24.50/8.13	MAYBE
24.75/8.14	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
24.75/8.14	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
24.75/8.14	
24.75/8.14	
24.75/8.14	Quasi decreasingness of the given CTRS could not be shown:
24.75/8.14	
24.75/8.14	(0) CTRS
24.75/8.14	(1) CTRSToQTRSProof [SOUND, 0 ms]
24.75/8.14	(2) QTRS
24.75/8.14	(3) DependencyPairsProof [EQUIVALENT, 0 ms]
24.75/8.14	(4) QDP
24.75/8.14	(5) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.14	(6) QDP
24.75/8.14	(7) UsableRulesReductionPairsProof [EQUIVALENT, 6 ms]
24.75/8.14	(8) QDP
24.75/8.14	(9) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(10) QDP
24.75/8.14	(11) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(12) QDP
24.75/8.14	(13) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(14) QDP
24.75/8.14	(15) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(16) QDP
24.75/8.14	(17) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(18) QDP
24.75/8.14	(19) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(20) QDP
24.75/8.14	(21) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(22) QDP
24.75/8.14	(23) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(24) QDP
24.75/8.14	(25) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(26) QDP
24.75/8.14	(27) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(28) QDP
24.75/8.14	(29) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(30) QDP
24.75/8.14	(31) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(32) QDP
24.75/8.14	(33) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(34) QDP
24.75/8.14	(35) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(36) QDP
24.75/8.14	(37) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(38) QDP
24.75/8.14	(39) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(40) QDP
24.75/8.14	(41) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(42) QDP
24.75/8.14	(43) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(44) QDP
24.75/8.14	(45) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(46) QDP
24.75/8.14	(47) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(48) QDP
24.75/8.14	(49) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(50) QDP
24.75/8.14	(51) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(52) QDP
24.75/8.14	(53) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(54) QDP
24.75/8.14	(55) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(56) QDP
24.75/8.14	(57) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(58) QDP
24.75/8.14	(59) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(60) QDP
24.75/8.14	(61) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(62) QDP
24.75/8.14	(63) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(64) QDP
24.75/8.14	(65) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(66) QDP
24.75/8.14	(67) TransformationProof [EQUIVALENT, 2 ms]
24.75/8.14	(68) QDP
24.75/8.14	(69) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(70) QDP
24.75/8.14	(71) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(72) QDP
24.75/8.14	(73) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(74) QDP
24.75/8.14	(75) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(76) QDP
24.75/8.14	(77) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(78) QDP
24.75/8.14	(79) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(80) QDP
24.75/8.14	(81) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(82) QDP
24.75/8.14	(83) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(84) QDP
24.75/8.14	(85) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(86) QDP
24.75/8.14	(87) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(88) QDP
24.75/8.14	(89) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(90) QDP
24.75/8.14	(91) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(92) QDP
24.75/8.14	(93) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(94) QDP
24.75/8.14	(95) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(96) QDP
24.75/8.14	(97) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(98) QDP
24.75/8.14	(99) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(100) QDP
24.75/8.14	(101) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(102) QDP
24.75/8.14	(103) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(104) QDP
24.75/8.14	(105) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(106) QDP
24.75/8.14	(107) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(108) QDP
24.75/8.14	(109) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(110) QDP
24.75/8.14	(111) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(112) QDP
24.75/8.14	(113) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(114) QDP
24.75/8.14	(115) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(116) QDP
24.75/8.14	(117) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(118) QDP
24.75/8.14	(119) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(120) QDP
24.75/8.14	(121) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(122) QDP
24.75/8.14	(123) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(124) QDP
24.75/8.14	(125) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(126) QDP
24.75/8.14	(127) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(128) QDP
24.75/8.14	(129) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(130) QDP
24.75/8.14	(131) TransformationProof [EQUIVALENT, 2 ms]
24.75/8.14	(132) QDP
24.75/8.14	(133) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(134) QDP
24.75/8.14	(135) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(136) QDP
24.75/8.14	(137) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(138) QDP
24.75/8.14	(139) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(140) QDP
24.75/8.14	(141) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(142) QDP
24.75/8.14	(143) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(144) QDP
24.75/8.14	(145) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(146) QDP
24.75/8.14	(147) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(148) QDP
24.75/8.14	(149) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(150) QDP
24.75/8.14	(151) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(152) QDP
24.75/8.14	(153) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(154) QDP
24.75/8.14	(155) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(156) QDP
24.75/8.14	(157) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(158) QDP
24.75/8.14	(159) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(160) QDP
24.75/8.14	(161) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(162) QDP
24.75/8.14	(163) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(164) QDP
24.75/8.14	(165) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(166) QDP
24.75/8.14	(167) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(168) QDP
24.75/8.14	(169) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(170) QDP
24.75/8.14	(171) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(172) QDP
24.75/8.14	(173) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(174) QDP
24.75/8.14	(175) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(176) QDP
24.75/8.14	(177) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(178) QDP
24.75/8.14	(179) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(180) QDP
24.75/8.14	(181) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(182) QDP
24.75/8.14	(183) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(184) QDP
24.75/8.14	(185) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(186) QDP
24.75/8.14	(187) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(188) QDP
24.75/8.14	(189) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(190) QDP
24.75/8.14	(191) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(192) QDP
24.75/8.14	(193) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(194) QDP
24.75/8.14	(195) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(196) QDP
24.75/8.14	(197) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(198) QDP
24.75/8.14	(199) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(200) QDP
24.75/8.14	(201) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(202) QDP
24.75/8.14	(203) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(204) QDP
24.75/8.14	(205) TransformationProof [EQUIVALENT, 1 ms]
24.75/8.14	(206) QDP
24.75/8.14	(207) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(208) QDP
24.75/8.14	(209) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(210) QDP
24.75/8.14	(211) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(212) QDP
24.75/8.14	(213) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(214) QDP
24.75/8.14	(215) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(216) QDP
24.75/8.14	(217) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(218) QDP
24.75/8.14	(219) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(220) QDP
24.75/8.14	(221) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(222) QDP
24.75/8.14	(223) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(224) QDP
24.75/8.14	(225) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(226) QDP
24.75/8.14	(227) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(228) QDP
24.75/8.14	(229) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(230) QDP
24.75/8.14	(231) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(232) QDP
24.75/8.14	(233) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(234) QDP
24.75/8.14	(235) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(236) QDP
24.75/8.14	(237) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(238) QDP
24.75/8.14	(239) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(240) QDP
24.75/8.14	(241) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(242) QDP
24.75/8.14	(243) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(244) QDP
24.75/8.14	(245) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(246) QDP
24.75/8.14	(247) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(248) QDP
24.75/8.14	(249) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(250) QDP
24.75/8.14	(251) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(252) QDP
24.75/8.14	(253) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(254) QDP
24.75/8.14	(255) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(256) QDP
24.75/8.14	(257) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(258) QDP
24.75/8.14	(259) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(260) QDP
24.75/8.14	(261) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(262) QDP
24.75/8.14	(263) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(264) QDP
24.75/8.14	(265) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(266) QDP
24.75/8.14	(267) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(268) QDP
24.75/8.14	(269) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(270) QDP
24.75/8.14	(271) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(272) QDP
24.75/8.14	(273) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(274) QDP
24.75/8.14	(275) TransformationProof [EQUIVALENT, 1 ms]
24.75/8.14	(276) QDP
24.75/8.14	(277) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(278) QDP
24.75/8.14	(279) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(280) QDP
24.75/8.14	(281) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(282) QDP
24.75/8.14	(283) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(284) QDP
24.75/8.14	(285) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(286) QDP
24.75/8.14	(287) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(288) QDP
24.75/8.14	(289) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(290) QDP
24.75/8.14	(291) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.14	(292) QDP
24.75/8.14	(293) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(294) QDP
24.75/8.15	(295) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(296) QDP
24.75/8.15	(297) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(298) QDP
24.75/8.15	(299) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(300) QDP
24.75/8.15	(301) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(302) QDP
24.75/8.15	(303) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(304) QDP
24.75/8.15	(305) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(306) QDP
24.75/8.15	(307) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(308) QDP
24.75/8.15	(309) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(310) QDP
24.75/8.15	(311) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(312) QDP
24.75/8.15	(313) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(314) QDP
24.75/8.15	(315) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(316) QDP
24.75/8.15	(317) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(318) QDP
24.75/8.15	(319) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(320) QDP
24.75/8.15	(321) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(322) QDP
24.75/8.15	(323) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(324) QDP
24.75/8.15	(325) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(326) QDP
24.75/8.15	(327) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(328) QDP
24.75/8.15	(329) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(330) QDP
24.75/8.15	(331) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(332) QDP
24.75/8.15	(333) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(334) QDP
24.75/8.15	(335) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(336) QDP
24.75/8.15	(337) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(338) QDP
24.75/8.15	(339) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(340) QDP
24.75/8.15	(341) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(342) QDP
24.75/8.15	(343) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(344) QDP
24.75/8.15	(345) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(346) QDP
24.75/8.15	(347) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(348) QDP
24.75/8.15	(349) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(350) QDP
24.75/8.15	(351) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(352) QDP
24.75/8.15	(353) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(354) QDP
24.75/8.15	(355) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(356) QDP
24.75/8.15	(357) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(358) QDP
24.75/8.15	(359) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(360) QDP
24.75/8.15	(361) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(362) QDP
24.75/8.15	(363) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(364) QDP
24.75/8.15	(365) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(366) QDP
24.75/8.15	(367) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(368) QDP
24.75/8.15	(369) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(370) QDP
24.75/8.15	(371) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(372) QDP
24.75/8.15	(373) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(374) QDP
24.75/8.15	(375) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(376) QDP
24.75/8.15	(377) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(378) QDP
24.75/8.15	(379) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(380) QDP
24.75/8.15	(381) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(382) QDP
24.75/8.15	(383) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(384) QDP
24.75/8.15	(385) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(386) QDP
24.75/8.15	(387) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(388) QDP
24.75/8.15	(389) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(390) QDP
24.75/8.15	(391) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(392) QDP
24.75/8.15	(393) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(394) QDP
24.75/8.15	(395) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(396) QDP
24.75/8.15	(397) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(398) QDP
24.75/8.15	(399) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(400) QDP
24.75/8.15	(401) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(402) QDP
24.75/8.15	(403) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(404) QDP
24.75/8.15	(405) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(406) QDP
24.75/8.15	(407) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(408) QDP
24.75/8.15	(409) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(410) QDP
24.75/8.15	(411) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(412) QDP
24.75/8.15	(413) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(414) QDP
24.75/8.15	(415) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(416) QDP
24.75/8.15	(417) TransformationProof [EQUIVALENT, 2 ms]
24.75/8.15	(418) QDP
24.75/8.15	(419) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(420) QDP
24.75/8.15	(421) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(422) QDP
24.75/8.15	(423) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(424) QDP
24.75/8.15	(425) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(426) QDP
24.75/8.15	(427) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(428) QDP
24.75/8.15	(429) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(430) QDP
24.75/8.15	(431) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(432) QDP
24.75/8.15	(433) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(434) QDP
24.75/8.15	(435) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(436) QDP
24.75/8.15	(437) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(438) QDP
24.75/8.15	(439) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(440) QDP
24.75/8.15	(441) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(442) QDP
24.75/8.15	(443) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(444) QDP
24.75/8.15	(445) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(446) QDP
24.75/8.15	(447) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(448) QDP
24.75/8.15	(449) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(450) QDP
24.75/8.15	(451) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(452) QDP
24.75/8.15	(453) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(454) QDP
24.75/8.15	(455) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(456) QDP
24.75/8.15	(457) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(458) QDP
24.75/8.15	(459) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(460) QDP
24.75/8.15	(461) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(462) QDP
24.75/8.15	(463) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(464) QDP
24.75/8.15	(465) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(466) QDP
24.75/8.15	(467) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(468) QDP
24.75/8.15	(469) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(470) QDP
24.75/8.15	(471) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(472) QDP
24.75/8.15	(473) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(474) QDP
24.75/8.15	(475) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(476) QDP
24.75/8.15	(477) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(478) QDP
24.75/8.15	(479) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(480) QDP
24.75/8.15	(481) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(482) QDP
24.75/8.15	(483) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(484) QDP
24.75/8.15	(485) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(486) QDP
24.75/8.15	(487) TransformationProof [EQUIVALENT, 1 ms]
24.75/8.15	(488) QDP
24.75/8.15	(489) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(490) QDP
24.75/8.15	(491) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(492) QDP
24.75/8.15	(493) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(494) QDP
24.75/8.15	(495) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(496) QDP
24.75/8.15	(497) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(498) QDP
24.75/8.15	(499) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(500) QDP
24.75/8.15	(501) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(502) QDP
24.75/8.15	(503) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(504) QDP
24.75/8.15	(505) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(506) QDP
24.75/8.15	(507) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(508) QDP
24.75/8.15	(509) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(510) QDP
24.75/8.15	(511) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(512) QDP
24.75/8.15	(513) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(514) QDP
24.75/8.15	(515) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(516) QDP
24.75/8.15	(517) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(518) QDP
24.75/8.15	(519) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(520) QDP
24.75/8.15	(521) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(522) QDP
24.75/8.15	(523) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(524) QDP
24.75/8.15	(525) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(526) QDP
24.75/8.15	(527) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(528) QDP
24.75/8.15	(529) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(530) QDP
24.75/8.15	(531) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(532) QDP
24.75/8.15	(533) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(534) QDP
24.75/8.15	(535) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(536) QDP
24.75/8.15	(537) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(538) QDP
24.75/8.15	(539) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(540) QDP
24.75/8.15	(541) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(542) QDP
24.75/8.15	(543) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(544) QDP
24.75/8.15	(545) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(546) QDP
24.75/8.15	(547) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(548) QDP
24.75/8.15	(549) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(550) QDP
24.75/8.15	(551) TransformationProof [EQUIVALENT, 3 ms]
24.75/8.15	(552) QDP
24.75/8.15	(553) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(554) QDP
24.75/8.15	(555) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(556) QDP
24.75/8.15	(557) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(558) QDP
24.75/8.15	(559) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(560) QDP
24.75/8.15	(561) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(562) QDP
24.75/8.15	(563) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(564) QDP
24.75/8.15	(565) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(566) QDP
24.75/8.15	(567) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(568) QDP
24.75/8.15	(569) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(570) QDP
24.75/8.15	(571) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(572) QDP
24.75/8.15	(573) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(574) QDP
24.75/8.15	(575) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(576) QDP
24.75/8.15	(577) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(578) QDP
24.75/8.15	(579) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(580) QDP
24.75/8.15	(581) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(582) QDP
24.75/8.15	(583) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(584) QDP
24.75/8.15	(585) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(586) QDP
24.75/8.15	(587) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(588) QDP
24.75/8.15	(589) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(590) QDP
24.75/8.15	(591) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(592) QDP
24.75/8.15	(593) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(594) QDP
24.75/8.15	(595) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(596) QDP
24.75/8.15	(597) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(598) QDP
24.75/8.15	(599) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(600) QDP
24.75/8.15	(601) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(602) QDP
24.75/8.15	(603) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(604) QDP
24.75/8.15	(605) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(606) QDP
24.75/8.15	(607) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(608) QDP
24.75/8.15	(609) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(610) QDP
24.75/8.15	(611) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(612) QDP
24.75/8.15	(613) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(614) QDP
24.75/8.15	(615) TransformationProof [EQUIVALENT, 2 ms]
24.75/8.15	(616) QDP
24.75/8.15	(617) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(618) QDP
24.75/8.15	(619) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(620) QDP
24.75/8.15	(621) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(622) QDP
24.75/8.15	(623) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(624) QDP
24.75/8.15	(625) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(626) QDP
24.75/8.15	(627) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(628) QDP
24.75/8.15	(629) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(630) QDP
24.75/8.15	(631) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(632) QDP
24.75/8.15	(633) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(634) QDP
24.75/8.15	(635) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(636) QDP
24.75/8.15	(637) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(638) QDP
24.75/8.15	(639) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(640) QDP
24.75/8.15	(641) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(642) QDP
24.75/8.15	(643) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(644) QDP
24.75/8.15	(645) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(646) QDP
24.75/8.15	(647) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(648) QDP
24.75/8.15	(649) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(650) QDP
24.75/8.15	(651) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(652) QDP
24.75/8.15	(653) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(654) QDP
24.75/8.15	(655) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(656) QDP
24.75/8.15	(657) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(658) QDP
24.75/8.15	(659) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(660) QDP
24.75/8.15	(661) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(662) QDP
24.75/8.15	(663) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(664) QDP
24.75/8.15	(665) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(666) QDP
24.75/8.15	(667) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(668) QDP
24.75/8.15	(669) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(670) QDP
24.75/8.15	(671) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(672) QDP
24.75/8.15	(673) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(674) QDP
24.75/8.15	(675) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(676) QDP
24.75/8.15	(677) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(678) QDP
24.75/8.15	(679) TransformationProof [EQUIVALENT, 2 ms]
24.75/8.15	(680) QDP
24.75/8.15	(681) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(682) QDP
24.75/8.15	(683) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(684) QDP
24.75/8.15	(685) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(686) QDP
24.75/8.15	(687) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(688) QDP
24.75/8.15	(689) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(690) QDP
24.75/8.15	(691) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(692) QDP
24.75/8.15	(693) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(694) QDP
24.75/8.15	(695) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(696) QDP
24.75/8.15	(697) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(698) QDP
24.75/8.15	(699) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(700) QDP
24.75/8.15	(701) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(702) QDP
24.75/8.15	(703) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(704) QDP
24.75/8.15	(705) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(706) QDP
24.75/8.15	(707) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(708) QDP
24.75/8.15	(709) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(710) QDP
24.75/8.15	(711) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(712) QDP
24.75/8.15	(713) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(714) QDP
24.75/8.15	(715) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(716) QDP
24.75/8.15	(717) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(718) QDP
24.75/8.15	(719) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(720) QDP
24.75/8.15	(721) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(722) QDP
24.75/8.15	(723) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(724) QDP
24.75/8.15	(725) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(726) QDP
24.75/8.15	(727) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(728) QDP
24.75/8.15	(729) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(730) QDP
24.75/8.15	(731) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(732) QDP
24.75/8.15	(733) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(734) QDP
24.75/8.15	(735) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(736) QDP
24.75/8.15	(737) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(738) QDP
24.75/8.15	(739) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(740) QDP
24.75/8.15	(741) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(742) QDP
24.75/8.15	(743) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(744) QDP
24.75/8.15	(745) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(746) QDP
24.75/8.15	(747) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(748) QDP
24.75/8.15	(749) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(750) QDP
24.75/8.15	(751) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(752) QDP
24.75/8.15	(753) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(754) QDP
24.75/8.15	(755) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(756) QDP
24.75/8.15	(757) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(758) QDP
24.75/8.15	(759) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(760) QDP
24.75/8.15	(761) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(762) QDP
24.75/8.15	(763) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(764) QDP
24.75/8.15	(765) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(766) QDP
24.75/8.15	(767) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(768) QDP
24.75/8.15	(769) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(770) QDP
24.75/8.15	(771) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(772) QDP
24.75/8.15	(773) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(774) QDP
24.75/8.15	(775) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(776) QDP
24.75/8.15	(777) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(778) QDP
24.75/8.15	(779) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(780) QDP
24.75/8.15	(781) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(782) QDP
24.75/8.15	(783) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(784) QDP
24.75/8.15	(785) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(786) QDP
24.75/8.15	(787) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(788) QDP
24.75/8.15	(789) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(790) QDP
24.75/8.15	(791) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(792) QDP
24.75/8.15	(793) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(794) QDP
24.75/8.15	(795) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(796) QDP
24.75/8.15	(797) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(798) QDP
24.75/8.15	(799) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(800) QDP
24.75/8.15	(801) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(802) QDP
24.75/8.15	(803) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(804) QDP
24.75/8.15	(805) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(806) QDP
24.75/8.15	(807) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(808) QDP
24.75/8.15	(809) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(810) QDP
24.75/8.15	(811) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(812) QDP
24.75/8.15	(813) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(814) QDP
24.75/8.15	(815) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(816) QDP
24.75/8.15	(817) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(818) QDP
24.75/8.15	(819) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(820) QDP
24.75/8.15	(821) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(822) QDP
24.75/8.15	(823) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(824) QDP
24.75/8.15	(825) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(826) QDP
24.75/8.15	(827) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(828) QDP
24.75/8.15	(829) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(830) QDP
24.75/8.15	(831) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(832) QDP
24.75/8.15	(833) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(834) QDP
24.75/8.15	(835) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(836) QDP
24.75/8.15	(837) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(838) QDP
24.75/8.15	(839) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(840) QDP
24.75/8.15	(841) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(842) QDP
24.75/8.15	(843) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(844) QDP
24.75/8.15	(845) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(846) QDP
24.75/8.15	(847) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(848) QDP
24.75/8.15	(849) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(850) QDP
24.75/8.15	(851) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(852) QDP
24.75/8.15	(853) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(854) QDP
24.75/8.15	(855) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(856) QDP
24.75/8.15	(857) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(858) QDP
24.75/8.15	(859) TransformationProof [EQUIVALENT, 2 ms]
24.75/8.15	(860) QDP
24.75/8.15	(861) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(862) QDP
24.75/8.15	(863) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(864) QDP
24.75/8.15	(865) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(866) QDP
24.75/8.15	(867) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(868) QDP
24.75/8.15	(869) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(870) QDP
24.75/8.15	(871) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(872) QDP
24.75/8.15	(873) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(874) QDP
24.75/8.15	(875) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(876) QDP
24.75/8.15	(877) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(878) QDP
24.75/8.15	(879) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(880) QDP
24.75/8.15	(881) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(882) QDP
24.75/8.15	(883) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(884) QDP
24.75/8.15	(885) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(886) QDP
24.75/8.15	(887) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(888) QDP
24.75/8.15	(889) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(890) QDP
24.75/8.15	(891) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(892) QDP
24.75/8.15	(893) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(894) QDP
24.75/8.15	(895) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(896) QDP
24.75/8.15	(897) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(898) QDP
24.75/8.15	(899) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(900) QDP
24.75/8.15	(901) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(902) QDP
24.75/8.15	(903) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(904) QDP
24.75/8.15	(905) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(906) QDP
24.75/8.15	(907) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(908) QDP
24.75/8.15	(909) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(910) QDP
24.75/8.15	(911) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(912) QDP
24.75/8.15	(913) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(914) QDP
24.75/8.15	(915) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(916) QDP
24.75/8.15	(917) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(918) QDP
24.75/8.15	(919) TransformationProof [EQUIVALENT, 1 ms]
24.75/8.15	(920) QDP
24.75/8.15	(921) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(922) QDP
24.75/8.15	(923) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(924) QDP
24.75/8.15	(925) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(926) QDP
24.75/8.15	(927) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(928) QDP
24.75/8.15	(929) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(930) QDP
24.75/8.15	(931) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(932) QDP
24.75/8.15	(933) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(934) QDP
24.75/8.15	(935) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(936) QDP
24.75/8.15	(937) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(938) QDP
24.75/8.15	(939) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(940) QDP
24.75/8.15	(941) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(942) QDP
24.75/8.15	(943) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(944) QDP
24.75/8.15	(945) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(946) QDP
24.75/8.15	(947) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(948) QDP
24.75/8.15	(949) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(950) QDP
24.75/8.15	(951) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(952) QDP
24.75/8.15	(953) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(954) QDP
24.75/8.15	(955) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(956) QDP
24.75/8.15	(957) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(958) QDP
24.75/8.15	(959) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(960) QDP
24.75/8.15	(961) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(962) QDP
24.75/8.15	(963) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(964) QDP
24.75/8.15	(965) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(966) QDP
24.75/8.15	(967) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(968) QDP
24.75/8.15	(969) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(970) QDP
24.75/8.15	(971) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(972) QDP
24.75/8.15	(973) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(974) QDP
24.75/8.15	(975) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(976) QDP
24.75/8.15	(977) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(978) QDP
24.75/8.15	(979) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(980) QDP
24.75/8.15	(981) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(982) QDP
24.75/8.15	(983) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(984) QDP
24.75/8.15	(985) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(986) QDP
24.75/8.15	(987) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(988) QDP
24.75/8.15	(989) TransformationProof [EQUIVALENT, 2 ms]
24.75/8.15	(990) QDP
24.75/8.15	(991) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(992) QDP
24.75/8.15	(993) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(994) QDP
24.75/8.15	(995) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(996) QDP
24.75/8.15	(997) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(998) QDP
24.75/8.15	(999) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1000) QDP
24.75/8.15	(1001) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1002) QDP
24.75/8.15	(1003) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1004) QDP
24.75/8.15	(1005) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1006) QDP
24.75/8.15	(1007) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1008) QDP
24.75/8.15	(1009) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1010) QDP
24.75/8.15	(1011) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1012) QDP
24.75/8.15	(1013) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1014) QDP
24.75/8.15	(1015) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1016) QDP
24.75/8.15	(1017) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1018) QDP
24.75/8.15	(1019) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1020) QDP
24.75/8.15	(1021) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1022) QDP
24.75/8.15	(1023) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1024) QDP
24.75/8.15	(1025) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1026) QDP
24.75/8.15	(1027) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1028) QDP
24.75/8.15	(1029) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1030) QDP
24.75/8.15	(1031) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1032) QDP
24.75/8.15	(1033) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1034) QDP
24.75/8.15	(1035) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1036) QDP
24.75/8.15	(1037) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1038) QDP
24.75/8.15	(1039) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1040) QDP
24.75/8.15	(1041) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1042) QDP
24.75/8.15	(1043) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1044) QDP
24.75/8.15	(1045) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1046) QDP
24.75/8.15	(1047) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1048) QDP
24.75/8.15	(1049) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1050) QDP
24.75/8.15	(1051) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1052) QDP
24.75/8.15	(1053) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1054) QDP
24.75/8.15	(1055) TransformationProof [EQUIVALENT, 2 ms]
24.75/8.15	(1056) QDP
24.75/8.15	(1057) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1058) QDP
24.75/8.15	(1059) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1060) QDP
24.75/8.15	(1061) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1062) QDP
24.75/8.15	(1063) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1064) QDP
24.75/8.15	(1065) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1066) QDP
24.75/8.15	(1067) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1068) QDP
24.75/8.15	(1069) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1070) QDP
24.75/8.15	(1071) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1072) QDP
24.75/8.15	(1073) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1074) QDP
24.75/8.15	(1075) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1076) QDP
24.75/8.15	(1077) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1078) QDP
24.75/8.15	(1079) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1080) QDP
24.75/8.15	(1081) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1082) QDP
24.75/8.15	(1083) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1084) QDP
24.75/8.15	(1085) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1086) QDP
24.75/8.15	(1087) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1088) QDP
24.75/8.15	(1089) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1090) QDP
24.75/8.15	(1091) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1092) QDP
24.75/8.15	(1093) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1094) QDP
24.75/8.15	(1095) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1096) QDP
24.75/8.15	(1097) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1098) QDP
24.75/8.15	(1099) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1100) QDP
24.75/8.15	(1101) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1102) QDP
24.75/8.15	(1103) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1104) QDP
24.75/8.15	(1105) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1106) QDP
24.75/8.15	(1107) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1108) QDP
24.75/8.15	(1109) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1110) QDP
24.75/8.15	(1111) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1112) QDP
24.75/8.15	(1113) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1114) QDP
24.75/8.15	(1115) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1116) QDP
24.75/8.15	(1117) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1118) QDP
24.75/8.15	(1119) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1120) QDP
24.75/8.15	(1121) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1122) QDP
24.75/8.15	(1123) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1124) QDP
24.75/8.15	(1125) TransformationProof [EQUIVALENT, 1 ms]
24.75/8.15	(1126) QDP
24.75/8.15	(1127) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1128) QDP
24.75/8.15	(1129) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1130) QDP
24.75/8.15	(1131) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1132) QDP
24.75/8.15	(1133) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1134) QDP
24.75/8.15	(1135) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1136) QDP
24.75/8.15	(1137) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1138) QDP
24.75/8.15	(1139) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1140) QDP
24.75/8.15	(1141) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1142) QDP
24.75/8.15	(1143) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1144) QDP
24.75/8.15	(1145) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1146) QDP
24.75/8.15	(1147) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1148) QDP
24.75/8.15	(1149) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1150) QDP
24.75/8.15	(1151) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1152) QDP
24.75/8.15	(1153) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1154) QDP
24.75/8.15	(1155) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1156) QDP
24.75/8.15	(1157) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1158) QDP
24.75/8.15	(1159) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1160) QDP
24.75/8.15	(1161) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1162) QDP
24.75/8.15	(1163) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1164) QDP
24.75/8.15	(1165) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1166) QDP
24.75/8.15	(1167) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1168) QDP
24.75/8.15	(1169) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1170) QDP
24.75/8.15	(1171) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1172) QDP
24.75/8.15	(1173) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1174) QDP
24.75/8.15	(1175) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1176) QDP
24.75/8.15	(1177) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1178) QDP
24.75/8.15	(1179) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1180) QDP
24.75/8.15	(1181) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1182) QDP
24.75/8.15	(1183) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1184) QDP
24.75/8.15	(1185) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1186) QDP
24.75/8.15	(1187) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1188) QDP
24.75/8.15	(1189) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1190) QDP
24.75/8.15	(1191) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1192) QDP
24.75/8.15	(1193) TransformationProof [EQUIVALENT, 1 ms]
24.75/8.15	(1194) QDP
24.75/8.15	(1195) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1196) QDP
24.75/8.15	(1197) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1198) QDP
24.75/8.15	(1199) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1200) QDP
24.75/8.15	(1201) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1202) QDP
24.75/8.15	(1203) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1204) QDP
24.75/8.15	(1205) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1206) QDP
24.75/8.15	(1207) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1208) QDP
24.75/8.15	(1209) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1210) QDP
24.75/8.15	(1211) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1212) QDP
24.75/8.15	(1213) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1214) QDP
24.75/8.15	(1215) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1216) QDP
24.75/8.15	(1217) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1218) QDP
24.75/8.15	(1219) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1220) QDP
24.75/8.15	(1221) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1222) QDP
24.75/8.15	(1223) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1224) QDP
24.75/8.15	(1225) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1226) QDP
24.75/8.15	(1227) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1228) QDP
24.75/8.15	(1229) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1230) QDP
24.75/8.15	(1231) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1232) QDP
24.75/8.15	(1233) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1234) QDP
24.75/8.15	(1235) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1236) QDP
24.75/8.15	(1237) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1238) QDP
24.75/8.15	(1239) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1240) QDP
24.75/8.15	(1241) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1242) QDP
24.75/8.15	(1243) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1244) QDP
24.75/8.15	(1245) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1246) QDP
24.75/8.15	(1247) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1248) QDP
24.75/8.15	(1249) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1250) QDP
24.75/8.15	(1251) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1252) QDP
24.75/8.15	(1253) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1254) QDP
24.75/8.15	(1255) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1256) QDP
24.75/8.15	(1257) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1258) QDP
24.75/8.15	(1259) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1260) QDP
24.75/8.15	(1261) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1262) QDP
24.75/8.15	(1263) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1264) QDP
24.75/8.15	(1265) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1266) QDP
24.75/8.15	(1267) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1268) QDP
24.75/8.15	(1269) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1270) QDP
24.75/8.15	(1271) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1272) QDP
24.75/8.15	(1273) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1274) QDP
24.75/8.15	(1275) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1276) QDP
24.75/8.15	(1277) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1278) QDP
24.75/8.15	(1279) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1280) QDP
24.75/8.15	(1281) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1282) QDP
24.75/8.15	(1283) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1284) QDP
24.75/8.15	(1285) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1286) QDP
24.75/8.15	(1287) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1288) QDP
24.75/8.15	(1289) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1290) QDP
24.75/8.15	(1291) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1292) QDP
24.75/8.15	(1293) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1294) QDP
24.75/8.15	(1295) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1296) QDP
24.75/8.15	(1297) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1298) QDP
24.75/8.15	(1299) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1300) QDP
24.75/8.15	(1301) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1302) QDP
24.75/8.15	(1303) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1304) QDP
24.75/8.15	(1305) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1306) QDP
24.75/8.15	(1307) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1308) QDP
24.75/8.15	(1309) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1310) QDP
24.75/8.15	(1311) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1312) QDP
24.75/8.15	(1313) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1314) QDP
24.75/8.15	(1315) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1316) QDP
24.75/8.15	(1317) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1318) QDP
24.75/8.15	(1319) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1320) QDP
24.75/8.15	(1321) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1322) QDP
24.75/8.15	(1323) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1324) QDP
24.75/8.15	(1325) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1326) QDP
24.75/8.15	(1327) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1328) QDP
24.75/8.15	(1329) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1330) QDP
24.75/8.15	(1331) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1332) QDP
24.75/8.15	(1333) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1334) QDP
24.75/8.15	(1335) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1336) QDP
24.75/8.15	(1337) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1338) QDP
24.75/8.15	(1339) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1340) QDP
24.75/8.15	(1341) TransformationProof [EQUIVALENT, 2 ms]
24.75/8.15	(1342) QDP
24.75/8.15	(1343) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1344) QDP
24.75/8.15	(1345) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1346) QDP
24.75/8.15	(1347) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1348) QDP
24.75/8.15	(1349) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1350) QDP
24.75/8.15	(1351) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1352) QDP
24.75/8.15	(1353) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1354) QDP
24.75/8.15	(1355) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1356) QDP
24.75/8.15	(1357) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1358) QDP
24.75/8.15	(1359) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1360) QDP
24.75/8.15	(1361) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1362) QDP
24.75/8.15	(1363) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1364) QDP
24.75/8.15	(1365) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1366) QDP
24.75/8.15	(1367) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1368) QDP
24.75/8.15	(1369) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1370) QDP
24.75/8.15	(1371) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1372) QDP
24.75/8.15	(1373) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1374) QDP
24.75/8.15	(1375) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1376) QDP
24.75/8.15	(1377) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1378) QDP
24.75/8.15	(1379) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1380) QDP
24.75/8.15	(1381) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1382) QDP
24.75/8.15	(1383) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1384) QDP
24.75/8.15	(1385) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1386) QDP
24.75/8.15	(1387) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1388) QDP
24.75/8.15	(1389) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1390) QDP
24.75/8.15	(1391) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1392) QDP
24.75/8.15	(1393) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1394) QDP
24.75/8.15	(1395) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1396) QDP
24.75/8.15	(1397) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1398) QDP
24.75/8.15	(1399) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1400) QDP
24.75/8.15	(1401) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1402) QDP
24.75/8.15	(1403) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1404) QDP
24.75/8.15	(1405) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1406) QDP
24.75/8.15	(1407) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1408) QDP
24.75/8.15	(1409) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1410) QDP
24.75/8.15	(1411) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1412) QDP
24.75/8.15	(1413) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1414) QDP
24.75/8.15	(1415) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1416) QDP
24.75/8.15	(1417) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1418) QDP
24.75/8.15	(1419) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1420) QDP
24.75/8.15	(1421) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1422) QDP
24.75/8.15	(1423) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1424) QDP
24.75/8.15	(1425) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1426) QDP
24.75/8.15	(1427) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1428) QDP
24.75/8.15	(1429) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1430) QDP
24.75/8.15	(1431) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1432) QDP
24.75/8.15	(1433) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1434) QDP
24.75/8.15	(1435) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1436) QDP
24.75/8.15	(1437) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1438) QDP
24.75/8.15	(1439) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1440) QDP
24.75/8.15	(1441) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1442) QDP
24.75/8.15	(1443) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1444) QDP
24.75/8.15	(1445) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1446) QDP
24.75/8.15	(1447) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1448) QDP
24.75/8.15	(1449) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1450) QDP
24.75/8.15	(1451) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1452) QDP
24.75/8.15	(1453) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1454) QDP
24.75/8.15	(1455) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1456) QDP
24.75/8.15	(1457) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1458) QDP
24.75/8.15	(1459) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1460) QDP
24.75/8.15	(1461) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1462) QDP
24.75/8.15	(1463) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1464) QDP
24.75/8.15	(1465) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1466) QDP
24.75/8.15	(1467) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1468) QDP
24.75/8.15	(1469) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1470) QDP
24.75/8.15	(1471) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1472) QDP
24.75/8.15	(1473) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1474) QDP
24.75/8.15	(1475) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1476) QDP
24.75/8.15	(1477) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1478) QDP
24.75/8.15	(1479) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1480) QDP
24.75/8.15	(1481) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1482) QDP
24.75/8.15	(1483) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1484) QDP
24.75/8.15	(1485) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1486) QDP
24.75/8.15	(1487) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1488) QDP
24.75/8.15	(1489) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1490) QDP
24.75/8.15	(1491) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1492) QDP
24.75/8.15	(1493) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1494) QDP
24.75/8.15	(1495) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1496) QDP
24.75/8.15	(1497) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1498) QDP
24.75/8.15	(1499) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1500) QDP
24.75/8.15	(1501) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1502) QDP
24.75/8.15	(1503) TransformationProof [EQUIVALENT, 1 ms]
24.75/8.15	(1504) QDP
24.75/8.15	(1505) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1506) QDP
24.75/8.15	(1507) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1508) QDP
24.75/8.15	(1509) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1510) QDP
24.75/8.15	(1511) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1512) QDP
24.75/8.15	(1513) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1514) QDP
24.75/8.15	(1515) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1516) QDP
24.75/8.15	(1517) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1518) QDP
24.75/8.15	(1519) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1520) QDP
24.75/8.15	(1521) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1522) QDP
24.75/8.15	(1523) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1524) QDP
24.75/8.15	(1525) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1526) QDP
24.75/8.15	(1527) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1528) QDP
24.75/8.15	(1529) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1530) QDP
24.75/8.15	(1531) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1532) QDP
24.75/8.15	(1533) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1534) QDP
24.75/8.15	(1535) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1536) QDP
24.75/8.15	(1537) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1538) QDP
24.75/8.15	(1539) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1540) QDP
24.75/8.15	(1541) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1542) QDP
24.75/8.15	(1543) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1544) QDP
24.75/8.15	(1545) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1546) QDP
24.75/8.15	(1547) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1548) QDP
24.75/8.15	(1549) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1550) QDP
24.75/8.15	(1551) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1552) QDP
24.75/8.15	(1553) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1554) QDP
24.75/8.15	(1555) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1556) QDP
24.75/8.15	(1557) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1558) QDP
24.75/8.15	(1559) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1560) QDP
24.75/8.15	(1561) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1562) QDP
24.75/8.15	(1563) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1564) QDP
24.75/8.15	(1565) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1566) QDP
24.75/8.15	(1567) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1568) QDP
24.75/8.15	(1569) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1570) QDP
24.75/8.15	(1571) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1572) QDP
24.75/8.15	(1573) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1574) QDP
24.75/8.15	(1575) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1576) QDP
24.75/8.15	(1577) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1578) QDP
24.75/8.15	(1579) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1580) QDP
24.75/8.15	(1581) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1582) QDP
24.75/8.15	(1583) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1584) QDP
24.75/8.15	(1585) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1586) QDP
24.75/8.15	(1587) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1588) QDP
24.75/8.15	(1589) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1590) QDP
24.75/8.15	(1591) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1592) QDP
24.75/8.15	(1593) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1594) QDP
24.75/8.15	(1595) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1596) QDP
24.75/8.15	(1597) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1598) QDP
24.75/8.15	(1599) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1600) QDP
24.75/8.15	(1601) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1602) QDP
24.75/8.15	(1603) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1604) QDP
24.75/8.15	(1605) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1606) QDP
24.75/8.15	(1607) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1608) QDP
24.75/8.15	(1609) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1610) QDP
24.75/8.15	(1611) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1612) QDP
24.75/8.15	(1613) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1614) QDP
24.75/8.15	(1615) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1616) QDP
24.75/8.15	(1617) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1618) QDP
24.75/8.15	(1619) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1620) QDP
24.75/8.15	(1621) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1622) QDP
24.75/8.15	(1623) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1624) QDP
24.75/8.15	(1625) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1626) QDP
24.75/8.15	(1627) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1628) QDP
24.75/8.15	(1629) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1630) QDP
24.75/8.15	(1631) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1632) QDP
24.75/8.15	(1633) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1634) QDP
24.75/8.15	(1635) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1636) QDP
24.75/8.15	(1637) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1638) QDP
24.75/8.15	(1639) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1640) QDP
24.75/8.15	(1641) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1642) QDP
24.75/8.15	(1643) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1644) QDP
24.75/8.15	(1645) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1646) QDP
24.75/8.15	(1647) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1648) QDP
24.75/8.15	(1649) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1650) QDP
24.75/8.15	(1651) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1652) QDP
24.75/8.15	(1653) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1654) QDP
24.75/8.15	(1655) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1656) QDP
24.75/8.15	(1657) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1658) QDP
24.75/8.15	(1659) TransformationProof [EQUIVALENT, 1 ms]
24.75/8.15	(1660) QDP
24.75/8.15	(1661) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1662) QDP
24.75/8.15	(1663) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1664) QDP
24.75/8.15	(1665) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1666) QDP
24.75/8.15	(1667) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1668) QDP
24.75/8.15	(1669) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1670) QDP
24.75/8.15	(1671) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1672) QDP
24.75/8.15	(1673) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1674) QDP
24.75/8.15	(1675) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1676) QDP
24.75/8.15	(1677) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1678) QDP
24.75/8.15	(1679) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1680) QDP
24.75/8.15	(1681) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1682) QDP
24.75/8.15	(1683) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1684) QDP
24.75/8.15	(1685) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1686) QDP
24.75/8.15	(1687) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1688) QDP
24.75/8.15	(1689) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1690) QDP
24.75/8.15	(1691) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1692) QDP
24.75/8.15	(1693) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1694) QDP
24.75/8.15	(1695) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1696) QDP
24.75/8.15	(1697) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1698) QDP
24.75/8.15	(1699) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1700) QDP
24.75/8.15	(1701) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1702) QDP
24.75/8.15	(1703) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1704) QDP
24.75/8.15	(1705) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1706) QDP
24.75/8.15	(1707) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1708) QDP
24.75/8.15	(1709) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1710) QDP
24.75/8.15	(1711) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1712) QDP
24.75/8.15	(1713) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1714) QDP
24.75/8.15	(1715) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1716) QDP
24.75/8.15	(1717) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1718) QDP
24.75/8.15	(1719) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1720) QDP
24.75/8.15	(1721) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1722) QDP
24.75/8.15	(1723) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1724) QDP
24.75/8.15	(1725) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1726) QDP
24.75/8.15	(1727) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1728) QDP
24.75/8.15	(1729) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1730) QDP
24.75/8.15	(1731) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1732) QDP
24.75/8.15	(1733) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1734) QDP
24.75/8.15	(1735) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1736) QDP
24.75/8.15	(1737) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1738) QDP
24.75/8.15	(1739) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1740) QDP
24.75/8.15	(1741) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1742) QDP
24.75/8.15	(1743) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1744) QDP
24.75/8.15	(1745) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1746) QDP
24.75/8.15	(1747) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1748) QDP
24.75/8.15	(1749) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1750) QDP
24.75/8.15	(1751) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1752) QDP
24.75/8.15	(1753) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1754) QDP
24.75/8.15	(1755) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1756) QDP
24.75/8.15	(1757) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1758) QDP
24.75/8.15	(1759) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1760) QDP
24.75/8.15	(1761) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1762) QDP
24.75/8.15	(1763) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1764) QDP
24.75/8.15	(1765) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1766) QDP
24.75/8.15	(1767) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1768) QDP
24.75/8.15	(1769) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1770) QDP
24.75/8.15	(1771) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1772) QDP
24.75/8.15	(1773) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1774) QDP
24.75/8.15	(1775) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1776) QDP
24.75/8.15	(1777) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1778) QDP
24.75/8.15	(1779) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1780) QDP
24.75/8.15	(1781) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1782) QDP
24.75/8.15	(1783) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1784) QDP
24.75/8.15	(1785) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1786) QDP
24.75/8.15	(1787) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1788) QDP
24.75/8.15	(1789) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1790) QDP
24.75/8.15	(1791) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1792) QDP
24.75/8.15	(1793) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1794) QDP
24.75/8.15	(1795) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1796) QDP
24.75/8.15	(1797) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1798) QDP
24.75/8.15	(1799) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1800) QDP
24.75/8.15	(1801) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1802) QDP
24.75/8.15	(1803) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1804) QDP
24.75/8.15	(1805) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1806) QDP
24.75/8.15	(1807) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1808) QDP
24.75/8.15	(1809) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1810) QDP
24.75/8.15	(1811) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1812) QDP
24.75/8.15	(1813) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1814) QDP
24.75/8.15	(1815) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1816) QDP
24.75/8.15	(1817) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1818) QDP
24.75/8.15	(1819) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1820) QDP
24.75/8.15	(1821) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1822) QDP
24.75/8.15	(1823) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1824) QDP
24.75/8.15	(1825) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1826) QDP
24.75/8.15	(1827) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1828) QDP
24.75/8.15	(1829) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1830) QDP
24.75/8.15	(1831) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1832) QDP
24.75/8.15	(1833) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1834) QDP
24.75/8.15	(1835) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1836) QDP
24.75/8.15	(1837) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1838) QDP
24.75/8.15	(1839) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1840) QDP
24.75/8.15	(1841) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1842) QDP
24.75/8.15	(1843) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1844) QDP
24.75/8.15	(1845) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1846) QDP
24.75/8.15	(1847) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1848) QDP
24.75/8.15	(1849) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1850) QDP
24.75/8.15	(1851) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1852) QDP
24.75/8.15	(1853) TransformationProof [EQUIVALENT, 1 ms]
24.75/8.15	(1854) QDP
24.75/8.15	(1855) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1856) QDP
24.75/8.15	(1857) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1858) QDP
24.75/8.15	(1859) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1860) QDP
24.75/8.15	(1861) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1862) QDP
24.75/8.15	(1863) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1864) QDP
24.75/8.15	(1865) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1866) QDP
24.75/8.15	(1867) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1868) QDP
24.75/8.15	(1869) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1870) QDP
24.75/8.15	(1871) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1872) QDP
24.75/8.15	(1873) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1874) QDP
24.75/8.15	(1875) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1876) QDP
24.75/8.15	(1877) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1878) QDP
24.75/8.15	(1879) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1880) QDP
24.75/8.15	(1881) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1882) QDP
24.75/8.15	(1883) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1884) QDP
24.75/8.15	(1885) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1886) QDP
24.75/8.15	(1887) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1888) QDP
24.75/8.15	(1889) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1890) QDP
24.75/8.15	(1891) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1892) QDP
24.75/8.15	(1893) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1894) QDP
24.75/8.15	(1895) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1896) QDP
24.75/8.15	(1897) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1898) QDP
24.75/8.15	(1899) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1900) QDP
24.75/8.15	(1901) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1902) QDP
24.75/8.15	(1903) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1904) QDP
24.75/8.15	(1905) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1906) QDP
24.75/8.15	(1907) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1908) QDP
24.75/8.15	(1909) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1910) QDP
24.75/8.15	(1911) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1912) QDP
24.75/8.15	(1913) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1914) QDP
24.75/8.15	(1915) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1916) QDP
24.75/8.15	(1917) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1918) QDP
24.75/8.15	(1919) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1920) QDP
24.75/8.15	(1921) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1922) QDP
24.75/8.15	(1923) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1924) QDP
24.75/8.15	(1925) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1926) QDP
24.75/8.15	(1927) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1928) QDP
24.75/8.15	(1929) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1930) QDP
24.75/8.15	(1931) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1932) QDP
24.75/8.15	(1933) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1934) QDP
24.75/8.15	(1935) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1936) QDP
24.75/8.15	(1937) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1938) QDP
24.75/8.15	(1939) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1940) QDP
24.75/8.15	(1941) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1942) QDP
24.75/8.15	(1943) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1944) QDP
24.75/8.15	(1945) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1946) QDP
24.75/8.15	(1947) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1948) QDP
24.75/8.15	(1949) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1950) QDP
24.75/8.15	(1951) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1952) QDP
24.75/8.15	(1953) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1954) QDP
24.75/8.15	(1955) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1956) QDP
24.75/8.15	(1957) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1958) QDP
24.75/8.15	(1959) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1960) QDP
24.75/8.15	(1961) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1962) QDP
24.75/8.15	(1963) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1964) QDP
24.75/8.15	(1965) TransformationProof [EQUIVALENT, 1 ms]
24.75/8.15	(1966) QDP
24.75/8.15	(1967) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1968) QDP
24.75/8.15	(1969) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1970) QDP
24.75/8.15	(1971) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1972) QDP
24.75/8.15	(1973) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1974) QDP
24.75/8.15	(1975) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1976) QDP
24.75/8.15	(1977) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(1978) QDP
24.75/8.15	(1979) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1980) QDP
24.75/8.15	(1981) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1982) QDP
24.75/8.15	(1983) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1984) QDP
24.75/8.15	(1985) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1986) QDP
24.75/8.15	(1987) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1988) QDP
24.75/8.15	(1989) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1990) QDP
24.75/8.15	(1991) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1992) QDP
24.75/8.15	(1993) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1994) QDP
24.75/8.15	(1995) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1996) QDP
24.75/8.15	(1997) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(1998) QDP
24.75/8.15	(1999) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2000) QDP
24.75/8.15	(2001) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2002) QDP
24.75/8.15	(2003) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2004) QDP
24.75/8.15	(2005) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2006) QDP
24.75/8.15	(2007) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2008) QDP
24.75/8.15	(2009) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2010) QDP
24.75/8.15	(2011) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2012) QDP
24.75/8.15	(2013) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2014) QDP
24.75/8.15	(2015) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2016) QDP
24.75/8.15	(2017) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2018) QDP
24.75/8.15	(2019) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2020) QDP
24.75/8.15	(2021) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2022) QDP
24.75/8.15	(2023) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2024) QDP
24.75/8.15	(2025) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2026) QDP
24.75/8.15	(2027) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2028) QDP
24.75/8.15	(2029) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2030) QDP
24.75/8.15	(2031) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2032) QDP
24.75/8.15	(2033) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2034) QDP
24.75/8.15	(2035) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2036) QDP
24.75/8.15	(2037) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2038) QDP
24.75/8.15	(2039) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2040) QDP
24.75/8.15	(2041) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2042) QDP
24.75/8.15	(2043) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2044) QDP
24.75/8.15	(2045) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2046) QDP
24.75/8.15	(2047) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2048) QDP
24.75/8.15	(2049) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2050) QDP
24.75/8.15	(2051) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2052) QDP
24.75/8.15	(2053) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2054) QDP
24.75/8.15	(2055) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2056) QDP
24.75/8.15	(2057) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2058) QDP
24.75/8.15	(2059) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2060) QDP
24.75/8.15	(2061) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2062) QDP
24.75/8.15	(2063) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2064) QDP
24.75/8.15	(2065) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2066) QDP
24.75/8.15	(2067) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2068) QDP
24.75/8.15	(2069) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2070) QDP
24.75/8.15	(2071) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2072) QDP
24.75/8.15	(2073) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2074) QDP
24.75/8.15	(2075) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2076) QDP
24.75/8.15	(2077) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2078) QDP
24.75/8.15	(2079) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2080) QDP
24.75/8.15	(2081) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2082) QDP
24.75/8.15	(2083) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2084) QDP
24.75/8.15	(2085) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2086) QDP
24.75/8.15	(2087) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2088) QDP
24.75/8.15	(2089) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2090) QDP
24.75/8.15	(2091) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2092) QDP
24.75/8.15	(2093) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2094) QDP
24.75/8.15	(2095) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2096) QDP
24.75/8.15	(2097) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2098) QDP
24.75/8.15	(2099) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2100) QDP
24.75/8.15	(2101) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2102) QDP
24.75/8.15	(2103) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2104) QDP
24.75/8.15	(2105) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2106) QDP
24.75/8.15	(2107) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2108) QDP
24.75/8.15	(2109) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2110) QDP
24.75/8.15	(2111) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2112) QDP
24.75/8.15	(2113) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2114) QDP
24.75/8.15	(2115) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2116) QDP
24.75/8.15	(2117) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2118) QDP
24.75/8.15	(2119) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2120) QDP
24.75/8.15	(2121) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2122) QDP
24.75/8.15	(2123) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2124) QDP
24.75/8.15	(2125) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2126) QDP
24.75/8.15	(2127) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2128) QDP
24.75/8.15	(2129) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2130) QDP
24.75/8.15	(2131) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2132) QDP
24.75/8.15	(2133) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2134) QDP
24.75/8.15	(2135) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2136) QDP
24.75/8.15	(2137) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2138) QDP
24.75/8.15	(2139) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2140) QDP
24.75/8.15	(2141) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2142) QDP
24.75/8.15	(2143) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2144) QDP
24.75/8.15	(2145) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2146) QDP
24.75/8.15	(2147) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2148) QDP
24.75/8.15	(2149) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2150) QDP
24.75/8.15	(2151) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2152) QDP
24.75/8.15	(2153) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2154) QDP
24.75/8.15	(2155) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2156) QDP
24.75/8.15	(2157) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2158) QDP
24.75/8.15	(2159) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2160) QDP
24.75/8.15	(2161) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2162) QDP
24.75/8.15	(2163) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2164) QDP
24.75/8.15	(2165) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2166) QDP
24.75/8.15	(2167) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2168) QDP
24.75/8.15	(2169) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2170) QDP
24.75/8.15	(2171) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2172) QDP
24.75/8.15	(2173) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2174) QDP
24.75/8.15	(2175) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2176) QDP
24.75/8.15	(2177) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2178) QDP
24.75/8.15	(2179) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2180) QDP
24.75/8.15	(2181) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2182) QDP
24.75/8.15	(2183) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2184) QDP
24.75/8.15	(2185) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2186) QDP
24.75/8.15	(2187) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2188) QDP
24.75/8.15	(2189) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2190) QDP
24.75/8.15	(2191) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2192) QDP
24.75/8.15	(2193) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2194) QDP
24.75/8.15	(2195) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2196) QDP
24.75/8.15	(2197) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2198) QDP
24.75/8.15	(2199) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2200) QDP
24.75/8.15	(2201) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2202) QDP
24.75/8.15	(2203) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2204) QDP
24.75/8.15	(2205) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2206) QDP
24.75/8.15	(2207) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2208) QDP
24.75/8.15	(2209) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2210) QDP
24.75/8.15	(2211) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2212) QDP
24.75/8.15	(2213) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2214) QDP
24.75/8.15	(2215) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2216) QDP
24.75/8.15	(2217) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2218) QDP
24.75/8.15	(2219) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2220) QDP
24.75/8.15	(2221) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2222) QDP
24.75/8.15	(2223) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2224) QDP
24.75/8.15	(2225) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2226) QDP
24.75/8.15	(2227) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2228) QDP
24.75/8.15	(2229) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2230) QDP
24.75/8.15	(2231) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2232) QDP
24.75/8.15	(2233) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2234) QDP
24.75/8.15	(2235) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2236) QDP
24.75/8.15	(2237) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2238) QDP
24.75/8.15	(2239) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2240) QDP
24.75/8.15	(2241) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2242) QDP
24.75/8.15	(2243) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2244) QDP
24.75/8.15	(2245) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2246) QDP
24.75/8.15	(2247) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2248) QDP
24.75/8.15	(2249) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2250) QDP
24.75/8.15	(2251) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2252) QDP
24.75/8.15	(2253) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2254) QDP
24.75/8.15	(2255) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2256) QDP
24.75/8.15	(2257) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2258) QDP
24.75/8.15	(2259) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2260) QDP
24.75/8.15	(2261) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2262) QDP
24.75/8.15	(2263) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2264) QDP
24.75/8.15	(2265) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2266) QDP
24.75/8.15	(2267) TransformationProof [EQUIVALENT, 1 ms]
24.75/8.15	(2268) QDP
24.75/8.15	(2269) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2270) QDP
24.75/8.15	(2271) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2272) QDP
24.75/8.15	(2273) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2274) QDP
24.75/8.15	(2275) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2276) QDP
24.75/8.15	(2277) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2278) QDP
24.75/8.15	(2279) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2280) QDP
24.75/8.15	(2281) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2282) QDP
24.75/8.15	(2283) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2284) QDP
24.75/8.15	(2285) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2286) QDP
24.75/8.15	(2287) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2288) QDP
24.75/8.15	(2289) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2290) QDP
24.75/8.15	(2291) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2292) QDP
24.75/8.15	(2293) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2294) QDP
24.75/8.15	(2295) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2296) QDP
24.75/8.15	(2297) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2298) QDP
24.75/8.15	(2299) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2300) QDP
24.75/8.15	(2301) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2302) QDP
24.75/8.15	(2303) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2304) QDP
24.75/8.15	(2305) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2306) QDP
24.75/8.15	(2307) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2308) QDP
24.75/8.15	(2309) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2310) QDP
24.75/8.15	(2311) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2312) QDP
24.75/8.15	(2313) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2314) QDP
24.75/8.15	(2315) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2316) QDP
24.75/8.15	(2317) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2318) QDP
24.75/8.15	(2319) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2320) QDP
24.75/8.15	(2321) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2322) QDP
24.75/8.15	(2323) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2324) QDP
24.75/8.15	(2325) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.15	(2326) QDP
24.75/8.15	(2327) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.15	(2328) QDP
24.75/8.16	(2329) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2330) QDP
24.75/8.16	(2331) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2332) QDP
24.75/8.16	(2333) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2334) QDP
24.75/8.16	(2335) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2336) QDP
24.75/8.16	(2337) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2338) QDP
24.75/8.16	(2339) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2340) QDP
24.75/8.16	(2341) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2342) QDP
24.75/8.16	(2343) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2344) QDP
24.75/8.16	(2345) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2346) QDP
24.75/8.16	(2347) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2348) QDP
24.75/8.16	(2349) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2350) QDP
24.75/8.16	(2351) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2352) QDP
24.75/8.16	(2353) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2354) QDP
24.75/8.16	(2355) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2356) QDP
24.75/8.16	(2357) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2358) QDP
24.75/8.16	(2359) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2360) QDP
24.75/8.16	(2361) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2362) QDP
24.75/8.16	(2363) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2364) QDP
24.75/8.16	(2365) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2366) QDP
24.75/8.16	(2367) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2368) QDP
24.75/8.16	(2369) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2370) QDP
24.75/8.16	(2371) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2372) QDP
24.75/8.16	(2373) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2374) QDP
24.75/8.16	(2375) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2376) QDP
24.75/8.16	(2377) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2378) QDP
24.75/8.16	(2379) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2380) QDP
24.75/8.16	(2381) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2382) QDP
24.75/8.16	(2383) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2384) QDP
24.75/8.16	(2385) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2386) QDP
24.75/8.16	(2387) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2388) QDP
24.75/8.16	(2389) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2390) QDP
24.75/8.16	(2391) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2392) QDP
24.75/8.16	(2393) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2394) QDP
24.75/8.16	(2395) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2396) QDP
24.75/8.16	(2397) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2398) QDP
24.75/8.16	(2399) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2400) QDP
24.75/8.16	(2401) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2402) QDP
24.75/8.16	(2403) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2404) QDP
24.75/8.16	(2405) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2406) QDP
24.75/8.16	(2407) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2408) QDP
24.75/8.16	(2409) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2410) QDP
24.75/8.16	(2411) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2412) QDP
24.75/8.16	(2413) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2414) QDP
24.75/8.16	(2415) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2416) QDP
24.75/8.16	(2417) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2418) QDP
24.75/8.16	(2419) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2420) QDP
24.75/8.16	(2421) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2422) QDP
24.75/8.16	(2423) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2424) QDP
24.75/8.16	(2425) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2426) QDP
24.75/8.16	(2427) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2428) QDP
24.75/8.16	(2429) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2430) QDP
24.75/8.16	(2431) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2432) QDP
24.75/8.16	(2433) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2434) QDP
24.75/8.16	(2435) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2436) QDP
24.75/8.16	(2437) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2438) QDP
24.75/8.16	(2439) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2440) QDP
24.75/8.16	(2441) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2442) QDP
24.75/8.16	(2443) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2444) QDP
24.75/8.16	(2445) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2446) QDP
24.75/8.16	(2447) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2448) QDP
24.75/8.16	(2449) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2450) QDP
24.75/8.16	(2451) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2452) QDP
24.75/8.16	(2453) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2454) QDP
24.75/8.16	(2455) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2456) QDP
24.75/8.16	(2457) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2458) QDP
24.75/8.16	(2459) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2460) QDP
24.75/8.16	(2461) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2462) QDP
24.75/8.16	(2463) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2464) QDP
24.75/8.16	(2465) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2466) QDP
24.75/8.16	(2467) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2468) QDP
24.75/8.16	(2469) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2470) QDP
24.75/8.16	(2471) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2472) QDP
24.75/8.16	(2473) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2474) QDP
24.75/8.16	(2475) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2476) QDP
24.75/8.16	(2477) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2478) QDP
24.75/8.16	(2479) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2480) QDP
24.75/8.16	(2481) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2482) QDP
24.75/8.16	(2483) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2484) QDP
24.75/8.16	(2485) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2486) QDP
24.75/8.16	(2487) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2488) QDP
24.75/8.16	(2489) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2490) QDP
24.75/8.16	(2491) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2492) QDP
24.75/8.16	(2493) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2494) QDP
24.75/8.16	(2495) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2496) QDP
24.75/8.16	(2497) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2498) QDP
24.75/8.16	(2499) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2500) QDP
24.75/8.16	(2501) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2502) QDP
24.75/8.16	(2503) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2504) QDP
24.75/8.16	(2505) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2506) QDP
24.75/8.16	(2507) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2508) QDP
24.75/8.16	(2509) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2510) QDP
24.75/8.16	(2511) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2512) QDP
24.75/8.16	(2513) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2514) QDP
24.75/8.16	(2515) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2516) QDP
24.75/8.16	(2517) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2518) QDP
24.75/8.16	(2519) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2520) QDP
24.75/8.16	(2521) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2522) QDP
24.75/8.16	(2523) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2524) QDP
24.75/8.16	(2525) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2526) QDP
24.75/8.16	(2527) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2528) QDP
24.75/8.16	(2529) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2530) QDP
24.75/8.16	(2531) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2532) QDP
24.75/8.16	(2533) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2534) QDP
24.75/8.16	(2535) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2536) QDP
24.75/8.16	(2537) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2538) QDP
24.75/8.16	(2539) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2540) QDP
24.75/8.16	(2541) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2542) QDP
24.75/8.16	(2543) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2544) QDP
24.75/8.16	(2545) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2546) QDP
24.75/8.16	(2547) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2548) QDP
24.75/8.16	(2549) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2550) QDP
24.75/8.16	(2551) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2552) QDP
24.75/8.16	(2553) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2554) QDP
24.75/8.16	(2555) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2556) QDP
24.75/8.16	(2557) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2558) QDP
24.75/8.16	(2559) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2560) QDP
24.75/8.16	(2561) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2562) QDP
24.75/8.16	(2563) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2564) QDP
24.75/8.16	(2565) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2566) QDP
24.75/8.16	(2567) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2568) QDP
24.75/8.16	(2569) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2570) QDP
24.75/8.16	(2571) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2572) QDP
24.75/8.16	(2573) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2574) QDP
24.75/8.16	(2575) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2576) QDP
24.75/8.16	(2577) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2578) QDP
24.75/8.16	(2579) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2580) QDP
24.75/8.16	(2581) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2582) QDP
24.75/8.16	(2583) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2584) QDP
24.75/8.16	(2585) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2586) QDP
24.75/8.16	(2587) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2588) QDP
24.75/8.16	(2589) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2590) QDP
24.75/8.16	(2591) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2592) QDP
24.75/8.16	(2593) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2594) QDP
24.75/8.16	(2595) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2596) QDP
24.75/8.16	(2597) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2598) QDP
24.75/8.16	(2599) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2600) QDP
24.75/8.16	(2601) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2602) QDP
24.75/8.16	(2603) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2604) QDP
24.75/8.16	(2605) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2606) QDP
24.75/8.16	(2607) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2608) QDP
24.75/8.16	(2609) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2610) QDP
24.75/8.16	(2611) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2612) QDP
24.75/8.16	(2613) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2614) QDP
24.75/8.16	(2615) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2616) QDP
24.75/8.16	(2617) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2618) QDP
24.75/8.16	(2619) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2620) QDP
24.75/8.16	(2621) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2622) QDP
24.75/8.16	(2623) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2624) QDP
24.75/8.16	(2625) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2626) QDP
24.75/8.16	(2627) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2628) QDP
24.75/8.16	(2629) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2630) QDP
24.75/8.16	(2631) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2632) QDP
24.75/8.16	(2633) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2634) QDP
24.75/8.16	(2635) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2636) QDP
24.75/8.16	(2637) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2638) QDP
24.75/8.16	(2639) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2640) QDP
24.75/8.16	(2641) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2642) QDP
24.75/8.16	(2643) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2644) QDP
24.75/8.16	(2645) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2646) QDP
24.75/8.16	(2647) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2648) QDP
24.75/8.16	(2649) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2650) QDP
24.75/8.16	(2651) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2652) QDP
24.75/8.16	(2653) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2654) QDP
24.75/8.16	(2655) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2656) QDP
24.75/8.16	(2657) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2658) QDP
24.75/8.16	(2659) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2660) QDP
24.75/8.16	(2661) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2662) QDP
24.75/8.16	(2663) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2664) QDP
24.75/8.16	(2665) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2666) QDP
24.75/8.16	(2667) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2668) QDP
24.75/8.16	(2669) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2670) QDP
24.75/8.16	(2671) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2672) QDP
24.75/8.16	(2673) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2674) QDP
24.75/8.16	(2675) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2676) QDP
24.75/8.16	(2677) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2678) QDP
24.75/8.16	(2679) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2680) QDP
24.75/8.16	(2681) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2682) QDP
24.75/8.16	(2683) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2684) QDP
24.75/8.16	(2685) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2686) QDP
24.75/8.16	(2687) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2688) QDP
24.75/8.16	(2689) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2690) QDP
24.75/8.16	(2691) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2692) QDP
24.75/8.16	(2693) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2694) QDP
24.75/8.16	(2695) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2696) QDP
24.75/8.16	(2697) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2698) QDP
24.75/8.16	(2699) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2700) QDP
24.75/8.16	(2701) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2702) QDP
24.75/8.16	(2703) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2704) QDP
24.75/8.16	(2705) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2706) QDP
24.75/8.16	(2707) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2708) QDP
24.75/8.16	(2709) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2710) QDP
24.75/8.16	(2711) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2712) QDP
24.75/8.16	(2713) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2714) QDP
24.75/8.16	(2715) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2716) QDP
24.75/8.16	(2717) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2718) QDP
24.75/8.16	(2719) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2720) QDP
24.75/8.16	(2721) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2722) QDP
24.75/8.16	(2723) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2724) QDP
24.75/8.16	(2725) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2726) QDP
24.75/8.16	(2727) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2728) QDP
24.75/8.16	(2729) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2730) QDP
24.75/8.16	(2731) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2732) QDP
24.75/8.16	(2733) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2734) QDP
24.75/8.16	(2735) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2736) QDP
24.75/8.16	(2737) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2738) QDP
24.75/8.16	(2739) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2740) QDP
24.75/8.16	(2741) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2742) QDP
24.75/8.16	(2743) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2744) QDP
24.75/8.16	(2745) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2746) QDP
24.75/8.16	(2747) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2748) QDP
24.75/8.16	(2749) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2750) QDP
24.75/8.16	(2751) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2752) QDP
24.75/8.16	(2753) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2754) QDP
24.75/8.16	(2755) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2756) QDP
24.75/8.16	(2757) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2758) QDP
24.75/8.16	(2759) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2760) QDP
24.75/8.16	(2761) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2762) QDP
24.75/8.16	(2763) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2764) QDP
24.75/8.16	(2765) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2766) QDP
24.75/8.16	(2767) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2768) QDP
24.75/8.16	(2769) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2770) QDP
24.75/8.16	(2771) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2772) QDP
24.75/8.16	(2773) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2774) QDP
24.75/8.16	(2775) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2776) QDP
24.75/8.16	(2777) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2778) QDP
24.75/8.16	(2779) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2780) QDP
24.75/8.16	(2781) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2782) QDP
24.75/8.16	(2783) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2784) QDP
24.75/8.16	(2785) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2786) QDP
24.75/8.16	(2787) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2788) QDP
24.75/8.16	(2789) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2790) QDP
24.75/8.16	(2791) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2792) QDP
24.75/8.16	(2793) DependencyGraphProof [EQUIVALENT, 0 ms]
24.75/8.16	(2794) QDP
24.75/8.16	(2795) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2796) QDP
24.75/8.16	(2797) TransformationProof [EQUIVALENT, 0 ms]
24.75/8.16	(2798) QDP
24.75/8.16	(2799) UsableRulesReductionPairsProof [EQUIVALENT, 51 ms]
24.75/8.16	(2800) QDP
24.75/8.16	(2801) QDPOrderProof [EQUIVALENT, 99 ms]
24.75/8.16	(2802) QDP
24.75/8.16	(2803) NonTerminationLoopProof [COMPLETE, 878 ms]
24.75/8.16	(2804) NO
24.75/8.16	
24.75/8.16	
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(0)
24.75/8.16	Obligation:
24.75/8.16	Conditional term rewrite system:
24.75/8.16	The TRS R consists of the following rules:
24.75/8.16	
24.75/8.16	   a -> c
24.75/8.16	   b -> c
24.75/8.16	   a -> d
24.75/8.16	   b -> d
24.75/8.16	   c -> e
24.75/8.16	   c -> k
24.75/8.16	   d -> k
24.75/8.16	   A -> h(f(a), f(b))
24.75/8.16	   h(x, x) -> g(x, x, f(k))
24.75/8.16	   g(d, x, x) -> A
24.75/8.16	
24.75/8.16	The conditional TRS C consists of the following conditional rules:
24.75/8.16	
24.75/8.16	   f(x) -> x <= x -> e
24.75/8.16	
24.75/8.16	
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(1) CTRSToQTRSProof (SOUND)
24.75/8.16	The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC].
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(2)
24.75/8.16	Obligation:
24.75/8.16	Q restricted rewrite system:
24.75/8.16	The TRS R consists of the following rules:
24.75/8.16	
24.75/8.16	   f(x) -> U1(x, x)
24.75/8.16	   U1(e, x) -> x
24.75/8.16	   a -> c
24.75/8.16	   b -> c
24.75/8.16	   a -> d
24.75/8.16	   b -> d
24.75/8.16	   c -> e
24.75/8.16	   c -> k
24.75/8.16	   d -> k
24.75/8.16	   A -> h(f(a), f(b))
24.75/8.16	   h(x, x) -> g(x, x, f(k))
24.75/8.16	   g(d, x, x) -> A
24.75/8.16	
24.75/8.16	Q is empty.
24.75/8.16	
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(3) DependencyPairsProof (EQUIVALENT)
24.75/8.16	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(4)
24.75/8.16	Obligation:
24.75/8.16	Q DP problem:
24.75/8.16	The TRS P consists of the following rules:
24.75/8.16	
24.75/8.16	   F(x) -> U1^1(x, x)
24.75/8.16	   A^1 -> C
24.75/8.16	   B -> C
24.75/8.16	   A^1 -> D
24.75/8.16	   B -> D
24.75/8.16	   A^2 -> H(f(a), f(b))
24.75/8.16	   A^2 -> F(a)
24.75/8.16	   A^2 -> A^1
24.75/8.16	   A^2 -> F(b)
24.75/8.16	   A^2 -> B
24.75/8.16	   H(x, x) -> G(x, x, f(k))
24.75/8.16	   H(x, x) -> F(k)
24.75/8.16	   G(d, x, x) -> A^2
24.75/8.16	
24.75/8.16	The TRS R consists of the following rules:
24.75/8.16	
24.75/8.16	   f(x) -> U1(x, x)
24.75/8.16	   U1(e, x) -> x
24.75/8.16	   a -> c
24.75/8.16	   b -> c
24.75/8.16	   a -> d
24.75/8.16	   b -> d
24.75/8.16	   c -> e
24.75/8.16	   c -> k
24.75/8.16	   d -> k
24.75/8.16	   A -> h(f(a), f(b))
24.75/8.16	   h(x, x) -> g(x, x, f(k))
24.75/8.16	   g(d, x, x) -> A
24.75/8.16	
24.75/8.16	Q is empty.
24.75/8.16	We have to consider all minimal (P,Q,R)-chains.
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(5) DependencyGraphProof (EQUIVALENT)
24.75/8.16	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 10 less nodes.
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(6)
24.75/8.16	Obligation:
24.75/8.16	Q DP problem:
24.75/8.16	The TRS P consists of the following rules:
24.75/8.16	
24.75/8.16	   A^2 -> H(f(a), f(b))
24.75/8.16	   H(x, x) -> G(x, x, f(k))
24.75/8.16	   G(d, x, x) -> A^2
24.75/8.16	
24.75/8.16	The TRS R consists of the following rules:
24.75/8.16	
24.75/8.16	   f(x) -> U1(x, x)
24.75/8.16	   U1(e, x) -> x
24.75/8.16	   a -> c
24.75/8.16	   b -> c
24.75/8.16	   a -> d
24.75/8.16	   b -> d
24.75/8.16	   c -> e
24.75/8.16	   c -> k
24.75/8.16	   d -> k
24.75/8.16	   A -> h(f(a), f(b))
24.75/8.16	   h(x, x) -> g(x, x, f(k))
24.75/8.16	   g(d, x, x) -> A
24.75/8.16	
24.75/8.16	Q is empty.
24.75/8.16	We have to consider all minimal (P,Q,R)-chains.
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(7) UsableRulesReductionPairsProof (EQUIVALENT)
24.75/8.16	By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.
24.75/8.16	
24.75/8.16	No dependency pairs are removed.
24.75/8.16	
24.75/8.16	The following rules are removed from R:
24.75/8.16	
24.75/8.16	   A -> h(f(a), f(b))
24.75/8.16	   h(x, x) -> g(x, x, f(k))
24.75/8.16	   g(d, x, x) -> A
24.75/8.16	Used ordering: POLO with Polynomial interpretation [POLO]:
24.75/8.16	
24.75/8.16	   POL(A^2) = 0
24.75/8.16	   POL(G(x_1, x_2, x_3)) = x_1 + x_2 + x_3
24.75/8.16	   POL(H(x_1, x_2)) = 2*x_1 + 2*x_2
24.75/8.16	   POL(U1(x_1, x_2)) = x_1 + x_2
24.75/8.16	   POL(a) = 0
24.75/8.16	   POL(b) = 0
24.75/8.16	   POL(c) = 0
24.75/8.16	   POL(d) = 0
24.75/8.16	   POL(e) = 0
24.75/8.16	   POL(f(x_1)) = 2*x_1
24.75/8.16	   POL(k) = 0
24.75/8.16	
24.75/8.16	
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(8)
24.75/8.16	Obligation:
24.75/8.16	Q DP problem:
24.75/8.16	The TRS P consists of the following rules:
24.75/8.16	
24.75/8.16	   A^2 -> H(f(a), f(b))
24.75/8.16	   H(x, x) -> G(x, x, f(k))
24.75/8.16	   G(d, x, x) -> A^2
24.75/8.16	
24.75/8.16	The TRS R consists of the following rules:
24.75/8.16	
24.75/8.16	   f(x) -> U1(x, x)
24.75/8.16	   U1(e, x) -> x
24.75/8.16	   a -> c
24.75/8.16	   a -> d
24.75/8.16	   b -> c
24.75/8.16	   b -> d
24.75/8.16	   d -> k
24.75/8.16	   c -> e
24.75/8.16	   c -> k
24.75/8.16	
24.75/8.16	Q is empty.
24.75/8.16	We have to consider all minimal (P,Q,R)-chains.
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(9) TransformationProof (EQUIVALENT)
24.75/8.16	By narrowing [LPAR04] the rule A^2 -> H(f(a), f(b)) at position [] we obtained the following new rules [LPAR04]:
24.75/8.16	
24.75/8.16	   (A^2 -> H(U1(a, a), f(b)),A^2 -> H(U1(a, a), f(b)))
24.75/8.16	   (A^2 -> H(f(c), f(b)),A^2 -> H(f(c), f(b)))
24.75/8.16	   (A^2 -> H(f(d), f(b)),A^2 -> H(f(d), f(b)))
24.75/8.16	   (A^2 -> H(f(a), U1(b, b)),A^2 -> H(f(a), U1(b, b)))
24.75/8.16	   (A^2 -> H(f(a), f(c)),A^2 -> H(f(a), f(c)))
24.75/8.16	   (A^2 -> H(f(a), f(d)),A^2 -> H(f(a), f(d)))
24.75/8.16	
24.75/8.16	
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(10)
24.75/8.16	Obligation:
24.75/8.16	Q DP problem:
24.75/8.16	The TRS P consists of the following rules:
24.75/8.16	
24.75/8.16	   H(x, x) -> G(x, x, f(k))
24.75/8.16	   G(d, x, x) -> A^2
24.75/8.16	   A^2 -> H(U1(a, a), f(b))
24.75/8.16	   A^2 -> H(f(c), f(b))
24.75/8.16	   A^2 -> H(f(d), f(b))
24.75/8.16	   A^2 -> H(f(a), U1(b, b))
24.75/8.16	   A^2 -> H(f(a), f(c))
24.75/8.16	   A^2 -> H(f(a), f(d))
24.75/8.16	
24.75/8.16	The TRS R consists of the following rules:
24.75/8.16	
24.75/8.16	   f(x) -> U1(x, x)
24.75/8.16	   U1(e, x) -> x
24.75/8.16	   a -> c
24.75/8.16	   a -> d
24.75/8.16	   b -> c
24.75/8.16	   b -> d
24.75/8.16	   d -> k
24.75/8.16	   c -> e
24.75/8.16	   c -> k
24.75/8.16	
24.75/8.16	Q is empty.
24.75/8.16	We have to consider all minimal (P,Q,R)-chains.
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(11) TransformationProof (EQUIVALENT)
24.75/8.16	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), f(b)) at position [] we obtained the following new rules [LPAR04]:
24.75/8.16	
24.75/8.16	   (A^2 -> H(U1(c, a), f(b)),A^2 -> H(U1(c, a), f(b)))
24.75/8.16	   (A^2 -> H(U1(d, a), f(b)),A^2 -> H(U1(d, a), f(b)))
24.75/8.16	   (A^2 -> H(U1(a, c), f(b)),A^2 -> H(U1(a, c), f(b)))
24.75/8.16	   (A^2 -> H(U1(a, d), f(b)),A^2 -> H(U1(a, d), f(b)))
24.75/8.16	   (A^2 -> H(U1(a, a), U1(b, b)),A^2 -> H(U1(a, a), U1(b, b)))
24.75/8.16	   (A^2 -> H(U1(a, a), f(c)),A^2 -> H(U1(a, a), f(c)))
24.75/8.16	   (A^2 -> H(U1(a, a), f(d)),A^2 -> H(U1(a, a), f(d)))
24.75/8.16	
24.75/8.16	
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(12)
24.75/8.16	Obligation:
24.75/8.16	Q DP problem:
24.75/8.16	The TRS P consists of the following rules:
24.75/8.16	
24.75/8.16	   H(x, x) -> G(x, x, f(k))
24.75/8.16	   G(d, x, x) -> A^2
24.75/8.16	   A^2 -> H(f(c), f(b))
24.75/8.16	   A^2 -> H(f(d), f(b))
24.75/8.16	   A^2 -> H(f(a), U1(b, b))
24.75/8.16	   A^2 -> H(f(a), f(c))
24.75/8.16	   A^2 -> H(f(a), f(d))
24.75/8.16	   A^2 -> H(U1(c, a), f(b))
24.75/8.16	   A^2 -> H(U1(d, a), f(b))
24.75/8.16	   A^2 -> H(U1(a, c), f(b))
24.75/8.16	   A^2 -> H(U1(a, d), f(b))
24.75/8.16	   A^2 -> H(U1(a, a), U1(b, b))
24.75/8.16	   A^2 -> H(U1(a, a), f(c))
24.75/8.16	   A^2 -> H(U1(a, a), f(d))
24.75/8.16	
24.75/8.16	The TRS R consists of the following rules:
24.75/8.16	
24.75/8.16	   f(x) -> U1(x, x)
24.75/8.16	   U1(e, x) -> x
24.75/8.16	   a -> c
24.75/8.16	   a -> d
24.75/8.16	   b -> c
24.75/8.16	   b -> d
24.75/8.16	   d -> k
24.75/8.16	   c -> e
24.75/8.16	   c -> k
24.75/8.16	
24.75/8.16	Q is empty.
24.75/8.16	We have to consider all minimal (P,Q,R)-chains.
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(13) TransformationProof (EQUIVALENT)
24.75/8.16	By narrowing [LPAR04] the rule A^2 -> H(f(c), f(b)) at position [] we obtained the following new rules [LPAR04]:
24.75/8.16	
24.75/8.16	   (A^2 -> H(U1(c, c), f(b)),A^2 -> H(U1(c, c), f(b)))
24.75/8.16	   (A^2 -> H(f(e), f(b)),A^2 -> H(f(e), f(b)))
24.75/8.16	   (A^2 -> H(f(k), f(b)),A^2 -> H(f(k), f(b)))
24.75/8.16	   (A^2 -> H(f(c), U1(b, b)),A^2 -> H(f(c), U1(b, b)))
24.75/8.16	   (A^2 -> H(f(c), f(c)),A^2 -> H(f(c), f(c)))
24.75/8.16	   (A^2 -> H(f(c), f(d)),A^2 -> H(f(c), f(d)))
24.75/8.16	
24.75/8.16	
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(14)
24.75/8.16	Obligation:
24.75/8.16	Q DP problem:
24.75/8.16	The TRS P consists of the following rules:
24.75/8.16	
24.75/8.16	   H(x, x) -> G(x, x, f(k))
24.75/8.16	   G(d, x, x) -> A^2
24.75/8.16	   A^2 -> H(f(d), f(b))
24.75/8.16	   A^2 -> H(f(a), U1(b, b))
24.75/8.16	   A^2 -> H(f(a), f(c))
24.75/8.16	   A^2 -> H(f(a), f(d))
24.75/8.16	   A^2 -> H(U1(c, a), f(b))
24.75/8.16	   A^2 -> H(U1(d, a), f(b))
24.75/8.16	   A^2 -> H(U1(a, c), f(b))
24.75/8.16	   A^2 -> H(U1(a, d), f(b))
24.75/8.16	   A^2 -> H(U1(a, a), U1(b, b))
24.75/8.16	   A^2 -> H(U1(a, a), f(c))
24.75/8.16	   A^2 -> H(U1(a, a), f(d))
24.75/8.16	   A^2 -> H(U1(c, c), f(b))
24.75/8.16	   A^2 -> H(f(e), f(b))
24.75/8.16	   A^2 -> H(f(k), f(b))
24.75/8.16	   A^2 -> H(f(c), U1(b, b))
24.75/8.16	   A^2 -> H(f(c), f(c))
24.75/8.16	   A^2 -> H(f(c), f(d))
24.75/8.16	
24.75/8.16	The TRS R consists of the following rules:
24.75/8.16	
24.75/8.16	   f(x) -> U1(x, x)
24.75/8.16	   U1(e, x) -> x
24.75/8.16	   a -> c
24.75/8.16	   a -> d
24.75/8.16	   b -> c
24.75/8.16	   b -> d
24.75/8.16	   d -> k
24.75/8.16	   c -> e
24.75/8.16	   c -> k
24.75/8.16	
24.75/8.16	Q is empty.
24.75/8.16	We have to consider all minimal (P,Q,R)-chains.
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(15) TransformationProof (EQUIVALENT)
24.75/8.16	By narrowing [LPAR04] the rule A^2 -> H(f(d), f(b)) at position [] we obtained the following new rules [LPAR04]:
24.75/8.16	
24.75/8.16	   (A^2 -> H(U1(d, d), f(b)),A^2 -> H(U1(d, d), f(b)))
24.75/8.16	   (A^2 -> H(f(k), f(b)),A^2 -> H(f(k), f(b)))
24.75/8.16	   (A^2 -> H(f(d), U1(b, b)),A^2 -> H(f(d), U1(b, b)))
24.75/8.16	   (A^2 -> H(f(d), f(c)),A^2 -> H(f(d), f(c)))
24.75/8.16	   (A^2 -> H(f(d), f(d)),A^2 -> H(f(d), f(d)))
24.75/8.16	
24.75/8.16	
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(16)
24.75/8.16	Obligation:
24.75/8.16	Q DP problem:
24.75/8.16	The TRS P consists of the following rules:
24.75/8.16	
24.75/8.16	   H(x, x) -> G(x, x, f(k))
24.75/8.16	   G(d, x, x) -> A^2
24.75/8.16	   A^2 -> H(f(a), U1(b, b))
24.75/8.16	   A^2 -> H(f(a), f(c))
24.75/8.16	   A^2 -> H(f(a), f(d))
24.75/8.16	   A^2 -> H(U1(c, a), f(b))
24.75/8.16	   A^2 -> H(U1(d, a), f(b))
24.75/8.16	   A^2 -> H(U1(a, c), f(b))
24.75/8.16	   A^2 -> H(U1(a, d), f(b))
24.75/8.16	   A^2 -> H(U1(a, a), U1(b, b))
24.75/8.16	   A^2 -> H(U1(a, a), f(c))
24.75/8.16	   A^2 -> H(U1(a, a), f(d))
24.75/8.16	   A^2 -> H(U1(c, c), f(b))
24.75/8.16	   A^2 -> H(f(e), f(b))
24.75/8.16	   A^2 -> H(f(k), f(b))
24.75/8.16	   A^2 -> H(f(c), U1(b, b))
24.75/8.16	   A^2 -> H(f(c), f(c))
24.75/8.16	   A^2 -> H(f(c), f(d))
24.75/8.16	   A^2 -> H(U1(d, d), f(b))
24.75/8.16	   A^2 -> H(f(d), U1(b, b))
24.75/8.16	   A^2 -> H(f(d), f(c))
24.75/8.16	   A^2 -> H(f(d), f(d))
24.75/8.16	
24.75/8.16	The TRS R consists of the following rules:
24.75/8.16	
24.75/8.16	   f(x) -> U1(x, x)
24.75/8.16	   U1(e, x) -> x
24.75/8.16	   a -> c
24.75/8.16	   a -> d
24.75/8.16	   b -> c
24.75/8.16	   b -> d
24.75/8.16	   d -> k
24.75/8.16	   c -> e
24.75/8.16	   c -> k
24.75/8.16	
24.75/8.16	Q is empty.
24.75/8.16	We have to consider all minimal (P,Q,R)-chains.
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(17) TransformationProof (EQUIVALENT)
24.75/8.16	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
24.75/8.16	
24.75/8.16	   (A^2 -> H(U1(a, a), U1(b, b)),A^2 -> H(U1(a, a), U1(b, b)))
24.75/8.16	   (A^2 -> H(f(c), U1(b, b)),A^2 -> H(f(c), U1(b, b)))
24.75/8.16	   (A^2 -> H(f(d), U1(b, b)),A^2 -> H(f(d), U1(b, b)))
24.75/8.16	   (A^2 -> H(f(a), U1(c, b)),A^2 -> H(f(a), U1(c, b)))
24.75/8.16	   (A^2 -> H(f(a), U1(d, b)),A^2 -> H(f(a), U1(d, b)))
24.75/8.16	   (A^2 -> H(f(a), U1(b, c)),A^2 -> H(f(a), U1(b, c)))
24.75/8.16	   (A^2 -> H(f(a), U1(b, d)),A^2 -> H(f(a), U1(b, d)))
24.75/8.16	
24.75/8.16	
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(18)
24.75/8.16	Obligation:
24.75/8.16	Q DP problem:
24.75/8.16	The TRS P consists of the following rules:
24.75/8.16	
24.75/8.16	   H(x, x) -> G(x, x, f(k))
24.75/8.16	   G(d, x, x) -> A^2
24.75/8.16	   A^2 -> H(f(a), f(c))
24.75/8.16	   A^2 -> H(f(a), f(d))
24.75/8.16	   A^2 -> H(U1(c, a), f(b))
24.75/8.16	   A^2 -> H(U1(d, a), f(b))
24.75/8.16	   A^2 -> H(U1(a, c), f(b))
24.75/8.16	   A^2 -> H(U1(a, d), f(b))
24.75/8.16	   A^2 -> H(U1(a, a), U1(b, b))
24.75/8.16	   A^2 -> H(U1(a, a), f(c))
24.75/8.16	   A^2 -> H(U1(a, a), f(d))
24.75/8.16	   A^2 -> H(U1(c, c), f(b))
24.75/8.16	   A^2 -> H(f(e), f(b))
24.75/8.16	   A^2 -> H(f(k), f(b))
24.75/8.16	   A^2 -> H(f(c), U1(b, b))
24.75/8.16	   A^2 -> H(f(c), f(c))
24.75/8.16	   A^2 -> H(f(c), f(d))
24.75/8.16	   A^2 -> H(U1(d, d), f(b))
24.75/8.16	   A^2 -> H(f(d), U1(b, b))
24.75/8.16	   A^2 -> H(f(d), f(c))
24.75/8.16	   A^2 -> H(f(d), f(d))
24.75/8.16	   A^2 -> H(f(a), U1(c, b))
24.75/8.16	   A^2 -> H(f(a), U1(d, b))
24.75/8.16	   A^2 -> H(f(a), U1(b, c))
24.75/8.16	   A^2 -> H(f(a), U1(b, d))
24.75/8.16	
24.75/8.16	The TRS R consists of the following rules:
24.75/8.16	
24.75/8.16	   f(x) -> U1(x, x)
24.75/8.16	   U1(e, x) -> x
24.75/8.16	   a -> c
24.75/8.16	   a -> d
24.75/8.16	   b -> c
24.75/8.16	   b -> d
24.75/8.16	   d -> k
24.75/8.16	   c -> e
24.75/8.16	   c -> k
24.75/8.16	
24.75/8.16	Q is empty.
24.75/8.16	We have to consider all minimal (P,Q,R)-chains.
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(19) TransformationProof (EQUIVALENT)
24.75/8.16	By narrowing [LPAR04] the rule A^2 -> H(f(a), f(c)) at position [] we obtained the following new rules [LPAR04]:
24.75/8.16	
24.75/8.16	   (A^2 -> H(U1(a, a), f(c)),A^2 -> H(U1(a, a), f(c)))
24.75/8.16	   (A^2 -> H(f(c), f(c)),A^2 -> H(f(c), f(c)))
24.75/8.16	   (A^2 -> H(f(d), f(c)),A^2 -> H(f(d), f(c)))
24.75/8.16	   (A^2 -> H(f(a), U1(c, c)),A^2 -> H(f(a), U1(c, c)))
24.75/8.16	   (A^2 -> H(f(a), f(e)),A^2 -> H(f(a), f(e)))
24.75/8.16	   (A^2 -> H(f(a), f(k)),A^2 -> H(f(a), f(k)))
24.75/8.16	
24.75/8.16	
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(20)
24.75/8.16	Obligation:
24.75/8.16	Q DP problem:
24.75/8.16	The TRS P consists of the following rules:
24.75/8.16	
24.75/8.16	   H(x, x) -> G(x, x, f(k))
24.75/8.16	   G(d, x, x) -> A^2
24.75/8.16	   A^2 -> H(f(a), f(d))
24.75/8.16	   A^2 -> H(U1(c, a), f(b))
24.75/8.16	   A^2 -> H(U1(d, a), f(b))
24.75/8.16	   A^2 -> H(U1(a, c), f(b))
24.75/8.16	   A^2 -> H(U1(a, d), f(b))
24.75/8.16	   A^2 -> H(U1(a, a), U1(b, b))
24.75/8.16	   A^2 -> H(U1(a, a), f(c))
24.75/8.16	   A^2 -> H(U1(a, a), f(d))
24.75/8.16	   A^2 -> H(U1(c, c), f(b))
24.75/8.16	   A^2 -> H(f(e), f(b))
24.75/8.16	   A^2 -> H(f(k), f(b))
24.75/8.16	   A^2 -> H(f(c), U1(b, b))
24.75/8.16	   A^2 -> H(f(c), f(c))
24.75/8.16	   A^2 -> H(f(c), f(d))
24.75/8.16	   A^2 -> H(U1(d, d), f(b))
24.75/8.16	   A^2 -> H(f(d), U1(b, b))
24.75/8.16	   A^2 -> H(f(d), f(c))
24.75/8.16	   A^2 -> H(f(d), f(d))
24.75/8.16	   A^2 -> H(f(a), U1(c, b))
24.75/8.16	   A^2 -> H(f(a), U1(d, b))
24.75/8.16	   A^2 -> H(f(a), U1(b, c))
24.75/8.16	   A^2 -> H(f(a), U1(b, d))
24.75/8.16	   A^2 -> H(f(a), U1(c, c))
24.75/8.16	   A^2 -> H(f(a), f(e))
24.75/8.16	   A^2 -> H(f(a), f(k))
24.75/8.16	
24.75/8.16	The TRS R consists of the following rules:
24.75/8.16	
24.75/8.16	   f(x) -> U1(x, x)
24.75/8.16	   U1(e, x) -> x
24.75/8.16	   a -> c
24.75/8.16	   a -> d
24.75/8.16	   b -> c
24.75/8.16	   b -> d
24.75/8.16	   d -> k
24.75/8.16	   c -> e
24.75/8.16	   c -> k
24.75/8.16	
24.75/8.16	Q is empty.
24.75/8.16	We have to consider all minimal (P,Q,R)-chains.
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(21) TransformationProof (EQUIVALENT)
24.75/8.16	By narrowing [LPAR04] the rule A^2 -> H(f(a), f(d)) at position [] we obtained the following new rules [LPAR04]:
24.75/8.16	
24.75/8.16	   (A^2 -> H(U1(a, a), f(d)),A^2 -> H(U1(a, a), f(d)))
24.75/8.16	   (A^2 -> H(f(c), f(d)),A^2 -> H(f(c), f(d)))
24.75/8.16	   (A^2 -> H(f(d), f(d)),A^2 -> H(f(d), f(d)))
24.75/8.16	   (A^2 -> H(f(a), U1(d, d)),A^2 -> H(f(a), U1(d, d)))
24.75/8.16	   (A^2 -> H(f(a), f(k)),A^2 -> H(f(a), f(k)))
24.75/8.16	
24.75/8.16	
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(22)
24.75/8.16	Obligation:
24.75/8.16	Q DP problem:
24.75/8.16	The TRS P consists of the following rules:
24.75/8.16	
24.75/8.16	   H(x, x) -> G(x, x, f(k))
24.75/8.16	   G(d, x, x) -> A^2
24.75/8.16	   A^2 -> H(U1(c, a), f(b))
24.75/8.16	   A^2 -> H(U1(d, a), f(b))
24.75/8.16	   A^2 -> H(U1(a, c), f(b))
24.75/8.16	   A^2 -> H(U1(a, d), f(b))
24.75/8.16	   A^2 -> H(U1(a, a), U1(b, b))
24.75/8.16	   A^2 -> H(U1(a, a), f(c))
24.75/8.16	   A^2 -> H(U1(a, a), f(d))
24.75/8.16	   A^2 -> H(U1(c, c), f(b))
24.75/8.16	   A^2 -> H(f(e), f(b))
24.75/8.16	   A^2 -> H(f(k), f(b))
24.75/8.16	   A^2 -> H(f(c), U1(b, b))
24.75/8.16	   A^2 -> H(f(c), f(c))
24.75/8.16	   A^2 -> H(f(c), f(d))
24.75/8.16	   A^2 -> H(U1(d, d), f(b))
24.75/8.16	   A^2 -> H(f(d), U1(b, b))
24.75/8.16	   A^2 -> H(f(d), f(c))
24.75/8.16	   A^2 -> H(f(d), f(d))
24.75/8.16	   A^2 -> H(f(a), U1(c, b))
24.75/8.16	   A^2 -> H(f(a), U1(d, b))
24.75/8.16	   A^2 -> H(f(a), U1(b, c))
24.75/8.16	   A^2 -> H(f(a), U1(b, d))
24.75/8.16	   A^2 -> H(f(a), U1(c, c))
24.75/8.16	   A^2 -> H(f(a), f(e))
24.75/8.16	   A^2 -> H(f(a), f(k))
24.75/8.16	   A^2 -> H(f(a), U1(d, d))
24.75/8.16	
24.75/8.16	The TRS R consists of the following rules:
24.75/8.16	
24.75/8.16	   f(x) -> U1(x, x)
24.75/8.16	   U1(e, x) -> x
24.75/8.16	   a -> c
24.75/8.16	   a -> d
24.75/8.16	   b -> c
24.75/8.16	   b -> d
24.75/8.16	   d -> k
24.75/8.16	   c -> e
24.75/8.16	   c -> k
24.75/8.16	
24.75/8.16	Q is empty.
24.75/8.16	We have to consider all minimal (P,Q,R)-chains.
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(23) TransformationProof (EQUIVALENT)
24.75/8.16	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), f(b)) at position [] we obtained the following new rules [LPAR04]:
24.75/8.16	
24.75/8.16	   (A^2 -> H(U1(e, a), f(b)),A^2 -> H(U1(e, a), f(b)))
24.75/8.16	   (A^2 -> H(U1(k, a), f(b)),A^2 -> H(U1(k, a), f(b)))
24.75/8.16	   (A^2 -> H(U1(c, c), f(b)),A^2 -> H(U1(c, c), f(b)))
24.75/8.16	   (A^2 -> H(U1(c, d), f(b)),A^2 -> H(U1(c, d), f(b)))
24.75/8.16	   (A^2 -> H(U1(c, a), U1(b, b)),A^2 -> H(U1(c, a), U1(b, b)))
24.75/8.16	   (A^2 -> H(U1(c, a), f(c)),A^2 -> H(U1(c, a), f(c)))
24.75/8.16	   (A^2 -> H(U1(c, a), f(d)),A^2 -> H(U1(c, a), f(d)))
24.75/8.16	
24.75/8.16	
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(24)
24.75/8.16	Obligation:
24.75/8.16	Q DP problem:
24.75/8.16	The TRS P consists of the following rules:
24.75/8.16	
24.75/8.16	   H(x, x) -> G(x, x, f(k))
24.75/8.16	   G(d, x, x) -> A^2
24.75/8.16	   A^2 -> H(U1(d, a), f(b))
24.75/8.16	   A^2 -> H(U1(a, c), f(b))
24.75/8.16	   A^2 -> H(U1(a, d), f(b))
24.75/8.16	   A^2 -> H(U1(a, a), U1(b, b))
24.75/8.16	   A^2 -> H(U1(a, a), f(c))
24.75/8.16	   A^2 -> H(U1(a, a), f(d))
24.75/8.16	   A^2 -> H(U1(c, c), f(b))
24.75/8.16	   A^2 -> H(f(e), f(b))
24.75/8.16	   A^2 -> H(f(k), f(b))
24.75/8.16	   A^2 -> H(f(c), U1(b, b))
24.75/8.16	   A^2 -> H(f(c), f(c))
24.75/8.16	   A^2 -> H(f(c), f(d))
24.75/8.16	   A^2 -> H(U1(d, d), f(b))
24.75/8.16	   A^2 -> H(f(d), U1(b, b))
24.75/8.16	   A^2 -> H(f(d), f(c))
24.75/8.16	   A^2 -> H(f(d), f(d))
24.75/8.16	   A^2 -> H(f(a), U1(c, b))
24.75/8.16	   A^2 -> H(f(a), U1(d, b))
24.75/8.16	   A^2 -> H(f(a), U1(b, c))
24.75/8.16	   A^2 -> H(f(a), U1(b, d))
24.75/8.16	   A^2 -> H(f(a), U1(c, c))
24.75/8.16	   A^2 -> H(f(a), f(e))
24.75/8.16	   A^2 -> H(f(a), f(k))
24.75/8.16	   A^2 -> H(f(a), U1(d, d))
24.75/8.16	   A^2 -> H(U1(e, a), f(b))
24.75/8.16	   A^2 -> H(U1(k, a), f(b))
24.75/8.16	   A^2 -> H(U1(c, d), f(b))
24.75/8.16	   A^2 -> H(U1(c, a), U1(b, b))
24.75/8.16	   A^2 -> H(U1(c, a), f(c))
24.75/8.16	   A^2 -> H(U1(c, a), f(d))
24.75/8.16	
24.75/8.16	The TRS R consists of the following rules:
24.75/8.16	
24.75/8.16	   f(x) -> U1(x, x)
24.75/8.16	   U1(e, x) -> x
24.75/8.16	   a -> c
24.75/8.16	   a -> d
24.75/8.16	   b -> c
24.75/8.16	   b -> d
24.75/8.16	   d -> k
24.75/8.16	   c -> e
24.75/8.16	   c -> k
24.75/8.16	
24.75/8.16	Q is empty.
24.75/8.16	We have to consider all minimal (P,Q,R)-chains.
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(25) TransformationProof (EQUIVALENT)
24.75/8.16	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), f(b)) at position [] we obtained the following new rules [LPAR04]:
24.75/8.16	
24.75/8.16	   (A^2 -> H(U1(k, a), f(b)),A^2 -> H(U1(k, a), f(b)))
24.75/8.16	   (A^2 -> H(U1(d, c), f(b)),A^2 -> H(U1(d, c), f(b)))
24.75/8.16	   (A^2 -> H(U1(d, d), f(b)),A^2 -> H(U1(d, d), f(b)))
24.75/8.16	   (A^2 -> H(U1(d, a), U1(b, b)),A^2 -> H(U1(d, a), U1(b, b)))
24.75/8.16	   (A^2 -> H(U1(d, a), f(c)),A^2 -> H(U1(d, a), f(c)))
24.75/8.16	   (A^2 -> H(U1(d, a), f(d)),A^2 -> H(U1(d, a), f(d)))
24.75/8.16	
24.75/8.16	
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(26)
24.75/8.16	Obligation:
24.75/8.16	Q DP problem:
24.75/8.16	The TRS P consists of the following rules:
24.75/8.16	
24.75/8.16	   H(x, x) -> G(x, x, f(k))
24.75/8.16	   G(d, x, x) -> A^2
24.75/8.16	   A^2 -> H(U1(a, c), f(b))
24.75/8.16	   A^2 -> H(U1(a, d), f(b))
24.75/8.16	   A^2 -> H(U1(a, a), U1(b, b))
24.75/8.16	   A^2 -> H(U1(a, a), f(c))
24.75/8.16	   A^2 -> H(U1(a, a), f(d))
24.75/8.16	   A^2 -> H(U1(c, c), f(b))
24.75/8.16	   A^2 -> H(f(e), f(b))
24.75/8.16	   A^2 -> H(f(k), f(b))
24.75/8.16	   A^2 -> H(f(c), U1(b, b))
24.75/8.16	   A^2 -> H(f(c), f(c))
24.75/8.16	   A^2 -> H(f(c), f(d))
24.75/8.16	   A^2 -> H(U1(d, d), f(b))
24.75/8.16	   A^2 -> H(f(d), U1(b, b))
24.75/8.16	   A^2 -> H(f(d), f(c))
24.75/8.16	   A^2 -> H(f(d), f(d))
24.75/8.16	   A^2 -> H(f(a), U1(c, b))
24.75/8.16	   A^2 -> H(f(a), U1(d, b))
24.75/8.16	   A^2 -> H(f(a), U1(b, c))
24.75/8.16	   A^2 -> H(f(a), U1(b, d))
24.75/8.16	   A^2 -> H(f(a), U1(c, c))
24.75/8.16	   A^2 -> H(f(a), f(e))
24.75/8.16	   A^2 -> H(f(a), f(k))
24.75/8.16	   A^2 -> H(f(a), U1(d, d))
24.75/8.16	   A^2 -> H(U1(e, a), f(b))
24.75/8.16	   A^2 -> H(U1(k, a), f(b))
24.75/8.16	   A^2 -> H(U1(c, d), f(b))
24.75/8.16	   A^2 -> H(U1(c, a), U1(b, b))
24.75/8.16	   A^2 -> H(U1(c, a), f(c))
24.75/8.16	   A^2 -> H(U1(c, a), f(d))
24.75/8.16	   A^2 -> H(U1(d, c), f(b))
24.75/8.16	   A^2 -> H(U1(d, a), U1(b, b))
24.75/8.16	   A^2 -> H(U1(d, a), f(c))
24.75/8.16	   A^2 -> H(U1(d, a), f(d))
24.75/8.16	
24.75/8.16	The TRS R consists of the following rules:
24.75/8.16	
24.75/8.16	   f(x) -> U1(x, x)
24.75/8.16	   U1(e, x) -> x
24.75/8.16	   a -> c
24.75/8.16	   a -> d
24.75/8.16	   b -> c
24.75/8.16	   b -> d
24.75/8.16	   d -> k
24.75/8.16	   c -> e
24.75/8.16	   c -> k
24.75/8.16	
24.75/8.16	Q is empty.
24.75/8.16	We have to consider all minimal (P,Q,R)-chains.
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(27) TransformationProof (EQUIVALENT)
24.75/8.16	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), f(b)) at position [] we obtained the following new rules [LPAR04]:
24.75/8.16	
24.75/8.16	   (A^2 -> H(U1(c, c), f(b)),A^2 -> H(U1(c, c), f(b)))
24.75/8.16	   (A^2 -> H(U1(d, c), f(b)),A^2 -> H(U1(d, c), f(b)))
24.75/8.16	   (A^2 -> H(U1(a, e), f(b)),A^2 -> H(U1(a, e), f(b)))
24.75/8.16	   (A^2 -> H(U1(a, k), f(b)),A^2 -> H(U1(a, k), f(b)))
24.75/8.16	   (A^2 -> H(U1(a, c), U1(b, b)),A^2 -> H(U1(a, c), U1(b, b)))
24.75/8.16	   (A^2 -> H(U1(a, c), f(c)),A^2 -> H(U1(a, c), f(c)))
24.75/8.16	   (A^2 -> H(U1(a, c), f(d)),A^2 -> H(U1(a, c), f(d)))
24.75/8.16	
24.75/8.16	
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(28)
24.75/8.16	Obligation:
24.75/8.16	Q DP problem:
24.75/8.16	The TRS P consists of the following rules:
24.75/8.16	
24.75/8.16	   H(x, x) -> G(x, x, f(k))
24.75/8.16	   G(d, x, x) -> A^2
24.75/8.16	   A^2 -> H(U1(a, d), f(b))
24.75/8.16	   A^2 -> H(U1(a, a), U1(b, b))
24.75/8.16	   A^2 -> H(U1(a, a), f(c))
24.75/8.16	   A^2 -> H(U1(a, a), f(d))
24.75/8.16	   A^2 -> H(U1(c, c), f(b))
24.75/8.16	   A^2 -> H(f(e), f(b))
24.75/8.16	   A^2 -> H(f(k), f(b))
24.75/8.16	   A^2 -> H(f(c), U1(b, b))
24.75/8.16	   A^2 -> H(f(c), f(c))
24.75/8.16	   A^2 -> H(f(c), f(d))
24.75/8.16	   A^2 -> H(U1(d, d), f(b))
24.75/8.16	   A^2 -> H(f(d), U1(b, b))
24.75/8.16	   A^2 -> H(f(d), f(c))
24.75/8.16	   A^2 -> H(f(d), f(d))
24.75/8.16	   A^2 -> H(f(a), U1(c, b))
24.75/8.16	   A^2 -> H(f(a), U1(d, b))
24.75/8.16	   A^2 -> H(f(a), U1(b, c))
24.75/8.16	   A^2 -> H(f(a), U1(b, d))
24.75/8.16	   A^2 -> H(f(a), U1(c, c))
24.75/8.16	   A^2 -> H(f(a), f(e))
24.75/8.16	   A^2 -> H(f(a), f(k))
24.75/8.16	   A^2 -> H(f(a), U1(d, d))
24.75/8.16	   A^2 -> H(U1(e, a), f(b))
24.75/8.16	   A^2 -> H(U1(k, a), f(b))
24.75/8.16	   A^2 -> H(U1(c, d), f(b))
24.75/8.16	   A^2 -> H(U1(c, a), U1(b, b))
24.75/8.16	   A^2 -> H(U1(c, a), f(c))
24.75/8.16	   A^2 -> H(U1(c, a), f(d))
24.75/8.16	   A^2 -> H(U1(d, c), f(b))
24.75/8.16	   A^2 -> H(U1(d, a), U1(b, b))
24.75/8.16	   A^2 -> H(U1(d, a), f(c))
24.75/8.16	   A^2 -> H(U1(d, a), f(d))
24.75/8.16	   A^2 -> H(U1(a, e), f(b))
24.75/8.16	   A^2 -> H(U1(a, k), f(b))
24.75/8.16	   A^2 -> H(U1(a, c), U1(b, b))
24.75/8.16	   A^2 -> H(U1(a, c), f(c))
24.75/8.16	   A^2 -> H(U1(a, c), f(d))
24.75/8.16	
24.75/8.16	The TRS R consists of the following rules:
24.75/8.16	
24.75/8.16	   f(x) -> U1(x, x)
24.75/8.16	   U1(e, x) -> x
24.75/8.16	   a -> c
24.75/8.16	   a -> d
24.75/8.16	   b -> c
24.75/8.16	   b -> d
24.75/8.16	   d -> k
24.75/8.16	   c -> e
24.75/8.16	   c -> k
24.75/8.16	
24.75/8.16	Q is empty.
24.75/8.16	We have to consider all minimal (P,Q,R)-chains.
24.75/8.16	----------------------------------------
24.75/8.16	
24.75/8.16	(29) TransformationProof (EQUIVALENT)
24.75/8.16	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), f(b)) at position [] we obtained the following new rules [LPAR04]:
24.75/8.16	
24.75/8.16	   (A^2 -> H(U1(c, d), f(b)),A^2 -> H(U1(c, d), f(b)))
24.75/8.16	   (A^2 -> H(U1(d, d), f(b)),A^2 -> H(U1(d, d), f(b)))
24.91/8.19	   (A^2 -> H(U1(a, k), f(b)),A^2 -> H(U1(a, k), f(b)))
24.91/8.19	   (A^2 -> H(U1(a, d), U1(b, b)),A^2 -> H(U1(a, d), U1(b, b)))
24.91/8.19	   (A^2 -> H(U1(a, d), f(c)),A^2 -> H(U1(a, d), f(c)))
24.91/8.19	   (A^2 -> H(U1(a, d), f(d)),A^2 -> H(U1(a, d), f(d)))
24.91/8.19	
24.91/8.19	
24.91/8.19	----------------------------------------
24.91/8.19	
24.91/8.19	(30)
24.91/8.19	Obligation:
24.91/8.19	Q DP problem:
24.91/8.19	The TRS P consists of the following rules:
24.91/8.19	
24.91/8.19	   H(x, x) -> G(x, x, f(k))
24.91/8.19	   G(d, x, x) -> A^2
24.91/8.19	   A^2 -> H(U1(a, a), U1(b, b))
24.91/8.19	   A^2 -> H(U1(a, a), f(c))
24.91/8.19	   A^2 -> H(U1(a, a), f(d))
24.91/8.19	   A^2 -> H(U1(c, c), f(b))
24.91/8.19	   A^2 -> H(f(e), f(b))
24.91/8.19	   A^2 -> H(f(k), f(b))
24.91/8.19	   A^2 -> H(f(c), U1(b, b))
24.91/8.19	   A^2 -> H(f(c), f(c))
24.91/8.19	   A^2 -> H(f(c), f(d))
24.91/8.19	   A^2 -> H(U1(d, d), f(b))
24.91/8.19	   A^2 -> H(f(d), U1(b, b))
24.91/8.19	   A^2 -> H(f(d), f(c))
24.91/8.19	   A^2 -> H(f(d), f(d))
24.91/8.19	   A^2 -> H(f(a), U1(c, b))
24.91/8.19	   A^2 -> H(f(a), U1(d, b))
24.91/8.19	   A^2 -> H(f(a), U1(b, c))
24.91/8.19	   A^2 -> H(f(a), U1(b, d))
24.91/8.19	   A^2 -> H(f(a), U1(c, c))
24.91/8.19	   A^2 -> H(f(a), f(e))
24.91/8.19	   A^2 -> H(f(a), f(k))
24.91/8.19	   A^2 -> H(f(a), U1(d, d))
24.91/8.19	   A^2 -> H(U1(e, a), f(b))
24.91/8.19	   A^2 -> H(U1(k, a), f(b))
24.91/8.19	   A^2 -> H(U1(c, d), f(b))
24.91/8.19	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.19	   A^2 -> H(U1(c, a), f(c))
24.91/8.19	   A^2 -> H(U1(c, a), f(d))
24.91/8.19	   A^2 -> H(U1(d, c), f(b))
24.91/8.19	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.19	   A^2 -> H(U1(d, a), f(c))
24.91/8.19	   A^2 -> H(U1(d, a), f(d))
24.91/8.19	   A^2 -> H(U1(a, e), f(b))
24.91/8.19	   A^2 -> H(U1(a, k), f(b))
24.91/8.19	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.19	   A^2 -> H(U1(a, c), f(c))
24.91/8.19	   A^2 -> H(U1(a, c), f(d))
24.91/8.19	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.19	   A^2 -> H(U1(a, d), f(c))
24.91/8.19	   A^2 -> H(U1(a, d), f(d))
24.91/8.19	
24.91/8.19	The TRS R consists of the following rules:
24.91/8.19	
24.91/8.19	   f(x) -> U1(x, x)
24.91/8.19	   U1(e, x) -> x
24.91/8.19	   a -> c
24.91/8.19	   a -> d
24.91/8.19	   b -> c
24.91/8.19	   b -> d
24.91/8.19	   d -> k
24.91/8.19	   c -> e
24.91/8.19	   c -> k
24.91/8.19	
24.91/8.19	Q is empty.
24.91/8.19	We have to consider all minimal (P,Q,R)-chains.
24.91/8.19	----------------------------------------
24.91/8.19	
24.91/8.19	(31) TransformationProof (EQUIVALENT)
24.91/8.19	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.19	
24.91/8.19	   (A^2 -> H(U1(c, a), U1(b, b)),A^2 -> H(U1(c, a), U1(b, b)))
24.91/8.19	   (A^2 -> H(U1(d, a), U1(b, b)),A^2 -> H(U1(d, a), U1(b, b)))
24.91/8.19	   (A^2 -> H(U1(a, c), U1(b, b)),A^2 -> H(U1(a, c), U1(b, b)))
24.91/8.19	   (A^2 -> H(U1(a, d), U1(b, b)),A^2 -> H(U1(a, d), U1(b, b)))
24.91/8.19	   (A^2 -> H(U1(a, a), U1(c, b)),A^2 -> H(U1(a, a), U1(c, b)))
24.91/8.19	   (A^2 -> H(U1(a, a), U1(d, b)),A^2 -> H(U1(a, a), U1(d, b)))
24.91/8.19	   (A^2 -> H(U1(a, a), U1(b, c)),A^2 -> H(U1(a, a), U1(b, c)))
24.91/8.19	   (A^2 -> H(U1(a, a), U1(b, d)),A^2 -> H(U1(a, a), U1(b, d)))
24.91/8.19	
24.91/8.19	
24.91/8.19	----------------------------------------
24.91/8.19	
24.91/8.19	(32)
24.91/8.19	Obligation:
24.91/8.19	Q DP problem:
24.91/8.19	The TRS P consists of the following rules:
24.91/8.19	
24.91/8.19	   H(x, x) -> G(x, x, f(k))
24.91/8.19	   G(d, x, x) -> A^2
24.91/8.19	   A^2 -> H(U1(a, a), f(c))
24.91/8.19	   A^2 -> H(U1(a, a), f(d))
24.91/8.19	   A^2 -> H(U1(c, c), f(b))
24.91/8.19	   A^2 -> H(f(e), f(b))
24.91/8.19	   A^2 -> H(f(k), f(b))
24.91/8.19	   A^2 -> H(f(c), U1(b, b))
24.91/8.19	   A^2 -> H(f(c), f(c))
24.91/8.19	   A^2 -> H(f(c), f(d))
24.91/8.19	   A^2 -> H(U1(d, d), f(b))
24.91/8.19	   A^2 -> H(f(d), U1(b, b))
24.91/8.19	   A^2 -> H(f(d), f(c))
24.91/8.19	   A^2 -> H(f(d), f(d))
24.91/8.19	   A^2 -> H(f(a), U1(c, b))
24.91/8.19	   A^2 -> H(f(a), U1(d, b))
24.91/8.19	   A^2 -> H(f(a), U1(b, c))
24.91/8.19	   A^2 -> H(f(a), U1(b, d))
24.91/8.19	   A^2 -> H(f(a), U1(c, c))
24.91/8.19	   A^2 -> H(f(a), f(e))
24.91/8.19	   A^2 -> H(f(a), f(k))
24.91/8.19	   A^2 -> H(f(a), U1(d, d))
24.91/8.19	   A^2 -> H(U1(e, a), f(b))
24.91/8.19	   A^2 -> H(U1(k, a), f(b))
24.91/8.19	   A^2 -> H(U1(c, d), f(b))
24.91/8.19	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.19	   A^2 -> H(U1(c, a), f(c))
24.91/8.19	   A^2 -> H(U1(c, a), f(d))
24.91/8.19	   A^2 -> H(U1(d, c), f(b))
24.91/8.19	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.19	   A^2 -> H(U1(d, a), f(c))
24.91/8.19	   A^2 -> H(U1(d, a), f(d))
24.91/8.19	   A^2 -> H(U1(a, e), f(b))
24.91/8.19	   A^2 -> H(U1(a, k), f(b))
24.91/8.19	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.19	   A^2 -> H(U1(a, c), f(c))
24.91/8.19	   A^2 -> H(U1(a, c), f(d))
24.91/8.19	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.19	   A^2 -> H(U1(a, d), f(c))
24.91/8.19	   A^2 -> H(U1(a, d), f(d))
24.91/8.19	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.19	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.19	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.19	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.19	
24.91/8.19	The TRS R consists of the following rules:
24.91/8.19	
24.91/8.19	   f(x) -> U1(x, x)
24.91/8.19	   U1(e, x) -> x
24.91/8.19	   a -> c
24.91/8.19	   a -> d
24.91/8.19	   b -> c
24.91/8.19	   b -> d
24.91/8.19	   d -> k
24.91/8.19	   c -> e
24.91/8.19	   c -> k
24.91/8.19	
24.91/8.19	Q is empty.
24.91/8.19	We have to consider all minimal (P,Q,R)-chains.
24.91/8.19	----------------------------------------
24.91/8.19	
24.91/8.19	(33) TransformationProof (EQUIVALENT)
24.91/8.19	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), f(c)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.19	
24.91/8.19	   (A^2 -> H(U1(c, a), f(c)),A^2 -> H(U1(c, a), f(c)))
24.91/8.19	   (A^2 -> H(U1(d, a), f(c)),A^2 -> H(U1(d, a), f(c)))
24.91/8.19	   (A^2 -> H(U1(a, c), f(c)),A^2 -> H(U1(a, c), f(c)))
24.91/8.19	   (A^2 -> H(U1(a, d), f(c)),A^2 -> H(U1(a, d), f(c)))
24.91/8.19	   (A^2 -> H(U1(a, a), U1(c, c)),A^2 -> H(U1(a, a), U1(c, c)))
24.91/8.19	   (A^2 -> H(U1(a, a), f(e)),A^2 -> H(U1(a, a), f(e)))
24.91/8.19	   (A^2 -> H(U1(a, a), f(k)),A^2 -> H(U1(a, a), f(k)))
24.91/8.19	
24.91/8.19	
24.91/8.19	----------------------------------------
24.91/8.19	
24.91/8.19	(34)
24.91/8.19	Obligation:
24.91/8.19	Q DP problem:
24.91/8.19	The TRS P consists of the following rules:
24.91/8.19	
24.91/8.19	   H(x, x) -> G(x, x, f(k))
24.91/8.19	   G(d, x, x) -> A^2
24.91/8.19	   A^2 -> H(U1(a, a), f(d))
24.91/8.19	   A^2 -> H(U1(c, c), f(b))
24.91/8.19	   A^2 -> H(f(e), f(b))
24.91/8.19	   A^2 -> H(f(k), f(b))
24.91/8.19	   A^2 -> H(f(c), U1(b, b))
24.91/8.19	   A^2 -> H(f(c), f(c))
24.91/8.19	   A^2 -> H(f(c), f(d))
24.91/8.19	   A^2 -> H(U1(d, d), f(b))
24.91/8.19	   A^2 -> H(f(d), U1(b, b))
24.91/8.19	   A^2 -> H(f(d), f(c))
24.91/8.19	   A^2 -> H(f(d), f(d))
24.91/8.19	   A^2 -> H(f(a), U1(c, b))
24.91/8.19	   A^2 -> H(f(a), U1(d, b))
24.91/8.19	   A^2 -> H(f(a), U1(b, c))
24.91/8.19	   A^2 -> H(f(a), U1(b, d))
24.91/8.19	   A^2 -> H(f(a), U1(c, c))
24.91/8.19	   A^2 -> H(f(a), f(e))
24.91/8.19	   A^2 -> H(f(a), f(k))
24.91/8.19	   A^2 -> H(f(a), U1(d, d))
24.91/8.19	   A^2 -> H(U1(e, a), f(b))
24.91/8.19	   A^2 -> H(U1(k, a), f(b))
24.91/8.19	   A^2 -> H(U1(c, d), f(b))
24.91/8.19	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.19	   A^2 -> H(U1(c, a), f(c))
24.91/8.19	   A^2 -> H(U1(c, a), f(d))
24.91/8.19	   A^2 -> H(U1(d, c), f(b))
24.91/8.19	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.19	   A^2 -> H(U1(d, a), f(c))
24.91/8.19	   A^2 -> H(U1(d, a), f(d))
24.91/8.19	   A^2 -> H(U1(a, e), f(b))
24.91/8.19	   A^2 -> H(U1(a, k), f(b))
24.91/8.19	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.19	   A^2 -> H(U1(a, c), f(c))
24.91/8.19	   A^2 -> H(U1(a, c), f(d))
24.91/8.19	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.19	   A^2 -> H(U1(a, d), f(c))
24.91/8.19	   A^2 -> H(U1(a, d), f(d))
24.91/8.19	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.19	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.19	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.19	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.19	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.19	   A^2 -> H(U1(a, a), f(e))
24.91/8.19	   A^2 -> H(U1(a, a), f(k))
24.91/8.19	
24.91/8.19	The TRS R consists of the following rules:
24.91/8.19	
24.91/8.19	   f(x) -> U1(x, x)
24.91/8.19	   U1(e, x) -> x
24.91/8.19	   a -> c
24.91/8.19	   a -> d
24.91/8.19	   b -> c
24.91/8.19	   b -> d
24.91/8.19	   d -> k
24.91/8.19	   c -> e
24.91/8.19	   c -> k
24.91/8.19	
24.91/8.19	Q is empty.
24.91/8.19	We have to consider all minimal (P,Q,R)-chains.
24.91/8.19	----------------------------------------
24.91/8.19	
24.91/8.19	(35) TransformationProof (EQUIVALENT)
24.91/8.19	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), f(d)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.19	
24.91/8.19	   (A^2 -> H(U1(c, a), f(d)),A^2 -> H(U1(c, a), f(d)))
24.91/8.19	   (A^2 -> H(U1(d, a), f(d)),A^2 -> H(U1(d, a), f(d)))
24.91/8.19	   (A^2 -> H(U1(a, c), f(d)),A^2 -> H(U1(a, c), f(d)))
24.91/8.19	   (A^2 -> H(U1(a, d), f(d)),A^2 -> H(U1(a, d), f(d)))
24.91/8.19	   (A^2 -> H(U1(a, a), U1(d, d)),A^2 -> H(U1(a, a), U1(d, d)))
24.91/8.19	   (A^2 -> H(U1(a, a), f(k)),A^2 -> H(U1(a, a), f(k)))
24.91/8.19	
24.91/8.19	
24.91/8.19	----------------------------------------
24.91/8.19	
24.91/8.19	(36)
24.91/8.19	Obligation:
24.91/8.19	Q DP problem:
24.91/8.19	The TRS P consists of the following rules:
24.91/8.19	
24.91/8.19	   H(x, x) -> G(x, x, f(k))
24.91/8.19	   G(d, x, x) -> A^2
24.91/8.19	   A^2 -> H(U1(c, c), f(b))
24.91/8.19	   A^2 -> H(f(e), f(b))
24.91/8.19	   A^2 -> H(f(k), f(b))
24.91/8.19	   A^2 -> H(f(c), U1(b, b))
24.91/8.19	   A^2 -> H(f(c), f(c))
24.91/8.19	   A^2 -> H(f(c), f(d))
24.91/8.19	   A^2 -> H(U1(d, d), f(b))
24.91/8.19	   A^2 -> H(f(d), U1(b, b))
24.91/8.19	   A^2 -> H(f(d), f(c))
24.91/8.19	   A^2 -> H(f(d), f(d))
24.91/8.19	   A^2 -> H(f(a), U1(c, b))
24.91/8.19	   A^2 -> H(f(a), U1(d, b))
24.91/8.19	   A^2 -> H(f(a), U1(b, c))
24.91/8.19	   A^2 -> H(f(a), U1(b, d))
24.91/8.19	   A^2 -> H(f(a), U1(c, c))
24.91/8.19	   A^2 -> H(f(a), f(e))
24.91/8.19	   A^2 -> H(f(a), f(k))
24.91/8.19	   A^2 -> H(f(a), U1(d, d))
24.91/8.19	   A^2 -> H(U1(e, a), f(b))
24.91/8.19	   A^2 -> H(U1(k, a), f(b))
24.91/8.19	   A^2 -> H(U1(c, d), f(b))
24.91/8.19	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.19	   A^2 -> H(U1(c, a), f(c))
24.91/8.19	   A^2 -> H(U1(c, a), f(d))
24.91/8.19	   A^2 -> H(U1(d, c), f(b))
24.91/8.19	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.19	   A^2 -> H(U1(d, a), f(c))
24.91/8.19	   A^2 -> H(U1(d, a), f(d))
24.91/8.19	   A^2 -> H(U1(a, e), f(b))
24.91/8.19	   A^2 -> H(U1(a, k), f(b))
24.91/8.19	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.19	   A^2 -> H(U1(a, c), f(c))
24.91/8.19	   A^2 -> H(U1(a, c), f(d))
24.91/8.19	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.19	   A^2 -> H(U1(a, d), f(c))
24.91/8.19	   A^2 -> H(U1(a, d), f(d))
24.91/8.19	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.19	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.19	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.19	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.19	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.19	   A^2 -> H(U1(a, a), f(e))
24.91/8.19	   A^2 -> H(U1(a, a), f(k))
24.91/8.19	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.19	
24.91/8.19	The TRS R consists of the following rules:
24.91/8.19	
24.91/8.19	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(37) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), f(b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(e, c), f(b)),A^2 -> H(U1(e, c), f(b)))
24.91/8.20	   (A^2 -> H(U1(k, c), f(b)),A^2 -> H(U1(k, c), f(b)))
24.91/8.20	   (A^2 -> H(U1(c, e), f(b)),A^2 -> H(U1(c, e), f(b)))
24.91/8.20	   (A^2 -> H(U1(c, k), f(b)),A^2 -> H(U1(c, k), f(b)))
24.91/8.20	   (A^2 -> H(U1(c, c), U1(b, b)),A^2 -> H(U1(c, c), U1(b, b)))
24.91/8.20	   (A^2 -> H(U1(c, c), f(c)),A^2 -> H(U1(c, c), f(c)))
24.91/8.20	   (A^2 -> H(U1(c, c), f(d)),A^2 -> H(U1(c, c), f(d)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(38)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(e), f(b))
24.91/8.20	   A^2 -> H(f(k), f(b))
24.91/8.20	   A^2 -> H(f(c), U1(b, b))
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(c), f(d))
24.91/8.20	   A^2 -> H(U1(d, d), f(b))
24.91/8.20	   A^2 -> H(f(d), U1(b, b))
24.91/8.20	   A^2 -> H(f(d), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(f(a), U1(c, b))
24.91/8.20	   A^2 -> H(f(a), U1(d, b))
24.91/8.20	   A^2 -> H(f(a), U1(b, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, d))
24.91/8.20	   A^2 -> H(f(a), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), f(e))
24.91/8.20	   A^2 -> H(f(a), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, a), f(b))
24.91/8.20	   A^2 -> H(U1(k, a), f(b))
24.91/8.20	   A^2 -> H(U1(c, d), f(b))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(39) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(f(e), f(b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(e, e), f(b)),A^2 -> H(U1(e, e), f(b)))
24.91/8.20	   (A^2 -> H(f(e), U1(b, b)),A^2 -> H(f(e), U1(b, b)))
24.91/8.20	   (A^2 -> H(f(e), f(c)),A^2 -> H(f(e), f(c)))
24.91/8.20	   (A^2 -> H(f(e), f(d)),A^2 -> H(f(e), f(d)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(40)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(k), f(b))
24.91/8.20	   A^2 -> H(f(c), U1(b, b))
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(c), f(d))
24.91/8.20	   A^2 -> H(U1(d, d), f(b))
24.91/8.20	   A^2 -> H(f(d), U1(b, b))
24.91/8.20	   A^2 -> H(f(d), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(f(a), U1(c, b))
24.91/8.20	   A^2 -> H(f(a), U1(d, b))
24.91/8.20	   A^2 -> H(f(a), U1(b, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, d))
24.91/8.20	   A^2 -> H(f(a), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), f(e))
24.91/8.20	   A^2 -> H(f(a), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, a), f(b))
24.91/8.20	   A^2 -> H(U1(k, a), f(b))
24.91/8.20	   A^2 -> H(U1(c, d), f(b))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(41) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(f(k), f(b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(k, k), f(b)),A^2 -> H(U1(k, k), f(b)))
24.91/8.20	   (A^2 -> H(f(k), U1(b, b)),A^2 -> H(f(k), U1(b, b)))
24.91/8.20	   (A^2 -> H(f(k), f(c)),A^2 -> H(f(k), f(c)))
24.91/8.20	   (A^2 -> H(f(k), f(d)),A^2 -> H(f(k), f(d)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(42)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(c), U1(b, b))
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(c), f(d))
24.91/8.20	   A^2 -> H(U1(d, d), f(b))
24.91/8.20	   A^2 -> H(f(d), U1(b, b))
24.91/8.20	   A^2 -> H(f(d), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(f(a), U1(c, b))
24.91/8.20	   A^2 -> H(f(a), U1(d, b))
24.91/8.20	   A^2 -> H(f(a), U1(b, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, d))
24.91/8.20	   A^2 -> H(f(a), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), f(e))
24.91/8.20	   A^2 -> H(f(a), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, a), f(b))
24.91/8.20	   A^2 -> H(U1(k, a), f(b))
24.91/8.20	   A^2 -> H(U1(c, d), f(b))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	   A^2 -> H(U1(k, k), f(b))
24.91/8.20	   A^2 -> H(f(k), U1(b, b))
24.91/8.20	   A^2 -> H(f(k), f(c))
24.91/8.20	   A^2 -> H(f(k), f(d))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(43) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(c, c), U1(b, b)),A^2 -> H(U1(c, c), U1(b, b)))
24.91/8.20	   (A^2 -> H(f(e), U1(b, b)),A^2 -> H(f(e), U1(b, b)))
24.91/8.20	   (A^2 -> H(f(k), U1(b, b)),A^2 -> H(f(k), U1(b, b)))
24.91/8.20	   (A^2 -> H(f(c), U1(c, b)),A^2 -> H(f(c), U1(c, b)))
24.91/8.20	   (A^2 -> H(f(c), U1(d, b)),A^2 -> H(f(c), U1(d, b)))
24.91/8.20	   (A^2 -> H(f(c), U1(b, c)),A^2 -> H(f(c), U1(b, c)))
24.91/8.20	   (A^2 -> H(f(c), U1(b, d)),A^2 -> H(f(c), U1(b, d)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(44)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(c), f(d))
24.91/8.20	   A^2 -> H(U1(d, d), f(b))
24.91/8.20	   A^2 -> H(f(d), U1(b, b))
24.91/8.20	   A^2 -> H(f(d), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(f(a), U1(c, b))
24.91/8.20	   A^2 -> H(f(a), U1(d, b))
24.91/8.20	   A^2 -> H(f(a), U1(b, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, d))
24.91/8.20	   A^2 -> H(f(a), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), f(e))
24.91/8.20	   A^2 -> H(f(a), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, a), f(b))
24.91/8.20	   A^2 -> H(U1(k, a), f(b))
24.91/8.20	   A^2 -> H(U1(c, d), f(b))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	   A^2 -> H(U1(k, k), f(b))
24.91/8.20	   A^2 -> H(f(k), U1(b, b))
24.91/8.20	   A^2 -> H(f(k), f(c))
24.91/8.20	   A^2 -> H(f(k), f(d))
24.91/8.20	   A^2 -> H(f(c), U1(c, b))
24.91/8.20	   A^2 -> H(f(c), U1(d, b))
24.91/8.20	   A^2 -> H(f(c), U1(b, c))
24.91/8.20	   A^2 -> H(f(c), U1(b, d))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(45) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(f(c), f(d)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(c, c), f(d)),A^2 -> H(U1(c, c), f(d)))
24.91/8.20	   (A^2 -> H(f(e), f(d)),A^2 -> H(f(e), f(d)))
24.91/8.20	   (A^2 -> H(f(k), f(d)),A^2 -> H(f(k), f(d)))
24.91/8.20	   (A^2 -> H(f(c), U1(d, d)),A^2 -> H(f(c), U1(d, d)))
24.91/8.20	   (A^2 -> H(f(c), f(k)),A^2 -> H(f(c), f(k)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(46)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(U1(d, d), f(b))
24.91/8.20	   A^2 -> H(f(d), U1(b, b))
24.91/8.20	   A^2 -> H(f(d), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(f(a), U1(c, b))
24.91/8.20	   A^2 -> H(f(a), U1(d, b))
24.91/8.20	   A^2 -> H(f(a), U1(b, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, d))
24.91/8.20	   A^2 -> H(f(a), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), f(e))
24.91/8.20	   A^2 -> H(f(a), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, a), f(b))
24.91/8.20	   A^2 -> H(U1(k, a), f(b))
24.91/8.20	   A^2 -> H(U1(c, d), f(b))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	   A^2 -> H(U1(k, k), f(b))
24.91/8.20	   A^2 -> H(f(k), U1(b, b))
24.91/8.20	   A^2 -> H(f(k), f(c))
24.91/8.20	   A^2 -> H(f(k), f(d))
24.91/8.20	   A^2 -> H(f(c), U1(c, b))
24.91/8.20	   A^2 -> H(f(c), U1(d, b))
24.91/8.20	   A^2 -> H(f(c), U1(b, c))
24.91/8.20	   A^2 -> H(f(c), U1(b, d))
24.91/8.20	   A^2 -> H(f(c), U1(d, d))
24.91/8.20	   A^2 -> H(f(c), f(k))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(47) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), f(b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(k, d), f(b)),A^2 -> H(U1(k, d), f(b)))
24.91/8.20	   (A^2 -> H(U1(d, k), f(b)),A^2 -> H(U1(d, k), f(b)))
24.91/8.20	   (A^2 -> H(U1(d, d), U1(b, b)),A^2 -> H(U1(d, d), U1(b, b)))
24.91/8.20	   (A^2 -> H(U1(d, d), f(c)),A^2 -> H(U1(d, d), f(c)))
24.91/8.20	   (A^2 -> H(U1(d, d), f(d)),A^2 -> H(U1(d, d), f(d)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(48)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(d), U1(b, b))
24.91/8.20	   A^2 -> H(f(d), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(f(a), U1(c, b))
24.91/8.20	   A^2 -> H(f(a), U1(d, b))
24.91/8.20	   A^2 -> H(f(a), U1(b, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, d))
24.91/8.20	   A^2 -> H(f(a), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), f(e))
24.91/8.20	   A^2 -> H(f(a), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, a), f(b))
24.91/8.20	   A^2 -> H(U1(k, a), f(b))
24.91/8.20	   A^2 -> H(U1(c, d), f(b))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	   A^2 -> H(U1(k, k), f(b))
24.91/8.20	   A^2 -> H(f(k), U1(b, b))
24.91/8.20	   A^2 -> H(f(k), f(c))
24.91/8.20	   A^2 -> H(f(k), f(d))
24.91/8.20	   A^2 -> H(f(c), U1(c, b))
24.91/8.20	   A^2 -> H(f(c), U1(d, b))
24.91/8.20	   A^2 -> H(f(c), U1(b, c))
24.91/8.20	   A^2 -> H(f(c), U1(b, d))
24.91/8.20	   A^2 -> H(f(c), U1(d, d))
24.91/8.20	   A^2 -> H(f(c), f(k))
24.91/8.20	   A^2 -> H(U1(k, d), f(b))
24.91/8.20	   A^2 -> H(U1(d, k), f(b))
24.91/8.20	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, d), f(c))
24.91/8.20	   A^2 -> H(U1(d, d), f(d))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(49) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(d, d), U1(b, b)),A^2 -> H(U1(d, d), U1(b, b)))
24.91/8.20	   (A^2 -> H(f(k), U1(b, b)),A^2 -> H(f(k), U1(b, b)))
24.91/8.20	   (A^2 -> H(f(d), U1(c, b)),A^2 -> H(f(d), U1(c, b)))
24.91/8.20	   (A^2 -> H(f(d), U1(d, b)),A^2 -> H(f(d), U1(d, b)))
24.91/8.20	   (A^2 -> H(f(d), U1(b, c)),A^2 -> H(f(d), U1(b, c)))
24.91/8.20	   (A^2 -> H(f(d), U1(b, d)),A^2 -> H(f(d), U1(b, d)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(50)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(d), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(f(a), U1(c, b))
24.91/8.20	   A^2 -> H(f(a), U1(d, b))
24.91/8.20	   A^2 -> H(f(a), U1(b, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, d))
24.91/8.20	   A^2 -> H(f(a), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), f(e))
24.91/8.20	   A^2 -> H(f(a), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, a), f(b))
24.91/8.20	   A^2 -> H(U1(k, a), f(b))
24.91/8.20	   A^2 -> H(U1(c, d), f(b))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	   A^2 -> H(U1(k, k), f(b))
24.91/8.20	   A^2 -> H(f(k), U1(b, b))
24.91/8.20	   A^2 -> H(f(k), f(c))
24.91/8.20	   A^2 -> H(f(k), f(d))
24.91/8.20	   A^2 -> H(f(c), U1(c, b))
24.91/8.20	   A^2 -> H(f(c), U1(d, b))
24.91/8.20	   A^2 -> H(f(c), U1(b, c))
24.91/8.20	   A^2 -> H(f(c), U1(b, d))
24.91/8.20	   A^2 -> H(f(c), U1(d, d))
24.91/8.20	   A^2 -> H(f(c), f(k))
24.91/8.20	   A^2 -> H(U1(k, d), f(b))
24.91/8.20	   A^2 -> H(U1(d, k), f(b))
24.91/8.20	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, d), f(c))
24.91/8.20	   A^2 -> H(U1(d, d), f(d))
24.91/8.20	   A^2 -> H(f(d), U1(c, b))
24.91/8.20	   A^2 -> H(f(d), U1(d, b))
24.91/8.20	   A^2 -> H(f(d), U1(b, c))
24.91/8.20	   A^2 -> H(f(d), U1(b, d))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(51) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(f(d), f(c)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(d, d), f(c)),A^2 -> H(U1(d, d), f(c)))
24.91/8.20	   (A^2 -> H(f(k), f(c)),A^2 -> H(f(k), f(c)))
24.91/8.20	   (A^2 -> H(f(d), U1(c, c)),A^2 -> H(f(d), U1(c, c)))
24.91/8.20	   (A^2 -> H(f(d), f(e)),A^2 -> H(f(d), f(e)))
24.91/8.20	   (A^2 -> H(f(d), f(k)),A^2 -> H(f(d), f(k)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(52)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(f(a), U1(c, b))
24.91/8.20	   A^2 -> H(f(a), U1(d, b))
24.91/8.20	   A^2 -> H(f(a), U1(b, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, d))
24.91/8.20	   A^2 -> H(f(a), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), f(e))
24.91/8.20	   A^2 -> H(f(a), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, a), f(b))
24.91/8.20	   A^2 -> H(U1(k, a), f(b))
24.91/8.20	   A^2 -> H(U1(c, d), f(b))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	   A^2 -> H(U1(k, k), f(b))
24.91/8.20	   A^2 -> H(f(k), U1(b, b))
24.91/8.20	   A^2 -> H(f(k), f(c))
24.91/8.20	   A^2 -> H(f(k), f(d))
24.91/8.20	   A^2 -> H(f(c), U1(c, b))
24.91/8.20	   A^2 -> H(f(c), U1(d, b))
24.91/8.20	   A^2 -> H(f(c), U1(b, c))
24.91/8.20	   A^2 -> H(f(c), U1(b, d))
24.91/8.20	   A^2 -> H(f(c), U1(d, d))
24.91/8.20	   A^2 -> H(f(c), f(k))
24.91/8.20	   A^2 -> H(U1(k, d), f(b))
24.91/8.20	   A^2 -> H(U1(d, k), f(b))
24.91/8.20	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, d), f(c))
24.91/8.20	   A^2 -> H(U1(d, d), f(d))
24.91/8.20	   A^2 -> H(f(d), U1(c, b))
24.91/8.20	   A^2 -> H(f(d), U1(d, b))
24.91/8.20	   A^2 -> H(f(d), U1(b, c))
24.91/8.20	   A^2 -> H(f(d), U1(b, d))
24.91/8.20	   A^2 -> H(f(d), U1(c, c))
24.91/8.20	   A^2 -> H(f(d), f(e))
24.91/8.20	   A^2 -> H(f(d), f(k))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(53) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(a, a), U1(c, b)),A^2 -> H(U1(a, a), U1(c, b)))
24.91/8.20	   (A^2 -> H(f(c), U1(c, b)),A^2 -> H(f(c), U1(c, b)))
24.91/8.20	   (A^2 -> H(f(d), U1(c, b)),A^2 -> H(f(d), U1(c, b)))
24.91/8.20	   (A^2 -> H(f(a), U1(e, b)),A^2 -> H(f(a), U1(e, b)))
24.91/8.20	   (A^2 -> H(f(a), U1(k, b)),A^2 -> H(f(a), U1(k, b)))
24.91/8.20	   (A^2 -> H(f(a), U1(c, c)),A^2 -> H(f(a), U1(c, c)))
24.91/8.20	   (A^2 -> H(f(a), U1(c, d)),A^2 -> H(f(a), U1(c, d)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(54)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(f(a), U1(d, b))
24.91/8.20	   A^2 -> H(f(a), U1(b, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, d))
24.91/8.20	   A^2 -> H(f(a), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), f(e))
24.91/8.20	   A^2 -> H(f(a), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, a), f(b))
24.91/8.20	   A^2 -> H(U1(k, a), f(b))
24.91/8.20	   A^2 -> H(U1(c, d), f(b))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	   A^2 -> H(U1(k, k), f(b))
24.91/8.20	   A^2 -> H(f(k), U1(b, b))
24.91/8.20	   A^2 -> H(f(k), f(c))
24.91/8.20	   A^2 -> H(f(k), f(d))
24.91/8.20	   A^2 -> H(f(c), U1(c, b))
24.91/8.20	   A^2 -> H(f(c), U1(d, b))
24.91/8.20	   A^2 -> H(f(c), U1(b, c))
24.91/8.20	   A^2 -> H(f(c), U1(b, d))
24.91/8.20	   A^2 -> H(f(c), U1(d, d))
24.91/8.20	   A^2 -> H(f(c), f(k))
24.91/8.20	   A^2 -> H(U1(k, d), f(b))
24.91/8.20	   A^2 -> H(U1(d, k), f(b))
24.91/8.20	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, d), f(c))
24.91/8.20	   A^2 -> H(U1(d, d), f(d))
24.91/8.20	   A^2 -> H(f(d), U1(c, b))
24.91/8.20	   A^2 -> H(f(d), U1(d, b))
24.91/8.20	   A^2 -> H(f(d), U1(b, c))
24.91/8.20	   A^2 -> H(f(d), U1(b, d))
24.91/8.20	   A^2 -> H(f(d), U1(c, c))
24.91/8.20	   A^2 -> H(f(d), f(e))
24.91/8.20	   A^2 -> H(f(d), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(e, b))
24.91/8.20	   A^2 -> H(f(a), U1(k, b))
24.91/8.20	   A^2 -> H(f(a), U1(c, d))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(55) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(a, a), U1(d, b)),A^2 -> H(U1(a, a), U1(d, b)))
24.91/8.20	   (A^2 -> H(f(c), U1(d, b)),A^2 -> H(f(c), U1(d, b)))
24.91/8.20	   (A^2 -> H(f(d), U1(d, b)),A^2 -> H(f(d), U1(d, b)))
24.91/8.20	   (A^2 -> H(f(a), U1(k, b)),A^2 -> H(f(a), U1(k, b)))
24.91/8.20	   (A^2 -> H(f(a), U1(d, c)),A^2 -> H(f(a), U1(d, c)))
24.91/8.20	   (A^2 -> H(f(a), U1(d, d)),A^2 -> H(f(a), U1(d, d)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(56)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(f(a), U1(b, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, d))
24.91/8.20	   A^2 -> H(f(a), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), f(e))
24.91/8.20	   A^2 -> H(f(a), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, a), f(b))
24.91/8.20	   A^2 -> H(U1(k, a), f(b))
24.91/8.20	   A^2 -> H(U1(c, d), f(b))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	   A^2 -> H(U1(k, k), f(b))
24.91/8.20	   A^2 -> H(f(k), U1(b, b))
24.91/8.20	   A^2 -> H(f(k), f(c))
24.91/8.20	   A^2 -> H(f(k), f(d))
24.91/8.20	   A^2 -> H(f(c), U1(c, b))
24.91/8.20	   A^2 -> H(f(c), U1(d, b))
24.91/8.20	   A^2 -> H(f(c), U1(b, c))
24.91/8.20	   A^2 -> H(f(c), U1(b, d))
24.91/8.20	   A^2 -> H(f(c), U1(d, d))
24.91/8.20	   A^2 -> H(f(c), f(k))
24.91/8.20	   A^2 -> H(U1(k, d), f(b))
24.91/8.20	   A^2 -> H(U1(d, k), f(b))
24.91/8.20	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, d), f(c))
24.91/8.20	   A^2 -> H(U1(d, d), f(d))
24.91/8.20	   A^2 -> H(f(d), U1(c, b))
24.91/8.20	   A^2 -> H(f(d), U1(d, b))
24.91/8.20	   A^2 -> H(f(d), U1(b, c))
24.91/8.20	   A^2 -> H(f(d), U1(b, d))
24.91/8.20	   A^2 -> H(f(d), U1(c, c))
24.91/8.20	   A^2 -> H(f(d), f(e))
24.91/8.20	   A^2 -> H(f(d), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(e, b))
24.91/8.20	   A^2 -> H(f(a), U1(k, b))
24.91/8.20	   A^2 -> H(f(a), U1(c, d))
24.91/8.20	   A^2 -> H(f(a), U1(d, c))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(57) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(a, a), U1(b, c)),A^2 -> H(U1(a, a), U1(b, c)))
24.91/8.20	   (A^2 -> H(f(c), U1(b, c)),A^2 -> H(f(c), U1(b, c)))
24.91/8.20	   (A^2 -> H(f(d), U1(b, c)),A^2 -> H(f(d), U1(b, c)))
24.91/8.20	   (A^2 -> H(f(a), U1(c, c)),A^2 -> H(f(a), U1(c, c)))
24.91/8.20	   (A^2 -> H(f(a), U1(d, c)),A^2 -> H(f(a), U1(d, c)))
24.91/8.20	   (A^2 -> H(f(a), U1(b, e)),A^2 -> H(f(a), U1(b, e)))
24.91/8.20	   (A^2 -> H(f(a), U1(b, k)),A^2 -> H(f(a), U1(b, k)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(58)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(f(a), U1(b, d))
24.91/8.20	   A^2 -> H(f(a), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), f(e))
24.91/8.20	   A^2 -> H(f(a), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, a), f(b))
24.91/8.20	   A^2 -> H(U1(k, a), f(b))
24.91/8.20	   A^2 -> H(U1(c, d), f(b))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	   A^2 -> H(U1(k, k), f(b))
24.91/8.20	   A^2 -> H(f(k), U1(b, b))
24.91/8.20	   A^2 -> H(f(k), f(c))
24.91/8.20	   A^2 -> H(f(k), f(d))
24.91/8.20	   A^2 -> H(f(c), U1(c, b))
24.91/8.20	   A^2 -> H(f(c), U1(d, b))
24.91/8.20	   A^2 -> H(f(c), U1(b, c))
24.91/8.20	   A^2 -> H(f(c), U1(b, d))
24.91/8.20	   A^2 -> H(f(c), U1(d, d))
24.91/8.20	   A^2 -> H(f(c), f(k))
24.91/8.20	   A^2 -> H(U1(k, d), f(b))
24.91/8.20	   A^2 -> H(U1(d, k), f(b))
24.91/8.20	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, d), f(c))
24.91/8.20	   A^2 -> H(U1(d, d), f(d))
24.91/8.20	   A^2 -> H(f(d), U1(c, b))
24.91/8.20	   A^2 -> H(f(d), U1(d, b))
24.91/8.20	   A^2 -> H(f(d), U1(b, c))
24.91/8.20	   A^2 -> H(f(d), U1(b, d))
24.91/8.20	   A^2 -> H(f(d), U1(c, c))
24.91/8.20	   A^2 -> H(f(d), f(e))
24.91/8.20	   A^2 -> H(f(d), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(e, b))
24.91/8.20	   A^2 -> H(f(a), U1(k, b))
24.91/8.20	   A^2 -> H(f(a), U1(c, d))
24.91/8.20	   A^2 -> H(f(a), U1(d, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, e))
24.91/8.20	   A^2 -> H(f(a), U1(b, k))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(59) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(a, a), U1(b, d)),A^2 -> H(U1(a, a), U1(b, d)))
24.91/8.20	   (A^2 -> H(f(c), U1(b, d)),A^2 -> H(f(c), U1(b, d)))
24.91/8.20	   (A^2 -> H(f(d), U1(b, d)),A^2 -> H(f(d), U1(b, d)))
24.91/8.20	   (A^2 -> H(f(a), U1(c, d)),A^2 -> H(f(a), U1(c, d)))
24.91/8.20	   (A^2 -> H(f(a), U1(d, d)),A^2 -> H(f(a), U1(d, d)))
24.91/8.20	   (A^2 -> H(f(a), U1(b, k)),A^2 -> H(f(a), U1(b, k)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(60)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(f(a), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), f(e))
24.91/8.20	   A^2 -> H(f(a), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, a), f(b))
24.91/8.20	   A^2 -> H(U1(k, a), f(b))
24.91/8.20	   A^2 -> H(U1(c, d), f(b))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	   A^2 -> H(U1(k, k), f(b))
24.91/8.20	   A^2 -> H(f(k), U1(b, b))
24.91/8.20	   A^2 -> H(f(k), f(c))
24.91/8.20	   A^2 -> H(f(k), f(d))
24.91/8.20	   A^2 -> H(f(c), U1(c, b))
24.91/8.20	   A^2 -> H(f(c), U1(d, b))
24.91/8.20	   A^2 -> H(f(c), U1(b, c))
24.91/8.20	   A^2 -> H(f(c), U1(b, d))
24.91/8.20	   A^2 -> H(f(c), U1(d, d))
24.91/8.20	   A^2 -> H(f(c), f(k))
24.91/8.20	   A^2 -> H(U1(k, d), f(b))
24.91/8.20	   A^2 -> H(U1(d, k), f(b))
24.91/8.20	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, d), f(c))
24.91/8.20	   A^2 -> H(U1(d, d), f(d))
24.91/8.20	   A^2 -> H(f(d), U1(c, b))
24.91/8.20	   A^2 -> H(f(d), U1(d, b))
24.91/8.20	   A^2 -> H(f(d), U1(b, c))
24.91/8.20	   A^2 -> H(f(d), U1(b, d))
24.91/8.20	   A^2 -> H(f(d), U1(c, c))
24.91/8.20	   A^2 -> H(f(d), f(e))
24.91/8.20	   A^2 -> H(f(d), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(e, b))
24.91/8.20	   A^2 -> H(f(a), U1(k, b))
24.91/8.20	   A^2 -> H(f(a), U1(c, d))
24.91/8.20	   A^2 -> H(f(a), U1(d, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, e))
24.91/8.20	   A^2 -> H(f(a), U1(b, k))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(61) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(a, a), U1(c, c)),A^2 -> H(U1(a, a), U1(c, c)))
24.91/8.20	   (A^2 -> H(f(c), U1(c, c)),A^2 -> H(f(c), U1(c, c)))
24.91/8.20	   (A^2 -> H(f(d), U1(c, c)),A^2 -> H(f(d), U1(c, c)))
24.91/8.20	   (A^2 -> H(f(a), U1(e, c)),A^2 -> H(f(a), U1(e, c)))
24.91/8.20	   (A^2 -> H(f(a), U1(k, c)),A^2 -> H(f(a), U1(k, c)))
24.91/8.20	   (A^2 -> H(f(a), U1(c, e)),A^2 -> H(f(a), U1(c, e)))
24.91/8.20	   (A^2 -> H(f(a), U1(c, k)),A^2 -> H(f(a), U1(c, k)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(62)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(f(a), f(e))
24.91/8.20	   A^2 -> H(f(a), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, a), f(b))
24.91/8.20	   A^2 -> H(U1(k, a), f(b))
24.91/8.20	   A^2 -> H(U1(c, d), f(b))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	   A^2 -> H(U1(k, k), f(b))
24.91/8.20	   A^2 -> H(f(k), U1(b, b))
24.91/8.20	   A^2 -> H(f(k), f(c))
24.91/8.20	   A^2 -> H(f(k), f(d))
24.91/8.20	   A^2 -> H(f(c), U1(c, b))
24.91/8.20	   A^2 -> H(f(c), U1(d, b))
24.91/8.20	   A^2 -> H(f(c), U1(b, c))
24.91/8.20	   A^2 -> H(f(c), U1(b, d))
24.91/8.20	   A^2 -> H(f(c), U1(d, d))
24.91/8.20	   A^2 -> H(f(c), f(k))
24.91/8.20	   A^2 -> H(U1(k, d), f(b))
24.91/8.20	   A^2 -> H(U1(d, k), f(b))
24.91/8.20	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, d), f(c))
24.91/8.20	   A^2 -> H(U1(d, d), f(d))
24.91/8.20	   A^2 -> H(f(d), U1(c, b))
24.91/8.20	   A^2 -> H(f(d), U1(d, b))
24.91/8.20	   A^2 -> H(f(d), U1(b, c))
24.91/8.20	   A^2 -> H(f(d), U1(b, d))
24.91/8.20	   A^2 -> H(f(d), U1(c, c))
24.91/8.20	   A^2 -> H(f(d), f(e))
24.91/8.20	   A^2 -> H(f(d), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(e, b))
24.91/8.20	   A^2 -> H(f(a), U1(k, b))
24.91/8.20	   A^2 -> H(f(a), U1(c, d))
24.91/8.20	   A^2 -> H(f(a), U1(d, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, e))
24.91/8.20	   A^2 -> H(f(a), U1(b, k))
24.91/8.20	   A^2 -> H(f(c), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), U1(e, c))
24.91/8.20	   A^2 -> H(f(a), U1(k, c))
24.91/8.20	   A^2 -> H(f(a), U1(c, e))
24.91/8.20	   A^2 -> H(f(a), U1(c, k))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(63) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(f(a), f(e)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(a, a), f(e)),A^2 -> H(U1(a, a), f(e)))
24.91/8.20	   (A^2 -> H(f(c), f(e)),A^2 -> H(f(c), f(e)))
24.91/8.20	   (A^2 -> H(f(d), f(e)),A^2 -> H(f(d), f(e)))
24.91/8.20	   (A^2 -> H(f(a), U1(e, e)),A^2 -> H(f(a), U1(e, e)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(64)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(f(a), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, a), f(b))
24.91/8.20	   A^2 -> H(U1(k, a), f(b))
24.91/8.20	   A^2 -> H(U1(c, d), f(b))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	   A^2 -> H(U1(k, k), f(b))
24.91/8.20	   A^2 -> H(f(k), U1(b, b))
24.91/8.20	   A^2 -> H(f(k), f(c))
24.91/8.20	   A^2 -> H(f(k), f(d))
24.91/8.20	   A^2 -> H(f(c), U1(c, b))
24.91/8.20	   A^2 -> H(f(c), U1(d, b))
24.91/8.20	   A^2 -> H(f(c), U1(b, c))
24.91/8.20	   A^2 -> H(f(c), U1(b, d))
24.91/8.20	   A^2 -> H(f(c), U1(d, d))
24.91/8.20	   A^2 -> H(f(c), f(k))
24.91/8.20	   A^2 -> H(U1(k, d), f(b))
24.91/8.20	   A^2 -> H(U1(d, k), f(b))
24.91/8.20	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, d), f(c))
24.91/8.20	   A^2 -> H(U1(d, d), f(d))
24.91/8.20	   A^2 -> H(f(d), U1(c, b))
24.91/8.20	   A^2 -> H(f(d), U1(d, b))
24.91/8.20	   A^2 -> H(f(d), U1(b, c))
24.91/8.20	   A^2 -> H(f(d), U1(b, d))
24.91/8.20	   A^2 -> H(f(d), U1(c, c))
24.91/8.20	   A^2 -> H(f(d), f(e))
24.91/8.20	   A^2 -> H(f(d), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(e, b))
24.91/8.20	   A^2 -> H(f(a), U1(k, b))
24.91/8.20	   A^2 -> H(f(a), U1(c, d))
24.91/8.20	   A^2 -> H(f(a), U1(d, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, e))
24.91/8.20	   A^2 -> H(f(a), U1(b, k))
24.91/8.20	   A^2 -> H(f(c), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), U1(e, c))
24.91/8.20	   A^2 -> H(f(a), U1(k, c))
24.91/8.20	   A^2 -> H(f(a), U1(c, e))
24.91/8.20	   A^2 -> H(f(a), U1(c, k))
24.91/8.20	   A^2 -> H(f(c), f(e))
24.91/8.20	   A^2 -> H(f(a), U1(e, e))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(65) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(f(a), f(k)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(a, a), f(k)),A^2 -> H(U1(a, a), f(k)))
24.91/8.20	   (A^2 -> H(f(c), f(k)),A^2 -> H(f(c), f(k)))
24.91/8.20	   (A^2 -> H(f(d), f(k)),A^2 -> H(f(d), f(k)))
24.91/8.20	   (A^2 -> H(f(a), U1(k, k)),A^2 -> H(f(a), U1(k, k)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(66)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(f(a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, a), f(b))
24.91/8.20	   A^2 -> H(U1(k, a), f(b))
24.91/8.20	   A^2 -> H(U1(c, d), f(b))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	   A^2 -> H(U1(k, k), f(b))
24.91/8.20	   A^2 -> H(f(k), U1(b, b))
24.91/8.20	   A^2 -> H(f(k), f(c))
24.91/8.20	   A^2 -> H(f(k), f(d))
24.91/8.20	   A^2 -> H(f(c), U1(c, b))
24.91/8.20	   A^2 -> H(f(c), U1(d, b))
24.91/8.20	   A^2 -> H(f(c), U1(b, c))
24.91/8.20	   A^2 -> H(f(c), U1(b, d))
24.91/8.20	   A^2 -> H(f(c), U1(d, d))
24.91/8.20	   A^2 -> H(f(c), f(k))
24.91/8.20	   A^2 -> H(U1(k, d), f(b))
24.91/8.20	   A^2 -> H(U1(d, k), f(b))
24.91/8.20	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, d), f(c))
24.91/8.20	   A^2 -> H(U1(d, d), f(d))
24.91/8.20	   A^2 -> H(f(d), U1(c, b))
24.91/8.20	   A^2 -> H(f(d), U1(d, b))
24.91/8.20	   A^2 -> H(f(d), U1(b, c))
24.91/8.20	   A^2 -> H(f(d), U1(b, d))
24.91/8.20	   A^2 -> H(f(d), U1(c, c))
24.91/8.20	   A^2 -> H(f(d), f(e))
24.91/8.20	   A^2 -> H(f(d), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(e, b))
24.91/8.20	   A^2 -> H(f(a), U1(k, b))
24.91/8.20	   A^2 -> H(f(a), U1(c, d))
24.91/8.20	   A^2 -> H(f(a), U1(d, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, e))
24.91/8.20	   A^2 -> H(f(a), U1(b, k))
24.91/8.20	   A^2 -> H(f(c), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), U1(e, c))
24.91/8.20	   A^2 -> H(f(a), U1(k, c))
24.91/8.20	   A^2 -> H(f(a), U1(c, e))
24.91/8.20	   A^2 -> H(f(a), U1(c, k))
24.91/8.20	   A^2 -> H(f(c), f(e))
24.91/8.20	   A^2 -> H(f(a), U1(e, e))
24.91/8.20	   A^2 -> H(f(a), U1(k, k))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(67) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(a, a), U1(d, d)),A^2 -> H(U1(a, a), U1(d, d)))
24.91/8.20	   (A^2 -> H(f(c), U1(d, d)),A^2 -> H(f(c), U1(d, d)))
24.91/8.20	   (A^2 -> H(f(d), U1(d, d)),A^2 -> H(f(d), U1(d, d)))
24.91/8.20	   (A^2 -> H(f(a), U1(k, d)),A^2 -> H(f(a), U1(k, d)))
24.91/8.20	   (A^2 -> H(f(a), U1(d, k)),A^2 -> H(f(a), U1(d, k)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(68)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(U1(e, a), f(b))
24.91/8.20	   A^2 -> H(U1(k, a), f(b))
24.91/8.20	   A^2 -> H(U1(c, d), f(b))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	   A^2 -> H(U1(k, k), f(b))
24.91/8.20	   A^2 -> H(f(k), U1(b, b))
24.91/8.20	   A^2 -> H(f(k), f(c))
24.91/8.20	   A^2 -> H(f(k), f(d))
24.91/8.20	   A^2 -> H(f(c), U1(c, b))
24.91/8.20	   A^2 -> H(f(c), U1(d, b))
24.91/8.20	   A^2 -> H(f(c), U1(b, c))
24.91/8.20	   A^2 -> H(f(c), U1(b, d))
24.91/8.20	   A^2 -> H(f(c), U1(d, d))
24.91/8.20	   A^2 -> H(f(c), f(k))
24.91/8.20	   A^2 -> H(U1(k, d), f(b))
24.91/8.20	   A^2 -> H(U1(d, k), f(b))
24.91/8.20	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, d), f(c))
24.91/8.20	   A^2 -> H(U1(d, d), f(d))
24.91/8.20	   A^2 -> H(f(d), U1(c, b))
24.91/8.20	   A^2 -> H(f(d), U1(d, b))
24.91/8.20	   A^2 -> H(f(d), U1(b, c))
24.91/8.20	   A^2 -> H(f(d), U1(b, d))
24.91/8.20	   A^2 -> H(f(d), U1(c, c))
24.91/8.20	   A^2 -> H(f(d), f(e))
24.91/8.20	   A^2 -> H(f(d), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(e, b))
24.91/8.20	   A^2 -> H(f(a), U1(k, b))
24.91/8.20	   A^2 -> H(f(a), U1(c, d))
24.91/8.20	   A^2 -> H(f(a), U1(d, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, e))
24.91/8.20	   A^2 -> H(f(a), U1(b, k))
24.91/8.20	   A^2 -> H(f(c), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), U1(e, c))
24.91/8.20	   A^2 -> H(f(a), U1(k, c))
24.91/8.20	   A^2 -> H(f(a), U1(c, e))
24.91/8.20	   A^2 -> H(f(a), U1(c, k))
24.91/8.20	   A^2 -> H(f(c), f(e))
24.91/8.20	   A^2 -> H(f(a), U1(e, e))
24.91/8.20	   A^2 -> H(f(a), U1(k, k))
24.91/8.20	   A^2 -> H(f(d), U1(d, d))
24.91/8.20	   A^2 -> H(f(a), U1(k, d))
24.91/8.20	   A^2 -> H(f(a), U1(d, k))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(69) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), f(b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(a, f(b)),A^2 -> H(a, f(b)))
24.91/8.20	   (A^2 -> H(U1(e, c), f(b)),A^2 -> H(U1(e, c), f(b)))
24.91/8.20	   (A^2 -> H(U1(e, d), f(b)),A^2 -> H(U1(e, d), f(b)))
24.91/8.20	   (A^2 -> H(U1(e, a), U1(b, b)),A^2 -> H(U1(e, a), U1(b, b)))
24.91/8.20	   (A^2 -> H(U1(e, a), f(c)),A^2 -> H(U1(e, a), f(c)))
24.91/8.20	   (A^2 -> H(U1(e, a), f(d)),A^2 -> H(U1(e, a), f(d)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(70)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(U1(k, a), f(b))
24.91/8.20	   A^2 -> H(U1(c, d), f(b))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	   A^2 -> H(U1(k, k), f(b))
24.91/8.20	   A^2 -> H(f(k), U1(b, b))
24.91/8.20	   A^2 -> H(f(k), f(c))
24.91/8.20	   A^2 -> H(f(k), f(d))
24.91/8.20	   A^2 -> H(f(c), U1(c, b))
24.91/8.20	   A^2 -> H(f(c), U1(d, b))
24.91/8.20	   A^2 -> H(f(c), U1(b, c))
24.91/8.20	   A^2 -> H(f(c), U1(b, d))
24.91/8.20	   A^2 -> H(f(c), U1(d, d))
24.91/8.20	   A^2 -> H(f(c), f(k))
24.91/8.20	   A^2 -> H(U1(k, d), f(b))
24.91/8.20	   A^2 -> H(U1(d, k), f(b))
24.91/8.20	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, d), f(c))
24.91/8.20	   A^2 -> H(U1(d, d), f(d))
24.91/8.20	   A^2 -> H(f(d), U1(c, b))
24.91/8.20	   A^2 -> H(f(d), U1(d, b))
24.91/8.20	   A^2 -> H(f(d), U1(b, c))
24.91/8.20	   A^2 -> H(f(d), U1(b, d))
24.91/8.20	   A^2 -> H(f(d), U1(c, c))
24.91/8.20	   A^2 -> H(f(d), f(e))
24.91/8.20	   A^2 -> H(f(d), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(e, b))
24.91/8.20	   A^2 -> H(f(a), U1(k, b))
24.91/8.20	   A^2 -> H(f(a), U1(c, d))
24.91/8.20	   A^2 -> H(f(a), U1(d, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, e))
24.91/8.20	   A^2 -> H(f(a), U1(b, k))
24.91/8.20	   A^2 -> H(f(c), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), U1(e, c))
24.91/8.20	   A^2 -> H(f(a), U1(k, c))
24.91/8.20	   A^2 -> H(f(a), U1(c, e))
24.91/8.20	   A^2 -> H(f(a), U1(c, k))
24.91/8.20	   A^2 -> H(f(c), f(e))
24.91/8.20	   A^2 -> H(f(a), U1(e, e))
24.91/8.20	   A^2 -> H(f(a), U1(k, k))
24.91/8.20	   A^2 -> H(f(d), U1(d, d))
24.91/8.20	   A^2 -> H(f(a), U1(k, d))
24.91/8.20	   A^2 -> H(f(a), U1(d, k))
24.91/8.20	   A^2 -> H(a, f(b))
24.91/8.20	   A^2 -> H(U1(e, d), f(b))
24.91/8.20	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(e, a), f(c))
24.91/8.20	   A^2 -> H(U1(e, a), f(d))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(71) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), f(b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(k, c), f(b)),A^2 -> H(U1(k, c), f(b)))
24.91/8.20	   (A^2 -> H(U1(k, d), f(b)),A^2 -> H(U1(k, d), f(b)))
24.91/8.20	   (A^2 -> H(U1(k, a), U1(b, b)),A^2 -> H(U1(k, a), U1(b, b)))
24.91/8.20	   (A^2 -> H(U1(k, a), f(c)),A^2 -> H(U1(k, a), f(c)))
24.91/8.20	   (A^2 -> H(U1(k, a), f(d)),A^2 -> H(U1(k, a), f(d)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(72)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(U1(c, d), f(b))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	   A^2 -> H(U1(k, k), f(b))
24.91/8.20	   A^2 -> H(f(k), U1(b, b))
24.91/8.20	   A^2 -> H(f(k), f(c))
24.91/8.20	   A^2 -> H(f(k), f(d))
24.91/8.20	   A^2 -> H(f(c), U1(c, b))
24.91/8.20	   A^2 -> H(f(c), U1(d, b))
24.91/8.20	   A^2 -> H(f(c), U1(b, c))
24.91/8.20	   A^2 -> H(f(c), U1(b, d))
24.91/8.20	   A^2 -> H(f(c), U1(d, d))
24.91/8.20	   A^2 -> H(f(c), f(k))
24.91/8.20	   A^2 -> H(U1(k, d), f(b))
24.91/8.20	   A^2 -> H(U1(d, k), f(b))
24.91/8.20	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, d), f(c))
24.91/8.20	   A^2 -> H(U1(d, d), f(d))
24.91/8.20	   A^2 -> H(f(d), U1(c, b))
24.91/8.20	   A^2 -> H(f(d), U1(d, b))
24.91/8.20	   A^2 -> H(f(d), U1(b, c))
24.91/8.20	   A^2 -> H(f(d), U1(b, d))
24.91/8.20	   A^2 -> H(f(d), U1(c, c))
24.91/8.20	   A^2 -> H(f(d), f(e))
24.91/8.20	   A^2 -> H(f(d), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(e, b))
24.91/8.20	   A^2 -> H(f(a), U1(k, b))
24.91/8.20	   A^2 -> H(f(a), U1(c, d))
24.91/8.20	   A^2 -> H(f(a), U1(d, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, e))
24.91/8.20	   A^2 -> H(f(a), U1(b, k))
24.91/8.20	   A^2 -> H(f(c), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), U1(e, c))
24.91/8.20	   A^2 -> H(f(a), U1(k, c))
24.91/8.20	   A^2 -> H(f(a), U1(c, e))
24.91/8.20	   A^2 -> H(f(a), U1(c, k))
24.91/8.20	   A^2 -> H(f(c), f(e))
24.91/8.20	   A^2 -> H(f(a), U1(e, e))
24.91/8.20	   A^2 -> H(f(a), U1(k, k))
24.91/8.20	   A^2 -> H(f(d), U1(d, d))
24.91/8.20	   A^2 -> H(f(a), U1(k, d))
24.91/8.20	   A^2 -> H(f(a), U1(d, k))
24.91/8.20	   A^2 -> H(a, f(b))
24.91/8.20	   A^2 -> H(U1(e, d), f(b))
24.91/8.20	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(e, a), f(c))
24.91/8.20	   A^2 -> H(U1(e, a), f(d))
24.91/8.20	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(k, a), f(c))
24.91/8.20	   A^2 -> H(U1(k, a), f(d))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(73) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), f(b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(e, d), f(b)),A^2 -> H(U1(e, d), f(b)))
24.91/8.20	   (A^2 -> H(U1(k, d), f(b)),A^2 -> H(U1(k, d), f(b)))
24.91/8.20	   (A^2 -> H(U1(c, k), f(b)),A^2 -> H(U1(c, k), f(b)))
24.91/8.20	   (A^2 -> H(U1(c, d), U1(b, b)),A^2 -> H(U1(c, d), U1(b, b)))
24.91/8.20	   (A^2 -> H(U1(c, d), f(c)),A^2 -> H(U1(c, d), f(c)))
24.91/8.20	   (A^2 -> H(U1(c, d), f(d)),A^2 -> H(U1(c, d), f(d)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(74)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(U1(c, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	   A^2 -> H(U1(k, k), f(b))
24.91/8.20	   A^2 -> H(f(k), U1(b, b))
24.91/8.20	   A^2 -> H(f(k), f(c))
24.91/8.20	   A^2 -> H(f(k), f(d))
24.91/8.20	   A^2 -> H(f(c), U1(c, b))
24.91/8.20	   A^2 -> H(f(c), U1(d, b))
24.91/8.20	   A^2 -> H(f(c), U1(b, c))
24.91/8.20	   A^2 -> H(f(c), U1(b, d))
24.91/8.20	   A^2 -> H(f(c), U1(d, d))
24.91/8.20	   A^2 -> H(f(c), f(k))
24.91/8.20	   A^2 -> H(U1(k, d), f(b))
24.91/8.20	   A^2 -> H(U1(d, k), f(b))
24.91/8.20	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, d), f(c))
24.91/8.20	   A^2 -> H(U1(d, d), f(d))
24.91/8.20	   A^2 -> H(f(d), U1(c, b))
24.91/8.20	   A^2 -> H(f(d), U1(d, b))
24.91/8.20	   A^2 -> H(f(d), U1(b, c))
24.91/8.20	   A^2 -> H(f(d), U1(b, d))
24.91/8.20	   A^2 -> H(f(d), U1(c, c))
24.91/8.20	   A^2 -> H(f(d), f(e))
24.91/8.20	   A^2 -> H(f(d), f(k))
24.91/8.20	   A^2 -> H(f(a), U1(e, b))
24.91/8.20	   A^2 -> H(f(a), U1(k, b))
24.91/8.20	   A^2 -> H(f(a), U1(c, d))
24.91/8.20	   A^2 -> H(f(a), U1(d, c))
24.91/8.20	   A^2 -> H(f(a), U1(b, e))
24.91/8.20	   A^2 -> H(f(a), U1(b, k))
24.91/8.20	   A^2 -> H(f(c), U1(c, c))
24.91/8.20	   A^2 -> H(f(a), U1(e, c))
24.91/8.20	   A^2 -> H(f(a), U1(k, c))
24.91/8.20	   A^2 -> H(f(a), U1(c, e))
24.91/8.20	   A^2 -> H(f(a), U1(c, k))
24.91/8.20	   A^2 -> H(f(c), f(e))
24.91/8.20	   A^2 -> H(f(a), U1(e, e))
24.91/8.20	   A^2 -> H(f(a), U1(k, k))
24.91/8.20	   A^2 -> H(f(d), U1(d, d))
24.91/8.20	   A^2 -> H(f(a), U1(k, d))
24.91/8.20	   A^2 -> H(f(a), U1(d, k))
24.91/8.20	   A^2 -> H(a, f(b))
24.91/8.20	   A^2 -> H(U1(e, d), f(b))
24.91/8.20	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(e, a), f(c))
24.91/8.20	   A^2 -> H(U1(e, a), f(d))
24.91/8.20	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(k, a), f(c))
24.91/8.20	   A^2 -> H(U1(k, a), f(d))
24.91/8.20	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, d), f(c))
24.91/8.20	   A^2 -> H(U1(c, d), f(d))
24.91/8.20	
24.91/8.20	The TRS R consists of the following rules:
24.91/8.20	
24.91/8.20	   f(x) -> U1(x, x)
24.91/8.20	   U1(e, x) -> x
24.91/8.20	   a -> c
24.91/8.20	   a -> d
24.91/8.20	   b -> c
24.91/8.20	   b -> d
24.91/8.20	   d -> k
24.91/8.20	   c -> e
24.91/8.20	   c -> k
24.91/8.20	
24.91/8.20	Q is empty.
24.91/8.20	We have to consider all minimal (P,Q,R)-chains.
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(75) TransformationProof (EQUIVALENT)
24.91/8.20	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.20	
24.91/8.20	   (A^2 -> H(U1(e, a), U1(b, b)),A^2 -> H(U1(e, a), U1(b, b)))
24.91/8.20	   (A^2 -> H(U1(k, a), U1(b, b)),A^2 -> H(U1(k, a), U1(b, b)))
24.91/8.20	   (A^2 -> H(U1(c, c), U1(b, b)),A^2 -> H(U1(c, c), U1(b, b)))
24.91/8.20	   (A^2 -> H(U1(c, d), U1(b, b)),A^2 -> H(U1(c, d), U1(b, b)))
24.91/8.20	   (A^2 -> H(U1(c, a), U1(c, b)),A^2 -> H(U1(c, a), U1(c, b)))
24.91/8.20	   (A^2 -> H(U1(c, a), U1(d, b)),A^2 -> H(U1(c, a), U1(d, b)))
24.91/8.20	   (A^2 -> H(U1(c, a), U1(b, c)),A^2 -> H(U1(c, a), U1(b, c)))
24.91/8.20	   (A^2 -> H(U1(c, a), U1(b, d)),A^2 -> H(U1(c, a), U1(b, d)))
24.91/8.20	
24.91/8.20	
24.91/8.20	----------------------------------------
24.91/8.20	
24.91/8.20	(76)
24.91/8.20	Obligation:
24.91/8.20	Q DP problem:
24.91/8.20	The TRS P consists of the following rules:
24.91/8.20	
24.91/8.20	   H(x, x) -> G(x, x, f(k))
24.91/8.20	   G(d, x, x) -> A^2
24.91/8.20	   A^2 -> H(f(c), f(c))
24.91/8.20	   A^2 -> H(f(d), f(d))
24.91/8.20	   A^2 -> H(U1(c, a), f(c))
24.91/8.20	   A^2 -> H(U1(c, a), f(d))
24.91/8.20	   A^2 -> H(U1(d, c), f(b))
24.91/8.20	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, a), f(c))
24.91/8.20	   A^2 -> H(U1(d, a), f(d))
24.91/8.20	   A^2 -> H(U1(a, e), f(b))
24.91/8.20	   A^2 -> H(U1(a, k), f(b))
24.91/8.20	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, c), f(c))
24.91/8.20	   A^2 -> H(U1(a, c), f(d))
24.91/8.20	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(a, d), f(c))
24.91/8.20	   A^2 -> H(U1(a, d), f(d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.20	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.20	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.20	   A^2 -> H(U1(a, a), f(e))
24.91/8.20	   A^2 -> H(U1(a, a), f(k))
24.91/8.20	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.20	   A^2 -> H(U1(e, c), f(b))
24.91/8.20	   A^2 -> H(U1(k, c), f(b))
24.91/8.20	   A^2 -> H(U1(c, e), f(b))
24.91/8.20	   A^2 -> H(U1(c, k), f(b))
24.91/8.20	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.20	   A^2 -> H(U1(c, c), f(c))
24.91/8.20	   A^2 -> H(U1(c, c), f(d))
24.91/8.20	   A^2 -> H(U1(e, e), f(b))
24.91/8.20	   A^2 -> H(f(e), U1(b, b))
24.91/8.20	   A^2 -> H(f(e), f(c))
24.91/8.20	   A^2 -> H(f(e), f(d))
24.91/8.20	   A^2 -> H(U1(k, k), f(b))
24.91/8.20	   A^2 -> H(f(k), U1(b, b))
24.91/8.20	   A^2 -> H(f(k), f(c))
24.91/8.20	   A^2 -> H(f(k), f(d))
24.91/8.20	   A^2 -> H(f(c), U1(c, b))
24.91/8.20	   A^2 -> H(f(c), U1(d, b))
24.91/8.20	   A^2 -> H(f(c), U1(b, c))
24.91/8.20	   A^2 -> H(f(c), U1(b, d))
24.91/8.20	   A^2 -> H(f(c), U1(d, d))
24.91/8.20	   A^2 -> H(f(c), f(k))
24.91/8.20	   A^2 -> H(U1(k, d), f(b))
24.91/8.20	   A^2 -> H(U1(d, k), f(b))
24.91/8.20	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.20	   A^2 -> H(U1(d, d), f(c))
24.91/8.20	   A^2 -> H(U1(d, d), f(d))
24.91/8.20	   A^2 -> H(f(d), U1(c, b))
24.91/8.21	   A^2 -> H(f(d), U1(d, b))
24.91/8.21	   A^2 -> H(f(d), U1(b, c))
24.91/8.21	   A^2 -> H(f(d), U1(b, d))
24.91/8.21	   A^2 -> H(f(d), U1(c, c))
24.91/8.21	   A^2 -> H(f(d), f(e))
24.91/8.21	   A^2 -> H(f(d), f(k))
24.91/8.21	   A^2 -> H(f(a), U1(e, b))
24.91/8.21	   A^2 -> H(f(a), U1(k, b))
24.91/8.21	   A^2 -> H(f(a), U1(c, d))
24.91/8.21	   A^2 -> H(f(a), U1(d, c))
24.91/8.21	   A^2 -> H(f(a), U1(b, e))
24.91/8.21	   A^2 -> H(f(a), U1(b, k))
24.91/8.21	   A^2 -> H(f(c), U1(c, c))
24.91/8.21	   A^2 -> H(f(a), U1(e, c))
24.91/8.21	   A^2 -> H(f(a), U1(k, c))
24.91/8.21	   A^2 -> H(f(a), U1(c, e))
24.91/8.21	   A^2 -> H(f(a), U1(c, k))
24.91/8.21	   A^2 -> H(f(c), f(e))
24.91/8.21	   A^2 -> H(f(a), U1(e, e))
24.91/8.21	   A^2 -> H(f(a), U1(k, k))
24.91/8.21	   A^2 -> H(f(d), U1(d, d))
24.91/8.21	   A^2 -> H(f(a), U1(k, d))
24.91/8.21	   A^2 -> H(f(a), U1(d, k))
24.91/8.21	   A^2 -> H(a, f(b))
24.91/8.21	   A^2 -> H(U1(e, d), f(b))
24.91/8.21	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.21	   A^2 -> H(U1(e, a), f(c))
24.91/8.21	   A^2 -> H(U1(e, a), f(d))
24.91/8.21	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.21	   A^2 -> H(U1(k, a), f(c))
24.91/8.21	   A^2 -> H(U1(k, a), f(d))
24.91/8.21	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.21	   A^2 -> H(U1(c, d), f(c))
24.91/8.21	   A^2 -> H(U1(c, d), f(d))
24.91/8.21	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.21	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.21	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.21	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.21	
24.91/8.21	The TRS R consists of the following rules:
24.91/8.21	
24.91/8.21	   f(x) -> U1(x, x)
24.91/8.21	   U1(e, x) -> x
24.91/8.21	   a -> c
24.91/8.21	   a -> d
24.91/8.21	   b -> c
24.91/8.21	   b -> d
24.91/8.21	   d -> k
24.91/8.21	   c -> e
24.91/8.21	   c -> k
24.91/8.21	
24.91/8.21	Q is empty.
24.91/8.21	We have to consider all minimal (P,Q,R)-chains.
24.91/8.21	----------------------------------------
24.91/8.21	
24.91/8.21	(77) TransformationProof (EQUIVALENT)
24.91/8.21	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), f(c)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.21	
24.91/8.21	   (A^2 -> H(U1(e, a), f(c)),A^2 -> H(U1(e, a), f(c)))
24.91/8.21	   (A^2 -> H(U1(k, a), f(c)),A^2 -> H(U1(k, a), f(c)))
24.91/8.21	   (A^2 -> H(U1(c, c), f(c)),A^2 -> H(U1(c, c), f(c)))
24.91/8.21	   (A^2 -> H(U1(c, d), f(c)),A^2 -> H(U1(c, d), f(c)))
24.91/8.21	   (A^2 -> H(U1(c, a), U1(c, c)),A^2 -> H(U1(c, a), U1(c, c)))
24.91/8.21	   (A^2 -> H(U1(c, a), f(e)),A^2 -> H(U1(c, a), f(e)))
24.91/8.21	   (A^2 -> H(U1(c, a), f(k)),A^2 -> H(U1(c, a), f(k)))
24.91/8.21	
24.91/8.21	
24.91/8.21	----------------------------------------
24.91/8.21	
24.91/8.21	(78)
24.91/8.21	Obligation:
24.91/8.21	Q DP problem:
24.91/8.21	The TRS P consists of the following rules:
24.91/8.21	
24.91/8.21	   H(x, x) -> G(x, x, f(k))
24.91/8.21	   G(d, x, x) -> A^2
24.91/8.21	   A^2 -> H(f(c), f(c))
24.91/8.21	   A^2 -> H(f(d), f(d))
24.91/8.21	   A^2 -> H(U1(c, a), f(d))
24.91/8.21	   A^2 -> H(U1(d, c), f(b))
24.91/8.21	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.21	   A^2 -> H(U1(d, a), f(c))
24.91/8.21	   A^2 -> H(U1(d, a), f(d))
24.91/8.21	   A^2 -> H(U1(a, e), f(b))
24.91/8.21	   A^2 -> H(U1(a, k), f(b))
24.91/8.21	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.21	   A^2 -> H(U1(a, c), f(c))
24.91/8.21	   A^2 -> H(U1(a, c), f(d))
24.91/8.21	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.21	   A^2 -> H(U1(a, d), f(c))
24.91/8.21	   A^2 -> H(U1(a, d), f(d))
24.91/8.21	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.21	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.21	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.21	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.21	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.21	   A^2 -> H(U1(a, a), f(e))
24.91/8.21	   A^2 -> H(U1(a, a), f(k))
24.91/8.21	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.21	   A^2 -> H(U1(e, c), f(b))
24.91/8.21	   A^2 -> H(U1(k, c), f(b))
24.91/8.21	   A^2 -> H(U1(c, e), f(b))
24.91/8.21	   A^2 -> H(U1(c, k), f(b))
24.91/8.21	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.21	   A^2 -> H(U1(c, c), f(c))
24.91/8.21	   A^2 -> H(U1(c, c), f(d))
24.91/8.21	   A^2 -> H(U1(e, e), f(b))
24.91/8.21	   A^2 -> H(f(e), U1(b, b))
24.91/8.21	   A^2 -> H(f(e), f(c))
24.91/8.21	   A^2 -> H(f(e), f(d))
24.91/8.21	   A^2 -> H(U1(k, k), f(b))
24.91/8.21	   A^2 -> H(f(k), U1(b, b))
24.91/8.21	   A^2 -> H(f(k), f(c))
24.91/8.21	   A^2 -> H(f(k), f(d))
24.91/8.21	   A^2 -> H(f(c), U1(c, b))
24.91/8.21	   A^2 -> H(f(c), U1(d, b))
24.91/8.21	   A^2 -> H(f(c), U1(b, c))
24.91/8.21	   A^2 -> H(f(c), U1(b, d))
24.91/8.21	   A^2 -> H(f(c), U1(d, d))
24.91/8.21	   A^2 -> H(f(c), f(k))
24.91/8.21	   A^2 -> H(U1(k, d), f(b))
24.91/8.21	   A^2 -> H(U1(d, k), f(b))
24.91/8.21	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.21	   A^2 -> H(U1(d, d), f(c))
24.91/8.21	   A^2 -> H(U1(d, d), f(d))
24.91/8.21	   A^2 -> H(f(d), U1(c, b))
24.91/8.21	   A^2 -> H(f(d), U1(d, b))
24.91/8.21	   A^2 -> H(f(d), U1(b, c))
24.91/8.21	   A^2 -> H(f(d), U1(b, d))
24.91/8.21	   A^2 -> H(f(d), U1(c, c))
24.91/8.21	   A^2 -> H(f(d), f(e))
24.91/8.21	   A^2 -> H(f(d), f(k))
24.91/8.21	   A^2 -> H(f(a), U1(e, b))
24.91/8.21	   A^2 -> H(f(a), U1(k, b))
24.91/8.21	   A^2 -> H(f(a), U1(c, d))
24.91/8.21	   A^2 -> H(f(a), U1(d, c))
24.91/8.21	   A^2 -> H(f(a), U1(b, e))
24.91/8.21	   A^2 -> H(f(a), U1(b, k))
24.91/8.21	   A^2 -> H(f(c), U1(c, c))
24.91/8.21	   A^2 -> H(f(a), U1(e, c))
24.91/8.21	   A^2 -> H(f(a), U1(k, c))
24.91/8.21	   A^2 -> H(f(a), U1(c, e))
24.91/8.21	   A^2 -> H(f(a), U1(c, k))
24.91/8.21	   A^2 -> H(f(c), f(e))
24.91/8.21	   A^2 -> H(f(a), U1(e, e))
24.91/8.21	   A^2 -> H(f(a), U1(k, k))
24.91/8.21	   A^2 -> H(f(d), U1(d, d))
24.91/8.21	   A^2 -> H(f(a), U1(k, d))
24.91/8.21	   A^2 -> H(f(a), U1(d, k))
24.91/8.21	   A^2 -> H(a, f(b))
24.91/8.21	   A^2 -> H(U1(e, d), f(b))
24.91/8.21	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.21	   A^2 -> H(U1(e, a), f(c))
24.91/8.21	   A^2 -> H(U1(e, a), f(d))
24.91/8.21	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.21	   A^2 -> H(U1(k, a), f(c))
24.91/8.21	   A^2 -> H(U1(k, a), f(d))
24.91/8.21	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.21	   A^2 -> H(U1(c, d), f(c))
24.91/8.21	   A^2 -> H(U1(c, d), f(d))
24.91/8.21	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.21	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.21	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.21	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.21	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.21	   A^2 -> H(U1(c, a), f(e))
24.91/8.21	   A^2 -> H(U1(c, a), f(k))
24.91/8.21	
24.91/8.21	The TRS R consists of the following rules:
24.91/8.21	
24.91/8.21	   f(x) -> U1(x, x)
24.91/8.21	   U1(e, x) -> x
24.91/8.21	   a -> c
24.91/8.21	   a -> d
24.91/8.21	   b -> c
24.91/8.21	   b -> d
24.91/8.21	   d -> k
24.91/8.21	   c -> e
24.91/8.21	   c -> k
24.91/8.21	
24.91/8.21	Q is empty.
24.91/8.21	We have to consider all minimal (P,Q,R)-chains.
24.91/8.21	----------------------------------------
24.91/8.21	
24.91/8.21	(79) TransformationProof (EQUIVALENT)
24.91/8.21	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), f(d)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.21	
24.91/8.21	   (A^2 -> H(U1(e, a), f(d)),A^2 -> H(U1(e, a), f(d)))
24.91/8.21	   (A^2 -> H(U1(k, a), f(d)),A^2 -> H(U1(k, a), f(d)))
24.91/8.21	   (A^2 -> H(U1(c, c), f(d)),A^2 -> H(U1(c, c), f(d)))
24.91/8.21	   (A^2 -> H(U1(c, d), f(d)),A^2 -> H(U1(c, d), f(d)))
24.91/8.21	   (A^2 -> H(U1(c, a), U1(d, d)),A^2 -> H(U1(c, a), U1(d, d)))
24.91/8.21	   (A^2 -> H(U1(c, a), f(k)),A^2 -> H(U1(c, a), f(k)))
24.91/8.21	
24.91/8.21	
24.91/8.21	----------------------------------------
24.91/8.21	
24.91/8.21	(80)
24.91/8.21	Obligation:
24.91/8.21	Q DP problem:
24.91/8.21	The TRS P consists of the following rules:
24.91/8.21	
24.91/8.21	   H(x, x) -> G(x, x, f(k))
24.91/8.21	   G(d, x, x) -> A^2
24.91/8.21	   A^2 -> H(f(c), f(c))
24.91/8.21	   A^2 -> H(f(d), f(d))
24.91/8.21	   A^2 -> H(U1(d, c), f(b))
24.91/8.21	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.21	   A^2 -> H(U1(d, a), f(c))
24.91/8.21	   A^2 -> H(U1(d, a), f(d))
24.91/8.21	   A^2 -> H(U1(a, e), f(b))
24.91/8.21	   A^2 -> H(U1(a, k), f(b))
24.91/8.21	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.21	   A^2 -> H(U1(a, c), f(c))
24.91/8.21	   A^2 -> H(U1(a, c), f(d))
24.91/8.21	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.21	   A^2 -> H(U1(a, d), f(c))
24.91/8.21	   A^2 -> H(U1(a, d), f(d))
24.91/8.21	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.21	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.21	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.21	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.21	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.21	   A^2 -> H(U1(a, a), f(e))
24.91/8.21	   A^2 -> H(U1(a, a), f(k))
24.91/8.21	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.21	   A^2 -> H(U1(e, c), f(b))
24.91/8.21	   A^2 -> H(U1(k, c), f(b))
24.91/8.21	   A^2 -> H(U1(c, e), f(b))
24.91/8.21	   A^2 -> H(U1(c, k), f(b))
24.91/8.21	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.21	   A^2 -> H(U1(c, c), f(c))
24.91/8.21	   A^2 -> H(U1(c, c), f(d))
24.91/8.21	   A^2 -> H(U1(e, e), f(b))
24.91/8.21	   A^2 -> H(f(e), U1(b, b))
24.91/8.21	   A^2 -> H(f(e), f(c))
24.91/8.21	   A^2 -> H(f(e), f(d))
24.91/8.21	   A^2 -> H(U1(k, k), f(b))
24.91/8.21	   A^2 -> H(f(k), U1(b, b))
24.91/8.21	   A^2 -> H(f(k), f(c))
24.91/8.21	   A^2 -> H(f(k), f(d))
24.91/8.21	   A^2 -> H(f(c), U1(c, b))
24.91/8.21	   A^2 -> H(f(c), U1(d, b))
24.91/8.21	   A^2 -> H(f(c), U1(b, c))
24.91/8.21	   A^2 -> H(f(c), U1(b, d))
24.91/8.21	   A^2 -> H(f(c), U1(d, d))
24.91/8.21	   A^2 -> H(f(c), f(k))
24.91/8.21	   A^2 -> H(U1(k, d), f(b))
24.91/8.21	   A^2 -> H(U1(d, k), f(b))
24.91/8.21	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.21	   A^2 -> H(U1(d, d), f(c))
24.91/8.21	   A^2 -> H(U1(d, d), f(d))
24.91/8.21	   A^2 -> H(f(d), U1(c, b))
24.91/8.21	   A^2 -> H(f(d), U1(d, b))
24.91/8.21	   A^2 -> H(f(d), U1(b, c))
24.91/8.21	   A^2 -> H(f(d), U1(b, d))
24.91/8.21	   A^2 -> H(f(d), U1(c, c))
24.91/8.21	   A^2 -> H(f(d), f(e))
24.91/8.21	   A^2 -> H(f(d), f(k))
24.91/8.21	   A^2 -> H(f(a), U1(e, b))
24.91/8.21	   A^2 -> H(f(a), U1(k, b))
24.91/8.21	   A^2 -> H(f(a), U1(c, d))
24.91/8.21	   A^2 -> H(f(a), U1(d, c))
24.91/8.21	   A^2 -> H(f(a), U1(b, e))
24.91/8.21	   A^2 -> H(f(a), U1(b, k))
24.91/8.21	   A^2 -> H(f(c), U1(c, c))
24.91/8.21	   A^2 -> H(f(a), U1(e, c))
24.91/8.21	   A^2 -> H(f(a), U1(k, c))
24.91/8.21	   A^2 -> H(f(a), U1(c, e))
24.91/8.21	   A^2 -> H(f(a), U1(c, k))
24.91/8.21	   A^2 -> H(f(c), f(e))
24.91/8.21	   A^2 -> H(f(a), U1(e, e))
24.91/8.21	   A^2 -> H(f(a), U1(k, k))
24.91/8.21	   A^2 -> H(f(d), U1(d, d))
24.91/8.21	   A^2 -> H(f(a), U1(k, d))
24.91/8.21	   A^2 -> H(f(a), U1(d, k))
24.91/8.21	   A^2 -> H(a, f(b))
24.91/8.21	   A^2 -> H(U1(e, d), f(b))
24.91/8.21	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.21	   A^2 -> H(U1(e, a), f(c))
24.91/8.21	   A^2 -> H(U1(e, a), f(d))
24.91/8.21	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.21	   A^2 -> H(U1(k, a), f(c))
24.91/8.21	   A^2 -> H(U1(k, a), f(d))
24.91/8.21	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.21	   A^2 -> H(U1(c, d), f(c))
24.91/8.21	   A^2 -> H(U1(c, d), f(d))
24.91/8.21	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.21	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.21	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.21	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.21	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.21	   A^2 -> H(U1(c, a), f(e))
24.91/8.21	   A^2 -> H(U1(c, a), f(k))
24.91/8.21	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.21	
24.91/8.21	The TRS R consists of the following rules:
24.91/8.21	
24.91/8.21	   f(x) -> U1(x, x)
24.91/8.22	   U1(e, x) -> x
24.91/8.22	   a -> c
24.91/8.22	   a -> d
24.91/8.22	   b -> c
24.91/8.22	   b -> d
24.91/8.22	   d -> k
24.91/8.22	   c -> e
24.91/8.22	   c -> k
24.91/8.22	
24.91/8.22	Q is empty.
24.91/8.22	We have to consider all minimal (P,Q,R)-chains.
24.91/8.22	----------------------------------------
24.91/8.22	
24.91/8.22	(81) TransformationProof (EQUIVALENT)
24.91/8.22	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), f(b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.22	
24.91/8.22	   (A^2 -> H(U1(k, c), f(b)),A^2 -> H(U1(k, c), f(b)))
24.91/8.22	   (A^2 -> H(U1(d, e), f(b)),A^2 -> H(U1(d, e), f(b)))
24.91/8.22	   (A^2 -> H(U1(d, k), f(b)),A^2 -> H(U1(d, k), f(b)))
24.91/8.22	   (A^2 -> H(U1(d, c), U1(b, b)),A^2 -> H(U1(d, c), U1(b, b)))
24.91/8.22	   (A^2 -> H(U1(d, c), f(c)),A^2 -> H(U1(d, c), f(c)))
24.91/8.22	   (A^2 -> H(U1(d, c), f(d)),A^2 -> H(U1(d, c), f(d)))
24.91/8.22	
24.91/8.22	
24.91/8.22	----------------------------------------
24.91/8.22	
24.91/8.22	(82)
24.91/8.22	Obligation:
24.91/8.22	Q DP problem:
24.91/8.22	The TRS P consists of the following rules:
24.91/8.22	
24.91/8.22	   H(x, x) -> G(x, x, f(k))
24.91/8.22	   G(d, x, x) -> A^2
24.91/8.22	   A^2 -> H(f(c), f(c))
24.91/8.22	   A^2 -> H(f(d), f(d))
24.91/8.22	   A^2 -> H(U1(d, a), U1(b, b))
24.91/8.22	   A^2 -> H(U1(d, a), f(c))
24.91/8.22	   A^2 -> H(U1(d, a), f(d))
24.91/8.22	   A^2 -> H(U1(a, e), f(b))
24.91/8.22	   A^2 -> H(U1(a, k), f(b))
24.91/8.22	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, c), f(c))
24.91/8.22	   A^2 -> H(U1(a, c), f(d))
24.91/8.22	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, d), f(c))
24.91/8.22	   A^2 -> H(U1(a, d), f(d))
24.91/8.22	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(a, a), f(e))
24.91/8.22	   A^2 -> H(U1(a, a), f(k))
24.91/8.22	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(e, c), f(b))
24.91/8.22	   A^2 -> H(U1(k, c), f(b))
24.91/8.22	   A^2 -> H(U1(c, e), f(b))
24.91/8.22	   A^2 -> H(U1(c, k), f(b))
24.91/8.22	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(c, c), f(c))
24.91/8.22	   A^2 -> H(U1(c, c), f(d))
24.91/8.22	   A^2 -> H(U1(e, e), f(b))
24.91/8.22	   A^2 -> H(f(e), U1(b, b))
24.91/8.22	   A^2 -> H(f(e), f(c))
24.91/8.22	   A^2 -> H(f(e), f(d))
24.91/8.22	   A^2 -> H(U1(k, k), f(b))
24.91/8.22	   A^2 -> H(f(k), U1(b, b))
24.91/8.22	   A^2 -> H(f(k), f(c))
24.91/8.22	   A^2 -> H(f(k), f(d))
24.91/8.22	   A^2 -> H(f(c), U1(c, b))
24.91/8.22	   A^2 -> H(f(c), U1(d, b))
24.91/8.22	   A^2 -> H(f(c), U1(b, c))
24.91/8.22	   A^2 -> H(f(c), U1(b, d))
24.91/8.22	   A^2 -> H(f(c), U1(d, d))
24.91/8.22	   A^2 -> H(f(c), f(k))
24.91/8.22	   A^2 -> H(U1(k, d), f(b))
24.91/8.22	   A^2 -> H(U1(d, k), f(b))
24.91/8.22	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(d, d), f(c))
24.91/8.22	   A^2 -> H(U1(d, d), f(d))
24.91/8.22	   A^2 -> H(f(d), U1(c, b))
24.91/8.22	   A^2 -> H(f(d), U1(d, b))
24.91/8.22	   A^2 -> H(f(d), U1(b, c))
24.91/8.22	   A^2 -> H(f(d), U1(b, d))
24.91/8.22	   A^2 -> H(f(d), U1(c, c))
24.91/8.22	   A^2 -> H(f(d), f(e))
24.91/8.22	   A^2 -> H(f(d), f(k))
24.91/8.22	   A^2 -> H(f(a), U1(e, b))
24.91/8.22	   A^2 -> H(f(a), U1(k, b))
24.91/8.22	   A^2 -> H(f(a), U1(c, d))
24.91/8.22	   A^2 -> H(f(a), U1(d, c))
24.91/8.22	   A^2 -> H(f(a), U1(b, e))
24.91/8.22	   A^2 -> H(f(a), U1(b, k))
24.91/8.22	   A^2 -> H(f(c), U1(c, c))
24.91/8.22	   A^2 -> H(f(a), U1(e, c))
24.91/8.22	   A^2 -> H(f(a), U1(k, c))
24.91/8.22	   A^2 -> H(f(a), U1(c, e))
24.91/8.22	   A^2 -> H(f(a), U1(c, k))
24.91/8.22	   A^2 -> H(f(c), f(e))
24.91/8.22	   A^2 -> H(f(a), U1(e, e))
24.91/8.22	   A^2 -> H(f(a), U1(k, k))
24.91/8.22	   A^2 -> H(f(d), U1(d, d))
24.91/8.22	   A^2 -> H(f(a), U1(k, d))
24.91/8.22	   A^2 -> H(f(a), U1(d, k))
24.91/8.22	   A^2 -> H(a, f(b))
24.91/8.22	   A^2 -> H(U1(e, d), f(b))
24.91/8.22	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.22	   A^2 -> H(U1(e, a), f(c))
24.91/8.22	   A^2 -> H(U1(e, a), f(d))
24.91/8.22	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.22	   A^2 -> H(U1(k, a), f(c))
24.91/8.22	   A^2 -> H(U1(k, a), f(d))
24.91/8.22	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(c, d), f(c))
24.91/8.22	   A^2 -> H(U1(c, d), f(d))
24.91/8.22	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(c, a), f(e))
24.91/8.22	   A^2 -> H(U1(c, a), f(k))
24.91/8.22	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(d, e), f(b))
24.91/8.22	   A^2 -> H(U1(d, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(d, c), f(c))
24.91/8.22	   A^2 -> H(U1(d, c), f(d))
24.91/8.22	
24.91/8.22	The TRS R consists of the following rules:
24.91/8.22	
24.91/8.22	   f(x) -> U1(x, x)
24.91/8.22	   U1(e, x) -> x
24.91/8.22	   a -> c
24.91/8.22	   a -> d
24.91/8.22	   b -> c
24.91/8.22	   b -> d
24.91/8.22	   d -> k
24.91/8.22	   c -> e
24.91/8.22	   c -> k
24.91/8.22	
24.91/8.22	Q is empty.
24.91/8.22	We have to consider all minimal (P,Q,R)-chains.
24.91/8.22	----------------------------------------
24.91/8.22	
24.91/8.22	(83) TransformationProof (EQUIVALENT)
24.91/8.22	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.22	
24.91/8.22	   (A^2 -> H(U1(k, a), U1(b, b)),A^2 -> H(U1(k, a), U1(b, b)))
24.91/8.22	   (A^2 -> H(U1(d, c), U1(b, b)),A^2 -> H(U1(d, c), U1(b, b)))
24.91/8.22	   (A^2 -> H(U1(d, d), U1(b, b)),A^2 -> H(U1(d, d), U1(b, b)))
24.91/8.22	   (A^2 -> H(U1(d, a), U1(c, b)),A^2 -> H(U1(d, a), U1(c, b)))
24.91/8.22	   (A^2 -> H(U1(d, a), U1(d, b)),A^2 -> H(U1(d, a), U1(d, b)))
24.91/8.22	   (A^2 -> H(U1(d, a), U1(b, c)),A^2 -> H(U1(d, a), U1(b, c)))
24.91/8.22	   (A^2 -> H(U1(d, a), U1(b, d)),A^2 -> H(U1(d, a), U1(b, d)))
24.91/8.22	
24.91/8.22	
24.91/8.22	----------------------------------------
24.91/8.22	
24.91/8.22	(84)
24.91/8.22	Obligation:
24.91/8.22	Q DP problem:
24.91/8.22	The TRS P consists of the following rules:
24.91/8.22	
24.91/8.22	   H(x, x) -> G(x, x, f(k))
24.91/8.22	   G(d, x, x) -> A^2
24.91/8.22	   A^2 -> H(f(c), f(c))
24.91/8.22	   A^2 -> H(f(d), f(d))
24.91/8.22	   A^2 -> H(U1(d, a), f(c))
24.91/8.22	   A^2 -> H(U1(d, a), f(d))
24.91/8.22	   A^2 -> H(U1(a, e), f(b))
24.91/8.22	   A^2 -> H(U1(a, k), f(b))
24.91/8.22	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, c), f(c))
24.91/8.22	   A^2 -> H(U1(a, c), f(d))
24.91/8.22	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, d), f(c))
24.91/8.22	   A^2 -> H(U1(a, d), f(d))
24.91/8.22	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(a, a), f(e))
24.91/8.22	   A^2 -> H(U1(a, a), f(k))
24.91/8.22	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(e, c), f(b))
24.91/8.22	   A^2 -> H(U1(k, c), f(b))
24.91/8.22	   A^2 -> H(U1(c, e), f(b))
24.91/8.22	   A^2 -> H(U1(c, k), f(b))
24.91/8.22	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(c, c), f(c))
24.91/8.22	   A^2 -> H(U1(c, c), f(d))
24.91/8.22	   A^2 -> H(U1(e, e), f(b))
24.91/8.22	   A^2 -> H(f(e), U1(b, b))
24.91/8.22	   A^2 -> H(f(e), f(c))
24.91/8.22	   A^2 -> H(f(e), f(d))
24.91/8.22	   A^2 -> H(U1(k, k), f(b))
24.91/8.22	   A^2 -> H(f(k), U1(b, b))
24.91/8.22	   A^2 -> H(f(k), f(c))
24.91/8.22	   A^2 -> H(f(k), f(d))
24.91/8.22	   A^2 -> H(f(c), U1(c, b))
24.91/8.22	   A^2 -> H(f(c), U1(d, b))
24.91/8.22	   A^2 -> H(f(c), U1(b, c))
24.91/8.22	   A^2 -> H(f(c), U1(b, d))
24.91/8.22	   A^2 -> H(f(c), U1(d, d))
24.91/8.22	   A^2 -> H(f(c), f(k))
24.91/8.22	   A^2 -> H(U1(k, d), f(b))
24.91/8.22	   A^2 -> H(U1(d, k), f(b))
24.91/8.22	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(d, d), f(c))
24.91/8.22	   A^2 -> H(U1(d, d), f(d))
24.91/8.22	   A^2 -> H(f(d), U1(c, b))
24.91/8.22	   A^2 -> H(f(d), U1(d, b))
24.91/8.22	   A^2 -> H(f(d), U1(b, c))
24.91/8.22	   A^2 -> H(f(d), U1(b, d))
24.91/8.22	   A^2 -> H(f(d), U1(c, c))
24.91/8.22	   A^2 -> H(f(d), f(e))
24.91/8.22	   A^2 -> H(f(d), f(k))
24.91/8.22	   A^2 -> H(f(a), U1(e, b))
24.91/8.22	   A^2 -> H(f(a), U1(k, b))
24.91/8.22	   A^2 -> H(f(a), U1(c, d))
24.91/8.22	   A^2 -> H(f(a), U1(d, c))
24.91/8.22	   A^2 -> H(f(a), U1(b, e))
24.91/8.22	   A^2 -> H(f(a), U1(b, k))
24.91/8.22	   A^2 -> H(f(c), U1(c, c))
24.91/8.22	   A^2 -> H(f(a), U1(e, c))
24.91/8.22	   A^2 -> H(f(a), U1(k, c))
24.91/8.22	   A^2 -> H(f(a), U1(c, e))
24.91/8.22	   A^2 -> H(f(a), U1(c, k))
24.91/8.22	   A^2 -> H(f(c), f(e))
24.91/8.22	   A^2 -> H(f(a), U1(e, e))
24.91/8.22	   A^2 -> H(f(a), U1(k, k))
24.91/8.22	   A^2 -> H(f(d), U1(d, d))
24.91/8.22	   A^2 -> H(f(a), U1(k, d))
24.91/8.22	   A^2 -> H(f(a), U1(d, k))
24.91/8.22	   A^2 -> H(a, f(b))
24.91/8.22	   A^2 -> H(U1(e, d), f(b))
24.91/8.22	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.22	   A^2 -> H(U1(e, a), f(c))
24.91/8.22	   A^2 -> H(U1(e, a), f(d))
24.91/8.22	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.22	   A^2 -> H(U1(k, a), f(c))
24.91/8.22	   A^2 -> H(U1(k, a), f(d))
24.91/8.22	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(c, d), f(c))
24.91/8.22	   A^2 -> H(U1(c, d), f(d))
24.91/8.22	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(c, a), f(e))
24.91/8.22	   A^2 -> H(U1(c, a), f(k))
24.91/8.22	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(d, e), f(b))
24.91/8.22	   A^2 -> H(U1(d, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(d, c), f(c))
24.91/8.22	   A^2 -> H(U1(d, c), f(d))
24.91/8.22	   A^2 -> H(U1(d, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(d, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(d, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(d, a), U1(b, d))
24.91/8.22	
24.91/8.22	The TRS R consists of the following rules:
24.91/8.22	
24.91/8.22	   f(x) -> U1(x, x)
24.91/8.22	   U1(e, x) -> x
24.91/8.22	   a -> c
24.91/8.22	   a -> d
24.91/8.22	   b -> c
24.91/8.22	   b -> d
24.91/8.22	   d -> k
24.91/8.22	   c -> e
24.91/8.22	   c -> k
24.91/8.22	
24.91/8.22	Q is empty.
24.91/8.22	We have to consider all minimal (P,Q,R)-chains.
24.91/8.22	----------------------------------------
24.91/8.22	
24.91/8.22	(85) TransformationProof (EQUIVALENT)
24.91/8.22	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), f(c)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.22	
24.91/8.22	   (A^2 -> H(U1(k, a), f(c)),A^2 -> H(U1(k, a), f(c)))
24.91/8.22	   (A^2 -> H(U1(d, c), f(c)),A^2 -> H(U1(d, c), f(c)))
24.91/8.22	   (A^2 -> H(U1(d, d), f(c)),A^2 -> H(U1(d, d), f(c)))
24.91/8.22	   (A^2 -> H(U1(d, a), U1(c, c)),A^2 -> H(U1(d, a), U1(c, c)))
24.91/8.22	   (A^2 -> H(U1(d, a), f(e)),A^2 -> H(U1(d, a), f(e)))
24.91/8.22	   (A^2 -> H(U1(d, a), f(k)),A^2 -> H(U1(d, a), f(k)))
24.91/8.22	
24.91/8.22	
24.91/8.22	----------------------------------------
24.91/8.22	
24.91/8.22	(86)
24.91/8.22	Obligation:
24.91/8.22	Q DP problem:
24.91/8.22	The TRS P consists of the following rules:
24.91/8.22	
24.91/8.22	   H(x, x) -> G(x, x, f(k))
24.91/8.22	   G(d, x, x) -> A^2
24.91/8.22	   A^2 -> H(f(c), f(c))
24.91/8.22	   A^2 -> H(f(d), f(d))
24.91/8.22	   A^2 -> H(U1(d, a), f(d))
24.91/8.22	   A^2 -> H(U1(a, e), f(b))
24.91/8.22	   A^2 -> H(U1(a, k), f(b))
24.91/8.22	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, c), f(c))
24.91/8.22	   A^2 -> H(U1(a, c), f(d))
24.91/8.22	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, d), f(c))
24.91/8.22	   A^2 -> H(U1(a, d), f(d))
24.91/8.22	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(a, a), f(e))
24.91/8.22	   A^2 -> H(U1(a, a), f(k))
24.91/8.22	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(e, c), f(b))
24.91/8.22	   A^2 -> H(U1(k, c), f(b))
24.91/8.22	   A^2 -> H(U1(c, e), f(b))
24.91/8.22	   A^2 -> H(U1(c, k), f(b))
24.91/8.22	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(c, c), f(c))
24.91/8.22	   A^2 -> H(U1(c, c), f(d))
24.91/8.22	   A^2 -> H(U1(e, e), f(b))
24.91/8.22	   A^2 -> H(f(e), U1(b, b))
24.91/8.22	   A^2 -> H(f(e), f(c))
24.91/8.22	   A^2 -> H(f(e), f(d))
24.91/8.22	   A^2 -> H(U1(k, k), f(b))
24.91/8.22	   A^2 -> H(f(k), U1(b, b))
24.91/8.22	   A^2 -> H(f(k), f(c))
24.91/8.22	   A^2 -> H(f(k), f(d))
24.91/8.22	   A^2 -> H(f(c), U1(c, b))
24.91/8.22	   A^2 -> H(f(c), U1(d, b))
24.91/8.22	   A^2 -> H(f(c), U1(b, c))
24.91/8.22	   A^2 -> H(f(c), U1(b, d))
24.91/8.22	   A^2 -> H(f(c), U1(d, d))
24.91/8.22	   A^2 -> H(f(c), f(k))
24.91/8.22	   A^2 -> H(U1(k, d), f(b))
24.91/8.22	   A^2 -> H(U1(d, k), f(b))
24.91/8.22	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(d, d), f(c))
24.91/8.22	   A^2 -> H(U1(d, d), f(d))
24.91/8.22	   A^2 -> H(f(d), U1(c, b))
24.91/8.22	   A^2 -> H(f(d), U1(d, b))
24.91/8.22	   A^2 -> H(f(d), U1(b, c))
24.91/8.22	   A^2 -> H(f(d), U1(b, d))
24.91/8.22	   A^2 -> H(f(d), U1(c, c))
24.91/8.22	   A^2 -> H(f(d), f(e))
24.91/8.22	   A^2 -> H(f(d), f(k))
24.91/8.22	   A^2 -> H(f(a), U1(e, b))
24.91/8.22	   A^2 -> H(f(a), U1(k, b))
24.91/8.22	   A^2 -> H(f(a), U1(c, d))
24.91/8.22	   A^2 -> H(f(a), U1(d, c))
24.91/8.22	   A^2 -> H(f(a), U1(b, e))
24.91/8.22	   A^2 -> H(f(a), U1(b, k))
24.91/8.22	   A^2 -> H(f(c), U1(c, c))
24.91/8.22	   A^2 -> H(f(a), U1(e, c))
24.91/8.22	   A^2 -> H(f(a), U1(k, c))
24.91/8.22	   A^2 -> H(f(a), U1(c, e))
24.91/8.22	   A^2 -> H(f(a), U1(c, k))
24.91/8.22	   A^2 -> H(f(c), f(e))
24.91/8.22	   A^2 -> H(f(a), U1(e, e))
24.91/8.22	   A^2 -> H(f(a), U1(k, k))
24.91/8.22	   A^2 -> H(f(d), U1(d, d))
24.91/8.22	   A^2 -> H(f(a), U1(k, d))
24.91/8.22	   A^2 -> H(f(a), U1(d, k))
24.91/8.22	   A^2 -> H(a, f(b))
24.91/8.22	   A^2 -> H(U1(e, d), f(b))
24.91/8.22	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.22	   A^2 -> H(U1(e, a), f(c))
24.91/8.22	   A^2 -> H(U1(e, a), f(d))
24.91/8.22	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.22	   A^2 -> H(U1(k, a), f(c))
24.91/8.22	   A^2 -> H(U1(k, a), f(d))
24.91/8.22	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(c, d), f(c))
24.91/8.22	   A^2 -> H(U1(c, d), f(d))
24.91/8.22	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(c, a), f(e))
24.91/8.22	   A^2 -> H(U1(c, a), f(k))
24.91/8.22	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(d, e), f(b))
24.91/8.22	   A^2 -> H(U1(d, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(d, c), f(c))
24.91/8.22	   A^2 -> H(U1(d, c), f(d))
24.91/8.22	   A^2 -> H(U1(d, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(d, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(d, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(d, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(d, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(d, a), f(e))
24.91/8.22	   A^2 -> H(U1(d, a), f(k))
24.91/8.22	
24.91/8.22	The TRS R consists of the following rules:
24.91/8.22	
24.91/8.22	   f(x) -> U1(x, x)
24.91/8.22	   U1(e, x) -> x
24.91/8.22	   a -> c
24.91/8.22	   a -> d
24.91/8.22	   b -> c
24.91/8.22	   b -> d
24.91/8.22	   d -> k
24.91/8.22	   c -> e
24.91/8.22	   c -> k
24.91/8.22	
24.91/8.22	Q is empty.
24.91/8.22	We have to consider all minimal (P,Q,R)-chains.
24.91/8.22	----------------------------------------
24.91/8.22	
24.91/8.22	(87) TransformationProof (EQUIVALENT)
24.91/8.22	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), f(d)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.22	
24.91/8.22	   (A^2 -> H(U1(k, a), f(d)),A^2 -> H(U1(k, a), f(d)))
24.91/8.22	   (A^2 -> H(U1(d, c), f(d)),A^2 -> H(U1(d, c), f(d)))
24.91/8.22	   (A^2 -> H(U1(d, d), f(d)),A^2 -> H(U1(d, d), f(d)))
24.91/8.22	   (A^2 -> H(U1(d, a), U1(d, d)),A^2 -> H(U1(d, a), U1(d, d)))
24.91/8.22	   (A^2 -> H(U1(d, a), f(k)),A^2 -> H(U1(d, a), f(k)))
24.91/8.22	
24.91/8.22	
24.91/8.22	----------------------------------------
24.91/8.22	
24.91/8.22	(88)
24.91/8.22	Obligation:
24.91/8.22	Q DP problem:
24.91/8.22	The TRS P consists of the following rules:
24.91/8.22	
24.91/8.22	   H(x, x) -> G(x, x, f(k))
24.91/8.22	   G(d, x, x) -> A^2
24.91/8.22	   A^2 -> H(f(c), f(c))
24.91/8.22	   A^2 -> H(f(d), f(d))
24.91/8.22	   A^2 -> H(U1(a, e), f(b))
24.91/8.22	   A^2 -> H(U1(a, k), f(b))
24.91/8.22	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, c), f(c))
24.91/8.22	   A^2 -> H(U1(a, c), f(d))
24.91/8.22	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, d), f(c))
24.91/8.22	   A^2 -> H(U1(a, d), f(d))
24.91/8.22	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(a, a), f(e))
24.91/8.22	   A^2 -> H(U1(a, a), f(k))
24.91/8.22	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(e, c), f(b))
24.91/8.22	   A^2 -> H(U1(k, c), f(b))
24.91/8.22	   A^2 -> H(U1(c, e), f(b))
24.91/8.22	   A^2 -> H(U1(c, k), f(b))
24.91/8.22	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(c, c), f(c))
24.91/8.22	   A^2 -> H(U1(c, c), f(d))
24.91/8.22	   A^2 -> H(U1(e, e), f(b))
24.91/8.22	   A^2 -> H(f(e), U1(b, b))
24.91/8.22	   A^2 -> H(f(e), f(c))
24.91/8.22	   A^2 -> H(f(e), f(d))
24.91/8.22	   A^2 -> H(U1(k, k), f(b))
24.91/8.22	   A^2 -> H(f(k), U1(b, b))
24.91/8.22	   A^2 -> H(f(k), f(c))
24.91/8.22	   A^2 -> H(f(k), f(d))
24.91/8.22	   A^2 -> H(f(c), U1(c, b))
24.91/8.22	   A^2 -> H(f(c), U1(d, b))
24.91/8.22	   A^2 -> H(f(c), U1(b, c))
24.91/8.22	   A^2 -> H(f(c), U1(b, d))
24.91/8.22	   A^2 -> H(f(c), U1(d, d))
24.91/8.22	   A^2 -> H(f(c), f(k))
24.91/8.22	   A^2 -> H(U1(k, d), f(b))
24.91/8.22	   A^2 -> H(U1(d, k), f(b))
24.91/8.22	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(d, d), f(c))
24.91/8.22	   A^2 -> H(U1(d, d), f(d))
24.91/8.22	   A^2 -> H(f(d), U1(c, b))
24.91/8.22	   A^2 -> H(f(d), U1(d, b))
24.91/8.22	   A^2 -> H(f(d), U1(b, c))
24.91/8.22	   A^2 -> H(f(d), U1(b, d))
24.91/8.22	   A^2 -> H(f(d), U1(c, c))
24.91/8.22	   A^2 -> H(f(d), f(e))
24.91/8.22	   A^2 -> H(f(d), f(k))
24.91/8.22	   A^2 -> H(f(a), U1(e, b))
24.91/8.22	   A^2 -> H(f(a), U1(k, b))
24.91/8.22	   A^2 -> H(f(a), U1(c, d))
24.91/8.22	   A^2 -> H(f(a), U1(d, c))
24.91/8.22	   A^2 -> H(f(a), U1(b, e))
24.91/8.22	   A^2 -> H(f(a), U1(b, k))
24.91/8.22	   A^2 -> H(f(c), U1(c, c))
24.91/8.22	   A^2 -> H(f(a), U1(e, c))
24.91/8.22	   A^2 -> H(f(a), U1(k, c))
24.91/8.22	   A^2 -> H(f(a), U1(c, e))
24.91/8.22	   A^2 -> H(f(a), U1(c, k))
24.91/8.22	   A^2 -> H(f(c), f(e))
24.91/8.22	   A^2 -> H(f(a), U1(e, e))
24.91/8.22	   A^2 -> H(f(a), U1(k, k))
24.91/8.22	   A^2 -> H(f(d), U1(d, d))
24.91/8.22	   A^2 -> H(f(a), U1(k, d))
24.91/8.22	   A^2 -> H(f(a), U1(d, k))
24.91/8.22	   A^2 -> H(a, f(b))
24.91/8.22	   A^2 -> H(U1(e, d), f(b))
24.91/8.22	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.22	   A^2 -> H(U1(e, a), f(c))
24.91/8.22	   A^2 -> H(U1(e, a), f(d))
24.91/8.22	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.22	   A^2 -> H(U1(k, a), f(c))
24.91/8.22	   A^2 -> H(U1(k, a), f(d))
24.91/8.22	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(c, d), f(c))
24.91/8.22	   A^2 -> H(U1(c, d), f(d))
24.91/8.22	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(c, a), f(e))
24.91/8.22	   A^2 -> H(U1(c, a), f(k))
24.91/8.22	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(d, e), f(b))
24.91/8.22	   A^2 -> H(U1(d, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(d, c), f(c))
24.91/8.22	   A^2 -> H(U1(d, c), f(d))
24.91/8.22	   A^2 -> H(U1(d, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(d, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(d, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(d, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(d, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(d, a), f(e))
24.91/8.22	   A^2 -> H(U1(d, a), f(k))
24.91/8.22	   A^2 -> H(U1(d, a), U1(d, d))
24.91/8.22	
24.91/8.22	The TRS R consists of the following rules:
24.91/8.22	
24.91/8.22	   f(x) -> U1(x, x)
24.91/8.22	   U1(e, x) -> x
24.91/8.22	   a -> c
24.91/8.22	   a -> d
24.91/8.22	   b -> c
24.91/8.22	   b -> d
24.91/8.22	   d -> k
24.91/8.22	   c -> e
24.91/8.22	   c -> k
24.91/8.22	
24.91/8.22	Q is empty.
24.91/8.22	We have to consider all minimal (P,Q,R)-chains.
24.91/8.22	----------------------------------------
24.91/8.22	
24.91/8.22	(89) TransformationProof (EQUIVALENT)
24.91/8.22	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), f(b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.22	
24.91/8.22	   (A^2 -> H(U1(c, e), f(b)),A^2 -> H(U1(c, e), f(b)))
24.91/8.22	   (A^2 -> H(U1(d, e), f(b)),A^2 -> H(U1(d, e), f(b)))
24.91/8.22	   (A^2 -> H(U1(a, e), U1(b, b)),A^2 -> H(U1(a, e), U1(b, b)))
24.91/8.22	   (A^2 -> H(U1(a, e), f(c)),A^2 -> H(U1(a, e), f(c)))
24.91/8.22	   (A^2 -> H(U1(a, e), f(d)),A^2 -> H(U1(a, e), f(d)))
24.91/8.22	
24.91/8.22	
24.91/8.22	----------------------------------------
24.91/8.22	
24.91/8.22	(90)
24.91/8.22	Obligation:
24.91/8.22	Q DP problem:
24.91/8.22	The TRS P consists of the following rules:
24.91/8.22	
24.91/8.22	   H(x, x) -> G(x, x, f(k))
24.91/8.22	   G(d, x, x) -> A^2
24.91/8.22	   A^2 -> H(f(c), f(c))
24.91/8.22	   A^2 -> H(f(d), f(d))
24.91/8.22	   A^2 -> H(U1(a, k), f(b))
24.91/8.22	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, c), f(c))
24.91/8.22	   A^2 -> H(U1(a, c), f(d))
24.91/8.22	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, d), f(c))
24.91/8.22	   A^2 -> H(U1(a, d), f(d))
24.91/8.22	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(a, a), f(e))
24.91/8.22	   A^2 -> H(U1(a, a), f(k))
24.91/8.22	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(e, c), f(b))
24.91/8.22	   A^2 -> H(U1(k, c), f(b))
24.91/8.22	   A^2 -> H(U1(c, e), f(b))
24.91/8.22	   A^2 -> H(U1(c, k), f(b))
24.91/8.22	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(c, c), f(c))
24.91/8.22	   A^2 -> H(U1(c, c), f(d))
24.91/8.22	   A^2 -> H(U1(e, e), f(b))
24.91/8.22	   A^2 -> H(f(e), U1(b, b))
24.91/8.22	   A^2 -> H(f(e), f(c))
24.91/8.22	   A^2 -> H(f(e), f(d))
24.91/8.22	   A^2 -> H(U1(k, k), f(b))
24.91/8.22	   A^2 -> H(f(k), U1(b, b))
24.91/8.22	   A^2 -> H(f(k), f(c))
24.91/8.22	   A^2 -> H(f(k), f(d))
24.91/8.22	   A^2 -> H(f(c), U1(c, b))
24.91/8.22	   A^2 -> H(f(c), U1(d, b))
24.91/8.22	   A^2 -> H(f(c), U1(b, c))
24.91/8.22	   A^2 -> H(f(c), U1(b, d))
24.91/8.22	   A^2 -> H(f(c), U1(d, d))
24.91/8.22	   A^2 -> H(f(c), f(k))
24.91/8.22	   A^2 -> H(U1(k, d), f(b))
24.91/8.22	   A^2 -> H(U1(d, k), f(b))
24.91/8.22	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(d, d), f(c))
24.91/8.22	   A^2 -> H(U1(d, d), f(d))
24.91/8.22	   A^2 -> H(f(d), U1(c, b))
24.91/8.22	   A^2 -> H(f(d), U1(d, b))
24.91/8.22	   A^2 -> H(f(d), U1(b, c))
24.91/8.22	   A^2 -> H(f(d), U1(b, d))
24.91/8.22	   A^2 -> H(f(d), U1(c, c))
24.91/8.22	   A^2 -> H(f(d), f(e))
24.91/8.22	   A^2 -> H(f(d), f(k))
24.91/8.22	   A^2 -> H(f(a), U1(e, b))
24.91/8.22	   A^2 -> H(f(a), U1(k, b))
24.91/8.22	   A^2 -> H(f(a), U1(c, d))
24.91/8.22	   A^2 -> H(f(a), U1(d, c))
24.91/8.22	   A^2 -> H(f(a), U1(b, e))
24.91/8.22	   A^2 -> H(f(a), U1(b, k))
24.91/8.22	   A^2 -> H(f(c), U1(c, c))
24.91/8.22	   A^2 -> H(f(a), U1(e, c))
24.91/8.22	   A^2 -> H(f(a), U1(k, c))
24.91/8.22	   A^2 -> H(f(a), U1(c, e))
24.91/8.22	   A^2 -> H(f(a), U1(c, k))
24.91/8.22	   A^2 -> H(f(c), f(e))
24.91/8.22	   A^2 -> H(f(a), U1(e, e))
24.91/8.22	   A^2 -> H(f(a), U1(k, k))
24.91/8.22	   A^2 -> H(f(d), U1(d, d))
24.91/8.22	   A^2 -> H(f(a), U1(k, d))
24.91/8.22	   A^2 -> H(f(a), U1(d, k))
24.91/8.22	   A^2 -> H(a, f(b))
24.91/8.22	   A^2 -> H(U1(e, d), f(b))
24.91/8.22	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.22	   A^2 -> H(U1(e, a), f(c))
24.91/8.22	   A^2 -> H(U1(e, a), f(d))
24.91/8.22	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.22	   A^2 -> H(U1(k, a), f(c))
24.91/8.22	   A^2 -> H(U1(k, a), f(d))
24.91/8.22	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(c, d), f(c))
24.91/8.22	   A^2 -> H(U1(c, d), f(d))
24.91/8.22	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(c, a), f(e))
24.91/8.22	   A^2 -> H(U1(c, a), f(k))
24.91/8.22	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(d, e), f(b))
24.91/8.22	   A^2 -> H(U1(d, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(d, c), f(c))
24.91/8.22	   A^2 -> H(U1(d, c), f(d))
24.91/8.22	   A^2 -> H(U1(d, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(d, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(d, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(d, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(d, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(d, a), f(e))
24.91/8.22	   A^2 -> H(U1(d, a), f(k))
24.91/8.22	   A^2 -> H(U1(d, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(a, e), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, e), f(c))
24.91/8.22	   A^2 -> H(U1(a, e), f(d))
24.91/8.22	
24.91/8.22	The TRS R consists of the following rules:
24.91/8.22	
24.91/8.22	   f(x) -> U1(x, x)
24.91/8.22	   U1(e, x) -> x
24.91/8.22	   a -> c
24.91/8.22	   a -> d
24.91/8.22	   b -> c
24.91/8.22	   b -> d
24.91/8.22	   d -> k
24.91/8.22	   c -> e
24.91/8.22	   c -> k
24.91/8.22	
24.91/8.22	Q is empty.
24.91/8.22	We have to consider all minimal (P,Q,R)-chains.
24.91/8.22	----------------------------------------
24.91/8.22	
24.91/8.22	(91) TransformationProof (EQUIVALENT)
24.91/8.22	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), f(b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.22	
24.91/8.22	   (A^2 -> H(U1(c, k), f(b)),A^2 -> H(U1(c, k), f(b)))
24.91/8.22	   (A^2 -> H(U1(d, k), f(b)),A^2 -> H(U1(d, k), f(b)))
24.91/8.22	   (A^2 -> H(U1(a, k), U1(b, b)),A^2 -> H(U1(a, k), U1(b, b)))
24.91/8.22	   (A^2 -> H(U1(a, k), f(c)),A^2 -> H(U1(a, k), f(c)))
24.91/8.22	   (A^2 -> H(U1(a, k), f(d)),A^2 -> H(U1(a, k), f(d)))
24.91/8.22	
24.91/8.22	
24.91/8.22	----------------------------------------
24.91/8.22	
24.91/8.22	(92)
24.91/8.22	Obligation:
24.91/8.22	Q DP problem:
24.91/8.22	The TRS P consists of the following rules:
24.91/8.22	
24.91/8.22	   H(x, x) -> G(x, x, f(k))
24.91/8.22	   G(d, x, x) -> A^2
24.91/8.22	   A^2 -> H(f(c), f(c))
24.91/8.22	   A^2 -> H(f(d), f(d))
24.91/8.22	   A^2 -> H(U1(a, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, c), f(c))
24.91/8.22	   A^2 -> H(U1(a, c), f(d))
24.91/8.22	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, d), f(c))
24.91/8.22	   A^2 -> H(U1(a, d), f(d))
24.91/8.22	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(a, a), f(e))
24.91/8.22	   A^2 -> H(U1(a, a), f(k))
24.91/8.22	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(e, c), f(b))
24.91/8.22	   A^2 -> H(U1(k, c), f(b))
24.91/8.22	   A^2 -> H(U1(c, e), f(b))
24.91/8.22	   A^2 -> H(U1(c, k), f(b))
24.91/8.22	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(c, c), f(c))
24.91/8.22	   A^2 -> H(U1(c, c), f(d))
24.91/8.22	   A^2 -> H(U1(e, e), f(b))
24.91/8.22	   A^2 -> H(f(e), U1(b, b))
24.91/8.22	   A^2 -> H(f(e), f(c))
24.91/8.22	   A^2 -> H(f(e), f(d))
24.91/8.22	   A^2 -> H(U1(k, k), f(b))
24.91/8.22	   A^2 -> H(f(k), U1(b, b))
24.91/8.22	   A^2 -> H(f(k), f(c))
24.91/8.22	   A^2 -> H(f(k), f(d))
24.91/8.22	   A^2 -> H(f(c), U1(c, b))
24.91/8.22	   A^2 -> H(f(c), U1(d, b))
24.91/8.22	   A^2 -> H(f(c), U1(b, c))
24.91/8.22	   A^2 -> H(f(c), U1(b, d))
24.91/8.22	   A^2 -> H(f(c), U1(d, d))
24.91/8.22	   A^2 -> H(f(c), f(k))
24.91/8.22	   A^2 -> H(U1(k, d), f(b))
24.91/8.22	   A^2 -> H(U1(d, k), f(b))
24.91/8.22	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(d, d), f(c))
24.91/8.22	   A^2 -> H(U1(d, d), f(d))
24.91/8.22	   A^2 -> H(f(d), U1(c, b))
24.91/8.22	   A^2 -> H(f(d), U1(d, b))
24.91/8.22	   A^2 -> H(f(d), U1(b, c))
24.91/8.22	   A^2 -> H(f(d), U1(b, d))
24.91/8.22	   A^2 -> H(f(d), U1(c, c))
24.91/8.22	   A^2 -> H(f(d), f(e))
24.91/8.22	   A^2 -> H(f(d), f(k))
24.91/8.22	   A^2 -> H(f(a), U1(e, b))
24.91/8.22	   A^2 -> H(f(a), U1(k, b))
24.91/8.22	   A^2 -> H(f(a), U1(c, d))
24.91/8.22	   A^2 -> H(f(a), U1(d, c))
24.91/8.22	   A^2 -> H(f(a), U1(b, e))
24.91/8.22	   A^2 -> H(f(a), U1(b, k))
24.91/8.22	   A^2 -> H(f(c), U1(c, c))
24.91/8.22	   A^2 -> H(f(a), U1(e, c))
24.91/8.22	   A^2 -> H(f(a), U1(k, c))
24.91/8.22	   A^2 -> H(f(a), U1(c, e))
24.91/8.22	   A^2 -> H(f(a), U1(c, k))
24.91/8.22	   A^2 -> H(f(c), f(e))
24.91/8.22	   A^2 -> H(f(a), U1(e, e))
24.91/8.22	   A^2 -> H(f(a), U1(k, k))
24.91/8.22	   A^2 -> H(f(d), U1(d, d))
24.91/8.22	   A^2 -> H(f(a), U1(k, d))
24.91/8.22	   A^2 -> H(f(a), U1(d, k))
24.91/8.22	   A^2 -> H(a, f(b))
24.91/8.22	   A^2 -> H(U1(e, d), f(b))
24.91/8.22	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.22	   A^2 -> H(U1(e, a), f(c))
24.91/8.22	   A^2 -> H(U1(e, a), f(d))
24.91/8.22	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.22	   A^2 -> H(U1(k, a), f(c))
24.91/8.22	   A^2 -> H(U1(k, a), f(d))
24.91/8.22	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(c, d), f(c))
24.91/8.22	   A^2 -> H(U1(c, d), f(d))
24.91/8.22	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(c, a), f(e))
24.91/8.22	   A^2 -> H(U1(c, a), f(k))
24.91/8.22	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(d, e), f(b))
24.91/8.22	   A^2 -> H(U1(d, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(d, c), f(c))
24.91/8.22	   A^2 -> H(U1(d, c), f(d))
24.91/8.22	   A^2 -> H(U1(d, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(d, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(d, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(d, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(d, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(d, a), f(e))
24.91/8.22	   A^2 -> H(U1(d, a), f(k))
24.91/8.22	   A^2 -> H(U1(d, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(a, e), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, e), f(c))
24.91/8.22	   A^2 -> H(U1(a, e), f(d))
24.91/8.22	   A^2 -> H(U1(a, k), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, k), f(c))
24.91/8.22	   A^2 -> H(U1(a, k), f(d))
24.91/8.22	
24.91/8.22	The TRS R consists of the following rules:
24.91/8.22	
24.91/8.22	   f(x) -> U1(x, x)
24.91/8.22	   U1(e, x) -> x
24.91/8.22	   a -> c
24.91/8.22	   a -> d
24.91/8.22	   b -> c
24.91/8.22	   b -> d
24.91/8.22	   d -> k
24.91/8.22	   c -> e
24.91/8.22	   c -> k
24.91/8.22	
24.91/8.22	Q is empty.
24.91/8.22	We have to consider all minimal (P,Q,R)-chains.
24.91/8.22	----------------------------------------
24.91/8.22	
24.91/8.22	(93) TransformationProof (EQUIVALENT)
24.91/8.22	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.22	
24.91/8.22	   (A^2 -> H(U1(c, c), U1(b, b)),A^2 -> H(U1(c, c), U1(b, b)))
24.91/8.22	   (A^2 -> H(U1(d, c), U1(b, b)),A^2 -> H(U1(d, c), U1(b, b)))
24.91/8.22	   (A^2 -> H(U1(a, e), U1(b, b)),A^2 -> H(U1(a, e), U1(b, b)))
24.91/8.22	   (A^2 -> H(U1(a, k), U1(b, b)),A^2 -> H(U1(a, k), U1(b, b)))
24.91/8.22	   (A^2 -> H(U1(a, c), U1(c, b)),A^2 -> H(U1(a, c), U1(c, b)))
24.91/8.22	   (A^2 -> H(U1(a, c), U1(d, b)),A^2 -> H(U1(a, c), U1(d, b)))
24.91/8.22	   (A^2 -> H(U1(a, c), U1(b, c)),A^2 -> H(U1(a, c), U1(b, c)))
24.91/8.22	   (A^2 -> H(U1(a, c), U1(b, d)),A^2 -> H(U1(a, c), U1(b, d)))
24.91/8.22	
24.91/8.22	
24.91/8.22	----------------------------------------
24.91/8.22	
24.91/8.22	(94)
24.91/8.22	Obligation:
24.91/8.22	Q DP problem:
24.91/8.22	The TRS P consists of the following rules:
24.91/8.22	
24.91/8.22	   H(x, x) -> G(x, x, f(k))
24.91/8.22	   G(d, x, x) -> A^2
24.91/8.22	   A^2 -> H(f(c), f(c))
24.91/8.22	   A^2 -> H(f(d), f(d))
24.91/8.22	   A^2 -> H(U1(a, c), f(c))
24.91/8.22	   A^2 -> H(U1(a, c), f(d))
24.91/8.22	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, d), f(c))
24.91/8.22	   A^2 -> H(U1(a, d), f(d))
24.91/8.22	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(a, a), f(e))
24.91/8.22	   A^2 -> H(U1(a, a), f(k))
24.91/8.22	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(e, c), f(b))
24.91/8.22	   A^2 -> H(U1(k, c), f(b))
24.91/8.22	   A^2 -> H(U1(c, e), f(b))
24.91/8.22	   A^2 -> H(U1(c, k), f(b))
24.91/8.22	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(c, c), f(c))
24.91/8.22	   A^2 -> H(U1(c, c), f(d))
24.91/8.22	   A^2 -> H(U1(e, e), f(b))
24.91/8.22	   A^2 -> H(f(e), U1(b, b))
24.91/8.22	   A^2 -> H(f(e), f(c))
24.91/8.22	   A^2 -> H(f(e), f(d))
24.91/8.22	   A^2 -> H(U1(k, k), f(b))
24.91/8.22	   A^2 -> H(f(k), U1(b, b))
24.91/8.22	   A^2 -> H(f(k), f(c))
24.91/8.22	   A^2 -> H(f(k), f(d))
24.91/8.22	   A^2 -> H(f(c), U1(c, b))
24.91/8.22	   A^2 -> H(f(c), U1(d, b))
24.91/8.22	   A^2 -> H(f(c), U1(b, c))
24.91/8.22	   A^2 -> H(f(c), U1(b, d))
24.91/8.22	   A^2 -> H(f(c), U1(d, d))
24.91/8.22	   A^2 -> H(f(c), f(k))
24.91/8.22	   A^2 -> H(U1(k, d), f(b))
24.91/8.22	   A^2 -> H(U1(d, k), f(b))
24.91/8.22	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(d, d), f(c))
24.91/8.22	   A^2 -> H(U1(d, d), f(d))
24.91/8.22	   A^2 -> H(f(d), U1(c, b))
24.91/8.22	   A^2 -> H(f(d), U1(d, b))
24.91/8.22	   A^2 -> H(f(d), U1(b, c))
24.91/8.22	   A^2 -> H(f(d), U1(b, d))
24.91/8.22	   A^2 -> H(f(d), U1(c, c))
24.91/8.22	   A^2 -> H(f(d), f(e))
24.91/8.22	   A^2 -> H(f(d), f(k))
24.91/8.22	   A^2 -> H(f(a), U1(e, b))
24.91/8.22	   A^2 -> H(f(a), U1(k, b))
24.91/8.22	   A^2 -> H(f(a), U1(c, d))
24.91/8.22	   A^2 -> H(f(a), U1(d, c))
24.91/8.22	   A^2 -> H(f(a), U1(b, e))
24.91/8.22	   A^2 -> H(f(a), U1(b, k))
24.91/8.22	   A^2 -> H(f(c), U1(c, c))
24.91/8.22	   A^2 -> H(f(a), U1(e, c))
24.91/8.22	   A^2 -> H(f(a), U1(k, c))
24.91/8.22	   A^2 -> H(f(a), U1(c, e))
24.91/8.22	   A^2 -> H(f(a), U1(c, k))
24.91/8.22	   A^2 -> H(f(c), f(e))
24.91/8.22	   A^2 -> H(f(a), U1(e, e))
24.91/8.22	   A^2 -> H(f(a), U1(k, k))
24.91/8.22	   A^2 -> H(f(d), U1(d, d))
24.91/8.22	   A^2 -> H(f(a), U1(k, d))
24.91/8.22	   A^2 -> H(f(a), U1(d, k))
24.91/8.22	   A^2 -> H(a, f(b))
24.91/8.22	   A^2 -> H(U1(e, d), f(b))
24.91/8.22	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.22	   A^2 -> H(U1(e, a), f(c))
24.91/8.22	   A^2 -> H(U1(e, a), f(d))
24.91/8.22	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.22	   A^2 -> H(U1(k, a), f(c))
24.91/8.22	   A^2 -> H(U1(k, a), f(d))
24.91/8.22	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(c, d), f(c))
24.91/8.22	   A^2 -> H(U1(c, d), f(d))
24.91/8.22	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(c, a), f(e))
24.91/8.22	   A^2 -> H(U1(c, a), f(k))
24.91/8.22	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(d, e), f(b))
24.91/8.22	   A^2 -> H(U1(d, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(d, c), f(c))
24.91/8.22	   A^2 -> H(U1(d, c), f(d))
24.91/8.22	   A^2 -> H(U1(d, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(d, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(d, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(d, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(d, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(d, a), f(e))
24.91/8.22	   A^2 -> H(U1(d, a), f(k))
24.91/8.22	   A^2 -> H(U1(d, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(a, e), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, e), f(c))
24.91/8.22	   A^2 -> H(U1(a, e), f(d))
24.91/8.22	   A^2 -> H(U1(a, k), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, k), f(c))
24.91/8.22	   A^2 -> H(U1(a, k), f(d))
24.91/8.22	   A^2 -> H(U1(a, c), U1(c, b))
24.91/8.22	   A^2 -> H(U1(a, c), U1(d, b))
24.91/8.22	   A^2 -> H(U1(a, c), U1(b, c))
24.91/8.22	   A^2 -> H(U1(a, c), U1(b, d))
24.91/8.22	
24.91/8.22	The TRS R consists of the following rules:
24.91/8.22	
24.91/8.22	   f(x) -> U1(x, x)
24.91/8.22	   U1(e, x) -> x
24.91/8.22	   a -> c
24.91/8.22	   a -> d
24.91/8.22	   b -> c
24.91/8.22	   b -> d
24.91/8.22	   d -> k
24.91/8.22	   c -> e
24.91/8.22	   c -> k
24.91/8.22	
24.91/8.22	Q is empty.
24.91/8.22	We have to consider all minimal (P,Q,R)-chains.
24.91/8.22	----------------------------------------
24.91/8.22	
24.91/8.22	(95) TransformationProof (EQUIVALENT)
24.91/8.22	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), f(c)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.22	
24.91/8.22	   (A^2 -> H(U1(c, c), f(c)),A^2 -> H(U1(c, c), f(c)))
24.91/8.22	   (A^2 -> H(U1(d, c), f(c)),A^2 -> H(U1(d, c), f(c)))
24.91/8.22	   (A^2 -> H(U1(a, e), f(c)),A^2 -> H(U1(a, e), f(c)))
24.91/8.22	   (A^2 -> H(U1(a, k), f(c)),A^2 -> H(U1(a, k), f(c)))
24.91/8.22	   (A^2 -> H(U1(a, c), U1(c, c)),A^2 -> H(U1(a, c), U1(c, c)))
24.91/8.22	   (A^2 -> H(U1(a, c), f(e)),A^2 -> H(U1(a, c), f(e)))
24.91/8.22	   (A^2 -> H(U1(a, c), f(k)),A^2 -> H(U1(a, c), f(k)))
24.91/8.22	
24.91/8.22	
24.91/8.22	----------------------------------------
24.91/8.22	
24.91/8.22	(96)
24.91/8.22	Obligation:
24.91/8.22	Q DP problem:
24.91/8.22	The TRS P consists of the following rules:
24.91/8.22	
24.91/8.22	   H(x, x) -> G(x, x, f(k))
24.91/8.22	   G(d, x, x) -> A^2
24.91/8.22	   A^2 -> H(f(c), f(c))
24.91/8.22	   A^2 -> H(f(d), f(d))
24.91/8.22	   A^2 -> H(U1(a, c), f(d))
24.91/8.22	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, d), f(c))
24.91/8.22	   A^2 -> H(U1(a, d), f(d))
24.91/8.22	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(a, a), f(e))
24.91/8.22	   A^2 -> H(U1(a, a), f(k))
24.91/8.22	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(e, c), f(b))
24.91/8.22	   A^2 -> H(U1(k, c), f(b))
24.91/8.22	   A^2 -> H(U1(c, e), f(b))
24.91/8.22	   A^2 -> H(U1(c, k), f(b))
24.91/8.22	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(c, c), f(c))
24.91/8.22	   A^2 -> H(U1(c, c), f(d))
24.91/8.22	   A^2 -> H(U1(e, e), f(b))
24.91/8.22	   A^2 -> H(f(e), U1(b, b))
24.91/8.22	   A^2 -> H(f(e), f(c))
24.91/8.22	   A^2 -> H(f(e), f(d))
24.91/8.22	   A^2 -> H(U1(k, k), f(b))
24.91/8.22	   A^2 -> H(f(k), U1(b, b))
24.91/8.22	   A^2 -> H(f(k), f(c))
24.91/8.22	   A^2 -> H(f(k), f(d))
24.91/8.22	   A^2 -> H(f(c), U1(c, b))
24.91/8.22	   A^2 -> H(f(c), U1(d, b))
24.91/8.22	   A^2 -> H(f(c), U1(b, c))
24.91/8.22	   A^2 -> H(f(c), U1(b, d))
24.91/8.22	   A^2 -> H(f(c), U1(d, d))
24.91/8.22	   A^2 -> H(f(c), f(k))
24.91/8.22	   A^2 -> H(U1(k, d), f(b))
24.91/8.22	   A^2 -> H(U1(d, k), f(b))
24.91/8.22	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(d, d), f(c))
24.91/8.22	   A^2 -> H(U1(d, d), f(d))
24.91/8.22	   A^2 -> H(f(d), U1(c, b))
24.91/8.22	   A^2 -> H(f(d), U1(d, b))
24.91/8.22	   A^2 -> H(f(d), U1(b, c))
24.91/8.22	   A^2 -> H(f(d), U1(b, d))
24.91/8.22	   A^2 -> H(f(d), U1(c, c))
24.91/8.22	   A^2 -> H(f(d), f(e))
24.91/8.22	   A^2 -> H(f(d), f(k))
24.91/8.22	   A^2 -> H(f(a), U1(e, b))
24.91/8.22	   A^2 -> H(f(a), U1(k, b))
24.91/8.22	   A^2 -> H(f(a), U1(c, d))
24.91/8.22	   A^2 -> H(f(a), U1(d, c))
24.91/8.22	   A^2 -> H(f(a), U1(b, e))
24.91/8.22	   A^2 -> H(f(a), U1(b, k))
24.91/8.22	   A^2 -> H(f(c), U1(c, c))
24.91/8.22	   A^2 -> H(f(a), U1(e, c))
24.91/8.22	   A^2 -> H(f(a), U1(k, c))
24.91/8.22	   A^2 -> H(f(a), U1(c, e))
24.91/8.22	   A^2 -> H(f(a), U1(c, k))
24.91/8.22	   A^2 -> H(f(c), f(e))
24.91/8.22	   A^2 -> H(f(a), U1(e, e))
24.91/8.22	   A^2 -> H(f(a), U1(k, k))
24.91/8.22	   A^2 -> H(f(d), U1(d, d))
24.91/8.22	   A^2 -> H(f(a), U1(k, d))
24.91/8.22	   A^2 -> H(f(a), U1(d, k))
24.91/8.22	   A^2 -> H(a, f(b))
24.91/8.22	   A^2 -> H(U1(e, d), f(b))
24.91/8.22	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.22	   A^2 -> H(U1(e, a), f(c))
24.91/8.22	   A^2 -> H(U1(e, a), f(d))
24.91/8.22	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.22	   A^2 -> H(U1(k, a), f(c))
24.91/8.22	   A^2 -> H(U1(k, a), f(d))
24.91/8.22	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.22	   A^2 -> H(U1(c, d), f(c))
24.91/8.22	   A^2 -> H(U1(c, d), f(d))
24.91/8.22	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(c, a), f(e))
24.91/8.22	   A^2 -> H(U1(c, a), f(k))
24.91/8.22	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(d, e), f(b))
24.91/8.22	   A^2 -> H(U1(d, c), U1(b, b))
24.91/8.22	   A^2 -> H(U1(d, c), f(c))
24.91/8.22	   A^2 -> H(U1(d, c), f(d))
24.91/8.22	   A^2 -> H(U1(d, a), U1(c, b))
24.91/8.22	   A^2 -> H(U1(d, a), U1(d, b))
24.91/8.22	   A^2 -> H(U1(d, a), U1(b, c))
24.91/8.22	   A^2 -> H(U1(d, a), U1(b, d))
24.91/8.22	   A^2 -> H(U1(d, a), U1(c, c))
24.91/8.22	   A^2 -> H(U1(d, a), f(e))
24.91/8.22	   A^2 -> H(U1(d, a), f(k))
24.91/8.22	   A^2 -> H(U1(d, a), U1(d, d))
24.91/8.22	   A^2 -> H(U1(a, e), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, e), f(c))
24.91/8.22	   A^2 -> H(U1(a, e), f(d))
24.91/8.22	   A^2 -> H(U1(a, k), U1(b, b))
24.91/8.22	   A^2 -> H(U1(a, k), f(c))
24.91/8.22	   A^2 -> H(U1(a, k), f(d))
24.91/8.22	   A^2 -> H(U1(a, c), U1(c, b))
24.91/8.22	   A^2 -> H(U1(a, c), U1(d, b))
24.91/8.22	   A^2 -> H(U1(a, c), U1(b, c))
24.91/8.22	   A^2 -> H(U1(a, c), U1(b, d))
24.91/8.22	   A^2 -> H(U1(a, c), U1(c, c))
24.91/8.22	   A^2 -> H(U1(a, c), f(e))
24.91/8.22	   A^2 -> H(U1(a, c), f(k))
24.91/8.22	
24.91/8.22	The TRS R consists of the following rules:
24.91/8.22	
24.91/8.22	   f(x) -> U1(x, x)
24.91/8.22	   U1(e, x) -> x
24.91/8.22	   a -> c
24.91/8.22	   a -> d
24.91/8.22	   b -> c
24.91/8.22	   b -> d
24.91/8.22	   d -> k
24.91/8.22	   c -> e
24.91/8.22	   c -> k
24.91/8.22	
24.91/8.22	Q is empty.
24.91/8.22	We have to consider all minimal (P,Q,R)-chains.
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(97) TransformationProof (EQUIVALENT)
24.91/8.23	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), f(d)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.23	
24.91/8.23	   (A^2 -> H(U1(c, c), f(d)),A^2 -> H(U1(c, c), f(d)))
24.91/8.23	   (A^2 -> H(U1(d, c), f(d)),A^2 -> H(U1(d, c), f(d)))
24.91/8.23	   (A^2 -> H(U1(a, e), f(d)),A^2 -> H(U1(a, e), f(d)))
24.91/8.23	   (A^2 -> H(U1(a, k), f(d)),A^2 -> H(U1(a, k), f(d)))
24.91/8.23	   (A^2 -> H(U1(a, c), U1(d, d)),A^2 -> H(U1(a, c), U1(d, d)))
24.91/8.23	   (A^2 -> H(U1(a, c), f(k)),A^2 -> H(U1(a, c), f(k)))
24.91/8.23	
24.91/8.23	
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(98)
24.91/8.23	Obligation:
24.91/8.23	Q DP problem:
24.91/8.23	The TRS P consists of the following rules:
24.91/8.23	
24.91/8.23	   H(x, x) -> G(x, x, f(k))
24.91/8.23	   G(d, x, x) -> A^2
24.91/8.23	   A^2 -> H(f(c), f(c))
24.91/8.23	   A^2 -> H(f(d), f(d))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, d), f(c))
24.91/8.23	   A^2 -> H(U1(a, d), f(d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, a), f(e))
24.91/8.23	   A^2 -> H(U1(a, a), f(k))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(e, c), f(b))
24.91/8.23	   A^2 -> H(U1(k, c), f(b))
24.91/8.23	   A^2 -> H(U1(c, e), f(b))
24.91/8.23	   A^2 -> H(U1(c, k), f(b))
24.91/8.23	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, c), f(c))
24.91/8.23	   A^2 -> H(U1(c, c), f(d))
24.91/8.23	   A^2 -> H(U1(e, e), f(b))
24.91/8.23	   A^2 -> H(f(e), U1(b, b))
24.91/8.23	   A^2 -> H(f(e), f(c))
24.91/8.23	   A^2 -> H(f(e), f(d))
24.91/8.23	   A^2 -> H(U1(k, k), f(b))
24.91/8.23	   A^2 -> H(f(k), U1(b, b))
24.91/8.23	   A^2 -> H(f(k), f(c))
24.91/8.23	   A^2 -> H(f(k), f(d))
24.91/8.23	   A^2 -> H(f(c), U1(c, b))
24.91/8.23	   A^2 -> H(f(c), U1(d, b))
24.91/8.23	   A^2 -> H(f(c), U1(b, c))
24.91/8.23	   A^2 -> H(f(c), U1(b, d))
24.91/8.23	   A^2 -> H(f(c), U1(d, d))
24.91/8.23	   A^2 -> H(f(c), f(k))
24.91/8.23	   A^2 -> H(U1(k, d), f(b))
24.91/8.23	   A^2 -> H(U1(d, k), f(b))
24.91/8.23	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, d), f(c))
24.91/8.23	   A^2 -> H(U1(d, d), f(d))
24.91/8.23	   A^2 -> H(f(d), U1(c, b))
24.91/8.23	   A^2 -> H(f(d), U1(d, b))
24.91/8.23	   A^2 -> H(f(d), U1(b, c))
24.91/8.23	   A^2 -> H(f(d), U1(b, d))
24.91/8.23	   A^2 -> H(f(d), U1(c, c))
24.91/8.23	   A^2 -> H(f(d), f(e))
24.91/8.23	   A^2 -> H(f(d), f(k))
24.91/8.23	   A^2 -> H(f(a), U1(e, b))
24.91/8.23	   A^2 -> H(f(a), U1(k, b))
24.91/8.23	   A^2 -> H(f(a), U1(c, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, c))
24.91/8.23	   A^2 -> H(f(a), U1(b, e))
24.91/8.23	   A^2 -> H(f(a), U1(b, k))
24.91/8.23	   A^2 -> H(f(c), U1(c, c))
24.91/8.23	   A^2 -> H(f(a), U1(e, c))
24.91/8.23	   A^2 -> H(f(a), U1(k, c))
24.91/8.23	   A^2 -> H(f(a), U1(c, e))
24.91/8.23	   A^2 -> H(f(a), U1(c, k))
24.91/8.23	   A^2 -> H(f(c), f(e))
24.91/8.23	   A^2 -> H(f(a), U1(e, e))
24.91/8.23	   A^2 -> H(f(a), U1(k, k))
24.91/8.23	   A^2 -> H(f(d), U1(d, d))
24.91/8.23	   A^2 -> H(f(a), U1(k, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, k))
24.91/8.23	   A^2 -> H(a, f(b))
24.91/8.23	   A^2 -> H(U1(e, d), f(b))
24.91/8.23	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(e, a), f(c))
24.91/8.23	   A^2 -> H(U1(e, a), f(d))
24.91/8.23	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(k, a), f(c))
24.91/8.23	   A^2 -> H(U1(k, a), f(d))
24.91/8.23	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, d), f(c))
24.91/8.23	   A^2 -> H(U1(c, d), f(d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(c, a), f(e))
24.91/8.23	   A^2 -> H(U1(c, a), f(k))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(d, e), f(b))
24.91/8.23	   A^2 -> H(U1(d, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, c), f(c))
24.91/8.23	   A^2 -> H(U1(d, c), f(d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(d, a), f(e))
24.91/8.23	   A^2 -> H(U1(d, a), f(k))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, e), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, e), f(c))
24.91/8.23	   A^2 -> H(U1(a, e), f(d))
24.91/8.23	   A^2 -> H(U1(a, k), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, k), f(c))
24.91/8.23	   A^2 -> H(U1(a, k), f(d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, c), f(e))
24.91/8.23	   A^2 -> H(U1(a, c), f(k))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, d))
24.91/8.23	
24.91/8.23	The TRS R consists of the following rules:
24.91/8.23	
24.91/8.23	   f(x) -> U1(x, x)
24.91/8.23	   U1(e, x) -> x
24.91/8.23	   a -> c
24.91/8.23	   a -> d
24.91/8.23	   b -> c
24.91/8.23	   b -> d
24.91/8.23	   d -> k
24.91/8.23	   c -> e
24.91/8.23	   c -> k
24.91/8.23	
24.91/8.23	Q is empty.
24.91/8.23	We have to consider all minimal (P,Q,R)-chains.
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(99) TransformationProof (EQUIVALENT)
24.91/8.23	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.23	
24.91/8.23	   (A^2 -> H(U1(c, d), U1(b, b)),A^2 -> H(U1(c, d), U1(b, b)))
24.91/8.23	   (A^2 -> H(U1(d, d), U1(b, b)),A^2 -> H(U1(d, d), U1(b, b)))
24.91/8.23	   (A^2 -> H(U1(a, k), U1(b, b)),A^2 -> H(U1(a, k), U1(b, b)))
24.91/8.23	   (A^2 -> H(U1(a, d), U1(c, b)),A^2 -> H(U1(a, d), U1(c, b)))
24.91/8.23	   (A^2 -> H(U1(a, d), U1(d, b)),A^2 -> H(U1(a, d), U1(d, b)))
24.91/8.23	   (A^2 -> H(U1(a, d), U1(b, c)),A^2 -> H(U1(a, d), U1(b, c)))
24.91/8.23	   (A^2 -> H(U1(a, d), U1(b, d)),A^2 -> H(U1(a, d), U1(b, d)))
24.91/8.23	
24.91/8.23	
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(100)
24.91/8.23	Obligation:
24.91/8.23	Q DP problem:
24.91/8.23	The TRS P consists of the following rules:
24.91/8.23	
24.91/8.23	   H(x, x) -> G(x, x, f(k))
24.91/8.23	   G(d, x, x) -> A^2
24.91/8.23	   A^2 -> H(f(c), f(c))
24.91/8.23	   A^2 -> H(f(d), f(d))
24.91/8.23	   A^2 -> H(U1(a, d), f(c))
24.91/8.23	   A^2 -> H(U1(a, d), f(d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, a), f(e))
24.91/8.23	   A^2 -> H(U1(a, a), f(k))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(e, c), f(b))
24.91/8.23	   A^2 -> H(U1(k, c), f(b))
24.91/8.23	   A^2 -> H(U1(c, e), f(b))
24.91/8.23	   A^2 -> H(U1(c, k), f(b))
24.91/8.23	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, c), f(c))
24.91/8.23	   A^2 -> H(U1(c, c), f(d))
24.91/8.23	   A^2 -> H(U1(e, e), f(b))
24.91/8.23	   A^2 -> H(f(e), U1(b, b))
24.91/8.23	   A^2 -> H(f(e), f(c))
24.91/8.23	   A^2 -> H(f(e), f(d))
24.91/8.23	   A^2 -> H(U1(k, k), f(b))
24.91/8.23	   A^2 -> H(f(k), U1(b, b))
24.91/8.23	   A^2 -> H(f(k), f(c))
24.91/8.23	   A^2 -> H(f(k), f(d))
24.91/8.23	   A^2 -> H(f(c), U1(c, b))
24.91/8.23	   A^2 -> H(f(c), U1(d, b))
24.91/8.23	   A^2 -> H(f(c), U1(b, c))
24.91/8.23	   A^2 -> H(f(c), U1(b, d))
24.91/8.23	   A^2 -> H(f(c), U1(d, d))
24.91/8.23	   A^2 -> H(f(c), f(k))
24.91/8.23	   A^2 -> H(U1(k, d), f(b))
24.91/8.23	   A^2 -> H(U1(d, k), f(b))
24.91/8.23	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, d), f(c))
24.91/8.23	   A^2 -> H(U1(d, d), f(d))
24.91/8.23	   A^2 -> H(f(d), U1(c, b))
24.91/8.23	   A^2 -> H(f(d), U1(d, b))
24.91/8.23	   A^2 -> H(f(d), U1(b, c))
24.91/8.23	   A^2 -> H(f(d), U1(b, d))
24.91/8.23	   A^2 -> H(f(d), U1(c, c))
24.91/8.23	   A^2 -> H(f(d), f(e))
24.91/8.23	   A^2 -> H(f(d), f(k))
24.91/8.23	   A^2 -> H(f(a), U1(e, b))
24.91/8.23	   A^2 -> H(f(a), U1(k, b))
24.91/8.23	   A^2 -> H(f(a), U1(c, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, c))
24.91/8.23	   A^2 -> H(f(a), U1(b, e))
24.91/8.23	   A^2 -> H(f(a), U1(b, k))
24.91/8.23	   A^2 -> H(f(c), U1(c, c))
24.91/8.23	   A^2 -> H(f(a), U1(e, c))
24.91/8.23	   A^2 -> H(f(a), U1(k, c))
24.91/8.23	   A^2 -> H(f(a), U1(c, e))
24.91/8.23	   A^2 -> H(f(a), U1(c, k))
24.91/8.23	   A^2 -> H(f(c), f(e))
24.91/8.23	   A^2 -> H(f(a), U1(e, e))
24.91/8.23	   A^2 -> H(f(a), U1(k, k))
24.91/8.23	   A^2 -> H(f(d), U1(d, d))
24.91/8.23	   A^2 -> H(f(a), U1(k, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, k))
24.91/8.23	   A^2 -> H(a, f(b))
24.91/8.23	   A^2 -> H(U1(e, d), f(b))
24.91/8.23	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(e, a), f(c))
24.91/8.23	   A^2 -> H(U1(e, a), f(d))
24.91/8.23	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(k, a), f(c))
24.91/8.23	   A^2 -> H(U1(k, a), f(d))
24.91/8.23	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, d), f(c))
24.91/8.23	   A^2 -> H(U1(c, d), f(d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(c, a), f(e))
24.91/8.23	   A^2 -> H(U1(c, a), f(k))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(d, e), f(b))
24.91/8.23	   A^2 -> H(U1(d, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, c), f(c))
24.91/8.23	   A^2 -> H(U1(d, c), f(d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(d, a), f(e))
24.91/8.23	   A^2 -> H(U1(d, a), f(k))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, e), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, e), f(c))
24.91/8.23	   A^2 -> H(U1(a, e), f(d))
24.91/8.23	   A^2 -> H(U1(a, k), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, k), f(c))
24.91/8.23	   A^2 -> H(U1(a, k), f(d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, c), f(e))
24.91/8.23	   A^2 -> H(U1(a, c), f(k))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, d), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, d), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, d))
24.91/8.23	
24.91/8.23	The TRS R consists of the following rules:
24.91/8.23	
24.91/8.23	   f(x) -> U1(x, x)
24.91/8.23	   U1(e, x) -> x
24.91/8.23	   a -> c
24.91/8.23	   a -> d
24.91/8.23	   b -> c
24.91/8.23	   b -> d
24.91/8.23	   d -> k
24.91/8.23	   c -> e
24.91/8.23	   c -> k
24.91/8.23	
24.91/8.23	Q is empty.
24.91/8.23	We have to consider all minimal (P,Q,R)-chains.
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(101) TransformationProof (EQUIVALENT)
24.91/8.23	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), f(c)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.23	
24.91/8.23	   (A^2 -> H(U1(c, d), f(c)),A^2 -> H(U1(c, d), f(c)))
24.91/8.23	   (A^2 -> H(U1(d, d), f(c)),A^2 -> H(U1(d, d), f(c)))
24.91/8.23	   (A^2 -> H(U1(a, k), f(c)),A^2 -> H(U1(a, k), f(c)))
24.91/8.23	   (A^2 -> H(U1(a, d), U1(c, c)),A^2 -> H(U1(a, d), U1(c, c)))
24.91/8.23	   (A^2 -> H(U1(a, d), f(e)),A^2 -> H(U1(a, d), f(e)))
24.91/8.23	   (A^2 -> H(U1(a, d), f(k)),A^2 -> H(U1(a, d), f(k)))
24.91/8.23	
24.91/8.23	
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(102)
24.91/8.23	Obligation:
24.91/8.23	Q DP problem:
24.91/8.23	The TRS P consists of the following rules:
24.91/8.23	
24.91/8.23	   H(x, x) -> G(x, x, f(k))
24.91/8.23	   G(d, x, x) -> A^2
24.91/8.23	   A^2 -> H(f(c), f(c))
24.91/8.23	   A^2 -> H(f(d), f(d))
24.91/8.23	   A^2 -> H(U1(a, d), f(d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, a), f(e))
24.91/8.23	   A^2 -> H(U1(a, a), f(k))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(e, c), f(b))
24.91/8.23	   A^2 -> H(U1(k, c), f(b))
24.91/8.23	   A^2 -> H(U1(c, e), f(b))
24.91/8.23	   A^2 -> H(U1(c, k), f(b))
24.91/8.23	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, c), f(c))
24.91/8.23	   A^2 -> H(U1(c, c), f(d))
24.91/8.23	   A^2 -> H(U1(e, e), f(b))
24.91/8.23	   A^2 -> H(f(e), U1(b, b))
24.91/8.23	   A^2 -> H(f(e), f(c))
24.91/8.23	   A^2 -> H(f(e), f(d))
24.91/8.23	   A^2 -> H(U1(k, k), f(b))
24.91/8.23	   A^2 -> H(f(k), U1(b, b))
24.91/8.23	   A^2 -> H(f(k), f(c))
24.91/8.23	   A^2 -> H(f(k), f(d))
24.91/8.23	   A^2 -> H(f(c), U1(c, b))
24.91/8.23	   A^2 -> H(f(c), U1(d, b))
24.91/8.23	   A^2 -> H(f(c), U1(b, c))
24.91/8.23	   A^2 -> H(f(c), U1(b, d))
24.91/8.23	   A^2 -> H(f(c), U1(d, d))
24.91/8.23	   A^2 -> H(f(c), f(k))
24.91/8.23	   A^2 -> H(U1(k, d), f(b))
24.91/8.23	   A^2 -> H(U1(d, k), f(b))
24.91/8.23	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, d), f(c))
24.91/8.23	   A^2 -> H(U1(d, d), f(d))
24.91/8.23	   A^2 -> H(f(d), U1(c, b))
24.91/8.23	   A^2 -> H(f(d), U1(d, b))
24.91/8.23	   A^2 -> H(f(d), U1(b, c))
24.91/8.23	   A^2 -> H(f(d), U1(b, d))
24.91/8.23	   A^2 -> H(f(d), U1(c, c))
24.91/8.23	   A^2 -> H(f(d), f(e))
24.91/8.23	   A^2 -> H(f(d), f(k))
24.91/8.23	   A^2 -> H(f(a), U1(e, b))
24.91/8.23	   A^2 -> H(f(a), U1(k, b))
24.91/8.23	   A^2 -> H(f(a), U1(c, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, c))
24.91/8.23	   A^2 -> H(f(a), U1(b, e))
24.91/8.23	   A^2 -> H(f(a), U1(b, k))
24.91/8.23	   A^2 -> H(f(c), U1(c, c))
24.91/8.23	   A^2 -> H(f(a), U1(e, c))
24.91/8.23	   A^2 -> H(f(a), U1(k, c))
24.91/8.23	   A^2 -> H(f(a), U1(c, e))
24.91/8.23	   A^2 -> H(f(a), U1(c, k))
24.91/8.23	   A^2 -> H(f(c), f(e))
24.91/8.23	   A^2 -> H(f(a), U1(e, e))
24.91/8.23	   A^2 -> H(f(a), U1(k, k))
24.91/8.23	   A^2 -> H(f(d), U1(d, d))
24.91/8.23	   A^2 -> H(f(a), U1(k, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, k))
24.91/8.23	   A^2 -> H(a, f(b))
24.91/8.23	   A^2 -> H(U1(e, d), f(b))
24.91/8.23	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(e, a), f(c))
24.91/8.23	   A^2 -> H(U1(e, a), f(d))
24.91/8.23	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(k, a), f(c))
24.91/8.23	   A^2 -> H(U1(k, a), f(d))
24.91/8.23	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, d), f(c))
24.91/8.23	   A^2 -> H(U1(c, d), f(d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(c, a), f(e))
24.91/8.23	   A^2 -> H(U1(c, a), f(k))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(d, e), f(b))
24.91/8.23	   A^2 -> H(U1(d, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, c), f(c))
24.91/8.23	   A^2 -> H(U1(d, c), f(d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(d, a), f(e))
24.91/8.23	   A^2 -> H(U1(d, a), f(k))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, e), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, e), f(c))
24.91/8.23	   A^2 -> H(U1(a, e), f(d))
24.91/8.23	   A^2 -> H(U1(a, k), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, k), f(c))
24.91/8.23	   A^2 -> H(U1(a, k), f(d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, c), f(e))
24.91/8.23	   A^2 -> H(U1(a, c), f(k))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, d), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, d), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, d), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, d), f(e))
24.91/8.23	   A^2 -> H(U1(a, d), f(k))
24.91/8.23	
24.91/8.23	The TRS R consists of the following rules:
24.91/8.23	
24.91/8.23	   f(x) -> U1(x, x)
24.91/8.23	   U1(e, x) -> x
24.91/8.23	   a -> c
24.91/8.23	   a -> d
24.91/8.23	   b -> c
24.91/8.23	   b -> d
24.91/8.23	   d -> k
24.91/8.23	   c -> e
24.91/8.23	   c -> k
24.91/8.23	
24.91/8.23	Q is empty.
24.91/8.23	We have to consider all minimal (P,Q,R)-chains.
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(103) TransformationProof (EQUIVALENT)
24.91/8.23	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), f(d)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.23	
24.91/8.23	   (A^2 -> H(U1(c, d), f(d)),A^2 -> H(U1(c, d), f(d)))
24.91/8.23	   (A^2 -> H(U1(d, d), f(d)),A^2 -> H(U1(d, d), f(d)))
24.91/8.23	   (A^2 -> H(U1(a, k), f(d)),A^2 -> H(U1(a, k), f(d)))
24.91/8.23	   (A^2 -> H(U1(a, d), U1(d, d)),A^2 -> H(U1(a, d), U1(d, d)))
24.91/8.23	   (A^2 -> H(U1(a, d), f(k)),A^2 -> H(U1(a, d), f(k)))
24.91/8.23	
24.91/8.23	
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(104)
24.91/8.23	Obligation:
24.91/8.23	Q DP problem:
24.91/8.23	The TRS P consists of the following rules:
24.91/8.23	
24.91/8.23	   H(x, x) -> G(x, x, f(k))
24.91/8.23	   G(d, x, x) -> A^2
24.91/8.23	   A^2 -> H(f(c), f(c))
24.91/8.23	   A^2 -> H(f(d), f(d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, a), f(e))
24.91/8.23	   A^2 -> H(U1(a, a), f(k))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(e, c), f(b))
24.91/8.23	   A^2 -> H(U1(k, c), f(b))
24.91/8.23	   A^2 -> H(U1(c, e), f(b))
24.91/8.23	   A^2 -> H(U1(c, k), f(b))
24.91/8.23	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, c), f(c))
24.91/8.23	   A^2 -> H(U1(c, c), f(d))
24.91/8.23	   A^2 -> H(U1(e, e), f(b))
24.91/8.23	   A^2 -> H(f(e), U1(b, b))
24.91/8.23	   A^2 -> H(f(e), f(c))
24.91/8.23	   A^2 -> H(f(e), f(d))
24.91/8.23	   A^2 -> H(U1(k, k), f(b))
24.91/8.23	   A^2 -> H(f(k), U1(b, b))
24.91/8.23	   A^2 -> H(f(k), f(c))
24.91/8.23	   A^2 -> H(f(k), f(d))
24.91/8.23	   A^2 -> H(f(c), U1(c, b))
24.91/8.23	   A^2 -> H(f(c), U1(d, b))
24.91/8.23	   A^2 -> H(f(c), U1(b, c))
24.91/8.23	   A^2 -> H(f(c), U1(b, d))
24.91/8.23	   A^2 -> H(f(c), U1(d, d))
24.91/8.23	   A^2 -> H(f(c), f(k))
24.91/8.23	   A^2 -> H(U1(k, d), f(b))
24.91/8.23	   A^2 -> H(U1(d, k), f(b))
24.91/8.23	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, d), f(c))
24.91/8.23	   A^2 -> H(U1(d, d), f(d))
24.91/8.23	   A^2 -> H(f(d), U1(c, b))
24.91/8.23	   A^2 -> H(f(d), U1(d, b))
24.91/8.23	   A^2 -> H(f(d), U1(b, c))
24.91/8.23	   A^2 -> H(f(d), U1(b, d))
24.91/8.23	   A^2 -> H(f(d), U1(c, c))
24.91/8.23	   A^2 -> H(f(d), f(e))
24.91/8.23	   A^2 -> H(f(d), f(k))
24.91/8.23	   A^2 -> H(f(a), U1(e, b))
24.91/8.23	   A^2 -> H(f(a), U1(k, b))
24.91/8.23	   A^2 -> H(f(a), U1(c, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, c))
24.91/8.23	   A^2 -> H(f(a), U1(b, e))
24.91/8.23	   A^2 -> H(f(a), U1(b, k))
24.91/8.23	   A^2 -> H(f(c), U1(c, c))
24.91/8.23	   A^2 -> H(f(a), U1(e, c))
24.91/8.23	   A^2 -> H(f(a), U1(k, c))
24.91/8.23	   A^2 -> H(f(a), U1(c, e))
24.91/8.23	   A^2 -> H(f(a), U1(c, k))
24.91/8.23	   A^2 -> H(f(c), f(e))
24.91/8.23	   A^2 -> H(f(a), U1(e, e))
24.91/8.23	   A^2 -> H(f(a), U1(k, k))
24.91/8.23	   A^2 -> H(f(d), U1(d, d))
24.91/8.23	   A^2 -> H(f(a), U1(k, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, k))
24.91/8.23	   A^2 -> H(a, f(b))
24.91/8.23	   A^2 -> H(U1(e, d), f(b))
24.91/8.23	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(e, a), f(c))
24.91/8.23	   A^2 -> H(U1(e, a), f(d))
24.91/8.23	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(k, a), f(c))
24.91/8.23	   A^2 -> H(U1(k, a), f(d))
24.91/8.23	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, d), f(c))
24.91/8.23	   A^2 -> H(U1(c, d), f(d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(c, a), f(e))
24.91/8.23	   A^2 -> H(U1(c, a), f(k))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(d, e), f(b))
24.91/8.23	   A^2 -> H(U1(d, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, c), f(c))
24.91/8.23	   A^2 -> H(U1(d, c), f(d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(d, a), f(e))
24.91/8.23	   A^2 -> H(U1(d, a), f(k))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, e), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, e), f(c))
24.91/8.23	   A^2 -> H(U1(a, e), f(d))
24.91/8.23	   A^2 -> H(U1(a, k), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, k), f(c))
24.91/8.23	   A^2 -> H(U1(a, k), f(d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, c), f(e))
24.91/8.23	   A^2 -> H(U1(a, c), f(k))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, d), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, d), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, d), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, d), f(e))
24.91/8.23	   A^2 -> H(U1(a, d), f(k))
24.91/8.23	   A^2 -> H(U1(a, d), U1(d, d))
24.91/8.23	
24.91/8.23	The TRS R consists of the following rules:
24.91/8.23	
24.91/8.23	   f(x) -> U1(x, x)
24.91/8.23	   U1(e, x) -> x
24.91/8.23	   a -> c
24.91/8.23	   a -> d
24.91/8.23	   b -> c
24.91/8.23	   b -> d
24.91/8.23	   d -> k
24.91/8.23	   c -> e
24.91/8.23	   c -> k
24.91/8.23	
24.91/8.23	Q is empty.
24.91/8.23	We have to consider all minimal (P,Q,R)-chains.
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(105) TransformationProof (EQUIVALENT)
24.91/8.23	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.23	
24.91/8.23	   (A^2 -> H(U1(c, a), U1(c, b)),A^2 -> H(U1(c, a), U1(c, b)))
24.91/8.23	   (A^2 -> H(U1(d, a), U1(c, b)),A^2 -> H(U1(d, a), U1(c, b)))
24.91/8.23	   (A^2 -> H(U1(a, c), U1(c, b)),A^2 -> H(U1(a, c), U1(c, b)))
24.91/8.23	   (A^2 -> H(U1(a, d), U1(c, b)),A^2 -> H(U1(a, d), U1(c, b)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(e, b)),A^2 -> H(U1(a, a), U1(e, b)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(k, b)),A^2 -> H(U1(a, a), U1(k, b)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(c, c)),A^2 -> H(U1(a, a), U1(c, c)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(c, d)),A^2 -> H(U1(a, a), U1(c, d)))
24.91/8.23	
24.91/8.23	
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(106)
24.91/8.23	Obligation:
24.91/8.23	Q DP problem:
24.91/8.23	The TRS P consists of the following rules:
24.91/8.23	
24.91/8.23	   H(x, x) -> G(x, x, f(k))
24.91/8.23	   G(d, x, x) -> A^2
24.91/8.23	   A^2 -> H(f(c), f(c))
24.91/8.23	   A^2 -> H(f(d), f(d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, a), f(e))
24.91/8.23	   A^2 -> H(U1(a, a), f(k))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(e, c), f(b))
24.91/8.23	   A^2 -> H(U1(k, c), f(b))
24.91/8.23	   A^2 -> H(U1(c, e), f(b))
24.91/8.23	   A^2 -> H(U1(c, k), f(b))
24.91/8.23	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, c), f(c))
24.91/8.23	   A^2 -> H(U1(c, c), f(d))
24.91/8.23	   A^2 -> H(U1(e, e), f(b))
24.91/8.23	   A^2 -> H(f(e), U1(b, b))
24.91/8.23	   A^2 -> H(f(e), f(c))
24.91/8.23	   A^2 -> H(f(e), f(d))
24.91/8.23	   A^2 -> H(U1(k, k), f(b))
24.91/8.23	   A^2 -> H(f(k), U1(b, b))
24.91/8.23	   A^2 -> H(f(k), f(c))
24.91/8.23	   A^2 -> H(f(k), f(d))
24.91/8.23	   A^2 -> H(f(c), U1(c, b))
24.91/8.23	   A^2 -> H(f(c), U1(d, b))
24.91/8.23	   A^2 -> H(f(c), U1(b, c))
24.91/8.23	   A^2 -> H(f(c), U1(b, d))
24.91/8.23	   A^2 -> H(f(c), U1(d, d))
24.91/8.23	   A^2 -> H(f(c), f(k))
24.91/8.23	   A^2 -> H(U1(k, d), f(b))
24.91/8.23	   A^2 -> H(U1(d, k), f(b))
24.91/8.23	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, d), f(c))
24.91/8.23	   A^2 -> H(U1(d, d), f(d))
24.91/8.23	   A^2 -> H(f(d), U1(c, b))
24.91/8.23	   A^2 -> H(f(d), U1(d, b))
24.91/8.23	   A^2 -> H(f(d), U1(b, c))
24.91/8.23	   A^2 -> H(f(d), U1(b, d))
24.91/8.23	   A^2 -> H(f(d), U1(c, c))
24.91/8.23	   A^2 -> H(f(d), f(e))
24.91/8.23	   A^2 -> H(f(d), f(k))
24.91/8.23	   A^2 -> H(f(a), U1(e, b))
24.91/8.23	   A^2 -> H(f(a), U1(k, b))
24.91/8.23	   A^2 -> H(f(a), U1(c, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, c))
24.91/8.23	   A^2 -> H(f(a), U1(b, e))
24.91/8.23	   A^2 -> H(f(a), U1(b, k))
24.91/8.23	   A^2 -> H(f(c), U1(c, c))
24.91/8.23	   A^2 -> H(f(a), U1(e, c))
24.91/8.23	   A^2 -> H(f(a), U1(k, c))
24.91/8.23	   A^2 -> H(f(a), U1(c, e))
24.91/8.23	   A^2 -> H(f(a), U1(c, k))
24.91/8.23	   A^2 -> H(f(c), f(e))
24.91/8.23	   A^2 -> H(f(a), U1(e, e))
24.91/8.23	   A^2 -> H(f(a), U1(k, k))
24.91/8.23	   A^2 -> H(f(d), U1(d, d))
24.91/8.23	   A^2 -> H(f(a), U1(k, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, k))
24.91/8.23	   A^2 -> H(a, f(b))
24.91/8.23	   A^2 -> H(U1(e, d), f(b))
24.91/8.23	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(e, a), f(c))
24.91/8.23	   A^2 -> H(U1(e, a), f(d))
24.91/8.23	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(k, a), f(c))
24.91/8.23	   A^2 -> H(U1(k, a), f(d))
24.91/8.23	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, d), f(c))
24.91/8.23	   A^2 -> H(U1(c, d), f(d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(c, a), f(e))
24.91/8.23	   A^2 -> H(U1(c, a), f(k))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(d, e), f(b))
24.91/8.23	   A^2 -> H(U1(d, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, c), f(c))
24.91/8.23	   A^2 -> H(U1(d, c), f(d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(d, a), f(e))
24.91/8.23	   A^2 -> H(U1(d, a), f(k))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, e), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, e), f(c))
24.91/8.23	   A^2 -> H(U1(a, e), f(d))
24.91/8.23	   A^2 -> H(U1(a, k), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, k), f(c))
24.91/8.23	   A^2 -> H(U1(a, k), f(d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, c), f(e))
24.91/8.23	   A^2 -> H(U1(a, c), f(k))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, d), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, d), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, d), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, d), f(e))
24.91/8.23	   A^2 -> H(U1(a, d), f(k))
24.91/8.23	   A^2 -> H(U1(a, d), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(e, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(k, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, d))
24.91/8.23	
24.91/8.23	The TRS R consists of the following rules:
24.91/8.23	
24.91/8.23	   f(x) -> U1(x, x)
24.91/8.23	   U1(e, x) -> x
24.91/8.23	   a -> c
24.91/8.23	   a -> d
24.91/8.23	   b -> c
24.91/8.23	   b -> d
24.91/8.23	   d -> k
24.91/8.23	   c -> e
24.91/8.23	   c -> k
24.91/8.23	
24.91/8.23	Q is empty.
24.91/8.23	We have to consider all minimal (P,Q,R)-chains.
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(107) TransformationProof (EQUIVALENT)
24.91/8.23	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.23	
24.91/8.23	   (A^2 -> H(U1(c, a), U1(d, b)),A^2 -> H(U1(c, a), U1(d, b)))
24.91/8.23	   (A^2 -> H(U1(d, a), U1(d, b)),A^2 -> H(U1(d, a), U1(d, b)))
24.91/8.23	   (A^2 -> H(U1(a, c), U1(d, b)),A^2 -> H(U1(a, c), U1(d, b)))
24.91/8.23	   (A^2 -> H(U1(a, d), U1(d, b)),A^2 -> H(U1(a, d), U1(d, b)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(k, b)),A^2 -> H(U1(a, a), U1(k, b)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(d, c)),A^2 -> H(U1(a, a), U1(d, c)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(d, d)),A^2 -> H(U1(a, a), U1(d, d)))
24.91/8.23	
24.91/8.23	
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(108)
24.91/8.23	Obligation:
24.91/8.23	Q DP problem:
24.91/8.23	The TRS P consists of the following rules:
24.91/8.23	
24.91/8.23	   H(x, x) -> G(x, x, f(k))
24.91/8.23	   G(d, x, x) -> A^2
24.91/8.23	   A^2 -> H(f(c), f(c))
24.91/8.23	   A^2 -> H(f(d), f(d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, a), f(e))
24.91/8.23	   A^2 -> H(U1(a, a), f(k))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(e, c), f(b))
24.91/8.23	   A^2 -> H(U1(k, c), f(b))
24.91/8.23	   A^2 -> H(U1(c, e), f(b))
24.91/8.23	   A^2 -> H(U1(c, k), f(b))
24.91/8.23	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, c), f(c))
24.91/8.23	   A^2 -> H(U1(c, c), f(d))
24.91/8.23	   A^2 -> H(U1(e, e), f(b))
24.91/8.23	   A^2 -> H(f(e), U1(b, b))
24.91/8.23	   A^2 -> H(f(e), f(c))
24.91/8.23	   A^2 -> H(f(e), f(d))
24.91/8.23	   A^2 -> H(U1(k, k), f(b))
24.91/8.23	   A^2 -> H(f(k), U1(b, b))
24.91/8.23	   A^2 -> H(f(k), f(c))
24.91/8.23	   A^2 -> H(f(k), f(d))
24.91/8.23	   A^2 -> H(f(c), U1(c, b))
24.91/8.23	   A^2 -> H(f(c), U1(d, b))
24.91/8.23	   A^2 -> H(f(c), U1(b, c))
24.91/8.23	   A^2 -> H(f(c), U1(b, d))
24.91/8.23	   A^2 -> H(f(c), U1(d, d))
24.91/8.23	   A^2 -> H(f(c), f(k))
24.91/8.23	   A^2 -> H(U1(k, d), f(b))
24.91/8.23	   A^2 -> H(U1(d, k), f(b))
24.91/8.23	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, d), f(c))
24.91/8.23	   A^2 -> H(U1(d, d), f(d))
24.91/8.23	   A^2 -> H(f(d), U1(c, b))
24.91/8.23	   A^2 -> H(f(d), U1(d, b))
24.91/8.23	   A^2 -> H(f(d), U1(b, c))
24.91/8.23	   A^2 -> H(f(d), U1(b, d))
24.91/8.23	   A^2 -> H(f(d), U1(c, c))
24.91/8.23	   A^2 -> H(f(d), f(e))
24.91/8.23	   A^2 -> H(f(d), f(k))
24.91/8.23	   A^2 -> H(f(a), U1(e, b))
24.91/8.23	   A^2 -> H(f(a), U1(k, b))
24.91/8.23	   A^2 -> H(f(a), U1(c, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, c))
24.91/8.23	   A^2 -> H(f(a), U1(b, e))
24.91/8.23	   A^2 -> H(f(a), U1(b, k))
24.91/8.23	   A^2 -> H(f(c), U1(c, c))
24.91/8.23	   A^2 -> H(f(a), U1(e, c))
24.91/8.23	   A^2 -> H(f(a), U1(k, c))
24.91/8.23	   A^2 -> H(f(a), U1(c, e))
24.91/8.23	   A^2 -> H(f(a), U1(c, k))
24.91/8.23	   A^2 -> H(f(c), f(e))
24.91/8.23	   A^2 -> H(f(a), U1(e, e))
24.91/8.23	   A^2 -> H(f(a), U1(k, k))
24.91/8.23	   A^2 -> H(f(d), U1(d, d))
24.91/8.23	   A^2 -> H(f(a), U1(k, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, k))
24.91/8.23	   A^2 -> H(a, f(b))
24.91/8.23	   A^2 -> H(U1(e, d), f(b))
24.91/8.23	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(e, a), f(c))
24.91/8.23	   A^2 -> H(U1(e, a), f(d))
24.91/8.23	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(k, a), f(c))
24.91/8.23	   A^2 -> H(U1(k, a), f(d))
24.91/8.23	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, d), f(c))
24.91/8.23	   A^2 -> H(U1(c, d), f(d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(c, a), f(e))
24.91/8.23	   A^2 -> H(U1(c, a), f(k))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(d, e), f(b))
24.91/8.23	   A^2 -> H(U1(d, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, c), f(c))
24.91/8.23	   A^2 -> H(U1(d, c), f(d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(d, a), f(e))
24.91/8.23	   A^2 -> H(U1(d, a), f(k))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, e), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, e), f(c))
24.91/8.23	   A^2 -> H(U1(a, e), f(d))
24.91/8.23	   A^2 -> H(U1(a, k), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, k), f(c))
24.91/8.23	   A^2 -> H(U1(a, k), f(d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, c), f(e))
24.91/8.23	   A^2 -> H(U1(a, c), f(k))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, d), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, d), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, d), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, d), f(e))
24.91/8.23	   A^2 -> H(U1(a, d), f(k))
24.91/8.23	   A^2 -> H(U1(a, d), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(e, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(k, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, c))
24.91/8.23	
24.91/8.23	The TRS R consists of the following rules:
24.91/8.23	
24.91/8.23	   f(x) -> U1(x, x)
24.91/8.23	   U1(e, x) -> x
24.91/8.23	   a -> c
24.91/8.23	   a -> d
24.91/8.23	   b -> c
24.91/8.23	   b -> d
24.91/8.23	   d -> k
24.91/8.23	   c -> e
24.91/8.23	   c -> k
24.91/8.23	
24.91/8.23	Q is empty.
24.91/8.23	We have to consider all minimal (P,Q,R)-chains.
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(109) TransformationProof (EQUIVALENT)
24.91/8.23	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.23	
24.91/8.23	   (A^2 -> H(U1(c, a), U1(b, c)),A^2 -> H(U1(c, a), U1(b, c)))
24.91/8.23	   (A^2 -> H(U1(d, a), U1(b, c)),A^2 -> H(U1(d, a), U1(b, c)))
24.91/8.23	   (A^2 -> H(U1(a, c), U1(b, c)),A^2 -> H(U1(a, c), U1(b, c)))
24.91/8.23	   (A^2 -> H(U1(a, d), U1(b, c)),A^2 -> H(U1(a, d), U1(b, c)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(c, c)),A^2 -> H(U1(a, a), U1(c, c)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(d, c)),A^2 -> H(U1(a, a), U1(d, c)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(b, e)),A^2 -> H(U1(a, a), U1(b, e)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(b, k)),A^2 -> H(U1(a, a), U1(b, k)))
24.91/8.23	
24.91/8.23	
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(110)
24.91/8.23	Obligation:
24.91/8.23	Q DP problem:
24.91/8.23	The TRS P consists of the following rules:
24.91/8.23	
24.91/8.23	   H(x, x) -> G(x, x, f(k))
24.91/8.23	   G(d, x, x) -> A^2
24.91/8.23	   A^2 -> H(f(c), f(c))
24.91/8.23	   A^2 -> H(f(d), f(d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, a), f(e))
24.91/8.23	   A^2 -> H(U1(a, a), f(k))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(e, c), f(b))
24.91/8.23	   A^2 -> H(U1(k, c), f(b))
24.91/8.23	   A^2 -> H(U1(c, e), f(b))
24.91/8.23	   A^2 -> H(U1(c, k), f(b))
24.91/8.23	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, c), f(c))
24.91/8.23	   A^2 -> H(U1(c, c), f(d))
24.91/8.23	   A^2 -> H(U1(e, e), f(b))
24.91/8.23	   A^2 -> H(f(e), U1(b, b))
24.91/8.23	   A^2 -> H(f(e), f(c))
24.91/8.23	   A^2 -> H(f(e), f(d))
24.91/8.23	   A^2 -> H(U1(k, k), f(b))
24.91/8.23	   A^2 -> H(f(k), U1(b, b))
24.91/8.23	   A^2 -> H(f(k), f(c))
24.91/8.23	   A^2 -> H(f(k), f(d))
24.91/8.23	   A^2 -> H(f(c), U1(c, b))
24.91/8.23	   A^2 -> H(f(c), U1(d, b))
24.91/8.23	   A^2 -> H(f(c), U1(b, c))
24.91/8.23	   A^2 -> H(f(c), U1(b, d))
24.91/8.23	   A^2 -> H(f(c), U1(d, d))
24.91/8.23	   A^2 -> H(f(c), f(k))
24.91/8.23	   A^2 -> H(U1(k, d), f(b))
24.91/8.23	   A^2 -> H(U1(d, k), f(b))
24.91/8.23	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, d), f(c))
24.91/8.23	   A^2 -> H(U1(d, d), f(d))
24.91/8.23	   A^2 -> H(f(d), U1(c, b))
24.91/8.23	   A^2 -> H(f(d), U1(d, b))
24.91/8.23	   A^2 -> H(f(d), U1(b, c))
24.91/8.23	   A^2 -> H(f(d), U1(b, d))
24.91/8.23	   A^2 -> H(f(d), U1(c, c))
24.91/8.23	   A^2 -> H(f(d), f(e))
24.91/8.23	   A^2 -> H(f(d), f(k))
24.91/8.23	   A^2 -> H(f(a), U1(e, b))
24.91/8.23	   A^2 -> H(f(a), U1(k, b))
24.91/8.23	   A^2 -> H(f(a), U1(c, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, c))
24.91/8.23	   A^2 -> H(f(a), U1(b, e))
24.91/8.23	   A^2 -> H(f(a), U1(b, k))
24.91/8.23	   A^2 -> H(f(c), U1(c, c))
24.91/8.23	   A^2 -> H(f(a), U1(e, c))
24.91/8.23	   A^2 -> H(f(a), U1(k, c))
24.91/8.23	   A^2 -> H(f(a), U1(c, e))
24.91/8.23	   A^2 -> H(f(a), U1(c, k))
24.91/8.23	   A^2 -> H(f(c), f(e))
24.91/8.23	   A^2 -> H(f(a), U1(e, e))
24.91/8.23	   A^2 -> H(f(a), U1(k, k))
24.91/8.23	   A^2 -> H(f(d), U1(d, d))
24.91/8.23	   A^2 -> H(f(a), U1(k, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, k))
24.91/8.23	   A^2 -> H(a, f(b))
24.91/8.23	   A^2 -> H(U1(e, d), f(b))
24.91/8.23	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(e, a), f(c))
24.91/8.23	   A^2 -> H(U1(e, a), f(d))
24.91/8.23	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(k, a), f(c))
24.91/8.23	   A^2 -> H(U1(k, a), f(d))
24.91/8.23	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, d), f(c))
24.91/8.23	   A^2 -> H(U1(c, d), f(d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(c, a), f(e))
24.91/8.23	   A^2 -> H(U1(c, a), f(k))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(d, e), f(b))
24.91/8.23	   A^2 -> H(U1(d, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, c), f(c))
24.91/8.23	   A^2 -> H(U1(d, c), f(d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(d, a), f(e))
24.91/8.23	   A^2 -> H(U1(d, a), f(k))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, e), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, e), f(c))
24.91/8.23	   A^2 -> H(U1(a, e), f(d))
24.91/8.23	   A^2 -> H(U1(a, k), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, k), f(c))
24.91/8.23	   A^2 -> H(U1(a, k), f(d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, c), f(e))
24.91/8.23	   A^2 -> H(U1(a, c), f(k))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, d), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, d), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, d), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, d), f(e))
24.91/8.23	   A^2 -> H(U1(a, d), f(k))
24.91/8.23	   A^2 -> H(U1(a, d), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(e, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(k, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, c))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, e))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, k))
24.91/8.23	
24.91/8.23	The TRS R consists of the following rules:
24.91/8.23	
24.91/8.23	   f(x) -> U1(x, x)
24.91/8.23	   U1(e, x) -> x
24.91/8.23	   a -> c
24.91/8.23	   a -> d
24.91/8.23	   b -> c
24.91/8.23	   b -> d
24.91/8.23	   d -> k
24.91/8.23	   c -> e
24.91/8.23	   c -> k
24.91/8.23	
24.91/8.23	Q is empty.
24.91/8.23	We have to consider all minimal (P,Q,R)-chains.
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(111) TransformationProof (EQUIVALENT)
24.91/8.23	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.23	
24.91/8.23	   (A^2 -> H(U1(c, a), U1(b, d)),A^2 -> H(U1(c, a), U1(b, d)))
24.91/8.23	   (A^2 -> H(U1(d, a), U1(b, d)),A^2 -> H(U1(d, a), U1(b, d)))
24.91/8.23	   (A^2 -> H(U1(a, c), U1(b, d)),A^2 -> H(U1(a, c), U1(b, d)))
24.91/8.23	   (A^2 -> H(U1(a, d), U1(b, d)),A^2 -> H(U1(a, d), U1(b, d)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(c, d)),A^2 -> H(U1(a, a), U1(c, d)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(d, d)),A^2 -> H(U1(a, a), U1(d, d)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(b, k)),A^2 -> H(U1(a, a), U1(b, k)))
24.91/8.23	
24.91/8.23	
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(112)
24.91/8.23	Obligation:
24.91/8.23	Q DP problem:
24.91/8.23	The TRS P consists of the following rules:
24.91/8.23	
24.91/8.23	   H(x, x) -> G(x, x, f(k))
24.91/8.23	   G(d, x, x) -> A^2
24.91/8.23	   A^2 -> H(f(c), f(c))
24.91/8.23	   A^2 -> H(f(d), f(d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, a), f(e))
24.91/8.23	   A^2 -> H(U1(a, a), f(k))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(e, c), f(b))
24.91/8.23	   A^2 -> H(U1(k, c), f(b))
24.91/8.23	   A^2 -> H(U1(c, e), f(b))
24.91/8.23	   A^2 -> H(U1(c, k), f(b))
24.91/8.23	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, c), f(c))
24.91/8.23	   A^2 -> H(U1(c, c), f(d))
24.91/8.23	   A^2 -> H(U1(e, e), f(b))
24.91/8.23	   A^2 -> H(f(e), U1(b, b))
24.91/8.23	   A^2 -> H(f(e), f(c))
24.91/8.23	   A^2 -> H(f(e), f(d))
24.91/8.23	   A^2 -> H(U1(k, k), f(b))
24.91/8.23	   A^2 -> H(f(k), U1(b, b))
24.91/8.23	   A^2 -> H(f(k), f(c))
24.91/8.23	   A^2 -> H(f(k), f(d))
24.91/8.23	   A^2 -> H(f(c), U1(c, b))
24.91/8.23	   A^2 -> H(f(c), U1(d, b))
24.91/8.23	   A^2 -> H(f(c), U1(b, c))
24.91/8.23	   A^2 -> H(f(c), U1(b, d))
24.91/8.23	   A^2 -> H(f(c), U1(d, d))
24.91/8.23	   A^2 -> H(f(c), f(k))
24.91/8.23	   A^2 -> H(U1(k, d), f(b))
24.91/8.23	   A^2 -> H(U1(d, k), f(b))
24.91/8.23	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, d), f(c))
24.91/8.23	   A^2 -> H(U1(d, d), f(d))
24.91/8.23	   A^2 -> H(f(d), U1(c, b))
24.91/8.23	   A^2 -> H(f(d), U1(d, b))
24.91/8.23	   A^2 -> H(f(d), U1(b, c))
24.91/8.23	   A^2 -> H(f(d), U1(b, d))
24.91/8.23	   A^2 -> H(f(d), U1(c, c))
24.91/8.23	   A^2 -> H(f(d), f(e))
24.91/8.23	   A^2 -> H(f(d), f(k))
24.91/8.23	   A^2 -> H(f(a), U1(e, b))
24.91/8.23	   A^2 -> H(f(a), U1(k, b))
24.91/8.23	   A^2 -> H(f(a), U1(c, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, c))
24.91/8.23	   A^2 -> H(f(a), U1(b, e))
24.91/8.23	   A^2 -> H(f(a), U1(b, k))
24.91/8.23	   A^2 -> H(f(c), U1(c, c))
24.91/8.23	   A^2 -> H(f(a), U1(e, c))
24.91/8.23	   A^2 -> H(f(a), U1(k, c))
24.91/8.23	   A^2 -> H(f(a), U1(c, e))
24.91/8.23	   A^2 -> H(f(a), U1(c, k))
24.91/8.23	   A^2 -> H(f(c), f(e))
24.91/8.23	   A^2 -> H(f(a), U1(e, e))
24.91/8.23	   A^2 -> H(f(a), U1(k, k))
24.91/8.23	   A^2 -> H(f(d), U1(d, d))
24.91/8.23	   A^2 -> H(f(a), U1(k, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, k))
24.91/8.23	   A^2 -> H(a, f(b))
24.91/8.23	   A^2 -> H(U1(e, d), f(b))
24.91/8.23	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(e, a), f(c))
24.91/8.23	   A^2 -> H(U1(e, a), f(d))
24.91/8.23	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(k, a), f(c))
24.91/8.23	   A^2 -> H(U1(k, a), f(d))
24.91/8.23	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, d), f(c))
24.91/8.23	   A^2 -> H(U1(c, d), f(d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(c, a), f(e))
24.91/8.23	   A^2 -> H(U1(c, a), f(k))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(d, e), f(b))
24.91/8.23	   A^2 -> H(U1(d, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, c), f(c))
24.91/8.23	   A^2 -> H(U1(d, c), f(d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(d, a), f(e))
24.91/8.23	   A^2 -> H(U1(d, a), f(k))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, e), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, e), f(c))
24.91/8.23	   A^2 -> H(U1(a, e), f(d))
24.91/8.23	   A^2 -> H(U1(a, k), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, k), f(c))
24.91/8.23	   A^2 -> H(U1(a, k), f(d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, c), f(e))
24.91/8.23	   A^2 -> H(U1(a, c), f(k))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, d), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, d), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, d), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, d), f(e))
24.91/8.23	   A^2 -> H(U1(a, d), f(k))
24.91/8.23	   A^2 -> H(U1(a, d), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(e, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(k, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, c))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, e))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, k))
24.91/8.23	
24.91/8.23	The TRS R consists of the following rules:
24.91/8.23	
24.91/8.23	   f(x) -> U1(x, x)
24.91/8.23	   U1(e, x) -> x
24.91/8.23	   a -> c
24.91/8.23	   a -> d
24.91/8.23	   b -> c
24.91/8.23	   b -> d
24.91/8.23	   d -> k
24.91/8.23	   c -> e
24.91/8.23	   c -> k
24.91/8.23	
24.91/8.23	Q is empty.
24.91/8.23	We have to consider all minimal (P,Q,R)-chains.
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(113) TransformationProof (EQUIVALENT)
24.91/8.23	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.23	
24.91/8.23	   (A^2 -> H(U1(c, a), U1(c, c)),A^2 -> H(U1(c, a), U1(c, c)))
24.91/8.23	   (A^2 -> H(U1(d, a), U1(c, c)),A^2 -> H(U1(d, a), U1(c, c)))
24.91/8.23	   (A^2 -> H(U1(a, c), U1(c, c)),A^2 -> H(U1(a, c), U1(c, c)))
24.91/8.23	   (A^2 -> H(U1(a, d), U1(c, c)),A^2 -> H(U1(a, d), U1(c, c)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(e, c)),A^2 -> H(U1(a, a), U1(e, c)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(k, c)),A^2 -> H(U1(a, a), U1(k, c)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(c, e)),A^2 -> H(U1(a, a), U1(c, e)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(c, k)),A^2 -> H(U1(a, a), U1(c, k)))
24.91/8.23	
24.91/8.23	
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(114)
24.91/8.23	Obligation:
24.91/8.23	Q DP problem:
24.91/8.23	The TRS P consists of the following rules:
24.91/8.23	
24.91/8.23	   H(x, x) -> G(x, x, f(k))
24.91/8.23	   G(d, x, x) -> A^2
24.91/8.23	   A^2 -> H(f(c), f(c))
24.91/8.23	   A^2 -> H(f(d), f(d))
24.91/8.23	   A^2 -> H(U1(a, a), f(e))
24.91/8.23	   A^2 -> H(U1(a, a), f(k))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(e, c), f(b))
24.91/8.23	   A^2 -> H(U1(k, c), f(b))
24.91/8.23	   A^2 -> H(U1(c, e), f(b))
24.91/8.23	   A^2 -> H(U1(c, k), f(b))
24.91/8.23	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, c), f(c))
24.91/8.23	   A^2 -> H(U1(c, c), f(d))
24.91/8.23	   A^2 -> H(U1(e, e), f(b))
24.91/8.23	   A^2 -> H(f(e), U1(b, b))
24.91/8.23	   A^2 -> H(f(e), f(c))
24.91/8.23	   A^2 -> H(f(e), f(d))
24.91/8.23	   A^2 -> H(U1(k, k), f(b))
24.91/8.23	   A^2 -> H(f(k), U1(b, b))
24.91/8.23	   A^2 -> H(f(k), f(c))
24.91/8.23	   A^2 -> H(f(k), f(d))
24.91/8.23	   A^2 -> H(f(c), U1(c, b))
24.91/8.23	   A^2 -> H(f(c), U1(d, b))
24.91/8.23	   A^2 -> H(f(c), U1(b, c))
24.91/8.23	   A^2 -> H(f(c), U1(b, d))
24.91/8.23	   A^2 -> H(f(c), U1(d, d))
24.91/8.23	   A^2 -> H(f(c), f(k))
24.91/8.23	   A^2 -> H(U1(k, d), f(b))
24.91/8.23	   A^2 -> H(U1(d, k), f(b))
24.91/8.23	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, d), f(c))
24.91/8.23	   A^2 -> H(U1(d, d), f(d))
24.91/8.23	   A^2 -> H(f(d), U1(c, b))
24.91/8.23	   A^2 -> H(f(d), U1(d, b))
24.91/8.23	   A^2 -> H(f(d), U1(b, c))
24.91/8.23	   A^2 -> H(f(d), U1(b, d))
24.91/8.23	   A^2 -> H(f(d), U1(c, c))
24.91/8.23	   A^2 -> H(f(d), f(e))
24.91/8.23	   A^2 -> H(f(d), f(k))
24.91/8.23	   A^2 -> H(f(a), U1(e, b))
24.91/8.23	   A^2 -> H(f(a), U1(k, b))
24.91/8.23	   A^2 -> H(f(a), U1(c, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, c))
24.91/8.23	   A^2 -> H(f(a), U1(b, e))
24.91/8.23	   A^2 -> H(f(a), U1(b, k))
24.91/8.23	   A^2 -> H(f(c), U1(c, c))
24.91/8.23	   A^2 -> H(f(a), U1(e, c))
24.91/8.23	   A^2 -> H(f(a), U1(k, c))
24.91/8.23	   A^2 -> H(f(a), U1(c, e))
24.91/8.23	   A^2 -> H(f(a), U1(c, k))
24.91/8.23	   A^2 -> H(f(c), f(e))
24.91/8.23	   A^2 -> H(f(a), U1(e, e))
24.91/8.23	   A^2 -> H(f(a), U1(k, k))
24.91/8.23	   A^2 -> H(f(d), U1(d, d))
24.91/8.23	   A^2 -> H(f(a), U1(k, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, k))
24.91/8.23	   A^2 -> H(a, f(b))
24.91/8.23	   A^2 -> H(U1(e, d), f(b))
24.91/8.23	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(e, a), f(c))
24.91/8.23	   A^2 -> H(U1(e, a), f(d))
24.91/8.23	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(k, a), f(c))
24.91/8.23	   A^2 -> H(U1(k, a), f(d))
24.91/8.23	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, d), f(c))
24.91/8.23	   A^2 -> H(U1(c, d), f(d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(c, a), f(e))
24.91/8.23	   A^2 -> H(U1(c, a), f(k))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(d, e), f(b))
24.91/8.23	   A^2 -> H(U1(d, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, c), f(c))
24.91/8.23	   A^2 -> H(U1(d, c), f(d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(d, a), f(e))
24.91/8.23	   A^2 -> H(U1(d, a), f(k))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, e), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, e), f(c))
24.91/8.23	   A^2 -> H(U1(a, e), f(d))
24.91/8.23	   A^2 -> H(U1(a, k), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, k), f(c))
24.91/8.23	   A^2 -> H(U1(a, k), f(d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, c), f(e))
24.91/8.23	   A^2 -> H(U1(a, c), f(k))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, d), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, d), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, d), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, d), f(e))
24.91/8.23	   A^2 -> H(U1(a, d), f(k))
24.91/8.23	   A^2 -> H(U1(a, d), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(e, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(k, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, c))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, e))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, k))
24.91/8.23	   A^2 -> H(U1(a, a), U1(e, c))
24.91/8.23	   A^2 -> H(U1(a, a), U1(k, c))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, e))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, k))
24.91/8.23	
24.91/8.23	The TRS R consists of the following rules:
24.91/8.23	
24.91/8.23	   f(x) -> U1(x, x)
24.91/8.23	   U1(e, x) -> x
24.91/8.23	   a -> c
24.91/8.23	   a -> d
24.91/8.23	   b -> c
24.91/8.23	   b -> d
24.91/8.23	   d -> k
24.91/8.23	   c -> e
24.91/8.23	   c -> k
24.91/8.23	
24.91/8.23	Q is empty.
24.91/8.23	We have to consider all minimal (P,Q,R)-chains.
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(115) TransformationProof (EQUIVALENT)
24.91/8.23	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), f(e)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.23	
24.91/8.23	   (A^2 -> H(U1(c, a), f(e)),A^2 -> H(U1(c, a), f(e)))
24.91/8.23	   (A^2 -> H(U1(d, a), f(e)),A^2 -> H(U1(d, a), f(e)))
24.91/8.23	   (A^2 -> H(U1(a, c), f(e)),A^2 -> H(U1(a, c), f(e)))
24.91/8.23	   (A^2 -> H(U1(a, d), f(e)),A^2 -> H(U1(a, d), f(e)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(e, e)),A^2 -> H(U1(a, a), U1(e, e)))
24.91/8.23	
24.91/8.23	
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(116)
24.91/8.23	Obligation:
24.91/8.23	Q DP problem:
24.91/8.23	The TRS P consists of the following rules:
24.91/8.23	
24.91/8.23	   H(x, x) -> G(x, x, f(k))
24.91/8.23	   G(d, x, x) -> A^2
24.91/8.23	   A^2 -> H(f(c), f(c))
24.91/8.23	   A^2 -> H(f(d), f(d))
24.91/8.23	   A^2 -> H(U1(a, a), f(k))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(e, c), f(b))
24.91/8.23	   A^2 -> H(U1(k, c), f(b))
24.91/8.23	   A^2 -> H(U1(c, e), f(b))
24.91/8.23	   A^2 -> H(U1(c, k), f(b))
24.91/8.23	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, c), f(c))
24.91/8.23	   A^2 -> H(U1(c, c), f(d))
24.91/8.23	   A^2 -> H(U1(e, e), f(b))
24.91/8.23	   A^2 -> H(f(e), U1(b, b))
24.91/8.23	   A^2 -> H(f(e), f(c))
24.91/8.23	   A^2 -> H(f(e), f(d))
24.91/8.23	   A^2 -> H(U1(k, k), f(b))
24.91/8.23	   A^2 -> H(f(k), U1(b, b))
24.91/8.23	   A^2 -> H(f(k), f(c))
24.91/8.23	   A^2 -> H(f(k), f(d))
24.91/8.23	   A^2 -> H(f(c), U1(c, b))
24.91/8.23	   A^2 -> H(f(c), U1(d, b))
24.91/8.23	   A^2 -> H(f(c), U1(b, c))
24.91/8.23	   A^2 -> H(f(c), U1(b, d))
24.91/8.23	   A^2 -> H(f(c), U1(d, d))
24.91/8.23	   A^2 -> H(f(c), f(k))
24.91/8.23	   A^2 -> H(U1(k, d), f(b))
24.91/8.23	   A^2 -> H(U1(d, k), f(b))
24.91/8.23	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, d), f(c))
24.91/8.23	   A^2 -> H(U1(d, d), f(d))
24.91/8.23	   A^2 -> H(f(d), U1(c, b))
24.91/8.23	   A^2 -> H(f(d), U1(d, b))
24.91/8.23	   A^2 -> H(f(d), U1(b, c))
24.91/8.23	   A^2 -> H(f(d), U1(b, d))
24.91/8.23	   A^2 -> H(f(d), U1(c, c))
24.91/8.23	   A^2 -> H(f(d), f(e))
24.91/8.23	   A^2 -> H(f(d), f(k))
24.91/8.23	   A^2 -> H(f(a), U1(e, b))
24.91/8.23	   A^2 -> H(f(a), U1(k, b))
24.91/8.23	   A^2 -> H(f(a), U1(c, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, c))
24.91/8.23	   A^2 -> H(f(a), U1(b, e))
24.91/8.23	   A^2 -> H(f(a), U1(b, k))
24.91/8.23	   A^2 -> H(f(c), U1(c, c))
24.91/8.23	   A^2 -> H(f(a), U1(e, c))
24.91/8.23	   A^2 -> H(f(a), U1(k, c))
24.91/8.23	   A^2 -> H(f(a), U1(c, e))
24.91/8.23	   A^2 -> H(f(a), U1(c, k))
24.91/8.23	   A^2 -> H(f(c), f(e))
24.91/8.23	   A^2 -> H(f(a), U1(e, e))
24.91/8.23	   A^2 -> H(f(a), U1(k, k))
24.91/8.23	   A^2 -> H(f(d), U1(d, d))
24.91/8.23	   A^2 -> H(f(a), U1(k, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, k))
24.91/8.23	   A^2 -> H(a, f(b))
24.91/8.23	   A^2 -> H(U1(e, d), f(b))
24.91/8.23	   A^2 -> H(U1(e, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(e, a), f(c))
24.91/8.23	   A^2 -> H(U1(e, a), f(d))
24.91/8.23	   A^2 -> H(U1(k, a), U1(b, b))
24.91/8.23	   A^2 -> H(U1(k, a), f(c))
24.91/8.23	   A^2 -> H(U1(k, a), f(d))
24.91/8.23	   A^2 -> H(U1(c, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, d), f(c))
24.91/8.23	   A^2 -> H(U1(c, d), f(d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(c, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(c, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(c, a), f(e))
24.91/8.23	   A^2 -> H(U1(c, a), f(k))
24.91/8.23	   A^2 -> H(U1(c, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(d, e), f(b))
24.91/8.23	   A^2 -> H(U1(d, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, c), f(c))
24.91/8.23	   A^2 -> H(U1(d, c), f(d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, b))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, c))
24.91/8.23	   A^2 -> H(U1(d, a), U1(b, d))
24.91/8.23	   A^2 -> H(U1(d, a), U1(c, c))
24.91/8.23	   A^2 -> H(U1(d, a), f(e))
24.91/8.23	   A^2 -> H(U1(d, a), f(k))
24.91/8.23	   A^2 -> H(U1(d, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, e), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, e), f(c))
24.91/8.23	   A^2 -> H(U1(a, e), f(d))
24.91/8.23	   A^2 -> H(U1(a, k), U1(b, b))
24.91/8.23	   A^2 -> H(U1(a, k), f(c))
24.91/8.23	   A^2 -> H(U1(a, k), f(d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, c), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, c), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, c), f(e))
24.91/8.23	   A^2 -> H(U1(a, c), f(k))
24.91/8.23	   A^2 -> H(U1(a, c), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, d), U1(c, b))
24.91/8.23	   A^2 -> H(U1(a, d), U1(d, b))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, c))
24.91/8.23	   A^2 -> H(U1(a, d), U1(b, d))
24.91/8.23	   A^2 -> H(U1(a, d), U1(c, c))
24.91/8.23	   A^2 -> H(U1(a, d), f(e))
24.91/8.23	   A^2 -> H(U1(a, d), f(k))
24.91/8.23	   A^2 -> H(U1(a, d), U1(d, d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(e, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(k, b))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, c))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, e))
24.91/8.23	   A^2 -> H(U1(a, a), U1(b, k))
24.91/8.23	   A^2 -> H(U1(a, a), U1(e, c))
24.91/8.23	   A^2 -> H(U1(a, a), U1(k, c))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, e))
24.91/8.23	   A^2 -> H(U1(a, a), U1(c, k))
24.91/8.23	   A^2 -> H(U1(a, a), U1(e, e))
24.91/8.23	
24.91/8.23	The TRS R consists of the following rules:
24.91/8.23	
24.91/8.23	   f(x) -> U1(x, x)
24.91/8.23	   U1(e, x) -> x
24.91/8.23	   a -> c
24.91/8.23	   a -> d
24.91/8.23	   b -> c
24.91/8.23	   b -> d
24.91/8.23	   d -> k
24.91/8.23	   c -> e
24.91/8.23	   c -> k
24.91/8.23	
24.91/8.23	Q is empty.
24.91/8.23	We have to consider all minimal (P,Q,R)-chains.
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(117) TransformationProof (EQUIVALENT)
24.91/8.23	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), f(k)) at position [] we obtained the following new rules [LPAR04]:
24.91/8.23	
24.91/8.23	   (A^2 -> H(U1(c, a), f(k)),A^2 -> H(U1(c, a), f(k)))
24.91/8.23	   (A^2 -> H(U1(d, a), f(k)),A^2 -> H(U1(d, a), f(k)))
24.91/8.23	   (A^2 -> H(U1(a, c), f(k)),A^2 -> H(U1(a, c), f(k)))
24.91/8.23	   (A^2 -> H(U1(a, d), f(k)),A^2 -> H(U1(a, d), f(k)))
24.91/8.23	   (A^2 -> H(U1(a, a), U1(k, k)),A^2 -> H(U1(a, a), U1(k, k)))
24.91/8.23	
24.91/8.23	
24.91/8.23	----------------------------------------
24.91/8.23	
24.91/8.23	(118)
24.91/8.23	Obligation:
24.91/8.23	Q DP problem:
24.91/8.23	The TRS P consists of the following rules:
24.91/8.23	
24.91/8.23	   H(x, x) -> G(x, x, f(k))
24.91/8.23	   G(d, x, x) -> A^2
24.91/8.23	   A^2 -> H(f(c), f(c))
24.91/8.23	   A^2 -> H(f(d), f(d))
24.91/8.23	   A^2 -> H(U1(a, a), U1(d, d))
24.91/8.23	   A^2 -> H(U1(e, c), f(b))
24.91/8.23	   A^2 -> H(U1(k, c), f(b))
24.91/8.23	   A^2 -> H(U1(c, e), f(b))
24.91/8.23	   A^2 -> H(U1(c, k), f(b))
24.91/8.23	   A^2 -> H(U1(c, c), U1(b, b))
24.91/8.23	   A^2 -> H(U1(c, c), f(c))
24.91/8.23	   A^2 -> H(U1(c, c), f(d))
24.91/8.23	   A^2 -> H(U1(e, e), f(b))
24.91/8.23	   A^2 -> H(f(e), U1(b, b))
24.91/8.23	   A^2 -> H(f(e), f(c))
24.91/8.23	   A^2 -> H(f(e), f(d))
24.91/8.23	   A^2 -> H(U1(k, k), f(b))
24.91/8.23	   A^2 -> H(f(k), U1(b, b))
24.91/8.23	   A^2 -> H(f(k), f(c))
24.91/8.23	   A^2 -> H(f(k), f(d))
24.91/8.23	   A^2 -> H(f(c), U1(c, b))
24.91/8.23	   A^2 -> H(f(c), U1(d, b))
24.91/8.23	   A^2 -> H(f(c), U1(b, c))
24.91/8.23	   A^2 -> H(f(c), U1(b, d))
24.91/8.23	   A^2 -> H(f(c), U1(d, d))
24.91/8.23	   A^2 -> H(f(c), f(k))
24.91/8.23	   A^2 -> H(U1(k, d), f(b))
24.91/8.23	   A^2 -> H(U1(d, k), f(b))
24.91/8.23	   A^2 -> H(U1(d, d), U1(b, b))
24.91/8.23	   A^2 -> H(U1(d, d), f(c))
24.91/8.23	   A^2 -> H(U1(d, d), f(d))
24.91/8.23	   A^2 -> H(f(d), U1(c, b))
24.91/8.23	   A^2 -> H(f(d), U1(d, b))
24.91/8.23	   A^2 -> H(f(d), U1(b, c))
24.91/8.23	   A^2 -> H(f(d), U1(b, d))
24.91/8.23	   A^2 -> H(f(d), U1(c, c))
24.91/8.23	   A^2 -> H(f(d), f(e))
24.91/8.23	   A^2 -> H(f(d), f(k))
24.91/8.23	   A^2 -> H(f(a), U1(e, b))
24.91/8.23	   A^2 -> H(f(a), U1(k, b))
24.91/8.23	   A^2 -> H(f(a), U1(c, d))
24.91/8.23	   A^2 -> H(f(a), U1(d, c))
24.91/8.23	   A^2 -> H(f(a), U1(b, e))
24.91/8.23	   A^2 -> H(f(a), U1(b, k))
24.91/8.23	   A^2 -> H(f(c), U1(c, c))
24.91/8.23	   A^2 -> H(f(a), U1(e, c))
24.91/8.23	   A^2 -> H(f(a), U1(k, c))
24.91/8.23	   A^2 -> H(f(a), U1(c, e))
24.91/8.23	   A^2 -> H(f(a), U1(c, k))
24.91/8.23	   A^2 -> H(f(c), f(e))
24.91/8.23	   A^2 -> H(f(a), U1(e, e))
24.91/8.23	   A^2 -> H(f(a), U1(k, k))
24.91/8.23	   A^2 -> H(f(d), U1(d, d))
24.91/8.23	   A^2 -> H(f(a), U1(k, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, k))
25.13/8.25	   A^2 -> H(a, f(b))
25.13/8.25	   A^2 -> H(U1(e, d), f(b))
25.13/8.25	   A^2 -> H(U1(e, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, a), f(c))
25.13/8.25	   A^2 -> H(U1(e, a), f(d))
25.13/8.25	   A^2 -> H(U1(k, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, a), f(c))
25.13/8.25	   A^2 -> H(U1(k, a), f(d))
25.13/8.25	   A^2 -> H(U1(c, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, d), f(c))
25.13/8.25	   A^2 -> H(U1(c, d), f(d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(c, a), f(e))
25.13/8.25	   A^2 -> H(U1(c, a), f(k))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(d, e), f(b))
25.13/8.25	   A^2 -> H(U1(d, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, c), f(c))
25.13/8.25	   A^2 -> H(U1(d, c), f(d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(d, a), f(e))
25.13/8.25	   A^2 -> H(U1(d, a), f(k))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, e), f(c))
25.13/8.25	   A^2 -> H(U1(a, e), f(d))
25.13/8.25	   A^2 -> H(U1(a, k), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, k), f(c))
25.13/8.25	   A^2 -> H(U1(a, k), f(d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, c), f(e))
25.13/8.25	   A^2 -> H(U1(a, c), f(k))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, d), f(e))
25.13/8.25	   A^2 -> H(U1(a, d), f(k))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, k))
25.13/8.25	
25.13/8.25	The TRS R consists of the following rules:
25.13/8.25	
25.13/8.25	   f(x) -> U1(x, x)
25.13/8.25	   U1(e, x) -> x
25.13/8.25	   a -> c
25.13/8.25	   a -> d
25.13/8.25	   b -> c
25.13/8.25	   b -> d
25.13/8.25	   d -> k
25.13/8.25	   c -> e
25.13/8.25	   c -> k
25.13/8.25	
25.13/8.25	Q is empty.
25.13/8.25	We have to consider all minimal (P,Q,R)-chains.
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(119) TransformationProof (EQUIVALENT)
25.13/8.25	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
25.13/8.25	
25.13/8.25	   (A^2 -> H(U1(c, a), U1(d, d)),A^2 -> H(U1(c, a), U1(d, d)))
25.13/8.25	   (A^2 -> H(U1(d, a), U1(d, d)),A^2 -> H(U1(d, a), U1(d, d)))
25.13/8.25	   (A^2 -> H(U1(a, c), U1(d, d)),A^2 -> H(U1(a, c), U1(d, d)))
25.13/8.25	   (A^2 -> H(U1(a, d), U1(d, d)),A^2 -> H(U1(a, d), U1(d, d)))
25.13/8.25	   (A^2 -> H(U1(a, a), U1(k, d)),A^2 -> H(U1(a, a), U1(k, d)))
25.13/8.25	   (A^2 -> H(U1(a, a), U1(d, k)),A^2 -> H(U1(a, a), U1(d, k)))
25.13/8.25	
25.13/8.25	
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(120)
25.13/8.25	Obligation:
25.13/8.25	Q DP problem:
25.13/8.25	The TRS P consists of the following rules:
25.13/8.25	
25.13/8.25	   H(x, x) -> G(x, x, f(k))
25.13/8.25	   G(d, x, x) -> A^2
25.13/8.25	   A^2 -> H(f(c), f(c))
25.13/8.25	   A^2 -> H(f(d), f(d))
25.13/8.25	   A^2 -> H(U1(e, c), f(b))
25.13/8.25	   A^2 -> H(U1(k, c), f(b))
25.13/8.25	   A^2 -> H(U1(c, e), f(b))
25.13/8.25	   A^2 -> H(U1(c, k), f(b))
25.13/8.25	   A^2 -> H(U1(c, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, c), f(c))
25.13/8.25	   A^2 -> H(U1(c, c), f(d))
25.13/8.25	   A^2 -> H(U1(e, e), f(b))
25.13/8.25	   A^2 -> H(f(e), U1(b, b))
25.13/8.25	   A^2 -> H(f(e), f(c))
25.13/8.25	   A^2 -> H(f(e), f(d))
25.13/8.25	   A^2 -> H(U1(k, k), f(b))
25.13/8.25	   A^2 -> H(f(k), U1(b, b))
25.13/8.25	   A^2 -> H(f(k), f(c))
25.13/8.25	   A^2 -> H(f(k), f(d))
25.13/8.25	   A^2 -> H(f(c), U1(c, b))
25.13/8.25	   A^2 -> H(f(c), U1(d, b))
25.13/8.25	   A^2 -> H(f(c), U1(b, c))
25.13/8.25	   A^2 -> H(f(c), U1(b, d))
25.13/8.25	   A^2 -> H(f(c), U1(d, d))
25.13/8.25	   A^2 -> H(f(c), f(k))
25.13/8.25	   A^2 -> H(U1(k, d), f(b))
25.13/8.25	   A^2 -> H(U1(d, k), f(b))
25.13/8.25	   A^2 -> H(U1(d, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, d), f(c))
25.13/8.25	   A^2 -> H(U1(d, d), f(d))
25.13/8.25	   A^2 -> H(f(d), U1(c, b))
25.13/8.25	   A^2 -> H(f(d), U1(d, b))
25.13/8.25	   A^2 -> H(f(d), U1(b, c))
25.13/8.25	   A^2 -> H(f(d), U1(b, d))
25.13/8.25	   A^2 -> H(f(d), U1(c, c))
25.13/8.25	   A^2 -> H(f(d), f(e))
25.13/8.25	   A^2 -> H(f(d), f(k))
25.13/8.25	   A^2 -> H(f(a), U1(e, b))
25.13/8.25	   A^2 -> H(f(a), U1(k, b))
25.13/8.25	   A^2 -> H(f(a), U1(c, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, c))
25.13/8.25	   A^2 -> H(f(a), U1(b, e))
25.13/8.25	   A^2 -> H(f(a), U1(b, k))
25.13/8.25	   A^2 -> H(f(c), U1(c, c))
25.13/8.25	   A^2 -> H(f(a), U1(e, c))
25.13/8.25	   A^2 -> H(f(a), U1(k, c))
25.13/8.25	   A^2 -> H(f(a), U1(c, e))
25.13/8.25	   A^2 -> H(f(a), U1(c, k))
25.13/8.25	   A^2 -> H(f(c), f(e))
25.13/8.25	   A^2 -> H(f(a), U1(e, e))
25.13/8.25	   A^2 -> H(f(a), U1(k, k))
25.13/8.25	   A^2 -> H(f(d), U1(d, d))
25.13/8.25	   A^2 -> H(f(a), U1(k, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, k))
25.13/8.25	   A^2 -> H(a, f(b))
25.13/8.25	   A^2 -> H(U1(e, d), f(b))
25.13/8.25	   A^2 -> H(U1(e, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, a), f(c))
25.13/8.25	   A^2 -> H(U1(e, a), f(d))
25.13/8.25	   A^2 -> H(U1(k, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, a), f(c))
25.13/8.25	   A^2 -> H(U1(k, a), f(d))
25.13/8.25	   A^2 -> H(U1(c, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, d), f(c))
25.13/8.25	   A^2 -> H(U1(c, d), f(d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(c, a), f(e))
25.13/8.25	   A^2 -> H(U1(c, a), f(k))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(d, e), f(b))
25.13/8.25	   A^2 -> H(U1(d, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, c), f(c))
25.13/8.25	   A^2 -> H(U1(d, c), f(d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(d, a), f(e))
25.13/8.25	   A^2 -> H(U1(d, a), f(k))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, e), f(c))
25.13/8.25	   A^2 -> H(U1(a, e), f(d))
25.13/8.25	   A^2 -> H(U1(a, k), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, k), f(c))
25.13/8.25	   A^2 -> H(U1(a, k), f(d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, c), f(e))
25.13/8.25	   A^2 -> H(U1(a, c), f(k))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, d), f(e))
25.13/8.25	   A^2 -> H(U1(a, d), f(k))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, k))
25.13/8.25	
25.13/8.25	The TRS R consists of the following rules:
25.13/8.25	
25.13/8.25	   f(x) -> U1(x, x)
25.13/8.25	   U1(e, x) -> x
25.13/8.25	   a -> c
25.13/8.25	   a -> d
25.13/8.25	   b -> c
25.13/8.25	   b -> d
25.13/8.25	   d -> k
25.13/8.25	   c -> e
25.13/8.25	   c -> k
25.13/8.25	
25.13/8.25	Q is empty.
25.13/8.25	We have to consider all minimal (P,Q,R)-chains.
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(121) TransformationProof (EQUIVALENT)
25.13/8.25	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), f(b)) at position [] we obtained the following new rules [LPAR04]:
25.13/8.25	
25.13/8.25	   (A^2 -> H(c, f(b)),A^2 -> H(c, f(b)))
25.13/8.25	   (A^2 -> H(U1(e, e), f(b)),A^2 -> H(U1(e, e), f(b)))
25.13/8.25	   (A^2 -> H(U1(e, k), f(b)),A^2 -> H(U1(e, k), f(b)))
25.13/8.25	   (A^2 -> H(U1(e, c), U1(b, b)),A^2 -> H(U1(e, c), U1(b, b)))
25.13/8.25	   (A^2 -> H(U1(e, c), f(c)),A^2 -> H(U1(e, c), f(c)))
25.13/8.25	   (A^2 -> H(U1(e, c), f(d)),A^2 -> H(U1(e, c), f(d)))
25.13/8.25	
25.13/8.25	
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(122)
25.13/8.25	Obligation:
25.13/8.25	Q DP problem:
25.13/8.25	The TRS P consists of the following rules:
25.13/8.25	
25.13/8.25	   H(x, x) -> G(x, x, f(k))
25.13/8.25	   G(d, x, x) -> A^2
25.13/8.25	   A^2 -> H(f(c), f(c))
25.13/8.25	   A^2 -> H(f(d), f(d))
25.13/8.25	   A^2 -> H(U1(k, c), f(b))
25.13/8.25	   A^2 -> H(U1(c, e), f(b))
25.13/8.25	   A^2 -> H(U1(c, k), f(b))
25.13/8.25	   A^2 -> H(U1(c, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, c), f(c))
25.13/8.25	   A^2 -> H(U1(c, c), f(d))
25.13/8.25	   A^2 -> H(U1(e, e), f(b))
25.13/8.25	   A^2 -> H(f(e), U1(b, b))
25.13/8.25	   A^2 -> H(f(e), f(c))
25.13/8.25	   A^2 -> H(f(e), f(d))
25.13/8.25	   A^2 -> H(U1(k, k), f(b))
25.13/8.25	   A^2 -> H(f(k), U1(b, b))
25.13/8.25	   A^2 -> H(f(k), f(c))
25.13/8.25	   A^2 -> H(f(k), f(d))
25.13/8.25	   A^2 -> H(f(c), U1(c, b))
25.13/8.25	   A^2 -> H(f(c), U1(d, b))
25.13/8.25	   A^2 -> H(f(c), U1(b, c))
25.13/8.25	   A^2 -> H(f(c), U1(b, d))
25.13/8.25	   A^2 -> H(f(c), U1(d, d))
25.13/8.25	   A^2 -> H(f(c), f(k))
25.13/8.25	   A^2 -> H(U1(k, d), f(b))
25.13/8.25	   A^2 -> H(U1(d, k), f(b))
25.13/8.25	   A^2 -> H(U1(d, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, d), f(c))
25.13/8.25	   A^2 -> H(U1(d, d), f(d))
25.13/8.25	   A^2 -> H(f(d), U1(c, b))
25.13/8.25	   A^2 -> H(f(d), U1(d, b))
25.13/8.25	   A^2 -> H(f(d), U1(b, c))
25.13/8.25	   A^2 -> H(f(d), U1(b, d))
25.13/8.25	   A^2 -> H(f(d), U1(c, c))
25.13/8.25	   A^2 -> H(f(d), f(e))
25.13/8.25	   A^2 -> H(f(d), f(k))
25.13/8.25	   A^2 -> H(f(a), U1(e, b))
25.13/8.25	   A^2 -> H(f(a), U1(k, b))
25.13/8.25	   A^2 -> H(f(a), U1(c, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, c))
25.13/8.25	   A^2 -> H(f(a), U1(b, e))
25.13/8.25	   A^2 -> H(f(a), U1(b, k))
25.13/8.25	   A^2 -> H(f(c), U1(c, c))
25.13/8.25	   A^2 -> H(f(a), U1(e, c))
25.13/8.25	   A^2 -> H(f(a), U1(k, c))
25.13/8.25	   A^2 -> H(f(a), U1(c, e))
25.13/8.25	   A^2 -> H(f(a), U1(c, k))
25.13/8.25	   A^2 -> H(f(c), f(e))
25.13/8.25	   A^2 -> H(f(a), U1(e, e))
25.13/8.25	   A^2 -> H(f(a), U1(k, k))
25.13/8.25	   A^2 -> H(f(d), U1(d, d))
25.13/8.25	   A^2 -> H(f(a), U1(k, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, k))
25.13/8.25	   A^2 -> H(a, f(b))
25.13/8.25	   A^2 -> H(U1(e, d), f(b))
25.13/8.25	   A^2 -> H(U1(e, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, a), f(c))
25.13/8.25	   A^2 -> H(U1(e, a), f(d))
25.13/8.25	   A^2 -> H(U1(k, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, a), f(c))
25.13/8.25	   A^2 -> H(U1(k, a), f(d))
25.13/8.25	   A^2 -> H(U1(c, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, d), f(c))
25.13/8.25	   A^2 -> H(U1(c, d), f(d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(c, a), f(e))
25.13/8.25	   A^2 -> H(U1(c, a), f(k))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(d, e), f(b))
25.13/8.25	   A^2 -> H(U1(d, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, c), f(c))
25.13/8.25	   A^2 -> H(U1(d, c), f(d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(d, a), f(e))
25.13/8.25	   A^2 -> H(U1(d, a), f(k))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, e), f(c))
25.13/8.25	   A^2 -> H(U1(a, e), f(d))
25.13/8.25	   A^2 -> H(U1(a, k), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, k), f(c))
25.13/8.25	   A^2 -> H(U1(a, k), f(d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, c), f(e))
25.13/8.25	   A^2 -> H(U1(a, c), f(k))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, d), f(e))
25.13/8.25	   A^2 -> H(U1(a, d), f(k))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, k))
25.13/8.25	   A^2 -> H(c, f(b))
25.13/8.25	   A^2 -> H(U1(e, k), f(b))
25.13/8.25	   A^2 -> H(U1(e, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, c), f(c))
25.13/8.25	   A^2 -> H(U1(e, c), f(d))
25.13/8.25	
25.13/8.25	The TRS R consists of the following rules:
25.13/8.25	
25.13/8.25	   f(x) -> U1(x, x)
25.13/8.25	   U1(e, x) -> x
25.13/8.25	   a -> c
25.13/8.25	   a -> d
25.13/8.25	   b -> c
25.13/8.25	   b -> d
25.13/8.25	   d -> k
25.13/8.25	   c -> e
25.13/8.25	   c -> k
25.13/8.25	
25.13/8.25	Q is empty.
25.13/8.25	We have to consider all minimal (P,Q,R)-chains.
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(123) TransformationProof (EQUIVALENT)
25.13/8.25	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), f(b)) at position [] we obtained the following new rules [LPAR04]:
25.13/8.25	
25.13/8.25	   (A^2 -> H(U1(k, e), f(b)),A^2 -> H(U1(k, e), f(b)))
25.13/8.25	   (A^2 -> H(U1(k, k), f(b)),A^2 -> H(U1(k, k), f(b)))
25.13/8.25	   (A^2 -> H(U1(k, c), U1(b, b)),A^2 -> H(U1(k, c), U1(b, b)))
25.13/8.25	   (A^2 -> H(U1(k, c), f(c)),A^2 -> H(U1(k, c), f(c)))
25.13/8.25	   (A^2 -> H(U1(k, c), f(d)),A^2 -> H(U1(k, c), f(d)))
25.13/8.25	
25.13/8.25	
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(124)
25.13/8.25	Obligation:
25.13/8.25	Q DP problem:
25.13/8.25	The TRS P consists of the following rules:
25.13/8.25	
25.13/8.25	   H(x, x) -> G(x, x, f(k))
25.13/8.25	   G(d, x, x) -> A^2
25.13/8.25	   A^2 -> H(f(c), f(c))
25.13/8.25	   A^2 -> H(f(d), f(d))
25.13/8.25	   A^2 -> H(U1(c, e), f(b))
25.13/8.25	   A^2 -> H(U1(c, k), f(b))
25.13/8.25	   A^2 -> H(U1(c, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, c), f(c))
25.13/8.25	   A^2 -> H(U1(c, c), f(d))
25.13/8.25	   A^2 -> H(U1(e, e), f(b))
25.13/8.25	   A^2 -> H(f(e), U1(b, b))
25.13/8.25	   A^2 -> H(f(e), f(c))
25.13/8.25	   A^2 -> H(f(e), f(d))
25.13/8.25	   A^2 -> H(U1(k, k), f(b))
25.13/8.25	   A^2 -> H(f(k), U1(b, b))
25.13/8.25	   A^2 -> H(f(k), f(c))
25.13/8.25	   A^2 -> H(f(k), f(d))
25.13/8.25	   A^2 -> H(f(c), U1(c, b))
25.13/8.25	   A^2 -> H(f(c), U1(d, b))
25.13/8.25	   A^2 -> H(f(c), U1(b, c))
25.13/8.25	   A^2 -> H(f(c), U1(b, d))
25.13/8.25	   A^2 -> H(f(c), U1(d, d))
25.13/8.25	   A^2 -> H(f(c), f(k))
25.13/8.25	   A^2 -> H(U1(k, d), f(b))
25.13/8.25	   A^2 -> H(U1(d, k), f(b))
25.13/8.25	   A^2 -> H(U1(d, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, d), f(c))
25.13/8.25	   A^2 -> H(U1(d, d), f(d))
25.13/8.25	   A^2 -> H(f(d), U1(c, b))
25.13/8.25	   A^2 -> H(f(d), U1(d, b))
25.13/8.25	   A^2 -> H(f(d), U1(b, c))
25.13/8.25	   A^2 -> H(f(d), U1(b, d))
25.13/8.25	   A^2 -> H(f(d), U1(c, c))
25.13/8.25	   A^2 -> H(f(d), f(e))
25.13/8.25	   A^2 -> H(f(d), f(k))
25.13/8.25	   A^2 -> H(f(a), U1(e, b))
25.13/8.25	   A^2 -> H(f(a), U1(k, b))
25.13/8.25	   A^2 -> H(f(a), U1(c, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, c))
25.13/8.25	   A^2 -> H(f(a), U1(b, e))
25.13/8.25	   A^2 -> H(f(a), U1(b, k))
25.13/8.25	   A^2 -> H(f(c), U1(c, c))
25.13/8.25	   A^2 -> H(f(a), U1(e, c))
25.13/8.25	   A^2 -> H(f(a), U1(k, c))
25.13/8.25	   A^2 -> H(f(a), U1(c, e))
25.13/8.25	   A^2 -> H(f(a), U1(c, k))
25.13/8.25	   A^2 -> H(f(c), f(e))
25.13/8.25	   A^2 -> H(f(a), U1(e, e))
25.13/8.25	   A^2 -> H(f(a), U1(k, k))
25.13/8.25	   A^2 -> H(f(d), U1(d, d))
25.13/8.25	   A^2 -> H(f(a), U1(k, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, k))
25.13/8.25	   A^2 -> H(a, f(b))
25.13/8.25	   A^2 -> H(U1(e, d), f(b))
25.13/8.25	   A^2 -> H(U1(e, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, a), f(c))
25.13/8.25	   A^2 -> H(U1(e, a), f(d))
25.13/8.25	   A^2 -> H(U1(k, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, a), f(c))
25.13/8.25	   A^2 -> H(U1(k, a), f(d))
25.13/8.25	   A^2 -> H(U1(c, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, d), f(c))
25.13/8.25	   A^2 -> H(U1(c, d), f(d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(c, a), f(e))
25.13/8.25	   A^2 -> H(U1(c, a), f(k))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(d, e), f(b))
25.13/8.25	   A^2 -> H(U1(d, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, c), f(c))
25.13/8.25	   A^2 -> H(U1(d, c), f(d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(d, a), f(e))
25.13/8.25	   A^2 -> H(U1(d, a), f(k))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, e), f(c))
25.13/8.25	   A^2 -> H(U1(a, e), f(d))
25.13/8.25	   A^2 -> H(U1(a, k), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, k), f(c))
25.13/8.25	   A^2 -> H(U1(a, k), f(d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, c), f(e))
25.13/8.25	   A^2 -> H(U1(a, c), f(k))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, d), f(e))
25.13/8.25	   A^2 -> H(U1(a, d), f(k))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, k))
25.13/8.25	   A^2 -> H(c, f(b))
25.13/8.25	   A^2 -> H(U1(e, k), f(b))
25.13/8.25	   A^2 -> H(U1(e, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, c), f(c))
25.13/8.25	   A^2 -> H(U1(e, c), f(d))
25.13/8.25	   A^2 -> H(U1(k, e), f(b))
25.13/8.25	   A^2 -> H(U1(k, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, c), f(c))
25.13/8.25	   A^2 -> H(U1(k, c), f(d))
25.13/8.25	
25.13/8.25	The TRS R consists of the following rules:
25.13/8.25	
25.13/8.25	   f(x) -> U1(x, x)
25.13/8.25	   U1(e, x) -> x
25.13/8.25	   a -> c
25.13/8.25	   a -> d
25.13/8.25	   b -> c
25.13/8.25	   b -> d
25.13/8.25	   d -> k
25.13/8.25	   c -> e
25.13/8.25	   c -> k
25.13/8.25	
25.13/8.25	Q is empty.
25.13/8.25	We have to consider all minimal (P,Q,R)-chains.
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(125) TransformationProof (EQUIVALENT)
25.13/8.25	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), f(b)) at position [] we obtained the following new rules [LPAR04]:
25.13/8.25	
25.13/8.25	   (A^2 -> H(U1(e, e), f(b)),A^2 -> H(U1(e, e), f(b)))
25.13/8.25	   (A^2 -> H(U1(k, e), f(b)),A^2 -> H(U1(k, e), f(b)))
25.13/8.25	   (A^2 -> H(U1(c, e), U1(b, b)),A^2 -> H(U1(c, e), U1(b, b)))
25.13/8.25	   (A^2 -> H(U1(c, e), f(c)),A^2 -> H(U1(c, e), f(c)))
25.13/8.25	   (A^2 -> H(U1(c, e), f(d)),A^2 -> H(U1(c, e), f(d)))
25.13/8.25	
25.13/8.25	
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(126)
25.13/8.25	Obligation:
25.13/8.25	Q DP problem:
25.13/8.25	The TRS P consists of the following rules:
25.13/8.25	
25.13/8.25	   H(x, x) -> G(x, x, f(k))
25.13/8.25	   G(d, x, x) -> A^2
25.13/8.25	   A^2 -> H(f(c), f(c))
25.13/8.25	   A^2 -> H(f(d), f(d))
25.13/8.25	   A^2 -> H(U1(c, k), f(b))
25.13/8.25	   A^2 -> H(U1(c, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, c), f(c))
25.13/8.25	   A^2 -> H(U1(c, c), f(d))
25.13/8.25	   A^2 -> H(U1(e, e), f(b))
25.13/8.25	   A^2 -> H(f(e), U1(b, b))
25.13/8.25	   A^2 -> H(f(e), f(c))
25.13/8.25	   A^2 -> H(f(e), f(d))
25.13/8.25	   A^2 -> H(U1(k, k), f(b))
25.13/8.25	   A^2 -> H(f(k), U1(b, b))
25.13/8.25	   A^2 -> H(f(k), f(c))
25.13/8.25	   A^2 -> H(f(k), f(d))
25.13/8.25	   A^2 -> H(f(c), U1(c, b))
25.13/8.25	   A^2 -> H(f(c), U1(d, b))
25.13/8.25	   A^2 -> H(f(c), U1(b, c))
25.13/8.25	   A^2 -> H(f(c), U1(b, d))
25.13/8.25	   A^2 -> H(f(c), U1(d, d))
25.13/8.25	   A^2 -> H(f(c), f(k))
25.13/8.25	   A^2 -> H(U1(k, d), f(b))
25.13/8.25	   A^2 -> H(U1(d, k), f(b))
25.13/8.25	   A^2 -> H(U1(d, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, d), f(c))
25.13/8.25	   A^2 -> H(U1(d, d), f(d))
25.13/8.25	   A^2 -> H(f(d), U1(c, b))
25.13/8.25	   A^2 -> H(f(d), U1(d, b))
25.13/8.25	   A^2 -> H(f(d), U1(b, c))
25.13/8.25	   A^2 -> H(f(d), U1(b, d))
25.13/8.25	   A^2 -> H(f(d), U1(c, c))
25.13/8.25	   A^2 -> H(f(d), f(e))
25.13/8.25	   A^2 -> H(f(d), f(k))
25.13/8.25	   A^2 -> H(f(a), U1(e, b))
25.13/8.25	   A^2 -> H(f(a), U1(k, b))
25.13/8.25	   A^2 -> H(f(a), U1(c, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, c))
25.13/8.25	   A^2 -> H(f(a), U1(b, e))
25.13/8.25	   A^2 -> H(f(a), U1(b, k))
25.13/8.25	   A^2 -> H(f(c), U1(c, c))
25.13/8.25	   A^2 -> H(f(a), U1(e, c))
25.13/8.25	   A^2 -> H(f(a), U1(k, c))
25.13/8.25	   A^2 -> H(f(a), U1(c, e))
25.13/8.25	   A^2 -> H(f(a), U1(c, k))
25.13/8.25	   A^2 -> H(f(c), f(e))
25.13/8.25	   A^2 -> H(f(a), U1(e, e))
25.13/8.25	   A^2 -> H(f(a), U1(k, k))
25.13/8.25	   A^2 -> H(f(d), U1(d, d))
25.13/8.25	   A^2 -> H(f(a), U1(k, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, k))
25.13/8.25	   A^2 -> H(a, f(b))
25.13/8.25	   A^2 -> H(U1(e, d), f(b))
25.13/8.25	   A^2 -> H(U1(e, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, a), f(c))
25.13/8.25	   A^2 -> H(U1(e, a), f(d))
25.13/8.25	   A^2 -> H(U1(k, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, a), f(c))
25.13/8.25	   A^2 -> H(U1(k, a), f(d))
25.13/8.25	   A^2 -> H(U1(c, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, d), f(c))
25.13/8.25	   A^2 -> H(U1(c, d), f(d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(c, a), f(e))
25.13/8.25	   A^2 -> H(U1(c, a), f(k))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(d, e), f(b))
25.13/8.25	   A^2 -> H(U1(d, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, c), f(c))
25.13/8.25	   A^2 -> H(U1(d, c), f(d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(d, a), f(e))
25.13/8.25	   A^2 -> H(U1(d, a), f(k))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, e), f(c))
25.13/8.25	   A^2 -> H(U1(a, e), f(d))
25.13/8.25	   A^2 -> H(U1(a, k), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, k), f(c))
25.13/8.25	   A^2 -> H(U1(a, k), f(d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, c), f(e))
25.13/8.25	   A^2 -> H(U1(a, c), f(k))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, d), f(e))
25.13/8.25	   A^2 -> H(U1(a, d), f(k))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, k))
25.13/8.25	   A^2 -> H(c, f(b))
25.13/8.25	   A^2 -> H(U1(e, k), f(b))
25.13/8.25	   A^2 -> H(U1(e, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, c), f(c))
25.13/8.25	   A^2 -> H(U1(e, c), f(d))
25.13/8.25	   A^2 -> H(U1(k, e), f(b))
25.13/8.25	   A^2 -> H(U1(k, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, c), f(c))
25.13/8.25	   A^2 -> H(U1(k, c), f(d))
25.13/8.25	   A^2 -> H(U1(c, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, e), f(c))
25.13/8.25	   A^2 -> H(U1(c, e), f(d))
25.13/8.25	
25.13/8.25	The TRS R consists of the following rules:
25.13/8.25	
25.13/8.25	   f(x) -> U1(x, x)
25.13/8.25	   U1(e, x) -> x
25.13/8.25	   a -> c
25.13/8.25	   a -> d
25.13/8.25	   b -> c
25.13/8.25	   b -> d
25.13/8.25	   d -> k
25.13/8.25	   c -> e
25.13/8.25	   c -> k
25.13/8.25	
25.13/8.25	Q is empty.
25.13/8.25	We have to consider all minimal (P,Q,R)-chains.
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(127) TransformationProof (EQUIVALENT)
25.13/8.25	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), f(b)) at position [] we obtained the following new rules [LPAR04]:
25.13/8.25	
25.13/8.25	   (A^2 -> H(U1(e, k), f(b)),A^2 -> H(U1(e, k), f(b)))
25.13/8.25	   (A^2 -> H(U1(k, k), f(b)),A^2 -> H(U1(k, k), f(b)))
25.13/8.25	   (A^2 -> H(U1(c, k), U1(b, b)),A^2 -> H(U1(c, k), U1(b, b)))
25.13/8.25	   (A^2 -> H(U1(c, k), f(c)),A^2 -> H(U1(c, k), f(c)))
25.13/8.25	   (A^2 -> H(U1(c, k), f(d)),A^2 -> H(U1(c, k), f(d)))
25.13/8.25	
25.13/8.25	
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(128)
25.13/8.25	Obligation:
25.13/8.25	Q DP problem:
25.13/8.25	The TRS P consists of the following rules:
25.13/8.25	
25.13/8.25	   H(x, x) -> G(x, x, f(k))
25.13/8.25	   G(d, x, x) -> A^2
25.13/8.25	   A^2 -> H(f(c), f(c))
25.13/8.25	   A^2 -> H(f(d), f(d))
25.13/8.25	   A^2 -> H(U1(c, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, c), f(c))
25.13/8.25	   A^2 -> H(U1(c, c), f(d))
25.13/8.25	   A^2 -> H(U1(e, e), f(b))
25.13/8.25	   A^2 -> H(f(e), U1(b, b))
25.13/8.25	   A^2 -> H(f(e), f(c))
25.13/8.25	   A^2 -> H(f(e), f(d))
25.13/8.25	   A^2 -> H(U1(k, k), f(b))
25.13/8.25	   A^2 -> H(f(k), U1(b, b))
25.13/8.25	   A^2 -> H(f(k), f(c))
25.13/8.25	   A^2 -> H(f(k), f(d))
25.13/8.25	   A^2 -> H(f(c), U1(c, b))
25.13/8.25	   A^2 -> H(f(c), U1(d, b))
25.13/8.25	   A^2 -> H(f(c), U1(b, c))
25.13/8.25	   A^2 -> H(f(c), U1(b, d))
25.13/8.25	   A^2 -> H(f(c), U1(d, d))
25.13/8.25	   A^2 -> H(f(c), f(k))
25.13/8.25	   A^2 -> H(U1(k, d), f(b))
25.13/8.25	   A^2 -> H(U1(d, k), f(b))
25.13/8.25	   A^2 -> H(U1(d, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, d), f(c))
25.13/8.25	   A^2 -> H(U1(d, d), f(d))
25.13/8.25	   A^2 -> H(f(d), U1(c, b))
25.13/8.25	   A^2 -> H(f(d), U1(d, b))
25.13/8.25	   A^2 -> H(f(d), U1(b, c))
25.13/8.25	   A^2 -> H(f(d), U1(b, d))
25.13/8.25	   A^2 -> H(f(d), U1(c, c))
25.13/8.25	   A^2 -> H(f(d), f(e))
25.13/8.25	   A^2 -> H(f(d), f(k))
25.13/8.25	   A^2 -> H(f(a), U1(e, b))
25.13/8.25	   A^2 -> H(f(a), U1(k, b))
25.13/8.25	   A^2 -> H(f(a), U1(c, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, c))
25.13/8.25	   A^2 -> H(f(a), U1(b, e))
25.13/8.25	   A^2 -> H(f(a), U1(b, k))
25.13/8.25	   A^2 -> H(f(c), U1(c, c))
25.13/8.25	   A^2 -> H(f(a), U1(e, c))
25.13/8.25	   A^2 -> H(f(a), U1(k, c))
25.13/8.25	   A^2 -> H(f(a), U1(c, e))
25.13/8.25	   A^2 -> H(f(a), U1(c, k))
25.13/8.25	   A^2 -> H(f(c), f(e))
25.13/8.25	   A^2 -> H(f(a), U1(e, e))
25.13/8.25	   A^2 -> H(f(a), U1(k, k))
25.13/8.25	   A^2 -> H(f(d), U1(d, d))
25.13/8.25	   A^2 -> H(f(a), U1(k, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, k))
25.13/8.25	   A^2 -> H(a, f(b))
25.13/8.25	   A^2 -> H(U1(e, d), f(b))
25.13/8.25	   A^2 -> H(U1(e, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, a), f(c))
25.13/8.25	   A^2 -> H(U1(e, a), f(d))
25.13/8.25	   A^2 -> H(U1(k, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, a), f(c))
25.13/8.25	   A^2 -> H(U1(k, a), f(d))
25.13/8.25	   A^2 -> H(U1(c, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, d), f(c))
25.13/8.25	   A^2 -> H(U1(c, d), f(d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(c, a), f(e))
25.13/8.25	   A^2 -> H(U1(c, a), f(k))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(d, e), f(b))
25.13/8.25	   A^2 -> H(U1(d, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, c), f(c))
25.13/8.25	   A^2 -> H(U1(d, c), f(d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(d, a), f(e))
25.13/8.25	   A^2 -> H(U1(d, a), f(k))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, e), f(c))
25.13/8.25	   A^2 -> H(U1(a, e), f(d))
25.13/8.25	   A^2 -> H(U1(a, k), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, k), f(c))
25.13/8.25	   A^2 -> H(U1(a, k), f(d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, c), f(e))
25.13/8.25	   A^2 -> H(U1(a, c), f(k))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, d), f(e))
25.13/8.25	   A^2 -> H(U1(a, d), f(k))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, k))
25.13/8.25	   A^2 -> H(c, f(b))
25.13/8.25	   A^2 -> H(U1(e, k), f(b))
25.13/8.25	   A^2 -> H(U1(e, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, c), f(c))
25.13/8.25	   A^2 -> H(U1(e, c), f(d))
25.13/8.25	   A^2 -> H(U1(k, e), f(b))
25.13/8.25	   A^2 -> H(U1(k, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, c), f(c))
25.13/8.25	   A^2 -> H(U1(k, c), f(d))
25.13/8.25	   A^2 -> H(U1(c, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, e), f(c))
25.13/8.25	   A^2 -> H(U1(c, e), f(d))
25.13/8.25	   A^2 -> H(U1(c, k), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, k), f(c))
25.13/8.25	   A^2 -> H(U1(c, k), f(d))
25.13/8.25	
25.13/8.25	The TRS R consists of the following rules:
25.13/8.25	
25.13/8.25	   f(x) -> U1(x, x)
25.13/8.25	   U1(e, x) -> x
25.13/8.25	   a -> c
25.13/8.25	   a -> d
25.13/8.25	   b -> c
25.13/8.25	   b -> d
25.13/8.25	   d -> k
25.13/8.25	   c -> e
25.13/8.25	   c -> k
25.13/8.25	
25.13/8.25	Q is empty.
25.13/8.25	We have to consider all minimal (P,Q,R)-chains.
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(129) TransformationProof (EQUIVALENT)
25.13/8.25	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
25.13/8.25	
25.13/8.25	   (A^2 -> H(U1(e, c), U1(b, b)),A^2 -> H(U1(e, c), U1(b, b)))
25.13/8.25	   (A^2 -> H(U1(k, c), U1(b, b)),A^2 -> H(U1(k, c), U1(b, b)))
25.13/8.25	   (A^2 -> H(U1(c, e), U1(b, b)),A^2 -> H(U1(c, e), U1(b, b)))
25.13/8.25	   (A^2 -> H(U1(c, k), U1(b, b)),A^2 -> H(U1(c, k), U1(b, b)))
25.13/8.25	   (A^2 -> H(U1(c, c), U1(c, b)),A^2 -> H(U1(c, c), U1(c, b)))
25.13/8.25	   (A^2 -> H(U1(c, c), U1(d, b)),A^2 -> H(U1(c, c), U1(d, b)))
25.13/8.25	   (A^2 -> H(U1(c, c), U1(b, c)),A^2 -> H(U1(c, c), U1(b, c)))
25.13/8.25	   (A^2 -> H(U1(c, c), U1(b, d)),A^2 -> H(U1(c, c), U1(b, d)))
25.13/8.25	
25.13/8.25	
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(130)
25.13/8.25	Obligation:
25.13/8.25	Q DP problem:
25.13/8.25	The TRS P consists of the following rules:
25.13/8.25	
25.13/8.25	   H(x, x) -> G(x, x, f(k))
25.13/8.25	   G(d, x, x) -> A^2
25.13/8.25	   A^2 -> H(f(c), f(c))
25.13/8.25	   A^2 -> H(f(d), f(d))
25.13/8.25	   A^2 -> H(U1(c, c), f(c))
25.13/8.25	   A^2 -> H(U1(c, c), f(d))
25.13/8.25	   A^2 -> H(U1(e, e), f(b))
25.13/8.25	   A^2 -> H(f(e), U1(b, b))
25.13/8.25	   A^2 -> H(f(e), f(c))
25.13/8.25	   A^2 -> H(f(e), f(d))
25.13/8.25	   A^2 -> H(U1(k, k), f(b))
25.13/8.25	   A^2 -> H(f(k), U1(b, b))
25.13/8.25	   A^2 -> H(f(k), f(c))
25.13/8.25	   A^2 -> H(f(k), f(d))
25.13/8.25	   A^2 -> H(f(c), U1(c, b))
25.13/8.25	   A^2 -> H(f(c), U1(d, b))
25.13/8.25	   A^2 -> H(f(c), U1(b, c))
25.13/8.25	   A^2 -> H(f(c), U1(b, d))
25.13/8.25	   A^2 -> H(f(c), U1(d, d))
25.13/8.25	   A^2 -> H(f(c), f(k))
25.13/8.25	   A^2 -> H(U1(k, d), f(b))
25.13/8.25	   A^2 -> H(U1(d, k), f(b))
25.13/8.25	   A^2 -> H(U1(d, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, d), f(c))
25.13/8.25	   A^2 -> H(U1(d, d), f(d))
25.13/8.25	   A^2 -> H(f(d), U1(c, b))
25.13/8.25	   A^2 -> H(f(d), U1(d, b))
25.13/8.25	   A^2 -> H(f(d), U1(b, c))
25.13/8.25	   A^2 -> H(f(d), U1(b, d))
25.13/8.25	   A^2 -> H(f(d), U1(c, c))
25.13/8.25	   A^2 -> H(f(d), f(e))
25.13/8.25	   A^2 -> H(f(d), f(k))
25.13/8.25	   A^2 -> H(f(a), U1(e, b))
25.13/8.25	   A^2 -> H(f(a), U1(k, b))
25.13/8.25	   A^2 -> H(f(a), U1(c, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, c))
25.13/8.25	   A^2 -> H(f(a), U1(b, e))
25.13/8.25	   A^2 -> H(f(a), U1(b, k))
25.13/8.25	   A^2 -> H(f(c), U1(c, c))
25.13/8.25	   A^2 -> H(f(a), U1(e, c))
25.13/8.25	   A^2 -> H(f(a), U1(k, c))
25.13/8.25	   A^2 -> H(f(a), U1(c, e))
25.13/8.25	   A^2 -> H(f(a), U1(c, k))
25.13/8.25	   A^2 -> H(f(c), f(e))
25.13/8.25	   A^2 -> H(f(a), U1(e, e))
25.13/8.25	   A^2 -> H(f(a), U1(k, k))
25.13/8.25	   A^2 -> H(f(d), U1(d, d))
25.13/8.25	   A^2 -> H(f(a), U1(k, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, k))
25.13/8.25	   A^2 -> H(a, f(b))
25.13/8.25	   A^2 -> H(U1(e, d), f(b))
25.13/8.25	   A^2 -> H(U1(e, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, a), f(c))
25.13/8.25	   A^2 -> H(U1(e, a), f(d))
25.13/8.25	   A^2 -> H(U1(k, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, a), f(c))
25.13/8.25	   A^2 -> H(U1(k, a), f(d))
25.13/8.25	   A^2 -> H(U1(c, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, d), f(c))
25.13/8.25	   A^2 -> H(U1(c, d), f(d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(c, a), f(e))
25.13/8.25	   A^2 -> H(U1(c, a), f(k))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(d, e), f(b))
25.13/8.25	   A^2 -> H(U1(d, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, c), f(c))
25.13/8.25	   A^2 -> H(U1(d, c), f(d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(d, a), f(e))
25.13/8.25	   A^2 -> H(U1(d, a), f(k))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, e), f(c))
25.13/8.25	   A^2 -> H(U1(a, e), f(d))
25.13/8.25	   A^2 -> H(U1(a, k), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, k), f(c))
25.13/8.25	   A^2 -> H(U1(a, k), f(d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, c), f(e))
25.13/8.25	   A^2 -> H(U1(a, c), f(k))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, d), f(e))
25.13/8.25	   A^2 -> H(U1(a, d), f(k))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, k))
25.13/8.25	   A^2 -> H(c, f(b))
25.13/8.25	   A^2 -> H(U1(e, k), f(b))
25.13/8.25	   A^2 -> H(U1(e, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, c), f(c))
25.13/8.25	   A^2 -> H(U1(e, c), f(d))
25.13/8.25	   A^2 -> H(U1(k, e), f(b))
25.13/8.25	   A^2 -> H(U1(k, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, c), f(c))
25.13/8.25	   A^2 -> H(U1(k, c), f(d))
25.13/8.25	   A^2 -> H(U1(c, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, e), f(c))
25.13/8.25	   A^2 -> H(U1(c, e), f(d))
25.13/8.25	   A^2 -> H(U1(c, k), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, k), f(c))
25.13/8.25	   A^2 -> H(U1(c, k), f(d))
25.13/8.25	   A^2 -> H(U1(c, c), U1(c, b))
25.13/8.25	   A^2 -> H(U1(c, c), U1(d, b))
25.13/8.25	   A^2 -> H(U1(c, c), U1(b, c))
25.13/8.25	   A^2 -> H(U1(c, c), U1(b, d))
25.13/8.25	
25.13/8.25	The TRS R consists of the following rules:
25.13/8.25	
25.13/8.25	   f(x) -> U1(x, x)
25.13/8.25	   U1(e, x) -> x
25.13/8.25	   a -> c
25.13/8.25	   a -> d
25.13/8.25	   b -> c
25.13/8.25	   b -> d
25.13/8.25	   d -> k
25.13/8.25	   c -> e
25.13/8.25	   c -> k
25.13/8.25	
25.13/8.25	Q is empty.
25.13/8.25	We have to consider all minimal (P,Q,R)-chains.
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(131) TransformationProof (EQUIVALENT)
25.13/8.25	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), f(c)) at position [] we obtained the following new rules [LPAR04]:
25.13/8.25	
25.13/8.25	   (A^2 -> H(U1(e, c), f(c)),A^2 -> H(U1(e, c), f(c)))
25.13/8.25	   (A^2 -> H(U1(k, c), f(c)),A^2 -> H(U1(k, c), f(c)))
25.13/8.25	   (A^2 -> H(U1(c, e), f(c)),A^2 -> H(U1(c, e), f(c)))
25.13/8.25	   (A^2 -> H(U1(c, k), f(c)),A^2 -> H(U1(c, k), f(c)))
25.13/8.25	   (A^2 -> H(U1(c, c), U1(c, c)),A^2 -> H(U1(c, c), U1(c, c)))
25.13/8.25	   (A^2 -> H(U1(c, c), f(e)),A^2 -> H(U1(c, c), f(e)))
25.13/8.25	   (A^2 -> H(U1(c, c), f(k)),A^2 -> H(U1(c, c), f(k)))
25.13/8.25	
25.13/8.25	
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(132)
25.13/8.25	Obligation:
25.13/8.25	Q DP problem:
25.13/8.25	The TRS P consists of the following rules:
25.13/8.25	
25.13/8.25	   H(x, x) -> G(x, x, f(k))
25.13/8.25	   G(d, x, x) -> A^2
25.13/8.25	   A^2 -> H(f(c), f(c))
25.13/8.25	   A^2 -> H(f(d), f(d))
25.13/8.25	   A^2 -> H(U1(c, c), f(d))
25.13/8.25	   A^2 -> H(U1(e, e), f(b))
25.13/8.25	   A^2 -> H(f(e), U1(b, b))
25.13/8.25	   A^2 -> H(f(e), f(c))
25.13/8.25	   A^2 -> H(f(e), f(d))
25.13/8.25	   A^2 -> H(U1(k, k), f(b))
25.13/8.25	   A^2 -> H(f(k), U1(b, b))
25.13/8.25	   A^2 -> H(f(k), f(c))
25.13/8.25	   A^2 -> H(f(k), f(d))
25.13/8.25	   A^2 -> H(f(c), U1(c, b))
25.13/8.25	   A^2 -> H(f(c), U1(d, b))
25.13/8.25	   A^2 -> H(f(c), U1(b, c))
25.13/8.25	   A^2 -> H(f(c), U1(b, d))
25.13/8.25	   A^2 -> H(f(c), U1(d, d))
25.13/8.25	   A^2 -> H(f(c), f(k))
25.13/8.25	   A^2 -> H(U1(k, d), f(b))
25.13/8.25	   A^2 -> H(U1(d, k), f(b))
25.13/8.25	   A^2 -> H(U1(d, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, d), f(c))
25.13/8.25	   A^2 -> H(U1(d, d), f(d))
25.13/8.25	   A^2 -> H(f(d), U1(c, b))
25.13/8.25	   A^2 -> H(f(d), U1(d, b))
25.13/8.25	   A^2 -> H(f(d), U1(b, c))
25.13/8.25	   A^2 -> H(f(d), U1(b, d))
25.13/8.25	   A^2 -> H(f(d), U1(c, c))
25.13/8.25	   A^2 -> H(f(d), f(e))
25.13/8.25	   A^2 -> H(f(d), f(k))
25.13/8.25	   A^2 -> H(f(a), U1(e, b))
25.13/8.25	   A^2 -> H(f(a), U1(k, b))
25.13/8.25	   A^2 -> H(f(a), U1(c, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, c))
25.13/8.25	   A^2 -> H(f(a), U1(b, e))
25.13/8.25	   A^2 -> H(f(a), U1(b, k))
25.13/8.25	   A^2 -> H(f(c), U1(c, c))
25.13/8.25	   A^2 -> H(f(a), U1(e, c))
25.13/8.25	   A^2 -> H(f(a), U1(k, c))
25.13/8.25	   A^2 -> H(f(a), U1(c, e))
25.13/8.25	   A^2 -> H(f(a), U1(c, k))
25.13/8.25	   A^2 -> H(f(c), f(e))
25.13/8.25	   A^2 -> H(f(a), U1(e, e))
25.13/8.25	   A^2 -> H(f(a), U1(k, k))
25.13/8.25	   A^2 -> H(f(d), U1(d, d))
25.13/8.25	   A^2 -> H(f(a), U1(k, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, k))
25.13/8.25	   A^2 -> H(a, f(b))
25.13/8.25	   A^2 -> H(U1(e, d), f(b))
25.13/8.25	   A^2 -> H(U1(e, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, a), f(c))
25.13/8.25	   A^2 -> H(U1(e, a), f(d))
25.13/8.25	   A^2 -> H(U1(k, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, a), f(c))
25.13/8.25	   A^2 -> H(U1(k, a), f(d))
25.13/8.25	   A^2 -> H(U1(c, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, d), f(c))
25.13/8.25	   A^2 -> H(U1(c, d), f(d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(c, a), f(e))
25.13/8.25	   A^2 -> H(U1(c, a), f(k))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(d, e), f(b))
25.13/8.25	   A^2 -> H(U1(d, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, c), f(c))
25.13/8.25	   A^2 -> H(U1(d, c), f(d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(d, a), f(e))
25.13/8.25	   A^2 -> H(U1(d, a), f(k))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, e), f(c))
25.13/8.25	   A^2 -> H(U1(a, e), f(d))
25.13/8.25	   A^2 -> H(U1(a, k), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, k), f(c))
25.13/8.25	   A^2 -> H(U1(a, k), f(d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, c), f(e))
25.13/8.25	   A^2 -> H(U1(a, c), f(k))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, d), f(e))
25.13/8.25	   A^2 -> H(U1(a, d), f(k))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, k))
25.13/8.25	   A^2 -> H(c, f(b))
25.13/8.25	   A^2 -> H(U1(e, k), f(b))
25.13/8.25	   A^2 -> H(U1(e, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, c), f(c))
25.13/8.25	   A^2 -> H(U1(e, c), f(d))
25.13/8.25	   A^2 -> H(U1(k, e), f(b))
25.13/8.25	   A^2 -> H(U1(k, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, c), f(c))
25.13/8.25	   A^2 -> H(U1(k, c), f(d))
25.13/8.25	   A^2 -> H(U1(c, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, e), f(c))
25.13/8.25	   A^2 -> H(U1(c, e), f(d))
25.13/8.25	   A^2 -> H(U1(c, k), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, k), f(c))
25.13/8.25	   A^2 -> H(U1(c, k), f(d))
25.13/8.25	   A^2 -> H(U1(c, c), U1(c, b))
25.13/8.25	   A^2 -> H(U1(c, c), U1(d, b))
25.13/8.25	   A^2 -> H(U1(c, c), U1(b, c))
25.13/8.25	   A^2 -> H(U1(c, c), U1(b, d))
25.13/8.25	   A^2 -> H(U1(c, c), U1(c, c))
25.13/8.25	   A^2 -> H(U1(c, c), f(e))
25.13/8.25	   A^2 -> H(U1(c, c), f(k))
25.13/8.25	
25.13/8.25	The TRS R consists of the following rules:
25.13/8.25	
25.13/8.25	   f(x) -> U1(x, x)
25.13/8.25	   U1(e, x) -> x
25.13/8.25	   a -> c
25.13/8.25	   a -> d
25.13/8.25	   b -> c
25.13/8.25	   b -> d
25.13/8.25	   d -> k
25.13/8.25	   c -> e
25.13/8.25	   c -> k
25.13/8.25	
25.13/8.25	Q is empty.
25.13/8.25	We have to consider all minimal (P,Q,R)-chains.
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(133) TransformationProof (EQUIVALENT)
25.13/8.25	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), f(d)) at position [] we obtained the following new rules [LPAR04]:
25.13/8.25	
25.13/8.25	   (A^2 -> H(U1(e, c), f(d)),A^2 -> H(U1(e, c), f(d)))
25.13/8.25	   (A^2 -> H(U1(k, c), f(d)),A^2 -> H(U1(k, c), f(d)))
25.13/8.25	   (A^2 -> H(U1(c, e), f(d)),A^2 -> H(U1(c, e), f(d)))
25.13/8.25	   (A^2 -> H(U1(c, k), f(d)),A^2 -> H(U1(c, k), f(d)))
25.13/8.25	   (A^2 -> H(U1(c, c), U1(d, d)),A^2 -> H(U1(c, c), U1(d, d)))
25.13/8.25	   (A^2 -> H(U1(c, c), f(k)),A^2 -> H(U1(c, c), f(k)))
25.13/8.25	
25.13/8.25	
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(134)
25.13/8.25	Obligation:
25.13/8.25	Q DP problem:
25.13/8.25	The TRS P consists of the following rules:
25.13/8.25	
25.13/8.25	   H(x, x) -> G(x, x, f(k))
25.13/8.25	   G(d, x, x) -> A^2
25.13/8.25	   A^2 -> H(f(c), f(c))
25.13/8.25	   A^2 -> H(f(d), f(d))
25.13/8.25	   A^2 -> H(U1(e, e), f(b))
25.13/8.25	   A^2 -> H(f(e), U1(b, b))
25.13/8.25	   A^2 -> H(f(e), f(c))
25.13/8.25	   A^2 -> H(f(e), f(d))
25.13/8.25	   A^2 -> H(U1(k, k), f(b))
25.13/8.25	   A^2 -> H(f(k), U1(b, b))
25.13/8.25	   A^2 -> H(f(k), f(c))
25.13/8.25	   A^2 -> H(f(k), f(d))
25.13/8.25	   A^2 -> H(f(c), U1(c, b))
25.13/8.25	   A^2 -> H(f(c), U1(d, b))
25.13/8.25	   A^2 -> H(f(c), U1(b, c))
25.13/8.25	   A^2 -> H(f(c), U1(b, d))
25.13/8.25	   A^2 -> H(f(c), U1(d, d))
25.13/8.25	   A^2 -> H(f(c), f(k))
25.13/8.25	   A^2 -> H(U1(k, d), f(b))
25.13/8.25	   A^2 -> H(U1(d, k), f(b))
25.13/8.25	   A^2 -> H(U1(d, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, d), f(c))
25.13/8.25	   A^2 -> H(U1(d, d), f(d))
25.13/8.25	   A^2 -> H(f(d), U1(c, b))
25.13/8.25	   A^2 -> H(f(d), U1(d, b))
25.13/8.25	   A^2 -> H(f(d), U1(b, c))
25.13/8.25	   A^2 -> H(f(d), U1(b, d))
25.13/8.25	   A^2 -> H(f(d), U1(c, c))
25.13/8.25	   A^2 -> H(f(d), f(e))
25.13/8.25	   A^2 -> H(f(d), f(k))
25.13/8.25	   A^2 -> H(f(a), U1(e, b))
25.13/8.25	   A^2 -> H(f(a), U1(k, b))
25.13/8.25	   A^2 -> H(f(a), U1(c, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, c))
25.13/8.25	   A^2 -> H(f(a), U1(b, e))
25.13/8.25	   A^2 -> H(f(a), U1(b, k))
25.13/8.25	   A^2 -> H(f(c), U1(c, c))
25.13/8.25	   A^2 -> H(f(a), U1(e, c))
25.13/8.25	   A^2 -> H(f(a), U1(k, c))
25.13/8.25	   A^2 -> H(f(a), U1(c, e))
25.13/8.25	   A^2 -> H(f(a), U1(c, k))
25.13/8.25	   A^2 -> H(f(c), f(e))
25.13/8.25	   A^2 -> H(f(a), U1(e, e))
25.13/8.25	   A^2 -> H(f(a), U1(k, k))
25.13/8.25	   A^2 -> H(f(d), U1(d, d))
25.13/8.25	   A^2 -> H(f(a), U1(k, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, k))
25.13/8.25	   A^2 -> H(a, f(b))
25.13/8.25	   A^2 -> H(U1(e, d), f(b))
25.13/8.25	   A^2 -> H(U1(e, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, a), f(c))
25.13/8.25	   A^2 -> H(U1(e, a), f(d))
25.13/8.25	   A^2 -> H(U1(k, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, a), f(c))
25.13/8.25	   A^2 -> H(U1(k, a), f(d))
25.13/8.25	   A^2 -> H(U1(c, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, d), f(c))
25.13/8.25	   A^2 -> H(U1(c, d), f(d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(c, a), f(e))
25.13/8.25	   A^2 -> H(U1(c, a), f(k))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(d, e), f(b))
25.13/8.25	   A^2 -> H(U1(d, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, c), f(c))
25.13/8.25	   A^2 -> H(U1(d, c), f(d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(d, a), f(e))
25.13/8.25	   A^2 -> H(U1(d, a), f(k))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, e), f(c))
25.13/8.25	   A^2 -> H(U1(a, e), f(d))
25.13/8.25	   A^2 -> H(U1(a, k), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, k), f(c))
25.13/8.25	   A^2 -> H(U1(a, k), f(d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, c), f(e))
25.13/8.25	   A^2 -> H(U1(a, c), f(k))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, d), f(e))
25.13/8.25	   A^2 -> H(U1(a, d), f(k))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, k))
25.13/8.25	   A^2 -> H(c, f(b))
25.13/8.25	   A^2 -> H(U1(e, k), f(b))
25.13/8.25	   A^2 -> H(U1(e, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, c), f(c))
25.13/8.25	   A^2 -> H(U1(e, c), f(d))
25.13/8.25	   A^2 -> H(U1(k, e), f(b))
25.13/8.25	   A^2 -> H(U1(k, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, c), f(c))
25.13/8.25	   A^2 -> H(U1(k, c), f(d))
25.13/8.25	   A^2 -> H(U1(c, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, e), f(c))
25.13/8.25	   A^2 -> H(U1(c, e), f(d))
25.13/8.25	   A^2 -> H(U1(c, k), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, k), f(c))
25.13/8.25	   A^2 -> H(U1(c, k), f(d))
25.13/8.25	   A^2 -> H(U1(c, c), U1(c, b))
25.13/8.25	   A^2 -> H(U1(c, c), U1(d, b))
25.13/8.25	   A^2 -> H(U1(c, c), U1(b, c))
25.13/8.25	   A^2 -> H(U1(c, c), U1(b, d))
25.13/8.25	   A^2 -> H(U1(c, c), U1(c, c))
25.13/8.25	   A^2 -> H(U1(c, c), f(e))
25.13/8.25	   A^2 -> H(U1(c, c), f(k))
25.13/8.25	   A^2 -> H(U1(c, c), U1(d, d))
25.13/8.25	
25.13/8.25	The TRS R consists of the following rules:
25.13/8.25	
25.13/8.25	   f(x) -> U1(x, x)
25.13/8.25	   U1(e, x) -> x
25.13/8.25	   a -> c
25.13/8.25	   a -> d
25.13/8.25	   b -> c
25.13/8.25	   b -> d
25.13/8.25	   d -> k
25.13/8.25	   c -> e
25.13/8.25	   c -> k
25.13/8.25	
25.13/8.25	Q is empty.
25.13/8.25	We have to consider all minimal (P,Q,R)-chains.
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(135) TransformationProof (EQUIVALENT)
25.13/8.25	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), f(b)) at position [] we obtained the following new rules [LPAR04]:
25.13/8.25	
25.13/8.25	   (A^2 -> H(e, f(b)),A^2 -> H(e, f(b)))
25.13/8.25	   (A^2 -> H(U1(e, e), U1(b, b)),A^2 -> H(U1(e, e), U1(b, b)))
25.13/8.25	   (A^2 -> H(U1(e, e), f(c)),A^2 -> H(U1(e, e), f(c)))
25.13/8.25	   (A^2 -> H(U1(e, e), f(d)),A^2 -> H(U1(e, e), f(d)))
25.13/8.25	
25.13/8.25	
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(136)
25.13/8.25	Obligation:
25.13/8.25	Q DP problem:
25.13/8.25	The TRS P consists of the following rules:
25.13/8.25	
25.13/8.25	   H(x, x) -> G(x, x, f(k))
25.13/8.25	   G(d, x, x) -> A^2
25.13/8.25	   A^2 -> H(f(c), f(c))
25.13/8.25	   A^2 -> H(f(d), f(d))
25.13/8.25	   A^2 -> H(f(e), U1(b, b))
25.13/8.25	   A^2 -> H(f(e), f(c))
25.13/8.25	   A^2 -> H(f(e), f(d))
25.13/8.25	   A^2 -> H(U1(k, k), f(b))
25.13/8.25	   A^2 -> H(f(k), U1(b, b))
25.13/8.25	   A^2 -> H(f(k), f(c))
25.13/8.25	   A^2 -> H(f(k), f(d))
25.13/8.25	   A^2 -> H(f(c), U1(c, b))
25.13/8.25	   A^2 -> H(f(c), U1(d, b))
25.13/8.25	   A^2 -> H(f(c), U1(b, c))
25.13/8.25	   A^2 -> H(f(c), U1(b, d))
25.13/8.25	   A^2 -> H(f(c), U1(d, d))
25.13/8.25	   A^2 -> H(f(c), f(k))
25.13/8.25	   A^2 -> H(U1(k, d), f(b))
25.13/8.25	   A^2 -> H(U1(d, k), f(b))
25.13/8.25	   A^2 -> H(U1(d, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, d), f(c))
25.13/8.25	   A^2 -> H(U1(d, d), f(d))
25.13/8.25	   A^2 -> H(f(d), U1(c, b))
25.13/8.25	   A^2 -> H(f(d), U1(d, b))
25.13/8.25	   A^2 -> H(f(d), U1(b, c))
25.13/8.25	   A^2 -> H(f(d), U1(b, d))
25.13/8.25	   A^2 -> H(f(d), U1(c, c))
25.13/8.25	   A^2 -> H(f(d), f(e))
25.13/8.25	   A^2 -> H(f(d), f(k))
25.13/8.25	   A^2 -> H(f(a), U1(e, b))
25.13/8.25	   A^2 -> H(f(a), U1(k, b))
25.13/8.25	   A^2 -> H(f(a), U1(c, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, c))
25.13/8.25	   A^2 -> H(f(a), U1(b, e))
25.13/8.25	   A^2 -> H(f(a), U1(b, k))
25.13/8.25	   A^2 -> H(f(c), U1(c, c))
25.13/8.25	   A^2 -> H(f(a), U1(e, c))
25.13/8.25	   A^2 -> H(f(a), U1(k, c))
25.13/8.25	   A^2 -> H(f(a), U1(c, e))
25.13/8.25	   A^2 -> H(f(a), U1(c, k))
25.13/8.25	   A^2 -> H(f(c), f(e))
25.13/8.25	   A^2 -> H(f(a), U1(e, e))
25.13/8.25	   A^2 -> H(f(a), U1(k, k))
25.13/8.25	   A^2 -> H(f(d), U1(d, d))
25.13/8.25	   A^2 -> H(f(a), U1(k, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, k))
25.13/8.25	   A^2 -> H(a, f(b))
25.13/8.25	   A^2 -> H(U1(e, d), f(b))
25.13/8.25	   A^2 -> H(U1(e, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, a), f(c))
25.13/8.25	   A^2 -> H(U1(e, a), f(d))
25.13/8.25	   A^2 -> H(U1(k, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, a), f(c))
25.13/8.25	   A^2 -> H(U1(k, a), f(d))
25.13/8.25	   A^2 -> H(U1(c, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, d), f(c))
25.13/8.25	   A^2 -> H(U1(c, d), f(d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(c, a), f(e))
25.13/8.25	   A^2 -> H(U1(c, a), f(k))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(d, e), f(b))
25.13/8.25	   A^2 -> H(U1(d, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, c), f(c))
25.13/8.25	   A^2 -> H(U1(d, c), f(d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(d, a), f(e))
25.13/8.25	   A^2 -> H(U1(d, a), f(k))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, e), f(c))
25.13/8.25	   A^2 -> H(U1(a, e), f(d))
25.13/8.25	   A^2 -> H(U1(a, k), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, k), f(c))
25.13/8.25	   A^2 -> H(U1(a, k), f(d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, c), f(e))
25.13/8.25	   A^2 -> H(U1(a, c), f(k))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, d), f(e))
25.13/8.25	   A^2 -> H(U1(a, d), f(k))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, k))
25.13/8.25	   A^2 -> H(c, f(b))
25.13/8.25	   A^2 -> H(U1(e, k), f(b))
25.13/8.25	   A^2 -> H(U1(e, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, c), f(c))
25.13/8.25	   A^2 -> H(U1(e, c), f(d))
25.13/8.25	   A^2 -> H(U1(k, e), f(b))
25.13/8.25	   A^2 -> H(U1(k, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, c), f(c))
25.13/8.25	   A^2 -> H(U1(k, c), f(d))
25.13/8.25	   A^2 -> H(U1(c, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, e), f(c))
25.13/8.25	   A^2 -> H(U1(c, e), f(d))
25.13/8.25	   A^2 -> H(U1(c, k), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, k), f(c))
25.13/8.25	   A^2 -> H(U1(c, k), f(d))
25.13/8.25	   A^2 -> H(U1(c, c), U1(c, b))
25.13/8.25	   A^2 -> H(U1(c, c), U1(d, b))
25.13/8.25	   A^2 -> H(U1(c, c), U1(b, c))
25.13/8.25	   A^2 -> H(U1(c, c), U1(b, d))
25.13/8.25	   A^2 -> H(U1(c, c), U1(c, c))
25.13/8.25	   A^2 -> H(U1(c, c), f(e))
25.13/8.25	   A^2 -> H(U1(c, c), f(k))
25.13/8.25	   A^2 -> H(U1(c, c), U1(d, d))
25.13/8.25	   A^2 -> H(e, f(b))
25.13/8.25	   A^2 -> H(U1(e, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, e), f(c))
25.13/8.25	   A^2 -> H(U1(e, e), f(d))
25.13/8.25	
25.13/8.25	The TRS R consists of the following rules:
25.13/8.25	
25.13/8.25	   f(x) -> U1(x, x)
25.13/8.25	   U1(e, x) -> x
25.13/8.25	   a -> c
25.13/8.25	   a -> d
25.13/8.25	   b -> c
25.13/8.25	   b -> d
25.13/8.25	   d -> k
25.13/8.25	   c -> e
25.13/8.25	   c -> k
25.13/8.25	
25.13/8.25	Q is empty.
25.13/8.25	We have to consider all minimal (P,Q,R)-chains.
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(137) TransformationProof (EQUIVALENT)
25.13/8.25	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
25.13/8.25	
25.13/8.25	   (A^2 -> H(U1(e, e), U1(b, b)),A^2 -> H(U1(e, e), U1(b, b)))
25.13/8.25	   (A^2 -> H(f(e), U1(c, b)),A^2 -> H(f(e), U1(c, b)))
25.13/8.25	   (A^2 -> H(f(e), U1(d, b)),A^2 -> H(f(e), U1(d, b)))
25.13/8.25	   (A^2 -> H(f(e), U1(b, c)),A^2 -> H(f(e), U1(b, c)))
25.13/8.25	   (A^2 -> H(f(e), U1(b, d)),A^2 -> H(f(e), U1(b, d)))
25.13/8.25	
25.13/8.25	
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(138)
25.13/8.25	Obligation:
25.13/8.25	Q DP problem:
25.13/8.25	The TRS P consists of the following rules:
25.13/8.25	
25.13/8.25	   H(x, x) -> G(x, x, f(k))
25.13/8.25	   G(d, x, x) -> A^2
25.13/8.25	   A^2 -> H(f(c), f(c))
25.13/8.25	   A^2 -> H(f(d), f(d))
25.13/8.25	   A^2 -> H(f(e), f(c))
25.13/8.25	   A^2 -> H(f(e), f(d))
25.13/8.25	   A^2 -> H(U1(k, k), f(b))
25.13/8.25	   A^2 -> H(f(k), U1(b, b))
25.13/8.25	   A^2 -> H(f(k), f(c))
25.13/8.25	   A^2 -> H(f(k), f(d))
25.13/8.25	   A^2 -> H(f(c), U1(c, b))
25.13/8.25	   A^2 -> H(f(c), U1(d, b))
25.13/8.25	   A^2 -> H(f(c), U1(b, c))
25.13/8.25	   A^2 -> H(f(c), U1(b, d))
25.13/8.25	   A^2 -> H(f(c), U1(d, d))
25.13/8.25	   A^2 -> H(f(c), f(k))
25.13/8.25	   A^2 -> H(U1(k, d), f(b))
25.13/8.25	   A^2 -> H(U1(d, k), f(b))
25.13/8.25	   A^2 -> H(U1(d, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, d), f(c))
25.13/8.25	   A^2 -> H(U1(d, d), f(d))
25.13/8.25	   A^2 -> H(f(d), U1(c, b))
25.13/8.25	   A^2 -> H(f(d), U1(d, b))
25.13/8.25	   A^2 -> H(f(d), U1(b, c))
25.13/8.25	   A^2 -> H(f(d), U1(b, d))
25.13/8.25	   A^2 -> H(f(d), U1(c, c))
25.13/8.25	   A^2 -> H(f(d), f(e))
25.13/8.25	   A^2 -> H(f(d), f(k))
25.13/8.25	   A^2 -> H(f(a), U1(e, b))
25.13/8.25	   A^2 -> H(f(a), U1(k, b))
25.13/8.25	   A^2 -> H(f(a), U1(c, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, c))
25.13/8.25	   A^2 -> H(f(a), U1(b, e))
25.13/8.25	   A^2 -> H(f(a), U1(b, k))
25.13/8.25	   A^2 -> H(f(c), U1(c, c))
25.13/8.25	   A^2 -> H(f(a), U1(e, c))
25.13/8.25	   A^2 -> H(f(a), U1(k, c))
25.13/8.25	   A^2 -> H(f(a), U1(c, e))
25.13/8.25	   A^2 -> H(f(a), U1(c, k))
25.13/8.25	   A^2 -> H(f(c), f(e))
25.13/8.25	   A^2 -> H(f(a), U1(e, e))
25.13/8.25	   A^2 -> H(f(a), U1(k, k))
25.13/8.25	   A^2 -> H(f(d), U1(d, d))
25.13/8.25	   A^2 -> H(f(a), U1(k, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, k))
25.13/8.25	   A^2 -> H(a, f(b))
25.13/8.25	   A^2 -> H(U1(e, d), f(b))
25.13/8.25	   A^2 -> H(U1(e, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, a), f(c))
25.13/8.25	   A^2 -> H(U1(e, a), f(d))
25.13/8.25	   A^2 -> H(U1(k, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, a), f(c))
25.13/8.25	   A^2 -> H(U1(k, a), f(d))
25.13/8.25	   A^2 -> H(U1(c, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, d), f(c))
25.13/8.25	   A^2 -> H(U1(c, d), f(d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(c, a), f(e))
25.13/8.25	   A^2 -> H(U1(c, a), f(k))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(d, e), f(b))
25.13/8.25	   A^2 -> H(U1(d, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, c), f(c))
25.13/8.25	   A^2 -> H(U1(d, c), f(d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(d, a), f(e))
25.13/8.25	   A^2 -> H(U1(d, a), f(k))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, e), f(c))
25.13/8.25	   A^2 -> H(U1(a, e), f(d))
25.13/8.25	   A^2 -> H(U1(a, k), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, k), f(c))
25.13/8.25	   A^2 -> H(U1(a, k), f(d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, c), f(e))
25.13/8.25	   A^2 -> H(U1(a, c), f(k))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, d), f(e))
25.13/8.25	   A^2 -> H(U1(a, d), f(k))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, k))
25.13/8.25	   A^2 -> H(c, f(b))
25.13/8.25	   A^2 -> H(U1(e, k), f(b))
25.13/8.25	   A^2 -> H(U1(e, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, c), f(c))
25.13/8.25	   A^2 -> H(U1(e, c), f(d))
25.13/8.25	   A^2 -> H(U1(k, e), f(b))
25.13/8.25	   A^2 -> H(U1(k, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, c), f(c))
25.13/8.25	   A^2 -> H(U1(k, c), f(d))
25.13/8.25	   A^2 -> H(U1(c, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, e), f(c))
25.13/8.25	   A^2 -> H(U1(c, e), f(d))
25.13/8.25	   A^2 -> H(U1(c, k), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, k), f(c))
25.13/8.25	   A^2 -> H(U1(c, k), f(d))
25.13/8.25	   A^2 -> H(U1(c, c), U1(c, b))
25.13/8.25	   A^2 -> H(U1(c, c), U1(d, b))
25.13/8.25	   A^2 -> H(U1(c, c), U1(b, c))
25.13/8.25	   A^2 -> H(U1(c, c), U1(b, d))
25.13/8.25	   A^2 -> H(U1(c, c), U1(c, c))
25.13/8.25	   A^2 -> H(U1(c, c), f(e))
25.13/8.25	   A^2 -> H(U1(c, c), f(k))
25.13/8.25	   A^2 -> H(U1(c, c), U1(d, d))
25.13/8.25	   A^2 -> H(e, f(b))
25.13/8.25	   A^2 -> H(U1(e, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, e), f(c))
25.13/8.25	   A^2 -> H(U1(e, e), f(d))
25.13/8.25	   A^2 -> H(f(e), U1(c, b))
25.13/8.25	   A^2 -> H(f(e), U1(d, b))
25.13/8.25	   A^2 -> H(f(e), U1(b, c))
25.13/8.25	   A^2 -> H(f(e), U1(b, d))
25.13/8.25	
25.13/8.25	The TRS R consists of the following rules:
25.13/8.25	
25.13/8.25	   f(x) -> U1(x, x)
25.13/8.25	   U1(e, x) -> x
25.13/8.25	   a -> c
25.13/8.25	   a -> d
25.13/8.25	   b -> c
25.13/8.25	   b -> d
25.13/8.25	   d -> k
25.13/8.25	   c -> e
25.13/8.25	   c -> k
25.13/8.25	
25.13/8.25	Q is empty.
25.13/8.25	We have to consider all minimal (P,Q,R)-chains.
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(139) TransformationProof (EQUIVALENT)
25.13/8.25	By narrowing [LPAR04] the rule A^2 -> H(f(e), f(c)) at position [] we obtained the following new rules [LPAR04]:
25.13/8.25	
25.13/8.25	   (A^2 -> H(U1(e, e), f(c)),A^2 -> H(U1(e, e), f(c)))
25.13/8.25	   (A^2 -> H(f(e), U1(c, c)),A^2 -> H(f(e), U1(c, c)))
25.13/8.25	   (A^2 -> H(f(e), f(e)),A^2 -> H(f(e), f(e)))
25.13/8.25	   (A^2 -> H(f(e), f(k)),A^2 -> H(f(e), f(k)))
25.13/8.25	
25.13/8.25	
25.13/8.25	----------------------------------------
25.13/8.25	
25.13/8.25	(140)
25.13/8.25	Obligation:
25.13/8.25	Q DP problem:
25.13/8.25	The TRS P consists of the following rules:
25.13/8.25	
25.13/8.25	   H(x, x) -> G(x, x, f(k))
25.13/8.25	   G(d, x, x) -> A^2
25.13/8.25	   A^2 -> H(f(c), f(c))
25.13/8.25	   A^2 -> H(f(d), f(d))
25.13/8.25	   A^2 -> H(f(e), f(d))
25.13/8.25	   A^2 -> H(U1(k, k), f(b))
25.13/8.25	   A^2 -> H(f(k), U1(b, b))
25.13/8.25	   A^2 -> H(f(k), f(c))
25.13/8.25	   A^2 -> H(f(k), f(d))
25.13/8.25	   A^2 -> H(f(c), U1(c, b))
25.13/8.25	   A^2 -> H(f(c), U1(d, b))
25.13/8.25	   A^2 -> H(f(c), U1(b, c))
25.13/8.25	   A^2 -> H(f(c), U1(b, d))
25.13/8.25	   A^2 -> H(f(c), U1(d, d))
25.13/8.25	   A^2 -> H(f(c), f(k))
25.13/8.25	   A^2 -> H(U1(k, d), f(b))
25.13/8.25	   A^2 -> H(U1(d, k), f(b))
25.13/8.25	   A^2 -> H(U1(d, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, d), f(c))
25.13/8.25	   A^2 -> H(U1(d, d), f(d))
25.13/8.25	   A^2 -> H(f(d), U1(c, b))
25.13/8.25	   A^2 -> H(f(d), U1(d, b))
25.13/8.25	   A^2 -> H(f(d), U1(b, c))
25.13/8.25	   A^2 -> H(f(d), U1(b, d))
25.13/8.25	   A^2 -> H(f(d), U1(c, c))
25.13/8.25	   A^2 -> H(f(d), f(e))
25.13/8.25	   A^2 -> H(f(d), f(k))
25.13/8.25	   A^2 -> H(f(a), U1(e, b))
25.13/8.25	   A^2 -> H(f(a), U1(k, b))
25.13/8.25	   A^2 -> H(f(a), U1(c, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, c))
25.13/8.25	   A^2 -> H(f(a), U1(b, e))
25.13/8.25	   A^2 -> H(f(a), U1(b, k))
25.13/8.25	   A^2 -> H(f(c), U1(c, c))
25.13/8.25	   A^2 -> H(f(a), U1(e, c))
25.13/8.25	   A^2 -> H(f(a), U1(k, c))
25.13/8.25	   A^2 -> H(f(a), U1(c, e))
25.13/8.25	   A^2 -> H(f(a), U1(c, k))
25.13/8.25	   A^2 -> H(f(c), f(e))
25.13/8.25	   A^2 -> H(f(a), U1(e, e))
25.13/8.25	   A^2 -> H(f(a), U1(k, k))
25.13/8.25	   A^2 -> H(f(d), U1(d, d))
25.13/8.25	   A^2 -> H(f(a), U1(k, d))
25.13/8.25	   A^2 -> H(f(a), U1(d, k))
25.13/8.25	   A^2 -> H(a, f(b))
25.13/8.25	   A^2 -> H(U1(e, d), f(b))
25.13/8.25	   A^2 -> H(U1(e, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(e, a), f(c))
25.13/8.25	   A^2 -> H(U1(e, a), f(d))
25.13/8.25	   A^2 -> H(U1(k, a), U1(b, b))
25.13/8.25	   A^2 -> H(U1(k, a), f(c))
25.13/8.25	   A^2 -> H(U1(k, a), f(d))
25.13/8.25	   A^2 -> H(U1(c, d), U1(b, b))
25.13/8.25	   A^2 -> H(U1(c, d), f(c))
25.13/8.25	   A^2 -> H(U1(c, d), f(d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(c, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(c, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(c, a), f(e))
25.13/8.25	   A^2 -> H(U1(c, a), f(k))
25.13/8.25	   A^2 -> H(U1(c, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(d, e), f(b))
25.13/8.25	   A^2 -> H(U1(d, c), U1(b, b))
25.13/8.25	   A^2 -> H(U1(d, c), f(c))
25.13/8.25	   A^2 -> H(U1(d, c), f(d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, b))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, c))
25.13/8.25	   A^2 -> H(U1(d, a), U1(b, d))
25.13/8.25	   A^2 -> H(U1(d, a), U1(c, c))
25.13/8.25	   A^2 -> H(U1(d, a), f(e))
25.13/8.25	   A^2 -> H(U1(d, a), f(k))
25.13/8.25	   A^2 -> H(U1(d, a), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, e), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, e), f(c))
25.13/8.25	   A^2 -> H(U1(a, e), f(d))
25.13/8.25	   A^2 -> H(U1(a, k), U1(b, b))
25.13/8.25	   A^2 -> H(U1(a, k), f(c))
25.13/8.25	   A^2 -> H(U1(a, k), f(d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, c), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, c), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, c), f(e))
25.13/8.25	   A^2 -> H(U1(a, c), f(k))
25.13/8.25	   A^2 -> H(U1(a, c), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, b))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, c))
25.13/8.25	   A^2 -> H(U1(a, d), U1(b, d))
25.13/8.25	   A^2 -> H(U1(a, d), U1(c, c))
25.13/8.25	   A^2 -> H(U1(a, d), f(e))
25.13/8.25	   A^2 -> H(U1(a, d), f(k))
25.13/8.25	   A^2 -> H(U1(a, d), U1(d, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, b))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(b, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, c))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(c, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(e, e))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, k))
25.13/8.25	   A^2 -> H(U1(a, a), U1(k, d))
25.13/8.25	   A^2 -> H(U1(a, a), U1(d, k))
25.13/8.25	   A^2 -> H(c, f(b))
25.13/8.26	   A^2 -> H(U1(e, k), f(b))
25.13/8.26	   A^2 -> H(U1(e, c), U1(b, b))
25.13/8.26	   A^2 -> H(U1(e, c), f(c))
25.13/8.26	   A^2 -> H(U1(e, c), f(d))
25.13/8.26	   A^2 -> H(U1(k, e), f(b))
25.13/8.26	   A^2 -> H(U1(k, c), U1(b, b))
25.13/8.26	   A^2 -> H(U1(k, c), f(c))
25.13/8.26	   A^2 -> H(U1(k, c), f(d))
25.13/8.26	   A^2 -> H(U1(c, e), U1(b, b))
25.13/8.26	   A^2 -> H(U1(c, e), f(c))
25.13/8.26	   A^2 -> H(U1(c, e), f(d))
25.13/8.26	   A^2 -> H(U1(c, k), U1(b, b))
25.13/8.26	   A^2 -> H(U1(c, k), f(c))
25.13/8.26	   A^2 -> H(U1(c, k), f(d))
25.13/8.26	   A^2 -> H(U1(c, c), U1(c, b))
25.13/8.26	   A^2 -> H(U1(c, c), U1(d, b))
25.13/8.26	   A^2 -> H(U1(c, c), U1(b, c))
25.13/8.26	   A^2 -> H(U1(c, c), U1(b, d))
25.13/8.26	   A^2 -> H(U1(c, c), U1(c, c))
25.13/8.26	   A^2 -> H(U1(c, c), f(e))
25.13/8.26	   A^2 -> H(U1(c, c), f(k))
25.13/8.26	   A^2 -> H(U1(c, c), U1(d, d))
25.13/8.26	   A^2 -> H(e, f(b))
25.13/8.26	   A^2 -> H(U1(e, e), U1(b, b))
25.13/8.26	   A^2 -> H(U1(e, e), f(c))
25.13/8.26	   A^2 -> H(U1(e, e), f(d))
25.13/8.26	   A^2 -> H(f(e), U1(c, b))
25.13/8.26	   A^2 -> H(f(e), U1(d, b))
25.13/8.26	   A^2 -> H(f(e), U1(b, c))
25.13/8.26	   A^2 -> H(f(e), U1(b, d))
25.13/8.26	   A^2 -> H(f(e), U1(c, c))
25.13/8.26	   A^2 -> H(f(e), f(e))
25.13/8.26	   A^2 -> H(f(e), f(k))
25.13/8.26	
25.13/8.26	The TRS R consists of the following rules:
25.13/8.26	
25.13/8.26	   f(x) -> U1(x, x)
25.13/8.26	   U1(e, x) -> x
25.13/8.26	   a -> c
25.13/8.26	   a -> d
25.13/8.26	   b -> c
25.13/8.26	   b -> d
25.13/8.26	   d -> k
25.13/8.26	   c -> e
25.13/8.26	   c -> k
25.13/8.26	
25.13/8.26	Q is empty.
25.13/8.26	We have to consider all minimal (P,Q,R)-chains.
25.13/8.26	----------------------------------------
25.13/8.26	
25.13/8.26	(141) TransformationProof (EQUIVALENT)
25.13/8.26	By narrowing [LPAR04] the rule A^2 -> H(f(e), f(d)) at position [] we obtained the following new rules [LPAR04]:
25.13/8.26	
25.13/8.26	   (A^2 -> H(U1(e, e), f(d)),A^2 -> H(U1(e, e), f(d)))
25.13/8.26	   (A^2 -> H(f(e), U1(d, d)),A^2 -> H(f(e), U1(d, d)))
25.13/8.26	   (A^2 -> H(f(e), f(k)),A^2 -> H(f(e), f(k)))
25.13/8.26	
25.13/8.26	
25.13/8.26	----------------------------------------
25.13/8.26	
25.13/8.26	(142)
25.13/8.26	Obligation:
25.13/8.26	Q DP problem:
25.13/8.26	The TRS P consists of the following rules:
25.13/8.26	
25.13/8.26	   H(x, x) -> G(x, x, f(k))
25.13/8.26	   G(d, x, x) -> A^2
25.13/8.26	   A^2 -> H(f(c), f(c))
25.13/8.26	   A^2 -> H(f(d), f(d))
25.13/8.26	   A^2 -> H(U1(k, k), f(b))
25.13/8.26	   A^2 -> H(f(k), U1(b, b))
25.13/8.26	   A^2 -> H(f(k), f(c))
25.13/8.26	   A^2 -> H(f(k), f(d))
25.13/8.26	   A^2 -> H(f(c), U1(c, b))
25.13/8.26	   A^2 -> H(f(c), U1(d, b))
25.13/8.26	   A^2 -> H(f(c), U1(b, c))
25.13/8.26	   A^2 -> H(f(c), U1(b, d))
25.13/8.26	   A^2 -> H(f(c), U1(d, d))
25.13/8.26	   A^2 -> H(f(c), f(k))
25.13/8.26	   A^2 -> H(U1(k, d), f(b))
25.13/8.26	   A^2 -> H(U1(d, k), f(b))
25.13/8.26	   A^2 -> H(U1(d, d), U1(b, b))
25.13/8.26	   A^2 -> H(U1(d, d), f(c))
25.13/8.26	   A^2 -> H(U1(d, d), f(d))
25.13/8.26	   A^2 -> H(f(d), U1(c, b))
25.13/8.26	   A^2 -> H(f(d), U1(d, b))
25.13/8.26	   A^2 -> H(f(d), U1(b, c))
25.13/8.26	   A^2 -> H(f(d), U1(b, d))
25.13/8.26	   A^2 -> H(f(d), U1(c, c))
25.13/8.26	   A^2 -> H(f(d), f(e))
25.13/8.26	   A^2 -> H(f(d), f(k))
25.13/8.26	   A^2 -> H(f(a), U1(e, b))
25.13/8.26	   A^2 -> H(f(a), U1(k, b))
25.13/8.26	   A^2 -> H(f(a), U1(c, d))
25.13/8.26	   A^2 -> H(f(a), U1(d, c))
25.13/8.26	   A^2 -> H(f(a), U1(b, e))
25.13/8.26	   A^2 -> H(f(a), U1(b, k))
25.13/8.26	   A^2 -> H(f(c), U1(c, c))
25.13/8.26	   A^2 -> H(f(a), U1(e, c))
25.13/8.26	   A^2 -> H(f(a), U1(k, c))
25.13/8.26	   A^2 -> H(f(a), U1(c, e))
25.13/8.26	   A^2 -> H(f(a), U1(c, k))
25.13/8.26	   A^2 -> H(f(c), f(e))
25.13/8.26	   A^2 -> H(f(a), U1(e, e))
25.13/8.26	   A^2 -> H(f(a), U1(k, k))
25.13/8.26	   A^2 -> H(f(d), U1(d, d))
25.13/8.26	   A^2 -> H(f(a), U1(k, d))
25.13/8.26	   A^2 -> H(f(a), U1(d, k))
25.13/8.26	   A^2 -> H(a, f(b))
25.13/8.26	   A^2 -> H(U1(e, d), f(b))
25.13/8.26	   A^2 -> H(U1(e, a), U1(b, b))
25.13/8.26	   A^2 -> H(U1(e, a), f(c))
25.13/8.26	   A^2 -> H(U1(e, a), f(d))
25.13/8.26	   A^2 -> H(U1(k, a), U1(b, b))
25.13/8.26	   A^2 -> H(U1(k, a), f(c))
25.13/8.26	   A^2 -> H(U1(k, a), f(d))
25.13/8.26	   A^2 -> H(U1(c, d), U1(b, b))
25.13/8.26	   A^2 -> H(U1(c, d), f(c))
25.13/8.26	   A^2 -> H(U1(c, d), f(d))
25.13/8.26	   A^2 -> H(U1(c, a), U1(c, b))
25.13/8.26	   A^2 -> H(U1(c, a), U1(d, b))
25.13/8.26	   A^2 -> H(U1(c, a), U1(b, c))
25.13/8.26	   A^2 -> H(U1(c, a), U1(b, d))
25.13/8.26	   A^2 -> H(U1(c, a), U1(c, c))
25.13/8.26	   A^2 -> H(U1(c, a), f(e))
25.13/8.26	   A^2 -> H(U1(c, a), f(k))
25.13/8.26	   A^2 -> H(U1(c, a), U1(d, d))
25.13/8.26	   A^2 -> H(U1(d, e), f(b))
25.13/8.26	   A^2 -> H(U1(d, c), U1(b, b))
25.13/8.26	   A^2 -> H(U1(d, c), f(c))
25.13/8.26	   A^2 -> H(U1(d, c), f(d))
25.13/8.26	   A^2 -> H(U1(d, a), U1(c, b))
25.13/8.26	   A^2 -> H(U1(d, a), U1(d, b))
25.13/8.26	   A^2 -> H(U1(d, a), U1(b, c))
25.13/8.26	   A^2 -> H(U1(d, a), U1(b, d))
25.13/8.26	   A^2 -> H(U1(d, a), U1(c, c))
25.13/8.26	   A^2 -> H(U1(d, a), f(e))
25.13/8.26	   A^2 -> H(U1(d, a), f(k))
25.13/8.26	   A^2 -> H(U1(d, a), U1(d, d))
25.13/8.26	   A^2 -> H(U1(a, e), U1(b, b))
25.13/8.26	   A^2 -> H(U1(a, e), f(c))
25.13/8.26	   A^2 -> H(U1(a, e), f(d))
25.13/8.26	   A^2 -> H(U1(a, k), U1(b, b))
25.13/8.26	   A^2 -> H(U1(a, k), f(c))
25.13/8.26	   A^2 -> H(U1(a, k), f(d))
25.13/8.26	   A^2 -> H(U1(a, c), U1(c, b))
25.13/8.26	   A^2 -> H(U1(a, c), U1(d, b))
25.13/8.26	   A^2 -> H(U1(a, c), U1(b, c))
25.13/8.26	   A^2 -> H(U1(a, c), U1(b, d))
25.13/8.26	   A^2 -> H(U1(a, c), U1(c, c))
25.13/8.26	   A^2 -> H(U1(a, c), f(e))
25.13/8.26	   A^2 -> H(U1(a, c), f(k))
25.13/8.26	   A^2 -> H(U1(a, c), U1(d, d))
25.13/8.26	   A^2 -> H(U1(a, d), U1(c, b))
25.13/8.26	   A^2 -> H(U1(a, d), U1(d, b))
25.13/8.26	   A^2 -> H(U1(a, d), U1(b, c))
25.13/8.26	   A^2 -> H(U1(a, d), U1(b, d))
25.13/8.26	   A^2 -> H(U1(a, d), U1(c, c))
25.13/8.26	   A^2 -> H(U1(a, d), f(e))
25.13/8.26	   A^2 -> H(U1(a, d), f(k))
25.13/8.26	   A^2 -> H(U1(a, d), U1(d, d))
25.13/8.26	   A^2 -> H(U1(a, a), U1(e, b))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, b))
25.13/8.26	   A^2 -> H(U1(a, a), U1(c, d))
25.13/8.26	   A^2 -> H(U1(a, a), U1(d, c))
25.13/8.26	   A^2 -> H(U1(a, a), U1(b, e))
25.13/8.26	   A^2 -> H(U1(a, a), U1(b, k))
25.13/8.26	   A^2 -> H(U1(a, a), U1(e, c))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, c))
25.13/8.26	   A^2 -> H(U1(a, a), U1(c, e))
25.13/8.26	   A^2 -> H(U1(a, a), U1(c, k))
25.13/8.26	   A^2 -> H(U1(a, a), U1(e, e))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, k))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, d))
25.13/8.26	   A^2 -> H(U1(a, a), U1(d, k))
25.13/8.26	   A^2 -> H(c, f(b))
25.13/8.26	   A^2 -> H(U1(e, k), f(b))
25.13/8.26	   A^2 -> H(U1(e, c), U1(b, b))
25.13/8.26	   A^2 -> H(U1(e, c), f(c))
25.13/8.26	   A^2 -> H(U1(e, c), f(d))
25.13/8.26	   A^2 -> H(U1(k, e), f(b))
25.13/8.26	   A^2 -> H(U1(k, c), U1(b, b))
25.13/8.26	   A^2 -> H(U1(k, c), f(c))
25.13/8.26	   A^2 -> H(U1(k, c), f(d))
25.13/8.26	   A^2 -> H(U1(c, e), U1(b, b))
25.13/8.26	   A^2 -> H(U1(c, e), f(c))
25.13/8.26	   A^2 -> H(U1(c, e), f(d))
25.13/8.26	   A^2 -> H(U1(c, k), U1(b, b))
25.13/8.26	   A^2 -> H(U1(c, k), f(c))
25.13/8.26	   A^2 -> H(U1(c, k), f(d))
25.13/8.26	   A^2 -> H(U1(c, c), U1(c, b))
25.13/8.26	   A^2 -> H(U1(c, c), U1(d, b))
25.13/8.26	   A^2 -> H(U1(c, c), U1(b, c))
25.13/8.26	   A^2 -> H(U1(c, c), U1(b, d))
25.13/8.26	   A^2 -> H(U1(c, c), U1(c, c))
25.13/8.26	   A^2 -> H(U1(c, c), f(e))
25.13/8.26	   A^2 -> H(U1(c, c), f(k))
25.13/8.26	   A^2 -> H(U1(c, c), U1(d, d))
25.13/8.26	   A^2 -> H(e, f(b))
25.13/8.26	   A^2 -> H(U1(e, e), U1(b, b))
25.13/8.26	   A^2 -> H(U1(e, e), f(c))
25.13/8.26	   A^2 -> H(U1(e, e), f(d))
25.13/8.26	   A^2 -> H(f(e), U1(c, b))
25.13/8.26	   A^2 -> H(f(e), U1(d, b))
25.13/8.26	   A^2 -> H(f(e), U1(b, c))
25.13/8.26	   A^2 -> H(f(e), U1(b, d))
25.13/8.26	   A^2 -> H(f(e), U1(c, c))
25.13/8.26	   A^2 -> H(f(e), f(e))
25.13/8.26	   A^2 -> H(f(e), f(k))
25.13/8.26	   A^2 -> H(f(e), U1(d, d))
25.13/8.26	
25.13/8.26	The TRS R consists of the following rules:
25.13/8.26	
25.13/8.26	   f(x) -> U1(x, x)
25.13/8.26	   U1(e, x) -> x
25.13/8.26	   a -> c
25.13/8.26	   a -> d
25.13/8.26	   b -> c
25.13/8.26	   b -> d
25.13/8.26	   d -> k
25.13/8.26	   c -> e
25.13/8.26	   c -> k
25.13/8.26	
25.13/8.26	Q is empty.
25.13/8.26	We have to consider all minimal (P,Q,R)-chains.
25.13/8.26	----------------------------------------
25.13/8.26	
25.13/8.26	(143) TransformationProof (EQUIVALENT)
25.13/8.26	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), f(b)) at position [] we obtained the following new rules [LPAR04]:
25.13/8.26	
25.13/8.26	   (A^2 -> H(U1(k, k), U1(b, b)),A^2 -> H(U1(k, k), U1(b, b)))
25.13/8.26	   (A^2 -> H(U1(k, k), f(c)),A^2 -> H(U1(k, k), f(c)))
25.13/8.26	   (A^2 -> H(U1(k, k), f(d)),A^2 -> H(U1(k, k), f(d)))
25.13/8.26	
25.13/8.26	
25.13/8.26	----------------------------------------
25.13/8.26	
25.13/8.26	(144)
25.13/8.26	Obligation:
25.13/8.26	Q DP problem:
25.13/8.26	The TRS P consists of the following rules:
25.13/8.26	
25.13/8.26	   H(x, x) -> G(x, x, f(k))
25.13/8.26	   G(d, x, x) -> A^2
25.13/8.26	   A^2 -> H(f(c), f(c))
25.13/8.26	   A^2 -> H(f(d), f(d))
25.13/8.26	   A^2 -> H(f(k), U1(b, b))
25.13/8.26	   A^2 -> H(f(k), f(c))
25.13/8.26	   A^2 -> H(f(k), f(d))
25.13/8.26	   A^2 -> H(f(c), U1(c, b))
25.13/8.26	   A^2 -> H(f(c), U1(d, b))
25.13/8.26	   A^2 -> H(f(c), U1(b, c))
25.13/8.26	   A^2 -> H(f(c), U1(b, d))
25.13/8.26	   A^2 -> H(f(c), U1(d, d))
25.13/8.26	   A^2 -> H(f(c), f(k))
25.13/8.26	   A^2 -> H(U1(k, d), f(b))
25.13/8.26	   A^2 -> H(U1(d, k), f(b))
25.13/8.26	   A^2 -> H(U1(d, d), U1(b, b))
25.13/8.26	   A^2 -> H(U1(d, d), f(c))
25.13/8.26	   A^2 -> H(U1(d, d), f(d))
25.13/8.26	   A^2 -> H(f(d), U1(c, b))
25.13/8.26	   A^2 -> H(f(d), U1(d, b))
25.13/8.26	   A^2 -> H(f(d), U1(b, c))
25.13/8.26	   A^2 -> H(f(d), U1(b, d))
25.13/8.26	   A^2 -> H(f(d), U1(c, c))
25.13/8.26	   A^2 -> H(f(d), f(e))
25.13/8.26	   A^2 -> H(f(d), f(k))
25.13/8.26	   A^2 -> H(f(a), U1(e, b))
25.13/8.26	   A^2 -> H(f(a), U1(k, b))
25.13/8.26	   A^2 -> H(f(a), U1(c, d))
25.13/8.26	   A^2 -> H(f(a), U1(d, c))
25.13/8.26	   A^2 -> H(f(a), U1(b, e))
25.13/8.26	   A^2 -> H(f(a), U1(b, k))
25.13/8.26	   A^2 -> H(f(c), U1(c, c))
25.13/8.26	   A^2 -> H(f(a), U1(e, c))
25.13/8.26	   A^2 -> H(f(a), U1(k, c))
25.13/8.26	   A^2 -> H(f(a), U1(c, e))
25.13/8.26	   A^2 -> H(f(a), U1(c, k))
25.13/8.26	   A^2 -> H(f(c), f(e))
25.13/8.26	   A^2 -> H(f(a), U1(e, e))
25.13/8.26	   A^2 -> H(f(a), U1(k, k))
25.13/8.26	   A^2 -> H(f(d), U1(d, d))
25.13/8.26	   A^2 -> H(f(a), U1(k, d))
25.13/8.26	   A^2 -> H(f(a), U1(d, k))
25.13/8.26	   A^2 -> H(a, f(b))
25.13/8.26	   A^2 -> H(U1(e, d), f(b))
25.13/8.26	   A^2 -> H(U1(e, a), U1(b, b))
25.13/8.26	   A^2 -> H(U1(e, a), f(c))
25.13/8.26	   A^2 -> H(U1(e, a), f(d))
25.13/8.26	   A^2 -> H(U1(k, a), U1(b, b))
25.13/8.26	   A^2 -> H(U1(k, a), f(c))
25.13/8.26	   A^2 -> H(U1(k, a), f(d))
25.13/8.26	   A^2 -> H(U1(c, d), U1(b, b))
25.13/8.26	   A^2 -> H(U1(c, d), f(c))
25.13/8.26	   A^2 -> H(U1(c, d), f(d))
25.13/8.26	   A^2 -> H(U1(c, a), U1(c, b))
25.13/8.26	   A^2 -> H(U1(c, a), U1(d, b))
25.13/8.26	   A^2 -> H(U1(c, a), U1(b, c))
25.13/8.26	   A^2 -> H(U1(c, a), U1(b, d))
25.13/8.26	   A^2 -> H(U1(c, a), U1(c, c))
25.13/8.26	   A^2 -> H(U1(c, a), f(e))
25.13/8.26	   A^2 -> H(U1(c, a), f(k))
25.13/8.26	   A^2 -> H(U1(c, a), U1(d, d))
25.13/8.26	   A^2 -> H(U1(d, e), f(b))
25.13/8.26	   A^2 -> H(U1(d, c), U1(b, b))
25.13/8.26	   A^2 -> H(U1(d, c), f(c))
25.13/8.26	   A^2 -> H(U1(d, c), f(d))
25.13/8.26	   A^2 -> H(U1(d, a), U1(c, b))
25.13/8.26	   A^2 -> H(U1(d, a), U1(d, b))
25.13/8.26	   A^2 -> H(U1(d, a), U1(b, c))
25.13/8.26	   A^2 -> H(U1(d, a), U1(b, d))
25.13/8.26	   A^2 -> H(U1(d, a), U1(c, c))
25.13/8.26	   A^2 -> H(U1(d, a), f(e))
25.13/8.26	   A^2 -> H(U1(d, a), f(k))
25.13/8.26	   A^2 -> H(U1(d, a), U1(d, d))
25.13/8.26	   A^2 -> H(U1(a, e), U1(b, b))
25.13/8.26	   A^2 -> H(U1(a, e), f(c))
25.13/8.26	   A^2 -> H(U1(a, e), f(d))
25.13/8.26	   A^2 -> H(U1(a, k), U1(b, b))
25.13/8.26	   A^2 -> H(U1(a, k), f(c))
25.13/8.26	   A^2 -> H(U1(a, k), f(d))
25.13/8.26	   A^2 -> H(U1(a, c), U1(c, b))
25.13/8.26	   A^2 -> H(U1(a, c), U1(d, b))
25.13/8.26	   A^2 -> H(U1(a, c), U1(b, c))
25.13/8.26	   A^2 -> H(U1(a, c), U1(b, d))
25.13/8.26	   A^2 -> H(U1(a, c), U1(c, c))
25.13/8.26	   A^2 -> H(U1(a, c), f(e))
25.13/8.26	   A^2 -> H(U1(a, c), f(k))
25.13/8.26	   A^2 -> H(U1(a, c), U1(d, d))
25.13/8.26	   A^2 -> H(U1(a, d), U1(c, b))
25.13/8.26	   A^2 -> H(U1(a, d), U1(d, b))
25.13/8.26	   A^2 -> H(U1(a, d), U1(b, c))
25.13/8.26	   A^2 -> H(U1(a, d), U1(b, d))
25.13/8.26	   A^2 -> H(U1(a, d), U1(c, c))
25.13/8.26	   A^2 -> H(U1(a, d), f(e))
25.13/8.26	   A^2 -> H(U1(a, d), f(k))
25.13/8.26	   A^2 -> H(U1(a, d), U1(d, d))
25.13/8.26	   A^2 -> H(U1(a, a), U1(e, b))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, b))
25.13/8.26	   A^2 -> H(U1(a, a), U1(c, d))
25.13/8.26	   A^2 -> H(U1(a, a), U1(d, c))
25.13/8.26	   A^2 -> H(U1(a, a), U1(b, e))
25.13/8.26	   A^2 -> H(U1(a, a), U1(b, k))
25.13/8.26	   A^2 -> H(U1(a, a), U1(e, c))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, c))
25.13/8.26	   A^2 -> H(U1(a, a), U1(c, e))
25.13/8.26	   A^2 -> H(U1(a, a), U1(c, k))
25.13/8.26	   A^2 -> H(U1(a, a), U1(e, e))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, k))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, d))
25.13/8.26	   A^2 -> H(U1(a, a), U1(d, k))
25.13/8.26	   A^2 -> H(c, f(b))
25.13/8.26	   A^2 -> H(U1(e, k), f(b))
25.13/8.26	   A^2 -> H(U1(e, c), U1(b, b))
25.13/8.26	   A^2 -> H(U1(e, c), f(c))
25.13/8.26	   A^2 -> H(U1(e, c), f(d))
25.13/8.26	   A^2 -> H(U1(k, e), f(b))
25.13/8.26	   A^2 -> H(U1(k, c), U1(b, b))
25.13/8.26	   A^2 -> H(U1(k, c), f(c))
25.13/8.26	   A^2 -> H(U1(k, c), f(d))
25.13/8.26	   A^2 -> H(U1(c, e), U1(b, b))
25.13/8.26	   A^2 -> H(U1(c, e), f(c))
25.13/8.26	   A^2 -> H(U1(c, e), f(d))
25.13/8.26	   A^2 -> H(U1(c, k), U1(b, b))
25.13/8.26	   A^2 -> H(U1(c, k), f(c))
25.13/8.26	   A^2 -> H(U1(c, k), f(d))
25.13/8.26	   A^2 -> H(U1(c, c), U1(c, b))
25.13/8.26	   A^2 -> H(U1(c, c), U1(d, b))
25.13/8.26	   A^2 -> H(U1(c, c), U1(b, c))
25.13/8.26	   A^2 -> H(U1(c, c), U1(b, d))
25.13/8.26	   A^2 -> H(U1(c, c), U1(c, c))
25.13/8.26	   A^2 -> H(U1(c, c), f(e))
25.13/8.26	   A^2 -> H(U1(c, c), f(k))
25.13/8.26	   A^2 -> H(U1(c, c), U1(d, d))
25.13/8.26	   A^2 -> H(e, f(b))
25.13/8.26	   A^2 -> H(U1(e, e), U1(b, b))
25.13/8.26	   A^2 -> H(U1(e, e), f(c))
25.13/8.26	   A^2 -> H(U1(e, e), f(d))
25.13/8.26	   A^2 -> H(f(e), U1(c, b))
25.13/8.26	   A^2 -> H(f(e), U1(d, b))
25.13/8.26	   A^2 -> H(f(e), U1(b, c))
25.13/8.26	   A^2 -> H(f(e), U1(b, d))
25.13/8.26	   A^2 -> H(f(e), U1(c, c))
25.13/8.26	   A^2 -> H(f(e), f(e))
25.13/8.26	   A^2 -> H(f(e), f(k))
25.13/8.26	   A^2 -> H(f(e), U1(d, d))
25.13/8.26	   A^2 -> H(U1(k, k), U1(b, b))
25.13/8.26	   A^2 -> H(U1(k, k), f(c))
25.13/8.26	   A^2 -> H(U1(k, k), f(d))
25.13/8.26	
25.13/8.26	The TRS R consists of the following rules:
25.13/8.26	
25.13/8.26	   f(x) -> U1(x, x)
25.13/8.26	   U1(e, x) -> x
25.13/8.26	   a -> c
25.13/8.26	   a -> d
25.13/8.26	   b -> c
25.13/8.26	   b -> d
25.13/8.26	   d -> k
25.13/8.26	   c -> e
25.13/8.26	   c -> k
25.13/8.26	
25.13/8.26	Q is empty.
25.13/8.26	We have to consider all minimal (P,Q,R)-chains.
25.13/8.26	----------------------------------------
25.13/8.26	
25.13/8.26	(145) TransformationProof (EQUIVALENT)
25.13/8.26	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
25.13/8.26	
25.13/8.26	   (A^2 -> H(U1(k, k), U1(b, b)),A^2 -> H(U1(k, k), U1(b, b)))
25.13/8.26	   (A^2 -> H(f(k), U1(c, b)),A^2 -> H(f(k), U1(c, b)))
25.13/8.26	   (A^2 -> H(f(k), U1(d, b)),A^2 -> H(f(k), U1(d, b)))
25.13/8.26	   (A^2 -> H(f(k), U1(b, c)),A^2 -> H(f(k), U1(b, c)))
25.13/8.26	   (A^2 -> H(f(k), U1(b, d)),A^2 -> H(f(k), U1(b, d)))
25.13/8.26	
25.13/8.26	
25.13/8.26	----------------------------------------
25.13/8.26	
25.13/8.26	(146)
25.13/8.26	Obligation:
25.13/8.26	Q DP problem:
25.13/8.26	The TRS P consists of the following rules:
25.13/8.26	
25.13/8.26	   H(x, x) -> G(x, x, f(k))
25.13/8.26	   G(d, x, x) -> A^2
25.13/8.26	   A^2 -> H(f(c), f(c))
25.13/8.26	   A^2 -> H(f(d), f(d))
25.13/8.26	   A^2 -> H(f(k), f(c))
25.13/8.26	   A^2 -> H(f(k), f(d))
25.13/8.26	   A^2 -> H(f(c), U1(c, b))
25.13/8.26	   A^2 -> H(f(c), U1(d, b))
25.13/8.26	   A^2 -> H(f(c), U1(b, c))
25.13/8.26	   A^2 -> H(f(c), U1(b, d))
25.13/8.26	   A^2 -> H(f(c), U1(d, d))
25.13/8.26	   A^2 -> H(f(c), f(k))
25.13/8.26	   A^2 -> H(U1(k, d), f(b))
25.13/8.26	   A^2 -> H(U1(d, k), f(b))
25.13/8.26	   A^2 -> H(U1(d, d), U1(b, b))
25.13/8.26	   A^2 -> H(U1(d, d), f(c))
25.13/8.26	   A^2 -> H(U1(d, d), f(d))
25.13/8.26	   A^2 -> H(f(d), U1(c, b))
25.13/8.26	   A^2 -> H(f(d), U1(d, b))
25.13/8.26	   A^2 -> H(f(d), U1(b, c))
25.13/8.26	   A^2 -> H(f(d), U1(b, d))
25.13/8.26	   A^2 -> H(f(d), U1(c, c))
25.13/8.26	   A^2 -> H(f(d), f(e))
25.13/8.26	   A^2 -> H(f(d), f(k))
25.13/8.26	   A^2 -> H(f(a), U1(e, b))
25.13/8.26	   A^2 -> H(f(a), U1(k, b))
25.13/8.26	   A^2 -> H(f(a), U1(c, d))
25.13/8.26	   A^2 -> H(f(a), U1(d, c))
25.13/8.26	   A^2 -> H(f(a), U1(b, e))
25.13/8.26	   A^2 -> H(f(a), U1(b, k))
25.13/8.26	   A^2 -> H(f(c), U1(c, c))
25.13/8.26	   A^2 -> H(f(a), U1(e, c))
25.13/8.26	   A^2 -> H(f(a), U1(k, c))
25.13/8.26	   A^2 -> H(f(a), U1(c, e))
25.13/8.26	   A^2 -> H(f(a), U1(c, k))
25.13/8.26	   A^2 -> H(f(c), f(e))
25.13/8.26	   A^2 -> H(f(a), U1(e, e))
25.13/8.26	   A^2 -> H(f(a), U1(k, k))
25.13/8.26	   A^2 -> H(f(d), U1(d, d))
25.13/8.26	   A^2 -> H(f(a), U1(k, d))
25.13/8.26	   A^2 -> H(f(a), U1(d, k))
25.13/8.26	   A^2 -> H(a, f(b))
25.13/8.26	   A^2 -> H(U1(e, d), f(b))
25.13/8.26	   A^2 -> H(U1(e, a), U1(b, b))
25.13/8.26	   A^2 -> H(U1(e, a), f(c))
25.13/8.26	   A^2 -> H(U1(e, a), f(d))
25.13/8.26	   A^2 -> H(U1(k, a), U1(b, b))
25.13/8.26	   A^2 -> H(U1(k, a), f(c))
25.13/8.26	   A^2 -> H(U1(k, a), f(d))
25.13/8.26	   A^2 -> H(U1(c, d), U1(b, b))
25.13/8.26	   A^2 -> H(U1(c, d), f(c))
25.13/8.26	   A^2 -> H(U1(c, d), f(d))
25.13/8.26	   A^2 -> H(U1(c, a), U1(c, b))
25.13/8.26	   A^2 -> H(U1(c, a), U1(d, b))
25.13/8.26	   A^2 -> H(U1(c, a), U1(b, c))
25.13/8.26	   A^2 -> H(U1(c, a), U1(b, d))
25.13/8.26	   A^2 -> H(U1(c, a), U1(c, c))
25.13/8.26	   A^2 -> H(U1(c, a), f(e))
25.13/8.26	   A^2 -> H(U1(c, a), f(k))
25.13/8.26	   A^2 -> H(U1(c, a), U1(d, d))
25.13/8.26	   A^2 -> H(U1(d, e), f(b))
25.13/8.26	   A^2 -> H(U1(d, c), U1(b, b))
25.13/8.26	   A^2 -> H(U1(d, c), f(c))
25.13/8.26	   A^2 -> H(U1(d, c), f(d))
25.13/8.26	   A^2 -> H(U1(d, a), U1(c, b))
25.13/8.26	   A^2 -> H(U1(d, a), U1(d, b))
25.13/8.26	   A^2 -> H(U1(d, a), U1(b, c))
25.13/8.26	   A^2 -> H(U1(d, a), U1(b, d))
25.13/8.26	   A^2 -> H(U1(d, a), U1(c, c))
25.13/8.26	   A^2 -> H(U1(d, a), f(e))
25.13/8.26	   A^2 -> H(U1(d, a), f(k))
25.13/8.26	   A^2 -> H(U1(d, a), U1(d, d))
25.13/8.26	   A^2 -> H(U1(a, e), U1(b, b))
25.13/8.26	   A^2 -> H(U1(a, e), f(c))
25.13/8.26	   A^2 -> H(U1(a, e), f(d))
25.13/8.26	   A^2 -> H(U1(a, k), U1(b, b))
25.13/8.26	   A^2 -> H(U1(a, k), f(c))
25.13/8.26	   A^2 -> H(U1(a, k), f(d))
25.13/8.26	   A^2 -> H(U1(a, c), U1(c, b))
25.13/8.26	   A^2 -> H(U1(a, c), U1(d, b))
25.13/8.26	   A^2 -> H(U1(a, c), U1(b, c))
25.13/8.26	   A^2 -> H(U1(a, c), U1(b, d))
25.13/8.26	   A^2 -> H(U1(a, c), U1(c, c))
25.13/8.26	   A^2 -> H(U1(a, c), f(e))
25.13/8.26	   A^2 -> H(U1(a, c), f(k))
25.13/8.26	   A^2 -> H(U1(a, c), U1(d, d))
25.13/8.26	   A^2 -> H(U1(a, d), U1(c, b))
25.13/8.26	   A^2 -> H(U1(a, d), U1(d, b))
25.13/8.26	   A^2 -> H(U1(a, d), U1(b, c))
25.13/8.26	   A^2 -> H(U1(a, d), U1(b, d))
25.13/8.26	   A^2 -> H(U1(a, d), U1(c, c))
25.13/8.26	   A^2 -> H(U1(a, d), f(e))
25.13/8.26	   A^2 -> H(U1(a, d), f(k))
25.13/8.26	   A^2 -> H(U1(a, d), U1(d, d))
25.13/8.26	   A^2 -> H(U1(a, a), U1(e, b))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, b))
25.13/8.26	   A^2 -> H(U1(a, a), U1(c, d))
25.13/8.26	   A^2 -> H(U1(a, a), U1(d, c))
25.13/8.26	   A^2 -> H(U1(a, a), U1(b, e))
25.13/8.26	   A^2 -> H(U1(a, a), U1(b, k))
25.13/8.26	   A^2 -> H(U1(a, a), U1(e, c))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, c))
25.13/8.26	   A^2 -> H(U1(a, a), U1(c, e))
25.13/8.26	   A^2 -> H(U1(a, a), U1(c, k))
25.13/8.26	   A^2 -> H(U1(a, a), U1(e, e))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, k))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, d))
25.13/8.26	   A^2 -> H(U1(a, a), U1(d, k))
25.13/8.26	   A^2 -> H(c, f(b))
25.13/8.26	   A^2 -> H(U1(e, k), f(b))
25.13/8.26	   A^2 -> H(U1(e, c), U1(b, b))
25.13/8.26	   A^2 -> H(U1(e, c), f(c))
25.13/8.26	   A^2 -> H(U1(e, c), f(d))
25.13/8.26	   A^2 -> H(U1(k, e), f(b))
25.13/8.26	   A^2 -> H(U1(k, c), U1(b, b))
25.13/8.26	   A^2 -> H(U1(k, c), f(c))
25.13/8.26	   A^2 -> H(U1(k, c), f(d))
25.13/8.26	   A^2 -> H(U1(c, e), U1(b, b))
25.13/8.26	   A^2 -> H(U1(c, e), f(c))
25.13/8.26	   A^2 -> H(U1(c, e), f(d))
25.13/8.26	   A^2 -> H(U1(c, k), U1(b, b))
25.13/8.26	   A^2 -> H(U1(c, k), f(c))
25.13/8.26	   A^2 -> H(U1(c, k), f(d))
25.13/8.26	   A^2 -> H(U1(c, c), U1(c, b))
25.13/8.26	   A^2 -> H(U1(c, c), U1(d, b))
25.13/8.26	   A^2 -> H(U1(c, c), U1(b, c))
25.13/8.26	   A^2 -> H(U1(c, c), U1(b, d))
25.13/8.26	   A^2 -> H(U1(c, c), U1(c, c))
25.13/8.26	   A^2 -> H(U1(c, c), f(e))
25.13/8.26	   A^2 -> H(U1(c, c), f(k))
25.13/8.26	   A^2 -> H(U1(c, c), U1(d, d))
25.13/8.26	   A^2 -> H(e, f(b))
25.13/8.26	   A^2 -> H(U1(e, e), U1(b, b))
25.13/8.26	   A^2 -> H(U1(e, e), f(c))
25.13/8.26	   A^2 -> H(U1(e, e), f(d))
25.13/8.26	   A^2 -> H(f(e), U1(c, b))
25.13/8.26	   A^2 -> H(f(e), U1(d, b))
25.13/8.26	   A^2 -> H(f(e), U1(b, c))
25.13/8.26	   A^2 -> H(f(e), U1(b, d))
25.13/8.26	   A^2 -> H(f(e), U1(c, c))
25.13/8.26	   A^2 -> H(f(e), f(e))
25.13/8.26	   A^2 -> H(f(e), f(k))
25.13/8.26	   A^2 -> H(f(e), U1(d, d))
25.13/8.26	   A^2 -> H(U1(k, k), U1(b, b))
25.13/8.26	   A^2 -> H(U1(k, k), f(c))
25.13/8.26	   A^2 -> H(U1(k, k), f(d))
25.13/8.26	   A^2 -> H(f(k), U1(c, b))
25.13/8.26	   A^2 -> H(f(k), U1(d, b))
25.13/8.26	   A^2 -> H(f(k), U1(b, c))
25.13/8.26	   A^2 -> H(f(k), U1(b, d))
25.13/8.26	
25.13/8.26	The TRS R consists of the following rules:
25.13/8.26	
25.13/8.26	   f(x) -> U1(x, x)
25.13/8.26	   U1(e, x) -> x
25.13/8.26	   a -> c
25.13/8.26	   a -> d
25.13/8.26	   b -> c
25.13/8.26	   b -> d
25.13/8.26	   d -> k
25.13/8.26	   c -> e
25.13/8.26	   c -> k
25.13/8.26	
25.13/8.26	Q is empty.
25.13/8.26	We have to consider all minimal (P,Q,R)-chains.
25.13/8.26	----------------------------------------
25.13/8.26	
25.13/8.26	(147) TransformationProof (EQUIVALENT)
25.13/8.26	By narrowing [LPAR04] the rule A^2 -> H(f(k), f(c)) at position [] we obtained the following new rules [LPAR04]:
25.13/8.26	
25.13/8.26	   (A^2 -> H(U1(k, k), f(c)),A^2 -> H(U1(k, k), f(c)))
25.13/8.26	   (A^2 -> H(f(k), U1(c, c)),A^2 -> H(f(k), U1(c, c)))
25.13/8.26	   (A^2 -> H(f(k), f(e)),A^2 -> H(f(k), f(e)))
25.13/8.26	   (A^2 -> H(f(k), f(k)),A^2 -> H(f(k), f(k)))
25.13/8.26	
25.13/8.26	
25.13/8.26	----------------------------------------
25.13/8.26	
25.13/8.26	(148)
25.13/8.26	Obligation:
25.13/8.26	Q DP problem:
25.13/8.26	The TRS P consists of the following rules:
25.13/8.26	
25.13/8.26	   H(x, x) -> G(x, x, f(k))
25.13/8.26	   G(d, x, x) -> A^2
25.13/8.26	   A^2 -> H(f(c), f(c))
25.13/8.26	   A^2 -> H(f(d), f(d))
25.13/8.26	   A^2 -> H(f(k), f(d))
25.13/8.26	   A^2 -> H(f(c), U1(c, b))
25.13/8.26	   A^2 -> H(f(c), U1(d, b))
25.13/8.26	   A^2 -> H(f(c), U1(b, c))
25.13/8.26	   A^2 -> H(f(c), U1(b, d))
25.13/8.26	   A^2 -> H(f(c), U1(d, d))
25.13/8.26	   A^2 -> H(f(c), f(k))
25.13/8.26	   A^2 -> H(U1(k, d), f(b))
25.13/8.26	   A^2 -> H(U1(d, k), f(b))
25.13/8.26	   A^2 -> H(U1(d, d), U1(b, b))
25.13/8.26	   A^2 -> H(U1(d, d), f(c))
25.13/8.26	   A^2 -> H(U1(d, d), f(d))
25.13/8.26	   A^2 -> H(f(d), U1(c, b))
25.13/8.26	   A^2 -> H(f(d), U1(d, b))
25.13/8.26	   A^2 -> H(f(d), U1(b, c))
25.13/8.26	   A^2 -> H(f(d), U1(b, d))
25.13/8.26	   A^2 -> H(f(d), U1(c, c))
25.13/8.26	   A^2 -> H(f(d), f(e))
25.13/8.26	   A^2 -> H(f(d), f(k))
25.13/8.26	   A^2 -> H(f(a), U1(e, b))
25.13/8.26	   A^2 -> H(f(a), U1(k, b))
25.13/8.26	   A^2 -> H(f(a), U1(c, d))
25.13/8.26	   A^2 -> H(f(a), U1(d, c))
25.13/8.26	   A^2 -> H(f(a), U1(b, e))
25.13/8.26	   A^2 -> H(f(a), U1(b, k))
25.13/8.26	   A^2 -> H(f(c), U1(c, c))
25.13/8.26	   A^2 -> H(f(a), U1(e, c))
25.13/8.26	   A^2 -> H(f(a), U1(k, c))
25.13/8.26	   A^2 -> H(f(a), U1(c, e))
25.13/8.26	   A^2 -> H(f(a), U1(c, k))
25.13/8.26	   A^2 -> H(f(c), f(e))
25.13/8.26	   A^2 -> H(f(a), U1(e, e))
25.13/8.26	   A^2 -> H(f(a), U1(k, k))
25.13/8.26	   A^2 -> H(f(d), U1(d, d))
25.13/8.26	   A^2 -> H(f(a), U1(k, d))
25.13/8.26	   A^2 -> H(f(a), U1(d, k))
25.13/8.26	   A^2 -> H(a, f(b))
25.13/8.26	   A^2 -> H(U1(e, d), f(b))
25.13/8.26	   A^2 -> H(U1(e, a), U1(b, b))
25.13/8.26	   A^2 -> H(U1(e, a), f(c))
25.13/8.26	   A^2 -> H(U1(e, a), f(d))
25.13/8.26	   A^2 -> H(U1(k, a), U1(b, b))
25.13/8.26	   A^2 -> H(U1(k, a), f(c))
25.13/8.26	   A^2 -> H(U1(k, a), f(d))
25.13/8.26	   A^2 -> H(U1(c, d), U1(b, b))
25.13/8.26	   A^2 -> H(U1(c, d), f(c))
25.13/8.26	   A^2 -> H(U1(c, d), f(d))
25.13/8.26	   A^2 -> H(U1(c, a), U1(c, b))
25.13/8.26	   A^2 -> H(U1(c, a), U1(d, b))
25.13/8.26	   A^2 -> H(U1(c, a), U1(b, c))
25.13/8.26	   A^2 -> H(U1(c, a), U1(b, d))
25.13/8.26	   A^2 -> H(U1(c, a), U1(c, c))
25.13/8.26	   A^2 -> H(U1(c, a), f(e))
25.13/8.26	   A^2 -> H(U1(c, a), f(k))
25.13/8.26	   A^2 -> H(U1(c, a), U1(d, d))
25.13/8.26	   A^2 -> H(U1(d, e), f(b))
25.13/8.26	   A^2 -> H(U1(d, c), U1(b, b))
25.13/8.26	   A^2 -> H(U1(d, c), f(c))
25.13/8.26	   A^2 -> H(U1(d, c), f(d))
25.13/8.26	   A^2 -> H(U1(d, a), U1(c, b))
25.13/8.26	   A^2 -> H(U1(d, a), U1(d, b))
25.13/8.26	   A^2 -> H(U1(d, a), U1(b, c))
25.13/8.26	   A^2 -> H(U1(d, a), U1(b, d))
25.13/8.26	   A^2 -> H(U1(d, a), U1(c, c))
25.13/8.26	   A^2 -> H(U1(d, a), f(e))
25.13/8.26	   A^2 -> H(U1(d, a), f(k))
25.13/8.26	   A^2 -> H(U1(d, a), U1(d, d))
25.13/8.26	   A^2 -> H(U1(a, e), U1(b, b))
25.13/8.26	   A^2 -> H(U1(a, e), f(c))
25.13/8.26	   A^2 -> H(U1(a, e), f(d))
25.13/8.26	   A^2 -> H(U1(a, k), U1(b, b))
25.13/8.26	   A^2 -> H(U1(a, k), f(c))
25.13/8.26	   A^2 -> H(U1(a, k), f(d))
25.13/8.26	   A^2 -> H(U1(a, c), U1(c, b))
25.13/8.26	   A^2 -> H(U1(a, c), U1(d, b))
25.13/8.26	   A^2 -> H(U1(a, c), U1(b, c))
25.13/8.26	   A^2 -> H(U1(a, c), U1(b, d))
25.13/8.26	   A^2 -> H(U1(a, c), U1(c, c))
25.13/8.26	   A^2 -> H(U1(a, c), f(e))
25.13/8.26	   A^2 -> H(U1(a, c), f(k))
25.13/8.26	   A^2 -> H(U1(a, c), U1(d, d))
25.13/8.26	   A^2 -> H(U1(a, d), U1(c, b))
25.13/8.26	   A^2 -> H(U1(a, d), U1(d, b))
25.13/8.26	   A^2 -> H(U1(a, d), U1(b, c))
25.13/8.26	   A^2 -> H(U1(a, d), U1(b, d))
25.13/8.26	   A^2 -> H(U1(a, d), U1(c, c))
25.13/8.26	   A^2 -> H(U1(a, d), f(e))
25.13/8.26	   A^2 -> H(U1(a, d), f(k))
25.13/8.26	   A^2 -> H(U1(a, d), U1(d, d))
25.13/8.26	   A^2 -> H(U1(a, a), U1(e, b))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, b))
25.13/8.26	   A^2 -> H(U1(a, a), U1(c, d))
25.13/8.26	   A^2 -> H(U1(a, a), U1(d, c))
25.13/8.26	   A^2 -> H(U1(a, a), U1(b, e))
25.13/8.26	   A^2 -> H(U1(a, a), U1(b, k))
25.13/8.26	   A^2 -> H(U1(a, a), U1(e, c))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, c))
25.13/8.26	   A^2 -> H(U1(a, a), U1(c, e))
25.13/8.26	   A^2 -> H(U1(a, a), U1(c, k))
25.13/8.26	   A^2 -> H(U1(a, a), U1(e, e))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, k))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, d))
25.13/8.26	   A^2 -> H(U1(a, a), U1(d, k))
25.13/8.26	   A^2 -> H(c, f(b))
25.13/8.26	   A^2 -> H(U1(e, k), f(b))
25.13/8.26	   A^2 -> H(U1(e, c), U1(b, b))
25.13/8.26	   A^2 -> H(U1(e, c), f(c))
25.13/8.26	   A^2 -> H(U1(e, c), f(d))
25.13/8.26	   A^2 -> H(U1(k, e), f(b))
25.13/8.26	   A^2 -> H(U1(k, c), U1(b, b))
25.13/8.26	   A^2 -> H(U1(k, c), f(c))
25.13/8.26	   A^2 -> H(U1(k, c), f(d))
25.13/8.26	   A^2 -> H(U1(c, e), U1(b, b))
25.13/8.26	   A^2 -> H(U1(c, e), f(c))
25.13/8.26	   A^2 -> H(U1(c, e), f(d))
25.13/8.26	   A^2 -> H(U1(c, k), U1(b, b))
25.13/8.26	   A^2 -> H(U1(c, k), f(c))
25.13/8.26	   A^2 -> H(U1(c, k), f(d))
25.13/8.26	   A^2 -> H(U1(c, c), U1(c, b))
25.13/8.26	   A^2 -> H(U1(c, c), U1(d, b))
25.13/8.26	   A^2 -> H(U1(c, c), U1(b, c))
25.13/8.26	   A^2 -> H(U1(c, c), U1(b, d))
25.13/8.26	   A^2 -> H(U1(c, c), U1(c, c))
25.13/8.26	   A^2 -> H(U1(c, c), f(e))
25.13/8.26	   A^2 -> H(U1(c, c), f(k))
25.13/8.26	   A^2 -> H(U1(c, c), U1(d, d))
25.13/8.26	   A^2 -> H(e, f(b))
25.13/8.26	   A^2 -> H(U1(e, e), U1(b, b))
25.13/8.26	   A^2 -> H(U1(e, e), f(c))
25.13/8.26	   A^2 -> H(U1(e, e), f(d))
25.13/8.26	   A^2 -> H(f(e), U1(c, b))
25.13/8.26	   A^2 -> H(f(e), U1(d, b))
25.13/8.26	   A^2 -> H(f(e), U1(b, c))
25.13/8.26	   A^2 -> H(f(e), U1(b, d))
25.13/8.26	   A^2 -> H(f(e), U1(c, c))
25.13/8.26	   A^2 -> H(f(e), f(e))
25.13/8.26	   A^2 -> H(f(e), f(k))
25.13/8.26	   A^2 -> H(f(e), U1(d, d))
25.13/8.26	   A^2 -> H(U1(k, k), U1(b, b))
25.13/8.26	   A^2 -> H(U1(k, k), f(c))
25.13/8.26	   A^2 -> H(U1(k, k), f(d))
25.13/8.26	   A^2 -> H(f(k), U1(c, b))
25.13/8.26	   A^2 -> H(f(k), U1(d, b))
25.13/8.26	   A^2 -> H(f(k), U1(b, c))
25.13/8.26	   A^2 -> H(f(k), U1(b, d))
25.13/8.26	   A^2 -> H(f(k), U1(c, c))
25.13/8.26	   A^2 -> H(f(k), f(e))
25.13/8.26	   A^2 -> H(f(k), f(k))
25.13/8.26	
25.13/8.26	The TRS R consists of the following rules:
25.13/8.26	
25.13/8.26	   f(x) -> U1(x, x)
25.13/8.26	   U1(e, x) -> x
25.13/8.26	   a -> c
25.13/8.26	   a -> d
25.13/8.26	   b -> c
25.13/8.26	   b -> d
25.13/8.26	   d -> k
25.13/8.26	   c -> e
25.13/8.26	   c -> k
25.13/8.26	
25.13/8.26	Q is empty.
25.13/8.26	We have to consider all minimal (P,Q,R)-chains.
25.13/8.26	----------------------------------------
25.13/8.26	
25.13/8.26	(149) TransformationProof (EQUIVALENT)
25.13/8.26	By narrowing [LPAR04] the rule A^2 -> H(f(k), f(d)) at position [] we obtained the following new rules [LPAR04]:
25.13/8.26	
25.13/8.26	   (A^2 -> H(U1(k, k), f(d)),A^2 -> H(U1(k, k), f(d)))
25.13/8.26	   (A^2 -> H(f(k), U1(d, d)),A^2 -> H(f(k), U1(d, d)))
25.13/8.26	   (A^2 -> H(f(k), f(k)),A^2 -> H(f(k), f(k)))
25.13/8.26	
25.13/8.26	
25.13/8.26	----------------------------------------
25.13/8.26	
25.13/8.26	(150)
25.13/8.26	Obligation:
25.13/8.26	Q DP problem:
25.13/8.26	The TRS P consists of the following rules:
25.13/8.26	
25.13/8.26	   H(x, x) -> G(x, x, f(k))
25.13/8.26	   G(d, x, x) -> A^2
25.13/8.26	   A^2 -> H(f(c), f(c))
25.13/8.26	   A^2 -> H(f(d), f(d))
25.13/8.26	   A^2 -> H(f(c), U1(c, b))
25.13/8.26	   A^2 -> H(f(c), U1(d, b))
25.13/8.26	   A^2 -> H(f(c), U1(b, c))
25.13/8.26	   A^2 -> H(f(c), U1(b, d))
25.13/8.26	   A^2 -> H(f(c), U1(d, d))
25.13/8.26	   A^2 -> H(f(c), f(k))
25.13/8.26	   A^2 -> H(U1(k, d), f(b))
25.13/8.26	   A^2 -> H(U1(d, k), f(b))
25.13/8.26	   A^2 -> H(U1(d, d), U1(b, b))
25.13/8.26	   A^2 -> H(U1(d, d), f(c))
25.13/8.26	   A^2 -> H(U1(d, d), f(d))
25.13/8.26	   A^2 -> H(f(d), U1(c, b))
25.13/8.26	   A^2 -> H(f(d), U1(d, b))
25.13/8.26	   A^2 -> H(f(d), U1(b, c))
25.13/8.26	   A^2 -> H(f(d), U1(b, d))
25.13/8.26	   A^2 -> H(f(d), U1(c, c))
25.13/8.26	   A^2 -> H(f(d), f(e))
25.13/8.26	   A^2 -> H(f(d), f(k))
25.13/8.26	   A^2 -> H(f(a), U1(e, b))
25.13/8.26	   A^2 -> H(f(a), U1(k, b))
25.13/8.26	   A^2 -> H(f(a), U1(c, d))
25.13/8.26	   A^2 -> H(f(a), U1(d, c))
25.13/8.26	   A^2 -> H(f(a), U1(b, e))
25.13/8.26	   A^2 -> H(f(a), U1(b, k))
25.13/8.26	   A^2 -> H(f(c), U1(c, c))
25.13/8.26	   A^2 -> H(f(a), U1(e, c))
25.13/8.26	   A^2 -> H(f(a), U1(k, c))
25.13/8.26	   A^2 -> H(f(a), U1(c, e))
25.13/8.26	   A^2 -> H(f(a), U1(c, k))
25.13/8.26	   A^2 -> H(f(c), f(e))
25.13/8.26	   A^2 -> H(f(a), U1(e, e))
25.13/8.26	   A^2 -> H(f(a), U1(k, k))
25.13/8.26	   A^2 -> H(f(d), U1(d, d))
25.13/8.26	   A^2 -> H(f(a), U1(k, d))
25.13/8.26	   A^2 -> H(f(a), U1(d, k))
25.13/8.26	   A^2 -> H(a, f(b))
25.13/8.26	   A^2 -> H(U1(e, d), f(b))
25.13/8.26	   A^2 -> H(U1(e, a), U1(b, b))
25.13/8.26	   A^2 -> H(U1(e, a), f(c))
25.13/8.26	   A^2 -> H(U1(e, a), f(d))
25.13/8.26	   A^2 -> H(U1(k, a), U1(b, b))
25.13/8.26	   A^2 -> H(U1(k, a), f(c))
25.13/8.26	   A^2 -> H(U1(k, a), f(d))
25.13/8.26	   A^2 -> H(U1(c, d), U1(b, b))
25.13/8.26	   A^2 -> H(U1(c, d), f(c))
25.13/8.26	   A^2 -> H(U1(c, d), f(d))
25.13/8.26	   A^2 -> H(U1(c, a), U1(c, b))
25.13/8.26	   A^2 -> H(U1(c, a), U1(d, b))
25.13/8.26	   A^2 -> H(U1(c, a), U1(b, c))
25.13/8.26	   A^2 -> H(U1(c, a), U1(b, d))
25.13/8.26	   A^2 -> H(U1(c, a), U1(c, c))
25.13/8.26	   A^2 -> H(U1(c, a), f(e))
25.13/8.26	   A^2 -> H(U1(c, a), f(k))
25.13/8.26	   A^2 -> H(U1(c, a), U1(d, d))
25.13/8.26	   A^2 -> H(U1(d, e), f(b))
25.13/8.26	   A^2 -> H(U1(d, c), U1(b, b))
25.13/8.26	   A^2 -> H(U1(d, c), f(c))
25.13/8.26	   A^2 -> H(U1(d, c), f(d))
25.13/8.26	   A^2 -> H(U1(d, a), U1(c, b))
25.13/8.26	   A^2 -> H(U1(d, a), U1(d, b))
25.13/8.26	   A^2 -> H(U1(d, a), U1(b, c))
25.13/8.26	   A^2 -> H(U1(d, a), U1(b, d))
25.13/8.26	   A^2 -> H(U1(d, a), U1(c, c))
25.13/8.26	   A^2 -> H(U1(d, a), f(e))
25.13/8.26	   A^2 -> H(U1(d, a), f(k))
25.13/8.26	   A^2 -> H(U1(d, a), U1(d, d))
25.13/8.26	   A^2 -> H(U1(a, e), U1(b, b))
25.13/8.26	   A^2 -> H(U1(a, e), f(c))
25.13/8.26	   A^2 -> H(U1(a, e), f(d))
25.13/8.26	   A^2 -> H(U1(a, k), U1(b, b))
25.13/8.26	   A^2 -> H(U1(a, k), f(c))
25.13/8.26	   A^2 -> H(U1(a, k), f(d))
25.13/8.26	   A^2 -> H(U1(a, c), U1(c, b))
25.13/8.26	   A^2 -> H(U1(a, c), U1(d, b))
25.13/8.26	   A^2 -> H(U1(a, c), U1(b, c))
25.13/8.26	   A^2 -> H(U1(a, c), U1(b, d))
25.13/8.26	   A^2 -> H(U1(a, c), U1(c, c))
25.13/8.26	   A^2 -> H(U1(a, c), f(e))
25.13/8.26	   A^2 -> H(U1(a, c), f(k))
25.13/8.26	   A^2 -> H(U1(a, c), U1(d, d))
25.13/8.26	   A^2 -> H(U1(a, d), U1(c, b))
25.13/8.26	   A^2 -> H(U1(a, d), U1(d, b))
25.13/8.26	   A^2 -> H(U1(a, d), U1(b, c))
25.13/8.26	   A^2 -> H(U1(a, d), U1(b, d))
25.13/8.26	   A^2 -> H(U1(a, d), U1(c, c))
25.13/8.26	   A^2 -> H(U1(a, d), f(e))
25.13/8.26	   A^2 -> H(U1(a, d), f(k))
25.13/8.26	   A^2 -> H(U1(a, d), U1(d, d))
25.13/8.26	   A^2 -> H(U1(a, a), U1(e, b))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, b))
25.13/8.26	   A^2 -> H(U1(a, a), U1(c, d))
25.13/8.26	   A^2 -> H(U1(a, a), U1(d, c))
25.13/8.26	   A^2 -> H(U1(a, a), U1(b, e))
25.13/8.26	   A^2 -> H(U1(a, a), U1(b, k))
25.13/8.26	   A^2 -> H(U1(a, a), U1(e, c))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, c))
25.13/8.26	   A^2 -> H(U1(a, a), U1(c, e))
25.13/8.26	   A^2 -> H(U1(a, a), U1(c, k))
25.13/8.26	   A^2 -> H(U1(a, a), U1(e, e))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, k))
25.13/8.26	   A^2 -> H(U1(a, a), U1(k, d))
25.13/8.26	   A^2 -> H(U1(a, a), U1(d, k))
25.13/8.26	   A^2 -> H(c, f(b))
25.13/8.26	   A^2 -> H(U1(e, k), f(b))
25.13/8.26	   A^2 -> H(U1(e, c), U1(b, b))
25.13/8.26	   A^2 -> H(U1(e, c), f(c))
25.13/8.26	   A^2 -> H(U1(e, c), f(d))
25.13/8.26	   A^2 -> H(U1(k, e), f(b))
25.13/8.26	   A^2 -> H(U1(k, c), U1(b, b))
25.13/8.26	   A^2 -> H(U1(k, c), f(c))
25.13/8.26	   A^2 -> H(U1(k, c), f(d))
25.13/8.26	   A^2 -> H(U1(c, e), U1(b, b))
25.13/8.26	   A^2 -> H(U1(c, e), f(c))
25.13/8.26	   A^2 -> H(U1(c, e), f(d))
25.13/8.26	   A^2 -> H(U1(c, k), U1(b, b))
25.13/8.26	   A^2 -> H(U1(c, k), f(c))
25.13/8.26	   A^2 -> H(U1(c, k), f(d))
25.13/8.26	   A^2 -> H(U1(c, c), U1(c, b))
25.13/8.26	   A^2 -> H(U1(c, c), U1(d, b))
25.13/8.26	   A^2 -> H(U1(c, c), U1(b, c))
25.13/8.26	   A^2 -> H(U1(c, c), U1(b, d))
25.13/8.26	   A^2 -> H(U1(c, c), U1(c, c))
25.13/8.26	   A^2 -> H(U1(c, c), f(e))
25.13/8.26	   A^2 -> H(U1(c, c), f(k))
25.13/8.26	   A^2 -> H(U1(c, c), U1(d, d))
25.13/8.26	   A^2 -> H(e, f(b))
25.13/8.26	   A^2 -> H(U1(e, e), U1(b, b))
25.13/8.26	   A^2 -> H(U1(e, e), f(c))
25.13/8.26	   A^2 -> H(U1(e, e), f(d))
25.13/8.26	   A^2 -> H(f(e), U1(c, b))
25.13/8.26	   A^2 -> H(f(e), U1(d, b))
25.13/8.26	   A^2 -> H(f(e), U1(b, c))
25.13/8.26	   A^2 -> H(f(e), U1(b, d))
25.13/8.26	   A^2 -> H(f(e), U1(c, c))
25.13/8.26	   A^2 -> H(f(e), f(e))
25.13/8.26	   A^2 -> H(f(e), f(k))
25.13/8.26	   A^2 -> H(f(e), U1(d, d))
25.13/8.26	   A^2 -> H(U1(k, k), U1(b, b))
25.13/8.26	   A^2 -> H(U1(k, k), f(c))
25.13/8.26	   A^2 -> H(U1(k, k), f(d))
25.13/8.26	   A^2 -> H(f(k), U1(c, b))
25.13/8.26	   A^2 -> H(f(k), U1(d, b))
25.13/8.26	   A^2 -> H(f(k), U1(b, c))
25.13/8.26	   A^2 -> H(f(k), U1(b, d))
25.13/8.26	   A^2 -> H(f(k), U1(c, c))
25.13/8.26	   A^2 -> H(f(k), f(e))
25.13/8.26	   A^2 -> H(f(k), f(k))
25.13/8.26	   A^2 -> H(f(k), U1(d, d))
25.13/8.26	
25.13/8.26	The TRS R consists of the following rules:
25.13/8.26	
25.13/8.26	   f(x) -> U1(x, x)
25.13/8.26	   U1(e, x) -> x
25.13/8.26	   a -> c
25.13/8.26	   a -> d
25.13/8.26	   b -> c
25.13/8.26	   b -> d
25.13/8.26	   d -> k
25.13/8.26	   c -> e
25.13/8.26	   c -> k
25.13/8.26	
25.13/8.26	Q is empty.
25.13/8.26	We have to consider all minimal (P,Q,R)-chains.
25.13/8.26	----------------------------------------
25.13/8.26	
25.13/8.26	(151) TransformationProof (EQUIVALENT)
25.13/8.26	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
25.13/8.26	
25.13/8.26	   (A^2 -> H(U1(c, c), U1(c, b)),A^2 -> H(U1(c, c), U1(c, b)))
25.13/8.26	   (A^2 -> H(f(e), U1(c, b)),A^2 -> H(f(e), U1(c, b)))
25.13/8.26	   (A^2 -> H(f(k), U1(c, b)),A^2 -> H(f(k), U1(c, b)))
25.13/8.26	   (A^2 -> H(f(c), U1(e, b)),A^2 -> H(f(c), U1(e, b)))
25.13/8.26	   (A^2 -> H(f(c), U1(k, b)),A^2 -> H(f(c), U1(k, b)))
25.13/8.26	   (A^2 -> H(f(c), U1(c, c)),A^2 -> H(f(c), U1(c, c)))
25.13/8.26	   (A^2 -> H(f(c), U1(c, d)),A^2 -> H(f(c), U1(c, d)))
25.13/8.26	
25.13/8.26	
25.13/8.26	----------------------------------------
25.13/8.26	
25.13/8.26	(152)
25.13/8.26	Obligation:
25.13/8.26	Q DP problem:
25.13/8.26	The TRS P consists of the following rules:
25.13/8.26	
25.13/8.26	   H(x, x) -> G(x, x, f(k))
25.13/8.26	   G(d, x, x) -> A^2
25.13/8.26	   A^2 -> H(f(c), f(c))
25.13/8.26	   A^2 -> H(f(d), f(d))
25.13/8.26	   A^2 -> H(f(c), U1(d, b))
25.13/8.26	   A^2 -> H(f(c), U1(b, c))
25.13/8.26	   A^2 -> H(f(c), U1(b, d))
25.13/8.26	   A^2 -> H(f(c), U1(d, d))
25.13/8.26	   A^2 -> H(f(c), f(k))
25.13/8.26	   A^2 -> H(U1(k, d), f(b))
25.13/8.26	   A^2 -> H(U1(d, k), f(b))
25.13/8.26	   A^2 -> H(U1(d, d), U1(b, b))
25.13/8.26	   A^2 -> H(U1(d, d), f(c))
25.13/8.26	   A^2 -> H(U1(d, d), f(d))
25.13/8.26	   A^2 -> H(f(d), U1(c, b))
25.13/8.26	   A^2 -> H(f(d), U1(d, b))
25.13/8.26	   A^2 -> H(f(d), U1(b, c))
25.13/8.26	   A^2 -> H(f(d), U1(b, d))
25.13/8.26	   A^2 -> H(f(d), U1(c, c))
25.13/8.26	   A^2 -> H(f(d), f(e))
25.13/8.26	   A^2 -> H(f(d), f(k))
25.13/8.26	   A^2 -> H(f(a), U1(e, b))
25.13/8.26	   A^2 -> H(f(a), U1(k, b))
25.13/8.26	   A^2 -> H(f(a), U1(c, d))
25.13/8.26	   A^2 -> H(f(a), U1(d, c))
25.13/8.26	   A^2 -> H(f(a), U1(b, e))
25.13/8.26	   A^2 -> H(f(a), U1(b, k))
25.13/8.26	   A^2 -> H(f(c), U1(c, c))
25.13/8.26	   A^2 -> H(f(a), U1(e, c))
25.13/8.26	   A^2 -> H(f(a), U1(k, c))
25.13/8.26	   A^2 -> H(f(a), U1(c, e))
25.13/8.26	   A^2 -> H(f(a), U1(c, k))
25.13/8.26	   A^2 -> H(f(c), f(e))
25.13/8.26	   A^2 -> H(f(a), U1(e, e))
25.13/8.26	   A^2 -> H(f(a), U1(k, k))
25.13/8.26	   A^2 -> H(f(d), U1(d, d))
25.13/8.26	   A^2 -> H(f(a), U1(k, d))
25.13/8.26	   A^2 -> H(f(a), U1(d, k))
25.13/8.26	   A^2 -> H(a, f(b))
25.13/8.26	   A^2 -> H(U1(e, d), f(b))
25.13/8.26	   A^2 -> H(U1(e, a), U1(b, b))
25.13/8.26	   A^2 -> H(U1(e, a), f(c))
25.13/8.26	   A^2 -> H(U1(e, a), f(d))
25.13/8.26	   A^2 -> H(U1(k, a), U1(b, b))
25.13/8.26	   A^2 -> H(U1(k, a), f(c))
25.13/8.26	   A^2 -> H(U1(k, a), f(d))
25.13/8.26	   A^2 -> H(U1(c, d), U1(b, b))
25.13/8.26	   A^2 -> H(U1(c, d), f(c))
25.13/8.26	   A^2 -> H(U1(c, d), f(d))
25.13/8.26	   A^2 -> H(U1(c, a), U1(c, b))
25.13/8.26	   A^2 -> H(U1(c, a), U1(d, b))
25.13/8.26	   A^2 -> H(U1(c, a), U1(b, c))
25.13/8.26	   A^2 -> H(U1(c, a), U1(b, d))
25.13/8.26	   A^2 -> H(U1(c, a), U1(c, c))
25.13/8.26	   A^2 -> H(U1(c, a), f(e))
25.13/8.26	   A^2 -> H(U1(c, a), f(k))
25.13/8.26	   A^2 -> H(U1(c, a), U1(d, d))
25.13/8.26	   A^2 -> H(U1(d, e), f(b))
25.13/8.26	   A^2 -> H(U1(d, c), U1(b, b))
25.13/8.26	   A^2 -> H(U1(d, c), f(c))
25.13/8.26	   A^2 -> H(U1(d, c), f(d))
25.13/8.26	   A^2 -> H(U1(d, a), U1(c, b))
25.13/8.26	   A^2 -> H(U1(d, a), U1(d, b))
25.13/8.26	   A^2 -> H(U1(d, a), U1(b, c))
25.13/8.26	   A^2 -> H(U1(d, a), U1(b, d))
25.13/8.26	   A^2 -> H(U1(d, a), U1(c, c))
25.13/8.26	   A^2 -> H(U1(d, a), f(e))
25.13/8.26	   A^2 -> H(U1(d, a), f(k))
25.13/8.26	   A^2 -> H(U1(d, a), U1(d, d))
25.13/8.26	   A^2 -> H(U1(a, e), U1(b, b))
25.13/8.26	   A^2 -> H(U1(a, e), f(c))
25.13/8.26	   A^2 -> H(U1(a, e), f(d))
25.13/8.26	   A^2 -> H(U1(a, k), U1(b, b))
25.13/8.26	   A^2 -> H(U1(a, k), f(c))
25.13/8.26	   A^2 -> H(U1(a, k), f(d))
25.13/8.26	   A^2 -> H(U1(a, c), U1(c, b))
25.13/8.26	   A^2 -> H(U1(a, c), U1(d, b))
25.13/8.26	   A^2 -> H(U1(a, c), U1(b, c))
25.13/8.26	   A^2 -> H(U1(a, c), U1(b, d))
25.13/8.26	   A^2 -> H(U1(a, c), U1(c, c))
25.13/8.26	   A^2 -> H(U1(a, c), f(e))
25.13/8.26	   A^2 -> H(U1(a, c), f(k))
25.13/8.26	   A^2 -> H(U1(a, c), U1(d, d))
25.13/8.26	   A^2 -> H(U1(a, d), U1(c, b))
25.13/8.26	   A^2 -> H(U1(a, d), U1(d, b))
25.13/8.26	   A^2 -> H(U1(a, d), U1(b, c))
25.13/8.26	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.26	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.26	   A^2 -> H(U1(a, d), f(e))
25.19/8.26	   A^2 -> H(U1(a, d), f(k))
25.19/8.26	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.26	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.26	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.26	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.26	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.26	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.26	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.26	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.26	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.26	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.26	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.26	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.26	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.26	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.26	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.26	   A^2 -> H(c, f(b))
25.19/8.26	   A^2 -> H(U1(e, k), f(b))
25.19/8.26	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.26	   A^2 -> H(U1(e, c), f(c))
25.19/8.26	   A^2 -> H(U1(e, c), f(d))
25.19/8.26	   A^2 -> H(U1(k, e), f(b))
25.19/8.26	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.26	   A^2 -> H(U1(k, c), f(c))
25.19/8.26	   A^2 -> H(U1(k, c), f(d))
25.19/8.26	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.26	   A^2 -> H(U1(c, e), f(c))
25.19/8.26	   A^2 -> H(U1(c, e), f(d))
25.19/8.26	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.26	   A^2 -> H(U1(c, k), f(c))
25.19/8.26	   A^2 -> H(U1(c, k), f(d))
25.19/8.26	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.26	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.26	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.26	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.26	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.26	   A^2 -> H(U1(c, c), f(e))
25.19/8.26	   A^2 -> H(U1(c, c), f(k))
25.19/8.26	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.26	   A^2 -> H(e, f(b))
25.19/8.26	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.26	   A^2 -> H(U1(e, e), f(c))
25.19/8.26	   A^2 -> H(U1(e, e), f(d))
25.19/8.26	   A^2 -> H(f(e), U1(c, b))
25.19/8.26	   A^2 -> H(f(e), U1(d, b))
25.19/8.26	   A^2 -> H(f(e), U1(b, c))
25.19/8.26	   A^2 -> H(f(e), U1(b, d))
25.19/8.26	   A^2 -> H(f(e), U1(c, c))
25.19/8.26	   A^2 -> H(f(e), f(e))
25.19/8.26	   A^2 -> H(f(e), f(k))
25.19/8.26	   A^2 -> H(f(e), U1(d, d))
25.19/8.26	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.26	   A^2 -> H(U1(k, k), f(c))
25.19/8.26	   A^2 -> H(U1(k, k), f(d))
25.19/8.26	   A^2 -> H(f(k), U1(c, b))
25.19/8.26	   A^2 -> H(f(k), U1(d, b))
25.19/8.26	   A^2 -> H(f(k), U1(b, c))
25.19/8.26	   A^2 -> H(f(k), U1(b, d))
25.19/8.26	   A^2 -> H(f(k), U1(c, c))
25.19/8.26	   A^2 -> H(f(k), f(e))
25.19/8.26	   A^2 -> H(f(k), f(k))
25.19/8.26	   A^2 -> H(f(k), U1(d, d))
25.19/8.26	   A^2 -> H(f(c), U1(e, b))
25.19/8.26	   A^2 -> H(f(c), U1(k, b))
25.19/8.26	   A^2 -> H(f(c), U1(c, d))
25.19/8.26	
25.19/8.26	The TRS R consists of the following rules:
25.19/8.26	
25.19/8.26	   f(x) -> U1(x, x)
25.19/8.26	   U1(e, x) -> x
25.19/8.26	   a -> c
25.19/8.26	   a -> d
25.19/8.26	   b -> c
25.19/8.26	   b -> d
25.19/8.26	   d -> k
25.19/8.26	   c -> e
25.19/8.26	   c -> k
25.19/8.26	
25.19/8.26	Q is empty.
25.19/8.26	We have to consider all minimal (P,Q,R)-chains.
25.19/8.26	----------------------------------------
25.19/8.26	
25.19/8.26	(153) TransformationProof (EQUIVALENT)
25.19/8.26	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.26	
25.19/8.26	   (A^2 -> H(U1(c, c), U1(d, b)),A^2 -> H(U1(c, c), U1(d, b)))
25.19/8.26	   (A^2 -> H(f(e), U1(d, b)),A^2 -> H(f(e), U1(d, b)))
25.19/8.26	   (A^2 -> H(f(k), U1(d, b)),A^2 -> H(f(k), U1(d, b)))
25.19/8.26	   (A^2 -> H(f(c), U1(k, b)),A^2 -> H(f(c), U1(k, b)))
25.19/8.26	   (A^2 -> H(f(c), U1(d, c)),A^2 -> H(f(c), U1(d, c)))
25.19/8.26	   (A^2 -> H(f(c), U1(d, d)),A^2 -> H(f(c), U1(d, d)))
25.19/8.26	
25.19/8.26	
25.19/8.26	----------------------------------------
25.19/8.26	
25.19/8.26	(154)
25.19/8.26	Obligation:
25.19/8.26	Q DP problem:
25.19/8.26	The TRS P consists of the following rules:
25.19/8.26	
25.19/8.26	   H(x, x) -> G(x, x, f(k))
25.19/8.26	   G(d, x, x) -> A^2
25.19/8.26	   A^2 -> H(f(c), f(c))
25.19/8.26	   A^2 -> H(f(d), f(d))
25.19/8.26	   A^2 -> H(f(c), U1(b, c))
25.19/8.26	   A^2 -> H(f(c), U1(b, d))
25.19/8.26	   A^2 -> H(f(c), U1(d, d))
25.19/8.26	   A^2 -> H(f(c), f(k))
25.19/8.26	   A^2 -> H(U1(k, d), f(b))
25.19/8.26	   A^2 -> H(U1(d, k), f(b))
25.19/8.26	   A^2 -> H(U1(d, d), U1(b, b))
25.19/8.26	   A^2 -> H(U1(d, d), f(c))
25.19/8.26	   A^2 -> H(U1(d, d), f(d))
25.19/8.26	   A^2 -> H(f(d), U1(c, b))
25.19/8.26	   A^2 -> H(f(d), U1(d, b))
25.19/8.26	   A^2 -> H(f(d), U1(b, c))
25.19/8.26	   A^2 -> H(f(d), U1(b, d))
25.19/8.26	   A^2 -> H(f(d), U1(c, c))
25.19/8.26	   A^2 -> H(f(d), f(e))
25.19/8.26	   A^2 -> H(f(d), f(k))
25.19/8.26	   A^2 -> H(f(a), U1(e, b))
25.19/8.26	   A^2 -> H(f(a), U1(k, b))
25.19/8.26	   A^2 -> H(f(a), U1(c, d))
25.19/8.26	   A^2 -> H(f(a), U1(d, c))
25.19/8.26	   A^2 -> H(f(a), U1(b, e))
25.19/8.26	   A^2 -> H(f(a), U1(b, k))
25.19/8.26	   A^2 -> H(f(c), U1(c, c))
25.19/8.26	   A^2 -> H(f(a), U1(e, c))
25.19/8.26	   A^2 -> H(f(a), U1(k, c))
25.19/8.26	   A^2 -> H(f(a), U1(c, e))
25.19/8.26	   A^2 -> H(f(a), U1(c, k))
25.19/8.26	   A^2 -> H(f(c), f(e))
25.19/8.26	   A^2 -> H(f(a), U1(e, e))
25.19/8.26	   A^2 -> H(f(a), U1(k, k))
25.19/8.26	   A^2 -> H(f(d), U1(d, d))
25.19/8.26	   A^2 -> H(f(a), U1(k, d))
25.19/8.26	   A^2 -> H(f(a), U1(d, k))
25.19/8.26	   A^2 -> H(a, f(b))
25.19/8.26	   A^2 -> H(U1(e, d), f(b))
25.19/8.26	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.26	   A^2 -> H(U1(e, a), f(c))
25.19/8.26	   A^2 -> H(U1(e, a), f(d))
25.19/8.26	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.26	   A^2 -> H(U1(k, a), f(c))
25.19/8.26	   A^2 -> H(U1(k, a), f(d))
25.19/8.26	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.26	   A^2 -> H(U1(c, d), f(c))
25.19/8.26	   A^2 -> H(U1(c, d), f(d))
25.19/8.26	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.26	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.26	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.26	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.26	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.26	   A^2 -> H(U1(c, a), f(e))
25.19/8.26	   A^2 -> H(U1(c, a), f(k))
25.19/8.26	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.26	   A^2 -> H(U1(d, e), f(b))
25.19/8.26	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.26	   A^2 -> H(U1(d, c), f(c))
25.19/8.26	   A^2 -> H(U1(d, c), f(d))
25.19/8.26	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.26	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.26	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.26	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.26	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.26	   A^2 -> H(U1(d, a), f(e))
25.19/8.26	   A^2 -> H(U1(d, a), f(k))
25.19/8.26	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.26	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.26	   A^2 -> H(U1(a, e), f(c))
25.19/8.26	   A^2 -> H(U1(a, e), f(d))
25.19/8.26	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.26	   A^2 -> H(U1(a, k), f(c))
25.19/8.26	   A^2 -> H(U1(a, k), f(d))
25.19/8.26	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.26	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.26	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.26	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.26	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.26	   A^2 -> H(U1(a, c), f(e))
25.19/8.26	   A^2 -> H(U1(a, c), f(k))
25.19/8.26	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.26	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.26	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.26	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.26	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.26	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.26	   A^2 -> H(U1(a, d), f(e))
25.19/8.26	   A^2 -> H(U1(a, d), f(k))
25.19/8.26	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.26	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.26	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.26	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.26	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.26	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.26	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.26	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.26	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.26	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.26	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.26	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.26	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.26	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.26	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.26	   A^2 -> H(c, f(b))
25.19/8.26	   A^2 -> H(U1(e, k), f(b))
25.19/8.26	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.26	   A^2 -> H(U1(e, c), f(c))
25.19/8.26	   A^2 -> H(U1(e, c), f(d))
25.19/8.26	   A^2 -> H(U1(k, e), f(b))
25.19/8.26	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.26	   A^2 -> H(U1(k, c), f(c))
25.19/8.26	   A^2 -> H(U1(k, c), f(d))
25.19/8.26	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.26	   A^2 -> H(U1(c, e), f(c))
25.19/8.26	   A^2 -> H(U1(c, e), f(d))
25.19/8.26	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.26	   A^2 -> H(U1(c, k), f(c))
25.19/8.26	   A^2 -> H(U1(c, k), f(d))
25.19/8.26	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.26	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.26	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.26	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.26	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.26	   A^2 -> H(U1(c, c), f(e))
25.19/8.26	   A^2 -> H(U1(c, c), f(k))
25.19/8.26	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.26	   A^2 -> H(e, f(b))
25.19/8.26	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.26	   A^2 -> H(U1(e, e), f(c))
25.19/8.26	   A^2 -> H(U1(e, e), f(d))
25.19/8.26	   A^2 -> H(f(e), U1(c, b))
25.19/8.26	   A^2 -> H(f(e), U1(d, b))
25.19/8.26	   A^2 -> H(f(e), U1(b, c))
25.19/8.26	   A^2 -> H(f(e), U1(b, d))
25.19/8.26	   A^2 -> H(f(e), U1(c, c))
25.19/8.26	   A^2 -> H(f(e), f(e))
25.19/8.26	   A^2 -> H(f(e), f(k))
25.19/8.26	   A^2 -> H(f(e), U1(d, d))
25.19/8.26	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.26	   A^2 -> H(U1(k, k), f(c))
25.19/8.26	   A^2 -> H(U1(k, k), f(d))
25.19/8.26	   A^2 -> H(f(k), U1(c, b))
25.19/8.26	   A^2 -> H(f(k), U1(d, b))
25.19/8.26	   A^2 -> H(f(k), U1(b, c))
25.19/8.26	   A^2 -> H(f(k), U1(b, d))
25.19/8.26	   A^2 -> H(f(k), U1(c, c))
25.19/8.26	   A^2 -> H(f(k), f(e))
25.19/8.26	   A^2 -> H(f(k), f(k))
25.19/8.26	   A^2 -> H(f(k), U1(d, d))
25.19/8.26	   A^2 -> H(f(c), U1(e, b))
25.19/8.26	   A^2 -> H(f(c), U1(k, b))
25.19/8.26	   A^2 -> H(f(c), U1(c, d))
25.19/8.26	   A^2 -> H(f(c), U1(d, c))
25.19/8.26	
25.19/8.26	The TRS R consists of the following rules:
25.19/8.26	
25.19/8.26	   f(x) -> U1(x, x)
25.19/8.26	   U1(e, x) -> x
25.19/8.26	   a -> c
25.19/8.26	   a -> d
25.19/8.26	   b -> c
25.19/8.26	   b -> d
25.19/8.26	   d -> k
25.19/8.26	   c -> e
25.19/8.26	   c -> k
25.19/8.26	
25.19/8.26	Q is empty.
25.19/8.26	We have to consider all minimal (P,Q,R)-chains.
25.19/8.26	----------------------------------------
25.19/8.26	
25.19/8.26	(155) TransformationProof (EQUIVALENT)
25.19/8.26	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.26	
25.19/8.26	   (A^2 -> H(U1(c, c), U1(b, c)),A^2 -> H(U1(c, c), U1(b, c)))
25.19/8.26	   (A^2 -> H(f(e), U1(b, c)),A^2 -> H(f(e), U1(b, c)))
25.19/8.26	   (A^2 -> H(f(k), U1(b, c)),A^2 -> H(f(k), U1(b, c)))
25.19/8.26	   (A^2 -> H(f(c), U1(c, c)),A^2 -> H(f(c), U1(c, c)))
25.19/8.26	   (A^2 -> H(f(c), U1(d, c)),A^2 -> H(f(c), U1(d, c)))
25.19/8.26	   (A^2 -> H(f(c), U1(b, e)),A^2 -> H(f(c), U1(b, e)))
25.19/8.26	   (A^2 -> H(f(c), U1(b, k)),A^2 -> H(f(c), U1(b, k)))
25.19/8.26	
25.19/8.26	
25.19/8.26	----------------------------------------
25.19/8.26	
25.19/8.26	(156)
25.19/8.26	Obligation:
25.19/8.26	Q DP problem:
25.19/8.26	The TRS P consists of the following rules:
25.19/8.26	
25.19/8.26	   H(x, x) -> G(x, x, f(k))
25.19/8.26	   G(d, x, x) -> A^2
25.19/8.26	   A^2 -> H(f(c), f(c))
25.19/8.26	   A^2 -> H(f(d), f(d))
25.19/8.26	   A^2 -> H(f(c), U1(b, d))
25.19/8.26	   A^2 -> H(f(c), U1(d, d))
25.19/8.26	   A^2 -> H(f(c), f(k))
25.19/8.26	   A^2 -> H(U1(k, d), f(b))
25.19/8.26	   A^2 -> H(U1(d, k), f(b))
25.19/8.26	   A^2 -> H(U1(d, d), U1(b, b))
25.19/8.26	   A^2 -> H(U1(d, d), f(c))
25.19/8.26	   A^2 -> H(U1(d, d), f(d))
25.19/8.26	   A^2 -> H(f(d), U1(c, b))
25.19/8.26	   A^2 -> H(f(d), U1(d, b))
25.19/8.26	   A^2 -> H(f(d), U1(b, c))
25.19/8.26	   A^2 -> H(f(d), U1(b, d))
25.19/8.26	   A^2 -> H(f(d), U1(c, c))
25.19/8.26	   A^2 -> H(f(d), f(e))
25.19/8.26	   A^2 -> H(f(d), f(k))
25.19/8.26	   A^2 -> H(f(a), U1(e, b))
25.19/8.26	   A^2 -> H(f(a), U1(k, b))
25.19/8.26	   A^2 -> H(f(a), U1(c, d))
25.19/8.26	   A^2 -> H(f(a), U1(d, c))
25.19/8.26	   A^2 -> H(f(a), U1(b, e))
25.19/8.26	   A^2 -> H(f(a), U1(b, k))
25.19/8.26	   A^2 -> H(f(c), U1(c, c))
25.19/8.26	   A^2 -> H(f(a), U1(e, c))
25.19/8.26	   A^2 -> H(f(a), U1(k, c))
25.19/8.26	   A^2 -> H(f(a), U1(c, e))
25.19/8.26	   A^2 -> H(f(a), U1(c, k))
25.19/8.26	   A^2 -> H(f(c), f(e))
25.19/8.26	   A^2 -> H(f(a), U1(e, e))
25.19/8.26	   A^2 -> H(f(a), U1(k, k))
25.19/8.26	   A^2 -> H(f(d), U1(d, d))
25.19/8.26	   A^2 -> H(f(a), U1(k, d))
25.19/8.26	   A^2 -> H(f(a), U1(d, k))
25.19/8.26	   A^2 -> H(a, f(b))
25.19/8.26	   A^2 -> H(U1(e, d), f(b))
25.19/8.26	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.26	   A^2 -> H(U1(e, a), f(c))
25.19/8.26	   A^2 -> H(U1(e, a), f(d))
25.19/8.26	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.26	   A^2 -> H(U1(k, a), f(c))
25.19/8.26	   A^2 -> H(U1(k, a), f(d))
25.19/8.26	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.26	   A^2 -> H(U1(c, d), f(c))
25.19/8.26	   A^2 -> H(U1(c, d), f(d))
25.19/8.26	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.26	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.26	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.26	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.26	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.26	   A^2 -> H(U1(c, a), f(e))
25.19/8.26	   A^2 -> H(U1(c, a), f(k))
25.19/8.26	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.26	   A^2 -> H(U1(d, e), f(b))
25.19/8.26	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.26	   A^2 -> H(U1(d, c), f(c))
25.19/8.26	   A^2 -> H(U1(d, c), f(d))
25.19/8.26	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.26	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.26	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.26	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.26	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.26	   A^2 -> H(U1(d, a), f(e))
25.19/8.26	   A^2 -> H(U1(d, a), f(k))
25.19/8.26	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.26	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.26	   A^2 -> H(U1(a, e), f(c))
25.19/8.26	   A^2 -> H(U1(a, e), f(d))
25.19/8.26	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.26	   A^2 -> H(U1(a, k), f(c))
25.19/8.26	   A^2 -> H(U1(a, k), f(d))
25.19/8.26	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.26	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.26	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.26	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.26	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.26	   A^2 -> H(U1(a, c), f(e))
25.19/8.26	   A^2 -> H(U1(a, c), f(k))
25.19/8.26	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.26	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.26	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.26	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.26	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.26	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.26	   A^2 -> H(U1(a, d), f(e))
25.19/8.26	   A^2 -> H(U1(a, d), f(k))
25.19/8.26	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.26	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.26	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.26	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.26	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.26	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.26	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.26	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.26	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.26	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.26	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.26	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.26	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.26	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.26	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.26	   A^2 -> H(c, f(b))
25.19/8.26	   A^2 -> H(U1(e, k), f(b))
25.19/8.26	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.26	   A^2 -> H(U1(e, c), f(c))
25.19/8.26	   A^2 -> H(U1(e, c), f(d))
25.19/8.26	   A^2 -> H(U1(k, e), f(b))
25.19/8.26	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.26	   A^2 -> H(U1(k, c), f(c))
25.19/8.26	   A^2 -> H(U1(k, c), f(d))
25.19/8.26	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.26	   A^2 -> H(U1(c, e), f(c))
25.19/8.26	   A^2 -> H(U1(c, e), f(d))
25.19/8.26	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.26	   A^2 -> H(U1(c, k), f(c))
25.19/8.26	   A^2 -> H(U1(c, k), f(d))
25.19/8.26	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.26	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.26	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.26	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.26	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.26	   A^2 -> H(U1(c, c), f(e))
25.19/8.26	   A^2 -> H(U1(c, c), f(k))
25.19/8.26	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.26	   A^2 -> H(e, f(b))
25.19/8.26	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.26	   A^2 -> H(U1(e, e), f(c))
25.19/8.26	   A^2 -> H(U1(e, e), f(d))
25.19/8.26	   A^2 -> H(f(e), U1(c, b))
25.19/8.26	   A^2 -> H(f(e), U1(d, b))
25.19/8.26	   A^2 -> H(f(e), U1(b, c))
25.19/8.26	   A^2 -> H(f(e), U1(b, d))
25.19/8.26	   A^2 -> H(f(e), U1(c, c))
25.19/8.26	   A^2 -> H(f(e), f(e))
25.19/8.26	   A^2 -> H(f(e), f(k))
25.19/8.26	   A^2 -> H(f(e), U1(d, d))
25.19/8.26	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.26	   A^2 -> H(U1(k, k), f(c))
25.19/8.26	   A^2 -> H(U1(k, k), f(d))
25.19/8.26	   A^2 -> H(f(k), U1(c, b))
25.19/8.26	   A^2 -> H(f(k), U1(d, b))
25.19/8.26	   A^2 -> H(f(k), U1(b, c))
25.19/8.26	   A^2 -> H(f(k), U1(b, d))
25.19/8.26	   A^2 -> H(f(k), U1(c, c))
25.19/8.26	   A^2 -> H(f(k), f(e))
25.19/8.26	   A^2 -> H(f(k), f(k))
25.19/8.26	   A^2 -> H(f(k), U1(d, d))
25.19/8.26	   A^2 -> H(f(c), U1(e, b))
25.19/8.26	   A^2 -> H(f(c), U1(k, b))
25.19/8.26	   A^2 -> H(f(c), U1(c, d))
25.19/8.26	   A^2 -> H(f(c), U1(d, c))
25.19/8.26	   A^2 -> H(f(c), U1(b, e))
25.19/8.26	   A^2 -> H(f(c), U1(b, k))
25.19/8.26	
25.19/8.26	The TRS R consists of the following rules:
25.19/8.26	
25.19/8.26	   f(x) -> U1(x, x)
25.19/8.26	   U1(e, x) -> x
25.19/8.26	   a -> c
25.19/8.26	   a -> d
25.19/8.26	   b -> c
25.19/8.26	   b -> d
25.19/8.26	   d -> k
25.19/8.26	   c -> e
25.19/8.26	   c -> k
25.19/8.26	
25.19/8.26	Q is empty.
25.19/8.26	We have to consider all minimal (P,Q,R)-chains.
25.19/8.26	----------------------------------------
25.19/8.26	
25.19/8.26	(157) TransformationProof (EQUIVALENT)
25.19/8.26	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.26	
25.19/8.26	   (A^2 -> H(U1(c, c), U1(b, d)),A^2 -> H(U1(c, c), U1(b, d)))
25.19/8.26	   (A^2 -> H(f(e), U1(b, d)),A^2 -> H(f(e), U1(b, d)))
25.19/8.26	   (A^2 -> H(f(k), U1(b, d)),A^2 -> H(f(k), U1(b, d)))
25.19/8.26	   (A^2 -> H(f(c), U1(c, d)),A^2 -> H(f(c), U1(c, d)))
25.19/8.26	   (A^2 -> H(f(c), U1(d, d)),A^2 -> H(f(c), U1(d, d)))
25.19/8.26	   (A^2 -> H(f(c), U1(b, k)),A^2 -> H(f(c), U1(b, k)))
25.19/8.26	
25.19/8.26	
25.19/8.26	----------------------------------------
25.19/8.26	
25.19/8.26	(158)
25.19/8.26	Obligation:
25.19/8.26	Q DP problem:
25.19/8.26	The TRS P consists of the following rules:
25.19/8.26	
25.19/8.26	   H(x, x) -> G(x, x, f(k))
25.19/8.26	   G(d, x, x) -> A^2
25.19/8.26	   A^2 -> H(f(c), f(c))
25.19/8.26	   A^2 -> H(f(d), f(d))
25.19/8.26	   A^2 -> H(f(c), U1(d, d))
25.19/8.26	   A^2 -> H(f(c), f(k))
25.19/8.26	   A^2 -> H(U1(k, d), f(b))
25.19/8.26	   A^2 -> H(U1(d, k), f(b))
25.19/8.26	   A^2 -> H(U1(d, d), U1(b, b))
25.19/8.26	   A^2 -> H(U1(d, d), f(c))
25.19/8.26	   A^2 -> H(U1(d, d), f(d))
25.19/8.26	   A^2 -> H(f(d), U1(c, b))
25.19/8.26	   A^2 -> H(f(d), U1(d, b))
25.19/8.26	   A^2 -> H(f(d), U1(b, c))
25.19/8.26	   A^2 -> H(f(d), U1(b, d))
25.19/8.26	   A^2 -> H(f(d), U1(c, c))
25.19/8.26	   A^2 -> H(f(d), f(e))
25.19/8.26	   A^2 -> H(f(d), f(k))
25.19/8.26	   A^2 -> H(f(a), U1(e, b))
25.19/8.26	   A^2 -> H(f(a), U1(k, b))
25.19/8.26	   A^2 -> H(f(a), U1(c, d))
25.19/8.26	   A^2 -> H(f(a), U1(d, c))
25.19/8.26	   A^2 -> H(f(a), U1(b, e))
25.19/8.26	   A^2 -> H(f(a), U1(b, k))
25.19/8.26	   A^2 -> H(f(c), U1(c, c))
25.19/8.26	   A^2 -> H(f(a), U1(e, c))
25.19/8.26	   A^2 -> H(f(a), U1(k, c))
25.19/8.26	   A^2 -> H(f(a), U1(c, e))
25.19/8.26	   A^2 -> H(f(a), U1(c, k))
25.19/8.26	   A^2 -> H(f(c), f(e))
25.19/8.26	   A^2 -> H(f(a), U1(e, e))
25.19/8.26	   A^2 -> H(f(a), U1(k, k))
25.19/8.26	   A^2 -> H(f(d), U1(d, d))
25.19/8.26	   A^2 -> H(f(a), U1(k, d))
25.19/8.26	   A^2 -> H(f(a), U1(d, k))
25.19/8.26	   A^2 -> H(a, f(b))
25.19/8.26	   A^2 -> H(U1(e, d), f(b))
25.19/8.26	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.26	   A^2 -> H(U1(e, a), f(c))
25.19/8.26	   A^2 -> H(U1(e, a), f(d))
25.19/8.26	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.26	   A^2 -> H(U1(k, a), f(c))
25.19/8.26	   A^2 -> H(U1(k, a), f(d))
25.19/8.26	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.26	   A^2 -> H(U1(c, d), f(c))
25.19/8.26	   A^2 -> H(U1(c, d), f(d))
25.19/8.26	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.26	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.26	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.26	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.26	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.26	   A^2 -> H(U1(c, a), f(e))
25.19/8.26	   A^2 -> H(U1(c, a), f(k))
25.19/8.26	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.26	   A^2 -> H(U1(d, e), f(b))
25.19/8.26	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.26	   A^2 -> H(U1(d, c), f(c))
25.19/8.26	   A^2 -> H(U1(d, c), f(d))
25.19/8.26	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.26	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.26	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.26	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.26	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.26	   A^2 -> H(U1(d, a), f(e))
25.19/8.26	   A^2 -> H(U1(d, a), f(k))
25.19/8.26	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.26	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.26	   A^2 -> H(U1(a, e), f(c))
25.19/8.26	   A^2 -> H(U1(a, e), f(d))
25.19/8.26	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.26	   A^2 -> H(U1(a, k), f(c))
25.19/8.26	   A^2 -> H(U1(a, k), f(d))
25.19/8.26	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.26	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.26	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.26	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.26	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.26	   A^2 -> H(U1(a, c), f(e))
25.19/8.26	   A^2 -> H(U1(a, c), f(k))
25.19/8.26	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.26	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.26	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.26	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.26	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.26	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.26	   A^2 -> H(U1(a, d), f(e))
25.19/8.26	   A^2 -> H(U1(a, d), f(k))
25.19/8.26	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.26	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.26	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.26	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.26	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.26	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.26	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.26	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.26	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.26	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.26	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.26	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.26	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.26	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.26	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.26	   A^2 -> H(c, f(b))
25.19/8.26	   A^2 -> H(U1(e, k), f(b))
25.19/8.26	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.26	   A^2 -> H(U1(e, c), f(c))
25.19/8.26	   A^2 -> H(U1(e, c), f(d))
25.19/8.26	   A^2 -> H(U1(k, e), f(b))
25.19/8.26	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.26	   A^2 -> H(U1(k, c), f(c))
25.19/8.26	   A^2 -> H(U1(k, c), f(d))
25.19/8.26	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.26	   A^2 -> H(U1(c, e), f(c))
25.19/8.26	   A^2 -> H(U1(c, e), f(d))
25.19/8.26	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.26	   A^2 -> H(U1(c, k), f(c))
25.19/8.26	   A^2 -> H(U1(c, k), f(d))
25.19/8.26	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.26	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.26	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.26	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.26	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.26	   A^2 -> H(U1(c, c), f(e))
25.19/8.26	   A^2 -> H(U1(c, c), f(k))
25.19/8.26	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.26	   A^2 -> H(e, f(b))
25.19/8.26	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.26	   A^2 -> H(U1(e, e), f(c))
25.19/8.26	   A^2 -> H(U1(e, e), f(d))
25.19/8.26	   A^2 -> H(f(e), U1(c, b))
25.19/8.26	   A^2 -> H(f(e), U1(d, b))
25.19/8.26	   A^2 -> H(f(e), U1(b, c))
25.19/8.26	   A^2 -> H(f(e), U1(b, d))
25.19/8.26	   A^2 -> H(f(e), U1(c, c))
25.19/8.26	   A^2 -> H(f(e), f(e))
25.19/8.26	   A^2 -> H(f(e), f(k))
25.19/8.26	   A^2 -> H(f(e), U1(d, d))
25.19/8.26	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.26	   A^2 -> H(U1(k, k), f(c))
25.19/8.26	   A^2 -> H(U1(k, k), f(d))
25.19/8.26	   A^2 -> H(f(k), U1(c, b))
25.19/8.26	   A^2 -> H(f(k), U1(d, b))
25.19/8.26	   A^2 -> H(f(k), U1(b, c))
25.19/8.26	   A^2 -> H(f(k), U1(b, d))
25.19/8.26	   A^2 -> H(f(k), U1(c, c))
25.19/8.26	   A^2 -> H(f(k), f(e))
25.19/8.26	   A^2 -> H(f(k), f(k))
25.19/8.26	   A^2 -> H(f(k), U1(d, d))
25.19/8.26	   A^2 -> H(f(c), U1(e, b))
25.19/8.26	   A^2 -> H(f(c), U1(k, b))
25.19/8.26	   A^2 -> H(f(c), U1(c, d))
25.19/8.26	   A^2 -> H(f(c), U1(d, c))
25.19/8.26	   A^2 -> H(f(c), U1(b, e))
25.19/8.26	   A^2 -> H(f(c), U1(b, k))
25.19/8.26	
25.19/8.26	The TRS R consists of the following rules:
25.19/8.26	
25.19/8.26	   f(x) -> U1(x, x)
25.19/8.26	   U1(e, x) -> x
25.19/8.26	   a -> c
25.19/8.26	   a -> d
25.19/8.26	   b -> c
25.19/8.26	   b -> d
25.19/8.26	   d -> k
25.19/8.26	   c -> e
25.19/8.26	   c -> k
25.19/8.26	
25.19/8.26	Q is empty.
25.19/8.26	We have to consider all minimal (P,Q,R)-chains.
25.19/8.26	----------------------------------------
25.19/8.26	
25.19/8.26	(159) TransformationProof (EQUIVALENT)
25.19/8.26	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.26	
25.19/8.26	   (A^2 -> H(U1(c, c), U1(d, d)),A^2 -> H(U1(c, c), U1(d, d)))
25.19/8.26	   (A^2 -> H(f(e), U1(d, d)),A^2 -> H(f(e), U1(d, d)))
25.19/8.26	   (A^2 -> H(f(k), U1(d, d)),A^2 -> H(f(k), U1(d, d)))
25.19/8.26	   (A^2 -> H(f(c), U1(k, d)),A^2 -> H(f(c), U1(k, d)))
25.19/8.26	   (A^2 -> H(f(c), U1(d, k)),A^2 -> H(f(c), U1(d, k)))
25.19/8.26	
25.19/8.26	
25.19/8.26	----------------------------------------
25.19/8.26	
25.19/8.26	(160)
25.19/8.26	Obligation:
25.19/8.26	Q DP problem:
25.19/8.26	The TRS P consists of the following rules:
25.19/8.26	
25.19/8.26	   H(x, x) -> G(x, x, f(k))
25.19/8.26	   G(d, x, x) -> A^2
25.19/8.26	   A^2 -> H(f(c), f(c))
25.19/8.26	   A^2 -> H(f(d), f(d))
25.19/8.26	   A^2 -> H(f(c), f(k))
25.19/8.26	   A^2 -> H(U1(k, d), f(b))
25.19/8.26	   A^2 -> H(U1(d, k), f(b))
25.19/8.26	   A^2 -> H(U1(d, d), U1(b, b))
25.19/8.26	   A^2 -> H(U1(d, d), f(c))
25.19/8.26	   A^2 -> H(U1(d, d), f(d))
25.19/8.26	   A^2 -> H(f(d), U1(c, b))
25.19/8.26	   A^2 -> H(f(d), U1(d, b))
25.19/8.26	   A^2 -> H(f(d), U1(b, c))
25.19/8.26	   A^2 -> H(f(d), U1(b, d))
25.19/8.26	   A^2 -> H(f(d), U1(c, c))
25.19/8.26	   A^2 -> H(f(d), f(e))
25.19/8.26	   A^2 -> H(f(d), f(k))
25.19/8.26	   A^2 -> H(f(a), U1(e, b))
25.19/8.26	   A^2 -> H(f(a), U1(k, b))
25.19/8.26	   A^2 -> H(f(a), U1(c, d))
25.19/8.26	   A^2 -> H(f(a), U1(d, c))
25.19/8.26	   A^2 -> H(f(a), U1(b, e))
25.19/8.26	   A^2 -> H(f(a), U1(b, k))
25.19/8.26	   A^2 -> H(f(c), U1(c, c))
25.19/8.26	   A^2 -> H(f(a), U1(e, c))
25.19/8.26	   A^2 -> H(f(a), U1(k, c))
25.19/8.26	   A^2 -> H(f(a), U1(c, e))
25.19/8.26	   A^2 -> H(f(a), U1(c, k))
25.19/8.26	   A^2 -> H(f(c), f(e))
25.19/8.26	   A^2 -> H(f(a), U1(e, e))
25.19/8.26	   A^2 -> H(f(a), U1(k, k))
25.19/8.26	   A^2 -> H(f(d), U1(d, d))
25.19/8.26	   A^2 -> H(f(a), U1(k, d))
25.19/8.26	   A^2 -> H(f(a), U1(d, k))
25.19/8.26	   A^2 -> H(a, f(b))
25.19/8.26	   A^2 -> H(U1(e, d), f(b))
25.19/8.26	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.26	   A^2 -> H(U1(e, a), f(c))
25.19/8.26	   A^2 -> H(U1(e, a), f(d))
25.19/8.26	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.26	   A^2 -> H(U1(k, a), f(c))
25.19/8.26	   A^2 -> H(U1(k, a), f(d))
25.19/8.26	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.26	   A^2 -> H(U1(c, d), f(c))
25.19/8.26	   A^2 -> H(U1(c, d), f(d))
25.19/8.26	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.26	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.26	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.26	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.26	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.26	   A^2 -> H(U1(c, a), f(e))
25.19/8.26	   A^2 -> H(U1(c, a), f(k))
25.19/8.26	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.26	   A^2 -> H(U1(d, e), f(b))
25.19/8.26	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.26	   A^2 -> H(U1(d, c), f(c))
25.19/8.26	   A^2 -> H(U1(d, c), f(d))
25.19/8.27	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.27	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.27	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.27	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.27	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.27	   A^2 -> H(U1(d, a), f(e))
25.19/8.27	   A^2 -> H(U1(d, a), f(k))
25.19/8.27	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.27	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.27	   A^2 -> H(U1(a, e), f(c))
25.19/8.27	   A^2 -> H(U1(a, e), f(d))
25.19/8.27	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.27	   A^2 -> H(U1(a, k), f(c))
25.19/8.27	   A^2 -> H(U1(a, k), f(d))
25.19/8.27	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.27	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.27	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.27	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.27	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.27	   A^2 -> H(U1(a, c), f(e))
25.19/8.27	   A^2 -> H(U1(a, c), f(k))
25.19/8.27	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.27	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.27	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.27	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.27	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.27	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.27	   A^2 -> H(U1(a, d), f(e))
25.19/8.27	   A^2 -> H(U1(a, d), f(k))
25.19/8.27	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.27	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.27	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.27	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.27	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.27	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.27	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.27	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.27	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.27	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.27	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.27	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.27	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.27	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.27	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.27	   A^2 -> H(c, f(b))
25.19/8.27	   A^2 -> H(U1(e, k), f(b))
25.19/8.27	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.27	   A^2 -> H(U1(e, c), f(c))
25.19/8.27	   A^2 -> H(U1(e, c), f(d))
25.19/8.27	   A^2 -> H(U1(k, e), f(b))
25.19/8.27	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.27	   A^2 -> H(U1(k, c), f(c))
25.19/8.27	   A^2 -> H(U1(k, c), f(d))
25.19/8.27	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.27	   A^2 -> H(U1(c, e), f(c))
25.19/8.27	   A^2 -> H(U1(c, e), f(d))
25.19/8.27	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.27	   A^2 -> H(U1(c, k), f(c))
25.19/8.27	   A^2 -> H(U1(c, k), f(d))
25.19/8.27	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.27	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.27	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.27	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.27	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.27	   A^2 -> H(U1(c, c), f(e))
25.19/8.27	   A^2 -> H(U1(c, c), f(k))
25.19/8.27	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.27	   A^2 -> H(e, f(b))
25.19/8.27	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.27	   A^2 -> H(U1(e, e), f(c))
25.19/8.27	   A^2 -> H(U1(e, e), f(d))
25.19/8.27	   A^2 -> H(f(e), U1(c, b))
25.19/8.27	   A^2 -> H(f(e), U1(d, b))
25.19/8.27	   A^2 -> H(f(e), U1(b, c))
25.19/8.27	   A^2 -> H(f(e), U1(b, d))
25.19/8.27	   A^2 -> H(f(e), U1(c, c))
25.19/8.27	   A^2 -> H(f(e), f(e))
25.19/8.27	   A^2 -> H(f(e), f(k))
25.19/8.27	   A^2 -> H(f(e), U1(d, d))
25.19/8.27	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.27	   A^2 -> H(U1(k, k), f(c))
25.19/8.27	   A^2 -> H(U1(k, k), f(d))
25.19/8.27	   A^2 -> H(f(k), U1(c, b))
25.19/8.27	   A^2 -> H(f(k), U1(d, b))
25.19/8.27	   A^2 -> H(f(k), U1(b, c))
25.19/8.27	   A^2 -> H(f(k), U1(b, d))
25.19/8.27	   A^2 -> H(f(k), U1(c, c))
25.19/8.27	   A^2 -> H(f(k), f(e))
25.19/8.27	   A^2 -> H(f(k), f(k))
25.19/8.27	   A^2 -> H(f(k), U1(d, d))
25.19/8.27	   A^2 -> H(f(c), U1(e, b))
25.19/8.27	   A^2 -> H(f(c), U1(k, b))
25.19/8.27	   A^2 -> H(f(c), U1(c, d))
25.19/8.27	   A^2 -> H(f(c), U1(d, c))
25.19/8.27	   A^2 -> H(f(c), U1(b, e))
25.19/8.27	   A^2 -> H(f(c), U1(b, k))
25.19/8.27	   A^2 -> H(f(c), U1(k, d))
25.19/8.27	   A^2 -> H(f(c), U1(d, k))
25.19/8.27	
25.19/8.27	The TRS R consists of the following rules:
25.19/8.27	
25.19/8.27	   f(x) -> U1(x, x)
25.19/8.27	   U1(e, x) -> x
25.19/8.27	   a -> c
25.19/8.27	   a -> d
25.19/8.27	   b -> c
25.19/8.27	   b -> d
25.19/8.27	   d -> k
25.19/8.27	   c -> e
25.19/8.27	   c -> k
25.19/8.27	
25.19/8.27	Q is empty.
25.19/8.27	We have to consider all minimal (P,Q,R)-chains.
25.19/8.27	----------------------------------------
25.19/8.27	
25.19/8.27	(161) TransformationProof (EQUIVALENT)
25.19/8.27	By narrowing [LPAR04] the rule A^2 -> H(f(c), f(k)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.27	
25.19/8.27	   (A^2 -> H(U1(c, c), f(k)),A^2 -> H(U1(c, c), f(k)))
25.19/8.27	   (A^2 -> H(f(e), f(k)),A^2 -> H(f(e), f(k)))
25.19/8.27	   (A^2 -> H(f(k), f(k)),A^2 -> H(f(k), f(k)))
25.19/8.27	   (A^2 -> H(f(c), U1(k, k)),A^2 -> H(f(c), U1(k, k)))
25.19/8.27	
25.19/8.27	
25.19/8.27	----------------------------------------
25.19/8.27	
25.19/8.27	(162)
25.19/8.27	Obligation:
25.19/8.27	Q DP problem:
25.19/8.27	The TRS P consists of the following rules:
25.19/8.27	
25.19/8.27	   H(x, x) -> G(x, x, f(k))
25.19/8.27	   G(d, x, x) -> A^2
25.19/8.27	   A^2 -> H(f(c), f(c))
25.19/8.27	   A^2 -> H(f(d), f(d))
25.19/8.27	   A^2 -> H(U1(k, d), f(b))
25.19/8.27	   A^2 -> H(U1(d, k), f(b))
25.19/8.27	   A^2 -> H(U1(d, d), U1(b, b))
25.19/8.27	   A^2 -> H(U1(d, d), f(c))
25.19/8.27	   A^2 -> H(U1(d, d), f(d))
25.19/8.27	   A^2 -> H(f(d), U1(c, b))
25.19/8.27	   A^2 -> H(f(d), U1(d, b))
25.19/8.27	   A^2 -> H(f(d), U1(b, c))
25.19/8.27	   A^2 -> H(f(d), U1(b, d))
25.19/8.27	   A^2 -> H(f(d), U1(c, c))
25.19/8.27	   A^2 -> H(f(d), f(e))
25.19/8.27	   A^2 -> H(f(d), f(k))
25.19/8.27	   A^2 -> H(f(a), U1(e, b))
25.19/8.27	   A^2 -> H(f(a), U1(k, b))
25.19/8.27	   A^2 -> H(f(a), U1(c, d))
25.19/8.27	   A^2 -> H(f(a), U1(d, c))
25.19/8.27	   A^2 -> H(f(a), U1(b, e))
25.19/8.27	   A^2 -> H(f(a), U1(b, k))
25.19/8.27	   A^2 -> H(f(c), U1(c, c))
25.19/8.27	   A^2 -> H(f(a), U1(e, c))
25.19/8.27	   A^2 -> H(f(a), U1(k, c))
25.19/8.27	   A^2 -> H(f(a), U1(c, e))
25.19/8.27	   A^2 -> H(f(a), U1(c, k))
25.19/8.27	   A^2 -> H(f(c), f(e))
25.19/8.27	   A^2 -> H(f(a), U1(e, e))
25.19/8.27	   A^2 -> H(f(a), U1(k, k))
25.19/8.27	   A^2 -> H(f(d), U1(d, d))
25.19/8.27	   A^2 -> H(f(a), U1(k, d))
25.19/8.27	   A^2 -> H(f(a), U1(d, k))
25.19/8.27	   A^2 -> H(a, f(b))
25.19/8.27	   A^2 -> H(U1(e, d), f(b))
25.19/8.27	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.27	   A^2 -> H(U1(e, a), f(c))
25.19/8.27	   A^2 -> H(U1(e, a), f(d))
25.19/8.27	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.27	   A^2 -> H(U1(k, a), f(c))
25.19/8.27	   A^2 -> H(U1(k, a), f(d))
25.19/8.27	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.27	   A^2 -> H(U1(c, d), f(c))
25.19/8.27	   A^2 -> H(U1(c, d), f(d))
25.19/8.27	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.27	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.27	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.27	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.27	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.27	   A^2 -> H(U1(c, a), f(e))
25.19/8.27	   A^2 -> H(U1(c, a), f(k))
25.19/8.27	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.27	   A^2 -> H(U1(d, e), f(b))
25.19/8.27	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.27	   A^2 -> H(U1(d, c), f(c))
25.19/8.27	   A^2 -> H(U1(d, c), f(d))
25.19/8.27	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.27	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.27	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.27	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.27	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.27	   A^2 -> H(U1(d, a), f(e))
25.19/8.27	   A^2 -> H(U1(d, a), f(k))
25.19/8.27	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.27	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.27	   A^2 -> H(U1(a, e), f(c))
25.19/8.27	   A^2 -> H(U1(a, e), f(d))
25.19/8.27	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.27	   A^2 -> H(U1(a, k), f(c))
25.19/8.27	   A^2 -> H(U1(a, k), f(d))
25.19/8.27	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.27	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.27	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.27	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.27	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.27	   A^2 -> H(U1(a, c), f(e))
25.19/8.27	   A^2 -> H(U1(a, c), f(k))
25.19/8.27	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.27	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.27	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.27	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.27	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.27	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.27	   A^2 -> H(U1(a, d), f(e))
25.19/8.27	   A^2 -> H(U1(a, d), f(k))
25.19/8.27	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.27	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.27	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.27	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.27	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.27	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.27	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.27	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.27	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.27	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.27	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.27	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.27	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.27	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.27	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.27	   A^2 -> H(c, f(b))
25.19/8.27	   A^2 -> H(U1(e, k), f(b))
25.19/8.27	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.27	   A^2 -> H(U1(e, c), f(c))
25.19/8.27	   A^2 -> H(U1(e, c), f(d))
25.19/8.27	   A^2 -> H(U1(k, e), f(b))
25.19/8.27	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.27	   A^2 -> H(U1(k, c), f(c))
25.19/8.27	   A^2 -> H(U1(k, c), f(d))
25.19/8.27	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.27	   A^2 -> H(U1(c, e), f(c))
25.19/8.27	   A^2 -> H(U1(c, e), f(d))
25.19/8.27	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.27	   A^2 -> H(U1(c, k), f(c))
25.19/8.27	   A^2 -> H(U1(c, k), f(d))
25.19/8.27	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.27	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.27	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.27	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.27	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.27	   A^2 -> H(U1(c, c), f(e))
25.19/8.27	   A^2 -> H(U1(c, c), f(k))
25.19/8.27	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.27	   A^2 -> H(e, f(b))
25.19/8.27	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.27	   A^2 -> H(U1(e, e), f(c))
25.19/8.27	   A^2 -> H(U1(e, e), f(d))
25.19/8.27	   A^2 -> H(f(e), U1(c, b))
25.19/8.27	   A^2 -> H(f(e), U1(d, b))
25.19/8.27	   A^2 -> H(f(e), U1(b, c))
25.19/8.27	   A^2 -> H(f(e), U1(b, d))
25.19/8.27	   A^2 -> H(f(e), U1(c, c))
25.19/8.27	   A^2 -> H(f(e), f(e))
25.19/8.27	   A^2 -> H(f(e), f(k))
25.19/8.27	   A^2 -> H(f(e), U1(d, d))
25.19/8.27	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.27	   A^2 -> H(U1(k, k), f(c))
25.19/8.27	   A^2 -> H(U1(k, k), f(d))
25.19/8.27	   A^2 -> H(f(k), U1(c, b))
25.19/8.27	   A^2 -> H(f(k), U1(d, b))
25.19/8.27	   A^2 -> H(f(k), U1(b, c))
25.19/8.27	   A^2 -> H(f(k), U1(b, d))
25.19/8.27	   A^2 -> H(f(k), U1(c, c))
25.19/8.27	   A^2 -> H(f(k), f(e))
25.19/8.27	   A^2 -> H(f(k), f(k))
25.19/8.27	   A^2 -> H(f(k), U1(d, d))
25.19/8.27	   A^2 -> H(f(c), U1(e, b))
25.19/8.27	   A^2 -> H(f(c), U1(k, b))
25.19/8.27	   A^2 -> H(f(c), U1(c, d))
25.19/8.27	   A^2 -> H(f(c), U1(d, c))
25.19/8.27	   A^2 -> H(f(c), U1(b, e))
25.19/8.27	   A^2 -> H(f(c), U1(b, k))
25.19/8.27	   A^2 -> H(f(c), U1(k, d))
25.19/8.27	   A^2 -> H(f(c), U1(d, k))
25.19/8.27	   A^2 -> H(f(c), U1(k, k))
25.19/8.27	
25.19/8.27	The TRS R consists of the following rules:
25.19/8.27	
25.19/8.27	   f(x) -> U1(x, x)
25.19/8.28	   U1(e, x) -> x
25.19/8.28	   a -> c
25.19/8.28	   a -> d
25.19/8.28	   b -> c
25.19/8.28	   b -> d
25.19/8.28	   d -> k
25.19/8.28	   c -> e
25.19/8.28	   c -> k
25.19/8.28	
25.19/8.28	Q is empty.
25.19/8.28	We have to consider all minimal (P,Q,R)-chains.
25.19/8.28	----------------------------------------
25.19/8.28	
25.19/8.28	(163) TransformationProof (EQUIVALENT)
25.19/8.28	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), f(b)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.28	
25.19/8.28	   (A^2 -> H(U1(k, k), f(b)),A^2 -> H(U1(k, k), f(b)))
25.19/8.28	   (A^2 -> H(U1(k, d), U1(b, b)),A^2 -> H(U1(k, d), U1(b, b)))
25.19/8.28	   (A^2 -> H(U1(k, d), f(c)),A^2 -> H(U1(k, d), f(c)))
25.19/8.28	   (A^2 -> H(U1(k, d), f(d)),A^2 -> H(U1(k, d), f(d)))
25.19/8.28	
25.19/8.28	
25.19/8.28	----------------------------------------
25.19/8.28	
25.19/8.28	(164)
25.19/8.28	Obligation:
25.19/8.28	Q DP problem:
25.19/8.28	The TRS P consists of the following rules:
25.19/8.28	
25.19/8.28	   H(x, x) -> G(x, x, f(k))
25.19/8.28	   G(d, x, x) -> A^2
25.19/8.28	   A^2 -> H(f(c), f(c))
25.19/8.28	   A^2 -> H(f(d), f(d))
25.19/8.28	   A^2 -> H(U1(d, k), f(b))
25.19/8.28	   A^2 -> H(U1(d, d), U1(b, b))
25.19/8.28	   A^2 -> H(U1(d, d), f(c))
25.19/8.28	   A^2 -> H(U1(d, d), f(d))
25.19/8.28	   A^2 -> H(f(d), U1(c, b))
25.19/8.28	   A^2 -> H(f(d), U1(d, b))
25.19/8.28	   A^2 -> H(f(d), U1(b, c))
25.19/8.28	   A^2 -> H(f(d), U1(b, d))
25.19/8.28	   A^2 -> H(f(d), U1(c, c))
25.19/8.28	   A^2 -> H(f(d), f(e))
25.19/8.28	   A^2 -> H(f(d), f(k))
25.19/8.28	   A^2 -> H(f(a), U1(e, b))
25.19/8.28	   A^2 -> H(f(a), U1(k, b))
25.19/8.28	   A^2 -> H(f(a), U1(c, d))
25.19/8.28	   A^2 -> H(f(a), U1(d, c))
25.19/8.28	   A^2 -> H(f(a), U1(b, e))
25.19/8.28	   A^2 -> H(f(a), U1(b, k))
25.19/8.28	   A^2 -> H(f(c), U1(c, c))
25.19/8.28	   A^2 -> H(f(a), U1(e, c))
25.19/8.28	   A^2 -> H(f(a), U1(k, c))
25.19/8.28	   A^2 -> H(f(a), U1(c, e))
25.19/8.28	   A^2 -> H(f(a), U1(c, k))
25.19/8.28	   A^2 -> H(f(c), f(e))
25.19/8.28	   A^2 -> H(f(a), U1(e, e))
25.19/8.28	   A^2 -> H(f(a), U1(k, k))
25.19/8.28	   A^2 -> H(f(d), U1(d, d))
25.19/8.28	   A^2 -> H(f(a), U1(k, d))
25.19/8.28	   A^2 -> H(f(a), U1(d, k))
25.19/8.28	   A^2 -> H(a, f(b))
25.19/8.28	   A^2 -> H(U1(e, d), f(b))
25.19/8.28	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, a), f(c))
25.19/8.28	   A^2 -> H(U1(e, a), f(d))
25.19/8.28	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, a), f(c))
25.19/8.28	   A^2 -> H(U1(k, a), f(d))
25.19/8.28	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, d), f(c))
25.19/8.28	   A^2 -> H(U1(c, d), f(d))
25.19/8.28	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.28	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.28	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.28	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.28	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.28	   A^2 -> H(U1(c, a), f(e))
25.19/8.28	   A^2 -> H(U1(c, a), f(k))
25.19/8.28	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.28	   A^2 -> H(U1(d, e), f(b))
25.19/8.28	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(d, c), f(c))
25.19/8.28	   A^2 -> H(U1(d, c), f(d))
25.19/8.28	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.28	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.28	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.28	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.28	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.28	   A^2 -> H(U1(d, a), f(e))
25.19/8.28	   A^2 -> H(U1(d, a), f(k))
25.19/8.28	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(a, e), f(c))
25.19/8.28	   A^2 -> H(U1(a, e), f(d))
25.19/8.28	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(a, k), f(c))
25.19/8.28	   A^2 -> H(U1(a, k), f(d))
25.19/8.28	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.28	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.28	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.28	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.28	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.28	   A^2 -> H(U1(a, c), f(e))
25.19/8.28	   A^2 -> H(U1(a, c), f(k))
25.19/8.28	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.28	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.28	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.28	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.28	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.28	   A^2 -> H(U1(a, d), f(e))
25.19/8.28	   A^2 -> H(U1(a, d), f(k))
25.19/8.28	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.28	   A^2 -> H(c, f(b))
25.19/8.28	   A^2 -> H(U1(e, k), f(b))
25.19/8.28	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, c), f(c))
25.19/8.28	   A^2 -> H(U1(e, c), f(d))
25.19/8.28	   A^2 -> H(U1(k, e), f(b))
25.19/8.28	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, c), f(c))
25.19/8.28	   A^2 -> H(U1(k, c), f(d))
25.19/8.28	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, e), f(c))
25.19/8.28	   A^2 -> H(U1(c, e), f(d))
25.19/8.28	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, k), f(c))
25.19/8.28	   A^2 -> H(U1(c, k), f(d))
25.19/8.28	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.28	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.28	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.28	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.28	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.28	   A^2 -> H(U1(c, c), f(e))
25.19/8.28	   A^2 -> H(U1(c, c), f(k))
25.19/8.28	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.28	   A^2 -> H(e, f(b))
25.19/8.28	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, e), f(c))
25.19/8.28	   A^2 -> H(U1(e, e), f(d))
25.19/8.28	   A^2 -> H(f(e), U1(c, b))
25.19/8.28	   A^2 -> H(f(e), U1(d, b))
25.19/8.28	   A^2 -> H(f(e), U1(b, c))
25.19/8.28	   A^2 -> H(f(e), U1(b, d))
25.19/8.28	   A^2 -> H(f(e), U1(c, c))
25.19/8.28	   A^2 -> H(f(e), f(e))
25.19/8.28	   A^2 -> H(f(e), f(k))
25.19/8.28	   A^2 -> H(f(e), U1(d, d))
25.19/8.28	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, k), f(c))
25.19/8.28	   A^2 -> H(U1(k, k), f(d))
25.19/8.28	   A^2 -> H(f(k), U1(c, b))
25.19/8.28	   A^2 -> H(f(k), U1(d, b))
25.19/8.28	   A^2 -> H(f(k), U1(b, c))
25.19/8.28	   A^2 -> H(f(k), U1(b, d))
25.19/8.28	   A^2 -> H(f(k), U1(c, c))
25.19/8.28	   A^2 -> H(f(k), f(e))
25.19/8.28	   A^2 -> H(f(k), f(k))
25.19/8.28	   A^2 -> H(f(k), U1(d, d))
25.19/8.28	   A^2 -> H(f(c), U1(e, b))
25.19/8.28	   A^2 -> H(f(c), U1(k, b))
25.19/8.28	   A^2 -> H(f(c), U1(c, d))
25.19/8.28	   A^2 -> H(f(c), U1(d, c))
25.19/8.28	   A^2 -> H(f(c), U1(b, e))
25.19/8.28	   A^2 -> H(f(c), U1(b, k))
25.19/8.28	   A^2 -> H(f(c), U1(k, d))
25.19/8.28	   A^2 -> H(f(c), U1(d, k))
25.19/8.28	   A^2 -> H(f(c), U1(k, k))
25.19/8.28	   A^2 -> H(U1(k, k), f(b))
25.19/8.28	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, d), f(c))
25.19/8.28	   A^2 -> H(U1(k, d), f(d))
25.19/8.28	
25.19/8.28	The TRS R consists of the following rules:
25.19/8.28	
25.19/8.28	   f(x) -> U1(x, x)
25.19/8.28	   U1(e, x) -> x
25.19/8.28	   a -> c
25.19/8.28	   a -> d
25.19/8.28	   b -> c
25.19/8.28	   b -> d
25.19/8.28	   d -> k
25.19/8.28	   c -> e
25.19/8.28	   c -> k
25.19/8.28	
25.19/8.28	Q is empty.
25.19/8.28	We have to consider all minimal (P,Q,R)-chains.
25.19/8.28	----------------------------------------
25.19/8.28	
25.19/8.28	(165) TransformationProof (EQUIVALENT)
25.19/8.28	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), f(b)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.28	
25.19/8.28	   (A^2 -> H(U1(k, k), f(b)),A^2 -> H(U1(k, k), f(b)))
25.19/8.28	   (A^2 -> H(U1(d, k), U1(b, b)),A^2 -> H(U1(d, k), U1(b, b)))
25.19/8.28	   (A^2 -> H(U1(d, k), f(c)),A^2 -> H(U1(d, k), f(c)))
25.19/8.28	   (A^2 -> H(U1(d, k), f(d)),A^2 -> H(U1(d, k), f(d)))
25.19/8.28	
25.19/8.28	
25.19/8.28	----------------------------------------
25.19/8.28	
25.19/8.28	(166)
25.19/8.28	Obligation:
25.19/8.28	Q DP problem:
25.19/8.28	The TRS P consists of the following rules:
25.19/8.28	
25.19/8.28	   H(x, x) -> G(x, x, f(k))
25.19/8.28	   G(d, x, x) -> A^2
25.19/8.28	   A^2 -> H(f(c), f(c))
25.19/8.28	   A^2 -> H(f(d), f(d))
25.19/8.28	   A^2 -> H(U1(d, d), U1(b, b))
25.19/8.28	   A^2 -> H(U1(d, d), f(c))
25.19/8.28	   A^2 -> H(U1(d, d), f(d))
25.19/8.28	   A^2 -> H(f(d), U1(c, b))
25.19/8.28	   A^2 -> H(f(d), U1(d, b))
25.19/8.28	   A^2 -> H(f(d), U1(b, c))
25.19/8.28	   A^2 -> H(f(d), U1(b, d))
25.19/8.28	   A^2 -> H(f(d), U1(c, c))
25.19/8.28	   A^2 -> H(f(d), f(e))
25.19/8.28	   A^2 -> H(f(d), f(k))
25.19/8.28	   A^2 -> H(f(a), U1(e, b))
25.19/8.28	   A^2 -> H(f(a), U1(k, b))
25.19/8.28	   A^2 -> H(f(a), U1(c, d))
25.19/8.28	   A^2 -> H(f(a), U1(d, c))
25.19/8.28	   A^2 -> H(f(a), U1(b, e))
25.19/8.28	   A^2 -> H(f(a), U1(b, k))
25.19/8.28	   A^2 -> H(f(c), U1(c, c))
25.19/8.28	   A^2 -> H(f(a), U1(e, c))
25.19/8.28	   A^2 -> H(f(a), U1(k, c))
25.19/8.28	   A^2 -> H(f(a), U1(c, e))
25.19/8.28	   A^2 -> H(f(a), U1(c, k))
25.19/8.28	   A^2 -> H(f(c), f(e))
25.19/8.28	   A^2 -> H(f(a), U1(e, e))
25.19/8.28	   A^2 -> H(f(a), U1(k, k))
25.19/8.28	   A^2 -> H(f(d), U1(d, d))
25.19/8.28	   A^2 -> H(f(a), U1(k, d))
25.19/8.28	   A^2 -> H(f(a), U1(d, k))
25.19/8.28	   A^2 -> H(a, f(b))
25.19/8.28	   A^2 -> H(U1(e, d), f(b))
25.19/8.28	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, a), f(c))
25.19/8.28	   A^2 -> H(U1(e, a), f(d))
25.19/8.28	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, a), f(c))
25.19/8.28	   A^2 -> H(U1(k, a), f(d))
25.19/8.28	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, d), f(c))
25.19/8.28	   A^2 -> H(U1(c, d), f(d))
25.19/8.28	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.28	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.28	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.28	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.28	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.28	   A^2 -> H(U1(c, a), f(e))
25.19/8.28	   A^2 -> H(U1(c, a), f(k))
25.19/8.28	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.28	   A^2 -> H(U1(d, e), f(b))
25.19/8.28	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(d, c), f(c))
25.19/8.28	   A^2 -> H(U1(d, c), f(d))
25.19/8.28	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.28	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.28	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.28	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.28	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.28	   A^2 -> H(U1(d, a), f(e))
25.19/8.28	   A^2 -> H(U1(d, a), f(k))
25.19/8.28	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(a, e), f(c))
25.19/8.28	   A^2 -> H(U1(a, e), f(d))
25.19/8.28	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(a, k), f(c))
25.19/8.28	   A^2 -> H(U1(a, k), f(d))
25.19/8.28	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.28	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.28	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.28	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.28	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.28	   A^2 -> H(U1(a, c), f(e))
25.19/8.28	   A^2 -> H(U1(a, c), f(k))
25.19/8.28	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.28	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.28	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.28	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.28	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.28	   A^2 -> H(U1(a, d), f(e))
25.19/8.28	   A^2 -> H(U1(a, d), f(k))
25.19/8.28	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.28	   A^2 -> H(c, f(b))
25.19/8.28	   A^2 -> H(U1(e, k), f(b))
25.19/8.28	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, c), f(c))
25.19/8.28	   A^2 -> H(U1(e, c), f(d))
25.19/8.28	   A^2 -> H(U1(k, e), f(b))
25.19/8.28	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, c), f(c))
25.19/8.28	   A^2 -> H(U1(k, c), f(d))
25.19/8.28	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, e), f(c))
25.19/8.28	   A^2 -> H(U1(c, e), f(d))
25.19/8.28	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, k), f(c))
25.19/8.28	   A^2 -> H(U1(c, k), f(d))
25.19/8.28	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.28	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.28	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.28	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.28	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.28	   A^2 -> H(U1(c, c), f(e))
25.19/8.28	   A^2 -> H(U1(c, c), f(k))
25.19/8.28	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.28	   A^2 -> H(e, f(b))
25.19/8.28	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, e), f(c))
25.19/8.28	   A^2 -> H(U1(e, e), f(d))
25.19/8.28	   A^2 -> H(f(e), U1(c, b))
25.19/8.28	   A^2 -> H(f(e), U1(d, b))
25.19/8.28	   A^2 -> H(f(e), U1(b, c))
25.19/8.28	   A^2 -> H(f(e), U1(b, d))
25.19/8.28	   A^2 -> H(f(e), U1(c, c))
25.19/8.28	   A^2 -> H(f(e), f(e))
25.19/8.28	   A^2 -> H(f(e), f(k))
25.19/8.28	   A^2 -> H(f(e), U1(d, d))
25.19/8.28	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, k), f(c))
25.19/8.28	   A^2 -> H(U1(k, k), f(d))
25.19/8.28	   A^2 -> H(f(k), U1(c, b))
25.19/8.28	   A^2 -> H(f(k), U1(d, b))
25.19/8.28	   A^2 -> H(f(k), U1(b, c))
25.19/8.28	   A^2 -> H(f(k), U1(b, d))
25.19/8.28	   A^2 -> H(f(k), U1(c, c))
25.19/8.28	   A^2 -> H(f(k), f(e))
25.19/8.28	   A^2 -> H(f(k), f(k))
25.19/8.28	   A^2 -> H(f(k), U1(d, d))
25.19/8.28	   A^2 -> H(f(c), U1(e, b))
25.19/8.28	   A^2 -> H(f(c), U1(k, b))
25.19/8.28	   A^2 -> H(f(c), U1(c, d))
25.19/8.28	   A^2 -> H(f(c), U1(d, c))
25.19/8.28	   A^2 -> H(f(c), U1(b, e))
25.19/8.28	   A^2 -> H(f(c), U1(b, k))
25.19/8.28	   A^2 -> H(f(c), U1(k, d))
25.19/8.28	   A^2 -> H(f(c), U1(d, k))
25.19/8.28	   A^2 -> H(f(c), U1(k, k))
25.19/8.28	   A^2 -> H(U1(k, k), f(b))
25.19/8.28	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, d), f(c))
25.19/8.28	   A^2 -> H(U1(k, d), f(d))
25.19/8.28	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(d, k), f(c))
25.19/8.28	   A^2 -> H(U1(d, k), f(d))
25.19/8.28	
25.19/8.28	The TRS R consists of the following rules:
25.19/8.28	
25.19/8.28	   f(x) -> U1(x, x)
25.19/8.28	   U1(e, x) -> x
25.19/8.28	   a -> c
25.19/8.28	   a -> d
25.19/8.28	   b -> c
25.19/8.28	   b -> d
25.19/8.28	   d -> k
25.19/8.28	   c -> e
25.19/8.28	   c -> k
25.19/8.28	
25.19/8.28	Q is empty.
25.19/8.28	We have to consider all minimal (P,Q,R)-chains.
25.19/8.28	----------------------------------------
25.19/8.28	
25.19/8.28	(167) TransformationProof (EQUIVALENT)
25.19/8.28	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.28	
25.19/8.28	   (A^2 -> H(U1(k, d), U1(b, b)),A^2 -> H(U1(k, d), U1(b, b)))
25.19/8.28	   (A^2 -> H(U1(d, k), U1(b, b)),A^2 -> H(U1(d, k), U1(b, b)))
25.19/8.28	   (A^2 -> H(U1(d, d), U1(c, b)),A^2 -> H(U1(d, d), U1(c, b)))
25.19/8.28	   (A^2 -> H(U1(d, d), U1(d, b)),A^2 -> H(U1(d, d), U1(d, b)))
25.19/8.28	   (A^2 -> H(U1(d, d), U1(b, c)),A^2 -> H(U1(d, d), U1(b, c)))
25.19/8.28	   (A^2 -> H(U1(d, d), U1(b, d)),A^2 -> H(U1(d, d), U1(b, d)))
25.19/8.28	
25.19/8.28	
25.19/8.28	----------------------------------------
25.19/8.28	
25.19/8.28	(168)
25.19/8.28	Obligation:
25.19/8.28	Q DP problem:
25.19/8.28	The TRS P consists of the following rules:
25.19/8.28	
25.19/8.28	   H(x, x) -> G(x, x, f(k))
25.19/8.28	   G(d, x, x) -> A^2
25.19/8.28	   A^2 -> H(f(c), f(c))
25.19/8.28	   A^2 -> H(f(d), f(d))
25.19/8.28	   A^2 -> H(U1(d, d), f(c))
25.19/8.28	   A^2 -> H(U1(d, d), f(d))
25.19/8.28	   A^2 -> H(f(d), U1(c, b))
25.19/8.28	   A^2 -> H(f(d), U1(d, b))
25.19/8.28	   A^2 -> H(f(d), U1(b, c))
25.19/8.28	   A^2 -> H(f(d), U1(b, d))
25.19/8.28	   A^2 -> H(f(d), U1(c, c))
25.19/8.28	   A^2 -> H(f(d), f(e))
25.19/8.28	   A^2 -> H(f(d), f(k))
25.19/8.28	   A^2 -> H(f(a), U1(e, b))
25.19/8.28	   A^2 -> H(f(a), U1(k, b))
25.19/8.28	   A^2 -> H(f(a), U1(c, d))
25.19/8.28	   A^2 -> H(f(a), U1(d, c))
25.19/8.28	   A^2 -> H(f(a), U1(b, e))
25.19/8.28	   A^2 -> H(f(a), U1(b, k))
25.19/8.28	   A^2 -> H(f(c), U1(c, c))
25.19/8.28	   A^2 -> H(f(a), U1(e, c))
25.19/8.28	   A^2 -> H(f(a), U1(k, c))
25.19/8.28	   A^2 -> H(f(a), U1(c, e))
25.19/8.28	   A^2 -> H(f(a), U1(c, k))
25.19/8.28	   A^2 -> H(f(c), f(e))
25.19/8.28	   A^2 -> H(f(a), U1(e, e))
25.19/8.28	   A^2 -> H(f(a), U1(k, k))
25.19/8.28	   A^2 -> H(f(d), U1(d, d))
25.19/8.28	   A^2 -> H(f(a), U1(k, d))
25.19/8.28	   A^2 -> H(f(a), U1(d, k))
25.19/8.28	   A^2 -> H(a, f(b))
25.19/8.28	   A^2 -> H(U1(e, d), f(b))
25.19/8.28	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, a), f(c))
25.19/8.28	   A^2 -> H(U1(e, a), f(d))
25.19/8.28	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, a), f(c))
25.19/8.28	   A^2 -> H(U1(k, a), f(d))
25.19/8.28	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, d), f(c))
25.19/8.28	   A^2 -> H(U1(c, d), f(d))
25.19/8.28	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.28	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.28	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.28	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.28	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.28	   A^2 -> H(U1(c, a), f(e))
25.19/8.28	   A^2 -> H(U1(c, a), f(k))
25.19/8.28	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.28	   A^2 -> H(U1(d, e), f(b))
25.19/8.28	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(d, c), f(c))
25.19/8.28	   A^2 -> H(U1(d, c), f(d))
25.19/8.28	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.28	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.28	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.28	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.28	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.28	   A^2 -> H(U1(d, a), f(e))
25.19/8.28	   A^2 -> H(U1(d, a), f(k))
25.19/8.28	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(a, e), f(c))
25.19/8.28	   A^2 -> H(U1(a, e), f(d))
25.19/8.28	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(a, k), f(c))
25.19/8.28	   A^2 -> H(U1(a, k), f(d))
25.19/8.28	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.28	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.28	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.28	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.28	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.28	   A^2 -> H(U1(a, c), f(e))
25.19/8.28	   A^2 -> H(U1(a, c), f(k))
25.19/8.28	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.28	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.28	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.28	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.28	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.28	   A^2 -> H(U1(a, d), f(e))
25.19/8.28	   A^2 -> H(U1(a, d), f(k))
25.19/8.28	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.28	   A^2 -> H(c, f(b))
25.19/8.28	   A^2 -> H(U1(e, k), f(b))
25.19/8.28	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, c), f(c))
25.19/8.28	   A^2 -> H(U1(e, c), f(d))
25.19/8.28	   A^2 -> H(U1(k, e), f(b))
25.19/8.28	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, c), f(c))
25.19/8.28	   A^2 -> H(U1(k, c), f(d))
25.19/8.28	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, e), f(c))
25.19/8.28	   A^2 -> H(U1(c, e), f(d))
25.19/8.28	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, k), f(c))
25.19/8.28	   A^2 -> H(U1(c, k), f(d))
25.19/8.28	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.28	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.28	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.28	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.28	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.28	   A^2 -> H(U1(c, c), f(e))
25.19/8.28	   A^2 -> H(U1(c, c), f(k))
25.19/8.28	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.28	   A^2 -> H(e, f(b))
25.19/8.28	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, e), f(c))
25.19/8.28	   A^2 -> H(U1(e, e), f(d))
25.19/8.28	   A^2 -> H(f(e), U1(c, b))
25.19/8.28	   A^2 -> H(f(e), U1(d, b))
25.19/8.28	   A^2 -> H(f(e), U1(b, c))
25.19/8.28	   A^2 -> H(f(e), U1(b, d))
25.19/8.28	   A^2 -> H(f(e), U1(c, c))
25.19/8.28	   A^2 -> H(f(e), f(e))
25.19/8.28	   A^2 -> H(f(e), f(k))
25.19/8.28	   A^2 -> H(f(e), U1(d, d))
25.19/8.28	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, k), f(c))
25.19/8.28	   A^2 -> H(U1(k, k), f(d))
25.19/8.28	   A^2 -> H(f(k), U1(c, b))
25.19/8.28	   A^2 -> H(f(k), U1(d, b))
25.19/8.28	   A^2 -> H(f(k), U1(b, c))
25.19/8.28	   A^2 -> H(f(k), U1(b, d))
25.19/8.28	   A^2 -> H(f(k), U1(c, c))
25.19/8.28	   A^2 -> H(f(k), f(e))
25.19/8.28	   A^2 -> H(f(k), f(k))
25.19/8.28	   A^2 -> H(f(k), U1(d, d))
25.19/8.28	   A^2 -> H(f(c), U1(e, b))
25.19/8.28	   A^2 -> H(f(c), U1(k, b))
25.19/8.28	   A^2 -> H(f(c), U1(c, d))
25.19/8.28	   A^2 -> H(f(c), U1(d, c))
25.19/8.28	   A^2 -> H(f(c), U1(b, e))
25.19/8.28	   A^2 -> H(f(c), U1(b, k))
25.19/8.28	   A^2 -> H(f(c), U1(k, d))
25.19/8.28	   A^2 -> H(f(c), U1(d, k))
25.19/8.28	   A^2 -> H(f(c), U1(k, k))
25.19/8.28	   A^2 -> H(U1(k, k), f(b))
25.19/8.28	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, d), f(c))
25.19/8.28	   A^2 -> H(U1(k, d), f(d))
25.19/8.28	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(d, k), f(c))
25.19/8.28	   A^2 -> H(U1(d, k), f(d))
25.19/8.28	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.28	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.28	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.28	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.28	
25.19/8.28	The TRS R consists of the following rules:
25.19/8.28	
25.19/8.28	   f(x) -> U1(x, x)
25.19/8.28	   U1(e, x) -> x
25.19/8.28	   a -> c
25.19/8.28	   a -> d
25.19/8.28	   b -> c
25.19/8.28	   b -> d
25.19/8.28	   d -> k
25.19/8.28	   c -> e
25.19/8.28	   c -> k
25.19/8.28	
25.19/8.28	Q is empty.
25.19/8.28	We have to consider all minimal (P,Q,R)-chains.
25.19/8.28	----------------------------------------
25.19/8.28	
25.19/8.28	(169) TransformationProof (EQUIVALENT)
25.19/8.28	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), f(c)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.28	
25.19/8.28	   (A^2 -> H(U1(k, d), f(c)),A^2 -> H(U1(k, d), f(c)))
25.19/8.28	   (A^2 -> H(U1(d, k), f(c)),A^2 -> H(U1(d, k), f(c)))
25.19/8.28	   (A^2 -> H(U1(d, d), U1(c, c)),A^2 -> H(U1(d, d), U1(c, c)))
25.19/8.28	   (A^2 -> H(U1(d, d), f(e)),A^2 -> H(U1(d, d), f(e)))
25.19/8.28	   (A^2 -> H(U1(d, d), f(k)),A^2 -> H(U1(d, d), f(k)))
25.19/8.28	
25.19/8.28	
25.19/8.28	----------------------------------------
25.19/8.28	
25.19/8.28	(170)
25.19/8.28	Obligation:
25.19/8.28	Q DP problem:
25.19/8.28	The TRS P consists of the following rules:
25.19/8.28	
25.19/8.28	   H(x, x) -> G(x, x, f(k))
25.19/8.28	   G(d, x, x) -> A^2
25.19/8.28	   A^2 -> H(f(c), f(c))
25.19/8.28	   A^2 -> H(f(d), f(d))
25.19/8.28	   A^2 -> H(U1(d, d), f(d))
25.19/8.28	   A^2 -> H(f(d), U1(c, b))
25.19/8.28	   A^2 -> H(f(d), U1(d, b))
25.19/8.28	   A^2 -> H(f(d), U1(b, c))
25.19/8.28	   A^2 -> H(f(d), U1(b, d))
25.19/8.28	   A^2 -> H(f(d), U1(c, c))
25.19/8.28	   A^2 -> H(f(d), f(e))
25.19/8.28	   A^2 -> H(f(d), f(k))
25.19/8.28	   A^2 -> H(f(a), U1(e, b))
25.19/8.28	   A^2 -> H(f(a), U1(k, b))
25.19/8.28	   A^2 -> H(f(a), U1(c, d))
25.19/8.28	   A^2 -> H(f(a), U1(d, c))
25.19/8.28	   A^2 -> H(f(a), U1(b, e))
25.19/8.28	   A^2 -> H(f(a), U1(b, k))
25.19/8.28	   A^2 -> H(f(c), U1(c, c))
25.19/8.28	   A^2 -> H(f(a), U1(e, c))
25.19/8.28	   A^2 -> H(f(a), U1(k, c))
25.19/8.28	   A^2 -> H(f(a), U1(c, e))
25.19/8.28	   A^2 -> H(f(a), U1(c, k))
25.19/8.28	   A^2 -> H(f(c), f(e))
25.19/8.28	   A^2 -> H(f(a), U1(e, e))
25.19/8.28	   A^2 -> H(f(a), U1(k, k))
25.19/8.28	   A^2 -> H(f(d), U1(d, d))
25.19/8.28	   A^2 -> H(f(a), U1(k, d))
25.19/8.28	   A^2 -> H(f(a), U1(d, k))
25.19/8.28	   A^2 -> H(a, f(b))
25.19/8.28	   A^2 -> H(U1(e, d), f(b))
25.19/8.28	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, a), f(c))
25.19/8.28	   A^2 -> H(U1(e, a), f(d))
25.19/8.28	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, a), f(c))
25.19/8.28	   A^2 -> H(U1(k, a), f(d))
25.19/8.28	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, d), f(c))
25.19/8.28	   A^2 -> H(U1(c, d), f(d))
25.19/8.28	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.28	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.28	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.28	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.28	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.28	   A^2 -> H(U1(c, a), f(e))
25.19/8.28	   A^2 -> H(U1(c, a), f(k))
25.19/8.28	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.28	   A^2 -> H(U1(d, e), f(b))
25.19/8.28	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(d, c), f(c))
25.19/8.28	   A^2 -> H(U1(d, c), f(d))
25.19/8.28	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.28	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.28	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.28	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.28	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.28	   A^2 -> H(U1(d, a), f(e))
25.19/8.28	   A^2 -> H(U1(d, a), f(k))
25.19/8.28	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(a, e), f(c))
25.19/8.28	   A^2 -> H(U1(a, e), f(d))
25.19/8.28	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(a, k), f(c))
25.19/8.28	   A^2 -> H(U1(a, k), f(d))
25.19/8.28	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.28	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.28	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.28	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.28	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.28	   A^2 -> H(U1(a, c), f(e))
25.19/8.28	   A^2 -> H(U1(a, c), f(k))
25.19/8.28	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.28	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.28	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.28	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.28	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.28	   A^2 -> H(U1(a, d), f(e))
25.19/8.28	   A^2 -> H(U1(a, d), f(k))
25.19/8.28	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.28	   A^2 -> H(c, f(b))
25.19/8.28	   A^2 -> H(U1(e, k), f(b))
25.19/8.28	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, c), f(c))
25.19/8.28	   A^2 -> H(U1(e, c), f(d))
25.19/8.28	   A^2 -> H(U1(k, e), f(b))
25.19/8.28	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, c), f(c))
25.19/8.28	   A^2 -> H(U1(k, c), f(d))
25.19/8.28	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, e), f(c))
25.19/8.28	   A^2 -> H(U1(c, e), f(d))
25.19/8.28	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, k), f(c))
25.19/8.28	   A^2 -> H(U1(c, k), f(d))
25.19/8.28	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.28	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.28	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.28	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.28	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.28	   A^2 -> H(U1(c, c), f(e))
25.19/8.28	   A^2 -> H(U1(c, c), f(k))
25.19/8.28	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.28	   A^2 -> H(e, f(b))
25.19/8.28	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, e), f(c))
25.19/8.28	   A^2 -> H(U1(e, e), f(d))
25.19/8.28	   A^2 -> H(f(e), U1(c, b))
25.19/8.28	   A^2 -> H(f(e), U1(d, b))
25.19/8.28	   A^2 -> H(f(e), U1(b, c))
25.19/8.28	   A^2 -> H(f(e), U1(b, d))
25.19/8.28	   A^2 -> H(f(e), U1(c, c))
25.19/8.28	   A^2 -> H(f(e), f(e))
25.19/8.28	   A^2 -> H(f(e), f(k))
25.19/8.28	   A^2 -> H(f(e), U1(d, d))
25.19/8.28	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, k), f(c))
25.19/8.28	   A^2 -> H(U1(k, k), f(d))
25.19/8.28	   A^2 -> H(f(k), U1(c, b))
25.19/8.28	   A^2 -> H(f(k), U1(d, b))
25.19/8.28	   A^2 -> H(f(k), U1(b, c))
25.19/8.28	   A^2 -> H(f(k), U1(b, d))
25.19/8.28	   A^2 -> H(f(k), U1(c, c))
25.19/8.28	   A^2 -> H(f(k), f(e))
25.19/8.28	   A^2 -> H(f(k), f(k))
25.19/8.28	   A^2 -> H(f(k), U1(d, d))
25.19/8.28	   A^2 -> H(f(c), U1(e, b))
25.19/8.28	   A^2 -> H(f(c), U1(k, b))
25.19/8.28	   A^2 -> H(f(c), U1(c, d))
25.19/8.28	   A^2 -> H(f(c), U1(d, c))
25.19/8.28	   A^2 -> H(f(c), U1(b, e))
25.19/8.28	   A^2 -> H(f(c), U1(b, k))
25.19/8.28	   A^2 -> H(f(c), U1(k, d))
25.19/8.28	   A^2 -> H(f(c), U1(d, k))
25.19/8.28	   A^2 -> H(f(c), U1(k, k))
25.19/8.28	   A^2 -> H(U1(k, k), f(b))
25.19/8.28	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, d), f(c))
25.19/8.28	   A^2 -> H(U1(k, d), f(d))
25.19/8.28	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(d, k), f(c))
25.19/8.28	   A^2 -> H(U1(d, k), f(d))
25.19/8.28	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.28	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.28	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.28	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.28	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.28	   A^2 -> H(U1(d, d), f(e))
25.19/8.28	   A^2 -> H(U1(d, d), f(k))
25.19/8.28	
25.19/8.28	The TRS R consists of the following rules:
25.19/8.28	
25.19/8.28	   f(x) -> U1(x, x)
25.19/8.28	   U1(e, x) -> x
25.19/8.28	   a -> c
25.19/8.28	   a -> d
25.19/8.28	   b -> c
25.19/8.28	   b -> d
25.19/8.28	   d -> k
25.19/8.28	   c -> e
25.19/8.28	   c -> k
25.19/8.28	
25.19/8.28	Q is empty.
25.19/8.28	We have to consider all minimal (P,Q,R)-chains.
25.19/8.28	----------------------------------------
25.19/8.28	
25.19/8.28	(171) TransformationProof (EQUIVALENT)
25.19/8.28	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), f(d)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.28	
25.19/8.28	   (A^2 -> H(U1(k, d), f(d)),A^2 -> H(U1(k, d), f(d)))
25.19/8.28	   (A^2 -> H(U1(d, k), f(d)),A^2 -> H(U1(d, k), f(d)))
25.19/8.28	   (A^2 -> H(U1(d, d), U1(d, d)),A^2 -> H(U1(d, d), U1(d, d)))
25.19/8.28	   (A^2 -> H(U1(d, d), f(k)),A^2 -> H(U1(d, d), f(k)))
25.19/8.28	
25.19/8.28	
25.19/8.28	----------------------------------------
25.19/8.28	
25.19/8.28	(172)
25.19/8.28	Obligation:
25.19/8.28	Q DP problem:
25.19/8.28	The TRS P consists of the following rules:
25.19/8.28	
25.19/8.28	   H(x, x) -> G(x, x, f(k))
25.19/8.28	   G(d, x, x) -> A^2
25.19/8.28	   A^2 -> H(f(c), f(c))
25.19/8.28	   A^2 -> H(f(d), f(d))
25.19/8.28	   A^2 -> H(f(d), U1(c, b))
25.19/8.28	   A^2 -> H(f(d), U1(d, b))
25.19/8.28	   A^2 -> H(f(d), U1(b, c))
25.19/8.28	   A^2 -> H(f(d), U1(b, d))
25.19/8.28	   A^2 -> H(f(d), U1(c, c))
25.19/8.28	   A^2 -> H(f(d), f(e))
25.19/8.28	   A^2 -> H(f(d), f(k))
25.19/8.28	   A^2 -> H(f(a), U1(e, b))
25.19/8.28	   A^2 -> H(f(a), U1(k, b))
25.19/8.28	   A^2 -> H(f(a), U1(c, d))
25.19/8.28	   A^2 -> H(f(a), U1(d, c))
25.19/8.28	   A^2 -> H(f(a), U1(b, e))
25.19/8.28	   A^2 -> H(f(a), U1(b, k))
25.19/8.28	   A^2 -> H(f(c), U1(c, c))
25.19/8.28	   A^2 -> H(f(a), U1(e, c))
25.19/8.28	   A^2 -> H(f(a), U1(k, c))
25.19/8.28	   A^2 -> H(f(a), U1(c, e))
25.19/8.28	   A^2 -> H(f(a), U1(c, k))
25.19/8.28	   A^2 -> H(f(c), f(e))
25.19/8.28	   A^2 -> H(f(a), U1(e, e))
25.19/8.28	   A^2 -> H(f(a), U1(k, k))
25.19/8.28	   A^2 -> H(f(d), U1(d, d))
25.19/8.28	   A^2 -> H(f(a), U1(k, d))
25.19/8.28	   A^2 -> H(f(a), U1(d, k))
25.19/8.28	   A^2 -> H(a, f(b))
25.19/8.28	   A^2 -> H(U1(e, d), f(b))
25.19/8.28	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, a), f(c))
25.19/8.28	   A^2 -> H(U1(e, a), f(d))
25.19/8.28	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, a), f(c))
25.19/8.28	   A^2 -> H(U1(k, a), f(d))
25.19/8.28	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, d), f(c))
25.19/8.28	   A^2 -> H(U1(c, d), f(d))
25.19/8.28	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.28	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.28	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.28	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.28	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.28	   A^2 -> H(U1(c, a), f(e))
25.19/8.28	   A^2 -> H(U1(c, a), f(k))
25.19/8.28	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.28	   A^2 -> H(U1(d, e), f(b))
25.19/8.28	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(d, c), f(c))
25.19/8.28	   A^2 -> H(U1(d, c), f(d))
25.19/8.28	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.28	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.28	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.28	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.28	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.28	   A^2 -> H(U1(d, a), f(e))
25.19/8.28	   A^2 -> H(U1(d, a), f(k))
25.19/8.28	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(a, e), f(c))
25.19/8.28	   A^2 -> H(U1(a, e), f(d))
25.19/8.28	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(a, k), f(c))
25.19/8.28	   A^2 -> H(U1(a, k), f(d))
25.19/8.28	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.28	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.28	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.28	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.28	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.28	   A^2 -> H(U1(a, c), f(e))
25.19/8.28	   A^2 -> H(U1(a, c), f(k))
25.19/8.28	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.28	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.28	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.28	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.28	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.28	   A^2 -> H(U1(a, d), f(e))
25.19/8.28	   A^2 -> H(U1(a, d), f(k))
25.19/8.28	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.28	   A^2 -> H(c, f(b))
25.19/8.28	   A^2 -> H(U1(e, k), f(b))
25.19/8.28	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, c), f(c))
25.19/8.28	   A^2 -> H(U1(e, c), f(d))
25.19/8.28	   A^2 -> H(U1(k, e), f(b))
25.19/8.28	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, c), f(c))
25.19/8.28	   A^2 -> H(U1(k, c), f(d))
25.19/8.28	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, e), f(c))
25.19/8.28	   A^2 -> H(U1(c, e), f(d))
25.19/8.28	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, k), f(c))
25.19/8.28	   A^2 -> H(U1(c, k), f(d))
25.19/8.28	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.28	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.28	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.28	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.28	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.28	   A^2 -> H(U1(c, c), f(e))
25.19/8.28	   A^2 -> H(U1(c, c), f(k))
25.19/8.28	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.28	   A^2 -> H(e, f(b))
25.19/8.28	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, e), f(c))
25.19/8.28	   A^2 -> H(U1(e, e), f(d))
25.19/8.28	   A^2 -> H(f(e), U1(c, b))
25.19/8.28	   A^2 -> H(f(e), U1(d, b))
25.19/8.28	   A^2 -> H(f(e), U1(b, c))
25.19/8.28	   A^2 -> H(f(e), U1(b, d))
25.19/8.28	   A^2 -> H(f(e), U1(c, c))
25.19/8.28	   A^2 -> H(f(e), f(e))
25.19/8.28	   A^2 -> H(f(e), f(k))
25.19/8.28	   A^2 -> H(f(e), U1(d, d))
25.19/8.28	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, k), f(c))
25.19/8.28	   A^2 -> H(U1(k, k), f(d))
25.19/8.28	   A^2 -> H(f(k), U1(c, b))
25.19/8.28	   A^2 -> H(f(k), U1(d, b))
25.19/8.28	   A^2 -> H(f(k), U1(b, c))
25.19/8.28	   A^2 -> H(f(k), U1(b, d))
25.19/8.28	   A^2 -> H(f(k), U1(c, c))
25.19/8.28	   A^2 -> H(f(k), f(e))
25.19/8.28	   A^2 -> H(f(k), f(k))
25.19/8.28	   A^2 -> H(f(k), U1(d, d))
25.19/8.28	   A^2 -> H(f(c), U1(e, b))
25.19/8.28	   A^2 -> H(f(c), U1(k, b))
25.19/8.28	   A^2 -> H(f(c), U1(c, d))
25.19/8.28	   A^2 -> H(f(c), U1(d, c))
25.19/8.28	   A^2 -> H(f(c), U1(b, e))
25.19/8.28	   A^2 -> H(f(c), U1(b, k))
25.19/8.28	   A^2 -> H(f(c), U1(k, d))
25.19/8.28	   A^2 -> H(f(c), U1(d, k))
25.19/8.28	   A^2 -> H(f(c), U1(k, k))
25.19/8.28	   A^2 -> H(U1(k, k), f(b))
25.19/8.28	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, d), f(c))
25.19/8.28	   A^2 -> H(U1(k, d), f(d))
25.19/8.28	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(d, k), f(c))
25.19/8.28	   A^2 -> H(U1(d, k), f(d))
25.19/8.28	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.28	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.28	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.28	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.28	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.28	   A^2 -> H(U1(d, d), f(e))
25.19/8.28	   A^2 -> H(U1(d, d), f(k))
25.19/8.28	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.28	
25.19/8.28	The TRS R consists of the following rules:
25.19/8.28	
25.19/8.28	   f(x) -> U1(x, x)
25.19/8.28	   U1(e, x) -> x
25.19/8.28	   a -> c
25.19/8.28	   a -> d
25.19/8.28	   b -> c
25.19/8.28	   b -> d
25.19/8.28	   d -> k
25.19/8.28	   c -> e
25.19/8.28	   c -> k
25.19/8.28	
25.19/8.28	Q is empty.
25.19/8.28	We have to consider all minimal (P,Q,R)-chains.
25.19/8.28	----------------------------------------
25.19/8.28	
25.19/8.28	(173) TransformationProof (EQUIVALENT)
25.19/8.28	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.28	
25.19/8.28	   (A^2 -> H(U1(d, d), U1(c, b)),A^2 -> H(U1(d, d), U1(c, b)))
25.19/8.28	   (A^2 -> H(f(k), U1(c, b)),A^2 -> H(f(k), U1(c, b)))
25.19/8.28	   (A^2 -> H(f(d), U1(e, b)),A^2 -> H(f(d), U1(e, b)))
25.19/8.28	   (A^2 -> H(f(d), U1(k, b)),A^2 -> H(f(d), U1(k, b)))
25.19/8.28	   (A^2 -> H(f(d), U1(c, c)),A^2 -> H(f(d), U1(c, c)))
25.19/8.28	   (A^2 -> H(f(d), U1(c, d)),A^2 -> H(f(d), U1(c, d)))
25.19/8.28	
25.19/8.28	
25.19/8.28	----------------------------------------
25.19/8.28	
25.19/8.28	(174)
25.19/8.28	Obligation:
25.19/8.28	Q DP problem:
25.19/8.28	The TRS P consists of the following rules:
25.19/8.28	
25.19/8.28	   H(x, x) -> G(x, x, f(k))
25.19/8.28	   G(d, x, x) -> A^2
25.19/8.28	   A^2 -> H(f(c), f(c))
25.19/8.28	   A^2 -> H(f(d), f(d))
25.19/8.28	   A^2 -> H(f(d), U1(d, b))
25.19/8.28	   A^2 -> H(f(d), U1(b, c))
25.19/8.28	   A^2 -> H(f(d), U1(b, d))
25.19/8.28	   A^2 -> H(f(d), U1(c, c))
25.19/8.28	   A^2 -> H(f(d), f(e))
25.19/8.28	   A^2 -> H(f(d), f(k))
25.19/8.28	   A^2 -> H(f(a), U1(e, b))
25.19/8.28	   A^2 -> H(f(a), U1(k, b))
25.19/8.28	   A^2 -> H(f(a), U1(c, d))
25.19/8.28	   A^2 -> H(f(a), U1(d, c))
25.19/8.28	   A^2 -> H(f(a), U1(b, e))
25.19/8.28	   A^2 -> H(f(a), U1(b, k))
25.19/8.28	   A^2 -> H(f(c), U1(c, c))
25.19/8.28	   A^2 -> H(f(a), U1(e, c))
25.19/8.28	   A^2 -> H(f(a), U1(k, c))
25.19/8.28	   A^2 -> H(f(a), U1(c, e))
25.19/8.28	   A^2 -> H(f(a), U1(c, k))
25.19/8.28	   A^2 -> H(f(c), f(e))
25.19/8.28	   A^2 -> H(f(a), U1(e, e))
25.19/8.28	   A^2 -> H(f(a), U1(k, k))
25.19/8.28	   A^2 -> H(f(d), U1(d, d))
25.19/8.28	   A^2 -> H(f(a), U1(k, d))
25.19/8.28	   A^2 -> H(f(a), U1(d, k))
25.19/8.28	   A^2 -> H(a, f(b))
25.19/8.28	   A^2 -> H(U1(e, d), f(b))
25.19/8.28	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, a), f(c))
25.19/8.28	   A^2 -> H(U1(e, a), f(d))
25.19/8.28	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, a), f(c))
25.19/8.28	   A^2 -> H(U1(k, a), f(d))
25.19/8.28	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, d), f(c))
25.19/8.28	   A^2 -> H(U1(c, d), f(d))
25.19/8.28	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.28	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.28	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.28	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.28	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.28	   A^2 -> H(U1(c, a), f(e))
25.19/8.28	   A^2 -> H(U1(c, a), f(k))
25.19/8.28	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.28	   A^2 -> H(U1(d, e), f(b))
25.19/8.28	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(d, c), f(c))
25.19/8.28	   A^2 -> H(U1(d, c), f(d))
25.19/8.28	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.28	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.28	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.28	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.28	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.28	   A^2 -> H(U1(d, a), f(e))
25.19/8.28	   A^2 -> H(U1(d, a), f(k))
25.19/8.28	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(a, e), f(c))
25.19/8.28	   A^2 -> H(U1(a, e), f(d))
25.19/8.28	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(a, k), f(c))
25.19/8.28	   A^2 -> H(U1(a, k), f(d))
25.19/8.28	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.28	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.28	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.28	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.28	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.28	   A^2 -> H(U1(a, c), f(e))
25.19/8.28	   A^2 -> H(U1(a, c), f(k))
25.19/8.28	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.28	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.28	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.28	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.28	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.28	   A^2 -> H(U1(a, d), f(e))
25.19/8.28	   A^2 -> H(U1(a, d), f(k))
25.19/8.28	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.28	   A^2 -> H(c, f(b))
25.19/8.28	   A^2 -> H(U1(e, k), f(b))
25.19/8.28	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, c), f(c))
25.19/8.28	   A^2 -> H(U1(e, c), f(d))
25.19/8.28	   A^2 -> H(U1(k, e), f(b))
25.19/8.28	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, c), f(c))
25.19/8.28	   A^2 -> H(U1(k, c), f(d))
25.19/8.28	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, e), f(c))
25.19/8.28	   A^2 -> H(U1(c, e), f(d))
25.19/8.28	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, k), f(c))
25.19/8.28	   A^2 -> H(U1(c, k), f(d))
25.19/8.28	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.28	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.28	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.28	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.28	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.28	   A^2 -> H(U1(c, c), f(e))
25.19/8.28	   A^2 -> H(U1(c, c), f(k))
25.19/8.28	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.28	   A^2 -> H(e, f(b))
25.19/8.28	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, e), f(c))
25.19/8.28	   A^2 -> H(U1(e, e), f(d))
25.19/8.28	   A^2 -> H(f(e), U1(c, b))
25.19/8.28	   A^2 -> H(f(e), U1(d, b))
25.19/8.28	   A^2 -> H(f(e), U1(b, c))
25.19/8.28	   A^2 -> H(f(e), U1(b, d))
25.19/8.28	   A^2 -> H(f(e), U1(c, c))
25.19/8.28	   A^2 -> H(f(e), f(e))
25.19/8.28	   A^2 -> H(f(e), f(k))
25.19/8.28	   A^2 -> H(f(e), U1(d, d))
25.19/8.28	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, k), f(c))
25.19/8.28	   A^2 -> H(U1(k, k), f(d))
25.19/8.28	   A^2 -> H(f(k), U1(c, b))
25.19/8.28	   A^2 -> H(f(k), U1(d, b))
25.19/8.28	   A^2 -> H(f(k), U1(b, c))
25.19/8.28	   A^2 -> H(f(k), U1(b, d))
25.19/8.28	   A^2 -> H(f(k), U1(c, c))
25.19/8.28	   A^2 -> H(f(k), f(e))
25.19/8.28	   A^2 -> H(f(k), f(k))
25.19/8.28	   A^2 -> H(f(k), U1(d, d))
25.19/8.28	   A^2 -> H(f(c), U1(e, b))
25.19/8.28	   A^2 -> H(f(c), U1(k, b))
25.19/8.28	   A^2 -> H(f(c), U1(c, d))
25.19/8.28	   A^2 -> H(f(c), U1(d, c))
25.19/8.28	   A^2 -> H(f(c), U1(b, e))
25.19/8.28	   A^2 -> H(f(c), U1(b, k))
25.19/8.28	   A^2 -> H(f(c), U1(k, d))
25.19/8.28	   A^2 -> H(f(c), U1(d, k))
25.19/8.28	   A^2 -> H(f(c), U1(k, k))
25.19/8.28	   A^2 -> H(U1(k, k), f(b))
25.19/8.28	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, d), f(c))
25.19/8.28	   A^2 -> H(U1(k, d), f(d))
25.19/8.28	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(d, k), f(c))
25.19/8.28	   A^2 -> H(U1(d, k), f(d))
25.19/8.28	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.28	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.28	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.28	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.28	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.28	   A^2 -> H(U1(d, d), f(e))
25.19/8.28	   A^2 -> H(U1(d, d), f(k))
25.19/8.28	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.28	   A^2 -> H(f(d), U1(e, b))
25.19/8.28	   A^2 -> H(f(d), U1(k, b))
25.19/8.28	   A^2 -> H(f(d), U1(c, d))
25.19/8.28	
25.19/8.28	The TRS R consists of the following rules:
25.19/8.28	
25.19/8.28	   f(x) -> U1(x, x)
25.19/8.28	   U1(e, x) -> x
25.19/8.28	   a -> c
25.19/8.28	   a -> d
25.19/8.28	   b -> c
25.19/8.28	   b -> d
25.19/8.28	   d -> k
25.19/8.28	   c -> e
25.19/8.28	   c -> k
25.19/8.28	
25.19/8.28	Q is empty.
25.19/8.28	We have to consider all minimal (P,Q,R)-chains.
25.19/8.28	----------------------------------------
25.19/8.28	
25.19/8.28	(175) TransformationProof (EQUIVALENT)
25.19/8.28	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.28	
25.19/8.28	   (A^2 -> H(U1(d, d), U1(d, b)),A^2 -> H(U1(d, d), U1(d, b)))
25.19/8.28	   (A^2 -> H(f(k), U1(d, b)),A^2 -> H(f(k), U1(d, b)))
25.19/8.28	   (A^2 -> H(f(d), U1(k, b)),A^2 -> H(f(d), U1(k, b)))
25.19/8.28	   (A^2 -> H(f(d), U1(d, c)),A^2 -> H(f(d), U1(d, c)))
25.19/8.28	   (A^2 -> H(f(d), U1(d, d)),A^2 -> H(f(d), U1(d, d)))
25.19/8.28	
25.19/8.28	
25.19/8.28	----------------------------------------
25.19/8.28	
25.19/8.28	(176)
25.19/8.28	Obligation:
25.19/8.28	Q DP problem:
25.19/8.28	The TRS P consists of the following rules:
25.19/8.28	
25.19/8.28	   H(x, x) -> G(x, x, f(k))
25.19/8.28	   G(d, x, x) -> A^2
25.19/8.28	   A^2 -> H(f(c), f(c))
25.19/8.28	   A^2 -> H(f(d), f(d))
25.19/8.28	   A^2 -> H(f(d), U1(b, c))
25.19/8.28	   A^2 -> H(f(d), U1(b, d))
25.19/8.28	   A^2 -> H(f(d), U1(c, c))
25.19/8.28	   A^2 -> H(f(d), f(e))
25.19/8.28	   A^2 -> H(f(d), f(k))
25.19/8.28	   A^2 -> H(f(a), U1(e, b))
25.19/8.28	   A^2 -> H(f(a), U1(k, b))
25.19/8.28	   A^2 -> H(f(a), U1(c, d))
25.19/8.28	   A^2 -> H(f(a), U1(d, c))
25.19/8.28	   A^2 -> H(f(a), U1(b, e))
25.19/8.28	   A^2 -> H(f(a), U1(b, k))
25.19/8.28	   A^2 -> H(f(c), U1(c, c))
25.19/8.28	   A^2 -> H(f(a), U1(e, c))
25.19/8.28	   A^2 -> H(f(a), U1(k, c))
25.19/8.28	   A^2 -> H(f(a), U1(c, e))
25.19/8.28	   A^2 -> H(f(a), U1(c, k))
25.19/8.28	   A^2 -> H(f(c), f(e))
25.19/8.28	   A^2 -> H(f(a), U1(e, e))
25.19/8.28	   A^2 -> H(f(a), U1(k, k))
25.19/8.28	   A^2 -> H(f(d), U1(d, d))
25.19/8.28	   A^2 -> H(f(a), U1(k, d))
25.19/8.28	   A^2 -> H(f(a), U1(d, k))
25.19/8.28	   A^2 -> H(a, f(b))
25.19/8.28	   A^2 -> H(U1(e, d), f(b))
25.19/8.28	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, a), f(c))
25.19/8.28	   A^2 -> H(U1(e, a), f(d))
25.19/8.28	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, a), f(c))
25.19/8.28	   A^2 -> H(U1(k, a), f(d))
25.19/8.28	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, d), f(c))
25.19/8.28	   A^2 -> H(U1(c, d), f(d))
25.19/8.28	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.28	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.28	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.28	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.28	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.28	   A^2 -> H(U1(c, a), f(e))
25.19/8.28	   A^2 -> H(U1(c, a), f(k))
25.19/8.28	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.28	   A^2 -> H(U1(d, e), f(b))
25.19/8.28	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(d, c), f(c))
25.19/8.28	   A^2 -> H(U1(d, c), f(d))
25.19/8.28	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.28	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.28	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.28	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.28	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.28	   A^2 -> H(U1(d, a), f(e))
25.19/8.28	   A^2 -> H(U1(d, a), f(k))
25.19/8.28	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(a, e), f(c))
25.19/8.28	   A^2 -> H(U1(a, e), f(d))
25.19/8.28	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(a, k), f(c))
25.19/8.28	   A^2 -> H(U1(a, k), f(d))
25.19/8.28	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.28	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.28	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.28	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.28	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.28	   A^2 -> H(U1(a, c), f(e))
25.19/8.28	   A^2 -> H(U1(a, c), f(k))
25.19/8.28	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.28	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.28	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.28	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.28	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.28	   A^2 -> H(U1(a, d), f(e))
25.19/8.28	   A^2 -> H(U1(a, d), f(k))
25.19/8.28	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.28	   A^2 -> H(c, f(b))
25.19/8.28	   A^2 -> H(U1(e, k), f(b))
25.19/8.28	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, c), f(c))
25.19/8.28	   A^2 -> H(U1(e, c), f(d))
25.19/8.28	   A^2 -> H(U1(k, e), f(b))
25.19/8.28	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, c), f(c))
25.19/8.28	   A^2 -> H(U1(k, c), f(d))
25.19/8.28	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, e), f(c))
25.19/8.28	   A^2 -> H(U1(c, e), f(d))
25.19/8.28	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, k), f(c))
25.19/8.28	   A^2 -> H(U1(c, k), f(d))
25.19/8.28	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.28	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.28	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.28	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.28	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.28	   A^2 -> H(U1(c, c), f(e))
25.19/8.28	   A^2 -> H(U1(c, c), f(k))
25.19/8.28	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.28	   A^2 -> H(e, f(b))
25.19/8.28	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, e), f(c))
25.19/8.28	   A^2 -> H(U1(e, e), f(d))
25.19/8.28	   A^2 -> H(f(e), U1(c, b))
25.19/8.28	   A^2 -> H(f(e), U1(d, b))
25.19/8.28	   A^2 -> H(f(e), U1(b, c))
25.19/8.28	   A^2 -> H(f(e), U1(b, d))
25.19/8.28	   A^2 -> H(f(e), U1(c, c))
25.19/8.28	   A^2 -> H(f(e), f(e))
25.19/8.28	   A^2 -> H(f(e), f(k))
25.19/8.28	   A^2 -> H(f(e), U1(d, d))
25.19/8.28	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, k), f(c))
25.19/8.28	   A^2 -> H(U1(k, k), f(d))
25.19/8.28	   A^2 -> H(f(k), U1(c, b))
25.19/8.28	   A^2 -> H(f(k), U1(d, b))
25.19/8.28	   A^2 -> H(f(k), U1(b, c))
25.19/8.28	   A^2 -> H(f(k), U1(b, d))
25.19/8.28	   A^2 -> H(f(k), U1(c, c))
25.19/8.28	   A^2 -> H(f(k), f(e))
25.19/8.28	   A^2 -> H(f(k), f(k))
25.19/8.28	   A^2 -> H(f(k), U1(d, d))
25.19/8.28	   A^2 -> H(f(c), U1(e, b))
25.19/8.28	   A^2 -> H(f(c), U1(k, b))
25.19/8.28	   A^2 -> H(f(c), U1(c, d))
25.19/8.28	   A^2 -> H(f(c), U1(d, c))
25.19/8.28	   A^2 -> H(f(c), U1(b, e))
25.19/8.28	   A^2 -> H(f(c), U1(b, k))
25.19/8.28	   A^2 -> H(f(c), U1(k, d))
25.19/8.28	   A^2 -> H(f(c), U1(d, k))
25.19/8.28	   A^2 -> H(f(c), U1(k, k))
25.19/8.28	   A^2 -> H(U1(k, k), f(b))
25.19/8.28	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, d), f(c))
25.19/8.28	   A^2 -> H(U1(k, d), f(d))
25.19/8.28	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(d, k), f(c))
25.19/8.28	   A^2 -> H(U1(d, k), f(d))
25.19/8.28	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.28	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.28	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.28	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.28	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.28	   A^2 -> H(U1(d, d), f(e))
25.19/8.28	   A^2 -> H(U1(d, d), f(k))
25.19/8.28	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.28	   A^2 -> H(f(d), U1(e, b))
25.19/8.28	   A^2 -> H(f(d), U1(k, b))
25.19/8.28	   A^2 -> H(f(d), U1(c, d))
25.19/8.28	   A^2 -> H(f(d), U1(d, c))
25.19/8.28	
25.19/8.28	The TRS R consists of the following rules:
25.19/8.28	
25.19/8.28	   f(x) -> U1(x, x)
25.19/8.28	   U1(e, x) -> x
25.19/8.28	   a -> c
25.19/8.28	   a -> d
25.19/8.28	   b -> c
25.19/8.28	   b -> d
25.19/8.28	   d -> k
25.19/8.28	   c -> e
25.19/8.28	   c -> k
25.19/8.28	
25.19/8.28	Q is empty.
25.19/8.28	We have to consider all minimal (P,Q,R)-chains.
25.19/8.28	----------------------------------------
25.19/8.28	
25.19/8.28	(177) TransformationProof (EQUIVALENT)
25.19/8.28	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.28	
25.19/8.28	   (A^2 -> H(U1(d, d), U1(b, c)),A^2 -> H(U1(d, d), U1(b, c)))
25.19/8.28	   (A^2 -> H(f(k), U1(b, c)),A^2 -> H(f(k), U1(b, c)))
25.19/8.28	   (A^2 -> H(f(d), U1(c, c)),A^2 -> H(f(d), U1(c, c)))
25.19/8.28	   (A^2 -> H(f(d), U1(d, c)),A^2 -> H(f(d), U1(d, c)))
25.19/8.28	   (A^2 -> H(f(d), U1(b, e)),A^2 -> H(f(d), U1(b, e)))
25.19/8.28	   (A^2 -> H(f(d), U1(b, k)),A^2 -> H(f(d), U1(b, k)))
25.19/8.28	
25.19/8.28	
25.19/8.28	----------------------------------------
25.19/8.28	
25.19/8.28	(178)
25.19/8.28	Obligation:
25.19/8.28	Q DP problem:
25.19/8.28	The TRS P consists of the following rules:
25.19/8.28	
25.19/8.28	   H(x, x) -> G(x, x, f(k))
25.19/8.28	   G(d, x, x) -> A^2
25.19/8.28	   A^2 -> H(f(c), f(c))
25.19/8.28	   A^2 -> H(f(d), f(d))
25.19/8.28	   A^2 -> H(f(d), U1(b, d))
25.19/8.28	   A^2 -> H(f(d), U1(c, c))
25.19/8.28	   A^2 -> H(f(d), f(e))
25.19/8.28	   A^2 -> H(f(d), f(k))
25.19/8.28	   A^2 -> H(f(a), U1(e, b))
25.19/8.28	   A^2 -> H(f(a), U1(k, b))
25.19/8.28	   A^2 -> H(f(a), U1(c, d))
25.19/8.28	   A^2 -> H(f(a), U1(d, c))
25.19/8.28	   A^2 -> H(f(a), U1(b, e))
25.19/8.28	   A^2 -> H(f(a), U1(b, k))
25.19/8.28	   A^2 -> H(f(c), U1(c, c))
25.19/8.28	   A^2 -> H(f(a), U1(e, c))
25.19/8.28	   A^2 -> H(f(a), U1(k, c))
25.19/8.28	   A^2 -> H(f(a), U1(c, e))
25.19/8.28	   A^2 -> H(f(a), U1(c, k))
25.19/8.28	   A^2 -> H(f(c), f(e))
25.19/8.28	   A^2 -> H(f(a), U1(e, e))
25.19/8.28	   A^2 -> H(f(a), U1(k, k))
25.19/8.28	   A^2 -> H(f(d), U1(d, d))
25.19/8.28	   A^2 -> H(f(a), U1(k, d))
25.19/8.28	   A^2 -> H(f(a), U1(d, k))
25.19/8.28	   A^2 -> H(a, f(b))
25.19/8.28	   A^2 -> H(U1(e, d), f(b))
25.19/8.28	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, a), f(c))
25.19/8.28	   A^2 -> H(U1(e, a), f(d))
25.19/8.28	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, a), f(c))
25.19/8.28	   A^2 -> H(U1(k, a), f(d))
25.19/8.28	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, d), f(c))
25.19/8.28	   A^2 -> H(U1(c, d), f(d))
25.19/8.28	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.28	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.28	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.28	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.28	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.28	   A^2 -> H(U1(c, a), f(e))
25.19/8.28	   A^2 -> H(U1(c, a), f(k))
25.19/8.28	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.28	   A^2 -> H(U1(d, e), f(b))
25.19/8.28	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(d, c), f(c))
25.19/8.28	   A^2 -> H(U1(d, c), f(d))
25.19/8.28	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.28	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.28	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.28	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.28	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.28	   A^2 -> H(U1(d, a), f(e))
25.19/8.28	   A^2 -> H(U1(d, a), f(k))
25.19/8.28	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(a, e), f(c))
25.19/8.28	   A^2 -> H(U1(a, e), f(d))
25.19/8.28	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(a, k), f(c))
25.19/8.28	   A^2 -> H(U1(a, k), f(d))
25.19/8.28	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.28	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.28	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.28	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.28	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.28	   A^2 -> H(U1(a, c), f(e))
25.19/8.28	   A^2 -> H(U1(a, c), f(k))
25.19/8.28	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.28	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.28	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.28	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.28	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.28	   A^2 -> H(U1(a, d), f(e))
25.19/8.28	   A^2 -> H(U1(a, d), f(k))
25.19/8.28	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.28	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.28	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.28	   A^2 -> H(c, f(b))
25.19/8.28	   A^2 -> H(U1(e, k), f(b))
25.19/8.28	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, c), f(c))
25.19/8.28	   A^2 -> H(U1(e, c), f(d))
25.19/8.28	   A^2 -> H(U1(k, e), f(b))
25.19/8.28	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, c), f(c))
25.19/8.28	   A^2 -> H(U1(k, c), f(d))
25.19/8.28	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, e), f(c))
25.19/8.28	   A^2 -> H(U1(c, e), f(d))
25.19/8.28	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(c, k), f(c))
25.19/8.28	   A^2 -> H(U1(c, k), f(d))
25.19/8.28	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.28	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.28	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.28	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.28	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.28	   A^2 -> H(U1(c, c), f(e))
25.19/8.28	   A^2 -> H(U1(c, c), f(k))
25.19/8.28	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.28	   A^2 -> H(e, f(b))
25.19/8.28	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.28	   A^2 -> H(U1(e, e), f(c))
25.19/8.28	   A^2 -> H(U1(e, e), f(d))
25.19/8.28	   A^2 -> H(f(e), U1(c, b))
25.19/8.28	   A^2 -> H(f(e), U1(d, b))
25.19/8.28	   A^2 -> H(f(e), U1(b, c))
25.19/8.28	   A^2 -> H(f(e), U1(b, d))
25.19/8.28	   A^2 -> H(f(e), U1(c, c))
25.19/8.28	   A^2 -> H(f(e), f(e))
25.19/8.28	   A^2 -> H(f(e), f(k))
25.19/8.28	   A^2 -> H(f(e), U1(d, d))
25.19/8.28	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, k), f(c))
25.19/8.28	   A^2 -> H(U1(k, k), f(d))
25.19/8.28	   A^2 -> H(f(k), U1(c, b))
25.19/8.28	   A^2 -> H(f(k), U1(d, b))
25.19/8.28	   A^2 -> H(f(k), U1(b, c))
25.19/8.28	   A^2 -> H(f(k), U1(b, d))
25.19/8.28	   A^2 -> H(f(k), U1(c, c))
25.19/8.28	   A^2 -> H(f(k), f(e))
25.19/8.28	   A^2 -> H(f(k), f(k))
25.19/8.28	   A^2 -> H(f(k), U1(d, d))
25.19/8.28	   A^2 -> H(f(c), U1(e, b))
25.19/8.28	   A^2 -> H(f(c), U1(k, b))
25.19/8.28	   A^2 -> H(f(c), U1(c, d))
25.19/8.28	   A^2 -> H(f(c), U1(d, c))
25.19/8.28	   A^2 -> H(f(c), U1(b, e))
25.19/8.28	   A^2 -> H(f(c), U1(b, k))
25.19/8.28	   A^2 -> H(f(c), U1(k, d))
25.19/8.28	   A^2 -> H(f(c), U1(d, k))
25.19/8.28	   A^2 -> H(f(c), U1(k, k))
25.19/8.28	   A^2 -> H(U1(k, k), f(b))
25.19/8.28	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.28	   A^2 -> H(U1(k, d), f(c))
25.19/8.28	   A^2 -> H(U1(k, d), f(d))
25.19/8.28	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.28	   A^2 -> H(U1(d, k), f(c))
25.19/8.28	   A^2 -> H(U1(d, k), f(d))
25.19/8.28	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.28	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.28	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.28	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.28	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.28	   A^2 -> H(U1(d, d), f(e))
25.19/8.28	   A^2 -> H(U1(d, d), f(k))
25.19/8.28	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.28	   A^2 -> H(f(d), U1(e, b))
25.19/8.28	   A^2 -> H(f(d), U1(k, b))
25.19/8.28	   A^2 -> H(f(d), U1(c, d))
25.19/8.28	   A^2 -> H(f(d), U1(d, c))
25.19/8.28	   A^2 -> H(f(d), U1(b, e))
25.19/8.28	   A^2 -> H(f(d), U1(b, k))
25.19/8.28	
25.19/8.28	The TRS R consists of the following rules:
25.19/8.28	
25.19/8.28	   f(x) -> U1(x, x)
25.19/8.28	   U1(e, x) -> x
25.19/8.28	   a -> c
25.19/8.28	   a -> d
25.19/8.28	   b -> c
25.19/8.28	   b -> d
25.19/8.28	   d -> k
25.19/8.28	   c -> e
25.19/8.28	   c -> k
25.19/8.28	
25.19/8.28	Q is empty.
25.19/8.28	We have to consider all minimal (P,Q,R)-chains.
25.19/8.28	----------------------------------------
25.19/8.28	
25.19/8.28	(179) TransformationProof (EQUIVALENT)
25.19/8.28	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.29	
25.19/8.29	   (A^2 -> H(U1(d, d), U1(b, d)),A^2 -> H(U1(d, d), U1(b, d)))
25.19/8.29	   (A^2 -> H(f(k), U1(b, d)),A^2 -> H(f(k), U1(b, d)))
25.19/8.29	   (A^2 -> H(f(d), U1(c, d)),A^2 -> H(f(d), U1(c, d)))
25.19/8.29	   (A^2 -> H(f(d), U1(d, d)),A^2 -> H(f(d), U1(d, d)))
25.19/8.29	   (A^2 -> H(f(d), U1(b, k)),A^2 -> H(f(d), U1(b, k)))
25.19/8.29	
25.19/8.29	
25.19/8.29	----------------------------------------
25.19/8.29	
25.19/8.29	(180)
25.19/8.29	Obligation:
25.19/8.29	Q DP problem:
25.19/8.29	The TRS P consists of the following rules:
25.19/8.29	
25.19/8.29	   H(x, x) -> G(x, x, f(k))
25.19/8.29	   G(d, x, x) -> A^2
25.19/8.29	   A^2 -> H(f(c), f(c))
25.19/8.29	   A^2 -> H(f(d), f(d))
25.19/8.29	   A^2 -> H(f(d), U1(c, c))
25.19/8.29	   A^2 -> H(f(d), f(e))
25.19/8.29	   A^2 -> H(f(d), f(k))
25.19/8.29	   A^2 -> H(f(a), U1(e, b))
25.19/8.29	   A^2 -> H(f(a), U1(k, b))
25.19/8.29	   A^2 -> H(f(a), U1(c, d))
25.19/8.29	   A^2 -> H(f(a), U1(d, c))
25.19/8.29	   A^2 -> H(f(a), U1(b, e))
25.19/8.29	   A^2 -> H(f(a), U1(b, k))
25.19/8.29	   A^2 -> H(f(c), U1(c, c))
25.19/8.29	   A^2 -> H(f(a), U1(e, c))
25.19/8.29	   A^2 -> H(f(a), U1(k, c))
25.19/8.29	   A^2 -> H(f(a), U1(c, e))
25.19/8.29	   A^2 -> H(f(a), U1(c, k))
25.19/8.29	   A^2 -> H(f(c), f(e))
25.19/8.29	   A^2 -> H(f(a), U1(e, e))
25.19/8.29	   A^2 -> H(f(a), U1(k, k))
25.19/8.29	   A^2 -> H(f(d), U1(d, d))
25.19/8.29	   A^2 -> H(f(a), U1(k, d))
25.19/8.29	   A^2 -> H(f(a), U1(d, k))
25.19/8.29	   A^2 -> H(a, f(b))
25.19/8.29	   A^2 -> H(U1(e, d), f(b))
25.19/8.29	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, a), f(c))
25.19/8.29	   A^2 -> H(U1(e, a), f(d))
25.19/8.29	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, a), f(c))
25.19/8.29	   A^2 -> H(U1(k, a), f(d))
25.19/8.29	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, d), f(c))
25.19/8.29	   A^2 -> H(U1(c, d), f(d))
25.19/8.29	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.29	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.29	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.29	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.29	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.29	   A^2 -> H(U1(c, a), f(e))
25.19/8.29	   A^2 -> H(U1(c, a), f(k))
25.19/8.29	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.29	   A^2 -> H(U1(d, e), f(b))
25.19/8.29	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(d, c), f(c))
25.19/8.29	   A^2 -> H(U1(d, c), f(d))
25.19/8.29	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.29	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.29	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.29	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.29	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.29	   A^2 -> H(U1(d, a), f(e))
25.19/8.29	   A^2 -> H(U1(d, a), f(k))
25.19/8.29	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(a, e), f(c))
25.19/8.29	   A^2 -> H(U1(a, e), f(d))
25.19/8.29	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(a, k), f(c))
25.19/8.29	   A^2 -> H(U1(a, k), f(d))
25.19/8.29	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.29	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.29	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.29	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.29	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.29	   A^2 -> H(U1(a, c), f(e))
25.19/8.29	   A^2 -> H(U1(a, c), f(k))
25.19/8.29	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.29	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.29	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.29	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.29	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.29	   A^2 -> H(U1(a, d), f(e))
25.19/8.29	   A^2 -> H(U1(a, d), f(k))
25.19/8.29	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.29	   A^2 -> H(c, f(b))
25.19/8.29	   A^2 -> H(U1(e, k), f(b))
25.19/8.29	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, c), f(c))
25.19/8.29	   A^2 -> H(U1(e, c), f(d))
25.19/8.29	   A^2 -> H(U1(k, e), f(b))
25.19/8.29	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, c), f(c))
25.19/8.29	   A^2 -> H(U1(k, c), f(d))
25.19/8.29	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, e), f(c))
25.19/8.29	   A^2 -> H(U1(c, e), f(d))
25.19/8.29	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, k), f(c))
25.19/8.29	   A^2 -> H(U1(c, k), f(d))
25.19/8.29	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.29	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.29	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.29	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.29	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.29	   A^2 -> H(U1(c, c), f(e))
25.19/8.29	   A^2 -> H(U1(c, c), f(k))
25.19/8.29	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.29	   A^2 -> H(e, f(b))
25.19/8.29	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, e), f(c))
25.19/8.29	   A^2 -> H(U1(e, e), f(d))
25.19/8.29	   A^2 -> H(f(e), U1(c, b))
25.19/8.29	   A^2 -> H(f(e), U1(d, b))
25.19/8.29	   A^2 -> H(f(e), U1(b, c))
25.19/8.29	   A^2 -> H(f(e), U1(b, d))
25.19/8.29	   A^2 -> H(f(e), U1(c, c))
25.19/8.29	   A^2 -> H(f(e), f(e))
25.19/8.29	   A^2 -> H(f(e), f(k))
25.19/8.29	   A^2 -> H(f(e), U1(d, d))
25.19/8.29	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, k), f(c))
25.19/8.29	   A^2 -> H(U1(k, k), f(d))
25.19/8.29	   A^2 -> H(f(k), U1(c, b))
25.19/8.29	   A^2 -> H(f(k), U1(d, b))
25.19/8.29	   A^2 -> H(f(k), U1(b, c))
25.19/8.29	   A^2 -> H(f(k), U1(b, d))
25.19/8.29	   A^2 -> H(f(k), U1(c, c))
25.19/8.29	   A^2 -> H(f(k), f(e))
25.19/8.29	   A^2 -> H(f(k), f(k))
25.19/8.29	   A^2 -> H(f(k), U1(d, d))
25.19/8.29	   A^2 -> H(f(c), U1(e, b))
25.19/8.29	   A^2 -> H(f(c), U1(k, b))
25.19/8.29	   A^2 -> H(f(c), U1(c, d))
25.19/8.29	   A^2 -> H(f(c), U1(d, c))
25.19/8.29	   A^2 -> H(f(c), U1(b, e))
25.19/8.29	   A^2 -> H(f(c), U1(b, k))
25.19/8.29	   A^2 -> H(f(c), U1(k, d))
25.19/8.29	   A^2 -> H(f(c), U1(d, k))
25.19/8.29	   A^2 -> H(f(c), U1(k, k))
25.19/8.29	   A^2 -> H(U1(k, k), f(b))
25.19/8.29	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, d), f(c))
25.19/8.29	   A^2 -> H(U1(k, d), f(d))
25.19/8.29	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(d, k), f(c))
25.19/8.29	   A^2 -> H(U1(d, k), f(d))
25.19/8.29	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.29	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.29	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.29	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.29	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.29	   A^2 -> H(U1(d, d), f(e))
25.19/8.29	   A^2 -> H(U1(d, d), f(k))
25.19/8.29	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.29	   A^2 -> H(f(d), U1(e, b))
25.19/8.29	   A^2 -> H(f(d), U1(k, b))
25.19/8.29	   A^2 -> H(f(d), U1(c, d))
25.19/8.29	   A^2 -> H(f(d), U1(d, c))
25.19/8.29	   A^2 -> H(f(d), U1(b, e))
25.19/8.29	   A^2 -> H(f(d), U1(b, k))
25.19/8.29	
25.19/8.29	The TRS R consists of the following rules:
25.19/8.29	
25.19/8.29	   f(x) -> U1(x, x)
25.19/8.29	   U1(e, x) -> x
25.19/8.29	   a -> c
25.19/8.29	   a -> d
25.19/8.29	   b -> c
25.19/8.29	   b -> d
25.19/8.29	   d -> k
25.19/8.29	   c -> e
25.19/8.29	   c -> k
25.19/8.29	
25.19/8.29	Q is empty.
25.19/8.29	We have to consider all minimal (P,Q,R)-chains.
25.19/8.29	----------------------------------------
25.19/8.29	
25.19/8.29	(181) TransformationProof (EQUIVALENT)
25.19/8.29	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.29	
25.19/8.29	   (A^2 -> H(U1(d, d), U1(c, c)),A^2 -> H(U1(d, d), U1(c, c)))
25.19/8.29	   (A^2 -> H(f(k), U1(c, c)),A^2 -> H(f(k), U1(c, c)))
25.19/8.29	   (A^2 -> H(f(d), U1(e, c)),A^2 -> H(f(d), U1(e, c)))
25.19/8.29	   (A^2 -> H(f(d), U1(k, c)),A^2 -> H(f(d), U1(k, c)))
25.19/8.29	   (A^2 -> H(f(d), U1(c, e)),A^2 -> H(f(d), U1(c, e)))
25.19/8.29	   (A^2 -> H(f(d), U1(c, k)),A^2 -> H(f(d), U1(c, k)))
25.19/8.29	
25.19/8.29	
25.19/8.29	----------------------------------------
25.19/8.29	
25.19/8.29	(182)
25.19/8.29	Obligation:
25.19/8.29	Q DP problem:
25.19/8.29	The TRS P consists of the following rules:
25.19/8.29	
25.19/8.29	   H(x, x) -> G(x, x, f(k))
25.19/8.29	   G(d, x, x) -> A^2
25.19/8.29	   A^2 -> H(f(c), f(c))
25.19/8.29	   A^2 -> H(f(d), f(d))
25.19/8.29	   A^2 -> H(f(d), f(e))
25.19/8.29	   A^2 -> H(f(d), f(k))
25.19/8.29	   A^2 -> H(f(a), U1(e, b))
25.19/8.29	   A^2 -> H(f(a), U1(k, b))
25.19/8.29	   A^2 -> H(f(a), U1(c, d))
25.19/8.29	   A^2 -> H(f(a), U1(d, c))
25.19/8.29	   A^2 -> H(f(a), U1(b, e))
25.19/8.29	   A^2 -> H(f(a), U1(b, k))
25.19/8.29	   A^2 -> H(f(c), U1(c, c))
25.19/8.29	   A^2 -> H(f(a), U1(e, c))
25.19/8.29	   A^2 -> H(f(a), U1(k, c))
25.19/8.29	   A^2 -> H(f(a), U1(c, e))
25.19/8.29	   A^2 -> H(f(a), U1(c, k))
25.19/8.29	   A^2 -> H(f(c), f(e))
25.19/8.29	   A^2 -> H(f(a), U1(e, e))
25.19/8.29	   A^2 -> H(f(a), U1(k, k))
25.19/8.29	   A^2 -> H(f(d), U1(d, d))
25.19/8.29	   A^2 -> H(f(a), U1(k, d))
25.19/8.29	   A^2 -> H(f(a), U1(d, k))
25.19/8.29	   A^2 -> H(a, f(b))
25.19/8.29	   A^2 -> H(U1(e, d), f(b))
25.19/8.29	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, a), f(c))
25.19/8.29	   A^2 -> H(U1(e, a), f(d))
25.19/8.29	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, a), f(c))
25.19/8.29	   A^2 -> H(U1(k, a), f(d))
25.19/8.29	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, d), f(c))
25.19/8.29	   A^2 -> H(U1(c, d), f(d))
25.19/8.29	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.29	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.29	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.29	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.29	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.29	   A^2 -> H(U1(c, a), f(e))
25.19/8.29	   A^2 -> H(U1(c, a), f(k))
25.19/8.29	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.29	   A^2 -> H(U1(d, e), f(b))
25.19/8.29	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(d, c), f(c))
25.19/8.29	   A^2 -> H(U1(d, c), f(d))
25.19/8.29	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.29	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.29	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.29	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.29	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.29	   A^2 -> H(U1(d, a), f(e))
25.19/8.29	   A^2 -> H(U1(d, a), f(k))
25.19/8.29	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(a, e), f(c))
25.19/8.29	   A^2 -> H(U1(a, e), f(d))
25.19/8.29	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(a, k), f(c))
25.19/8.29	   A^2 -> H(U1(a, k), f(d))
25.19/8.29	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.29	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.29	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.29	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.29	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.29	   A^2 -> H(U1(a, c), f(e))
25.19/8.29	   A^2 -> H(U1(a, c), f(k))
25.19/8.29	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.29	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.29	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.29	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.29	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.29	   A^2 -> H(U1(a, d), f(e))
25.19/8.29	   A^2 -> H(U1(a, d), f(k))
25.19/8.29	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.29	   A^2 -> H(c, f(b))
25.19/8.29	   A^2 -> H(U1(e, k), f(b))
25.19/8.29	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, c), f(c))
25.19/8.29	   A^2 -> H(U1(e, c), f(d))
25.19/8.29	   A^2 -> H(U1(k, e), f(b))
25.19/8.29	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, c), f(c))
25.19/8.29	   A^2 -> H(U1(k, c), f(d))
25.19/8.29	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, e), f(c))
25.19/8.29	   A^2 -> H(U1(c, e), f(d))
25.19/8.29	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, k), f(c))
25.19/8.29	   A^2 -> H(U1(c, k), f(d))
25.19/8.29	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.29	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.29	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.29	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.29	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.29	   A^2 -> H(U1(c, c), f(e))
25.19/8.29	   A^2 -> H(U1(c, c), f(k))
25.19/8.29	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.29	   A^2 -> H(e, f(b))
25.19/8.29	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, e), f(c))
25.19/8.29	   A^2 -> H(U1(e, e), f(d))
25.19/8.29	   A^2 -> H(f(e), U1(c, b))
25.19/8.29	   A^2 -> H(f(e), U1(d, b))
25.19/8.29	   A^2 -> H(f(e), U1(b, c))
25.19/8.29	   A^2 -> H(f(e), U1(b, d))
25.19/8.29	   A^2 -> H(f(e), U1(c, c))
25.19/8.29	   A^2 -> H(f(e), f(e))
25.19/8.29	   A^2 -> H(f(e), f(k))
25.19/8.29	   A^2 -> H(f(e), U1(d, d))
25.19/8.29	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, k), f(c))
25.19/8.29	   A^2 -> H(U1(k, k), f(d))
25.19/8.29	   A^2 -> H(f(k), U1(c, b))
25.19/8.29	   A^2 -> H(f(k), U1(d, b))
25.19/8.29	   A^2 -> H(f(k), U1(b, c))
25.19/8.29	   A^2 -> H(f(k), U1(b, d))
25.19/8.29	   A^2 -> H(f(k), U1(c, c))
25.19/8.29	   A^2 -> H(f(k), f(e))
25.19/8.29	   A^2 -> H(f(k), f(k))
25.19/8.29	   A^2 -> H(f(k), U1(d, d))
25.19/8.29	   A^2 -> H(f(c), U1(e, b))
25.19/8.29	   A^2 -> H(f(c), U1(k, b))
25.19/8.29	   A^2 -> H(f(c), U1(c, d))
25.19/8.29	   A^2 -> H(f(c), U1(d, c))
25.19/8.29	   A^2 -> H(f(c), U1(b, e))
25.19/8.29	   A^2 -> H(f(c), U1(b, k))
25.19/8.29	   A^2 -> H(f(c), U1(k, d))
25.19/8.29	   A^2 -> H(f(c), U1(d, k))
25.19/8.29	   A^2 -> H(f(c), U1(k, k))
25.19/8.29	   A^2 -> H(U1(k, k), f(b))
25.19/8.29	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, d), f(c))
25.19/8.29	   A^2 -> H(U1(k, d), f(d))
25.19/8.29	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(d, k), f(c))
25.19/8.29	   A^2 -> H(U1(d, k), f(d))
25.19/8.29	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.29	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.29	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.29	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.29	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.29	   A^2 -> H(U1(d, d), f(e))
25.19/8.29	   A^2 -> H(U1(d, d), f(k))
25.19/8.29	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.29	   A^2 -> H(f(d), U1(e, b))
25.19/8.29	   A^2 -> H(f(d), U1(k, b))
25.19/8.29	   A^2 -> H(f(d), U1(c, d))
25.19/8.29	   A^2 -> H(f(d), U1(d, c))
25.19/8.29	   A^2 -> H(f(d), U1(b, e))
25.19/8.29	   A^2 -> H(f(d), U1(b, k))
25.19/8.29	   A^2 -> H(f(d), U1(e, c))
25.19/8.29	   A^2 -> H(f(d), U1(k, c))
25.19/8.29	   A^2 -> H(f(d), U1(c, e))
25.19/8.29	   A^2 -> H(f(d), U1(c, k))
25.19/8.29	
25.19/8.29	The TRS R consists of the following rules:
25.19/8.29	
25.19/8.29	   f(x) -> U1(x, x)
25.19/8.29	   U1(e, x) -> x
25.19/8.29	   a -> c
25.19/8.29	   a -> d
25.19/8.29	   b -> c
25.19/8.29	   b -> d
25.19/8.29	   d -> k
25.19/8.29	   c -> e
25.19/8.29	   c -> k
25.19/8.29	
25.19/8.29	Q is empty.
25.19/8.29	We have to consider all minimal (P,Q,R)-chains.
25.19/8.29	----------------------------------------
25.19/8.29	
25.19/8.29	(183) TransformationProof (EQUIVALENT)
25.19/8.29	By narrowing [LPAR04] the rule A^2 -> H(f(d), f(e)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.29	
25.19/8.29	   (A^2 -> H(U1(d, d), f(e)),A^2 -> H(U1(d, d), f(e)))
25.19/8.29	   (A^2 -> H(f(k), f(e)),A^2 -> H(f(k), f(e)))
25.19/8.29	   (A^2 -> H(f(d), U1(e, e)),A^2 -> H(f(d), U1(e, e)))
25.19/8.29	
25.19/8.29	
25.19/8.29	----------------------------------------
25.19/8.29	
25.19/8.29	(184)
25.19/8.29	Obligation:
25.19/8.29	Q DP problem:
25.19/8.29	The TRS P consists of the following rules:
25.19/8.29	
25.19/8.29	   H(x, x) -> G(x, x, f(k))
25.19/8.29	   G(d, x, x) -> A^2
25.19/8.29	   A^2 -> H(f(c), f(c))
25.19/8.29	   A^2 -> H(f(d), f(d))
25.19/8.29	   A^2 -> H(f(d), f(k))
25.19/8.29	   A^2 -> H(f(a), U1(e, b))
25.19/8.29	   A^2 -> H(f(a), U1(k, b))
25.19/8.29	   A^2 -> H(f(a), U1(c, d))
25.19/8.29	   A^2 -> H(f(a), U1(d, c))
25.19/8.29	   A^2 -> H(f(a), U1(b, e))
25.19/8.29	   A^2 -> H(f(a), U1(b, k))
25.19/8.29	   A^2 -> H(f(c), U1(c, c))
25.19/8.29	   A^2 -> H(f(a), U1(e, c))
25.19/8.29	   A^2 -> H(f(a), U1(k, c))
25.19/8.29	   A^2 -> H(f(a), U1(c, e))
25.19/8.29	   A^2 -> H(f(a), U1(c, k))
25.19/8.29	   A^2 -> H(f(c), f(e))
25.19/8.29	   A^2 -> H(f(a), U1(e, e))
25.19/8.29	   A^2 -> H(f(a), U1(k, k))
25.19/8.29	   A^2 -> H(f(d), U1(d, d))
25.19/8.29	   A^2 -> H(f(a), U1(k, d))
25.19/8.29	   A^2 -> H(f(a), U1(d, k))
25.19/8.29	   A^2 -> H(a, f(b))
25.19/8.29	   A^2 -> H(U1(e, d), f(b))
25.19/8.29	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, a), f(c))
25.19/8.29	   A^2 -> H(U1(e, a), f(d))
25.19/8.29	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, a), f(c))
25.19/8.29	   A^2 -> H(U1(k, a), f(d))
25.19/8.29	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, d), f(c))
25.19/8.29	   A^2 -> H(U1(c, d), f(d))
25.19/8.29	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.29	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.29	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.29	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.29	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.29	   A^2 -> H(U1(c, a), f(e))
25.19/8.29	   A^2 -> H(U1(c, a), f(k))
25.19/8.29	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.29	   A^2 -> H(U1(d, e), f(b))
25.19/8.29	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(d, c), f(c))
25.19/8.29	   A^2 -> H(U1(d, c), f(d))
25.19/8.29	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.29	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.29	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.29	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.29	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.29	   A^2 -> H(U1(d, a), f(e))
25.19/8.29	   A^2 -> H(U1(d, a), f(k))
25.19/8.29	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(a, e), f(c))
25.19/8.29	   A^2 -> H(U1(a, e), f(d))
25.19/8.29	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(a, k), f(c))
25.19/8.29	   A^2 -> H(U1(a, k), f(d))
25.19/8.29	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.29	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.29	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.29	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.29	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.29	   A^2 -> H(U1(a, c), f(e))
25.19/8.29	   A^2 -> H(U1(a, c), f(k))
25.19/8.29	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.29	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.29	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.29	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.29	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.29	   A^2 -> H(U1(a, d), f(e))
25.19/8.29	   A^2 -> H(U1(a, d), f(k))
25.19/8.29	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.29	   A^2 -> H(c, f(b))
25.19/8.29	   A^2 -> H(U1(e, k), f(b))
25.19/8.29	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, c), f(c))
25.19/8.29	   A^2 -> H(U1(e, c), f(d))
25.19/8.29	   A^2 -> H(U1(k, e), f(b))
25.19/8.29	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, c), f(c))
25.19/8.29	   A^2 -> H(U1(k, c), f(d))
25.19/8.29	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, e), f(c))
25.19/8.29	   A^2 -> H(U1(c, e), f(d))
25.19/8.29	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, k), f(c))
25.19/8.29	   A^2 -> H(U1(c, k), f(d))
25.19/8.29	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.29	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.29	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.29	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.29	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.29	   A^2 -> H(U1(c, c), f(e))
25.19/8.29	   A^2 -> H(U1(c, c), f(k))
25.19/8.29	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.29	   A^2 -> H(e, f(b))
25.19/8.29	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, e), f(c))
25.19/8.29	   A^2 -> H(U1(e, e), f(d))
25.19/8.29	   A^2 -> H(f(e), U1(c, b))
25.19/8.29	   A^2 -> H(f(e), U1(d, b))
25.19/8.29	   A^2 -> H(f(e), U1(b, c))
25.19/8.29	   A^2 -> H(f(e), U1(b, d))
25.19/8.29	   A^2 -> H(f(e), U1(c, c))
25.19/8.29	   A^2 -> H(f(e), f(e))
25.19/8.29	   A^2 -> H(f(e), f(k))
25.19/8.29	   A^2 -> H(f(e), U1(d, d))
25.19/8.29	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, k), f(c))
25.19/8.29	   A^2 -> H(U1(k, k), f(d))
25.19/8.29	   A^2 -> H(f(k), U1(c, b))
25.19/8.29	   A^2 -> H(f(k), U1(d, b))
25.19/8.29	   A^2 -> H(f(k), U1(b, c))
25.19/8.29	   A^2 -> H(f(k), U1(b, d))
25.19/8.29	   A^2 -> H(f(k), U1(c, c))
25.19/8.29	   A^2 -> H(f(k), f(e))
25.19/8.29	   A^2 -> H(f(k), f(k))
25.19/8.29	   A^2 -> H(f(k), U1(d, d))
25.19/8.29	   A^2 -> H(f(c), U1(e, b))
25.19/8.29	   A^2 -> H(f(c), U1(k, b))
25.19/8.29	   A^2 -> H(f(c), U1(c, d))
25.19/8.29	   A^2 -> H(f(c), U1(d, c))
25.19/8.29	   A^2 -> H(f(c), U1(b, e))
25.19/8.29	   A^2 -> H(f(c), U1(b, k))
25.19/8.29	   A^2 -> H(f(c), U1(k, d))
25.19/8.29	   A^2 -> H(f(c), U1(d, k))
25.19/8.29	   A^2 -> H(f(c), U1(k, k))
25.19/8.29	   A^2 -> H(U1(k, k), f(b))
25.19/8.29	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, d), f(c))
25.19/8.29	   A^2 -> H(U1(k, d), f(d))
25.19/8.29	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(d, k), f(c))
25.19/8.29	   A^2 -> H(U1(d, k), f(d))
25.19/8.29	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.29	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.29	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.29	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.29	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.29	   A^2 -> H(U1(d, d), f(e))
25.19/8.29	   A^2 -> H(U1(d, d), f(k))
25.19/8.29	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.29	   A^2 -> H(f(d), U1(e, b))
25.19/8.29	   A^2 -> H(f(d), U1(k, b))
25.19/8.29	   A^2 -> H(f(d), U1(c, d))
25.19/8.29	   A^2 -> H(f(d), U1(d, c))
25.19/8.29	   A^2 -> H(f(d), U1(b, e))
25.19/8.29	   A^2 -> H(f(d), U1(b, k))
25.19/8.29	   A^2 -> H(f(d), U1(e, c))
25.19/8.29	   A^2 -> H(f(d), U1(k, c))
25.19/8.29	   A^2 -> H(f(d), U1(c, e))
25.19/8.29	   A^2 -> H(f(d), U1(c, k))
25.19/8.29	   A^2 -> H(f(d), U1(e, e))
25.19/8.29	
25.19/8.29	The TRS R consists of the following rules:
25.19/8.29	
25.19/8.29	   f(x) -> U1(x, x)
25.19/8.29	   U1(e, x) -> x
25.19/8.29	   a -> c
25.19/8.29	   a -> d
25.19/8.29	   b -> c
25.19/8.29	   b -> d
25.19/8.29	   d -> k
25.19/8.29	   c -> e
25.19/8.29	   c -> k
25.19/8.29	
25.19/8.29	Q is empty.
25.19/8.29	We have to consider all minimal (P,Q,R)-chains.
25.19/8.29	----------------------------------------
25.19/8.29	
25.19/8.29	(185) TransformationProof (EQUIVALENT)
25.19/8.29	By narrowing [LPAR04] the rule A^2 -> H(f(d), f(k)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.29	
25.19/8.29	   (A^2 -> H(U1(d, d), f(k)),A^2 -> H(U1(d, d), f(k)))
25.19/8.29	   (A^2 -> H(f(k), f(k)),A^2 -> H(f(k), f(k)))
25.19/8.29	   (A^2 -> H(f(d), U1(k, k)),A^2 -> H(f(d), U1(k, k)))
25.19/8.29	
25.19/8.29	
25.19/8.29	----------------------------------------
25.19/8.29	
25.19/8.29	(186)
25.19/8.29	Obligation:
25.19/8.29	Q DP problem:
25.19/8.29	The TRS P consists of the following rules:
25.19/8.29	
25.19/8.29	   H(x, x) -> G(x, x, f(k))
25.19/8.29	   G(d, x, x) -> A^2
25.19/8.29	   A^2 -> H(f(c), f(c))
25.19/8.29	   A^2 -> H(f(d), f(d))
25.19/8.29	   A^2 -> H(f(a), U1(e, b))
25.19/8.29	   A^2 -> H(f(a), U1(k, b))
25.19/8.29	   A^2 -> H(f(a), U1(c, d))
25.19/8.29	   A^2 -> H(f(a), U1(d, c))
25.19/8.29	   A^2 -> H(f(a), U1(b, e))
25.19/8.29	   A^2 -> H(f(a), U1(b, k))
25.19/8.29	   A^2 -> H(f(c), U1(c, c))
25.19/8.29	   A^2 -> H(f(a), U1(e, c))
25.19/8.29	   A^2 -> H(f(a), U1(k, c))
25.19/8.29	   A^2 -> H(f(a), U1(c, e))
25.19/8.29	   A^2 -> H(f(a), U1(c, k))
25.19/8.29	   A^2 -> H(f(c), f(e))
25.19/8.29	   A^2 -> H(f(a), U1(e, e))
25.19/8.29	   A^2 -> H(f(a), U1(k, k))
25.19/8.29	   A^2 -> H(f(d), U1(d, d))
25.19/8.29	   A^2 -> H(f(a), U1(k, d))
25.19/8.29	   A^2 -> H(f(a), U1(d, k))
25.19/8.29	   A^2 -> H(a, f(b))
25.19/8.29	   A^2 -> H(U1(e, d), f(b))
25.19/8.29	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, a), f(c))
25.19/8.29	   A^2 -> H(U1(e, a), f(d))
25.19/8.29	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, a), f(c))
25.19/8.29	   A^2 -> H(U1(k, a), f(d))
25.19/8.29	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, d), f(c))
25.19/8.29	   A^2 -> H(U1(c, d), f(d))
25.19/8.29	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.29	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.29	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.29	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.29	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.29	   A^2 -> H(U1(c, a), f(e))
25.19/8.29	   A^2 -> H(U1(c, a), f(k))
25.19/8.29	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.29	   A^2 -> H(U1(d, e), f(b))
25.19/8.29	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(d, c), f(c))
25.19/8.29	   A^2 -> H(U1(d, c), f(d))
25.19/8.29	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.29	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.29	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.29	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.29	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.29	   A^2 -> H(U1(d, a), f(e))
25.19/8.29	   A^2 -> H(U1(d, a), f(k))
25.19/8.29	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(a, e), f(c))
25.19/8.29	   A^2 -> H(U1(a, e), f(d))
25.19/8.29	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(a, k), f(c))
25.19/8.29	   A^2 -> H(U1(a, k), f(d))
25.19/8.29	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.29	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.29	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.29	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.29	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.29	   A^2 -> H(U1(a, c), f(e))
25.19/8.29	   A^2 -> H(U1(a, c), f(k))
25.19/8.29	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.29	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.29	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.29	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.29	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.29	   A^2 -> H(U1(a, d), f(e))
25.19/8.29	   A^2 -> H(U1(a, d), f(k))
25.19/8.29	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.29	   A^2 -> H(c, f(b))
25.19/8.29	   A^2 -> H(U1(e, k), f(b))
25.19/8.29	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, c), f(c))
25.19/8.29	   A^2 -> H(U1(e, c), f(d))
25.19/8.29	   A^2 -> H(U1(k, e), f(b))
25.19/8.29	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, c), f(c))
25.19/8.29	   A^2 -> H(U1(k, c), f(d))
25.19/8.29	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, e), f(c))
25.19/8.29	   A^2 -> H(U1(c, e), f(d))
25.19/8.29	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, k), f(c))
25.19/8.29	   A^2 -> H(U1(c, k), f(d))
25.19/8.29	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.29	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.29	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.29	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.29	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.29	   A^2 -> H(U1(c, c), f(e))
25.19/8.29	   A^2 -> H(U1(c, c), f(k))
25.19/8.29	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.29	   A^2 -> H(e, f(b))
25.19/8.29	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, e), f(c))
25.19/8.29	   A^2 -> H(U1(e, e), f(d))
25.19/8.29	   A^2 -> H(f(e), U1(c, b))
25.19/8.29	   A^2 -> H(f(e), U1(d, b))
25.19/8.29	   A^2 -> H(f(e), U1(b, c))
25.19/8.29	   A^2 -> H(f(e), U1(b, d))
25.19/8.29	   A^2 -> H(f(e), U1(c, c))
25.19/8.29	   A^2 -> H(f(e), f(e))
25.19/8.29	   A^2 -> H(f(e), f(k))
25.19/8.29	   A^2 -> H(f(e), U1(d, d))
25.19/8.29	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, k), f(c))
25.19/8.29	   A^2 -> H(U1(k, k), f(d))
25.19/8.29	   A^2 -> H(f(k), U1(c, b))
25.19/8.29	   A^2 -> H(f(k), U1(d, b))
25.19/8.29	   A^2 -> H(f(k), U1(b, c))
25.19/8.29	   A^2 -> H(f(k), U1(b, d))
25.19/8.29	   A^2 -> H(f(k), U1(c, c))
25.19/8.29	   A^2 -> H(f(k), f(e))
25.19/8.29	   A^2 -> H(f(k), f(k))
25.19/8.29	   A^2 -> H(f(k), U1(d, d))
25.19/8.29	   A^2 -> H(f(c), U1(e, b))
25.19/8.29	   A^2 -> H(f(c), U1(k, b))
25.19/8.29	   A^2 -> H(f(c), U1(c, d))
25.19/8.29	   A^2 -> H(f(c), U1(d, c))
25.19/8.29	   A^2 -> H(f(c), U1(b, e))
25.19/8.29	   A^2 -> H(f(c), U1(b, k))
25.19/8.29	   A^2 -> H(f(c), U1(k, d))
25.19/8.29	   A^2 -> H(f(c), U1(d, k))
25.19/8.29	   A^2 -> H(f(c), U1(k, k))
25.19/8.29	   A^2 -> H(U1(k, k), f(b))
25.19/8.29	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, d), f(c))
25.19/8.29	   A^2 -> H(U1(k, d), f(d))
25.19/8.29	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(d, k), f(c))
25.19/8.29	   A^2 -> H(U1(d, k), f(d))
25.19/8.29	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.29	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.29	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.29	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.29	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.29	   A^2 -> H(U1(d, d), f(e))
25.19/8.29	   A^2 -> H(U1(d, d), f(k))
25.19/8.29	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.29	   A^2 -> H(f(d), U1(e, b))
25.19/8.29	   A^2 -> H(f(d), U1(k, b))
25.19/8.29	   A^2 -> H(f(d), U1(c, d))
25.19/8.29	   A^2 -> H(f(d), U1(d, c))
25.19/8.29	   A^2 -> H(f(d), U1(b, e))
25.19/8.29	   A^2 -> H(f(d), U1(b, k))
25.19/8.29	   A^2 -> H(f(d), U1(e, c))
25.19/8.29	   A^2 -> H(f(d), U1(k, c))
25.19/8.29	   A^2 -> H(f(d), U1(c, e))
25.19/8.29	   A^2 -> H(f(d), U1(c, k))
25.19/8.29	   A^2 -> H(f(d), U1(e, e))
25.19/8.29	   A^2 -> H(f(d), U1(k, k))
25.19/8.29	
25.19/8.29	The TRS R consists of the following rules:
25.19/8.29	
25.19/8.29	   f(x) -> U1(x, x)
25.19/8.29	   U1(e, x) -> x
25.19/8.29	   a -> c
25.19/8.29	   a -> d
25.19/8.29	   b -> c
25.19/8.29	   b -> d
25.19/8.29	   d -> k
25.19/8.29	   c -> e
25.19/8.29	   c -> k
25.19/8.29	
25.19/8.29	Q is empty.
25.19/8.29	We have to consider all minimal (P,Q,R)-chains.
25.19/8.29	----------------------------------------
25.19/8.29	
25.19/8.29	(187) TransformationProof (EQUIVALENT)
25.19/8.29	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.29	
25.19/8.29	   (A^2 -> H(U1(a, a), U1(e, b)),A^2 -> H(U1(a, a), U1(e, b)))
25.19/8.29	   (A^2 -> H(f(c), U1(e, b)),A^2 -> H(f(c), U1(e, b)))
25.19/8.29	   (A^2 -> H(f(d), U1(e, b)),A^2 -> H(f(d), U1(e, b)))
25.19/8.29	   (A^2 -> H(f(a), b),A^2 -> H(f(a), b))
25.19/8.29	   (A^2 -> H(f(a), U1(e, c)),A^2 -> H(f(a), U1(e, c)))
25.19/8.29	   (A^2 -> H(f(a), U1(e, d)),A^2 -> H(f(a), U1(e, d)))
25.19/8.29	
25.19/8.29	
25.19/8.29	----------------------------------------
25.19/8.29	
25.19/8.29	(188)
25.19/8.29	Obligation:
25.19/8.29	Q DP problem:
25.19/8.29	The TRS P consists of the following rules:
25.19/8.29	
25.19/8.29	   H(x, x) -> G(x, x, f(k))
25.19/8.29	   G(d, x, x) -> A^2
25.19/8.29	   A^2 -> H(f(c), f(c))
25.19/8.29	   A^2 -> H(f(d), f(d))
25.19/8.29	   A^2 -> H(f(a), U1(k, b))
25.19/8.29	   A^2 -> H(f(a), U1(c, d))
25.19/8.29	   A^2 -> H(f(a), U1(d, c))
25.19/8.29	   A^2 -> H(f(a), U1(b, e))
25.19/8.29	   A^2 -> H(f(a), U1(b, k))
25.19/8.29	   A^2 -> H(f(c), U1(c, c))
25.19/8.29	   A^2 -> H(f(a), U1(e, c))
25.19/8.29	   A^2 -> H(f(a), U1(k, c))
25.19/8.29	   A^2 -> H(f(a), U1(c, e))
25.19/8.29	   A^2 -> H(f(a), U1(c, k))
25.19/8.29	   A^2 -> H(f(c), f(e))
25.19/8.29	   A^2 -> H(f(a), U1(e, e))
25.19/8.29	   A^2 -> H(f(a), U1(k, k))
25.19/8.29	   A^2 -> H(f(d), U1(d, d))
25.19/8.29	   A^2 -> H(f(a), U1(k, d))
25.19/8.29	   A^2 -> H(f(a), U1(d, k))
25.19/8.29	   A^2 -> H(a, f(b))
25.19/8.29	   A^2 -> H(U1(e, d), f(b))
25.19/8.29	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, a), f(c))
25.19/8.29	   A^2 -> H(U1(e, a), f(d))
25.19/8.29	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, a), f(c))
25.19/8.29	   A^2 -> H(U1(k, a), f(d))
25.19/8.29	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, d), f(c))
25.19/8.29	   A^2 -> H(U1(c, d), f(d))
25.19/8.29	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.29	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.29	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.29	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.29	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.29	   A^2 -> H(U1(c, a), f(e))
25.19/8.29	   A^2 -> H(U1(c, a), f(k))
25.19/8.29	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.29	   A^2 -> H(U1(d, e), f(b))
25.19/8.29	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(d, c), f(c))
25.19/8.29	   A^2 -> H(U1(d, c), f(d))
25.19/8.29	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.29	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.29	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.29	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.29	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.29	   A^2 -> H(U1(d, a), f(e))
25.19/8.29	   A^2 -> H(U1(d, a), f(k))
25.19/8.29	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(a, e), f(c))
25.19/8.29	   A^2 -> H(U1(a, e), f(d))
25.19/8.29	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(a, k), f(c))
25.19/8.29	   A^2 -> H(U1(a, k), f(d))
25.19/8.29	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.29	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.29	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.29	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.29	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.29	   A^2 -> H(U1(a, c), f(e))
25.19/8.29	   A^2 -> H(U1(a, c), f(k))
25.19/8.29	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.29	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.29	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.29	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.29	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.29	   A^2 -> H(U1(a, d), f(e))
25.19/8.29	   A^2 -> H(U1(a, d), f(k))
25.19/8.29	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.29	   A^2 -> H(c, f(b))
25.19/8.29	   A^2 -> H(U1(e, k), f(b))
25.19/8.29	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, c), f(c))
25.19/8.29	   A^2 -> H(U1(e, c), f(d))
25.19/8.29	   A^2 -> H(U1(k, e), f(b))
25.19/8.29	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, c), f(c))
25.19/8.29	   A^2 -> H(U1(k, c), f(d))
25.19/8.29	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, e), f(c))
25.19/8.29	   A^2 -> H(U1(c, e), f(d))
25.19/8.29	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, k), f(c))
25.19/8.29	   A^2 -> H(U1(c, k), f(d))
25.19/8.29	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.29	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.29	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.29	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.29	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.29	   A^2 -> H(U1(c, c), f(e))
25.19/8.29	   A^2 -> H(U1(c, c), f(k))
25.19/8.29	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.29	   A^2 -> H(e, f(b))
25.19/8.29	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, e), f(c))
25.19/8.29	   A^2 -> H(U1(e, e), f(d))
25.19/8.29	   A^2 -> H(f(e), U1(c, b))
25.19/8.29	   A^2 -> H(f(e), U1(d, b))
25.19/8.29	   A^2 -> H(f(e), U1(b, c))
25.19/8.29	   A^2 -> H(f(e), U1(b, d))
25.19/8.29	   A^2 -> H(f(e), U1(c, c))
25.19/8.29	   A^2 -> H(f(e), f(e))
25.19/8.29	   A^2 -> H(f(e), f(k))
25.19/8.29	   A^2 -> H(f(e), U1(d, d))
25.19/8.29	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, k), f(c))
25.19/8.29	   A^2 -> H(U1(k, k), f(d))
25.19/8.29	   A^2 -> H(f(k), U1(c, b))
25.19/8.29	   A^2 -> H(f(k), U1(d, b))
25.19/8.29	   A^2 -> H(f(k), U1(b, c))
25.19/8.29	   A^2 -> H(f(k), U1(b, d))
25.19/8.29	   A^2 -> H(f(k), U1(c, c))
25.19/8.29	   A^2 -> H(f(k), f(e))
25.19/8.29	   A^2 -> H(f(k), f(k))
25.19/8.29	   A^2 -> H(f(k), U1(d, d))
25.19/8.29	   A^2 -> H(f(c), U1(e, b))
25.19/8.29	   A^2 -> H(f(c), U1(k, b))
25.19/8.29	   A^2 -> H(f(c), U1(c, d))
25.19/8.29	   A^2 -> H(f(c), U1(d, c))
25.19/8.29	   A^2 -> H(f(c), U1(b, e))
25.19/8.29	   A^2 -> H(f(c), U1(b, k))
25.19/8.29	   A^2 -> H(f(c), U1(k, d))
25.19/8.29	   A^2 -> H(f(c), U1(d, k))
25.19/8.29	   A^2 -> H(f(c), U1(k, k))
25.19/8.29	   A^2 -> H(U1(k, k), f(b))
25.19/8.29	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, d), f(c))
25.19/8.29	   A^2 -> H(U1(k, d), f(d))
25.19/8.29	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(d, k), f(c))
25.19/8.29	   A^2 -> H(U1(d, k), f(d))
25.19/8.29	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.29	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.29	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.29	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.29	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.29	   A^2 -> H(U1(d, d), f(e))
25.19/8.29	   A^2 -> H(U1(d, d), f(k))
25.19/8.29	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.29	   A^2 -> H(f(d), U1(e, b))
25.19/8.29	   A^2 -> H(f(d), U1(k, b))
25.19/8.29	   A^2 -> H(f(d), U1(c, d))
25.19/8.29	   A^2 -> H(f(d), U1(d, c))
25.19/8.29	   A^2 -> H(f(d), U1(b, e))
25.19/8.29	   A^2 -> H(f(d), U1(b, k))
25.19/8.29	   A^2 -> H(f(d), U1(e, c))
25.19/8.29	   A^2 -> H(f(d), U1(k, c))
25.19/8.29	   A^2 -> H(f(d), U1(c, e))
25.19/8.29	   A^2 -> H(f(d), U1(c, k))
25.19/8.29	   A^2 -> H(f(d), U1(e, e))
25.19/8.29	   A^2 -> H(f(d), U1(k, k))
25.19/8.29	   A^2 -> H(f(a), b)
25.19/8.29	   A^2 -> H(f(a), U1(e, d))
25.19/8.29	
25.19/8.29	The TRS R consists of the following rules:
25.19/8.29	
25.19/8.29	   f(x) -> U1(x, x)
25.19/8.29	   U1(e, x) -> x
25.19/8.29	   a -> c
25.19/8.29	   a -> d
25.19/8.29	   b -> c
25.19/8.29	   b -> d
25.19/8.29	   d -> k
25.19/8.29	   c -> e
25.19/8.29	   c -> k
25.19/8.29	
25.19/8.29	Q is empty.
25.19/8.29	We have to consider all minimal (P,Q,R)-chains.
25.19/8.29	----------------------------------------
25.19/8.29	
25.19/8.29	(189) TransformationProof (EQUIVALENT)
25.19/8.29	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.29	
25.19/8.29	   (A^2 -> H(U1(a, a), U1(k, b)),A^2 -> H(U1(a, a), U1(k, b)))
25.19/8.29	   (A^2 -> H(f(c), U1(k, b)),A^2 -> H(f(c), U1(k, b)))
25.19/8.29	   (A^2 -> H(f(d), U1(k, b)),A^2 -> H(f(d), U1(k, b)))
25.19/8.29	   (A^2 -> H(f(a), U1(k, c)),A^2 -> H(f(a), U1(k, c)))
25.19/8.29	   (A^2 -> H(f(a), U1(k, d)),A^2 -> H(f(a), U1(k, d)))
25.19/8.29	
25.19/8.29	
25.19/8.29	----------------------------------------
25.19/8.29	
25.19/8.29	(190)
25.19/8.29	Obligation:
25.19/8.29	Q DP problem:
25.19/8.29	The TRS P consists of the following rules:
25.19/8.29	
25.19/8.29	   H(x, x) -> G(x, x, f(k))
25.19/8.29	   G(d, x, x) -> A^2
25.19/8.29	   A^2 -> H(f(c), f(c))
25.19/8.29	   A^2 -> H(f(d), f(d))
25.19/8.29	   A^2 -> H(f(a), U1(c, d))
25.19/8.29	   A^2 -> H(f(a), U1(d, c))
25.19/8.29	   A^2 -> H(f(a), U1(b, e))
25.19/8.29	   A^2 -> H(f(a), U1(b, k))
25.19/8.29	   A^2 -> H(f(c), U1(c, c))
25.19/8.29	   A^2 -> H(f(a), U1(e, c))
25.19/8.29	   A^2 -> H(f(a), U1(k, c))
25.19/8.29	   A^2 -> H(f(a), U1(c, e))
25.19/8.29	   A^2 -> H(f(a), U1(c, k))
25.19/8.29	   A^2 -> H(f(c), f(e))
25.19/8.29	   A^2 -> H(f(a), U1(e, e))
25.19/8.29	   A^2 -> H(f(a), U1(k, k))
25.19/8.29	   A^2 -> H(f(d), U1(d, d))
25.19/8.29	   A^2 -> H(f(a), U1(k, d))
25.19/8.29	   A^2 -> H(f(a), U1(d, k))
25.19/8.29	   A^2 -> H(a, f(b))
25.19/8.29	   A^2 -> H(U1(e, d), f(b))
25.19/8.29	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, a), f(c))
25.19/8.29	   A^2 -> H(U1(e, a), f(d))
25.19/8.29	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, a), f(c))
25.19/8.29	   A^2 -> H(U1(k, a), f(d))
25.19/8.29	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, d), f(c))
25.19/8.29	   A^2 -> H(U1(c, d), f(d))
25.19/8.29	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.29	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.29	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.29	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.29	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.29	   A^2 -> H(U1(c, a), f(e))
25.19/8.29	   A^2 -> H(U1(c, a), f(k))
25.19/8.29	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.29	   A^2 -> H(U1(d, e), f(b))
25.19/8.29	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(d, c), f(c))
25.19/8.29	   A^2 -> H(U1(d, c), f(d))
25.19/8.29	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.29	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.29	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.29	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.29	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.29	   A^2 -> H(U1(d, a), f(e))
25.19/8.29	   A^2 -> H(U1(d, a), f(k))
25.19/8.29	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(a, e), f(c))
25.19/8.29	   A^2 -> H(U1(a, e), f(d))
25.19/8.29	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(a, k), f(c))
25.19/8.29	   A^2 -> H(U1(a, k), f(d))
25.19/8.29	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.29	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.29	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.29	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.29	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.29	   A^2 -> H(U1(a, c), f(e))
25.19/8.29	   A^2 -> H(U1(a, c), f(k))
25.19/8.29	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.29	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.29	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.29	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.29	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.29	   A^2 -> H(U1(a, d), f(e))
25.19/8.29	   A^2 -> H(U1(a, d), f(k))
25.19/8.29	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.29	   A^2 -> H(c, f(b))
25.19/8.29	   A^2 -> H(U1(e, k), f(b))
25.19/8.29	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, c), f(c))
25.19/8.29	   A^2 -> H(U1(e, c), f(d))
25.19/8.29	   A^2 -> H(U1(k, e), f(b))
25.19/8.29	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, c), f(c))
25.19/8.29	   A^2 -> H(U1(k, c), f(d))
25.19/8.29	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, e), f(c))
25.19/8.29	   A^2 -> H(U1(c, e), f(d))
25.19/8.29	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, k), f(c))
25.19/8.29	   A^2 -> H(U1(c, k), f(d))
25.19/8.29	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.29	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.29	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.29	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.29	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.29	   A^2 -> H(U1(c, c), f(e))
25.19/8.29	   A^2 -> H(U1(c, c), f(k))
25.19/8.29	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.29	   A^2 -> H(e, f(b))
25.19/8.29	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, e), f(c))
25.19/8.29	   A^2 -> H(U1(e, e), f(d))
25.19/8.29	   A^2 -> H(f(e), U1(c, b))
25.19/8.29	   A^2 -> H(f(e), U1(d, b))
25.19/8.29	   A^2 -> H(f(e), U1(b, c))
25.19/8.29	   A^2 -> H(f(e), U1(b, d))
25.19/8.29	   A^2 -> H(f(e), U1(c, c))
25.19/8.29	   A^2 -> H(f(e), f(e))
25.19/8.29	   A^2 -> H(f(e), f(k))
25.19/8.29	   A^2 -> H(f(e), U1(d, d))
25.19/8.29	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, k), f(c))
25.19/8.29	   A^2 -> H(U1(k, k), f(d))
25.19/8.29	   A^2 -> H(f(k), U1(c, b))
25.19/8.29	   A^2 -> H(f(k), U1(d, b))
25.19/8.29	   A^2 -> H(f(k), U1(b, c))
25.19/8.29	   A^2 -> H(f(k), U1(b, d))
25.19/8.29	   A^2 -> H(f(k), U1(c, c))
25.19/8.29	   A^2 -> H(f(k), f(e))
25.19/8.29	   A^2 -> H(f(k), f(k))
25.19/8.29	   A^2 -> H(f(k), U1(d, d))
25.19/8.29	   A^2 -> H(f(c), U1(e, b))
25.19/8.29	   A^2 -> H(f(c), U1(k, b))
25.19/8.29	   A^2 -> H(f(c), U1(c, d))
25.19/8.29	   A^2 -> H(f(c), U1(d, c))
25.19/8.29	   A^2 -> H(f(c), U1(b, e))
25.19/8.29	   A^2 -> H(f(c), U1(b, k))
25.19/8.29	   A^2 -> H(f(c), U1(k, d))
25.19/8.29	   A^2 -> H(f(c), U1(d, k))
25.19/8.29	   A^2 -> H(f(c), U1(k, k))
25.19/8.29	   A^2 -> H(U1(k, k), f(b))
25.19/8.29	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, d), f(c))
25.19/8.29	   A^2 -> H(U1(k, d), f(d))
25.19/8.29	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(d, k), f(c))
25.19/8.29	   A^2 -> H(U1(d, k), f(d))
25.19/8.29	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.29	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.29	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.29	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.29	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.29	   A^2 -> H(U1(d, d), f(e))
25.19/8.29	   A^2 -> H(U1(d, d), f(k))
25.19/8.29	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.29	   A^2 -> H(f(d), U1(e, b))
25.19/8.29	   A^2 -> H(f(d), U1(k, b))
25.19/8.29	   A^2 -> H(f(d), U1(c, d))
25.19/8.29	   A^2 -> H(f(d), U1(d, c))
25.19/8.29	   A^2 -> H(f(d), U1(b, e))
25.19/8.29	   A^2 -> H(f(d), U1(b, k))
25.19/8.29	   A^2 -> H(f(d), U1(e, c))
25.19/8.29	   A^2 -> H(f(d), U1(k, c))
25.19/8.29	   A^2 -> H(f(d), U1(c, e))
25.19/8.29	   A^2 -> H(f(d), U1(c, k))
25.19/8.29	   A^2 -> H(f(d), U1(e, e))
25.19/8.29	   A^2 -> H(f(d), U1(k, k))
25.19/8.29	   A^2 -> H(f(a), b)
25.19/8.29	   A^2 -> H(f(a), U1(e, d))
25.19/8.29	
25.19/8.29	The TRS R consists of the following rules:
25.19/8.29	
25.19/8.29	   f(x) -> U1(x, x)
25.19/8.29	   U1(e, x) -> x
25.19/8.29	   a -> c
25.19/8.29	   a -> d
25.19/8.29	   b -> c
25.19/8.29	   b -> d
25.19/8.29	   d -> k
25.19/8.29	   c -> e
25.19/8.29	   c -> k
25.19/8.29	
25.19/8.29	Q is empty.
25.19/8.29	We have to consider all minimal (P,Q,R)-chains.
25.19/8.29	----------------------------------------
25.19/8.29	
25.19/8.29	(191) TransformationProof (EQUIVALENT)
25.19/8.29	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.29	
25.19/8.29	   (A^2 -> H(U1(a, a), U1(c, d)),A^2 -> H(U1(a, a), U1(c, d)))
25.19/8.29	   (A^2 -> H(f(c), U1(c, d)),A^2 -> H(f(c), U1(c, d)))
25.19/8.29	   (A^2 -> H(f(d), U1(c, d)),A^2 -> H(f(d), U1(c, d)))
25.19/8.29	   (A^2 -> H(f(a), U1(e, d)),A^2 -> H(f(a), U1(e, d)))
25.19/8.29	   (A^2 -> H(f(a), U1(k, d)),A^2 -> H(f(a), U1(k, d)))
25.19/8.29	   (A^2 -> H(f(a), U1(c, k)),A^2 -> H(f(a), U1(c, k)))
25.19/8.29	
25.19/8.29	
25.19/8.29	----------------------------------------
25.19/8.29	
25.19/8.29	(192)
25.19/8.29	Obligation:
25.19/8.29	Q DP problem:
25.19/8.29	The TRS P consists of the following rules:
25.19/8.29	
25.19/8.29	   H(x, x) -> G(x, x, f(k))
25.19/8.29	   G(d, x, x) -> A^2
25.19/8.29	   A^2 -> H(f(c), f(c))
25.19/8.29	   A^2 -> H(f(d), f(d))
25.19/8.29	   A^2 -> H(f(a), U1(d, c))
25.19/8.29	   A^2 -> H(f(a), U1(b, e))
25.19/8.29	   A^2 -> H(f(a), U1(b, k))
25.19/8.29	   A^2 -> H(f(c), U1(c, c))
25.19/8.29	   A^2 -> H(f(a), U1(e, c))
25.19/8.29	   A^2 -> H(f(a), U1(k, c))
25.19/8.29	   A^2 -> H(f(a), U1(c, e))
25.19/8.29	   A^2 -> H(f(a), U1(c, k))
25.19/8.29	   A^2 -> H(f(c), f(e))
25.19/8.29	   A^2 -> H(f(a), U1(e, e))
25.19/8.29	   A^2 -> H(f(a), U1(k, k))
25.19/8.29	   A^2 -> H(f(d), U1(d, d))
25.19/8.29	   A^2 -> H(f(a), U1(k, d))
25.19/8.29	   A^2 -> H(f(a), U1(d, k))
25.19/8.29	   A^2 -> H(a, f(b))
25.19/8.29	   A^2 -> H(U1(e, d), f(b))
25.19/8.29	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, a), f(c))
25.19/8.29	   A^2 -> H(U1(e, a), f(d))
25.19/8.29	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, a), f(c))
25.19/8.29	   A^2 -> H(U1(k, a), f(d))
25.19/8.29	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, d), f(c))
25.19/8.29	   A^2 -> H(U1(c, d), f(d))
25.19/8.29	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.29	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.29	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.29	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.29	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.29	   A^2 -> H(U1(c, a), f(e))
25.19/8.29	   A^2 -> H(U1(c, a), f(k))
25.19/8.29	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.29	   A^2 -> H(U1(d, e), f(b))
25.19/8.29	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(d, c), f(c))
25.19/8.29	   A^2 -> H(U1(d, c), f(d))
25.19/8.29	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.29	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.29	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.29	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.29	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.29	   A^2 -> H(U1(d, a), f(e))
25.19/8.29	   A^2 -> H(U1(d, a), f(k))
25.19/8.29	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(a, e), f(c))
25.19/8.29	   A^2 -> H(U1(a, e), f(d))
25.19/8.29	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(a, k), f(c))
25.19/8.29	   A^2 -> H(U1(a, k), f(d))
25.19/8.29	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.29	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.29	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.29	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.29	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.29	   A^2 -> H(U1(a, c), f(e))
25.19/8.29	   A^2 -> H(U1(a, c), f(k))
25.19/8.29	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.29	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.29	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.29	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.29	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.29	   A^2 -> H(U1(a, d), f(e))
25.19/8.29	   A^2 -> H(U1(a, d), f(k))
25.19/8.29	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.29	   A^2 -> H(c, f(b))
25.19/8.29	   A^2 -> H(U1(e, k), f(b))
25.19/8.29	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, c), f(c))
25.19/8.29	   A^2 -> H(U1(e, c), f(d))
25.19/8.29	   A^2 -> H(U1(k, e), f(b))
25.19/8.29	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, c), f(c))
25.19/8.29	   A^2 -> H(U1(k, c), f(d))
25.19/8.29	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, e), f(c))
25.19/8.29	   A^2 -> H(U1(c, e), f(d))
25.19/8.29	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, k), f(c))
25.19/8.29	   A^2 -> H(U1(c, k), f(d))
25.19/8.29	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.29	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.29	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.29	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.29	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.29	   A^2 -> H(U1(c, c), f(e))
25.19/8.29	   A^2 -> H(U1(c, c), f(k))
25.19/8.29	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.29	   A^2 -> H(e, f(b))
25.19/8.29	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, e), f(c))
25.19/8.29	   A^2 -> H(U1(e, e), f(d))
25.19/8.29	   A^2 -> H(f(e), U1(c, b))
25.19/8.29	   A^2 -> H(f(e), U1(d, b))
25.19/8.29	   A^2 -> H(f(e), U1(b, c))
25.19/8.29	   A^2 -> H(f(e), U1(b, d))
25.19/8.29	   A^2 -> H(f(e), U1(c, c))
25.19/8.29	   A^2 -> H(f(e), f(e))
25.19/8.29	   A^2 -> H(f(e), f(k))
25.19/8.29	   A^2 -> H(f(e), U1(d, d))
25.19/8.29	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, k), f(c))
25.19/8.29	   A^2 -> H(U1(k, k), f(d))
25.19/8.29	   A^2 -> H(f(k), U1(c, b))
25.19/8.29	   A^2 -> H(f(k), U1(d, b))
25.19/8.29	   A^2 -> H(f(k), U1(b, c))
25.19/8.29	   A^2 -> H(f(k), U1(b, d))
25.19/8.29	   A^2 -> H(f(k), U1(c, c))
25.19/8.29	   A^2 -> H(f(k), f(e))
25.19/8.29	   A^2 -> H(f(k), f(k))
25.19/8.29	   A^2 -> H(f(k), U1(d, d))
25.19/8.29	   A^2 -> H(f(c), U1(e, b))
25.19/8.29	   A^2 -> H(f(c), U1(k, b))
25.19/8.29	   A^2 -> H(f(c), U1(c, d))
25.19/8.29	   A^2 -> H(f(c), U1(d, c))
25.19/8.29	   A^2 -> H(f(c), U1(b, e))
25.19/8.29	   A^2 -> H(f(c), U1(b, k))
25.19/8.29	   A^2 -> H(f(c), U1(k, d))
25.19/8.29	   A^2 -> H(f(c), U1(d, k))
25.19/8.29	   A^2 -> H(f(c), U1(k, k))
25.19/8.29	   A^2 -> H(U1(k, k), f(b))
25.19/8.29	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, d), f(c))
25.19/8.29	   A^2 -> H(U1(k, d), f(d))
25.19/8.29	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(d, k), f(c))
25.19/8.29	   A^2 -> H(U1(d, k), f(d))
25.19/8.29	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.29	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.29	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.29	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.29	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.29	   A^2 -> H(U1(d, d), f(e))
25.19/8.29	   A^2 -> H(U1(d, d), f(k))
25.19/8.29	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.29	   A^2 -> H(f(d), U1(e, b))
25.19/8.29	   A^2 -> H(f(d), U1(k, b))
25.19/8.29	   A^2 -> H(f(d), U1(c, d))
25.19/8.29	   A^2 -> H(f(d), U1(d, c))
25.19/8.29	   A^2 -> H(f(d), U1(b, e))
25.19/8.29	   A^2 -> H(f(d), U1(b, k))
25.19/8.29	   A^2 -> H(f(d), U1(e, c))
25.19/8.29	   A^2 -> H(f(d), U1(k, c))
25.19/8.29	   A^2 -> H(f(d), U1(c, e))
25.19/8.29	   A^2 -> H(f(d), U1(c, k))
25.19/8.29	   A^2 -> H(f(d), U1(e, e))
25.19/8.29	   A^2 -> H(f(d), U1(k, k))
25.19/8.29	   A^2 -> H(f(a), b)
25.19/8.29	   A^2 -> H(f(a), U1(e, d))
25.19/8.29	
25.19/8.29	The TRS R consists of the following rules:
25.19/8.29	
25.19/8.29	   f(x) -> U1(x, x)
25.19/8.29	   U1(e, x) -> x
25.19/8.29	   a -> c
25.19/8.29	   a -> d
25.19/8.29	   b -> c
25.19/8.29	   b -> d
25.19/8.29	   d -> k
25.19/8.29	   c -> e
25.19/8.29	   c -> k
25.19/8.29	
25.19/8.29	Q is empty.
25.19/8.29	We have to consider all minimal (P,Q,R)-chains.
25.19/8.29	----------------------------------------
25.19/8.29	
25.19/8.29	(193) TransformationProof (EQUIVALENT)
25.19/8.29	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.29	
25.19/8.29	   (A^2 -> H(U1(a, a), U1(d, c)),A^2 -> H(U1(a, a), U1(d, c)))
25.19/8.29	   (A^2 -> H(f(c), U1(d, c)),A^2 -> H(f(c), U1(d, c)))
25.19/8.29	   (A^2 -> H(f(d), U1(d, c)),A^2 -> H(f(d), U1(d, c)))
25.19/8.29	   (A^2 -> H(f(a), U1(k, c)),A^2 -> H(f(a), U1(k, c)))
25.19/8.29	   (A^2 -> H(f(a), U1(d, e)),A^2 -> H(f(a), U1(d, e)))
25.19/8.29	   (A^2 -> H(f(a), U1(d, k)),A^2 -> H(f(a), U1(d, k)))
25.19/8.29	
25.19/8.29	
25.19/8.29	----------------------------------------
25.19/8.29	
25.19/8.29	(194)
25.19/8.29	Obligation:
25.19/8.29	Q DP problem:
25.19/8.29	The TRS P consists of the following rules:
25.19/8.29	
25.19/8.29	   H(x, x) -> G(x, x, f(k))
25.19/8.29	   G(d, x, x) -> A^2
25.19/8.29	   A^2 -> H(f(c), f(c))
25.19/8.29	   A^2 -> H(f(d), f(d))
25.19/8.29	   A^2 -> H(f(a), U1(b, e))
25.19/8.29	   A^2 -> H(f(a), U1(b, k))
25.19/8.29	   A^2 -> H(f(c), U1(c, c))
25.19/8.29	   A^2 -> H(f(a), U1(e, c))
25.19/8.29	   A^2 -> H(f(a), U1(k, c))
25.19/8.29	   A^2 -> H(f(a), U1(c, e))
25.19/8.29	   A^2 -> H(f(a), U1(c, k))
25.19/8.29	   A^2 -> H(f(c), f(e))
25.19/8.29	   A^2 -> H(f(a), U1(e, e))
25.19/8.29	   A^2 -> H(f(a), U1(k, k))
25.19/8.29	   A^2 -> H(f(d), U1(d, d))
25.19/8.29	   A^2 -> H(f(a), U1(k, d))
25.19/8.29	   A^2 -> H(f(a), U1(d, k))
25.19/8.29	   A^2 -> H(a, f(b))
25.19/8.29	   A^2 -> H(U1(e, d), f(b))
25.19/8.29	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, a), f(c))
25.19/8.29	   A^2 -> H(U1(e, a), f(d))
25.19/8.29	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, a), f(c))
25.19/8.29	   A^2 -> H(U1(k, a), f(d))
25.19/8.29	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, d), f(c))
25.19/8.29	   A^2 -> H(U1(c, d), f(d))
25.19/8.29	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.29	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.29	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.29	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.29	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.29	   A^2 -> H(U1(c, a), f(e))
25.19/8.29	   A^2 -> H(U1(c, a), f(k))
25.19/8.29	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.29	   A^2 -> H(U1(d, e), f(b))
25.19/8.29	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(d, c), f(c))
25.19/8.29	   A^2 -> H(U1(d, c), f(d))
25.19/8.29	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.29	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.29	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.29	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.29	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.29	   A^2 -> H(U1(d, a), f(e))
25.19/8.29	   A^2 -> H(U1(d, a), f(k))
25.19/8.29	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(a, e), f(c))
25.19/8.29	   A^2 -> H(U1(a, e), f(d))
25.19/8.29	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(a, k), f(c))
25.19/8.29	   A^2 -> H(U1(a, k), f(d))
25.19/8.29	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.29	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.29	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.29	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.29	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.29	   A^2 -> H(U1(a, c), f(e))
25.19/8.29	   A^2 -> H(U1(a, c), f(k))
25.19/8.29	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.29	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.29	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.29	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.29	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.29	   A^2 -> H(U1(a, d), f(e))
25.19/8.29	   A^2 -> H(U1(a, d), f(k))
25.19/8.29	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.29	   A^2 -> H(c, f(b))
25.19/8.29	   A^2 -> H(U1(e, k), f(b))
25.19/8.29	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, c), f(c))
25.19/8.29	   A^2 -> H(U1(e, c), f(d))
25.19/8.29	   A^2 -> H(U1(k, e), f(b))
25.19/8.29	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, c), f(c))
25.19/8.29	   A^2 -> H(U1(k, c), f(d))
25.19/8.29	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, e), f(c))
25.19/8.29	   A^2 -> H(U1(c, e), f(d))
25.19/8.29	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, k), f(c))
25.19/8.29	   A^2 -> H(U1(c, k), f(d))
25.19/8.29	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.29	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.29	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.29	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.29	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.29	   A^2 -> H(U1(c, c), f(e))
25.19/8.29	   A^2 -> H(U1(c, c), f(k))
25.19/8.29	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.29	   A^2 -> H(e, f(b))
25.19/8.29	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, e), f(c))
25.19/8.29	   A^2 -> H(U1(e, e), f(d))
25.19/8.29	   A^2 -> H(f(e), U1(c, b))
25.19/8.29	   A^2 -> H(f(e), U1(d, b))
25.19/8.29	   A^2 -> H(f(e), U1(b, c))
25.19/8.29	   A^2 -> H(f(e), U1(b, d))
25.19/8.29	   A^2 -> H(f(e), U1(c, c))
25.19/8.29	   A^2 -> H(f(e), f(e))
25.19/8.29	   A^2 -> H(f(e), f(k))
25.19/8.29	   A^2 -> H(f(e), U1(d, d))
25.19/8.29	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, k), f(c))
25.19/8.29	   A^2 -> H(U1(k, k), f(d))
25.19/8.29	   A^2 -> H(f(k), U1(c, b))
25.19/8.29	   A^2 -> H(f(k), U1(d, b))
25.19/8.29	   A^2 -> H(f(k), U1(b, c))
25.19/8.29	   A^2 -> H(f(k), U1(b, d))
25.19/8.29	   A^2 -> H(f(k), U1(c, c))
25.19/8.29	   A^2 -> H(f(k), f(e))
25.19/8.29	   A^2 -> H(f(k), f(k))
25.19/8.29	   A^2 -> H(f(k), U1(d, d))
25.19/8.29	   A^2 -> H(f(c), U1(e, b))
25.19/8.29	   A^2 -> H(f(c), U1(k, b))
25.19/8.29	   A^2 -> H(f(c), U1(c, d))
25.19/8.29	   A^2 -> H(f(c), U1(d, c))
25.19/8.29	   A^2 -> H(f(c), U1(b, e))
25.19/8.29	   A^2 -> H(f(c), U1(b, k))
25.19/8.29	   A^2 -> H(f(c), U1(k, d))
25.19/8.29	   A^2 -> H(f(c), U1(d, k))
25.19/8.29	   A^2 -> H(f(c), U1(k, k))
25.19/8.29	   A^2 -> H(U1(k, k), f(b))
25.19/8.29	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, d), f(c))
25.19/8.29	   A^2 -> H(U1(k, d), f(d))
25.19/8.29	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(d, k), f(c))
25.19/8.29	   A^2 -> H(U1(d, k), f(d))
25.19/8.29	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.29	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.29	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.29	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.29	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.29	   A^2 -> H(U1(d, d), f(e))
25.19/8.29	   A^2 -> H(U1(d, d), f(k))
25.19/8.29	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.29	   A^2 -> H(f(d), U1(e, b))
25.19/8.29	   A^2 -> H(f(d), U1(k, b))
25.19/8.29	   A^2 -> H(f(d), U1(c, d))
25.19/8.29	   A^2 -> H(f(d), U1(d, c))
25.19/8.29	   A^2 -> H(f(d), U1(b, e))
25.19/8.29	   A^2 -> H(f(d), U1(b, k))
25.19/8.29	   A^2 -> H(f(d), U1(e, c))
25.19/8.29	   A^2 -> H(f(d), U1(k, c))
25.19/8.29	   A^2 -> H(f(d), U1(c, e))
25.19/8.29	   A^2 -> H(f(d), U1(c, k))
25.19/8.29	   A^2 -> H(f(d), U1(e, e))
25.19/8.29	   A^2 -> H(f(d), U1(k, k))
25.19/8.29	   A^2 -> H(f(a), b)
25.19/8.29	   A^2 -> H(f(a), U1(e, d))
25.19/8.29	   A^2 -> H(f(a), U1(d, e))
25.19/8.29	
25.19/8.29	The TRS R consists of the following rules:
25.19/8.29	
25.19/8.29	   f(x) -> U1(x, x)
25.19/8.29	   U1(e, x) -> x
25.19/8.29	   a -> c
25.19/8.29	   a -> d
25.19/8.29	   b -> c
25.19/8.29	   b -> d
25.19/8.29	   d -> k
25.19/8.29	   c -> e
25.19/8.29	   c -> k
25.19/8.29	
25.19/8.29	Q is empty.
25.19/8.29	We have to consider all minimal (P,Q,R)-chains.
25.19/8.29	----------------------------------------
25.19/8.29	
25.19/8.29	(195) TransformationProof (EQUIVALENT)
25.19/8.29	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.29	
25.19/8.29	   (A^2 -> H(U1(a, a), U1(b, e)),A^2 -> H(U1(a, a), U1(b, e)))
25.19/8.29	   (A^2 -> H(f(c), U1(b, e)),A^2 -> H(f(c), U1(b, e)))
25.19/8.29	   (A^2 -> H(f(d), U1(b, e)),A^2 -> H(f(d), U1(b, e)))
25.19/8.29	   (A^2 -> H(f(a), U1(c, e)),A^2 -> H(f(a), U1(c, e)))
25.19/8.29	   (A^2 -> H(f(a), U1(d, e)),A^2 -> H(f(a), U1(d, e)))
25.19/8.29	
25.19/8.29	
25.19/8.29	----------------------------------------
25.19/8.29	
25.19/8.29	(196)
25.19/8.29	Obligation:
25.19/8.29	Q DP problem:
25.19/8.29	The TRS P consists of the following rules:
25.19/8.29	
25.19/8.29	   H(x, x) -> G(x, x, f(k))
25.19/8.29	   G(d, x, x) -> A^2
25.19/8.29	   A^2 -> H(f(c), f(c))
25.19/8.29	   A^2 -> H(f(d), f(d))
25.19/8.29	   A^2 -> H(f(a), U1(b, k))
25.19/8.29	   A^2 -> H(f(c), U1(c, c))
25.19/8.29	   A^2 -> H(f(a), U1(e, c))
25.19/8.29	   A^2 -> H(f(a), U1(k, c))
25.19/8.29	   A^2 -> H(f(a), U1(c, e))
25.19/8.29	   A^2 -> H(f(a), U1(c, k))
25.19/8.29	   A^2 -> H(f(c), f(e))
25.19/8.29	   A^2 -> H(f(a), U1(e, e))
25.19/8.29	   A^2 -> H(f(a), U1(k, k))
25.19/8.29	   A^2 -> H(f(d), U1(d, d))
25.19/8.29	   A^2 -> H(f(a), U1(k, d))
25.19/8.29	   A^2 -> H(f(a), U1(d, k))
25.19/8.29	   A^2 -> H(a, f(b))
25.19/8.29	   A^2 -> H(U1(e, d), f(b))
25.19/8.29	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, a), f(c))
25.19/8.29	   A^2 -> H(U1(e, a), f(d))
25.19/8.29	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.29	   A^2 -> H(U1(k, a), f(c))
25.19/8.29	   A^2 -> H(U1(k, a), f(d))
25.19/8.29	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.29	   A^2 -> H(U1(c, d), f(c))
25.19/8.29	   A^2 -> H(U1(c, d), f(d))
25.19/8.29	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.29	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.29	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.29	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.29	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.29	   A^2 -> H(U1(c, a), f(e))
25.19/8.29	   A^2 -> H(U1(c, a), f(k))
25.19/8.29	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.29	   A^2 -> H(U1(d, e), f(b))
25.19/8.29	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(d, c), f(c))
25.19/8.29	   A^2 -> H(U1(d, c), f(d))
25.19/8.29	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.29	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.29	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.29	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.29	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.29	   A^2 -> H(U1(d, a), f(e))
25.19/8.29	   A^2 -> H(U1(d, a), f(k))
25.19/8.29	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.29	   A^2 -> H(U1(a, e), f(c))
25.19/8.29	   A^2 -> H(U1(a, e), f(d))
25.19/8.29	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.29	   A^2 -> H(U1(a, k), f(c))
25.19/8.29	   A^2 -> H(U1(a, k), f(d))
25.19/8.29	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.29	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.29	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.29	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.29	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.29	   A^2 -> H(U1(a, c), f(e))
25.19/8.29	   A^2 -> H(U1(a, c), f(k))
25.19/8.29	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.29	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.29	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.29	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.29	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.29	   A^2 -> H(U1(a, d), f(e))
25.19/8.29	   A^2 -> H(U1(a, d), f(k))
25.19/8.29	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.29	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.29	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.29	   A^2 -> H(c, f(b))
25.19/8.29	   A^2 -> H(U1(e, k), f(b))
25.19/8.29	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.29	   A^2 -> H(U1(e, c), f(c))
25.19/8.29	   A^2 -> H(U1(e, c), f(d))
25.19/8.29	   A^2 -> H(U1(k, e), f(b))
25.19/8.29	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, c), f(c))
25.19/8.31	   A^2 -> H(U1(k, c), f(d))
25.19/8.31	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, e), f(c))
25.19/8.31	   A^2 -> H(U1(c, e), f(d))
25.19/8.31	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, k), f(c))
25.19/8.31	   A^2 -> H(U1(c, k), f(d))
25.19/8.31	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.31	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.31	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.31	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.31	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.31	   A^2 -> H(U1(c, c), f(e))
25.19/8.31	   A^2 -> H(U1(c, c), f(k))
25.19/8.31	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.31	   A^2 -> H(e, f(b))
25.19/8.31	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, e), f(c))
25.19/8.31	   A^2 -> H(U1(e, e), f(d))
25.19/8.31	   A^2 -> H(f(e), U1(c, b))
25.19/8.31	   A^2 -> H(f(e), U1(d, b))
25.19/8.31	   A^2 -> H(f(e), U1(b, c))
25.19/8.31	   A^2 -> H(f(e), U1(b, d))
25.19/8.31	   A^2 -> H(f(e), U1(c, c))
25.19/8.31	   A^2 -> H(f(e), f(e))
25.19/8.31	   A^2 -> H(f(e), f(k))
25.19/8.31	   A^2 -> H(f(e), U1(d, d))
25.19/8.31	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, k), f(c))
25.19/8.31	   A^2 -> H(U1(k, k), f(d))
25.19/8.31	   A^2 -> H(f(k), U1(c, b))
25.19/8.31	   A^2 -> H(f(k), U1(d, b))
25.19/8.31	   A^2 -> H(f(k), U1(b, c))
25.19/8.31	   A^2 -> H(f(k), U1(b, d))
25.19/8.31	   A^2 -> H(f(k), U1(c, c))
25.19/8.31	   A^2 -> H(f(k), f(e))
25.19/8.31	   A^2 -> H(f(k), f(k))
25.19/8.31	   A^2 -> H(f(k), U1(d, d))
25.19/8.31	   A^2 -> H(f(c), U1(e, b))
25.19/8.31	   A^2 -> H(f(c), U1(k, b))
25.19/8.31	   A^2 -> H(f(c), U1(c, d))
25.19/8.31	   A^2 -> H(f(c), U1(d, c))
25.19/8.31	   A^2 -> H(f(c), U1(b, e))
25.19/8.31	   A^2 -> H(f(c), U1(b, k))
25.19/8.31	   A^2 -> H(f(c), U1(k, d))
25.19/8.31	   A^2 -> H(f(c), U1(d, k))
25.19/8.31	   A^2 -> H(f(c), U1(k, k))
25.19/8.31	   A^2 -> H(U1(k, k), f(b))
25.19/8.31	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, d), f(c))
25.19/8.31	   A^2 -> H(U1(k, d), f(d))
25.19/8.31	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(d, k), f(c))
25.19/8.31	   A^2 -> H(U1(d, k), f(d))
25.19/8.31	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.31	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.31	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.31	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.31	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.31	   A^2 -> H(U1(d, d), f(e))
25.19/8.31	   A^2 -> H(U1(d, d), f(k))
25.19/8.31	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.31	   A^2 -> H(f(d), U1(e, b))
25.19/8.31	   A^2 -> H(f(d), U1(k, b))
25.19/8.31	   A^2 -> H(f(d), U1(c, d))
25.19/8.31	   A^2 -> H(f(d), U1(d, c))
25.19/8.31	   A^2 -> H(f(d), U1(b, e))
25.19/8.31	   A^2 -> H(f(d), U1(b, k))
25.19/8.31	   A^2 -> H(f(d), U1(e, c))
25.19/8.31	   A^2 -> H(f(d), U1(k, c))
25.19/8.31	   A^2 -> H(f(d), U1(c, e))
25.19/8.31	   A^2 -> H(f(d), U1(c, k))
25.19/8.31	   A^2 -> H(f(d), U1(e, e))
25.19/8.31	   A^2 -> H(f(d), U1(k, k))
25.19/8.31	   A^2 -> H(f(a), b)
25.19/8.31	   A^2 -> H(f(a), U1(e, d))
25.19/8.31	   A^2 -> H(f(a), U1(d, e))
25.19/8.31	
25.19/8.31	The TRS R consists of the following rules:
25.19/8.31	
25.19/8.31	   f(x) -> U1(x, x)
25.19/8.31	   U1(e, x) -> x
25.19/8.31	   a -> c
25.19/8.31	   a -> d
25.19/8.31	   b -> c
25.19/8.31	   b -> d
25.19/8.31	   d -> k
25.19/8.31	   c -> e
25.19/8.31	   c -> k
25.19/8.31	
25.19/8.31	Q is empty.
25.19/8.31	We have to consider all minimal (P,Q,R)-chains.
25.19/8.31	----------------------------------------
25.19/8.31	
25.19/8.31	(197) TransformationProof (EQUIVALENT)
25.19/8.31	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.31	
25.19/8.31	   (A^2 -> H(U1(a, a), U1(b, k)),A^2 -> H(U1(a, a), U1(b, k)))
25.19/8.31	   (A^2 -> H(f(c), U1(b, k)),A^2 -> H(f(c), U1(b, k)))
25.19/8.31	   (A^2 -> H(f(d), U1(b, k)),A^2 -> H(f(d), U1(b, k)))
25.19/8.31	   (A^2 -> H(f(a), U1(c, k)),A^2 -> H(f(a), U1(c, k)))
25.19/8.31	   (A^2 -> H(f(a), U1(d, k)),A^2 -> H(f(a), U1(d, k)))
25.19/8.31	
25.19/8.31	
25.19/8.31	----------------------------------------
25.19/8.31	
25.19/8.31	(198)
25.19/8.31	Obligation:
25.19/8.31	Q DP problem:
25.19/8.31	The TRS P consists of the following rules:
25.19/8.31	
25.19/8.31	   H(x, x) -> G(x, x, f(k))
25.19/8.31	   G(d, x, x) -> A^2
25.19/8.31	   A^2 -> H(f(c), f(c))
25.19/8.31	   A^2 -> H(f(d), f(d))
25.19/8.31	   A^2 -> H(f(c), U1(c, c))
25.19/8.31	   A^2 -> H(f(a), U1(e, c))
25.19/8.31	   A^2 -> H(f(a), U1(k, c))
25.19/8.31	   A^2 -> H(f(a), U1(c, e))
25.19/8.31	   A^2 -> H(f(a), U1(c, k))
25.19/8.31	   A^2 -> H(f(c), f(e))
25.19/8.31	   A^2 -> H(f(a), U1(e, e))
25.19/8.31	   A^2 -> H(f(a), U1(k, k))
25.19/8.31	   A^2 -> H(f(d), U1(d, d))
25.19/8.31	   A^2 -> H(f(a), U1(k, d))
25.19/8.31	   A^2 -> H(f(a), U1(d, k))
25.19/8.31	   A^2 -> H(a, f(b))
25.19/8.31	   A^2 -> H(U1(e, d), f(b))
25.19/8.31	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, a), f(c))
25.19/8.31	   A^2 -> H(U1(e, a), f(d))
25.19/8.31	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, a), f(c))
25.19/8.31	   A^2 -> H(U1(k, a), f(d))
25.19/8.31	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, d), f(c))
25.19/8.31	   A^2 -> H(U1(c, d), f(d))
25.19/8.31	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.31	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.31	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.31	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.31	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.31	   A^2 -> H(U1(c, a), f(e))
25.19/8.31	   A^2 -> H(U1(c, a), f(k))
25.19/8.31	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.31	   A^2 -> H(U1(d, e), f(b))
25.19/8.31	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(d, c), f(c))
25.19/8.31	   A^2 -> H(U1(d, c), f(d))
25.19/8.31	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.31	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.31	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.31	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.31	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.31	   A^2 -> H(U1(d, a), f(e))
25.19/8.31	   A^2 -> H(U1(d, a), f(k))
25.19/8.31	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(a, e), f(c))
25.19/8.31	   A^2 -> H(U1(a, e), f(d))
25.19/8.31	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(a, k), f(c))
25.19/8.31	   A^2 -> H(U1(a, k), f(d))
25.19/8.31	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.31	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.31	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.31	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.31	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.31	   A^2 -> H(U1(a, c), f(e))
25.19/8.31	   A^2 -> H(U1(a, c), f(k))
25.19/8.31	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.31	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.31	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.31	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.31	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.31	   A^2 -> H(U1(a, d), f(e))
25.19/8.31	   A^2 -> H(U1(a, d), f(k))
25.19/8.31	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.31	   A^2 -> H(c, f(b))
25.19/8.31	   A^2 -> H(U1(e, k), f(b))
25.19/8.31	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, c), f(c))
25.19/8.31	   A^2 -> H(U1(e, c), f(d))
25.19/8.31	   A^2 -> H(U1(k, e), f(b))
25.19/8.31	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, c), f(c))
25.19/8.31	   A^2 -> H(U1(k, c), f(d))
25.19/8.31	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, e), f(c))
25.19/8.31	   A^2 -> H(U1(c, e), f(d))
25.19/8.31	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, k), f(c))
25.19/8.31	   A^2 -> H(U1(c, k), f(d))
25.19/8.31	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.31	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.31	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.31	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.31	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.31	   A^2 -> H(U1(c, c), f(e))
25.19/8.31	   A^2 -> H(U1(c, c), f(k))
25.19/8.31	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.31	   A^2 -> H(e, f(b))
25.19/8.31	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, e), f(c))
25.19/8.31	   A^2 -> H(U1(e, e), f(d))
25.19/8.31	   A^2 -> H(f(e), U1(c, b))
25.19/8.31	   A^2 -> H(f(e), U1(d, b))
25.19/8.31	   A^2 -> H(f(e), U1(b, c))
25.19/8.31	   A^2 -> H(f(e), U1(b, d))
25.19/8.31	   A^2 -> H(f(e), U1(c, c))
25.19/8.31	   A^2 -> H(f(e), f(e))
25.19/8.31	   A^2 -> H(f(e), f(k))
25.19/8.31	   A^2 -> H(f(e), U1(d, d))
25.19/8.31	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, k), f(c))
25.19/8.31	   A^2 -> H(U1(k, k), f(d))
25.19/8.31	   A^2 -> H(f(k), U1(c, b))
25.19/8.31	   A^2 -> H(f(k), U1(d, b))
25.19/8.31	   A^2 -> H(f(k), U1(b, c))
25.19/8.31	   A^2 -> H(f(k), U1(b, d))
25.19/8.31	   A^2 -> H(f(k), U1(c, c))
25.19/8.31	   A^2 -> H(f(k), f(e))
25.19/8.31	   A^2 -> H(f(k), f(k))
25.19/8.31	   A^2 -> H(f(k), U1(d, d))
25.19/8.31	   A^2 -> H(f(c), U1(e, b))
25.19/8.31	   A^2 -> H(f(c), U1(k, b))
25.19/8.31	   A^2 -> H(f(c), U1(c, d))
25.19/8.31	   A^2 -> H(f(c), U1(d, c))
25.19/8.31	   A^2 -> H(f(c), U1(b, e))
25.19/8.31	   A^2 -> H(f(c), U1(b, k))
25.19/8.31	   A^2 -> H(f(c), U1(k, d))
25.19/8.31	   A^2 -> H(f(c), U1(d, k))
25.19/8.31	   A^2 -> H(f(c), U1(k, k))
25.19/8.31	   A^2 -> H(U1(k, k), f(b))
25.19/8.31	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, d), f(c))
25.19/8.31	   A^2 -> H(U1(k, d), f(d))
25.19/8.31	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(d, k), f(c))
25.19/8.31	   A^2 -> H(U1(d, k), f(d))
25.19/8.31	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.31	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.31	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.31	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.31	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.31	   A^2 -> H(U1(d, d), f(e))
25.19/8.31	   A^2 -> H(U1(d, d), f(k))
25.19/8.31	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.31	   A^2 -> H(f(d), U1(e, b))
25.19/8.31	   A^2 -> H(f(d), U1(k, b))
25.19/8.31	   A^2 -> H(f(d), U1(c, d))
25.19/8.31	   A^2 -> H(f(d), U1(d, c))
25.19/8.31	   A^2 -> H(f(d), U1(b, e))
25.19/8.31	   A^2 -> H(f(d), U1(b, k))
25.19/8.31	   A^2 -> H(f(d), U1(e, c))
25.19/8.31	   A^2 -> H(f(d), U1(k, c))
25.19/8.31	   A^2 -> H(f(d), U1(c, e))
25.19/8.31	   A^2 -> H(f(d), U1(c, k))
25.19/8.31	   A^2 -> H(f(d), U1(e, e))
25.19/8.31	   A^2 -> H(f(d), U1(k, k))
25.19/8.31	   A^2 -> H(f(a), b)
25.19/8.31	   A^2 -> H(f(a), U1(e, d))
25.19/8.31	   A^2 -> H(f(a), U1(d, e))
25.19/8.31	
25.19/8.31	The TRS R consists of the following rules:
25.19/8.31	
25.19/8.31	   f(x) -> U1(x, x)
25.19/8.31	   U1(e, x) -> x
25.19/8.31	   a -> c
25.19/8.31	   a -> d
25.19/8.31	   b -> c
25.19/8.31	   b -> d
25.19/8.31	   d -> k
25.19/8.31	   c -> e
25.19/8.31	   c -> k
25.19/8.31	
25.19/8.31	Q is empty.
25.19/8.31	We have to consider all minimal (P,Q,R)-chains.
25.19/8.31	----------------------------------------
25.19/8.31	
25.19/8.31	(199) TransformationProof (EQUIVALENT)
25.19/8.31	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.31	
25.19/8.31	   (A^2 -> H(U1(c, c), U1(c, c)),A^2 -> H(U1(c, c), U1(c, c)))
25.19/8.31	   (A^2 -> H(f(e), U1(c, c)),A^2 -> H(f(e), U1(c, c)))
25.19/8.31	   (A^2 -> H(f(k), U1(c, c)),A^2 -> H(f(k), U1(c, c)))
25.19/8.31	   (A^2 -> H(f(c), U1(e, c)),A^2 -> H(f(c), U1(e, c)))
25.19/8.31	   (A^2 -> H(f(c), U1(k, c)),A^2 -> H(f(c), U1(k, c)))
25.19/8.31	   (A^2 -> H(f(c), U1(c, e)),A^2 -> H(f(c), U1(c, e)))
25.19/8.31	   (A^2 -> H(f(c), U1(c, k)),A^2 -> H(f(c), U1(c, k)))
25.19/8.31	
25.19/8.31	
25.19/8.31	----------------------------------------
25.19/8.31	
25.19/8.31	(200)
25.19/8.31	Obligation:
25.19/8.31	Q DP problem:
25.19/8.31	The TRS P consists of the following rules:
25.19/8.31	
25.19/8.31	   H(x, x) -> G(x, x, f(k))
25.19/8.31	   G(d, x, x) -> A^2
25.19/8.31	   A^2 -> H(f(c), f(c))
25.19/8.31	   A^2 -> H(f(d), f(d))
25.19/8.31	   A^2 -> H(f(a), U1(e, c))
25.19/8.31	   A^2 -> H(f(a), U1(k, c))
25.19/8.31	   A^2 -> H(f(a), U1(c, e))
25.19/8.31	   A^2 -> H(f(a), U1(c, k))
25.19/8.31	   A^2 -> H(f(c), f(e))
25.19/8.31	   A^2 -> H(f(a), U1(e, e))
25.19/8.31	   A^2 -> H(f(a), U1(k, k))
25.19/8.31	   A^2 -> H(f(d), U1(d, d))
25.19/8.31	   A^2 -> H(f(a), U1(k, d))
25.19/8.31	   A^2 -> H(f(a), U1(d, k))
25.19/8.31	   A^2 -> H(a, f(b))
25.19/8.31	   A^2 -> H(U1(e, d), f(b))
25.19/8.31	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, a), f(c))
25.19/8.31	   A^2 -> H(U1(e, a), f(d))
25.19/8.31	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, a), f(c))
25.19/8.31	   A^2 -> H(U1(k, a), f(d))
25.19/8.31	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, d), f(c))
25.19/8.31	   A^2 -> H(U1(c, d), f(d))
25.19/8.31	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.31	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.31	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.31	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.31	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.31	   A^2 -> H(U1(c, a), f(e))
25.19/8.31	   A^2 -> H(U1(c, a), f(k))
25.19/8.31	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.31	   A^2 -> H(U1(d, e), f(b))
25.19/8.31	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(d, c), f(c))
25.19/8.31	   A^2 -> H(U1(d, c), f(d))
25.19/8.31	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.31	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.31	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.31	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.31	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.31	   A^2 -> H(U1(d, a), f(e))
25.19/8.31	   A^2 -> H(U1(d, a), f(k))
25.19/8.31	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(a, e), f(c))
25.19/8.31	   A^2 -> H(U1(a, e), f(d))
25.19/8.31	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(a, k), f(c))
25.19/8.31	   A^2 -> H(U1(a, k), f(d))
25.19/8.31	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.31	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.31	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.31	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.31	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.31	   A^2 -> H(U1(a, c), f(e))
25.19/8.31	   A^2 -> H(U1(a, c), f(k))
25.19/8.31	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.31	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.31	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.31	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.31	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.31	   A^2 -> H(U1(a, d), f(e))
25.19/8.31	   A^2 -> H(U1(a, d), f(k))
25.19/8.31	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.31	   A^2 -> H(c, f(b))
25.19/8.31	   A^2 -> H(U1(e, k), f(b))
25.19/8.31	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, c), f(c))
25.19/8.31	   A^2 -> H(U1(e, c), f(d))
25.19/8.31	   A^2 -> H(U1(k, e), f(b))
25.19/8.31	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, c), f(c))
25.19/8.31	   A^2 -> H(U1(k, c), f(d))
25.19/8.31	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, e), f(c))
25.19/8.31	   A^2 -> H(U1(c, e), f(d))
25.19/8.31	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, k), f(c))
25.19/8.31	   A^2 -> H(U1(c, k), f(d))
25.19/8.31	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.31	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.31	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.31	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.31	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.31	   A^2 -> H(U1(c, c), f(e))
25.19/8.31	   A^2 -> H(U1(c, c), f(k))
25.19/8.31	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.31	   A^2 -> H(e, f(b))
25.19/8.31	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, e), f(c))
25.19/8.31	   A^2 -> H(U1(e, e), f(d))
25.19/8.31	   A^2 -> H(f(e), U1(c, b))
25.19/8.31	   A^2 -> H(f(e), U1(d, b))
25.19/8.31	   A^2 -> H(f(e), U1(b, c))
25.19/8.31	   A^2 -> H(f(e), U1(b, d))
25.19/8.31	   A^2 -> H(f(e), U1(c, c))
25.19/8.31	   A^2 -> H(f(e), f(e))
25.19/8.31	   A^2 -> H(f(e), f(k))
25.19/8.31	   A^2 -> H(f(e), U1(d, d))
25.19/8.31	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, k), f(c))
25.19/8.31	   A^2 -> H(U1(k, k), f(d))
25.19/8.31	   A^2 -> H(f(k), U1(c, b))
25.19/8.31	   A^2 -> H(f(k), U1(d, b))
25.19/8.31	   A^2 -> H(f(k), U1(b, c))
25.19/8.31	   A^2 -> H(f(k), U1(b, d))
25.19/8.31	   A^2 -> H(f(k), U1(c, c))
25.19/8.31	   A^2 -> H(f(k), f(e))
25.19/8.31	   A^2 -> H(f(k), f(k))
25.19/8.31	   A^2 -> H(f(k), U1(d, d))
25.19/8.31	   A^2 -> H(f(c), U1(e, b))
25.19/8.31	   A^2 -> H(f(c), U1(k, b))
25.19/8.31	   A^2 -> H(f(c), U1(c, d))
25.19/8.31	   A^2 -> H(f(c), U1(d, c))
25.19/8.31	   A^2 -> H(f(c), U1(b, e))
25.19/8.31	   A^2 -> H(f(c), U1(b, k))
25.19/8.31	   A^2 -> H(f(c), U1(k, d))
25.19/8.31	   A^2 -> H(f(c), U1(d, k))
25.19/8.31	   A^2 -> H(f(c), U1(k, k))
25.19/8.31	   A^2 -> H(U1(k, k), f(b))
25.19/8.31	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, d), f(c))
25.19/8.31	   A^2 -> H(U1(k, d), f(d))
25.19/8.31	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(d, k), f(c))
25.19/8.31	   A^2 -> H(U1(d, k), f(d))
25.19/8.31	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.31	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.31	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.31	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.31	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.31	   A^2 -> H(U1(d, d), f(e))
25.19/8.31	   A^2 -> H(U1(d, d), f(k))
25.19/8.31	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.31	   A^2 -> H(f(d), U1(e, b))
25.19/8.31	   A^2 -> H(f(d), U1(k, b))
25.19/8.31	   A^2 -> H(f(d), U1(c, d))
25.19/8.31	   A^2 -> H(f(d), U1(d, c))
25.19/8.31	   A^2 -> H(f(d), U1(b, e))
25.19/8.31	   A^2 -> H(f(d), U1(b, k))
25.19/8.31	   A^2 -> H(f(d), U1(e, c))
25.19/8.31	   A^2 -> H(f(d), U1(k, c))
25.19/8.31	   A^2 -> H(f(d), U1(c, e))
25.19/8.31	   A^2 -> H(f(d), U1(c, k))
25.19/8.31	   A^2 -> H(f(d), U1(e, e))
25.19/8.31	   A^2 -> H(f(d), U1(k, k))
25.19/8.31	   A^2 -> H(f(a), b)
25.19/8.31	   A^2 -> H(f(a), U1(e, d))
25.19/8.31	   A^2 -> H(f(a), U1(d, e))
25.19/8.31	   A^2 -> H(f(c), U1(e, c))
25.19/8.31	   A^2 -> H(f(c), U1(k, c))
25.19/8.31	   A^2 -> H(f(c), U1(c, e))
25.19/8.31	   A^2 -> H(f(c), U1(c, k))
25.19/8.31	
25.19/8.31	The TRS R consists of the following rules:
25.19/8.31	
25.19/8.31	   f(x) -> U1(x, x)
25.19/8.31	   U1(e, x) -> x
25.19/8.31	   a -> c
25.19/8.31	   a -> d
25.19/8.31	   b -> c
25.19/8.31	   b -> d
25.19/8.31	   d -> k
25.19/8.31	   c -> e
25.19/8.31	   c -> k
25.19/8.31	
25.19/8.31	Q is empty.
25.19/8.31	We have to consider all minimal (P,Q,R)-chains.
25.19/8.31	----------------------------------------
25.19/8.31	
25.19/8.31	(201) TransformationProof (EQUIVALENT)
25.19/8.31	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.31	
25.19/8.31	   (A^2 -> H(U1(a, a), U1(e, c)),A^2 -> H(U1(a, a), U1(e, c)))
25.19/8.31	   (A^2 -> H(f(c), U1(e, c)),A^2 -> H(f(c), U1(e, c)))
25.19/8.31	   (A^2 -> H(f(d), U1(e, c)),A^2 -> H(f(d), U1(e, c)))
25.19/8.31	   (A^2 -> H(f(a), c),A^2 -> H(f(a), c))
25.19/8.31	   (A^2 -> H(f(a), U1(e, e)),A^2 -> H(f(a), U1(e, e)))
25.19/8.31	   (A^2 -> H(f(a), U1(e, k)),A^2 -> H(f(a), U1(e, k)))
25.19/8.31	
25.19/8.31	
25.19/8.31	----------------------------------------
25.19/8.31	
25.19/8.31	(202)
25.19/8.31	Obligation:
25.19/8.31	Q DP problem:
25.19/8.31	The TRS P consists of the following rules:
25.19/8.31	
25.19/8.31	   H(x, x) -> G(x, x, f(k))
25.19/8.31	   G(d, x, x) -> A^2
25.19/8.31	   A^2 -> H(f(c), f(c))
25.19/8.31	   A^2 -> H(f(d), f(d))
25.19/8.31	   A^2 -> H(f(a), U1(k, c))
25.19/8.31	   A^2 -> H(f(a), U1(c, e))
25.19/8.31	   A^2 -> H(f(a), U1(c, k))
25.19/8.31	   A^2 -> H(f(c), f(e))
25.19/8.31	   A^2 -> H(f(a), U1(e, e))
25.19/8.31	   A^2 -> H(f(a), U1(k, k))
25.19/8.31	   A^2 -> H(f(d), U1(d, d))
25.19/8.31	   A^2 -> H(f(a), U1(k, d))
25.19/8.31	   A^2 -> H(f(a), U1(d, k))
25.19/8.31	   A^2 -> H(a, f(b))
25.19/8.31	   A^2 -> H(U1(e, d), f(b))
25.19/8.31	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, a), f(c))
25.19/8.31	   A^2 -> H(U1(e, a), f(d))
25.19/8.31	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, a), f(c))
25.19/8.31	   A^2 -> H(U1(k, a), f(d))
25.19/8.31	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, d), f(c))
25.19/8.31	   A^2 -> H(U1(c, d), f(d))
25.19/8.31	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.31	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.31	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.31	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.31	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.31	   A^2 -> H(U1(c, a), f(e))
25.19/8.31	   A^2 -> H(U1(c, a), f(k))
25.19/8.31	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.31	   A^2 -> H(U1(d, e), f(b))
25.19/8.31	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(d, c), f(c))
25.19/8.31	   A^2 -> H(U1(d, c), f(d))
25.19/8.31	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.31	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.31	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.31	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.31	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.31	   A^2 -> H(U1(d, a), f(e))
25.19/8.31	   A^2 -> H(U1(d, a), f(k))
25.19/8.31	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(a, e), f(c))
25.19/8.31	   A^2 -> H(U1(a, e), f(d))
25.19/8.31	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(a, k), f(c))
25.19/8.31	   A^2 -> H(U1(a, k), f(d))
25.19/8.31	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.31	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.31	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.31	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.31	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.31	   A^2 -> H(U1(a, c), f(e))
25.19/8.31	   A^2 -> H(U1(a, c), f(k))
25.19/8.31	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.31	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.31	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.31	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.31	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.31	   A^2 -> H(U1(a, d), f(e))
25.19/8.31	   A^2 -> H(U1(a, d), f(k))
25.19/8.31	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.31	   A^2 -> H(c, f(b))
25.19/8.31	   A^2 -> H(U1(e, k), f(b))
25.19/8.31	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, c), f(c))
25.19/8.31	   A^2 -> H(U1(e, c), f(d))
25.19/8.31	   A^2 -> H(U1(k, e), f(b))
25.19/8.31	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, c), f(c))
25.19/8.31	   A^2 -> H(U1(k, c), f(d))
25.19/8.31	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, e), f(c))
25.19/8.31	   A^2 -> H(U1(c, e), f(d))
25.19/8.31	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, k), f(c))
25.19/8.31	   A^2 -> H(U1(c, k), f(d))
25.19/8.31	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.31	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.31	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.31	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.31	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.31	   A^2 -> H(U1(c, c), f(e))
25.19/8.31	   A^2 -> H(U1(c, c), f(k))
25.19/8.31	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.31	   A^2 -> H(e, f(b))
25.19/8.31	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, e), f(c))
25.19/8.31	   A^2 -> H(U1(e, e), f(d))
25.19/8.31	   A^2 -> H(f(e), U1(c, b))
25.19/8.31	   A^2 -> H(f(e), U1(d, b))
25.19/8.31	   A^2 -> H(f(e), U1(b, c))
25.19/8.31	   A^2 -> H(f(e), U1(b, d))
25.19/8.31	   A^2 -> H(f(e), U1(c, c))
25.19/8.31	   A^2 -> H(f(e), f(e))
25.19/8.31	   A^2 -> H(f(e), f(k))
25.19/8.31	   A^2 -> H(f(e), U1(d, d))
25.19/8.31	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, k), f(c))
25.19/8.31	   A^2 -> H(U1(k, k), f(d))
25.19/8.31	   A^2 -> H(f(k), U1(c, b))
25.19/8.31	   A^2 -> H(f(k), U1(d, b))
25.19/8.31	   A^2 -> H(f(k), U1(b, c))
25.19/8.31	   A^2 -> H(f(k), U1(b, d))
25.19/8.31	   A^2 -> H(f(k), U1(c, c))
25.19/8.31	   A^2 -> H(f(k), f(e))
25.19/8.31	   A^2 -> H(f(k), f(k))
25.19/8.31	   A^2 -> H(f(k), U1(d, d))
25.19/8.31	   A^2 -> H(f(c), U1(e, b))
25.19/8.31	   A^2 -> H(f(c), U1(k, b))
25.19/8.31	   A^2 -> H(f(c), U1(c, d))
25.19/8.31	   A^2 -> H(f(c), U1(d, c))
25.19/8.31	   A^2 -> H(f(c), U1(b, e))
25.19/8.31	   A^2 -> H(f(c), U1(b, k))
25.19/8.31	   A^2 -> H(f(c), U1(k, d))
25.19/8.31	   A^2 -> H(f(c), U1(d, k))
25.19/8.31	   A^2 -> H(f(c), U1(k, k))
25.19/8.31	   A^2 -> H(U1(k, k), f(b))
25.19/8.31	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, d), f(c))
25.19/8.31	   A^2 -> H(U1(k, d), f(d))
25.19/8.31	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(d, k), f(c))
25.19/8.31	   A^2 -> H(U1(d, k), f(d))
25.19/8.31	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.31	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.31	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.31	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.31	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.31	   A^2 -> H(U1(d, d), f(e))
25.19/8.31	   A^2 -> H(U1(d, d), f(k))
25.19/8.31	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.31	   A^2 -> H(f(d), U1(e, b))
25.19/8.31	   A^2 -> H(f(d), U1(k, b))
25.19/8.31	   A^2 -> H(f(d), U1(c, d))
25.19/8.31	   A^2 -> H(f(d), U1(d, c))
25.19/8.31	   A^2 -> H(f(d), U1(b, e))
25.19/8.31	   A^2 -> H(f(d), U1(b, k))
25.19/8.31	   A^2 -> H(f(d), U1(e, c))
25.19/8.31	   A^2 -> H(f(d), U1(k, c))
25.19/8.31	   A^2 -> H(f(d), U1(c, e))
25.19/8.31	   A^2 -> H(f(d), U1(c, k))
25.19/8.31	   A^2 -> H(f(d), U1(e, e))
25.19/8.31	   A^2 -> H(f(d), U1(k, k))
25.19/8.31	   A^2 -> H(f(a), b)
25.19/8.31	   A^2 -> H(f(a), U1(e, d))
25.19/8.31	   A^2 -> H(f(a), U1(d, e))
25.19/8.31	   A^2 -> H(f(c), U1(e, c))
25.19/8.31	   A^2 -> H(f(c), U1(k, c))
25.19/8.31	   A^2 -> H(f(c), U1(c, e))
25.19/8.31	   A^2 -> H(f(c), U1(c, k))
25.19/8.31	   A^2 -> H(f(a), c)
25.19/8.31	   A^2 -> H(f(a), U1(e, k))
25.19/8.31	
25.19/8.31	The TRS R consists of the following rules:
25.19/8.31	
25.19/8.31	   f(x) -> U1(x, x)
25.19/8.31	   U1(e, x) -> x
25.19/8.31	   a -> c
25.19/8.31	   a -> d
25.19/8.31	   b -> c
25.19/8.31	   b -> d
25.19/8.31	   d -> k
25.19/8.31	   c -> e
25.19/8.31	   c -> k
25.19/8.31	
25.19/8.31	Q is empty.
25.19/8.31	We have to consider all minimal (P,Q,R)-chains.
25.19/8.31	----------------------------------------
25.19/8.31	
25.19/8.31	(203) TransformationProof (EQUIVALENT)
25.19/8.31	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.31	
25.19/8.31	   (A^2 -> H(U1(a, a), U1(k, c)),A^2 -> H(U1(a, a), U1(k, c)))
25.19/8.31	   (A^2 -> H(f(c), U1(k, c)),A^2 -> H(f(c), U1(k, c)))
25.19/8.31	   (A^2 -> H(f(d), U1(k, c)),A^2 -> H(f(d), U1(k, c)))
25.19/8.31	   (A^2 -> H(f(a), U1(k, e)),A^2 -> H(f(a), U1(k, e)))
25.19/8.31	   (A^2 -> H(f(a), U1(k, k)),A^2 -> H(f(a), U1(k, k)))
25.19/8.31	
25.19/8.31	
25.19/8.31	----------------------------------------
25.19/8.31	
25.19/8.31	(204)
25.19/8.31	Obligation:
25.19/8.31	Q DP problem:
25.19/8.31	The TRS P consists of the following rules:
25.19/8.31	
25.19/8.31	   H(x, x) -> G(x, x, f(k))
25.19/8.31	   G(d, x, x) -> A^2
25.19/8.31	   A^2 -> H(f(c), f(c))
25.19/8.31	   A^2 -> H(f(d), f(d))
25.19/8.31	   A^2 -> H(f(a), U1(c, e))
25.19/8.31	   A^2 -> H(f(a), U1(c, k))
25.19/8.31	   A^2 -> H(f(c), f(e))
25.19/8.31	   A^2 -> H(f(a), U1(e, e))
25.19/8.31	   A^2 -> H(f(a), U1(k, k))
25.19/8.31	   A^2 -> H(f(d), U1(d, d))
25.19/8.31	   A^2 -> H(f(a), U1(k, d))
25.19/8.31	   A^2 -> H(f(a), U1(d, k))
25.19/8.31	   A^2 -> H(a, f(b))
25.19/8.31	   A^2 -> H(U1(e, d), f(b))
25.19/8.31	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, a), f(c))
25.19/8.31	   A^2 -> H(U1(e, a), f(d))
25.19/8.31	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, a), f(c))
25.19/8.31	   A^2 -> H(U1(k, a), f(d))
25.19/8.31	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, d), f(c))
25.19/8.31	   A^2 -> H(U1(c, d), f(d))
25.19/8.31	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.31	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.31	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.31	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.31	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.31	   A^2 -> H(U1(c, a), f(e))
25.19/8.31	   A^2 -> H(U1(c, a), f(k))
25.19/8.31	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.31	   A^2 -> H(U1(d, e), f(b))
25.19/8.31	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(d, c), f(c))
25.19/8.31	   A^2 -> H(U1(d, c), f(d))
25.19/8.31	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.31	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.31	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.31	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.31	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.31	   A^2 -> H(U1(d, a), f(e))
25.19/8.31	   A^2 -> H(U1(d, a), f(k))
25.19/8.31	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(a, e), f(c))
25.19/8.31	   A^2 -> H(U1(a, e), f(d))
25.19/8.31	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(a, k), f(c))
25.19/8.31	   A^2 -> H(U1(a, k), f(d))
25.19/8.31	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.31	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.31	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.31	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.31	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.31	   A^2 -> H(U1(a, c), f(e))
25.19/8.31	   A^2 -> H(U1(a, c), f(k))
25.19/8.31	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.31	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.31	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.31	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.31	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.31	   A^2 -> H(U1(a, d), f(e))
25.19/8.31	   A^2 -> H(U1(a, d), f(k))
25.19/8.31	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.31	   A^2 -> H(c, f(b))
25.19/8.31	   A^2 -> H(U1(e, k), f(b))
25.19/8.31	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, c), f(c))
25.19/8.31	   A^2 -> H(U1(e, c), f(d))
25.19/8.31	   A^2 -> H(U1(k, e), f(b))
25.19/8.31	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, c), f(c))
25.19/8.31	   A^2 -> H(U1(k, c), f(d))
25.19/8.31	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, e), f(c))
25.19/8.31	   A^2 -> H(U1(c, e), f(d))
25.19/8.31	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, k), f(c))
25.19/8.31	   A^2 -> H(U1(c, k), f(d))
25.19/8.31	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.31	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.31	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.31	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.31	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.31	   A^2 -> H(U1(c, c), f(e))
25.19/8.31	   A^2 -> H(U1(c, c), f(k))
25.19/8.31	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.31	   A^2 -> H(e, f(b))
25.19/8.31	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, e), f(c))
25.19/8.31	   A^2 -> H(U1(e, e), f(d))
25.19/8.31	   A^2 -> H(f(e), U1(c, b))
25.19/8.31	   A^2 -> H(f(e), U1(d, b))
25.19/8.31	   A^2 -> H(f(e), U1(b, c))
25.19/8.31	   A^2 -> H(f(e), U1(b, d))
25.19/8.31	   A^2 -> H(f(e), U1(c, c))
25.19/8.31	   A^2 -> H(f(e), f(e))
25.19/8.31	   A^2 -> H(f(e), f(k))
25.19/8.31	   A^2 -> H(f(e), U1(d, d))
25.19/8.31	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, k), f(c))
25.19/8.31	   A^2 -> H(U1(k, k), f(d))
25.19/8.31	   A^2 -> H(f(k), U1(c, b))
25.19/8.31	   A^2 -> H(f(k), U1(d, b))
25.19/8.31	   A^2 -> H(f(k), U1(b, c))
25.19/8.31	   A^2 -> H(f(k), U1(b, d))
25.19/8.31	   A^2 -> H(f(k), U1(c, c))
25.19/8.31	   A^2 -> H(f(k), f(e))
25.19/8.31	   A^2 -> H(f(k), f(k))
25.19/8.31	   A^2 -> H(f(k), U1(d, d))
25.19/8.31	   A^2 -> H(f(c), U1(e, b))
25.19/8.31	   A^2 -> H(f(c), U1(k, b))
25.19/8.31	   A^2 -> H(f(c), U1(c, d))
25.19/8.31	   A^2 -> H(f(c), U1(d, c))
25.19/8.31	   A^2 -> H(f(c), U1(b, e))
25.19/8.31	   A^2 -> H(f(c), U1(b, k))
25.19/8.31	   A^2 -> H(f(c), U1(k, d))
25.19/8.31	   A^2 -> H(f(c), U1(d, k))
25.19/8.31	   A^2 -> H(f(c), U1(k, k))
25.19/8.31	   A^2 -> H(U1(k, k), f(b))
25.19/8.31	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, d), f(c))
25.19/8.31	   A^2 -> H(U1(k, d), f(d))
25.19/8.31	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(d, k), f(c))
25.19/8.31	   A^2 -> H(U1(d, k), f(d))
25.19/8.31	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.31	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.31	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.31	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.31	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.31	   A^2 -> H(U1(d, d), f(e))
25.19/8.31	   A^2 -> H(U1(d, d), f(k))
25.19/8.31	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.31	   A^2 -> H(f(d), U1(e, b))
25.19/8.31	   A^2 -> H(f(d), U1(k, b))
25.19/8.31	   A^2 -> H(f(d), U1(c, d))
25.19/8.31	   A^2 -> H(f(d), U1(d, c))
25.19/8.31	   A^2 -> H(f(d), U1(b, e))
25.19/8.31	   A^2 -> H(f(d), U1(b, k))
25.19/8.31	   A^2 -> H(f(d), U1(e, c))
25.19/8.31	   A^2 -> H(f(d), U1(k, c))
25.19/8.31	   A^2 -> H(f(d), U1(c, e))
25.19/8.31	   A^2 -> H(f(d), U1(c, k))
25.19/8.31	   A^2 -> H(f(d), U1(e, e))
25.19/8.31	   A^2 -> H(f(d), U1(k, k))
25.19/8.31	   A^2 -> H(f(a), b)
25.19/8.31	   A^2 -> H(f(a), U1(e, d))
25.19/8.31	   A^2 -> H(f(a), U1(d, e))
25.19/8.31	   A^2 -> H(f(c), U1(e, c))
25.19/8.31	   A^2 -> H(f(c), U1(k, c))
25.19/8.31	   A^2 -> H(f(c), U1(c, e))
25.19/8.31	   A^2 -> H(f(c), U1(c, k))
25.19/8.31	   A^2 -> H(f(a), c)
25.19/8.31	   A^2 -> H(f(a), U1(e, k))
25.19/8.31	   A^2 -> H(f(a), U1(k, e))
25.19/8.31	
25.19/8.31	The TRS R consists of the following rules:
25.19/8.31	
25.19/8.31	   f(x) -> U1(x, x)
25.19/8.31	   U1(e, x) -> x
25.19/8.31	   a -> c
25.19/8.31	   a -> d
25.19/8.31	   b -> c
25.19/8.31	   b -> d
25.19/8.31	   d -> k
25.19/8.31	   c -> e
25.19/8.31	   c -> k
25.19/8.31	
25.19/8.31	Q is empty.
25.19/8.31	We have to consider all minimal (P,Q,R)-chains.
25.19/8.31	----------------------------------------
25.19/8.31	
25.19/8.31	(205) TransformationProof (EQUIVALENT)
25.19/8.31	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.31	
25.19/8.31	   (A^2 -> H(U1(a, a), U1(c, e)),A^2 -> H(U1(a, a), U1(c, e)))
25.19/8.31	   (A^2 -> H(f(c), U1(c, e)),A^2 -> H(f(c), U1(c, e)))
25.19/8.31	   (A^2 -> H(f(d), U1(c, e)),A^2 -> H(f(d), U1(c, e)))
25.19/8.31	   (A^2 -> H(f(a), U1(e, e)),A^2 -> H(f(a), U1(e, e)))
25.19/8.31	   (A^2 -> H(f(a), U1(k, e)),A^2 -> H(f(a), U1(k, e)))
25.19/8.31	
25.19/8.31	
25.19/8.31	----------------------------------------
25.19/8.31	
25.19/8.31	(206)
25.19/8.31	Obligation:
25.19/8.31	Q DP problem:
25.19/8.31	The TRS P consists of the following rules:
25.19/8.31	
25.19/8.31	   H(x, x) -> G(x, x, f(k))
25.19/8.31	   G(d, x, x) -> A^2
25.19/8.31	   A^2 -> H(f(c), f(c))
25.19/8.31	   A^2 -> H(f(d), f(d))
25.19/8.31	   A^2 -> H(f(a), U1(c, k))
25.19/8.31	   A^2 -> H(f(c), f(e))
25.19/8.31	   A^2 -> H(f(a), U1(e, e))
25.19/8.31	   A^2 -> H(f(a), U1(k, k))
25.19/8.31	   A^2 -> H(f(d), U1(d, d))
25.19/8.31	   A^2 -> H(f(a), U1(k, d))
25.19/8.31	   A^2 -> H(f(a), U1(d, k))
25.19/8.31	   A^2 -> H(a, f(b))
25.19/8.31	   A^2 -> H(U1(e, d), f(b))
25.19/8.31	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, a), f(c))
25.19/8.31	   A^2 -> H(U1(e, a), f(d))
25.19/8.31	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, a), f(c))
25.19/8.31	   A^2 -> H(U1(k, a), f(d))
25.19/8.31	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, d), f(c))
25.19/8.31	   A^2 -> H(U1(c, d), f(d))
25.19/8.31	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.31	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.31	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.31	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.31	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.31	   A^2 -> H(U1(c, a), f(e))
25.19/8.31	   A^2 -> H(U1(c, a), f(k))
25.19/8.31	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.31	   A^2 -> H(U1(d, e), f(b))
25.19/8.31	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(d, c), f(c))
25.19/8.31	   A^2 -> H(U1(d, c), f(d))
25.19/8.31	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.31	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.31	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.31	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.31	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.31	   A^2 -> H(U1(d, a), f(e))
25.19/8.31	   A^2 -> H(U1(d, a), f(k))
25.19/8.31	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(a, e), f(c))
25.19/8.31	   A^2 -> H(U1(a, e), f(d))
25.19/8.31	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(a, k), f(c))
25.19/8.31	   A^2 -> H(U1(a, k), f(d))
25.19/8.31	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.31	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.31	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.31	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.31	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.31	   A^2 -> H(U1(a, c), f(e))
25.19/8.31	   A^2 -> H(U1(a, c), f(k))
25.19/8.31	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.31	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.31	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.31	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.31	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.31	   A^2 -> H(U1(a, d), f(e))
25.19/8.31	   A^2 -> H(U1(a, d), f(k))
25.19/8.31	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.31	   A^2 -> H(c, f(b))
25.19/8.31	   A^2 -> H(U1(e, k), f(b))
25.19/8.31	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, c), f(c))
25.19/8.31	   A^2 -> H(U1(e, c), f(d))
25.19/8.31	   A^2 -> H(U1(k, e), f(b))
25.19/8.31	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, c), f(c))
25.19/8.31	   A^2 -> H(U1(k, c), f(d))
25.19/8.31	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, e), f(c))
25.19/8.31	   A^2 -> H(U1(c, e), f(d))
25.19/8.31	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, k), f(c))
25.19/8.31	   A^2 -> H(U1(c, k), f(d))
25.19/8.31	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.31	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.31	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.31	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.31	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.31	   A^2 -> H(U1(c, c), f(e))
25.19/8.31	   A^2 -> H(U1(c, c), f(k))
25.19/8.31	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.31	   A^2 -> H(e, f(b))
25.19/8.31	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, e), f(c))
25.19/8.31	   A^2 -> H(U1(e, e), f(d))
25.19/8.31	   A^2 -> H(f(e), U1(c, b))
25.19/8.31	   A^2 -> H(f(e), U1(d, b))
25.19/8.31	   A^2 -> H(f(e), U1(b, c))
25.19/8.31	   A^2 -> H(f(e), U1(b, d))
25.19/8.31	   A^2 -> H(f(e), U1(c, c))
25.19/8.31	   A^2 -> H(f(e), f(e))
25.19/8.31	   A^2 -> H(f(e), f(k))
25.19/8.31	   A^2 -> H(f(e), U1(d, d))
25.19/8.31	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, k), f(c))
25.19/8.31	   A^2 -> H(U1(k, k), f(d))
25.19/8.31	   A^2 -> H(f(k), U1(c, b))
25.19/8.31	   A^2 -> H(f(k), U1(d, b))
25.19/8.31	   A^2 -> H(f(k), U1(b, c))
25.19/8.31	   A^2 -> H(f(k), U1(b, d))
25.19/8.31	   A^2 -> H(f(k), U1(c, c))
25.19/8.31	   A^2 -> H(f(k), f(e))
25.19/8.31	   A^2 -> H(f(k), f(k))
25.19/8.31	   A^2 -> H(f(k), U1(d, d))
25.19/8.31	   A^2 -> H(f(c), U1(e, b))
25.19/8.31	   A^2 -> H(f(c), U1(k, b))
25.19/8.31	   A^2 -> H(f(c), U1(c, d))
25.19/8.31	   A^2 -> H(f(c), U1(d, c))
25.19/8.31	   A^2 -> H(f(c), U1(b, e))
25.19/8.31	   A^2 -> H(f(c), U1(b, k))
25.19/8.31	   A^2 -> H(f(c), U1(k, d))
25.19/8.31	   A^2 -> H(f(c), U1(d, k))
25.19/8.31	   A^2 -> H(f(c), U1(k, k))
25.19/8.31	   A^2 -> H(U1(k, k), f(b))
25.19/8.31	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, d), f(c))
25.19/8.31	   A^2 -> H(U1(k, d), f(d))
25.19/8.31	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(d, k), f(c))
25.19/8.31	   A^2 -> H(U1(d, k), f(d))
25.19/8.31	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.31	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.31	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.31	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.31	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.31	   A^2 -> H(U1(d, d), f(e))
25.19/8.31	   A^2 -> H(U1(d, d), f(k))
25.19/8.31	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.31	   A^2 -> H(f(d), U1(e, b))
25.19/8.31	   A^2 -> H(f(d), U1(k, b))
25.19/8.31	   A^2 -> H(f(d), U1(c, d))
25.19/8.31	   A^2 -> H(f(d), U1(d, c))
25.19/8.31	   A^2 -> H(f(d), U1(b, e))
25.19/8.31	   A^2 -> H(f(d), U1(b, k))
25.19/8.31	   A^2 -> H(f(d), U1(e, c))
25.19/8.31	   A^2 -> H(f(d), U1(k, c))
25.19/8.31	   A^2 -> H(f(d), U1(c, e))
25.19/8.31	   A^2 -> H(f(d), U1(c, k))
25.19/8.31	   A^2 -> H(f(d), U1(e, e))
25.19/8.31	   A^2 -> H(f(d), U1(k, k))
25.19/8.31	   A^2 -> H(f(a), b)
25.19/8.31	   A^2 -> H(f(a), U1(e, d))
25.19/8.31	   A^2 -> H(f(a), U1(d, e))
25.19/8.31	   A^2 -> H(f(c), U1(e, c))
25.19/8.31	   A^2 -> H(f(c), U1(k, c))
25.19/8.31	   A^2 -> H(f(c), U1(c, e))
25.19/8.31	   A^2 -> H(f(c), U1(c, k))
25.19/8.31	   A^2 -> H(f(a), c)
25.19/8.31	   A^2 -> H(f(a), U1(e, k))
25.19/8.31	   A^2 -> H(f(a), U1(k, e))
25.19/8.31	
25.19/8.31	The TRS R consists of the following rules:
25.19/8.31	
25.19/8.31	   f(x) -> U1(x, x)
25.19/8.31	   U1(e, x) -> x
25.19/8.31	   a -> c
25.19/8.31	   a -> d
25.19/8.31	   b -> c
25.19/8.31	   b -> d
25.19/8.31	   d -> k
25.19/8.31	   c -> e
25.19/8.31	   c -> k
25.19/8.31	
25.19/8.31	Q is empty.
25.19/8.31	We have to consider all minimal (P,Q,R)-chains.
25.19/8.31	----------------------------------------
25.19/8.31	
25.19/8.31	(207) TransformationProof (EQUIVALENT)
25.19/8.31	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.31	
25.19/8.31	   (A^2 -> H(U1(a, a), U1(c, k)),A^2 -> H(U1(a, a), U1(c, k)))
25.19/8.31	   (A^2 -> H(f(c), U1(c, k)),A^2 -> H(f(c), U1(c, k)))
25.19/8.31	   (A^2 -> H(f(d), U1(c, k)),A^2 -> H(f(d), U1(c, k)))
25.19/8.31	   (A^2 -> H(f(a), U1(e, k)),A^2 -> H(f(a), U1(e, k)))
25.19/8.31	   (A^2 -> H(f(a), U1(k, k)),A^2 -> H(f(a), U1(k, k)))
25.19/8.31	
25.19/8.31	
25.19/8.31	----------------------------------------
25.19/8.31	
25.19/8.31	(208)
25.19/8.31	Obligation:
25.19/8.31	Q DP problem:
25.19/8.31	The TRS P consists of the following rules:
25.19/8.31	
25.19/8.31	   H(x, x) -> G(x, x, f(k))
25.19/8.31	   G(d, x, x) -> A^2
25.19/8.31	   A^2 -> H(f(c), f(c))
25.19/8.31	   A^2 -> H(f(d), f(d))
25.19/8.31	   A^2 -> H(f(c), f(e))
25.19/8.31	   A^2 -> H(f(a), U1(e, e))
25.19/8.31	   A^2 -> H(f(a), U1(k, k))
25.19/8.31	   A^2 -> H(f(d), U1(d, d))
25.19/8.31	   A^2 -> H(f(a), U1(k, d))
25.19/8.31	   A^2 -> H(f(a), U1(d, k))
25.19/8.31	   A^2 -> H(a, f(b))
25.19/8.31	   A^2 -> H(U1(e, d), f(b))
25.19/8.31	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, a), f(c))
25.19/8.31	   A^2 -> H(U1(e, a), f(d))
25.19/8.31	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, a), f(c))
25.19/8.31	   A^2 -> H(U1(k, a), f(d))
25.19/8.31	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, d), f(c))
25.19/8.31	   A^2 -> H(U1(c, d), f(d))
25.19/8.31	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.31	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.31	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.31	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.31	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.31	   A^2 -> H(U1(c, a), f(e))
25.19/8.31	   A^2 -> H(U1(c, a), f(k))
25.19/8.31	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.31	   A^2 -> H(U1(d, e), f(b))
25.19/8.31	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(d, c), f(c))
25.19/8.31	   A^2 -> H(U1(d, c), f(d))
25.19/8.31	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.31	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.31	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.31	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.31	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.31	   A^2 -> H(U1(d, a), f(e))
25.19/8.31	   A^2 -> H(U1(d, a), f(k))
25.19/8.31	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(a, e), f(c))
25.19/8.31	   A^2 -> H(U1(a, e), f(d))
25.19/8.31	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(a, k), f(c))
25.19/8.31	   A^2 -> H(U1(a, k), f(d))
25.19/8.31	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.31	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.31	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.31	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.31	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.31	   A^2 -> H(U1(a, c), f(e))
25.19/8.31	   A^2 -> H(U1(a, c), f(k))
25.19/8.31	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.31	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.31	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.31	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.31	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.31	   A^2 -> H(U1(a, d), f(e))
25.19/8.31	   A^2 -> H(U1(a, d), f(k))
25.19/8.31	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.31	   A^2 -> H(c, f(b))
25.19/8.31	   A^2 -> H(U1(e, k), f(b))
25.19/8.31	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, c), f(c))
25.19/8.31	   A^2 -> H(U1(e, c), f(d))
25.19/8.31	   A^2 -> H(U1(k, e), f(b))
25.19/8.31	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, c), f(c))
25.19/8.31	   A^2 -> H(U1(k, c), f(d))
25.19/8.31	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, e), f(c))
25.19/8.31	   A^2 -> H(U1(c, e), f(d))
25.19/8.31	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, k), f(c))
25.19/8.31	   A^2 -> H(U1(c, k), f(d))
25.19/8.31	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.31	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.31	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.31	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.31	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.31	   A^2 -> H(U1(c, c), f(e))
25.19/8.31	   A^2 -> H(U1(c, c), f(k))
25.19/8.31	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.31	   A^2 -> H(e, f(b))
25.19/8.31	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, e), f(c))
25.19/8.31	   A^2 -> H(U1(e, e), f(d))
25.19/8.31	   A^2 -> H(f(e), U1(c, b))
25.19/8.31	   A^2 -> H(f(e), U1(d, b))
25.19/8.31	   A^2 -> H(f(e), U1(b, c))
25.19/8.31	   A^2 -> H(f(e), U1(b, d))
25.19/8.31	   A^2 -> H(f(e), U1(c, c))
25.19/8.31	   A^2 -> H(f(e), f(e))
25.19/8.31	   A^2 -> H(f(e), f(k))
25.19/8.31	   A^2 -> H(f(e), U1(d, d))
25.19/8.31	   A^2 -> H(U1(k, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, k), f(c))
25.19/8.31	   A^2 -> H(U1(k, k), f(d))
25.19/8.31	   A^2 -> H(f(k), U1(c, b))
25.19/8.31	   A^2 -> H(f(k), U1(d, b))
25.19/8.31	   A^2 -> H(f(k), U1(b, c))
25.19/8.31	   A^2 -> H(f(k), U1(b, d))
25.19/8.31	   A^2 -> H(f(k), U1(c, c))
25.19/8.31	   A^2 -> H(f(k), f(e))
25.19/8.31	   A^2 -> H(f(k), f(k))
25.19/8.31	   A^2 -> H(f(k), U1(d, d))
25.19/8.31	   A^2 -> H(f(c), U1(e, b))
25.19/8.31	   A^2 -> H(f(c), U1(k, b))
25.19/8.31	   A^2 -> H(f(c), U1(c, d))
25.19/8.31	   A^2 -> H(f(c), U1(d, c))
25.19/8.31	   A^2 -> H(f(c), U1(b, e))
25.19/8.31	   A^2 -> H(f(c), U1(b, k))
25.19/8.31	   A^2 -> H(f(c), U1(k, d))
25.19/8.31	   A^2 -> H(f(c), U1(d, k))
25.19/8.31	   A^2 -> H(f(c), U1(k, k))
25.19/8.31	   A^2 -> H(U1(k, k), f(b))
25.19/8.31	   A^2 -> H(U1(k, d), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, d), f(c))
25.19/8.31	   A^2 -> H(U1(k, d), f(d))
25.19/8.31	   A^2 -> H(U1(d, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(d, k), f(c))
25.19/8.31	   A^2 -> H(U1(d, k), f(d))
25.19/8.31	   A^2 -> H(U1(d, d), U1(c, b))
25.19/8.31	   A^2 -> H(U1(d, d), U1(d, b))
25.19/8.31	   A^2 -> H(U1(d, d), U1(b, c))
25.19/8.31	   A^2 -> H(U1(d, d), U1(b, d))
25.19/8.31	   A^2 -> H(U1(d, d), U1(c, c))
25.19/8.31	   A^2 -> H(U1(d, d), f(e))
25.19/8.31	   A^2 -> H(U1(d, d), f(k))
25.19/8.31	   A^2 -> H(U1(d, d), U1(d, d))
25.19/8.31	   A^2 -> H(f(d), U1(e, b))
25.19/8.31	   A^2 -> H(f(d), U1(k, b))
25.19/8.31	   A^2 -> H(f(d), U1(c, d))
25.19/8.31	   A^2 -> H(f(d), U1(d, c))
25.19/8.31	   A^2 -> H(f(d), U1(b, e))
25.19/8.31	   A^2 -> H(f(d), U1(b, k))
25.19/8.31	   A^2 -> H(f(d), U1(e, c))
25.19/8.31	   A^2 -> H(f(d), U1(k, c))
25.19/8.31	   A^2 -> H(f(d), U1(c, e))
25.19/8.31	   A^2 -> H(f(d), U1(c, k))
25.19/8.31	   A^2 -> H(f(d), U1(e, e))
25.19/8.31	   A^2 -> H(f(d), U1(k, k))
25.19/8.31	   A^2 -> H(f(a), b)
25.19/8.31	   A^2 -> H(f(a), U1(e, d))
25.19/8.31	   A^2 -> H(f(a), U1(d, e))
25.19/8.31	   A^2 -> H(f(c), U1(e, c))
25.19/8.31	   A^2 -> H(f(c), U1(k, c))
25.19/8.31	   A^2 -> H(f(c), U1(c, e))
25.19/8.31	   A^2 -> H(f(c), U1(c, k))
25.19/8.31	   A^2 -> H(f(a), c)
25.19/8.31	   A^2 -> H(f(a), U1(e, k))
25.19/8.31	   A^2 -> H(f(a), U1(k, e))
25.19/8.31	
25.19/8.31	The TRS R consists of the following rules:
25.19/8.31	
25.19/8.31	   f(x) -> U1(x, x)
25.19/8.31	   U1(e, x) -> x
25.19/8.31	   a -> c
25.19/8.31	   a -> d
25.19/8.31	   b -> c
25.19/8.31	   b -> d
25.19/8.31	   d -> k
25.19/8.31	   c -> e
25.19/8.31	   c -> k
25.19/8.31	
25.19/8.31	Q is empty.
25.19/8.31	We have to consider all minimal (P,Q,R)-chains.
25.19/8.31	----------------------------------------
25.19/8.31	
25.19/8.31	(209) TransformationProof (EQUIVALENT)
25.19/8.31	By narrowing [LPAR04] the rule A^2 -> H(f(c), f(e)) at position [] we obtained the following new rules [LPAR04]:
25.19/8.31	
25.19/8.31	   (A^2 -> H(U1(c, c), f(e)),A^2 -> H(U1(c, c), f(e)))
25.19/8.31	   (A^2 -> H(f(e), f(e)),A^2 -> H(f(e), f(e)))
25.19/8.31	   (A^2 -> H(f(k), f(e)),A^2 -> H(f(k), f(e)))
25.19/8.31	   (A^2 -> H(f(c), U1(e, e)),A^2 -> H(f(c), U1(e, e)))
25.19/8.31	
25.19/8.31	
25.19/8.31	----------------------------------------
25.19/8.31	
25.19/8.31	(210)
25.19/8.31	Obligation:
25.19/8.31	Q DP problem:
25.19/8.31	The TRS P consists of the following rules:
25.19/8.31	
25.19/8.31	   H(x, x) -> G(x, x, f(k))
25.19/8.31	   G(d, x, x) -> A^2
25.19/8.31	   A^2 -> H(f(c), f(c))
25.19/8.31	   A^2 -> H(f(d), f(d))
25.19/8.31	   A^2 -> H(f(a), U1(e, e))
25.19/8.31	   A^2 -> H(f(a), U1(k, k))
25.19/8.31	   A^2 -> H(f(d), U1(d, d))
25.19/8.31	   A^2 -> H(f(a), U1(k, d))
25.19/8.31	   A^2 -> H(f(a), U1(d, k))
25.19/8.31	   A^2 -> H(a, f(b))
25.19/8.31	   A^2 -> H(U1(e, d), f(b))
25.19/8.31	   A^2 -> H(U1(e, a), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, a), f(c))
25.19/8.31	   A^2 -> H(U1(e, a), f(d))
25.19/8.31	   A^2 -> H(U1(k, a), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, a), f(c))
25.19/8.31	   A^2 -> H(U1(k, a), f(d))
25.19/8.31	   A^2 -> H(U1(c, d), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, d), f(c))
25.19/8.31	   A^2 -> H(U1(c, d), f(d))
25.19/8.31	   A^2 -> H(U1(c, a), U1(c, b))
25.19/8.31	   A^2 -> H(U1(c, a), U1(d, b))
25.19/8.31	   A^2 -> H(U1(c, a), U1(b, c))
25.19/8.31	   A^2 -> H(U1(c, a), U1(b, d))
25.19/8.31	   A^2 -> H(U1(c, a), U1(c, c))
25.19/8.31	   A^2 -> H(U1(c, a), f(e))
25.19/8.31	   A^2 -> H(U1(c, a), f(k))
25.19/8.31	   A^2 -> H(U1(c, a), U1(d, d))
25.19/8.31	   A^2 -> H(U1(d, e), f(b))
25.19/8.31	   A^2 -> H(U1(d, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(d, c), f(c))
25.19/8.31	   A^2 -> H(U1(d, c), f(d))
25.19/8.31	   A^2 -> H(U1(d, a), U1(c, b))
25.19/8.31	   A^2 -> H(U1(d, a), U1(d, b))
25.19/8.31	   A^2 -> H(U1(d, a), U1(b, c))
25.19/8.31	   A^2 -> H(U1(d, a), U1(b, d))
25.19/8.31	   A^2 -> H(U1(d, a), U1(c, c))
25.19/8.31	   A^2 -> H(U1(d, a), f(e))
25.19/8.31	   A^2 -> H(U1(d, a), f(k))
25.19/8.31	   A^2 -> H(U1(d, a), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(a, e), f(c))
25.19/8.31	   A^2 -> H(U1(a, e), f(d))
25.19/8.31	   A^2 -> H(U1(a, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(a, k), f(c))
25.19/8.31	   A^2 -> H(U1(a, k), f(d))
25.19/8.31	   A^2 -> H(U1(a, c), U1(c, b))
25.19/8.31	   A^2 -> H(U1(a, c), U1(d, b))
25.19/8.31	   A^2 -> H(U1(a, c), U1(b, c))
25.19/8.31	   A^2 -> H(U1(a, c), U1(b, d))
25.19/8.31	   A^2 -> H(U1(a, c), U1(c, c))
25.19/8.31	   A^2 -> H(U1(a, c), f(e))
25.19/8.31	   A^2 -> H(U1(a, c), f(k))
25.19/8.31	   A^2 -> H(U1(a, c), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, d), U1(c, b))
25.19/8.31	   A^2 -> H(U1(a, d), U1(d, b))
25.19/8.31	   A^2 -> H(U1(a, d), U1(b, c))
25.19/8.31	   A^2 -> H(U1(a, d), U1(b, d))
25.19/8.31	   A^2 -> H(U1(a, d), U1(c, c))
25.19/8.31	   A^2 -> H(U1(a, d), f(e))
25.19/8.31	   A^2 -> H(U1(a, d), f(k))
25.19/8.31	   A^2 -> H(U1(a, d), U1(d, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, b))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, b))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(d, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(b, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(b, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, c))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(c, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(e, e))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, k))
25.19/8.31	   A^2 -> H(U1(a, a), U1(k, d))
25.19/8.31	   A^2 -> H(U1(a, a), U1(d, k))
25.19/8.31	   A^2 -> H(c, f(b))
25.19/8.31	   A^2 -> H(U1(e, k), f(b))
25.19/8.31	   A^2 -> H(U1(e, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, c), f(c))
25.19/8.31	   A^2 -> H(U1(e, c), f(d))
25.19/8.31	   A^2 -> H(U1(k, e), f(b))
25.19/8.31	   A^2 -> H(U1(k, c), U1(b, b))
25.19/8.31	   A^2 -> H(U1(k, c), f(c))
25.19/8.31	   A^2 -> H(U1(k, c), f(d))
25.19/8.31	   A^2 -> H(U1(c, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, e), f(c))
25.19/8.31	   A^2 -> H(U1(c, e), f(d))
25.19/8.31	   A^2 -> H(U1(c, k), U1(b, b))
25.19/8.31	   A^2 -> H(U1(c, k), f(c))
25.19/8.31	   A^2 -> H(U1(c, k), f(d))
25.19/8.31	   A^2 -> H(U1(c, c), U1(c, b))
25.19/8.31	   A^2 -> H(U1(c, c), U1(d, b))
25.19/8.31	   A^2 -> H(U1(c, c), U1(b, c))
25.19/8.31	   A^2 -> H(U1(c, c), U1(b, d))
25.19/8.31	   A^2 -> H(U1(c, c), U1(c, c))
25.19/8.31	   A^2 -> H(U1(c, c), f(e))
25.19/8.31	   A^2 -> H(U1(c, c), f(k))
25.19/8.31	   A^2 -> H(U1(c, c), U1(d, d))
25.19/8.31	   A^2 -> H(e, f(b))
25.19/8.31	   A^2 -> H(U1(e, e), U1(b, b))
25.19/8.31	   A^2 -> H(U1(e, e), f(c))
25.19/8.31	   A^2 -> H(U1(e, e), f(d))
25.19/8.31	   A^2 -> H(f(e), U1(c, b))
25.19/8.31	   A^2 -> H(f(e), U1(d, b))
25.19/8.31	   A^2 -> H(f(e), U1(b, c))
25.19/8.31	   A^2 -> H(f(e), U1(b, d))
25.19/8.31	   A^2 -> H(f(e), U1(c, c))
25.19/8.31	   A^2 -> H(f(e), f(e))
25.19/8.31	   A^2 -> H(f(e), f(k))
25.19/8.31	   A^2 -> H(f(e), U1(d, d))
25.19/8.31	   A^2 -> H(U1(k, k), U1(b, b))
25.37/8.31	   A^2 -> H(U1(k, k), f(c))
25.37/8.31	   A^2 -> H(U1(k, k), f(d))
25.37/8.31	   A^2 -> H(f(k), U1(c, b))
25.37/8.31	   A^2 -> H(f(k), U1(d, b))
25.37/8.31	   A^2 -> H(f(k), U1(b, c))
25.37/8.31	   A^2 -> H(f(k), U1(b, d))
25.37/8.31	   A^2 -> H(f(k), U1(c, c))
25.37/8.31	   A^2 -> H(f(k), f(e))
25.37/8.31	   A^2 -> H(f(k), f(k))
25.37/8.31	   A^2 -> H(f(k), U1(d, d))
25.37/8.31	   A^2 -> H(f(c), U1(e, b))
25.37/8.31	   A^2 -> H(f(c), U1(k, b))
25.37/8.31	   A^2 -> H(f(c), U1(c, d))
25.37/8.31	   A^2 -> H(f(c), U1(d, c))
25.37/8.31	   A^2 -> H(f(c), U1(b, e))
25.37/8.31	   A^2 -> H(f(c), U1(b, k))
25.37/8.31	   A^2 -> H(f(c), U1(k, d))
25.37/8.31	   A^2 -> H(f(c), U1(d, k))
25.37/8.31	   A^2 -> H(f(c), U1(k, k))
25.37/8.31	   A^2 -> H(U1(k, k), f(b))
25.37/8.31	   A^2 -> H(U1(k, d), U1(b, b))
25.37/8.31	   A^2 -> H(U1(k, d), f(c))
25.37/8.31	   A^2 -> H(U1(k, d), f(d))
25.37/8.31	   A^2 -> H(U1(d, k), U1(b, b))
25.37/8.31	   A^2 -> H(U1(d, k), f(c))
25.37/8.31	   A^2 -> H(U1(d, k), f(d))
25.37/8.31	   A^2 -> H(U1(d, d), U1(c, b))
25.37/8.31	   A^2 -> H(U1(d, d), U1(d, b))
25.37/8.31	   A^2 -> H(U1(d, d), U1(b, c))
25.37/8.31	   A^2 -> H(U1(d, d), U1(b, d))
25.37/8.31	   A^2 -> H(U1(d, d), U1(c, c))
25.37/8.31	   A^2 -> H(U1(d, d), f(e))
25.37/8.31	   A^2 -> H(U1(d, d), f(k))
25.37/8.31	   A^2 -> H(U1(d, d), U1(d, d))
25.37/8.31	   A^2 -> H(f(d), U1(e, b))
25.37/8.31	   A^2 -> H(f(d), U1(k, b))
25.37/8.31	   A^2 -> H(f(d), U1(c, d))
25.37/8.31	   A^2 -> H(f(d), U1(d, c))
25.37/8.31	   A^2 -> H(f(d), U1(b, e))
25.37/8.31	   A^2 -> H(f(d), U1(b, k))
25.37/8.31	   A^2 -> H(f(d), U1(e, c))
25.37/8.31	   A^2 -> H(f(d), U1(k, c))
25.37/8.31	   A^2 -> H(f(d), U1(c, e))
25.37/8.31	   A^2 -> H(f(d), U1(c, k))
25.37/8.31	   A^2 -> H(f(d), U1(e, e))
25.37/8.31	   A^2 -> H(f(d), U1(k, k))
25.37/8.31	   A^2 -> H(f(a), b)
25.37/8.31	   A^2 -> H(f(a), U1(e, d))
25.37/8.31	   A^2 -> H(f(a), U1(d, e))
25.37/8.31	   A^2 -> H(f(c), U1(e, c))
25.37/8.31	   A^2 -> H(f(c), U1(k, c))
25.37/8.31	   A^2 -> H(f(c), U1(c, e))
25.37/8.31	   A^2 -> H(f(c), U1(c, k))
25.37/8.31	   A^2 -> H(f(a), c)
25.37/8.31	   A^2 -> H(f(a), U1(e, k))
25.37/8.31	   A^2 -> H(f(a), U1(k, e))
25.37/8.31	   A^2 -> H(f(c), U1(e, e))
25.37/8.31	
25.37/8.31	The TRS R consists of the following rules:
25.37/8.31	
25.37/8.31	   f(x) -> U1(x, x)
25.37/8.31	   U1(e, x) -> x
25.37/8.31	   a -> c
25.37/8.31	   a -> d
25.37/8.31	   b -> c
25.37/8.31	   b -> d
25.37/8.31	   d -> k
25.37/8.31	   c -> e
25.37/8.31	   c -> k
25.37/8.31	
25.37/8.31	Q is empty.
25.37/8.31	We have to consider all minimal (P,Q,R)-chains.
25.37/8.31	----------------------------------------
25.37/8.31	
25.37/8.31	(211) TransformationProof (EQUIVALENT)
25.37/8.31	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
25.37/8.31	
25.37/8.31	   (A^2 -> H(U1(a, a), U1(e, e)),A^2 -> H(U1(a, a), U1(e, e)))
25.37/8.31	   (A^2 -> H(f(c), U1(e, e)),A^2 -> H(f(c), U1(e, e)))
25.37/8.31	   (A^2 -> H(f(d), U1(e, e)),A^2 -> H(f(d), U1(e, e)))
25.37/8.31	   (A^2 -> H(f(a), e),A^2 -> H(f(a), e))
25.37/8.31	
25.37/8.31	
25.37/8.31	----------------------------------------
25.37/8.31	
25.37/8.31	(212)
25.37/8.31	Obligation:
25.37/8.31	Q DP problem:
25.37/8.31	The TRS P consists of the following rules:
25.37/8.31	
25.37/8.31	   H(x, x) -> G(x, x, f(k))
25.37/8.31	   G(d, x, x) -> A^2
25.37/8.31	   A^2 -> H(f(c), f(c))
25.37/8.31	   A^2 -> H(f(d), f(d))
25.37/8.31	   A^2 -> H(f(a), U1(k, k))
25.37/8.31	   A^2 -> H(f(d), U1(d, d))
25.37/8.31	   A^2 -> H(f(a), U1(k, d))
25.37/8.31	   A^2 -> H(f(a), U1(d, k))
25.37/8.31	   A^2 -> H(a, f(b))
25.37/8.31	   A^2 -> H(U1(e, d), f(b))
25.37/8.31	   A^2 -> H(U1(e, a), U1(b, b))
25.37/8.31	   A^2 -> H(U1(e, a), f(c))
25.37/8.31	   A^2 -> H(U1(e, a), f(d))
25.37/8.31	   A^2 -> H(U1(k, a), U1(b, b))
25.37/8.31	   A^2 -> H(U1(k, a), f(c))
25.37/8.31	   A^2 -> H(U1(k, a), f(d))
25.37/8.31	   A^2 -> H(U1(c, d), U1(b, b))
25.37/8.31	   A^2 -> H(U1(c, d), f(c))
25.37/8.31	   A^2 -> H(U1(c, d), f(d))
25.37/8.31	   A^2 -> H(U1(c, a), U1(c, b))
25.37/8.31	   A^2 -> H(U1(c, a), U1(d, b))
25.37/8.31	   A^2 -> H(U1(c, a), U1(b, c))
25.37/8.31	   A^2 -> H(U1(c, a), U1(b, d))
25.37/8.31	   A^2 -> H(U1(c, a), U1(c, c))
25.37/8.31	   A^2 -> H(U1(c, a), f(e))
25.37/8.31	   A^2 -> H(U1(c, a), f(k))
25.37/8.31	   A^2 -> H(U1(c, a), U1(d, d))
25.37/8.31	   A^2 -> H(U1(d, e), f(b))
25.37/8.31	   A^2 -> H(U1(d, c), U1(b, b))
25.37/8.31	   A^2 -> H(U1(d, c), f(c))
25.37/8.31	   A^2 -> H(U1(d, c), f(d))
25.37/8.31	   A^2 -> H(U1(d, a), U1(c, b))
25.37/8.31	   A^2 -> H(U1(d, a), U1(d, b))
25.37/8.31	   A^2 -> H(U1(d, a), U1(b, c))
25.37/8.31	   A^2 -> H(U1(d, a), U1(b, d))
25.37/8.31	   A^2 -> H(U1(d, a), U1(c, c))
25.37/8.31	   A^2 -> H(U1(d, a), f(e))
25.37/8.31	   A^2 -> H(U1(d, a), f(k))
25.37/8.31	   A^2 -> H(U1(d, a), U1(d, d))
25.37/8.31	   A^2 -> H(U1(a, e), U1(b, b))
25.37/8.31	   A^2 -> H(U1(a, e), f(c))
25.37/8.31	   A^2 -> H(U1(a, e), f(d))
25.37/8.31	   A^2 -> H(U1(a, k), U1(b, b))
25.37/8.31	   A^2 -> H(U1(a, k), f(c))
25.37/8.31	   A^2 -> H(U1(a, k), f(d))
25.37/8.31	   A^2 -> H(U1(a, c), U1(c, b))
25.37/8.31	   A^2 -> H(U1(a, c), U1(d, b))
25.37/8.31	   A^2 -> H(U1(a, c), U1(b, c))
25.37/8.31	   A^2 -> H(U1(a, c), U1(b, d))
25.37/8.31	   A^2 -> H(U1(a, c), U1(c, c))
25.37/8.31	   A^2 -> H(U1(a, c), f(e))
25.37/8.31	   A^2 -> H(U1(a, c), f(k))
25.37/8.31	   A^2 -> H(U1(a, c), U1(d, d))
25.37/8.31	   A^2 -> H(U1(a, d), U1(c, b))
25.37/8.31	   A^2 -> H(U1(a, d), U1(d, b))
25.37/8.31	   A^2 -> H(U1(a, d), U1(b, c))
25.37/8.31	   A^2 -> H(U1(a, d), U1(b, d))
25.37/8.31	   A^2 -> H(U1(a, d), U1(c, c))
25.37/8.31	   A^2 -> H(U1(a, d), f(e))
25.37/8.31	   A^2 -> H(U1(a, d), f(k))
25.37/8.31	   A^2 -> H(U1(a, d), U1(d, d))
25.37/8.31	   A^2 -> H(U1(a, a), U1(e, b))
25.37/8.31	   A^2 -> H(U1(a, a), U1(k, b))
25.37/8.31	   A^2 -> H(U1(a, a), U1(c, d))
25.37/8.31	   A^2 -> H(U1(a, a), U1(d, c))
25.37/8.31	   A^2 -> H(U1(a, a), U1(b, e))
25.37/8.31	   A^2 -> H(U1(a, a), U1(b, k))
25.37/8.31	   A^2 -> H(U1(a, a), U1(e, c))
25.37/8.31	   A^2 -> H(U1(a, a), U1(k, c))
25.37/8.31	   A^2 -> H(U1(a, a), U1(c, e))
25.37/8.31	   A^2 -> H(U1(a, a), U1(c, k))
25.37/8.31	   A^2 -> H(U1(a, a), U1(e, e))
25.37/8.31	   A^2 -> H(U1(a, a), U1(k, k))
25.37/8.31	   A^2 -> H(U1(a, a), U1(k, d))
25.37/8.31	   A^2 -> H(U1(a, a), U1(d, k))
25.37/8.31	   A^2 -> H(c, f(b))
25.37/8.31	   A^2 -> H(U1(e, k), f(b))
25.37/8.31	   A^2 -> H(U1(e, c), U1(b, b))
25.37/8.31	   A^2 -> H(U1(e, c), f(c))
25.37/8.31	   A^2 -> H(U1(e, c), f(d))
25.37/8.31	   A^2 -> H(U1(k, e), f(b))
25.37/8.31	   A^2 -> H(U1(k, c), U1(b, b))
25.37/8.31	   A^2 -> H(U1(k, c), f(c))
25.37/8.31	   A^2 -> H(U1(k, c), f(d))
25.37/8.31	   A^2 -> H(U1(c, e), U1(b, b))
25.37/8.31	   A^2 -> H(U1(c, e), f(c))
25.37/8.31	   A^2 -> H(U1(c, e), f(d))
25.37/8.31	   A^2 -> H(U1(c, k), U1(b, b))
25.37/8.31	   A^2 -> H(U1(c, k), f(c))
25.37/8.31	   A^2 -> H(U1(c, k), f(d))
25.37/8.31	   A^2 -> H(U1(c, c), U1(c, b))
25.37/8.31	   A^2 -> H(U1(c, c), U1(d, b))
25.37/8.31	   A^2 -> H(U1(c, c), U1(b, c))
25.37/8.31	   A^2 -> H(U1(c, c), U1(b, d))
25.37/8.31	   A^2 -> H(U1(c, c), U1(c, c))
25.37/8.31	   A^2 -> H(U1(c, c), f(e))
25.37/8.31	   A^2 -> H(U1(c, c), f(k))
25.37/8.31	   A^2 -> H(U1(c, c), U1(d, d))
25.37/8.31	   A^2 -> H(e, f(b))
25.37/8.31	   A^2 -> H(U1(e, e), U1(b, b))
25.37/8.31	   A^2 -> H(U1(e, e), f(c))
25.37/8.31	   A^2 -> H(U1(e, e), f(d))
25.37/8.31	   A^2 -> H(f(e), U1(c, b))
25.37/8.31	   A^2 -> H(f(e), U1(d, b))
25.37/8.31	   A^2 -> H(f(e), U1(b, c))
25.37/8.31	   A^2 -> H(f(e), U1(b, d))
25.37/8.31	   A^2 -> H(f(e), U1(c, c))
25.37/8.31	   A^2 -> H(f(e), f(e))
25.37/8.31	   A^2 -> H(f(e), f(k))
25.37/8.31	   A^2 -> H(f(e), U1(d, d))
25.37/8.31	   A^2 -> H(U1(k, k), U1(b, b))
25.37/8.31	   A^2 -> H(U1(k, k), f(c))
25.37/8.31	   A^2 -> H(U1(k, k), f(d))
25.37/8.31	   A^2 -> H(f(k), U1(c, b))
25.37/8.31	   A^2 -> H(f(k), U1(d, b))
25.37/8.31	   A^2 -> H(f(k), U1(b, c))
25.37/8.31	   A^2 -> H(f(k), U1(b, d))
25.37/8.31	   A^2 -> H(f(k), U1(c, c))
25.37/8.31	   A^2 -> H(f(k), f(e))
25.37/8.31	   A^2 -> H(f(k), f(k))
25.37/8.31	   A^2 -> H(f(k), U1(d, d))
25.37/8.31	   A^2 -> H(f(c), U1(e, b))
25.37/8.31	   A^2 -> H(f(c), U1(k, b))
25.37/8.31	   A^2 -> H(f(c), U1(c, d))
25.37/8.31	   A^2 -> H(f(c), U1(d, c))
25.37/8.31	   A^2 -> H(f(c), U1(b, e))
25.37/8.31	   A^2 -> H(f(c), U1(b, k))
25.37/8.31	   A^2 -> H(f(c), U1(k, d))
25.37/8.31	   A^2 -> H(f(c), U1(d, k))
25.37/8.31	   A^2 -> H(f(c), U1(k, k))
25.37/8.31	   A^2 -> H(U1(k, k), f(b))
25.37/8.31	   A^2 -> H(U1(k, d), U1(b, b))
25.37/8.31	   A^2 -> H(U1(k, d), f(c))
25.37/8.31	   A^2 -> H(U1(k, d), f(d))
25.37/8.31	   A^2 -> H(U1(d, k), U1(b, b))
25.37/8.31	   A^2 -> H(U1(d, k), f(c))
25.37/8.31	   A^2 -> H(U1(d, k), f(d))
25.37/8.31	   A^2 -> H(U1(d, d), U1(c, b))
25.37/8.31	   A^2 -> H(U1(d, d), U1(d, b))
25.37/8.31	   A^2 -> H(U1(d, d), U1(b, c))
25.37/8.31	   A^2 -> H(U1(d, d), U1(b, d))
25.37/8.31	   A^2 -> H(U1(d, d), U1(c, c))
25.37/8.31	   A^2 -> H(U1(d, d), f(e))
25.37/8.31	   A^2 -> H(U1(d, d), f(k))
25.37/8.31	   A^2 -> H(U1(d, d), U1(d, d))
25.37/8.31	   A^2 -> H(f(d), U1(e, b))
25.37/8.31	   A^2 -> H(f(d), U1(k, b))
25.37/8.31	   A^2 -> H(f(d), U1(c, d))
25.37/8.31	   A^2 -> H(f(d), U1(d, c))
25.37/8.31	   A^2 -> H(f(d), U1(b, e))
25.37/8.31	   A^2 -> H(f(d), U1(b, k))
25.37/8.31	   A^2 -> H(f(d), U1(e, c))
25.37/8.31	   A^2 -> H(f(d), U1(k, c))
25.37/8.31	   A^2 -> H(f(d), U1(c, e))
25.37/8.31	   A^2 -> H(f(d), U1(c, k))
25.37/8.31	   A^2 -> H(f(d), U1(e, e))
25.37/8.31	   A^2 -> H(f(d), U1(k, k))
25.37/8.31	   A^2 -> H(f(a), b)
25.37/8.31	   A^2 -> H(f(a), U1(e, d))
25.37/8.31	   A^2 -> H(f(a), U1(d, e))
25.37/8.31	   A^2 -> H(f(c), U1(e, c))
25.37/8.31	   A^2 -> H(f(c), U1(k, c))
25.37/8.31	   A^2 -> H(f(c), U1(c, e))
25.37/8.31	   A^2 -> H(f(c), U1(c, k))
25.37/8.31	   A^2 -> H(f(a), c)
25.37/8.31	   A^2 -> H(f(a), U1(e, k))
25.37/8.31	   A^2 -> H(f(a), U1(k, e))
25.37/8.31	   A^2 -> H(f(c), U1(e, e))
25.37/8.31	   A^2 -> H(f(a), e)
25.37/8.31	
25.37/8.31	The TRS R consists of the following rules:
25.37/8.31	
25.37/8.31	   f(x) -> U1(x, x)
25.37/8.31	   U1(e, x) -> x
25.37/8.31	   a -> c
25.37/8.31	   a -> d
25.37/8.31	   b -> c
25.37/8.31	   b -> d
25.37/8.31	   d -> k
25.37/8.31	   c -> e
25.37/8.31	   c -> k
25.37/8.31	
25.37/8.31	Q is empty.
25.37/8.31	We have to consider all minimal (P,Q,R)-chains.
25.37/8.31	----------------------------------------
25.37/8.31	
25.37/8.31	(213) TransformationProof (EQUIVALENT)
25.37/8.31	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
25.37/8.31	
25.37/8.31	   (A^2 -> H(U1(a, a), U1(k, k)),A^2 -> H(U1(a, a), U1(k, k)))
25.37/8.31	   (A^2 -> H(f(c), U1(k, k)),A^2 -> H(f(c), U1(k, k)))
25.37/8.31	   (A^2 -> H(f(d), U1(k, k)),A^2 -> H(f(d), U1(k, k)))
25.37/8.31	
25.37/8.31	
25.37/8.31	----------------------------------------
25.37/8.31	
25.37/8.31	(214)
25.37/8.31	Obligation:
25.37/8.31	Q DP problem:
25.37/8.31	The TRS P consists of the following rules:
25.37/8.31	
25.37/8.31	   H(x, x) -> G(x, x, f(k))
25.37/8.31	   G(d, x, x) -> A^2
25.37/8.31	   A^2 -> H(f(c), f(c))
25.37/8.31	   A^2 -> H(f(d), f(d))
25.37/8.31	   A^2 -> H(f(d), U1(d, d))
25.37/8.31	   A^2 -> H(f(a), U1(k, d))
25.37/8.31	   A^2 -> H(f(a), U1(d, k))
25.37/8.31	   A^2 -> H(a, f(b))
25.37/8.31	   A^2 -> H(U1(e, d), f(b))
25.37/8.32	   A^2 -> H(U1(e, a), U1(b, b))
25.37/8.32	   A^2 -> H(U1(e, a), f(c))
25.37/8.32	   A^2 -> H(U1(e, a), f(d))
25.37/8.32	   A^2 -> H(U1(k, a), U1(b, b))
25.37/8.32	   A^2 -> H(U1(k, a), f(c))
25.37/8.32	   A^2 -> H(U1(k, a), f(d))
25.37/8.32	   A^2 -> H(U1(c, d), U1(b, b))
25.37/8.32	   A^2 -> H(U1(c, d), f(c))
25.37/8.32	   A^2 -> H(U1(c, d), f(d))
25.37/8.32	   A^2 -> H(U1(c, a), U1(c, b))
25.37/8.32	   A^2 -> H(U1(c, a), U1(d, b))
25.37/8.32	   A^2 -> H(U1(c, a), U1(b, c))
25.37/8.32	   A^2 -> H(U1(c, a), U1(b, d))
25.37/8.32	   A^2 -> H(U1(c, a), U1(c, c))
25.37/8.32	   A^2 -> H(U1(c, a), f(e))
25.37/8.32	   A^2 -> H(U1(c, a), f(k))
25.37/8.32	   A^2 -> H(U1(c, a), U1(d, d))
25.37/8.32	   A^2 -> H(U1(d, e), f(b))
25.37/8.32	   A^2 -> H(U1(d, c), U1(b, b))
25.37/8.32	   A^2 -> H(U1(d, c), f(c))
25.37/8.32	   A^2 -> H(U1(d, c), f(d))
25.37/8.32	   A^2 -> H(U1(d, a), U1(c, b))
25.37/8.32	   A^2 -> H(U1(d, a), U1(d, b))
25.37/8.32	   A^2 -> H(U1(d, a), U1(b, c))
25.37/8.32	   A^2 -> H(U1(d, a), U1(b, d))
25.37/8.32	   A^2 -> H(U1(d, a), U1(c, c))
25.37/8.32	   A^2 -> H(U1(d, a), f(e))
25.37/8.32	   A^2 -> H(U1(d, a), f(k))
25.37/8.32	   A^2 -> H(U1(d, a), U1(d, d))
25.37/8.32	   A^2 -> H(U1(a, e), U1(b, b))
25.37/8.32	   A^2 -> H(U1(a, e), f(c))
25.37/8.32	   A^2 -> H(U1(a, e), f(d))
25.37/8.32	   A^2 -> H(U1(a, k), U1(b, b))
25.37/8.32	   A^2 -> H(U1(a, k), f(c))
25.37/8.32	   A^2 -> H(U1(a, k), f(d))
25.37/8.32	   A^2 -> H(U1(a, c), U1(c, b))
25.37/8.32	   A^2 -> H(U1(a, c), U1(d, b))
25.37/8.32	   A^2 -> H(U1(a, c), U1(b, c))
25.37/8.32	   A^2 -> H(U1(a, c), U1(b, d))
25.37/8.32	   A^2 -> H(U1(a, c), U1(c, c))
25.37/8.32	   A^2 -> H(U1(a, c), f(e))
25.37/8.32	   A^2 -> H(U1(a, c), f(k))
25.37/8.32	   A^2 -> H(U1(a, c), U1(d, d))
25.37/8.32	   A^2 -> H(U1(a, d), U1(c, b))
25.37/8.32	   A^2 -> H(U1(a, d), U1(d, b))
25.37/8.32	   A^2 -> H(U1(a, d), U1(b, c))
25.37/8.32	   A^2 -> H(U1(a, d), U1(b, d))
25.37/8.32	   A^2 -> H(U1(a, d), U1(c, c))
25.37/8.32	   A^2 -> H(U1(a, d), f(e))
25.37/8.32	   A^2 -> H(U1(a, d), f(k))
25.37/8.32	   A^2 -> H(U1(a, d), U1(d, d))
25.37/8.32	   A^2 -> H(U1(a, a), U1(e, b))
25.37/8.32	   A^2 -> H(U1(a, a), U1(k, b))
25.37/8.32	   A^2 -> H(U1(a, a), U1(c, d))
25.37/8.32	   A^2 -> H(U1(a, a), U1(d, c))
25.37/8.32	   A^2 -> H(U1(a, a), U1(b, e))
25.37/8.32	   A^2 -> H(U1(a, a), U1(b, k))
25.37/8.32	   A^2 -> H(U1(a, a), U1(e, c))
25.37/8.32	   A^2 -> H(U1(a, a), U1(k, c))
25.37/8.32	   A^2 -> H(U1(a, a), U1(c, e))
25.37/8.32	   A^2 -> H(U1(a, a), U1(c, k))
25.37/8.32	   A^2 -> H(U1(a, a), U1(e, e))
25.37/8.32	   A^2 -> H(U1(a, a), U1(k, k))
25.37/8.32	   A^2 -> H(U1(a, a), U1(k, d))
25.37/8.32	   A^2 -> H(U1(a, a), U1(d, k))
25.37/8.32	   A^2 -> H(c, f(b))
25.37/8.32	   A^2 -> H(U1(e, k), f(b))
25.37/8.32	   A^2 -> H(U1(e, c), U1(b, b))
25.37/8.32	   A^2 -> H(U1(e, c), f(c))
25.37/8.32	   A^2 -> H(U1(e, c), f(d))
25.37/8.32	   A^2 -> H(U1(k, e), f(b))
25.37/8.32	   A^2 -> H(U1(k, c), U1(b, b))
25.37/8.32	   A^2 -> H(U1(k, c), f(c))
25.37/8.32	   A^2 -> H(U1(k, c), f(d))
25.37/8.32	   A^2 -> H(U1(c, e), U1(b, b))
25.37/8.32	   A^2 -> H(U1(c, e), f(c))
25.37/8.32	   A^2 -> H(U1(c, e), f(d))
25.37/8.32	   A^2 -> H(U1(c, k), U1(b, b))
25.37/8.32	   A^2 -> H(U1(c, k), f(c))
25.37/8.32	   A^2 -> H(U1(c, k), f(d))
25.37/8.32	   A^2 -> H(U1(c, c), U1(c, b))
25.37/8.32	   A^2 -> H(U1(c, c), U1(d, b))
25.37/8.32	   A^2 -> H(U1(c, c), U1(b, c))
25.37/8.32	   A^2 -> H(U1(c, c), U1(b, d))
25.37/8.32	   A^2 -> H(U1(c, c), U1(c, c))
25.37/8.32	   A^2 -> H(U1(c, c), f(e))
25.37/8.32	   A^2 -> H(U1(c, c), f(k))
25.37/8.32	   A^2 -> H(U1(c, c), U1(d, d))
25.37/8.32	   A^2 -> H(e, f(b))
25.37/8.32	   A^2 -> H(U1(e, e), U1(b, b))
25.37/8.32	   A^2 -> H(U1(e, e), f(c))
25.37/8.32	   A^2 -> H(U1(e, e), f(d))
25.37/8.32	   A^2 -> H(f(e), U1(c, b))
25.37/8.32	   A^2 -> H(f(e), U1(d, b))
25.37/8.32	   A^2 -> H(f(e), U1(b, c))
25.37/8.32	   A^2 -> H(f(e), U1(b, d))
25.37/8.32	   A^2 -> H(f(e), U1(c, c))
25.37/8.32	   A^2 -> H(f(e), f(e))
25.37/8.32	   A^2 -> H(f(e), f(k))
25.37/8.32	   A^2 -> H(f(e), U1(d, d))
25.37/8.32	   A^2 -> H(U1(k, k), U1(b, b))
25.37/8.32	   A^2 -> H(U1(k, k), f(c))
25.37/8.32	   A^2 -> H(U1(k, k), f(d))
25.37/8.32	   A^2 -> H(f(k), U1(c, b))
25.37/8.32	   A^2 -> H(f(k), U1(d, b))
25.37/8.32	   A^2 -> H(f(k), U1(b, c))
25.37/8.32	   A^2 -> H(f(k), U1(b, d))
25.37/8.32	   A^2 -> H(f(k), U1(c, c))
25.37/8.32	   A^2 -> H(f(k), f(e))
25.37/8.32	   A^2 -> H(f(k), f(k))
25.37/8.32	   A^2 -> H(f(k), U1(d, d))
25.37/8.32	   A^2 -> H(f(c), U1(e, b))
25.37/8.32	   A^2 -> H(f(c), U1(k, b))
25.37/8.32	   A^2 -> H(f(c), U1(c, d))
25.37/8.32	   A^2 -> H(f(c), U1(d, c))
25.37/8.32	   A^2 -> H(f(c), U1(b, e))
25.37/8.32	   A^2 -> H(f(c), U1(b, k))
25.37/8.32	   A^2 -> H(f(c), U1(k, d))
25.37/8.32	   A^2 -> H(f(c), U1(d, k))
25.37/8.32	   A^2 -> H(f(c), U1(k, k))
25.37/8.32	   A^2 -> H(U1(k, k), f(b))
25.37/8.32	   A^2 -> H(U1(k, d), U1(b, b))
25.37/8.32	   A^2 -> H(U1(k, d), f(c))
25.37/8.32	   A^2 -> H(U1(k, d), f(d))
25.37/8.32	   A^2 -> H(U1(d, k), U1(b, b))
25.37/8.32	   A^2 -> H(U1(d, k), f(c))
25.37/8.32	   A^2 -> H(U1(d, k), f(d))
25.37/8.32	   A^2 -> H(U1(d, d), U1(c, b))
25.37/8.32	   A^2 -> H(U1(d, d), U1(d, b))
25.37/8.32	   A^2 -> H(U1(d, d), U1(b, c))
25.37/8.32	   A^2 -> H(U1(d, d), U1(b, d))
25.37/8.32	   A^2 -> H(U1(d, d), U1(c, c))
25.37/8.32	   A^2 -> H(U1(d, d), f(e))
25.37/8.32	   A^2 -> H(U1(d, d), f(k))
25.37/8.32	   A^2 -> H(U1(d, d), U1(d, d))
25.37/8.32	   A^2 -> H(f(d), U1(e, b))
25.37/8.32	   A^2 -> H(f(d), U1(k, b))
25.37/8.32	   A^2 -> H(f(d), U1(c, d))
25.37/8.33	   A^2 -> H(f(d), U1(d, c))
25.37/8.33	   A^2 -> H(f(d), U1(b, e))
25.37/8.33	   A^2 -> H(f(d), U1(b, k))
25.37/8.33	   A^2 -> H(f(d), U1(e, c))
25.37/8.33	   A^2 -> H(f(d), U1(k, c))
25.37/8.33	   A^2 -> H(f(d), U1(c, e))
25.37/8.33	   A^2 -> H(f(d), U1(c, k))
25.37/8.33	   A^2 -> H(f(d), U1(e, e))
25.37/8.33	   A^2 -> H(f(d), U1(k, k))
25.37/8.33	   A^2 -> H(f(a), b)
25.37/8.33	   A^2 -> H(f(a), U1(e, d))
25.37/8.33	   A^2 -> H(f(a), U1(d, e))
25.37/8.33	   A^2 -> H(f(c), U1(e, c))
25.37/8.33	   A^2 -> H(f(c), U1(k, c))
25.37/8.33	   A^2 -> H(f(c), U1(c, e))
25.37/8.33	   A^2 -> H(f(c), U1(c, k))
25.37/8.33	   A^2 -> H(f(a), c)
25.37/8.33	   A^2 -> H(f(a), U1(e, k))
25.37/8.33	   A^2 -> H(f(a), U1(k, e))
25.37/8.33	   A^2 -> H(f(c), U1(e, e))
25.37/8.33	   A^2 -> H(f(a), e)
25.37/8.33	
25.37/8.33	The TRS R consists of the following rules:
25.37/8.33	
25.37/8.33	   f(x) -> U1(x, x)
25.37/8.33	   U1(e, x) -> x
25.37/8.33	   a -> c
25.37/8.33	   a -> d
25.37/8.33	   b -> c
25.37/8.33	   b -> d
25.37/8.33	   d -> k
25.37/8.33	   c -> e
25.37/8.33	   c -> k
25.37/8.33	
25.37/8.33	Q is empty.
25.37/8.33	We have to consider all minimal (P,Q,R)-chains.
25.37/8.33	----------------------------------------
25.37/8.33	
25.37/8.33	(215) TransformationProof (EQUIVALENT)
25.37/8.33	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
25.37/8.33	
25.37/8.33	   (A^2 -> H(U1(d, d), U1(d, d)),A^2 -> H(U1(d, d), U1(d, d)))
25.37/8.33	   (A^2 -> H(f(k), U1(d, d)),A^2 -> H(f(k), U1(d, d)))
25.37/8.33	   (A^2 -> H(f(d), U1(k, d)),A^2 -> H(f(d), U1(k, d)))
25.37/8.33	   (A^2 -> H(f(d), U1(d, k)),A^2 -> H(f(d), U1(d, k)))
25.37/8.33	
25.37/8.33	
25.37/8.33	----------------------------------------
25.37/8.33	
25.37/8.33	(216)
25.37/8.33	Obligation:
25.37/8.33	Q DP problem:
25.37/8.33	The TRS P consists of the following rules:
25.37/8.33	
25.37/8.33	   H(x, x) -> G(x, x, f(k))
25.37/8.33	   G(d, x, x) -> A^2
25.37/8.33	   A^2 -> H(f(c), f(c))
25.37/8.33	   A^2 -> H(f(d), f(d))
25.37/8.33	   A^2 -> H(f(a), U1(k, d))
25.37/8.33	   A^2 -> H(f(a), U1(d, k))
25.37/8.33	   A^2 -> H(a, f(b))
25.37/8.33	   A^2 -> H(U1(e, d), f(b))
25.37/8.33	   A^2 -> H(U1(e, a), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, a), f(c))
25.37/8.33	   A^2 -> H(U1(e, a), f(d))
25.37/8.33	   A^2 -> H(U1(k, a), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, a), f(c))
25.37/8.33	   A^2 -> H(U1(k, a), f(d))
25.37/8.33	   A^2 -> H(U1(c, d), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, d), f(c))
25.37/8.33	   A^2 -> H(U1(c, d), f(d))
25.37/8.33	   A^2 -> H(U1(c, a), U1(c, b))
25.37/8.33	   A^2 -> H(U1(c, a), U1(d, b))
25.37/8.33	   A^2 -> H(U1(c, a), U1(b, c))
25.37/8.33	   A^2 -> H(U1(c, a), U1(b, d))
25.37/8.33	   A^2 -> H(U1(c, a), U1(c, c))
25.37/8.33	   A^2 -> H(U1(c, a), f(e))
25.37/8.33	   A^2 -> H(U1(c, a), f(k))
25.37/8.33	   A^2 -> H(U1(c, a), U1(d, d))
25.37/8.33	   A^2 -> H(U1(d, e), f(b))
25.37/8.33	   A^2 -> H(U1(d, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(d, c), f(c))
25.37/8.33	   A^2 -> H(U1(d, c), f(d))
25.37/8.33	   A^2 -> H(U1(d, a), U1(c, b))
25.37/8.33	   A^2 -> H(U1(d, a), U1(d, b))
25.37/8.33	   A^2 -> H(U1(d, a), U1(b, c))
25.37/8.33	   A^2 -> H(U1(d, a), U1(b, d))
25.37/8.33	   A^2 -> H(U1(d, a), U1(c, c))
25.37/8.33	   A^2 -> H(U1(d, a), f(e))
25.37/8.33	   A^2 -> H(U1(d, a), f(k))
25.37/8.33	   A^2 -> H(U1(d, a), U1(d, d))
25.37/8.33	   A^2 -> H(U1(a, e), U1(b, b))
25.37/8.33	   A^2 -> H(U1(a, e), f(c))
25.37/8.33	   A^2 -> H(U1(a, e), f(d))
25.37/8.33	   A^2 -> H(U1(a, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(a, k), f(c))
25.37/8.33	   A^2 -> H(U1(a, k), f(d))
25.37/8.33	   A^2 -> H(U1(a, c), U1(c, b))
25.37/8.33	   A^2 -> H(U1(a, c), U1(d, b))
25.37/8.33	   A^2 -> H(U1(a, c), U1(b, c))
25.37/8.33	   A^2 -> H(U1(a, c), U1(b, d))
25.37/8.33	   A^2 -> H(U1(a, c), U1(c, c))
25.37/8.33	   A^2 -> H(U1(a, c), f(e))
25.37/8.33	   A^2 -> H(U1(a, c), f(k))
25.37/8.33	   A^2 -> H(U1(a, c), U1(d, d))
25.37/8.33	   A^2 -> H(U1(a, d), U1(c, b))
25.37/8.33	   A^2 -> H(U1(a, d), U1(d, b))
25.37/8.33	   A^2 -> H(U1(a, d), U1(b, c))
25.37/8.33	   A^2 -> H(U1(a, d), U1(b, d))
25.37/8.33	   A^2 -> H(U1(a, d), U1(c, c))
25.37/8.33	   A^2 -> H(U1(a, d), f(e))
25.37/8.33	   A^2 -> H(U1(a, d), f(k))
25.37/8.33	   A^2 -> H(U1(a, d), U1(d, d))
25.37/8.33	   A^2 -> H(U1(a, a), U1(e, b))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, b))
25.37/8.33	   A^2 -> H(U1(a, a), U1(c, d))
25.37/8.33	   A^2 -> H(U1(a, a), U1(d, c))
25.37/8.33	   A^2 -> H(U1(a, a), U1(b, e))
25.37/8.33	   A^2 -> H(U1(a, a), U1(b, k))
25.37/8.33	   A^2 -> H(U1(a, a), U1(e, c))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, c))
25.37/8.33	   A^2 -> H(U1(a, a), U1(c, e))
25.37/8.33	   A^2 -> H(U1(a, a), U1(c, k))
25.37/8.33	   A^2 -> H(U1(a, a), U1(e, e))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, k))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, d))
25.37/8.33	   A^2 -> H(U1(a, a), U1(d, k))
25.37/8.33	   A^2 -> H(c, f(b))
25.37/8.33	   A^2 -> H(U1(e, k), f(b))
25.37/8.33	   A^2 -> H(U1(e, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, c), f(c))
25.37/8.33	   A^2 -> H(U1(e, c), f(d))
25.37/8.33	   A^2 -> H(U1(k, e), f(b))
25.37/8.33	   A^2 -> H(U1(k, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, c), f(c))
25.37/8.33	   A^2 -> H(U1(k, c), f(d))
25.37/8.33	   A^2 -> H(U1(c, e), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, e), f(c))
25.37/8.33	   A^2 -> H(U1(c, e), f(d))
25.37/8.33	   A^2 -> H(U1(c, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, k), f(c))
25.37/8.33	   A^2 -> H(U1(c, k), f(d))
25.37/8.33	   A^2 -> H(U1(c, c), U1(c, b))
25.37/8.33	   A^2 -> H(U1(c, c), U1(d, b))
25.37/8.33	   A^2 -> H(U1(c, c), U1(b, c))
25.37/8.33	   A^2 -> H(U1(c, c), U1(b, d))
25.37/8.33	   A^2 -> H(U1(c, c), U1(c, c))
25.37/8.33	   A^2 -> H(U1(c, c), f(e))
25.37/8.33	   A^2 -> H(U1(c, c), f(k))
25.37/8.33	   A^2 -> H(U1(c, c), U1(d, d))
25.37/8.33	   A^2 -> H(e, f(b))
25.37/8.33	   A^2 -> H(U1(e, e), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, e), f(c))
25.37/8.33	   A^2 -> H(U1(e, e), f(d))
25.37/8.33	   A^2 -> H(f(e), U1(c, b))
25.37/8.33	   A^2 -> H(f(e), U1(d, b))
25.37/8.33	   A^2 -> H(f(e), U1(b, c))
25.37/8.33	   A^2 -> H(f(e), U1(b, d))
25.37/8.33	   A^2 -> H(f(e), U1(c, c))
25.37/8.33	   A^2 -> H(f(e), f(e))
25.37/8.33	   A^2 -> H(f(e), f(k))
25.37/8.33	   A^2 -> H(f(e), U1(d, d))
25.37/8.33	   A^2 -> H(U1(k, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, k), f(c))
25.37/8.33	   A^2 -> H(U1(k, k), f(d))
25.37/8.33	   A^2 -> H(f(k), U1(c, b))
25.37/8.33	   A^2 -> H(f(k), U1(d, b))
25.37/8.33	   A^2 -> H(f(k), U1(b, c))
25.37/8.33	   A^2 -> H(f(k), U1(b, d))
25.37/8.33	   A^2 -> H(f(k), U1(c, c))
25.37/8.33	   A^2 -> H(f(k), f(e))
25.37/8.33	   A^2 -> H(f(k), f(k))
25.37/8.33	   A^2 -> H(f(k), U1(d, d))
25.37/8.33	   A^2 -> H(f(c), U1(e, b))
25.37/8.33	   A^2 -> H(f(c), U1(k, b))
25.37/8.33	   A^2 -> H(f(c), U1(c, d))
25.37/8.33	   A^2 -> H(f(c), U1(d, c))
25.37/8.33	   A^2 -> H(f(c), U1(b, e))
25.37/8.33	   A^2 -> H(f(c), U1(b, k))
25.37/8.33	   A^2 -> H(f(c), U1(k, d))
25.37/8.33	   A^2 -> H(f(c), U1(d, k))
25.37/8.33	   A^2 -> H(f(c), U1(k, k))
25.37/8.33	   A^2 -> H(U1(k, k), f(b))
25.37/8.33	   A^2 -> H(U1(k, d), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, d), f(c))
25.37/8.33	   A^2 -> H(U1(k, d), f(d))
25.37/8.33	   A^2 -> H(U1(d, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(d, k), f(c))
25.37/8.33	   A^2 -> H(U1(d, k), f(d))
25.37/8.33	   A^2 -> H(U1(d, d), U1(c, b))
25.37/8.33	   A^2 -> H(U1(d, d), U1(d, b))
25.37/8.33	   A^2 -> H(U1(d, d), U1(b, c))
25.37/8.33	   A^2 -> H(U1(d, d), U1(b, d))
25.37/8.33	   A^2 -> H(U1(d, d), U1(c, c))
25.37/8.33	   A^2 -> H(U1(d, d), f(e))
25.37/8.33	   A^2 -> H(U1(d, d), f(k))
25.37/8.33	   A^2 -> H(U1(d, d), U1(d, d))
25.37/8.33	   A^2 -> H(f(d), U1(e, b))
25.37/8.33	   A^2 -> H(f(d), U1(k, b))
25.37/8.33	   A^2 -> H(f(d), U1(c, d))
25.37/8.33	   A^2 -> H(f(d), U1(d, c))
25.37/8.33	   A^2 -> H(f(d), U1(b, e))
25.37/8.33	   A^2 -> H(f(d), U1(b, k))
25.37/8.33	   A^2 -> H(f(d), U1(e, c))
25.37/8.33	   A^2 -> H(f(d), U1(k, c))
25.37/8.33	   A^2 -> H(f(d), U1(c, e))
25.37/8.33	   A^2 -> H(f(d), U1(c, k))
25.37/8.33	   A^2 -> H(f(d), U1(e, e))
25.37/8.33	   A^2 -> H(f(d), U1(k, k))
25.37/8.33	   A^2 -> H(f(a), b)
25.37/8.33	   A^2 -> H(f(a), U1(e, d))
25.37/8.33	   A^2 -> H(f(a), U1(d, e))
25.37/8.33	   A^2 -> H(f(c), U1(e, c))
25.37/8.33	   A^2 -> H(f(c), U1(k, c))
25.37/8.33	   A^2 -> H(f(c), U1(c, e))
25.37/8.33	   A^2 -> H(f(c), U1(c, k))
25.37/8.33	   A^2 -> H(f(a), c)
25.37/8.33	   A^2 -> H(f(a), U1(e, k))
25.37/8.33	   A^2 -> H(f(a), U1(k, e))
25.37/8.33	   A^2 -> H(f(c), U1(e, e))
25.37/8.33	   A^2 -> H(f(a), e)
25.37/8.33	   A^2 -> H(f(d), U1(k, d))
25.37/8.33	   A^2 -> H(f(d), U1(d, k))
25.37/8.33	
25.37/8.33	The TRS R consists of the following rules:
25.37/8.33	
25.37/8.33	   f(x) -> U1(x, x)
25.37/8.33	   U1(e, x) -> x
25.37/8.33	   a -> c
25.37/8.33	   a -> d
25.37/8.33	   b -> c
25.37/8.33	   b -> d
25.37/8.33	   d -> k
25.37/8.33	   c -> e
25.37/8.33	   c -> k
25.37/8.33	
25.37/8.33	Q is empty.
25.37/8.33	We have to consider all minimal (P,Q,R)-chains.
25.37/8.33	----------------------------------------
25.37/8.33	
25.37/8.33	(217) TransformationProof (EQUIVALENT)
25.37/8.33	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
25.37/8.33	
25.37/8.33	   (A^2 -> H(U1(a, a), U1(k, d)),A^2 -> H(U1(a, a), U1(k, d)))
25.37/8.33	   (A^2 -> H(f(c), U1(k, d)),A^2 -> H(f(c), U1(k, d)))
25.37/8.33	   (A^2 -> H(f(d), U1(k, d)),A^2 -> H(f(d), U1(k, d)))
25.37/8.33	   (A^2 -> H(f(a), U1(k, k)),A^2 -> H(f(a), U1(k, k)))
25.37/8.33	
25.37/8.33	
25.37/8.33	----------------------------------------
25.37/8.33	
25.37/8.33	(218)
25.37/8.33	Obligation:
25.37/8.33	Q DP problem:
25.37/8.33	The TRS P consists of the following rules:
25.37/8.33	
25.37/8.33	   H(x, x) -> G(x, x, f(k))
25.37/8.33	   G(d, x, x) -> A^2
25.37/8.33	   A^2 -> H(f(c), f(c))
25.37/8.33	   A^2 -> H(f(d), f(d))
25.37/8.33	   A^2 -> H(f(a), U1(d, k))
25.37/8.33	   A^2 -> H(a, f(b))
25.37/8.33	   A^2 -> H(U1(e, d), f(b))
25.37/8.33	   A^2 -> H(U1(e, a), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, a), f(c))
25.37/8.33	   A^2 -> H(U1(e, a), f(d))
25.37/8.33	   A^2 -> H(U1(k, a), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, a), f(c))
25.37/8.33	   A^2 -> H(U1(k, a), f(d))
25.37/8.33	   A^2 -> H(U1(c, d), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, d), f(c))
25.37/8.33	   A^2 -> H(U1(c, d), f(d))
25.37/8.33	   A^2 -> H(U1(c, a), U1(c, b))
25.37/8.33	   A^2 -> H(U1(c, a), U1(d, b))
25.37/8.33	   A^2 -> H(U1(c, a), U1(b, c))
25.37/8.33	   A^2 -> H(U1(c, a), U1(b, d))
25.37/8.33	   A^2 -> H(U1(c, a), U1(c, c))
25.37/8.33	   A^2 -> H(U1(c, a), f(e))
25.37/8.33	   A^2 -> H(U1(c, a), f(k))
25.37/8.33	   A^2 -> H(U1(c, a), U1(d, d))
25.37/8.33	   A^2 -> H(U1(d, e), f(b))
25.37/8.33	   A^2 -> H(U1(d, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(d, c), f(c))
25.37/8.33	   A^2 -> H(U1(d, c), f(d))
25.37/8.33	   A^2 -> H(U1(d, a), U1(c, b))
25.37/8.33	   A^2 -> H(U1(d, a), U1(d, b))
25.37/8.33	   A^2 -> H(U1(d, a), U1(b, c))
25.37/8.33	   A^2 -> H(U1(d, a), U1(b, d))
25.37/8.33	   A^2 -> H(U1(d, a), U1(c, c))
25.37/8.33	   A^2 -> H(U1(d, a), f(e))
25.37/8.33	   A^2 -> H(U1(d, a), f(k))
25.37/8.33	   A^2 -> H(U1(d, a), U1(d, d))
25.37/8.33	   A^2 -> H(U1(a, e), U1(b, b))
25.37/8.33	   A^2 -> H(U1(a, e), f(c))
25.37/8.33	   A^2 -> H(U1(a, e), f(d))
25.37/8.33	   A^2 -> H(U1(a, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(a, k), f(c))
25.37/8.33	   A^2 -> H(U1(a, k), f(d))
25.37/8.33	   A^2 -> H(U1(a, c), U1(c, b))
25.37/8.33	   A^2 -> H(U1(a, c), U1(d, b))
25.37/8.33	   A^2 -> H(U1(a, c), U1(b, c))
25.37/8.33	   A^2 -> H(U1(a, c), U1(b, d))
25.37/8.33	   A^2 -> H(U1(a, c), U1(c, c))
25.37/8.33	   A^2 -> H(U1(a, c), f(e))
25.37/8.33	   A^2 -> H(U1(a, c), f(k))
25.37/8.33	   A^2 -> H(U1(a, c), U1(d, d))
25.37/8.33	   A^2 -> H(U1(a, d), U1(c, b))
25.37/8.33	   A^2 -> H(U1(a, d), U1(d, b))
25.37/8.33	   A^2 -> H(U1(a, d), U1(b, c))
25.37/8.33	   A^2 -> H(U1(a, d), U1(b, d))
25.37/8.33	   A^2 -> H(U1(a, d), U1(c, c))
25.37/8.33	   A^2 -> H(U1(a, d), f(e))
25.37/8.33	   A^2 -> H(U1(a, d), f(k))
25.37/8.33	   A^2 -> H(U1(a, d), U1(d, d))
25.37/8.33	   A^2 -> H(U1(a, a), U1(e, b))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, b))
25.37/8.33	   A^2 -> H(U1(a, a), U1(c, d))
25.37/8.33	   A^2 -> H(U1(a, a), U1(d, c))
25.37/8.33	   A^2 -> H(U1(a, a), U1(b, e))
25.37/8.33	   A^2 -> H(U1(a, a), U1(b, k))
25.37/8.33	   A^2 -> H(U1(a, a), U1(e, c))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, c))
25.37/8.33	   A^2 -> H(U1(a, a), U1(c, e))
25.37/8.33	   A^2 -> H(U1(a, a), U1(c, k))
25.37/8.33	   A^2 -> H(U1(a, a), U1(e, e))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, k))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, d))
25.37/8.33	   A^2 -> H(U1(a, a), U1(d, k))
25.37/8.33	   A^2 -> H(c, f(b))
25.37/8.33	   A^2 -> H(U1(e, k), f(b))
25.37/8.33	   A^2 -> H(U1(e, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, c), f(c))
25.37/8.33	   A^2 -> H(U1(e, c), f(d))
25.37/8.33	   A^2 -> H(U1(k, e), f(b))
25.37/8.33	   A^2 -> H(U1(k, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, c), f(c))
25.37/8.33	   A^2 -> H(U1(k, c), f(d))
25.37/8.33	   A^2 -> H(U1(c, e), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, e), f(c))
25.37/8.33	   A^2 -> H(U1(c, e), f(d))
25.37/8.33	   A^2 -> H(U1(c, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, k), f(c))
25.37/8.33	   A^2 -> H(U1(c, k), f(d))
25.37/8.33	   A^2 -> H(U1(c, c), U1(c, b))
25.37/8.33	   A^2 -> H(U1(c, c), U1(d, b))
25.37/8.33	   A^2 -> H(U1(c, c), U1(b, c))
25.37/8.33	   A^2 -> H(U1(c, c), U1(b, d))
25.37/8.33	   A^2 -> H(U1(c, c), U1(c, c))
25.37/8.33	   A^2 -> H(U1(c, c), f(e))
25.37/8.33	   A^2 -> H(U1(c, c), f(k))
25.37/8.33	   A^2 -> H(U1(c, c), U1(d, d))
25.37/8.33	   A^2 -> H(e, f(b))
25.37/8.33	   A^2 -> H(U1(e, e), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, e), f(c))
25.37/8.33	   A^2 -> H(U1(e, e), f(d))
25.37/8.33	   A^2 -> H(f(e), U1(c, b))
25.37/8.33	   A^2 -> H(f(e), U1(d, b))
25.37/8.33	   A^2 -> H(f(e), U1(b, c))
25.37/8.33	   A^2 -> H(f(e), U1(b, d))
25.37/8.33	   A^2 -> H(f(e), U1(c, c))
25.37/8.33	   A^2 -> H(f(e), f(e))
25.37/8.33	   A^2 -> H(f(e), f(k))
25.37/8.33	   A^2 -> H(f(e), U1(d, d))
25.37/8.33	   A^2 -> H(U1(k, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, k), f(c))
25.37/8.33	   A^2 -> H(U1(k, k), f(d))
25.37/8.33	   A^2 -> H(f(k), U1(c, b))
25.37/8.33	   A^2 -> H(f(k), U1(d, b))
25.37/8.33	   A^2 -> H(f(k), U1(b, c))
25.37/8.33	   A^2 -> H(f(k), U1(b, d))
25.37/8.33	   A^2 -> H(f(k), U1(c, c))
25.37/8.33	   A^2 -> H(f(k), f(e))
25.37/8.33	   A^2 -> H(f(k), f(k))
25.37/8.33	   A^2 -> H(f(k), U1(d, d))
25.37/8.33	   A^2 -> H(f(c), U1(e, b))
25.37/8.33	   A^2 -> H(f(c), U1(k, b))
25.37/8.33	   A^2 -> H(f(c), U1(c, d))
25.37/8.33	   A^2 -> H(f(c), U1(d, c))
25.37/8.33	   A^2 -> H(f(c), U1(b, e))
25.37/8.33	   A^2 -> H(f(c), U1(b, k))
25.37/8.33	   A^2 -> H(f(c), U1(k, d))
25.37/8.33	   A^2 -> H(f(c), U1(d, k))
25.37/8.33	   A^2 -> H(f(c), U1(k, k))
25.37/8.33	   A^2 -> H(U1(k, k), f(b))
25.37/8.33	   A^2 -> H(U1(k, d), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, d), f(c))
25.37/8.33	   A^2 -> H(U1(k, d), f(d))
25.37/8.33	   A^2 -> H(U1(d, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(d, k), f(c))
25.37/8.33	   A^2 -> H(U1(d, k), f(d))
25.37/8.33	   A^2 -> H(U1(d, d), U1(c, b))
25.37/8.33	   A^2 -> H(U1(d, d), U1(d, b))
25.37/8.33	   A^2 -> H(U1(d, d), U1(b, c))
25.37/8.33	   A^2 -> H(U1(d, d), U1(b, d))
25.37/8.33	   A^2 -> H(U1(d, d), U1(c, c))
25.37/8.33	   A^2 -> H(U1(d, d), f(e))
25.37/8.33	   A^2 -> H(U1(d, d), f(k))
25.37/8.33	   A^2 -> H(U1(d, d), U1(d, d))
25.37/8.33	   A^2 -> H(f(d), U1(e, b))
25.37/8.33	   A^2 -> H(f(d), U1(k, b))
25.37/8.33	   A^2 -> H(f(d), U1(c, d))
25.37/8.33	   A^2 -> H(f(d), U1(d, c))
25.37/8.33	   A^2 -> H(f(d), U1(b, e))
25.37/8.33	   A^2 -> H(f(d), U1(b, k))
25.37/8.33	   A^2 -> H(f(d), U1(e, c))
25.37/8.33	   A^2 -> H(f(d), U1(k, c))
25.37/8.33	   A^2 -> H(f(d), U1(c, e))
25.37/8.33	   A^2 -> H(f(d), U1(c, k))
25.37/8.33	   A^2 -> H(f(d), U1(e, e))
25.37/8.33	   A^2 -> H(f(d), U1(k, k))
25.37/8.33	   A^2 -> H(f(a), b)
25.37/8.33	   A^2 -> H(f(a), U1(e, d))
25.37/8.33	   A^2 -> H(f(a), U1(d, e))
25.37/8.33	   A^2 -> H(f(c), U1(e, c))
25.37/8.33	   A^2 -> H(f(c), U1(k, c))
25.37/8.33	   A^2 -> H(f(c), U1(c, e))
25.37/8.33	   A^2 -> H(f(c), U1(c, k))
25.37/8.33	   A^2 -> H(f(a), c)
25.37/8.33	   A^2 -> H(f(a), U1(e, k))
25.37/8.33	   A^2 -> H(f(a), U1(k, e))
25.37/8.33	   A^2 -> H(f(c), U1(e, e))
25.37/8.33	   A^2 -> H(f(a), e)
25.37/8.33	   A^2 -> H(f(d), U1(k, d))
25.37/8.33	   A^2 -> H(f(d), U1(d, k))
25.37/8.33	   A^2 -> H(f(a), U1(k, k))
25.37/8.33	
25.37/8.33	The TRS R consists of the following rules:
25.37/8.33	
25.37/8.33	   f(x) -> U1(x, x)
25.37/8.33	   U1(e, x) -> x
25.37/8.33	   a -> c
25.37/8.33	   a -> d
25.37/8.33	   b -> c
25.37/8.33	   b -> d
25.37/8.33	   d -> k
25.37/8.33	   c -> e
25.37/8.33	   c -> k
25.37/8.33	
25.37/8.33	Q is empty.
25.37/8.33	We have to consider all minimal (P,Q,R)-chains.
25.37/8.33	----------------------------------------
25.37/8.33	
25.37/8.33	(219) TransformationProof (EQUIVALENT)
25.37/8.33	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
25.37/8.33	
25.37/8.33	   (A^2 -> H(U1(a, a), U1(d, k)),A^2 -> H(U1(a, a), U1(d, k)))
25.37/8.33	   (A^2 -> H(f(c), U1(d, k)),A^2 -> H(f(c), U1(d, k)))
25.37/8.33	   (A^2 -> H(f(d), U1(d, k)),A^2 -> H(f(d), U1(d, k)))
25.37/8.33	   (A^2 -> H(f(a), U1(k, k)),A^2 -> H(f(a), U1(k, k)))
25.37/8.33	
25.37/8.33	
25.37/8.33	----------------------------------------
25.37/8.33	
25.37/8.33	(220)
25.37/8.33	Obligation:
25.37/8.33	Q DP problem:
25.37/8.33	The TRS P consists of the following rules:
25.37/8.33	
25.37/8.33	   H(x, x) -> G(x, x, f(k))
25.37/8.33	   G(d, x, x) -> A^2
25.37/8.33	   A^2 -> H(f(c), f(c))
25.37/8.33	   A^2 -> H(f(d), f(d))
25.37/8.33	   A^2 -> H(a, f(b))
25.37/8.33	   A^2 -> H(U1(e, d), f(b))
25.37/8.33	   A^2 -> H(U1(e, a), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, a), f(c))
25.37/8.33	   A^2 -> H(U1(e, a), f(d))
25.37/8.33	   A^2 -> H(U1(k, a), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, a), f(c))
25.37/8.33	   A^2 -> H(U1(k, a), f(d))
25.37/8.33	   A^2 -> H(U1(c, d), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, d), f(c))
25.37/8.33	   A^2 -> H(U1(c, d), f(d))
25.37/8.33	   A^2 -> H(U1(c, a), U1(c, b))
25.37/8.33	   A^2 -> H(U1(c, a), U1(d, b))
25.37/8.33	   A^2 -> H(U1(c, a), U1(b, c))
25.37/8.33	   A^2 -> H(U1(c, a), U1(b, d))
25.37/8.33	   A^2 -> H(U1(c, a), U1(c, c))
25.37/8.33	   A^2 -> H(U1(c, a), f(e))
25.37/8.33	   A^2 -> H(U1(c, a), f(k))
25.37/8.33	   A^2 -> H(U1(c, a), U1(d, d))
25.37/8.33	   A^2 -> H(U1(d, e), f(b))
25.37/8.33	   A^2 -> H(U1(d, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(d, c), f(c))
25.37/8.33	   A^2 -> H(U1(d, c), f(d))
25.37/8.33	   A^2 -> H(U1(d, a), U1(c, b))
25.37/8.33	   A^2 -> H(U1(d, a), U1(d, b))
25.37/8.33	   A^2 -> H(U1(d, a), U1(b, c))
25.37/8.33	   A^2 -> H(U1(d, a), U1(b, d))
25.37/8.33	   A^2 -> H(U1(d, a), U1(c, c))
25.37/8.33	   A^2 -> H(U1(d, a), f(e))
25.37/8.33	   A^2 -> H(U1(d, a), f(k))
25.37/8.33	   A^2 -> H(U1(d, a), U1(d, d))
25.37/8.33	   A^2 -> H(U1(a, e), U1(b, b))
25.37/8.33	   A^2 -> H(U1(a, e), f(c))
25.37/8.33	   A^2 -> H(U1(a, e), f(d))
25.37/8.33	   A^2 -> H(U1(a, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(a, k), f(c))
25.37/8.33	   A^2 -> H(U1(a, k), f(d))
25.37/8.33	   A^2 -> H(U1(a, c), U1(c, b))
25.37/8.33	   A^2 -> H(U1(a, c), U1(d, b))
25.37/8.33	   A^2 -> H(U1(a, c), U1(b, c))
25.37/8.33	   A^2 -> H(U1(a, c), U1(b, d))
25.37/8.33	   A^2 -> H(U1(a, c), U1(c, c))
25.37/8.33	   A^2 -> H(U1(a, c), f(e))
25.37/8.33	   A^2 -> H(U1(a, c), f(k))
25.37/8.33	   A^2 -> H(U1(a, c), U1(d, d))
25.37/8.33	   A^2 -> H(U1(a, d), U1(c, b))
25.37/8.33	   A^2 -> H(U1(a, d), U1(d, b))
25.37/8.33	   A^2 -> H(U1(a, d), U1(b, c))
25.37/8.33	   A^2 -> H(U1(a, d), U1(b, d))
25.37/8.33	   A^2 -> H(U1(a, d), U1(c, c))
25.37/8.33	   A^2 -> H(U1(a, d), f(e))
25.37/8.33	   A^2 -> H(U1(a, d), f(k))
25.37/8.33	   A^2 -> H(U1(a, d), U1(d, d))
25.37/8.33	   A^2 -> H(U1(a, a), U1(e, b))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, b))
25.37/8.33	   A^2 -> H(U1(a, a), U1(c, d))
25.37/8.33	   A^2 -> H(U1(a, a), U1(d, c))
25.37/8.33	   A^2 -> H(U1(a, a), U1(b, e))
25.37/8.33	   A^2 -> H(U1(a, a), U1(b, k))
25.37/8.33	   A^2 -> H(U1(a, a), U1(e, c))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, c))
25.37/8.33	   A^2 -> H(U1(a, a), U1(c, e))
25.37/8.33	   A^2 -> H(U1(a, a), U1(c, k))
25.37/8.33	   A^2 -> H(U1(a, a), U1(e, e))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, k))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, d))
25.37/8.33	   A^2 -> H(U1(a, a), U1(d, k))
25.37/8.33	   A^2 -> H(c, f(b))
25.37/8.33	   A^2 -> H(U1(e, k), f(b))
25.37/8.33	   A^2 -> H(U1(e, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, c), f(c))
25.37/8.33	   A^2 -> H(U1(e, c), f(d))
25.37/8.33	   A^2 -> H(U1(k, e), f(b))
25.37/8.33	   A^2 -> H(U1(k, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, c), f(c))
25.37/8.33	   A^2 -> H(U1(k, c), f(d))
25.37/8.33	   A^2 -> H(U1(c, e), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, e), f(c))
25.37/8.33	   A^2 -> H(U1(c, e), f(d))
25.37/8.33	   A^2 -> H(U1(c, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, k), f(c))
25.37/8.33	   A^2 -> H(U1(c, k), f(d))
25.37/8.33	   A^2 -> H(U1(c, c), U1(c, b))
25.37/8.33	   A^2 -> H(U1(c, c), U1(d, b))
25.37/8.33	   A^2 -> H(U1(c, c), U1(b, c))
25.37/8.33	   A^2 -> H(U1(c, c), U1(b, d))
25.37/8.33	   A^2 -> H(U1(c, c), U1(c, c))
25.37/8.33	   A^2 -> H(U1(c, c), f(e))
25.37/8.33	   A^2 -> H(U1(c, c), f(k))
25.37/8.33	   A^2 -> H(U1(c, c), U1(d, d))
25.37/8.33	   A^2 -> H(e, f(b))
25.37/8.33	   A^2 -> H(U1(e, e), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, e), f(c))
25.37/8.33	   A^2 -> H(U1(e, e), f(d))
25.37/8.33	   A^2 -> H(f(e), U1(c, b))
25.37/8.33	   A^2 -> H(f(e), U1(d, b))
25.37/8.33	   A^2 -> H(f(e), U1(b, c))
25.37/8.33	   A^2 -> H(f(e), U1(b, d))
25.37/8.33	   A^2 -> H(f(e), U1(c, c))
25.37/8.33	   A^2 -> H(f(e), f(e))
25.37/8.33	   A^2 -> H(f(e), f(k))
25.37/8.33	   A^2 -> H(f(e), U1(d, d))
25.37/8.33	   A^2 -> H(U1(k, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, k), f(c))
25.37/8.33	   A^2 -> H(U1(k, k), f(d))
25.37/8.33	   A^2 -> H(f(k), U1(c, b))
25.37/8.33	   A^2 -> H(f(k), U1(d, b))
25.37/8.33	   A^2 -> H(f(k), U1(b, c))
25.37/8.33	   A^2 -> H(f(k), U1(b, d))
25.37/8.33	   A^2 -> H(f(k), U1(c, c))
25.37/8.33	   A^2 -> H(f(k), f(e))
25.37/8.33	   A^2 -> H(f(k), f(k))
25.37/8.33	   A^2 -> H(f(k), U1(d, d))
25.37/8.33	   A^2 -> H(f(c), U1(e, b))
25.37/8.33	   A^2 -> H(f(c), U1(k, b))
25.37/8.33	   A^2 -> H(f(c), U1(c, d))
25.37/8.33	   A^2 -> H(f(c), U1(d, c))
25.37/8.33	   A^2 -> H(f(c), U1(b, e))
25.37/8.33	   A^2 -> H(f(c), U1(b, k))
25.37/8.33	   A^2 -> H(f(c), U1(k, d))
25.37/8.33	   A^2 -> H(f(c), U1(d, k))
25.37/8.33	   A^2 -> H(f(c), U1(k, k))
25.37/8.33	   A^2 -> H(U1(k, k), f(b))
25.37/8.33	   A^2 -> H(U1(k, d), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, d), f(c))
25.37/8.33	   A^2 -> H(U1(k, d), f(d))
25.37/8.33	   A^2 -> H(U1(d, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(d, k), f(c))
25.37/8.33	   A^2 -> H(U1(d, k), f(d))
25.37/8.33	   A^2 -> H(U1(d, d), U1(c, b))
25.37/8.33	   A^2 -> H(U1(d, d), U1(d, b))
25.37/8.33	   A^2 -> H(U1(d, d), U1(b, c))
25.37/8.33	   A^2 -> H(U1(d, d), U1(b, d))
25.37/8.33	   A^2 -> H(U1(d, d), U1(c, c))
25.37/8.33	   A^2 -> H(U1(d, d), f(e))
25.37/8.33	   A^2 -> H(U1(d, d), f(k))
25.37/8.33	   A^2 -> H(U1(d, d), U1(d, d))
25.37/8.33	   A^2 -> H(f(d), U1(e, b))
25.37/8.33	   A^2 -> H(f(d), U1(k, b))
25.37/8.33	   A^2 -> H(f(d), U1(c, d))
25.37/8.33	   A^2 -> H(f(d), U1(d, c))
25.37/8.33	   A^2 -> H(f(d), U1(b, e))
25.37/8.33	   A^2 -> H(f(d), U1(b, k))
25.37/8.33	   A^2 -> H(f(d), U1(e, c))
25.37/8.33	   A^2 -> H(f(d), U1(k, c))
25.37/8.33	   A^2 -> H(f(d), U1(c, e))
25.37/8.33	   A^2 -> H(f(d), U1(c, k))
25.37/8.33	   A^2 -> H(f(d), U1(e, e))
25.37/8.33	   A^2 -> H(f(d), U1(k, k))
25.37/8.33	   A^2 -> H(f(a), b)
25.37/8.33	   A^2 -> H(f(a), U1(e, d))
25.37/8.33	   A^2 -> H(f(a), U1(d, e))
25.37/8.33	   A^2 -> H(f(c), U1(e, c))
25.37/8.33	   A^2 -> H(f(c), U1(k, c))
25.37/8.33	   A^2 -> H(f(c), U1(c, e))
25.37/8.33	   A^2 -> H(f(c), U1(c, k))
25.37/8.33	   A^2 -> H(f(a), c)
25.37/8.33	   A^2 -> H(f(a), U1(e, k))
25.37/8.33	   A^2 -> H(f(a), U1(k, e))
25.37/8.33	   A^2 -> H(f(c), U1(e, e))
25.37/8.33	   A^2 -> H(f(a), e)
25.37/8.33	   A^2 -> H(f(d), U1(k, d))
25.37/8.33	   A^2 -> H(f(d), U1(d, k))
25.37/8.33	   A^2 -> H(f(a), U1(k, k))
25.37/8.33	
25.37/8.33	The TRS R consists of the following rules:
25.37/8.33	
25.37/8.33	   f(x) -> U1(x, x)
25.37/8.33	   U1(e, x) -> x
25.37/8.33	   a -> c
25.37/8.33	   a -> d
25.37/8.33	   b -> c
25.37/8.33	   b -> d
25.37/8.33	   d -> k
25.37/8.33	   c -> e
25.37/8.33	   c -> k
25.37/8.33	
25.37/8.33	Q is empty.
25.37/8.33	We have to consider all minimal (P,Q,R)-chains.
25.37/8.33	----------------------------------------
25.37/8.33	
25.37/8.33	(221) TransformationProof (EQUIVALENT)
25.37/8.33	By narrowing [LPAR04] the rule A^2 -> H(a, f(b)) at position [] we obtained the following new rules [LPAR04]:
25.37/8.33	
25.37/8.33	   (A^2 -> H(c, f(b)),A^2 -> H(c, f(b)))
25.37/8.33	   (A^2 -> H(d, f(b)),A^2 -> H(d, f(b)))
25.37/8.33	   (A^2 -> H(a, U1(b, b)),A^2 -> H(a, U1(b, b)))
25.37/8.33	   (A^2 -> H(a, f(c)),A^2 -> H(a, f(c)))
25.37/8.33	   (A^2 -> H(a, f(d)),A^2 -> H(a, f(d)))
25.37/8.33	
25.37/8.33	
25.37/8.33	----------------------------------------
25.37/8.33	
25.37/8.33	(222)
25.37/8.33	Obligation:
25.37/8.33	Q DP problem:
25.37/8.33	The TRS P consists of the following rules:
25.37/8.33	
25.37/8.33	   H(x, x) -> G(x, x, f(k))
25.37/8.33	   G(d, x, x) -> A^2
25.37/8.33	   A^2 -> H(f(c), f(c))
25.37/8.33	   A^2 -> H(f(d), f(d))
25.37/8.33	   A^2 -> H(U1(e, d), f(b))
25.37/8.33	   A^2 -> H(U1(e, a), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, a), f(c))
25.37/8.33	   A^2 -> H(U1(e, a), f(d))
25.37/8.33	   A^2 -> H(U1(k, a), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, a), f(c))
25.37/8.33	   A^2 -> H(U1(k, a), f(d))
25.37/8.33	   A^2 -> H(U1(c, d), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, d), f(c))
25.37/8.33	   A^2 -> H(U1(c, d), f(d))
25.37/8.33	   A^2 -> H(U1(c, a), U1(c, b))
25.37/8.33	   A^2 -> H(U1(c, a), U1(d, b))
25.37/8.33	   A^2 -> H(U1(c, a), U1(b, c))
25.37/8.33	   A^2 -> H(U1(c, a), U1(b, d))
25.37/8.33	   A^2 -> H(U1(c, a), U1(c, c))
25.37/8.33	   A^2 -> H(U1(c, a), f(e))
25.37/8.33	   A^2 -> H(U1(c, a), f(k))
25.37/8.33	   A^2 -> H(U1(c, a), U1(d, d))
25.37/8.33	   A^2 -> H(U1(d, e), f(b))
25.37/8.33	   A^2 -> H(U1(d, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(d, c), f(c))
25.37/8.33	   A^2 -> H(U1(d, c), f(d))
25.37/8.33	   A^2 -> H(U1(d, a), U1(c, b))
25.37/8.33	   A^2 -> H(U1(d, a), U1(d, b))
25.37/8.33	   A^2 -> H(U1(d, a), U1(b, c))
25.37/8.33	   A^2 -> H(U1(d, a), U1(b, d))
25.37/8.33	   A^2 -> H(U1(d, a), U1(c, c))
25.37/8.33	   A^2 -> H(U1(d, a), f(e))
25.37/8.33	   A^2 -> H(U1(d, a), f(k))
25.37/8.33	   A^2 -> H(U1(d, a), U1(d, d))
25.37/8.33	   A^2 -> H(U1(a, e), U1(b, b))
25.37/8.33	   A^2 -> H(U1(a, e), f(c))
25.37/8.33	   A^2 -> H(U1(a, e), f(d))
25.37/8.33	   A^2 -> H(U1(a, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(a, k), f(c))
25.37/8.33	   A^2 -> H(U1(a, k), f(d))
25.37/8.33	   A^2 -> H(U1(a, c), U1(c, b))
25.37/8.33	   A^2 -> H(U1(a, c), U1(d, b))
25.37/8.33	   A^2 -> H(U1(a, c), U1(b, c))
25.37/8.33	   A^2 -> H(U1(a, c), U1(b, d))
25.37/8.33	   A^2 -> H(U1(a, c), U1(c, c))
25.37/8.33	   A^2 -> H(U1(a, c), f(e))
25.37/8.33	   A^2 -> H(U1(a, c), f(k))
25.37/8.33	   A^2 -> H(U1(a, c), U1(d, d))
25.37/8.33	   A^2 -> H(U1(a, d), U1(c, b))
25.37/8.33	   A^2 -> H(U1(a, d), U1(d, b))
25.37/8.33	   A^2 -> H(U1(a, d), U1(b, c))
25.37/8.33	   A^2 -> H(U1(a, d), U1(b, d))
25.37/8.33	   A^2 -> H(U1(a, d), U1(c, c))
25.37/8.33	   A^2 -> H(U1(a, d), f(e))
25.37/8.33	   A^2 -> H(U1(a, d), f(k))
25.37/8.33	   A^2 -> H(U1(a, d), U1(d, d))
25.37/8.33	   A^2 -> H(U1(a, a), U1(e, b))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, b))
25.37/8.33	   A^2 -> H(U1(a, a), U1(c, d))
25.37/8.33	   A^2 -> H(U1(a, a), U1(d, c))
25.37/8.33	   A^2 -> H(U1(a, a), U1(b, e))
25.37/8.33	   A^2 -> H(U1(a, a), U1(b, k))
25.37/8.33	   A^2 -> H(U1(a, a), U1(e, c))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, c))
25.37/8.33	   A^2 -> H(U1(a, a), U1(c, e))
25.37/8.33	   A^2 -> H(U1(a, a), U1(c, k))
25.37/8.33	   A^2 -> H(U1(a, a), U1(e, e))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, k))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, d))
25.37/8.33	   A^2 -> H(U1(a, a), U1(d, k))
25.37/8.33	   A^2 -> H(c, f(b))
25.37/8.33	   A^2 -> H(U1(e, k), f(b))
25.37/8.33	   A^2 -> H(U1(e, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, c), f(c))
25.37/8.33	   A^2 -> H(U1(e, c), f(d))
25.37/8.33	   A^2 -> H(U1(k, e), f(b))
25.37/8.33	   A^2 -> H(U1(k, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, c), f(c))
25.37/8.33	   A^2 -> H(U1(k, c), f(d))
25.37/8.33	   A^2 -> H(U1(c, e), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, e), f(c))
25.37/8.33	   A^2 -> H(U1(c, e), f(d))
25.37/8.33	   A^2 -> H(U1(c, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, k), f(c))
25.37/8.33	   A^2 -> H(U1(c, k), f(d))
25.37/8.33	   A^2 -> H(U1(c, c), U1(c, b))
25.37/8.33	   A^2 -> H(U1(c, c), U1(d, b))
25.37/8.33	   A^2 -> H(U1(c, c), U1(b, c))
25.37/8.33	   A^2 -> H(U1(c, c), U1(b, d))
25.37/8.33	   A^2 -> H(U1(c, c), U1(c, c))
25.37/8.33	   A^2 -> H(U1(c, c), f(e))
25.37/8.33	   A^2 -> H(U1(c, c), f(k))
25.37/8.33	   A^2 -> H(U1(c, c), U1(d, d))
25.37/8.33	   A^2 -> H(e, f(b))
25.37/8.33	   A^2 -> H(U1(e, e), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, e), f(c))
25.37/8.33	   A^2 -> H(U1(e, e), f(d))
25.37/8.33	   A^2 -> H(f(e), U1(c, b))
25.37/8.33	   A^2 -> H(f(e), U1(d, b))
25.37/8.33	   A^2 -> H(f(e), U1(b, c))
25.37/8.33	   A^2 -> H(f(e), U1(b, d))
25.37/8.33	   A^2 -> H(f(e), U1(c, c))
25.37/8.33	   A^2 -> H(f(e), f(e))
25.37/8.33	   A^2 -> H(f(e), f(k))
25.37/8.33	   A^2 -> H(f(e), U1(d, d))
25.37/8.33	   A^2 -> H(U1(k, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, k), f(c))
25.37/8.33	   A^2 -> H(U1(k, k), f(d))
25.37/8.33	   A^2 -> H(f(k), U1(c, b))
25.37/8.33	   A^2 -> H(f(k), U1(d, b))
25.37/8.33	   A^2 -> H(f(k), U1(b, c))
25.37/8.33	   A^2 -> H(f(k), U1(b, d))
25.37/8.33	   A^2 -> H(f(k), U1(c, c))
25.37/8.33	   A^2 -> H(f(k), f(e))
25.37/8.33	   A^2 -> H(f(k), f(k))
25.37/8.33	   A^2 -> H(f(k), U1(d, d))
25.37/8.33	   A^2 -> H(f(c), U1(e, b))
25.37/8.33	   A^2 -> H(f(c), U1(k, b))
25.37/8.33	   A^2 -> H(f(c), U1(c, d))
25.37/8.33	   A^2 -> H(f(c), U1(d, c))
25.37/8.33	   A^2 -> H(f(c), U1(b, e))
25.37/8.33	   A^2 -> H(f(c), U1(b, k))
25.37/8.33	   A^2 -> H(f(c), U1(k, d))
25.37/8.33	   A^2 -> H(f(c), U1(d, k))
25.37/8.33	   A^2 -> H(f(c), U1(k, k))
25.37/8.33	   A^2 -> H(U1(k, k), f(b))
25.37/8.33	   A^2 -> H(U1(k, d), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, d), f(c))
25.37/8.33	   A^2 -> H(U1(k, d), f(d))
25.37/8.33	   A^2 -> H(U1(d, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(d, k), f(c))
25.37/8.33	   A^2 -> H(U1(d, k), f(d))
25.37/8.33	   A^2 -> H(U1(d, d), U1(c, b))
25.37/8.33	   A^2 -> H(U1(d, d), U1(d, b))
25.37/8.33	   A^2 -> H(U1(d, d), U1(b, c))
25.37/8.33	   A^2 -> H(U1(d, d), U1(b, d))
25.37/8.33	   A^2 -> H(U1(d, d), U1(c, c))
25.37/8.33	   A^2 -> H(U1(d, d), f(e))
25.37/8.33	   A^2 -> H(U1(d, d), f(k))
25.37/8.33	   A^2 -> H(U1(d, d), U1(d, d))
25.37/8.33	   A^2 -> H(f(d), U1(e, b))
25.37/8.33	   A^2 -> H(f(d), U1(k, b))
25.37/8.33	   A^2 -> H(f(d), U1(c, d))
25.37/8.33	   A^2 -> H(f(d), U1(d, c))
25.37/8.33	   A^2 -> H(f(d), U1(b, e))
25.37/8.33	   A^2 -> H(f(d), U1(b, k))
25.37/8.33	   A^2 -> H(f(d), U1(e, c))
25.37/8.33	   A^2 -> H(f(d), U1(k, c))
25.37/8.33	   A^2 -> H(f(d), U1(c, e))
25.37/8.33	   A^2 -> H(f(d), U1(c, k))
25.37/8.33	   A^2 -> H(f(d), U1(e, e))
25.37/8.33	   A^2 -> H(f(d), U1(k, k))
25.37/8.33	   A^2 -> H(f(a), b)
25.37/8.33	   A^2 -> H(f(a), U1(e, d))
25.37/8.33	   A^2 -> H(f(a), U1(d, e))
25.37/8.33	   A^2 -> H(f(c), U1(e, c))
25.37/8.33	   A^2 -> H(f(c), U1(k, c))
25.37/8.33	   A^2 -> H(f(c), U1(c, e))
25.37/8.33	   A^2 -> H(f(c), U1(c, k))
25.37/8.33	   A^2 -> H(f(a), c)
25.37/8.33	   A^2 -> H(f(a), U1(e, k))
25.37/8.33	   A^2 -> H(f(a), U1(k, e))
25.37/8.33	   A^2 -> H(f(c), U1(e, e))
25.37/8.33	   A^2 -> H(f(a), e)
25.37/8.33	   A^2 -> H(f(d), U1(k, d))
25.37/8.33	   A^2 -> H(f(d), U1(d, k))
25.37/8.33	   A^2 -> H(f(a), U1(k, k))
25.37/8.33	   A^2 -> H(d, f(b))
25.37/8.33	   A^2 -> H(a, U1(b, b))
25.37/8.33	   A^2 -> H(a, f(c))
25.37/8.33	   A^2 -> H(a, f(d))
25.37/8.33	
25.37/8.33	The TRS R consists of the following rules:
25.37/8.33	
25.37/8.33	   f(x) -> U1(x, x)
25.37/8.33	   U1(e, x) -> x
25.37/8.33	   a -> c
25.37/8.33	   a -> d
25.37/8.33	   b -> c
25.37/8.33	   b -> d
25.37/8.33	   d -> k
25.37/8.33	   c -> e
25.37/8.33	   c -> k
25.37/8.33	
25.37/8.33	Q is empty.
25.37/8.33	We have to consider all minimal (P,Q,R)-chains.
25.37/8.33	----------------------------------------
25.37/8.33	
25.37/8.33	(223) TransformationProof (EQUIVALENT)
25.37/8.33	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), f(b)) at position [] we obtained the following new rules [LPAR04]:
25.37/8.33	
25.37/8.33	   (A^2 -> H(d, f(b)),A^2 -> H(d, f(b)))
25.37/8.33	   (A^2 -> H(U1(e, k), f(b)),A^2 -> H(U1(e, k), f(b)))
25.37/8.33	   (A^2 -> H(U1(e, d), U1(b, b)),A^2 -> H(U1(e, d), U1(b, b)))
25.37/8.33	   (A^2 -> H(U1(e, d), f(c)),A^2 -> H(U1(e, d), f(c)))
25.37/8.33	   (A^2 -> H(U1(e, d), f(d)),A^2 -> H(U1(e, d), f(d)))
25.37/8.33	
25.37/8.33	
25.37/8.33	----------------------------------------
25.37/8.33	
25.37/8.33	(224)
25.37/8.33	Obligation:
25.37/8.33	Q DP problem:
25.37/8.33	The TRS P consists of the following rules:
25.37/8.33	
25.37/8.33	   H(x, x) -> G(x, x, f(k))
25.37/8.33	   G(d, x, x) -> A^2
25.37/8.33	   A^2 -> H(f(c), f(c))
25.37/8.33	   A^2 -> H(f(d), f(d))
25.37/8.33	   A^2 -> H(U1(e, a), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, a), f(c))
25.37/8.33	   A^2 -> H(U1(e, a), f(d))
25.37/8.33	   A^2 -> H(U1(k, a), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, a), f(c))
25.37/8.33	   A^2 -> H(U1(k, a), f(d))
25.37/8.33	   A^2 -> H(U1(c, d), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, d), f(c))
25.37/8.33	   A^2 -> H(U1(c, d), f(d))
25.37/8.33	   A^2 -> H(U1(c, a), U1(c, b))
25.37/8.33	   A^2 -> H(U1(c, a), U1(d, b))
25.37/8.33	   A^2 -> H(U1(c, a), U1(b, c))
25.37/8.33	   A^2 -> H(U1(c, a), U1(b, d))
25.37/8.33	   A^2 -> H(U1(c, a), U1(c, c))
25.37/8.33	   A^2 -> H(U1(c, a), f(e))
25.37/8.33	   A^2 -> H(U1(c, a), f(k))
25.37/8.33	   A^2 -> H(U1(c, a), U1(d, d))
25.37/8.33	   A^2 -> H(U1(d, e), f(b))
25.37/8.33	   A^2 -> H(U1(d, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(d, c), f(c))
25.37/8.33	   A^2 -> H(U1(d, c), f(d))
25.37/8.33	   A^2 -> H(U1(d, a), U1(c, b))
25.37/8.33	   A^2 -> H(U1(d, a), U1(d, b))
25.37/8.33	   A^2 -> H(U1(d, a), U1(b, c))
25.37/8.33	   A^2 -> H(U1(d, a), U1(b, d))
25.37/8.33	   A^2 -> H(U1(d, a), U1(c, c))
25.37/8.33	   A^2 -> H(U1(d, a), f(e))
25.37/8.33	   A^2 -> H(U1(d, a), f(k))
25.37/8.33	   A^2 -> H(U1(d, a), U1(d, d))
25.37/8.33	   A^2 -> H(U1(a, e), U1(b, b))
25.37/8.33	   A^2 -> H(U1(a, e), f(c))
25.37/8.33	   A^2 -> H(U1(a, e), f(d))
25.37/8.33	   A^2 -> H(U1(a, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(a, k), f(c))
25.37/8.33	   A^2 -> H(U1(a, k), f(d))
25.37/8.33	   A^2 -> H(U1(a, c), U1(c, b))
25.37/8.33	   A^2 -> H(U1(a, c), U1(d, b))
25.37/8.33	   A^2 -> H(U1(a, c), U1(b, c))
25.37/8.33	   A^2 -> H(U1(a, c), U1(b, d))
25.37/8.33	   A^2 -> H(U1(a, c), U1(c, c))
25.37/8.33	   A^2 -> H(U1(a, c), f(e))
25.37/8.33	   A^2 -> H(U1(a, c), f(k))
25.37/8.33	   A^2 -> H(U1(a, c), U1(d, d))
25.37/8.33	   A^2 -> H(U1(a, d), U1(c, b))
25.37/8.33	   A^2 -> H(U1(a, d), U1(d, b))
25.37/8.33	   A^2 -> H(U1(a, d), U1(b, c))
25.37/8.33	   A^2 -> H(U1(a, d), U1(b, d))
25.37/8.33	   A^2 -> H(U1(a, d), U1(c, c))
25.37/8.33	   A^2 -> H(U1(a, d), f(e))
25.37/8.33	   A^2 -> H(U1(a, d), f(k))
25.37/8.33	   A^2 -> H(U1(a, d), U1(d, d))
25.37/8.33	   A^2 -> H(U1(a, a), U1(e, b))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, b))
25.37/8.33	   A^2 -> H(U1(a, a), U1(c, d))
25.37/8.33	   A^2 -> H(U1(a, a), U1(d, c))
25.37/8.33	   A^2 -> H(U1(a, a), U1(b, e))
25.37/8.33	   A^2 -> H(U1(a, a), U1(b, k))
25.37/8.33	   A^2 -> H(U1(a, a), U1(e, c))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, c))
25.37/8.33	   A^2 -> H(U1(a, a), U1(c, e))
25.37/8.33	   A^2 -> H(U1(a, a), U1(c, k))
25.37/8.33	   A^2 -> H(U1(a, a), U1(e, e))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, k))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, d))
25.37/8.33	   A^2 -> H(U1(a, a), U1(d, k))
25.37/8.33	   A^2 -> H(c, f(b))
25.37/8.33	   A^2 -> H(U1(e, k), f(b))
25.37/8.33	   A^2 -> H(U1(e, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, c), f(c))
25.37/8.33	   A^2 -> H(U1(e, c), f(d))
25.37/8.33	   A^2 -> H(U1(k, e), f(b))
25.37/8.33	   A^2 -> H(U1(k, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, c), f(c))
25.37/8.33	   A^2 -> H(U1(k, c), f(d))
25.37/8.33	   A^2 -> H(U1(c, e), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, e), f(c))
25.37/8.33	   A^2 -> H(U1(c, e), f(d))
25.37/8.33	   A^2 -> H(U1(c, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, k), f(c))
25.37/8.33	   A^2 -> H(U1(c, k), f(d))
25.37/8.33	   A^2 -> H(U1(c, c), U1(c, b))
25.37/8.33	   A^2 -> H(U1(c, c), U1(d, b))
25.37/8.33	   A^2 -> H(U1(c, c), U1(b, c))
25.37/8.33	   A^2 -> H(U1(c, c), U1(b, d))
25.37/8.33	   A^2 -> H(U1(c, c), U1(c, c))
25.37/8.33	   A^2 -> H(U1(c, c), f(e))
25.37/8.33	   A^2 -> H(U1(c, c), f(k))
25.37/8.33	   A^2 -> H(U1(c, c), U1(d, d))
25.37/8.33	   A^2 -> H(e, f(b))
25.37/8.33	   A^2 -> H(U1(e, e), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, e), f(c))
25.37/8.33	   A^2 -> H(U1(e, e), f(d))
25.37/8.33	   A^2 -> H(f(e), U1(c, b))
25.37/8.33	   A^2 -> H(f(e), U1(d, b))
25.37/8.33	   A^2 -> H(f(e), U1(b, c))
25.37/8.33	   A^2 -> H(f(e), U1(b, d))
25.37/8.33	   A^2 -> H(f(e), U1(c, c))
25.37/8.33	   A^2 -> H(f(e), f(e))
25.37/8.33	   A^2 -> H(f(e), f(k))
25.37/8.33	   A^2 -> H(f(e), U1(d, d))
25.37/8.33	   A^2 -> H(U1(k, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, k), f(c))
25.37/8.33	   A^2 -> H(U1(k, k), f(d))
25.37/8.33	   A^2 -> H(f(k), U1(c, b))
25.37/8.33	   A^2 -> H(f(k), U1(d, b))
25.37/8.33	   A^2 -> H(f(k), U1(b, c))
25.37/8.33	   A^2 -> H(f(k), U1(b, d))
25.37/8.33	   A^2 -> H(f(k), U1(c, c))
25.37/8.33	   A^2 -> H(f(k), f(e))
25.37/8.33	   A^2 -> H(f(k), f(k))
25.37/8.33	   A^2 -> H(f(k), U1(d, d))
25.37/8.33	   A^2 -> H(f(c), U1(e, b))
25.37/8.33	   A^2 -> H(f(c), U1(k, b))
25.37/8.33	   A^2 -> H(f(c), U1(c, d))
25.37/8.33	   A^2 -> H(f(c), U1(d, c))
25.37/8.33	   A^2 -> H(f(c), U1(b, e))
25.37/8.33	   A^2 -> H(f(c), U1(b, k))
25.37/8.33	   A^2 -> H(f(c), U1(k, d))
25.37/8.33	   A^2 -> H(f(c), U1(d, k))
25.37/8.33	   A^2 -> H(f(c), U1(k, k))
25.37/8.33	   A^2 -> H(U1(k, k), f(b))
25.37/8.33	   A^2 -> H(U1(k, d), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, d), f(c))
25.37/8.33	   A^2 -> H(U1(k, d), f(d))
25.37/8.33	   A^2 -> H(U1(d, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(d, k), f(c))
25.37/8.33	   A^2 -> H(U1(d, k), f(d))
25.37/8.33	   A^2 -> H(U1(d, d), U1(c, b))
25.37/8.33	   A^2 -> H(U1(d, d), U1(d, b))
25.37/8.33	   A^2 -> H(U1(d, d), U1(b, c))
25.37/8.33	   A^2 -> H(U1(d, d), U1(b, d))
25.37/8.33	   A^2 -> H(U1(d, d), U1(c, c))
25.37/8.33	   A^2 -> H(U1(d, d), f(e))
25.37/8.33	   A^2 -> H(U1(d, d), f(k))
25.37/8.33	   A^2 -> H(U1(d, d), U1(d, d))
25.37/8.33	   A^2 -> H(f(d), U1(e, b))
25.37/8.33	   A^2 -> H(f(d), U1(k, b))
25.37/8.33	   A^2 -> H(f(d), U1(c, d))
25.37/8.33	   A^2 -> H(f(d), U1(d, c))
25.37/8.33	   A^2 -> H(f(d), U1(b, e))
25.37/8.33	   A^2 -> H(f(d), U1(b, k))
25.37/8.33	   A^2 -> H(f(d), U1(e, c))
25.37/8.33	   A^2 -> H(f(d), U1(k, c))
25.37/8.33	   A^2 -> H(f(d), U1(c, e))
25.37/8.33	   A^2 -> H(f(d), U1(c, k))
25.37/8.33	   A^2 -> H(f(d), U1(e, e))
25.37/8.33	   A^2 -> H(f(d), U1(k, k))
25.37/8.33	   A^2 -> H(f(a), b)
25.37/8.33	   A^2 -> H(f(a), U1(e, d))
25.37/8.33	   A^2 -> H(f(a), U1(d, e))
25.37/8.33	   A^2 -> H(f(c), U1(e, c))
25.37/8.33	   A^2 -> H(f(c), U1(k, c))
25.37/8.33	   A^2 -> H(f(c), U1(c, e))
25.37/8.33	   A^2 -> H(f(c), U1(c, k))
25.37/8.33	   A^2 -> H(f(a), c)
25.37/8.33	   A^2 -> H(f(a), U1(e, k))
25.37/8.33	   A^2 -> H(f(a), U1(k, e))
25.37/8.33	   A^2 -> H(f(c), U1(e, e))
25.37/8.33	   A^2 -> H(f(a), e)
25.37/8.33	   A^2 -> H(f(d), U1(k, d))
25.37/8.33	   A^2 -> H(f(d), U1(d, k))
25.37/8.33	   A^2 -> H(f(a), U1(k, k))
25.37/8.33	   A^2 -> H(d, f(b))
25.37/8.33	   A^2 -> H(a, U1(b, b))
25.37/8.33	   A^2 -> H(a, f(c))
25.37/8.33	   A^2 -> H(a, f(d))
25.37/8.33	   A^2 -> H(U1(e, d), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, d), f(c))
25.37/8.33	   A^2 -> H(U1(e, d), f(d))
25.37/8.33	
25.37/8.33	The TRS R consists of the following rules:
25.37/8.33	
25.37/8.33	   f(x) -> U1(x, x)
25.37/8.33	   U1(e, x) -> x
25.37/8.33	   a -> c
25.37/8.33	   a -> d
25.37/8.33	   b -> c
25.37/8.33	   b -> d
25.37/8.33	   d -> k
25.37/8.33	   c -> e
25.37/8.33	   c -> k
25.37/8.33	
25.37/8.33	Q is empty.
25.37/8.33	We have to consider all minimal (P,Q,R)-chains.
25.37/8.33	----------------------------------------
25.37/8.33	
25.37/8.33	(225) TransformationProof (EQUIVALENT)
25.37/8.33	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
25.37/8.33	
25.37/8.33	   (A^2 -> H(a, U1(b, b)),A^2 -> H(a, U1(b, b)))
25.37/8.33	   (A^2 -> H(U1(e, c), U1(b, b)),A^2 -> H(U1(e, c), U1(b, b)))
25.37/8.33	   (A^2 -> H(U1(e, d), U1(b, b)),A^2 -> H(U1(e, d), U1(b, b)))
25.37/8.33	   (A^2 -> H(U1(e, a), U1(c, b)),A^2 -> H(U1(e, a), U1(c, b)))
25.37/8.33	   (A^2 -> H(U1(e, a), U1(d, b)),A^2 -> H(U1(e, a), U1(d, b)))
25.37/8.33	   (A^2 -> H(U1(e, a), U1(b, c)),A^2 -> H(U1(e, a), U1(b, c)))
25.37/8.33	   (A^2 -> H(U1(e, a), U1(b, d)),A^2 -> H(U1(e, a), U1(b, d)))
25.37/8.33	
25.37/8.33	
25.37/8.33	----------------------------------------
25.37/8.33	
25.37/8.33	(226)
25.37/8.33	Obligation:
25.37/8.33	Q DP problem:
25.37/8.33	The TRS P consists of the following rules:
25.37/8.33	
25.37/8.33	   H(x, x) -> G(x, x, f(k))
25.37/8.33	   G(d, x, x) -> A^2
25.37/8.33	   A^2 -> H(f(c), f(c))
25.37/8.33	   A^2 -> H(f(d), f(d))
25.37/8.33	   A^2 -> H(U1(e, a), f(c))
25.37/8.33	   A^2 -> H(U1(e, a), f(d))
25.37/8.33	   A^2 -> H(U1(k, a), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, a), f(c))
25.37/8.33	   A^2 -> H(U1(k, a), f(d))
25.37/8.33	   A^2 -> H(U1(c, d), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, d), f(c))
25.37/8.33	   A^2 -> H(U1(c, d), f(d))
25.37/8.33	   A^2 -> H(U1(c, a), U1(c, b))
25.37/8.33	   A^2 -> H(U1(c, a), U1(d, b))
25.37/8.33	   A^2 -> H(U1(c, a), U1(b, c))
25.37/8.33	   A^2 -> H(U1(c, a), U1(b, d))
25.37/8.33	   A^2 -> H(U1(c, a), U1(c, c))
25.37/8.33	   A^2 -> H(U1(c, a), f(e))
25.37/8.33	   A^2 -> H(U1(c, a), f(k))
25.37/8.33	   A^2 -> H(U1(c, a), U1(d, d))
25.37/8.33	   A^2 -> H(U1(d, e), f(b))
25.37/8.33	   A^2 -> H(U1(d, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(d, c), f(c))
25.37/8.33	   A^2 -> H(U1(d, c), f(d))
25.37/8.33	   A^2 -> H(U1(d, a), U1(c, b))
25.37/8.33	   A^2 -> H(U1(d, a), U1(d, b))
25.37/8.33	   A^2 -> H(U1(d, a), U1(b, c))
25.37/8.33	   A^2 -> H(U1(d, a), U1(b, d))
25.37/8.33	   A^2 -> H(U1(d, a), U1(c, c))
25.37/8.33	   A^2 -> H(U1(d, a), f(e))
25.37/8.33	   A^2 -> H(U1(d, a), f(k))
25.37/8.33	   A^2 -> H(U1(d, a), U1(d, d))
25.37/8.33	   A^2 -> H(U1(a, e), U1(b, b))
25.37/8.33	   A^2 -> H(U1(a, e), f(c))
25.37/8.33	   A^2 -> H(U1(a, e), f(d))
25.37/8.33	   A^2 -> H(U1(a, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(a, k), f(c))
25.37/8.33	   A^2 -> H(U1(a, k), f(d))
25.37/8.33	   A^2 -> H(U1(a, c), U1(c, b))
25.37/8.33	   A^2 -> H(U1(a, c), U1(d, b))
25.37/8.33	   A^2 -> H(U1(a, c), U1(b, c))
25.37/8.33	   A^2 -> H(U1(a, c), U1(b, d))
25.37/8.33	   A^2 -> H(U1(a, c), U1(c, c))
25.37/8.33	   A^2 -> H(U1(a, c), f(e))
25.37/8.33	   A^2 -> H(U1(a, c), f(k))
25.37/8.33	   A^2 -> H(U1(a, c), U1(d, d))
25.37/8.33	   A^2 -> H(U1(a, d), U1(c, b))
25.37/8.33	   A^2 -> H(U1(a, d), U1(d, b))
25.37/8.33	   A^2 -> H(U1(a, d), U1(b, c))
25.37/8.33	   A^2 -> H(U1(a, d), U1(b, d))
25.37/8.33	   A^2 -> H(U1(a, d), U1(c, c))
25.37/8.33	   A^2 -> H(U1(a, d), f(e))
25.37/8.33	   A^2 -> H(U1(a, d), f(k))
25.37/8.33	   A^2 -> H(U1(a, d), U1(d, d))
25.37/8.33	   A^2 -> H(U1(a, a), U1(e, b))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, b))
25.37/8.33	   A^2 -> H(U1(a, a), U1(c, d))
25.37/8.33	   A^2 -> H(U1(a, a), U1(d, c))
25.37/8.33	   A^2 -> H(U1(a, a), U1(b, e))
25.37/8.33	   A^2 -> H(U1(a, a), U1(b, k))
25.37/8.33	   A^2 -> H(U1(a, a), U1(e, c))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, c))
25.37/8.33	   A^2 -> H(U1(a, a), U1(c, e))
25.37/8.33	   A^2 -> H(U1(a, a), U1(c, k))
25.37/8.33	   A^2 -> H(U1(a, a), U1(e, e))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, k))
25.37/8.33	   A^2 -> H(U1(a, a), U1(k, d))
25.37/8.33	   A^2 -> H(U1(a, a), U1(d, k))
25.37/8.33	   A^2 -> H(c, f(b))
25.37/8.33	   A^2 -> H(U1(e, k), f(b))
25.37/8.33	   A^2 -> H(U1(e, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, c), f(c))
25.37/8.33	   A^2 -> H(U1(e, c), f(d))
25.37/8.33	   A^2 -> H(U1(k, e), f(b))
25.37/8.33	   A^2 -> H(U1(k, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, c), f(c))
25.37/8.33	   A^2 -> H(U1(k, c), f(d))
25.37/8.33	   A^2 -> H(U1(c, e), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, e), f(c))
25.37/8.33	   A^2 -> H(U1(c, e), f(d))
25.37/8.33	   A^2 -> H(U1(c, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, k), f(c))
25.37/8.33	   A^2 -> H(U1(c, k), f(d))
25.37/8.33	   A^2 -> H(U1(c, c), U1(c, b))
25.37/8.33	   A^2 -> H(U1(c, c), U1(d, b))
25.37/8.33	   A^2 -> H(U1(c, c), U1(b, c))
25.37/8.33	   A^2 -> H(U1(c, c), U1(b, d))
25.37/8.33	   A^2 -> H(U1(c, c), U1(c, c))
25.37/8.33	   A^2 -> H(U1(c, c), f(e))
25.37/8.33	   A^2 -> H(U1(c, c), f(k))
25.37/8.33	   A^2 -> H(U1(c, c), U1(d, d))
25.37/8.33	   A^2 -> H(e, f(b))
25.37/8.33	   A^2 -> H(U1(e, e), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, e), f(c))
25.37/8.33	   A^2 -> H(U1(e, e), f(d))
25.37/8.33	   A^2 -> H(f(e), U1(c, b))
25.37/8.33	   A^2 -> H(f(e), U1(d, b))
25.37/8.33	   A^2 -> H(f(e), U1(b, c))
25.37/8.33	   A^2 -> H(f(e), U1(b, d))
25.37/8.33	   A^2 -> H(f(e), U1(c, c))
25.37/8.33	   A^2 -> H(f(e), f(e))
25.37/8.33	   A^2 -> H(f(e), f(k))
25.37/8.33	   A^2 -> H(f(e), U1(d, d))
25.37/8.33	   A^2 -> H(U1(k, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, k), f(c))
25.37/8.33	   A^2 -> H(U1(k, k), f(d))
25.37/8.33	   A^2 -> H(f(k), U1(c, b))
25.37/8.33	   A^2 -> H(f(k), U1(d, b))
25.37/8.33	   A^2 -> H(f(k), U1(b, c))
25.37/8.33	   A^2 -> H(f(k), U1(b, d))
25.37/8.33	   A^2 -> H(f(k), U1(c, c))
25.37/8.33	   A^2 -> H(f(k), f(e))
25.37/8.33	   A^2 -> H(f(k), f(k))
25.37/8.33	   A^2 -> H(f(k), U1(d, d))
25.37/8.33	   A^2 -> H(f(c), U1(e, b))
25.37/8.33	   A^2 -> H(f(c), U1(k, b))
25.37/8.33	   A^2 -> H(f(c), U1(c, d))
25.37/8.33	   A^2 -> H(f(c), U1(d, c))
25.37/8.33	   A^2 -> H(f(c), U1(b, e))
25.37/8.33	   A^2 -> H(f(c), U1(b, k))
25.37/8.33	   A^2 -> H(f(c), U1(k, d))
25.37/8.33	   A^2 -> H(f(c), U1(d, k))
25.37/8.33	   A^2 -> H(f(c), U1(k, k))
25.37/8.33	   A^2 -> H(U1(k, k), f(b))
25.37/8.33	   A^2 -> H(U1(k, d), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, d), f(c))
25.37/8.33	   A^2 -> H(U1(k, d), f(d))
25.37/8.33	   A^2 -> H(U1(d, k), U1(b, b))
25.37/8.33	   A^2 -> H(U1(d, k), f(c))
25.37/8.33	   A^2 -> H(U1(d, k), f(d))
25.37/8.33	   A^2 -> H(U1(d, d), U1(c, b))
25.37/8.33	   A^2 -> H(U1(d, d), U1(d, b))
25.37/8.33	   A^2 -> H(U1(d, d), U1(b, c))
25.37/8.33	   A^2 -> H(U1(d, d), U1(b, d))
25.37/8.33	   A^2 -> H(U1(d, d), U1(c, c))
25.37/8.33	   A^2 -> H(U1(d, d), f(e))
25.37/8.33	   A^2 -> H(U1(d, d), f(k))
25.37/8.33	   A^2 -> H(U1(d, d), U1(d, d))
25.37/8.33	   A^2 -> H(f(d), U1(e, b))
25.37/8.33	   A^2 -> H(f(d), U1(k, b))
25.37/8.33	   A^2 -> H(f(d), U1(c, d))
25.37/8.33	   A^2 -> H(f(d), U1(d, c))
25.37/8.33	   A^2 -> H(f(d), U1(b, e))
25.37/8.33	   A^2 -> H(f(d), U1(b, k))
25.37/8.33	   A^2 -> H(f(d), U1(e, c))
25.37/8.33	   A^2 -> H(f(d), U1(k, c))
25.37/8.33	   A^2 -> H(f(d), U1(c, e))
25.37/8.33	   A^2 -> H(f(d), U1(c, k))
25.37/8.33	   A^2 -> H(f(d), U1(e, e))
25.37/8.33	   A^2 -> H(f(d), U1(k, k))
25.37/8.33	   A^2 -> H(f(a), b)
25.37/8.33	   A^2 -> H(f(a), U1(e, d))
25.37/8.33	   A^2 -> H(f(a), U1(d, e))
25.37/8.33	   A^2 -> H(f(c), U1(e, c))
25.37/8.33	   A^2 -> H(f(c), U1(k, c))
25.37/8.33	   A^2 -> H(f(c), U1(c, e))
25.37/8.33	   A^2 -> H(f(c), U1(c, k))
25.37/8.33	   A^2 -> H(f(a), c)
25.37/8.33	   A^2 -> H(f(a), U1(e, k))
25.37/8.33	   A^2 -> H(f(a), U1(k, e))
25.37/8.33	   A^2 -> H(f(c), U1(e, e))
25.37/8.33	   A^2 -> H(f(a), e)
25.37/8.33	   A^2 -> H(f(d), U1(k, d))
25.37/8.33	   A^2 -> H(f(d), U1(d, k))
25.37/8.33	   A^2 -> H(f(a), U1(k, k))
25.37/8.33	   A^2 -> H(d, f(b))
25.37/8.33	   A^2 -> H(a, U1(b, b))
25.37/8.33	   A^2 -> H(a, f(c))
25.37/8.33	   A^2 -> H(a, f(d))
25.37/8.33	   A^2 -> H(U1(e, d), U1(b, b))
25.37/8.33	   A^2 -> H(U1(e, d), f(c))
25.37/8.33	   A^2 -> H(U1(e, d), f(d))
25.37/8.33	   A^2 -> H(U1(e, a), U1(c, b))
25.37/8.33	   A^2 -> H(U1(e, a), U1(d, b))
25.37/8.33	   A^2 -> H(U1(e, a), U1(b, c))
25.37/8.33	   A^2 -> H(U1(e, a), U1(b, d))
25.37/8.33	
25.37/8.33	The TRS R consists of the following rules:
25.37/8.33	
25.37/8.33	   f(x) -> U1(x, x)
25.37/8.33	   U1(e, x) -> x
25.37/8.33	   a -> c
25.37/8.33	   a -> d
25.37/8.33	   b -> c
25.37/8.33	   b -> d
25.37/8.33	   d -> k
25.37/8.33	   c -> e
25.37/8.33	   c -> k
25.37/8.33	
25.37/8.33	Q is empty.
25.37/8.33	We have to consider all minimal (P,Q,R)-chains.
25.37/8.33	----------------------------------------
25.37/8.33	
25.37/8.33	(227) TransformationProof (EQUIVALENT)
25.37/8.33	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), f(c)) at position [] we obtained the following new rules [LPAR04]:
25.37/8.33	
25.37/8.33	   (A^2 -> H(a, f(c)),A^2 -> H(a, f(c)))
25.37/8.33	   (A^2 -> H(U1(e, c), f(c)),A^2 -> H(U1(e, c), f(c)))
25.37/8.33	   (A^2 -> H(U1(e, d), f(c)),A^2 -> H(U1(e, d), f(c)))
25.37/8.33	   (A^2 -> H(U1(e, a), U1(c, c)),A^2 -> H(U1(e, a), U1(c, c)))
25.37/8.33	   (A^2 -> H(U1(e, a), f(e)),A^2 -> H(U1(e, a), f(e)))
25.37/8.33	   (A^2 -> H(U1(e, a), f(k)),A^2 -> H(U1(e, a), f(k)))
25.37/8.33	
25.37/8.33	
25.37/8.33	----------------------------------------
25.37/8.33	
25.37/8.33	(228)
25.37/8.33	Obligation:
25.37/8.33	Q DP problem:
25.37/8.33	The TRS P consists of the following rules:
25.37/8.33	
25.37/8.33	   H(x, x) -> G(x, x, f(k))
25.37/8.33	   G(d, x, x) -> A^2
25.37/8.33	   A^2 -> H(f(c), f(c))
25.37/8.33	   A^2 -> H(f(d), f(d))
25.37/8.33	   A^2 -> H(U1(e, a), f(d))
25.37/8.33	   A^2 -> H(U1(k, a), U1(b, b))
25.37/8.33	   A^2 -> H(U1(k, a), f(c))
25.37/8.33	   A^2 -> H(U1(k, a), f(d))
25.37/8.33	   A^2 -> H(U1(c, d), U1(b, b))
25.37/8.33	   A^2 -> H(U1(c, d), f(c))
25.37/8.33	   A^2 -> H(U1(c, d), f(d))
25.37/8.33	   A^2 -> H(U1(c, a), U1(c, b))
25.37/8.33	   A^2 -> H(U1(c, a), U1(d, b))
25.37/8.33	   A^2 -> H(U1(c, a), U1(b, c))
25.37/8.33	   A^2 -> H(U1(c, a), U1(b, d))
25.37/8.33	   A^2 -> H(U1(c, a), U1(c, c))
25.37/8.33	   A^2 -> H(U1(c, a), f(e))
25.37/8.33	   A^2 -> H(U1(c, a), f(k))
25.37/8.33	   A^2 -> H(U1(c, a), U1(d, d))
25.37/8.33	   A^2 -> H(U1(d, e), f(b))
25.37/8.33	   A^2 -> H(U1(d, c), U1(b, b))
25.37/8.33	   A^2 -> H(U1(d, c), f(c))
25.37/8.33	   A^2 -> H(U1(d, c), f(d))
25.37/8.33	   A^2 -> H(U1(d, a), U1(c, b))
25.37/8.33	   A^2 -> H(U1(d, a), U1(d, b))
25.37/8.33	   A^2 -> H(U1(d, a), U1(b, c))
25.37/8.33	   A^2 -> H(U1(d, a), U1(b, d))
25.37/8.33	   A^2 -> H(U1(d, a), U1(c, c))
25.37/8.33	   A^2 -> H(U1(d, a), f(e))
25.37/8.34	   A^2 -> H(U1(d, a), f(k))
25.37/8.34	   A^2 -> H(U1(d, a), U1(d, d))
25.37/8.34	   A^2 -> H(U1(a, e), U1(b, b))
25.37/8.34	   A^2 -> H(U1(a, e), f(c))
25.37/8.34	   A^2 -> H(U1(a, e), f(d))
25.37/8.34	   A^2 -> H(U1(a, k), U1(b, b))
25.37/8.34	   A^2 -> H(U1(a, k), f(c))
25.37/8.34	   A^2 -> H(U1(a, k), f(d))
25.37/8.34	   A^2 -> H(U1(a, c), U1(c, b))
25.37/8.34	   A^2 -> H(U1(a, c), U1(d, b))
25.37/8.34	   A^2 -> H(U1(a, c), U1(b, c))
25.37/8.34	   A^2 -> H(U1(a, c), U1(b, d))
25.37/8.34	   A^2 -> H(U1(a, c), U1(c, c))
25.37/8.34	   A^2 -> H(U1(a, c), f(e))
25.37/8.34	   A^2 -> H(U1(a, c), f(k))
25.37/8.34	   A^2 -> H(U1(a, c), U1(d, d))
25.37/8.34	   A^2 -> H(U1(a, d), U1(c, b))
25.37/8.34	   A^2 -> H(U1(a, d), U1(d, b))
25.37/8.34	   A^2 -> H(U1(a, d), U1(b, c))
25.37/8.34	   A^2 -> H(U1(a, d), U1(b, d))
25.37/8.34	   A^2 -> H(U1(a, d), U1(c, c))
25.37/8.34	   A^2 -> H(U1(a, d), f(e))
25.37/8.34	   A^2 -> H(U1(a, d), f(k))
25.37/8.34	   A^2 -> H(U1(a, d), U1(d, d))
25.37/8.34	   A^2 -> H(U1(a, a), U1(e, b))
25.37/8.34	   A^2 -> H(U1(a, a), U1(k, b))
25.37/8.34	   A^2 -> H(U1(a, a), U1(c, d))
25.37/8.34	   A^2 -> H(U1(a, a), U1(d, c))
25.37/8.34	   A^2 -> H(U1(a, a), U1(b, e))
25.37/8.34	   A^2 -> H(U1(a, a), U1(b, k))
25.37/8.34	   A^2 -> H(U1(a, a), U1(e, c))
25.37/8.34	   A^2 -> H(U1(a, a), U1(k, c))
25.37/8.34	   A^2 -> H(U1(a, a), U1(c, e))
25.37/8.34	   A^2 -> H(U1(a, a), U1(c, k))
25.37/8.34	   A^2 -> H(U1(a, a), U1(e, e))
25.37/8.34	   A^2 -> H(U1(a, a), U1(k, k))
25.37/8.34	   A^2 -> H(U1(a, a), U1(k, d))
25.37/8.34	   A^2 -> H(U1(a, a), U1(d, k))
25.37/8.34	   A^2 -> H(c, f(b))
25.37/8.34	   A^2 -> H(U1(e, k), f(b))
25.37/8.34	   A^2 -> H(U1(e, c), U1(b, b))
25.37/8.34	   A^2 -> H(U1(e, c), f(c))
25.37/8.34	   A^2 -> H(U1(e, c), f(d))
25.37/8.34	   A^2 -> H(U1(k, e), f(b))
25.37/8.34	   A^2 -> H(U1(k, c), U1(b, b))
25.37/8.34	   A^2 -> H(U1(k, c), f(c))
25.37/8.34	   A^2 -> H(U1(k, c), f(d))
25.37/8.34	   A^2 -> H(U1(c, e), U1(b, b))
25.37/8.34	   A^2 -> H(U1(c, e), f(c))
25.37/8.34	   A^2 -> H(U1(c, e), f(d))
25.37/8.34	   A^2 -> H(U1(c, k), U1(b, b))
25.37/8.34	   A^2 -> H(U1(c, k), f(c))
25.37/8.34	   A^2 -> H(U1(c, k), f(d))
25.37/8.34	   A^2 -> H(U1(c, c), U1(c, b))
25.37/8.34	   A^2 -> H(U1(c, c), U1(d, b))
25.37/8.34	   A^2 -> H(U1(c, c), U1(b, c))
25.37/8.34	   A^2 -> H(U1(c, c), U1(b, d))
25.37/8.34	   A^2 -> H(U1(c, c), U1(c, c))
25.37/8.34	   A^2 -> H(U1(c, c), f(e))
25.37/8.34	   A^2 -> H(U1(c, c), f(k))
25.37/8.34	   A^2 -> H(U1(c, c), U1(d, d))
25.37/8.34	   A^2 -> H(e, f(b))
25.37/8.34	   A^2 -> H(U1(e, e), U1(b, b))
25.37/8.34	   A^2 -> H(U1(e, e), f(c))
25.37/8.34	   A^2 -> H(U1(e, e), f(d))
25.37/8.34	   A^2 -> H(f(e), U1(c, b))
25.37/8.34	   A^2 -> H(f(e), U1(d, b))
25.37/8.34	   A^2 -> H(f(e), U1(b, c))
25.37/8.34	   A^2 -> H(f(e), U1(b, d))
25.37/8.34	   A^2 -> H(f(e), U1(c, c))
25.37/8.34	   A^2 -> H(f(e), f(e))
25.37/8.34	   A^2 -> H(f(e), f(k))
25.37/8.34	   A^2 -> H(f(e), U1(d, d))
25.37/8.34	   A^2 -> H(U1(k, k), U1(b, b))
25.37/8.34	   A^2 -> H(U1(k, k), f(c))
25.37/8.34	   A^2 -> H(U1(k, k), f(d))
25.37/8.34	   A^2 -> H(f(k), U1(c, b))
25.37/8.34	   A^2 -> H(f(k), U1(d, b))
25.37/8.34	   A^2 -> H(f(k), U1(b, c))
25.37/8.34	   A^2 -> H(f(k), U1(b, d))
25.37/8.34	   A^2 -> H(f(k), U1(c, c))
25.37/8.34	   A^2 -> H(f(k), f(e))
25.37/8.34	   A^2 -> H(f(k), f(k))
25.37/8.34	   A^2 -> H(f(k), U1(d, d))
25.37/8.34	   A^2 -> H(f(c), U1(e, b))
25.37/8.34	   A^2 -> H(f(c), U1(k, b))
25.37/8.34	   A^2 -> H(f(c), U1(c, d))
25.37/8.34	   A^2 -> H(f(c), U1(d, c))
25.37/8.34	   A^2 -> H(f(c), U1(b, e))
25.37/8.34	   A^2 -> H(f(c), U1(b, k))
25.37/8.34	   A^2 -> H(f(c), U1(k, d))
25.37/8.34	   A^2 -> H(f(c), U1(d, k))
25.37/8.34	   A^2 -> H(f(c), U1(k, k))
25.37/8.34	   A^2 -> H(U1(k, k), f(b))
25.37/8.34	   A^2 -> H(U1(k, d), U1(b, b))
25.37/8.34	   A^2 -> H(U1(k, d), f(c))
25.37/8.34	   A^2 -> H(U1(k, d), f(d))
25.37/8.34	   A^2 -> H(U1(d, k), U1(b, b))
25.37/8.34	   A^2 -> H(U1(d, k), f(c))
25.37/8.34	   A^2 -> H(U1(d, k), f(d))
25.37/8.34	   A^2 -> H(U1(d, d), U1(c, b))
25.37/8.34	   A^2 -> H(U1(d, d), U1(d, b))
25.37/8.34	   A^2 -> H(U1(d, d), U1(b, c))
25.37/8.34	   A^2 -> H(U1(d, d), U1(b, d))
25.37/8.34	   A^2 -> H(U1(d, d), U1(c, c))
25.37/8.34	   A^2 -> H(U1(d, d), f(e))
25.37/8.34	   A^2 -> H(U1(d, d), f(k))
25.37/8.34	   A^2 -> H(U1(d, d), U1(d, d))
25.37/8.34	   A^2 -> H(f(d), U1(e, b))
25.37/8.34	   A^2 -> H(f(d), U1(k, b))
25.37/8.34	   A^2 -> H(f(d), U1(c, d))
25.37/8.34	   A^2 -> H(f(d), U1(d, c))
25.37/8.34	   A^2 -> H(f(d), U1(b, e))
25.37/8.34	   A^2 -> H(f(d), U1(b, k))
25.37/8.34	   A^2 -> H(f(d), U1(e, c))
25.37/8.34	   A^2 -> H(f(d), U1(k, c))
25.37/8.34	   A^2 -> H(f(d), U1(c, e))
25.37/8.34	   A^2 -> H(f(d), U1(c, k))
25.37/8.34	   A^2 -> H(f(d), U1(e, e))
25.37/8.34	   A^2 -> H(f(d), U1(k, k))
25.37/8.34	   A^2 -> H(f(a), b)
25.37/8.34	   A^2 -> H(f(a), U1(e, d))
25.37/8.34	   A^2 -> H(f(a), U1(d, e))
25.37/8.34	   A^2 -> H(f(c), U1(e, c))
25.37/8.34	   A^2 -> H(f(c), U1(k, c))
25.37/8.34	   A^2 -> H(f(c), U1(c, e))
25.37/8.34	   A^2 -> H(f(c), U1(c, k))
25.37/8.34	   A^2 -> H(f(a), c)
25.37/8.34	   A^2 -> H(f(a), U1(e, k))
25.37/8.34	   A^2 -> H(f(a), U1(k, e))
25.37/8.34	   A^2 -> H(f(c), U1(e, e))
25.37/8.34	   A^2 -> H(f(a), e)
25.37/8.34	   A^2 -> H(f(d), U1(k, d))
25.37/8.34	   A^2 -> H(f(d), U1(d, k))
25.37/8.34	   A^2 -> H(f(a), U1(k, k))
25.37/8.34	   A^2 -> H(d, f(b))
25.37/8.34	   A^2 -> H(a, U1(b, b))
25.37/8.34	   A^2 -> H(a, f(c))
25.37/8.34	   A^2 -> H(a, f(d))
25.37/8.34	   A^2 -> H(U1(e, d), U1(b, b))
25.37/8.34	   A^2 -> H(U1(e, d), f(c))
25.37/8.34	   A^2 -> H(U1(e, d), f(d))
25.37/8.34	   A^2 -> H(U1(e, a), U1(c, b))
25.37/8.34	   A^2 -> H(U1(e, a), U1(d, b))
25.37/8.34	   A^2 -> H(U1(e, a), U1(b, c))
25.37/8.34	   A^2 -> H(U1(e, a), U1(b, d))
25.37/8.34	   A^2 -> H(U1(e, a), U1(c, c))
25.37/8.34	   A^2 -> H(U1(e, a), f(e))
25.37/8.34	   A^2 -> H(U1(e, a), f(k))
25.37/8.34	
25.37/8.34	The TRS R consists of the following rules:
25.37/8.34	
25.37/8.34	   f(x) -> U1(x, x)
25.37/8.34	   U1(e, x) -> x
25.37/8.34	   a -> c
25.37/8.34	   a -> d
25.37/8.34	   b -> c
25.37/8.34	   b -> d
25.37/8.34	   d -> k
25.37/8.34	   c -> e
25.37/8.34	   c -> k
25.37/8.34	
25.37/8.34	Q is empty.
25.37/8.34	We have to consider all minimal (P,Q,R)-chains.
25.37/8.34	----------------------------------------
25.37/8.34	
25.37/8.34	(229) TransformationProof (EQUIVALENT)
25.37/8.34	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), f(d)) at position [] we obtained the following new rules [LPAR04]:
25.37/8.34	
25.37/8.34	   (A^2 -> H(a, f(d)),A^2 -> H(a, f(d)))
25.37/8.34	   (A^2 -> H(U1(e, c), f(d)),A^2 -> H(U1(e, c), f(d)))
25.37/8.34	   (A^2 -> H(U1(e, d), f(d)),A^2 -> H(U1(e, d), f(d)))
25.37/8.34	   (A^2 -> H(U1(e, a), U1(d, d)),A^2 -> H(U1(e, a), U1(d, d)))
25.37/8.34	   (A^2 -> H(U1(e, a), f(k)),A^2 -> H(U1(e, a), f(k)))
25.37/8.34	
25.37/8.34	
25.37/8.34	----------------------------------------
25.37/8.34	
25.37/8.34	(230)
25.37/8.34	Obligation:
25.37/8.34	Q DP problem:
25.37/8.34	The TRS P consists of the following rules:
25.37/8.34	
25.37/8.34	   H(x, x) -> G(x, x, f(k))
25.37/8.34	   G(d, x, x) -> A^2
25.37/8.34	   A^2 -> H(f(c), f(c))
25.37/8.34	   A^2 -> H(f(d), f(d))
25.37/8.34	   A^2 -> H(U1(k, a), U1(b, b))
25.37/8.34	   A^2 -> H(U1(k, a), f(c))
25.37/8.34	   A^2 -> H(U1(k, a), f(d))
25.37/8.34	   A^2 -> H(U1(c, d), U1(b, b))
25.37/8.34	   A^2 -> H(U1(c, d), f(c))
25.37/8.34	   A^2 -> H(U1(c, d), f(d))
25.37/8.34	   A^2 -> H(U1(c, a), U1(c, b))
25.37/8.34	   A^2 -> H(U1(c, a), U1(d, b))
25.37/8.34	   A^2 -> H(U1(c, a), U1(b, c))
25.37/8.34	   A^2 -> H(U1(c, a), U1(b, d))
25.37/8.34	   A^2 -> H(U1(c, a), U1(c, c))
25.37/8.34	   A^2 -> H(U1(c, a), f(e))
25.37/8.34	   A^2 -> H(U1(c, a), f(k))
25.37/8.34	   A^2 -> H(U1(c, a), U1(d, d))
25.37/8.34	   A^2 -> H(U1(d, e), f(b))
25.37/8.34	   A^2 -> H(U1(d, c), U1(b, b))
25.37/8.34	   A^2 -> H(U1(d, c), f(c))
25.37/8.34	   A^2 -> H(U1(d, c), f(d))
25.37/8.34	   A^2 -> H(U1(d, a), U1(c, b))
25.37/8.34	   A^2 -> H(U1(d, a), U1(d, b))
25.37/8.34	   A^2 -> H(U1(d, a), U1(b, c))
25.37/8.34	   A^2 -> H(U1(d, a), U1(b, d))
25.37/8.34	   A^2 -> H(U1(d, a), U1(c, c))
25.37/8.34	   A^2 -> H(U1(d, a), f(e))
25.37/8.34	   A^2 -> H(U1(d, a), f(k))
25.37/8.34	   A^2 -> H(U1(d, a), U1(d, d))
25.37/8.34	   A^2 -> H(U1(a, e), U1(b, b))
25.37/8.34	   A^2 -> H(U1(a, e), f(c))
25.37/8.34	   A^2 -> H(U1(a, e), f(d))
25.37/8.34	   A^2 -> H(U1(a, k), U1(b, b))
25.37/8.34	   A^2 -> H(U1(a, k), f(c))
25.37/8.34	   A^2 -> H(U1(a, k), f(d))
25.37/8.34	   A^2 -> H(U1(a, c), U1(c, b))
25.37/8.34	   A^2 -> H(U1(a, c), U1(d, b))
25.37/8.34	   A^2 -> H(U1(a, c), U1(b, c))
25.37/8.34	   A^2 -> H(U1(a, c), U1(b, d))
25.37/8.34	   A^2 -> H(U1(a, c), U1(c, c))
25.37/8.34	   A^2 -> H(U1(a, c), f(e))
25.37/8.34	   A^2 -> H(U1(a, c), f(k))
25.37/8.34	   A^2 -> H(U1(a, c), U1(d, d))
25.37/8.34	   A^2 -> H(U1(a, d), U1(c, b))
25.37/8.34	   A^2 -> H(U1(a, d), U1(d, b))
25.37/8.34	   A^2 -> H(U1(a, d), U1(b, c))
25.37/8.34	   A^2 -> H(U1(a, d), U1(b, d))
25.37/8.34	   A^2 -> H(U1(a, d), U1(c, c))
25.37/8.34	   A^2 -> H(U1(a, d), f(e))
25.37/8.34	   A^2 -> H(U1(a, d), f(k))
25.37/8.34	   A^2 -> H(U1(a, d), U1(d, d))
25.37/8.34	   A^2 -> H(U1(a, a), U1(e, b))
25.37/8.34	   A^2 -> H(U1(a, a), U1(k, b))
25.37/8.34	   A^2 -> H(U1(a, a), U1(c, d))
25.37/8.34	   A^2 -> H(U1(a, a), U1(d, c))
25.37/8.34	   A^2 -> H(U1(a, a), U1(b, e))
25.37/8.34	   A^2 -> H(U1(a, a), U1(b, k))
25.37/8.34	   A^2 -> H(U1(a, a), U1(e, c))
25.37/8.34	   A^2 -> H(U1(a, a), U1(k, c))
25.37/8.34	   A^2 -> H(U1(a, a), U1(c, e))
25.37/8.34	   A^2 -> H(U1(a, a), U1(c, k))
25.37/8.34	   A^2 -> H(U1(a, a), U1(e, e))
25.37/8.34	   A^2 -> H(U1(a, a), U1(k, k))
25.37/8.34	   A^2 -> H(U1(a, a), U1(k, d))
25.37/8.34	   A^2 -> H(U1(a, a), U1(d, k))
25.37/8.34	   A^2 -> H(c, f(b))
25.37/8.34	   A^2 -> H(U1(e, k), f(b))
25.37/8.34	   A^2 -> H(U1(e, c), U1(b, b))
25.37/8.34	   A^2 -> H(U1(e, c), f(c))
25.37/8.34	   A^2 -> H(U1(e, c), f(d))
25.37/8.34	   A^2 -> H(U1(k, e), f(b))
25.37/8.34	   A^2 -> H(U1(k, c), U1(b, b))
25.37/8.34	   A^2 -> H(U1(k, c), f(c))
25.37/8.34	   A^2 -> H(U1(k, c), f(d))
25.37/8.34	   A^2 -> H(U1(c, e), U1(b, b))
25.37/8.34	   A^2 -> H(U1(c, e), f(c))
25.37/8.34	   A^2 -> H(U1(c, e), f(d))
25.37/8.34	   A^2 -> H(U1(c, k), U1(b, b))
25.37/8.34	   A^2 -> H(U1(c, k), f(c))
25.37/8.34	   A^2 -> H(U1(c, k), f(d))
25.37/8.34	   A^2 -> H(U1(c, c), U1(c, b))
25.37/8.34	   A^2 -> H(U1(c, c), U1(d, b))
25.37/8.34	   A^2 -> H(U1(c, c), U1(b, c))
25.37/8.34	   A^2 -> H(U1(c, c), U1(b, d))
25.37/8.34	   A^2 -> H(U1(c, c), U1(c, c))
25.37/8.34	   A^2 -> H(U1(c, c), f(e))
25.37/8.34	   A^2 -> H(U1(c, c), f(k))
25.37/8.34	   A^2 -> H(U1(c, c), U1(d, d))
25.37/8.34	   A^2 -> H(e, f(b))
25.37/8.34	   A^2 -> H(U1(e, e), U1(b, b))
25.37/8.34	   A^2 -> H(U1(e, e), f(c))
25.37/8.34	   A^2 -> H(U1(e, e), f(d))
25.37/8.34	   A^2 -> H(f(e), U1(c, b))
25.37/8.34	   A^2 -> H(f(e), U1(d, b))
25.37/8.34	   A^2 -> H(f(e), U1(b, c))
25.37/8.34	   A^2 -> H(f(e), U1(b, d))
25.37/8.34	   A^2 -> H(f(e), U1(c, c))
25.37/8.34	   A^2 -> H(f(e), f(e))
25.37/8.34	   A^2 -> H(f(e), f(k))
25.37/8.34	   A^2 -> H(f(e), U1(d, d))
25.37/8.34	   A^2 -> H(U1(k, k), U1(b, b))
25.37/8.34	   A^2 -> H(U1(k, k), f(c))
25.37/8.34	   A^2 -> H(U1(k, k), f(d))
25.37/8.34	   A^2 -> H(f(k), U1(c, b))
25.37/8.34	   A^2 -> H(f(k), U1(d, b))
25.37/8.34	   A^2 -> H(f(k), U1(b, c))
25.37/8.34	   A^2 -> H(f(k), U1(b, d))
25.37/8.34	   A^2 -> H(f(k), U1(c, c))
25.37/8.34	   A^2 -> H(f(k), f(e))
25.37/8.34	   A^2 -> H(f(k), f(k))
25.37/8.34	   A^2 -> H(f(k), U1(d, d))
25.37/8.34	   A^2 -> H(f(c), U1(e, b))
25.37/8.34	   A^2 -> H(f(c), U1(k, b))
25.37/8.34	   A^2 -> H(f(c), U1(c, d))
25.37/8.34	   A^2 -> H(f(c), U1(d, c))
25.37/8.34	   A^2 -> H(f(c), U1(b, e))
25.37/8.34	   A^2 -> H(f(c), U1(b, k))
25.37/8.34	   A^2 -> H(f(c), U1(k, d))
25.37/8.34	   A^2 -> H(f(c), U1(d, k))
25.37/8.34	   A^2 -> H(f(c), U1(k, k))
25.37/8.34	   A^2 -> H(U1(k, k), f(b))
25.37/8.34	   A^2 -> H(U1(k, d), U1(b, b))
25.37/8.34	   A^2 -> H(U1(k, d), f(c))
25.37/8.34	   A^2 -> H(U1(k, d), f(d))
25.37/8.34	   A^2 -> H(U1(d, k), U1(b, b))
25.37/8.34	   A^2 -> H(U1(d, k), f(c))
25.37/8.34	   A^2 -> H(U1(d, k), f(d))
25.37/8.34	   A^2 -> H(U1(d, d), U1(c, b))
25.37/8.34	   A^2 -> H(U1(d, d), U1(d, b))
25.37/8.34	   A^2 -> H(U1(d, d), U1(b, c))
25.37/8.34	   A^2 -> H(U1(d, d), U1(b, d))
25.37/8.34	   A^2 -> H(U1(d, d), U1(c, c))
25.37/8.34	   A^2 -> H(U1(d, d), f(e))
25.37/8.34	   A^2 -> H(U1(d, d), f(k))
25.37/8.34	   A^2 -> H(U1(d, d), U1(d, d))
25.37/8.34	   A^2 -> H(f(d), U1(e, b))
25.37/8.34	   A^2 -> H(f(d), U1(k, b))
25.37/8.34	   A^2 -> H(f(d), U1(c, d))
25.37/8.34	   A^2 -> H(f(d), U1(d, c))
25.37/8.34	   A^2 -> H(f(d), U1(b, e))
25.37/8.34	   A^2 -> H(f(d), U1(b, k))
25.37/8.34	   A^2 -> H(f(d), U1(e, c))
25.37/8.34	   A^2 -> H(f(d), U1(k, c))
25.37/8.34	   A^2 -> H(f(d), U1(c, e))
25.37/8.34	   A^2 -> H(f(d), U1(c, k))
25.37/8.34	   A^2 -> H(f(d), U1(e, e))
25.37/8.34	   A^2 -> H(f(d), U1(k, k))
25.37/8.34	   A^2 -> H(f(a), b)
25.37/8.34	   A^2 -> H(f(a), U1(e, d))
25.37/8.34	   A^2 -> H(f(a), U1(d, e))
25.37/8.34	   A^2 -> H(f(c), U1(e, c))
25.37/8.34	   A^2 -> H(f(c), U1(k, c))
25.37/8.34	   A^2 -> H(f(c), U1(c, e))
25.37/8.34	   A^2 -> H(f(c), U1(c, k))
25.37/8.34	   A^2 -> H(f(a), c)
25.37/8.34	   A^2 -> H(f(a), U1(e, k))
25.37/8.34	   A^2 -> H(f(a), U1(k, e))
25.37/8.34	   A^2 -> H(f(c), U1(e, e))
25.37/8.34	   A^2 -> H(f(a), e)
25.37/8.34	   A^2 -> H(f(d), U1(k, d))
25.37/8.34	   A^2 -> H(f(d), U1(d, k))
25.37/8.34	   A^2 -> H(f(a), U1(k, k))
25.37/8.34	   A^2 -> H(d, f(b))
25.37/8.34	   A^2 -> H(a, U1(b, b))
25.37/8.34	   A^2 -> H(a, f(c))
25.37/8.34	   A^2 -> H(a, f(d))
25.37/8.34	   A^2 -> H(U1(e, d), U1(b, b))
25.37/8.34	   A^2 -> H(U1(e, d), f(c))
25.37/8.34	   A^2 -> H(U1(e, d), f(d))
25.37/8.34	   A^2 -> H(U1(e, a), U1(c, b))
25.37/8.34	   A^2 -> H(U1(e, a), U1(d, b))
25.37/8.34	   A^2 -> H(U1(e, a), U1(b, c))
25.37/8.34	   A^2 -> H(U1(e, a), U1(b, d))
25.37/8.34	   A^2 -> H(U1(e, a), U1(c, c))
25.37/8.34	   A^2 -> H(U1(e, a), f(e))
25.37/8.34	   A^2 -> H(U1(e, a), f(k))
25.37/8.34	   A^2 -> H(U1(e, a), U1(d, d))
25.37/8.34	
25.37/8.34	The TRS R consists of the following rules:
25.37/8.34	
25.37/8.34	   f(x) -> U1(x, x)
25.37/8.34	   U1(e, x) -> x
25.37/8.34	   a -> c
25.37/8.34	   a -> d
25.37/8.34	   b -> c
25.37/8.34	   b -> d
25.37/8.34	   d -> k
25.37/8.34	   c -> e
25.37/8.34	   c -> k
25.37/8.34	
25.37/8.34	Q is empty.
25.37/8.34	We have to consider all minimal (P,Q,R)-chains.
25.37/8.34	----------------------------------------
25.37/8.34	
25.37/8.34	(231) TransformationProof (EQUIVALENT)
25.37/8.34	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
25.37/8.34	
25.37/8.34	   (A^2 -> H(U1(k, c), U1(b, b)),A^2 -> H(U1(k, c), U1(b, b)))
25.37/8.34	   (A^2 -> H(U1(k, d), U1(b, b)),A^2 -> H(U1(k, d), U1(b, b)))
25.37/8.34	   (A^2 -> H(U1(k, a), U1(c, b)),A^2 -> H(U1(k, a), U1(c, b)))
25.37/8.34	   (A^2 -> H(U1(k, a), U1(d, b)),A^2 -> H(U1(k, a), U1(d, b)))
25.37/8.34	   (A^2 -> H(U1(k, a), U1(b, c)),A^2 -> H(U1(k, a), U1(b, c)))
25.37/8.34	   (A^2 -> H(U1(k, a), U1(b, d)),A^2 -> H(U1(k, a), U1(b, d)))
25.37/8.34	
25.37/8.34	
25.37/8.34	----------------------------------------
25.37/8.34	
25.37/8.34	(232)
25.37/8.34	Obligation:
25.37/8.34	Q DP problem:
25.37/8.34	The TRS P consists of the following rules:
25.37/8.34	
25.37/8.34	   H(x, x) -> G(x, x, f(k))
25.37/8.34	   G(d, x, x) -> A^2
25.37/8.34	   A^2 -> H(f(c), f(c))
25.37/8.34	   A^2 -> H(f(d), f(d))
25.37/8.34	   A^2 -> H(U1(k, a), f(c))
25.37/8.34	   A^2 -> H(U1(k, a), f(d))
25.37/8.34	   A^2 -> H(U1(c, d), U1(b, b))
25.37/8.34	   A^2 -> H(U1(c, d), f(c))
25.37/8.34	   A^2 -> H(U1(c, d), f(d))
25.37/8.34	   A^2 -> H(U1(c, a), U1(c, b))
25.37/8.34	   A^2 -> H(U1(c, a), U1(d, b))
25.37/8.34	   A^2 -> H(U1(c, a), U1(b, c))
25.37/8.34	   A^2 -> H(U1(c, a), U1(b, d))
25.37/8.34	   A^2 -> H(U1(c, a), U1(c, c))
25.37/8.34	   A^2 -> H(U1(c, a), f(e))
25.37/8.34	   A^2 -> H(U1(c, a), f(k))
25.37/8.34	   A^2 -> H(U1(c, a), U1(d, d))
25.37/8.34	   A^2 -> H(U1(d, e), f(b))
25.37/8.34	   A^2 -> H(U1(d, c), U1(b, b))
25.37/8.34	   A^2 -> H(U1(d, c), f(c))
25.37/8.34	   A^2 -> H(U1(d, c), f(d))
25.37/8.34	   A^2 -> H(U1(d, a), U1(c, b))
25.37/8.34	   A^2 -> H(U1(d, a), U1(d, b))
25.37/8.34	   A^2 -> H(U1(d, a), U1(b, c))
25.37/8.34	   A^2 -> H(U1(d, a), U1(b, d))
25.37/8.34	   A^2 -> H(U1(d, a), U1(c, c))
25.37/8.34	   A^2 -> H(U1(d, a), f(e))
25.37/8.34	   A^2 -> H(U1(d, a), f(k))
25.37/8.34	   A^2 -> H(U1(d, a), U1(d, d))
25.37/8.34	   A^2 -> H(U1(a, e), U1(b, b))
25.37/8.34	   A^2 -> H(U1(a, e), f(c))
25.37/8.34	   A^2 -> H(U1(a, e), f(d))
25.37/8.34	   A^2 -> H(U1(a, k), U1(b, b))
25.37/8.34	   A^2 -> H(U1(a, k), f(c))
25.37/8.34	   A^2 -> H(U1(a, k), f(d))
25.37/8.34	   A^2 -> H(U1(a, c), U1(c, b))
25.37/8.34	   A^2 -> H(U1(a, c), U1(d, b))
25.37/8.34	   A^2 -> H(U1(a, c), U1(b, c))
25.37/8.34	   A^2 -> H(U1(a, c), U1(b, d))
25.37/8.34	   A^2 -> H(U1(a, c), U1(c, c))
25.37/8.34	   A^2 -> H(U1(a, c), f(e))
25.37/8.34	   A^2 -> H(U1(a, c), f(k))
25.37/8.34	   A^2 -> H(U1(a, c), U1(d, d))
25.37/8.34	   A^2 -> H(U1(a, d), U1(c, b))
25.37/8.34	   A^2 -> H(U1(a, d), U1(d, b))
25.37/8.34	   A^2 -> H(U1(a, d), U1(b, c))
25.37/8.34	   A^2 -> H(U1(a, d), U1(b, d))
25.37/8.34	   A^2 -> H(U1(a, d), U1(c, c))
25.37/8.34	   A^2 -> H(U1(a, d), f(e))
25.37/8.34	   A^2 -> H(U1(a, d), f(k))
25.37/8.34	   A^2 -> H(U1(a, d), U1(d, d))
25.37/8.34	   A^2 -> H(U1(a, a), U1(e, b))
25.37/8.34	   A^2 -> H(U1(a, a), U1(k, b))
25.37/8.34	   A^2 -> H(U1(a, a), U1(c, d))
25.37/8.34	   A^2 -> H(U1(a, a), U1(d, c))
25.37/8.34	   A^2 -> H(U1(a, a), U1(b, e))
25.37/8.34	   A^2 -> H(U1(a, a), U1(b, k))
25.37/8.34	   A^2 -> H(U1(a, a), U1(e, c))
25.37/8.34	   A^2 -> H(U1(a, a), U1(k, c))
25.37/8.34	   A^2 -> H(U1(a, a), U1(c, e))
25.37/8.34	   A^2 -> H(U1(a, a), U1(c, k))
25.37/8.34	   A^2 -> H(U1(a, a), U1(e, e))
25.37/8.34	   A^2 -> H(U1(a, a), U1(k, k))
25.37/8.34	   A^2 -> H(U1(a, a), U1(k, d))
25.37/8.34	   A^2 -> H(U1(a, a), U1(d, k))
25.37/8.34	   A^2 -> H(c, f(b))
25.37/8.34	   A^2 -> H(U1(e, k), f(b))
25.37/8.34	   A^2 -> H(U1(e, c), U1(b, b))
25.37/8.34	   A^2 -> H(U1(e, c), f(c))
25.37/8.34	   A^2 -> H(U1(e, c), f(d))
25.37/8.34	   A^2 -> H(U1(k, e), f(b))
25.37/8.34	   A^2 -> H(U1(k, c), U1(b, b))
25.37/8.34	   A^2 -> H(U1(k, c), f(c))
25.37/8.34	   A^2 -> H(U1(k, c), f(d))
25.37/8.34	   A^2 -> H(U1(c, e), U1(b, b))
25.37/8.34	   A^2 -> H(U1(c, e), f(c))
25.37/8.34	   A^2 -> H(U1(c, e), f(d))
25.37/8.34	   A^2 -> H(U1(c, k), U1(b, b))
25.37/8.34	   A^2 -> H(U1(c, k), f(c))
25.37/8.34	   A^2 -> H(U1(c, k), f(d))
25.37/8.34	   A^2 -> H(U1(c, c), U1(c, b))
25.37/8.34	   A^2 -> H(U1(c, c), U1(d, b))
25.37/8.34	   A^2 -> H(U1(c, c), U1(b, c))
25.37/8.34	   A^2 -> H(U1(c, c), U1(b, d))
25.37/8.34	   A^2 -> H(U1(c, c), U1(c, c))
25.37/8.34	   A^2 -> H(U1(c, c), f(e))
25.37/8.34	   A^2 -> H(U1(c, c), f(k))
25.37/8.34	   A^2 -> H(U1(c, c), U1(d, d))
25.37/8.34	   A^2 -> H(e, f(b))
25.37/8.34	   A^2 -> H(U1(e, e), U1(b, b))
25.37/8.34	   A^2 -> H(U1(e, e), f(c))
25.37/8.34	   A^2 -> H(U1(e, e), f(d))
25.37/8.34	   A^2 -> H(f(e), U1(c, b))
25.37/8.34	   A^2 -> H(f(e), U1(d, b))
25.37/8.34	   A^2 -> H(f(e), U1(b, c))
25.37/8.34	   A^2 -> H(f(e), U1(b, d))
25.37/8.34	   A^2 -> H(f(e), U1(c, c))
25.37/8.34	   A^2 -> H(f(e), f(e))
25.37/8.34	   A^2 -> H(f(e), f(k))
25.37/8.34	   A^2 -> H(f(e), U1(d, d))
25.37/8.34	   A^2 -> H(U1(k, k), U1(b, b))
25.37/8.34	   A^2 -> H(U1(k, k), f(c))
25.37/8.34	   A^2 -> H(U1(k, k), f(d))
25.37/8.34	   A^2 -> H(f(k), U1(c, b))
25.37/8.34	   A^2 -> H(f(k), U1(d, b))
25.37/8.34	   A^2 -> H(f(k), U1(b, c))
25.37/8.34	   A^2 -> H(f(k), U1(b, d))
25.37/8.34	   A^2 -> H(f(k), U1(c, c))
25.37/8.34	   A^2 -> H(f(k), f(e))
25.37/8.34	   A^2 -> H(f(k), f(k))
25.37/8.34	   A^2 -> H(f(k), U1(d, d))
25.37/8.34	   A^2 -> H(f(c), U1(e, b))
25.37/8.34	   A^2 -> H(f(c), U1(k, b))
25.37/8.34	   A^2 -> H(f(c), U1(c, d))
25.37/8.34	   A^2 -> H(f(c), U1(d, c))
25.37/8.34	   A^2 -> H(f(c), U1(b, e))
25.37/8.34	   A^2 -> H(f(c), U1(b, k))
25.37/8.34	   A^2 -> H(f(c), U1(k, d))
25.37/8.34	   A^2 -> H(f(c), U1(d, k))
25.37/8.34	   A^2 -> H(f(c), U1(k, k))
25.37/8.34	   A^2 -> H(U1(k, k), f(b))
25.37/8.34	   A^2 -> H(U1(k, d), U1(b, b))
25.37/8.34	   A^2 -> H(U1(k, d), f(c))
25.37/8.34	   A^2 -> H(U1(k, d), f(d))
25.37/8.34	   A^2 -> H(U1(d, k), U1(b, b))
25.37/8.34	   A^2 -> H(U1(d, k), f(c))
25.37/8.34	   A^2 -> H(U1(d, k), f(d))
25.37/8.34	   A^2 -> H(U1(d, d), U1(c, b))
25.37/8.34	   A^2 -> H(U1(d, d), U1(d, b))
25.37/8.34	   A^2 -> H(U1(d, d), U1(b, c))
25.37/8.34	   A^2 -> H(U1(d, d), U1(b, d))
25.37/8.34	   A^2 -> H(U1(d, d), U1(c, c))
25.37/8.34	   A^2 -> H(U1(d, d), f(e))
25.37/8.34	   A^2 -> H(U1(d, d), f(k))
25.37/8.34	   A^2 -> H(U1(d, d), U1(d, d))
25.37/8.34	   A^2 -> H(f(d), U1(e, b))
25.37/8.34	   A^2 -> H(f(d), U1(k, b))
25.37/8.34	   A^2 -> H(f(d), U1(c, d))
25.37/8.34	   A^2 -> H(f(d), U1(d, c))
25.37/8.34	   A^2 -> H(f(d), U1(b, e))
25.37/8.34	   A^2 -> H(f(d), U1(b, k))
25.37/8.34	   A^2 -> H(f(d), U1(e, c))
25.51/8.35	   A^2 -> H(f(d), U1(k, c))
25.51/8.35	   A^2 -> H(f(d), U1(c, e))
25.51/8.35	   A^2 -> H(f(d), U1(c, k))
25.51/8.35	   A^2 -> H(f(d), U1(e, e))
25.51/8.35	   A^2 -> H(f(d), U1(k, k))
25.51/8.35	   A^2 -> H(f(a), b)
25.51/8.35	   A^2 -> H(f(a), U1(e, d))
25.51/8.35	   A^2 -> H(f(a), U1(d, e))
25.51/8.35	   A^2 -> H(f(c), U1(e, c))
25.51/8.35	   A^2 -> H(f(c), U1(k, c))
25.51/8.35	   A^2 -> H(f(c), U1(c, e))
25.51/8.35	   A^2 -> H(f(c), U1(c, k))
25.51/8.35	   A^2 -> H(f(a), c)
25.51/8.35	   A^2 -> H(f(a), U1(e, k))
25.51/8.35	   A^2 -> H(f(a), U1(k, e))
25.51/8.35	   A^2 -> H(f(c), U1(e, e))
25.51/8.35	   A^2 -> H(f(a), e)
25.51/8.35	   A^2 -> H(f(d), U1(k, d))
25.51/8.35	   A^2 -> H(f(d), U1(d, k))
25.51/8.35	   A^2 -> H(f(a), U1(k, k))
25.51/8.35	   A^2 -> H(d, f(b))
25.51/8.35	   A^2 -> H(a, U1(b, b))
25.51/8.35	   A^2 -> H(a, f(c))
25.51/8.35	   A^2 -> H(a, f(d))
25.51/8.35	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.35	   A^2 -> H(U1(e, d), f(c))
25.51/8.35	   A^2 -> H(U1(e, d), f(d))
25.51/8.35	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.35	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.35	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.35	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.35	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.35	   A^2 -> H(U1(e, a), f(e))
25.51/8.35	   A^2 -> H(U1(e, a), f(k))
25.51/8.35	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.35	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.35	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.35	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.35	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.35	
25.51/8.35	The TRS R consists of the following rules:
25.51/8.35	
25.51/8.35	   f(x) -> U1(x, x)
25.51/8.35	   U1(e, x) -> x
25.51/8.35	   a -> c
25.51/8.35	   a -> d
25.51/8.35	   b -> c
25.51/8.35	   b -> d
25.51/8.35	   d -> k
25.51/8.35	   c -> e
25.51/8.35	   c -> k
25.51/8.35	
25.51/8.35	Q is empty.
25.51/8.35	We have to consider all minimal (P,Q,R)-chains.
25.51/8.35	----------------------------------------
25.51/8.35	
25.51/8.35	(233) TransformationProof (EQUIVALENT)
25.51/8.35	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), f(c)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.35	
25.51/8.35	   (A^2 -> H(U1(k, c), f(c)),A^2 -> H(U1(k, c), f(c)))
25.51/8.35	   (A^2 -> H(U1(k, d), f(c)),A^2 -> H(U1(k, d), f(c)))
25.51/8.35	   (A^2 -> H(U1(k, a), U1(c, c)),A^2 -> H(U1(k, a), U1(c, c)))
25.51/8.35	   (A^2 -> H(U1(k, a), f(e)),A^2 -> H(U1(k, a), f(e)))
25.51/8.35	   (A^2 -> H(U1(k, a), f(k)),A^2 -> H(U1(k, a), f(k)))
25.51/8.35	
25.51/8.35	
25.51/8.35	----------------------------------------
25.51/8.35	
25.51/8.35	(234)
25.51/8.35	Obligation:
25.51/8.35	Q DP problem:
25.51/8.35	The TRS P consists of the following rules:
25.51/8.35	
25.51/8.35	   H(x, x) -> G(x, x, f(k))
25.51/8.35	   G(d, x, x) -> A^2
25.51/8.35	   A^2 -> H(f(c), f(c))
25.51/8.35	   A^2 -> H(f(d), f(d))
25.51/8.35	   A^2 -> H(U1(k, a), f(d))
25.51/8.35	   A^2 -> H(U1(c, d), U1(b, b))
25.51/8.35	   A^2 -> H(U1(c, d), f(c))
25.51/8.35	   A^2 -> H(U1(c, d), f(d))
25.51/8.35	   A^2 -> H(U1(c, a), U1(c, b))
25.51/8.35	   A^2 -> H(U1(c, a), U1(d, b))
25.51/8.35	   A^2 -> H(U1(c, a), U1(b, c))
25.51/8.35	   A^2 -> H(U1(c, a), U1(b, d))
25.51/8.35	   A^2 -> H(U1(c, a), U1(c, c))
25.51/8.35	   A^2 -> H(U1(c, a), f(e))
25.51/8.35	   A^2 -> H(U1(c, a), f(k))
25.51/8.35	   A^2 -> H(U1(c, a), U1(d, d))
25.51/8.35	   A^2 -> H(U1(d, e), f(b))
25.51/8.35	   A^2 -> H(U1(d, c), U1(b, b))
25.51/8.35	   A^2 -> H(U1(d, c), f(c))
25.51/8.35	   A^2 -> H(U1(d, c), f(d))
25.51/8.35	   A^2 -> H(U1(d, a), U1(c, b))
25.51/8.35	   A^2 -> H(U1(d, a), U1(d, b))
25.51/8.35	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.35	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.35	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.35	   A^2 -> H(U1(d, a), f(e))
25.51/8.35	   A^2 -> H(U1(d, a), f(k))
25.51/8.35	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.35	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.35	   A^2 -> H(U1(a, e), f(c))
25.51/8.35	   A^2 -> H(U1(a, e), f(d))
25.51/8.35	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.35	   A^2 -> H(U1(a, k), f(c))
25.51/8.35	   A^2 -> H(U1(a, k), f(d))
25.51/8.35	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.35	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.35	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.35	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.35	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.35	   A^2 -> H(U1(a, c), f(e))
25.51/8.35	   A^2 -> H(U1(a, c), f(k))
25.51/8.35	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.35	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.35	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.35	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.35	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.35	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.35	   A^2 -> H(U1(a, d), f(e))
25.51/8.35	   A^2 -> H(U1(a, d), f(k))
25.51/8.35	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.35	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.35	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.35	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.35	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.35	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.35	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.35	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.35	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.35	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.35	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.35	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.35	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.35	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.35	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.35	   A^2 -> H(c, f(b))
25.51/8.35	   A^2 -> H(U1(e, k), f(b))
25.51/8.35	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.35	   A^2 -> H(U1(e, c), f(c))
25.51/8.35	   A^2 -> H(U1(e, c), f(d))
25.51/8.35	   A^2 -> H(U1(k, e), f(b))
25.51/8.35	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.35	   A^2 -> H(U1(k, c), f(c))
25.51/8.35	   A^2 -> H(U1(k, c), f(d))
25.51/8.35	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.35	   A^2 -> H(U1(c, e), f(c))
25.51/8.35	   A^2 -> H(U1(c, e), f(d))
25.51/8.35	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.35	   A^2 -> H(U1(c, k), f(c))
25.51/8.35	   A^2 -> H(U1(c, k), f(d))
25.51/8.35	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.35	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.35	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.35	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.35	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.35	   A^2 -> H(U1(c, c), f(e))
25.51/8.35	   A^2 -> H(U1(c, c), f(k))
25.51/8.35	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.35	   A^2 -> H(e, f(b))
25.51/8.35	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.35	   A^2 -> H(U1(e, e), f(c))
25.51/8.35	   A^2 -> H(U1(e, e), f(d))
25.51/8.35	   A^2 -> H(f(e), U1(c, b))
25.51/8.35	   A^2 -> H(f(e), U1(d, b))
25.51/8.35	   A^2 -> H(f(e), U1(b, c))
25.51/8.35	   A^2 -> H(f(e), U1(b, d))
25.51/8.35	   A^2 -> H(f(e), U1(c, c))
25.51/8.35	   A^2 -> H(f(e), f(e))
25.51/8.35	   A^2 -> H(f(e), f(k))
25.51/8.35	   A^2 -> H(f(e), U1(d, d))
25.51/8.35	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.35	   A^2 -> H(U1(k, k), f(c))
25.51/8.35	   A^2 -> H(U1(k, k), f(d))
25.51/8.35	   A^2 -> H(f(k), U1(c, b))
25.51/8.35	   A^2 -> H(f(k), U1(d, b))
25.51/8.35	   A^2 -> H(f(k), U1(b, c))
25.51/8.35	   A^2 -> H(f(k), U1(b, d))
25.51/8.35	   A^2 -> H(f(k), U1(c, c))
25.51/8.35	   A^2 -> H(f(k), f(e))
25.51/8.35	   A^2 -> H(f(k), f(k))
25.51/8.35	   A^2 -> H(f(k), U1(d, d))
25.51/8.35	   A^2 -> H(f(c), U1(e, b))
25.51/8.35	   A^2 -> H(f(c), U1(k, b))
25.51/8.35	   A^2 -> H(f(c), U1(c, d))
25.51/8.35	   A^2 -> H(f(c), U1(d, c))
25.51/8.35	   A^2 -> H(f(c), U1(b, e))
25.51/8.35	   A^2 -> H(f(c), U1(b, k))
25.51/8.35	   A^2 -> H(f(c), U1(k, d))
25.51/8.35	   A^2 -> H(f(c), U1(d, k))
25.51/8.35	   A^2 -> H(f(c), U1(k, k))
25.51/8.35	   A^2 -> H(U1(k, k), f(b))
25.51/8.35	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.35	   A^2 -> H(U1(k, d), f(c))
25.51/8.35	   A^2 -> H(U1(k, d), f(d))
25.51/8.35	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.35	   A^2 -> H(U1(d, k), f(c))
25.51/8.35	   A^2 -> H(U1(d, k), f(d))
25.51/8.35	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.35	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.35	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.35	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.35	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.35	   A^2 -> H(U1(d, d), f(e))
25.51/8.35	   A^2 -> H(U1(d, d), f(k))
25.51/8.35	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.35	   A^2 -> H(f(d), U1(e, b))
25.51/8.35	   A^2 -> H(f(d), U1(k, b))
25.51/8.35	   A^2 -> H(f(d), U1(c, d))
25.51/8.35	   A^2 -> H(f(d), U1(d, c))
25.51/8.35	   A^2 -> H(f(d), U1(b, e))
25.51/8.35	   A^2 -> H(f(d), U1(b, k))
25.51/8.35	   A^2 -> H(f(d), U1(e, c))
25.51/8.35	   A^2 -> H(f(d), U1(k, c))
25.51/8.35	   A^2 -> H(f(d), U1(c, e))
25.51/8.35	   A^2 -> H(f(d), U1(c, k))
25.51/8.35	   A^2 -> H(f(d), U1(e, e))
25.51/8.35	   A^2 -> H(f(d), U1(k, k))
25.51/8.35	   A^2 -> H(f(a), b)
25.51/8.35	   A^2 -> H(f(a), U1(e, d))
25.51/8.35	   A^2 -> H(f(a), U1(d, e))
25.51/8.35	   A^2 -> H(f(c), U1(e, c))
25.51/8.35	   A^2 -> H(f(c), U1(k, c))
25.51/8.35	   A^2 -> H(f(c), U1(c, e))
25.51/8.35	   A^2 -> H(f(c), U1(c, k))
25.51/8.35	   A^2 -> H(f(a), c)
25.51/8.35	   A^2 -> H(f(a), U1(e, k))
25.51/8.35	   A^2 -> H(f(a), U1(k, e))
25.51/8.35	   A^2 -> H(f(c), U1(e, e))
25.51/8.35	   A^2 -> H(f(a), e)
25.51/8.35	   A^2 -> H(f(d), U1(k, d))
25.51/8.35	   A^2 -> H(f(d), U1(d, k))
25.51/8.35	   A^2 -> H(f(a), U1(k, k))
25.51/8.35	   A^2 -> H(d, f(b))
25.51/8.35	   A^2 -> H(a, U1(b, b))
25.51/8.35	   A^2 -> H(a, f(c))
25.51/8.35	   A^2 -> H(a, f(d))
25.51/8.35	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.35	   A^2 -> H(U1(e, d), f(c))
25.51/8.35	   A^2 -> H(U1(e, d), f(d))
25.51/8.35	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.35	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.35	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.35	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.35	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.35	   A^2 -> H(U1(e, a), f(e))
25.51/8.35	   A^2 -> H(U1(e, a), f(k))
25.51/8.35	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.35	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.35	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.35	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.35	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.35	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.35	   A^2 -> H(U1(k, a), f(e))
25.51/8.35	   A^2 -> H(U1(k, a), f(k))
25.51/8.35	
25.51/8.35	The TRS R consists of the following rules:
25.51/8.35	
25.51/8.35	   f(x) -> U1(x, x)
25.51/8.35	   U1(e, x) -> x
25.51/8.35	   a -> c
25.51/8.35	   a -> d
25.51/8.35	   b -> c
25.51/8.35	   b -> d
25.51/8.35	   d -> k
25.51/8.35	   c -> e
25.51/8.35	   c -> k
25.51/8.35	
25.51/8.35	Q is empty.
25.51/8.35	We have to consider all minimal (P,Q,R)-chains.
25.51/8.35	----------------------------------------
25.51/8.35	
25.51/8.35	(235) TransformationProof (EQUIVALENT)
25.51/8.35	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), f(d)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.35	
25.51/8.35	   (A^2 -> H(U1(k, c), f(d)),A^2 -> H(U1(k, c), f(d)))
25.51/8.35	   (A^2 -> H(U1(k, d), f(d)),A^2 -> H(U1(k, d), f(d)))
25.51/8.35	   (A^2 -> H(U1(k, a), U1(d, d)),A^2 -> H(U1(k, a), U1(d, d)))
25.51/8.35	   (A^2 -> H(U1(k, a), f(k)),A^2 -> H(U1(k, a), f(k)))
25.51/8.35	
25.51/8.35	
25.51/8.35	----------------------------------------
25.51/8.35	
25.51/8.35	(236)
25.51/8.35	Obligation:
25.51/8.35	Q DP problem:
25.51/8.35	The TRS P consists of the following rules:
25.51/8.35	
25.51/8.35	   H(x, x) -> G(x, x, f(k))
25.51/8.35	   G(d, x, x) -> A^2
25.51/8.35	   A^2 -> H(f(c), f(c))
25.51/8.35	   A^2 -> H(f(d), f(d))
25.51/8.35	   A^2 -> H(U1(c, d), U1(b, b))
25.51/8.35	   A^2 -> H(U1(c, d), f(c))
25.51/8.35	   A^2 -> H(U1(c, d), f(d))
25.51/8.35	   A^2 -> H(U1(c, a), U1(c, b))
25.51/8.35	   A^2 -> H(U1(c, a), U1(d, b))
25.51/8.35	   A^2 -> H(U1(c, a), U1(b, c))
25.51/8.35	   A^2 -> H(U1(c, a), U1(b, d))
25.51/8.35	   A^2 -> H(U1(c, a), U1(c, c))
25.51/8.35	   A^2 -> H(U1(c, a), f(e))
25.51/8.35	   A^2 -> H(U1(c, a), f(k))
25.51/8.35	   A^2 -> H(U1(c, a), U1(d, d))
25.51/8.35	   A^2 -> H(U1(d, e), f(b))
25.51/8.35	   A^2 -> H(U1(d, c), U1(b, b))
25.51/8.35	   A^2 -> H(U1(d, c), f(c))
25.51/8.35	   A^2 -> H(U1(d, c), f(d))
25.51/8.35	   A^2 -> H(U1(d, a), U1(c, b))
25.51/8.35	   A^2 -> H(U1(d, a), U1(d, b))
25.51/8.35	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.35	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.35	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.35	   A^2 -> H(U1(d, a), f(e))
25.51/8.35	   A^2 -> H(U1(d, a), f(k))
25.51/8.35	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.35	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.35	   A^2 -> H(U1(a, e), f(c))
25.51/8.35	   A^2 -> H(U1(a, e), f(d))
25.51/8.35	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.35	   A^2 -> H(U1(a, k), f(c))
25.51/8.35	   A^2 -> H(U1(a, k), f(d))
25.51/8.35	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.35	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.35	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.35	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.35	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.35	   A^2 -> H(U1(a, c), f(e))
25.51/8.35	   A^2 -> H(U1(a, c), f(k))
25.51/8.35	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.35	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.35	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.35	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.35	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.35	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.35	   A^2 -> H(U1(a, d), f(e))
25.51/8.35	   A^2 -> H(U1(a, d), f(k))
25.51/8.35	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.35	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.35	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.35	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.35	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.35	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.35	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.35	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.35	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.35	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.35	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.35	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.35	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.35	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.35	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.35	   A^2 -> H(c, f(b))
25.51/8.35	   A^2 -> H(U1(e, k), f(b))
25.51/8.35	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.35	   A^2 -> H(U1(e, c), f(c))
25.51/8.35	   A^2 -> H(U1(e, c), f(d))
25.51/8.35	   A^2 -> H(U1(k, e), f(b))
25.51/8.35	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.35	   A^2 -> H(U1(k, c), f(c))
25.51/8.35	   A^2 -> H(U1(k, c), f(d))
25.51/8.35	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.35	   A^2 -> H(U1(c, e), f(c))
25.51/8.35	   A^2 -> H(U1(c, e), f(d))
25.51/8.35	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.35	   A^2 -> H(U1(c, k), f(c))
25.51/8.35	   A^2 -> H(U1(c, k), f(d))
25.51/8.35	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.35	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.35	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.35	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.35	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.35	   A^2 -> H(U1(c, c), f(e))
25.51/8.35	   A^2 -> H(U1(c, c), f(k))
25.51/8.35	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.35	   A^2 -> H(e, f(b))
25.51/8.35	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.35	   A^2 -> H(U1(e, e), f(c))
25.51/8.35	   A^2 -> H(U1(e, e), f(d))
25.51/8.35	   A^2 -> H(f(e), U1(c, b))
25.51/8.35	   A^2 -> H(f(e), U1(d, b))
25.51/8.35	   A^2 -> H(f(e), U1(b, c))
25.51/8.35	   A^2 -> H(f(e), U1(b, d))
25.51/8.35	   A^2 -> H(f(e), U1(c, c))
25.51/8.35	   A^2 -> H(f(e), f(e))
25.51/8.35	   A^2 -> H(f(e), f(k))
25.51/8.35	   A^2 -> H(f(e), U1(d, d))
25.51/8.35	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.35	   A^2 -> H(U1(k, k), f(c))
25.51/8.35	   A^2 -> H(U1(k, k), f(d))
25.51/8.35	   A^2 -> H(f(k), U1(c, b))
25.51/8.35	   A^2 -> H(f(k), U1(d, b))
25.51/8.35	   A^2 -> H(f(k), U1(b, c))
25.51/8.35	   A^2 -> H(f(k), U1(b, d))
25.51/8.35	   A^2 -> H(f(k), U1(c, c))
25.51/8.35	   A^2 -> H(f(k), f(e))
25.51/8.35	   A^2 -> H(f(k), f(k))
25.51/8.35	   A^2 -> H(f(k), U1(d, d))
25.51/8.35	   A^2 -> H(f(c), U1(e, b))
25.51/8.35	   A^2 -> H(f(c), U1(k, b))
25.51/8.35	   A^2 -> H(f(c), U1(c, d))
25.51/8.35	   A^2 -> H(f(c), U1(d, c))
25.51/8.35	   A^2 -> H(f(c), U1(b, e))
25.51/8.35	   A^2 -> H(f(c), U1(b, k))
25.51/8.35	   A^2 -> H(f(c), U1(k, d))
25.51/8.35	   A^2 -> H(f(c), U1(d, k))
25.51/8.35	   A^2 -> H(f(c), U1(k, k))
25.51/8.35	   A^2 -> H(U1(k, k), f(b))
25.51/8.35	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.35	   A^2 -> H(U1(k, d), f(c))
25.51/8.35	   A^2 -> H(U1(k, d), f(d))
25.51/8.35	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.35	   A^2 -> H(U1(d, k), f(c))
25.51/8.35	   A^2 -> H(U1(d, k), f(d))
25.51/8.35	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.35	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.35	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.35	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.35	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.35	   A^2 -> H(U1(d, d), f(e))
25.51/8.35	   A^2 -> H(U1(d, d), f(k))
25.51/8.35	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.35	   A^2 -> H(f(d), U1(e, b))
25.51/8.35	   A^2 -> H(f(d), U1(k, b))
25.51/8.35	   A^2 -> H(f(d), U1(c, d))
25.51/8.35	   A^2 -> H(f(d), U1(d, c))
25.51/8.35	   A^2 -> H(f(d), U1(b, e))
25.51/8.35	   A^2 -> H(f(d), U1(b, k))
25.51/8.35	   A^2 -> H(f(d), U1(e, c))
25.51/8.35	   A^2 -> H(f(d), U1(k, c))
25.51/8.35	   A^2 -> H(f(d), U1(c, e))
25.51/8.35	   A^2 -> H(f(d), U1(c, k))
25.51/8.35	   A^2 -> H(f(d), U1(e, e))
25.51/8.35	   A^2 -> H(f(d), U1(k, k))
25.51/8.35	   A^2 -> H(f(a), b)
25.51/8.35	   A^2 -> H(f(a), U1(e, d))
25.51/8.35	   A^2 -> H(f(a), U1(d, e))
25.51/8.35	   A^2 -> H(f(c), U1(e, c))
25.51/8.35	   A^2 -> H(f(c), U1(k, c))
25.51/8.35	   A^2 -> H(f(c), U1(c, e))
25.51/8.35	   A^2 -> H(f(c), U1(c, k))
25.51/8.35	   A^2 -> H(f(a), c)
25.51/8.35	   A^2 -> H(f(a), U1(e, k))
25.51/8.35	   A^2 -> H(f(a), U1(k, e))
25.51/8.35	   A^2 -> H(f(c), U1(e, e))
25.51/8.35	   A^2 -> H(f(a), e)
25.51/8.35	   A^2 -> H(f(d), U1(k, d))
25.51/8.35	   A^2 -> H(f(d), U1(d, k))
25.51/8.35	   A^2 -> H(f(a), U1(k, k))
25.51/8.35	   A^2 -> H(d, f(b))
25.51/8.35	   A^2 -> H(a, U1(b, b))
25.51/8.35	   A^2 -> H(a, f(c))
25.51/8.35	   A^2 -> H(a, f(d))
25.51/8.35	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.35	   A^2 -> H(U1(e, d), f(c))
25.51/8.35	   A^2 -> H(U1(e, d), f(d))
25.51/8.35	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.35	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.35	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.35	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.35	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.35	   A^2 -> H(U1(e, a), f(e))
25.51/8.35	   A^2 -> H(U1(e, a), f(k))
25.51/8.35	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.35	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.35	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.35	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.35	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.35	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.35	   A^2 -> H(U1(k, a), f(e))
25.51/8.35	   A^2 -> H(U1(k, a), f(k))
25.51/8.35	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.35	
25.51/8.35	The TRS R consists of the following rules:
25.51/8.35	
25.51/8.35	   f(x) -> U1(x, x)
25.51/8.35	   U1(e, x) -> x
25.51/8.35	   a -> c
25.51/8.35	   a -> d
25.51/8.35	   b -> c
25.51/8.35	   b -> d
25.51/8.35	   d -> k
25.51/8.35	   c -> e
25.51/8.35	   c -> k
25.51/8.35	
25.51/8.35	Q is empty.
25.51/8.35	We have to consider all minimal (P,Q,R)-chains.
25.51/8.35	----------------------------------------
25.51/8.35	
25.51/8.35	(237) TransformationProof (EQUIVALENT)
25.51/8.35	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.35	
25.51/8.35	   (A^2 -> H(U1(e, d), U1(b, b)),A^2 -> H(U1(e, d), U1(b, b)))
25.51/8.35	   (A^2 -> H(U1(k, d), U1(b, b)),A^2 -> H(U1(k, d), U1(b, b)))
25.51/8.35	   (A^2 -> H(U1(c, k), U1(b, b)),A^2 -> H(U1(c, k), U1(b, b)))
25.51/8.35	   (A^2 -> H(U1(c, d), U1(c, b)),A^2 -> H(U1(c, d), U1(c, b)))
25.51/8.35	   (A^2 -> H(U1(c, d), U1(d, b)),A^2 -> H(U1(c, d), U1(d, b)))
25.51/8.35	   (A^2 -> H(U1(c, d), U1(b, c)),A^2 -> H(U1(c, d), U1(b, c)))
25.51/8.35	   (A^2 -> H(U1(c, d), U1(b, d)),A^2 -> H(U1(c, d), U1(b, d)))
25.51/8.35	
25.51/8.35	
25.51/8.35	----------------------------------------
25.51/8.35	
25.51/8.35	(238)
25.51/8.35	Obligation:
25.51/8.35	Q DP problem:
25.51/8.35	The TRS P consists of the following rules:
25.51/8.35	
25.51/8.35	   H(x, x) -> G(x, x, f(k))
25.51/8.35	   G(d, x, x) -> A^2
25.51/8.35	   A^2 -> H(f(c), f(c))
25.51/8.35	   A^2 -> H(f(d), f(d))
25.51/8.35	   A^2 -> H(U1(c, d), f(c))
25.51/8.35	   A^2 -> H(U1(c, d), f(d))
25.51/8.35	   A^2 -> H(U1(c, a), U1(c, b))
25.51/8.35	   A^2 -> H(U1(c, a), U1(d, b))
25.51/8.35	   A^2 -> H(U1(c, a), U1(b, c))
25.51/8.35	   A^2 -> H(U1(c, a), U1(b, d))
25.51/8.35	   A^2 -> H(U1(c, a), U1(c, c))
25.51/8.35	   A^2 -> H(U1(c, a), f(e))
25.51/8.35	   A^2 -> H(U1(c, a), f(k))
25.51/8.35	   A^2 -> H(U1(c, a), U1(d, d))
25.51/8.35	   A^2 -> H(U1(d, e), f(b))
25.51/8.35	   A^2 -> H(U1(d, c), U1(b, b))
25.51/8.35	   A^2 -> H(U1(d, c), f(c))
25.51/8.35	   A^2 -> H(U1(d, c), f(d))
25.51/8.35	   A^2 -> H(U1(d, a), U1(c, b))
25.51/8.35	   A^2 -> H(U1(d, a), U1(d, b))
25.51/8.35	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.35	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.35	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.35	   A^2 -> H(U1(d, a), f(e))
25.51/8.35	   A^2 -> H(U1(d, a), f(k))
25.51/8.35	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.35	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.35	   A^2 -> H(U1(a, e), f(c))
25.51/8.35	   A^2 -> H(U1(a, e), f(d))
25.51/8.35	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.35	   A^2 -> H(U1(a, k), f(c))
25.51/8.35	   A^2 -> H(U1(a, k), f(d))
25.51/8.35	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.35	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.35	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.35	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.35	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.35	   A^2 -> H(U1(a, c), f(e))
25.51/8.35	   A^2 -> H(U1(a, c), f(k))
25.51/8.35	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.35	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.35	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.35	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.35	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.35	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.35	   A^2 -> H(U1(a, d), f(e))
25.51/8.35	   A^2 -> H(U1(a, d), f(k))
25.51/8.35	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.35	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.35	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.35	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.35	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.35	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.35	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.35	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.35	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.35	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.35	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.35	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.35	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.35	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.35	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.35	   A^2 -> H(c, f(b))
25.51/8.35	   A^2 -> H(U1(e, k), f(b))
25.51/8.35	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.35	   A^2 -> H(U1(e, c), f(c))
25.51/8.35	   A^2 -> H(U1(e, c), f(d))
25.51/8.35	   A^2 -> H(U1(k, e), f(b))
25.51/8.35	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.35	   A^2 -> H(U1(k, c), f(c))
25.51/8.35	   A^2 -> H(U1(k, c), f(d))
25.51/8.35	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.35	   A^2 -> H(U1(c, e), f(c))
25.51/8.35	   A^2 -> H(U1(c, e), f(d))
25.51/8.35	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.35	   A^2 -> H(U1(c, k), f(c))
25.51/8.35	   A^2 -> H(U1(c, k), f(d))
25.51/8.35	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.35	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.35	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.35	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.35	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.35	   A^2 -> H(U1(c, c), f(e))
25.51/8.35	   A^2 -> H(U1(c, c), f(k))
25.51/8.35	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.35	   A^2 -> H(e, f(b))
25.51/8.35	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.35	   A^2 -> H(U1(e, e), f(c))
25.51/8.35	   A^2 -> H(U1(e, e), f(d))
25.51/8.35	   A^2 -> H(f(e), U1(c, b))
25.51/8.35	   A^2 -> H(f(e), U1(d, b))
25.51/8.35	   A^2 -> H(f(e), U1(b, c))
25.51/8.35	   A^2 -> H(f(e), U1(b, d))
25.51/8.35	   A^2 -> H(f(e), U1(c, c))
25.51/8.35	   A^2 -> H(f(e), f(e))
25.51/8.35	   A^2 -> H(f(e), f(k))
25.51/8.35	   A^2 -> H(f(e), U1(d, d))
25.51/8.35	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.35	   A^2 -> H(U1(k, k), f(c))
25.51/8.35	   A^2 -> H(U1(k, k), f(d))
25.51/8.35	   A^2 -> H(f(k), U1(c, b))
25.51/8.35	   A^2 -> H(f(k), U1(d, b))
25.51/8.35	   A^2 -> H(f(k), U1(b, c))
25.51/8.35	   A^2 -> H(f(k), U1(b, d))
25.51/8.35	   A^2 -> H(f(k), U1(c, c))
25.51/8.35	   A^2 -> H(f(k), f(e))
25.51/8.35	   A^2 -> H(f(k), f(k))
25.51/8.35	   A^2 -> H(f(k), U1(d, d))
25.51/8.35	   A^2 -> H(f(c), U1(e, b))
25.51/8.35	   A^2 -> H(f(c), U1(k, b))
25.51/8.35	   A^2 -> H(f(c), U1(c, d))
25.51/8.35	   A^2 -> H(f(c), U1(d, c))
25.51/8.35	   A^2 -> H(f(c), U1(b, e))
25.51/8.35	   A^2 -> H(f(c), U1(b, k))
25.51/8.35	   A^2 -> H(f(c), U1(k, d))
25.51/8.35	   A^2 -> H(f(c), U1(d, k))
25.51/8.35	   A^2 -> H(f(c), U1(k, k))
25.51/8.35	   A^2 -> H(U1(k, k), f(b))
25.51/8.35	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.35	   A^2 -> H(U1(k, d), f(c))
25.51/8.35	   A^2 -> H(U1(k, d), f(d))
25.51/8.35	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.35	   A^2 -> H(U1(d, k), f(c))
25.51/8.35	   A^2 -> H(U1(d, k), f(d))
25.51/8.35	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.35	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.35	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.35	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.35	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.35	   A^2 -> H(U1(d, d), f(e))
25.51/8.35	   A^2 -> H(U1(d, d), f(k))
25.51/8.35	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.35	   A^2 -> H(f(d), U1(e, b))
25.51/8.35	   A^2 -> H(f(d), U1(k, b))
25.51/8.35	   A^2 -> H(f(d), U1(c, d))
25.51/8.35	   A^2 -> H(f(d), U1(d, c))
25.51/8.35	   A^2 -> H(f(d), U1(b, e))
25.51/8.35	   A^2 -> H(f(d), U1(b, k))
25.51/8.35	   A^2 -> H(f(d), U1(e, c))
25.51/8.35	   A^2 -> H(f(d), U1(k, c))
25.51/8.35	   A^2 -> H(f(d), U1(c, e))
25.51/8.35	   A^2 -> H(f(d), U1(c, k))
25.51/8.35	   A^2 -> H(f(d), U1(e, e))
25.51/8.35	   A^2 -> H(f(d), U1(k, k))
25.51/8.35	   A^2 -> H(f(a), b)
25.51/8.35	   A^2 -> H(f(a), U1(e, d))
25.51/8.35	   A^2 -> H(f(a), U1(d, e))
25.51/8.35	   A^2 -> H(f(c), U1(e, c))
25.51/8.35	   A^2 -> H(f(c), U1(k, c))
25.51/8.35	   A^2 -> H(f(c), U1(c, e))
25.51/8.35	   A^2 -> H(f(c), U1(c, k))
25.51/8.35	   A^2 -> H(f(a), c)
25.51/8.35	   A^2 -> H(f(a), U1(e, k))
25.51/8.35	   A^2 -> H(f(a), U1(k, e))
25.51/8.35	   A^2 -> H(f(c), U1(e, e))
25.51/8.35	   A^2 -> H(f(a), e)
25.51/8.35	   A^2 -> H(f(d), U1(k, d))
25.51/8.35	   A^2 -> H(f(d), U1(d, k))
25.51/8.35	   A^2 -> H(f(a), U1(k, k))
25.51/8.35	   A^2 -> H(d, f(b))
25.51/8.35	   A^2 -> H(a, U1(b, b))
25.51/8.35	   A^2 -> H(a, f(c))
25.51/8.35	   A^2 -> H(a, f(d))
25.51/8.35	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.35	   A^2 -> H(U1(e, d), f(c))
25.51/8.35	   A^2 -> H(U1(e, d), f(d))
25.51/8.35	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.35	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.35	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.35	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.35	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.35	   A^2 -> H(U1(e, a), f(e))
25.51/8.35	   A^2 -> H(U1(e, a), f(k))
25.51/8.35	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.35	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.35	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.35	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.35	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.35	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.35	   A^2 -> H(U1(k, a), f(e))
25.51/8.35	   A^2 -> H(U1(k, a), f(k))
25.51/8.35	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.35	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.35	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.35	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.35	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.35	
25.51/8.35	The TRS R consists of the following rules:
25.51/8.35	
25.51/8.35	   f(x) -> U1(x, x)
25.51/8.35	   U1(e, x) -> x
25.51/8.35	   a -> c
25.51/8.35	   a -> d
25.51/8.35	   b -> c
25.51/8.35	   b -> d
25.51/8.35	   d -> k
25.51/8.35	   c -> e
25.51/8.35	   c -> k
25.51/8.35	
25.51/8.35	Q is empty.
25.51/8.35	We have to consider all minimal (P,Q,R)-chains.
25.51/8.35	----------------------------------------
25.51/8.35	
25.51/8.35	(239) TransformationProof (EQUIVALENT)
25.51/8.35	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), f(c)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.35	
25.51/8.35	   (A^2 -> H(U1(e, d), f(c)),A^2 -> H(U1(e, d), f(c)))
25.51/8.35	   (A^2 -> H(U1(k, d), f(c)),A^2 -> H(U1(k, d), f(c)))
25.51/8.35	   (A^2 -> H(U1(c, k), f(c)),A^2 -> H(U1(c, k), f(c)))
25.51/8.35	   (A^2 -> H(U1(c, d), U1(c, c)),A^2 -> H(U1(c, d), U1(c, c)))
25.51/8.35	   (A^2 -> H(U1(c, d), f(e)),A^2 -> H(U1(c, d), f(e)))
25.51/8.35	   (A^2 -> H(U1(c, d), f(k)),A^2 -> H(U1(c, d), f(k)))
25.51/8.35	
25.51/8.35	
25.51/8.35	----------------------------------------
25.51/8.35	
25.51/8.35	(240)
25.51/8.35	Obligation:
25.51/8.35	Q DP problem:
25.51/8.35	The TRS P consists of the following rules:
25.51/8.35	
25.51/8.35	   H(x, x) -> G(x, x, f(k))
25.51/8.35	   G(d, x, x) -> A^2
25.51/8.35	   A^2 -> H(f(c), f(c))
25.51/8.35	   A^2 -> H(f(d), f(d))
25.51/8.35	   A^2 -> H(U1(c, d), f(d))
25.51/8.35	   A^2 -> H(U1(c, a), U1(c, b))
25.51/8.35	   A^2 -> H(U1(c, a), U1(d, b))
25.51/8.35	   A^2 -> H(U1(c, a), U1(b, c))
25.51/8.35	   A^2 -> H(U1(c, a), U1(b, d))
25.51/8.35	   A^2 -> H(U1(c, a), U1(c, c))
25.51/8.35	   A^2 -> H(U1(c, a), f(e))
25.51/8.35	   A^2 -> H(U1(c, a), f(k))
25.51/8.35	   A^2 -> H(U1(c, a), U1(d, d))
25.51/8.35	   A^2 -> H(U1(d, e), f(b))
25.51/8.35	   A^2 -> H(U1(d, c), U1(b, b))
25.51/8.35	   A^2 -> H(U1(d, c), f(c))
25.51/8.35	   A^2 -> H(U1(d, c), f(d))
25.51/8.35	   A^2 -> H(U1(d, a), U1(c, b))
25.51/8.35	   A^2 -> H(U1(d, a), U1(d, b))
25.51/8.35	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.35	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.35	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.35	   A^2 -> H(U1(d, a), f(e))
25.51/8.35	   A^2 -> H(U1(d, a), f(k))
25.51/8.35	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.35	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.35	   A^2 -> H(U1(a, e), f(c))
25.51/8.35	   A^2 -> H(U1(a, e), f(d))
25.51/8.35	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.35	   A^2 -> H(U1(a, k), f(c))
25.51/8.35	   A^2 -> H(U1(a, k), f(d))
25.51/8.35	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.35	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.35	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.35	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.35	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.35	   A^2 -> H(U1(a, c), f(e))
25.51/8.35	   A^2 -> H(U1(a, c), f(k))
25.51/8.35	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.35	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.35	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.35	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.35	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.35	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.35	   A^2 -> H(U1(a, d), f(e))
25.51/8.35	   A^2 -> H(U1(a, d), f(k))
25.51/8.35	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.35	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.35	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.35	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.35	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.35	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.35	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.35	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.35	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.35	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.35	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.35	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.35	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.35	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.35	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.35	   A^2 -> H(c, f(b))
25.51/8.35	   A^2 -> H(U1(e, k), f(b))
25.51/8.35	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.35	   A^2 -> H(U1(e, c), f(c))
25.51/8.35	   A^2 -> H(U1(e, c), f(d))
25.51/8.35	   A^2 -> H(U1(k, e), f(b))
25.51/8.35	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.35	   A^2 -> H(U1(k, c), f(c))
25.51/8.35	   A^2 -> H(U1(k, c), f(d))
25.51/8.35	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.35	   A^2 -> H(U1(c, e), f(c))
25.51/8.35	   A^2 -> H(U1(c, e), f(d))
25.51/8.35	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.35	   A^2 -> H(U1(c, k), f(c))
25.51/8.35	   A^2 -> H(U1(c, k), f(d))
25.51/8.35	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.35	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.35	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.35	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.35	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.35	   A^2 -> H(U1(c, c), f(e))
25.51/8.35	   A^2 -> H(U1(c, c), f(k))
25.51/8.35	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.35	   A^2 -> H(e, f(b))
25.51/8.35	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.35	   A^2 -> H(U1(e, e), f(c))
25.51/8.35	   A^2 -> H(U1(e, e), f(d))
25.51/8.35	   A^2 -> H(f(e), U1(c, b))
25.51/8.35	   A^2 -> H(f(e), U1(d, b))
25.51/8.35	   A^2 -> H(f(e), U1(b, c))
25.51/8.35	   A^2 -> H(f(e), U1(b, d))
25.51/8.35	   A^2 -> H(f(e), U1(c, c))
25.51/8.35	   A^2 -> H(f(e), f(e))
25.51/8.35	   A^2 -> H(f(e), f(k))
25.51/8.35	   A^2 -> H(f(e), U1(d, d))
25.51/8.35	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.35	   A^2 -> H(U1(k, k), f(c))
25.51/8.35	   A^2 -> H(U1(k, k), f(d))
25.51/8.35	   A^2 -> H(f(k), U1(c, b))
25.51/8.35	   A^2 -> H(f(k), U1(d, b))
25.51/8.35	   A^2 -> H(f(k), U1(b, c))
25.51/8.35	   A^2 -> H(f(k), U1(b, d))
25.51/8.35	   A^2 -> H(f(k), U1(c, c))
25.51/8.35	   A^2 -> H(f(k), f(e))
25.51/8.35	   A^2 -> H(f(k), f(k))
25.51/8.35	   A^2 -> H(f(k), U1(d, d))
25.51/8.35	   A^2 -> H(f(c), U1(e, b))
25.51/8.35	   A^2 -> H(f(c), U1(k, b))
25.51/8.35	   A^2 -> H(f(c), U1(c, d))
25.51/8.35	   A^2 -> H(f(c), U1(d, c))
25.51/8.35	   A^2 -> H(f(c), U1(b, e))
25.51/8.35	   A^2 -> H(f(c), U1(b, k))
25.51/8.35	   A^2 -> H(f(c), U1(k, d))
25.51/8.35	   A^2 -> H(f(c), U1(d, k))
25.51/8.35	   A^2 -> H(f(c), U1(k, k))
25.51/8.35	   A^2 -> H(U1(k, k), f(b))
25.51/8.35	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.35	   A^2 -> H(U1(k, d), f(c))
25.51/8.35	   A^2 -> H(U1(k, d), f(d))
25.51/8.35	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.35	   A^2 -> H(U1(d, k), f(c))
25.51/8.35	   A^2 -> H(U1(d, k), f(d))
25.51/8.35	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.35	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.35	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.35	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.35	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.35	   A^2 -> H(U1(d, d), f(e))
25.51/8.35	   A^2 -> H(U1(d, d), f(k))
25.51/8.35	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.35	   A^2 -> H(f(d), U1(e, b))
25.51/8.35	   A^2 -> H(f(d), U1(k, b))
25.51/8.35	   A^2 -> H(f(d), U1(c, d))
25.51/8.35	   A^2 -> H(f(d), U1(d, c))
25.51/8.35	   A^2 -> H(f(d), U1(b, e))
25.51/8.35	   A^2 -> H(f(d), U1(b, k))
25.51/8.35	   A^2 -> H(f(d), U1(e, c))
25.51/8.35	   A^2 -> H(f(d), U1(k, c))
25.51/8.35	   A^2 -> H(f(d), U1(c, e))
25.51/8.35	   A^2 -> H(f(d), U1(c, k))
25.51/8.35	   A^2 -> H(f(d), U1(e, e))
25.51/8.35	   A^2 -> H(f(d), U1(k, k))
25.51/8.35	   A^2 -> H(f(a), b)
25.51/8.35	   A^2 -> H(f(a), U1(e, d))
25.51/8.35	   A^2 -> H(f(a), U1(d, e))
25.51/8.35	   A^2 -> H(f(c), U1(e, c))
25.51/8.35	   A^2 -> H(f(c), U1(k, c))
25.51/8.35	   A^2 -> H(f(c), U1(c, e))
25.51/8.35	   A^2 -> H(f(c), U1(c, k))
25.51/8.35	   A^2 -> H(f(a), c)
25.51/8.35	   A^2 -> H(f(a), U1(e, k))
25.51/8.35	   A^2 -> H(f(a), U1(k, e))
25.51/8.35	   A^2 -> H(f(c), U1(e, e))
25.51/8.35	   A^2 -> H(f(a), e)
25.51/8.35	   A^2 -> H(f(d), U1(k, d))
25.51/8.35	   A^2 -> H(f(d), U1(d, k))
25.51/8.35	   A^2 -> H(f(a), U1(k, k))
25.51/8.35	   A^2 -> H(d, f(b))
25.51/8.35	   A^2 -> H(a, U1(b, b))
25.51/8.35	   A^2 -> H(a, f(c))
25.51/8.35	   A^2 -> H(a, f(d))
25.51/8.35	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.35	   A^2 -> H(U1(e, d), f(c))
25.51/8.35	   A^2 -> H(U1(e, d), f(d))
25.51/8.35	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.35	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.35	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.35	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.35	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.35	   A^2 -> H(U1(e, a), f(e))
25.51/8.35	   A^2 -> H(U1(e, a), f(k))
25.51/8.36	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(k, a), f(e))
25.51/8.36	   A^2 -> H(U1(k, a), f(k))
25.51/8.36	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, d), f(e))
25.51/8.36	   A^2 -> H(U1(c, d), f(k))
25.51/8.36	
25.51/8.36	The TRS R consists of the following rules:
25.51/8.36	
25.51/8.36	   f(x) -> U1(x, x)
25.51/8.36	   U1(e, x) -> x
25.51/8.36	   a -> c
25.51/8.36	   a -> d
25.51/8.36	   b -> c
25.51/8.36	   b -> d
25.51/8.36	   d -> k
25.51/8.36	   c -> e
25.51/8.36	   c -> k
25.51/8.36	
25.51/8.36	Q is empty.
25.51/8.36	We have to consider all minimal (P,Q,R)-chains.
25.51/8.36	----------------------------------------
25.51/8.36	
25.51/8.36	(241) TransformationProof (EQUIVALENT)
25.51/8.36	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), f(d)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.36	
25.51/8.36	   (A^2 -> H(U1(e, d), f(d)),A^2 -> H(U1(e, d), f(d)))
25.51/8.36	   (A^2 -> H(U1(k, d), f(d)),A^2 -> H(U1(k, d), f(d)))
25.51/8.36	   (A^2 -> H(U1(c, k), f(d)),A^2 -> H(U1(c, k), f(d)))
25.51/8.36	   (A^2 -> H(U1(c, d), U1(d, d)),A^2 -> H(U1(c, d), U1(d, d)))
25.51/8.36	   (A^2 -> H(U1(c, d), f(k)),A^2 -> H(U1(c, d), f(k)))
25.51/8.36	
25.51/8.36	
25.51/8.36	----------------------------------------
25.51/8.36	
25.51/8.36	(242)
25.51/8.36	Obligation:
25.51/8.36	Q DP problem:
25.51/8.36	The TRS P consists of the following rules:
25.51/8.36	
25.51/8.36	   H(x, x) -> G(x, x, f(k))
25.51/8.36	   G(d, x, x) -> A^2
25.51/8.36	   A^2 -> H(f(c), f(c))
25.51/8.36	   A^2 -> H(f(d), f(d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, a), f(e))
25.51/8.36	   A^2 -> H(U1(c, a), f(k))
25.51/8.36	   A^2 -> H(U1(c, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(d, e), f(b))
25.51/8.36	   A^2 -> H(U1(d, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(d, c), f(c))
25.51/8.36	   A^2 -> H(U1(d, c), f(d))
25.51/8.36	   A^2 -> H(U1(d, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(d, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(d, a), f(e))
25.51/8.36	   A^2 -> H(U1(d, a), f(k))
25.51/8.36	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(a, e), f(c))
25.51/8.36	   A^2 -> H(U1(a, e), f(d))
25.51/8.36	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(a, k), f(c))
25.51/8.36	   A^2 -> H(U1(a, k), f(d))
25.51/8.36	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.36	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.36	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.36	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.36	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.36	   A^2 -> H(U1(a, c), f(e))
25.51/8.36	   A^2 -> H(U1(a, c), f(k))
25.51/8.36	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(a, d), f(e))
25.51/8.36	   A^2 -> H(U1(a, d), f(k))
25.51/8.36	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.36	   A^2 -> H(c, f(b))
25.51/8.36	   A^2 -> H(U1(e, k), f(b))
25.51/8.36	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, c), f(c))
25.51/8.36	   A^2 -> H(U1(e, c), f(d))
25.51/8.36	   A^2 -> H(U1(k, e), f(b))
25.51/8.36	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, c), f(c))
25.51/8.36	   A^2 -> H(U1(k, c), f(d))
25.51/8.36	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(c, e), f(c))
25.51/8.36	   A^2 -> H(U1(c, e), f(d))
25.51/8.36	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(c, k), f(c))
25.51/8.36	   A^2 -> H(U1(c, k), f(d))
25.51/8.36	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, c), f(e))
25.51/8.36	   A^2 -> H(U1(c, c), f(k))
25.51/8.36	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.36	   A^2 -> H(e, f(b))
25.51/8.36	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, e), f(c))
25.51/8.36	   A^2 -> H(U1(e, e), f(d))
25.51/8.36	   A^2 -> H(f(e), U1(c, b))
25.51/8.36	   A^2 -> H(f(e), U1(d, b))
25.51/8.36	   A^2 -> H(f(e), U1(b, c))
25.51/8.36	   A^2 -> H(f(e), U1(b, d))
25.51/8.36	   A^2 -> H(f(e), U1(c, c))
25.51/8.36	   A^2 -> H(f(e), f(e))
25.51/8.36	   A^2 -> H(f(e), f(k))
25.51/8.36	   A^2 -> H(f(e), U1(d, d))
25.51/8.36	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, k), f(c))
25.51/8.36	   A^2 -> H(U1(k, k), f(d))
25.51/8.36	   A^2 -> H(f(k), U1(c, b))
25.51/8.36	   A^2 -> H(f(k), U1(d, b))
25.51/8.36	   A^2 -> H(f(k), U1(b, c))
25.51/8.36	   A^2 -> H(f(k), U1(b, d))
25.51/8.36	   A^2 -> H(f(k), U1(c, c))
25.51/8.36	   A^2 -> H(f(k), f(e))
25.51/8.36	   A^2 -> H(f(k), f(k))
25.51/8.36	   A^2 -> H(f(k), U1(d, d))
25.51/8.36	   A^2 -> H(f(c), U1(e, b))
25.51/8.36	   A^2 -> H(f(c), U1(k, b))
25.51/8.36	   A^2 -> H(f(c), U1(c, d))
25.51/8.36	   A^2 -> H(f(c), U1(d, c))
25.51/8.36	   A^2 -> H(f(c), U1(b, e))
25.51/8.36	   A^2 -> H(f(c), U1(b, k))
25.51/8.36	   A^2 -> H(f(c), U1(k, d))
25.51/8.36	   A^2 -> H(f(c), U1(d, k))
25.51/8.36	   A^2 -> H(f(c), U1(k, k))
25.51/8.36	   A^2 -> H(U1(k, k), f(b))
25.51/8.36	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, d), f(c))
25.51/8.36	   A^2 -> H(U1(k, d), f(d))
25.51/8.36	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(d, k), f(c))
25.51/8.36	   A^2 -> H(U1(d, k), f(d))
25.51/8.36	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(d, d), f(e))
25.51/8.36	   A^2 -> H(U1(d, d), f(k))
25.51/8.36	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.36	   A^2 -> H(f(d), U1(e, b))
25.51/8.36	   A^2 -> H(f(d), U1(k, b))
25.51/8.36	   A^2 -> H(f(d), U1(c, d))
25.51/8.36	   A^2 -> H(f(d), U1(d, c))
25.51/8.36	   A^2 -> H(f(d), U1(b, e))
25.51/8.36	   A^2 -> H(f(d), U1(b, k))
25.51/8.36	   A^2 -> H(f(d), U1(e, c))
25.51/8.36	   A^2 -> H(f(d), U1(k, c))
25.51/8.36	   A^2 -> H(f(d), U1(c, e))
25.51/8.36	   A^2 -> H(f(d), U1(c, k))
25.51/8.36	   A^2 -> H(f(d), U1(e, e))
25.51/8.36	   A^2 -> H(f(d), U1(k, k))
25.51/8.36	   A^2 -> H(f(a), b)
25.51/8.36	   A^2 -> H(f(a), U1(e, d))
25.51/8.36	   A^2 -> H(f(a), U1(d, e))
25.51/8.36	   A^2 -> H(f(c), U1(e, c))
25.51/8.36	   A^2 -> H(f(c), U1(k, c))
25.51/8.36	   A^2 -> H(f(c), U1(c, e))
25.51/8.36	   A^2 -> H(f(c), U1(c, k))
25.51/8.36	   A^2 -> H(f(a), c)
25.51/8.36	   A^2 -> H(f(a), U1(e, k))
25.51/8.36	   A^2 -> H(f(a), U1(k, e))
25.51/8.36	   A^2 -> H(f(c), U1(e, e))
25.51/8.36	   A^2 -> H(f(a), e)
25.51/8.36	   A^2 -> H(f(d), U1(k, d))
25.51/8.36	   A^2 -> H(f(d), U1(d, k))
25.51/8.36	   A^2 -> H(f(a), U1(k, k))
25.51/8.36	   A^2 -> H(d, f(b))
25.51/8.36	   A^2 -> H(a, U1(b, b))
25.51/8.36	   A^2 -> H(a, f(c))
25.51/8.36	   A^2 -> H(a, f(d))
25.51/8.36	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, d), f(c))
25.51/8.36	   A^2 -> H(U1(e, d), f(d))
25.51/8.36	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(e, a), f(e))
25.51/8.36	   A^2 -> H(U1(e, a), f(k))
25.51/8.36	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(k, a), f(e))
25.51/8.36	   A^2 -> H(U1(k, a), f(k))
25.51/8.36	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, d), f(e))
25.51/8.36	   A^2 -> H(U1(c, d), f(k))
25.51/8.36	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.36	
25.51/8.36	The TRS R consists of the following rules:
25.51/8.36	
25.51/8.36	   f(x) -> U1(x, x)
25.51/8.36	   U1(e, x) -> x
25.51/8.36	   a -> c
25.51/8.36	   a -> d
25.51/8.36	   b -> c
25.51/8.36	   b -> d
25.51/8.36	   d -> k
25.51/8.36	   c -> e
25.51/8.36	   c -> k
25.51/8.36	
25.51/8.36	Q is empty.
25.51/8.36	We have to consider all minimal (P,Q,R)-chains.
25.51/8.36	----------------------------------------
25.51/8.36	
25.51/8.36	(243) TransformationProof (EQUIVALENT)
25.51/8.36	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.36	
25.51/8.36	   (A^2 -> H(U1(e, a), U1(c, b)),A^2 -> H(U1(e, a), U1(c, b)))
25.51/8.36	   (A^2 -> H(U1(k, a), U1(c, b)),A^2 -> H(U1(k, a), U1(c, b)))
25.51/8.36	   (A^2 -> H(U1(c, c), U1(c, b)),A^2 -> H(U1(c, c), U1(c, b)))
25.51/8.36	   (A^2 -> H(U1(c, d), U1(c, b)),A^2 -> H(U1(c, d), U1(c, b)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(e, b)),A^2 -> H(U1(c, a), U1(e, b)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(k, b)),A^2 -> H(U1(c, a), U1(k, b)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(c, c)),A^2 -> H(U1(c, a), U1(c, c)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(c, d)),A^2 -> H(U1(c, a), U1(c, d)))
25.51/8.36	
25.51/8.36	
25.51/8.36	----------------------------------------
25.51/8.36	
25.51/8.36	(244)
25.51/8.36	Obligation:
25.51/8.36	Q DP problem:
25.51/8.36	The TRS P consists of the following rules:
25.51/8.36	
25.51/8.36	   H(x, x) -> G(x, x, f(k))
25.51/8.36	   G(d, x, x) -> A^2
25.51/8.36	   A^2 -> H(f(c), f(c))
25.51/8.36	   A^2 -> H(f(d), f(d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, a), f(e))
25.51/8.36	   A^2 -> H(U1(c, a), f(k))
25.51/8.36	   A^2 -> H(U1(c, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(d, e), f(b))
25.51/8.36	   A^2 -> H(U1(d, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(d, c), f(c))
25.51/8.36	   A^2 -> H(U1(d, c), f(d))
25.51/8.36	   A^2 -> H(U1(d, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(d, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(d, a), f(e))
25.51/8.36	   A^2 -> H(U1(d, a), f(k))
25.51/8.36	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(a, e), f(c))
25.51/8.36	   A^2 -> H(U1(a, e), f(d))
25.51/8.36	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(a, k), f(c))
25.51/8.36	   A^2 -> H(U1(a, k), f(d))
25.51/8.36	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.36	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.36	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.36	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.36	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.36	   A^2 -> H(U1(a, c), f(e))
25.51/8.36	   A^2 -> H(U1(a, c), f(k))
25.51/8.36	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(a, d), f(e))
25.51/8.36	   A^2 -> H(U1(a, d), f(k))
25.51/8.36	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.36	   A^2 -> H(c, f(b))
25.51/8.36	   A^2 -> H(U1(e, k), f(b))
25.51/8.36	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, c), f(c))
25.51/8.36	   A^2 -> H(U1(e, c), f(d))
25.51/8.36	   A^2 -> H(U1(k, e), f(b))
25.51/8.36	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, c), f(c))
25.51/8.36	   A^2 -> H(U1(k, c), f(d))
25.51/8.36	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(c, e), f(c))
25.51/8.36	   A^2 -> H(U1(c, e), f(d))
25.51/8.36	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(c, k), f(c))
25.51/8.36	   A^2 -> H(U1(c, k), f(d))
25.51/8.36	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, c), f(e))
25.51/8.36	   A^2 -> H(U1(c, c), f(k))
25.51/8.36	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.36	   A^2 -> H(e, f(b))
25.51/8.36	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, e), f(c))
25.51/8.36	   A^2 -> H(U1(e, e), f(d))
25.51/8.36	   A^2 -> H(f(e), U1(c, b))
25.51/8.36	   A^2 -> H(f(e), U1(d, b))
25.51/8.36	   A^2 -> H(f(e), U1(b, c))
25.51/8.36	   A^2 -> H(f(e), U1(b, d))
25.51/8.36	   A^2 -> H(f(e), U1(c, c))
25.51/8.36	   A^2 -> H(f(e), f(e))
25.51/8.36	   A^2 -> H(f(e), f(k))
25.51/8.36	   A^2 -> H(f(e), U1(d, d))
25.51/8.36	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, k), f(c))
25.51/8.36	   A^2 -> H(U1(k, k), f(d))
25.51/8.36	   A^2 -> H(f(k), U1(c, b))
25.51/8.36	   A^2 -> H(f(k), U1(d, b))
25.51/8.36	   A^2 -> H(f(k), U1(b, c))
25.51/8.36	   A^2 -> H(f(k), U1(b, d))
25.51/8.36	   A^2 -> H(f(k), U1(c, c))
25.51/8.36	   A^2 -> H(f(k), f(e))
25.51/8.36	   A^2 -> H(f(k), f(k))
25.51/8.36	   A^2 -> H(f(k), U1(d, d))
25.51/8.36	   A^2 -> H(f(c), U1(e, b))
25.51/8.36	   A^2 -> H(f(c), U1(k, b))
25.51/8.36	   A^2 -> H(f(c), U1(c, d))
25.51/8.36	   A^2 -> H(f(c), U1(d, c))
25.51/8.36	   A^2 -> H(f(c), U1(b, e))
25.51/8.36	   A^2 -> H(f(c), U1(b, k))
25.51/8.36	   A^2 -> H(f(c), U1(k, d))
25.51/8.36	   A^2 -> H(f(c), U1(d, k))
25.51/8.36	   A^2 -> H(f(c), U1(k, k))
25.51/8.36	   A^2 -> H(U1(k, k), f(b))
25.51/8.36	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, d), f(c))
25.51/8.36	   A^2 -> H(U1(k, d), f(d))
25.51/8.36	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(d, k), f(c))
25.51/8.36	   A^2 -> H(U1(d, k), f(d))
25.51/8.36	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(d, d), f(e))
25.51/8.36	   A^2 -> H(U1(d, d), f(k))
25.51/8.36	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.36	   A^2 -> H(f(d), U1(e, b))
25.51/8.36	   A^2 -> H(f(d), U1(k, b))
25.51/8.36	   A^2 -> H(f(d), U1(c, d))
25.51/8.36	   A^2 -> H(f(d), U1(d, c))
25.51/8.36	   A^2 -> H(f(d), U1(b, e))
25.51/8.36	   A^2 -> H(f(d), U1(b, k))
25.51/8.36	   A^2 -> H(f(d), U1(e, c))
25.51/8.36	   A^2 -> H(f(d), U1(k, c))
25.51/8.36	   A^2 -> H(f(d), U1(c, e))
25.51/8.36	   A^2 -> H(f(d), U1(c, k))
25.51/8.36	   A^2 -> H(f(d), U1(e, e))
25.51/8.36	   A^2 -> H(f(d), U1(k, k))
25.51/8.36	   A^2 -> H(f(a), b)
25.51/8.36	   A^2 -> H(f(a), U1(e, d))
25.51/8.36	   A^2 -> H(f(a), U1(d, e))
25.51/8.36	   A^2 -> H(f(c), U1(e, c))
25.51/8.36	   A^2 -> H(f(c), U1(k, c))
25.51/8.36	   A^2 -> H(f(c), U1(c, e))
25.51/8.36	   A^2 -> H(f(c), U1(c, k))
25.51/8.36	   A^2 -> H(f(a), c)
25.51/8.36	   A^2 -> H(f(a), U1(e, k))
25.51/8.36	   A^2 -> H(f(a), U1(k, e))
25.51/8.36	   A^2 -> H(f(c), U1(e, e))
25.51/8.36	   A^2 -> H(f(a), e)
25.51/8.36	   A^2 -> H(f(d), U1(k, d))
25.51/8.36	   A^2 -> H(f(d), U1(d, k))
25.51/8.36	   A^2 -> H(f(a), U1(k, k))
25.51/8.36	   A^2 -> H(d, f(b))
25.51/8.36	   A^2 -> H(a, U1(b, b))
25.51/8.36	   A^2 -> H(a, f(c))
25.51/8.36	   A^2 -> H(a, f(d))
25.51/8.36	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, d), f(c))
25.51/8.36	   A^2 -> H(U1(e, d), f(d))
25.51/8.36	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(e, a), f(e))
25.51/8.36	   A^2 -> H(U1(e, a), f(k))
25.51/8.36	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(k, a), f(e))
25.51/8.36	   A^2 -> H(U1(k, a), f(k))
25.51/8.36	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, d), f(e))
25.51/8.36	   A^2 -> H(U1(c, d), f(k))
25.51/8.36	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.36	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.36	
25.51/8.36	The TRS R consists of the following rules:
25.51/8.36	
25.51/8.36	   f(x) -> U1(x, x)
25.51/8.36	   U1(e, x) -> x
25.51/8.36	   a -> c
25.51/8.36	   a -> d
25.51/8.36	   b -> c
25.51/8.36	   b -> d
25.51/8.36	   d -> k
25.51/8.36	   c -> e
25.51/8.36	   c -> k
25.51/8.36	
25.51/8.36	Q is empty.
25.51/8.36	We have to consider all minimal (P,Q,R)-chains.
25.51/8.36	----------------------------------------
25.51/8.36	
25.51/8.36	(245) TransformationProof (EQUIVALENT)
25.51/8.36	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.36	
25.51/8.36	   (A^2 -> H(U1(e, a), U1(d, b)),A^2 -> H(U1(e, a), U1(d, b)))
25.51/8.36	   (A^2 -> H(U1(k, a), U1(d, b)),A^2 -> H(U1(k, a), U1(d, b)))
25.51/8.36	   (A^2 -> H(U1(c, c), U1(d, b)),A^2 -> H(U1(c, c), U1(d, b)))
25.51/8.36	   (A^2 -> H(U1(c, d), U1(d, b)),A^2 -> H(U1(c, d), U1(d, b)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(k, b)),A^2 -> H(U1(c, a), U1(k, b)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(d, c)),A^2 -> H(U1(c, a), U1(d, c)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(d, d)),A^2 -> H(U1(c, a), U1(d, d)))
25.51/8.36	
25.51/8.36	
25.51/8.36	----------------------------------------
25.51/8.36	
25.51/8.36	(246)
25.51/8.36	Obligation:
25.51/8.36	Q DP problem:
25.51/8.36	The TRS P consists of the following rules:
25.51/8.36	
25.51/8.36	   H(x, x) -> G(x, x, f(k))
25.51/8.36	   G(d, x, x) -> A^2
25.51/8.36	   A^2 -> H(f(c), f(c))
25.51/8.36	   A^2 -> H(f(d), f(d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, a), f(e))
25.51/8.36	   A^2 -> H(U1(c, a), f(k))
25.51/8.36	   A^2 -> H(U1(c, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(d, e), f(b))
25.51/8.36	   A^2 -> H(U1(d, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(d, c), f(c))
25.51/8.36	   A^2 -> H(U1(d, c), f(d))
25.51/8.36	   A^2 -> H(U1(d, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(d, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(d, a), f(e))
25.51/8.36	   A^2 -> H(U1(d, a), f(k))
25.51/8.36	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(a, e), f(c))
25.51/8.36	   A^2 -> H(U1(a, e), f(d))
25.51/8.36	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(a, k), f(c))
25.51/8.36	   A^2 -> H(U1(a, k), f(d))
25.51/8.36	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.36	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.36	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.36	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.36	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.36	   A^2 -> H(U1(a, c), f(e))
25.51/8.36	   A^2 -> H(U1(a, c), f(k))
25.51/8.36	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(a, d), f(e))
25.51/8.36	   A^2 -> H(U1(a, d), f(k))
25.51/8.36	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.36	   A^2 -> H(c, f(b))
25.51/8.36	   A^2 -> H(U1(e, k), f(b))
25.51/8.36	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, c), f(c))
25.51/8.36	   A^2 -> H(U1(e, c), f(d))
25.51/8.36	   A^2 -> H(U1(k, e), f(b))
25.51/8.36	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, c), f(c))
25.51/8.36	   A^2 -> H(U1(k, c), f(d))
25.51/8.36	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(c, e), f(c))
25.51/8.36	   A^2 -> H(U1(c, e), f(d))
25.51/8.36	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(c, k), f(c))
25.51/8.36	   A^2 -> H(U1(c, k), f(d))
25.51/8.36	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, c), f(e))
25.51/8.36	   A^2 -> H(U1(c, c), f(k))
25.51/8.36	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.36	   A^2 -> H(e, f(b))
25.51/8.36	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, e), f(c))
25.51/8.36	   A^2 -> H(U1(e, e), f(d))
25.51/8.36	   A^2 -> H(f(e), U1(c, b))
25.51/8.36	   A^2 -> H(f(e), U1(d, b))
25.51/8.36	   A^2 -> H(f(e), U1(b, c))
25.51/8.36	   A^2 -> H(f(e), U1(b, d))
25.51/8.36	   A^2 -> H(f(e), U1(c, c))
25.51/8.36	   A^2 -> H(f(e), f(e))
25.51/8.36	   A^2 -> H(f(e), f(k))
25.51/8.36	   A^2 -> H(f(e), U1(d, d))
25.51/8.36	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, k), f(c))
25.51/8.36	   A^2 -> H(U1(k, k), f(d))
25.51/8.36	   A^2 -> H(f(k), U1(c, b))
25.51/8.36	   A^2 -> H(f(k), U1(d, b))
25.51/8.36	   A^2 -> H(f(k), U1(b, c))
25.51/8.36	   A^2 -> H(f(k), U1(b, d))
25.51/8.36	   A^2 -> H(f(k), U1(c, c))
25.51/8.36	   A^2 -> H(f(k), f(e))
25.51/8.36	   A^2 -> H(f(k), f(k))
25.51/8.36	   A^2 -> H(f(k), U1(d, d))
25.51/8.36	   A^2 -> H(f(c), U1(e, b))
25.51/8.36	   A^2 -> H(f(c), U1(k, b))
25.51/8.36	   A^2 -> H(f(c), U1(c, d))
25.51/8.36	   A^2 -> H(f(c), U1(d, c))
25.51/8.36	   A^2 -> H(f(c), U1(b, e))
25.51/8.36	   A^2 -> H(f(c), U1(b, k))
25.51/8.36	   A^2 -> H(f(c), U1(k, d))
25.51/8.36	   A^2 -> H(f(c), U1(d, k))
25.51/8.36	   A^2 -> H(f(c), U1(k, k))
25.51/8.36	   A^2 -> H(U1(k, k), f(b))
25.51/8.36	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, d), f(c))
25.51/8.36	   A^2 -> H(U1(k, d), f(d))
25.51/8.36	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(d, k), f(c))
25.51/8.36	   A^2 -> H(U1(d, k), f(d))
25.51/8.36	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(d, d), f(e))
25.51/8.36	   A^2 -> H(U1(d, d), f(k))
25.51/8.36	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.36	   A^2 -> H(f(d), U1(e, b))
25.51/8.36	   A^2 -> H(f(d), U1(k, b))
25.51/8.36	   A^2 -> H(f(d), U1(c, d))
25.51/8.36	   A^2 -> H(f(d), U1(d, c))
25.51/8.36	   A^2 -> H(f(d), U1(b, e))
25.51/8.36	   A^2 -> H(f(d), U1(b, k))
25.51/8.36	   A^2 -> H(f(d), U1(e, c))
25.51/8.36	   A^2 -> H(f(d), U1(k, c))
25.51/8.36	   A^2 -> H(f(d), U1(c, e))
25.51/8.36	   A^2 -> H(f(d), U1(c, k))
25.51/8.36	   A^2 -> H(f(d), U1(e, e))
25.51/8.36	   A^2 -> H(f(d), U1(k, k))
25.51/8.36	   A^2 -> H(f(a), b)
25.51/8.36	   A^2 -> H(f(a), U1(e, d))
25.51/8.36	   A^2 -> H(f(a), U1(d, e))
25.51/8.36	   A^2 -> H(f(c), U1(e, c))
25.51/8.36	   A^2 -> H(f(c), U1(k, c))
25.51/8.36	   A^2 -> H(f(c), U1(c, e))
25.51/8.36	   A^2 -> H(f(c), U1(c, k))
25.51/8.36	   A^2 -> H(f(a), c)
25.51/8.36	   A^2 -> H(f(a), U1(e, k))
25.51/8.36	   A^2 -> H(f(a), U1(k, e))
25.51/8.36	   A^2 -> H(f(c), U1(e, e))
25.51/8.36	   A^2 -> H(f(a), e)
25.51/8.36	   A^2 -> H(f(d), U1(k, d))
25.51/8.36	   A^2 -> H(f(d), U1(d, k))
25.51/8.36	   A^2 -> H(f(a), U1(k, k))
25.51/8.36	   A^2 -> H(d, f(b))
25.51/8.36	   A^2 -> H(a, U1(b, b))
25.51/8.36	   A^2 -> H(a, f(c))
25.51/8.36	   A^2 -> H(a, f(d))
25.51/8.36	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, d), f(c))
25.51/8.36	   A^2 -> H(U1(e, d), f(d))
25.51/8.36	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(e, a), f(e))
25.51/8.36	   A^2 -> H(U1(e, a), f(k))
25.51/8.36	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(k, a), f(e))
25.51/8.36	   A^2 -> H(U1(k, a), f(k))
25.51/8.36	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, d), f(e))
25.51/8.36	   A^2 -> H(U1(c, d), f(k))
25.51/8.36	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.36	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.36	
25.51/8.36	The TRS R consists of the following rules:
25.51/8.36	
25.51/8.36	   f(x) -> U1(x, x)
25.51/8.36	   U1(e, x) -> x
25.51/8.36	   a -> c
25.51/8.36	   a -> d
25.51/8.36	   b -> c
25.51/8.36	   b -> d
25.51/8.36	   d -> k
25.51/8.36	   c -> e
25.51/8.36	   c -> k
25.51/8.36	
25.51/8.36	Q is empty.
25.51/8.36	We have to consider all minimal (P,Q,R)-chains.
25.51/8.36	----------------------------------------
25.51/8.36	
25.51/8.36	(247) TransformationProof (EQUIVALENT)
25.51/8.36	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.36	
25.51/8.36	   (A^2 -> H(U1(e, a), U1(b, c)),A^2 -> H(U1(e, a), U1(b, c)))
25.51/8.36	   (A^2 -> H(U1(k, a), U1(b, c)),A^2 -> H(U1(k, a), U1(b, c)))
25.51/8.36	   (A^2 -> H(U1(c, c), U1(b, c)),A^2 -> H(U1(c, c), U1(b, c)))
25.51/8.36	   (A^2 -> H(U1(c, d), U1(b, c)),A^2 -> H(U1(c, d), U1(b, c)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(c, c)),A^2 -> H(U1(c, a), U1(c, c)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(d, c)),A^2 -> H(U1(c, a), U1(d, c)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(b, e)),A^2 -> H(U1(c, a), U1(b, e)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(b, k)),A^2 -> H(U1(c, a), U1(b, k)))
25.51/8.36	
25.51/8.36	
25.51/8.36	----------------------------------------
25.51/8.36	
25.51/8.36	(248)
25.51/8.36	Obligation:
25.51/8.36	Q DP problem:
25.51/8.36	The TRS P consists of the following rules:
25.51/8.36	
25.51/8.36	   H(x, x) -> G(x, x, f(k))
25.51/8.36	   G(d, x, x) -> A^2
25.51/8.36	   A^2 -> H(f(c), f(c))
25.51/8.36	   A^2 -> H(f(d), f(d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, a), f(e))
25.51/8.36	   A^2 -> H(U1(c, a), f(k))
25.51/8.36	   A^2 -> H(U1(c, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(d, e), f(b))
25.51/8.36	   A^2 -> H(U1(d, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(d, c), f(c))
25.51/8.36	   A^2 -> H(U1(d, c), f(d))
25.51/8.36	   A^2 -> H(U1(d, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(d, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(d, a), f(e))
25.51/8.36	   A^2 -> H(U1(d, a), f(k))
25.51/8.36	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(a, e), f(c))
25.51/8.36	   A^2 -> H(U1(a, e), f(d))
25.51/8.36	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(a, k), f(c))
25.51/8.36	   A^2 -> H(U1(a, k), f(d))
25.51/8.36	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.36	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.36	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.36	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.36	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.36	   A^2 -> H(U1(a, c), f(e))
25.51/8.36	   A^2 -> H(U1(a, c), f(k))
25.51/8.36	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(a, d), f(e))
25.51/8.36	   A^2 -> H(U1(a, d), f(k))
25.51/8.36	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.36	   A^2 -> H(c, f(b))
25.51/8.36	   A^2 -> H(U1(e, k), f(b))
25.51/8.36	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, c), f(c))
25.51/8.36	   A^2 -> H(U1(e, c), f(d))
25.51/8.36	   A^2 -> H(U1(k, e), f(b))
25.51/8.36	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, c), f(c))
25.51/8.36	   A^2 -> H(U1(k, c), f(d))
25.51/8.36	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(c, e), f(c))
25.51/8.36	   A^2 -> H(U1(c, e), f(d))
25.51/8.36	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(c, k), f(c))
25.51/8.36	   A^2 -> H(U1(c, k), f(d))
25.51/8.36	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, c), f(e))
25.51/8.36	   A^2 -> H(U1(c, c), f(k))
25.51/8.36	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.36	   A^2 -> H(e, f(b))
25.51/8.36	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, e), f(c))
25.51/8.36	   A^2 -> H(U1(e, e), f(d))
25.51/8.36	   A^2 -> H(f(e), U1(c, b))
25.51/8.36	   A^2 -> H(f(e), U1(d, b))
25.51/8.36	   A^2 -> H(f(e), U1(b, c))
25.51/8.36	   A^2 -> H(f(e), U1(b, d))
25.51/8.36	   A^2 -> H(f(e), U1(c, c))
25.51/8.36	   A^2 -> H(f(e), f(e))
25.51/8.36	   A^2 -> H(f(e), f(k))
25.51/8.36	   A^2 -> H(f(e), U1(d, d))
25.51/8.36	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, k), f(c))
25.51/8.36	   A^2 -> H(U1(k, k), f(d))
25.51/8.36	   A^2 -> H(f(k), U1(c, b))
25.51/8.36	   A^2 -> H(f(k), U1(d, b))
25.51/8.36	   A^2 -> H(f(k), U1(b, c))
25.51/8.36	   A^2 -> H(f(k), U1(b, d))
25.51/8.36	   A^2 -> H(f(k), U1(c, c))
25.51/8.36	   A^2 -> H(f(k), f(e))
25.51/8.36	   A^2 -> H(f(k), f(k))
25.51/8.36	   A^2 -> H(f(k), U1(d, d))
25.51/8.36	   A^2 -> H(f(c), U1(e, b))
25.51/8.36	   A^2 -> H(f(c), U1(k, b))
25.51/8.36	   A^2 -> H(f(c), U1(c, d))
25.51/8.36	   A^2 -> H(f(c), U1(d, c))
25.51/8.36	   A^2 -> H(f(c), U1(b, e))
25.51/8.36	   A^2 -> H(f(c), U1(b, k))
25.51/8.36	   A^2 -> H(f(c), U1(k, d))
25.51/8.36	   A^2 -> H(f(c), U1(d, k))
25.51/8.36	   A^2 -> H(f(c), U1(k, k))
25.51/8.36	   A^2 -> H(U1(k, k), f(b))
25.51/8.36	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, d), f(c))
25.51/8.36	   A^2 -> H(U1(k, d), f(d))
25.51/8.36	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(d, k), f(c))
25.51/8.36	   A^2 -> H(U1(d, k), f(d))
25.51/8.36	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(d, d), f(e))
25.51/8.36	   A^2 -> H(U1(d, d), f(k))
25.51/8.36	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.36	   A^2 -> H(f(d), U1(e, b))
25.51/8.36	   A^2 -> H(f(d), U1(k, b))
25.51/8.36	   A^2 -> H(f(d), U1(c, d))
25.51/8.36	   A^2 -> H(f(d), U1(d, c))
25.51/8.36	   A^2 -> H(f(d), U1(b, e))
25.51/8.36	   A^2 -> H(f(d), U1(b, k))
25.51/8.36	   A^2 -> H(f(d), U1(e, c))
25.51/8.36	   A^2 -> H(f(d), U1(k, c))
25.51/8.36	   A^2 -> H(f(d), U1(c, e))
25.51/8.36	   A^2 -> H(f(d), U1(c, k))
25.51/8.36	   A^2 -> H(f(d), U1(e, e))
25.51/8.36	   A^2 -> H(f(d), U1(k, k))
25.51/8.36	   A^2 -> H(f(a), b)
25.51/8.36	   A^2 -> H(f(a), U1(e, d))
25.51/8.36	   A^2 -> H(f(a), U1(d, e))
25.51/8.36	   A^2 -> H(f(c), U1(e, c))
25.51/8.36	   A^2 -> H(f(c), U1(k, c))
25.51/8.36	   A^2 -> H(f(c), U1(c, e))
25.51/8.36	   A^2 -> H(f(c), U1(c, k))
25.51/8.36	   A^2 -> H(f(a), c)
25.51/8.36	   A^2 -> H(f(a), U1(e, k))
25.51/8.36	   A^2 -> H(f(a), U1(k, e))
25.51/8.36	   A^2 -> H(f(c), U1(e, e))
25.51/8.36	   A^2 -> H(f(a), e)
25.51/8.36	   A^2 -> H(f(d), U1(k, d))
25.51/8.36	   A^2 -> H(f(d), U1(d, k))
25.51/8.36	   A^2 -> H(f(a), U1(k, k))
25.51/8.36	   A^2 -> H(d, f(b))
25.51/8.36	   A^2 -> H(a, U1(b, b))
25.51/8.36	   A^2 -> H(a, f(c))
25.51/8.36	   A^2 -> H(a, f(d))
25.51/8.36	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, d), f(c))
25.51/8.36	   A^2 -> H(U1(e, d), f(d))
25.51/8.36	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(e, a), f(e))
25.51/8.36	   A^2 -> H(U1(e, a), f(k))
25.51/8.36	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(k, a), f(e))
25.51/8.36	   A^2 -> H(U1(k, a), f(k))
25.51/8.36	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, d), f(e))
25.51/8.36	   A^2 -> H(U1(c, d), f(k))
25.51/8.36	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.36	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.36	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.36	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.36	
25.51/8.36	The TRS R consists of the following rules:
25.51/8.36	
25.51/8.36	   f(x) -> U1(x, x)
25.51/8.36	   U1(e, x) -> x
25.51/8.36	   a -> c
25.51/8.36	   a -> d
25.51/8.36	   b -> c
25.51/8.36	   b -> d
25.51/8.36	   d -> k
25.51/8.36	   c -> e
25.51/8.36	   c -> k
25.51/8.36	
25.51/8.36	Q is empty.
25.51/8.36	We have to consider all minimal (P,Q,R)-chains.
25.51/8.36	----------------------------------------
25.51/8.36	
25.51/8.36	(249) TransformationProof (EQUIVALENT)
25.51/8.36	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.36	
25.51/8.36	   (A^2 -> H(U1(e, a), U1(b, d)),A^2 -> H(U1(e, a), U1(b, d)))
25.51/8.36	   (A^2 -> H(U1(k, a), U1(b, d)),A^2 -> H(U1(k, a), U1(b, d)))
25.51/8.36	   (A^2 -> H(U1(c, c), U1(b, d)),A^2 -> H(U1(c, c), U1(b, d)))
25.51/8.36	   (A^2 -> H(U1(c, d), U1(b, d)),A^2 -> H(U1(c, d), U1(b, d)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(c, d)),A^2 -> H(U1(c, a), U1(c, d)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(d, d)),A^2 -> H(U1(c, a), U1(d, d)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(b, k)),A^2 -> H(U1(c, a), U1(b, k)))
25.51/8.36	
25.51/8.36	
25.51/8.36	----------------------------------------
25.51/8.36	
25.51/8.36	(250)
25.51/8.36	Obligation:
25.51/8.36	Q DP problem:
25.51/8.36	The TRS P consists of the following rules:
25.51/8.36	
25.51/8.36	   H(x, x) -> G(x, x, f(k))
25.51/8.36	   G(d, x, x) -> A^2
25.51/8.36	   A^2 -> H(f(c), f(c))
25.51/8.36	   A^2 -> H(f(d), f(d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, a), f(e))
25.51/8.36	   A^2 -> H(U1(c, a), f(k))
25.51/8.36	   A^2 -> H(U1(c, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(d, e), f(b))
25.51/8.36	   A^2 -> H(U1(d, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(d, c), f(c))
25.51/8.36	   A^2 -> H(U1(d, c), f(d))
25.51/8.36	   A^2 -> H(U1(d, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(d, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(d, a), f(e))
25.51/8.36	   A^2 -> H(U1(d, a), f(k))
25.51/8.36	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(a, e), f(c))
25.51/8.36	   A^2 -> H(U1(a, e), f(d))
25.51/8.36	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(a, k), f(c))
25.51/8.36	   A^2 -> H(U1(a, k), f(d))
25.51/8.36	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.36	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.36	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.36	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.36	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.36	   A^2 -> H(U1(a, c), f(e))
25.51/8.36	   A^2 -> H(U1(a, c), f(k))
25.51/8.36	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(a, d), f(e))
25.51/8.36	   A^2 -> H(U1(a, d), f(k))
25.51/8.36	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.36	   A^2 -> H(c, f(b))
25.51/8.36	   A^2 -> H(U1(e, k), f(b))
25.51/8.36	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, c), f(c))
25.51/8.36	   A^2 -> H(U1(e, c), f(d))
25.51/8.36	   A^2 -> H(U1(k, e), f(b))
25.51/8.36	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, c), f(c))
25.51/8.36	   A^2 -> H(U1(k, c), f(d))
25.51/8.36	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(c, e), f(c))
25.51/8.36	   A^2 -> H(U1(c, e), f(d))
25.51/8.36	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(c, k), f(c))
25.51/8.36	   A^2 -> H(U1(c, k), f(d))
25.51/8.36	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, c), f(e))
25.51/8.36	   A^2 -> H(U1(c, c), f(k))
25.51/8.36	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.36	   A^2 -> H(e, f(b))
25.51/8.36	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, e), f(c))
25.51/8.36	   A^2 -> H(U1(e, e), f(d))
25.51/8.36	   A^2 -> H(f(e), U1(c, b))
25.51/8.36	   A^2 -> H(f(e), U1(d, b))
25.51/8.36	   A^2 -> H(f(e), U1(b, c))
25.51/8.36	   A^2 -> H(f(e), U1(b, d))
25.51/8.36	   A^2 -> H(f(e), U1(c, c))
25.51/8.36	   A^2 -> H(f(e), f(e))
25.51/8.36	   A^2 -> H(f(e), f(k))
25.51/8.36	   A^2 -> H(f(e), U1(d, d))
25.51/8.36	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, k), f(c))
25.51/8.36	   A^2 -> H(U1(k, k), f(d))
25.51/8.36	   A^2 -> H(f(k), U1(c, b))
25.51/8.36	   A^2 -> H(f(k), U1(d, b))
25.51/8.36	   A^2 -> H(f(k), U1(b, c))
25.51/8.36	   A^2 -> H(f(k), U1(b, d))
25.51/8.36	   A^2 -> H(f(k), U1(c, c))
25.51/8.36	   A^2 -> H(f(k), f(e))
25.51/8.36	   A^2 -> H(f(k), f(k))
25.51/8.36	   A^2 -> H(f(k), U1(d, d))
25.51/8.36	   A^2 -> H(f(c), U1(e, b))
25.51/8.36	   A^2 -> H(f(c), U1(k, b))
25.51/8.36	   A^2 -> H(f(c), U1(c, d))
25.51/8.36	   A^2 -> H(f(c), U1(d, c))
25.51/8.36	   A^2 -> H(f(c), U1(b, e))
25.51/8.36	   A^2 -> H(f(c), U1(b, k))
25.51/8.36	   A^2 -> H(f(c), U1(k, d))
25.51/8.36	   A^2 -> H(f(c), U1(d, k))
25.51/8.36	   A^2 -> H(f(c), U1(k, k))
25.51/8.36	   A^2 -> H(U1(k, k), f(b))
25.51/8.36	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, d), f(c))
25.51/8.36	   A^2 -> H(U1(k, d), f(d))
25.51/8.36	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(d, k), f(c))
25.51/8.36	   A^2 -> H(U1(d, k), f(d))
25.51/8.36	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(d, d), f(e))
25.51/8.36	   A^2 -> H(U1(d, d), f(k))
25.51/8.36	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.36	   A^2 -> H(f(d), U1(e, b))
25.51/8.36	   A^2 -> H(f(d), U1(k, b))
25.51/8.36	   A^2 -> H(f(d), U1(c, d))
25.51/8.36	   A^2 -> H(f(d), U1(d, c))
25.51/8.36	   A^2 -> H(f(d), U1(b, e))
25.51/8.36	   A^2 -> H(f(d), U1(b, k))
25.51/8.36	   A^2 -> H(f(d), U1(e, c))
25.51/8.36	   A^2 -> H(f(d), U1(k, c))
25.51/8.36	   A^2 -> H(f(d), U1(c, e))
25.51/8.36	   A^2 -> H(f(d), U1(c, k))
25.51/8.36	   A^2 -> H(f(d), U1(e, e))
25.51/8.36	   A^2 -> H(f(d), U1(k, k))
25.51/8.36	   A^2 -> H(f(a), b)
25.51/8.36	   A^2 -> H(f(a), U1(e, d))
25.51/8.36	   A^2 -> H(f(a), U1(d, e))
25.51/8.36	   A^2 -> H(f(c), U1(e, c))
25.51/8.36	   A^2 -> H(f(c), U1(k, c))
25.51/8.36	   A^2 -> H(f(c), U1(c, e))
25.51/8.36	   A^2 -> H(f(c), U1(c, k))
25.51/8.36	   A^2 -> H(f(a), c)
25.51/8.36	   A^2 -> H(f(a), U1(e, k))
25.51/8.36	   A^2 -> H(f(a), U1(k, e))
25.51/8.36	   A^2 -> H(f(c), U1(e, e))
25.51/8.36	   A^2 -> H(f(a), e)
25.51/8.36	   A^2 -> H(f(d), U1(k, d))
25.51/8.36	   A^2 -> H(f(d), U1(d, k))
25.51/8.36	   A^2 -> H(f(a), U1(k, k))
25.51/8.36	   A^2 -> H(d, f(b))
25.51/8.36	   A^2 -> H(a, U1(b, b))
25.51/8.36	   A^2 -> H(a, f(c))
25.51/8.36	   A^2 -> H(a, f(d))
25.51/8.36	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, d), f(c))
25.51/8.36	   A^2 -> H(U1(e, d), f(d))
25.51/8.36	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(e, a), f(e))
25.51/8.36	   A^2 -> H(U1(e, a), f(k))
25.51/8.36	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(k, a), f(e))
25.51/8.36	   A^2 -> H(U1(k, a), f(k))
25.51/8.36	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, d), f(e))
25.51/8.36	   A^2 -> H(U1(c, d), f(k))
25.51/8.36	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.36	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.36	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.36	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.36	
25.51/8.36	The TRS R consists of the following rules:
25.51/8.36	
25.51/8.36	   f(x) -> U1(x, x)
25.51/8.36	   U1(e, x) -> x
25.51/8.36	   a -> c
25.51/8.36	   a -> d
25.51/8.36	   b -> c
25.51/8.36	   b -> d
25.51/8.36	   d -> k
25.51/8.36	   c -> e
25.51/8.36	   c -> k
25.51/8.36	
25.51/8.36	Q is empty.
25.51/8.36	We have to consider all minimal (P,Q,R)-chains.
25.51/8.36	----------------------------------------
25.51/8.36	
25.51/8.36	(251) TransformationProof (EQUIVALENT)
25.51/8.36	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.36	
25.51/8.36	   (A^2 -> H(U1(e, a), U1(c, c)),A^2 -> H(U1(e, a), U1(c, c)))
25.51/8.36	   (A^2 -> H(U1(k, a), U1(c, c)),A^2 -> H(U1(k, a), U1(c, c)))
25.51/8.36	   (A^2 -> H(U1(c, c), U1(c, c)),A^2 -> H(U1(c, c), U1(c, c)))
25.51/8.36	   (A^2 -> H(U1(c, d), U1(c, c)),A^2 -> H(U1(c, d), U1(c, c)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(e, c)),A^2 -> H(U1(c, a), U1(e, c)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(k, c)),A^2 -> H(U1(c, a), U1(k, c)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(c, e)),A^2 -> H(U1(c, a), U1(c, e)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(c, k)),A^2 -> H(U1(c, a), U1(c, k)))
25.51/8.36	
25.51/8.36	
25.51/8.36	----------------------------------------
25.51/8.36	
25.51/8.36	(252)
25.51/8.36	Obligation:
25.51/8.36	Q DP problem:
25.51/8.36	The TRS P consists of the following rules:
25.51/8.36	
25.51/8.36	   H(x, x) -> G(x, x, f(k))
25.51/8.36	   G(d, x, x) -> A^2
25.51/8.36	   A^2 -> H(f(c), f(c))
25.51/8.36	   A^2 -> H(f(d), f(d))
25.51/8.36	   A^2 -> H(U1(c, a), f(e))
25.51/8.36	   A^2 -> H(U1(c, a), f(k))
25.51/8.36	   A^2 -> H(U1(c, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(d, e), f(b))
25.51/8.36	   A^2 -> H(U1(d, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(d, c), f(c))
25.51/8.36	   A^2 -> H(U1(d, c), f(d))
25.51/8.36	   A^2 -> H(U1(d, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(d, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(d, a), f(e))
25.51/8.36	   A^2 -> H(U1(d, a), f(k))
25.51/8.36	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(a, e), f(c))
25.51/8.36	   A^2 -> H(U1(a, e), f(d))
25.51/8.36	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(a, k), f(c))
25.51/8.36	   A^2 -> H(U1(a, k), f(d))
25.51/8.36	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.36	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.36	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.36	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.36	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.36	   A^2 -> H(U1(a, c), f(e))
25.51/8.36	   A^2 -> H(U1(a, c), f(k))
25.51/8.36	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(a, d), f(e))
25.51/8.36	   A^2 -> H(U1(a, d), f(k))
25.51/8.36	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.36	   A^2 -> H(c, f(b))
25.51/8.36	   A^2 -> H(U1(e, k), f(b))
25.51/8.36	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, c), f(c))
25.51/8.36	   A^2 -> H(U1(e, c), f(d))
25.51/8.36	   A^2 -> H(U1(k, e), f(b))
25.51/8.36	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, c), f(c))
25.51/8.36	   A^2 -> H(U1(k, c), f(d))
25.51/8.36	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(c, e), f(c))
25.51/8.36	   A^2 -> H(U1(c, e), f(d))
25.51/8.36	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(c, k), f(c))
25.51/8.36	   A^2 -> H(U1(c, k), f(d))
25.51/8.36	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, c), f(e))
25.51/8.36	   A^2 -> H(U1(c, c), f(k))
25.51/8.36	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.36	   A^2 -> H(e, f(b))
25.51/8.36	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, e), f(c))
25.51/8.36	   A^2 -> H(U1(e, e), f(d))
25.51/8.36	   A^2 -> H(f(e), U1(c, b))
25.51/8.36	   A^2 -> H(f(e), U1(d, b))
25.51/8.36	   A^2 -> H(f(e), U1(b, c))
25.51/8.36	   A^2 -> H(f(e), U1(b, d))
25.51/8.36	   A^2 -> H(f(e), U1(c, c))
25.51/8.36	   A^2 -> H(f(e), f(e))
25.51/8.36	   A^2 -> H(f(e), f(k))
25.51/8.36	   A^2 -> H(f(e), U1(d, d))
25.51/8.36	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, k), f(c))
25.51/8.36	   A^2 -> H(U1(k, k), f(d))
25.51/8.36	   A^2 -> H(f(k), U1(c, b))
25.51/8.36	   A^2 -> H(f(k), U1(d, b))
25.51/8.36	   A^2 -> H(f(k), U1(b, c))
25.51/8.36	   A^2 -> H(f(k), U1(b, d))
25.51/8.36	   A^2 -> H(f(k), U1(c, c))
25.51/8.36	   A^2 -> H(f(k), f(e))
25.51/8.36	   A^2 -> H(f(k), f(k))
25.51/8.36	   A^2 -> H(f(k), U1(d, d))
25.51/8.36	   A^2 -> H(f(c), U1(e, b))
25.51/8.36	   A^2 -> H(f(c), U1(k, b))
25.51/8.36	   A^2 -> H(f(c), U1(c, d))
25.51/8.36	   A^2 -> H(f(c), U1(d, c))
25.51/8.36	   A^2 -> H(f(c), U1(b, e))
25.51/8.36	   A^2 -> H(f(c), U1(b, k))
25.51/8.36	   A^2 -> H(f(c), U1(k, d))
25.51/8.36	   A^2 -> H(f(c), U1(d, k))
25.51/8.36	   A^2 -> H(f(c), U1(k, k))
25.51/8.36	   A^2 -> H(U1(k, k), f(b))
25.51/8.36	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, d), f(c))
25.51/8.36	   A^2 -> H(U1(k, d), f(d))
25.51/8.36	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(d, k), f(c))
25.51/8.36	   A^2 -> H(U1(d, k), f(d))
25.51/8.36	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(d, d), f(e))
25.51/8.36	   A^2 -> H(U1(d, d), f(k))
25.51/8.36	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.36	   A^2 -> H(f(d), U1(e, b))
25.51/8.36	   A^2 -> H(f(d), U1(k, b))
25.51/8.36	   A^2 -> H(f(d), U1(c, d))
25.51/8.36	   A^2 -> H(f(d), U1(d, c))
25.51/8.36	   A^2 -> H(f(d), U1(b, e))
25.51/8.36	   A^2 -> H(f(d), U1(b, k))
25.51/8.36	   A^2 -> H(f(d), U1(e, c))
25.51/8.36	   A^2 -> H(f(d), U1(k, c))
25.51/8.36	   A^2 -> H(f(d), U1(c, e))
25.51/8.36	   A^2 -> H(f(d), U1(c, k))
25.51/8.36	   A^2 -> H(f(d), U1(e, e))
25.51/8.36	   A^2 -> H(f(d), U1(k, k))
25.51/8.36	   A^2 -> H(f(a), b)
25.51/8.36	   A^2 -> H(f(a), U1(e, d))
25.51/8.36	   A^2 -> H(f(a), U1(d, e))
25.51/8.36	   A^2 -> H(f(c), U1(e, c))
25.51/8.36	   A^2 -> H(f(c), U1(k, c))
25.51/8.36	   A^2 -> H(f(c), U1(c, e))
25.51/8.36	   A^2 -> H(f(c), U1(c, k))
25.51/8.36	   A^2 -> H(f(a), c)
25.51/8.36	   A^2 -> H(f(a), U1(e, k))
25.51/8.36	   A^2 -> H(f(a), U1(k, e))
25.51/8.36	   A^2 -> H(f(c), U1(e, e))
25.51/8.36	   A^2 -> H(f(a), e)
25.51/8.36	   A^2 -> H(f(d), U1(k, d))
25.51/8.36	   A^2 -> H(f(d), U1(d, k))
25.51/8.36	   A^2 -> H(f(a), U1(k, k))
25.51/8.36	   A^2 -> H(d, f(b))
25.51/8.36	   A^2 -> H(a, U1(b, b))
25.51/8.36	   A^2 -> H(a, f(c))
25.51/8.36	   A^2 -> H(a, f(d))
25.51/8.36	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, d), f(c))
25.51/8.36	   A^2 -> H(U1(e, d), f(d))
25.51/8.36	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(e, a), f(e))
25.51/8.36	   A^2 -> H(U1(e, a), f(k))
25.51/8.36	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(k, a), f(e))
25.51/8.36	   A^2 -> H(U1(k, a), f(k))
25.51/8.36	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, d), f(e))
25.51/8.36	   A^2 -> H(U1(c, d), f(k))
25.51/8.36	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.36	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.36	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.36	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.36	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.36	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.36	
25.51/8.36	The TRS R consists of the following rules:
25.51/8.36	
25.51/8.36	   f(x) -> U1(x, x)
25.51/8.36	   U1(e, x) -> x
25.51/8.36	   a -> c
25.51/8.36	   a -> d
25.51/8.36	   b -> c
25.51/8.36	   b -> d
25.51/8.36	   d -> k
25.51/8.36	   c -> e
25.51/8.36	   c -> k
25.51/8.36	
25.51/8.36	Q is empty.
25.51/8.36	We have to consider all minimal (P,Q,R)-chains.
25.51/8.36	----------------------------------------
25.51/8.36	
25.51/8.36	(253) TransformationProof (EQUIVALENT)
25.51/8.36	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), f(e)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.36	
25.51/8.36	   (A^2 -> H(U1(e, a), f(e)),A^2 -> H(U1(e, a), f(e)))
25.51/8.36	   (A^2 -> H(U1(k, a), f(e)),A^2 -> H(U1(k, a), f(e)))
25.51/8.36	   (A^2 -> H(U1(c, c), f(e)),A^2 -> H(U1(c, c), f(e)))
25.51/8.36	   (A^2 -> H(U1(c, d), f(e)),A^2 -> H(U1(c, d), f(e)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(e, e)),A^2 -> H(U1(c, a), U1(e, e)))
25.51/8.36	
25.51/8.36	
25.51/8.36	----------------------------------------
25.51/8.36	
25.51/8.36	(254)
25.51/8.36	Obligation:
25.51/8.36	Q DP problem:
25.51/8.36	The TRS P consists of the following rules:
25.51/8.36	
25.51/8.36	   H(x, x) -> G(x, x, f(k))
25.51/8.36	   G(d, x, x) -> A^2
25.51/8.36	   A^2 -> H(f(c), f(c))
25.51/8.36	   A^2 -> H(f(d), f(d))
25.51/8.36	   A^2 -> H(U1(c, a), f(k))
25.51/8.36	   A^2 -> H(U1(c, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(d, e), f(b))
25.51/8.36	   A^2 -> H(U1(d, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(d, c), f(c))
25.51/8.36	   A^2 -> H(U1(d, c), f(d))
25.51/8.36	   A^2 -> H(U1(d, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(d, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(d, a), f(e))
25.51/8.36	   A^2 -> H(U1(d, a), f(k))
25.51/8.36	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(a, e), f(c))
25.51/8.36	   A^2 -> H(U1(a, e), f(d))
25.51/8.36	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(a, k), f(c))
25.51/8.36	   A^2 -> H(U1(a, k), f(d))
25.51/8.36	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.36	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.36	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.36	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.36	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.36	   A^2 -> H(U1(a, c), f(e))
25.51/8.36	   A^2 -> H(U1(a, c), f(k))
25.51/8.36	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(a, d), f(e))
25.51/8.36	   A^2 -> H(U1(a, d), f(k))
25.51/8.36	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.36	   A^2 -> H(c, f(b))
25.51/8.36	   A^2 -> H(U1(e, k), f(b))
25.51/8.36	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, c), f(c))
25.51/8.36	   A^2 -> H(U1(e, c), f(d))
25.51/8.36	   A^2 -> H(U1(k, e), f(b))
25.51/8.36	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, c), f(c))
25.51/8.36	   A^2 -> H(U1(k, c), f(d))
25.51/8.36	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(c, e), f(c))
25.51/8.36	   A^2 -> H(U1(c, e), f(d))
25.51/8.36	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(c, k), f(c))
25.51/8.36	   A^2 -> H(U1(c, k), f(d))
25.51/8.36	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, c), f(e))
25.51/8.36	   A^2 -> H(U1(c, c), f(k))
25.51/8.36	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.36	   A^2 -> H(e, f(b))
25.51/8.36	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, e), f(c))
25.51/8.36	   A^2 -> H(U1(e, e), f(d))
25.51/8.36	   A^2 -> H(f(e), U1(c, b))
25.51/8.36	   A^2 -> H(f(e), U1(d, b))
25.51/8.36	   A^2 -> H(f(e), U1(b, c))
25.51/8.36	   A^2 -> H(f(e), U1(b, d))
25.51/8.36	   A^2 -> H(f(e), U1(c, c))
25.51/8.36	   A^2 -> H(f(e), f(e))
25.51/8.36	   A^2 -> H(f(e), f(k))
25.51/8.36	   A^2 -> H(f(e), U1(d, d))
25.51/8.36	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, k), f(c))
25.51/8.36	   A^2 -> H(U1(k, k), f(d))
25.51/8.36	   A^2 -> H(f(k), U1(c, b))
25.51/8.36	   A^2 -> H(f(k), U1(d, b))
25.51/8.36	   A^2 -> H(f(k), U1(b, c))
25.51/8.36	   A^2 -> H(f(k), U1(b, d))
25.51/8.36	   A^2 -> H(f(k), U1(c, c))
25.51/8.36	   A^2 -> H(f(k), f(e))
25.51/8.36	   A^2 -> H(f(k), f(k))
25.51/8.36	   A^2 -> H(f(k), U1(d, d))
25.51/8.36	   A^2 -> H(f(c), U1(e, b))
25.51/8.36	   A^2 -> H(f(c), U1(k, b))
25.51/8.36	   A^2 -> H(f(c), U1(c, d))
25.51/8.36	   A^2 -> H(f(c), U1(d, c))
25.51/8.36	   A^2 -> H(f(c), U1(b, e))
25.51/8.36	   A^2 -> H(f(c), U1(b, k))
25.51/8.36	   A^2 -> H(f(c), U1(k, d))
25.51/8.36	   A^2 -> H(f(c), U1(d, k))
25.51/8.36	   A^2 -> H(f(c), U1(k, k))
25.51/8.36	   A^2 -> H(U1(k, k), f(b))
25.51/8.36	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, d), f(c))
25.51/8.36	   A^2 -> H(U1(k, d), f(d))
25.51/8.36	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(d, k), f(c))
25.51/8.36	   A^2 -> H(U1(d, k), f(d))
25.51/8.36	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(d, d), f(e))
25.51/8.36	   A^2 -> H(U1(d, d), f(k))
25.51/8.36	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.36	   A^2 -> H(f(d), U1(e, b))
25.51/8.36	   A^2 -> H(f(d), U1(k, b))
25.51/8.36	   A^2 -> H(f(d), U1(c, d))
25.51/8.36	   A^2 -> H(f(d), U1(d, c))
25.51/8.36	   A^2 -> H(f(d), U1(b, e))
25.51/8.36	   A^2 -> H(f(d), U1(b, k))
25.51/8.36	   A^2 -> H(f(d), U1(e, c))
25.51/8.36	   A^2 -> H(f(d), U1(k, c))
25.51/8.36	   A^2 -> H(f(d), U1(c, e))
25.51/8.36	   A^2 -> H(f(d), U1(c, k))
25.51/8.36	   A^2 -> H(f(d), U1(e, e))
25.51/8.36	   A^2 -> H(f(d), U1(k, k))
25.51/8.36	   A^2 -> H(f(a), b)
25.51/8.36	   A^2 -> H(f(a), U1(e, d))
25.51/8.36	   A^2 -> H(f(a), U1(d, e))
25.51/8.36	   A^2 -> H(f(c), U1(e, c))
25.51/8.36	   A^2 -> H(f(c), U1(k, c))
25.51/8.36	   A^2 -> H(f(c), U1(c, e))
25.51/8.36	   A^2 -> H(f(c), U1(c, k))
25.51/8.36	   A^2 -> H(f(a), c)
25.51/8.36	   A^2 -> H(f(a), U1(e, k))
25.51/8.36	   A^2 -> H(f(a), U1(k, e))
25.51/8.36	   A^2 -> H(f(c), U1(e, e))
25.51/8.36	   A^2 -> H(f(a), e)
25.51/8.36	   A^2 -> H(f(d), U1(k, d))
25.51/8.36	   A^2 -> H(f(d), U1(d, k))
25.51/8.36	   A^2 -> H(f(a), U1(k, k))
25.51/8.36	   A^2 -> H(d, f(b))
25.51/8.36	   A^2 -> H(a, U1(b, b))
25.51/8.36	   A^2 -> H(a, f(c))
25.51/8.36	   A^2 -> H(a, f(d))
25.51/8.36	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, d), f(c))
25.51/8.36	   A^2 -> H(U1(e, d), f(d))
25.51/8.36	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(e, a), f(e))
25.51/8.36	   A^2 -> H(U1(e, a), f(k))
25.51/8.36	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(k, a), f(e))
25.51/8.36	   A^2 -> H(U1(k, a), f(k))
25.51/8.36	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, d), f(e))
25.51/8.36	   A^2 -> H(U1(c, d), f(k))
25.51/8.36	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.36	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.36	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.36	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.36	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.36	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.36	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.36	
25.51/8.36	The TRS R consists of the following rules:
25.51/8.36	
25.51/8.36	   f(x) -> U1(x, x)
25.51/8.36	   U1(e, x) -> x
25.51/8.36	   a -> c
25.51/8.36	   a -> d
25.51/8.36	   b -> c
25.51/8.36	   b -> d
25.51/8.36	   d -> k
25.51/8.36	   c -> e
25.51/8.36	   c -> k
25.51/8.36	
25.51/8.36	Q is empty.
25.51/8.36	We have to consider all minimal (P,Q,R)-chains.
25.51/8.36	----------------------------------------
25.51/8.36	
25.51/8.36	(255) TransformationProof (EQUIVALENT)
25.51/8.36	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), f(k)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.36	
25.51/8.36	   (A^2 -> H(U1(e, a), f(k)),A^2 -> H(U1(e, a), f(k)))
25.51/8.36	   (A^2 -> H(U1(k, a), f(k)),A^2 -> H(U1(k, a), f(k)))
25.51/8.36	   (A^2 -> H(U1(c, c), f(k)),A^2 -> H(U1(c, c), f(k)))
25.51/8.36	   (A^2 -> H(U1(c, d), f(k)),A^2 -> H(U1(c, d), f(k)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(k, k)),A^2 -> H(U1(c, a), U1(k, k)))
25.51/8.36	
25.51/8.36	
25.51/8.36	----------------------------------------
25.51/8.36	
25.51/8.36	(256)
25.51/8.36	Obligation:
25.51/8.36	Q DP problem:
25.51/8.36	The TRS P consists of the following rules:
25.51/8.36	
25.51/8.36	   H(x, x) -> G(x, x, f(k))
25.51/8.36	   G(d, x, x) -> A^2
25.51/8.36	   A^2 -> H(f(c), f(c))
25.51/8.36	   A^2 -> H(f(d), f(d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(d, e), f(b))
25.51/8.36	   A^2 -> H(U1(d, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(d, c), f(c))
25.51/8.36	   A^2 -> H(U1(d, c), f(d))
25.51/8.36	   A^2 -> H(U1(d, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(d, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(d, a), f(e))
25.51/8.36	   A^2 -> H(U1(d, a), f(k))
25.51/8.36	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(a, e), f(c))
25.51/8.36	   A^2 -> H(U1(a, e), f(d))
25.51/8.36	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(a, k), f(c))
25.51/8.36	   A^2 -> H(U1(a, k), f(d))
25.51/8.36	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.36	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.36	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.36	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.36	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.36	   A^2 -> H(U1(a, c), f(e))
25.51/8.36	   A^2 -> H(U1(a, c), f(k))
25.51/8.36	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(a, d), f(e))
25.51/8.36	   A^2 -> H(U1(a, d), f(k))
25.51/8.36	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.36	   A^2 -> H(c, f(b))
25.51/8.36	   A^2 -> H(U1(e, k), f(b))
25.51/8.36	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, c), f(c))
25.51/8.36	   A^2 -> H(U1(e, c), f(d))
25.51/8.36	   A^2 -> H(U1(k, e), f(b))
25.51/8.36	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, c), f(c))
25.51/8.36	   A^2 -> H(U1(k, c), f(d))
25.51/8.36	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(c, e), f(c))
25.51/8.36	   A^2 -> H(U1(c, e), f(d))
25.51/8.36	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(c, k), f(c))
25.51/8.36	   A^2 -> H(U1(c, k), f(d))
25.51/8.36	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, c), f(e))
25.51/8.36	   A^2 -> H(U1(c, c), f(k))
25.51/8.36	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.36	   A^2 -> H(e, f(b))
25.51/8.36	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, e), f(c))
25.51/8.36	   A^2 -> H(U1(e, e), f(d))
25.51/8.36	   A^2 -> H(f(e), U1(c, b))
25.51/8.36	   A^2 -> H(f(e), U1(d, b))
25.51/8.36	   A^2 -> H(f(e), U1(b, c))
25.51/8.36	   A^2 -> H(f(e), U1(b, d))
25.51/8.36	   A^2 -> H(f(e), U1(c, c))
25.51/8.36	   A^2 -> H(f(e), f(e))
25.51/8.36	   A^2 -> H(f(e), f(k))
25.51/8.36	   A^2 -> H(f(e), U1(d, d))
25.51/8.36	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, k), f(c))
25.51/8.36	   A^2 -> H(U1(k, k), f(d))
25.51/8.36	   A^2 -> H(f(k), U1(c, b))
25.51/8.36	   A^2 -> H(f(k), U1(d, b))
25.51/8.36	   A^2 -> H(f(k), U1(b, c))
25.51/8.36	   A^2 -> H(f(k), U1(b, d))
25.51/8.36	   A^2 -> H(f(k), U1(c, c))
25.51/8.36	   A^2 -> H(f(k), f(e))
25.51/8.36	   A^2 -> H(f(k), f(k))
25.51/8.36	   A^2 -> H(f(k), U1(d, d))
25.51/8.36	   A^2 -> H(f(c), U1(e, b))
25.51/8.36	   A^2 -> H(f(c), U1(k, b))
25.51/8.36	   A^2 -> H(f(c), U1(c, d))
25.51/8.36	   A^2 -> H(f(c), U1(d, c))
25.51/8.36	   A^2 -> H(f(c), U1(b, e))
25.51/8.36	   A^2 -> H(f(c), U1(b, k))
25.51/8.36	   A^2 -> H(f(c), U1(k, d))
25.51/8.36	   A^2 -> H(f(c), U1(d, k))
25.51/8.36	   A^2 -> H(f(c), U1(k, k))
25.51/8.36	   A^2 -> H(U1(k, k), f(b))
25.51/8.36	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, d), f(c))
25.51/8.36	   A^2 -> H(U1(k, d), f(d))
25.51/8.36	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(d, k), f(c))
25.51/8.36	   A^2 -> H(U1(d, k), f(d))
25.51/8.36	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(d, d), f(e))
25.51/8.36	   A^2 -> H(U1(d, d), f(k))
25.51/8.36	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.36	   A^2 -> H(f(d), U1(e, b))
25.51/8.36	   A^2 -> H(f(d), U1(k, b))
25.51/8.36	   A^2 -> H(f(d), U1(c, d))
25.51/8.36	   A^2 -> H(f(d), U1(d, c))
25.51/8.36	   A^2 -> H(f(d), U1(b, e))
25.51/8.36	   A^2 -> H(f(d), U1(b, k))
25.51/8.36	   A^2 -> H(f(d), U1(e, c))
25.51/8.36	   A^2 -> H(f(d), U1(k, c))
25.51/8.36	   A^2 -> H(f(d), U1(c, e))
25.51/8.36	   A^2 -> H(f(d), U1(c, k))
25.51/8.36	   A^2 -> H(f(d), U1(e, e))
25.51/8.36	   A^2 -> H(f(d), U1(k, k))
25.51/8.36	   A^2 -> H(f(a), b)
25.51/8.36	   A^2 -> H(f(a), U1(e, d))
25.51/8.36	   A^2 -> H(f(a), U1(d, e))
25.51/8.36	   A^2 -> H(f(c), U1(e, c))
25.51/8.36	   A^2 -> H(f(c), U1(k, c))
25.51/8.36	   A^2 -> H(f(c), U1(c, e))
25.51/8.36	   A^2 -> H(f(c), U1(c, k))
25.51/8.36	   A^2 -> H(f(a), c)
25.51/8.36	   A^2 -> H(f(a), U1(e, k))
25.51/8.36	   A^2 -> H(f(a), U1(k, e))
25.51/8.36	   A^2 -> H(f(c), U1(e, e))
25.51/8.36	   A^2 -> H(f(a), e)
25.51/8.36	   A^2 -> H(f(d), U1(k, d))
25.51/8.36	   A^2 -> H(f(d), U1(d, k))
25.51/8.36	   A^2 -> H(f(a), U1(k, k))
25.51/8.36	   A^2 -> H(d, f(b))
25.51/8.36	   A^2 -> H(a, U1(b, b))
25.51/8.36	   A^2 -> H(a, f(c))
25.51/8.36	   A^2 -> H(a, f(d))
25.51/8.36	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, d), f(c))
25.51/8.36	   A^2 -> H(U1(e, d), f(d))
25.51/8.36	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(e, a), f(e))
25.51/8.36	   A^2 -> H(U1(e, a), f(k))
25.51/8.36	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(k, a), f(e))
25.51/8.36	   A^2 -> H(U1(k, a), f(k))
25.51/8.36	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, d), f(e))
25.51/8.36	   A^2 -> H(U1(c, d), f(k))
25.51/8.36	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.36	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.36	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.36	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.36	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.36	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.36	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.36	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.36	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.36	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.36	
25.51/8.36	The TRS R consists of the following rules:
25.51/8.36	
25.51/8.36	   f(x) -> U1(x, x)
25.51/8.36	   U1(e, x) -> x
25.51/8.36	   a -> c
25.51/8.36	   a -> d
25.51/8.36	   b -> c
25.51/8.36	   b -> d
25.51/8.36	   d -> k
25.51/8.36	   c -> e
25.51/8.36	   c -> k
25.51/8.36	
25.51/8.36	Q is empty.
25.51/8.36	We have to consider all minimal (P,Q,R)-chains.
25.51/8.36	----------------------------------------
25.51/8.36	
25.51/8.36	(257) TransformationProof (EQUIVALENT)
25.51/8.36	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.36	
25.51/8.36	   (A^2 -> H(U1(e, a), U1(d, d)),A^2 -> H(U1(e, a), U1(d, d)))
25.51/8.36	   (A^2 -> H(U1(k, a), U1(d, d)),A^2 -> H(U1(k, a), U1(d, d)))
25.51/8.36	   (A^2 -> H(U1(c, c), U1(d, d)),A^2 -> H(U1(c, c), U1(d, d)))
25.51/8.36	   (A^2 -> H(U1(c, d), U1(d, d)),A^2 -> H(U1(c, d), U1(d, d)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(k, d)),A^2 -> H(U1(c, a), U1(k, d)))
25.51/8.36	   (A^2 -> H(U1(c, a), U1(d, k)),A^2 -> H(U1(c, a), U1(d, k)))
25.51/8.36	
25.51/8.36	
25.51/8.36	----------------------------------------
25.51/8.36	
25.51/8.36	(258)
25.51/8.36	Obligation:
25.51/8.36	Q DP problem:
25.51/8.36	The TRS P consists of the following rules:
25.51/8.36	
25.51/8.36	   H(x, x) -> G(x, x, f(k))
25.51/8.36	   G(d, x, x) -> A^2
25.51/8.36	   A^2 -> H(f(c), f(c))
25.51/8.36	   A^2 -> H(f(d), f(d))
25.51/8.36	   A^2 -> H(U1(d, e), f(b))
25.51/8.36	   A^2 -> H(U1(d, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(d, c), f(c))
25.51/8.36	   A^2 -> H(U1(d, c), f(d))
25.51/8.36	   A^2 -> H(U1(d, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(d, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(d, a), f(e))
25.51/8.36	   A^2 -> H(U1(d, a), f(k))
25.51/8.36	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(a, e), f(c))
25.51/8.36	   A^2 -> H(U1(a, e), f(d))
25.51/8.36	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(a, k), f(c))
25.51/8.36	   A^2 -> H(U1(a, k), f(d))
25.51/8.36	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.36	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.36	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.36	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.36	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.36	   A^2 -> H(U1(a, c), f(e))
25.51/8.36	   A^2 -> H(U1(a, c), f(k))
25.51/8.36	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(a, d), f(e))
25.51/8.36	   A^2 -> H(U1(a, d), f(k))
25.51/8.36	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.36	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.36	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.36	   A^2 -> H(c, f(b))
25.51/8.36	   A^2 -> H(U1(e, k), f(b))
25.51/8.36	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, c), f(c))
25.51/8.36	   A^2 -> H(U1(e, c), f(d))
25.51/8.36	   A^2 -> H(U1(k, e), f(b))
25.51/8.36	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, c), f(c))
25.51/8.36	   A^2 -> H(U1(k, c), f(d))
25.51/8.36	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(c, e), f(c))
25.51/8.36	   A^2 -> H(U1(c, e), f(d))
25.51/8.36	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(c, k), f(c))
25.51/8.36	   A^2 -> H(U1(c, k), f(d))
25.51/8.36	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.36	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.36	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.36	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.36	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.36	   A^2 -> H(U1(c, c), f(e))
25.51/8.36	   A^2 -> H(U1(c, c), f(k))
25.51/8.36	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.36	   A^2 -> H(e, f(b))
25.51/8.36	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, e), f(c))
25.51/8.36	   A^2 -> H(U1(e, e), f(d))
25.51/8.36	   A^2 -> H(f(e), U1(c, b))
25.51/8.36	   A^2 -> H(f(e), U1(d, b))
25.51/8.36	   A^2 -> H(f(e), U1(b, c))
25.51/8.36	   A^2 -> H(f(e), U1(b, d))
25.51/8.36	   A^2 -> H(f(e), U1(c, c))
25.51/8.36	   A^2 -> H(f(e), f(e))
25.51/8.36	   A^2 -> H(f(e), f(k))
25.51/8.36	   A^2 -> H(f(e), U1(d, d))
25.51/8.36	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, k), f(c))
25.51/8.36	   A^2 -> H(U1(k, k), f(d))
25.51/8.36	   A^2 -> H(f(k), U1(c, b))
25.51/8.36	   A^2 -> H(f(k), U1(d, b))
25.51/8.36	   A^2 -> H(f(k), U1(b, c))
25.51/8.36	   A^2 -> H(f(k), U1(b, d))
25.51/8.36	   A^2 -> H(f(k), U1(c, c))
25.51/8.36	   A^2 -> H(f(k), f(e))
25.51/8.36	   A^2 -> H(f(k), f(k))
25.51/8.36	   A^2 -> H(f(k), U1(d, d))
25.51/8.36	   A^2 -> H(f(c), U1(e, b))
25.51/8.36	   A^2 -> H(f(c), U1(k, b))
25.51/8.36	   A^2 -> H(f(c), U1(c, d))
25.51/8.36	   A^2 -> H(f(c), U1(d, c))
25.51/8.36	   A^2 -> H(f(c), U1(b, e))
25.51/8.36	   A^2 -> H(f(c), U1(b, k))
25.51/8.36	   A^2 -> H(f(c), U1(k, d))
25.51/8.36	   A^2 -> H(f(c), U1(d, k))
25.51/8.36	   A^2 -> H(f(c), U1(k, k))
25.51/8.36	   A^2 -> H(U1(k, k), f(b))
25.51/8.36	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.36	   A^2 -> H(U1(k, d), f(c))
25.51/8.36	   A^2 -> H(U1(k, d), f(d))
25.51/8.36	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.36	   A^2 -> H(U1(d, k), f(c))
25.51/8.36	   A^2 -> H(U1(d, k), f(d))
25.51/8.36	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.36	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.36	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.36	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.36	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.36	   A^2 -> H(U1(d, d), f(e))
25.51/8.36	   A^2 -> H(U1(d, d), f(k))
25.51/8.36	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.36	   A^2 -> H(f(d), U1(e, b))
25.51/8.36	   A^2 -> H(f(d), U1(k, b))
25.51/8.36	   A^2 -> H(f(d), U1(c, d))
25.51/8.36	   A^2 -> H(f(d), U1(d, c))
25.51/8.36	   A^2 -> H(f(d), U1(b, e))
25.51/8.36	   A^2 -> H(f(d), U1(b, k))
25.51/8.36	   A^2 -> H(f(d), U1(e, c))
25.51/8.36	   A^2 -> H(f(d), U1(k, c))
25.51/8.36	   A^2 -> H(f(d), U1(c, e))
25.51/8.36	   A^2 -> H(f(d), U1(c, k))
25.51/8.36	   A^2 -> H(f(d), U1(e, e))
25.51/8.36	   A^2 -> H(f(d), U1(k, k))
25.51/8.36	   A^2 -> H(f(a), b)
25.51/8.36	   A^2 -> H(f(a), U1(e, d))
25.51/8.36	   A^2 -> H(f(a), U1(d, e))
25.51/8.36	   A^2 -> H(f(c), U1(e, c))
25.51/8.36	   A^2 -> H(f(c), U1(k, c))
25.51/8.36	   A^2 -> H(f(c), U1(c, e))
25.51/8.36	   A^2 -> H(f(c), U1(c, k))
25.51/8.36	   A^2 -> H(f(a), c)
25.51/8.36	   A^2 -> H(f(a), U1(e, k))
25.51/8.36	   A^2 -> H(f(a), U1(k, e))
25.51/8.36	   A^2 -> H(f(c), U1(e, e))
25.51/8.36	   A^2 -> H(f(a), e)
25.51/8.36	   A^2 -> H(f(d), U1(k, d))
25.51/8.36	   A^2 -> H(f(d), U1(d, k))
25.51/8.36	   A^2 -> H(f(a), U1(k, k))
25.51/8.36	   A^2 -> H(d, f(b))
25.51/8.36	   A^2 -> H(a, U1(b, b))
25.51/8.36	   A^2 -> H(a, f(c))
25.51/8.36	   A^2 -> H(a, f(d))
25.51/8.36	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.36	   A^2 -> H(U1(e, d), f(c))
25.51/8.36	   A^2 -> H(U1(e, d), f(d))
25.51/8.36	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.36	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.36	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.36	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.36	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.36	   A^2 -> H(U1(e, a), f(e))
25.51/8.37	   A^2 -> H(U1(e, a), f(k))
25.51/8.37	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.37	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.37	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.37	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.37	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.37	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.37	   A^2 -> H(U1(k, a), f(e))
25.51/8.37	   A^2 -> H(U1(k, a), f(k))
25.51/8.37	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.37	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.37	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.37	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.37	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.37	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.37	   A^2 -> H(U1(c, d), f(e))
25.51/8.37	   A^2 -> H(U1(c, d), f(k))
25.51/8.37	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.37	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.37	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.37	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.37	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.37	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.37	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.37	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.37	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.37	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.37	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.37	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.37	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.37	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.37	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.37	
25.51/8.37	The TRS R consists of the following rules:
25.51/8.37	
25.51/8.37	   f(x) -> U1(x, x)
25.51/8.37	   U1(e, x) -> x
25.51/8.37	   a -> c
25.51/8.37	   a -> d
25.51/8.37	   b -> c
25.51/8.37	   b -> d
25.51/8.37	   d -> k
25.51/8.37	   c -> e
25.51/8.37	   c -> k
25.51/8.37	
25.51/8.37	Q is empty.
25.51/8.37	We have to consider all minimal (P,Q,R)-chains.
25.51/8.37	----------------------------------------
25.51/8.37	
25.51/8.37	(259) TransformationProof (EQUIVALENT)
25.51/8.37	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), f(b)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.37	
25.51/8.37	   (A^2 -> H(U1(k, e), f(b)),A^2 -> H(U1(k, e), f(b)))
25.51/8.37	   (A^2 -> H(U1(d, e), U1(b, b)),A^2 -> H(U1(d, e), U1(b, b)))
25.51/8.37	   (A^2 -> H(U1(d, e), f(c)),A^2 -> H(U1(d, e), f(c)))
25.51/8.37	   (A^2 -> H(U1(d, e), f(d)),A^2 -> H(U1(d, e), f(d)))
25.51/8.37	
25.51/8.37	
25.51/8.37	----------------------------------------
25.51/8.37	
25.51/8.37	(260)
25.51/8.37	Obligation:
25.51/8.37	Q DP problem:
25.51/8.37	The TRS P consists of the following rules:
25.51/8.37	
25.51/8.37	   H(x, x) -> G(x, x, f(k))
25.51/8.37	   G(d, x, x) -> A^2
25.51/8.37	   A^2 -> H(f(c), f(c))
25.51/8.37	   A^2 -> H(f(d), f(d))
25.51/8.37	   A^2 -> H(U1(d, c), U1(b, b))
25.51/8.37	   A^2 -> H(U1(d, c), f(c))
25.51/8.37	   A^2 -> H(U1(d, c), f(d))
25.51/8.37	   A^2 -> H(U1(d, a), U1(c, b))
25.51/8.37	   A^2 -> H(U1(d, a), U1(d, b))
25.51/8.37	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.37	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.37	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.37	   A^2 -> H(U1(d, a), f(e))
25.51/8.37	   A^2 -> H(U1(d, a), f(k))
25.51/8.37	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.37	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.37	   A^2 -> H(U1(a, e), f(c))
25.51/8.37	   A^2 -> H(U1(a, e), f(d))
25.51/8.37	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.37	   A^2 -> H(U1(a, k), f(c))
25.51/8.37	   A^2 -> H(U1(a, k), f(d))
25.51/8.37	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.37	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.37	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.37	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.37	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.37	   A^2 -> H(U1(a, c), f(e))
25.51/8.37	   A^2 -> H(U1(a, c), f(k))
25.51/8.37	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.37	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.37	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.37	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.37	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.37	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.37	   A^2 -> H(U1(a, d), f(e))
25.51/8.37	   A^2 -> H(U1(a, d), f(k))
25.51/8.37	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.37	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.37	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.37	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.37	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.37	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.37	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.37	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.37	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.37	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.37	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.37	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.37	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.37	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.37	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.37	   A^2 -> H(c, f(b))
25.51/8.37	   A^2 -> H(U1(e, k), f(b))
25.51/8.37	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.37	   A^2 -> H(U1(e, c), f(c))
25.51/8.37	   A^2 -> H(U1(e, c), f(d))
25.51/8.37	   A^2 -> H(U1(k, e), f(b))
25.51/8.37	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.37	   A^2 -> H(U1(k, c), f(c))
25.51/8.37	   A^2 -> H(U1(k, c), f(d))
25.51/8.37	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.37	   A^2 -> H(U1(c, e), f(c))
25.51/8.37	   A^2 -> H(U1(c, e), f(d))
25.51/8.37	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.37	   A^2 -> H(U1(c, k), f(c))
25.51/8.37	   A^2 -> H(U1(c, k), f(d))
25.51/8.37	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.37	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.37	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.37	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.37	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.37	   A^2 -> H(U1(c, c), f(e))
25.51/8.37	   A^2 -> H(U1(c, c), f(k))
25.51/8.37	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.37	   A^2 -> H(e, f(b))
25.51/8.37	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.37	   A^2 -> H(U1(e, e), f(c))
25.51/8.37	   A^2 -> H(U1(e, e), f(d))
25.51/8.37	   A^2 -> H(f(e), U1(c, b))
25.51/8.37	   A^2 -> H(f(e), U1(d, b))
25.51/8.37	   A^2 -> H(f(e), U1(b, c))
25.51/8.37	   A^2 -> H(f(e), U1(b, d))
25.51/8.37	   A^2 -> H(f(e), U1(c, c))
25.51/8.37	   A^2 -> H(f(e), f(e))
25.51/8.37	   A^2 -> H(f(e), f(k))
25.51/8.37	   A^2 -> H(f(e), U1(d, d))
25.51/8.37	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.37	   A^2 -> H(U1(k, k), f(c))
25.51/8.37	   A^2 -> H(U1(k, k), f(d))
25.51/8.37	   A^2 -> H(f(k), U1(c, b))
25.51/8.37	   A^2 -> H(f(k), U1(d, b))
25.51/8.37	   A^2 -> H(f(k), U1(b, c))
25.51/8.37	   A^2 -> H(f(k), U1(b, d))
25.51/8.37	   A^2 -> H(f(k), U1(c, c))
25.51/8.37	   A^2 -> H(f(k), f(e))
25.51/8.37	   A^2 -> H(f(k), f(k))
25.51/8.37	   A^2 -> H(f(k), U1(d, d))
25.51/8.37	   A^2 -> H(f(c), U1(e, b))
25.51/8.37	   A^2 -> H(f(c), U1(k, b))
25.51/8.37	   A^2 -> H(f(c), U1(c, d))
25.51/8.37	   A^2 -> H(f(c), U1(d, c))
25.51/8.37	   A^2 -> H(f(c), U1(b, e))
25.51/8.37	   A^2 -> H(f(c), U1(b, k))
25.51/8.37	   A^2 -> H(f(c), U1(k, d))
25.51/8.37	   A^2 -> H(f(c), U1(d, k))
25.51/8.37	   A^2 -> H(f(c), U1(k, k))
25.51/8.37	   A^2 -> H(U1(k, k), f(b))
25.51/8.37	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.37	   A^2 -> H(U1(k, d), f(c))
25.51/8.37	   A^2 -> H(U1(k, d), f(d))
25.51/8.37	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.37	   A^2 -> H(U1(d, k), f(c))
25.51/8.37	   A^2 -> H(U1(d, k), f(d))
25.51/8.37	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.37	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.37	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.37	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.37	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.37	   A^2 -> H(U1(d, d), f(e))
25.51/8.37	   A^2 -> H(U1(d, d), f(k))
25.51/8.37	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.37	   A^2 -> H(f(d), U1(e, b))
25.51/8.37	   A^2 -> H(f(d), U1(k, b))
25.51/8.37	   A^2 -> H(f(d), U1(c, d))
25.51/8.37	   A^2 -> H(f(d), U1(d, c))
25.51/8.37	   A^2 -> H(f(d), U1(b, e))
25.51/8.37	   A^2 -> H(f(d), U1(b, k))
25.51/8.37	   A^2 -> H(f(d), U1(e, c))
25.51/8.37	   A^2 -> H(f(d), U1(k, c))
25.51/8.37	   A^2 -> H(f(d), U1(c, e))
25.51/8.37	   A^2 -> H(f(d), U1(c, k))
25.51/8.37	   A^2 -> H(f(d), U1(e, e))
25.51/8.37	   A^2 -> H(f(d), U1(k, k))
25.51/8.37	   A^2 -> H(f(a), b)
25.51/8.37	   A^2 -> H(f(a), U1(e, d))
25.51/8.37	   A^2 -> H(f(a), U1(d, e))
25.51/8.37	   A^2 -> H(f(c), U1(e, c))
25.51/8.37	   A^2 -> H(f(c), U1(k, c))
25.51/8.37	   A^2 -> H(f(c), U1(c, e))
25.51/8.37	   A^2 -> H(f(c), U1(c, k))
25.51/8.37	   A^2 -> H(f(a), c)
25.51/8.37	   A^2 -> H(f(a), U1(e, k))
25.51/8.37	   A^2 -> H(f(a), U1(k, e))
25.51/8.37	   A^2 -> H(f(c), U1(e, e))
25.51/8.37	   A^2 -> H(f(a), e)
25.51/8.37	   A^2 -> H(f(d), U1(k, d))
25.51/8.37	   A^2 -> H(f(d), U1(d, k))
25.51/8.37	   A^2 -> H(f(a), U1(k, k))
25.51/8.37	   A^2 -> H(d, f(b))
25.51/8.37	   A^2 -> H(a, U1(b, b))
25.51/8.37	   A^2 -> H(a, f(c))
25.51/8.37	   A^2 -> H(a, f(d))
25.51/8.37	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.37	   A^2 -> H(U1(e, d), f(c))
25.51/8.37	   A^2 -> H(U1(e, d), f(d))
25.51/8.37	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.37	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.37	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.37	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.37	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.37	   A^2 -> H(U1(e, a), f(e))
25.51/8.37	   A^2 -> H(U1(e, a), f(k))
25.51/8.37	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.37	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.37	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.37	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.37	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.37	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.37	   A^2 -> H(U1(k, a), f(e))
25.51/8.37	   A^2 -> H(U1(k, a), f(k))
25.51/8.37	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.37	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.37	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.37	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.37	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.37	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.37	   A^2 -> H(U1(c, d), f(e))
25.51/8.37	   A^2 -> H(U1(c, d), f(k))
25.51/8.37	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.37	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.37	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.37	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.37	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.37	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.37	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.37	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.37	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.37	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.37	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.37	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.37	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.37	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.37	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.37	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.37	   A^2 -> H(U1(d, e), f(c))
25.51/8.37	   A^2 -> H(U1(d, e), f(d))
25.51/8.37	
25.51/8.37	The TRS R consists of the following rules:
25.51/8.37	
25.51/8.37	   f(x) -> U1(x, x)
25.51/8.37	   U1(e, x) -> x
25.51/8.37	   a -> c
25.51/8.37	   a -> d
25.51/8.37	   b -> c
25.51/8.37	   b -> d
25.51/8.37	   d -> k
25.51/8.37	   c -> e
25.51/8.37	   c -> k
25.51/8.37	
25.51/8.37	Q is empty.
25.51/8.37	We have to consider all minimal (P,Q,R)-chains.
25.51/8.37	----------------------------------------
25.51/8.37	
25.51/8.37	(261) TransformationProof (EQUIVALENT)
25.51/8.37	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.37	
25.51/8.37	   (A^2 -> H(U1(k, c), U1(b, b)),A^2 -> H(U1(k, c), U1(b, b)))
25.51/8.37	   (A^2 -> H(U1(d, e), U1(b, b)),A^2 -> H(U1(d, e), U1(b, b)))
25.51/8.37	   (A^2 -> H(U1(d, k), U1(b, b)),A^2 -> H(U1(d, k), U1(b, b)))
25.51/8.37	   (A^2 -> H(U1(d, c), U1(c, b)),A^2 -> H(U1(d, c), U1(c, b)))
25.51/8.37	   (A^2 -> H(U1(d, c), U1(d, b)),A^2 -> H(U1(d, c), U1(d, b)))
25.51/8.37	   (A^2 -> H(U1(d, c), U1(b, c)),A^2 -> H(U1(d, c), U1(b, c)))
25.51/8.37	   (A^2 -> H(U1(d, c), U1(b, d)),A^2 -> H(U1(d, c), U1(b, d)))
25.51/8.37	
25.51/8.37	
25.51/8.37	----------------------------------------
25.51/8.37	
25.51/8.37	(262)
25.51/8.37	Obligation:
25.51/8.37	Q DP problem:
25.51/8.37	The TRS P consists of the following rules:
25.51/8.37	
25.51/8.37	   H(x, x) -> G(x, x, f(k))
25.51/8.37	   G(d, x, x) -> A^2
25.51/8.37	   A^2 -> H(f(c), f(c))
25.51/8.37	   A^2 -> H(f(d), f(d))
25.51/8.37	   A^2 -> H(U1(d, c), f(c))
25.51/8.37	   A^2 -> H(U1(d, c), f(d))
25.51/8.37	   A^2 -> H(U1(d, a), U1(c, b))
25.51/8.37	   A^2 -> H(U1(d, a), U1(d, b))
25.51/8.37	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.37	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.37	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.37	   A^2 -> H(U1(d, a), f(e))
25.51/8.37	   A^2 -> H(U1(d, a), f(k))
25.51/8.37	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.37	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.37	   A^2 -> H(U1(a, e), f(c))
25.51/8.37	   A^2 -> H(U1(a, e), f(d))
25.51/8.37	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.37	   A^2 -> H(U1(a, k), f(c))
25.51/8.37	   A^2 -> H(U1(a, k), f(d))
25.51/8.37	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.37	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.37	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.37	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.37	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.37	   A^2 -> H(U1(a, c), f(e))
25.51/8.37	   A^2 -> H(U1(a, c), f(k))
25.51/8.37	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.37	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.37	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.37	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.37	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.37	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.37	   A^2 -> H(U1(a, d), f(e))
25.51/8.37	   A^2 -> H(U1(a, d), f(k))
25.51/8.37	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.37	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.37	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.37	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.37	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.37	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.37	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.37	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.37	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.37	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.37	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.37	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.37	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.37	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.37	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.37	   A^2 -> H(c, f(b))
25.51/8.37	   A^2 -> H(U1(e, k), f(b))
25.51/8.37	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.37	   A^2 -> H(U1(e, c), f(c))
25.51/8.37	   A^2 -> H(U1(e, c), f(d))
25.51/8.37	   A^2 -> H(U1(k, e), f(b))
25.51/8.37	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.37	   A^2 -> H(U1(k, c), f(c))
25.51/8.37	   A^2 -> H(U1(k, c), f(d))
25.51/8.37	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.37	   A^2 -> H(U1(c, e), f(c))
25.51/8.37	   A^2 -> H(U1(c, e), f(d))
25.51/8.37	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.37	   A^2 -> H(U1(c, k), f(c))
25.51/8.37	   A^2 -> H(U1(c, k), f(d))
25.51/8.37	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.37	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.37	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.37	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.37	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.37	   A^2 -> H(U1(c, c), f(e))
25.51/8.37	   A^2 -> H(U1(c, c), f(k))
25.51/8.37	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.37	   A^2 -> H(e, f(b))
25.51/8.37	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.37	   A^2 -> H(U1(e, e), f(c))
25.51/8.37	   A^2 -> H(U1(e, e), f(d))
25.51/8.37	   A^2 -> H(f(e), U1(c, b))
25.51/8.37	   A^2 -> H(f(e), U1(d, b))
25.51/8.37	   A^2 -> H(f(e), U1(b, c))
25.51/8.37	   A^2 -> H(f(e), U1(b, d))
25.51/8.37	   A^2 -> H(f(e), U1(c, c))
25.51/8.37	   A^2 -> H(f(e), f(e))
25.51/8.37	   A^2 -> H(f(e), f(k))
25.51/8.37	   A^2 -> H(f(e), U1(d, d))
25.51/8.37	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.37	   A^2 -> H(U1(k, k), f(c))
25.51/8.37	   A^2 -> H(U1(k, k), f(d))
25.51/8.37	   A^2 -> H(f(k), U1(c, b))
25.51/8.37	   A^2 -> H(f(k), U1(d, b))
25.51/8.37	   A^2 -> H(f(k), U1(b, c))
25.51/8.37	   A^2 -> H(f(k), U1(b, d))
25.51/8.37	   A^2 -> H(f(k), U1(c, c))
25.51/8.37	   A^2 -> H(f(k), f(e))
25.51/8.37	   A^2 -> H(f(k), f(k))
25.51/8.37	   A^2 -> H(f(k), U1(d, d))
25.51/8.37	   A^2 -> H(f(c), U1(e, b))
25.51/8.37	   A^2 -> H(f(c), U1(k, b))
25.51/8.37	   A^2 -> H(f(c), U1(c, d))
25.51/8.37	   A^2 -> H(f(c), U1(d, c))
25.51/8.37	   A^2 -> H(f(c), U1(b, e))
25.51/8.37	   A^2 -> H(f(c), U1(b, k))
25.51/8.37	   A^2 -> H(f(c), U1(k, d))
25.51/8.37	   A^2 -> H(f(c), U1(d, k))
25.51/8.37	   A^2 -> H(f(c), U1(k, k))
25.51/8.37	   A^2 -> H(U1(k, k), f(b))
25.51/8.37	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.37	   A^2 -> H(U1(k, d), f(c))
25.51/8.37	   A^2 -> H(U1(k, d), f(d))
25.51/8.37	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.37	   A^2 -> H(U1(d, k), f(c))
25.51/8.37	   A^2 -> H(U1(d, k), f(d))
25.51/8.37	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.37	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.37	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.37	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.37	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.37	   A^2 -> H(U1(d, d), f(e))
25.51/8.37	   A^2 -> H(U1(d, d), f(k))
25.51/8.37	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.37	   A^2 -> H(f(d), U1(e, b))
25.51/8.37	   A^2 -> H(f(d), U1(k, b))
25.51/8.37	   A^2 -> H(f(d), U1(c, d))
25.51/8.37	   A^2 -> H(f(d), U1(d, c))
25.51/8.37	   A^2 -> H(f(d), U1(b, e))
25.51/8.37	   A^2 -> H(f(d), U1(b, k))
25.51/8.37	   A^2 -> H(f(d), U1(e, c))
25.51/8.37	   A^2 -> H(f(d), U1(k, c))
25.51/8.37	   A^2 -> H(f(d), U1(c, e))
25.51/8.37	   A^2 -> H(f(d), U1(c, k))
25.51/8.37	   A^2 -> H(f(d), U1(e, e))
25.51/8.37	   A^2 -> H(f(d), U1(k, k))
25.51/8.37	   A^2 -> H(f(a), b)
25.51/8.37	   A^2 -> H(f(a), U1(e, d))
25.51/8.37	   A^2 -> H(f(a), U1(d, e))
25.51/8.37	   A^2 -> H(f(c), U1(e, c))
25.51/8.37	   A^2 -> H(f(c), U1(k, c))
25.51/8.37	   A^2 -> H(f(c), U1(c, e))
25.51/8.37	   A^2 -> H(f(c), U1(c, k))
25.51/8.37	   A^2 -> H(f(a), c)
25.51/8.37	   A^2 -> H(f(a), U1(e, k))
25.51/8.37	   A^2 -> H(f(a), U1(k, e))
25.51/8.37	   A^2 -> H(f(c), U1(e, e))
25.51/8.37	   A^2 -> H(f(a), e)
25.51/8.37	   A^2 -> H(f(d), U1(k, d))
25.51/8.37	   A^2 -> H(f(d), U1(d, k))
25.51/8.37	   A^2 -> H(f(a), U1(k, k))
25.51/8.37	   A^2 -> H(d, f(b))
25.51/8.37	   A^2 -> H(a, U1(b, b))
25.51/8.37	   A^2 -> H(a, f(c))
25.51/8.37	   A^2 -> H(a, f(d))
25.51/8.37	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.37	   A^2 -> H(U1(e, d), f(c))
25.51/8.37	   A^2 -> H(U1(e, d), f(d))
25.51/8.37	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.37	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.37	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.37	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.37	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.37	   A^2 -> H(U1(e, a), f(e))
25.51/8.37	   A^2 -> H(U1(e, a), f(k))
25.51/8.37	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.37	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.37	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.37	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.37	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.37	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.37	   A^2 -> H(U1(k, a), f(e))
25.51/8.37	   A^2 -> H(U1(k, a), f(k))
25.51/8.37	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.37	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.37	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.37	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.37	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.37	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.37	   A^2 -> H(U1(c, d), f(e))
25.51/8.37	   A^2 -> H(U1(c, d), f(k))
25.51/8.37	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.37	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.37	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.37	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.37	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.37	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.37	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.37	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.37	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.37	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.37	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.37	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.37	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.37	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.37	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.37	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.37	   A^2 -> H(U1(d, e), f(c))
25.51/8.37	   A^2 -> H(U1(d, e), f(d))
25.51/8.37	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.37	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.37	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.37	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.37	
25.51/8.37	The TRS R consists of the following rules:
25.51/8.37	
25.51/8.37	   f(x) -> U1(x, x)
25.51/8.37	   U1(e, x) -> x
25.51/8.37	   a -> c
25.51/8.37	   a -> d
25.51/8.37	   b -> c
25.51/8.37	   b -> d
25.51/8.37	   d -> k
25.51/8.37	   c -> e
25.51/8.37	   c -> k
25.51/8.37	
25.51/8.37	Q is empty.
25.51/8.37	We have to consider all minimal (P,Q,R)-chains.
25.51/8.37	----------------------------------------
25.51/8.37	
25.51/8.37	(263) TransformationProof (EQUIVALENT)
25.51/8.37	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), f(c)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.37	
25.51/8.37	   (A^2 -> H(U1(k, c), f(c)),A^2 -> H(U1(k, c), f(c)))
25.51/8.37	   (A^2 -> H(U1(d, e), f(c)),A^2 -> H(U1(d, e), f(c)))
25.51/8.37	   (A^2 -> H(U1(d, k), f(c)),A^2 -> H(U1(d, k), f(c)))
25.51/8.37	   (A^2 -> H(U1(d, c), U1(c, c)),A^2 -> H(U1(d, c), U1(c, c)))
25.51/8.37	   (A^2 -> H(U1(d, c), f(e)),A^2 -> H(U1(d, c), f(e)))
25.51/8.37	   (A^2 -> H(U1(d, c), f(k)),A^2 -> H(U1(d, c), f(k)))
25.51/8.37	
25.51/8.37	
25.51/8.37	----------------------------------------
25.51/8.37	
25.51/8.37	(264)
25.51/8.37	Obligation:
25.51/8.37	Q DP problem:
25.51/8.37	The TRS P consists of the following rules:
25.51/8.37	
25.51/8.37	   H(x, x) -> G(x, x, f(k))
25.51/8.37	   G(d, x, x) -> A^2
25.51/8.37	   A^2 -> H(f(c), f(c))
25.51/8.37	   A^2 -> H(f(d), f(d))
25.51/8.37	   A^2 -> H(U1(d, c), f(d))
25.51/8.37	   A^2 -> H(U1(d, a), U1(c, b))
25.51/8.37	   A^2 -> H(U1(d, a), U1(d, b))
25.51/8.37	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.37	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.37	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.37	   A^2 -> H(U1(d, a), f(e))
25.51/8.37	   A^2 -> H(U1(d, a), f(k))
25.51/8.37	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.37	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.37	   A^2 -> H(U1(a, e), f(c))
25.51/8.37	   A^2 -> H(U1(a, e), f(d))
25.51/8.37	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.37	   A^2 -> H(U1(a, k), f(c))
25.51/8.37	   A^2 -> H(U1(a, k), f(d))
25.51/8.37	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.37	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.37	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.37	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.37	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.37	   A^2 -> H(U1(a, c), f(e))
25.51/8.37	   A^2 -> H(U1(a, c), f(k))
25.51/8.37	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.37	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.37	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.37	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.37	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.37	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.37	   A^2 -> H(U1(a, d), f(e))
25.51/8.37	   A^2 -> H(U1(a, d), f(k))
25.51/8.37	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.37	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.37	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.37	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.37	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.37	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.37	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.37	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.37	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.37	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.37	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.37	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.37	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.37	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.37	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.37	   A^2 -> H(c, f(b))
25.51/8.37	   A^2 -> H(U1(e, k), f(b))
25.51/8.37	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.37	   A^2 -> H(U1(e, c), f(c))
25.51/8.37	   A^2 -> H(U1(e, c), f(d))
25.51/8.37	   A^2 -> H(U1(k, e), f(b))
25.51/8.37	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.37	   A^2 -> H(U1(k, c), f(c))
25.51/8.37	   A^2 -> H(U1(k, c), f(d))
25.51/8.37	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.37	   A^2 -> H(U1(c, e), f(c))
25.51/8.37	   A^2 -> H(U1(c, e), f(d))
25.51/8.37	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.37	   A^2 -> H(U1(c, k), f(c))
25.51/8.37	   A^2 -> H(U1(c, k), f(d))
25.51/8.37	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.37	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.37	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.37	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.37	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.37	   A^2 -> H(U1(c, c), f(e))
25.51/8.37	   A^2 -> H(U1(c, c), f(k))
25.51/8.37	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.37	   A^2 -> H(e, f(b))
25.51/8.37	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.37	   A^2 -> H(U1(e, e), f(c))
25.51/8.37	   A^2 -> H(U1(e, e), f(d))
25.51/8.37	   A^2 -> H(f(e), U1(c, b))
25.51/8.37	   A^2 -> H(f(e), U1(d, b))
25.51/8.37	   A^2 -> H(f(e), U1(b, c))
25.51/8.37	   A^2 -> H(f(e), U1(b, d))
25.51/8.37	   A^2 -> H(f(e), U1(c, c))
25.51/8.37	   A^2 -> H(f(e), f(e))
25.51/8.37	   A^2 -> H(f(e), f(k))
25.51/8.37	   A^2 -> H(f(e), U1(d, d))
25.51/8.37	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.37	   A^2 -> H(U1(k, k), f(c))
25.51/8.37	   A^2 -> H(U1(k, k), f(d))
25.51/8.37	   A^2 -> H(f(k), U1(c, b))
25.51/8.37	   A^2 -> H(f(k), U1(d, b))
25.51/8.37	   A^2 -> H(f(k), U1(b, c))
25.51/8.37	   A^2 -> H(f(k), U1(b, d))
25.51/8.37	   A^2 -> H(f(k), U1(c, c))
25.51/8.37	   A^2 -> H(f(k), f(e))
25.51/8.37	   A^2 -> H(f(k), f(k))
25.51/8.37	   A^2 -> H(f(k), U1(d, d))
25.51/8.37	   A^2 -> H(f(c), U1(e, b))
25.51/8.37	   A^2 -> H(f(c), U1(k, b))
25.51/8.37	   A^2 -> H(f(c), U1(c, d))
25.51/8.37	   A^2 -> H(f(c), U1(d, c))
25.51/8.37	   A^2 -> H(f(c), U1(b, e))
25.51/8.37	   A^2 -> H(f(c), U1(b, k))
25.51/8.37	   A^2 -> H(f(c), U1(k, d))
25.51/8.37	   A^2 -> H(f(c), U1(d, k))
25.51/8.37	   A^2 -> H(f(c), U1(k, k))
25.51/8.37	   A^2 -> H(U1(k, k), f(b))
25.51/8.37	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.37	   A^2 -> H(U1(k, d), f(c))
25.51/8.37	   A^2 -> H(U1(k, d), f(d))
25.51/8.37	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.37	   A^2 -> H(U1(d, k), f(c))
25.51/8.37	   A^2 -> H(U1(d, k), f(d))
25.51/8.37	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.37	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.37	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.37	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.37	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.37	   A^2 -> H(U1(d, d), f(e))
25.51/8.37	   A^2 -> H(U1(d, d), f(k))
25.51/8.37	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.37	   A^2 -> H(f(d), U1(e, b))
25.51/8.37	   A^2 -> H(f(d), U1(k, b))
25.51/8.37	   A^2 -> H(f(d), U1(c, d))
25.51/8.37	   A^2 -> H(f(d), U1(d, c))
25.51/8.37	   A^2 -> H(f(d), U1(b, e))
25.51/8.37	   A^2 -> H(f(d), U1(b, k))
25.51/8.37	   A^2 -> H(f(d), U1(e, c))
25.51/8.37	   A^2 -> H(f(d), U1(k, c))
25.51/8.37	   A^2 -> H(f(d), U1(c, e))
25.51/8.37	   A^2 -> H(f(d), U1(c, k))
25.51/8.37	   A^2 -> H(f(d), U1(e, e))
25.51/8.37	   A^2 -> H(f(d), U1(k, k))
25.51/8.37	   A^2 -> H(f(a), b)
25.51/8.37	   A^2 -> H(f(a), U1(e, d))
25.51/8.37	   A^2 -> H(f(a), U1(d, e))
25.51/8.37	   A^2 -> H(f(c), U1(e, c))
25.51/8.37	   A^2 -> H(f(c), U1(k, c))
25.51/8.37	   A^2 -> H(f(c), U1(c, e))
25.51/8.37	   A^2 -> H(f(c), U1(c, k))
25.51/8.37	   A^2 -> H(f(a), c)
25.51/8.37	   A^2 -> H(f(a), U1(e, k))
25.51/8.37	   A^2 -> H(f(a), U1(k, e))
25.51/8.37	   A^2 -> H(f(c), U1(e, e))
25.51/8.37	   A^2 -> H(f(a), e)
25.51/8.37	   A^2 -> H(f(d), U1(k, d))
25.51/8.37	   A^2 -> H(f(d), U1(d, k))
25.51/8.37	   A^2 -> H(f(a), U1(k, k))
25.51/8.37	   A^2 -> H(d, f(b))
25.51/8.37	   A^2 -> H(a, U1(b, b))
25.51/8.37	   A^2 -> H(a, f(c))
25.51/8.37	   A^2 -> H(a, f(d))
25.51/8.37	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.37	   A^2 -> H(U1(e, d), f(c))
25.51/8.37	   A^2 -> H(U1(e, d), f(d))
25.51/8.37	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.37	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.37	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.37	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.37	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.37	   A^2 -> H(U1(e, a), f(e))
25.51/8.37	   A^2 -> H(U1(e, a), f(k))
25.51/8.37	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.37	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.37	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.37	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.37	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.37	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.37	   A^2 -> H(U1(k, a), f(e))
25.51/8.37	   A^2 -> H(U1(k, a), f(k))
25.51/8.37	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.37	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.37	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.37	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.37	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.37	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.37	   A^2 -> H(U1(c, d), f(e))
25.51/8.37	   A^2 -> H(U1(c, d), f(k))
25.51/8.37	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.37	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.37	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.37	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.37	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.37	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.37	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.37	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.37	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.37	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.37	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.37	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.37	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.37	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.37	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.37	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.37	   A^2 -> H(U1(d, e), f(c))
25.51/8.37	   A^2 -> H(U1(d, e), f(d))
25.51/8.37	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.37	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.37	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.37	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.37	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.37	   A^2 -> H(U1(d, c), f(e))
25.51/8.37	   A^2 -> H(U1(d, c), f(k))
25.51/8.37	
25.51/8.37	The TRS R consists of the following rules:
25.51/8.37	
25.51/8.37	   f(x) -> U1(x, x)
25.51/8.37	   U1(e, x) -> x
25.51/8.37	   a -> c
25.51/8.37	   a -> d
25.51/8.37	   b -> c
25.51/8.37	   b -> d
25.51/8.37	   d -> k
25.51/8.37	   c -> e
25.51/8.37	   c -> k
25.51/8.37	
25.51/8.37	Q is empty.
25.51/8.37	We have to consider all minimal (P,Q,R)-chains.
25.51/8.37	----------------------------------------
25.51/8.37	
25.51/8.37	(265) TransformationProof (EQUIVALENT)
25.51/8.37	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), f(d)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.38	
25.51/8.38	   (A^2 -> H(U1(k, c), f(d)),A^2 -> H(U1(k, c), f(d)))
25.51/8.38	   (A^2 -> H(U1(d, e), f(d)),A^2 -> H(U1(d, e), f(d)))
25.51/8.38	   (A^2 -> H(U1(d, k), f(d)),A^2 -> H(U1(d, k), f(d)))
25.51/8.38	   (A^2 -> H(U1(d, c), U1(d, d)),A^2 -> H(U1(d, c), U1(d, d)))
25.51/8.38	   (A^2 -> H(U1(d, c), f(k)),A^2 -> H(U1(d, c), f(k)))
25.51/8.38	
25.51/8.38	
25.51/8.38	----------------------------------------
25.51/8.38	
25.51/8.38	(266)
25.51/8.38	Obligation:
25.51/8.38	Q DP problem:
25.51/8.38	The TRS P consists of the following rules:
25.51/8.38	
25.51/8.38	   H(x, x) -> G(x, x, f(k))
25.51/8.38	   G(d, x, x) -> A^2
25.51/8.38	   A^2 -> H(f(c), f(c))
25.51/8.38	   A^2 -> H(f(d), f(d))
25.51/8.38	   A^2 -> H(U1(d, a), U1(c, b))
25.51/8.38	   A^2 -> H(U1(d, a), U1(d, b))
25.51/8.38	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.38	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.38	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.38	   A^2 -> H(U1(d, a), f(e))
25.51/8.38	   A^2 -> H(U1(d, a), f(k))
25.51/8.38	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.38	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.38	   A^2 -> H(U1(a, e), f(c))
25.51/8.38	   A^2 -> H(U1(a, e), f(d))
25.51/8.38	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.38	   A^2 -> H(U1(a, k), f(c))
25.51/8.38	   A^2 -> H(U1(a, k), f(d))
25.51/8.38	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.38	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.38	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.38	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.38	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.38	   A^2 -> H(U1(a, c), f(e))
25.51/8.38	   A^2 -> H(U1(a, c), f(k))
25.51/8.38	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.38	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.38	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.38	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.38	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.38	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.38	   A^2 -> H(U1(a, d), f(e))
25.51/8.38	   A^2 -> H(U1(a, d), f(k))
25.51/8.38	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.38	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.38	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.38	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.38	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.38	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.38	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.38	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.38	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.38	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.38	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.38	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.38	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.38	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.38	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.38	   A^2 -> H(c, f(b))
25.51/8.38	   A^2 -> H(U1(e, k), f(b))
25.51/8.38	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.38	   A^2 -> H(U1(e, c), f(c))
25.51/8.38	   A^2 -> H(U1(e, c), f(d))
25.51/8.38	   A^2 -> H(U1(k, e), f(b))
25.51/8.38	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.38	   A^2 -> H(U1(k, c), f(c))
25.51/8.38	   A^2 -> H(U1(k, c), f(d))
25.51/8.38	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.38	   A^2 -> H(U1(c, e), f(c))
25.51/8.38	   A^2 -> H(U1(c, e), f(d))
25.51/8.38	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.38	   A^2 -> H(U1(c, k), f(c))
25.51/8.38	   A^2 -> H(U1(c, k), f(d))
25.51/8.38	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.38	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.38	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.38	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.38	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.38	   A^2 -> H(U1(c, c), f(e))
25.51/8.38	   A^2 -> H(U1(c, c), f(k))
25.51/8.38	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.38	   A^2 -> H(e, f(b))
25.51/8.38	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.38	   A^2 -> H(U1(e, e), f(c))
25.51/8.38	   A^2 -> H(U1(e, e), f(d))
25.51/8.38	   A^2 -> H(f(e), U1(c, b))
25.51/8.38	   A^2 -> H(f(e), U1(d, b))
25.51/8.38	   A^2 -> H(f(e), U1(b, c))
25.51/8.38	   A^2 -> H(f(e), U1(b, d))
25.51/8.38	   A^2 -> H(f(e), U1(c, c))
25.51/8.38	   A^2 -> H(f(e), f(e))
25.51/8.38	   A^2 -> H(f(e), f(k))
25.51/8.38	   A^2 -> H(f(e), U1(d, d))
25.51/8.38	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.38	   A^2 -> H(U1(k, k), f(c))
25.51/8.38	   A^2 -> H(U1(k, k), f(d))
25.51/8.38	   A^2 -> H(f(k), U1(c, b))
25.51/8.38	   A^2 -> H(f(k), U1(d, b))
25.51/8.38	   A^2 -> H(f(k), U1(b, c))
25.51/8.38	   A^2 -> H(f(k), U1(b, d))
25.51/8.38	   A^2 -> H(f(k), U1(c, c))
25.51/8.38	   A^2 -> H(f(k), f(e))
25.51/8.38	   A^2 -> H(f(k), f(k))
25.51/8.38	   A^2 -> H(f(k), U1(d, d))
25.51/8.38	   A^2 -> H(f(c), U1(e, b))
25.51/8.38	   A^2 -> H(f(c), U1(k, b))
25.51/8.38	   A^2 -> H(f(c), U1(c, d))
25.51/8.38	   A^2 -> H(f(c), U1(d, c))
25.51/8.38	   A^2 -> H(f(c), U1(b, e))
25.51/8.38	   A^2 -> H(f(c), U1(b, k))
25.51/8.38	   A^2 -> H(f(c), U1(k, d))
25.51/8.38	   A^2 -> H(f(c), U1(d, k))
25.51/8.38	   A^2 -> H(f(c), U1(k, k))
25.51/8.38	   A^2 -> H(U1(k, k), f(b))
25.51/8.38	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.38	   A^2 -> H(U1(k, d), f(c))
25.51/8.38	   A^2 -> H(U1(k, d), f(d))
25.51/8.38	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.38	   A^2 -> H(U1(d, k), f(c))
25.51/8.38	   A^2 -> H(U1(d, k), f(d))
25.51/8.38	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.38	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.38	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.38	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.38	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.38	   A^2 -> H(U1(d, d), f(e))
25.51/8.38	   A^2 -> H(U1(d, d), f(k))
25.51/8.38	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.38	   A^2 -> H(f(d), U1(e, b))
25.51/8.38	   A^2 -> H(f(d), U1(k, b))
25.51/8.38	   A^2 -> H(f(d), U1(c, d))
25.51/8.38	   A^2 -> H(f(d), U1(d, c))
25.51/8.38	   A^2 -> H(f(d), U1(b, e))
25.51/8.38	   A^2 -> H(f(d), U1(b, k))
25.51/8.38	   A^2 -> H(f(d), U1(e, c))
25.51/8.38	   A^2 -> H(f(d), U1(k, c))
25.51/8.38	   A^2 -> H(f(d), U1(c, e))
25.51/8.38	   A^2 -> H(f(d), U1(c, k))
25.51/8.38	   A^2 -> H(f(d), U1(e, e))
25.51/8.38	   A^2 -> H(f(d), U1(k, k))
25.51/8.38	   A^2 -> H(f(a), b)
25.51/8.38	   A^2 -> H(f(a), U1(e, d))
25.51/8.38	   A^2 -> H(f(a), U1(d, e))
25.51/8.38	   A^2 -> H(f(c), U1(e, c))
25.51/8.38	   A^2 -> H(f(c), U1(k, c))
25.51/8.38	   A^2 -> H(f(c), U1(c, e))
25.51/8.38	   A^2 -> H(f(c), U1(c, k))
25.51/8.38	   A^2 -> H(f(a), c)
25.51/8.38	   A^2 -> H(f(a), U1(e, k))
25.51/8.38	   A^2 -> H(f(a), U1(k, e))
25.51/8.38	   A^2 -> H(f(c), U1(e, e))
25.51/8.38	   A^2 -> H(f(a), e)
25.51/8.38	   A^2 -> H(f(d), U1(k, d))
25.51/8.38	   A^2 -> H(f(d), U1(d, k))
25.51/8.38	   A^2 -> H(f(a), U1(k, k))
25.51/8.38	   A^2 -> H(d, f(b))
25.51/8.38	   A^2 -> H(a, U1(b, b))
25.51/8.38	   A^2 -> H(a, f(c))
25.51/8.38	   A^2 -> H(a, f(d))
25.51/8.38	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.38	   A^2 -> H(U1(e, d), f(c))
25.51/8.38	   A^2 -> H(U1(e, d), f(d))
25.51/8.38	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.38	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.38	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.38	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.38	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.38	   A^2 -> H(U1(e, a), f(e))
25.51/8.38	   A^2 -> H(U1(e, a), f(k))
25.51/8.38	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.38	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.38	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.38	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.38	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.38	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.38	   A^2 -> H(U1(k, a), f(e))
25.51/8.38	   A^2 -> H(U1(k, a), f(k))
25.51/8.38	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.38	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.38	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.38	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.38	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.38	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.38	   A^2 -> H(U1(c, d), f(e))
25.51/8.38	   A^2 -> H(U1(c, d), f(k))
25.51/8.38	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.38	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.38	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.38	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.38	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.38	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.38	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.38	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.38	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.38	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.38	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.38	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.38	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.38	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.38	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.38	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.38	   A^2 -> H(U1(d, e), f(c))
25.51/8.38	   A^2 -> H(U1(d, e), f(d))
25.51/8.38	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.38	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.38	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.38	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.38	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.38	   A^2 -> H(U1(d, c), f(e))
25.51/8.38	   A^2 -> H(U1(d, c), f(k))
25.51/8.38	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.38	
25.51/8.38	The TRS R consists of the following rules:
25.51/8.38	
25.51/8.38	   f(x) -> U1(x, x)
25.51/8.38	   U1(e, x) -> x
25.51/8.38	   a -> c
25.51/8.38	   a -> d
25.51/8.38	   b -> c
25.51/8.38	   b -> d
25.51/8.38	   d -> k
25.51/8.38	   c -> e
25.51/8.38	   c -> k
25.51/8.38	
25.51/8.38	Q is empty.
25.51/8.38	We have to consider all minimal (P,Q,R)-chains.
25.51/8.38	----------------------------------------
25.51/8.38	
25.51/8.38	(267) TransformationProof (EQUIVALENT)
25.51/8.38	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.38	
25.51/8.38	   (A^2 -> H(U1(k, a), U1(c, b)),A^2 -> H(U1(k, a), U1(c, b)))
25.51/8.38	   (A^2 -> H(U1(d, c), U1(c, b)),A^2 -> H(U1(d, c), U1(c, b)))
25.51/8.38	   (A^2 -> H(U1(d, d), U1(c, b)),A^2 -> H(U1(d, d), U1(c, b)))
25.51/8.38	   (A^2 -> H(U1(d, a), U1(e, b)),A^2 -> H(U1(d, a), U1(e, b)))
25.51/8.38	   (A^2 -> H(U1(d, a), U1(k, b)),A^2 -> H(U1(d, a), U1(k, b)))
25.51/8.38	   (A^2 -> H(U1(d, a), U1(c, c)),A^2 -> H(U1(d, a), U1(c, c)))
25.51/8.38	   (A^2 -> H(U1(d, a), U1(c, d)),A^2 -> H(U1(d, a), U1(c, d)))
25.51/8.38	
25.51/8.38	
25.51/8.38	----------------------------------------
25.51/8.38	
25.51/8.38	(268)
25.51/8.38	Obligation:
25.51/8.38	Q DP problem:
25.51/8.38	The TRS P consists of the following rules:
25.51/8.38	
25.51/8.38	   H(x, x) -> G(x, x, f(k))
25.51/8.38	   G(d, x, x) -> A^2
25.51/8.38	   A^2 -> H(f(c), f(c))
25.51/8.38	   A^2 -> H(f(d), f(d))
25.51/8.38	   A^2 -> H(U1(d, a), U1(d, b))
25.51/8.38	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.38	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.38	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.38	   A^2 -> H(U1(d, a), f(e))
25.51/8.38	   A^2 -> H(U1(d, a), f(k))
25.51/8.38	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.38	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.38	   A^2 -> H(U1(a, e), f(c))
25.51/8.38	   A^2 -> H(U1(a, e), f(d))
25.51/8.38	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.38	   A^2 -> H(U1(a, k), f(c))
25.51/8.38	   A^2 -> H(U1(a, k), f(d))
25.51/8.38	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.38	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.38	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.38	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.38	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.38	   A^2 -> H(U1(a, c), f(e))
25.51/8.38	   A^2 -> H(U1(a, c), f(k))
25.51/8.38	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.38	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.38	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.38	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.38	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.38	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.38	   A^2 -> H(U1(a, d), f(e))
25.51/8.38	   A^2 -> H(U1(a, d), f(k))
25.51/8.38	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.38	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.38	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.38	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.38	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.38	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.38	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.38	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.38	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.38	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.38	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.38	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.38	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.38	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.38	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.38	   A^2 -> H(c, f(b))
25.51/8.38	   A^2 -> H(U1(e, k), f(b))
25.51/8.38	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.38	   A^2 -> H(U1(e, c), f(c))
25.51/8.38	   A^2 -> H(U1(e, c), f(d))
25.51/8.38	   A^2 -> H(U1(k, e), f(b))
25.51/8.38	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.38	   A^2 -> H(U1(k, c), f(c))
25.51/8.38	   A^2 -> H(U1(k, c), f(d))
25.51/8.38	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.38	   A^2 -> H(U1(c, e), f(c))
25.51/8.38	   A^2 -> H(U1(c, e), f(d))
25.51/8.38	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.38	   A^2 -> H(U1(c, k), f(c))
25.51/8.38	   A^2 -> H(U1(c, k), f(d))
25.51/8.38	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.38	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.38	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.38	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.38	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.38	   A^2 -> H(U1(c, c), f(e))
25.51/8.38	   A^2 -> H(U1(c, c), f(k))
25.51/8.38	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.38	   A^2 -> H(e, f(b))
25.51/8.38	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.38	   A^2 -> H(U1(e, e), f(c))
25.51/8.38	   A^2 -> H(U1(e, e), f(d))
25.51/8.38	   A^2 -> H(f(e), U1(c, b))
25.51/8.38	   A^2 -> H(f(e), U1(d, b))
25.51/8.38	   A^2 -> H(f(e), U1(b, c))
25.51/8.38	   A^2 -> H(f(e), U1(b, d))
25.51/8.38	   A^2 -> H(f(e), U1(c, c))
25.51/8.38	   A^2 -> H(f(e), f(e))
25.51/8.38	   A^2 -> H(f(e), f(k))
25.51/8.38	   A^2 -> H(f(e), U1(d, d))
25.51/8.38	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.38	   A^2 -> H(U1(k, k), f(c))
25.51/8.38	   A^2 -> H(U1(k, k), f(d))
25.51/8.38	   A^2 -> H(f(k), U1(c, b))
25.51/8.38	   A^2 -> H(f(k), U1(d, b))
25.51/8.38	   A^2 -> H(f(k), U1(b, c))
25.51/8.38	   A^2 -> H(f(k), U1(b, d))
25.51/8.38	   A^2 -> H(f(k), U1(c, c))
25.51/8.38	   A^2 -> H(f(k), f(e))
25.51/8.38	   A^2 -> H(f(k), f(k))
25.51/8.38	   A^2 -> H(f(k), U1(d, d))
25.51/8.38	   A^2 -> H(f(c), U1(e, b))
25.51/8.38	   A^2 -> H(f(c), U1(k, b))
25.51/8.38	   A^2 -> H(f(c), U1(c, d))
25.51/8.38	   A^2 -> H(f(c), U1(d, c))
25.51/8.38	   A^2 -> H(f(c), U1(b, e))
25.51/8.38	   A^2 -> H(f(c), U1(b, k))
25.51/8.38	   A^2 -> H(f(c), U1(k, d))
25.51/8.38	   A^2 -> H(f(c), U1(d, k))
25.51/8.38	   A^2 -> H(f(c), U1(k, k))
25.51/8.38	   A^2 -> H(U1(k, k), f(b))
25.51/8.38	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.38	   A^2 -> H(U1(k, d), f(c))
25.51/8.38	   A^2 -> H(U1(k, d), f(d))
25.51/8.38	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.38	   A^2 -> H(U1(d, k), f(c))
25.51/8.38	   A^2 -> H(U1(d, k), f(d))
25.51/8.38	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.38	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.38	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.38	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.38	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.38	   A^2 -> H(U1(d, d), f(e))
25.51/8.38	   A^2 -> H(U1(d, d), f(k))
25.51/8.38	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.38	   A^2 -> H(f(d), U1(e, b))
25.51/8.38	   A^2 -> H(f(d), U1(k, b))
25.51/8.38	   A^2 -> H(f(d), U1(c, d))
25.51/8.38	   A^2 -> H(f(d), U1(d, c))
25.51/8.38	   A^2 -> H(f(d), U1(b, e))
25.51/8.38	   A^2 -> H(f(d), U1(b, k))
25.51/8.38	   A^2 -> H(f(d), U1(e, c))
25.51/8.38	   A^2 -> H(f(d), U1(k, c))
25.51/8.38	   A^2 -> H(f(d), U1(c, e))
25.51/8.38	   A^2 -> H(f(d), U1(c, k))
25.51/8.38	   A^2 -> H(f(d), U1(e, e))
25.51/8.38	   A^2 -> H(f(d), U1(k, k))
25.51/8.38	   A^2 -> H(f(a), b)
25.51/8.38	   A^2 -> H(f(a), U1(e, d))
25.51/8.38	   A^2 -> H(f(a), U1(d, e))
25.51/8.38	   A^2 -> H(f(c), U1(e, c))
25.51/8.38	   A^2 -> H(f(c), U1(k, c))
25.51/8.38	   A^2 -> H(f(c), U1(c, e))
25.51/8.38	   A^2 -> H(f(c), U1(c, k))
25.51/8.38	   A^2 -> H(f(a), c)
25.51/8.38	   A^2 -> H(f(a), U1(e, k))
25.51/8.38	   A^2 -> H(f(a), U1(k, e))
25.51/8.38	   A^2 -> H(f(c), U1(e, e))
25.51/8.38	   A^2 -> H(f(a), e)
25.51/8.38	   A^2 -> H(f(d), U1(k, d))
25.51/8.38	   A^2 -> H(f(d), U1(d, k))
25.51/8.38	   A^2 -> H(f(a), U1(k, k))
25.51/8.38	   A^2 -> H(d, f(b))
25.51/8.38	   A^2 -> H(a, U1(b, b))
25.51/8.38	   A^2 -> H(a, f(c))
25.51/8.38	   A^2 -> H(a, f(d))
25.51/8.38	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.38	   A^2 -> H(U1(e, d), f(c))
25.51/8.38	   A^2 -> H(U1(e, d), f(d))
25.51/8.38	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.38	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.38	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.38	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.38	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.38	   A^2 -> H(U1(e, a), f(e))
25.51/8.38	   A^2 -> H(U1(e, a), f(k))
25.51/8.38	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.38	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.38	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.38	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.38	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.38	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.38	   A^2 -> H(U1(k, a), f(e))
25.51/8.38	   A^2 -> H(U1(k, a), f(k))
25.51/8.38	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.38	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.38	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.38	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.38	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.38	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.38	   A^2 -> H(U1(c, d), f(e))
25.51/8.38	   A^2 -> H(U1(c, d), f(k))
25.51/8.38	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.38	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.38	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.38	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.38	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.38	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.38	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.38	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.38	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.38	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.38	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.38	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.38	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.38	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.38	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.38	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.38	   A^2 -> H(U1(d, e), f(c))
25.51/8.38	   A^2 -> H(U1(d, e), f(d))
25.51/8.38	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.38	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.38	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.38	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.38	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.38	   A^2 -> H(U1(d, c), f(e))
25.51/8.38	   A^2 -> H(U1(d, c), f(k))
25.51/8.38	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.38	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.38	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.38	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.38	
25.51/8.38	The TRS R consists of the following rules:
25.51/8.38	
25.51/8.38	   f(x) -> U1(x, x)
25.51/8.38	   U1(e, x) -> x
25.51/8.38	   a -> c
25.51/8.38	   a -> d
25.51/8.38	   b -> c
25.51/8.38	   b -> d
25.51/8.38	   d -> k
25.51/8.38	   c -> e
25.51/8.38	   c -> k
25.51/8.38	
25.51/8.38	Q is empty.
25.51/8.38	We have to consider all minimal (P,Q,R)-chains.
25.51/8.38	----------------------------------------
25.51/8.38	
25.51/8.38	(269) TransformationProof (EQUIVALENT)
25.51/8.38	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.38	
25.51/8.38	   (A^2 -> H(U1(k, a), U1(d, b)),A^2 -> H(U1(k, a), U1(d, b)))
25.51/8.38	   (A^2 -> H(U1(d, c), U1(d, b)),A^2 -> H(U1(d, c), U1(d, b)))
25.51/8.38	   (A^2 -> H(U1(d, d), U1(d, b)),A^2 -> H(U1(d, d), U1(d, b)))
25.51/8.38	   (A^2 -> H(U1(d, a), U1(k, b)),A^2 -> H(U1(d, a), U1(k, b)))
25.51/8.38	   (A^2 -> H(U1(d, a), U1(d, c)),A^2 -> H(U1(d, a), U1(d, c)))
25.51/8.38	   (A^2 -> H(U1(d, a), U1(d, d)),A^2 -> H(U1(d, a), U1(d, d)))
25.51/8.38	
25.51/8.38	
25.51/8.38	----------------------------------------
25.51/8.38	
25.51/8.38	(270)
25.51/8.38	Obligation:
25.51/8.38	Q DP problem:
25.51/8.38	The TRS P consists of the following rules:
25.51/8.38	
25.51/8.38	   H(x, x) -> G(x, x, f(k))
25.51/8.38	   G(d, x, x) -> A^2
25.51/8.38	   A^2 -> H(f(c), f(c))
25.51/8.38	   A^2 -> H(f(d), f(d))
25.51/8.38	   A^2 -> H(U1(d, a), U1(b, c))
25.51/8.38	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.38	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.38	   A^2 -> H(U1(d, a), f(e))
25.51/8.38	   A^2 -> H(U1(d, a), f(k))
25.51/8.38	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.38	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.38	   A^2 -> H(U1(a, e), f(c))
25.51/8.38	   A^2 -> H(U1(a, e), f(d))
25.51/8.38	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.38	   A^2 -> H(U1(a, k), f(c))
25.51/8.38	   A^2 -> H(U1(a, k), f(d))
25.51/8.38	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.38	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.38	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.38	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.38	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.38	   A^2 -> H(U1(a, c), f(e))
25.51/8.38	   A^2 -> H(U1(a, c), f(k))
25.51/8.38	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.38	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.38	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.38	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.38	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.38	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.38	   A^2 -> H(U1(a, d), f(e))
25.51/8.38	   A^2 -> H(U1(a, d), f(k))
25.51/8.38	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.38	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.38	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.38	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.38	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.38	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.38	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.38	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.38	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.38	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.38	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.38	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.38	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.38	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.38	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.38	   A^2 -> H(c, f(b))
25.51/8.38	   A^2 -> H(U1(e, k), f(b))
25.51/8.38	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.38	   A^2 -> H(U1(e, c), f(c))
25.51/8.38	   A^2 -> H(U1(e, c), f(d))
25.51/8.38	   A^2 -> H(U1(k, e), f(b))
25.51/8.38	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.38	   A^2 -> H(U1(k, c), f(c))
25.51/8.38	   A^2 -> H(U1(k, c), f(d))
25.51/8.38	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.38	   A^2 -> H(U1(c, e), f(c))
25.51/8.38	   A^2 -> H(U1(c, e), f(d))
25.51/8.38	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.38	   A^2 -> H(U1(c, k), f(c))
25.51/8.38	   A^2 -> H(U1(c, k), f(d))
25.51/8.38	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.38	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.38	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.38	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.38	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.38	   A^2 -> H(U1(c, c), f(e))
25.51/8.38	   A^2 -> H(U1(c, c), f(k))
25.51/8.38	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.38	   A^2 -> H(e, f(b))
25.51/8.38	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.38	   A^2 -> H(U1(e, e), f(c))
25.51/8.38	   A^2 -> H(U1(e, e), f(d))
25.51/8.38	   A^2 -> H(f(e), U1(c, b))
25.51/8.38	   A^2 -> H(f(e), U1(d, b))
25.51/8.38	   A^2 -> H(f(e), U1(b, c))
25.51/8.38	   A^2 -> H(f(e), U1(b, d))
25.51/8.38	   A^2 -> H(f(e), U1(c, c))
25.51/8.38	   A^2 -> H(f(e), f(e))
25.51/8.38	   A^2 -> H(f(e), f(k))
25.51/8.38	   A^2 -> H(f(e), U1(d, d))
25.51/8.38	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.38	   A^2 -> H(U1(k, k), f(c))
25.51/8.38	   A^2 -> H(U1(k, k), f(d))
25.51/8.38	   A^2 -> H(f(k), U1(c, b))
25.51/8.38	   A^2 -> H(f(k), U1(d, b))
25.51/8.38	   A^2 -> H(f(k), U1(b, c))
25.51/8.38	   A^2 -> H(f(k), U1(b, d))
25.51/8.38	   A^2 -> H(f(k), U1(c, c))
25.51/8.38	   A^2 -> H(f(k), f(e))
25.51/8.38	   A^2 -> H(f(k), f(k))
25.51/8.38	   A^2 -> H(f(k), U1(d, d))
25.51/8.38	   A^2 -> H(f(c), U1(e, b))
25.51/8.38	   A^2 -> H(f(c), U1(k, b))
25.51/8.38	   A^2 -> H(f(c), U1(c, d))
25.51/8.38	   A^2 -> H(f(c), U1(d, c))
25.51/8.38	   A^2 -> H(f(c), U1(b, e))
25.51/8.38	   A^2 -> H(f(c), U1(b, k))
25.51/8.38	   A^2 -> H(f(c), U1(k, d))
25.51/8.38	   A^2 -> H(f(c), U1(d, k))
25.51/8.38	   A^2 -> H(f(c), U1(k, k))
25.51/8.38	   A^2 -> H(U1(k, k), f(b))
25.51/8.38	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.38	   A^2 -> H(U1(k, d), f(c))
25.51/8.38	   A^2 -> H(U1(k, d), f(d))
25.51/8.38	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.38	   A^2 -> H(U1(d, k), f(c))
25.51/8.38	   A^2 -> H(U1(d, k), f(d))
25.51/8.38	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.38	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.38	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.38	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.38	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.38	   A^2 -> H(U1(d, d), f(e))
25.51/8.38	   A^2 -> H(U1(d, d), f(k))
25.51/8.38	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.38	   A^2 -> H(f(d), U1(e, b))
25.51/8.38	   A^2 -> H(f(d), U1(k, b))
25.51/8.38	   A^2 -> H(f(d), U1(c, d))
25.51/8.38	   A^2 -> H(f(d), U1(d, c))
25.51/8.38	   A^2 -> H(f(d), U1(b, e))
25.51/8.38	   A^2 -> H(f(d), U1(b, k))
25.51/8.38	   A^2 -> H(f(d), U1(e, c))
25.51/8.38	   A^2 -> H(f(d), U1(k, c))
25.51/8.38	   A^2 -> H(f(d), U1(c, e))
25.51/8.38	   A^2 -> H(f(d), U1(c, k))
25.51/8.38	   A^2 -> H(f(d), U1(e, e))
25.51/8.38	   A^2 -> H(f(d), U1(k, k))
25.51/8.38	   A^2 -> H(f(a), b)
25.51/8.38	   A^2 -> H(f(a), U1(e, d))
25.51/8.38	   A^2 -> H(f(a), U1(d, e))
25.51/8.38	   A^2 -> H(f(c), U1(e, c))
25.51/8.38	   A^2 -> H(f(c), U1(k, c))
25.51/8.38	   A^2 -> H(f(c), U1(c, e))
25.51/8.38	   A^2 -> H(f(c), U1(c, k))
25.51/8.38	   A^2 -> H(f(a), c)
25.51/8.38	   A^2 -> H(f(a), U1(e, k))
25.51/8.38	   A^2 -> H(f(a), U1(k, e))
25.51/8.38	   A^2 -> H(f(c), U1(e, e))
25.51/8.38	   A^2 -> H(f(a), e)
25.51/8.38	   A^2 -> H(f(d), U1(k, d))
25.51/8.38	   A^2 -> H(f(d), U1(d, k))
25.51/8.38	   A^2 -> H(f(a), U1(k, k))
25.51/8.38	   A^2 -> H(d, f(b))
25.51/8.38	   A^2 -> H(a, U1(b, b))
25.51/8.38	   A^2 -> H(a, f(c))
25.51/8.38	   A^2 -> H(a, f(d))
25.51/8.38	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.38	   A^2 -> H(U1(e, d), f(c))
25.51/8.38	   A^2 -> H(U1(e, d), f(d))
25.51/8.38	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.38	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.38	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.38	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.38	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.38	   A^2 -> H(U1(e, a), f(e))
25.51/8.38	   A^2 -> H(U1(e, a), f(k))
25.51/8.38	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.38	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.38	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.38	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.38	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.38	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.38	   A^2 -> H(U1(k, a), f(e))
25.51/8.38	   A^2 -> H(U1(k, a), f(k))
25.51/8.38	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.38	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.38	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.38	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.38	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.38	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.38	   A^2 -> H(U1(c, d), f(e))
25.51/8.38	   A^2 -> H(U1(c, d), f(k))
25.51/8.38	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.38	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.38	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.38	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.38	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.38	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.38	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.39	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.39	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.39	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.39	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.39	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.39	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(d, e), f(c))
25.51/8.39	   A^2 -> H(U1(d, e), f(d))
25.51/8.39	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.39	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.39	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.39	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.39	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.39	   A^2 -> H(U1(d, c), f(e))
25.51/8.39	   A^2 -> H(U1(d, c), f(k))
25.51/8.39	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.39	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.39	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.39	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.39	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.39	
25.51/8.39	The TRS R consists of the following rules:
25.51/8.39	
25.51/8.39	   f(x) -> U1(x, x)
25.51/8.39	   U1(e, x) -> x
25.51/8.39	   a -> c
25.51/8.39	   a -> d
25.51/8.39	   b -> c
25.51/8.39	   b -> d
25.51/8.39	   d -> k
25.51/8.39	   c -> e
25.51/8.39	   c -> k
25.51/8.39	
25.51/8.39	Q is empty.
25.51/8.39	We have to consider all minimal (P,Q,R)-chains.
25.51/8.39	----------------------------------------
25.51/8.39	
25.51/8.39	(271) TransformationProof (EQUIVALENT)
25.51/8.39	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.39	
25.51/8.39	   (A^2 -> H(U1(k, a), U1(b, c)),A^2 -> H(U1(k, a), U1(b, c)))
25.51/8.39	   (A^2 -> H(U1(d, c), U1(b, c)),A^2 -> H(U1(d, c), U1(b, c)))
25.51/8.39	   (A^2 -> H(U1(d, d), U1(b, c)),A^2 -> H(U1(d, d), U1(b, c)))
25.51/8.39	   (A^2 -> H(U1(d, a), U1(c, c)),A^2 -> H(U1(d, a), U1(c, c)))
25.51/8.39	   (A^2 -> H(U1(d, a), U1(d, c)),A^2 -> H(U1(d, a), U1(d, c)))
25.51/8.39	   (A^2 -> H(U1(d, a), U1(b, e)),A^2 -> H(U1(d, a), U1(b, e)))
25.51/8.39	   (A^2 -> H(U1(d, a), U1(b, k)),A^2 -> H(U1(d, a), U1(b, k)))
25.51/8.39	
25.51/8.39	
25.51/8.39	----------------------------------------
25.51/8.39	
25.51/8.39	(272)
25.51/8.39	Obligation:
25.51/8.39	Q DP problem:
25.51/8.39	The TRS P consists of the following rules:
25.51/8.39	
25.51/8.39	   H(x, x) -> G(x, x, f(k))
25.51/8.39	   G(d, x, x) -> A^2
25.51/8.39	   A^2 -> H(f(c), f(c))
25.51/8.39	   A^2 -> H(f(d), f(d))
25.51/8.39	   A^2 -> H(U1(d, a), U1(b, d))
25.51/8.39	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.39	   A^2 -> H(U1(d, a), f(e))
25.51/8.39	   A^2 -> H(U1(d, a), f(k))
25.51/8.39	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.39	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(a, e), f(c))
25.51/8.39	   A^2 -> H(U1(a, e), f(d))
25.51/8.39	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(a, k), f(c))
25.51/8.39	   A^2 -> H(U1(a, k), f(d))
25.51/8.39	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.39	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.39	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.39	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.39	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.39	   A^2 -> H(U1(a, c), f(e))
25.51/8.39	   A^2 -> H(U1(a, c), f(k))
25.51/8.39	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.39	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.39	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.39	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.39	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.39	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.39	   A^2 -> H(U1(a, d), f(e))
25.51/8.39	   A^2 -> H(U1(a, d), f(k))
25.51/8.39	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.39	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.39	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.39	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.39	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.39	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.39	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.39	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.39	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.39	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.39	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.39	   A^2 -> H(c, f(b))
25.51/8.39	   A^2 -> H(U1(e, k), f(b))
25.51/8.39	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.39	   A^2 -> H(U1(e, c), f(c))
25.51/8.39	   A^2 -> H(U1(e, c), f(d))
25.51/8.39	   A^2 -> H(U1(k, e), f(b))
25.51/8.39	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.39	   A^2 -> H(U1(k, c), f(c))
25.51/8.39	   A^2 -> H(U1(k, c), f(d))
25.51/8.39	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(c, e), f(c))
25.51/8.39	   A^2 -> H(U1(c, e), f(d))
25.51/8.39	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(c, k), f(c))
25.51/8.39	   A^2 -> H(U1(c, k), f(d))
25.51/8.39	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.39	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.39	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.39	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.39	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.39	   A^2 -> H(U1(c, c), f(e))
25.51/8.39	   A^2 -> H(U1(c, c), f(k))
25.51/8.39	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.39	   A^2 -> H(e, f(b))
25.51/8.39	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(e, e), f(c))
25.51/8.39	   A^2 -> H(U1(e, e), f(d))
25.51/8.39	   A^2 -> H(f(e), U1(c, b))
25.51/8.39	   A^2 -> H(f(e), U1(d, b))
25.51/8.39	   A^2 -> H(f(e), U1(b, c))
25.51/8.39	   A^2 -> H(f(e), U1(b, d))
25.51/8.39	   A^2 -> H(f(e), U1(c, c))
25.51/8.39	   A^2 -> H(f(e), f(e))
25.51/8.39	   A^2 -> H(f(e), f(k))
25.51/8.39	   A^2 -> H(f(e), U1(d, d))
25.51/8.39	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(k, k), f(c))
25.51/8.39	   A^2 -> H(U1(k, k), f(d))
25.51/8.39	   A^2 -> H(f(k), U1(c, b))
25.51/8.39	   A^2 -> H(f(k), U1(d, b))
25.51/8.39	   A^2 -> H(f(k), U1(b, c))
25.51/8.39	   A^2 -> H(f(k), U1(b, d))
25.51/8.39	   A^2 -> H(f(k), U1(c, c))
25.51/8.39	   A^2 -> H(f(k), f(e))
25.51/8.39	   A^2 -> H(f(k), f(k))
25.51/8.39	   A^2 -> H(f(k), U1(d, d))
25.51/8.39	   A^2 -> H(f(c), U1(e, b))
25.51/8.39	   A^2 -> H(f(c), U1(k, b))
25.51/8.39	   A^2 -> H(f(c), U1(c, d))
25.51/8.39	   A^2 -> H(f(c), U1(d, c))
25.51/8.39	   A^2 -> H(f(c), U1(b, e))
25.51/8.39	   A^2 -> H(f(c), U1(b, k))
25.51/8.39	   A^2 -> H(f(c), U1(k, d))
25.51/8.39	   A^2 -> H(f(c), U1(d, k))
25.51/8.39	   A^2 -> H(f(c), U1(k, k))
25.51/8.39	   A^2 -> H(U1(k, k), f(b))
25.51/8.39	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.39	   A^2 -> H(U1(k, d), f(c))
25.51/8.39	   A^2 -> H(U1(k, d), f(d))
25.51/8.39	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(d, k), f(c))
25.51/8.39	   A^2 -> H(U1(d, k), f(d))
25.51/8.39	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.39	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.39	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.39	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.39	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.39	   A^2 -> H(U1(d, d), f(e))
25.51/8.39	   A^2 -> H(U1(d, d), f(k))
25.51/8.39	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.39	   A^2 -> H(f(d), U1(e, b))
25.51/8.39	   A^2 -> H(f(d), U1(k, b))
25.51/8.39	   A^2 -> H(f(d), U1(c, d))
25.51/8.39	   A^2 -> H(f(d), U1(d, c))
25.51/8.39	   A^2 -> H(f(d), U1(b, e))
25.51/8.39	   A^2 -> H(f(d), U1(b, k))
25.51/8.39	   A^2 -> H(f(d), U1(e, c))
25.51/8.39	   A^2 -> H(f(d), U1(k, c))
25.51/8.39	   A^2 -> H(f(d), U1(c, e))
25.51/8.39	   A^2 -> H(f(d), U1(c, k))
25.51/8.39	   A^2 -> H(f(d), U1(e, e))
25.51/8.39	   A^2 -> H(f(d), U1(k, k))
25.51/8.39	   A^2 -> H(f(a), b)
25.51/8.39	   A^2 -> H(f(a), U1(e, d))
25.51/8.39	   A^2 -> H(f(a), U1(d, e))
25.51/8.39	   A^2 -> H(f(c), U1(e, c))
25.51/8.39	   A^2 -> H(f(c), U1(k, c))
25.51/8.39	   A^2 -> H(f(c), U1(c, e))
25.51/8.39	   A^2 -> H(f(c), U1(c, k))
25.51/8.39	   A^2 -> H(f(a), c)
25.51/8.39	   A^2 -> H(f(a), U1(e, k))
25.51/8.39	   A^2 -> H(f(a), U1(k, e))
25.51/8.39	   A^2 -> H(f(c), U1(e, e))
25.51/8.39	   A^2 -> H(f(a), e)
25.51/8.39	   A^2 -> H(f(d), U1(k, d))
25.51/8.39	   A^2 -> H(f(d), U1(d, k))
25.51/8.39	   A^2 -> H(f(a), U1(k, k))
25.51/8.39	   A^2 -> H(d, f(b))
25.51/8.39	   A^2 -> H(a, U1(b, b))
25.51/8.39	   A^2 -> H(a, f(c))
25.51/8.39	   A^2 -> H(a, f(d))
25.51/8.39	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.39	   A^2 -> H(U1(e, d), f(c))
25.51/8.39	   A^2 -> H(U1(e, d), f(d))
25.51/8.39	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.39	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.39	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.39	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.39	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.39	   A^2 -> H(U1(e, a), f(e))
25.51/8.39	   A^2 -> H(U1(e, a), f(k))
25.51/8.39	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.39	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.39	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.39	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.39	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.39	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.39	   A^2 -> H(U1(k, a), f(e))
25.51/8.39	   A^2 -> H(U1(k, a), f(k))
25.51/8.39	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.39	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.39	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.39	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.39	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.39	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.39	   A^2 -> H(U1(c, d), f(e))
25.51/8.39	   A^2 -> H(U1(c, d), f(k))
25.51/8.39	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.39	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.39	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.39	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.39	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.39	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.39	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.39	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.39	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.39	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.39	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.39	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(d, e), f(c))
25.51/8.39	   A^2 -> H(U1(d, e), f(d))
25.51/8.39	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.39	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.39	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.39	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.39	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.39	   A^2 -> H(U1(d, c), f(e))
25.51/8.39	   A^2 -> H(U1(d, c), f(k))
25.51/8.39	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.39	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.39	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.39	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.39	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.39	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.39	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.39	
25.51/8.39	The TRS R consists of the following rules:
25.51/8.39	
25.51/8.39	   f(x) -> U1(x, x)
25.51/8.39	   U1(e, x) -> x
25.51/8.39	   a -> c
25.51/8.39	   a -> d
25.51/8.39	   b -> c
25.51/8.39	   b -> d
25.51/8.39	   d -> k
25.51/8.39	   c -> e
25.51/8.39	   c -> k
25.51/8.39	
25.51/8.39	Q is empty.
25.51/8.39	We have to consider all minimal (P,Q,R)-chains.
25.51/8.39	----------------------------------------
25.51/8.39	
25.51/8.39	(273) TransformationProof (EQUIVALENT)
25.51/8.39	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.39	
25.51/8.39	   (A^2 -> H(U1(k, a), U1(b, d)),A^2 -> H(U1(k, a), U1(b, d)))
25.51/8.39	   (A^2 -> H(U1(d, c), U1(b, d)),A^2 -> H(U1(d, c), U1(b, d)))
25.51/8.39	   (A^2 -> H(U1(d, d), U1(b, d)),A^2 -> H(U1(d, d), U1(b, d)))
25.51/8.39	   (A^2 -> H(U1(d, a), U1(c, d)),A^2 -> H(U1(d, a), U1(c, d)))
25.51/8.39	   (A^2 -> H(U1(d, a), U1(d, d)),A^2 -> H(U1(d, a), U1(d, d)))
25.51/8.39	   (A^2 -> H(U1(d, a), U1(b, k)),A^2 -> H(U1(d, a), U1(b, k)))
25.51/8.39	
25.51/8.39	
25.51/8.39	----------------------------------------
25.51/8.39	
25.51/8.39	(274)
25.51/8.39	Obligation:
25.51/8.39	Q DP problem:
25.51/8.39	The TRS P consists of the following rules:
25.51/8.39	
25.51/8.39	   H(x, x) -> G(x, x, f(k))
25.51/8.39	   G(d, x, x) -> A^2
25.51/8.39	   A^2 -> H(f(c), f(c))
25.51/8.39	   A^2 -> H(f(d), f(d))
25.51/8.39	   A^2 -> H(U1(d, a), U1(c, c))
25.51/8.39	   A^2 -> H(U1(d, a), f(e))
25.51/8.39	   A^2 -> H(U1(d, a), f(k))
25.51/8.39	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.39	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(a, e), f(c))
25.51/8.39	   A^2 -> H(U1(a, e), f(d))
25.51/8.39	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(a, k), f(c))
25.51/8.39	   A^2 -> H(U1(a, k), f(d))
25.51/8.39	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.39	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.39	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.39	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.39	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.39	   A^2 -> H(U1(a, c), f(e))
25.51/8.39	   A^2 -> H(U1(a, c), f(k))
25.51/8.39	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.39	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.39	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.39	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.39	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.39	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.39	   A^2 -> H(U1(a, d), f(e))
25.51/8.39	   A^2 -> H(U1(a, d), f(k))
25.51/8.39	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.39	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.39	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.39	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.39	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.39	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.39	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.39	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.39	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.39	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.39	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.39	   A^2 -> H(c, f(b))
25.51/8.39	   A^2 -> H(U1(e, k), f(b))
25.51/8.39	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.39	   A^2 -> H(U1(e, c), f(c))
25.51/8.39	   A^2 -> H(U1(e, c), f(d))
25.51/8.39	   A^2 -> H(U1(k, e), f(b))
25.51/8.39	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.39	   A^2 -> H(U1(k, c), f(c))
25.51/8.39	   A^2 -> H(U1(k, c), f(d))
25.51/8.39	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(c, e), f(c))
25.51/8.39	   A^2 -> H(U1(c, e), f(d))
25.51/8.39	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(c, k), f(c))
25.51/8.39	   A^2 -> H(U1(c, k), f(d))
25.51/8.39	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.39	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.39	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.39	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.39	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.39	   A^2 -> H(U1(c, c), f(e))
25.51/8.39	   A^2 -> H(U1(c, c), f(k))
25.51/8.39	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.39	   A^2 -> H(e, f(b))
25.51/8.39	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(e, e), f(c))
25.51/8.39	   A^2 -> H(U1(e, e), f(d))
25.51/8.39	   A^2 -> H(f(e), U1(c, b))
25.51/8.39	   A^2 -> H(f(e), U1(d, b))
25.51/8.39	   A^2 -> H(f(e), U1(b, c))
25.51/8.39	   A^2 -> H(f(e), U1(b, d))
25.51/8.39	   A^2 -> H(f(e), U1(c, c))
25.51/8.39	   A^2 -> H(f(e), f(e))
25.51/8.39	   A^2 -> H(f(e), f(k))
25.51/8.39	   A^2 -> H(f(e), U1(d, d))
25.51/8.39	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(k, k), f(c))
25.51/8.39	   A^2 -> H(U1(k, k), f(d))
25.51/8.39	   A^2 -> H(f(k), U1(c, b))
25.51/8.39	   A^2 -> H(f(k), U1(d, b))
25.51/8.39	   A^2 -> H(f(k), U1(b, c))
25.51/8.39	   A^2 -> H(f(k), U1(b, d))
25.51/8.39	   A^2 -> H(f(k), U1(c, c))
25.51/8.39	   A^2 -> H(f(k), f(e))
25.51/8.39	   A^2 -> H(f(k), f(k))
25.51/8.39	   A^2 -> H(f(k), U1(d, d))
25.51/8.39	   A^2 -> H(f(c), U1(e, b))
25.51/8.39	   A^2 -> H(f(c), U1(k, b))
25.51/8.39	   A^2 -> H(f(c), U1(c, d))
25.51/8.39	   A^2 -> H(f(c), U1(d, c))
25.51/8.39	   A^2 -> H(f(c), U1(b, e))
25.51/8.39	   A^2 -> H(f(c), U1(b, k))
25.51/8.39	   A^2 -> H(f(c), U1(k, d))
25.51/8.39	   A^2 -> H(f(c), U1(d, k))
25.51/8.39	   A^2 -> H(f(c), U1(k, k))
25.51/8.39	   A^2 -> H(U1(k, k), f(b))
25.51/8.39	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.39	   A^2 -> H(U1(k, d), f(c))
25.51/8.39	   A^2 -> H(U1(k, d), f(d))
25.51/8.39	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(d, k), f(c))
25.51/8.39	   A^2 -> H(U1(d, k), f(d))
25.51/8.39	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.39	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.39	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.39	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.39	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.39	   A^2 -> H(U1(d, d), f(e))
25.51/8.39	   A^2 -> H(U1(d, d), f(k))
25.51/8.39	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.39	   A^2 -> H(f(d), U1(e, b))
25.51/8.39	   A^2 -> H(f(d), U1(k, b))
25.51/8.39	   A^2 -> H(f(d), U1(c, d))
25.51/8.39	   A^2 -> H(f(d), U1(d, c))
25.51/8.39	   A^2 -> H(f(d), U1(b, e))
25.51/8.39	   A^2 -> H(f(d), U1(b, k))
25.51/8.39	   A^2 -> H(f(d), U1(e, c))
25.51/8.39	   A^2 -> H(f(d), U1(k, c))
25.51/8.39	   A^2 -> H(f(d), U1(c, e))
25.51/8.39	   A^2 -> H(f(d), U1(c, k))
25.51/8.39	   A^2 -> H(f(d), U1(e, e))
25.51/8.39	   A^2 -> H(f(d), U1(k, k))
25.51/8.39	   A^2 -> H(f(a), b)
25.51/8.39	   A^2 -> H(f(a), U1(e, d))
25.51/8.39	   A^2 -> H(f(a), U1(d, e))
25.51/8.39	   A^2 -> H(f(c), U1(e, c))
25.51/8.39	   A^2 -> H(f(c), U1(k, c))
25.51/8.39	   A^2 -> H(f(c), U1(c, e))
25.51/8.39	   A^2 -> H(f(c), U1(c, k))
25.51/8.39	   A^2 -> H(f(a), c)
25.51/8.39	   A^2 -> H(f(a), U1(e, k))
25.51/8.39	   A^2 -> H(f(a), U1(k, e))
25.51/8.39	   A^2 -> H(f(c), U1(e, e))
25.51/8.39	   A^2 -> H(f(a), e)
25.51/8.39	   A^2 -> H(f(d), U1(k, d))
25.51/8.39	   A^2 -> H(f(d), U1(d, k))
25.51/8.39	   A^2 -> H(f(a), U1(k, k))
25.51/8.39	   A^2 -> H(d, f(b))
25.51/8.39	   A^2 -> H(a, U1(b, b))
25.51/8.39	   A^2 -> H(a, f(c))
25.51/8.39	   A^2 -> H(a, f(d))
25.51/8.39	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.39	   A^2 -> H(U1(e, d), f(c))
25.51/8.39	   A^2 -> H(U1(e, d), f(d))
25.51/8.39	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.39	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.39	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.39	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.39	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.39	   A^2 -> H(U1(e, a), f(e))
25.51/8.39	   A^2 -> H(U1(e, a), f(k))
25.51/8.39	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.39	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.39	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.39	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.39	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.39	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.39	   A^2 -> H(U1(k, a), f(e))
25.51/8.39	   A^2 -> H(U1(k, a), f(k))
25.51/8.39	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.39	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.39	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.39	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.39	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.39	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.39	   A^2 -> H(U1(c, d), f(e))
25.51/8.39	   A^2 -> H(U1(c, d), f(k))
25.51/8.39	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.39	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.39	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.39	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.39	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.39	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.39	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.39	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.39	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.39	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.39	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.39	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(d, e), f(c))
25.51/8.39	   A^2 -> H(U1(d, e), f(d))
25.51/8.39	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.39	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.39	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.39	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.39	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.39	   A^2 -> H(U1(d, c), f(e))
25.51/8.39	   A^2 -> H(U1(d, c), f(k))
25.51/8.39	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.39	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.39	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.39	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.39	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.39	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.39	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.39	
25.51/8.39	The TRS R consists of the following rules:
25.51/8.39	
25.51/8.39	   f(x) -> U1(x, x)
25.51/8.39	   U1(e, x) -> x
25.51/8.39	   a -> c
25.51/8.39	   a -> d
25.51/8.39	   b -> c
25.51/8.39	   b -> d
25.51/8.39	   d -> k
25.51/8.39	   c -> e
25.51/8.39	   c -> k
25.51/8.39	
25.51/8.39	Q is empty.
25.51/8.39	We have to consider all minimal (P,Q,R)-chains.
25.51/8.39	----------------------------------------
25.51/8.39	
25.51/8.39	(275) TransformationProof (EQUIVALENT)
25.51/8.39	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.39	
25.51/8.39	   (A^2 -> H(U1(k, a), U1(c, c)),A^2 -> H(U1(k, a), U1(c, c)))
25.51/8.39	   (A^2 -> H(U1(d, c), U1(c, c)),A^2 -> H(U1(d, c), U1(c, c)))
25.51/8.39	   (A^2 -> H(U1(d, d), U1(c, c)),A^2 -> H(U1(d, d), U1(c, c)))
25.51/8.39	   (A^2 -> H(U1(d, a), U1(e, c)),A^2 -> H(U1(d, a), U1(e, c)))
25.51/8.39	   (A^2 -> H(U1(d, a), U1(k, c)),A^2 -> H(U1(d, a), U1(k, c)))
25.51/8.39	   (A^2 -> H(U1(d, a), U1(c, e)),A^2 -> H(U1(d, a), U1(c, e)))
25.51/8.39	   (A^2 -> H(U1(d, a), U1(c, k)),A^2 -> H(U1(d, a), U1(c, k)))
25.51/8.39	
25.51/8.39	
25.51/8.39	----------------------------------------
25.51/8.39	
25.51/8.39	(276)
25.51/8.39	Obligation:
25.51/8.39	Q DP problem:
25.51/8.39	The TRS P consists of the following rules:
25.51/8.39	
25.51/8.39	   H(x, x) -> G(x, x, f(k))
25.51/8.39	   G(d, x, x) -> A^2
25.51/8.39	   A^2 -> H(f(c), f(c))
25.51/8.39	   A^2 -> H(f(d), f(d))
25.51/8.39	   A^2 -> H(U1(d, a), f(e))
25.51/8.39	   A^2 -> H(U1(d, a), f(k))
25.51/8.39	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.39	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(a, e), f(c))
25.51/8.39	   A^2 -> H(U1(a, e), f(d))
25.51/8.39	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(a, k), f(c))
25.51/8.39	   A^2 -> H(U1(a, k), f(d))
25.51/8.39	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.39	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.39	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.39	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.39	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.39	   A^2 -> H(U1(a, c), f(e))
25.51/8.39	   A^2 -> H(U1(a, c), f(k))
25.51/8.39	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.39	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.39	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.39	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.39	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.39	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.39	   A^2 -> H(U1(a, d), f(e))
25.51/8.39	   A^2 -> H(U1(a, d), f(k))
25.51/8.39	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.39	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.39	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.39	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.39	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.39	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.39	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.39	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.39	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.39	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.39	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.39	   A^2 -> H(c, f(b))
25.51/8.39	   A^2 -> H(U1(e, k), f(b))
25.51/8.39	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.39	   A^2 -> H(U1(e, c), f(c))
25.51/8.39	   A^2 -> H(U1(e, c), f(d))
25.51/8.39	   A^2 -> H(U1(k, e), f(b))
25.51/8.39	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.39	   A^2 -> H(U1(k, c), f(c))
25.51/8.39	   A^2 -> H(U1(k, c), f(d))
25.51/8.39	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(c, e), f(c))
25.51/8.39	   A^2 -> H(U1(c, e), f(d))
25.51/8.39	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(c, k), f(c))
25.51/8.39	   A^2 -> H(U1(c, k), f(d))
25.51/8.39	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.39	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.39	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.39	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.39	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.39	   A^2 -> H(U1(c, c), f(e))
25.51/8.39	   A^2 -> H(U1(c, c), f(k))
25.51/8.39	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.39	   A^2 -> H(e, f(b))
25.51/8.39	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(e, e), f(c))
25.51/8.39	   A^2 -> H(U1(e, e), f(d))
25.51/8.39	   A^2 -> H(f(e), U1(c, b))
25.51/8.39	   A^2 -> H(f(e), U1(d, b))
25.51/8.39	   A^2 -> H(f(e), U1(b, c))
25.51/8.39	   A^2 -> H(f(e), U1(b, d))
25.51/8.39	   A^2 -> H(f(e), U1(c, c))
25.51/8.39	   A^2 -> H(f(e), f(e))
25.51/8.39	   A^2 -> H(f(e), f(k))
25.51/8.39	   A^2 -> H(f(e), U1(d, d))
25.51/8.39	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(k, k), f(c))
25.51/8.39	   A^2 -> H(U1(k, k), f(d))
25.51/8.39	   A^2 -> H(f(k), U1(c, b))
25.51/8.39	   A^2 -> H(f(k), U1(d, b))
25.51/8.39	   A^2 -> H(f(k), U1(b, c))
25.51/8.39	   A^2 -> H(f(k), U1(b, d))
25.51/8.39	   A^2 -> H(f(k), U1(c, c))
25.51/8.39	   A^2 -> H(f(k), f(e))
25.51/8.39	   A^2 -> H(f(k), f(k))
25.51/8.39	   A^2 -> H(f(k), U1(d, d))
25.51/8.39	   A^2 -> H(f(c), U1(e, b))
25.51/8.39	   A^2 -> H(f(c), U1(k, b))
25.51/8.39	   A^2 -> H(f(c), U1(c, d))
25.51/8.39	   A^2 -> H(f(c), U1(d, c))
25.51/8.39	   A^2 -> H(f(c), U1(b, e))
25.51/8.39	   A^2 -> H(f(c), U1(b, k))
25.51/8.39	   A^2 -> H(f(c), U1(k, d))
25.51/8.39	   A^2 -> H(f(c), U1(d, k))
25.51/8.39	   A^2 -> H(f(c), U1(k, k))
25.51/8.39	   A^2 -> H(U1(k, k), f(b))
25.51/8.39	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.39	   A^2 -> H(U1(k, d), f(c))
25.51/8.39	   A^2 -> H(U1(k, d), f(d))
25.51/8.39	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(d, k), f(c))
25.51/8.39	   A^2 -> H(U1(d, k), f(d))
25.51/8.39	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.39	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.39	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.39	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.39	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.39	   A^2 -> H(U1(d, d), f(e))
25.51/8.39	   A^2 -> H(U1(d, d), f(k))
25.51/8.39	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.39	   A^2 -> H(f(d), U1(e, b))
25.51/8.39	   A^2 -> H(f(d), U1(k, b))
25.51/8.39	   A^2 -> H(f(d), U1(c, d))
25.51/8.39	   A^2 -> H(f(d), U1(d, c))
25.51/8.39	   A^2 -> H(f(d), U1(b, e))
25.51/8.39	   A^2 -> H(f(d), U1(b, k))
25.51/8.39	   A^2 -> H(f(d), U1(e, c))
25.51/8.39	   A^2 -> H(f(d), U1(k, c))
25.51/8.39	   A^2 -> H(f(d), U1(c, e))
25.51/8.39	   A^2 -> H(f(d), U1(c, k))
25.51/8.39	   A^2 -> H(f(d), U1(e, e))
25.51/8.39	   A^2 -> H(f(d), U1(k, k))
25.51/8.39	   A^2 -> H(f(a), b)
25.51/8.39	   A^2 -> H(f(a), U1(e, d))
25.51/8.39	   A^2 -> H(f(a), U1(d, e))
25.51/8.39	   A^2 -> H(f(c), U1(e, c))
25.51/8.39	   A^2 -> H(f(c), U1(k, c))
25.51/8.39	   A^2 -> H(f(c), U1(c, e))
25.51/8.39	   A^2 -> H(f(c), U1(c, k))
25.51/8.39	   A^2 -> H(f(a), c)
25.51/8.39	   A^2 -> H(f(a), U1(e, k))
25.51/8.39	   A^2 -> H(f(a), U1(k, e))
25.51/8.39	   A^2 -> H(f(c), U1(e, e))
25.51/8.39	   A^2 -> H(f(a), e)
25.51/8.39	   A^2 -> H(f(d), U1(k, d))
25.51/8.39	   A^2 -> H(f(d), U1(d, k))
25.51/8.39	   A^2 -> H(f(a), U1(k, k))
25.51/8.39	   A^2 -> H(d, f(b))
25.51/8.39	   A^2 -> H(a, U1(b, b))
25.51/8.39	   A^2 -> H(a, f(c))
25.51/8.39	   A^2 -> H(a, f(d))
25.51/8.39	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.39	   A^2 -> H(U1(e, d), f(c))
25.51/8.39	   A^2 -> H(U1(e, d), f(d))
25.51/8.39	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.39	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.39	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.39	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.39	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.39	   A^2 -> H(U1(e, a), f(e))
25.51/8.39	   A^2 -> H(U1(e, a), f(k))
25.51/8.39	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.39	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.39	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.39	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.39	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.39	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.39	   A^2 -> H(U1(k, a), f(e))
25.51/8.39	   A^2 -> H(U1(k, a), f(k))
25.51/8.39	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.39	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.39	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.39	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.39	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.39	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.39	   A^2 -> H(U1(c, d), f(e))
25.51/8.39	   A^2 -> H(U1(c, d), f(k))
25.51/8.39	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.39	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.39	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.39	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.39	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.39	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.39	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.39	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.39	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.39	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.39	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.39	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(d, e), f(c))
25.51/8.39	   A^2 -> H(U1(d, e), f(d))
25.51/8.39	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.39	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.39	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.39	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.39	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.39	   A^2 -> H(U1(d, c), f(e))
25.51/8.39	   A^2 -> H(U1(d, c), f(k))
25.51/8.39	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.39	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.39	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.39	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.39	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.39	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.39	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.39	   A^2 -> H(U1(d, a), U1(e, c))
25.51/8.39	   A^2 -> H(U1(d, a), U1(k, c))
25.51/8.39	   A^2 -> H(U1(d, a), U1(c, e))
25.51/8.39	   A^2 -> H(U1(d, a), U1(c, k))
25.51/8.39	
25.51/8.39	The TRS R consists of the following rules:
25.51/8.39	
25.51/8.39	   f(x) -> U1(x, x)
25.51/8.39	   U1(e, x) -> x
25.51/8.39	   a -> c
25.51/8.39	   a -> d
25.51/8.39	   b -> c
25.51/8.39	   b -> d
25.51/8.39	   d -> k
25.51/8.39	   c -> e
25.51/8.39	   c -> k
25.51/8.39	
25.51/8.39	Q is empty.
25.51/8.39	We have to consider all minimal (P,Q,R)-chains.
25.51/8.39	----------------------------------------
25.51/8.39	
25.51/8.39	(277) TransformationProof (EQUIVALENT)
25.51/8.39	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), f(e)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.39	
25.51/8.39	   (A^2 -> H(U1(k, a), f(e)),A^2 -> H(U1(k, a), f(e)))
25.51/8.39	   (A^2 -> H(U1(d, c), f(e)),A^2 -> H(U1(d, c), f(e)))
25.51/8.39	   (A^2 -> H(U1(d, d), f(e)),A^2 -> H(U1(d, d), f(e)))
25.51/8.39	   (A^2 -> H(U1(d, a), U1(e, e)),A^2 -> H(U1(d, a), U1(e, e)))
25.51/8.39	
25.51/8.39	
25.51/8.39	----------------------------------------
25.51/8.39	
25.51/8.39	(278)
25.51/8.39	Obligation:
25.51/8.39	Q DP problem:
25.51/8.39	The TRS P consists of the following rules:
25.51/8.39	
25.51/8.39	   H(x, x) -> G(x, x, f(k))
25.51/8.39	   G(d, x, x) -> A^2
25.51/8.39	   A^2 -> H(f(c), f(c))
25.51/8.39	   A^2 -> H(f(d), f(d))
25.51/8.39	   A^2 -> H(U1(d, a), f(k))
25.51/8.39	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.39	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(a, e), f(c))
25.51/8.39	   A^2 -> H(U1(a, e), f(d))
25.51/8.39	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(a, k), f(c))
25.51/8.39	   A^2 -> H(U1(a, k), f(d))
25.51/8.39	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.39	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.39	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.39	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.39	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.39	   A^2 -> H(U1(a, c), f(e))
25.51/8.39	   A^2 -> H(U1(a, c), f(k))
25.51/8.39	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.39	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.39	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.39	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.39	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.39	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.39	   A^2 -> H(U1(a, d), f(e))
25.51/8.39	   A^2 -> H(U1(a, d), f(k))
25.51/8.39	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.39	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.39	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.39	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.39	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.39	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.39	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.39	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.39	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.39	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.39	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.39	   A^2 -> H(c, f(b))
25.51/8.39	   A^2 -> H(U1(e, k), f(b))
25.51/8.39	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.39	   A^2 -> H(U1(e, c), f(c))
25.51/8.39	   A^2 -> H(U1(e, c), f(d))
25.51/8.39	   A^2 -> H(U1(k, e), f(b))
25.51/8.39	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.39	   A^2 -> H(U1(k, c), f(c))
25.51/8.39	   A^2 -> H(U1(k, c), f(d))
25.51/8.39	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(c, e), f(c))
25.51/8.39	   A^2 -> H(U1(c, e), f(d))
25.51/8.39	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(c, k), f(c))
25.51/8.39	   A^2 -> H(U1(c, k), f(d))
25.51/8.39	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.39	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.39	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.39	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.39	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.39	   A^2 -> H(U1(c, c), f(e))
25.51/8.39	   A^2 -> H(U1(c, c), f(k))
25.51/8.39	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.39	   A^2 -> H(e, f(b))
25.51/8.39	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(e, e), f(c))
25.51/8.39	   A^2 -> H(U1(e, e), f(d))
25.51/8.39	   A^2 -> H(f(e), U1(c, b))
25.51/8.39	   A^2 -> H(f(e), U1(d, b))
25.51/8.39	   A^2 -> H(f(e), U1(b, c))
25.51/8.39	   A^2 -> H(f(e), U1(b, d))
25.51/8.39	   A^2 -> H(f(e), U1(c, c))
25.51/8.39	   A^2 -> H(f(e), f(e))
25.51/8.39	   A^2 -> H(f(e), f(k))
25.51/8.39	   A^2 -> H(f(e), U1(d, d))
25.51/8.39	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(k, k), f(c))
25.51/8.39	   A^2 -> H(U1(k, k), f(d))
25.51/8.39	   A^2 -> H(f(k), U1(c, b))
25.51/8.39	   A^2 -> H(f(k), U1(d, b))
25.51/8.39	   A^2 -> H(f(k), U1(b, c))
25.51/8.39	   A^2 -> H(f(k), U1(b, d))
25.51/8.39	   A^2 -> H(f(k), U1(c, c))
25.51/8.39	   A^2 -> H(f(k), f(e))
25.51/8.39	   A^2 -> H(f(k), f(k))
25.51/8.39	   A^2 -> H(f(k), U1(d, d))
25.51/8.39	   A^2 -> H(f(c), U1(e, b))
25.51/8.39	   A^2 -> H(f(c), U1(k, b))
25.51/8.39	   A^2 -> H(f(c), U1(c, d))
25.51/8.39	   A^2 -> H(f(c), U1(d, c))
25.51/8.39	   A^2 -> H(f(c), U1(b, e))
25.51/8.39	   A^2 -> H(f(c), U1(b, k))
25.51/8.39	   A^2 -> H(f(c), U1(k, d))
25.51/8.39	   A^2 -> H(f(c), U1(d, k))
25.51/8.39	   A^2 -> H(f(c), U1(k, k))
25.51/8.39	   A^2 -> H(U1(k, k), f(b))
25.51/8.39	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.39	   A^2 -> H(U1(k, d), f(c))
25.51/8.39	   A^2 -> H(U1(k, d), f(d))
25.51/8.39	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(d, k), f(c))
25.51/8.39	   A^2 -> H(U1(d, k), f(d))
25.51/8.39	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.39	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.39	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.39	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.39	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.39	   A^2 -> H(U1(d, d), f(e))
25.51/8.39	   A^2 -> H(U1(d, d), f(k))
25.51/8.39	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.39	   A^2 -> H(f(d), U1(e, b))
25.51/8.39	   A^2 -> H(f(d), U1(k, b))
25.51/8.39	   A^2 -> H(f(d), U1(c, d))
25.51/8.39	   A^2 -> H(f(d), U1(d, c))
25.51/8.39	   A^2 -> H(f(d), U1(b, e))
25.51/8.39	   A^2 -> H(f(d), U1(b, k))
25.51/8.39	   A^2 -> H(f(d), U1(e, c))
25.51/8.39	   A^2 -> H(f(d), U1(k, c))
25.51/8.39	   A^2 -> H(f(d), U1(c, e))
25.51/8.39	   A^2 -> H(f(d), U1(c, k))
25.51/8.39	   A^2 -> H(f(d), U1(e, e))
25.51/8.39	   A^2 -> H(f(d), U1(k, k))
25.51/8.39	   A^2 -> H(f(a), b)
25.51/8.39	   A^2 -> H(f(a), U1(e, d))
25.51/8.39	   A^2 -> H(f(a), U1(d, e))
25.51/8.39	   A^2 -> H(f(c), U1(e, c))
25.51/8.39	   A^2 -> H(f(c), U1(k, c))
25.51/8.39	   A^2 -> H(f(c), U1(c, e))
25.51/8.39	   A^2 -> H(f(c), U1(c, k))
25.51/8.39	   A^2 -> H(f(a), c)
25.51/8.39	   A^2 -> H(f(a), U1(e, k))
25.51/8.39	   A^2 -> H(f(a), U1(k, e))
25.51/8.39	   A^2 -> H(f(c), U1(e, e))
25.51/8.39	   A^2 -> H(f(a), e)
25.51/8.39	   A^2 -> H(f(d), U1(k, d))
25.51/8.39	   A^2 -> H(f(d), U1(d, k))
25.51/8.39	   A^2 -> H(f(a), U1(k, k))
25.51/8.39	   A^2 -> H(d, f(b))
25.51/8.39	   A^2 -> H(a, U1(b, b))
25.51/8.39	   A^2 -> H(a, f(c))
25.51/8.39	   A^2 -> H(a, f(d))
25.51/8.39	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.39	   A^2 -> H(U1(e, d), f(c))
25.51/8.39	   A^2 -> H(U1(e, d), f(d))
25.51/8.39	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.39	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.39	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.39	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.39	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.39	   A^2 -> H(U1(e, a), f(e))
25.51/8.39	   A^2 -> H(U1(e, a), f(k))
25.51/8.39	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.39	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.39	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.39	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.39	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.39	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.39	   A^2 -> H(U1(k, a), f(e))
25.51/8.39	   A^2 -> H(U1(k, a), f(k))
25.51/8.39	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.39	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.39	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.39	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.39	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.39	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.39	   A^2 -> H(U1(c, d), f(e))
25.51/8.39	   A^2 -> H(U1(c, d), f(k))
25.51/8.39	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.39	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.39	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.39	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.39	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.39	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.39	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.39	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.39	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.39	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.39	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.39	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.39	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(d, e), f(c))
25.51/8.39	   A^2 -> H(U1(d, e), f(d))
25.51/8.39	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.39	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.39	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.39	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.39	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.39	   A^2 -> H(U1(d, c), f(e))
25.51/8.39	   A^2 -> H(U1(d, c), f(k))
25.51/8.39	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.39	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.39	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.39	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.39	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.39	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.39	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.39	   A^2 -> H(U1(d, a), U1(e, c))
25.51/8.39	   A^2 -> H(U1(d, a), U1(k, c))
25.51/8.39	   A^2 -> H(U1(d, a), U1(c, e))
25.51/8.39	   A^2 -> H(U1(d, a), U1(c, k))
25.51/8.39	   A^2 -> H(U1(d, a), U1(e, e))
25.51/8.39	
25.51/8.39	The TRS R consists of the following rules:
25.51/8.39	
25.51/8.39	   f(x) -> U1(x, x)
25.51/8.39	   U1(e, x) -> x
25.51/8.39	   a -> c
25.51/8.39	   a -> d
25.51/8.39	   b -> c
25.51/8.39	   b -> d
25.51/8.39	   d -> k
25.51/8.39	   c -> e
25.51/8.39	   c -> k
25.51/8.39	
25.51/8.39	Q is empty.
25.51/8.39	We have to consider all minimal (P,Q,R)-chains.
25.51/8.39	----------------------------------------
25.51/8.39	
25.51/8.39	(279) TransformationProof (EQUIVALENT)
25.51/8.39	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), f(k)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.39	
25.51/8.39	   (A^2 -> H(U1(k, a), f(k)),A^2 -> H(U1(k, a), f(k)))
25.51/8.39	   (A^2 -> H(U1(d, c), f(k)),A^2 -> H(U1(d, c), f(k)))
25.51/8.39	   (A^2 -> H(U1(d, d), f(k)),A^2 -> H(U1(d, d), f(k)))
25.51/8.39	   (A^2 -> H(U1(d, a), U1(k, k)),A^2 -> H(U1(d, a), U1(k, k)))
25.51/8.39	
25.51/8.39	
25.51/8.39	----------------------------------------
25.51/8.39	
25.51/8.39	(280)
25.51/8.39	Obligation:
25.51/8.39	Q DP problem:
25.51/8.39	The TRS P consists of the following rules:
25.51/8.39	
25.51/8.39	   H(x, x) -> G(x, x, f(k))
25.51/8.39	   G(d, x, x) -> A^2
25.51/8.39	   A^2 -> H(f(c), f(c))
25.51/8.39	   A^2 -> H(f(d), f(d))
25.51/8.39	   A^2 -> H(U1(d, a), U1(d, d))
25.51/8.39	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(a, e), f(c))
25.51/8.39	   A^2 -> H(U1(a, e), f(d))
25.51/8.39	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(a, k), f(c))
25.51/8.39	   A^2 -> H(U1(a, k), f(d))
25.51/8.39	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.39	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.39	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.39	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.39	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.39	   A^2 -> H(U1(a, c), f(e))
25.51/8.39	   A^2 -> H(U1(a, c), f(k))
25.51/8.39	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.39	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.39	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.39	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.39	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.39	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.39	   A^2 -> H(U1(a, d), f(e))
25.51/8.39	   A^2 -> H(U1(a, d), f(k))
25.51/8.39	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.39	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.39	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.39	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.39	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.39	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.39	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.39	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.39	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.39	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.39	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.39	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.39	   A^2 -> H(c, f(b))
25.51/8.39	   A^2 -> H(U1(e, k), f(b))
25.51/8.39	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.39	   A^2 -> H(U1(e, c), f(c))
25.51/8.39	   A^2 -> H(U1(e, c), f(d))
25.51/8.39	   A^2 -> H(U1(k, e), f(b))
25.51/8.39	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.39	   A^2 -> H(U1(k, c), f(c))
25.51/8.39	   A^2 -> H(U1(k, c), f(d))
25.51/8.39	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(c, e), f(c))
25.51/8.39	   A^2 -> H(U1(c, e), f(d))
25.51/8.39	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(c, k), f(c))
25.51/8.39	   A^2 -> H(U1(c, k), f(d))
25.51/8.39	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.39	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.39	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.39	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.39	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.39	   A^2 -> H(U1(c, c), f(e))
25.51/8.39	   A^2 -> H(U1(c, c), f(k))
25.51/8.39	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.39	   A^2 -> H(e, f(b))
25.51/8.39	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.39	   A^2 -> H(U1(e, e), f(c))
25.51/8.39	   A^2 -> H(U1(e, e), f(d))
25.51/8.39	   A^2 -> H(f(e), U1(c, b))
25.51/8.39	   A^2 -> H(f(e), U1(d, b))
25.51/8.39	   A^2 -> H(f(e), U1(b, c))
25.51/8.39	   A^2 -> H(f(e), U1(b, d))
25.51/8.39	   A^2 -> H(f(e), U1(c, c))
25.51/8.39	   A^2 -> H(f(e), f(e))
25.51/8.39	   A^2 -> H(f(e), f(k))
25.51/8.39	   A^2 -> H(f(e), U1(d, d))
25.51/8.39	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(k, k), f(c))
25.51/8.39	   A^2 -> H(U1(k, k), f(d))
25.51/8.39	   A^2 -> H(f(k), U1(c, b))
25.51/8.39	   A^2 -> H(f(k), U1(d, b))
25.51/8.39	   A^2 -> H(f(k), U1(b, c))
25.51/8.39	   A^2 -> H(f(k), U1(b, d))
25.51/8.39	   A^2 -> H(f(k), U1(c, c))
25.51/8.39	   A^2 -> H(f(k), f(e))
25.51/8.39	   A^2 -> H(f(k), f(k))
25.51/8.39	   A^2 -> H(f(k), U1(d, d))
25.51/8.39	   A^2 -> H(f(c), U1(e, b))
25.51/8.39	   A^2 -> H(f(c), U1(k, b))
25.51/8.39	   A^2 -> H(f(c), U1(c, d))
25.51/8.39	   A^2 -> H(f(c), U1(d, c))
25.51/8.39	   A^2 -> H(f(c), U1(b, e))
25.51/8.39	   A^2 -> H(f(c), U1(b, k))
25.51/8.39	   A^2 -> H(f(c), U1(k, d))
25.51/8.39	   A^2 -> H(f(c), U1(d, k))
25.51/8.39	   A^2 -> H(f(c), U1(k, k))
25.51/8.39	   A^2 -> H(U1(k, k), f(b))
25.51/8.39	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.39	   A^2 -> H(U1(k, d), f(c))
25.51/8.39	   A^2 -> H(U1(k, d), f(d))
25.51/8.39	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.39	   A^2 -> H(U1(d, k), f(c))
25.51/8.39	   A^2 -> H(U1(d, k), f(d))
25.51/8.39	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.39	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.39	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.39	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.39	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.39	   A^2 -> H(U1(d, d), f(e))
25.51/8.39	   A^2 -> H(U1(d, d), f(k))
25.51/8.39	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.39	   A^2 -> H(f(d), U1(e, b))
25.51/8.39	   A^2 -> H(f(d), U1(k, b))
25.51/8.39	   A^2 -> H(f(d), U1(c, d))
25.51/8.39	   A^2 -> H(f(d), U1(d, c))
25.51/8.39	   A^2 -> H(f(d), U1(b, e))
25.51/8.39	   A^2 -> H(f(d), U1(b, k))
25.51/8.39	   A^2 -> H(f(d), U1(e, c))
25.51/8.39	   A^2 -> H(f(d), U1(k, c))
25.51/8.39	   A^2 -> H(f(d), U1(c, e))
25.51/8.39	   A^2 -> H(f(d), U1(c, k))
25.51/8.39	   A^2 -> H(f(d), U1(e, e))
25.51/8.39	   A^2 -> H(f(d), U1(k, k))
25.51/8.39	   A^2 -> H(f(a), b)
25.51/8.39	   A^2 -> H(f(a), U1(e, d))
25.51/8.39	   A^2 -> H(f(a), U1(d, e))
25.51/8.39	   A^2 -> H(f(c), U1(e, c))
25.51/8.39	   A^2 -> H(f(c), U1(k, c))
25.51/8.39	   A^2 -> H(f(c), U1(c, e))
25.51/8.39	   A^2 -> H(f(c), U1(c, k))
25.51/8.39	   A^2 -> H(f(a), c)
25.51/8.39	   A^2 -> H(f(a), U1(e, k))
25.51/8.39	   A^2 -> H(f(a), U1(k, e))
25.51/8.39	   A^2 -> H(f(c), U1(e, e))
25.51/8.39	   A^2 -> H(f(a), e)
25.51/8.39	   A^2 -> H(f(d), U1(k, d))
25.51/8.39	   A^2 -> H(f(d), U1(d, k))
25.51/8.39	   A^2 -> H(f(a), U1(k, k))
25.51/8.39	   A^2 -> H(d, f(b))
25.51/8.39	   A^2 -> H(a, U1(b, b))
25.51/8.39	   A^2 -> H(a, f(c))
25.51/8.39	   A^2 -> H(a, f(d))
25.51/8.39	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.39	   A^2 -> H(U1(e, d), f(c))
25.51/8.39	   A^2 -> H(U1(e, d), f(d))
25.51/8.39	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.39	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.39	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.39	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.39	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.39	   A^2 -> H(U1(e, a), f(e))
25.51/8.39	   A^2 -> H(U1(e, a), f(k))
25.51/8.39	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.39	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.39	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.39	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.40	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.40	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.40	   A^2 -> H(U1(k, a), f(e))
25.51/8.40	   A^2 -> H(U1(k, a), f(k))
25.51/8.40	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.40	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.40	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.40	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.40	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.40	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.40	   A^2 -> H(U1(c, d), f(e))
25.51/8.40	   A^2 -> H(U1(c, d), f(k))
25.51/8.40	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.40	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.40	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.40	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.40	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.40	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.40	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.40	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.40	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.40	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.40	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.40	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.40	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.40	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.40	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.40	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.40	   A^2 -> H(U1(d, e), f(c))
25.51/8.40	   A^2 -> H(U1(d, e), f(d))
25.51/8.40	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.40	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.40	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.40	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.40	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.40	   A^2 -> H(U1(d, c), f(e))
25.51/8.40	   A^2 -> H(U1(d, c), f(k))
25.51/8.40	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.40	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.40	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.40	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.40	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.40	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.40	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.40	   A^2 -> H(U1(d, a), U1(e, c))
25.51/8.40	   A^2 -> H(U1(d, a), U1(k, c))
25.51/8.40	   A^2 -> H(U1(d, a), U1(c, e))
25.51/8.40	   A^2 -> H(U1(d, a), U1(c, k))
25.51/8.40	   A^2 -> H(U1(d, a), U1(e, e))
25.51/8.40	   A^2 -> H(U1(d, a), U1(k, k))
25.51/8.40	
25.51/8.40	The TRS R consists of the following rules:
25.51/8.40	
25.51/8.40	   f(x) -> U1(x, x)
25.51/8.40	   U1(e, x) -> x
25.51/8.40	   a -> c
25.51/8.40	   a -> d
25.51/8.40	   b -> c
25.51/8.40	   b -> d
25.51/8.40	   d -> k
25.51/8.40	   c -> e
25.51/8.40	   c -> k
25.51/8.40	
25.51/8.40	Q is empty.
25.51/8.40	We have to consider all minimal (P,Q,R)-chains.
25.51/8.40	----------------------------------------
25.51/8.40	
25.51/8.40	(281) TransformationProof (EQUIVALENT)
25.51/8.40	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.40	
25.51/8.40	   (A^2 -> H(U1(k, a), U1(d, d)),A^2 -> H(U1(k, a), U1(d, d)))
25.51/8.40	   (A^2 -> H(U1(d, c), U1(d, d)),A^2 -> H(U1(d, c), U1(d, d)))
25.51/8.40	   (A^2 -> H(U1(d, d), U1(d, d)),A^2 -> H(U1(d, d), U1(d, d)))
25.51/8.40	   (A^2 -> H(U1(d, a), U1(k, d)),A^2 -> H(U1(d, a), U1(k, d)))
25.51/8.40	   (A^2 -> H(U1(d, a), U1(d, k)),A^2 -> H(U1(d, a), U1(d, k)))
25.51/8.40	
25.51/8.40	
25.51/8.40	----------------------------------------
25.51/8.40	
25.51/8.40	(282)
25.51/8.40	Obligation:
25.51/8.40	Q DP problem:
25.51/8.40	The TRS P consists of the following rules:
25.51/8.40	
25.51/8.40	   H(x, x) -> G(x, x, f(k))
25.51/8.40	   G(d, x, x) -> A^2
25.51/8.40	   A^2 -> H(f(c), f(c))
25.51/8.40	   A^2 -> H(f(d), f(d))
25.51/8.40	   A^2 -> H(U1(a, e), U1(b, b))
25.51/8.40	   A^2 -> H(U1(a, e), f(c))
25.51/8.40	   A^2 -> H(U1(a, e), f(d))
25.51/8.40	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.40	   A^2 -> H(U1(a, k), f(c))
25.51/8.40	   A^2 -> H(U1(a, k), f(d))
25.51/8.40	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.40	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.40	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.40	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.40	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.40	   A^2 -> H(U1(a, c), f(e))
25.51/8.40	   A^2 -> H(U1(a, c), f(k))
25.51/8.40	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.40	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.40	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.40	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.40	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.40	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.40	   A^2 -> H(U1(a, d), f(e))
25.51/8.40	   A^2 -> H(U1(a, d), f(k))
25.51/8.40	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.40	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.40	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.40	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.40	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.40	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.40	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.40	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.40	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.40	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.40	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.40	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.40	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.40	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.40	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.40	   A^2 -> H(c, f(b))
25.51/8.40	   A^2 -> H(U1(e, k), f(b))
25.51/8.40	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.40	   A^2 -> H(U1(e, c), f(c))
25.51/8.40	   A^2 -> H(U1(e, c), f(d))
25.51/8.40	   A^2 -> H(U1(k, e), f(b))
25.51/8.40	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.40	   A^2 -> H(U1(k, c), f(c))
25.51/8.40	   A^2 -> H(U1(k, c), f(d))
25.51/8.40	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.40	   A^2 -> H(U1(c, e), f(c))
25.51/8.40	   A^2 -> H(U1(c, e), f(d))
25.51/8.40	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.40	   A^2 -> H(U1(c, k), f(c))
25.51/8.40	   A^2 -> H(U1(c, k), f(d))
25.51/8.40	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.40	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.40	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.40	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.40	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.40	   A^2 -> H(U1(c, c), f(e))
25.51/8.40	   A^2 -> H(U1(c, c), f(k))
25.51/8.40	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.40	   A^2 -> H(e, f(b))
25.51/8.40	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.40	   A^2 -> H(U1(e, e), f(c))
25.51/8.40	   A^2 -> H(U1(e, e), f(d))
25.51/8.40	   A^2 -> H(f(e), U1(c, b))
25.51/8.40	   A^2 -> H(f(e), U1(d, b))
25.51/8.40	   A^2 -> H(f(e), U1(b, c))
25.51/8.40	   A^2 -> H(f(e), U1(b, d))
25.51/8.40	   A^2 -> H(f(e), U1(c, c))
25.51/8.40	   A^2 -> H(f(e), f(e))
25.51/8.40	   A^2 -> H(f(e), f(k))
25.51/8.40	   A^2 -> H(f(e), U1(d, d))
25.51/8.40	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.40	   A^2 -> H(U1(k, k), f(c))
25.51/8.40	   A^2 -> H(U1(k, k), f(d))
25.51/8.40	   A^2 -> H(f(k), U1(c, b))
25.51/8.40	   A^2 -> H(f(k), U1(d, b))
25.51/8.40	   A^2 -> H(f(k), U1(b, c))
25.51/8.40	   A^2 -> H(f(k), U1(b, d))
25.51/8.40	   A^2 -> H(f(k), U1(c, c))
25.51/8.40	   A^2 -> H(f(k), f(e))
25.51/8.40	   A^2 -> H(f(k), f(k))
25.51/8.40	   A^2 -> H(f(k), U1(d, d))
25.51/8.40	   A^2 -> H(f(c), U1(e, b))
25.51/8.40	   A^2 -> H(f(c), U1(k, b))
25.51/8.40	   A^2 -> H(f(c), U1(c, d))
25.51/8.40	   A^2 -> H(f(c), U1(d, c))
25.51/8.40	   A^2 -> H(f(c), U1(b, e))
25.51/8.40	   A^2 -> H(f(c), U1(b, k))
25.51/8.40	   A^2 -> H(f(c), U1(k, d))
25.51/8.40	   A^2 -> H(f(c), U1(d, k))
25.51/8.40	   A^2 -> H(f(c), U1(k, k))
25.51/8.40	   A^2 -> H(U1(k, k), f(b))
25.51/8.40	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.40	   A^2 -> H(U1(k, d), f(c))
25.51/8.40	   A^2 -> H(U1(k, d), f(d))
25.51/8.40	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.40	   A^2 -> H(U1(d, k), f(c))
25.51/8.40	   A^2 -> H(U1(d, k), f(d))
25.51/8.40	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.40	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.40	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.40	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.40	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.40	   A^2 -> H(U1(d, d), f(e))
25.51/8.40	   A^2 -> H(U1(d, d), f(k))
25.51/8.40	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.40	   A^2 -> H(f(d), U1(e, b))
25.51/8.40	   A^2 -> H(f(d), U1(k, b))
25.51/8.40	   A^2 -> H(f(d), U1(c, d))
25.51/8.40	   A^2 -> H(f(d), U1(d, c))
25.51/8.40	   A^2 -> H(f(d), U1(b, e))
25.51/8.40	   A^2 -> H(f(d), U1(b, k))
25.51/8.40	   A^2 -> H(f(d), U1(e, c))
25.51/8.40	   A^2 -> H(f(d), U1(k, c))
25.51/8.40	   A^2 -> H(f(d), U1(c, e))
25.51/8.40	   A^2 -> H(f(d), U1(c, k))
25.51/8.40	   A^2 -> H(f(d), U1(e, e))
25.51/8.40	   A^2 -> H(f(d), U1(k, k))
25.51/8.40	   A^2 -> H(f(a), b)
25.51/8.40	   A^2 -> H(f(a), U1(e, d))
25.51/8.40	   A^2 -> H(f(a), U1(d, e))
25.51/8.40	   A^2 -> H(f(c), U1(e, c))
25.51/8.40	   A^2 -> H(f(c), U1(k, c))
25.51/8.40	   A^2 -> H(f(c), U1(c, e))
25.51/8.40	   A^2 -> H(f(c), U1(c, k))
25.51/8.40	   A^2 -> H(f(a), c)
25.51/8.40	   A^2 -> H(f(a), U1(e, k))
25.51/8.40	   A^2 -> H(f(a), U1(k, e))
25.51/8.40	   A^2 -> H(f(c), U1(e, e))
25.51/8.40	   A^2 -> H(f(a), e)
25.51/8.40	   A^2 -> H(f(d), U1(k, d))
25.51/8.40	   A^2 -> H(f(d), U1(d, k))
25.51/8.40	   A^2 -> H(f(a), U1(k, k))
25.51/8.40	   A^2 -> H(d, f(b))
25.51/8.40	   A^2 -> H(a, U1(b, b))
25.51/8.40	   A^2 -> H(a, f(c))
25.51/8.40	   A^2 -> H(a, f(d))
25.51/8.40	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.40	   A^2 -> H(U1(e, d), f(c))
25.51/8.40	   A^2 -> H(U1(e, d), f(d))
25.51/8.40	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.40	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.40	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.40	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.40	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.40	   A^2 -> H(U1(e, a), f(e))
25.51/8.40	   A^2 -> H(U1(e, a), f(k))
25.51/8.40	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.40	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.40	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.40	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.40	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.40	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.40	   A^2 -> H(U1(k, a), f(e))
25.51/8.40	   A^2 -> H(U1(k, a), f(k))
25.51/8.40	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.40	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.40	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.40	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.40	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.40	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.40	   A^2 -> H(U1(c, d), f(e))
25.51/8.40	   A^2 -> H(U1(c, d), f(k))
25.51/8.40	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.40	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.40	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.40	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.40	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.40	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.40	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.40	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.40	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.40	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.40	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.40	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.40	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.40	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.40	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.40	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.40	   A^2 -> H(U1(d, e), f(c))
25.51/8.40	   A^2 -> H(U1(d, e), f(d))
25.51/8.40	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.40	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.40	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.40	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.40	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.40	   A^2 -> H(U1(d, c), f(e))
25.51/8.40	   A^2 -> H(U1(d, c), f(k))
25.51/8.40	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.40	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.40	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.40	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.40	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(d, k))
25.51/8.41	
25.51/8.41	The TRS R consists of the following rules:
25.51/8.41	
25.51/8.41	   f(x) -> U1(x, x)
25.51/8.41	   U1(e, x) -> x
25.51/8.41	   a -> c
25.51/8.41	   a -> d
25.51/8.41	   b -> c
25.51/8.41	   b -> d
25.51/8.41	   d -> k
25.51/8.41	   c -> e
25.51/8.41	   c -> k
25.51/8.41	
25.51/8.41	Q is empty.
25.51/8.41	We have to consider all minimal (P,Q,R)-chains.
25.51/8.41	----------------------------------------
25.51/8.41	
25.51/8.41	(283) TransformationProof (EQUIVALENT)
25.51/8.41	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.41	
25.51/8.41	   (A^2 -> H(U1(c, e), U1(b, b)),A^2 -> H(U1(c, e), U1(b, b)))
25.51/8.41	   (A^2 -> H(U1(d, e), U1(b, b)),A^2 -> H(U1(d, e), U1(b, b)))
25.51/8.41	   (A^2 -> H(U1(a, e), U1(c, b)),A^2 -> H(U1(a, e), U1(c, b)))
25.51/8.41	   (A^2 -> H(U1(a, e), U1(d, b)),A^2 -> H(U1(a, e), U1(d, b)))
25.51/8.41	   (A^2 -> H(U1(a, e), U1(b, c)),A^2 -> H(U1(a, e), U1(b, c)))
25.51/8.41	   (A^2 -> H(U1(a, e), U1(b, d)),A^2 -> H(U1(a, e), U1(b, d)))
25.51/8.41	
25.51/8.41	
25.51/8.41	----------------------------------------
25.51/8.41	
25.51/8.41	(284)
25.51/8.41	Obligation:
25.51/8.41	Q DP problem:
25.51/8.41	The TRS P consists of the following rules:
25.51/8.41	
25.51/8.41	   H(x, x) -> G(x, x, f(k))
25.51/8.41	   G(d, x, x) -> A^2
25.51/8.41	   A^2 -> H(f(c), f(c))
25.51/8.41	   A^2 -> H(f(d), f(d))
25.51/8.41	   A^2 -> H(U1(a, e), f(c))
25.51/8.41	   A^2 -> H(U1(a, e), f(d))
25.51/8.41	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(a, k), f(c))
25.51/8.41	   A^2 -> H(U1(a, k), f(d))
25.51/8.41	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, c), f(e))
25.51/8.41	   A^2 -> H(U1(a, c), f(k))
25.51/8.41	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.41	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, d), f(e))
25.51/8.41	   A^2 -> H(U1(a, d), f(k))
25.51/8.41	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.41	   A^2 -> H(c, f(b))
25.51/8.41	   A^2 -> H(U1(e, k), f(b))
25.51/8.41	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.41	   A^2 -> H(U1(e, c), f(c))
25.51/8.41	   A^2 -> H(U1(e, c), f(d))
25.51/8.41	   A^2 -> H(U1(k, e), f(b))
25.51/8.41	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.41	   A^2 -> H(U1(k, c), f(c))
25.51/8.41	   A^2 -> H(U1(k, c), f(d))
25.51/8.41	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.41	   A^2 -> H(U1(c, e), f(c))
25.51/8.41	   A^2 -> H(U1(c, e), f(d))
25.51/8.41	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(c, k), f(c))
25.51/8.41	   A^2 -> H(U1(c, k), f(d))
25.51/8.41	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.41	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(c, c), f(e))
25.51/8.41	   A^2 -> H(U1(c, c), f(k))
25.51/8.41	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.41	   A^2 -> H(e, f(b))
25.51/8.41	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.41	   A^2 -> H(U1(e, e), f(c))
25.51/8.41	   A^2 -> H(U1(e, e), f(d))
25.51/8.41	   A^2 -> H(f(e), U1(c, b))
25.51/8.41	   A^2 -> H(f(e), U1(d, b))
25.51/8.41	   A^2 -> H(f(e), U1(b, c))
25.51/8.41	   A^2 -> H(f(e), U1(b, d))
25.51/8.41	   A^2 -> H(f(e), U1(c, c))
25.51/8.41	   A^2 -> H(f(e), f(e))
25.51/8.41	   A^2 -> H(f(e), f(k))
25.51/8.41	   A^2 -> H(f(e), U1(d, d))
25.51/8.41	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(k, k), f(c))
25.51/8.41	   A^2 -> H(U1(k, k), f(d))
25.51/8.41	   A^2 -> H(f(k), U1(c, b))
25.51/8.41	   A^2 -> H(f(k), U1(d, b))
25.51/8.41	   A^2 -> H(f(k), U1(b, c))
25.51/8.41	   A^2 -> H(f(k), U1(b, d))
25.51/8.41	   A^2 -> H(f(k), U1(c, c))
25.51/8.41	   A^2 -> H(f(k), f(e))
25.51/8.41	   A^2 -> H(f(k), f(k))
25.51/8.41	   A^2 -> H(f(k), U1(d, d))
25.51/8.41	   A^2 -> H(f(c), U1(e, b))
25.51/8.41	   A^2 -> H(f(c), U1(k, b))
25.51/8.41	   A^2 -> H(f(c), U1(c, d))
25.51/8.41	   A^2 -> H(f(c), U1(d, c))
25.51/8.41	   A^2 -> H(f(c), U1(b, e))
25.51/8.41	   A^2 -> H(f(c), U1(b, k))
25.51/8.41	   A^2 -> H(f(c), U1(k, d))
25.51/8.41	   A^2 -> H(f(c), U1(d, k))
25.51/8.41	   A^2 -> H(f(c), U1(k, k))
25.51/8.41	   A^2 -> H(U1(k, k), f(b))
25.51/8.41	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.41	   A^2 -> H(U1(k, d), f(c))
25.51/8.41	   A^2 -> H(U1(k, d), f(d))
25.51/8.41	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(d, k), f(c))
25.51/8.41	   A^2 -> H(U1(d, k), f(d))
25.51/8.41	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(d, d), f(e))
25.51/8.41	   A^2 -> H(U1(d, d), f(k))
25.51/8.41	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.41	   A^2 -> H(f(d), U1(e, b))
25.51/8.41	   A^2 -> H(f(d), U1(k, b))
25.51/8.41	   A^2 -> H(f(d), U1(c, d))
25.51/8.41	   A^2 -> H(f(d), U1(d, c))
25.51/8.41	   A^2 -> H(f(d), U1(b, e))
25.51/8.41	   A^2 -> H(f(d), U1(b, k))
25.51/8.41	   A^2 -> H(f(d), U1(e, c))
25.51/8.41	   A^2 -> H(f(d), U1(k, c))
25.51/8.41	   A^2 -> H(f(d), U1(c, e))
25.51/8.41	   A^2 -> H(f(d), U1(c, k))
25.51/8.41	   A^2 -> H(f(d), U1(e, e))
25.51/8.41	   A^2 -> H(f(d), U1(k, k))
25.51/8.41	   A^2 -> H(f(a), b)
25.51/8.41	   A^2 -> H(f(a), U1(e, d))
25.51/8.41	   A^2 -> H(f(a), U1(d, e))
25.51/8.41	   A^2 -> H(f(c), U1(e, c))
25.51/8.41	   A^2 -> H(f(c), U1(k, c))
25.51/8.41	   A^2 -> H(f(c), U1(c, e))
25.51/8.41	   A^2 -> H(f(c), U1(c, k))
25.51/8.41	   A^2 -> H(f(a), c)
25.51/8.41	   A^2 -> H(f(a), U1(e, k))
25.51/8.41	   A^2 -> H(f(a), U1(k, e))
25.51/8.41	   A^2 -> H(f(c), U1(e, e))
25.51/8.41	   A^2 -> H(f(a), e)
25.51/8.41	   A^2 -> H(f(d), U1(k, d))
25.51/8.41	   A^2 -> H(f(d), U1(d, k))
25.51/8.41	   A^2 -> H(f(a), U1(k, k))
25.51/8.41	   A^2 -> H(d, f(b))
25.51/8.41	   A^2 -> H(a, U1(b, b))
25.51/8.41	   A^2 -> H(a, f(c))
25.51/8.41	   A^2 -> H(a, f(d))
25.51/8.41	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.41	   A^2 -> H(U1(e, d), f(c))
25.51/8.41	   A^2 -> H(U1(e, d), f(d))
25.51/8.41	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.41	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.41	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.41	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.41	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.41	   A^2 -> H(U1(e, a), f(e))
25.51/8.41	   A^2 -> H(U1(e, a), f(k))
25.51/8.41	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.41	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.41	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.41	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.41	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.41	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.41	   A^2 -> H(U1(k, a), f(e))
25.51/8.41	   A^2 -> H(U1(k, a), f(k))
25.51/8.41	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.41	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(c, d), f(e))
25.51/8.41	   A^2 -> H(U1(c, d), f(k))
25.51/8.41	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.41	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.41	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.41	   A^2 -> H(U1(d, e), f(c))
25.51/8.41	   A^2 -> H(U1(d, e), f(d))
25.51/8.41	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.41	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(d, c), f(e))
25.51/8.41	   A^2 -> H(U1(d, c), f(k))
25.51/8.41	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(d, k))
25.51/8.41	   A^2 -> H(U1(a, e), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, e), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, e), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, e), U1(b, d))
25.51/8.41	
25.51/8.41	The TRS R consists of the following rules:
25.51/8.41	
25.51/8.41	   f(x) -> U1(x, x)
25.51/8.41	   U1(e, x) -> x
25.51/8.41	   a -> c
25.51/8.41	   a -> d
25.51/8.41	   b -> c
25.51/8.41	   b -> d
25.51/8.41	   d -> k
25.51/8.41	   c -> e
25.51/8.41	   c -> k
25.51/8.41	
25.51/8.41	Q is empty.
25.51/8.41	We have to consider all minimal (P,Q,R)-chains.
25.51/8.41	----------------------------------------
25.51/8.41	
25.51/8.41	(285) TransformationProof (EQUIVALENT)
25.51/8.41	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), f(c)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.41	
25.51/8.41	   (A^2 -> H(U1(c, e), f(c)),A^2 -> H(U1(c, e), f(c)))
25.51/8.41	   (A^2 -> H(U1(d, e), f(c)),A^2 -> H(U1(d, e), f(c)))
25.51/8.41	   (A^2 -> H(U1(a, e), U1(c, c)),A^2 -> H(U1(a, e), U1(c, c)))
25.51/8.41	   (A^2 -> H(U1(a, e), f(e)),A^2 -> H(U1(a, e), f(e)))
25.51/8.41	   (A^2 -> H(U1(a, e), f(k)),A^2 -> H(U1(a, e), f(k)))
25.51/8.41	
25.51/8.41	
25.51/8.41	----------------------------------------
25.51/8.41	
25.51/8.41	(286)
25.51/8.41	Obligation:
25.51/8.41	Q DP problem:
25.51/8.41	The TRS P consists of the following rules:
25.51/8.41	
25.51/8.41	   H(x, x) -> G(x, x, f(k))
25.51/8.41	   G(d, x, x) -> A^2
25.51/8.41	   A^2 -> H(f(c), f(c))
25.51/8.41	   A^2 -> H(f(d), f(d))
25.51/8.41	   A^2 -> H(U1(a, e), f(d))
25.51/8.41	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(a, k), f(c))
25.51/8.41	   A^2 -> H(U1(a, k), f(d))
25.51/8.41	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, c), f(e))
25.51/8.41	   A^2 -> H(U1(a, c), f(k))
25.51/8.41	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.41	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, d), f(e))
25.51/8.41	   A^2 -> H(U1(a, d), f(k))
25.51/8.41	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.41	   A^2 -> H(c, f(b))
25.51/8.41	   A^2 -> H(U1(e, k), f(b))
25.51/8.41	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.41	   A^2 -> H(U1(e, c), f(c))
25.51/8.41	   A^2 -> H(U1(e, c), f(d))
25.51/8.41	   A^2 -> H(U1(k, e), f(b))
25.51/8.41	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.41	   A^2 -> H(U1(k, c), f(c))
25.51/8.41	   A^2 -> H(U1(k, c), f(d))
25.51/8.41	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.41	   A^2 -> H(U1(c, e), f(c))
25.51/8.41	   A^2 -> H(U1(c, e), f(d))
25.51/8.41	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(c, k), f(c))
25.51/8.41	   A^2 -> H(U1(c, k), f(d))
25.51/8.41	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.41	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(c, c), f(e))
25.51/8.41	   A^2 -> H(U1(c, c), f(k))
25.51/8.41	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.41	   A^2 -> H(e, f(b))
25.51/8.41	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.41	   A^2 -> H(U1(e, e), f(c))
25.51/8.41	   A^2 -> H(U1(e, e), f(d))
25.51/8.41	   A^2 -> H(f(e), U1(c, b))
25.51/8.41	   A^2 -> H(f(e), U1(d, b))
25.51/8.41	   A^2 -> H(f(e), U1(b, c))
25.51/8.41	   A^2 -> H(f(e), U1(b, d))
25.51/8.41	   A^2 -> H(f(e), U1(c, c))
25.51/8.41	   A^2 -> H(f(e), f(e))
25.51/8.41	   A^2 -> H(f(e), f(k))
25.51/8.41	   A^2 -> H(f(e), U1(d, d))
25.51/8.41	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(k, k), f(c))
25.51/8.41	   A^2 -> H(U1(k, k), f(d))
25.51/8.41	   A^2 -> H(f(k), U1(c, b))
25.51/8.41	   A^2 -> H(f(k), U1(d, b))
25.51/8.41	   A^2 -> H(f(k), U1(b, c))
25.51/8.41	   A^2 -> H(f(k), U1(b, d))
25.51/8.41	   A^2 -> H(f(k), U1(c, c))
25.51/8.41	   A^2 -> H(f(k), f(e))
25.51/8.41	   A^2 -> H(f(k), f(k))
25.51/8.41	   A^2 -> H(f(k), U1(d, d))
25.51/8.41	   A^2 -> H(f(c), U1(e, b))
25.51/8.41	   A^2 -> H(f(c), U1(k, b))
25.51/8.41	   A^2 -> H(f(c), U1(c, d))
25.51/8.41	   A^2 -> H(f(c), U1(d, c))
25.51/8.41	   A^2 -> H(f(c), U1(b, e))
25.51/8.41	   A^2 -> H(f(c), U1(b, k))
25.51/8.41	   A^2 -> H(f(c), U1(k, d))
25.51/8.41	   A^2 -> H(f(c), U1(d, k))
25.51/8.41	   A^2 -> H(f(c), U1(k, k))
25.51/8.41	   A^2 -> H(U1(k, k), f(b))
25.51/8.41	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.41	   A^2 -> H(U1(k, d), f(c))
25.51/8.41	   A^2 -> H(U1(k, d), f(d))
25.51/8.41	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(d, k), f(c))
25.51/8.41	   A^2 -> H(U1(d, k), f(d))
25.51/8.41	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(d, d), f(e))
25.51/8.41	   A^2 -> H(U1(d, d), f(k))
25.51/8.41	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.41	   A^2 -> H(f(d), U1(e, b))
25.51/8.41	   A^2 -> H(f(d), U1(k, b))
25.51/8.41	   A^2 -> H(f(d), U1(c, d))
25.51/8.41	   A^2 -> H(f(d), U1(d, c))
25.51/8.41	   A^2 -> H(f(d), U1(b, e))
25.51/8.41	   A^2 -> H(f(d), U1(b, k))
25.51/8.41	   A^2 -> H(f(d), U1(e, c))
25.51/8.41	   A^2 -> H(f(d), U1(k, c))
25.51/8.41	   A^2 -> H(f(d), U1(c, e))
25.51/8.41	   A^2 -> H(f(d), U1(c, k))
25.51/8.41	   A^2 -> H(f(d), U1(e, e))
25.51/8.41	   A^2 -> H(f(d), U1(k, k))
25.51/8.41	   A^2 -> H(f(a), b)
25.51/8.41	   A^2 -> H(f(a), U1(e, d))
25.51/8.41	   A^2 -> H(f(a), U1(d, e))
25.51/8.41	   A^2 -> H(f(c), U1(e, c))
25.51/8.41	   A^2 -> H(f(c), U1(k, c))
25.51/8.41	   A^2 -> H(f(c), U1(c, e))
25.51/8.41	   A^2 -> H(f(c), U1(c, k))
25.51/8.41	   A^2 -> H(f(a), c)
25.51/8.41	   A^2 -> H(f(a), U1(e, k))
25.51/8.41	   A^2 -> H(f(a), U1(k, e))
25.51/8.41	   A^2 -> H(f(c), U1(e, e))
25.51/8.41	   A^2 -> H(f(a), e)
25.51/8.41	   A^2 -> H(f(d), U1(k, d))
25.51/8.41	   A^2 -> H(f(d), U1(d, k))
25.51/8.41	   A^2 -> H(f(a), U1(k, k))
25.51/8.41	   A^2 -> H(d, f(b))
25.51/8.41	   A^2 -> H(a, U1(b, b))
25.51/8.41	   A^2 -> H(a, f(c))
25.51/8.41	   A^2 -> H(a, f(d))
25.51/8.41	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.41	   A^2 -> H(U1(e, d), f(c))
25.51/8.41	   A^2 -> H(U1(e, d), f(d))
25.51/8.41	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.41	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.41	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.41	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.41	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.41	   A^2 -> H(U1(e, a), f(e))
25.51/8.41	   A^2 -> H(U1(e, a), f(k))
25.51/8.41	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.41	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.41	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.41	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.41	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.41	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.41	   A^2 -> H(U1(k, a), f(e))
25.51/8.41	   A^2 -> H(U1(k, a), f(k))
25.51/8.41	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.41	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(c, d), f(e))
25.51/8.41	   A^2 -> H(U1(c, d), f(k))
25.51/8.41	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.41	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.41	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.41	   A^2 -> H(U1(d, e), f(c))
25.51/8.41	   A^2 -> H(U1(d, e), f(d))
25.51/8.41	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.41	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(d, c), f(e))
25.51/8.41	   A^2 -> H(U1(d, c), f(k))
25.51/8.41	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(d, k))
25.51/8.41	   A^2 -> H(U1(a, e), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, e), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, e), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, e), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, e), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, e), f(e))
25.51/8.41	   A^2 -> H(U1(a, e), f(k))
25.51/8.41	
25.51/8.41	The TRS R consists of the following rules:
25.51/8.41	
25.51/8.41	   f(x) -> U1(x, x)
25.51/8.41	   U1(e, x) -> x
25.51/8.41	   a -> c
25.51/8.41	   a -> d
25.51/8.41	   b -> c
25.51/8.41	   b -> d
25.51/8.41	   d -> k
25.51/8.41	   c -> e
25.51/8.41	   c -> k
25.51/8.41	
25.51/8.41	Q is empty.
25.51/8.41	We have to consider all minimal (P,Q,R)-chains.
25.51/8.41	----------------------------------------
25.51/8.41	
25.51/8.41	(287) TransformationProof (EQUIVALENT)
25.51/8.41	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), f(d)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.41	
25.51/8.41	   (A^2 -> H(U1(c, e), f(d)),A^2 -> H(U1(c, e), f(d)))
25.51/8.41	   (A^2 -> H(U1(d, e), f(d)),A^2 -> H(U1(d, e), f(d)))
25.51/8.41	   (A^2 -> H(U1(a, e), U1(d, d)),A^2 -> H(U1(a, e), U1(d, d)))
25.51/8.41	   (A^2 -> H(U1(a, e), f(k)),A^2 -> H(U1(a, e), f(k)))
25.51/8.41	
25.51/8.41	
25.51/8.41	----------------------------------------
25.51/8.41	
25.51/8.41	(288)
25.51/8.41	Obligation:
25.51/8.41	Q DP problem:
25.51/8.41	The TRS P consists of the following rules:
25.51/8.41	
25.51/8.41	   H(x, x) -> G(x, x, f(k))
25.51/8.41	   G(d, x, x) -> A^2
25.51/8.41	   A^2 -> H(f(c), f(c))
25.51/8.41	   A^2 -> H(f(d), f(d))
25.51/8.41	   A^2 -> H(U1(a, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(a, k), f(c))
25.51/8.41	   A^2 -> H(U1(a, k), f(d))
25.51/8.41	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, c), f(e))
25.51/8.41	   A^2 -> H(U1(a, c), f(k))
25.51/8.41	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.41	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, d), f(e))
25.51/8.41	   A^2 -> H(U1(a, d), f(k))
25.51/8.41	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.41	   A^2 -> H(c, f(b))
25.51/8.41	   A^2 -> H(U1(e, k), f(b))
25.51/8.41	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.41	   A^2 -> H(U1(e, c), f(c))
25.51/8.41	   A^2 -> H(U1(e, c), f(d))
25.51/8.41	   A^2 -> H(U1(k, e), f(b))
25.51/8.41	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.41	   A^2 -> H(U1(k, c), f(c))
25.51/8.41	   A^2 -> H(U1(k, c), f(d))
25.51/8.41	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.41	   A^2 -> H(U1(c, e), f(c))
25.51/8.41	   A^2 -> H(U1(c, e), f(d))
25.51/8.41	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(c, k), f(c))
25.51/8.41	   A^2 -> H(U1(c, k), f(d))
25.51/8.41	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.41	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(c, c), f(e))
25.51/8.41	   A^2 -> H(U1(c, c), f(k))
25.51/8.41	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.41	   A^2 -> H(e, f(b))
25.51/8.41	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.41	   A^2 -> H(U1(e, e), f(c))
25.51/8.41	   A^2 -> H(U1(e, e), f(d))
25.51/8.41	   A^2 -> H(f(e), U1(c, b))
25.51/8.41	   A^2 -> H(f(e), U1(d, b))
25.51/8.41	   A^2 -> H(f(e), U1(b, c))
25.51/8.41	   A^2 -> H(f(e), U1(b, d))
25.51/8.41	   A^2 -> H(f(e), U1(c, c))
25.51/8.41	   A^2 -> H(f(e), f(e))
25.51/8.41	   A^2 -> H(f(e), f(k))
25.51/8.41	   A^2 -> H(f(e), U1(d, d))
25.51/8.41	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(k, k), f(c))
25.51/8.41	   A^2 -> H(U1(k, k), f(d))
25.51/8.41	   A^2 -> H(f(k), U1(c, b))
25.51/8.41	   A^2 -> H(f(k), U1(d, b))
25.51/8.41	   A^2 -> H(f(k), U1(b, c))
25.51/8.41	   A^2 -> H(f(k), U1(b, d))
25.51/8.41	   A^2 -> H(f(k), U1(c, c))
25.51/8.41	   A^2 -> H(f(k), f(e))
25.51/8.41	   A^2 -> H(f(k), f(k))
25.51/8.41	   A^2 -> H(f(k), U1(d, d))
25.51/8.41	   A^2 -> H(f(c), U1(e, b))
25.51/8.41	   A^2 -> H(f(c), U1(k, b))
25.51/8.41	   A^2 -> H(f(c), U1(c, d))
25.51/8.41	   A^2 -> H(f(c), U1(d, c))
25.51/8.41	   A^2 -> H(f(c), U1(b, e))
25.51/8.41	   A^2 -> H(f(c), U1(b, k))
25.51/8.41	   A^2 -> H(f(c), U1(k, d))
25.51/8.41	   A^2 -> H(f(c), U1(d, k))
25.51/8.41	   A^2 -> H(f(c), U1(k, k))
25.51/8.41	   A^2 -> H(U1(k, k), f(b))
25.51/8.41	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.41	   A^2 -> H(U1(k, d), f(c))
25.51/8.41	   A^2 -> H(U1(k, d), f(d))
25.51/8.41	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(d, k), f(c))
25.51/8.41	   A^2 -> H(U1(d, k), f(d))
25.51/8.41	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(d, d), f(e))
25.51/8.41	   A^2 -> H(U1(d, d), f(k))
25.51/8.41	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.41	   A^2 -> H(f(d), U1(e, b))
25.51/8.41	   A^2 -> H(f(d), U1(k, b))
25.51/8.41	   A^2 -> H(f(d), U1(c, d))
25.51/8.41	   A^2 -> H(f(d), U1(d, c))
25.51/8.41	   A^2 -> H(f(d), U1(b, e))
25.51/8.41	   A^2 -> H(f(d), U1(b, k))
25.51/8.41	   A^2 -> H(f(d), U1(e, c))
25.51/8.41	   A^2 -> H(f(d), U1(k, c))
25.51/8.41	   A^2 -> H(f(d), U1(c, e))
25.51/8.41	   A^2 -> H(f(d), U1(c, k))
25.51/8.41	   A^2 -> H(f(d), U1(e, e))
25.51/8.41	   A^2 -> H(f(d), U1(k, k))
25.51/8.41	   A^2 -> H(f(a), b)
25.51/8.41	   A^2 -> H(f(a), U1(e, d))
25.51/8.41	   A^2 -> H(f(a), U1(d, e))
25.51/8.41	   A^2 -> H(f(c), U1(e, c))
25.51/8.41	   A^2 -> H(f(c), U1(k, c))
25.51/8.41	   A^2 -> H(f(c), U1(c, e))
25.51/8.41	   A^2 -> H(f(c), U1(c, k))
25.51/8.41	   A^2 -> H(f(a), c)
25.51/8.41	   A^2 -> H(f(a), U1(e, k))
25.51/8.41	   A^2 -> H(f(a), U1(k, e))
25.51/8.41	   A^2 -> H(f(c), U1(e, e))
25.51/8.41	   A^2 -> H(f(a), e)
25.51/8.41	   A^2 -> H(f(d), U1(k, d))
25.51/8.41	   A^2 -> H(f(d), U1(d, k))
25.51/8.41	   A^2 -> H(f(a), U1(k, k))
25.51/8.41	   A^2 -> H(d, f(b))
25.51/8.41	   A^2 -> H(a, U1(b, b))
25.51/8.41	   A^2 -> H(a, f(c))
25.51/8.41	   A^2 -> H(a, f(d))
25.51/8.41	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.41	   A^2 -> H(U1(e, d), f(c))
25.51/8.41	   A^2 -> H(U1(e, d), f(d))
25.51/8.41	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.41	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.41	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.41	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.41	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.41	   A^2 -> H(U1(e, a), f(e))
25.51/8.41	   A^2 -> H(U1(e, a), f(k))
25.51/8.41	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.41	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.41	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.41	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.41	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.41	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.41	   A^2 -> H(U1(k, a), f(e))
25.51/8.41	   A^2 -> H(U1(k, a), f(k))
25.51/8.41	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.41	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(c, d), f(e))
25.51/8.41	   A^2 -> H(U1(c, d), f(k))
25.51/8.41	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.41	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.41	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.41	   A^2 -> H(U1(d, e), f(c))
25.51/8.41	   A^2 -> H(U1(d, e), f(d))
25.51/8.41	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.41	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(d, c), f(e))
25.51/8.41	   A^2 -> H(U1(d, c), f(k))
25.51/8.41	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(d, k))
25.51/8.41	   A^2 -> H(U1(a, e), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, e), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, e), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, e), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, e), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, e), f(e))
25.51/8.41	   A^2 -> H(U1(a, e), f(k))
25.51/8.41	   A^2 -> H(U1(a, e), U1(d, d))
25.51/8.41	
25.51/8.41	The TRS R consists of the following rules:
25.51/8.41	
25.51/8.41	   f(x) -> U1(x, x)
25.51/8.41	   U1(e, x) -> x
25.51/8.41	   a -> c
25.51/8.41	   a -> d
25.51/8.41	   b -> c
25.51/8.41	   b -> d
25.51/8.41	   d -> k
25.51/8.41	   c -> e
25.51/8.41	   c -> k
25.51/8.41	
25.51/8.41	Q is empty.
25.51/8.41	We have to consider all minimal (P,Q,R)-chains.
25.51/8.41	----------------------------------------
25.51/8.41	
25.51/8.41	(289) TransformationProof (EQUIVALENT)
25.51/8.41	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.41	
25.51/8.41	   (A^2 -> H(U1(c, k), U1(b, b)),A^2 -> H(U1(c, k), U1(b, b)))
25.51/8.41	   (A^2 -> H(U1(d, k), U1(b, b)),A^2 -> H(U1(d, k), U1(b, b)))
25.51/8.41	   (A^2 -> H(U1(a, k), U1(c, b)),A^2 -> H(U1(a, k), U1(c, b)))
25.51/8.41	   (A^2 -> H(U1(a, k), U1(d, b)),A^2 -> H(U1(a, k), U1(d, b)))
25.51/8.41	   (A^2 -> H(U1(a, k), U1(b, c)),A^2 -> H(U1(a, k), U1(b, c)))
25.51/8.41	   (A^2 -> H(U1(a, k), U1(b, d)),A^2 -> H(U1(a, k), U1(b, d)))
25.51/8.41	
25.51/8.41	
25.51/8.41	----------------------------------------
25.51/8.41	
25.51/8.41	(290)
25.51/8.41	Obligation:
25.51/8.41	Q DP problem:
25.51/8.41	The TRS P consists of the following rules:
25.51/8.41	
25.51/8.41	   H(x, x) -> G(x, x, f(k))
25.51/8.41	   G(d, x, x) -> A^2
25.51/8.41	   A^2 -> H(f(c), f(c))
25.51/8.41	   A^2 -> H(f(d), f(d))
25.51/8.41	   A^2 -> H(U1(a, k), f(c))
25.51/8.41	   A^2 -> H(U1(a, k), f(d))
25.51/8.41	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, c), f(e))
25.51/8.41	   A^2 -> H(U1(a, c), f(k))
25.51/8.41	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.41	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, d), f(e))
25.51/8.41	   A^2 -> H(U1(a, d), f(k))
25.51/8.41	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.41	   A^2 -> H(c, f(b))
25.51/8.41	   A^2 -> H(U1(e, k), f(b))
25.51/8.41	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.41	   A^2 -> H(U1(e, c), f(c))
25.51/8.41	   A^2 -> H(U1(e, c), f(d))
25.51/8.41	   A^2 -> H(U1(k, e), f(b))
25.51/8.41	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.41	   A^2 -> H(U1(k, c), f(c))
25.51/8.41	   A^2 -> H(U1(k, c), f(d))
25.51/8.41	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.41	   A^2 -> H(U1(c, e), f(c))
25.51/8.41	   A^2 -> H(U1(c, e), f(d))
25.51/8.41	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(c, k), f(c))
25.51/8.41	   A^2 -> H(U1(c, k), f(d))
25.51/8.41	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.41	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(c, c), f(e))
25.51/8.41	   A^2 -> H(U1(c, c), f(k))
25.51/8.41	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.41	   A^2 -> H(e, f(b))
25.51/8.41	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.41	   A^2 -> H(U1(e, e), f(c))
25.51/8.41	   A^2 -> H(U1(e, e), f(d))
25.51/8.41	   A^2 -> H(f(e), U1(c, b))
25.51/8.41	   A^2 -> H(f(e), U1(d, b))
25.51/8.41	   A^2 -> H(f(e), U1(b, c))
25.51/8.41	   A^2 -> H(f(e), U1(b, d))
25.51/8.41	   A^2 -> H(f(e), U1(c, c))
25.51/8.41	   A^2 -> H(f(e), f(e))
25.51/8.41	   A^2 -> H(f(e), f(k))
25.51/8.41	   A^2 -> H(f(e), U1(d, d))
25.51/8.41	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(k, k), f(c))
25.51/8.41	   A^2 -> H(U1(k, k), f(d))
25.51/8.41	   A^2 -> H(f(k), U1(c, b))
25.51/8.41	   A^2 -> H(f(k), U1(d, b))
25.51/8.41	   A^2 -> H(f(k), U1(b, c))
25.51/8.41	   A^2 -> H(f(k), U1(b, d))
25.51/8.41	   A^2 -> H(f(k), U1(c, c))
25.51/8.41	   A^2 -> H(f(k), f(e))
25.51/8.41	   A^2 -> H(f(k), f(k))
25.51/8.41	   A^2 -> H(f(k), U1(d, d))
25.51/8.41	   A^2 -> H(f(c), U1(e, b))
25.51/8.41	   A^2 -> H(f(c), U1(k, b))
25.51/8.41	   A^2 -> H(f(c), U1(c, d))
25.51/8.41	   A^2 -> H(f(c), U1(d, c))
25.51/8.41	   A^2 -> H(f(c), U1(b, e))
25.51/8.41	   A^2 -> H(f(c), U1(b, k))
25.51/8.41	   A^2 -> H(f(c), U1(k, d))
25.51/8.41	   A^2 -> H(f(c), U1(d, k))
25.51/8.41	   A^2 -> H(f(c), U1(k, k))
25.51/8.41	   A^2 -> H(U1(k, k), f(b))
25.51/8.41	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.41	   A^2 -> H(U1(k, d), f(c))
25.51/8.41	   A^2 -> H(U1(k, d), f(d))
25.51/8.41	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(d, k), f(c))
25.51/8.41	   A^2 -> H(U1(d, k), f(d))
25.51/8.41	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(d, d), f(e))
25.51/8.41	   A^2 -> H(U1(d, d), f(k))
25.51/8.41	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.41	   A^2 -> H(f(d), U1(e, b))
25.51/8.41	   A^2 -> H(f(d), U1(k, b))
25.51/8.41	   A^2 -> H(f(d), U1(c, d))
25.51/8.41	   A^2 -> H(f(d), U1(d, c))
25.51/8.41	   A^2 -> H(f(d), U1(b, e))
25.51/8.41	   A^2 -> H(f(d), U1(b, k))
25.51/8.41	   A^2 -> H(f(d), U1(e, c))
25.51/8.41	   A^2 -> H(f(d), U1(k, c))
25.51/8.41	   A^2 -> H(f(d), U1(c, e))
25.51/8.41	   A^2 -> H(f(d), U1(c, k))
25.51/8.41	   A^2 -> H(f(d), U1(e, e))
25.51/8.41	   A^2 -> H(f(d), U1(k, k))
25.51/8.41	   A^2 -> H(f(a), b)
25.51/8.41	   A^2 -> H(f(a), U1(e, d))
25.51/8.41	   A^2 -> H(f(a), U1(d, e))
25.51/8.41	   A^2 -> H(f(c), U1(e, c))
25.51/8.41	   A^2 -> H(f(c), U1(k, c))
25.51/8.41	   A^2 -> H(f(c), U1(c, e))
25.51/8.41	   A^2 -> H(f(c), U1(c, k))
25.51/8.41	   A^2 -> H(f(a), c)
25.51/8.41	   A^2 -> H(f(a), U1(e, k))
25.51/8.41	   A^2 -> H(f(a), U1(k, e))
25.51/8.41	   A^2 -> H(f(c), U1(e, e))
25.51/8.41	   A^2 -> H(f(a), e)
25.51/8.41	   A^2 -> H(f(d), U1(k, d))
25.51/8.41	   A^2 -> H(f(d), U1(d, k))
25.51/8.41	   A^2 -> H(f(a), U1(k, k))
25.51/8.41	   A^2 -> H(d, f(b))
25.51/8.41	   A^2 -> H(a, U1(b, b))
25.51/8.41	   A^2 -> H(a, f(c))
25.51/8.41	   A^2 -> H(a, f(d))
25.51/8.41	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.41	   A^2 -> H(U1(e, d), f(c))
25.51/8.41	   A^2 -> H(U1(e, d), f(d))
25.51/8.41	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.41	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.41	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.41	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.41	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.41	   A^2 -> H(U1(e, a), f(e))
25.51/8.41	   A^2 -> H(U1(e, a), f(k))
25.51/8.41	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.41	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.41	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.41	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.41	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.41	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.41	   A^2 -> H(U1(k, a), f(e))
25.51/8.41	   A^2 -> H(U1(k, a), f(k))
25.51/8.41	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.41	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(c, d), f(e))
25.51/8.41	   A^2 -> H(U1(c, d), f(k))
25.51/8.41	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.41	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.41	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.41	   A^2 -> H(U1(d, e), f(c))
25.51/8.41	   A^2 -> H(U1(d, e), f(d))
25.51/8.41	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.41	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(d, c), f(e))
25.51/8.41	   A^2 -> H(U1(d, c), f(k))
25.51/8.41	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(d, k))
25.51/8.41	   A^2 -> H(U1(a, e), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, e), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, e), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, e), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, e), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, e), f(e))
25.51/8.41	   A^2 -> H(U1(a, e), f(k))
25.51/8.41	   A^2 -> H(U1(a, e), U1(d, d))
25.51/8.41	   A^2 -> H(U1(a, k), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, k), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, k), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, k), U1(b, d))
25.51/8.41	
25.51/8.41	The TRS R consists of the following rules:
25.51/8.41	
25.51/8.41	   f(x) -> U1(x, x)
25.51/8.41	   U1(e, x) -> x
25.51/8.41	   a -> c
25.51/8.41	   a -> d
25.51/8.41	   b -> c
25.51/8.41	   b -> d
25.51/8.41	   d -> k
25.51/8.41	   c -> e
25.51/8.41	   c -> k
25.51/8.41	
25.51/8.41	Q is empty.
25.51/8.41	We have to consider all minimal (P,Q,R)-chains.
25.51/8.41	----------------------------------------
25.51/8.41	
25.51/8.41	(291) TransformationProof (EQUIVALENT)
25.51/8.41	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), f(c)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.41	
25.51/8.41	   (A^2 -> H(U1(c, k), f(c)),A^2 -> H(U1(c, k), f(c)))
25.51/8.41	   (A^2 -> H(U1(d, k), f(c)),A^2 -> H(U1(d, k), f(c)))
25.51/8.41	   (A^2 -> H(U1(a, k), U1(c, c)),A^2 -> H(U1(a, k), U1(c, c)))
25.51/8.41	   (A^2 -> H(U1(a, k), f(e)),A^2 -> H(U1(a, k), f(e)))
25.51/8.41	   (A^2 -> H(U1(a, k), f(k)),A^2 -> H(U1(a, k), f(k)))
25.51/8.41	
25.51/8.41	
25.51/8.41	----------------------------------------
25.51/8.41	
25.51/8.41	(292)
25.51/8.41	Obligation:
25.51/8.41	Q DP problem:
25.51/8.41	The TRS P consists of the following rules:
25.51/8.41	
25.51/8.41	   H(x, x) -> G(x, x, f(k))
25.51/8.41	   G(d, x, x) -> A^2
25.51/8.41	   A^2 -> H(f(c), f(c))
25.51/8.41	   A^2 -> H(f(d), f(d))
25.51/8.41	   A^2 -> H(U1(a, k), f(d))
25.51/8.41	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, c), f(e))
25.51/8.41	   A^2 -> H(U1(a, c), f(k))
25.51/8.41	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.41	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, d), f(e))
25.51/8.41	   A^2 -> H(U1(a, d), f(k))
25.51/8.41	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.41	   A^2 -> H(c, f(b))
25.51/8.41	   A^2 -> H(U1(e, k), f(b))
25.51/8.41	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.41	   A^2 -> H(U1(e, c), f(c))
25.51/8.41	   A^2 -> H(U1(e, c), f(d))
25.51/8.41	   A^2 -> H(U1(k, e), f(b))
25.51/8.41	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.41	   A^2 -> H(U1(k, c), f(c))
25.51/8.41	   A^2 -> H(U1(k, c), f(d))
25.51/8.41	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.41	   A^2 -> H(U1(c, e), f(c))
25.51/8.41	   A^2 -> H(U1(c, e), f(d))
25.51/8.41	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(c, k), f(c))
25.51/8.41	   A^2 -> H(U1(c, k), f(d))
25.51/8.41	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.41	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(c, c), f(e))
25.51/8.41	   A^2 -> H(U1(c, c), f(k))
25.51/8.41	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.41	   A^2 -> H(e, f(b))
25.51/8.41	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.41	   A^2 -> H(U1(e, e), f(c))
25.51/8.41	   A^2 -> H(U1(e, e), f(d))
25.51/8.41	   A^2 -> H(f(e), U1(c, b))
25.51/8.41	   A^2 -> H(f(e), U1(d, b))
25.51/8.41	   A^2 -> H(f(e), U1(b, c))
25.51/8.41	   A^2 -> H(f(e), U1(b, d))
25.51/8.41	   A^2 -> H(f(e), U1(c, c))
25.51/8.41	   A^2 -> H(f(e), f(e))
25.51/8.41	   A^2 -> H(f(e), f(k))
25.51/8.41	   A^2 -> H(f(e), U1(d, d))
25.51/8.41	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(k, k), f(c))
25.51/8.41	   A^2 -> H(U1(k, k), f(d))
25.51/8.41	   A^2 -> H(f(k), U1(c, b))
25.51/8.41	   A^2 -> H(f(k), U1(d, b))
25.51/8.41	   A^2 -> H(f(k), U1(b, c))
25.51/8.41	   A^2 -> H(f(k), U1(b, d))
25.51/8.41	   A^2 -> H(f(k), U1(c, c))
25.51/8.41	   A^2 -> H(f(k), f(e))
25.51/8.41	   A^2 -> H(f(k), f(k))
25.51/8.41	   A^2 -> H(f(k), U1(d, d))
25.51/8.41	   A^2 -> H(f(c), U1(e, b))
25.51/8.41	   A^2 -> H(f(c), U1(k, b))
25.51/8.41	   A^2 -> H(f(c), U1(c, d))
25.51/8.41	   A^2 -> H(f(c), U1(d, c))
25.51/8.41	   A^2 -> H(f(c), U1(b, e))
25.51/8.41	   A^2 -> H(f(c), U1(b, k))
25.51/8.41	   A^2 -> H(f(c), U1(k, d))
25.51/8.41	   A^2 -> H(f(c), U1(d, k))
25.51/8.41	   A^2 -> H(f(c), U1(k, k))
25.51/8.41	   A^2 -> H(U1(k, k), f(b))
25.51/8.41	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.41	   A^2 -> H(U1(k, d), f(c))
25.51/8.41	   A^2 -> H(U1(k, d), f(d))
25.51/8.41	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(d, k), f(c))
25.51/8.41	   A^2 -> H(U1(d, k), f(d))
25.51/8.41	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(d, d), f(e))
25.51/8.41	   A^2 -> H(U1(d, d), f(k))
25.51/8.41	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.41	   A^2 -> H(f(d), U1(e, b))
25.51/8.41	   A^2 -> H(f(d), U1(k, b))
25.51/8.41	   A^2 -> H(f(d), U1(c, d))
25.51/8.41	   A^2 -> H(f(d), U1(d, c))
25.51/8.41	   A^2 -> H(f(d), U1(b, e))
25.51/8.41	   A^2 -> H(f(d), U1(b, k))
25.51/8.41	   A^2 -> H(f(d), U1(e, c))
25.51/8.41	   A^2 -> H(f(d), U1(k, c))
25.51/8.41	   A^2 -> H(f(d), U1(c, e))
25.51/8.41	   A^2 -> H(f(d), U1(c, k))
25.51/8.41	   A^2 -> H(f(d), U1(e, e))
25.51/8.41	   A^2 -> H(f(d), U1(k, k))
25.51/8.41	   A^2 -> H(f(a), b)
25.51/8.41	   A^2 -> H(f(a), U1(e, d))
25.51/8.41	   A^2 -> H(f(a), U1(d, e))
25.51/8.41	   A^2 -> H(f(c), U1(e, c))
25.51/8.41	   A^2 -> H(f(c), U1(k, c))
25.51/8.41	   A^2 -> H(f(c), U1(c, e))
25.51/8.41	   A^2 -> H(f(c), U1(c, k))
25.51/8.41	   A^2 -> H(f(a), c)
25.51/8.41	   A^2 -> H(f(a), U1(e, k))
25.51/8.41	   A^2 -> H(f(a), U1(k, e))
25.51/8.41	   A^2 -> H(f(c), U1(e, e))
25.51/8.41	   A^2 -> H(f(a), e)
25.51/8.41	   A^2 -> H(f(d), U1(k, d))
25.51/8.41	   A^2 -> H(f(d), U1(d, k))
25.51/8.41	   A^2 -> H(f(a), U1(k, k))
25.51/8.41	   A^2 -> H(d, f(b))
25.51/8.41	   A^2 -> H(a, U1(b, b))
25.51/8.41	   A^2 -> H(a, f(c))
25.51/8.41	   A^2 -> H(a, f(d))
25.51/8.41	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.41	   A^2 -> H(U1(e, d), f(c))
25.51/8.41	   A^2 -> H(U1(e, d), f(d))
25.51/8.41	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.41	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.41	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.41	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.41	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.41	   A^2 -> H(U1(e, a), f(e))
25.51/8.41	   A^2 -> H(U1(e, a), f(k))
25.51/8.41	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.41	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.41	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.41	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.41	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.41	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.41	   A^2 -> H(U1(k, a), f(e))
25.51/8.41	   A^2 -> H(U1(k, a), f(k))
25.51/8.41	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.41	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(c, d), f(e))
25.51/8.41	   A^2 -> H(U1(c, d), f(k))
25.51/8.41	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.41	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.41	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.41	   A^2 -> H(U1(d, e), f(c))
25.51/8.41	   A^2 -> H(U1(d, e), f(d))
25.51/8.41	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.41	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(d, c), f(e))
25.51/8.41	   A^2 -> H(U1(d, c), f(k))
25.51/8.41	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(d, k))
25.51/8.41	   A^2 -> H(U1(a, e), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, e), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, e), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, e), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, e), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, e), f(e))
25.51/8.41	   A^2 -> H(U1(a, e), f(k))
25.51/8.41	   A^2 -> H(U1(a, e), U1(d, d))
25.51/8.41	   A^2 -> H(U1(a, k), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, k), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, k), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, k), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, k), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, k), f(e))
25.51/8.41	   A^2 -> H(U1(a, k), f(k))
25.51/8.41	
25.51/8.41	The TRS R consists of the following rules:
25.51/8.41	
25.51/8.41	   f(x) -> U1(x, x)
25.51/8.41	   U1(e, x) -> x
25.51/8.41	   a -> c
25.51/8.41	   a -> d
25.51/8.41	   b -> c
25.51/8.41	   b -> d
25.51/8.41	   d -> k
25.51/8.41	   c -> e
25.51/8.41	   c -> k
25.51/8.41	
25.51/8.41	Q is empty.
25.51/8.41	We have to consider all minimal (P,Q,R)-chains.
25.51/8.41	----------------------------------------
25.51/8.41	
25.51/8.41	(293) TransformationProof (EQUIVALENT)
25.51/8.41	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), f(d)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.41	
25.51/8.41	   (A^2 -> H(U1(c, k), f(d)),A^2 -> H(U1(c, k), f(d)))
25.51/8.41	   (A^2 -> H(U1(d, k), f(d)),A^2 -> H(U1(d, k), f(d)))
25.51/8.41	   (A^2 -> H(U1(a, k), U1(d, d)),A^2 -> H(U1(a, k), U1(d, d)))
25.51/8.41	   (A^2 -> H(U1(a, k), f(k)),A^2 -> H(U1(a, k), f(k)))
25.51/8.41	
25.51/8.41	
25.51/8.41	----------------------------------------
25.51/8.41	
25.51/8.41	(294)
25.51/8.41	Obligation:
25.51/8.41	Q DP problem:
25.51/8.41	The TRS P consists of the following rules:
25.51/8.41	
25.51/8.41	   H(x, x) -> G(x, x, f(k))
25.51/8.41	   G(d, x, x) -> A^2
25.51/8.41	   A^2 -> H(f(c), f(c))
25.51/8.41	   A^2 -> H(f(d), f(d))
25.51/8.41	   A^2 -> H(U1(a, c), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, c), f(e))
25.51/8.41	   A^2 -> H(U1(a, c), f(k))
25.51/8.41	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.41	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, d), f(e))
25.51/8.41	   A^2 -> H(U1(a, d), f(k))
25.51/8.41	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.41	   A^2 -> H(c, f(b))
25.51/8.41	   A^2 -> H(U1(e, k), f(b))
25.51/8.41	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.41	   A^2 -> H(U1(e, c), f(c))
25.51/8.41	   A^2 -> H(U1(e, c), f(d))
25.51/8.41	   A^2 -> H(U1(k, e), f(b))
25.51/8.41	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.41	   A^2 -> H(U1(k, c), f(c))
25.51/8.41	   A^2 -> H(U1(k, c), f(d))
25.51/8.41	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.41	   A^2 -> H(U1(c, e), f(c))
25.51/8.41	   A^2 -> H(U1(c, e), f(d))
25.51/8.41	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(c, k), f(c))
25.51/8.41	   A^2 -> H(U1(c, k), f(d))
25.51/8.41	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.41	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(c, c), f(e))
25.51/8.41	   A^2 -> H(U1(c, c), f(k))
25.51/8.41	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.41	   A^2 -> H(e, f(b))
25.51/8.41	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.41	   A^2 -> H(U1(e, e), f(c))
25.51/8.41	   A^2 -> H(U1(e, e), f(d))
25.51/8.41	   A^2 -> H(f(e), U1(c, b))
25.51/8.41	   A^2 -> H(f(e), U1(d, b))
25.51/8.41	   A^2 -> H(f(e), U1(b, c))
25.51/8.41	   A^2 -> H(f(e), U1(b, d))
25.51/8.41	   A^2 -> H(f(e), U1(c, c))
25.51/8.41	   A^2 -> H(f(e), f(e))
25.51/8.41	   A^2 -> H(f(e), f(k))
25.51/8.41	   A^2 -> H(f(e), U1(d, d))
25.51/8.41	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(k, k), f(c))
25.51/8.41	   A^2 -> H(U1(k, k), f(d))
25.51/8.41	   A^2 -> H(f(k), U1(c, b))
25.51/8.41	   A^2 -> H(f(k), U1(d, b))
25.51/8.41	   A^2 -> H(f(k), U1(b, c))
25.51/8.41	   A^2 -> H(f(k), U1(b, d))
25.51/8.41	   A^2 -> H(f(k), U1(c, c))
25.51/8.41	   A^2 -> H(f(k), f(e))
25.51/8.41	   A^2 -> H(f(k), f(k))
25.51/8.41	   A^2 -> H(f(k), U1(d, d))
25.51/8.41	   A^2 -> H(f(c), U1(e, b))
25.51/8.41	   A^2 -> H(f(c), U1(k, b))
25.51/8.41	   A^2 -> H(f(c), U1(c, d))
25.51/8.41	   A^2 -> H(f(c), U1(d, c))
25.51/8.41	   A^2 -> H(f(c), U1(b, e))
25.51/8.41	   A^2 -> H(f(c), U1(b, k))
25.51/8.41	   A^2 -> H(f(c), U1(k, d))
25.51/8.41	   A^2 -> H(f(c), U1(d, k))
25.51/8.41	   A^2 -> H(f(c), U1(k, k))
25.51/8.41	   A^2 -> H(U1(k, k), f(b))
25.51/8.41	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.41	   A^2 -> H(U1(k, d), f(c))
25.51/8.41	   A^2 -> H(U1(k, d), f(d))
25.51/8.41	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.41	   A^2 -> H(U1(d, k), f(c))
25.51/8.41	   A^2 -> H(U1(d, k), f(d))
25.51/8.41	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(d, d), f(e))
25.51/8.41	   A^2 -> H(U1(d, d), f(k))
25.51/8.41	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.41	   A^2 -> H(f(d), U1(e, b))
25.51/8.41	   A^2 -> H(f(d), U1(k, b))
25.51/8.41	   A^2 -> H(f(d), U1(c, d))
25.51/8.41	   A^2 -> H(f(d), U1(d, c))
25.51/8.41	   A^2 -> H(f(d), U1(b, e))
25.51/8.41	   A^2 -> H(f(d), U1(b, k))
25.51/8.41	   A^2 -> H(f(d), U1(e, c))
25.51/8.41	   A^2 -> H(f(d), U1(k, c))
25.51/8.41	   A^2 -> H(f(d), U1(c, e))
25.51/8.41	   A^2 -> H(f(d), U1(c, k))
25.51/8.41	   A^2 -> H(f(d), U1(e, e))
25.51/8.41	   A^2 -> H(f(d), U1(k, k))
25.51/8.41	   A^2 -> H(f(a), b)
25.51/8.41	   A^2 -> H(f(a), U1(e, d))
25.51/8.41	   A^2 -> H(f(a), U1(d, e))
25.51/8.41	   A^2 -> H(f(c), U1(e, c))
25.51/8.41	   A^2 -> H(f(c), U1(k, c))
25.51/8.41	   A^2 -> H(f(c), U1(c, e))
25.51/8.41	   A^2 -> H(f(c), U1(c, k))
25.51/8.41	   A^2 -> H(f(a), c)
25.51/8.41	   A^2 -> H(f(a), U1(e, k))
25.51/8.41	   A^2 -> H(f(a), U1(k, e))
25.51/8.41	   A^2 -> H(f(c), U1(e, e))
25.51/8.41	   A^2 -> H(f(a), e)
25.51/8.41	   A^2 -> H(f(d), U1(k, d))
25.51/8.41	   A^2 -> H(f(d), U1(d, k))
25.51/8.41	   A^2 -> H(f(a), U1(k, k))
25.51/8.41	   A^2 -> H(d, f(b))
25.51/8.41	   A^2 -> H(a, U1(b, b))
25.51/8.41	   A^2 -> H(a, f(c))
25.51/8.41	   A^2 -> H(a, f(d))
25.51/8.41	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.41	   A^2 -> H(U1(e, d), f(c))
25.51/8.41	   A^2 -> H(U1(e, d), f(d))
25.51/8.41	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.41	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.41	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.41	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.41	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.41	   A^2 -> H(U1(e, a), f(e))
25.51/8.41	   A^2 -> H(U1(e, a), f(k))
25.51/8.41	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.41	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.41	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.41	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.41	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.41	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.41	   A^2 -> H(U1(k, a), f(e))
25.51/8.41	   A^2 -> H(U1(k, a), f(k))
25.51/8.41	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.41	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(c, d), f(e))
25.51/8.41	   A^2 -> H(U1(c, d), f(k))
25.51/8.41	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.41	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.41	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.41	   A^2 -> H(U1(d, e), f(c))
25.51/8.41	   A^2 -> H(U1(d, e), f(d))
25.51/8.41	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.41	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(d, c), f(e))
25.51/8.41	   A^2 -> H(U1(d, c), f(k))
25.51/8.41	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, c))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(c, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(e, e))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, k))
25.51/8.41	   A^2 -> H(U1(d, a), U1(k, d))
25.51/8.41	   A^2 -> H(U1(d, a), U1(d, k))
25.51/8.41	   A^2 -> H(U1(a, e), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, e), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, e), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, e), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, e), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, e), f(e))
25.51/8.41	   A^2 -> H(U1(a, e), f(k))
25.51/8.41	   A^2 -> H(U1(a, e), U1(d, d))
25.51/8.41	   A^2 -> H(U1(a, k), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, k), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, k), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, k), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, k), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, k), f(e))
25.51/8.41	   A^2 -> H(U1(a, k), f(k))
25.51/8.41	   A^2 -> H(U1(a, k), U1(d, d))
25.51/8.41	
25.51/8.41	The TRS R consists of the following rules:
25.51/8.41	
25.51/8.41	   f(x) -> U1(x, x)
25.51/8.41	   U1(e, x) -> x
25.51/8.41	   a -> c
25.51/8.41	   a -> d
25.51/8.41	   b -> c
25.51/8.41	   b -> d
25.51/8.41	   d -> k
25.51/8.41	   c -> e
25.51/8.41	   c -> k
25.51/8.41	
25.51/8.41	Q is empty.
25.51/8.41	We have to consider all minimal (P,Q,R)-chains.
25.51/8.41	----------------------------------------
25.51/8.41	
25.51/8.41	(295) TransformationProof (EQUIVALENT)
25.51/8.41	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.41	
25.51/8.41	   (A^2 -> H(U1(c, c), U1(c, b)),A^2 -> H(U1(c, c), U1(c, b)))
25.51/8.41	   (A^2 -> H(U1(d, c), U1(c, b)),A^2 -> H(U1(d, c), U1(c, b)))
25.51/8.41	   (A^2 -> H(U1(a, e), U1(c, b)),A^2 -> H(U1(a, e), U1(c, b)))
25.51/8.41	   (A^2 -> H(U1(a, k), U1(c, b)),A^2 -> H(U1(a, k), U1(c, b)))
25.51/8.41	   (A^2 -> H(U1(a, c), U1(e, b)),A^2 -> H(U1(a, c), U1(e, b)))
25.51/8.41	   (A^2 -> H(U1(a, c), U1(k, b)),A^2 -> H(U1(a, c), U1(k, b)))
25.51/8.41	   (A^2 -> H(U1(a, c), U1(c, c)),A^2 -> H(U1(a, c), U1(c, c)))
25.51/8.41	   (A^2 -> H(U1(a, c), U1(c, d)),A^2 -> H(U1(a, c), U1(c, d)))
25.51/8.41	
25.51/8.41	
25.51/8.41	----------------------------------------
25.51/8.41	
25.51/8.41	(296)
25.51/8.41	Obligation:
25.51/8.41	Q DP problem:
25.51/8.41	The TRS P consists of the following rules:
25.51/8.41	
25.51/8.41	   H(x, x) -> G(x, x, f(k))
25.51/8.41	   G(d, x, x) -> A^2
25.51/8.41	   A^2 -> H(f(c), f(c))
25.51/8.41	   A^2 -> H(f(d), f(d))
25.51/8.41	   A^2 -> H(U1(a, c), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, c), f(e))
25.51/8.41	   A^2 -> H(U1(a, c), f(k))
25.51/8.41	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.41	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.41	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.41	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.41	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.41	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.41	   A^2 -> H(U1(a, d), f(e))
25.51/8.41	   A^2 -> H(U1(a, d), f(k))
25.51/8.41	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.41	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.41	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.41	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.41	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.43	   A^2 -> H(c, f(b))
25.51/8.43	   A^2 -> H(U1(e, k), f(b))
25.51/8.43	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, c), f(c))
25.51/8.43	   A^2 -> H(U1(e, c), f(d))
25.51/8.43	   A^2 -> H(U1(k, e), f(b))
25.51/8.43	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, c), f(c))
25.51/8.43	   A^2 -> H(U1(k, c), f(d))
25.51/8.43	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(c, e), f(c))
25.51/8.43	   A^2 -> H(U1(c, e), f(d))
25.51/8.43	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(c, k), f(c))
25.51/8.43	   A^2 -> H(U1(c, k), f(d))
25.51/8.43	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.43	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.43	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.43	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.43	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.43	   A^2 -> H(U1(c, c), f(e))
25.51/8.43	   A^2 -> H(U1(c, c), f(k))
25.51/8.43	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.43	   A^2 -> H(e, f(b))
25.51/8.43	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, e), f(c))
25.51/8.43	   A^2 -> H(U1(e, e), f(d))
25.51/8.43	   A^2 -> H(f(e), U1(c, b))
25.51/8.43	   A^2 -> H(f(e), U1(d, b))
25.51/8.43	   A^2 -> H(f(e), U1(b, c))
25.51/8.43	   A^2 -> H(f(e), U1(b, d))
25.51/8.43	   A^2 -> H(f(e), U1(c, c))
25.51/8.43	   A^2 -> H(f(e), f(e))
25.51/8.43	   A^2 -> H(f(e), f(k))
25.51/8.43	   A^2 -> H(f(e), U1(d, d))
25.51/8.43	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, k), f(c))
25.51/8.43	   A^2 -> H(U1(k, k), f(d))
25.51/8.43	   A^2 -> H(f(k), U1(c, b))
25.51/8.43	   A^2 -> H(f(k), U1(d, b))
25.51/8.43	   A^2 -> H(f(k), U1(b, c))
25.51/8.43	   A^2 -> H(f(k), U1(b, d))
25.51/8.43	   A^2 -> H(f(k), U1(c, c))
25.51/8.43	   A^2 -> H(f(k), f(e))
25.51/8.43	   A^2 -> H(f(k), f(k))
25.51/8.43	   A^2 -> H(f(k), U1(d, d))
25.51/8.43	   A^2 -> H(f(c), U1(e, b))
25.51/8.43	   A^2 -> H(f(c), U1(k, b))
25.51/8.43	   A^2 -> H(f(c), U1(c, d))
25.51/8.43	   A^2 -> H(f(c), U1(d, c))
25.51/8.43	   A^2 -> H(f(c), U1(b, e))
25.51/8.43	   A^2 -> H(f(c), U1(b, k))
25.51/8.43	   A^2 -> H(f(c), U1(k, d))
25.51/8.43	   A^2 -> H(f(c), U1(d, k))
25.51/8.43	   A^2 -> H(f(c), U1(k, k))
25.51/8.43	   A^2 -> H(U1(k, k), f(b))
25.51/8.43	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, d), f(c))
25.51/8.43	   A^2 -> H(U1(k, d), f(d))
25.51/8.43	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(d, k), f(c))
25.51/8.43	   A^2 -> H(U1(d, k), f(d))
25.51/8.43	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(d, d), f(e))
25.51/8.43	   A^2 -> H(U1(d, d), f(k))
25.51/8.43	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.43	   A^2 -> H(f(d), U1(e, b))
25.51/8.43	   A^2 -> H(f(d), U1(k, b))
25.51/8.43	   A^2 -> H(f(d), U1(c, d))
25.51/8.43	   A^2 -> H(f(d), U1(d, c))
25.51/8.43	   A^2 -> H(f(d), U1(b, e))
25.51/8.43	   A^2 -> H(f(d), U1(b, k))
25.51/8.43	   A^2 -> H(f(d), U1(e, c))
25.51/8.43	   A^2 -> H(f(d), U1(k, c))
25.51/8.43	   A^2 -> H(f(d), U1(c, e))
25.51/8.43	   A^2 -> H(f(d), U1(c, k))
25.51/8.43	   A^2 -> H(f(d), U1(e, e))
25.51/8.43	   A^2 -> H(f(d), U1(k, k))
25.51/8.43	   A^2 -> H(f(a), b)
25.51/8.43	   A^2 -> H(f(a), U1(e, d))
25.51/8.43	   A^2 -> H(f(a), U1(d, e))
25.51/8.43	   A^2 -> H(f(c), U1(e, c))
25.51/8.43	   A^2 -> H(f(c), U1(k, c))
25.51/8.43	   A^2 -> H(f(c), U1(c, e))
25.51/8.43	   A^2 -> H(f(c), U1(c, k))
25.51/8.43	   A^2 -> H(f(a), c)
25.51/8.43	   A^2 -> H(f(a), U1(e, k))
25.51/8.43	   A^2 -> H(f(a), U1(k, e))
25.51/8.43	   A^2 -> H(f(c), U1(e, e))
25.51/8.43	   A^2 -> H(f(a), e)
25.51/8.43	   A^2 -> H(f(d), U1(k, d))
25.51/8.43	   A^2 -> H(f(d), U1(d, k))
25.51/8.43	   A^2 -> H(f(a), U1(k, k))
25.51/8.43	   A^2 -> H(d, f(b))
25.51/8.43	   A^2 -> H(a, U1(b, b))
25.51/8.43	   A^2 -> H(a, f(c))
25.51/8.43	   A^2 -> H(a, f(d))
25.51/8.43	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, d), f(c))
25.51/8.43	   A^2 -> H(U1(e, d), f(d))
25.51/8.43	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.43	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.43	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.43	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.43	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.43	   A^2 -> H(U1(e, a), f(e))
25.51/8.43	   A^2 -> H(U1(e, a), f(k))
25.51/8.43	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.43	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.43	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.43	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.43	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.43	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.43	   A^2 -> H(U1(k, a), f(e))
25.51/8.43	   A^2 -> H(U1(k, a), f(k))
25.51/8.43	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.43	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(c, d), f(e))
25.51/8.43	   A^2 -> H(U1(c, d), f(k))
25.51/8.43	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.43	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(d, e), f(c))
25.51/8.43	   A^2 -> H(U1(d, e), f(d))
25.51/8.43	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.43	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.43	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.43	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.43	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.43	   A^2 -> H(U1(d, c), f(e))
25.51/8.43	   A^2 -> H(U1(d, c), f(k))
25.51/8.43	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(d, k))
25.51/8.43	   A^2 -> H(U1(a, e), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, e), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, e), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, e), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, e), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, e), f(e))
25.51/8.43	   A^2 -> H(U1(a, e), f(k))
25.51/8.43	   A^2 -> H(U1(a, e), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, k), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, k), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, k), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, k), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, k), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, k), f(e))
25.51/8.43	   A^2 -> H(U1(a, k), f(k))
25.51/8.43	   A^2 -> H(U1(a, k), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(e, b))
25.51/8.43	   A^2 -> H(U1(a, c), U1(k, b))
25.51/8.43	   A^2 -> H(U1(a, c), U1(c, d))
25.51/8.43	
25.51/8.43	The TRS R consists of the following rules:
25.51/8.43	
25.51/8.43	   f(x) -> U1(x, x)
25.51/8.43	   U1(e, x) -> x
25.51/8.43	   a -> c
25.51/8.43	   a -> d
25.51/8.43	   b -> c
25.51/8.43	   b -> d
25.51/8.43	   d -> k
25.51/8.43	   c -> e
25.51/8.43	   c -> k
25.51/8.43	
25.51/8.43	Q is empty.
25.51/8.43	We have to consider all minimal (P,Q,R)-chains.
25.51/8.43	----------------------------------------
25.51/8.43	
25.51/8.43	(297) TransformationProof (EQUIVALENT)
25.51/8.43	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.43	
25.51/8.43	   (A^2 -> H(U1(c, c), U1(d, b)),A^2 -> H(U1(c, c), U1(d, b)))
25.51/8.43	   (A^2 -> H(U1(d, c), U1(d, b)),A^2 -> H(U1(d, c), U1(d, b)))
25.51/8.43	   (A^2 -> H(U1(a, e), U1(d, b)),A^2 -> H(U1(a, e), U1(d, b)))
25.51/8.43	   (A^2 -> H(U1(a, k), U1(d, b)),A^2 -> H(U1(a, k), U1(d, b)))
25.51/8.43	   (A^2 -> H(U1(a, c), U1(k, b)),A^2 -> H(U1(a, c), U1(k, b)))
25.51/8.43	   (A^2 -> H(U1(a, c), U1(d, c)),A^2 -> H(U1(a, c), U1(d, c)))
25.51/8.43	   (A^2 -> H(U1(a, c), U1(d, d)),A^2 -> H(U1(a, c), U1(d, d)))
25.51/8.43	
25.51/8.43	
25.51/8.43	----------------------------------------
25.51/8.43	
25.51/8.43	(298)
25.51/8.43	Obligation:
25.51/8.43	Q DP problem:
25.51/8.43	The TRS P consists of the following rules:
25.51/8.43	
25.51/8.43	   H(x, x) -> G(x, x, f(k))
25.51/8.43	   G(d, x, x) -> A^2
25.51/8.43	   A^2 -> H(f(c), f(c))
25.51/8.43	   A^2 -> H(f(d), f(d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, c), f(e))
25.51/8.43	   A^2 -> H(U1(a, c), f(k))
25.51/8.43	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, d), f(e))
25.51/8.43	   A^2 -> H(U1(a, d), f(k))
25.51/8.43	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.43	   A^2 -> H(c, f(b))
25.51/8.43	   A^2 -> H(U1(e, k), f(b))
25.51/8.43	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, c), f(c))
25.51/8.43	   A^2 -> H(U1(e, c), f(d))
25.51/8.43	   A^2 -> H(U1(k, e), f(b))
25.51/8.43	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, c), f(c))
25.51/8.43	   A^2 -> H(U1(k, c), f(d))
25.51/8.43	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(c, e), f(c))
25.51/8.43	   A^2 -> H(U1(c, e), f(d))
25.51/8.43	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(c, k), f(c))
25.51/8.43	   A^2 -> H(U1(c, k), f(d))
25.51/8.43	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.43	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.43	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.43	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.43	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.43	   A^2 -> H(U1(c, c), f(e))
25.51/8.43	   A^2 -> H(U1(c, c), f(k))
25.51/8.43	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.43	   A^2 -> H(e, f(b))
25.51/8.43	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, e), f(c))
25.51/8.43	   A^2 -> H(U1(e, e), f(d))
25.51/8.43	   A^2 -> H(f(e), U1(c, b))
25.51/8.43	   A^2 -> H(f(e), U1(d, b))
25.51/8.43	   A^2 -> H(f(e), U1(b, c))
25.51/8.43	   A^2 -> H(f(e), U1(b, d))
25.51/8.43	   A^2 -> H(f(e), U1(c, c))
25.51/8.43	   A^2 -> H(f(e), f(e))
25.51/8.43	   A^2 -> H(f(e), f(k))
25.51/8.43	   A^2 -> H(f(e), U1(d, d))
25.51/8.43	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, k), f(c))
25.51/8.43	   A^2 -> H(U1(k, k), f(d))
25.51/8.43	   A^2 -> H(f(k), U1(c, b))
25.51/8.43	   A^2 -> H(f(k), U1(d, b))
25.51/8.43	   A^2 -> H(f(k), U1(b, c))
25.51/8.43	   A^2 -> H(f(k), U1(b, d))
25.51/8.43	   A^2 -> H(f(k), U1(c, c))
25.51/8.43	   A^2 -> H(f(k), f(e))
25.51/8.43	   A^2 -> H(f(k), f(k))
25.51/8.43	   A^2 -> H(f(k), U1(d, d))
25.51/8.43	   A^2 -> H(f(c), U1(e, b))
25.51/8.43	   A^2 -> H(f(c), U1(k, b))
25.51/8.43	   A^2 -> H(f(c), U1(c, d))
25.51/8.43	   A^2 -> H(f(c), U1(d, c))
25.51/8.43	   A^2 -> H(f(c), U1(b, e))
25.51/8.43	   A^2 -> H(f(c), U1(b, k))
25.51/8.43	   A^2 -> H(f(c), U1(k, d))
25.51/8.43	   A^2 -> H(f(c), U1(d, k))
25.51/8.43	   A^2 -> H(f(c), U1(k, k))
25.51/8.43	   A^2 -> H(U1(k, k), f(b))
25.51/8.43	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, d), f(c))
25.51/8.43	   A^2 -> H(U1(k, d), f(d))
25.51/8.43	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(d, k), f(c))
25.51/8.43	   A^2 -> H(U1(d, k), f(d))
25.51/8.43	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(d, d), f(e))
25.51/8.43	   A^2 -> H(U1(d, d), f(k))
25.51/8.43	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.43	   A^2 -> H(f(d), U1(e, b))
25.51/8.43	   A^2 -> H(f(d), U1(k, b))
25.51/8.43	   A^2 -> H(f(d), U1(c, d))
25.51/8.43	   A^2 -> H(f(d), U1(d, c))
25.51/8.43	   A^2 -> H(f(d), U1(b, e))
25.51/8.43	   A^2 -> H(f(d), U1(b, k))
25.51/8.43	   A^2 -> H(f(d), U1(e, c))
25.51/8.43	   A^2 -> H(f(d), U1(k, c))
25.51/8.43	   A^2 -> H(f(d), U1(c, e))
25.51/8.43	   A^2 -> H(f(d), U1(c, k))
25.51/8.43	   A^2 -> H(f(d), U1(e, e))
25.51/8.43	   A^2 -> H(f(d), U1(k, k))
25.51/8.43	   A^2 -> H(f(a), b)
25.51/8.43	   A^2 -> H(f(a), U1(e, d))
25.51/8.43	   A^2 -> H(f(a), U1(d, e))
25.51/8.43	   A^2 -> H(f(c), U1(e, c))
25.51/8.43	   A^2 -> H(f(c), U1(k, c))
25.51/8.43	   A^2 -> H(f(c), U1(c, e))
25.51/8.43	   A^2 -> H(f(c), U1(c, k))
25.51/8.43	   A^2 -> H(f(a), c)
25.51/8.43	   A^2 -> H(f(a), U1(e, k))
25.51/8.43	   A^2 -> H(f(a), U1(k, e))
25.51/8.43	   A^2 -> H(f(c), U1(e, e))
25.51/8.43	   A^2 -> H(f(a), e)
25.51/8.43	   A^2 -> H(f(d), U1(k, d))
25.51/8.43	   A^2 -> H(f(d), U1(d, k))
25.51/8.43	   A^2 -> H(f(a), U1(k, k))
25.51/8.43	   A^2 -> H(d, f(b))
25.51/8.43	   A^2 -> H(a, U1(b, b))
25.51/8.43	   A^2 -> H(a, f(c))
25.51/8.43	   A^2 -> H(a, f(d))
25.51/8.43	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, d), f(c))
25.51/8.43	   A^2 -> H(U1(e, d), f(d))
25.51/8.43	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.43	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.43	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.43	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.43	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.43	   A^2 -> H(U1(e, a), f(e))
25.51/8.43	   A^2 -> H(U1(e, a), f(k))
25.51/8.43	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.43	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.43	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.43	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.43	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.43	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.43	   A^2 -> H(U1(k, a), f(e))
25.51/8.43	   A^2 -> H(U1(k, a), f(k))
25.51/8.43	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.43	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(c, d), f(e))
25.51/8.43	   A^2 -> H(U1(c, d), f(k))
25.51/8.43	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.43	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(d, e), f(c))
25.51/8.43	   A^2 -> H(U1(d, e), f(d))
25.51/8.43	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.43	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.43	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.43	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.43	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.43	   A^2 -> H(U1(d, c), f(e))
25.51/8.43	   A^2 -> H(U1(d, c), f(k))
25.51/8.43	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(d, k))
25.51/8.43	   A^2 -> H(U1(a, e), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, e), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, e), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, e), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, e), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, e), f(e))
25.51/8.43	   A^2 -> H(U1(a, e), f(k))
25.51/8.43	   A^2 -> H(U1(a, e), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, k), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, k), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, k), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, k), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, k), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, k), f(e))
25.51/8.43	   A^2 -> H(U1(a, k), f(k))
25.51/8.43	   A^2 -> H(U1(a, k), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(e, b))
25.51/8.43	   A^2 -> H(U1(a, c), U1(k, b))
25.51/8.43	   A^2 -> H(U1(a, c), U1(c, d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(d, c))
25.51/8.43	
25.51/8.43	The TRS R consists of the following rules:
25.51/8.43	
25.51/8.43	   f(x) -> U1(x, x)
25.51/8.43	   U1(e, x) -> x
25.51/8.43	   a -> c
25.51/8.43	   a -> d
25.51/8.43	   b -> c
25.51/8.43	   b -> d
25.51/8.43	   d -> k
25.51/8.43	   c -> e
25.51/8.43	   c -> k
25.51/8.43	
25.51/8.43	Q is empty.
25.51/8.43	We have to consider all minimal (P,Q,R)-chains.
25.51/8.43	----------------------------------------
25.51/8.43	
25.51/8.43	(299) TransformationProof (EQUIVALENT)
25.51/8.43	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.43	
25.51/8.43	   (A^2 -> H(U1(c, c), U1(b, c)),A^2 -> H(U1(c, c), U1(b, c)))
25.51/8.43	   (A^2 -> H(U1(d, c), U1(b, c)),A^2 -> H(U1(d, c), U1(b, c)))
25.51/8.43	   (A^2 -> H(U1(a, e), U1(b, c)),A^2 -> H(U1(a, e), U1(b, c)))
25.51/8.43	   (A^2 -> H(U1(a, k), U1(b, c)),A^2 -> H(U1(a, k), U1(b, c)))
25.51/8.43	   (A^2 -> H(U1(a, c), U1(c, c)),A^2 -> H(U1(a, c), U1(c, c)))
25.51/8.43	   (A^2 -> H(U1(a, c), U1(d, c)),A^2 -> H(U1(a, c), U1(d, c)))
25.51/8.43	   (A^2 -> H(U1(a, c), U1(b, e)),A^2 -> H(U1(a, c), U1(b, e)))
25.51/8.43	   (A^2 -> H(U1(a, c), U1(b, k)),A^2 -> H(U1(a, c), U1(b, k)))
25.51/8.43	
25.51/8.43	
25.51/8.43	----------------------------------------
25.51/8.43	
25.51/8.43	(300)
25.51/8.43	Obligation:
25.51/8.43	Q DP problem:
25.51/8.43	The TRS P consists of the following rules:
25.51/8.43	
25.51/8.43	   H(x, x) -> G(x, x, f(k))
25.51/8.43	   G(d, x, x) -> A^2
25.51/8.43	   A^2 -> H(f(c), f(c))
25.51/8.43	   A^2 -> H(f(d), f(d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, c), f(e))
25.51/8.43	   A^2 -> H(U1(a, c), f(k))
25.51/8.43	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, d), f(e))
25.51/8.43	   A^2 -> H(U1(a, d), f(k))
25.51/8.43	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.43	   A^2 -> H(c, f(b))
25.51/8.43	   A^2 -> H(U1(e, k), f(b))
25.51/8.43	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, c), f(c))
25.51/8.43	   A^2 -> H(U1(e, c), f(d))
25.51/8.43	   A^2 -> H(U1(k, e), f(b))
25.51/8.43	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, c), f(c))
25.51/8.43	   A^2 -> H(U1(k, c), f(d))
25.51/8.43	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(c, e), f(c))
25.51/8.43	   A^2 -> H(U1(c, e), f(d))
25.51/8.43	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(c, k), f(c))
25.51/8.43	   A^2 -> H(U1(c, k), f(d))
25.51/8.43	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.43	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.43	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.43	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.43	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.43	   A^2 -> H(U1(c, c), f(e))
25.51/8.43	   A^2 -> H(U1(c, c), f(k))
25.51/8.43	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.43	   A^2 -> H(e, f(b))
25.51/8.43	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, e), f(c))
25.51/8.43	   A^2 -> H(U1(e, e), f(d))
25.51/8.43	   A^2 -> H(f(e), U1(c, b))
25.51/8.43	   A^2 -> H(f(e), U1(d, b))
25.51/8.43	   A^2 -> H(f(e), U1(b, c))
25.51/8.43	   A^2 -> H(f(e), U1(b, d))
25.51/8.43	   A^2 -> H(f(e), U1(c, c))
25.51/8.43	   A^2 -> H(f(e), f(e))
25.51/8.43	   A^2 -> H(f(e), f(k))
25.51/8.43	   A^2 -> H(f(e), U1(d, d))
25.51/8.43	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, k), f(c))
25.51/8.43	   A^2 -> H(U1(k, k), f(d))
25.51/8.43	   A^2 -> H(f(k), U1(c, b))
25.51/8.43	   A^2 -> H(f(k), U1(d, b))
25.51/8.43	   A^2 -> H(f(k), U1(b, c))
25.51/8.43	   A^2 -> H(f(k), U1(b, d))
25.51/8.43	   A^2 -> H(f(k), U1(c, c))
25.51/8.43	   A^2 -> H(f(k), f(e))
25.51/8.43	   A^2 -> H(f(k), f(k))
25.51/8.43	   A^2 -> H(f(k), U1(d, d))
25.51/8.43	   A^2 -> H(f(c), U1(e, b))
25.51/8.43	   A^2 -> H(f(c), U1(k, b))
25.51/8.43	   A^2 -> H(f(c), U1(c, d))
25.51/8.43	   A^2 -> H(f(c), U1(d, c))
25.51/8.43	   A^2 -> H(f(c), U1(b, e))
25.51/8.43	   A^2 -> H(f(c), U1(b, k))
25.51/8.43	   A^2 -> H(f(c), U1(k, d))
25.51/8.43	   A^2 -> H(f(c), U1(d, k))
25.51/8.43	   A^2 -> H(f(c), U1(k, k))
25.51/8.43	   A^2 -> H(U1(k, k), f(b))
25.51/8.43	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, d), f(c))
25.51/8.43	   A^2 -> H(U1(k, d), f(d))
25.51/8.43	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(d, k), f(c))
25.51/8.43	   A^2 -> H(U1(d, k), f(d))
25.51/8.43	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(d, d), f(e))
25.51/8.43	   A^2 -> H(U1(d, d), f(k))
25.51/8.43	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.43	   A^2 -> H(f(d), U1(e, b))
25.51/8.43	   A^2 -> H(f(d), U1(k, b))
25.51/8.43	   A^2 -> H(f(d), U1(c, d))
25.51/8.43	   A^2 -> H(f(d), U1(d, c))
25.51/8.43	   A^2 -> H(f(d), U1(b, e))
25.51/8.43	   A^2 -> H(f(d), U1(b, k))
25.51/8.43	   A^2 -> H(f(d), U1(e, c))
25.51/8.43	   A^2 -> H(f(d), U1(k, c))
25.51/8.43	   A^2 -> H(f(d), U1(c, e))
25.51/8.43	   A^2 -> H(f(d), U1(c, k))
25.51/8.43	   A^2 -> H(f(d), U1(e, e))
25.51/8.43	   A^2 -> H(f(d), U1(k, k))
25.51/8.43	   A^2 -> H(f(a), b)
25.51/8.43	   A^2 -> H(f(a), U1(e, d))
25.51/8.43	   A^2 -> H(f(a), U1(d, e))
25.51/8.43	   A^2 -> H(f(c), U1(e, c))
25.51/8.43	   A^2 -> H(f(c), U1(k, c))
25.51/8.43	   A^2 -> H(f(c), U1(c, e))
25.51/8.43	   A^2 -> H(f(c), U1(c, k))
25.51/8.43	   A^2 -> H(f(a), c)
25.51/8.43	   A^2 -> H(f(a), U1(e, k))
25.51/8.43	   A^2 -> H(f(a), U1(k, e))
25.51/8.43	   A^2 -> H(f(c), U1(e, e))
25.51/8.43	   A^2 -> H(f(a), e)
25.51/8.43	   A^2 -> H(f(d), U1(k, d))
25.51/8.43	   A^2 -> H(f(d), U1(d, k))
25.51/8.43	   A^2 -> H(f(a), U1(k, k))
25.51/8.43	   A^2 -> H(d, f(b))
25.51/8.43	   A^2 -> H(a, U1(b, b))
25.51/8.43	   A^2 -> H(a, f(c))
25.51/8.43	   A^2 -> H(a, f(d))
25.51/8.43	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, d), f(c))
25.51/8.43	   A^2 -> H(U1(e, d), f(d))
25.51/8.43	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.43	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.43	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.43	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.43	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.43	   A^2 -> H(U1(e, a), f(e))
25.51/8.43	   A^2 -> H(U1(e, a), f(k))
25.51/8.43	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.43	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.43	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.43	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.43	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.43	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.43	   A^2 -> H(U1(k, a), f(e))
25.51/8.43	   A^2 -> H(U1(k, a), f(k))
25.51/8.43	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.43	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(c, d), f(e))
25.51/8.43	   A^2 -> H(U1(c, d), f(k))
25.51/8.43	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.43	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(d, e), f(c))
25.51/8.43	   A^2 -> H(U1(d, e), f(d))
25.51/8.43	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.43	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.43	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.43	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.43	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.43	   A^2 -> H(U1(d, c), f(e))
25.51/8.43	   A^2 -> H(U1(d, c), f(k))
25.51/8.43	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(d, k))
25.51/8.43	   A^2 -> H(U1(a, e), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, e), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, e), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, e), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, e), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, e), f(e))
25.51/8.43	   A^2 -> H(U1(a, e), f(k))
25.51/8.43	   A^2 -> H(U1(a, e), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, k), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, k), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, k), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, k), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, k), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, k), f(e))
25.51/8.43	   A^2 -> H(U1(a, k), f(k))
25.51/8.43	   A^2 -> H(U1(a, k), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(e, b))
25.51/8.43	   A^2 -> H(U1(a, c), U1(k, b))
25.51/8.43	   A^2 -> H(U1(a, c), U1(c, d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(d, c))
25.51/8.43	   A^2 -> H(U1(a, c), U1(b, e))
25.51/8.43	   A^2 -> H(U1(a, c), U1(b, k))
25.51/8.43	
25.51/8.43	The TRS R consists of the following rules:
25.51/8.43	
25.51/8.43	   f(x) -> U1(x, x)
25.51/8.43	   U1(e, x) -> x
25.51/8.43	   a -> c
25.51/8.43	   a -> d
25.51/8.43	   b -> c
25.51/8.43	   b -> d
25.51/8.43	   d -> k
25.51/8.43	   c -> e
25.51/8.43	   c -> k
25.51/8.43	
25.51/8.43	Q is empty.
25.51/8.43	We have to consider all minimal (P,Q,R)-chains.
25.51/8.43	----------------------------------------
25.51/8.43	
25.51/8.43	(301) TransformationProof (EQUIVALENT)
25.51/8.43	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.43	
25.51/8.43	   (A^2 -> H(U1(c, c), U1(b, d)),A^2 -> H(U1(c, c), U1(b, d)))
25.51/8.43	   (A^2 -> H(U1(d, c), U1(b, d)),A^2 -> H(U1(d, c), U1(b, d)))
25.51/8.43	   (A^2 -> H(U1(a, e), U1(b, d)),A^2 -> H(U1(a, e), U1(b, d)))
25.51/8.43	   (A^2 -> H(U1(a, k), U1(b, d)),A^2 -> H(U1(a, k), U1(b, d)))
25.51/8.43	   (A^2 -> H(U1(a, c), U1(c, d)),A^2 -> H(U1(a, c), U1(c, d)))
25.51/8.43	   (A^2 -> H(U1(a, c), U1(d, d)),A^2 -> H(U1(a, c), U1(d, d)))
25.51/8.43	   (A^2 -> H(U1(a, c), U1(b, k)),A^2 -> H(U1(a, c), U1(b, k)))
25.51/8.43	
25.51/8.43	
25.51/8.43	----------------------------------------
25.51/8.43	
25.51/8.43	(302)
25.51/8.43	Obligation:
25.51/8.43	Q DP problem:
25.51/8.43	The TRS P consists of the following rules:
25.51/8.43	
25.51/8.43	   H(x, x) -> G(x, x, f(k))
25.51/8.43	   G(d, x, x) -> A^2
25.51/8.43	   A^2 -> H(f(c), f(c))
25.51/8.43	   A^2 -> H(f(d), f(d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, c), f(e))
25.51/8.43	   A^2 -> H(U1(a, c), f(k))
25.51/8.43	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, d), f(e))
25.51/8.43	   A^2 -> H(U1(a, d), f(k))
25.51/8.43	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.43	   A^2 -> H(c, f(b))
25.51/8.43	   A^2 -> H(U1(e, k), f(b))
25.51/8.43	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, c), f(c))
25.51/8.43	   A^2 -> H(U1(e, c), f(d))
25.51/8.43	   A^2 -> H(U1(k, e), f(b))
25.51/8.43	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, c), f(c))
25.51/8.43	   A^2 -> H(U1(k, c), f(d))
25.51/8.43	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(c, e), f(c))
25.51/8.43	   A^2 -> H(U1(c, e), f(d))
25.51/8.43	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(c, k), f(c))
25.51/8.43	   A^2 -> H(U1(c, k), f(d))
25.51/8.43	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.43	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.43	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.43	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.43	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.43	   A^2 -> H(U1(c, c), f(e))
25.51/8.43	   A^2 -> H(U1(c, c), f(k))
25.51/8.43	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.43	   A^2 -> H(e, f(b))
25.51/8.43	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, e), f(c))
25.51/8.43	   A^2 -> H(U1(e, e), f(d))
25.51/8.43	   A^2 -> H(f(e), U1(c, b))
25.51/8.43	   A^2 -> H(f(e), U1(d, b))
25.51/8.43	   A^2 -> H(f(e), U1(b, c))
25.51/8.43	   A^2 -> H(f(e), U1(b, d))
25.51/8.43	   A^2 -> H(f(e), U1(c, c))
25.51/8.43	   A^2 -> H(f(e), f(e))
25.51/8.43	   A^2 -> H(f(e), f(k))
25.51/8.43	   A^2 -> H(f(e), U1(d, d))
25.51/8.43	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, k), f(c))
25.51/8.43	   A^2 -> H(U1(k, k), f(d))
25.51/8.43	   A^2 -> H(f(k), U1(c, b))
25.51/8.43	   A^2 -> H(f(k), U1(d, b))
25.51/8.43	   A^2 -> H(f(k), U1(b, c))
25.51/8.43	   A^2 -> H(f(k), U1(b, d))
25.51/8.43	   A^2 -> H(f(k), U1(c, c))
25.51/8.43	   A^2 -> H(f(k), f(e))
25.51/8.43	   A^2 -> H(f(k), f(k))
25.51/8.43	   A^2 -> H(f(k), U1(d, d))
25.51/8.43	   A^2 -> H(f(c), U1(e, b))
25.51/8.43	   A^2 -> H(f(c), U1(k, b))
25.51/8.43	   A^2 -> H(f(c), U1(c, d))
25.51/8.43	   A^2 -> H(f(c), U1(d, c))
25.51/8.43	   A^2 -> H(f(c), U1(b, e))
25.51/8.43	   A^2 -> H(f(c), U1(b, k))
25.51/8.43	   A^2 -> H(f(c), U1(k, d))
25.51/8.43	   A^2 -> H(f(c), U1(d, k))
25.51/8.43	   A^2 -> H(f(c), U1(k, k))
25.51/8.43	   A^2 -> H(U1(k, k), f(b))
25.51/8.43	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, d), f(c))
25.51/8.43	   A^2 -> H(U1(k, d), f(d))
25.51/8.43	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(d, k), f(c))
25.51/8.43	   A^2 -> H(U1(d, k), f(d))
25.51/8.43	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(d, d), f(e))
25.51/8.43	   A^2 -> H(U1(d, d), f(k))
25.51/8.43	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.43	   A^2 -> H(f(d), U1(e, b))
25.51/8.43	   A^2 -> H(f(d), U1(k, b))
25.51/8.43	   A^2 -> H(f(d), U1(c, d))
25.51/8.43	   A^2 -> H(f(d), U1(d, c))
25.51/8.43	   A^2 -> H(f(d), U1(b, e))
25.51/8.43	   A^2 -> H(f(d), U1(b, k))
25.51/8.43	   A^2 -> H(f(d), U1(e, c))
25.51/8.43	   A^2 -> H(f(d), U1(k, c))
25.51/8.43	   A^2 -> H(f(d), U1(c, e))
25.51/8.43	   A^2 -> H(f(d), U1(c, k))
25.51/8.43	   A^2 -> H(f(d), U1(e, e))
25.51/8.43	   A^2 -> H(f(d), U1(k, k))
25.51/8.43	   A^2 -> H(f(a), b)
25.51/8.43	   A^2 -> H(f(a), U1(e, d))
25.51/8.43	   A^2 -> H(f(a), U1(d, e))
25.51/8.43	   A^2 -> H(f(c), U1(e, c))
25.51/8.43	   A^2 -> H(f(c), U1(k, c))
25.51/8.43	   A^2 -> H(f(c), U1(c, e))
25.51/8.43	   A^2 -> H(f(c), U1(c, k))
25.51/8.43	   A^2 -> H(f(a), c)
25.51/8.43	   A^2 -> H(f(a), U1(e, k))
25.51/8.43	   A^2 -> H(f(a), U1(k, e))
25.51/8.43	   A^2 -> H(f(c), U1(e, e))
25.51/8.43	   A^2 -> H(f(a), e)
25.51/8.43	   A^2 -> H(f(d), U1(k, d))
25.51/8.43	   A^2 -> H(f(d), U1(d, k))
25.51/8.43	   A^2 -> H(f(a), U1(k, k))
25.51/8.43	   A^2 -> H(d, f(b))
25.51/8.43	   A^2 -> H(a, U1(b, b))
25.51/8.43	   A^2 -> H(a, f(c))
25.51/8.43	   A^2 -> H(a, f(d))
25.51/8.43	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, d), f(c))
25.51/8.43	   A^2 -> H(U1(e, d), f(d))
25.51/8.43	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.43	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.43	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.43	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.43	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.43	   A^2 -> H(U1(e, a), f(e))
25.51/8.43	   A^2 -> H(U1(e, a), f(k))
25.51/8.43	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.43	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.43	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.43	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.43	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.43	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.43	   A^2 -> H(U1(k, a), f(e))
25.51/8.43	   A^2 -> H(U1(k, a), f(k))
25.51/8.43	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.43	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(c, d), f(e))
25.51/8.43	   A^2 -> H(U1(c, d), f(k))
25.51/8.43	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.43	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(d, e), f(c))
25.51/8.43	   A^2 -> H(U1(d, e), f(d))
25.51/8.43	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.43	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.43	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.43	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.43	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.43	   A^2 -> H(U1(d, c), f(e))
25.51/8.43	   A^2 -> H(U1(d, c), f(k))
25.51/8.43	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(d, k))
25.51/8.43	   A^2 -> H(U1(a, e), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, e), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, e), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, e), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, e), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, e), f(e))
25.51/8.43	   A^2 -> H(U1(a, e), f(k))
25.51/8.43	   A^2 -> H(U1(a, e), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, k), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, k), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, k), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, k), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, k), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, k), f(e))
25.51/8.43	   A^2 -> H(U1(a, k), f(k))
25.51/8.43	   A^2 -> H(U1(a, k), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(e, b))
25.51/8.43	   A^2 -> H(U1(a, c), U1(k, b))
25.51/8.43	   A^2 -> H(U1(a, c), U1(c, d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(d, c))
25.51/8.43	   A^2 -> H(U1(a, c), U1(b, e))
25.51/8.43	   A^2 -> H(U1(a, c), U1(b, k))
25.51/8.43	
25.51/8.43	The TRS R consists of the following rules:
25.51/8.43	
25.51/8.43	   f(x) -> U1(x, x)
25.51/8.43	   U1(e, x) -> x
25.51/8.43	   a -> c
25.51/8.43	   a -> d
25.51/8.43	   b -> c
25.51/8.43	   b -> d
25.51/8.43	   d -> k
25.51/8.43	   c -> e
25.51/8.43	   c -> k
25.51/8.43	
25.51/8.43	Q is empty.
25.51/8.43	We have to consider all minimal (P,Q,R)-chains.
25.51/8.43	----------------------------------------
25.51/8.43	
25.51/8.43	(303) TransformationProof (EQUIVALENT)
25.51/8.43	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.43	
25.51/8.43	   (A^2 -> H(U1(c, c), U1(c, c)),A^2 -> H(U1(c, c), U1(c, c)))
25.51/8.43	   (A^2 -> H(U1(d, c), U1(c, c)),A^2 -> H(U1(d, c), U1(c, c)))
25.51/8.43	   (A^2 -> H(U1(a, e), U1(c, c)),A^2 -> H(U1(a, e), U1(c, c)))
25.51/8.43	   (A^2 -> H(U1(a, k), U1(c, c)),A^2 -> H(U1(a, k), U1(c, c)))
25.51/8.43	   (A^2 -> H(U1(a, c), U1(e, c)),A^2 -> H(U1(a, c), U1(e, c)))
25.51/8.43	   (A^2 -> H(U1(a, c), U1(k, c)),A^2 -> H(U1(a, c), U1(k, c)))
25.51/8.43	   (A^2 -> H(U1(a, c), U1(c, e)),A^2 -> H(U1(a, c), U1(c, e)))
25.51/8.43	   (A^2 -> H(U1(a, c), U1(c, k)),A^2 -> H(U1(a, c), U1(c, k)))
25.51/8.43	
25.51/8.43	
25.51/8.43	----------------------------------------
25.51/8.43	
25.51/8.43	(304)
25.51/8.43	Obligation:
25.51/8.43	Q DP problem:
25.51/8.43	The TRS P consists of the following rules:
25.51/8.43	
25.51/8.43	   H(x, x) -> G(x, x, f(k))
25.51/8.43	   G(d, x, x) -> A^2
25.51/8.43	   A^2 -> H(f(c), f(c))
25.51/8.43	   A^2 -> H(f(d), f(d))
25.51/8.43	   A^2 -> H(U1(a, c), f(e))
25.51/8.43	   A^2 -> H(U1(a, c), f(k))
25.51/8.43	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, d), f(e))
25.51/8.43	   A^2 -> H(U1(a, d), f(k))
25.51/8.43	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.43	   A^2 -> H(c, f(b))
25.51/8.43	   A^2 -> H(U1(e, k), f(b))
25.51/8.43	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, c), f(c))
25.51/8.43	   A^2 -> H(U1(e, c), f(d))
25.51/8.43	   A^2 -> H(U1(k, e), f(b))
25.51/8.43	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, c), f(c))
25.51/8.43	   A^2 -> H(U1(k, c), f(d))
25.51/8.43	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(c, e), f(c))
25.51/8.43	   A^2 -> H(U1(c, e), f(d))
25.51/8.43	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(c, k), f(c))
25.51/8.43	   A^2 -> H(U1(c, k), f(d))
25.51/8.43	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.43	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.43	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.43	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.43	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.43	   A^2 -> H(U1(c, c), f(e))
25.51/8.43	   A^2 -> H(U1(c, c), f(k))
25.51/8.43	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.43	   A^2 -> H(e, f(b))
25.51/8.43	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, e), f(c))
25.51/8.43	   A^2 -> H(U1(e, e), f(d))
25.51/8.43	   A^2 -> H(f(e), U1(c, b))
25.51/8.43	   A^2 -> H(f(e), U1(d, b))
25.51/8.43	   A^2 -> H(f(e), U1(b, c))
25.51/8.43	   A^2 -> H(f(e), U1(b, d))
25.51/8.43	   A^2 -> H(f(e), U1(c, c))
25.51/8.43	   A^2 -> H(f(e), f(e))
25.51/8.43	   A^2 -> H(f(e), f(k))
25.51/8.43	   A^2 -> H(f(e), U1(d, d))
25.51/8.43	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, k), f(c))
25.51/8.43	   A^2 -> H(U1(k, k), f(d))
25.51/8.43	   A^2 -> H(f(k), U1(c, b))
25.51/8.43	   A^2 -> H(f(k), U1(d, b))
25.51/8.43	   A^2 -> H(f(k), U1(b, c))
25.51/8.43	   A^2 -> H(f(k), U1(b, d))
25.51/8.43	   A^2 -> H(f(k), U1(c, c))
25.51/8.43	   A^2 -> H(f(k), f(e))
25.51/8.43	   A^2 -> H(f(k), f(k))
25.51/8.43	   A^2 -> H(f(k), U1(d, d))
25.51/8.43	   A^2 -> H(f(c), U1(e, b))
25.51/8.43	   A^2 -> H(f(c), U1(k, b))
25.51/8.43	   A^2 -> H(f(c), U1(c, d))
25.51/8.43	   A^2 -> H(f(c), U1(d, c))
25.51/8.43	   A^2 -> H(f(c), U1(b, e))
25.51/8.43	   A^2 -> H(f(c), U1(b, k))
25.51/8.43	   A^2 -> H(f(c), U1(k, d))
25.51/8.43	   A^2 -> H(f(c), U1(d, k))
25.51/8.43	   A^2 -> H(f(c), U1(k, k))
25.51/8.43	   A^2 -> H(U1(k, k), f(b))
25.51/8.43	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, d), f(c))
25.51/8.43	   A^2 -> H(U1(k, d), f(d))
25.51/8.43	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(d, k), f(c))
25.51/8.43	   A^2 -> H(U1(d, k), f(d))
25.51/8.43	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(d, d), f(e))
25.51/8.43	   A^2 -> H(U1(d, d), f(k))
25.51/8.43	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.43	   A^2 -> H(f(d), U1(e, b))
25.51/8.43	   A^2 -> H(f(d), U1(k, b))
25.51/8.43	   A^2 -> H(f(d), U1(c, d))
25.51/8.43	   A^2 -> H(f(d), U1(d, c))
25.51/8.43	   A^2 -> H(f(d), U1(b, e))
25.51/8.43	   A^2 -> H(f(d), U1(b, k))
25.51/8.43	   A^2 -> H(f(d), U1(e, c))
25.51/8.43	   A^2 -> H(f(d), U1(k, c))
25.51/8.43	   A^2 -> H(f(d), U1(c, e))
25.51/8.43	   A^2 -> H(f(d), U1(c, k))
25.51/8.43	   A^2 -> H(f(d), U1(e, e))
25.51/8.43	   A^2 -> H(f(d), U1(k, k))
25.51/8.43	   A^2 -> H(f(a), b)
25.51/8.43	   A^2 -> H(f(a), U1(e, d))
25.51/8.43	   A^2 -> H(f(a), U1(d, e))
25.51/8.43	   A^2 -> H(f(c), U1(e, c))
25.51/8.43	   A^2 -> H(f(c), U1(k, c))
25.51/8.43	   A^2 -> H(f(c), U1(c, e))
25.51/8.43	   A^2 -> H(f(c), U1(c, k))
25.51/8.43	   A^2 -> H(f(a), c)
25.51/8.43	   A^2 -> H(f(a), U1(e, k))
25.51/8.43	   A^2 -> H(f(a), U1(k, e))
25.51/8.43	   A^2 -> H(f(c), U1(e, e))
25.51/8.43	   A^2 -> H(f(a), e)
25.51/8.43	   A^2 -> H(f(d), U1(k, d))
25.51/8.43	   A^2 -> H(f(d), U1(d, k))
25.51/8.43	   A^2 -> H(f(a), U1(k, k))
25.51/8.43	   A^2 -> H(d, f(b))
25.51/8.43	   A^2 -> H(a, U1(b, b))
25.51/8.43	   A^2 -> H(a, f(c))
25.51/8.43	   A^2 -> H(a, f(d))
25.51/8.43	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, d), f(c))
25.51/8.43	   A^2 -> H(U1(e, d), f(d))
25.51/8.43	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.43	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.43	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.43	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.43	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.43	   A^2 -> H(U1(e, a), f(e))
25.51/8.43	   A^2 -> H(U1(e, a), f(k))
25.51/8.43	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.43	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.43	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.43	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.43	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.43	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.43	   A^2 -> H(U1(k, a), f(e))
25.51/8.43	   A^2 -> H(U1(k, a), f(k))
25.51/8.43	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.43	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(c, d), f(e))
25.51/8.43	   A^2 -> H(U1(c, d), f(k))
25.51/8.43	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.43	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(d, e), f(c))
25.51/8.43	   A^2 -> H(U1(d, e), f(d))
25.51/8.43	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.43	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.43	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.43	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.43	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.43	   A^2 -> H(U1(d, c), f(e))
25.51/8.43	   A^2 -> H(U1(d, c), f(k))
25.51/8.43	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(d, k))
25.51/8.43	   A^2 -> H(U1(a, e), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, e), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, e), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, e), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, e), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, e), f(e))
25.51/8.43	   A^2 -> H(U1(a, e), f(k))
25.51/8.43	   A^2 -> H(U1(a, e), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, k), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, k), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, k), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, k), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, k), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, k), f(e))
25.51/8.43	   A^2 -> H(U1(a, k), f(k))
25.51/8.43	   A^2 -> H(U1(a, k), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(e, b))
25.51/8.43	   A^2 -> H(U1(a, c), U1(k, b))
25.51/8.43	   A^2 -> H(U1(a, c), U1(c, d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(d, c))
25.51/8.43	   A^2 -> H(U1(a, c), U1(b, e))
25.51/8.43	   A^2 -> H(U1(a, c), U1(b, k))
25.51/8.43	   A^2 -> H(U1(a, c), U1(e, c))
25.51/8.43	   A^2 -> H(U1(a, c), U1(k, c))
25.51/8.43	   A^2 -> H(U1(a, c), U1(c, e))
25.51/8.43	   A^2 -> H(U1(a, c), U1(c, k))
25.51/8.43	
25.51/8.43	The TRS R consists of the following rules:
25.51/8.43	
25.51/8.43	   f(x) -> U1(x, x)
25.51/8.43	   U1(e, x) -> x
25.51/8.43	   a -> c
25.51/8.43	   a -> d
25.51/8.43	   b -> c
25.51/8.43	   b -> d
25.51/8.43	   d -> k
25.51/8.43	   c -> e
25.51/8.43	   c -> k
25.51/8.43	
25.51/8.43	Q is empty.
25.51/8.43	We have to consider all minimal (P,Q,R)-chains.
25.51/8.43	----------------------------------------
25.51/8.43	
25.51/8.43	(305) TransformationProof (EQUIVALENT)
25.51/8.43	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), f(e)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.43	
25.51/8.43	   (A^2 -> H(U1(c, c), f(e)),A^2 -> H(U1(c, c), f(e)))
25.51/8.43	   (A^2 -> H(U1(d, c), f(e)),A^2 -> H(U1(d, c), f(e)))
25.51/8.43	   (A^2 -> H(U1(a, e), f(e)),A^2 -> H(U1(a, e), f(e)))
25.51/8.43	   (A^2 -> H(U1(a, k), f(e)),A^2 -> H(U1(a, k), f(e)))
25.51/8.43	   (A^2 -> H(U1(a, c), U1(e, e)),A^2 -> H(U1(a, c), U1(e, e)))
25.51/8.43	
25.51/8.43	
25.51/8.43	----------------------------------------
25.51/8.43	
25.51/8.43	(306)
25.51/8.43	Obligation:
25.51/8.43	Q DP problem:
25.51/8.43	The TRS P consists of the following rules:
25.51/8.43	
25.51/8.43	   H(x, x) -> G(x, x, f(k))
25.51/8.43	   G(d, x, x) -> A^2
25.51/8.43	   A^2 -> H(f(c), f(c))
25.51/8.43	   A^2 -> H(f(d), f(d))
25.51/8.43	   A^2 -> H(U1(a, c), f(k))
25.51/8.43	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, d), f(e))
25.51/8.43	   A^2 -> H(U1(a, d), f(k))
25.51/8.43	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.43	   A^2 -> H(c, f(b))
25.51/8.43	   A^2 -> H(U1(e, k), f(b))
25.51/8.43	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, c), f(c))
25.51/8.43	   A^2 -> H(U1(e, c), f(d))
25.51/8.43	   A^2 -> H(U1(k, e), f(b))
25.51/8.43	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, c), f(c))
25.51/8.43	   A^2 -> H(U1(k, c), f(d))
25.51/8.43	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(c, e), f(c))
25.51/8.43	   A^2 -> H(U1(c, e), f(d))
25.51/8.43	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(c, k), f(c))
25.51/8.43	   A^2 -> H(U1(c, k), f(d))
25.51/8.43	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.43	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.43	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.43	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.43	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.43	   A^2 -> H(U1(c, c), f(e))
25.51/8.43	   A^2 -> H(U1(c, c), f(k))
25.51/8.43	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.43	   A^2 -> H(e, f(b))
25.51/8.43	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, e), f(c))
25.51/8.43	   A^2 -> H(U1(e, e), f(d))
25.51/8.43	   A^2 -> H(f(e), U1(c, b))
25.51/8.43	   A^2 -> H(f(e), U1(d, b))
25.51/8.43	   A^2 -> H(f(e), U1(b, c))
25.51/8.43	   A^2 -> H(f(e), U1(b, d))
25.51/8.43	   A^2 -> H(f(e), U1(c, c))
25.51/8.43	   A^2 -> H(f(e), f(e))
25.51/8.43	   A^2 -> H(f(e), f(k))
25.51/8.43	   A^2 -> H(f(e), U1(d, d))
25.51/8.43	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, k), f(c))
25.51/8.43	   A^2 -> H(U1(k, k), f(d))
25.51/8.43	   A^2 -> H(f(k), U1(c, b))
25.51/8.43	   A^2 -> H(f(k), U1(d, b))
25.51/8.43	   A^2 -> H(f(k), U1(b, c))
25.51/8.43	   A^2 -> H(f(k), U1(b, d))
25.51/8.43	   A^2 -> H(f(k), U1(c, c))
25.51/8.43	   A^2 -> H(f(k), f(e))
25.51/8.43	   A^2 -> H(f(k), f(k))
25.51/8.43	   A^2 -> H(f(k), U1(d, d))
25.51/8.43	   A^2 -> H(f(c), U1(e, b))
25.51/8.43	   A^2 -> H(f(c), U1(k, b))
25.51/8.43	   A^2 -> H(f(c), U1(c, d))
25.51/8.43	   A^2 -> H(f(c), U1(d, c))
25.51/8.43	   A^2 -> H(f(c), U1(b, e))
25.51/8.43	   A^2 -> H(f(c), U1(b, k))
25.51/8.43	   A^2 -> H(f(c), U1(k, d))
25.51/8.43	   A^2 -> H(f(c), U1(d, k))
25.51/8.43	   A^2 -> H(f(c), U1(k, k))
25.51/8.43	   A^2 -> H(U1(k, k), f(b))
25.51/8.43	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, d), f(c))
25.51/8.43	   A^2 -> H(U1(k, d), f(d))
25.51/8.43	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(d, k), f(c))
25.51/8.43	   A^2 -> H(U1(d, k), f(d))
25.51/8.43	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(d, d), f(e))
25.51/8.43	   A^2 -> H(U1(d, d), f(k))
25.51/8.43	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.43	   A^2 -> H(f(d), U1(e, b))
25.51/8.43	   A^2 -> H(f(d), U1(k, b))
25.51/8.43	   A^2 -> H(f(d), U1(c, d))
25.51/8.43	   A^2 -> H(f(d), U1(d, c))
25.51/8.43	   A^2 -> H(f(d), U1(b, e))
25.51/8.43	   A^2 -> H(f(d), U1(b, k))
25.51/8.43	   A^2 -> H(f(d), U1(e, c))
25.51/8.43	   A^2 -> H(f(d), U1(k, c))
25.51/8.43	   A^2 -> H(f(d), U1(c, e))
25.51/8.43	   A^2 -> H(f(d), U1(c, k))
25.51/8.43	   A^2 -> H(f(d), U1(e, e))
25.51/8.43	   A^2 -> H(f(d), U1(k, k))
25.51/8.43	   A^2 -> H(f(a), b)
25.51/8.43	   A^2 -> H(f(a), U1(e, d))
25.51/8.43	   A^2 -> H(f(a), U1(d, e))
25.51/8.43	   A^2 -> H(f(c), U1(e, c))
25.51/8.43	   A^2 -> H(f(c), U1(k, c))
25.51/8.43	   A^2 -> H(f(c), U1(c, e))
25.51/8.43	   A^2 -> H(f(c), U1(c, k))
25.51/8.43	   A^2 -> H(f(a), c)
25.51/8.43	   A^2 -> H(f(a), U1(e, k))
25.51/8.43	   A^2 -> H(f(a), U1(k, e))
25.51/8.43	   A^2 -> H(f(c), U1(e, e))
25.51/8.43	   A^2 -> H(f(a), e)
25.51/8.43	   A^2 -> H(f(d), U1(k, d))
25.51/8.43	   A^2 -> H(f(d), U1(d, k))
25.51/8.43	   A^2 -> H(f(a), U1(k, k))
25.51/8.43	   A^2 -> H(d, f(b))
25.51/8.43	   A^2 -> H(a, U1(b, b))
25.51/8.43	   A^2 -> H(a, f(c))
25.51/8.43	   A^2 -> H(a, f(d))
25.51/8.43	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, d), f(c))
25.51/8.43	   A^2 -> H(U1(e, d), f(d))
25.51/8.43	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.43	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.43	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.43	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.43	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.43	   A^2 -> H(U1(e, a), f(e))
25.51/8.43	   A^2 -> H(U1(e, a), f(k))
25.51/8.43	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.43	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.43	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.43	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.43	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.43	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.43	   A^2 -> H(U1(k, a), f(e))
25.51/8.43	   A^2 -> H(U1(k, a), f(k))
25.51/8.43	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.43	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(c, d), f(e))
25.51/8.43	   A^2 -> H(U1(c, d), f(k))
25.51/8.43	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.43	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(d, e), f(c))
25.51/8.43	   A^2 -> H(U1(d, e), f(d))
25.51/8.43	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.43	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.43	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.43	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.43	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.43	   A^2 -> H(U1(d, c), f(e))
25.51/8.43	   A^2 -> H(U1(d, c), f(k))
25.51/8.43	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(d, k))
25.51/8.43	   A^2 -> H(U1(a, e), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, e), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, e), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, e), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, e), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, e), f(e))
25.51/8.43	   A^2 -> H(U1(a, e), f(k))
25.51/8.43	   A^2 -> H(U1(a, e), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, k), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, k), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, k), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, k), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, k), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, k), f(e))
25.51/8.43	   A^2 -> H(U1(a, k), f(k))
25.51/8.43	   A^2 -> H(U1(a, k), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(e, b))
25.51/8.43	   A^2 -> H(U1(a, c), U1(k, b))
25.51/8.43	   A^2 -> H(U1(a, c), U1(c, d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(d, c))
25.51/8.43	   A^2 -> H(U1(a, c), U1(b, e))
25.51/8.43	   A^2 -> H(U1(a, c), U1(b, k))
25.51/8.43	   A^2 -> H(U1(a, c), U1(e, c))
25.51/8.43	   A^2 -> H(U1(a, c), U1(k, c))
25.51/8.43	   A^2 -> H(U1(a, c), U1(c, e))
25.51/8.43	   A^2 -> H(U1(a, c), U1(c, k))
25.51/8.43	   A^2 -> H(U1(a, c), U1(e, e))
25.51/8.43	
25.51/8.43	The TRS R consists of the following rules:
25.51/8.43	
25.51/8.43	   f(x) -> U1(x, x)
25.51/8.43	   U1(e, x) -> x
25.51/8.43	   a -> c
25.51/8.43	   a -> d
25.51/8.43	   b -> c
25.51/8.43	   b -> d
25.51/8.43	   d -> k
25.51/8.43	   c -> e
25.51/8.43	   c -> k
25.51/8.43	
25.51/8.43	Q is empty.
25.51/8.43	We have to consider all minimal (P,Q,R)-chains.
25.51/8.43	----------------------------------------
25.51/8.43	
25.51/8.43	(307) TransformationProof (EQUIVALENT)
25.51/8.43	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), f(k)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.43	
25.51/8.43	   (A^2 -> H(U1(c, c), f(k)),A^2 -> H(U1(c, c), f(k)))
25.51/8.43	   (A^2 -> H(U1(d, c), f(k)),A^2 -> H(U1(d, c), f(k)))
25.51/8.43	   (A^2 -> H(U1(a, e), f(k)),A^2 -> H(U1(a, e), f(k)))
25.51/8.43	   (A^2 -> H(U1(a, k), f(k)),A^2 -> H(U1(a, k), f(k)))
25.51/8.43	   (A^2 -> H(U1(a, c), U1(k, k)),A^2 -> H(U1(a, c), U1(k, k)))
25.51/8.43	
25.51/8.43	
25.51/8.43	----------------------------------------
25.51/8.43	
25.51/8.43	(308)
25.51/8.43	Obligation:
25.51/8.43	Q DP problem:
25.51/8.43	The TRS P consists of the following rules:
25.51/8.43	
25.51/8.43	   H(x, x) -> G(x, x, f(k))
25.51/8.43	   G(d, x, x) -> A^2
25.51/8.43	   A^2 -> H(f(c), f(c))
25.51/8.43	   A^2 -> H(f(d), f(d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, d), f(e))
25.51/8.43	   A^2 -> H(U1(a, d), f(k))
25.51/8.43	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.43	   A^2 -> H(c, f(b))
25.51/8.43	   A^2 -> H(U1(e, k), f(b))
25.51/8.43	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, c), f(c))
25.51/8.43	   A^2 -> H(U1(e, c), f(d))
25.51/8.43	   A^2 -> H(U1(k, e), f(b))
25.51/8.43	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, c), f(c))
25.51/8.43	   A^2 -> H(U1(k, c), f(d))
25.51/8.43	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(c, e), f(c))
25.51/8.43	   A^2 -> H(U1(c, e), f(d))
25.51/8.43	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(c, k), f(c))
25.51/8.43	   A^2 -> H(U1(c, k), f(d))
25.51/8.43	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.43	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.43	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.43	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.43	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.43	   A^2 -> H(U1(c, c), f(e))
25.51/8.43	   A^2 -> H(U1(c, c), f(k))
25.51/8.43	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.43	   A^2 -> H(e, f(b))
25.51/8.43	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, e), f(c))
25.51/8.43	   A^2 -> H(U1(e, e), f(d))
25.51/8.43	   A^2 -> H(f(e), U1(c, b))
25.51/8.43	   A^2 -> H(f(e), U1(d, b))
25.51/8.43	   A^2 -> H(f(e), U1(b, c))
25.51/8.43	   A^2 -> H(f(e), U1(b, d))
25.51/8.43	   A^2 -> H(f(e), U1(c, c))
25.51/8.43	   A^2 -> H(f(e), f(e))
25.51/8.43	   A^2 -> H(f(e), f(k))
25.51/8.43	   A^2 -> H(f(e), U1(d, d))
25.51/8.43	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, k), f(c))
25.51/8.43	   A^2 -> H(U1(k, k), f(d))
25.51/8.43	   A^2 -> H(f(k), U1(c, b))
25.51/8.43	   A^2 -> H(f(k), U1(d, b))
25.51/8.43	   A^2 -> H(f(k), U1(b, c))
25.51/8.43	   A^2 -> H(f(k), U1(b, d))
25.51/8.43	   A^2 -> H(f(k), U1(c, c))
25.51/8.43	   A^2 -> H(f(k), f(e))
25.51/8.43	   A^2 -> H(f(k), f(k))
25.51/8.43	   A^2 -> H(f(k), U1(d, d))
25.51/8.43	   A^2 -> H(f(c), U1(e, b))
25.51/8.43	   A^2 -> H(f(c), U1(k, b))
25.51/8.43	   A^2 -> H(f(c), U1(c, d))
25.51/8.43	   A^2 -> H(f(c), U1(d, c))
25.51/8.43	   A^2 -> H(f(c), U1(b, e))
25.51/8.43	   A^2 -> H(f(c), U1(b, k))
25.51/8.43	   A^2 -> H(f(c), U1(k, d))
25.51/8.43	   A^2 -> H(f(c), U1(d, k))
25.51/8.43	   A^2 -> H(f(c), U1(k, k))
25.51/8.43	   A^2 -> H(U1(k, k), f(b))
25.51/8.43	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, d), f(c))
25.51/8.43	   A^2 -> H(U1(k, d), f(d))
25.51/8.43	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(d, k), f(c))
25.51/8.43	   A^2 -> H(U1(d, k), f(d))
25.51/8.43	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(d, d), f(e))
25.51/8.43	   A^2 -> H(U1(d, d), f(k))
25.51/8.43	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.43	   A^2 -> H(f(d), U1(e, b))
25.51/8.43	   A^2 -> H(f(d), U1(k, b))
25.51/8.43	   A^2 -> H(f(d), U1(c, d))
25.51/8.43	   A^2 -> H(f(d), U1(d, c))
25.51/8.43	   A^2 -> H(f(d), U1(b, e))
25.51/8.43	   A^2 -> H(f(d), U1(b, k))
25.51/8.43	   A^2 -> H(f(d), U1(e, c))
25.51/8.43	   A^2 -> H(f(d), U1(k, c))
25.51/8.43	   A^2 -> H(f(d), U1(c, e))
25.51/8.43	   A^2 -> H(f(d), U1(c, k))
25.51/8.43	   A^2 -> H(f(d), U1(e, e))
25.51/8.43	   A^2 -> H(f(d), U1(k, k))
25.51/8.43	   A^2 -> H(f(a), b)
25.51/8.43	   A^2 -> H(f(a), U1(e, d))
25.51/8.43	   A^2 -> H(f(a), U1(d, e))
25.51/8.43	   A^2 -> H(f(c), U1(e, c))
25.51/8.43	   A^2 -> H(f(c), U1(k, c))
25.51/8.43	   A^2 -> H(f(c), U1(c, e))
25.51/8.43	   A^2 -> H(f(c), U1(c, k))
25.51/8.43	   A^2 -> H(f(a), c)
25.51/8.43	   A^2 -> H(f(a), U1(e, k))
25.51/8.43	   A^2 -> H(f(a), U1(k, e))
25.51/8.43	   A^2 -> H(f(c), U1(e, e))
25.51/8.43	   A^2 -> H(f(a), e)
25.51/8.43	   A^2 -> H(f(d), U1(k, d))
25.51/8.43	   A^2 -> H(f(d), U1(d, k))
25.51/8.43	   A^2 -> H(f(a), U1(k, k))
25.51/8.43	   A^2 -> H(d, f(b))
25.51/8.43	   A^2 -> H(a, U1(b, b))
25.51/8.43	   A^2 -> H(a, f(c))
25.51/8.43	   A^2 -> H(a, f(d))
25.51/8.43	   A^2 -> H(U1(e, d), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, d), f(c))
25.51/8.43	   A^2 -> H(U1(e, d), f(d))
25.51/8.43	   A^2 -> H(U1(e, a), U1(c, b))
25.51/8.43	   A^2 -> H(U1(e, a), U1(d, b))
25.51/8.43	   A^2 -> H(U1(e, a), U1(b, c))
25.51/8.43	   A^2 -> H(U1(e, a), U1(b, d))
25.51/8.43	   A^2 -> H(U1(e, a), U1(c, c))
25.51/8.43	   A^2 -> H(U1(e, a), f(e))
25.51/8.43	   A^2 -> H(U1(e, a), f(k))
25.51/8.43	   A^2 -> H(U1(e, a), U1(d, d))
25.51/8.43	   A^2 -> H(U1(k, a), U1(c, b))
25.51/8.43	   A^2 -> H(U1(k, a), U1(d, b))
25.51/8.43	   A^2 -> H(U1(k, a), U1(b, c))
25.51/8.43	   A^2 -> H(U1(k, a), U1(b, d))
25.51/8.43	   A^2 -> H(U1(k, a), U1(c, c))
25.51/8.43	   A^2 -> H(U1(k, a), f(e))
25.51/8.43	   A^2 -> H(U1(k, a), f(k))
25.51/8.43	   A^2 -> H(U1(k, a), U1(d, d))
25.51/8.43	   A^2 -> H(U1(c, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(c, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(c, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(c, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(c, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(c, d), f(e))
25.51/8.43	   A^2 -> H(U1(c, d), f(k))
25.51/8.43	   A^2 -> H(U1(c, d), U1(d, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(c, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(c, a), U1(d, k))
25.51/8.43	   A^2 -> H(U1(d, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(d, e), f(c))
25.51/8.43	   A^2 -> H(U1(d, e), f(d))
25.51/8.43	   A^2 -> H(U1(d, c), U1(c, b))
25.51/8.43	   A^2 -> H(U1(d, c), U1(d, b))
25.51/8.43	   A^2 -> H(U1(d, c), U1(b, c))
25.51/8.43	   A^2 -> H(U1(d, c), U1(b, d))
25.51/8.43	   A^2 -> H(U1(d, c), U1(c, c))
25.51/8.43	   A^2 -> H(U1(d, c), f(e))
25.51/8.43	   A^2 -> H(U1(d, c), f(k))
25.51/8.43	   A^2 -> H(U1(d, c), U1(d, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(d, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(d, a), U1(d, k))
25.51/8.43	   A^2 -> H(U1(a, e), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, e), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, e), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, e), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, e), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, e), f(e))
25.51/8.43	   A^2 -> H(U1(a, e), f(k))
25.51/8.43	   A^2 -> H(U1(a, e), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, k), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, k), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, k), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, k), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, k), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, k), f(e))
25.51/8.43	   A^2 -> H(U1(a, k), f(k))
25.51/8.43	   A^2 -> H(U1(a, k), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(e, b))
25.51/8.43	   A^2 -> H(U1(a, c), U1(k, b))
25.51/8.43	   A^2 -> H(U1(a, c), U1(c, d))
25.51/8.43	   A^2 -> H(U1(a, c), U1(d, c))
25.51/8.43	   A^2 -> H(U1(a, c), U1(b, e))
25.51/8.43	   A^2 -> H(U1(a, c), U1(b, k))
25.51/8.43	   A^2 -> H(U1(a, c), U1(e, c))
25.51/8.43	   A^2 -> H(U1(a, c), U1(k, c))
25.51/8.43	   A^2 -> H(U1(a, c), U1(c, e))
25.51/8.43	   A^2 -> H(U1(a, c), U1(c, k))
25.51/8.43	   A^2 -> H(U1(a, c), U1(e, e))
25.51/8.43	   A^2 -> H(U1(a, c), U1(k, k))
25.51/8.43	
25.51/8.43	The TRS R consists of the following rules:
25.51/8.43	
25.51/8.43	   f(x) -> U1(x, x)
25.51/8.43	   U1(e, x) -> x
25.51/8.43	   a -> c
25.51/8.43	   a -> d
25.51/8.43	   b -> c
25.51/8.43	   b -> d
25.51/8.43	   d -> k
25.51/8.43	   c -> e
25.51/8.43	   c -> k
25.51/8.43	
25.51/8.43	Q is empty.
25.51/8.43	We have to consider all minimal (P,Q,R)-chains.
25.51/8.43	----------------------------------------
25.51/8.43	
25.51/8.43	(309) TransformationProof (EQUIVALENT)
25.51/8.43	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
25.51/8.43	
25.51/8.43	   (A^2 -> H(U1(c, c), U1(d, d)),A^2 -> H(U1(c, c), U1(d, d)))
25.51/8.43	   (A^2 -> H(U1(d, c), U1(d, d)),A^2 -> H(U1(d, c), U1(d, d)))
25.51/8.43	   (A^2 -> H(U1(a, e), U1(d, d)),A^2 -> H(U1(a, e), U1(d, d)))
25.51/8.43	   (A^2 -> H(U1(a, k), U1(d, d)),A^2 -> H(U1(a, k), U1(d, d)))
25.51/8.43	   (A^2 -> H(U1(a, c), U1(k, d)),A^2 -> H(U1(a, c), U1(k, d)))
25.51/8.43	   (A^2 -> H(U1(a, c), U1(d, k)),A^2 -> H(U1(a, c), U1(d, k)))
25.51/8.43	
25.51/8.43	
25.51/8.43	----------------------------------------
25.51/8.43	
25.51/8.43	(310)
25.51/8.43	Obligation:
25.51/8.43	Q DP problem:
25.51/8.43	The TRS P consists of the following rules:
25.51/8.43	
25.51/8.43	   H(x, x) -> G(x, x, f(k))
25.51/8.43	   G(d, x, x) -> A^2
25.51/8.43	   A^2 -> H(f(c), f(c))
25.51/8.43	   A^2 -> H(f(d), f(d))
25.51/8.43	   A^2 -> H(U1(a, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(a, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(a, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(a, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(a, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(a, d), f(e))
25.51/8.43	   A^2 -> H(U1(a, d), f(k))
25.51/8.43	   A^2 -> H(U1(a, d), U1(d, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, b))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, b))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(d, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(b, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(b, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, c))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(c, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(e, e))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, k))
25.51/8.43	   A^2 -> H(U1(a, a), U1(k, d))
25.51/8.43	   A^2 -> H(U1(a, a), U1(d, k))
25.51/8.43	   A^2 -> H(c, f(b))
25.51/8.43	   A^2 -> H(U1(e, k), f(b))
25.51/8.43	   A^2 -> H(U1(e, c), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, c), f(c))
25.51/8.43	   A^2 -> H(U1(e, c), f(d))
25.51/8.43	   A^2 -> H(U1(k, e), f(b))
25.51/8.43	   A^2 -> H(U1(k, c), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, c), f(c))
25.51/8.43	   A^2 -> H(U1(k, c), f(d))
25.51/8.43	   A^2 -> H(U1(c, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(c, e), f(c))
25.51/8.43	   A^2 -> H(U1(c, e), f(d))
25.51/8.43	   A^2 -> H(U1(c, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(c, k), f(c))
25.51/8.43	   A^2 -> H(U1(c, k), f(d))
25.51/8.43	   A^2 -> H(U1(c, c), U1(c, b))
25.51/8.43	   A^2 -> H(U1(c, c), U1(d, b))
25.51/8.43	   A^2 -> H(U1(c, c), U1(b, c))
25.51/8.43	   A^2 -> H(U1(c, c), U1(b, d))
25.51/8.43	   A^2 -> H(U1(c, c), U1(c, c))
25.51/8.43	   A^2 -> H(U1(c, c), f(e))
25.51/8.43	   A^2 -> H(U1(c, c), f(k))
25.51/8.43	   A^2 -> H(U1(c, c), U1(d, d))
25.51/8.43	   A^2 -> H(e, f(b))
25.51/8.43	   A^2 -> H(U1(e, e), U1(b, b))
25.51/8.43	   A^2 -> H(U1(e, e), f(c))
25.51/8.43	   A^2 -> H(U1(e, e), f(d))
25.51/8.43	   A^2 -> H(f(e), U1(c, b))
25.51/8.43	   A^2 -> H(f(e), U1(d, b))
25.51/8.43	   A^2 -> H(f(e), U1(b, c))
25.51/8.43	   A^2 -> H(f(e), U1(b, d))
25.51/8.43	   A^2 -> H(f(e), U1(c, c))
25.51/8.43	   A^2 -> H(f(e), f(e))
25.51/8.43	   A^2 -> H(f(e), f(k))
25.51/8.43	   A^2 -> H(f(e), U1(d, d))
25.51/8.43	   A^2 -> H(U1(k, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, k), f(c))
25.51/8.43	   A^2 -> H(U1(k, k), f(d))
25.51/8.43	   A^2 -> H(f(k), U1(c, b))
25.51/8.43	   A^2 -> H(f(k), U1(d, b))
25.51/8.43	   A^2 -> H(f(k), U1(b, c))
25.51/8.43	   A^2 -> H(f(k), U1(b, d))
25.51/8.43	   A^2 -> H(f(k), U1(c, c))
25.51/8.43	   A^2 -> H(f(k), f(e))
25.51/8.43	   A^2 -> H(f(k), f(k))
25.51/8.43	   A^2 -> H(f(k), U1(d, d))
25.51/8.43	   A^2 -> H(f(c), U1(e, b))
25.51/8.43	   A^2 -> H(f(c), U1(k, b))
25.51/8.43	   A^2 -> H(f(c), U1(c, d))
25.51/8.43	   A^2 -> H(f(c), U1(d, c))
25.51/8.43	   A^2 -> H(f(c), U1(b, e))
25.51/8.43	   A^2 -> H(f(c), U1(b, k))
25.51/8.43	   A^2 -> H(f(c), U1(k, d))
25.51/8.43	   A^2 -> H(f(c), U1(d, k))
25.51/8.43	   A^2 -> H(f(c), U1(k, k))
25.51/8.43	   A^2 -> H(U1(k, k), f(b))
25.51/8.43	   A^2 -> H(U1(k, d), U1(b, b))
25.51/8.43	   A^2 -> H(U1(k, d), f(c))
25.51/8.43	   A^2 -> H(U1(k, d), f(d))
25.51/8.43	   A^2 -> H(U1(d, k), U1(b, b))
25.51/8.43	   A^2 -> H(U1(d, k), f(c))
25.51/8.43	   A^2 -> H(U1(d, k), f(d))
25.51/8.43	   A^2 -> H(U1(d, d), U1(c, b))
25.51/8.43	   A^2 -> H(U1(d, d), U1(d, b))
25.51/8.43	   A^2 -> H(U1(d, d), U1(b, c))
25.51/8.43	   A^2 -> H(U1(d, d), U1(b, d))
25.51/8.43	   A^2 -> H(U1(d, d), U1(c, c))
25.51/8.43	   A^2 -> H(U1(d, d), f(e))
25.51/8.43	   A^2 -> H(U1(d, d), f(k))
25.51/8.43	   A^2 -> H(U1(d, d), U1(d, d))
25.51/8.43	   A^2 -> H(f(d), U1(e, b))
25.51/8.43	   A^2 -> H(f(d), U1(k, b))
25.51/8.43	   A^2 -> H(f(d), U1(c, d))
25.51/8.43	   A^2 -> H(f(d), U1(d, c))
25.51/8.43	   A^2 -> H(f(d), U1(b, e))
25.51/8.43	   A^2 -> H(f(d), U1(b, k))
25.51/8.43	   A^2 -> H(f(d), U1(e, c))
25.51/8.43	   A^2 -> H(f(d), U1(k, c))
25.51/8.43	   A^2 -> H(f(d), U1(c, e))
25.51/8.43	   A^2 -> H(f(d), U1(c, k))
25.51/8.43	   A^2 -> H(f(d), U1(e, e))
25.51/8.43	   A^2 -> H(f(d), U1(k, k))
25.51/8.43	   A^2 -> H(f(a), b)
25.51/8.43	   A^2 -> H(f(a), U1(e, d))
25.51/8.43	   A^2 -> H(f(a), U1(d, e))
25.51/8.43	   A^2 -> H(f(c), U1(e, c))
25.51/8.43	   A^2 -> H(f(c), U1(k, c))
25.51/8.43	   A^2 -> H(f(c), U1(c, e))
25.51/8.43	   A^2 -> H(f(c), U1(c, k))
25.51/8.43	   A^2 -> H(f(a), c)
25.51/8.43	   A^2 -> H(f(a), U1(e, k))
25.51/8.43	   A^2 -> H(f(a), U1(k, e))
25.51/8.43	   A^2 -> H(f(c), U1(e, e))
25.51/8.43	   A^2 -> H(f(a), e)
25.51/8.43	   A^2 -> H(f(d), U1(k, d))
25.51/8.43	   A^2 -> H(f(d), U1(d, k))
25.51/8.43	   A^2 -> H(f(a), U1(k, k))
25.51/8.43	   A^2 -> H(d, f(b))
25.51/8.43	   A^2 -> H(a, U1(b, b))
25.51/8.43	   A^2 -> H(a, f(c))
25.51/8.43	   A^2 -> H(a, f(d))
25.79/8.44	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, d), f(c))
25.79/8.44	   A^2 -> H(U1(e, d), f(d))
25.79/8.44	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.44	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.44	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.44	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.44	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.44	   A^2 -> H(U1(e, a), f(e))
25.79/8.44	   A^2 -> H(U1(e, a), f(k))
25.79/8.44	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.44	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.44	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.44	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.44	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.44	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.44	   A^2 -> H(U1(k, a), f(e))
25.79/8.44	   A^2 -> H(U1(k, a), f(k))
25.79/8.44	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.44	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.44	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.44	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.44	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.44	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.44	   A^2 -> H(U1(c, d), f(e))
25.79/8.44	   A^2 -> H(U1(c, d), f(k))
25.79/8.44	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.44	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(d, e), f(c))
25.79/8.44	   A^2 -> H(U1(d, e), f(d))
25.79/8.44	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.44	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.44	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.44	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.44	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.44	   A^2 -> H(U1(d, c), f(e))
25.79/8.44	   A^2 -> H(U1(d, c), f(k))
25.79/8.44	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.44	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.44	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.44	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.44	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.44	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.44	   A^2 -> H(U1(a, e), f(e))
25.79/8.44	   A^2 -> H(U1(a, e), f(k))
25.79/8.44	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.44	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.44	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.44	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.44	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.44	   A^2 -> H(U1(a, k), f(e))
25.79/8.44	   A^2 -> H(U1(a, k), f(k))
25.79/8.44	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.44	
25.79/8.44	The TRS R consists of the following rules:
25.79/8.44	
25.79/8.44	   f(x) -> U1(x, x)
25.79/8.44	   U1(e, x) -> x
25.79/8.44	   a -> c
25.79/8.44	   a -> d
25.79/8.44	   b -> c
25.79/8.44	   b -> d
25.79/8.44	   d -> k
25.79/8.44	   c -> e
25.79/8.44	   c -> k
25.79/8.44	
25.79/8.44	Q is empty.
25.79/8.44	We have to consider all minimal (P,Q,R)-chains.
25.79/8.44	----------------------------------------
25.79/8.44	
25.79/8.44	(311) TransformationProof (EQUIVALENT)
25.79/8.44	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.44	
25.79/8.44	   (A^2 -> H(U1(c, d), U1(c, b)),A^2 -> H(U1(c, d), U1(c, b)))
25.79/8.44	   (A^2 -> H(U1(d, d), U1(c, b)),A^2 -> H(U1(d, d), U1(c, b)))
25.79/8.44	   (A^2 -> H(U1(a, k), U1(c, b)),A^2 -> H(U1(a, k), U1(c, b)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(e, b)),A^2 -> H(U1(a, d), U1(e, b)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(k, b)),A^2 -> H(U1(a, d), U1(k, b)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(c, c)),A^2 -> H(U1(a, d), U1(c, c)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(c, d)),A^2 -> H(U1(a, d), U1(c, d)))
25.79/8.44	
25.79/8.44	
25.79/8.44	----------------------------------------
25.79/8.44	
25.79/8.44	(312)
25.79/8.44	Obligation:
25.79/8.44	Q DP problem:
25.79/8.44	The TRS P consists of the following rules:
25.79/8.44	
25.79/8.44	   H(x, x) -> G(x, x, f(k))
25.79/8.44	   G(d, x, x) -> A^2
25.79/8.44	   A^2 -> H(f(c), f(c))
25.79/8.44	   A^2 -> H(f(d), f(d))
25.79/8.44	   A^2 -> H(U1(a, d), U1(d, b))
25.79/8.44	   A^2 -> H(U1(a, d), U1(b, c))
25.79/8.44	   A^2 -> H(U1(a, d), U1(b, d))
25.79/8.44	   A^2 -> H(U1(a, d), U1(c, c))
25.79/8.44	   A^2 -> H(U1(a, d), f(e))
25.79/8.44	   A^2 -> H(U1(a, d), f(k))
25.79/8.44	   A^2 -> H(U1(a, d), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.44	   A^2 -> H(c, f(b))
25.79/8.44	   A^2 -> H(U1(e, k), f(b))
25.79/8.44	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, c), f(c))
25.79/8.44	   A^2 -> H(U1(e, c), f(d))
25.79/8.44	   A^2 -> H(U1(k, e), f(b))
25.79/8.44	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, c), f(c))
25.79/8.44	   A^2 -> H(U1(k, c), f(d))
25.79/8.44	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(c, e), f(c))
25.79/8.44	   A^2 -> H(U1(c, e), f(d))
25.79/8.44	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(c, k), f(c))
25.79/8.44	   A^2 -> H(U1(c, k), f(d))
25.79/8.44	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.44	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.44	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.44	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.44	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.44	   A^2 -> H(U1(c, c), f(e))
25.79/8.44	   A^2 -> H(U1(c, c), f(k))
25.79/8.44	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.44	   A^2 -> H(e, f(b))
25.79/8.44	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, e), f(c))
25.79/8.44	   A^2 -> H(U1(e, e), f(d))
25.79/8.44	   A^2 -> H(f(e), U1(c, b))
25.79/8.44	   A^2 -> H(f(e), U1(d, b))
25.79/8.44	   A^2 -> H(f(e), U1(b, c))
25.79/8.44	   A^2 -> H(f(e), U1(b, d))
25.79/8.44	   A^2 -> H(f(e), U1(c, c))
25.79/8.44	   A^2 -> H(f(e), f(e))
25.79/8.44	   A^2 -> H(f(e), f(k))
25.79/8.44	   A^2 -> H(f(e), U1(d, d))
25.79/8.44	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, k), f(c))
25.79/8.44	   A^2 -> H(U1(k, k), f(d))
25.79/8.44	   A^2 -> H(f(k), U1(c, b))
25.79/8.44	   A^2 -> H(f(k), U1(d, b))
25.79/8.44	   A^2 -> H(f(k), U1(b, c))
25.79/8.44	   A^2 -> H(f(k), U1(b, d))
25.79/8.44	   A^2 -> H(f(k), U1(c, c))
25.79/8.44	   A^2 -> H(f(k), f(e))
25.79/8.44	   A^2 -> H(f(k), f(k))
25.79/8.44	   A^2 -> H(f(k), U1(d, d))
25.79/8.44	   A^2 -> H(f(c), U1(e, b))
25.79/8.44	   A^2 -> H(f(c), U1(k, b))
25.79/8.44	   A^2 -> H(f(c), U1(c, d))
25.79/8.44	   A^2 -> H(f(c), U1(d, c))
25.79/8.44	   A^2 -> H(f(c), U1(b, e))
25.79/8.44	   A^2 -> H(f(c), U1(b, k))
25.79/8.44	   A^2 -> H(f(c), U1(k, d))
25.79/8.44	   A^2 -> H(f(c), U1(d, k))
25.79/8.44	   A^2 -> H(f(c), U1(k, k))
25.79/8.44	   A^2 -> H(U1(k, k), f(b))
25.79/8.44	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, d), f(c))
25.79/8.44	   A^2 -> H(U1(k, d), f(d))
25.79/8.44	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(d, k), f(c))
25.79/8.44	   A^2 -> H(U1(d, k), f(d))
25.79/8.44	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.44	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.44	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.44	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.44	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.44	   A^2 -> H(U1(d, d), f(e))
25.79/8.44	   A^2 -> H(U1(d, d), f(k))
25.79/8.44	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.44	   A^2 -> H(f(d), U1(e, b))
25.79/8.44	   A^2 -> H(f(d), U1(k, b))
25.79/8.44	   A^2 -> H(f(d), U1(c, d))
25.79/8.44	   A^2 -> H(f(d), U1(d, c))
25.79/8.44	   A^2 -> H(f(d), U1(b, e))
25.79/8.44	   A^2 -> H(f(d), U1(b, k))
25.79/8.44	   A^2 -> H(f(d), U1(e, c))
25.79/8.44	   A^2 -> H(f(d), U1(k, c))
25.79/8.44	   A^2 -> H(f(d), U1(c, e))
25.79/8.44	   A^2 -> H(f(d), U1(c, k))
25.79/8.44	   A^2 -> H(f(d), U1(e, e))
25.79/8.44	   A^2 -> H(f(d), U1(k, k))
25.79/8.44	   A^2 -> H(f(a), b)
25.79/8.44	   A^2 -> H(f(a), U1(e, d))
25.79/8.44	   A^2 -> H(f(a), U1(d, e))
25.79/8.44	   A^2 -> H(f(c), U1(e, c))
25.79/8.44	   A^2 -> H(f(c), U1(k, c))
25.79/8.44	   A^2 -> H(f(c), U1(c, e))
25.79/8.44	   A^2 -> H(f(c), U1(c, k))
25.79/8.44	   A^2 -> H(f(a), c)
25.79/8.44	   A^2 -> H(f(a), U1(e, k))
25.79/8.44	   A^2 -> H(f(a), U1(k, e))
25.79/8.44	   A^2 -> H(f(c), U1(e, e))
25.79/8.44	   A^2 -> H(f(a), e)
25.79/8.44	   A^2 -> H(f(d), U1(k, d))
25.79/8.44	   A^2 -> H(f(d), U1(d, k))
25.79/8.44	   A^2 -> H(f(a), U1(k, k))
25.79/8.44	   A^2 -> H(d, f(b))
25.79/8.44	   A^2 -> H(a, U1(b, b))
25.79/8.44	   A^2 -> H(a, f(c))
25.79/8.44	   A^2 -> H(a, f(d))
25.79/8.44	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, d), f(c))
25.79/8.44	   A^2 -> H(U1(e, d), f(d))
25.79/8.44	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.44	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.44	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.44	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.44	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.44	   A^2 -> H(U1(e, a), f(e))
25.79/8.44	   A^2 -> H(U1(e, a), f(k))
25.79/8.44	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.44	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.44	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.44	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.44	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.44	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.44	   A^2 -> H(U1(k, a), f(e))
25.79/8.44	   A^2 -> H(U1(k, a), f(k))
25.79/8.44	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.44	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.44	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.44	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.44	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.44	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.44	   A^2 -> H(U1(c, d), f(e))
25.79/8.44	   A^2 -> H(U1(c, d), f(k))
25.79/8.44	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.44	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(d, e), f(c))
25.79/8.44	   A^2 -> H(U1(d, e), f(d))
25.79/8.44	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.44	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.44	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.44	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.44	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.44	   A^2 -> H(U1(d, c), f(e))
25.79/8.44	   A^2 -> H(U1(d, c), f(k))
25.79/8.44	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.44	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.44	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.44	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.44	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.44	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.44	   A^2 -> H(U1(a, e), f(e))
25.79/8.44	   A^2 -> H(U1(a, e), f(k))
25.79/8.44	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.44	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.44	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.44	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.44	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.44	   A^2 -> H(U1(a, k), f(e))
25.79/8.44	   A^2 -> H(U1(a, k), f(k))
25.79/8.44	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.44	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.44	
25.79/8.44	The TRS R consists of the following rules:
25.79/8.44	
25.79/8.44	   f(x) -> U1(x, x)
25.79/8.44	   U1(e, x) -> x
25.79/8.44	   a -> c
25.79/8.44	   a -> d
25.79/8.44	   b -> c
25.79/8.44	   b -> d
25.79/8.44	   d -> k
25.79/8.44	   c -> e
25.79/8.44	   c -> k
25.79/8.44	
25.79/8.44	Q is empty.
25.79/8.44	We have to consider all minimal (P,Q,R)-chains.
25.79/8.44	----------------------------------------
25.79/8.44	
25.79/8.44	(313) TransformationProof (EQUIVALENT)
25.79/8.44	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.44	
25.79/8.44	   (A^2 -> H(U1(c, d), U1(d, b)),A^2 -> H(U1(c, d), U1(d, b)))
25.79/8.44	   (A^2 -> H(U1(d, d), U1(d, b)),A^2 -> H(U1(d, d), U1(d, b)))
25.79/8.44	   (A^2 -> H(U1(a, k), U1(d, b)),A^2 -> H(U1(a, k), U1(d, b)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(k, b)),A^2 -> H(U1(a, d), U1(k, b)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(d, c)),A^2 -> H(U1(a, d), U1(d, c)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(d, d)),A^2 -> H(U1(a, d), U1(d, d)))
25.79/8.44	
25.79/8.44	
25.79/8.44	----------------------------------------
25.79/8.44	
25.79/8.44	(314)
25.79/8.44	Obligation:
25.79/8.44	Q DP problem:
25.79/8.44	The TRS P consists of the following rules:
25.79/8.44	
25.79/8.44	   H(x, x) -> G(x, x, f(k))
25.79/8.44	   G(d, x, x) -> A^2
25.79/8.44	   A^2 -> H(f(c), f(c))
25.79/8.44	   A^2 -> H(f(d), f(d))
25.79/8.44	   A^2 -> H(U1(a, d), U1(b, c))
25.79/8.44	   A^2 -> H(U1(a, d), U1(b, d))
25.79/8.44	   A^2 -> H(U1(a, d), U1(c, c))
25.79/8.44	   A^2 -> H(U1(a, d), f(e))
25.79/8.44	   A^2 -> H(U1(a, d), f(k))
25.79/8.44	   A^2 -> H(U1(a, d), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.44	   A^2 -> H(c, f(b))
25.79/8.44	   A^2 -> H(U1(e, k), f(b))
25.79/8.44	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, c), f(c))
25.79/8.44	   A^2 -> H(U1(e, c), f(d))
25.79/8.44	   A^2 -> H(U1(k, e), f(b))
25.79/8.44	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, c), f(c))
25.79/8.44	   A^2 -> H(U1(k, c), f(d))
25.79/8.44	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(c, e), f(c))
25.79/8.44	   A^2 -> H(U1(c, e), f(d))
25.79/8.44	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(c, k), f(c))
25.79/8.44	   A^2 -> H(U1(c, k), f(d))
25.79/8.44	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.44	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.44	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.44	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.44	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.44	   A^2 -> H(U1(c, c), f(e))
25.79/8.44	   A^2 -> H(U1(c, c), f(k))
25.79/8.44	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.44	   A^2 -> H(e, f(b))
25.79/8.44	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, e), f(c))
25.79/8.44	   A^2 -> H(U1(e, e), f(d))
25.79/8.44	   A^2 -> H(f(e), U1(c, b))
25.79/8.44	   A^2 -> H(f(e), U1(d, b))
25.79/8.44	   A^2 -> H(f(e), U1(b, c))
25.79/8.44	   A^2 -> H(f(e), U1(b, d))
25.79/8.44	   A^2 -> H(f(e), U1(c, c))
25.79/8.44	   A^2 -> H(f(e), f(e))
25.79/8.44	   A^2 -> H(f(e), f(k))
25.79/8.44	   A^2 -> H(f(e), U1(d, d))
25.79/8.44	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, k), f(c))
25.79/8.44	   A^2 -> H(U1(k, k), f(d))
25.79/8.44	   A^2 -> H(f(k), U1(c, b))
25.79/8.44	   A^2 -> H(f(k), U1(d, b))
25.79/8.44	   A^2 -> H(f(k), U1(b, c))
25.79/8.44	   A^2 -> H(f(k), U1(b, d))
25.79/8.44	   A^2 -> H(f(k), U1(c, c))
25.79/8.44	   A^2 -> H(f(k), f(e))
25.79/8.44	   A^2 -> H(f(k), f(k))
25.79/8.44	   A^2 -> H(f(k), U1(d, d))
25.79/8.44	   A^2 -> H(f(c), U1(e, b))
25.79/8.44	   A^2 -> H(f(c), U1(k, b))
25.79/8.44	   A^2 -> H(f(c), U1(c, d))
25.79/8.44	   A^2 -> H(f(c), U1(d, c))
25.79/8.44	   A^2 -> H(f(c), U1(b, e))
25.79/8.44	   A^2 -> H(f(c), U1(b, k))
25.79/8.44	   A^2 -> H(f(c), U1(k, d))
25.79/8.44	   A^2 -> H(f(c), U1(d, k))
25.79/8.44	   A^2 -> H(f(c), U1(k, k))
25.79/8.44	   A^2 -> H(U1(k, k), f(b))
25.79/8.44	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, d), f(c))
25.79/8.44	   A^2 -> H(U1(k, d), f(d))
25.79/8.44	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(d, k), f(c))
25.79/8.44	   A^2 -> H(U1(d, k), f(d))
25.79/8.44	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.44	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.44	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.44	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.44	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.44	   A^2 -> H(U1(d, d), f(e))
25.79/8.44	   A^2 -> H(U1(d, d), f(k))
25.79/8.44	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.44	   A^2 -> H(f(d), U1(e, b))
25.79/8.44	   A^2 -> H(f(d), U1(k, b))
25.79/8.44	   A^2 -> H(f(d), U1(c, d))
25.79/8.44	   A^2 -> H(f(d), U1(d, c))
25.79/8.44	   A^2 -> H(f(d), U1(b, e))
25.79/8.44	   A^2 -> H(f(d), U1(b, k))
25.79/8.44	   A^2 -> H(f(d), U1(e, c))
25.79/8.44	   A^2 -> H(f(d), U1(k, c))
25.79/8.44	   A^2 -> H(f(d), U1(c, e))
25.79/8.44	   A^2 -> H(f(d), U1(c, k))
25.79/8.44	   A^2 -> H(f(d), U1(e, e))
25.79/8.44	   A^2 -> H(f(d), U1(k, k))
25.79/8.44	   A^2 -> H(f(a), b)
25.79/8.44	   A^2 -> H(f(a), U1(e, d))
25.79/8.44	   A^2 -> H(f(a), U1(d, e))
25.79/8.44	   A^2 -> H(f(c), U1(e, c))
25.79/8.44	   A^2 -> H(f(c), U1(k, c))
25.79/8.44	   A^2 -> H(f(c), U1(c, e))
25.79/8.44	   A^2 -> H(f(c), U1(c, k))
25.79/8.44	   A^2 -> H(f(a), c)
25.79/8.44	   A^2 -> H(f(a), U1(e, k))
25.79/8.44	   A^2 -> H(f(a), U1(k, e))
25.79/8.44	   A^2 -> H(f(c), U1(e, e))
25.79/8.44	   A^2 -> H(f(a), e)
25.79/8.44	   A^2 -> H(f(d), U1(k, d))
25.79/8.44	   A^2 -> H(f(d), U1(d, k))
25.79/8.44	   A^2 -> H(f(a), U1(k, k))
25.79/8.44	   A^2 -> H(d, f(b))
25.79/8.44	   A^2 -> H(a, U1(b, b))
25.79/8.44	   A^2 -> H(a, f(c))
25.79/8.44	   A^2 -> H(a, f(d))
25.79/8.44	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, d), f(c))
25.79/8.44	   A^2 -> H(U1(e, d), f(d))
25.79/8.44	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.44	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.44	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.44	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.44	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.44	   A^2 -> H(U1(e, a), f(e))
25.79/8.44	   A^2 -> H(U1(e, a), f(k))
25.79/8.44	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.44	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.44	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.44	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.44	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.44	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.44	   A^2 -> H(U1(k, a), f(e))
25.79/8.44	   A^2 -> H(U1(k, a), f(k))
25.79/8.44	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.44	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.44	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.44	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.44	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.44	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.44	   A^2 -> H(U1(c, d), f(e))
25.79/8.44	   A^2 -> H(U1(c, d), f(k))
25.79/8.44	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.44	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(d, e), f(c))
25.79/8.44	   A^2 -> H(U1(d, e), f(d))
25.79/8.44	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.44	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.44	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.44	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.44	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.44	   A^2 -> H(U1(d, c), f(e))
25.79/8.44	   A^2 -> H(U1(d, c), f(k))
25.79/8.44	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.44	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.44	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.44	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.44	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.44	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.44	   A^2 -> H(U1(a, e), f(e))
25.79/8.44	   A^2 -> H(U1(a, e), f(k))
25.79/8.44	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.44	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.44	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.44	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.44	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.44	   A^2 -> H(U1(a, k), f(e))
25.79/8.44	   A^2 -> H(U1(a, k), f(k))
25.79/8.44	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.44	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.44	
25.79/8.44	The TRS R consists of the following rules:
25.79/8.44	
25.79/8.44	   f(x) -> U1(x, x)
25.79/8.44	   U1(e, x) -> x
25.79/8.44	   a -> c
25.79/8.44	   a -> d
25.79/8.44	   b -> c
25.79/8.44	   b -> d
25.79/8.44	   d -> k
25.79/8.44	   c -> e
25.79/8.44	   c -> k
25.79/8.44	
25.79/8.44	Q is empty.
25.79/8.44	We have to consider all minimal (P,Q,R)-chains.
25.79/8.44	----------------------------------------
25.79/8.44	
25.79/8.44	(315) TransformationProof (EQUIVALENT)
25.79/8.44	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.44	
25.79/8.44	   (A^2 -> H(U1(c, d), U1(b, c)),A^2 -> H(U1(c, d), U1(b, c)))
25.79/8.44	   (A^2 -> H(U1(d, d), U1(b, c)),A^2 -> H(U1(d, d), U1(b, c)))
25.79/8.44	   (A^2 -> H(U1(a, k), U1(b, c)),A^2 -> H(U1(a, k), U1(b, c)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(c, c)),A^2 -> H(U1(a, d), U1(c, c)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(d, c)),A^2 -> H(U1(a, d), U1(d, c)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(b, e)),A^2 -> H(U1(a, d), U1(b, e)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(b, k)),A^2 -> H(U1(a, d), U1(b, k)))
25.79/8.44	
25.79/8.44	
25.79/8.44	----------------------------------------
25.79/8.44	
25.79/8.44	(316)
25.79/8.44	Obligation:
25.79/8.44	Q DP problem:
25.79/8.44	The TRS P consists of the following rules:
25.79/8.44	
25.79/8.44	   H(x, x) -> G(x, x, f(k))
25.79/8.44	   G(d, x, x) -> A^2
25.79/8.44	   A^2 -> H(f(c), f(c))
25.79/8.44	   A^2 -> H(f(d), f(d))
25.79/8.44	   A^2 -> H(U1(a, d), U1(b, d))
25.79/8.44	   A^2 -> H(U1(a, d), U1(c, c))
25.79/8.44	   A^2 -> H(U1(a, d), f(e))
25.79/8.44	   A^2 -> H(U1(a, d), f(k))
25.79/8.44	   A^2 -> H(U1(a, d), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.44	   A^2 -> H(c, f(b))
25.79/8.44	   A^2 -> H(U1(e, k), f(b))
25.79/8.44	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, c), f(c))
25.79/8.44	   A^2 -> H(U1(e, c), f(d))
25.79/8.44	   A^2 -> H(U1(k, e), f(b))
25.79/8.44	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, c), f(c))
25.79/8.44	   A^2 -> H(U1(k, c), f(d))
25.79/8.44	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(c, e), f(c))
25.79/8.44	   A^2 -> H(U1(c, e), f(d))
25.79/8.44	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(c, k), f(c))
25.79/8.44	   A^2 -> H(U1(c, k), f(d))
25.79/8.44	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.44	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.44	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.44	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.44	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.44	   A^2 -> H(U1(c, c), f(e))
25.79/8.44	   A^2 -> H(U1(c, c), f(k))
25.79/8.44	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.44	   A^2 -> H(e, f(b))
25.79/8.44	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, e), f(c))
25.79/8.44	   A^2 -> H(U1(e, e), f(d))
25.79/8.44	   A^2 -> H(f(e), U1(c, b))
25.79/8.44	   A^2 -> H(f(e), U1(d, b))
25.79/8.44	   A^2 -> H(f(e), U1(b, c))
25.79/8.44	   A^2 -> H(f(e), U1(b, d))
25.79/8.44	   A^2 -> H(f(e), U1(c, c))
25.79/8.44	   A^2 -> H(f(e), f(e))
25.79/8.44	   A^2 -> H(f(e), f(k))
25.79/8.44	   A^2 -> H(f(e), U1(d, d))
25.79/8.44	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, k), f(c))
25.79/8.44	   A^2 -> H(U1(k, k), f(d))
25.79/8.44	   A^2 -> H(f(k), U1(c, b))
25.79/8.44	   A^2 -> H(f(k), U1(d, b))
25.79/8.44	   A^2 -> H(f(k), U1(b, c))
25.79/8.44	   A^2 -> H(f(k), U1(b, d))
25.79/8.44	   A^2 -> H(f(k), U1(c, c))
25.79/8.44	   A^2 -> H(f(k), f(e))
25.79/8.44	   A^2 -> H(f(k), f(k))
25.79/8.44	   A^2 -> H(f(k), U1(d, d))
25.79/8.44	   A^2 -> H(f(c), U1(e, b))
25.79/8.44	   A^2 -> H(f(c), U1(k, b))
25.79/8.44	   A^2 -> H(f(c), U1(c, d))
25.79/8.44	   A^2 -> H(f(c), U1(d, c))
25.79/8.44	   A^2 -> H(f(c), U1(b, e))
25.79/8.44	   A^2 -> H(f(c), U1(b, k))
25.79/8.44	   A^2 -> H(f(c), U1(k, d))
25.79/8.44	   A^2 -> H(f(c), U1(d, k))
25.79/8.44	   A^2 -> H(f(c), U1(k, k))
25.79/8.44	   A^2 -> H(U1(k, k), f(b))
25.79/8.44	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, d), f(c))
25.79/8.44	   A^2 -> H(U1(k, d), f(d))
25.79/8.44	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(d, k), f(c))
25.79/8.44	   A^2 -> H(U1(d, k), f(d))
25.79/8.44	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.44	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.44	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.44	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.44	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.44	   A^2 -> H(U1(d, d), f(e))
25.79/8.44	   A^2 -> H(U1(d, d), f(k))
25.79/8.44	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.44	   A^2 -> H(f(d), U1(e, b))
25.79/8.44	   A^2 -> H(f(d), U1(k, b))
25.79/8.44	   A^2 -> H(f(d), U1(c, d))
25.79/8.44	   A^2 -> H(f(d), U1(d, c))
25.79/8.44	   A^2 -> H(f(d), U1(b, e))
25.79/8.44	   A^2 -> H(f(d), U1(b, k))
25.79/8.44	   A^2 -> H(f(d), U1(e, c))
25.79/8.44	   A^2 -> H(f(d), U1(k, c))
25.79/8.44	   A^2 -> H(f(d), U1(c, e))
25.79/8.44	   A^2 -> H(f(d), U1(c, k))
25.79/8.44	   A^2 -> H(f(d), U1(e, e))
25.79/8.44	   A^2 -> H(f(d), U1(k, k))
25.79/8.44	   A^2 -> H(f(a), b)
25.79/8.44	   A^2 -> H(f(a), U1(e, d))
25.79/8.44	   A^2 -> H(f(a), U1(d, e))
25.79/8.44	   A^2 -> H(f(c), U1(e, c))
25.79/8.44	   A^2 -> H(f(c), U1(k, c))
25.79/8.44	   A^2 -> H(f(c), U1(c, e))
25.79/8.44	   A^2 -> H(f(c), U1(c, k))
25.79/8.44	   A^2 -> H(f(a), c)
25.79/8.44	   A^2 -> H(f(a), U1(e, k))
25.79/8.44	   A^2 -> H(f(a), U1(k, e))
25.79/8.44	   A^2 -> H(f(c), U1(e, e))
25.79/8.44	   A^2 -> H(f(a), e)
25.79/8.44	   A^2 -> H(f(d), U1(k, d))
25.79/8.44	   A^2 -> H(f(d), U1(d, k))
25.79/8.44	   A^2 -> H(f(a), U1(k, k))
25.79/8.44	   A^2 -> H(d, f(b))
25.79/8.44	   A^2 -> H(a, U1(b, b))
25.79/8.44	   A^2 -> H(a, f(c))
25.79/8.44	   A^2 -> H(a, f(d))
25.79/8.44	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, d), f(c))
25.79/8.44	   A^2 -> H(U1(e, d), f(d))
25.79/8.44	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.44	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.44	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.44	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.44	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.44	   A^2 -> H(U1(e, a), f(e))
25.79/8.44	   A^2 -> H(U1(e, a), f(k))
25.79/8.44	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.44	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.44	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.44	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.44	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.44	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.44	   A^2 -> H(U1(k, a), f(e))
25.79/8.44	   A^2 -> H(U1(k, a), f(k))
25.79/8.44	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.44	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.44	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.44	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.44	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.44	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.44	   A^2 -> H(U1(c, d), f(e))
25.79/8.44	   A^2 -> H(U1(c, d), f(k))
25.79/8.44	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.44	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(d, e), f(c))
25.79/8.44	   A^2 -> H(U1(d, e), f(d))
25.79/8.44	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.44	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.44	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.44	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.44	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.44	   A^2 -> H(U1(d, c), f(e))
25.79/8.44	   A^2 -> H(U1(d, c), f(k))
25.79/8.44	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.44	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.44	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.44	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.44	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.44	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.44	   A^2 -> H(U1(a, e), f(e))
25.79/8.44	   A^2 -> H(U1(a, e), f(k))
25.79/8.44	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.44	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.44	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.44	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.44	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.44	   A^2 -> H(U1(a, k), f(e))
25.79/8.44	   A^2 -> H(U1(a, k), f(k))
25.79/8.44	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.44	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.44	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.44	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.44	
25.79/8.44	The TRS R consists of the following rules:
25.79/8.44	
25.79/8.44	   f(x) -> U1(x, x)
25.79/8.44	   U1(e, x) -> x
25.79/8.44	   a -> c
25.79/8.44	   a -> d
25.79/8.44	   b -> c
25.79/8.44	   b -> d
25.79/8.44	   d -> k
25.79/8.44	   c -> e
25.79/8.44	   c -> k
25.79/8.44	
25.79/8.44	Q is empty.
25.79/8.44	We have to consider all minimal (P,Q,R)-chains.
25.79/8.44	----------------------------------------
25.79/8.44	
25.79/8.44	(317) TransformationProof (EQUIVALENT)
25.79/8.44	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.44	
25.79/8.44	   (A^2 -> H(U1(c, d), U1(b, d)),A^2 -> H(U1(c, d), U1(b, d)))
25.79/8.44	   (A^2 -> H(U1(d, d), U1(b, d)),A^2 -> H(U1(d, d), U1(b, d)))
25.79/8.44	   (A^2 -> H(U1(a, k), U1(b, d)),A^2 -> H(U1(a, k), U1(b, d)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(c, d)),A^2 -> H(U1(a, d), U1(c, d)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(d, d)),A^2 -> H(U1(a, d), U1(d, d)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(b, k)),A^2 -> H(U1(a, d), U1(b, k)))
25.79/8.44	
25.79/8.44	
25.79/8.44	----------------------------------------
25.79/8.44	
25.79/8.44	(318)
25.79/8.44	Obligation:
25.79/8.44	Q DP problem:
25.79/8.44	The TRS P consists of the following rules:
25.79/8.44	
25.79/8.44	   H(x, x) -> G(x, x, f(k))
25.79/8.44	   G(d, x, x) -> A^2
25.79/8.44	   A^2 -> H(f(c), f(c))
25.79/8.44	   A^2 -> H(f(d), f(d))
25.79/8.44	   A^2 -> H(U1(a, d), U1(c, c))
25.79/8.44	   A^2 -> H(U1(a, d), f(e))
25.79/8.44	   A^2 -> H(U1(a, d), f(k))
25.79/8.44	   A^2 -> H(U1(a, d), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.44	   A^2 -> H(c, f(b))
25.79/8.44	   A^2 -> H(U1(e, k), f(b))
25.79/8.44	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, c), f(c))
25.79/8.44	   A^2 -> H(U1(e, c), f(d))
25.79/8.44	   A^2 -> H(U1(k, e), f(b))
25.79/8.44	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, c), f(c))
25.79/8.44	   A^2 -> H(U1(k, c), f(d))
25.79/8.44	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(c, e), f(c))
25.79/8.44	   A^2 -> H(U1(c, e), f(d))
25.79/8.44	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(c, k), f(c))
25.79/8.44	   A^2 -> H(U1(c, k), f(d))
25.79/8.44	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.44	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.44	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.44	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.44	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.44	   A^2 -> H(U1(c, c), f(e))
25.79/8.44	   A^2 -> H(U1(c, c), f(k))
25.79/8.44	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.44	   A^2 -> H(e, f(b))
25.79/8.44	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, e), f(c))
25.79/8.44	   A^2 -> H(U1(e, e), f(d))
25.79/8.44	   A^2 -> H(f(e), U1(c, b))
25.79/8.44	   A^2 -> H(f(e), U1(d, b))
25.79/8.44	   A^2 -> H(f(e), U1(b, c))
25.79/8.44	   A^2 -> H(f(e), U1(b, d))
25.79/8.44	   A^2 -> H(f(e), U1(c, c))
25.79/8.44	   A^2 -> H(f(e), f(e))
25.79/8.44	   A^2 -> H(f(e), f(k))
25.79/8.44	   A^2 -> H(f(e), U1(d, d))
25.79/8.44	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, k), f(c))
25.79/8.44	   A^2 -> H(U1(k, k), f(d))
25.79/8.44	   A^2 -> H(f(k), U1(c, b))
25.79/8.44	   A^2 -> H(f(k), U1(d, b))
25.79/8.44	   A^2 -> H(f(k), U1(b, c))
25.79/8.44	   A^2 -> H(f(k), U1(b, d))
25.79/8.44	   A^2 -> H(f(k), U1(c, c))
25.79/8.44	   A^2 -> H(f(k), f(e))
25.79/8.44	   A^2 -> H(f(k), f(k))
25.79/8.44	   A^2 -> H(f(k), U1(d, d))
25.79/8.44	   A^2 -> H(f(c), U1(e, b))
25.79/8.44	   A^2 -> H(f(c), U1(k, b))
25.79/8.44	   A^2 -> H(f(c), U1(c, d))
25.79/8.44	   A^2 -> H(f(c), U1(d, c))
25.79/8.44	   A^2 -> H(f(c), U1(b, e))
25.79/8.44	   A^2 -> H(f(c), U1(b, k))
25.79/8.44	   A^2 -> H(f(c), U1(k, d))
25.79/8.44	   A^2 -> H(f(c), U1(d, k))
25.79/8.44	   A^2 -> H(f(c), U1(k, k))
25.79/8.44	   A^2 -> H(U1(k, k), f(b))
25.79/8.44	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, d), f(c))
25.79/8.44	   A^2 -> H(U1(k, d), f(d))
25.79/8.44	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(d, k), f(c))
25.79/8.44	   A^2 -> H(U1(d, k), f(d))
25.79/8.44	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.44	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.44	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.44	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.44	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.44	   A^2 -> H(U1(d, d), f(e))
25.79/8.44	   A^2 -> H(U1(d, d), f(k))
25.79/8.44	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.44	   A^2 -> H(f(d), U1(e, b))
25.79/8.44	   A^2 -> H(f(d), U1(k, b))
25.79/8.44	   A^2 -> H(f(d), U1(c, d))
25.79/8.44	   A^2 -> H(f(d), U1(d, c))
25.79/8.44	   A^2 -> H(f(d), U1(b, e))
25.79/8.44	   A^2 -> H(f(d), U1(b, k))
25.79/8.44	   A^2 -> H(f(d), U1(e, c))
25.79/8.44	   A^2 -> H(f(d), U1(k, c))
25.79/8.44	   A^2 -> H(f(d), U1(c, e))
25.79/8.44	   A^2 -> H(f(d), U1(c, k))
25.79/8.44	   A^2 -> H(f(d), U1(e, e))
25.79/8.44	   A^2 -> H(f(d), U1(k, k))
25.79/8.44	   A^2 -> H(f(a), b)
25.79/8.44	   A^2 -> H(f(a), U1(e, d))
25.79/8.44	   A^2 -> H(f(a), U1(d, e))
25.79/8.44	   A^2 -> H(f(c), U1(e, c))
25.79/8.44	   A^2 -> H(f(c), U1(k, c))
25.79/8.44	   A^2 -> H(f(c), U1(c, e))
25.79/8.44	   A^2 -> H(f(c), U1(c, k))
25.79/8.44	   A^2 -> H(f(a), c)
25.79/8.44	   A^2 -> H(f(a), U1(e, k))
25.79/8.44	   A^2 -> H(f(a), U1(k, e))
25.79/8.44	   A^2 -> H(f(c), U1(e, e))
25.79/8.44	   A^2 -> H(f(a), e)
25.79/8.44	   A^2 -> H(f(d), U1(k, d))
25.79/8.44	   A^2 -> H(f(d), U1(d, k))
25.79/8.44	   A^2 -> H(f(a), U1(k, k))
25.79/8.44	   A^2 -> H(d, f(b))
25.79/8.44	   A^2 -> H(a, U1(b, b))
25.79/8.44	   A^2 -> H(a, f(c))
25.79/8.44	   A^2 -> H(a, f(d))
25.79/8.44	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, d), f(c))
25.79/8.44	   A^2 -> H(U1(e, d), f(d))
25.79/8.44	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.44	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.44	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.44	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.44	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.44	   A^2 -> H(U1(e, a), f(e))
25.79/8.44	   A^2 -> H(U1(e, a), f(k))
25.79/8.44	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.44	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.44	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.44	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.44	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.44	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.44	   A^2 -> H(U1(k, a), f(e))
25.79/8.44	   A^2 -> H(U1(k, a), f(k))
25.79/8.44	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.44	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.44	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.44	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.44	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.44	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.44	   A^2 -> H(U1(c, d), f(e))
25.79/8.44	   A^2 -> H(U1(c, d), f(k))
25.79/8.44	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.44	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(d, e), f(c))
25.79/8.44	   A^2 -> H(U1(d, e), f(d))
25.79/8.44	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.44	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.44	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.44	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.44	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.44	   A^2 -> H(U1(d, c), f(e))
25.79/8.44	   A^2 -> H(U1(d, c), f(k))
25.79/8.44	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.44	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.44	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.44	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.44	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.44	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.44	   A^2 -> H(U1(a, e), f(e))
25.79/8.44	   A^2 -> H(U1(a, e), f(k))
25.79/8.44	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.44	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.44	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.44	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.44	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.44	   A^2 -> H(U1(a, k), f(e))
25.79/8.44	   A^2 -> H(U1(a, k), f(k))
25.79/8.44	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.44	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.44	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.44	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.44	
25.79/8.44	The TRS R consists of the following rules:
25.79/8.44	
25.79/8.44	   f(x) -> U1(x, x)
25.79/8.44	   U1(e, x) -> x
25.79/8.44	   a -> c
25.79/8.44	   a -> d
25.79/8.44	   b -> c
25.79/8.44	   b -> d
25.79/8.44	   d -> k
25.79/8.44	   c -> e
25.79/8.44	   c -> k
25.79/8.44	
25.79/8.44	Q is empty.
25.79/8.44	We have to consider all minimal (P,Q,R)-chains.
25.79/8.44	----------------------------------------
25.79/8.44	
25.79/8.44	(319) TransformationProof (EQUIVALENT)
25.79/8.44	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.44	
25.79/8.44	   (A^2 -> H(U1(c, d), U1(c, c)),A^2 -> H(U1(c, d), U1(c, c)))
25.79/8.44	   (A^2 -> H(U1(d, d), U1(c, c)),A^2 -> H(U1(d, d), U1(c, c)))
25.79/8.44	   (A^2 -> H(U1(a, k), U1(c, c)),A^2 -> H(U1(a, k), U1(c, c)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(e, c)),A^2 -> H(U1(a, d), U1(e, c)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(k, c)),A^2 -> H(U1(a, d), U1(k, c)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(c, e)),A^2 -> H(U1(a, d), U1(c, e)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(c, k)),A^2 -> H(U1(a, d), U1(c, k)))
25.79/8.44	
25.79/8.44	
25.79/8.44	----------------------------------------
25.79/8.44	
25.79/8.44	(320)
25.79/8.44	Obligation:
25.79/8.44	Q DP problem:
25.79/8.44	The TRS P consists of the following rules:
25.79/8.44	
25.79/8.44	   H(x, x) -> G(x, x, f(k))
25.79/8.44	   G(d, x, x) -> A^2
25.79/8.44	   A^2 -> H(f(c), f(c))
25.79/8.44	   A^2 -> H(f(d), f(d))
25.79/8.44	   A^2 -> H(U1(a, d), f(e))
25.79/8.44	   A^2 -> H(U1(a, d), f(k))
25.79/8.44	   A^2 -> H(U1(a, d), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.44	   A^2 -> H(c, f(b))
25.79/8.44	   A^2 -> H(U1(e, k), f(b))
25.79/8.44	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, c), f(c))
25.79/8.44	   A^2 -> H(U1(e, c), f(d))
25.79/8.44	   A^2 -> H(U1(k, e), f(b))
25.79/8.44	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, c), f(c))
25.79/8.44	   A^2 -> H(U1(k, c), f(d))
25.79/8.44	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(c, e), f(c))
25.79/8.44	   A^2 -> H(U1(c, e), f(d))
25.79/8.44	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(c, k), f(c))
25.79/8.44	   A^2 -> H(U1(c, k), f(d))
25.79/8.44	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.44	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.44	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.44	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.44	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.44	   A^2 -> H(U1(c, c), f(e))
25.79/8.44	   A^2 -> H(U1(c, c), f(k))
25.79/8.44	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.44	   A^2 -> H(e, f(b))
25.79/8.44	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, e), f(c))
25.79/8.44	   A^2 -> H(U1(e, e), f(d))
25.79/8.44	   A^2 -> H(f(e), U1(c, b))
25.79/8.44	   A^2 -> H(f(e), U1(d, b))
25.79/8.44	   A^2 -> H(f(e), U1(b, c))
25.79/8.44	   A^2 -> H(f(e), U1(b, d))
25.79/8.44	   A^2 -> H(f(e), U1(c, c))
25.79/8.44	   A^2 -> H(f(e), f(e))
25.79/8.44	   A^2 -> H(f(e), f(k))
25.79/8.44	   A^2 -> H(f(e), U1(d, d))
25.79/8.44	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, k), f(c))
25.79/8.44	   A^2 -> H(U1(k, k), f(d))
25.79/8.44	   A^2 -> H(f(k), U1(c, b))
25.79/8.44	   A^2 -> H(f(k), U1(d, b))
25.79/8.44	   A^2 -> H(f(k), U1(b, c))
25.79/8.44	   A^2 -> H(f(k), U1(b, d))
25.79/8.44	   A^2 -> H(f(k), U1(c, c))
25.79/8.44	   A^2 -> H(f(k), f(e))
25.79/8.44	   A^2 -> H(f(k), f(k))
25.79/8.44	   A^2 -> H(f(k), U1(d, d))
25.79/8.44	   A^2 -> H(f(c), U1(e, b))
25.79/8.44	   A^2 -> H(f(c), U1(k, b))
25.79/8.44	   A^2 -> H(f(c), U1(c, d))
25.79/8.44	   A^2 -> H(f(c), U1(d, c))
25.79/8.44	   A^2 -> H(f(c), U1(b, e))
25.79/8.44	   A^2 -> H(f(c), U1(b, k))
25.79/8.44	   A^2 -> H(f(c), U1(k, d))
25.79/8.44	   A^2 -> H(f(c), U1(d, k))
25.79/8.44	   A^2 -> H(f(c), U1(k, k))
25.79/8.44	   A^2 -> H(U1(k, k), f(b))
25.79/8.44	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, d), f(c))
25.79/8.44	   A^2 -> H(U1(k, d), f(d))
25.79/8.44	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(d, k), f(c))
25.79/8.44	   A^2 -> H(U1(d, k), f(d))
25.79/8.44	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.44	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.44	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.44	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.44	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.44	   A^2 -> H(U1(d, d), f(e))
25.79/8.44	   A^2 -> H(U1(d, d), f(k))
25.79/8.44	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.44	   A^2 -> H(f(d), U1(e, b))
25.79/8.44	   A^2 -> H(f(d), U1(k, b))
25.79/8.44	   A^2 -> H(f(d), U1(c, d))
25.79/8.44	   A^2 -> H(f(d), U1(d, c))
25.79/8.44	   A^2 -> H(f(d), U1(b, e))
25.79/8.44	   A^2 -> H(f(d), U1(b, k))
25.79/8.44	   A^2 -> H(f(d), U1(e, c))
25.79/8.44	   A^2 -> H(f(d), U1(k, c))
25.79/8.44	   A^2 -> H(f(d), U1(c, e))
25.79/8.44	   A^2 -> H(f(d), U1(c, k))
25.79/8.44	   A^2 -> H(f(d), U1(e, e))
25.79/8.44	   A^2 -> H(f(d), U1(k, k))
25.79/8.44	   A^2 -> H(f(a), b)
25.79/8.44	   A^2 -> H(f(a), U1(e, d))
25.79/8.44	   A^2 -> H(f(a), U1(d, e))
25.79/8.44	   A^2 -> H(f(c), U1(e, c))
25.79/8.44	   A^2 -> H(f(c), U1(k, c))
25.79/8.44	   A^2 -> H(f(c), U1(c, e))
25.79/8.44	   A^2 -> H(f(c), U1(c, k))
25.79/8.44	   A^2 -> H(f(a), c)
25.79/8.44	   A^2 -> H(f(a), U1(e, k))
25.79/8.44	   A^2 -> H(f(a), U1(k, e))
25.79/8.44	   A^2 -> H(f(c), U1(e, e))
25.79/8.44	   A^2 -> H(f(a), e)
25.79/8.44	   A^2 -> H(f(d), U1(k, d))
25.79/8.44	   A^2 -> H(f(d), U1(d, k))
25.79/8.44	   A^2 -> H(f(a), U1(k, k))
25.79/8.44	   A^2 -> H(d, f(b))
25.79/8.44	   A^2 -> H(a, U1(b, b))
25.79/8.44	   A^2 -> H(a, f(c))
25.79/8.44	   A^2 -> H(a, f(d))
25.79/8.44	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, d), f(c))
25.79/8.44	   A^2 -> H(U1(e, d), f(d))
25.79/8.44	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.44	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.44	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.44	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.44	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.44	   A^2 -> H(U1(e, a), f(e))
25.79/8.44	   A^2 -> H(U1(e, a), f(k))
25.79/8.44	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.44	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.44	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.44	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.44	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.44	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.44	   A^2 -> H(U1(k, a), f(e))
25.79/8.44	   A^2 -> H(U1(k, a), f(k))
25.79/8.44	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.44	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.44	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.44	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.44	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.44	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.44	   A^2 -> H(U1(c, d), f(e))
25.79/8.44	   A^2 -> H(U1(c, d), f(k))
25.79/8.44	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.44	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(d, e), f(c))
25.79/8.44	   A^2 -> H(U1(d, e), f(d))
25.79/8.44	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.44	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.44	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.44	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.44	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.44	   A^2 -> H(U1(d, c), f(e))
25.79/8.44	   A^2 -> H(U1(d, c), f(k))
25.79/8.44	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.44	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.44	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.44	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.44	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.44	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.44	   A^2 -> H(U1(a, e), f(e))
25.79/8.44	   A^2 -> H(U1(a, e), f(k))
25.79/8.44	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.44	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.44	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.44	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.44	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.44	   A^2 -> H(U1(a, k), f(e))
25.79/8.44	   A^2 -> H(U1(a, k), f(k))
25.79/8.44	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.44	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.44	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.44	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.44	   A^2 -> H(U1(a, d), U1(e, c))
25.79/8.44	   A^2 -> H(U1(a, d), U1(k, c))
25.79/8.44	   A^2 -> H(U1(a, d), U1(c, e))
25.79/8.44	   A^2 -> H(U1(a, d), U1(c, k))
25.79/8.44	
25.79/8.44	The TRS R consists of the following rules:
25.79/8.44	
25.79/8.44	   f(x) -> U1(x, x)
25.79/8.44	   U1(e, x) -> x
25.79/8.44	   a -> c
25.79/8.44	   a -> d
25.79/8.44	   b -> c
25.79/8.44	   b -> d
25.79/8.44	   d -> k
25.79/8.44	   c -> e
25.79/8.44	   c -> k
25.79/8.44	
25.79/8.44	Q is empty.
25.79/8.44	We have to consider all minimal (P,Q,R)-chains.
25.79/8.44	----------------------------------------
25.79/8.44	
25.79/8.44	(321) TransformationProof (EQUIVALENT)
25.79/8.44	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), f(e)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.44	
25.79/8.44	   (A^2 -> H(U1(c, d), f(e)),A^2 -> H(U1(c, d), f(e)))
25.79/8.44	   (A^2 -> H(U1(d, d), f(e)),A^2 -> H(U1(d, d), f(e)))
25.79/8.44	   (A^2 -> H(U1(a, k), f(e)),A^2 -> H(U1(a, k), f(e)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(e, e)),A^2 -> H(U1(a, d), U1(e, e)))
25.79/8.44	
25.79/8.44	
25.79/8.44	----------------------------------------
25.79/8.44	
25.79/8.44	(322)
25.79/8.44	Obligation:
25.79/8.44	Q DP problem:
25.79/8.44	The TRS P consists of the following rules:
25.79/8.44	
25.79/8.44	   H(x, x) -> G(x, x, f(k))
25.79/8.44	   G(d, x, x) -> A^2
25.79/8.44	   A^2 -> H(f(c), f(c))
25.79/8.44	   A^2 -> H(f(d), f(d))
25.79/8.44	   A^2 -> H(U1(a, d), f(k))
25.79/8.44	   A^2 -> H(U1(a, d), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.44	   A^2 -> H(c, f(b))
25.79/8.44	   A^2 -> H(U1(e, k), f(b))
25.79/8.44	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, c), f(c))
25.79/8.44	   A^2 -> H(U1(e, c), f(d))
25.79/8.44	   A^2 -> H(U1(k, e), f(b))
25.79/8.44	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, c), f(c))
25.79/8.44	   A^2 -> H(U1(k, c), f(d))
25.79/8.44	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(c, e), f(c))
25.79/8.44	   A^2 -> H(U1(c, e), f(d))
25.79/8.44	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(c, k), f(c))
25.79/8.44	   A^2 -> H(U1(c, k), f(d))
25.79/8.44	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.44	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.44	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.44	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.44	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.44	   A^2 -> H(U1(c, c), f(e))
25.79/8.44	   A^2 -> H(U1(c, c), f(k))
25.79/8.44	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.44	   A^2 -> H(e, f(b))
25.79/8.44	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, e), f(c))
25.79/8.44	   A^2 -> H(U1(e, e), f(d))
25.79/8.44	   A^2 -> H(f(e), U1(c, b))
25.79/8.44	   A^2 -> H(f(e), U1(d, b))
25.79/8.44	   A^2 -> H(f(e), U1(b, c))
25.79/8.44	   A^2 -> H(f(e), U1(b, d))
25.79/8.44	   A^2 -> H(f(e), U1(c, c))
25.79/8.44	   A^2 -> H(f(e), f(e))
25.79/8.44	   A^2 -> H(f(e), f(k))
25.79/8.44	   A^2 -> H(f(e), U1(d, d))
25.79/8.44	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, k), f(c))
25.79/8.44	   A^2 -> H(U1(k, k), f(d))
25.79/8.44	   A^2 -> H(f(k), U1(c, b))
25.79/8.44	   A^2 -> H(f(k), U1(d, b))
25.79/8.44	   A^2 -> H(f(k), U1(b, c))
25.79/8.44	   A^2 -> H(f(k), U1(b, d))
25.79/8.44	   A^2 -> H(f(k), U1(c, c))
25.79/8.44	   A^2 -> H(f(k), f(e))
25.79/8.44	   A^2 -> H(f(k), f(k))
25.79/8.44	   A^2 -> H(f(k), U1(d, d))
25.79/8.44	   A^2 -> H(f(c), U1(e, b))
25.79/8.44	   A^2 -> H(f(c), U1(k, b))
25.79/8.44	   A^2 -> H(f(c), U1(c, d))
25.79/8.44	   A^2 -> H(f(c), U1(d, c))
25.79/8.44	   A^2 -> H(f(c), U1(b, e))
25.79/8.44	   A^2 -> H(f(c), U1(b, k))
25.79/8.44	   A^2 -> H(f(c), U1(k, d))
25.79/8.44	   A^2 -> H(f(c), U1(d, k))
25.79/8.44	   A^2 -> H(f(c), U1(k, k))
25.79/8.44	   A^2 -> H(U1(k, k), f(b))
25.79/8.44	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, d), f(c))
25.79/8.44	   A^2 -> H(U1(k, d), f(d))
25.79/8.44	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(d, k), f(c))
25.79/8.44	   A^2 -> H(U1(d, k), f(d))
25.79/8.44	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.44	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.44	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.44	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.44	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.44	   A^2 -> H(U1(d, d), f(e))
25.79/8.44	   A^2 -> H(U1(d, d), f(k))
25.79/8.44	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.44	   A^2 -> H(f(d), U1(e, b))
25.79/8.44	   A^2 -> H(f(d), U1(k, b))
25.79/8.44	   A^2 -> H(f(d), U1(c, d))
25.79/8.44	   A^2 -> H(f(d), U1(d, c))
25.79/8.44	   A^2 -> H(f(d), U1(b, e))
25.79/8.44	   A^2 -> H(f(d), U1(b, k))
25.79/8.44	   A^2 -> H(f(d), U1(e, c))
25.79/8.44	   A^2 -> H(f(d), U1(k, c))
25.79/8.44	   A^2 -> H(f(d), U1(c, e))
25.79/8.44	   A^2 -> H(f(d), U1(c, k))
25.79/8.44	   A^2 -> H(f(d), U1(e, e))
25.79/8.44	   A^2 -> H(f(d), U1(k, k))
25.79/8.44	   A^2 -> H(f(a), b)
25.79/8.44	   A^2 -> H(f(a), U1(e, d))
25.79/8.44	   A^2 -> H(f(a), U1(d, e))
25.79/8.44	   A^2 -> H(f(c), U1(e, c))
25.79/8.44	   A^2 -> H(f(c), U1(k, c))
25.79/8.44	   A^2 -> H(f(c), U1(c, e))
25.79/8.44	   A^2 -> H(f(c), U1(c, k))
25.79/8.44	   A^2 -> H(f(a), c)
25.79/8.44	   A^2 -> H(f(a), U1(e, k))
25.79/8.44	   A^2 -> H(f(a), U1(k, e))
25.79/8.44	   A^2 -> H(f(c), U1(e, e))
25.79/8.44	   A^2 -> H(f(a), e)
25.79/8.44	   A^2 -> H(f(d), U1(k, d))
25.79/8.44	   A^2 -> H(f(d), U1(d, k))
25.79/8.44	   A^2 -> H(f(a), U1(k, k))
25.79/8.44	   A^2 -> H(d, f(b))
25.79/8.44	   A^2 -> H(a, U1(b, b))
25.79/8.44	   A^2 -> H(a, f(c))
25.79/8.44	   A^2 -> H(a, f(d))
25.79/8.44	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, d), f(c))
25.79/8.44	   A^2 -> H(U1(e, d), f(d))
25.79/8.44	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.44	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.44	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.44	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.44	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.44	   A^2 -> H(U1(e, a), f(e))
25.79/8.44	   A^2 -> H(U1(e, a), f(k))
25.79/8.44	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.44	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.44	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.44	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.44	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.44	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.44	   A^2 -> H(U1(k, a), f(e))
25.79/8.44	   A^2 -> H(U1(k, a), f(k))
25.79/8.44	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.44	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.44	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.44	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.44	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.44	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.44	   A^2 -> H(U1(c, d), f(e))
25.79/8.44	   A^2 -> H(U1(c, d), f(k))
25.79/8.44	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.44	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(d, e), f(c))
25.79/8.44	   A^2 -> H(U1(d, e), f(d))
25.79/8.44	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.44	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.44	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.44	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.44	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.44	   A^2 -> H(U1(d, c), f(e))
25.79/8.44	   A^2 -> H(U1(d, c), f(k))
25.79/8.44	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.44	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.44	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.44	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.44	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.44	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.44	   A^2 -> H(U1(a, e), f(e))
25.79/8.44	   A^2 -> H(U1(a, e), f(k))
25.79/8.44	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.44	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.44	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.44	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.44	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.44	   A^2 -> H(U1(a, k), f(e))
25.79/8.44	   A^2 -> H(U1(a, k), f(k))
25.79/8.44	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.44	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.44	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.44	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.44	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.44	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.44	   A^2 -> H(U1(a, d), U1(e, c))
25.79/8.44	   A^2 -> H(U1(a, d), U1(k, c))
25.79/8.44	   A^2 -> H(U1(a, d), U1(c, e))
25.79/8.44	   A^2 -> H(U1(a, d), U1(c, k))
25.79/8.44	   A^2 -> H(U1(a, d), U1(e, e))
25.79/8.44	
25.79/8.44	The TRS R consists of the following rules:
25.79/8.44	
25.79/8.44	   f(x) -> U1(x, x)
25.79/8.44	   U1(e, x) -> x
25.79/8.44	   a -> c
25.79/8.44	   a -> d
25.79/8.44	   b -> c
25.79/8.44	   b -> d
25.79/8.44	   d -> k
25.79/8.44	   c -> e
25.79/8.44	   c -> k
25.79/8.44	
25.79/8.44	Q is empty.
25.79/8.44	We have to consider all minimal (P,Q,R)-chains.
25.79/8.44	----------------------------------------
25.79/8.44	
25.79/8.44	(323) TransformationProof (EQUIVALENT)
25.79/8.44	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), f(k)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.44	
25.79/8.44	   (A^2 -> H(U1(c, d), f(k)),A^2 -> H(U1(c, d), f(k)))
25.79/8.44	   (A^2 -> H(U1(d, d), f(k)),A^2 -> H(U1(d, d), f(k)))
25.79/8.44	   (A^2 -> H(U1(a, k), f(k)),A^2 -> H(U1(a, k), f(k)))
25.79/8.44	   (A^2 -> H(U1(a, d), U1(k, k)),A^2 -> H(U1(a, d), U1(k, k)))
25.79/8.44	
25.79/8.44	
25.79/8.44	----------------------------------------
25.79/8.44	
25.79/8.44	(324)
25.79/8.44	Obligation:
25.79/8.44	Q DP problem:
25.79/8.44	The TRS P consists of the following rules:
25.79/8.44	
25.79/8.44	   H(x, x) -> G(x, x, f(k))
25.79/8.44	   G(d, x, x) -> A^2
25.79/8.44	   A^2 -> H(f(c), f(c))
25.79/8.44	   A^2 -> H(f(d), f(d))
25.79/8.44	   A^2 -> H(U1(a, d), U1(d, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, b))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, b))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(d, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(b, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(b, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, c))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(c, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(e, e))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.44	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.44	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.44	   A^2 -> H(c, f(b))
25.79/8.44	   A^2 -> H(U1(e, k), f(b))
25.79/8.44	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, c), f(c))
25.79/8.44	   A^2 -> H(U1(e, c), f(d))
25.79/8.44	   A^2 -> H(U1(k, e), f(b))
25.79/8.44	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, c), f(c))
25.79/8.44	   A^2 -> H(U1(k, c), f(d))
25.79/8.44	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(c, e), f(c))
25.79/8.44	   A^2 -> H(U1(c, e), f(d))
25.79/8.44	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(c, k), f(c))
25.79/8.44	   A^2 -> H(U1(c, k), f(d))
25.79/8.44	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.44	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.44	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.44	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.44	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.44	   A^2 -> H(U1(c, c), f(e))
25.79/8.44	   A^2 -> H(U1(c, c), f(k))
25.79/8.44	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.44	   A^2 -> H(e, f(b))
25.79/8.44	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, e), f(c))
25.79/8.44	   A^2 -> H(U1(e, e), f(d))
25.79/8.44	   A^2 -> H(f(e), U1(c, b))
25.79/8.44	   A^2 -> H(f(e), U1(d, b))
25.79/8.44	   A^2 -> H(f(e), U1(b, c))
25.79/8.44	   A^2 -> H(f(e), U1(b, d))
25.79/8.44	   A^2 -> H(f(e), U1(c, c))
25.79/8.44	   A^2 -> H(f(e), f(e))
25.79/8.44	   A^2 -> H(f(e), f(k))
25.79/8.44	   A^2 -> H(f(e), U1(d, d))
25.79/8.44	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, k), f(c))
25.79/8.44	   A^2 -> H(U1(k, k), f(d))
25.79/8.44	   A^2 -> H(f(k), U1(c, b))
25.79/8.44	   A^2 -> H(f(k), U1(d, b))
25.79/8.44	   A^2 -> H(f(k), U1(b, c))
25.79/8.44	   A^2 -> H(f(k), U1(b, d))
25.79/8.44	   A^2 -> H(f(k), U1(c, c))
25.79/8.44	   A^2 -> H(f(k), f(e))
25.79/8.44	   A^2 -> H(f(k), f(k))
25.79/8.44	   A^2 -> H(f(k), U1(d, d))
25.79/8.44	   A^2 -> H(f(c), U1(e, b))
25.79/8.44	   A^2 -> H(f(c), U1(k, b))
25.79/8.44	   A^2 -> H(f(c), U1(c, d))
25.79/8.44	   A^2 -> H(f(c), U1(d, c))
25.79/8.44	   A^2 -> H(f(c), U1(b, e))
25.79/8.44	   A^2 -> H(f(c), U1(b, k))
25.79/8.44	   A^2 -> H(f(c), U1(k, d))
25.79/8.44	   A^2 -> H(f(c), U1(d, k))
25.79/8.44	   A^2 -> H(f(c), U1(k, k))
25.79/8.44	   A^2 -> H(U1(k, k), f(b))
25.79/8.44	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.44	   A^2 -> H(U1(k, d), f(c))
25.79/8.44	   A^2 -> H(U1(k, d), f(d))
25.79/8.44	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.44	   A^2 -> H(U1(d, k), f(c))
25.79/8.44	   A^2 -> H(U1(d, k), f(d))
25.79/8.44	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.44	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.44	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.44	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.44	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.44	   A^2 -> H(U1(d, d), f(e))
25.79/8.44	   A^2 -> H(U1(d, d), f(k))
25.79/8.44	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.44	   A^2 -> H(f(d), U1(e, b))
25.79/8.44	   A^2 -> H(f(d), U1(k, b))
25.79/8.44	   A^2 -> H(f(d), U1(c, d))
25.79/8.44	   A^2 -> H(f(d), U1(d, c))
25.79/8.44	   A^2 -> H(f(d), U1(b, e))
25.79/8.44	   A^2 -> H(f(d), U1(b, k))
25.79/8.44	   A^2 -> H(f(d), U1(e, c))
25.79/8.44	   A^2 -> H(f(d), U1(k, c))
25.79/8.44	   A^2 -> H(f(d), U1(c, e))
25.79/8.44	   A^2 -> H(f(d), U1(c, k))
25.79/8.44	   A^2 -> H(f(d), U1(e, e))
25.79/8.44	   A^2 -> H(f(d), U1(k, k))
25.79/8.44	   A^2 -> H(f(a), b)
25.79/8.44	   A^2 -> H(f(a), U1(e, d))
25.79/8.44	   A^2 -> H(f(a), U1(d, e))
25.79/8.44	   A^2 -> H(f(c), U1(e, c))
25.79/8.44	   A^2 -> H(f(c), U1(k, c))
25.79/8.44	   A^2 -> H(f(c), U1(c, e))
25.79/8.44	   A^2 -> H(f(c), U1(c, k))
25.79/8.44	   A^2 -> H(f(a), c)
25.79/8.44	   A^2 -> H(f(a), U1(e, k))
25.79/8.44	   A^2 -> H(f(a), U1(k, e))
25.79/8.44	   A^2 -> H(f(c), U1(e, e))
25.79/8.44	   A^2 -> H(f(a), e)
25.79/8.44	   A^2 -> H(f(d), U1(k, d))
25.79/8.44	   A^2 -> H(f(d), U1(d, k))
25.79/8.44	   A^2 -> H(f(a), U1(k, k))
25.79/8.44	   A^2 -> H(d, f(b))
25.79/8.44	   A^2 -> H(a, U1(b, b))
25.79/8.44	   A^2 -> H(a, f(c))
25.79/8.44	   A^2 -> H(a, f(d))
25.79/8.44	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.44	   A^2 -> H(U1(e, d), f(c))
25.79/8.44	   A^2 -> H(U1(e, d), f(d))
25.79/8.44	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.46	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.46	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.46	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.46	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.46	   A^2 -> H(U1(e, a), f(e))
25.79/8.46	   A^2 -> H(U1(e, a), f(k))
25.79/8.46	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.46	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.46	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.46	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.46	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.46	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.46	   A^2 -> H(U1(k, a), f(e))
25.79/8.46	   A^2 -> H(U1(k, a), f(k))
25.79/8.46	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.46	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.46	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.46	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.46	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.46	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.46	   A^2 -> H(U1(c, d), f(e))
25.79/8.46	   A^2 -> H(U1(c, d), f(k))
25.79/8.46	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.46	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(d, e), f(c))
25.79/8.46	   A^2 -> H(U1(d, e), f(d))
25.79/8.46	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.46	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.46	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.46	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.46	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.46	   A^2 -> H(U1(d, c), f(e))
25.79/8.46	   A^2 -> H(U1(d, c), f(k))
25.79/8.46	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.46	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.46	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.46	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.46	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.46	   A^2 -> H(U1(a, e), f(e))
25.79/8.46	   A^2 -> H(U1(a, e), f(k))
25.79/8.46	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.46	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.46	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.46	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.46	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.46	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.46	   A^2 -> H(U1(a, k), f(e))
25.79/8.46	   A^2 -> H(U1(a, k), f(k))
25.79/8.46	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.46	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, k))
25.79/8.46	
25.79/8.46	The TRS R consists of the following rules:
25.79/8.46	
25.79/8.46	   f(x) -> U1(x, x)
25.79/8.46	   U1(e, x) -> x
25.79/8.46	   a -> c
25.79/8.46	   a -> d
25.79/8.46	   b -> c
25.79/8.46	   b -> d
25.79/8.46	   d -> k
25.79/8.46	   c -> e
25.79/8.46	   c -> k
25.79/8.46	
25.79/8.46	Q is empty.
25.79/8.46	We have to consider all minimal (P,Q,R)-chains.
25.79/8.46	----------------------------------------
25.79/8.46	
25.79/8.46	(325) TransformationProof (EQUIVALENT)
25.79/8.46	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.46	
25.79/8.46	   (A^2 -> H(U1(c, d), U1(d, d)),A^2 -> H(U1(c, d), U1(d, d)))
25.79/8.46	   (A^2 -> H(U1(d, d), U1(d, d)),A^2 -> H(U1(d, d), U1(d, d)))
25.79/8.46	   (A^2 -> H(U1(a, k), U1(d, d)),A^2 -> H(U1(a, k), U1(d, d)))
25.79/8.46	   (A^2 -> H(U1(a, d), U1(k, d)),A^2 -> H(U1(a, d), U1(k, d)))
25.79/8.46	   (A^2 -> H(U1(a, d), U1(d, k)),A^2 -> H(U1(a, d), U1(d, k)))
25.79/8.46	
25.79/8.46	
25.79/8.46	----------------------------------------
25.79/8.46	
25.79/8.46	(326)
25.79/8.46	Obligation:
25.79/8.46	Q DP problem:
25.79/8.46	The TRS P consists of the following rules:
25.79/8.46	
25.79/8.46	   H(x, x) -> G(x, x, f(k))
25.79/8.46	   G(d, x, x) -> A^2
25.79/8.46	   A^2 -> H(f(c), f(c))
25.79/8.46	   A^2 -> H(f(d), f(d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, b))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, b))
25.79/8.46	   A^2 -> H(U1(a, a), U1(c, d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(d, c))
25.79/8.46	   A^2 -> H(U1(a, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.46	   A^2 -> H(c, f(b))
25.79/8.46	   A^2 -> H(U1(e, k), f(b))
25.79/8.46	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, c), f(c))
25.79/8.46	   A^2 -> H(U1(e, c), f(d))
25.79/8.46	   A^2 -> H(U1(k, e), f(b))
25.79/8.46	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.46	   A^2 -> H(U1(k, c), f(c))
25.79/8.46	   A^2 -> H(U1(k, c), f(d))
25.79/8.46	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(c, e), f(c))
25.79/8.46	   A^2 -> H(U1(c, e), f(d))
25.79/8.46	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.46	   A^2 -> H(U1(c, k), f(c))
25.79/8.46	   A^2 -> H(U1(c, k), f(d))
25.79/8.46	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.46	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.46	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.46	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.46	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.46	   A^2 -> H(U1(c, c), f(e))
25.79/8.46	   A^2 -> H(U1(c, c), f(k))
25.79/8.46	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.46	   A^2 -> H(e, f(b))
25.79/8.46	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, e), f(c))
25.79/8.46	   A^2 -> H(U1(e, e), f(d))
25.79/8.46	   A^2 -> H(f(e), U1(c, b))
25.79/8.46	   A^2 -> H(f(e), U1(d, b))
25.79/8.46	   A^2 -> H(f(e), U1(b, c))
25.79/8.46	   A^2 -> H(f(e), U1(b, d))
25.79/8.46	   A^2 -> H(f(e), U1(c, c))
25.79/8.46	   A^2 -> H(f(e), f(e))
25.79/8.46	   A^2 -> H(f(e), f(k))
25.79/8.46	   A^2 -> H(f(e), U1(d, d))
25.79/8.46	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.46	   A^2 -> H(U1(k, k), f(c))
25.79/8.46	   A^2 -> H(U1(k, k), f(d))
25.79/8.46	   A^2 -> H(f(k), U1(c, b))
25.79/8.46	   A^2 -> H(f(k), U1(d, b))
25.79/8.46	   A^2 -> H(f(k), U1(b, c))
25.79/8.46	   A^2 -> H(f(k), U1(b, d))
25.79/8.46	   A^2 -> H(f(k), U1(c, c))
25.79/8.46	   A^2 -> H(f(k), f(e))
25.79/8.46	   A^2 -> H(f(k), f(k))
25.79/8.46	   A^2 -> H(f(k), U1(d, d))
25.79/8.46	   A^2 -> H(f(c), U1(e, b))
25.79/8.46	   A^2 -> H(f(c), U1(k, b))
25.79/8.46	   A^2 -> H(f(c), U1(c, d))
25.79/8.46	   A^2 -> H(f(c), U1(d, c))
25.79/8.46	   A^2 -> H(f(c), U1(b, e))
25.79/8.46	   A^2 -> H(f(c), U1(b, k))
25.79/8.46	   A^2 -> H(f(c), U1(k, d))
25.79/8.46	   A^2 -> H(f(c), U1(d, k))
25.79/8.46	   A^2 -> H(f(c), U1(k, k))
25.79/8.46	   A^2 -> H(U1(k, k), f(b))
25.79/8.46	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.46	   A^2 -> H(U1(k, d), f(c))
25.79/8.46	   A^2 -> H(U1(k, d), f(d))
25.79/8.46	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.46	   A^2 -> H(U1(d, k), f(c))
25.79/8.46	   A^2 -> H(U1(d, k), f(d))
25.79/8.46	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.46	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.46	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.46	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.46	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.46	   A^2 -> H(U1(d, d), f(e))
25.79/8.46	   A^2 -> H(U1(d, d), f(k))
25.79/8.46	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.46	   A^2 -> H(f(d), U1(e, b))
25.79/8.46	   A^2 -> H(f(d), U1(k, b))
25.79/8.46	   A^2 -> H(f(d), U1(c, d))
25.79/8.46	   A^2 -> H(f(d), U1(d, c))
25.79/8.46	   A^2 -> H(f(d), U1(b, e))
25.79/8.46	   A^2 -> H(f(d), U1(b, k))
25.79/8.46	   A^2 -> H(f(d), U1(e, c))
25.79/8.46	   A^2 -> H(f(d), U1(k, c))
25.79/8.46	   A^2 -> H(f(d), U1(c, e))
25.79/8.46	   A^2 -> H(f(d), U1(c, k))
25.79/8.46	   A^2 -> H(f(d), U1(e, e))
25.79/8.46	   A^2 -> H(f(d), U1(k, k))
25.79/8.46	   A^2 -> H(f(a), b)
25.79/8.46	   A^2 -> H(f(a), U1(e, d))
25.79/8.46	   A^2 -> H(f(a), U1(d, e))
25.79/8.46	   A^2 -> H(f(c), U1(e, c))
25.79/8.46	   A^2 -> H(f(c), U1(k, c))
25.79/8.46	   A^2 -> H(f(c), U1(c, e))
25.79/8.46	   A^2 -> H(f(c), U1(c, k))
25.79/8.46	   A^2 -> H(f(a), c)
25.79/8.46	   A^2 -> H(f(a), U1(e, k))
25.79/8.46	   A^2 -> H(f(a), U1(k, e))
25.79/8.46	   A^2 -> H(f(c), U1(e, e))
25.79/8.46	   A^2 -> H(f(a), e)
25.79/8.46	   A^2 -> H(f(d), U1(k, d))
25.79/8.46	   A^2 -> H(f(d), U1(d, k))
25.79/8.46	   A^2 -> H(f(a), U1(k, k))
25.79/8.46	   A^2 -> H(d, f(b))
25.79/8.46	   A^2 -> H(a, U1(b, b))
25.79/8.46	   A^2 -> H(a, f(c))
25.79/8.46	   A^2 -> H(a, f(d))
25.79/8.46	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, d), f(c))
25.79/8.46	   A^2 -> H(U1(e, d), f(d))
25.79/8.46	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.46	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.46	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.46	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.46	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.46	   A^2 -> H(U1(e, a), f(e))
25.79/8.46	   A^2 -> H(U1(e, a), f(k))
25.79/8.46	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.46	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.46	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.46	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.46	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.46	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.46	   A^2 -> H(U1(k, a), f(e))
25.79/8.46	   A^2 -> H(U1(k, a), f(k))
25.79/8.46	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.46	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.46	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.46	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.46	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.46	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.46	   A^2 -> H(U1(c, d), f(e))
25.79/8.46	   A^2 -> H(U1(c, d), f(k))
25.79/8.46	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.46	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(d, e), f(c))
25.79/8.46	   A^2 -> H(U1(d, e), f(d))
25.79/8.46	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.46	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.46	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.46	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.46	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.46	   A^2 -> H(U1(d, c), f(e))
25.79/8.46	   A^2 -> H(U1(d, c), f(k))
25.79/8.46	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.46	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.46	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.46	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.46	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.46	   A^2 -> H(U1(a, e), f(e))
25.79/8.46	   A^2 -> H(U1(a, e), f(k))
25.79/8.46	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.46	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.46	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.46	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.46	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.46	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.46	   A^2 -> H(U1(a, k), f(e))
25.79/8.46	   A^2 -> H(U1(a, k), f(k))
25.79/8.46	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.46	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, d), U1(d, k))
25.79/8.46	
25.79/8.46	The TRS R consists of the following rules:
25.79/8.46	
25.79/8.46	   f(x) -> U1(x, x)
25.79/8.46	   U1(e, x) -> x
25.79/8.46	   a -> c
25.79/8.46	   a -> d
25.79/8.46	   b -> c
25.79/8.46	   b -> d
25.79/8.46	   d -> k
25.79/8.46	   c -> e
25.79/8.46	   c -> k
25.79/8.46	
25.79/8.46	Q is empty.
25.79/8.46	We have to consider all minimal (P,Q,R)-chains.
25.79/8.46	----------------------------------------
25.79/8.46	
25.79/8.46	(327) TransformationProof (EQUIVALENT)
25.79/8.46	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.46	
25.79/8.46	   (A^2 -> H(U1(c, a), U1(e, b)),A^2 -> H(U1(c, a), U1(e, b)))
25.79/8.46	   (A^2 -> H(U1(d, a), U1(e, b)),A^2 -> H(U1(d, a), U1(e, b)))
25.79/8.46	   (A^2 -> H(U1(a, c), U1(e, b)),A^2 -> H(U1(a, c), U1(e, b)))
25.79/8.46	   (A^2 -> H(U1(a, d), U1(e, b)),A^2 -> H(U1(a, d), U1(e, b)))
25.79/8.46	   (A^2 -> H(U1(a, a), b),A^2 -> H(U1(a, a), b))
25.79/8.46	   (A^2 -> H(U1(a, a), U1(e, c)),A^2 -> H(U1(a, a), U1(e, c)))
25.79/8.46	   (A^2 -> H(U1(a, a), U1(e, d)),A^2 -> H(U1(a, a), U1(e, d)))
25.79/8.46	
25.79/8.46	
25.79/8.46	----------------------------------------
25.79/8.46	
25.79/8.46	(328)
25.79/8.46	Obligation:
25.79/8.46	Q DP problem:
25.79/8.46	The TRS P consists of the following rules:
25.79/8.46	
25.79/8.46	   H(x, x) -> G(x, x, f(k))
25.79/8.46	   G(d, x, x) -> A^2
25.79/8.46	   A^2 -> H(f(c), f(c))
25.79/8.46	   A^2 -> H(f(d), f(d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, b))
25.79/8.46	   A^2 -> H(U1(a, a), U1(c, d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(d, c))
25.79/8.46	   A^2 -> H(U1(a, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.46	   A^2 -> H(c, f(b))
25.79/8.46	   A^2 -> H(U1(e, k), f(b))
25.79/8.46	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, c), f(c))
25.79/8.46	   A^2 -> H(U1(e, c), f(d))
25.79/8.46	   A^2 -> H(U1(k, e), f(b))
25.79/8.46	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.46	   A^2 -> H(U1(k, c), f(c))
25.79/8.46	   A^2 -> H(U1(k, c), f(d))
25.79/8.46	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(c, e), f(c))
25.79/8.46	   A^2 -> H(U1(c, e), f(d))
25.79/8.46	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.46	   A^2 -> H(U1(c, k), f(c))
25.79/8.46	   A^2 -> H(U1(c, k), f(d))
25.79/8.46	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.46	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.46	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.46	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.46	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.46	   A^2 -> H(U1(c, c), f(e))
25.79/8.46	   A^2 -> H(U1(c, c), f(k))
25.79/8.46	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.46	   A^2 -> H(e, f(b))
25.79/8.46	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, e), f(c))
25.79/8.46	   A^2 -> H(U1(e, e), f(d))
25.79/8.46	   A^2 -> H(f(e), U1(c, b))
25.79/8.46	   A^2 -> H(f(e), U1(d, b))
25.79/8.46	   A^2 -> H(f(e), U1(b, c))
25.79/8.46	   A^2 -> H(f(e), U1(b, d))
25.79/8.46	   A^2 -> H(f(e), U1(c, c))
25.79/8.46	   A^2 -> H(f(e), f(e))
25.79/8.46	   A^2 -> H(f(e), f(k))
25.79/8.46	   A^2 -> H(f(e), U1(d, d))
25.79/8.46	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.46	   A^2 -> H(U1(k, k), f(c))
25.79/8.46	   A^2 -> H(U1(k, k), f(d))
25.79/8.46	   A^2 -> H(f(k), U1(c, b))
25.79/8.46	   A^2 -> H(f(k), U1(d, b))
25.79/8.46	   A^2 -> H(f(k), U1(b, c))
25.79/8.46	   A^2 -> H(f(k), U1(b, d))
25.79/8.46	   A^2 -> H(f(k), U1(c, c))
25.79/8.46	   A^2 -> H(f(k), f(e))
25.79/8.46	   A^2 -> H(f(k), f(k))
25.79/8.46	   A^2 -> H(f(k), U1(d, d))
25.79/8.46	   A^2 -> H(f(c), U1(e, b))
25.79/8.46	   A^2 -> H(f(c), U1(k, b))
25.79/8.46	   A^2 -> H(f(c), U1(c, d))
25.79/8.46	   A^2 -> H(f(c), U1(d, c))
25.79/8.46	   A^2 -> H(f(c), U1(b, e))
25.79/8.46	   A^2 -> H(f(c), U1(b, k))
25.79/8.46	   A^2 -> H(f(c), U1(k, d))
25.79/8.46	   A^2 -> H(f(c), U1(d, k))
25.79/8.46	   A^2 -> H(f(c), U1(k, k))
25.79/8.46	   A^2 -> H(U1(k, k), f(b))
25.79/8.46	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.46	   A^2 -> H(U1(k, d), f(c))
25.79/8.46	   A^2 -> H(U1(k, d), f(d))
25.79/8.46	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.46	   A^2 -> H(U1(d, k), f(c))
25.79/8.46	   A^2 -> H(U1(d, k), f(d))
25.79/8.46	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.46	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.46	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.46	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.46	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.46	   A^2 -> H(U1(d, d), f(e))
25.79/8.46	   A^2 -> H(U1(d, d), f(k))
25.79/8.46	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.46	   A^2 -> H(f(d), U1(e, b))
25.79/8.46	   A^2 -> H(f(d), U1(k, b))
25.79/8.46	   A^2 -> H(f(d), U1(c, d))
25.79/8.46	   A^2 -> H(f(d), U1(d, c))
25.79/8.46	   A^2 -> H(f(d), U1(b, e))
25.79/8.46	   A^2 -> H(f(d), U1(b, k))
25.79/8.46	   A^2 -> H(f(d), U1(e, c))
25.79/8.46	   A^2 -> H(f(d), U1(k, c))
25.79/8.46	   A^2 -> H(f(d), U1(c, e))
25.79/8.46	   A^2 -> H(f(d), U1(c, k))
25.79/8.46	   A^2 -> H(f(d), U1(e, e))
25.79/8.46	   A^2 -> H(f(d), U1(k, k))
25.79/8.46	   A^2 -> H(f(a), b)
25.79/8.46	   A^2 -> H(f(a), U1(e, d))
25.79/8.46	   A^2 -> H(f(a), U1(d, e))
25.79/8.46	   A^2 -> H(f(c), U1(e, c))
25.79/8.46	   A^2 -> H(f(c), U1(k, c))
25.79/8.46	   A^2 -> H(f(c), U1(c, e))
25.79/8.46	   A^2 -> H(f(c), U1(c, k))
25.79/8.46	   A^2 -> H(f(a), c)
25.79/8.46	   A^2 -> H(f(a), U1(e, k))
25.79/8.46	   A^2 -> H(f(a), U1(k, e))
25.79/8.46	   A^2 -> H(f(c), U1(e, e))
25.79/8.46	   A^2 -> H(f(a), e)
25.79/8.46	   A^2 -> H(f(d), U1(k, d))
25.79/8.46	   A^2 -> H(f(d), U1(d, k))
25.79/8.46	   A^2 -> H(f(a), U1(k, k))
25.79/8.46	   A^2 -> H(d, f(b))
25.79/8.46	   A^2 -> H(a, U1(b, b))
25.79/8.46	   A^2 -> H(a, f(c))
25.79/8.46	   A^2 -> H(a, f(d))
25.79/8.46	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, d), f(c))
25.79/8.46	   A^2 -> H(U1(e, d), f(d))
25.79/8.46	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.46	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.46	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.46	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.46	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.46	   A^2 -> H(U1(e, a), f(e))
25.79/8.46	   A^2 -> H(U1(e, a), f(k))
25.79/8.46	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.46	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.46	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.46	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.46	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.46	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.46	   A^2 -> H(U1(k, a), f(e))
25.79/8.46	   A^2 -> H(U1(k, a), f(k))
25.79/8.46	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.46	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.46	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.46	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.46	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.46	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.46	   A^2 -> H(U1(c, d), f(e))
25.79/8.46	   A^2 -> H(U1(c, d), f(k))
25.79/8.46	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.46	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(d, e), f(c))
25.79/8.46	   A^2 -> H(U1(d, e), f(d))
25.79/8.46	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.46	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.46	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.46	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.46	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.46	   A^2 -> H(U1(d, c), f(e))
25.79/8.46	   A^2 -> H(U1(d, c), f(k))
25.79/8.46	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.46	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.46	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.46	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.46	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.46	   A^2 -> H(U1(a, e), f(e))
25.79/8.46	   A^2 -> H(U1(a, e), f(k))
25.79/8.46	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.46	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.46	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.46	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.46	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.46	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.46	   A^2 -> H(U1(a, k), f(e))
25.79/8.46	   A^2 -> H(U1(a, k), f(k))
25.79/8.46	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.46	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, d), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, a), b)
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, d))
25.79/8.46	
25.79/8.46	The TRS R consists of the following rules:
25.79/8.46	
25.79/8.46	   f(x) -> U1(x, x)
25.79/8.46	   U1(e, x) -> x
25.79/8.46	   a -> c
25.79/8.46	   a -> d
25.79/8.46	   b -> c
25.79/8.46	   b -> d
25.79/8.46	   d -> k
25.79/8.46	   c -> e
25.79/8.46	   c -> k
25.79/8.46	
25.79/8.46	Q is empty.
25.79/8.46	We have to consider all minimal (P,Q,R)-chains.
25.79/8.46	----------------------------------------
25.79/8.46	
25.79/8.46	(329) TransformationProof (EQUIVALENT)
25.79/8.46	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.46	
25.79/8.46	   (A^2 -> H(U1(c, a), U1(k, b)),A^2 -> H(U1(c, a), U1(k, b)))
25.79/8.46	   (A^2 -> H(U1(d, a), U1(k, b)),A^2 -> H(U1(d, a), U1(k, b)))
25.79/8.46	   (A^2 -> H(U1(a, c), U1(k, b)),A^2 -> H(U1(a, c), U1(k, b)))
25.79/8.46	   (A^2 -> H(U1(a, d), U1(k, b)),A^2 -> H(U1(a, d), U1(k, b)))
25.79/8.46	   (A^2 -> H(U1(a, a), U1(k, c)),A^2 -> H(U1(a, a), U1(k, c)))
25.79/8.46	   (A^2 -> H(U1(a, a), U1(k, d)),A^2 -> H(U1(a, a), U1(k, d)))
25.79/8.46	
25.79/8.46	
25.79/8.46	----------------------------------------
25.79/8.46	
25.79/8.46	(330)
25.79/8.46	Obligation:
25.79/8.46	Q DP problem:
25.79/8.46	The TRS P consists of the following rules:
25.79/8.46	
25.79/8.46	   H(x, x) -> G(x, x, f(k))
25.79/8.46	   G(d, x, x) -> A^2
25.79/8.46	   A^2 -> H(f(c), f(c))
25.79/8.46	   A^2 -> H(f(d), f(d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(c, d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(d, c))
25.79/8.46	   A^2 -> H(U1(a, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.46	   A^2 -> H(c, f(b))
25.79/8.46	   A^2 -> H(U1(e, k), f(b))
25.79/8.46	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, c), f(c))
25.79/8.46	   A^2 -> H(U1(e, c), f(d))
25.79/8.46	   A^2 -> H(U1(k, e), f(b))
25.79/8.46	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.46	   A^2 -> H(U1(k, c), f(c))
25.79/8.46	   A^2 -> H(U1(k, c), f(d))
25.79/8.46	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(c, e), f(c))
25.79/8.46	   A^2 -> H(U1(c, e), f(d))
25.79/8.46	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.46	   A^2 -> H(U1(c, k), f(c))
25.79/8.46	   A^2 -> H(U1(c, k), f(d))
25.79/8.46	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.46	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.46	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.46	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.46	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.46	   A^2 -> H(U1(c, c), f(e))
25.79/8.46	   A^2 -> H(U1(c, c), f(k))
25.79/8.46	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.46	   A^2 -> H(e, f(b))
25.79/8.46	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, e), f(c))
25.79/8.46	   A^2 -> H(U1(e, e), f(d))
25.79/8.46	   A^2 -> H(f(e), U1(c, b))
25.79/8.46	   A^2 -> H(f(e), U1(d, b))
25.79/8.46	   A^2 -> H(f(e), U1(b, c))
25.79/8.46	   A^2 -> H(f(e), U1(b, d))
25.79/8.46	   A^2 -> H(f(e), U1(c, c))
25.79/8.46	   A^2 -> H(f(e), f(e))
25.79/8.46	   A^2 -> H(f(e), f(k))
25.79/8.46	   A^2 -> H(f(e), U1(d, d))
25.79/8.46	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.46	   A^2 -> H(U1(k, k), f(c))
25.79/8.46	   A^2 -> H(U1(k, k), f(d))
25.79/8.46	   A^2 -> H(f(k), U1(c, b))
25.79/8.46	   A^2 -> H(f(k), U1(d, b))
25.79/8.46	   A^2 -> H(f(k), U1(b, c))
25.79/8.46	   A^2 -> H(f(k), U1(b, d))
25.79/8.46	   A^2 -> H(f(k), U1(c, c))
25.79/8.46	   A^2 -> H(f(k), f(e))
25.79/8.46	   A^2 -> H(f(k), f(k))
25.79/8.46	   A^2 -> H(f(k), U1(d, d))
25.79/8.46	   A^2 -> H(f(c), U1(e, b))
25.79/8.46	   A^2 -> H(f(c), U1(k, b))
25.79/8.46	   A^2 -> H(f(c), U1(c, d))
25.79/8.46	   A^2 -> H(f(c), U1(d, c))
25.79/8.46	   A^2 -> H(f(c), U1(b, e))
25.79/8.46	   A^2 -> H(f(c), U1(b, k))
25.79/8.46	   A^2 -> H(f(c), U1(k, d))
25.79/8.46	   A^2 -> H(f(c), U1(d, k))
25.79/8.46	   A^2 -> H(f(c), U1(k, k))
25.79/8.46	   A^2 -> H(U1(k, k), f(b))
25.79/8.46	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.46	   A^2 -> H(U1(k, d), f(c))
25.79/8.46	   A^2 -> H(U1(k, d), f(d))
25.79/8.46	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.46	   A^2 -> H(U1(d, k), f(c))
25.79/8.46	   A^2 -> H(U1(d, k), f(d))
25.79/8.46	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.46	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.46	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.46	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.46	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.46	   A^2 -> H(U1(d, d), f(e))
25.79/8.46	   A^2 -> H(U1(d, d), f(k))
25.79/8.46	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.46	   A^2 -> H(f(d), U1(e, b))
25.79/8.46	   A^2 -> H(f(d), U1(k, b))
25.79/8.46	   A^2 -> H(f(d), U1(c, d))
25.79/8.46	   A^2 -> H(f(d), U1(d, c))
25.79/8.46	   A^2 -> H(f(d), U1(b, e))
25.79/8.46	   A^2 -> H(f(d), U1(b, k))
25.79/8.46	   A^2 -> H(f(d), U1(e, c))
25.79/8.46	   A^2 -> H(f(d), U1(k, c))
25.79/8.46	   A^2 -> H(f(d), U1(c, e))
25.79/8.46	   A^2 -> H(f(d), U1(c, k))
25.79/8.46	   A^2 -> H(f(d), U1(e, e))
25.79/8.46	   A^2 -> H(f(d), U1(k, k))
25.79/8.46	   A^2 -> H(f(a), b)
25.79/8.46	   A^2 -> H(f(a), U1(e, d))
25.79/8.46	   A^2 -> H(f(a), U1(d, e))
25.79/8.46	   A^2 -> H(f(c), U1(e, c))
25.79/8.46	   A^2 -> H(f(c), U1(k, c))
25.79/8.46	   A^2 -> H(f(c), U1(c, e))
25.79/8.46	   A^2 -> H(f(c), U1(c, k))
25.79/8.46	   A^2 -> H(f(a), c)
25.79/8.46	   A^2 -> H(f(a), U1(e, k))
25.79/8.46	   A^2 -> H(f(a), U1(k, e))
25.79/8.46	   A^2 -> H(f(c), U1(e, e))
25.79/8.46	   A^2 -> H(f(a), e)
25.79/8.46	   A^2 -> H(f(d), U1(k, d))
25.79/8.46	   A^2 -> H(f(d), U1(d, k))
25.79/8.46	   A^2 -> H(f(a), U1(k, k))
25.79/8.46	   A^2 -> H(d, f(b))
25.79/8.46	   A^2 -> H(a, U1(b, b))
25.79/8.46	   A^2 -> H(a, f(c))
25.79/8.46	   A^2 -> H(a, f(d))
25.79/8.46	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, d), f(c))
25.79/8.46	   A^2 -> H(U1(e, d), f(d))
25.79/8.46	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.46	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.46	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.46	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.46	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.46	   A^2 -> H(U1(e, a), f(e))
25.79/8.46	   A^2 -> H(U1(e, a), f(k))
25.79/8.46	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.46	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.46	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.46	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.46	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.46	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.46	   A^2 -> H(U1(k, a), f(e))
25.79/8.46	   A^2 -> H(U1(k, a), f(k))
25.79/8.46	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.46	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.46	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.46	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.46	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.46	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.46	   A^2 -> H(U1(c, d), f(e))
25.79/8.46	   A^2 -> H(U1(c, d), f(k))
25.79/8.46	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.46	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(d, e), f(c))
25.79/8.46	   A^2 -> H(U1(d, e), f(d))
25.79/8.46	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.46	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.46	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.46	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.46	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.46	   A^2 -> H(U1(d, c), f(e))
25.79/8.46	   A^2 -> H(U1(d, c), f(k))
25.79/8.46	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.46	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.46	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.46	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.46	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.46	   A^2 -> H(U1(a, e), f(e))
25.79/8.46	   A^2 -> H(U1(a, e), f(k))
25.79/8.46	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.46	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.46	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.46	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.46	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.46	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.46	   A^2 -> H(U1(a, k), f(e))
25.79/8.46	   A^2 -> H(U1(a, k), f(k))
25.79/8.46	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.46	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, d), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, a), b)
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, d))
25.79/8.46	
25.79/8.46	The TRS R consists of the following rules:
25.79/8.46	
25.79/8.46	   f(x) -> U1(x, x)
25.79/8.46	   U1(e, x) -> x
25.79/8.46	   a -> c
25.79/8.46	   a -> d
25.79/8.46	   b -> c
25.79/8.46	   b -> d
25.79/8.46	   d -> k
25.79/8.46	   c -> e
25.79/8.46	   c -> k
25.79/8.46	
25.79/8.46	Q is empty.
25.79/8.46	We have to consider all minimal (P,Q,R)-chains.
25.79/8.46	----------------------------------------
25.79/8.46	
25.79/8.46	(331) TransformationProof (EQUIVALENT)
25.79/8.46	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.46	
25.79/8.46	   (A^2 -> H(U1(c, a), U1(c, d)),A^2 -> H(U1(c, a), U1(c, d)))
25.79/8.46	   (A^2 -> H(U1(d, a), U1(c, d)),A^2 -> H(U1(d, a), U1(c, d)))
25.79/8.46	   (A^2 -> H(U1(a, c), U1(c, d)),A^2 -> H(U1(a, c), U1(c, d)))
25.79/8.46	   (A^2 -> H(U1(a, d), U1(c, d)),A^2 -> H(U1(a, d), U1(c, d)))
25.79/8.46	   (A^2 -> H(U1(a, a), U1(e, d)),A^2 -> H(U1(a, a), U1(e, d)))
25.79/8.46	   (A^2 -> H(U1(a, a), U1(k, d)),A^2 -> H(U1(a, a), U1(k, d)))
25.79/8.46	   (A^2 -> H(U1(a, a), U1(c, k)),A^2 -> H(U1(a, a), U1(c, k)))
25.79/8.46	
25.79/8.46	
25.79/8.46	----------------------------------------
25.79/8.46	
25.79/8.46	(332)
25.79/8.46	Obligation:
25.79/8.46	Q DP problem:
25.79/8.46	The TRS P consists of the following rules:
25.79/8.46	
25.79/8.46	   H(x, x) -> G(x, x, f(k))
25.79/8.46	   G(d, x, x) -> A^2
25.79/8.46	   A^2 -> H(f(c), f(c))
25.79/8.46	   A^2 -> H(f(d), f(d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(d, c))
25.79/8.46	   A^2 -> H(U1(a, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.46	   A^2 -> H(c, f(b))
25.79/8.46	   A^2 -> H(U1(e, k), f(b))
25.79/8.46	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, c), f(c))
25.79/8.46	   A^2 -> H(U1(e, c), f(d))
25.79/8.46	   A^2 -> H(U1(k, e), f(b))
25.79/8.46	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.46	   A^2 -> H(U1(k, c), f(c))
25.79/8.46	   A^2 -> H(U1(k, c), f(d))
25.79/8.46	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(c, e), f(c))
25.79/8.46	   A^2 -> H(U1(c, e), f(d))
25.79/8.46	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.46	   A^2 -> H(U1(c, k), f(c))
25.79/8.46	   A^2 -> H(U1(c, k), f(d))
25.79/8.46	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.46	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.46	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.46	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.46	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.46	   A^2 -> H(U1(c, c), f(e))
25.79/8.46	   A^2 -> H(U1(c, c), f(k))
25.79/8.46	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.46	   A^2 -> H(e, f(b))
25.79/8.46	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, e), f(c))
25.79/8.46	   A^2 -> H(U1(e, e), f(d))
25.79/8.46	   A^2 -> H(f(e), U1(c, b))
25.79/8.46	   A^2 -> H(f(e), U1(d, b))
25.79/8.46	   A^2 -> H(f(e), U1(b, c))
25.79/8.46	   A^2 -> H(f(e), U1(b, d))
25.79/8.46	   A^2 -> H(f(e), U1(c, c))
25.79/8.46	   A^2 -> H(f(e), f(e))
25.79/8.46	   A^2 -> H(f(e), f(k))
25.79/8.46	   A^2 -> H(f(e), U1(d, d))
25.79/8.46	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.46	   A^2 -> H(U1(k, k), f(c))
25.79/8.46	   A^2 -> H(U1(k, k), f(d))
25.79/8.46	   A^2 -> H(f(k), U1(c, b))
25.79/8.46	   A^2 -> H(f(k), U1(d, b))
25.79/8.46	   A^2 -> H(f(k), U1(b, c))
25.79/8.46	   A^2 -> H(f(k), U1(b, d))
25.79/8.46	   A^2 -> H(f(k), U1(c, c))
25.79/8.46	   A^2 -> H(f(k), f(e))
25.79/8.46	   A^2 -> H(f(k), f(k))
25.79/8.46	   A^2 -> H(f(k), U1(d, d))
25.79/8.46	   A^2 -> H(f(c), U1(e, b))
25.79/8.46	   A^2 -> H(f(c), U1(k, b))
25.79/8.46	   A^2 -> H(f(c), U1(c, d))
25.79/8.46	   A^2 -> H(f(c), U1(d, c))
25.79/8.46	   A^2 -> H(f(c), U1(b, e))
25.79/8.46	   A^2 -> H(f(c), U1(b, k))
25.79/8.46	   A^2 -> H(f(c), U1(k, d))
25.79/8.46	   A^2 -> H(f(c), U1(d, k))
25.79/8.46	   A^2 -> H(f(c), U1(k, k))
25.79/8.46	   A^2 -> H(U1(k, k), f(b))
25.79/8.46	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.46	   A^2 -> H(U1(k, d), f(c))
25.79/8.46	   A^2 -> H(U1(k, d), f(d))
25.79/8.46	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.46	   A^2 -> H(U1(d, k), f(c))
25.79/8.46	   A^2 -> H(U1(d, k), f(d))
25.79/8.46	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.46	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.46	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.46	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.46	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.46	   A^2 -> H(U1(d, d), f(e))
25.79/8.46	   A^2 -> H(U1(d, d), f(k))
25.79/8.46	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.46	   A^2 -> H(f(d), U1(e, b))
25.79/8.46	   A^2 -> H(f(d), U1(k, b))
25.79/8.46	   A^2 -> H(f(d), U1(c, d))
25.79/8.46	   A^2 -> H(f(d), U1(d, c))
25.79/8.46	   A^2 -> H(f(d), U1(b, e))
25.79/8.46	   A^2 -> H(f(d), U1(b, k))
25.79/8.46	   A^2 -> H(f(d), U1(e, c))
25.79/8.46	   A^2 -> H(f(d), U1(k, c))
25.79/8.46	   A^2 -> H(f(d), U1(c, e))
25.79/8.46	   A^2 -> H(f(d), U1(c, k))
25.79/8.46	   A^2 -> H(f(d), U1(e, e))
25.79/8.46	   A^2 -> H(f(d), U1(k, k))
25.79/8.46	   A^2 -> H(f(a), b)
25.79/8.46	   A^2 -> H(f(a), U1(e, d))
25.79/8.46	   A^2 -> H(f(a), U1(d, e))
25.79/8.46	   A^2 -> H(f(c), U1(e, c))
25.79/8.46	   A^2 -> H(f(c), U1(k, c))
25.79/8.46	   A^2 -> H(f(c), U1(c, e))
25.79/8.46	   A^2 -> H(f(c), U1(c, k))
25.79/8.46	   A^2 -> H(f(a), c)
25.79/8.46	   A^2 -> H(f(a), U1(e, k))
25.79/8.46	   A^2 -> H(f(a), U1(k, e))
25.79/8.46	   A^2 -> H(f(c), U1(e, e))
25.79/8.46	   A^2 -> H(f(a), e)
25.79/8.46	   A^2 -> H(f(d), U1(k, d))
25.79/8.46	   A^2 -> H(f(d), U1(d, k))
25.79/8.46	   A^2 -> H(f(a), U1(k, k))
25.79/8.46	   A^2 -> H(d, f(b))
25.79/8.46	   A^2 -> H(a, U1(b, b))
25.79/8.46	   A^2 -> H(a, f(c))
25.79/8.46	   A^2 -> H(a, f(d))
25.79/8.46	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, d), f(c))
25.79/8.46	   A^2 -> H(U1(e, d), f(d))
25.79/8.46	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.46	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.46	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.46	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.46	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.46	   A^2 -> H(U1(e, a), f(e))
25.79/8.46	   A^2 -> H(U1(e, a), f(k))
25.79/8.46	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.46	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.46	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.46	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.46	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.46	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.46	   A^2 -> H(U1(k, a), f(e))
25.79/8.46	   A^2 -> H(U1(k, a), f(k))
25.79/8.46	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.46	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.46	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.46	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.46	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.46	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.46	   A^2 -> H(U1(c, d), f(e))
25.79/8.46	   A^2 -> H(U1(c, d), f(k))
25.79/8.46	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.46	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(d, e), f(c))
25.79/8.46	   A^2 -> H(U1(d, e), f(d))
25.79/8.46	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.46	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.46	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.46	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.46	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.46	   A^2 -> H(U1(d, c), f(e))
25.79/8.46	   A^2 -> H(U1(d, c), f(k))
25.79/8.46	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.46	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.46	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.46	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.46	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.46	   A^2 -> H(U1(a, e), f(e))
25.79/8.46	   A^2 -> H(U1(a, e), f(k))
25.79/8.46	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.46	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.46	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.46	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.46	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.46	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.46	   A^2 -> H(U1(a, k), f(e))
25.79/8.46	   A^2 -> H(U1(a, k), f(k))
25.79/8.46	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.46	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, d), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, a), b)
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, d))
25.79/8.46	
25.79/8.46	The TRS R consists of the following rules:
25.79/8.46	
25.79/8.46	   f(x) -> U1(x, x)
25.79/8.46	   U1(e, x) -> x
25.79/8.46	   a -> c
25.79/8.46	   a -> d
25.79/8.46	   b -> c
25.79/8.46	   b -> d
25.79/8.46	   d -> k
25.79/8.46	   c -> e
25.79/8.46	   c -> k
25.79/8.46	
25.79/8.46	Q is empty.
25.79/8.46	We have to consider all minimal (P,Q,R)-chains.
25.79/8.46	----------------------------------------
25.79/8.46	
25.79/8.46	(333) TransformationProof (EQUIVALENT)
25.79/8.46	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.46	
25.79/8.46	   (A^2 -> H(U1(c, a), U1(d, c)),A^2 -> H(U1(c, a), U1(d, c)))
25.79/8.46	   (A^2 -> H(U1(d, a), U1(d, c)),A^2 -> H(U1(d, a), U1(d, c)))
25.79/8.46	   (A^2 -> H(U1(a, c), U1(d, c)),A^2 -> H(U1(a, c), U1(d, c)))
25.79/8.46	   (A^2 -> H(U1(a, d), U1(d, c)),A^2 -> H(U1(a, d), U1(d, c)))
25.79/8.46	   (A^2 -> H(U1(a, a), U1(k, c)),A^2 -> H(U1(a, a), U1(k, c)))
25.79/8.46	   (A^2 -> H(U1(a, a), U1(d, e)),A^2 -> H(U1(a, a), U1(d, e)))
25.79/8.46	   (A^2 -> H(U1(a, a), U1(d, k)),A^2 -> H(U1(a, a), U1(d, k)))
25.79/8.46	
25.79/8.46	
25.79/8.46	----------------------------------------
25.79/8.46	
25.79/8.46	(334)
25.79/8.46	Obligation:
25.79/8.46	Q DP problem:
25.79/8.46	The TRS P consists of the following rules:
25.79/8.46	
25.79/8.46	   H(x, x) -> G(x, x, f(k))
25.79/8.46	   G(d, x, x) -> A^2
25.79/8.46	   A^2 -> H(f(c), f(c))
25.79/8.46	   A^2 -> H(f(d), f(d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.46	   A^2 -> H(c, f(b))
25.79/8.46	   A^2 -> H(U1(e, k), f(b))
25.79/8.46	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, c), f(c))
25.79/8.46	   A^2 -> H(U1(e, c), f(d))
25.79/8.46	   A^2 -> H(U1(k, e), f(b))
25.79/8.46	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.46	   A^2 -> H(U1(k, c), f(c))
25.79/8.46	   A^2 -> H(U1(k, c), f(d))
25.79/8.46	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(c, e), f(c))
25.79/8.46	   A^2 -> H(U1(c, e), f(d))
25.79/8.46	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.46	   A^2 -> H(U1(c, k), f(c))
25.79/8.46	   A^2 -> H(U1(c, k), f(d))
25.79/8.46	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.46	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.46	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.46	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.46	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.46	   A^2 -> H(U1(c, c), f(e))
25.79/8.46	   A^2 -> H(U1(c, c), f(k))
25.79/8.46	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.46	   A^2 -> H(e, f(b))
25.79/8.46	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, e), f(c))
25.79/8.46	   A^2 -> H(U1(e, e), f(d))
25.79/8.46	   A^2 -> H(f(e), U1(c, b))
25.79/8.46	   A^2 -> H(f(e), U1(d, b))
25.79/8.46	   A^2 -> H(f(e), U1(b, c))
25.79/8.46	   A^2 -> H(f(e), U1(b, d))
25.79/8.46	   A^2 -> H(f(e), U1(c, c))
25.79/8.46	   A^2 -> H(f(e), f(e))
25.79/8.46	   A^2 -> H(f(e), f(k))
25.79/8.46	   A^2 -> H(f(e), U1(d, d))
25.79/8.46	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.46	   A^2 -> H(U1(k, k), f(c))
25.79/8.46	   A^2 -> H(U1(k, k), f(d))
25.79/8.46	   A^2 -> H(f(k), U1(c, b))
25.79/8.46	   A^2 -> H(f(k), U1(d, b))
25.79/8.46	   A^2 -> H(f(k), U1(b, c))
25.79/8.46	   A^2 -> H(f(k), U1(b, d))
25.79/8.46	   A^2 -> H(f(k), U1(c, c))
25.79/8.46	   A^2 -> H(f(k), f(e))
25.79/8.46	   A^2 -> H(f(k), f(k))
25.79/8.46	   A^2 -> H(f(k), U1(d, d))
25.79/8.46	   A^2 -> H(f(c), U1(e, b))
25.79/8.46	   A^2 -> H(f(c), U1(k, b))
25.79/8.46	   A^2 -> H(f(c), U1(c, d))
25.79/8.46	   A^2 -> H(f(c), U1(d, c))
25.79/8.46	   A^2 -> H(f(c), U1(b, e))
25.79/8.46	   A^2 -> H(f(c), U1(b, k))
25.79/8.46	   A^2 -> H(f(c), U1(k, d))
25.79/8.46	   A^2 -> H(f(c), U1(d, k))
25.79/8.46	   A^2 -> H(f(c), U1(k, k))
25.79/8.46	   A^2 -> H(U1(k, k), f(b))
25.79/8.46	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.46	   A^2 -> H(U1(k, d), f(c))
25.79/8.46	   A^2 -> H(U1(k, d), f(d))
25.79/8.46	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.46	   A^2 -> H(U1(d, k), f(c))
25.79/8.46	   A^2 -> H(U1(d, k), f(d))
25.79/8.46	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.46	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.46	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.46	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.46	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.46	   A^2 -> H(U1(d, d), f(e))
25.79/8.46	   A^2 -> H(U1(d, d), f(k))
25.79/8.46	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.46	   A^2 -> H(f(d), U1(e, b))
25.79/8.46	   A^2 -> H(f(d), U1(k, b))
25.79/8.46	   A^2 -> H(f(d), U1(c, d))
25.79/8.46	   A^2 -> H(f(d), U1(d, c))
25.79/8.46	   A^2 -> H(f(d), U1(b, e))
25.79/8.46	   A^2 -> H(f(d), U1(b, k))
25.79/8.46	   A^2 -> H(f(d), U1(e, c))
25.79/8.46	   A^2 -> H(f(d), U1(k, c))
25.79/8.46	   A^2 -> H(f(d), U1(c, e))
25.79/8.46	   A^2 -> H(f(d), U1(c, k))
25.79/8.46	   A^2 -> H(f(d), U1(e, e))
25.79/8.46	   A^2 -> H(f(d), U1(k, k))
25.79/8.46	   A^2 -> H(f(a), b)
25.79/8.46	   A^2 -> H(f(a), U1(e, d))
25.79/8.46	   A^2 -> H(f(a), U1(d, e))
25.79/8.46	   A^2 -> H(f(c), U1(e, c))
25.79/8.46	   A^2 -> H(f(c), U1(k, c))
25.79/8.46	   A^2 -> H(f(c), U1(c, e))
25.79/8.46	   A^2 -> H(f(c), U1(c, k))
25.79/8.46	   A^2 -> H(f(a), c)
25.79/8.46	   A^2 -> H(f(a), U1(e, k))
25.79/8.46	   A^2 -> H(f(a), U1(k, e))
25.79/8.46	   A^2 -> H(f(c), U1(e, e))
25.79/8.46	   A^2 -> H(f(a), e)
25.79/8.46	   A^2 -> H(f(d), U1(k, d))
25.79/8.46	   A^2 -> H(f(d), U1(d, k))
25.79/8.46	   A^2 -> H(f(a), U1(k, k))
25.79/8.46	   A^2 -> H(d, f(b))
25.79/8.46	   A^2 -> H(a, U1(b, b))
25.79/8.46	   A^2 -> H(a, f(c))
25.79/8.46	   A^2 -> H(a, f(d))
25.79/8.46	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, d), f(c))
25.79/8.46	   A^2 -> H(U1(e, d), f(d))
25.79/8.46	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.46	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.46	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.46	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.46	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.46	   A^2 -> H(U1(e, a), f(e))
25.79/8.46	   A^2 -> H(U1(e, a), f(k))
25.79/8.46	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.46	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.46	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.46	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.46	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.46	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.46	   A^2 -> H(U1(k, a), f(e))
25.79/8.46	   A^2 -> H(U1(k, a), f(k))
25.79/8.46	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.46	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.46	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.46	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.46	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.46	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.46	   A^2 -> H(U1(c, d), f(e))
25.79/8.46	   A^2 -> H(U1(c, d), f(k))
25.79/8.46	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.46	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(d, e), f(c))
25.79/8.46	   A^2 -> H(U1(d, e), f(d))
25.79/8.46	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.46	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.46	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.46	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.46	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.46	   A^2 -> H(U1(d, c), f(e))
25.79/8.46	   A^2 -> H(U1(d, c), f(k))
25.79/8.46	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.46	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.46	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.46	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.46	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.46	   A^2 -> H(U1(a, e), f(e))
25.79/8.46	   A^2 -> H(U1(a, e), f(k))
25.79/8.46	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.46	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.46	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.46	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.46	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.46	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.46	   A^2 -> H(U1(a, k), f(e))
25.79/8.46	   A^2 -> H(U1(a, k), f(k))
25.79/8.46	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.46	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, d), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, a), b)
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(d, e))
25.79/8.46	
25.79/8.46	The TRS R consists of the following rules:
25.79/8.46	
25.79/8.46	   f(x) -> U1(x, x)
25.79/8.46	   U1(e, x) -> x
25.79/8.46	   a -> c
25.79/8.46	   a -> d
25.79/8.46	   b -> c
25.79/8.46	   b -> d
25.79/8.46	   d -> k
25.79/8.46	   c -> e
25.79/8.46	   c -> k
25.79/8.46	
25.79/8.46	Q is empty.
25.79/8.46	We have to consider all minimal (P,Q,R)-chains.
25.79/8.46	----------------------------------------
25.79/8.46	
25.79/8.46	(335) TransformationProof (EQUIVALENT)
25.79/8.46	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.46	
25.79/8.46	   (A^2 -> H(U1(c, a), U1(b, e)),A^2 -> H(U1(c, a), U1(b, e)))
25.79/8.46	   (A^2 -> H(U1(d, a), U1(b, e)),A^2 -> H(U1(d, a), U1(b, e)))
25.79/8.46	   (A^2 -> H(U1(a, c), U1(b, e)),A^2 -> H(U1(a, c), U1(b, e)))
25.79/8.46	   (A^2 -> H(U1(a, d), U1(b, e)),A^2 -> H(U1(a, d), U1(b, e)))
25.79/8.46	   (A^2 -> H(U1(a, a), U1(c, e)),A^2 -> H(U1(a, a), U1(c, e)))
25.79/8.46	   (A^2 -> H(U1(a, a), U1(d, e)),A^2 -> H(U1(a, a), U1(d, e)))
25.79/8.46	
25.79/8.46	
25.79/8.46	----------------------------------------
25.79/8.46	
25.79/8.46	(336)
25.79/8.46	Obligation:
25.79/8.46	Q DP problem:
25.79/8.46	The TRS P consists of the following rules:
25.79/8.46	
25.79/8.46	   H(x, x) -> G(x, x, f(k))
25.79/8.46	   G(d, x, x) -> A^2
25.79/8.46	   A^2 -> H(f(c), f(c))
25.79/8.46	   A^2 -> H(f(d), f(d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.46	   A^2 -> H(c, f(b))
25.79/8.46	   A^2 -> H(U1(e, k), f(b))
25.79/8.46	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, c), f(c))
25.79/8.46	   A^2 -> H(U1(e, c), f(d))
25.79/8.46	   A^2 -> H(U1(k, e), f(b))
25.79/8.46	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.46	   A^2 -> H(U1(k, c), f(c))
25.79/8.46	   A^2 -> H(U1(k, c), f(d))
25.79/8.46	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(c, e), f(c))
25.79/8.46	   A^2 -> H(U1(c, e), f(d))
25.79/8.46	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.46	   A^2 -> H(U1(c, k), f(c))
25.79/8.46	   A^2 -> H(U1(c, k), f(d))
25.79/8.46	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.46	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.46	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.46	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.46	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.46	   A^2 -> H(U1(c, c), f(e))
25.79/8.46	   A^2 -> H(U1(c, c), f(k))
25.79/8.46	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.46	   A^2 -> H(e, f(b))
25.79/8.46	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, e), f(c))
25.79/8.46	   A^2 -> H(U1(e, e), f(d))
25.79/8.46	   A^2 -> H(f(e), U1(c, b))
25.79/8.46	   A^2 -> H(f(e), U1(d, b))
25.79/8.46	   A^2 -> H(f(e), U1(b, c))
25.79/8.46	   A^2 -> H(f(e), U1(b, d))
25.79/8.46	   A^2 -> H(f(e), U1(c, c))
25.79/8.46	   A^2 -> H(f(e), f(e))
25.79/8.46	   A^2 -> H(f(e), f(k))
25.79/8.46	   A^2 -> H(f(e), U1(d, d))
25.79/8.46	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.46	   A^2 -> H(U1(k, k), f(c))
25.79/8.46	   A^2 -> H(U1(k, k), f(d))
25.79/8.46	   A^2 -> H(f(k), U1(c, b))
25.79/8.46	   A^2 -> H(f(k), U1(d, b))
25.79/8.46	   A^2 -> H(f(k), U1(b, c))
25.79/8.46	   A^2 -> H(f(k), U1(b, d))
25.79/8.46	   A^2 -> H(f(k), U1(c, c))
25.79/8.46	   A^2 -> H(f(k), f(e))
25.79/8.46	   A^2 -> H(f(k), f(k))
25.79/8.46	   A^2 -> H(f(k), U1(d, d))
25.79/8.46	   A^2 -> H(f(c), U1(e, b))
25.79/8.46	   A^2 -> H(f(c), U1(k, b))
25.79/8.46	   A^2 -> H(f(c), U1(c, d))
25.79/8.46	   A^2 -> H(f(c), U1(d, c))
25.79/8.46	   A^2 -> H(f(c), U1(b, e))
25.79/8.46	   A^2 -> H(f(c), U1(b, k))
25.79/8.46	   A^2 -> H(f(c), U1(k, d))
25.79/8.46	   A^2 -> H(f(c), U1(d, k))
25.79/8.46	   A^2 -> H(f(c), U1(k, k))
25.79/8.46	   A^2 -> H(U1(k, k), f(b))
25.79/8.46	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.46	   A^2 -> H(U1(k, d), f(c))
25.79/8.46	   A^2 -> H(U1(k, d), f(d))
25.79/8.46	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.46	   A^2 -> H(U1(d, k), f(c))
25.79/8.46	   A^2 -> H(U1(d, k), f(d))
25.79/8.46	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.46	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.46	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.46	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.46	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.46	   A^2 -> H(U1(d, d), f(e))
25.79/8.46	   A^2 -> H(U1(d, d), f(k))
25.79/8.46	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.46	   A^2 -> H(f(d), U1(e, b))
25.79/8.46	   A^2 -> H(f(d), U1(k, b))
25.79/8.46	   A^2 -> H(f(d), U1(c, d))
25.79/8.46	   A^2 -> H(f(d), U1(d, c))
25.79/8.46	   A^2 -> H(f(d), U1(b, e))
25.79/8.46	   A^2 -> H(f(d), U1(b, k))
25.79/8.46	   A^2 -> H(f(d), U1(e, c))
25.79/8.46	   A^2 -> H(f(d), U1(k, c))
25.79/8.46	   A^2 -> H(f(d), U1(c, e))
25.79/8.46	   A^2 -> H(f(d), U1(c, k))
25.79/8.46	   A^2 -> H(f(d), U1(e, e))
25.79/8.46	   A^2 -> H(f(d), U1(k, k))
25.79/8.46	   A^2 -> H(f(a), b)
25.79/8.46	   A^2 -> H(f(a), U1(e, d))
25.79/8.46	   A^2 -> H(f(a), U1(d, e))
25.79/8.46	   A^2 -> H(f(c), U1(e, c))
25.79/8.46	   A^2 -> H(f(c), U1(k, c))
25.79/8.46	   A^2 -> H(f(c), U1(c, e))
25.79/8.46	   A^2 -> H(f(c), U1(c, k))
25.79/8.46	   A^2 -> H(f(a), c)
25.79/8.46	   A^2 -> H(f(a), U1(e, k))
25.79/8.46	   A^2 -> H(f(a), U1(k, e))
25.79/8.46	   A^2 -> H(f(c), U1(e, e))
25.79/8.46	   A^2 -> H(f(a), e)
25.79/8.46	   A^2 -> H(f(d), U1(k, d))
25.79/8.46	   A^2 -> H(f(d), U1(d, k))
25.79/8.46	   A^2 -> H(f(a), U1(k, k))
25.79/8.46	   A^2 -> H(d, f(b))
25.79/8.46	   A^2 -> H(a, U1(b, b))
25.79/8.46	   A^2 -> H(a, f(c))
25.79/8.46	   A^2 -> H(a, f(d))
25.79/8.46	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, d), f(c))
25.79/8.46	   A^2 -> H(U1(e, d), f(d))
25.79/8.46	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.46	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.46	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.46	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.46	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.46	   A^2 -> H(U1(e, a), f(e))
25.79/8.46	   A^2 -> H(U1(e, a), f(k))
25.79/8.46	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.46	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.46	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.46	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.46	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.46	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.46	   A^2 -> H(U1(k, a), f(e))
25.79/8.46	   A^2 -> H(U1(k, a), f(k))
25.79/8.46	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.46	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.46	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.46	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.46	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.46	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.46	   A^2 -> H(U1(c, d), f(e))
25.79/8.46	   A^2 -> H(U1(c, d), f(k))
25.79/8.46	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.46	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.46	   A^2 -> H(U1(d, e), f(c))
25.79/8.46	   A^2 -> H(U1(d, e), f(d))
25.79/8.46	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.46	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.46	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.46	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.46	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.46	   A^2 -> H(U1(d, c), f(e))
25.79/8.46	   A^2 -> H(U1(d, c), f(k))
25.79/8.46	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.46	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.46	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.46	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.46	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.46	   A^2 -> H(U1(a, e), f(e))
25.79/8.46	   A^2 -> H(U1(a, e), f(k))
25.79/8.46	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.46	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.46	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.46	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.46	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.46	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.46	   A^2 -> H(U1(a, k), f(e))
25.79/8.46	   A^2 -> H(U1(a, k), f(k))
25.79/8.46	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.46	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, d), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, d), U1(d, k))
25.79/8.46	   A^2 -> H(U1(a, a), b)
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(d, e))
25.79/8.46	
25.79/8.46	The TRS R consists of the following rules:
25.79/8.46	
25.79/8.46	   f(x) -> U1(x, x)
25.79/8.46	   U1(e, x) -> x
25.79/8.46	   a -> c
25.79/8.46	   a -> d
25.79/8.46	   b -> c
25.79/8.46	   b -> d
25.79/8.46	   d -> k
25.79/8.46	   c -> e
25.79/8.46	   c -> k
25.79/8.46	
25.79/8.46	Q is empty.
25.79/8.46	We have to consider all minimal (P,Q,R)-chains.
25.79/8.46	----------------------------------------
25.79/8.46	
25.79/8.46	(337) TransformationProof (EQUIVALENT)
25.79/8.46	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.46	
25.79/8.46	   (A^2 -> H(U1(c, a), U1(b, k)),A^2 -> H(U1(c, a), U1(b, k)))
25.79/8.46	   (A^2 -> H(U1(d, a), U1(b, k)),A^2 -> H(U1(d, a), U1(b, k)))
25.79/8.46	   (A^2 -> H(U1(a, c), U1(b, k)),A^2 -> H(U1(a, c), U1(b, k)))
25.79/8.46	   (A^2 -> H(U1(a, d), U1(b, k)),A^2 -> H(U1(a, d), U1(b, k)))
25.79/8.46	   (A^2 -> H(U1(a, a), U1(c, k)),A^2 -> H(U1(a, a), U1(c, k)))
25.79/8.46	   (A^2 -> H(U1(a, a), U1(d, k)),A^2 -> H(U1(a, a), U1(d, k)))
25.79/8.46	
25.79/8.46	
25.79/8.46	----------------------------------------
25.79/8.46	
25.79/8.46	(338)
25.79/8.46	Obligation:
25.79/8.46	Q DP problem:
25.79/8.46	The TRS P consists of the following rules:
25.79/8.46	
25.79/8.46	   H(x, x) -> G(x, x, f(k))
25.79/8.46	   G(d, x, x) -> A^2
25.79/8.46	   A^2 -> H(f(c), f(c))
25.79/8.46	   A^2 -> H(f(d), f(d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, c))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, c))
25.79/8.46	   A^2 -> H(U1(a, a), U1(c, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(c, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(e, e))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.46	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.46	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.46	   A^2 -> H(c, f(b))
25.79/8.46	   A^2 -> H(U1(e, k), f(b))
25.79/8.46	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.46	   A^2 -> H(U1(e, c), f(c))
25.79/8.46	   A^2 -> H(U1(e, c), f(d))
25.79/8.46	   A^2 -> H(U1(k, e), f(b))
25.79/8.46	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.47	   A^2 -> H(U1(k, c), f(c))
25.79/8.47	   A^2 -> H(U1(k, c), f(d))
25.79/8.47	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.47	   A^2 -> H(U1(c, e), f(c))
25.79/8.47	   A^2 -> H(U1(c, e), f(d))
25.79/8.47	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.47	   A^2 -> H(U1(c, k), f(c))
25.79/8.47	   A^2 -> H(U1(c, k), f(d))
25.79/8.47	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.47	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.47	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.47	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.47	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.47	   A^2 -> H(U1(c, c), f(e))
25.79/8.47	   A^2 -> H(U1(c, c), f(k))
25.79/8.47	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.47	   A^2 -> H(e, f(b))
25.79/8.47	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.47	   A^2 -> H(U1(e, e), f(c))
25.79/8.47	   A^2 -> H(U1(e, e), f(d))
25.79/8.47	   A^2 -> H(f(e), U1(c, b))
25.79/8.47	   A^2 -> H(f(e), U1(d, b))
25.79/8.47	   A^2 -> H(f(e), U1(b, c))
25.79/8.47	   A^2 -> H(f(e), U1(b, d))
25.79/8.47	   A^2 -> H(f(e), U1(c, c))
25.79/8.47	   A^2 -> H(f(e), f(e))
25.79/8.47	   A^2 -> H(f(e), f(k))
25.79/8.47	   A^2 -> H(f(e), U1(d, d))
25.79/8.47	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.47	   A^2 -> H(U1(k, k), f(c))
25.79/8.47	   A^2 -> H(U1(k, k), f(d))
25.79/8.47	   A^2 -> H(f(k), U1(c, b))
25.79/8.47	   A^2 -> H(f(k), U1(d, b))
25.79/8.47	   A^2 -> H(f(k), U1(b, c))
25.79/8.47	   A^2 -> H(f(k), U1(b, d))
25.79/8.47	   A^2 -> H(f(k), U1(c, c))
25.79/8.47	   A^2 -> H(f(k), f(e))
25.79/8.47	   A^2 -> H(f(k), f(k))
25.79/8.47	   A^2 -> H(f(k), U1(d, d))
25.79/8.47	   A^2 -> H(f(c), U1(e, b))
25.79/8.47	   A^2 -> H(f(c), U1(k, b))
25.79/8.47	   A^2 -> H(f(c), U1(c, d))
25.79/8.47	   A^2 -> H(f(c), U1(d, c))
25.79/8.47	   A^2 -> H(f(c), U1(b, e))
25.79/8.47	   A^2 -> H(f(c), U1(b, k))
25.79/8.47	   A^2 -> H(f(c), U1(k, d))
25.79/8.47	   A^2 -> H(f(c), U1(d, k))
25.79/8.47	   A^2 -> H(f(c), U1(k, k))
25.79/8.47	   A^2 -> H(U1(k, k), f(b))
25.79/8.47	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.47	   A^2 -> H(U1(k, d), f(c))
25.79/8.47	   A^2 -> H(U1(k, d), f(d))
25.79/8.47	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.47	   A^2 -> H(U1(d, k), f(c))
25.79/8.47	   A^2 -> H(U1(d, k), f(d))
25.79/8.47	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.47	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.47	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.47	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.47	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.47	   A^2 -> H(U1(d, d), f(e))
25.79/8.47	   A^2 -> H(U1(d, d), f(k))
25.79/8.47	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.47	   A^2 -> H(f(d), U1(e, b))
25.79/8.47	   A^2 -> H(f(d), U1(k, b))
25.79/8.47	   A^2 -> H(f(d), U1(c, d))
25.79/8.47	   A^2 -> H(f(d), U1(d, c))
25.79/8.47	   A^2 -> H(f(d), U1(b, e))
25.79/8.47	   A^2 -> H(f(d), U1(b, k))
25.79/8.47	   A^2 -> H(f(d), U1(e, c))
25.79/8.47	   A^2 -> H(f(d), U1(k, c))
25.79/8.47	   A^2 -> H(f(d), U1(c, e))
25.79/8.47	   A^2 -> H(f(d), U1(c, k))
25.79/8.47	   A^2 -> H(f(d), U1(e, e))
25.79/8.47	   A^2 -> H(f(d), U1(k, k))
25.79/8.47	   A^2 -> H(f(a), b)
25.79/8.47	   A^2 -> H(f(a), U1(e, d))
25.79/8.47	   A^2 -> H(f(a), U1(d, e))
25.79/8.47	   A^2 -> H(f(c), U1(e, c))
25.79/8.47	   A^2 -> H(f(c), U1(k, c))
25.79/8.47	   A^2 -> H(f(c), U1(c, e))
25.79/8.47	   A^2 -> H(f(c), U1(c, k))
25.79/8.47	   A^2 -> H(f(a), c)
25.79/8.47	   A^2 -> H(f(a), U1(e, k))
25.79/8.47	   A^2 -> H(f(a), U1(k, e))
25.79/8.47	   A^2 -> H(f(c), U1(e, e))
25.79/8.47	   A^2 -> H(f(a), e)
25.79/8.47	   A^2 -> H(f(d), U1(k, d))
25.79/8.47	   A^2 -> H(f(d), U1(d, k))
25.79/8.47	   A^2 -> H(f(a), U1(k, k))
25.79/8.47	   A^2 -> H(d, f(b))
25.79/8.47	   A^2 -> H(a, U1(b, b))
25.79/8.47	   A^2 -> H(a, f(c))
25.79/8.47	   A^2 -> H(a, f(d))
25.79/8.47	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.47	   A^2 -> H(U1(e, d), f(c))
25.79/8.47	   A^2 -> H(U1(e, d), f(d))
25.79/8.47	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.47	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.47	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.47	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.47	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.47	   A^2 -> H(U1(e, a), f(e))
25.79/8.47	   A^2 -> H(U1(e, a), f(k))
25.79/8.47	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.47	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.47	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.47	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.48	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.48	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.48	   A^2 -> H(U1(k, a), f(e))
25.79/8.48	   A^2 -> H(U1(k, a), f(k))
25.79/8.48	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.48	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.48	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.48	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.48	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.48	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.48	   A^2 -> H(U1(c, d), f(e))
25.79/8.48	   A^2 -> H(U1(c, d), f(k))
25.79/8.48	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.48	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.48	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.48	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.48	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.48	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.48	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.48	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.48	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.48	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.48	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.48	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.48	   A^2 -> H(U1(d, e), f(c))
25.79/8.48	   A^2 -> H(U1(d, e), f(d))
25.79/8.48	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.48	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.48	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.48	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.48	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.48	   A^2 -> H(U1(d, c), f(e))
25.79/8.48	   A^2 -> H(U1(d, c), f(k))
25.79/8.48	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.48	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.48	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.48	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.48	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.48	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.48	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.48	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.48	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.48	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.48	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.48	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.48	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.48	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.48	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.48	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.48	   A^2 -> H(U1(a, e), f(e))
25.79/8.48	   A^2 -> H(U1(a, e), f(k))
25.79/8.48	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.48	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.48	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.48	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.48	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.48	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.48	   A^2 -> H(U1(a, k), f(e))
25.79/8.48	   A^2 -> H(U1(a, k), f(k))
25.79/8.48	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.48	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.48	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.48	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.48	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.48	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.48	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.48	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.48	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.48	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.48	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.48	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.48	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.48	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.48	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(e, c))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, c))
25.79/8.48	   A^2 -> H(U1(a, d), U1(c, e))
25.79/8.48	   A^2 -> H(U1(a, d), U1(c, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(e, e))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, d))
25.79/8.48	   A^2 -> H(U1(a, d), U1(d, k))
25.79/8.48	   A^2 -> H(U1(a, a), b)
25.79/8.48	   A^2 -> H(U1(a, a), U1(e, d))
25.79/8.48	   A^2 -> H(U1(a, a), U1(d, e))
25.79/8.48	
25.79/8.48	The TRS R consists of the following rules:
25.79/8.48	
25.79/8.48	   f(x) -> U1(x, x)
25.79/8.48	   U1(e, x) -> x
25.79/8.48	   a -> c
25.79/8.48	   a -> d
25.79/8.48	   b -> c
25.79/8.48	   b -> d
25.79/8.48	   d -> k
25.79/8.48	   c -> e
25.79/8.48	   c -> k
25.79/8.48	
25.79/8.48	Q is empty.
25.79/8.48	We have to consider all minimal (P,Q,R)-chains.
25.79/8.48	----------------------------------------
25.79/8.48	
25.79/8.48	(339) TransformationProof (EQUIVALENT)
25.79/8.48	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.48	
25.79/8.48	   (A^2 -> H(U1(c, a), U1(e, c)),A^2 -> H(U1(c, a), U1(e, c)))
25.79/8.48	   (A^2 -> H(U1(d, a), U1(e, c)),A^2 -> H(U1(d, a), U1(e, c)))
25.79/8.48	   (A^2 -> H(U1(a, c), U1(e, c)),A^2 -> H(U1(a, c), U1(e, c)))
25.79/8.48	   (A^2 -> H(U1(a, d), U1(e, c)),A^2 -> H(U1(a, d), U1(e, c)))
25.79/8.48	   (A^2 -> H(U1(a, a), c),A^2 -> H(U1(a, a), c))
25.79/8.48	   (A^2 -> H(U1(a, a), U1(e, e)),A^2 -> H(U1(a, a), U1(e, e)))
25.79/8.48	   (A^2 -> H(U1(a, a), U1(e, k)),A^2 -> H(U1(a, a), U1(e, k)))
25.79/8.48	
25.79/8.48	
25.79/8.48	----------------------------------------
25.79/8.48	
25.79/8.48	(340)
25.79/8.48	Obligation:
25.79/8.48	Q DP problem:
25.79/8.48	The TRS P consists of the following rules:
25.79/8.48	
25.79/8.48	   H(x, x) -> G(x, x, f(k))
25.79/8.48	   G(d, x, x) -> A^2
25.79/8.48	   A^2 -> H(f(c), f(c))
25.79/8.48	   A^2 -> H(f(d), f(d))
25.79/8.48	   A^2 -> H(U1(a, a), U1(k, c))
25.79/8.48	   A^2 -> H(U1(a, a), U1(c, e))
25.79/8.48	   A^2 -> H(U1(a, a), U1(c, k))
25.79/8.48	   A^2 -> H(U1(a, a), U1(e, e))
25.79/8.48	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.48	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.48	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.48	   A^2 -> H(c, f(b))
25.79/8.48	   A^2 -> H(U1(e, k), f(b))
25.79/8.48	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.48	   A^2 -> H(U1(e, c), f(c))
25.79/8.48	   A^2 -> H(U1(e, c), f(d))
25.79/8.48	   A^2 -> H(U1(k, e), f(b))
25.79/8.48	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.48	   A^2 -> H(U1(k, c), f(c))
25.79/8.48	   A^2 -> H(U1(k, c), f(d))
25.79/8.48	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.48	   A^2 -> H(U1(c, e), f(c))
25.79/8.48	   A^2 -> H(U1(c, e), f(d))
25.79/8.48	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.48	   A^2 -> H(U1(c, k), f(c))
25.79/8.48	   A^2 -> H(U1(c, k), f(d))
25.79/8.48	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.48	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.48	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.48	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.48	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.48	   A^2 -> H(U1(c, c), f(e))
25.79/8.48	   A^2 -> H(U1(c, c), f(k))
25.79/8.48	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.48	   A^2 -> H(e, f(b))
25.79/8.48	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.48	   A^2 -> H(U1(e, e), f(c))
25.79/8.48	   A^2 -> H(U1(e, e), f(d))
25.79/8.48	   A^2 -> H(f(e), U1(c, b))
25.79/8.48	   A^2 -> H(f(e), U1(d, b))
25.79/8.48	   A^2 -> H(f(e), U1(b, c))
25.79/8.48	   A^2 -> H(f(e), U1(b, d))
25.79/8.48	   A^2 -> H(f(e), U1(c, c))
25.79/8.48	   A^2 -> H(f(e), f(e))
25.79/8.48	   A^2 -> H(f(e), f(k))
25.79/8.48	   A^2 -> H(f(e), U1(d, d))
25.79/8.48	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.48	   A^2 -> H(U1(k, k), f(c))
25.79/8.48	   A^2 -> H(U1(k, k), f(d))
25.79/8.48	   A^2 -> H(f(k), U1(c, b))
25.79/8.48	   A^2 -> H(f(k), U1(d, b))
25.79/8.48	   A^2 -> H(f(k), U1(b, c))
25.79/8.48	   A^2 -> H(f(k), U1(b, d))
25.79/8.48	   A^2 -> H(f(k), U1(c, c))
25.79/8.48	   A^2 -> H(f(k), f(e))
25.79/8.48	   A^2 -> H(f(k), f(k))
25.79/8.48	   A^2 -> H(f(k), U1(d, d))
25.79/8.48	   A^2 -> H(f(c), U1(e, b))
25.79/8.48	   A^2 -> H(f(c), U1(k, b))
25.79/8.48	   A^2 -> H(f(c), U1(c, d))
25.79/8.48	   A^2 -> H(f(c), U1(d, c))
25.79/8.48	   A^2 -> H(f(c), U1(b, e))
25.79/8.48	   A^2 -> H(f(c), U1(b, k))
25.79/8.48	   A^2 -> H(f(c), U1(k, d))
25.79/8.48	   A^2 -> H(f(c), U1(d, k))
25.79/8.48	   A^2 -> H(f(c), U1(k, k))
25.79/8.48	   A^2 -> H(U1(k, k), f(b))
25.79/8.48	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.48	   A^2 -> H(U1(k, d), f(c))
25.79/8.48	   A^2 -> H(U1(k, d), f(d))
25.79/8.48	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.48	   A^2 -> H(U1(d, k), f(c))
25.79/8.48	   A^2 -> H(U1(d, k), f(d))
25.79/8.48	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.48	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.48	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.48	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.48	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.48	   A^2 -> H(U1(d, d), f(e))
25.79/8.48	   A^2 -> H(U1(d, d), f(k))
25.79/8.48	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.48	   A^2 -> H(f(d), U1(e, b))
25.79/8.48	   A^2 -> H(f(d), U1(k, b))
25.79/8.48	   A^2 -> H(f(d), U1(c, d))
25.79/8.48	   A^2 -> H(f(d), U1(d, c))
25.79/8.48	   A^2 -> H(f(d), U1(b, e))
25.79/8.48	   A^2 -> H(f(d), U1(b, k))
25.79/8.48	   A^2 -> H(f(d), U1(e, c))
25.79/8.48	   A^2 -> H(f(d), U1(k, c))
25.79/8.48	   A^2 -> H(f(d), U1(c, e))
25.79/8.48	   A^2 -> H(f(d), U1(c, k))
25.79/8.48	   A^2 -> H(f(d), U1(e, e))
25.79/8.48	   A^2 -> H(f(d), U1(k, k))
25.79/8.48	   A^2 -> H(f(a), b)
25.79/8.48	   A^2 -> H(f(a), U1(e, d))
25.79/8.48	   A^2 -> H(f(a), U1(d, e))
25.79/8.48	   A^2 -> H(f(c), U1(e, c))
25.79/8.48	   A^2 -> H(f(c), U1(k, c))
25.79/8.48	   A^2 -> H(f(c), U1(c, e))
25.79/8.48	   A^2 -> H(f(c), U1(c, k))
25.79/8.48	   A^2 -> H(f(a), c)
25.79/8.48	   A^2 -> H(f(a), U1(e, k))
25.79/8.48	   A^2 -> H(f(a), U1(k, e))
25.79/8.48	   A^2 -> H(f(c), U1(e, e))
25.79/8.48	   A^2 -> H(f(a), e)
25.79/8.48	   A^2 -> H(f(d), U1(k, d))
25.79/8.48	   A^2 -> H(f(d), U1(d, k))
25.79/8.48	   A^2 -> H(f(a), U1(k, k))
25.79/8.48	   A^2 -> H(d, f(b))
25.79/8.48	   A^2 -> H(a, U1(b, b))
25.79/8.48	   A^2 -> H(a, f(c))
25.79/8.48	   A^2 -> H(a, f(d))
25.79/8.48	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.48	   A^2 -> H(U1(e, d), f(c))
25.79/8.48	   A^2 -> H(U1(e, d), f(d))
25.79/8.48	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.48	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.48	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.48	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.48	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.48	   A^2 -> H(U1(e, a), f(e))
25.79/8.48	   A^2 -> H(U1(e, a), f(k))
25.79/8.48	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.48	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.48	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.48	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.48	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.48	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.48	   A^2 -> H(U1(k, a), f(e))
25.79/8.48	   A^2 -> H(U1(k, a), f(k))
25.79/8.48	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.48	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.48	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.48	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.48	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.48	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.48	   A^2 -> H(U1(c, d), f(e))
25.79/8.48	   A^2 -> H(U1(c, d), f(k))
25.79/8.48	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.48	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.48	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.48	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.48	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.48	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.48	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.48	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.48	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.48	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.48	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.48	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.48	   A^2 -> H(U1(d, e), f(c))
25.79/8.48	   A^2 -> H(U1(d, e), f(d))
25.79/8.48	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.48	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.48	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.48	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.48	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.48	   A^2 -> H(U1(d, c), f(e))
25.79/8.48	   A^2 -> H(U1(d, c), f(k))
25.79/8.48	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.48	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.48	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.48	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.48	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.48	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.48	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.48	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.48	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.48	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.48	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.48	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.48	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.48	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.48	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.48	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.48	   A^2 -> H(U1(a, e), f(e))
25.79/8.48	   A^2 -> H(U1(a, e), f(k))
25.79/8.48	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.48	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.48	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.48	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.48	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.48	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.48	   A^2 -> H(U1(a, k), f(e))
25.79/8.48	   A^2 -> H(U1(a, k), f(k))
25.79/8.48	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.48	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.48	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.48	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.48	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.48	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.48	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.48	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.48	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.48	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.48	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.48	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.48	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.48	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.48	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(e, c))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, c))
25.79/8.48	   A^2 -> H(U1(a, d), U1(c, e))
25.79/8.48	   A^2 -> H(U1(a, d), U1(c, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(e, e))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, d))
25.79/8.48	   A^2 -> H(U1(a, d), U1(d, k))
25.79/8.48	   A^2 -> H(U1(a, a), b)
25.79/8.48	   A^2 -> H(U1(a, a), U1(e, d))
25.79/8.48	   A^2 -> H(U1(a, a), U1(d, e))
25.79/8.48	   A^2 -> H(U1(a, a), c)
25.79/8.48	   A^2 -> H(U1(a, a), U1(e, k))
25.79/8.48	
25.79/8.48	The TRS R consists of the following rules:
25.79/8.48	
25.79/8.48	   f(x) -> U1(x, x)
25.79/8.48	   U1(e, x) -> x
25.79/8.48	   a -> c
25.79/8.48	   a -> d
25.79/8.48	   b -> c
25.79/8.48	   b -> d
25.79/8.48	   d -> k
25.79/8.48	   c -> e
25.79/8.48	   c -> k
25.79/8.48	
25.79/8.48	Q is empty.
25.79/8.48	We have to consider all minimal (P,Q,R)-chains.
25.79/8.48	----------------------------------------
25.79/8.48	
25.79/8.48	(341) TransformationProof (EQUIVALENT)
25.79/8.48	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.48	
25.79/8.48	   (A^2 -> H(U1(c, a), U1(k, c)),A^2 -> H(U1(c, a), U1(k, c)))
25.79/8.48	   (A^2 -> H(U1(d, a), U1(k, c)),A^2 -> H(U1(d, a), U1(k, c)))
25.79/8.48	   (A^2 -> H(U1(a, c), U1(k, c)),A^2 -> H(U1(a, c), U1(k, c)))
25.79/8.48	   (A^2 -> H(U1(a, d), U1(k, c)),A^2 -> H(U1(a, d), U1(k, c)))
25.79/8.48	   (A^2 -> H(U1(a, a), U1(k, e)),A^2 -> H(U1(a, a), U1(k, e)))
25.79/8.48	   (A^2 -> H(U1(a, a), U1(k, k)),A^2 -> H(U1(a, a), U1(k, k)))
25.79/8.48	
25.79/8.48	
25.79/8.48	----------------------------------------
25.79/8.48	
25.79/8.48	(342)
25.79/8.48	Obligation:
25.79/8.48	Q DP problem:
25.79/8.48	The TRS P consists of the following rules:
25.79/8.48	
25.79/8.48	   H(x, x) -> G(x, x, f(k))
25.79/8.48	   G(d, x, x) -> A^2
25.79/8.48	   A^2 -> H(f(c), f(c))
25.79/8.48	   A^2 -> H(f(d), f(d))
25.79/8.48	   A^2 -> H(U1(a, a), U1(c, e))
25.79/8.48	   A^2 -> H(U1(a, a), U1(c, k))
25.79/8.48	   A^2 -> H(U1(a, a), U1(e, e))
25.79/8.48	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.48	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.48	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.48	   A^2 -> H(c, f(b))
25.79/8.48	   A^2 -> H(U1(e, k), f(b))
25.79/8.48	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.48	   A^2 -> H(U1(e, c), f(c))
25.79/8.48	   A^2 -> H(U1(e, c), f(d))
25.79/8.48	   A^2 -> H(U1(k, e), f(b))
25.79/8.48	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.48	   A^2 -> H(U1(k, c), f(c))
25.79/8.48	   A^2 -> H(U1(k, c), f(d))
25.79/8.48	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.48	   A^2 -> H(U1(c, e), f(c))
25.79/8.48	   A^2 -> H(U1(c, e), f(d))
25.79/8.48	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.48	   A^2 -> H(U1(c, k), f(c))
25.79/8.48	   A^2 -> H(U1(c, k), f(d))
25.79/8.48	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.48	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.48	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.48	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.48	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.48	   A^2 -> H(U1(c, c), f(e))
25.79/8.48	   A^2 -> H(U1(c, c), f(k))
25.79/8.48	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.48	   A^2 -> H(e, f(b))
25.79/8.48	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.48	   A^2 -> H(U1(e, e), f(c))
25.79/8.48	   A^2 -> H(U1(e, e), f(d))
25.79/8.48	   A^2 -> H(f(e), U1(c, b))
25.79/8.48	   A^2 -> H(f(e), U1(d, b))
25.79/8.48	   A^2 -> H(f(e), U1(b, c))
25.79/8.48	   A^2 -> H(f(e), U1(b, d))
25.79/8.48	   A^2 -> H(f(e), U1(c, c))
25.79/8.48	   A^2 -> H(f(e), f(e))
25.79/8.48	   A^2 -> H(f(e), f(k))
25.79/8.48	   A^2 -> H(f(e), U1(d, d))
25.79/8.48	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.48	   A^2 -> H(U1(k, k), f(c))
25.79/8.48	   A^2 -> H(U1(k, k), f(d))
25.79/8.48	   A^2 -> H(f(k), U1(c, b))
25.79/8.48	   A^2 -> H(f(k), U1(d, b))
25.79/8.48	   A^2 -> H(f(k), U1(b, c))
25.79/8.48	   A^2 -> H(f(k), U1(b, d))
25.79/8.48	   A^2 -> H(f(k), U1(c, c))
25.79/8.48	   A^2 -> H(f(k), f(e))
25.79/8.48	   A^2 -> H(f(k), f(k))
25.79/8.48	   A^2 -> H(f(k), U1(d, d))
25.79/8.48	   A^2 -> H(f(c), U1(e, b))
25.79/8.48	   A^2 -> H(f(c), U1(k, b))
25.79/8.48	   A^2 -> H(f(c), U1(c, d))
25.79/8.48	   A^2 -> H(f(c), U1(d, c))
25.79/8.48	   A^2 -> H(f(c), U1(b, e))
25.79/8.48	   A^2 -> H(f(c), U1(b, k))
25.79/8.48	   A^2 -> H(f(c), U1(k, d))
25.79/8.48	   A^2 -> H(f(c), U1(d, k))
25.79/8.48	   A^2 -> H(f(c), U1(k, k))
25.79/8.48	   A^2 -> H(U1(k, k), f(b))
25.79/8.48	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.48	   A^2 -> H(U1(k, d), f(c))
25.79/8.48	   A^2 -> H(U1(k, d), f(d))
25.79/8.48	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.48	   A^2 -> H(U1(d, k), f(c))
25.79/8.48	   A^2 -> H(U1(d, k), f(d))
25.79/8.48	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.48	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.48	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.48	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.48	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.48	   A^2 -> H(U1(d, d), f(e))
25.79/8.48	   A^2 -> H(U1(d, d), f(k))
25.79/8.48	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.48	   A^2 -> H(f(d), U1(e, b))
25.79/8.48	   A^2 -> H(f(d), U1(k, b))
25.79/8.48	   A^2 -> H(f(d), U1(c, d))
25.79/8.48	   A^2 -> H(f(d), U1(d, c))
25.79/8.48	   A^2 -> H(f(d), U1(b, e))
25.79/8.48	   A^2 -> H(f(d), U1(b, k))
25.79/8.48	   A^2 -> H(f(d), U1(e, c))
25.79/8.48	   A^2 -> H(f(d), U1(k, c))
25.79/8.48	   A^2 -> H(f(d), U1(c, e))
25.79/8.48	   A^2 -> H(f(d), U1(c, k))
25.79/8.48	   A^2 -> H(f(d), U1(e, e))
25.79/8.48	   A^2 -> H(f(d), U1(k, k))
25.79/8.48	   A^2 -> H(f(a), b)
25.79/8.48	   A^2 -> H(f(a), U1(e, d))
25.79/8.48	   A^2 -> H(f(a), U1(d, e))
25.79/8.48	   A^2 -> H(f(c), U1(e, c))
25.79/8.48	   A^2 -> H(f(c), U1(k, c))
25.79/8.48	   A^2 -> H(f(c), U1(c, e))
25.79/8.48	   A^2 -> H(f(c), U1(c, k))
25.79/8.48	   A^2 -> H(f(a), c)
25.79/8.48	   A^2 -> H(f(a), U1(e, k))
25.79/8.48	   A^2 -> H(f(a), U1(k, e))
25.79/8.48	   A^2 -> H(f(c), U1(e, e))
25.79/8.48	   A^2 -> H(f(a), e)
25.79/8.48	   A^2 -> H(f(d), U1(k, d))
25.79/8.48	   A^2 -> H(f(d), U1(d, k))
25.79/8.48	   A^2 -> H(f(a), U1(k, k))
25.79/8.48	   A^2 -> H(d, f(b))
25.79/8.48	   A^2 -> H(a, U1(b, b))
25.79/8.48	   A^2 -> H(a, f(c))
25.79/8.48	   A^2 -> H(a, f(d))
25.79/8.48	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.48	   A^2 -> H(U1(e, d), f(c))
25.79/8.48	   A^2 -> H(U1(e, d), f(d))
25.79/8.48	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.48	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.48	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.48	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.48	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.48	   A^2 -> H(U1(e, a), f(e))
25.79/8.48	   A^2 -> H(U1(e, a), f(k))
25.79/8.48	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.48	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.48	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.48	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.48	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.48	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.48	   A^2 -> H(U1(k, a), f(e))
25.79/8.48	   A^2 -> H(U1(k, a), f(k))
25.79/8.48	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.48	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.48	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.48	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.48	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.48	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.48	   A^2 -> H(U1(c, d), f(e))
25.79/8.48	   A^2 -> H(U1(c, d), f(k))
25.79/8.48	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.48	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.48	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.48	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.48	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.48	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.48	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.48	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.48	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.48	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.48	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.48	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.48	   A^2 -> H(U1(d, e), f(c))
25.79/8.48	   A^2 -> H(U1(d, e), f(d))
25.79/8.48	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.48	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.48	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.48	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.48	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.48	   A^2 -> H(U1(d, c), f(e))
25.79/8.48	   A^2 -> H(U1(d, c), f(k))
25.79/8.48	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.48	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.48	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.48	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.48	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.48	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.48	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.48	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.48	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.48	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.48	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.48	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.48	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.48	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.48	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.48	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.48	   A^2 -> H(U1(a, e), f(e))
25.79/8.48	   A^2 -> H(U1(a, e), f(k))
25.79/8.48	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.48	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.48	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.48	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.48	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.48	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.48	   A^2 -> H(U1(a, k), f(e))
25.79/8.48	   A^2 -> H(U1(a, k), f(k))
25.79/8.48	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.48	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.48	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.48	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.48	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.48	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.48	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.48	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.48	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.48	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.48	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.48	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.48	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.48	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.48	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(e, c))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, c))
25.79/8.48	   A^2 -> H(U1(a, d), U1(c, e))
25.79/8.48	   A^2 -> H(U1(a, d), U1(c, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(e, e))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, d))
25.79/8.48	   A^2 -> H(U1(a, d), U1(d, k))
25.79/8.48	   A^2 -> H(U1(a, a), b)
25.79/8.48	   A^2 -> H(U1(a, a), U1(e, d))
25.79/8.48	   A^2 -> H(U1(a, a), U1(d, e))
25.79/8.48	   A^2 -> H(U1(a, a), c)
25.79/8.48	   A^2 -> H(U1(a, a), U1(e, k))
25.79/8.48	   A^2 -> H(U1(a, a), U1(k, e))
25.79/8.48	
25.79/8.48	The TRS R consists of the following rules:
25.79/8.48	
25.79/8.48	   f(x) -> U1(x, x)
25.79/8.48	   U1(e, x) -> x
25.79/8.48	   a -> c
25.79/8.48	   a -> d
25.79/8.48	   b -> c
25.79/8.48	   b -> d
25.79/8.48	   d -> k
25.79/8.48	   c -> e
25.79/8.48	   c -> k
25.79/8.48	
25.79/8.48	Q is empty.
25.79/8.48	We have to consider all minimal (P,Q,R)-chains.
25.79/8.48	----------------------------------------
25.79/8.48	
25.79/8.48	(343) TransformationProof (EQUIVALENT)
25.79/8.48	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.48	
25.79/8.48	   (A^2 -> H(U1(c, a), U1(c, e)),A^2 -> H(U1(c, a), U1(c, e)))
25.79/8.48	   (A^2 -> H(U1(d, a), U1(c, e)),A^2 -> H(U1(d, a), U1(c, e)))
25.79/8.48	   (A^2 -> H(U1(a, c), U1(c, e)),A^2 -> H(U1(a, c), U1(c, e)))
25.79/8.48	   (A^2 -> H(U1(a, d), U1(c, e)),A^2 -> H(U1(a, d), U1(c, e)))
25.79/8.48	   (A^2 -> H(U1(a, a), U1(e, e)),A^2 -> H(U1(a, a), U1(e, e)))
25.79/8.48	   (A^2 -> H(U1(a, a), U1(k, e)),A^2 -> H(U1(a, a), U1(k, e)))
25.79/8.48	
25.79/8.48	
25.79/8.48	----------------------------------------
25.79/8.48	
25.79/8.48	(344)
25.79/8.48	Obligation:
25.79/8.48	Q DP problem:
25.79/8.48	The TRS P consists of the following rules:
25.79/8.48	
25.79/8.48	   H(x, x) -> G(x, x, f(k))
25.79/8.48	   G(d, x, x) -> A^2
25.79/8.48	   A^2 -> H(f(c), f(c))
25.79/8.48	   A^2 -> H(f(d), f(d))
25.79/8.48	   A^2 -> H(U1(a, a), U1(c, k))
25.79/8.48	   A^2 -> H(U1(a, a), U1(e, e))
25.79/8.48	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.48	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.48	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.48	   A^2 -> H(c, f(b))
25.79/8.48	   A^2 -> H(U1(e, k), f(b))
25.79/8.48	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.48	   A^2 -> H(U1(e, c), f(c))
25.79/8.48	   A^2 -> H(U1(e, c), f(d))
25.79/8.48	   A^2 -> H(U1(k, e), f(b))
25.79/8.48	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.48	   A^2 -> H(U1(k, c), f(c))
25.79/8.48	   A^2 -> H(U1(k, c), f(d))
25.79/8.48	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.48	   A^2 -> H(U1(c, e), f(c))
25.79/8.48	   A^2 -> H(U1(c, e), f(d))
25.79/8.48	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.48	   A^2 -> H(U1(c, k), f(c))
25.79/8.48	   A^2 -> H(U1(c, k), f(d))
25.79/8.48	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.48	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.48	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.48	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.48	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.48	   A^2 -> H(U1(c, c), f(e))
25.79/8.48	   A^2 -> H(U1(c, c), f(k))
25.79/8.48	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.48	   A^2 -> H(e, f(b))
25.79/8.48	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.48	   A^2 -> H(U1(e, e), f(c))
25.79/8.48	   A^2 -> H(U1(e, e), f(d))
25.79/8.48	   A^2 -> H(f(e), U1(c, b))
25.79/8.48	   A^2 -> H(f(e), U1(d, b))
25.79/8.48	   A^2 -> H(f(e), U1(b, c))
25.79/8.48	   A^2 -> H(f(e), U1(b, d))
25.79/8.48	   A^2 -> H(f(e), U1(c, c))
25.79/8.48	   A^2 -> H(f(e), f(e))
25.79/8.48	   A^2 -> H(f(e), f(k))
25.79/8.48	   A^2 -> H(f(e), U1(d, d))
25.79/8.48	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.48	   A^2 -> H(U1(k, k), f(c))
25.79/8.48	   A^2 -> H(U1(k, k), f(d))
25.79/8.48	   A^2 -> H(f(k), U1(c, b))
25.79/8.48	   A^2 -> H(f(k), U1(d, b))
25.79/8.48	   A^2 -> H(f(k), U1(b, c))
25.79/8.48	   A^2 -> H(f(k), U1(b, d))
25.79/8.48	   A^2 -> H(f(k), U1(c, c))
25.79/8.48	   A^2 -> H(f(k), f(e))
25.79/8.48	   A^2 -> H(f(k), f(k))
25.79/8.48	   A^2 -> H(f(k), U1(d, d))
25.79/8.48	   A^2 -> H(f(c), U1(e, b))
25.79/8.48	   A^2 -> H(f(c), U1(k, b))
25.79/8.48	   A^2 -> H(f(c), U1(c, d))
25.79/8.48	   A^2 -> H(f(c), U1(d, c))
25.79/8.48	   A^2 -> H(f(c), U1(b, e))
25.79/8.48	   A^2 -> H(f(c), U1(b, k))
25.79/8.48	   A^2 -> H(f(c), U1(k, d))
25.79/8.48	   A^2 -> H(f(c), U1(d, k))
25.79/8.48	   A^2 -> H(f(c), U1(k, k))
25.79/8.48	   A^2 -> H(U1(k, k), f(b))
25.79/8.48	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.48	   A^2 -> H(U1(k, d), f(c))
25.79/8.48	   A^2 -> H(U1(k, d), f(d))
25.79/8.48	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.48	   A^2 -> H(U1(d, k), f(c))
25.79/8.48	   A^2 -> H(U1(d, k), f(d))
25.79/8.48	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.48	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.48	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.48	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.48	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.48	   A^2 -> H(U1(d, d), f(e))
25.79/8.48	   A^2 -> H(U1(d, d), f(k))
25.79/8.48	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.48	   A^2 -> H(f(d), U1(e, b))
25.79/8.48	   A^2 -> H(f(d), U1(k, b))
25.79/8.48	   A^2 -> H(f(d), U1(c, d))
25.79/8.48	   A^2 -> H(f(d), U1(d, c))
25.79/8.48	   A^2 -> H(f(d), U1(b, e))
25.79/8.48	   A^2 -> H(f(d), U1(b, k))
25.79/8.48	   A^2 -> H(f(d), U1(e, c))
25.79/8.48	   A^2 -> H(f(d), U1(k, c))
25.79/8.48	   A^2 -> H(f(d), U1(c, e))
25.79/8.48	   A^2 -> H(f(d), U1(c, k))
25.79/8.48	   A^2 -> H(f(d), U1(e, e))
25.79/8.48	   A^2 -> H(f(d), U1(k, k))
25.79/8.48	   A^2 -> H(f(a), b)
25.79/8.48	   A^2 -> H(f(a), U1(e, d))
25.79/8.48	   A^2 -> H(f(a), U1(d, e))
25.79/8.48	   A^2 -> H(f(c), U1(e, c))
25.79/8.48	   A^2 -> H(f(c), U1(k, c))
25.79/8.48	   A^2 -> H(f(c), U1(c, e))
25.79/8.48	   A^2 -> H(f(c), U1(c, k))
25.79/8.48	   A^2 -> H(f(a), c)
25.79/8.48	   A^2 -> H(f(a), U1(e, k))
25.79/8.48	   A^2 -> H(f(a), U1(k, e))
25.79/8.48	   A^2 -> H(f(c), U1(e, e))
25.79/8.48	   A^2 -> H(f(a), e)
25.79/8.48	   A^2 -> H(f(d), U1(k, d))
25.79/8.48	   A^2 -> H(f(d), U1(d, k))
25.79/8.48	   A^2 -> H(f(a), U1(k, k))
25.79/8.48	   A^2 -> H(d, f(b))
25.79/8.48	   A^2 -> H(a, U1(b, b))
25.79/8.48	   A^2 -> H(a, f(c))
25.79/8.48	   A^2 -> H(a, f(d))
25.79/8.48	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.48	   A^2 -> H(U1(e, d), f(c))
25.79/8.48	   A^2 -> H(U1(e, d), f(d))
25.79/8.48	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.48	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.48	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.48	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.48	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.48	   A^2 -> H(U1(e, a), f(e))
25.79/8.48	   A^2 -> H(U1(e, a), f(k))
25.79/8.48	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.48	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.48	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.48	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.48	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.48	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.48	   A^2 -> H(U1(k, a), f(e))
25.79/8.48	   A^2 -> H(U1(k, a), f(k))
25.79/8.48	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.48	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.48	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.48	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.48	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.48	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.48	   A^2 -> H(U1(c, d), f(e))
25.79/8.48	   A^2 -> H(U1(c, d), f(k))
25.79/8.48	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.48	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.48	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.48	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.48	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.48	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.48	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.48	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.48	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.48	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.48	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.48	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.48	   A^2 -> H(U1(d, e), f(c))
25.79/8.48	   A^2 -> H(U1(d, e), f(d))
25.79/8.48	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.48	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.48	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.48	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.48	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.48	   A^2 -> H(U1(d, c), f(e))
25.79/8.48	   A^2 -> H(U1(d, c), f(k))
25.79/8.48	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.48	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.48	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.48	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.48	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.48	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.48	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.48	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.48	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.48	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.48	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.48	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.48	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.48	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.48	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.48	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.48	   A^2 -> H(U1(a, e), f(e))
25.79/8.48	   A^2 -> H(U1(a, e), f(k))
25.79/8.48	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.48	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.48	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.48	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.48	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.48	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.48	   A^2 -> H(U1(a, k), f(e))
25.79/8.48	   A^2 -> H(U1(a, k), f(k))
25.79/8.48	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.48	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.48	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.48	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.48	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.48	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.48	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.48	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.48	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.48	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.48	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.48	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.48	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.48	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.48	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(e, c))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, c))
25.79/8.48	   A^2 -> H(U1(a, d), U1(c, e))
25.79/8.48	   A^2 -> H(U1(a, d), U1(c, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(e, e))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, d))
25.79/8.48	   A^2 -> H(U1(a, d), U1(d, k))
25.79/8.48	   A^2 -> H(U1(a, a), b)
25.79/8.48	   A^2 -> H(U1(a, a), U1(e, d))
25.79/8.48	   A^2 -> H(U1(a, a), U1(d, e))
25.79/8.48	   A^2 -> H(U1(a, a), c)
25.79/8.48	   A^2 -> H(U1(a, a), U1(e, k))
25.79/8.48	   A^2 -> H(U1(a, a), U1(k, e))
25.79/8.48	
25.79/8.48	The TRS R consists of the following rules:
25.79/8.48	
25.79/8.48	   f(x) -> U1(x, x)
25.79/8.48	   U1(e, x) -> x
25.79/8.48	   a -> c
25.79/8.48	   a -> d
25.79/8.48	   b -> c
25.79/8.48	   b -> d
25.79/8.48	   d -> k
25.79/8.48	   c -> e
25.79/8.48	   c -> k
25.79/8.48	
25.79/8.48	Q is empty.
25.79/8.48	We have to consider all minimal (P,Q,R)-chains.
25.79/8.48	----------------------------------------
25.79/8.48	
25.79/8.48	(345) TransformationProof (EQUIVALENT)
25.79/8.48	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.48	
25.79/8.48	   (A^2 -> H(U1(c, a), U1(c, k)),A^2 -> H(U1(c, a), U1(c, k)))
25.79/8.48	   (A^2 -> H(U1(d, a), U1(c, k)),A^2 -> H(U1(d, a), U1(c, k)))
25.79/8.48	   (A^2 -> H(U1(a, c), U1(c, k)),A^2 -> H(U1(a, c), U1(c, k)))
25.79/8.48	   (A^2 -> H(U1(a, d), U1(c, k)),A^2 -> H(U1(a, d), U1(c, k)))
25.79/8.48	   (A^2 -> H(U1(a, a), U1(e, k)),A^2 -> H(U1(a, a), U1(e, k)))
25.79/8.48	   (A^2 -> H(U1(a, a), U1(k, k)),A^2 -> H(U1(a, a), U1(k, k)))
25.79/8.48	
25.79/8.48	
25.79/8.48	----------------------------------------
25.79/8.48	
25.79/8.48	(346)
25.79/8.48	Obligation:
25.79/8.48	Q DP problem:
25.79/8.48	The TRS P consists of the following rules:
25.79/8.48	
25.79/8.48	   H(x, x) -> G(x, x, f(k))
25.79/8.48	   G(d, x, x) -> A^2
25.79/8.48	   A^2 -> H(f(c), f(c))
25.79/8.48	   A^2 -> H(f(d), f(d))
25.79/8.48	   A^2 -> H(U1(a, a), U1(e, e))
25.79/8.48	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.48	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.48	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.48	   A^2 -> H(c, f(b))
25.79/8.48	   A^2 -> H(U1(e, k), f(b))
25.79/8.48	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.48	   A^2 -> H(U1(e, c), f(c))
25.79/8.48	   A^2 -> H(U1(e, c), f(d))
25.79/8.48	   A^2 -> H(U1(k, e), f(b))
25.79/8.48	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.48	   A^2 -> H(U1(k, c), f(c))
25.79/8.48	   A^2 -> H(U1(k, c), f(d))
25.79/8.48	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.48	   A^2 -> H(U1(c, e), f(c))
25.79/8.48	   A^2 -> H(U1(c, e), f(d))
25.79/8.48	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.48	   A^2 -> H(U1(c, k), f(c))
25.79/8.48	   A^2 -> H(U1(c, k), f(d))
25.79/8.48	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.48	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.48	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.48	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.48	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.48	   A^2 -> H(U1(c, c), f(e))
25.79/8.48	   A^2 -> H(U1(c, c), f(k))
25.79/8.48	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.48	   A^2 -> H(e, f(b))
25.79/8.48	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.48	   A^2 -> H(U1(e, e), f(c))
25.79/8.48	   A^2 -> H(U1(e, e), f(d))
25.79/8.48	   A^2 -> H(f(e), U1(c, b))
25.79/8.48	   A^2 -> H(f(e), U1(d, b))
25.79/8.48	   A^2 -> H(f(e), U1(b, c))
25.79/8.48	   A^2 -> H(f(e), U1(b, d))
25.79/8.48	   A^2 -> H(f(e), U1(c, c))
25.79/8.48	   A^2 -> H(f(e), f(e))
25.79/8.48	   A^2 -> H(f(e), f(k))
25.79/8.48	   A^2 -> H(f(e), U1(d, d))
25.79/8.48	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.48	   A^2 -> H(U1(k, k), f(c))
25.79/8.48	   A^2 -> H(U1(k, k), f(d))
25.79/8.48	   A^2 -> H(f(k), U1(c, b))
25.79/8.48	   A^2 -> H(f(k), U1(d, b))
25.79/8.48	   A^2 -> H(f(k), U1(b, c))
25.79/8.48	   A^2 -> H(f(k), U1(b, d))
25.79/8.48	   A^2 -> H(f(k), U1(c, c))
25.79/8.48	   A^2 -> H(f(k), f(e))
25.79/8.48	   A^2 -> H(f(k), f(k))
25.79/8.48	   A^2 -> H(f(k), U1(d, d))
25.79/8.48	   A^2 -> H(f(c), U1(e, b))
25.79/8.48	   A^2 -> H(f(c), U1(k, b))
25.79/8.48	   A^2 -> H(f(c), U1(c, d))
25.79/8.48	   A^2 -> H(f(c), U1(d, c))
25.79/8.48	   A^2 -> H(f(c), U1(b, e))
25.79/8.48	   A^2 -> H(f(c), U1(b, k))
25.79/8.48	   A^2 -> H(f(c), U1(k, d))
25.79/8.48	   A^2 -> H(f(c), U1(d, k))
25.79/8.48	   A^2 -> H(f(c), U1(k, k))
25.79/8.48	   A^2 -> H(U1(k, k), f(b))
25.79/8.48	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.48	   A^2 -> H(U1(k, d), f(c))
25.79/8.48	   A^2 -> H(U1(k, d), f(d))
25.79/8.48	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.48	   A^2 -> H(U1(d, k), f(c))
25.79/8.48	   A^2 -> H(U1(d, k), f(d))
25.79/8.48	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.48	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.48	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.48	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.48	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.48	   A^2 -> H(U1(d, d), f(e))
25.79/8.48	   A^2 -> H(U1(d, d), f(k))
25.79/8.48	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.48	   A^2 -> H(f(d), U1(e, b))
25.79/8.48	   A^2 -> H(f(d), U1(k, b))
25.79/8.48	   A^2 -> H(f(d), U1(c, d))
25.79/8.48	   A^2 -> H(f(d), U1(d, c))
25.79/8.48	   A^2 -> H(f(d), U1(b, e))
25.79/8.48	   A^2 -> H(f(d), U1(b, k))
25.79/8.48	   A^2 -> H(f(d), U1(e, c))
25.79/8.48	   A^2 -> H(f(d), U1(k, c))
25.79/8.48	   A^2 -> H(f(d), U1(c, e))
25.79/8.48	   A^2 -> H(f(d), U1(c, k))
25.79/8.48	   A^2 -> H(f(d), U1(e, e))
25.79/8.48	   A^2 -> H(f(d), U1(k, k))
25.79/8.48	   A^2 -> H(f(a), b)
25.79/8.48	   A^2 -> H(f(a), U1(e, d))
25.79/8.48	   A^2 -> H(f(a), U1(d, e))
25.79/8.48	   A^2 -> H(f(c), U1(e, c))
25.79/8.48	   A^2 -> H(f(c), U1(k, c))
25.79/8.48	   A^2 -> H(f(c), U1(c, e))
25.79/8.48	   A^2 -> H(f(c), U1(c, k))
25.79/8.48	   A^2 -> H(f(a), c)
25.79/8.48	   A^2 -> H(f(a), U1(e, k))
25.79/8.48	   A^2 -> H(f(a), U1(k, e))
25.79/8.48	   A^2 -> H(f(c), U1(e, e))
25.79/8.48	   A^2 -> H(f(a), e)
25.79/8.48	   A^2 -> H(f(d), U1(k, d))
25.79/8.48	   A^2 -> H(f(d), U1(d, k))
25.79/8.48	   A^2 -> H(f(a), U1(k, k))
25.79/8.48	   A^2 -> H(d, f(b))
25.79/8.48	   A^2 -> H(a, U1(b, b))
25.79/8.48	   A^2 -> H(a, f(c))
25.79/8.48	   A^2 -> H(a, f(d))
25.79/8.48	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.48	   A^2 -> H(U1(e, d), f(c))
25.79/8.48	   A^2 -> H(U1(e, d), f(d))
25.79/8.48	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.48	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.48	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.48	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.48	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.48	   A^2 -> H(U1(e, a), f(e))
25.79/8.48	   A^2 -> H(U1(e, a), f(k))
25.79/8.48	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.48	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.48	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.48	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.48	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.48	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.48	   A^2 -> H(U1(k, a), f(e))
25.79/8.48	   A^2 -> H(U1(k, a), f(k))
25.79/8.48	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.48	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.48	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.48	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.48	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.48	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.48	   A^2 -> H(U1(c, d), f(e))
25.79/8.48	   A^2 -> H(U1(c, d), f(k))
25.79/8.48	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.48	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.48	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.48	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.48	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.48	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.48	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.48	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.48	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.48	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.48	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.48	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.48	   A^2 -> H(U1(d, e), f(c))
25.79/8.48	   A^2 -> H(U1(d, e), f(d))
25.79/8.48	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.48	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.48	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.48	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.48	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.48	   A^2 -> H(U1(d, c), f(e))
25.79/8.48	   A^2 -> H(U1(d, c), f(k))
25.79/8.48	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.48	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.48	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.48	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.48	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.48	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.48	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.48	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.48	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.48	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.48	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.48	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.48	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.48	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.48	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.48	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.48	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.48	   A^2 -> H(U1(a, e), f(e))
25.79/8.48	   A^2 -> H(U1(a, e), f(k))
25.79/8.48	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.48	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.48	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.48	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.48	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.48	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.48	   A^2 -> H(U1(a, k), f(e))
25.79/8.48	   A^2 -> H(U1(a, k), f(k))
25.79/8.48	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.48	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.48	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.48	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.48	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.48	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.48	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.48	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.48	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.48	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.48	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.48	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.48	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.48	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.48	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.48	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(e, c))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, c))
25.79/8.48	   A^2 -> H(U1(a, d), U1(c, e))
25.79/8.48	   A^2 -> H(U1(a, d), U1(c, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(e, e))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, k))
25.79/8.48	   A^2 -> H(U1(a, d), U1(k, d))
25.79/8.48	   A^2 -> H(U1(a, d), U1(d, k))
25.79/8.48	   A^2 -> H(U1(a, a), b)
25.79/8.48	   A^2 -> H(U1(a, a), U1(e, d))
25.79/8.48	   A^2 -> H(U1(a, a), U1(d, e))
25.79/8.48	   A^2 -> H(U1(a, a), c)
25.79/8.48	   A^2 -> H(U1(a, a), U1(e, k))
25.79/8.48	   A^2 -> H(U1(a, a), U1(k, e))
25.79/8.48	
25.79/8.48	The TRS R consists of the following rules:
25.79/8.48	
25.79/8.48	   f(x) -> U1(x, x)
25.79/8.48	   U1(e, x) -> x
25.79/8.48	   a -> c
25.79/8.48	   a -> d
25.79/8.48	   b -> c
25.79/8.48	   b -> d
25.79/8.48	   d -> k
25.79/8.48	   c -> e
25.79/8.48	   c -> k
25.79/8.48	
25.79/8.48	Q is empty.
25.79/8.48	We have to consider all minimal (P,Q,R)-chains.
25.79/8.48	----------------------------------------
25.79/8.48	
25.79/8.48	(347) TransformationProof (EQUIVALENT)
25.79/8.48	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.48	
25.79/8.48	   (A^2 -> H(U1(c, a), U1(e, e)),A^2 -> H(U1(c, a), U1(e, e)))
25.79/8.48	   (A^2 -> H(U1(d, a), U1(e, e)),A^2 -> H(U1(d, a), U1(e, e)))
25.79/8.48	   (A^2 -> H(U1(a, c), U1(e, e)),A^2 -> H(U1(a, c), U1(e, e)))
25.79/8.48	   (A^2 -> H(U1(a, d), U1(e, e)),A^2 -> H(U1(a, d), U1(e, e)))
25.79/8.48	   (A^2 -> H(U1(a, a), e),A^2 -> H(U1(a, a), e))
25.79/8.48	
25.79/8.48	
25.79/8.48	----------------------------------------
25.79/8.48	
25.79/8.48	(348)
25.79/8.48	Obligation:
25.79/8.48	Q DP problem:
25.79/8.48	The TRS P consists of the following rules:
25.79/8.48	
25.79/8.48	   H(x, x) -> G(x, x, f(k))
25.79/8.48	   G(d, x, x) -> A^2
25.79/8.48	   A^2 -> H(f(c), f(c))
25.79/8.48	   A^2 -> H(f(d), f(d))
25.79/8.48	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.48	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.48	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.48	   A^2 -> H(c, f(b))
25.79/8.48	   A^2 -> H(U1(e, k), f(b))
25.79/8.48	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.48	   A^2 -> H(U1(e, c), f(c))
25.79/8.48	   A^2 -> H(U1(e, c), f(d))
25.79/8.48	   A^2 -> H(U1(k, e), f(b))
25.79/8.48	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.48	   A^2 -> H(U1(k, c), f(c))
25.79/8.48	   A^2 -> H(U1(k, c), f(d))
25.79/8.48	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.48	   A^2 -> H(U1(c, e), f(c))
25.79/8.48	   A^2 -> H(U1(c, e), f(d))
25.79/8.48	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.48	   A^2 -> H(U1(c, k), f(c))
25.79/8.48	   A^2 -> H(U1(c, k), f(d))
25.79/8.48	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.48	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.48	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.48	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.48	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.48	   A^2 -> H(U1(c, c), f(e))
25.79/8.48	   A^2 -> H(U1(c, c), f(k))
25.79/8.48	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.48	   A^2 -> H(e, f(b))
25.79/8.48	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.48	   A^2 -> H(U1(e, e), f(c))
25.79/8.48	   A^2 -> H(U1(e, e), f(d))
25.79/8.48	   A^2 -> H(f(e), U1(c, b))
25.79/8.48	   A^2 -> H(f(e), U1(d, b))
25.79/8.48	   A^2 -> H(f(e), U1(b, c))
25.79/8.48	   A^2 -> H(f(e), U1(b, d))
25.79/8.48	   A^2 -> H(f(e), U1(c, c))
25.79/8.48	   A^2 -> H(f(e), f(e))
25.79/8.48	   A^2 -> H(f(e), f(k))
25.79/8.48	   A^2 -> H(f(e), U1(d, d))
25.79/8.48	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.48	   A^2 -> H(U1(k, k), f(c))
25.79/8.48	   A^2 -> H(U1(k, k), f(d))
25.79/8.48	   A^2 -> H(f(k), U1(c, b))
25.79/8.48	   A^2 -> H(f(k), U1(d, b))
25.79/8.48	   A^2 -> H(f(k), U1(b, c))
25.79/8.48	   A^2 -> H(f(k), U1(b, d))
25.79/8.48	   A^2 -> H(f(k), U1(c, c))
25.79/8.48	   A^2 -> H(f(k), f(e))
25.79/8.48	   A^2 -> H(f(k), f(k))
25.79/8.48	   A^2 -> H(f(k), U1(d, d))
25.79/8.48	   A^2 -> H(f(c), U1(e, b))
25.79/8.48	   A^2 -> H(f(c), U1(k, b))
25.79/8.48	   A^2 -> H(f(c), U1(c, d))
25.79/8.48	   A^2 -> H(f(c), U1(d, c))
25.79/8.48	   A^2 -> H(f(c), U1(b, e))
25.79/8.48	   A^2 -> H(f(c), U1(b, k))
25.79/8.48	   A^2 -> H(f(c), U1(k, d))
25.79/8.48	   A^2 -> H(f(c), U1(d, k))
25.79/8.48	   A^2 -> H(f(c), U1(k, k))
25.79/8.48	   A^2 -> H(U1(k, k), f(b))
25.79/8.48	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.48	   A^2 -> H(U1(k, d), f(c))
25.79/8.48	   A^2 -> H(U1(k, d), f(d))
25.79/8.48	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.48	   A^2 -> H(U1(d, k), f(c))
25.79/8.48	   A^2 -> H(U1(d, k), f(d))
25.79/8.48	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.48	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.48	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.48	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.48	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.48	   A^2 -> H(U1(d, d), f(e))
25.79/8.48	   A^2 -> H(U1(d, d), f(k))
25.79/8.48	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.48	   A^2 -> H(f(d), U1(e, b))
25.79/8.48	   A^2 -> H(f(d), U1(k, b))
25.79/8.48	   A^2 -> H(f(d), U1(c, d))
25.79/8.48	   A^2 -> H(f(d), U1(d, c))
25.79/8.48	   A^2 -> H(f(d), U1(b, e))
25.79/8.48	   A^2 -> H(f(d), U1(b, k))
25.79/8.48	   A^2 -> H(f(d), U1(e, c))
25.79/8.48	   A^2 -> H(f(d), U1(k, c))
25.79/8.48	   A^2 -> H(f(d), U1(c, e))
25.79/8.48	   A^2 -> H(f(d), U1(c, k))
25.79/8.48	   A^2 -> H(f(d), U1(e, e))
25.79/8.48	   A^2 -> H(f(d), U1(k, k))
25.79/8.48	   A^2 -> H(f(a), b)
25.79/8.48	   A^2 -> H(f(a), U1(e, d))
25.79/8.48	   A^2 -> H(f(a), U1(d, e))
25.79/8.48	   A^2 -> H(f(c), U1(e, c))
25.79/8.48	   A^2 -> H(f(c), U1(k, c))
25.79/8.48	   A^2 -> H(f(c), U1(c, e))
25.79/8.48	   A^2 -> H(f(c), U1(c, k))
25.79/8.48	   A^2 -> H(f(a), c)
25.79/8.48	   A^2 -> H(f(a), U1(e, k))
25.79/8.48	   A^2 -> H(f(a), U1(k, e))
25.79/8.48	   A^2 -> H(f(c), U1(e, e))
25.79/8.48	   A^2 -> H(f(a), e)
25.79/8.48	   A^2 -> H(f(d), U1(k, d))
25.79/8.48	   A^2 -> H(f(d), U1(d, k))
25.79/8.48	   A^2 -> H(f(a), U1(k, k))
25.79/8.48	   A^2 -> H(d, f(b))
25.79/8.48	   A^2 -> H(a, U1(b, b))
25.79/8.48	   A^2 -> H(a, f(c))
25.79/8.48	   A^2 -> H(a, f(d))
25.79/8.48	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.48	   A^2 -> H(U1(e, d), f(c))
25.79/8.48	   A^2 -> H(U1(e, d), f(d))
25.79/8.48	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.48	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.48	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.48	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.48	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.48	   A^2 -> H(U1(e, a), f(e))
25.79/8.48	   A^2 -> H(U1(e, a), f(k))
25.79/8.48	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.48	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.48	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.48	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.48	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.48	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.48	   A^2 -> H(U1(k, a), f(e))
25.79/8.48	   A^2 -> H(U1(k, a), f(k))
25.79/8.48	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.48	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.48	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.48	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.48	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.48	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.48	   A^2 -> H(U1(c, d), f(e))
25.79/8.48	   A^2 -> H(U1(c, d), f(k))
25.79/8.48	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.48	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.48	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.48	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.48	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.48	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.48	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.48	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.48	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.48	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.48	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.48	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.48	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.49	   A^2 -> H(U1(d, e), f(c))
25.79/8.49	   A^2 -> H(U1(d, e), f(d))
25.79/8.49	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.49	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.49	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.49	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.49	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.49	   A^2 -> H(U1(d, c), f(e))
25.79/8.49	   A^2 -> H(U1(d, c), f(k))
25.79/8.49	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.49	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.49	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.49	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.49	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.49	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.49	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.49	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.49	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.49	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.49	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.49	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.49	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.49	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.49	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.49	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.49	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.49	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.49	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.49	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.49	   A^2 -> H(U1(a, e), f(e))
25.79/8.49	   A^2 -> H(U1(a, e), f(k))
25.79/8.49	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.49	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.49	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.49	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.49	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.49	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.49	   A^2 -> H(U1(a, k), f(e))
25.79/8.49	   A^2 -> H(U1(a, k), f(k))
25.79/8.49	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.49	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.49	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.49	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.49	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.49	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.49	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.49	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.49	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.49	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.49	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.49	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.49	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.49	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.49	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.49	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.49	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.49	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.49	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.49	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.49	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.49	   A^2 -> H(U1(a, d), U1(e, c))
25.79/8.49	   A^2 -> H(U1(a, d), U1(k, c))
25.79/8.49	   A^2 -> H(U1(a, d), U1(c, e))
25.79/8.49	   A^2 -> H(U1(a, d), U1(c, k))
25.79/8.49	   A^2 -> H(U1(a, d), U1(e, e))
25.79/8.49	   A^2 -> H(U1(a, d), U1(k, k))
25.79/8.49	   A^2 -> H(U1(a, d), U1(k, d))
25.79/8.49	   A^2 -> H(U1(a, d), U1(d, k))
25.79/8.49	   A^2 -> H(U1(a, a), b)
25.79/8.49	   A^2 -> H(U1(a, a), U1(e, d))
25.79/8.49	   A^2 -> H(U1(a, a), U1(d, e))
25.79/8.49	   A^2 -> H(U1(a, a), c)
25.79/8.49	   A^2 -> H(U1(a, a), U1(e, k))
25.79/8.49	   A^2 -> H(U1(a, a), U1(k, e))
25.79/8.49	   A^2 -> H(U1(a, a), e)
25.79/8.49	
25.79/8.49	The TRS R consists of the following rules:
25.79/8.49	
25.79/8.49	   f(x) -> U1(x, x)
25.79/8.49	   U1(e, x) -> x
25.79/8.49	   a -> c
25.79/8.49	   a -> d
25.79/8.49	   b -> c
25.79/8.49	   b -> d
25.79/8.49	   d -> k
25.79/8.49	   c -> e
25.79/8.49	   c -> k
25.79/8.49	
25.79/8.49	Q is empty.
25.79/8.49	We have to consider all minimal (P,Q,R)-chains.
25.79/8.49	----------------------------------------
25.79/8.49	
25.79/8.49	(349) TransformationProof (EQUIVALENT)
25.79/8.49	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.49	
25.79/8.49	   (A^2 -> H(U1(c, a), U1(k, k)),A^2 -> H(U1(c, a), U1(k, k)))
25.79/8.49	   (A^2 -> H(U1(d, a), U1(k, k)),A^2 -> H(U1(d, a), U1(k, k)))
25.79/8.49	   (A^2 -> H(U1(a, c), U1(k, k)),A^2 -> H(U1(a, c), U1(k, k)))
25.79/8.49	   (A^2 -> H(U1(a, d), U1(k, k)),A^2 -> H(U1(a, d), U1(k, k)))
25.79/8.49	
25.79/8.49	
25.79/8.49	----------------------------------------
25.79/8.49	
25.79/8.49	(350)
25.79/8.49	Obligation:
25.79/8.49	Q DP problem:
25.79/8.49	The TRS P consists of the following rules:
25.79/8.49	
25.79/8.49	   H(x, x) -> G(x, x, f(k))
25.79/8.49	   G(d, x, x) -> A^2
25.79/8.49	   A^2 -> H(f(c), f(c))
25.79/8.49	   A^2 -> H(f(d), f(d))
25.79/8.49	   A^2 -> H(U1(a, a), U1(k, d))
25.79/8.49	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.49	   A^2 -> H(c, f(b))
25.79/8.49	   A^2 -> H(U1(e, k), f(b))
25.79/8.49	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.49	   A^2 -> H(U1(e, c), f(c))
25.79/8.49	   A^2 -> H(U1(e, c), f(d))
25.79/8.49	   A^2 -> H(U1(k, e), f(b))
25.79/8.49	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.49	   A^2 -> H(U1(k, c), f(c))
25.79/8.49	   A^2 -> H(U1(k, c), f(d))
25.79/8.49	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.49	   A^2 -> H(U1(c, e), f(c))
25.79/8.49	   A^2 -> H(U1(c, e), f(d))
25.79/8.49	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.49	   A^2 -> H(U1(c, k), f(c))
25.79/8.49	   A^2 -> H(U1(c, k), f(d))
25.79/8.49	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.49	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.49	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.49	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.49	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.49	   A^2 -> H(U1(c, c), f(e))
25.79/8.49	   A^2 -> H(U1(c, c), f(k))
25.79/8.49	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.49	   A^2 -> H(e, f(b))
25.79/8.49	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.49	   A^2 -> H(U1(e, e), f(c))
25.79/8.49	   A^2 -> H(U1(e, e), f(d))
25.79/8.49	   A^2 -> H(f(e), U1(c, b))
25.79/8.49	   A^2 -> H(f(e), U1(d, b))
25.79/8.49	   A^2 -> H(f(e), U1(b, c))
25.79/8.49	   A^2 -> H(f(e), U1(b, d))
25.79/8.49	   A^2 -> H(f(e), U1(c, c))
25.79/8.49	   A^2 -> H(f(e), f(e))
25.79/8.49	   A^2 -> H(f(e), f(k))
25.79/8.49	   A^2 -> H(f(e), U1(d, d))
25.79/8.49	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.49	   A^2 -> H(U1(k, k), f(c))
25.79/8.49	   A^2 -> H(U1(k, k), f(d))
25.79/8.49	   A^2 -> H(f(k), U1(c, b))
25.79/8.49	   A^2 -> H(f(k), U1(d, b))
25.79/8.49	   A^2 -> H(f(k), U1(b, c))
25.79/8.49	   A^2 -> H(f(k), U1(b, d))
25.79/8.49	   A^2 -> H(f(k), U1(c, c))
25.79/8.49	   A^2 -> H(f(k), f(e))
25.79/8.49	   A^2 -> H(f(k), f(k))
25.79/8.49	   A^2 -> H(f(k), U1(d, d))
25.79/8.49	   A^2 -> H(f(c), U1(e, b))
25.79/8.49	   A^2 -> H(f(c), U1(k, b))
25.79/8.49	   A^2 -> H(f(c), U1(c, d))
25.79/8.49	   A^2 -> H(f(c), U1(d, c))
25.79/8.49	   A^2 -> H(f(c), U1(b, e))
25.79/8.49	   A^2 -> H(f(c), U1(b, k))
25.79/8.49	   A^2 -> H(f(c), U1(k, d))
25.79/8.49	   A^2 -> H(f(c), U1(d, k))
25.79/8.49	   A^2 -> H(f(c), U1(k, k))
25.79/8.49	   A^2 -> H(U1(k, k), f(b))
25.79/8.49	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.49	   A^2 -> H(U1(k, d), f(c))
25.79/8.49	   A^2 -> H(U1(k, d), f(d))
25.79/8.49	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.49	   A^2 -> H(U1(d, k), f(c))
25.79/8.49	   A^2 -> H(U1(d, k), f(d))
25.79/8.49	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.49	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.49	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.49	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.49	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.49	   A^2 -> H(U1(d, d), f(e))
25.79/8.49	   A^2 -> H(U1(d, d), f(k))
25.79/8.49	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.49	   A^2 -> H(f(d), U1(e, b))
25.79/8.49	   A^2 -> H(f(d), U1(k, b))
25.79/8.49	   A^2 -> H(f(d), U1(c, d))
25.79/8.49	   A^2 -> H(f(d), U1(d, c))
25.79/8.49	   A^2 -> H(f(d), U1(b, e))
25.79/8.49	   A^2 -> H(f(d), U1(b, k))
25.79/8.49	   A^2 -> H(f(d), U1(e, c))
25.79/8.49	   A^2 -> H(f(d), U1(k, c))
25.79/8.49	   A^2 -> H(f(d), U1(c, e))
25.79/8.49	   A^2 -> H(f(d), U1(c, k))
25.79/8.49	   A^2 -> H(f(d), U1(e, e))
25.79/8.49	   A^2 -> H(f(d), U1(k, k))
25.79/8.49	   A^2 -> H(f(a), b)
25.79/8.49	   A^2 -> H(f(a), U1(e, d))
25.79/8.49	   A^2 -> H(f(a), U1(d, e))
25.79/8.49	   A^2 -> H(f(c), U1(e, c))
25.79/8.49	   A^2 -> H(f(c), U1(k, c))
25.79/8.49	   A^2 -> H(f(c), U1(c, e))
25.79/8.49	   A^2 -> H(f(c), U1(c, k))
25.79/8.49	   A^2 -> H(f(a), c)
25.79/8.49	   A^2 -> H(f(a), U1(e, k))
25.79/8.49	   A^2 -> H(f(a), U1(k, e))
25.79/8.49	   A^2 -> H(f(c), U1(e, e))
25.79/8.49	   A^2 -> H(f(a), e)
25.79/8.49	   A^2 -> H(f(d), U1(k, d))
25.79/8.49	   A^2 -> H(f(d), U1(d, k))
25.79/8.49	   A^2 -> H(f(a), U1(k, k))
25.79/8.49	   A^2 -> H(d, f(b))
25.79/8.49	   A^2 -> H(a, U1(b, b))
25.79/8.49	   A^2 -> H(a, f(c))
25.79/8.49	   A^2 -> H(a, f(d))
25.79/8.49	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.49	   A^2 -> H(U1(e, d), f(c))
25.79/8.49	   A^2 -> H(U1(e, d), f(d))
25.79/8.49	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.49	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.49	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.49	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.49	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.49	   A^2 -> H(U1(e, a), f(e))
25.79/8.49	   A^2 -> H(U1(e, a), f(k))
25.79/8.49	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.49	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.49	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.49	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.49	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.49	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.49	   A^2 -> H(U1(k, a), f(e))
25.79/8.49	   A^2 -> H(U1(k, a), f(k))
25.79/8.49	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.49	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.49	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.49	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.49	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.49	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.49	   A^2 -> H(U1(c, d), f(e))
25.79/8.49	   A^2 -> H(U1(c, d), f(k))
25.79/8.49	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.49	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.49	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.49	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.49	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.49	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.49	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.49	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.49	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.49	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.49	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.49	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.49	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.49	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.49	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.49	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.49	   A^2 -> H(U1(d, e), f(c))
25.79/8.49	   A^2 -> H(U1(d, e), f(d))
25.79/8.49	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.49	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.49	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.49	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.49	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.49	   A^2 -> H(U1(d, c), f(e))
25.79/8.49	   A^2 -> H(U1(d, c), f(k))
25.79/8.49	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.49	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.49	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.49	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.49	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.49	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.49	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.49	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.49	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.49	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.49	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.49	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.49	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.49	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.49	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.49	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.49	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.49	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.49	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.49	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.49	   A^2 -> H(U1(a, e), f(e))
25.79/8.49	   A^2 -> H(U1(a, e), f(k))
25.79/8.49	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.49	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.49	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.49	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.49	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.49	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.49	   A^2 -> H(U1(a, k), f(e))
25.79/8.49	   A^2 -> H(U1(a, k), f(k))
25.79/8.49	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.49	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.49	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.49	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.49	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.49	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.49	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.49	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.49	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.49	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.49	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.49	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.49	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.49	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.49	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.49	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.49	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.49	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.49	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.49	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.49	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.49	   A^2 -> H(U1(a, d), U1(e, c))
25.79/8.49	   A^2 -> H(U1(a, d), U1(k, c))
25.79/8.49	   A^2 -> H(U1(a, d), U1(c, e))
25.79/8.49	   A^2 -> H(U1(a, d), U1(c, k))
25.79/8.49	   A^2 -> H(U1(a, d), U1(e, e))
25.79/8.49	   A^2 -> H(U1(a, d), U1(k, k))
25.79/8.49	   A^2 -> H(U1(a, d), U1(k, d))
25.79/8.49	   A^2 -> H(U1(a, d), U1(d, k))
25.79/8.49	   A^2 -> H(U1(a, a), b)
25.79/8.49	   A^2 -> H(U1(a, a), U1(e, d))
25.79/8.49	   A^2 -> H(U1(a, a), U1(d, e))
25.79/8.49	   A^2 -> H(U1(a, a), c)
25.79/8.49	   A^2 -> H(U1(a, a), U1(e, k))
25.79/8.49	   A^2 -> H(U1(a, a), U1(k, e))
25.79/8.49	   A^2 -> H(U1(a, a), e)
25.79/8.49	
25.79/8.49	The TRS R consists of the following rules:
25.79/8.49	
25.79/8.49	   f(x) -> U1(x, x)
25.79/8.49	   U1(e, x) -> x
25.79/8.49	   a -> c
25.79/8.49	   a -> d
25.79/8.49	   b -> c
25.79/8.49	   b -> d
25.79/8.49	   d -> k
25.79/8.49	   c -> e
25.79/8.49	   c -> k
25.79/8.49	
25.79/8.49	Q is empty.
25.79/8.49	We have to consider all minimal (P,Q,R)-chains.
25.79/8.49	----------------------------------------
25.79/8.49	
25.79/8.49	(351) TransformationProof (EQUIVALENT)
25.79/8.49	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.49	
25.79/8.49	   (A^2 -> H(U1(c, a), U1(k, d)),A^2 -> H(U1(c, a), U1(k, d)))
25.79/8.49	   (A^2 -> H(U1(d, a), U1(k, d)),A^2 -> H(U1(d, a), U1(k, d)))
25.79/8.49	   (A^2 -> H(U1(a, c), U1(k, d)),A^2 -> H(U1(a, c), U1(k, d)))
25.79/8.49	   (A^2 -> H(U1(a, d), U1(k, d)),A^2 -> H(U1(a, d), U1(k, d)))
25.79/8.49	   (A^2 -> H(U1(a, a), U1(k, k)),A^2 -> H(U1(a, a), U1(k, k)))
25.79/8.49	
25.79/8.49	
25.79/8.49	----------------------------------------
25.79/8.49	
25.79/8.49	(352)
25.79/8.49	Obligation:
25.79/8.49	Q DP problem:
25.79/8.49	The TRS P consists of the following rules:
25.79/8.49	
25.79/8.49	   H(x, x) -> G(x, x, f(k))
25.79/8.49	   G(d, x, x) -> A^2
25.79/8.49	   A^2 -> H(f(c), f(c))
25.79/8.49	   A^2 -> H(f(d), f(d))
25.79/8.49	   A^2 -> H(U1(a, a), U1(d, k))
25.79/8.49	   A^2 -> H(c, f(b))
25.79/8.49	   A^2 -> H(U1(e, k), f(b))
25.79/8.49	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.49	   A^2 -> H(U1(e, c), f(c))
25.79/8.49	   A^2 -> H(U1(e, c), f(d))
25.79/8.49	   A^2 -> H(U1(k, e), f(b))
25.79/8.49	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.49	   A^2 -> H(U1(k, c), f(c))
25.79/8.49	   A^2 -> H(U1(k, c), f(d))
25.79/8.49	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.49	   A^2 -> H(U1(c, e), f(c))
25.79/8.49	   A^2 -> H(U1(c, e), f(d))
25.79/8.49	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.49	   A^2 -> H(U1(c, k), f(c))
25.79/8.49	   A^2 -> H(U1(c, k), f(d))
25.79/8.49	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.49	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.49	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.49	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.49	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.49	   A^2 -> H(U1(c, c), f(e))
25.79/8.49	   A^2 -> H(U1(c, c), f(k))
25.79/8.49	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.49	   A^2 -> H(e, f(b))
25.79/8.49	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.49	   A^2 -> H(U1(e, e), f(c))
25.79/8.49	   A^2 -> H(U1(e, e), f(d))
25.79/8.49	   A^2 -> H(f(e), U1(c, b))
25.79/8.49	   A^2 -> H(f(e), U1(d, b))
25.79/8.49	   A^2 -> H(f(e), U1(b, c))
25.79/8.49	   A^2 -> H(f(e), U1(b, d))
25.79/8.49	   A^2 -> H(f(e), U1(c, c))
25.79/8.49	   A^2 -> H(f(e), f(e))
25.79/8.49	   A^2 -> H(f(e), f(k))
25.79/8.49	   A^2 -> H(f(e), U1(d, d))
25.79/8.49	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.49	   A^2 -> H(U1(k, k), f(c))
25.79/8.49	   A^2 -> H(U1(k, k), f(d))
25.79/8.49	   A^2 -> H(f(k), U1(c, b))
25.79/8.49	   A^2 -> H(f(k), U1(d, b))
25.79/8.49	   A^2 -> H(f(k), U1(b, c))
25.79/8.49	   A^2 -> H(f(k), U1(b, d))
25.79/8.49	   A^2 -> H(f(k), U1(c, c))
25.79/8.49	   A^2 -> H(f(k), f(e))
25.79/8.49	   A^2 -> H(f(k), f(k))
25.79/8.49	   A^2 -> H(f(k), U1(d, d))
25.79/8.49	   A^2 -> H(f(c), U1(e, b))
25.79/8.49	   A^2 -> H(f(c), U1(k, b))
25.79/8.49	   A^2 -> H(f(c), U1(c, d))
25.79/8.49	   A^2 -> H(f(c), U1(d, c))
25.79/8.49	   A^2 -> H(f(c), U1(b, e))
25.79/8.49	   A^2 -> H(f(c), U1(b, k))
25.79/8.49	   A^2 -> H(f(c), U1(k, d))
25.79/8.49	   A^2 -> H(f(c), U1(d, k))
25.79/8.49	   A^2 -> H(f(c), U1(k, k))
25.79/8.49	   A^2 -> H(U1(k, k), f(b))
25.79/8.49	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.49	   A^2 -> H(U1(k, d), f(c))
25.79/8.49	   A^2 -> H(U1(k, d), f(d))
25.79/8.49	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.49	   A^2 -> H(U1(d, k), f(c))
25.79/8.49	   A^2 -> H(U1(d, k), f(d))
25.79/8.49	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.49	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.49	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.49	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.49	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.49	   A^2 -> H(U1(d, d), f(e))
25.79/8.49	   A^2 -> H(U1(d, d), f(k))
25.79/8.49	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.49	   A^2 -> H(f(d), U1(e, b))
25.79/8.49	   A^2 -> H(f(d), U1(k, b))
25.79/8.49	   A^2 -> H(f(d), U1(c, d))
25.79/8.49	   A^2 -> H(f(d), U1(d, c))
25.79/8.49	   A^2 -> H(f(d), U1(b, e))
25.79/8.49	   A^2 -> H(f(d), U1(b, k))
25.79/8.49	   A^2 -> H(f(d), U1(e, c))
25.79/8.49	   A^2 -> H(f(d), U1(k, c))
25.79/8.49	   A^2 -> H(f(d), U1(c, e))
25.79/8.49	   A^2 -> H(f(d), U1(c, k))
25.79/8.49	   A^2 -> H(f(d), U1(e, e))
25.79/8.49	   A^2 -> H(f(d), U1(k, k))
25.79/8.49	   A^2 -> H(f(a), b)
25.79/8.49	   A^2 -> H(f(a), U1(e, d))
25.79/8.49	   A^2 -> H(f(a), U1(d, e))
25.79/8.49	   A^2 -> H(f(c), U1(e, c))
25.79/8.49	   A^2 -> H(f(c), U1(k, c))
25.79/8.49	   A^2 -> H(f(c), U1(c, e))
25.79/8.49	   A^2 -> H(f(c), U1(c, k))
25.79/8.49	   A^2 -> H(f(a), c)
25.79/8.49	   A^2 -> H(f(a), U1(e, k))
25.79/8.49	   A^2 -> H(f(a), U1(k, e))
25.79/8.49	   A^2 -> H(f(c), U1(e, e))
25.79/8.49	   A^2 -> H(f(a), e)
25.79/8.49	   A^2 -> H(f(d), U1(k, d))
25.79/8.49	   A^2 -> H(f(d), U1(d, k))
25.79/8.49	   A^2 -> H(f(a), U1(k, k))
25.79/8.49	   A^2 -> H(d, f(b))
25.79/8.49	   A^2 -> H(a, U1(b, b))
25.79/8.49	   A^2 -> H(a, f(c))
25.79/8.49	   A^2 -> H(a, f(d))
25.79/8.49	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.49	   A^2 -> H(U1(e, d), f(c))
25.79/8.49	   A^2 -> H(U1(e, d), f(d))
25.79/8.49	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.49	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.49	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.49	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.49	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.49	   A^2 -> H(U1(e, a), f(e))
25.79/8.49	   A^2 -> H(U1(e, a), f(k))
25.79/8.49	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.49	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.49	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.49	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.49	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.49	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.49	   A^2 -> H(U1(k, a), f(e))
25.79/8.49	   A^2 -> H(U1(k, a), f(k))
25.79/8.49	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.49	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.49	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.49	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.49	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.49	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.49	   A^2 -> H(U1(c, d), f(e))
25.79/8.49	   A^2 -> H(U1(c, d), f(k))
25.79/8.49	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.49	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.49	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.49	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.49	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.49	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.49	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.49	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.49	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.49	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.49	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.49	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.49	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.49	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.49	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.49	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.49	   A^2 -> H(U1(d, e), f(c))
25.79/8.49	   A^2 -> H(U1(d, e), f(d))
25.79/8.49	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.49	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.49	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.49	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.49	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.49	   A^2 -> H(U1(d, c), f(e))
25.79/8.49	   A^2 -> H(U1(d, c), f(k))
25.79/8.49	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.49	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.49	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.49	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.49	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.49	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.49	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.49	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.49	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.49	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.49	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.49	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.49	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.49	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.49	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.49	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.49	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.49	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.49	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.49	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.49	   A^2 -> H(U1(a, e), f(e))
25.79/8.49	   A^2 -> H(U1(a, e), f(k))
25.79/8.49	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.49	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.49	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.49	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.49	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.49	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.49	   A^2 -> H(U1(a, k), f(e))
25.79/8.49	   A^2 -> H(U1(a, k), f(k))
25.79/8.49	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.49	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.49	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.49	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.49	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.49	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.49	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.49	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.49	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.49	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.49	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.49	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.49	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.49	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.49	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.49	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.49	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.49	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.49	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.49	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.49	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.49	   A^2 -> H(U1(a, d), U1(e, c))
25.79/8.49	   A^2 -> H(U1(a, d), U1(k, c))
25.79/8.49	   A^2 -> H(U1(a, d), U1(c, e))
25.79/8.49	   A^2 -> H(U1(a, d), U1(c, k))
25.79/8.49	   A^2 -> H(U1(a, d), U1(e, e))
25.79/8.49	   A^2 -> H(U1(a, d), U1(k, k))
25.79/8.49	   A^2 -> H(U1(a, d), U1(k, d))
25.79/8.49	   A^2 -> H(U1(a, d), U1(d, k))
25.79/8.49	   A^2 -> H(U1(a, a), b)
25.79/8.49	   A^2 -> H(U1(a, a), U1(e, d))
25.79/8.49	   A^2 -> H(U1(a, a), U1(d, e))
25.79/8.49	   A^2 -> H(U1(a, a), c)
25.79/8.49	   A^2 -> H(U1(a, a), U1(e, k))
25.79/8.49	   A^2 -> H(U1(a, a), U1(k, e))
25.79/8.49	   A^2 -> H(U1(a, a), e)
25.79/8.49	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.49	
25.79/8.49	The TRS R consists of the following rules:
25.79/8.49	
25.79/8.49	   f(x) -> U1(x, x)
25.79/8.49	   U1(e, x) -> x
25.79/8.49	   a -> c
25.79/8.49	   a -> d
25.79/8.49	   b -> c
25.79/8.49	   b -> d
25.79/8.49	   d -> k
25.79/8.49	   c -> e
25.79/8.49	   c -> k
25.79/8.49	
25.79/8.49	Q is empty.
25.79/8.49	We have to consider all minimal (P,Q,R)-chains.
25.79/8.49	----------------------------------------
25.79/8.49	
25.79/8.49	(353) TransformationProof (EQUIVALENT)
25.79/8.49	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.49	
25.79/8.49	   (A^2 -> H(U1(c, a), U1(d, k)),A^2 -> H(U1(c, a), U1(d, k)))
25.79/8.49	   (A^2 -> H(U1(d, a), U1(d, k)),A^2 -> H(U1(d, a), U1(d, k)))
25.79/8.49	   (A^2 -> H(U1(a, c), U1(d, k)),A^2 -> H(U1(a, c), U1(d, k)))
25.79/8.49	   (A^2 -> H(U1(a, d), U1(d, k)),A^2 -> H(U1(a, d), U1(d, k)))
25.79/8.49	   (A^2 -> H(U1(a, a), U1(k, k)),A^2 -> H(U1(a, a), U1(k, k)))
25.79/8.49	
25.79/8.49	
25.79/8.49	----------------------------------------
25.79/8.49	
25.79/8.49	(354)
25.79/8.49	Obligation:
25.79/8.49	Q DP problem:
25.79/8.49	The TRS P consists of the following rules:
25.79/8.49	
25.79/8.49	   H(x, x) -> G(x, x, f(k))
25.79/8.49	   G(d, x, x) -> A^2
25.79/8.49	   A^2 -> H(f(c), f(c))
25.79/8.49	   A^2 -> H(f(d), f(d))
25.79/8.49	   A^2 -> H(c, f(b))
25.79/8.49	   A^2 -> H(U1(e, k), f(b))
25.79/8.49	   A^2 -> H(U1(e, c), U1(b, b))
25.79/8.49	   A^2 -> H(U1(e, c), f(c))
25.79/8.49	   A^2 -> H(U1(e, c), f(d))
25.79/8.49	   A^2 -> H(U1(k, e), f(b))
25.79/8.49	   A^2 -> H(U1(k, c), U1(b, b))
25.79/8.49	   A^2 -> H(U1(k, c), f(c))
25.79/8.49	   A^2 -> H(U1(k, c), f(d))
25.79/8.49	   A^2 -> H(U1(c, e), U1(b, b))
25.79/8.49	   A^2 -> H(U1(c, e), f(c))
25.79/8.49	   A^2 -> H(U1(c, e), f(d))
25.79/8.49	   A^2 -> H(U1(c, k), U1(b, b))
25.79/8.49	   A^2 -> H(U1(c, k), f(c))
25.79/8.49	   A^2 -> H(U1(c, k), f(d))
25.79/8.49	   A^2 -> H(U1(c, c), U1(c, b))
25.79/8.49	   A^2 -> H(U1(c, c), U1(d, b))
25.79/8.49	   A^2 -> H(U1(c, c), U1(b, c))
25.79/8.49	   A^2 -> H(U1(c, c), U1(b, d))
25.79/8.49	   A^2 -> H(U1(c, c), U1(c, c))
25.79/8.49	   A^2 -> H(U1(c, c), f(e))
25.79/8.49	   A^2 -> H(U1(c, c), f(k))
25.79/8.49	   A^2 -> H(U1(c, c), U1(d, d))
25.79/8.49	   A^2 -> H(e, f(b))
25.79/8.49	   A^2 -> H(U1(e, e), U1(b, b))
25.79/8.49	   A^2 -> H(U1(e, e), f(c))
25.79/8.49	   A^2 -> H(U1(e, e), f(d))
25.79/8.49	   A^2 -> H(f(e), U1(c, b))
25.79/8.49	   A^2 -> H(f(e), U1(d, b))
25.79/8.49	   A^2 -> H(f(e), U1(b, c))
25.79/8.49	   A^2 -> H(f(e), U1(b, d))
25.79/8.49	   A^2 -> H(f(e), U1(c, c))
25.79/8.49	   A^2 -> H(f(e), f(e))
25.79/8.49	   A^2 -> H(f(e), f(k))
25.79/8.49	   A^2 -> H(f(e), U1(d, d))
25.79/8.49	   A^2 -> H(U1(k, k), U1(b, b))
25.79/8.49	   A^2 -> H(U1(k, k), f(c))
25.79/8.49	   A^2 -> H(U1(k, k), f(d))
25.79/8.49	   A^2 -> H(f(k), U1(c, b))
25.79/8.49	   A^2 -> H(f(k), U1(d, b))
25.79/8.49	   A^2 -> H(f(k), U1(b, c))
25.79/8.49	   A^2 -> H(f(k), U1(b, d))
25.79/8.49	   A^2 -> H(f(k), U1(c, c))
25.79/8.49	   A^2 -> H(f(k), f(e))
25.79/8.49	   A^2 -> H(f(k), f(k))
25.79/8.49	   A^2 -> H(f(k), U1(d, d))
25.79/8.49	   A^2 -> H(f(c), U1(e, b))
25.79/8.49	   A^2 -> H(f(c), U1(k, b))
25.79/8.49	   A^2 -> H(f(c), U1(c, d))
25.79/8.49	   A^2 -> H(f(c), U1(d, c))
25.79/8.49	   A^2 -> H(f(c), U1(b, e))
25.79/8.49	   A^2 -> H(f(c), U1(b, k))
25.79/8.49	   A^2 -> H(f(c), U1(k, d))
25.79/8.49	   A^2 -> H(f(c), U1(d, k))
25.79/8.49	   A^2 -> H(f(c), U1(k, k))
25.79/8.49	   A^2 -> H(U1(k, k), f(b))
25.79/8.49	   A^2 -> H(U1(k, d), U1(b, b))
25.79/8.49	   A^2 -> H(U1(k, d), f(c))
25.79/8.49	   A^2 -> H(U1(k, d), f(d))
25.79/8.49	   A^2 -> H(U1(d, k), U1(b, b))
25.79/8.49	   A^2 -> H(U1(d, k), f(c))
25.79/8.49	   A^2 -> H(U1(d, k), f(d))
25.79/8.49	   A^2 -> H(U1(d, d), U1(c, b))
25.79/8.49	   A^2 -> H(U1(d, d), U1(d, b))
25.79/8.49	   A^2 -> H(U1(d, d), U1(b, c))
25.79/8.49	   A^2 -> H(U1(d, d), U1(b, d))
25.79/8.49	   A^2 -> H(U1(d, d), U1(c, c))
25.79/8.49	   A^2 -> H(U1(d, d), f(e))
25.79/8.49	   A^2 -> H(U1(d, d), f(k))
25.79/8.49	   A^2 -> H(U1(d, d), U1(d, d))
25.79/8.49	   A^2 -> H(f(d), U1(e, b))
25.79/8.49	   A^2 -> H(f(d), U1(k, b))
25.79/8.49	   A^2 -> H(f(d), U1(c, d))
25.79/8.49	   A^2 -> H(f(d), U1(d, c))
25.79/8.49	   A^2 -> H(f(d), U1(b, e))
25.79/8.49	   A^2 -> H(f(d), U1(b, k))
25.79/8.49	   A^2 -> H(f(d), U1(e, c))
25.79/8.49	   A^2 -> H(f(d), U1(k, c))
25.79/8.49	   A^2 -> H(f(d), U1(c, e))
25.79/8.49	   A^2 -> H(f(d), U1(c, k))
25.79/8.49	   A^2 -> H(f(d), U1(e, e))
25.79/8.49	   A^2 -> H(f(d), U1(k, k))
25.79/8.49	   A^2 -> H(f(a), b)
25.79/8.49	   A^2 -> H(f(a), U1(e, d))
25.79/8.49	   A^2 -> H(f(a), U1(d, e))
25.79/8.49	   A^2 -> H(f(c), U1(e, c))
25.79/8.49	   A^2 -> H(f(c), U1(k, c))
25.79/8.49	   A^2 -> H(f(c), U1(c, e))
25.79/8.49	   A^2 -> H(f(c), U1(c, k))
25.79/8.49	   A^2 -> H(f(a), c)
25.79/8.49	   A^2 -> H(f(a), U1(e, k))
25.79/8.49	   A^2 -> H(f(a), U1(k, e))
25.79/8.49	   A^2 -> H(f(c), U1(e, e))
25.79/8.49	   A^2 -> H(f(a), e)
25.79/8.49	   A^2 -> H(f(d), U1(k, d))
25.79/8.49	   A^2 -> H(f(d), U1(d, k))
25.79/8.49	   A^2 -> H(f(a), U1(k, k))
25.79/8.49	   A^2 -> H(d, f(b))
25.79/8.49	   A^2 -> H(a, U1(b, b))
25.79/8.49	   A^2 -> H(a, f(c))
25.79/8.49	   A^2 -> H(a, f(d))
25.79/8.49	   A^2 -> H(U1(e, d), U1(b, b))
25.79/8.49	   A^2 -> H(U1(e, d), f(c))
25.79/8.49	   A^2 -> H(U1(e, d), f(d))
25.79/8.49	   A^2 -> H(U1(e, a), U1(c, b))
25.79/8.49	   A^2 -> H(U1(e, a), U1(d, b))
25.79/8.49	   A^2 -> H(U1(e, a), U1(b, c))
25.79/8.49	   A^2 -> H(U1(e, a), U1(b, d))
25.79/8.49	   A^2 -> H(U1(e, a), U1(c, c))
25.79/8.49	   A^2 -> H(U1(e, a), f(e))
25.79/8.49	   A^2 -> H(U1(e, a), f(k))
25.79/8.49	   A^2 -> H(U1(e, a), U1(d, d))
25.79/8.49	   A^2 -> H(U1(k, a), U1(c, b))
25.79/8.49	   A^2 -> H(U1(k, a), U1(d, b))
25.79/8.49	   A^2 -> H(U1(k, a), U1(b, c))
25.79/8.49	   A^2 -> H(U1(k, a), U1(b, d))
25.79/8.49	   A^2 -> H(U1(k, a), U1(c, c))
25.79/8.49	   A^2 -> H(U1(k, a), f(e))
25.79/8.49	   A^2 -> H(U1(k, a), f(k))
25.79/8.49	   A^2 -> H(U1(k, a), U1(d, d))
25.79/8.49	   A^2 -> H(U1(c, d), U1(c, b))
25.79/8.49	   A^2 -> H(U1(c, d), U1(d, b))
25.79/8.49	   A^2 -> H(U1(c, d), U1(b, c))
25.79/8.49	   A^2 -> H(U1(c, d), U1(b, d))
25.79/8.49	   A^2 -> H(U1(c, d), U1(c, c))
25.79/8.49	   A^2 -> H(U1(c, d), f(e))
25.79/8.49	   A^2 -> H(U1(c, d), f(k))
25.79/8.49	   A^2 -> H(U1(c, d), U1(d, d))
25.79/8.49	   A^2 -> H(U1(c, a), U1(e, b))
25.79/8.49	   A^2 -> H(U1(c, a), U1(k, b))
25.79/8.49	   A^2 -> H(U1(c, a), U1(c, d))
25.79/8.49	   A^2 -> H(U1(c, a), U1(d, c))
25.79/8.49	   A^2 -> H(U1(c, a), U1(b, e))
25.79/8.49	   A^2 -> H(U1(c, a), U1(b, k))
25.79/8.49	   A^2 -> H(U1(c, a), U1(e, c))
25.79/8.49	   A^2 -> H(U1(c, a), U1(k, c))
25.79/8.49	   A^2 -> H(U1(c, a), U1(c, e))
25.79/8.49	   A^2 -> H(U1(c, a), U1(c, k))
25.79/8.49	   A^2 -> H(U1(c, a), U1(e, e))
25.79/8.49	   A^2 -> H(U1(c, a), U1(k, k))
25.79/8.49	   A^2 -> H(U1(c, a), U1(k, d))
25.79/8.49	   A^2 -> H(U1(c, a), U1(d, k))
25.79/8.49	   A^2 -> H(U1(d, e), U1(b, b))
25.79/8.49	   A^2 -> H(U1(d, e), f(c))
25.79/8.49	   A^2 -> H(U1(d, e), f(d))
25.79/8.49	   A^2 -> H(U1(d, c), U1(c, b))
25.79/8.49	   A^2 -> H(U1(d, c), U1(d, b))
25.79/8.49	   A^2 -> H(U1(d, c), U1(b, c))
25.79/8.49	   A^2 -> H(U1(d, c), U1(b, d))
25.79/8.49	   A^2 -> H(U1(d, c), U1(c, c))
25.79/8.49	   A^2 -> H(U1(d, c), f(e))
25.79/8.49	   A^2 -> H(U1(d, c), f(k))
25.79/8.49	   A^2 -> H(U1(d, c), U1(d, d))
25.79/8.49	   A^2 -> H(U1(d, a), U1(e, b))
25.79/8.49	   A^2 -> H(U1(d, a), U1(k, b))
25.79/8.49	   A^2 -> H(U1(d, a), U1(c, d))
25.79/8.49	   A^2 -> H(U1(d, a), U1(d, c))
25.79/8.49	   A^2 -> H(U1(d, a), U1(b, e))
25.79/8.49	   A^2 -> H(U1(d, a), U1(b, k))
25.79/8.49	   A^2 -> H(U1(d, a), U1(e, c))
25.79/8.49	   A^2 -> H(U1(d, a), U1(k, c))
25.79/8.49	   A^2 -> H(U1(d, a), U1(c, e))
25.79/8.49	   A^2 -> H(U1(d, a), U1(c, k))
25.79/8.49	   A^2 -> H(U1(d, a), U1(e, e))
25.79/8.49	   A^2 -> H(U1(d, a), U1(k, k))
25.79/8.49	   A^2 -> H(U1(d, a), U1(k, d))
25.79/8.49	   A^2 -> H(U1(d, a), U1(d, k))
25.79/8.49	   A^2 -> H(U1(a, e), U1(c, b))
25.79/8.49	   A^2 -> H(U1(a, e), U1(d, b))
25.79/8.49	   A^2 -> H(U1(a, e), U1(b, c))
25.79/8.49	   A^2 -> H(U1(a, e), U1(b, d))
25.79/8.49	   A^2 -> H(U1(a, e), U1(c, c))
25.79/8.49	   A^2 -> H(U1(a, e), f(e))
25.79/8.49	   A^2 -> H(U1(a, e), f(k))
25.79/8.49	   A^2 -> H(U1(a, e), U1(d, d))
25.79/8.49	   A^2 -> H(U1(a, k), U1(c, b))
25.79/8.49	   A^2 -> H(U1(a, k), U1(d, b))
25.79/8.49	   A^2 -> H(U1(a, k), U1(b, c))
25.79/8.49	   A^2 -> H(U1(a, k), U1(b, d))
25.79/8.49	   A^2 -> H(U1(a, k), U1(c, c))
25.79/8.49	   A^2 -> H(U1(a, k), f(e))
25.79/8.49	   A^2 -> H(U1(a, k), f(k))
25.79/8.49	   A^2 -> H(U1(a, k), U1(d, d))
25.79/8.49	   A^2 -> H(U1(a, c), U1(e, b))
25.79/8.49	   A^2 -> H(U1(a, c), U1(k, b))
25.79/8.49	   A^2 -> H(U1(a, c), U1(c, d))
25.79/8.49	   A^2 -> H(U1(a, c), U1(d, c))
25.79/8.49	   A^2 -> H(U1(a, c), U1(b, e))
25.79/8.49	   A^2 -> H(U1(a, c), U1(b, k))
25.79/8.49	   A^2 -> H(U1(a, c), U1(e, c))
25.79/8.49	   A^2 -> H(U1(a, c), U1(k, c))
25.79/8.49	   A^2 -> H(U1(a, c), U1(c, e))
25.79/8.49	   A^2 -> H(U1(a, c), U1(c, k))
25.79/8.49	   A^2 -> H(U1(a, c), U1(e, e))
25.79/8.49	   A^2 -> H(U1(a, c), U1(k, k))
25.79/8.49	   A^2 -> H(U1(a, c), U1(k, d))
25.79/8.49	   A^2 -> H(U1(a, c), U1(d, k))
25.79/8.49	   A^2 -> H(U1(a, d), U1(e, b))
25.79/8.49	   A^2 -> H(U1(a, d), U1(k, b))
25.79/8.49	   A^2 -> H(U1(a, d), U1(c, d))
25.79/8.49	   A^2 -> H(U1(a, d), U1(d, c))
25.79/8.49	   A^2 -> H(U1(a, d), U1(b, e))
25.79/8.49	   A^2 -> H(U1(a, d), U1(b, k))
25.79/8.49	   A^2 -> H(U1(a, d), U1(e, c))
25.79/8.49	   A^2 -> H(U1(a, d), U1(k, c))
25.79/8.49	   A^2 -> H(U1(a, d), U1(c, e))
25.79/8.49	   A^2 -> H(U1(a, d), U1(c, k))
25.79/8.49	   A^2 -> H(U1(a, d), U1(e, e))
25.79/8.49	   A^2 -> H(U1(a, d), U1(k, k))
25.79/8.49	   A^2 -> H(U1(a, d), U1(k, d))
25.79/8.49	   A^2 -> H(U1(a, d), U1(d, k))
25.79/8.49	   A^2 -> H(U1(a, a), b)
25.79/8.49	   A^2 -> H(U1(a, a), U1(e, d))
25.79/8.49	   A^2 -> H(U1(a, a), U1(d, e))
25.79/8.49	   A^2 -> H(U1(a, a), c)
25.79/8.49	   A^2 -> H(U1(a, a), U1(e, k))
25.79/8.49	   A^2 -> H(U1(a, a), U1(k, e))
25.79/8.49	   A^2 -> H(U1(a, a), e)
25.79/8.49	   A^2 -> H(U1(a, a), U1(k, k))
25.79/8.49	
25.79/8.49	The TRS R consists of the following rules:
25.79/8.49	
25.79/8.49	   f(x) -> U1(x, x)
25.79/8.49	   U1(e, x) -> x
25.79/8.49	   a -> c
25.79/8.49	   a -> d
25.79/8.49	   b -> c
25.79/8.49	   b -> d
25.79/8.49	   d -> k
25.79/8.49	   c -> e
25.79/8.49	   c -> k
25.79/8.49	
25.79/8.49	Q is empty.
25.79/8.49	We have to consider all minimal (P,Q,R)-chains.
25.79/8.49	----------------------------------------
25.79/8.49	
25.79/8.49	(355) TransformationProof (EQUIVALENT)
25.79/8.49	By narrowing [LPAR04] the rule A^2 -> H(c, f(b)) at position [] we obtained the following new rules [LPAR04]:
25.79/8.49	
25.79/8.49	   (A^2 -> H(e, f(b)),A^2 -> H(e, f(b)))
25.79/8.49	   (A^2 -> H(k, f(b)),A^2 -> H(k, f(b)))
25.79/8.49	   (A^2 -> H(c, U1(b, b)),A^2 -> H(c, U1(b, b)))
25.79/8.49	   (A^2 -> H(c, f(c)),A^2 -> H(c, f(c)))
25.79/8.49	   (A^2 -> H(c, f(d)),A^2 -> H(c, f(d)))
25.79/8.49	
25.79/8.49	
25.79/8.49	----------------------------------------
25.79/8.49	
25.79/8.49	(356)
25.79/8.49	Obligation:
25.79/8.49	Q DP problem:
25.79/8.49	The TRS P consists of the following rules:
25.79/8.49	
25.79/8.49	   H(x, x) -> G(x, x, f(k))
25.79/8.49	   G(d, x, x) -> A^2
25.79/8.49	   A^2 -> H(f(c), f(c))
25.79/8.49	   A^2 -> H(f(d), f(d))
25.98/8.49	   A^2 -> H(U1(e, k), f(b))
25.98/8.49	   A^2 -> H(U1(e, c), U1(b, b))
25.98/8.49	   A^2 -> H(U1(e, c), f(c))
25.98/8.49	   A^2 -> H(U1(e, c), f(d))
25.98/8.49	   A^2 -> H(U1(k, e), f(b))
25.98/8.49	   A^2 -> H(U1(k, c), U1(b, b))
25.98/8.49	   A^2 -> H(U1(k, c), f(c))
25.98/8.49	   A^2 -> H(U1(k, c), f(d))
25.98/8.49	   A^2 -> H(U1(c, e), U1(b, b))
25.98/8.49	   A^2 -> H(U1(c, e), f(c))
25.98/8.49	   A^2 -> H(U1(c, e), f(d))
25.98/8.49	   A^2 -> H(U1(c, k), U1(b, b))
25.98/8.49	   A^2 -> H(U1(c, k), f(c))
25.98/8.49	   A^2 -> H(U1(c, k), f(d))
25.98/8.49	   A^2 -> H(U1(c, c), U1(c, b))
25.98/8.49	   A^2 -> H(U1(c, c), U1(d, b))
25.98/8.49	   A^2 -> H(U1(c, c), U1(b, c))
25.98/8.49	   A^2 -> H(U1(c, c), U1(b, d))
25.98/8.49	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.49	   A^2 -> H(U1(c, c), f(e))
25.98/8.49	   A^2 -> H(U1(c, c), f(k))
25.98/8.49	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.49	   A^2 -> H(e, f(b))
25.98/8.49	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.49	   A^2 -> H(U1(e, e), f(c))
25.98/8.49	   A^2 -> H(U1(e, e), f(d))
25.98/8.49	   A^2 -> H(f(e), U1(c, b))
25.98/8.49	   A^2 -> H(f(e), U1(d, b))
25.98/8.49	   A^2 -> H(f(e), U1(b, c))
25.98/8.49	   A^2 -> H(f(e), U1(b, d))
25.98/8.49	   A^2 -> H(f(e), U1(c, c))
25.98/8.49	   A^2 -> H(f(e), f(e))
25.98/8.49	   A^2 -> H(f(e), f(k))
25.98/8.49	   A^2 -> H(f(e), U1(d, d))
25.98/8.49	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.49	   A^2 -> H(U1(k, k), f(c))
25.98/8.49	   A^2 -> H(U1(k, k), f(d))
25.98/8.49	   A^2 -> H(f(k), U1(c, b))
25.98/8.49	   A^2 -> H(f(k), U1(d, b))
25.98/8.49	   A^2 -> H(f(k), U1(b, c))
25.98/8.49	   A^2 -> H(f(k), U1(b, d))
25.98/8.49	   A^2 -> H(f(k), U1(c, c))
25.98/8.49	   A^2 -> H(f(k), f(e))
25.98/8.49	   A^2 -> H(f(k), f(k))
25.98/8.49	   A^2 -> H(f(k), U1(d, d))
25.98/8.49	   A^2 -> H(f(c), U1(e, b))
25.98/8.49	   A^2 -> H(f(c), U1(k, b))
25.98/8.49	   A^2 -> H(f(c), U1(c, d))
25.98/8.49	   A^2 -> H(f(c), U1(d, c))
25.98/8.49	   A^2 -> H(f(c), U1(b, e))
25.98/8.49	   A^2 -> H(f(c), U1(b, k))
25.98/8.49	   A^2 -> H(f(c), U1(k, d))
25.98/8.49	   A^2 -> H(f(c), U1(d, k))
25.98/8.49	   A^2 -> H(f(c), U1(k, k))
25.98/8.49	   A^2 -> H(U1(k, k), f(b))
25.98/8.49	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.49	   A^2 -> H(U1(k, d), f(c))
25.98/8.49	   A^2 -> H(U1(k, d), f(d))
25.98/8.49	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.49	   A^2 -> H(U1(d, k), f(c))
25.98/8.49	   A^2 -> H(U1(d, k), f(d))
25.98/8.49	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.49	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.49	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.49	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.49	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.49	   A^2 -> H(U1(d, d), f(e))
25.98/8.49	   A^2 -> H(U1(d, d), f(k))
25.98/8.49	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.49	   A^2 -> H(f(d), U1(e, b))
25.98/8.49	   A^2 -> H(f(d), U1(k, b))
25.98/8.49	   A^2 -> H(f(d), U1(c, d))
25.98/8.49	   A^2 -> H(f(d), U1(d, c))
25.98/8.49	   A^2 -> H(f(d), U1(b, e))
25.98/8.49	   A^2 -> H(f(d), U1(b, k))
25.98/8.49	   A^2 -> H(f(d), U1(e, c))
25.98/8.49	   A^2 -> H(f(d), U1(k, c))
25.98/8.49	   A^2 -> H(f(d), U1(c, e))
25.98/8.49	   A^2 -> H(f(d), U1(c, k))
25.98/8.49	   A^2 -> H(f(d), U1(e, e))
25.98/8.49	   A^2 -> H(f(d), U1(k, k))
25.98/8.49	   A^2 -> H(f(a), b)
25.98/8.49	   A^2 -> H(f(a), U1(e, d))
25.98/8.49	   A^2 -> H(f(a), U1(d, e))
25.98/8.49	   A^2 -> H(f(c), U1(e, c))
25.98/8.49	   A^2 -> H(f(c), U1(k, c))
25.98/8.49	   A^2 -> H(f(c), U1(c, e))
25.98/8.49	   A^2 -> H(f(c), U1(c, k))
25.98/8.49	   A^2 -> H(f(a), c)
25.98/8.49	   A^2 -> H(f(a), U1(e, k))
25.98/8.49	   A^2 -> H(f(a), U1(k, e))
25.98/8.49	   A^2 -> H(f(c), U1(e, e))
25.98/8.49	   A^2 -> H(f(a), e)
25.98/8.49	   A^2 -> H(f(d), U1(k, d))
25.98/8.49	   A^2 -> H(f(d), U1(d, k))
25.98/8.49	   A^2 -> H(f(a), U1(k, k))
25.98/8.49	   A^2 -> H(d, f(b))
25.98/8.49	   A^2 -> H(a, U1(b, b))
25.98/8.49	   A^2 -> H(a, f(c))
25.98/8.49	   A^2 -> H(a, f(d))
25.98/8.49	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.49	   A^2 -> H(U1(e, d), f(c))
25.98/8.49	   A^2 -> H(U1(e, d), f(d))
25.98/8.49	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.49	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.49	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.49	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.49	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.49	   A^2 -> H(U1(e, a), f(e))
25.98/8.49	   A^2 -> H(U1(e, a), f(k))
25.98/8.49	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.49	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.49	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.49	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.49	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.49	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.49	   A^2 -> H(U1(k, a), f(e))
25.98/8.49	   A^2 -> H(U1(k, a), f(k))
25.98/8.49	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.49	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.49	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.49	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.49	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.49	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.49	   A^2 -> H(U1(c, d), f(e))
25.98/8.49	   A^2 -> H(U1(c, d), f(k))
25.98/8.49	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.49	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.49	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.49	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.49	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.49	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.49	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.49	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.49	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.49	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.49	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.49	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.49	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.49	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.49	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.49	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.49	   A^2 -> H(U1(d, e), f(c))
25.98/8.49	   A^2 -> H(U1(d, e), f(d))
25.98/8.49	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.49	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.49	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.49	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.49	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.49	   A^2 -> H(U1(d, c), f(e))
25.98/8.49	   A^2 -> H(U1(d, c), f(k))
25.98/8.49	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.49	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.49	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.49	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.49	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.49	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.49	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.49	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.49	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.49	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.49	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.49	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.49	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.49	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.49	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.49	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.49	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.49	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.49	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.49	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.49	   A^2 -> H(U1(a, e), f(e))
25.98/8.49	   A^2 -> H(U1(a, e), f(k))
25.98/8.49	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.49	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.49	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.49	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.49	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.49	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.49	   A^2 -> H(U1(a, k), f(e))
25.98/8.49	   A^2 -> H(U1(a, k), f(k))
25.98/8.49	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.49	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.49	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.49	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.49	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.49	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.49	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.49	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.49	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.49	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.49	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.49	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.49	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.49	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.49	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.49	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.49	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.49	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.49	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.49	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.49	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.49	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.49	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.49	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.49	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.49	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.49	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.49	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.49	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.49	   A^2 -> H(U1(a, a), b)
25.98/8.49	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.49	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.49	   A^2 -> H(U1(a, a), c)
25.98/8.49	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.49	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.49	   A^2 -> H(U1(a, a), e)
25.98/8.49	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.49	   A^2 -> H(k, f(b))
25.98/8.49	   A^2 -> H(c, U1(b, b))
25.98/8.49	   A^2 -> H(c, f(c))
25.98/8.49	   A^2 -> H(c, f(d))
25.98/8.49	
25.98/8.49	The TRS R consists of the following rules:
25.98/8.49	
25.98/8.49	   f(x) -> U1(x, x)
25.98/8.49	   U1(e, x) -> x
25.98/8.49	   a -> c
25.98/8.49	   a -> d
25.98/8.49	   b -> c
25.98/8.49	   b -> d
25.98/8.49	   d -> k
25.98/8.49	   c -> e
25.98/8.49	   c -> k
25.98/8.49	
25.98/8.49	Q is empty.
25.98/8.49	We have to consider all minimal (P,Q,R)-chains.
25.98/8.49	----------------------------------------
25.98/8.49	
25.98/8.49	(357) TransformationProof (EQUIVALENT)
25.98/8.49	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), f(b)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.49	
25.98/8.49	   (A^2 -> H(k, f(b)),A^2 -> H(k, f(b)))
25.98/8.49	   (A^2 -> H(U1(e, k), U1(b, b)),A^2 -> H(U1(e, k), U1(b, b)))
25.98/8.49	   (A^2 -> H(U1(e, k), f(c)),A^2 -> H(U1(e, k), f(c)))
25.98/8.49	   (A^2 -> H(U1(e, k), f(d)),A^2 -> H(U1(e, k), f(d)))
25.98/8.49	
25.98/8.49	
25.98/8.49	----------------------------------------
25.98/8.49	
25.98/8.49	(358)
25.98/8.49	Obligation:
25.98/8.49	Q DP problem:
25.98/8.49	The TRS P consists of the following rules:
25.98/8.49	
25.98/8.49	   H(x, x) -> G(x, x, f(k))
25.98/8.49	   G(d, x, x) -> A^2
25.98/8.49	   A^2 -> H(f(c), f(c))
25.98/8.49	   A^2 -> H(f(d), f(d))
25.98/8.49	   A^2 -> H(U1(e, c), U1(b, b))
25.98/8.49	   A^2 -> H(U1(e, c), f(c))
25.98/8.49	   A^2 -> H(U1(e, c), f(d))
25.98/8.49	   A^2 -> H(U1(k, e), f(b))
25.98/8.49	   A^2 -> H(U1(k, c), U1(b, b))
25.98/8.49	   A^2 -> H(U1(k, c), f(c))
25.98/8.49	   A^2 -> H(U1(k, c), f(d))
25.98/8.49	   A^2 -> H(U1(c, e), U1(b, b))
25.98/8.49	   A^2 -> H(U1(c, e), f(c))
25.98/8.49	   A^2 -> H(U1(c, e), f(d))
25.98/8.49	   A^2 -> H(U1(c, k), U1(b, b))
25.98/8.49	   A^2 -> H(U1(c, k), f(c))
25.98/8.49	   A^2 -> H(U1(c, k), f(d))
25.98/8.49	   A^2 -> H(U1(c, c), U1(c, b))
25.98/8.49	   A^2 -> H(U1(c, c), U1(d, b))
25.98/8.49	   A^2 -> H(U1(c, c), U1(b, c))
25.98/8.49	   A^2 -> H(U1(c, c), U1(b, d))
25.98/8.49	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.49	   A^2 -> H(U1(c, c), f(e))
25.98/8.49	   A^2 -> H(U1(c, c), f(k))
25.98/8.49	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.49	   A^2 -> H(e, f(b))
25.98/8.49	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.49	   A^2 -> H(U1(e, e), f(c))
25.98/8.49	   A^2 -> H(U1(e, e), f(d))
25.98/8.49	   A^2 -> H(f(e), U1(c, b))
25.98/8.49	   A^2 -> H(f(e), U1(d, b))
25.98/8.49	   A^2 -> H(f(e), U1(b, c))
25.98/8.49	   A^2 -> H(f(e), U1(b, d))
25.98/8.49	   A^2 -> H(f(e), U1(c, c))
25.98/8.49	   A^2 -> H(f(e), f(e))
25.98/8.49	   A^2 -> H(f(e), f(k))
25.98/8.49	   A^2 -> H(f(e), U1(d, d))
25.98/8.49	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.49	   A^2 -> H(U1(k, k), f(c))
25.98/8.49	   A^2 -> H(U1(k, k), f(d))
25.98/8.49	   A^2 -> H(f(k), U1(c, b))
25.98/8.49	   A^2 -> H(f(k), U1(d, b))
25.98/8.49	   A^2 -> H(f(k), U1(b, c))
25.98/8.49	   A^2 -> H(f(k), U1(b, d))
25.98/8.49	   A^2 -> H(f(k), U1(c, c))
25.98/8.49	   A^2 -> H(f(k), f(e))
25.98/8.49	   A^2 -> H(f(k), f(k))
25.98/8.49	   A^2 -> H(f(k), U1(d, d))
25.98/8.49	   A^2 -> H(f(c), U1(e, b))
25.98/8.49	   A^2 -> H(f(c), U1(k, b))
25.98/8.49	   A^2 -> H(f(c), U1(c, d))
25.98/8.49	   A^2 -> H(f(c), U1(d, c))
25.98/8.49	   A^2 -> H(f(c), U1(b, e))
25.98/8.49	   A^2 -> H(f(c), U1(b, k))
25.98/8.49	   A^2 -> H(f(c), U1(k, d))
25.98/8.49	   A^2 -> H(f(c), U1(d, k))
25.98/8.49	   A^2 -> H(f(c), U1(k, k))
25.98/8.49	   A^2 -> H(U1(k, k), f(b))
25.98/8.49	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.49	   A^2 -> H(U1(k, d), f(c))
25.98/8.49	   A^2 -> H(U1(k, d), f(d))
25.98/8.49	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.49	   A^2 -> H(U1(d, k), f(c))
25.98/8.49	   A^2 -> H(U1(d, k), f(d))
25.98/8.49	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.49	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.49	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.49	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.49	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.49	   A^2 -> H(U1(d, d), f(e))
25.98/8.49	   A^2 -> H(U1(d, d), f(k))
25.98/8.49	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.49	   A^2 -> H(f(d), U1(e, b))
25.98/8.49	   A^2 -> H(f(d), U1(k, b))
25.98/8.49	   A^2 -> H(f(d), U1(c, d))
25.98/8.49	   A^2 -> H(f(d), U1(d, c))
25.98/8.49	   A^2 -> H(f(d), U1(b, e))
25.98/8.49	   A^2 -> H(f(d), U1(b, k))
25.98/8.49	   A^2 -> H(f(d), U1(e, c))
25.98/8.49	   A^2 -> H(f(d), U1(k, c))
25.98/8.49	   A^2 -> H(f(d), U1(c, e))
25.98/8.49	   A^2 -> H(f(d), U1(c, k))
25.98/8.49	   A^2 -> H(f(d), U1(e, e))
25.98/8.49	   A^2 -> H(f(d), U1(k, k))
25.98/8.49	   A^2 -> H(f(a), b)
25.98/8.49	   A^2 -> H(f(a), U1(e, d))
25.98/8.49	   A^2 -> H(f(a), U1(d, e))
25.98/8.49	   A^2 -> H(f(c), U1(e, c))
25.98/8.49	   A^2 -> H(f(c), U1(k, c))
25.98/8.49	   A^2 -> H(f(c), U1(c, e))
25.98/8.49	   A^2 -> H(f(c), U1(c, k))
25.98/8.49	   A^2 -> H(f(a), c)
25.98/8.49	   A^2 -> H(f(a), U1(e, k))
25.98/8.49	   A^2 -> H(f(a), U1(k, e))
25.98/8.49	   A^2 -> H(f(c), U1(e, e))
25.98/8.49	   A^2 -> H(f(a), e)
25.98/8.49	   A^2 -> H(f(d), U1(k, d))
25.98/8.49	   A^2 -> H(f(d), U1(d, k))
25.98/8.49	   A^2 -> H(f(a), U1(k, k))
25.98/8.49	   A^2 -> H(d, f(b))
25.98/8.49	   A^2 -> H(a, U1(b, b))
25.98/8.49	   A^2 -> H(a, f(c))
25.98/8.49	   A^2 -> H(a, f(d))
25.98/8.49	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.49	   A^2 -> H(U1(e, d), f(c))
25.98/8.49	   A^2 -> H(U1(e, d), f(d))
25.98/8.49	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.49	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.49	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.49	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.49	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.49	   A^2 -> H(U1(e, a), f(e))
25.98/8.49	   A^2 -> H(U1(e, a), f(k))
25.98/8.49	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.49	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.49	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.49	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.49	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.49	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.49	   A^2 -> H(U1(k, a), f(e))
25.98/8.49	   A^2 -> H(U1(k, a), f(k))
25.98/8.49	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.49	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.49	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.49	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.49	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.49	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.49	   A^2 -> H(U1(c, d), f(e))
25.98/8.49	   A^2 -> H(U1(c, d), f(k))
25.98/8.49	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.49	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.49	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.49	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.49	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.49	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.49	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.49	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.49	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.49	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.49	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.49	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.49	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.49	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.49	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.49	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.49	   A^2 -> H(U1(d, e), f(c))
25.98/8.49	   A^2 -> H(U1(d, e), f(d))
25.98/8.49	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.49	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.49	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.49	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.49	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.49	   A^2 -> H(U1(d, c), f(e))
25.98/8.49	   A^2 -> H(U1(d, c), f(k))
25.98/8.49	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.49	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.49	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.49	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.49	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.49	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.49	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.49	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.49	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.49	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.49	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.49	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.49	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.49	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.49	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.49	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.49	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.49	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.49	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.49	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.49	   A^2 -> H(U1(a, e), f(e))
25.98/8.49	   A^2 -> H(U1(a, e), f(k))
25.98/8.49	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.49	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.49	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.49	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.49	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.49	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.49	   A^2 -> H(U1(a, k), f(e))
25.98/8.49	   A^2 -> H(U1(a, k), f(k))
25.98/8.49	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.49	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.49	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.49	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.49	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.49	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.49	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.49	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.49	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.49	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.49	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.49	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.49	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.49	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.49	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.49	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.49	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.49	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.49	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.49	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.49	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.49	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.49	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.49	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.49	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.49	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.49	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.49	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.49	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.49	   A^2 -> H(U1(a, a), b)
25.98/8.49	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.49	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.49	   A^2 -> H(U1(a, a), c)
25.98/8.49	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.49	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.49	   A^2 -> H(U1(a, a), e)
25.98/8.49	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.49	   A^2 -> H(k, f(b))
25.98/8.49	   A^2 -> H(c, U1(b, b))
25.98/8.49	   A^2 -> H(c, f(c))
25.98/8.49	   A^2 -> H(c, f(d))
25.98/8.49	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.49	   A^2 -> H(U1(e, k), f(c))
25.98/8.49	   A^2 -> H(U1(e, k), f(d))
25.98/8.49	
25.98/8.49	The TRS R consists of the following rules:
25.98/8.49	
25.98/8.49	   f(x) -> U1(x, x)
25.98/8.49	   U1(e, x) -> x
25.98/8.49	   a -> c
25.98/8.49	   a -> d
25.98/8.49	   b -> c
25.98/8.49	   b -> d
25.98/8.49	   d -> k
25.98/8.49	   c -> e
25.98/8.49	   c -> k
25.98/8.49	
25.98/8.49	Q is empty.
25.98/8.49	We have to consider all minimal (P,Q,R)-chains.
25.98/8.49	----------------------------------------
25.98/8.49	
25.98/8.49	(359) TransformationProof (EQUIVALENT)
25.98/8.49	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.49	
25.98/8.49	   (A^2 -> H(c, U1(b, b)),A^2 -> H(c, U1(b, b)))
25.98/8.49	   (A^2 -> H(U1(e, e), U1(b, b)),A^2 -> H(U1(e, e), U1(b, b)))
25.98/8.49	   (A^2 -> H(U1(e, k), U1(b, b)),A^2 -> H(U1(e, k), U1(b, b)))
25.98/8.49	   (A^2 -> H(U1(e, c), U1(c, b)),A^2 -> H(U1(e, c), U1(c, b)))
25.98/8.49	   (A^2 -> H(U1(e, c), U1(d, b)),A^2 -> H(U1(e, c), U1(d, b)))
25.98/8.49	   (A^2 -> H(U1(e, c), U1(b, c)),A^2 -> H(U1(e, c), U1(b, c)))
25.98/8.49	   (A^2 -> H(U1(e, c), U1(b, d)),A^2 -> H(U1(e, c), U1(b, d)))
25.98/8.49	
25.98/8.49	
25.98/8.49	----------------------------------------
25.98/8.49	
25.98/8.49	(360)
25.98/8.49	Obligation:
25.98/8.49	Q DP problem:
25.98/8.49	The TRS P consists of the following rules:
25.98/8.49	
25.98/8.49	   H(x, x) -> G(x, x, f(k))
25.98/8.49	   G(d, x, x) -> A^2
25.98/8.49	   A^2 -> H(f(c), f(c))
25.98/8.49	   A^2 -> H(f(d), f(d))
25.98/8.49	   A^2 -> H(U1(e, c), f(c))
25.98/8.49	   A^2 -> H(U1(e, c), f(d))
25.98/8.49	   A^2 -> H(U1(k, e), f(b))
25.98/8.49	   A^2 -> H(U1(k, c), U1(b, b))
25.98/8.49	   A^2 -> H(U1(k, c), f(c))
25.98/8.49	   A^2 -> H(U1(k, c), f(d))
25.98/8.49	   A^2 -> H(U1(c, e), U1(b, b))
25.98/8.49	   A^2 -> H(U1(c, e), f(c))
25.98/8.49	   A^2 -> H(U1(c, e), f(d))
25.98/8.49	   A^2 -> H(U1(c, k), U1(b, b))
25.98/8.49	   A^2 -> H(U1(c, k), f(c))
25.98/8.49	   A^2 -> H(U1(c, k), f(d))
25.98/8.49	   A^2 -> H(U1(c, c), U1(c, b))
25.98/8.49	   A^2 -> H(U1(c, c), U1(d, b))
25.98/8.49	   A^2 -> H(U1(c, c), U1(b, c))
25.98/8.49	   A^2 -> H(U1(c, c), U1(b, d))
25.98/8.49	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.49	   A^2 -> H(U1(c, c), f(e))
25.98/8.49	   A^2 -> H(U1(c, c), f(k))
25.98/8.49	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.49	   A^2 -> H(e, f(b))
25.98/8.49	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.49	   A^2 -> H(U1(e, e), f(c))
25.98/8.49	   A^2 -> H(U1(e, e), f(d))
25.98/8.49	   A^2 -> H(f(e), U1(c, b))
25.98/8.49	   A^2 -> H(f(e), U1(d, b))
25.98/8.49	   A^2 -> H(f(e), U1(b, c))
25.98/8.49	   A^2 -> H(f(e), U1(b, d))
25.98/8.49	   A^2 -> H(f(e), U1(c, c))
25.98/8.49	   A^2 -> H(f(e), f(e))
25.98/8.49	   A^2 -> H(f(e), f(k))
25.98/8.49	   A^2 -> H(f(e), U1(d, d))
25.98/8.49	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.49	   A^2 -> H(U1(k, k), f(c))
25.98/8.49	   A^2 -> H(U1(k, k), f(d))
25.98/8.49	   A^2 -> H(f(k), U1(c, b))
25.98/8.49	   A^2 -> H(f(k), U1(d, b))
25.98/8.49	   A^2 -> H(f(k), U1(b, c))
25.98/8.49	   A^2 -> H(f(k), U1(b, d))
25.98/8.49	   A^2 -> H(f(k), U1(c, c))
25.98/8.49	   A^2 -> H(f(k), f(e))
25.98/8.49	   A^2 -> H(f(k), f(k))
25.98/8.49	   A^2 -> H(f(k), U1(d, d))
25.98/8.49	   A^2 -> H(f(c), U1(e, b))
25.98/8.49	   A^2 -> H(f(c), U1(k, b))
25.98/8.49	   A^2 -> H(f(c), U1(c, d))
25.98/8.49	   A^2 -> H(f(c), U1(d, c))
25.98/8.49	   A^2 -> H(f(c), U1(b, e))
25.98/8.49	   A^2 -> H(f(c), U1(b, k))
25.98/8.49	   A^2 -> H(f(c), U1(k, d))
25.98/8.49	   A^2 -> H(f(c), U1(d, k))
25.98/8.49	   A^2 -> H(f(c), U1(k, k))
25.98/8.49	   A^2 -> H(U1(k, k), f(b))
25.98/8.49	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.49	   A^2 -> H(U1(k, d), f(c))
25.98/8.49	   A^2 -> H(U1(k, d), f(d))
25.98/8.49	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.49	   A^2 -> H(U1(d, k), f(c))
25.98/8.49	   A^2 -> H(U1(d, k), f(d))
25.98/8.49	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.49	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.49	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.49	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.49	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.49	   A^2 -> H(U1(d, d), f(e))
25.98/8.49	   A^2 -> H(U1(d, d), f(k))
25.98/8.49	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.49	   A^2 -> H(f(d), U1(e, b))
25.98/8.49	   A^2 -> H(f(d), U1(k, b))
25.98/8.49	   A^2 -> H(f(d), U1(c, d))
25.98/8.49	   A^2 -> H(f(d), U1(d, c))
25.98/8.49	   A^2 -> H(f(d), U1(b, e))
25.98/8.49	   A^2 -> H(f(d), U1(b, k))
25.98/8.49	   A^2 -> H(f(d), U1(e, c))
25.98/8.49	   A^2 -> H(f(d), U1(k, c))
25.98/8.49	   A^2 -> H(f(d), U1(c, e))
25.98/8.49	   A^2 -> H(f(d), U1(c, k))
25.98/8.49	   A^2 -> H(f(d), U1(e, e))
25.98/8.49	   A^2 -> H(f(d), U1(k, k))
25.98/8.49	   A^2 -> H(f(a), b)
25.98/8.49	   A^2 -> H(f(a), U1(e, d))
25.98/8.49	   A^2 -> H(f(a), U1(d, e))
25.98/8.49	   A^2 -> H(f(c), U1(e, c))
25.98/8.49	   A^2 -> H(f(c), U1(k, c))
25.98/8.49	   A^2 -> H(f(c), U1(c, e))
25.98/8.49	   A^2 -> H(f(c), U1(c, k))
25.98/8.49	   A^2 -> H(f(a), c)
25.98/8.49	   A^2 -> H(f(a), U1(e, k))
25.98/8.49	   A^2 -> H(f(a), U1(k, e))
25.98/8.49	   A^2 -> H(f(c), U1(e, e))
25.98/8.49	   A^2 -> H(f(a), e)
25.98/8.49	   A^2 -> H(f(d), U1(k, d))
25.98/8.49	   A^2 -> H(f(d), U1(d, k))
25.98/8.49	   A^2 -> H(f(a), U1(k, k))
25.98/8.49	   A^2 -> H(d, f(b))
25.98/8.49	   A^2 -> H(a, U1(b, b))
25.98/8.49	   A^2 -> H(a, f(c))
25.98/8.49	   A^2 -> H(a, f(d))
25.98/8.49	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.49	   A^2 -> H(U1(e, d), f(c))
25.98/8.49	   A^2 -> H(U1(e, d), f(d))
25.98/8.49	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.49	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.49	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.49	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.49	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.49	   A^2 -> H(U1(e, a), f(e))
25.98/8.49	   A^2 -> H(U1(e, a), f(k))
25.98/8.49	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.49	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.49	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.49	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.49	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.49	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.49	   A^2 -> H(U1(k, a), f(e))
25.98/8.49	   A^2 -> H(U1(k, a), f(k))
25.98/8.49	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.49	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.49	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.49	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.49	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.49	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.49	   A^2 -> H(U1(c, d), f(e))
25.98/8.49	   A^2 -> H(U1(c, d), f(k))
25.98/8.49	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.49	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.49	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.49	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.49	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.49	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.49	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.49	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.49	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.49	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.49	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.49	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.49	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.49	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.49	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.49	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.49	   A^2 -> H(U1(d, e), f(c))
25.98/8.49	   A^2 -> H(U1(d, e), f(d))
25.98/8.49	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.49	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.49	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.49	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.49	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.49	   A^2 -> H(U1(d, c), f(e))
25.98/8.49	   A^2 -> H(U1(d, c), f(k))
25.98/8.49	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.49	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.49	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.49	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.49	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.49	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.49	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.49	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.49	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.49	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.49	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.49	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.49	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.49	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.49	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.49	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.49	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.49	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.49	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.49	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.49	   A^2 -> H(U1(a, e), f(e))
25.98/8.49	   A^2 -> H(U1(a, e), f(k))
25.98/8.49	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.49	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.49	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.49	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.49	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.49	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.49	   A^2 -> H(U1(a, k), f(e))
25.98/8.49	   A^2 -> H(U1(a, k), f(k))
25.98/8.49	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.49	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.49	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.49	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.49	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.49	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.49	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.49	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.49	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.49	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.49	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.49	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.49	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.49	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.49	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.49	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.49	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.49	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.49	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.49	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.49	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.49	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.49	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.49	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.49	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.49	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.49	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.49	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.49	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.49	   A^2 -> H(U1(a, a), b)
25.98/8.49	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.49	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.49	   A^2 -> H(U1(a, a), c)
25.98/8.49	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.49	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.49	   A^2 -> H(U1(a, a), e)
25.98/8.49	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.49	   A^2 -> H(k, f(b))
25.98/8.49	   A^2 -> H(c, U1(b, b))
25.98/8.49	   A^2 -> H(c, f(c))
25.98/8.49	   A^2 -> H(c, f(d))
25.98/8.49	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.49	   A^2 -> H(U1(e, k), f(c))
25.98/8.49	   A^2 -> H(U1(e, k), f(d))
25.98/8.49	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.49	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.49	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.49	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.49	
25.98/8.49	The TRS R consists of the following rules:
25.98/8.49	
25.98/8.49	   f(x) -> U1(x, x)
25.98/8.49	   U1(e, x) -> x
25.98/8.49	   a -> c
25.98/8.49	   a -> d
25.98/8.49	   b -> c
25.98/8.49	   b -> d
25.98/8.49	   d -> k
25.98/8.49	   c -> e
25.98/8.49	   c -> k
25.98/8.49	
25.98/8.49	Q is empty.
25.98/8.49	We have to consider all minimal (P,Q,R)-chains.
25.98/8.49	----------------------------------------
25.98/8.49	
25.98/8.49	(361) TransformationProof (EQUIVALENT)
25.98/8.49	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), f(c)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.49	
25.98/8.49	   (A^2 -> H(c, f(c)),A^2 -> H(c, f(c)))
25.98/8.49	   (A^2 -> H(U1(e, e), f(c)),A^2 -> H(U1(e, e), f(c)))
25.98/8.49	   (A^2 -> H(U1(e, k), f(c)),A^2 -> H(U1(e, k), f(c)))
25.98/8.49	   (A^2 -> H(U1(e, c), U1(c, c)),A^2 -> H(U1(e, c), U1(c, c)))
25.98/8.49	   (A^2 -> H(U1(e, c), f(e)),A^2 -> H(U1(e, c), f(e)))
25.98/8.49	   (A^2 -> H(U1(e, c), f(k)),A^2 -> H(U1(e, c), f(k)))
25.98/8.49	
25.98/8.49	
25.98/8.49	----------------------------------------
25.98/8.49	
25.98/8.49	(362)
25.98/8.49	Obligation:
25.98/8.49	Q DP problem:
25.98/8.49	The TRS P consists of the following rules:
25.98/8.49	
25.98/8.49	   H(x, x) -> G(x, x, f(k))
25.98/8.49	   G(d, x, x) -> A^2
25.98/8.49	   A^2 -> H(f(c), f(c))
25.98/8.49	   A^2 -> H(f(d), f(d))
25.98/8.49	   A^2 -> H(U1(e, c), f(d))
25.98/8.49	   A^2 -> H(U1(k, e), f(b))
25.98/8.49	   A^2 -> H(U1(k, c), U1(b, b))
25.98/8.49	   A^2 -> H(U1(k, c), f(c))
25.98/8.49	   A^2 -> H(U1(k, c), f(d))
25.98/8.49	   A^2 -> H(U1(c, e), U1(b, b))
25.98/8.49	   A^2 -> H(U1(c, e), f(c))
25.98/8.49	   A^2 -> H(U1(c, e), f(d))
25.98/8.49	   A^2 -> H(U1(c, k), U1(b, b))
25.98/8.49	   A^2 -> H(U1(c, k), f(c))
25.98/8.49	   A^2 -> H(U1(c, k), f(d))
25.98/8.49	   A^2 -> H(U1(c, c), U1(c, b))
25.98/8.49	   A^2 -> H(U1(c, c), U1(d, b))
25.98/8.49	   A^2 -> H(U1(c, c), U1(b, c))
25.98/8.49	   A^2 -> H(U1(c, c), U1(b, d))
25.98/8.49	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.49	   A^2 -> H(U1(c, c), f(e))
25.98/8.49	   A^2 -> H(U1(c, c), f(k))
25.98/8.49	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.49	   A^2 -> H(e, f(b))
25.98/8.49	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.49	   A^2 -> H(U1(e, e), f(c))
25.98/8.49	   A^2 -> H(U1(e, e), f(d))
25.98/8.49	   A^2 -> H(f(e), U1(c, b))
25.98/8.49	   A^2 -> H(f(e), U1(d, b))
25.98/8.49	   A^2 -> H(f(e), U1(b, c))
25.98/8.49	   A^2 -> H(f(e), U1(b, d))
25.98/8.49	   A^2 -> H(f(e), U1(c, c))
25.98/8.49	   A^2 -> H(f(e), f(e))
25.98/8.49	   A^2 -> H(f(e), f(k))
25.98/8.49	   A^2 -> H(f(e), U1(d, d))
25.98/8.49	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.49	   A^2 -> H(U1(k, k), f(c))
25.98/8.49	   A^2 -> H(U1(k, k), f(d))
25.98/8.49	   A^2 -> H(f(k), U1(c, b))
25.98/8.49	   A^2 -> H(f(k), U1(d, b))
25.98/8.49	   A^2 -> H(f(k), U1(b, c))
25.98/8.49	   A^2 -> H(f(k), U1(b, d))
25.98/8.49	   A^2 -> H(f(k), U1(c, c))
25.98/8.49	   A^2 -> H(f(k), f(e))
25.98/8.49	   A^2 -> H(f(k), f(k))
25.98/8.49	   A^2 -> H(f(k), U1(d, d))
25.98/8.49	   A^2 -> H(f(c), U1(e, b))
25.98/8.49	   A^2 -> H(f(c), U1(k, b))
25.98/8.49	   A^2 -> H(f(c), U1(c, d))
25.98/8.49	   A^2 -> H(f(c), U1(d, c))
25.98/8.49	   A^2 -> H(f(c), U1(b, e))
25.98/8.49	   A^2 -> H(f(c), U1(b, k))
25.98/8.49	   A^2 -> H(f(c), U1(k, d))
25.98/8.49	   A^2 -> H(f(c), U1(d, k))
25.98/8.49	   A^2 -> H(f(c), U1(k, k))
25.98/8.49	   A^2 -> H(U1(k, k), f(b))
25.98/8.49	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.49	   A^2 -> H(U1(k, d), f(c))
25.98/8.49	   A^2 -> H(U1(k, d), f(d))
25.98/8.49	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.49	   A^2 -> H(U1(d, k), f(c))
25.98/8.49	   A^2 -> H(U1(d, k), f(d))
25.98/8.49	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.49	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.49	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.49	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.49	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.49	   A^2 -> H(U1(d, d), f(e))
25.98/8.49	   A^2 -> H(U1(d, d), f(k))
25.98/8.49	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.49	   A^2 -> H(f(d), U1(e, b))
25.98/8.49	   A^2 -> H(f(d), U1(k, b))
25.98/8.49	   A^2 -> H(f(d), U1(c, d))
25.98/8.49	   A^2 -> H(f(d), U1(d, c))
25.98/8.49	   A^2 -> H(f(d), U1(b, e))
25.98/8.49	   A^2 -> H(f(d), U1(b, k))
25.98/8.49	   A^2 -> H(f(d), U1(e, c))
25.98/8.49	   A^2 -> H(f(d), U1(k, c))
25.98/8.49	   A^2 -> H(f(d), U1(c, e))
25.98/8.49	   A^2 -> H(f(d), U1(c, k))
25.98/8.49	   A^2 -> H(f(d), U1(e, e))
25.98/8.49	   A^2 -> H(f(d), U1(k, k))
25.98/8.49	   A^2 -> H(f(a), b)
25.98/8.49	   A^2 -> H(f(a), U1(e, d))
25.98/8.49	   A^2 -> H(f(a), U1(d, e))
25.98/8.49	   A^2 -> H(f(c), U1(e, c))
25.98/8.49	   A^2 -> H(f(c), U1(k, c))
25.98/8.49	   A^2 -> H(f(c), U1(c, e))
25.98/8.49	   A^2 -> H(f(c), U1(c, k))
25.98/8.49	   A^2 -> H(f(a), c)
25.98/8.49	   A^2 -> H(f(a), U1(e, k))
25.98/8.49	   A^2 -> H(f(a), U1(k, e))
25.98/8.49	   A^2 -> H(f(c), U1(e, e))
25.98/8.49	   A^2 -> H(f(a), e)
25.98/8.49	   A^2 -> H(f(d), U1(k, d))
25.98/8.49	   A^2 -> H(f(d), U1(d, k))
25.98/8.49	   A^2 -> H(f(a), U1(k, k))
25.98/8.49	   A^2 -> H(d, f(b))
25.98/8.49	   A^2 -> H(a, U1(b, b))
25.98/8.49	   A^2 -> H(a, f(c))
25.98/8.49	   A^2 -> H(a, f(d))
25.98/8.49	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.49	   A^2 -> H(U1(e, d), f(c))
25.98/8.49	   A^2 -> H(U1(e, d), f(d))
25.98/8.49	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.49	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.49	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.49	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.49	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.49	   A^2 -> H(U1(e, a), f(e))
25.98/8.49	   A^2 -> H(U1(e, a), f(k))
25.98/8.49	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.49	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.49	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.49	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.49	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.49	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.49	   A^2 -> H(U1(k, a), f(e))
25.98/8.49	   A^2 -> H(U1(k, a), f(k))
25.98/8.49	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.49	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.49	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.49	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.49	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.49	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.49	   A^2 -> H(U1(c, d), f(e))
25.98/8.49	   A^2 -> H(U1(c, d), f(k))
25.98/8.49	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.49	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.49	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.49	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.49	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.49	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.49	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.49	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.49	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.49	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.49	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.49	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.49	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.49	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.49	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.49	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.49	   A^2 -> H(U1(d, e), f(c))
25.98/8.49	   A^2 -> H(U1(d, e), f(d))
25.98/8.49	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.49	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.49	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.49	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.49	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.49	   A^2 -> H(U1(d, c), f(e))
25.98/8.49	   A^2 -> H(U1(d, c), f(k))
25.98/8.49	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.49	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.49	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.49	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.49	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.49	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.49	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.49	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.49	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.49	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.49	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.49	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.49	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.49	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.49	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.49	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.49	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.49	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.49	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.49	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.49	   A^2 -> H(U1(a, e), f(e))
25.98/8.49	   A^2 -> H(U1(a, e), f(k))
25.98/8.49	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.49	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.49	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.49	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.49	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.49	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.49	   A^2 -> H(U1(a, k), f(e))
25.98/8.49	   A^2 -> H(U1(a, k), f(k))
25.98/8.49	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.49	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.49	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.49	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.49	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.49	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.49	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.49	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.49	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.49	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.49	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.49	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.49	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.49	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.49	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.49	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.49	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.49	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.49	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.49	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.49	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.49	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.49	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.49	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.49	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.49	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.49	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.49	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.49	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.49	   A^2 -> H(U1(a, a), b)
25.98/8.49	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.49	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.49	   A^2 -> H(U1(a, a), c)
25.98/8.49	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.49	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.49	   A^2 -> H(U1(a, a), e)
25.98/8.49	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.49	   A^2 -> H(k, f(b))
25.98/8.49	   A^2 -> H(c, U1(b, b))
25.98/8.49	   A^2 -> H(c, f(c))
25.98/8.49	   A^2 -> H(c, f(d))
25.98/8.49	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.49	   A^2 -> H(U1(e, k), f(c))
25.98/8.49	   A^2 -> H(U1(e, k), f(d))
25.98/8.49	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.49	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.49	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.49	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.49	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.49	   A^2 -> H(U1(e, c), f(e))
25.98/8.49	   A^2 -> H(U1(e, c), f(k))
25.98/8.49	
25.98/8.49	The TRS R consists of the following rules:
25.98/8.49	
25.98/8.49	   f(x) -> U1(x, x)
25.98/8.49	   U1(e, x) -> x
25.98/8.49	   a -> c
25.98/8.49	   a -> d
25.98/8.49	   b -> c
25.98/8.49	   b -> d
25.98/8.49	   d -> k
25.98/8.49	   c -> e
25.98/8.49	   c -> k
25.98/8.49	
25.98/8.49	Q is empty.
25.98/8.49	We have to consider all minimal (P,Q,R)-chains.
25.98/8.49	----------------------------------------
25.98/8.49	
25.98/8.49	(363) TransformationProof (EQUIVALENT)
25.98/8.49	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), f(d)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.49	
25.98/8.49	   (A^2 -> H(c, f(d)),A^2 -> H(c, f(d)))
25.98/8.49	   (A^2 -> H(U1(e, e), f(d)),A^2 -> H(U1(e, e), f(d)))
25.98/8.49	   (A^2 -> H(U1(e, k), f(d)),A^2 -> H(U1(e, k), f(d)))
25.98/8.49	   (A^2 -> H(U1(e, c), U1(d, d)),A^2 -> H(U1(e, c), U1(d, d)))
25.98/8.49	   (A^2 -> H(U1(e, c), f(k)),A^2 -> H(U1(e, c), f(k)))
25.98/8.49	
25.98/8.49	
25.98/8.49	----------------------------------------
25.98/8.49	
25.98/8.49	(364)
25.98/8.49	Obligation:
25.98/8.49	Q DP problem:
25.98/8.49	The TRS P consists of the following rules:
25.98/8.49	
25.98/8.49	   H(x, x) -> G(x, x, f(k))
25.98/8.49	   G(d, x, x) -> A^2
25.98/8.49	   A^2 -> H(f(c), f(c))
25.98/8.49	   A^2 -> H(f(d), f(d))
25.98/8.49	   A^2 -> H(U1(k, e), f(b))
25.98/8.49	   A^2 -> H(U1(k, c), U1(b, b))
25.98/8.49	   A^2 -> H(U1(k, c), f(c))
25.98/8.49	   A^2 -> H(U1(k, c), f(d))
25.98/8.49	   A^2 -> H(U1(c, e), U1(b, b))
25.98/8.49	   A^2 -> H(U1(c, e), f(c))
25.98/8.49	   A^2 -> H(U1(c, e), f(d))
25.98/8.49	   A^2 -> H(U1(c, k), U1(b, b))
25.98/8.49	   A^2 -> H(U1(c, k), f(c))
25.98/8.49	   A^2 -> H(U1(c, k), f(d))
25.98/8.49	   A^2 -> H(U1(c, c), U1(c, b))
25.98/8.49	   A^2 -> H(U1(c, c), U1(d, b))
25.98/8.49	   A^2 -> H(U1(c, c), U1(b, c))
25.98/8.49	   A^2 -> H(U1(c, c), U1(b, d))
25.98/8.49	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.49	   A^2 -> H(U1(c, c), f(e))
25.98/8.49	   A^2 -> H(U1(c, c), f(k))
25.98/8.49	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.49	   A^2 -> H(e, f(b))
25.98/8.49	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.49	   A^2 -> H(U1(e, e), f(c))
25.98/8.49	   A^2 -> H(U1(e, e), f(d))
25.98/8.49	   A^2 -> H(f(e), U1(c, b))
25.98/8.49	   A^2 -> H(f(e), U1(d, b))
25.98/8.49	   A^2 -> H(f(e), U1(b, c))
25.98/8.49	   A^2 -> H(f(e), U1(b, d))
25.98/8.49	   A^2 -> H(f(e), U1(c, c))
25.98/8.49	   A^2 -> H(f(e), f(e))
25.98/8.49	   A^2 -> H(f(e), f(k))
25.98/8.49	   A^2 -> H(f(e), U1(d, d))
25.98/8.49	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.49	   A^2 -> H(U1(k, k), f(c))
25.98/8.49	   A^2 -> H(U1(k, k), f(d))
25.98/8.49	   A^2 -> H(f(k), U1(c, b))
25.98/8.49	   A^2 -> H(f(k), U1(d, b))
25.98/8.49	   A^2 -> H(f(k), U1(b, c))
25.98/8.49	   A^2 -> H(f(k), U1(b, d))
25.98/8.49	   A^2 -> H(f(k), U1(c, c))
25.98/8.49	   A^2 -> H(f(k), f(e))
25.98/8.49	   A^2 -> H(f(k), f(k))
25.98/8.49	   A^2 -> H(f(k), U1(d, d))
25.98/8.49	   A^2 -> H(f(c), U1(e, b))
25.98/8.49	   A^2 -> H(f(c), U1(k, b))
25.98/8.49	   A^2 -> H(f(c), U1(c, d))
25.98/8.49	   A^2 -> H(f(c), U1(d, c))
25.98/8.49	   A^2 -> H(f(c), U1(b, e))
25.98/8.49	   A^2 -> H(f(c), U1(b, k))
25.98/8.49	   A^2 -> H(f(c), U1(k, d))
25.98/8.49	   A^2 -> H(f(c), U1(d, k))
25.98/8.49	   A^2 -> H(f(c), U1(k, k))
25.98/8.49	   A^2 -> H(U1(k, k), f(b))
25.98/8.49	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.49	   A^2 -> H(U1(k, d), f(c))
25.98/8.49	   A^2 -> H(U1(k, d), f(d))
25.98/8.49	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.49	   A^2 -> H(U1(d, k), f(c))
25.98/8.49	   A^2 -> H(U1(d, k), f(d))
25.98/8.49	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.49	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.49	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.49	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.49	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.49	   A^2 -> H(U1(d, d), f(e))
25.98/8.49	   A^2 -> H(U1(d, d), f(k))
25.98/8.49	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.49	   A^2 -> H(f(d), U1(e, b))
25.98/8.49	   A^2 -> H(f(d), U1(k, b))
25.98/8.49	   A^2 -> H(f(d), U1(c, d))
25.98/8.49	   A^2 -> H(f(d), U1(d, c))
25.98/8.49	   A^2 -> H(f(d), U1(b, e))
25.98/8.49	   A^2 -> H(f(d), U1(b, k))
25.98/8.49	   A^2 -> H(f(d), U1(e, c))
25.98/8.49	   A^2 -> H(f(d), U1(k, c))
25.98/8.49	   A^2 -> H(f(d), U1(c, e))
25.98/8.49	   A^2 -> H(f(d), U1(c, k))
25.98/8.49	   A^2 -> H(f(d), U1(e, e))
25.98/8.49	   A^2 -> H(f(d), U1(k, k))
25.98/8.50	   A^2 -> H(f(a), b)
25.98/8.50	   A^2 -> H(f(a), U1(e, d))
25.98/8.50	   A^2 -> H(f(a), U1(d, e))
25.98/8.50	   A^2 -> H(f(c), U1(e, c))
25.98/8.50	   A^2 -> H(f(c), U1(k, c))
25.98/8.50	   A^2 -> H(f(c), U1(c, e))
25.98/8.50	   A^2 -> H(f(c), U1(c, k))
25.98/8.50	   A^2 -> H(f(a), c)
25.98/8.50	   A^2 -> H(f(a), U1(e, k))
25.98/8.50	   A^2 -> H(f(a), U1(k, e))
25.98/8.50	   A^2 -> H(f(c), U1(e, e))
25.98/8.50	   A^2 -> H(f(a), e)
25.98/8.50	   A^2 -> H(f(d), U1(k, d))
25.98/8.50	   A^2 -> H(f(d), U1(d, k))
25.98/8.50	   A^2 -> H(f(a), U1(k, k))
25.98/8.50	   A^2 -> H(d, f(b))
25.98/8.50	   A^2 -> H(a, U1(b, b))
25.98/8.50	   A^2 -> H(a, f(c))
25.98/8.50	   A^2 -> H(a, f(d))
25.98/8.50	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.50	   A^2 -> H(U1(e, d), f(c))
25.98/8.50	   A^2 -> H(U1(e, d), f(d))
25.98/8.50	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.50	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.50	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.50	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.50	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.50	   A^2 -> H(U1(e, a), f(e))
25.98/8.50	   A^2 -> H(U1(e, a), f(k))
25.98/8.50	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.50	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.50	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.50	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.50	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.50	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.50	   A^2 -> H(U1(k, a), f(e))
25.98/8.50	   A^2 -> H(U1(k, a), f(k))
25.98/8.50	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.50	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.50	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.50	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.50	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.50	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.50	   A^2 -> H(U1(c, d), f(e))
25.98/8.50	   A^2 -> H(U1(c, d), f(k))
25.98/8.50	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.50	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.50	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.50	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.50	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.50	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.50	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.50	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.50	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.50	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.50	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.50	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.50	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.50	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.50	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.50	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.50	   A^2 -> H(U1(d, e), f(c))
25.98/8.50	   A^2 -> H(U1(d, e), f(d))
25.98/8.50	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.50	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.50	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.50	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.50	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.50	   A^2 -> H(U1(d, c), f(e))
25.98/8.50	   A^2 -> H(U1(d, c), f(k))
25.98/8.50	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.50	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.50	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.50	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.50	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.50	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.50	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.50	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.50	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.50	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.50	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.50	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.50	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.50	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.50	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.50	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.50	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.50	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.50	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.50	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.50	   A^2 -> H(U1(a, e), f(e))
25.98/8.50	   A^2 -> H(U1(a, e), f(k))
25.98/8.50	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.50	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.50	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.50	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.50	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.50	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.50	   A^2 -> H(U1(a, k), f(e))
25.98/8.50	   A^2 -> H(U1(a, k), f(k))
25.98/8.50	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.50	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.50	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.50	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.50	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.50	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.50	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.50	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.50	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.50	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.50	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.50	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.50	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.50	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.50	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.50	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.50	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.50	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.50	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.50	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.50	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.50	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.50	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.50	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.50	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.50	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.50	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.50	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.50	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.50	   A^2 -> H(U1(a, a), b)
25.98/8.50	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.50	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.50	   A^2 -> H(U1(a, a), c)
25.98/8.50	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.50	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.50	   A^2 -> H(U1(a, a), e)
25.98/8.50	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.50	   A^2 -> H(k, f(b))
25.98/8.50	   A^2 -> H(c, U1(b, b))
25.98/8.50	   A^2 -> H(c, f(c))
25.98/8.50	   A^2 -> H(c, f(d))
25.98/8.50	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.50	   A^2 -> H(U1(e, k), f(c))
25.98/8.50	   A^2 -> H(U1(e, k), f(d))
25.98/8.50	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.50	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.50	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.50	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.50	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.50	   A^2 -> H(U1(e, c), f(e))
25.98/8.50	   A^2 -> H(U1(e, c), f(k))
25.98/8.50	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.50	
25.98/8.50	The TRS R consists of the following rules:
25.98/8.50	
25.98/8.50	   f(x) -> U1(x, x)
25.98/8.50	   U1(e, x) -> x
25.98/8.50	   a -> c
25.98/8.50	   a -> d
25.98/8.50	   b -> c
25.98/8.50	   b -> d
25.98/8.50	   d -> k
25.98/8.50	   c -> e
25.98/8.50	   c -> k
25.98/8.50	
25.98/8.50	Q is empty.
25.98/8.50	We have to consider all minimal (P,Q,R)-chains.
25.98/8.50	----------------------------------------
25.98/8.50	
25.98/8.50	(365) TransformationProof (EQUIVALENT)
25.98/8.50	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), f(b)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.50	
25.98/8.50	   (A^2 -> H(U1(k, e), U1(b, b)),A^2 -> H(U1(k, e), U1(b, b)))
25.98/8.50	   (A^2 -> H(U1(k, e), f(c)),A^2 -> H(U1(k, e), f(c)))
25.98/8.50	   (A^2 -> H(U1(k, e), f(d)),A^2 -> H(U1(k, e), f(d)))
25.98/8.50	
25.98/8.50	
25.98/8.50	----------------------------------------
25.98/8.50	
25.98/8.50	(366)
25.98/8.50	Obligation:
25.98/8.50	Q DP problem:
25.98/8.50	The TRS P consists of the following rules:
25.98/8.50	
25.98/8.50	   H(x, x) -> G(x, x, f(k))
25.98/8.50	   G(d, x, x) -> A^2
25.98/8.50	   A^2 -> H(f(c), f(c))
25.98/8.50	   A^2 -> H(f(d), f(d))
25.98/8.50	   A^2 -> H(U1(k, c), U1(b, b))
25.98/8.50	   A^2 -> H(U1(k, c), f(c))
25.98/8.50	   A^2 -> H(U1(k, c), f(d))
25.98/8.50	   A^2 -> H(U1(c, e), U1(b, b))
25.98/8.50	   A^2 -> H(U1(c, e), f(c))
25.98/8.50	   A^2 -> H(U1(c, e), f(d))
25.98/8.50	   A^2 -> H(U1(c, k), U1(b, b))
25.98/8.50	   A^2 -> H(U1(c, k), f(c))
25.98/8.50	   A^2 -> H(U1(c, k), f(d))
25.98/8.50	   A^2 -> H(U1(c, c), U1(c, b))
25.98/8.50	   A^2 -> H(U1(c, c), U1(d, b))
25.98/8.50	   A^2 -> H(U1(c, c), U1(b, c))
25.98/8.50	   A^2 -> H(U1(c, c), U1(b, d))
25.98/8.50	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.50	   A^2 -> H(U1(c, c), f(e))
25.98/8.50	   A^2 -> H(U1(c, c), f(k))
25.98/8.50	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.50	   A^2 -> H(e, f(b))
25.98/8.50	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.50	   A^2 -> H(U1(e, e), f(c))
25.98/8.50	   A^2 -> H(U1(e, e), f(d))
25.98/8.50	   A^2 -> H(f(e), U1(c, b))
25.98/8.50	   A^2 -> H(f(e), U1(d, b))
25.98/8.50	   A^2 -> H(f(e), U1(b, c))
25.98/8.50	   A^2 -> H(f(e), U1(b, d))
25.98/8.50	   A^2 -> H(f(e), U1(c, c))
25.98/8.50	   A^2 -> H(f(e), f(e))
25.98/8.50	   A^2 -> H(f(e), f(k))
25.98/8.50	   A^2 -> H(f(e), U1(d, d))
25.98/8.50	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.50	   A^2 -> H(U1(k, k), f(c))
25.98/8.50	   A^2 -> H(U1(k, k), f(d))
25.98/8.50	   A^2 -> H(f(k), U1(c, b))
25.98/8.50	   A^2 -> H(f(k), U1(d, b))
25.98/8.50	   A^2 -> H(f(k), U1(b, c))
25.98/8.50	   A^2 -> H(f(k), U1(b, d))
25.98/8.50	   A^2 -> H(f(k), U1(c, c))
25.98/8.50	   A^2 -> H(f(k), f(e))
25.98/8.50	   A^2 -> H(f(k), f(k))
25.98/8.50	   A^2 -> H(f(k), U1(d, d))
25.98/8.50	   A^2 -> H(f(c), U1(e, b))
25.98/8.50	   A^2 -> H(f(c), U1(k, b))
25.98/8.50	   A^2 -> H(f(c), U1(c, d))
25.98/8.50	   A^2 -> H(f(c), U1(d, c))
25.98/8.50	   A^2 -> H(f(c), U1(b, e))
25.98/8.50	   A^2 -> H(f(c), U1(b, k))
25.98/8.50	   A^2 -> H(f(c), U1(k, d))
25.98/8.50	   A^2 -> H(f(c), U1(d, k))
25.98/8.50	   A^2 -> H(f(c), U1(k, k))
25.98/8.50	   A^2 -> H(U1(k, k), f(b))
25.98/8.50	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.50	   A^2 -> H(U1(k, d), f(c))
25.98/8.50	   A^2 -> H(U1(k, d), f(d))
25.98/8.50	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.50	   A^2 -> H(U1(d, k), f(c))
25.98/8.50	   A^2 -> H(U1(d, k), f(d))
25.98/8.50	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.50	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.50	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.50	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.50	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.50	   A^2 -> H(U1(d, d), f(e))
25.98/8.50	   A^2 -> H(U1(d, d), f(k))
25.98/8.50	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.50	   A^2 -> H(f(d), U1(e, b))
25.98/8.50	   A^2 -> H(f(d), U1(k, b))
25.98/8.50	   A^2 -> H(f(d), U1(c, d))
25.98/8.50	   A^2 -> H(f(d), U1(d, c))
25.98/8.50	   A^2 -> H(f(d), U1(b, e))
25.98/8.50	   A^2 -> H(f(d), U1(b, k))
25.98/8.50	   A^2 -> H(f(d), U1(e, c))
25.98/8.50	   A^2 -> H(f(d), U1(k, c))
25.98/8.50	   A^2 -> H(f(d), U1(c, e))
25.98/8.50	   A^2 -> H(f(d), U1(c, k))
25.98/8.50	   A^2 -> H(f(d), U1(e, e))
25.98/8.50	   A^2 -> H(f(d), U1(k, k))
25.98/8.50	   A^2 -> H(f(a), b)
25.98/8.50	   A^2 -> H(f(a), U1(e, d))
25.98/8.50	   A^2 -> H(f(a), U1(d, e))
25.98/8.50	   A^2 -> H(f(c), U1(e, c))
25.98/8.50	   A^2 -> H(f(c), U1(k, c))
25.98/8.50	   A^2 -> H(f(c), U1(c, e))
25.98/8.50	   A^2 -> H(f(c), U1(c, k))
25.98/8.50	   A^2 -> H(f(a), c)
25.98/8.50	   A^2 -> H(f(a), U1(e, k))
25.98/8.50	   A^2 -> H(f(a), U1(k, e))
25.98/8.50	   A^2 -> H(f(c), U1(e, e))
25.98/8.50	   A^2 -> H(f(a), e)
25.98/8.50	   A^2 -> H(f(d), U1(k, d))
25.98/8.50	   A^2 -> H(f(d), U1(d, k))
25.98/8.50	   A^2 -> H(f(a), U1(k, k))
25.98/8.50	   A^2 -> H(d, f(b))
25.98/8.50	   A^2 -> H(a, U1(b, b))
25.98/8.50	   A^2 -> H(a, f(c))
25.98/8.50	   A^2 -> H(a, f(d))
25.98/8.50	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.50	   A^2 -> H(U1(e, d), f(c))
25.98/8.50	   A^2 -> H(U1(e, d), f(d))
25.98/8.50	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.50	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.50	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.50	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.50	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.50	   A^2 -> H(U1(e, a), f(e))
25.98/8.50	   A^2 -> H(U1(e, a), f(k))
25.98/8.50	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.50	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.50	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.50	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.50	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.50	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.50	   A^2 -> H(U1(k, a), f(e))
25.98/8.50	   A^2 -> H(U1(k, a), f(k))
25.98/8.50	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.50	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.50	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.50	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.50	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.50	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.50	   A^2 -> H(U1(c, d), f(e))
25.98/8.50	   A^2 -> H(U1(c, d), f(k))
25.98/8.50	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.50	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.50	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.50	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.50	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.50	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.50	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.50	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.50	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.50	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.50	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.51	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.51	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.51	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.51	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.51	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.51	   A^2 -> H(U1(d, e), f(c))
25.98/8.51	   A^2 -> H(U1(d, e), f(d))
25.98/8.51	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.51	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.51	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.51	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.51	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.51	   A^2 -> H(U1(d, c), f(e))
25.98/8.51	   A^2 -> H(U1(d, c), f(k))
25.98/8.51	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.51	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.51	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.51	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.51	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.51	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.51	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.51	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.51	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.51	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.51	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.51	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.51	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.51	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.51	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.51	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.51	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.51	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.51	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.51	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.51	   A^2 -> H(U1(a, e), f(e))
25.98/8.51	   A^2 -> H(U1(a, e), f(k))
25.98/8.51	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.51	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.51	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.51	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.51	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.51	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.51	   A^2 -> H(U1(a, k), f(e))
25.98/8.51	   A^2 -> H(U1(a, k), f(k))
25.98/8.51	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.51	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.51	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.51	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.51	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.51	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.51	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.51	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.51	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.51	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.51	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.51	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.51	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.51	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.51	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.51	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.51	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.51	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.51	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.51	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.51	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.51	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.51	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.51	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.51	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.51	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.51	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.51	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.51	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.51	   A^2 -> H(U1(a, a), b)
25.98/8.51	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.51	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.51	   A^2 -> H(U1(a, a), c)
25.98/8.51	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.51	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.51	   A^2 -> H(U1(a, a), e)
25.98/8.51	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.51	   A^2 -> H(k, f(b))
25.98/8.51	   A^2 -> H(c, U1(b, b))
25.98/8.51	   A^2 -> H(c, f(c))
25.98/8.51	   A^2 -> H(c, f(d))
25.98/8.51	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.51	   A^2 -> H(U1(e, k), f(c))
25.98/8.51	   A^2 -> H(U1(e, k), f(d))
25.98/8.51	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.51	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.51	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.51	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.51	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.51	   A^2 -> H(U1(e, c), f(e))
25.98/8.51	   A^2 -> H(U1(e, c), f(k))
25.98/8.51	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.51	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.51	   A^2 -> H(U1(k, e), f(c))
25.98/8.51	   A^2 -> H(U1(k, e), f(d))
25.98/8.51	
25.98/8.51	The TRS R consists of the following rules:
25.98/8.51	
25.98/8.51	   f(x) -> U1(x, x)
25.98/8.51	   U1(e, x) -> x
25.98/8.51	   a -> c
25.98/8.51	   a -> d
25.98/8.51	   b -> c
25.98/8.51	   b -> d
25.98/8.51	   d -> k
25.98/8.51	   c -> e
25.98/8.51	   c -> k
25.98/8.51	
25.98/8.51	Q is empty.
25.98/8.51	We have to consider all minimal (P,Q,R)-chains.
25.98/8.51	----------------------------------------
25.98/8.51	
25.98/8.51	(367) TransformationProof (EQUIVALENT)
25.98/8.51	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.51	
25.98/8.51	   (A^2 -> H(U1(k, e), U1(b, b)),A^2 -> H(U1(k, e), U1(b, b)))
25.98/8.51	   (A^2 -> H(U1(k, k), U1(b, b)),A^2 -> H(U1(k, k), U1(b, b)))
25.98/8.51	   (A^2 -> H(U1(k, c), U1(c, b)),A^2 -> H(U1(k, c), U1(c, b)))
25.98/8.51	   (A^2 -> H(U1(k, c), U1(d, b)),A^2 -> H(U1(k, c), U1(d, b)))
25.98/8.51	   (A^2 -> H(U1(k, c), U1(b, c)),A^2 -> H(U1(k, c), U1(b, c)))
25.98/8.51	   (A^2 -> H(U1(k, c), U1(b, d)),A^2 -> H(U1(k, c), U1(b, d)))
25.98/8.51	
25.98/8.51	
25.98/8.51	----------------------------------------
25.98/8.51	
25.98/8.51	(368)
25.98/8.51	Obligation:
25.98/8.51	Q DP problem:
25.98/8.51	The TRS P consists of the following rules:
25.98/8.51	
25.98/8.51	   H(x, x) -> G(x, x, f(k))
25.98/8.51	   G(d, x, x) -> A^2
25.98/8.51	   A^2 -> H(f(c), f(c))
25.98/8.51	   A^2 -> H(f(d), f(d))
25.98/8.51	   A^2 -> H(U1(k, c), f(c))
25.98/8.51	   A^2 -> H(U1(k, c), f(d))
25.98/8.51	   A^2 -> H(U1(c, e), U1(b, b))
25.98/8.51	   A^2 -> H(U1(c, e), f(c))
25.98/8.51	   A^2 -> H(U1(c, e), f(d))
25.98/8.51	   A^2 -> H(U1(c, k), U1(b, b))
25.98/8.51	   A^2 -> H(U1(c, k), f(c))
25.98/8.51	   A^2 -> H(U1(c, k), f(d))
25.98/8.51	   A^2 -> H(U1(c, c), U1(c, b))
25.98/8.51	   A^2 -> H(U1(c, c), U1(d, b))
25.98/8.51	   A^2 -> H(U1(c, c), U1(b, c))
25.98/8.51	   A^2 -> H(U1(c, c), U1(b, d))
25.98/8.51	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.51	   A^2 -> H(U1(c, c), f(e))
25.98/8.51	   A^2 -> H(U1(c, c), f(k))
25.98/8.51	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.51	   A^2 -> H(e, f(b))
25.98/8.51	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.51	   A^2 -> H(U1(e, e), f(c))
25.98/8.51	   A^2 -> H(U1(e, e), f(d))
25.98/8.51	   A^2 -> H(f(e), U1(c, b))
25.98/8.51	   A^2 -> H(f(e), U1(d, b))
25.98/8.51	   A^2 -> H(f(e), U1(b, c))
25.98/8.51	   A^2 -> H(f(e), U1(b, d))
25.98/8.51	   A^2 -> H(f(e), U1(c, c))
25.98/8.51	   A^2 -> H(f(e), f(e))
25.98/8.51	   A^2 -> H(f(e), f(k))
25.98/8.51	   A^2 -> H(f(e), U1(d, d))
25.98/8.51	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.51	   A^2 -> H(U1(k, k), f(c))
25.98/8.51	   A^2 -> H(U1(k, k), f(d))
25.98/8.51	   A^2 -> H(f(k), U1(c, b))
25.98/8.51	   A^2 -> H(f(k), U1(d, b))
25.98/8.51	   A^2 -> H(f(k), U1(b, c))
25.98/8.51	   A^2 -> H(f(k), U1(b, d))
25.98/8.51	   A^2 -> H(f(k), U1(c, c))
25.98/8.51	   A^2 -> H(f(k), f(e))
25.98/8.51	   A^2 -> H(f(k), f(k))
25.98/8.51	   A^2 -> H(f(k), U1(d, d))
25.98/8.51	   A^2 -> H(f(c), U1(e, b))
25.98/8.51	   A^2 -> H(f(c), U1(k, b))
25.98/8.51	   A^2 -> H(f(c), U1(c, d))
25.98/8.51	   A^2 -> H(f(c), U1(d, c))
25.98/8.51	   A^2 -> H(f(c), U1(b, e))
25.98/8.51	   A^2 -> H(f(c), U1(b, k))
25.98/8.51	   A^2 -> H(f(c), U1(k, d))
25.98/8.51	   A^2 -> H(f(c), U1(d, k))
25.98/8.51	   A^2 -> H(f(c), U1(k, k))
25.98/8.51	   A^2 -> H(U1(k, k), f(b))
25.98/8.51	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.51	   A^2 -> H(U1(k, d), f(c))
25.98/8.51	   A^2 -> H(U1(k, d), f(d))
25.98/8.51	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.51	   A^2 -> H(U1(d, k), f(c))
25.98/8.51	   A^2 -> H(U1(d, k), f(d))
25.98/8.51	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.51	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.51	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.51	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.51	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.51	   A^2 -> H(U1(d, d), f(e))
25.98/8.51	   A^2 -> H(U1(d, d), f(k))
25.98/8.51	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.51	   A^2 -> H(f(d), U1(e, b))
25.98/8.51	   A^2 -> H(f(d), U1(k, b))
25.98/8.51	   A^2 -> H(f(d), U1(c, d))
25.98/8.51	   A^2 -> H(f(d), U1(d, c))
25.98/8.51	   A^2 -> H(f(d), U1(b, e))
25.98/8.51	   A^2 -> H(f(d), U1(b, k))
25.98/8.51	   A^2 -> H(f(d), U1(e, c))
25.98/8.51	   A^2 -> H(f(d), U1(k, c))
25.98/8.51	   A^2 -> H(f(d), U1(c, e))
25.98/8.51	   A^2 -> H(f(d), U1(c, k))
25.98/8.51	   A^2 -> H(f(d), U1(e, e))
25.98/8.51	   A^2 -> H(f(d), U1(k, k))
25.98/8.51	   A^2 -> H(f(a), b)
25.98/8.51	   A^2 -> H(f(a), U1(e, d))
25.98/8.51	   A^2 -> H(f(a), U1(d, e))
25.98/8.51	   A^2 -> H(f(c), U1(e, c))
25.98/8.51	   A^2 -> H(f(c), U1(k, c))
25.98/8.51	   A^2 -> H(f(c), U1(c, e))
25.98/8.51	   A^2 -> H(f(c), U1(c, k))
25.98/8.51	   A^2 -> H(f(a), c)
25.98/8.51	   A^2 -> H(f(a), U1(e, k))
25.98/8.51	   A^2 -> H(f(a), U1(k, e))
25.98/8.51	   A^2 -> H(f(c), U1(e, e))
25.98/8.51	   A^2 -> H(f(a), e)
25.98/8.51	   A^2 -> H(f(d), U1(k, d))
25.98/8.51	   A^2 -> H(f(d), U1(d, k))
25.98/8.51	   A^2 -> H(f(a), U1(k, k))
25.98/8.51	   A^2 -> H(d, f(b))
25.98/8.51	   A^2 -> H(a, U1(b, b))
25.98/8.51	   A^2 -> H(a, f(c))
25.98/8.51	   A^2 -> H(a, f(d))
25.98/8.51	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.51	   A^2 -> H(U1(e, d), f(c))
25.98/8.51	   A^2 -> H(U1(e, d), f(d))
25.98/8.51	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.51	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.51	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.51	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.51	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.51	   A^2 -> H(U1(e, a), f(e))
25.98/8.51	   A^2 -> H(U1(e, a), f(k))
25.98/8.51	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.51	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.51	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.51	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.51	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.51	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.51	   A^2 -> H(U1(k, a), f(e))
25.98/8.51	   A^2 -> H(U1(k, a), f(k))
25.98/8.51	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.51	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.51	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.51	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.51	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.51	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.51	   A^2 -> H(U1(c, d), f(e))
25.98/8.51	   A^2 -> H(U1(c, d), f(k))
25.98/8.51	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.51	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.51	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.51	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.51	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.51	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.51	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.51	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.51	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.51	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.51	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.51	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.51	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.51	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.51	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.51	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.51	   A^2 -> H(U1(d, e), f(c))
25.98/8.51	   A^2 -> H(U1(d, e), f(d))
25.98/8.51	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.51	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.51	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.51	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.51	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.51	   A^2 -> H(U1(d, c), f(e))
25.98/8.51	   A^2 -> H(U1(d, c), f(k))
25.98/8.51	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.51	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.51	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.51	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.51	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.51	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.51	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.51	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.51	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.51	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.51	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.51	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.51	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.51	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.51	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.51	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.51	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.51	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.51	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.51	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.51	   A^2 -> H(U1(a, e), f(e))
25.98/8.51	   A^2 -> H(U1(a, e), f(k))
25.98/8.51	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.51	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.51	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.51	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.51	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.51	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.51	   A^2 -> H(U1(a, k), f(e))
25.98/8.51	   A^2 -> H(U1(a, k), f(k))
25.98/8.51	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.51	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.51	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.51	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.51	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.51	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.51	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.51	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.51	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.51	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.51	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.51	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.51	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.51	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.51	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.51	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.51	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.51	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.51	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.51	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.51	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.51	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.51	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.51	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.51	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.51	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.51	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.51	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.51	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.51	   A^2 -> H(U1(a, a), b)
25.98/8.51	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.51	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.51	   A^2 -> H(U1(a, a), c)
25.98/8.51	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.51	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.51	   A^2 -> H(U1(a, a), e)
25.98/8.51	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.51	   A^2 -> H(k, f(b))
25.98/8.51	   A^2 -> H(c, U1(b, b))
25.98/8.51	   A^2 -> H(c, f(c))
25.98/8.51	   A^2 -> H(c, f(d))
25.98/8.51	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.51	   A^2 -> H(U1(e, k), f(c))
25.98/8.51	   A^2 -> H(U1(e, k), f(d))
25.98/8.51	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.51	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.51	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.51	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.51	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.51	   A^2 -> H(U1(e, c), f(e))
25.98/8.51	   A^2 -> H(U1(e, c), f(k))
25.98/8.51	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.51	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.51	   A^2 -> H(U1(k, e), f(c))
25.98/8.51	   A^2 -> H(U1(k, e), f(d))
25.98/8.51	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.51	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.51	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.51	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.51	
25.98/8.51	The TRS R consists of the following rules:
25.98/8.51	
25.98/8.51	   f(x) -> U1(x, x)
25.98/8.51	   U1(e, x) -> x
25.98/8.51	   a -> c
25.98/8.51	   a -> d
25.98/8.51	   b -> c
25.98/8.51	   b -> d
25.98/8.51	   d -> k
25.98/8.51	   c -> e
25.98/8.51	   c -> k
25.98/8.51	
25.98/8.51	Q is empty.
25.98/8.51	We have to consider all minimal (P,Q,R)-chains.
25.98/8.51	----------------------------------------
25.98/8.51	
25.98/8.51	(369) TransformationProof (EQUIVALENT)
25.98/8.51	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), f(c)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.51	
25.98/8.51	   (A^2 -> H(U1(k, e), f(c)),A^2 -> H(U1(k, e), f(c)))
25.98/8.51	   (A^2 -> H(U1(k, k), f(c)),A^2 -> H(U1(k, k), f(c)))
25.98/8.51	   (A^2 -> H(U1(k, c), U1(c, c)),A^2 -> H(U1(k, c), U1(c, c)))
25.98/8.51	   (A^2 -> H(U1(k, c), f(e)),A^2 -> H(U1(k, c), f(e)))
25.98/8.51	   (A^2 -> H(U1(k, c), f(k)),A^2 -> H(U1(k, c), f(k)))
25.98/8.51	
25.98/8.51	
25.98/8.51	----------------------------------------
25.98/8.51	
25.98/8.51	(370)
25.98/8.51	Obligation:
25.98/8.51	Q DP problem:
25.98/8.51	The TRS P consists of the following rules:
25.98/8.51	
25.98/8.51	   H(x, x) -> G(x, x, f(k))
25.98/8.51	   G(d, x, x) -> A^2
25.98/8.51	   A^2 -> H(f(c), f(c))
25.98/8.51	   A^2 -> H(f(d), f(d))
25.98/8.51	   A^2 -> H(U1(k, c), f(d))
25.98/8.51	   A^2 -> H(U1(c, e), U1(b, b))
25.98/8.51	   A^2 -> H(U1(c, e), f(c))
25.98/8.51	   A^2 -> H(U1(c, e), f(d))
25.98/8.51	   A^2 -> H(U1(c, k), U1(b, b))
25.98/8.51	   A^2 -> H(U1(c, k), f(c))
25.98/8.51	   A^2 -> H(U1(c, k), f(d))
25.98/8.51	   A^2 -> H(U1(c, c), U1(c, b))
25.98/8.51	   A^2 -> H(U1(c, c), U1(d, b))
25.98/8.51	   A^2 -> H(U1(c, c), U1(b, c))
25.98/8.51	   A^2 -> H(U1(c, c), U1(b, d))
25.98/8.51	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.51	   A^2 -> H(U1(c, c), f(e))
25.98/8.51	   A^2 -> H(U1(c, c), f(k))
25.98/8.51	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.51	   A^2 -> H(e, f(b))
25.98/8.51	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.51	   A^2 -> H(U1(e, e), f(c))
25.98/8.51	   A^2 -> H(U1(e, e), f(d))
25.98/8.51	   A^2 -> H(f(e), U1(c, b))
25.98/8.51	   A^2 -> H(f(e), U1(d, b))
25.98/8.51	   A^2 -> H(f(e), U1(b, c))
25.98/8.51	   A^2 -> H(f(e), U1(b, d))
25.98/8.51	   A^2 -> H(f(e), U1(c, c))
25.98/8.51	   A^2 -> H(f(e), f(e))
25.98/8.51	   A^2 -> H(f(e), f(k))
25.98/8.51	   A^2 -> H(f(e), U1(d, d))
25.98/8.51	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.51	   A^2 -> H(U1(k, k), f(c))
25.98/8.51	   A^2 -> H(U1(k, k), f(d))
25.98/8.51	   A^2 -> H(f(k), U1(c, b))
25.98/8.51	   A^2 -> H(f(k), U1(d, b))
25.98/8.51	   A^2 -> H(f(k), U1(b, c))
25.98/8.51	   A^2 -> H(f(k), U1(b, d))
25.98/8.51	   A^2 -> H(f(k), U1(c, c))
25.98/8.51	   A^2 -> H(f(k), f(e))
25.98/8.51	   A^2 -> H(f(k), f(k))
25.98/8.51	   A^2 -> H(f(k), U1(d, d))
25.98/8.51	   A^2 -> H(f(c), U1(e, b))
25.98/8.51	   A^2 -> H(f(c), U1(k, b))
25.98/8.51	   A^2 -> H(f(c), U1(c, d))
25.98/8.51	   A^2 -> H(f(c), U1(d, c))
25.98/8.51	   A^2 -> H(f(c), U1(b, e))
25.98/8.51	   A^2 -> H(f(c), U1(b, k))
25.98/8.51	   A^2 -> H(f(c), U1(k, d))
25.98/8.51	   A^2 -> H(f(c), U1(d, k))
25.98/8.51	   A^2 -> H(f(c), U1(k, k))
25.98/8.51	   A^2 -> H(U1(k, k), f(b))
25.98/8.51	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.51	   A^2 -> H(U1(k, d), f(c))
25.98/8.51	   A^2 -> H(U1(k, d), f(d))
25.98/8.51	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.51	   A^2 -> H(U1(d, k), f(c))
25.98/8.51	   A^2 -> H(U1(d, k), f(d))
25.98/8.51	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.51	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.51	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.51	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.51	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.51	   A^2 -> H(U1(d, d), f(e))
25.98/8.51	   A^2 -> H(U1(d, d), f(k))
25.98/8.51	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.51	   A^2 -> H(f(d), U1(e, b))
25.98/8.51	   A^2 -> H(f(d), U1(k, b))
25.98/8.51	   A^2 -> H(f(d), U1(c, d))
25.98/8.51	   A^2 -> H(f(d), U1(d, c))
25.98/8.51	   A^2 -> H(f(d), U1(b, e))
25.98/8.51	   A^2 -> H(f(d), U1(b, k))
25.98/8.51	   A^2 -> H(f(d), U1(e, c))
25.98/8.51	   A^2 -> H(f(d), U1(k, c))
25.98/8.51	   A^2 -> H(f(d), U1(c, e))
25.98/8.51	   A^2 -> H(f(d), U1(c, k))
25.98/8.51	   A^2 -> H(f(d), U1(e, e))
25.98/8.51	   A^2 -> H(f(d), U1(k, k))
25.98/8.51	   A^2 -> H(f(a), b)
25.98/8.51	   A^2 -> H(f(a), U1(e, d))
25.98/8.51	   A^2 -> H(f(a), U1(d, e))
25.98/8.51	   A^2 -> H(f(c), U1(e, c))
25.98/8.51	   A^2 -> H(f(c), U1(k, c))
25.98/8.51	   A^2 -> H(f(c), U1(c, e))
25.98/8.51	   A^2 -> H(f(c), U1(c, k))
25.98/8.51	   A^2 -> H(f(a), c)
25.98/8.51	   A^2 -> H(f(a), U1(e, k))
25.98/8.51	   A^2 -> H(f(a), U1(k, e))
25.98/8.51	   A^2 -> H(f(c), U1(e, e))
25.98/8.51	   A^2 -> H(f(a), e)
25.98/8.51	   A^2 -> H(f(d), U1(k, d))
25.98/8.51	   A^2 -> H(f(d), U1(d, k))
25.98/8.51	   A^2 -> H(f(a), U1(k, k))
25.98/8.51	   A^2 -> H(d, f(b))
25.98/8.51	   A^2 -> H(a, U1(b, b))
25.98/8.51	   A^2 -> H(a, f(c))
25.98/8.51	   A^2 -> H(a, f(d))
25.98/8.51	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.51	   A^2 -> H(U1(e, d), f(c))
25.98/8.51	   A^2 -> H(U1(e, d), f(d))
25.98/8.51	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.51	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.51	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.51	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.51	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.51	   A^2 -> H(U1(e, a), f(e))
25.98/8.51	   A^2 -> H(U1(e, a), f(k))
25.98/8.51	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.51	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.51	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.51	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.51	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.51	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.51	   A^2 -> H(U1(k, a), f(e))
25.98/8.51	   A^2 -> H(U1(k, a), f(k))
25.98/8.51	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.51	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.51	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.51	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.51	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.51	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.51	   A^2 -> H(U1(c, d), f(e))
25.98/8.51	   A^2 -> H(U1(c, d), f(k))
25.98/8.51	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.51	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.51	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.51	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.51	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.51	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.51	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.51	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.51	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.51	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.51	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.51	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.51	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.51	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.51	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.51	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.51	   A^2 -> H(U1(d, e), f(c))
25.98/8.51	   A^2 -> H(U1(d, e), f(d))
25.98/8.51	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.51	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.51	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.51	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.51	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.51	   A^2 -> H(U1(d, c), f(e))
25.98/8.51	   A^2 -> H(U1(d, c), f(k))
25.98/8.51	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.51	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.51	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.51	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.51	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.51	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.51	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.51	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.51	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.51	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.51	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.51	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.51	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.51	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.51	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.51	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.51	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.51	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.51	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.51	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.51	   A^2 -> H(U1(a, e), f(e))
25.98/8.51	   A^2 -> H(U1(a, e), f(k))
25.98/8.51	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.51	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.51	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.51	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.51	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.51	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.51	   A^2 -> H(U1(a, k), f(e))
25.98/8.51	   A^2 -> H(U1(a, k), f(k))
25.98/8.51	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.51	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.51	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.51	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.51	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.51	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.51	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.51	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.51	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.51	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.51	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.51	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.51	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.51	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.51	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.51	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.51	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.51	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.51	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.51	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.51	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.51	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.51	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.51	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.51	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.51	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.51	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.51	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.51	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.51	   A^2 -> H(U1(a, a), b)
25.98/8.51	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.51	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.51	   A^2 -> H(U1(a, a), c)
25.98/8.51	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.51	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.51	   A^2 -> H(U1(a, a), e)
25.98/8.51	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.51	   A^2 -> H(k, f(b))
25.98/8.51	   A^2 -> H(c, U1(b, b))
25.98/8.51	   A^2 -> H(c, f(c))
25.98/8.51	   A^2 -> H(c, f(d))
25.98/8.51	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.51	   A^2 -> H(U1(e, k), f(c))
25.98/8.51	   A^2 -> H(U1(e, k), f(d))
25.98/8.51	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.51	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.51	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.51	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.51	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.51	   A^2 -> H(U1(e, c), f(e))
25.98/8.51	   A^2 -> H(U1(e, c), f(k))
25.98/8.51	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.51	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.51	   A^2 -> H(U1(k, e), f(c))
25.98/8.51	   A^2 -> H(U1(k, e), f(d))
25.98/8.51	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.51	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.51	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.51	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.51	   A^2 -> H(U1(k, c), U1(c, c))
25.98/8.51	   A^2 -> H(U1(k, c), f(e))
25.98/8.51	   A^2 -> H(U1(k, c), f(k))
25.98/8.51	
25.98/8.51	The TRS R consists of the following rules:
25.98/8.51	
25.98/8.51	   f(x) -> U1(x, x)
25.98/8.51	   U1(e, x) -> x
25.98/8.51	   a -> c
25.98/8.51	   a -> d
25.98/8.51	   b -> c
25.98/8.51	   b -> d
25.98/8.51	   d -> k
25.98/8.51	   c -> e
25.98/8.51	   c -> k
25.98/8.51	
25.98/8.51	Q is empty.
25.98/8.51	We have to consider all minimal (P,Q,R)-chains.
25.98/8.51	----------------------------------------
25.98/8.51	
25.98/8.51	(371) TransformationProof (EQUIVALENT)
25.98/8.51	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), f(d)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.51	
25.98/8.51	   (A^2 -> H(U1(k, e), f(d)),A^2 -> H(U1(k, e), f(d)))
25.98/8.51	   (A^2 -> H(U1(k, k), f(d)),A^2 -> H(U1(k, k), f(d)))
25.98/8.51	   (A^2 -> H(U1(k, c), U1(d, d)),A^2 -> H(U1(k, c), U1(d, d)))
25.98/8.51	   (A^2 -> H(U1(k, c), f(k)),A^2 -> H(U1(k, c), f(k)))
25.98/8.51	
25.98/8.51	
25.98/8.51	----------------------------------------
25.98/8.51	
25.98/8.51	(372)
25.98/8.51	Obligation:
25.98/8.51	Q DP problem:
25.98/8.51	The TRS P consists of the following rules:
25.98/8.51	
25.98/8.51	   H(x, x) -> G(x, x, f(k))
25.98/8.51	   G(d, x, x) -> A^2
25.98/8.51	   A^2 -> H(f(c), f(c))
25.98/8.51	   A^2 -> H(f(d), f(d))
25.98/8.51	   A^2 -> H(U1(c, e), U1(b, b))
25.98/8.51	   A^2 -> H(U1(c, e), f(c))
25.98/8.51	   A^2 -> H(U1(c, e), f(d))
25.98/8.51	   A^2 -> H(U1(c, k), U1(b, b))
25.98/8.51	   A^2 -> H(U1(c, k), f(c))
25.98/8.51	   A^2 -> H(U1(c, k), f(d))
25.98/8.51	   A^2 -> H(U1(c, c), U1(c, b))
25.98/8.51	   A^2 -> H(U1(c, c), U1(d, b))
25.98/8.51	   A^2 -> H(U1(c, c), U1(b, c))
25.98/8.51	   A^2 -> H(U1(c, c), U1(b, d))
25.98/8.51	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.51	   A^2 -> H(U1(c, c), f(e))
25.98/8.51	   A^2 -> H(U1(c, c), f(k))
25.98/8.51	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.51	   A^2 -> H(e, f(b))
25.98/8.51	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.51	   A^2 -> H(U1(e, e), f(c))
25.98/8.51	   A^2 -> H(U1(e, e), f(d))
25.98/8.51	   A^2 -> H(f(e), U1(c, b))
25.98/8.51	   A^2 -> H(f(e), U1(d, b))
25.98/8.51	   A^2 -> H(f(e), U1(b, c))
25.98/8.51	   A^2 -> H(f(e), U1(b, d))
25.98/8.51	   A^2 -> H(f(e), U1(c, c))
25.98/8.51	   A^2 -> H(f(e), f(e))
25.98/8.51	   A^2 -> H(f(e), f(k))
25.98/8.51	   A^2 -> H(f(e), U1(d, d))
25.98/8.51	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.51	   A^2 -> H(U1(k, k), f(c))
25.98/8.51	   A^2 -> H(U1(k, k), f(d))
25.98/8.51	   A^2 -> H(f(k), U1(c, b))
25.98/8.51	   A^2 -> H(f(k), U1(d, b))
25.98/8.51	   A^2 -> H(f(k), U1(b, c))
25.98/8.51	   A^2 -> H(f(k), U1(b, d))
25.98/8.51	   A^2 -> H(f(k), U1(c, c))
25.98/8.51	   A^2 -> H(f(k), f(e))
25.98/8.51	   A^2 -> H(f(k), f(k))
25.98/8.51	   A^2 -> H(f(k), U1(d, d))
25.98/8.51	   A^2 -> H(f(c), U1(e, b))
25.98/8.51	   A^2 -> H(f(c), U1(k, b))
25.98/8.51	   A^2 -> H(f(c), U1(c, d))
25.98/8.51	   A^2 -> H(f(c), U1(d, c))
25.98/8.51	   A^2 -> H(f(c), U1(b, e))
25.98/8.51	   A^2 -> H(f(c), U1(b, k))
25.98/8.51	   A^2 -> H(f(c), U1(k, d))
25.98/8.51	   A^2 -> H(f(c), U1(d, k))
25.98/8.51	   A^2 -> H(f(c), U1(k, k))
25.98/8.51	   A^2 -> H(U1(k, k), f(b))
25.98/8.51	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.51	   A^2 -> H(U1(k, d), f(c))
25.98/8.51	   A^2 -> H(U1(k, d), f(d))
25.98/8.51	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.51	   A^2 -> H(U1(d, k), f(c))
25.98/8.51	   A^2 -> H(U1(d, k), f(d))
25.98/8.51	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.51	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.51	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.51	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.51	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.51	   A^2 -> H(U1(d, d), f(e))
25.98/8.51	   A^2 -> H(U1(d, d), f(k))
25.98/8.51	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.51	   A^2 -> H(f(d), U1(e, b))
25.98/8.51	   A^2 -> H(f(d), U1(k, b))
25.98/8.51	   A^2 -> H(f(d), U1(c, d))
25.98/8.51	   A^2 -> H(f(d), U1(d, c))
25.98/8.51	   A^2 -> H(f(d), U1(b, e))
25.98/8.51	   A^2 -> H(f(d), U1(b, k))
25.98/8.51	   A^2 -> H(f(d), U1(e, c))
25.98/8.51	   A^2 -> H(f(d), U1(k, c))
25.98/8.51	   A^2 -> H(f(d), U1(c, e))
25.98/8.51	   A^2 -> H(f(d), U1(c, k))
25.98/8.51	   A^2 -> H(f(d), U1(e, e))
25.98/8.51	   A^2 -> H(f(d), U1(k, k))
25.98/8.51	   A^2 -> H(f(a), b)
25.98/8.51	   A^2 -> H(f(a), U1(e, d))
25.98/8.51	   A^2 -> H(f(a), U1(d, e))
25.98/8.51	   A^2 -> H(f(c), U1(e, c))
25.98/8.51	   A^2 -> H(f(c), U1(k, c))
25.98/8.51	   A^2 -> H(f(c), U1(c, e))
25.98/8.51	   A^2 -> H(f(c), U1(c, k))
25.98/8.51	   A^2 -> H(f(a), c)
25.98/8.51	   A^2 -> H(f(a), U1(e, k))
25.98/8.51	   A^2 -> H(f(a), U1(k, e))
25.98/8.51	   A^2 -> H(f(c), U1(e, e))
25.98/8.51	   A^2 -> H(f(a), e)
25.98/8.51	   A^2 -> H(f(d), U1(k, d))
25.98/8.51	   A^2 -> H(f(d), U1(d, k))
25.98/8.51	   A^2 -> H(f(a), U1(k, k))
25.98/8.51	   A^2 -> H(d, f(b))
25.98/8.51	   A^2 -> H(a, U1(b, b))
25.98/8.51	   A^2 -> H(a, f(c))
25.98/8.51	   A^2 -> H(a, f(d))
25.98/8.51	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.51	   A^2 -> H(U1(e, d), f(c))
25.98/8.51	   A^2 -> H(U1(e, d), f(d))
25.98/8.51	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.51	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.51	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.51	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.51	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.51	   A^2 -> H(U1(e, a), f(e))
25.98/8.51	   A^2 -> H(U1(e, a), f(k))
25.98/8.51	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.51	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.51	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.51	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.51	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.51	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.51	   A^2 -> H(U1(k, a), f(e))
25.98/8.51	   A^2 -> H(U1(k, a), f(k))
25.98/8.51	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.51	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.51	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.51	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.51	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.51	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.51	   A^2 -> H(U1(c, d), f(e))
25.98/8.51	   A^2 -> H(U1(c, d), f(k))
25.98/8.51	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.51	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.51	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.51	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.51	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.51	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.51	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.51	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.51	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.51	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.51	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.51	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.51	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.51	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.51	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.51	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.51	   A^2 -> H(U1(d, e), f(c))
25.98/8.51	   A^2 -> H(U1(d, e), f(d))
25.98/8.51	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.51	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.51	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.51	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.51	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.51	   A^2 -> H(U1(d, c), f(e))
25.98/8.51	   A^2 -> H(U1(d, c), f(k))
25.98/8.51	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.51	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.51	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.51	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.51	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.51	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.51	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.51	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.51	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.51	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.51	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.51	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.51	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.51	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.51	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.51	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.51	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.51	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.51	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.51	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.51	   A^2 -> H(U1(a, e), f(e))
25.98/8.51	   A^2 -> H(U1(a, e), f(k))
25.98/8.51	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.51	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.51	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.51	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.51	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.51	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.51	   A^2 -> H(U1(a, k), f(e))
25.98/8.51	   A^2 -> H(U1(a, k), f(k))
25.98/8.51	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.51	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.51	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.51	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.51	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.51	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.51	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.51	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.51	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.51	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.51	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.51	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.51	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.51	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.51	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.51	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.51	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.51	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.51	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.51	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.51	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.51	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.51	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.51	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.51	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.51	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.51	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.51	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.51	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.51	   A^2 -> H(U1(a, a), b)
25.98/8.51	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.51	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.51	   A^2 -> H(U1(a, a), c)
25.98/8.51	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.51	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.51	   A^2 -> H(U1(a, a), e)
25.98/8.51	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.51	   A^2 -> H(k, f(b))
25.98/8.51	   A^2 -> H(c, U1(b, b))
25.98/8.51	   A^2 -> H(c, f(c))
25.98/8.51	   A^2 -> H(c, f(d))
25.98/8.51	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.51	   A^2 -> H(U1(e, k), f(c))
25.98/8.51	   A^2 -> H(U1(e, k), f(d))
25.98/8.51	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.51	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.51	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.51	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.51	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.51	   A^2 -> H(U1(e, c), f(e))
25.98/8.51	   A^2 -> H(U1(e, c), f(k))
25.98/8.51	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.51	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.51	   A^2 -> H(U1(k, e), f(c))
25.98/8.51	   A^2 -> H(U1(k, e), f(d))
25.98/8.51	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.51	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.51	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.51	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.51	   A^2 -> H(U1(k, c), U1(c, c))
25.98/8.51	   A^2 -> H(U1(k, c), f(e))
25.98/8.51	   A^2 -> H(U1(k, c), f(k))
25.98/8.51	   A^2 -> H(U1(k, c), U1(d, d))
25.98/8.51	
25.98/8.51	The TRS R consists of the following rules:
25.98/8.51	
25.98/8.51	   f(x) -> U1(x, x)
25.98/8.51	   U1(e, x) -> x
25.98/8.51	   a -> c
25.98/8.51	   a -> d
25.98/8.51	   b -> c
25.98/8.51	   b -> d
25.98/8.51	   d -> k
25.98/8.51	   c -> e
25.98/8.51	   c -> k
25.98/8.51	
25.98/8.51	Q is empty.
25.98/8.51	We have to consider all minimal (P,Q,R)-chains.
25.98/8.51	----------------------------------------
25.98/8.51	
25.98/8.51	(373) TransformationProof (EQUIVALENT)
25.98/8.51	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.51	
25.98/8.51	   (A^2 -> H(U1(e, e), U1(b, b)),A^2 -> H(U1(e, e), U1(b, b)))
25.98/8.51	   (A^2 -> H(U1(k, e), U1(b, b)),A^2 -> H(U1(k, e), U1(b, b)))
25.98/8.51	   (A^2 -> H(U1(c, e), U1(c, b)),A^2 -> H(U1(c, e), U1(c, b)))
25.98/8.51	   (A^2 -> H(U1(c, e), U1(d, b)),A^2 -> H(U1(c, e), U1(d, b)))
25.98/8.51	   (A^2 -> H(U1(c, e), U1(b, c)),A^2 -> H(U1(c, e), U1(b, c)))
25.98/8.51	   (A^2 -> H(U1(c, e), U1(b, d)),A^2 -> H(U1(c, e), U1(b, d)))
25.98/8.51	
25.98/8.51	
25.98/8.51	----------------------------------------
25.98/8.51	
25.98/8.51	(374)
25.98/8.51	Obligation:
25.98/8.51	Q DP problem:
25.98/8.51	The TRS P consists of the following rules:
25.98/8.51	
25.98/8.51	   H(x, x) -> G(x, x, f(k))
25.98/8.51	   G(d, x, x) -> A^2
25.98/8.51	   A^2 -> H(f(c), f(c))
25.98/8.51	   A^2 -> H(f(d), f(d))
25.98/8.51	   A^2 -> H(U1(c, e), f(c))
25.98/8.51	   A^2 -> H(U1(c, e), f(d))
25.98/8.51	   A^2 -> H(U1(c, k), U1(b, b))
25.98/8.51	   A^2 -> H(U1(c, k), f(c))
25.98/8.51	   A^2 -> H(U1(c, k), f(d))
25.98/8.51	   A^2 -> H(U1(c, c), U1(c, b))
25.98/8.51	   A^2 -> H(U1(c, c), U1(d, b))
25.98/8.51	   A^2 -> H(U1(c, c), U1(b, c))
25.98/8.51	   A^2 -> H(U1(c, c), U1(b, d))
25.98/8.51	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.51	   A^2 -> H(U1(c, c), f(e))
25.98/8.51	   A^2 -> H(U1(c, c), f(k))
25.98/8.51	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.51	   A^2 -> H(e, f(b))
25.98/8.51	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.51	   A^2 -> H(U1(e, e), f(c))
25.98/8.51	   A^2 -> H(U1(e, e), f(d))
25.98/8.51	   A^2 -> H(f(e), U1(c, b))
25.98/8.51	   A^2 -> H(f(e), U1(d, b))
25.98/8.51	   A^2 -> H(f(e), U1(b, c))
25.98/8.51	   A^2 -> H(f(e), U1(b, d))
25.98/8.51	   A^2 -> H(f(e), U1(c, c))
25.98/8.51	   A^2 -> H(f(e), f(e))
25.98/8.51	   A^2 -> H(f(e), f(k))
25.98/8.51	   A^2 -> H(f(e), U1(d, d))
25.98/8.51	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.51	   A^2 -> H(U1(k, k), f(c))
25.98/8.51	   A^2 -> H(U1(k, k), f(d))
25.98/8.51	   A^2 -> H(f(k), U1(c, b))
25.98/8.51	   A^2 -> H(f(k), U1(d, b))
25.98/8.51	   A^2 -> H(f(k), U1(b, c))
25.98/8.51	   A^2 -> H(f(k), U1(b, d))
25.98/8.51	   A^2 -> H(f(k), U1(c, c))
25.98/8.51	   A^2 -> H(f(k), f(e))
25.98/8.51	   A^2 -> H(f(k), f(k))
25.98/8.51	   A^2 -> H(f(k), U1(d, d))
25.98/8.51	   A^2 -> H(f(c), U1(e, b))
25.98/8.51	   A^2 -> H(f(c), U1(k, b))
25.98/8.51	   A^2 -> H(f(c), U1(c, d))
25.98/8.51	   A^2 -> H(f(c), U1(d, c))
25.98/8.51	   A^2 -> H(f(c), U1(b, e))
25.98/8.51	   A^2 -> H(f(c), U1(b, k))
25.98/8.51	   A^2 -> H(f(c), U1(k, d))
25.98/8.51	   A^2 -> H(f(c), U1(d, k))
25.98/8.51	   A^2 -> H(f(c), U1(k, k))
25.98/8.51	   A^2 -> H(U1(k, k), f(b))
25.98/8.51	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.51	   A^2 -> H(U1(k, d), f(c))
25.98/8.51	   A^2 -> H(U1(k, d), f(d))
25.98/8.51	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.51	   A^2 -> H(U1(d, k), f(c))
25.98/8.51	   A^2 -> H(U1(d, k), f(d))
25.98/8.51	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.51	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.51	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.51	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.51	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.51	   A^2 -> H(U1(d, d), f(e))
25.98/8.51	   A^2 -> H(U1(d, d), f(k))
25.98/8.51	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.51	   A^2 -> H(f(d), U1(e, b))
25.98/8.51	   A^2 -> H(f(d), U1(k, b))
25.98/8.51	   A^2 -> H(f(d), U1(c, d))
25.98/8.51	   A^2 -> H(f(d), U1(d, c))
25.98/8.51	   A^2 -> H(f(d), U1(b, e))
25.98/8.51	   A^2 -> H(f(d), U1(b, k))
25.98/8.51	   A^2 -> H(f(d), U1(e, c))
25.98/8.51	   A^2 -> H(f(d), U1(k, c))
25.98/8.51	   A^2 -> H(f(d), U1(c, e))
25.98/8.51	   A^2 -> H(f(d), U1(c, k))
25.98/8.51	   A^2 -> H(f(d), U1(e, e))
25.98/8.51	   A^2 -> H(f(d), U1(k, k))
25.98/8.51	   A^2 -> H(f(a), b)
25.98/8.51	   A^2 -> H(f(a), U1(e, d))
25.98/8.51	   A^2 -> H(f(a), U1(d, e))
25.98/8.51	   A^2 -> H(f(c), U1(e, c))
25.98/8.51	   A^2 -> H(f(c), U1(k, c))
25.98/8.51	   A^2 -> H(f(c), U1(c, e))
25.98/8.51	   A^2 -> H(f(c), U1(c, k))
25.98/8.51	   A^2 -> H(f(a), c)
25.98/8.51	   A^2 -> H(f(a), U1(e, k))
25.98/8.51	   A^2 -> H(f(a), U1(k, e))
25.98/8.51	   A^2 -> H(f(c), U1(e, e))
25.98/8.51	   A^2 -> H(f(a), e)
25.98/8.51	   A^2 -> H(f(d), U1(k, d))
25.98/8.51	   A^2 -> H(f(d), U1(d, k))
25.98/8.51	   A^2 -> H(f(a), U1(k, k))
25.98/8.51	   A^2 -> H(d, f(b))
25.98/8.51	   A^2 -> H(a, U1(b, b))
25.98/8.51	   A^2 -> H(a, f(c))
25.98/8.51	   A^2 -> H(a, f(d))
25.98/8.51	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.51	   A^2 -> H(U1(e, d), f(c))
25.98/8.51	   A^2 -> H(U1(e, d), f(d))
25.98/8.51	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.51	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.51	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.51	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.51	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.51	   A^2 -> H(U1(e, a), f(e))
25.98/8.51	   A^2 -> H(U1(e, a), f(k))
25.98/8.51	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.51	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.51	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.51	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.51	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.51	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.51	   A^2 -> H(U1(k, a), f(e))
25.98/8.51	   A^2 -> H(U1(k, a), f(k))
25.98/8.51	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.51	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.51	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.51	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.51	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.51	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.51	   A^2 -> H(U1(c, d), f(e))
25.98/8.51	   A^2 -> H(U1(c, d), f(k))
25.98/8.51	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.51	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.51	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.51	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.51	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.51	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.51	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.51	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.51	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.51	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.51	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.51	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.51	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.51	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.51	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.51	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.51	   A^2 -> H(U1(d, e), f(c))
25.98/8.52	   A^2 -> H(U1(d, e), f(d))
25.98/8.52	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.52	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.52	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.52	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.52	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.52	   A^2 -> H(U1(d, c), f(e))
25.98/8.52	   A^2 -> H(U1(d, c), f(k))
25.98/8.52	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.52	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.52	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.52	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.52	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.52	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.52	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.52	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.52	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.52	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.52	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.52	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.52	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.52	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.52	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.52	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.52	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.52	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.52	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.52	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.52	   A^2 -> H(U1(a, e), f(e))
25.98/8.52	   A^2 -> H(U1(a, e), f(k))
25.98/8.52	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.52	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.52	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.52	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.52	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.52	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.52	   A^2 -> H(U1(a, k), f(e))
25.98/8.52	   A^2 -> H(U1(a, k), f(k))
25.98/8.52	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.52	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.52	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.52	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.52	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.52	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.52	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.52	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.52	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.52	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.52	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.52	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.52	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.52	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.52	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.52	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.52	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.52	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.52	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.52	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.52	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.52	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.52	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.52	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.52	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.52	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.52	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.52	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.52	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.52	   A^2 -> H(U1(a, a), b)
25.98/8.52	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.52	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.52	   A^2 -> H(U1(a, a), c)
25.98/8.52	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.52	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.52	   A^2 -> H(U1(a, a), e)
25.98/8.52	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.52	   A^2 -> H(k, f(b))
25.98/8.52	   A^2 -> H(c, U1(b, b))
25.98/8.52	   A^2 -> H(c, f(c))
25.98/8.52	   A^2 -> H(c, f(d))
25.98/8.52	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.52	   A^2 -> H(U1(e, k), f(c))
25.98/8.52	   A^2 -> H(U1(e, k), f(d))
25.98/8.52	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.52	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.52	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.52	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.52	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.52	   A^2 -> H(U1(e, c), f(e))
25.98/8.52	   A^2 -> H(U1(e, c), f(k))
25.98/8.52	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.52	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.52	   A^2 -> H(U1(k, e), f(c))
25.98/8.52	   A^2 -> H(U1(k, e), f(d))
25.98/8.52	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.52	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.52	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.52	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.52	   A^2 -> H(U1(k, c), U1(c, c))
25.98/8.52	   A^2 -> H(U1(k, c), f(e))
25.98/8.52	   A^2 -> H(U1(k, c), f(k))
25.98/8.52	   A^2 -> H(U1(k, c), U1(d, d))
25.98/8.52	   A^2 -> H(U1(c, e), U1(c, b))
25.98/8.52	   A^2 -> H(U1(c, e), U1(d, b))
25.98/8.52	   A^2 -> H(U1(c, e), U1(b, c))
25.98/8.52	   A^2 -> H(U1(c, e), U1(b, d))
25.98/8.52	
25.98/8.52	The TRS R consists of the following rules:
25.98/8.52	
25.98/8.52	   f(x) -> U1(x, x)
25.98/8.52	   U1(e, x) -> x
25.98/8.52	   a -> c
25.98/8.52	   a -> d
25.98/8.52	   b -> c
25.98/8.52	   b -> d
25.98/8.52	   d -> k
25.98/8.52	   c -> e
25.98/8.52	   c -> k
25.98/8.52	
25.98/8.52	Q is empty.
25.98/8.52	We have to consider all minimal (P,Q,R)-chains.
25.98/8.52	----------------------------------------
25.98/8.52	
25.98/8.52	(375) TransformationProof (EQUIVALENT)
25.98/8.52	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), f(c)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.52	
25.98/8.52	   (A^2 -> H(U1(e, e), f(c)),A^2 -> H(U1(e, e), f(c)))
25.98/8.52	   (A^2 -> H(U1(k, e), f(c)),A^2 -> H(U1(k, e), f(c)))
25.98/8.52	   (A^2 -> H(U1(c, e), U1(c, c)),A^2 -> H(U1(c, e), U1(c, c)))
25.98/8.52	   (A^2 -> H(U1(c, e), f(e)),A^2 -> H(U1(c, e), f(e)))
25.98/8.52	   (A^2 -> H(U1(c, e), f(k)),A^2 -> H(U1(c, e), f(k)))
25.98/8.52	
25.98/8.52	
25.98/8.52	----------------------------------------
25.98/8.52	
25.98/8.52	(376)
25.98/8.52	Obligation:
25.98/8.52	Q DP problem:
25.98/8.52	The TRS P consists of the following rules:
25.98/8.52	
25.98/8.52	   H(x, x) -> G(x, x, f(k))
25.98/8.52	   G(d, x, x) -> A^2
25.98/8.52	   A^2 -> H(f(c), f(c))
25.98/8.52	   A^2 -> H(f(d), f(d))
25.98/8.52	   A^2 -> H(U1(c, e), f(d))
25.98/8.52	   A^2 -> H(U1(c, k), U1(b, b))
25.98/8.52	   A^2 -> H(U1(c, k), f(c))
25.98/8.52	   A^2 -> H(U1(c, k), f(d))
25.98/8.52	   A^2 -> H(U1(c, c), U1(c, b))
25.98/8.52	   A^2 -> H(U1(c, c), U1(d, b))
25.98/8.52	   A^2 -> H(U1(c, c), U1(b, c))
25.98/8.52	   A^2 -> H(U1(c, c), U1(b, d))
25.98/8.52	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.52	   A^2 -> H(U1(c, c), f(e))
25.98/8.52	   A^2 -> H(U1(c, c), f(k))
25.98/8.52	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.52	   A^2 -> H(e, f(b))
25.98/8.52	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.52	   A^2 -> H(U1(e, e), f(c))
25.98/8.52	   A^2 -> H(U1(e, e), f(d))
25.98/8.52	   A^2 -> H(f(e), U1(c, b))
25.98/8.52	   A^2 -> H(f(e), U1(d, b))
25.98/8.52	   A^2 -> H(f(e), U1(b, c))
25.98/8.52	   A^2 -> H(f(e), U1(b, d))
25.98/8.52	   A^2 -> H(f(e), U1(c, c))
25.98/8.52	   A^2 -> H(f(e), f(e))
25.98/8.52	   A^2 -> H(f(e), f(k))
25.98/8.52	   A^2 -> H(f(e), U1(d, d))
25.98/8.52	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.52	   A^2 -> H(U1(k, k), f(c))
25.98/8.52	   A^2 -> H(U1(k, k), f(d))
25.98/8.52	   A^2 -> H(f(k), U1(c, b))
25.98/8.52	   A^2 -> H(f(k), U1(d, b))
25.98/8.52	   A^2 -> H(f(k), U1(b, c))
25.98/8.52	   A^2 -> H(f(k), U1(b, d))
25.98/8.52	   A^2 -> H(f(k), U1(c, c))
25.98/8.52	   A^2 -> H(f(k), f(e))
25.98/8.52	   A^2 -> H(f(k), f(k))
25.98/8.52	   A^2 -> H(f(k), U1(d, d))
25.98/8.52	   A^2 -> H(f(c), U1(e, b))
25.98/8.52	   A^2 -> H(f(c), U1(k, b))
25.98/8.52	   A^2 -> H(f(c), U1(c, d))
25.98/8.52	   A^2 -> H(f(c), U1(d, c))
25.98/8.52	   A^2 -> H(f(c), U1(b, e))
25.98/8.52	   A^2 -> H(f(c), U1(b, k))
25.98/8.52	   A^2 -> H(f(c), U1(k, d))
25.98/8.52	   A^2 -> H(f(c), U1(d, k))
25.98/8.52	   A^2 -> H(f(c), U1(k, k))
25.98/8.52	   A^2 -> H(U1(k, k), f(b))
25.98/8.52	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.52	   A^2 -> H(U1(k, d), f(c))
25.98/8.52	   A^2 -> H(U1(k, d), f(d))
25.98/8.52	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.52	   A^2 -> H(U1(d, k), f(c))
25.98/8.52	   A^2 -> H(U1(d, k), f(d))
25.98/8.52	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.52	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.52	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.52	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.52	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.52	   A^2 -> H(U1(d, d), f(e))
25.98/8.52	   A^2 -> H(U1(d, d), f(k))
25.98/8.52	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.52	   A^2 -> H(f(d), U1(e, b))
25.98/8.52	   A^2 -> H(f(d), U1(k, b))
25.98/8.52	   A^2 -> H(f(d), U1(c, d))
25.98/8.52	   A^2 -> H(f(d), U1(d, c))
25.98/8.52	   A^2 -> H(f(d), U1(b, e))
25.98/8.52	   A^2 -> H(f(d), U1(b, k))
25.98/8.52	   A^2 -> H(f(d), U1(e, c))
25.98/8.52	   A^2 -> H(f(d), U1(k, c))
25.98/8.52	   A^2 -> H(f(d), U1(c, e))
25.98/8.52	   A^2 -> H(f(d), U1(c, k))
25.98/8.52	   A^2 -> H(f(d), U1(e, e))
25.98/8.52	   A^2 -> H(f(d), U1(k, k))
25.98/8.52	   A^2 -> H(f(a), b)
25.98/8.52	   A^2 -> H(f(a), U1(e, d))
25.98/8.52	   A^2 -> H(f(a), U1(d, e))
25.98/8.52	   A^2 -> H(f(c), U1(e, c))
25.98/8.52	   A^2 -> H(f(c), U1(k, c))
25.98/8.52	   A^2 -> H(f(c), U1(c, e))
25.98/8.52	   A^2 -> H(f(c), U1(c, k))
25.98/8.52	   A^2 -> H(f(a), c)
25.98/8.52	   A^2 -> H(f(a), U1(e, k))
25.98/8.52	   A^2 -> H(f(a), U1(k, e))
25.98/8.52	   A^2 -> H(f(c), U1(e, e))
25.98/8.52	   A^2 -> H(f(a), e)
25.98/8.52	   A^2 -> H(f(d), U1(k, d))
25.98/8.52	   A^2 -> H(f(d), U1(d, k))
25.98/8.52	   A^2 -> H(f(a), U1(k, k))
25.98/8.52	   A^2 -> H(d, f(b))
25.98/8.52	   A^2 -> H(a, U1(b, b))
25.98/8.52	   A^2 -> H(a, f(c))
25.98/8.52	   A^2 -> H(a, f(d))
25.98/8.52	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.52	   A^2 -> H(U1(e, d), f(c))
25.98/8.52	   A^2 -> H(U1(e, d), f(d))
25.98/8.52	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.52	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.52	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.52	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.52	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.52	   A^2 -> H(U1(e, a), f(e))
25.98/8.52	   A^2 -> H(U1(e, a), f(k))
25.98/8.52	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.52	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.52	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.52	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.52	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.52	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.52	   A^2 -> H(U1(k, a), f(e))
25.98/8.52	   A^2 -> H(U1(k, a), f(k))
25.98/8.52	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.52	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.52	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.52	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.52	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.52	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.52	   A^2 -> H(U1(c, d), f(e))
25.98/8.52	   A^2 -> H(U1(c, d), f(k))
25.98/8.52	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.52	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.52	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.52	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.52	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.52	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.52	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.52	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.52	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.52	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.52	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.52	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.52	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.52	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.52	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.52	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.52	   A^2 -> H(U1(d, e), f(c))
25.98/8.52	   A^2 -> H(U1(d, e), f(d))
25.98/8.52	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.52	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.52	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.52	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.52	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.52	   A^2 -> H(U1(d, c), f(e))
25.98/8.52	   A^2 -> H(U1(d, c), f(k))
25.98/8.52	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.52	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.52	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.52	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.52	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.52	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.52	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.52	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.52	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.52	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.52	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.52	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.52	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.52	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.52	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.52	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.52	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.52	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.52	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.52	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.52	   A^2 -> H(U1(a, e), f(e))
25.98/8.52	   A^2 -> H(U1(a, e), f(k))
25.98/8.52	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.52	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.52	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.52	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.52	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.52	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.52	   A^2 -> H(U1(a, k), f(e))
25.98/8.52	   A^2 -> H(U1(a, k), f(k))
25.98/8.52	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.52	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.52	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.52	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.52	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.52	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.52	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.52	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.52	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.52	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.52	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.52	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.52	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.52	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.52	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.52	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.52	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.52	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.52	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.52	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.52	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.52	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.52	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.52	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.52	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.52	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.52	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.52	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.52	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.52	   A^2 -> H(U1(a, a), b)
25.98/8.52	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.52	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.52	   A^2 -> H(U1(a, a), c)
25.98/8.52	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.52	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.52	   A^2 -> H(U1(a, a), e)
25.98/8.52	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.52	   A^2 -> H(k, f(b))
25.98/8.52	   A^2 -> H(c, U1(b, b))
25.98/8.52	   A^2 -> H(c, f(c))
25.98/8.52	   A^2 -> H(c, f(d))
25.98/8.52	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.52	   A^2 -> H(U1(e, k), f(c))
25.98/8.52	   A^2 -> H(U1(e, k), f(d))
25.98/8.52	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.52	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.52	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.52	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.52	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.52	   A^2 -> H(U1(e, c), f(e))
25.98/8.52	   A^2 -> H(U1(e, c), f(k))
25.98/8.52	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.52	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.52	   A^2 -> H(U1(k, e), f(c))
25.98/8.52	   A^2 -> H(U1(k, e), f(d))
25.98/8.52	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.52	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.52	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.52	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.52	   A^2 -> H(U1(k, c), U1(c, c))
25.98/8.52	   A^2 -> H(U1(k, c), f(e))
25.98/8.52	   A^2 -> H(U1(k, c), f(k))
25.98/8.52	   A^2 -> H(U1(k, c), U1(d, d))
25.98/8.52	   A^2 -> H(U1(c, e), U1(c, b))
25.98/8.52	   A^2 -> H(U1(c, e), U1(d, b))
25.98/8.52	   A^2 -> H(U1(c, e), U1(b, c))
25.98/8.52	   A^2 -> H(U1(c, e), U1(b, d))
25.98/8.52	   A^2 -> H(U1(c, e), U1(c, c))
25.98/8.52	   A^2 -> H(U1(c, e), f(e))
25.98/8.52	   A^2 -> H(U1(c, e), f(k))
25.98/8.52	
25.98/8.52	The TRS R consists of the following rules:
25.98/8.52	
25.98/8.52	   f(x) -> U1(x, x)
25.98/8.52	   U1(e, x) -> x
25.98/8.52	   a -> c
25.98/8.52	   a -> d
25.98/8.52	   b -> c
25.98/8.52	   b -> d
25.98/8.52	   d -> k
25.98/8.52	   c -> e
25.98/8.52	   c -> k
25.98/8.52	
25.98/8.52	Q is empty.
25.98/8.52	We have to consider all minimal (P,Q,R)-chains.
25.98/8.52	----------------------------------------
25.98/8.52	
25.98/8.52	(377) TransformationProof (EQUIVALENT)
25.98/8.52	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), f(d)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.52	
25.98/8.52	   (A^2 -> H(U1(e, e), f(d)),A^2 -> H(U1(e, e), f(d)))
25.98/8.52	   (A^2 -> H(U1(k, e), f(d)),A^2 -> H(U1(k, e), f(d)))
25.98/8.52	   (A^2 -> H(U1(c, e), U1(d, d)),A^2 -> H(U1(c, e), U1(d, d)))
25.98/8.52	   (A^2 -> H(U1(c, e), f(k)),A^2 -> H(U1(c, e), f(k)))
25.98/8.52	
25.98/8.52	
25.98/8.52	----------------------------------------
25.98/8.52	
25.98/8.52	(378)
25.98/8.52	Obligation:
25.98/8.52	Q DP problem:
25.98/8.52	The TRS P consists of the following rules:
25.98/8.52	
25.98/8.52	   H(x, x) -> G(x, x, f(k))
25.98/8.52	   G(d, x, x) -> A^2
25.98/8.52	   A^2 -> H(f(c), f(c))
25.98/8.52	   A^2 -> H(f(d), f(d))
25.98/8.52	   A^2 -> H(U1(c, k), U1(b, b))
25.98/8.52	   A^2 -> H(U1(c, k), f(c))
25.98/8.52	   A^2 -> H(U1(c, k), f(d))
25.98/8.52	   A^2 -> H(U1(c, c), U1(c, b))
25.98/8.52	   A^2 -> H(U1(c, c), U1(d, b))
25.98/8.52	   A^2 -> H(U1(c, c), U1(b, c))
25.98/8.52	   A^2 -> H(U1(c, c), U1(b, d))
25.98/8.52	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.52	   A^2 -> H(U1(c, c), f(e))
25.98/8.52	   A^2 -> H(U1(c, c), f(k))
25.98/8.52	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.52	   A^2 -> H(e, f(b))
25.98/8.52	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.52	   A^2 -> H(U1(e, e), f(c))
25.98/8.52	   A^2 -> H(U1(e, e), f(d))
25.98/8.52	   A^2 -> H(f(e), U1(c, b))
25.98/8.52	   A^2 -> H(f(e), U1(d, b))
25.98/8.52	   A^2 -> H(f(e), U1(b, c))
25.98/8.52	   A^2 -> H(f(e), U1(b, d))
25.98/8.52	   A^2 -> H(f(e), U1(c, c))
25.98/8.52	   A^2 -> H(f(e), f(e))
25.98/8.52	   A^2 -> H(f(e), f(k))
25.98/8.52	   A^2 -> H(f(e), U1(d, d))
25.98/8.52	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.52	   A^2 -> H(U1(k, k), f(c))
25.98/8.52	   A^2 -> H(U1(k, k), f(d))
25.98/8.52	   A^2 -> H(f(k), U1(c, b))
25.98/8.52	   A^2 -> H(f(k), U1(d, b))
25.98/8.52	   A^2 -> H(f(k), U1(b, c))
25.98/8.52	   A^2 -> H(f(k), U1(b, d))
25.98/8.52	   A^2 -> H(f(k), U1(c, c))
25.98/8.52	   A^2 -> H(f(k), f(e))
25.98/8.52	   A^2 -> H(f(k), f(k))
25.98/8.52	   A^2 -> H(f(k), U1(d, d))
25.98/8.52	   A^2 -> H(f(c), U1(e, b))
25.98/8.52	   A^2 -> H(f(c), U1(k, b))
25.98/8.52	   A^2 -> H(f(c), U1(c, d))
25.98/8.52	   A^2 -> H(f(c), U1(d, c))
25.98/8.52	   A^2 -> H(f(c), U1(b, e))
25.98/8.52	   A^2 -> H(f(c), U1(b, k))
25.98/8.52	   A^2 -> H(f(c), U1(k, d))
25.98/8.52	   A^2 -> H(f(c), U1(d, k))
25.98/8.52	   A^2 -> H(f(c), U1(k, k))
25.98/8.52	   A^2 -> H(U1(k, k), f(b))
25.98/8.52	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.52	   A^2 -> H(U1(k, d), f(c))
25.98/8.52	   A^2 -> H(U1(k, d), f(d))
25.98/8.52	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.52	   A^2 -> H(U1(d, k), f(c))
25.98/8.52	   A^2 -> H(U1(d, k), f(d))
25.98/8.52	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.52	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.52	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.52	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.52	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.52	   A^2 -> H(U1(d, d), f(e))
25.98/8.52	   A^2 -> H(U1(d, d), f(k))
25.98/8.52	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.52	   A^2 -> H(f(d), U1(e, b))
25.98/8.52	   A^2 -> H(f(d), U1(k, b))
25.98/8.52	   A^2 -> H(f(d), U1(c, d))
25.98/8.52	   A^2 -> H(f(d), U1(d, c))
25.98/8.52	   A^2 -> H(f(d), U1(b, e))
25.98/8.52	   A^2 -> H(f(d), U1(b, k))
25.98/8.52	   A^2 -> H(f(d), U1(e, c))
25.98/8.52	   A^2 -> H(f(d), U1(k, c))
25.98/8.52	   A^2 -> H(f(d), U1(c, e))
25.98/8.52	   A^2 -> H(f(d), U1(c, k))
25.98/8.52	   A^2 -> H(f(d), U1(e, e))
25.98/8.52	   A^2 -> H(f(d), U1(k, k))
25.98/8.52	   A^2 -> H(f(a), b)
25.98/8.52	   A^2 -> H(f(a), U1(e, d))
25.98/8.52	   A^2 -> H(f(a), U1(d, e))
25.98/8.52	   A^2 -> H(f(c), U1(e, c))
25.98/8.52	   A^2 -> H(f(c), U1(k, c))
25.98/8.52	   A^2 -> H(f(c), U1(c, e))
25.98/8.52	   A^2 -> H(f(c), U1(c, k))
25.98/8.52	   A^2 -> H(f(a), c)
25.98/8.52	   A^2 -> H(f(a), U1(e, k))
25.98/8.52	   A^2 -> H(f(a), U1(k, e))
25.98/8.52	   A^2 -> H(f(c), U1(e, e))
25.98/8.52	   A^2 -> H(f(a), e)
25.98/8.52	   A^2 -> H(f(d), U1(k, d))
25.98/8.52	   A^2 -> H(f(d), U1(d, k))
25.98/8.52	   A^2 -> H(f(a), U1(k, k))
25.98/8.52	   A^2 -> H(d, f(b))
25.98/8.52	   A^2 -> H(a, U1(b, b))
25.98/8.52	   A^2 -> H(a, f(c))
25.98/8.52	   A^2 -> H(a, f(d))
25.98/8.52	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.52	   A^2 -> H(U1(e, d), f(c))
25.98/8.52	   A^2 -> H(U1(e, d), f(d))
25.98/8.52	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.52	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.52	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.52	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.52	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.52	   A^2 -> H(U1(e, a), f(e))
25.98/8.52	   A^2 -> H(U1(e, a), f(k))
25.98/8.52	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.52	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.52	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.52	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.52	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.52	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.52	   A^2 -> H(U1(k, a), f(e))
25.98/8.52	   A^2 -> H(U1(k, a), f(k))
25.98/8.52	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.52	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.52	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.52	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.52	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.52	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.52	   A^2 -> H(U1(c, d), f(e))
25.98/8.52	   A^2 -> H(U1(c, d), f(k))
25.98/8.52	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.52	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.52	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.52	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.52	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.52	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.52	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.52	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.52	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.52	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.52	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.52	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.52	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.52	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.52	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.52	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.52	   A^2 -> H(U1(d, e), f(c))
25.98/8.52	   A^2 -> H(U1(d, e), f(d))
25.98/8.52	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.52	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.52	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.52	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.52	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.52	   A^2 -> H(U1(d, c), f(e))
25.98/8.52	   A^2 -> H(U1(d, c), f(k))
25.98/8.52	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.52	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.52	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.52	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.52	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.52	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.52	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.52	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.52	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.52	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.52	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.52	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.52	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.52	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.52	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.52	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.52	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.52	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.52	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.52	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.52	   A^2 -> H(U1(a, e), f(e))
25.98/8.52	   A^2 -> H(U1(a, e), f(k))
25.98/8.52	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.52	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.52	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.52	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.52	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.52	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.52	   A^2 -> H(U1(a, k), f(e))
25.98/8.52	   A^2 -> H(U1(a, k), f(k))
25.98/8.52	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.52	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.52	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.52	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.52	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.52	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.52	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.52	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.52	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.52	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.52	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.52	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.52	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.52	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.52	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.52	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.52	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.52	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.52	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.52	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.52	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.52	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.52	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.52	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.52	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.52	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.52	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.52	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.52	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.52	   A^2 -> H(U1(a, a), b)
25.98/8.52	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.52	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.52	   A^2 -> H(U1(a, a), c)
25.98/8.52	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.52	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.52	   A^2 -> H(U1(a, a), e)
25.98/8.52	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.52	   A^2 -> H(k, f(b))
25.98/8.52	   A^2 -> H(c, U1(b, b))
25.98/8.52	   A^2 -> H(c, f(c))
25.98/8.52	   A^2 -> H(c, f(d))
25.98/8.52	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.52	   A^2 -> H(U1(e, k), f(c))
25.98/8.52	   A^2 -> H(U1(e, k), f(d))
25.98/8.52	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.52	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.52	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.52	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.52	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.52	   A^2 -> H(U1(e, c), f(e))
25.98/8.52	   A^2 -> H(U1(e, c), f(k))
25.98/8.52	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.52	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.52	   A^2 -> H(U1(k, e), f(c))
25.98/8.52	   A^2 -> H(U1(k, e), f(d))
25.98/8.52	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.52	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.52	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.52	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.52	   A^2 -> H(U1(k, c), U1(c, c))
25.98/8.52	   A^2 -> H(U1(k, c), f(e))
25.98/8.52	   A^2 -> H(U1(k, c), f(k))
25.98/8.52	   A^2 -> H(U1(k, c), U1(d, d))
25.98/8.52	   A^2 -> H(U1(c, e), U1(c, b))
25.98/8.52	   A^2 -> H(U1(c, e), U1(d, b))
25.98/8.52	   A^2 -> H(U1(c, e), U1(b, c))
25.98/8.52	   A^2 -> H(U1(c, e), U1(b, d))
25.98/8.52	   A^2 -> H(U1(c, e), U1(c, c))
25.98/8.52	   A^2 -> H(U1(c, e), f(e))
25.98/8.52	   A^2 -> H(U1(c, e), f(k))
25.98/8.52	   A^2 -> H(U1(c, e), U1(d, d))
25.98/8.52	
25.98/8.52	The TRS R consists of the following rules:
25.98/8.52	
25.98/8.52	   f(x) -> U1(x, x)
25.98/8.52	   U1(e, x) -> x
25.98/8.52	   a -> c
25.98/8.52	   a -> d
25.98/8.52	   b -> c
25.98/8.52	   b -> d
25.98/8.52	   d -> k
25.98/8.52	   c -> e
25.98/8.52	   c -> k
25.98/8.52	
25.98/8.52	Q is empty.
25.98/8.52	We have to consider all minimal (P,Q,R)-chains.
25.98/8.52	----------------------------------------
25.98/8.52	
25.98/8.52	(379) TransformationProof (EQUIVALENT)
25.98/8.52	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.52	
25.98/8.52	   (A^2 -> H(U1(e, k), U1(b, b)),A^2 -> H(U1(e, k), U1(b, b)))
25.98/8.52	   (A^2 -> H(U1(k, k), U1(b, b)),A^2 -> H(U1(k, k), U1(b, b)))
25.98/8.52	   (A^2 -> H(U1(c, k), U1(c, b)),A^2 -> H(U1(c, k), U1(c, b)))
25.98/8.52	   (A^2 -> H(U1(c, k), U1(d, b)),A^2 -> H(U1(c, k), U1(d, b)))
25.98/8.52	   (A^2 -> H(U1(c, k), U1(b, c)),A^2 -> H(U1(c, k), U1(b, c)))
25.98/8.52	   (A^2 -> H(U1(c, k), U1(b, d)),A^2 -> H(U1(c, k), U1(b, d)))
25.98/8.52	
25.98/8.52	
25.98/8.52	----------------------------------------
25.98/8.52	
25.98/8.52	(380)
25.98/8.52	Obligation:
25.98/8.52	Q DP problem:
25.98/8.52	The TRS P consists of the following rules:
25.98/8.52	
25.98/8.52	   H(x, x) -> G(x, x, f(k))
25.98/8.52	   G(d, x, x) -> A^2
25.98/8.52	   A^2 -> H(f(c), f(c))
25.98/8.52	   A^2 -> H(f(d), f(d))
25.98/8.52	   A^2 -> H(U1(c, k), f(c))
25.98/8.52	   A^2 -> H(U1(c, k), f(d))
25.98/8.52	   A^2 -> H(U1(c, c), U1(c, b))
25.98/8.52	   A^2 -> H(U1(c, c), U1(d, b))
25.98/8.52	   A^2 -> H(U1(c, c), U1(b, c))
25.98/8.52	   A^2 -> H(U1(c, c), U1(b, d))
25.98/8.52	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.52	   A^2 -> H(U1(c, c), f(e))
25.98/8.52	   A^2 -> H(U1(c, c), f(k))
25.98/8.52	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.52	   A^2 -> H(e, f(b))
25.98/8.52	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.52	   A^2 -> H(U1(e, e), f(c))
25.98/8.52	   A^2 -> H(U1(e, e), f(d))
25.98/8.52	   A^2 -> H(f(e), U1(c, b))
25.98/8.52	   A^2 -> H(f(e), U1(d, b))
25.98/8.52	   A^2 -> H(f(e), U1(b, c))
25.98/8.52	   A^2 -> H(f(e), U1(b, d))
25.98/8.52	   A^2 -> H(f(e), U1(c, c))
25.98/8.52	   A^2 -> H(f(e), f(e))
25.98/8.52	   A^2 -> H(f(e), f(k))
25.98/8.52	   A^2 -> H(f(e), U1(d, d))
25.98/8.52	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.52	   A^2 -> H(U1(k, k), f(c))
25.98/8.52	   A^2 -> H(U1(k, k), f(d))
25.98/8.52	   A^2 -> H(f(k), U1(c, b))
25.98/8.52	   A^2 -> H(f(k), U1(d, b))
25.98/8.52	   A^2 -> H(f(k), U1(b, c))
25.98/8.52	   A^2 -> H(f(k), U1(b, d))
25.98/8.52	   A^2 -> H(f(k), U1(c, c))
25.98/8.52	   A^2 -> H(f(k), f(e))
25.98/8.52	   A^2 -> H(f(k), f(k))
25.98/8.52	   A^2 -> H(f(k), U1(d, d))
25.98/8.52	   A^2 -> H(f(c), U1(e, b))
25.98/8.52	   A^2 -> H(f(c), U1(k, b))
25.98/8.52	   A^2 -> H(f(c), U1(c, d))
25.98/8.52	   A^2 -> H(f(c), U1(d, c))
25.98/8.52	   A^2 -> H(f(c), U1(b, e))
25.98/8.52	   A^2 -> H(f(c), U1(b, k))
25.98/8.53	   A^2 -> H(f(c), U1(k, d))
25.98/8.53	   A^2 -> H(f(c), U1(d, k))
25.98/8.53	   A^2 -> H(f(c), U1(k, k))
25.98/8.53	   A^2 -> H(U1(k, k), f(b))
25.98/8.53	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.53	   A^2 -> H(U1(k, d), f(c))
25.98/8.53	   A^2 -> H(U1(k, d), f(d))
25.98/8.53	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.53	   A^2 -> H(U1(d, k), f(c))
25.98/8.53	   A^2 -> H(U1(d, k), f(d))
25.98/8.53	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.53	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.53	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.53	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.53	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.53	   A^2 -> H(U1(d, d), f(e))
25.98/8.53	   A^2 -> H(U1(d, d), f(k))
25.98/8.53	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.53	   A^2 -> H(f(d), U1(e, b))
25.98/8.53	   A^2 -> H(f(d), U1(k, b))
25.98/8.53	   A^2 -> H(f(d), U1(c, d))
25.98/8.53	   A^2 -> H(f(d), U1(d, c))
25.98/8.53	   A^2 -> H(f(d), U1(b, e))
25.98/8.53	   A^2 -> H(f(d), U1(b, k))
25.98/8.53	   A^2 -> H(f(d), U1(e, c))
25.98/8.53	   A^2 -> H(f(d), U1(k, c))
25.98/8.53	   A^2 -> H(f(d), U1(c, e))
25.98/8.53	   A^2 -> H(f(d), U1(c, k))
25.98/8.53	   A^2 -> H(f(d), U1(e, e))
25.98/8.53	   A^2 -> H(f(d), U1(k, k))
25.98/8.53	   A^2 -> H(f(a), b)
25.98/8.53	   A^2 -> H(f(a), U1(e, d))
25.98/8.53	   A^2 -> H(f(a), U1(d, e))
25.98/8.53	   A^2 -> H(f(c), U1(e, c))
25.98/8.53	   A^2 -> H(f(c), U1(k, c))
25.98/8.53	   A^2 -> H(f(c), U1(c, e))
25.98/8.53	   A^2 -> H(f(c), U1(c, k))
25.98/8.53	   A^2 -> H(f(a), c)
25.98/8.53	   A^2 -> H(f(a), U1(e, k))
25.98/8.53	   A^2 -> H(f(a), U1(k, e))
25.98/8.53	   A^2 -> H(f(c), U1(e, e))
25.98/8.53	   A^2 -> H(f(a), e)
25.98/8.53	   A^2 -> H(f(d), U1(k, d))
25.98/8.53	   A^2 -> H(f(d), U1(d, k))
25.98/8.53	   A^2 -> H(f(a), U1(k, k))
25.98/8.53	   A^2 -> H(d, f(b))
25.98/8.53	   A^2 -> H(a, U1(b, b))
25.98/8.53	   A^2 -> H(a, f(c))
25.98/8.53	   A^2 -> H(a, f(d))
25.98/8.53	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.53	   A^2 -> H(U1(e, d), f(c))
25.98/8.53	   A^2 -> H(U1(e, d), f(d))
25.98/8.53	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.53	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.53	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.53	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.53	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.53	   A^2 -> H(U1(e, a), f(e))
25.98/8.53	   A^2 -> H(U1(e, a), f(k))
25.98/8.53	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.53	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.53	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.53	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.53	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.53	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.53	   A^2 -> H(U1(k, a), f(e))
25.98/8.53	   A^2 -> H(U1(k, a), f(k))
25.98/8.53	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.53	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.53	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.53	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.53	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.53	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.53	   A^2 -> H(U1(c, d), f(e))
25.98/8.53	   A^2 -> H(U1(c, d), f(k))
25.98/8.53	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.53	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.53	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.53	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.53	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.53	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.53	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.53	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.53	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.53	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.53	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.53	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.53	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.53	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.53	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.53	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.53	   A^2 -> H(U1(d, e), f(c))
25.98/8.53	   A^2 -> H(U1(d, e), f(d))
25.98/8.53	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.53	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.53	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.53	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.53	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.53	   A^2 -> H(U1(d, c), f(e))
25.98/8.53	   A^2 -> H(U1(d, c), f(k))
25.98/8.53	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.53	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.53	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.53	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.53	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.53	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.53	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.53	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.53	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.53	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.53	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.53	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.53	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.53	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.53	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.53	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.53	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.53	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.53	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.53	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.53	   A^2 -> H(U1(a, e), f(e))
25.98/8.53	   A^2 -> H(U1(a, e), f(k))
25.98/8.53	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.53	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.53	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.53	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.53	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.53	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.53	   A^2 -> H(U1(a, k), f(e))
25.98/8.53	   A^2 -> H(U1(a, k), f(k))
25.98/8.53	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.53	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.53	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.53	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.53	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.53	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.53	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.53	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.53	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.53	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.53	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.53	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.53	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.53	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.53	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.53	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.53	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.53	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.53	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.53	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.53	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.53	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.53	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.53	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.53	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.53	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.53	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.53	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.53	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.53	   A^2 -> H(U1(a, a), b)
25.98/8.53	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.53	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.53	   A^2 -> H(U1(a, a), c)
25.98/8.53	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.53	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.53	   A^2 -> H(U1(a, a), e)
25.98/8.53	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.53	   A^2 -> H(k, f(b))
25.98/8.53	   A^2 -> H(c, U1(b, b))
25.98/8.53	   A^2 -> H(c, f(c))
25.98/8.53	   A^2 -> H(c, f(d))
25.98/8.53	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.53	   A^2 -> H(U1(e, k), f(c))
25.98/8.53	   A^2 -> H(U1(e, k), f(d))
25.98/8.53	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.53	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.53	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.53	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.53	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.53	   A^2 -> H(U1(e, c), f(e))
25.98/8.53	   A^2 -> H(U1(e, c), f(k))
25.98/8.53	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.53	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.53	   A^2 -> H(U1(k, e), f(c))
25.98/8.53	   A^2 -> H(U1(k, e), f(d))
25.98/8.53	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.53	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.53	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.53	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.53	   A^2 -> H(U1(k, c), U1(c, c))
25.98/8.53	   A^2 -> H(U1(k, c), f(e))
25.98/8.53	   A^2 -> H(U1(k, c), f(k))
25.98/8.53	   A^2 -> H(U1(k, c), U1(d, d))
25.98/8.53	   A^2 -> H(U1(c, e), U1(c, b))
25.98/8.53	   A^2 -> H(U1(c, e), U1(d, b))
25.98/8.53	   A^2 -> H(U1(c, e), U1(b, c))
25.98/8.53	   A^2 -> H(U1(c, e), U1(b, d))
25.98/8.53	   A^2 -> H(U1(c, e), U1(c, c))
25.98/8.53	   A^2 -> H(U1(c, e), f(e))
25.98/8.53	   A^2 -> H(U1(c, e), f(k))
25.98/8.53	   A^2 -> H(U1(c, e), U1(d, d))
25.98/8.53	   A^2 -> H(U1(c, k), U1(c, b))
25.98/8.53	   A^2 -> H(U1(c, k), U1(d, b))
25.98/8.53	   A^2 -> H(U1(c, k), U1(b, c))
25.98/8.53	   A^2 -> H(U1(c, k), U1(b, d))
25.98/8.53	
25.98/8.53	The TRS R consists of the following rules:
25.98/8.53	
25.98/8.53	   f(x) -> U1(x, x)
25.98/8.53	   U1(e, x) -> x
25.98/8.53	   a -> c
25.98/8.53	   a -> d
25.98/8.53	   b -> c
25.98/8.53	   b -> d
25.98/8.53	   d -> k
25.98/8.53	   c -> e
25.98/8.53	   c -> k
25.98/8.53	
25.98/8.53	Q is empty.
25.98/8.53	We have to consider all minimal (P,Q,R)-chains.
25.98/8.53	----------------------------------------
25.98/8.53	
25.98/8.53	(381) TransformationProof (EQUIVALENT)
25.98/8.53	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), f(c)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.53	
25.98/8.53	   (A^2 -> H(U1(e, k), f(c)),A^2 -> H(U1(e, k), f(c)))
25.98/8.53	   (A^2 -> H(U1(k, k), f(c)),A^2 -> H(U1(k, k), f(c)))
25.98/8.53	   (A^2 -> H(U1(c, k), U1(c, c)),A^2 -> H(U1(c, k), U1(c, c)))
25.98/8.53	   (A^2 -> H(U1(c, k), f(e)),A^2 -> H(U1(c, k), f(e)))
25.98/8.53	   (A^2 -> H(U1(c, k), f(k)),A^2 -> H(U1(c, k), f(k)))
25.98/8.53	
25.98/8.53	
25.98/8.53	----------------------------------------
25.98/8.53	
25.98/8.53	(382)
25.98/8.53	Obligation:
25.98/8.53	Q DP problem:
25.98/8.53	The TRS P consists of the following rules:
25.98/8.53	
25.98/8.53	   H(x, x) -> G(x, x, f(k))
25.98/8.53	   G(d, x, x) -> A^2
25.98/8.53	   A^2 -> H(f(c), f(c))
25.98/8.53	   A^2 -> H(f(d), f(d))
25.98/8.53	   A^2 -> H(U1(c, k), f(d))
25.98/8.53	   A^2 -> H(U1(c, c), U1(c, b))
25.98/8.53	   A^2 -> H(U1(c, c), U1(d, b))
25.98/8.53	   A^2 -> H(U1(c, c), U1(b, c))
25.98/8.53	   A^2 -> H(U1(c, c), U1(b, d))
25.98/8.53	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.53	   A^2 -> H(U1(c, c), f(e))
25.98/8.53	   A^2 -> H(U1(c, c), f(k))
25.98/8.53	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.53	   A^2 -> H(e, f(b))
25.98/8.53	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.53	   A^2 -> H(U1(e, e), f(c))
25.98/8.53	   A^2 -> H(U1(e, e), f(d))
25.98/8.53	   A^2 -> H(f(e), U1(c, b))
25.98/8.53	   A^2 -> H(f(e), U1(d, b))
25.98/8.53	   A^2 -> H(f(e), U1(b, c))
25.98/8.53	   A^2 -> H(f(e), U1(b, d))
25.98/8.53	   A^2 -> H(f(e), U1(c, c))
25.98/8.53	   A^2 -> H(f(e), f(e))
25.98/8.53	   A^2 -> H(f(e), f(k))
25.98/8.53	   A^2 -> H(f(e), U1(d, d))
25.98/8.53	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.53	   A^2 -> H(U1(k, k), f(c))
25.98/8.53	   A^2 -> H(U1(k, k), f(d))
25.98/8.53	   A^2 -> H(f(k), U1(c, b))
25.98/8.53	   A^2 -> H(f(k), U1(d, b))
25.98/8.53	   A^2 -> H(f(k), U1(b, c))
25.98/8.53	   A^2 -> H(f(k), U1(b, d))
25.98/8.53	   A^2 -> H(f(k), U1(c, c))
25.98/8.53	   A^2 -> H(f(k), f(e))
25.98/8.53	   A^2 -> H(f(k), f(k))
25.98/8.53	   A^2 -> H(f(k), U1(d, d))
25.98/8.53	   A^2 -> H(f(c), U1(e, b))
25.98/8.53	   A^2 -> H(f(c), U1(k, b))
25.98/8.53	   A^2 -> H(f(c), U1(c, d))
25.98/8.53	   A^2 -> H(f(c), U1(d, c))
25.98/8.53	   A^2 -> H(f(c), U1(b, e))
25.98/8.53	   A^2 -> H(f(c), U1(b, k))
25.98/8.53	   A^2 -> H(f(c), U1(k, d))
25.98/8.53	   A^2 -> H(f(c), U1(d, k))
25.98/8.53	   A^2 -> H(f(c), U1(k, k))
25.98/8.53	   A^2 -> H(U1(k, k), f(b))
25.98/8.53	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.53	   A^2 -> H(U1(k, d), f(c))
25.98/8.53	   A^2 -> H(U1(k, d), f(d))
25.98/8.53	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.53	   A^2 -> H(U1(d, k), f(c))
25.98/8.53	   A^2 -> H(U1(d, k), f(d))
25.98/8.53	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.53	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.53	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.53	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.53	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.53	   A^2 -> H(U1(d, d), f(e))
25.98/8.53	   A^2 -> H(U1(d, d), f(k))
25.98/8.53	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.53	   A^2 -> H(f(d), U1(e, b))
25.98/8.53	   A^2 -> H(f(d), U1(k, b))
25.98/8.53	   A^2 -> H(f(d), U1(c, d))
25.98/8.53	   A^2 -> H(f(d), U1(d, c))
25.98/8.53	   A^2 -> H(f(d), U1(b, e))
25.98/8.53	   A^2 -> H(f(d), U1(b, k))
25.98/8.53	   A^2 -> H(f(d), U1(e, c))
25.98/8.53	   A^2 -> H(f(d), U1(k, c))
25.98/8.53	   A^2 -> H(f(d), U1(c, e))
25.98/8.53	   A^2 -> H(f(d), U1(c, k))
25.98/8.53	   A^2 -> H(f(d), U1(e, e))
25.98/8.53	   A^2 -> H(f(d), U1(k, k))
25.98/8.53	   A^2 -> H(f(a), b)
25.98/8.53	   A^2 -> H(f(a), U1(e, d))
25.98/8.53	   A^2 -> H(f(a), U1(d, e))
25.98/8.53	   A^2 -> H(f(c), U1(e, c))
25.98/8.53	   A^2 -> H(f(c), U1(k, c))
25.98/8.53	   A^2 -> H(f(c), U1(c, e))
25.98/8.53	   A^2 -> H(f(c), U1(c, k))
25.98/8.53	   A^2 -> H(f(a), c)
25.98/8.53	   A^2 -> H(f(a), U1(e, k))
25.98/8.53	   A^2 -> H(f(a), U1(k, e))
25.98/8.53	   A^2 -> H(f(c), U1(e, e))
25.98/8.53	   A^2 -> H(f(a), e)
25.98/8.53	   A^2 -> H(f(d), U1(k, d))
25.98/8.53	   A^2 -> H(f(d), U1(d, k))
25.98/8.53	   A^2 -> H(f(a), U1(k, k))
25.98/8.53	   A^2 -> H(d, f(b))
25.98/8.53	   A^2 -> H(a, U1(b, b))
25.98/8.53	   A^2 -> H(a, f(c))
25.98/8.53	   A^2 -> H(a, f(d))
25.98/8.53	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.53	   A^2 -> H(U1(e, d), f(c))
25.98/8.53	   A^2 -> H(U1(e, d), f(d))
25.98/8.53	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.53	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.53	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.53	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.53	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.53	   A^2 -> H(U1(e, a), f(e))
25.98/8.53	   A^2 -> H(U1(e, a), f(k))
25.98/8.53	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.53	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.53	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.53	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.53	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.53	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.53	   A^2 -> H(U1(k, a), f(e))
25.98/8.53	   A^2 -> H(U1(k, a), f(k))
25.98/8.53	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.53	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.53	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.53	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.53	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.53	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.53	   A^2 -> H(U1(c, d), f(e))
25.98/8.53	   A^2 -> H(U1(c, d), f(k))
25.98/8.53	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.53	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.53	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.53	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.53	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.53	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.53	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.53	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.53	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.53	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.53	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.53	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.53	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.53	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.53	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.53	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.53	   A^2 -> H(U1(d, e), f(c))
25.98/8.53	   A^2 -> H(U1(d, e), f(d))
25.98/8.53	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.53	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.53	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.53	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.53	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.53	   A^2 -> H(U1(d, c), f(e))
25.98/8.53	   A^2 -> H(U1(d, c), f(k))
25.98/8.53	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.53	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.53	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.53	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.53	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.53	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.53	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.53	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.53	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.53	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.53	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.53	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.53	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.53	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.53	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.53	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.53	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.53	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.53	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.53	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.53	   A^2 -> H(U1(a, e), f(e))
25.98/8.53	   A^2 -> H(U1(a, e), f(k))
25.98/8.53	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.53	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.53	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.53	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.53	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.53	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.53	   A^2 -> H(U1(a, k), f(e))
25.98/8.53	   A^2 -> H(U1(a, k), f(k))
25.98/8.53	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.53	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.53	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.53	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.53	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.53	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.53	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.53	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.53	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.53	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.53	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.53	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.53	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.53	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.53	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.53	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.53	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.53	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.53	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.53	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.53	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.53	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.53	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.53	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.53	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.53	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.53	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.53	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.53	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.53	   A^2 -> H(U1(a, a), b)
25.98/8.53	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.53	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.53	   A^2 -> H(U1(a, a), c)
25.98/8.53	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.53	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.53	   A^2 -> H(U1(a, a), e)
25.98/8.53	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.53	   A^2 -> H(k, f(b))
25.98/8.53	   A^2 -> H(c, U1(b, b))
25.98/8.53	   A^2 -> H(c, f(c))
25.98/8.53	   A^2 -> H(c, f(d))
25.98/8.53	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.53	   A^2 -> H(U1(e, k), f(c))
25.98/8.53	   A^2 -> H(U1(e, k), f(d))
25.98/8.53	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.53	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.53	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.53	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.53	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.53	   A^2 -> H(U1(e, c), f(e))
25.98/8.53	   A^2 -> H(U1(e, c), f(k))
25.98/8.53	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.53	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.53	   A^2 -> H(U1(k, e), f(c))
25.98/8.53	   A^2 -> H(U1(k, e), f(d))
25.98/8.53	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.53	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.53	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.53	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.53	   A^2 -> H(U1(k, c), U1(c, c))
25.98/8.53	   A^2 -> H(U1(k, c), f(e))
25.98/8.53	   A^2 -> H(U1(k, c), f(k))
25.98/8.53	   A^2 -> H(U1(k, c), U1(d, d))
25.98/8.53	   A^2 -> H(U1(c, e), U1(c, b))
25.98/8.53	   A^2 -> H(U1(c, e), U1(d, b))
25.98/8.53	   A^2 -> H(U1(c, e), U1(b, c))
25.98/8.53	   A^2 -> H(U1(c, e), U1(b, d))
25.98/8.53	   A^2 -> H(U1(c, e), U1(c, c))
25.98/8.53	   A^2 -> H(U1(c, e), f(e))
25.98/8.53	   A^2 -> H(U1(c, e), f(k))
25.98/8.53	   A^2 -> H(U1(c, e), U1(d, d))
25.98/8.53	   A^2 -> H(U1(c, k), U1(c, b))
25.98/8.53	   A^2 -> H(U1(c, k), U1(d, b))
25.98/8.53	   A^2 -> H(U1(c, k), U1(b, c))
25.98/8.53	   A^2 -> H(U1(c, k), U1(b, d))
25.98/8.53	   A^2 -> H(U1(c, k), U1(c, c))
25.98/8.53	   A^2 -> H(U1(c, k), f(e))
25.98/8.53	   A^2 -> H(U1(c, k), f(k))
25.98/8.53	
25.98/8.53	The TRS R consists of the following rules:
25.98/8.53	
25.98/8.53	   f(x) -> U1(x, x)
25.98/8.53	   U1(e, x) -> x
25.98/8.53	   a -> c
25.98/8.53	   a -> d
25.98/8.53	   b -> c
25.98/8.53	   b -> d
25.98/8.53	   d -> k
25.98/8.53	   c -> e
25.98/8.53	   c -> k
25.98/8.53	
25.98/8.53	Q is empty.
25.98/8.53	We have to consider all minimal (P,Q,R)-chains.
25.98/8.53	----------------------------------------
25.98/8.53	
25.98/8.53	(383) TransformationProof (EQUIVALENT)
25.98/8.53	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), f(d)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.53	
25.98/8.53	   (A^2 -> H(U1(e, k), f(d)),A^2 -> H(U1(e, k), f(d)))
25.98/8.53	   (A^2 -> H(U1(k, k), f(d)),A^2 -> H(U1(k, k), f(d)))
25.98/8.53	   (A^2 -> H(U1(c, k), U1(d, d)),A^2 -> H(U1(c, k), U1(d, d)))
25.98/8.53	   (A^2 -> H(U1(c, k), f(k)),A^2 -> H(U1(c, k), f(k)))
25.98/8.53	
25.98/8.53	
25.98/8.53	----------------------------------------
25.98/8.53	
25.98/8.53	(384)
25.98/8.53	Obligation:
25.98/8.53	Q DP problem:
25.98/8.53	The TRS P consists of the following rules:
25.98/8.53	
25.98/8.53	   H(x, x) -> G(x, x, f(k))
25.98/8.53	   G(d, x, x) -> A^2
25.98/8.53	   A^2 -> H(f(c), f(c))
25.98/8.53	   A^2 -> H(f(d), f(d))
25.98/8.53	   A^2 -> H(U1(c, c), U1(c, b))
25.98/8.53	   A^2 -> H(U1(c, c), U1(d, b))
25.98/8.53	   A^2 -> H(U1(c, c), U1(b, c))
25.98/8.53	   A^2 -> H(U1(c, c), U1(b, d))
25.98/8.53	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.53	   A^2 -> H(U1(c, c), f(e))
25.98/8.53	   A^2 -> H(U1(c, c), f(k))
25.98/8.53	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.53	   A^2 -> H(e, f(b))
25.98/8.53	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.53	   A^2 -> H(U1(e, e), f(c))
25.98/8.53	   A^2 -> H(U1(e, e), f(d))
25.98/8.53	   A^2 -> H(f(e), U1(c, b))
25.98/8.53	   A^2 -> H(f(e), U1(d, b))
25.98/8.53	   A^2 -> H(f(e), U1(b, c))
25.98/8.53	   A^2 -> H(f(e), U1(b, d))
25.98/8.53	   A^2 -> H(f(e), U1(c, c))
25.98/8.53	   A^2 -> H(f(e), f(e))
25.98/8.53	   A^2 -> H(f(e), f(k))
25.98/8.53	   A^2 -> H(f(e), U1(d, d))
25.98/8.53	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.53	   A^2 -> H(U1(k, k), f(c))
25.98/8.53	   A^2 -> H(U1(k, k), f(d))
25.98/8.53	   A^2 -> H(f(k), U1(c, b))
25.98/8.53	   A^2 -> H(f(k), U1(d, b))
25.98/8.53	   A^2 -> H(f(k), U1(b, c))
25.98/8.53	   A^2 -> H(f(k), U1(b, d))
25.98/8.53	   A^2 -> H(f(k), U1(c, c))
25.98/8.53	   A^2 -> H(f(k), f(e))
25.98/8.53	   A^2 -> H(f(k), f(k))
25.98/8.53	   A^2 -> H(f(k), U1(d, d))
25.98/8.53	   A^2 -> H(f(c), U1(e, b))
25.98/8.53	   A^2 -> H(f(c), U1(k, b))
25.98/8.53	   A^2 -> H(f(c), U1(c, d))
25.98/8.53	   A^2 -> H(f(c), U1(d, c))
25.98/8.53	   A^2 -> H(f(c), U1(b, e))
25.98/8.53	   A^2 -> H(f(c), U1(b, k))
25.98/8.53	   A^2 -> H(f(c), U1(k, d))
25.98/8.53	   A^2 -> H(f(c), U1(d, k))
25.98/8.53	   A^2 -> H(f(c), U1(k, k))
25.98/8.53	   A^2 -> H(U1(k, k), f(b))
25.98/8.53	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.53	   A^2 -> H(U1(k, d), f(c))
25.98/8.53	   A^2 -> H(U1(k, d), f(d))
25.98/8.53	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.53	   A^2 -> H(U1(d, k), f(c))
25.98/8.53	   A^2 -> H(U1(d, k), f(d))
25.98/8.53	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.53	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.53	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.53	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.53	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.53	   A^2 -> H(U1(d, d), f(e))
25.98/8.53	   A^2 -> H(U1(d, d), f(k))
25.98/8.53	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.53	   A^2 -> H(f(d), U1(e, b))
25.98/8.53	   A^2 -> H(f(d), U1(k, b))
25.98/8.53	   A^2 -> H(f(d), U1(c, d))
25.98/8.53	   A^2 -> H(f(d), U1(d, c))
25.98/8.53	   A^2 -> H(f(d), U1(b, e))
25.98/8.53	   A^2 -> H(f(d), U1(b, k))
25.98/8.53	   A^2 -> H(f(d), U1(e, c))
25.98/8.53	   A^2 -> H(f(d), U1(k, c))
25.98/8.53	   A^2 -> H(f(d), U1(c, e))
25.98/8.53	   A^2 -> H(f(d), U1(c, k))
25.98/8.53	   A^2 -> H(f(d), U1(e, e))
25.98/8.53	   A^2 -> H(f(d), U1(k, k))
25.98/8.53	   A^2 -> H(f(a), b)
25.98/8.53	   A^2 -> H(f(a), U1(e, d))
25.98/8.53	   A^2 -> H(f(a), U1(d, e))
25.98/8.53	   A^2 -> H(f(c), U1(e, c))
25.98/8.53	   A^2 -> H(f(c), U1(k, c))
25.98/8.53	   A^2 -> H(f(c), U1(c, e))
25.98/8.53	   A^2 -> H(f(c), U1(c, k))
25.98/8.53	   A^2 -> H(f(a), c)
25.98/8.53	   A^2 -> H(f(a), U1(e, k))
25.98/8.53	   A^2 -> H(f(a), U1(k, e))
25.98/8.53	   A^2 -> H(f(c), U1(e, e))
25.98/8.53	   A^2 -> H(f(a), e)
25.98/8.53	   A^2 -> H(f(d), U1(k, d))
25.98/8.53	   A^2 -> H(f(d), U1(d, k))
25.98/8.53	   A^2 -> H(f(a), U1(k, k))
25.98/8.53	   A^2 -> H(d, f(b))
25.98/8.53	   A^2 -> H(a, U1(b, b))
25.98/8.53	   A^2 -> H(a, f(c))
25.98/8.53	   A^2 -> H(a, f(d))
25.98/8.53	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.53	   A^2 -> H(U1(e, d), f(c))
25.98/8.53	   A^2 -> H(U1(e, d), f(d))
25.98/8.53	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.53	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.53	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.53	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.53	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.53	   A^2 -> H(U1(e, a), f(e))
25.98/8.53	   A^2 -> H(U1(e, a), f(k))
25.98/8.53	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.53	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.53	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.53	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.53	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.53	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.53	   A^2 -> H(U1(k, a), f(e))
25.98/8.53	   A^2 -> H(U1(k, a), f(k))
25.98/8.53	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.53	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.53	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.53	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.53	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.53	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.53	   A^2 -> H(U1(c, d), f(e))
25.98/8.53	   A^2 -> H(U1(c, d), f(k))
25.98/8.53	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.53	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.53	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.53	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.53	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.53	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.53	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.53	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.53	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.53	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.53	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.53	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.53	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.53	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.53	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.53	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.53	   A^2 -> H(U1(d, e), f(c))
25.98/8.53	   A^2 -> H(U1(d, e), f(d))
25.98/8.53	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.53	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.53	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.53	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.53	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.53	   A^2 -> H(U1(d, c), f(e))
25.98/8.53	   A^2 -> H(U1(d, c), f(k))
25.98/8.53	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.53	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.53	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.53	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.53	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.53	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.53	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.53	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.53	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.53	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.53	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.53	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.53	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.53	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.53	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.53	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.53	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.53	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.53	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.53	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.53	   A^2 -> H(U1(a, e), f(e))
25.98/8.53	   A^2 -> H(U1(a, e), f(k))
25.98/8.53	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.53	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.53	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.53	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.53	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.53	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.53	   A^2 -> H(U1(a, k), f(e))
25.98/8.53	   A^2 -> H(U1(a, k), f(k))
25.98/8.53	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.53	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.53	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.53	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.53	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.53	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.53	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.53	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.54	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.54	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, a), b)
25.98/8.54	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.54	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.54	   A^2 -> H(U1(a, a), c)
25.98/8.54	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.54	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.54	   A^2 -> H(U1(a, a), e)
25.98/8.54	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.54	   A^2 -> H(k, f(b))
25.98/8.54	   A^2 -> H(c, U1(b, b))
25.98/8.54	   A^2 -> H(c, f(c))
25.98/8.54	   A^2 -> H(c, f(d))
25.98/8.54	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, k), f(c))
25.98/8.54	   A^2 -> H(U1(e, k), f(d))
25.98/8.54	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(e, c), f(e))
25.98/8.54	   A^2 -> H(U1(e, c), f(k))
25.98/8.54	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, e), f(c))
25.98/8.54	   A^2 -> H(U1(k, e), f(d))
25.98/8.54	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(k, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(k, c), f(e))
25.98/8.54	   A^2 -> H(U1(k, c), f(k))
25.98/8.54	   A^2 -> H(U1(k, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, e), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, e), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, e), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, e), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, e), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, e), f(e))
25.98/8.54	   A^2 -> H(U1(c, e), f(k))
25.98/8.54	   A^2 -> H(U1(c, e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, k), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, k), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, k), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, k), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, k), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, k), f(e))
25.98/8.54	   A^2 -> H(U1(c, k), f(k))
25.98/8.54	   A^2 -> H(U1(c, k), U1(d, d))
25.98/8.54	
25.98/8.54	The TRS R consists of the following rules:
25.98/8.54	
25.98/8.54	   f(x) -> U1(x, x)
25.98/8.54	   U1(e, x) -> x
25.98/8.54	   a -> c
25.98/8.54	   a -> d
25.98/8.54	   b -> c
25.98/8.54	   b -> d
25.98/8.54	   d -> k
25.98/8.54	   c -> e
25.98/8.54	   c -> k
25.98/8.54	
25.98/8.54	Q is empty.
25.98/8.54	We have to consider all minimal (P,Q,R)-chains.
25.98/8.54	----------------------------------------
25.98/8.54	
25.98/8.54	(385) TransformationProof (EQUIVALENT)
25.98/8.54	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.54	
25.98/8.54	   (A^2 -> H(U1(e, c), U1(c, b)),A^2 -> H(U1(e, c), U1(c, b)))
25.98/8.54	   (A^2 -> H(U1(k, c), U1(c, b)),A^2 -> H(U1(k, c), U1(c, b)))
25.98/8.54	   (A^2 -> H(U1(c, e), U1(c, b)),A^2 -> H(U1(c, e), U1(c, b)))
25.98/8.54	   (A^2 -> H(U1(c, k), U1(c, b)),A^2 -> H(U1(c, k), U1(c, b)))
25.98/8.54	   (A^2 -> H(U1(c, c), U1(e, b)),A^2 -> H(U1(c, c), U1(e, b)))
25.98/8.54	   (A^2 -> H(U1(c, c), U1(k, b)),A^2 -> H(U1(c, c), U1(k, b)))
25.98/8.54	   (A^2 -> H(U1(c, c), U1(c, c)),A^2 -> H(U1(c, c), U1(c, c)))
25.98/8.54	   (A^2 -> H(U1(c, c), U1(c, d)),A^2 -> H(U1(c, c), U1(c, d)))
25.98/8.54	
25.98/8.54	
25.98/8.54	----------------------------------------
25.98/8.54	
25.98/8.54	(386)
25.98/8.54	Obligation:
25.98/8.54	Q DP problem:
25.98/8.54	The TRS P consists of the following rules:
25.98/8.54	
25.98/8.54	   H(x, x) -> G(x, x, f(k))
25.98/8.54	   G(d, x, x) -> A^2
25.98/8.54	   A^2 -> H(f(c), f(c))
25.98/8.54	   A^2 -> H(f(d), f(d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, c), f(e))
25.98/8.54	   A^2 -> H(U1(c, c), f(k))
25.98/8.54	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.54	   A^2 -> H(e, f(b))
25.98/8.54	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, e), f(c))
25.98/8.54	   A^2 -> H(U1(e, e), f(d))
25.98/8.54	   A^2 -> H(f(e), U1(c, b))
25.98/8.54	   A^2 -> H(f(e), U1(d, b))
25.98/8.54	   A^2 -> H(f(e), U1(b, c))
25.98/8.54	   A^2 -> H(f(e), U1(b, d))
25.98/8.54	   A^2 -> H(f(e), U1(c, c))
25.98/8.54	   A^2 -> H(f(e), f(e))
25.98/8.54	   A^2 -> H(f(e), f(k))
25.98/8.54	   A^2 -> H(f(e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, k), f(c))
25.98/8.54	   A^2 -> H(U1(k, k), f(d))
25.98/8.54	   A^2 -> H(f(k), U1(c, b))
25.98/8.54	   A^2 -> H(f(k), U1(d, b))
25.98/8.54	   A^2 -> H(f(k), U1(b, c))
25.98/8.54	   A^2 -> H(f(k), U1(b, d))
25.98/8.54	   A^2 -> H(f(k), U1(c, c))
25.98/8.54	   A^2 -> H(f(k), f(e))
25.98/8.54	   A^2 -> H(f(k), f(k))
25.98/8.54	   A^2 -> H(f(k), U1(d, d))
25.98/8.54	   A^2 -> H(f(c), U1(e, b))
25.98/8.54	   A^2 -> H(f(c), U1(k, b))
25.98/8.54	   A^2 -> H(f(c), U1(c, d))
25.98/8.54	   A^2 -> H(f(c), U1(d, c))
25.98/8.54	   A^2 -> H(f(c), U1(b, e))
25.98/8.54	   A^2 -> H(f(c), U1(b, k))
25.98/8.54	   A^2 -> H(f(c), U1(k, d))
25.98/8.54	   A^2 -> H(f(c), U1(d, k))
25.98/8.54	   A^2 -> H(f(c), U1(k, k))
25.98/8.54	   A^2 -> H(U1(k, k), f(b))
25.98/8.54	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, d), f(c))
25.98/8.54	   A^2 -> H(U1(k, d), f(d))
25.98/8.54	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(d, k), f(c))
25.98/8.54	   A^2 -> H(U1(d, k), f(d))
25.98/8.54	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.54	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.54	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.54	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.54	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.54	   A^2 -> H(U1(d, d), f(e))
25.98/8.54	   A^2 -> H(U1(d, d), f(k))
25.98/8.54	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.54	   A^2 -> H(f(d), U1(e, b))
25.98/8.54	   A^2 -> H(f(d), U1(k, b))
25.98/8.54	   A^2 -> H(f(d), U1(c, d))
25.98/8.54	   A^2 -> H(f(d), U1(d, c))
25.98/8.54	   A^2 -> H(f(d), U1(b, e))
25.98/8.54	   A^2 -> H(f(d), U1(b, k))
25.98/8.54	   A^2 -> H(f(d), U1(e, c))
25.98/8.54	   A^2 -> H(f(d), U1(k, c))
25.98/8.54	   A^2 -> H(f(d), U1(c, e))
25.98/8.54	   A^2 -> H(f(d), U1(c, k))
25.98/8.54	   A^2 -> H(f(d), U1(e, e))
25.98/8.54	   A^2 -> H(f(d), U1(k, k))
25.98/8.54	   A^2 -> H(f(a), b)
25.98/8.54	   A^2 -> H(f(a), U1(e, d))
25.98/8.54	   A^2 -> H(f(a), U1(d, e))
25.98/8.54	   A^2 -> H(f(c), U1(e, c))
25.98/8.54	   A^2 -> H(f(c), U1(k, c))
25.98/8.54	   A^2 -> H(f(c), U1(c, e))
25.98/8.54	   A^2 -> H(f(c), U1(c, k))
25.98/8.54	   A^2 -> H(f(a), c)
25.98/8.54	   A^2 -> H(f(a), U1(e, k))
25.98/8.54	   A^2 -> H(f(a), U1(k, e))
25.98/8.54	   A^2 -> H(f(c), U1(e, e))
25.98/8.54	   A^2 -> H(f(a), e)
25.98/8.54	   A^2 -> H(f(d), U1(k, d))
25.98/8.54	   A^2 -> H(f(d), U1(d, k))
25.98/8.54	   A^2 -> H(f(a), U1(k, k))
25.98/8.54	   A^2 -> H(d, f(b))
25.98/8.54	   A^2 -> H(a, U1(b, b))
25.98/8.54	   A^2 -> H(a, f(c))
25.98/8.54	   A^2 -> H(a, f(d))
25.98/8.54	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, d), f(c))
25.98/8.54	   A^2 -> H(U1(e, d), f(d))
25.98/8.54	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.54	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.54	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.54	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.54	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.54	   A^2 -> H(U1(e, a), f(e))
25.98/8.54	   A^2 -> H(U1(e, a), f(k))
25.98/8.54	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.54	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.54	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.54	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.54	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.54	   A^2 -> H(U1(k, a), f(e))
25.98/8.54	   A^2 -> H(U1(k, a), f(k))
25.98/8.54	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, d), f(e))
25.98/8.54	   A^2 -> H(U1(c, d), f(k))
25.98/8.54	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.54	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(d, e), f(c))
25.98/8.54	   A^2 -> H(U1(d, e), f(d))
25.98/8.54	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(d, c), f(e))
25.98/8.54	   A^2 -> H(U1(d, c), f(k))
25.98/8.54	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.54	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.54	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.54	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.54	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.54	   A^2 -> H(U1(a, e), f(e))
25.98/8.54	   A^2 -> H(U1(a, e), f(k))
25.98/8.54	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.54	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.54	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.54	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.54	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.54	   A^2 -> H(U1(a, k), f(e))
25.98/8.54	   A^2 -> H(U1(a, k), f(k))
25.98/8.54	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.54	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.54	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, a), b)
25.98/8.54	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.54	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.54	   A^2 -> H(U1(a, a), c)
25.98/8.54	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.54	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.54	   A^2 -> H(U1(a, a), e)
25.98/8.54	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.54	   A^2 -> H(k, f(b))
25.98/8.54	   A^2 -> H(c, U1(b, b))
25.98/8.54	   A^2 -> H(c, f(c))
25.98/8.54	   A^2 -> H(c, f(d))
25.98/8.54	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, k), f(c))
25.98/8.54	   A^2 -> H(U1(e, k), f(d))
25.98/8.54	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(e, c), f(e))
25.98/8.54	   A^2 -> H(U1(e, c), f(k))
25.98/8.54	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, e), f(c))
25.98/8.54	   A^2 -> H(U1(k, e), f(d))
25.98/8.54	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(k, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(k, c), f(e))
25.98/8.54	   A^2 -> H(U1(k, c), f(k))
25.98/8.54	   A^2 -> H(U1(k, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, e), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, e), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, e), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, e), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, e), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, e), f(e))
25.98/8.54	   A^2 -> H(U1(c, e), f(k))
25.98/8.54	   A^2 -> H(U1(c, e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, k), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, k), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, k), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, k), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, k), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, k), f(e))
25.98/8.54	   A^2 -> H(U1(c, k), f(k))
25.98/8.54	   A^2 -> H(U1(c, k), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(e, b))
25.98/8.54	   A^2 -> H(U1(c, c), U1(k, b))
25.98/8.54	   A^2 -> H(U1(c, c), U1(c, d))
25.98/8.54	
25.98/8.54	The TRS R consists of the following rules:
25.98/8.54	
25.98/8.54	   f(x) -> U1(x, x)
25.98/8.54	   U1(e, x) -> x
25.98/8.54	   a -> c
25.98/8.54	   a -> d
25.98/8.54	   b -> c
25.98/8.54	   b -> d
25.98/8.54	   d -> k
25.98/8.54	   c -> e
25.98/8.54	   c -> k
25.98/8.54	
25.98/8.54	Q is empty.
25.98/8.54	We have to consider all minimal (P,Q,R)-chains.
25.98/8.54	----------------------------------------
25.98/8.54	
25.98/8.54	(387) TransformationProof (EQUIVALENT)
25.98/8.54	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.54	
25.98/8.54	   (A^2 -> H(U1(e, c), U1(d, b)),A^2 -> H(U1(e, c), U1(d, b)))
25.98/8.54	   (A^2 -> H(U1(k, c), U1(d, b)),A^2 -> H(U1(k, c), U1(d, b)))
25.98/8.54	   (A^2 -> H(U1(c, e), U1(d, b)),A^2 -> H(U1(c, e), U1(d, b)))
25.98/8.54	   (A^2 -> H(U1(c, k), U1(d, b)),A^2 -> H(U1(c, k), U1(d, b)))
25.98/8.54	   (A^2 -> H(U1(c, c), U1(k, b)),A^2 -> H(U1(c, c), U1(k, b)))
25.98/8.54	   (A^2 -> H(U1(c, c), U1(d, c)),A^2 -> H(U1(c, c), U1(d, c)))
25.98/8.54	   (A^2 -> H(U1(c, c), U1(d, d)),A^2 -> H(U1(c, c), U1(d, d)))
25.98/8.54	
25.98/8.54	
25.98/8.54	----------------------------------------
25.98/8.54	
25.98/8.54	(388)
25.98/8.54	Obligation:
25.98/8.54	Q DP problem:
25.98/8.54	The TRS P consists of the following rules:
25.98/8.54	
25.98/8.54	   H(x, x) -> G(x, x, f(k))
25.98/8.54	   G(d, x, x) -> A^2
25.98/8.54	   A^2 -> H(f(c), f(c))
25.98/8.54	   A^2 -> H(f(d), f(d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, c), f(e))
25.98/8.54	   A^2 -> H(U1(c, c), f(k))
25.98/8.54	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.54	   A^2 -> H(e, f(b))
25.98/8.54	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, e), f(c))
25.98/8.54	   A^2 -> H(U1(e, e), f(d))
25.98/8.54	   A^2 -> H(f(e), U1(c, b))
25.98/8.54	   A^2 -> H(f(e), U1(d, b))
25.98/8.54	   A^2 -> H(f(e), U1(b, c))
25.98/8.54	   A^2 -> H(f(e), U1(b, d))
25.98/8.54	   A^2 -> H(f(e), U1(c, c))
25.98/8.54	   A^2 -> H(f(e), f(e))
25.98/8.54	   A^2 -> H(f(e), f(k))
25.98/8.54	   A^2 -> H(f(e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, k), f(c))
25.98/8.54	   A^2 -> H(U1(k, k), f(d))
25.98/8.54	   A^2 -> H(f(k), U1(c, b))
25.98/8.54	   A^2 -> H(f(k), U1(d, b))
25.98/8.54	   A^2 -> H(f(k), U1(b, c))
25.98/8.54	   A^2 -> H(f(k), U1(b, d))
25.98/8.54	   A^2 -> H(f(k), U1(c, c))
25.98/8.54	   A^2 -> H(f(k), f(e))
25.98/8.54	   A^2 -> H(f(k), f(k))
25.98/8.54	   A^2 -> H(f(k), U1(d, d))
25.98/8.54	   A^2 -> H(f(c), U1(e, b))
25.98/8.54	   A^2 -> H(f(c), U1(k, b))
25.98/8.54	   A^2 -> H(f(c), U1(c, d))
25.98/8.54	   A^2 -> H(f(c), U1(d, c))
25.98/8.54	   A^2 -> H(f(c), U1(b, e))
25.98/8.54	   A^2 -> H(f(c), U1(b, k))
25.98/8.54	   A^2 -> H(f(c), U1(k, d))
25.98/8.54	   A^2 -> H(f(c), U1(d, k))
25.98/8.54	   A^2 -> H(f(c), U1(k, k))
25.98/8.54	   A^2 -> H(U1(k, k), f(b))
25.98/8.54	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, d), f(c))
25.98/8.54	   A^2 -> H(U1(k, d), f(d))
25.98/8.54	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(d, k), f(c))
25.98/8.54	   A^2 -> H(U1(d, k), f(d))
25.98/8.54	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.54	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.54	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.54	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.54	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.54	   A^2 -> H(U1(d, d), f(e))
25.98/8.54	   A^2 -> H(U1(d, d), f(k))
25.98/8.54	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.54	   A^2 -> H(f(d), U1(e, b))
25.98/8.54	   A^2 -> H(f(d), U1(k, b))
25.98/8.54	   A^2 -> H(f(d), U1(c, d))
25.98/8.54	   A^2 -> H(f(d), U1(d, c))
25.98/8.54	   A^2 -> H(f(d), U1(b, e))
25.98/8.54	   A^2 -> H(f(d), U1(b, k))
25.98/8.54	   A^2 -> H(f(d), U1(e, c))
25.98/8.54	   A^2 -> H(f(d), U1(k, c))
25.98/8.54	   A^2 -> H(f(d), U1(c, e))
25.98/8.54	   A^2 -> H(f(d), U1(c, k))
25.98/8.54	   A^2 -> H(f(d), U1(e, e))
25.98/8.54	   A^2 -> H(f(d), U1(k, k))
25.98/8.54	   A^2 -> H(f(a), b)
25.98/8.54	   A^2 -> H(f(a), U1(e, d))
25.98/8.54	   A^2 -> H(f(a), U1(d, e))
25.98/8.54	   A^2 -> H(f(c), U1(e, c))
25.98/8.54	   A^2 -> H(f(c), U1(k, c))
25.98/8.54	   A^2 -> H(f(c), U1(c, e))
25.98/8.54	   A^2 -> H(f(c), U1(c, k))
25.98/8.54	   A^2 -> H(f(a), c)
25.98/8.54	   A^2 -> H(f(a), U1(e, k))
25.98/8.54	   A^2 -> H(f(a), U1(k, e))
25.98/8.54	   A^2 -> H(f(c), U1(e, e))
25.98/8.54	   A^2 -> H(f(a), e)
25.98/8.54	   A^2 -> H(f(d), U1(k, d))
25.98/8.54	   A^2 -> H(f(d), U1(d, k))
25.98/8.54	   A^2 -> H(f(a), U1(k, k))
25.98/8.54	   A^2 -> H(d, f(b))
25.98/8.54	   A^2 -> H(a, U1(b, b))
25.98/8.54	   A^2 -> H(a, f(c))
25.98/8.54	   A^2 -> H(a, f(d))
25.98/8.54	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, d), f(c))
25.98/8.54	   A^2 -> H(U1(e, d), f(d))
25.98/8.54	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.54	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.54	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.54	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.54	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.54	   A^2 -> H(U1(e, a), f(e))
25.98/8.54	   A^2 -> H(U1(e, a), f(k))
25.98/8.54	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.54	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.54	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.54	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.54	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.54	   A^2 -> H(U1(k, a), f(e))
25.98/8.54	   A^2 -> H(U1(k, a), f(k))
25.98/8.54	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, d), f(e))
25.98/8.54	   A^2 -> H(U1(c, d), f(k))
25.98/8.54	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.54	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(d, e), f(c))
25.98/8.54	   A^2 -> H(U1(d, e), f(d))
25.98/8.54	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(d, c), f(e))
25.98/8.54	   A^2 -> H(U1(d, c), f(k))
25.98/8.54	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.54	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.54	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.54	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.54	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.54	   A^2 -> H(U1(a, e), f(e))
25.98/8.54	   A^2 -> H(U1(a, e), f(k))
25.98/8.54	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.54	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.54	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.54	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.54	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.54	   A^2 -> H(U1(a, k), f(e))
25.98/8.54	   A^2 -> H(U1(a, k), f(k))
25.98/8.54	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.54	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.54	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, a), b)
25.98/8.54	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.54	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.54	   A^2 -> H(U1(a, a), c)
25.98/8.54	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.54	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.54	   A^2 -> H(U1(a, a), e)
25.98/8.54	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.54	   A^2 -> H(k, f(b))
25.98/8.54	   A^2 -> H(c, U1(b, b))
25.98/8.54	   A^2 -> H(c, f(c))
25.98/8.54	   A^2 -> H(c, f(d))
25.98/8.54	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, k), f(c))
25.98/8.54	   A^2 -> H(U1(e, k), f(d))
25.98/8.54	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(e, c), f(e))
25.98/8.54	   A^2 -> H(U1(e, c), f(k))
25.98/8.54	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, e), f(c))
25.98/8.54	   A^2 -> H(U1(k, e), f(d))
25.98/8.54	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(k, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(k, c), f(e))
25.98/8.54	   A^2 -> H(U1(k, c), f(k))
25.98/8.54	   A^2 -> H(U1(k, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, e), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, e), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, e), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, e), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, e), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, e), f(e))
25.98/8.54	   A^2 -> H(U1(c, e), f(k))
25.98/8.54	   A^2 -> H(U1(c, e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, k), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, k), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, k), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, k), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, k), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, k), f(e))
25.98/8.54	   A^2 -> H(U1(c, k), f(k))
25.98/8.54	   A^2 -> H(U1(c, k), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(e, b))
25.98/8.54	   A^2 -> H(U1(c, c), U1(k, b))
25.98/8.54	   A^2 -> H(U1(c, c), U1(c, d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(d, c))
25.98/8.54	
25.98/8.54	The TRS R consists of the following rules:
25.98/8.54	
25.98/8.54	   f(x) -> U1(x, x)
25.98/8.54	   U1(e, x) -> x
25.98/8.54	   a -> c
25.98/8.54	   a -> d
25.98/8.54	   b -> c
25.98/8.54	   b -> d
25.98/8.54	   d -> k
25.98/8.54	   c -> e
25.98/8.54	   c -> k
25.98/8.54	
25.98/8.54	Q is empty.
25.98/8.54	We have to consider all minimal (P,Q,R)-chains.
25.98/8.54	----------------------------------------
25.98/8.54	
25.98/8.54	(389) TransformationProof (EQUIVALENT)
25.98/8.54	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.54	
25.98/8.54	   (A^2 -> H(U1(e, c), U1(b, c)),A^2 -> H(U1(e, c), U1(b, c)))
25.98/8.54	   (A^2 -> H(U1(k, c), U1(b, c)),A^2 -> H(U1(k, c), U1(b, c)))
25.98/8.54	   (A^2 -> H(U1(c, e), U1(b, c)),A^2 -> H(U1(c, e), U1(b, c)))
25.98/8.54	   (A^2 -> H(U1(c, k), U1(b, c)),A^2 -> H(U1(c, k), U1(b, c)))
25.98/8.54	   (A^2 -> H(U1(c, c), U1(c, c)),A^2 -> H(U1(c, c), U1(c, c)))
25.98/8.54	   (A^2 -> H(U1(c, c), U1(d, c)),A^2 -> H(U1(c, c), U1(d, c)))
25.98/8.54	   (A^2 -> H(U1(c, c), U1(b, e)),A^2 -> H(U1(c, c), U1(b, e)))
25.98/8.54	   (A^2 -> H(U1(c, c), U1(b, k)),A^2 -> H(U1(c, c), U1(b, k)))
25.98/8.54	
25.98/8.54	
25.98/8.54	----------------------------------------
25.98/8.54	
25.98/8.54	(390)
25.98/8.54	Obligation:
25.98/8.54	Q DP problem:
25.98/8.54	The TRS P consists of the following rules:
25.98/8.54	
25.98/8.54	   H(x, x) -> G(x, x, f(k))
25.98/8.54	   G(d, x, x) -> A^2
25.98/8.54	   A^2 -> H(f(c), f(c))
25.98/8.54	   A^2 -> H(f(d), f(d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, c), f(e))
25.98/8.54	   A^2 -> H(U1(c, c), f(k))
25.98/8.54	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.54	   A^2 -> H(e, f(b))
25.98/8.54	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, e), f(c))
25.98/8.54	   A^2 -> H(U1(e, e), f(d))
25.98/8.54	   A^2 -> H(f(e), U1(c, b))
25.98/8.54	   A^2 -> H(f(e), U1(d, b))
25.98/8.54	   A^2 -> H(f(e), U1(b, c))
25.98/8.54	   A^2 -> H(f(e), U1(b, d))
25.98/8.54	   A^2 -> H(f(e), U1(c, c))
25.98/8.54	   A^2 -> H(f(e), f(e))
25.98/8.54	   A^2 -> H(f(e), f(k))
25.98/8.54	   A^2 -> H(f(e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, k), f(c))
25.98/8.54	   A^2 -> H(U1(k, k), f(d))
25.98/8.54	   A^2 -> H(f(k), U1(c, b))
25.98/8.54	   A^2 -> H(f(k), U1(d, b))
25.98/8.54	   A^2 -> H(f(k), U1(b, c))
25.98/8.54	   A^2 -> H(f(k), U1(b, d))
25.98/8.54	   A^2 -> H(f(k), U1(c, c))
25.98/8.54	   A^2 -> H(f(k), f(e))
25.98/8.54	   A^2 -> H(f(k), f(k))
25.98/8.54	   A^2 -> H(f(k), U1(d, d))
25.98/8.54	   A^2 -> H(f(c), U1(e, b))
25.98/8.54	   A^2 -> H(f(c), U1(k, b))
25.98/8.54	   A^2 -> H(f(c), U1(c, d))
25.98/8.54	   A^2 -> H(f(c), U1(d, c))
25.98/8.54	   A^2 -> H(f(c), U1(b, e))
25.98/8.54	   A^2 -> H(f(c), U1(b, k))
25.98/8.54	   A^2 -> H(f(c), U1(k, d))
25.98/8.54	   A^2 -> H(f(c), U1(d, k))
25.98/8.54	   A^2 -> H(f(c), U1(k, k))
25.98/8.54	   A^2 -> H(U1(k, k), f(b))
25.98/8.54	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, d), f(c))
25.98/8.54	   A^2 -> H(U1(k, d), f(d))
25.98/8.54	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(d, k), f(c))
25.98/8.54	   A^2 -> H(U1(d, k), f(d))
25.98/8.54	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.54	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.54	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.54	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.54	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.54	   A^2 -> H(U1(d, d), f(e))
25.98/8.54	   A^2 -> H(U1(d, d), f(k))
25.98/8.54	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.54	   A^2 -> H(f(d), U1(e, b))
25.98/8.54	   A^2 -> H(f(d), U1(k, b))
25.98/8.54	   A^2 -> H(f(d), U1(c, d))
25.98/8.54	   A^2 -> H(f(d), U1(d, c))
25.98/8.54	   A^2 -> H(f(d), U1(b, e))
25.98/8.54	   A^2 -> H(f(d), U1(b, k))
25.98/8.54	   A^2 -> H(f(d), U1(e, c))
25.98/8.54	   A^2 -> H(f(d), U1(k, c))
25.98/8.54	   A^2 -> H(f(d), U1(c, e))
25.98/8.54	   A^2 -> H(f(d), U1(c, k))
25.98/8.54	   A^2 -> H(f(d), U1(e, e))
25.98/8.54	   A^2 -> H(f(d), U1(k, k))
25.98/8.54	   A^2 -> H(f(a), b)
25.98/8.54	   A^2 -> H(f(a), U1(e, d))
25.98/8.54	   A^2 -> H(f(a), U1(d, e))
25.98/8.54	   A^2 -> H(f(c), U1(e, c))
25.98/8.54	   A^2 -> H(f(c), U1(k, c))
25.98/8.54	   A^2 -> H(f(c), U1(c, e))
25.98/8.54	   A^2 -> H(f(c), U1(c, k))
25.98/8.54	   A^2 -> H(f(a), c)
25.98/8.54	   A^2 -> H(f(a), U1(e, k))
25.98/8.54	   A^2 -> H(f(a), U1(k, e))
25.98/8.54	   A^2 -> H(f(c), U1(e, e))
25.98/8.54	   A^2 -> H(f(a), e)
25.98/8.54	   A^2 -> H(f(d), U1(k, d))
25.98/8.54	   A^2 -> H(f(d), U1(d, k))
25.98/8.54	   A^2 -> H(f(a), U1(k, k))
25.98/8.54	   A^2 -> H(d, f(b))
25.98/8.54	   A^2 -> H(a, U1(b, b))
25.98/8.54	   A^2 -> H(a, f(c))
25.98/8.54	   A^2 -> H(a, f(d))
25.98/8.54	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, d), f(c))
25.98/8.54	   A^2 -> H(U1(e, d), f(d))
25.98/8.54	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.54	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.54	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.54	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.54	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.54	   A^2 -> H(U1(e, a), f(e))
25.98/8.54	   A^2 -> H(U1(e, a), f(k))
25.98/8.54	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.54	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.54	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.54	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.54	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.54	   A^2 -> H(U1(k, a), f(e))
25.98/8.54	   A^2 -> H(U1(k, a), f(k))
25.98/8.54	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, d), f(e))
25.98/8.54	   A^2 -> H(U1(c, d), f(k))
25.98/8.54	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.54	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(d, e), f(c))
25.98/8.54	   A^2 -> H(U1(d, e), f(d))
25.98/8.54	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(d, c), f(e))
25.98/8.54	   A^2 -> H(U1(d, c), f(k))
25.98/8.54	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.54	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.54	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.54	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.54	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.54	   A^2 -> H(U1(a, e), f(e))
25.98/8.54	   A^2 -> H(U1(a, e), f(k))
25.98/8.54	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.54	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.54	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.54	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.54	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.54	   A^2 -> H(U1(a, k), f(e))
25.98/8.54	   A^2 -> H(U1(a, k), f(k))
25.98/8.54	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.54	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.54	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, a), b)
25.98/8.54	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.54	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.54	   A^2 -> H(U1(a, a), c)
25.98/8.54	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.54	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.54	   A^2 -> H(U1(a, a), e)
25.98/8.54	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.54	   A^2 -> H(k, f(b))
25.98/8.54	   A^2 -> H(c, U1(b, b))
25.98/8.54	   A^2 -> H(c, f(c))
25.98/8.54	   A^2 -> H(c, f(d))
25.98/8.54	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, k), f(c))
25.98/8.54	   A^2 -> H(U1(e, k), f(d))
25.98/8.54	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(e, c), f(e))
25.98/8.54	   A^2 -> H(U1(e, c), f(k))
25.98/8.54	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, e), f(c))
25.98/8.54	   A^2 -> H(U1(k, e), f(d))
25.98/8.54	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(k, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(k, c), f(e))
25.98/8.54	   A^2 -> H(U1(k, c), f(k))
25.98/8.54	   A^2 -> H(U1(k, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, e), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, e), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, e), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, e), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, e), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, e), f(e))
25.98/8.54	   A^2 -> H(U1(c, e), f(k))
25.98/8.54	   A^2 -> H(U1(c, e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, k), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, k), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, k), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, k), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, k), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, k), f(e))
25.98/8.54	   A^2 -> H(U1(c, k), f(k))
25.98/8.54	   A^2 -> H(U1(c, k), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(e, b))
25.98/8.54	   A^2 -> H(U1(c, c), U1(k, b))
25.98/8.54	   A^2 -> H(U1(c, c), U1(c, d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(d, c))
25.98/8.54	   A^2 -> H(U1(c, c), U1(b, e))
25.98/8.54	   A^2 -> H(U1(c, c), U1(b, k))
25.98/8.54	
25.98/8.54	The TRS R consists of the following rules:
25.98/8.54	
25.98/8.54	   f(x) -> U1(x, x)
25.98/8.54	   U1(e, x) -> x
25.98/8.54	   a -> c
25.98/8.54	   a -> d
25.98/8.54	   b -> c
25.98/8.54	   b -> d
25.98/8.54	   d -> k
25.98/8.54	   c -> e
25.98/8.54	   c -> k
25.98/8.54	
25.98/8.54	Q is empty.
25.98/8.54	We have to consider all minimal (P,Q,R)-chains.
25.98/8.54	----------------------------------------
25.98/8.54	
25.98/8.54	(391) TransformationProof (EQUIVALENT)
25.98/8.54	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.54	
25.98/8.54	   (A^2 -> H(U1(e, c), U1(b, d)),A^2 -> H(U1(e, c), U1(b, d)))
25.98/8.54	   (A^2 -> H(U1(k, c), U1(b, d)),A^2 -> H(U1(k, c), U1(b, d)))
25.98/8.54	   (A^2 -> H(U1(c, e), U1(b, d)),A^2 -> H(U1(c, e), U1(b, d)))
25.98/8.54	   (A^2 -> H(U1(c, k), U1(b, d)),A^2 -> H(U1(c, k), U1(b, d)))
25.98/8.54	   (A^2 -> H(U1(c, c), U1(c, d)),A^2 -> H(U1(c, c), U1(c, d)))
25.98/8.54	   (A^2 -> H(U1(c, c), U1(d, d)),A^2 -> H(U1(c, c), U1(d, d)))
25.98/8.54	   (A^2 -> H(U1(c, c), U1(b, k)),A^2 -> H(U1(c, c), U1(b, k)))
25.98/8.54	
25.98/8.54	
25.98/8.54	----------------------------------------
25.98/8.54	
25.98/8.54	(392)
25.98/8.54	Obligation:
25.98/8.54	Q DP problem:
25.98/8.54	The TRS P consists of the following rules:
25.98/8.54	
25.98/8.54	   H(x, x) -> G(x, x, f(k))
25.98/8.54	   G(d, x, x) -> A^2
25.98/8.54	   A^2 -> H(f(c), f(c))
25.98/8.54	   A^2 -> H(f(d), f(d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, c), f(e))
25.98/8.54	   A^2 -> H(U1(c, c), f(k))
25.98/8.54	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.54	   A^2 -> H(e, f(b))
25.98/8.54	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, e), f(c))
25.98/8.54	   A^2 -> H(U1(e, e), f(d))
25.98/8.54	   A^2 -> H(f(e), U1(c, b))
25.98/8.54	   A^2 -> H(f(e), U1(d, b))
25.98/8.54	   A^2 -> H(f(e), U1(b, c))
25.98/8.54	   A^2 -> H(f(e), U1(b, d))
25.98/8.54	   A^2 -> H(f(e), U1(c, c))
25.98/8.54	   A^2 -> H(f(e), f(e))
25.98/8.54	   A^2 -> H(f(e), f(k))
25.98/8.54	   A^2 -> H(f(e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, k), f(c))
25.98/8.54	   A^2 -> H(U1(k, k), f(d))
25.98/8.54	   A^2 -> H(f(k), U1(c, b))
25.98/8.54	   A^2 -> H(f(k), U1(d, b))
25.98/8.54	   A^2 -> H(f(k), U1(b, c))
25.98/8.54	   A^2 -> H(f(k), U1(b, d))
25.98/8.54	   A^2 -> H(f(k), U1(c, c))
25.98/8.54	   A^2 -> H(f(k), f(e))
25.98/8.54	   A^2 -> H(f(k), f(k))
25.98/8.54	   A^2 -> H(f(k), U1(d, d))
25.98/8.54	   A^2 -> H(f(c), U1(e, b))
25.98/8.54	   A^2 -> H(f(c), U1(k, b))
25.98/8.54	   A^2 -> H(f(c), U1(c, d))
25.98/8.54	   A^2 -> H(f(c), U1(d, c))
25.98/8.54	   A^2 -> H(f(c), U1(b, e))
25.98/8.54	   A^2 -> H(f(c), U1(b, k))
25.98/8.54	   A^2 -> H(f(c), U1(k, d))
25.98/8.54	   A^2 -> H(f(c), U1(d, k))
25.98/8.54	   A^2 -> H(f(c), U1(k, k))
25.98/8.54	   A^2 -> H(U1(k, k), f(b))
25.98/8.54	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, d), f(c))
25.98/8.54	   A^2 -> H(U1(k, d), f(d))
25.98/8.54	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(d, k), f(c))
25.98/8.54	   A^2 -> H(U1(d, k), f(d))
25.98/8.54	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.54	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.54	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.54	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.54	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.54	   A^2 -> H(U1(d, d), f(e))
25.98/8.54	   A^2 -> H(U1(d, d), f(k))
25.98/8.54	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.54	   A^2 -> H(f(d), U1(e, b))
25.98/8.54	   A^2 -> H(f(d), U1(k, b))
25.98/8.54	   A^2 -> H(f(d), U1(c, d))
25.98/8.54	   A^2 -> H(f(d), U1(d, c))
25.98/8.54	   A^2 -> H(f(d), U1(b, e))
25.98/8.54	   A^2 -> H(f(d), U1(b, k))
25.98/8.54	   A^2 -> H(f(d), U1(e, c))
25.98/8.54	   A^2 -> H(f(d), U1(k, c))
25.98/8.54	   A^2 -> H(f(d), U1(c, e))
25.98/8.54	   A^2 -> H(f(d), U1(c, k))
25.98/8.54	   A^2 -> H(f(d), U1(e, e))
25.98/8.54	   A^2 -> H(f(d), U1(k, k))
25.98/8.54	   A^2 -> H(f(a), b)
25.98/8.54	   A^2 -> H(f(a), U1(e, d))
25.98/8.54	   A^2 -> H(f(a), U1(d, e))
25.98/8.54	   A^2 -> H(f(c), U1(e, c))
25.98/8.54	   A^2 -> H(f(c), U1(k, c))
25.98/8.54	   A^2 -> H(f(c), U1(c, e))
25.98/8.54	   A^2 -> H(f(c), U1(c, k))
25.98/8.54	   A^2 -> H(f(a), c)
25.98/8.54	   A^2 -> H(f(a), U1(e, k))
25.98/8.54	   A^2 -> H(f(a), U1(k, e))
25.98/8.54	   A^2 -> H(f(c), U1(e, e))
25.98/8.54	   A^2 -> H(f(a), e)
25.98/8.54	   A^2 -> H(f(d), U1(k, d))
25.98/8.54	   A^2 -> H(f(d), U1(d, k))
25.98/8.54	   A^2 -> H(f(a), U1(k, k))
25.98/8.54	   A^2 -> H(d, f(b))
25.98/8.54	   A^2 -> H(a, U1(b, b))
25.98/8.54	   A^2 -> H(a, f(c))
25.98/8.54	   A^2 -> H(a, f(d))
25.98/8.54	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, d), f(c))
25.98/8.54	   A^2 -> H(U1(e, d), f(d))
25.98/8.54	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.54	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.54	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.54	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.54	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.54	   A^2 -> H(U1(e, a), f(e))
25.98/8.54	   A^2 -> H(U1(e, a), f(k))
25.98/8.54	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.54	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.54	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.54	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.54	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.54	   A^2 -> H(U1(k, a), f(e))
25.98/8.54	   A^2 -> H(U1(k, a), f(k))
25.98/8.54	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, d), f(e))
25.98/8.54	   A^2 -> H(U1(c, d), f(k))
25.98/8.54	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.54	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(d, e), f(c))
25.98/8.54	   A^2 -> H(U1(d, e), f(d))
25.98/8.54	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(d, c), f(e))
25.98/8.54	   A^2 -> H(U1(d, c), f(k))
25.98/8.54	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.54	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.54	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.54	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.54	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.54	   A^2 -> H(U1(a, e), f(e))
25.98/8.54	   A^2 -> H(U1(a, e), f(k))
25.98/8.54	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.54	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.54	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.54	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.54	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.54	   A^2 -> H(U1(a, k), f(e))
25.98/8.54	   A^2 -> H(U1(a, k), f(k))
25.98/8.54	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.54	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.54	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, a), b)
25.98/8.54	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.54	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.54	   A^2 -> H(U1(a, a), c)
25.98/8.54	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.54	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.54	   A^2 -> H(U1(a, a), e)
25.98/8.54	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.54	   A^2 -> H(k, f(b))
25.98/8.54	   A^2 -> H(c, U1(b, b))
25.98/8.54	   A^2 -> H(c, f(c))
25.98/8.54	   A^2 -> H(c, f(d))
25.98/8.54	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, k), f(c))
25.98/8.54	   A^2 -> H(U1(e, k), f(d))
25.98/8.54	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(e, c), f(e))
25.98/8.54	   A^2 -> H(U1(e, c), f(k))
25.98/8.54	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, e), f(c))
25.98/8.54	   A^2 -> H(U1(k, e), f(d))
25.98/8.54	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(k, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(k, c), f(e))
25.98/8.54	   A^2 -> H(U1(k, c), f(k))
25.98/8.54	   A^2 -> H(U1(k, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, e), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, e), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, e), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, e), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, e), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, e), f(e))
25.98/8.54	   A^2 -> H(U1(c, e), f(k))
25.98/8.54	   A^2 -> H(U1(c, e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, k), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, k), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, k), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, k), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, k), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, k), f(e))
25.98/8.54	   A^2 -> H(U1(c, k), f(k))
25.98/8.54	   A^2 -> H(U1(c, k), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(e, b))
25.98/8.54	   A^2 -> H(U1(c, c), U1(k, b))
25.98/8.54	   A^2 -> H(U1(c, c), U1(c, d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(d, c))
25.98/8.54	   A^2 -> H(U1(c, c), U1(b, e))
25.98/8.54	   A^2 -> H(U1(c, c), U1(b, k))
25.98/8.54	
25.98/8.54	The TRS R consists of the following rules:
25.98/8.54	
25.98/8.54	   f(x) -> U1(x, x)
25.98/8.54	   U1(e, x) -> x
25.98/8.54	   a -> c
25.98/8.54	   a -> d
25.98/8.54	   b -> c
25.98/8.54	   b -> d
25.98/8.54	   d -> k
25.98/8.54	   c -> e
25.98/8.54	   c -> k
25.98/8.54	
25.98/8.54	Q is empty.
25.98/8.54	We have to consider all minimal (P,Q,R)-chains.
25.98/8.54	----------------------------------------
25.98/8.54	
25.98/8.54	(393) TransformationProof (EQUIVALENT)
25.98/8.54	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), f(e)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.54	
25.98/8.54	   (A^2 -> H(U1(e, c), f(e)),A^2 -> H(U1(e, c), f(e)))
25.98/8.54	   (A^2 -> H(U1(k, c), f(e)),A^2 -> H(U1(k, c), f(e)))
25.98/8.54	   (A^2 -> H(U1(c, e), f(e)),A^2 -> H(U1(c, e), f(e)))
25.98/8.54	   (A^2 -> H(U1(c, k), f(e)),A^2 -> H(U1(c, k), f(e)))
25.98/8.54	   (A^2 -> H(U1(c, c), U1(e, e)),A^2 -> H(U1(c, c), U1(e, e)))
25.98/8.54	
25.98/8.54	
25.98/8.54	----------------------------------------
25.98/8.54	
25.98/8.54	(394)
25.98/8.54	Obligation:
25.98/8.54	Q DP problem:
25.98/8.54	The TRS P consists of the following rules:
25.98/8.54	
25.98/8.54	   H(x, x) -> G(x, x, f(k))
25.98/8.54	   G(d, x, x) -> A^2
25.98/8.54	   A^2 -> H(f(c), f(c))
25.98/8.54	   A^2 -> H(f(d), f(d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, c), f(k))
25.98/8.54	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.54	   A^2 -> H(e, f(b))
25.98/8.54	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, e), f(c))
25.98/8.54	   A^2 -> H(U1(e, e), f(d))
25.98/8.54	   A^2 -> H(f(e), U1(c, b))
25.98/8.54	   A^2 -> H(f(e), U1(d, b))
25.98/8.54	   A^2 -> H(f(e), U1(b, c))
25.98/8.54	   A^2 -> H(f(e), U1(b, d))
25.98/8.54	   A^2 -> H(f(e), U1(c, c))
25.98/8.54	   A^2 -> H(f(e), f(e))
25.98/8.54	   A^2 -> H(f(e), f(k))
25.98/8.54	   A^2 -> H(f(e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, k), f(c))
25.98/8.54	   A^2 -> H(U1(k, k), f(d))
25.98/8.54	   A^2 -> H(f(k), U1(c, b))
25.98/8.54	   A^2 -> H(f(k), U1(d, b))
25.98/8.54	   A^2 -> H(f(k), U1(b, c))
25.98/8.54	   A^2 -> H(f(k), U1(b, d))
25.98/8.54	   A^2 -> H(f(k), U1(c, c))
25.98/8.54	   A^2 -> H(f(k), f(e))
25.98/8.54	   A^2 -> H(f(k), f(k))
25.98/8.54	   A^2 -> H(f(k), U1(d, d))
25.98/8.54	   A^2 -> H(f(c), U1(e, b))
25.98/8.54	   A^2 -> H(f(c), U1(k, b))
25.98/8.54	   A^2 -> H(f(c), U1(c, d))
25.98/8.54	   A^2 -> H(f(c), U1(d, c))
25.98/8.54	   A^2 -> H(f(c), U1(b, e))
25.98/8.54	   A^2 -> H(f(c), U1(b, k))
25.98/8.54	   A^2 -> H(f(c), U1(k, d))
25.98/8.54	   A^2 -> H(f(c), U1(d, k))
25.98/8.54	   A^2 -> H(f(c), U1(k, k))
25.98/8.54	   A^2 -> H(U1(k, k), f(b))
25.98/8.54	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, d), f(c))
25.98/8.54	   A^2 -> H(U1(k, d), f(d))
25.98/8.54	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(d, k), f(c))
25.98/8.54	   A^2 -> H(U1(d, k), f(d))
25.98/8.54	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.54	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.54	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.54	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.54	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.54	   A^2 -> H(U1(d, d), f(e))
25.98/8.54	   A^2 -> H(U1(d, d), f(k))
25.98/8.54	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.54	   A^2 -> H(f(d), U1(e, b))
25.98/8.54	   A^2 -> H(f(d), U1(k, b))
25.98/8.54	   A^2 -> H(f(d), U1(c, d))
25.98/8.54	   A^2 -> H(f(d), U1(d, c))
25.98/8.54	   A^2 -> H(f(d), U1(b, e))
25.98/8.54	   A^2 -> H(f(d), U1(b, k))
25.98/8.54	   A^2 -> H(f(d), U1(e, c))
25.98/8.54	   A^2 -> H(f(d), U1(k, c))
25.98/8.54	   A^2 -> H(f(d), U1(c, e))
25.98/8.54	   A^2 -> H(f(d), U1(c, k))
25.98/8.54	   A^2 -> H(f(d), U1(e, e))
25.98/8.54	   A^2 -> H(f(d), U1(k, k))
25.98/8.54	   A^2 -> H(f(a), b)
25.98/8.54	   A^2 -> H(f(a), U1(e, d))
25.98/8.54	   A^2 -> H(f(a), U1(d, e))
25.98/8.54	   A^2 -> H(f(c), U1(e, c))
25.98/8.54	   A^2 -> H(f(c), U1(k, c))
25.98/8.54	   A^2 -> H(f(c), U1(c, e))
25.98/8.54	   A^2 -> H(f(c), U1(c, k))
25.98/8.54	   A^2 -> H(f(a), c)
25.98/8.54	   A^2 -> H(f(a), U1(e, k))
25.98/8.54	   A^2 -> H(f(a), U1(k, e))
25.98/8.54	   A^2 -> H(f(c), U1(e, e))
25.98/8.54	   A^2 -> H(f(a), e)
25.98/8.54	   A^2 -> H(f(d), U1(k, d))
25.98/8.54	   A^2 -> H(f(d), U1(d, k))
25.98/8.54	   A^2 -> H(f(a), U1(k, k))
25.98/8.54	   A^2 -> H(d, f(b))
25.98/8.54	   A^2 -> H(a, U1(b, b))
25.98/8.54	   A^2 -> H(a, f(c))
25.98/8.54	   A^2 -> H(a, f(d))
25.98/8.54	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, d), f(c))
25.98/8.54	   A^2 -> H(U1(e, d), f(d))
25.98/8.54	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.54	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.54	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.54	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.54	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.54	   A^2 -> H(U1(e, a), f(e))
25.98/8.54	   A^2 -> H(U1(e, a), f(k))
25.98/8.54	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.54	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.54	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.54	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.54	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.54	   A^2 -> H(U1(k, a), f(e))
25.98/8.54	   A^2 -> H(U1(k, a), f(k))
25.98/8.54	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, d), f(e))
25.98/8.54	   A^2 -> H(U1(c, d), f(k))
25.98/8.54	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.54	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(d, e), f(c))
25.98/8.54	   A^2 -> H(U1(d, e), f(d))
25.98/8.54	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(d, c), f(e))
25.98/8.54	   A^2 -> H(U1(d, c), f(k))
25.98/8.54	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.54	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.54	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.54	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.54	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.54	   A^2 -> H(U1(a, e), f(e))
25.98/8.54	   A^2 -> H(U1(a, e), f(k))
25.98/8.54	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.54	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.54	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.54	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.54	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.54	   A^2 -> H(U1(a, k), f(e))
25.98/8.54	   A^2 -> H(U1(a, k), f(k))
25.98/8.54	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.54	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.54	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, a), b)
25.98/8.54	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.54	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.54	   A^2 -> H(U1(a, a), c)
25.98/8.54	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.54	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.54	   A^2 -> H(U1(a, a), e)
25.98/8.54	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.54	   A^2 -> H(k, f(b))
25.98/8.54	   A^2 -> H(c, U1(b, b))
25.98/8.54	   A^2 -> H(c, f(c))
25.98/8.54	   A^2 -> H(c, f(d))
25.98/8.54	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, k), f(c))
25.98/8.54	   A^2 -> H(U1(e, k), f(d))
25.98/8.54	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(e, c), f(e))
25.98/8.54	   A^2 -> H(U1(e, c), f(k))
25.98/8.54	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, e), f(c))
25.98/8.54	   A^2 -> H(U1(k, e), f(d))
25.98/8.54	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(k, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(k, c), f(e))
25.98/8.54	   A^2 -> H(U1(k, c), f(k))
25.98/8.54	   A^2 -> H(U1(k, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, e), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, e), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, e), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, e), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, e), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, e), f(e))
25.98/8.54	   A^2 -> H(U1(c, e), f(k))
25.98/8.54	   A^2 -> H(U1(c, e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, k), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, k), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, k), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, k), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, k), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, k), f(e))
25.98/8.54	   A^2 -> H(U1(c, k), f(k))
25.98/8.54	   A^2 -> H(U1(c, k), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(e, b))
25.98/8.54	   A^2 -> H(U1(c, c), U1(k, b))
25.98/8.54	   A^2 -> H(U1(c, c), U1(c, d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(d, c))
25.98/8.54	   A^2 -> H(U1(c, c), U1(b, e))
25.98/8.54	   A^2 -> H(U1(c, c), U1(b, k))
25.98/8.54	   A^2 -> H(U1(c, c), U1(e, e))
25.98/8.54	
25.98/8.54	The TRS R consists of the following rules:
25.98/8.54	
25.98/8.54	   f(x) -> U1(x, x)
25.98/8.54	   U1(e, x) -> x
25.98/8.54	   a -> c
25.98/8.54	   a -> d
25.98/8.54	   b -> c
25.98/8.54	   b -> d
25.98/8.54	   d -> k
25.98/8.54	   c -> e
25.98/8.54	   c -> k
25.98/8.54	
25.98/8.54	Q is empty.
25.98/8.54	We have to consider all minimal (P,Q,R)-chains.
25.98/8.54	----------------------------------------
25.98/8.54	
25.98/8.54	(395) TransformationProof (EQUIVALENT)
25.98/8.54	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), f(k)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.54	
25.98/8.54	   (A^2 -> H(U1(e, c), f(k)),A^2 -> H(U1(e, c), f(k)))
25.98/8.54	   (A^2 -> H(U1(k, c), f(k)),A^2 -> H(U1(k, c), f(k)))
25.98/8.54	   (A^2 -> H(U1(c, e), f(k)),A^2 -> H(U1(c, e), f(k)))
25.98/8.54	   (A^2 -> H(U1(c, k), f(k)),A^2 -> H(U1(c, k), f(k)))
25.98/8.54	   (A^2 -> H(U1(c, c), U1(k, k)),A^2 -> H(U1(c, c), U1(k, k)))
25.98/8.54	
25.98/8.54	
25.98/8.54	----------------------------------------
25.98/8.54	
25.98/8.54	(396)
25.98/8.54	Obligation:
25.98/8.54	Q DP problem:
25.98/8.54	The TRS P consists of the following rules:
25.98/8.54	
25.98/8.54	   H(x, x) -> G(x, x, f(k))
25.98/8.54	   G(d, x, x) -> A^2
25.98/8.54	   A^2 -> H(f(c), f(c))
25.98/8.54	   A^2 -> H(f(d), f(d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, c), U1(d, d))
25.98/8.54	   A^2 -> H(e, f(b))
25.98/8.54	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, e), f(c))
25.98/8.54	   A^2 -> H(U1(e, e), f(d))
25.98/8.54	   A^2 -> H(f(e), U1(c, b))
25.98/8.54	   A^2 -> H(f(e), U1(d, b))
25.98/8.54	   A^2 -> H(f(e), U1(b, c))
25.98/8.54	   A^2 -> H(f(e), U1(b, d))
25.98/8.54	   A^2 -> H(f(e), U1(c, c))
25.98/8.54	   A^2 -> H(f(e), f(e))
25.98/8.54	   A^2 -> H(f(e), f(k))
25.98/8.54	   A^2 -> H(f(e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, k), f(c))
25.98/8.54	   A^2 -> H(U1(k, k), f(d))
25.98/8.54	   A^2 -> H(f(k), U1(c, b))
25.98/8.54	   A^2 -> H(f(k), U1(d, b))
25.98/8.54	   A^2 -> H(f(k), U1(b, c))
25.98/8.54	   A^2 -> H(f(k), U1(b, d))
25.98/8.54	   A^2 -> H(f(k), U1(c, c))
25.98/8.54	   A^2 -> H(f(k), f(e))
25.98/8.54	   A^2 -> H(f(k), f(k))
25.98/8.54	   A^2 -> H(f(k), U1(d, d))
25.98/8.54	   A^2 -> H(f(c), U1(e, b))
25.98/8.54	   A^2 -> H(f(c), U1(k, b))
25.98/8.54	   A^2 -> H(f(c), U1(c, d))
25.98/8.54	   A^2 -> H(f(c), U1(d, c))
25.98/8.54	   A^2 -> H(f(c), U1(b, e))
25.98/8.54	   A^2 -> H(f(c), U1(b, k))
25.98/8.54	   A^2 -> H(f(c), U1(k, d))
25.98/8.54	   A^2 -> H(f(c), U1(d, k))
25.98/8.54	   A^2 -> H(f(c), U1(k, k))
25.98/8.54	   A^2 -> H(U1(k, k), f(b))
25.98/8.54	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, d), f(c))
25.98/8.54	   A^2 -> H(U1(k, d), f(d))
25.98/8.54	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(d, k), f(c))
25.98/8.54	   A^2 -> H(U1(d, k), f(d))
25.98/8.54	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.54	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.54	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.54	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.54	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.54	   A^2 -> H(U1(d, d), f(e))
25.98/8.54	   A^2 -> H(U1(d, d), f(k))
25.98/8.54	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.54	   A^2 -> H(f(d), U1(e, b))
25.98/8.54	   A^2 -> H(f(d), U1(k, b))
25.98/8.54	   A^2 -> H(f(d), U1(c, d))
25.98/8.54	   A^2 -> H(f(d), U1(d, c))
25.98/8.54	   A^2 -> H(f(d), U1(b, e))
25.98/8.54	   A^2 -> H(f(d), U1(b, k))
25.98/8.54	   A^2 -> H(f(d), U1(e, c))
25.98/8.54	   A^2 -> H(f(d), U1(k, c))
25.98/8.54	   A^2 -> H(f(d), U1(c, e))
25.98/8.54	   A^2 -> H(f(d), U1(c, k))
25.98/8.54	   A^2 -> H(f(d), U1(e, e))
25.98/8.54	   A^2 -> H(f(d), U1(k, k))
25.98/8.54	   A^2 -> H(f(a), b)
25.98/8.54	   A^2 -> H(f(a), U1(e, d))
25.98/8.54	   A^2 -> H(f(a), U1(d, e))
25.98/8.54	   A^2 -> H(f(c), U1(e, c))
25.98/8.54	   A^2 -> H(f(c), U1(k, c))
25.98/8.54	   A^2 -> H(f(c), U1(c, e))
25.98/8.54	   A^2 -> H(f(c), U1(c, k))
25.98/8.54	   A^2 -> H(f(a), c)
25.98/8.54	   A^2 -> H(f(a), U1(e, k))
25.98/8.54	   A^2 -> H(f(a), U1(k, e))
25.98/8.54	   A^2 -> H(f(c), U1(e, e))
25.98/8.54	   A^2 -> H(f(a), e)
25.98/8.54	   A^2 -> H(f(d), U1(k, d))
25.98/8.54	   A^2 -> H(f(d), U1(d, k))
25.98/8.54	   A^2 -> H(f(a), U1(k, k))
25.98/8.54	   A^2 -> H(d, f(b))
25.98/8.54	   A^2 -> H(a, U1(b, b))
25.98/8.54	   A^2 -> H(a, f(c))
25.98/8.54	   A^2 -> H(a, f(d))
25.98/8.54	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, d), f(c))
25.98/8.54	   A^2 -> H(U1(e, d), f(d))
25.98/8.54	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.54	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.54	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.54	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.54	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.54	   A^2 -> H(U1(e, a), f(e))
25.98/8.54	   A^2 -> H(U1(e, a), f(k))
25.98/8.54	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.54	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.54	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.54	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.54	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.54	   A^2 -> H(U1(k, a), f(e))
25.98/8.54	   A^2 -> H(U1(k, a), f(k))
25.98/8.54	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, d), f(e))
25.98/8.54	   A^2 -> H(U1(c, d), f(k))
25.98/8.54	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.54	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(d, e), f(c))
25.98/8.54	   A^2 -> H(U1(d, e), f(d))
25.98/8.54	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(d, c), f(e))
25.98/8.54	   A^2 -> H(U1(d, c), f(k))
25.98/8.54	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.54	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.54	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.54	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.54	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.54	   A^2 -> H(U1(a, e), f(e))
25.98/8.54	   A^2 -> H(U1(a, e), f(k))
25.98/8.54	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.54	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.54	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.54	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.54	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.54	   A^2 -> H(U1(a, k), f(e))
25.98/8.54	   A^2 -> H(U1(a, k), f(k))
25.98/8.54	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.54	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.54	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, a), b)
25.98/8.54	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.54	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.54	   A^2 -> H(U1(a, a), c)
25.98/8.54	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.54	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.54	   A^2 -> H(U1(a, a), e)
25.98/8.54	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.54	   A^2 -> H(k, f(b))
25.98/8.54	   A^2 -> H(c, U1(b, b))
25.98/8.54	   A^2 -> H(c, f(c))
25.98/8.54	   A^2 -> H(c, f(d))
25.98/8.54	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, k), f(c))
25.98/8.54	   A^2 -> H(U1(e, k), f(d))
25.98/8.54	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(e, c), f(e))
25.98/8.54	   A^2 -> H(U1(e, c), f(k))
25.98/8.54	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, e), f(c))
25.98/8.54	   A^2 -> H(U1(k, e), f(d))
25.98/8.54	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(k, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(k, c), f(e))
25.98/8.54	   A^2 -> H(U1(k, c), f(k))
25.98/8.54	   A^2 -> H(U1(k, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, e), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, e), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, e), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, e), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, e), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, e), f(e))
25.98/8.54	   A^2 -> H(U1(c, e), f(k))
25.98/8.54	   A^2 -> H(U1(c, e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, k), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, k), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, k), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, k), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, k), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, k), f(e))
25.98/8.54	   A^2 -> H(U1(c, k), f(k))
25.98/8.54	   A^2 -> H(U1(c, k), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(e, b))
25.98/8.54	   A^2 -> H(U1(c, c), U1(k, b))
25.98/8.54	   A^2 -> H(U1(c, c), U1(c, d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(d, c))
25.98/8.54	   A^2 -> H(U1(c, c), U1(b, e))
25.98/8.54	   A^2 -> H(U1(c, c), U1(b, k))
25.98/8.54	   A^2 -> H(U1(c, c), U1(e, e))
25.98/8.54	   A^2 -> H(U1(c, c), U1(k, k))
25.98/8.54	
25.98/8.54	The TRS R consists of the following rules:
25.98/8.54	
25.98/8.54	   f(x) -> U1(x, x)
25.98/8.54	   U1(e, x) -> x
25.98/8.54	   a -> c
25.98/8.54	   a -> d
25.98/8.54	   b -> c
25.98/8.54	   b -> d
25.98/8.54	   d -> k
25.98/8.54	   c -> e
25.98/8.54	   c -> k
25.98/8.54	
25.98/8.54	Q is empty.
25.98/8.54	We have to consider all minimal (P,Q,R)-chains.
25.98/8.54	----------------------------------------
25.98/8.54	
25.98/8.54	(397) TransformationProof (EQUIVALENT)
25.98/8.54	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.54	
25.98/8.54	   (A^2 -> H(U1(e, c), U1(d, d)),A^2 -> H(U1(e, c), U1(d, d)))
25.98/8.54	   (A^2 -> H(U1(k, c), U1(d, d)),A^2 -> H(U1(k, c), U1(d, d)))
25.98/8.54	   (A^2 -> H(U1(c, e), U1(d, d)),A^2 -> H(U1(c, e), U1(d, d)))
25.98/8.54	   (A^2 -> H(U1(c, k), U1(d, d)),A^2 -> H(U1(c, k), U1(d, d)))
25.98/8.54	   (A^2 -> H(U1(c, c), U1(k, d)),A^2 -> H(U1(c, c), U1(k, d)))
25.98/8.54	   (A^2 -> H(U1(c, c), U1(d, k)),A^2 -> H(U1(c, c), U1(d, k)))
25.98/8.54	
25.98/8.54	
25.98/8.54	----------------------------------------
25.98/8.54	
25.98/8.54	(398)
25.98/8.54	Obligation:
25.98/8.54	Q DP problem:
25.98/8.54	The TRS P consists of the following rules:
25.98/8.54	
25.98/8.54	   H(x, x) -> G(x, x, f(k))
25.98/8.54	   G(d, x, x) -> A^2
25.98/8.54	   A^2 -> H(f(c), f(c))
25.98/8.54	   A^2 -> H(f(d), f(d))
25.98/8.54	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.54	   A^2 -> H(e, f(b))
25.98/8.54	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, e), f(c))
25.98/8.54	   A^2 -> H(U1(e, e), f(d))
25.98/8.54	   A^2 -> H(f(e), U1(c, b))
25.98/8.54	   A^2 -> H(f(e), U1(d, b))
25.98/8.54	   A^2 -> H(f(e), U1(b, c))
25.98/8.54	   A^2 -> H(f(e), U1(b, d))
25.98/8.54	   A^2 -> H(f(e), U1(c, c))
25.98/8.54	   A^2 -> H(f(e), f(e))
25.98/8.54	   A^2 -> H(f(e), f(k))
25.98/8.54	   A^2 -> H(f(e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, k), f(c))
25.98/8.54	   A^2 -> H(U1(k, k), f(d))
25.98/8.54	   A^2 -> H(f(k), U1(c, b))
25.98/8.54	   A^2 -> H(f(k), U1(d, b))
25.98/8.54	   A^2 -> H(f(k), U1(b, c))
25.98/8.54	   A^2 -> H(f(k), U1(b, d))
25.98/8.54	   A^2 -> H(f(k), U1(c, c))
25.98/8.54	   A^2 -> H(f(k), f(e))
25.98/8.54	   A^2 -> H(f(k), f(k))
25.98/8.54	   A^2 -> H(f(k), U1(d, d))
25.98/8.54	   A^2 -> H(f(c), U1(e, b))
25.98/8.54	   A^2 -> H(f(c), U1(k, b))
25.98/8.54	   A^2 -> H(f(c), U1(c, d))
25.98/8.54	   A^2 -> H(f(c), U1(d, c))
25.98/8.54	   A^2 -> H(f(c), U1(b, e))
25.98/8.54	   A^2 -> H(f(c), U1(b, k))
25.98/8.54	   A^2 -> H(f(c), U1(k, d))
25.98/8.54	   A^2 -> H(f(c), U1(d, k))
25.98/8.54	   A^2 -> H(f(c), U1(k, k))
25.98/8.54	   A^2 -> H(U1(k, k), f(b))
25.98/8.54	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, d), f(c))
25.98/8.54	   A^2 -> H(U1(k, d), f(d))
25.98/8.54	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(d, k), f(c))
25.98/8.54	   A^2 -> H(U1(d, k), f(d))
25.98/8.54	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.54	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.54	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.54	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.54	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.54	   A^2 -> H(U1(d, d), f(e))
25.98/8.54	   A^2 -> H(U1(d, d), f(k))
25.98/8.54	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.54	   A^2 -> H(f(d), U1(e, b))
25.98/8.54	   A^2 -> H(f(d), U1(k, b))
25.98/8.54	   A^2 -> H(f(d), U1(c, d))
25.98/8.54	   A^2 -> H(f(d), U1(d, c))
25.98/8.54	   A^2 -> H(f(d), U1(b, e))
25.98/8.54	   A^2 -> H(f(d), U1(b, k))
25.98/8.54	   A^2 -> H(f(d), U1(e, c))
25.98/8.54	   A^2 -> H(f(d), U1(k, c))
25.98/8.54	   A^2 -> H(f(d), U1(c, e))
25.98/8.54	   A^2 -> H(f(d), U1(c, k))
25.98/8.54	   A^2 -> H(f(d), U1(e, e))
25.98/8.54	   A^2 -> H(f(d), U1(k, k))
25.98/8.54	   A^2 -> H(f(a), b)
25.98/8.54	   A^2 -> H(f(a), U1(e, d))
25.98/8.54	   A^2 -> H(f(a), U1(d, e))
25.98/8.54	   A^2 -> H(f(c), U1(e, c))
25.98/8.54	   A^2 -> H(f(c), U1(k, c))
25.98/8.54	   A^2 -> H(f(c), U1(c, e))
25.98/8.54	   A^2 -> H(f(c), U1(c, k))
25.98/8.54	   A^2 -> H(f(a), c)
25.98/8.54	   A^2 -> H(f(a), U1(e, k))
25.98/8.54	   A^2 -> H(f(a), U1(k, e))
25.98/8.54	   A^2 -> H(f(c), U1(e, e))
25.98/8.54	   A^2 -> H(f(a), e)
25.98/8.54	   A^2 -> H(f(d), U1(k, d))
25.98/8.54	   A^2 -> H(f(d), U1(d, k))
25.98/8.54	   A^2 -> H(f(a), U1(k, k))
25.98/8.54	   A^2 -> H(d, f(b))
25.98/8.54	   A^2 -> H(a, U1(b, b))
25.98/8.54	   A^2 -> H(a, f(c))
25.98/8.54	   A^2 -> H(a, f(d))
25.98/8.54	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, d), f(c))
25.98/8.54	   A^2 -> H(U1(e, d), f(d))
25.98/8.54	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.54	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.54	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.54	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.54	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.54	   A^2 -> H(U1(e, a), f(e))
25.98/8.54	   A^2 -> H(U1(e, a), f(k))
25.98/8.54	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.54	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.54	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.54	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.54	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.54	   A^2 -> H(U1(k, a), f(e))
25.98/8.54	   A^2 -> H(U1(k, a), f(k))
25.98/8.54	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.54	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.54	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.54	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.54	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.54	   A^2 -> H(U1(c, d), f(e))
25.98/8.54	   A^2 -> H(U1(c, d), f(k))
25.98/8.54	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.54	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.54	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.54	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(d, e), f(c))
25.98/8.54	   A^2 -> H(U1(d, e), f(d))
25.98/8.54	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(d, c), f(e))
25.98/8.54	   A^2 -> H(U1(d, c), f(k))
25.98/8.54	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.54	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.54	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.54	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.54	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.54	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.54	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.54	   A^2 -> H(U1(a, e), f(e))
25.98/8.54	   A^2 -> H(U1(a, e), f(k))
25.98/8.54	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.54	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.54	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.54	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.54	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.54	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.54	   A^2 -> H(U1(a, k), f(e))
25.98/8.54	   A^2 -> H(U1(a, k), f(k))
25.98/8.54	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.54	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.54	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.54	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.54	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.54	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.54	   A^2 -> H(U1(a, a), b)
25.98/8.54	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.54	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.54	   A^2 -> H(U1(a, a), c)
25.98/8.54	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.54	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.54	   A^2 -> H(U1(a, a), e)
25.98/8.54	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.54	   A^2 -> H(k, f(b))
25.98/8.54	   A^2 -> H(c, U1(b, b))
25.98/8.54	   A^2 -> H(c, f(c))
25.98/8.54	   A^2 -> H(c, f(d))
25.98/8.54	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.54	   A^2 -> H(U1(e, k), f(c))
25.98/8.54	   A^2 -> H(U1(e, k), f(d))
25.98/8.54	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.54	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.54	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.54	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.54	   A^2 -> H(U1(e, c), f(e))
25.98/8.54	   A^2 -> H(U1(e, c), f(k))
25.98/8.54	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.54	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.54	   A^2 -> H(U1(k, e), f(c))
25.98/8.54	   A^2 -> H(U1(k, e), f(d))
25.98/8.54	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.54	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.55	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.55	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.55	   A^2 -> H(U1(k, c), U1(c, c))
25.98/8.55	   A^2 -> H(U1(k, c), f(e))
25.98/8.55	   A^2 -> H(U1(k, c), f(k))
25.98/8.55	   A^2 -> H(U1(k, c), U1(d, d))
25.98/8.55	   A^2 -> H(U1(c, e), U1(c, b))
25.98/8.55	   A^2 -> H(U1(c, e), U1(d, b))
25.98/8.55	   A^2 -> H(U1(c, e), U1(b, c))
25.98/8.55	   A^2 -> H(U1(c, e), U1(b, d))
25.98/8.55	   A^2 -> H(U1(c, e), U1(c, c))
25.98/8.55	   A^2 -> H(U1(c, e), f(e))
25.98/8.55	   A^2 -> H(U1(c, e), f(k))
25.98/8.55	   A^2 -> H(U1(c, e), U1(d, d))
25.98/8.55	   A^2 -> H(U1(c, k), U1(c, b))
25.98/8.55	   A^2 -> H(U1(c, k), U1(d, b))
25.98/8.55	   A^2 -> H(U1(c, k), U1(b, c))
25.98/8.55	   A^2 -> H(U1(c, k), U1(b, d))
25.98/8.55	   A^2 -> H(U1(c, k), U1(c, c))
25.98/8.55	   A^2 -> H(U1(c, k), f(e))
25.98/8.55	   A^2 -> H(U1(c, k), f(k))
25.98/8.55	   A^2 -> H(U1(c, k), U1(d, d))
25.98/8.55	   A^2 -> H(U1(c, c), U1(e, b))
25.98/8.55	   A^2 -> H(U1(c, c), U1(k, b))
25.98/8.55	   A^2 -> H(U1(c, c), U1(c, d))
25.98/8.55	   A^2 -> H(U1(c, c), U1(d, c))
25.98/8.55	   A^2 -> H(U1(c, c), U1(b, e))
25.98/8.55	   A^2 -> H(U1(c, c), U1(b, k))
25.98/8.55	   A^2 -> H(U1(c, c), U1(e, e))
25.98/8.55	   A^2 -> H(U1(c, c), U1(k, k))
25.98/8.55	   A^2 -> H(U1(c, c), U1(k, d))
25.98/8.55	   A^2 -> H(U1(c, c), U1(d, k))
25.98/8.55	
25.98/8.55	The TRS R consists of the following rules:
25.98/8.55	
25.98/8.55	   f(x) -> U1(x, x)
25.98/8.55	   U1(e, x) -> x
25.98/8.55	   a -> c
25.98/8.55	   a -> d
25.98/8.55	   b -> c
25.98/8.55	   b -> d
25.98/8.55	   d -> k
25.98/8.55	   c -> e
25.98/8.55	   c -> k
25.98/8.55	
25.98/8.55	Q is empty.
25.98/8.55	We have to consider all minimal (P,Q,R)-chains.
25.98/8.55	----------------------------------------
25.98/8.55	
25.98/8.55	(399) TransformationProof (EQUIVALENT)
25.98/8.55	By narrowing [LPAR04] the rule A^2 -> H(e, f(b)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.55	
25.98/8.55	   (A^2 -> H(e, U1(b, b)),A^2 -> H(e, U1(b, b)))
25.98/8.55	   (A^2 -> H(e, f(c)),A^2 -> H(e, f(c)))
25.98/8.55	   (A^2 -> H(e, f(d)),A^2 -> H(e, f(d)))
25.98/8.55	
25.98/8.55	
25.98/8.55	----------------------------------------
25.98/8.55	
25.98/8.55	(400)
25.98/8.55	Obligation:
25.98/8.55	Q DP problem:
25.98/8.55	The TRS P consists of the following rules:
25.98/8.55	
25.98/8.55	   H(x, x) -> G(x, x, f(k))
25.98/8.55	   G(d, x, x) -> A^2
25.98/8.55	   A^2 -> H(f(c), f(c))
25.98/8.55	   A^2 -> H(f(d), f(d))
25.98/8.55	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.55	   A^2 -> H(U1(e, e), U1(b, b))
25.98/8.55	   A^2 -> H(U1(e, e), f(c))
25.98/8.55	   A^2 -> H(U1(e, e), f(d))
25.98/8.55	   A^2 -> H(f(e), U1(c, b))
25.98/8.55	   A^2 -> H(f(e), U1(d, b))
25.98/8.55	   A^2 -> H(f(e), U1(b, c))
25.98/8.55	   A^2 -> H(f(e), U1(b, d))
25.98/8.55	   A^2 -> H(f(e), U1(c, c))
25.98/8.55	   A^2 -> H(f(e), f(e))
25.98/8.55	   A^2 -> H(f(e), f(k))
25.98/8.55	   A^2 -> H(f(e), U1(d, d))
25.98/8.55	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.55	   A^2 -> H(U1(k, k), f(c))
25.98/8.55	   A^2 -> H(U1(k, k), f(d))
25.98/8.55	   A^2 -> H(f(k), U1(c, b))
25.98/8.55	   A^2 -> H(f(k), U1(d, b))
25.98/8.55	   A^2 -> H(f(k), U1(b, c))
25.98/8.55	   A^2 -> H(f(k), U1(b, d))
25.98/8.55	   A^2 -> H(f(k), U1(c, c))
25.98/8.55	   A^2 -> H(f(k), f(e))
25.98/8.55	   A^2 -> H(f(k), f(k))
25.98/8.55	   A^2 -> H(f(k), U1(d, d))
25.98/8.55	   A^2 -> H(f(c), U1(e, b))
25.98/8.55	   A^2 -> H(f(c), U1(k, b))
25.98/8.55	   A^2 -> H(f(c), U1(c, d))
25.98/8.55	   A^2 -> H(f(c), U1(d, c))
25.98/8.55	   A^2 -> H(f(c), U1(b, e))
25.98/8.55	   A^2 -> H(f(c), U1(b, k))
25.98/8.55	   A^2 -> H(f(c), U1(k, d))
25.98/8.55	   A^2 -> H(f(c), U1(d, k))
25.98/8.55	   A^2 -> H(f(c), U1(k, k))
25.98/8.55	   A^2 -> H(U1(k, k), f(b))
25.98/8.55	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.55	   A^2 -> H(U1(k, d), f(c))
25.98/8.55	   A^2 -> H(U1(k, d), f(d))
25.98/8.55	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.55	   A^2 -> H(U1(d, k), f(c))
25.98/8.55	   A^2 -> H(U1(d, k), f(d))
25.98/8.55	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.55	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.55	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.55	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.55	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.55	   A^2 -> H(U1(d, d), f(e))
25.98/8.55	   A^2 -> H(U1(d, d), f(k))
25.98/8.55	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.55	   A^2 -> H(f(d), U1(e, b))
25.98/8.55	   A^2 -> H(f(d), U1(k, b))
25.98/8.55	   A^2 -> H(f(d), U1(c, d))
25.98/8.55	   A^2 -> H(f(d), U1(d, c))
25.98/8.55	   A^2 -> H(f(d), U1(b, e))
25.98/8.55	   A^2 -> H(f(d), U1(b, k))
25.98/8.55	   A^2 -> H(f(d), U1(e, c))
25.98/8.55	   A^2 -> H(f(d), U1(k, c))
25.98/8.55	   A^2 -> H(f(d), U1(c, e))
25.98/8.55	   A^2 -> H(f(d), U1(c, k))
25.98/8.55	   A^2 -> H(f(d), U1(e, e))
25.98/8.55	   A^2 -> H(f(d), U1(k, k))
25.98/8.55	   A^2 -> H(f(a), b)
25.98/8.55	   A^2 -> H(f(a), U1(e, d))
25.98/8.55	   A^2 -> H(f(a), U1(d, e))
25.98/8.55	   A^2 -> H(f(c), U1(e, c))
25.98/8.55	   A^2 -> H(f(c), U1(k, c))
25.98/8.55	   A^2 -> H(f(c), U1(c, e))
25.98/8.55	   A^2 -> H(f(c), U1(c, k))
25.98/8.55	   A^2 -> H(f(a), c)
25.98/8.55	   A^2 -> H(f(a), U1(e, k))
25.98/8.55	   A^2 -> H(f(a), U1(k, e))
25.98/8.55	   A^2 -> H(f(c), U1(e, e))
25.98/8.55	   A^2 -> H(f(a), e)
25.98/8.55	   A^2 -> H(f(d), U1(k, d))
25.98/8.55	   A^2 -> H(f(d), U1(d, k))
25.98/8.55	   A^2 -> H(f(a), U1(k, k))
25.98/8.55	   A^2 -> H(d, f(b))
25.98/8.55	   A^2 -> H(a, U1(b, b))
25.98/8.55	   A^2 -> H(a, f(c))
25.98/8.55	   A^2 -> H(a, f(d))
25.98/8.55	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.55	   A^2 -> H(U1(e, d), f(c))
25.98/8.55	   A^2 -> H(U1(e, d), f(d))
25.98/8.55	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.55	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.55	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.55	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.55	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.55	   A^2 -> H(U1(e, a), f(e))
25.98/8.55	   A^2 -> H(U1(e, a), f(k))
25.98/8.55	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.55	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.55	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.55	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.55	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.55	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.55	   A^2 -> H(U1(k, a), f(e))
25.98/8.55	   A^2 -> H(U1(k, a), f(k))
25.98/8.55	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.55	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.55	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.55	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.55	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.55	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.55	   A^2 -> H(U1(c, d), f(e))
25.98/8.55	   A^2 -> H(U1(c, d), f(k))
25.98/8.55	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.55	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.55	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.55	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.55	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.55	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.55	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.55	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.55	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.55	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.55	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.55	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.55	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.55	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.55	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.55	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.55	   A^2 -> H(U1(d, e), f(c))
25.98/8.55	   A^2 -> H(U1(d, e), f(d))
25.98/8.55	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.55	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.55	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.55	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.55	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.55	   A^2 -> H(U1(d, c), f(e))
25.98/8.55	   A^2 -> H(U1(d, c), f(k))
25.98/8.55	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.55	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.55	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.55	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.55	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.55	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.55	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.55	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.55	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.55	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.55	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.55	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.55	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.55	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.55	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.55	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.55	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.55	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.55	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.55	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.55	   A^2 -> H(U1(a, e), f(e))
25.98/8.55	   A^2 -> H(U1(a, e), f(k))
25.98/8.55	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.55	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.55	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.55	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.55	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.55	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.55	   A^2 -> H(U1(a, k), f(e))
25.98/8.55	   A^2 -> H(U1(a, k), f(k))
25.98/8.55	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.55	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.55	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.55	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.55	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.55	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.55	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.55	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.55	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.55	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.55	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.55	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.55	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.55	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.55	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.55	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.55	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.55	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.55	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.55	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.55	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.55	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.55	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.55	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.55	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.55	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.55	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.55	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.55	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.55	   A^2 -> H(U1(a, a), b)
25.98/8.55	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.55	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.55	   A^2 -> H(U1(a, a), c)
25.98/8.55	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.55	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.55	   A^2 -> H(U1(a, a), e)
25.98/8.55	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.55	   A^2 -> H(k, f(b))
25.98/8.55	   A^2 -> H(c, U1(b, b))
25.98/8.55	   A^2 -> H(c, f(c))
25.98/8.55	   A^2 -> H(c, f(d))
25.98/8.55	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.55	   A^2 -> H(U1(e, k), f(c))
25.98/8.55	   A^2 -> H(U1(e, k), f(d))
25.98/8.55	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.55	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.55	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.55	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.55	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.55	   A^2 -> H(U1(e, c), f(e))
25.98/8.55	   A^2 -> H(U1(e, c), f(k))
25.98/8.55	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.55	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.55	   A^2 -> H(U1(k, e), f(c))
25.98/8.55	   A^2 -> H(U1(k, e), f(d))
25.98/8.55	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.55	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.55	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.55	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.55	   A^2 -> H(U1(k, c), U1(c, c))
25.98/8.55	   A^2 -> H(U1(k, c), f(e))
25.98/8.55	   A^2 -> H(U1(k, c), f(k))
25.98/8.55	   A^2 -> H(U1(k, c), U1(d, d))
25.98/8.55	   A^2 -> H(U1(c, e), U1(c, b))
25.98/8.55	   A^2 -> H(U1(c, e), U1(d, b))
25.98/8.55	   A^2 -> H(U1(c, e), U1(b, c))
25.98/8.55	   A^2 -> H(U1(c, e), U1(b, d))
25.98/8.55	   A^2 -> H(U1(c, e), U1(c, c))
25.98/8.55	   A^2 -> H(U1(c, e), f(e))
25.98/8.55	   A^2 -> H(U1(c, e), f(k))
25.98/8.55	   A^2 -> H(U1(c, e), U1(d, d))
25.98/8.55	   A^2 -> H(U1(c, k), U1(c, b))
25.98/8.55	   A^2 -> H(U1(c, k), U1(d, b))
25.98/8.55	   A^2 -> H(U1(c, k), U1(b, c))
25.98/8.55	   A^2 -> H(U1(c, k), U1(b, d))
25.98/8.55	   A^2 -> H(U1(c, k), U1(c, c))
25.98/8.55	   A^2 -> H(U1(c, k), f(e))
25.98/8.55	   A^2 -> H(U1(c, k), f(k))
25.98/8.55	   A^2 -> H(U1(c, k), U1(d, d))
25.98/8.55	   A^2 -> H(U1(c, c), U1(e, b))
25.98/8.55	   A^2 -> H(U1(c, c), U1(k, b))
25.98/8.55	   A^2 -> H(U1(c, c), U1(c, d))
25.98/8.55	   A^2 -> H(U1(c, c), U1(d, c))
25.98/8.55	   A^2 -> H(U1(c, c), U1(b, e))
25.98/8.55	   A^2 -> H(U1(c, c), U1(b, k))
25.98/8.55	   A^2 -> H(U1(c, c), U1(e, e))
25.98/8.55	   A^2 -> H(U1(c, c), U1(k, k))
25.98/8.55	   A^2 -> H(U1(c, c), U1(k, d))
25.98/8.55	   A^2 -> H(U1(c, c), U1(d, k))
25.98/8.55	   A^2 -> H(e, U1(b, b))
25.98/8.55	   A^2 -> H(e, f(c))
25.98/8.55	   A^2 -> H(e, f(d))
25.98/8.55	
25.98/8.55	The TRS R consists of the following rules:
25.98/8.55	
25.98/8.55	   f(x) -> U1(x, x)
25.98/8.55	   U1(e, x) -> x
25.98/8.55	   a -> c
25.98/8.55	   a -> d
25.98/8.55	   b -> c
25.98/8.55	   b -> d
25.98/8.55	   d -> k
25.98/8.55	   c -> e
25.98/8.55	   c -> k
25.98/8.55	
25.98/8.55	Q is empty.
25.98/8.55	We have to consider all minimal (P,Q,R)-chains.
25.98/8.55	----------------------------------------
25.98/8.55	
25.98/8.55	(401) TransformationProof (EQUIVALENT)
25.98/8.55	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.55	
25.98/8.55	   (A^2 -> H(e, U1(b, b)),A^2 -> H(e, U1(b, b)))
25.98/8.55	   (A^2 -> H(U1(e, e), U1(c, b)),A^2 -> H(U1(e, e), U1(c, b)))
25.98/8.55	   (A^2 -> H(U1(e, e), U1(d, b)),A^2 -> H(U1(e, e), U1(d, b)))
25.98/8.55	   (A^2 -> H(U1(e, e), U1(b, c)),A^2 -> H(U1(e, e), U1(b, c)))
25.98/8.55	   (A^2 -> H(U1(e, e), U1(b, d)),A^2 -> H(U1(e, e), U1(b, d)))
25.98/8.55	
25.98/8.55	
25.98/8.55	----------------------------------------
25.98/8.55	
25.98/8.55	(402)
25.98/8.55	Obligation:
25.98/8.55	Q DP problem:
25.98/8.55	The TRS P consists of the following rules:
25.98/8.55	
25.98/8.55	   H(x, x) -> G(x, x, f(k))
25.98/8.55	   G(d, x, x) -> A^2
25.98/8.55	   A^2 -> H(f(c), f(c))
25.98/8.55	   A^2 -> H(f(d), f(d))
25.98/8.55	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.55	   A^2 -> H(U1(e, e), f(c))
25.98/8.55	   A^2 -> H(U1(e, e), f(d))
25.98/8.55	   A^2 -> H(f(e), U1(c, b))
25.98/8.55	   A^2 -> H(f(e), U1(d, b))
25.98/8.55	   A^2 -> H(f(e), U1(b, c))
25.98/8.55	   A^2 -> H(f(e), U1(b, d))
25.98/8.55	   A^2 -> H(f(e), U1(c, c))
25.98/8.55	   A^2 -> H(f(e), f(e))
25.98/8.55	   A^2 -> H(f(e), f(k))
25.98/8.55	   A^2 -> H(f(e), U1(d, d))
25.98/8.55	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.55	   A^2 -> H(U1(k, k), f(c))
25.98/8.55	   A^2 -> H(U1(k, k), f(d))
25.98/8.55	   A^2 -> H(f(k), U1(c, b))
25.98/8.55	   A^2 -> H(f(k), U1(d, b))
25.98/8.55	   A^2 -> H(f(k), U1(b, c))
25.98/8.55	   A^2 -> H(f(k), U1(b, d))
25.98/8.55	   A^2 -> H(f(k), U1(c, c))
25.98/8.55	   A^2 -> H(f(k), f(e))
25.98/8.55	   A^2 -> H(f(k), f(k))
25.98/8.55	   A^2 -> H(f(k), U1(d, d))
25.98/8.55	   A^2 -> H(f(c), U1(e, b))
25.98/8.55	   A^2 -> H(f(c), U1(k, b))
25.98/8.55	   A^2 -> H(f(c), U1(c, d))
25.98/8.55	   A^2 -> H(f(c), U1(d, c))
25.98/8.55	   A^2 -> H(f(c), U1(b, e))
25.98/8.55	   A^2 -> H(f(c), U1(b, k))
25.98/8.55	   A^2 -> H(f(c), U1(k, d))
25.98/8.55	   A^2 -> H(f(c), U1(d, k))
25.98/8.55	   A^2 -> H(f(c), U1(k, k))
25.98/8.55	   A^2 -> H(U1(k, k), f(b))
25.98/8.55	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.55	   A^2 -> H(U1(k, d), f(c))
25.98/8.55	   A^2 -> H(U1(k, d), f(d))
25.98/8.55	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.55	   A^2 -> H(U1(d, k), f(c))
25.98/8.55	   A^2 -> H(U1(d, k), f(d))
25.98/8.55	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.55	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.55	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.55	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.55	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.55	   A^2 -> H(U1(d, d), f(e))
25.98/8.55	   A^2 -> H(U1(d, d), f(k))
25.98/8.55	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.55	   A^2 -> H(f(d), U1(e, b))
25.98/8.55	   A^2 -> H(f(d), U1(k, b))
25.98/8.55	   A^2 -> H(f(d), U1(c, d))
25.98/8.55	   A^2 -> H(f(d), U1(d, c))
25.98/8.55	   A^2 -> H(f(d), U1(b, e))
25.98/8.55	   A^2 -> H(f(d), U1(b, k))
25.98/8.55	   A^2 -> H(f(d), U1(e, c))
25.98/8.55	   A^2 -> H(f(d), U1(k, c))
25.98/8.55	   A^2 -> H(f(d), U1(c, e))
25.98/8.55	   A^2 -> H(f(d), U1(c, k))
25.98/8.55	   A^2 -> H(f(d), U1(e, e))
25.98/8.55	   A^2 -> H(f(d), U1(k, k))
25.98/8.55	   A^2 -> H(f(a), b)
25.98/8.55	   A^2 -> H(f(a), U1(e, d))
25.98/8.55	   A^2 -> H(f(a), U1(d, e))
25.98/8.55	   A^2 -> H(f(c), U1(e, c))
25.98/8.55	   A^2 -> H(f(c), U1(k, c))
25.98/8.55	   A^2 -> H(f(c), U1(c, e))
25.98/8.55	   A^2 -> H(f(c), U1(c, k))
25.98/8.55	   A^2 -> H(f(a), c)
25.98/8.55	   A^2 -> H(f(a), U1(e, k))
25.98/8.55	   A^2 -> H(f(a), U1(k, e))
25.98/8.55	   A^2 -> H(f(c), U1(e, e))
25.98/8.55	   A^2 -> H(f(a), e)
25.98/8.55	   A^2 -> H(f(d), U1(k, d))
25.98/8.55	   A^2 -> H(f(d), U1(d, k))
25.98/8.55	   A^2 -> H(f(a), U1(k, k))
25.98/8.55	   A^2 -> H(d, f(b))
25.98/8.55	   A^2 -> H(a, U1(b, b))
25.98/8.55	   A^2 -> H(a, f(c))
25.98/8.55	   A^2 -> H(a, f(d))
25.98/8.55	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.55	   A^2 -> H(U1(e, d), f(c))
25.98/8.55	   A^2 -> H(U1(e, d), f(d))
25.98/8.55	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.55	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.55	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.55	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.55	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.55	   A^2 -> H(U1(e, a), f(e))
25.98/8.55	   A^2 -> H(U1(e, a), f(k))
25.98/8.55	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.55	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.55	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.55	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.55	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.55	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.55	   A^2 -> H(U1(k, a), f(e))
25.98/8.55	   A^2 -> H(U1(k, a), f(k))
25.98/8.55	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.55	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.55	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.55	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.55	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.55	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.55	   A^2 -> H(U1(c, d), f(e))
25.98/8.55	   A^2 -> H(U1(c, d), f(k))
25.98/8.55	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.55	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.55	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.55	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.55	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.55	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.55	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.55	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.55	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.55	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.55	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.55	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.55	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.55	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.55	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.55	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.55	   A^2 -> H(U1(d, e), f(c))
25.98/8.55	   A^2 -> H(U1(d, e), f(d))
25.98/8.55	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.55	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.55	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.55	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.55	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.55	   A^2 -> H(U1(d, c), f(e))
25.98/8.55	   A^2 -> H(U1(d, c), f(k))
25.98/8.55	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.55	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.55	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.55	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.55	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.55	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.55	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.55	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.55	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.55	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.55	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.55	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.55	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.55	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.55	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.55	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.55	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.55	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.55	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.55	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.55	   A^2 -> H(U1(a, e), f(e))
25.98/8.55	   A^2 -> H(U1(a, e), f(k))
25.98/8.55	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.55	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.55	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.55	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.55	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.55	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.55	   A^2 -> H(U1(a, k), f(e))
25.98/8.55	   A^2 -> H(U1(a, k), f(k))
25.98/8.55	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.55	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.55	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.55	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.55	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.55	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.55	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.55	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.55	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.55	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.55	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.55	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.55	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.55	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.55	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.55	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.55	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.55	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.55	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.55	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.55	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.55	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.55	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.55	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.55	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.55	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.55	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.55	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.55	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.55	   A^2 -> H(U1(a, a), b)
25.98/8.55	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.55	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.55	   A^2 -> H(U1(a, a), c)
25.98/8.55	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.55	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.55	   A^2 -> H(U1(a, a), e)
25.98/8.55	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.55	   A^2 -> H(k, f(b))
25.98/8.55	   A^2 -> H(c, U1(b, b))
25.98/8.55	   A^2 -> H(c, f(c))
25.98/8.55	   A^2 -> H(c, f(d))
25.98/8.55	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.55	   A^2 -> H(U1(e, k), f(c))
25.98/8.55	   A^2 -> H(U1(e, k), f(d))
25.98/8.55	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.55	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.55	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.55	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.55	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.55	   A^2 -> H(U1(e, c), f(e))
25.98/8.55	   A^2 -> H(U1(e, c), f(k))
25.98/8.55	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.55	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.55	   A^2 -> H(U1(k, e), f(c))
25.98/8.55	   A^2 -> H(U1(k, e), f(d))
25.98/8.55	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.55	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.55	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.55	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.55	   A^2 -> H(U1(k, c), U1(c, c))
25.98/8.55	   A^2 -> H(U1(k, c), f(e))
25.98/8.55	   A^2 -> H(U1(k, c), f(k))
25.98/8.55	   A^2 -> H(U1(k, c), U1(d, d))
25.98/8.55	   A^2 -> H(U1(c, e), U1(c, b))
25.98/8.55	   A^2 -> H(U1(c, e), U1(d, b))
25.98/8.55	   A^2 -> H(U1(c, e), U1(b, c))
25.98/8.55	   A^2 -> H(U1(c, e), U1(b, d))
25.98/8.55	   A^2 -> H(U1(c, e), U1(c, c))
25.98/8.55	   A^2 -> H(U1(c, e), f(e))
25.98/8.55	   A^2 -> H(U1(c, e), f(k))
25.98/8.55	   A^2 -> H(U1(c, e), U1(d, d))
25.98/8.55	   A^2 -> H(U1(c, k), U1(c, b))
25.98/8.55	   A^2 -> H(U1(c, k), U1(d, b))
25.98/8.55	   A^2 -> H(U1(c, k), U1(b, c))
25.98/8.55	   A^2 -> H(U1(c, k), U1(b, d))
25.98/8.55	   A^2 -> H(U1(c, k), U1(c, c))
25.98/8.55	   A^2 -> H(U1(c, k), f(e))
25.98/8.55	   A^2 -> H(U1(c, k), f(k))
25.98/8.55	   A^2 -> H(U1(c, k), U1(d, d))
25.98/8.55	   A^2 -> H(U1(c, c), U1(e, b))
25.98/8.55	   A^2 -> H(U1(c, c), U1(k, b))
25.98/8.55	   A^2 -> H(U1(c, c), U1(c, d))
25.98/8.55	   A^2 -> H(U1(c, c), U1(d, c))
25.98/8.55	   A^2 -> H(U1(c, c), U1(b, e))
25.98/8.55	   A^2 -> H(U1(c, c), U1(b, k))
25.98/8.55	   A^2 -> H(U1(c, c), U1(e, e))
25.98/8.55	   A^2 -> H(U1(c, c), U1(k, k))
25.98/8.55	   A^2 -> H(U1(c, c), U1(k, d))
25.98/8.55	   A^2 -> H(U1(c, c), U1(d, k))
25.98/8.55	   A^2 -> H(e, U1(b, b))
25.98/8.55	   A^2 -> H(e, f(c))
25.98/8.55	   A^2 -> H(e, f(d))
25.98/8.55	   A^2 -> H(U1(e, e), U1(c, b))
25.98/8.55	   A^2 -> H(U1(e, e), U1(d, b))
25.98/8.55	   A^2 -> H(U1(e, e), U1(b, c))
25.98/8.55	   A^2 -> H(U1(e, e), U1(b, d))
25.98/8.55	
25.98/8.55	The TRS R consists of the following rules:
25.98/8.55	
25.98/8.55	   f(x) -> U1(x, x)
25.98/8.55	   U1(e, x) -> x
25.98/8.55	   a -> c
25.98/8.55	   a -> d
25.98/8.55	   b -> c
25.98/8.55	   b -> d
25.98/8.55	   d -> k
25.98/8.55	   c -> e
25.98/8.55	   c -> k
25.98/8.55	
25.98/8.55	Q is empty.
25.98/8.55	We have to consider all minimal (P,Q,R)-chains.
25.98/8.55	----------------------------------------
25.98/8.55	
25.98/8.55	(403) TransformationProof (EQUIVALENT)
25.98/8.55	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), f(c)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.55	
25.98/8.55	   (A^2 -> H(e, f(c)),A^2 -> H(e, f(c)))
25.98/8.55	   (A^2 -> H(U1(e, e), U1(c, c)),A^2 -> H(U1(e, e), U1(c, c)))
25.98/8.55	   (A^2 -> H(U1(e, e), f(e)),A^2 -> H(U1(e, e), f(e)))
25.98/8.55	   (A^2 -> H(U1(e, e), f(k)),A^2 -> H(U1(e, e), f(k)))
25.98/8.55	
25.98/8.55	
25.98/8.55	----------------------------------------
25.98/8.55	
25.98/8.55	(404)
25.98/8.55	Obligation:
25.98/8.55	Q DP problem:
25.98/8.55	The TRS P consists of the following rules:
25.98/8.55	
25.98/8.55	   H(x, x) -> G(x, x, f(k))
25.98/8.55	   G(d, x, x) -> A^2
25.98/8.55	   A^2 -> H(f(c), f(c))
25.98/8.55	   A^2 -> H(f(d), f(d))
25.98/8.55	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.55	   A^2 -> H(U1(e, e), f(d))
25.98/8.55	   A^2 -> H(f(e), U1(c, b))
25.98/8.55	   A^2 -> H(f(e), U1(d, b))
25.98/8.55	   A^2 -> H(f(e), U1(b, c))
25.98/8.55	   A^2 -> H(f(e), U1(b, d))
25.98/8.55	   A^2 -> H(f(e), U1(c, c))
25.98/8.55	   A^2 -> H(f(e), f(e))
25.98/8.55	   A^2 -> H(f(e), f(k))
25.98/8.55	   A^2 -> H(f(e), U1(d, d))
25.98/8.55	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.55	   A^2 -> H(U1(k, k), f(c))
25.98/8.55	   A^2 -> H(U1(k, k), f(d))
25.98/8.55	   A^2 -> H(f(k), U1(c, b))
25.98/8.55	   A^2 -> H(f(k), U1(d, b))
25.98/8.55	   A^2 -> H(f(k), U1(b, c))
25.98/8.55	   A^2 -> H(f(k), U1(b, d))
25.98/8.55	   A^2 -> H(f(k), U1(c, c))
25.98/8.55	   A^2 -> H(f(k), f(e))
25.98/8.55	   A^2 -> H(f(k), f(k))
25.98/8.55	   A^2 -> H(f(k), U1(d, d))
25.98/8.55	   A^2 -> H(f(c), U1(e, b))
25.98/8.55	   A^2 -> H(f(c), U1(k, b))
25.98/8.55	   A^2 -> H(f(c), U1(c, d))
25.98/8.55	   A^2 -> H(f(c), U1(d, c))
25.98/8.55	   A^2 -> H(f(c), U1(b, e))
25.98/8.55	   A^2 -> H(f(c), U1(b, k))
25.98/8.55	   A^2 -> H(f(c), U1(k, d))
25.98/8.55	   A^2 -> H(f(c), U1(d, k))
25.98/8.55	   A^2 -> H(f(c), U1(k, k))
25.98/8.55	   A^2 -> H(U1(k, k), f(b))
25.98/8.55	   A^2 -> H(U1(k, d), U1(b, b))
25.98/8.55	   A^2 -> H(U1(k, d), f(c))
25.98/8.55	   A^2 -> H(U1(k, d), f(d))
25.98/8.55	   A^2 -> H(U1(d, k), U1(b, b))
25.98/8.55	   A^2 -> H(U1(d, k), f(c))
25.98/8.55	   A^2 -> H(U1(d, k), f(d))
25.98/8.55	   A^2 -> H(U1(d, d), U1(c, b))
25.98/8.55	   A^2 -> H(U1(d, d), U1(d, b))
25.98/8.55	   A^2 -> H(U1(d, d), U1(b, c))
25.98/8.55	   A^2 -> H(U1(d, d), U1(b, d))
25.98/8.55	   A^2 -> H(U1(d, d), U1(c, c))
25.98/8.55	   A^2 -> H(U1(d, d), f(e))
25.98/8.55	   A^2 -> H(U1(d, d), f(k))
25.98/8.55	   A^2 -> H(U1(d, d), U1(d, d))
25.98/8.55	   A^2 -> H(f(d), U1(e, b))
25.98/8.55	   A^2 -> H(f(d), U1(k, b))
25.98/8.55	   A^2 -> H(f(d), U1(c, d))
25.98/8.55	   A^2 -> H(f(d), U1(d, c))
25.98/8.55	   A^2 -> H(f(d), U1(b, e))
25.98/8.55	   A^2 -> H(f(d), U1(b, k))
25.98/8.55	   A^2 -> H(f(d), U1(e, c))
25.98/8.55	   A^2 -> H(f(d), U1(k, c))
25.98/8.55	   A^2 -> H(f(d), U1(c, e))
25.98/8.55	   A^2 -> H(f(d), U1(c, k))
25.98/8.55	   A^2 -> H(f(d), U1(e, e))
25.98/8.55	   A^2 -> H(f(d), U1(k, k))
25.98/8.55	   A^2 -> H(f(a), b)
25.98/8.55	   A^2 -> H(f(a), U1(e, d))
25.98/8.55	   A^2 -> H(f(a), U1(d, e))
25.98/8.55	   A^2 -> H(f(c), U1(e, c))
25.98/8.55	   A^2 -> H(f(c), U1(k, c))
25.98/8.55	   A^2 -> H(f(c), U1(c, e))
25.98/8.55	   A^2 -> H(f(c), U1(c, k))
25.98/8.55	   A^2 -> H(f(a), c)
25.98/8.55	   A^2 -> H(f(a), U1(e, k))
25.98/8.55	   A^2 -> H(f(a), U1(k, e))
25.98/8.55	   A^2 -> H(f(c), U1(e, e))
25.98/8.55	   A^2 -> H(f(a), e)
25.98/8.55	   A^2 -> H(f(d), U1(k, d))
25.98/8.55	   A^2 -> H(f(d), U1(d, k))
25.98/8.55	   A^2 -> H(f(a), U1(k, k))
25.98/8.55	   A^2 -> H(d, f(b))
25.98/8.55	   A^2 -> H(a, U1(b, b))
25.98/8.55	   A^2 -> H(a, f(c))
25.98/8.55	   A^2 -> H(a, f(d))
25.98/8.55	   A^2 -> H(U1(e, d), U1(b, b))
25.98/8.55	   A^2 -> H(U1(e, d), f(c))
25.98/8.55	   A^2 -> H(U1(e, d), f(d))
25.98/8.55	   A^2 -> H(U1(e, a), U1(c, b))
25.98/8.55	   A^2 -> H(U1(e, a), U1(d, b))
25.98/8.55	   A^2 -> H(U1(e, a), U1(b, c))
25.98/8.55	   A^2 -> H(U1(e, a), U1(b, d))
25.98/8.55	   A^2 -> H(U1(e, a), U1(c, c))
25.98/8.55	   A^2 -> H(U1(e, a), f(e))
25.98/8.55	   A^2 -> H(U1(e, a), f(k))
25.98/8.55	   A^2 -> H(U1(e, a), U1(d, d))
25.98/8.55	   A^2 -> H(U1(k, a), U1(c, b))
25.98/8.55	   A^2 -> H(U1(k, a), U1(d, b))
25.98/8.55	   A^2 -> H(U1(k, a), U1(b, c))
25.98/8.55	   A^2 -> H(U1(k, a), U1(b, d))
25.98/8.55	   A^2 -> H(U1(k, a), U1(c, c))
25.98/8.55	   A^2 -> H(U1(k, a), f(e))
25.98/8.55	   A^2 -> H(U1(k, a), f(k))
25.98/8.55	   A^2 -> H(U1(k, a), U1(d, d))
25.98/8.55	   A^2 -> H(U1(c, d), U1(c, b))
25.98/8.55	   A^2 -> H(U1(c, d), U1(d, b))
25.98/8.55	   A^2 -> H(U1(c, d), U1(b, c))
25.98/8.55	   A^2 -> H(U1(c, d), U1(b, d))
25.98/8.55	   A^2 -> H(U1(c, d), U1(c, c))
25.98/8.55	   A^2 -> H(U1(c, d), f(e))
25.98/8.55	   A^2 -> H(U1(c, d), f(k))
25.98/8.55	   A^2 -> H(U1(c, d), U1(d, d))
25.98/8.55	   A^2 -> H(U1(c, a), U1(e, b))
25.98/8.55	   A^2 -> H(U1(c, a), U1(k, b))
25.98/8.55	   A^2 -> H(U1(c, a), U1(c, d))
25.98/8.55	   A^2 -> H(U1(c, a), U1(d, c))
25.98/8.55	   A^2 -> H(U1(c, a), U1(b, e))
25.98/8.55	   A^2 -> H(U1(c, a), U1(b, k))
25.98/8.55	   A^2 -> H(U1(c, a), U1(e, c))
25.98/8.55	   A^2 -> H(U1(c, a), U1(k, c))
25.98/8.55	   A^2 -> H(U1(c, a), U1(c, e))
25.98/8.55	   A^2 -> H(U1(c, a), U1(c, k))
25.98/8.55	   A^2 -> H(U1(c, a), U1(e, e))
25.98/8.55	   A^2 -> H(U1(c, a), U1(k, k))
25.98/8.55	   A^2 -> H(U1(c, a), U1(k, d))
25.98/8.55	   A^2 -> H(U1(c, a), U1(d, k))
25.98/8.55	   A^2 -> H(U1(d, e), U1(b, b))
25.98/8.55	   A^2 -> H(U1(d, e), f(c))
25.98/8.55	   A^2 -> H(U1(d, e), f(d))
25.98/8.55	   A^2 -> H(U1(d, c), U1(c, b))
25.98/8.55	   A^2 -> H(U1(d, c), U1(d, b))
25.98/8.55	   A^2 -> H(U1(d, c), U1(b, c))
25.98/8.55	   A^2 -> H(U1(d, c), U1(b, d))
25.98/8.55	   A^2 -> H(U1(d, c), U1(c, c))
25.98/8.55	   A^2 -> H(U1(d, c), f(e))
25.98/8.55	   A^2 -> H(U1(d, c), f(k))
25.98/8.55	   A^2 -> H(U1(d, c), U1(d, d))
25.98/8.55	   A^2 -> H(U1(d, a), U1(e, b))
25.98/8.55	   A^2 -> H(U1(d, a), U1(k, b))
25.98/8.55	   A^2 -> H(U1(d, a), U1(c, d))
25.98/8.55	   A^2 -> H(U1(d, a), U1(d, c))
25.98/8.55	   A^2 -> H(U1(d, a), U1(b, e))
25.98/8.55	   A^2 -> H(U1(d, a), U1(b, k))
25.98/8.55	   A^2 -> H(U1(d, a), U1(e, c))
25.98/8.55	   A^2 -> H(U1(d, a), U1(k, c))
25.98/8.55	   A^2 -> H(U1(d, a), U1(c, e))
25.98/8.55	   A^2 -> H(U1(d, a), U1(c, k))
25.98/8.55	   A^2 -> H(U1(d, a), U1(e, e))
25.98/8.55	   A^2 -> H(U1(d, a), U1(k, k))
25.98/8.55	   A^2 -> H(U1(d, a), U1(k, d))
25.98/8.55	   A^2 -> H(U1(d, a), U1(d, k))
25.98/8.55	   A^2 -> H(U1(a, e), U1(c, b))
25.98/8.55	   A^2 -> H(U1(a, e), U1(d, b))
25.98/8.55	   A^2 -> H(U1(a, e), U1(b, c))
25.98/8.55	   A^2 -> H(U1(a, e), U1(b, d))
25.98/8.55	   A^2 -> H(U1(a, e), U1(c, c))
25.98/8.55	   A^2 -> H(U1(a, e), f(e))
25.98/8.55	   A^2 -> H(U1(a, e), f(k))
25.98/8.55	   A^2 -> H(U1(a, e), U1(d, d))
25.98/8.55	   A^2 -> H(U1(a, k), U1(c, b))
25.98/8.55	   A^2 -> H(U1(a, k), U1(d, b))
25.98/8.55	   A^2 -> H(U1(a, k), U1(b, c))
25.98/8.55	   A^2 -> H(U1(a, k), U1(b, d))
25.98/8.55	   A^2 -> H(U1(a, k), U1(c, c))
25.98/8.55	   A^2 -> H(U1(a, k), f(e))
25.98/8.55	   A^2 -> H(U1(a, k), f(k))
25.98/8.55	   A^2 -> H(U1(a, k), U1(d, d))
25.98/8.55	   A^2 -> H(U1(a, c), U1(e, b))
25.98/8.55	   A^2 -> H(U1(a, c), U1(k, b))
25.98/8.55	   A^2 -> H(U1(a, c), U1(c, d))
25.98/8.55	   A^2 -> H(U1(a, c), U1(d, c))
25.98/8.55	   A^2 -> H(U1(a, c), U1(b, e))
25.98/8.55	   A^2 -> H(U1(a, c), U1(b, k))
25.98/8.55	   A^2 -> H(U1(a, c), U1(e, c))
25.98/8.55	   A^2 -> H(U1(a, c), U1(k, c))
25.98/8.55	   A^2 -> H(U1(a, c), U1(c, e))
25.98/8.55	   A^2 -> H(U1(a, c), U1(c, k))
25.98/8.55	   A^2 -> H(U1(a, c), U1(e, e))
25.98/8.55	   A^2 -> H(U1(a, c), U1(k, k))
25.98/8.55	   A^2 -> H(U1(a, c), U1(k, d))
25.98/8.55	   A^2 -> H(U1(a, c), U1(d, k))
25.98/8.55	   A^2 -> H(U1(a, d), U1(e, b))
25.98/8.55	   A^2 -> H(U1(a, d), U1(k, b))
25.98/8.55	   A^2 -> H(U1(a, d), U1(c, d))
25.98/8.55	   A^2 -> H(U1(a, d), U1(d, c))
25.98/8.55	   A^2 -> H(U1(a, d), U1(b, e))
25.98/8.55	   A^2 -> H(U1(a, d), U1(b, k))
25.98/8.55	   A^2 -> H(U1(a, d), U1(e, c))
25.98/8.55	   A^2 -> H(U1(a, d), U1(k, c))
25.98/8.55	   A^2 -> H(U1(a, d), U1(c, e))
25.98/8.55	   A^2 -> H(U1(a, d), U1(c, k))
25.98/8.55	   A^2 -> H(U1(a, d), U1(e, e))
25.98/8.55	   A^2 -> H(U1(a, d), U1(k, k))
25.98/8.55	   A^2 -> H(U1(a, d), U1(k, d))
25.98/8.55	   A^2 -> H(U1(a, d), U1(d, k))
25.98/8.55	   A^2 -> H(U1(a, a), b)
25.98/8.55	   A^2 -> H(U1(a, a), U1(e, d))
25.98/8.55	   A^2 -> H(U1(a, a), U1(d, e))
25.98/8.55	   A^2 -> H(U1(a, a), c)
25.98/8.55	   A^2 -> H(U1(a, a), U1(e, k))
25.98/8.55	   A^2 -> H(U1(a, a), U1(k, e))
25.98/8.55	   A^2 -> H(U1(a, a), e)
25.98/8.55	   A^2 -> H(U1(a, a), U1(k, k))
25.98/8.55	   A^2 -> H(k, f(b))
25.98/8.55	   A^2 -> H(c, U1(b, b))
25.98/8.55	   A^2 -> H(c, f(c))
25.98/8.55	   A^2 -> H(c, f(d))
25.98/8.55	   A^2 -> H(U1(e, k), U1(b, b))
25.98/8.55	   A^2 -> H(U1(e, k), f(c))
25.98/8.55	   A^2 -> H(U1(e, k), f(d))
25.98/8.55	   A^2 -> H(U1(e, c), U1(c, b))
25.98/8.55	   A^2 -> H(U1(e, c), U1(d, b))
25.98/8.55	   A^2 -> H(U1(e, c), U1(b, c))
25.98/8.55	   A^2 -> H(U1(e, c), U1(b, d))
25.98/8.55	   A^2 -> H(U1(e, c), U1(c, c))
25.98/8.55	   A^2 -> H(U1(e, c), f(e))
25.98/8.55	   A^2 -> H(U1(e, c), f(k))
25.98/8.55	   A^2 -> H(U1(e, c), U1(d, d))
25.98/8.55	   A^2 -> H(U1(k, e), U1(b, b))
25.98/8.55	   A^2 -> H(U1(k, e), f(c))
25.98/8.55	   A^2 -> H(U1(k, e), f(d))
25.98/8.55	   A^2 -> H(U1(k, c), U1(c, b))
25.98/8.55	   A^2 -> H(U1(k, c), U1(d, b))
25.98/8.55	   A^2 -> H(U1(k, c), U1(b, c))
25.98/8.55	   A^2 -> H(U1(k, c), U1(b, d))
25.98/8.55	   A^2 -> H(U1(k, c), U1(c, c))
25.98/8.55	   A^2 -> H(U1(k, c), f(e))
25.98/8.55	   A^2 -> H(U1(k, c), f(k))
25.98/8.55	   A^2 -> H(U1(k, c), U1(d, d))
25.98/8.55	   A^2 -> H(U1(c, e), U1(c, b))
25.98/8.55	   A^2 -> H(U1(c, e), U1(d, b))
25.98/8.55	   A^2 -> H(U1(c, e), U1(b, c))
25.98/8.55	   A^2 -> H(U1(c, e), U1(b, d))
25.98/8.55	   A^2 -> H(U1(c, e), U1(c, c))
25.98/8.55	   A^2 -> H(U1(c, e), f(e))
25.98/8.55	   A^2 -> H(U1(c, e), f(k))
25.98/8.55	   A^2 -> H(U1(c, e), U1(d, d))
25.98/8.55	   A^2 -> H(U1(c, k), U1(c, b))
25.98/8.55	   A^2 -> H(U1(c, k), U1(d, b))
25.98/8.55	   A^2 -> H(U1(c, k), U1(b, c))
25.98/8.55	   A^2 -> H(U1(c, k), U1(b, d))
25.98/8.55	   A^2 -> H(U1(c, k), U1(c, c))
25.98/8.55	   A^2 -> H(U1(c, k), f(e))
25.98/8.55	   A^2 -> H(U1(c, k), f(k))
25.98/8.55	   A^2 -> H(U1(c, k), U1(d, d))
25.98/8.55	   A^2 -> H(U1(c, c), U1(e, b))
25.98/8.55	   A^2 -> H(U1(c, c), U1(k, b))
25.98/8.55	   A^2 -> H(U1(c, c), U1(c, d))
25.98/8.55	   A^2 -> H(U1(c, c), U1(d, c))
25.98/8.55	   A^2 -> H(U1(c, c), U1(b, e))
25.98/8.55	   A^2 -> H(U1(c, c), U1(b, k))
25.98/8.55	   A^2 -> H(U1(c, c), U1(e, e))
25.98/8.55	   A^2 -> H(U1(c, c), U1(k, k))
25.98/8.55	   A^2 -> H(U1(c, c), U1(k, d))
25.98/8.55	   A^2 -> H(U1(c, c), U1(d, k))
25.98/8.55	   A^2 -> H(e, U1(b, b))
25.98/8.55	   A^2 -> H(e, f(c))
25.98/8.55	   A^2 -> H(e, f(d))
25.98/8.55	   A^2 -> H(U1(e, e), U1(c, b))
25.98/8.55	   A^2 -> H(U1(e, e), U1(d, b))
25.98/8.55	   A^2 -> H(U1(e, e), U1(b, c))
25.98/8.55	   A^2 -> H(U1(e, e), U1(b, d))
25.98/8.55	   A^2 -> H(U1(e, e), U1(c, c))
25.98/8.55	   A^2 -> H(U1(e, e), f(e))
25.98/8.55	   A^2 -> H(U1(e, e), f(k))
25.98/8.55	
25.98/8.55	The TRS R consists of the following rules:
25.98/8.55	
25.98/8.55	   f(x) -> U1(x, x)
25.98/8.55	   U1(e, x) -> x
25.98/8.55	   a -> c
25.98/8.55	   a -> d
25.98/8.55	   b -> c
25.98/8.55	   b -> d
25.98/8.55	   d -> k
25.98/8.55	   c -> e
25.98/8.55	   c -> k
25.98/8.55	
25.98/8.55	Q is empty.
25.98/8.55	We have to consider all minimal (P,Q,R)-chains.
25.98/8.55	----------------------------------------
25.98/8.55	
25.98/8.55	(405) TransformationProof (EQUIVALENT)
25.98/8.55	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), f(d)) at position [] we obtained the following new rules [LPAR04]:
25.98/8.55	
25.98/8.55	   (A^2 -> H(e, f(d)),A^2 -> H(e, f(d)))
25.98/8.55	   (A^2 -> H(U1(e, e), U1(d, d)),A^2 -> H(U1(e, e), U1(d, d)))
25.98/8.55	   (A^2 -> H(U1(e, e), f(k)),A^2 -> H(U1(e, e), f(k)))
25.98/8.55	
25.98/8.55	
25.98/8.55	----------------------------------------
25.98/8.55	
25.98/8.55	(406)
25.98/8.55	Obligation:
25.98/8.55	Q DP problem:
25.98/8.55	The TRS P consists of the following rules:
25.98/8.55	
25.98/8.55	   H(x, x) -> G(x, x, f(k))
25.98/8.55	   G(d, x, x) -> A^2
25.98/8.55	   A^2 -> H(f(c), f(c))
25.98/8.55	   A^2 -> H(f(d), f(d))
25.98/8.55	   A^2 -> H(U1(c, c), U1(c, c))
25.98/8.55	   A^2 -> H(f(e), U1(c, b))
25.98/8.55	   A^2 -> H(f(e), U1(d, b))
25.98/8.55	   A^2 -> H(f(e), U1(b, c))
25.98/8.55	   A^2 -> H(f(e), U1(b, d))
25.98/8.55	   A^2 -> H(f(e), U1(c, c))
25.98/8.55	   A^2 -> H(f(e), f(e))
25.98/8.55	   A^2 -> H(f(e), f(k))
25.98/8.55	   A^2 -> H(f(e), U1(d, d))
25.98/8.55	   A^2 -> H(U1(k, k), U1(b, b))
25.98/8.55	   A^2 -> H(U1(k, k), f(c))
25.98/8.55	   A^2 -> H(U1(k, k), f(d))
25.98/8.55	   A^2 -> H(f(k), U1(c, b))
25.98/8.55	   A^2 -> H(f(k), U1(d, b))
25.98/8.55	   A^2 -> H(f(k), U1(b, c))
25.98/8.55	   A^2 -> H(f(k), U1(b, d))
25.98/8.55	   A^2 -> H(f(k), U1(c, c))
25.98/8.55	   A^2 -> H(f(k), f(e))
25.98/8.55	   A^2 -> H(f(k), f(k))
25.98/8.55	   A^2 -> H(f(k), U1(d, d))
25.98/8.55	   A^2 -> H(f(c), U1(e, b))
26.23/8.56	   A^2 -> H(f(c), U1(k, b))
26.23/8.56	   A^2 -> H(f(c), U1(c, d))
26.23/8.56	   A^2 -> H(f(c), U1(d, c))
26.23/8.56	   A^2 -> H(f(c), U1(b, e))
26.23/8.56	   A^2 -> H(f(c), U1(b, k))
26.23/8.56	   A^2 -> H(f(c), U1(k, d))
26.23/8.56	   A^2 -> H(f(c), U1(d, k))
26.23/8.56	   A^2 -> H(f(c), U1(k, k))
26.23/8.56	   A^2 -> H(U1(k, k), f(b))
26.23/8.56	   A^2 -> H(U1(k, d), U1(b, b))
26.23/8.56	   A^2 -> H(U1(k, d), f(c))
26.23/8.56	   A^2 -> H(U1(k, d), f(d))
26.23/8.56	   A^2 -> H(U1(d, k), U1(b, b))
26.23/8.56	   A^2 -> H(U1(d, k), f(c))
26.23/8.56	   A^2 -> H(U1(d, k), f(d))
26.23/8.56	   A^2 -> H(U1(d, d), U1(c, b))
26.23/8.56	   A^2 -> H(U1(d, d), U1(d, b))
26.23/8.56	   A^2 -> H(U1(d, d), U1(b, c))
26.23/8.56	   A^2 -> H(U1(d, d), U1(b, d))
26.23/8.56	   A^2 -> H(U1(d, d), U1(c, c))
26.23/8.56	   A^2 -> H(U1(d, d), f(e))
26.23/8.56	   A^2 -> H(U1(d, d), f(k))
26.23/8.56	   A^2 -> H(U1(d, d), U1(d, d))
26.23/8.56	   A^2 -> H(f(d), U1(e, b))
26.23/8.56	   A^2 -> H(f(d), U1(k, b))
26.23/8.56	   A^2 -> H(f(d), U1(c, d))
26.23/8.56	   A^2 -> H(f(d), U1(d, c))
26.23/8.56	   A^2 -> H(f(d), U1(b, e))
26.23/8.56	   A^2 -> H(f(d), U1(b, k))
26.23/8.56	   A^2 -> H(f(d), U1(e, c))
26.23/8.56	   A^2 -> H(f(d), U1(k, c))
26.23/8.56	   A^2 -> H(f(d), U1(c, e))
26.23/8.56	   A^2 -> H(f(d), U1(c, k))
26.23/8.56	   A^2 -> H(f(d), U1(e, e))
26.23/8.56	   A^2 -> H(f(d), U1(k, k))
26.23/8.56	   A^2 -> H(f(a), b)
26.23/8.56	   A^2 -> H(f(a), U1(e, d))
26.23/8.56	   A^2 -> H(f(a), U1(d, e))
26.23/8.56	   A^2 -> H(f(c), U1(e, c))
26.23/8.56	   A^2 -> H(f(c), U1(k, c))
26.23/8.56	   A^2 -> H(f(c), U1(c, e))
26.23/8.56	   A^2 -> H(f(c), U1(c, k))
26.23/8.56	   A^2 -> H(f(a), c)
26.23/8.56	   A^2 -> H(f(a), U1(e, k))
26.23/8.56	   A^2 -> H(f(a), U1(k, e))
26.23/8.56	   A^2 -> H(f(c), U1(e, e))
26.23/8.56	   A^2 -> H(f(a), e)
26.23/8.56	   A^2 -> H(f(d), U1(k, d))
26.23/8.56	   A^2 -> H(f(d), U1(d, k))
26.23/8.56	   A^2 -> H(f(a), U1(k, k))
26.23/8.56	   A^2 -> H(d, f(b))
26.23/8.56	   A^2 -> H(a, U1(b, b))
26.23/8.56	   A^2 -> H(a, f(c))
26.23/8.56	   A^2 -> H(a, f(d))
26.23/8.56	   A^2 -> H(U1(e, d), U1(b, b))
26.23/8.56	   A^2 -> H(U1(e, d), f(c))
26.23/8.56	   A^2 -> H(U1(e, d), f(d))
26.23/8.56	   A^2 -> H(U1(e, a), U1(c, b))
26.23/8.56	   A^2 -> H(U1(e, a), U1(d, b))
26.23/8.56	   A^2 -> H(U1(e, a), U1(b, c))
26.23/8.56	   A^2 -> H(U1(e, a), U1(b, d))
26.23/8.56	   A^2 -> H(U1(e, a), U1(c, c))
26.23/8.56	   A^2 -> H(U1(e, a), f(e))
26.23/8.56	   A^2 -> H(U1(e, a), f(k))
26.23/8.56	   A^2 -> H(U1(e, a), U1(d, d))
26.23/8.56	   A^2 -> H(U1(k, a), U1(c, b))
26.23/8.56	   A^2 -> H(U1(k, a), U1(d, b))
26.23/8.56	   A^2 -> H(U1(k, a), U1(b, c))
26.23/8.56	   A^2 -> H(U1(k, a), U1(b, d))
26.23/8.56	   A^2 -> H(U1(k, a), U1(c, c))
26.23/8.56	   A^2 -> H(U1(k, a), f(e))
26.23/8.56	   A^2 -> H(U1(k, a), f(k))
26.23/8.56	   A^2 -> H(U1(k, a), U1(d, d))
26.23/8.56	   A^2 -> H(U1(c, d), U1(c, b))
26.23/8.56	   A^2 -> H(U1(c, d), U1(d, b))
26.23/8.56	   A^2 -> H(U1(c, d), U1(b, c))
26.23/8.56	   A^2 -> H(U1(c, d), U1(b, d))
26.23/8.56	   A^2 -> H(U1(c, d), U1(c, c))
26.23/8.56	   A^2 -> H(U1(c, d), f(e))
26.23/8.56	   A^2 -> H(U1(c, d), f(k))
26.23/8.56	   A^2 -> H(U1(c, d), U1(d, d))
26.23/8.56	   A^2 -> H(U1(c, a), U1(e, b))
26.23/8.56	   A^2 -> H(U1(c, a), U1(k, b))
26.23/8.56	   A^2 -> H(U1(c, a), U1(c, d))
26.23/8.56	   A^2 -> H(U1(c, a), U1(d, c))
26.23/8.56	   A^2 -> H(U1(c, a), U1(b, e))
26.23/8.56	   A^2 -> H(U1(c, a), U1(b, k))
26.23/8.56	   A^2 -> H(U1(c, a), U1(e, c))
26.23/8.56	   A^2 -> H(U1(c, a), U1(k, c))
26.23/8.56	   A^2 -> H(U1(c, a), U1(c, e))
26.23/8.56	   A^2 -> H(U1(c, a), U1(c, k))
26.23/8.56	   A^2 -> H(U1(c, a), U1(e, e))
26.23/8.56	   A^2 -> H(U1(c, a), U1(k, k))
26.23/8.56	   A^2 -> H(U1(c, a), U1(k, d))
26.23/8.56	   A^2 -> H(U1(c, a), U1(d, k))
26.23/8.56	   A^2 -> H(U1(d, e), U1(b, b))
26.23/8.56	   A^2 -> H(U1(d, e), f(c))
26.23/8.56	   A^2 -> H(U1(d, e), f(d))
26.23/8.56	   A^2 -> H(U1(d, c), U1(c, b))
26.23/8.56	   A^2 -> H(U1(d, c), U1(d, b))
26.23/8.56	   A^2 -> H(U1(d, c), U1(b, c))
26.23/8.56	   A^2 -> H(U1(d, c), U1(b, d))
26.23/8.56	   A^2 -> H(U1(d, c), U1(c, c))
26.23/8.56	   A^2 -> H(U1(d, c), f(e))
26.23/8.56	   A^2 -> H(U1(d, c), f(k))
26.23/8.56	   A^2 -> H(U1(d, c), U1(d, d))
26.23/8.56	   A^2 -> H(U1(d, a), U1(e, b))
26.23/8.56	   A^2 -> H(U1(d, a), U1(k, b))
26.23/8.56	   A^2 -> H(U1(d, a), U1(c, d))
26.23/8.56	   A^2 -> H(U1(d, a), U1(d, c))
26.23/8.56	   A^2 -> H(U1(d, a), U1(b, e))
26.23/8.56	   A^2 -> H(U1(d, a), U1(b, k))
26.23/8.56	   A^2 -> H(U1(d, a), U1(e, c))
26.23/8.56	   A^2 -> H(U1(d, a), U1(k, c))
26.23/8.56	   A^2 -> H(U1(d, a), U1(c, e))
26.23/8.56	   A^2 -> H(U1(d, a), U1(c, k))
26.23/8.56	   A^2 -> H(U1(d, a), U1(e, e))
26.23/8.56	   A^2 -> H(U1(d, a), U1(k, k))
26.23/8.56	   A^2 -> H(U1(d, a), U1(k, d))
26.23/8.56	   A^2 -> H(U1(d, a), U1(d, k))
26.23/8.56	   A^2 -> H(U1(a, e), U1(c, b))
26.23/8.56	   A^2 -> H(U1(a, e), U1(d, b))
26.23/8.56	   A^2 -> H(U1(a, e), U1(b, c))
26.23/8.56	   A^2 -> H(U1(a, e), U1(b, d))
26.23/8.56	   A^2 -> H(U1(a, e), U1(c, c))
26.23/8.56	   A^2 -> H(U1(a, e), f(e))
26.23/8.56	   A^2 -> H(U1(a, e), f(k))
26.23/8.56	   A^2 -> H(U1(a, e), U1(d, d))
26.23/8.56	   A^2 -> H(U1(a, k), U1(c, b))
26.23/8.56	   A^2 -> H(U1(a, k), U1(d, b))
26.23/8.56	   A^2 -> H(U1(a, k), U1(b, c))
26.23/8.56	   A^2 -> H(U1(a, k), U1(b, d))
26.23/8.56	   A^2 -> H(U1(a, k), U1(c, c))
26.23/8.56	   A^2 -> H(U1(a, k), f(e))
26.23/8.56	   A^2 -> H(U1(a, k), f(k))
26.23/8.56	   A^2 -> H(U1(a, k), U1(d, d))
26.23/8.56	   A^2 -> H(U1(a, c), U1(e, b))
26.23/8.56	   A^2 -> H(U1(a, c), U1(k, b))
26.23/8.56	   A^2 -> H(U1(a, c), U1(c, d))
26.23/8.56	   A^2 -> H(U1(a, c), U1(d, c))
26.23/8.56	   A^2 -> H(U1(a, c), U1(b, e))
26.23/8.56	   A^2 -> H(U1(a, c), U1(b, k))
26.23/8.56	   A^2 -> H(U1(a, c), U1(e, c))
26.23/8.56	   A^2 -> H(U1(a, c), U1(k, c))
26.23/8.56	   A^2 -> H(U1(a, c), U1(c, e))
26.23/8.56	   A^2 -> H(U1(a, c), U1(c, k))
26.23/8.56	   A^2 -> H(U1(a, c), U1(e, e))
26.23/8.56	   A^2 -> H(U1(a, c), U1(k, k))
26.23/8.56	   A^2 -> H(U1(a, c), U1(k, d))
26.23/8.56	   A^2 -> H(U1(a, c), U1(d, k))
26.23/8.56	   A^2 -> H(U1(a, d), U1(e, b))
26.23/8.56	   A^2 -> H(U1(a, d), U1(k, b))
26.23/8.56	   A^2 -> H(U1(a, d), U1(c, d))
26.23/8.56	   A^2 -> H(U1(a, d), U1(d, c))
26.23/8.56	   A^2 -> H(U1(a, d), U1(b, e))
26.23/8.56	   A^2 -> H(U1(a, d), U1(b, k))
26.23/8.56	   A^2 -> H(U1(a, d), U1(e, c))
26.23/8.56	   A^2 -> H(U1(a, d), U1(k, c))
26.23/8.56	   A^2 -> H(U1(a, d), U1(c, e))
26.23/8.56	   A^2 -> H(U1(a, d), U1(c, k))
26.23/8.56	   A^2 -> H(U1(a, d), U1(e, e))
26.23/8.56	   A^2 -> H(U1(a, d), U1(k, k))
26.23/8.56	   A^2 -> H(U1(a, d), U1(k, d))
26.23/8.56	   A^2 -> H(U1(a, d), U1(d, k))
26.23/8.56	   A^2 -> H(U1(a, a), b)
26.23/8.56	   A^2 -> H(U1(a, a), U1(e, d))
26.23/8.56	   A^2 -> H(U1(a, a), U1(d, e))
26.23/8.56	   A^2 -> H(U1(a, a), c)
26.23/8.56	   A^2 -> H(U1(a, a), U1(e, k))
26.23/8.56	   A^2 -> H(U1(a, a), U1(k, e))
26.23/8.56	   A^2 -> H(U1(a, a), e)
26.23/8.56	   A^2 -> H(U1(a, a), U1(k, k))
26.23/8.56	   A^2 -> H(k, f(b))
26.23/8.56	   A^2 -> H(c, U1(b, b))
26.23/8.56	   A^2 -> H(c, f(c))
26.23/8.56	   A^2 -> H(c, f(d))
26.23/8.56	   A^2 -> H(U1(e, k), U1(b, b))
26.23/8.56	   A^2 -> H(U1(e, k), f(c))
26.23/8.56	   A^2 -> H(U1(e, k), f(d))
26.23/8.56	   A^2 -> H(U1(e, c), U1(c, b))
26.23/8.56	   A^2 -> H(U1(e, c), U1(d, b))
26.23/8.56	   A^2 -> H(U1(e, c), U1(b, c))
26.23/8.56	   A^2 -> H(U1(e, c), U1(b, d))
26.23/8.56	   A^2 -> H(U1(e, c), U1(c, c))
26.23/8.56	   A^2 -> H(U1(e, c), f(e))
26.23/8.56	   A^2 -> H(U1(e, c), f(k))
26.23/8.56	   A^2 -> H(U1(e, c), U1(d, d))
26.23/8.56	   A^2 -> H(U1(k, e), U1(b, b))
26.23/8.56	   A^2 -> H(U1(k, e), f(c))
26.23/8.56	   A^2 -> H(U1(k, e), f(d))
26.23/8.56	   A^2 -> H(U1(k, c), U1(c, b))
26.23/8.56	   A^2 -> H(U1(k, c), U1(d, b))
26.23/8.56	   A^2 -> H(U1(k, c), U1(b, c))
26.23/8.56	   A^2 -> H(U1(k, c), U1(b, d))
26.23/8.56	   A^2 -> H(U1(k, c), U1(c, c))
26.23/8.56	   A^2 -> H(U1(k, c), f(e))
26.23/8.56	   A^2 -> H(U1(k, c), f(k))
26.23/8.56	   A^2 -> H(U1(k, c), U1(d, d))
26.23/8.56	   A^2 -> H(U1(c, e), U1(c, b))
26.23/8.56	   A^2 -> H(U1(c, e), U1(d, b))
26.23/8.56	   A^2 -> H(U1(c, e), U1(b, c))
26.23/8.56	   A^2 -> H(U1(c, e), U1(b, d))
26.23/8.56	   A^2 -> H(U1(c, e), U1(c, c))
26.23/8.56	   A^2 -> H(U1(c, e), f(e))
26.23/8.56	   A^2 -> H(U1(c, e), f(k))
26.23/8.56	   A^2 -> H(U1(c, e), U1(d, d))
26.23/8.56	   A^2 -> H(U1(c, k), U1(c, b))
26.23/8.56	   A^2 -> H(U1(c, k), U1(d, b))
26.23/8.56	   A^2 -> H(U1(c, k), U1(b, c))
26.23/8.56	   A^2 -> H(U1(c, k), U1(b, d))
26.23/8.56	   A^2 -> H(U1(c, k), U1(c, c))
26.23/8.56	   A^2 -> H(U1(c, k), f(e))
26.23/8.56	   A^2 -> H(U1(c, k), f(k))
26.23/8.56	   A^2 -> H(U1(c, k), U1(d, d))
26.23/8.56	   A^2 -> H(U1(c, c), U1(e, b))
26.23/8.56	   A^2 -> H(U1(c, c), U1(k, b))
26.23/8.56	   A^2 -> H(U1(c, c), U1(c, d))
26.23/8.56	   A^2 -> H(U1(c, c), U1(d, c))
26.23/8.56	   A^2 -> H(U1(c, c), U1(b, e))
26.23/8.56	   A^2 -> H(U1(c, c), U1(b, k))
26.23/8.56	   A^2 -> H(U1(c, c), U1(e, e))
26.23/8.56	   A^2 -> H(U1(c, c), U1(k, k))
26.23/8.56	   A^2 -> H(U1(c, c), U1(k, d))
26.23/8.56	   A^2 -> H(U1(c, c), U1(d, k))
26.23/8.56	   A^2 -> H(e, U1(b, b))
26.23/8.56	   A^2 -> H(e, f(c))
26.23/8.56	   A^2 -> H(e, f(d))
26.23/8.56	   A^2 -> H(U1(e, e), U1(c, b))
26.23/8.56	   A^2 -> H(U1(e, e), U1(d, b))
26.23/8.56	   A^2 -> H(U1(e, e), U1(b, c))
26.23/8.56	   A^2 -> H(U1(e, e), U1(b, d))
26.23/8.56	   A^2 -> H(U1(e, e), U1(c, c))
26.23/8.56	   A^2 -> H(U1(e, e), f(e))
26.23/8.56	   A^2 -> H(U1(e, e), f(k))
26.23/8.56	   A^2 -> H(U1(e, e), U1(d, d))
26.23/8.56	
26.23/8.56	The TRS R consists of the following rules:
26.23/8.56	
26.23/8.56	   f(x) -> U1(x, x)
26.23/8.56	   U1(e, x) -> x
26.23/8.56	   a -> c
26.23/8.56	   a -> d
26.23/8.56	   b -> c
26.23/8.56	   b -> d
26.23/8.56	   d -> k
26.23/8.56	   c -> e
26.23/8.56	   c -> k
26.23/8.56	
26.23/8.56	Q is empty.
26.23/8.56	We have to consider all minimal (P,Q,R)-chains.
26.23/8.56	----------------------------------------
26.23/8.56	
26.23/8.56	(407) TransformationProof (EQUIVALENT)
26.23/8.56	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
26.23/8.56	
26.23/8.56	   (A^2 -> H(U1(e, e), U1(c, b)),A^2 -> H(U1(e, e), U1(c, b)))
26.23/8.56	   (A^2 -> H(f(e), U1(e, b)),A^2 -> H(f(e), U1(e, b)))
26.23/8.56	   (A^2 -> H(f(e), U1(k, b)),A^2 -> H(f(e), U1(k, b)))
26.23/8.56	   (A^2 -> H(f(e), U1(c, c)),A^2 -> H(f(e), U1(c, c)))
26.23/8.56	   (A^2 -> H(f(e), U1(c, d)),A^2 -> H(f(e), U1(c, d)))
26.23/8.56	
26.23/8.56	
26.23/8.56	----------------------------------------
26.23/8.56	
26.23/8.56	(408)
26.23/8.56	Obligation:
26.23/8.56	Q DP problem:
26.23/8.56	The TRS P consists of the following rules:
26.23/8.56	
26.23/8.56	   H(x, x) -> G(x, x, f(k))
26.23/8.56	   G(d, x, x) -> A^2
26.23/8.56	   A^2 -> H(f(c), f(c))
26.23/8.56	   A^2 -> H(f(d), f(d))
26.23/8.56	   A^2 -> H(U1(c, c), U1(c, c))
26.23/8.56	   A^2 -> H(f(e), U1(d, b))
26.23/8.56	   A^2 -> H(f(e), U1(b, c))
26.23/8.56	   A^2 -> H(f(e), U1(b, d))
26.23/8.56	   A^2 -> H(f(e), U1(c, c))
26.23/8.56	   A^2 -> H(f(e), f(e))
26.23/8.56	   A^2 -> H(f(e), f(k))
26.23/8.56	   A^2 -> H(f(e), U1(d, d))
26.23/8.56	   A^2 -> H(U1(k, k), U1(b, b))
26.23/8.56	   A^2 -> H(U1(k, k), f(c))
26.23/8.56	   A^2 -> H(U1(k, k), f(d))
26.23/8.56	   A^2 -> H(f(k), U1(c, b))
26.23/8.56	   A^2 -> H(f(k), U1(d, b))
26.23/8.56	   A^2 -> H(f(k), U1(b, c))
26.23/8.56	   A^2 -> H(f(k), U1(b, d))
26.23/8.56	   A^2 -> H(f(k), U1(c, c))
26.23/8.56	   A^2 -> H(f(k), f(e))
26.23/8.56	   A^2 -> H(f(k), f(k))
26.23/8.56	   A^2 -> H(f(k), U1(d, d))
26.23/8.56	   A^2 -> H(f(c), U1(e, b))
26.23/8.56	   A^2 -> H(f(c), U1(k, b))
26.23/8.56	   A^2 -> H(f(c), U1(c, d))
26.23/8.56	   A^2 -> H(f(c), U1(d, c))
26.23/8.56	   A^2 -> H(f(c), U1(b, e))
26.23/8.56	   A^2 -> H(f(c), U1(b, k))
26.23/8.56	   A^2 -> H(f(c), U1(k, d))
26.23/8.56	   A^2 -> H(f(c), U1(d, k))
26.23/8.56	   A^2 -> H(f(c), U1(k, k))
26.23/8.56	   A^2 -> H(U1(k, k), f(b))
26.23/8.56	   A^2 -> H(U1(k, d), U1(b, b))
26.23/8.56	   A^2 -> H(U1(k, d), f(c))
26.23/8.56	   A^2 -> H(U1(k, d), f(d))
26.23/8.56	   A^2 -> H(U1(d, k), U1(b, b))
26.23/8.56	   A^2 -> H(U1(d, k), f(c))
26.23/8.56	   A^2 -> H(U1(d, k), f(d))
26.23/8.56	   A^2 -> H(U1(d, d), U1(c, b))
26.23/8.56	   A^2 -> H(U1(d, d), U1(d, b))
26.23/8.56	   A^2 -> H(U1(d, d), U1(b, c))
26.23/8.56	   A^2 -> H(U1(d, d), U1(b, d))
26.23/8.56	   A^2 -> H(U1(d, d), U1(c, c))
26.23/8.56	   A^2 -> H(U1(d, d), f(e))
26.23/8.56	   A^2 -> H(U1(d, d), f(k))
26.23/8.56	   A^2 -> H(U1(d, d), U1(d, d))
26.23/8.56	   A^2 -> H(f(d), U1(e, b))
26.23/8.56	   A^2 -> H(f(d), U1(k, b))
26.23/8.56	   A^2 -> H(f(d), U1(c, d))
26.23/8.56	   A^2 -> H(f(d), U1(d, c))
26.23/8.56	   A^2 -> H(f(d), U1(b, e))
26.23/8.56	   A^2 -> H(f(d), U1(b, k))
26.23/8.56	   A^2 -> H(f(d), U1(e, c))
26.23/8.56	   A^2 -> H(f(d), U1(k, c))
26.23/8.56	   A^2 -> H(f(d), U1(c, e))
26.23/8.56	   A^2 -> H(f(d), U1(c, k))
26.23/8.56	   A^2 -> H(f(d), U1(e, e))
26.23/8.56	   A^2 -> H(f(d), U1(k, k))
26.23/8.56	   A^2 -> H(f(a), b)
26.23/8.56	   A^2 -> H(f(a), U1(e, d))
26.23/8.56	   A^2 -> H(f(a), U1(d, e))
26.23/8.56	   A^2 -> H(f(c), U1(e, c))
26.23/8.56	   A^2 -> H(f(c), U1(k, c))
26.23/8.56	   A^2 -> H(f(c), U1(c, e))
26.23/8.56	   A^2 -> H(f(c), U1(c, k))
26.23/8.56	   A^2 -> H(f(a), c)
26.23/8.56	   A^2 -> H(f(a), U1(e, k))
26.23/8.56	   A^2 -> H(f(a), U1(k, e))
26.23/8.56	   A^2 -> H(f(c), U1(e, e))
26.23/8.56	   A^2 -> H(f(a), e)
26.23/8.56	   A^2 -> H(f(d), U1(k, d))
26.23/8.56	   A^2 -> H(f(d), U1(d, k))
26.23/8.56	   A^2 -> H(f(a), U1(k, k))
26.23/8.56	   A^2 -> H(d, f(b))
26.23/8.56	   A^2 -> H(a, U1(b, b))
26.23/8.56	   A^2 -> H(a, f(c))
26.23/8.56	   A^2 -> H(a, f(d))
26.23/8.56	   A^2 -> H(U1(e, d), U1(b, b))
26.23/8.56	   A^2 -> H(U1(e, d), f(c))
26.23/8.56	   A^2 -> H(U1(e, d), f(d))
26.23/8.56	   A^2 -> H(U1(e, a), U1(c, b))
26.23/8.56	   A^2 -> H(U1(e, a), U1(d, b))
26.23/8.56	   A^2 -> H(U1(e, a), U1(b, c))
26.23/8.56	   A^2 -> H(U1(e, a), U1(b, d))
26.23/8.56	   A^2 -> H(U1(e, a), U1(c, c))
26.23/8.56	   A^2 -> H(U1(e, a), f(e))
26.23/8.56	   A^2 -> H(U1(e, a), f(k))
26.23/8.56	   A^2 -> H(U1(e, a), U1(d, d))
26.23/8.56	   A^2 -> H(U1(k, a), U1(c, b))
26.23/8.56	   A^2 -> H(U1(k, a), U1(d, b))
26.23/8.56	   A^2 -> H(U1(k, a), U1(b, c))
26.23/8.56	   A^2 -> H(U1(k, a), U1(b, d))
26.23/8.56	   A^2 -> H(U1(k, a), U1(c, c))
26.23/8.56	   A^2 -> H(U1(k, a), f(e))
26.23/8.56	   A^2 -> H(U1(k, a), f(k))
26.23/8.56	   A^2 -> H(U1(k, a), U1(d, d))
26.23/8.56	   A^2 -> H(U1(c, d), U1(c, b))
26.23/8.56	   A^2 -> H(U1(c, d), U1(d, b))
26.23/8.56	   A^2 -> H(U1(c, d), U1(b, c))
26.23/8.56	   A^2 -> H(U1(c, d), U1(b, d))
26.23/8.56	   A^2 -> H(U1(c, d), U1(c, c))
26.23/8.56	   A^2 -> H(U1(c, d), f(e))
26.23/8.56	   A^2 -> H(U1(c, d), f(k))
26.23/8.56	   A^2 -> H(U1(c, d), U1(d, d))
26.23/8.56	   A^2 -> H(U1(c, a), U1(e, b))
26.23/8.56	   A^2 -> H(U1(c, a), U1(k, b))
26.23/8.56	   A^2 -> H(U1(c, a), U1(c, d))
26.23/8.56	   A^2 -> H(U1(c, a), U1(d, c))
26.23/8.56	   A^2 -> H(U1(c, a), U1(b, e))
26.23/8.56	   A^2 -> H(U1(c, a), U1(b, k))
26.23/8.56	   A^2 -> H(U1(c, a), U1(e, c))
26.23/8.56	   A^2 -> H(U1(c, a), U1(k, c))
26.23/8.56	   A^2 -> H(U1(c, a), U1(c, e))
26.23/8.56	   A^2 -> H(U1(c, a), U1(c, k))
26.23/8.56	   A^2 -> H(U1(c, a), U1(e, e))
26.23/8.56	   A^2 -> H(U1(c, a), U1(k, k))
26.23/8.56	   A^2 -> H(U1(c, a), U1(k, d))
26.23/8.56	   A^2 -> H(U1(c, a), U1(d, k))
26.23/8.56	   A^2 -> H(U1(d, e), U1(b, b))
26.23/8.56	   A^2 -> H(U1(d, e), f(c))
26.23/8.56	   A^2 -> H(U1(d, e), f(d))
26.23/8.56	   A^2 -> H(U1(d, c), U1(c, b))
26.23/8.56	   A^2 -> H(U1(d, c), U1(d, b))
26.23/8.56	   A^2 -> H(U1(d, c), U1(b, c))
26.23/8.56	   A^2 -> H(U1(d, c), U1(b, d))
26.23/8.56	   A^2 -> H(U1(d, c), U1(c, c))
26.23/8.56	   A^2 -> H(U1(d, c), f(e))
26.23/8.56	   A^2 -> H(U1(d, c), f(k))
26.23/8.56	   A^2 -> H(U1(d, c), U1(d, d))
26.23/8.56	   A^2 -> H(U1(d, a), U1(e, b))
26.23/8.56	   A^2 -> H(U1(d, a), U1(k, b))
26.23/8.56	   A^2 -> H(U1(d, a), U1(c, d))
26.23/8.56	   A^2 -> H(U1(d, a), U1(d, c))
26.23/8.56	   A^2 -> H(U1(d, a), U1(b, e))
26.23/8.56	   A^2 -> H(U1(d, a), U1(b, k))
26.23/8.56	   A^2 -> H(U1(d, a), U1(e, c))
26.23/8.56	   A^2 -> H(U1(d, a), U1(k, c))
26.23/8.56	   A^2 -> H(U1(d, a), U1(c, e))
26.23/8.56	   A^2 -> H(U1(d, a), U1(c, k))
26.23/8.56	   A^2 -> H(U1(d, a), U1(e, e))
26.23/8.56	   A^2 -> H(U1(d, a), U1(k, k))
26.23/8.56	   A^2 -> H(U1(d, a), U1(k, d))
26.23/8.56	   A^2 -> H(U1(d, a), U1(d, k))
26.23/8.56	   A^2 -> H(U1(a, e), U1(c, b))
26.23/8.56	   A^2 -> H(U1(a, e), U1(d, b))
26.23/8.56	   A^2 -> H(U1(a, e), U1(b, c))
26.23/8.56	   A^2 -> H(U1(a, e), U1(b, d))
26.23/8.56	   A^2 -> H(U1(a, e), U1(c, c))
26.23/8.56	   A^2 -> H(U1(a, e), f(e))
26.23/8.56	   A^2 -> H(U1(a, e), f(k))
26.23/8.56	   A^2 -> H(U1(a, e), U1(d, d))
26.23/8.56	   A^2 -> H(U1(a, k), U1(c, b))
26.23/8.56	   A^2 -> H(U1(a, k), U1(d, b))
26.23/8.56	   A^2 -> H(U1(a, k), U1(b, c))
26.23/8.56	   A^2 -> H(U1(a, k), U1(b, d))
26.23/8.56	   A^2 -> H(U1(a, k), U1(c, c))
26.23/8.56	   A^2 -> H(U1(a, k), f(e))
26.23/8.56	   A^2 -> H(U1(a, k), f(k))
26.23/8.56	   A^2 -> H(U1(a, k), U1(d, d))
26.23/8.56	   A^2 -> H(U1(a, c), U1(e, b))
26.23/8.56	   A^2 -> H(U1(a, c), U1(k, b))
26.23/8.56	   A^2 -> H(U1(a, c), U1(c, d))
26.23/8.56	   A^2 -> H(U1(a, c), U1(d, c))
26.23/8.56	   A^2 -> H(U1(a, c), U1(b, e))
26.23/8.56	   A^2 -> H(U1(a, c), U1(b, k))
26.23/8.56	   A^2 -> H(U1(a, c), U1(e, c))
26.23/8.56	   A^2 -> H(U1(a, c), U1(k, c))
26.23/8.56	   A^2 -> H(U1(a, c), U1(c, e))
26.23/8.56	   A^2 -> H(U1(a, c), U1(c, k))
26.23/8.56	   A^2 -> H(U1(a, c), U1(e, e))
26.23/8.56	   A^2 -> H(U1(a, c), U1(k, k))
26.23/8.56	   A^2 -> H(U1(a, c), U1(k, d))
26.23/8.56	   A^2 -> H(U1(a, c), U1(d, k))
26.23/8.56	   A^2 -> H(U1(a, d), U1(e, b))
26.23/8.56	   A^2 -> H(U1(a, d), U1(k, b))
26.23/8.56	   A^2 -> H(U1(a, d), U1(c, d))
26.23/8.56	   A^2 -> H(U1(a, d), U1(d, c))
26.23/8.56	   A^2 -> H(U1(a, d), U1(b, e))
26.23/8.56	   A^2 -> H(U1(a, d), U1(b, k))
26.23/8.56	   A^2 -> H(U1(a, d), U1(e, c))
26.23/8.56	   A^2 -> H(U1(a, d), U1(k, c))
26.23/8.56	   A^2 -> H(U1(a, d), U1(c, e))
26.23/8.56	   A^2 -> H(U1(a, d), U1(c, k))
26.23/8.56	   A^2 -> H(U1(a, d), U1(e, e))
26.23/8.56	   A^2 -> H(U1(a, d), U1(k, k))
26.23/8.56	   A^2 -> H(U1(a, d), U1(k, d))
26.23/8.56	   A^2 -> H(U1(a, d), U1(d, k))
26.23/8.56	   A^2 -> H(U1(a, a), b)
26.23/8.56	   A^2 -> H(U1(a, a), U1(e, d))
26.23/8.56	   A^2 -> H(U1(a, a), U1(d, e))
26.23/8.56	   A^2 -> H(U1(a, a), c)
26.23/8.56	   A^2 -> H(U1(a, a), U1(e, k))
26.23/8.56	   A^2 -> H(U1(a, a), U1(k, e))
26.23/8.56	   A^2 -> H(U1(a, a), e)
26.23/8.56	   A^2 -> H(U1(a, a), U1(k, k))
26.23/8.56	   A^2 -> H(k, f(b))
26.23/8.56	   A^2 -> H(c, U1(b, b))
26.23/8.56	   A^2 -> H(c, f(c))
26.23/8.56	   A^2 -> H(c, f(d))
26.23/8.56	   A^2 -> H(U1(e, k), U1(b, b))
26.23/8.56	   A^2 -> H(U1(e, k), f(c))
26.23/8.56	   A^2 -> H(U1(e, k), f(d))
26.23/8.56	   A^2 -> H(U1(e, c), U1(c, b))
26.23/8.56	   A^2 -> H(U1(e, c), U1(d, b))
26.23/8.56	   A^2 -> H(U1(e, c), U1(b, c))
26.23/8.56	   A^2 -> H(U1(e, c), U1(b, d))
26.23/8.56	   A^2 -> H(U1(e, c), U1(c, c))
26.23/8.56	   A^2 -> H(U1(e, c), f(e))
26.23/8.56	   A^2 -> H(U1(e, c), f(k))
26.23/8.56	   A^2 -> H(U1(e, c), U1(d, d))
26.23/8.56	   A^2 -> H(U1(k, e), U1(b, b))
26.23/8.56	   A^2 -> H(U1(k, e), f(c))
26.23/8.56	   A^2 -> H(U1(k, e), f(d))
26.23/8.56	   A^2 -> H(U1(k, c), U1(c, b))
26.23/8.56	   A^2 -> H(U1(k, c), U1(d, b))
26.23/8.56	   A^2 -> H(U1(k, c), U1(b, c))
26.23/8.57	   A^2 -> H(U1(k, c), U1(b, d))
26.23/8.57	   A^2 -> H(U1(k, c), U1(c, c))
26.23/8.57	   A^2 -> H(U1(k, c), f(e))
26.23/8.57	   A^2 -> H(U1(k, c), f(k))
26.23/8.57	   A^2 -> H(U1(k, c), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, e), U1(c, b))
26.23/8.57	   A^2 -> H(U1(c, e), U1(d, b))
26.23/8.57	   A^2 -> H(U1(c, e), U1(b, c))
26.23/8.57	   A^2 -> H(U1(c, e), U1(b, d))
26.23/8.57	   A^2 -> H(U1(c, e), U1(c, c))
26.23/8.57	   A^2 -> H(U1(c, e), f(e))
26.23/8.57	   A^2 -> H(U1(c, e), f(k))
26.23/8.57	   A^2 -> H(U1(c, e), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, k), U1(c, b))
26.23/8.57	   A^2 -> H(U1(c, k), U1(d, b))
26.23/8.57	   A^2 -> H(U1(c, k), U1(b, c))
26.23/8.57	   A^2 -> H(U1(c, k), U1(b, d))
26.23/8.57	   A^2 -> H(U1(c, k), U1(c, c))
26.23/8.57	   A^2 -> H(U1(c, k), f(e))
26.23/8.57	   A^2 -> H(U1(c, k), f(k))
26.23/8.57	   A^2 -> H(U1(c, k), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(e, b))
26.23/8.57	   A^2 -> H(U1(c, c), U1(k, b))
26.23/8.57	   A^2 -> H(U1(c, c), U1(c, d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(d, c))
26.23/8.57	   A^2 -> H(U1(c, c), U1(b, e))
26.23/8.57	   A^2 -> H(U1(c, c), U1(b, k))
26.23/8.57	   A^2 -> H(U1(c, c), U1(e, e))
26.23/8.57	   A^2 -> H(U1(c, c), U1(k, k))
26.23/8.57	   A^2 -> H(U1(c, c), U1(k, d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(d, k))
26.23/8.57	   A^2 -> H(e, U1(b, b))
26.23/8.57	   A^2 -> H(e, f(c))
26.23/8.57	   A^2 -> H(e, f(d))
26.23/8.57	   A^2 -> H(U1(e, e), U1(c, b))
26.23/8.57	   A^2 -> H(U1(e, e), U1(d, b))
26.23/8.57	   A^2 -> H(U1(e, e), U1(b, c))
26.23/8.57	   A^2 -> H(U1(e, e), U1(b, d))
26.23/8.57	   A^2 -> H(U1(e, e), U1(c, c))
26.23/8.57	   A^2 -> H(U1(e, e), f(e))
26.23/8.57	   A^2 -> H(U1(e, e), f(k))
26.23/8.57	   A^2 -> H(U1(e, e), U1(d, d))
26.23/8.57	   A^2 -> H(f(e), U1(e, b))
26.23/8.57	   A^2 -> H(f(e), U1(k, b))
26.23/8.57	   A^2 -> H(f(e), U1(c, d))
26.23/8.57	
26.23/8.57	The TRS R consists of the following rules:
26.23/8.57	
26.23/8.57	   f(x) -> U1(x, x)
26.23/8.57	   U1(e, x) -> x
26.23/8.57	   a -> c
26.23/8.57	   a -> d
26.23/8.57	   b -> c
26.23/8.57	   b -> d
26.23/8.57	   d -> k
26.23/8.57	   c -> e
26.23/8.57	   c -> k
26.23/8.57	
26.23/8.57	Q is empty.
26.23/8.57	We have to consider all minimal (P,Q,R)-chains.
26.23/8.57	----------------------------------------
26.23/8.57	
26.23/8.57	(409) TransformationProof (EQUIVALENT)
26.23/8.57	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
26.23/8.57	
26.23/8.57	   (A^2 -> H(U1(e, e), U1(d, b)),A^2 -> H(U1(e, e), U1(d, b)))
26.23/8.57	   (A^2 -> H(f(e), U1(k, b)),A^2 -> H(f(e), U1(k, b)))
26.23/8.57	   (A^2 -> H(f(e), U1(d, c)),A^2 -> H(f(e), U1(d, c)))
26.23/8.57	   (A^2 -> H(f(e), U1(d, d)),A^2 -> H(f(e), U1(d, d)))
26.23/8.57	
26.23/8.57	
26.23/8.57	----------------------------------------
26.23/8.57	
26.23/8.57	(410)
26.23/8.57	Obligation:
26.23/8.57	Q DP problem:
26.23/8.57	The TRS P consists of the following rules:
26.23/8.57	
26.23/8.57	   H(x, x) -> G(x, x, f(k))
26.23/8.57	   G(d, x, x) -> A^2
26.23/8.57	   A^2 -> H(f(c), f(c))
26.23/8.57	   A^2 -> H(f(d), f(d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(c, c))
26.23/8.57	   A^2 -> H(f(e), U1(b, c))
26.23/8.57	   A^2 -> H(f(e), U1(b, d))
26.23/8.57	   A^2 -> H(f(e), U1(c, c))
26.23/8.57	   A^2 -> H(f(e), f(e))
26.23/8.57	   A^2 -> H(f(e), f(k))
26.23/8.57	   A^2 -> H(f(e), U1(d, d))
26.23/8.57	   A^2 -> H(U1(k, k), U1(b, b))
26.23/8.57	   A^2 -> H(U1(k, k), f(c))
26.23/8.57	   A^2 -> H(U1(k, k), f(d))
26.23/8.57	   A^2 -> H(f(k), U1(c, b))
26.23/8.57	   A^2 -> H(f(k), U1(d, b))
26.23/8.57	   A^2 -> H(f(k), U1(b, c))
26.23/8.57	   A^2 -> H(f(k), U1(b, d))
26.23/8.57	   A^2 -> H(f(k), U1(c, c))
26.23/8.57	   A^2 -> H(f(k), f(e))
26.23/8.57	   A^2 -> H(f(k), f(k))
26.23/8.57	   A^2 -> H(f(k), U1(d, d))
26.23/8.57	   A^2 -> H(f(c), U1(e, b))
26.23/8.57	   A^2 -> H(f(c), U1(k, b))
26.23/8.57	   A^2 -> H(f(c), U1(c, d))
26.23/8.57	   A^2 -> H(f(c), U1(d, c))
26.23/8.57	   A^2 -> H(f(c), U1(b, e))
26.23/8.57	   A^2 -> H(f(c), U1(b, k))
26.23/8.57	   A^2 -> H(f(c), U1(k, d))
26.23/8.57	   A^2 -> H(f(c), U1(d, k))
26.23/8.57	   A^2 -> H(f(c), U1(k, k))
26.23/8.57	   A^2 -> H(U1(k, k), f(b))
26.23/8.57	   A^2 -> H(U1(k, d), U1(b, b))
26.23/8.57	   A^2 -> H(U1(k, d), f(c))
26.23/8.57	   A^2 -> H(U1(k, d), f(d))
26.23/8.57	   A^2 -> H(U1(d, k), U1(b, b))
26.23/8.57	   A^2 -> H(U1(d, k), f(c))
26.23/8.57	   A^2 -> H(U1(d, k), f(d))
26.23/8.57	   A^2 -> H(U1(d, d), U1(c, b))
26.23/8.57	   A^2 -> H(U1(d, d), U1(d, b))
26.23/8.57	   A^2 -> H(U1(d, d), U1(b, c))
26.23/8.57	   A^2 -> H(U1(d, d), U1(b, d))
26.23/8.57	   A^2 -> H(U1(d, d), U1(c, c))
26.23/8.57	   A^2 -> H(U1(d, d), f(e))
26.23/8.57	   A^2 -> H(U1(d, d), f(k))
26.23/8.57	   A^2 -> H(U1(d, d), U1(d, d))
26.23/8.57	   A^2 -> H(f(d), U1(e, b))
26.23/8.57	   A^2 -> H(f(d), U1(k, b))
26.23/8.57	   A^2 -> H(f(d), U1(c, d))
26.23/8.57	   A^2 -> H(f(d), U1(d, c))
26.23/8.57	   A^2 -> H(f(d), U1(b, e))
26.23/8.57	   A^2 -> H(f(d), U1(b, k))
26.23/8.57	   A^2 -> H(f(d), U1(e, c))
26.23/8.57	   A^2 -> H(f(d), U1(k, c))
26.23/8.57	   A^2 -> H(f(d), U1(c, e))
26.23/8.57	   A^2 -> H(f(d), U1(c, k))
26.23/8.57	   A^2 -> H(f(d), U1(e, e))
26.23/8.57	   A^2 -> H(f(d), U1(k, k))
26.23/8.57	   A^2 -> H(f(a), b)
26.23/8.57	   A^2 -> H(f(a), U1(e, d))
26.23/8.57	   A^2 -> H(f(a), U1(d, e))
26.23/8.57	   A^2 -> H(f(c), U1(e, c))
26.23/8.57	   A^2 -> H(f(c), U1(k, c))
26.23/8.57	   A^2 -> H(f(c), U1(c, e))
26.23/8.57	   A^2 -> H(f(c), U1(c, k))
26.23/8.57	   A^2 -> H(f(a), c)
26.23/8.57	   A^2 -> H(f(a), U1(e, k))
26.23/8.57	   A^2 -> H(f(a), U1(k, e))
26.23/8.57	   A^2 -> H(f(c), U1(e, e))
26.23/8.57	   A^2 -> H(f(a), e)
26.23/8.57	   A^2 -> H(f(d), U1(k, d))
26.23/8.57	   A^2 -> H(f(d), U1(d, k))
26.23/8.57	   A^2 -> H(f(a), U1(k, k))
26.23/8.57	   A^2 -> H(d, f(b))
26.23/8.57	   A^2 -> H(a, U1(b, b))
26.23/8.57	   A^2 -> H(a, f(c))
26.23/8.57	   A^2 -> H(a, f(d))
26.23/8.57	   A^2 -> H(U1(e, d), U1(b, b))
26.23/8.57	   A^2 -> H(U1(e, d), f(c))
26.23/8.57	   A^2 -> H(U1(e, d), f(d))
26.23/8.57	   A^2 -> H(U1(e, a), U1(c, b))
26.23/8.57	   A^2 -> H(U1(e, a), U1(d, b))
26.23/8.57	   A^2 -> H(U1(e, a), U1(b, c))
26.23/8.57	   A^2 -> H(U1(e, a), U1(b, d))
26.23/8.57	   A^2 -> H(U1(e, a), U1(c, c))
26.23/8.57	   A^2 -> H(U1(e, a), f(e))
26.23/8.57	   A^2 -> H(U1(e, a), f(k))
26.23/8.57	   A^2 -> H(U1(e, a), U1(d, d))
26.23/8.57	   A^2 -> H(U1(k, a), U1(c, b))
26.23/8.57	   A^2 -> H(U1(k, a), U1(d, b))
26.23/8.57	   A^2 -> H(U1(k, a), U1(b, c))
26.23/8.57	   A^2 -> H(U1(k, a), U1(b, d))
26.23/8.57	   A^2 -> H(U1(k, a), U1(c, c))
26.23/8.57	   A^2 -> H(U1(k, a), f(e))
26.23/8.57	   A^2 -> H(U1(k, a), f(k))
26.23/8.57	   A^2 -> H(U1(k, a), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, d), U1(c, b))
26.23/8.57	   A^2 -> H(U1(c, d), U1(d, b))
26.23/8.57	   A^2 -> H(U1(c, d), U1(b, c))
26.23/8.57	   A^2 -> H(U1(c, d), U1(b, d))
26.23/8.57	   A^2 -> H(U1(c, d), U1(c, c))
26.23/8.57	   A^2 -> H(U1(c, d), f(e))
26.23/8.57	   A^2 -> H(U1(c, d), f(k))
26.23/8.57	   A^2 -> H(U1(c, d), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, a), U1(e, b))
26.23/8.57	   A^2 -> H(U1(c, a), U1(k, b))
26.23/8.57	   A^2 -> H(U1(c, a), U1(c, d))
26.23/8.57	   A^2 -> H(U1(c, a), U1(d, c))
26.23/8.57	   A^2 -> H(U1(c, a), U1(b, e))
26.23/8.57	   A^2 -> H(U1(c, a), U1(b, k))
26.23/8.57	   A^2 -> H(U1(c, a), U1(e, c))
26.23/8.57	   A^2 -> H(U1(c, a), U1(k, c))
26.23/8.57	   A^2 -> H(U1(c, a), U1(c, e))
26.23/8.57	   A^2 -> H(U1(c, a), U1(c, k))
26.23/8.57	   A^2 -> H(U1(c, a), U1(e, e))
26.23/8.57	   A^2 -> H(U1(c, a), U1(k, k))
26.23/8.57	   A^2 -> H(U1(c, a), U1(k, d))
26.23/8.57	   A^2 -> H(U1(c, a), U1(d, k))
26.23/8.57	   A^2 -> H(U1(d, e), U1(b, b))
26.23/8.57	   A^2 -> H(U1(d, e), f(c))
26.23/8.57	   A^2 -> H(U1(d, e), f(d))
26.23/8.57	   A^2 -> H(U1(d, c), U1(c, b))
26.23/8.57	   A^2 -> H(U1(d, c), U1(d, b))
26.23/8.57	   A^2 -> H(U1(d, c), U1(b, c))
26.23/8.57	   A^2 -> H(U1(d, c), U1(b, d))
26.23/8.57	   A^2 -> H(U1(d, c), U1(c, c))
26.23/8.57	   A^2 -> H(U1(d, c), f(e))
26.23/8.57	   A^2 -> H(U1(d, c), f(k))
26.23/8.57	   A^2 -> H(U1(d, c), U1(d, d))
26.23/8.57	   A^2 -> H(U1(d, a), U1(e, b))
26.23/8.57	   A^2 -> H(U1(d, a), U1(k, b))
26.23/8.57	   A^2 -> H(U1(d, a), U1(c, d))
26.23/8.57	   A^2 -> H(U1(d, a), U1(d, c))
26.23/8.57	   A^2 -> H(U1(d, a), U1(b, e))
26.23/8.57	   A^2 -> H(U1(d, a), U1(b, k))
26.23/8.57	   A^2 -> H(U1(d, a), U1(e, c))
26.23/8.57	   A^2 -> H(U1(d, a), U1(k, c))
26.23/8.57	   A^2 -> H(U1(d, a), U1(c, e))
26.23/8.57	   A^2 -> H(U1(d, a), U1(c, k))
26.23/8.57	   A^2 -> H(U1(d, a), U1(e, e))
26.23/8.57	   A^2 -> H(U1(d, a), U1(k, k))
26.23/8.57	   A^2 -> H(U1(d, a), U1(k, d))
26.23/8.57	   A^2 -> H(U1(d, a), U1(d, k))
26.23/8.57	   A^2 -> H(U1(a, e), U1(c, b))
26.23/8.57	   A^2 -> H(U1(a, e), U1(d, b))
26.23/8.57	   A^2 -> H(U1(a, e), U1(b, c))
26.23/8.57	   A^2 -> H(U1(a, e), U1(b, d))
26.23/8.57	   A^2 -> H(U1(a, e), U1(c, c))
26.23/8.57	   A^2 -> H(U1(a, e), f(e))
26.23/8.57	   A^2 -> H(U1(a, e), f(k))
26.23/8.57	   A^2 -> H(U1(a, e), U1(d, d))
26.23/8.57	   A^2 -> H(U1(a, k), U1(c, b))
26.23/8.57	   A^2 -> H(U1(a, k), U1(d, b))
26.23/8.57	   A^2 -> H(U1(a, k), U1(b, c))
26.23/8.57	   A^2 -> H(U1(a, k), U1(b, d))
26.23/8.57	   A^2 -> H(U1(a, k), U1(c, c))
26.23/8.57	   A^2 -> H(U1(a, k), f(e))
26.23/8.57	   A^2 -> H(U1(a, k), f(k))
26.23/8.57	   A^2 -> H(U1(a, k), U1(d, d))
26.23/8.57	   A^2 -> H(U1(a, c), U1(e, b))
26.23/8.57	   A^2 -> H(U1(a, c), U1(k, b))
26.23/8.57	   A^2 -> H(U1(a, c), U1(c, d))
26.23/8.57	   A^2 -> H(U1(a, c), U1(d, c))
26.23/8.57	   A^2 -> H(U1(a, c), U1(b, e))
26.23/8.57	   A^2 -> H(U1(a, c), U1(b, k))
26.23/8.57	   A^2 -> H(U1(a, c), U1(e, c))
26.23/8.57	   A^2 -> H(U1(a, c), U1(k, c))
26.23/8.57	   A^2 -> H(U1(a, c), U1(c, e))
26.23/8.57	   A^2 -> H(U1(a, c), U1(c, k))
26.23/8.57	   A^2 -> H(U1(a, c), U1(e, e))
26.23/8.57	   A^2 -> H(U1(a, c), U1(k, k))
26.23/8.57	   A^2 -> H(U1(a, c), U1(k, d))
26.23/8.57	   A^2 -> H(U1(a, c), U1(d, k))
26.23/8.57	   A^2 -> H(U1(a, d), U1(e, b))
26.23/8.57	   A^2 -> H(U1(a, d), U1(k, b))
26.23/8.57	   A^2 -> H(U1(a, d), U1(c, d))
26.23/8.57	   A^2 -> H(U1(a, d), U1(d, c))
26.23/8.57	   A^2 -> H(U1(a, d), U1(b, e))
26.23/8.57	   A^2 -> H(U1(a, d), U1(b, k))
26.23/8.57	   A^2 -> H(U1(a, d), U1(e, c))
26.23/8.57	   A^2 -> H(U1(a, d), U1(k, c))
26.23/8.57	   A^2 -> H(U1(a, d), U1(c, e))
26.23/8.57	   A^2 -> H(U1(a, d), U1(c, k))
26.23/8.57	   A^2 -> H(U1(a, d), U1(e, e))
26.23/8.57	   A^2 -> H(U1(a, d), U1(k, k))
26.23/8.57	   A^2 -> H(U1(a, d), U1(k, d))
26.23/8.57	   A^2 -> H(U1(a, d), U1(d, k))
26.23/8.57	   A^2 -> H(U1(a, a), b)
26.23/8.57	   A^2 -> H(U1(a, a), U1(e, d))
26.23/8.57	   A^2 -> H(U1(a, a), U1(d, e))
26.23/8.57	   A^2 -> H(U1(a, a), c)
26.23/8.57	   A^2 -> H(U1(a, a), U1(e, k))
26.23/8.57	   A^2 -> H(U1(a, a), U1(k, e))
26.23/8.57	   A^2 -> H(U1(a, a), e)
26.23/8.57	   A^2 -> H(U1(a, a), U1(k, k))
26.23/8.57	   A^2 -> H(k, f(b))
26.23/8.57	   A^2 -> H(c, U1(b, b))
26.23/8.57	   A^2 -> H(c, f(c))
26.23/8.57	   A^2 -> H(c, f(d))
26.23/8.57	   A^2 -> H(U1(e, k), U1(b, b))
26.23/8.57	   A^2 -> H(U1(e, k), f(c))
26.23/8.57	   A^2 -> H(U1(e, k), f(d))
26.23/8.57	   A^2 -> H(U1(e, c), U1(c, b))
26.23/8.57	   A^2 -> H(U1(e, c), U1(d, b))
26.23/8.57	   A^2 -> H(U1(e, c), U1(b, c))
26.23/8.57	   A^2 -> H(U1(e, c), U1(b, d))
26.23/8.57	   A^2 -> H(U1(e, c), U1(c, c))
26.23/8.57	   A^2 -> H(U1(e, c), f(e))
26.23/8.57	   A^2 -> H(U1(e, c), f(k))
26.23/8.57	   A^2 -> H(U1(e, c), U1(d, d))
26.23/8.57	   A^2 -> H(U1(k, e), U1(b, b))
26.23/8.57	   A^2 -> H(U1(k, e), f(c))
26.23/8.57	   A^2 -> H(U1(k, e), f(d))
26.23/8.57	   A^2 -> H(U1(k, c), U1(c, b))
26.23/8.57	   A^2 -> H(U1(k, c), U1(d, b))
26.23/8.57	   A^2 -> H(U1(k, c), U1(b, c))
26.23/8.57	   A^2 -> H(U1(k, c), U1(b, d))
26.23/8.57	   A^2 -> H(U1(k, c), U1(c, c))
26.23/8.57	   A^2 -> H(U1(k, c), f(e))
26.23/8.57	   A^2 -> H(U1(k, c), f(k))
26.23/8.57	   A^2 -> H(U1(k, c), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, e), U1(c, b))
26.23/8.57	   A^2 -> H(U1(c, e), U1(d, b))
26.23/8.57	   A^2 -> H(U1(c, e), U1(b, c))
26.23/8.57	   A^2 -> H(U1(c, e), U1(b, d))
26.23/8.57	   A^2 -> H(U1(c, e), U1(c, c))
26.23/8.57	   A^2 -> H(U1(c, e), f(e))
26.23/8.57	   A^2 -> H(U1(c, e), f(k))
26.23/8.57	   A^2 -> H(U1(c, e), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, k), U1(c, b))
26.23/8.57	   A^2 -> H(U1(c, k), U1(d, b))
26.23/8.57	   A^2 -> H(U1(c, k), U1(b, c))
26.23/8.57	   A^2 -> H(U1(c, k), U1(b, d))
26.23/8.57	   A^2 -> H(U1(c, k), U1(c, c))
26.23/8.57	   A^2 -> H(U1(c, k), f(e))
26.23/8.57	   A^2 -> H(U1(c, k), f(k))
26.23/8.57	   A^2 -> H(U1(c, k), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(e, b))
26.23/8.57	   A^2 -> H(U1(c, c), U1(k, b))
26.23/8.57	   A^2 -> H(U1(c, c), U1(c, d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(d, c))
26.23/8.57	   A^2 -> H(U1(c, c), U1(b, e))
26.23/8.57	   A^2 -> H(U1(c, c), U1(b, k))
26.23/8.57	   A^2 -> H(U1(c, c), U1(e, e))
26.23/8.57	   A^2 -> H(U1(c, c), U1(k, k))
26.23/8.57	   A^2 -> H(U1(c, c), U1(k, d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(d, k))
26.23/8.57	   A^2 -> H(e, U1(b, b))
26.23/8.57	   A^2 -> H(e, f(c))
26.23/8.57	   A^2 -> H(e, f(d))
26.23/8.57	   A^2 -> H(U1(e, e), U1(c, b))
26.23/8.57	   A^2 -> H(U1(e, e), U1(d, b))
26.23/8.57	   A^2 -> H(U1(e, e), U1(b, c))
26.23/8.57	   A^2 -> H(U1(e, e), U1(b, d))
26.23/8.57	   A^2 -> H(U1(e, e), U1(c, c))
26.23/8.57	   A^2 -> H(U1(e, e), f(e))
26.23/8.57	   A^2 -> H(U1(e, e), f(k))
26.23/8.57	   A^2 -> H(U1(e, e), U1(d, d))
26.23/8.57	   A^2 -> H(f(e), U1(e, b))
26.23/8.57	   A^2 -> H(f(e), U1(k, b))
26.23/8.57	   A^2 -> H(f(e), U1(c, d))
26.23/8.57	   A^2 -> H(f(e), U1(d, c))
26.23/8.57	
26.23/8.57	The TRS R consists of the following rules:
26.23/8.57	
26.23/8.57	   f(x) -> U1(x, x)
26.23/8.57	   U1(e, x) -> x
26.23/8.57	   a -> c
26.23/8.57	   a -> d
26.23/8.57	   b -> c
26.23/8.57	   b -> d
26.23/8.57	   d -> k
26.23/8.57	   c -> e
26.23/8.57	   c -> k
26.23/8.57	
26.23/8.57	Q is empty.
26.23/8.57	We have to consider all minimal (P,Q,R)-chains.
26.23/8.57	----------------------------------------
26.23/8.57	
26.23/8.57	(411) TransformationProof (EQUIVALENT)
26.23/8.57	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
26.23/8.57	
26.23/8.57	   (A^2 -> H(U1(e, e), U1(b, c)),A^2 -> H(U1(e, e), U1(b, c)))
26.23/8.57	   (A^2 -> H(f(e), U1(c, c)),A^2 -> H(f(e), U1(c, c)))
26.23/8.57	   (A^2 -> H(f(e), U1(d, c)),A^2 -> H(f(e), U1(d, c)))
26.23/8.57	   (A^2 -> H(f(e), U1(b, e)),A^2 -> H(f(e), U1(b, e)))
26.23/8.57	   (A^2 -> H(f(e), U1(b, k)),A^2 -> H(f(e), U1(b, k)))
26.23/8.57	
26.23/8.57	
26.23/8.57	----------------------------------------
26.23/8.57	
26.23/8.57	(412)
26.23/8.57	Obligation:
26.23/8.57	Q DP problem:
26.23/8.57	The TRS P consists of the following rules:
26.23/8.57	
26.23/8.57	   H(x, x) -> G(x, x, f(k))
26.23/8.57	   G(d, x, x) -> A^2
26.23/8.57	   A^2 -> H(f(c), f(c))
26.23/8.57	   A^2 -> H(f(d), f(d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(c, c))
26.23/8.57	   A^2 -> H(f(e), U1(b, d))
26.23/8.57	   A^2 -> H(f(e), U1(c, c))
26.23/8.57	   A^2 -> H(f(e), f(e))
26.23/8.57	   A^2 -> H(f(e), f(k))
26.23/8.57	   A^2 -> H(f(e), U1(d, d))
26.23/8.57	   A^2 -> H(U1(k, k), U1(b, b))
26.23/8.57	   A^2 -> H(U1(k, k), f(c))
26.23/8.57	   A^2 -> H(U1(k, k), f(d))
26.23/8.57	   A^2 -> H(f(k), U1(c, b))
26.23/8.57	   A^2 -> H(f(k), U1(d, b))
26.23/8.57	   A^2 -> H(f(k), U1(b, c))
26.23/8.57	   A^2 -> H(f(k), U1(b, d))
26.23/8.57	   A^2 -> H(f(k), U1(c, c))
26.23/8.57	   A^2 -> H(f(k), f(e))
26.23/8.57	   A^2 -> H(f(k), f(k))
26.23/8.57	   A^2 -> H(f(k), U1(d, d))
26.23/8.57	   A^2 -> H(f(c), U1(e, b))
26.23/8.57	   A^2 -> H(f(c), U1(k, b))
26.23/8.57	   A^2 -> H(f(c), U1(c, d))
26.23/8.57	   A^2 -> H(f(c), U1(d, c))
26.23/8.57	   A^2 -> H(f(c), U1(b, e))
26.23/8.57	   A^2 -> H(f(c), U1(b, k))
26.23/8.57	   A^2 -> H(f(c), U1(k, d))
26.23/8.57	   A^2 -> H(f(c), U1(d, k))
26.23/8.57	   A^2 -> H(f(c), U1(k, k))
26.23/8.57	   A^2 -> H(U1(k, k), f(b))
26.23/8.57	   A^2 -> H(U1(k, d), U1(b, b))
26.23/8.57	   A^2 -> H(U1(k, d), f(c))
26.23/8.57	   A^2 -> H(U1(k, d), f(d))
26.23/8.57	   A^2 -> H(U1(d, k), U1(b, b))
26.23/8.57	   A^2 -> H(U1(d, k), f(c))
26.23/8.57	   A^2 -> H(U1(d, k), f(d))
26.23/8.57	   A^2 -> H(U1(d, d), U1(c, b))
26.23/8.57	   A^2 -> H(U1(d, d), U1(d, b))
26.23/8.57	   A^2 -> H(U1(d, d), U1(b, c))
26.23/8.57	   A^2 -> H(U1(d, d), U1(b, d))
26.23/8.57	   A^2 -> H(U1(d, d), U1(c, c))
26.23/8.57	   A^2 -> H(U1(d, d), f(e))
26.23/8.57	   A^2 -> H(U1(d, d), f(k))
26.23/8.57	   A^2 -> H(U1(d, d), U1(d, d))
26.23/8.57	   A^2 -> H(f(d), U1(e, b))
26.23/8.57	   A^2 -> H(f(d), U1(k, b))
26.23/8.57	   A^2 -> H(f(d), U1(c, d))
26.23/8.57	   A^2 -> H(f(d), U1(d, c))
26.23/8.57	   A^2 -> H(f(d), U1(b, e))
26.23/8.57	   A^2 -> H(f(d), U1(b, k))
26.23/8.57	   A^2 -> H(f(d), U1(e, c))
26.23/8.57	   A^2 -> H(f(d), U1(k, c))
26.23/8.57	   A^2 -> H(f(d), U1(c, e))
26.23/8.57	   A^2 -> H(f(d), U1(c, k))
26.23/8.57	   A^2 -> H(f(d), U1(e, e))
26.23/8.57	   A^2 -> H(f(d), U1(k, k))
26.23/8.57	   A^2 -> H(f(a), b)
26.23/8.57	   A^2 -> H(f(a), U1(e, d))
26.23/8.57	   A^2 -> H(f(a), U1(d, e))
26.23/8.57	   A^2 -> H(f(c), U1(e, c))
26.23/8.57	   A^2 -> H(f(c), U1(k, c))
26.23/8.57	   A^2 -> H(f(c), U1(c, e))
26.23/8.57	   A^2 -> H(f(c), U1(c, k))
26.23/8.57	   A^2 -> H(f(a), c)
26.23/8.57	   A^2 -> H(f(a), U1(e, k))
26.23/8.57	   A^2 -> H(f(a), U1(k, e))
26.23/8.57	   A^2 -> H(f(c), U1(e, e))
26.23/8.57	   A^2 -> H(f(a), e)
26.23/8.57	   A^2 -> H(f(d), U1(k, d))
26.23/8.57	   A^2 -> H(f(d), U1(d, k))
26.23/8.57	   A^2 -> H(f(a), U1(k, k))
26.23/8.57	   A^2 -> H(d, f(b))
26.23/8.57	   A^2 -> H(a, U1(b, b))
26.23/8.57	   A^2 -> H(a, f(c))
26.23/8.57	   A^2 -> H(a, f(d))
26.23/8.57	   A^2 -> H(U1(e, d), U1(b, b))
26.23/8.57	   A^2 -> H(U1(e, d), f(c))
26.23/8.57	   A^2 -> H(U1(e, d), f(d))
26.23/8.57	   A^2 -> H(U1(e, a), U1(c, b))
26.23/8.57	   A^2 -> H(U1(e, a), U1(d, b))
26.23/8.57	   A^2 -> H(U1(e, a), U1(b, c))
26.23/8.57	   A^2 -> H(U1(e, a), U1(b, d))
26.23/8.57	   A^2 -> H(U1(e, a), U1(c, c))
26.23/8.57	   A^2 -> H(U1(e, a), f(e))
26.23/8.57	   A^2 -> H(U1(e, a), f(k))
26.23/8.57	   A^2 -> H(U1(e, a), U1(d, d))
26.23/8.57	   A^2 -> H(U1(k, a), U1(c, b))
26.23/8.57	   A^2 -> H(U1(k, a), U1(d, b))
26.23/8.57	   A^2 -> H(U1(k, a), U1(b, c))
26.23/8.57	   A^2 -> H(U1(k, a), U1(b, d))
26.23/8.57	   A^2 -> H(U1(k, a), U1(c, c))
26.23/8.57	   A^2 -> H(U1(k, a), f(e))
26.23/8.57	   A^2 -> H(U1(k, a), f(k))
26.23/8.57	   A^2 -> H(U1(k, a), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, d), U1(c, b))
26.23/8.57	   A^2 -> H(U1(c, d), U1(d, b))
26.23/8.57	   A^2 -> H(U1(c, d), U1(b, c))
26.23/8.57	   A^2 -> H(U1(c, d), U1(b, d))
26.23/8.57	   A^2 -> H(U1(c, d), U1(c, c))
26.23/8.57	   A^2 -> H(U1(c, d), f(e))
26.23/8.57	   A^2 -> H(U1(c, d), f(k))
26.23/8.57	   A^2 -> H(U1(c, d), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, a), U1(e, b))
26.23/8.57	   A^2 -> H(U1(c, a), U1(k, b))
26.23/8.57	   A^2 -> H(U1(c, a), U1(c, d))
26.23/8.57	   A^2 -> H(U1(c, a), U1(d, c))
26.23/8.57	   A^2 -> H(U1(c, a), U1(b, e))
26.23/8.57	   A^2 -> H(U1(c, a), U1(b, k))
26.23/8.57	   A^2 -> H(U1(c, a), U1(e, c))
26.23/8.57	   A^2 -> H(U1(c, a), U1(k, c))
26.23/8.57	   A^2 -> H(U1(c, a), U1(c, e))
26.23/8.57	   A^2 -> H(U1(c, a), U1(c, k))
26.23/8.57	   A^2 -> H(U1(c, a), U1(e, e))
26.23/8.57	   A^2 -> H(U1(c, a), U1(k, k))
26.23/8.57	   A^2 -> H(U1(c, a), U1(k, d))
26.23/8.57	   A^2 -> H(U1(c, a), U1(d, k))
26.23/8.57	   A^2 -> H(U1(d, e), U1(b, b))
26.23/8.57	   A^2 -> H(U1(d, e), f(c))
26.23/8.57	   A^2 -> H(U1(d, e), f(d))
26.23/8.57	   A^2 -> H(U1(d, c), U1(c, b))
26.23/8.57	   A^2 -> H(U1(d, c), U1(d, b))
26.23/8.57	   A^2 -> H(U1(d, c), U1(b, c))
26.23/8.57	   A^2 -> H(U1(d, c), U1(b, d))
26.23/8.57	   A^2 -> H(U1(d, c), U1(c, c))
26.23/8.57	   A^2 -> H(U1(d, c), f(e))
26.23/8.57	   A^2 -> H(U1(d, c), f(k))
26.23/8.57	   A^2 -> H(U1(d, c), U1(d, d))
26.23/8.57	   A^2 -> H(U1(d, a), U1(e, b))
26.23/8.57	   A^2 -> H(U1(d, a), U1(k, b))
26.23/8.57	   A^2 -> H(U1(d, a), U1(c, d))
26.23/8.57	   A^2 -> H(U1(d, a), U1(d, c))
26.23/8.57	   A^2 -> H(U1(d, a), U1(b, e))
26.23/8.57	   A^2 -> H(U1(d, a), U1(b, k))
26.23/8.57	   A^2 -> H(U1(d, a), U1(e, c))
26.23/8.57	   A^2 -> H(U1(d, a), U1(k, c))
26.23/8.57	   A^2 -> H(U1(d, a), U1(c, e))
26.23/8.57	   A^2 -> H(U1(d, a), U1(c, k))
26.23/8.57	   A^2 -> H(U1(d, a), U1(e, e))
26.23/8.57	   A^2 -> H(U1(d, a), U1(k, k))
26.23/8.57	   A^2 -> H(U1(d, a), U1(k, d))
26.23/8.57	   A^2 -> H(U1(d, a), U1(d, k))
26.23/8.57	   A^2 -> H(U1(a, e), U1(c, b))
26.23/8.57	   A^2 -> H(U1(a, e), U1(d, b))
26.23/8.57	   A^2 -> H(U1(a, e), U1(b, c))
26.23/8.57	   A^2 -> H(U1(a, e), U1(b, d))
26.23/8.57	   A^2 -> H(U1(a, e), U1(c, c))
26.23/8.57	   A^2 -> H(U1(a, e), f(e))
26.23/8.57	   A^2 -> H(U1(a, e), f(k))
26.23/8.57	   A^2 -> H(U1(a, e), U1(d, d))
26.23/8.57	   A^2 -> H(U1(a, k), U1(c, b))
26.23/8.57	   A^2 -> H(U1(a, k), U1(d, b))
26.23/8.57	   A^2 -> H(U1(a, k), U1(b, c))
26.23/8.57	   A^2 -> H(U1(a, k), U1(b, d))
26.23/8.57	   A^2 -> H(U1(a, k), U1(c, c))
26.23/8.57	   A^2 -> H(U1(a, k), f(e))
26.23/8.57	   A^2 -> H(U1(a, k), f(k))
26.23/8.57	   A^2 -> H(U1(a, k), U1(d, d))
26.23/8.57	   A^2 -> H(U1(a, c), U1(e, b))
26.23/8.57	   A^2 -> H(U1(a, c), U1(k, b))
26.23/8.57	   A^2 -> H(U1(a, c), U1(c, d))
26.23/8.57	   A^2 -> H(U1(a, c), U1(d, c))
26.23/8.57	   A^2 -> H(U1(a, c), U1(b, e))
26.23/8.57	   A^2 -> H(U1(a, c), U1(b, k))
26.23/8.57	   A^2 -> H(U1(a, c), U1(e, c))
26.23/8.57	   A^2 -> H(U1(a, c), U1(k, c))
26.23/8.57	   A^2 -> H(U1(a, c), U1(c, e))
26.23/8.57	   A^2 -> H(U1(a, c), U1(c, k))
26.23/8.57	   A^2 -> H(U1(a, c), U1(e, e))
26.23/8.57	   A^2 -> H(U1(a, c), U1(k, k))
26.23/8.57	   A^2 -> H(U1(a, c), U1(k, d))
26.23/8.57	   A^2 -> H(U1(a, c), U1(d, k))
26.23/8.57	   A^2 -> H(U1(a, d), U1(e, b))
26.23/8.57	   A^2 -> H(U1(a, d), U1(k, b))
26.23/8.57	   A^2 -> H(U1(a, d), U1(c, d))
26.23/8.57	   A^2 -> H(U1(a, d), U1(d, c))
26.23/8.57	   A^2 -> H(U1(a, d), U1(b, e))
26.23/8.57	   A^2 -> H(U1(a, d), U1(b, k))
26.23/8.57	   A^2 -> H(U1(a, d), U1(e, c))
26.23/8.57	   A^2 -> H(U1(a, d), U1(k, c))
26.23/8.57	   A^2 -> H(U1(a, d), U1(c, e))
26.23/8.57	   A^2 -> H(U1(a, d), U1(c, k))
26.23/8.57	   A^2 -> H(U1(a, d), U1(e, e))
26.23/8.57	   A^2 -> H(U1(a, d), U1(k, k))
26.23/8.57	   A^2 -> H(U1(a, d), U1(k, d))
26.23/8.57	   A^2 -> H(U1(a, d), U1(d, k))
26.23/8.57	   A^2 -> H(U1(a, a), b)
26.23/8.57	   A^2 -> H(U1(a, a), U1(e, d))
26.23/8.57	   A^2 -> H(U1(a, a), U1(d, e))
26.23/8.57	   A^2 -> H(U1(a, a), c)
26.23/8.57	   A^2 -> H(U1(a, a), U1(e, k))
26.23/8.57	   A^2 -> H(U1(a, a), U1(k, e))
26.23/8.57	   A^2 -> H(U1(a, a), e)
26.23/8.57	   A^2 -> H(U1(a, a), U1(k, k))
26.23/8.57	   A^2 -> H(k, f(b))
26.23/8.57	   A^2 -> H(c, U1(b, b))
26.23/8.57	   A^2 -> H(c, f(c))
26.23/8.57	   A^2 -> H(c, f(d))
26.23/8.57	   A^2 -> H(U1(e, k), U1(b, b))
26.23/8.57	   A^2 -> H(U1(e, k), f(c))
26.23/8.57	   A^2 -> H(U1(e, k), f(d))
26.23/8.57	   A^2 -> H(U1(e, c), U1(c, b))
26.23/8.57	   A^2 -> H(U1(e, c), U1(d, b))
26.23/8.57	   A^2 -> H(U1(e, c), U1(b, c))
26.23/8.57	   A^2 -> H(U1(e, c), U1(b, d))
26.23/8.57	   A^2 -> H(U1(e, c), U1(c, c))
26.23/8.57	   A^2 -> H(U1(e, c), f(e))
26.23/8.57	   A^2 -> H(U1(e, c), f(k))
26.23/8.57	   A^2 -> H(U1(e, c), U1(d, d))
26.23/8.57	   A^2 -> H(U1(k, e), U1(b, b))
26.23/8.57	   A^2 -> H(U1(k, e), f(c))
26.23/8.57	   A^2 -> H(U1(k, e), f(d))
26.23/8.57	   A^2 -> H(U1(k, c), U1(c, b))
26.23/8.57	   A^2 -> H(U1(k, c), U1(d, b))
26.23/8.57	   A^2 -> H(U1(k, c), U1(b, c))
26.23/8.57	   A^2 -> H(U1(k, c), U1(b, d))
26.23/8.57	   A^2 -> H(U1(k, c), U1(c, c))
26.23/8.57	   A^2 -> H(U1(k, c), f(e))
26.23/8.57	   A^2 -> H(U1(k, c), f(k))
26.23/8.57	   A^2 -> H(U1(k, c), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, e), U1(c, b))
26.23/8.57	   A^2 -> H(U1(c, e), U1(d, b))
26.23/8.57	   A^2 -> H(U1(c, e), U1(b, c))
26.23/8.57	   A^2 -> H(U1(c, e), U1(b, d))
26.23/8.57	   A^2 -> H(U1(c, e), U1(c, c))
26.23/8.57	   A^2 -> H(U1(c, e), f(e))
26.23/8.57	   A^2 -> H(U1(c, e), f(k))
26.23/8.57	   A^2 -> H(U1(c, e), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, k), U1(c, b))
26.23/8.57	   A^2 -> H(U1(c, k), U1(d, b))
26.23/8.57	   A^2 -> H(U1(c, k), U1(b, c))
26.23/8.57	   A^2 -> H(U1(c, k), U1(b, d))
26.23/8.57	   A^2 -> H(U1(c, k), U1(c, c))
26.23/8.57	   A^2 -> H(U1(c, k), f(e))
26.23/8.57	   A^2 -> H(U1(c, k), f(k))
26.23/8.57	   A^2 -> H(U1(c, k), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(e, b))
26.23/8.57	   A^2 -> H(U1(c, c), U1(k, b))
26.23/8.57	   A^2 -> H(U1(c, c), U1(c, d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(d, c))
26.23/8.57	   A^2 -> H(U1(c, c), U1(b, e))
26.23/8.57	   A^2 -> H(U1(c, c), U1(b, k))
26.23/8.57	   A^2 -> H(U1(c, c), U1(e, e))
26.23/8.57	   A^2 -> H(U1(c, c), U1(k, k))
26.23/8.57	   A^2 -> H(U1(c, c), U1(k, d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(d, k))
26.23/8.57	   A^2 -> H(e, U1(b, b))
26.23/8.57	   A^2 -> H(e, f(c))
26.23/8.57	   A^2 -> H(e, f(d))
26.23/8.57	   A^2 -> H(U1(e, e), U1(c, b))
26.23/8.57	   A^2 -> H(U1(e, e), U1(d, b))
26.23/8.57	   A^2 -> H(U1(e, e), U1(b, c))
26.23/8.57	   A^2 -> H(U1(e, e), U1(b, d))
26.23/8.57	   A^2 -> H(U1(e, e), U1(c, c))
26.23/8.57	   A^2 -> H(U1(e, e), f(e))
26.23/8.57	   A^2 -> H(U1(e, e), f(k))
26.23/8.57	   A^2 -> H(U1(e, e), U1(d, d))
26.23/8.57	   A^2 -> H(f(e), U1(e, b))
26.23/8.57	   A^2 -> H(f(e), U1(k, b))
26.23/8.57	   A^2 -> H(f(e), U1(c, d))
26.23/8.57	   A^2 -> H(f(e), U1(d, c))
26.23/8.57	   A^2 -> H(f(e), U1(b, e))
26.23/8.57	   A^2 -> H(f(e), U1(b, k))
26.23/8.57	
26.23/8.57	The TRS R consists of the following rules:
26.23/8.57	
26.23/8.57	   f(x) -> U1(x, x)
26.23/8.57	   U1(e, x) -> x
26.23/8.57	   a -> c
26.23/8.57	   a -> d
26.23/8.57	   b -> c
26.23/8.57	   b -> d
26.23/8.57	   d -> k
26.23/8.57	   c -> e
26.23/8.57	   c -> k
26.23/8.57	
26.23/8.57	Q is empty.
26.23/8.57	We have to consider all minimal (P,Q,R)-chains.
26.23/8.57	----------------------------------------
26.23/8.57	
26.23/8.57	(413) TransformationProof (EQUIVALENT)
26.23/8.57	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
26.23/8.57	
26.23/8.57	   (A^2 -> H(U1(e, e), U1(b, d)),A^2 -> H(U1(e, e), U1(b, d)))
26.23/8.57	   (A^2 -> H(f(e), U1(c, d)),A^2 -> H(f(e), U1(c, d)))
26.23/8.57	   (A^2 -> H(f(e), U1(d, d)),A^2 -> H(f(e), U1(d, d)))
26.23/8.57	   (A^2 -> H(f(e), U1(b, k)),A^2 -> H(f(e), U1(b, k)))
26.23/8.57	
26.23/8.57	
26.23/8.57	----------------------------------------
26.23/8.57	
26.23/8.57	(414)
26.23/8.57	Obligation:
26.23/8.57	Q DP problem:
26.23/8.57	The TRS P consists of the following rules:
26.23/8.57	
26.23/8.57	   H(x, x) -> G(x, x, f(k))
26.23/8.57	   G(d, x, x) -> A^2
26.23/8.57	   A^2 -> H(f(c), f(c))
26.23/8.57	   A^2 -> H(f(d), f(d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(c, c))
26.23/8.57	   A^2 -> H(f(e), U1(c, c))
26.23/8.57	   A^2 -> H(f(e), f(e))
26.23/8.57	   A^2 -> H(f(e), f(k))
26.23/8.57	   A^2 -> H(f(e), U1(d, d))
26.23/8.57	   A^2 -> H(U1(k, k), U1(b, b))
26.23/8.57	   A^2 -> H(U1(k, k), f(c))
26.23/8.57	   A^2 -> H(U1(k, k), f(d))
26.23/8.57	   A^2 -> H(f(k), U1(c, b))
26.23/8.57	   A^2 -> H(f(k), U1(d, b))
26.23/8.57	   A^2 -> H(f(k), U1(b, c))
26.23/8.57	   A^2 -> H(f(k), U1(b, d))
26.23/8.57	   A^2 -> H(f(k), U1(c, c))
26.23/8.57	   A^2 -> H(f(k), f(e))
26.23/8.57	   A^2 -> H(f(k), f(k))
26.23/8.57	   A^2 -> H(f(k), U1(d, d))
26.23/8.57	   A^2 -> H(f(c), U1(e, b))
26.23/8.57	   A^2 -> H(f(c), U1(k, b))
26.23/8.57	   A^2 -> H(f(c), U1(c, d))
26.23/8.57	   A^2 -> H(f(c), U1(d, c))
26.23/8.57	   A^2 -> H(f(c), U1(b, e))
26.23/8.57	   A^2 -> H(f(c), U1(b, k))
26.23/8.57	   A^2 -> H(f(c), U1(k, d))
26.23/8.57	   A^2 -> H(f(c), U1(d, k))
26.23/8.57	   A^2 -> H(f(c), U1(k, k))
26.23/8.57	   A^2 -> H(U1(k, k), f(b))
26.23/8.57	   A^2 -> H(U1(k, d), U1(b, b))
26.23/8.57	   A^2 -> H(U1(k, d), f(c))
26.23/8.57	   A^2 -> H(U1(k, d), f(d))
26.23/8.57	   A^2 -> H(U1(d, k), U1(b, b))
26.23/8.57	   A^2 -> H(U1(d, k), f(c))
26.23/8.57	   A^2 -> H(U1(d, k), f(d))
26.23/8.57	   A^2 -> H(U1(d, d), U1(c, b))
26.23/8.57	   A^2 -> H(U1(d, d), U1(d, b))
26.23/8.57	   A^2 -> H(U1(d, d), U1(b, c))
26.23/8.57	   A^2 -> H(U1(d, d), U1(b, d))
26.23/8.57	   A^2 -> H(U1(d, d), U1(c, c))
26.23/8.57	   A^2 -> H(U1(d, d), f(e))
26.23/8.57	   A^2 -> H(U1(d, d), f(k))
26.23/8.57	   A^2 -> H(U1(d, d), U1(d, d))
26.23/8.57	   A^2 -> H(f(d), U1(e, b))
26.23/8.57	   A^2 -> H(f(d), U1(k, b))
26.23/8.57	   A^2 -> H(f(d), U1(c, d))
26.23/8.57	   A^2 -> H(f(d), U1(d, c))
26.23/8.57	   A^2 -> H(f(d), U1(b, e))
26.23/8.57	   A^2 -> H(f(d), U1(b, k))
26.23/8.57	   A^2 -> H(f(d), U1(e, c))
26.23/8.57	   A^2 -> H(f(d), U1(k, c))
26.23/8.57	   A^2 -> H(f(d), U1(c, e))
26.23/8.57	   A^2 -> H(f(d), U1(c, k))
26.23/8.57	   A^2 -> H(f(d), U1(e, e))
26.23/8.57	   A^2 -> H(f(d), U1(k, k))
26.23/8.57	   A^2 -> H(f(a), b)
26.23/8.57	   A^2 -> H(f(a), U1(e, d))
26.23/8.57	   A^2 -> H(f(a), U1(d, e))
26.23/8.57	   A^2 -> H(f(c), U1(e, c))
26.23/8.57	   A^2 -> H(f(c), U1(k, c))
26.23/8.57	   A^2 -> H(f(c), U1(c, e))
26.23/8.57	   A^2 -> H(f(c), U1(c, k))
26.23/8.57	   A^2 -> H(f(a), c)
26.23/8.57	   A^2 -> H(f(a), U1(e, k))
26.23/8.57	   A^2 -> H(f(a), U1(k, e))
26.23/8.57	   A^2 -> H(f(c), U1(e, e))
26.23/8.57	   A^2 -> H(f(a), e)
26.23/8.57	   A^2 -> H(f(d), U1(k, d))
26.23/8.57	   A^2 -> H(f(d), U1(d, k))
26.23/8.57	   A^2 -> H(f(a), U1(k, k))
26.23/8.57	   A^2 -> H(d, f(b))
26.23/8.57	   A^2 -> H(a, U1(b, b))
26.23/8.57	   A^2 -> H(a, f(c))
26.23/8.57	   A^2 -> H(a, f(d))
26.23/8.57	   A^2 -> H(U1(e, d), U1(b, b))
26.23/8.57	   A^2 -> H(U1(e, d), f(c))
26.23/8.57	   A^2 -> H(U1(e, d), f(d))
26.23/8.57	   A^2 -> H(U1(e, a), U1(c, b))
26.23/8.57	   A^2 -> H(U1(e, a), U1(d, b))
26.23/8.57	   A^2 -> H(U1(e, a), U1(b, c))
26.23/8.57	   A^2 -> H(U1(e, a), U1(b, d))
26.23/8.57	   A^2 -> H(U1(e, a), U1(c, c))
26.23/8.57	   A^2 -> H(U1(e, a), f(e))
26.23/8.57	   A^2 -> H(U1(e, a), f(k))
26.23/8.57	   A^2 -> H(U1(e, a), U1(d, d))
26.23/8.57	   A^2 -> H(U1(k, a), U1(c, b))
26.23/8.57	   A^2 -> H(U1(k, a), U1(d, b))
26.23/8.57	   A^2 -> H(U1(k, a), U1(b, c))
26.23/8.57	   A^2 -> H(U1(k, a), U1(b, d))
26.23/8.57	   A^2 -> H(U1(k, a), U1(c, c))
26.23/8.57	   A^2 -> H(U1(k, a), f(e))
26.23/8.57	   A^2 -> H(U1(k, a), f(k))
26.23/8.57	   A^2 -> H(U1(k, a), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, d), U1(c, b))
26.23/8.57	   A^2 -> H(U1(c, d), U1(d, b))
26.23/8.57	   A^2 -> H(U1(c, d), U1(b, c))
26.23/8.57	   A^2 -> H(U1(c, d), U1(b, d))
26.23/8.57	   A^2 -> H(U1(c, d), U1(c, c))
26.23/8.57	   A^2 -> H(U1(c, d), f(e))
26.23/8.57	   A^2 -> H(U1(c, d), f(k))
26.23/8.57	   A^2 -> H(U1(c, d), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, a), U1(e, b))
26.23/8.57	   A^2 -> H(U1(c, a), U1(k, b))
26.23/8.57	   A^2 -> H(U1(c, a), U1(c, d))
26.23/8.57	   A^2 -> H(U1(c, a), U1(d, c))
26.23/8.57	   A^2 -> H(U1(c, a), U1(b, e))
26.23/8.57	   A^2 -> H(U1(c, a), U1(b, k))
26.23/8.57	   A^2 -> H(U1(c, a), U1(e, c))
26.23/8.57	   A^2 -> H(U1(c, a), U1(k, c))
26.23/8.57	   A^2 -> H(U1(c, a), U1(c, e))
26.23/8.57	   A^2 -> H(U1(c, a), U1(c, k))
26.23/8.57	   A^2 -> H(U1(c, a), U1(e, e))
26.23/8.57	   A^2 -> H(U1(c, a), U1(k, k))
26.23/8.57	   A^2 -> H(U1(c, a), U1(k, d))
26.23/8.57	   A^2 -> H(U1(c, a), U1(d, k))
26.23/8.57	   A^2 -> H(U1(d, e), U1(b, b))
26.23/8.57	   A^2 -> H(U1(d, e), f(c))
26.23/8.57	   A^2 -> H(U1(d, e), f(d))
26.23/8.57	   A^2 -> H(U1(d, c), U1(c, b))
26.23/8.57	   A^2 -> H(U1(d, c), U1(d, b))
26.23/8.57	   A^2 -> H(U1(d, c), U1(b, c))
26.23/8.57	   A^2 -> H(U1(d, c), U1(b, d))
26.23/8.57	   A^2 -> H(U1(d, c), U1(c, c))
26.23/8.57	   A^2 -> H(U1(d, c), f(e))
26.23/8.57	   A^2 -> H(U1(d, c), f(k))
26.23/8.57	   A^2 -> H(U1(d, c), U1(d, d))
26.23/8.57	   A^2 -> H(U1(d, a), U1(e, b))
26.23/8.57	   A^2 -> H(U1(d, a), U1(k, b))
26.23/8.57	   A^2 -> H(U1(d, a), U1(c, d))
26.23/8.57	   A^2 -> H(U1(d, a), U1(d, c))
26.23/8.57	   A^2 -> H(U1(d, a), U1(b, e))
26.23/8.57	   A^2 -> H(U1(d, a), U1(b, k))
26.23/8.57	   A^2 -> H(U1(d, a), U1(e, c))
26.23/8.57	   A^2 -> H(U1(d, a), U1(k, c))
26.23/8.57	   A^2 -> H(U1(d, a), U1(c, e))
26.23/8.57	   A^2 -> H(U1(d, a), U1(c, k))
26.23/8.57	   A^2 -> H(U1(d, a), U1(e, e))
26.23/8.57	   A^2 -> H(U1(d, a), U1(k, k))
26.23/8.57	   A^2 -> H(U1(d, a), U1(k, d))
26.23/8.57	   A^2 -> H(U1(d, a), U1(d, k))
26.23/8.57	   A^2 -> H(U1(a, e), U1(c, b))
26.23/8.57	   A^2 -> H(U1(a, e), U1(d, b))
26.23/8.57	   A^2 -> H(U1(a, e), U1(b, c))
26.23/8.57	   A^2 -> H(U1(a, e), U1(b, d))
26.23/8.57	   A^2 -> H(U1(a, e), U1(c, c))
26.23/8.57	   A^2 -> H(U1(a, e), f(e))
26.23/8.57	   A^2 -> H(U1(a, e), f(k))
26.23/8.57	   A^2 -> H(U1(a, e), U1(d, d))
26.23/8.57	   A^2 -> H(U1(a, k), U1(c, b))
26.23/8.57	   A^2 -> H(U1(a, k), U1(d, b))
26.23/8.57	   A^2 -> H(U1(a, k), U1(b, c))
26.23/8.57	   A^2 -> H(U1(a, k), U1(b, d))
26.23/8.57	   A^2 -> H(U1(a, k), U1(c, c))
26.23/8.57	   A^2 -> H(U1(a, k), f(e))
26.23/8.57	   A^2 -> H(U1(a, k), f(k))
26.23/8.57	   A^2 -> H(U1(a, k), U1(d, d))
26.23/8.57	   A^2 -> H(U1(a, c), U1(e, b))
26.23/8.57	   A^2 -> H(U1(a, c), U1(k, b))
26.23/8.57	   A^2 -> H(U1(a, c), U1(c, d))
26.23/8.57	   A^2 -> H(U1(a, c), U1(d, c))
26.23/8.57	   A^2 -> H(U1(a, c), U1(b, e))
26.23/8.57	   A^2 -> H(U1(a, c), U1(b, k))
26.23/8.57	   A^2 -> H(U1(a, c), U1(e, c))
26.23/8.57	   A^2 -> H(U1(a, c), U1(k, c))
26.23/8.57	   A^2 -> H(U1(a, c), U1(c, e))
26.23/8.57	   A^2 -> H(U1(a, c), U1(c, k))
26.23/8.57	   A^2 -> H(U1(a, c), U1(e, e))
26.23/8.57	   A^2 -> H(U1(a, c), U1(k, k))
26.23/8.57	   A^2 -> H(U1(a, c), U1(k, d))
26.23/8.57	   A^2 -> H(U1(a, c), U1(d, k))
26.23/8.57	   A^2 -> H(U1(a, d), U1(e, b))
26.23/8.57	   A^2 -> H(U1(a, d), U1(k, b))
26.23/8.57	   A^2 -> H(U1(a, d), U1(c, d))
26.23/8.57	   A^2 -> H(U1(a, d), U1(d, c))
26.23/8.57	   A^2 -> H(U1(a, d), U1(b, e))
26.23/8.57	   A^2 -> H(U1(a, d), U1(b, k))
26.23/8.57	   A^2 -> H(U1(a, d), U1(e, c))
26.23/8.57	   A^2 -> H(U1(a, d), U1(k, c))
26.23/8.57	   A^2 -> H(U1(a, d), U1(c, e))
26.23/8.57	   A^2 -> H(U1(a, d), U1(c, k))
26.23/8.57	   A^2 -> H(U1(a, d), U1(e, e))
26.23/8.57	   A^2 -> H(U1(a, d), U1(k, k))
26.23/8.57	   A^2 -> H(U1(a, d), U1(k, d))
26.23/8.57	   A^2 -> H(U1(a, d), U1(d, k))
26.23/8.57	   A^2 -> H(U1(a, a), b)
26.23/8.57	   A^2 -> H(U1(a, a), U1(e, d))
26.23/8.57	   A^2 -> H(U1(a, a), U1(d, e))
26.23/8.57	   A^2 -> H(U1(a, a), c)
26.23/8.57	   A^2 -> H(U1(a, a), U1(e, k))
26.23/8.57	   A^2 -> H(U1(a, a), U1(k, e))
26.23/8.57	   A^2 -> H(U1(a, a), e)
26.23/8.57	   A^2 -> H(U1(a, a), U1(k, k))
26.23/8.57	   A^2 -> H(k, f(b))
26.23/8.57	   A^2 -> H(c, U1(b, b))
26.23/8.57	   A^2 -> H(c, f(c))
26.23/8.57	   A^2 -> H(c, f(d))
26.23/8.57	   A^2 -> H(U1(e, k), U1(b, b))
26.23/8.57	   A^2 -> H(U1(e, k), f(c))
26.23/8.57	   A^2 -> H(U1(e, k), f(d))
26.23/8.57	   A^2 -> H(U1(e, c), U1(c, b))
26.23/8.57	   A^2 -> H(U1(e, c), U1(d, b))
26.23/8.57	   A^2 -> H(U1(e, c), U1(b, c))
26.23/8.57	   A^2 -> H(U1(e, c), U1(b, d))
26.23/8.57	   A^2 -> H(U1(e, c), U1(c, c))
26.23/8.57	   A^2 -> H(U1(e, c), f(e))
26.23/8.57	   A^2 -> H(U1(e, c), f(k))
26.23/8.57	   A^2 -> H(U1(e, c), U1(d, d))
26.23/8.57	   A^2 -> H(U1(k, e), U1(b, b))
26.23/8.57	   A^2 -> H(U1(k, e), f(c))
26.23/8.57	   A^2 -> H(U1(k, e), f(d))
26.23/8.57	   A^2 -> H(U1(k, c), U1(c, b))
26.23/8.57	   A^2 -> H(U1(k, c), U1(d, b))
26.23/8.57	   A^2 -> H(U1(k, c), U1(b, c))
26.23/8.57	   A^2 -> H(U1(k, c), U1(b, d))
26.23/8.57	   A^2 -> H(U1(k, c), U1(c, c))
26.23/8.57	   A^2 -> H(U1(k, c), f(e))
26.23/8.57	   A^2 -> H(U1(k, c), f(k))
26.23/8.57	   A^2 -> H(U1(k, c), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, e), U1(c, b))
26.23/8.57	   A^2 -> H(U1(c, e), U1(d, b))
26.23/8.57	   A^2 -> H(U1(c, e), U1(b, c))
26.23/8.57	   A^2 -> H(U1(c, e), U1(b, d))
26.23/8.57	   A^2 -> H(U1(c, e), U1(c, c))
26.23/8.57	   A^2 -> H(U1(c, e), f(e))
26.23/8.57	   A^2 -> H(U1(c, e), f(k))
26.23/8.57	   A^2 -> H(U1(c, e), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, k), U1(c, b))
26.23/8.57	   A^2 -> H(U1(c, k), U1(d, b))
26.23/8.57	   A^2 -> H(U1(c, k), U1(b, c))
26.23/8.57	   A^2 -> H(U1(c, k), U1(b, d))
26.23/8.57	   A^2 -> H(U1(c, k), U1(c, c))
26.23/8.57	   A^2 -> H(U1(c, k), f(e))
26.23/8.57	   A^2 -> H(U1(c, k), f(k))
26.23/8.57	   A^2 -> H(U1(c, k), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(e, b))
26.23/8.57	   A^2 -> H(U1(c, c), U1(k, b))
26.23/8.57	   A^2 -> H(U1(c, c), U1(c, d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(d, c))
26.23/8.57	   A^2 -> H(U1(c, c), U1(b, e))
26.23/8.57	   A^2 -> H(U1(c, c), U1(b, k))
26.23/8.57	   A^2 -> H(U1(c, c), U1(e, e))
26.23/8.57	   A^2 -> H(U1(c, c), U1(k, k))
26.23/8.57	   A^2 -> H(U1(c, c), U1(k, d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(d, k))
26.23/8.57	   A^2 -> H(e, U1(b, b))
26.23/8.57	   A^2 -> H(e, f(c))
26.23/8.57	   A^2 -> H(e, f(d))
26.23/8.57	   A^2 -> H(U1(e, e), U1(c, b))
26.23/8.57	   A^2 -> H(U1(e, e), U1(d, b))
26.23/8.57	   A^2 -> H(U1(e, e), U1(b, c))
26.23/8.57	   A^2 -> H(U1(e, e), U1(b, d))
26.23/8.57	   A^2 -> H(U1(e, e), U1(c, c))
26.23/8.57	   A^2 -> H(U1(e, e), f(e))
26.23/8.57	   A^2 -> H(U1(e, e), f(k))
26.23/8.57	   A^2 -> H(U1(e, e), U1(d, d))
26.23/8.57	   A^2 -> H(f(e), U1(e, b))
26.23/8.57	   A^2 -> H(f(e), U1(k, b))
26.23/8.57	   A^2 -> H(f(e), U1(c, d))
26.23/8.57	   A^2 -> H(f(e), U1(d, c))
26.23/8.57	   A^2 -> H(f(e), U1(b, e))
26.23/8.57	   A^2 -> H(f(e), U1(b, k))
26.23/8.57	
26.23/8.57	The TRS R consists of the following rules:
26.23/8.57	
26.23/8.57	   f(x) -> U1(x, x)
26.23/8.57	   U1(e, x) -> x
26.23/8.57	   a -> c
26.23/8.57	   a -> d
26.23/8.57	   b -> c
26.23/8.57	   b -> d
26.23/8.57	   d -> k
26.23/8.57	   c -> e
26.23/8.57	   c -> k
26.23/8.57	
26.23/8.57	Q is empty.
26.23/8.57	We have to consider all minimal (P,Q,R)-chains.
26.23/8.57	----------------------------------------
26.23/8.57	
26.23/8.57	(415) TransformationProof (EQUIVALENT)
26.23/8.57	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
26.23/8.57	
26.23/8.57	   (A^2 -> H(U1(e, e), U1(c, c)),A^2 -> H(U1(e, e), U1(c, c)))
26.23/8.57	   (A^2 -> H(f(e), U1(e, c)),A^2 -> H(f(e), U1(e, c)))
26.23/8.57	   (A^2 -> H(f(e), U1(k, c)),A^2 -> H(f(e), U1(k, c)))
26.23/8.57	   (A^2 -> H(f(e), U1(c, e)),A^2 -> H(f(e), U1(c, e)))
26.23/8.57	   (A^2 -> H(f(e), U1(c, k)),A^2 -> H(f(e), U1(c, k)))
26.23/8.57	
26.23/8.57	
26.23/8.57	----------------------------------------
26.23/8.57	
26.23/8.57	(416)
26.23/8.57	Obligation:
26.23/8.57	Q DP problem:
26.23/8.57	The TRS P consists of the following rules:
26.23/8.57	
26.23/8.57	   H(x, x) -> G(x, x, f(k))
26.23/8.57	   G(d, x, x) -> A^2
26.23/8.57	   A^2 -> H(f(c), f(c))
26.23/8.57	   A^2 -> H(f(d), f(d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(c, c))
26.23/8.57	   A^2 -> H(f(e), f(e))
26.23/8.57	   A^2 -> H(f(e), f(k))
26.23/8.57	   A^2 -> H(f(e), U1(d, d))
26.23/8.57	   A^2 -> H(U1(k, k), U1(b, b))
26.23/8.57	   A^2 -> H(U1(k, k), f(c))
26.23/8.57	   A^2 -> H(U1(k, k), f(d))
26.23/8.57	   A^2 -> H(f(k), U1(c, b))
26.23/8.57	   A^2 -> H(f(k), U1(d, b))
26.23/8.57	   A^2 -> H(f(k), U1(b, c))
26.23/8.57	   A^2 -> H(f(k), U1(b, d))
26.23/8.57	   A^2 -> H(f(k), U1(c, c))
26.23/8.57	   A^2 -> H(f(k), f(e))
26.23/8.57	   A^2 -> H(f(k), f(k))
26.23/8.57	   A^2 -> H(f(k), U1(d, d))
26.23/8.57	   A^2 -> H(f(c), U1(e, b))
26.23/8.57	   A^2 -> H(f(c), U1(k, b))
26.23/8.57	   A^2 -> H(f(c), U1(c, d))
26.23/8.57	   A^2 -> H(f(c), U1(d, c))
26.23/8.57	   A^2 -> H(f(c), U1(b, e))
26.23/8.57	   A^2 -> H(f(c), U1(b, k))
26.23/8.57	   A^2 -> H(f(c), U1(k, d))
26.23/8.57	   A^2 -> H(f(c), U1(d, k))
26.23/8.57	   A^2 -> H(f(c), U1(k, k))
26.23/8.57	   A^2 -> H(U1(k, k), f(b))
26.23/8.57	   A^2 -> H(U1(k, d), U1(b, b))
26.23/8.57	   A^2 -> H(U1(k, d), f(c))
26.23/8.57	   A^2 -> H(U1(k, d), f(d))
26.23/8.57	   A^2 -> H(U1(d, k), U1(b, b))
26.23/8.57	   A^2 -> H(U1(d, k), f(c))
26.23/8.57	   A^2 -> H(U1(d, k), f(d))
26.23/8.57	   A^2 -> H(U1(d, d), U1(c, b))
26.23/8.57	   A^2 -> H(U1(d, d), U1(d, b))
26.23/8.57	   A^2 -> H(U1(d, d), U1(b, c))
26.23/8.57	   A^2 -> H(U1(d, d), U1(b, d))
26.23/8.57	   A^2 -> H(U1(d, d), U1(c, c))
26.23/8.57	   A^2 -> H(U1(d, d), f(e))
26.23/8.57	   A^2 -> H(U1(d, d), f(k))
26.23/8.57	   A^2 -> H(U1(d, d), U1(d, d))
26.23/8.57	   A^2 -> H(f(d), U1(e, b))
26.23/8.57	   A^2 -> H(f(d), U1(k, b))
26.23/8.57	   A^2 -> H(f(d), U1(c, d))
26.23/8.57	   A^2 -> H(f(d), U1(d, c))
26.23/8.57	   A^2 -> H(f(d), U1(b, e))
26.23/8.57	   A^2 -> H(f(d), U1(b, k))
26.23/8.57	   A^2 -> H(f(d), U1(e, c))
26.23/8.57	   A^2 -> H(f(d), U1(k, c))
26.23/8.57	   A^2 -> H(f(d), U1(c, e))
26.23/8.57	   A^2 -> H(f(d), U1(c, k))
26.23/8.57	   A^2 -> H(f(d), U1(e, e))
26.23/8.57	   A^2 -> H(f(d), U1(k, k))
26.23/8.57	   A^2 -> H(f(a), b)
26.23/8.57	   A^2 -> H(f(a), U1(e, d))
26.23/8.57	   A^2 -> H(f(a), U1(d, e))
26.23/8.57	   A^2 -> H(f(c), U1(e, c))
26.23/8.57	   A^2 -> H(f(c), U1(k, c))
26.23/8.57	   A^2 -> H(f(c), U1(c, e))
26.23/8.57	   A^2 -> H(f(c), U1(c, k))
26.23/8.57	   A^2 -> H(f(a), c)
26.23/8.57	   A^2 -> H(f(a), U1(e, k))
26.23/8.57	   A^2 -> H(f(a), U1(k, e))
26.23/8.57	   A^2 -> H(f(c), U1(e, e))
26.23/8.57	   A^2 -> H(f(a), e)
26.23/8.57	   A^2 -> H(f(d), U1(k, d))
26.23/8.57	   A^2 -> H(f(d), U1(d, k))
26.23/8.57	   A^2 -> H(f(a), U1(k, k))
26.23/8.57	   A^2 -> H(d, f(b))
26.23/8.57	   A^2 -> H(a, U1(b, b))
26.23/8.57	   A^2 -> H(a, f(c))
26.23/8.57	   A^2 -> H(a, f(d))
26.23/8.57	   A^2 -> H(U1(e, d), U1(b, b))
26.23/8.57	   A^2 -> H(U1(e, d), f(c))
26.23/8.57	   A^2 -> H(U1(e, d), f(d))
26.23/8.57	   A^2 -> H(U1(e, a), U1(c, b))
26.23/8.57	   A^2 -> H(U1(e, a), U1(d, b))
26.23/8.57	   A^2 -> H(U1(e, a), U1(b, c))
26.23/8.57	   A^2 -> H(U1(e, a), U1(b, d))
26.23/8.57	   A^2 -> H(U1(e, a), U1(c, c))
26.23/8.57	   A^2 -> H(U1(e, a), f(e))
26.23/8.57	   A^2 -> H(U1(e, a), f(k))
26.23/8.57	   A^2 -> H(U1(e, a), U1(d, d))
26.23/8.57	   A^2 -> H(U1(k, a), U1(c, b))
26.23/8.57	   A^2 -> H(U1(k, a), U1(d, b))
26.23/8.57	   A^2 -> H(U1(k, a), U1(b, c))
26.23/8.57	   A^2 -> H(U1(k, a), U1(b, d))
26.23/8.57	   A^2 -> H(U1(k, a), U1(c, c))
26.23/8.57	   A^2 -> H(U1(k, a), f(e))
26.23/8.57	   A^2 -> H(U1(k, a), f(k))
26.23/8.57	   A^2 -> H(U1(k, a), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, d), U1(c, b))
26.23/8.57	   A^2 -> H(U1(c, d), U1(d, b))
26.23/8.57	   A^2 -> H(U1(c, d), U1(b, c))
26.23/8.57	   A^2 -> H(U1(c, d), U1(b, d))
26.23/8.57	   A^2 -> H(U1(c, d), U1(c, c))
26.23/8.57	   A^2 -> H(U1(c, d), f(e))
26.23/8.57	   A^2 -> H(U1(c, d), f(k))
26.23/8.57	   A^2 -> H(U1(c, d), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, a), U1(e, b))
26.23/8.57	   A^2 -> H(U1(c, a), U1(k, b))
26.23/8.57	   A^2 -> H(U1(c, a), U1(c, d))
26.23/8.57	   A^2 -> H(U1(c, a), U1(d, c))
26.23/8.57	   A^2 -> H(U1(c, a), U1(b, e))
26.23/8.57	   A^2 -> H(U1(c, a), U1(b, k))
26.23/8.57	   A^2 -> H(U1(c, a), U1(e, c))
26.23/8.57	   A^2 -> H(U1(c, a), U1(k, c))
26.23/8.57	   A^2 -> H(U1(c, a), U1(c, e))
26.23/8.57	   A^2 -> H(U1(c, a), U1(c, k))
26.23/8.57	   A^2 -> H(U1(c, a), U1(e, e))
26.23/8.57	   A^2 -> H(U1(c, a), U1(k, k))
26.23/8.57	   A^2 -> H(U1(c, a), U1(k, d))
26.23/8.57	   A^2 -> H(U1(c, a), U1(d, k))
26.23/8.57	   A^2 -> H(U1(d, e), U1(b, b))
26.23/8.57	   A^2 -> H(U1(d, e), f(c))
26.23/8.57	   A^2 -> H(U1(d, e), f(d))
26.23/8.57	   A^2 -> H(U1(d, c), U1(c, b))
26.23/8.57	   A^2 -> H(U1(d, c), U1(d, b))
26.23/8.57	   A^2 -> H(U1(d, c), U1(b, c))
26.23/8.57	   A^2 -> H(U1(d, c), U1(b, d))
26.23/8.57	   A^2 -> H(U1(d, c), U1(c, c))
26.23/8.57	   A^2 -> H(U1(d, c), f(e))
26.23/8.57	   A^2 -> H(U1(d, c), f(k))
26.23/8.57	   A^2 -> H(U1(d, c), U1(d, d))
26.23/8.57	   A^2 -> H(U1(d, a), U1(e, b))
26.23/8.57	   A^2 -> H(U1(d, a), U1(k, b))
26.23/8.57	   A^2 -> H(U1(d, a), U1(c, d))
26.23/8.57	   A^2 -> H(U1(d, a), U1(d, c))
26.23/8.57	   A^2 -> H(U1(d, a), U1(b, e))
26.23/8.57	   A^2 -> H(U1(d, a), U1(b, k))
26.23/8.57	   A^2 -> H(U1(d, a), U1(e, c))
26.23/8.57	   A^2 -> H(U1(d, a), U1(k, c))
26.23/8.57	   A^2 -> H(U1(d, a), U1(c, e))
26.23/8.57	   A^2 -> H(U1(d, a), U1(c, k))
26.23/8.57	   A^2 -> H(U1(d, a), U1(e, e))
26.23/8.57	   A^2 -> H(U1(d, a), U1(k, k))
26.23/8.57	   A^2 -> H(U1(d, a), U1(k, d))
26.23/8.57	   A^2 -> H(U1(d, a), U1(d, k))
26.23/8.57	   A^2 -> H(U1(a, e), U1(c, b))
26.23/8.57	   A^2 -> H(U1(a, e), U1(d, b))
26.23/8.57	   A^2 -> H(U1(a, e), U1(b, c))
26.23/8.57	   A^2 -> H(U1(a, e), U1(b, d))
26.23/8.57	   A^2 -> H(U1(a, e), U1(c, c))
26.23/8.57	   A^2 -> H(U1(a, e), f(e))
26.23/8.57	   A^2 -> H(U1(a, e), f(k))
26.23/8.57	   A^2 -> H(U1(a, e), U1(d, d))
26.23/8.57	   A^2 -> H(U1(a, k), U1(c, b))
26.23/8.57	   A^2 -> H(U1(a, k), U1(d, b))
26.23/8.57	   A^2 -> H(U1(a, k), U1(b, c))
26.23/8.57	   A^2 -> H(U1(a, k), U1(b, d))
26.23/8.57	   A^2 -> H(U1(a, k), U1(c, c))
26.23/8.57	   A^2 -> H(U1(a, k), f(e))
26.23/8.57	   A^2 -> H(U1(a, k), f(k))
26.23/8.57	   A^2 -> H(U1(a, k), U1(d, d))
26.23/8.57	   A^2 -> H(U1(a, c), U1(e, b))
26.23/8.57	   A^2 -> H(U1(a, c), U1(k, b))
26.23/8.57	   A^2 -> H(U1(a, c), U1(c, d))
26.23/8.57	   A^2 -> H(U1(a, c), U1(d, c))
26.23/8.57	   A^2 -> H(U1(a, c), U1(b, e))
26.23/8.57	   A^2 -> H(U1(a, c), U1(b, k))
26.23/8.57	   A^2 -> H(U1(a, c), U1(e, c))
26.23/8.57	   A^2 -> H(U1(a, c), U1(k, c))
26.23/8.57	   A^2 -> H(U1(a, c), U1(c, e))
26.23/8.57	   A^2 -> H(U1(a, c), U1(c, k))
26.23/8.57	   A^2 -> H(U1(a, c), U1(e, e))
26.23/8.57	   A^2 -> H(U1(a, c), U1(k, k))
26.23/8.57	   A^2 -> H(U1(a, c), U1(k, d))
26.23/8.57	   A^2 -> H(U1(a, c), U1(d, k))
26.23/8.57	   A^2 -> H(U1(a, d), U1(e, b))
26.23/8.57	   A^2 -> H(U1(a, d), U1(k, b))
26.23/8.57	   A^2 -> H(U1(a, d), U1(c, d))
26.23/8.57	   A^2 -> H(U1(a, d), U1(d, c))
26.23/8.57	   A^2 -> H(U1(a, d), U1(b, e))
26.23/8.57	   A^2 -> H(U1(a, d), U1(b, k))
26.23/8.57	   A^2 -> H(U1(a, d), U1(e, c))
26.23/8.57	   A^2 -> H(U1(a, d), U1(k, c))
26.23/8.57	   A^2 -> H(U1(a, d), U1(c, e))
26.23/8.57	   A^2 -> H(U1(a, d), U1(c, k))
26.23/8.57	   A^2 -> H(U1(a, d), U1(e, e))
26.23/8.57	   A^2 -> H(U1(a, d), U1(k, k))
26.23/8.57	   A^2 -> H(U1(a, d), U1(k, d))
26.23/8.57	   A^2 -> H(U1(a, d), U1(d, k))
26.23/8.57	   A^2 -> H(U1(a, a), b)
26.23/8.57	   A^2 -> H(U1(a, a), U1(e, d))
26.23/8.57	   A^2 -> H(U1(a, a), U1(d, e))
26.23/8.57	   A^2 -> H(U1(a, a), c)
26.23/8.57	   A^2 -> H(U1(a, a), U1(e, k))
26.23/8.57	   A^2 -> H(U1(a, a), U1(k, e))
26.23/8.57	   A^2 -> H(U1(a, a), e)
26.23/8.57	   A^2 -> H(U1(a, a), U1(k, k))
26.23/8.57	   A^2 -> H(k, f(b))
26.23/8.57	   A^2 -> H(c, U1(b, b))
26.23/8.57	   A^2 -> H(c, f(c))
26.23/8.57	   A^2 -> H(c, f(d))
26.23/8.57	   A^2 -> H(U1(e, k), U1(b, b))
26.23/8.57	   A^2 -> H(U1(e, k), f(c))
26.23/8.57	   A^2 -> H(U1(e, k), f(d))
26.23/8.57	   A^2 -> H(U1(e, c), U1(c, b))
26.23/8.57	   A^2 -> H(U1(e, c), U1(d, b))
26.23/8.57	   A^2 -> H(U1(e, c), U1(b, c))
26.23/8.57	   A^2 -> H(U1(e, c), U1(b, d))
26.23/8.57	   A^2 -> H(U1(e, c), U1(c, c))
26.23/8.57	   A^2 -> H(U1(e, c), f(e))
26.23/8.57	   A^2 -> H(U1(e, c), f(k))
26.23/8.57	   A^2 -> H(U1(e, c), U1(d, d))
26.23/8.57	   A^2 -> H(U1(k, e), U1(b, b))
26.23/8.57	   A^2 -> H(U1(k, e), f(c))
26.23/8.57	   A^2 -> H(U1(k, e), f(d))
26.23/8.57	   A^2 -> H(U1(k, c), U1(c, b))
26.23/8.57	   A^2 -> H(U1(k, c), U1(d, b))
26.23/8.57	   A^2 -> H(U1(k, c), U1(b, c))
26.23/8.57	   A^2 -> H(U1(k, c), U1(b, d))
26.23/8.57	   A^2 -> H(U1(k, c), U1(c, c))
26.23/8.57	   A^2 -> H(U1(k, c), f(e))
26.23/8.57	   A^2 -> H(U1(k, c), f(k))
26.23/8.57	   A^2 -> H(U1(k, c), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, e), U1(c, b))
26.23/8.57	   A^2 -> H(U1(c, e), U1(d, b))
26.23/8.57	   A^2 -> H(U1(c, e), U1(b, c))
26.23/8.57	   A^2 -> H(U1(c, e), U1(b, d))
26.23/8.57	   A^2 -> H(U1(c, e), U1(c, c))
26.23/8.57	   A^2 -> H(U1(c, e), f(e))
26.23/8.57	   A^2 -> H(U1(c, e), f(k))
26.23/8.57	   A^2 -> H(U1(c, e), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, k), U1(c, b))
26.23/8.57	   A^2 -> H(U1(c, k), U1(d, b))
26.23/8.57	   A^2 -> H(U1(c, k), U1(b, c))
26.23/8.57	   A^2 -> H(U1(c, k), U1(b, d))
26.23/8.57	   A^2 -> H(U1(c, k), U1(c, c))
26.23/8.57	   A^2 -> H(U1(c, k), f(e))
26.23/8.57	   A^2 -> H(U1(c, k), f(k))
26.23/8.57	   A^2 -> H(U1(c, k), U1(d, d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(e, b))
26.23/8.57	   A^2 -> H(U1(c, c), U1(k, b))
26.23/8.57	   A^2 -> H(U1(c, c), U1(c, d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(d, c))
26.23/8.57	   A^2 -> H(U1(c, c), U1(b, e))
26.23/8.57	   A^2 -> H(U1(c, c), U1(b, k))
26.23/8.57	   A^2 -> H(U1(c, c), U1(e, e))
26.23/8.57	   A^2 -> H(U1(c, c), U1(k, k))
26.23/8.57	   A^2 -> H(U1(c, c), U1(k, d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(d, k))
26.23/8.57	   A^2 -> H(e, U1(b, b))
26.23/8.57	   A^2 -> H(e, f(c))
26.23/8.57	   A^2 -> H(e, f(d))
26.23/8.57	   A^2 -> H(U1(e, e), U1(c, b))
26.23/8.57	   A^2 -> H(U1(e, e), U1(d, b))
26.23/8.57	   A^2 -> H(U1(e, e), U1(b, c))
26.23/8.57	   A^2 -> H(U1(e, e), U1(b, d))
26.23/8.57	   A^2 -> H(U1(e, e), U1(c, c))
26.23/8.57	   A^2 -> H(U1(e, e), f(e))
26.23/8.57	   A^2 -> H(U1(e, e), f(k))
26.23/8.57	   A^2 -> H(U1(e, e), U1(d, d))
26.23/8.57	   A^2 -> H(f(e), U1(e, b))
26.23/8.57	   A^2 -> H(f(e), U1(k, b))
26.23/8.57	   A^2 -> H(f(e), U1(c, d))
26.23/8.57	   A^2 -> H(f(e), U1(d, c))
26.23/8.57	   A^2 -> H(f(e), U1(b, e))
26.23/8.57	   A^2 -> H(f(e), U1(b, k))
26.23/8.57	   A^2 -> H(f(e), U1(e, c))
26.23/8.57	   A^2 -> H(f(e), U1(k, c))
26.23/8.57	   A^2 -> H(f(e), U1(c, e))
26.23/8.57	   A^2 -> H(f(e), U1(c, k))
26.23/8.57	
26.23/8.57	The TRS R consists of the following rules:
26.23/8.57	
26.23/8.57	   f(x) -> U1(x, x)
26.23/8.57	   U1(e, x) -> x
26.23/8.57	   a -> c
26.23/8.57	   a -> d
26.23/8.57	   b -> c
26.23/8.57	   b -> d
26.23/8.57	   d -> k
26.23/8.57	   c -> e
26.23/8.57	   c -> k
26.23/8.57	
26.23/8.57	Q is empty.
26.23/8.57	We have to consider all minimal (P,Q,R)-chains.
26.23/8.57	----------------------------------------
26.23/8.57	
26.23/8.57	(417) TransformationProof (EQUIVALENT)
26.23/8.57	By narrowing [LPAR04] the rule A^2 -> H(f(e), f(k)) at position [] we obtained the following new rules [LPAR04]:
26.23/8.57	
26.23/8.57	   (A^2 -> H(U1(e, e), f(k)),A^2 -> H(U1(e, e), f(k)))
26.23/8.57	   (A^2 -> H(f(e), U1(k, k)),A^2 -> H(f(e), U1(k, k)))
26.23/8.57	
26.23/8.57	
26.23/8.57	----------------------------------------
26.23/8.57	
26.23/8.57	(418)
26.23/8.57	Obligation:
26.23/8.57	Q DP problem:
26.23/8.57	The TRS P consists of the following rules:
26.23/8.57	
26.23/8.57	   H(x, x) -> G(x, x, f(k))
26.23/8.57	   G(d, x, x) -> A^2
26.23/8.57	   A^2 -> H(f(c), f(c))
26.23/8.57	   A^2 -> H(f(d), f(d))
26.23/8.57	   A^2 -> H(U1(c, c), U1(c, c))
26.23/8.57	   A^2 -> H(f(e), f(e))
26.23/8.57	   A^2 -> H(f(e), U1(d, d))
26.23/8.57	   A^2 -> H(U1(k, k), U1(b, b))
26.23/8.57	   A^2 -> H(U1(k, k), f(c))
26.23/8.57	   A^2 -> H(U1(k, k), f(d))
26.23/8.57	   A^2 -> H(f(k), U1(c, b))
26.23/8.57	   A^2 -> H(f(k), U1(d, b))
26.23/8.57	   A^2 -> H(f(k), U1(b, c))
26.23/8.57	   A^2 -> H(f(k), U1(b, d))
26.23/8.57	   A^2 -> H(f(k), U1(c, c))
26.23/8.57	   A^2 -> H(f(k), f(e))
26.23/8.57	   A^2 -> H(f(k), f(k))
26.23/8.57	   A^2 -> H(f(k), U1(d, d))
26.23/8.57	   A^2 -> H(f(c), U1(e, b))
26.23/8.57	   A^2 -> H(f(c), U1(k, b))
26.23/8.57	   A^2 -> H(f(c), U1(c, d))
26.23/8.57	   A^2 -> H(f(c), U1(d, c))
26.23/8.57	   A^2 -> H(f(c), U1(b, e))
26.23/8.57	   A^2 -> H(f(c), U1(b, k))
26.23/8.57	   A^2 -> H(f(c), U1(k, d))
26.23/8.57	   A^2 -> H(f(c), U1(d, k))
26.23/8.57	   A^2 -> H(f(c), U1(k, k))
26.23/8.57	   A^2 -> H(U1(k, k), f(b))
26.23/8.57	   A^2 -> H(U1(k, d), U1(b, b))
26.23/8.57	   A^2 -> H(U1(k, d), f(c))
26.23/8.57	   A^2 -> H(U1(k, d), f(d))
26.23/8.57	   A^2 -> H(U1(d, k), U1(b, b))
26.23/8.57	   A^2 -> H(U1(d, k), f(c))
26.23/8.57	   A^2 -> H(U1(d, k), f(d))
26.23/8.57	   A^2 -> H(U1(d, d), U1(c, b))
26.23/8.57	   A^2 -> H(U1(d, d), U1(d, b))
26.23/8.57	   A^2 -> H(U1(d, d), U1(b, c))
26.23/8.57	   A^2 -> H(U1(d, d), U1(b, d))
26.23/8.57	   A^2 -> H(U1(d, d), U1(c, c))
26.23/8.57	   A^2 -> H(U1(d, d), f(e))
26.23/8.57	   A^2 -> H(U1(d, d), f(k))
26.23/8.57	   A^2 -> H(U1(d, d), U1(d, d))
26.23/8.57	   A^2 -> H(f(d), U1(e, b))
26.23/8.57	   A^2 -> H(f(d), U1(k, b))
26.23/8.57	   A^2 -> H(f(d), U1(c, d))
26.23/8.57	   A^2 -> H(f(d), U1(d, c))
26.23/8.57	   A^2 -> H(f(d), U1(b, e))
26.23/8.57	   A^2 -> H(f(d), U1(b, k))
26.23/8.57	   A^2 -> H(f(d), U1(e, c))
26.23/8.57	   A^2 -> H(f(d), U1(k, c))
26.23/8.57	   A^2 -> H(f(d), U1(c, e))
26.23/8.57	   A^2 -> H(f(d), U1(c, k))
26.23/8.57	   A^2 -> H(f(d), U1(e, e))
26.23/8.57	   A^2 -> H(f(d), U1(k, k))
26.23/8.57	   A^2 -> H(f(a), b)
26.23/8.57	   A^2 -> H(f(a), U1(e, d))
26.23/8.57	   A^2 -> H(f(a), U1(d, e))
26.23/8.57	   A^2 -> H(f(c), U1(e, c))
26.23/8.57	   A^2 -> H(f(c), U1(k, c))
26.23/8.57	   A^2 -> H(f(c), U1(c, e))
26.23/8.57	   A^2 -> H(f(c), U1(c, k))
26.23/8.57	   A^2 -> H(f(a), c)
26.23/8.57	   A^2 -> H(f(a), U1(e, k))
26.23/8.57	   A^2 -> H(f(a), U1(k, e))
26.23/8.57	   A^2 -> H(f(c), U1(e, e))
26.23/8.57	   A^2 -> H(f(a), e)
26.23/8.57	   A^2 -> H(f(d), U1(k, d))
26.23/8.57	   A^2 -> H(f(d), U1(d, k))
26.23/8.57	   A^2 -> H(f(a), U1(k, k))
26.23/8.57	   A^2 -> H(d, f(b))
26.23/8.57	   A^2 -> H(a, U1(b, b))
26.23/8.57	   A^2 -> H(a, f(c))
26.23/8.57	   A^2 -> H(a, f(d))
26.23/8.57	   A^2 -> H(U1(e, d), U1(b, b))
26.23/8.57	   A^2 -> H(U1(e, d), f(c))
26.23/8.57	   A^2 -> H(U1(e, d), f(d))
26.23/8.57	   A^2 -> H(U1(e, a), U1(c, b))
26.23/8.57	   A^2 -> H(U1(e, a), U1(d, b))
26.23/8.57	   A^2 -> H(U1(e, a), U1(b, c))
26.23/8.57	   A^2 -> H(U1(e, a), U1(b, d))
26.23/8.57	   A^2 -> H(U1(e, a), U1(c, c))
26.23/8.57	   A^2 -> H(U1(e, a), f(e))
26.23/8.57	   A^2 -> H(U1(e, a), f(k))
26.23/8.57	   A^2 -> H(U1(e, a), U1(d, d))
26.23/8.57	   A^2 -> H(U1(k, a), U1(c, b))
26.26/8.58	   A^2 -> H(U1(k, a), U1(d, b))
26.26/8.58	   A^2 -> H(U1(k, a), U1(b, c))
26.26/8.58	   A^2 -> H(U1(k, a), U1(b, d))
26.26/8.58	   A^2 -> H(U1(k, a), U1(c, c))
26.26/8.58	   A^2 -> H(U1(k, a), f(e))
26.26/8.58	   A^2 -> H(U1(k, a), f(k))
26.26/8.58	   A^2 -> H(U1(k, a), U1(d, d))
26.26/8.58	   A^2 -> H(U1(c, d), U1(c, b))
26.26/8.58	   A^2 -> H(U1(c, d), U1(d, b))
26.26/8.58	   A^2 -> H(U1(c, d), U1(b, c))
26.26/8.58	   A^2 -> H(U1(c, d), U1(b, d))
26.26/8.58	   A^2 -> H(U1(c, d), U1(c, c))
26.26/8.58	   A^2 -> H(U1(c, d), f(e))
26.26/8.58	   A^2 -> H(U1(c, d), f(k))
26.26/8.58	   A^2 -> H(U1(c, d), U1(d, d))
26.26/8.58	   A^2 -> H(U1(c, a), U1(e, b))
26.26/8.58	   A^2 -> H(U1(c, a), U1(k, b))
26.26/8.58	   A^2 -> H(U1(c, a), U1(c, d))
26.26/8.58	   A^2 -> H(U1(c, a), U1(d, c))
26.26/8.58	   A^2 -> H(U1(c, a), U1(b, e))
26.26/8.58	   A^2 -> H(U1(c, a), U1(b, k))
26.26/8.58	   A^2 -> H(U1(c, a), U1(e, c))
26.26/8.58	   A^2 -> H(U1(c, a), U1(k, c))
26.26/8.58	   A^2 -> H(U1(c, a), U1(c, e))
26.26/8.58	   A^2 -> H(U1(c, a), U1(c, k))
26.26/8.58	   A^2 -> H(U1(c, a), U1(e, e))
26.26/8.58	   A^2 -> H(U1(c, a), U1(k, k))
26.26/8.58	   A^2 -> H(U1(c, a), U1(k, d))
26.26/8.58	   A^2 -> H(U1(c, a), U1(d, k))
26.26/8.58	   A^2 -> H(U1(d, e), U1(b, b))
26.26/8.58	   A^2 -> H(U1(d, e), f(c))
26.26/8.58	   A^2 -> H(U1(d, e), f(d))
26.26/8.58	   A^2 -> H(U1(d, c), U1(c, b))
26.26/8.58	   A^2 -> H(U1(d, c), U1(d, b))
26.26/8.58	   A^2 -> H(U1(d, c), U1(b, c))
26.26/8.58	   A^2 -> H(U1(d, c), U1(b, d))
26.26/8.58	   A^2 -> H(U1(d, c), U1(c, c))
26.26/8.58	   A^2 -> H(U1(d, c), f(e))
26.26/8.58	   A^2 -> H(U1(d, c), f(k))
26.26/8.58	   A^2 -> H(U1(d, c), U1(d, d))
26.26/8.58	   A^2 -> H(U1(d, a), U1(e, b))
26.26/8.58	   A^2 -> H(U1(d, a), U1(k, b))
26.26/8.58	   A^2 -> H(U1(d, a), U1(c, d))
26.26/8.58	   A^2 -> H(U1(d, a), U1(d, c))
26.26/8.58	   A^2 -> H(U1(d, a), U1(b, e))
26.26/8.58	   A^2 -> H(U1(d, a), U1(b, k))
26.26/8.58	   A^2 -> H(U1(d, a), U1(e, c))
26.26/8.58	   A^2 -> H(U1(d, a), U1(k, c))
26.26/8.58	   A^2 -> H(U1(d, a), U1(c, e))
26.26/8.58	   A^2 -> H(U1(d, a), U1(c, k))
26.26/8.58	   A^2 -> H(U1(d, a), U1(e, e))
26.26/8.58	   A^2 -> H(U1(d, a), U1(k, k))
26.26/8.58	   A^2 -> H(U1(d, a), U1(k, d))
26.26/8.58	   A^2 -> H(U1(d, a), U1(d, k))
26.26/8.58	   A^2 -> H(U1(a, e), U1(c, b))
26.26/8.58	   A^2 -> H(U1(a, e), U1(d, b))
26.26/8.58	   A^2 -> H(U1(a, e), U1(b, c))
26.26/8.58	   A^2 -> H(U1(a, e), U1(b, d))
26.26/8.58	   A^2 -> H(U1(a, e), U1(c, c))
26.26/8.58	   A^2 -> H(U1(a, e), f(e))
26.26/8.58	   A^2 -> H(U1(a, e), f(k))
26.26/8.58	   A^2 -> H(U1(a, e), U1(d, d))
26.26/8.58	   A^2 -> H(U1(a, k), U1(c, b))
26.26/8.58	   A^2 -> H(U1(a, k), U1(d, b))
26.26/8.58	   A^2 -> H(U1(a, k), U1(b, c))
26.26/8.59	   A^2 -> H(U1(a, k), U1(b, d))
26.26/8.59	   A^2 -> H(U1(a, k), U1(c, c))
26.26/8.59	   A^2 -> H(U1(a, k), f(e))
26.26/8.59	   A^2 -> H(U1(a, k), f(k))
26.26/8.59	   A^2 -> H(U1(a, k), U1(d, d))
26.26/8.59	   A^2 -> H(U1(a, c), U1(e, b))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, b))
26.26/8.59	   A^2 -> H(U1(a, c), U1(c, d))
26.26/8.59	   A^2 -> H(U1(a, c), U1(d, c))
26.26/8.59	   A^2 -> H(U1(a, c), U1(b, e))
26.26/8.59	   A^2 -> H(U1(a, c), U1(b, k))
26.26/8.59	   A^2 -> H(U1(a, c), U1(e, c))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, c))
26.26/8.59	   A^2 -> H(U1(a, c), U1(c, e))
26.26/8.59	   A^2 -> H(U1(a, c), U1(c, k))
26.26/8.59	   A^2 -> H(U1(a, c), U1(e, e))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, k))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, d))
26.26/8.59	   A^2 -> H(U1(a, c), U1(d, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(e, b))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, b))
26.26/8.59	   A^2 -> H(U1(a, d), U1(c, d))
26.26/8.59	   A^2 -> H(U1(a, d), U1(d, c))
26.26/8.59	   A^2 -> H(U1(a, d), U1(b, e))
26.26/8.59	   A^2 -> H(U1(a, d), U1(b, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(e, c))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, c))
26.26/8.59	   A^2 -> H(U1(a, d), U1(c, e))
26.26/8.59	   A^2 -> H(U1(a, d), U1(c, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(e, e))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, d))
26.26/8.59	   A^2 -> H(U1(a, d), U1(d, k))
26.26/8.59	   A^2 -> H(U1(a, a), b)
26.26/8.59	   A^2 -> H(U1(a, a), U1(e, d))
26.26/8.59	   A^2 -> H(U1(a, a), U1(d, e))
26.26/8.59	   A^2 -> H(U1(a, a), c)
26.26/8.59	   A^2 -> H(U1(a, a), U1(e, k))
26.26/8.59	   A^2 -> H(U1(a, a), U1(k, e))
26.26/8.59	   A^2 -> H(U1(a, a), e)
26.26/8.59	   A^2 -> H(U1(a, a), U1(k, k))
26.26/8.59	   A^2 -> H(k, f(b))
26.26/8.59	   A^2 -> H(c, U1(b, b))
26.26/8.59	   A^2 -> H(c, f(c))
26.26/8.59	   A^2 -> H(c, f(d))
26.26/8.59	   A^2 -> H(U1(e, k), U1(b, b))
26.26/8.59	   A^2 -> H(U1(e, k), f(c))
26.26/8.59	   A^2 -> H(U1(e, k), f(d))
26.26/8.59	   A^2 -> H(U1(e, c), U1(c, b))
26.26/8.59	   A^2 -> H(U1(e, c), U1(d, b))
26.26/8.59	   A^2 -> H(U1(e, c), U1(b, c))
26.26/8.59	   A^2 -> H(U1(e, c), U1(b, d))
26.26/8.59	   A^2 -> H(U1(e, c), U1(c, c))
26.26/8.59	   A^2 -> H(U1(e, c), f(e))
26.26/8.59	   A^2 -> H(U1(e, c), f(k))
26.26/8.59	   A^2 -> H(U1(e, c), U1(d, d))
26.26/8.59	   A^2 -> H(U1(k, e), U1(b, b))
26.26/8.59	   A^2 -> H(U1(k, e), f(c))
26.26/8.59	   A^2 -> H(U1(k, e), f(d))
26.26/8.59	   A^2 -> H(U1(k, c), U1(c, b))
26.26/8.59	   A^2 -> H(U1(k, c), U1(d, b))
26.26/8.59	   A^2 -> H(U1(k, c), U1(b, c))
26.26/8.59	   A^2 -> H(U1(k, c), U1(b, d))
26.26/8.59	   A^2 -> H(U1(k, c), U1(c, c))
26.26/8.59	   A^2 -> H(U1(k, c), f(e))
26.26/8.59	   A^2 -> H(U1(k, c), f(k))
26.26/8.59	   A^2 -> H(U1(k, c), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, e), U1(c, b))
26.26/8.59	   A^2 -> H(U1(c, e), U1(d, b))
26.26/8.59	   A^2 -> H(U1(c, e), U1(b, c))
26.26/8.59	   A^2 -> H(U1(c, e), U1(b, d))
26.26/8.59	   A^2 -> H(U1(c, e), U1(c, c))
26.26/8.59	   A^2 -> H(U1(c, e), f(e))
26.26/8.59	   A^2 -> H(U1(c, e), f(k))
26.26/8.59	   A^2 -> H(U1(c, e), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, k), U1(c, b))
26.26/8.59	   A^2 -> H(U1(c, k), U1(d, b))
26.26/8.59	   A^2 -> H(U1(c, k), U1(b, c))
26.26/8.59	   A^2 -> H(U1(c, k), U1(b, d))
26.26/8.59	   A^2 -> H(U1(c, k), U1(c, c))
26.26/8.59	   A^2 -> H(U1(c, k), f(e))
26.26/8.59	   A^2 -> H(U1(c, k), f(k))
26.26/8.59	   A^2 -> H(U1(c, k), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(e, b))
26.26/8.59	   A^2 -> H(U1(c, c), U1(k, b))
26.26/8.59	   A^2 -> H(U1(c, c), U1(c, d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(d, c))
26.26/8.59	   A^2 -> H(U1(c, c), U1(b, e))
26.26/8.59	   A^2 -> H(U1(c, c), U1(b, k))
26.26/8.59	   A^2 -> H(U1(c, c), U1(e, e))
26.26/8.59	   A^2 -> H(U1(c, c), U1(k, k))
26.26/8.59	   A^2 -> H(U1(c, c), U1(k, d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(d, k))
26.26/8.59	   A^2 -> H(e, U1(b, b))
26.26/8.59	   A^2 -> H(e, f(c))
26.26/8.59	   A^2 -> H(e, f(d))
26.26/8.59	   A^2 -> H(U1(e, e), U1(c, b))
26.26/8.59	   A^2 -> H(U1(e, e), U1(d, b))
26.26/8.59	   A^2 -> H(U1(e, e), U1(b, c))
26.26/8.59	   A^2 -> H(U1(e, e), U1(b, d))
26.26/8.59	   A^2 -> H(U1(e, e), U1(c, c))
26.26/8.59	   A^2 -> H(U1(e, e), f(e))
26.26/8.59	   A^2 -> H(U1(e, e), f(k))
26.26/8.59	   A^2 -> H(U1(e, e), U1(d, d))
26.26/8.59	   A^2 -> H(f(e), U1(e, b))
26.26/8.59	   A^2 -> H(f(e), U1(k, b))
26.26/8.59	   A^2 -> H(f(e), U1(c, d))
26.26/8.59	   A^2 -> H(f(e), U1(d, c))
26.26/8.59	   A^2 -> H(f(e), U1(b, e))
26.26/8.59	   A^2 -> H(f(e), U1(b, k))
26.26/8.59	   A^2 -> H(f(e), U1(e, c))
26.26/8.59	   A^2 -> H(f(e), U1(k, c))
26.26/8.59	   A^2 -> H(f(e), U1(c, e))
26.26/8.59	   A^2 -> H(f(e), U1(c, k))
26.26/8.59	   A^2 -> H(f(e), U1(k, k))
26.26/8.59	
26.26/8.59	The TRS R consists of the following rules:
26.26/8.59	
26.26/8.59	   f(x) -> U1(x, x)
26.26/8.59	   U1(e, x) -> x
26.26/8.59	   a -> c
26.26/8.59	   a -> d
26.26/8.59	   b -> c
26.26/8.59	   b -> d
26.26/8.59	   d -> k
26.26/8.59	   c -> e
26.26/8.59	   c -> k
26.26/8.59	
26.26/8.59	Q is empty.
26.26/8.59	We have to consider all minimal (P,Q,R)-chains.
26.26/8.59	----------------------------------------
26.26/8.59	
26.26/8.59	(419) TransformationProof (EQUIVALENT)
26.26/8.59	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
26.26/8.59	
26.26/8.59	   (A^2 -> H(U1(e, e), U1(d, d)),A^2 -> H(U1(e, e), U1(d, d)))
26.26/8.59	   (A^2 -> H(f(e), U1(k, d)),A^2 -> H(f(e), U1(k, d)))
26.26/8.59	   (A^2 -> H(f(e), U1(d, k)),A^2 -> H(f(e), U1(d, k)))
26.26/8.59	
26.26/8.59	
26.26/8.59	----------------------------------------
26.26/8.59	
26.26/8.59	(420)
26.26/8.59	Obligation:
26.26/8.59	Q DP problem:
26.26/8.59	The TRS P consists of the following rules:
26.26/8.59	
26.26/8.59	   H(x, x) -> G(x, x, f(k))
26.26/8.59	   G(d, x, x) -> A^2
26.26/8.59	   A^2 -> H(f(c), f(c))
26.26/8.59	   A^2 -> H(f(d), f(d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(c, c))
26.26/8.59	   A^2 -> H(f(e), f(e))
26.26/8.59	   A^2 -> H(U1(k, k), U1(b, b))
26.26/8.59	   A^2 -> H(U1(k, k), f(c))
26.26/8.59	   A^2 -> H(U1(k, k), f(d))
26.26/8.59	   A^2 -> H(f(k), U1(c, b))
26.26/8.59	   A^2 -> H(f(k), U1(d, b))
26.26/8.59	   A^2 -> H(f(k), U1(b, c))
26.26/8.59	   A^2 -> H(f(k), U1(b, d))
26.26/8.59	   A^2 -> H(f(k), U1(c, c))
26.26/8.59	   A^2 -> H(f(k), f(e))
26.26/8.59	   A^2 -> H(f(k), f(k))
26.26/8.59	   A^2 -> H(f(k), U1(d, d))
26.26/8.59	   A^2 -> H(f(c), U1(e, b))
26.26/8.59	   A^2 -> H(f(c), U1(k, b))
26.26/8.59	   A^2 -> H(f(c), U1(c, d))
26.26/8.59	   A^2 -> H(f(c), U1(d, c))
26.26/8.59	   A^2 -> H(f(c), U1(b, e))
26.26/8.59	   A^2 -> H(f(c), U1(b, k))
26.26/8.59	   A^2 -> H(f(c), U1(k, d))
26.26/8.59	   A^2 -> H(f(c), U1(d, k))
26.26/8.59	   A^2 -> H(f(c), U1(k, k))
26.26/8.59	   A^2 -> H(U1(k, k), f(b))
26.26/8.59	   A^2 -> H(U1(k, d), U1(b, b))
26.26/8.59	   A^2 -> H(U1(k, d), f(c))
26.26/8.59	   A^2 -> H(U1(k, d), f(d))
26.26/8.59	   A^2 -> H(U1(d, k), U1(b, b))
26.26/8.59	   A^2 -> H(U1(d, k), f(c))
26.26/8.59	   A^2 -> H(U1(d, k), f(d))
26.26/8.59	   A^2 -> H(U1(d, d), U1(c, b))
26.26/8.59	   A^2 -> H(U1(d, d), U1(d, b))
26.26/8.59	   A^2 -> H(U1(d, d), U1(b, c))
26.26/8.59	   A^2 -> H(U1(d, d), U1(b, d))
26.26/8.59	   A^2 -> H(U1(d, d), U1(c, c))
26.26/8.59	   A^2 -> H(U1(d, d), f(e))
26.26/8.59	   A^2 -> H(U1(d, d), f(k))
26.26/8.59	   A^2 -> H(U1(d, d), U1(d, d))
26.26/8.59	   A^2 -> H(f(d), U1(e, b))
26.26/8.59	   A^2 -> H(f(d), U1(k, b))
26.26/8.59	   A^2 -> H(f(d), U1(c, d))
26.26/8.59	   A^2 -> H(f(d), U1(d, c))
26.26/8.59	   A^2 -> H(f(d), U1(b, e))
26.26/8.59	   A^2 -> H(f(d), U1(b, k))
26.26/8.59	   A^2 -> H(f(d), U1(e, c))
26.26/8.59	   A^2 -> H(f(d), U1(k, c))
26.26/8.59	   A^2 -> H(f(d), U1(c, e))
26.26/8.59	   A^2 -> H(f(d), U1(c, k))
26.26/8.59	   A^2 -> H(f(d), U1(e, e))
26.26/8.59	   A^2 -> H(f(d), U1(k, k))
26.26/8.59	   A^2 -> H(f(a), b)
26.26/8.59	   A^2 -> H(f(a), U1(e, d))
26.26/8.59	   A^2 -> H(f(a), U1(d, e))
26.26/8.59	   A^2 -> H(f(c), U1(e, c))
26.26/8.59	   A^2 -> H(f(c), U1(k, c))
26.26/8.59	   A^2 -> H(f(c), U1(c, e))
26.26/8.59	   A^2 -> H(f(c), U1(c, k))
26.26/8.59	   A^2 -> H(f(a), c)
26.26/8.59	   A^2 -> H(f(a), U1(e, k))
26.26/8.59	   A^2 -> H(f(a), U1(k, e))
26.26/8.59	   A^2 -> H(f(c), U1(e, e))
26.26/8.59	   A^2 -> H(f(a), e)
26.26/8.59	   A^2 -> H(f(d), U1(k, d))
26.26/8.59	   A^2 -> H(f(d), U1(d, k))
26.26/8.59	   A^2 -> H(f(a), U1(k, k))
26.26/8.59	   A^2 -> H(d, f(b))
26.26/8.59	   A^2 -> H(a, U1(b, b))
26.26/8.59	   A^2 -> H(a, f(c))
26.26/8.59	   A^2 -> H(a, f(d))
26.26/8.59	   A^2 -> H(U1(e, d), U1(b, b))
26.26/8.59	   A^2 -> H(U1(e, d), f(c))
26.26/8.59	   A^2 -> H(U1(e, d), f(d))
26.26/8.59	   A^2 -> H(U1(e, a), U1(c, b))
26.26/8.59	   A^2 -> H(U1(e, a), U1(d, b))
26.26/8.59	   A^2 -> H(U1(e, a), U1(b, c))
26.26/8.59	   A^2 -> H(U1(e, a), U1(b, d))
26.26/8.59	   A^2 -> H(U1(e, a), U1(c, c))
26.26/8.59	   A^2 -> H(U1(e, a), f(e))
26.26/8.59	   A^2 -> H(U1(e, a), f(k))
26.26/8.59	   A^2 -> H(U1(e, a), U1(d, d))
26.26/8.59	   A^2 -> H(U1(k, a), U1(c, b))
26.26/8.59	   A^2 -> H(U1(k, a), U1(d, b))
26.26/8.59	   A^2 -> H(U1(k, a), U1(b, c))
26.26/8.59	   A^2 -> H(U1(k, a), U1(b, d))
26.26/8.59	   A^2 -> H(U1(k, a), U1(c, c))
26.26/8.59	   A^2 -> H(U1(k, a), f(e))
26.26/8.59	   A^2 -> H(U1(k, a), f(k))
26.26/8.59	   A^2 -> H(U1(k, a), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, d), U1(c, b))
26.26/8.59	   A^2 -> H(U1(c, d), U1(d, b))
26.26/8.59	   A^2 -> H(U1(c, d), U1(b, c))
26.26/8.59	   A^2 -> H(U1(c, d), U1(b, d))
26.26/8.59	   A^2 -> H(U1(c, d), U1(c, c))
26.26/8.59	   A^2 -> H(U1(c, d), f(e))
26.26/8.59	   A^2 -> H(U1(c, d), f(k))
26.26/8.59	   A^2 -> H(U1(c, d), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, a), U1(e, b))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, b))
26.26/8.59	   A^2 -> H(U1(c, a), U1(c, d))
26.26/8.59	   A^2 -> H(U1(c, a), U1(d, c))
26.26/8.59	   A^2 -> H(U1(c, a), U1(b, e))
26.26/8.59	   A^2 -> H(U1(c, a), U1(b, k))
26.26/8.59	   A^2 -> H(U1(c, a), U1(e, c))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, c))
26.26/8.59	   A^2 -> H(U1(c, a), U1(c, e))
26.26/8.59	   A^2 -> H(U1(c, a), U1(c, k))
26.26/8.59	   A^2 -> H(U1(c, a), U1(e, e))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, k))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, d))
26.26/8.59	   A^2 -> H(U1(c, a), U1(d, k))
26.26/8.59	   A^2 -> H(U1(d, e), U1(b, b))
26.26/8.59	   A^2 -> H(U1(d, e), f(c))
26.26/8.59	   A^2 -> H(U1(d, e), f(d))
26.26/8.59	   A^2 -> H(U1(d, c), U1(c, b))
26.26/8.59	   A^2 -> H(U1(d, c), U1(d, b))
26.26/8.59	   A^2 -> H(U1(d, c), U1(b, c))
26.26/8.59	   A^2 -> H(U1(d, c), U1(b, d))
26.26/8.59	   A^2 -> H(U1(d, c), U1(c, c))
26.26/8.59	   A^2 -> H(U1(d, c), f(e))
26.26/8.59	   A^2 -> H(U1(d, c), f(k))
26.26/8.59	   A^2 -> H(U1(d, c), U1(d, d))
26.26/8.59	   A^2 -> H(U1(d, a), U1(e, b))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, b))
26.26/8.59	   A^2 -> H(U1(d, a), U1(c, d))
26.26/8.59	   A^2 -> H(U1(d, a), U1(d, c))
26.26/8.59	   A^2 -> H(U1(d, a), U1(b, e))
26.26/8.59	   A^2 -> H(U1(d, a), U1(b, k))
26.26/8.59	   A^2 -> H(U1(d, a), U1(e, c))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, c))
26.26/8.59	   A^2 -> H(U1(d, a), U1(c, e))
26.26/8.59	   A^2 -> H(U1(d, a), U1(c, k))
26.26/8.59	   A^2 -> H(U1(d, a), U1(e, e))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, k))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, d))
26.26/8.59	   A^2 -> H(U1(d, a), U1(d, k))
26.26/8.59	   A^2 -> H(U1(a, e), U1(c, b))
26.26/8.59	   A^2 -> H(U1(a, e), U1(d, b))
26.26/8.59	   A^2 -> H(U1(a, e), U1(b, c))
26.26/8.59	   A^2 -> H(U1(a, e), U1(b, d))
26.26/8.59	   A^2 -> H(U1(a, e), U1(c, c))
26.26/8.59	   A^2 -> H(U1(a, e), f(e))
26.26/8.59	   A^2 -> H(U1(a, e), f(k))
26.26/8.59	   A^2 -> H(U1(a, e), U1(d, d))
26.26/8.59	   A^2 -> H(U1(a, k), U1(c, b))
26.26/8.59	   A^2 -> H(U1(a, k), U1(d, b))
26.26/8.59	   A^2 -> H(U1(a, k), U1(b, c))
26.26/8.59	   A^2 -> H(U1(a, k), U1(b, d))
26.26/8.59	   A^2 -> H(U1(a, k), U1(c, c))
26.26/8.59	   A^2 -> H(U1(a, k), f(e))
26.26/8.59	   A^2 -> H(U1(a, k), f(k))
26.26/8.59	   A^2 -> H(U1(a, k), U1(d, d))
26.26/8.59	   A^2 -> H(U1(a, c), U1(e, b))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, b))
26.26/8.59	   A^2 -> H(U1(a, c), U1(c, d))
26.26/8.59	   A^2 -> H(U1(a, c), U1(d, c))
26.26/8.59	   A^2 -> H(U1(a, c), U1(b, e))
26.26/8.59	   A^2 -> H(U1(a, c), U1(b, k))
26.26/8.59	   A^2 -> H(U1(a, c), U1(e, c))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, c))
26.26/8.59	   A^2 -> H(U1(a, c), U1(c, e))
26.26/8.59	   A^2 -> H(U1(a, c), U1(c, k))
26.26/8.59	   A^2 -> H(U1(a, c), U1(e, e))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, k))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, d))
26.26/8.59	   A^2 -> H(U1(a, c), U1(d, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(e, b))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, b))
26.26/8.59	   A^2 -> H(U1(a, d), U1(c, d))
26.26/8.59	   A^2 -> H(U1(a, d), U1(d, c))
26.26/8.59	   A^2 -> H(U1(a, d), U1(b, e))
26.26/8.59	   A^2 -> H(U1(a, d), U1(b, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(e, c))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, c))
26.26/8.59	   A^2 -> H(U1(a, d), U1(c, e))
26.26/8.59	   A^2 -> H(U1(a, d), U1(c, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(e, e))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, d))
26.26/8.59	   A^2 -> H(U1(a, d), U1(d, k))
26.26/8.59	   A^2 -> H(U1(a, a), b)
26.26/8.59	   A^2 -> H(U1(a, a), U1(e, d))
26.26/8.59	   A^2 -> H(U1(a, a), U1(d, e))
26.26/8.59	   A^2 -> H(U1(a, a), c)
26.26/8.59	   A^2 -> H(U1(a, a), U1(e, k))
26.26/8.59	   A^2 -> H(U1(a, a), U1(k, e))
26.26/8.59	   A^2 -> H(U1(a, a), e)
26.26/8.59	   A^2 -> H(U1(a, a), U1(k, k))
26.26/8.59	   A^2 -> H(k, f(b))
26.26/8.59	   A^2 -> H(c, U1(b, b))
26.26/8.59	   A^2 -> H(c, f(c))
26.26/8.59	   A^2 -> H(c, f(d))
26.26/8.59	   A^2 -> H(U1(e, k), U1(b, b))
26.26/8.59	   A^2 -> H(U1(e, k), f(c))
26.26/8.59	   A^2 -> H(U1(e, k), f(d))
26.26/8.59	   A^2 -> H(U1(e, c), U1(c, b))
26.26/8.59	   A^2 -> H(U1(e, c), U1(d, b))
26.26/8.59	   A^2 -> H(U1(e, c), U1(b, c))
26.26/8.59	   A^2 -> H(U1(e, c), U1(b, d))
26.26/8.59	   A^2 -> H(U1(e, c), U1(c, c))
26.26/8.59	   A^2 -> H(U1(e, c), f(e))
26.26/8.59	   A^2 -> H(U1(e, c), f(k))
26.26/8.59	   A^2 -> H(U1(e, c), U1(d, d))
26.26/8.59	   A^2 -> H(U1(k, e), U1(b, b))
26.26/8.59	   A^2 -> H(U1(k, e), f(c))
26.26/8.59	   A^2 -> H(U1(k, e), f(d))
26.26/8.59	   A^2 -> H(U1(k, c), U1(c, b))
26.26/8.59	   A^2 -> H(U1(k, c), U1(d, b))
26.26/8.59	   A^2 -> H(U1(k, c), U1(b, c))
26.26/8.59	   A^2 -> H(U1(k, c), U1(b, d))
26.26/8.59	   A^2 -> H(U1(k, c), U1(c, c))
26.26/8.59	   A^2 -> H(U1(k, c), f(e))
26.26/8.59	   A^2 -> H(U1(k, c), f(k))
26.26/8.59	   A^2 -> H(U1(k, c), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, e), U1(c, b))
26.26/8.59	   A^2 -> H(U1(c, e), U1(d, b))
26.26/8.59	   A^2 -> H(U1(c, e), U1(b, c))
26.26/8.59	   A^2 -> H(U1(c, e), U1(b, d))
26.26/8.59	   A^2 -> H(U1(c, e), U1(c, c))
26.26/8.59	   A^2 -> H(U1(c, e), f(e))
26.26/8.59	   A^2 -> H(U1(c, e), f(k))
26.26/8.59	   A^2 -> H(U1(c, e), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, k), U1(c, b))
26.26/8.59	   A^2 -> H(U1(c, k), U1(d, b))
26.26/8.59	   A^2 -> H(U1(c, k), U1(b, c))
26.26/8.59	   A^2 -> H(U1(c, k), U1(b, d))
26.26/8.59	   A^2 -> H(U1(c, k), U1(c, c))
26.26/8.59	   A^2 -> H(U1(c, k), f(e))
26.26/8.59	   A^2 -> H(U1(c, k), f(k))
26.26/8.59	   A^2 -> H(U1(c, k), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(e, b))
26.26/8.59	   A^2 -> H(U1(c, c), U1(k, b))
26.26/8.59	   A^2 -> H(U1(c, c), U1(c, d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(d, c))
26.26/8.59	   A^2 -> H(U1(c, c), U1(b, e))
26.26/8.59	   A^2 -> H(U1(c, c), U1(b, k))
26.26/8.59	   A^2 -> H(U1(c, c), U1(e, e))
26.26/8.59	   A^2 -> H(U1(c, c), U1(k, k))
26.26/8.59	   A^2 -> H(U1(c, c), U1(k, d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(d, k))
26.26/8.59	   A^2 -> H(e, U1(b, b))
26.26/8.59	   A^2 -> H(e, f(c))
26.26/8.59	   A^2 -> H(e, f(d))
26.26/8.59	   A^2 -> H(U1(e, e), U1(c, b))
26.26/8.59	   A^2 -> H(U1(e, e), U1(d, b))
26.26/8.59	   A^2 -> H(U1(e, e), U1(b, c))
26.26/8.59	   A^2 -> H(U1(e, e), U1(b, d))
26.26/8.59	   A^2 -> H(U1(e, e), U1(c, c))
26.26/8.59	   A^2 -> H(U1(e, e), f(e))
26.26/8.59	   A^2 -> H(U1(e, e), f(k))
26.26/8.59	   A^2 -> H(U1(e, e), U1(d, d))
26.26/8.59	   A^2 -> H(f(e), U1(e, b))
26.26/8.59	   A^2 -> H(f(e), U1(k, b))
26.26/8.59	   A^2 -> H(f(e), U1(c, d))
26.26/8.59	   A^2 -> H(f(e), U1(d, c))
26.26/8.59	   A^2 -> H(f(e), U1(b, e))
26.26/8.59	   A^2 -> H(f(e), U1(b, k))
26.26/8.59	   A^2 -> H(f(e), U1(e, c))
26.26/8.59	   A^2 -> H(f(e), U1(k, c))
26.26/8.59	   A^2 -> H(f(e), U1(c, e))
26.26/8.59	   A^2 -> H(f(e), U1(c, k))
26.26/8.59	   A^2 -> H(f(e), U1(k, k))
26.26/8.59	   A^2 -> H(f(e), U1(k, d))
26.26/8.59	   A^2 -> H(f(e), U1(d, k))
26.26/8.59	
26.26/8.59	The TRS R consists of the following rules:
26.26/8.59	
26.26/8.59	   f(x) -> U1(x, x)
26.26/8.59	   U1(e, x) -> x
26.26/8.59	   a -> c
26.26/8.59	   a -> d
26.26/8.59	   b -> c
26.26/8.59	   b -> d
26.26/8.59	   d -> k
26.26/8.59	   c -> e
26.26/8.59	   c -> k
26.26/8.59	
26.26/8.59	Q is empty.
26.26/8.59	We have to consider all minimal (P,Q,R)-chains.
26.26/8.59	----------------------------------------
26.26/8.59	
26.26/8.59	(421) TransformationProof (EQUIVALENT)
26.26/8.59	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
26.26/8.59	
26.26/8.59	   (A^2 -> H(U1(k, k), U1(c, b)),A^2 -> H(U1(k, k), U1(c, b)))
26.26/8.59	   (A^2 -> H(U1(k, k), U1(d, b)),A^2 -> H(U1(k, k), U1(d, b)))
26.26/8.59	   (A^2 -> H(U1(k, k), U1(b, c)),A^2 -> H(U1(k, k), U1(b, c)))
26.26/8.59	   (A^2 -> H(U1(k, k), U1(b, d)),A^2 -> H(U1(k, k), U1(b, d)))
26.26/8.59	
26.26/8.59	
26.26/8.59	----------------------------------------
26.26/8.59	
26.26/8.59	(422)
26.26/8.59	Obligation:
26.26/8.59	Q DP problem:
26.26/8.59	The TRS P consists of the following rules:
26.26/8.59	
26.26/8.59	   H(x, x) -> G(x, x, f(k))
26.26/8.59	   G(d, x, x) -> A^2
26.26/8.59	   A^2 -> H(f(c), f(c))
26.26/8.59	   A^2 -> H(f(d), f(d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(c, c))
26.26/8.59	   A^2 -> H(f(e), f(e))
26.26/8.59	   A^2 -> H(U1(k, k), f(c))
26.26/8.59	   A^2 -> H(U1(k, k), f(d))
26.26/8.59	   A^2 -> H(f(k), U1(c, b))
26.26/8.59	   A^2 -> H(f(k), U1(d, b))
26.26/8.59	   A^2 -> H(f(k), U1(b, c))
26.26/8.59	   A^2 -> H(f(k), U1(b, d))
26.26/8.59	   A^2 -> H(f(k), U1(c, c))
26.26/8.59	   A^2 -> H(f(k), f(e))
26.26/8.59	   A^2 -> H(f(k), f(k))
26.26/8.59	   A^2 -> H(f(k), U1(d, d))
26.26/8.59	   A^2 -> H(f(c), U1(e, b))
26.26/8.59	   A^2 -> H(f(c), U1(k, b))
26.26/8.59	   A^2 -> H(f(c), U1(c, d))
26.26/8.59	   A^2 -> H(f(c), U1(d, c))
26.26/8.59	   A^2 -> H(f(c), U1(b, e))
26.26/8.59	   A^2 -> H(f(c), U1(b, k))
26.26/8.59	   A^2 -> H(f(c), U1(k, d))
26.26/8.59	   A^2 -> H(f(c), U1(d, k))
26.26/8.59	   A^2 -> H(f(c), U1(k, k))
26.26/8.59	   A^2 -> H(U1(k, k), f(b))
26.26/8.59	   A^2 -> H(U1(k, d), U1(b, b))
26.26/8.59	   A^2 -> H(U1(k, d), f(c))
26.26/8.59	   A^2 -> H(U1(k, d), f(d))
26.26/8.59	   A^2 -> H(U1(d, k), U1(b, b))
26.26/8.59	   A^2 -> H(U1(d, k), f(c))
26.26/8.59	   A^2 -> H(U1(d, k), f(d))
26.26/8.59	   A^2 -> H(U1(d, d), U1(c, b))
26.26/8.59	   A^2 -> H(U1(d, d), U1(d, b))
26.26/8.59	   A^2 -> H(U1(d, d), U1(b, c))
26.26/8.59	   A^2 -> H(U1(d, d), U1(b, d))
26.26/8.59	   A^2 -> H(U1(d, d), U1(c, c))
26.26/8.59	   A^2 -> H(U1(d, d), f(e))
26.26/8.59	   A^2 -> H(U1(d, d), f(k))
26.26/8.59	   A^2 -> H(U1(d, d), U1(d, d))
26.26/8.59	   A^2 -> H(f(d), U1(e, b))
26.26/8.59	   A^2 -> H(f(d), U1(k, b))
26.26/8.59	   A^2 -> H(f(d), U1(c, d))
26.26/8.59	   A^2 -> H(f(d), U1(d, c))
26.26/8.59	   A^2 -> H(f(d), U1(b, e))
26.26/8.59	   A^2 -> H(f(d), U1(b, k))
26.26/8.59	   A^2 -> H(f(d), U1(e, c))
26.26/8.59	   A^2 -> H(f(d), U1(k, c))
26.26/8.59	   A^2 -> H(f(d), U1(c, e))
26.26/8.59	   A^2 -> H(f(d), U1(c, k))
26.26/8.59	   A^2 -> H(f(d), U1(e, e))
26.26/8.59	   A^2 -> H(f(d), U1(k, k))
26.26/8.59	   A^2 -> H(f(a), b)
26.26/8.59	   A^2 -> H(f(a), U1(e, d))
26.26/8.59	   A^2 -> H(f(a), U1(d, e))
26.26/8.59	   A^2 -> H(f(c), U1(e, c))
26.26/8.59	   A^2 -> H(f(c), U1(k, c))
26.26/8.59	   A^2 -> H(f(c), U1(c, e))
26.26/8.59	   A^2 -> H(f(c), U1(c, k))
26.26/8.59	   A^2 -> H(f(a), c)
26.26/8.59	   A^2 -> H(f(a), U1(e, k))
26.26/8.59	   A^2 -> H(f(a), U1(k, e))
26.26/8.59	   A^2 -> H(f(c), U1(e, e))
26.26/8.59	   A^2 -> H(f(a), e)
26.26/8.59	   A^2 -> H(f(d), U1(k, d))
26.26/8.59	   A^2 -> H(f(d), U1(d, k))
26.26/8.59	   A^2 -> H(f(a), U1(k, k))
26.26/8.59	   A^2 -> H(d, f(b))
26.26/8.59	   A^2 -> H(a, U1(b, b))
26.26/8.59	   A^2 -> H(a, f(c))
26.26/8.59	   A^2 -> H(a, f(d))
26.26/8.59	   A^2 -> H(U1(e, d), U1(b, b))
26.26/8.59	   A^2 -> H(U1(e, d), f(c))
26.26/8.59	   A^2 -> H(U1(e, d), f(d))
26.26/8.59	   A^2 -> H(U1(e, a), U1(c, b))
26.26/8.59	   A^2 -> H(U1(e, a), U1(d, b))
26.26/8.59	   A^2 -> H(U1(e, a), U1(b, c))
26.26/8.59	   A^2 -> H(U1(e, a), U1(b, d))
26.26/8.59	   A^2 -> H(U1(e, a), U1(c, c))
26.26/8.59	   A^2 -> H(U1(e, a), f(e))
26.26/8.59	   A^2 -> H(U1(e, a), f(k))
26.26/8.59	   A^2 -> H(U1(e, a), U1(d, d))
26.26/8.59	   A^2 -> H(U1(k, a), U1(c, b))
26.26/8.59	   A^2 -> H(U1(k, a), U1(d, b))
26.26/8.59	   A^2 -> H(U1(k, a), U1(b, c))
26.26/8.59	   A^2 -> H(U1(k, a), U1(b, d))
26.26/8.59	   A^2 -> H(U1(k, a), U1(c, c))
26.26/8.59	   A^2 -> H(U1(k, a), f(e))
26.26/8.59	   A^2 -> H(U1(k, a), f(k))
26.26/8.59	   A^2 -> H(U1(k, a), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, d), U1(c, b))
26.26/8.59	   A^2 -> H(U1(c, d), U1(d, b))
26.26/8.59	   A^2 -> H(U1(c, d), U1(b, c))
26.26/8.59	   A^2 -> H(U1(c, d), U1(b, d))
26.26/8.59	   A^2 -> H(U1(c, d), U1(c, c))
26.26/8.59	   A^2 -> H(U1(c, d), f(e))
26.26/8.59	   A^2 -> H(U1(c, d), f(k))
26.26/8.59	   A^2 -> H(U1(c, d), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, a), U1(e, b))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, b))
26.26/8.59	   A^2 -> H(U1(c, a), U1(c, d))
26.26/8.59	   A^2 -> H(U1(c, a), U1(d, c))
26.26/8.59	   A^2 -> H(U1(c, a), U1(b, e))
26.26/8.59	   A^2 -> H(U1(c, a), U1(b, k))
26.26/8.59	   A^2 -> H(U1(c, a), U1(e, c))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, c))
26.26/8.59	   A^2 -> H(U1(c, a), U1(c, e))
26.26/8.59	   A^2 -> H(U1(c, a), U1(c, k))
26.26/8.59	   A^2 -> H(U1(c, a), U1(e, e))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, k))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, d))
26.26/8.59	   A^2 -> H(U1(c, a), U1(d, k))
26.26/8.59	   A^2 -> H(U1(d, e), U1(b, b))
26.26/8.59	   A^2 -> H(U1(d, e), f(c))
26.26/8.59	   A^2 -> H(U1(d, e), f(d))
26.26/8.59	   A^2 -> H(U1(d, c), U1(c, b))
26.26/8.59	   A^2 -> H(U1(d, c), U1(d, b))
26.26/8.59	   A^2 -> H(U1(d, c), U1(b, c))
26.26/8.59	   A^2 -> H(U1(d, c), U1(b, d))
26.26/8.59	   A^2 -> H(U1(d, c), U1(c, c))
26.26/8.59	   A^2 -> H(U1(d, c), f(e))
26.26/8.59	   A^2 -> H(U1(d, c), f(k))
26.26/8.59	   A^2 -> H(U1(d, c), U1(d, d))
26.26/8.59	   A^2 -> H(U1(d, a), U1(e, b))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, b))
26.26/8.59	   A^2 -> H(U1(d, a), U1(c, d))
26.26/8.59	   A^2 -> H(U1(d, a), U1(d, c))
26.26/8.59	   A^2 -> H(U1(d, a), U1(b, e))
26.26/8.59	   A^2 -> H(U1(d, a), U1(b, k))
26.26/8.59	   A^2 -> H(U1(d, a), U1(e, c))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, c))
26.26/8.59	   A^2 -> H(U1(d, a), U1(c, e))
26.26/8.59	   A^2 -> H(U1(d, a), U1(c, k))
26.26/8.59	   A^2 -> H(U1(d, a), U1(e, e))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, k))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, d))
26.26/8.59	   A^2 -> H(U1(d, a), U1(d, k))
26.26/8.59	   A^2 -> H(U1(a, e), U1(c, b))
26.26/8.59	   A^2 -> H(U1(a, e), U1(d, b))
26.26/8.59	   A^2 -> H(U1(a, e), U1(b, c))
26.26/8.59	   A^2 -> H(U1(a, e), U1(b, d))
26.26/8.59	   A^2 -> H(U1(a, e), U1(c, c))
26.26/8.59	   A^2 -> H(U1(a, e), f(e))
26.26/8.59	   A^2 -> H(U1(a, e), f(k))
26.26/8.59	   A^2 -> H(U1(a, e), U1(d, d))
26.26/8.59	   A^2 -> H(U1(a, k), U1(c, b))
26.26/8.59	   A^2 -> H(U1(a, k), U1(d, b))
26.26/8.59	   A^2 -> H(U1(a, k), U1(b, c))
26.26/8.59	   A^2 -> H(U1(a, k), U1(b, d))
26.26/8.59	   A^2 -> H(U1(a, k), U1(c, c))
26.26/8.59	   A^2 -> H(U1(a, k), f(e))
26.26/8.59	   A^2 -> H(U1(a, k), f(k))
26.26/8.59	   A^2 -> H(U1(a, k), U1(d, d))
26.26/8.59	   A^2 -> H(U1(a, c), U1(e, b))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, b))
26.26/8.59	   A^2 -> H(U1(a, c), U1(c, d))
26.26/8.59	   A^2 -> H(U1(a, c), U1(d, c))
26.26/8.59	   A^2 -> H(U1(a, c), U1(b, e))
26.26/8.59	   A^2 -> H(U1(a, c), U1(b, k))
26.26/8.59	   A^2 -> H(U1(a, c), U1(e, c))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, c))
26.26/8.59	   A^2 -> H(U1(a, c), U1(c, e))
26.26/8.59	   A^2 -> H(U1(a, c), U1(c, k))
26.26/8.59	   A^2 -> H(U1(a, c), U1(e, e))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, k))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, d))
26.26/8.59	   A^2 -> H(U1(a, c), U1(d, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(e, b))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, b))
26.26/8.59	   A^2 -> H(U1(a, d), U1(c, d))
26.26/8.59	   A^2 -> H(U1(a, d), U1(d, c))
26.26/8.59	   A^2 -> H(U1(a, d), U1(b, e))
26.26/8.59	   A^2 -> H(U1(a, d), U1(b, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(e, c))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, c))
26.26/8.59	   A^2 -> H(U1(a, d), U1(c, e))
26.26/8.59	   A^2 -> H(U1(a, d), U1(c, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(e, e))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, d))
26.26/8.59	   A^2 -> H(U1(a, d), U1(d, k))
26.26/8.59	   A^2 -> H(U1(a, a), b)
26.26/8.59	   A^2 -> H(U1(a, a), U1(e, d))
26.26/8.59	   A^2 -> H(U1(a, a), U1(d, e))
26.26/8.59	   A^2 -> H(U1(a, a), c)
26.26/8.59	   A^2 -> H(U1(a, a), U1(e, k))
26.26/8.59	   A^2 -> H(U1(a, a), U1(k, e))
26.26/8.59	   A^2 -> H(U1(a, a), e)
26.26/8.59	   A^2 -> H(U1(a, a), U1(k, k))
26.26/8.59	   A^2 -> H(k, f(b))
26.26/8.59	   A^2 -> H(c, U1(b, b))
26.26/8.59	   A^2 -> H(c, f(c))
26.26/8.59	   A^2 -> H(c, f(d))
26.26/8.59	   A^2 -> H(U1(e, k), U1(b, b))
26.26/8.59	   A^2 -> H(U1(e, k), f(c))
26.26/8.59	   A^2 -> H(U1(e, k), f(d))
26.26/8.59	   A^2 -> H(U1(e, c), U1(c, b))
26.26/8.59	   A^2 -> H(U1(e, c), U1(d, b))
26.26/8.59	   A^2 -> H(U1(e, c), U1(b, c))
26.26/8.59	   A^2 -> H(U1(e, c), U1(b, d))
26.26/8.59	   A^2 -> H(U1(e, c), U1(c, c))
26.26/8.59	   A^2 -> H(U1(e, c), f(e))
26.26/8.59	   A^2 -> H(U1(e, c), f(k))
26.26/8.59	   A^2 -> H(U1(e, c), U1(d, d))
26.26/8.59	   A^2 -> H(U1(k, e), U1(b, b))
26.26/8.59	   A^2 -> H(U1(k, e), f(c))
26.26/8.59	   A^2 -> H(U1(k, e), f(d))
26.26/8.59	   A^2 -> H(U1(k, c), U1(c, b))
26.26/8.59	   A^2 -> H(U1(k, c), U1(d, b))
26.26/8.59	   A^2 -> H(U1(k, c), U1(b, c))
26.26/8.59	   A^2 -> H(U1(k, c), U1(b, d))
26.26/8.59	   A^2 -> H(U1(k, c), U1(c, c))
26.26/8.59	   A^2 -> H(U1(k, c), f(e))
26.26/8.59	   A^2 -> H(U1(k, c), f(k))
26.26/8.59	   A^2 -> H(U1(k, c), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, e), U1(c, b))
26.26/8.59	   A^2 -> H(U1(c, e), U1(d, b))
26.26/8.59	   A^2 -> H(U1(c, e), U1(b, c))
26.26/8.59	   A^2 -> H(U1(c, e), U1(b, d))
26.26/8.59	   A^2 -> H(U1(c, e), U1(c, c))
26.26/8.59	   A^2 -> H(U1(c, e), f(e))
26.26/8.59	   A^2 -> H(U1(c, e), f(k))
26.26/8.59	   A^2 -> H(U1(c, e), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, k), U1(c, b))
26.26/8.59	   A^2 -> H(U1(c, k), U1(d, b))
26.26/8.59	   A^2 -> H(U1(c, k), U1(b, c))
26.26/8.59	   A^2 -> H(U1(c, k), U1(b, d))
26.26/8.59	   A^2 -> H(U1(c, k), U1(c, c))
26.26/8.59	   A^2 -> H(U1(c, k), f(e))
26.26/8.59	   A^2 -> H(U1(c, k), f(k))
26.26/8.59	   A^2 -> H(U1(c, k), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(e, b))
26.26/8.59	   A^2 -> H(U1(c, c), U1(k, b))
26.26/8.59	   A^2 -> H(U1(c, c), U1(c, d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(d, c))
26.26/8.59	   A^2 -> H(U1(c, c), U1(b, e))
26.26/8.59	   A^2 -> H(U1(c, c), U1(b, k))
26.26/8.59	   A^2 -> H(U1(c, c), U1(e, e))
26.26/8.59	   A^2 -> H(U1(c, c), U1(k, k))
26.26/8.59	   A^2 -> H(U1(c, c), U1(k, d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(d, k))
26.26/8.59	   A^2 -> H(e, U1(b, b))
26.26/8.59	   A^2 -> H(e, f(c))
26.26/8.59	   A^2 -> H(e, f(d))
26.26/8.59	   A^2 -> H(U1(e, e), U1(c, b))
26.26/8.59	   A^2 -> H(U1(e, e), U1(d, b))
26.26/8.59	   A^2 -> H(U1(e, e), U1(b, c))
26.26/8.59	   A^2 -> H(U1(e, e), U1(b, d))
26.26/8.59	   A^2 -> H(U1(e, e), U1(c, c))
26.26/8.59	   A^2 -> H(U1(e, e), f(e))
26.26/8.59	   A^2 -> H(U1(e, e), f(k))
26.26/8.59	   A^2 -> H(U1(e, e), U1(d, d))
26.26/8.59	   A^2 -> H(f(e), U1(e, b))
26.26/8.59	   A^2 -> H(f(e), U1(k, b))
26.26/8.59	   A^2 -> H(f(e), U1(c, d))
26.26/8.59	   A^2 -> H(f(e), U1(d, c))
26.26/8.59	   A^2 -> H(f(e), U1(b, e))
26.26/8.59	   A^2 -> H(f(e), U1(b, k))
26.26/8.59	   A^2 -> H(f(e), U1(e, c))
26.26/8.59	   A^2 -> H(f(e), U1(k, c))
26.26/8.59	   A^2 -> H(f(e), U1(c, e))
26.26/8.59	   A^2 -> H(f(e), U1(c, k))
26.26/8.59	   A^2 -> H(f(e), U1(k, k))
26.26/8.59	   A^2 -> H(f(e), U1(k, d))
26.26/8.59	   A^2 -> H(f(e), U1(d, k))
26.26/8.59	   A^2 -> H(U1(k, k), U1(c, b))
26.26/8.59	   A^2 -> H(U1(k, k), U1(d, b))
26.26/8.59	   A^2 -> H(U1(k, k), U1(b, c))
26.26/8.59	   A^2 -> H(U1(k, k), U1(b, d))
26.26/8.59	
26.26/8.59	The TRS R consists of the following rules:
26.26/8.59	
26.26/8.59	   f(x) -> U1(x, x)
26.26/8.59	   U1(e, x) -> x
26.26/8.59	   a -> c
26.26/8.59	   a -> d
26.26/8.59	   b -> c
26.26/8.59	   b -> d
26.26/8.59	   d -> k
26.26/8.59	   c -> e
26.26/8.59	   c -> k
26.26/8.59	
26.26/8.59	Q is empty.
26.26/8.59	We have to consider all minimal (P,Q,R)-chains.
26.26/8.59	----------------------------------------
26.26/8.59	
26.26/8.59	(423) TransformationProof (EQUIVALENT)
26.26/8.59	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), f(c)) at position [] we obtained the following new rules [LPAR04]:
26.26/8.59	
26.26/8.59	   (A^2 -> H(U1(k, k), U1(c, c)),A^2 -> H(U1(k, k), U1(c, c)))
26.26/8.59	   (A^2 -> H(U1(k, k), f(e)),A^2 -> H(U1(k, k), f(e)))
26.26/8.59	   (A^2 -> H(U1(k, k), f(k)),A^2 -> H(U1(k, k), f(k)))
26.26/8.59	
26.26/8.59	
26.26/8.59	----------------------------------------
26.26/8.59	
26.26/8.59	(424)
26.26/8.59	Obligation:
26.26/8.59	Q DP problem:
26.26/8.59	The TRS P consists of the following rules:
26.26/8.59	
26.26/8.59	   H(x, x) -> G(x, x, f(k))
26.26/8.59	   G(d, x, x) -> A^2
26.26/8.59	   A^2 -> H(f(c), f(c))
26.26/8.59	   A^2 -> H(f(d), f(d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(c, c))
26.26/8.59	   A^2 -> H(f(e), f(e))
26.26/8.59	   A^2 -> H(U1(k, k), f(d))
26.26/8.59	   A^2 -> H(f(k), U1(c, b))
26.26/8.59	   A^2 -> H(f(k), U1(d, b))
26.26/8.59	   A^2 -> H(f(k), U1(b, c))
26.26/8.59	   A^2 -> H(f(k), U1(b, d))
26.26/8.59	   A^2 -> H(f(k), U1(c, c))
26.26/8.59	   A^2 -> H(f(k), f(e))
26.26/8.59	   A^2 -> H(f(k), f(k))
26.26/8.59	   A^2 -> H(f(k), U1(d, d))
26.26/8.59	   A^2 -> H(f(c), U1(e, b))
26.26/8.59	   A^2 -> H(f(c), U1(k, b))
26.26/8.59	   A^2 -> H(f(c), U1(c, d))
26.26/8.59	   A^2 -> H(f(c), U1(d, c))
26.26/8.59	   A^2 -> H(f(c), U1(b, e))
26.26/8.59	   A^2 -> H(f(c), U1(b, k))
26.26/8.59	   A^2 -> H(f(c), U1(k, d))
26.26/8.59	   A^2 -> H(f(c), U1(d, k))
26.26/8.59	   A^2 -> H(f(c), U1(k, k))
26.26/8.59	   A^2 -> H(U1(k, k), f(b))
26.26/8.59	   A^2 -> H(U1(k, d), U1(b, b))
26.26/8.59	   A^2 -> H(U1(k, d), f(c))
26.26/8.59	   A^2 -> H(U1(k, d), f(d))
26.26/8.59	   A^2 -> H(U1(d, k), U1(b, b))
26.26/8.59	   A^2 -> H(U1(d, k), f(c))
26.26/8.59	   A^2 -> H(U1(d, k), f(d))
26.26/8.59	   A^2 -> H(U1(d, d), U1(c, b))
26.26/8.59	   A^2 -> H(U1(d, d), U1(d, b))
26.26/8.59	   A^2 -> H(U1(d, d), U1(b, c))
26.26/8.59	   A^2 -> H(U1(d, d), U1(b, d))
26.26/8.59	   A^2 -> H(U1(d, d), U1(c, c))
26.26/8.59	   A^2 -> H(U1(d, d), f(e))
26.26/8.59	   A^2 -> H(U1(d, d), f(k))
26.26/8.59	   A^2 -> H(U1(d, d), U1(d, d))
26.26/8.59	   A^2 -> H(f(d), U1(e, b))
26.26/8.59	   A^2 -> H(f(d), U1(k, b))
26.26/8.59	   A^2 -> H(f(d), U1(c, d))
26.26/8.59	   A^2 -> H(f(d), U1(d, c))
26.26/8.59	   A^2 -> H(f(d), U1(b, e))
26.26/8.59	   A^2 -> H(f(d), U1(b, k))
26.26/8.59	   A^2 -> H(f(d), U1(e, c))
26.26/8.59	   A^2 -> H(f(d), U1(k, c))
26.26/8.59	   A^2 -> H(f(d), U1(c, e))
26.26/8.59	   A^2 -> H(f(d), U1(c, k))
26.26/8.59	   A^2 -> H(f(d), U1(e, e))
26.26/8.59	   A^2 -> H(f(d), U1(k, k))
26.26/8.59	   A^2 -> H(f(a), b)
26.26/8.59	   A^2 -> H(f(a), U1(e, d))
26.26/8.59	   A^2 -> H(f(a), U1(d, e))
26.26/8.59	   A^2 -> H(f(c), U1(e, c))
26.26/8.59	   A^2 -> H(f(c), U1(k, c))
26.26/8.59	   A^2 -> H(f(c), U1(c, e))
26.26/8.59	   A^2 -> H(f(c), U1(c, k))
26.26/8.59	   A^2 -> H(f(a), c)
26.26/8.59	   A^2 -> H(f(a), U1(e, k))
26.26/8.59	   A^2 -> H(f(a), U1(k, e))
26.26/8.59	   A^2 -> H(f(c), U1(e, e))
26.26/8.59	   A^2 -> H(f(a), e)
26.26/8.59	   A^2 -> H(f(d), U1(k, d))
26.26/8.59	   A^2 -> H(f(d), U1(d, k))
26.26/8.59	   A^2 -> H(f(a), U1(k, k))
26.26/8.59	   A^2 -> H(d, f(b))
26.26/8.59	   A^2 -> H(a, U1(b, b))
26.26/8.59	   A^2 -> H(a, f(c))
26.26/8.59	   A^2 -> H(a, f(d))
26.26/8.59	   A^2 -> H(U1(e, d), U1(b, b))
26.26/8.59	   A^2 -> H(U1(e, d), f(c))
26.26/8.59	   A^2 -> H(U1(e, d), f(d))
26.26/8.59	   A^2 -> H(U1(e, a), U1(c, b))
26.26/8.59	   A^2 -> H(U1(e, a), U1(d, b))
26.26/8.59	   A^2 -> H(U1(e, a), U1(b, c))
26.26/8.59	   A^2 -> H(U1(e, a), U1(b, d))
26.26/8.59	   A^2 -> H(U1(e, a), U1(c, c))
26.26/8.59	   A^2 -> H(U1(e, a), f(e))
26.26/8.59	   A^2 -> H(U1(e, a), f(k))
26.26/8.59	   A^2 -> H(U1(e, a), U1(d, d))
26.26/8.59	   A^2 -> H(U1(k, a), U1(c, b))
26.26/8.59	   A^2 -> H(U1(k, a), U1(d, b))
26.26/8.59	   A^2 -> H(U1(k, a), U1(b, c))
26.26/8.59	   A^2 -> H(U1(k, a), U1(b, d))
26.26/8.59	   A^2 -> H(U1(k, a), U1(c, c))
26.26/8.59	   A^2 -> H(U1(k, a), f(e))
26.26/8.59	   A^2 -> H(U1(k, a), f(k))
26.26/8.59	   A^2 -> H(U1(k, a), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, d), U1(c, b))
26.26/8.59	   A^2 -> H(U1(c, d), U1(d, b))
26.26/8.59	   A^2 -> H(U1(c, d), U1(b, c))
26.26/8.59	   A^2 -> H(U1(c, d), U1(b, d))
26.26/8.59	   A^2 -> H(U1(c, d), U1(c, c))
26.26/8.59	   A^2 -> H(U1(c, d), f(e))
26.26/8.59	   A^2 -> H(U1(c, d), f(k))
26.26/8.59	   A^2 -> H(U1(c, d), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, a), U1(e, b))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, b))
26.26/8.59	   A^2 -> H(U1(c, a), U1(c, d))
26.26/8.59	   A^2 -> H(U1(c, a), U1(d, c))
26.26/8.59	   A^2 -> H(U1(c, a), U1(b, e))
26.26/8.59	   A^2 -> H(U1(c, a), U1(b, k))
26.26/8.59	   A^2 -> H(U1(c, a), U1(e, c))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, c))
26.26/8.59	   A^2 -> H(U1(c, a), U1(c, e))
26.26/8.59	   A^2 -> H(U1(c, a), U1(c, k))
26.26/8.59	   A^2 -> H(U1(c, a), U1(e, e))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, k))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, d))
26.26/8.59	   A^2 -> H(U1(c, a), U1(d, k))
26.26/8.59	   A^2 -> H(U1(d, e), U1(b, b))
26.26/8.59	   A^2 -> H(U1(d, e), f(c))
26.26/8.59	   A^2 -> H(U1(d, e), f(d))
26.26/8.59	   A^2 -> H(U1(d, c), U1(c, b))
26.26/8.59	   A^2 -> H(U1(d, c), U1(d, b))
26.26/8.59	   A^2 -> H(U1(d, c), U1(b, c))
26.26/8.59	   A^2 -> H(U1(d, c), U1(b, d))
26.26/8.59	   A^2 -> H(U1(d, c), U1(c, c))
26.26/8.59	   A^2 -> H(U1(d, c), f(e))
26.26/8.59	   A^2 -> H(U1(d, c), f(k))
26.26/8.59	   A^2 -> H(U1(d, c), U1(d, d))
26.26/8.59	   A^2 -> H(U1(d, a), U1(e, b))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, b))
26.26/8.59	   A^2 -> H(U1(d, a), U1(c, d))
26.26/8.59	   A^2 -> H(U1(d, a), U1(d, c))
26.26/8.59	   A^2 -> H(U1(d, a), U1(b, e))
26.26/8.59	   A^2 -> H(U1(d, a), U1(b, k))
26.26/8.59	   A^2 -> H(U1(d, a), U1(e, c))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, c))
26.26/8.59	   A^2 -> H(U1(d, a), U1(c, e))
26.26/8.59	   A^2 -> H(U1(d, a), U1(c, k))
26.26/8.59	   A^2 -> H(U1(d, a), U1(e, e))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, k))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, d))
26.26/8.59	   A^2 -> H(U1(d, a), U1(d, k))
26.26/8.59	   A^2 -> H(U1(a, e), U1(c, b))
26.26/8.59	   A^2 -> H(U1(a, e), U1(d, b))
26.26/8.59	   A^2 -> H(U1(a, e), U1(b, c))
26.26/8.59	   A^2 -> H(U1(a, e), U1(b, d))
26.26/8.59	   A^2 -> H(U1(a, e), U1(c, c))
26.26/8.59	   A^2 -> H(U1(a, e), f(e))
26.26/8.59	   A^2 -> H(U1(a, e), f(k))
26.26/8.59	   A^2 -> H(U1(a, e), U1(d, d))
26.26/8.59	   A^2 -> H(U1(a, k), U1(c, b))
26.26/8.59	   A^2 -> H(U1(a, k), U1(d, b))
26.26/8.59	   A^2 -> H(U1(a, k), U1(b, c))
26.26/8.59	   A^2 -> H(U1(a, k), U1(b, d))
26.26/8.59	   A^2 -> H(U1(a, k), U1(c, c))
26.26/8.59	   A^2 -> H(U1(a, k), f(e))
26.26/8.59	   A^2 -> H(U1(a, k), f(k))
26.26/8.59	   A^2 -> H(U1(a, k), U1(d, d))
26.26/8.59	   A^2 -> H(U1(a, c), U1(e, b))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, b))
26.26/8.59	   A^2 -> H(U1(a, c), U1(c, d))
26.26/8.59	   A^2 -> H(U1(a, c), U1(d, c))
26.26/8.59	   A^2 -> H(U1(a, c), U1(b, e))
26.26/8.59	   A^2 -> H(U1(a, c), U1(b, k))
26.26/8.59	   A^2 -> H(U1(a, c), U1(e, c))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, c))
26.26/8.59	   A^2 -> H(U1(a, c), U1(c, e))
26.26/8.59	   A^2 -> H(U1(a, c), U1(c, k))
26.26/8.59	   A^2 -> H(U1(a, c), U1(e, e))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, k))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, d))
26.26/8.59	   A^2 -> H(U1(a, c), U1(d, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(e, b))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, b))
26.26/8.59	   A^2 -> H(U1(a, d), U1(c, d))
26.26/8.59	   A^2 -> H(U1(a, d), U1(d, c))
26.26/8.59	   A^2 -> H(U1(a, d), U1(b, e))
26.26/8.59	   A^2 -> H(U1(a, d), U1(b, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(e, c))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, c))
26.26/8.59	   A^2 -> H(U1(a, d), U1(c, e))
26.26/8.59	   A^2 -> H(U1(a, d), U1(c, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(e, e))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, d))
26.26/8.59	   A^2 -> H(U1(a, d), U1(d, k))
26.26/8.59	   A^2 -> H(U1(a, a), b)
26.26/8.59	   A^2 -> H(U1(a, a), U1(e, d))
26.26/8.59	   A^2 -> H(U1(a, a), U1(d, e))
26.26/8.59	   A^2 -> H(U1(a, a), c)
26.26/8.59	   A^2 -> H(U1(a, a), U1(e, k))
26.26/8.59	   A^2 -> H(U1(a, a), U1(k, e))
26.26/8.59	   A^2 -> H(U1(a, a), e)
26.26/8.59	   A^2 -> H(U1(a, a), U1(k, k))
26.26/8.59	   A^2 -> H(k, f(b))
26.26/8.59	   A^2 -> H(c, U1(b, b))
26.26/8.59	   A^2 -> H(c, f(c))
26.26/8.59	   A^2 -> H(c, f(d))
26.26/8.59	   A^2 -> H(U1(e, k), U1(b, b))
26.26/8.59	   A^2 -> H(U1(e, k), f(c))
26.26/8.59	   A^2 -> H(U1(e, k), f(d))
26.26/8.59	   A^2 -> H(U1(e, c), U1(c, b))
26.26/8.59	   A^2 -> H(U1(e, c), U1(d, b))
26.26/8.59	   A^2 -> H(U1(e, c), U1(b, c))
26.26/8.59	   A^2 -> H(U1(e, c), U1(b, d))
26.26/8.59	   A^2 -> H(U1(e, c), U1(c, c))
26.26/8.59	   A^2 -> H(U1(e, c), f(e))
26.26/8.59	   A^2 -> H(U1(e, c), f(k))
26.26/8.59	   A^2 -> H(U1(e, c), U1(d, d))
26.26/8.59	   A^2 -> H(U1(k, e), U1(b, b))
26.26/8.59	   A^2 -> H(U1(k, e), f(c))
26.26/8.59	   A^2 -> H(U1(k, e), f(d))
26.26/8.59	   A^2 -> H(U1(k, c), U1(c, b))
26.26/8.59	   A^2 -> H(U1(k, c), U1(d, b))
26.26/8.59	   A^2 -> H(U1(k, c), U1(b, c))
26.26/8.59	   A^2 -> H(U1(k, c), U1(b, d))
26.26/8.59	   A^2 -> H(U1(k, c), U1(c, c))
26.26/8.59	   A^2 -> H(U1(k, c), f(e))
26.26/8.59	   A^2 -> H(U1(k, c), f(k))
26.26/8.59	   A^2 -> H(U1(k, c), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, e), U1(c, b))
26.26/8.59	   A^2 -> H(U1(c, e), U1(d, b))
26.26/8.59	   A^2 -> H(U1(c, e), U1(b, c))
26.26/8.59	   A^2 -> H(U1(c, e), U1(b, d))
26.26/8.59	   A^2 -> H(U1(c, e), U1(c, c))
26.26/8.59	   A^2 -> H(U1(c, e), f(e))
26.26/8.59	   A^2 -> H(U1(c, e), f(k))
26.26/8.59	   A^2 -> H(U1(c, e), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, k), U1(c, b))
26.26/8.59	   A^2 -> H(U1(c, k), U1(d, b))
26.26/8.59	   A^2 -> H(U1(c, k), U1(b, c))
26.26/8.59	   A^2 -> H(U1(c, k), U1(b, d))
26.26/8.59	   A^2 -> H(U1(c, k), U1(c, c))
26.26/8.59	   A^2 -> H(U1(c, k), f(e))
26.26/8.59	   A^2 -> H(U1(c, k), f(k))
26.26/8.59	   A^2 -> H(U1(c, k), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(e, b))
26.26/8.59	   A^2 -> H(U1(c, c), U1(k, b))
26.26/8.59	   A^2 -> H(U1(c, c), U1(c, d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(d, c))
26.26/8.59	   A^2 -> H(U1(c, c), U1(b, e))
26.26/8.59	   A^2 -> H(U1(c, c), U1(b, k))
26.26/8.59	   A^2 -> H(U1(c, c), U1(e, e))
26.26/8.59	   A^2 -> H(U1(c, c), U1(k, k))
26.26/8.59	   A^2 -> H(U1(c, c), U1(k, d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(d, k))
26.26/8.59	   A^2 -> H(e, U1(b, b))
26.26/8.59	   A^2 -> H(e, f(c))
26.26/8.59	   A^2 -> H(e, f(d))
26.26/8.59	   A^2 -> H(U1(e, e), U1(c, b))
26.26/8.59	   A^2 -> H(U1(e, e), U1(d, b))
26.26/8.59	   A^2 -> H(U1(e, e), U1(b, c))
26.26/8.59	   A^2 -> H(U1(e, e), U1(b, d))
26.26/8.59	   A^2 -> H(U1(e, e), U1(c, c))
26.26/8.59	   A^2 -> H(U1(e, e), f(e))
26.26/8.59	   A^2 -> H(U1(e, e), f(k))
26.26/8.59	   A^2 -> H(U1(e, e), U1(d, d))
26.26/8.59	   A^2 -> H(f(e), U1(e, b))
26.26/8.59	   A^2 -> H(f(e), U1(k, b))
26.26/8.59	   A^2 -> H(f(e), U1(c, d))
26.26/8.59	   A^2 -> H(f(e), U1(d, c))
26.26/8.59	   A^2 -> H(f(e), U1(b, e))
26.26/8.59	   A^2 -> H(f(e), U1(b, k))
26.26/8.59	   A^2 -> H(f(e), U1(e, c))
26.26/8.59	   A^2 -> H(f(e), U1(k, c))
26.26/8.59	   A^2 -> H(f(e), U1(c, e))
26.26/8.59	   A^2 -> H(f(e), U1(c, k))
26.26/8.59	   A^2 -> H(f(e), U1(k, k))
26.26/8.59	   A^2 -> H(f(e), U1(k, d))
26.26/8.59	   A^2 -> H(f(e), U1(d, k))
26.26/8.59	   A^2 -> H(U1(k, k), U1(c, b))
26.26/8.59	   A^2 -> H(U1(k, k), U1(d, b))
26.26/8.59	   A^2 -> H(U1(k, k), U1(b, c))
26.26/8.59	   A^2 -> H(U1(k, k), U1(b, d))
26.26/8.59	   A^2 -> H(U1(k, k), U1(c, c))
26.26/8.59	   A^2 -> H(U1(k, k), f(e))
26.26/8.59	   A^2 -> H(U1(k, k), f(k))
26.26/8.59	
26.26/8.59	The TRS R consists of the following rules:
26.26/8.59	
26.26/8.59	   f(x) -> U1(x, x)
26.26/8.59	   U1(e, x) -> x
26.26/8.59	   a -> c
26.26/8.59	   a -> d
26.26/8.59	   b -> c
26.26/8.59	   b -> d
26.26/8.59	   d -> k
26.26/8.59	   c -> e
26.26/8.59	   c -> k
26.26/8.59	
26.26/8.59	Q is empty.
26.26/8.59	We have to consider all minimal (P,Q,R)-chains.
26.26/8.59	----------------------------------------
26.26/8.59	
26.26/8.59	(425) TransformationProof (EQUIVALENT)
26.26/8.59	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), f(d)) at position [] we obtained the following new rules [LPAR04]:
26.26/8.59	
26.26/8.59	   (A^2 -> H(U1(k, k), U1(d, d)),A^2 -> H(U1(k, k), U1(d, d)))
26.26/8.59	   (A^2 -> H(U1(k, k), f(k)),A^2 -> H(U1(k, k), f(k)))
26.26/8.59	
26.26/8.59	
26.26/8.59	----------------------------------------
26.26/8.59	
26.26/8.59	(426)
26.26/8.59	Obligation:
26.26/8.59	Q DP problem:
26.26/8.59	The TRS P consists of the following rules:
26.26/8.59	
26.26/8.59	   H(x, x) -> G(x, x, f(k))
26.26/8.59	   G(d, x, x) -> A^2
26.26/8.59	   A^2 -> H(f(c), f(c))
26.26/8.59	   A^2 -> H(f(d), f(d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(c, c))
26.26/8.59	   A^2 -> H(f(e), f(e))
26.26/8.59	   A^2 -> H(f(k), U1(c, b))
26.26/8.59	   A^2 -> H(f(k), U1(d, b))
26.26/8.59	   A^2 -> H(f(k), U1(b, c))
26.26/8.59	   A^2 -> H(f(k), U1(b, d))
26.26/8.59	   A^2 -> H(f(k), U1(c, c))
26.26/8.59	   A^2 -> H(f(k), f(e))
26.26/8.59	   A^2 -> H(f(k), f(k))
26.26/8.59	   A^2 -> H(f(k), U1(d, d))
26.26/8.59	   A^2 -> H(f(c), U1(e, b))
26.26/8.59	   A^2 -> H(f(c), U1(k, b))
26.26/8.59	   A^2 -> H(f(c), U1(c, d))
26.26/8.59	   A^2 -> H(f(c), U1(d, c))
26.26/8.59	   A^2 -> H(f(c), U1(b, e))
26.26/8.59	   A^2 -> H(f(c), U1(b, k))
26.26/8.59	   A^2 -> H(f(c), U1(k, d))
26.26/8.59	   A^2 -> H(f(c), U1(d, k))
26.26/8.59	   A^2 -> H(f(c), U1(k, k))
26.26/8.59	   A^2 -> H(U1(k, k), f(b))
26.26/8.59	   A^2 -> H(U1(k, d), U1(b, b))
26.26/8.59	   A^2 -> H(U1(k, d), f(c))
26.26/8.59	   A^2 -> H(U1(k, d), f(d))
26.26/8.59	   A^2 -> H(U1(d, k), U1(b, b))
26.26/8.59	   A^2 -> H(U1(d, k), f(c))
26.26/8.59	   A^2 -> H(U1(d, k), f(d))
26.26/8.59	   A^2 -> H(U1(d, d), U1(c, b))
26.26/8.59	   A^2 -> H(U1(d, d), U1(d, b))
26.26/8.59	   A^2 -> H(U1(d, d), U1(b, c))
26.26/8.59	   A^2 -> H(U1(d, d), U1(b, d))
26.26/8.59	   A^2 -> H(U1(d, d), U1(c, c))
26.26/8.59	   A^2 -> H(U1(d, d), f(e))
26.26/8.59	   A^2 -> H(U1(d, d), f(k))
26.26/8.59	   A^2 -> H(U1(d, d), U1(d, d))
26.26/8.59	   A^2 -> H(f(d), U1(e, b))
26.26/8.59	   A^2 -> H(f(d), U1(k, b))
26.26/8.59	   A^2 -> H(f(d), U1(c, d))
26.26/8.59	   A^2 -> H(f(d), U1(d, c))
26.26/8.59	   A^2 -> H(f(d), U1(b, e))
26.26/8.59	   A^2 -> H(f(d), U1(b, k))
26.26/8.59	   A^2 -> H(f(d), U1(e, c))
26.26/8.59	   A^2 -> H(f(d), U1(k, c))
26.26/8.59	   A^2 -> H(f(d), U1(c, e))
26.26/8.59	   A^2 -> H(f(d), U1(c, k))
26.26/8.59	   A^2 -> H(f(d), U1(e, e))
26.26/8.59	   A^2 -> H(f(d), U1(k, k))
26.26/8.59	   A^2 -> H(f(a), b)
26.26/8.59	   A^2 -> H(f(a), U1(e, d))
26.26/8.59	   A^2 -> H(f(a), U1(d, e))
26.26/8.59	   A^2 -> H(f(c), U1(e, c))
26.26/8.59	   A^2 -> H(f(c), U1(k, c))
26.26/8.59	   A^2 -> H(f(c), U1(c, e))
26.26/8.59	   A^2 -> H(f(c), U1(c, k))
26.26/8.59	   A^2 -> H(f(a), c)
26.26/8.59	   A^2 -> H(f(a), U1(e, k))
26.26/8.59	   A^2 -> H(f(a), U1(k, e))
26.26/8.59	   A^2 -> H(f(c), U1(e, e))
26.26/8.59	   A^2 -> H(f(a), e)
26.26/8.59	   A^2 -> H(f(d), U1(k, d))
26.26/8.59	   A^2 -> H(f(d), U1(d, k))
26.26/8.59	   A^2 -> H(f(a), U1(k, k))
26.26/8.59	   A^2 -> H(d, f(b))
26.26/8.59	   A^2 -> H(a, U1(b, b))
26.26/8.59	   A^2 -> H(a, f(c))
26.26/8.59	   A^2 -> H(a, f(d))
26.26/8.59	   A^2 -> H(U1(e, d), U1(b, b))
26.26/8.59	   A^2 -> H(U1(e, d), f(c))
26.26/8.59	   A^2 -> H(U1(e, d), f(d))
26.26/8.59	   A^2 -> H(U1(e, a), U1(c, b))
26.26/8.59	   A^2 -> H(U1(e, a), U1(d, b))
26.26/8.59	   A^2 -> H(U1(e, a), U1(b, c))
26.26/8.59	   A^2 -> H(U1(e, a), U1(b, d))
26.26/8.59	   A^2 -> H(U1(e, a), U1(c, c))
26.26/8.59	   A^2 -> H(U1(e, a), f(e))
26.26/8.59	   A^2 -> H(U1(e, a), f(k))
26.26/8.59	   A^2 -> H(U1(e, a), U1(d, d))
26.26/8.59	   A^2 -> H(U1(k, a), U1(c, b))
26.26/8.59	   A^2 -> H(U1(k, a), U1(d, b))
26.26/8.59	   A^2 -> H(U1(k, a), U1(b, c))
26.26/8.59	   A^2 -> H(U1(k, a), U1(b, d))
26.26/8.59	   A^2 -> H(U1(k, a), U1(c, c))
26.26/8.59	   A^2 -> H(U1(k, a), f(e))
26.26/8.59	   A^2 -> H(U1(k, a), f(k))
26.26/8.59	   A^2 -> H(U1(k, a), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, d), U1(c, b))
26.26/8.59	   A^2 -> H(U1(c, d), U1(d, b))
26.26/8.59	   A^2 -> H(U1(c, d), U1(b, c))
26.26/8.59	   A^2 -> H(U1(c, d), U1(b, d))
26.26/8.59	   A^2 -> H(U1(c, d), U1(c, c))
26.26/8.59	   A^2 -> H(U1(c, d), f(e))
26.26/8.59	   A^2 -> H(U1(c, d), f(k))
26.26/8.59	   A^2 -> H(U1(c, d), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, a), U1(e, b))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, b))
26.26/8.59	   A^2 -> H(U1(c, a), U1(c, d))
26.26/8.59	   A^2 -> H(U1(c, a), U1(d, c))
26.26/8.59	   A^2 -> H(U1(c, a), U1(b, e))
26.26/8.59	   A^2 -> H(U1(c, a), U1(b, k))
26.26/8.59	   A^2 -> H(U1(c, a), U1(e, c))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, c))
26.26/8.59	   A^2 -> H(U1(c, a), U1(c, e))
26.26/8.59	   A^2 -> H(U1(c, a), U1(c, k))
26.26/8.59	   A^2 -> H(U1(c, a), U1(e, e))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, k))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, d))
26.26/8.59	   A^2 -> H(U1(c, a), U1(d, k))
26.26/8.59	   A^2 -> H(U1(d, e), U1(b, b))
26.26/8.59	   A^2 -> H(U1(d, e), f(c))
26.26/8.59	   A^2 -> H(U1(d, e), f(d))
26.26/8.59	   A^2 -> H(U1(d, c), U1(c, b))
26.26/8.59	   A^2 -> H(U1(d, c), U1(d, b))
26.26/8.59	   A^2 -> H(U1(d, c), U1(b, c))
26.26/8.59	   A^2 -> H(U1(d, c), U1(b, d))
26.26/8.59	   A^2 -> H(U1(d, c), U1(c, c))
26.26/8.59	   A^2 -> H(U1(d, c), f(e))
26.26/8.59	   A^2 -> H(U1(d, c), f(k))
26.26/8.59	   A^2 -> H(U1(d, c), U1(d, d))
26.26/8.59	   A^2 -> H(U1(d, a), U1(e, b))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, b))
26.26/8.59	   A^2 -> H(U1(d, a), U1(c, d))
26.26/8.59	   A^2 -> H(U1(d, a), U1(d, c))
26.26/8.59	   A^2 -> H(U1(d, a), U1(b, e))
26.26/8.59	   A^2 -> H(U1(d, a), U1(b, k))
26.26/8.59	   A^2 -> H(U1(d, a), U1(e, c))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, c))
26.26/8.59	   A^2 -> H(U1(d, a), U1(c, e))
26.26/8.59	   A^2 -> H(U1(d, a), U1(c, k))
26.26/8.59	   A^2 -> H(U1(d, a), U1(e, e))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, k))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, d))
26.26/8.59	   A^2 -> H(U1(d, a), U1(d, k))
26.26/8.59	   A^2 -> H(U1(a, e), U1(c, b))
26.26/8.59	   A^2 -> H(U1(a, e), U1(d, b))
26.26/8.59	   A^2 -> H(U1(a, e), U1(b, c))
26.26/8.59	   A^2 -> H(U1(a, e), U1(b, d))
26.26/8.59	   A^2 -> H(U1(a, e), U1(c, c))
26.26/8.59	   A^2 -> H(U1(a, e), f(e))
26.26/8.59	   A^2 -> H(U1(a, e), f(k))
26.26/8.59	   A^2 -> H(U1(a, e), U1(d, d))
26.26/8.59	   A^2 -> H(U1(a, k), U1(c, b))
26.26/8.59	   A^2 -> H(U1(a, k), U1(d, b))
26.26/8.59	   A^2 -> H(U1(a, k), U1(b, c))
26.26/8.59	   A^2 -> H(U1(a, k), U1(b, d))
26.26/8.59	   A^2 -> H(U1(a, k), U1(c, c))
26.26/8.59	   A^2 -> H(U1(a, k), f(e))
26.26/8.59	   A^2 -> H(U1(a, k), f(k))
26.26/8.59	   A^2 -> H(U1(a, k), U1(d, d))
26.26/8.59	   A^2 -> H(U1(a, c), U1(e, b))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, b))
26.26/8.59	   A^2 -> H(U1(a, c), U1(c, d))
26.26/8.59	   A^2 -> H(U1(a, c), U1(d, c))
26.26/8.59	   A^2 -> H(U1(a, c), U1(b, e))
26.26/8.59	   A^2 -> H(U1(a, c), U1(b, k))
26.26/8.59	   A^2 -> H(U1(a, c), U1(e, c))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, c))
26.26/8.59	   A^2 -> H(U1(a, c), U1(c, e))
26.26/8.59	   A^2 -> H(U1(a, c), U1(c, k))
26.26/8.59	   A^2 -> H(U1(a, c), U1(e, e))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, k))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, d))
26.26/8.59	   A^2 -> H(U1(a, c), U1(d, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(e, b))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, b))
26.26/8.59	   A^2 -> H(U1(a, d), U1(c, d))
26.26/8.59	   A^2 -> H(U1(a, d), U1(d, c))
26.26/8.59	   A^2 -> H(U1(a, d), U1(b, e))
26.26/8.59	   A^2 -> H(U1(a, d), U1(b, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(e, c))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, c))
26.26/8.59	   A^2 -> H(U1(a, d), U1(c, e))
26.26/8.59	   A^2 -> H(U1(a, d), U1(c, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(e, e))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, d))
26.26/8.59	   A^2 -> H(U1(a, d), U1(d, k))
26.26/8.59	   A^2 -> H(U1(a, a), b)
26.26/8.59	   A^2 -> H(U1(a, a), U1(e, d))
26.26/8.59	   A^2 -> H(U1(a, a), U1(d, e))
26.26/8.59	   A^2 -> H(U1(a, a), c)
26.26/8.59	   A^2 -> H(U1(a, a), U1(e, k))
26.26/8.59	   A^2 -> H(U1(a, a), U1(k, e))
26.26/8.59	   A^2 -> H(U1(a, a), e)
26.26/8.59	   A^2 -> H(U1(a, a), U1(k, k))
26.26/8.59	   A^2 -> H(k, f(b))
26.26/8.59	   A^2 -> H(c, U1(b, b))
26.26/8.59	   A^2 -> H(c, f(c))
26.26/8.59	   A^2 -> H(c, f(d))
26.26/8.59	   A^2 -> H(U1(e, k), U1(b, b))
26.26/8.59	   A^2 -> H(U1(e, k), f(c))
26.26/8.59	   A^2 -> H(U1(e, k), f(d))
26.26/8.59	   A^2 -> H(U1(e, c), U1(c, b))
26.26/8.59	   A^2 -> H(U1(e, c), U1(d, b))
26.26/8.59	   A^2 -> H(U1(e, c), U1(b, c))
26.26/8.59	   A^2 -> H(U1(e, c), U1(b, d))
26.26/8.59	   A^2 -> H(U1(e, c), U1(c, c))
26.26/8.59	   A^2 -> H(U1(e, c), f(e))
26.26/8.59	   A^2 -> H(U1(e, c), f(k))
26.26/8.59	   A^2 -> H(U1(e, c), U1(d, d))
26.26/8.59	   A^2 -> H(U1(k, e), U1(b, b))
26.26/8.59	   A^2 -> H(U1(k, e), f(c))
26.26/8.59	   A^2 -> H(U1(k, e), f(d))
26.26/8.59	   A^2 -> H(U1(k, c), U1(c, b))
26.26/8.59	   A^2 -> H(U1(k, c), U1(d, b))
26.26/8.59	   A^2 -> H(U1(k, c), U1(b, c))
26.26/8.59	   A^2 -> H(U1(k, c), U1(b, d))
26.26/8.59	   A^2 -> H(U1(k, c), U1(c, c))
26.26/8.59	   A^2 -> H(U1(k, c), f(e))
26.26/8.59	   A^2 -> H(U1(k, c), f(k))
26.26/8.59	   A^2 -> H(U1(k, c), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, e), U1(c, b))
26.26/8.59	   A^2 -> H(U1(c, e), U1(d, b))
26.26/8.59	   A^2 -> H(U1(c, e), U1(b, c))
26.26/8.59	   A^2 -> H(U1(c, e), U1(b, d))
26.26/8.59	   A^2 -> H(U1(c, e), U1(c, c))
26.26/8.59	   A^2 -> H(U1(c, e), f(e))
26.26/8.59	   A^2 -> H(U1(c, e), f(k))
26.26/8.59	   A^2 -> H(U1(c, e), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, k), U1(c, b))
26.26/8.59	   A^2 -> H(U1(c, k), U1(d, b))
26.26/8.59	   A^2 -> H(U1(c, k), U1(b, c))
26.26/8.59	   A^2 -> H(U1(c, k), U1(b, d))
26.26/8.59	   A^2 -> H(U1(c, k), U1(c, c))
26.26/8.59	   A^2 -> H(U1(c, k), f(e))
26.26/8.59	   A^2 -> H(U1(c, k), f(k))
26.26/8.59	   A^2 -> H(U1(c, k), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(e, b))
26.26/8.59	   A^2 -> H(U1(c, c), U1(k, b))
26.26/8.59	   A^2 -> H(U1(c, c), U1(c, d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(d, c))
26.26/8.59	   A^2 -> H(U1(c, c), U1(b, e))
26.26/8.59	   A^2 -> H(U1(c, c), U1(b, k))
26.26/8.59	   A^2 -> H(U1(c, c), U1(e, e))
26.26/8.59	   A^2 -> H(U1(c, c), U1(k, k))
26.26/8.59	   A^2 -> H(U1(c, c), U1(k, d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(d, k))
26.26/8.59	   A^2 -> H(e, U1(b, b))
26.26/8.59	   A^2 -> H(e, f(c))
26.26/8.59	   A^2 -> H(e, f(d))
26.26/8.59	   A^2 -> H(U1(e, e), U1(c, b))
26.26/8.59	   A^2 -> H(U1(e, e), U1(d, b))
26.26/8.59	   A^2 -> H(U1(e, e), U1(b, c))
26.26/8.59	   A^2 -> H(U1(e, e), U1(b, d))
26.26/8.59	   A^2 -> H(U1(e, e), U1(c, c))
26.26/8.59	   A^2 -> H(U1(e, e), f(e))
26.26/8.59	   A^2 -> H(U1(e, e), f(k))
26.26/8.59	   A^2 -> H(U1(e, e), U1(d, d))
26.26/8.59	   A^2 -> H(f(e), U1(e, b))
26.26/8.59	   A^2 -> H(f(e), U1(k, b))
26.26/8.59	   A^2 -> H(f(e), U1(c, d))
26.26/8.59	   A^2 -> H(f(e), U1(d, c))
26.26/8.59	   A^2 -> H(f(e), U1(b, e))
26.26/8.59	   A^2 -> H(f(e), U1(b, k))
26.26/8.59	   A^2 -> H(f(e), U1(e, c))
26.26/8.59	   A^2 -> H(f(e), U1(k, c))
26.26/8.59	   A^2 -> H(f(e), U1(c, e))
26.26/8.59	   A^2 -> H(f(e), U1(c, k))
26.26/8.59	   A^2 -> H(f(e), U1(k, k))
26.26/8.59	   A^2 -> H(f(e), U1(k, d))
26.26/8.59	   A^2 -> H(f(e), U1(d, k))
26.26/8.59	   A^2 -> H(U1(k, k), U1(c, b))
26.26/8.59	   A^2 -> H(U1(k, k), U1(d, b))
26.26/8.59	   A^2 -> H(U1(k, k), U1(b, c))
26.26/8.59	   A^2 -> H(U1(k, k), U1(b, d))
26.26/8.59	   A^2 -> H(U1(k, k), U1(c, c))
26.26/8.59	   A^2 -> H(U1(k, k), f(e))
26.26/8.59	   A^2 -> H(U1(k, k), f(k))
26.26/8.59	   A^2 -> H(U1(k, k), U1(d, d))
26.26/8.59	
26.26/8.59	The TRS R consists of the following rules:
26.26/8.59	
26.26/8.59	   f(x) -> U1(x, x)
26.26/8.59	   U1(e, x) -> x
26.26/8.59	   a -> c
26.26/8.59	   a -> d
26.26/8.59	   b -> c
26.26/8.59	   b -> d
26.26/8.59	   d -> k
26.26/8.59	   c -> e
26.26/8.59	   c -> k
26.26/8.59	
26.26/8.59	Q is empty.
26.26/8.59	We have to consider all minimal (P,Q,R)-chains.
26.26/8.59	----------------------------------------
26.26/8.59	
26.26/8.59	(427) TransformationProof (EQUIVALENT)
26.26/8.59	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
26.26/8.59	
26.26/8.59	   (A^2 -> H(U1(k, k), U1(c, b)),A^2 -> H(U1(k, k), U1(c, b)))
26.26/8.59	   (A^2 -> H(f(k), U1(e, b)),A^2 -> H(f(k), U1(e, b)))
26.26/8.59	   (A^2 -> H(f(k), U1(k, b)),A^2 -> H(f(k), U1(k, b)))
26.26/8.59	   (A^2 -> H(f(k), U1(c, c)),A^2 -> H(f(k), U1(c, c)))
26.26/8.59	   (A^2 -> H(f(k), U1(c, d)),A^2 -> H(f(k), U1(c, d)))
26.26/8.59	
26.26/8.59	
26.26/8.59	----------------------------------------
26.26/8.59	
26.26/8.59	(428)
26.26/8.59	Obligation:
26.26/8.59	Q DP problem:
26.26/8.59	The TRS P consists of the following rules:
26.26/8.59	
26.26/8.59	   H(x, x) -> G(x, x, f(k))
26.26/8.59	   G(d, x, x) -> A^2
26.26/8.59	   A^2 -> H(f(c), f(c))
26.26/8.59	   A^2 -> H(f(d), f(d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(c, c))
26.26/8.59	   A^2 -> H(f(e), f(e))
26.26/8.59	   A^2 -> H(f(k), U1(d, b))
26.26/8.59	   A^2 -> H(f(k), U1(b, c))
26.26/8.59	   A^2 -> H(f(k), U1(b, d))
26.26/8.59	   A^2 -> H(f(k), U1(c, c))
26.26/8.59	   A^2 -> H(f(k), f(e))
26.26/8.59	   A^2 -> H(f(k), f(k))
26.26/8.59	   A^2 -> H(f(k), U1(d, d))
26.26/8.59	   A^2 -> H(f(c), U1(e, b))
26.26/8.59	   A^2 -> H(f(c), U1(k, b))
26.26/8.59	   A^2 -> H(f(c), U1(c, d))
26.26/8.59	   A^2 -> H(f(c), U1(d, c))
26.26/8.59	   A^2 -> H(f(c), U1(b, e))
26.26/8.59	   A^2 -> H(f(c), U1(b, k))
26.26/8.59	   A^2 -> H(f(c), U1(k, d))
26.26/8.59	   A^2 -> H(f(c), U1(d, k))
26.26/8.59	   A^2 -> H(f(c), U1(k, k))
26.26/8.59	   A^2 -> H(U1(k, k), f(b))
26.26/8.59	   A^2 -> H(U1(k, d), U1(b, b))
26.26/8.59	   A^2 -> H(U1(k, d), f(c))
26.26/8.59	   A^2 -> H(U1(k, d), f(d))
26.26/8.59	   A^2 -> H(U1(d, k), U1(b, b))
26.26/8.59	   A^2 -> H(U1(d, k), f(c))
26.26/8.59	   A^2 -> H(U1(d, k), f(d))
26.26/8.59	   A^2 -> H(U1(d, d), U1(c, b))
26.26/8.59	   A^2 -> H(U1(d, d), U1(d, b))
26.26/8.59	   A^2 -> H(U1(d, d), U1(b, c))
26.26/8.59	   A^2 -> H(U1(d, d), U1(b, d))
26.26/8.59	   A^2 -> H(U1(d, d), U1(c, c))
26.26/8.59	   A^2 -> H(U1(d, d), f(e))
26.26/8.59	   A^2 -> H(U1(d, d), f(k))
26.26/8.59	   A^2 -> H(U1(d, d), U1(d, d))
26.26/8.59	   A^2 -> H(f(d), U1(e, b))
26.26/8.59	   A^2 -> H(f(d), U1(k, b))
26.26/8.59	   A^2 -> H(f(d), U1(c, d))
26.26/8.59	   A^2 -> H(f(d), U1(d, c))
26.26/8.59	   A^2 -> H(f(d), U1(b, e))
26.26/8.59	   A^2 -> H(f(d), U1(b, k))
26.26/8.59	   A^2 -> H(f(d), U1(e, c))
26.26/8.59	   A^2 -> H(f(d), U1(k, c))
26.26/8.59	   A^2 -> H(f(d), U1(c, e))
26.26/8.59	   A^2 -> H(f(d), U1(c, k))
26.26/8.59	   A^2 -> H(f(d), U1(e, e))
26.26/8.59	   A^2 -> H(f(d), U1(k, k))
26.26/8.59	   A^2 -> H(f(a), b)
26.26/8.59	   A^2 -> H(f(a), U1(e, d))
26.26/8.59	   A^2 -> H(f(a), U1(d, e))
26.26/8.59	   A^2 -> H(f(c), U1(e, c))
26.26/8.59	   A^2 -> H(f(c), U1(k, c))
26.26/8.59	   A^2 -> H(f(c), U1(c, e))
26.26/8.59	   A^2 -> H(f(c), U1(c, k))
26.26/8.59	   A^2 -> H(f(a), c)
26.26/8.59	   A^2 -> H(f(a), U1(e, k))
26.26/8.59	   A^2 -> H(f(a), U1(k, e))
26.26/8.59	   A^2 -> H(f(c), U1(e, e))
26.26/8.59	   A^2 -> H(f(a), e)
26.26/8.59	   A^2 -> H(f(d), U1(k, d))
26.26/8.59	   A^2 -> H(f(d), U1(d, k))
26.26/8.59	   A^2 -> H(f(a), U1(k, k))
26.26/8.59	   A^2 -> H(d, f(b))
26.26/8.59	   A^2 -> H(a, U1(b, b))
26.26/8.59	   A^2 -> H(a, f(c))
26.26/8.59	   A^2 -> H(a, f(d))
26.26/8.59	   A^2 -> H(U1(e, d), U1(b, b))
26.26/8.59	   A^2 -> H(U1(e, d), f(c))
26.26/8.59	   A^2 -> H(U1(e, d), f(d))
26.26/8.59	   A^2 -> H(U1(e, a), U1(c, b))
26.26/8.59	   A^2 -> H(U1(e, a), U1(d, b))
26.26/8.59	   A^2 -> H(U1(e, a), U1(b, c))
26.26/8.59	   A^2 -> H(U1(e, a), U1(b, d))
26.26/8.59	   A^2 -> H(U1(e, a), U1(c, c))
26.26/8.59	   A^2 -> H(U1(e, a), f(e))
26.26/8.59	   A^2 -> H(U1(e, a), f(k))
26.26/8.59	   A^2 -> H(U1(e, a), U1(d, d))
26.26/8.59	   A^2 -> H(U1(k, a), U1(c, b))
26.26/8.59	   A^2 -> H(U1(k, a), U1(d, b))
26.26/8.59	   A^2 -> H(U1(k, a), U1(b, c))
26.26/8.59	   A^2 -> H(U1(k, a), U1(b, d))
26.26/8.59	   A^2 -> H(U1(k, a), U1(c, c))
26.26/8.59	   A^2 -> H(U1(k, a), f(e))
26.26/8.59	   A^2 -> H(U1(k, a), f(k))
26.26/8.59	   A^2 -> H(U1(k, a), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, d), U1(c, b))
26.26/8.59	   A^2 -> H(U1(c, d), U1(d, b))
26.26/8.59	   A^2 -> H(U1(c, d), U1(b, c))
26.26/8.59	   A^2 -> H(U1(c, d), U1(b, d))
26.26/8.59	   A^2 -> H(U1(c, d), U1(c, c))
26.26/8.59	   A^2 -> H(U1(c, d), f(e))
26.26/8.59	   A^2 -> H(U1(c, d), f(k))
26.26/8.59	   A^2 -> H(U1(c, d), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, a), U1(e, b))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, b))
26.26/8.59	   A^2 -> H(U1(c, a), U1(c, d))
26.26/8.59	   A^2 -> H(U1(c, a), U1(d, c))
26.26/8.59	   A^2 -> H(U1(c, a), U1(b, e))
26.26/8.59	   A^2 -> H(U1(c, a), U1(b, k))
26.26/8.59	   A^2 -> H(U1(c, a), U1(e, c))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, c))
26.26/8.59	   A^2 -> H(U1(c, a), U1(c, e))
26.26/8.59	   A^2 -> H(U1(c, a), U1(c, k))
26.26/8.59	   A^2 -> H(U1(c, a), U1(e, e))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, k))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, d))
26.26/8.59	   A^2 -> H(U1(c, a), U1(d, k))
26.26/8.59	   A^2 -> H(U1(d, e), U1(b, b))
26.26/8.59	   A^2 -> H(U1(d, e), f(c))
26.26/8.59	   A^2 -> H(U1(d, e), f(d))
26.26/8.59	   A^2 -> H(U1(d, c), U1(c, b))
26.26/8.59	   A^2 -> H(U1(d, c), U1(d, b))
26.26/8.59	   A^2 -> H(U1(d, c), U1(b, c))
26.26/8.59	   A^2 -> H(U1(d, c), U1(b, d))
26.26/8.59	   A^2 -> H(U1(d, c), U1(c, c))
26.26/8.59	   A^2 -> H(U1(d, c), f(e))
26.26/8.59	   A^2 -> H(U1(d, c), f(k))
26.26/8.59	   A^2 -> H(U1(d, c), U1(d, d))
26.26/8.59	   A^2 -> H(U1(d, a), U1(e, b))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, b))
26.26/8.59	   A^2 -> H(U1(d, a), U1(c, d))
26.26/8.59	   A^2 -> H(U1(d, a), U1(d, c))
26.26/8.59	   A^2 -> H(U1(d, a), U1(b, e))
26.26/8.59	   A^2 -> H(U1(d, a), U1(b, k))
26.26/8.59	   A^2 -> H(U1(d, a), U1(e, c))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, c))
26.26/8.59	   A^2 -> H(U1(d, a), U1(c, e))
26.26/8.59	   A^2 -> H(U1(d, a), U1(c, k))
26.26/8.59	   A^2 -> H(U1(d, a), U1(e, e))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, k))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, d))
26.26/8.59	   A^2 -> H(U1(d, a), U1(d, k))
26.26/8.59	   A^2 -> H(U1(a, e), U1(c, b))
26.26/8.59	   A^2 -> H(U1(a, e), U1(d, b))
26.26/8.59	   A^2 -> H(U1(a, e), U1(b, c))
26.26/8.59	   A^2 -> H(U1(a, e), U1(b, d))
26.26/8.59	   A^2 -> H(U1(a, e), U1(c, c))
26.26/8.59	   A^2 -> H(U1(a, e), f(e))
26.26/8.59	   A^2 -> H(U1(a, e), f(k))
26.26/8.59	   A^2 -> H(U1(a, e), U1(d, d))
26.26/8.59	   A^2 -> H(U1(a, k), U1(c, b))
26.26/8.59	   A^2 -> H(U1(a, k), U1(d, b))
26.26/8.59	   A^2 -> H(U1(a, k), U1(b, c))
26.26/8.59	   A^2 -> H(U1(a, k), U1(b, d))
26.26/8.59	   A^2 -> H(U1(a, k), U1(c, c))
26.26/8.59	   A^2 -> H(U1(a, k), f(e))
26.26/8.59	   A^2 -> H(U1(a, k), f(k))
26.26/8.59	   A^2 -> H(U1(a, k), U1(d, d))
26.26/8.59	   A^2 -> H(U1(a, c), U1(e, b))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, b))
26.26/8.59	   A^2 -> H(U1(a, c), U1(c, d))
26.26/8.59	   A^2 -> H(U1(a, c), U1(d, c))
26.26/8.59	   A^2 -> H(U1(a, c), U1(b, e))
26.26/8.59	   A^2 -> H(U1(a, c), U1(b, k))
26.26/8.59	   A^2 -> H(U1(a, c), U1(e, c))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, c))
26.26/8.59	   A^2 -> H(U1(a, c), U1(c, e))
26.26/8.59	   A^2 -> H(U1(a, c), U1(c, k))
26.26/8.59	   A^2 -> H(U1(a, c), U1(e, e))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, k))
26.26/8.59	   A^2 -> H(U1(a, c), U1(k, d))
26.26/8.59	   A^2 -> H(U1(a, c), U1(d, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(e, b))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, b))
26.26/8.59	   A^2 -> H(U1(a, d), U1(c, d))
26.26/8.59	   A^2 -> H(U1(a, d), U1(d, c))
26.26/8.59	   A^2 -> H(U1(a, d), U1(b, e))
26.26/8.59	   A^2 -> H(U1(a, d), U1(b, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(e, c))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, c))
26.26/8.59	   A^2 -> H(U1(a, d), U1(c, e))
26.26/8.59	   A^2 -> H(U1(a, d), U1(c, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(e, e))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, k))
26.26/8.59	   A^2 -> H(U1(a, d), U1(k, d))
26.26/8.59	   A^2 -> H(U1(a, d), U1(d, k))
26.26/8.59	   A^2 -> H(U1(a, a), b)
26.26/8.59	   A^2 -> H(U1(a, a), U1(e, d))
26.26/8.59	   A^2 -> H(U1(a, a), U1(d, e))
26.26/8.59	   A^2 -> H(U1(a, a), c)
26.26/8.59	   A^2 -> H(U1(a, a), U1(e, k))
26.26/8.59	   A^2 -> H(U1(a, a), U1(k, e))
26.26/8.59	   A^2 -> H(U1(a, a), e)
26.26/8.59	   A^2 -> H(U1(a, a), U1(k, k))
26.26/8.59	   A^2 -> H(k, f(b))
26.26/8.59	   A^2 -> H(c, U1(b, b))
26.26/8.59	   A^2 -> H(c, f(c))
26.26/8.59	   A^2 -> H(c, f(d))
26.26/8.59	   A^2 -> H(U1(e, k), U1(b, b))
26.26/8.59	   A^2 -> H(U1(e, k), f(c))
26.26/8.59	   A^2 -> H(U1(e, k), f(d))
26.26/8.59	   A^2 -> H(U1(e, c), U1(c, b))
26.26/8.59	   A^2 -> H(U1(e, c), U1(d, b))
26.26/8.59	   A^2 -> H(U1(e, c), U1(b, c))
26.26/8.59	   A^2 -> H(U1(e, c), U1(b, d))
26.26/8.59	   A^2 -> H(U1(e, c), U1(c, c))
26.26/8.59	   A^2 -> H(U1(e, c), f(e))
26.26/8.59	   A^2 -> H(U1(e, c), f(k))
26.26/8.59	   A^2 -> H(U1(e, c), U1(d, d))
26.26/8.59	   A^2 -> H(U1(k, e), U1(b, b))
26.26/8.59	   A^2 -> H(U1(k, e), f(c))
26.26/8.59	   A^2 -> H(U1(k, e), f(d))
26.26/8.59	   A^2 -> H(U1(k, c), U1(c, b))
26.26/8.59	   A^2 -> H(U1(k, c), U1(d, b))
26.26/8.59	   A^2 -> H(U1(k, c), U1(b, c))
26.26/8.59	   A^2 -> H(U1(k, c), U1(b, d))
26.26/8.59	   A^2 -> H(U1(k, c), U1(c, c))
26.26/8.59	   A^2 -> H(U1(k, c), f(e))
26.26/8.59	   A^2 -> H(U1(k, c), f(k))
26.26/8.59	   A^2 -> H(U1(k, c), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, e), U1(c, b))
26.26/8.59	   A^2 -> H(U1(c, e), U1(d, b))
26.26/8.59	   A^2 -> H(U1(c, e), U1(b, c))
26.26/8.59	   A^2 -> H(U1(c, e), U1(b, d))
26.26/8.59	   A^2 -> H(U1(c, e), U1(c, c))
26.26/8.59	   A^2 -> H(U1(c, e), f(e))
26.26/8.59	   A^2 -> H(U1(c, e), f(k))
26.26/8.59	   A^2 -> H(U1(c, e), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, k), U1(c, b))
26.26/8.59	   A^2 -> H(U1(c, k), U1(d, b))
26.26/8.59	   A^2 -> H(U1(c, k), U1(b, c))
26.26/8.59	   A^2 -> H(U1(c, k), U1(b, d))
26.26/8.59	   A^2 -> H(U1(c, k), U1(c, c))
26.26/8.59	   A^2 -> H(U1(c, k), f(e))
26.26/8.59	   A^2 -> H(U1(c, k), f(k))
26.26/8.59	   A^2 -> H(U1(c, k), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(e, b))
26.26/8.59	   A^2 -> H(U1(c, c), U1(k, b))
26.26/8.59	   A^2 -> H(U1(c, c), U1(c, d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(d, c))
26.26/8.59	   A^2 -> H(U1(c, c), U1(b, e))
26.26/8.59	   A^2 -> H(U1(c, c), U1(b, k))
26.26/8.59	   A^2 -> H(U1(c, c), U1(e, e))
26.26/8.59	   A^2 -> H(U1(c, c), U1(k, k))
26.26/8.59	   A^2 -> H(U1(c, c), U1(k, d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(d, k))
26.26/8.59	   A^2 -> H(e, U1(b, b))
26.26/8.59	   A^2 -> H(e, f(c))
26.26/8.59	   A^2 -> H(e, f(d))
26.26/8.59	   A^2 -> H(U1(e, e), U1(c, b))
26.26/8.59	   A^2 -> H(U1(e, e), U1(d, b))
26.26/8.59	   A^2 -> H(U1(e, e), U1(b, c))
26.26/8.59	   A^2 -> H(U1(e, e), U1(b, d))
26.26/8.59	   A^2 -> H(U1(e, e), U1(c, c))
26.26/8.59	   A^2 -> H(U1(e, e), f(e))
26.26/8.59	   A^2 -> H(U1(e, e), f(k))
26.26/8.59	   A^2 -> H(U1(e, e), U1(d, d))
26.26/8.59	   A^2 -> H(f(e), U1(e, b))
26.26/8.59	   A^2 -> H(f(e), U1(k, b))
26.26/8.59	   A^2 -> H(f(e), U1(c, d))
26.26/8.59	   A^2 -> H(f(e), U1(d, c))
26.26/8.59	   A^2 -> H(f(e), U1(b, e))
26.26/8.59	   A^2 -> H(f(e), U1(b, k))
26.26/8.59	   A^2 -> H(f(e), U1(e, c))
26.26/8.59	   A^2 -> H(f(e), U1(k, c))
26.26/8.59	   A^2 -> H(f(e), U1(c, e))
26.26/8.59	   A^2 -> H(f(e), U1(c, k))
26.26/8.59	   A^2 -> H(f(e), U1(k, k))
26.26/8.59	   A^2 -> H(f(e), U1(k, d))
26.26/8.59	   A^2 -> H(f(e), U1(d, k))
26.26/8.59	   A^2 -> H(U1(k, k), U1(c, b))
26.26/8.59	   A^2 -> H(U1(k, k), U1(d, b))
26.26/8.59	   A^2 -> H(U1(k, k), U1(b, c))
26.26/8.59	   A^2 -> H(U1(k, k), U1(b, d))
26.26/8.59	   A^2 -> H(U1(k, k), U1(c, c))
26.26/8.59	   A^2 -> H(U1(k, k), f(e))
26.26/8.59	   A^2 -> H(U1(k, k), f(k))
26.26/8.59	   A^2 -> H(U1(k, k), U1(d, d))
26.26/8.59	   A^2 -> H(f(k), U1(e, b))
26.26/8.59	   A^2 -> H(f(k), U1(k, b))
26.26/8.59	   A^2 -> H(f(k), U1(c, d))
26.26/8.59	
26.26/8.59	The TRS R consists of the following rules:
26.26/8.59	
26.26/8.59	   f(x) -> U1(x, x)
26.26/8.59	   U1(e, x) -> x
26.26/8.59	   a -> c
26.26/8.59	   a -> d
26.26/8.59	   b -> c
26.26/8.59	   b -> d
26.26/8.59	   d -> k
26.26/8.59	   c -> e
26.26/8.59	   c -> k
26.26/8.59	
26.26/8.59	Q is empty.
26.26/8.59	We have to consider all minimal (P,Q,R)-chains.
26.26/8.59	----------------------------------------
26.26/8.59	
26.26/8.59	(429) TransformationProof (EQUIVALENT)
26.26/8.59	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
26.26/8.59	
26.26/8.59	   (A^2 -> H(U1(k, k), U1(d, b)),A^2 -> H(U1(k, k), U1(d, b)))
26.26/8.59	   (A^2 -> H(f(k), U1(k, b)),A^2 -> H(f(k), U1(k, b)))
26.26/8.59	   (A^2 -> H(f(k), U1(d, c)),A^2 -> H(f(k), U1(d, c)))
26.26/8.59	   (A^2 -> H(f(k), U1(d, d)),A^2 -> H(f(k), U1(d, d)))
26.26/8.59	
26.26/8.59	
26.26/8.59	----------------------------------------
26.26/8.59	
26.26/8.59	(430)
26.26/8.59	Obligation:
26.26/8.59	Q DP problem:
26.26/8.59	The TRS P consists of the following rules:
26.26/8.59	
26.26/8.59	   H(x, x) -> G(x, x, f(k))
26.26/8.59	   G(d, x, x) -> A^2
26.26/8.59	   A^2 -> H(f(c), f(c))
26.26/8.59	   A^2 -> H(f(d), f(d))
26.26/8.59	   A^2 -> H(U1(c, c), U1(c, c))
26.26/8.59	   A^2 -> H(f(e), f(e))
26.26/8.59	   A^2 -> H(f(k), U1(b, c))
26.26/8.59	   A^2 -> H(f(k), U1(b, d))
26.26/8.59	   A^2 -> H(f(k), U1(c, c))
26.26/8.59	   A^2 -> H(f(k), f(e))
26.26/8.59	   A^2 -> H(f(k), f(k))
26.26/8.59	   A^2 -> H(f(k), U1(d, d))
26.26/8.59	   A^2 -> H(f(c), U1(e, b))
26.26/8.59	   A^2 -> H(f(c), U1(k, b))
26.26/8.59	   A^2 -> H(f(c), U1(c, d))
26.26/8.59	   A^2 -> H(f(c), U1(d, c))
26.26/8.59	   A^2 -> H(f(c), U1(b, e))
26.26/8.59	   A^2 -> H(f(c), U1(b, k))
26.26/8.59	   A^2 -> H(f(c), U1(k, d))
26.26/8.59	   A^2 -> H(f(c), U1(d, k))
26.26/8.59	   A^2 -> H(f(c), U1(k, k))
26.26/8.59	   A^2 -> H(U1(k, k), f(b))
26.26/8.59	   A^2 -> H(U1(k, d), U1(b, b))
26.26/8.59	   A^2 -> H(U1(k, d), f(c))
26.26/8.59	   A^2 -> H(U1(k, d), f(d))
26.26/8.59	   A^2 -> H(U1(d, k), U1(b, b))
26.26/8.59	   A^2 -> H(U1(d, k), f(c))
26.26/8.59	   A^2 -> H(U1(d, k), f(d))
26.26/8.59	   A^2 -> H(U1(d, d), U1(c, b))
26.26/8.59	   A^2 -> H(U1(d, d), U1(d, b))
26.26/8.59	   A^2 -> H(U1(d, d), U1(b, c))
26.26/8.59	   A^2 -> H(U1(d, d), U1(b, d))
26.26/8.59	   A^2 -> H(U1(d, d), U1(c, c))
26.26/8.59	   A^2 -> H(U1(d, d), f(e))
26.26/8.59	   A^2 -> H(U1(d, d), f(k))
26.26/8.59	   A^2 -> H(U1(d, d), U1(d, d))
26.26/8.59	   A^2 -> H(f(d), U1(e, b))
26.26/8.59	   A^2 -> H(f(d), U1(k, b))
26.26/8.59	   A^2 -> H(f(d), U1(c, d))
26.26/8.59	   A^2 -> H(f(d), U1(d, c))
26.26/8.59	   A^2 -> H(f(d), U1(b, e))
26.26/8.59	   A^2 -> H(f(d), U1(b, k))
26.26/8.59	   A^2 -> H(f(d), U1(e, c))
26.26/8.59	   A^2 -> H(f(d), U1(k, c))
26.26/8.59	   A^2 -> H(f(d), U1(c, e))
26.26/8.59	   A^2 -> H(f(d), U1(c, k))
26.26/8.59	   A^2 -> H(f(d), U1(e, e))
26.26/8.59	   A^2 -> H(f(d), U1(k, k))
26.26/8.59	   A^2 -> H(f(a), b)
26.26/8.59	   A^2 -> H(f(a), U1(e, d))
26.26/8.59	   A^2 -> H(f(a), U1(d, e))
26.26/8.59	   A^2 -> H(f(c), U1(e, c))
26.26/8.59	   A^2 -> H(f(c), U1(k, c))
26.26/8.59	   A^2 -> H(f(c), U1(c, e))
26.26/8.59	   A^2 -> H(f(c), U1(c, k))
26.26/8.59	   A^2 -> H(f(a), c)
26.26/8.59	   A^2 -> H(f(a), U1(e, k))
26.26/8.59	   A^2 -> H(f(a), U1(k, e))
26.26/8.59	   A^2 -> H(f(c), U1(e, e))
26.26/8.59	   A^2 -> H(f(a), e)
26.26/8.59	   A^2 -> H(f(d), U1(k, d))
26.26/8.59	   A^2 -> H(f(d), U1(d, k))
26.26/8.59	   A^2 -> H(f(a), U1(k, k))
26.26/8.59	   A^2 -> H(d, f(b))
26.26/8.59	   A^2 -> H(a, U1(b, b))
26.26/8.59	   A^2 -> H(a, f(c))
26.26/8.59	   A^2 -> H(a, f(d))
26.26/8.59	   A^2 -> H(U1(e, d), U1(b, b))
26.26/8.59	   A^2 -> H(U1(e, d), f(c))
26.26/8.59	   A^2 -> H(U1(e, d), f(d))
26.26/8.59	   A^2 -> H(U1(e, a), U1(c, b))
26.26/8.59	   A^2 -> H(U1(e, a), U1(d, b))
26.26/8.59	   A^2 -> H(U1(e, a), U1(b, c))
26.26/8.59	   A^2 -> H(U1(e, a), U1(b, d))
26.26/8.59	   A^2 -> H(U1(e, a), U1(c, c))
26.26/8.59	   A^2 -> H(U1(e, a), f(e))
26.26/8.59	   A^2 -> H(U1(e, a), f(k))
26.26/8.59	   A^2 -> H(U1(e, a), U1(d, d))
26.26/8.59	   A^2 -> H(U1(k, a), U1(c, b))
26.26/8.59	   A^2 -> H(U1(k, a), U1(d, b))
26.26/8.59	   A^2 -> H(U1(k, a), U1(b, c))
26.26/8.59	   A^2 -> H(U1(k, a), U1(b, d))
26.26/8.59	   A^2 -> H(U1(k, a), U1(c, c))
26.26/8.59	   A^2 -> H(U1(k, a), f(e))
26.26/8.59	   A^2 -> H(U1(k, a), f(k))
26.26/8.59	   A^2 -> H(U1(k, a), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, d), U1(c, b))
26.26/8.59	   A^2 -> H(U1(c, d), U1(d, b))
26.26/8.59	   A^2 -> H(U1(c, d), U1(b, c))
26.26/8.59	   A^2 -> H(U1(c, d), U1(b, d))
26.26/8.59	   A^2 -> H(U1(c, d), U1(c, c))
26.26/8.59	   A^2 -> H(U1(c, d), f(e))
26.26/8.59	   A^2 -> H(U1(c, d), f(k))
26.26/8.59	   A^2 -> H(U1(c, d), U1(d, d))
26.26/8.59	   A^2 -> H(U1(c, a), U1(e, b))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, b))
26.26/8.59	   A^2 -> H(U1(c, a), U1(c, d))
26.26/8.59	   A^2 -> H(U1(c, a), U1(d, c))
26.26/8.59	   A^2 -> H(U1(c, a), U1(b, e))
26.26/8.59	   A^2 -> H(U1(c, a), U1(b, k))
26.26/8.59	   A^2 -> H(U1(c, a), U1(e, c))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, c))
26.26/8.59	   A^2 -> H(U1(c, a), U1(c, e))
26.26/8.59	   A^2 -> H(U1(c, a), U1(c, k))
26.26/8.59	   A^2 -> H(U1(c, a), U1(e, e))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, k))
26.26/8.59	   A^2 -> H(U1(c, a), U1(k, d))
26.26/8.59	   A^2 -> H(U1(c, a), U1(d, k))
26.26/8.59	   A^2 -> H(U1(d, e), U1(b, b))
26.26/8.59	   A^2 -> H(U1(d, e), f(c))
26.26/8.59	   A^2 -> H(U1(d, e), f(d))
26.26/8.59	   A^2 -> H(U1(d, c), U1(c, b))
26.26/8.59	   A^2 -> H(U1(d, c), U1(d, b))
26.26/8.59	   A^2 -> H(U1(d, c), U1(b, c))
26.26/8.59	   A^2 -> H(U1(d, c), U1(b, d))
26.26/8.59	   A^2 -> H(U1(d, c), U1(c, c))
26.26/8.59	   A^2 -> H(U1(d, c), f(e))
26.26/8.59	   A^2 -> H(U1(d, c), f(k))
26.26/8.59	   A^2 -> H(U1(d, c), U1(d, d))
26.26/8.59	   A^2 -> H(U1(d, a), U1(e, b))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, b))
26.26/8.59	   A^2 -> H(U1(d, a), U1(c, d))
26.26/8.59	   A^2 -> H(U1(d, a), U1(d, c))
26.26/8.59	   A^2 -> H(U1(d, a), U1(b, e))
26.26/8.59	   A^2 -> H(U1(d, a), U1(b, k))
26.26/8.59	   A^2 -> H(U1(d, a), U1(e, c))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, c))
26.26/8.59	   A^2 -> H(U1(d, a), U1(c, e))
26.26/8.59	   A^2 -> H(U1(d, a), U1(c, k))
26.26/8.59	   A^2 -> H(U1(d, a), U1(e, e))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, k))
26.26/8.59	   A^2 -> H(U1(d, a), U1(k, d))
26.26/8.59	   A^2 -> H(U1(d, a), U1(d, k))
26.26/8.59	   A^2 -> H(U1(a, e), U1(c, b))
26.26/8.59	   A^2 -> H(U1(a, e), U1(d, b))
26.26/8.59	   A^2 -> H(U1(a, e), U1(b, c))
26.26/8.59	   A^2 -> H(U1(a, e), U1(b, d))
26.26/8.61	   A^2 -> H(U1(a, e), U1(c, c))
26.26/8.61	   A^2 -> H(U1(a, e), f(e))
26.26/8.61	   A^2 -> H(U1(a, e), f(k))
26.26/8.61	   A^2 -> H(U1(a, e), U1(d, d))
26.26/8.61	   A^2 -> H(U1(a, k), U1(c, b))
26.26/8.61	   A^2 -> H(U1(a, k), U1(d, b))
26.26/8.61	   A^2 -> H(U1(a, k), U1(b, c))
26.26/8.61	   A^2 -> H(U1(a, k), U1(b, d))
26.26/8.61	   A^2 -> H(U1(a, k), U1(c, c))
26.26/8.61	   A^2 -> H(U1(a, k), f(e))
26.26/8.61	   A^2 -> H(U1(a, k), f(k))
26.26/8.61	   A^2 -> H(U1(a, k), U1(d, d))
26.26/8.61	   A^2 -> H(U1(a, c), U1(e, b))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, b))
26.26/8.61	   A^2 -> H(U1(a, c), U1(c, d))
26.26/8.61	   A^2 -> H(U1(a, c), U1(d, c))
26.26/8.61	   A^2 -> H(U1(a, c), U1(b, e))
26.26/8.61	   A^2 -> H(U1(a, c), U1(b, k))
26.26/8.61	   A^2 -> H(U1(a, c), U1(e, c))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, c))
26.26/8.61	   A^2 -> H(U1(a, c), U1(c, e))
26.26/8.61	   A^2 -> H(U1(a, c), U1(c, k))
26.26/8.61	   A^2 -> H(U1(a, c), U1(e, e))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, k))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, d))
26.26/8.61	   A^2 -> H(U1(a, c), U1(d, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(e, b))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, b))
26.26/8.61	   A^2 -> H(U1(a, d), U1(c, d))
26.26/8.61	   A^2 -> H(U1(a, d), U1(d, c))
26.26/8.61	   A^2 -> H(U1(a, d), U1(b, e))
26.26/8.61	   A^2 -> H(U1(a, d), U1(b, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(e, c))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, c))
26.26/8.61	   A^2 -> H(U1(a, d), U1(c, e))
26.26/8.61	   A^2 -> H(U1(a, d), U1(c, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(e, e))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, d))
26.26/8.61	   A^2 -> H(U1(a, d), U1(d, k))
26.26/8.61	   A^2 -> H(U1(a, a), b)
26.26/8.61	   A^2 -> H(U1(a, a), U1(e, d))
26.26/8.61	   A^2 -> H(U1(a, a), U1(d, e))
26.26/8.61	   A^2 -> H(U1(a, a), c)
26.26/8.61	   A^2 -> H(U1(a, a), U1(e, k))
26.26/8.61	   A^2 -> H(U1(a, a), U1(k, e))
26.26/8.61	   A^2 -> H(U1(a, a), e)
26.26/8.61	   A^2 -> H(U1(a, a), U1(k, k))
26.26/8.61	   A^2 -> H(k, f(b))
26.26/8.61	   A^2 -> H(c, U1(b, b))
26.26/8.61	   A^2 -> H(c, f(c))
26.26/8.61	   A^2 -> H(c, f(d))
26.26/8.61	   A^2 -> H(U1(e, k), U1(b, b))
26.26/8.61	   A^2 -> H(U1(e, k), f(c))
26.26/8.61	   A^2 -> H(U1(e, k), f(d))
26.26/8.61	   A^2 -> H(U1(e, c), U1(c, b))
26.26/8.61	   A^2 -> H(U1(e, c), U1(d, b))
26.26/8.61	   A^2 -> H(U1(e, c), U1(b, c))
26.26/8.61	   A^2 -> H(U1(e, c), U1(b, d))
26.26/8.61	   A^2 -> H(U1(e, c), U1(c, c))
26.26/8.61	   A^2 -> H(U1(e, c), f(e))
26.26/8.61	   A^2 -> H(U1(e, c), f(k))
26.26/8.61	   A^2 -> H(U1(e, c), U1(d, d))
26.26/8.61	   A^2 -> H(U1(k, e), U1(b, b))
26.26/8.61	   A^2 -> H(U1(k, e), f(c))
26.26/8.61	   A^2 -> H(U1(k, e), f(d))
26.26/8.61	   A^2 -> H(U1(k, c), U1(c, b))
26.26/8.61	   A^2 -> H(U1(k, c), U1(d, b))
26.26/8.61	   A^2 -> H(U1(k, c), U1(b, c))
26.26/8.61	   A^2 -> H(U1(k, c), U1(b, d))
26.26/8.61	   A^2 -> H(U1(k, c), U1(c, c))
26.26/8.61	   A^2 -> H(U1(k, c), f(e))
26.26/8.61	   A^2 -> H(U1(k, c), f(k))
26.26/8.61	   A^2 -> H(U1(k, c), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, e), U1(c, b))
26.26/8.61	   A^2 -> H(U1(c, e), U1(d, b))
26.26/8.61	   A^2 -> H(U1(c, e), U1(b, c))
26.26/8.61	   A^2 -> H(U1(c, e), U1(b, d))
26.26/8.61	   A^2 -> H(U1(c, e), U1(c, c))
26.26/8.61	   A^2 -> H(U1(c, e), f(e))
26.26/8.61	   A^2 -> H(U1(c, e), f(k))
26.26/8.61	   A^2 -> H(U1(c, e), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, k), U1(c, b))
26.26/8.61	   A^2 -> H(U1(c, k), U1(d, b))
26.26/8.61	   A^2 -> H(U1(c, k), U1(b, c))
26.26/8.61	   A^2 -> H(U1(c, k), U1(b, d))
26.26/8.61	   A^2 -> H(U1(c, k), U1(c, c))
26.26/8.61	   A^2 -> H(U1(c, k), f(e))
26.26/8.61	   A^2 -> H(U1(c, k), f(k))
26.26/8.61	   A^2 -> H(U1(c, k), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(e, b))
26.26/8.61	   A^2 -> H(U1(c, c), U1(k, b))
26.26/8.61	   A^2 -> H(U1(c, c), U1(c, d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(d, c))
26.26/8.61	   A^2 -> H(U1(c, c), U1(b, e))
26.26/8.61	   A^2 -> H(U1(c, c), U1(b, k))
26.26/8.61	   A^2 -> H(U1(c, c), U1(e, e))
26.26/8.61	   A^2 -> H(U1(c, c), U1(k, k))
26.26/8.61	   A^2 -> H(U1(c, c), U1(k, d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(d, k))
26.26/8.61	   A^2 -> H(e, U1(b, b))
26.26/8.61	   A^2 -> H(e, f(c))
26.26/8.61	   A^2 -> H(e, f(d))
26.26/8.61	   A^2 -> H(U1(e, e), U1(c, b))
26.26/8.61	   A^2 -> H(U1(e, e), U1(d, b))
26.26/8.61	   A^2 -> H(U1(e, e), U1(b, c))
26.26/8.61	   A^2 -> H(U1(e, e), U1(b, d))
26.26/8.61	   A^2 -> H(U1(e, e), U1(c, c))
26.26/8.61	   A^2 -> H(U1(e, e), f(e))
26.26/8.61	   A^2 -> H(U1(e, e), f(k))
26.26/8.61	   A^2 -> H(U1(e, e), U1(d, d))
26.26/8.61	   A^2 -> H(f(e), U1(e, b))
26.26/8.61	   A^2 -> H(f(e), U1(k, b))
26.26/8.61	   A^2 -> H(f(e), U1(c, d))
26.26/8.61	   A^2 -> H(f(e), U1(d, c))
26.26/8.61	   A^2 -> H(f(e), U1(b, e))
26.26/8.61	   A^2 -> H(f(e), U1(b, k))
26.26/8.61	   A^2 -> H(f(e), U1(e, c))
26.26/8.61	   A^2 -> H(f(e), U1(k, c))
26.26/8.61	   A^2 -> H(f(e), U1(c, e))
26.26/8.61	   A^2 -> H(f(e), U1(c, k))
26.26/8.61	   A^2 -> H(f(e), U1(k, k))
26.26/8.61	   A^2 -> H(f(e), U1(k, d))
26.26/8.61	   A^2 -> H(f(e), U1(d, k))
26.26/8.61	   A^2 -> H(U1(k, k), U1(c, b))
26.26/8.61	   A^2 -> H(U1(k, k), U1(d, b))
26.26/8.61	   A^2 -> H(U1(k, k), U1(b, c))
26.26/8.61	   A^2 -> H(U1(k, k), U1(b, d))
26.26/8.61	   A^2 -> H(U1(k, k), U1(c, c))
26.26/8.61	   A^2 -> H(U1(k, k), f(e))
26.26/8.61	   A^2 -> H(U1(k, k), f(k))
26.26/8.61	   A^2 -> H(U1(k, k), U1(d, d))
26.26/8.61	   A^2 -> H(f(k), U1(e, b))
26.26/8.61	   A^2 -> H(f(k), U1(k, b))
26.26/8.61	   A^2 -> H(f(k), U1(c, d))
26.26/8.61	   A^2 -> H(f(k), U1(d, c))
26.26/8.61	
26.26/8.61	The TRS R consists of the following rules:
26.26/8.61	
26.26/8.61	   f(x) -> U1(x, x)
26.26/8.61	   U1(e, x) -> x
26.26/8.61	   a -> c
26.26/8.61	   a -> d
26.26/8.61	   b -> c
26.26/8.61	   b -> d
26.26/8.61	   d -> k
26.26/8.61	   c -> e
26.26/8.61	   c -> k
26.26/8.61	
26.26/8.61	Q is empty.
26.26/8.61	We have to consider all minimal (P,Q,R)-chains.
26.26/8.61	----------------------------------------
26.26/8.61	
26.26/8.61	(431) TransformationProof (EQUIVALENT)
26.26/8.61	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
26.26/8.61	
26.26/8.61	   (A^2 -> H(U1(k, k), U1(b, c)),A^2 -> H(U1(k, k), U1(b, c)))
26.26/8.61	   (A^2 -> H(f(k), U1(c, c)),A^2 -> H(f(k), U1(c, c)))
26.26/8.61	   (A^2 -> H(f(k), U1(d, c)),A^2 -> H(f(k), U1(d, c)))
26.26/8.61	   (A^2 -> H(f(k), U1(b, e)),A^2 -> H(f(k), U1(b, e)))
26.26/8.61	   (A^2 -> H(f(k), U1(b, k)),A^2 -> H(f(k), U1(b, k)))
26.26/8.61	
26.26/8.61	
26.26/8.61	----------------------------------------
26.26/8.61	
26.26/8.61	(432)
26.26/8.61	Obligation:
26.26/8.61	Q DP problem:
26.26/8.61	The TRS P consists of the following rules:
26.26/8.61	
26.26/8.61	   H(x, x) -> G(x, x, f(k))
26.26/8.61	   G(d, x, x) -> A^2
26.26/8.61	   A^2 -> H(f(c), f(c))
26.26/8.61	   A^2 -> H(f(d), f(d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(c, c))
26.26/8.61	   A^2 -> H(f(e), f(e))
26.26/8.61	   A^2 -> H(f(k), U1(b, d))
26.26/8.61	   A^2 -> H(f(k), U1(c, c))
26.26/8.61	   A^2 -> H(f(k), f(e))
26.26/8.61	   A^2 -> H(f(k), f(k))
26.26/8.61	   A^2 -> H(f(k), U1(d, d))
26.26/8.61	   A^2 -> H(f(c), U1(e, b))
26.26/8.61	   A^2 -> H(f(c), U1(k, b))
26.26/8.61	   A^2 -> H(f(c), U1(c, d))
26.26/8.61	   A^2 -> H(f(c), U1(d, c))
26.26/8.61	   A^2 -> H(f(c), U1(b, e))
26.26/8.61	   A^2 -> H(f(c), U1(b, k))
26.26/8.61	   A^2 -> H(f(c), U1(k, d))
26.26/8.61	   A^2 -> H(f(c), U1(d, k))
26.26/8.61	   A^2 -> H(f(c), U1(k, k))
26.26/8.61	   A^2 -> H(U1(k, k), f(b))
26.26/8.61	   A^2 -> H(U1(k, d), U1(b, b))
26.26/8.61	   A^2 -> H(U1(k, d), f(c))
26.26/8.61	   A^2 -> H(U1(k, d), f(d))
26.26/8.61	   A^2 -> H(U1(d, k), U1(b, b))
26.26/8.61	   A^2 -> H(U1(d, k), f(c))
26.26/8.61	   A^2 -> H(U1(d, k), f(d))
26.26/8.61	   A^2 -> H(U1(d, d), U1(c, b))
26.26/8.61	   A^2 -> H(U1(d, d), U1(d, b))
26.26/8.61	   A^2 -> H(U1(d, d), U1(b, c))
26.26/8.61	   A^2 -> H(U1(d, d), U1(b, d))
26.26/8.61	   A^2 -> H(U1(d, d), U1(c, c))
26.26/8.61	   A^2 -> H(U1(d, d), f(e))
26.26/8.61	   A^2 -> H(U1(d, d), f(k))
26.26/8.61	   A^2 -> H(U1(d, d), U1(d, d))
26.26/8.61	   A^2 -> H(f(d), U1(e, b))
26.26/8.61	   A^2 -> H(f(d), U1(k, b))
26.26/8.61	   A^2 -> H(f(d), U1(c, d))
26.26/8.61	   A^2 -> H(f(d), U1(d, c))
26.26/8.61	   A^2 -> H(f(d), U1(b, e))
26.26/8.61	   A^2 -> H(f(d), U1(b, k))
26.26/8.61	   A^2 -> H(f(d), U1(e, c))
26.26/8.61	   A^2 -> H(f(d), U1(k, c))
26.26/8.61	   A^2 -> H(f(d), U1(c, e))
26.26/8.61	   A^2 -> H(f(d), U1(c, k))
26.26/8.61	   A^2 -> H(f(d), U1(e, e))
26.26/8.61	   A^2 -> H(f(d), U1(k, k))
26.26/8.61	   A^2 -> H(f(a), b)
26.26/8.61	   A^2 -> H(f(a), U1(e, d))
26.26/8.61	   A^2 -> H(f(a), U1(d, e))
26.26/8.61	   A^2 -> H(f(c), U1(e, c))
26.26/8.61	   A^2 -> H(f(c), U1(k, c))
26.26/8.61	   A^2 -> H(f(c), U1(c, e))
26.26/8.61	   A^2 -> H(f(c), U1(c, k))
26.26/8.61	   A^2 -> H(f(a), c)
26.26/8.61	   A^2 -> H(f(a), U1(e, k))
26.26/8.61	   A^2 -> H(f(a), U1(k, e))
26.26/8.61	   A^2 -> H(f(c), U1(e, e))
26.26/8.61	   A^2 -> H(f(a), e)
26.26/8.61	   A^2 -> H(f(d), U1(k, d))
26.26/8.61	   A^2 -> H(f(d), U1(d, k))
26.26/8.61	   A^2 -> H(f(a), U1(k, k))
26.26/8.61	   A^2 -> H(d, f(b))
26.26/8.61	   A^2 -> H(a, U1(b, b))
26.26/8.61	   A^2 -> H(a, f(c))
26.26/8.61	   A^2 -> H(a, f(d))
26.26/8.61	   A^2 -> H(U1(e, d), U1(b, b))
26.26/8.61	   A^2 -> H(U1(e, d), f(c))
26.26/8.61	   A^2 -> H(U1(e, d), f(d))
26.26/8.61	   A^2 -> H(U1(e, a), U1(c, b))
26.26/8.61	   A^2 -> H(U1(e, a), U1(d, b))
26.26/8.61	   A^2 -> H(U1(e, a), U1(b, c))
26.26/8.61	   A^2 -> H(U1(e, a), U1(b, d))
26.26/8.61	   A^2 -> H(U1(e, a), U1(c, c))
26.26/8.61	   A^2 -> H(U1(e, a), f(e))
26.26/8.61	   A^2 -> H(U1(e, a), f(k))
26.26/8.61	   A^2 -> H(U1(e, a), U1(d, d))
26.26/8.61	   A^2 -> H(U1(k, a), U1(c, b))
26.26/8.61	   A^2 -> H(U1(k, a), U1(d, b))
26.26/8.61	   A^2 -> H(U1(k, a), U1(b, c))
26.26/8.61	   A^2 -> H(U1(k, a), U1(b, d))
26.26/8.61	   A^2 -> H(U1(k, a), U1(c, c))
26.26/8.61	   A^2 -> H(U1(k, a), f(e))
26.26/8.61	   A^2 -> H(U1(k, a), f(k))
26.26/8.61	   A^2 -> H(U1(k, a), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, d), U1(c, b))
26.26/8.61	   A^2 -> H(U1(c, d), U1(d, b))
26.26/8.61	   A^2 -> H(U1(c, d), U1(b, c))
26.26/8.61	   A^2 -> H(U1(c, d), U1(b, d))
26.26/8.61	   A^2 -> H(U1(c, d), U1(c, c))
26.26/8.61	   A^2 -> H(U1(c, d), f(e))
26.26/8.61	   A^2 -> H(U1(c, d), f(k))
26.26/8.61	   A^2 -> H(U1(c, d), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, a), U1(e, b))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, b))
26.26/8.61	   A^2 -> H(U1(c, a), U1(c, d))
26.26/8.61	   A^2 -> H(U1(c, a), U1(d, c))
26.26/8.61	   A^2 -> H(U1(c, a), U1(b, e))
26.26/8.61	   A^2 -> H(U1(c, a), U1(b, k))
26.26/8.61	   A^2 -> H(U1(c, a), U1(e, c))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, c))
26.26/8.61	   A^2 -> H(U1(c, a), U1(c, e))
26.26/8.61	   A^2 -> H(U1(c, a), U1(c, k))
26.26/8.61	   A^2 -> H(U1(c, a), U1(e, e))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, k))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, d))
26.26/8.61	   A^2 -> H(U1(c, a), U1(d, k))
26.26/8.61	   A^2 -> H(U1(d, e), U1(b, b))
26.26/8.61	   A^2 -> H(U1(d, e), f(c))
26.26/8.61	   A^2 -> H(U1(d, e), f(d))
26.26/8.61	   A^2 -> H(U1(d, c), U1(c, b))
26.26/8.61	   A^2 -> H(U1(d, c), U1(d, b))
26.26/8.61	   A^2 -> H(U1(d, c), U1(b, c))
26.26/8.61	   A^2 -> H(U1(d, c), U1(b, d))
26.26/8.61	   A^2 -> H(U1(d, c), U1(c, c))
26.26/8.61	   A^2 -> H(U1(d, c), f(e))
26.26/8.61	   A^2 -> H(U1(d, c), f(k))
26.26/8.61	   A^2 -> H(U1(d, c), U1(d, d))
26.26/8.61	   A^2 -> H(U1(d, a), U1(e, b))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, b))
26.26/8.61	   A^2 -> H(U1(d, a), U1(c, d))
26.26/8.61	   A^2 -> H(U1(d, a), U1(d, c))
26.26/8.61	   A^2 -> H(U1(d, a), U1(b, e))
26.26/8.61	   A^2 -> H(U1(d, a), U1(b, k))
26.26/8.61	   A^2 -> H(U1(d, a), U1(e, c))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, c))
26.26/8.61	   A^2 -> H(U1(d, a), U1(c, e))
26.26/8.61	   A^2 -> H(U1(d, a), U1(c, k))
26.26/8.61	   A^2 -> H(U1(d, a), U1(e, e))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, k))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, d))
26.26/8.61	   A^2 -> H(U1(d, a), U1(d, k))
26.26/8.61	   A^2 -> H(U1(a, e), U1(c, b))
26.26/8.61	   A^2 -> H(U1(a, e), U1(d, b))
26.26/8.61	   A^2 -> H(U1(a, e), U1(b, c))
26.26/8.61	   A^2 -> H(U1(a, e), U1(b, d))
26.26/8.61	   A^2 -> H(U1(a, e), U1(c, c))
26.26/8.61	   A^2 -> H(U1(a, e), f(e))
26.26/8.61	   A^2 -> H(U1(a, e), f(k))
26.26/8.61	   A^2 -> H(U1(a, e), U1(d, d))
26.26/8.61	   A^2 -> H(U1(a, k), U1(c, b))
26.26/8.61	   A^2 -> H(U1(a, k), U1(d, b))
26.26/8.61	   A^2 -> H(U1(a, k), U1(b, c))
26.26/8.61	   A^2 -> H(U1(a, k), U1(b, d))
26.26/8.61	   A^2 -> H(U1(a, k), U1(c, c))
26.26/8.61	   A^2 -> H(U1(a, k), f(e))
26.26/8.61	   A^2 -> H(U1(a, k), f(k))
26.26/8.61	   A^2 -> H(U1(a, k), U1(d, d))
26.26/8.61	   A^2 -> H(U1(a, c), U1(e, b))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, b))
26.26/8.61	   A^2 -> H(U1(a, c), U1(c, d))
26.26/8.61	   A^2 -> H(U1(a, c), U1(d, c))
26.26/8.61	   A^2 -> H(U1(a, c), U1(b, e))
26.26/8.61	   A^2 -> H(U1(a, c), U1(b, k))
26.26/8.61	   A^2 -> H(U1(a, c), U1(e, c))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, c))
26.26/8.61	   A^2 -> H(U1(a, c), U1(c, e))
26.26/8.61	   A^2 -> H(U1(a, c), U1(c, k))
26.26/8.61	   A^2 -> H(U1(a, c), U1(e, e))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, k))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, d))
26.26/8.61	   A^2 -> H(U1(a, c), U1(d, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(e, b))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, b))
26.26/8.61	   A^2 -> H(U1(a, d), U1(c, d))
26.26/8.61	   A^2 -> H(U1(a, d), U1(d, c))
26.26/8.61	   A^2 -> H(U1(a, d), U1(b, e))
26.26/8.61	   A^2 -> H(U1(a, d), U1(b, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(e, c))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, c))
26.26/8.61	   A^2 -> H(U1(a, d), U1(c, e))
26.26/8.61	   A^2 -> H(U1(a, d), U1(c, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(e, e))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, d))
26.26/8.61	   A^2 -> H(U1(a, d), U1(d, k))
26.26/8.61	   A^2 -> H(U1(a, a), b)
26.26/8.61	   A^2 -> H(U1(a, a), U1(e, d))
26.26/8.61	   A^2 -> H(U1(a, a), U1(d, e))
26.26/8.61	   A^2 -> H(U1(a, a), c)
26.26/8.61	   A^2 -> H(U1(a, a), U1(e, k))
26.26/8.61	   A^2 -> H(U1(a, a), U1(k, e))
26.26/8.61	   A^2 -> H(U1(a, a), e)
26.26/8.61	   A^2 -> H(U1(a, a), U1(k, k))
26.26/8.61	   A^2 -> H(k, f(b))
26.26/8.61	   A^2 -> H(c, U1(b, b))
26.26/8.61	   A^2 -> H(c, f(c))
26.26/8.61	   A^2 -> H(c, f(d))
26.26/8.61	   A^2 -> H(U1(e, k), U1(b, b))
26.26/8.61	   A^2 -> H(U1(e, k), f(c))
26.26/8.61	   A^2 -> H(U1(e, k), f(d))
26.26/8.61	   A^2 -> H(U1(e, c), U1(c, b))
26.26/8.61	   A^2 -> H(U1(e, c), U1(d, b))
26.26/8.61	   A^2 -> H(U1(e, c), U1(b, c))
26.26/8.61	   A^2 -> H(U1(e, c), U1(b, d))
26.26/8.61	   A^2 -> H(U1(e, c), U1(c, c))
26.26/8.61	   A^2 -> H(U1(e, c), f(e))
26.26/8.61	   A^2 -> H(U1(e, c), f(k))
26.26/8.61	   A^2 -> H(U1(e, c), U1(d, d))
26.26/8.61	   A^2 -> H(U1(k, e), U1(b, b))
26.26/8.61	   A^2 -> H(U1(k, e), f(c))
26.26/8.61	   A^2 -> H(U1(k, e), f(d))
26.26/8.61	   A^2 -> H(U1(k, c), U1(c, b))
26.26/8.61	   A^2 -> H(U1(k, c), U1(d, b))
26.26/8.61	   A^2 -> H(U1(k, c), U1(b, c))
26.26/8.61	   A^2 -> H(U1(k, c), U1(b, d))
26.26/8.61	   A^2 -> H(U1(k, c), U1(c, c))
26.26/8.61	   A^2 -> H(U1(k, c), f(e))
26.26/8.61	   A^2 -> H(U1(k, c), f(k))
26.26/8.61	   A^2 -> H(U1(k, c), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, e), U1(c, b))
26.26/8.61	   A^2 -> H(U1(c, e), U1(d, b))
26.26/8.61	   A^2 -> H(U1(c, e), U1(b, c))
26.26/8.61	   A^2 -> H(U1(c, e), U1(b, d))
26.26/8.61	   A^2 -> H(U1(c, e), U1(c, c))
26.26/8.61	   A^2 -> H(U1(c, e), f(e))
26.26/8.61	   A^2 -> H(U1(c, e), f(k))
26.26/8.61	   A^2 -> H(U1(c, e), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, k), U1(c, b))
26.26/8.61	   A^2 -> H(U1(c, k), U1(d, b))
26.26/8.61	   A^2 -> H(U1(c, k), U1(b, c))
26.26/8.61	   A^2 -> H(U1(c, k), U1(b, d))
26.26/8.61	   A^2 -> H(U1(c, k), U1(c, c))
26.26/8.61	   A^2 -> H(U1(c, k), f(e))
26.26/8.61	   A^2 -> H(U1(c, k), f(k))
26.26/8.61	   A^2 -> H(U1(c, k), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(e, b))
26.26/8.61	   A^2 -> H(U1(c, c), U1(k, b))
26.26/8.61	   A^2 -> H(U1(c, c), U1(c, d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(d, c))
26.26/8.61	   A^2 -> H(U1(c, c), U1(b, e))
26.26/8.61	   A^2 -> H(U1(c, c), U1(b, k))
26.26/8.61	   A^2 -> H(U1(c, c), U1(e, e))
26.26/8.61	   A^2 -> H(U1(c, c), U1(k, k))
26.26/8.61	   A^2 -> H(U1(c, c), U1(k, d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(d, k))
26.26/8.61	   A^2 -> H(e, U1(b, b))
26.26/8.61	   A^2 -> H(e, f(c))
26.26/8.61	   A^2 -> H(e, f(d))
26.26/8.61	   A^2 -> H(U1(e, e), U1(c, b))
26.26/8.61	   A^2 -> H(U1(e, e), U1(d, b))
26.26/8.61	   A^2 -> H(U1(e, e), U1(b, c))
26.26/8.61	   A^2 -> H(U1(e, e), U1(b, d))
26.26/8.61	   A^2 -> H(U1(e, e), U1(c, c))
26.26/8.61	   A^2 -> H(U1(e, e), f(e))
26.26/8.61	   A^2 -> H(U1(e, e), f(k))
26.26/8.61	   A^2 -> H(U1(e, e), U1(d, d))
26.26/8.61	   A^2 -> H(f(e), U1(e, b))
26.26/8.61	   A^2 -> H(f(e), U1(k, b))
26.26/8.61	   A^2 -> H(f(e), U1(c, d))
26.26/8.61	   A^2 -> H(f(e), U1(d, c))
26.26/8.61	   A^2 -> H(f(e), U1(b, e))
26.26/8.61	   A^2 -> H(f(e), U1(b, k))
26.26/8.61	   A^2 -> H(f(e), U1(e, c))
26.26/8.61	   A^2 -> H(f(e), U1(k, c))
26.26/8.61	   A^2 -> H(f(e), U1(c, e))
26.26/8.61	   A^2 -> H(f(e), U1(c, k))
26.26/8.61	   A^2 -> H(f(e), U1(k, k))
26.26/8.61	   A^2 -> H(f(e), U1(k, d))
26.26/8.61	   A^2 -> H(f(e), U1(d, k))
26.26/8.61	   A^2 -> H(U1(k, k), U1(c, b))
26.26/8.61	   A^2 -> H(U1(k, k), U1(d, b))
26.26/8.61	   A^2 -> H(U1(k, k), U1(b, c))
26.26/8.61	   A^2 -> H(U1(k, k), U1(b, d))
26.26/8.61	   A^2 -> H(U1(k, k), U1(c, c))
26.26/8.61	   A^2 -> H(U1(k, k), f(e))
26.26/8.61	   A^2 -> H(U1(k, k), f(k))
26.26/8.61	   A^2 -> H(U1(k, k), U1(d, d))
26.26/8.61	   A^2 -> H(f(k), U1(e, b))
26.26/8.61	   A^2 -> H(f(k), U1(k, b))
26.26/8.61	   A^2 -> H(f(k), U1(c, d))
26.26/8.61	   A^2 -> H(f(k), U1(d, c))
26.26/8.61	   A^2 -> H(f(k), U1(b, e))
26.26/8.61	   A^2 -> H(f(k), U1(b, k))
26.26/8.61	
26.26/8.61	The TRS R consists of the following rules:
26.26/8.61	
26.26/8.61	   f(x) -> U1(x, x)
26.26/8.61	   U1(e, x) -> x
26.26/8.61	   a -> c
26.26/8.61	   a -> d
26.26/8.61	   b -> c
26.26/8.61	   b -> d
26.26/8.61	   d -> k
26.26/8.61	   c -> e
26.26/8.61	   c -> k
26.26/8.61	
26.26/8.61	Q is empty.
26.26/8.61	We have to consider all minimal (P,Q,R)-chains.
26.26/8.61	----------------------------------------
26.26/8.61	
26.26/8.61	(433) TransformationProof (EQUIVALENT)
26.26/8.61	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
26.26/8.61	
26.26/8.61	   (A^2 -> H(U1(k, k), U1(b, d)),A^2 -> H(U1(k, k), U1(b, d)))
26.26/8.61	   (A^2 -> H(f(k), U1(c, d)),A^2 -> H(f(k), U1(c, d)))
26.26/8.61	   (A^2 -> H(f(k), U1(d, d)),A^2 -> H(f(k), U1(d, d)))
26.26/8.61	   (A^2 -> H(f(k), U1(b, k)),A^2 -> H(f(k), U1(b, k)))
26.26/8.61	
26.26/8.61	
26.26/8.61	----------------------------------------
26.26/8.61	
26.26/8.61	(434)
26.26/8.61	Obligation:
26.26/8.61	Q DP problem:
26.26/8.61	The TRS P consists of the following rules:
26.26/8.61	
26.26/8.61	   H(x, x) -> G(x, x, f(k))
26.26/8.61	   G(d, x, x) -> A^2
26.26/8.61	   A^2 -> H(f(c), f(c))
26.26/8.61	   A^2 -> H(f(d), f(d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(c, c))
26.26/8.61	   A^2 -> H(f(e), f(e))
26.26/8.61	   A^2 -> H(f(k), U1(c, c))
26.26/8.61	   A^2 -> H(f(k), f(e))
26.26/8.61	   A^2 -> H(f(k), f(k))
26.26/8.61	   A^2 -> H(f(k), U1(d, d))
26.26/8.61	   A^2 -> H(f(c), U1(e, b))
26.26/8.61	   A^2 -> H(f(c), U1(k, b))
26.26/8.61	   A^2 -> H(f(c), U1(c, d))
26.26/8.61	   A^2 -> H(f(c), U1(d, c))
26.26/8.61	   A^2 -> H(f(c), U1(b, e))
26.26/8.61	   A^2 -> H(f(c), U1(b, k))
26.26/8.61	   A^2 -> H(f(c), U1(k, d))
26.26/8.61	   A^2 -> H(f(c), U1(d, k))
26.26/8.61	   A^2 -> H(f(c), U1(k, k))
26.26/8.61	   A^2 -> H(U1(k, k), f(b))
26.26/8.61	   A^2 -> H(U1(k, d), U1(b, b))
26.26/8.61	   A^2 -> H(U1(k, d), f(c))
26.26/8.61	   A^2 -> H(U1(k, d), f(d))
26.26/8.61	   A^2 -> H(U1(d, k), U1(b, b))
26.26/8.61	   A^2 -> H(U1(d, k), f(c))
26.26/8.61	   A^2 -> H(U1(d, k), f(d))
26.26/8.61	   A^2 -> H(U1(d, d), U1(c, b))
26.26/8.61	   A^2 -> H(U1(d, d), U1(d, b))
26.26/8.61	   A^2 -> H(U1(d, d), U1(b, c))
26.26/8.61	   A^2 -> H(U1(d, d), U1(b, d))
26.26/8.61	   A^2 -> H(U1(d, d), U1(c, c))
26.26/8.61	   A^2 -> H(U1(d, d), f(e))
26.26/8.61	   A^2 -> H(U1(d, d), f(k))
26.26/8.61	   A^2 -> H(U1(d, d), U1(d, d))
26.26/8.61	   A^2 -> H(f(d), U1(e, b))
26.26/8.61	   A^2 -> H(f(d), U1(k, b))
26.26/8.61	   A^2 -> H(f(d), U1(c, d))
26.26/8.61	   A^2 -> H(f(d), U1(d, c))
26.26/8.61	   A^2 -> H(f(d), U1(b, e))
26.26/8.61	   A^2 -> H(f(d), U1(b, k))
26.26/8.61	   A^2 -> H(f(d), U1(e, c))
26.26/8.61	   A^2 -> H(f(d), U1(k, c))
26.26/8.61	   A^2 -> H(f(d), U1(c, e))
26.26/8.61	   A^2 -> H(f(d), U1(c, k))
26.26/8.61	   A^2 -> H(f(d), U1(e, e))
26.26/8.61	   A^2 -> H(f(d), U1(k, k))
26.26/8.61	   A^2 -> H(f(a), b)
26.26/8.61	   A^2 -> H(f(a), U1(e, d))
26.26/8.61	   A^2 -> H(f(a), U1(d, e))
26.26/8.61	   A^2 -> H(f(c), U1(e, c))
26.26/8.61	   A^2 -> H(f(c), U1(k, c))
26.26/8.61	   A^2 -> H(f(c), U1(c, e))
26.26/8.61	   A^2 -> H(f(c), U1(c, k))
26.26/8.61	   A^2 -> H(f(a), c)
26.26/8.61	   A^2 -> H(f(a), U1(e, k))
26.26/8.61	   A^2 -> H(f(a), U1(k, e))
26.26/8.61	   A^2 -> H(f(c), U1(e, e))
26.26/8.61	   A^2 -> H(f(a), e)
26.26/8.61	   A^2 -> H(f(d), U1(k, d))
26.26/8.61	   A^2 -> H(f(d), U1(d, k))
26.26/8.61	   A^2 -> H(f(a), U1(k, k))
26.26/8.61	   A^2 -> H(d, f(b))
26.26/8.61	   A^2 -> H(a, U1(b, b))
26.26/8.61	   A^2 -> H(a, f(c))
26.26/8.61	   A^2 -> H(a, f(d))
26.26/8.61	   A^2 -> H(U1(e, d), U1(b, b))
26.26/8.61	   A^2 -> H(U1(e, d), f(c))
26.26/8.61	   A^2 -> H(U1(e, d), f(d))
26.26/8.61	   A^2 -> H(U1(e, a), U1(c, b))
26.26/8.61	   A^2 -> H(U1(e, a), U1(d, b))
26.26/8.61	   A^2 -> H(U1(e, a), U1(b, c))
26.26/8.61	   A^2 -> H(U1(e, a), U1(b, d))
26.26/8.61	   A^2 -> H(U1(e, a), U1(c, c))
26.26/8.61	   A^2 -> H(U1(e, a), f(e))
26.26/8.61	   A^2 -> H(U1(e, a), f(k))
26.26/8.61	   A^2 -> H(U1(e, a), U1(d, d))
26.26/8.61	   A^2 -> H(U1(k, a), U1(c, b))
26.26/8.61	   A^2 -> H(U1(k, a), U1(d, b))
26.26/8.61	   A^2 -> H(U1(k, a), U1(b, c))
26.26/8.61	   A^2 -> H(U1(k, a), U1(b, d))
26.26/8.61	   A^2 -> H(U1(k, a), U1(c, c))
26.26/8.61	   A^2 -> H(U1(k, a), f(e))
26.26/8.61	   A^2 -> H(U1(k, a), f(k))
26.26/8.61	   A^2 -> H(U1(k, a), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, d), U1(c, b))
26.26/8.61	   A^2 -> H(U1(c, d), U1(d, b))
26.26/8.61	   A^2 -> H(U1(c, d), U1(b, c))
26.26/8.61	   A^2 -> H(U1(c, d), U1(b, d))
26.26/8.61	   A^2 -> H(U1(c, d), U1(c, c))
26.26/8.61	   A^2 -> H(U1(c, d), f(e))
26.26/8.61	   A^2 -> H(U1(c, d), f(k))
26.26/8.61	   A^2 -> H(U1(c, d), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, a), U1(e, b))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, b))
26.26/8.61	   A^2 -> H(U1(c, a), U1(c, d))
26.26/8.61	   A^2 -> H(U1(c, a), U1(d, c))
26.26/8.61	   A^2 -> H(U1(c, a), U1(b, e))
26.26/8.61	   A^2 -> H(U1(c, a), U1(b, k))
26.26/8.61	   A^2 -> H(U1(c, a), U1(e, c))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, c))
26.26/8.61	   A^2 -> H(U1(c, a), U1(c, e))
26.26/8.61	   A^2 -> H(U1(c, a), U1(c, k))
26.26/8.61	   A^2 -> H(U1(c, a), U1(e, e))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, k))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, d))
26.26/8.61	   A^2 -> H(U1(c, a), U1(d, k))
26.26/8.61	   A^2 -> H(U1(d, e), U1(b, b))
26.26/8.61	   A^2 -> H(U1(d, e), f(c))
26.26/8.61	   A^2 -> H(U1(d, e), f(d))
26.26/8.61	   A^2 -> H(U1(d, c), U1(c, b))
26.26/8.61	   A^2 -> H(U1(d, c), U1(d, b))
26.26/8.61	   A^2 -> H(U1(d, c), U1(b, c))
26.26/8.61	   A^2 -> H(U1(d, c), U1(b, d))
26.26/8.61	   A^2 -> H(U1(d, c), U1(c, c))
26.26/8.61	   A^2 -> H(U1(d, c), f(e))
26.26/8.61	   A^2 -> H(U1(d, c), f(k))
26.26/8.61	   A^2 -> H(U1(d, c), U1(d, d))
26.26/8.61	   A^2 -> H(U1(d, a), U1(e, b))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, b))
26.26/8.61	   A^2 -> H(U1(d, a), U1(c, d))
26.26/8.61	   A^2 -> H(U1(d, a), U1(d, c))
26.26/8.61	   A^2 -> H(U1(d, a), U1(b, e))
26.26/8.61	   A^2 -> H(U1(d, a), U1(b, k))
26.26/8.61	   A^2 -> H(U1(d, a), U1(e, c))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, c))
26.26/8.61	   A^2 -> H(U1(d, a), U1(c, e))
26.26/8.61	   A^2 -> H(U1(d, a), U1(c, k))
26.26/8.61	   A^2 -> H(U1(d, a), U1(e, e))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, k))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, d))
26.26/8.61	   A^2 -> H(U1(d, a), U1(d, k))
26.26/8.61	   A^2 -> H(U1(a, e), U1(c, b))
26.26/8.61	   A^2 -> H(U1(a, e), U1(d, b))
26.26/8.61	   A^2 -> H(U1(a, e), U1(b, c))
26.26/8.61	   A^2 -> H(U1(a, e), U1(b, d))
26.26/8.61	   A^2 -> H(U1(a, e), U1(c, c))
26.26/8.61	   A^2 -> H(U1(a, e), f(e))
26.26/8.61	   A^2 -> H(U1(a, e), f(k))
26.26/8.61	   A^2 -> H(U1(a, e), U1(d, d))
26.26/8.61	   A^2 -> H(U1(a, k), U1(c, b))
26.26/8.61	   A^2 -> H(U1(a, k), U1(d, b))
26.26/8.61	   A^2 -> H(U1(a, k), U1(b, c))
26.26/8.61	   A^2 -> H(U1(a, k), U1(b, d))
26.26/8.61	   A^2 -> H(U1(a, k), U1(c, c))
26.26/8.61	   A^2 -> H(U1(a, k), f(e))
26.26/8.61	   A^2 -> H(U1(a, k), f(k))
26.26/8.61	   A^2 -> H(U1(a, k), U1(d, d))
26.26/8.61	   A^2 -> H(U1(a, c), U1(e, b))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, b))
26.26/8.61	   A^2 -> H(U1(a, c), U1(c, d))
26.26/8.61	   A^2 -> H(U1(a, c), U1(d, c))
26.26/8.61	   A^2 -> H(U1(a, c), U1(b, e))
26.26/8.61	   A^2 -> H(U1(a, c), U1(b, k))
26.26/8.61	   A^2 -> H(U1(a, c), U1(e, c))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, c))
26.26/8.61	   A^2 -> H(U1(a, c), U1(c, e))
26.26/8.61	   A^2 -> H(U1(a, c), U1(c, k))
26.26/8.61	   A^2 -> H(U1(a, c), U1(e, e))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, k))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, d))
26.26/8.61	   A^2 -> H(U1(a, c), U1(d, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(e, b))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, b))
26.26/8.61	   A^2 -> H(U1(a, d), U1(c, d))
26.26/8.61	   A^2 -> H(U1(a, d), U1(d, c))
26.26/8.61	   A^2 -> H(U1(a, d), U1(b, e))
26.26/8.61	   A^2 -> H(U1(a, d), U1(b, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(e, c))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, c))
26.26/8.61	   A^2 -> H(U1(a, d), U1(c, e))
26.26/8.61	   A^2 -> H(U1(a, d), U1(c, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(e, e))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, d))
26.26/8.61	   A^2 -> H(U1(a, d), U1(d, k))
26.26/8.61	   A^2 -> H(U1(a, a), b)
26.26/8.61	   A^2 -> H(U1(a, a), U1(e, d))
26.26/8.61	   A^2 -> H(U1(a, a), U1(d, e))
26.26/8.61	   A^2 -> H(U1(a, a), c)
26.26/8.61	   A^2 -> H(U1(a, a), U1(e, k))
26.26/8.61	   A^2 -> H(U1(a, a), U1(k, e))
26.26/8.61	   A^2 -> H(U1(a, a), e)
26.26/8.61	   A^2 -> H(U1(a, a), U1(k, k))
26.26/8.61	   A^2 -> H(k, f(b))
26.26/8.61	   A^2 -> H(c, U1(b, b))
26.26/8.61	   A^2 -> H(c, f(c))
26.26/8.61	   A^2 -> H(c, f(d))
26.26/8.61	   A^2 -> H(U1(e, k), U1(b, b))
26.26/8.61	   A^2 -> H(U1(e, k), f(c))
26.26/8.61	   A^2 -> H(U1(e, k), f(d))
26.26/8.61	   A^2 -> H(U1(e, c), U1(c, b))
26.26/8.61	   A^2 -> H(U1(e, c), U1(d, b))
26.26/8.61	   A^2 -> H(U1(e, c), U1(b, c))
26.26/8.61	   A^2 -> H(U1(e, c), U1(b, d))
26.26/8.61	   A^2 -> H(U1(e, c), U1(c, c))
26.26/8.61	   A^2 -> H(U1(e, c), f(e))
26.26/8.61	   A^2 -> H(U1(e, c), f(k))
26.26/8.61	   A^2 -> H(U1(e, c), U1(d, d))
26.26/8.61	   A^2 -> H(U1(k, e), U1(b, b))
26.26/8.61	   A^2 -> H(U1(k, e), f(c))
26.26/8.61	   A^2 -> H(U1(k, e), f(d))
26.26/8.61	   A^2 -> H(U1(k, c), U1(c, b))
26.26/8.61	   A^2 -> H(U1(k, c), U1(d, b))
26.26/8.61	   A^2 -> H(U1(k, c), U1(b, c))
26.26/8.61	   A^2 -> H(U1(k, c), U1(b, d))
26.26/8.61	   A^2 -> H(U1(k, c), U1(c, c))
26.26/8.61	   A^2 -> H(U1(k, c), f(e))
26.26/8.61	   A^2 -> H(U1(k, c), f(k))
26.26/8.61	   A^2 -> H(U1(k, c), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, e), U1(c, b))
26.26/8.61	   A^2 -> H(U1(c, e), U1(d, b))
26.26/8.61	   A^2 -> H(U1(c, e), U1(b, c))
26.26/8.61	   A^2 -> H(U1(c, e), U1(b, d))
26.26/8.61	   A^2 -> H(U1(c, e), U1(c, c))
26.26/8.61	   A^2 -> H(U1(c, e), f(e))
26.26/8.61	   A^2 -> H(U1(c, e), f(k))
26.26/8.61	   A^2 -> H(U1(c, e), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, k), U1(c, b))
26.26/8.61	   A^2 -> H(U1(c, k), U1(d, b))
26.26/8.61	   A^2 -> H(U1(c, k), U1(b, c))
26.26/8.61	   A^2 -> H(U1(c, k), U1(b, d))
26.26/8.61	   A^2 -> H(U1(c, k), U1(c, c))
26.26/8.61	   A^2 -> H(U1(c, k), f(e))
26.26/8.61	   A^2 -> H(U1(c, k), f(k))
26.26/8.61	   A^2 -> H(U1(c, k), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(e, b))
26.26/8.61	   A^2 -> H(U1(c, c), U1(k, b))
26.26/8.61	   A^2 -> H(U1(c, c), U1(c, d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(d, c))
26.26/8.61	   A^2 -> H(U1(c, c), U1(b, e))
26.26/8.61	   A^2 -> H(U1(c, c), U1(b, k))
26.26/8.61	   A^2 -> H(U1(c, c), U1(e, e))
26.26/8.61	   A^2 -> H(U1(c, c), U1(k, k))
26.26/8.61	   A^2 -> H(U1(c, c), U1(k, d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(d, k))
26.26/8.61	   A^2 -> H(e, U1(b, b))
26.26/8.61	   A^2 -> H(e, f(c))
26.26/8.61	   A^2 -> H(e, f(d))
26.26/8.61	   A^2 -> H(U1(e, e), U1(c, b))
26.26/8.61	   A^2 -> H(U1(e, e), U1(d, b))
26.26/8.61	   A^2 -> H(U1(e, e), U1(b, c))
26.26/8.61	   A^2 -> H(U1(e, e), U1(b, d))
26.26/8.61	   A^2 -> H(U1(e, e), U1(c, c))
26.26/8.61	   A^2 -> H(U1(e, e), f(e))
26.26/8.61	   A^2 -> H(U1(e, e), f(k))
26.26/8.61	   A^2 -> H(U1(e, e), U1(d, d))
26.26/8.61	   A^2 -> H(f(e), U1(e, b))
26.26/8.61	   A^2 -> H(f(e), U1(k, b))
26.26/8.61	   A^2 -> H(f(e), U1(c, d))
26.26/8.61	   A^2 -> H(f(e), U1(d, c))
26.26/8.61	   A^2 -> H(f(e), U1(b, e))
26.26/8.61	   A^2 -> H(f(e), U1(b, k))
26.26/8.61	   A^2 -> H(f(e), U1(e, c))
26.26/8.61	   A^2 -> H(f(e), U1(k, c))
26.26/8.61	   A^2 -> H(f(e), U1(c, e))
26.26/8.61	   A^2 -> H(f(e), U1(c, k))
26.26/8.61	   A^2 -> H(f(e), U1(k, k))
26.26/8.61	   A^2 -> H(f(e), U1(k, d))
26.26/8.61	   A^2 -> H(f(e), U1(d, k))
26.26/8.61	   A^2 -> H(U1(k, k), U1(c, b))
26.26/8.61	   A^2 -> H(U1(k, k), U1(d, b))
26.26/8.61	   A^2 -> H(U1(k, k), U1(b, c))
26.26/8.61	   A^2 -> H(U1(k, k), U1(b, d))
26.26/8.61	   A^2 -> H(U1(k, k), U1(c, c))
26.26/8.61	   A^2 -> H(U1(k, k), f(e))
26.26/8.61	   A^2 -> H(U1(k, k), f(k))
26.26/8.61	   A^2 -> H(U1(k, k), U1(d, d))
26.26/8.61	   A^2 -> H(f(k), U1(e, b))
26.26/8.61	   A^2 -> H(f(k), U1(k, b))
26.26/8.61	   A^2 -> H(f(k), U1(c, d))
26.26/8.61	   A^2 -> H(f(k), U1(d, c))
26.26/8.61	   A^2 -> H(f(k), U1(b, e))
26.26/8.61	   A^2 -> H(f(k), U1(b, k))
26.26/8.61	
26.26/8.61	The TRS R consists of the following rules:
26.26/8.61	
26.26/8.61	   f(x) -> U1(x, x)
26.26/8.61	   U1(e, x) -> x
26.26/8.61	   a -> c
26.26/8.61	   a -> d
26.26/8.61	   b -> c
26.26/8.61	   b -> d
26.26/8.61	   d -> k
26.26/8.61	   c -> e
26.26/8.61	   c -> k
26.26/8.61	
26.26/8.61	Q is empty.
26.26/8.61	We have to consider all minimal (P,Q,R)-chains.
26.26/8.61	----------------------------------------
26.26/8.61	
26.26/8.61	(435) TransformationProof (EQUIVALENT)
26.26/8.61	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
26.26/8.61	
26.26/8.61	   (A^2 -> H(U1(k, k), U1(c, c)),A^2 -> H(U1(k, k), U1(c, c)))
26.26/8.61	   (A^2 -> H(f(k), U1(e, c)),A^2 -> H(f(k), U1(e, c)))
26.26/8.61	   (A^2 -> H(f(k), U1(k, c)),A^2 -> H(f(k), U1(k, c)))
26.26/8.61	   (A^2 -> H(f(k), U1(c, e)),A^2 -> H(f(k), U1(c, e)))
26.26/8.61	   (A^2 -> H(f(k), U1(c, k)),A^2 -> H(f(k), U1(c, k)))
26.26/8.61	
26.26/8.61	
26.26/8.61	----------------------------------------
26.26/8.61	
26.26/8.61	(436)
26.26/8.61	Obligation:
26.26/8.61	Q DP problem:
26.26/8.61	The TRS P consists of the following rules:
26.26/8.61	
26.26/8.61	   H(x, x) -> G(x, x, f(k))
26.26/8.61	   G(d, x, x) -> A^2
26.26/8.61	   A^2 -> H(f(c), f(c))
26.26/8.61	   A^2 -> H(f(d), f(d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(c, c))
26.26/8.61	   A^2 -> H(f(e), f(e))
26.26/8.61	   A^2 -> H(f(k), f(e))
26.26/8.61	   A^2 -> H(f(k), f(k))
26.26/8.61	   A^2 -> H(f(k), U1(d, d))
26.26/8.61	   A^2 -> H(f(c), U1(e, b))
26.26/8.61	   A^2 -> H(f(c), U1(k, b))
26.26/8.61	   A^2 -> H(f(c), U1(c, d))
26.26/8.61	   A^2 -> H(f(c), U1(d, c))
26.26/8.61	   A^2 -> H(f(c), U1(b, e))
26.26/8.61	   A^2 -> H(f(c), U1(b, k))
26.26/8.61	   A^2 -> H(f(c), U1(k, d))
26.26/8.61	   A^2 -> H(f(c), U1(d, k))
26.26/8.61	   A^2 -> H(f(c), U1(k, k))
26.26/8.61	   A^2 -> H(U1(k, k), f(b))
26.26/8.61	   A^2 -> H(U1(k, d), U1(b, b))
26.26/8.61	   A^2 -> H(U1(k, d), f(c))
26.26/8.61	   A^2 -> H(U1(k, d), f(d))
26.26/8.61	   A^2 -> H(U1(d, k), U1(b, b))
26.26/8.61	   A^2 -> H(U1(d, k), f(c))
26.26/8.61	   A^2 -> H(U1(d, k), f(d))
26.26/8.61	   A^2 -> H(U1(d, d), U1(c, b))
26.26/8.61	   A^2 -> H(U1(d, d), U1(d, b))
26.26/8.61	   A^2 -> H(U1(d, d), U1(b, c))
26.26/8.61	   A^2 -> H(U1(d, d), U1(b, d))
26.26/8.61	   A^2 -> H(U1(d, d), U1(c, c))
26.26/8.61	   A^2 -> H(U1(d, d), f(e))
26.26/8.61	   A^2 -> H(U1(d, d), f(k))
26.26/8.61	   A^2 -> H(U1(d, d), U1(d, d))
26.26/8.61	   A^2 -> H(f(d), U1(e, b))
26.26/8.61	   A^2 -> H(f(d), U1(k, b))
26.26/8.61	   A^2 -> H(f(d), U1(c, d))
26.26/8.61	   A^2 -> H(f(d), U1(d, c))
26.26/8.61	   A^2 -> H(f(d), U1(b, e))
26.26/8.61	   A^2 -> H(f(d), U1(b, k))
26.26/8.61	   A^2 -> H(f(d), U1(e, c))
26.26/8.61	   A^2 -> H(f(d), U1(k, c))
26.26/8.61	   A^2 -> H(f(d), U1(c, e))
26.26/8.61	   A^2 -> H(f(d), U1(c, k))
26.26/8.61	   A^2 -> H(f(d), U1(e, e))
26.26/8.61	   A^2 -> H(f(d), U1(k, k))
26.26/8.61	   A^2 -> H(f(a), b)
26.26/8.61	   A^2 -> H(f(a), U1(e, d))
26.26/8.61	   A^2 -> H(f(a), U1(d, e))
26.26/8.61	   A^2 -> H(f(c), U1(e, c))
26.26/8.61	   A^2 -> H(f(c), U1(k, c))
26.26/8.61	   A^2 -> H(f(c), U1(c, e))
26.26/8.61	   A^2 -> H(f(c), U1(c, k))
26.26/8.61	   A^2 -> H(f(a), c)
26.26/8.61	   A^2 -> H(f(a), U1(e, k))
26.26/8.61	   A^2 -> H(f(a), U1(k, e))
26.26/8.61	   A^2 -> H(f(c), U1(e, e))
26.26/8.61	   A^2 -> H(f(a), e)
26.26/8.61	   A^2 -> H(f(d), U1(k, d))
26.26/8.61	   A^2 -> H(f(d), U1(d, k))
26.26/8.61	   A^2 -> H(f(a), U1(k, k))
26.26/8.61	   A^2 -> H(d, f(b))
26.26/8.61	   A^2 -> H(a, U1(b, b))
26.26/8.61	   A^2 -> H(a, f(c))
26.26/8.61	   A^2 -> H(a, f(d))
26.26/8.61	   A^2 -> H(U1(e, d), U1(b, b))
26.26/8.61	   A^2 -> H(U1(e, d), f(c))
26.26/8.61	   A^2 -> H(U1(e, d), f(d))
26.26/8.61	   A^2 -> H(U1(e, a), U1(c, b))
26.26/8.61	   A^2 -> H(U1(e, a), U1(d, b))
26.26/8.61	   A^2 -> H(U1(e, a), U1(b, c))
26.26/8.61	   A^2 -> H(U1(e, a), U1(b, d))
26.26/8.61	   A^2 -> H(U1(e, a), U1(c, c))
26.26/8.61	   A^2 -> H(U1(e, a), f(e))
26.26/8.61	   A^2 -> H(U1(e, a), f(k))
26.26/8.61	   A^2 -> H(U1(e, a), U1(d, d))
26.26/8.61	   A^2 -> H(U1(k, a), U1(c, b))
26.26/8.61	   A^2 -> H(U1(k, a), U1(d, b))
26.26/8.61	   A^2 -> H(U1(k, a), U1(b, c))
26.26/8.61	   A^2 -> H(U1(k, a), U1(b, d))
26.26/8.61	   A^2 -> H(U1(k, a), U1(c, c))
26.26/8.61	   A^2 -> H(U1(k, a), f(e))
26.26/8.61	   A^2 -> H(U1(k, a), f(k))
26.26/8.61	   A^2 -> H(U1(k, a), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, d), U1(c, b))
26.26/8.61	   A^2 -> H(U1(c, d), U1(d, b))
26.26/8.61	   A^2 -> H(U1(c, d), U1(b, c))
26.26/8.61	   A^2 -> H(U1(c, d), U1(b, d))
26.26/8.61	   A^2 -> H(U1(c, d), U1(c, c))
26.26/8.61	   A^2 -> H(U1(c, d), f(e))
26.26/8.61	   A^2 -> H(U1(c, d), f(k))
26.26/8.61	   A^2 -> H(U1(c, d), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, a), U1(e, b))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, b))
26.26/8.61	   A^2 -> H(U1(c, a), U1(c, d))
26.26/8.61	   A^2 -> H(U1(c, a), U1(d, c))
26.26/8.61	   A^2 -> H(U1(c, a), U1(b, e))
26.26/8.61	   A^2 -> H(U1(c, a), U1(b, k))
26.26/8.61	   A^2 -> H(U1(c, a), U1(e, c))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, c))
26.26/8.61	   A^2 -> H(U1(c, a), U1(c, e))
26.26/8.61	   A^2 -> H(U1(c, a), U1(c, k))
26.26/8.61	   A^2 -> H(U1(c, a), U1(e, e))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, k))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, d))
26.26/8.61	   A^2 -> H(U1(c, a), U1(d, k))
26.26/8.61	   A^2 -> H(U1(d, e), U1(b, b))
26.26/8.61	   A^2 -> H(U1(d, e), f(c))
26.26/8.61	   A^2 -> H(U1(d, e), f(d))
26.26/8.61	   A^2 -> H(U1(d, c), U1(c, b))
26.26/8.61	   A^2 -> H(U1(d, c), U1(d, b))
26.26/8.61	   A^2 -> H(U1(d, c), U1(b, c))
26.26/8.61	   A^2 -> H(U1(d, c), U1(b, d))
26.26/8.61	   A^2 -> H(U1(d, c), U1(c, c))
26.26/8.61	   A^2 -> H(U1(d, c), f(e))
26.26/8.61	   A^2 -> H(U1(d, c), f(k))
26.26/8.61	   A^2 -> H(U1(d, c), U1(d, d))
26.26/8.61	   A^2 -> H(U1(d, a), U1(e, b))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, b))
26.26/8.61	   A^2 -> H(U1(d, a), U1(c, d))
26.26/8.61	   A^2 -> H(U1(d, a), U1(d, c))
26.26/8.61	   A^2 -> H(U1(d, a), U1(b, e))
26.26/8.61	   A^2 -> H(U1(d, a), U1(b, k))
26.26/8.61	   A^2 -> H(U1(d, a), U1(e, c))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, c))
26.26/8.61	   A^2 -> H(U1(d, a), U1(c, e))
26.26/8.61	   A^2 -> H(U1(d, a), U1(c, k))
26.26/8.61	   A^2 -> H(U1(d, a), U1(e, e))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, k))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, d))
26.26/8.61	   A^2 -> H(U1(d, a), U1(d, k))
26.26/8.61	   A^2 -> H(U1(a, e), U1(c, b))
26.26/8.61	   A^2 -> H(U1(a, e), U1(d, b))
26.26/8.61	   A^2 -> H(U1(a, e), U1(b, c))
26.26/8.61	   A^2 -> H(U1(a, e), U1(b, d))
26.26/8.61	   A^2 -> H(U1(a, e), U1(c, c))
26.26/8.61	   A^2 -> H(U1(a, e), f(e))
26.26/8.61	   A^2 -> H(U1(a, e), f(k))
26.26/8.61	   A^2 -> H(U1(a, e), U1(d, d))
26.26/8.61	   A^2 -> H(U1(a, k), U1(c, b))
26.26/8.61	   A^2 -> H(U1(a, k), U1(d, b))
26.26/8.61	   A^2 -> H(U1(a, k), U1(b, c))
26.26/8.61	   A^2 -> H(U1(a, k), U1(b, d))
26.26/8.61	   A^2 -> H(U1(a, k), U1(c, c))
26.26/8.61	   A^2 -> H(U1(a, k), f(e))
26.26/8.61	   A^2 -> H(U1(a, k), f(k))
26.26/8.61	   A^2 -> H(U1(a, k), U1(d, d))
26.26/8.61	   A^2 -> H(U1(a, c), U1(e, b))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, b))
26.26/8.61	   A^2 -> H(U1(a, c), U1(c, d))
26.26/8.61	   A^2 -> H(U1(a, c), U1(d, c))
26.26/8.61	   A^2 -> H(U1(a, c), U1(b, e))
26.26/8.61	   A^2 -> H(U1(a, c), U1(b, k))
26.26/8.61	   A^2 -> H(U1(a, c), U1(e, c))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, c))
26.26/8.61	   A^2 -> H(U1(a, c), U1(c, e))
26.26/8.61	   A^2 -> H(U1(a, c), U1(c, k))
26.26/8.61	   A^2 -> H(U1(a, c), U1(e, e))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, k))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, d))
26.26/8.61	   A^2 -> H(U1(a, c), U1(d, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(e, b))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, b))
26.26/8.61	   A^2 -> H(U1(a, d), U1(c, d))
26.26/8.61	   A^2 -> H(U1(a, d), U1(d, c))
26.26/8.61	   A^2 -> H(U1(a, d), U1(b, e))
26.26/8.61	   A^2 -> H(U1(a, d), U1(b, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(e, c))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, c))
26.26/8.61	   A^2 -> H(U1(a, d), U1(c, e))
26.26/8.61	   A^2 -> H(U1(a, d), U1(c, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(e, e))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, d))
26.26/8.61	   A^2 -> H(U1(a, d), U1(d, k))
26.26/8.61	   A^2 -> H(U1(a, a), b)
26.26/8.61	   A^2 -> H(U1(a, a), U1(e, d))
26.26/8.61	   A^2 -> H(U1(a, a), U1(d, e))
26.26/8.61	   A^2 -> H(U1(a, a), c)
26.26/8.61	   A^2 -> H(U1(a, a), U1(e, k))
26.26/8.61	   A^2 -> H(U1(a, a), U1(k, e))
26.26/8.61	   A^2 -> H(U1(a, a), e)
26.26/8.61	   A^2 -> H(U1(a, a), U1(k, k))
26.26/8.61	   A^2 -> H(k, f(b))
26.26/8.61	   A^2 -> H(c, U1(b, b))
26.26/8.61	   A^2 -> H(c, f(c))
26.26/8.61	   A^2 -> H(c, f(d))
26.26/8.61	   A^2 -> H(U1(e, k), U1(b, b))
26.26/8.61	   A^2 -> H(U1(e, k), f(c))
26.26/8.61	   A^2 -> H(U1(e, k), f(d))
26.26/8.61	   A^2 -> H(U1(e, c), U1(c, b))
26.26/8.61	   A^2 -> H(U1(e, c), U1(d, b))
26.26/8.61	   A^2 -> H(U1(e, c), U1(b, c))
26.26/8.61	   A^2 -> H(U1(e, c), U1(b, d))
26.26/8.61	   A^2 -> H(U1(e, c), U1(c, c))
26.26/8.61	   A^2 -> H(U1(e, c), f(e))
26.26/8.61	   A^2 -> H(U1(e, c), f(k))
26.26/8.61	   A^2 -> H(U1(e, c), U1(d, d))
26.26/8.61	   A^2 -> H(U1(k, e), U1(b, b))
26.26/8.61	   A^2 -> H(U1(k, e), f(c))
26.26/8.61	   A^2 -> H(U1(k, e), f(d))
26.26/8.61	   A^2 -> H(U1(k, c), U1(c, b))
26.26/8.61	   A^2 -> H(U1(k, c), U1(d, b))
26.26/8.61	   A^2 -> H(U1(k, c), U1(b, c))
26.26/8.61	   A^2 -> H(U1(k, c), U1(b, d))
26.26/8.61	   A^2 -> H(U1(k, c), U1(c, c))
26.26/8.61	   A^2 -> H(U1(k, c), f(e))
26.26/8.61	   A^2 -> H(U1(k, c), f(k))
26.26/8.61	   A^2 -> H(U1(k, c), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, e), U1(c, b))
26.26/8.61	   A^2 -> H(U1(c, e), U1(d, b))
26.26/8.61	   A^2 -> H(U1(c, e), U1(b, c))
26.26/8.61	   A^2 -> H(U1(c, e), U1(b, d))
26.26/8.61	   A^2 -> H(U1(c, e), U1(c, c))
26.26/8.61	   A^2 -> H(U1(c, e), f(e))
26.26/8.61	   A^2 -> H(U1(c, e), f(k))
26.26/8.61	   A^2 -> H(U1(c, e), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, k), U1(c, b))
26.26/8.61	   A^2 -> H(U1(c, k), U1(d, b))
26.26/8.61	   A^2 -> H(U1(c, k), U1(b, c))
26.26/8.61	   A^2 -> H(U1(c, k), U1(b, d))
26.26/8.61	   A^2 -> H(U1(c, k), U1(c, c))
26.26/8.61	   A^2 -> H(U1(c, k), f(e))
26.26/8.61	   A^2 -> H(U1(c, k), f(k))
26.26/8.61	   A^2 -> H(U1(c, k), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(e, b))
26.26/8.61	   A^2 -> H(U1(c, c), U1(k, b))
26.26/8.61	   A^2 -> H(U1(c, c), U1(c, d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(d, c))
26.26/8.61	   A^2 -> H(U1(c, c), U1(b, e))
26.26/8.61	   A^2 -> H(U1(c, c), U1(b, k))
26.26/8.61	   A^2 -> H(U1(c, c), U1(e, e))
26.26/8.61	   A^2 -> H(U1(c, c), U1(k, k))
26.26/8.61	   A^2 -> H(U1(c, c), U1(k, d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(d, k))
26.26/8.61	   A^2 -> H(e, U1(b, b))
26.26/8.61	   A^2 -> H(e, f(c))
26.26/8.61	   A^2 -> H(e, f(d))
26.26/8.61	   A^2 -> H(U1(e, e), U1(c, b))
26.26/8.61	   A^2 -> H(U1(e, e), U1(d, b))
26.26/8.61	   A^2 -> H(U1(e, e), U1(b, c))
26.26/8.61	   A^2 -> H(U1(e, e), U1(b, d))
26.26/8.61	   A^2 -> H(U1(e, e), U1(c, c))
26.26/8.61	   A^2 -> H(U1(e, e), f(e))
26.26/8.61	   A^2 -> H(U1(e, e), f(k))
26.26/8.61	   A^2 -> H(U1(e, e), U1(d, d))
26.26/8.61	   A^2 -> H(f(e), U1(e, b))
26.26/8.61	   A^2 -> H(f(e), U1(k, b))
26.26/8.61	   A^2 -> H(f(e), U1(c, d))
26.26/8.61	   A^2 -> H(f(e), U1(d, c))
26.26/8.61	   A^2 -> H(f(e), U1(b, e))
26.26/8.61	   A^2 -> H(f(e), U1(b, k))
26.26/8.61	   A^2 -> H(f(e), U1(e, c))
26.26/8.61	   A^2 -> H(f(e), U1(k, c))
26.26/8.61	   A^2 -> H(f(e), U1(c, e))
26.26/8.61	   A^2 -> H(f(e), U1(c, k))
26.26/8.61	   A^2 -> H(f(e), U1(k, k))
26.26/8.61	   A^2 -> H(f(e), U1(k, d))
26.26/8.61	   A^2 -> H(f(e), U1(d, k))
26.26/8.61	   A^2 -> H(U1(k, k), U1(c, b))
26.26/8.61	   A^2 -> H(U1(k, k), U1(d, b))
26.26/8.61	   A^2 -> H(U1(k, k), U1(b, c))
26.26/8.61	   A^2 -> H(U1(k, k), U1(b, d))
26.26/8.61	   A^2 -> H(U1(k, k), U1(c, c))
26.26/8.61	   A^2 -> H(U1(k, k), f(e))
26.26/8.61	   A^2 -> H(U1(k, k), f(k))
26.26/8.61	   A^2 -> H(U1(k, k), U1(d, d))
26.26/8.61	   A^2 -> H(f(k), U1(e, b))
26.26/8.61	   A^2 -> H(f(k), U1(k, b))
26.26/8.61	   A^2 -> H(f(k), U1(c, d))
26.26/8.61	   A^2 -> H(f(k), U1(d, c))
26.26/8.61	   A^2 -> H(f(k), U1(b, e))
26.26/8.61	   A^2 -> H(f(k), U1(b, k))
26.26/8.61	   A^2 -> H(f(k), U1(e, c))
26.26/8.61	   A^2 -> H(f(k), U1(k, c))
26.26/8.61	   A^2 -> H(f(k), U1(c, e))
26.26/8.61	   A^2 -> H(f(k), U1(c, k))
26.26/8.61	
26.26/8.61	The TRS R consists of the following rules:
26.26/8.61	
26.26/8.61	   f(x) -> U1(x, x)
26.26/8.61	   U1(e, x) -> x
26.26/8.61	   a -> c
26.26/8.61	   a -> d
26.26/8.61	   b -> c
26.26/8.61	   b -> d
26.26/8.61	   d -> k
26.26/8.61	   c -> e
26.26/8.61	   c -> k
26.26/8.61	
26.26/8.61	Q is empty.
26.26/8.61	We have to consider all minimal (P,Q,R)-chains.
26.26/8.61	----------------------------------------
26.26/8.61	
26.26/8.61	(437) TransformationProof (EQUIVALENT)
26.26/8.61	By narrowing [LPAR04] the rule A^2 -> H(f(k), f(e)) at position [] we obtained the following new rules [LPAR04]:
26.26/8.61	
26.26/8.61	   (A^2 -> H(U1(k, k), f(e)),A^2 -> H(U1(k, k), f(e)))
26.26/8.61	   (A^2 -> H(f(k), U1(e, e)),A^2 -> H(f(k), U1(e, e)))
26.26/8.61	
26.26/8.61	
26.26/8.61	----------------------------------------
26.26/8.61	
26.26/8.61	(438)
26.26/8.61	Obligation:
26.26/8.61	Q DP problem:
26.26/8.61	The TRS P consists of the following rules:
26.26/8.61	
26.26/8.61	   H(x, x) -> G(x, x, f(k))
26.26/8.61	   G(d, x, x) -> A^2
26.26/8.61	   A^2 -> H(f(c), f(c))
26.26/8.61	   A^2 -> H(f(d), f(d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(c, c))
26.26/8.61	   A^2 -> H(f(e), f(e))
26.26/8.61	   A^2 -> H(f(k), f(k))
26.26/8.61	   A^2 -> H(f(k), U1(d, d))
26.26/8.61	   A^2 -> H(f(c), U1(e, b))
26.26/8.61	   A^2 -> H(f(c), U1(k, b))
26.26/8.61	   A^2 -> H(f(c), U1(c, d))
26.26/8.61	   A^2 -> H(f(c), U1(d, c))
26.26/8.61	   A^2 -> H(f(c), U1(b, e))
26.26/8.61	   A^2 -> H(f(c), U1(b, k))
26.26/8.61	   A^2 -> H(f(c), U1(k, d))
26.26/8.61	   A^2 -> H(f(c), U1(d, k))
26.26/8.61	   A^2 -> H(f(c), U1(k, k))
26.26/8.61	   A^2 -> H(U1(k, k), f(b))
26.26/8.61	   A^2 -> H(U1(k, d), U1(b, b))
26.26/8.61	   A^2 -> H(U1(k, d), f(c))
26.26/8.61	   A^2 -> H(U1(k, d), f(d))
26.26/8.61	   A^2 -> H(U1(d, k), U1(b, b))
26.26/8.61	   A^2 -> H(U1(d, k), f(c))
26.26/8.61	   A^2 -> H(U1(d, k), f(d))
26.26/8.61	   A^2 -> H(U1(d, d), U1(c, b))
26.26/8.61	   A^2 -> H(U1(d, d), U1(d, b))
26.26/8.61	   A^2 -> H(U1(d, d), U1(b, c))
26.26/8.61	   A^2 -> H(U1(d, d), U1(b, d))
26.26/8.61	   A^2 -> H(U1(d, d), U1(c, c))
26.26/8.61	   A^2 -> H(U1(d, d), f(e))
26.26/8.61	   A^2 -> H(U1(d, d), f(k))
26.26/8.61	   A^2 -> H(U1(d, d), U1(d, d))
26.26/8.61	   A^2 -> H(f(d), U1(e, b))
26.26/8.61	   A^2 -> H(f(d), U1(k, b))
26.26/8.61	   A^2 -> H(f(d), U1(c, d))
26.26/8.61	   A^2 -> H(f(d), U1(d, c))
26.26/8.61	   A^2 -> H(f(d), U1(b, e))
26.26/8.61	   A^2 -> H(f(d), U1(b, k))
26.26/8.61	   A^2 -> H(f(d), U1(e, c))
26.26/8.61	   A^2 -> H(f(d), U1(k, c))
26.26/8.61	   A^2 -> H(f(d), U1(c, e))
26.26/8.61	   A^2 -> H(f(d), U1(c, k))
26.26/8.61	   A^2 -> H(f(d), U1(e, e))
26.26/8.61	   A^2 -> H(f(d), U1(k, k))
26.26/8.61	   A^2 -> H(f(a), b)
26.26/8.61	   A^2 -> H(f(a), U1(e, d))
26.26/8.61	   A^2 -> H(f(a), U1(d, e))
26.26/8.61	   A^2 -> H(f(c), U1(e, c))
26.26/8.61	   A^2 -> H(f(c), U1(k, c))
26.26/8.61	   A^2 -> H(f(c), U1(c, e))
26.26/8.61	   A^2 -> H(f(c), U1(c, k))
26.26/8.61	   A^2 -> H(f(a), c)
26.26/8.61	   A^2 -> H(f(a), U1(e, k))
26.26/8.61	   A^2 -> H(f(a), U1(k, e))
26.26/8.61	   A^2 -> H(f(c), U1(e, e))
26.26/8.61	   A^2 -> H(f(a), e)
26.26/8.61	   A^2 -> H(f(d), U1(k, d))
26.26/8.61	   A^2 -> H(f(d), U1(d, k))
26.26/8.61	   A^2 -> H(f(a), U1(k, k))
26.26/8.61	   A^2 -> H(d, f(b))
26.26/8.61	   A^2 -> H(a, U1(b, b))
26.26/8.61	   A^2 -> H(a, f(c))
26.26/8.61	   A^2 -> H(a, f(d))
26.26/8.61	   A^2 -> H(U1(e, d), U1(b, b))
26.26/8.61	   A^2 -> H(U1(e, d), f(c))
26.26/8.61	   A^2 -> H(U1(e, d), f(d))
26.26/8.61	   A^2 -> H(U1(e, a), U1(c, b))
26.26/8.61	   A^2 -> H(U1(e, a), U1(d, b))
26.26/8.61	   A^2 -> H(U1(e, a), U1(b, c))
26.26/8.61	   A^2 -> H(U1(e, a), U1(b, d))
26.26/8.61	   A^2 -> H(U1(e, a), U1(c, c))
26.26/8.61	   A^2 -> H(U1(e, a), f(e))
26.26/8.61	   A^2 -> H(U1(e, a), f(k))
26.26/8.61	   A^2 -> H(U1(e, a), U1(d, d))
26.26/8.61	   A^2 -> H(U1(k, a), U1(c, b))
26.26/8.61	   A^2 -> H(U1(k, a), U1(d, b))
26.26/8.61	   A^2 -> H(U1(k, a), U1(b, c))
26.26/8.61	   A^2 -> H(U1(k, a), U1(b, d))
26.26/8.61	   A^2 -> H(U1(k, a), U1(c, c))
26.26/8.61	   A^2 -> H(U1(k, a), f(e))
26.26/8.61	   A^2 -> H(U1(k, a), f(k))
26.26/8.61	   A^2 -> H(U1(k, a), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, d), U1(c, b))
26.26/8.61	   A^2 -> H(U1(c, d), U1(d, b))
26.26/8.61	   A^2 -> H(U1(c, d), U1(b, c))
26.26/8.61	   A^2 -> H(U1(c, d), U1(b, d))
26.26/8.61	   A^2 -> H(U1(c, d), U1(c, c))
26.26/8.61	   A^2 -> H(U1(c, d), f(e))
26.26/8.61	   A^2 -> H(U1(c, d), f(k))
26.26/8.61	   A^2 -> H(U1(c, d), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, a), U1(e, b))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, b))
26.26/8.61	   A^2 -> H(U1(c, a), U1(c, d))
26.26/8.61	   A^2 -> H(U1(c, a), U1(d, c))
26.26/8.61	   A^2 -> H(U1(c, a), U1(b, e))
26.26/8.61	   A^2 -> H(U1(c, a), U1(b, k))
26.26/8.61	   A^2 -> H(U1(c, a), U1(e, c))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, c))
26.26/8.61	   A^2 -> H(U1(c, a), U1(c, e))
26.26/8.61	   A^2 -> H(U1(c, a), U1(c, k))
26.26/8.61	   A^2 -> H(U1(c, a), U1(e, e))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, k))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, d))
26.26/8.61	   A^2 -> H(U1(c, a), U1(d, k))
26.26/8.61	   A^2 -> H(U1(d, e), U1(b, b))
26.26/8.61	   A^2 -> H(U1(d, e), f(c))
26.26/8.61	   A^2 -> H(U1(d, e), f(d))
26.26/8.61	   A^2 -> H(U1(d, c), U1(c, b))
26.26/8.61	   A^2 -> H(U1(d, c), U1(d, b))
26.26/8.61	   A^2 -> H(U1(d, c), U1(b, c))
26.26/8.61	   A^2 -> H(U1(d, c), U1(b, d))
26.26/8.61	   A^2 -> H(U1(d, c), U1(c, c))
26.26/8.61	   A^2 -> H(U1(d, c), f(e))
26.26/8.61	   A^2 -> H(U1(d, c), f(k))
26.26/8.61	   A^2 -> H(U1(d, c), U1(d, d))
26.26/8.61	   A^2 -> H(U1(d, a), U1(e, b))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, b))
26.26/8.61	   A^2 -> H(U1(d, a), U1(c, d))
26.26/8.61	   A^2 -> H(U1(d, a), U1(d, c))
26.26/8.61	   A^2 -> H(U1(d, a), U1(b, e))
26.26/8.61	   A^2 -> H(U1(d, a), U1(b, k))
26.26/8.61	   A^2 -> H(U1(d, a), U1(e, c))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, c))
26.26/8.61	   A^2 -> H(U1(d, a), U1(c, e))
26.26/8.61	   A^2 -> H(U1(d, a), U1(c, k))
26.26/8.61	   A^2 -> H(U1(d, a), U1(e, e))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, k))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, d))
26.26/8.61	   A^2 -> H(U1(d, a), U1(d, k))
26.26/8.61	   A^2 -> H(U1(a, e), U1(c, b))
26.26/8.61	   A^2 -> H(U1(a, e), U1(d, b))
26.26/8.61	   A^2 -> H(U1(a, e), U1(b, c))
26.26/8.61	   A^2 -> H(U1(a, e), U1(b, d))
26.26/8.61	   A^2 -> H(U1(a, e), U1(c, c))
26.26/8.61	   A^2 -> H(U1(a, e), f(e))
26.26/8.61	   A^2 -> H(U1(a, e), f(k))
26.26/8.61	   A^2 -> H(U1(a, e), U1(d, d))
26.26/8.61	   A^2 -> H(U1(a, k), U1(c, b))
26.26/8.61	   A^2 -> H(U1(a, k), U1(d, b))
26.26/8.61	   A^2 -> H(U1(a, k), U1(b, c))
26.26/8.61	   A^2 -> H(U1(a, k), U1(b, d))
26.26/8.61	   A^2 -> H(U1(a, k), U1(c, c))
26.26/8.61	   A^2 -> H(U1(a, k), f(e))
26.26/8.61	   A^2 -> H(U1(a, k), f(k))
26.26/8.61	   A^2 -> H(U1(a, k), U1(d, d))
26.26/8.61	   A^2 -> H(U1(a, c), U1(e, b))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, b))
26.26/8.61	   A^2 -> H(U1(a, c), U1(c, d))
26.26/8.61	   A^2 -> H(U1(a, c), U1(d, c))
26.26/8.61	   A^2 -> H(U1(a, c), U1(b, e))
26.26/8.61	   A^2 -> H(U1(a, c), U1(b, k))
26.26/8.61	   A^2 -> H(U1(a, c), U1(e, c))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, c))
26.26/8.61	   A^2 -> H(U1(a, c), U1(c, e))
26.26/8.61	   A^2 -> H(U1(a, c), U1(c, k))
26.26/8.61	   A^2 -> H(U1(a, c), U1(e, e))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, k))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, d))
26.26/8.61	   A^2 -> H(U1(a, c), U1(d, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(e, b))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, b))
26.26/8.61	   A^2 -> H(U1(a, d), U1(c, d))
26.26/8.61	   A^2 -> H(U1(a, d), U1(d, c))
26.26/8.61	   A^2 -> H(U1(a, d), U1(b, e))
26.26/8.61	   A^2 -> H(U1(a, d), U1(b, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(e, c))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, c))
26.26/8.61	   A^2 -> H(U1(a, d), U1(c, e))
26.26/8.61	   A^2 -> H(U1(a, d), U1(c, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(e, e))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, d))
26.26/8.61	   A^2 -> H(U1(a, d), U1(d, k))
26.26/8.61	   A^2 -> H(U1(a, a), b)
26.26/8.61	   A^2 -> H(U1(a, a), U1(e, d))
26.26/8.61	   A^2 -> H(U1(a, a), U1(d, e))
26.26/8.61	   A^2 -> H(U1(a, a), c)
26.26/8.61	   A^2 -> H(U1(a, a), U1(e, k))
26.26/8.61	   A^2 -> H(U1(a, a), U1(k, e))
26.26/8.61	   A^2 -> H(U1(a, a), e)
26.26/8.61	   A^2 -> H(U1(a, a), U1(k, k))
26.26/8.61	   A^2 -> H(k, f(b))
26.26/8.61	   A^2 -> H(c, U1(b, b))
26.26/8.61	   A^2 -> H(c, f(c))
26.26/8.61	   A^2 -> H(c, f(d))
26.26/8.61	   A^2 -> H(U1(e, k), U1(b, b))
26.26/8.61	   A^2 -> H(U1(e, k), f(c))
26.26/8.61	   A^2 -> H(U1(e, k), f(d))
26.26/8.61	   A^2 -> H(U1(e, c), U1(c, b))
26.26/8.61	   A^2 -> H(U1(e, c), U1(d, b))
26.26/8.61	   A^2 -> H(U1(e, c), U1(b, c))
26.26/8.61	   A^2 -> H(U1(e, c), U1(b, d))
26.26/8.61	   A^2 -> H(U1(e, c), U1(c, c))
26.26/8.61	   A^2 -> H(U1(e, c), f(e))
26.26/8.61	   A^2 -> H(U1(e, c), f(k))
26.26/8.61	   A^2 -> H(U1(e, c), U1(d, d))
26.26/8.61	   A^2 -> H(U1(k, e), U1(b, b))
26.26/8.61	   A^2 -> H(U1(k, e), f(c))
26.26/8.61	   A^2 -> H(U1(k, e), f(d))
26.26/8.61	   A^2 -> H(U1(k, c), U1(c, b))
26.26/8.61	   A^2 -> H(U1(k, c), U1(d, b))
26.26/8.61	   A^2 -> H(U1(k, c), U1(b, c))
26.26/8.61	   A^2 -> H(U1(k, c), U1(b, d))
26.26/8.61	   A^2 -> H(U1(k, c), U1(c, c))
26.26/8.61	   A^2 -> H(U1(k, c), f(e))
26.26/8.61	   A^2 -> H(U1(k, c), f(k))
26.26/8.61	   A^2 -> H(U1(k, c), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, e), U1(c, b))
26.26/8.61	   A^2 -> H(U1(c, e), U1(d, b))
26.26/8.61	   A^2 -> H(U1(c, e), U1(b, c))
26.26/8.61	   A^2 -> H(U1(c, e), U1(b, d))
26.26/8.61	   A^2 -> H(U1(c, e), U1(c, c))
26.26/8.61	   A^2 -> H(U1(c, e), f(e))
26.26/8.61	   A^2 -> H(U1(c, e), f(k))
26.26/8.61	   A^2 -> H(U1(c, e), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, k), U1(c, b))
26.26/8.61	   A^2 -> H(U1(c, k), U1(d, b))
26.26/8.61	   A^2 -> H(U1(c, k), U1(b, c))
26.26/8.61	   A^2 -> H(U1(c, k), U1(b, d))
26.26/8.61	   A^2 -> H(U1(c, k), U1(c, c))
26.26/8.61	   A^2 -> H(U1(c, k), f(e))
26.26/8.61	   A^2 -> H(U1(c, k), f(k))
26.26/8.61	   A^2 -> H(U1(c, k), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(e, b))
26.26/8.61	   A^2 -> H(U1(c, c), U1(k, b))
26.26/8.61	   A^2 -> H(U1(c, c), U1(c, d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(d, c))
26.26/8.61	   A^2 -> H(U1(c, c), U1(b, e))
26.26/8.61	   A^2 -> H(U1(c, c), U1(b, k))
26.26/8.61	   A^2 -> H(U1(c, c), U1(e, e))
26.26/8.61	   A^2 -> H(U1(c, c), U1(k, k))
26.26/8.61	   A^2 -> H(U1(c, c), U1(k, d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(d, k))
26.26/8.61	   A^2 -> H(e, U1(b, b))
26.26/8.61	   A^2 -> H(e, f(c))
26.26/8.61	   A^2 -> H(e, f(d))
26.26/8.61	   A^2 -> H(U1(e, e), U1(c, b))
26.26/8.61	   A^2 -> H(U1(e, e), U1(d, b))
26.26/8.61	   A^2 -> H(U1(e, e), U1(b, c))
26.26/8.61	   A^2 -> H(U1(e, e), U1(b, d))
26.26/8.61	   A^2 -> H(U1(e, e), U1(c, c))
26.26/8.61	   A^2 -> H(U1(e, e), f(e))
26.26/8.61	   A^2 -> H(U1(e, e), f(k))
26.26/8.61	   A^2 -> H(U1(e, e), U1(d, d))
26.26/8.61	   A^2 -> H(f(e), U1(e, b))
26.26/8.61	   A^2 -> H(f(e), U1(k, b))
26.26/8.61	   A^2 -> H(f(e), U1(c, d))
26.26/8.61	   A^2 -> H(f(e), U1(d, c))
26.26/8.61	   A^2 -> H(f(e), U1(b, e))
26.26/8.61	   A^2 -> H(f(e), U1(b, k))
26.26/8.61	   A^2 -> H(f(e), U1(e, c))
26.26/8.61	   A^2 -> H(f(e), U1(k, c))
26.26/8.61	   A^2 -> H(f(e), U1(c, e))
26.26/8.61	   A^2 -> H(f(e), U1(c, k))
26.26/8.61	   A^2 -> H(f(e), U1(k, k))
26.26/8.61	   A^2 -> H(f(e), U1(k, d))
26.26/8.61	   A^2 -> H(f(e), U1(d, k))
26.26/8.61	   A^2 -> H(U1(k, k), U1(c, b))
26.26/8.61	   A^2 -> H(U1(k, k), U1(d, b))
26.26/8.61	   A^2 -> H(U1(k, k), U1(b, c))
26.26/8.61	   A^2 -> H(U1(k, k), U1(b, d))
26.26/8.61	   A^2 -> H(U1(k, k), U1(c, c))
26.26/8.61	   A^2 -> H(U1(k, k), f(e))
26.26/8.61	   A^2 -> H(U1(k, k), f(k))
26.26/8.61	   A^2 -> H(U1(k, k), U1(d, d))
26.26/8.61	   A^2 -> H(f(k), U1(e, b))
26.26/8.61	   A^2 -> H(f(k), U1(k, b))
26.26/8.61	   A^2 -> H(f(k), U1(c, d))
26.26/8.61	   A^2 -> H(f(k), U1(d, c))
26.26/8.61	   A^2 -> H(f(k), U1(b, e))
26.26/8.61	   A^2 -> H(f(k), U1(b, k))
26.26/8.61	   A^2 -> H(f(k), U1(e, c))
26.26/8.61	   A^2 -> H(f(k), U1(k, c))
26.26/8.61	   A^2 -> H(f(k), U1(c, e))
26.26/8.61	   A^2 -> H(f(k), U1(c, k))
26.26/8.61	   A^2 -> H(f(k), U1(e, e))
26.26/8.61	
26.26/8.61	The TRS R consists of the following rules:
26.26/8.61	
26.26/8.61	   f(x) -> U1(x, x)
26.26/8.61	   U1(e, x) -> x
26.26/8.61	   a -> c
26.26/8.61	   a -> d
26.26/8.61	   b -> c
26.26/8.61	   b -> d
26.26/8.61	   d -> k
26.26/8.61	   c -> e
26.26/8.61	   c -> k
26.26/8.61	
26.26/8.61	Q is empty.
26.26/8.61	We have to consider all minimal (P,Q,R)-chains.
26.26/8.61	----------------------------------------
26.26/8.61	
26.26/8.61	(439) TransformationProof (EQUIVALENT)
26.26/8.61	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
26.26/8.61	
26.26/8.61	   (A^2 -> H(U1(k, k), U1(d, d)),A^2 -> H(U1(k, k), U1(d, d)))
26.26/8.61	   (A^2 -> H(f(k), U1(k, d)),A^2 -> H(f(k), U1(k, d)))
26.26/8.61	   (A^2 -> H(f(k), U1(d, k)),A^2 -> H(f(k), U1(d, k)))
26.26/8.61	
26.26/8.61	
26.26/8.61	----------------------------------------
26.26/8.61	
26.26/8.61	(440)
26.26/8.61	Obligation:
26.26/8.61	Q DP problem:
26.26/8.61	The TRS P consists of the following rules:
26.26/8.61	
26.26/8.61	   H(x, x) -> G(x, x, f(k))
26.26/8.61	   G(d, x, x) -> A^2
26.26/8.61	   A^2 -> H(f(c), f(c))
26.26/8.61	   A^2 -> H(f(d), f(d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(c, c))
26.26/8.61	   A^2 -> H(f(e), f(e))
26.26/8.61	   A^2 -> H(f(k), f(k))
26.26/8.61	   A^2 -> H(f(c), U1(e, b))
26.26/8.61	   A^2 -> H(f(c), U1(k, b))
26.26/8.61	   A^2 -> H(f(c), U1(c, d))
26.26/8.61	   A^2 -> H(f(c), U1(d, c))
26.26/8.61	   A^2 -> H(f(c), U1(b, e))
26.26/8.61	   A^2 -> H(f(c), U1(b, k))
26.26/8.61	   A^2 -> H(f(c), U1(k, d))
26.26/8.61	   A^2 -> H(f(c), U1(d, k))
26.26/8.61	   A^2 -> H(f(c), U1(k, k))
26.26/8.61	   A^2 -> H(U1(k, k), f(b))
26.26/8.61	   A^2 -> H(U1(k, d), U1(b, b))
26.26/8.61	   A^2 -> H(U1(k, d), f(c))
26.26/8.61	   A^2 -> H(U1(k, d), f(d))
26.26/8.61	   A^2 -> H(U1(d, k), U1(b, b))
26.26/8.61	   A^2 -> H(U1(d, k), f(c))
26.26/8.61	   A^2 -> H(U1(d, k), f(d))
26.26/8.61	   A^2 -> H(U1(d, d), U1(c, b))
26.26/8.61	   A^2 -> H(U1(d, d), U1(d, b))
26.26/8.61	   A^2 -> H(U1(d, d), U1(b, c))
26.26/8.61	   A^2 -> H(U1(d, d), U1(b, d))
26.26/8.61	   A^2 -> H(U1(d, d), U1(c, c))
26.26/8.61	   A^2 -> H(U1(d, d), f(e))
26.26/8.61	   A^2 -> H(U1(d, d), f(k))
26.26/8.61	   A^2 -> H(U1(d, d), U1(d, d))
26.26/8.61	   A^2 -> H(f(d), U1(e, b))
26.26/8.61	   A^2 -> H(f(d), U1(k, b))
26.26/8.61	   A^2 -> H(f(d), U1(c, d))
26.26/8.61	   A^2 -> H(f(d), U1(d, c))
26.26/8.61	   A^2 -> H(f(d), U1(b, e))
26.26/8.61	   A^2 -> H(f(d), U1(b, k))
26.26/8.61	   A^2 -> H(f(d), U1(e, c))
26.26/8.61	   A^2 -> H(f(d), U1(k, c))
26.26/8.61	   A^2 -> H(f(d), U1(c, e))
26.26/8.61	   A^2 -> H(f(d), U1(c, k))
26.26/8.61	   A^2 -> H(f(d), U1(e, e))
26.26/8.61	   A^2 -> H(f(d), U1(k, k))
26.26/8.61	   A^2 -> H(f(a), b)
26.26/8.61	   A^2 -> H(f(a), U1(e, d))
26.26/8.61	   A^2 -> H(f(a), U1(d, e))
26.26/8.61	   A^2 -> H(f(c), U1(e, c))
26.26/8.61	   A^2 -> H(f(c), U1(k, c))
26.26/8.61	   A^2 -> H(f(c), U1(c, e))
26.26/8.61	   A^2 -> H(f(c), U1(c, k))
26.26/8.61	   A^2 -> H(f(a), c)
26.26/8.61	   A^2 -> H(f(a), U1(e, k))
26.26/8.61	   A^2 -> H(f(a), U1(k, e))
26.26/8.61	   A^2 -> H(f(c), U1(e, e))
26.26/8.61	   A^2 -> H(f(a), e)
26.26/8.61	   A^2 -> H(f(d), U1(k, d))
26.26/8.61	   A^2 -> H(f(d), U1(d, k))
26.26/8.61	   A^2 -> H(f(a), U1(k, k))
26.26/8.61	   A^2 -> H(d, f(b))
26.26/8.61	   A^2 -> H(a, U1(b, b))
26.26/8.61	   A^2 -> H(a, f(c))
26.26/8.61	   A^2 -> H(a, f(d))
26.26/8.61	   A^2 -> H(U1(e, d), U1(b, b))
26.26/8.61	   A^2 -> H(U1(e, d), f(c))
26.26/8.61	   A^2 -> H(U1(e, d), f(d))
26.26/8.61	   A^2 -> H(U1(e, a), U1(c, b))
26.26/8.61	   A^2 -> H(U1(e, a), U1(d, b))
26.26/8.61	   A^2 -> H(U1(e, a), U1(b, c))
26.26/8.61	   A^2 -> H(U1(e, a), U1(b, d))
26.26/8.61	   A^2 -> H(U1(e, a), U1(c, c))
26.26/8.61	   A^2 -> H(U1(e, a), f(e))
26.26/8.61	   A^2 -> H(U1(e, a), f(k))
26.26/8.61	   A^2 -> H(U1(e, a), U1(d, d))
26.26/8.61	   A^2 -> H(U1(k, a), U1(c, b))
26.26/8.61	   A^2 -> H(U1(k, a), U1(d, b))
26.26/8.61	   A^2 -> H(U1(k, a), U1(b, c))
26.26/8.61	   A^2 -> H(U1(k, a), U1(b, d))
26.26/8.61	   A^2 -> H(U1(k, a), U1(c, c))
26.26/8.61	   A^2 -> H(U1(k, a), f(e))
26.26/8.61	   A^2 -> H(U1(k, a), f(k))
26.26/8.61	   A^2 -> H(U1(k, a), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, d), U1(c, b))
26.26/8.61	   A^2 -> H(U1(c, d), U1(d, b))
26.26/8.61	   A^2 -> H(U1(c, d), U1(b, c))
26.26/8.61	   A^2 -> H(U1(c, d), U1(b, d))
26.26/8.61	   A^2 -> H(U1(c, d), U1(c, c))
26.26/8.61	   A^2 -> H(U1(c, d), f(e))
26.26/8.61	   A^2 -> H(U1(c, d), f(k))
26.26/8.61	   A^2 -> H(U1(c, d), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, a), U1(e, b))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, b))
26.26/8.61	   A^2 -> H(U1(c, a), U1(c, d))
26.26/8.61	   A^2 -> H(U1(c, a), U1(d, c))
26.26/8.61	   A^2 -> H(U1(c, a), U1(b, e))
26.26/8.61	   A^2 -> H(U1(c, a), U1(b, k))
26.26/8.61	   A^2 -> H(U1(c, a), U1(e, c))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, c))
26.26/8.61	   A^2 -> H(U1(c, a), U1(c, e))
26.26/8.61	   A^2 -> H(U1(c, a), U1(c, k))
26.26/8.61	   A^2 -> H(U1(c, a), U1(e, e))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, k))
26.26/8.61	   A^2 -> H(U1(c, a), U1(k, d))
26.26/8.61	   A^2 -> H(U1(c, a), U1(d, k))
26.26/8.61	   A^2 -> H(U1(d, e), U1(b, b))
26.26/8.61	   A^2 -> H(U1(d, e), f(c))
26.26/8.61	   A^2 -> H(U1(d, e), f(d))
26.26/8.61	   A^2 -> H(U1(d, c), U1(c, b))
26.26/8.61	   A^2 -> H(U1(d, c), U1(d, b))
26.26/8.61	   A^2 -> H(U1(d, c), U1(b, c))
26.26/8.61	   A^2 -> H(U1(d, c), U1(b, d))
26.26/8.61	   A^2 -> H(U1(d, c), U1(c, c))
26.26/8.61	   A^2 -> H(U1(d, c), f(e))
26.26/8.61	   A^2 -> H(U1(d, c), f(k))
26.26/8.61	   A^2 -> H(U1(d, c), U1(d, d))
26.26/8.61	   A^2 -> H(U1(d, a), U1(e, b))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, b))
26.26/8.61	   A^2 -> H(U1(d, a), U1(c, d))
26.26/8.61	   A^2 -> H(U1(d, a), U1(d, c))
26.26/8.61	   A^2 -> H(U1(d, a), U1(b, e))
26.26/8.61	   A^2 -> H(U1(d, a), U1(b, k))
26.26/8.61	   A^2 -> H(U1(d, a), U1(e, c))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, c))
26.26/8.61	   A^2 -> H(U1(d, a), U1(c, e))
26.26/8.61	   A^2 -> H(U1(d, a), U1(c, k))
26.26/8.61	   A^2 -> H(U1(d, a), U1(e, e))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, k))
26.26/8.61	   A^2 -> H(U1(d, a), U1(k, d))
26.26/8.61	   A^2 -> H(U1(d, a), U1(d, k))
26.26/8.61	   A^2 -> H(U1(a, e), U1(c, b))
26.26/8.61	   A^2 -> H(U1(a, e), U1(d, b))
26.26/8.61	   A^2 -> H(U1(a, e), U1(b, c))
26.26/8.61	   A^2 -> H(U1(a, e), U1(b, d))
26.26/8.61	   A^2 -> H(U1(a, e), U1(c, c))
26.26/8.61	   A^2 -> H(U1(a, e), f(e))
26.26/8.61	   A^2 -> H(U1(a, e), f(k))
26.26/8.61	   A^2 -> H(U1(a, e), U1(d, d))
26.26/8.61	   A^2 -> H(U1(a, k), U1(c, b))
26.26/8.61	   A^2 -> H(U1(a, k), U1(d, b))
26.26/8.61	   A^2 -> H(U1(a, k), U1(b, c))
26.26/8.61	   A^2 -> H(U1(a, k), U1(b, d))
26.26/8.61	   A^2 -> H(U1(a, k), U1(c, c))
26.26/8.61	   A^2 -> H(U1(a, k), f(e))
26.26/8.61	   A^2 -> H(U1(a, k), f(k))
26.26/8.61	   A^2 -> H(U1(a, k), U1(d, d))
26.26/8.61	   A^2 -> H(U1(a, c), U1(e, b))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, b))
26.26/8.61	   A^2 -> H(U1(a, c), U1(c, d))
26.26/8.61	   A^2 -> H(U1(a, c), U1(d, c))
26.26/8.61	   A^2 -> H(U1(a, c), U1(b, e))
26.26/8.61	   A^2 -> H(U1(a, c), U1(b, k))
26.26/8.61	   A^2 -> H(U1(a, c), U1(e, c))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, c))
26.26/8.61	   A^2 -> H(U1(a, c), U1(c, e))
26.26/8.61	   A^2 -> H(U1(a, c), U1(c, k))
26.26/8.61	   A^2 -> H(U1(a, c), U1(e, e))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, k))
26.26/8.61	   A^2 -> H(U1(a, c), U1(k, d))
26.26/8.61	   A^2 -> H(U1(a, c), U1(d, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(e, b))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, b))
26.26/8.61	   A^2 -> H(U1(a, d), U1(c, d))
26.26/8.61	   A^2 -> H(U1(a, d), U1(d, c))
26.26/8.61	   A^2 -> H(U1(a, d), U1(b, e))
26.26/8.61	   A^2 -> H(U1(a, d), U1(b, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(e, c))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, c))
26.26/8.61	   A^2 -> H(U1(a, d), U1(c, e))
26.26/8.61	   A^2 -> H(U1(a, d), U1(c, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(e, e))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, k))
26.26/8.61	   A^2 -> H(U1(a, d), U1(k, d))
26.26/8.61	   A^2 -> H(U1(a, d), U1(d, k))
26.26/8.61	   A^2 -> H(U1(a, a), b)
26.26/8.61	   A^2 -> H(U1(a, a), U1(e, d))
26.26/8.61	   A^2 -> H(U1(a, a), U1(d, e))
26.26/8.61	   A^2 -> H(U1(a, a), c)
26.26/8.61	   A^2 -> H(U1(a, a), U1(e, k))
26.26/8.61	   A^2 -> H(U1(a, a), U1(k, e))
26.26/8.61	   A^2 -> H(U1(a, a), e)
26.26/8.61	   A^2 -> H(U1(a, a), U1(k, k))
26.26/8.61	   A^2 -> H(k, f(b))
26.26/8.61	   A^2 -> H(c, U1(b, b))
26.26/8.61	   A^2 -> H(c, f(c))
26.26/8.61	   A^2 -> H(c, f(d))
26.26/8.61	   A^2 -> H(U1(e, k), U1(b, b))
26.26/8.61	   A^2 -> H(U1(e, k), f(c))
26.26/8.61	   A^2 -> H(U1(e, k), f(d))
26.26/8.61	   A^2 -> H(U1(e, c), U1(c, b))
26.26/8.61	   A^2 -> H(U1(e, c), U1(d, b))
26.26/8.61	   A^2 -> H(U1(e, c), U1(b, c))
26.26/8.61	   A^2 -> H(U1(e, c), U1(b, d))
26.26/8.61	   A^2 -> H(U1(e, c), U1(c, c))
26.26/8.61	   A^2 -> H(U1(e, c), f(e))
26.26/8.61	   A^2 -> H(U1(e, c), f(k))
26.26/8.61	   A^2 -> H(U1(e, c), U1(d, d))
26.26/8.61	   A^2 -> H(U1(k, e), U1(b, b))
26.26/8.61	   A^2 -> H(U1(k, e), f(c))
26.26/8.61	   A^2 -> H(U1(k, e), f(d))
26.26/8.61	   A^2 -> H(U1(k, c), U1(c, b))
26.26/8.61	   A^2 -> H(U1(k, c), U1(d, b))
26.26/8.61	   A^2 -> H(U1(k, c), U1(b, c))
26.26/8.61	   A^2 -> H(U1(k, c), U1(b, d))
26.26/8.61	   A^2 -> H(U1(k, c), U1(c, c))
26.26/8.61	   A^2 -> H(U1(k, c), f(e))
26.26/8.61	   A^2 -> H(U1(k, c), f(k))
26.26/8.61	   A^2 -> H(U1(k, c), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, e), U1(c, b))
26.26/8.61	   A^2 -> H(U1(c, e), U1(d, b))
26.26/8.61	   A^2 -> H(U1(c, e), U1(b, c))
26.26/8.61	   A^2 -> H(U1(c, e), U1(b, d))
26.26/8.61	   A^2 -> H(U1(c, e), U1(c, c))
26.26/8.61	   A^2 -> H(U1(c, e), f(e))
26.26/8.61	   A^2 -> H(U1(c, e), f(k))
26.26/8.61	   A^2 -> H(U1(c, e), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, k), U1(c, b))
26.26/8.61	   A^2 -> H(U1(c, k), U1(d, b))
26.26/8.61	   A^2 -> H(U1(c, k), U1(b, c))
26.26/8.61	   A^2 -> H(U1(c, k), U1(b, d))
26.26/8.61	   A^2 -> H(U1(c, k), U1(c, c))
26.26/8.61	   A^2 -> H(U1(c, k), f(e))
26.26/8.61	   A^2 -> H(U1(c, k), f(k))
26.26/8.61	   A^2 -> H(U1(c, k), U1(d, d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(e, b))
26.26/8.61	   A^2 -> H(U1(c, c), U1(k, b))
26.26/8.61	   A^2 -> H(U1(c, c), U1(c, d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(d, c))
26.26/8.61	   A^2 -> H(U1(c, c), U1(b, e))
26.26/8.61	   A^2 -> H(U1(c, c), U1(b, k))
26.26/8.61	   A^2 -> H(U1(c, c), U1(e, e))
26.26/8.61	   A^2 -> H(U1(c, c), U1(k, k))
26.26/8.61	   A^2 -> H(U1(c, c), U1(k, d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(d, k))
26.26/8.61	   A^2 -> H(e, U1(b, b))
26.26/8.61	   A^2 -> H(e, f(c))
26.26/8.61	   A^2 -> H(e, f(d))
26.26/8.61	   A^2 -> H(U1(e, e), U1(c, b))
26.26/8.61	   A^2 -> H(U1(e, e), U1(d, b))
26.26/8.61	   A^2 -> H(U1(e, e), U1(b, c))
26.26/8.61	   A^2 -> H(U1(e, e), U1(b, d))
26.26/8.61	   A^2 -> H(U1(e, e), U1(c, c))
26.26/8.61	   A^2 -> H(U1(e, e), f(e))
26.26/8.61	   A^2 -> H(U1(e, e), f(k))
26.26/8.61	   A^2 -> H(U1(e, e), U1(d, d))
26.26/8.61	   A^2 -> H(f(e), U1(e, b))
26.26/8.61	   A^2 -> H(f(e), U1(k, b))
26.26/8.61	   A^2 -> H(f(e), U1(c, d))
26.26/8.61	   A^2 -> H(f(e), U1(d, c))
26.26/8.61	   A^2 -> H(f(e), U1(b, e))
26.26/8.61	   A^2 -> H(f(e), U1(b, k))
26.26/8.61	   A^2 -> H(f(e), U1(e, c))
26.26/8.61	   A^2 -> H(f(e), U1(k, c))
26.26/8.61	   A^2 -> H(f(e), U1(c, e))
26.26/8.61	   A^2 -> H(f(e), U1(c, k))
26.26/8.61	   A^2 -> H(f(e), U1(k, k))
26.26/8.61	   A^2 -> H(f(e), U1(k, d))
26.26/8.61	   A^2 -> H(f(e), U1(d, k))
26.26/8.61	   A^2 -> H(U1(k, k), U1(c, b))
26.26/8.61	   A^2 -> H(U1(k, k), U1(d, b))
26.26/8.61	   A^2 -> H(U1(k, k), U1(b, c))
26.26/8.61	   A^2 -> H(U1(k, k), U1(b, d))
26.26/8.61	   A^2 -> H(U1(k, k), U1(c, c))
26.26/8.61	   A^2 -> H(U1(k, k), f(e))
26.26/8.61	   A^2 -> H(U1(k, k), f(k))
26.26/8.61	   A^2 -> H(U1(k, k), U1(d, d))
26.26/8.61	   A^2 -> H(f(k), U1(e, b))
26.26/8.61	   A^2 -> H(f(k), U1(k, b))
26.26/8.61	   A^2 -> H(f(k), U1(c, d))
26.26/8.61	   A^2 -> H(f(k), U1(d, c))
26.26/8.61	   A^2 -> H(f(k), U1(b, e))
26.26/8.61	   A^2 -> H(f(k), U1(b, k))
26.26/8.61	   A^2 -> H(f(k), U1(e, c))
26.26/8.61	   A^2 -> H(f(k), U1(k, c))
26.26/8.61	   A^2 -> H(f(k), U1(c, e))
26.26/8.61	   A^2 -> H(f(k), U1(c, k))
26.26/8.61	   A^2 -> H(f(k), U1(e, e))
26.26/8.61	   A^2 -> H(f(k), U1(k, d))
26.26/8.61	   A^2 -> H(f(k), U1(d, k))
26.26/8.61	
26.26/8.61	The TRS R consists of the following rules:
26.26/8.61	
26.26/8.61	   f(x) -> U1(x, x)
26.26/8.61	   U1(e, x) -> x
26.26/8.61	   a -> c
26.26/8.61	   a -> d
26.26/8.61	   b -> c
26.26/8.61	   b -> d
26.26/8.61	   d -> k
26.26/8.61	   c -> e
26.26/8.61	   c -> k
26.26/8.61	
26.26/8.61	Q is empty.
26.26/8.61	We have to consider all minimal (P,Q,R)-chains.
26.26/8.61	----------------------------------------
26.26/8.61	
26.26/8.61	(441) TransformationProof (EQUIVALENT)
26.26/8.61	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
26.26/8.61	
26.26/8.61	   (A^2 -> H(U1(c, c), U1(e, b)),A^2 -> H(U1(c, c), U1(e, b)))
26.26/8.61	   (A^2 -> H(f(e), U1(e, b)),A^2 -> H(f(e), U1(e, b)))
26.26/8.61	   (A^2 -> H(f(k), U1(e, b)),A^2 -> H(f(k), U1(e, b)))
26.26/8.61	   (A^2 -> H(f(c), b),A^2 -> H(f(c), b))
26.26/8.61	   (A^2 -> H(f(c), U1(e, c)),A^2 -> H(f(c), U1(e, c)))
26.26/8.61	   (A^2 -> H(f(c), U1(e, d)),A^2 -> H(f(c), U1(e, d)))
26.26/8.61	
26.26/8.61	
26.26/8.61	----------------------------------------
26.26/8.61	
26.26/8.61	(442)
26.26/8.61	Obligation:
26.26/8.61	Q DP problem:
26.26/8.61	The TRS P consists of the following rules:
26.26/8.61	
26.26/8.61	   H(x, x) -> G(x, x, f(k))
26.26/8.61	   G(d, x, x) -> A^2
26.26/8.61	   A^2 -> H(f(c), f(c))
26.26/8.61	   A^2 -> H(f(d), f(d))
26.26/8.61	   A^2 -> H(U1(c, c), U1(c, c))
26.26/8.61	   A^2 -> H(f(e), f(e))
26.26/8.61	   A^2 -> H(f(k), f(k))
26.26/8.61	   A^2 -> H(f(c), U1(k, b))
26.26/8.61	   A^2 -> H(f(c), U1(c, d))
26.26/8.61	   A^2 -> H(f(c), U1(d, c))
26.26/8.61	   A^2 -> H(f(c), U1(b, e))
26.26/8.61	   A^2 -> H(f(c), U1(b, k))
26.26/8.61	   A^2 -> H(f(c), U1(k, d))
26.26/8.61	   A^2 -> H(f(c), U1(d, k))
26.26/8.61	   A^2 -> H(f(c), U1(k, k))
26.26/8.61	   A^2 -> H(U1(k, k), f(b))
26.26/8.61	   A^2 -> H(U1(k, d), U1(b, b))
26.26/8.61	   A^2 -> H(U1(k, d), f(c))
26.26/8.61	   A^2 -> H(U1(k, d), f(d))
26.26/8.61	   A^2 -> H(U1(d, k), U1(b, b))
26.26/8.61	   A^2 -> H(U1(d, k), f(c))
26.26/8.61	   A^2 -> H(U1(d, k), f(d))
26.26/8.61	   A^2 -> H(U1(d, d), U1(c, b))
26.26/8.61	   A^2 -> H(U1(d, d), U1(d, b))
26.26/8.61	   A^2 -> H(U1(d, d), U1(b, c))
26.26/8.61	   A^2 -> H(U1(d, d), U1(b, d))
26.26/8.61	   A^2 -> H(U1(d, d), U1(c, c))
26.26/8.61	   A^2 -> H(U1(d, d), f(e))
26.26/8.61	   A^2 -> H(U1(d, d), f(k))
26.26/8.61	   A^2 -> H(U1(d, d), U1(d, d))
26.26/8.61	   A^2 -> H(f(d), U1(e, b))
26.26/8.61	   A^2 -> H(f(d), U1(k, b))
26.26/8.61	   A^2 -> H(f(d), U1(c, d))
26.26/8.61	   A^2 -> H(f(d), U1(d, c))
26.26/8.61	   A^2 -> H(f(d), U1(b, e))
26.26/8.61	   A^2 -> H(f(d), U1(b, k))
26.26/8.61	   A^2 -> H(f(d), U1(e, c))
26.26/8.61	   A^2 -> H(f(d), U1(k, c))
26.26/8.61	   A^2 -> H(f(d), U1(c, e))
26.26/8.61	   A^2 -> H(f(d), U1(c, k))
26.26/8.61	   A^2 -> H(f(d), U1(e, e))
26.26/8.61	   A^2 -> H(f(d), U1(k, k))
26.26/8.61	   A^2 -> H(f(a), b)
26.26/8.61	   A^2 -> H(f(a), U1(e, d))
26.26/8.61	   A^2 -> H(f(a), U1(d, e))
26.26/8.61	   A^2 -> H(f(c), U1(e, c))
26.26/8.61	   A^2 -> H(f(c), U1(k, c))
26.26/8.61	   A^2 -> H(f(c), U1(c, e))
26.26/8.61	   A^2 -> H(f(c), U1(c, k))
26.26/8.61	   A^2 -> H(f(a), c)
26.26/8.61	   A^2 -> H(f(a), U1(e, k))
26.26/8.61	   A^2 -> H(f(a), U1(k, e))
26.26/8.62	   A^2 -> H(f(c), U1(e, e))
26.26/8.62	   A^2 -> H(f(a), e)
26.26/8.62	   A^2 -> H(f(d), U1(k, d))
26.26/8.62	   A^2 -> H(f(d), U1(d, k))
26.26/8.62	   A^2 -> H(f(a), U1(k, k))
26.26/8.62	   A^2 -> H(d, f(b))
26.26/8.62	   A^2 -> H(a, U1(b, b))
26.26/8.62	   A^2 -> H(a, f(c))
26.26/8.62	   A^2 -> H(a, f(d))
26.26/8.62	   A^2 -> H(U1(e, d), U1(b, b))
26.26/8.62	   A^2 -> H(U1(e, d), f(c))
26.26/8.62	   A^2 -> H(U1(e, d), f(d))
26.26/8.62	   A^2 -> H(U1(e, a), U1(c, b))
26.26/8.62	   A^2 -> H(U1(e, a), U1(d, b))
26.26/8.62	   A^2 -> H(U1(e, a), U1(b, c))
26.26/8.62	   A^2 -> H(U1(e, a), U1(b, d))
26.26/8.62	   A^2 -> H(U1(e, a), U1(c, c))
26.26/8.62	   A^2 -> H(U1(e, a), f(e))
26.26/8.62	   A^2 -> H(U1(e, a), f(k))
26.26/8.62	   A^2 -> H(U1(e, a), U1(d, d))
26.26/8.62	   A^2 -> H(U1(k, a), U1(c, b))
26.26/8.62	   A^2 -> H(U1(k, a), U1(d, b))
26.26/8.62	   A^2 -> H(U1(k, a), U1(b, c))
26.26/8.62	   A^2 -> H(U1(k, a), U1(b, d))
26.26/8.62	   A^2 -> H(U1(k, a), U1(c, c))
26.26/8.62	   A^2 -> H(U1(k, a), f(e))
26.26/8.62	   A^2 -> H(U1(k, a), f(k))
26.26/8.62	   A^2 -> H(U1(k, a), U1(d, d))
26.26/8.62	   A^2 -> H(U1(c, d), U1(c, b))
26.26/8.62	   A^2 -> H(U1(c, d), U1(d, b))
26.26/8.62	   A^2 -> H(U1(c, d), U1(b, c))
26.26/8.62	   A^2 -> H(U1(c, d), U1(b, d))
26.26/8.62	   A^2 -> H(U1(c, d), U1(c, c))
26.26/8.62	   A^2 -> H(U1(c, d), f(e))
26.26/8.62	   A^2 -> H(U1(c, d), f(k))
26.26/8.62	   A^2 -> H(U1(c, d), U1(d, d))
26.26/8.62	   A^2 -> H(U1(c, a), U1(e, b))
26.26/8.62	   A^2 -> H(U1(c, a), U1(k, b))
26.26/8.62	   A^2 -> H(U1(c, a), U1(c, d))
26.26/8.62	   A^2 -> H(U1(c, a), U1(d, c))
26.26/8.62	   A^2 -> H(U1(c, a), U1(b, e))
26.26/8.62	   A^2 -> H(U1(c, a), U1(b, k))
26.26/8.62	   A^2 -> H(U1(c, a), U1(e, c))
26.26/8.62	   A^2 -> H(U1(c, a), U1(k, c))
26.26/8.62	   A^2 -> H(U1(c, a), U1(c, e))
26.26/8.62	   A^2 -> H(U1(c, a), U1(c, k))
26.26/8.62	   A^2 -> H(U1(c, a), U1(e, e))
26.26/8.62	   A^2 -> H(U1(c, a), U1(k, k))
26.26/8.62	   A^2 -> H(U1(c, a), U1(k, d))
26.26/8.62	   A^2 -> H(U1(c, a), U1(d, k))
26.26/8.62	   A^2 -> H(U1(d, e), U1(b, b))
26.26/8.62	   A^2 -> H(U1(d, e), f(c))
26.26/8.62	   A^2 -> H(U1(d, e), f(d))
26.26/8.62	   A^2 -> H(U1(d, c), U1(c, b))
26.26/8.62	   A^2 -> H(U1(d, c), U1(d, b))
26.26/8.62	   A^2 -> H(U1(d, c), U1(b, c))
26.26/8.62	   A^2 -> H(U1(d, c), U1(b, d))
26.26/8.62	   A^2 -> H(U1(d, c), U1(c, c))
26.26/8.62	   A^2 -> H(U1(d, c), f(e))
26.26/8.62	   A^2 -> H(U1(d, c), f(k))
26.26/8.62	   A^2 -> H(U1(d, c), U1(d, d))
26.26/8.62	   A^2 -> H(U1(d, a), U1(e, b))
26.26/8.62	   A^2 -> H(U1(d, a), U1(k, b))
26.26/8.62	   A^2 -> H(U1(d, a), U1(c, d))
26.26/8.62	   A^2 -> H(U1(d, a), U1(d, c))
26.26/8.62	   A^2 -> H(U1(d, a), U1(b, e))
26.26/8.62	   A^2 -> H(U1(d, a), U1(b, k))
26.26/8.62	   A^2 -> H(U1(d, a), U1(e, c))
26.26/8.62	   A^2 -> H(U1(d, a), U1(k, c))
26.26/8.62	   A^2 -> H(U1(d, a), U1(c, e))
26.26/8.62	   A^2 -> H(U1(d, a), U1(c, k))
26.26/8.62	   A^2 -> H(U1(d, a), U1(e, e))
26.26/8.62	   A^2 -> H(U1(d, a), U1(k, k))
26.26/8.62	   A^2 -> H(U1(d, a), U1(k, d))
26.26/8.62	   A^2 -> H(U1(d, a), U1(d, k))
26.26/8.62	   A^2 -> H(U1(a, e), U1(c, b))
26.26/8.62	   A^2 -> H(U1(a, e), U1(d, b))
26.26/8.62	   A^2 -> H(U1(a, e), U1(b, c))
26.26/8.62	   A^2 -> H(U1(a, e), U1(b, d))
26.26/8.62	   A^2 -> H(U1(a, e), U1(c, c))
26.26/8.62	   A^2 -> H(U1(a, e), f(e))
26.26/8.62	   A^2 -> H(U1(a, e), f(k))
26.26/8.62	   A^2 -> H(U1(a, e), U1(d, d))
26.26/8.62	   A^2 -> H(U1(a, k), U1(c, b))
26.26/8.62	   A^2 -> H(U1(a, k), U1(d, b))
26.26/8.62	   A^2 -> H(U1(a, k), U1(b, c))
26.26/8.62	   A^2 -> H(U1(a, k), U1(b, d))
26.26/8.62	   A^2 -> H(U1(a, k), U1(c, c))
26.26/8.62	   A^2 -> H(U1(a, k), f(e))
26.26/8.62	   A^2 -> H(U1(a, k), f(k))
26.26/8.62	   A^2 -> H(U1(a, k), U1(d, d))
26.26/8.62	   A^2 -> H(U1(a, c), U1(e, b))
26.26/8.62	   A^2 -> H(U1(a, c), U1(k, b))
26.26/8.62	   A^2 -> H(U1(a, c), U1(c, d))
26.26/8.62	   A^2 -> H(U1(a, c), U1(d, c))
26.26/8.62	   A^2 -> H(U1(a, c), U1(b, e))
26.26/8.62	   A^2 -> H(U1(a, c), U1(b, k))
26.26/8.62	   A^2 -> H(U1(a, c), U1(e, c))
26.26/8.62	   A^2 -> H(U1(a, c), U1(k, c))
26.26/8.62	   A^2 -> H(U1(a, c), U1(c, e))
26.26/8.62	   A^2 -> H(U1(a, c), U1(c, k))
26.26/8.62	   A^2 -> H(U1(a, c), U1(e, e))
26.26/8.62	   A^2 -> H(U1(a, c), U1(k, k))
26.26/8.62	   A^2 -> H(U1(a, c), U1(k, d))
26.26/8.62	   A^2 -> H(U1(a, c), U1(d, k))
26.26/8.62	   A^2 -> H(U1(a, d), U1(e, b))
26.26/8.62	   A^2 -> H(U1(a, d), U1(k, b))
26.26/8.62	   A^2 -> H(U1(a, d), U1(c, d))
26.26/8.62	   A^2 -> H(U1(a, d), U1(d, c))
26.26/8.62	   A^2 -> H(U1(a, d), U1(b, e))
26.26/8.62	   A^2 -> H(U1(a, d), U1(b, k))
26.26/8.62	   A^2 -> H(U1(a, d), U1(e, c))
26.26/8.62	   A^2 -> H(U1(a, d), U1(k, c))
26.26/8.62	   A^2 -> H(U1(a, d), U1(c, e))
26.26/8.62	   A^2 -> H(U1(a, d), U1(c, k))
26.26/8.62	   A^2 -> H(U1(a, d), U1(e, e))
26.26/8.62	   A^2 -> H(U1(a, d), U1(k, k))
26.26/8.62	   A^2 -> H(U1(a, d), U1(k, d))
26.26/8.62	   A^2 -> H(U1(a, d), U1(d, k))
26.26/8.62	   A^2 -> H(U1(a, a), b)
26.26/8.62	   A^2 -> H(U1(a, a), U1(e, d))
26.26/8.62	   A^2 -> H(U1(a, a), U1(d, e))
26.26/8.62	   A^2 -> H(U1(a, a), c)
26.26/8.62	   A^2 -> H(U1(a, a), U1(e, k))
26.26/8.62	   A^2 -> H(U1(a, a), U1(k, e))
26.26/8.62	   A^2 -> H(U1(a, a), e)
26.26/8.62	   A^2 -> H(U1(a, a), U1(k, k))
26.26/8.62	   A^2 -> H(k, f(b))
26.26/8.62	   A^2 -> H(c, U1(b, b))
26.26/8.62	   A^2 -> H(c, f(c))
26.26/8.62	   A^2 -> H(c, f(d))
26.26/8.62	   A^2 -> H(U1(e, k), U1(b, b))
26.26/8.62	   A^2 -> H(U1(e, k), f(c))
26.26/8.62	   A^2 -> H(U1(e, k), f(d))
26.26/8.62	   A^2 -> H(U1(e, c), U1(c, b))
26.26/8.62	   A^2 -> H(U1(e, c), U1(d, b))
26.26/8.62	   A^2 -> H(U1(e, c), U1(b, c))
26.26/8.62	   A^2 -> H(U1(e, c), U1(b, d))
26.26/8.62	   A^2 -> H(U1(e, c), U1(c, c))
26.26/8.62	   A^2 -> H(U1(e, c), f(e))
26.26/8.62	   A^2 -> H(U1(e, c), f(k))
26.26/8.62	   A^2 -> H(U1(e, c), U1(d, d))
26.26/8.62	   A^2 -> H(U1(k, e), U1(b, b))
26.26/8.62	   A^2 -> H(U1(k, e), f(c))
26.26/8.62	   A^2 -> H(U1(k, e), f(d))
26.26/8.62	   A^2 -> H(U1(k, c), U1(c, b))
26.26/8.62	   A^2 -> H(U1(k, c), U1(d, b))
26.26/8.62	   A^2 -> H(U1(k, c), U1(b, c))
26.26/8.62	   A^2 -> H(U1(k, c), U1(b, d))
26.26/8.62	   A^2 -> H(U1(k, c), U1(c, c))
26.26/8.62	   A^2 -> H(U1(k, c), f(e))
26.26/8.62	   A^2 -> H(U1(k, c), f(k))
26.26/8.62	   A^2 -> H(U1(k, c), U1(d, d))
26.26/8.62	   A^2 -> H(U1(c, e), U1(c, b))
26.26/8.62	   A^2 -> H(U1(c, e), U1(d, b))
26.26/8.62	   A^2 -> H(U1(c, e), U1(b, c))
26.26/8.62	   A^2 -> H(U1(c, e), U1(b, d))
26.26/8.62	   A^2 -> H(U1(c, e), U1(c, c))
26.26/8.62	   A^2 -> H(U1(c, e), f(e))
26.26/8.62	   A^2 -> H(U1(c, e), f(k))
26.26/8.62	   A^2 -> H(U1(c, e), U1(d, d))
26.26/8.62	   A^2 -> H(U1(c, k), U1(c, b))
26.26/8.62	   A^2 -> H(U1(c, k), U1(d, b))
26.26/8.62	   A^2 -> H(U1(c, k), U1(b, c))
26.26/8.62	   A^2 -> H(U1(c, k), U1(b, d))
26.26/8.62	   A^2 -> H(U1(c, k), U1(c, c))
26.26/8.62	   A^2 -> H(U1(c, k), f(e))
26.26/8.62	   A^2 -> H(U1(c, k), f(k))
26.26/8.62	   A^2 -> H(U1(c, k), U1(d, d))
26.26/8.62	   A^2 -> H(U1(c, c), U1(e, b))
26.26/8.62	   A^2 -> H(U1(c, c), U1(k, b))
26.26/8.62	   A^2 -> H(U1(c, c), U1(c, d))
26.26/8.62	   A^2 -> H(U1(c, c), U1(d, c))
26.26/8.62	   A^2 -> H(U1(c, c), U1(b, e))
26.26/8.62	   A^2 -> H(U1(c, c), U1(b, k))
26.26/8.62	   A^2 -> H(U1(c, c), U1(e, e))
26.26/8.62	   A^2 -> H(U1(c, c), U1(k, k))
26.26/8.62	   A^2 -> H(U1(c, c), U1(k, d))
26.26/8.62	   A^2 -> H(U1(c, c), U1(d, k))
26.26/8.62	   A^2 -> H(e, U1(b, b))
26.26/8.62	   A^2 -> H(e, f(c))
26.26/8.62	   A^2 -> H(e, f(d))
26.26/8.62	   A^2 -> H(U1(e, e), U1(c, b))
26.26/8.62	   A^2 -> H(U1(e, e), U1(d, b))
26.26/8.62	   A^2 -> H(U1(e, e), U1(b, c))
26.26/8.62	   A^2 -> H(U1(e, e), U1(b, d))
26.26/8.62	   A^2 -> H(U1(e, e), U1(c, c))
26.26/8.62	   A^2 -> H(U1(e, e), f(e))
26.26/8.62	   A^2 -> H(U1(e, e), f(k))
26.26/8.62	   A^2 -> H(U1(e, e), U1(d, d))
26.26/8.62	   A^2 -> H(f(e), U1(e, b))
26.26/8.62	   A^2 -> H(f(e), U1(k, b))
26.26/8.62	   A^2 -> H(f(e), U1(c, d))
26.26/8.62	   A^2 -> H(f(e), U1(d, c))
26.26/8.62	   A^2 -> H(f(e), U1(b, e))
26.26/8.62	   A^2 -> H(f(e), U1(b, k))
26.26/8.62	   A^2 -> H(f(e), U1(e, c))
26.26/8.62	   A^2 -> H(f(e), U1(k, c))
26.26/8.62	   A^2 -> H(f(e), U1(c, e))
26.26/8.62	   A^2 -> H(f(e), U1(c, k))
26.26/8.62	   A^2 -> H(f(e), U1(k, k))
26.26/8.62	   A^2 -> H(f(e), U1(k, d))
26.26/8.62	   A^2 -> H(f(e), U1(d, k))
26.26/8.62	   A^2 -> H(U1(k, k), U1(c, b))
26.26/8.62	   A^2 -> H(U1(k, k), U1(d, b))
26.26/8.62	   A^2 -> H(U1(k, k), U1(b, c))
26.26/8.62	   A^2 -> H(U1(k, k), U1(b, d))
26.26/8.62	   A^2 -> H(U1(k, k), U1(c, c))
26.26/8.62	   A^2 -> H(U1(k, k), f(e))
26.26/8.62	   A^2 -> H(U1(k, k), f(k))
26.26/8.62	   A^2 -> H(U1(k, k), U1(d, d))
26.26/8.62	   A^2 -> H(f(k), U1(e, b))
26.26/8.62	   A^2 -> H(f(k), U1(k, b))
26.26/8.62	   A^2 -> H(f(k), U1(c, d))
26.26/8.62	   A^2 -> H(f(k), U1(d, c))
26.26/8.62	   A^2 -> H(f(k), U1(b, e))
26.26/8.62	   A^2 -> H(f(k), U1(b, k))
26.26/8.62	   A^2 -> H(f(k), U1(e, c))
26.26/8.62	   A^2 -> H(f(k), U1(k, c))
26.26/8.62	   A^2 -> H(f(k), U1(c, e))
26.26/8.62	   A^2 -> H(f(k), U1(c, k))
26.26/8.62	   A^2 -> H(f(k), U1(e, e))
26.26/8.62	   A^2 -> H(f(k), U1(k, d))
26.26/8.62	   A^2 -> H(f(k), U1(d, k))
26.26/8.62	   A^2 -> H(f(c), b)
26.26/8.62	   A^2 -> H(f(c), U1(e, d))
26.26/8.62	
26.26/8.62	The TRS R consists of the following rules:
26.26/8.62	
26.26/8.62	   f(x) -> U1(x, x)
26.26/8.62	   U1(e, x) -> x
26.26/8.62	   a -> c
26.26/8.62	   a -> d
26.26/8.62	   b -> c
26.26/8.62	   b -> d
26.26/8.62	   d -> k
26.26/8.62	   c -> e
26.26/8.62	   c -> k
26.26/8.62	
26.26/8.62	Q is empty.
26.26/8.62	We have to consider all minimal (P,Q,R)-chains.
26.26/8.62	----------------------------------------
26.26/8.62	
26.26/8.62	(443) TransformationProof (EQUIVALENT)
26.26/8.62	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
26.26/8.62	
26.26/8.62	   (A^2 -> H(U1(c, c), U1(k, b)),A^2 -> H(U1(c, c), U1(k, b)))
26.26/8.62	   (A^2 -> H(f(e), U1(k, b)),A^2 -> H(f(e), U1(k, b)))
26.26/8.62	   (A^2 -> H(f(k), U1(k, b)),A^2 -> H(f(k), U1(k, b)))
26.26/8.62	   (A^2 -> H(f(c), U1(k, c)),A^2 -> H(f(c), U1(k, c)))
26.26/8.62	   (A^2 -> H(f(c), U1(k, d)),A^2 -> H(f(c), U1(k, d)))
26.26/8.62	
26.26/8.62	
26.26/8.62	----------------------------------------
26.26/8.62	
26.26/8.62	(444)
26.26/8.62	Obligation:
26.26/8.62	Q DP problem:
26.26/8.62	The TRS P consists of the following rules:
26.26/8.62	
26.26/8.62	   H(x, x) -> G(x, x, f(k))
26.26/8.62	   G(d, x, x) -> A^2
26.26/8.62	   A^2 -> H(f(c), f(c))
26.26/8.62	   A^2 -> H(f(d), f(d))
26.26/8.62	   A^2 -> H(U1(c, c), U1(c, c))
26.26/8.62	   A^2 -> H(f(e), f(e))
26.26/8.62	   A^2 -> H(f(k), f(k))
26.26/8.62	   A^2 -> H(f(c), U1(c, d))
26.26/8.62	   A^2 -> H(f(c), U1(d, c))
26.26/8.62	   A^2 -> H(f(c), U1(b, e))
26.26/8.62	   A^2 -> H(f(c), U1(b, k))
26.26/8.62	   A^2 -> H(f(c), U1(k, d))
26.26/8.62	   A^2 -> H(f(c), U1(d, k))
26.26/8.62	   A^2 -> H(f(c), U1(k, k))
26.26/8.62	   A^2 -> H(U1(k, k), f(b))
26.26/8.62	   A^2 -> H(U1(k, d), U1(b, b))
26.26/8.62	   A^2 -> H(U1(k, d), f(c))
26.26/8.62	   A^2 -> H(U1(k, d), f(d))
26.26/8.62	   A^2 -> H(U1(d, k), U1(b, b))
26.26/8.62	   A^2 -> H(U1(d, k), f(c))
26.42/8.62	   A^2 -> H(U1(d, k), f(d))
26.42/8.62	   A^2 -> H(U1(d, d), U1(c, b))
26.42/8.62	   A^2 -> H(U1(d, d), U1(d, b))
26.42/8.62	   A^2 -> H(U1(d, d), U1(b, c))
26.42/8.62	   A^2 -> H(U1(d, d), U1(b, d))
26.42/8.62	   A^2 -> H(U1(d, d), U1(c, c))
26.42/8.62	   A^2 -> H(U1(d, d), f(e))
26.42/8.62	   A^2 -> H(U1(d, d), f(k))
26.42/8.62	   A^2 -> H(U1(d, d), U1(d, d))
26.42/8.62	   A^2 -> H(f(d), U1(e, b))
26.42/8.62	   A^2 -> H(f(d), U1(k, b))
26.42/8.62	   A^2 -> H(f(d), U1(c, d))
26.42/8.62	   A^2 -> H(f(d), U1(d, c))
26.42/8.62	   A^2 -> H(f(d), U1(b, e))
26.42/8.62	   A^2 -> H(f(d), U1(b, k))
26.42/8.62	   A^2 -> H(f(d), U1(e, c))
26.42/8.62	   A^2 -> H(f(d), U1(k, c))
26.42/8.62	   A^2 -> H(f(d), U1(c, e))
26.42/8.62	   A^2 -> H(f(d), U1(c, k))
26.42/8.62	   A^2 -> H(f(d), U1(e, e))
26.42/8.62	   A^2 -> H(f(d), U1(k, k))
26.42/8.62	   A^2 -> H(f(a), b)
26.42/8.62	   A^2 -> H(f(a), U1(e, d))
26.42/8.62	   A^2 -> H(f(a), U1(d, e))
26.42/8.62	   A^2 -> H(f(c), U1(e, c))
26.42/8.62	   A^2 -> H(f(c), U1(k, c))
26.42/8.62	   A^2 -> H(f(c), U1(c, e))
26.42/8.62	   A^2 -> H(f(c), U1(c, k))
26.42/8.62	   A^2 -> H(f(a), c)
26.42/8.62	   A^2 -> H(f(a), U1(e, k))
26.42/8.62	   A^2 -> H(f(a), U1(k, e))
26.42/8.62	   A^2 -> H(f(c), U1(e, e))
26.42/8.62	   A^2 -> H(f(a), e)
26.42/8.62	   A^2 -> H(f(d), U1(k, d))
26.42/8.62	   A^2 -> H(f(d), U1(d, k))
26.42/8.62	   A^2 -> H(f(a), U1(k, k))
26.42/8.62	   A^2 -> H(d, f(b))
26.42/8.62	   A^2 -> H(a, U1(b, b))
26.42/8.62	   A^2 -> H(a, f(c))
26.42/8.62	   A^2 -> H(a, f(d))
26.42/8.62	   A^2 -> H(U1(e, d), U1(b, b))
26.42/8.62	   A^2 -> H(U1(e, d), f(c))
26.42/8.62	   A^2 -> H(U1(e, d), f(d))
26.42/8.62	   A^2 -> H(U1(e, a), U1(c, b))
26.42/8.62	   A^2 -> H(U1(e, a), U1(d, b))
26.42/8.62	   A^2 -> H(U1(e, a), U1(b, c))
26.42/8.62	   A^2 -> H(U1(e, a), U1(b, d))
26.42/8.62	   A^2 -> H(U1(e, a), U1(c, c))
26.42/8.62	   A^2 -> H(U1(e, a), f(e))
26.42/8.62	   A^2 -> H(U1(e, a), f(k))
26.42/8.62	   A^2 -> H(U1(e, a), U1(d, d))
26.42/8.62	   A^2 -> H(U1(k, a), U1(c, b))
26.42/8.62	   A^2 -> H(U1(k, a), U1(d, b))
26.42/8.62	   A^2 -> H(U1(k, a), U1(b, c))
26.42/8.62	   A^2 -> H(U1(k, a), U1(b, d))
26.42/8.62	   A^2 -> H(U1(k, a), U1(c, c))
26.42/8.62	   A^2 -> H(U1(k, a), f(e))
26.42/8.62	   A^2 -> H(U1(k, a), f(k))
26.42/8.62	   A^2 -> H(U1(k, a), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, d), U1(c, b))
26.42/8.62	   A^2 -> H(U1(c, d), U1(d, b))
26.42/8.62	   A^2 -> H(U1(c, d), U1(b, c))
26.42/8.62	   A^2 -> H(U1(c, d), U1(b, d))
26.42/8.62	   A^2 -> H(U1(c, d), U1(c, c))
26.42/8.62	   A^2 -> H(U1(c, d), f(e))
26.42/8.62	   A^2 -> H(U1(c, d), f(k))
26.42/8.62	   A^2 -> H(U1(c, d), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, a), U1(e, b))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, b))
26.42/8.62	   A^2 -> H(U1(c, a), U1(c, d))
26.42/8.62	   A^2 -> H(U1(c, a), U1(d, c))
26.42/8.62	   A^2 -> H(U1(c, a), U1(b, e))
26.42/8.62	   A^2 -> H(U1(c, a), U1(b, k))
26.42/8.62	   A^2 -> H(U1(c, a), U1(e, c))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, c))
26.42/8.62	   A^2 -> H(U1(c, a), U1(c, e))
26.42/8.62	   A^2 -> H(U1(c, a), U1(c, k))
26.42/8.62	   A^2 -> H(U1(c, a), U1(e, e))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, k))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, d))
26.42/8.62	   A^2 -> H(U1(c, a), U1(d, k))
26.42/8.62	   A^2 -> H(U1(d, e), U1(b, b))
26.42/8.62	   A^2 -> H(U1(d, e), f(c))
26.42/8.62	   A^2 -> H(U1(d, e), f(d))
26.42/8.62	   A^2 -> H(U1(d, c), U1(c, b))
26.42/8.62	   A^2 -> H(U1(d, c), U1(d, b))
26.42/8.62	   A^2 -> H(U1(d, c), U1(b, c))
26.42/8.62	   A^2 -> H(U1(d, c), U1(b, d))
26.42/8.62	   A^2 -> H(U1(d, c), U1(c, c))
26.42/8.62	   A^2 -> H(U1(d, c), f(e))
26.42/8.62	   A^2 -> H(U1(d, c), f(k))
26.42/8.62	   A^2 -> H(U1(d, c), U1(d, d))
26.42/8.62	   A^2 -> H(U1(d, a), U1(e, b))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, b))
26.42/8.62	   A^2 -> H(U1(d, a), U1(c, d))
26.42/8.62	   A^2 -> H(U1(d, a), U1(d, c))
26.42/8.62	   A^2 -> H(U1(d, a), U1(b, e))
26.42/8.62	   A^2 -> H(U1(d, a), U1(b, k))
26.42/8.62	   A^2 -> H(U1(d, a), U1(e, c))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, c))
26.42/8.62	   A^2 -> H(U1(d, a), U1(c, e))
26.42/8.62	   A^2 -> H(U1(d, a), U1(c, k))
26.42/8.62	   A^2 -> H(U1(d, a), U1(e, e))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, k))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, d))
26.42/8.62	   A^2 -> H(U1(d, a), U1(d, k))
26.42/8.62	   A^2 -> H(U1(a, e), U1(c, b))
26.42/8.62	   A^2 -> H(U1(a, e), U1(d, b))
26.42/8.62	   A^2 -> H(U1(a, e), U1(b, c))
26.42/8.62	   A^2 -> H(U1(a, e), U1(b, d))
26.42/8.62	   A^2 -> H(U1(a, e), U1(c, c))
26.42/8.62	   A^2 -> H(U1(a, e), f(e))
26.42/8.62	   A^2 -> H(U1(a, e), f(k))
26.42/8.62	   A^2 -> H(U1(a, e), U1(d, d))
26.42/8.62	   A^2 -> H(U1(a, k), U1(c, b))
26.42/8.62	   A^2 -> H(U1(a, k), U1(d, b))
26.42/8.62	   A^2 -> H(U1(a, k), U1(b, c))
26.42/8.62	   A^2 -> H(U1(a, k), U1(b, d))
26.42/8.62	   A^2 -> H(U1(a, k), U1(c, c))
26.42/8.62	   A^2 -> H(U1(a, k), f(e))
26.42/8.62	   A^2 -> H(U1(a, k), f(k))
26.42/8.62	   A^2 -> H(U1(a, k), U1(d, d))
26.42/8.62	   A^2 -> H(U1(a, c), U1(e, b))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, b))
26.42/8.62	   A^2 -> H(U1(a, c), U1(c, d))
26.42/8.62	   A^2 -> H(U1(a, c), U1(d, c))
26.42/8.62	   A^2 -> H(U1(a, c), U1(b, e))
26.42/8.62	   A^2 -> H(U1(a, c), U1(b, k))
26.42/8.62	   A^2 -> H(U1(a, c), U1(e, c))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, c))
26.42/8.62	   A^2 -> H(U1(a, c), U1(c, e))
26.42/8.62	   A^2 -> H(U1(a, c), U1(c, k))
26.42/8.62	   A^2 -> H(U1(a, c), U1(e, e))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, k))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, d))
26.42/8.62	   A^2 -> H(U1(a, c), U1(d, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(e, b))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, b))
26.42/8.62	   A^2 -> H(U1(a, d), U1(c, d))
26.42/8.62	   A^2 -> H(U1(a, d), U1(d, c))
26.42/8.62	   A^2 -> H(U1(a, d), U1(b, e))
26.42/8.62	   A^2 -> H(U1(a, d), U1(b, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(e, c))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, c))
26.42/8.62	   A^2 -> H(U1(a, d), U1(c, e))
26.42/8.62	   A^2 -> H(U1(a, d), U1(c, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(e, e))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, d))
26.42/8.62	   A^2 -> H(U1(a, d), U1(d, k))
26.42/8.62	   A^2 -> H(U1(a, a), b)
26.42/8.62	   A^2 -> H(U1(a, a), U1(e, d))
26.42/8.62	   A^2 -> H(U1(a, a), U1(d, e))
26.42/8.62	   A^2 -> H(U1(a, a), c)
26.42/8.62	   A^2 -> H(U1(a, a), U1(e, k))
26.42/8.62	   A^2 -> H(U1(a, a), U1(k, e))
26.42/8.62	   A^2 -> H(U1(a, a), e)
26.42/8.62	   A^2 -> H(U1(a, a), U1(k, k))
26.42/8.62	   A^2 -> H(k, f(b))
26.42/8.62	   A^2 -> H(c, U1(b, b))
26.42/8.62	   A^2 -> H(c, f(c))
26.42/8.62	   A^2 -> H(c, f(d))
26.42/8.62	   A^2 -> H(U1(e, k), U1(b, b))
26.42/8.62	   A^2 -> H(U1(e, k), f(c))
26.42/8.62	   A^2 -> H(U1(e, k), f(d))
26.42/8.62	   A^2 -> H(U1(e, c), U1(c, b))
26.42/8.62	   A^2 -> H(U1(e, c), U1(d, b))
26.42/8.62	   A^2 -> H(U1(e, c), U1(b, c))
26.42/8.62	   A^2 -> H(U1(e, c), U1(b, d))
26.42/8.62	   A^2 -> H(U1(e, c), U1(c, c))
26.42/8.62	   A^2 -> H(U1(e, c), f(e))
26.42/8.62	   A^2 -> H(U1(e, c), f(k))
26.42/8.62	   A^2 -> H(U1(e, c), U1(d, d))
26.42/8.62	   A^2 -> H(U1(k, e), U1(b, b))
26.42/8.62	   A^2 -> H(U1(k, e), f(c))
26.42/8.62	   A^2 -> H(U1(k, e), f(d))
26.42/8.62	   A^2 -> H(U1(k, c), U1(c, b))
26.42/8.62	   A^2 -> H(U1(k, c), U1(d, b))
26.42/8.62	   A^2 -> H(U1(k, c), U1(b, c))
26.42/8.62	   A^2 -> H(U1(k, c), U1(b, d))
26.42/8.62	   A^2 -> H(U1(k, c), U1(c, c))
26.42/8.62	   A^2 -> H(U1(k, c), f(e))
26.42/8.62	   A^2 -> H(U1(k, c), f(k))
26.42/8.62	   A^2 -> H(U1(k, c), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, e), U1(c, b))
26.42/8.62	   A^2 -> H(U1(c, e), U1(d, b))
26.42/8.62	   A^2 -> H(U1(c, e), U1(b, c))
26.42/8.62	   A^2 -> H(U1(c, e), U1(b, d))
26.42/8.62	   A^2 -> H(U1(c, e), U1(c, c))
26.42/8.62	   A^2 -> H(U1(c, e), f(e))
26.42/8.62	   A^2 -> H(U1(c, e), f(k))
26.42/8.62	   A^2 -> H(U1(c, e), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, k), U1(c, b))
26.42/8.62	   A^2 -> H(U1(c, k), U1(d, b))
26.42/8.62	   A^2 -> H(U1(c, k), U1(b, c))
26.42/8.62	   A^2 -> H(U1(c, k), U1(b, d))
26.42/8.62	   A^2 -> H(U1(c, k), U1(c, c))
26.42/8.62	   A^2 -> H(U1(c, k), f(e))
26.42/8.62	   A^2 -> H(U1(c, k), f(k))
26.42/8.62	   A^2 -> H(U1(c, k), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(e, b))
26.42/8.62	   A^2 -> H(U1(c, c), U1(k, b))
26.42/8.62	   A^2 -> H(U1(c, c), U1(c, d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(d, c))
26.42/8.62	   A^2 -> H(U1(c, c), U1(b, e))
26.42/8.62	   A^2 -> H(U1(c, c), U1(b, k))
26.42/8.62	   A^2 -> H(U1(c, c), U1(e, e))
26.42/8.62	   A^2 -> H(U1(c, c), U1(k, k))
26.42/8.62	   A^2 -> H(U1(c, c), U1(k, d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(d, k))
26.42/8.62	   A^2 -> H(e, U1(b, b))
26.42/8.62	   A^2 -> H(e, f(c))
26.42/8.62	   A^2 -> H(e, f(d))
26.42/8.62	   A^2 -> H(U1(e, e), U1(c, b))
26.42/8.62	   A^2 -> H(U1(e, e), U1(d, b))
26.42/8.62	   A^2 -> H(U1(e, e), U1(b, c))
26.42/8.62	   A^2 -> H(U1(e, e), U1(b, d))
26.42/8.62	   A^2 -> H(U1(e, e), U1(c, c))
26.42/8.62	   A^2 -> H(U1(e, e), f(e))
26.42/8.62	   A^2 -> H(U1(e, e), f(k))
26.42/8.62	   A^2 -> H(U1(e, e), U1(d, d))
26.42/8.62	   A^2 -> H(f(e), U1(e, b))
26.42/8.62	   A^2 -> H(f(e), U1(k, b))
26.42/8.62	   A^2 -> H(f(e), U1(c, d))
26.42/8.62	   A^2 -> H(f(e), U1(d, c))
26.42/8.62	   A^2 -> H(f(e), U1(b, e))
26.42/8.62	   A^2 -> H(f(e), U1(b, k))
26.42/8.62	   A^2 -> H(f(e), U1(e, c))
26.42/8.62	   A^2 -> H(f(e), U1(k, c))
26.42/8.62	   A^2 -> H(f(e), U1(c, e))
26.42/8.62	   A^2 -> H(f(e), U1(c, k))
26.42/8.62	   A^2 -> H(f(e), U1(k, k))
26.42/8.62	   A^2 -> H(f(e), U1(k, d))
26.42/8.62	   A^2 -> H(f(e), U1(d, k))
26.42/8.62	   A^2 -> H(U1(k, k), U1(c, b))
26.42/8.62	   A^2 -> H(U1(k, k), U1(d, b))
26.42/8.62	   A^2 -> H(U1(k, k), U1(b, c))
26.42/8.62	   A^2 -> H(U1(k, k), U1(b, d))
26.42/8.62	   A^2 -> H(U1(k, k), U1(c, c))
26.42/8.62	   A^2 -> H(U1(k, k), f(e))
26.42/8.62	   A^2 -> H(U1(k, k), f(k))
26.42/8.62	   A^2 -> H(U1(k, k), U1(d, d))
26.42/8.62	   A^2 -> H(f(k), U1(e, b))
26.42/8.62	   A^2 -> H(f(k), U1(k, b))
26.42/8.62	   A^2 -> H(f(k), U1(c, d))
26.42/8.62	   A^2 -> H(f(k), U1(d, c))
26.42/8.62	   A^2 -> H(f(k), U1(b, e))
26.42/8.62	   A^2 -> H(f(k), U1(b, k))
26.42/8.62	   A^2 -> H(f(k), U1(e, c))
26.42/8.62	   A^2 -> H(f(k), U1(k, c))
26.42/8.62	   A^2 -> H(f(k), U1(c, e))
26.42/8.62	   A^2 -> H(f(k), U1(c, k))
26.42/8.62	   A^2 -> H(f(k), U1(e, e))
26.42/8.62	   A^2 -> H(f(k), U1(k, d))
26.42/8.62	   A^2 -> H(f(k), U1(d, k))
26.42/8.62	   A^2 -> H(f(c), b)
26.42/8.62	   A^2 -> H(f(c), U1(e, d))
26.42/8.62	
26.42/8.62	The TRS R consists of the following rules:
26.42/8.62	
26.42/8.62	   f(x) -> U1(x, x)
26.42/8.62	   U1(e, x) -> x
26.42/8.62	   a -> c
26.42/8.62	   a -> d
26.42/8.62	   b -> c
26.42/8.62	   b -> d
26.42/8.62	   d -> k
26.42/8.62	   c -> e
26.42/8.62	   c -> k
26.42/8.62	
26.42/8.62	Q is empty.
26.42/8.62	We have to consider all minimal (P,Q,R)-chains.
26.42/8.62	----------------------------------------
26.42/8.62	
26.42/8.62	(445) TransformationProof (EQUIVALENT)
26.42/8.62	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
26.42/8.62	
26.42/8.62	   (A^2 -> H(U1(c, c), U1(c, d)),A^2 -> H(U1(c, c), U1(c, d)))
26.42/8.62	   (A^2 -> H(f(e), U1(c, d)),A^2 -> H(f(e), U1(c, d)))
26.42/8.62	   (A^2 -> H(f(k), U1(c, d)),A^2 -> H(f(k), U1(c, d)))
26.42/8.62	   (A^2 -> H(f(c), U1(e, d)),A^2 -> H(f(c), U1(e, d)))
26.42/8.62	   (A^2 -> H(f(c), U1(k, d)),A^2 -> H(f(c), U1(k, d)))
26.42/8.62	   (A^2 -> H(f(c), U1(c, k)),A^2 -> H(f(c), U1(c, k)))
26.42/8.62	
26.42/8.62	
26.42/8.62	----------------------------------------
26.42/8.62	
26.42/8.62	(446)
26.42/8.62	Obligation:
26.42/8.62	Q DP problem:
26.42/8.62	The TRS P consists of the following rules:
26.42/8.62	
26.42/8.62	   H(x, x) -> G(x, x, f(k))
26.42/8.62	   G(d, x, x) -> A^2
26.42/8.62	   A^2 -> H(f(c), f(c))
26.42/8.62	   A^2 -> H(f(d), f(d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(c, c))
26.42/8.62	   A^2 -> H(f(e), f(e))
26.42/8.62	   A^2 -> H(f(k), f(k))
26.42/8.62	   A^2 -> H(f(c), U1(d, c))
26.42/8.62	   A^2 -> H(f(c), U1(b, e))
26.42/8.62	   A^2 -> H(f(c), U1(b, k))
26.42/8.62	   A^2 -> H(f(c), U1(k, d))
26.42/8.62	   A^2 -> H(f(c), U1(d, k))
26.42/8.62	   A^2 -> H(f(c), U1(k, k))
26.42/8.62	   A^2 -> H(U1(k, k), f(b))
26.42/8.62	   A^2 -> H(U1(k, d), U1(b, b))
26.42/8.62	   A^2 -> H(U1(k, d), f(c))
26.42/8.62	   A^2 -> H(U1(k, d), f(d))
26.42/8.62	   A^2 -> H(U1(d, k), U1(b, b))
26.42/8.62	   A^2 -> H(U1(d, k), f(c))
26.42/8.62	   A^2 -> H(U1(d, k), f(d))
26.42/8.62	   A^2 -> H(U1(d, d), U1(c, b))
26.42/8.62	   A^2 -> H(U1(d, d), U1(d, b))
26.42/8.62	   A^2 -> H(U1(d, d), U1(b, c))
26.42/8.62	   A^2 -> H(U1(d, d), U1(b, d))
26.42/8.62	   A^2 -> H(U1(d, d), U1(c, c))
26.42/8.62	   A^2 -> H(U1(d, d), f(e))
26.42/8.62	   A^2 -> H(U1(d, d), f(k))
26.42/8.62	   A^2 -> H(U1(d, d), U1(d, d))
26.42/8.62	   A^2 -> H(f(d), U1(e, b))
26.42/8.62	   A^2 -> H(f(d), U1(k, b))
26.42/8.62	   A^2 -> H(f(d), U1(c, d))
26.42/8.62	   A^2 -> H(f(d), U1(d, c))
26.42/8.62	   A^2 -> H(f(d), U1(b, e))
26.42/8.62	   A^2 -> H(f(d), U1(b, k))
26.42/8.62	   A^2 -> H(f(d), U1(e, c))
26.42/8.62	   A^2 -> H(f(d), U1(k, c))
26.42/8.62	   A^2 -> H(f(d), U1(c, e))
26.42/8.62	   A^2 -> H(f(d), U1(c, k))
26.42/8.62	   A^2 -> H(f(d), U1(e, e))
26.42/8.62	   A^2 -> H(f(d), U1(k, k))
26.42/8.62	   A^2 -> H(f(a), b)
26.42/8.62	   A^2 -> H(f(a), U1(e, d))
26.42/8.62	   A^2 -> H(f(a), U1(d, e))
26.42/8.62	   A^2 -> H(f(c), U1(e, c))
26.42/8.62	   A^2 -> H(f(c), U1(k, c))
26.42/8.62	   A^2 -> H(f(c), U1(c, e))
26.42/8.62	   A^2 -> H(f(c), U1(c, k))
26.42/8.62	   A^2 -> H(f(a), c)
26.42/8.62	   A^2 -> H(f(a), U1(e, k))
26.42/8.62	   A^2 -> H(f(a), U1(k, e))
26.42/8.62	   A^2 -> H(f(c), U1(e, e))
26.42/8.62	   A^2 -> H(f(a), e)
26.42/8.62	   A^2 -> H(f(d), U1(k, d))
26.42/8.62	   A^2 -> H(f(d), U1(d, k))
26.42/8.62	   A^2 -> H(f(a), U1(k, k))
26.42/8.62	   A^2 -> H(d, f(b))
26.42/8.62	   A^2 -> H(a, U1(b, b))
26.42/8.62	   A^2 -> H(a, f(c))
26.42/8.62	   A^2 -> H(a, f(d))
26.42/8.62	   A^2 -> H(U1(e, d), U1(b, b))
26.42/8.62	   A^2 -> H(U1(e, d), f(c))
26.42/8.62	   A^2 -> H(U1(e, d), f(d))
26.42/8.62	   A^2 -> H(U1(e, a), U1(c, b))
26.42/8.62	   A^2 -> H(U1(e, a), U1(d, b))
26.42/8.62	   A^2 -> H(U1(e, a), U1(b, c))
26.42/8.62	   A^2 -> H(U1(e, a), U1(b, d))
26.42/8.62	   A^2 -> H(U1(e, a), U1(c, c))
26.42/8.62	   A^2 -> H(U1(e, a), f(e))
26.42/8.62	   A^2 -> H(U1(e, a), f(k))
26.42/8.62	   A^2 -> H(U1(e, a), U1(d, d))
26.42/8.62	   A^2 -> H(U1(k, a), U1(c, b))
26.42/8.62	   A^2 -> H(U1(k, a), U1(d, b))
26.42/8.62	   A^2 -> H(U1(k, a), U1(b, c))
26.42/8.62	   A^2 -> H(U1(k, a), U1(b, d))
26.42/8.62	   A^2 -> H(U1(k, a), U1(c, c))
26.42/8.62	   A^2 -> H(U1(k, a), f(e))
26.42/8.62	   A^2 -> H(U1(k, a), f(k))
26.42/8.62	   A^2 -> H(U1(k, a), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, d), U1(c, b))
26.42/8.62	   A^2 -> H(U1(c, d), U1(d, b))
26.42/8.62	   A^2 -> H(U1(c, d), U1(b, c))
26.42/8.62	   A^2 -> H(U1(c, d), U1(b, d))
26.42/8.62	   A^2 -> H(U1(c, d), U1(c, c))
26.42/8.62	   A^2 -> H(U1(c, d), f(e))
26.42/8.62	   A^2 -> H(U1(c, d), f(k))
26.42/8.62	   A^2 -> H(U1(c, d), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, a), U1(e, b))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, b))
26.42/8.62	   A^2 -> H(U1(c, a), U1(c, d))
26.42/8.62	   A^2 -> H(U1(c, a), U1(d, c))
26.42/8.62	   A^2 -> H(U1(c, a), U1(b, e))
26.42/8.62	   A^2 -> H(U1(c, a), U1(b, k))
26.42/8.62	   A^2 -> H(U1(c, a), U1(e, c))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, c))
26.42/8.62	   A^2 -> H(U1(c, a), U1(c, e))
26.42/8.62	   A^2 -> H(U1(c, a), U1(c, k))
26.42/8.62	   A^2 -> H(U1(c, a), U1(e, e))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, k))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, d))
26.42/8.62	   A^2 -> H(U1(c, a), U1(d, k))
26.42/8.62	   A^2 -> H(U1(d, e), U1(b, b))
26.42/8.62	   A^2 -> H(U1(d, e), f(c))
26.42/8.62	   A^2 -> H(U1(d, e), f(d))
26.42/8.62	   A^2 -> H(U1(d, c), U1(c, b))
26.42/8.62	   A^2 -> H(U1(d, c), U1(d, b))
26.42/8.62	   A^2 -> H(U1(d, c), U1(b, c))
26.42/8.62	   A^2 -> H(U1(d, c), U1(b, d))
26.42/8.62	   A^2 -> H(U1(d, c), U1(c, c))
26.42/8.62	   A^2 -> H(U1(d, c), f(e))
26.42/8.62	   A^2 -> H(U1(d, c), f(k))
26.42/8.62	   A^2 -> H(U1(d, c), U1(d, d))
26.42/8.62	   A^2 -> H(U1(d, a), U1(e, b))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, b))
26.42/8.62	   A^2 -> H(U1(d, a), U1(c, d))
26.42/8.62	   A^2 -> H(U1(d, a), U1(d, c))
26.42/8.62	   A^2 -> H(U1(d, a), U1(b, e))
26.42/8.62	   A^2 -> H(U1(d, a), U1(b, k))
26.42/8.62	   A^2 -> H(U1(d, a), U1(e, c))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, c))
26.42/8.62	   A^2 -> H(U1(d, a), U1(c, e))
26.42/8.62	   A^2 -> H(U1(d, a), U1(c, k))
26.42/8.62	   A^2 -> H(U1(d, a), U1(e, e))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, k))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, d))
26.42/8.62	   A^2 -> H(U1(d, a), U1(d, k))
26.42/8.62	   A^2 -> H(U1(a, e), U1(c, b))
26.42/8.62	   A^2 -> H(U1(a, e), U1(d, b))
26.42/8.62	   A^2 -> H(U1(a, e), U1(b, c))
26.42/8.62	   A^2 -> H(U1(a, e), U1(b, d))
26.42/8.62	   A^2 -> H(U1(a, e), U1(c, c))
26.42/8.62	   A^2 -> H(U1(a, e), f(e))
26.42/8.62	   A^2 -> H(U1(a, e), f(k))
26.42/8.62	   A^2 -> H(U1(a, e), U1(d, d))
26.42/8.62	   A^2 -> H(U1(a, k), U1(c, b))
26.42/8.62	   A^2 -> H(U1(a, k), U1(d, b))
26.42/8.62	   A^2 -> H(U1(a, k), U1(b, c))
26.42/8.62	   A^2 -> H(U1(a, k), U1(b, d))
26.42/8.62	   A^2 -> H(U1(a, k), U1(c, c))
26.42/8.62	   A^2 -> H(U1(a, k), f(e))
26.42/8.62	   A^2 -> H(U1(a, k), f(k))
26.42/8.62	   A^2 -> H(U1(a, k), U1(d, d))
26.42/8.62	   A^2 -> H(U1(a, c), U1(e, b))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, b))
26.42/8.62	   A^2 -> H(U1(a, c), U1(c, d))
26.42/8.62	   A^2 -> H(U1(a, c), U1(d, c))
26.42/8.62	   A^2 -> H(U1(a, c), U1(b, e))
26.42/8.62	   A^2 -> H(U1(a, c), U1(b, k))
26.42/8.62	   A^2 -> H(U1(a, c), U1(e, c))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, c))
26.42/8.62	   A^2 -> H(U1(a, c), U1(c, e))
26.42/8.62	   A^2 -> H(U1(a, c), U1(c, k))
26.42/8.62	   A^2 -> H(U1(a, c), U1(e, e))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, k))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, d))
26.42/8.62	   A^2 -> H(U1(a, c), U1(d, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(e, b))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, b))
26.42/8.62	   A^2 -> H(U1(a, d), U1(c, d))
26.42/8.62	   A^2 -> H(U1(a, d), U1(d, c))
26.42/8.62	   A^2 -> H(U1(a, d), U1(b, e))
26.42/8.62	   A^2 -> H(U1(a, d), U1(b, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(e, c))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, c))
26.42/8.62	   A^2 -> H(U1(a, d), U1(c, e))
26.42/8.62	   A^2 -> H(U1(a, d), U1(c, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(e, e))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, d))
26.42/8.62	   A^2 -> H(U1(a, d), U1(d, k))
26.42/8.62	   A^2 -> H(U1(a, a), b)
26.42/8.62	   A^2 -> H(U1(a, a), U1(e, d))
26.42/8.62	   A^2 -> H(U1(a, a), U1(d, e))
26.42/8.62	   A^2 -> H(U1(a, a), c)
26.42/8.62	   A^2 -> H(U1(a, a), U1(e, k))
26.42/8.62	   A^2 -> H(U1(a, a), U1(k, e))
26.42/8.62	   A^2 -> H(U1(a, a), e)
26.42/8.62	   A^2 -> H(U1(a, a), U1(k, k))
26.42/8.62	   A^2 -> H(k, f(b))
26.42/8.62	   A^2 -> H(c, U1(b, b))
26.42/8.62	   A^2 -> H(c, f(c))
26.42/8.62	   A^2 -> H(c, f(d))
26.42/8.62	   A^2 -> H(U1(e, k), U1(b, b))
26.42/8.62	   A^2 -> H(U1(e, k), f(c))
26.42/8.62	   A^2 -> H(U1(e, k), f(d))
26.42/8.62	   A^2 -> H(U1(e, c), U1(c, b))
26.42/8.62	   A^2 -> H(U1(e, c), U1(d, b))
26.42/8.62	   A^2 -> H(U1(e, c), U1(b, c))
26.42/8.62	   A^2 -> H(U1(e, c), U1(b, d))
26.42/8.62	   A^2 -> H(U1(e, c), U1(c, c))
26.42/8.62	   A^2 -> H(U1(e, c), f(e))
26.42/8.62	   A^2 -> H(U1(e, c), f(k))
26.42/8.62	   A^2 -> H(U1(e, c), U1(d, d))
26.42/8.62	   A^2 -> H(U1(k, e), U1(b, b))
26.42/8.62	   A^2 -> H(U1(k, e), f(c))
26.42/8.62	   A^2 -> H(U1(k, e), f(d))
26.42/8.62	   A^2 -> H(U1(k, c), U1(c, b))
26.42/8.62	   A^2 -> H(U1(k, c), U1(d, b))
26.42/8.62	   A^2 -> H(U1(k, c), U1(b, c))
26.42/8.62	   A^2 -> H(U1(k, c), U1(b, d))
26.42/8.62	   A^2 -> H(U1(k, c), U1(c, c))
26.42/8.62	   A^2 -> H(U1(k, c), f(e))
26.42/8.62	   A^2 -> H(U1(k, c), f(k))
26.42/8.62	   A^2 -> H(U1(k, c), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, e), U1(c, b))
26.42/8.62	   A^2 -> H(U1(c, e), U1(d, b))
26.42/8.62	   A^2 -> H(U1(c, e), U1(b, c))
26.42/8.62	   A^2 -> H(U1(c, e), U1(b, d))
26.42/8.62	   A^2 -> H(U1(c, e), U1(c, c))
26.42/8.62	   A^2 -> H(U1(c, e), f(e))
26.42/8.62	   A^2 -> H(U1(c, e), f(k))
26.42/8.62	   A^2 -> H(U1(c, e), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, k), U1(c, b))
26.42/8.62	   A^2 -> H(U1(c, k), U1(d, b))
26.42/8.62	   A^2 -> H(U1(c, k), U1(b, c))
26.42/8.62	   A^2 -> H(U1(c, k), U1(b, d))
26.42/8.62	   A^2 -> H(U1(c, k), U1(c, c))
26.42/8.62	   A^2 -> H(U1(c, k), f(e))
26.42/8.62	   A^2 -> H(U1(c, k), f(k))
26.42/8.62	   A^2 -> H(U1(c, k), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(e, b))
26.42/8.62	   A^2 -> H(U1(c, c), U1(k, b))
26.42/8.62	   A^2 -> H(U1(c, c), U1(c, d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(d, c))
26.42/8.62	   A^2 -> H(U1(c, c), U1(b, e))
26.42/8.62	   A^2 -> H(U1(c, c), U1(b, k))
26.42/8.62	   A^2 -> H(U1(c, c), U1(e, e))
26.42/8.62	   A^2 -> H(U1(c, c), U1(k, k))
26.42/8.62	   A^2 -> H(U1(c, c), U1(k, d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(d, k))
26.42/8.62	   A^2 -> H(e, U1(b, b))
26.42/8.62	   A^2 -> H(e, f(c))
26.42/8.62	   A^2 -> H(e, f(d))
26.42/8.62	   A^2 -> H(U1(e, e), U1(c, b))
26.42/8.62	   A^2 -> H(U1(e, e), U1(d, b))
26.42/8.62	   A^2 -> H(U1(e, e), U1(b, c))
26.42/8.62	   A^2 -> H(U1(e, e), U1(b, d))
26.42/8.62	   A^2 -> H(U1(e, e), U1(c, c))
26.42/8.62	   A^2 -> H(U1(e, e), f(e))
26.42/8.62	   A^2 -> H(U1(e, e), f(k))
26.42/8.62	   A^2 -> H(U1(e, e), U1(d, d))
26.42/8.62	   A^2 -> H(f(e), U1(e, b))
26.42/8.62	   A^2 -> H(f(e), U1(k, b))
26.42/8.62	   A^2 -> H(f(e), U1(c, d))
26.42/8.62	   A^2 -> H(f(e), U1(d, c))
26.42/8.62	   A^2 -> H(f(e), U1(b, e))
26.42/8.62	   A^2 -> H(f(e), U1(b, k))
26.42/8.62	   A^2 -> H(f(e), U1(e, c))
26.42/8.62	   A^2 -> H(f(e), U1(k, c))
26.42/8.62	   A^2 -> H(f(e), U1(c, e))
26.42/8.62	   A^2 -> H(f(e), U1(c, k))
26.42/8.62	   A^2 -> H(f(e), U1(k, k))
26.42/8.62	   A^2 -> H(f(e), U1(k, d))
26.42/8.62	   A^2 -> H(f(e), U1(d, k))
26.42/8.62	   A^2 -> H(U1(k, k), U1(c, b))
26.42/8.62	   A^2 -> H(U1(k, k), U1(d, b))
26.42/8.62	   A^2 -> H(U1(k, k), U1(b, c))
26.42/8.62	   A^2 -> H(U1(k, k), U1(b, d))
26.42/8.62	   A^2 -> H(U1(k, k), U1(c, c))
26.42/8.62	   A^2 -> H(U1(k, k), f(e))
26.42/8.62	   A^2 -> H(U1(k, k), f(k))
26.42/8.62	   A^2 -> H(U1(k, k), U1(d, d))
26.42/8.62	   A^2 -> H(f(k), U1(e, b))
26.42/8.62	   A^2 -> H(f(k), U1(k, b))
26.42/8.62	   A^2 -> H(f(k), U1(c, d))
26.42/8.62	   A^2 -> H(f(k), U1(d, c))
26.42/8.62	   A^2 -> H(f(k), U1(b, e))
26.42/8.62	   A^2 -> H(f(k), U1(b, k))
26.42/8.62	   A^2 -> H(f(k), U1(e, c))
26.42/8.62	   A^2 -> H(f(k), U1(k, c))
26.42/8.62	   A^2 -> H(f(k), U1(c, e))
26.42/8.62	   A^2 -> H(f(k), U1(c, k))
26.42/8.62	   A^2 -> H(f(k), U1(e, e))
26.42/8.62	   A^2 -> H(f(k), U1(k, d))
26.42/8.62	   A^2 -> H(f(k), U1(d, k))
26.42/8.62	   A^2 -> H(f(c), b)
26.42/8.62	   A^2 -> H(f(c), U1(e, d))
26.42/8.62	
26.42/8.62	The TRS R consists of the following rules:
26.42/8.62	
26.42/8.62	   f(x) -> U1(x, x)
26.42/8.62	   U1(e, x) -> x
26.42/8.62	   a -> c
26.42/8.62	   a -> d
26.42/8.62	   b -> c
26.42/8.62	   b -> d
26.42/8.62	   d -> k
26.42/8.62	   c -> e
26.42/8.62	   c -> k
26.42/8.62	
26.42/8.62	Q is empty.
26.42/8.62	We have to consider all minimal (P,Q,R)-chains.
26.42/8.62	----------------------------------------
26.42/8.62	
26.42/8.62	(447) TransformationProof (EQUIVALENT)
26.42/8.62	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
26.42/8.62	
26.42/8.62	   (A^2 -> H(U1(c, c), U1(d, c)),A^2 -> H(U1(c, c), U1(d, c)))
26.42/8.62	   (A^2 -> H(f(e), U1(d, c)),A^2 -> H(f(e), U1(d, c)))
26.42/8.62	   (A^2 -> H(f(k), U1(d, c)),A^2 -> H(f(k), U1(d, c)))
26.42/8.62	   (A^2 -> H(f(c), U1(k, c)),A^2 -> H(f(c), U1(k, c)))
26.42/8.62	   (A^2 -> H(f(c), U1(d, e)),A^2 -> H(f(c), U1(d, e)))
26.42/8.62	   (A^2 -> H(f(c), U1(d, k)),A^2 -> H(f(c), U1(d, k)))
26.42/8.62	
26.42/8.62	
26.42/8.62	----------------------------------------
26.42/8.62	
26.42/8.62	(448)
26.42/8.62	Obligation:
26.42/8.62	Q DP problem:
26.42/8.62	The TRS P consists of the following rules:
26.42/8.62	
26.42/8.62	   H(x, x) -> G(x, x, f(k))
26.42/8.62	   G(d, x, x) -> A^2
26.42/8.62	   A^2 -> H(f(c), f(c))
26.42/8.62	   A^2 -> H(f(d), f(d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(c, c))
26.42/8.62	   A^2 -> H(f(e), f(e))
26.42/8.62	   A^2 -> H(f(k), f(k))
26.42/8.62	   A^2 -> H(f(c), U1(b, e))
26.42/8.62	   A^2 -> H(f(c), U1(b, k))
26.42/8.62	   A^2 -> H(f(c), U1(k, d))
26.42/8.62	   A^2 -> H(f(c), U1(d, k))
26.42/8.62	   A^2 -> H(f(c), U1(k, k))
26.42/8.62	   A^2 -> H(U1(k, k), f(b))
26.42/8.62	   A^2 -> H(U1(k, d), U1(b, b))
26.42/8.62	   A^2 -> H(U1(k, d), f(c))
26.42/8.62	   A^2 -> H(U1(k, d), f(d))
26.42/8.62	   A^2 -> H(U1(d, k), U1(b, b))
26.42/8.62	   A^2 -> H(U1(d, k), f(c))
26.42/8.62	   A^2 -> H(U1(d, k), f(d))
26.42/8.62	   A^2 -> H(U1(d, d), U1(c, b))
26.42/8.62	   A^2 -> H(U1(d, d), U1(d, b))
26.42/8.62	   A^2 -> H(U1(d, d), U1(b, c))
26.42/8.62	   A^2 -> H(U1(d, d), U1(b, d))
26.42/8.62	   A^2 -> H(U1(d, d), U1(c, c))
26.42/8.62	   A^2 -> H(U1(d, d), f(e))
26.42/8.62	   A^2 -> H(U1(d, d), f(k))
26.42/8.62	   A^2 -> H(U1(d, d), U1(d, d))
26.42/8.62	   A^2 -> H(f(d), U1(e, b))
26.42/8.62	   A^2 -> H(f(d), U1(k, b))
26.42/8.62	   A^2 -> H(f(d), U1(c, d))
26.42/8.62	   A^2 -> H(f(d), U1(d, c))
26.42/8.62	   A^2 -> H(f(d), U1(b, e))
26.42/8.62	   A^2 -> H(f(d), U1(b, k))
26.42/8.62	   A^2 -> H(f(d), U1(e, c))
26.42/8.62	   A^2 -> H(f(d), U1(k, c))
26.42/8.62	   A^2 -> H(f(d), U1(c, e))
26.42/8.62	   A^2 -> H(f(d), U1(c, k))
26.42/8.62	   A^2 -> H(f(d), U1(e, e))
26.42/8.62	   A^2 -> H(f(d), U1(k, k))
26.42/8.62	   A^2 -> H(f(a), b)
26.42/8.62	   A^2 -> H(f(a), U1(e, d))
26.42/8.62	   A^2 -> H(f(a), U1(d, e))
26.42/8.62	   A^2 -> H(f(c), U1(e, c))
26.42/8.62	   A^2 -> H(f(c), U1(k, c))
26.42/8.62	   A^2 -> H(f(c), U1(c, e))
26.42/8.62	   A^2 -> H(f(c), U1(c, k))
26.42/8.62	   A^2 -> H(f(a), c)
26.42/8.62	   A^2 -> H(f(a), U1(e, k))
26.42/8.62	   A^2 -> H(f(a), U1(k, e))
26.42/8.62	   A^2 -> H(f(c), U1(e, e))
26.42/8.62	   A^2 -> H(f(a), e)
26.42/8.62	   A^2 -> H(f(d), U1(k, d))
26.42/8.62	   A^2 -> H(f(d), U1(d, k))
26.42/8.62	   A^2 -> H(f(a), U1(k, k))
26.42/8.62	   A^2 -> H(d, f(b))
26.42/8.62	   A^2 -> H(a, U1(b, b))
26.42/8.62	   A^2 -> H(a, f(c))
26.42/8.62	   A^2 -> H(a, f(d))
26.42/8.62	   A^2 -> H(U1(e, d), U1(b, b))
26.42/8.62	   A^2 -> H(U1(e, d), f(c))
26.42/8.62	   A^2 -> H(U1(e, d), f(d))
26.42/8.62	   A^2 -> H(U1(e, a), U1(c, b))
26.42/8.62	   A^2 -> H(U1(e, a), U1(d, b))
26.42/8.62	   A^2 -> H(U1(e, a), U1(b, c))
26.42/8.62	   A^2 -> H(U1(e, a), U1(b, d))
26.42/8.62	   A^2 -> H(U1(e, a), U1(c, c))
26.42/8.62	   A^2 -> H(U1(e, a), f(e))
26.42/8.62	   A^2 -> H(U1(e, a), f(k))
26.42/8.62	   A^2 -> H(U1(e, a), U1(d, d))
26.42/8.62	   A^2 -> H(U1(k, a), U1(c, b))
26.42/8.62	   A^2 -> H(U1(k, a), U1(d, b))
26.42/8.62	   A^2 -> H(U1(k, a), U1(b, c))
26.42/8.62	   A^2 -> H(U1(k, a), U1(b, d))
26.42/8.62	   A^2 -> H(U1(k, a), U1(c, c))
26.42/8.62	   A^2 -> H(U1(k, a), f(e))
26.42/8.62	   A^2 -> H(U1(k, a), f(k))
26.42/8.62	   A^2 -> H(U1(k, a), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, d), U1(c, b))
26.42/8.62	   A^2 -> H(U1(c, d), U1(d, b))
26.42/8.62	   A^2 -> H(U1(c, d), U1(b, c))
26.42/8.62	   A^2 -> H(U1(c, d), U1(b, d))
26.42/8.62	   A^2 -> H(U1(c, d), U1(c, c))
26.42/8.62	   A^2 -> H(U1(c, d), f(e))
26.42/8.62	   A^2 -> H(U1(c, d), f(k))
26.42/8.62	   A^2 -> H(U1(c, d), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, a), U1(e, b))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, b))
26.42/8.62	   A^2 -> H(U1(c, a), U1(c, d))
26.42/8.62	   A^2 -> H(U1(c, a), U1(d, c))
26.42/8.62	   A^2 -> H(U1(c, a), U1(b, e))
26.42/8.62	   A^2 -> H(U1(c, a), U1(b, k))
26.42/8.62	   A^2 -> H(U1(c, a), U1(e, c))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, c))
26.42/8.62	   A^2 -> H(U1(c, a), U1(c, e))
26.42/8.62	   A^2 -> H(U1(c, a), U1(c, k))
26.42/8.62	   A^2 -> H(U1(c, a), U1(e, e))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, k))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, d))
26.42/8.62	   A^2 -> H(U1(c, a), U1(d, k))
26.42/8.62	   A^2 -> H(U1(d, e), U1(b, b))
26.42/8.62	   A^2 -> H(U1(d, e), f(c))
26.42/8.62	   A^2 -> H(U1(d, e), f(d))
26.42/8.62	   A^2 -> H(U1(d, c), U1(c, b))
26.42/8.62	   A^2 -> H(U1(d, c), U1(d, b))
26.42/8.62	   A^2 -> H(U1(d, c), U1(b, c))
26.42/8.62	   A^2 -> H(U1(d, c), U1(b, d))
26.42/8.62	   A^2 -> H(U1(d, c), U1(c, c))
26.42/8.62	   A^2 -> H(U1(d, c), f(e))
26.42/8.62	   A^2 -> H(U1(d, c), f(k))
26.42/8.62	   A^2 -> H(U1(d, c), U1(d, d))
26.42/8.62	   A^2 -> H(U1(d, a), U1(e, b))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, b))
26.42/8.62	   A^2 -> H(U1(d, a), U1(c, d))
26.42/8.62	   A^2 -> H(U1(d, a), U1(d, c))
26.42/8.62	   A^2 -> H(U1(d, a), U1(b, e))
26.42/8.62	   A^2 -> H(U1(d, a), U1(b, k))
26.42/8.62	   A^2 -> H(U1(d, a), U1(e, c))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, c))
26.42/8.62	   A^2 -> H(U1(d, a), U1(c, e))
26.42/8.62	   A^2 -> H(U1(d, a), U1(c, k))
26.42/8.62	   A^2 -> H(U1(d, a), U1(e, e))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, k))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, d))
26.42/8.62	   A^2 -> H(U1(d, a), U1(d, k))
26.42/8.62	   A^2 -> H(U1(a, e), U1(c, b))
26.42/8.62	   A^2 -> H(U1(a, e), U1(d, b))
26.42/8.62	   A^2 -> H(U1(a, e), U1(b, c))
26.42/8.62	   A^2 -> H(U1(a, e), U1(b, d))
26.42/8.62	   A^2 -> H(U1(a, e), U1(c, c))
26.42/8.62	   A^2 -> H(U1(a, e), f(e))
26.42/8.62	   A^2 -> H(U1(a, e), f(k))
26.42/8.62	   A^2 -> H(U1(a, e), U1(d, d))
26.42/8.62	   A^2 -> H(U1(a, k), U1(c, b))
26.42/8.62	   A^2 -> H(U1(a, k), U1(d, b))
26.42/8.62	   A^2 -> H(U1(a, k), U1(b, c))
26.42/8.62	   A^2 -> H(U1(a, k), U1(b, d))
26.42/8.62	   A^2 -> H(U1(a, k), U1(c, c))
26.42/8.62	   A^2 -> H(U1(a, k), f(e))
26.42/8.62	   A^2 -> H(U1(a, k), f(k))
26.42/8.62	   A^2 -> H(U1(a, k), U1(d, d))
26.42/8.62	   A^2 -> H(U1(a, c), U1(e, b))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, b))
26.42/8.62	   A^2 -> H(U1(a, c), U1(c, d))
26.42/8.62	   A^2 -> H(U1(a, c), U1(d, c))
26.42/8.62	   A^2 -> H(U1(a, c), U1(b, e))
26.42/8.62	   A^2 -> H(U1(a, c), U1(b, k))
26.42/8.62	   A^2 -> H(U1(a, c), U1(e, c))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, c))
26.42/8.62	   A^2 -> H(U1(a, c), U1(c, e))
26.42/8.62	   A^2 -> H(U1(a, c), U1(c, k))
26.42/8.62	   A^2 -> H(U1(a, c), U1(e, e))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, k))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, d))
26.42/8.62	   A^2 -> H(U1(a, c), U1(d, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(e, b))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, b))
26.42/8.62	   A^2 -> H(U1(a, d), U1(c, d))
26.42/8.62	   A^2 -> H(U1(a, d), U1(d, c))
26.42/8.62	   A^2 -> H(U1(a, d), U1(b, e))
26.42/8.62	   A^2 -> H(U1(a, d), U1(b, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(e, c))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, c))
26.42/8.62	   A^2 -> H(U1(a, d), U1(c, e))
26.42/8.62	   A^2 -> H(U1(a, d), U1(c, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(e, e))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, d))
26.42/8.62	   A^2 -> H(U1(a, d), U1(d, k))
26.42/8.62	   A^2 -> H(U1(a, a), b)
26.42/8.62	   A^2 -> H(U1(a, a), U1(e, d))
26.42/8.62	   A^2 -> H(U1(a, a), U1(d, e))
26.42/8.62	   A^2 -> H(U1(a, a), c)
26.42/8.62	   A^2 -> H(U1(a, a), U1(e, k))
26.42/8.62	   A^2 -> H(U1(a, a), U1(k, e))
26.42/8.62	   A^2 -> H(U1(a, a), e)
26.42/8.62	   A^2 -> H(U1(a, a), U1(k, k))
26.42/8.62	   A^2 -> H(k, f(b))
26.42/8.62	   A^2 -> H(c, U1(b, b))
26.42/8.62	   A^2 -> H(c, f(c))
26.42/8.62	   A^2 -> H(c, f(d))
26.42/8.62	   A^2 -> H(U1(e, k), U1(b, b))
26.42/8.62	   A^2 -> H(U1(e, k), f(c))
26.42/8.62	   A^2 -> H(U1(e, k), f(d))
26.42/8.62	   A^2 -> H(U1(e, c), U1(c, b))
26.42/8.62	   A^2 -> H(U1(e, c), U1(d, b))
26.42/8.62	   A^2 -> H(U1(e, c), U1(b, c))
26.42/8.62	   A^2 -> H(U1(e, c), U1(b, d))
26.42/8.62	   A^2 -> H(U1(e, c), U1(c, c))
26.42/8.62	   A^2 -> H(U1(e, c), f(e))
26.42/8.62	   A^2 -> H(U1(e, c), f(k))
26.42/8.62	   A^2 -> H(U1(e, c), U1(d, d))
26.42/8.62	   A^2 -> H(U1(k, e), U1(b, b))
26.42/8.62	   A^2 -> H(U1(k, e), f(c))
26.42/8.62	   A^2 -> H(U1(k, e), f(d))
26.42/8.62	   A^2 -> H(U1(k, c), U1(c, b))
26.42/8.62	   A^2 -> H(U1(k, c), U1(d, b))
26.42/8.62	   A^2 -> H(U1(k, c), U1(b, c))
26.42/8.62	   A^2 -> H(U1(k, c), U1(b, d))
26.42/8.62	   A^2 -> H(U1(k, c), U1(c, c))
26.42/8.62	   A^2 -> H(U1(k, c), f(e))
26.42/8.62	   A^2 -> H(U1(k, c), f(k))
26.42/8.62	   A^2 -> H(U1(k, c), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, e), U1(c, b))
26.42/8.62	   A^2 -> H(U1(c, e), U1(d, b))
26.42/8.62	   A^2 -> H(U1(c, e), U1(b, c))
26.42/8.62	   A^2 -> H(U1(c, e), U1(b, d))
26.42/8.62	   A^2 -> H(U1(c, e), U1(c, c))
26.42/8.62	   A^2 -> H(U1(c, e), f(e))
26.42/8.62	   A^2 -> H(U1(c, e), f(k))
26.42/8.62	   A^2 -> H(U1(c, e), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, k), U1(c, b))
26.42/8.62	   A^2 -> H(U1(c, k), U1(d, b))
26.42/8.62	   A^2 -> H(U1(c, k), U1(b, c))
26.42/8.62	   A^2 -> H(U1(c, k), U1(b, d))
26.42/8.62	   A^2 -> H(U1(c, k), U1(c, c))
26.42/8.62	   A^2 -> H(U1(c, k), f(e))
26.42/8.62	   A^2 -> H(U1(c, k), f(k))
26.42/8.62	   A^2 -> H(U1(c, k), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(e, b))
26.42/8.62	   A^2 -> H(U1(c, c), U1(k, b))
26.42/8.62	   A^2 -> H(U1(c, c), U1(c, d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(d, c))
26.42/8.62	   A^2 -> H(U1(c, c), U1(b, e))
26.42/8.62	   A^2 -> H(U1(c, c), U1(b, k))
26.42/8.62	   A^2 -> H(U1(c, c), U1(e, e))
26.42/8.62	   A^2 -> H(U1(c, c), U1(k, k))
26.42/8.62	   A^2 -> H(U1(c, c), U1(k, d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(d, k))
26.42/8.62	   A^2 -> H(e, U1(b, b))
26.42/8.62	   A^2 -> H(e, f(c))
26.42/8.62	   A^2 -> H(e, f(d))
26.42/8.62	   A^2 -> H(U1(e, e), U1(c, b))
26.42/8.62	   A^2 -> H(U1(e, e), U1(d, b))
26.42/8.62	   A^2 -> H(U1(e, e), U1(b, c))
26.42/8.62	   A^2 -> H(U1(e, e), U1(b, d))
26.42/8.62	   A^2 -> H(U1(e, e), U1(c, c))
26.42/8.62	   A^2 -> H(U1(e, e), f(e))
26.42/8.62	   A^2 -> H(U1(e, e), f(k))
26.42/8.62	   A^2 -> H(U1(e, e), U1(d, d))
26.42/8.62	   A^2 -> H(f(e), U1(e, b))
26.42/8.62	   A^2 -> H(f(e), U1(k, b))
26.42/8.62	   A^2 -> H(f(e), U1(c, d))
26.42/8.62	   A^2 -> H(f(e), U1(d, c))
26.42/8.62	   A^2 -> H(f(e), U1(b, e))
26.42/8.62	   A^2 -> H(f(e), U1(b, k))
26.42/8.62	   A^2 -> H(f(e), U1(e, c))
26.42/8.62	   A^2 -> H(f(e), U1(k, c))
26.42/8.62	   A^2 -> H(f(e), U1(c, e))
26.42/8.62	   A^2 -> H(f(e), U1(c, k))
26.42/8.62	   A^2 -> H(f(e), U1(k, k))
26.42/8.62	   A^2 -> H(f(e), U1(k, d))
26.42/8.62	   A^2 -> H(f(e), U1(d, k))
26.42/8.62	   A^2 -> H(U1(k, k), U1(c, b))
26.42/8.62	   A^2 -> H(U1(k, k), U1(d, b))
26.42/8.62	   A^2 -> H(U1(k, k), U1(b, c))
26.42/8.62	   A^2 -> H(U1(k, k), U1(b, d))
26.42/8.62	   A^2 -> H(U1(k, k), U1(c, c))
26.42/8.62	   A^2 -> H(U1(k, k), f(e))
26.42/8.62	   A^2 -> H(U1(k, k), f(k))
26.42/8.62	   A^2 -> H(U1(k, k), U1(d, d))
26.42/8.62	   A^2 -> H(f(k), U1(e, b))
26.42/8.62	   A^2 -> H(f(k), U1(k, b))
26.42/8.62	   A^2 -> H(f(k), U1(c, d))
26.42/8.62	   A^2 -> H(f(k), U1(d, c))
26.42/8.62	   A^2 -> H(f(k), U1(b, e))
26.42/8.62	   A^2 -> H(f(k), U1(b, k))
26.42/8.62	   A^2 -> H(f(k), U1(e, c))
26.42/8.62	   A^2 -> H(f(k), U1(k, c))
26.42/8.62	   A^2 -> H(f(k), U1(c, e))
26.42/8.62	   A^2 -> H(f(k), U1(c, k))
26.42/8.62	   A^2 -> H(f(k), U1(e, e))
26.42/8.62	   A^2 -> H(f(k), U1(k, d))
26.42/8.62	   A^2 -> H(f(k), U1(d, k))
26.42/8.62	   A^2 -> H(f(c), b)
26.42/8.62	   A^2 -> H(f(c), U1(e, d))
26.42/8.62	   A^2 -> H(f(c), U1(d, e))
26.42/8.62	
26.42/8.62	The TRS R consists of the following rules:
26.42/8.62	
26.42/8.62	   f(x) -> U1(x, x)
26.42/8.62	   U1(e, x) -> x
26.42/8.62	   a -> c
26.42/8.62	   a -> d
26.42/8.62	   b -> c
26.42/8.62	   b -> d
26.42/8.62	   d -> k
26.42/8.62	   c -> e
26.42/8.62	   c -> k
26.42/8.62	
26.42/8.62	Q is empty.
26.42/8.62	We have to consider all minimal (P,Q,R)-chains.
26.42/8.62	----------------------------------------
26.42/8.62	
26.42/8.62	(449) TransformationProof (EQUIVALENT)
26.42/8.62	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
26.42/8.62	
26.42/8.62	   (A^2 -> H(U1(c, c), U1(b, e)),A^2 -> H(U1(c, c), U1(b, e)))
26.42/8.62	   (A^2 -> H(f(e), U1(b, e)),A^2 -> H(f(e), U1(b, e)))
26.42/8.62	   (A^2 -> H(f(k), U1(b, e)),A^2 -> H(f(k), U1(b, e)))
26.42/8.62	   (A^2 -> H(f(c), U1(c, e)),A^2 -> H(f(c), U1(c, e)))
26.42/8.62	   (A^2 -> H(f(c), U1(d, e)),A^2 -> H(f(c), U1(d, e)))
26.42/8.62	
26.42/8.62	
26.42/8.62	----------------------------------------
26.42/8.62	
26.42/8.62	(450)
26.42/8.62	Obligation:
26.42/8.62	Q DP problem:
26.42/8.62	The TRS P consists of the following rules:
26.42/8.62	
26.42/8.62	   H(x, x) -> G(x, x, f(k))
26.42/8.62	   G(d, x, x) -> A^2
26.42/8.62	   A^2 -> H(f(c), f(c))
26.42/8.62	   A^2 -> H(f(d), f(d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(c, c))
26.42/8.62	   A^2 -> H(f(e), f(e))
26.42/8.62	   A^2 -> H(f(k), f(k))
26.42/8.62	   A^2 -> H(f(c), U1(b, k))
26.42/8.62	   A^2 -> H(f(c), U1(k, d))
26.42/8.62	   A^2 -> H(f(c), U1(d, k))
26.42/8.62	   A^2 -> H(f(c), U1(k, k))
26.42/8.62	   A^2 -> H(U1(k, k), f(b))
26.42/8.62	   A^2 -> H(U1(k, d), U1(b, b))
26.42/8.62	   A^2 -> H(U1(k, d), f(c))
26.42/8.62	   A^2 -> H(U1(k, d), f(d))
26.42/8.62	   A^2 -> H(U1(d, k), U1(b, b))
26.42/8.62	   A^2 -> H(U1(d, k), f(c))
26.42/8.62	   A^2 -> H(U1(d, k), f(d))
26.42/8.62	   A^2 -> H(U1(d, d), U1(c, b))
26.42/8.62	   A^2 -> H(U1(d, d), U1(d, b))
26.42/8.62	   A^2 -> H(U1(d, d), U1(b, c))
26.42/8.62	   A^2 -> H(U1(d, d), U1(b, d))
26.42/8.62	   A^2 -> H(U1(d, d), U1(c, c))
26.42/8.62	   A^2 -> H(U1(d, d), f(e))
26.42/8.62	   A^2 -> H(U1(d, d), f(k))
26.42/8.62	   A^2 -> H(U1(d, d), U1(d, d))
26.42/8.62	   A^2 -> H(f(d), U1(e, b))
26.42/8.62	   A^2 -> H(f(d), U1(k, b))
26.42/8.62	   A^2 -> H(f(d), U1(c, d))
26.42/8.62	   A^2 -> H(f(d), U1(d, c))
26.42/8.62	   A^2 -> H(f(d), U1(b, e))
26.42/8.62	   A^2 -> H(f(d), U1(b, k))
26.42/8.62	   A^2 -> H(f(d), U1(e, c))
26.42/8.62	   A^2 -> H(f(d), U1(k, c))
26.42/8.62	   A^2 -> H(f(d), U1(c, e))
26.42/8.62	   A^2 -> H(f(d), U1(c, k))
26.42/8.62	   A^2 -> H(f(d), U1(e, e))
26.42/8.62	   A^2 -> H(f(d), U1(k, k))
26.42/8.62	   A^2 -> H(f(a), b)
26.42/8.62	   A^2 -> H(f(a), U1(e, d))
26.42/8.62	   A^2 -> H(f(a), U1(d, e))
26.42/8.62	   A^2 -> H(f(c), U1(e, c))
26.42/8.62	   A^2 -> H(f(c), U1(k, c))
26.42/8.62	   A^2 -> H(f(c), U1(c, e))
26.42/8.62	   A^2 -> H(f(c), U1(c, k))
26.42/8.62	   A^2 -> H(f(a), c)
26.42/8.62	   A^2 -> H(f(a), U1(e, k))
26.42/8.62	   A^2 -> H(f(a), U1(k, e))
26.42/8.62	   A^2 -> H(f(c), U1(e, e))
26.42/8.62	   A^2 -> H(f(a), e)
26.42/8.62	   A^2 -> H(f(d), U1(k, d))
26.42/8.62	   A^2 -> H(f(d), U1(d, k))
26.42/8.62	   A^2 -> H(f(a), U1(k, k))
26.42/8.62	   A^2 -> H(d, f(b))
26.42/8.62	   A^2 -> H(a, U1(b, b))
26.42/8.62	   A^2 -> H(a, f(c))
26.42/8.62	   A^2 -> H(a, f(d))
26.42/8.62	   A^2 -> H(U1(e, d), U1(b, b))
26.42/8.62	   A^2 -> H(U1(e, d), f(c))
26.42/8.62	   A^2 -> H(U1(e, d), f(d))
26.42/8.62	   A^2 -> H(U1(e, a), U1(c, b))
26.42/8.62	   A^2 -> H(U1(e, a), U1(d, b))
26.42/8.62	   A^2 -> H(U1(e, a), U1(b, c))
26.42/8.62	   A^2 -> H(U1(e, a), U1(b, d))
26.42/8.62	   A^2 -> H(U1(e, a), U1(c, c))
26.42/8.62	   A^2 -> H(U1(e, a), f(e))
26.42/8.62	   A^2 -> H(U1(e, a), f(k))
26.42/8.62	   A^2 -> H(U1(e, a), U1(d, d))
26.42/8.62	   A^2 -> H(U1(k, a), U1(c, b))
26.42/8.62	   A^2 -> H(U1(k, a), U1(d, b))
26.42/8.62	   A^2 -> H(U1(k, a), U1(b, c))
26.42/8.62	   A^2 -> H(U1(k, a), U1(b, d))
26.42/8.62	   A^2 -> H(U1(k, a), U1(c, c))
26.42/8.62	   A^2 -> H(U1(k, a), f(e))
26.42/8.62	   A^2 -> H(U1(k, a), f(k))
26.42/8.62	   A^2 -> H(U1(k, a), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, d), U1(c, b))
26.42/8.62	   A^2 -> H(U1(c, d), U1(d, b))
26.42/8.62	   A^2 -> H(U1(c, d), U1(b, c))
26.42/8.62	   A^2 -> H(U1(c, d), U1(b, d))
26.42/8.62	   A^2 -> H(U1(c, d), U1(c, c))
26.42/8.62	   A^2 -> H(U1(c, d), f(e))
26.42/8.62	   A^2 -> H(U1(c, d), f(k))
26.42/8.62	   A^2 -> H(U1(c, d), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, a), U1(e, b))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, b))
26.42/8.62	   A^2 -> H(U1(c, a), U1(c, d))
26.42/8.62	   A^2 -> H(U1(c, a), U1(d, c))
26.42/8.62	   A^2 -> H(U1(c, a), U1(b, e))
26.42/8.62	   A^2 -> H(U1(c, a), U1(b, k))
26.42/8.62	   A^2 -> H(U1(c, a), U1(e, c))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, c))
26.42/8.62	   A^2 -> H(U1(c, a), U1(c, e))
26.42/8.62	   A^2 -> H(U1(c, a), U1(c, k))
26.42/8.62	   A^2 -> H(U1(c, a), U1(e, e))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, k))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, d))
26.42/8.62	   A^2 -> H(U1(c, a), U1(d, k))
26.42/8.62	   A^2 -> H(U1(d, e), U1(b, b))
26.42/8.62	   A^2 -> H(U1(d, e), f(c))
26.42/8.62	   A^2 -> H(U1(d, e), f(d))
26.42/8.62	   A^2 -> H(U1(d, c), U1(c, b))
26.42/8.62	   A^2 -> H(U1(d, c), U1(d, b))
26.42/8.62	   A^2 -> H(U1(d, c), U1(b, c))
26.42/8.62	   A^2 -> H(U1(d, c), U1(b, d))
26.42/8.62	   A^2 -> H(U1(d, c), U1(c, c))
26.42/8.62	   A^2 -> H(U1(d, c), f(e))
26.42/8.62	   A^2 -> H(U1(d, c), f(k))
26.42/8.62	   A^2 -> H(U1(d, c), U1(d, d))
26.42/8.62	   A^2 -> H(U1(d, a), U1(e, b))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, b))
26.42/8.62	   A^2 -> H(U1(d, a), U1(c, d))
26.42/8.62	   A^2 -> H(U1(d, a), U1(d, c))
26.42/8.62	   A^2 -> H(U1(d, a), U1(b, e))
26.42/8.62	   A^2 -> H(U1(d, a), U1(b, k))
26.42/8.62	   A^2 -> H(U1(d, a), U1(e, c))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, c))
26.42/8.62	   A^2 -> H(U1(d, a), U1(c, e))
26.42/8.62	   A^2 -> H(U1(d, a), U1(c, k))
26.42/8.62	   A^2 -> H(U1(d, a), U1(e, e))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, k))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, d))
26.42/8.62	   A^2 -> H(U1(d, a), U1(d, k))
26.42/8.62	   A^2 -> H(U1(a, e), U1(c, b))
26.42/8.62	   A^2 -> H(U1(a, e), U1(d, b))
26.42/8.62	   A^2 -> H(U1(a, e), U1(b, c))
26.42/8.62	   A^2 -> H(U1(a, e), U1(b, d))
26.42/8.62	   A^2 -> H(U1(a, e), U1(c, c))
26.42/8.62	   A^2 -> H(U1(a, e), f(e))
26.42/8.62	   A^2 -> H(U1(a, e), f(k))
26.42/8.62	   A^2 -> H(U1(a, e), U1(d, d))
26.42/8.62	   A^2 -> H(U1(a, k), U1(c, b))
26.42/8.62	   A^2 -> H(U1(a, k), U1(d, b))
26.42/8.62	   A^2 -> H(U1(a, k), U1(b, c))
26.42/8.62	   A^2 -> H(U1(a, k), U1(b, d))
26.42/8.62	   A^2 -> H(U1(a, k), U1(c, c))
26.42/8.62	   A^2 -> H(U1(a, k), f(e))
26.42/8.62	   A^2 -> H(U1(a, k), f(k))
26.42/8.62	   A^2 -> H(U1(a, k), U1(d, d))
26.42/8.62	   A^2 -> H(U1(a, c), U1(e, b))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, b))
26.42/8.62	   A^2 -> H(U1(a, c), U1(c, d))
26.42/8.62	   A^2 -> H(U1(a, c), U1(d, c))
26.42/8.62	   A^2 -> H(U1(a, c), U1(b, e))
26.42/8.62	   A^2 -> H(U1(a, c), U1(b, k))
26.42/8.62	   A^2 -> H(U1(a, c), U1(e, c))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, c))
26.42/8.62	   A^2 -> H(U1(a, c), U1(c, e))
26.42/8.62	   A^2 -> H(U1(a, c), U1(c, k))
26.42/8.62	   A^2 -> H(U1(a, c), U1(e, e))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, k))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, d))
26.42/8.62	   A^2 -> H(U1(a, c), U1(d, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(e, b))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, b))
26.42/8.62	   A^2 -> H(U1(a, d), U1(c, d))
26.42/8.62	   A^2 -> H(U1(a, d), U1(d, c))
26.42/8.62	   A^2 -> H(U1(a, d), U1(b, e))
26.42/8.62	   A^2 -> H(U1(a, d), U1(b, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(e, c))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, c))
26.42/8.62	   A^2 -> H(U1(a, d), U1(c, e))
26.42/8.62	   A^2 -> H(U1(a, d), U1(c, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(e, e))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, d))
26.42/8.62	   A^2 -> H(U1(a, d), U1(d, k))
26.42/8.62	   A^2 -> H(U1(a, a), b)
26.42/8.62	   A^2 -> H(U1(a, a), U1(e, d))
26.42/8.62	   A^2 -> H(U1(a, a), U1(d, e))
26.42/8.62	   A^2 -> H(U1(a, a), c)
26.42/8.62	   A^2 -> H(U1(a, a), U1(e, k))
26.42/8.62	   A^2 -> H(U1(a, a), U1(k, e))
26.42/8.62	   A^2 -> H(U1(a, a), e)
26.42/8.62	   A^2 -> H(U1(a, a), U1(k, k))
26.42/8.62	   A^2 -> H(k, f(b))
26.42/8.62	   A^2 -> H(c, U1(b, b))
26.42/8.62	   A^2 -> H(c, f(c))
26.42/8.62	   A^2 -> H(c, f(d))
26.42/8.62	   A^2 -> H(U1(e, k), U1(b, b))
26.42/8.62	   A^2 -> H(U1(e, k), f(c))
26.42/8.62	   A^2 -> H(U1(e, k), f(d))
26.42/8.62	   A^2 -> H(U1(e, c), U1(c, b))
26.42/8.62	   A^2 -> H(U1(e, c), U1(d, b))
26.42/8.62	   A^2 -> H(U1(e, c), U1(b, c))
26.42/8.62	   A^2 -> H(U1(e, c), U1(b, d))
26.42/8.62	   A^2 -> H(U1(e, c), U1(c, c))
26.42/8.62	   A^2 -> H(U1(e, c), f(e))
26.42/8.62	   A^2 -> H(U1(e, c), f(k))
26.42/8.62	   A^2 -> H(U1(e, c), U1(d, d))
26.42/8.62	   A^2 -> H(U1(k, e), U1(b, b))
26.42/8.62	   A^2 -> H(U1(k, e), f(c))
26.42/8.62	   A^2 -> H(U1(k, e), f(d))
26.42/8.62	   A^2 -> H(U1(k, c), U1(c, b))
26.42/8.62	   A^2 -> H(U1(k, c), U1(d, b))
26.42/8.62	   A^2 -> H(U1(k, c), U1(b, c))
26.42/8.62	   A^2 -> H(U1(k, c), U1(b, d))
26.42/8.62	   A^2 -> H(U1(k, c), U1(c, c))
26.42/8.62	   A^2 -> H(U1(k, c), f(e))
26.42/8.62	   A^2 -> H(U1(k, c), f(k))
26.42/8.62	   A^2 -> H(U1(k, c), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, e), U1(c, b))
26.42/8.62	   A^2 -> H(U1(c, e), U1(d, b))
26.42/8.62	   A^2 -> H(U1(c, e), U1(b, c))
26.42/8.62	   A^2 -> H(U1(c, e), U1(b, d))
26.42/8.62	   A^2 -> H(U1(c, e), U1(c, c))
26.42/8.62	   A^2 -> H(U1(c, e), f(e))
26.42/8.62	   A^2 -> H(U1(c, e), f(k))
26.42/8.62	   A^2 -> H(U1(c, e), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, k), U1(c, b))
26.42/8.62	   A^2 -> H(U1(c, k), U1(d, b))
26.42/8.62	   A^2 -> H(U1(c, k), U1(b, c))
26.42/8.62	   A^2 -> H(U1(c, k), U1(b, d))
26.42/8.62	   A^2 -> H(U1(c, k), U1(c, c))
26.42/8.62	   A^2 -> H(U1(c, k), f(e))
26.42/8.62	   A^2 -> H(U1(c, k), f(k))
26.42/8.62	   A^2 -> H(U1(c, k), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(e, b))
26.42/8.62	   A^2 -> H(U1(c, c), U1(k, b))
26.42/8.62	   A^2 -> H(U1(c, c), U1(c, d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(d, c))
26.42/8.62	   A^2 -> H(U1(c, c), U1(b, e))
26.42/8.62	   A^2 -> H(U1(c, c), U1(b, k))
26.42/8.62	   A^2 -> H(U1(c, c), U1(e, e))
26.42/8.62	   A^2 -> H(U1(c, c), U1(k, k))
26.42/8.62	   A^2 -> H(U1(c, c), U1(k, d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(d, k))
26.42/8.62	   A^2 -> H(e, U1(b, b))
26.42/8.62	   A^2 -> H(e, f(c))
26.42/8.62	   A^2 -> H(e, f(d))
26.42/8.62	   A^2 -> H(U1(e, e), U1(c, b))
26.42/8.62	   A^2 -> H(U1(e, e), U1(d, b))
26.42/8.62	   A^2 -> H(U1(e, e), U1(b, c))
26.42/8.62	   A^2 -> H(U1(e, e), U1(b, d))
26.42/8.62	   A^2 -> H(U1(e, e), U1(c, c))
26.42/8.62	   A^2 -> H(U1(e, e), f(e))
26.42/8.62	   A^2 -> H(U1(e, e), f(k))
26.42/8.62	   A^2 -> H(U1(e, e), U1(d, d))
26.42/8.62	   A^2 -> H(f(e), U1(e, b))
26.42/8.62	   A^2 -> H(f(e), U1(k, b))
26.42/8.62	   A^2 -> H(f(e), U1(c, d))
26.42/8.62	   A^2 -> H(f(e), U1(d, c))
26.42/8.62	   A^2 -> H(f(e), U1(b, e))
26.42/8.62	   A^2 -> H(f(e), U1(b, k))
26.42/8.62	   A^2 -> H(f(e), U1(e, c))
26.42/8.62	   A^2 -> H(f(e), U1(k, c))
26.42/8.62	   A^2 -> H(f(e), U1(c, e))
26.42/8.62	   A^2 -> H(f(e), U1(c, k))
26.42/8.62	   A^2 -> H(f(e), U1(k, k))
26.42/8.62	   A^2 -> H(f(e), U1(k, d))
26.42/8.62	   A^2 -> H(f(e), U1(d, k))
26.42/8.62	   A^2 -> H(U1(k, k), U1(c, b))
26.42/8.62	   A^2 -> H(U1(k, k), U1(d, b))
26.42/8.62	   A^2 -> H(U1(k, k), U1(b, c))
26.42/8.62	   A^2 -> H(U1(k, k), U1(b, d))
26.42/8.62	   A^2 -> H(U1(k, k), U1(c, c))
26.42/8.62	   A^2 -> H(U1(k, k), f(e))
26.42/8.62	   A^2 -> H(U1(k, k), f(k))
26.42/8.62	   A^2 -> H(U1(k, k), U1(d, d))
26.42/8.62	   A^2 -> H(f(k), U1(e, b))
26.42/8.62	   A^2 -> H(f(k), U1(k, b))
26.42/8.62	   A^2 -> H(f(k), U1(c, d))
26.42/8.62	   A^2 -> H(f(k), U1(d, c))
26.42/8.62	   A^2 -> H(f(k), U1(b, e))
26.42/8.62	   A^2 -> H(f(k), U1(b, k))
26.42/8.62	   A^2 -> H(f(k), U1(e, c))
26.42/8.62	   A^2 -> H(f(k), U1(k, c))
26.42/8.62	   A^2 -> H(f(k), U1(c, e))
26.42/8.62	   A^2 -> H(f(k), U1(c, k))
26.42/8.62	   A^2 -> H(f(k), U1(e, e))
26.42/8.62	   A^2 -> H(f(k), U1(k, d))
26.42/8.62	   A^2 -> H(f(k), U1(d, k))
26.42/8.62	   A^2 -> H(f(c), b)
26.42/8.62	   A^2 -> H(f(c), U1(e, d))
26.42/8.62	   A^2 -> H(f(c), U1(d, e))
26.42/8.62	
26.42/8.62	The TRS R consists of the following rules:
26.42/8.62	
26.42/8.62	   f(x) -> U1(x, x)
26.42/8.62	   U1(e, x) -> x
26.42/8.62	   a -> c
26.42/8.62	   a -> d
26.42/8.62	   b -> c
26.42/8.62	   b -> d
26.42/8.62	   d -> k
26.42/8.62	   c -> e
26.42/8.62	   c -> k
26.42/8.62	
26.42/8.62	Q is empty.
26.42/8.62	We have to consider all minimal (P,Q,R)-chains.
26.42/8.62	----------------------------------------
26.42/8.62	
26.42/8.62	(451) TransformationProof (EQUIVALENT)
26.42/8.62	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
26.42/8.62	
26.42/8.62	   (A^2 -> H(U1(c, c), U1(b, k)),A^2 -> H(U1(c, c), U1(b, k)))
26.42/8.62	   (A^2 -> H(f(e), U1(b, k)),A^2 -> H(f(e), U1(b, k)))
26.42/8.62	   (A^2 -> H(f(k), U1(b, k)),A^2 -> H(f(k), U1(b, k)))
26.42/8.62	   (A^2 -> H(f(c), U1(c, k)),A^2 -> H(f(c), U1(c, k)))
26.42/8.62	   (A^2 -> H(f(c), U1(d, k)),A^2 -> H(f(c), U1(d, k)))
26.42/8.62	
26.42/8.62	
26.42/8.62	----------------------------------------
26.42/8.62	
26.42/8.62	(452)
26.42/8.62	Obligation:
26.42/8.62	Q DP problem:
26.42/8.62	The TRS P consists of the following rules:
26.42/8.62	
26.42/8.62	   H(x, x) -> G(x, x, f(k))
26.42/8.62	   G(d, x, x) -> A^2
26.42/8.62	   A^2 -> H(f(c), f(c))
26.42/8.62	   A^2 -> H(f(d), f(d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(c, c))
26.42/8.62	   A^2 -> H(f(e), f(e))
26.42/8.62	   A^2 -> H(f(k), f(k))
26.42/8.62	   A^2 -> H(f(c), U1(k, d))
26.42/8.62	   A^2 -> H(f(c), U1(d, k))
26.42/8.62	   A^2 -> H(f(c), U1(k, k))
26.42/8.62	   A^2 -> H(U1(k, k), f(b))
26.42/8.62	   A^2 -> H(U1(k, d), U1(b, b))
26.42/8.62	   A^2 -> H(U1(k, d), f(c))
26.42/8.62	   A^2 -> H(U1(k, d), f(d))
26.42/8.62	   A^2 -> H(U1(d, k), U1(b, b))
26.42/8.62	   A^2 -> H(U1(d, k), f(c))
26.42/8.62	   A^2 -> H(U1(d, k), f(d))
26.42/8.62	   A^2 -> H(U1(d, d), U1(c, b))
26.42/8.62	   A^2 -> H(U1(d, d), U1(d, b))
26.42/8.62	   A^2 -> H(U1(d, d), U1(b, c))
26.42/8.62	   A^2 -> H(U1(d, d), U1(b, d))
26.42/8.62	   A^2 -> H(U1(d, d), U1(c, c))
26.42/8.62	   A^2 -> H(U1(d, d), f(e))
26.42/8.62	   A^2 -> H(U1(d, d), f(k))
26.42/8.62	   A^2 -> H(U1(d, d), U1(d, d))
26.42/8.62	   A^2 -> H(f(d), U1(e, b))
26.42/8.62	   A^2 -> H(f(d), U1(k, b))
26.42/8.62	   A^2 -> H(f(d), U1(c, d))
26.42/8.62	   A^2 -> H(f(d), U1(d, c))
26.42/8.62	   A^2 -> H(f(d), U1(b, e))
26.42/8.62	   A^2 -> H(f(d), U1(b, k))
26.42/8.62	   A^2 -> H(f(d), U1(e, c))
26.42/8.62	   A^2 -> H(f(d), U1(k, c))
26.42/8.62	   A^2 -> H(f(d), U1(c, e))
26.42/8.62	   A^2 -> H(f(d), U1(c, k))
26.42/8.62	   A^2 -> H(f(d), U1(e, e))
26.42/8.62	   A^2 -> H(f(d), U1(k, k))
26.42/8.62	   A^2 -> H(f(a), b)
26.42/8.62	   A^2 -> H(f(a), U1(e, d))
26.42/8.62	   A^2 -> H(f(a), U1(d, e))
26.42/8.62	   A^2 -> H(f(c), U1(e, c))
26.42/8.62	   A^2 -> H(f(c), U1(k, c))
26.42/8.62	   A^2 -> H(f(c), U1(c, e))
26.42/8.62	   A^2 -> H(f(c), U1(c, k))
26.42/8.62	   A^2 -> H(f(a), c)
26.42/8.62	   A^2 -> H(f(a), U1(e, k))
26.42/8.62	   A^2 -> H(f(a), U1(k, e))
26.42/8.62	   A^2 -> H(f(c), U1(e, e))
26.42/8.62	   A^2 -> H(f(a), e)
26.42/8.62	   A^2 -> H(f(d), U1(k, d))
26.42/8.62	   A^2 -> H(f(d), U1(d, k))
26.42/8.62	   A^2 -> H(f(a), U1(k, k))
26.42/8.62	   A^2 -> H(d, f(b))
26.42/8.62	   A^2 -> H(a, U1(b, b))
26.42/8.62	   A^2 -> H(a, f(c))
26.42/8.62	   A^2 -> H(a, f(d))
26.42/8.62	   A^2 -> H(U1(e, d), U1(b, b))
26.42/8.62	   A^2 -> H(U1(e, d), f(c))
26.42/8.62	   A^2 -> H(U1(e, d), f(d))
26.42/8.62	   A^2 -> H(U1(e, a), U1(c, b))
26.42/8.62	   A^2 -> H(U1(e, a), U1(d, b))
26.42/8.62	   A^2 -> H(U1(e, a), U1(b, c))
26.42/8.62	   A^2 -> H(U1(e, a), U1(b, d))
26.42/8.62	   A^2 -> H(U1(e, a), U1(c, c))
26.42/8.62	   A^2 -> H(U1(e, a), f(e))
26.42/8.62	   A^2 -> H(U1(e, a), f(k))
26.42/8.62	   A^2 -> H(U1(e, a), U1(d, d))
26.42/8.62	   A^2 -> H(U1(k, a), U1(c, b))
26.42/8.62	   A^2 -> H(U1(k, a), U1(d, b))
26.42/8.62	   A^2 -> H(U1(k, a), U1(b, c))
26.42/8.62	   A^2 -> H(U1(k, a), U1(b, d))
26.42/8.62	   A^2 -> H(U1(k, a), U1(c, c))
26.42/8.62	   A^2 -> H(U1(k, a), f(e))
26.42/8.62	   A^2 -> H(U1(k, a), f(k))
26.42/8.62	   A^2 -> H(U1(k, a), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, d), U1(c, b))
26.42/8.62	   A^2 -> H(U1(c, d), U1(d, b))
26.42/8.62	   A^2 -> H(U1(c, d), U1(b, c))
26.42/8.62	   A^2 -> H(U1(c, d), U1(b, d))
26.42/8.62	   A^2 -> H(U1(c, d), U1(c, c))
26.42/8.62	   A^2 -> H(U1(c, d), f(e))
26.42/8.62	   A^2 -> H(U1(c, d), f(k))
26.42/8.62	   A^2 -> H(U1(c, d), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, a), U1(e, b))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, b))
26.42/8.62	   A^2 -> H(U1(c, a), U1(c, d))
26.42/8.62	   A^2 -> H(U1(c, a), U1(d, c))
26.42/8.62	   A^2 -> H(U1(c, a), U1(b, e))
26.42/8.62	   A^2 -> H(U1(c, a), U1(b, k))
26.42/8.62	   A^2 -> H(U1(c, a), U1(e, c))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, c))
26.42/8.62	   A^2 -> H(U1(c, a), U1(c, e))
26.42/8.62	   A^2 -> H(U1(c, a), U1(c, k))
26.42/8.62	   A^2 -> H(U1(c, a), U1(e, e))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, k))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, d))
26.42/8.62	   A^2 -> H(U1(c, a), U1(d, k))
26.42/8.62	   A^2 -> H(U1(d, e), U1(b, b))
26.42/8.62	   A^2 -> H(U1(d, e), f(c))
26.42/8.62	   A^2 -> H(U1(d, e), f(d))
26.42/8.62	   A^2 -> H(U1(d, c), U1(c, b))
26.42/8.62	   A^2 -> H(U1(d, c), U1(d, b))
26.42/8.62	   A^2 -> H(U1(d, c), U1(b, c))
26.42/8.62	   A^2 -> H(U1(d, c), U1(b, d))
26.42/8.62	   A^2 -> H(U1(d, c), U1(c, c))
26.42/8.62	   A^2 -> H(U1(d, c), f(e))
26.42/8.62	   A^2 -> H(U1(d, c), f(k))
26.42/8.62	   A^2 -> H(U1(d, c), U1(d, d))
26.42/8.62	   A^2 -> H(U1(d, a), U1(e, b))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, b))
26.42/8.62	   A^2 -> H(U1(d, a), U1(c, d))
26.42/8.62	   A^2 -> H(U1(d, a), U1(d, c))
26.42/8.62	   A^2 -> H(U1(d, a), U1(b, e))
26.42/8.62	   A^2 -> H(U1(d, a), U1(b, k))
26.42/8.62	   A^2 -> H(U1(d, a), U1(e, c))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, c))
26.42/8.62	   A^2 -> H(U1(d, a), U1(c, e))
26.42/8.62	   A^2 -> H(U1(d, a), U1(c, k))
26.42/8.62	   A^2 -> H(U1(d, a), U1(e, e))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, k))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, d))
26.42/8.62	   A^2 -> H(U1(d, a), U1(d, k))
26.42/8.62	   A^2 -> H(U1(a, e), U1(c, b))
26.42/8.62	   A^2 -> H(U1(a, e), U1(d, b))
26.42/8.62	   A^2 -> H(U1(a, e), U1(b, c))
26.42/8.62	   A^2 -> H(U1(a, e), U1(b, d))
26.42/8.62	   A^2 -> H(U1(a, e), U1(c, c))
26.42/8.62	   A^2 -> H(U1(a, e), f(e))
26.42/8.62	   A^2 -> H(U1(a, e), f(k))
26.42/8.62	   A^2 -> H(U1(a, e), U1(d, d))
26.42/8.62	   A^2 -> H(U1(a, k), U1(c, b))
26.42/8.62	   A^2 -> H(U1(a, k), U1(d, b))
26.42/8.62	   A^2 -> H(U1(a, k), U1(b, c))
26.42/8.62	   A^2 -> H(U1(a, k), U1(b, d))
26.42/8.62	   A^2 -> H(U1(a, k), U1(c, c))
26.42/8.62	   A^2 -> H(U1(a, k), f(e))
26.42/8.62	   A^2 -> H(U1(a, k), f(k))
26.42/8.62	   A^2 -> H(U1(a, k), U1(d, d))
26.42/8.62	   A^2 -> H(U1(a, c), U1(e, b))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, b))
26.42/8.62	   A^2 -> H(U1(a, c), U1(c, d))
26.42/8.62	   A^2 -> H(U1(a, c), U1(d, c))
26.42/8.62	   A^2 -> H(U1(a, c), U1(b, e))
26.42/8.62	   A^2 -> H(U1(a, c), U1(b, k))
26.42/8.62	   A^2 -> H(U1(a, c), U1(e, c))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, c))
26.42/8.62	   A^2 -> H(U1(a, c), U1(c, e))
26.42/8.62	   A^2 -> H(U1(a, c), U1(c, k))
26.42/8.62	   A^2 -> H(U1(a, c), U1(e, e))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, k))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, d))
26.42/8.62	   A^2 -> H(U1(a, c), U1(d, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(e, b))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, b))
26.42/8.62	   A^2 -> H(U1(a, d), U1(c, d))
26.42/8.62	   A^2 -> H(U1(a, d), U1(d, c))
26.42/8.62	   A^2 -> H(U1(a, d), U1(b, e))
26.42/8.62	   A^2 -> H(U1(a, d), U1(b, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(e, c))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, c))
26.42/8.62	   A^2 -> H(U1(a, d), U1(c, e))
26.42/8.62	   A^2 -> H(U1(a, d), U1(c, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(e, e))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, k))
26.42/8.62	   A^2 -> H(U1(a, d), U1(k, d))
26.42/8.62	   A^2 -> H(U1(a, d), U1(d, k))
26.42/8.62	   A^2 -> H(U1(a, a), b)
26.42/8.62	   A^2 -> H(U1(a, a), U1(e, d))
26.42/8.62	   A^2 -> H(U1(a, a), U1(d, e))
26.42/8.62	   A^2 -> H(U1(a, a), c)
26.42/8.62	   A^2 -> H(U1(a, a), U1(e, k))
26.42/8.62	   A^2 -> H(U1(a, a), U1(k, e))
26.42/8.62	   A^2 -> H(U1(a, a), e)
26.42/8.62	   A^2 -> H(U1(a, a), U1(k, k))
26.42/8.62	   A^2 -> H(k, f(b))
26.42/8.62	   A^2 -> H(c, U1(b, b))
26.42/8.62	   A^2 -> H(c, f(c))
26.42/8.62	   A^2 -> H(c, f(d))
26.42/8.62	   A^2 -> H(U1(e, k), U1(b, b))
26.42/8.62	   A^2 -> H(U1(e, k), f(c))
26.42/8.62	   A^2 -> H(U1(e, k), f(d))
26.42/8.62	   A^2 -> H(U1(e, c), U1(c, b))
26.42/8.62	   A^2 -> H(U1(e, c), U1(d, b))
26.42/8.62	   A^2 -> H(U1(e, c), U1(b, c))
26.42/8.62	   A^2 -> H(U1(e, c), U1(b, d))
26.42/8.62	   A^2 -> H(U1(e, c), U1(c, c))
26.42/8.62	   A^2 -> H(U1(e, c), f(e))
26.42/8.62	   A^2 -> H(U1(e, c), f(k))
26.42/8.62	   A^2 -> H(U1(e, c), U1(d, d))
26.42/8.62	   A^2 -> H(U1(k, e), U1(b, b))
26.42/8.62	   A^2 -> H(U1(k, e), f(c))
26.42/8.62	   A^2 -> H(U1(k, e), f(d))
26.42/8.62	   A^2 -> H(U1(k, c), U1(c, b))
26.42/8.62	   A^2 -> H(U1(k, c), U1(d, b))
26.42/8.62	   A^2 -> H(U1(k, c), U1(b, c))
26.42/8.62	   A^2 -> H(U1(k, c), U1(b, d))
26.42/8.62	   A^2 -> H(U1(k, c), U1(c, c))
26.42/8.62	   A^2 -> H(U1(k, c), f(e))
26.42/8.62	   A^2 -> H(U1(k, c), f(k))
26.42/8.62	   A^2 -> H(U1(k, c), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, e), U1(c, b))
26.42/8.62	   A^2 -> H(U1(c, e), U1(d, b))
26.42/8.62	   A^2 -> H(U1(c, e), U1(b, c))
26.42/8.62	   A^2 -> H(U1(c, e), U1(b, d))
26.42/8.62	   A^2 -> H(U1(c, e), U1(c, c))
26.42/8.62	   A^2 -> H(U1(c, e), f(e))
26.42/8.62	   A^2 -> H(U1(c, e), f(k))
26.42/8.62	   A^2 -> H(U1(c, e), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, k), U1(c, b))
26.42/8.62	   A^2 -> H(U1(c, k), U1(d, b))
26.42/8.62	   A^2 -> H(U1(c, k), U1(b, c))
26.42/8.62	   A^2 -> H(U1(c, k), U1(b, d))
26.42/8.62	   A^2 -> H(U1(c, k), U1(c, c))
26.42/8.62	   A^2 -> H(U1(c, k), f(e))
26.42/8.62	   A^2 -> H(U1(c, k), f(k))
26.42/8.62	   A^2 -> H(U1(c, k), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(e, b))
26.42/8.62	   A^2 -> H(U1(c, c), U1(k, b))
26.42/8.62	   A^2 -> H(U1(c, c), U1(c, d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(d, c))
26.42/8.62	   A^2 -> H(U1(c, c), U1(b, e))
26.42/8.62	   A^2 -> H(U1(c, c), U1(b, k))
26.42/8.62	   A^2 -> H(U1(c, c), U1(e, e))
26.42/8.62	   A^2 -> H(U1(c, c), U1(k, k))
26.42/8.62	   A^2 -> H(U1(c, c), U1(k, d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(d, k))
26.42/8.62	   A^2 -> H(e, U1(b, b))
26.42/8.62	   A^2 -> H(e, f(c))
26.42/8.62	   A^2 -> H(e, f(d))
26.42/8.62	   A^2 -> H(U1(e, e), U1(c, b))
26.42/8.62	   A^2 -> H(U1(e, e), U1(d, b))
26.42/8.62	   A^2 -> H(U1(e, e), U1(b, c))
26.42/8.62	   A^2 -> H(U1(e, e), U1(b, d))
26.42/8.62	   A^2 -> H(U1(e, e), U1(c, c))
26.42/8.62	   A^2 -> H(U1(e, e), f(e))
26.42/8.62	   A^2 -> H(U1(e, e), f(k))
26.42/8.62	   A^2 -> H(U1(e, e), U1(d, d))
26.42/8.62	   A^2 -> H(f(e), U1(e, b))
26.42/8.62	   A^2 -> H(f(e), U1(k, b))
26.42/8.62	   A^2 -> H(f(e), U1(c, d))
26.42/8.62	   A^2 -> H(f(e), U1(d, c))
26.42/8.62	   A^2 -> H(f(e), U1(b, e))
26.42/8.62	   A^2 -> H(f(e), U1(b, k))
26.42/8.62	   A^2 -> H(f(e), U1(e, c))
26.42/8.62	   A^2 -> H(f(e), U1(k, c))
26.42/8.62	   A^2 -> H(f(e), U1(c, e))
26.42/8.62	   A^2 -> H(f(e), U1(c, k))
26.42/8.62	   A^2 -> H(f(e), U1(k, k))
26.42/8.62	   A^2 -> H(f(e), U1(k, d))
26.42/8.62	   A^2 -> H(f(e), U1(d, k))
26.42/8.62	   A^2 -> H(U1(k, k), U1(c, b))
26.42/8.62	   A^2 -> H(U1(k, k), U1(d, b))
26.42/8.62	   A^2 -> H(U1(k, k), U1(b, c))
26.42/8.62	   A^2 -> H(U1(k, k), U1(b, d))
26.42/8.62	   A^2 -> H(U1(k, k), U1(c, c))
26.42/8.62	   A^2 -> H(U1(k, k), f(e))
26.42/8.62	   A^2 -> H(U1(k, k), f(k))
26.42/8.62	   A^2 -> H(U1(k, k), U1(d, d))
26.42/8.62	   A^2 -> H(f(k), U1(e, b))
26.42/8.62	   A^2 -> H(f(k), U1(k, b))
26.42/8.62	   A^2 -> H(f(k), U1(c, d))
26.42/8.62	   A^2 -> H(f(k), U1(d, c))
26.42/8.62	   A^2 -> H(f(k), U1(b, e))
26.42/8.62	   A^2 -> H(f(k), U1(b, k))
26.42/8.62	   A^2 -> H(f(k), U1(e, c))
26.42/8.62	   A^2 -> H(f(k), U1(k, c))
26.42/8.62	   A^2 -> H(f(k), U1(c, e))
26.42/8.62	   A^2 -> H(f(k), U1(c, k))
26.42/8.62	   A^2 -> H(f(k), U1(e, e))
26.42/8.62	   A^2 -> H(f(k), U1(k, d))
26.42/8.62	   A^2 -> H(f(k), U1(d, k))
26.42/8.62	   A^2 -> H(f(c), b)
26.42/8.62	   A^2 -> H(f(c), U1(e, d))
26.42/8.62	   A^2 -> H(f(c), U1(d, e))
26.42/8.62	
26.42/8.62	The TRS R consists of the following rules:
26.42/8.62	
26.42/8.62	   f(x) -> U1(x, x)
26.42/8.62	   U1(e, x) -> x
26.42/8.62	   a -> c
26.42/8.62	   a -> d
26.42/8.62	   b -> c
26.42/8.62	   b -> d
26.42/8.62	   d -> k
26.42/8.62	   c -> e
26.42/8.62	   c -> k
26.42/8.62	
26.42/8.62	Q is empty.
26.42/8.62	We have to consider all minimal (P,Q,R)-chains.
26.42/8.62	----------------------------------------
26.42/8.62	
26.42/8.62	(453) TransformationProof (EQUIVALENT)
26.42/8.62	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
26.42/8.62	
26.42/8.62	   (A^2 -> H(U1(c, c), U1(k, d)),A^2 -> H(U1(c, c), U1(k, d)))
26.42/8.62	   (A^2 -> H(f(e), U1(k, d)),A^2 -> H(f(e), U1(k, d)))
26.42/8.62	   (A^2 -> H(f(k), U1(k, d)),A^2 -> H(f(k), U1(k, d)))
26.42/8.62	   (A^2 -> H(f(c), U1(k, k)),A^2 -> H(f(c), U1(k, k)))
26.42/8.62	
26.42/8.62	
26.42/8.62	----------------------------------------
26.42/8.62	
26.42/8.62	(454)
26.42/8.62	Obligation:
26.42/8.62	Q DP problem:
26.42/8.62	The TRS P consists of the following rules:
26.42/8.62	
26.42/8.62	   H(x, x) -> G(x, x, f(k))
26.42/8.62	   G(d, x, x) -> A^2
26.42/8.62	   A^2 -> H(f(c), f(c))
26.42/8.62	   A^2 -> H(f(d), f(d))
26.42/8.62	   A^2 -> H(U1(c, c), U1(c, c))
26.42/8.62	   A^2 -> H(f(e), f(e))
26.42/8.62	   A^2 -> H(f(k), f(k))
26.42/8.62	   A^2 -> H(f(c), U1(d, k))
26.42/8.62	   A^2 -> H(f(c), U1(k, k))
26.42/8.62	   A^2 -> H(U1(k, k), f(b))
26.42/8.62	   A^2 -> H(U1(k, d), U1(b, b))
26.42/8.62	   A^2 -> H(U1(k, d), f(c))
26.42/8.62	   A^2 -> H(U1(k, d), f(d))
26.42/8.62	   A^2 -> H(U1(d, k), U1(b, b))
26.42/8.62	   A^2 -> H(U1(d, k), f(c))
26.42/8.62	   A^2 -> H(U1(d, k), f(d))
26.42/8.62	   A^2 -> H(U1(d, d), U1(c, b))
26.42/8.62	   A^2 -> H(U1(d, d), U1(d, b))
26.42/8.62	   A^2 -> H(U1(d, d), U1(b, c))
26.42/8.62	   A^2 -> H(U1(d, d), U1(b, d))
26.42/8.62	   A^2 -> H(U1(d, d), U1(c, c))
26.42/8.62	   A^2 -> H(U1(d, d), f(e))
26.42/8.62	   A^2 -> H(U1(d, d), f(k))
26.42/8.62	   A^2 -> H(U1(d, d), U1(d, d))
26.42/8.62	   A^2 -> H(f(d), U1(e, b))
26.42/8.62	   A^2 -> H(f(d), U1(k, b))
26.42/8.62	   A^2 -> H(f(d), U1(c, d))
26.42/8.62	   A^2 -> H(f(d), U1(d, c))
26.42/8.62	   A^2 -> H(f(d), U1(b, e))
26.42/8.62	   A^2 -> H(f(d), U1(b, k))
26.42/8.62	   A^2 -> H(f(d), U1(e, c))
26.42/8.62	   A^2 -> H(f(d), U1(k, c))
26.42/8.62	   A^2 -> H(f(d), U1(c, e))
26.42/8.62	   A^2 -> H(f(d), U1(c, k))
26.42/8.62	   A^2 -> H(f(d), U1(e, e))
26.42/8.62	   A^2 -> H(f(d), U1(k, k))
26.42/8.62	   A^2 -> H(f(a), b)
26.42/8.62	   A^2 -> H(f(a), U1(e, d))
26.42/8.62	   A^2 -> H(f(a), U1(d, e))
26.42/8.62	   A^2 -> H(f(c), U1(e, c))
26.42/8.62	   A^2 -> H(f(c), U1(k, c))
26.42/8.62	   A^2 -> H(f(c), U1(c, e))
26.42/8.62	   A^2 -> H(f(c), U1(c, k))
26.42/8.62	   A^2 -> H(f(a), c)
26.42/8.62	   A^2 -> H(f(a), U1(e, k))
26.42/8.62	   A^2 -> H(f(a), U1(k, e))
26.42/8.62	   A^2 -> H(f(c), U1(e, e))
26.42/8.62	   A^2 -> H(f(a), e)
26.42/8.62	   A^2 -> H(f(d), U1(k, d))
26.42/8.62	   A^2 -> H(f(d), U1(d, k))
26.42/8.62	   A^2 -> H(f(a), U1(k, k))
26.42/8.62	   A^2 -> H(d, f(b))
26.42/8.62	   A^2 -> H(a, U1(b, b))
26.42/8.62	   A^2 -> H(a, f(c))
26.42/8.62	   A^2 -> H(a, f(d))
26.42/8.62	   A^2 -> H(U1(e, d), U1(b, b))
26.42/8.62	   A^2 -> H(U1(e, d), f(c))
26.42/8.62	   A^2 -> H(U1(e, d), f(d))
26.42/8.62	   A^2 -> H(U1(e, a), U1(c, b))
26.42/8.62	   A^2 -> H(U1(e, a), U1(d, b))
26.42/8.62	   A^2 -> H(U1(e, a), U1(b, c))
26.42/8.62	   A^2 -> H(U1(e, a), U1(b, d))
26.42/8.62	   A^2 -> H(U1(e, a), U1(c, c))
26.42/8.62	   A^2 -> H(U1(e, a), f(e))
26.42/8.62	   A^2 -> H(U1(e, a), f(k))
26.42/8.62	   A^2 -> H(U1(e, a), U1(d, d))
26.42/8.62	   A^2 -> H(U1(k, a), U1(c, b))
26.42/8.62	   A^2 -> H(U1(k, a), U1(d, b))
26.42/8.62	   A^2 -> H(U1(k, a), U1(b, c))
26.42/8.62	   A^2 -> H(U1(k, a), U1(b, d))
26.42/8.62	   A^2 -> H(U1(k, a), U1(c, c))
26.42/8.62	   A^2 -> H(U1(k, a), f(e))
26.42/8.62	   A^2 -> H(U1(k, a), f(k))
26.42/8.62	   A^2 -> H(U1(k, a), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, d), U1(c, b))
26.42/8.62	   A^2 -> H(U1(c, d), U1(d, b))
26.42/8.62	   A^2 -> H(U1(c, d), U1(b, c))
26.42/8.62	   A^2 -> H(U1(c, d), U1(b, d))
26.42/8.62	   A^2 -> H(U1(c, d), U1(c, c))
26.42/8.62	   A^2 -> H(U1(c, d), f(e))
26.42/8.62	   A^2 -> H(U1(c, d), f(k))
26.42/8.62	   A^2 -> H(U1(c, d), U1(d, d))
26.42/8.62	   A^2 -> H(U1(c, a), U1(e, b))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, b))
26.42/8.62	   A^2 -> H(U1(c, a), U1(c, d))
26.42/8.62	   A^2 -> H(U1(c, a), U1(d, c))
26.42/8.62	   A^2 -> H(U1(c, a), U1(b, e))
26.42/8.62	   A^2 -> H(U1(c, a), U1(b, k))
26.42/8.62	   A^2 -> H(U1(c, a), U1(e, c))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, c))
26.42/8.62	   A^2 -> H(U1(c, a), U1(c, e))
26.42/8.62	   A^2 -> H(U1(c, a), U1(c, k))
26.42/8.62	   A^2 -> H(U1(c, a), U1(e, e))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, k))
26.42/8.62	   A^2 -> H(U1(c, a), U1(k, d))
26.42/8.62	   A^2 -> H(U1(c, a), U1(d, k))
26.42/8.62	   A^2 -> H(U1(d, e), U1(b, b))
26.42/8.62	   A^2 -> H(U1(d, e), f(c))
26.42/8.62	   A^2 -> H(U1(d, e), f(d))
26.42/8.62	   A^2 -> H(U1(d, c), U1(c, b))
26.42/8.62	   A^2 -> H(U1(d, c), U1(d, b))
26.42/8.62	   A^2 -> H(U1(d, c), U1(b, c))
26.42/8.62	   A^2 -> H(U1(d, c), U1(b, d))
26.42/8.62	   A^2 -> H(U1(d, c), U1(c, c))
26.42/8.62	   A^2 -> H(U1(d, c), f(e))
26.42/8.62	   A^2 -> H(U1(d, c), f(k))
26.42/8.62	   A^2 -> H(U1(d, c), U1(d, d))
26.42/8.62	   A^2 -> H(U1(d, a), U1(e, b))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, b))
26.42/8.62	   A^2 -> H(U1(d, a), U1(c, d))
26.42/8.62	   A^2 -> H(U1(d, a), U1(d, c))
26.42/8.62	   A^2 -> H(U1(d, a), U1(b, e))
26.42/8.62	   A^2 -> H(U1(d, a), U1(b, k))
26.42/8.62	   A^2 -> H(U1(d, a), U1(e, c))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, c))
26.42/8.62	   A^2 -> H(U1(d, a), U1(c, e))
26.42/8.62	   A^2 -> H(U1(d, a), U1(c, k))
26.42/8.62	   A^2 -> H(U1(d, a), U1(e, e))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, k))
26.42/8.62	   A^2 -> H(U1(d, a), U1(k, d))
26.42/8.62	   A^2 -> H(U1(d, a), U1(d, k))
26.42/8.62	   A^2 -> H(U1(a, e), U1(c, b))
26.42/8.62	   A^2 -> H(U1(a, e), U1(d, b))
26.42/8.62	   A^2 -> H(U1(a, e), U1(b, c))
26.42/8.62	   A^2 -> H(U1(a, e), U1(b, d))
26.42/8.62	   A^2 -> H(U1(a, e), U1(c, c))
26.42/8.62	   A^2 -> H(U1(a, e), f(e))
26.42/8.62	   A^2 -> H(U1(a, e), f(k))
26.42/8.62	   A^2 -> H(U1(a, e), U1(d, d))
26.42/8.62	   A^2 -> H(U1(a, k), U1(c, b))
26.42/8.62	   A^2 -> H(U1(a, k), U1(d, b))
26.42/8.62	   A^2 -> H(U1(a, k), U1(b, c))
26.42/8.62	   A^2 -> H(U1(a, k), U1(b, d))
26.42/8.62	   A^2 -> H(U1(a, k), U1(c, c))
26.42/8.62	   A^2 -> H(U1(a, k), f(e))
26.42/8.62	   A^2 -> H(U1(a, k), f(k))
26.42/8.62	   A^2 -> H(U1(a, k), U1(d, d))
26.42/8.62	   A^2 -> H(U1(a, c), U1(e, b))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, b))
26.42/8.62	   A^2 -> H(U1(a, c), U1(c, d))
26.42/8.62	   A^2 -> H(U1(a, c), U1(d, c))
26.42/8.62	   A^2 -> H(U1(a, c), U1(b, e))
26.42/8.62	   A^2 -> H(U1(a, c), U1(b, k))
26.42/8.62	   A^2 -> H(U1(a, c), U1(e, c))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, c))
26.42/8.62	   A^2 -> H(U1(a, c), U1(c, e))
26.42/8.62	   A^2 -> H(U1(a, c), U1(c, k))
26.42/8.62	   A^2 -> H(U1(a, c), U1(e, e))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, k))
26.42/8.62	   A^2 -> H(U1(a, c), U1(k, d))
26.42/8.64	   A^2 -> H(U1(a, c), U1(d, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(e, b))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, b))
26.42/8.64	   A^2 -> H(U1(a, d), U1(c, d))
26.42/8.64	   A^2 -> H(U1(a, d), U1(d, c))
26.42/8.64	   A^2 -> H(U1(a, d), U1(b, e))
26.42/8.64	   A^2 -> H(U1(a, d), U1(b, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(e, c))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, c))
26.42/8.64	   A^2 -> H(U1(a, d), U1(c, e))
26.42/8.64	   A^2 -> H(U1(a, d), U1(c, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(e, e))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, d))
26.42/8.64	   A^2 -> H(U1(a, d), U1(d, k))
26.42/8.64	   A^2 -> H(U1(a, a), b)
26.42/8.64	   A^2 -> H(U1(a, a), U1(e, d))
26.42/8.64	   A^2 -> H(U1(a, a), U1(d, e))
26.42/8.64	   A^2 -> H(U1(a, a), c)
26.42/8.64	   A^2 -> H(U1(a, a), U1(e, k))
26.42/8.64	   A^2 -> H(U1(a, a), U1(k, e))
26.42/8.64	   A^2 -> H(U1(a, a), e)
26.42/8.64	   A^2 -> H(U1(a, a), U1(k, k))
26.42/8.64	   A^2 -> H(k, f(b))
26.42/8.64	   A^2 -> H(c, U1(b, b))
26.42/8.64	   A^2 -> H(c, f(c))
26.42/8.64	   A^2 -> H(c, f(d))
26.42/8.64	   A^2 -> H(U1(e, k), U1(b, b))
26.42/8.64	   A^2 -> H(U1(e, k), f(c))
26.42/8.64	   A^2 -> H(U1(e, k), f(d))
26.42/8.64	   A^2 -> H(U1(e, c), U1(c, b))
26.42/8.64	   A^2 -> H(U1(e, c), U1(d, b))
26.42/8.64	   A^2 -> H(U1(e, c), U1(b, c))
26.42/8.64	   A^2 -> H(U1(e, c), U1(b, d))
26.42/8.64	   A^2 -> H(U1(e, c), U1(c, c))
26.42/8.64	   A^2 -> H(U1(e, c), f(e))
26.42/8.64	   A^2 -> H(U1(e, c), f(k))
26.42/8.64	   A^2 -> H(U1(e, c), U1(d, d))
26.42/8.64	   A^2 -> H(U1(k, e), U1(b, b))
26.42/8.64	   A^2 -> H(U1(k, e), f(c))
26.42/8.64	   A^2 -> H(U1(k, e), f(d))
26.42/8.64	   A^2 -> H(U1(k, c), U1(c, b))
26.42/8.64	   A^2 -> H(U1(k, c), U1(d, b))
26.42/8.64	   A^2 -> H(U1(k, c), U1(b, c))
26.42/8.64	   A^2 -> H(U1(k, c), U1(b, d))
26.42/8.64	   A^2 -> H(U1(k, c), U1(c, c))
26.42/8.64	   A^2 -> H(U1(k, c), f(e))
26.42/8.64	   A^2 -> H(U1(k, c), f(k))
26.42/8.64	   A^2 -> H(U1(k, c), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, e), U1(c, b))
26.42/8.64	   A^2 -> H(U1(c, e), U1(d, b))
26.42/8.64	   A^2 -> H(U1(c, e), U1(b, c))
26.42/8.64	   A^2 -> H(U1(c, e), U1(b, d))
26.42/8.64	   A^2 -> H(U1(c, e), U1(c, c))
26.42/8.64	   A^2 -> H(U1(c, e), f(e))
26.42/8.64	   A^2 -> H(U1(c, e), f(k))
26.42/8.64	   A^2 -> H(U1(c, e), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, k), U1(c, b))
26.42/8.64	   A^2 -> H(U1(c, k), U1(d, b))
26.42/8.64	   A^2 -> H(U1(c, k), U1(b, c))
26.42/8.64	   A^2 -> H(U1(c, k), U1(b, d))
26.42/8.64	   A^2 -> H(U1(c, k), U1(c, c))
26.42/8.64	   A^2 -> H(U1(c, k), f(e))
26.42/8.64	   A^2 -> H(U1(c, k), f(k))
26.42/8.64	   A^2 -> H(U1(c, k), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(e, b))
26.42/8.64	   A^2 -> H(U1(c, c), U1(k, b))
26.42/8.64	   A^2 -> H(U1(c, c), U1(c, d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(d, c))
26.42/8.64	   A^2 -> H(U1(c, c), U1(b, e))
26.42/8.64	   A^2 -> H(U1(c, c), U1(b, k))
26.42/8.64	   A^2 -> H(U1(c, c), U1(e, e))
26.42/8.64	   A^2 -> H(U1(c, c), U1(k, k))
26.42/8.64	   A^2 -> H(U1(c, c), U1(k, d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(d, k))
26.42/8.64	   A^2 -> H(e, U1(b, b))
26.42/8.64	   A^2 -> H(e, f(c))
26.42/8.64	   A^2 -> H(e, f(d))
26.42/8.64	   A^2 -> H(U1(e, e), U1(c, b))
26.42/8.64	   A^2 -> H(U1(e, e), U1(d, b))
26.42/8.64	   A^2 -> H(U1(e, e), U1(b, c))
26.42/8.64	   A^2 -> H(U1(e, e), U1(b, d))
26.42/8.64	   A^2 -> H(U1(e, e), U1(c, c))
26.42/8.64	   A^2 -> H(U1(e, e), f(e))
26.42/8.64	   A^2 -> H(U1(e, e), f(k))
26.42/8.64	   A^2 -> H(U1(e, e), U1(d, d))
26.42/8.64	   A^2 -> H(f(e), U1(e, b))
26.42/8.64	   A^2 -> H(f(e), U1(k, b))
26.42/8.64	   A^2 -> H(f(e), U1(c, d))
26.42/8.64	   A^2 -> H(f(e), U1(d, c))
26.42/8.64	   A^2 -> H(f(e), U1(b, e))
26.42/8.64	   A^2 -> H(f(e), U1(b, k))
26.42/8.64	   A^2 -> H(f(e), U1(e, c))
26.42/8.64	   A^2 -> H(f(e), U1(k, c))
26.42/8.64	   A^2 -> H(f(e), U1(c, e))
26.42/8.64	   A^2 -> H(f(e), U1(c, k))
26.42/8.64	   A^2 -> H(f(e), U1(k, k))
26.42/8.64	   A^2 -> H(f(e), U1(k, d))
26.42/8.64	   A^2 -> H(f(e), U1(d, k))
26.42/8.64	   A^2 -> H(U1(k, k), U1(c, b))
26.42/8.64	   A^2 -> H(U1(k, k), U1(d, b))
26.42/8.64	   A^2 -> H(U1(k, k), U1(b, c))
26.42/8.64	   A^2 -> H(U1(k, k), U1(b, d))
26.42/8.64	   A^2 -> H(U1(k, k), U1(c, c))
26.42/8.64	   A^2 -> H(U1(k, k), f(e))
26.42/8.64	   A^2 -> H(U1(k, k), f(k))
26.42/8.64	   A^2 -> H(U1(k, k), U1(d, d))
26.42/8.64	   A^2 -> H(f(k), U1(e, b))
26.42/8.64	   A^2 -> H(f(k), U1(k, b))
26.42/8.64	   A^2 -> H(f(k), U1(c, d))
26.42/8.64	   A^2 -> H(f(k), U1(d, c))
26.42/8.64	   A^2 -> H(f(k), U1(b, e))
26.42/8.64	   A^2 -> H(f(k), U1(b, k))
26.42/8.64	   A^2 -> H(f(k), U1(e, c))
26.42/8.64	   A^2 -> H(f(k), U1(k, c))
26.42/8.64	   A^2 -> H(f(k), U1(c, e))
26.42/8.64	   A^2 -> H(f(k), U1(c, k))
26.42/8.64	   A^2 -> H(f(k), U1(e, e))
26.42/8.64	   A^2 -> H(f(k), U1(k, d))
26.42/8.64	   A^2 -> H(f(k), U1(d, k))
26.42/8.64	   A^2 -> H(f(c), b)
26.42/8.64	   A^2 -> H(f(c), U1(e, d))
26.42/8.64	   A^2 -> H(f(c), U1(d, e))
26.42/8.64	
26.42/8.64	The TRS R consists of the following rules:
26.42/8.64	
26.42/8.64	   f(x) -> U1(x, x)
26.42/8.64	   U1(e, x) -> x
26.42/8.64	   a -> c
26.42/8.64	   a -> d
26.42/8.64	   b -> c
26.42/8.64	   b -> d
26.42/8.64	   d -> k
26.42/8.64	   c -> e
26.42/8.64	   c -> k
26.42/8.64	
26.42/8.64	Q is empty.
26.42/8.64	We have to consider all minimal (P,Q,R)-chains.
26.42/8.64	----------------------------------------
26.42/8.64	
26.42/8.64	(455) TransformationProof (EQUIVALENT)
26.42/8.64	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
26.42/8.64	
26.42/8.64	   (A^2 -> H(U1(c, c), U1(d, k)),A^2 -> H(U1(c, c), U1(d, k)))
26.42/8.64	   (A^2 -> H(f(e), U1(d, k)),A^2 -> H(f(e), U1(d, k)))
26.42/8.64	   (A^2 -> H(f(k), U1(d, k)),A^2 -> H(f(k), U1(d, k)))
26.42/8.64	   (A^2 -> H(f(c), U1(k, k)),A^2 -> H(f(c), U1(k, k)))
26.42/8.64	
26.42/8.64	
26.42/8.64	----------------------------------------
26.42/8.64	
26.42/8.64	(456)
26.42/8.64	Obligation:
26.42/8.64	Q DP problem:
26.42/8.64	The TRS P consists of the following rules:
26.42/8.64	
26.42/8.64	   H(x, x) -> G(x, x, f(k))
26.42/8.64	   G(d, x, x) -> A^2
26.42/8.64	   A^2 -> H(f(c), f(c))
26.42/8.64	   A^2 -> H(f(d), f(d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(c, c))
26.42/8.64	   A^2 -> H(f(e), f(e))
26.42/8.64	   A^2 -> H(f(k), f(k))
26.42/8.64	   A^2 -> H(f(c), U1(k, k))
26.42/8.64	   A^2 -> H(U1(k, k), f(b))
26.42/8.64	   A^2 -> H(U1(k, d), U1(b, b))
26.42/8.64	   A^2 -> H(U1(k, d), f(c))
26.42/8.64	   A^2 -> H(U1(k, d), f(d))
26.42/8.64	   A^2 -> H(U1(d, k), U1(b, b))
26.42/8.64	   A^2 -> H(U1(d, k), f(c))
26.42/8.64	   A^2 -> H(U1(d, k), f(d))
26.42/8.64	   A^2 -> H(U1(d, d), U1(c, b))
26.42/8.64	   A^2 -> H(U1(d, d), U1(d, b))
26.42/8.64	   A^2 -> H(U1(d, d), U1(b, c))
26.42/8.64	   A^2 -> H(U1(d, d), U1(b, d))
26.42/8.64	   A^2 -> H(U1(d, d), U1(c, c))
26.42/8.64	   A^2 -> H(U1(d, d), f(e))
26.42/8.64	   A^2 -> H(U1(d, d), f(k))
26.42/8.64	   A^2 -> H(U1(d, d), U1(d, d))
26.42/8.64	   A^2 -> H(f(d), U1(e, b))
26.42/8.64	   A^2 -> H(f(d), U1(k, b))
26.42/8.64	   A^2 -> H(f(d), U1(c, d))
26.42/8.64	   A^2 -> H(f(d), U1(d, c))
26.42/8.64	   A^2 -> H(f(d), U1(b, e))
26.42/8.64	   A^2 -> H(f(d), U1(b, k))
26.42/8.64	   A^2 -> H(f(d), U1(e, c))
26.42/8.64	   A^2 -> H(f(d), U1(k, c))
26.42/8.64	   A^2 -> H(f(d), U1(c, e))
26.42/8.64	   A^2 -> H(f(d), U1(c, k))
26.42/8.64	   A^2 -> H(f(d), U1(e, e))
26.42/8.64	   A^2 -> H(f(d), U1(k, k))
26.42/8.64	   A^2 -> H(f(a), b)
26.42/8.64	   A^2 -> H(f(a), U1(e, d))
26.42/8.64	   A^2 -> H(f(a), U1(d, e))
26.42/8.64	   A^2 -> H(f(c), U1(e, c))
26.42/8.64	   A^2 -> H(f(c), U1(k, c))
26.42/8.64	   A^2 -> H(f(c), U1(c, e))
26.42/8.64	   A^2 -> H(f(c), U1(c, k))
26.42/8.64	   A^2 -> H(f(a), c)
26.42/8.64	   A^2 -> H(f(a), U1(e, k))
26.42/8.64	   A^2 -> H(f(a), U1(k, e))
26.42/8.64	   A^2 -> H(f(c), U1(e, e))
26.42/8.64	   A^2 -> H(f(a), e)
26.42/8.64	   A^2 -> H(f(d), U1(k, d))
26.42/8.64	   A^2 -> H(f(d), U1(d, k))
26.42/8.64	   A^2 -> H(f(a), U1(k, k))
26.42/8.64	   A^2 -> H(d, f(b))
26.42/8.64	   A^2 -> H(a, U1(b, b))
26.42/8.64	   A^2 -> H(a, f(c))
26.42/8.64	   A^2 -> H(a, f(d))
26.42/8.64	   A^2 -> H(U1(e, d), U1(b, b))
26.42/8.64	   A^2 -> H(U1(e, d), f(c))
26.42/8.64	   A^2 -> H(U1(e, d), f(d))
26.42/8.64	   A^2 -> H(U1(e, a), U1(c, b))
26.42/8.64	   A^2 -> H(U1(e, a), U1(d, b))
26.42/8.64	   A^2 -> H(U1(e, a), U1(b, c))
26.42/8.64	   A^2 -> H(U1(e, a), U1(b, d))
26.42/8.64	   A^2 -> H(U1(e, a), U1(c, c))
26.42/8.64	   A^2 -> H(U1(e, a), f(e))
26.42/8.64	   A^2 -> H(U1(e, a), f(k))
26.42/8.64	   A^2 -> H(U1(e, a), U1(d, d))
26.42/8.64	   A^2 -> H(U1(k, a), U1(c, b))
26.42/8.64	   A^2 -> H(U1(k, a), U1(d, b))
26.42/8.64	   A^2 -> H(U1(k, a), U1(b, c))
26.42/8.64	   A^2 -> H(U1(k, a), U1(b, d))
26.42/8.64	   A^2 -> H(U1(k, a), U1(c, c))
26.42/8.64	   A^2 -> H(U1(k, a), f(e))
26.42/8.64	   A^2 -> H(U1(k, a), f(k))
26.42/8.64	   A^2 -> H(U1(k, a), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, d), U1(c, b))
26.42/8.64	   A^2 -> H(U1(c, d), U1(d, b))
26.42/8.64	   A^2 -> H(U1(c, d), U1(b, c))
26.42/8.64	   A^2 -> H(U1(c, d), U1(b, d))
26.42/8.64	   A^2 -> H(U1(c, d), U1(c, c))
26.42/8.64	   A^2 -> H(U1(c, d), f(e))
26.42/8.64	   A^2 -> H(U1(c, d), f(k))
26.42/8.64	   A^2 -> H(U1(c, d), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, a), U1(e, b))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, b))
26.42/8.64	   A^2 -> H(U1(c, a), U1(c, d))
26.42/8.64	   A^2 -> H(U1(c, a), U1(d, c))
26.42/8.64	   A^2 -> H(U1(c, a), U1(b, e))
26.42/8.64	   A^2 -> H(U1(c, a), U1(b, k))
26.42/8.64	   A^2 -> H(U1(c, a), U1(e, c))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, c))
26.42/8.64	   A^2 -> H(U1(c, a), U1(c, e))
26.42/8.64	   A^2 -> H(U1(c, a), U1(c, k))
26.42/8.64	   A^2 -> H(U1(c, a), U1(e, e))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, k))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, d))
26.42/8.64	   A^2 -> H(U1(c, a), U1(d, k))
26.42/8.64	   A^2 -> H(U1(d, e), U1(b, b))
26.42/8.64	   A^2 -> H(U1(d, e), f(c))
26.42/8.64	   A^2 -> H(U1(d, e), f(d))
26.42/8.64	   A^2 -> H(U1(d, c), U1(c, b))
26.42/8.64	   A^2 -> H(U1(d, c), U1(d, b))
26.42/8.64	   A^2 -> H(U1(d, c), U1(b, c))
26.42/8.64	   A^2 -> H(U1(d, c), U1(b, d))
26.42/8.64	   A^2 -> H(U1(d, c), U1(c, c))
26.42/8.64	   A^2 -> H(U1(d, c), f(e))
26.42/8.64	   A^2 -> H(U1(d, c), f(k))
26.42/8.64	   A^2 -> H(U1(d, c), U1(d, d))
26.42/8.64	   A^2 -> H(U1(d, a), U1(e, b))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, b))
26.42/8.64	   A^2 -> H(U1(d, a), U1(c, d))
26.42/8.64	   A^2 -> H(U1(d, a), U1(d, c))
26.42/8.64	   A^2 -> H(U1(d, a), U1(b, e))
26.42/8.64	   A^2 -> H(U1(d, a), U1(b, k))
26.42/8.64	   A^2 -> H(U1(d, a), U1(e, c))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, c))
26.42/8.64	   A^2 -> H(U1(d, a), U1(c, e))
26.42/8.64	   A^2 -> H(U1(d, a), U1(c, k))
26.42/8.64	   A^2 -> H(U1(d, a), U1(e, e))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, k))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, d))
26.42/8.64	   A^2 -> H(U1(d, a), U1(d, k))
26.42/8.64	   A^2 -> H(U1(a, e), U1(c, b))
26.42/8.64	   A^2 -> H(U1(a, e), U1(d, b))
26.42/8.64	   A^2 -> H(U1(a, e), U1(b, c))
26.42/8.64	   A^2 -> H(U1(a, e), U1(b, d))
26.42/8.64	   A^2 -> H(U1(a, e), U1(c, c))
26.42/8.64	   A^2 -> H(U1(a, e), f(e))
26.42/8.64	   A^2 -> H(U1(a, e), f(k))
26.42/8.64	   A^2 -> H(U1(a, e), U1(d, d))
26.42/8.64	   A^2 -> H(U1(a, k), U1(c, b))
26.42/8.64	   A^2 -> H(U1(a, k), U1(d, b))
26.42/8.64	   A^2 -> H(U1(a, k), U1(b, c))
26.42/8.64	   A^2 -> H(U1(a, k), U1(b, d))
26.42/8.64	   A^2 -> H(U1(a, k), U1(c, c))
26.42/8.64	   A^2 -> H(U1(a, k), f(e))
26.42/8.64	   A^2 -> H(U1(a, k), f(k))
26.42/8.64	   A^2 -> H(U1(a, k), U1(d, d))
26.42/8.64	   A^2 -> H(U1(a, c), U1(e, b))
26.42/8.64	   A^2 -> H(U1(a, c), U1(k, b))
26.42/8.64	   A^2 -> H(U1(a, c), U1(c, d))
26.42/8.64	   A^2 -> H(U1(a, c), U1(d, c))
26.42/8.64	   A^2 -> H(U1(a, c), U1(b, e))
26.42/8.64	   A^2 -> H(U1(a, c), U1(b, k))
26.42/8.64	   A^2 -> H(U1(a, c), U1(e, c))
26.42/8.64	   A^2 -> H(U1(a, c), U1(k, c))
26.42/8.64	   A^2 -> H(U1(a, c), U1(c, e))
26.42/8.64	   A^2 -> H(U1(a, c), U1(c, k))
26.42/8.64	   A^2 -> H(U1(a, c), U1(e, e))
26.42/8.64	   A^2 -> H(U1(a, c), U1(k, k))
26.42/8.64	   A^2 -> H(U1(a, c), U1(k, d))
26.42/8.64	   A^2 -> H(U1(a, c), U1(d, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(e, b))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, b))
26.42/8.64	   A^2 -> H(U1(a, d), U1(c, d))
26.42/8.64	   A^2 -> H(U1(a, d), U1(d, c))
26.42/8.64	   A^2 -> H(U1(a, d), U1(b, e))
26.42/8.64	   A^2 -> H(U1(a, d), U1(b, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(e, c))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, c))
26.42/8.64	   A^2 -> H(U1(a, d), U1(c, e))
26.42/8.64	   A^2 -> H(U1(a, d), U1(c, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(e, e))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, d))
26.42/8.64	   A^2 -> H(U1(a, d), U1(d, k))
26.42/8.64	   A^2 -> H(U1(a, a), b)
26.42/8.64	   A^2 -> H(U1(a, a), U1(e, d))
26.42/8.64	   A^2 -> H(U1(a, a), U1(d, e))
26.42/8.64	   A^2 -> H(U1(a, a), c)
26.42/8.64	   A^2 -> H(U1(a, a), U1(e, k))
26.42/8.64	   A^2 -> H(U1(a, a), U1(k, e))
26.42/8.64	   A^2 -> H(U1(a, a), e)
26.42/8.64	   A^2 -> H(U1(a, a), U1(k, k))
26.42/8.64	   A^2 -> H(k, f(b))
26.42/8.64	   A^2 -> H(c, U1(b, b))
26.42/8.64	   A^2 -> H(c, f(c))
26.42/8.64	   A^2 -> H(c, f(d))
26.42/8.64	   A^2 -> H(U1(e, k), U1(b, b))
26.42/8.64	   A^2 -> H(U1(e, k), f(c))
26.42/8.64	   A^2 -> H(U1(e, k), f(d))
26.42/8.64	   A^2 -> H(U1(e, c), U1(c, b))
26.42/8.64	   A^2 -> H(U1(e, c), U1(d, b))
26.42/8.64	   A^2 -> H(U1(e, c), U1(b, c))
26.42/8.64	   A^2 -> H(U1(e, c), U1(b, d))
26.42/8.64	   A^2 -> H(U1(e, c), U1(c, c))
26.42/8.64	   A^2 -> H(U1(e, c), f(e))
26.42/8.64	   A^2 -> H(U1(e, c), f(k))
26.42/8.64	   A^2 -> H(U1(e, c), U1(d, d))
26.42/8.64	   A^2 -> H(U1(k, e), U1(b, b))
26.42/8.64	   A^2 -> H(U1(k, e), f(c))
26.42/8.64	   A^2 -> H(U1(k, e), f(d))
26.42/8.64	   A^2 -> H(U1(k, c), U1(c, b))
26.42/8.64	   A^2 -> H(U1(k, c), U1(d, b))
26.42/8.64	   A^2 -> H(U1(k, c), U1(b, c))
26.42/8.64	   A^2 -> H(U1(k, c), U1(b, d))
26.42/8.64	   A^2 -> H(U1(k, c), U1(c, c))
26.42/8.64	   A^2 -> H(U1(k, c), f(e))
26.42/8.64	   A^2 -> H(U1(k, c), f(k))
26.42/8.64	   A^2 -> H(U1(k, c), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, e), U1(c, b))
26.42/8.64	   A^2 -> H(U1(c, e), U1(d, b))
26.42/8.64	   A^2 -> H(U1(c, e), U1(b, c))
26.42/8.64	   A^2 -> H(U1(c, e), U1(b, d))
26.42/8.64	   A^2 -> H(U1(c, e), U1(c, c))
26.42/8.64	   A^2 -> H(U1(c, e), f(e))
26.42/8.64	   A^2 -> H(U1(c, e), f(k))
26.42/8.64	   A^2 -> H(U1(c, e), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, k), U1(c, b))
26.42/8.64	   A^2 -> H(U1(c, k), U1(d, b))
26.42/8.64	   A^2 -> H(U1(c, k), U1(b, c))
26.42/8.64	   A^2 -> H(U1(c, k), U1(b, d))
26.42/8.64	   A^2 -> H(U1(c, k), U1(c, c))
26.42/8.64	   A^2 -> H(U1(c, k), f(e))
26.42/8.64	   A^2 -> H(U1(c, k), f(k))
26.42/8.64	   A^2 -> H(U1(c, k), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(e, b))
26.42/8.64	   A^2 -> H(U1(c, c), U1(k, b))
26.42/8.64	   A^2 -> H(U1(c, c), U1(c, d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(d, c))
26.42/8.64	   A^2 -> H(U1(c, c), U1(b, e))
26.42/8.64	   A^2 -> H(U1(c, c), U1(b, k))
26.42/8.64	   A^2 -> H(U1(c, c), U1(e, e))
26.42/8.64	   A^2 -> H(U1(c, c), U1(k, k))
26.42/8.64	   A^2 -> H(U1(c, c), U1(k, d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(d, k))
26.42/8.64	   A^2 -> H(e, U1(b, b))
26.42/8.64	   A^2 -> H(e, f(c))
26.42/8.64	   A^2 -> H(e, f(d))
26.42/8.64	   A^2 -> H(U1(e, e), U1(c, b))
26.42/8.64	   A^2 -> H(U1(e, e), U1(d, b))
26.42/8.64	   A^2 -> H(U1(e, e), U1(b, c))
26.42/8.64	   A^2 -> H(U1(e, e), U1(b, d))
26.42/8.64	   A^2 -> H(U1(e, e), U1(c, c))
26.42/8.64	   A^2 -> H(U1(e, e), f(e))
26.42/8.64	   A^2 -> H(U1(e, e), f(k))
26.42/8.64	   A^2 -> H(U1(e, e), U1(d, d))
26.42/8.64	   A^2 -> H(f(e), U1(e, b))
26.42/8.64	   A^2 -> H(f(e), U1(k, b))
26.42/8.64	   A^2 -> H(f(e), U1(c, d))
26.42/8.64	   A^2 -> H(f(e), U1(d, c))
26.42/8.64	   A^2 -> H(f(e), U1(b, e))
26.42/8.64	   A^2 -> H(f(e), U1(b, k))
26.42/8.64	   A^2 -> H(f(e), U1(e, c))
26.42/8.64	   A^2 -> H(f(e), U1(k, c))
26.42/8.64	   A^2 -> H(f(e), U1(c, e))
26.42/8.64	   A^2 -> H(f(e), U1(c, k))
26.42/8.64	   A^2 -> H(f(e), U1(k, k))
26.42/8.64	   A^2 -> H(f(e), U1(k, d))
26.42/8.64	   A^2 -> H(f(e), U1(d, k))
26.42/8.64	   A^2 -> H(U1(k, k), U1(c, b))
26.42/8.64	   A^2 -> H(U1(k, k), U1(d, b))
26.42/8.64	   A^2 -> H(U1(k, k), U1(b, c))
26.42/8.64	   A^2 -> H(U1(k, k), U1(b, d))
26.42/8.64	   A^2 -> H(U1(k, k), U1(c, c))
26.42/8.64	   A^2 -> H(U1(k, k), f(e))
26.42/8.64	   A^2 -> H(U1(k, k), f(k))
26.42/8.64	   A^2 -> H(U1(k, k), U1(d, d))
26.42/8.64	   A^2 -> H(f(k), U1(e, b))
26.42/8.64	   A^2 -> H(f(k), U1(k, b))
26.42/8.64	   A^2 -> H(f(k), U1(c, d))
26.42/8.64	   A^2 -> H(f(k), U1(d, c))
26.42/8.64	   A^2 -> H(f(k), U1(b, e))
26.42/8.64	   A^2 -> H(f(k), U1(b, k))
26.42/8.64	   A^2 -> H(f(k), U1(e, c))
26.42/8.64	   A^2 -> H(f(k), U1(k, c))
26.42/8.64	   A^2 -> H(f(k), U1(c, e))
26.42/8.64	   A^2 -> H(f(k), U1(c, k))
26.42/8.64	   A^2 -> H(f(k), U1(e, e))
26.42/8.64	   A^2 -> H(f(k), U1(k, d))
26.42/8.64	   A^2 -> H(f(k), U1(d, k))
26.42/8.64	   A^2 -> H(f(c), b)
26.42/8.64	   A^2 -> H(f(c), U1(e, d))
26.42/8.64	   A^2 -> H(f(c), U1(d, e))
26.42/8.64	
26.42/8.64	The TRS R consists of the following rules:
26.42/8.64	
26.42/8.64	   f(x) -> U1(x, x)
26.42/8.64	   U1(e, x) -> x
26.42/8.64	   a -> c
26.42/8.64	   a -> d
26.42/8.64	   b -> c
26.42/8.64	   b -> d
26.42/8.64	   d -> k
26.42/8.64	   c -> e
26.42/8.64	   c -> k
26.42/8.64	
26.42/8.64	Q is empty.
26.42/8.64	We have to consider all minimal (P,Q,R)-chains.
26.42/8.64	----------------------------------------
26.42/8.64	
26.42/8.64	(457) TransformationProof (EQUIVALENT)
26.42/8.64	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
26.42/8.64	
26.42/8.64	   (A^2 -> H(U1(c, c), U1(k, k)),A^2 -> H(U1(c, c), U1(k, k)))
26.42/8.64	   (A^2 -> H(f(e), U1(k, k)),A^2 -> H(f(e), U1(k, k)))
26.42/8.64	   (A^2 -> H(f(k), U1(k, k)),A^2 -> H(f(k), U1(k, k)))
26.42/8.64	
26.42/8.64	
26.42/8.64	----------------------------------------
26.42/8.64	
26.42/8.64	(458)
26.42/8.64	Obligation:
26.42/8.64	Q DP problem:
26.42/8.64	The TRS P consists of the following rules:
26.42/8.64	
26.42/8.64	   H(x, x) -> G(x, x, f(k))
26.42/8.64	   G(d, x, x) -> A^2
26.42/8.64	   A^2 -> H(f(c), f(c))
26.42/8.64	   A^2 -> H(f(d), f(d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(c, c))
26.42/8.64	   A^2 -> H(f(e), f(e))
26.42/8.64	   A^2 -> H(f(k), f(k))
26.42/8.64	   A^2 -> H(U1(k, k), f(b))
26.42/8.64	   A^2 -> H(U1(k, d), U1(b, b))
26.42/8.64	   A^2 -> H(U1(k, d), f(c))
26.42/8.64	   A^2 -> H(U1(k, d), f(d))
26.42/8.64	   A^2 -> H(U1(d, k), U1(b, b))
26.42/8.64	   A^2 -> H(U1(d, k), f(c))
26.42/8.64	   A^2 -> H(U1(d, k), f(d))
26.42/8.64	   A^2 -> H(U1(d, d), U1(c, b))
26.42/8.64	   A^2 -> H(U1(d, d), U1(d, b))
26.42/8.64	   A^2 -> H(U1(d, d), U1(b, c))
26.42/8.64	   A^2 -> H(U1(d, d), U1(b, d))
26.42/8.64	   A^2 -> H(U1(d, d), U1(c, c))
26.42/8.64	   A^2 -> H(U1(d, d), f(e))
26.42/8.64	   A^2 -> H(U1(d, d), f(k))
26.42/8.64	   A^2 -> H(U1(d, d), U1(d, d))
26.42/8.64	   A^2 -> H(f(d), U1(e, b))
26.42/8.64	   A^2 -> H(f(d), U1(k, b))
26.42/8.64	   A^2 -> H(f(d), U1(c, d))
26.42/8.64	   A^2 -> H(f(d), U1(d, c))
26.42/8.64	   A^2 -> H(f(d), U1(b, e))
26.42/8.64	   A^2 -> H(f(d), U1(b, k))
26.42/8.64	   A^2 -> H(f(d), U1(e, c))
26.42/8.64	   A^2 -> H(f(d), U1(k, c))
26.42/8.64	   A^2 -> H(f(d), U1(c, e))
26.42/8.64	   A^2 -> H(f(d), U1(c, k))
26.42/8.64	   A^2 -> H(f(d), U1(e, e))
26.42/8.64	   A^2 -> H(f(d), U1(k, k))
26.42/8.64	   A^2 -> H(f(a), b)
26.42/8.64	   A^2 -> H(f(a), U1(e, d))
26.42/8.64	   A^2 -> H(f(a), U1(d, e))
26.42/8.64	   A^2 -> H(f(c), U1(e, c))
26.42/8.64	   A^2 -> H(f(c), U1(k, c))
26.42/8.64	   A^2 -> H(f(c), U1(c, e))
26.42/8.64	   A^2 -> H(f(c), U1(c, k))
26.42/8.64	   A^2 -> H(f(a), c)
26.42/8.64	   A^2 -> H(f(a), U1(e, k))
26.42/8.64	   A^2 -> H(f(a), U1(k, e))
26.42/8.64	   A^2 -> H(f(c), U1(e, e))
26.42/8.64	   A^2 -> H(f(a), e)
26.42/8.64	   A^2 -> H(f(d), U1(k, d))
26.42/8.64	   A^2 -> H(f(d), U1(d, k))
26.42/8.64	   A^2 -> H(f(a), U1(k, k))
26.42/8.64	   A^2 -> H(d, f(b))
26.42/8.64	   A^2 -> H(a, U1(b, b))
26.42/8.64	   A^2 -> H(a, f(c))
26.42/8.64	   A^2 -> H(a, f(d))
26.42/8.64	   A^2 -> H(U1(e, d), U1(b, b))
26.42/8.64	   A^2 -> H(U1(e, d), f(c))
26.42/8.64	   A^2 -> H(U1(e, d), f(d))
26.42/8.64	   A^2 -> H(U1(e, a), U1(c, b))
26.42/8.64	   A^2 -> H(U1(e, a), U1(d, b))
26.42/8.64	   A^2 -> H(U1(e, a), U1(b, c))
26.42/8.64	   A^2 -> H(U1(e, a), U1(b, d))
26.42/8.64	   A^2 -> H(U1(e, a), U1(c, c))
26.42/8.64	   A^2 -> H(U1(e, a), f(e))
26.42/8.64	   A^2 -> H(U1(e, a), f(k))
26.42/8.64	   A^2 -> H(U1(e, a), U1(d, d))
26.42/8.64	   A^2 -> H(U1(k, a), U1(c, b))
26.42/8.64	   A^2 -> H(U1(k, a), U1(d, b))
26.42/8.64	   A^2 -> H(U1(k, a), U1(b, c))
26.42/8.64	   A^2 -> H(U1(k, a), U1(b, d))
26.42/8.64	   A^2 -> H(U1(k, a), U1(c, c))
26.42/8.64	   A^2 -> H(U1(k, a), f(e))
26.42/8.64	   A^2 -> H(U1(k, a), f(k))
26.42/8.64	   A^2 -> H(U1(k, a), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, d), U1(c, b))
26.42/8.64	   A^2 -> H(U1(c, d), U1(d, b))
26.42/8.64	   A^2 -> H(U1(c, d), U1(b, c))
26.42/8.64	   A^2 -> H(U1(c, d), U1(b, d))
26.42/8.64	   A^2 -> H(U1(c, d), U1(c, c))
26.42/8.64	   A^2 -> H(U1(c, d), f(e))
26.42/8.64	   A^2 -> H(U1(c, d), f(k))
26.42/8.64	   A^2 -> H(U1(c, d), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, a), U1(e, b))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, b))
26.42/8.64	   A^2 -> H(U1(c, a), U1(c, d))
26.42/8.64	   A^2 -> H(U1(c, a), U1(d, c))
26.42/8.64	   A^2 -> H(U1(c, a), U1(b, e))
26.42/8.64	   A^2 -> H(U1(c, a), U1(b, k))
26.42/8.64	   A^2 -> H(U1(c, a), U1(e, c))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, c))
26.42/8.64	   A^2 -> H(U1(c, a), U1(c, e))
26.42/8.64	   A^2 -> H(U1(c, a), U1(c, k))
26.42/8.64	   A^2 -> H(U1(c, a), U1(e, e))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, k))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, d))
26.42/8.64	   A^2 -> H(U1(c, a), U1(d, k))
26.42/8.64	   A^2 -> H(U1(d, e), U1(b, b))
26.42/8.64	   A^2 -> H(U1(d, e), f(c))
26.42/8.64	   A^2 -> H(U1(d, e), f(d))
26.42/8.64	   A^2 -> H(U1(d, c), U1(c, b))
26.42/8.64	   A^2 -> H(U1(d, c), U1(d, b))
26.42/8.64	   A^2 -> H(U1(d, c), U1(b, c))
26.42/8.64	   A^2 -> H(U1(d, c), U1(b, d))
26.42/8.64	   A^2 -> H(U1(d, c), U1(c, c))
26.42/8.64	   A^2 -> H(U1(d, c), f(e))
26.42/8.64	   A^2 -> H(U1(d, c), f(k))
26.42/8.64	   A^2 -> H(U1(d, c), U1(d, d))
26.42/8.64	   A^2 -> H(U1(d, a), U1(e, b))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, b))
26.42/8.64	   A^2 -> H(U1(d, a), U1(c, d))
26.42/8.64	   A^2 -> H(U1(d, a), U1(d, c))
26.42/8.64	   A^2 -> H(U1(d, a), U1(b, e))
26.42/8.64	   A^2 -> H(U1(d, a), U1(b, k))
26.42/8.64	   A^2 -> H(U1(d, a), U1(e, c))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, c))
26.42/8.64	   A^2 -> H(U1(d, a), U1(c, e))
26.42/8.64	   A^2 -> H(U1(d, a), U1(c, k))
26.42/8.64	   A^2 -> H(U1(d, a), U1(e, e))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, k))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, d))
26.42/8.64	   A^2 -> H(U1(d, a), U1(d, k))
26.42/8.64	   A^2 -> H(U1(a, e), U1(c, b))
26.42/8.64	   A^2 -> H(U1(a, e), U1(d, b))
26.42/8.64	   A^2 -> H(U1(a, e), U1(b, c))
26.42/8.64	   A^2 -> H(U1(a, e), U1(b, d))
26.42/8.64	   A^2 -> H(U1(a, e), U1(c, c))
26.42/8.64	   A^2 -> H(U1(a, e), f(e))
26.42/8.64	   A^2 -> H(U1(a, e), f(k))
26.42/8.64	   A^2 -> H(U1(a, e), U1(d, d))
26.42/8.64	   A^2 -> H(U1(a, k), U1(c, b))
26.42/8.64	   A^2 -> H(U1(a, k), U1(d, b))
26.42/8.64	   A^2 -> H(U1(a, k), U1(b, c))
26.42/8.64	   A^2 -> H(U1(a, k), U1(b, d))
26.42/8.64	   A^2 -> H(U1(a, k), U1(c, c))
26.42/8.64	   A^2 -> H(U1(a, k), f(e))
26.42/8.64	   A^2 -> H(U1(a, k), f(k))
26.42/8.64	   A^2 -> H(U1(a, k), U1(d, d))
26.42/8.64	   A^2 -> H(U1(a, c), U1(e, b))
26.42/8.64	   A^2 -> H(U1(a, c), U1(k, b))
26.42/8.64	   A^2 -> H(U1(a, c), U1(c, d))
26.42/8.64	   A^2 -> H(U1(a, c), U1(d, c))
26.42/8.64	   A^2 -> H(U1(a, c), U1(b, e))
26.42/8.64	   A^2 -> H(U1(a, c), U1(b, k))
26.42/8.64	   A^2 -> H(U1(a, c), U1(e, c))
26.42/8.64	   A^2 -> H(U1(a, c), U1(k, c))
26.42/8.64	   A^2 -> H(U1(a, c), U1(c, e))
26.42/8.64	   A^2 -> H(U1(a, c), U1(c, k))
26.42/8.64	   A^2 -> H(U1(a, c), U1(e, e))
26.42/8.64	   A^2 -> H(U1(a, c), U1(k, k))
26.42/8.64	   A^2 -> H(U1(a, c), U1(k, d))
26.42/8.64	   A^2 -> H(U1(a, c), U1(d, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(e, b))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, b))
26.42/8.64	   A^2 -> H(U1(a, d), U1(c, d))
26.42/8.64	   A^2 -> H(U1(a, d), U1(d, c))
26.42/8.64	   A^2 -> H(U1(a, d), U1(b, e))
26.42/8.64	   A^2 -> H(U1(a, d), U1(b, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(e, c))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, c))
26.42/8.64	   A^2 -> H(U1(a, d), U1(c, e))
26.42/8.64	   A^2 -> H(U1(a, d), U1(c, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(e, e))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, d))
26.42/8.64	   A^2 -> H(U1(a, d), U1(d, k))
26.42/8.64	   A^2 -> H(U1(a, a), b)
26.42/8.64	   A^2 -> H(U1(a, a), U1(e, d))
26.42/8.64	   A^2 -> H(U1(a, a), U1(d, e))
26.42/8.64	   A^2 -> H(U1(a, a), c)
26.42/8.64	   A^2 -> H(U1(a, a), U1(e, k))
26.42/8.64	   A^2 -> H(U1(a, a), U1(k, e))
26.42/8.64	   A^2 -> H(U1(a, a), e)
26.42/8.64	   A^2 -> H(U1(a, a), U1(k, k))
26.42/8.64	   A^2 -> H(k, f(b))
26.42/8.64	   A^2 -> H(c, U1(b, b))
26.42/8.64	   A^2 -> H(c, f(c))
26.42/8.64	   A^2 -> H(c, f(d))
26.42/8.64	   A^2 -> H(U1(e, k), U1(b, b))
26.42/8.64	   A^2 -> H(U1(e, k), f(c))
26.42/8.64	   A^2 -> H(U1(e, k), f(d))
26.42/8.64	   A^2 -> H(U1(e, c), U1(c, b))
26.42/8.64	   A^2 -> H(U1(e, c), U1(d, b))
26.42/8.64	   A^2 -> H(U1(e, c), U1(b, c))
26.42/8.64	   A^2 -> H(U1(e, c), U1(b, d))
26.42/8.64	   A^2 -> H(U1(e, c), U1(c, c))
26.42/8.64	   A^2 -> H(U1(e, c), f(e))
26.42/8.64	   A^2 -> H(U1(e, c), f(k))
26.42/8.64	   A^2 -> H(U1(e, c), U1(d, d))
26.42/8.64	   A^2 -> H(U1(k, e), U1(b, b))
26.42/8.64	   A^2 -> H(U1(k, e), f(c))
26.42/8.64	   A^2 -> H(U1(k, e), f(d))
26.42/8.64	   A^2 -> H(U1(k, c), U1(c, b))
26.42/8.64	   A^2 -> H(U1(k, c), U1(d, b))
26.42/8.64	   A^2 -> H(U1(k, c), U1(b, c))
26.42/8.64	   A^2 -> H(U1(k, c), U1(b, d))
26.42/8.64	   A^2 -> H(U1(k, c), U1(c, c))
26.42/8.64	   A^2 -> H(U1(k, c), f(e))
26.42/8.64	   A^2 -> H(U1(k, c), f(k))
26.42/8.64	   A^2 -> H(U1(k, c), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, e), U1(c, b))
26.42/8.64	   A^2 -> H(U1(c, e), U1(d, b))
26.42/8.64	   A^2 -> H(U1(c, e), U1(b, c))
26.42/8.64	   A^2 -> H(U1(c, e), U1(b, d))
26.42/8.64	   A^2 -> H(U1(c, e), U1(c, c))
26.42/8.64	   A^2 -> H(U1(c, e), f(e))
26.42/8.64	   A^2 -> H(U1(c, e), f(k))
26.42/8.64	   A^2 -> H(U1(c, e), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, k), U1(c, b))
26.42/8.64	   A^2 -> H(U1(c, k), U1(d, b))
26.42/8.64	   A^2 -> H(U1(c, k), U1(b, c))
26.42/8.64	   A^2 -> H(U1(c, k), U1(b, d))
26.42/8.64	   A^2 -> H(U1(c, k), U1(c, c))
26.42/8.64	   A^2 -> H(U1(c, k), f(e))
26.42/8.64	   A^2 -> H(U1(c, k), f(k))
26.42/8.64	   A^2 -> H(U1(c, k), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(e, b))
26.42/8.64	   A^2 -> H(U1(c, c), U1(k, b))
26.42/8.64	   A^2 -> H(U1(c, c), U1(c, d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(d, c))
26.42/8.64	   A^2 -> H(U1(c, c), U1(b, e))
26.42/8.64	   A^2 -> H(U1(c, c), U1(b, k))
26.42/8.64	   A^2 -> H(U1(c, c), U1(e, e))
26.42/8.64	   A^2 -> H(U1(c, c), U1(k, k))
26.42/8.64	   A^2 -> H(U1(c, c), U1(k, d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(d, k))
26.42/8.64	   A^2 -> H(e, U1(b, b))
26.42/8.64	   A^2 -> H(e, f(c))
26.42/8.64	   A^2 -> H(e, f(d))
26.42/8.64	   A^2 -> H(U1(e, e), U1(c, b))
26.42/8.64	   A^2 -> H(U1(e, e), U1(d, b))
26.42/8.64	   A^2 -> H(U1(e, e), U1(b, c))
26.42/8.64	   A^2 -> H(U1(e, e), U1(b, d))
26.42/8.64	   A^2 -> H(U1(e, e), U1(c, c))
26.42/8.64	   A^2 -> H(U1(e, e), f(e))
26.42/8.64	   A^2 -> H(U1(e, e), f(k))
26.42/8.64	   A^2 -> H(U1(e, e), U1(d, d))
26.42/8.64	   A^2 -> H(f(e), U1(e, b))
26.42/8.64	   A^2 -> H(f(e), U1(k, b))
26.42/8.64	   A^2 -> H(f(e), U1(c, d))
26.42/8.64	   A^2 -> H(f(e), U1(d, c))
26.42/8.64	   A^2 -> H(f(e), U1(b, e))
26.42/8.64	   A^2 -> H(f(e), U1(b, k))
26.42/8.64	   A^2 -> H(f(e), U1(e, c))
26.42/8.64	   A^2 -> H(f(e), U1(k, c))
26.42/8.64	   A^2 -> H(f(e), U1(c, e))
26.42/8.64	   A^2 -> H(f(e), U1(c, k))
26.42/8.64	   A^2 -> H(f(e), U1(k, k))
26.42/8.64	   A^2 -> H(f(e), U1(k, d))
26.42/8.64	   A^2 -> H(f(e), U1(d, k))
26.42/8.64	   A^2 -> H(U1(k, k), U1(c, b))
26.42/8.64	   A^2 -> H(U1(k, k), U1(d, b))
26.42/8.64	   A^2 -> H(U1(k, k), U1(b, c))
26.42/8.64	   A^2 -> H(U1(k, k), U1(b, d))
26.42/8.64	   A^2 -> H(U1(k, k), U1(c, c))
26.42/8.64	   A^2 -> H(U1(k, k), f(e))
26.42/8.64	   A^2 -> H(U1(k, k), f(k))
26.42/8.64	   A^2 -> H(U1(k, k), U1(d, d))
26.42/8.64	   A^2 -> H(f(k), U1(e, b))
26.42/8.64	   A^2 -> H(f(k), U1(k, b))
26.42/8.64	   A^2 -> H(f(k), U1(c, d))
26.42/8.64	   A^2 -> H(f(k), U1(d, c))
26.42/8.64	   A^2 -> H(f(k), U1(b, e))
26.42/8.64	   A^2 -> H(f(k), U1(b, k))
26.42/8.64	   A^2 -> H(f(k), U1(e, c))
26.42/8.64	   A^2 -> H(f(k), U1(k, c))
26.42/8.64	   A^2 -> H(f(k), U1(c, e))
26.42/8.64	   A^2 -> H(f(k), U1(c, k))
26.42/8.64	   A^2 -> H(f(k), U1(e, e))
26.42/8.64	   A^2 -> H(f(k), U1(k, d))
26.42/8.64	   A^2 -> H(f(k), U1(d, k))
26.42/8.64	   A^2 -> H(f(c), b)
26.42/8.64	   A^2 -> H(f(c), U1(e, d))
26.42/8.64	   A^2 -> H(f(c), U1(d, e))
26.42/8.64	   A^2 -> H(f(k), U1(k, k))
26.42/8.64	
26.42/8.64	The TRS R consists of the following rules:
26.42/8.64	
26.42/8.64	   f(x) -> U1(x, x)
26.42/8.64	   U1(e, x) -> x
26.42/8.64	   a -> c
26.42/8.64	   a -> d
26.42/8.64	   b -> c
26.42/8.64	   b -> d
26.42/8.64	   d -> k
26.42/8.64	   c -> e
26.42/8.64	   c -> k
26.42/8.64	
26.42/8.64	Q is empty.
26.42/8.64	We have to consider all minimal (P,Q,R)-chains.
26.42/8.64	----------------------------------------
26.42/8.64	
26.42/8.64	(459) TransformationProof (EQUIVALENT)
26.42/8.64	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), f(b)) at position [] we obtained the following new rules [LPAR04]:
26.42/8.64	
26.42/8.64	   (A^2 -> H(U1(k, k), U1(b, b)),A^2 -> H(U1(k, k), U1(b, b)))
26.42/8.64	   (A^2 -> H(U1(k, k), f(c)),A^2 -> H(U1(k, k), f(c)))
26.42/8.64	   (A^2 -> H(U1(k, k), f(d)),A^2 -> H(U1(k, k), f(d)))
26.42/8.64	
26.42/8.64	
26.42/8.64	----------------------------------------
26.42/8.64	
26.42/8.64	(460)
26.42/8.64	Obligation:
26.42/8.64	Q DP problem:
26.42/8.64	The TRS P consists of the following rules:
26.42/8.64	
26.42/8.64	   H(x, x) -> G(x, x, f(k))
26.42/8.64	   G(d, x, x) -> A^2
26.42/8.64	   A^2 -> H(f(c), f(c))
26.42/8.64	   A^2 -> H(f(d), f(d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(c, c))
26.42/8.64	   A^2 -> H(f(e), f(e))
26.42/8.64	   A^2 -> H(f(k), f(k))
26.42/8.64	   A^2 -> H(U1(k, d), U1(b, b))
26.42/8.64	   A^2 -> H(U1(k, d), f(c))
26.42/8.64	   A^2 -> H(U1(k, d), f(d))
26.42/8.64	   A^2 -> H(U1(d, k), U1(b, b))
26.42/8.64	   A^2 -> H(U1(d, k), f(c))
26.42/8.64	   A^2 -> H(U1(d, k), f(d))
26.42/8.64	   A^2 -> H(U1(d, d), U1(c, b))
26.42/8.64	   A^2 -> H(U1(d, d), U1(d, b))
26.42/8.64	   A^2 -> H(U1(d, d), U1(b, c))
26.42/8.64	   A^2 -> H(U1(d, d), U1(b, d))
26.42/8.64	   A^2 -> H(U1(d, d), U1(c, c))
26.42/8.64	   A^2 -> H(U1(d, d), f(e))
26.42/8.64	   A^2 -> H(U1(d, d), f(k))
26.42/8.64	   A^2 -> H(U1(d, d), U1(d, d))
26.42/8.64	   A^2 -> H(f(d), U1(e, b))
26.42/8.64	   A^2 -> H(f(d), U1(k, b))
26.42/8.64	   A^2 -> H(f(d), U1(c, d))
26.42/8.64	   A^2 -> H(f(d), U1(d, c))
26.42/8.64	   A^2 -> H(f(d), U1(b, e))
26.42/8.64	   A^2 -> H(f(d), U1(b, k))
26.42/8.64	   A^2 -> H(f(d), U1(e, c))
26.42/8.64	   A^2 -> H(f(d), U1(k, c))
26.42/8.64	   A^2 -> H(f(d), U1(c, e))
26.42/8.64	   A^2 -> H(f(d), U1(c, k))
26.42/8.64	   A^2 -> H(f(d), U1(e, e))
26.42/8.64	   A^2 -> H(f(d), U1(k, k))
26.42/8.64	   A^2 -> H(f(a), b)
26.42/8.64	   A^2 -> H(f(a), U1(e, d))
26.42/8.64	   A^2 -> H(f(a), U1(d, e))
26.42/8.64	   A^2 -> H(f(c), U1(e, c))
26.42/8.64	   A^2 -> H(f(c), U1(k, c))
26.42/8.64	   A^2 -> H(f(c), U1(c, e))
26.42/8.64	   A^2 -> H(f(c), U1(c, k))
26.42/8.64	   A^2 -> H(f(a), c)
26.42/8.64	   A^2 -> H(f(a), U1(e, k))
26.42/8.64	   A^2 -> H(f(a), U1(k, e))
26.42/8.64	   A^2 -> H(f(c), U1(e, e))
26.42/8.64	   A^2 -> H(f(a), e)
26.42/8.64	   A^2 -> H(f(d), U1(k, d))
26.42/8.64	   A^2 -> H(f(d), U1(d, k))
26.42/8.64	   A^2 -> H(f(a), U1(k, k))
26.42/8.64	   A^2 -> H(d, f(b))
26.42/8.64	   A^2 -> H(a, U1(b, b))
26.42/8.64	   A^2 -> H(a, f(c))
26.42/8.64	   A^2 -> H(a, f(d))
26.42/8.64	   A^2 -> H(U1(e, d), U1(b, b))
26.42/8.64	   A^2 -> H(U1(e, d), f(c))
26.42/8.64	   A^2 -> H(U1(e, d), f(d))
26.42/8.64	   A^2 -> H(U1(e, a), U1(c, b))
26.42/8.64	   A^2 -> H(U1(e, a), U1(d, b))
26.42/8.64	   A^2 -> H(U1(e, a), U1(b, c))
26.42/8.64	   A^2 -> H(U1(e, a), U1(b, d))
26.42/8.64	   A^2 -> H(U1(e, a), U1(c, c))
26.42/8.64	   A^2 -> H(U1(e, a), f(e))
26.42/8.64	   A^2 -> H(U1(e, a), f(k))
26.42/8.64	   A^2 -> H(U1(e, a), U1(d, d))
26.42/8.64	   A^2 -> H(U1(k, a), U1(c, b))
26.42/8.64	   A^2 -> H(U1(k, a), U1(d, b))
26.42/8.64	   A^2 -> H(U1(k, a), U1(b, c))
26.42/8.64	   A^2 -> H(U1(k, a), U1(b, d))
26.42/8.64	   A^2 -> H(U1(k, a), U1(c, c))
26.42/8.64	   A^2 -> H(U1(k, a), f(e))
26.42/8.64	   A^2 -> H(U1(k, a), f(k))
26.42/8.64	   A^2 -> H(U1(k, a), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, d), U1(c, b))
26.42/8.64	   A^2 -> H(U1(c, d), U1(d, b))
26.42/8.64	   A^2 -> H(U1(c, d), U1(b, c))
26.42/8.64	   A^2 -> H(U1(c, d), U1(b, d))
26.42/8.64	   A^2 -> H(U1(c, d), U1(c, c))
26.42/8.64	   A^2 -> H(U1(c, d), f(e))
26.42/8.64	   A^2 -> H(U1(c, d), f(k))
26.42/8.64	   A^2 -> H(U1(c, d), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, a), U1(e, b))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, b))
26.42/8.64	   A^2 -> H(U1(c, a), U1(c, d))
26.42/8.64	   A^2 -> H(U1(c, a), U1(d, c))
26.42/8.64	   A^2 -> H(U1(c, a), U1(b, e))
26.42/8.64	   A^2 -> H(U1(c, a), U1(b, k))
26.42/8.64	   A^2 -> H(U1(c, a), U1(e, c))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, c))
26.42/8.64	   A^2 -> H(U1(c, a), U1(c, e))
26.42/8.64	   A^2 -> H(U1(c, a), U1(c, k))
26.42/8.64	   A^2 -> H(U1(c, a), U1(e, e))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, k))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, d))
26.42/8.64	   A^2 -> H(U1(c, a), U1(d, k))
26.42/8.64	   A^2 -> H(U1(d, e), U1(b, b))
26.42/8.64	   A^2 -> H(U1(d, e), f(c))
26.42/8.64	   A^2 -> H(U1(d, e), f(d))
26.42/8.64	   A^2 -> H(U1(d, c), U1(c, b))
26.42/8.64	   A^2 -> H(U1(d, c), U1(d, b))
26.42/8.64	   A^2 -> H(U1(d, c), U1(b, c))
26.42/8.64	   A^2 -> H(U1(d, c), U1(b, d))
26.42/8.64	   A^2 -> H(U1(d, c), U1(c, c))
26.42/8.64	   A^2 -> H(U1(d, c), f(e))
26.42/8.64	   A^2 -> H(U1(d, c), f(k))
26.42/8.64	   A^2 -> H(U1(d, c), U1(d, d))
26.42/8.64	   A^2 -> H(U1(d, a), U1(e, b))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, b))
26.42/8.64	   A^2 -> H(U1(d, a), U1(c, d))
26.42/8.64	   A^2 -> H(U1(d, a), U1(d, c))
26.42/8.64	   A^2 -> H(U1(d, a), U1(b, e))
26.42/8.64	   A^2 -> H(U1(d, a), U1(b, k))
26.42/8.64	   A^2 -> H(U1(d, a), U1(e, c))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, c))
26.42/8.64	   A^2 -> H(U1(d, a), U1(c, e))
26.42/8.64	   A^2 -> H(U1(d, a), U1(c, k))
26.42/8.64	   A^2 -> H(U1(d, a), U1(e, e))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, k))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, d))
26.42/8.64	   A^2 -> H(U1(d, a), U1(d, k))
26.42/8.64	   A^2 -> H(U1(a, e), U1(c, b))
26.42/8.64	   A^2 -> H(U1(a, e), U1(d, b))
26.42/8.64	   A^2 -> H(U1(a, e), U1(b, c))
26.42/8.64	   A^2 -> H(U1(a, e), U1(b, d))
26.42/8.64	   A^2 -> H(U1(a, e), U1(c, c))
26.42/8.64	   A^2 -> H(U1(a, e), f(e))
26.42/8.64	   A^2 -> H(U1(a, e), f(k))
26.42/8.64	   A^2 -> H(U1(a, e), U1(d, d))
26.42/8.64	   A^2 -> H(U1(a, k), U1(c, b))
26.42/8.64	   A^2 -> H(U1(a, k), U1(d, b))
26.42/8.64	   A^2 -> H(U1(a, k), U1(b, c))
26.42/8.64	   A^2 -> H(U1(a, k), U1(b, d))
26.42/8.64	   A^2 -> H(U1(a, k), U1(c, c))
26.42/8.64	   A^2 -> H(U1(a, k), f(e))
26.42/8.64	   A^2 -> H(U1(a, k), f(k))
26.42/8.64	   A^2 -> H(U1(a, k), U1(d, d))
26.42/8.64	   A^2 -> H(U1(a, c), U1(e, b))
26.42/8.64	   A^2 -> H(U1(a, c), U1(k, b))
26.42/8.64	   A^2 -> H(U1(a, c), U1(c, d))
26.42/8.64	   A^2 -> H(U1(a, c), U1(d, c))
26.42/8.64	   A^2 -> H(U1(a, c), U1(b, e))
26.42/8.64	   A^2 -> H(U1(a, c), U1(b, k))
26.42/8.64	   A^2 -> H(U1(a, c), U1(e, c))
26.42/8.64	   A^2 -> H(U1(a, c), U1(k, c))
26.42/8.64	   A^2 -> H(U1(a, c), U1(c, e))
26.42/8.64	   A^2 -> H(U1(a, c), U1(c, k))
26.42/8.64	   A^2 -> H(U1(a, c), U1(e, e))
26.42/8.64	   A^2 -> H(U1(a, c), U1(k, k))
26.42/8.64	   A^2 -> H(U1(a, c), U1(k, d))
26.42/8.64	   A^2 -> H(U1(a, c), U1(d, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(e, b))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, b))
26.42/8.64	   A^2 -> H(U1(a, d), U1(c, d))
26.42/8.64	   A^2 -> H(U1(a, d), U1(d, c))
26.42/8.64	   A^2 -> H(U1(a, d), U1(b, e))
26.42/8.64	   A^2 -> H(U1(a, d), U1(b, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(e, c))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, c))
26.42/8.64	   A^2 -> H(U1(a, d), U1(c, e))
26.42/8.64	   A^2 -> H(U1(a, d), U1(c, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(e, e))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, d))
26.42/8.64	   A^2 -> H(U1(a, d), U1(d, k))
26.42/8.64	   A^2 -> H(U1(a, a), b)
26.42/8.64	   A^2 -> H(U1(a, a), U1(e, d))
26.42/8.64	   A^2 -> H(U1(a, a), U1(d, e))
26.42/8.64	   A^2 -> H(U1(a, a), c)
26.42/8.64	   A^2 -> H(U1(a, a), U1(e, k))
26.42/8.64	   A^2 -> H(U1(a, a), U1(k, e))
26.42/8.64	   A^2 -> H(U1(a, a), e)
26.42/8.64	   A^2 -> H(U1(a, a), U1(k, k))
26.42/8.64	   A^2 -> H(k, f(b))
26.42/8.64	   A^2 -> H(c, U1(b, b))
26.42/8.64	   A^2 -> H(c, f(c))
26.42/8.64	   A^2 -> H(c, f(d))
26.42/8.64	   A^2 -> H(U1(e, k), U1(b, b))
26.42/8.64	   A^2 -> H(U1(e, k), f(c))
26.42/8.64	   A^2 -> H(U1(e, k), f(d))
26.42/8.64	   A^2 -> H(U1(e, c), U1(c, b))
26.42/8.64	   A^2 -> H(U1(e, c), U1(d, b))
26.42/8.64	   A^2 -> H(U1(e, c), U1(b, c))
26.42/8.64	   A^2 -> H(U1(e, c), U1(b, d))
26.42/8.64	   A^2 -> H(U1(e, c), U1(c, c))
26.42/8.64	   A^2 -> H(U1(e, c), f(e))
26.42/8.64	   A^2 -> H(U1(e, c), f(k))
26.42/8.64	   A^2 -> H(U1(e, c), U1(d, d))
26.42/8.64	   A^2 -> H(U1(k, e), U1(b, b))
26.42/8.64	   A^2 -> H(U1(k, e), f(c))
26.42/8.64	   A^2 -> H(U1(k, e), f(d))
26.42/8.64	   A^2 -> H(U1(k, c), U1(c, b))
26.42/8.64	   A^2 -> H(U1(k, c), U1(d, b))
26.42/8.64	   A^2 -> H(U1(k, c), U1(b, c))
26.42/8.64	   A^2 -> H(U1(k, c), U1(b, d))
26.42/8.64	   A^2 -> H(U1(k, c), U1(c, c))
26.42/8.64	   A^2 -> H(U1(k, c), f(e))
26.42/8.64	   A^2 -> H(U1(k, c), f(k))
26.42/8.64	   A^2 -> H(U1(k, c), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, e), U1(c, b))
26.42/8.64	   A^2 -> H(U1(c, e), U1(d, b))
26.42/8.64	   A^2 -> H(U1(c, e), U1(b, c))
26.42/8.64	   A^2 -> H(U1(c, e), U1(b, d))
26.42/8.64	   A^2 -> H(U1(c, e), U1(c, c))
26.42/8.64	   A^2 -> H(U1(c, e), f(e))
26.42/8.64	   A^2 -> H(U1(c, e), f(k))
26.42/8.64	   A^2 -> H(U1(c, e), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, k), U1(c, b))
26.42/8.64	   A^2 -> H(U1(c, k), U1(d, b))
26.42/8.64	   A^2 -> H(U1(c, k), U1(b, c))
26.42/8.64	   A^2 -> H(U1(c, k), U1(b, d))
26.42/8.64	   A^2 -> H(U1(c, k), U1(c, c))
26.42/8.64	   A^2 -> H(U1(c, k), f(e))
26.42/8.64	   A^2 -> H(U1(c, k), f(k))
26.42/8.64	   A^2 -> H(U1(c, k), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(e, b))
26.42/8.64	   A^2 -> H(U1(c, c), U1(k, b))
26.42/8.64	   A^2 -> H(U1(c, c), U1(c, d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(d, c))
26.42/8.64	   A^2 -> H(U1(c, c), U1(b, e))
26.42/8.64	   A^2 -> H(U1(c, c), U1(b, k))
26.42/8.64	   A^2 -> H(U1(c, c), U1(e, e))
26.42/8.64	   A^2 -> H(U1(c, c), U1(k, k))
26.42/8.64	   A^2 -> H(U1(c, c), U1(k, d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(d, k))
26.42/8.64	   A^2 -> H(e, U1(b, b))
26.42/8.64	   A^2 -> H(e, f(c))
26.42/8.64	   A^2 -> H(e, f(d))
26.42/8.64	   A^2 -> H(U1(e, e), U1(c, b))
26.42/8.64	   A^2 -> H(U1(e, e), U1(d, b))
26.42/8.64	   A^2 -> H(U1(e, e), U1(b, c))
26.42/8.64	   A^2 -> H(U1(e, e), U1(b, d))
26.42/8.64	   A^2 -> H(U1(e, e), U1(c, c))
26.42/8.64	   A^2 -> H(U1(e, e), f(e))
26.42/8.64	   A^2 -> H(U1(e, e), f(k))
26.42/8.64	   A^2 -> H(U1(e, e), U1(d, d))
26.42/8.64	   A^2 -> H(f(e), U1(e, b))
26.42/8.64	   A^2 -> H(f(e), U1(k, b))
26.42/8.64	   A^2 -> H(f(e), U1(c, d))
26.42/8.64	   A^2 -> H(f(e), U1(d, c))
26.42/8.64	   A^2 -> H(f(e), U1(b, e))
26.42/8.64	   A^2 -> H(f(e), U1(b, k))
26.42/8.64	   A^2 -> H(f(e), U1(e, c))
26.42/8.64	   A^2 -> H(f(e), U1(k, c))
26.42/8.64	   A^2 -> H(f(e), U1(c, e))
26.42/8.64	   A^2 -> H(f(e), U1(c, k))
26.42/8.64	   A^2 -> H(f(e), U1(k, k))
26.42/8.64	   A^2 -> H(f(e), U1(k, d))
26.42/8.64	   A^2 -> H(f(e), U1(d, k))
26.42/8.64	   A^2 -> H(U1(k, k), U1(c, b))
26.42/8.64	   A^2 -> H(U1(k, k), U1(d, b))
26.42/8.64	   A^2 -> H(U1(k, k), U1(b, c))
26.42/8.64	   A^2 -> H(U1(k, k), U1(b, d))
26.42/8.64	   A^2 -> H(U1(k, k), U1(c, c))
26.42/8.64	   A^2 -> H(U1(k, k), f(e))
26.42/8.64	   A^2 -> H(U1(k, k), f(k))
26.42/8.64	   A^2 -> H(U1(k, k), U1(d, d))
26.42/8.64	   A^2 -> H(f(k), U1(e, b))
26.42/8.64	   A^2 -> H(f(k), U1(k, b))
26.42/8.64	   A^2 -> H(f(k), U1(c, d))
26.42/8.64	   A^2 -> H(f(k), U1(d, c))
26.42/8.64	   A^2 -> H(f(k), U1(b, e))
26.42/8.64	   A^2 -> H(f(k), U1(b, k))
26.42/8.64	   A^2 -> H(f(k), U1(e, c))
26.42/8.64	   A^2 -> H(f(k), U1(k, c))
26.42/8.64	   A^2 -> H(f(k), U1(c, e))
26.42/8.64	   A^2 -> H(f(k), U1(c, k))
26.42/8.64	   A^2 -> H(f(k), U1(e, e))
26.42/8.64	   A^2 -> H(f(k), U1(k, d))
26.42/8.64	   A^2 -> H(f(k), U1(d, k))
26.42/8.64	   A^2 -> H(f(c), b)
26.42/8.64	   A^2 -> H(f(c), U1(e, d))
26.42/8.64	   A^2 -> H(f(c), U1(d, e))
26.42/8.64	   A^2 -> H(f(k), U1(k, k))
26.42/8.64	   A^2 -> H(U1(k, k), U1(b, b))
26.42/8.64	   A^2 -> H(U1(k, k), f(c))
26.42/8.64	   A^2 -> H(U1(k, k), f(d))
26.42/8.64	
26.42/8.64	The TRS R consists of the following rules:
26.42/8.64	
26.42/8.64	   f(x) -> U1(x, x)
26.42/8.64	   U1(e, x) -> x
26.42/8.64	   a -> c
26.42/8.64	   a -> d
26.42/8.64	   b -> c
26.42/8.64	   b -> d
26.42/8.64	   d -> k
26.42/8.64	   c -> e
26.42/8.64	   c -> k
26.42/8.64	
26.42/8.64	Q is empty.
26.42/8.64	We have to consider all minimal (P,Q,R)-chains.
26.42/8.64	----------------------------------------
26.42/8.64	
26.42/8.64	(461) TransformationProof (EQUIVALENT)
26.42/8.64	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
26.42/8.64	
26.42/8.64	   (A^2 -> H(U1(k, k), U1(b, b)),A^2 -> H(U1(k, k), U1(b, b)))
26.42/8.64	   (A^2 -> H(U1(k, d), U1(c, b)),A^2 -> H(U1(k, d), U1(c, b)))
26.42/8.64	   (A^2 -> H(U1(k, d), U1(d, b)),A^2 -> H(U1(k, d), U1(d, b)))
26.42/8.64	   (A^2 -> H(U1(k, d), U1(b, c)),A^2 -> H(U1(k, d), U1(b, c)))
26.42/8.64	   (A^2 -> H(U1(k, d), U1(b, d)),A^2 -> H(U1(k, d), U1(b, d)))
26.42/8.64	
26.42/8.64	
26.42/8.64	----------------------------------------
26.42/8.64	
26.42/8.64	(462)
26.42/8.64	Obligation:
26.42/8.64	Q DP problem:
26.42/8.64	The TRS P consists of the following rules:
26.42/8.64	
26.42/8.64	   H(x, x) -> G(x, x, f(k))
26.42/8.64	   G(d, x, x) -> A^2
26.42/8.64	   A^2 -> H(f(c), f(c))
26.42/8.64	   A^2 -> H(f(d), f(d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(c, c))
26.42/8.64	   A^2 -> H(f(e), f(e))
26.42/8.64	   A^2 -> H(f(k), f(k))
26.42/8.64	   A^2 -> H(U1(k, d), f(c))
26.42/8.64	   A^2 -> H(U1(k, d), f(d))
26.42/8.64	   A^2 -> H(U1(d, k), U1(b, b))
26.42/8.64	   A^2 -> H(U1(d, k), f(c))
26.42/8.64	   A^2 -> H(U1(d, k), f(d))
26.42/8.64	   A^2 -> H(U1(d, d), U1(c, b))
26.42/8.64	   A^2 -> H(U1(d, d), U1(d, b))
26.42/8.64	   A^2 -> H(U1(d, d), U1(b, c))
26.42/8.64	   A^2 -> H(U1(d, d), U1(b, d))
26.42/8.64	   A^2 -> H(U1(d, d), U1(c, c))
26.42/8.64	   A^2 -> H(U1(d, d), f(e))
26.42/8.64	   A^2 -> H(U1(d, d), f(k))
26.42/8.64	   A^2 -> H(U1(d, d), U1(d, d))
26.42/8.64	   A^2 -> H(f(d), U1(e, b))
26.42/8.64	   A^2 -> H(f(d), U1(k, b))
26.42/8.64	   A^2 -> H(f(d), U1(c, d))
26.42/8.64	   A^2 -> H(f(d), U1(d, c))
26.42/8.64	   A^2 -> H(f(d), U1(b, e))
26.42/8.64	   A^2 -> H(f(d), U1(b, k))
26.42/8.64	   A^2 -> H(f(d), U1(e, c))
26.42/8.64	   A^2 -> H(f(d), U1(k, c))
26.42/8.64	   A^2 -> H(f(d), U1(c, e))
26.42/8.64	   A^2 -> H(f(d), U1(c, k))
26.42/8.64	   A^2 -> H(f(d), U1(e, e))
26.42/8.64	   A^2 -> H(f(d), U1(k, k))
26.42/8.64	   A^2 -> H(f(a), b)
26.42/8.64	   A^2 -> H(f(a), U1(e, d))
26.42/8.64	   A^2 -> H(f(a), U1(d, e))
26.42/8.64	   A^2 -> H(f(c), U1(e, c))
26.42/8.64	   A^2 -> H(f(c), U1(k, c))
26.42/8.64	   A^2 -> H(f(c), U1(c, e))
26.42/8.64	   A^2 -> H(f(c), U1(c, k))
26.42/8.64	   A^2 -> H(f(a), c)
26.42/8.64	   A^2 -> H(f(a), U1(e, k))
26.42/8.64	   A^2 -> H(f(a), U1(k, e))
26.42/8.64	   A^2 -> H(f(c), U1(e, e))
26.42/8.64	   A^2 -> H(f(a), e)
26.42/8.64	   A^2 -> H(f(d), U1(k, d))
26.42/8.64	   A^2 -> H(f(d), U1(d, k))
26.42/8.64	   A^2 -> H(f(a), U1(k, k))
26.42/8.64	   A^2 -> H(d, f(b))
26.42/8.64	   A^2 -> H(a, U1(b, b))
26.42/8.64	   A^2 -> H(a, f(c))
26.42/8.64	   A^2 -> H(a, f(d))
26.42/8.64	   A^2 -> H(U1(e, d), U1(b, b))
26.42/8.64	   A^2 -> H(U1(e, d), f(c))
26.42/8.64	   A^2 -> H(U1(e, d), f(d))
26.42/8.64	   A^2 -> H(U1(e, a), U1(c, b))
26.42/8.64	   A^2 -> H(U1(e, a), U1(d, b))
26.42/8.64	   A^2 -> H(U1(e, a), U1(b, c))
26.42/8.64	   A^2 -> H(U1(e, a), U1(b, d))
26.42/8.64	   A^2 -> H(U1(e, a), U1(c, c))
26.42/8.64	   A^2 -> H(U1(e, a), f(e))
26.42/8.64	   A^2 -> H(U1(e, a), f(k))
26.42/8.64	   A^2 -> H(U1(e, a), U1(d, d))
26.42/8.64	   A^2 -> H(U1(k, a), U1(c, b))
26.42/8.64	   A^2 -> H(U1(k, a), U1(d, b))
26.42/8.64	   A^2 -> H(U1(k, a), U1(b, c))
26.42/8.64	   A^2 -> H(U1(k, a), U1(b, d))
26.42/8.64	   A^2 -> H(U1(k, a), U1(c, c))
26.42/8.64	   A^2 -> H(U1(k, a), f(e))
26.42/8.64	   A^2 -> H(U1(k, a), f(k))
26.42/8.64	   A^2 -> H(U1(k, a), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, d), U1(c, b))
26.42/8.64	   A^2 -> H(U1(c, d), U1(d, b))
26.42/8.64	   A^2 -> H(U1(c, d), U1(b, c))
26.42/8.64	   A^2 -> H(U1(c, d), U1(b, d))
26.42/8.64	   A^2 -> H(U1(c, d), U1(c, c))
26.42/8.64	   A^2 -> H(U1(c, d), f(e))
26.42/8.64	   A^2 -> H(U1(c, d), f(k))
26.42/8.64	   A^2 -> H(U1(c, d), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, a), U1(e, b))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, b))
26.42/8.64	   A^2 -> H(U1(c, a), U1(c, d))
26.42/8.64	   A^2 -> H(U1(c, a), U1(d, c))
26.42/8.64	   A^2 -> H(U1(c, a), U1(b, e))
26.42/8.64	   A^2 -> H(U1(c, a), U1(b, k))
26.42/8.64	   A^2 -> H(U1(c, a), U1(e, c))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, c))
26.42/8.64	   A^2 -> H(U1(c, a), U1(c, e))
26.42/8.64	   A^2 -> H(U1(c, a), U1(c, k))
26.42/8.64	   A^2 -> H(U1(c, a), U1(e, e))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, k))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, d))
26.42/8.64	   A^2 -> H(U1(c, a), U1(d, k))
26.42/8.64	   A^2 -> H(U1(d, e), U1(b, b))
26.42/8.64	   A^2 -> H(U1(d, e), f(c))
26.42/8.64	   A^2 -> H(U1(d, e), f(d))
26.42/8.64	   A^2 -> H(U1(d, c), U1(c, b))
26.42/8.64	   A^2 -> H(U1(d, c), U1(d, b))
26.42/8.64	   A^2 -> H(U1(d, c), U1(b, c))
26.42/8.64	   A^2 -> H(U1(d, c), U1(b, d))
26.42/8.64	   A^2 -> H(U1(d, c), U1(c, c))
26.42/8.64	   A^2 -> H(U1(d, c), f(e))
26.42/8.64	   A^2 -> H(U1(d, c), f(k))
26.42/8.64	   A^2 -> H(U1(d, c), U1(d, d))
26.42/8.64	   A^2 -> H(U1(d, a), U1(e, b))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, b))
26.42/8.64	   A^2 -> H(U1(d, a), U1(c, d))
26.42/8.64	   A^2 -> H(U1(d, a), U1(d, c))
26.42/8.64	   A^2 -> H(U1(d, a), U1(b, e))
26.42/8.64	   A^2 -> H(U1(d, a), U1(b, k))
26.42/8.64	   A^2 -> H(U1(d, a), U1(e, c))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, c))
26.42/8.64	   A^2 -> H(U1(d, a), U1(c, e))
26.42/8.64	   A^2 -> H(U1(d, a), U1(c, k))
26.42/8.64	   A^2 -> H(U1(d, a), U1(e, e))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, k))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, d))
26.42/8.64	   A^2 -> H(U1(d, a), U1(d, k))
26.42/8.64	   A^2 -> H(U1(a, e), U1(c, b))
26.42/8.64	   A^2 -> H(U1(a, e), U1(d, b))
26.42/8.64	   A^2 -> H(U1(a, e), U1(b, c))
26.42/8.64	   A^2 -> H(U1(a, e), U1(b, d))
26.42/8.64	   A^2 -> H(U1(a, e), U1(c, c))
26.42/8.64	   A^2 -> H(U1(a, e), f(e))
26.42/8.64	   A^2 -> H(U1(a, e), f(k))
26.42/8.64	   A^2 -> H(U1(a, e), U1(d, d))
26.42/8.64	   A^2 -> H(U1(a, k), U1(c, b))
26.42/8.64	   A^2 -> H(U1(a, k), U1(d, b))
26.42/8.64	   A^2 -> H(U1(a, k), U1(b, c))
26.42/8.64	   A^2 -> H(U1(a, k), U1(b, d))
26.42/8.64	   A^2 -> H(U1(a, k), U1(c, c))
26.42/8.64	   A^2 -> H(U1(a, k), f(e))
26.42/8.64	   A^2 -> H(U1(a, k), f(k))
26.42/8.64	   A^2 -> H(U1(a, k), U1(d, d))
26.42/8.64	   A^2 -> H(U1(a, c), U1(e, b))
26.42/8.64	   A^2 -> H(U1(a, c), U1(k, b))
26.42/8.64	   A^2 -> H(U1(a, c), U1(c, d))
26.42/8.64	   A^2 -> H(U1(a, c), U1(d, c))
26.42/8.64	   A^2 -> H(U1(a, c), U1(b, e))
26.42/8.64	   A^2 -> H(U1(a, c), U1(b, k))
26.42/8.64	   A^2 -> H(U1(a, c), U1(e, c))
26.42/8.64	   A^2 -> H(U1(a, c), U1(k, c))
26.42/8.64	   A^2 -> H(U1(a, c), U1(c, e))
26.42/8.64	   A^2 -> H(U1(a, c), U1(c, k))
26.42/8.64	   A^2 -> H(U1(a, c), U1(e, e))
26.42/8.64	   A^2 -> H(U1(a, c), U1(k, k))
26.42/8.64	   A^2 -> H(U1(a, c), U1(k, d))
26.42/8.64	   A^2 -> H(U1(a, c), U1(d, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(e, b))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, b))
26.42/8.64	   A^2 -> H(U1(a, d), U1(c, d))
26.42/8.64	   A^2 -> H(U1(a, d), U1(d, c))
26.42/8.64	   A^2 -> H(U1(a, d), U1(b, e))
26.42/8.64	   A^2 -> H(U1(a, d), U1(b, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(e, c))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, c))
26.42/8.64	   A^2 -> H(U1(a, d), U1(c, e))
26.42/8.64	   A^2 -> H(U1(a, d), U1(c, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(e, e))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, k))
26.42/8.64	   A^2 -> H(U1(a, d), U1(k, d))
26.42/8.64	   A^2 -> H(U1(a, d), U1(d, k))
26.42/8.64	   A^2 -> H(U1(a, a), b)
26.42/8.64	   A^2 -> H(U1(a, a), U1(e, d))
26.42/8.64	   A^2 -> H(U1(a, a), U1(d, e))
26.42/8.64	   A^2 -> H(U1(a, a), c)
26.42/8.64	   A^2 -> H(U1(a, a), U1(e, k))
26.42/8.64	   A^2 -> H(U1(a, a), U1(k, e))
26.42/8.64	   A^2 -> H(U1(a, a), e)
26.42/8.64	   A^2 -> H(U1(a, a), U1(k, k))
26.42/8.64	   A^2 -> H(k, f(b))
26.42/8.64	   A^2 -> H(c, U1(b, b))
26.42/8.64	   A^2 -> H(c, f(c))
26.42/8.64	   A^2 -> H(c, f(d))
26.42/8.64	   A^2 -> H(U1(e, k), U1(b, b))
26.42/8.64	   A^2 -> H(U1(e, k), f(c))
26.42/8.64	   A^2 -> H(U1(e, k), f(d))
26.42/8.64	   A^2 -> H(U1(e, c), U1(c, b))
26.42/8.64	   A^2 -> H(U1(e, c), U1(d, b))
26.42/8.64	   A^2 -> H(U1(e, c), U1(b, c))
26.42/8.64	   A^2 -> H(U1(e, c), U1(b, d))
26.42/8.64	   A^2 -> H(U1(e, c), U1(c, c))
26.42/8.64	   A^2 -> H(U1(e, c), f(e))
26.42/8.64	   A^2 -> H(U1(e, c), f(k))
26.42/8.64	   A^2 -> H(U1(e, c), U1(d, d))
26.42/8.64	   A^2 -> H(U1(k, e), U1(b, b))
26.42/8.64	   A^2 -> H(U1(k, e), f(c))
26.42/8.64	   A^2 -> H(U1(k, e), f(d))
26.42/8.64	   A^2 -> H(U1(k, c), U1(c, b))
26.42/8.64	   A^2 -> H(U1(k, c), U1(d, b))
26.42/8.64	   A^2 -> H(U1(k, c), U1(b, c))
26.42/8.64	   A^2 -> H(U1(k, c), U1(b, d))
26.42/8.64	   A^2 -> H(U1(k, c), U1(c, c))
26.42/8.64	   A^2 -> H(U1(k, c), f(e))
26.42/8.64	   A^2 -> H(U1(k, c), f(k))
26.42/8.64	   A^2 -> H(U1(k, c), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, e), U1(c, b))
26.42/8.64	   A^2 -> H(U1(c, e), U1(d, b))
26.42/8.64	   A^2 -> H(U1(c, e), U1(b, c))
26.42/8.64	   A^2 -> H(U1(c, e), U1(b, d))
26.42/8.64	   A^2 -> H(U1(c, e), U1(c, c))
26.42/8.64	   A^2 -> H(U1(c, e), f(e))
26.42/8.64	   A^2 -> H(U1(c, e), f(k))
26.42/8.64	   A^2 -> H(U1(c, e), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, k), U1(c, b))
26.42/8.64	   A^2 -> H(U1(c, k), U1(d, b))
26.42/8.64	   A^2 -> H(U1(c, k), U1(b, c))
26.42/8.64	   A^2 -> H(U1(c, k), U1(b, d))
26.42/8.64	   A^2 -> H(U1(c, k), U1(c, c))
26.42/8.64	   A^2 -> H(U1(c, k), f(e))
26.42/8.64	   A^2 -> H(U1(c, k), f(k))
26.42/8.64	   A^2 -> H(U1(c, k), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(e, b))
26.42/8.64	   A^2 -> H(U1(c, c), U1(k, b))
26.42/8.64	   A^2 -> H(U1(c, c), U1(c, d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(d, c))
26.42/8.64	   A^2 -> H(U1(c, c), U1(b, e))
26.42/8.64	   A^2 -> H(U1(c, c), U1(b, k))
26.42/8.64	   A^2 -> H(U1(c, c), U1(e, e))
26.42/8.64	   A^2 -> H(U1(c, c), U1(k, k))
26.42/8.64	   A^2 -> H(U1(c, c), U1(k, d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(d, k))
26.42/8.64	   A^2 -> H(e, U1(b, b))
26.42/8.64	   A^2 -> H(e, f(c))
26.42/8.64	   A^2 -> H(e, f(d))
26.42/8.64	   A^2 -> H(U1(e, e), U1(c, b))
26.42/8.64	   A^2 -> H(U1(e, e), U1(d, b))
26.42/8.64	   A^2 -> H(U1(e, e), U1(b, c))
26.42/8.64	   A^2 -> H(U1(e, e), U1(b, d))
26.42/8.64	   A^2 -> H(U1(e, e), U1(c, c))
26.42/8.64	   A^2 -> H(U1(e, e), f(e))
26.42/8.64	   A^2 -> H(U1(e, e), f(k))
26.42/8.64	   A^2 -> H(U1(e, e), U1(d, d))
26.42/8.64	   A^2 -> H(f(e), U1(e, b))
26.42/8.64	   A^2 -> H(f(e), U1(k, b))
26.42/8.64	   A^2 -> H(f(e), U1(c, d))
26.42/8.64	   A^2 -> H(f(e), U1(d, c))
26.42/8.64	   A^2 -> H(f(e), U1(b, e))
26.42/8.64	   A^2 -> H(f(e), U1(b, k))
26.42/8.64	   A^2 -> H(f(e), U1(e, c))
26.42/8.64	   A^2 -> H(f(e), U1(k, c))
26.42/8.64	   A^2 -> H(f(e), U1(c, e))
26.42/8.64	   A^2 -> H(f(e), U1(c, k))
26.42/8.64	   A^2 -> H(f(e), U1(k, k))
26.42/8.64	   A^2 -> H(f(e), U1(k, d))
26.42/8.64	   A^2 -> H(f(e), U1(d, k))
26.42/8.64	   A^2 -> H(U1(k, k), U1(c, b))
26.42/8.64	   A^2 -> H(U1(k, k), U1(d, b))
26.42/8.64	   A^2 -> H(U1(k, k), U1(b, c))
26.42/8.64	   A^2 -> H(U1(k, k), U1(b, d))
26.42/8.64	   A^2 -> H(U1(k, k), U1(c, c))
26.42/8.64	   A^2 -> H(U1(k, k), f(e))
26.42/8.64	   A^2 -> H(U1(k, k), f(k))
26.42/8.64	   A^2 -> H(U1(k, k), U1(d, d))
26.42/8.64	   A^2 -> H(f(k), U1(e, b))
26.42/8.64	   A^2 -> H(f(k), U1(k, b))
26.42/8.64	   A^2 -> H(f(k), U1(c, d))
26.42/8.64	   A^2 -> H(f(k), U1(d, c))
26.42/8.64	   A^2 -> H(f(k), U1(b, e))
26.42/8.64	   A^2 -> H(f(k), U1(b, k))
26.42/8.64	   A^2 -> H(f(k), U1(e, c))
26.42/8.64	   A^2 -> H(f(k), U1(k, c))
26.42/8.64	   A^2 -> H(f(k), U1(c, e))
26.42/8.64	   A^2 -> H(f(k), U1(c, k))
26.42/8.64	   A^2 -> H(f(k), U1(e, e))
26.42/8.64	   A^2 -> H(f(k), U1(k, d))
26.42/8.64	   A^2 -> H(f(k), U1(d, k))
26.42/8.64	   A^2 -> H(f(c), b)
26.42/8.64	   A^2 -> H(f(c), U1(e, d))
26.42/8.64	   A^2 -> H(f(c), U1(d, e))
26.42/8.64	   A^2 -> H(f(k), U1(k, k))
26.42/8.64	   A^2 -> H(U1(k, k), U1(b, b))
26.42/8.64	   A^2 -> H(U1(k, k), f(c))
26.42/8.64	   A^2 -> H(U1(k, k), f(d))
26.42/8.64	   A^2 -> H(U1(k, d), U1(c, b))
26.42/8.64	   A^2 -> H(U1(k, d), U1(d, b))
26.42/8.64	   A^2 -> H(U1(k, d), U1(b, c))
26.42/8.64	   A^2 -> H(U1(k, d), U1(b, d))
26.42/8.64	
26.42/8.64	The TRS R consists of the following rules:
26.42/8.64	
26.42/8.64	   f(x) -> U1(x, x)
26.42/8.64	   U1(e, x) -> x
26.42/8.64	   a -> c
26.42/8.64	   a -> d
26.42/8.64	   b -> c
26.42/8.64	   b -> d
26.42/8.64	   d -> k
26.42/8.64	   c -> e
26.42/8.64	   c -> k
26.42/8.64	
26.42/8.64	Q is empty.
26.42/8.64	We have to consider all minimal (P,Q,R)-chains.
26.42/8.64	----------------------------------------
26.42/8.64	
26.42/8.64	(463) TransformationProof (EQUIVALENT)
26.42/8.64	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), f(c)) at position [] we obtained the following new rules [LPAR04]:
26.42/8.64	
26.42/8.64	   (A^2 -> H(U1(k, k), f(c)),A^2 -> H(U1(k, k), f(c)))
26.42/8.64	   (A^2 -> H(U1(k, d), U1(c, c)),A^2 -> H(U1(k, d), U1(c, c)))
26.42/8.64	   (A^2 -> H(U1(k, d), f(e)),A^2 -> H(U1(k, d), f(e)))
26.42/8.64	   (A^2 -> H(U1(k, d), f(k)),A^2 -> H(U1(k, d), f(k)))
26.42/8.64	
26.42/8.64	
26.42/8.64	----------------------------------------
26.42/8.64	
26.42/8.64	(464)
26.42/8.64	Obligation:
26.42/8.64	Q DP problem:
26.42/8.64	The TRS P consists of the following rules:
26.42/8.64	
26.42/8.64	   H(x, x) -> G(x, x, f(k))
26.42/8.64	   G(d, x, x) -> A^2
26.42/8.64	   A^2 -> H(f(c), f(c))
26.42/8.64	   A^2 -> H(f(d), f(d))
26.42/8.64	   A^2 -> H(U1(c, c), U1(c, c))
26.42/8.64	   A^2 -> H(f(e), f(e))
26.42/8.64	   A^2 -> H(f(k), f(k))
26.42/8.64	   A^2 -> H(U1(k, d), f(d))
26.42/8.64	   A^2 -> H(U1(d, k), U1(b, b))
26.42/8.64	   A^2 -> H(U1(d, k), f(c))
26.42/8.64	   A^2 -> H(U1(d, k), f(d))
26.42/8.64	   A^2 -> H(U1(d, d), U1(c, b))
26.42/8.64	   A^2 -> H(U1(d, d), U1(d, b))
26.42/8.64	   A^2 -> H(U1(d, d), U1(b, c))
26.42/8.64	   A^2 -> H(U1(d, d), U1(b, d))
26.42/8.64	   A^2 -> H(U1(d, d), U1(c, c))
26.42/8.64	   A^2 -> H(U1(d, d), f(e))
26.42/8.64	   A^2 -> H(U1(d, d), f(k))
26.42/8.64	   A^2 -> H(U1(d, d), U1(d, d))
26.42/8.64	   A^2 -> H(f(d), U1(e, b))
26.42/8.64	   A^2 -> H(f(d), U1(k, b))
26.42/8.64	   A^2 -> H(f(d), U1(c, d))
26.42/8.64	   A^2 -> H(f(d), U1(d, c))
26.42/8.64	   A^2 -> H(f(d), U1(b, e))
26.42/8.64	   A^2 -> H(f(d), U1(b, k))
26.42/8.64	   A^2 -> H(f(d), U1(e, c))
26.42/8.64	   A^2 -> H(f(d), U1(k, c))
26.42/8.64	   A^2 -> H(f(d), U1(c, e))
26.42/8.64	   A^2 -> H(f(d), U1(c, k))
26.42/8.64	   A^2 -> H(f(d), U1(e, e))
26.42/8.64	   A^2 -> H(f(d), U1(k, k))
26.42/8.64	   A^2 -> H(f(a), b)
26.42/8.64	   A^2 -> H(f(a), U1(e, d))
26.42/8.64	   A^2 -> H(f(a), U1(d, e))
26.42/8.64	   A^2 -> H(f(c), U1(e, c))
26.42/8.64	   A^2 -> H(f(c), U1(k, c))
26.42/8.64	   A^2 -> H(f(c), U1(c, e))
26.42/8.64	   A^2 -> H(f(c), U1(c, k))
26.42/8.64	   A^2 -> H(f(a), c)
26.42/8.64	   A^2 -> H(f(a), U1(e, k))
26.42/8.64	   A^2 -> H(f(a), U1(k, e))
26.42/8.64	   A^2 -> H(f(c), U1(e, e))
26.42/8.64	   A^2 -> H(f(a), e)
26.42/8.64	   A^2 -> H(f(d), U1(k, d))
26.42/8.64	   A^2 -> H(f(d), U1(d, k))
26.42/8.64	   A^2 -> H(f(a), U1(k, k))
26.42/8.64	   A^2 -> H(d, f(b))
26.42/8.64	   A^2 -> H(a, U1(b, b))
26.42/8.64	   A^2 -> H(a, f(c))
26.42/8.64	   A^2 -> H(a, f(d))
26.42/8.64	   A^2 -> H(U1(e, d), U1(b, b))
26.42/8.64	   A^2 -> H(U1(e, d), f(c))
26.42/8.64	   A^2 -> H(U1(e, d), f(d))
26.42/8.64	   A^2 -> H(U1(e, a), U1(c, b))
26.42/8.64	   A^2 -> H(U1(e, a), U1(d, b))
26.42/8.64	   A^2 -> H(U1(e, a), U1(b, c))
26.42/8.64	   A^2 -> H(U1(e, a), U1(b, d))
26.42/8.64	   A^2 -> H(U1(e, a), U1(c, c))
26.42/8.64	   A^2 -> H(U1(e, a), f(e))
26.42/8.64	   A^2 -> H(U1(e, a), f(k))
26.42/8.64	   A^2 -> H(U1(e, a), U1(d, d))
26.42/8.64	   A^2 -> H(U1(k, a), U1(c, b))
26.42/8.64	   A^2 -> H(U1(k, a), U1(d, b))
26.42/8.64	   A^2 -> H(U1(k, a), U1(b, c))
26.42/8.64	   A^2 -> H(U1(k, a), U1(b, d))
26.42/8.64	   A^2 -> H(U1(k, a), U1(c, c))
26.42/8.64	   A^2 -> H(U1(k, a), f(e))
26.42/8.64	   A^2 -> H(U1(k, a), f(k))
26.42/8.64	   A^2 -> H(U1(k, a), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, d), U1(c, b))
26.42/8.64	   A^2 -> H(U1(c, d), U1(d, b))
26.42/8.64	   A^2 -> H(U1(c, d), U1(b, c))
26.42/8.64	   A^2 -> H(U1(c, d), U1(b, d))
26.42/8.64	   A^2 -> H(U1(c, d), U1(c, c))
26.42/8.64	   A^2 -> H(U1(c, d), f(e))
26.42/8.64	   A^2 -> H(U1(c, d), f(k))
26.42/8.64	   A^2 -> H(U1(c, d), U1(d, d))
26.42/8.64	   A^2 -> H(U1(c, a), U1(e, b))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, b))
26.42/8.64	   A^2 -> H(U1(c, a), U1(c, d))
26.42/8.64	   A^2 -> H(U1(c, a), U1(d, c))
26.42/8.64	   A^2 -> H(U1(c, a), U1(b, e))
26.42/8.64	   A^2 -> H(U1(c, a), U1(b, k))
26.42/8.64	   A^2 -> H(U1(c, a), U1(e, c))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, c))
26.42/8.64	   A^2 -> H(U1(c, a), U1(c, e))
26.42/8.64	   A^2 -> H(U1(c, a), U1(c, k))
26.42/8.64	   A^2 -> H(U1(c, a), U1(e, e))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, k))
26.42/8.64	   A^2 -> H(U1(c, a), U1(k, d))
26.42/8.64	   A^2 -> H(U1(c, a), U1(d, k))
26.42/8.64	   A^2 -> H(U1(d, e), U1(b, b))
26.42/8.64	   A^2 -> H(U1(d, e), f(c))
26.42/8.64	   A^2 -> H(U1(d, e), f(d))
26.42/8.64	   A^2 -> H(U1(d, c), U1(c, b))
26.42/8.64	   A^2 -> H(U1(d, c), U1(d, b))
26.42/8.64	   A^2 -> H(U1(d, c), U1(b, c))
26.42/8.64	   A^2 -> H(U1(d, c), U1(b, d))
26.42/8.64	   A^2 -> H(U1(d, c), U1(c, c))
26.42/8.64	   A^2 -> H(U1(d, c), f(e))
26.42/8.64	   A^2 -> H(U1(d, c), f(k))
26.42/8.64	   A^2 -> H(U1(d, c), U1(d, d))
26.42/8.64	   A^2 -> H(U1(d, a), U1(e, b))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, b))
26.42/8.64	   A^2 -> H(U1(d, a), U1(c, d))
26.42/8.64	   A^2 -> H(U1(d, a), U1(d, c))
26.42/8.64	   A^2 -> H(U1(d, a), U1(b, e))
26.42/8.64	   A^2 -> H(U1(d, a), U1(b, k))
26.42/8.64	   A^2 -> H(U1(d, a), U1(e, c))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, c))
26.42/8.64	   A^2 -> H(U1(d, a), U1(c, e))
26.42/8.64	   A^2 -> H(U1(d, a), U1(c, k))
26.42/8.64	   A^2 -> H(U1(d, a), U1(e, e))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, k))
26.42/8.64	   A^2 -> H(U1(d, a), U1(k, d))
26.42/8.64	   A^2 -> H(U1(d, a), U1(d, k))
26.42/8.64	   A^2 -> H(U1(a, e), U1(c, b))
26.42/8.64	   A^2 -> H(U1(a, e), U1(d, b))
26.42/8.64	   A^2 -> H(U1(a, e), U1(b, c))
26.42/8.64	   A^2 -> H(U1(a, e), U1(b, d))
26.42/8.64	   A^2 -> H(U1(a, e), U1(c, c))
26.42/8.64	   A^2 -> H(U1(a, e), f(e))
26.42/8.64	   A^2 -> H(U1(a, e), f(k))
26.42/8.64	   A^2 -> H(U1(a, e), U1(d, d))
26.42/8.64	   A^2 -> H(U1(a, k), U1(c, b))
26.42/8.64	   A^2 -> H(U1(a, k), U1(d, b))
26.42/8.64	   A^2 -> H(U1(a, k), U1(b, c))
26.42/8.64	   A^2 -> H(U1(a, k), U1(b, d))
26.42/8.64	   A^2 -> H(U1(a, k), U1(c, c))
26.42/8.64	   A^2 -> H(U1(a, k), f(e))
26.42/8.64	   A^2 -> H(U1(a, k), f(k))
26.42/8.64	   A^2 -> H(U1(a, k), U1(d, d))
26.42/8.65	   A^2 -> H(U1(a, c), U1(e, b))
26.42/8.65	   A^2 -> H(U1(a, c), U1(k, b))
26.42/8.65	   A^2 -> H(U1(a, c), U1(c, d))
26.42/8.65	   A^2 -> H(U1(a, c), U1(d, c))
26.42/8.65	   A^2 -> H(U1(a, c), U1(b, e))
26.42/8.65	   A^2 -> H(U1(a, c), U1(b, k))
26.42/8.65	   A^2 -> H(U1(a, c), U1(e, c))
26.42/8.65	   A^2 -> H(U1(a, c), U1(k, c))
26.42/8.65	   A^2 -> H(U1(a, c), U1(c, e))
26.42/8.65	   A^2 -> H(U1(a, c), U1(c, k))
26.42/8.65	   A^2 -> H(U1(a, c), U1(e, e))
26.42/8.65	   A^2 -> H(U1(a, c), U1(k, k))
26.42/8.65	   A^2 -> H(U1(a, c), U1(k, d))
26.42/8.65	   A^2 -> H(U1(a, c), U1(d, k))
26.42/8.65	   A^2 -> H(U1(a, d), U1(e, b))
26.42/8.65	   A^2 -> H(U1(a, d), U1(k, b))
26.42/8.65	   A^2 -> H(U1(a, d), U1(c, d))
26.42/8.65	   A^2 -> H(U1(a, d), U1(d, c))
26.42/8.65	   A^2 -> H(U1(a, d), U1(b, e))
26.42/8.65	   A^2 -> H(U1(a, d), U1(b, k))
26.42/8.65	   A^2 -> H(U1(a, d), U1(e, c))
26.42/8.65	   A^2 -> H(U1(a, d), U1(k, c))
26.42/8.65	   A^2 -> H(U1(a, d), U1(c, e))
26.42/8.65	   A^2 -> H(U1(a, d), U1(c, k))
26.42/8.65	   A^2 -> H(U1(a, d), U1(e, e))
26.42/8.65	   A^2 -> H(U1(a, d), U1(k, k))
26.42/8.65	   A^2 -> H(U1(a, d), U1(k, d))
26.42/8.65	   A^2 -> H(U1(a, d), U1(d, k))
26.42/8.65	   A^2 -> H(U1(a, a), b)
26.42/8.65	   A^2 -> H(U1(a, a), U1(e, d))
26.42/8.65	   A^2 -> H(U1(a, a), U1(d, e))
26.42/8.65	   A^2 -> H(U1(a, a), c)
26.42/8.65	   A^2 -> H(U1(a, a), U1(e, k))
26.42/8.65	   A^2 -> H(U1(a, a), U1(k, e))
26.42/8.65	   A^2 -> H(U1(a, a), e)
26.42/8.65	   A^2 -> H(U1(a, a), U1(k, k))
26.42/8.65	   A^2 -> H(k, f(b))
26.42/8.65	   A^2 -> H(c, U1(b, b))
26.42/8.65	   A^2 -> H(c, f(c))
26.42/8.65	   A^2 -> H(c, f(d))
26.42/8.65	   A^2 -> H(U1(e, k), U1(b, b))
26.42/8.65	   A^2 -> H(U1(e, k), f(c))
26.42/8.65	   A^2 -> H(U1(e, k), f(d))
26.42/8.65	   A^2 -> H(U1(e, c), U1(c, b))
26.42/8.65	   A^2 -> H(U1(e, c), U1(d, b))
26.42/8.65	   A^2 -> H(U1(e, c), U1(b, c))
26.42/8.65	   A^2 -> H(U1(e, c), U1(b, d))
26.42/8.65	   A^2 -> H(U1(e, c), U1(c, c))
26.42/8.65	   A^2 -> H(U1(e, c), f(e))
26.42/8.65	   A^2 -> H(U1(e, c), f(k))
26.42/8.65	   A^2 -> H(U1(e, c), U1(d, d))
26.42/8.65	   A^2 -> H(U1(k, e), U1(b, b))
26.42/8.65	   A^2 -> H(U1(k, e), f(c))
26.42/8.65	   A^2 -> H(U1(k, e), f(d))
26.42/8.65	   A^2 -> H(U1(k, c), U1(c, b))
26.42/8.65	   A^2 -> H(U1(k, c), U1(d, b))
26.42/8.65	   A^2 -> H(U1(k, c), U1(b, c))
26.42/8.65	   A^2 -> H(U1(k, c), U1(b, d))
26.42/8.65	   A^2 -> H(U1(k, c), U1(c, c))
26.42/8.65	   A^2 -> H(U1(k, c), f(e))
26.42/8.65	   A^2 -> H(U1(k, c), f(k))
26.42/8.65	   A^2 -> H(U1(k, c), U1(d, d))
26.42/8.65	   A^2 -> H(U1(c, e), U1(c, b))
26.42/8.65	   A^2 -> H(U1(c, e), U1(d, b))
26.42/8.65	   A^2 -> H(U1(c, e), U1(b, c))
26.42/8.65	   A^2 -> H(U1(c, e), U1(b, d))
26.42/8.65	   A^2 -> H(U1(c, e), U1(c, c))
26.42/8.65	   A^2 -> H(U1(c, e), f(e))
26.42/8.65	   A^2 -> H(U1(c, e), f(k))
26.42/8.65	   A^2 -> H(U1(c, e), U1(d, d))
26.42/8.65	   A^2 -> H(U1(c, k), U1(c, b))
26.42/8.65	   A^2 -> H(U1(c, k), U1(d, b))
26.42/8.65	   A^2 -> H(U1(c, k), U1(b, c))
26.42/8.65	   A^2 -> H(U1(c, k), U1(b, d))
26.42/8.65	   A^2 -> H(U1(c, k), U1(c, c))
26.42/8.65	   A^2 -> H(U1(c, k), f(e))
26.42/8.65	   A^2 -> H(U1(c, k), f(k))
26.42/8.65	   A^2 -> H(U1(c, k), U1(d, d))
26.42/8.65	   A^2 -> H(U1(c, c), U1(e, b))
26.42/8.65	   A^2 -> H(U1(c, c), U1(k, b))
26.42/8.65	   A^2 -> H(U1(c, c), U1(c, d))
26.42/8.65	   A^2 -> H(U1(c, c), U1(d, c))
26.42/8.65	   A^2 -> H(U1(c, c), U1(b, e))
26.42/8.65	   A^2 -> H(U1(c, c), U1(b, k))
26.42/8.65	   A^2 -> H(U1(c, c), U1(e, e))
26.42/8.65	   A^2 -> H(U1(c, c), U1(k, k))
26.42/8.65	   A^2 -> H(U1(c, c), U1(k, d))
26.42/8.65	   A^2 -> H(U1(c, c), U1(d, k))
26.42/8.65	   A^2 -> H(e, U1(b, b))
26.42/8.65	   A^2 -> H(e, f(c))
26.42/8.65	   A^2 -> H(e, f(d))
26.42/8.65	   A^2 -> H(U1(e, e), U1(c, b))
26.42/8.65	   A^2 -> H(U1(e, e), U1(d, b))
26.42/8.65	   A^2 -> H(U1(e, e), U1(b, c))
26.42/8.65	   A^2 -> H(U1(e, e), U1(b, d))
26.42/8.65	   A^2 -> H(U1(e, e), U1(c, c))
26.42/8.65	   A^2 -> H(U1(e, e), f(e))
26.42/8.65	   A^2 -> H(U1(e, e), f(k))
26.42/8.65	   A^2 -> H(U1(e, e), U1(d, d))
26.42/8.65	   A^2 -> H(f(e), U1(e, b))
26.42/8.65	   A^2 -> H(f(e), U1(k, b))
26.42/8.65	   A^2 -> H(f(e), U1(c, d))
26.42/8.65	   A^2 -> H(f(e), U1(d, c))
26.42/8.65	   A^2 -> H(f(e), U1(b, e))
26.42/8.65	   A^2 -> H(f(e), U1(b, k))
26.42/8.65	   A^2 -> H(f(e), U1(e, c))
26.42/8.65	   A^2 -> H(f(e), U1(k, c))
26.42/8.65	   A^2 -> H(f(e), U1(c, e))
26.42/8.65	   A^2 -> H(f(e), U1(c, k))
26.42/8.65	   A^2 -> H(f(e), U1(k, k))
26.42/8.65	   A^2 -> H(f(e), U1(k, d))
26.42/8.65	   A^2 -> H(f(e), U1(d, k))
26.42/8.65	   A^2 -> H(U1(k, k), U1(c, b))
26.42/8.65	   A^2 -> H(U1(k, k), U1(d, b))
26.42/8.65	   A^2 -> H(U1(k, k), U1(b, c))
26.42/8.65	   A^2 -> H(U1(k, k), U1(b, d))
26.42/8.65	   A^2 -> H(U1(k, k), U1(c, c))
26.42/8.65	   A^2 -> H(U1(k, k), f(e))
26.42/8.65	   A^2 -> H(U1(k, k), f(k))
26.42/8.65	   A^2 -> H(U1(k, k), U1(d, d))
26.42/8.65	   A^2 -> H(f(k), U1(e, b))
26.42/8.65	   A^2 -> H(f(k), U1(k, b))
26.42/8.65	   A^2 -> H(f(k), U1(c, d))
26.42/8.65	   A^2 -> H(f(k), U1(d, c))
26.42/8.65	   A^2 -> H(f(k), U1(b, e))
26.42/8.65	   A^2 -> H(f(k), U1(b, k))
26.42/8.65	   A^2 -> H(f(k), U1(e, c))
26.42/8.65	   A^2 -> H(f(k), U1(k, c))
26.42/8.65	   A^2 -> H(f(k), U1(c, e))
26.42/8.65	   A^2 -> H(f(k), U1(c, k))
26.42/8.65	   A^2 -> H(f(k), U1(e, e))
26.42/8.65	   A^2 -> H(f(k), U1(k, d))
26.42/8.65	   A^2 -> H(f(k), U1(d, k))
26.42/8.65	   A^2 -> H(f(c), b)
26.42/8.65	   A^2 -> H(f(c), U1(e, d))
26.42/8.65	   A^2 -> H(f(c), U1(d, e))
26.42/8.65	   A^2 -> H(f(k), U1(k, k))
26.42/8.65	   A^2 -> H(U1(k, k), U1(b, b))
26.42/8.65	   A^2 -> H(U1(k, k), f(c))
26.42/8.65	   A^2 -> H(U1(k, k), f(d))
26.42/8.65	   A^2 -> H(U1(k, d), U1(c, b))
26.42/8.65	   A^2 -> H(U1(k, d), U1(d, b))
26.42/8.65	   A^2 -> H(U1(k, d), U1(b, c))
26.42/8.65	   A^2 -> H(U1(k, d), U1(b, d))
26.42/8.65	   A^2 -> H(U1(k, d), U1(c, c))
26.42/8.65	   A^2 -> H(U1(k, d), f(e))
26.42/8.65	   A^2 -> H(U1(k, d), f(k))
26.42/8.65	
26.42/8.65	The TRS R consists of the following rules:
26.42/8.65	
26.42/8.65	   f(x) -> U1(x, x)
26.42/8.65	   U1(e, x) -> x
26.42/8.65	   a -> c
26.42/8.65	   a -> d
26.42/8.65	   b -> c
26.42/8.65	   b -> d
26.42/8.65	   d -> k
26.42/8.65	   c -> e
26.42/8.65	   c -> k
26.42/8.65	
26.42/8.65	Q is empty.
26.42/8.65	We have to consider all minimal (P,Q,R)-chains.
26.42/8.65	----------------------------------------
26.42/8.65	
26.42/8.65	(465) TransformationProof (EQUIVALENT)
26.42/8.65	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), f(d)) at position [] we obtained the following new rules [LPAR04]:
26.42/8.65	
26.42/8.65	   (A^2 -> H(U1(k, k), f(d)),A^2 -> H(U1(k, k), f(d)))
26.42/8.65	   (A^2 -> H(U1(k, d), U1(d, d)),A^2 -> H(U1(k, d), U1(d, d)))
26.42/8.65	   (A^2 -> H(U1(k, d), f(k)),A^2 -> H(U1(k, d), f(k)))
26.42/8.65	
26.42/8.65	
26.42/8.65	----------------------------------------
26.42/8.65	
26.42/8.65	(466)
26.42/8.65	Obligation:
26.42/8.65	Q DP problem:
26.42/8.65	The TRS P consists of the following rules:
26.42/8.65	
26.42/8.65	   H(x, x) -> G(x, x, f(k))
26.42/8.65	   G(d, x, x) -> A^2
26.42/8.65	   A^2 -> H(f(c), f(c))
26.42/8.65	   A^2 -> H(f(d), f(d))
26.42/8.65	   A^2 -> H(U1(c, c), U1(c, c))
26.42/8.65	   A^2 -> H(f(e), f(e))
26.42/8.65	   A^2 -> H(f(k), f(k))
26.42/8.65	   A^2 -> H(U1(d, k), U1(b, b))
26.42/8.65	   A^2 -> H(U1(d, k), f(c))
26.42/8.65	   A^2 -> H(U1(d, k), f(d))
26.42/8.65	   A^2 -> H(U1(d, d), U1(c, b))
26.42/8.65	   A^2 -> H(U1(d, d), U1(d, b))
26.42/8.65	   A^2 -> H(U1(d, d), U1(b, c))
26.42/8.65	   A^2 -> H(U1(d, d), U1(b, d))
26.42/8.65	   A^2 -> H(U1(d, d), U1(c, c))
26.42/8.65	   A^2 -> H(U1(d, d), f(e))
26.42/8.65	   A^2 -> H(U1(d, d), f(k))
26.42/8.65	   A^2 -> H(U1(d, d), U1(d, d))
26.42/8.65	   A^2 -> H(f(d), U1(e, b))
26.42/8.65	   A^2 -> H(f(d), U1(k, b))
26.42/8.65	   A^2 -> H(f(d), U1(c, d))
26.42/8.65	   A^2 -> H(f(d), U1(d, c))
26.42/8.65	   A^2 -> H(f(d), U1(b, e))
26.42/8.65	   A^2 -> H(f(d), U1(b, k))
26.42/8.65	   A^2 -> H(f(d), U1(e, c))
26.42/8.65	   A^2 -> H(f(d), U1(k, c))
26.42/8.65	   A^2 -> H(f(d), U1(c, e))
26.42/8.65	   A^2 -> H(f(d), U1(c, k))
26.42/8.65	   A^2 -> H(f(d), U1(e, e))
26.42/8.65	   A^2 -> H(f(d), U1(k, k))
26.42/8.65	   A^2 -> H(f(a), b)
26.42/8.65	   A^2 -> H(f(a), U1(e, d))
26.42/8.65	   A^2 -> H(f(a), U1(d, e))
26.42/8.65	   A^2 -> H(f(c), U1(e, c))
26.42/8.65	   A^2 -> H(f(c), U1(k, c))
26.42/8.65	   A^2 -> H(f(c), U1(c, e))
26.42/8.65	   A^2 -> H(f(c), U1(c, k))
26.42/8.65	   A^2 -> H(f(a), c)
26.42/8.65	   A^2 -> H(f(a), U1(e, k))
26.42/8.65	   A^2 -> H(f(a), U1(k, e))
26.42/8.65	   A^2 -> H(f(c), U1(e, e))
26.42/8.65	   A^2 -> H(f(a), e)
26.42/8.65	   A^2 -> H(f(d), U1(k, d))
26.42/8.65	   A^2 -> H(f(d), U1(d, k))
26.42/8.65	   A^2 -> H(f(a), U1(k, k))
26.42/8.65	   A^2 -> H(d, f(b))
26.42/8.65	   A^2 -> H(a, U1(b, b))
26.42/8.65	   A^2 -> H(a, f(c))
26.42/8.65	   A^2 -> H(a, f(d))
26.42/8.65	   A^2 -> H(U1(e, d), U1(b, b))
26.42/8.65	   A^2 -> H(U1(e, d), f(c))
26.42/8.65	   A^2 -> H(U1(e, d), f(d))
26.42/8.65	   A^2 -> H(U1(e, a), U1(c, b))
26.42/8.65	   A^2 -> H(U1(e, a), U1(d, b))
26.42/8.65	   A^2 -> H(U1(e, a), U1(b, c))
26.42/8.65	   A^2 -> H(U1(e, a), U1(b, d))
26.42/8.65	   A^2 -> H(U1(e, a), U1(c, c))
26.42/8.65	   A^2 -> H(U1(e, a), f(e))
26.42/8.65	   A^2 -> H(U1(e, a), f(k))
26.42/8.65	   A^2 -> H(U1(e, a), U1(d, d))
26.42/8.65	   A^2 -> H(U1(k, a), U1(c, b))
26.42/8.65	   A^2 -> H(U1(k, a), U1(d, b))
26.42/8.65	   A^2 -> H(U1(k, a), U1(b, c))
26.42/8.65	   A^2 -> H(U1(k, a), U1(b, d))
26.42/8.65	   A^2 -> H(U1(k, a), U1(c, c))
26.42/8.65	   A^2 -> H(U1(k, a), f(e))
26.42/8.65	   A^2 -> H(U1(k, a), f(k))
26.42/8.65	   A^2 -> H(U1(k, a), U1(d, d))
26.42/8.65	   A^2 -> H(U1(c, d), U1(c, b))
26.42/8.65	   A^2 -> H(U1(c, d), U1(d, b))
26.42/8.65	   A^2 -> H(U1(c, d), U1(b, c))
26.42/8.65	   A^2 -> H(U1(c, d), U1(b, d))
26.42/8.65	   A^2 -> H(U1(c, d), U1(c, c))
26.42/8.65	   A^2 -> H(U1(c, d), f(e))
26.42/8.65	   A^2 -> H(U1(c, d), f(k))
26.42/8.65	   A^2 -> H(U1(c, d), U1(d, d))
26.42/8.65	   A^2 -> H(U1(c, a), U1(e, b))
26.42/8.65	   A^2 -> H(U1(c, a), U1(k, b))
26.42/8.65	   A^2 -> H(U1(c, a), U1(c, d))
26.42/8.65	   A^2 -> H(U1(c, a), U1(d, c))
26.42/8.65	   A^2 -> H(U1(c, a), U1(b, e))
26.42/8.65	   A^2 -> H(U1(c, a), U1(b, k))
26.42/8.65	   A^2 -> H(U1(c, a), U1(e, c))
26.42/8.65	   A^2 -> H(U1(c, a), U1(k, c))
26.42/8.65	   A^2 -> H(U1(c, a), U1(c, e))
26.42/8.65	   A^2 -> H(U1(c, a), U1(c, k))
26.42/8.65	   A^2 -> H(U1(c, a), U1(e, e))
26.42/8.65	   A^2 -> H(U1(c, a), U1(k, k))
26.42/8.65	   A^2 -> H(U1(c, a), U1(k, d))
26.42/8.65	   A^2 -> H(U1(c, a), U1(d, k))
26.42/8.65	   A^2 -> H(U1(d, e), U1(b, b))
26.42/8.65	   A^2 -> H(U1(d, e), f(c))
26.42/8.65	   A^2 -> H(U1(d, e), f(d))
26.42/8.65	   A^2 -> H(U1(d, c), U1(c, b))
26.42/8.65	   A^2 -> H(U1(d, c), U1(d, b))
26.42/8.65	   A^2 -> H(U1(d, c), U1(b, c))
26.42/8.65	   A^2 -> H(U1(d, c), U1(b, d))
26.42/8.65	   A^2 -> H(U1(d, c), U1(c, c))
26.42/8.65	   A^2 -> H(U1(d, c), f(e))
26.42/8.65	   A^2 -> H(U1(d, c), f(k))
26.42/8.65	   A^2 -> H(U1(d, c), U1(d, d))
26.42/8.65	   A^2 -> H(U1(d, a), U1(e, b))
26.42/8.65	   A^2 -> H(U1(d, a), U1(k, b))
26.42/8.65	   A^2 -> H(U1(d, a), U1(c, d))
26.42/8.65	   A^2 -> H(U1(d, a), U1(d, c))
26.42/8.65	   A^2 -> H(U1(d, a), U1(b, e))
26.42/8.65	   A^2 -> H(U1(d, a), U1(b, k))
26.42/8.65	   A^2 -> H(U1(d, a), U1(e, c))
26.42/8.65	   A^2 -> H(U1(d, a), U1(k, c))
26.42/8.65	   A^2 -> H(U1(d, a), U1(c, e))
26.42/8.65	   A^2 -> H(U1(d, a), U1(c, k))
26.42/8.65	   A^2 -> H(U1(d, a), U1(e, e))
26.42/8.65	   A^2 -> H(U1(d, a), U1(k, k))
26.42/8.65	   A^2 -> H(U1(d, a), U1(k, d))
26.42/8.65	   A^2 -> H(U1(d, a), U1(d, k))
26.42/8.65	   A^2 -> H(U1(a, e), U1(c, b))
26.42/8.65	   A^2 -> H(U1(a, e), U1(d, b))
26.42/8.65	   A^2 -> H(U1(a, e), U1(b, c))
26.42/8.65	   A^2 -> H(U1(a, e), U1(b, d))
26.42/8.65	   A^2 -> H(U1(a, e), U1(c, c))
26.42/8.65	   A^2 -> H(U1(a, e), f(e))
26.42/8.65	   A^2 -> H(U1(a, e), f(k))
26.42/8.65	   A^2 -> H(U1(a, e), U1(d, d))
26.42/8.65	   A^2 -> H(U1(a, k), U1(c, b))
26.42/8.65	   A^2 -> H(U1(a, k), U1(d, b))
26.42/8.65	   A^2 -> H(U1(a, k), U1(b, c))
26.42/8.65	   A^2 -> H(U1(a, k), U1(b, d))
26.42/8.65	   A^2 -> H(U1(a, k), U1(c, c))
26.42/8.65	   A^2 -> H(U1(a, k), f(e))
26.42/8.65	   A^2 -> H(U1(a, k), f(k))
26.42/8.65	   A^2 -> H(U1(a, k), U1(d, d))
26.42/8.65	   A^2 -> H(U1(a, c), U1(e, b))
26.42/8.65	   A^2 -> H(U1(a, c), U1(k, b))
26.42/8.65	   A^2 -> H(U1(a, c), U1(c, d))
26.42/8.65	   A^2 -> H(U1(a, c), U1(d, c))
26.42/8.65	   A^2 -> H(U1(a, c), U1(b, e))
26.42/8.65	   A^2 -> H(U1(a, c), U1(b, k))
26.42/8.65	   A^2 -> H(U1(a, c), U1(e, c))
26.42/8.65	   A^2 -> H(U1(a, c), U1(k, c))
26.42/8.65	   A^2 -> H(U1(a, c), U1(c, e))
26.42/8.65	   A^2 -> H(U1(a, c), U1(c, k))
26.42/8.65	   A^2 -> H(U1(a, c), U1(e, e))
26.42/8.65	   A^2 -> H(U1(a, c), U1(k, k))
26.42/8.65	   A^2 -> H(U1(a, c), U1(k, d))
26.42/8.65	   A^2 -> H(U1(a, c), U1(d, k))
26.42/8.65	   A^2 -> H(U1(a, d), U1(e, b))
26.42/8.65	   A^2 -> H(U1(a, d), U1(k, b))
26.42/8.65	   A^2 -> H(U1(a, d), U1(c, d))
26.42/8.65	   A^2 -> H(U1(a, d), U1(d, c))
26.42/8.65	   A^2 -> H(U1(a, d), U1(b, e))
26.42/8.65	   A^2 -> H(U1(a, d), U1(b, k))
26.42/8.65	   A^2 -> H(U1(a, d), U1(e, c))
26.42/8.65	   A^2 -> H(U1(a, d), U1(k, c))
26.42/8.65	   A^2 -> H(U1(a, d), U1(c, e))
26.42/8.65	   A^2 -> H(U1(a, d), U1(c, k))
26.42/8.65	   A^2 -> H(U1(a, d), U1(e, e))
26.42/8.65	   A^2 -> H(U1(a, d), U1(k, k))
26.42/8.65	   A^2 -> H(U1(a, d), U1(k, d))
26.42/8.65	   A^2 -> H(U1(a, d), U1(d, k))
26.42/8.65	   A^2 -> H(U1(a, a), b)
26.42/8.65	   A^2 -> H(U1(a, a), U1(e, d))
26.42/8.65	   A^2 -> H(U1(a, a), U1(d, e))
26.42/8.65	   A^2 -> H(U1(a, a), c)
26.42/8.65	   A^2 -> H(U1(a, a), U1(e, k))
26.42/8.65	   A^2 -> H(U1(a, a), U1(k, e))
26.42/8.65	   A^2 -> H(U1(a, a), e)
26.42/8.65	   A^2 -> H(U1(a, a), U1(k, k))
26.42/8.65	   A^2 -> H(k, f(b))
26.42/8.65	   A^2 -> H(c, U1(b, b))
26.42/8.65	   A^2 -> H(c, f(c))
26.42/8.65	   A^2 -> H(c, f(d))
26.42/8.65	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.66	   A^2 -> H(U1(e, k), f(c))
26.53/8.66	   A^2 -> H(U1(e, k), f(d))
26.53/8.66	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.66	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.66	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.66	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.66	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.66	   A^2 -> H(U1(e, c), f(e))
26.53/8.66	   A^2 -> H(U1(e, c), f(k))
26.53/8.66	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.66	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.66	   A^2 -> H(U1(k, e), f(c))
26.53/8.66	   A^2 -> H(U1(k, e), f(d))
26.53/8.66	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.66	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.66	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.66	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.66	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.66	   A^2 -> H(U1(k, c), f(e))
26.53/8.66	   A^2 -> H(U1(k, c), f(k))
26.53/8.66	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.66	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.66	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.66	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.66	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.66	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.66	   A^2 -> H(U1(c, e), f(e))
26.53/8.66	   A^2 -> H(U1(c, e), f(k))
26.53/8.66	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.66	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.66	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.66	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.66	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.66	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.66	   A^2 -> H(U1(c, k), f(e))
26.53/8.66	   A^2 -> H(U1(c, k), f(k))
26.53/8.66	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.66	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.66	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.66	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.66	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.66	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.66	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.66	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.66	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.66	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.66	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.66	   A^2 -> H(e, U1(b, b))
26.53/8.66	   A^2 -> H(e, f(c))
26.53/8.66	   A^2 -> H(e, f(d))
26.53/8.66	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.66	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.66	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.66	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.66	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.66	   A^2 -> H(U1(e, e), f(e))
26.53/8.66	   A^2 -> H(U1(e, e), f(k))
26.53/8.66	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.66	   A^2 -> H(f(e), U1(e, b))
26.53/8.66	   A^2 -> H(f(e), U1(k, b))
26.53/8.66	   A^2 -> H(f(e), U1(c, d))
26.53/8.66	   A^2 -> H(f(e), U1(d, c))
26.53/8.66	   A^2 -> H(f(e), U1(b, e))
26.53/8.66	   A^2 -> H(f(e), U1(b, k))
26.53/8.66	   A^2 -> H(f(e), U1(e, c))
26.53/8.66	   A^2 -> H(f(e), U1(k, c))
26.53/8.66	   A^2 -> H(f(e), U1(c, e))
26.53/8.66	   A^2 -> H(f(e), U1(c, k))
26.53/8.66	   A^2 -> H(f(e), U1(k, k))
26.53/8.66	   A^2 -> H(f(e), U1(k, d))
26.53/8.66	   A^2 -> H(f(e), U1(d, k))
26.53/8.66	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.66	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.66	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.66	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.66	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.66	   A^2 -> H(U1(k, k), f(e))
26.53/8.66	   A^2 -> H(U1(k, k), f(k))
26.53/8.66	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.66	   A^2 -> H(f(k), U1(e, b))
26.53/8.66	   A^2 -> H(f(k), U1(k, b))
26.53/8.66	   A^2 -> H(f(k), U1(c, d))
26.53/8.66	   A^2 -> H(f(k), U1(d, c))
26.53/8.66	   A^2 -> H(f(k), U1(b, e))
26.53/8.66	   A^2 -> H(f(k), U1(b, k))
26.53/8.66	   A^2 -> H(f(k), U1(e, c))
26.53/8.66	   A^2 -> H(f(k), U1(k, c))
26.53/8.66	   A^2 -> H(f(k), U1(c, e))
26.53/8.66	   A^2 -> H(f(k), U1(c, k))
26.53/8.66	   A^2 -> H(f(k), U1(e, e))
26.53/8.66	   A^2 -> H(f(k), U1(k, d))
26.53/8.66	   A^2 -> H(f(k), U1(d, k))
26.53/8.66	   A^2 -> H(f(c), b)
26.53/8.66	   A^2 -> H(f(c), U1(e, d))
26.53/8.66	   A^2 -> H(f(c), U1(d, e))
26.53/8.66	   A^2 -> H(f(k), U1(k, k))
26.53/8.66	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.66	   A^2 -> H(U1(k, k), f(c))
26.53/8.66	   A^2 -> H(U1(k, k), f(d))
26.53/8.66	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.66	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.66	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.66	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.66	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.66	   A^2 -> H(U1(k, d), f(e))
26.53/8.66	   A^2 -> H(U1(k, d), f(k))
26.53/8.66	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.66	
26.53/8.66	The TRS R consists of the following rules:
26.53/8.66	
26.53/8.66	   f(x) -> U1(x, x)
26.53/8.66	   U1(e, x) -> x
26.53/8.66	   a -> c
26.53/8.66	   a -> d
26.53/8.66	   b -> c
26.53/8.66	   b -> d
26.53/8.66	   d -> k
26.53/8.66	   c -> e
26.53/8.66	   c -> k
26.53/8.66	
26.53/8.66	Q is empty.
26.53/8.66	We have to consider all minimal (P,Q,R)-chains.
26.53/8.66	----------------------------------------
26.53/8.66	
26.53/8.66	(467) TransformationProof (EQUIVALENT)
26.53/8.66	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.66	
26.53/8.66	   (A^2 -> H(U1(k, k), U1(b, b)),A^2 -> H(U1(k, k), U1(b, b)))
26.53/8.66	   (A^2 -> H(U1(d, k), U1(c, b)),A^2 -> H(U1(d, k), U1(c, b)))
26.53/8.66	   (A^2 -> H(U1(d, k), U1(d, b)),A^2 -> H(U1(d, k), U1(d, b)))
26.53/8.66	   (A^2 -> H(U1(d, k), U1(b, c)),A^2 -> H(U1(d, k), U1(b, c)))
26.53/8.66	   (A^2 -> H(U1(d, k), U1(b, d)),A^2 -> H(U1(d, k), U1(b, d)))
26.53/8.66	
26.53/8.66	
26.53/8.66	----------------------------------------
26.53/8.66	
26.53/8.66	(468)
26.53/8.66	Obligation:
26.53/8.66	Q DP problem:
26.53/8.66	The TRS P consists of the following rules:
26.53/8.66	
26.53/8.66	   H(x, x) -> G(x, x, f(k))
26.53/8.66	   G(d, x, x) -> A^2
26.53/8.66	   A^2 -> H(f(c), f(c))
26.53/8.66	   A^2 -> H(f(d), f(d))
26.53/8.66	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.66	   A^2 -> H(f(e), f(e))
26.53/8.66	   A^2 -> H(f(k), f(k))
26.53/8.66	   A^2 -> H(U1(d, k), f(c))
26.53/8.66	   A^2 -> H(U1(d, k), f(d))
26.53/8.66	   A^2 -> H(U1(d, d), U1(c, b))
26.53/8.66	   A^2 -> H(U1(d, d), U1(d, b))
26.53/8.66	   A^2 -> H(U1(d, d), U1(b, c))
26.53/8.66	   A^2 -> H(U1(d, d), U1(b, d))
26.53/8.66	   A^2 -> H(U1(d, d), U1(c, c))
26.53/8.66	   A^2 -> H(U1(d, d), f(e))
26.53/8.66	   A^2 -> H(U1(d, d), f(k))
26.53/8.66	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.66	   A^2 -> H(f(d), U1(e, b))
26.53/8.66	   A^2 -> H(f(d), U1(k, b))
26.53/8.66	   A^2 -> H(f(d), U1(c, d))
26.53/8.66	   A^2 -> H(f(d), U1(d, c))
26.53/8.66	   A^2 -> H(f(d), U1(b, e))
26.53/8.66	   A^2 -> H(f(d), U1(b, k))
26.53/8.66	   A^2 -> H(f(d), U1(e, c))
26.53/8.66	   A^2 -> H(f(d), U1(k, c))
26.53/8.66	   A^2 -> H(f(d), U1(c, e))
26.53/8.66	   A^2 -> H(f(d), U1(c, k))
26.53/8.66	   A^2 -> H(f(d), U1(e, e))
26.53/8.66	   A^2 -> H(f(d), U1(k, k))
26.53/8.66	   A^2 -> H(f(a), b)
26.53/8.66	   A^2 -> H(f(a), U1(e, d))
26.53/8.66	   A^2 -> H(f(a), U1(d, e))
26.53/8.66	   A^2 -> H(f(c), U1(e, c))
26.53/8.66	   A^2 -> H(f(c), U1(k, c))
26.53/8.66	   A^2 -> H(f(c), U1(c, e))
26.53/8.66	   A^2 -> H(f(c), U1(c, k))
26.53/8.66	   A^2 -> H(f(a), c)
26.53/8.66	   A^2 -> H(f(a), U1(e, k))
26.53/8.66	   A^2 -> H(f(a), U1(k, e))
26.53/8.66	   A^2 -> H(f(c), U1(e, e))
26.53/8.66	   A^2 -> H(f(a), e)
26.53/8.66	   A^2 -> H(f(d), U1(k, d))
26.53/8.66	   A^2 -> H(f(d), U1(d, k))
26.53/8.66	   A^2 -> H(f(a), U1(k, k))
26.53/8.66	   A^2 -> H(d, f(b))
26.53/8.66	   A^2 -> H(a, U1(b, b))
26.53/8.66	   A^2 -> H(a, f(c))
26.53/8.66	   A^2 -> H(a, f(d))
26.53/8.66	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.66	   A^2 -> H(U1(e, d), f(c))
26.53/8.66	   A^2 -> H(U1(e, d), f(d))
26.53/8.66	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.66	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.66	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.66	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.66	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.66	   A^2 -> H(U1(e, a), f(e))
26.53/8.66	   A^2 -> H(U1(e, a), f(k))
26.53/8.66	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.66	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.66	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.66	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.66	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.66	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.66	   A^2 -> H(U1(k, a), f(e))
26.53/8.66	   A^2 -> H(U1(k, a), f(k))
26.53/8.66	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.66	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.66	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.66	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.66	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.66	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.66	   A^2 -> H(U1(c, d), f(e))
26.53/8.66	   A^2 -> H(U1(c, d), f(k))
26.53/8.66	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.66	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.66	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.66	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.66	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.66	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.66	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.66	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.66	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.66	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.66	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.66	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.66	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.66	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.66	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.66	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.66	   A^2 -> H(U1(d, e), f(c))
26.53/8.66	   A^2 -> H(U1(d, e), f(d))
26.53/8.66	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.66	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.66	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.66	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.66	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.66	   A^2 -> H(U1(d, c), f(e))
26.53/8.66	   A^2 -> H(U1(d, c), f(k))
26.53/8.66	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.66	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.66	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.66	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.66	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.66	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.66	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.66	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.66	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.66	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.66	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.66	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.66	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.66	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.66	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.66	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.66	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.66	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.66	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.66	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.66	   A^2 -> H(U1(a, e), f(e))
26.53/8.66	   A^2 -> H(U1(a, e), f(k))
26.53/8.66	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.66	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.66	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.66	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.66	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.66	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.66	   A^2 -> H(U1(a, k), f(e))
26.53/8.66	   A^2 -> H(U1(a, k), f(k))
26.53/8.66	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.66	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.66	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.66	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.66	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.66	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.66	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.66	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.66	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.66	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.66	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.66	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.66	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.66	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.66	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.66	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.66	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.66	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.66	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.66	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.66	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.66	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.66	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.66	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.66	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.66	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.66	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.66	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.66	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.66	   A^2 -> H(U1(a, a), b)
26.53/8.66	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.66	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.66	   A^2 -> H(U1(a, a), c)
26.53/8.66	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.66	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.66	   A^2 -> H(U1(a, a), e)
26.53/8.66	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.66	   A^2 -> H(k, f(b))
26.53/8.66	   A^2 -> H(c, U1(b, b))
26.53/8.66	   A^2 -> H(c, f(c))
26.53/8.66	   A^2 -> H(c, f(d))
26.53/8.66	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.66	   A^2 -> H(U1(e, k), f(c))
26.53/8.66	   A^2 -> H(U1(e, k), f(d))
26.53/8.66	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.66	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.66	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.66	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.66	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.66	   A^2 -> H(U1(e, c), f(e))
26.53/8.66	   A^2 -> H(U1(e, c), f(k))
26.53/8.66	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.66	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.66	   A^2 -> H(U1(k, e), f(c))
26.53/8.66	   A^2 -> H(U1(k, e), f(d))
26.53/8.66	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.66	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.66	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.66	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.66	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.66	   A^2 -> H(U1(k, c), f(e))
26.53/8.66	   A^2 -> H(U1(k, c), f(k))
26.53/8.66	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.66	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.66	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.66	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.66	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.66	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.66	   A^2 -> H(U1(c, e), f(e))
26.53/8.66	   A^2 -> H(U1(c, e), f(k))
26.53/8.66	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.66	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.66	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.66	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.66	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.66	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.66	   A^2 -> H(U1(c, k), f(e))
26.53/8.66	   A^2 -> H(U1(c, k), f(k))
26.53/8.66	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.66	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.66	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.66	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.66	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.66	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.66	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.66	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.66	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.66	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.66	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.66	   A^2 -> H(e, U1(b, b))
26.53/8.66	   A^2 -> H(e, f(c))
26.53/8.66	   A^2 -> H(e, f(d))
26.53/8.66	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.66	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.66	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.66	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.66	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.66	   A^2 -> H(U1(e, e), f(e))
26.53/8.66	   A^2 -> H(U1(e, e), f(k))
26.53/8.66	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.66	   A^2 -> H(f(e), U1(e, b))
26.53/8.66	   A^2 -> H(f(e), U1(k, b))
26.53/8.66	   A^2 -> H(f(e), U1(c, d))
26.53/8.66	   A^2 -> H(f(e), U1(d, c))
26.53/8.66	   A^2 -> H(f(e), U1(b, e))
26.53/8.66	   A^2 -> H(f(e), U1(b, k))
26.53/8.66	   A^2 -> H(f(e), U1(e, c))
26.53/8.66	   A^2 -> H(f(e), U1(k, c))
26.53/8.66	   A^2 -> H(f(e), U1(c, e))
26.53/8.66	   A^2 -> H(f(e), U1(c, k))
26.53/8.66	   A^2 -> H(f(e), U1(k, k))
26.53/8.66	   A^2 -> H(f(e), U1(k, d))
26.53/8.66	   A^2 -> H(f(e), U1(d, k))
26.53/8.66	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.66	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.66	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.66	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.66	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.66	   A^2 -> H(U1(k, k), f(e))
26.53/8.66	   A^2 -> H(U1(k, k), f(k))
26.53/8.66	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.66	   A^2 -> H(f(k), U1(e, b))
26.53/8.66	   A^2 -> H(f(k), U1(k, b))
26.53/8.66	   A^2 -> H(f(k), U1(c, d))
26.53/8.66	   A^2 -> H(f(k), U1(d, c))
26.53/8.66	   A^2 -> H(f(k), U1(b, e))
26.53/8.66	   A^2 -> H(f(k), U1(b, k))
26.53/8.66	   A^2 -> H(f(k), U1(e, c))
26.53/8.66	   A^2 -> H(f(k), U1(k, c))
26.53/8.66	   A^2 -> H(f(k), U1(c, e))
26.53/8.66	   A^2 -> H(f(k), U1(c, k))
26.53/8.66	   A^2 -> H(f(k), U1(e, e))
26.53/8.66	   A^2 -> H(f(k), U1(k, d))
26.53/8.66	   A^2 -> H(f(k), U1(d, k))
26.53/8.66	   A^2 -> H(f(c), b)
26.53/8.66	   A^2 -> H(f(c), U1(e, d))
26.53/8.66	   A^2 -> H(f(c), U1(d, e))
26.53/8.66	   A^2 -> H(f(k), U1(k, k))
26.53/8.66	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.66	   A^2 -> H(U1(k, k), f(c))
26.53/8.66	   A^2 -> H(U1(k, k), f(d))
26.53/8.66	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.66	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.66	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.66	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.66	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.66	   A^2 -> H(U1(k, d), f(e))
26.53/8.66	   A^2 -> H(U1(k, d), f(k))
26.53/8.66	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.66	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.66	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.66	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.66	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.66	
26.53/8.66	The TRS R consists of the following rules:
26.53/8.66	
26.53/8.66	   f(x) -> U1(x, x)
26.53/8.66	   U1(e, x) -> x
26.53/8.66	   a -> c
26.53/8.66	   a -> d
26.53/8.66	   b -> c
26.53/8.66	   b -> d
26.53/8.66	   d -> k
26.53/8.66	   c -> e
26.53/8.66	   c -> k
26.53/8.66	
26.53/8.66	Q is empty.
26.53/8.66	We have to consider all minimal (P,Q,R)-chains.
26.53/8.66	----------------------------------------
26.53/8.66	
26.53/8.66	(469) TransformationProof (EQUIVALENT)
26.53/8.66	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), f(c)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.66	
26.53/8.66	   (A^2 -> H(U1(k, k), f(c)),A^2 -> H(U1(k, k), f(c)))
26.53/8.66	   (A^2 -> H(U1(d, k), U1(c, c)),A^2 -> H(U1(d, k), U1(c, c)))
26.53/8.66	   (A^2 -> H(U1(d, k), f(e)),A^2 -> H(U1(d, k), f(e)))
26.53/8.66	   (A^2 -> H(U1(d, k), f(k)),A^2 -> H(U1(d, k), f(k)))
26.53/8.66	
26.53/8.66	
26.53/8.66	----------------------------------------
26.53/8.66	
26.53/8.66	(470)
26.53/8.66	Obligation:
26.53/8.66	Q DP problem:
26.53/8.66	The TRS P consists of the following rules:
26.53/8.66	
26.53/8.66	   H(x, x) -> G(x, x, f(k))
26.53/8.66	   G(d, x, x) -> A^2
26.53/8.66	   A^2 -> H(f(c), f(c))
26.53/8.66	   A^2 -> H(f(d), f(d))
26.53/8.66	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.66	   A^2 -> H(f(e), f(e))
26.53/8.66	   A^2 -> H(f(k), f(k))
26.53/8.66	   A^2 -> H(U1(d, k), f(d))
26.53/8.66	   A^2 -> H(U1(d, d), U1(c, b))
26.53/8.66	   A^2 -> H(U1(d, d), U1(d, b))
26.53/8.66	   A^2 -> H(U1(d, d), U1(b, c))
26.53/8.66	   A^2 -> H(U1(d, d), U1(b, d))
26.53/8.66	   A^2 -> H(U1(d, d), U1(c, c))
26.53/8.66	   A^2 -> H(U1(d, d), f(e))
26.53/8.66	   A^2 -> H(U1(d, d), f(k))
26.53/8.66	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.66	   A^2 -> H(f(d), U1(e, b))
26.53/8.66	   A^2 -> H(f(d), U1(k, b))
26.53/8.66	   A^2 -> H(f(d), U1(c, d))
26.53/8.66	   A^2 -> H(f(d), U1(d, c))
26.53/8.66	   A^2 -> H(f(d), U1(b, e))
26.53/8.66	   A^2 -> H(f(d), U1(b, k))
26.53/8.66	   A^2 -> H(f(d), U1(e, c))
26.53/8.66	   A^2 -> H(f(d), U1(k, c))
26.53/8.66	   A^2 -> H(f(d), U1(c, e))
26.53/8.66	   A^2 -> H(f(d), U1(c, k))
26.53/8.66	   A^2 -> H(f(d), U1(e, e))
26.53/8.66	   A^2 -> H(f(d), U1(k, k))
26.53/8.66	   A^2 -> H(f(a), b)
26.53/8.66	   A^2 -> H(f(a), U1(e, d))
26.53/8.66	   A^2 -> H(f(a), U1(d, e))
26.53/8.66	   A^2 -> H(f(c), U1(e, c))
26.53/8.66	   A^2 -> H(f(c), U1(k, c))
26.53/8.66	   A^2 -> H(f(c), U1(c, e))
26.53/8.66	   A^2 -> H(f(c), U1(c, k))
26.53/8.66	   A^2 -> H(f(a), c)
26.53/8.66	   A^2 -> H(f(a), U1(e, k))
26.53/8.66	   A^2 -> H(f(a), U1(k, e))
26.53/8.66	   A^2 -> H(f(c), U1(e, e))
26.53/8.66	   A^2 -> H(f(a), e)
26.53/8.66	   A^2 -> H(f(d), U1(k, d))
26.53/8.66	   A^2 -> H(f(d), U1(d, k))
26.53/8.66	   A^2 -> H(f(a), U1(k, k))
26.53/8.66	   A^2 -> H(d, f(b))
26.53/8.66	   A^2 -> H(a, U1(b, b))
26.53/8.66	   A^2 -> H(a, f(c))
26.53/8.66	   A^2 -> H(a, f(d))
26.53/8.66	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.66	   A^2 -> H(U1(e, d), f(c))
26.53/8.66	   A^2 -> H(U1(e, d), f(d))
26.53/8.66	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.66	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.66	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.66	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.66	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.66	   A^2 -> H(U1(e, a), f(e))
26.53/8.66	   A^2 -> H(U1(e, a), f(k))
26.53/8.66	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.66	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.66	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.66	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.66	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.66	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.66	   A^2 -> H(U1(k, a), f(e))
26.53/8.66	   A^2 -> H(U1(k, a), f(k))
26.53/8.66	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.66	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.66	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.66	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.66	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.66	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.66	   A^2 -> H(U1(c, d), f(e))
26.53/8.66	   A^2 -> H(U1(c, d), f(k))
26.53/8.66	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.66	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.66	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.66	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.66	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.66	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.66	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.66	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.66	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.66	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.66	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.66	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.66	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.66	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.66	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.66	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.66	   A^2 -> H(U1(d, e), f(c))
26.53/8.66	   A^2 -> H(U1(d, e), f(d))
26.53/8.66	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.66	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.66	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.66	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.66	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.66	   A^2 -> H(U1(d, c), f(e))
26.53/8.66	   A^2 -> H(U1(d, c), f(k))
26.53/8.66	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.66	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.66	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.66	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.66	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.66	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.66	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.66	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.66	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.66	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.66	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.66	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.66	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.66	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.66	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.66	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.66	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.66	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.66	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.66	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.66	   A^2 -> H(U1(a, e), f(e))
26.53/8.66	   A^2 -> H(U1(a, e), f(k))
26.53/8.66	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.66	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.66	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.66	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.66	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.66	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.66	   A^2 -> H(U1(a, k), f(e))
26.53/8.66	   A^2 -> H(U1(a, k), f(k))
26.53/8.66	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.66	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.66	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.66	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.66	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.66	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.66	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.66	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.66	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.66	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.66	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.66	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.66	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.66	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.66	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.66	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.66	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.66	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.66	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.66	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.66	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.66	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.66	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.66	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.66	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.66	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.66	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.66	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.66	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.66	   A^2 -> H(U1(a, a), b)
26.53/8.66	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.66	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.66	   A^2 -> H(U1(a, a), c)
26.53/8.66	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.66	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.66	   A^2 -> H(U1(a, a), e)
26.53/8.66	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.66	   A^2 -> H(k, f(b))
26.53/8.66	   A^2 -> H(c, U1(b, b))
26.53/8.66	   A^2 -> H(c, f(c))
26.53/8.66	   A^2 -> H(c, f(d))
26.53/8.66	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.66	   A^2 -> H(U1(e, k), f(c))
26.53/8.66	   A^2 -> H(U1(e, k), f(d))
26.53/8.66	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.66	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.66	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.66	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.66	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.66	   A^2 -> H(U1(e, c), f(e))
26.53/8.66	   A^2 -> H(U1(e, c), f(k))
26.53/8.66	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.66	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.66	   A^2 -> H(U1(k, e), f(c))
26.53/8.66	   A^2 -> H(U1(k, e), f(d))
26.53/8.66	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.66	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.66	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.66	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.66	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.66	   A^2 -> H(U1(k, c), f(e))
26.53/8.66	   A^2 -> H(U1(k, c), f(k))
26.53/8.66	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.66	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.66	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.66	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.66	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.66	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.66	   A^2 -> H(U1(c, e), f(e))
26.53/8.66	   A^2 -> H(U1(c, e), f(k))
26.53/8.66	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.66	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.66	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.66	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.66	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.66	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.66	   A^2 -> H(U1(c, k), f(e))
26.53/8.66	   A^2 -> H(U1(c, k), f(k))
26.53/8.66	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.66	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.66	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.66	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.66	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.66	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.66	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.66	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.66	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.66	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.66	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.66	   A^2 -> H(e, U1(b, b))
26.53/8.66	   A^2 -> H(e, f(c))
26.53/8.66	   A^2 -> H(e, f(d))
26.53/8.66	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.66	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.66	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.66	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.66	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.66	   A^2 -> H(U1(e, e), f(e))
26.53/8.66	   A^2 -> H(U1(e, e), f(k))
26.53/8.66	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.66	   A^2 -> H(f(e), U1(e, b))
26.53/8.66	   A^2 -> H(f(e), U1(k, b))
26.53/8.66	   A^2 -> H(f(e), U1(c, d))
26.53/8.66	   A^2 -> H(f(e), U1(d, c))
26.53/8.66	   A^2 -> H(f(e), U1(b, e))
26.53/8.66	   A^2 -> H(f(e), U1(b, k))
26.53/8.66	   A^2 -> H(f(e), U1(e, c))
26.53/8.66	   A^2 -> H(f(e), U1(k, c))
26.53/8.66	   A^2 -> H(f(e), U1(c, e))
26.53/8.66	   A^2 -> H(f(e), U1(c, k))
26.53/8.66	   A^2 -> H(f(e), U1(k, k))
26.53/8.66	   A^2 -> H(f(e), U1(k, d))
26.53/8.66	   A^2 -> H(f(e), U1(d, k))
26.53/8.66	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.66	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.66	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.66	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.66	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.66	   A^2 -> H(U1(k, k), f(e))
26.53/8.66	   A^2 -> H(U1(k, k), f(k))
26.53/8.66	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.66	   A^2 -> H(f(k), U1(e, b))
26.53/8.66	   A^2 -> H(f(k), U1(k, b))
26.53/8.66	   A^2 -> H(f(k), U1(c, d))
26.53/8.66	   A^2 -> H(f(k), U1(d, c))
26.53/8.66	   A^2 -> H(f(k), U1(b, e))
26.53/8.66	   A^2 -> H(f(k), U1(b, k))
26.53/8.66	   A^2 -> H(f(k), U1(e, c))
26.53/8.66	   A^2 -> H(f(k), U1(k, c))
26.53/8.66	   A^2 -> H(f(k), U1(c, e))
26.53/8.66	   A^2 -> H(f(k), U1(c, k))
26.53/8.66	   A^2 -> H(f(k), U1(e, e))
26.53/8.66	   A^2 -> H(f(k), U1(k, d))
26.53/8.66	   A^2 -> H(f(k), U1(d, k))
26.53/8.66	   A^2 -> H(f(c), b)
26.53/8.66	   A^2 -> H(f(c), U1(e, d))
26.53/8.66	   A^2 -> H(f(c), U1(d, e))
26.53/8.66	   A^2 -> H(f(k), U1(k, k))
26.53/8.66	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.66	   A^2 -> H(U1(k, k), f(c))
26.53/8.66	   A^2 -> H(U1(k, k), f(d))
26.53/8.66	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.66	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.66	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.66	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.66	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.66	   A^2 -> H(U1(k, d), f(e))
26.53/8.66	   A^2 -> H(U1(k, d), f(k))
26.53/8.66	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.66	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.66	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.66	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.66	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.66	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.66	   A^2 -> H(U1(d, k), f(e))
26.53/8.66	   A^2 -> H(U1(d, k), f(k))
26.53/8.66	
26.53/8.66	The TRS R consists of the following rules:
26.53/8.66	
26.53/8.66	   f(x) -> U1(x, x)
26.53/8.66	   U1(e, x) -> x
26.53/8.66	   a -> c
26.53/8.66	   a -> d
26.53/8.66	   b -> c
26.53/8.66	   b -> d
26.53/8.66	   d -> k
26.53/8.66	   c -> e
26.53/8.66	   c -> k
26.53/8.66	
26.53/8.66	Q is empty.
26.53/8.66	We have to consider all minimal (P,Q,R)-chains.
26.53/8.66	----------------------------------------
26.53/8.66	
26.53/8.66	(471) TransformationProof (EQUIVALENT)
26.53/8.66	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), f(d)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.66	
26.53/8.66	   (A^2 -> H(U1(k, k), f(d)),A^2 -> H(U1(k, k), f(d)))
26.53/8.66	   (A^2 -> H(U1(d, k), U1(d, d)),A^2 -> H(U1(d, k), U1(d, d)))
26.53/8.66	   (A^2 -> H(U1(d, k), f(k)),A^2 -> H(U1(d, k), f(k)))
26.53/8.66	
26.53/8.66	
26.53/8.66	----------------------------------------
26.53/8.66	
26.53/8.66	(472)
26.53/8.66	Obligation:
26.53/8.66	Q DP problem:
26.53/8.66	The TRS P consists of the following rules:
26.53/8.66	
26.53/8.66	   H(x, x) -> G(x, x, f(k))
26.53/8.66	   G(d, x, x) -> A^2
26.53/8.66	   A^2 -> H(f(c), f(c))
26.53/8.66	   A^2 -> H(f(d), f(d))
26.53/8.66	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.66	   A^2 -> H(f(e), f(e))
26.53/8.66	   A^2 -> H(f(k), f(k))
26.53/8.66	   A^2 -> H(U1(d, d), U1(c, b))
26.53/8.66	   A^2 -> H(U1(d, d), U1(d, b))
26.53/8.66	   A^2 -> H(U1(d, d), U1(b, c))
26.53/8.66	   A^2 -> H(U1(d, d), U1(b, d))
26.53/8.66	   A^2 -> H(U1(d, d), U1(c, c))
26.53/8.66	   A^2 -> H(U1(d, d), f(e))
26.53/8.66	   A^2 -> H(U1(d, d), f(k))
26.53/8.66	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.66	   A^2 -> H(f(d), U1(e, b))
26.53/8.66	   A^2 -> H(f(d), U1(k, b))
26.53/8.66	   A^2 -> H(f(d), U1(c, d))
26.53/8.66	   A^2 -> H(f(d), U1(d, c))
26.53/8.66	   A^2 -> H(f(d), U1(b, e))
26.53/8.66	   A^2 -> H(f(d), U1(b, k))
26.53/8.66	   A^2 -> H(f(d), U1(e, c))
26.53/8.66	   A^2 -> H(f(d), U1(k, c))
26.53/8.66	   A^2 -> H(f(d), U1(c, e))
26.53/8.66	   A^2 -> H(f(d), U1(c, k))
26.53/8.66	   A^2 -> H(f(d), U1(e, e))
26.53/8.66	   A^2 -> H(f(d), U1(k, k))
26.53/8.66	   A^2 -> H(f(a), b)
26.53/8.66	   A^2 -> H(f(a), U1(e, d))
26.53/8.66	   A^2 -> H(f(a), U1(d, e))
26.53/8.66	   A^2 -> H(f(c), U1(e, c))
26.53/8.66	   A^2 -> H(f(c), U1(k, c))
26.53/8.66	   A^2 -> H(f(c), U1(c, e))
26.53/8.66	   A^2 -> H(f(c), U1(c, k))
26.53/8.66	   A^2 -> H(f(a), c)
26.53/8.66	   A^2 -> H(f(a), U1(e, k))
26.53/8.66	   A^2 -> H(f(a), U1(k, e))
26.53/8.66	   A^2 -> H(f(c), U1(e, e))
26.53/8.66	   A^2 -> H(f(a), e)
26.53/8.66	   A^2 -> H(f(d), U1(k, d))
26.53/8.66	   A^2 -> H(f(d), U1(d, k))
26.53/8.66	   A^2 -> H(f(a), U1(k, k))
26.53/8.66	   A^2 -> H(d, f(b))
26.53/8.66	   A^2 -> H(a, U1(b, b))
26.53/8.66	   A^2 -> H(a, f(c))
26.53/8.66	   A^2 -> H(a, f(d))
26.53/8.66	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.66	   A^2 -> H(U1(e, d), f(c))
26.53/8.66	   A^2 -> H(U1(e, d), f(d))
26.53/8.66	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.66	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.66	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.66	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.66	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.66	   A^2 -> H(U1(e, a), f(e))
26.53/8.66	   A^2 -> H(U1(e, a), f(k))
26.53/8.66	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.66	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.66	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.66	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.66	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.66	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.66	   A^2 -> H(U1(k, a), f(e))
26.53/8.66	   A^2 -> H(U1(k, a), f(k))
26.53/8.66	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.66	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.66	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.66	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.66	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.66	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.66	   A^2 -> H(U1(c, d), f(e))
26.53/8.66	   A^2 -> H(U1(c, d), f(k))
26.53/8.66	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.66	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.66	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.66	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.66	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.66	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.66	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.66	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.66	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.66	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.66	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.66	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.66	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.66	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.66	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.66	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.66	   A^2 -> H(U1(d, e), f(c))
26.53/8.66	   A^2 -> H(U1(d, e), f(d))
26.53/8.66	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.66	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.66	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.66	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.66	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.66	   A^2 -> H(U1(d, c), f(e))
26.53/8.66	   A^2 -> H(U1(d, c), f(k))
26.53/8.66	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.66	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.66	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.66	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.66	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.66	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.66	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.66	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.66	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.66	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.66	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.66	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.66	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.66	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.66	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.66	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.66	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.66	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.66	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.66	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.66	   A^2 -> H(U1(a, e), f(e))
26.53/8.66	   A^2 -> H(U1(a, e), f(k))
26.53/8.66	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.66	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.66	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.66	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.66	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.66	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.66	   A^2 -> H(U1(a, k), f(e))
26.53/8.66	   A^2 -> H(U1(a, k), f(k))
26.53/8.66	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.66	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.66	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.66	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.66	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.66	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.66	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.66	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.66	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.66	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.66	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.66	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.66	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.66	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.66	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.66	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.66	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.66	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.66	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.66	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.66	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.66	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.66	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.66	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.66	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.66	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.66	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.66	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.66	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.66	   A^2 -> H(U1(a, a), b)
26.53/8.66	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.66	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.66	   A^2 -> H(U1(a, a), c)
26.53/8.66	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.66	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.66	   A^2 -> H(U1(a, a), e)
26.53/8.66	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.66	   A^2 -> H(k, f(b))
26.53/8.66	   A^2 -> H(c, U1(b, b))
26.53/8.66	   A^2 -> H(c, f(c))
26.53/8.66	   A^2 -> H(c, f(d))
26.53/8.66	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.66	   A^2 -> H(U1(e, k), f(c))
26.53/8.66	   A^2 -> H(U1(e, k), f(d))
26.53/8.66	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.66	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.66	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.66	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.66	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.66	   A^2 -> H(U1(e, c), f(e))
26.53/8.66	   A^2 -> H(U1(e, c), f(k))
26.53/8.66	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.66	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.66	   A^2 -> H(U1(k, e), f(c))
26.53/8.66	   A^2 -> H(U1(k, e), f(d))
26.53/8.66	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.66	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.66	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.66	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.66	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.66	   A^2 -> H(U1(k, c), f(e))
26.53/8.66	   A^2 -> H(U1(k, c), f(k))
26.53/8.66	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.66	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.66	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.66	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.66	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.66	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.66	   A^2 -> H(U1(c, e), f(e))
26.53/8.66	   A^2 -> H(U1(c, e), f(k))
26.53/8.66	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.66	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.66	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.66	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.66	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.66	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.66	   A^2 -> H(U1(c, k), f(e))
26.53/8.66	   A^2 -> H(U1(c, k), f(k))
26.53/8.66	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.66	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.66	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.66	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.66	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.66	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.66	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.66	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.66	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.66	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.66	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.66	   A^2 -> H(e, U1(b, b))
26.53/8.66	   A^2 -> H(e, f(c))
26.53/8.66	   A^2 -> H(e, f(d))
26.53/8.66	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.66	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.66	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.66	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.66	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.66	   A^2 -> H(U1(e, e), f(e))
26.53/8.66	   A^2 -> H(U1(e, e), f(k))
26.53/8.66	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.66	   A^2 -> H(f(e), U1(e, b))
26.53/8.66	   A^2 -> H(f(e), U1(k, b))
26.53/8.66	   A^2 -> H(f(e), U1(c, d))
26.53/8.66	   A^2 -> H(f(e), U1(d, c))
26.53/8.66	   A^2 -> H(f(e), U1(b, e))
26.53/8.66	   A^2 -> H(f(e), U1(b, k))
26.53/8.66	   A^2 -> H(f(e), U1(e, c))
26.53/8.66	   A^2 -> H(f(e), U1(k, c))
26.53/8.66	   A^2 -> H(f(e), U1(c, e))
26.53/8.66	   A^2 -> H(f(e), U1(c, k))
26.53/8.66	   A^2 -> H(f(e), U1(k, k))
26.53/8.66	   A^2 -> H(f(e), U1(k, d))
26.53/8.66	   A^2 -> H(f(e), U1(d, k))
26.53/8.66	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.66	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.66	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.66	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.66	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.66	   A^2 -> H(U1(k, k), f(e))
26.53/8.66	   A^2 -> H(U1(k, k), f(k))
26.53/8.66	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.66	   A^2 -> H(f(k), U1(e, b))
26.53/8.66	   A^2 -> H(f(k), U1(k, b))
26.53/8.66	   A^2 -> H(f(k), U1(c, d))
26.53/8.66	   A^2 -> H(f(k), U1(d, c))
26.53/8.66	   A^2 -> H(f(k), U1(b, e))
26.53/8.66	   A^2 -> H(f(k), U1(b, k))
26.53/8.66	   A^2 -> H(f(k), U1(e, c))
26.53/8.66	   A^2 -> H(f(k), U1(k, c))
26.53/8.66	   A^2 -> H(f(k), U1(c, e))
26.53/8.66	   A^2 -> H(f(k), U1(c, k))
26.53/8.66	   A^2 -> H(f(k), U1(e, e))
26.53/8.66	   A^2 -> H(f(k), U1(k, d))
26.53/8.66	   A^2 -> H(f(k), U1(d, k))
26.53/8.66	   A^2 -> H(f(c), b)
26.53/8.66	   A^2 -> H(f(c), U1(e, d))
26.53/8.66	   A^2 -> H(f(c), U1(d, e))
26.53/8.66	   A^2 -> H(f(k), U1(k, k))
26.53/8.66	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.66	   A^2 -> H(U1(k, k), f(c))
26.53/8.66	   A^2 -> H(U1(k, k), f(d))
26.53/8.66	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.66	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.66	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.66	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.66	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.66	   A^2 -> H(U1(k, d), f(e))
26.53/8.66	   A^2 -> H(U1(k, d), f(k))
26.53/8.66	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.66	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.66	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.66	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.66	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.66	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.66	   A^2 -> H(U1(d, k), f(e))
26.53/8.66	   A^2 -> H(U1(d, k), f(k))
26.53/8.66	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.66	
26.53/8.66	The TRS R consists of the following rules:
26.53/8.66	
26.53/8.66	   f(x) -> U1(x, x)
26.53/8.66	   U1(e, x) -> x
26.53/8.66	   a -> c
26.53/8.66	   a -> d
26.53/8.66	   b -> c
26.53/8.66	   b -> d
26.53/8.66	   d -> k
26.53/8.66	   c -> e
26.53/8.66	   c -> k
26.53/8.66	
26.53/8.66	Q is empty.
26.53/8.66	We have to consider all minimal (P,Q,R)-chains.
26.53/8.66	----------------------------------------
26.53/8.66	
26.53/8.66	(473) TransformationProof (EQUIVALENT)
26.53/8.66	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.66	
26.53/8.66	   (A^2 -> H(U1(k, d), U1(c, b)),A^2 -> H(U1(k, d), U1(c, b)))
26.53/8.66	   (A^2 -> H(U1(d, k), U1(c, b)),A^2 -> H(U1(d, k), U1(c, b)))
26.53/8.66	   (A^2 -> H(U1(d, d), U1(e, b)),A^2 -> H(U1(d, d), U1(e, b)))
26.53/8.66	   (A^2 -> H(U1(d, d), U1(k, b)),A^2 -> H(U1(d, d), U1(k, b)))
26.53/8.66	   (A^2 -> H(U1(d, d), U1(c, c)),A^2 -> H(U1(d, d), U1(c, c)))
26.53/8.66	   (A^2 -> H(U1(d, d), U1(c, d)),A^2 -> H(U1(d, d), U1(c, d)))
26.53/8.66	
26.53/8.66	
26.53/8.66	----------------------------------------
26.53/8.66	
26.53/8.66	(474)
26.53/8.66	Obligation:
26.53/8.66	Q DP problem:
26.53/8.66	The TRS P consists of the following rules:
26.53/8.66	
26.53/8.66	   H(x, x) -> G(x, x, f(k))
26.53/8.66	   G(d, x, x) -> A^2
26.53/8.66	   A^2 -> H(f(c), f(c))
26.53/8.66	   A^2 -> H(f(d), f(d))
26.53/8.66	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.66	   A^2 -> H(f(e), f(e))
26.53/8.66	   A^2 -> H(f(k), f(k))
26.53/8.66	   A^2 -> H(U1(d, d), U1(d, b))
26.53/8.66	   A^2 -> H(U1(d, d), U1(b, c))
26.53/8.66	   A^2 -> H(U1(d, d), U1(b, d))
26.53/8.66	   A^2 -> H(U1(d, d), U1(c, c))
26.53/8.66	   A^2 -> H(U1(d, d), f(e))
26.53/8.66	   A^2 -> H(U1(d, d), f(k))
26.53/8.66	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.66	   A^2 -> H(f(d), U1(e, b))
26.53/8.66	   A^2 -> H(f(d), U1(k, b))
26.53/8.66	   A^2 -> H(f(d), U1(c, d))
26.53/8.66	   A^2 -> H(f(d), U1(d, c))
26.53/8.66	   A^2 -> H(f(d), U1(b, e))
26.53/8.66	   A^2 -> H(f(d), U1(b, k))
26.53/8.66	   A^2 -> H(f(d), U1(e, c))
26.53/8.66	   A^2 -> H(f(d), U1(k, c))
26.53/8.66	   A^2 -> H(f(d), U1(c, e))
26.53/8.66	   A^2 -> H(f(d), U1(c, k))
26.53/8.66	   A^2 -> H(f(d), U1(e, e))
26.53/8.66	   A^2 -> H(f(d), U1(k, k))
26.53/8.66	   A^2 -> H(f(a), b)
26.53/8.66	   A^2 -> H(f(a), U1(e, d))
26.53/8.66	   A^2 -> H(f(a), U1(d, e))
26.53/8.66	   A^2 -> H(f(c), U1(e, c))
26.53/8.66	   A^2 -> H(f(c), U1(k, c))
26.53/8.66	   A^2 -> H(f(c), U1(c, e))
26.53/8.66	   A^2 -> H(f(c), U1(c, k))
26.53/8.67	   A^2 -> H(f(a), c)
26.53/8.67	   A^2 -> H(f(a), U1(e, k))
26.53/8.67	   A^2 -> H(f(a), U1(k, e))
26.53/8.67	   A^2 -> H(f(c), U1(e, e))
26.53/8.67	   A^2 -> H(f(a), e)
26.53/8.67	   A^2 -> H(f(d), U1(k, d))
26.53/8.67	   A^2 -> H(f(d), U1(d, k))
26.53/8.67	   A^2 -> H(f(a), U1(k, k))
26.53/8.67	   A^2 -> H(d, f(b))
26.53/8.67	   A^2 -> H(a, U1(b, b))
26.53/8.67	   A^2 -> H(a, f(c))
26.53/8.67	   A^2 -> H(a, f(d))
26.53/8.67	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.67	   A^2 -> H(U1(e, d), f(c))
26.53/8.67	   A^2 -> H(U1(e, d), f(d))
26.53/8.67	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, a), f(e))
26.53/8.67	   A^2 -> H(U1(e, a), f(k))
26.53/8.67	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.67	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, a), f(e))
26.53/8.67	   A^2 -> H(U1(k, a), f(k))
26.53/8.67	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, d), f(e))
26.53/8.67	   A^2 -> H(U1(c, d), f(k))
26.53/8.67	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.67	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.67	   A^2 -> H(U1(d, e), f(c))
26.53/8.67	   A^2 -> H(U1(d, e), f(d))
26.53/8.67	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(d, c), f(e))
26.53/8.67	   A^2 -> H(U1(d, c), f(k))
26.53/8.67	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(a, e), f(e))
26.53/8.67	   A^2 -> H(U1(a, e), f(k))
26.53/8.67	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.67	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(a, k), f(e))
26.53/8.67	   A^2 -> H(U1(a, k), f(k))
26.53/8.67	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.67	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.67	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, a), b)
26.53/8.67	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.67	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.67	   A^2 -> H(U1(a, a), c)
26.53/8.67	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.67	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.67	   A^2 -> H(U1(a, a), e)
26.53/8.67	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.67	   A^2 -> H(k, f(b))
26.53/8.67	   A^2 -> H(c, U1(b, b))
26.53/8.67	   A^2 -> H(c, f(c))
26.53/8.67	   A^2 -> H(c, f(d))
26.53/8.67	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.67	   A^2 -> H(U1(e, k), f(c))
26.53/8.67	   A^2 -> H(U1(e, k), f(d))
26.53/8.67	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, c), f(e))
26.53/8.67	   A^2 -> H(U1(e, c), f(k))
26.53/8.67	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.67	   A^2 -> H(U1(k, e), f(c))
26.53/8.67	   A^2 -> H(U1(k, e), f(d))
26.53/8.67	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, c), f(e))
26.53/8.67	   A^2 -> H(U1(k, c), f(k))
26.53/8.67	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, e), f(e))
26.53/8.67	   A^2 -> H(U1(c, e), f(k))
26.53/8.67	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, k), f(e))
26.53/8.67	   A^2 -> H(U1(c, k), f(k))
26.53/8.67	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.67	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.67	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.67	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.67	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.67	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.67	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.67	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.67	   A^2 -> H(e, U1(b, b))
26.53/8.67	   A^2 -> H(e, f(c))
26.53/8.67	   A^2 -> H(e, f(d))
26.53/8.67	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, e), f(e))
26.53/8.67	   A^2 -> H(U1(e, e), f(k))
26.53/8.67	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.67	   A^2 -> H(f(e), U1(e, b))
26.53/8.67	   A^2 -> H(f(e), U1(k, b))
26.53/8.67	   A^2 -> H(f(e), U1(c, d))
26.53/8.67	   A^2 -> H(f(e), U1(d, c))
26.53/8.67	   A^2 -> H(f(e), U1(b, e))
26.53/8.67	   A^2 -> H(f(e), U1(b, k))
26.53/8.67	   A^2 -> H(f(e), U1(e, c))
26.53/8.67	   A^2 -> H(f(e), U1(k, c))
26.53/8.67	   A^2 -> H(f(e), U1(c, e))
26.53/8.67	   A^2 -> H(f(e), U1(c, k))
26.53/8.67	   A^2 -> H(f(e), U1(k, k))
26.53/8.67	   A^2 -> H(f(e), U1(k, d))
26.53/8.67	   A^2 -> H(f(e), U1(d, k))
26.53/8.67	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, k), f(e))
26.53/8.67	   A^2 -> H(U1(k, k), f(k))
26.53/8.67	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.67	   A^2 -> H(f(k), U1(e, b))
26.53/8.67	   A^2 -> H(f(k), U1(k, b))
26.53/8.67	   A^2 -> H(f(k), U1(c, d))
26.53/8.67	   A^2 -> H(f(k), U1(d, c))
26.53/8.67	   A^2 -> H(f(k), U1(b, e))
26.53/8.67	   A^2 -> H(f(k), U1(b, k))
26.53/8.67	   A^2 -> H(f(k), U1(e, c))
26.53/8.67	   A^2 -> H(f(k), U1(k, c))
26.53/8.67	   A^2 -> H(f(k), U1(c, e))
26.53/8.67	   A^2 -> H(f(k), U1(c, k))
26.53/8.67	   A^2 -> H(f(k), U1(e, e))
26.53/8.67	   A^2 -> H(f(k), U1(k, d))
26.53/8.67	   A^2 -> H(f(k), U1(d, k))
26.53/8.67	   A^2 -> H(f(c), b)
26.53/8.67	   A^2 -> H(f(c), U1(e, d))
26.53/8.67	   A^2 -> H(f(c), U1(d, e))
26.53/8.67	   A^2 -> H(f(k), U1(k, k))
26.53/8.67	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.67	   A^2 -> H(U1(k, k), f(c))
26.53/8.67	   A^2 -> H(U1(k, k), f(d))
26.53/8.67	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, d), f(e))
26.53/8.67	   A^2 -> H(U1(k, d), f(k))
26.53/8.67	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(d, k), f(e))
26.53/8.67	   A^2 -> H(U1(d, k), f(k))
26.53/8.67	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.67	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.67	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.67	
26.53/8.67	The TRS R consists of the following rules:
26.53/8.67	
26.53/8.67	   f(x) -> U1(x, x)
26.53/8.67	   U1(e, x) -> x
26.53/8.67	   a -> c
26.53/8.67	   a -> d
26.53/8.67	   b -> c
26.53/8.67	   b -> d
26.53/8.67	   d -> k
26.53/8.67	   c -> e
26.53/8.67	   c -> k
26.53/8.67	
26.53/8.67	Q is empty.
26.53/8.67	We have to consider all minimal (P,Q,R)-chains.
26.53/8.67	----------------------------------------
26.53/8.67	
26.53/8.67	(475) TransformationProof (EQUIVALENT)
26.53/8.67	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.67	
26.53/8.67	   (A^2 -> H(U1(k, d), U1(d, b)),A^2 -> H(U1(k, d), U1(d, b)))
26.53/8.67	   (A^2 -> H(U1(d, k), U1(d, b)),A^2 -> H(U1(d, k), U1(d, b)))
26.53/8.67	   (A^2 -> H(U1(d, d), U1(k, b)),A^2 -> H(U1(d, d), U1(k, b)))
26.53/8.67	   (A^2 -> H(U1(d, d), U1(d, c)),A^2 -> H(U1(d, d), U1(d, c)))
26.53/8.67	   (A^2 -> H(U1(d, d), U1(d, d)),A^2 -> H(U1(d, d), U1(d, d)))
26.53/8.67	
26.53/8.67	
26.53/8.67	----------------------------------------
26.53/8.67	
26.53/8.67	(476)
26.53/8.67	Obligation:
26.53/8.67	Q DP problem:
26.53/8.67	The TRS P consists of the following rules:
26.53/8.67	
26.53/8.67	   H(x, x) -> G(x, x, f(k))
26.53/8.67	   G(d, x, x) -> A^2
26.53/8.67	   A^2 -> H(f(c), f(c))
26.53/8.67	   A^2 -> H(f(d), f(d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.67	   A^2 -> H(f(e), f(e))
26.53/8.67	   A^2 -> H(f(k), f(k))
26.53/8.67	   A^2 -> H(U1(d, d), U1(b, c))
26.53/8.67	   A^2 -> H(U1(d, d), U1(b, d))
26.53/8.67	   A^2 -> H(U1(d, d), U1(c, c))
26.53/8.67	   A^2 -> H(U1(d, d), f(e))
26.53/8.67	   A^2 -> H(U1(d, d), f(k))
26.53/8.67	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.67	   A^2 -> H(f(d), U1(e, b))
26.53/8.67	   A^2 -> H(f(d), U1(k, b))
26.53/8.67	   A^2 -> H(f(d), U1(c, d))
26.53/8.67	   A^2 -> H(f(d), U1(d, c))
26.53/8.67	   A^2 -> H(f(d), U1(b, e))
26.53/8.67	   A^2 -> H(f(d), U1(b, k))
26.53/8.67	   A^2 -> H(f(d), U1(e, c))
26.53/8.67	   A^2 -> H(f(d), U1(k, c))
26.53/8.67	   A^2 -> H(f(d), U1(c, e))
26.53/8.67	   A^2 -> H(f(d), U1(c, k))
26.53/8.67	   A^2 -> H(f(d), U1(e, e))
26.53/8.67	   A^2 -> H(f(d), U1(k, k))
26.53/8.67	   A^2 -> H(f(a), b)
26.53/8.67	   A^2 -> H(f(a), U1(e, d))
26.53/8.67	   A^2 -> H(f(a), U1(d, e))
26.53/8.67	   A^2 -> H(f(c), U1(e, c))
26.53/8.67	   A^2 -> H(f(c), U1(k, c))
26.53/8.67	   A^2 -> H(f(c), U1(c, e))
26.53/8.67	   A^2 -> H(f(c), U1(c, k))
26.53/8.67	   A^2 -> H(f(a), c)
26.53/8.67	   A^2 -> H(f(a), U1(e, k))
26.53/8.67	   A^2 -> H(f(a), U1(k, e))
26.53/8.67	   A^2 -> H(f(c), U1(e, e))
26.53/8.67	   A^2 -> H(f(a), e)
26.53/8.67	   A^2 -> H(f(d), U1(k, d))
26.53/8.67	   A^2 -> H(f(d), U1(d, k))
26.53/8.67	   A^2 -> H(f(a), U1(k, k))
26.53/8.67	   A^2 -> H(d, f(b))
26.53/8.67	   A^2 -> H(a, U1(b, b))
26.53/8.67	   A^2 -> H(a, f(c))
26.53/8.67	   A^2 -> H(a, f(d))
26.53/8.67	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.67	   A^2 -> H(U1(e, d), f(c))
26.53/8.67	   A^2 -> H(U1(e, d), f(d))
26.53/8.67	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, a), f(e))
26.53/8.67	   A^2 -> H(U1(e, a), f(k))
26.53/8.67	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.67	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, a), f(e))
26.53/8.67	   A^2 -> H(U1(k, a), f(k))
26.53/8.67	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, d), f(e))
26.53/8.67	   A^2 -> H(U1(c, d), f(k))
26.53/8.67	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.67	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.67	   A^2 -> H(U1(d, e), f(c))
26.53/8.67	   A^2 -> H(U1(d, e), f(d))
26.53/8.67	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(d, c), f(e))
26.53/8.67	   A^2 -> H(U1(d, c), f(k))
26.53/8.67	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(a, e), f(e))
26.53/8.67	   A^2 -> H(U1(a, e), f(k))
26.53/8.67	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.67	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(a, k), f(e))
26.53/8.67	   A^2 -> H(U1(a, k), f(k))
26.53/8.67	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.67	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.67	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, a), b)
26.53/8.67	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.67	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.67	   A^2 -> H(U1(a, a), c)
26.53/8.67	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.67	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.67	   A^2 -> H(U1(a, a), e)
26.53/8.67	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.67	   A^2 -> H(k, f(b))
26.53/8.67	   A^2 -> H(c, U1(b, b))
26.53/8.67	   A^2 -> H(c, f(c))
26.53/8.67	   A^2 -> H(c, f(d))
26.53/8.67	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.67	   A^2 -> H(U1(e, k), f(c))
26.53/8.67	   A^2 -> H(U1(e, k), f(d))
26.53/8.67	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, c), f(e))
26.53/8.67	   A^2 -> H(U1(e, c), f(k))
26.53/8.67	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.67	   A^2 -> H(U1(k, e), f(c))
26.53/8.67	   A^2 -> H(U1(k, e), f(d))
26.53/8.67	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, c), f(e))
26.53/8.67	   A^2 -> H(U1(k, c), f(k))
26.53/8.67	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, e), f(e))
26.53/8.67	   A^2 -> H(U1(c, e), f(k))
26.53/8.67	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, k), f(e))
26.53/8.67	   A^2 -> H(U1(c, k), f(k))
26.53/8.67	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.67	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.67	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.67	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.67	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.67	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.67	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.67	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.67	   A^2 -> H(e, U1(b, b))
26.53/8.67	   A^2 -> H(e, f(c))
26.53/8.67	   A^2 -> H(e, f(d))
26.53/8.67	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, e), f(e))
26.53/8.67	   A^2 -> H(U1(e, e), f(k))
26.53/8.67	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.67	   A^2 -> H(f(e), U1(e, b))
26.53/8.67	   A^2 -> H(f(e), U1(k, b))
26.53/8.67	   A^2 -> H(f(e), U1(c, d))
26.53/8.67	   A^2 -> H(f(e), U1(d, c))
26.53/8.67	   A^2 -> H(f(e), U1(b, e))
26.53/8.67	   A^2 -> H(f(e), U1(b, k))
26.53/8.67	   A^2 -> H(f(e), U1(e, c))
26.53/8.67	   A^2 -> H(f(e), U1(k, c))
26.53/8.67	   A^2 -> H(f(e), U1(c, e))
26.53/8.67	   A^2 -> H(f(e), U1(c, k))
26.53/8.67	   A^2 -> H(f(e), U1(k, k))
26.53/8.67	   A^2 -> H(f(e), U1(k, d))
26.53/8.67	   A^2 -> H(f(e), U1(d, k))
26.53/8.67	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, k), f(e))
26.53/8.67	   A^2 -> H(U1(k, k), f(k))
26.53/8.67	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.67	   A^2 -> H(f(k), U1(e, b))
26.53/8.67	   A^2 -> H(f(k), U1(k, b))
26.53/8.67	   A^2 -> H(f(k), U1(c, d))
26.53/8.67	   A^2 -> H(f(k), U1(d, c))
26.53/8.67	   A^2 -> H(f(k), U1(b, e))
26.53/8.67	   A^2 -> H(f(k), U1(b, k))
26.53/8.67	   A^2 -> H(f(k), U1(e, c))
26.53/8.67	   A^2 -> H(f(k), U1(k, c))
26.53/8.67	   A^2 -> H(f(k), U1(c, e))
26.53/8.67	   A^2 -> H(f(k), U1(c, k))
26.53/8.67	   A^2 -> H(f(k), U1(e, e))
26.53/8.67	   A^2 -> H(f(k), U1(k, d))
26.53/8.67	   A^2 -> H(f(k), U1(d, k))
26.53/8.67	   A^2 -> H(f(c), b)
26.53/8.67	   A^2 -> H(f(c), U1(e, d))
26.53/8.67	   A^2 -> H(f(c), U1(d, e))
26.53/8.67	   A^2 -> H(f(k), U1(k, k))
26.53/8.67	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.67	   A^2 -> H(U1(k, k), f(c))
26.53/8.67	   A^2 -> H(U1(k, k), f(d))
26.53/8.67	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, d), f(e))
26.53/8.67	   A^2 -> H(U1(k, d), f(k))
26.53/8.67	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(d, k), f(e))
26.53/8.67	   A^2 -> H(U1(d, k), f(k))
26.53/8.67	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.67	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.67	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.67	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.67	
26.53/8.67	The TRS R consists of the following rules:
26.53/8.67	
26.53/8.67	   f(x) -> U1(x, x)
26.53/8.67	   U1(e, x) -> x
26.53/8.67	   a -> c
26.53/8.67	   a -> d
26.53/8.67	   b -> c
26.53/8.67	   b -> d
26.53/8.67	   d -> k
26.53/8.67	   c -> e
26.53/8.67	   c -> k
26.53/8.67	
26.53/8.67	Q is empty.
26.53/8.67	We have to consider all minimal (P,Q,R)-chains.
26.53/8.67	----------------------------------------
26.53/8.67	
26.53/8.67	(477) TransformationProof (EQUIVALENT)
26.53/8.67	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.67	
26.53/8.67	   (A^2 -> H(U1(k, d), U1(b, c)),A^2 -> H(U1(k, d), U1(b, c)))
26.53/8.67	   (A^2 -> H(U1(d, k), U1(b, c)),A^2 -> H(U1(d, k), U1(b, c)))
26.53/8.67	   (A^2 -> H(U1(d, d), U1(c, c)),A^2 -> H(U1(d, d), U1(c, c)))
26.53/8.67	   (A^2 -> H(U1(d, d), U1(d, c)),A^2 -> H(U1(d, d), U1(d, c)))
26.53/8.67	   (A^2 -> H(U1(d, d), U1(b, e)),A^2 -> H(U1(d, d), U1(b, e)))
26.53/8.67	   (A^2 -> H(U1(d, d), U1(b, k)),A^2 -> H(U1(d, d), U1(b, k)))
26.53/8.67	
26.53/8.67	
26.53/8.67	----------------------------------------
26.53/8.67	
26.53/8.67	(478)
26.53/8.67	Obligation:
26.53/8.67	Q DP problem:
26.53/8.67	The TRS P consists of the following rules:
26.53/8.67	
26.53/8.67	   H(x, x) -> G(x, x, f(k))
26.53/8.67	   G(d, x, x) -> A^2
26.53/8.67	   A^2 -> H(f(c), f(c))
26.53/8.67	   A^2 -> H(f(d), f(d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.67	   A^2 -> H(f(e), f(e))
26.53/8.67	   A^2 -> H(f(k), f(k))
26.53/8.67	   A^2 -> H(U1(d, d), U1(b, d))
26.53/8.67	   A^2 -> H(U1(d, d), U1(c, c))
26.53/8.67	   A^2 -> H(U1(d, d), f(e))
26.53/8.67	   A^2 -> H(U1(d, d), f(k))
26.53/8.67	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.67	   A^2 -> H(f(d), U1(e, b))
26.53/8.67	   A^2 -> H(f(d), U1(k, b))
26.53/8.67	   A^2 -> H(f(d), U1(c, d))
26.53/8.67	   A^2 -> H(f(d), U1(d, c))
26.53/8.67	   A^2 -> H(f(d), U1(b, e))
26.53/8.67	   A^2 -> H(f(d), U1(b, k))
26.53/8.67	   A^2 -> H(f(d), U1(e, c))
26.53/8.67	   A^2 -> H(f(d), U1(k, c))
26.53/8.67	   A^2 -> H(f(d), U1(c, e))
26.53/8.67	   A^2 -> H(f(d), U1(c, k))
26.53/8.67	   A^2 -> H(f(d), U1(e, e))
26.53/8.67	   A^2 -> H(f(d), U1(k, k))
26.53/8.67	   A^2 -> H(f(a), b)
26.53/8.67	   A^2 -> H(f(a), U1(e, d))
26.53/8.67	   A^2 -> H(f(a), U1(d, e))
26.53/8.67	   A^2 -> H(f(c), U1(e, c))
26.53/8.67	   A^2 -> H(f(c), U1(k, c))
26.53/8.67	   A^2 -> H(f(c), U1(c, e))
26.53/8.67	   A^2 -> H(f(c), U1(c, k))
26.53/8.67	   A^2 -> H(f(a), c)
26.53/8.67	   A^2 -> H(f(a), U1(e, k))
26.53/8.67	   A^2 -> H(f(a), U1(k, e))
26.53/8.67	   A^2 -> H(f(c), U1(e, e))
26.53/8.67	   A^2 -> H(f(a), e)
26.53/8.67	   A^2 -> H(f(d), U1(k, d))
26.53/8.67	   A^2 -> H(f(d), U1(d, k))
26.53/8.67	   A^2 -> H(f(a), U1(k, k))
26.53/8.67	   A^2 -> H(d, f(b))
26.53/8.67	   A^2 -> H(a, U1(b, b))
26.53/8.67	   A^2 -> H(a, f(c))
26.53/8.67	   A^2 -> H(a, f(d))
26.53/8.67	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.67	   A^2 -> H(U1(e, d), f(c))
26.53/8.67	   A^2 -> H(U1(e, d), f(d))
26.53/8.67	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, a), f(e))
26.53/8.67	   A^2 -> H(U1(e, a), f(k))
26.53/8.67	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.67	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, a), f(e))
26.53/8.67	   A^2 -> H(U1(k, a), f(k))
26.53/8.67	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, d), f(e))
26.53/8.67	   A^2 -> H(U1(c, d), f(k))
26.53/8.67	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.67	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.67	   A^2 -> H(U1(d, e), f(c))
26.53/8.67	   A^2 -> H(U1(d, e), f(d))
26.53/8.67	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(d, c), f(e))
26.53/8.67	   A^2 -> H(U1(d, c), f(k))
26.53/8.67	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(a, e), f(e))
26.53/8.67	   A^2 -> H(U1(a, e), f(k))
26.53/8.67	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.67	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(a, k), f(e))
26.53/8.67	   A^2 -> H(U1(a, k), f(k))
26.53/8.67	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.67	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.67	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, a), b)
26.53/8.67	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.67	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.67	   A^2 -> H(U1(a, a), c)
26.53/8.67	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.67	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.67	   A^2 -> H(U1(a, a), e)
26.53/8.67	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.67	   A^2 -> H(k, f(b))
26.53/8.67	   A^2 -> H(c, U1(b, b))
26.53/8.67	   A^2 -> H(c, f(c))
26.53/8.67	   A^2 -> H(c, f(d))
26.53/8.67	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.67	   A^2 -> H(U1(e, k), f(c))
26.53/8.67	   A^2 -> H(U1(e, k), f(d))
26.53/8.67	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, c), f(e))
26.53/8.67	   A^2 -> H(U1(e, c), f(k))
26.53/8.67	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.67	   A^2 -> H(U1(k, e), f(c))
26.53/8.67	   A^2 -> H(U1(k, e), f(d))
26.53/8.67	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, c), f(e))
26.53/8.67	   A^2 -> H(U1(k, c), f(k))
26.53/8.67	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, e), f(e))
26.53/8.67	   A^2 -> H(U1(c, e), f(k))
26.53/8.67	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, k), f(e))
26.53/8.67	   A^2 -> H(U1(c, k), f(k))
26.53/8.67	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.67	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.67	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.67	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.67	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.67	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.67	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.67	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.67	   A^2 -> H(e, U1(b, b))
26.53/8.67	   A^2 -> H(e, f(c))
26.53/8.67	   A^2 -> H(e, f(d))
26.53/8.67	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, e), f(e))
26.53/8.67	   A^2 -> H(U1(e, e), f(k))
26.53/8.67	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.67	   A^2 -> H(f(e), U1(e, b))
26.53/8.67	   A^2 -> H(f(e), U1(k, b))
26.53/8.67	   A^2 -> H(f(e), U1(c, d))
26.53/8.67	   A^2 -> H(f(e), U1(d, c))
26.53/8.67	   A^2 -> H(f(e), U1(b, e))
26.53/8.67	   A^2 -> H(f(e), U1(b, k))
26.53/8.67	   A^2 -> H(f(e), U1(e, c))
26.53/8.67	   A^2 -> H(f(e), U1(k, c))
26.53/8.67	   A^2 -> H(f(e), U1(c, e))
26.53/8.67	   A^2 -> H(f(e), U1(c, k))
26.53/8.67	   A^2 -> H(f(e), U1(k, k))
26.53/8.67	   A^2 -> H(f(e), U1(k, d))
26.53/8.67	   A^2 -> H(f(e), U1(d, k))
26.53/8.67	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, k), f(e))
26.53/8.67	   A^2 -> H(U1(k, k), f(k))
26.53/8.67	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.67	   A^2 -> H(f(k), U1(e, b))
26.53/8.67	   A^2 -> H(f(k), U1(k, b))
26.53/8.67	   A^2 -> H(f(k), U1(c, d))
26.53/8.67	   A^2 -> H(f(k), U1(d, c))
26.53/8.67	   A^2 -> H(f(k), U1(b, e))
26.53/8.67	   A^2 -> H(f(k), U1(b, k))
26.53/8.67	   A^2 -> H(f(k), U1(e, c))
26.53/8.67	   A^2 -> H(f(k), U1(k, c))
26.53/8.67	   A^2 -> H(f(k), U1(c, e))
26.53/8.67	   A^2 -> H(f(k), U1(c, k))
26.53/8.67	   A^2 -> H(f(k), U1(e, e))
26.53/8.67	   A^2 -> H(f(k), U1(k, d))
26.53/8.67	   A^2 -> H(f(k), U1(d, k))
26.53/8.67	   A^2 -> H(f(c), b)
26.53/8.67	   A^2 -> H(f(c), U1(e, d))
26.53/8.67	   A^2 -> H(f(c), U1(d, e))
26.53/8.67	   A^2 -> H(f(k), U1(k, k))
26.53/8.67	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.67	   A^2 -> H(U1(k, k), f(c))
26.53/8.67	   A^2 -> H(U1(k, k), f(d))
26.53/8.67	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, d), f(e))
26.53/8.67	   A^2 -> H(U1(k, d), f(k))
26.53/8.67	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(d, k), f(e))
26.53/8.67	   A^2 -> H(U1(d, k), f(k))
26.53/8.67	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.67	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.67	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.67	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.67	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.67	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.67	
26.53/8.67	The TRS R consists of the following rules:
26.53/8.67	
26.53/8.67	   f(x) -> U1(x, x)
26.53/8.67	   U1(e, x) -> x
26.53/8.67	   a -> c
26.53/8.67	   a -> d
26.53/8.67	   b -> c
26.53/8.67	   b -> d
26.53/8.67	   d -> k
26.53/8.67	   c -> e
26.53/8.67	   c -> k
26.53/8.67	
26.53/8.67	Q is empty.
26.53/8.67	We have to consider all minimal (P,Q,R)-chains.
26.53/8.67	----------------------------------------
26.53/8.67	
26.53/8.67	(479) TransformationProof (EQUIVALENT)
26.53/8.67	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.67	
26.53/8.67	   (A^2 -> H(U1(k, d), U1(b, d)),A^2 -> H(U1(k, d), U1(b, d)))
26.53/8.67	   (A^2 -> H(U1(d, k), U1(b, d)),A^2 -> H(U1(d, k), U1(b, d)))
26.53/8.67	   (A^2 -> H(U1(d, d), U1(c, d)),A^2 -> H(U1(d, d), U1(c, d)))
26.53/8.67	   (A^2 -> H(U1(d, d), U1(d, d)),A^2 -> H(U1(d, d), U1(d, d)))
26.53/8.67	   (A^2 -> H(U1(d, d), U1(b, k)),A^2 -> H(U1(d, d), U1(b, k)))
26.53/8.67	
26.53/8.67	
26.53/8.67	----------------------------------------
26.53/8.67	
26.53/8.67	(480)
26.53/8.67	Obligation:
26.53/8.67	Q DP problem:
26.53/8.67	The TRS P consists of the following rules:
26.53/8.67	
26.53/8.67	   H(x, x) -> G(x, x, f(k))
26.53/8.67	   G(d, x, x) -> A^2
26.53/8.67	   A^2 -> H(f(c), f(c))
26.53/8.67	   A^2 -> H(f(d), f(d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.67	   A^2 -> H(f(e), f(e))
26.53/8.67	   A^2 -> H(f(k), f(k))
26.53/8.67	   A^2 -> H(U1(d, d), U1(c, c))
26.53/8.67	   A^2 -> H(U1(d, d), f(e))
26.53/8.67	   A^2 -> H(U1(d, d), f(k))
26.53/8.67	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.67	   A^2 -> H(f(d), U1(e, b))
26.53/8.67	   A^2 -> H(f(d), U1(k, b))
26.53/8.67	   A^2 -> H(f(d), U1(c, d))
26.53/8.67	   A^2 -> H(f(d), U1(d, c))
26.53/8.67	   A^2 -> H(f(d), U1(b, e))
26.53/8.67	   A^2 -> H(f(d), U1(b, k))
26.53/8.67	   A^2 -> H(f(d), U1(e, c))
26.53/8.67	   A^2 -> H(f(d), U1(k, c))
26.53/8.67	   A^2 -> H(f(d), U1(c, e))
26.53/8.67	   A^2 -> H(f(d), U1(c, k))
26.53/8.67	   A^2 -> H(f(d), U1(e, e))
26.53/8.67	   A^2 -> H(f(d), U1(k, k))
26.53/8.67	   A^2 -> H(f(a), b)
26.53/8.67	   A^2 -> H(f(a), U1(e, d))
26.53/8.67	   A^2 -> H(f(a), U1(d, e))
26.53/8.67	   A^2 -> H(f(c), U1(e, c))
26.53/8.67	   A^2 -> H(f(c), U1(k, c))
26.53/8.67	   A^2 -> H(f(c), U1(c, e))
26.53/8.67	   A^2 -> H(f(c), U1(c, k))
26.53/8.67	   A^2 -> H(f(a), c)
26.53/8.67	   A^2 -> H(f(a), U1(e, k))
26.53/8.67	   A^2 -> H(f(a), U1(k, e))
26.53/8.67	   A^2 -> H(f(c), U1(e, e))
26.53/8.67	   A^2 -> H(f(a), e)
26.53/8.67	   A^2 -> H(f(d), U1(k, d))
26.53/8.67	   A^2 -> H(f(d), U1(d, k))
26.53/8.67	   A^2 -> H(f(a), U1(k, k))
26.53/8.67	   A^2 -> H(d, f(b))
26.53/8.67	   A^2 -> H(a, U1(b, b))
26.53/8.67	   A^2 -> H(a, f(c))
26.53/8.67	   A^2 -> H(a, f(d))
26.53/8.67	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.67	   A^2 -> H(U1(e, d), f(c))
26.53/8.67	   A^2 -> H(U1(e, d), f(d))
26.53/8.67	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, a), f(e))
26.53/8.67	   A^2 -> H(U1(e, a), f(k))
26.53/8.67	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.67	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, a), f(e))
26.53/8.67	   A^2 -> H(U1(k, a), f(k))
26.53/8.67	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, d), f(e))
26.53/8.67	   A^2 -> H(U1(c, d), f(k))
26.53/8.67	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.67	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.67	   A^2 -> H(U1(d, e), f(c))
26.53/8.67	   A^2 -> H(U1(d, e), f(d))
26.53/8.67	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(d, c), f(e))
26.53/8.67	   A^2 -> H(U1(d, c), f(k))
26.53/8.67	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(a, e), f(e))
26.53/8.67	   A^2 -> H(U1(a, e), f(k))
26.53/8.67	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.67	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(a, k), f(e))
26.53/8.67	   A^2 -> H(U1(a, k), f(k))
26.53/8.67	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.67	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.67	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, a), b)
26.53/8.67	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.67	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.67	   A^2 -> H(U1(a, a), c)
26.53/8.67	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.67	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.67	   A^2 -> H(U1(a, a), e)
26.53/8.67	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.67	   A^2 -> H(k, f(b))
26.53/8.67	   A^2 -> H(c, U1(b, b))
26.53/8.67	   A^2 -> H(c, f(c))
26.53/8.67	   A^2 -> H(c, f(d))
26.53/8.67	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.67	   A^2 -> H(U1(e, k), f(c))
26.53/8.67	   A^2 -> H(U1(e, k), f(d))
26.53/8.67	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, c), f(e))
26.53/8.67	   A^2 -> H(U1(e, c), f(k))
26.53/8.67	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.67	   A^2 -> H(U1(k, e), f(c))
26.53/8.67	   A^2 -> H(U1(k, e), f(d))
26.53/8.67	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, c), f(e))
26.53/8.67	   A^2 -> H(U1(k, c), f(k))
26.53/8.67	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, e), f(e))
26.53/8.67	   A^2 -> H(U1(c, e), f(k))
26.53/8.67	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, k), f(e))
26.53/8.67	   A^2 -> H(U1(c, k), f(k))
26.53/8.67	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.67	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.67	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.67	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.67	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.67	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.67	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.67	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.67	   A^2 -> H(e, U1(b, b))
26.53/8.67	   A^2 -> H(e, f(c))
26.53/8.67	   A^2 -> H(e, f(d))
26.53/8.67	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, e), f(e))
26.53/8.67	   A^2 -> H(U1(e, e), f(k))
26.53/8.67	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.67	   A^2 -> H(f(e), U1(e, b))
26.53/8.67	   A^2 -> H(f(e), U1(k, b))
26.53/8.67	   A^2 -> H(f(e), U1(c, d))
26.53/8.67	   A^2 -> H(f(e), U1(d, c))
26.53/8.67	   A^2 -> H(f(e), U1(b, e))
26.53/8.67	   A^2 -> H(f(e), U1(b, k))
26.53/8.67	   A^2 -> H(f(e), U1(e, c))
26.53/8.67	   A^2 -> H(f(e), U1(k, c))
26.53/8.67	   A^2 -> H(f(e), U1(c, e))
26.53/8.67	   A^2 -> H(f(e), U1(c, k))
26.53/8.67	   A^2 -> H(f(e), U1(k, k))
26.53/8.67	   A^2 -> H(f(e), U1(k, d))
26.53/8.67	   A^2 -> H(f(e), U1(d, k))
26.53/8.67	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, k), f(e))
26.53/8.67	   A^2 -> H(U1(k, k), f(k))
26.53/8.67	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.67	   A^2 -> H(f(k), U1(e, b))
26.53/8.67	   A^2 -> H(f(k), U1(k, b))
26.53/8.67	   A^2 -> H(f(k), U1(c, d))
26.53/8.67	   A^2 -> H(f(k), U1(d, c))
26.53/8.67	   A^2 -> H(f(k), U1(b, e))
26.53/8.67	   A^2 -> H(f(k), U1(b, k))
26.53/8.67	   A^2 -> H(f(k), U1(e, c))
26.53/8.67	   A^2 -> H(f(k), U1(k, c))
26.53/8.67	   A^2 -> H(f(k), U1(c, e))
26.53/8.67	   A^2 -> H(f(k), U1(c, k))
26.53/8.67	   A^2 -> H(f(k), U1(e, e))
26.53/8.67	   A^2 -> H(f(k), U1(k, d))
26.53/8.67	   A^2 -> H(f(k), U1(d, k))
26.53/8.67	   A^2 -> H(f(c), b)
26.53/8.67	   A^2 -> H(f(c), U1(e, d))
26.53/8.67	   A^2 -> H(f(c), U1(d, e))
26.53/8.67	   A^2 -> H(f(k), U1(k, k))
26.53/8.67	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.67	   A^2 -> H(U1(k, k), f(c))
26.53/8.67	   A^2 -> H(U1(k, k), f(d))
26.53/8.67	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, d), f(e))
26.53/8.67	   A^2 -> H(U1(k, d), f(k))
26.53/8.67	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(d, k), f(e))
26.53/8.67	   A^2 -> H(U1(d, k), f(k))
26.53/8.67	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.67	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.67	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.67	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.67	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.67	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.67	
26.53/8.67	The TRS R consists of the following rules:
26.53/8.67	
26.53/8.67	   f(x) -> U1(x, x)
26.53/8.67	   U1(e, x) -> x
26.53/8.67	   a -> c
26.53/8.67	   a -> d
26.53/8.67	   b -> c
26.53/8.67	   b -> d
26.53/8.67	   d -> k
26.53/8.67	   c -> e
26.53/8.67	   c -> k
26.53/8.67	
26.53/8.67	Q is empty.
26.53/8.67	We have to consider all minimal (P,Q,R)-chains.
26.53/8.67	----------------------------------------
26.53/8.67	
26.53/8.67	(481) TransformationProof (EQUIVALENT)
26.53/8.67	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.67	
26.53/8.67	   (A^2 -> H(U1(k, d), U1(c, c)),A^2 -> H(U1(k, d), U1(c, c)))
26.53/8.67	   (A^2 -> H(U1(d, k), U1(c, c)),A^2 -> H(U1(d, k), U1(c, c)))
26.53/8.67	   (A^2 -> H(U1(d, d), U1(e, c)),A^2 -> H(U1(d, d), U1(e, c)))
26.53/8.67	   (A^2 -> H(U1(d, d), U1(k, c)),A^2 -> H(U1(d, d), U1(k, c)))
26.53/8.67	   (A^2 -> H(U1(d, d), U1(c, e)),A^2 -> H(U1(d, d), U1(c, e)))
26.53/8.67	   (A^2 -> H(U1(d, d), U1(c, k)),A^2 -> H(U1(d, d), U1(c, k)))
26.53/8.67	
26.53/8.67	
26.53/8.67	----------------------------------------
26.53/8.67	
26.53/8.67	(482)
26.53/8.67	Obligation:
26.53/8.67	Q DP problem:
26.53/8.67	The TRS P consists of the following rules:
26.53/8.67	
26.53/8.67	   H(x, x) -> G(x, x, f(k))
26.53/8.67	   G(d, x, x) -> A^2
26.53/8.67	   A^2 -> H(f(c), f(c))
26.53/8.67	   A^2 -> H(f(d), f(d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.67	   A^2 -> H(f(e), f(e))
26.53/8.67	   A^2 -> H(f(k), f(k))
26.53/8.67	   A^2 -> H(U1(d, d), f(e))
26.53/8.67	   A^2 -> H(U1(d, d), f(k))
26.53/8.67	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.67	   A^2 -> H(f(d), U1(e, b))
26.53/8.67	   A^2 -> H(f(d), U1(k, b))
26.53/8.67	   A^2 -> H(f(d), U1(c, d))
26.53/8.67	   A^2 -> H(f(d), U1(d, c))
26.53/8.67	   A^2 -> H(f(d), U1(b, e))
26.53/8.67	   A^2 -> H(f(d), U1(b, k))
26.53/8.67	   A^2 -> H(f(d), U1(e, c))
26.53/8.67	   A^2 -> H(f(d), U1(k, c))
26.53/8.67	   A^2 -> H(f(d), U1(c, e))
26.53/8.67	   A^2 -> H(f(d), U1(c, k))
26.53/8.67	   A^2 -> H(f(d), U1(e, e))
26.53/8.67	   A^2 -> H(f(d), U1(k, k))
26.53/8.67	   A^2 -> H(f(a), b)
26.53/8.67	   A^2 -> H(f(a), U1(e, d))
26.53/8.67	   A^2 -> H(f(a), U1(d, e))
26.53/8.67	   A^2 -> H(f(c), U1(e, c))
26.53/8.67	   A^2 -> H(f(c), U1(k, c))
26.53/8.67	   A^2 -> H(f(c), U1(c, e))
26.53/8.67	   A^2 -> H(f(c), U1(c, k))
26.53/8.67	   A^2 -> H(f(a), c)
26.53/8.67	   A^2 -> H(f(a), U1(e, k))
26.53/8.67	   A^2 -> H(f(a), U1(k, e))
26.53/8.67	   A^2 -> H(f(c), U1(e, e))
26.53/8.67	   A^2 -> H(f(a), e)
26.53/8.67	   A^2 -> H(f(d), U1(k, d))
26.53/8.67	   A^2 -> H(f(d), U1(d, k))
26.53/8.67	   A^2 -> H(f(a), U1(k, k))
26.53/8.67	   A^2 -> H(d, f(b))
26.53/8.67	   A^2 -> H(a, U1(b, b))
26.53/8.67	   A^2 -> H(a, f(c))
26.53/8.67	   A^2 -> H(a, f(d))
26.53/8.67	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.67	   A^2 -> H(U1(e, d), f(c))
26.53/8.67	   A^2 -> H(U1(e, d), f(d))
26.53/8.67	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, a), f(e))
26.53/8.67	   A^2 -> H(U1(e, a), f(k))
26.53/8.67	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.67	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, a), f(e))
26.53/8.67	   A^2 -> H(U1(k, a), f(k))
26.53/8.67	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, d), f(e))
26.53/8.67	   A^2 -> H(U1(c, d), f(k))
26.53/8.67	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.67	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.67	   A^2 -> H(U1(d, e), f(c))
26.53/8.67	   A^2 -> H(U1(d, e), f(d))
26.53/8.67	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(d, c), f(e))
26.53/8.67	   A^2 -> H(U1(d, c), f(k))
26.53/8.67	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(a, e), f(e))
26.53/8.67	   A^2 -> H(U1(a, e), f(k))
26.53/8.67	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.67	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(a, k), f(e))
26.53/8.67	   A^2 -> H(U1(a, k), f(k))
26.53/8.67	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.67	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.67	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, a), b)
26.53/8.67	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.67	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.67	   A^2 -> H(U1(a, a), c)
26.53/8.67	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.67	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.67	   A^2 -> H(U1(a, a), e)
26.53/8.67	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.67	   A^2 -> H(k, f(b))
26.53/8.67	   A^2 -> H(c, U1(b, b))
26.53/8.67	   A^2 -> H(c, f(c))
26.53/8.67	   A^2 -> H(c, f(d))
26.53/8.67	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.67	   A^2 -> H(U1(e, k), f(c))
26.53/8.67	   A^2 -> H(U1(e, k), f(d))
26.53/8.67	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, c), f(e))
26.53/8.67	   A^2 -> H(U1(e, c), f(k))
26.53/8.67	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.67	   A^2 -> H(U1(k, e), f(c))
26.53/8.67	   A^2 -> H(U1(k, e), f(d))
26.53/8.67	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, c), f(e))
26.53/8.67	   A^2 -> H(U1(k, c), f(k))
26.53/8.67	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, e), f(e))
26.53/8.67	   A^2 -> H(U1(c, e), f(k))
26.53/8.67	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, k), f(e))
26.53/8.67	   A^2 -> H(U1(c, k), f(k))
26.53/8.67	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.67	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.67	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.67	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.67	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.67	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.67	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.67	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.67	   A^2 -> H(e, U1(b, b))
26.53/8.67	   A^2 -> H(e, f(c))
26.53/8.67	   A^2 -> H(e, f(d))
26.53/8.67	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, e), f(e))
26.53/8.67	   A^2 -> H(U1(e, e), f(k))
26.53/8.67	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.67	   A^2 -> H(f(e), U1(e, b))
26.53/8.67	   A^2 -> H(f(e), U1(k, b))
26.53/8.67	   A^2 -> H(f(e), U1(c, d))
26.53/8.67	   A^2 -> H(f(e), U1(d, c))
26.53/8.67	   A^2 -> H(f(e), U1(b, e))
26.53/8.67	   A^2 -> H(f(e), U1(b, k))
26.53/8.67	   A^2 -> H(f(e), U1(e, c))
26.53/8.67	   A^2 -> H(f(e), U1(k, c))
26.53/8.67	   A^2 -> H(f(e), U1(c, e))
26.53/8.67	   A^2 -> H(f(e), U1(c, k))
26.53/8.67	   A^2 -> H(f(e), U1(k, k))
26.53/8.67	   A^2 -> H(f(e), U1(k, d))
26.53/8.67	   A^2 -> H(f(e), U1(d, k))
26.53/8.67	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, k), f(e))
26.53/8.67	   A^2 -> H(U1(k, k), f(k))
26.53/8.67	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.67	   A^2 -> H(f(k), U1(e, b))
26.53/8.67	   A^2 -> H(f(k), U1(k, b))
26.53/8.67	   A^2 -> H(f(k), U1(c, d))
26.53/8.67	   A^2 -> H(f(k), U1(d, c))
26.53/8.67	   A^2 -> H(f(k), U1(b, e))
26.53/8.67	   A^2 -> H(f(k), U1(b, k))
26.53/8.67	   A^2 -> H(f(k), U1(e, c))
26.53/8.67	   A^2 -> H(f(k), U1(k, c))
26.53/8.67	   A^2 -> H(f(k), U1(c, e))
26.53/8.67	   A^2 -> H(f(k), U1(c, k))
26.53/8.67	   A^2 -> H(f(k), U1(e, e))
26.53/8.67	   A^2 -> H(f(k), U1(k, d))
26.53/8.67	   A^2 -> H(f(k), U1(d, k))
26.53/8.67	   A^2 -> H(f(c), b)
26.53/8.67	   A^2 -> H(f(c), U1(e, d))
26.53/8.67	   A^2 -> H(f(c), U1(d, e))
26.53/8.67	   A^2 -> H(f(k), U1(k, k))
26.53/8.67	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.67	   A^2 -> H(U1(k, k), f(c))
26.53/8.67	   A^2 -> H(U1(k, k), f(d))
26.53/8.67	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, d), f(e))
26.53/8.67	   A^2 -> H(U1(k, d), f(k))
26.53/8.67	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(d, k), f(e))
26.53/8.67	   A^2 -> H(U1(d, k), f(k))
26.53/8.67	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.67	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.67	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.67	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.67	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.67	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.67	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.67	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.67	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.67	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.67	
26.53/8.67	The TRS R consists of the following rules:
26.53/8.67	
26.53/8.67	   f(x) -> U1(x, x)
26.53/8.67	   U1(e, x) -> x
26.53/8.67	   a -> c
26.53/8.67	   a -> d
26.53/8.67	   b -> c
26.53/8.67	   b -> d
26.53/8.67	   d -> k
26.53/8.67	   c -> e
26.53/8.67	   c -> k
26.53/8.67	
26.53/8.67	Q is empty.
26.53/8.67	We have to consider all minimal (P,Q,R)-chains.
26.53/8.67	----------------------------------------
26.53/8.67	
26.53/8.67	(483) TransformationProof (EQUIVALENT)
26.53/8.67	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), f(e)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.67	
26.53/8.67	   (A^2 -> H(U1(k, d), f(e)),A^2 -> H(U1(k, d), f(e)))
26.53/8.67	   (A^2 -> H(U1(d, k), f(e)),A^2 -> H(U1(d, k), f(e)))
26.53/8.67	   (A^2 -> H(U1(d, d), U1(e, e)),A^2 -> H(U1(d, d), U1(e, e)))
26.53/8.67	
26.53/8.67	
26.53/8.67	----------------------------------------
26.53/8.67	
26.53/8.67	(484)
26.53/8.67	Obligation:
26.53/8.67	Q DP problem:
26.53/8.67	The TRS P consists of the following rules:
26.53/8.67	
26.53/8.67	   H(x, x) -> G(x, x, f(k))
26.53/8.67	   G(d, x, x) -> A^2
26.53/8.67	   A^2 -> H(f(c), f(c))
26.53/8.67	   A^2 -> H(f(d), f(d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.67	   A^2 -> H(f(e), f(e))
26.53/8.67	   A^2 -> H(f(k), f(k))
26.53/8.67	   A^2 -> H(U1(d, d), f(k))
26.53/8.67	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.67	   A^2 -> H(f(d), U1(e, b))
26.53/8.67	   A^2 -> H(f(d), U1(k, b))
26.53/8.67	   A^2 -> H(f(d), U1(c, d))
26.53/8.67	   A^2 -> H(f(d), U1(d, c))
26.53/8.67	   A^2 -> H(f(d), U1(b, e))
26.53/8.67	   A^2 -> H(f(d), U1(b, k))
26.53/8.67	   A^2 -> H(f(d), U1(e, c))
26.53/8.67	   A^2 -> H(f(d), U1(k, c))
26.53/8.67	   A^2 -> H(f(d), U1(c, e))
26.53/8.67	   A^2 -> H(f(d), U1(c, k))
26.53/8.67	   A^2 -> H(f(d), U1(e, e))
26.53/8.67	   A^2 -> H(f(d), U1(k, k))
26.53/8.67	   A^2 -> H(f(a), b)
26.53/8.67	   A^2 -> H(f(a), U1(e, d))
26.53/8.67	   A^2 -> H(f(a), U1(d, e))
26.53/8.67	   A^2 -> H(f(c), U1(e, c))
26.53/8.67	   A^2 -> H(f(c), U1(k, c))
26.53/8.67	   A^2 -> H(f(c), U1(c, e))
26.53/8.67	   A^2 -> H(f(c), U1(c, k))
26.53/8.67	   A^2 -> H(f(a), c)
26.53/8.67	   A^2 -> H(f(a), U1(e, k))
26.53/8.67	   A^2 -> H(f(a), U1(k, e))
26.53/8.67	   A^2 -> H(f(c), U1(e, e))
26.53/8.67	   A^2 -> H(f(a), e)
26.53/8.67	   A^2 -> H(f(d), U1(k, d))
26.53/8.67	   A^2 -> H(f(d), U1(d, k))
26.53/8.67	   A^2 -> H(f(a), U1(k, k))
26.53/8.67	   A^2 -> H(d, f(b))
26.53/8.67	   A^2 -> H(a, U1(b, b))
26.53/8.67	   A^2 -> H(a, f(c))
26.53/8.67	   A^2 -> H(a, f(d))
26.53/8.67	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.67	   A^2 -> H(U1(e, d), f(c))
26.53/8.67	   A^2 -> H(U1(e, d), f(d))
26.53/8.67	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, a), f(e))
26.53/8.67	   A^2 -> H(U1(e, a), f(k))
26.53/8.67	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.67	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, a), f(e))
26.53/8.67	   A^2 -> H(U1(k, a), f(k))
26.53/8.67	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, d), f(e))
26.53/8.67	   A^2 -> H(U1(c, d), f(k))
26.53/8.67	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.67	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.67	   A^2 -> H(U1(d, e), f(c))
26.53/8.67	   A^2 -> H(U1(d, e), f(d))
26.53/8.67	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(d, c), f(e))
26.53/8.67	   A^2 -> H(U1(d, c), f(k))
26.53/8.67	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(a, e), f(e))
26.53/8.67	   A^2 -> H(U1(a, e), f(k))
26.53/8.67	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.67	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(a, k), f(e))
26.53/8.67	   A^2 -> H(U1(a, k), f(k))
26.53/8.67	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.67	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.67	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, a), b)
26.53/8.67	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.67	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.67	   A^2 -> H(U1(a, a), c)
26.53/8.67	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.67	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.67	   A^2 -> H(U1(a, a), e)
26.53/8.67	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.67	   A^2 -> H(k, f(b))
26.53/8.67	   A^2 -> H(c, U1(b, b))
26.53/8.67	   A^2 -> H(c, f(c))
26.53/8.67	   A^2 -> H(c, f(d))
26.53/8.67	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.67	   A^2 -> H(U1(e, k), f(c))
26.53/8.67	   A^2 -> H(U1(e, k), f(d))
26.53/8.67	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, c), f(e))
26.53/8.67	   A^2 -> H(U1(e, c), f(k))
26.53/8.67	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.67	   A^2 -> H(U1(k, e), f(c))
26.53/8.67	   A^2 -> H(U1(k, e), f(d))
26.53/8.67	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, c), f(e))
26.53/8.67	   A^2 -> H(U1(k, c), f(k))
26.53/8.67	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, e), f(e))
26.53/8.67	   A^2 -> H(U1(c, e), f(k))
26.53/8.67	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, k), f(e))
26.53/8.67	   A^2 -> H(U1(c, k), f(k))
26.53/8.67	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.67	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.67	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.67	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.67	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.67	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.67	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.67	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.67	   A^2 -> H(e, U1(b, b))
26.53/8.67	   A^2 -> H(e, f(c))
26.53/8.67	   A^2 -> H(e, f(d))
26.53/8.67	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, e), f(e))
26.53/8.67	   A^2 -> H(U1(e, e), f(k))
26.53/8.67	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.67	   A^2 -> H(f(e), U1(e, b))
26.53/8.67	   A^2 -> H(f(e), U1(k, b))
26.53/8.67	   A^2 -> H(f(e), U1(c, d))
26.53/8.67	   A^2 -> H(f(e), U1(d, c))
26.53/8.67	   A^2 -> H(f(e), U1(b, e))
26.53/8.67	   A^2 -> H(f(e), U1(b, k))
26.53/8.67	   A^2 -> H(f(e), U1(e, c))
26.53/8.67	   A^2 -> H(f(e), U1(k, c))
26.53/8.67	   A^2 -> H(f(e), U1(c, e))
26.53/8.67	   A^2 -> H(f(e), U1(c, k))
26.53/8.67	   A^2 -> H(f(e), U1(k, k))
26.53/8.67	   A^2 -> H(f(e), U1(k, d))
26.53/8.67	   A^2 -> H(f(e), U1(d, k))
26.53/8.67	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, k), f(e))
26.53/8.67	   A^2 -> H(U1(k, k), f(k))
26.53/8.67	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.67	   A^2 -> H(f(k), U1(e, b))
26.53/8.67	   A^2 -> H(f(k), U1(k, b))
26.53/8.67	   A^2 -> H(f(k), U1(c, d))
26.53/8.67	   A^2 -> H(f(k), U1(d, c))
26.53/8.67	   A^2 -> H(f(k), U1(b, e))
26.53/8.67	   A^2 -> H(f(k), U1(b, k))
26.53/8.67	   A^2 -> H(f(k), U1(e, c))
26.53/8.67	   A^2 -> H(f(k), U1(k, c))
26.53/8.67	   A^2 -> H(f(k), U1(c, e))
26.53/8.67	   A^2 -> H(f(k), U1(c, k))
26.53/8.67	   A^2 -> H(f(k), U1(e, e))
26.53/8.67	   A^2 -> H(f(k), U1(k, d))
26.53/8.67	   A^2 -> H(f(k), U1(d, k))
26.53/8.67	   A^2 -> H(f(c), b)
26.53/8.67	   A^2 -> H(f(c), U1(e, d))
26.53/8.67	   A^2 -> H(f(c), U1(d, e))
26.53/8.67	   A^2 -> H(f(k), U1(k, k))
26.53/8.67	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.67	   A^2 -> H(U1(k, k), f(c))
26.53/8.67	   A^2 -> H(U1(k, k), f(d))
26.53/8.67	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, d), f(e))
26.53/8.67	   A^2 -> H(U1(k, d), f(k))
26.53/8.67	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(d, k), f(e))
26.53/8.67	   A^2 -> H(U1(d, k), f(k))
26.53/8.67	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.67	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.67	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.67	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.67	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.67	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.67	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.67	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.67	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.67	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.67	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.67	
26.53/8.67	The TRS R consists of the following rules:
26.53/8.67	
26.53/8.67	   f(x) -> U1(x, x)
26.53/8.67	   U1(e, x) -> x
26.53/8.67	   a -> c
26.53/8.67	   a -> d
26.53/8.67	   b -> c
26.53/8.67	   b -> d
26.53/8.67	   d -> k
26.53/8.67	   c -> e
26.53/8.67	   c -> k
26.53/8.67	
26.53/8.67	Q is empty.
26.53/8.67	We have to consider all minimal (P,Q,R)-chains.
26.53/8.67	----------------------------------------
26.53/8.67	
26.53/8.67	(485) TransformationProof (EQUIVALENT)
26.53/8.67	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), f(k)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.67	
26.53/8.67	   (A^2 -> H(U1(k, d), f(k)),A^2 -> H(U1(k, d), f(k)))
26.53/8.67	   (A^2 -> H(U1(d, k), f(k)),A^2 -> H(U1(d, k), f(k)))
26.53/8.67	   (A^2 -> H(U1(d, d), U1(k, k)),A^2 -> H(U1(d, d), U1(k, k)))
26.53/8.67	
26.53/8.67	
26.53/8.67	----------------------------------------
26.53/8.67	
26.53/8.67	(486)
26.53/8.67	Obligation:
26.53/8.67	Q DP problem:
26.53/8.67	The TRS P consists of the following rules:
26.53/8.67	
26.53/8.67	   H(x, x) -> G(x, x, f(k))
26.53/8.67	   G(d, x, x) -> A^2
26.53/8.67	   A^2 -> H(f(c), f(c))
26.53/8.67	   A^2 -> H(f(d), f(d))
26.53/8.67	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.67	   A^2 -> H(f(e), f(e))
26.53/8.67	   A^2 -> H(f(k), f(k))
26.53/8.67	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.67	   A^2 -> H(f(d), U1(e, b))
26.53/8.67	   A^2 -> H(f(d), U1(k, b))
26.53/8.67	   A^2 -> H(f(d), U1(c, d))
26.53/8.67	   A^2 -> H(f(d), U1(d, c))
26.53/8.67	   A^2 -> H(f(d), U1(b, e))
26.53/8.67	   A^2 -> H(f(d), U1(b, k))
26.53/8.67	   A^2 -> H(f(d), U1(e, c))
26.53/8.67	   A^2 -> H(f(d), U1(k, c))
26.53/8.67	   A^2 -> H(f(d), U1(c, e))
26.53/8.67	   A^2 -> H(f(d), U1(c, k))
26.53/8.67	   A^2 -> H(f(d), U1(e, e))
26.53/8.67	   A^2 -> H(f(d), U1(k, k))
26.53/8.67	   A^2 -> H(f(a), b)
26.53/8.67	   A^2 -> H(f(a), U1(e, d))
26.53/8.67	   A^2 -> H(f(a), U1(d, e))
26.53/8.67	   A^2 -> H(f(c), U1(e, c))
26.53/8.67	   A^2 -> H(f(c), U1(k, c))
26.53/8.67	   A^2 -> H(f(c), U1(c, e))
26.53/8.67	   A^2 -> H(f(c), U1(c, k))
26.53/8.67	   A^2 -> H(f(a), c)
26.53/8.67	   A^2 -> H(f(a), U1(e, k))
26.53/8.67	   A^2 -> H(f(a), U1(k, e))
26.53/8.67	   A^2 -> H(f(c), U1(e, e))
26.53/8.67	   A^2 -> H(f(a), e)
26.53/8.67	   A^2 -> H(f(d), U1(k, d))
26.53/8.67	   A^2 -> H(f(d), U1(d, k))
26.53/8.67	   A^2 -> H(f(a), U1(k, k))
26.53/8.67	   A^2 -> H(d, f(b))
26.53/8.67	   A^2 -> H(a, U1(b, b))
26.53/8.67	   A^2 -> H(a, f(c))
26.53/8.67	   A^2 -> H(a, f(d))
26.53/8.67	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.67	   A^2 -> H(U1(e, d), f(c))
26.53/8.67	   A^2 -> H(U1(e, d), f(d))
26.53/8.67	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.67	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.67	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.67	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.67	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.67	   A^2 -> H(U1(e, a), f(e))
26.53/8.67	   A^2 -> H(U1(e, a), f(k))
26.53/8.67	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.67	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.67	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.67	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.67	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.67	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.67	   A^2 -> H(U1(k, a), f(e))
26.53/8.67	   A^2 -> H(U1(k, a), f(k))
26.53/8.67	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.67	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.67	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.67	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.67	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.67	   A^2 -> H(U1(c, d), f(e))
26.53/8.67	   A^2 -> H(U1(c, d), f(k))
26.53/8.67	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.67	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.67	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.67	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.67	   A^2 -> H(U1(d, e), f(c))
26.53/8.67	   A^2 -> H(U1(d, e), f(d))
26.53/8.67	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.67	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.67	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.67	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.67	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.67	   A^2 -> H(U1(d, c), f(e))
26.53/8.67	   A^2 -> H(U1(d, c), f(k))
26.53/8.67	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.67	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.67	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.67	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.67	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.67	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.67	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.67	   A^2 -> H(U1(a, e), f(e))
26.53/8.67	   A^2 -> H(U1(a, e), f(k))
26.53/8.67	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.67	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.67	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.67	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.67	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.67	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.67	   A^2 -> H(U1(a, k), f(e))
26.53/8.67	   A^2 -> H(U1(a, k), f(k))
26.53/8.67	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.67	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.67	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.67	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.67	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.67	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.67	   A^2 -> H(U1(a, a), b)
26.53/8.67	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.67	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.67	   A^2 -> H(U1(a, a), c)
26.53/8.67	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.67	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.67	   A^2 -> H(U1(a, a), e)
26.53/8.67	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.67	   A^2 -> H(k, f(b))
26.53/8.67	   A^2 -> H(c, U1(b, b))
26.53/8.67	   A^2 -> H(c, f(c))
26.53/8.67	   A^2 -> H(c, f(d))
26.53/8.68	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.68	   A^2 -> H(U1(e, k), f(c))
26.53/8.68	   A^2 -> H(U1(e, k), f(d))
26.53/8.68	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.68	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.68	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.68	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.68	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.68	   A^2 -> H(U1(e, c), f(e))
26.53/8.68	   A^2 -> H(U1(e, c), f(k))
26.53/8.68	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.68	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.68	   A^2 -> H(U1(k, e), f(c))
26.53/8.68	   A^2 -> H(U1(k, e), f(d))
26.53/8.68	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.68	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.68	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.68	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.68	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.68	   A^2 -> H(U1(k, c), f(e))
26.53/8.68	   A^2 -> H(U1(k, c), f(k))
26.53/8.68	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.68	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.68	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.68	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.68	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.68	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.68	   A^2 -> H(U1(c, e), f(e))
26.53/8.68	   A^2 -> H(U1(c, e), f(k))
26.53/8.68	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.68	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.68	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.68	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.68	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.68	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.68	   A^2 -> H(U1(c, k), f(e))
26.53/8.68	   A^2 -> H(U1(c, k), f(k))
26.53/8.68	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.68	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.68	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.68	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.68	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.68	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.68	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.68	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.68	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.68	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.68	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.68	   A^2 -> H(e, U1(b, b))
26.53/8.68	   A^2 -> H(e, f(c))
26.53/8.68	   A^2 -> H(e, f(d))
26.53/8.68	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.68	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.68	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.68	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.68	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.68	   A^2 -> H(U1(e, e), f(e))
26.53/8.68	   A^2 -> H(U1(e, e), f(k))
26.53/8.68	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.68	   A^2 -> H(f(e), U1(e, b))
26.53/8.68	   A^2 -> H(f(e), U1(k, b))
26.53/8.68	   A^2 -> H(f(e), U1(c, d))
26.53/8.68	   A^2 -> H(f(e), U1(d, c))
26.53/8.68	   A^2 -> H(f(e), U1(b, e))
26.53/8.68	   A^2 -> H(f(e), U1(b, k))
26.53/8.68	   A^2 -> H(f(e), U1(e, c))
26.53/8.68	   A^2 -> H(f(e), U1(k, c))
26.53/8.68	   A^2 -> H(f(e), U1(c, e))
26.53/8.68	   A^2 -> H(f(e), U1(c, k))
26.53/8.68	   A^2 -> H(f(e), U1(k, k))
26.53/8.68	   A^2 -> H(f(e), U1(k, d))
26.53/8.68	   A^2 -> H(f(e), U1(d, k))
26.53/8.68	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.68	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.68	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.68	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.68	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.68	   A^2 -> H(U1(k, k), f(e))
26.53/8.68	   A^2 -> H(U1(k, k), f(k))
26.53/8.68	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.68	   A^2 -> H(f(k), U1(e, b))
26.53/8.68	   A^2 -> H(f(k), U1(k, b))
26.53/8.68	   A^2 -> H(f(k), U1(c, d))
26.53/8.68	   A^2 -> H(f(k), U1(d, c))
26.53/8.68	   A^2 -> H(f(k), U1(b, e))
26.53/8.68	   A^2 -> H(f(k), U1(b, k))
26.53/8.68	   A^2 -> H(f(k), U1(e, c))
26.53/8.68	   A^2 -> H(f(k), U1(k, c))
26.53/8.68	   A^2 -> H(f(k), U1(c, e))
26.53/8.68	   A^2 -> H(f(k), U1(c, k))
26.53/8.68	   A^2 -> H(f(k), U1(e, e))
26.53/8.68	   A^2 -> H(f(k), U1(k, d))
26.53/8.68	   A^2 -> H(f(k), U1(d, k))
26.53/8.68	   A^2 -> H(f(c), b)
26.53/8.68	   A^2 -> H(f(c), U1(e, d))
26.53/8.68	   A^2 -> H(f(c), U1(d, e))
26.53/8.68	   A^2 -> H(f(k), U1(k, k))
26.53/8.68	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.68	   A^2 -> H(U1(k, k), f(c))
26.53/8.68	   A^2 -> H(U1(k, k), f(d))
26.53/8.68	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.68	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.68	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.68	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.68	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.68	   A^2 -> H(U1(k, d), f(e))
26.53/8.68	   A^2 -> H(U1(k, d), f(k))
26.53/8.68	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.68	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.68	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.68	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.68	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.68	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.68	   A^2 -> H(U1(d, k), f(e))
26.53/8.68	   A^2 -> H(U1(d, k), f(k))
26.53/8.68	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.68	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.68	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.68	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.68	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.68	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.68	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.68	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.68	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.68	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.68	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.68	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.68	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.68	
26.53/8.68	The TRS R consists of the following rules:
26.53/8.68	
26.53/8.68	   f(x) -> U1(x, x)
26.53/8.68	   U1(e, x) -> x
26.53/8.68	   a -> c
26.53/8.68	   a -> d
26.53/8.68	   b -> c
26.53/8.68	   b -> d
26.53/8.68	   d -> k
26.53/8.68	   c -> e
26.53/8.68	   c -> k
26.53/8.68	
26.53/8.68	Q is empty.
26.53/8.68	We have to consider all minimal (P,Q,R)-chains.
26.53/8.68	----------------------------------------
26.53/8.68	
26.53/8.68	(487) TransformationProof (EQUIVALENT)
26.53/8.68	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.68	
26.53/8.68	   (A^2 -> H(U1(d, d), U1(e, b)),A^2 -> H(U1(d, d), U1(e, b)))
26.53/8.68	   (A^2 -> H(f(k), U1(e, b)),A^2 -> H(f(k), U1(e, b)))
26.53/8.68	   (A^2 -> H(f(d), b),A^2 -> H(f(d), b))
26.53/8.68	   (A^2 -> H(f(d), U1(e, c)),A^2 -> H(f(d), U1(e, c)))
26.53/8.68	   (A^2 -> H(f(d), U1(e, d)),A^2 -> H(f(d), U1(e, d)))
26.53/8.68	
26.53/8.68	
26.53/8.68	----------------------------------------
26.53/8.68	
26.53/8.68	(488)
26.53/8.68	Obligation:
26.53/8.68	Q DP problem:
26.53/8.68	The TRS P consists of the following rules:
26.53/8.68	
26.53/8.68	   H(x, x) -> G(x, x, f(k))
26.53/8.68	   G(d, x, x) -> A^2
26.53/8.68	   A^2 -> H(f(c), f(c))
26.53/8.68	   A^2 -> H(f(d), f(d))
26.53/8.68	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.68	   A^2 -> H(f(e), f(e))
26.53/8.68	   A^2 -> H(f(k), f(k))
26.53/8.68	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.68	   A^2 -> H(f(d), U1(k, b))
26.53/8.68	   A^2 -> H(f(d), U1(c, d))
26.53/8.68	   A^2 -> H(f(d), U1(d, c))
26.53/8.68	   A^2 -> H(f(d), U1(b, e))
26.53/8.68	   A^2 -> H(f(d), U1(b, k))
26.53/8.68	   A^2 -> H(f(d), U1(e, c))
26.53/8.68	   A^2 -> H(f(d), U1(k, c))
26.53/8.68	   A^2 -> H(f(d), U1(c, e))
26.53/8.68	   A^2 -> H(f(d), U1(c, k))
26.53/8.68	   A^2 -> H(f(d), U1(e, e))
26.53/8.68	   A^2 -> H(f(d), U1(k, k))
26.53/8.68	   A^2 -> H(f(a), b)
26.53/8.68	   A^2 -> H(f(a), U1(e, d))
26.53/8.68	   A^2 -> H(f(a), U1(d, e))
26.53/8.68	   A^2 -> H(f(c), U1(e, c))
26.53/8.68	   A^2 -> H(f(c), U1(k, c))
26.53/8.68	   A^2 -> H(f(c), U1(c, e))
26.53/8.68	   A^2 -> H(f(c), U1(c, k))
26.53/8.68	   A^2 -> H(f(a), c)
26.53/8.68	   A^2 -> H(f(a), U1(e, k))
26.53/8.68	   A^2 -> H(f(a), U1(k, e))
26.53/8.68	   A^2 -> H(f(c), U1(e, e))
26.53/8.68	   A^2 -> H(f(a), e)
26.53/8.68	   A^2 -> H(f(d), U1(k, d))
26.53/8.68	   A^2 -> H(f(d), U1(d, k))
26.53/8.68	   A^2 -> H(f(a), U1(k, k))
26.53/8.68	   A^2 -> H(d, f(b))
26.53/8.68	   A^2 -> H(a, U1(b, b))
26.53/8.68	   A^2 -> H(a, f(c))
26.53/8.68	   A^2 -> H(a, f(d))
26.53/8.68	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.68	   A^2 -> H(U1(e, d), f(c))
26.53/8.68	   A^2 -> H(U1(e, d), f(d))
26.53/8.68	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.68	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.68	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.68	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.68	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.68	   A^2 -> H(U1(e, a), f(e))
26.53/8.68	   A^2 -> H(U1(e, a), f(k))
26.53/8.68	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.68	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.68	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.68	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.68	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.68	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.68	   A^2 -> H(U1(k, a), f(e))
26.53/8.68	   A^2 -> H(U1(k, a), f(k))
26.53/8.68	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.68	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.68	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.68	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.68	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.68	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.68	   A^2 -> H(U1(c, d), f(e))
26.53/8.68	   A^2 -> H(U1(c, d), f(k))
26.53/8.68	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.68	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.68	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.68	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.68	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.68	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.68	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.68	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.68	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.68	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.68	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.68	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.68	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.68	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.68	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.68	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.68	   A^2 -> H(U1(d, e), f(c))
26.53/8.68	   A^2 -> H(U1(d, e), f(d))
26.53/8.68	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.68	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.68	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.68	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.68	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.68	   A^2 -> H(U1(d, c), f(e))
26.53/8.68	   A^2 -> H(U1(d, c), f(k))
26.53/8.68	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.68	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.68	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.68	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.68	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.68	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.68	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.68	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.68	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.68	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.68	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.68	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.68	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.68	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.68	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.68	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.68	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.68	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.68	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.68	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.68	   A^2 -> H(U1(a, e), f(e))
26.53/8.68	   A^2 -> H(U1(a, e), f(k))
26.53/8.68	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.68	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.68	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.68	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.68	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.68	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.68	   A^2 -> H(U1(a, k), f(e))
26.53/8.68	   A^2 -> H(U1(a, k), f(k))
26.53/8.68	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.68	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.68	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.68	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.68	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.68	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.68	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.68	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.68	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.68	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.68	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.68	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.68	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.68	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.68	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.68	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.68	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.68	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.68	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.68	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.68	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.68	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.68	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.68	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.68	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.68	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.68	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.68	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.68	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.68	   A^2 -> H(U1(a, a), b)
26.53/8.68	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.68	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.68	   A^2 -> H(U1(a, a), c)
26.53/8.68	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.68	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.68	   A^2 -> H(U1(a, a), e)
26.53/8.68	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.68	   A^2 -> H(k, f(b))
26.53/8.68	   A^2 -> H(c, U1(b, b))
26.53/8.68	   A^2 -> H(c, f(c))
26.53/8.68	   A^2 -> H(c, f(d))
26.53/8.68	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.68	   A^2 -> H(U1(e, k), f(c))
26.53/8.68	   A^2 -> H(U1(e, k), f(d))
26.53/8.68	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.68	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.68	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.68	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.68	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.68	   A^2 -> H(U1(e, c), f(e))
26.53/8.68	   A^2 -> H(U1(e, c), f(k))
26.53/8.68	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.68	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.68	   A^2 -> H(U1(k, e), f(c))
26.53/8.68	   A^2 -> H(U1(k, e), f(d))
26.53/8.68	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.68	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.68	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.68	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.68	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.68	   A^2 -> H(U1(k, c), f(e))
26.53/8.68	   A^2 -> H(U1(k, c), f(k))
26.53/8.68	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.68	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.68	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.68	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.68	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.68	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.68	   A^2 -> H(U1(c, e), f(e))
26.53/8.68	   A^2 -> H(U1(c, e), f(k))
26.53/8.68	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.68	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.68	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.68	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.68	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.68	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.68	   A^2 -> H(U1(c, k), f(e))
26.53/8.68	   A^2 -> H(U1(c, k), f(k))
26.53/8.68	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.68	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.68	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.68	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.68	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.68	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.68	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.68	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.68	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.68	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.68	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.68	   A^2 -> H(e, U1(b, b))
26.53/8.68	   A^2 -> H(e, f(c))
26.53/8.68	   A^2 -> H(e, f(d))
26.53/8.68	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.68	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.68	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.68	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.68	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.68	   A^2 -> H(U1(e, e), f(e))
26.53/8.68	   A^2 -> H(U1(e, e), f(k))
26.53/8.68	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.68	   A^2 -> H(f(e), U1(e, b))
26.53/8.68	   A^2 -> H(f(e), U1(k, b))
26.53/8.68	   A^2 -> H(f(e), U1(c, d))
26.53/8.68	   A^2 -> H(f(e), U1(d, c))
26.53/8.68	   A^2 -> H(f(e), U1(b, e))
26.53/8.68	   A^2 -> H(f(e), U1(b, k))
26.53/8.68	   A^2 -> H(f(e), U1(e, c))
26.53/8.68	   A^2 -> H(f(e), U1(k, c))
26.53/8.68	   A^2 -> H(f(e), U1(c, e))
26.53/8.68	   A^2 -> H(f(e), U1(c, k))
26.53/8.68	   A^2 -> H(f(e), U1(k, k))
26.53/8.68	   A^2 -> H(f(e), U1(k, d))
26.53/8.68	   A^2 -> H(f(e), U1(d, k))
26.53/8.68	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.68	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.68	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.68	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.68	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.68	   A^2 -> H(U1(k, k), f(e))
26.53/8.68	   A^2 -> H(U1(k, k), f(k))
26.53/8.68	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.68	   A^2 -> H(f(k), U1(e, b))
26.53/8.68	   A^2 -> H(f(k), U1(k, b))
26.53/8.68	   A^2 -> H(f(k), U1(c, d))
26.53/8.68	   A^2 -> H(f(k), U1(d, c))
26.53/8.68	   A^2 -> H(f(k), U1(b, e))
26.53/8.68	   A^2 -> H(f(k), U1(b, k))
26.53/8.68	   A^2 -> H(f(k), U1(e, c))
26.53/8.68	   A^2 -> H(f(k), U1(k, c))
26.53/8.68	   A^2 -> H(f(k), U1(c, e))
26.53/8.68	   A^2 -> H(f(k), U1(c, k))
26.53/8.68	   A^2 -> H(f(k), U1(e, e))
26.53/8.68	   A^2 -> H(f(k), U1(k, d))
26.53/8.68	   A^2 -> H(f(k), U1(d, k))
26.53/8.68	   A^2 -> H(f(c), b)
26.53/8.68	   A^2 -> H(f(c), U1(e, d))
26.53/8.68	   A^2 -> H(f(c), U1(d, e))
26.53/8.68	   A^2 -> H(f(k), U1(k, k))
26.53/8.68	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.68	   A^2 -> H(U1(k, k), f(c))
26.53/8.68	   A^2 -> H(U1(k, k), f(d))
26.53/8.68	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.68	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.68	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.68	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.68	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.68	   A^2 -> H(U1(k, d), f(e))
26.53/8.68	   A^2 -> H(U1(k, d), f(k))
26.53/8.68	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.68	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.68	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.68	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.68	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.68	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.68	   A^2 -> H(U1(d, k), f(e))
26.53/8.68	   A^2 -> H(U1(d, k), f(k))
26.53/8.68	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.68	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.68	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.68	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.68	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.68	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.68	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.68	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.68	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.68	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.68	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.68	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.68	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.68	   A^2 -> H(f(d), b)
26.53/8.68	   A^2 -> H(f(d), U1(e, d))
26.53/8.68	
26.53/8.68	The TRS R consists of the following rules:
26.53/8.68	
26.53/8.68	   f(x) -> U1(x, x)
26.53/8.68	   U1(e, x) -> x
26.53/8.68	   a -> c
26.53/8.68	   a -> d
26.53/8.68	   b -> c
26.53/8.68	   b -> d
26.53/8.68	   d -> k
26.53/8.68	   c -> e
26.53/8.68	   c -> k
26.53/8.68	
26.53/8.68	Q is empty.
26.53/8.68	We have to consider all minimal (P,Q,R)-chains.
26.53/8.68	----------------------------------------
26.53/8.68	
26.53/8.68	(489) TransformationProof (EQUIVALENT)
26.53/8.68	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.68	
26.53/8.68	   (A^2 -> H(U1(d, d), U1(k, b)),A^2 -> H(U1(d, d), U1(k, b)))
26.53/8.68	   (A^2 -> H(f(k), U1(k, b)),A^2 -> H(f(k), U1(k, b)))
26.53/8.68	   (A^2 -> H(f(d), U1(k, c)),A^2 -> H(f(d), U1(k, c)))
26.53/8.68	   (A^2 -> H(f(d), U1(k, d)),A^2 -> H(f(d), U1(k, d)))
26.53/8.68	
26.53/8.68	
26.53/8.68	----------------------------------------
26.53/8.68	
26.53/8.68	(490)
26.53/8.68	Obligation:
26.53/8.68	Q DP problem:
26.53/8.68	The TRS P consists of the following rules:
26.53/8.68	
26.53/8.68	   H(x, x) -> G(x, x, f(k))
26.53/8.68	   G(d, x, x) -> A^2
26.53/8.68	   A^2 -> H(f(c), f(c))
26.53/8.68	   A^2 -> H(f(d), f(d))
26.53/8.68	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.68	   A^2 -> H(f(e), f(e))
26.53/8.68	   A^2 -> H(f(k), f(k))
26.53/8.68	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.68	   A^2 -> H(f(d), U1(c, d))
26.53/8.68	   A^2 -> H(f(d), U1(d, c))
26.53/8.68	   A^2 -> H(f(d), U1(b, e))
26.53/8.68	   A^2 -> H(f(d), U1(b, k))
26.53/8.68	   A^2 -> H(f(d), U1(e, c))
26.53/8.68	   A^2 -> H(f(d), U1(k, c))
26.53/8.68	   A^2 -> H(f(d), U1(c, e))
26.53/8.68	   A^2 -> H(f(d), U1(c, k))
26.53/8.68	   A^2 -> H(f(d), U1(e, e))
26.53/8.68	   A^2 -> H(f(d), U1(k, k))
26.53/8.68	   A^2 -> H(f(a), b)
26.53/8.68	   A^2 -> H(f(a), U1(e, d))
26.53/8.68	   A^2 -> H(f(a), U1(d, e))
26.53/8.68	   A^2 -> H(f(c), U1(e, c))
26.53/8.68	   A^2 -> H(f(c), U1(k, c))
26.53/8.68	   A^2 -> H(f(c), U1(c, e))
26.53/8.68	   A^2 -> H(f(c), U1(c, k))
26.53/8.68	   A^2 -> H(f(a), c)
26.53/8.68	   A^2 -> H(f(a), U1(e, k))
26.53/8.68	   A^2 -> H(f(a), U1(k, e))
26.53/8.68	   A^2 -> H(f(c), U1(e, e))
26.53/8.68	   A^2 -> H(f(a), e)
26.53/8.68	   A^2 -> H(f(d), U1(k, d))
26.53/8.68	   A^2 -> H(f(d), U1(d, k))
26.53/8.68	   A^2 -> H(f(a), U1(k, k))
26.53/8.68	   A^2 -> H(d, f(b))
26.53/8.68	   A^2 -> H(a, U1(b, b))
26.53/8.68	   A^2 -> H(a, f(c))
26.53/8.68	   A^2 -> H(a, f(d))
26.53/8.68	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.68	   A^2 -> H(U1(e, d), f(c))
26.53/8.68	   A^2 -> H(U1(e, d), f(d))
26.53/8.68	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.68	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.68	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.68	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.68	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.68	   A^2 -> H(U1(e, a), f(e))
26.53/8.69	   A^2 -> H(U1(e, a), f(k))
26.53/8.69	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.69	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.69	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.69	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.69	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.69	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.69	   A^2 -> H(U1(k, a), f(e))
26.53/8.69	   A^2 -> H(U1(k, a), f(k))
26.53/8.69	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.69	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.69	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.69	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.69	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.69	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.69	   A^2 -> H(U1(c, d), f(e))
26.53/8.69	   A^2 -> H(U1(c, d), f(k))
26.53/8.69	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.69	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.69	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.69	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.69	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.69	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.69	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.69	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.69	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.69	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.69	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.69	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.69	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.69	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.69	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.69	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.69	   A^2 -> H(U1(d, e), f(c))
26.53/8.69	   A^2 -> H(U1(d, e), f(d))
26.53/8.69	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.69	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.69	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.69	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.69	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.69	   A^2 -> H(U1(d, c), f(e))
26.53/8.69	   A^2 -> H(U1(d, c), f(k))
26.53/8.69	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.69	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.69	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.69	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.69	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.69	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.69	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.69	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.69	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.69	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.69	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.69	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.69	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.69	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.69	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.69	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.69	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.69	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.69	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.69	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.69	   A^2 -> H(U1(a, e), f(e))
26.53/8.69	   A^2 -> H(U1(a, e), f(k))
26.53/8.69	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.69	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.69	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.69	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.69	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.69	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.69	   A^2 -> H(U1(a, k), f(e))
26.53/8.69	   A^2 -> H(U1(a, k), f(k))
26.53/8.69	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.69	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.69	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.69	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.69	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.69	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.69	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.69	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.69	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.69	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.69	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.69	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.69	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.69	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.69	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.69	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.69	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.69	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.69	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.69	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.69	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.69	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.69	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.69	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.69	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.69	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.69	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.69	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.69	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.69	   A^2 -> H(U1(a, a), b)
26.53/8.69	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.69	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.69	   A^2 -> H(U1(a, a), c)
26.53/8.69	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.69	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.69	   A^2 -> H(U1(a, a), e)
26.53/8.69	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.69	   A^2 -> H(k, f(b))
26.53/8.69	   A^2 -> H(c, U1(b, b))
26.53/8.69	   A^2 -> H(c, f(c))
26.53/8.69	   A^2 -> H(c, f(d))
26.53/8.69	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.69	   A^2 -> H(U1(e, k), f(c))
26.53/8.69	   A^2 -> H(U1(e, k), f(d))
26.53/8.69	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.69	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.69	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.69	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.69	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.69	   A^2 -> H(U1(e, c), f(e))
26.53/8.69	   A^2 -> H(U1(e, c), f(k))
26.53/8.69	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.69	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.69	   A^2 -> H(U1(k, e), f(c))
26.53/8.69	   A^2 -> H(U1(k, e), f(d))
26.53/8.69	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.69	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.69	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.69	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.69	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.69	   A^2 -> H(U1(k, c), f(e))
26.53/8.69	   A^2 -> H(U1(k, c), f(k))
26.53/8.69	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.69	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.69	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.69	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.69	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.69	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.69	   A^2 -> H(U1(c, e), f(e))
26.53/8.69	   A^2 -> H(U1(c, e), f(k))
26.53/8.69	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.69	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.69	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.69	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.69	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.69	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.69	   A^2 -> H(U1(c, k), f(e))
26.53/8.69	   A^2 -> H(U1(c, k), f(k))
26.53/8.69	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.69	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.69	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.69	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.69	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.69	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.69	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.69	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.69	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.69	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.69	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.69	   A^2 -> H(e, U1(b, b))
26.53/8.69	   A^2 -> H(e, f(c))
26.53/8.69	   A^2 -> H(e, f(d))
26.53/8.69	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.69	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.69	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.69	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.69	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.69	   A^2 -> H(U1(e, e), f(e))
26.53/8.69	   A^2 -> H(U1(e, e), f(k))
26.53/8.69	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.69	   A^2 -> H(f(e), U1(e, b))
26.53/8.69	   A^2 -> H(f(e), U1(k, b))
26.53/8.69	   A^2 -> H(f(e), U1(c, d))
26.53/8.69	   A^2 -> H(f(e), U1(d, c))
26.53/8.69	   A^2 -> H(f(e), U1(b, e))
26.53/8.69	   A^2 -> H(f(e), U1(b, k))
26.53/8.69	   A^2 -> H(f(e), U1(e, c))
26.53/8.69	   A^2 -> H(f(e), U1(k, c))
26.53/8.69	   A^2 -> H(f(e), U1(c, e))
26.53/8.69	   A^2 -> H(f(e), U1(c, k))
26.53/8.69	   A^2 -> H(f(e), U1(k, k))
26.53/8.69	   A^2 -> H(f(e), U1(k, d))
26.53/8.69	   A^2 -> H(f(e), U1(d, k))
26.53/8.69	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.69	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.69	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.69	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.69	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.69	   A^2 -> H(U1(k, k), f(e))
26.53/8.69	   A^2 -> H(U1(k, k), f(k))
26.53/8.69	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.69	   A^2 -> H(f(k), U1(e, b))
26.53/8.69	   A^2 -> H(f(k), U1(k, b))
26.53/8.69	   A^2 -> H(f(k), U1(c, d))
26.53/8.69	   A^2 -> H(f(k), U1(d, c))
26.53/8.69	   A^2 -> H(f(k), U1(b, e))
26.53/8.69	   A^2 -> H(f(k), U1(b, k))
26.53/8.69	   A^2 -> H(f(k), U1(e, c))
26.53/8.69	   A^2 -> H(f(k), U1(k, c))
26.53/8.69	   A^2 -> H(f(k), U1(c, e))
26.53/8.69	   A^2 -> H(f(k), U1(c, k))
26.53/8.69	   A^2 -> H(f(k), U1(e, e))
26.53/8.69	   A^2 -> H(f(k), U1(k, d))
26.53/8.69	   A^2 -> H(f(k), U1(d, k))
26.53/8.69	   A^2 -> H(f(c), b)
26.53/8.69	   A^2 -> H(f(c), U1(e, d))
26.53/8.69	   A^2 -> H(f(c), U1(d, e))
26.53/8.69	   A^2 -> H(f(k), U1(k, k))
26.53/8.69	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.69	   A^2 -> H(U1(k, k), f(c))
26.53/8.69	   A^2 -> H(U1(k, k), f(d))
26.53/8.69	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.69	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.69	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.69	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.69	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.69	   A^2 -> H(U1(k, d), f(e))
26.53/8.69	   A^2 -> H(U1(k, d), f(k))
26.53/8.69	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.69	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.69	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.69	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.69	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.69	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.69	   A^2 -> H(U1(d, k), f(e))
26.53/8.69	   A^2 -> H(U1(d, k), f(k))
26.53/8.69	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.69	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.69	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.69	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.69	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.69	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.69	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.69	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.69	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.69	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.69	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.69	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.69	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.69	   A^2 -> H(f(d), b)
26.53/8.69	   A^2 -> H(f(d), U1(e, d))
26.53/8.69	
26.53/8.69	The TRS R consists of the following rules:
26.53/8.69	
26.53/8.69	   f(x) -> U1(x, x)
26.53/8.69	   U1(e, x) -> x
26.53/8.69	   a -> c
26.53/8.69	   a -> d
26.53/8.69	   b -> c
26.53/8.69	   b -> d
26.53/8.69	   d -> k
26.53/8.69	   c -> e
26.53/8.69	   c -> k
26.53/8.69	
26.53/8.69	Q is empty.
26.53/8.69	We have to consider all minimal (P,Q,R)-chains.
26.53/8.69	----------------------------------------
26.53/8.69	
26.53/8.69	(491) TransformationProof (EQUIVALENT)
26.53/8.69	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.69	
26.53/8.69	   (A^2 -> H(U1(d, d), U1(c, d)),A^2 -> H(U1(d, d), U1(c, d)))
26.53/8.69	   (A^2 -> H(f(k), U1(c, d)),A^2 -> H(f(k), U1(c, d)))
26.53/8.69	   (A^2 -> H(f(d), U1(e, d)),A^2 -> H(f(d), U1(e, d)))
26.53/8.69	   (A^2 -> H(f(d), U1(k, d)),A^2 -> H(f(d), U1(k, d)))
26.53/8.69	   (A^2 -> H(f(d), U1(c, k)),A^2 -> H(f(d), U1(c, k)))
26.53/8.69	
26.53/8.69	
26.53/8.69	----------------------------------------
26.53/8.69	
26.53/8.69	(492)
26.53/8.69	Obligation:
26.53/8.69	Q DP problem:
26.53/8.69	The TRS P consists of the following rules:
26.53/8.69	
26.53/8.69	   H(x, x) -> G(x, x, f(k))
26.53/8.69	   G(d, x, x) -> A^2
26.53/8.69	   A^2 -> H(f(c), f(c))
26.53/8.69	   A^2 -> H(f(d), f(d))
26.53/8.69	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.69	   A^2 -> H(f(e), f(e))
26.53/8.69	   A^2 -> H(f(k), f(k))
26.53/8.69	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.69	   A^2 -> H(f(d), U1(d, c))
26.53/8.69	   A^2 -> H(f(d), U1(b, e))
26.53/8.69	   A^2 -> H(f(d), U1(b, k))
26.53/8.69	   A^2 -> H(f(d), U1(e, c))
26.53/8.69	   A^2 -> H(f(d), U1(k, c))
26.53/8.69	   A^2 -> H(f(d), U1(c, e))
26.53/8.69	   A^2 -> H(f(d), U1(c, k))
26.53/8.69	   A^2 -> H(f(d), U1(e, e))
26.53/8.69	   A^2 -> H(f(d), U1(k, k))
26.53/8.69	   A^2 -> H(f(a), b)
26.53/8.69	   A^2 -> H(f(a), U1(e, d))
26.53/8.69	   A^2 -> H(f(a), U1(d, e))
26.53/8.69	   A^2 -> H(f(c), U1(e, c))
26.53/8.69	   A^2 -> H(f(c), U1(k, c))
26.53/8.69	   A^2 -> H(f(c), U1(c, e))
26.53/8.69	   A^2 -> H(f(c), U1(c, k))
26.53/8.69	   A^2 -> H(f(a), c)
26.53/8.69	   A^2 -> H(f(a), U1(e, k))
26.53/8.69	   A^2 -> H(f(a), U1(k, e))
26.53/8.69	   A^2 -> H(f(c), U1(e, e))
26.53/8.69	   A^2 -> H(f(a), e)
26.53/8.69	   A^2 -> H(f(d), U1(k, d))
26.53/8.69	   A^2 -> H(f(d), U1(d, k))
26.53/8.69	   A^2 -> H(f(a), U1(k, k))
26.53/8.69	   A^2 -> H(d, f(b))
26.53/8.69	   A^2 -> H(a, U1(b, b))
26.53/8.69	   A^2 -> H(a, f(c))
26.53/8.69	   A^2 -> H(a, f(d))
26.53/8.69	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.69	   A^2 -> H(U1(e, d), f(c))
26.53/8.69	   A^2 -> H(U1(e, d), f(d))
26.53/8.69	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.69	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.69	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.69	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.69	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.69	   A^2 -> H(U1(e, a), f(e))
26.53/8.69	   A^2 -> H(U1(e, a), f(k))
26.53/8.69	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.69	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.69	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.69	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.69	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.69	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.69	   A^2 -> H(U1(k, a), f(e))
26.53/8.69	   A^2 -> H(U1(k, a), f(k))
26.53/8.69	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.69	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.69	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.69	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.69	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.69	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.69	   A^2 -> H(U1(c, d), f(e))
26.53/8.69	   A^2 -> H(U1(c, d), f(k))
26.53/8.69	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.69	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.69	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.69	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.69	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.69	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.69	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.69	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.69	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.69	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.69	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.69	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.69	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.69	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.69	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.69	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.69	   A^2 -> H(U1(d, e), f(c))
26.53/8.69	   A^2 -> H(U1(d, e), f(d))
26.53/8.69	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.69	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.69	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.69	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.69	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.69	   A^2 -> H(U1(d, c), f(e))
26.53/8.69	   A^2 -> H(U1(d, c), f(k))
26.53/8.69	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.69	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.69	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.69	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.69	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.69	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.69	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.69	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.69	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.69	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.69	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.69	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.69	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.69	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.69	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.69	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.69	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.69	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.69	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.69	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.69	   A^2 -> H(U1(a, e), f(e))
26.53/8.69	   A^2 -> H(U1(a, e), f(k))
26.53/8.69	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.69	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.69	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.69	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.69	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.69	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.69	   A^2 -> H(U1(a, k), f(e))
26.53/8.69	   A^2 -> H(U1(a, k), f(k))
26.53/8.69	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.69	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.69	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.69	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.69	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.69	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.69	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.69	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.69	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.69	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.69	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.69	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.69	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.69	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.69	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.69	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.69	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.69	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.69	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.69	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.69	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.69	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.69	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.69	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.69	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.69	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.69	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.69	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.69	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.69	   A^2 -> H(U1(a, a), b)
26.53/8.69	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.69	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.69	   A^2 -> H(U1(a, a), c)
26.53/8.69	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.69	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.69	   A^2 -> H(U1(a, a), e)
26.53/8.69	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.69	   A^2 -> H(k, f(b))
26.53/8.69	   A^2 -> H(c, U1(b, b))
26.53/8.69	   A^2 -> H(c, f(c))
26.53/8.69	   A^2 -> H(c, f(d))
26.53/8.69	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.69	   A^2 -> H(U1(e, k), f(c))
26.53/8.69	   A^2 -> H(U1(e, k), f(d))
26.53/8.69	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.69	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.69	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.69	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.69	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.69	   A^2 -> H(U1(e, c), f(e))
26.53/8.69	   A^2 -> H(U1(e, c), f(k))
26.53/8.69	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.69	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.69	   A^2 -> H(U1(k, e), f(c))
26.53/8.69	   A^2 -> H(U1(k, e), f(d))
26.53/8.69	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.69	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.69	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.69	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.69	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.69	   A^2 -> H(U1(k, c), f(e))
26.53/8.69	   A^2 -> H(U1(k, c), f(k))
26.53/8.69	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.69	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.69	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.69	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.69	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.69	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.69	   A^2 -> H(U1(c, e), f(e))
26.53/8.69	   A^2 -> H(U1(c, e), f(k))
26.53/8.69	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.69	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.69	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.69	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.69	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.69	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.69	   A^2 -> H(U1(c, k), f(e))
26.53/8.69	   A^2 -> H(U1(c, k), f(k))
26.53/8.69	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.69	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.69	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.69	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.69	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.69	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.69	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.69	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.69	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.69	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.69	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.69	   A^2 -> H(e, U1(b, b))
26.53/8.69	   A^2 -> H(e, f(c))
26.53/8.69	   A^2 -> H(e, f(d))
26.53/8.69	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.69	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.69	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.69	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.69	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.69	   A^2 -> H(U1(e, e), f(e))
26.53/8.69	   A^2 -> H(U1(e, e), f(k))
26.53/8.69	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.69	   A^2 -> H(f(e), U1(e, b))
26.53/8.69	   A^2 -> H(f(e), U1(k, b))
26.53/8.69	   A^2 -> H(f(e), U1(c, d))
26.53/8.69	   A^2 -> H(f(e), U1(d, c))
26.53/8.69	   A^2 -> H(f(e), U1(b, e))
26.53/8.69	   A^2 -> H(f(e), U1(b, k))
26.53/8.69	   A^2 -> H(f(e), U1(e, c))
26.53/8.69	   A^2 -> H(f(e), U1(k, c))
26.53/8.69	   A^2 -> H(f(e), U1(c, e))
26.53/8.69	   A^2 -> H(f(e), U1(c, k))
26.53/8.69	   A^2 -> H(f(e), U1(k, k))
26.53/8.69	   A^2 -> H(f(e), U1(k, d))
26.53/8.69	   A^2 -> H(f(e), U1(d, k))
26.53/8.69	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.69	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.69	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.69	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.69	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.69	   A^2 -> H(U1(k, k), f(e))
26.53/8.69	   A^2 -> H(U1(k, k), f(k))
26.53/8.69	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.69	   A^2 -> H(f(k), U1(e, b))
26.53/8.69	   A^2 -> H(f(k), U1(k, b))
26.53/8.69	   A^2 -> H(f(k), U1(c, d))
26.53/8.69	   A^2 -> H(f(k), U1(d, c))
26.53/8.69	   A^2 -> H(f(k), U1(b, e))
26.53/8.69	   A^2 -> H(f(k), U1(b, k))
26.53/8.69	   A^2 -> H(f(k), U1(e, c))
26.53/8.69	   A^2 -> H(f(k), U1(k, c))
26.53/8.69	   A^2 -> H(f(k), U1(c, e))
26.53/8.69	   A^2 -> H(f(k), U1(c, k))
26.53/8.69	   A^2 -> H(f(k), U1(e, e))
26.53/8.69	   A^2 -> H(f(k), U1(k, d))
26.53/8.69	   A^2 -> H(f(k), U1(d, k))
26.53/8.69	   A^2 -> H(f(c), b)
26.53/8.69	   A^2 -> H(f(c), U1(e, d))
26.53/8.69	   A^2 -> H(f(c), U1(d, e))
26.53/8.69	   A^2 -> H(f(k), U1(k, k))
26.53/8.69	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.69	   A^2 -> H(U1(k, k), f(c))
26.53/8.69	   A^2 -> H(U1(k, k), f(d))
26.53/8.69	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.69	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.69	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.69	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.69	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.69	   A^2 -> H(U1(k, d), f(e))
26.53/8.69	   A^2 -> H(U1(k, d), f(k))
26.53/8.69	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.69	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.69	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.69	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.69	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.69	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.69	   A^2 -> H(U1(d, k), f(e))
26.53/8.69	   A^2 -> H(U1(d, k), f(k))
26.53/8.69	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.69	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.69	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.69	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.69	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.69	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.69	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.69	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.69	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.69	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.69	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.69	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.69	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.69	   A^2 -> H(f(d), b)
26.53/8.69	   A^2 -> H(f(d), U1(e, d))
26.53/8.69	
26.53/8.69	The TRS R consists of the following rules:
26.53/8.69	
26.53/8.69	   f(x) -> U1(x, x)
26.53/8.69	   U1(e, x) -> x
26.53/8.69	   a -> c
26.53/8.69	   a -> d
26.53/8.69	   b -> c
26.53/8.69	   b -> d
26.53/8.69	   d -> k
26.53/8.69	   c -> e
26.53/8.69	   c -> k
26.53/8.69	
26.53/8.69	Q is empty.
26.53/8.69	We have to consider all minimal (P,Q,R)-chains.
26.53/8.69	----------------------------------------
26.53/8.69	
26.53/8.69	(493) TransformationProof (EQUIVALENT)
26.53/8.69	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.69	
26.53/8.69	   (A^2 -> H(U1(d, d), U1(d, c)),A^2 -> H(U1(d, d), U1(d, c)))
26.53/8.69	   (A^2 -> H(f(k), U1(d, c)),A^2 -> H(f(k), U1(d, c)))
26.53/8.69	   (A^2 -> H(f(d), U1(k, c)),A^2 -> H(f(d), U1(k, c)))
26.53/8.69	   (A^2 -> H(f(d), U1(d, e)),A^2 -> H(f(d), U1(d, e)))
26.53/8.69	   (A^2 -> H(f(d), U1(d, k)),A^2 -> H(f(d), U1(d, k)))
26.53/8.69	
26.53/8.69	
26.53/8.69	----------------------------------------
26.53/8.69	
26.53/8.69	(494)
26.53/8.69	Obligation:
26.53/8.69	Q DP problem:
26.53/8.69	The TRS P consists of the following rules:
26.53/8.69	
26.53/8.69	   H(x, x) -> G(x, x, f(k))
26.53/8.69	   G(d, x, x) -> A^2
26.53/8.69	   A^2 -> H(f(c), f(c))
26.53/8.69	   A^2 -> H(f(d), f(d))
26.53/8.69	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.69	   A^2 -> H(f(e), f(e))
26.53/8.69	   A^2 -> H(f(k), f(k))
26.53/8.69	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.69	   A^2 -> H(f(d), U1(b, e))
26.53/8.69	   A^2 -> H(f(d), U1(b, k))
26.53/8.69	   A^2 -> H(f(d), U1(e, c))
26.53/8.69	   A^2 -> H(f(d), U1(k, c))
26.53/8.69	   A^2 -> H(f(d), U1(c, e))
26.53/8.69	   A^2 -> H(f(d), U1(c, k))
26.53/8.69	   A^2 -> H(f(d), U1(e, e))
26.53/8.69	   A^2 -> H(f(d), U1(k, k))
26.53/8.69	   A^2 -> H(f(a), b)
26.53/8.69	   A^2 -> H(f(a), U1(e, d))
26.53/8.69	   A^2 -> H(f(a), U1(d, e))
26.53/8.69	   A^2 -> H(f(c), U1(e, c))
26.53/8.69	   A^2 -> H(f(c), U1(k, c))
26.53/8.69	   A^2 -> H(f(c), U1(c, e))
26.53/8.69	   A^2 -> H(f(c), U1(c, k))
26.53/8.69	   A^2 -> H(f(a), c)
26.53/8.69	   A^2 -> H(f(a), U1(e, k))
26.53/8.69	   A^2 -> H(f(a), U1(k, e))
26.53/8.69	   A^2 -> H(f(c), U1(e, e))
26.53/8.69	   A^2 -> H(f(a), e)
26.53/8.69	   A^2 -> H(f(d), U1(k, d))
26.53/8.69	   A^2 -> H(f(d), U1(d, k))
26.53/8.69	   A^2 -> H(f(a), U1(k, k))
26.53/8.69	   A^2 -> H(d, f(b))
26.53/8.69	   A^2 -> H(a, U1(b, b))
26.53/8.69	   A^2 -> H(a, f(c))
26.53/8.69	   A^2 -> H(a, f(d))
26.53/8.69	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.69	   A^2 -> H(U1(e, d), f(c))
26.53/8.69	   A^2 -> H(U1(e, d), f(d))
26.53/8.69	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.69	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.69	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.69	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.69	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.69	   A^2 -> H(U1(e, a), f(e))
26.53/8.69	   A^2 -> H(U1(e, a), f(k))
26.53/8.69	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.69	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.69	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.69	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.69	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.69	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.69	   A^2 -> H(U1(k, a), f(e))
26.53/8.69	   A^2 -> H(U1(k, a), f(k))
26.53/8.69	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.69	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.69	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.69	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.69	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.69	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.69	   A^2 -> H(U1(c, d), f(e))
26.53/8.69	   A^2 -> H(U1(c, d), f(k))
26.53/8.69	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.69	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.69	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.69	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.69	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.69	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.69	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.69	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.69	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.69	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.69	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.69	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.69	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.69	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.69	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.69	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.69	   A^2 -> H(U1(d, e), f(c))
26.53/8.69	   A^2 -> H(U1(d, e), f(d))
26.53/8.69	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.69	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.69	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.69	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.69	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.69	   A^2 -> H(U1(d, c), f(e))
26.53/8.69	   A^2 -> H(U1(d, c), f(k))
26.53/8.69	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.69	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.69	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.69	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.69	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.69	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.69	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.69	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.69	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.69	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.69	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.69	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.69	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.69	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.69	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.69	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.69	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.69	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.69	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.69	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.69	   A^2 -> H(U1(a, e), f(e))
26.53/8.69	   A^2 -> H(U1(a, e), f(k))
26.53/8.69	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.69	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.69	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.69	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.69	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.69	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.69	   A^2 -> H(U1(a, k), f(e))
26.53/8.69	   A^2 -> H(U1(a, k), f(k))
26.53/8.69	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.69	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.69	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.69	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.69	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.69	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.69	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.69	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.69	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.69	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.69	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.69	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.69	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.69	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.69	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.69	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.69	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.69	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.69	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.69	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.69	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.69	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.69	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.69	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.69	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.69	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.69	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.69	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.69	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.69	   A^2 -> H(U1(a, a), b)
26.53/8.69	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.69	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.69	   A^2 -> H(U1(a, a), c)
26.53/8.69	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.69	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.69	   A^2 -> H(U1(a, a), e)
26.53/8.69	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.69	   A^2 -> H(k, f(b))
26.53/8.69	   A^2 -> H(c, U1(b, b))
26.53/8.69	   A^2 -> H(c, f(c))
26.53/8.69	   A^2 -> H(c, f(d))
26.53/8.69	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.69	   A^2 -> H(U1(e, k), f(c))
26.53/8.69	   A^2 -> H(U1(e, k), f(d))
26.53/8.69	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.69	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.69	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.69	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.69	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.69	   A^2 -> H(U1(e, c), f(e))
26.53/8.69	   A^2 -> H(U1(e, c), f(k))
26.53/8.69	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.69	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.69	   A^2 -> H(U1(k, e), f(c))
26.53/8.69	   A^2 -> H(U1(k, e), f(d))
26.53/8.69	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.69	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.69	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.69	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.69	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.69	   A^2 -> H(U1(k, c), f(e))
26.53/8.69	   A^2 -> H(U1(k, c), f(k))
26.53/8.69	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.69	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.69	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.69	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.69	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.69	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.69	   A^2 -> H(U1(c, e), f(e))
26.53/8.69	   A^2 -> H(U1(c, e), f(k))
26.53/8.69	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.69	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.69	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.69	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.69	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.69	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.69	   A^2 -> H(U1(c, k), f(e))
26.53/8.69	   A^2 -> H(U1(c, k), f(k))
26.53/8.69	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.69	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.69	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.69	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.69	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.69	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.69	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.69	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.69	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.69	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.69	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.69	   A^2 -> H(e, U1(b, b))
26.53/8.69	   A^2 -> H(e, f(c))
26.53/8.69	   A^2 -> H(e, f(d))
26.53/8.69	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.69	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.69	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.69	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.69	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.69	   A^2 -> H(U1(e, e), f(e))
26.53/8.69	   A^2 -> H(U1(e, e), f(k))
26.53/8.69	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.69	   A^2 -> H(f(e), U1(e, b))
26.53/8.69	   A^2 -> H(f(e), U1(k, b))
26.53/8.69	   A^2 -> H(f(e), U1(c, d))
26.53/8.69	   A^2 -> H(f(e), U1(d, c))
26.53/8.69	   A^2 -> H(f(e), U1(b, e))
26.53/8.69	   A^2 -> H(f(e), U1(b, k))
26.53/8.69	   A^2 -> H(f(e), U1(e, c))
26.53/8.69	   A^2 -> H(f(e), U1(k, c))
26.53/8.69	   A^2 -> H(f(e), U1(c, e))
26.53/8.69	   A^2 -> H(f(e), U1(c, k))
26.53/8.69	   A^2 -> H(f(e), U1(k, k))
26.53/8.69	   A^2 -> H(f(e), U1(k, d))
26.53/8.69	   A^2 -> H(f(e), U1(d, k))
26.53/8.69	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.69	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.69	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.69	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.69	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.69	   A^2 -> H(U1(k, k), f(e))
26.53/8.69	   A^2 -> H(U1(k, k), f(k))
26.53/8.69	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.69	   A^2 -> H(f(k), U1(e, b))
26.53/8.69	   A^2 -> H(f(k), U1(k, b))
26.53/8.69	   A^2 -> H(f(k), U1(c, d))
26.53/8.69	   A^2 -> H(f(k), U1(d, c))
26.53/8.69	   A^2 -> H(f(k), U1(b, e))
26.53/8.69	   A^2 -> H(f(k), U1(b, k))
26.53/8.69	   A^2 -> H(f(k), U1(e, c))
26.53/8.69	   A^2 -> H(f(k), U1(k, c))
26.53/8.69	   A^2 -> H(f(k), U1(c, e))
26.53/8.69	   A^2 -> H(f(k), U1(c, k))
26.53/8.69	   A^2 -> H(f(k), U1(e, e))
26.53/8.69	   A^2 -> H(f(k), U1(k, d))
26.53/8.69	   A^2 -> H(f(k), U1(d, k))
26.53/8.69	   A^2 -> H(f(c), b)
26.53/8.69	   A^2 -> H(f(c), U1(e, d))
26.53/8.69	   A^2 -> H(f(c), U1(d, e))
26.53/8.69	   A^2 -> H(f(k), U1(k, k))
26.53/8.69	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.69	   A^2 -> H(U1(k, k), f(c))
26.53/8.69	   A^2 -> H(U1(k, k), f(d))
26.53/8.69	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.69	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.69	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.69	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.69	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.69	   A^2 -> H(U1(k, d), f(e))
26.53/8.69	   A^2 -> H(U1(k, d), f(k))
26.53/8.69	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.69	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.69	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.69	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.69	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.69	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.69	   A^2 -> H(U1(d, k), f(e))
26.53/8.69	   A^2 -> H(U1(d, k), f(k))
26.53/8.69	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.69	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.69	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.69	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.69	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.69	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.69	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.69	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.69	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.69	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.69	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.69	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.69	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.69	   A^2 -> H(f(d), b)
26.53/8.69	   A^2 -> H(f(d), U1(e, d))
26.53/8.69	   A^2 -> H(f(d), U1(d, e))
26.53/8.69	
26.53/8.69	The TRS R consists of the following rules:
26.53/8.69	
26.53/8.69	   f(x) -> U1(x, x)
26.53/8.69	   U1(e, x) -> x
26.53/8.69	   a -> c
26.53/8.69	   a -> d
26.53/8.69	   b -> c
26.53/8.69	   b -> d
26.53/8.69	   d -> k
26.53/8.69	   c -> e
26.53/8.69	   c -> k
26.53/8.69	
26.53/8.69	Q is empty.
26.53/8.69	We have to consider all minimal (P,Q,R)-chains.
26.53/8.69	----------------------------------------
26.53/8.69	
26.53/8.69	(495) TransformationProof (EQUIVALENT)
26.53/8.69	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.70	
26.53/8.70	   (A^2 -> H(U1(d, d), U1(b, e)),A^2 -> H(U1(d, d), U1(b, e)))
26.53/8.70	   (A^2 -> H(f(k), U1(b, e)),A^2 -> H(f(k), U1(b, e)))
26.53/8.70	   (A^2 -> H(f(d), U1(c, e)),A^2 -> H(f(d), U1(c, e)))
26.53/8.70	   (A^2 -> H(f(d), U1(d, e)),A^2 -> H(f(d), U1(d, e)))
26.53/8.70	
26.53/8.70	
26.53/8.70	----------------------------------------
26.53/8.70	
26.53/8.70	(496)
26.53/8.70	Obligation:
26.53/8.70	Q DP problem:
26.53/8.70	The TRS P consists of the following rules:
26.53/8.70	
26.53/8.70	   H(x, x) -> G(x, x, f(k))
26.53/8.70	   G(d, x, x) -> A^2
26.53/8.70	   A^2 -> H(f(c), f(c))
26.53/8.70	   A^2 -> H(f(d), f(d))
26.53/8.70	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.70	   A^2 -> H(f(e), f(e))
26.53/8.70	   A^2 -> H(f(k), f(k))
26.53/8.70	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.70	   A^2 -> H(f(d), U1(b, k))
26.53/8.70	   A^2 -> H(f(d), U1(e, c))
26.53/8.70	   A^2 -> H(f(d), U1(k, c))
26.53/8.70	   A^2 -> H(f(d), U1(c, e))
26.53/8.70	   A^2 -> H(f(d), U1(c, k))
26.53/8.70	   A^2 -> H(f(d), U1(e, e))
26.53/8.70	   A^2 -> H(f(d), U1(k, k))
26.53/8.70	   A^2 -> H(f(a), b)
26.53/8.70	   A^2 -> H(f(a), U1(e, d))
26.53/8.70	   A^2 -> H(f(a), U1(d, e))
26.53/8.70	   A^2 -> H(f(c), U1(e, c))
26.53/8.70	   A^2 -> H(f(c), U1(k, c))
26.53/8.70	   A^2 -> H(f(c), U1(c, e))
26.53/8.70	   A^2 -> H(f(c), U1(c, k))
26.53/8.70	   A^2 -> H(f(a), c)
26.53/8.70	   A^2 -> H(f(a), U1(e, k))
26.53/8.70	   A^2 -> H(f(a), U1(k, e))
26.53/8.70	   A^2 -> H(f(c), U1(e, e))
26.53/8.70	   A^2 -> H(f(a), e)
26.53/8.70	   A^2 -> H(f(d), U1(k, d))
26.53/8.70	   A^2 -> H(f(d), U1(d, k))
26.53/8.70	   A^2 -> H(f(a), U1(k, k))
26.53/8.70	   A^2 -> H(d, f(b))
26.53/8.70	   A^2 -> H(a, U1(b, b))
26.53/8.70	   A^2 -> H(a, f(c))
26.53/8.70	   A^2 -> H(a, f(d))
26.53/8.70	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.70	   A^2 -> H(U1(e, d), f(c))
26.53/8.70	   A^2 -> H(U1(e, d), f(d))
26.53/8.70	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.70	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.70	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.70	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.70	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.70	   A^2 -> H(U1(e, a), f(e))
26.53/8.70	   A^2 -> H(U1(e, a), f(k))
26.53/8.70	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.70	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.70	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.70	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.70	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.70	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.70	   A^2 -> H(U1(k, a), f(e))
26.53/8.70	   A^2 -> H(U1(k, a), f(k))
26.53/8.70	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.70	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.70	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.70	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.70	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.70	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.70	   A^2 -> H(U1(c, d), f(e))
26.53/8.70	   A^2 -> H(U1(c, d), f(k))
26.53/8.70	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.70	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.70	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.70	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.70	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.70	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.70	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.70	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.70	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.70	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.70	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.70	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.70	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.70	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.70	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.70	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.70	   A^2 -> H(U1(d, e), f(c))
26.53/8.70	   A^2 -> H(U1(d, e), f(d))
26.53/8.70	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.70	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.70	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.70	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.70	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.70	   A^2 -> H(U1(d, c), f(e))
26.53/8.70	   A^2 -> H(U1(d, c), f(k))
26.53/8.70	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.70	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.70	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.70	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.70	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.70	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.70	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.70	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.70	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.70	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.70	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.70	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.70	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.70	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.70	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.70	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.70	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.70	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.70	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.70	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.70	   A^2 -> H(U1(a, e), f(e))
26.53/8.70	   A^2 -> H(U1(a, e), f(k))
26.53/8.70	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.70	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.70	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.70	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.70	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.70	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.70	   A^2 -> H(U1(a, k), f(e))
26.53/8.70	   A^2 -> H(U1(a, k), f(k))
26.53/8.70	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.70	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.70	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.70	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.70	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.70	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.70	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.70	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.70	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.70	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.70	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.70	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.70	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.70	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.70	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.70	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.70	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.70	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.70	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.70	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.70	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.70	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.70	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.70	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.70	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.70	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.70	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.70	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.70	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.70	   A^2 -> H(U1(a, a), b)
26.53/8.70	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.70	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.70	   A^2 -> H(U1(a, a), c)
26.53/8.70	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.70	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.70	   A^2 -> H(U1(a, a), e)
26.53/8.70	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.70	   A^2 -> H(k, f(b))
26.53/8.70	   A^2 -> H(c, U1(b, b))
26.53/8.70	   A^2 -> H(c, f(c))
26.53/8.70	   A^2 -> H(c, f(d))
26.53/8.70	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.70	   A^2 -> H(U1(e, k), f(c))
26.53/8.70	   A^2 -> H(U1(e, k), f(d))
26.53/8.70	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.70	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.70	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.70	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.70	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.70	   A^2 -> H(U1(e, c), f(e))
26.53/8.70	   A^2 -> H(U1(e, c), f(k))
26.53/8.70	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.70	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.70	   A^2 -> H(U1(k, e), f(c))
26.53/8.70	   A^2 -> H(U1(k, e), f(d))
26.53/8.70	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.70	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.70	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.70	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.70	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.70	   A^2 -> H(U1(k, c), f(e))
26.53/8.70	   A^2 -> H(U1(k, c), f(k))
26.53/8.70	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.70	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.70	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.70	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.70	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.70	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.70	   A^2 -> H(U1(c, e), f(e))
26.53/8.70	   A^2 -> H(U1(c, e), f(k))
26.53/8.70	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.70	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.70	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.70	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.70	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.70	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.70	   A^2 -> H(U1(c, k), f(e))
26.53/8.70	   A^2 -> H(U1(c, k), f(k))
26.53/8.70	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.70	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.70	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.70	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.70	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.70	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.70	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.70	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.70	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.70	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.70	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.70	   A^2 -> H(e, U1(b, b))
26.53/8.70	   A^2 -> H(e, f(c))
26.53/8.70	   A^2 -> H(e, f(d))
26.53/8.70	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.70	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.70	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.70	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.70	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.70	   A^2 -> H(U1(e, e), f(e))
26.53/8.70	   A^2 -> H(U1(e, e), f(k))
26.53/8.70	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.70	   A^2 -> H(f(e), U1(e, b))
26.53/8.70	   A^2 -> H(f(e), U1(k, b))
26.53/8.70	   A^2 -> H(f(e), U1(c, d))
26.53/8.70	   A^2 -> H(f(e), U1(d, c))
26.53/8.70	   A^2 -> H(f(e), U1(b, e))
26.53/8.70	   A^2 -> H(f(e), U1(b, k))
26.53/8.70	   A^2 -> H(f(e), U1(e, c))
26.53/8.70	   A^2 -> H(f(e), U1(k, c))
26.53/8.70	   A^2 -> H(f(e), U1(c, e))
26.53/8.70	   A^2 -> H(f(e), U1(c, k))
26.53/8.70	   A^2 -> H(f(e), U1(k, k))
26.53/8.70	   A^2 -> H(f(e), U1(k, d))
26.53/8.70	   A^2 -> H(f(e), U1(d, k))
26.53/8.70	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.70	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.70	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.70	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.70	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.70	   A^2 -> H(U1(k, k), f(e))
26.53/8.70	   A^2 -> H(U1(k, k), f(k))
26.53/8.70	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.70	   A^2 -> H(f(k), U1(e, b))
26.53/8.70	   A^2 -> H(f(k), U1(k, b))
26.53/8.70	   A^2 -> H(f(k), U1(c, d))
26.53/8.70	   A^2 -> H(f(k), U1(d, c))
26.53/8.70	   A^2 -> H(f(k), U1(b, e))
26.53/8.70	   A^2 -> H(f(k), U1(b, k))
26.53/8.70	   A^2 -> H(f(k), U1(e, c))
26.53/8.70	   A^2 -> H(f(k), U1(k, c))
26.53/8.70	   A^2 -> H(f(k), U1(c, e))
26.53/8.70	   A^2 -> H(f(k), U1(c, k))
26.53/8.70	   A^2 -> H(f(k), U1(e, e))
26.53/8.70	   A^2 -> H(f(k), U1(k, d))
26.53/8.70	   A^2 -> H(f(k), U1(d, k))
26.53/8.70	   A^2 -> H(f(c), b)
26.53/8.70	   A^2 -> H(f(c), U1(e, d))
26.53/8.70	   A^2 -> H(f(c), U1(d, e))
26.53/8.70	   A^2 -> H(f(k), U1(k, k))
26.53/8.70	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.70	   A^2 -> H(U1(k, k), f(c))
26.53/8.70	   A^2 -> H(U1(k, k), f(d))
26.53/8.70	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.70	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.70	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.70	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.70	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.70	   A^2 -> H(U1(k, d), f(e))
26.53/8.70	   A^2 -> H(U1(k, d), f(k))
26.53/8.70	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.70	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.70	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.70	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.70	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.70	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.70	   A^2 -> H(U1(d, k), f(e))
26.53/8.70	   A^2 -> H(U1(d, k), f(k))
26.53/8.70	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.70	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.70	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.70	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.70	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.70	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.70	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.70	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.70	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.70	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.70	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.70	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.70	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.70	   A^2 -> H(f(d), b)
26.53/8.70	   A^2 -> H(f(d), U1(e, d))
26.53/8.70	   A^2 -> H(f(d), U1(d, e))
26.53/8.70	
26.53/8.70	The TRS R consists of the following rules:
26.53/8.70	
26.53/8.70	   f(x) -> U1(x, x)
26.53/8.70	   U1(e, x) -> x
26.53/8.70	   a -> c
26.53/8.70	   a -> d
26.53/8.70	   b -> c
26.53/8.70	   b -> d
26.53/8.70	   d -> k
26.53/8.70	   c -> e
26.53/8.70	   c -> k
26.53/8.70	
26.53/8.70	Q is empty.
26.53/8.70	We have to consider all minimal (P,Q,R)-chains.
26.53/8.70	----------------------------------------
26.53/8.70	
26.53/8.70	(497) TransformationProof (EQUIVALENT)
26.53/8.70	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.70	
26.53/8.70	   (A^2 -> H(U1(d, d), U1(b, k)),A^2 -> H(U1(d, d), U1(b, k)))
26.53/8.70	   (A^2 -> H(f(k), U1(b, k)),A^2 -> H(f(k), U1(b, k)))
26.53/8.70	   (A^2 -> H(f(d), U1(c, k)),A^2 -> H(f(d), U1(c, k)))
26.53/8.70	   (A^2 -> H(f(d), U1(d, k)),A^2 -> H(f(d), U1(d, k)))
26.53/8.70	
26.53/8.70	
26.53/8.70	----------------------------------------
26.53/8.70	
26.53/8.70	(498)
26.53/8.70	Obligation:
26.53/8.70	Q DP problem:
26.53/8.70	The TRS P consists of the following rules:
26.53/8.70	
26.53/8.70	   H(x, x) -> G(x, x, f(k))
26.53/8.70	   G(d, x, x) -> A^2
26.53/8.70	   A^2 -> H(f(c), f(c))
26.53/8.70	   A^2 -> H(f(d), f(d))
26.53/8.70	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.70	   A^2 -> H(f(e), f(e))
26.53/8.70	   A^2 -> H(f(k), f(k))
26.53/8.70	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.70	   A^2 -> H(f(d), U1(e, c))
26.53/8.70	   A^2 -> H(f(d), U1(k, c))
26.53/8.70	   A^2 -> H(f(d), U1(c, e))
26.53/8.70	   A^2 -> H(f(d), U1(c, k))
26.53/8.70	   A^2 -> H(f(d), U1(e, e))
26.53/8.70	   A^2 -> H(f(d), U1(k, k))
26.53/8.70	   A^2 -> H(f(a), b)
26.53/8.70	   A^2 -> H(f(a), U1(e, d))
26.53/8.70	   A^2 -> H(f(a), U1(d, e))
26.53/8.70	   A^2 -> H(f(c), U1(e, c))
26.53/8.70	   A^2 -> H(f(c), U1(k, c))
26.53/8.70	   A^2 -> H(f(c), U1(c, e))
26.53/8.70	   A^2 -> H(f(c), U1(c, k))
26.53/8.70	   A^2 -> H(f(a), c)
26.53/8.70	   A^2 -> H(f(a), U1(e, k))
26.53/8.70	   A^2 -> H(f(a), U1(k, e))
26.53/8.70	   A^2 -> H(f(c), U1(e, e))
26.53/8.70	   A^2 -> H(f(a), e)
26.53/8.70	   A^2 -> H(f(d), U1(k, d))
26.53/8.70	   A^2 -> H(f(d), U1(d, k))
26.53/8.70	   A^2 -> H(f(a), U1(k, k))
26.53/8.70	   A^2 -> H(d, f(b))
26.53/8.70	   A^2 -> H(a, U1(b, b))
26.53/8.70	   A^2 -> H(a, f(c))
26.53/8.70	   A^2 -> H(a, f(d))
26.53/8.70	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.70	   A^2 -> H(U1(e, d), f(c))
26.53/8.70	   A^2 -> H(U1(e, d), f(d))
26.53/8.70	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.70	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.70	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.70	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.70	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.70	   A^2 -> H(U1(e, a), f(e))
26.53/8.70	   A^2 -> H(U1(e, a), f(k))
26.53/8.70	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.70	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.70	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.70	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.70	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.70	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.70	   A^2 -> H(U1(k, a), f(e))
26.53/8.70	   A^2 -> H(U1(k, a), f(k))
26.53/8.70	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.70	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.70	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.70	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.70	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.70	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.70	   A^2 -> H(U1(c, d), f(e))
26.53/8.70	   A^2 -> H(U1(c, d), f(k))
26.53/8.70	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.70	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.70	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.70	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.70	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.70	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.70	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.70	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.70	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.70	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.70	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.70	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.70	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.70	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.70	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.70	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.70	   A^2 -> H(U1(d, e), f(c))
26.53/8.70	   A^2 -> H(U1(d, e), f(d))
26.53/8.70	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.70	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.70	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.70	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.70	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.70	   A^2 -> H(U1(d, c), f(e))
26.53/8.70	   A^2 -> H(U1(d, c), f(k))
26.53/8.70	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.70	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.70	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.70	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.70	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.70	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.70	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.70	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.70	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.70	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.70	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.70	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.70	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.70	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.70	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.70	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.70	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.70	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.70	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.70	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.70	   A^2 -> H(U1(a, e), f(e))
26.53/8.70	   A^2 -> H(U1(a, e), f(k))
26.53/8.70	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.70	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.70	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.70	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.70	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.70	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.70	   A^2 -> H(U1(a, k), f(e))
26.53/8.70	   A^2 -> H(U1(a, k), f(k))
26.53/8.70	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.70	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.70	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.70	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.70	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.70	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.70	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.70	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.70	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.70	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.70	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.70	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.70	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.70	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.70	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.70	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.70	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.70	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.70	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.70	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.70	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.70	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.70	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.70	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.70	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.70	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.70	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.70	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.70	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.70	   A^2 -> H(U1(a, a), b)
26.53/8.70	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.70	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.70	   A^2 -> H(U1(a, a), c)
26.53/8.70	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.70	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.70	   A^2 -> H(U1(a, a), e)
26.53/8.70	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.70	   A^2 -> H(k, f(b))
26.53/8.70	   A^2 -> H(c, U1(b, b))
26.53/8.70	   A^2 -> H(c, f(c))
26.53/8.70	   A^2 -> H(c, f(d))
26.53/8.70	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.70	   A^2 -> H(U1(e, k), f(c))
26.53/8.70	   A^2 -> H(U1(e, k), f(d))
26.53/8.70	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.70	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.70	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.70	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.70	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.70	   A^2 -> H(U1(e, c), f(e))
26.53/8.70	   A^2 -> H(U1(e, c), f(k))
26.53/8.70	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.70	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.70	   A^2 -> H(U1(k, e), f(c))
26.53/8.70	   A^2 -> H(U1(k, e), f(d))
26.53/8.70	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.70	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.70	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.70	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.70	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.70	   A^2 -> H(U1(k, c), f(e))
26.53/8.70	   A^2 -> H(U1(k, c), f(k))
26.53/8.70	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.70	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.70	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.70	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.70	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.70	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.70	   A^2 -> H(U1(c, e), f(e))
26.53/8.70	   A^2 -> H(U1(c, e), f(k))
26.53/8.70	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.70	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.70	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.70	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.70	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.70	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.70	   A^2 -> H(U1(c, k), f(e))
26.53/8.70	   A^2 -> H(U1(c, k), f(k))
26.53/8.70	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.70	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.70	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.70	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.70	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.70	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.70	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.70	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.70	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.70	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.70	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.70	   A^2 -> H(e, U1(b, b))
26.53/8.70	   A^2 -> H(e, f(c))
26.53/8.70	   A^2 -> H(e, f(d))
26.53/8.70	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.70	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.70	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.70	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.70	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.70	   A^2 -> H(U1(e, e), f(e))
26.53/8.70	   A^2 -> H(U1(e, e), f(k))
26.53/8.70	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.70	   A^2 -> H(f(e), U1(e, b))
26.53/8.70	   A^2 -> H(f(e), U1(k, b))
26.53/8.70	   A^2 -> H(f(e), U1(c, d))
26.53/8.70	   A^2 -> H(f(e), U1(d, c))
26.53/8.70	   A^2 -> H(f(e), U1(b, e))
26.53/8.70	   A^2 -> H(f(e), U1(b, k))
26.53/8.70	   A^2 -> H(f(e), U1(e, c))
26.53/8.70	   A^2 -> H(f(e), U1(k, c))
26.53/8.70	   A^2 -> H(f(e), U1(c, e))
26.53/8.70	   A^2 -> H(f(e), U1(c, k))
26.53/8.70	   A^2 -> H(f(e), U1(k, k))
26.53/8.70	   A^2 -> H(f(e), U1(k, d))
26.53/8.70	   A^2 -> H(f(e), U1(d, k))
26.53/8.70	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.70	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.70	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.70	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.70	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.70	   A^2 -> H(U1(k, k), f(e))
26.53/8.70	   A^2 -> H(U1(k, k), f(k))
26.53/8.70	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.70	   A^2 -> H(f(k), U1(e, b))
26.53/8.70	   A^2 -> H(f(k), U1(k, b))
26.53/8.70	   A^2 -> H(f(k), U1(c, d))
26.53/8.70	   A^2 -> H(f(k), U1(d, c))
26.53/8.70	   A^2 -> H(f(k), U1(b, e))
26.53/8.70	   A^2 -> H(f(k), U1(b, k))
26.53/8.70	   A^2 -> H(f(k), U1(e, c))
26.53/8.70	   A^2 -> H(f(k), U1(k, c))
26.53/8.70	   A^2 -> H(f(k), U1(c, e))
26.53/8.70	   A^2 -> H(f(k), U1(c, k))
26.53/8.70	   A^2 -> H(f(k), U1(e, e))
26.53/8.70	   A^2 -> H(f(k), U1(k, d))
26.53/8.70	   A^2 -> H(f(k), U1(d, k))
26.53/8.70	   A^2 -> H(f(c), b)
26.53/8.70	   A^2 -> H(f(c), U1(e, d))
26.53/8.70	   A^2 -> H(f(c), U1(d, e))
26.53/8.70	   A^2 -> H(f(k), U1(k, k))
26.53/8.70	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.70	   A^2 -> H(U1(k, k), f(c))
26.53/8.70	   A^2 -> H(U1(k, k), f(d))
26.53/8.70	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.70	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.70	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.70	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.70	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.70	   A^2 -> H(U1(k, d), f(e))
26.53/8.70	   A^2 -> H(U1(k, d), f(k))
26.53/8.70	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.70	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.70	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.70	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.70	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.70	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.70	   A^2 -> H(U1(d, k), f(e))
26.53/8.70	   A^2 -> H(U1(d, k), f(k))
26.53/8.70	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.70	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.70	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.70	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.70	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.70	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.70	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.70	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.70	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.70	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.70	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.70	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.70	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.70	   A^2 -> H(f(d), b)
26.53/8.70	   A^2 -> H(f(d), U1(e, d))
26.53/8.70	   A^2 -> H(f(d), U1(d, e))
26.53/8.70	
26.53/8.70	The TRS R consists of the following rules:
26.53/8.70	
26.53/8.70	   f(x) -> U1(x, x)
26.53/8.70	   U1(e, x) -> x
26.53/8.70	   a -> c
26.53/8.70	   a -> d
26.53/8.70	   b -> c
26.53/8.70	   b -> d
26.53/8.70	   d -> k
26.53/8.70	   c -> e
26.53/8.70	   c -> k
26.53/8.70	
26.53/8.70	Q is empty.
26.53/8.70	We have to consider all minimal (P,Q,R)-chains.
26.53/8.70	----------------------------------------
26.53/8.70	
26.53/8.70	(499) TransformationProof (EQUIVALENT)
26.53/8.70	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.70	
26.53/8.70	   (A^2 -> H(U1(d, d), U1(e, c)),A^2 -> H(U1(d, d), U1(e, c)))
26.53/8.70	   (A^2 -> H(f(k), U1(e, c)),A^2 -> H(f(k), U1(e, c)))
26.53/8.70	   (A^2 -> H(f(d), c),A^2 -> H(f(d), c))
26.53/8.70	   (A^2 -> H(f(d), U1(e, e)),A^2 -> H(f(d), U1(e, e)))
26.53/8.70	   (A^2 -> H(f(d), U1(e, k)),A^2 -> H(f(d), U1(e, k)))
26.53/8.70	
26.53/8.70	
26.53/8.70	----------------------------------------
26.53/8.70	
26.53/8.70	(500)
26.53/8.70	Obligation:
26.53/8.70	Q DP problem:
26.53/8.70	The TRS P consists of the following rules:
26.53/8.70	
26.53/8.70	   H(x, x) -> G(x, x, f(k))
26.53/8.70	   G(d, x, x) -> A^2
26.53/8.70	   A^2 -> H(f(c), f(c))
26.53/8.70	   A^2 -> H(f(d), f(d))
26.53/8.70	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.70	   A^2 -> H(f(e), f(e))
26.53/8.70	   A^2 -> H(f(k), f(k))
26.53/8.70	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.70	   A^2 -> H(f(d), U1(k, c))
26.53/8.70	   A^2 -> H(f(d), U1(c, e))
26.53/8.70	   A^2 -> H(f(d), U1(c, k))
26.53/8.70	   A^2 -> H(f(d), U1(e, e))
26.53/8.70	   A^2 -> H(f(d), U1(k, k))
26.53/8.70	   A^2 -> H(f(a), b)
26.53/8.70	   A^2 -> H(f(a), U1(e, d))
26.53/8.70	   A^2 -> H(f(a), U1(d, e))
26.53/8.70	   A^2 -> H(f(c), U1(e, c))
26.53/8.70	   A^2 -> H(f(c), U1(k, c))
26.53/8.70	   A^2 -> H(f(c), U1(c, e))
26.53/8.70	   A^2 -> H(f(c), U1(c, k))
26.53/8.70	   A^2 -> H(f(a), c)
26.53/8.70	   A^2 -> H(f(a), U1(e, k))
26.53/8.70	   A^2 -> H(f(a), U1(k, e))
26.53/8.70	   A^2 -> H(f(c), U1(e, e))
26.53/8.70	   A^2 -> H(f(a), e)
26.53/8.70	   A^2 -> H(f(d), U1(k, d))
26.53/8.70	   A^2 -> H(f(d), U1(d, k))
26.53/8.70	   A^2 -> H(f(a), U1(k, k))
26.53/8.70	   A^2 -> H(d, f(b))
26.53/8.70	   A^2 -> H(a, U1(b, b))
26.53/8.70	   A^2 -> H(a, f(c))
26.53/8.70	   A^2 -> H(a, f(d))
26.53/8.70	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.70	   A^2 -> H(U1(e, d), f(c))
26.53/8.70	   A^2 -> H(U1(e, d), f(d))
26.53/8.70	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.70	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.70	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.70	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.70	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.70	   A^2 -> H(U1(e, a), f(e))
26.53/8.70	   A^2 -> H(U1(e, a), f(k))
26.53/8.70	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.70	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.70	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.70	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.70	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.70	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.70	   A^2 -> H(U1(k, a), f(e))
26.53/8.70	   A^2 -> H(U1(k, a), f(k))
26.53/8.70	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.70	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.70	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.70	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.70	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.70	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.70	   A^2 -> H(U1(c, d), f(e))
26.53/8.70	   A^2 -> H(U1(c, d), f(k))
26.53/8.70	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.70	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.70	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.70	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.70	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.70	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.70	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.70	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.70	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.70	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.70	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.70	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.70	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.70	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.70	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.70	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.70	   A^2 -> H(U1(d, e), f(c))
26.53/8.70	   A^2 -> H(U1(d, e), f(d))
26.53/8.70	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.70	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.70	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.70	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.70	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.70	   A^2 -> H(U1(d, c), f(e))
26.53/8.70	   A^2 -> H(U1(d, c), f(k))
26.53/8.70	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.70	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.70	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.70	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.70	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.70	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.70	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.70	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.70	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.70	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.70	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.70	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.70	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.70	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.70	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.70	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.70	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.70	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.70	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.70	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.70	   A^2 -> H(U1(a, e), f(e))
26.53/8.70	   A^2 -> H(U1(a, e), f(k))
26.53/8.70	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.70	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.70	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.70	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.70	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.70	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.70	   A^2 -> H(U1(a, k), f(e))
26.53/8.70	   A^2 -> H(U1(a, k), f(k))
26.53/8.70	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.70	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.70	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.70	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.70	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.70	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.70	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.70	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.70	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.70	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.70	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.70	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.70	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.70	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.70	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.70	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.70	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.70	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.70	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.70	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.70	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.70	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.70	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.70	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.70	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.70	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.70	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.70	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.70	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.70	   A^2 -> H(U1(a, a), b)
26.53/8.70	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.70	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.70	   A^2 -> H(U1(a, a), c)
26.53/8.70	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.70	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.70	   A^2 -> H(U1(a, a), e)
26.53/8.70	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.70	   A^2 -> H(k, f(b))
26.53/8.70	   A^2 -> H(c, U1(b, b))
26.53/8.70	   A^2 -> H(c, f(c))
26.53/8.70	   A^2 -> H(c, f(d))
26.53/8.70	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.70	   A^2 -> H(U1(e, k), f(c))
26.53/8.70	   A^2 -> H(U1(e, k), f(d))
26.53/8.70	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.70	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.70	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.70	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.70	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.70	   A^2 -> H(U1(e, c), f(e))
26.53/8.70	   A^2 -> H(U1(e, c), f(k))
26.53/8.70	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.70	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.70	   A^2 -> H(U1(k, e), f(c))
26.53/8.70	   A^2 -> H(U1(k, e), f(d))
26.53/8.70	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.70	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.70	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.70	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.70	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.70	   A^2 -> H(U1(k, c), f(e))
26.53/8.70	   A^2 -> H(U1(k, c), f(k))
26.53/8.70	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.70	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.70	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.70	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.70	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.70	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.70	   A^2 -> H(U1(c, e), f(e))
26.53/8.70	   A^2 -> H(U1(c, e), f(k))
26.53/8.70	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.70	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.70	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.70	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.70	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.70	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.70	   A^2 -> H(U1(c, k), f(e))
26.53/8.70	   A^2 -> H(U1(c, k), f(k))
26.53/8.70	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.70	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.70	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.70	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.70	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.70	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.70	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.70	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.70	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.70	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.70	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.70	   A^2 -> H(e, U1(b, b))
26.53/8.70	   A^2 -> H(e, f(c))
26.53/8.70	   A^2 -> H(e, f(d))
26.53/8.70	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.70	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.70	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.70	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.70	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.70	   A^2 -> H(U1(e, e), f(e))
26.53/8.70	   A^2 -> H(U1(e, e), f(k))
26.53/8.70	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.70	   A^2 -> H(f(e), U1(e, b))
26.53/8.70	   A^2 -> H(f(e), U1(k, b))
26.53/8.70	   A^2 -> H(f(e), U1(c, d))
26.53/8.70	   A^2 -> H(f(e), U1(d, c))
26.53/8.70	   A^2 -> H(f(e), U1(b, e))
26.53/8.70	   A^2 -> H(f(e), U1(b, k))
26.53/8.70	   A^2 -> H(f(e), U1(e, c))
26.53/8.70	   A^2 -> H(f(e), U1(k, c))
26.53/8.70	   A^2 -> H(f(e), U1(c, e))
26.53/8.70	   A^2 -> H(f(e), U1(c, k))
26.53/8.70	   A^2 -> H(f(e), U1(k, k))
26.53/8.70	   A^2 -> H(f(e), U1(k, d))
26.53/8.70	   A^2 -> H(f(e), U1(d, k))
26.53/8.70	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.70	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.70	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.70	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.70	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.70	   A^2 -> H(U1(k, k), f(e))
26.53/8.70	   A^2 -> H(U1(k, k), f(k))
26.53/8.70	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.70	   A^2 -> H(f(k), U1(e, b))
26.53/8.70	   A^2 -> H(f(k), U1(k, b))
26.53/8.70	   A^2 -> H(f(k), U1(c, d))
26.53/8.70	   A^2 -> H(f(k), U1(d, c))
26.53/8.70	   A^2 -> H(f(k), U1(b, e))
26.53/8.70	   A^2 -> H(f(k), U1(b, k))
26.53/8.70	   A^2 -> H(f(k), U1(e, c))
26.53/8.70	   A^2 -> H(f(k), U1(k, c))
26.53/8.70	   A^2 -> H(f(k), U1(c, e))
26.53/8.70	   A^2 -> H(f(k), U1(c, k))
26.53/8.70	   A^2 -> H(f(k), U1(e, e))
26.53/8.70	   A^2 -> H(f(k), U1(k, d))
26.53/8.70	   A^2 -> H(f(k), U1(d, k))
26.53/8.70	   A^2 -> H(f(c), b)
26.53/8.70	   A^2 -> H(f(c), U1(e, d))
26.53/8.70	   A^2 -> H(f(c), U1(d, e))
26.53/8.70	   A^2 -> H(f(k), U1(k, k))
26.53/8.70	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.70	   A^2 -> H(U1(k, k), f(c))
26.53/8.70	   A^2 -> H(U1(k, k), f(d))
26.53/8.70	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.70	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.70	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.70	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.70	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.70	   A^2 -> H(U1(k, d), f(e))
26.53/8.70	   A^2 -> H(U1(k, d), f(k))
26.53/8.70	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.70	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.70	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.70	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.70	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.70	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.70	   A^2 -> H(U1(d, k), f(e))
26.53/8.70	   A^2 -> H(U1(d, k), f(k))
26.53/8.70	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.70	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.70	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.70	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.70	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.70	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.70	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.70	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.70	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.70	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.70	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.70	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.70	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.70	   A^2 -> H(f(d), b)
26.53/8.70	   A^2 -> H(f(d), U1(e, d))
26.53/8.70	   A^2 -> H(f(d), U1(d, e))
26.53/8.70	   A^2 -> H(f(d), c)
26.53/8.70	   A^2 -> H(f(d), U1(e, k))
26.53/8.70	
26.53/8.70	The TRS R consists of the following rules:
26.53/8.70	
26.53/8.70	   f(x) -> U1(x, x)
26.53/8.70	   U1(e, x) -> x
26.53/8.70	   a -> c
26.53/8.70	   a -> d
26.53/8.70	   b -> c
26.53/8.70	   b -> d
26.53/8.70	   d -> k
26.53/8.70	   c -> e
26.53/8.70	   c -> k
26.53/8.70	
26.53/8.70	Q is empty.
26.53/8.70	We have to consider all minimal (P,Q,R)-chains.
26.53/8.70	----------------------------------------
26.53/8.70	
26.53/8.70	(501) TransformationProof (EQUIVALENT)
26.53/8.70	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.70	
26.53/8.70	   (A^2 -> H(U1(d, d), U1(k, c)),A^2 -> H(U1(d, d), U1(k, c)))
26.53/8.70	   (A^2 -> H(f(k), U1(k, c)),A^2 -> H(f(k), U1(k, c)))
26.53/8.70	   (A^2 -> H(f(d), U1(k, e)),A^2 -> H(f(d), U1(k, e)))
26.53/8.70	   (A^2 -> H(f(d), U1(k, k)),A^2 -> H(f(d), U1(k, k)))
26.53/8.70	
26.53/8.70	
26.53/8.70	----------------------------------------
26.53/8.70	
26.53/8.70	(502)
26.53/8.70	Obligation:
26.53/8.70	Q DP problem:
26.53/8.70	The TRS P consists of the following rules:
26.53/8.70	
26.53/8.70	   H(x, x) -> G(x, x, f(k))
26.53/8.70	   G(d, x, x) -> A^2
26.53/8.70	   A^2 -> H(f(c), f(c))
26.53/8.70	   A^2 -> H(f(d), f(d))
26.53/8.70	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.70	   A^2 -> H(f(e), f(e))
26.53/8.70	   A^2 -> H(f(k), f(k))
26.53/8.71	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.71	   A^2 -> H(f(d), U1(c, e))
26.53/8.71	   A^2 -> H(f(d), U1(c, k))
26.53/8.71	   A^2 -> H(f(d), U1(e, e))
26.53/8.71	   A^2 -> H(f(d), U1(k, k))
26.53/8.71	   A^2 -> H(f(a), b)
26.53/8.71	   A^2 -> H(f(a), U1(e, d))
26.53/8.71	   A^2 -> H(f(a), U1(d, e))
26.53/8.71	   A^2 -> H(f(c), U1(e, c))
26.53/8.71	   A^2 -> H(f(c), U1(k, c))
26.53/8.71	   A^2 -> H(f(c), U1(c, e))
26.53/8.71	   A^2 -> H(f(c), U1(c, k))
26.53/8.71	   A^2 -> H(f(a), c)
26.53/8.71	   A^2 -> H(f(a), U1(e, k))
26.53/8.71	   A^2 -> H(f(a), U1(k, e))
26.53/8.71	   A^2 -> H(f(c), U1(e, e))
26.53/8.71	   A^2 -> H(f(a), e)
26.53/8.71	   A^2 -> H(f(d), U1(k, d))
26.53/8.71	   A^2 -> H(f(d), U1(d, k))
26.53/8.71	   A^2 -> H(f(a), U1(k, k))
26.53/8.71	   A^2 -> H(d, f(b))
26.53/8.71	   A^2 -> H(a, U1(b, b))
26.53/8.71	   A^2 -> H(a, f(c))
26.53/8.71	   A^2 -> H(a, f(d))
26.53/8.71	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.71	   A^2 -> H(U1(e, d), f(c))
26.53/8.71	   A^2 -> H(U1(e, d), f(d))
26.53/8.71	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.71	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.71	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.71	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.71	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.71	   A^2 -> H(U1(e, a), f(e))
26.53/8.71	   A^2 -> H(U1(e, a), f(k))
26.53/8.71	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.71	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.71	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.71	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.71	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.71	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.71	   A^2 -> H(U1(k, a), f(e))
26.53/8.71	   A^2 -> H(U1(k, a), f(k))
26.53/8.71	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.71	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.71	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.71	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.71	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.71	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.71	   A^2 -> H(U1(c, d), f(e))
26.53/8.71	   A^2 -> H(U1(c, d), f(k))
26.53/8.71	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.71	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.71	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.71	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.71	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.71	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.71	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.71	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.71	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.71	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.71	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.71	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.71	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.71	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.71	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.71	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.71	   A^2 -> H(U1(d, e), f(c))
26.53/8.71	   A^2 -> H(U1(d, e), f(d))
26.53/8.71	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.71	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.71	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.71	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.71	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.71	   A^2 -> H(U1(d, c), f(e))
26.53/8.71	   A^2 -> H(U1(d, c), f(k))
26.53/8.71	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.71	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.71	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.71	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.71	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.71	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.71	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.71	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.71	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.71	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.71	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.71	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.71	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.71	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.71	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.71	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.71	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.71	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.71	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.71	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.71	   A^2 -> H(U1(a, e), f(e))
26.53/8.71	   A^2 -> H(U1(a, e), f(k))
26.53/8.71	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.71	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.71	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.71	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.71	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.71	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.71	   A^2 -> H(U1(a, k), f(e))
26.53/8.71	   A^2 -> H(U1(a, k), f(k))
26.53/8.71	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.71	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.71	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.71	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.71	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.71	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.71	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.71	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.71	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.71	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.71	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.71	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.71	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.71	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.71	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.71	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.71	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.71	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.71	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.71	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.71	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.71	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.71	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.71	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.71	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.71	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.71	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.71	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.71	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.71	   A^2 -> H(U1(a, a), b)
26.53/8.71	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.71	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.71	   A^2 -> H(U1(a, a), c)
26.53/8.71	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.71	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.71	   A^2 -> H(U1(a, a), e)
26.53/8.71	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.71	   A^2 -> H(k, f(b))
26.53/8.71	   A^2 -> H(c, U1(b, b))
26.53/8.71	   A^2 -> H(c, f(c))
26.53/8.71	   A^2 -> H(c, f(d))
26.53/8.71	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.71	   A^2 -> H(U1(e, k), f(c))
26.53/8.71	   A^2 -> H(U1(e, k), f(d))
26.53/8.71	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.71	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.71	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.71	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.71	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.71	   A^2 -> H(U1(e, c), f(e))
26.53/8.71	   A^2 -> H(U1(e, c), f(k))
26.53/8.71	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.71	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.71	   A^2 -> H(U1(k, e), f(c))
26.53/8.71	   A^2 -> H(U1(k, e), f(d))
26.53/8.71	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.71	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.71	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.71	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.71	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.71	   A^2 -> H(U1(k, c), f(e))
26.53/8.71	   A^2 -> H(U1(k, c), f(k))
26.53/8.71	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.71	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.71	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.71	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.71	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.71	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.71	   A^2 -> H(U1(c, e), f(e))
26.53/8.71	   A^2 -> H(U1(c, e), f(k))
26.53/8.71	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.71	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.71	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.71	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.71	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.71	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.71	   A^2 -> H(U1(c, k), f(e))
26.53/8.71	   A^2 -> H(U1(c, k), f(k))
26.53/8.71	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.71	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.71	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.71	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.71	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.71	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.71	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.71	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.71	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.71	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.71	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.71	   A^2 -> H(e, U1(b, b))
26.53/8.71	   A^2 -> H(e, f(c))
26.53/8.71	   A^2 -> H(e, f(d))
26.53/8.71	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.71	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.71	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.71	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.71	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.71	   A^2 -> H(U1(e, e), f(e))
26.53/8.71	   A^2 -> H(U1(e, e), f(k))
26.53/8.71	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.71	   A^2 -> H(f(e), U1(e, b))
26.53/8.71	   A^2 -> H(f(e), U1(k, b))
26.53/8.71	   A^2 -> H(f(e), U1(c, d))
26.53/8.71	   A^2 -> H(f(e), U1(d, c))
26.53/8.71	   A^2 -> H(f(e), U1(b, e))
26.53/8.71	   A^2 -> H(f(e), U1(b, k))
26.53/8.71	   A^2 -> H(f(e), U1(e, c))
26.53/8.71	   A^2 -> H(f(e), U1(k, c))
26.53/8.71	   A^2 -> H(f(e), U1(c, e))
26.53/8.71	   A^2 -> H(f(e), U1(c, k))
26.53/8.71	   A^2 -> H(f(e), U1(k, k))
26.53/8.71	   A^2 -> H(f(e), U1(k, d))
26.53/8.71	   A^2 -> H(f(e), U1(d, k))
26.53/8.71	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.71	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.71	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.71	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.71	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.71	   A^2 -> H(U1(k, k), f(e))
26.53/8.71	   A^2 -> H(U1(k, k), f(k))
26.53/8.71	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.71	   A^2 -> H(f(k), U1(e, b))
26.53/8.71	   A^2 -> H(f(k), U1(k, b))
26.53/8.71	   A^2 -> H(f(k), U1(c, d))
26.53/8.71	   A^2 -> H(f(k), U1(d, c))
26.53/8.71	   A^2 -> H(f(k), U1(b, e))
26.53/8.71	   A^2 -> H(f(k), U1(b, k))
26.53/8.71	   A^2 -> H(f(k), U1(e, c))
26.53/8.71	   A^2 -> H(f(k), U1(k, c))
26.53/8.71	   A^2 -> H(f(k), U1(c, e))
26.53/8.71	   A^2 -> H(f(k), U1(c, k))
26.53/8.71	   A^2 -> H(f(k), U1(e, e))
26.53/8.71	   A^2 -> H(f(k), U1(k, d))
26.53/8.71	   A^2 -> H(f(k), U1(d, k))
26.53/8.71	   A^2 -> H(f(c), b)
26.53/8.71	   A^2 -> H(f(c), U1(e, d))
26.53/8.71	   A^2 -> H(f(c), U1(d, e))
26.53/8.71	   A^2 -> H(f(k), U1(k, k))
26.53/8.71	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.71	   A^2 -> H(U1(k, k), f(c))
26.53/8.71	   A^2 -> H(U1(k, k), f(d))
26.53/8.71	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.71	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.71	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.71	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.71	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.71	   A^2 -> H(U1(k, d), f(e))
26.53/8.71	   A^2 -> H(U1(k, d), f(k))
26.53/8.71	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.71	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.71	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.71	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.71	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.71	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.71	   A^2 -> H(U1(d, k), f(e))
26.53/8.71	   A^2 -> H(U1(d, k), f(k))
26.53/8.71	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.71	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.71	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.71	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.71	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.71	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.71	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.71	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.71	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.71	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.71	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.71	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.71	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.71	   A^2 -> H(f(d), b)
26.53/8.71	   A^2 -> H(f(d), U1(e, d))
26.53/8.71	   A^2 -> H(f(d), U1(d, e))
26.53/8.71	   A^2 -> H(f(d), c)
26.53/8.71	   A^2 -> H(f(d), U1(e, k))
26.53/8.71	   A^2 -> H(f(d), U1(k, e))
26.53/8.71	
26.53/8.71	The TRS R consists of the following rules:
26.53/8.71	
26.53/8.71	   f(x) -> U1(x, x)
26.53/8.71	   U1(e, x) -> x
26.53/8.71	   a -> c
26.53/8.71	   a -> d
26.53/8.71	   b -> c
26.53/8.71	   b -> d
26.53/8.71	   d -> k
26.53/8.71	   c -> e
26.53/8.71	   c -> k
26.53/8.71	
26.53/8.71	Q is empty.
26.53/8.71	We have to consider all minimal (P,Q,R)-chains.
26.53/8.71	----------------------------------------
26.53/8.71	
26.53/8.71	(503) TransformationProof (EQUIVALENT)
26.53/8.71	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.71	
26.53/8.71	   (A^2 -> H(U1(d, d), U1(c, e)),A^2 -> H(U1(d, d), U1(c, e)))
26.53/8.71	   (A^2 -> H(f(k), U1(c, e)),A^2 -> H(f(k), U1(c, e)))
26.53/8.71	   (A^2 -> H(f(d), U1(e, e)),A^2 -> H(f(d), U1(e, e)))
26.53/8.71	   (A^2 -> H(f(d), U1(k, e)),A^2 -> H(f(d), U1(k, e)))
26.53/8.71	
26.53/8.71	
26.53/8.71	----------------------------------------
26.53/8.71	
26.53/8.71	(504)
26.53/8.71	Obligation:
26.53/8.71	Q DP problem:
26.53/8.71	The TRS P consists of the following rules:
26.53/8.71	
26.53/8.71	   H(x, x) -> G(x, x, f(k))
26.53/8.71	   G(d, x, x) -> A^2
26.53/8.71	   A^2 -> H(f(c), f(c))
26.53/8.71	   A^2 -> H(f(d), f(d))
26.53/8.71	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.71	   A^2 -> H(f(e), f(e))
26.53/8.71	   A^2 -> H(f(k), f(k))
26.53/8.71	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.71	   A^2 -> H(f(d), U1(c, k))
26.53/8.71	   A^2 -> H(f(d), U1(e, e))
26.53/8.71	   A^2 -> H(f(d), U1(k, k))
26.53/8.71	   A^2 -> H(f(a), b)
26.53/8.71	   A^2 -> H(f(a), U1(e, d))
26.53/8.71	   A^2 -> H(f(a), U1(d, e))
26.53/8.71	   A^2 -> H(f(c), U1(e, c))
26.53/8.71	   A^2 -> H(f(c), U1(k, c))
26.53/8.71	   A^2 -> H(f(c), U1(c, e))
26.53/8.71	   A^2 -> H(f(c), U1(c, k))
26.53/8.71	   A^2 -> H(f(a), c)
26.53/8.71	   A^2 -> H(f(a), U1(e, k))
26.53/8.71	   A^2 -> H(f(a), U1(k, e))
26.53/8.71	   A^2 -> H(f(c), U1(e, e))
26.53/8.71	   A^2 -> H(f(a), e)
26.53/8.71	   A^2 -> H(f(d), U1(k, d))
26.53/8.71	   A^2 -> H(f(d), U1(d, k))
26.53/8.71	   A^2 -> H(f(a), U1(k, k))
26.53/8.71	   A^2 -> H(d, f(b))
26.53/8.71	   A^2 -> H(a, U1(b, b))
26.53/8.71	   A^2 -> H(a, f(c))
26.53/8.71	   A^2 -> H(a, f(d))
26.53/8.71	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.71	   A^2 -> H(U1(e, d), f(c))
26.53/8.71	   A^2 -> H(U1(e, d), f(d))
26.53/8.71	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.71	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.71	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.71	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.71	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.71	   A^2 -> H(U1(e, a), f(e))
26.53/8.71	   A^2 -> H(U1(e, a), f(k))
26.53/8.71	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.71	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.71	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.71	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.71	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.71	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.71	   A^2 -> H(U1(k, a), f(e))
26.53/8.71	   A^2 -> H(U1(k, a), f(k))
26.53/8.71	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.71	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.71	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.71	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.71	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.71	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.71	   A^2 -> H(U1(c, d), f(e))
26.53/8.71	   A^2 -> H(U1(c, d), f(k))
26.53/8.71	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.71	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.71	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.71	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.71	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.71	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.71	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.71	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.71	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.71	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.71	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.71	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.71	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.71	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.71	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.71	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.71	   A^2 -> H(U1(d, e), f(c))
26.53/8.71	   A^2 -> H(U1(d, e), f(d))
26.53/8.71	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.71	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.71	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.71	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.71	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.71	   A^2 -> H(U1(d, c), f(e))
26.53/8.71	   A^2 -> H(U1(d, c), f(k))
26.53/8.71	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.71	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.71	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.71	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.71	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.71	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.71	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.71	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.71	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.71	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.71	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.71	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.71	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.71	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.71	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.71	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.71	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.71	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.71	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.71	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.71	   A^2 -> H(U1(a, e), f(e))
26.53/8.71	   A^2 -> H(U1(a, e), f(k))
26.53/8.71	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.71	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.71	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.71	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.71	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.71	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.71	   A^2 -> H(U1(a, k), f(e))
26.53/8.71	   A^2 -> H(U1(a, k), f(k))
26.53/8.71	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.71	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.71	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.71	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.71	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.71	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.71	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.71	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.71	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.71	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.71	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.71	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.71	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.71	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.71	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.71	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.71	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.71	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.71	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.71	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.71	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.71	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.71	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.71	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.71	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.71	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.71	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.71	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.71	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.71	   A^2 -> H(U1(a, a), b)
26.53/8.71	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.71	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.71	   A^2 -> H(U1(a, a), c)
26.53/8.71	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.71	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.71	   A^2 -> H(U1(a, a), e)
26.53/8.71	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.71	   A^2 -> H(k, f(b))
26.53/8.71	   A^2 -> H(c, U1(b, b))
26.53/8.71	   A^2 -> H(c, f(c))
26.53/8.71	   A^2 -> H(c, f(d))
26.53/8.71	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.71	   A^2 -> H(U1(e, k), f(c))
26.53/8.71	   A^2 -> H(U1(e, k), f(d))
26.53/8.71	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.71	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.71	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.71	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.71	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.71	   A^2 -> H(U1(e, c), f(e))
26.53/8.71	   A^2 -> H(U1(e, c), f(k))
26.53/8.71	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.71	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.71	   A^2 -> H(U1(k, e), f(c))
26.53/8.71	   A^2 -> H(U1(k, e), f(d))
26.53/8.71	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.71	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.71	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.71	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.71	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, c), f(e))
26.53/8.72	   A^2 -> H(U1(k, c), f(k))
26.53/8.72	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, e), f(e))
26.53/8.72	   A^2 -> H(U1(c, e), f(k))
26.53/8.72	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, k), f(e))
26.53/8.72	   A^2 -> H(U1(c, k), f(k))
26.53/8.72	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.72	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.72	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.72	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.72	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.72	   A^2 -> H(e, U1(b, b))
26.53/8.72	   A^2 -> H(e, f(c))
26.53/8.72	   A^2 -> H(e, f(d))
26.53/8.72	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, e), f(e))
26.53/8.72	   A^2 -> H(U1(e, e), f(k))
26.53/8.72	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.72	   A^2 -> H(f(e), U1(e, b))
26.53/8.72	   A^2 -> H(f(e), U1(k, b))
26.53/8.72	   A^2 -> H(f(e), U1(c, d))
26.53/8.72	   A^2 -> H(f(e), U1(d, c))
26.53/8.72	   A^2 -> H(f(e), U1(b, e))
26.53/8.72	   A^2 -> H(f(e), U1(b, k))
26.53/8.72	   A^2 -> H(f(e), U1(e, c))
26.53/8.72	   A^2 -> H(f(e), U1(k, c))
26.53/8.72	   A^2 -> H(f(e), U1(c, e))
26.53/8.72	   A^2 -> H(f(e), U1(c, k))
26.53/8.72	   A^2 -> H(f(e), U1(k, k))
26.53/8.72	   A^2 -> H(f(e), U1(k, d))
26.53/8.72	   A^2 -> H(f(e), U1(d, k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, k), f(e))
26.53/8.72	   A^2 -> H(U1(k, k), f(k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.72	   A^2 -> H(f(k), U1(e, b))
26.53/8.72	   A^2 -> H(f(k), U1(k, b))
26.53/8.72	   A^2 -> H(f(k), U1(c, d))
26.53/8.72	   A^2 -> H(f(k), U1(d, c))
26.53/8.72	   A^2 -> H(f(k), U1(b, e))
26.53/8.72	   A^2 -> H(f(k), U1(b, k))
26.53/8.72	   A^2 -> H(f(k), U1(e, c))
26.53/8.72	   A^2 -> H(f(k), U1(k, c))
26.53/8.72	   A^2 -> H(f(k), U1(c, e))
26.53/8.72	   A^2 -> H(f(k), U1(c, k))
26.53/8.72	   A^2 -> H(f(k), U1(e, e))
26.53/8.72	   A^2 -> H(f(k), U1(k, d))
26.53/8.72	   A^2 -> H(f(k), U1(d, k))
26.53/8.72	   A^2 -> H(f(c), b)
26.53/8.72	   A^2 -> H(f(c), U1(e, d))
26.53/8.72	   A^2 -> H(f(c), U1(d, e))
26.53/8.72	   A^2 -> H(f(k), U1(k, k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.72	   A^2 -> H(U1(k, k), f(c))
26.53/8.72	   A^2 -> H(U1(k, k), f(d))
26.53/8.72	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, d), f(e))
26.53/8.72	   A^2 -> H(U1(k, d), f(k))
26.53/8.72	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(d, k), f(e))
26.53/8.72	   A^2 -> H(U1(d, k), f(k))
26.53/8.72	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.72	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.72	   A^2 -> H(f(d), b)
26.53/8.72	   A^2 -> H(f(d), U1(e, d))
26.53/8.72	   A^2 -> H(f(d), U1(d, e))
26.53/8.72	   A^2 -> H(f(d), c)
26.53/8.72	   A^2 -> H(f(d), U1(e, k))
26.53/8.72	   A^2 -> H(f(d), U1(k, e))
26.53/8.72	
26.53/8.72	The TRS R consists of the following rules:
26.53/8.72	
26.53/8.72	   f(x) -> U1(x, x)
26.53/8.72	   U1(e, x) -> x
26.53/8.72	   a -> c
26.53/8.72	   a -> d
26.53/8.72	   b -> c
26.53/8.72	   b -> d
26.53/8.72	   d -> k
26.53/8.72	   c -> e
26.53/8.72	   c -> k
26.53/8.72	
26.53/8.72	Q is empty.
26.53/8.72	We have to consider all minimal (P,Q,R)-chains.
26.53/8.72	----------------------------------------
26.53/8.72	
26.53/8.72	(505) TransformationProof (EQUIVALENT)
26.53/8.72	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.72	
26.53/8.72	   (A^2 -> H(U1(d, d), U1(c, k)),A^2 -> H(U1(d, d), U1(c, k)))
26.53/8.72	   (A^2 -> H(f(k), U1(c, k)),A^2 -> H(f(k), U1(c, k)))
26.53/8.72	   (A^2 -> H(f(d), U1(e, k)),A^2 -> H(f(d), U1(e, k)))
26.53/8.72	   (A^2 -> H(f(d), U1(k, k)),A^2 -> H(f(d), U1(k, k)))
26.53/8.72	
26.53/8.72	
26.53/8.72	----------------------------------------
26.53/8.72	
26.53/8.72	(506)
26.53/8.72	Obligation:
26.53/8.72	Q DP problem:
26.53/8.72	The TRS P consists of the following rules:
26.53/8.72	
26.53/8.72	   H(x, x) -> G(x, x, f(k))
26.53/8.72	   G(d, x, x) -> A^2
26.53/8.72	   A^2 -> H(f(c), f(c))
26.53/8.72	   A^2 -> H(f(d), f(d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.72	   A^2 -> H(f(e), f(e))
26.53/8.72	   A^2 -> H(f(k), f(k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.72	   A^2 -> H(f(d), U1(e, e))
26.53/8.72	   A^2 -> H(f(d), U1(k, k))
26.53/8.72	   A^2 -> H(f(a), b)
26.53/8.72	   A^2 -> H(f(a), U1(e, d))
26.53/8.72	   A^2 -> H(f(a), U1(d, e))
26.53/8.72	   A^2 -> H(f(c), U1(e, c))
26.53/8.72	   A^2 -> H(f(c), U1(k, c))
26.53/8.72	   A^2 -> H(f(c), U1(c, e))
26.53/8.72	   A^2 -> H(f(c), U1(c, k))
26.53/8.72	   A^2 -> H(f(a), c)
26.53/8.72	   A^2 -> H(f(a), U1(e, k))
26.53/8.72	   A^2 -> H(f(a), U1(k, e))
26.53/8.72	   A^2 -> H(f(c), U1(e, e))
26.53/8.72	   A^2 -> H(f(a), e)
26.53/8.72	   A^2 -> H(f(d), U1(k, d))
26.53/8.72	   A^2 -> H(f(d), U1(d, k))
26.53/8.72	   A^2 -> H(f(a), U1(k, k))
26.53/8.72	   A^2 -> H(d, f(b))
26.53/8.72	   A^2 -> H(a, U1(b, b))
26.53/8.72	   A^2 -> H(a, f(c))
26.53/8.72	   A^2 -> H(a, f(d))
26.53/8.72	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.72	   A^2 -> H(U1(e, d), f(c))
26.53/8.72	   A^2 -> H(U1(e, d), f(d))
26.53/8.72	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, a), f(e))
26.53/8.72	   A^2 -> H(U1(e, a), f(k))
26.53/8.72	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.72	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, a), f(e))
26.53/8.72	   A^2 -> H(U1(k, a), f(k))
26.53/8.72	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, d), f(e))
26.53/8.72	   A^2 -> H(U1(c, d), f(k))
26.53/8.72	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.72	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.72	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.72	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.72	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.72	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.72	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.72	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.72	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.72	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.72	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.72	   A^2 -> H(U1(d, e), f(c))
26.53/8.72	   A^2 -> H(U1(d, e), f(d))
26.53/8.72	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.72	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.72	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.72	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.72	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(d, c), f(e))
26.53/8.72	   A^2 -> H(U1(d, c), f(k))
26.53/8.72	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.72	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.72	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.72	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.72	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.72	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.72	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.72	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.72	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.72	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.72	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(a, e), f(e))
26.53/8.72	   A^2 -> H(U1(a, e), f(k))
26.53/8.72	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.72	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(a, k), f(e))
26.53/8.72	   A^2 -> H(U1(a, k), f(k))
26.53/8.72	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.72	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.72	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.72	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.72	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.72	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.72	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.72	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.72	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.72	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.72	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.72	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.72	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.72	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.72	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.72	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.72	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.72	   A^2 -> H(U1(a, a), b)
26.53/8.72	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.72	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.72	   A^2 -> H(U1(a, a), c)
26.53/8.72	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.72	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.72	   A^2 -> H(U1(a, a), e)
26.53/8.72	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.72	   A^2 -> H(k, f(b))
26.53/8.72	   A^2 -> H(c, U1(b, b))
26.53/8.72	   A^2 -> H(c, f(c))
26.53/8.72	   A^2 -> H(c, f(d))
26.53/8.72	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.72	   A^2 -> H(U1(e, k), f(c))
26.53/8.72	   A^2 -> H(U1(e, k), f(d))
26.53/8.72	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, c), f(e))
26.53/8.72	   A^2 -> H(U1(e, c), f(k))
26.53/8.72	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.72	   A^2 -> H(U1(k, e), f(c))
26.53/8.72	   A^2 -> H(U1(k, e), f(d))
26.53/8.72	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, c), f(e))
26.53/8.72	   A^2 -> H(U1(k, c), f(k))
26.53/8.72	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, e), f(e))
26.53/8.72	   A^2 -> H(U1(c, e), f(k))
26.53/8.72	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, k), f(e))
26.53/8.72	   A^2 -> H(U1(c, k), f(k))
26.53/8.72	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.72	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.72	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.72	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.72	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.72	   A^2 -> H(e, U1(b, b))
26.53/8.72	   A^2 -> H(e, f(c))
26.53/8.72	   A^2 -> H(e, f(d))
26.53/8.72	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, e), f(e))
26.53/8.72	   A^2 -> H(U1(e, e), f(k))
26.53/8.72	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.72	   A^2 -> H(f(e), U1(e, b))
26.53/8.72	   A^2 -> H(f(e), U1(k, b))
26.53/8.72	   A^2 -> H(f(e), U1(c, d))
26.53/8.72	   A^2 -> H(f(e), U1(d, c))
26.53/8.72	   A^2 -> H(f(e), U1(b, e))
26.53/8.72	   A^2 -> H(f(e), U1(b, k))
26.53/8.72	   A^2 -> H(f(e), U1(e, c))
26.53/8.72	   A^2 -> H(f(e), U1(k, c))
26.53/8.72	   A^2 -> H(f(e), U1(c, e))
26.53/8.72	   A^2 -> H(f(e), U1(c, k))
26.53/8.72	   A^2 -> H(f(e), U1(k, k))
26.53/8.72	   A^2 -> H(f(e), U1(k, d))
26.53/8.72	   A^2 -> H(f(e), U1(d, k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, k), f(e))
26.53/8.72	   A^2 -> H(U1(k, k), f(k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.72	   A^2 -> H(f(k), U1(e, b))
26.53/8.72	   A^2 -> H(f(k), U1(k, b))
26.53/8.72	   A^2 -> H(f(k), U1(c, d))
26.53/8.72	   A^2 -> H(f(k), U1(d, c))
26.53/8.72	   A^2 -> H(f(k), U1(b, e))
26.53/8.72	   A^2 -> H(f(k), U1(b, k))
26.53/8.72	   A^2 -> H(f(k), U1(e, c))
26.53/8.72	   A^2 -> H(f(k), U1(k, c))
26.53/8.72	   A^2 -> H(f(k), U1(c, e))
26.53/8.72	   A^2 -> H(f(k), U1(c, k))
26.53/8.72	   A^2 -> H(f(k), U1(e, e))
26.53/8.72	   A^2 -> H(f(k), U1(k, d))
26.53/8.72	   A^2 -> H(f(k), U1(d, k))
26.53/8.72	   A^2 -> H(f(c), b)
26.53/8.72	   A^2 -> H(f(c), U1(e, d))
26.53/8.72	   A^2 -> H(f(c), U1(d, e))
26.53/8.72	   A^2 -> H(f(k), U1(k, k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.72	   A^2 -> H(U1(k, k), f(c))
26.53/8.72	   A^2 -> H(U1(k, k), f(d))
26.53/8.72	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, d), f(e))
26.53/8.72	   A^2 -> H(U1(k, d), f(k))
26.53/8.72	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(d, k), f(e))
26.53/8.72	   A^2 -> H(U1(d, k), f(k))
26.53/8.72	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.72	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.72	   A^2 -> H(f(d), b)
26.53/8.72	   A^2 -> H(f(d), U1(e, d))
26.53/8.72	   A^2 -> H(f(d), U1(d, e))
26.53/8.72	   A^2 -> H(f(d), c)
26.53/8.72	   A^2 -> H(f(d), U1(e, k))
26.53/8.72	   A^2 -> H(f(d), U1(k, e))
26.53/8.72	
26.53/8.72	The TRS R consists of the following rules:
26.53/8.72	
26.53/8.72	   f(x) -> U1(x, x)
26.53/8.72	   U1(e, x) -> x
26.53/8.72	   a -> c
26.53/8.72	   a -> d
26.53/8.72	   b -> c
26.53/8.72	   b -> d
26.53/8.72	   d -> k
26.53/8.72	   c -> e
26.53/8.72	   c -> k
26.53/8.72	
26.53/8.72	Q is empty.
26.53/8.72	We have to consider all minimal (P,Q,R)-chains.
26.53/8.72	----------------------------------------
26.53/8.72	
26.53/8.72	(507) TransformationProof (EQUIVALENT)
26.53/8.72	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.72	
26.53/8.72	   (A^2 -> H(U1(d, d), U1(e, e)),A^2 -> H(U1(d, d), U1(e, e)))
26.53/8.72	   (A^2 -> H(f(k), U1(e, e)),A^2 -> H(f(k), U1(e, e)))
26.53/8.72	   (A^2 -> H(f(d), e),A^2 -> H(f(d), e))
26.53/8.72	
26.53/8.72	
26.53/8.72	----------------------------------------
26.53/8.72	
26.53/8.72	(508)
26.53/8.72	Obligation:
26.53/8.72	Q DP problem:
26.53/8.72	The TRS P consists of the following rules:
26.53/8.72	
26.53/8.72	   H(x, x) -> G(x, x, f(k))
26.53/8.72	   G(d, x, x) -> A^2
26.53/8.72	   A^2 -> H(f(c), f(c))
26.53/8.72	   A^2 -> H(f(d), f(d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.72	   A^2 -> H(f(e), f(e))
26.53/8.72	   A^2 -> H(f(k), f(k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.72	   A^2 -> H(f(d), U1(k, k))
26.53/8.72	   A^2 -> H(f(a), b)
26.53/8.72	   A^2 -> H(f(a), U1(e, d))
26.53/8.72	   A^2 -> H(f(a), U1(d, e))
26.53/8.72	   A^2 -> H(f(c), U1(e, c))
26.53/8.72	   A^2 -> H(f(c), U1(k, c))
26.53/8.72	   A^2 -> H(f(c), U1(c, e))
26.53/8.72	   A^2 -> H(f(c), U1(c, k))
26.53/8.72	   A^2 -> H(f(a), c)
26.53/8.72	   A^2 -> H(f(a), U1(e, k))
26.53/8.72	   A^2 -> H(f(a), U1(k, e))
26.53/8.72	   A^2 -> H(f(c), U1(e, e))
26.53/8.72	   A^2 -> H(f(a), e)
26.53/8.72	   A^2 -> H(f(d), U1(k, d))
26.53/8.72	   A^2 -> H(f(d), U1(d, k))
26.53/8.72	   A^2 -> H(f(a), U1(k, k))
26.53/8.72	   A^2 -> H(d, f(b))
26.53/8.72	   A^2 -> H(a, U1(b, b))
26.53/8.72	   A^2 -> H(a, f(c))
26.53/8.72	   A^2 -> H(a, f(d))
26.53/8.72	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.72	   A^2 -> H(U1(e, d), f(c))
26.53/8.72	   A^2 -> H(U1(e, d), f(d))
26.53/8.72	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, a), f(e))
26.53/8.72	   A^2 -> H(U1(e, a), f(k))
26.53/8.72	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.72	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, a), f(e))
26.53/8.72	   A^2 -> H(U1(k, a), f(k))
26.53/8.72	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, d), f(e))
26.53/8.72	   A^2 -> H(U1(c, d), f(k))
26.53/8.72	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.72	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.72	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.72	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.72	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.72	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.72	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.72	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.72	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.72	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.72	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.72	   A^2 -> H(U1(d, e), f(c))
26.53/8.72	   A^2 -> H(U1(d, e), f(d))
26.53/8.72	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.72	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.72	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.72	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.72	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(d, c), f(e))
26.53/8.72	   A^2 -> H(U1(d, c), f(k))
26.53/8.72	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.72	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.72	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.72	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.72	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.72	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.72	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.72	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.72	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.72	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.72	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(a, e), f(e))
26.53/8.72	   A^2 -> H(U1(a, e), f(k))
26.53/8.72	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.72	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(a, k), f(e))
26.53/8.72	   A^2 -> H(U1(a, k), f(k))
26.53/8.72	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.72	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.72	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.72	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.72	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.72	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.72	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.72	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.72	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.72	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.72	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.72	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.72	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.72	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.72	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.72	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.72	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.72	   A^2 -> H(U1(a, a), b)
26.53/8.72	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.72	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.72	   A^2 -> H(U1(a, a), c)
26.53/8.72	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.72	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.72	   A^2 -> H(U1(a, a), e)
26.53/8.72	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.72	   A^2 -> H(k, f(b))
26.53/8.72	   A^2 -> H(c, U1(b, b))
26.53/8.72	   A^2 -> H(c, f(c))
26.53/8.72	   A^2 -> H(c, f(d))
26.53/8.72	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.72	   A^2 -> H(U1(e, k), f(c))
26.53/8.72	   A^2 -> H(U1(e, k), f(d))
26.53/8.72	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, c), f(e))
26.53/8.72	   A^2 -> H(U1(e, c), f(k))
26.53/8.72	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.72	   A^2 -> H(U1(k, e), f(c))
26.53/8.72	   A^2 -> H(U1(k, e), f(d))
26.53/8.72	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, c), f(e))
26.53/8.72	   A^2 -> H(U1(k, c), f(k))
26.53/8.72	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, e), f(e))
26.53/8.72	   A^2 -> H(U1(c, e), f(k))
26.53/8.72	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, k), f(e))
26.53/8.72	   A^2 -> H(U1(c, k), f(k))
26.53/8.72	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.72	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.72	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.72	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.72	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.72	   A^2 -> H(e, U1(b, b))
26.53/8.72	   A^2 -> H(e, f(c))
26.53/8.72	   A^2 -> H(e, f(d))
26.53/8.72	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, e), f(e))
26.53/8.72	   A^2 -> H(U1(e, e), f(k))
26.53/8.72	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.72	   A^2 -> H(f(e), U1(e, b))
26.53/8.72	   A^2 -> H(f(e), U1(k, b))
26.53/8.72	   A^2 -> H(f(e), U1(c, d))
26.53/8.72	   A^2 -> H(f(e), U1(d, c))
26.53/8.72	   A^2 -> H(f(e), U1(b, e))
26.53/8.72	   A^2 -> H(f(e), U1(b, k))
26.53/8.72	   A^2 -> H(f(e), U1(e, c))
26.53/8.72	   A^2 -> H(f(e), U1(k, c))
26.53/8.72	   A^2 -> H(f(e), U1(c, e))
26.53/8.72	   A^2 -> H(f(e), U1(c, k))
26.53/8.72	   A^2 -> H(f(e), U1(k, k))
26.53/8.72	   A^2 -> H(f(e), U1(k, d))
26.53/8.72	   A^2 -> H(f(e), U1(d, k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, k), f(e))
26.53/8.72	   A^2 -> H(U1(k, k), f(k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.72	   A^2 -> H(f(k), U1(e, b))
26.53/8.72	   A^2 -> H(f(k), U1(k, b))
26.53/8.72	   A^2 -> H(f(k), U1(c, d))
26.53/8.72	   A^2 -> H(f(k), U1(d, c))
26.53/8.72	   A^2 -> H(f(k), U1(b, e))
26.53/8.72	   A^2 -> H(f(k), U1(b, k))
26.53/8.72	   A^2 -> H(f(k), U1(e, c))
26.53/8.72	   A^2 -> H(f(k), U1(k, c))
26.53/8.72	   A^2 -> H(f(k), U1(c, e))
26.53/8.72	   A^2 -> H(f(k), U1(c, k))
26.53/8.72	   A^2 -> H(f(k), U1(e, e))
26.53/8.72	   A^2 -> H(f(k), U1(k, d))
26.53/8.72	   A^2 -> H(f(k), U1(d, k))
26.53/8.72	   A^2 -> H(f(c), b)
26.53/8.72	   A^2 -> H(f(c), U1(e, d))
26.53/8.72	   A^2 -> H(f(c), U1(d, e))
26.53/8.72	   A^2 -> H(f(k), U1(k, k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.72	   A^2 -> H(U1(k, k), f(c))
26.53/8.72	   A^2 -> H(U1(k, k), f(d))
26.53/8.72	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, d), f(e))
26.53/8.72	   A^2 -> H(U1(k, d), f(k))
26.53/8.72	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(d, k), f(e))
26.53/8.72	   A^2 -> H(U1(d, k), f(k))
26.53/8.72	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.72	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.72	   A^2 -> H(f(d), b)
26.53/8.72	   A^2 -> H(f(d), U1(e, d))
26.53/8.72	   A^2 -> H(f(d), U1(d, e))
26.53/8.72	   A^2 -> H(f(d), c)
26.53/8.72	   A^2 -> H(f(d), U1(e, k))
26.53/8.72	   A^2 -> H(f(d), U1(k, e))
26.53/8.72	   A^2 -> H(f(d), e)
26.53/8.72	
26.53/8.72	The TRS R consists of the following rules:
26.53/8.72	
26.53/8.72	   f(x) -> U1(x, x)
26.53/8.72	   U1(e, x) -> x
26.53/8.72	   a -> c
26.53/8.72	   a -> d
26.53/8.72	   b -> c
26.53/8.72	   b -> d
26.53/8.72	   d -> k
26.53/8.72	   c -> e
26.53/8.72	   c -> k
26.53/8.72	
26.53/8.72	Q is empty.
26.53/8.72	We have to consider all minimal (P,Q,R)-chains.
26.53/8.72	----------------------------------------
26.53/8.72	
26.53/8.72	(509) TransformationProof (EQUIVALENT)
26.53/8.72	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.72	
26.53/8.72	   (A^2 -> H(U1(d, d), U1(k, k)),A^2 -> H(U1(d, d), U1(k, k)))
26.53/8.72	   (A^2 -> H(f(k), U1(k, k)),A^2 -> H(f(k), U1(k, k)))
26.53/8.72	
26.53/8.72	
26.53/8.72	----------------------------------------
26.53/8.72	
26.53/8.72	(510)
26.53/8.72	Obligation:
26.53/8.72	Q DP problem:
26.53/8.72	The TRS P consists of the following rules:
26.53/8.72	
26.53/8.72	   H(x, x) -> G(x, x, f(k))
26.53/8.72	   G(d, x, x) -> A^2
26.53/8.72	   A^2 -> H(f(c), f(c))
26.53/8.72	   A^2 -> H(f(d), f(d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.72	   A^2 -> H(f(e), f(e))
26.53/8.72	   A^2 -> H(f(k), f(k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.72	   A^2 -> H(f(a), b)
26.53/8.72	   A^2 -> H(f(a), U1(e, d))
26.53/8.72	   A^2 -> H(f(a), U1(d, e))
26.53/8.72	   A^2 -> H(f(c), U1(e, c))
26.53/8.72	   A^2 -> H(f(c), U1(k, c))
26.53/8.72	   A^2 -> H(f(c), U1(c, e))
26.53/8.72	   A^2 -> H(f(c), U1(c, k))
26.53/8.72	   A^2 -> H(f(a), c)
26.53/8.72	   A^2 -> H(f(a), U1(e, k))
26.53/8.72	   A^2 -> H(f(a), U1(k, e))
26.53/8.72	   A^2 -> H(f(c), U1(e, e))
26.53/8.72	   A^2 -> H(f(a), e)
26.53/8.72	   A^2 -> H(f(d), U1(k, d))
26.53/8.72	   A^2 -> H(f(d), U1(d, k))
26.53/8.72	   A^2 -> H(f(a), U1(k, k))
26.53/8.72	   A^2 -> H(d, f(b))
26.53/8.72	   A^2 -> H(a, U1(b, b))
26.53/8.72	   A^2 -> H(a, f(c))
26.53/8.72	   A^2 -> H(a, f(d))
26.53/8.72	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.72	   A^2 -> H(U1(e, d), f(c))
26.53/8.72	   A^2 -> H(U1(e, d), f(d))
26.53/8.72	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, a), f(e))
26.53/8.72	   A^2 -> H(U1(e, a), f(k))
26.53/8.72	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.72	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, a), f(e))
26.53/8.72	   A^2 -> H(U1(k, a), f(k))
26.53/8.72	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, d), f(e))
26.53/8.72	   A^2 -> H(U1(c, d), f(k))
26.53/8.72	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.72	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.72	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.72	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.72	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.72	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.72	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.72	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.72	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.72	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.72	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.72	   A^2 -> H(U1(d, e), f(c))
26.53/8.72	   A^2 -> H(U1(d, e), f(d))
26.53/8.72	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.72	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.72	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.72	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.72	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(d, c), f(e))
26.53/8.72	   A^2 -> H(U1(d, c), f(k))
26.53/8.72	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.72	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.72	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.72	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.72	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.72	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.72	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.72	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.72	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.72	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.72	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(a, e), f(e))
26.53/8.72	   A^2 -> H(U1(a, e), f(k))
26.53/8.72	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.72	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(a, k), f(e))
26.53/8.72	   A^2 -> H(U1(a, k), f(k))
26.53/8.72	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.72	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.72	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.72	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.72	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.72	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.72	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.72	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.72	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.72	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.72	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.72	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.72	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.72	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.72	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.72	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.72	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.72	   A^2 -> H(U1(a, a), b)
26.53/8.72	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.72	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.72	   A^2 -> H(U1(a, a), c)
26.53/8.72	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.72	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.72	   A^2 -> H(U1(a, a), e)
26.53/8.72	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.72	   A^2 -> H(k, f(b))
26.53/8.72	   A^2 -> H(c, U1(b, b))
26.53/8.72	   A^2 -> H(c, f(c))
26.53/8.72	   A^2 -> H(c, f(d))
26.53/8.72	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.72	   A^2 -> H(U1(e, k), f(c))
26.53/8.72	   A^2 -> H(U1(e, k), f(d))
26.53/8.72	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, c), f(e))
26.53/8.72	   A^2 -> H(U1(e, c), f(k))
26.53/8.72	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.72	   A^2 -> H(U1(k, e), f(c))
26.53/8.72	   A^2 -> H(U1(k, e), f(d))
26.53/8.72	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, c), f(e))
26.53/8.72	   A^2 -> H(U1(k, c), f(k))
26.53/8.72	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, e), f(e))
26.53/8.72	   A^2 -> H(U1(c, e), f(k))
26.53/8.72	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, k), f(e))
26.53/8.72	   A^2 -> H(U1(c, k), f(k))
26.53/8.72	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.72	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.72	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.72	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.72	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.72	   A^2 -> H(e, U1(b, b))
26.53/8.72	   A^2 -> H(e, f(c))
26.53/8.72	   A^2 -> H(e, f(d))
26.53/8.72	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, e), f(e))
26.53/8.72	   A^2 -> H(U1(e, e), f(k))
26.53/8.72	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.72	   A^2 -> H(f(e), U1(e, b))
26.53/8.72	   A^2 -> H(f(e), U1(k, b))
26.53/8.72	   A^2 -> H(f(e), U1(c, d))
26.53/8.72	   A^2 -> H(f(e), U1(d, c))
26.53/8.72	   A^2 -> H(f(e), U1(b, e))
26.53/8.72	   A^2 -> H(f(e), U1(b, k))
26.53/8.72	   A^2 -> H(f(e), U1(e, c))
26.53/8.72	   A^2 -> H(f(e), U1(k, c))
26.53/8.72	   A^2 -> H(f(e), U1(c, e))
26.53/8.72	   A^2 -> H(f(e), U1(c, k))
26.53/8.72	   A^2 -> H(f(e), U1(k, k))
26.53/8.72	   A^2 -> H(f(e), U1(k, d))
26.53/8.72	   A^2 -> H(f(e), U1(d, k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, k), f(e))
26.53/8.72	   A^2 -> H(U1(k, k), f(k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.72	   A^2 -> H(f(k), U1(e, b))
26.53/8.72	   A^2 -> H(f(k), U1(k, b))
26.53/8.72	   A^2 -> H(f(k), U1(c, d))
26.53/8.72	   A^2 -> H(f(k), U1(d, c))
26.53/8.72	   A^2 -> H(f(k), U1(b, e))
26.53/8.72	   A^2 -> H(f(k), U1(b, k))
26.53/8.72	   A^2 -> H(f(k), U1(e, c))
26.53/8.72	   A^2 -> H(f(k), U1(k, c))
26.53/8.72	   A^2 -> H(f(k), U1(c, e))
26.53/8.72	   A^2 -> H(f(k), U1(c, k))
26.53/8.72	   A^2 -> H(f(k), U1(e, e))
26.53/8.72	   A^2 -> H(f(k), U1(k, d))
26.53/8.72	   A^2 -> H(f(k), U1(d, k))
26.53/8.72	   A^2 -> H(f(c), b)
26.53/8.72	   A^2 -> H(f(c), U1(e, d))
26.53/8.72	   A^2 -> H(f(c), U1(d, e))
26.53/8.72	   A^2 -> H(f(k), U1(k, k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.72	   A^2 -> H(U1(k, k), f(c))
26.53/8.72	   A^2 -> H(U1(k, k), f(d))
26.53/8.72	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, d), f(e))
26.53/8.72	   A^2 -> H(U1(k, d), f(k))
26.53/8.72	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(d, k), f(e))
26.53/8.72	   A^2 -> H(U1(d, k), f(k))
26.53/8.72	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.72	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.72	   A^2 -> H(f(d), b)
26.53/8.72	   A^2 -> H(f(d), U1(e, d))
26.53/8.72	   A^2 -> H(f(d), U1(d, e))
26.53/8.72	   A^2 -> H(f(d), c)
26.53/8.72	   A^2 -> H(f(d), U1(e, k))
26.53/8.72	   A^2 -> H(f(d), U1(k, e))
26.53/8.72	   A^2 -> H(f(d), e)
26.53/8.72	
26.53/8.72	The TRS R consists of the following rules:
26.53/8.72	
26.53/8.72	   f(x) -> U1(x, x)
26.53/8.72	   U1(e, x) -> x
26.53/8.72	   a -> c
26.53/8.72	   a -> d
26.53/8.72	   b -> c
26.53/8.72	   b -> d
26.53/8.72	   d -> k
26.53/8.72	   c -> e
26.53/8.72	   c -> k
26.53/8.72	
26.53/8.72	Q is empty.
26.53/8.72	We have to consider all minimal (P,Q,R)-chains.
26.53/8.72	----------------------------------------
26.53/8.72	
26.53/8.72	(511) TransformationProof (EQUIVALENT)
26.53/8.72	By narrowing [LPAR04] the rule A^2 -> H(f(a), b) at position [] we obtained the following new rules [LPAR04]:
26.53/8.72	
26.53/8.72	   (A^2 -> H(U1(a, a), b),A^2 -> H(U1(a, a), b))
26.53/8.72	   (A^2 -> H(f(c), b),A^2 -> H(f(c), b))
26.53/8.72	   (A^2 -> H(f(d), b),A^2 -> H(f(d), b))
26.53/8.72	   (A^2 -> H(f(a), c),A^2 -> H(f(a), c))
26.53/8.72	   (A^2 -> H(f(a), d),A^2 -> H(f(a), d))
26.53/8.72	
26.53/8.72	
26.53/8.72	----------------------------------------
26.53/8.72	
26.53/8.72	(512)
26.53/8.72	Obligation:
26.53/8.72	Q DP problem:
26.53/8.72	The TRS P consists of the following rules:
26.53/8.72	
26.53/8.72	   H(x, x) -> G(x, x, f(k))
26.53/8.72	   G(d, x, x) -> A^2
26.53/8.72	   A^2 -> H(f(c), f(c))
26.53/8.72	   A^2 -> H(f(d), f(d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.72	   A^2 -> H(f(e), f(e))
26.53/8.72	   A^2 -> H(f(k), f(k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.72	   A^2 -> H(f(a), U1(e, d))
26.53/8.72	   A^2 -> H(f(a), U1(d, e))
26.53/8.72	   A^2 -> H(f(c), U1(e, c))
26.53/8.72	   A^2 -> H(f(c), U1(k, c))
26.53/8.72	   A^2 -> H(f(c), U1(c, e))
26.53/8.72	   A^2 -> H(f(c), U1(c, k))
26.53/8.72	   A^2 -> H(f(a), c)
26.53/8.72	   A^2 -> H(f(a), U1(e, k))
26.53/8.72	   A^2 -> H(f(a), U1(k, e))
26.53/8.72	   A^2 -> H(f(c), U1(e, e))
26.53/8.72	   A^2 -> H(f(a), e)
26.53/8.72	   A^2 -> H(f(d), U1(k, d))
26.53/8.72	   A^2 -> H(f(d), U1(d, k))
26.53/8.72	   A^2 -> H(f(a), U1(k, k))
26.53/8.72	   A^2 -> H(d, f(b))
26.53/8.72	   A^2 -> H(a, U1(b, b))
26.53/8.72	   A^2 -> H(a, f(c))
26.53/8.72	   A^2 -> H(a, f(d))
26.53/8.72	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.72	   A^2 -> H(U1(e, d), f(c))
26.53/8.72	   A^2 -> H(U1(e, d), f(d))
26.53/8.72	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, a), f(e))
26.53/8.72	   A^2 -> H(U1(e, a), f(k))
26.53/8.72	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.72	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, a), f(e))
26.53/8.72	   A^2 -> H(U1(k, a), f(k))
26.53/8.72	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, d), f(e))
26.53/8.72	   A^2 -> H(U1(c, d), f(k))
26.53/8.72	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.72	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.72	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.72	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.72	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.72	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.72	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.72	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.72	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.72	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.72	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.72	   A^2 -> H(U1(d, e), f(c))
26.53/8.72	   A^2 -> H(U1(d, e), f(d))
26.53/8.72	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.72	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.72	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.72	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.72	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(d, c), f(e))
26.53/8.72	   A^2 -> H(U1(d, c), f(k))
26.53/8.72	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.72	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.72	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.72	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.72	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.72	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.72	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.72	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.72	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.72	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.72	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(a, e), f(e))
26.53/8.72	   A^2 -> H(U1(a, e), f(k))
26.53/8.72	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.72	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(a, k), f(e))
26.53/8.72	   A^2 -> H(U1(a, k), f(k))
26.53/8.72	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.72	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.72	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.72	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.72	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.72	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.72	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.72	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.72	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.72	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.72	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.72	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.72	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.72	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.72	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.72	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.72	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.72	   A^2 -> H(U1(a, a), b)
26.53/8.72	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.72	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.72	   A^2 -> H(U1(a, a), c)
26.53/8.72	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.72	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.72	   A^2 -> H(U1(a, a), e)
26.53/8.72	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.72	   A^2 -> H(k, f(b))
26.53/8.72	   A^2 -> H(c, U1(b, b))
26.53/8.72	   A^2 -> H(c, f(c))
26.53/8.72	   A^2 -> H(c, f(d))
26.53/8.72	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.72	   A^2 -> H(U1(e, k), f(c))
26.53/8.72	   A^2 -> H(U1(e, k), f(d))
26.53/8.72	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, c), f(e))
26.53/8.72	   A^2 -> H(U1(e, c), f(k))
26.53/8.72	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.72	   A^2 -> H(U1(k, e), f(c))
26.53/8.72	   A^2 -> H(U1(k, e), f(d))
26.53/8.72	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, c), f(e))
26.53/8.72	   A^2 -> H(U1(k, c), f(k))
26.53/8.72	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, e), f(e))
26.53/8.72	   A^2 -> H(U1(c, e), f(k))
26.53/8.72	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, k), f(e))
26.53/8.72	   A^2 -> H(U1(c, k), f(k))
26.53/8.72	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.72	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.72	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.72	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.72	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.72	   A^2 -> H(e, U1(b, b))
26.53/8.72	   A^2 -> H(e, f(c))
26.53/8.72	   A^2 -> H(e, f(d))
26.53/8.72	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, e), f(e))
26.53/8.72	   A^2 -> H(U1(e, e), f(k))
26.53/8.72	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.72	   A^2 -> H(f(e), U1(e, b))
26.53/8.72	   A^2 -> H(f(e), U1(k, b))
26.53/8.72	   A^2 -> H(f(e), U1(c, d))
26.53/8.72	   A^2 -> H(f(e), U1(d, c))
26.53/8.72	   A^2 -> H(f(e), U1(b, e))
26.53/8.72	   A^2 -> H(f(e), U1(b, k))
26.53/8.72	   A^2 -> H(f(e), U1(e, c))
26.53/8.72	   A^2 -> H(f(e), U1(k, c))
26.53/8.72	   A^2 -> H(f(e), U1(c, e))
26.53/8.72	   A^2 -> H(f(e), U1(c, k))
26.53/8.72	   A^2 -> H(f(e), U1(k, k))
26.53/8.72	   A^2 -> H(f(e), U1(k, d))
26.53/8.72	   A^2 -> H(f(e), U1(d, k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, k), f(e))
26.53/8.72	   A^2 -> H(U1(k, k), f(k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.72	   A^2 -> H(f(k), U1(e, b))
26.53/8.72	   A^2 -> H(f(k), U1(k, b))
26.53/8.72	   A^2 -> H(f(k), U1(c, d))
26.53/8.72	   A^2 -> H(f(k), U1(d, c))
26.53/8.72	   A^2 -> H(f(k), U1(b, e))
26.53/8.72	   A^2 -> H(f(k), U1(b, k))
26.53/8.72	   A^2 -> H(f(k), U1(e, c))
26.53/8.72	   A^2 -> H(f(k), U1(k, c))
26.53/8.72	   A^2 -> H(f(k), U1(c, e))
26.53/8.72	   A^2 -> H(f(k), U1(c, k))
26.53/8.72	   A^2 -> H(f(k), U1(e, e))
26.53/8.72	   A^2 -> H(f(k), U1(k, d))
26.53/8.72	   A^2 -> H(f(k), U1(d, k))
26.53/8.72	   A^2 -> H(f(c), b)
26.53/8.72	   A^2 -> H(f(c), U1(e, d))
26.53/8.72	   A^2 -> H(f(c), U1(d, e))
26.53/8.72	   A^2 -> H(f(k), U1(k, k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.72	   A^2 -> H(U1(k, k), f(c))
26.53/8.72	   A^2 -> H(U1(k, k), f(d))
26.53/8.72	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, d), f(e))
26.53/8.72	   A^2 -> H(U1(k, d), f(k))
26.53/8.72	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(d, k), f(e))
26.53/8.72	   A^2 -> H(U1(d, k), f(k))
26.53/8.72	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.72	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.72	   A^2 -> H(f(d), b)
26.53/8.72	   A^2 -> H(f(d), U1(e, d))
26.53/8.72	   A^2 -> H(f(d), U1(d, e))
26.53/8.72	   A^2 -> H(f(d), c)
26.53/8.72	   A^2 -> H(f(d), U1(e, k))
26.53/8.72	   A^2 -> H(f(d), U1(k, e))
26.53/8.72	   A^2 -> H(f(d), e)
26.53/8.72	   A^2 -> H(f(a), d)
26.53/8.72	
26.53/8.72	The TRS R consists of the following rules:
26.53/8.72	
26.53/8.72	   f(x) -> U1(x, x)
26.53/8.72	   U1(e, x) -> x
26.53/8.72	   a -> c
26.53/8.72	   a -> d
26.53/8.72	   b -> c
26.53/8.72	   b -> d
26.53/8.72	   d -> k
26.53/8.72	   c -> e
26.53/8.72	   c -> k
26.53/8.72	
26.53/8.72	Q is empty.
26.53/8.72	We have to consider all minimal (P,Q,R)-chains.
26.53/8.72	----------------------------------------
26.53/8.72	
26.53/8.72	(513) TransformationProof (EQUIVALENT)
26.53/8.72	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.72	
26.53/8.72	   (A^2 -> H(U1(a, a), U1(e, d)),A^2 -> H(U1(a, a), U1(e, d)))
26.53/8.72	   (A^2 -> H(f(c), U1(e, d)),A^2 -> H(f(c), U1(e, d)))
26.53/8.72	   (A^2 -> H(f(d), U1(e, d)),A^2 -> H(f(d), U1(e, d)))
26.53/8.72	   (A^2 -> H(f(a), d),A^2 -> H(f(a), d))
26.53/8.72	   (A^2 -> H(f(a), U1(e, k)),A^2 -> H(f(a), U1(e, k)))
26.53/8.72	
26.53/8.72	
26.53/8.72	----------------------------------------
26.53/8.72	
26.53/8.72	(514)
26.53/8.72	Obligation:
26.53/8.72	Q DP problem:
26.53/8.72	The TRS P consists of the following rules:
26.53/8.72	
26.53/8.72	   H(x, x) -> G(x, x, f(k))
26.53/8.72	   G(d, x, x) -> A^2
26.53/8.72	   A^2 -> H(f(c), f(c))
26.53/8.72	   A^2 -> H(f(d), f(d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.72	   A^2 -> H(f(e), f(e))
26.53/8.72	   A^2 -> H(f(k), f(k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.72	   A^2 -> H(f(a), U1(d, e))
26.53/8.72	   A^2 -> H(f(c), U1(e, c))
26.53/8.72	   A^2 -> H(f(c), U1(k, c))
26.53/8.72	   A^2 -> H(f(c), U1(c, e))
26.53/8.72	   A^2 -> H(f(c), U1(c, k))
26.53/8.72	   A^2 -> H(f(a), c)
26.53/8.72	   A^2 -> H(f(a), U1(e, k))
26.53/8.72	   A^2 -> H(f(a), U1(k, e))
26.53/8.72	   A^2 -> H(f(c), U1(e, e))
26.53/8.72	   A^2 -> H(f(a), e)
26.53/8.72	   A^2 -> H(f(d), U1(k, d))
26.53/8.72	   A^2 -> H(f(d), U1(d, k))
26.53/8.72	   A^2 -> H(f(a), U1(k, k))
26.53/8.72	   A^2 -> H(d, f(b))
26.53/8.72	   A^2 -> H(a, U1(b, b))
26.53/8.72	   A^2 -> H(a, f(c))
26.53/8.72	   A^2 -> H(a, f(d))
26.53/8.72	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.72	   A^2 -> H(U1(e, d), f(c))
26.53/8.72	   A^2 -> H(U1(e, d), f(d))
26.53/8.72	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, a), f(e))
26.53/8.72	   A^2 -> H(U1(e, a), f(k))
26.53/8.72	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.72	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, a), f(e))
26.53/8.72	   A^2 -> H(U1(k, a), f(k))
26.53/8.72	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, d), f(e))
26.53/8.72	   A^2 -> H(U1(c, d), f(k))
26.53/8.72	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.72	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.72	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.72	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.72	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.72	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.72	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.72	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.72	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.72	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.72	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.72	   A^2 -> H(U1(d, e), f(c))
26.53/8.72	   A^2 -> H(U1(d, e), f(d))
26.53/8.72	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.72	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.72	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.72	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.72	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(d, c), f(e))
26.53/8.72	   A^2 -> H(U1(d, c), f(k))
26.53/8.72	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.72	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.72	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.72	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.72	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.72	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.72	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.72	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.72	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.72	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.72	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(a, e), f(e))
26.53/8.72	   A^2 -> H(U1(a, e), f(k))
26.53/8.72	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.72	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(a, k), f(e))
26.53/8.72	   A^2 -> H(U1(a, k), f(k))
26.53/8.72	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.72	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.72	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.72	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.72	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.72	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.72	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.72	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.72	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.72	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.72	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.72	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.72	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.72	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.72	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.72	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.72	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.72	   A^2 -> H(U1(a, a), b)
26.53/8.72	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.72	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.72	   A^2 -> H(U1(a, a), c)
26.53/8.72	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.72	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.72	   A^2 -> H(U1(a, a), e)
26.53/8.72	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.72	   A^2 -> H(k, f(b))
26.53/8.72	   A^2 -> H(c, U1(b, b))
26.53/8.72	   A^2 -> H(c, f(c))
26.53/8.72	   A^2 -> H(c, f(d))
26.53/8.72	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.72	   A^2 -> H(U1(e, k), f(c))
26.53/8.72	   A^2 -> H(U1(e, k), f(d))
26.53/8.72	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, c), f(e))
26.53/8.72	   A^2 -> H(U1(e, c), f(k))
26.53/8.72	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.72	   A^2 -> H(U1(k, e), f(c))
26.53/8.72	   A^2 -> H(U1(k, e), f(d))
26.53/8.72	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, c), f(e))
26.53/8.72	   A^2 -> H(U1(k, c), f(k))
26.53/8.72	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, e), f(e))
26.53/8.72	   A^2 -> H(U1(c, e), f(k))
26.53/8.72	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, k), f(e))
26.53/8.72	   A^2 -> H(U1(c, k), f(k))
26.53/8.72	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.72	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.72	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.72	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.72	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.72	   A^2 -> H(e, U1(b, b))
26.53/8.72	   A^2 -> H(e, f(c))
26.53/8.72	   A^2 -> H(e, f(d))
26.53/8.72	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, e), f(e))
26.53/8.72	   A^2 -> H(U1(e, e), f(k))
26.53/8.72	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.72	   A^2 -> H(f(e), U1(e, b))
26.53/8.72	   A^2 -> H(f(e), U1(k, b))
26.53/8.72	   A^2 -> H(f(e), U1(c, d))
26.53/8.72	   A^2 -> H(f(e), U1(d, c))
26.53/8.72	   A^2 -> H(f(e), U1(b, e))
26.53/8.72	   A^2 -> H(f(e), U1(b, k))
26.53/8.72	   A^2 -> H(f(e), U1(e, c))
26.53/8.72	   A^2 -> H(f(e), U1(k, c))
26.53/8.72	   A^2 -> H(f(e), U1(c, e))
26.53/8.72	   A^2 -> H(f(e), U1(c, k))
26.53/8.72	   A^2 -> H(f(e), U1(k, k))
26.53/8.72	   A^2 -> H(f(e), U1(k, d))
26.53/8.72	   A^2 -> H(f(e), U1(d, k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, k), f(e))
26.53/8.72	   A^2 -> H(U1(k, k), f(k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.72	   A^2 -> H(f(k), U1(e, b))
26.53/8.72	   A^2 -> H(f(k), U1(k, b))
26.53/8.72	   A^2 -> H(f(k), U1(c, d))
26.53/8.72	   A^2 -> H(f(k), U1(d, c))
26.53/8.72	   A^2 -> H(f(k), U1(b, e))
26.53/8.72	   A^2 -> H(f(k), U1(b, k))
26.53/8.72	   A^2 -> H(f(k), U1(e, c))
26.53/8.72	   A^2 -> H(f(k), U1(k, c))
26.53/8.72	   A^2 -> H(f(k), U1(c, e))
26.53/8.72	   A^2 -> H(f(k), U1(c, k))
26.53/8.72	   A^2 -> H(f(k), U1(e, e))
26.53/8.72	   A^2 -> H(f(k), U1(k, d))
26.53/8.72	   A^2 -> H(f(k), U1(d, k))
26.53/8.72	   A^2 -> H(f(c), b)
26.53/8.72	   A^2 -> H(f(c), U1(e, d))
26.53/8.72	   A^2 -> H(f(c), U1(d, e))
26.53/8.72	   A^2 -> H(f(k), U1(k, k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.72	   A^2 -> H(U1(k, k), f(c))
26.53/8.72	   A^2 -> H(U1(k, k), f(d))
26.53/8.72	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, d), f(e))
26.53/8.72	   A^2 -> H(U1(k, d), f(k))
26.53/8.72	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(d, k), f(e))
26.53/8.72	   A^2 -> H(U1(d, k), f(k))
26.53/8.72	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.72	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.72	   A^2 -> H(f(d), b)
26.53/8.72	   A^2 -> H(f(d), U1(e, d))
26.53/8.72	   A^2 -> H(f(d), U1(d, e))
26.53/8.72	   A^2 -> H(f(d), c)
26.53/8.72	   A^2 -> H(f(d), U1(e, k))
26.53/8.72	   A^2 -> H(f(d), U1(k, e))
26.53/8.72	   A^2 -> H(f(d), e)
26.53/8.72	   A^2 -> H(f(a), d)
26.53/8.72	
26.53/8.72	The TRS R consists of the following rules:
26.53/8.72	
26.53/8.72	   f(x) -> U1(x, x)
26.53/8.72	   U1(e, x) -> x
26.53/8.72	   a -> c
26.53/8.72	   a -> d
26.53/8.72	   b -> c
26.53/8.72	   b -> d
26.53/8.72	   d -> k
26.53/8.72	   c -> e
26.53/8.72	   c -> k
26.53/8.72	
26.53/8.72	Q is empty.
26.53/8.72	We have to consider all minimal (P,Q,R)-chains.
26.53/8.72	----------------------------------------
26.53/8.72	
26.53/8.72	(515) TransformationProof (EQUIVALENT)
26.53/8.72	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.72	
26.53/8.72	   (A^2 -> H(U1(a, a), U1(d, e)),A^2 -> H(U1(a, a), U1(d, e)))
26.53/8.72	   (A^2 -> H(f(c), U1(d, e)),A^2 -> H(f(c), U1(d, e)))
26.53/8.72	   (A^2 -> H(f(d), U1(d, e)),A^2 -> H(f(d), U1(d, e)))
26.53/8.72	   (A^2 -> H(f(a), U1(k, e)),A^2 -> H(f(a), U1(k, e)))
26.53/8.72	
26.53/8.72	
26.53/8.72	----------------------------------------
26.53/8.72	
26.53/8.72	(516)
26.53/8.72	Obligation:
26.53/8.72	Q DP problem:
26.53/8.72	The TRS P consists of the following rules:
26.53/8.72	
26.53/8.72	   H(x, x) -> G(x, x, f(k))
26.53/8.72	   G(d, x, x) -> A^2
26.53/8.72	   A^2 -> H(f(c), f(c))
26.53/8.72	   A^2 -> H(f(d), f(d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.72	   A^2 -> H(f(e), f(e))
26.53/8.72	   A^2 -> H(f(k), f(k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.72	   A^2 -> H(f(c), U1(e, c))
26.53/8.72	   A^2 -> H(f(c), U1(k, c))
26.53/8.72	   A^2 -> H(f(c), U1(c, e))
26.53/8.72	   A^2 -> H(f(c), U1(c, k))
26.53/8.72	   A^2 -> H(f(a), c)
26.53/8.72	   A^2 -> H(f(a), U1(e, k))
26.53/8.72	   A^2 -> H(f(a), U1(k, e))
26.53/8.72	   A^2 -> H(f(c), U1(e, e))
26.53/8.72	   A^2 -> H(f(a), e)
26.53/8.72	   A^2 -> H(f(d), U1(k, d))
26.53/8.72	   A^2 -> H(f(d), U1(d, k))
26.53/8.72	   A^2 -> H(f(a), U1(k, k))
26.53/8.72	   A^2 -> H(d, f(b))
26.53/8.72	   A^2 -> H(a, U1(b, b))
26.53/8.72	   A^2 -> H(a, f(c))
26.53/8.72	   A^2 -> H(a, f(d))
26.53/8.72	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.72	   A^2 -> H(U1(e, d), f(c))
26.53/8.72	   A^2 -> H(U1(e, d), f(d))
26.53/8.72	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, a), f(e))
26.53/8.72	   A^2 -> H(U1(e, a), f(k))
26.53/8.72	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.72	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, a), f(e))
26.53/8.72	   A^2 -> H(U1(k, a), f(k))
26.53/8.72	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, d), f(e))
26.53/8.72	   A^2 -> H(U1(c, d), f(k))
26.53/8.72	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.72	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.72	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.72	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.72	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.72	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.72	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.72	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.72	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.72	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.72	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.72	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.72	   A^2 -> H(U1(d, e), f(c))
26.53/8.72	   A^2 -> H(U1(d, e), f(d))
26.53/8.72	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.72	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.72	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.72	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.72	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(d, c), f(e))
26.53/8.72	   A^2 -> H(U1(d, c), f(k))
26.53/8.72	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.72	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.72	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.72	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.72	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.72	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.72	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.72	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.72	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.72	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.72	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.72	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(a, e), f(e))
26.53/8.72	   A^2 -> H(U1(a, e), f(k))
26.53/8.72	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.72	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(a, k), f(e))
26.53/8.72	   A^2 -> H(U1(a, k), f(k))
26.53/8.72	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.72	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.72	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.72	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.72	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.72	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.72	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.72	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.72	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.72	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.72	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.72	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.72	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.72	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.72	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.72	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.72	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.72	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.72	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.72	   A^2 -> H(U1(a, a), b)
26.53/8.72	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.72	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.72	   A^2 -> H(U1(a, a), c)
26.53/8.72	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.72	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.72	   A^2 -> H(U1(a, a), e)
26.53/8.72	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.72	   A^2 -> H(k, f(b))
26.53/8.72	   A^2 -> H(c, U1(b, b))
26.53/8.72	   A^2 -> H(c, f(c))
26.53/8.72	   A^2 -> H(c, f(d))
26.53/8.72	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.72	   A^2 -> H(U1(e, k), f(c))
26.53/8.72	   A^2 -> H(U1(e, k), f(d))
26.53/8.72	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, c), f(e))
26.53/8.72	   A^2 -> H(U1(e, c), f(k))
26.53/8.72	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.72	   A^2 -> H(U1(k, e), f(c))
26.53/8.72	   A^2 -> H(U1(k, e), f(d))
26.53/8.72	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, c), f(e))
26.53/8.72	   A^2 -> H(U1(k, c), f(k))
26.53/8.72	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, e), f(e))
26.53/8.72	   A^2 -> H(U1(c, e), f(k))
26.53/8.72	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(c, k), f(e))
26.53/8.72	   A^2 -> H(U1(c, k), f(k))
26.53/8.72	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.72	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.72	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.72	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.72	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.72	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.72	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.72	   A^2 -> H(e, U1(b, b))
26.53/8.72	   A^2 -> H(e, f(c))
26.53/8.72	   A^2 -> H(e, f(d))
26.53/8.72	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.72	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.72	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.72	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.72	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.72	   A^2 -> H(U1(e, e), f(e))
26.53/8.72	   A^2 -> H(U1(e, e), f(k))
26.53/8.72	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.72	   A^2 -> H(f(e), U1(e, b))
26.53/8.72	   A^2 -> H(f(e), U1(k, b))
26.53/8.72	   A^2 -> H(f(e), U1(c, d))
26.53/8.72	   A^2 -> H(f(e), U1(d, c))
26.53/8.72	   A^2 -> H(f(e), U1(b, e))
26.53/8.72	   A^2 -> H(f(e), U1(b, k))
26.53/8.72	   A^2 -> H(f(e), U1(e, c))
26.53/8.72	   A^2 -> H(f(e), U1(k, c))
26.53/8.72	   A^2 -> H(f(e), U1(c, e))
26.53/8.72	   A^2 -> H(f(e), U1(c, k))
26.53/8.72	   A^2 -> H(f(e), U1(k, k))
26.53/8.72	   A^2 -> H(f(e), U1(k, d))
26.53/8.72	   A^2 -> H(f(e), U1(d, k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, k), f(e))
26.53/8.72	   A^2 -> H(U1(k, k), f(k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.72	   A^2 -> H(f(k), U1(e, b))
26.53/8.72	   A^2 -> H(f(k), U1(k, b))
26.53/8.72	   A^2 -> H(f(k), U1(c, d))
26.53/8.72	   A^2 -> H(f(k), U1(d, c))
26.53/8.72	   A^2 -> H(f(k), U1(b, e))
26.53/8.72	   A^2 -> H(f(k), U1(b, k))
26.53/8.72	   A^2 -> H(f(k), U1(e, c))
26.53/8.72	   A^2 -> H(f(k), U1(k, c))
26.53/8.72	   A^2 -> H(f(k), U1(c, e))
26.53/8.72	   A^2 -> H(f(k), U1(c, k))
26.53/8.72	   A^2 -> H(f(k), U1(e, e))
26.53/8.72	   A^2 -> H(f(k), U1(k, d))
26.53/8.72	   A^2 -> H(f(k), U1(d, k))
26.53/8.72	   A^2 -> H(f(c), b)
26.53/8.72	   A^2 -> H(f(c), U1(e, d))
26.53/8.72	   A^2 -> H(f(c), U1(d, e))
26.53/8.72	   A^2 -> H(f(k), U1(k, k))
26.53/8.72	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.72	   A^2 -> H(U1(k, k), f(c))
26.53/8.72	   A^2 -> H(U1(k, k), f(d))
26.53/8.72	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.72	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.72	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.72	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.72	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.72	   A^2 -> H(U1(k, d), f(e))
26.53/8.72	   A^2 -> H(U1(k, d), f(k))
26.53/8.72	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.72	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.72	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.72	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.72	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.72	   A^2 -> H(U1(d, k), f(e))
26.53/8.72	   A^2 -> H(U1(d, k), f(k))
26.53/8.72	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.72	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.72	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.72	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.72	   A^2 -> H(f(d), b)
26.53/8.72	   A^2 -> H(f(d), U1(e, d))
26.53/8.72	   A^2 -> H(f(d), U1(d, e))
26.53/8.72	   A^2 -> H(f(d), c)
26.53/8.72	   A^2 -> H(f(d), U1(e, k))
26.53/8.72	   A^2 -> H(f(d), U1(k, e))
26.53/8.72	   A^2 -> H(f(d), e)
26.53/8.72	   A^2 -> H(f(a), d)
26.53/8.72	
26.53/8.72	The TRS R consists of the following rules:
26.53/8.72	
26.53/8.72	   f(x) -> U1(x, x)
26.53/8.72	   U1(e, x) -> x
26.53/8.72	   a -> c
26.53/8.72	   a -> d
26.53/8.72	   b -> c
26.53/8.72	   b -> d
26.53/8.72	   d -> k
26.53/8.72	   c -> e
26.53/8.72	   c -> k
26.53/8.72	
26.53/8.72	Q is empty.
26.53/8.72	We have to consider all minimal (P,Q,R)-chains.
26.53/8.72	----------------------------------------
26.53/8.72	
26.53/8.72	(517) TransformationProof (EQUIVALENT)
26.53/8.72	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.72	
26.53/8.72	   (A^2 -> H(U1(c, c), U1(e, c)),A^2 -> H(U1(c, c), U1(e, c)))
26.53/8.72	   (A^2 -> H(f(e), U1(e, c)),A^2 -> H(f(e), U1(e, c)))
26.53/8.72	   (A^2 -> H(f(k), U1(e, c)),A^2 -> H(f(k), U1(e, c)))
26.53/8.73	   (A^2 -> H(f(c), c),A^2 -> H(f(c), c))
26.53/8.73	   (A^2 -> H(f(c), U1(e, e)),A^2 -> H(f(c), U1(e, e)))
26.53/8.73	   (A^2 -> H(f(c), U1(e, k)),A^2 -> H(f(c), U1(e, k)))
26.53/8.73	
26.53/8.73	
26.53/8.73	----------------------------------------
26.53/8.73	
26.53/8.73	(518)
26.53/8.73	Obligation:
26.53/8.73	Q DP problem:
26.53/8.73	The TRS P consists of the following rules:
26.53/8.73	
26.53/8.73	   H(x, x) -> G(x, x, f(k))
26.53/8.73	   G(d, x, x) -> A^2
26.53/8.73	   A^2 -> H(f(c), f(c))
26.53/8.73	   A^2 -> H(f(d), f(d))
26.53/8.73	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.73	   A^2 -> H(f(e), f(e))
26.53/8.73	   A^2 -> H(f(k), f(k))
26.53/8.73	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.73	   A^2 -> H(f(c), U1(k, c))
26.53/8.73	   A^2 -> H(f(c), U1(c, e))
26.53/8.73	   A^2 -> H(f(c), U1(c, k))
26.53/8.73	   A^2 -> H(f(a), c)
26.53/8.73	   A^2 -> H(f(a), U1(e, k))
26.53/8.73	   A^2 -> H(f(a), U1(k, e))
26.53/8.73	   A^2 -> H(f(c), U1(e, e))
26.53/8.73	   A^2 -> H(f(a), e)
26.53/8.73	   A^2 -> H(f(d), U1(k, d))
26.53/8.73	   A^2 -> H(f(d), U1(d, k))
26.53/8.73	   A^2 -> H(f(a), U1(k, k))
26.53/8.73	   A^2 -> H(d, f(b))
26.53/8.73	   A^2 -> H(a, U1(b, b))
26.53/8.73	   A^2 -> H(a, f(c))
26.53/8.73	   A^2 -> H(a, f(d))
26.53/8.73	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.73	   A^2 -> H(U1(e, d), f(c))
26.53/8.73	   A^2 -> H(U1(e, d), f(d))
26.53/8.73	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.73	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.73	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.73	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.73	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.73	   A^2 -> H(U1(e, a), f(e))
26.53/8.73	   A^2 -> H(U1(e, a), f(k))
26.53/8.73	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.73	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.73	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.73	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.73	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.73	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.73	   A^2 -> H(U1(k, a), f(e))
26.53/8.73	   A^2 -> H(U1(k, a), f(k))
26.53/8.73	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.73	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.73	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.73	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.73	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.73	   A^2 -> H(U1(c, d), f(e))
26.53/8.73	   A^2 -> H(U1(c, d), f(k))
26.53/8.73	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.73	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.73	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.73	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.73	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.73	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.73	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.73	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.73	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.73	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.73	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.73	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.73	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.73	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.73	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.73	   A^2 -> H(U1(d, e), f(c))
26.53/8.73	   A^2 -> H(U1(d, e), f(d))
26.53/8.73	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.73	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.73	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.73	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.73	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.73	   A^2 -> H(U1(d, c), f(e))
26.53/8.73	   A^2 -> H(U1(d, c), f(k))
26.53/8.73	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.73	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.73	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.73	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.73	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.73	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.73	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.73	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.73	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.73	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.73	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.73	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.73	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.73	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.73	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.73	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.73	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.73	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.73	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.73	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.73	   A^2 -> H(U1(a, e), f(e))
26.53/8.73	   A^2 -> H(U1(a, e), f(k))
26.53/8.73	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.73	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.73	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.73	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.73	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.73	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.73	   A^2 -> H(U1(a, k), f(e))
26.53/8.73	   A^2 -> H(U1(a, k), f(k))
26.53/8.73	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.73	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.73	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.73	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.73	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.73	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.73	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.73	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.73	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.73	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.73	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.73	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.73	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.73	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.73	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.73	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.73	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.73	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.73	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.73	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.73	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.73	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.73	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.73	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.73	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.73	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.73	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.73	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.73	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.73	   A^2 -> H(U1(a, a), b)
26.53/8.73	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.73	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.73	   A^2 -> H(U1(a, a), c)
26.53/8.73	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.73	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.73	   A^2 -> H(U1(a, a), e)
26.53/8.73	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.73	   A^2 -> H(k, f(b))
26.53/8.73	   A^2 -> H(c, U1(b, b))
26.53/8.73	   A^2 -> H(c, f(c))
26.53/8.73	   A^2 -> H(c, f(d))
26.53/8.73	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.73	   A^2 -> H(U1(e, k), f(c))
26.53/8.73	   A^2 -> H(U1(e, k), f(d))
26.53/8.73	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.73	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.73	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.73	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.73	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.73	   A^2 -> H(U1(e, c), f(e))
26.53/8.73	   A^2 -> H(U1(e, c), f(k))
26.53/8.73	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.73	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.73	   A^2 -> H(U1(k, e), f(c))
26.53/8.73	   A^2 -> H(U1(k, e), f(d))
26.53/8.73	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.73	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.73	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.73	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.73	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.73	   A^2 -> H(U1(k, c), f(e))
26.53/8.73	   A^2 -> H(U1(k, c), f(k))
26.53/8.73	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.73	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.73	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.73	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.73	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.73	   A^2 -> H(U1(c, e), f(e))
26.53/8.73	   A^2 -> H(U1(c, e), f(k))
26.53/8.73	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.73	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.73	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.73	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.73	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.73	   A^2 -> H(U1(c, k), f(e))
26.53/8.73	   A^2 -> H(U1(c, k), f(k))
26.53/8.73	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.73	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.73	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.73	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.73	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.73	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.73	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.73	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.73	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.73	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.73	   A^2 -> H(e, U1(b, b))
26.53/8.73	   A^2 -> H(e, f(c))
26.53/8.73	   A^2 -> H(e, f(d))
26.53/8.73	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.73	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.73	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.73	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.73	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.73	   A^2 -> H(U1(e, e), f(e))
26.53/8.73	   A^2 -> H(U1(e, e), f(k))
26.53/8.73	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.73	   A^2 -> H(f(e), U1(e, b))
26.53/8.73	   A^2 -> H(f(e), U1(k, b))
26.53/8.73	   A^2 -> H(f(e), U1(c, d))
26.53/8.73	   A^2 -> H(f(e), U1(d, c))
26.53/8.73	   A^2 -> H(f(e), U1(b, e))
26.53/8.73	   A^2 -> H(f(e), U1(b, k))
26.53/8.73	   A^2 -> H(f(e), U1(e, c))
26.53/8.73	   A^2 -> H(f(e), U1(k, c))
26.53/8.73	   A^2 -> H(f(e), U1(c, e))
26.53/8.73	   A^2 -> H(f(e), U1(c, k))
26.53/8.73	   A^2 -> H(f(e), U1(k, k))
26.53/8.73	   A^2 -> H(f(e), U1(k, d))
26.53/8.73	   A^2 -> H(f(e), U1(d, k))
26.53/8.73	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.73	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.73	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.73	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.73	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.73	   A^2 -> H(U1(k, k), f(e))
26.53/8.73	   A^2 -> H(U1(k, k), f(k))
26.53/8.73	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.73	   A^2 -> H(f(k), U1(e, b))
26.53/8.73	   A^2 -> H(f(k), U1(k, b))
26.53/8.73	   A^2 -> H(f(k), U1(c, d))
26.53/8.73	   A^2 -> H(f(k), U1(d, c))
26.53/8.73	   A^2 -> H(f(k), U1(b, e))
26.53/8.73	   A^2 -> H(f(k), U1(b, k))
26.53/8.73	   A^2 -> H(f(k), U1(e, c))
26.53/8.73	   A^2 -> H(f(k), U1(k, c))
26.53/8.73	   A^2 -> H(f(k), U1(c, e))
26.53/8.73	   A^2 -> H(f(k), U1(c, k))
26.53/8.73	   A^2 -> H(f(k), U1(e, e))
26.53/8.73	   A^2 -> H(f(k), U1(k, d))
26.53/8.73	   A^2 -> H(f(k), U1(d, k))
26.53/8.73	   A^2 -> H(f(c), b)
26.53/8.73	   A^2 -> H(f(c), U1(e, d))
26.53/8.73	   A^2 -> H(f(c), U1(d, e))
26.53/8.73	   A^2 -> H(f(k), U1(k, k))
26.53/8.73	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.73	   A^2 -> H(U1(k, k), f(c))
26.53/8.73	   A^2 -> H(U1(k, k), f(d))
26.53/8.73	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.73	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.73	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.73	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.73	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.73	   A^2 -> H(U1(k, d), f(e))
26.53/8.73	   A^2 -> H(U1(k, d), f(k))
26.53/8.73	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.73	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.73	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.73	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.73	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.73	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.73	   A^2 -> H(U1(d, k), f(e))
26.53/8.73	   A^2 -> H(U1(d, k), f(k))
26.53/8.73	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.73	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.73	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.73	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.73	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.73	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.73	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.73	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.73	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.73	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.73	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.73	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.73	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.73	   A^2 -> H(f(d), b)
26.53/8.73	   A^2 -> H(f(d), U1(e, d))
26.53/8.73	   A^2 -> H(f(d), U1(d, e))
26.53/8.73	   A^2 -> H(f(d), c)
26.53/8.73	   A^2 -> H(f(d), U1(e, k))
26.53/8.73	   A^2 -> H(f(d), U1(k, e))
26.53/8.73	   A^2 -> H(f(d), e)
26.53/8.73	   A^2 -> H(f(a), d)
26.53/8.73	   A^2 -> H(U1(c, c), U1(e, c))
26.53/8.73	   A^2 -> H(f(c), c)
26.53/8.73	   A^2 -> H(f(c), U1(e, k))
26.53/8.73	
26.53/8.73	The TRS R consists of the following rules:
26.53/8.73	
26.53/8.73	   f(x) -> U1(x, x)
26.53/8.73	   U1(e, x) -> x
26.53/8.73	   a -> c
26.53/8.73	   a -> d
26.53/8.73	   b -> c
26.53/8.73	   b -> d
26.53/8.73	   d -> k
26.53/8.73	   c -> e
26.53/8.73	   c -> k
26.53/8.73	
26.53/8.73	Q is empty.
26.53/8.73	We have to consider all minimal (P,Q,R)-chains.
26.53/8.73	----------------------------------------
26.53/8.73	
26.53/8.73	(519) TransformationProof (EQUIVALENT)
26.53/8.73	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.73	
26.53/8.73	   (A^2 -> H(U1(c, c), U1(k, c)),A^2 -> H(U1(c, c), U1(k, c)))
26.53/8.73	   (A^2 -> H(f(e), U1(k, c)),A^2 -> H(f(e), U1(k, c)))
26.53/8.73	   (A^2 -> H(f(k), U1(k, c)),A^2 -> H(f(k), U1(k, c)))
26.53/8.73	   (A^2 -> H(f(c), U1(k, e)),A^2 -> H(f(c), U1(k, e)))
26.53/8.73	   (A^2 -> H(f(c), U1(k, k)),A^2 -> H(f(c), U1(k, k)))
26.53/8.73	
26.53/8.73	
26.53/8.73	----------------------------------------
26.53/8.73	
26.53/8.73	(520)
26.53/8.73	Obligation:
26.53/8.73	Q DP problem:
26.53/8.73	The TRS P consists of the following rules:
26.53/8.73	
26.53/8.73	   H(x, x) -> G(x, x, f(k))
26.53/8.73	   G(d, x, x) -> A^2
26.53/8.73	   A^2 -> H(f(c), f(c))
26.53/8.73	   A^2 -> H(f(d), f(d))
26.53/8.73	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.73	   A^2 -> H(f(e), f(e))
26.53/8.73	   A^2 -> H(f(k), f(k))
26.53/8.73	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.73	   A^2 -> H(f(c), U1(c, e))
26.53/8.73	   A^2 -> H(f(c), U1(c, k))
26.53/8.73	   A^2 -> H(f(a), c)
26.53/8.73	   A^2 -> H(f(a), U1(e, k))
26.53/8.73	   A^2 -> H(f(a), U1(k, e))
26.53/8.73	   A^2 -> H(f(c), U1(e, e))
26.53/8.73	   A^2 -> H(f(a), e)
26.53/8.73	   A^2 -> H(f(d), U1(k, d))
26.53/8.73	   A^2 -> H(f(d), U1(d, k))
26.53/8.73	   A^2 -> H(f(a), U1(k, k))
26.53/8.73	   A^2 -> H(d, f(b))
26.53/8.73	   A^2 -> H(a, U1(b, b))
26.53/8.73	   A^2 -> H(a, f(c))
26.53/8.73	   A^2 -> H(a, f(d))
26.53/8.73	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.73	   A^2 -> H(U1(e, d), f(c))
26.53/8.73	   A^2 -> H(U1(e, d), f(d))
26.53/8.73	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.73	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.73	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.73	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.73	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.73	   A^2 -> H(U1(e, a), f(e))
26.53/8.73	   A^2 -> H(U1(e, a), f(k))
26.53/8.73	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.73	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.73	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.73	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.73	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.73	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.73	   A^2 -> H(U1(k, a), f(e))
26.53/8.73	   A^2 -> H(U1(k, a), f(k))
26.53/8.73	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.73	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.73	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.73	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.73	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.73	   A^2 -> H(U1(c, d), f(e))
26.53/8.73	   A^2 -> H(U1(c, d), f(k))
26.53/8.73	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.73	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.73	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.73	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.73	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.73	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.73	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.73	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.73	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.73	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.73	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.73	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.73	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.73	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.73	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.73	   A^2 -> H(U1(d, e), f(c))
26.53/8.73	   A^2 -> H(U1(d, e), f(d))
26.53/8.73	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.73	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.73	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.73	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.73	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.73	   A^2 -> H(U1(d, c), f(e))
26.53/8.73	   A^2 -> H(U1(d, c), f(k))
26.53/8.73	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.73	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.73	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.73	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.73	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.73	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.73	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.73	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.73	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.73	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.73	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.73	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.73	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.73	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.73	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.73	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.73	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.73	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.73	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.73	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.73	   A^2 -> H(U1(a, e), f(e))
26.53/8.73	   A^2 -> H(U1(a, e), f(k))
26.53/8.73	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.73	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.73	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.73	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.73	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.73	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.73	   A^2 -> H(U1(a, k), f(e))
26.53/8.73	   A^2 -> H(U1(a, k), f(k))
26.53/8.73	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.73	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.73	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.73	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.73	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.73	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.73	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.73	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.73	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.73	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.73	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.73	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.73	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.73	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.73	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.73	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.73	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.73	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.73	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.73	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.73	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.73	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.73	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.73	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.73	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.73	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.73	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.73	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.73	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.73	   A^2 -> H(U1(a, a), b)
26.53/8.73	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.73	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.73	   A^2 -> H(U1(a, a), c)
26.53/8.73	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.73	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.73	   A^2 -> H(U1(a, a), e)
26.53/8.73	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.73	   A^2 -> H(k, f(b))
26.53/8.73	   A^2 -> H(c, U1(b, b))
26.53/8.73	   A^2 -> H(c, f(c))
26.53/8.73	   A^2 -> H(c, f(d))
26.53/8.73	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.73	   A^2 -> H(U1(e, k), f(c))
26.53/8.73	   A^2 -> H(U1(e, k), f(d))
26.53/8.73	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.73	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.73	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.73	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.73	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.73	   A^2 -> H(U1(e, c), f(e))
26.53/8.73	   A^2 -> H(U1(e, c), f(k))
26.53/8.73	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.73	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.73	   A^2 -> H(U1(k, e), f(c))
26.53/8.73	   A^2 -> H(U1(k, e), f(d))
26.53/8.73	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.73	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.73	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.73	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.73	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.73	   A^2 -> H(U1(k, c), f(e))
26.53/8.73	   A^2 -> H(U1(k, c), f(k))
26.53/8.73	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.73	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.73	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.73	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.73	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.73	   A^2 -> H(U1(c, e), f(e))
26.53/8.73	   A^2 -> H(U1(c, e), f(k))
26.53/8.73	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.73	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.73	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.73	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.73	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.73	   A^2 -> H(U1(c, k), f(e))
26.53/8.73	   A^2 -> H(U1(c, k), f(k))
26.53/8.73	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.73	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.73	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.73	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.73	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.73	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.73	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.73	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.73	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.73	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.73	   A^2 -> H(e, U1(b, b))
26.53/8.73	   A^2 -> H(e, f(c))
26.53/8.73	   A^2 -> H(e, f(d))
26.53/8.73	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.73	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.73	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.73	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.73	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.73	   A^2 -> H(U1(e, e), f(e))
26.53/8.73	   A^2 -> H(U1(e, e), f(k))
26.53/8.73	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.73	   A^2 -> H(f(e), U1(e, b))
26.53/8.73	   A^2 -> H(f(e), U1(k, b))
26.53/8.73	   A^2 -> H(f(e), U1(c, d))
26.53/8.73	   A^2 -> H(f(e), U1(d, c))
26.53/8.73	   A^2 -> H(f(e), U1(b, e))
26.53/8.73	   A^2 -> H(f(e), U1(b, k))
26.53/8.73	   A^2 -> H(f(e), U1(e, c))
26.53/8.73	   A^2 -> H(f(e), U1(k, c))
26.53/8.73	   A^2 -> H(f(e), U1(c, e))
26.53/8.73	   A^2 -> H(f(e), U1(c, k))
26.53/8.73	   A^2 -> H(f(e), U1(k, k))
26.53/8.73	   A^2 -> H(f(e), U1(k, d))
26.53/8.73	   A^2 -> H(f(e), U1(d, k))
26.53/8.73	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.73	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.73	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.73	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.73	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.73	   A^2 -> H(U1(k, k), f(e))
26.53/8.73	   A^2 -> H(U1(k, k), f(k))
26.53/8.73	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.73	   A^2 -> H(f(k), U1(e, b))
26.53/8.73	   A^2 -> H(f(k), U1(k, b))
26.53/8.73	   A^2 -> H(f(k), U1(c, d))
26.53/8.73	   A^2 -> H(f(k), U1(d, c))
26.53/8.73	   A^2 -> H(f(k), U1(b, e))
26.53/8.73	   A^2 -> H(f(k), U1(b, k))
26.53/8.73	   A^2 -> H(f(k), U1(e, c))
26.53/8.73	   A^2 -> H(f(k), U1(k, c))
26.53/8.73	   A^2 -> H(f(k), U1(c, e))
26.53/8.73	   A^2 -> H(f(k), U1(c, k))
26.53/8.73	   A^2 -> H(f(k), U1(e, e))
26.53/8.73	   A^2 -> H(f(k), U1(k, d))
26.53/8.73	   A^2 -> H(f(k), U1(d, k))
26.53/8.73	   A^2 -> H(f(c), b)
26.53/8.73	   A^2 -> H(f(c), U1(e, d))
26.53/8.73	   A^2 -> H(f(c), U1(d, e))
26.53/8.73	   A^2 -> H(f(k), U1(k, k))
26.53/8.73	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.73	   A^2 -> H(U1(k, k), f(c))
26.53/8.73	   A^2 -> H(U1(k, k), f(d))
26.53/8.73	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.73	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.73	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.73	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.73	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.73	   A^2 -> H(U1(k, d), f(e))
26.53/8.73	   A^2 -> H(U1(k, d), f(k))
26.53/8.73	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.73	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.73	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.73	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.73	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.73	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.73	   A^2 -> H(U1(d, k), f(e))
26.53/8.73	   A^2 -> H(U1(d, k), f(k))
26.53/8.73	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.73	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.73	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.73	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.73	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.73	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.73	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.73	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.73	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.73	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.73	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.73	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.73	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.73	   A^2 -> H(f(d), b)
26.53/8.73	   A^2 -> H(f(d), U1(e, d))
26.53/8.73	   A^2 -> H(f(d), U1(d, e))
26.53/8.73	   A^2 -> H(f(d), c)
26.53/8.73	   A^2 -> H(f(d), U1(e, k))
26.53/8.73	   A^2 -> H(f(d), U1(k, e))
26.53/8.73	   A^2 -> H(f(d), e)
26.53/8.73	   A^2 -> H(f(a), d)
26.53/8.73	   A^2 -> H(U1(c, c), U1(e, c))
26.53/8.73	   A^2 -> H(f(c), c)
26.53/8.73	   A^2 -> H(f(c), U1(e, k))
26.53/8.73	   A^2 -> H(U1(c, c), U1(k, c))
26.53/8.73	   A^2 -> H(f(c), U1(k, e))
26.53/8.73	   A^2 -> H(f(c), U1(k, k))
26.53/8.73	
26.53/8.73	The TRS R consists of the following rules:
26.53/8.73	
26.53/8.73	   f(x) -> U1(x, x)
26.53/8.73	   U1(e, x) -> x
26.53/8.73	   a -> c
26.53/8.73	   a -> d
26.53/8.73	   b -> c
26.53/8.73	   b -> d
26.53/8.73	   d -> k
26.53/8.73	   c -> e
26.53/8.73	   c -> k
26.53/8.73	
26.53/8.73	Q is empty.
26.53/8.73	We have to consider all minimal (P,Q,R)-chains.
26.53/8.73	----------------------------------------
26.53/8.73	
26.53/8.73	(521) TransformationProof (EQUIVALENT)
26.53/8.73	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.73	
26.53/8.73	   (A^2 -> H(U1(c, c), U1(c, e)),A^2 -> H(U1(c, c), U1(c, e)))
26.53/8.73	   (A^2 -> H(f(e), U1(c, e)),A^2 -> H(f(e), U1(c, e)))
26.53/8.73	   (A^2 -> H(f(k), U1(c, e)),A^2 -> H(f(k), U1(c, e)))
26.53/8.73	   (A^2 -> H(f(c), U1(e, e)),A^2 -> H(f(c), U1(e, e)))
26.53/8.73	   (A^2 -> H(f(c), U1(k, e)),A^2 -> H(f(c), U1(k, e)))
26.53/8.73	
26.53/8.73	
26.53/8.73	----------------------------------------
26.53/8.73	
26.53/8.73	(522)
26.53/8.73	Obligation:
26.53/8.73	Q DP problem:
26.53/8.73	The TRS P consists of the following rules:
26.53/8.73	
26.53/8.73	   H(x, x) -> G(x, x, f(k))
26.53/8.73	   G(d, x, x) -> A^2
26.53/8.73	   A^2 -> H(f(c), f(c))
26.53/8.73	   A^2 -> H(f(d), f(d))
26.53/8.73	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.73	   A^2 -> H(f(e), f(e))
26.53/8.73	   A^2 -> H(f(k), f(k))
26.53/8.73	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.73	   A^2 -> H(f(c), U1(c, k))
26.53/8.73	   A^2 -> H(f(a), c)
26.53/8.73	   A^2 -> H(f(a), U1(e, k))
26.53/8.73	   A^2 -> H(f(a), U1(k, e))
26.53/8.73	   A^2 -> H(f(c), U1(e, e))
26.53/8.73	   A^2 -> H(f(a), e)
26.53/8.73	   A^2 -> H(f(d), U1(k, d))
26.53/8.73	   A^2 -> H(f(d), U1(d, k))
26.53/8.73	   A^2 -> H(f(a), U1(k, k))
26.53/8.73	   A^2 -> H(d, f(b))
26.53/8.73	   A^2 -> H(a, U1(b, b))
26.53/8.73	   A^2 -> H(a, f(c))
26.53/8.73	   A^2 -> H(a, f(d))
26.53/8.73	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.73	   A^2 -> H(U1(e, d), f(c))
26.53/8.73	   A^2 -> H(U1(e, d), f(d))
26.53/8.73	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.73	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.73	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.73	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.73	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.73	   A^2 -> H(U1(e, a), f(e))
26.53/8.73	   A^2 -> H(U1(e, a), f(k))
26.53/8.73	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.73	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.73	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.73	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.73	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.73	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.73	   A^2 -> H(U1(k, a), f(e))
26.53/8.73	   A^2 -> H(U1(k, a), f(k))
26.53/8.73	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.73	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.73	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.73	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.73	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.73	   A^2 -> H(U1(c, d), f(e))
26.53/8.73	   A^2 -> H(U1(c, d), f(k))
26.53/8.73	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.73	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.73	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.73	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.73	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.73	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.73	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.73	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.73	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.73	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.73	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.73	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.73	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.73	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.73	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.73	   A^2 -> H(U1(d, e), f(c))
26.53/8.73	   A^2 -> H(U1(d, e), f(d))
26.53/8.73	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.73	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.73	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.73	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.73	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.73	   A^2 -> H(U1(d, c), f(e))
26.53/8.73	   A^2 -> H(U1(d, c), f(k))
26.53/8.73	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.73	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.73	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.73	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.73	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.73	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.73	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.73	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.73	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.73	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.73	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.73	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.73	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.73	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.73	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.73	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.73	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.73	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.73	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.73	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.73	   A^2 -> H(U1(a, e), f(e))
26.53/8.73	   A^2 -> H(U1(a, e), f(k))
26.53/8.73	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.73	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.73	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.73	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.73	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.73	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.73	   A^2 -> H(U1(a, k), f(e))
26.53/8.73	   A^2 -> H(U1(a, k), f(k))
26.53/8.73	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.73	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.73	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.73	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.73	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.73	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.73	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.73	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.73	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.73	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.73	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.73	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.73	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.73	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.73	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.73	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.73	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.73	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.73	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.73	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.73	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.73	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.73	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.73	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.73	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.73	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.73	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.73	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.73	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.73	   A^2 -> H(U1(a, a), b)
26.53/8.73	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.73	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.73	   A^2 -> H(U1(a, a), c)
26.53/8.73	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.73	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.73	   A^2 -> H(U1(a, a), e)
26.53/8.73	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.73	   A^2 -> H(k, f(b))
26.53/8.73	   A^2 -> H(c, U1(b, b))
26.53/8.73	   A^2 -> H(c, f(c))
26.53/8.73	   A^2 -> H(c, f(d))
26.53/8.73	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.73	   A^2 -> H(U1(e, k), f(c))
26.53/8.73	   A^2 -> H(U1(e, k), f(d))
26.53/8.73	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.73	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.73	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.73	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.73	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.73	   A^2 -> H(U1(e, c), f(e))
26.53/8.73	   A^2 -> H(U1(e, c), f(k))
26.53/8.73	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.73	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.73	   A^2 -> H(U1(k, e), f(c))
26.53/8.73	   A^2 -> H(U1(k, e), f(d))
26.53/8.73	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.73	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.73	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.73	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.73	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.73	   A^2 -> H(U1(k, c), f(e))
26.53/8.73	   A^2 -> H(U1(k, c), f(k))
26.53/8.73	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.73	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.73	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.73	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.73	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.73	   A^2 -> H(U1(c, e), f(e))
26.53/8.73	   A^2 -> H(U1(c, e), f(k))
26.53/8.73	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.73	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.73	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.73	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.73	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.73	   A^2 -> H(U1(c, k), f(e))
26.53/8.73	   A^2 -> H(U1(c, k), f(k))
26.53/8.73	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.73	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.73	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.73	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.73	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.73	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.73	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.73	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.73	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.73	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.73	   A^2 -> H(e, U1(b, b))
26.53/8.73	   A^2 -> H(e, f(c))
26.53/8.73	   A^2 -> H(e, f(d))
26.53/8.73	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.73	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.73	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.73	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.73	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.73	   A^2 -> H(U1(e, e), f(e))
26.53/8.73	   A^2 -> H(U1(e, e), f(k))
26.53/8.73	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.73	   A^2 -> H(f(e), U1(e, b))
26.53/8.73	   A^2 -> H(f(e), U1(k, b))
26.53/8.73	   A^2 -> H(f(e), U1(c, d))
26.53/8.73	   A^2 -> H(f(e), U1(d, c))
26.53/8.73	   A^2 -> H(f(e), U1(b, e))
26.53/8.73	   A^2 -> H(f(e), U1(b, k))
26.53/8.73	   A^2 -> H(f(e), U1(e, c))
26.53/8.73	   A^2 -> H(f(e), U1(k, c))
26.53/8.73	   A^2 -> H(f(e), U1(c, e))
26.53/8.73	   A^2 -> H(f(e), U1(c, k))
26.53/8.73	   A^2 -> H(f(e), U1(k, k))
26.53/8.73	   A^2 -> H(f(e), U1(k, d))
26.53/8.73	   A^2 -> H(f(e), U1(d, k))
26.53/8.73	   A^2 -> H(U1(k, k), U1(c, b))
26.53/8.73	   A^2 -> H(U1(k, k), U1(d, b))
26.53/8.73	   A^2 -> H(U1(k, k), U1(b, c))
26.53/8.73	   A^2 -> H(U1(k, k), U1(b, d))
26.53/8.73	   A^2 -> H(U1(k, k), U1(c, c))
26.53/8.73	   A^2 -> H(U1(k, k), f(e))
26.53/8.73	   A^2 -> H(U1(k, k), f(k))
26.53/8.73	   A^2 -> H(U1(k, k), U1(d, d))
26.53/8.73	   A^2 -> H(f(k), U1(e, b))
26.53/8.73	   A^2 -> H(f(k), U1(k, b))
26.53/8.73	   A^2 -> H(f(k), U1(c, d))
26.53/8.73	   A^2 -> H(f(k), U1(d, c))
26.53/8.73	   A^2 -> H(f(k), U1(b, e))
26.53/8.73	   A^2 -> H(f(k), U1(b, k))
26.53/8.73	   A^2 -> H(f(k), U1(e, c))
26.53/8.73	   A^2 -> H(f(k), U1(k, c))
26.53/8.73	   A^2 -> H(f(k), U1(c, e))
26.53/8.73	   A^2 -> H(f(k), U1(c, k))
26.53/8.73	   A^2 -> H(f(k), U1(e, e))
26.53/8.73	   A^2 -> H(f(k), U1(k, d))
26.53/8.73	   A^2 -> H(f(k), U1(d, k))
26.53/8.73	   A^2 -> H(f(c), b)
26.53/8.73	   A^2 -> H(f(c), U1(e, d))
26.53/8.73	   A^2 -> H(f(c), U1(d, e))
26.53/8.73	   A^2 -> H(f(k), U1(k, k))
26.53/8.73	   A^2 -> H(U1(k, k), U1(b, b))
26.53/8.73	   A^2 -> H(U1(k, k), f(c))
26.53/8.73	   A^2 -> H(U1(k, k), f(d))
26.53/8.73	   A^2 -> H(U1(k, d), U1(c, b))
26.53/8.73	   A^2 -> H(U1(k, d), U1(d, b))
26.53/8.73	   A^2 -> H(U1(k, d), U1(b, c))
26.53/8.73	   A^2 -> H(U1(k, d), U1(b, d))
26.53/8.73	   A^2 -> H(U1(k, d), U1(c, c))
26.53/8.73	   A^2 -> H(U1(k, d), f(e))
26.53/8.73	   A^2 -> H(U1(k, d), f(k))
26.53/8.73	   A^2 -> H(U1(k, d), U1(d, d))
26.53/8.73	   A^2 -> H(U1(d, k), U1(c, b))
26.53/8.73	   A^2 -> H(U1(d, k), U1(d, b))
26.53/8.73	   A^2 -> H(U1(d, k), U1(b, c))
26.53/8.73	   A^2 -> H(U1(d, k), U1(b, d))
26.53/8.73	   A^2 -> H(U1(d, k), U1(c, c))
26.53/8.73	   A^2 -> H(U1(d, k), f(e))
26.53/8.73	   A^2 -> H(U1(d, k), f(k))
26.53/8.73	   A^2 -> H(U1(d, k), U1(d, d))
26.53/8.73	   A^2 -> H(U1(d, d), U1(e, b))
26.53/8.73	   A^2 -> H(U1(d, d), U1(k, b))
26.53/8.73	   A^2 -> H(U1(d, d), U1(c, d))
26.53/8.73	   A^2 -> H(U1(d, d), U1(d, c))
26.53/8.73	   A^2 -> H(U1(d, d), U1(b, e))
26.53/8.73	   A^2 -> H(U1(d, d), U1(b, k))
26.53/8.73	   A^2 -> H(U1(d, d), U1(e, c))
26.53/8.73	   A^2 -> H(U1(d, d), U1(k, c))
26.53/8.73	   A^2 -> H(U1(d, d), U1(c, e))
26.53/8.73	   A^2 -> H(U1(d, d), U1(c, k))
26.53/8.73	   A^2 -> H(U1(d, d), U1(e, e))
26.53/8.73	   A^2 -> H(U1(d, d), U1(k, k))
26.53/8.73	   A^2 -> H(f(d), b)
26.53/8.73	   A^2 -> H(f(d), U1(e, d))
26.53/8.73	   A^2 -> H(f(d), U1(d, e))
26.53/8.73	   A^2 -> H(f(d), c)
26.53/8.73	   A^2 -> H(f(d), U1(e, k))
26.53/8.73	   A^2 -> H(f(d), U1(k, e))
26.53/8.73	   A^2 -> H(f(d), e)
26.53/8.73	   A^2 -> H(f(a), d)
26.53/8.73	   A^2 -> H(U1(c, c), U1(e, c))
26.53/8.73	   A^2 -> H(f(c), c)
26.53/8.73	   A^2 -> H(f(c), U1(e, k))
26.53/8.73	   A^2 -> H(U1(c, c), U1(k, c))
26.53/8.73	   A^2 -> H(f(c), U1(k, e))
26.53/8.73	   A^2 -> H(f(c), U1(k, k))
26.53/8.73	   A^2 -> H(U1(c, c), U1(c, e))
26.53/8.73	
26.53/8.73	The TRS R consists of the following rules:
26.53/8.73	
26.53/8.73	   f(x) -> U1(x, x)
26.53/8.73	   U1(e, x) -> x
26.53/8.73	   a -> c
26.53/8.73	   a -> d
26.53/8.73	   b -> c
26.53/8.73	   b -> d
26.53/8.73	   d -> k
26.53/8.73	   c -> e
26.53/8.73	   c -> k
26.53/8.73	
26.53/8.73	Q is empty.
26.53/8.73	We have to consider all minimal (P,Q,R)-chains.
26.53/8.73	----------------------------------------
26.53/8.73	
26.53/8.73	(523) TransformationProof (EQUIVALENT)
26.53/8.73	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
26.53/8.73	
26.53/8.73	   (A^2 -> H(U1(c, c), U1(c, k)),A^2 -> H(U1(c, c), U1(c, k)))
26.53/8.73	   (A^2 -> H(f(e), U1(c, k)),A^2 -> H(f(e), U1(c, k)))
26.53/8.73	   (A^2 -> H(f(k), U1(c, k)),A^2 -> H(f(k), U1(c, k)))
26.53/8.73	   (A^2 -> H(f(c), U1(e, k)),A^2 -> H(f(c), U1(e, k)))
26.53/8.73	   (A^2 -> H(f(c), U1(k, k)),A^2 -> H(f(c), U1(k, k)))
26.53/8.73	
26.53/8.73	
26.53/8.73	----------------------------------------
26.53/8.73	
26.53/8.73	(524)
26.53/8.73	Obligation:
26.53/8.73	Q DP problem:
26.53/8.73	The TRS P consists of the following rules:
26.53/8.73	
26.53/8.73	   H(x, x) -> G(x, x, f(k))
26.53/8.73	   G(d, x, x) -> A^2
26.53/8.73	   A^2 -> H(f(c), f(c))
26.53/8.73	   A^2 -> H(f(d), f(d))
26.53/8.73	   A^2 -> H(U1(c, c), U1(c, c))
26.53/8.73	   A^2 -> H(f(e), f(e))
26.53/8.73	   A^2 -> H(f(k), f(k))
26.53/8.73	   A^2 -> H(U1(d, d), U1(d, d))
26.53/8.73	   A^2 -> H(f(a), c)
26.53/8.73	   A^2 -> H(f(a), U1(e, k))
26.53/8.73	   A^2 -> H(f(a), U1(k, e))
26.53/8.73	   A^2 -> H(f(c), U1(e, e))
26.53/8.73	   A^2 -> H(f(a), e)
26.53/8.73	   A^2 -> H(f(d), U1(k, d))
26.53/8.73	   A^2 -> H(f(d), U1(d, k))
26.53/8.73	   A^2 -> H(f(a), U1(k, k))
26.53/8.73	   A^2 -> H(d, f(b))
26.53/8.73	   A^2 -> H(a, U1(b, b))
26.53/8.73	   A^2 -> H(a, f(c))
26.53/8.73	   A^2 -> H(a, f(d))
26.53/8.73	   A^2 -> H(U1(e, d), U1(b, b))
26.53/8.73	   A^2 -> H(U1(e, d), f(c))
26.53/8.73	   A^2 -> H(U1(e, d), f(d))
26.53/8.73	   A^2 -> H(U1(e, a), U1(c, b))
26.53/8.73	   A^2 -> H(U1(e, a), U1(d, b))
26.53/8.73	   A^2 -> H(U1(e, a), U1(b, c))
26.53/8.73	   A^2 -> H(U1(e, a), U1(b, d))
26.53/8.73	   A^2 -> H(U1(e, a), U1(c, c))
26.53/8.73	   A^2 -> H(U1(e, a), f(e))
26.53/8.73	   A^2 -> H(U1(e, a), f(k))
26.53/8.73	   A^2 -> H(U1(e, a), U1(d, d))
26.53/8.73	   A^2 -> H(U1(k, a), U1(c, b))
26.53/8.73	   A^2 -> H(U1(k, a), U1(d, b))
26.53/8.73	   A^2 -> H(U1(k, a), U1(b, c))
26.53/8.73	   A^2 -> H(U1(k, a), U1(b, d))
26.53/8.73	   A^2 -> H(U1(k, a), U1(c, c))
26.53/8.73	   A^2 -> H(U1(k, a), f(e))
26.53/8.73	   A^2 -> H(U1(k, a), f(k))
26.53/8.73	   A^2 -> H(U1(k, a), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, d), U1(c, b))
26.53/8.73	   A^2 -> H(U1(c, d), U1(d, b))
26.53/8.73	   A^2 -> H(U1(c, d), U1(b, c))
26.53/8.73	   A^2 -> H(U1(c, d), U1(b, d))
26.53/8.73	   A^2 -> H(U1(c, d), U1(c, c))
26.53/8.73	   A^2 -> H(U1(c, d), f(e))
26.53/8.73	   A^2 -> H(U1(c, d), f(k))
26.53/8.73	   A^2 -> H(U1(c, d), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, a), U1(e, b))
26.53/8.73	   A^2 -> H(U1(c, a), U1(k, b))
26.53/8.73	   A^2 -> H(U1(c, a), U1(c, d))
26.53/8.73	   A^2 -> H(U1(c, a), U1(d, c))
26.53/8.73	   A^2 -> H(U1(c, a), U1(b, e))
26.53/8.73	   A^2 -> H(U1(c, a), U1(b, k))
26.53/8.73	   A^2 -> H(U1(c, a), U1(e, c))
26.53/8.73	   A^2 -> H(U1(c, a), U1(k, c))
26.53/8.73	   A^2 -> H(U1(c, a), U1(c, e))
26.53/8.73	   A^2 -> H(U1(c, a), U1(c, k))
26.53/8.73	   A^2 -> H(U1(c, a), U1(e, e))
26.53/8.73	   A^2 -> H(U1(c, a), U1(k, k))
26.53/8.73	   A^2 -> H(U1(c, a), U1(k, d))
26.53/8.73	   A^2 -> H(U1(c, a), U1(d, k))
26.53/8.73	   A^2 -> H(U1(d, e), U1(b, b))
26.53/8.73	   A^2 -> H(U1(d, e), f(c))
26.53/8.73	   A^2 -> H(U1(d, e), f(d))
26.53/8.73	   A^2 -> H(U1(d, c), U1(c, b))
26.53/8.73	   A^2 -> H(U1(d, c), U1(d, b))
26.53/8.73	   A^2 -> H(U1(d, c), U1(b, c))
26.53/8.73	   A^2 -> H(U1(d, c), U1(b, d))
26.53/8.73	   A^2 -> H(U1(d, c), U1(c, c))
26.53/8.73	   A^2 -> H(U1(d, c), f(e))
26.53/8.73	   A^2 -> H(U1(d, c), f(k))
26.53/8.73	   A^2 -> H(U1(d, c), U1(d, d))
26.53/8.73	   A^2 -> H(U1(d, a), U1(e, b))
26.53/8.73	   A^2 -> H(U1(d, a), U1(k, b))
26.53/8.73	   A^2 -> H(U1(d, a), U1(c, d))
26.53/8.73	   A^2 -> H(U1(d, a), U1(d, c))
26.53/8.73	   A^2 -> H(U1(d, a), U1(b, e))
26.53/8.73	   A^2 -> H(U1(d, a), U1(b, k))
26.53/8.73	   A^2 -> H(U1(d, a), U1(e, c))
26.53/8.73	   A^2 -> H(U1(d, a), U1(k, c))
26.53/8.73	   A^2 -> H(U1(d, a), U1(c, e))
26.53/8.73	   A^2 -> H(U1(d, a), U1(c, k))
26.53/8.73	   A^2 -> H(U1(d, a), U1(e, e))
26.53/8.73	   A^2 -> H(U1(d, a), U1(k, k))
26.53/8.73	   A^2 -> H(U1(d, a), U1(k, d))
26.53/8.73	   A^2 -> H(U1(d, a), U1(d, k))
26.53/8.73	   A^2 -> H(U1(a, e), U1(c, b))
26.53/8.73	   A^2 -> H(U1(a, e), U1(d, b))
26.53/8.73	   A^2 -> H(U1(a, e), U1(b, c))
26.53/8.73	   A^2 -> H(U1(a, e), U1(b, d))
26.53/8.73	   A^2 -> H(U1(a, e), U1(c, c))
26.53/8.73	   A^2 -> H(U1(a, e), f(e))
26.53/8.73	   A^2 -> H(U1(a, e), f(k))
26.53/8.73	   A^2 -> H(U1(a, e), U1(d, d))
26.53/8.73	   A^2 -> H(U1(a, k), U1(c, b))
26.53/8.73	   A^2 -> H(U1(a, k), U1(d, b))
26.53/8.73	   A^2 -> H(U1(a, k), U1(b, c))
26.53/8.73	   A^2 -> H(U1(a, k), U1(b, d))
26.53/8.73	   A^2 -> H(U1(a, k), U1(c, c))
26.53/8.73	   A^2 -> H(U1(a, k), f(e))
26.53/8.73	   A^2 -> H(U1(a, k), f(k))
26.53/8.73	   A^2 -> H(U1(a, k), U1(d, d))
26.53/8.73	   A^2 -> H(U1(a, c), U1(e, b))
26.53/8.73	   A^2 -> H(U1(a, c), U1(k, b))
26.53/8.73	   A^2 -> H(U1(a, c), U1(c, d))
26.53/8.73	   A^2 -> H(U1(a, c), U1(d, c))
26.53/8.73	   A^2 -> H(U1(a, c), U1(b, e))
26.53/8.73	   A^2 -> H(U1(a, c), U1(b, k))
26.53/8.73	   A^2 -> H(U1(a, c), U1(e, c))
26.53/8.73	   A^2 -> H(U1(a, c), U1(k, c))
26.53/8.73	   A^2 -> H(U1(a, c), U1(c, e))
26.53/8.73	   A^2 -> H(U1(a, c), U1(c, k))
26.53/8.73	   A^2 -> H(U1(a, c), U1(e, e))
26.53/8.73	   A^2 -> H(U1(a, c), U1(k, k))
26.53/8.73	   A^2 -> H(U1(a, c), U1(k, d))
26.53/8.73	   A^2 -> H(U1(a, c), U1(d, k))
26.53/8.73	   A^2 -> H(U1(a, d), U1(e, b))
26.53/8.73	   A^2 -> H(U1(a, d), U1(k, b))
26.53/8.73	   A^2 -> H(U1(a, d), U1(c, d))
26.53/8.73	   A^2 -> H(U1(a, d), U1(d, c))
26.53/8.73	   A^2 -> H(U1(a, d), U1(b, e))
26.53/8.73	   A^2 -> H(U1(a, d), U1(b, k))
26.53/8.73	   A^2 -> H(U1(a, d), U1(e, c))
26.53/8.73	   A^2 -> H(U1(a, d), U1(k, c))
26.53/8.73	   A^2 -> H(U1(a, d), U1(c, e))
26.53/8.73	   A^2 -> H(U1(a, d), U1(c, k))
26.53/8.73	   A^2 -> H(U1(a, d), U1(e, e))
26.53/8.73	   A^2 -> H(U1(a, d), U1(k, k))
26.53/8.73	   A^2 -> H(U1(a, d), U1(k, d))
26.53/8.73	   A^2 -> H(U1(a, d), U1(d, k))
26.53/8.73	   A^2 -> H(U1(a, a), b)
26.53/8.73	   A^2 -> H(U1(a, a), U1(e, d))
26.53/8.73	   A^2 -> H(U1(a, a), U1(d, e))
26.53/8.73	   A^2 -> H(U1(a, a), c)
26.53/8.73	   A^2 -> H(U1(a, a), U1(e, k))
26.53/8.73	   A^2 -> H(U1(a, a), U1(k, e))
26.53/8.73	   A^2 -> H(U1(a, a), e)
26.53/8.73	   A^2 -> H(U1(a, a), U1(k, k))
26.53/8.73	   A^2 -> H(k, f(b))
26.53/8.73	   A^2 -> H(c, U1(b, b))
26.53/8.73	   A^2 -> H(c, f(c))
26.53/8.73	   A^2 -> H(c, f(d))
26.53/8.73	   A^2 -> H(U1(e, k), U1(b, b))
26.53/8.73	   A^2 -> H(U1(e, k), f(c))
26.53/8.73	   A^2 -> H(U1(e, k), f(d))
26.53/8.73	   A^2 -> H(U1(e, c), U1(c, b))
26.53/8.73	   A^2 -> H(U1(e, c), U1(d, b))
26.53/8.73	   A^2 -> H(U1(e, c), U1(b, c))
26.53/8.73	   A^2 -> H(U1(e, c), U1(b, d))
26.53/8.73	   A^2 -> H(U1(e, c), U1(c, c))
26.53/8.73	   A^2 -> H(U1(e, c), f(e))
26.53/8.73	   A^2 -> H(U1(e, c), f(k))
26.53/8.73	   A^2 -> H(U1(e, c), U1(d, d))
26.53/8.73	   A^2 -> H(U1(k, e), U1(b, b))
26.53/8.73	   A^2 -> H(U1(k, e), f(c))
26.53/8.73	   A^2 -> H(U1(k, e), f(d))
26.53/8.73	   A^2 -> H(U1(k, c), U1(c, b))
26.53/8.73	   A^2 -> H(U1(k, c), U1(d, b))
26.53/8.73	   A^2 -> H(U1(k, c), U1(b, c))
26.53/8.73	   A^2 -> H(U1(k, c), U1(b, d))
26.53/8.73	   A^2 -> H(U1(k, c), U1(c, c))
26.53/8.73	   A^2 -> H(U1(k, c), f(e))
26.53/8.73	   A^2 -> H(U1(k, c), f(k))
26.53/8.73	   A^2 -> H(U1(k, c), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, e), U1(c, b))
26.53/8.73	   A^2 -> H(U1(c, e), U1(d, b))
26.53/8.73	   A^2 -> H(U1(c, e), U1(b, c))
26.53/8.73	   A^2 -> H(U1(c, e), U1(b, d))
26.53/8.73	   A^2 -> H(U1(c, e), U1(c, c))
26.53/8.73	   A^2 -> H(U1(c, e), f(e))
26.53/8.73	   A^2 -> H(U1(c, e), f(k))
26.53/8.73	   A^2 -> H(U1(c, e), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, k), U1(c, b))
26.53/8.73	   A^2 -> H(U1(c, k), U1(d, b))
26.53/8.73	   A^2 -> H(U1(c, k), U1(b, c))
26.53/8.73	   A^2 -> H(U1(c, k), U1(b, d))
26.53/8.73	   A^2 -> H(U1(c, k), U1(c, c))
26.53/8.73	   A^2 -> H(U1(c, k), f(e))
26.53/8.73	   A^2 -> H(U1(c, k), f(k))
26.53/8.73	   A^2 -> H(U1(c, k), U1(d, d))
26.53/8.73	   A^2 -> H(U1(c, c), U1(e, b))
26.53/8.73	   A^2 -> H(U1(c, c), U1(k, b))
26.53/8.73	   A^2 -> H(U1(c, c), U1(c, d))
26.53/8.73	   A^2 -> H(U1(c, c), U1(d, c))
26.53/8.73	   A^2 -> H(U1(c, c), U1(b, e))
26.53/8.73	   A^2 -> H(U1(c, c), U1(b, k))
26.53/8.73	   A^2 -> H(U1(c, c), U1(e, e))
26.53/8.73	   A^2 -> H(U1(c, c), U1(k, k))
26.53/8.73	   A^2 -> H(U1(c, c), U1(k, d))
26.53/8.73	   A^2 -> H(U1(c, c), U1(d, k))
26.53/8.73	   A^2 -> H(e, U1(b, b))
26.53/8.73	   A^2 -> H(e, f(c))
26.53/8.73	   A^2 -> H(e, f(d))
26.53/8.73	   A^2 -> H(U1(e, e), U1(c, b))
26.53/8.73	   A^2 -> H(U1(e, e), U1(d, b))
26.53/8.73	   A^2 -> H(U1(e, e), U1(b, c))
26.53/8.73	   A^2 -> H(U1(e, e), U1(b, d))
26.53/8.73	   A^2 -> H(U1(e, e), U1(c, c))
26.53/8.73	   A^2 -> H(U1(e, e), f(e))
26.53/8.73	   A^2 -> H(U1(e, e), f(k))
26.53/8.73	   A^2 -> H(U1(e, e), U1(d, d))
26.53/8.73	   A^2 -> H(f(e), U1(e, b))
26.53/8.73	   A^2 -> H(f(e), U1(k, b))
26.53/8.73	   A^2 -> H(f(e), U1(c, d))
26.53/8.73	   A^2 -> H(f(e), U1(d, c))
26.53/8.73	   A^2 -> H(f(e), U1(b, e))
26.53/8.73	   A^2 -> H(f(e), U1(b, k))
26.53/8.73	   A^2 -> H(f(e), U1(e, c))
26.53/8.73	   A^2 -> H(f(e), U1(k, c))
26.53/8.73	   A^2 -> H(f(e), U1(c, e))
26.53/8.73	   A^2 -> H(f(e), U1(c, k))
26.53/8.73	   A^2 -> H(f(e), U1(k, k))
26.53/8.73	   A^2 -> H(f(e), U1(k, d))
26.53/8.73	   A^2 -> H(f(e), U1(d, k))
26.53/8.73	   A^2 -> H(U1(k, k), U1(c, b))
26.81/8.74	   A^2 -> H(U1(k, k), U1(d, b))
26.81/8.74	   A^2 -> H(U1(k, k), U1(b, c))
26.81/8.74	   A^2 -> H(U1(k, k), U1(b, d))
26.81/8.74	   A^2 -> H(U1(k, k), U1(c, c))
26.81/8.74	   A^2 -> H(U1(k, k), f(e))
26.81/8.74	   A^2 -> H(U1(k, k), f(k))
26.81/8.74	   A^2 -> H(U1(k, k), U1(d, d))
26.81/8.74	   A^2 -> H(f(k), U1(e, b))
26.81/8.74	   A^2 -> H(f(k), U1(k, b))
26.81/8.74	   A^2 -> H(f(k), U1(c, d))
26.81/8.74	   A^2 -> H(f(k), U1(d, c))
26.81/8.74	   A^2 -> H(f(k), U1(b, e))
26.81/8.74	   A^2 -> H(f(k), U1(b, k))
26.81/8.74	   A^2 -> H(f(k), U1(e, c))
26.81/8.74	   A^2 -> H(f(k), U1(k, c))
26.81/8.74	   A^2 -> H(f(k), U1(c, e))
26.81/8.74	   A^2 -> H(f(k), U1(c, k))
26.81/8.74	   A^2 -> H(f(k), U1(e, e))
26.81/8.74	   A^2 -> H(f(k), U1(k, d))
26.81/8.74	   A^2 -> H(f(k), U1(d, k))
26.81/8.74	   A^2 -> H(f(c), b)
26.81/8.74	   A^2 -> H(f(c), U1(e, d))
26.81/8.74	   A^2 -> H(f(c), U1(d, e))
26.81/8.74	   A^2 -> H(f(k), U1(k, k))
26.81/8.74	   A^2 -> H(U1(k, k), U1(b, b))
26.81/8.74	   A^2 -> H(U1(k, k), f(c))
26.81/8.74	   A^2 -> H(U1(k, k), f(d))
26.81/8.74	   A^2 -> H(U1(k, d), U1(c, b))
26.81/8.74	   A^2 -> H(U1(k, d), U1(d, b))
26.81/8.74	   A^2 -> H(U1(k, d), U1(b, c))
26.81/8.74	   A^2 -> H(U1(k, d), U1(b, d))
26.81/8.74	   A^2 -> H(U1(k, d), U1(c, c))
26.81/8.74	   A^2 -> H(U1(k, d), f(e))
26.81/8.74	   A^2 -> H(U1(k, d), f(k))
26.81/8.74	   A^2 -> H(U1(k, d), U1(d, d))
26.81/8.74	   A^2 -> H(U1(d, k), U1(c, b))
26.81/8.74	   A^2 -> H(U1(d, k), U1(d, b))
26.81/8.74	   A^2 -> H(U1(d, k), U1(b, c))
26.81/8.74	   A^2 -> H(U1(d, k), U1(b, d))
26.81/8.74	   A^2 -> H(U1(d, k), U1(c, c))
26.81/8.74	   A^2 -> H(U1(d, k), f(e))
26.81/8.74	   A^2 -> H(U1(d, k), f(k))
26.81/8.74	   A^2 -> H(U1(d, k), U1(d, d))
26.81/8.74	   A^2 -> H(U1(d, d), U1(e, b))
26.81/8.74	   A^2 -> H(U1(d, d), U1(k, b))
26.81/8.74	   A^2 -> H(U1(d, d), U1(c, d))
26.81/8.74	   A^2 -> H(U1(d, d), U1(d, c))
26.81/8.74	   A^2 -> H(U1(d, d), U1(b, e))
26.81/8.74	   A^2 -> H(U1(d, d), U1(b, k))
26.81/8.74	   A^2 -> H(U1(d, d), U1(e, c))
26.81/8.74	   A^2 -> H(U1(d, d), U1(k, c))
26.81/8.74	   A^2 -> H(U1(d, d), U1(c, e))
26.81/8.74	   A^2 -> H(U1(d, d), U1(c, k))
26.81/8.74	   A^2 -> H(U1(d, d), U1(e, e))
26.81/8.74	   A^2 -> H(U1(d, d), U1(k, k))
26.81/8.74	   A^2 -> H(f(d), b)
26.81/8.74	   A^2 -> H(f(d), U1(e, d))
26.81/8.74	   A^2 -> H(f(d), U1(d, e))
26.81/8.74	   A^2 -> H(f(d), c)
26.81/8.74	   A^2 -> H(f(d), U1(e, k))
26.81/8.74	   A^2 -> H(f(d), U1(k, e))
26.81/8.74	   A^2 -> H(f(d), e)
26.81/8.74	   A^2 -> H(f(a), d)
26.81/8.74	   A^2 -> H(U1(c, c), U1(e, c))
26.81/8.74	   A^2 -> H(f(c), c)
26.81/8.74	   A^2 -> H(f(c), U1(e, k))
26.81/8.74	   A^2 -> H(U1(c, c), U1(k, c))
26.81/8.74	   A^2 -> H(f(c), U1(k, e))
26.81/8.74	   A^2 -> H(f(c), U1(k, k))
26.81/8.74	   A^2 -> H(U1(c, c), U1(c, e))
26.81/8.74	   A^2 -> H(U1(c, c), U1(c, k))
26.81/8.74	
26.81/8.74	The TRS R consists of the following rules:
26.81/8.74	
26.81/8.74	   f(x) -> U1(x, x)
26.81/8.74	   U1(e, x) -> x
26.81/8.74	   a -> c
26.81/8.74	   a -> d
26.81/8.74	   b -> c
26.81/8.74	   b -> d
26.81/8.74	   d -> k
26.81/8.74	   c -> e
26.81/8.74	   c -> k
26.81/8.74	
26.81/8.74	Q is empty.
26.81/8.74	We have to consider all minimal (P,Q,R)-chains.
26.81/8.74	----------------------------------------
26.81/8.74	
26.81/8.74	(525) TransformationProof (EQUIVALENT)
26.81/8.74	By narrowing [LPAR04] the rule A^2 -> H(f(a), c) at position [] we obtained the following new rules [LPAR04]:
26.81/8.74	
26.81/8.74	   (A^2 -> H(U1(a, a), c),A^2 -> H(U1(a, a), c))
26.81/8.74	   (A^2 -> H(f(c), c),A^2 -> H(f(c), c))
26.81/8.74	   (A^2 -> H(f(d), c),A^2 -> H(f(d), c))
26.81/8.74	   (A^2 -> H(f(a), e),A^2 -> H(f(a), e))
26.81/8.74	   (A^2 -> H(f(a), k),A^2 -> H(f(a), k))
26.81/8.74	
26.81/8.74	
26.81/8.74	----------------------------------------
26.81/8.74	
26.81/8.74	(526)
26.81/8.74	Obligation:
26.81/8.74	Q DP problem:
26.81/8.74	The TRS P consists of the following rules:
26.81/8.74	
26.81/8.74	   H(x, x) -> G(x, x, f(k))
26.81/8.74	   G(d, x, x) -> A^2
26.81/8.74	   A^2 -> H(f(c), f(c))
26.81/8.74	   A^2 -> H(f(d), f(d))
26.81/8.74	   A^2 -> H(U1(c, c), U1(c, c))
26.81/8.74	   A^2 -> H(f(e), f(e))
26.81/8.74	   A^2 -> H(f(k), f(k))
26.81/8.74	   A^2 -> H(U1(d, d), U1(d, d))
26.81/8.74	   A^2 -> H(f(a), U1(e, k))
26.81/8.74	   A^2 -> H(f(a), U1(k, e))
26.81/8.74	   A^2 -> H(f(c), U1(e, e))
26.81/8.74	   A^2 -> H(f(a), e)
26.81/8.74	   A^2 -> H(f(d), U1(k, d))
26.81/8.74	   A^2 -> H(f(d), U1(d, k))
26.81/8.74	   A^2 -> H(f(a), U1(k, k))
26.81/8.74	   A^2 -> H(d, f(b))
26.81/8.74	   A^2 -> H(a, U1(b, b))
26.81/8.74	   A^2 -> H(a, f(c))
26.81/8.74	   A^2 -> H(a, f(d))
26.81/8.74	   A^2 -> H(U1(e, d), U1(b, b))
26.81/8.74	   A^2 -> H(U1(e, d), f(c))
26.81/8.74	   A^2 -> H(U1(e, d), f(d))
26.81/8.74	   A^2 -> H(U1(e, a), U1(c, b))
26.81/8.74	   A^2 -> H(U1(e, a), U1(d, b))
26.81/8.74	   A^2 -> H(U1(e, a), U1(b, c))
26.81/8.74	   A^2 -> H(U1(e, a), U1(b, d))
26.81/8.74	   A^2 -> H(U1(e, a), U1(c, c))
26.81/8.74	   A^2 -> H(U1(e, a), f(e))
26.81/8.74	   A^2 -> H(U1(e, a), f(k))
26.81/8.74	   A^2 -> H(U1(e, a), U1(d, d))
26.81/8.74	   A^2 -> H(U1(k, a), U1(c, b))
26.81/8.74	   A^2 -> H(U1(k, a), U1(d, b))
26.81/8.74	   A^2 -> H(U1(k, a), U1(b, c))
26.81/8.74	   A^2 -> H(U1(k, a), U1(b, d))
26.81/8.74	   A^2 -> H(U1(k, a), U1(c, c))
26.81/8.74	   A^2 -> H(U1(k, a), f(e))
26.81/8.74	   A^2 -> H(U1(k, a), f(k))
26.81/8.74	   A^2 -> H(U1(k, a), U1(d, d))
26.81/8.74	   A^2 -> H(U1(c, d), U1(c, b))
26.81/8.74	   A^2 -> H(U1(c, d), U1(d, b))
26.81/8.74	   A^2 -> H(U1(c, d), U1(b, c))
26.81/8.74	   A^2 -> H(U1(c, d), U1(b, d))
26.81/8.74	   A^2 -> H(U1(c, d), U1(c, c))
26.81/8.74	   A^2 -> H(U1(c, d), f(e))
26.81/8.74	   A^2 -> H(U1(c, d), f(k))
26.81/8.74	   A^2 -> H(U1(c, d), U1(d, d))
26.81/8.74	   A^2 -> H(U1(c, a), U1(e, b))
26.81/8.74	   A^2 -> H(U1(c, a), U1(k, b))
26.81/8.74	   A^2 -> H(U1(c, a), U1(c, d))
26.81/8.74	   A^2 -> H(U1(c, a), U1(d, c))
26.81/8.74	   A^2 -> H(U1(c, a), U1(b, e))
26.81/8.74	   A^2 -> H(U1(c, a), U1(b, k))
26.81/8.74	   A^2 -> H(U1(c, a), U1(e, c))
26.81/8.74	   A^2 -> H(U1(c, a), U1(k, c))
26.81/8.74	   A^2 -> H(U1(c, a), U1(c, e))
26.81/8.74	   A^2 -> H(U1(c, a), U1(c, k))
26.81/8.74	   A^2 -> H(U1(c, a), U1(e, e))
26.81/8.74	   A^2 -> H(U1(c, a), U1(k, k))
26.81/8.74	   A^2 -> H(U1(c, a), U1(k, d))
26.81/8.74	   A^2 -> H(U1(c, a), U1(d, k))
26.81/8.74	   A^2 -> H(U1(d, e), U1(b, b))
26.81/8.74	   A^2 -> H(U1(d, e), f(c))
26.81/8.74	   A^2 -> H(U1(d, e), f(d))
26.81/8.74	   A^2 -> H(U1(d, c), U1(c, b))
26.81/8.74	   A^2 -> H(U1(d, c), U1(d, b))
26.81/8.74	   A^2 -> H(U1(d, c), U1(b, c))
26.81/8.74	   A^2 -> H(U1(d, c), U1(b, d))
26.81/8.74	   A^2 -> H(U1(d, c), U1(c, c))
26.81/8.74	   A^2 -> H(U1(d, c), f(e))
26.81/8.74	   A^2 -> H(U1(d, c), f(k))
26.81/8.74	   A^2 -> H(U1(d, c), U1(d, d))
26.81/8.74	   A^2 -> H(U1(d, a), U1(e, b))
26.81/8.74	   A^2 -> H(U1(d, a), U1(k, b))
26.81/8.74	   A^2 -> H(U1(d, a), U1(c, d))
26.81/8.74	   A^2 -> H(U1(d, a), U1(d, c))
26.81/8.74	   A^2 -> H(U1(d, a), U1(b, e))
26.81/8.74	   A^2 -> H(U1(d, a), U1(b, k))
26.81/8.74	   A^2 -> H(U1(d, a), U1(e, c))
26.81/8.74	   A^2 -> H(U1(d, a), U1(k, c))
26.81/8.74	   A^2 -> H(U1(d, a), U1(c, e))
26.81/8.74	   A^2 -> H(U1(d, a), U1(c, k))
26.81/8.74	   A^2 -> H(U1(d, a), U1(e, e))
26.81/8.74	   A^2 -> H(U1(d, a), U1(k, k))
26.81/8.74	   A^2 -> H(U1(d, a), U1(k, d))
26.81/8.74	   A^2 -> H(U1(d, a), U1(d, k))
26.81/8.74	   A^2 -> H(U1(a, e), U1(c, b))
26.81/8.74	   A^2 -> H(U1(a, e), U1(d, b))
26.81/8.74	   A^2 -> H(U1(a, e), U1(b, c))
26.81/8.74	   A^2 -> H(U1(a, e), U1(b, d))
26.81/8.74	   A^2 -> H(U1(a, e), U1(c, c))
26.81/8.74	   A^2 -> H(U1(a, e), f(e))
26.81/8.74	   A^2 -> H(U1(a, e), f(k))
26.81/8.74	   A^2 -> H(U1(a, e), U1(d, d))
26.81/8.74	   A^2 -> H(U1(a, k), U1(c, b))
26.81/8.74	   A^2 -> H(U1(a, k), U1(d, b))
26.81/8.74	   A^2 -> H(U1(a, k), U1(b, c))
26.81/8.74	   A^2 -> H(U1(a, k), U1(b, d))
26.81/8.74	   A^2 -> H(U1(a, k), U1(c, c))
26.81/8.74	   A^2 -> H(U1(a, k), f(e))
26.81/8.74	   A^2 -> H(U1(a, k), f(k))
26.81/8.74	   A^2 -> H(U1(a, k), U1(d, d))
26.81/8.74	   A^2 -> H(U1(a, c), U1(e, b))
26.81/8.74	   A^2 -> H(U1(a, c), U1(k, b))
26.81/8.74	   A^2 -> H(U1(a, c), U1(c, d))
26.81/8.74	   A^2 -> H(U1(a, c), U1(d, c))
26.81/8.74	   A^2 -> H(U1(a, c), U1(b, e))
26.81/8.74	   A^2 -> H(U1(a, c), U1(b, k))
26.81/8.74	   A^2 -> H(U1(a, c), U1(e, c))
26.81/8.74	   A^2 -> H(U1(a, c), U1(k, c))
26.81/8.74	   A^2 -> H(U1(a, c), U1(c, e))
26.81/8.74	   A^2 -> H(U1(a, c), U1(c, k))
26.81/8.74	   A^2 -> H(U1(a, c), U1(e, e))
26.81/8.74	   A^2 -> H(U1(a, c), U1(k, k))
26.81/8.74	   A^2 -> H(U1(a, c), U1(k, d))
26.81/8.74	   A^2 -> H(U1(a, c), U1(d, k))
26.81/8.74	   A^2 -> H(U1(a, d), U1(e, b))
26.81/8.74	   A^2 -> H(U1(a, d), U1(k, b))
26.81/8.74	   A^2 -> H(U1(a, d), U1(c, d))
26.81/8.74	   A^2 -> H(U1(a, d), U1(d, c))
26.81/8.74	   A^2 -> H(U1(a, d), U1(b, e))
26.81/8.74	   A^2 -> H(U1(a, d), U1(b, k))
26.81/8.74	   A^2 -> H(U1(a, d), U1(e, c))
26.81/8.74	   A^2 -> H(U1(a, d), U1(k, c))
26.81/8.74	   A^2 -> H(U1(a, d), U1(c, e))
26.81/8.74	   A^2 -> H(U1(a, d), U1(c, k))
26.81/8.74	   A^2 -> H(U1(a, d), U1(e, e))
26.81/8.74	   A^2 -> H(U1(a, d), U1(k, k))
26.81/8.74	   A^2 -> H(U1(a, d), U1(k, d))
26.81/8.74	   A^2 -> H(U1(a, d), U1(d, k))
26.81/8.74	   A^2 -> H(U1(a, a), b)
26.81/8.74	   A^2 -> H(U1(a, a), U1(e, d))
26.81/8.74	   A^2 -> H(U1(a, a), U1(d, e))
26.81/8.74	   A^2 -> H(U1(a, a), c)
26.81/8.74	   A^2 -> H(U1(a, a), U1(e, k))
26.81/8.74	   A^2 -> H(U1(a, a), U1(k, e))
26.81/8.74	   A^2 -> H(U1(a, a), e)
26.81/8.74	   A^2 -> H(U1(a, a), U1(k, k))
26.81/8.74	   A^2 -> H(k, f(b))
26.81/8.74	   A^2 -> H(c, U1(b, b))
26.81/8.74	   A^2 -> H(c, f(c))
26.81/8.74	   A^2 -> H(c, f(d))
26.81/8.74	   A^2 -> H(U1(e, k), U1(b, b))
26.81/8.74	   A^2 -> H(U1(e, k), f(c))
26.81/8.74	   A^2 -> H(U1(e, k), f(d))
26.81/8.74	   A^2 -> H(U1(e, c), U1(c, b))
26.81/8.74	   A^2 -> H(U1(e, c), U1(d, b))
26.81/8.74	   A^2 -> H(U1(e, c), U1(b, c))
26.81/8.74	   A^2 -> H(U1(e, c), U1(b, d))
26.81/8.74	   A^2 -> H(U1(e, c), U1(c, c))
26.81/8.74	   A^2 -> H(U1(e, c), f(e))
26.81/8.74	   A^2 -> H(U1(e, c), f(k))
26.81/8.74	   A^2 -> H(U1(e, c), U1(d, d))
26.81/8.74	   A^2 -> H(U1(k, e), U1(b, b))
26.81/8.74	   A^2 -> H(U1(k, e), f(c))
26.81/8.74	   A^2 -> H(U1(k, e), f(d))
26.81/8.74	   A^2 -> H(U1(k, c), U1(c, b))
26.81/8.74	   A^2 -> H(U1(k, c), U1(d, b))
26.81/8.74	   A^2 -> H(U1(k, c), U1(b, c))
26.81/8.74	   A^2 -> H(U1(k, c), U1(b, d))
26.81/8.74	   A^2 -> H(U1(k, c), U1(c, c))
26.81/8.74	   A^2 -> H(U1(k, c), f(e))
26.81/8.74	   A^2 -> H(U1(k, c), f(k))
26.81/8.74	   A^2 -> H(U1(k, c), U1(d, d))
26.81/8.74	   A^2 -> H(U1(c, e), U1(c, b))
26.81/8.74	   A^2 -> H(U1(c, e), U1(d, b))
26.81/8.74	   A^2 -> H(U1(c, e), U1(b, c))
26.81/8.74	   A^2 -> H(U1(c, e), U1(b, d))
26.81/8.74	   A^2 -> H(U1(c, e), U1(c, c))
26.81/8.74	   A^2 -> H(U1(c, e), f(e))
26.81/8.74	   A^2 -> H(U1(c, e), f(k))
26.81/8.74	   A^2 -> H(U1(c, e), U1(d, d))
26.81/8.74	   A^2 -> H(U1(c, k), U1(c, b))
26.81/8.74	   A^2 -> H(U1(c, k), U1(d, b))
26.81/8.74	   A^2 -> H(U1(c, k), U1(b, c))
26.81/8.74	   A^2 -> H(U1(c, k), U1(b, d))
26.81/8.74	   A^2 -> H(U1(c, k), U1(c, c))
26.81/8.74	   A^2 -> H(U1(c, k), f(e))
26.81/8.75	   A^2 -> H(U1(c, k), f(k))
26.81/8.75	   A^2 -> H(U1(c, k), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(e, b))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, b))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(d, c))
26.81/8.75	   A^2 -> H(U1(c, c), U1(b, e))
26.81/8.75	   A^2 -> H(U1(c, c), U1(b, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(e, e))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(d, k))
26.81/8.75	   A^2 -> H(e, U1(b, b))
26.81/8.75	   A^2 -> H(e, f(c))
26.81/8.75	   A^2 -> H(e, f(d))
26.81/8.75	   A^2 -> H(U1(e, e), U1(c, b))
26.81/8.75	   A^2 -> H(U1(e, e), U1(d, b))
26.81/8.75	   A^2 -> H(U1(e, e), U1(b, c))
26.81/8.75	   A^2 -> H(U1(e, e), U1(b, d))
26.81/8.75	   A^2 -> H(U1(e, e), U1(c, c))
26.81/8.75	   A^2 -> H(U1(e, e), f(e))
26.81/8.75	   A^2 -> H(U1(e, e), f(k))
26.81/8.75	   A^2 -> H(U1(e, e), U1(d, d))
26.81/8.75	   A^2 -> H(f(e), U1(e, b))
26.81/8.75	   A^2 -> H(f(e), U1(k, b))
26.81/8.75	   A^2 -> H(f(e), U1(c, d))
26.81/8.75	   A^2 -> H(f(e), U1(d, c))
26.81/8.75	   A^2 -> H(f(e), U1(b, e))
26.81/8.75	   A^2 -> H(f(e), U1(b, k))
26.81/8.75	   A^2 -> H(f(e), U1(e, c))
26.81/8.75	   A^2 -> H(f(e), U1(k, c))
26.81/8.75	   A^2 -> H(f(e), U1(c, e))
26.81/8.75	   A^2 -> H(f(e), U1(c, k))
26.81/8.75	   A^2 -> H(f(e), U1(k, k))
26.81/8.75	   A^2 -> H(f(e), U1(k, d))
26.81/8.75	   A^2 -> H(f(e), U1(d, k))
26.81/8.75	   A^2 -> H(U1(k, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, k), f(e))
26.81/8.75	   A^2 -> H(U1(k, k), f(k))
26.81/8.75	   A^2 -> H(U1(k, k), U1(d, d))
26.81/8.75	   A^2 -> H(f(k), U1(e, b))
26.81/8.75	   A^2 -> H(f(k), U1(k, b))
26.81/8.75	   A^2 -> H(f(k), U1(c, d))
26.81/8.75	   A^2 -> H(f(k), U1(d, c))
26.81/8.75	   A^2 -> H(f(k), U1(b, e))
26.81/8.75	   A^2 -> H(f(k), U1(b, k))
26.81/8.75	   A^2 -> H(f(k), U1(e, c))
26.81/8.75	   A^2 -> H(f(k), U1(k, c))
26.81/8.75	   A^2 -> H(f(k), U1(c, e))
26.81/8.75	   A^2 -> H(f(k), U1(c, k))
26.81/8.75	   A^2 -> H(f(k), U1(e, e))
26.81/8.75	   A^2 -> H(f(k), U1(k, d))
26.81/8.75	   A^2 -> H(f(k), U1(d, k))
26.81/8.75	   A^2 -> H(f(c), b)
26.81/8.75	   A^2 -> H(f(c), U1(e, d))
26.81/8.75	   A^2 -> H(f(c), U1(d, e))
26.81/8.75	   A^2 -> H(f(k), U1(k, k))
26.81/8.75	   A^2 -> H(U1(k, k), U1(b, b))
26.81/8.75	   A^2 -> H(U1(k, k), f(c))
26.81/8.75	   A^2 -> H(U1(k, k), f(d))
26.81/8.75	   A^2 -> H(U1(k, d), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, d), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, d), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, d), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, d), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, d), f(e))
26.81/8.75	   A^2 -> H(U1(k, d), f(k))
26.81/8.75	   A^2 -> H(U1(k, d), U1(d, d))
26.81/8.75	   A^2 -> H(U1(d, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(d, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(d, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(d, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(d, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(d, k), f(e))
26.81/8.75	   A^2 -> H(U1(d, k), f(k))
26.81/8.75	   A^2 -> H(U1(d, k), U1(d, d))
26.81/8.75	   A^2 -> H(U1(d, d), U1(e, b))
26.81/8.75	   A^2 -> H(U1(d, d), U1(k, b))
26.81/8.75	   A^2 -> H(U1(d, d), U1(c, d))
26.81/8.75	   A^2 -> H(U1(d, d), U1(d, c))
26.81/8.75	   A^2 -> H(U1(d, d), U1(b, e))
26.81/8.75	   A^2 -> H(U1(d, d), U1(b, k))
26.81/8.75	   A^2 -> H(U1(d, d), U1(e, c))
26.81/8.75	   A^2 -> H(U1(d, d), U1(k, c))
26.81/8.75	   A^2 -> H(U1(d, d), U1(c, e))
26.81/8.75	   A^2 -> H(U1(d, d), U1(c, k))
26.81/8.75	   A^2 -> H(U1(d, d), U1(e, e))
26.81/8.75	   A^2 -> H(U1(d, d), U1(k, k))
26.81/8.75	   A^2 -> H(f(d), b)
26.81/8.75	   A^2 -> H(f(d), U1(e, d))
26.81/8.75	   A^2 -> H(f(d), U1(d, e))
26.81/8.75	   A^2 -> H(f(d), c)
26.81/8.75	   A^2 -> H(f(d), U1(e, k))
26.81/8.75	   A^2 -> H(f(d), U1(k, e))
26.81/8.75	   A^2 -> H(f(d), e)
26.81/8.75	   A^2 -> H(f(a), d)
26.81/8.75	   A^2 -> H(U1(c, c), U1(e, c))
26.81/8.75	   A^2 -> H(f(c), c)
26.81/8.75	   A^2 -> H(f(c), U1(e, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, c))
26.81/8.75	   A^2 -> H(f(c), U1(k, e))
26.81/8.75	   A^2 -> H(f(c), U1(k, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, e))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, k))
26.81/8.75	   A^2 -> H(f(a), k)
26.81/8.75	
26.81/8.75	The TRS R consists of the following rules:
26.81/8.75	
26.81/8.75	   f(x) -> U1(x, x)
26.81/8.75	   U1(e, x) -> x
26.81/8.75	   a -> c
26.81/8.75	   a -> d
26.81/8.75	   b -> c
26.81/8.75	   b -> d
26.81/8.75	   d -> k
26.81/8.75	   c -> e
26.81/8.75	   c -> k
26.81/8.75	
26.81/8.75	Q is empty.
26.81/8.75	We have to consider all minimal (P,Q,R)-chains.
26.81/8.75	----------------------------------------
26.81/8.75	
26.81/8.75	(527) TransformationProof (EQUIVALENT)
26.81/8.75	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
26.81/8.75	
26.81/8.75	   (A^2 -> H(U1(a, a), U1(e, k)),A^2 -> H(U1(a, a), U1(e, k)))
26.81/8.75	   (A^2 -> H(f(c), U1(e, k)),A^2 -> H(f(c), U1(e, k)))
26.81/8.75	   (A^2 -> H(f(d), U1(e, k)),A^2 -> H(f(d), U1(e, k)))
26.81/8.75	   (A^2 -> H(f(a), k),A^2 -> H(f(a), k))
26.81/8.75	
26.81/8.75	
26.81/8.75	----------------------------------------
26.81/8.75	
26.81/8.75	(528)
26.81/8.75	Obligation:
26.81/8.75	Q DP problem:
26.81/8.75	The TRS P consists of the following rules:
26.81/8.75	
26.81/8.75	   H(x, x) -> G(x, x, f(k))
26.81/8.75	   G(d, x, x) -> A^2
26.81/8.75	   A^2 -> H(f(c), f(c))
26.81/8.75	   A^2 -> H(f(d), f(d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, c))
26.81/8.75	   A^2 -> H(f(e), f(e))
26.81/8.75	   A^2 -> H(f(k), f(k))
26.81/8.75	   A^2 -> H(U1(d, d), U1(d, d))
26.81/8.75	   A^2 -> H(f(a), U1(k, e))
26.81/8.75	   A^2 -> H(f(c), U1(e, e))
26.81/8.75	   A^2 -> H(f(a), e)
26.81/8.75	   A^2 -> H(f(d), U1(k, d))
26.81/8.75	   A^2 -> H(f(d), U1(d, k))
26.81/8.75	   A^2 -> H(f(a), U1(k, k))
26.81/8.75	   A^2 -> H(d, f(b))
26.81/8.75	   A^2 -> H(a, U1(b, b))
26.81/8.75	   A^2 -> H(a, f(c))
26.81/8.75	   A^2 -> H(a, f(d))
26.81/8.75	   A^2 -> H(U1(e, d), U1(b, b))
26.81/8.75	   A^2 -> H(U1(e, d), f(c))
26.81/8.75	   A^2 -> H(U1(e, d), f(d))
26.81/8.75	   A^2 -> H(U1(e, a), U1(c, b))
26.81/8.75	   A^2 -> H(U1(e, a), U1(d, b))
26.81/8.75	   A^2 -> H(U1(e, a), U1(b, c))
26.81/8.75	   A^2 -> H(U1(e, a), U1(b, d))
26.81/8.75	   A^2 -> H(U1(e, a), U1(c, c))
26.81/8.75	   A^2 -> H(U1(e, a), f(e))
26.81/8.75	   A^2 -> H(U1(e, a), f(k))
26.81/8.75	   A^2 -> H(U1(e, a), U1(d, d))
26.81/8.75	   A^2 -> H(U1(k, a), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, a), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, a), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, a), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, a), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, a), f(e))
26.81/8.75	   A^2 -> H(U1(k, a), f(k))
26.81/8.75	   A^2 -> H(U1(k, a), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, d), U1(c, b))
26.81/8.75	   A^2 -> H(U1(c, d), U1(d, b))
26.81/8.75	   A^2 -> H(U1(c, d), U1(b, c))
26.81/8.75	   A^2 -> H(U1(c, d), U1(b, d))
26.81/8.75	   A^2 -> H(U1(c, d), U1(c, c))
26.81/8.75	   A^2 -> H(U1(c, d), f(e))
26.81/8.75	   A^2 -> H(U1(c, d), f(k))
26.81/8.75	   A^2 -> H(U1(c, d), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, a), U1(e, b))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, b))
26.81/8.75	   A^2 -> H(U1(c, a), U1(c, d))
26.81/8.75	   A^2 -> H(U1(c, a), U1(d, c))
26.81/8.75	   A^2 -> H(U1(c, a), U1(b, e))
26.81/8.75	   A^2 -> H(U1(c, a), U1(b, k))
26.81/8.75	   A^2 -> H(U1(c, a), U1(e, c))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, c))
26.81/8.75	   A^2 -> H(U1(c, a), U1(c, e))
26.81/8.75	   A^2 -> H(U1(c, a), U1(c, k))
26.81/8.75	   A^2 -> H(U1(c, a), U1(e, e))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, k))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, d))
26.81/8.75	   A^2 -> H(U1(c, a), U1(d, k))
26.81/8.75	   A^2 -> H(U1(d, e), U1(b, b))
26.81/8.75	   A^2 -> H(U1(d, e), f(c))
26.81/8.75	   A^2 -> H(U1(d, e), f(d))
26.81/8.75	   A^2 -> H(U1(d, c), U1(c, b))
26.81/8.75	   A^2 -> H(U1(d, c), U1(d, b))
26.81/8.75	   A^2 -> H(U1(d, c), U1(b, c))
26.81/8.75	   A^2 -> H(U1(d, c), U1(b, d))
26.81/8.75	   A^2 -> H(U1(d, c), U1(c, c))
26.81/8.75	   A^2 -> H(U1(d, c), f(e))
26.81/8.75	   A^2 -> H(U1(d, c), f(k))
26.81/8.75	   A^2 -> H(U1(d, c), U1(d, d))
26.81/8.75	   A^2 -> H(U1(d, a), U1(e, b))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, b))
26.81/8.75	   A^2 -> H(U1(d, a), U1(c, d))
26.81/8.75	   A^2 -> H(U1(d, a), U1(d, c))
26.81/8.75	   A^2 -> H(U1(d, a), U1(b, e))
26.81/8.75	   A^2 -> H(U1(d, a), U1(b, k))
26.81/8.75	   A^2 -> H(U1(d, a), U1(e, c))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, c))
26.81/8.75	   A^2 -> H(U1(d, a), U1(c, e))
26.81/8.75	   A^2 -> H(U1(d, a), U1(c, k))
26.81/8.75	   A^2 -> H(U1(d, a), U1(e, e))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, k))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, d))
26.81/8.75	   A^2 -> H(U1(d, a), U1(d, k))
26.81/8.75	   A^2 -> H(U1(a, e), U1(c, b))
26.81/8.75	   A^2 -> H(U1(a, e), U1(d, b))
26.81/8.75	   A^2 -> H(U1(a, e), U1(b, c))
26.81/8.75	   A^2 -> H(U1(a, e), U1(b, d))
26.81/8.75	   A^2 -> H(U1(a, e), U1(c, c))
26.81/8.75	   A^2 -> H(U1(a, e), f(e))
26.81/8.75	   A^2 -> H(U1(a, e), f(k))
26.81/8.75	   A^2 -> H(U1(a, e), U1(d, d))
26.81/8.75	   A^2 -> H(U1(a, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(a, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(a, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(a, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(a, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(a, k), f(e))
26.81/8.75	   A^2 -> H(U1(a, k), f(k))
26.81/8.75	   A^2 -> H(U1(a, k), U1(d, d))
26.81/8.75	   A^2 -> H(U1(a, c), U1(e, b))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, b))
26.81/8.75	   A^2 -> H(U1(a, c), U1(c, d))
26.81/8.75	   A^2 -> H(U1(a, c), U1(d, c))
26.81/8.75	   A^2 -> H(U1(a, c), U1(b, e))
26.81/8.75	   A^2 -> H(U1(a, c), U1(b, k))
26.81/8.75	   A^2 -> H(U1(a, c), U1(e, c))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, c))
26.81/8.75	   A^2 -> H(U1(a, c), U1(c, e))
26.81/8.75	   A^2 -> H(U1(a, c), U1(c, k))
26.81/8.75	   A^2 -> H(U1(a, c), U1(e, e))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, k))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, d))
26.81/8.75	   A^2 -> H(U1(a, c), U1(d, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(e, b))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, b))
26.81/8.75	   A^2 -> H(U1(a, d), U1(c, d))
26.81/8.75	   A^2 -> H(U1(a, d), U1(d, c))
26.81/8.75	   A^2 -> H(U1(a, d), U1(b, e))
26.81/8.75	   A^2 -> H(U1(a, d), U1(b, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(e, c))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, c))
26.81/8.75	   A^2 -> H(U1(a, d), U1(c, e))
26.81/8.75	   A^2 -> H(U1(a, d), U1(c, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(e, e))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, d))
26.81/8.75	   A^2 -> H(U1(a, d), U1(d, k))
26.81/8.75	   A^2 -> H(U1(a, a), b)
26.81/8.75	   A^2 -> H(U1(a, a), U1(e, d))
26.81/8.75	   A^2 -> H(U1(a, a), U1(d, e))
26.81/8.75	   A^2 -> H(U1(a, a), c)
26.81/8.75	   A^2 -> H(U1(a, a), U1(e, k))
26.81/8.75	   A^2 -> H(U1(a, a), U1(k, e))
26.81/8.75	   A^2 -> H(U1(a, a), e)
26.81/8.75	   A^2 -> H(U1(a, a), U1(k, k))
26.81/8.75	   A^2 -> H(k, f(b))
26.81/8.75	   A^2 -> H(c, U1(b, b))
26.81/8.75	   A^2 -> H(c, f(c))
26.81/8.75	   A^2 -> H(c, f(d))
26.81/8.75	   A^2 -> H(U1(e, k), U1(b, b))
26.81/8.75	   A^2 -> H(U1(e, k), f(c))
26.81/8.75	   A^2 -> H(U1(e, k), f(d))
26.81/8.75	   A^2 -> H(U1(e, c), U1(c, b))
26.81/8.75	   A^2 -> H(U1(e, c), U1(d, b))
26.81/8.75	   A^2 -> H(U1(e, c), U1(b, c))
26.81/8.75	   A^2 -> H(U1(e, c), U1(b, d))
26.81/8.75	   A^2 -> H(U1(e, c), U1(c, c))
26.81/8.75	   A^2 -> H(U1(e, c), f(e))
26.81/8.75	   A^2 -> H(U1(e, c), f(k))
26.81/8.75	   A^2 -> H(U1(e, c), U1(d, d))
26.81/8.75	   A^2 -> H(U1(k, e), U1(b, b))
26.81/8.75	   A^2 -> H(U1(k, e), f(c))
26.81/8.75	   A^2 -> H(U1(k, e), f(d))
26.81/8.75	   A^2 -> H(U1(k, c), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, c), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, c), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, c), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, c), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, c), f(e))
26.81/8.75	   A^2 -> H(U1(k, c), f(k))
26.81/8.75	   A^2 -> H(U1(k, c), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, e), U1(c, b))
26.81/8.75	   A^2 -> H(U1(c, e), U1(d, b))
26.81/8.75	   A^2 -> H(U1(c, e), U1(b, c))
26.81/8.75	   A^2 -> H(U1(c, e), U1(b, d))
26.81/8.75	   A^2 -> H(U1(c, e), U1(c, c))
26.81/8.75	   A^2 -> H(U1(c, e), f(e))
26.81/8.75	   A^2 -> H(U1(c, e), f(k))
26.81/8.75	   A^2 -> H(U1(c, e), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(c, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(c, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(c, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(c, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(c, k), f(e))
26.81/8.75	   A^2 -> H(U1(c, k), f(k))
26.81/8.75	   A^2 -> H(U1(c, k), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(e, b))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, b))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(d, c))
26.81/8.75	   A^2 -> H(U1(c, c), U1(b, e))
26.81/8.75	   A^2 -> H(U1(c, c), U1(b, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(e, e))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(d, k))
26.81/8.75	   A^2 -> H(e, U1(b, b))
26.81/8.75	   A^2 -> H(e, f(c))
26.81/8.75	   A^2 -> H(e, f(d))
26.81/8.75	   A^2 -> H(U1(e, e), U1(c, b))
26.81/8.75	   A^2 -> H(U1(e, e), U1(d, b))
26.81/8.75	   A^2 -> H(U1(e, e), U1(b, c))
26.81/8.75	   A^2 -> H(U1(e, e), U1(b, d))
26.81/8.75	   A^2 -> H(U1(e, e), U1(c, c))
26.81/8.75	   A^2 -> H(U1(e, e), f(e))
26.81/8.75	   A^2 -> H(U1(e, e), f(k))
26.81/8.75	   A^2 -> H(U1(e, e), U1(d, d))
26.81/8.75	   A^2 -> H(f(e), U1(e, b))
26.81/8.75	   A^2 -> H(f(e), U1(k, b))
26.81/8.75	   A^2 -> H(f(e), U1(c, d))
26.81/8.75	   A^2 -> H(f(e), U1(d, c))
26.81/8.75	   A^2 -> H(f(e), U1(b, e))
26.81/8.75	   A^2 -> H(f(e), U1(b, k))
26.81/8.75	   A^2 -> H(f(e), U1(e, c))
26.81/8.75	   A^2 -> H(f(e), U1(k, c))
26.81/8.75	   A^2 -> H(f(e), U1(c, e))
26.81/8.75	   A^2 -> H(f(e), U1(c, k))
26.81/8.75	   A^2 -> H(f(e), U1(k, k))
26.81/8.75	   A^2 -> H(f(e), U1(k, d))
26.81/8.75	   A^2 -> H(f(e), U1(d, k))
26.81/8.75	   A^2 -> H(U1(k, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, k), f(e))
26.81/8.75	   A^2 -> H(U1(k, k), f(k))
26.81/8.75	   A^2 -> H(U1(k, k), U1(d, d))
26.81/8.75	   A^2 -> H(f(k), U1(e, b))
26.81/8.75	   A^2 -> H(f(k), U1(k, b))
26.81/8.75	   A^2 -> H(f(k), U1(c, d))
26.81/8.75	   A^2 -> H(f(k), U1(d, c))
26.81/8.75	   A^2 -> H(f(k), U1(b, e))
26.81/8.75	   A^2 -> H(f(k), U1(b, k))
26.81/8.75	   A^2 -> H(f(k), U1(e, c))
26.81/8.75	   A^2 -> H(f(k), U1(k, c))
26.81/8.75	   A^2 -> H(f(k), U1(c, e))
26.81/8.75	   A^2 -> H(f(k), U1(c, k))
26.81/8.75	   A^2 -> H(f(k), U1(e, e))
26.81/8.75	   A^2 -> H(f(k), U1(k, d))
26.81/8.75	   A^2 -> H(f(k), U1(d, k))
26.81/8.75	   A^2 -> H(f(c), b)
26.81/8.75	   A^2 -> H(f(c), U1(e, d))
26.81/8.75	   A^2 -> H(f(c), U1(d, e))
26.81/8.75	   A^2 -> H(f(k), U1(k, k))
26.81/8.75	   A^2 -> H(U1(k, k), U1(b, b))
26.81/8.75	   A^2 -> H(U1(k, k), f(c))
26.81/8.75	   A^2 -> H(U1(k, k), f(d))
26.81/8.75	   A^2 -> H(U1(k, d), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, d), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, d), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, d), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, d), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, d), f(e))
26.81/8.75	   A^2 -> H(U1(k, d), f(k))
26.81/8.75	   A^2 -> H(U1(k, d), U1(d, d))
26.81/8.75	   A^2 -> H(U1(d, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(d, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(d, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(d, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(d, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(d, k), f(e))
26.81/8.75	   A^2 -> H(U1(d, k), f(k))
26.81/8.75	   A^2 -> H(U1(d, k), U1(d, d))
26.81/8.75	   A^2 -> H(U1(d, d), U1(e, b))
26.81/8.75	   A^2 -> H(U1(d, d), U1(k, b))
26.81/8.75	   A^2 -> H(U1(d, d), U1(c, d))
26.81/8.75	   A^2 -> H(U1(d, d), U1(d, c))
26.81/8.75	   A^2 -> H(U1(d, d), U1(b, e))
26.81/8.75	   A^2 -> H(U1(d, d), U1(b, k))
26.81/8.75	   A^2 -> H(U1(d, d), U1(e, c))
26.81/8.75	   A^2 -> H(U1(d, d), U1(k, c))
26.81/8.75	   A^2 -> H(U1(d, d), U1(c, e))
26.81/8.75	   A^2 -> H(U1(d, d), U1(c, k))
26.81/8.75	   A^2 -> H(U1(d, d), U1(e, e))
26.81/8.75	   A^2 -> H(U1(d, d), U1(k, k))
26.81/8.75	   A^2 -> H(f(d), b)
26.81/8.75	   A^2 -> H(f(d), U1(e, d))
26.81/8.75	   A^2 -> H(f(d), U1(d, e))
26.81/8.75	   A^2 -> H(f(d), c)
26.81/8.75	   A^2 -> H(f(d), U1(e, k))
26.81/8.75	   A^2 -> H(f(d), U1(k, e))
26.81/8.75	   A^2 -> H(f(d), e)
26.81/8.75	   A^2 -> H(f(a), d)
26.81/8.75	   A^2 -> H(U1(c, c), U1(e, c))
26.81/8.75	   A^2 -> H(f(c), c)
26.81/8.75	   A^2 -> H(f(c), U1(e, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, c))
26.81/8.75	   A^2 -> H(f(c), U1(k, e))
26.81/8.75	   A^2 -> H(f(c), U1(k, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, e))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, k))
26.81/8.75	   A^2 -> H(f(a), k)
26.81/8.75	
26.81/8.75	The TRS R consists of the following rules:
26.81/8.75	
26.81/8.75	   f(x) -> U1(x, x)
26.81/8.75	   U1(e, x) -> x
26.81/8.75	   a -> c
26.81/8.75	   a -> d
26.81/8.75	   b -> c
26.81/8.75	   b -> d
26.81/8.75	   d -> k
26.81/8.75	   c -> e
26.81/8.75	   c -> k
26.81/8.75	
26.81/8.75	Q is empty.
26.81/8.75	We have to consider all minimal (P,Q,R)-chains.
26.81/8.75	----------------------------------------
26.81/8.75	
26.81/8.75	(529) TransformationProof (EQUIVALENT)
26.81/8.75	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
26.81/8.75	
26.81/8.75	   (A^2 -> H(U1(a, a), U1(k, e)),A^2 -> H(U1(a, a), U1(k, e)))
26.81/8.75	   (A^2 -> H(f(c), U1(k, e)),A^2 -> H(f(c), U1(k, e)))
26.81/8.75	   (A^2 -> H(f(d), U1(k, e)),A^2 -> H(f(d), U1(k, e)))
26.81/8.75	
26.81/8.75	
26.81/8.75	----------------------------------------
26.81/8.75	
26.81/8.75	(530)
26.81/8.75	Obligation:
26.81/8.75	Q DP problem:
26.81/8.75	The TRS P consists of the following rules:
26.81/8.75	
26.81/8.75	   H(x, x) -> G(x, x, f(k))
26.81/8.75	   G(d, x, x) -> A^2
26.81/8.75	   A^2 -> H(f(c), f(c))
26.81/8.75	   A^2 -> H(f(d), f(d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, c))
26.81/8.75	   A^2 -> H(f(e), f(e))
26.81/8.75	   A^2 -> H(f(k), f(k))
26.81/8.75	   A^2 -> H(U1(d, d), U1(d, d))
26.81/8.75	   A^2 -> H(f(c), U1(e, e))
26.81/8.75	   A^2 -> H(f(a), e)
26.81/8.75	   A^2 -> H(f(d), U1(k, d))
26.81/8.75	   A^2 -> H(f(d), U1(d, k))
26.81/8.75	   A^2 -> H(f(a), U1(k, k))
26.81/8.75	   A^2 -> H(d, f(b))
26.81/8.75	   A^2 -> H(a, U1(b, b))
26.81/8.75	   A^2 -> H(a, f(c))
26.81/8.75	   A^2 -> H(a, f(d))
26.81/8.75	   A^2 -> H(U1(e, d), U1(b, b))
26.81/8.75	   A^2 -> H(U1(e, d), f(c))
26.81/8.75	   A^2 -> H(U1(e, d), f(d))
26.81/8.75	   A^2 -> H(U1(e, a), U1(c, b))
26.81/8.75	   A^2 -> H(U1(e, a), U1(d, b))
26.81/8.75	   A^2 -> H(U1(e, a), U1(b, c))
26.81/8.75	   A^2 -> H(U1(e, a), U1(b, d))
26.81/8.75	   A^2 -> H(U1(e, a), U1(c, c))
26.81/8.75	   A^2 -> H(U1(e, a), f(e))
26.81/8.75	   A^2 -> H(U1(e, a), f(k))
26.81/8.75	   A^2 -> H(U1(e, a), U1(d, d))
26.81/8.75	   A^2 -> H(U1(k, a), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, a), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, a), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, a), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, a), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, a), f(e))
26.81/8.75	   A^2 -> H(U1(k, a), f(k))
26.81/8.75	   A^2 -> H(U1(k, a), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, d), U1(c, b))
26.81/8.75	   A^2 -> H(U1(c, d), U1(d, b))
26.81/8.75	   A^2 -> H(U1(c, d), U1(b, c))
26.81/8.75	   A^2 -> H(U1(c, d), U1(b, d))
26.81/8.75	   A^2 -> H(U1(c, d), U1(c, c))
26.81/8.75	   A^2 -> H(U1(c, d), f(e))
26.81/8.75	   A^2 -> H(U1(c, d), f(k))
26.81/8.75	   A^2 -> H(U1(c, d), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, a), U1(e, b))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, b))
26.81/8.75	   A^2 -> H(U1(c, a), U1(c, d))
26.81/8.75	   A^2 -> H(U1(c, a), U1(d, c))
26.81/8.75	   A^2 -> H(U1(c, a), U1(b, e))
26.81/8.75	   A^2 -> H(U1(c, a), U1(b, k))
26.81/8.75	   A^2 -> H(U1(c, a), U1(e, c))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, c))
26.81/8.75	   A^2 -> H(U1(c, a), U1(c, e))
26.81/8.75	   A^2 -> H(U1(c, a), U1(c, k))
26.81/8.75	   A^2 -> H(U1(c, a), U1(e, e))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, k))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, d))
26.81/8.75	   A^2 -> H(U1(c, a), U1(d, k))
26.81/8.75	   A^2 -> H(U1(d, e), U1(b, b))
26.81/8.75	   A^2 -> H(U1(d, e), f(c))
26.81/8.75	   A^2 -> H(U1(d, e), f(d))
26.81/8.75	   A^2 -> H(U1(d, c), U1(c, b))
26.81/8.75	   A^2 -> H(U1(d, c), U1(d, b))
26.81/8.75	   A^2 -> H(U1(d, c), U1(b, c))
26.81/8.75	   A^2 -> H(U1(d, c), U1(b, d))
26.81/8.75	   A^2 -> H(U1(d, c), U1(c, c))
26.81/8.75	   A^2 -> H(U1(d, c), f(e))
26.81/8.75	   A^2 -> H(U1(d, c), f(k))
26.81/8.75	   A^2 -> H(U1(d, c), U1(d, d))
26.81/8.75	   A^2 -> H(U1(d, a), U1(e, b))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, b))
26.81/8.75	   A^2 -> H(U1(d, a), U1(c, d))
26.81/8.75	   A^2 -> H(U1(d, a), U1(d, c))
26.81/8.75	   A^2 -> H(U1(d, a), U1(b, e))
26.81/8.75	   A^2 -> H(U1(d, a), U1(b, k))
26.81/8.75	   A^2 -> H(U1(d, a), U1(e, c))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, c))
26.81/8.75	   A^2 -> H(U1(d, a), U1(c, e))
26.81/8.75	   A^2 -> H(U1(d, a), U1(c, k))
26.81/8.75	   A^2 -> H(U1(d, a), U1(e, e))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, k))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, d))
26.81/8.75	   A^2 -> H(U1(d, a), U1(d, k))
26.81/8.75	   A^2 -> H(U1(a, e), U1(c, b))
26.81/8.75	   A^2 -> H(U1(a, e), U1(d, b))
26.81/8.75	   A^2 -> H(U1(a, e), U1(b, c))
26.81/8.75	   A^2 -> H(U1(a, e), U1(b, d))
26.81/8.75	   A^2 -> H(U1(a, e), U1(c, c))
26.81/8.75	   A^2 -> H(U1(a, e), f(e))
26.81/8.75	   A^2 -> H(U1(a, e), f(k))
26.81/8.75	   A^2 -> H(U1(a, e), U1(d, d))
26.81/8.75	   A^2 -> H(U1(a, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(a, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(a, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(a, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(a, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(a, k), f(e))
26.81/8.75	   A^2 -> H(U1(a, k), f(k))
26.81/8.75	   A^2 -> H(U1(a, k), U1(d, d))
26.81/8.75	   A^2 -> H(U1(a, c), U1(e, b))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, b))
26.81/8.75	   A^2 -> H(U1(a, c), U1(c, d))
26.81/8.75	   A^2 -> H(U1(a, c), U1(d, c))
26.81/8.75	   A^2 -> H(U1(a, c), U1(b, e))
26.81/8.75	   A^2 -> H(U1(a, c), U1(b, k))
26.81/8.75	   A^2 -> H(U1(a, c), U1(e, c))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, c))
26.81/8.75	   A^2 -> H(U1(a, c), U1(c, e))
26.81/8.75	   A^2 -> H(U1(a, c), U1(c, k))
26.81/8.75	   A^2 -> H(U1(a, c), U1(e, e))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, k))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, d))
26.81/8.75	   A^2 -> H(U1(a, c), U1(d, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(e, b))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, b))
26.81/8.75	   A^2 -> H(U1(a, d), U1(c, d))
26.81/8.75	   A^2 -> H(U1(a, d), U1(d, c))
26.81/8.75	   A^2 -> H(U1(a, d), U1(b, e))
26.81/8.75	   A^2 -> H(U1(a, d), U1(b, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(e, c))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, c))
26.81/8.75	   A^2 -> H(U1(a, d), U1(c, e))
26.81/8.75	   A^2 -> H(U1(a, d), U1(c, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(e, e))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, d))
26.81/8.75	   A^2 -> H(U1(a, d), U1(d, k))
26.81/8.75	   A^2 -> H(U1(a, a), b)
26.81/8.75	   A^2 -> H(U1(a, a), U1(e, d))
26.81/8.75	   A^2 -> H(U1(a, a), U1(d, e))
26.81/8.75	   A^2 -> H(U1(a, a), c)
26.81/8.75	   A^2 -> H(U1(a, a), U1(e, k))
26.81/8.75	   A^2 -> H(U1(a, a), U1(k, e))
26.81/8.75	   A^2 -> H(U1(a, a), e)
26.81/8.75	   A^2 -> H(U1(a, a), U1(k, k))
26.81/8.75	   A^2 -> H(k, f(b))
26.81/8.75	   A^2 -> H(c, U1(b, b))
26.81/8.75	   A^2 -> H(c, f(c))
26.81/8.75	   A^2 -> H(c, f(d))
26.81/8.75	   A^2 -> H(U1(e, k), U1(b, b))
26.81/8.75	   A^2 -> H(U1(e, k), f(c))
26.81/8.75	   A^2 -> H(U1(e, k), f(d))
26.81/8.75	   A^2 -> H(U1(e, c), U1(c, b))
26.81/8.75	   A^2 -> H(U1(e, c), U1(d, b))
26.81/8.75	   A^2 -> H(U1(e, c), U1(b, c))
26.81/8.75	   A^2 -> H(U1(e, c), U1(b, d))
26.81/8.75	   A^2 -> H(U1(e, c), U1(c, c))
26.81/8.75	   A^2 -> H(U1(e, c), f(e))
26.81/8.75	   A^2 -> H(U1(e, c), f(k))
26.81/8.75	   A^2 -> H(U1(e, c), U1(d, d))
26.81/8.75	   A^2 -> H(U1(k, e), U1(b, b))
26.81/8.75	   A^2 -> H(U1(k, e), f(c))
26.81/8.75	   A^2 -> H(U1(k, e), f(d))
26.81/8.75	   A^2 -> H(U1(k, c), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, c), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, c), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, c), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, c), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, c), f(e))
26.81/8.75	   A^2 -> H(U1(k, c), f(k))
26.81/8.75	   A^2 -> H(U1(k, c), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, e), U1(c, b))
26.81/8.75	   A^2 -> H(U1(c, e), U1(d, b))
26.81/8.75	   A^2 -> H(U1(c, e), U1(b, c))
26.81/8.75	   A^2 -> H(U1(c, e), U1(b, d))
26.81/8.75	   A^2 -> H(U1(c, e), U1(c, c))
26.81/8.75	   A^2 -> H(U1(c, e), f(e))
26.81/8.75	   A^2 -> H(U1(c, e), f(k))
26.81/8.75	   A^2 -> H(U1(c, e), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(c, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(c, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(c, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(c, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(c, k), f(e))
26.81/8.75	   A^2 -> H(U1(c, k), f(k))
26.81/8.75	   A^2 -> H(U1(c, k), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(e, b))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, b))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(d, c))
26.81/8.75	   A^2 -> H(U1(c, c), U1(b, e))
26.81/8.75	   A^2 -> H(U1(c, c), U1(b, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(e, e))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(d, k))
26.81/8.75	   A^2 -> H(e, U1(b, b))
26.81/8.75	   A^2 -> H(e, f(c))
26.81/8.75	   A^2 -> H(e, f(d))
26.81/8.75	   A^2 -> H(U1(e, e), U1(c, b))
26.81/8.75	   A^2 -> H(U1(e, e), U1(d, b))
26.81/8.75	   A^2 -> H(U1(e, e), U1(b, c))
26.81/8.75	   A^2 -> H(U1(e, e), U1(b, d))
26.81/8.75	   A^2 -> H(U1(e, e), U1(c, c))
26.81/8.75	   A^2 -> H(U1(e, e), f(e))
26.81/8.75	   A^2 -> H(U1(e, e), f(k))
26.81/8.75	   A^2 -> H(U1(e, e), U1(d, d))
26.81/8.75	   A^2 -> H(f(e), U1(e, b))
26.81/8.75	   A^2 -> H(f(e), U1(k, b))
26.81/8.75	   A^2 -> H(f(e), U1(c, d))
26.81/8.75	   A^2 -> H(f(e), U1(d, c))
26.81/8.75	   A^2 -> H(f(e), U1(b, e))
26.81/8.75	   A^2 -> H(f(e), U1(b, k))
26.81/8.75	   A^2 -> H(f(e), U1(e, c))
26.81/8.75	   A^2 -> H(f(e), U1(k, c))
26.81/8.75	   A^2 -> H(f(e), U1(c, e))
26.81/8.75	   A^2 -> H(f(e), U1(c, k))
26.81/8.75	   A^2 -> H(f(e), U1(k, k))
26.81/8.75	   A^2 -> H(f(e), U1(k, d))
26.81/8.75	   A^2 -> H(f(e), U1(d, k))
26.81/8.75	   A^2 -> H(U1(k, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, k), f(e))
26.81/8.75	   A^2 -> H(U1(k, k), f(k))
26.81/8.75	   A^2 -> H(U1(k, k), U1(d, d))
26.81/8.75	   A^2 -> H(f(k), U1(e, b))
26.81/8.75	   A^2 -> H(f(k), U1(k, b))
26.81/8.75	   A^2 -> H(f(k), U1(c, d))
26.81/8.75	   A^2 -> H(f(k), U1(d, c))
26.81/8.75	   A^2 -> H(f(k), U1(b, e))
26.81/8.75	   A^2 -> H(f(k), U1(b, k))
26.81/8.75	   A^2 -> H(f(k), U1(e, c))
26.81/8.75	   A^2 -> H(f(k), U1(k, c))
26.81/8.75	   A^2 -> H(f(k), U1(c, e))
26.81/8.75	   A^2 -> H(f(k), U1(c, k))
26.81/8.75	   A^2 -> H(f(k), U1(e, e))
26.81/8.75	   A^2 -> H(f(k), U1(k, d))
26.81/8.75	   A^2 -> H(f(k), U1(d, k))
26.81/8.75	   A^2 -> H(f(c), b)
26.81/8.75	   A^2 -> H(f(c), U1(e, d))
26.81/8.75	   A^2 -> H(f(c), U1(d, e))
26.81/8.75	   A^2 -> H(f(k), U1(k, k))
26.81/8.75	   A^2 -> H(U1(k, k), U1(b, b))
26.81/8.75	   A^2 -> H(U1(k, k), f(c))
26.81/8.75	   A^2 -> H(U1(k, k), f(d))
26.81/8.75	   A^2 -> H(U1(k, d), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, d), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, d), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, d), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, d), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, d), f(e))
26.81/8.75	   A^2 -> H(U1(k, d), f(k))
26.81/8.75	   A^2 -> H(U1(k, d), U1(d, d))
26.81/8.75	   A^2 -> H(U1(d, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(d, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(d, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(d, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(d, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(d, k), f(e))
26.81/8.75	   A^2 -> H(U1(d, k), f(k))
26.81/8.75	   A^2 -> H(U1(d, k), U1(d, d))
26.81/8.75	   A^2 -> H(U1(d, d), U1(e, b))
26.81/8.75	   A^2 -> H(U1(d, d), U1(k, b))
26.81/8.75	   A^2 -> H(U1(d, d), U1(c, d))
26.81/8.75	   A^2 -> H(U1(d, d), U1(d, c))
26.81/8.75	   A^2 -> H(U1(d, d), U1(b, e))
26.81/8.75	   A^2 -> H(U1(d, d), U1(b, k))
26.81/8.75	   A^2 -> H(U1(d, d), U1(e, c))
26.81/8.75	   A^2 -> H(U1(d, d), U1(k, c))
26.81/8.75	   A^2 -> H(U1(d, d), U1(c, e))
26.81/8.75	   A^2 -> H(U1(d, d), U1(c, k))
26.81/8.75	   A^2 -> H(U1(d, d), U1(e, e))
26.81/8.75	   A^2 -> H(U1(d, d), U1(k, k))
26.81/8.75	   A^2 -> H(f(d), b)
26.81/8.75	   A^2 -> H(f(d), U1(e, d))
26.81/8.75	   A^2 -> H(f(d), U1(d, e))
26.81/8.75	   A^2 -> H(f(d), c)
26.81/8.75	   A^2 -> H(f(d), U1(e, k))
26.81/8.75	   A^2 -> H(f(d), U1(k, e))
26.81/8.75	   A^2 -> H(f(d), e)
26.81/8.75	   A^2 -> H(f(a), d)
26.81/8.75	   A^2 -> H(U1(c, c), U1(e, c))
26.81/8.75	   A^2 -> H(f(c), c)
26.81/8.75	   A^2 -> H(f(c), U1(e, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, c))
26.81/8.75	   A^2 -> H(f(c), U1(k, e))
26.81/8.75	   A^2 -> H(f(c), U1(k, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, e))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, k))
26.81/8.75	   A^2 -> H(f(a), k)
26.81/8.75	
26.81/8.75	The TRS R consists of the following rules:
26.81/8.75	
26.81/8.75	   f(x) -> U1(x, x)
26.81/8.75	   U1(e, x) -> x
26.81/8.75	   a -> c
26.81/8.75	   a -> d
26.81/8.75	   b -> c
26.81/8.75	   b -> d
26.81/8.75	   d -> k
26.81/8.75	   c -> e
26.81/8.75	   c -> k
26.81/8.75	
26.81/8.75	Q is empty.
26.81/8.75	We have to consider all minimal (P,Q,R)-chains.
26.81/8.75	----------------------------------------
26.81/8.75	
26.81/8.75	(531) TransformationProof (EQUIVALENT)
26.81/8.75	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
26.81/8.75	
26.81/8.75	   (A^2 -> H(U1(c, c), U1(e, e)),A^2 -> H(U1(c, c), U1(e, e)))
26.81/8.75	   (A^2 -> H(f(e), U1(e, e)),A^2 -> H(f(e), U1(e, e)))
26.81/8.75	   (A^2 -> H(f(k), U1(e, e)),A^2 -> H(f(k), U1(e, e)))
26.81/8.75	   (A^2 -> H(f(c), e),A^2 -> H(f(c), e))
26.81/8.75	
26.81/8.75	
26.81/8.75	----------------------------------------
26.81/8.75	
26.81/8.75	(532)
26.81/8.75	Obligation:
26.81/8.75	Q DP problem:
26.81/8.75	The TRS P consists of the following rules:
26.81/8.75	
26.81/8.75	   H(x, x) -> G(x, x, f(k))
26.81/8.75	   G(d, x, x) -> A^2
26.81/8.75	   A^2 -> H(f(c), f(c))
26.81/8.75	   A^2 -> H(f(d), f(d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, c))
26.81/8.75	   A^2 -> H(f(e), f(e))
26.81/8.75	   A^2 -> H(f(k), f(k))
26.81/8.75	   A^2 -> H(U1(d, d), U1(d, d))
26.81/8.75	   A^2 -> H(f(a), e)
26.81/8.75	   A^2 -> H(f(d), U1(k, d))
26.81/8.75	   A^2 -> H(f(d), U1(d, k))
26.81/8.75	   A^2 -> H(f(a), U1(k, k))
26.81/8.75	   A^2 -> H(d, f(b))
26.81/8.75	   A^2 -> H(a, U1(b, b))
26.81/8.75	   A^2 -> H(a, f(c))
26.81/8.75	   A^2 -> H(a, f(d))
26.81/8.75	   A^2 -> H(U1(e, d), U1(b, b))
26.81/8.75	   A^2 -> H(U1(e, d), f(c))
26.81/8.75	   A^2 -> H(U1(e, d), f(d))
26.81/8.75	   A^2 -> H(U1(e, a), U1(c, b))
26.81/8.75	   A^2 -> H(U1(e, a), U1(d, b))
26.81/8.75	   A^2 -> H(U1(e, a), U1(b, c))
26.81/8.75	   A^2 -> H(U1(e, a), U1(b, d))
26.81/8.75	   A^2 -> H(U1(e, a), U1(c, c))
26.81/8.75	   A^2 -> H(U1(e, a), f(e))
26.81/8.75	   A^2 -> H(U1(e, a), f(k))
26.81/8.75	   A^2 -> H(U1(e, a), U1(d, d))
26.81/8.75	   A^2 -> H(U1(k, a), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, a), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, a), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, a), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, a), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, a), f(e))
26.81/8.75	   A^2 -> H(U1(k, a), f(k))
26.81/8.75	   A^2 -> H(U1(k, a), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, d), U1(c, b))
26.81/8.75	   A^2 -> H(U1(c, d), U1(d, b))
26.81/8.75	   A^2 -> H(U1(c, d), U1(b, c))
26.81/8.75	   A^2 -> H(U1(c, d), U1(b, d))
26.81/8.75	   A^2 -> H(U1(c, d), U1(c, c))
26.81/8.75	   A^2 -> H(U1(c, d), f(e))
26.81/8.75	   A^2 -> H(U1(c, d), f(k))
26.81/8.75	   A^2 -> H(U1(c, d), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, a), U1(e, b))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, b))
26.81/8.75	   A^2 -> H(U1(c, a), U1(c, d))
26.81/8.75	   A^2 -> H(U1(c, a), U1(d, c))
26.81/8.75	   A^2 -> H(U1(c, a), U1(b, e))
26.81/8.75	   A^2 -> H(U1(c, a), U1(b, k))
26.81/8.75	   A^2 -> H(U1(c, a), U1(e, c))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, c))
26.81/8.75	   A^2 -> H(U1(c, a), U1(c, e))
26.81/8.75	   A^2 -> H(U1(c, a), U1(c, k))
26.81/8.75	   A^2 -> H(U1(c, a), U1(e, e))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, k))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, d))
26.81/8.75	   A^2 -> H(U1(c, a), U1(d, k))
26.81/8.75	   A^2 -> H(U1(d, e), U1(b, b))
26.81/8.75	   A^2 -> H(U1(d, e), f(c))
26.81/8.75	   A^2 -> H(U1(d, e), f(d))
26.81/8.75	   A^2 -> H(U1(d, c), U1(c, b))
26.81/8.75	   A^2 -> H(U1(d, c), U1(d, b))
26.81/8.75	   A^2 -> H(U1(d, c), U1(b, c))
26.81/8.75	   A^2 -> H(U1(d, c), U1(b, d))
26.81/8.75	   A^2 -> H(U1(d, c), U1(c, c))
26.81/8.75	   A^2 -> H(U1(d, c), f(e))
26.81/8.75	   A^2 -> H(U1(d, c), f(k))
26.81/8.75	   A^2 -> H(U1(d, c), U1(d, d))
26.81/8.75	   A^2 -> H(U1(d, a), U1(e, b))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, b))
26.81/8.75	   A^2 -> H(U1(d, a), U1(c, d))
26.81/8.75	   A^2 -> H(U1(d, a), U1(d, c))
26.81/8.75	   A^2 -> H(U1(d, a), U1(b, e))
26.81/8.75	   A^2 -> H(U1(d, a), U1(b, k))
26.81/8.75	   A^2 -> H(U1(d, a), U1(e, c))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, c))
26.81/8.75	   A^2 -> H(U1(d, a), U1(c, e))
26.81/8.75	   A^2 -> H(U1(d, a), U1(c, k))
26.81/8.75	   A^2 -> H(U1(d, a), U1(e, e))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, k))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, d))
26.81/8.75	   A^2 -> H(U1(d, a), U1(d, k))
26.81/8.75	   A^2 -> H(U1(a, e), U1(c, b))
26.81/8.75	   A^2 -> H(U1(a, e), U1(d, b))
26.81/8.75	   A^2 -> H(U1(a, e), U1(b, c))
26.81/8.75	   A^2 -> H(U1(a, e), U1(b, d))
26.81/8.75	   A^2 -> H(U1(a, e), U1(c, c))
26.81/8.75	   A^2 -> H(U1(a, e), f(e))
26.81/8.75	   A^2 -> H(U1(a, e), f(k))
26.81/8.75	   A^2 -> H(U1(a, e), U1(d, d))
26.81/8.75	   A^2 -> H(U1(a, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(a, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(a, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(a, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(a, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(a, k), f(e))
26.81/8.75	   A^2 -> H(U1(a, k), f(k))
26.81/8.75	   A^2 -> H(U1(a, k), U1(d, d))
26.81/8.75	   A^2 -> H(U1(a, c), U1(e, b))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, b))
26.81/8.75	   A^2 -> H(U1(a, c), U1(c, d))
26.81/8.75	   A^2 -> H(U1(a, c), U1(d, c))
26.81/8.75	   A^2 -> H(U1(a, c), U1(b, e))
26.81/8.75	   A^2 -> H(U1(a, c), U1(b, k))
26.81/8.75	   A^2 -> H(U1(a, c), U1(e, c))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, c))
26.81/8.75	   A^2 -> H(U1(a, c), U1(c, e))
26.81/8.75	   A^2 -> H(U1(a, c), U1(c, k))
26.81/8.75	   A^2 -> H(U1(a, c), U1(e, e))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, k))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, d))
26.81/8.75	   A^2 -> H(U1(a, c), U1(d, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(e, b))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, b))
26.81/8.75	   A^2 -> H(U1(a, d), U1(c, d))
26.81/8.75	   A^2 -> H(U1(a, d), U1(d, c))
26.81/8.75	   A^2 -> H(U1(a, d), U1(b, e))
26.81/8.75	   A^2 -> H(U1(a, d), U1(b, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(e, c))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, c))
26.81/8.75	   A^2 -> H(U1(a, d), U1(c, e))
26.81/8.75	   A^2 -> H(U1(a, d), U1(c, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(e, e))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, d))
26.81/8.75	   A^2 -> H(U1(a, d), U1(d, k))
26.81/8.75	   A^2 -> H(U1(a, a), b)
26.81/8.75	   A^2 -> H(U1(a, a), U1(e, d))
26.81/8.75	   A^2 -> H(U1(a, a), U1(d, e))
26.81/8.75	   A^2 -> H(U1(a, a), c)
26.81/8.75	   A^2 -> H(U1(a, a), U1(e, k))
26.81/8.75	   A^2 -> H(U1(a, a), U1(k, e))
26.81/8.75	   A^2 -> H(U1(a, a), e)
26.81/8.75	   A^2 -> H(U1(a, a), U1(k, k))
26.81/8.75	   A^2 -> H(k, f(b))
26.81/8.75	   A^2 -> H(c, U1(b, b))
26.81/8.75	   A^2 -> H(c, f(c))
26.81/8.75	   A^2 -> H(c, f(d))
26.81/8.75	   A^2 -> H(U1(e, k), U1(b, b))
26.81/8.75	   A^2 -> H(U1(e, k), f(c))
26.81/8.75	   A^2 -> H(U1(e, k), f(d))
26.81/8.75	   A^2 -> H(U1(e, c), U1(c, b))
26.81/8.75	   A^2 -> H(U1(e, c), U1(d, b))
26.81/8.75	   A^2 -> H(U1(e, c), U1(b, c))
26.81/8.75	   A^2 -> H(U1(e, c), U1(b, d))
26.81/8.75	   A^2 -> H(U1(e, c), U1(c, c))
26.81/8.75	   A^2 -> H(U1(e, c), f(e))
26.81/8.75	   A^2 -> H(U1(e, c), f(k))
26.81/8.75	   A^2 -> H(U1(e, c), U1(d, d))
26.81/8.75	   A^2 -> H(U1(k, e), U1(b, b))
26.81/8.75	   A^2 -> H(U1(k, e), f(c))
26.81/8.75	   A^2 -> H(U1(k, e), f(d))
26.81/8.75	   A^2 -> H(U1(k, c), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, c), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, c), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, c), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, c), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, c), f(e))
26.81/8.75	   A^2 -> H(U1(k, c), f(k))
26.81/8.75	   A^2 -> H(U1(k, c), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, e), U1(c, b))
26.81/8.75	   A^2 -> H(U1(c, e), U1(d, b))
26.81/8.75	   A^2 -> H(U1(c, e), U1(b, c))
26.81/8.75	   A^2 -> H(U1(c, e), U1(b, d))
26.81/8.75	   A^2 -> H(U1(c, e), U1(c, c))
26.81/8.75	   A^2 -> H(U1(c, e), f(e))
26.81/8.75	   A^2 -> H(U1(c, e), f(k))
26.81/8.75	   A^2 -> H(U1(c, e), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(c, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(c, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(c, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(c, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(c, k), f(e))
26.81/8.75	   A^2 -> H(U1(c, k), f(k))
26.81/8.75	   A^2 -> H(U1(c, k), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(e, b))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, b))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(d, c))
26.81/8.75	   A^2 -> H(U1(c, c), U1(b, e))
26.81/8.75	   A^2 -> H(U1(c, c), U1(b, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(e, e))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(d, k))
26.81/8.75	   A^2 -> H(e, U1(b, b))
26.81/8.75	   A^2 -> H(e, f(c))
26.81/8.75	   A^2 -> H(e, f(d))
26.81/8.75	   A^2 -> H(U1(e, e), U1(c, b))
26.81/8.75	   A^2 -> H(U1(e, e), U1(d, b))
26.81/8.75	   A^2 -> H(U1(e, e), U1(b, c))
26.81/8.75	   A^2 -> H(U1(e, e), U1(b, d))
26.81/8.75	   A^2 -> H(U1(e, e), U1(c, c))
26.81/8.75	   A^2 -> H(U1(e, e), f(e))
26.81/8.75	   A^2 -> H(U1(e, e), f(k))
26.81/8.75	   A^2 -> H(U1(e, e), U1(d, d))
26.81/8.75	   A^2 -> H(f(e), U1(e, b))
26.81/8.75	   A^2 -> H(f(e), U1(k, b))
26.81/8.75	   A^2 -> H(f(e), U1(c, d))
26.81/8.75	   A^2 -> H(f(e), U1(d, c))
26.81/8.75	   A^2 -> H(f(e), U1(b, e))
26.81/8.75	   A^2 -> H(f(e), U1(b, k))
26.81/8.75	   A^2 -> H(f(e), U1(e, c))
26.81/8.75	   A^2 -> H(f(e), U1(k, c))
26.81/8.75	   A^2 -> H(f(e), U1(c, e))
26.81/8.75	   A^2 -> H(f(e), U1(c, k))
26.81/8.75	   A^2 -> H(f(e), U1(k, k))
26.81/8.75	   A^2 -> H(f(e), U1(k, d))
26.81/8.75	   A^2 -> H(f(e), U1(d, k))
26.81/8.75	   A^2 -> H(U1(k, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, k), f(e))
26.81/8.75	   A^2 -> H(U1(k, k), f(k))
26.81/8.75	   A^2 -> H(U1(k, k), U1(d, d))
26.81/8.75	   A^2 -> H(f(k), U1(e, b))
26.81/8.75	   A^2 -> H(f(k), U1(k, b))
26.81/8.75	   A^2 -> H(f(k), U1(c, d))
26.81/8.75	   A^2 -> H(f(k), U1(d, c))
26.81/8.75	   A^2 -> H(f(k), U1(b, e))
26.81/8.75	   A^2 -> H(f(k), U1(b, k))
26.81/8.75	   A^2 -> H(f(k), U1(e, c))
26.81/8.75	   A^2 -> H(f(k), U1(k, c))
26.81/8.75	   A^2 -> H(f(k), U1(c, e))
26.81/8.75	   A^2 -> H(f(k), U1(c, k))
26.81/8.75	   A^2 -> H(f(k), U1(e, e))
26.81/8.75	   A^2 -> H(f(k), U1(k, d))
26.81/8.75	   A^2 -> H(f(k), U1(d, k))
26.81/8.75	   A^2 -> H(f(c), b)
26.81/8.75	   A^2 -> H(f(c), U1(e, d))
26.81/8.75	   A^2 -> H(f(c), U1(d, e))
26.81/8.75	   A^2 -> H(f(k), U1(k, k))
26.81/8.75	   A^2 -> H(U1(k, k), U1(b, b))
26.81/8.75	   A^2 -> H(U1(k, k), f(c))
26.81/8.75	   A^2 -> H(U1(k, k), f(d))
26.81/8.75	   A^2 -> H(U1(k, d), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, d), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, d), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, d), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, d), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, d), f(e))
26.81/8.75	   A^2 -> H(U1(k, d), f(k))
26.81/8.75	   A^2 -> H(U1(k, d), U1(d, d))
26.81/8.75	   A^2 -> H(U1(d, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(d, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(d, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(d, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(d, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(d, k), f(e))
26.81/8.75	   A^2 -> H(U1(d, k), f(k))
26.81/8.75	   A^2 -> H(U1(d, k), U1(d, d))
26.81/8.75	   A^2 -> H(U1(d, d), U1(e, b))
26.81/8.75	   A^2 -> H(U1(d, d), U1(k, b))
26.81/8.75	   A^2 -> H(U1(d, d), U1(c, d))
26.81/8.75	   A^2 -> H(U1(d, d), U1(d, c))
26.81/8.75	   A^2 -> H(U1(d, d), U1(b, e))
26.81/8.75	   A^2 -> H(U1(d, d), U1(b, k))
26.81/8.75	   A^2 -> H(U1(d, d), U1(e, c))
26.81/8.75	   A^2 -> H(U1(d, d), U1(k, c))
26.81/8.75	   A^2 -> H(U1(d, d), U1(c, e))
26.81/8.75	   A^2 -> H(U1(d, d), U1(c, k))
26.81/8.75	   A^2 -> H(U1(d, d), U1(e, e))
26.81/8.75	   A^2 -> H(U1(d, d), U1(k, k))
26.81/8.75	   A^2 -> H(f(d), b)
26.81/8.75	   A^2 -> H(f(d), U1(e, d))
26.81/8.75	   A^2 -> H(f(d), U1(d, e))
26.81/8.75	   A^2 -> H(f(d), c)
26.81/8.75	   A^2 -> H(f(d), U1(e, k))
26.81/8.75	   A^2 -> H(f(d), U1(k, e))
26.81/8.75	   A^2 -> H(f(d), e)
26.81/8.75	   A^2 -> H(f(a), d)
26.81/8.75	   A^2 -> H(U1(c, c), U1(e, c))
26.81/8.75	   A^2 -> H(f(c), c)
26.81/8.75	   A^2 -> H(f(c), U1(e, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, c))
26.81/8.75	   A^2 -> H(f(c), U1(k, e))
26.81/8.75	   A^2 -> H(f(c), U1(k, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, e))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, k))
26.81/8.75	   A^2 -> H(f(a), k)
26.81/8.75	   A^2 -> H(f(e), U1(e, e))
26.81/8.75	   A^2 -> H(f(c), e)
26.81/8.75	
26.81/8.75	The TRS R consists of the following rules:
26.81/8.75	
26.81/8.75	   f(x) -> U1(x, x)
26.81/8.75	   U1(e, x) -> x
26.81/8.75	   a -> c
26.81/8.75	   a -> d
26.81/8.75	   b -> c
26.81/8.75	   b -> d
26.81/8.75	   d -> k
26.81/8.75	   c -> e
26.81/8.75	   c -> k
26.81/8.75	
26.81/8.75	Q is empty.
26.81/8.75	We have to consider all minimal (P,Q,R)-chains.
26.81/8.75	----------------------------------------
26.81/8.75	
26.81/8.75	(533) TransformationProof (EQUIVALENT)
26.81/8.75	By narrowing [LPAR04] the rule A^2 -> H(f(a), e) at position [] we obtained the following new rules [LPAR04]:
26.81/8.75	
26.81/8.75	   (A^2 -> H(U1(a, a), e),A^2 -> H(U1(a, a), e))
26.81/8.75	   (A^2 -> H(f(c), e),A^2 -> H(f(c), e))
26.81/8.75	   (A^2 -> H(f(d), e),A^2 -> H(f(d), e))
26.81/8.75	
26.81/8.75	
26.81/8.75	----------------------------------------
26.81/8.75	
26.81/8.75	(534)
26.81/8.75	Obligation:
26.81/8.75	Q DP problem:
26.81/8.75	The TRS P consists of the following rules:
26.81/8.75	
26.81/8.75	   H(x, x) -> G(x, x, f(k))
26.81/8.75	   G(d, x, x) -> A^2
26.81/8.75	   A^2 -> H(f(c), f(c))
26.81/8.75	   A^2 -> H(f(d), f(d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, c))
26.81/8.75	   A^2 -> H(f(e), f(e))
26.81/8.75	   A^2 -> H(f(k), f(k))
26.81/8.75	   A^2 -> H(U1(d, d), U1(d, d))
26.81/8.75	   A^2 -> H(f(d), U1(k, d))
26.81/8.75	   A^2 -> H(f(d), U1(d, k))
26.81/8.75	   A^2 -> H(f(a), U1(k, k))
26.81/8.75	   A^2 -> H(d, f(b))
26.81/8.75	   A^2 -> H(a, U1(b, b))
26.81/8.75	   A^2 -> H(a, f(c))
26.81/8.75	   A^2 -> H(a, f(d))
26.81/8.75	   A^2 -> H(U1(e, d), U1(b, b))
26.81/8.75	   A^2 -> H(U1(e, d), f(c))
26.81/8.75	   A^2 -> H(U1(e, d), f(d))
26.81/8.75	   A^2 -> H(U1(e, a), U1(c, b))
26.81/8.75	   A^2 -> H(U1(e, a), U1(d, b))
26.81/8.75	   A^2 -> H(U1(e, a), U1(b, c))
26.81/8.75	   A^2 -> H(U1(e, a), U1(b, d))
26.81/8.75	   A^2 -> H(U1(e, a), U1(c, c))
26.81/8.75	   A^2 -> H(U1(e, a), f(e))
26.81/8.75	   A^2 -> H(U1(e, a), f(k))
26.81/8.75	   A^2 -> H(U1(e, a), U1(d, d))
26.81/8.75	   A^2 -> H(U1(k, a), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, a), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, a), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, a), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, a), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, a), f(e))
26.81/8.75	   A^2 -> H(U1(k, a), f(k))
26.81/8.75	   A^2 -> H(U1(k, a), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, d), U1(c, b))
26.81/8.75	   A^2 -> H(U1(c, d), U1(d, b))
26.81/8.75	   A^2 -> H(U1(c, d), U1(b, c))
26.81/8.75	   A^2 -> H(U1(c, d), U1(b, d))
26.81/8.75	   A^2 -> H(U1(c, d), U1(c, c))
26.81/8.75	   A^2 -> H(U1(c, d), f(e))
26.81/8.75	   A^2 -> H(U1(c, d), f(k))
26.81/8.75	   A^2 -> H(U1(c, d), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, a), U1(e, b))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, b))
26.81/8.75	   A^2 -> H(U1(c, a), U1(c, d))
26.81/8.75	   A^2 -> H(U1(c, a), U1(d, c))
26.81/8.75	   A^2 -> H(U1(c, a), U1(b, e))
26.81/8.75	   A^2 -> H(U1(c, a), U1(b, k))
26.81/8.75	   A^2 -> H(U1(c, a), U1(e, c))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, c))
26.81/8.75	   A^2 -> H(U1(c, a), U1(c, e))
26.81/8.75	   A^2 -> H(U1(c, a), U1(c, k))
26.81/8.75	   A^2 -> H(U1(c, a), U1(e, e))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, k))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, d))
26.81/8.75	   A^2 -> H(U1(c, a), U1(d, k))
26.81/8.75	   A^2 -> H(U1(d, e), U1(b, b))
26.81/8.75	   A^2 -> H(U1(d, e), f(c))
26.81/8.75	   A^2 -> H(U1(d, e), f(d))
26.81/8.75	   A^2 -> H(U1(d, c), U1(c, b))
26.81/8.75	   A^2 -> H(U1(d, c), U1(d, b))
26.81/8.75	   A^2 -> H(U1(d, c), U1(b, c))
26.81/8.75	   A^2 -> H(U1(d, c), U1(b, d))
26.81/8.75	   A^2 -> H(U1(d, c), U1(c, c))
26.81/8.75	   A^2 -> H(U1(d, c), f(e))
26.81/8.75	   A^2 -> H(U1(d, c), f(k))
26.81/8.75	   A^2 -> H(U1(d, c), U1(d, d))
26.81/8.75	   A^2 -> H(U1(d, a), U1(e, b))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, b))
26.81/8.75	   A^2 -> H(U1(d, a), U1(c, d))
26.81/8.75	   A^2 -> H(U1(d, a), U1(d, c))
26.81/8.75	   A^2 -> H(U1(d, a), U1(b, e))
26.81/8.75	   A^2 -> H(U1(d, a), U1(b, k))
26.81/8.75	   A^2 -> H(U1(d, a), U1(e, c))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, c))
26.81/8.75	   A^2 -> H(U1(d, a), U1(c, e))
26.81/8.75	   A^2 -> H(U1(d, a), U1(c, k))
26.81/8.75	   A^2 -> H(U1(d, a), U1(e, e))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, k))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, d))
26.81/8.75	   A^2 -> H(U1(d, a), U1(d, k))
26.81/8.75	   A^2 -> H(U1(a, e), U1(c, b))
26.81/8.75	   A^2 -> H(U1(a, e), U1(d, b))
26.81/8.75	   A^2 -> H(U1(a, e), U1(b, c))
26.81/8.75	   A^2 -> H(U1(a, e), U1(b, d))
26.81/8.75	   A^2 -> H(U1(a, e), U1(c, c))
26.81/8.75	   A^2 -> H(U1(a, e), f(e))
26.81/8.75	   A^2 -> H(U1(a, e), f(k))
26.81/8.75	   A^2 -> H(U1(a, e), U1(d, d))
26.81/8.75	   A^2 -> H(U1(a, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(a, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(a, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(a, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(a, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(a, k), f(e))
26.81/8.75	   A^2 -> H(U1(a, k), f(k))
26.81/8.75	   A^2 -> H(U1(a, k), U1(d, d))
26.81/8.75	   A^2 -> H(U1(a, c), U1(e, b))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, b))
26.81/8.75	   A^2 -> H(U1(a, c), U1(c, d))
26.81/8.75	   A^2 -> H(U1(a, c), U1(d, c))
26.81/8.75	   A^2 -> H(U1(a, c), U1(b, e))
26.81/8.75	   A^2 -> H(U1(a, c), U1(b, k))
26.81/8.75	   A^2 -> H(U1(a, c), U1(e, c))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, c))
26.81/8.75	   A^2 -> H(U1(a, c), U1(c, e))
26.81/8.75	   A^2 -> H(U1(a, c), U1(c, k))
26.81/8.75	   A^2 -> H(U1(a, c), U1(e, e))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, k))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, d))
26.81/8.75	   A^2 -> H(U1(a, c), U1(d, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(e, b))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, b))
26.81/8.75	   A^2 -> H(U1(a, d), U1(c, d))
26.81/8.75	   A^2 -> H(U1(a, d), U1(d, c))
26.81/8.75	   A^2 -> H(U1(a, d), U1(b, e))
26.81/8.75	   A^2 -> H(U1(a, d), U1(b, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(e, c))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, c))
26.81/8.75	   A^2 -> H(U1(a, d), U1(c, e))
26.81/8.75	   A^2 -> H(U1(a, d), U1(c, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(e, e))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, d))
26.81/8.75	   A^2 -> H(U1(a, d), U1(d, k))
26.81/8.75	   A^2 -> H(U1(a, a), b)
26.81/8.75	   A^2 -> H(U1(a, a), U1(e, d))
26.81/8.75	   A^2 -> H(U1(a, a), U1(d, e))
26.81/8.75	   A^2 -> H(U1(a, a), c)
26.81/8.75	   A^2 -> H(U1(a, a), U1(e, k))
26.81/8.75	   A^2 -> H(U1(a, a), U1(k, e))
26.81/8.75	   A^2 -> H(U1(a, a), e)
26.81/8.75	   A^2 -> H(U1(a, a), U1(k, k))
26.81/8.75	   A^2 -> H(k, f(b))
26.81/8.75	   A^2 -> H(c, U1(b, b))
26.81/8.75	   A^2 -> H(c, f(c))
26.81/8.75	   A^2 -> H(c, f(d))
26.81/8.75	   A^2 -> H(U1(e, k), U1(b, b))
26.81/8.75	   A^2 -> H(U1(e, k), f(c))
26.81/8.75	   A^2 -> H(U1(e, k), f(d))
26.81/8.75	   A^2 -> H(U1(e, c), U1(c, b))
26.81/8.75	   A^2 -> H(U1(e, c), U1(d, b))
26.81/8.75	   A^2 -> H(U1(e, c), U1(b, c))
26.81/8.75	   A^2 -> H(U1(e, c), U1(b, d))
26.81/8.75	   A^2 -> H(U1(e, c), U1(c, c))
26.81/8.75	   A^2 -> H(U1(e, c), f(e))
26.81/8.75	   A^2 -> H(U1(e, c), f(k))
26.81/8.75	   A^2 -> H(U1(e, c), U1(d, d))
26.81/8.75	   A^2 -> H(U1(k, e), U1(b, b))
26.81/8.75	   A^2 -> H(U1(k, e), f(c))
26.81/8.75	   A^2 -> H(U1(k, e), f(d))
26.81/8.75	   A^2 -> H(U1(k, c), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, c), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, c), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, c), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, c), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, c), f(e))
26.81/8.75	   A^2 -> H(U1(k, c), f(k))
26.81/8.75	   A^2 -> H(U1(k, c), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, e), U1(c, b))
26.81/8.75	   A^2 -> H(U1(c, e), U1(d, b))
26.81/8.75	   A^2 -> H(U1(c, e), U1(b, c))
26.81/8.75	   A^2 -> H(U1(c, e), U1(b, d))
26.81/8.75	   A^2 -> H(U1(c, e), U1(c, c))
26.81/8.75	   A^2 -> H(U1(c, e), f(e))
26.81/8.75	   A^2 -> H(U1(c, e), f(k))
26.81/8.75	   A^2 -> H(U1(c, e), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(c, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(c, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(c, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(c, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(c, k), f(e))
26.81/8.75	   A^2 -> H(U1(c, k), f(k))
26.81/8.75	   A^2 -> H(U1(c, k), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(e, b))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, b))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(d, c))
26.81/8.75	   A^2 -> H(U1(c, c), U1(b, e))
26.81/8.75	   A^2 -> H(U1(c, c), U1(b, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(e, e))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(d, k))
26.81/8.75	   A^2 -> H(e, U1(b, b))
26.81/8.75	   A^2 -> H(e, f(c))
26.81/8.75	   A^2 -> H(e, f(d))
26.81/8.75	   A^2 -> H(U1(e, e), U1(c, b))
26.81/8.75	   A^2 -> H(U1(e, e), U1(d, b))
26.81/8.75	   A^2 -> H(U1(e, e), U1(b, c))
26.81/8.75	   A^2 -> H(U1(e, e), U1(b, d))
26.81/8.75	   A^2 -> H(U1(e, e), U1(c, c))
26.81/8.75	   A^2 -> H(U1(e, e), f(e))
26.81/8.75	   A^2 -> H(U1(e, e), f(k))
26.81/8.75	   A^2 -> H(U1(e, e), U1(d, d))
26.81/8.75	   A^2 -> H(f(e), U1(e, b))
26.81/8.75	   A^2 -> H(f(e), U1(k, b))
26.81/8.75	   A^2 -> H(f(e), U1(c, d))
26.81/8.75	   A^2 -> H(f(e), U1(d, c))
26.81/8.75	   A^2 -> H(f(e), U1(b, e))
26.81/8.75	   A^2 -> H(f(e), U1(b, k))
26.81/8.75	   A^2 -> H(f(e), U1(e, c))
26.81/8.75	   A^2 -> H(f(e), U1(k, c))
26.81/8.75	   A^2 -> H(f(e), U1(c, e))
26.81/8.75	   A^2 -> H(f(e), U1(c, k))
26.81/8.75	   A^2 -> H(f(e), U1(k, k))
26.81/8.75	   A^2 -> H(f(e), U1(k, d))
26.81/8.75	   A^2 -> H(f(e), U1(d, k))
26.81/8.75	   A^2 -> H(U1(k, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, k), f(e))
26.81/8.75	   A^2 -> H(U1(k, k), f(k))
26.81/8.75	   A^2 -> H(U1(k, k), U1(d, d))
26.81/8.75	   A^2 -> H(f(k), U1(e, b))
26.81/8.75	   A^2 -> H(f(k), U1(k, b))
26.81/8.75	   A^2 -> H(f(k), U1(c, d))
26.81/8.75	   A^2 -> H(f(k), U1(d, c))
26.81/8.75	   A^2 -> H(f(k), U1(b, e))
26.81/8.75	   A^2 -> H(f(k), U1(b, k))
26.81/8.75	   A^2 -> H(f(k), U1(e, c))
26.81/8.75	   A^2 -> H(f(k), U1(k, c))
26.81/8.75	   A^2 -> H(f(k), U1(c, e))
26.81/8.75	   A^2 -> H(f(k), U1(c, k))
26.81/8.75	   A^2 -> H(f(k), U1(e, e))
26.81/8.75	   A^2 -> H(f(k), U1(k, d))
26.81/8.75	   A^2 -> H(f(k), U1(d, k))
26.81/8.75	   A^2 -> H(f(c), b)
26.81/8.75	   A^2 -> H(f(c), U1(e, d))
26.81/8.75	   A^2 -> H(f(c), U1(d, e))
26.81/8.75	   A^2 -> H(f(k), U1(k, k))
26.81/8.75	   A^2 -> H(U1(k, k), U1(b, b))
26.81/8.75	   A^2 -> H(U1(k, k), f(c))
26.81/8.75	   A^2 -> H(U1(k, k), f(d))
26.81/8.75	   A^2 -> H(U1(k, d), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, d), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, d), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, d), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, d), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, d), f(e))
26.81/8.75	   A^2 -> H(U1(k, d), f(k))
26.81/8.75	   A^2 -> H(U1(k, d), U1(d, d))
26.81/8.75	   A^2 -> H(U1(d, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(d, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(d, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(d, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(d, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(d, k), f(e))
26.81/8.75	   A^2 -> H(U1(d, k), f(k))
26.81/8.75	   A^2 -> H(U1(d, k), U1(d, d))
26.81/8.75	   A^2 -> H(U1(d, d), U1(e, b))
26.81/8.75	   A^2 -> H(U1(d, d), U1(k, b))
26.81/8.75	   A^2 -> H(U1(d, d), U1(c, d))
26.81/8.75	   A^2 -> H(U1(d, d), U1(d, c))
26.81/8.75	   A^2 -> H(U1(d, d), U1(b, e))
26.81/8.75	   A^2 -> H(U1(d, d), U1(b, k))
26.81/8.75	   A^2 -> H(U1(d, d), U1(e, c))
26.81/8.75	   A^2 -> H(U1(d, d), U1(k, c))
26.81/8.75	   A^2 -> H(U1(d, d), U1(c, e))
26.81/8.75	   A^2 -> H(U1(d, d), U1(c, k))
26.81/8.75	   A^2 -> H(U1(d, d), U1(e, e))
26.81/8.75	   A^2 -> H(U1(d, d), U1(k, k))
26.81/8.75	   A^2 -> H(f(d), b)
26.81/8.75	   A^2 -> H(f(d), U1(e, d))
26.81/8.75	   A^2 -> H(f(d), U1(d, e))
26.81/8.75	   A^2 -> H(f(d), c)
26.81/8.75	   A^2 -> H(f(d), U1(e, k))
26.81/8.75	   A^2 -> H(f(d), U1(k, e))
26.81/8.75	   A^2 -> H(f(d), e)
26.81/8.75	   A^2 -> H(f(a), d)
26.81/8.75	   A^2 -> H(U1(c, c), U1(e, c))
26.81/8.75	   A^2 -> H(f(c), c)
26.81/8.75	   A^2 -> H(f(c), U1(e, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(k, c))
26.81/8.75	   A^2 -> H(f(c), U1(k, e))
26.81/8.75	   A^2 -> H(f(c), U1(k, k))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, e))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, k))
26.81/8.75	   A^2 -> H(f(a), k)
26.81/8.75	   A^2 -> H(f(e), U1(e, e))
26.81/8.75	   A^2 -> H(f(c), e)
26.81/8.75	
26.81/8.75	The TRS R consists of the following rules:
26.81/8.75	
26.81/8.75	   f(x) -> U1(x, x)
26.81/8.75	   U1(e, x) -> x
26.81/8.75	   a -> c
26.81/8.75	   a -> d
26.81/8.75	   b -> c
26.81/8.75	   b -> d
26.81/8.75	   d -> k
26.81/8.75	   c -> e
26.81/8.75	   c -> k
26.81/8.75	
26.81/8.75	Q is empty.
26.81/8.75	We have to consider all minimal (P,Q,R)-chains.
26.81/8.75	----------------------------------------
26.81/8.75	
26.81/8.75	(535) TransformationProof (EQUIVALENT)
26.81/8.75	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
26.81/8.75	
26.81/8.75	   (A^2 -> H(U1(d, d), U1(k, d)),A^2 -> H(U1(d, d), U1(k, d)))
26.81/8.75	   (A^2 -> H(f(k), U1(k, d)),A^2 -> H(f(k), U1(k, d)))
26.81/8.75	   (A^2 -> H(f(d), U1(k, k)),A^2 -> H(f(d), U1(k, k)))
26.81/8.75	
26.81/8.75	
26.81/8.75	----------------------------------------
26.81/8.75	
26.81/8.75	(536)
26.81/8.75	Obligation:
26.81/8.75	Q DP problem:
26.81/8.75	The TRS P consists of the following rules:
26.81/8.75	
26.81/8.75	   H(x, x) -> G(x, x, f(k))
26.81/8.75	   G(d, x, x) -> A^2
26.81/8.75	   A^2 -> H(f(c), f(c))
26.81/8.75	   A^2 -> H(f(d), f(d))
26.81/8.75	   A^2 -> H(U1(c, c), U1(c, c))
26.81/8.75	   A^2 -> H(f(e), f(e))
26.81/8.75	   A^2 -> H(f(k), f(k))
26.81/8.75	   A^2 -> H(U1(d, d), U1(d, d))
26.81/8.75	   A^2 -> H(f(d), U1(d, k))
26.81/8.75	   A^2 -> H(f(a), U1(k, k))
26.81/8.75	   A^2 -> H(d, f(b))
26.81/8.75	   A^2 -> H(a, U1(b, b))
26.81/8.75	   A^2 -> H(a, f(c))
26.81/8.75	   A^2 -> H(a, f(d))
26.81/8.75	   A^2 -> H(U1(e, d), U1(b, b))
26.81/8.75	   A^2 -> H(U1(e, d), f(c))
26.81/8.75	   A^2 -> H(U1(e, d), f(d))
26.81/8.75	   A^2 -> H(U1(e, a), U1(c, b))
26.81/8.75	   A^2 -> H(U1(e, a), U1(d, b))
26.81/8.75	   A^2 -> H(U1(e, a), U1(b, c))
26.81/8.75	   A^2 -> H(U1(e, a), U1(b, d))
26.81/8.75	   A^2 -> H(U1(e, a), U1(c, c))
26.81/8.75	   A^2 -> H(U1(e, a), f(e))
26.81/8.75	   A^2 -> H(U1(e, a), f(k))
26.81/8.75	   A^2 -> H(U1(e, a), U1(d, d))
26.81/8.75	   A^2 -> H(U1(k, a), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, a), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, a), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, a), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, a), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, a), f(e))
26.81/8.75	   A^2 -> H(U1(k, a), f(k))
26.81/8.75	   A^2 -> H(U1(k, a), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, d), U1(c, b))
26.81/8.75	   A^2 -> H(U1(c, d), U1(d, b))
26.81/8.75	   A^2 -> H(U1(c, d), U1(b, c))
26.81/8.75	   A^2 -> H(U1(c, d), U1(b, d))
26.81/8.75	   A^2 -> H(U1(c, d), U1(c, c))
26.81/8.75	   A^2 -> H(U1(c, d), f(e))
26.81/8.75	   A^2 -> H(U1(c, d), f(k))
26.81/8.75	   A^2 -> H(U1(c, d), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, a), U1(e, b))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, b))
26.81/8.75	   A^2 -> H(U1(c, a), U1(c, d))
26.81/8.75	   A^2 -> H(U1(c, a), U1(d, c))
26.81/8.75	   A^2 -> H(U1(c, a), U1(b, e))
26.81/8.75	   A^2 -> H(U1(c, a), U1(b, k))
26.81/8.75	   A^2 -> H(U1(c, a), U1(e, c))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, c))
26.81/8.75	   A^2 -> H(U1(c, a), U1(c, e))
26.81/8.75	   A^2 -> H(U1(c, a), U1(c, k))
26.81/8.75	   A^2 -> H(U1(c, a), U1(e, e))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, k))
26.81/8.75	   A^2 -> H(U1(c, a), U1(k, d))
26.81/8.75	   A^2 -> H(U1(c, a), U1(d, k))
26.81/8.75	   A^2 -> H(U1(d, e), U1(b, b))
26.81/8.75	   A^2 -> H(U1(d, e), f(c))
26.81/8.75	   A^2 -> H(U1(d, e), f(d))
26.81/8.75	   A^2 -> H(U1(d, c), U1(c, b))
26.81/8.75	   A^2 -> H(U1(d, c), U1(d, b))
26.81/8.75	   A^2 -> H(U1(d, c), U1(b, c))
26.81/8.75	   A^2 -> H(U1(d, c), U1(b, d))
26.81/8.75	   A^2 -> H(U1(d, c), U1(c, c))
26.81/8.75	   A^2 -> H(U1(d, c), f(e))
26.81/8.75	   A^2 -> H(U1(d, c), f(k))
26.81/8.75	   A^2 -> H(U1(d, c), U1(d, d))
26.81/8.75	   A^2 -> H(U1(d, a), U1(e, b))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, b))
26.81/8.75	   A^2 -> H(U1(d, a), U1(c, d))
26.81/8.75	   A^2 -> H(U1(d, a), U1(d, c))
26.81/8.75	   A^2 -> H(U1(d, a), U1(b, e))
26.81/8.75	   A^2 -> H(U1(d, a), U1(b, k))
26.81/8.75	   A^2 -> H(U1(d, a), U1(e, c))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, c))
26.81/8.75	   A^2 -> H(U1(d, a), U1(c, e))
26.81/8.75	   A^2 -> H(U1(d, a), U1(c, k))
26.81/8.75	   A^2 -> H(U1(d, a), U1(e, e))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, k))
26.81/8.75	   A^2 -> H(U1(d, a), U1(k, d))
26.81/8.75	   A^2 -> H(U1(d, a), U1(d, k))
26.81/8.75	   A^2 -> H(U1(a, e), U1(c, b))
26.81/8.75	   A^2 -> H(U1(a, e), U1(d, b))
26.81/8.75	   A^2 -> H(U1(a, e), U1(b, c))
26.81/8.75	   A^2 -> H(U1(a, e), U1(b, d))
26.81/8.75	   A^2 -> H(U1(a, e), U1(c, c))
26.81/8.75	   A^2 -> H(U1(a, e), f(e))
26.81/8.75	   A^2 -> H(U1(a, e), f(k))
26.81/8.75	   A^2 -> H(U1(a, e), U1(d, d))
26.81/8.75	   A^2 -> H(U1(a, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(a, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(a, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(a, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(a, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(a, k), f(e))
26.81/8.75	   A^2 -> H(U1(a, k), f(k))
26.81/8.75	   A^2 -> H(U1(a, k), U1(d, d))
26.81/8.75	   A^2 -> H(U1(a, c), U1(e, b))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, b))
26.81/8.75	   A^2 -> H(U1(a, c), U1(c, d))
26.81/8.75	   A^2 -> H(U1(a, c), U1(d, c))
26.81/8.75	   A^2 -> H(U1(a, c), U1(b, e))
26.81/8.75	   A^2 -> H(U1(a, c), U1(b, k))
26.81/8.75	   A^2 -> H(U1(a, c), U1(e, c))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, c))
26.81/8.75	   A^2 -> H(U1(a, c), U1(c, e))
26.81/8.75	   A^2 -> H(U1(a, c), U1(c, k))
26.81/8.75	   A^2 -> H(U1(a, c), U1(e, e))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, k))
26.81/8.75	   A^2 -> H(U1(a, c), U1(k, d))
26.81/8.75	   A^2 -> H(U1(a, c), U1(d, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(e, b))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, b))
26.81/8.75	   A^2 -> H(U1(a, d), U1(c, d))
26.81/8.75	   A^2 -> H(U1(a, d), U1(d, c))
26.81/8.75	   A^2 -> H(U1(a, d), U1(b, e))
26.81/8.75	   A^2 -> H(U1(a, d), U1(b, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(e, c))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, c))
26.81/8.75	   A^2 -> H(U1(a, d), U1(c, e))
26.81/8.75	   A^2 -> H(U1(a, d), U1(c, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(e, e))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, k))
26.81/8.75	   A^2 -> H(U1(a, d), U1(k, d))
26.81/8.75	   A^2 -> H(U1(a, d), U1(d, k))
26.81/8.75	   A^2 -> H(U1(a, a), b)
26.81/8.75	   A^2 -> H(U1(a, a), U1(e, d))
26.81/8.75	   A^2 -> H(U1(a, a), U1(d, e))
26.81/8.75	   A^2 -> H(U1(a, a), c)
26.81/8.75	   A^2 -> H(U1(a, a), U1(e, k))
26.81/8.75	   A^2 -> H(U1(a, a), U1(k, e))
26.81/8.75	   A^2 -> H(U1(a, a), e)
26.81/8.75	   A^2 -> H(U1(a, a), U1(k, k))
26.81/8.75	   A^2 -> H(k, f(b))
26.81/8.75	   A^2 -> H(c, U1(b, b))
26.81/8.75	   A^2 -> H(c, f(c))
26.81/8.75	   A^2 -> H(c, f(d))
26.81/8.75	   A^2 -> H(U1(e, k), U1(b, b))
26.81/8.75	   A^2 -> H(U1(e, k), f(c))
26.81/8.75	   A^2 -> H(U1(e, k), f(d))
26.81/8.75	   A^2 -> H(U1(e, c), U1(c, b))
26.81/8.75	   A^2 -> H(U1(e, c), U1(d, b))
26.81/8.75	   A^2 -> H(U1(e, c), U1(b, c))
26.81/8.75	   A^2 -> H(U1(e, c), U1(b, d))
26.81/8.75	   A^2 -> H(U1(e, c), U1(c, c))
26.81/8.75	   A^2 -> H(U1(e, c), f(e))
26.81/8.75	   A^2 -> H(U1(e, c), f(k))
26.81/8.75	   A^2 -> H(U1(e, c), U1(d, d))
26.81/8.75	   A^2 -> H(U1(k, e), U1(b, b))
26.81/8.75	   A^2 -> H(U1(k, e), f(c))
26.81/8.75	   A^2 -> H(U1(k, e), f(d))
26.81/8.75	   A^2 -> H(U1(k, c), U1(c, b))
26.81/8.75	   A^2 -> H(U1(k, c), U1(d, b))
26.81/8.75	   A^2 -> H(U1(k, c), U1(b, c))
26.81/8.75	   A^2 -> H(U1(k, c), U1(b, d))
26.81/8.75	   A^2 -> H(U1(k, c), U1(c, c))
26.81/8.75	   A^2 -> H(U1(k, c), f(e))
26.81/8.75	   A^2 -> H(U1(k, c), f(k))
26.81/8.75	   A^2 -> H(U1(k, c), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, e), U1(c, b))
26.81/8.75	   A^2 -> H(U1(c, e), U1(d, b))
26.81/8.75	   A^2 -> H(U1(c, e), U1(b, c))
26.81/8.75	   A^2 -> H(U1(c, e), U1(b, d))
26.81/8.75	   A^2 -> H(U1(c, e), U1(c, c))
26.81/8.75	   A^2 -> H(U1(c, e), f(e))
26.81/8.75	   A^2 -> H(U1(c, e), f(k))
26.81/8.75	   A^2 -> H(U1(c, e), U1(d, d))
26.81/8.75	   A^2 -> H(U1(c, k), U1(c, b))
26.81/8.75	   A^2 -> H(U1(c, k), U1(d, b))
26.81/8.75	   A^2 -> H(U1(c, k), U1(b, c))
26.81/8.75	   A^2 -> H(U1(c, k), U1(b, d))
26.81/8.75	   A^2 -> H(U1(c, k), U1(c, c))
26.81/8.75	   A^2 -> H(U1(c, k), f(e))
26.81/8.77	   A^2 -> H(U1(c, k), f(k))
26.81/8.77	   A^2 -> H(U1(c, k), U1(d, d))
26.81/8.77	   A^2 -> H(U1(c, c), U1(e, b))
26.81/8.77	   A^2 -> H(U1(c, c), U1(k, b))
26.81/8.77	   A^2 -> H(U1(c, c), U1(c, d))
26.81/8.77	   A^2 -> H(U1(c, c), U1(d, c))
26.81/8.77	   A^2 -> H(U1(c, c), U1(b, e))
26.81/8.77	   A^2 -> H(U1(c, c), U1(b, k))
26.81/8.77	   A^2 -> H(U1(c, c), U1(e, e))
26.81/8.77	   A^2 -> H(U1(c, c), U1(k, k))
26.81/8.77	   A^2 -> H(U1(c, c), U1(k, d))
26.81/8.77	   A^2 -> H(U1(c, c), U1(d, k))
26.81/8.77	   A^2 -> H(e, U1(b, b))
26.81/8.77	   A^2 -> H(e, f(c))
26.81/8.77	   A^2 -> H(e, f(d))
26.81/8.77	   A^2 -> H(U1(e, e), U1(c, b))
26.81/8.77	   A^2 -> H(U1(e, e), U1(d, b))
26.81/8.77	   A^2 -> H(U1(e, e), U1(b, c))
26.81/8.77	   A^2 -> H(U1(e, e), U1(b, d))
26.81/8.77	   A^2 -> H(U1(e, e), U1(c, c))
26.81/8.77	   A^2 -> H(U1(e, e), f(e))
26.81/8.77	   A^2 -> H(U1(e, e), f(k))
26.81/8.77	   A^2 -> H(U1(e, e), U1(d, d))
26.81/8.77	   A^2 -> H(f(e), U1(e, b))
26.81/8.77	   A^2 -> H(f(e), U1(k, b))
26.81/8.77	   A^2 -> H(f(e), U1(c, d))
26.81/8.77	   A^2 -> H(f(e), U1(d, c))
26.81/8.77	   A^2 -> H(f(e), U1(b, e))
26.81/8.77	   A^2 -> H(f(e), U1(b, k))
26.81/8.77	   A^2 -> H(f(e), U1(e, c))
26.81/8.77	   A^2 -> H(f(e), U1(k, c))
26.81/8.77	   A^2 -> H(f(e), U1(c, e))
26.81/8.77	   A^2 -> H(f(e), U1(c, k))
26.81/8.77	   A^2 -> H(f(e), U1(k, k))
26.81/8.77	   A^2 -> H(f(e), U1(k, d))
26.81/8.77	   A^2 -> H(f(e), U1(d, k))
26.81/8.77	   A^2 -> H(U1(k, k), U1(c, b))
26.81/8.77	   A^2 -> H(U1(k, k), U1(d, b))
26.81/8.77	   A^2 -> H(U1(k, k), U1(b, c))
26.81/8.77	   A^2 -> H(U1(k, k), U1(b, d))
26.81/8.77	   A^2 -> H(U1(k, k), U1(c, c))
26.81/8.77	   A^2 -> H(U1(k, k), f(e))
26.81/8.77	   A^2 -> H(U1(k, k), f(k))
26.81/8.77	   A^2 -> H(U1(k, k), U1(d, d))
26.81/8.77	   A^2 -> H(f(k), U1(e, b))
26.81/8.77	   A^2 -> H(f(k), U1(k, b))
26.81/8.77	   A^2 -> H(f(k), U1(c, d))
26.81/8.77	   A^2 -> H(f(k), U1(d, c))
26.81/8.77	   A^2 -> H(f(k), U1(b, e))
26.81/8.77	   A^2 -> H(f(k), U1(b, k))
26.81/8.77	   A^2 -> H(f(k), U1(e, c))
26.81/8.77	   A^2 -> H(f(k), U1(k, c))
26.81/8.77	   A^2 -> H(f(k), U1(c, e))
26.81/8.77	   A^2 -> H(f(k), U1(c, k))
26.81/8.77	   A^2 -> H(f(k), U1(e, e))
26.81/8.77	   A^2 -> H(f(k), U1(k, d))
26.81/8.77	   A^2 -> H(f(k), U1(d, k))
26.81/8.77	   A^2 -> H(f(c), b)
26.81/8.77	   A^2 -> H(f(c), U1(e, d))
26.81/8.77	   A^2 -> H(f(c), U1(d, e))
26.81/8.77	   A^2 -> H(f(k), U1(k, k))
26.81/8.77	   A^2 -> H(U1(k, k), U1(b, b))
26.81/8.77	   A^2 -> H(U1(k, k), f(c))
26.81/8.77	   A^2 -> H(U1(k, k), f(d))
26.81/8.77	   A^2 -> H(U1(k, d), U1(c, b))
26.81/8.77	   A^2 -> H(U1(k, d), U1(d, b))
26.81/8.77	   A^2 -> H(U1(k, d), U1(b, c))
26.81/8.77	   A^2 -> H(U1(k, d), U1(b, d))
26.81/8.77	   A^2 -> H(U1(k, d), U1(c, c))
26.81/8.77	   A^2 -> H(U1(k, d), f(e))
26.81/8.77	   A^2 -> H(U1(k, d), f(k))
26.81/8.77	   A^2 -> H(U1(k, d), U1(d, d))
26.81/8.77	   A^2 -> H(U1(d, k), U1(c, b))
26.81/8.77	   A^2 -> H(U1(d, k), U1(d, b))
26.81/8.77	   A^2 -> H(U1(d, k), U1(b, c))
26.81/8.77	   A^2 -> H(U1(d, k), U1(b, d))
26.81/8.77	   A^2 -> H(U1(d, k), U1(c, c))
26.81/8.77	   A^2 -> H(U1(d, k), f(e))
26.81/8.77	   A^2 -> H(U1(d, k), f(k))
26.81/8.77	   A^2 -> H(U1(d, k), U1(d, d))
26.81/8.77	   A^2 -> H(U1(d, d), U1(e, b))
26.81/8.77	   A^2 -> H(U1(d, d), U1(k, b))
26.81/8.77	   A^2 -> H(U1(d, d), U1(c, d))
26.81/8.77	   A^2 -> H(U1(d, d), U1(d, c))
26.81/8.77	   A^2 -> H(U1(d, d), U1(b, e))
26.81/8.77	   A^2 -> H(U1(d, d), U1(b, k))
26.81/8.77	   A^2 -> H(U1(d, d), U1(e, c))
26.81/8.77	   A^2 -> H(U1(d, d), U1(k, c))
26.81/8.77	   A^2 -> H(U1(d, d), U1(c, e))
26.81/8.77	   A^2 -> H(U1(d, d), U1(c, k))
26.81/8.77	   A^2 -> H(U1(d, d), U1(e, e))
26.81/8.77	   A^2 -> H(U1(d, d), U1(k, k))
26.81/8.77	   A^2 -> H(f(d), b)
26.81/8.77	   A^2 -> H(f(d), U1(e, d))
26.81/8.77	   A^2 -> H(f(d), U1(d, e))
26.81/8.77	   A^2 -> H(f(d), c)
26.81/8.77	   A^2 -> H(f(d), U1(e, k))
26.81/8.77	   A^2 -> H(f(d), U1(k, e))
26.81/8.77	   A^2 -> H(f(d), e)
26.81/8.77	   A^2 -> H(f(a), d)
26.81/8.77	   A^2 -> H(U1(c, c), U1(e, c))
26.81/8.77	   A^2 -> H(f(c), c)
26.81/8.77	   A^2 -> H(f(c), U1(e, k))
26.81/8.77	   A^2 -> H(U1(c, c), U1(k, c))
26.81/8.77	   A^2 -> H(f(c), U1(k, e))
26.81/8.77	   A^2 -> H(f(c), U1(k, k))
26.81/8.77	   A^2 -> H(U1(c, c), U1(c, e))
26.81/8.77	   A^2 -> H(U1(c, c), U1(c, k))
26.81/8.77	   A^2 -> H(f(a), k)
26.81/8.77	   A^2 -> H(f(e), U1(e, e))
26.81/8.77	   A^2 -> H(f(c), e)
26.81/8.77	   A^2 -> H(U1(d, d), U1(k, d))
26.81/8.77	   A^2 -> H(f(d), U1(k, k))
26.81/8.77	
26.81/8.77	The TRS R consists of the following rules:
26.81/8.77	
26.81/8.77	   f(x) -> U1(x, x)
26.81/8.77	   U1(e, x) -> x
26.81/8.77	   a -> c
26.81/8.77	   a -> d
26.81/8.77	   b -> c
26.81/8.77	   b -> d
26.81/8.77	   d -> k
26.81/8.77	   c -> e
26.81/8.77	   c -> k
26.81/8.77	
26.81/8.77	Q is empty.
26.81/8.77	We have to consider all minimal (P,Q,R)-chains.
26.81/8.77	----------------------------------------
26.81/8.77	
26.81/8.77	(537) TransformationProof (EQUIVALENT)
26.81/8.77	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
26.81/8.77	
26.81/8.77	   (A^2 -> H(U1(d, d), U1(d, k)),A^2 -> H(U1(d, d), U1(d, k)))
26.81/8.77	   (A^2 -> H(f(k), U1(d, k)),A^2 -> H(f(k), U1(d, k)))
26.81/8.77	   (A^2 -> H(f(d), U1(k, k)),A^2 -> H(f(d), U1(k, k)))
26.81/8.77	
26.81/8.77	
26.81/8.77	----------------------------------------
26.81/8.77	
26.81/8.77	(538)
26.81/8.77	Obligation:
26.81/8.77	Q DP problem:
26.81/8.77	The TRS P consists of the following rules:
26.81/8.77	
26.81/8.77	   H(x, x) -> G(x, x, f(k))
26.81/8.77	   G(d, x, x) -> A^2
26.81/8.77	   A^2 -> H(f(c), f(c))
26.81/8.77	   A^2 -> H(f(d), f(d))
26.81/8.77	   A^2 -> H(U1(c, c), U1(c, c))
26.81/8.77	   A^2 -> H(f(e), f(e))
26.81/8.77	   A^2 -> H(f(k), f(k))
26.81/8.77	   A^2 -> H(U1(d, d), U1(d, d))
26.81/8.77	   A^2 -> H(f(a), U1(k, k))
26.81/8.77	   A^2 -> H(d, f(b))
26.81/8.77	   A^2 -> H(a, U1(b, b))
26.81/8.77	   A^2 -> H(a, f(c))
26.81/8.77	   A^2 -> H(a, f(d))
26.81/8.77	   A^2 -> H(U1(e, d), U1(b, b))
26.81/8.77	   A^2 -> H(U1(e, d), f(c))
26.81/8.77	   A^2 -> H(U1(e, d), f(d))
26.81/8.77	   A^2 -> H(U1(e, a), U1(c, b))
26.81/8.77	   A^2 -> H(U1(e, a), U1(d, b))
26.81/8.77	   A^2 -> H(U1(e, a), U1(b, c))
26.81/8.77	   A^2 -> H(U1(e, a), U1(b, d))
26.81/8.77	   A^2 -> H(U1(e, a), U1(c, c))
26.81/8.77	   A^2 -> H(U1(e, a), f(e))
26.81/8.77	   A^2 -> H(U1(e, a), f(k))
26.81/8.77	   A^2 -> H(U1(e, a), U1(d, d))
26.81/8.77	   A^2 -> H(U1(k, a), U1(c, b))
26.81/8.77	   A^2 -> H(U1(k, a), U1(d, b))
26.81/8.77	   A^2 -> H(U1(k, a), U1(b, c))
26.81/8.77	   A^2 -> H(U1(k, a), U1(b, d))
26.81/8.77	   A^2 -> H(U1(k, a), U1(c, c))
26.81/8.77	   A^2 -> H(U1(k, a), f(e))
26.81/8.77	   A^2 -> H(U1(k, a), f(k))
26.81/8.77	   A^2 -> H(U1(k, a), U1(d, d))
26.81/8.77	   A^2 -> H(U1(c, d), U1(c, b))
26.81/8.77	   A^2 -> H(U1(c, d), U1(d, b))
26.81/8.77	   A^2 -> H(U1(c, d), U1(b, c))
26.81/8.77	   A^2 -> H(U1(c, d), U1(b, d))
26.81/8.77	   A^2 -> H(U1(c, d), U1(c, c))
26.81/8.77	   A^2 -> H(U1(c, d), f(e))
26.81/8.77	   A^2 -> H(U1(c, d), f(k))
26.81/8.77	   A^2 -> H(U1(c, d), U1(d, d))
26.81/8.77	   A^2 -> H(U1(c, a), U1(e, b))
26.81/8.77	   A^2 -> H(U1(c, a), U1(k, b))
26.81/8.77	   A^2 -> H(U1(c, a), U1(c, d))
26.81/8.77	   A^2 -> H(U1(c, a), U1(d, c))
26.81/8.77	   A^2 -> H(U1(c, a), U1(b, e))
26.81/8.77	   A^2 -> H(U1(c, a), U1(b, k))
26.81/8.77	   A^2 -> H(U1(c, a), U1(e, c))
26.81/8.77	   A^2 -> H(U1(c, a), U1(k, c))
26.81/8.77	   A^2 -> H(U1(c, a), U1(c, e))
26.81/8.77	   A^2 -> H(U1(c, a), U1(c, k))
26.81/8.77	   A^2 -> H(U1(c, a), U1(e, e))
26.81/8.77	   A^2 -> H(U1(c, a), U1(k, k))
26.81/8.77	   A^2 -> H(U1(c, a), U1(k, d))
26.81/8.77	   A^2 -> H(U1(c, a), U1(d, k))
26.81/8.77	   A^2 -> H(U1(d, e), U1(b, b))
26.81/8.77	   A^2 -> H(U1(d, e), f(c))
26.81/8.77	   A^2 -> H(U1(d, e), f(d))
26.81/8.77	   A^2 -> H(U1(d, c), U1(c, b))
26.81/8.77	   A^2 -> H(U1(d, c), U1(d, b))
26.81/8.77	   A^2 -> H(U1(d, c), U1(b, c))
26.81/8.77	   A^2 -> H(U1(d, c), U1(b, d))
26.81/8.77	   A^2 -> H(U1(d, c), U1(c, c))
26.81/8.77	   A^2 -> H(U1(d, c), f(e))
26.81/8.77	   A^2 -> H(U1(d, c), f(k))
26.81/8.77	   A^2 -> H(U1(d, c), U1(d, d))
26.81/8.77	   A^2 -> H(U1(d, a), U1(e, b))
26.81/8.77	   A^2 -> H(U1(d, a), U1(k, b))
26.81/8.77	   A^2 -> H(U1(d, a), U1(c, d))
26.81/8.77	   A^2 -> H(U1(d, a), U1(d, c))
26.81/8.77	   A^2 -> H(U1(d, a), U1(b, e))
26.81/8.77	   A^2 -> H(U1(d, a), U1(b, k))
26.81/8.77	   A^2 -> H(U1(d, a), U1(e, c))
26.81/8.77	   A^2 -> H(U1(d, a), U1(k, c))
26.81/8.77	   A^2 -> H(U1(d, a), U1(c, e))
26.81/8.77	   A^2 -> H(U1(d, a), U1(c, k))
26.81/8.77	   A^2 -> H(U1(d, a), U1(e, e))
26.81/8.77	   A^2 -> H(U1(d, a), U1(k, k))
26.81/8.77	   A^2 -> H(U1(d, a), U1(k, d))
26.81/8.77	   A^2 -> H(U1(d, a), U1(d, k))
26.81/8.77	   A^2 -> H(U1(a, e), U1(c, b))
26.81/8.77	   A^2 -> H(U1(a, e), U1(d, b))
26.81/8.77	   A^2 -> H(U1(a, e), U1(b, c))
26.81/8.77	   A^2 -> H(U1(a, e), U1(b, d))
26.81/8.77	   A^2 -> H(U1(a, e), U1(c, c))
26.81/8.77	   A^2 -> H(U1(a, e), f(e))
26.81/8.77	   A^2 -> H(U1(a, e), f(k))
26.81/8.77	   A^2 -> H(U1(a, e), U1(d, d))
26.81/8.77	   A^2 -> H(U1(a, k), U1(c, b))
26.81/8.77	   A^2 -> H(U1(a, k), U1(d, b))
26.81/8.77	   A^2 -> H(U1(a, k), U1(b, c))
26.81/8.77	   A^2 -> H(U1(a, k), U1(b, d))
26.81/8.77	   A^2 -> H(U1(a, k), U1(c, c))
26.81/8.77	   A^2 -> H(U1(a, k), f(e))
26.81/8.77	   A^2 -> H(U1(a, k), f(k))
26.81/8.77	   A^2 -> H(U1(a, k), U1(d, d))
26.81/8.77	   A^2 -> H(U1(a, c), U1(e, b))
26.81/8.77	   A^2 -> H(U1(a, c), U1(k, b))
26.81/8.77	   A^2 -> H(U1(a, c), U1(c, d))
26.81/8.77	   A^2 -> H(U1(a, c), U1(d, c))
26.81/8.77	   A^2 -> H(U1(a, c), U1(b, e))
26.81/8.77	   A^2 -> H(U1(a, c), U1(b, k))
26.81/8.77	   A^2 -> H(U1(a, c), U1(e, c))
26.81/8.77	   A^2 -> H(U1(a, c), U1(k, c))
26.81/8.77	   A^2 -> H(U1(a, c), U1(c, e))
26.81/8.77	   A^2 -> H(U1(a, c), U1(c, k))
26.81/8.77	   A^2 -> H(U1(a, c), U1(e, e))
26.81/8.77	   A^2 -> H(U1(a, c), U1(k, k))
26.81/8.77	   A^2 -> H(U1(a, c), U1(k, d))
26.81/8.77	   A^2 -> H(U1(a, c), U1(d, k))
26.81/8.77	   A^2 -> H(U1(a, d), U1(e, b))
26.81/8.77	   A^2 -> H(U1(a, d), U1(k, b))
26.81/8.77	   A^2 -> H(U1(a, d), U1(c, d))
26.81/8.77	   A^2 -> H(U1(a, d), U1(d, c))
26.81/8.77	   A^2 -> H(U1(a, d), U1(b, e))
26.81/8.77	   A^2 -> H(U1(a, d), U1(b, k))
26.81/8.77	   A^2 -> H(U1(a, d), U1(e, c))
26.81/8.77	   A^2 -> H(U1(a, d), U1(k, c))
26.81/8.77	   A^2 -> H(U1(a, d), U1(c, e))
26.81/8.77	   A^2 -> H(U1(a, d), U1(c, k))
26.81/8.77	   A^2 -> H(U1(a, d), U1(e, e))
26.81/8.77	   A^2 -> H(U1(a, d), U1(k, k))
26.81/8.77	   A^2 -> H(U1(a, d), U1(k, d))
26.81/8.77	   A^2 -> H(U1(a, d), U1(d, k))
26.81/8.77	   A^2 -> H(U1(a, a), b)
26.81/8.77	   A^2 -> H(U1(a, a), U1(e, d))
26.81/8.77	   A^2 -> H(U1(a, a), U1(d, e))
26.81/8.77	   A^2 -> H(U1(a, a), c)
26.81/8.77	   A^2 -> H(U1(a, a), U1(e, k))
26.81/8.77	   A^2 -> H(U1(a, a), U1(k, e))
26.81/8.77	   A^2 -> H(U1(a, a), e)
26.81/8.77	   A^2 -> H(U1(a, a), U1(k, k))
26.81/8.77	   A^2 -> H(k, f(b))
26.81/8.77	   A^2 -> H(c, U1(b, b))
26.81/8.77	   A^2 -> H(c, f(c))
26.81/8.77	   A^2 -> H(c, f(d))
26.81/8.77	   A^2 -> H(U1(e, k), U1(b, b))
26.81/8.77	   A^2 -> H(U1(e, k), f(c))
26.81/8.77	   A^2 -> H(U1(e, k), f(d))
26.81/8.77	   A^2 -> H(U1(e, c), U1(c, b))
26.81/8.77	   A^2 -> H(U1(e, c), U1(d, b))
26.81/8.77	   A^2 -> H(U1(e, c), U1(b, c))
26.81/8.77	   A^2 -> H(U1(e, c), U1(b, d))
26.81/8.77	   A^2 -> H(U1(e, c), U1(c, c))
26.81/8.77	   A^2 -> H(U1(e, c), f(e))
26.81/8.77	   A^2 -> H(U1(e, c), f(k))
26.81/8.77	   A^2 -> H(U1(e, c), U1(d, d))
26.81/8.77	   A^2 -> H(U1(k, e), U1(b, b))
26.81/8.77	   A^2 -> H(U1(k, e), f(c))
26.81/8.77	   A^2 -> H(U1(k, e), f(d))
26.81/8.77	   A^2 -> H(U1(k, c), U1(c, b))
26.81/8.77	   A^2 -> H(U1(k, c), U1(d, b))
26.81/8.77	   A^2 -> H(U1(k, c), U1(b, c))
26.81/8.77	   A^2 -> H(U1(k, c), U1(b, d))
26.81/8.77	   A^2 -> H(U1(k, c), U1(c, c))
26.81/8.77	   A^2 -> H(U1(k, c), f(e))
26.81/8.77	   A^2 -> H(U1(k, c), f(k))
26.81/8.77	   A^2 -> H(U1(k, c), U1(d, d))
26.81/8.77	   A^2 -> H(U1(c, e), U1(c, b))
26.81/8.77	   A^2 -> H(U1(c, e), U1(d, b))
26.81/8.77	   A^2 -> H(U1(c, e), U1(b, c))
26.81/8.77	   A^2 -> H(U1(c, e), U1(b, d))
26.81/8.77	   A^2 -> H(U1(c, e), U1(c, c))
26.81/8.77	   A^2 -> H(U1(c, e), f(e))
26.81/8.77	   A^2 -> H(U1(c, e), f(k))
26.81/8.77	   A^2 -> H(U1(c, e), U1(d, d))
26.81/8.77	   A^2 -> H(U1(c, k), U1(c, b))
26.81/8.77	   A^2 -> H(U1(c, k), U1(d, b))
26.81/8.77	   A^2 -> H(U1(c, k), U1(b, c))
26.81/8.77	   A^2 -> H(U1(c, k), U1(b, d))
26.81/8.77	   A^2 -> H(U1(c, k), U1(c, c))
26.81/8.77	   A^2 -> H(U1(c, k), f(e))
26.81/8.77	   A^2 -> H(U1(c, k), f(k))
26.81/8.77	   A^2 -> H(U1(c, k), U1(d, d))
26.81/8.77	   A^2 -> H(U1(c, c), U1(e, b))
26.81/8.77	   A^2 -> H(U1(c, c), U1(k, b))
26.81/8.77	   A^2 -> H(U1(c, c), U1(c, d))
26.81/8.77	   A^2 -> H(U1(c, c), U1(d, c))
26.81/8.77	   A^2 -> H(U1(c, c), U1(b, e))
26.81/8.77	   A^2 -> H(U1(c, c), U1(b, k))
26.81/8.77	   A^2 -> H(U1(c, c), U1(e, e))
26.81/8.77	   A^2 -> H(U1(c, c), U1(k, k))
26.81/8.77	   A^2 -> H(U1(c, c), U1(k, d))
26.81/8.77	   A^2 -> H(U1(c, c), U1(d, k))
26.81/8.77	   A^2 -> H(e, U1(b, b))
26.81/8.77	   A^2 -> H(e, f(c))
26.81/8.77	   A^2 -> H(e, f(d))
26.81/8.77	   A^2 -> H(U1(e, e), U1(c, b))
26.81/8.77	   A^2 -> H(U1(e, e), U1(d, b))
26.81/8.77	   A^2 -> H(U1(e, e), U1(b, c))
26.81/8.77	   A^2 -> H(U1(e, e), U1(b, d))
26.81/8.77	   A^2 -> H(U1(e, e), U1(c, c))
26.81/8.77	   A^2 -> H(U1(e, e), f(e))
26.81/8.77	   A^2 -> H(U1(e, e), f(k))
26.81/8.77	   A^2 -> H(U1(e, e), U1(d, d))
26.81/8.77	   A^2 -> H(f(e), U1(e, b))
26.81/8.77	   A^2 -> H(f(e), U1(k, b))
26.81/8.77	   A^2 -> H(f(e), U1(c, d))
26.81/8.77	   A^2 -> H(f(e), U1(d, c))
26.81/8.77	   A^2 -> H(f(e), U1(b, e))
26.81/8.77	   A^2 -> H(f(e), U1(b, k))
26.81/8.77	   A^2 -> H(f(e), U1(e, c))
26.81/8.77	   A^2 -> H(f(e), U1(k, c))
26.81/8.77	   A^2 -> H(f(e), U1(c, e))
26.81/8.77	   A^2 -> H(f(e), U1(c, k))
26.81/8.77	   A^2 -> H(f(e), U1(k, k))
26.81/8.77	   A^2 -> H(f(e), U1(k, d))
26.81/8.77	   A^2 -> H(f(e), U1(d, k))
26.81/8.77	   A^2 -> H(U1(k, k), U1(c, b))
26.81/8.77	   A^2 -> H(U1(k, k), U1(d, b))
26.81/8.77	   A^2 -> H(U1(k, k), U1(b, c))
26.81/8.77	   A^2 -> H(U1(k, k), U1(b, d))
26.81/8.77	   A^2 -> H(U1(k, k), U1(c, c))
26.81/8.77	   A^2 -> H(U1(k, k), f(e))
26.81/8.77	   A^2 -> H(U1(k, k), f(k))
26.81/8.77	   A^2 -> H(U1(k, k), U1(d, d))
26.81/8.77	   A^2 -> H(f(k), U1(e, b))
26.81/8.77	   A^2 -> H(f(k), U1(k, b))
26.81/8.77	   A^2 -> H(f(k), U1(c, d))
26.81/8.77	   A^2 -> H(f(k), U1(d, c))
26.81/8.77	   A^2 -> H(f(k), U1(b, e))
26.81/8.77	   A^2 -> H(f(k), U1(b, k))
26.81/8.77	   A^2 -> H(f(k), U1(e, c))
26.81/8.77	   A^2 -> H(f(k), U1(k, c))
26.81/8.77	   A^2 -> H(f(k), U1(c, e))
26.81/8.77	   A^2 -> H(f(k), U1(c, k))
26.81/8.77	   A^2 -> H(f(k), U1(e, e))
26.81/8.77	   A^2 -> H(f(k), U1(k, d))
26.81/8.77	   A^2 -> H(f(k), U1(d, k))
26.81/8.77	   A^2 -> H(f(c), b)
26.81/8.77	   A^2 -> H(f(c), U1(e, d))
26.81/8.77	   A^2 -> H(f(c), U1(d, e))
26.81/8.77	   A^2 -> H(f(k), U1(k, k))
26.81/8.77	   A^2 -> H(U1(k, k), U1(b, b))
26.81/8.77	   A^2 -> H(U1(k, k), f(c))
26.81/8.77	   A^2 -> H(U1(k, k), f(d))
26.81/8.77	   A^2 -> H(U1(k, d), U1(c, b))
26.81/8.77	   A^2 -> H(U1(k, d), U1(d, b))
26.81/8.77	   A^2 -> H(U1(k, d), U1(b, c))
26.81/8.77	   A^2 -> H(U1(k, d), U1(b, d))
26.81/8.77	   A^2 -> H(U1(k, d), U1(c, c))
26.81/8.77	   A^2 -> H(U1(k, d), f(e))
26.81/8.77	   A^2 -> H(U1(k, d), f(k))
26.81/8.77	   A^2 -> H(U1(k, d), U1(d, d))
26.81/8.77	   A^2 -> H(U1(d, k), U1(c, b))
26.81/8.77	   A^2 -> H(U1(d, k), U1(d, b))
26.81/8.77	   A^2 -> H(U1(d, k), U1(b, c))
26.81/8.77	   A^2 -> H(U1(d, k), U1(b, d))
26.81/8.77	   A^2 -> H(U1(d, k), U1(c, c))
26.81/8.77	   A^2 -> H(U1(d, k), f(e))
26.81/8.77	   A^2 -> H(U1(d, k), f(k))
26.81/8.77	   A^2 -> H(U1(d, k), U1(d, d))
26.81/8.77	   A^2 -> H(U1(d, d), U1(e, b))
26.81/8.77	   A^2 -> H(U1(d, d), U1(k, b))
26.81/8.77	   A^2 -> H(U1(d, d), U1(c, d))
26.81/8.77	   A^2 -> H(U1(d, d), U1(d, c))
26.81/8.77	   A^2 -> H(U1(d, d), U1(b, e))
26.81/8.77	   A^2 -> H(U1(d, d), U1(b, k))
26.81/8.77	   A^2 -> H(U1(d, d), U1(e, c))
26.81/8.77	   A^2 -> H(U1(d, d), U1(k, c))
26.81/8.77	   A^2 -> H(U1(d, d), U1(c, e))
26.81/8.77	   A^2 -> H(U1(d, d), U1(c, k))
26.81/8.77	   A^2 -> H(U1(d, d), U1(e, e))
26.81/8.77	   A^2 -> H(U1(d, d), U1(k, k))
26.81/8.77	   A^2 -> H(f(d), b)
26.81/8.77	   A^2 -> H(f(d), U1(e, d))
26.81/8.77	   A^2 -> H(f(d), U1(d, e))
26.81/8.77	   A^2 -> H(f(d), c)
26.81/8.77	   A^2 -> H(f(d), U1(e, k))
26.81/8.77	   A^2 -> H(f(d), U1(k, e))
26.81/8.77	   A^2 -> H(f(d), e)
26.81/8.77	   A^2 -> H(f(a), d)
26.81/8.77	   A^2 -> H(U1(c, c), U1(e, c))
26.81/8.77	   A^2 -> H(f(c), c)
26.81/8.77	   A^2 -> H(f(c), U1(e, k))
26.81/8.77	   A^2 -> H(U1(c, c), U1(k, c))
26.81/8.77	   A^2 -> H(f(c), U1(k, e))
26.81/8.77	   A^2 -> H(f(c), U1(k, k))
26.81/8.77	   A^2 -> H(U1(c, c), U1(c, e))
26.81/8.77	   A^2 -> H(U1(c, c), U1(c, k))
26.81/8.77	   A^2 -> H(f(a), k)
26.81/8.77	   A^2 -> H(f(e), U1(e, e))
26.81/8.77	   A^2 -> H(f(c), e)
26.81/8.77	   A^2 -> H(U1(d, d), U1(k, d))
26.81/8.77	   A^2 -> H(f(d), U1(k, k))
26.81/8.77	   A^2 -> H(U1(d, d), U1(d, k))
26.81/8.77	
26.81/8.77	The TRS R consists of the following rules:
26.81/8.77	
26.81/8.77	   f(x) -> U1(x, x)
26.81/8.77	   U1(e, x) -> x
26.81/8.77	   a -> c
26.81/8.77	   a -> d
26.81/8.77	   b -> c
26.81/8.77	   b -> d
26.81/8.77	   d -> k
26.81/8.77	   c -> e
26.81/8.77	   c -> k
26.81/8.77	
26.81/8.77	Q is empty.
26.81/8.77	We have to consider all minimal (P,Q,R)-chains.
26.81/8.77	----------------------------------------
26.81/8.77	
26.81/8.77	(539) TransformationProof (EQUIVALENT)
26.81/8.77	By narrowing [LPAR04] the rule A^2 -> H(f(a), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
26.81/8.77	
26.81/8.77	   (A^2 -> H(U1(a, a), U1(k, k)),A^2 -> H(U1(a, a), U1(k, k)))
26.81/8.77	   (A^2 -> H(f(c), U1(k, k)),A^2 -> H(f(c), U1(k, k)))
26.81/8.77	   (A^2 -> H(f(d), U1(k, k)),A^2 -> H(f(d), U1(k, k)))
26.81/8.77	
26.81/8.77	
26.81/8.77	----------------------------------------
26.81/8.77	
26.81/8.77	(540)
26.81/8.77	Obligation:
26.81/8.77	Q DP problem:
26.81/8.77	The TRS P consists of the following rules:
26.81/8.77	
26.81/8.77	   H(x, x) -> G(x, x, f(k))
26.81/8.77	   G(d, x, x) -> A^2
26.81/8.77	   A^2 -> H(f(c), f(c))
26.81/8.77	   A^2 -> H(f(d), f(d))
26.81/8.77	   A^2 -> H(U1(c, c), U1(c, c))
26.81/8.77	   A^2 -> H(f(e), f(e))
26.81/8.77	   A^2 -> H(f(k), f(k))
26.81/8.77	   A^2 -> H(U1(d, d), U1(d, d))
26.81/8.77	   A^2 -> H(d, f(b))
26.81/8.77	   A^2 -> H(a, U1(b, b))
26.81/8.77	   A^2 -> H(a, f(c))
26.81/8.77	   A^2 -> H(a, f(d))
26.81/8.77	   A^2 -> H(U1(e, d), U1(b, b))
26.81/8.77	   A^2 -> H(U1(e, d), f(c))
26.81/8.77	   A^2 -> H(U1(e, d), f(d))
26.81/8.77	   A^2 -> H(U1(e, a), U1(c, b))
26.81/8.77	   A^2 -> H(U1(e, a), U1(d, b))
26.81/8.77	   A^2 -> H(U1(e, a), U1(b, c))
26.81/8.77	   A^2 -> H(U1(e, a), U1(b, d))
26.81/8.77	   A^2 -> H(U1(e, a), U1(c, c))
26.81/8.77	   A^2 -> H(U1(e, a), f(e))
26.81/8.77	   A^2 -> H(U1(e, a), f(k))
26.81/8.77	   A^2 -> H(U1(e, a), U1(d, d))
26.81/8.77	   A^2 -> H(U1(k, a), U1(c, b))
26.81/8.77	   A^2 -> H(U1(k, a), U1(d, b))
26.81/8.77	   A^2 -> H(U1(k, a), U1(b, c))
26.81/8.77	   A^2 -> H(U1(k, a), U1(b, d))
26.81/8.77	   A^2 -> H(U1(k, a), U1(c, c))
26.81/8.77	   A^2 -> H(U1(k, a), f(e))
26.81/8.77	   A^2 -> H(U1(k, a), f(k))
26.81/8.77	   A^2 -> H(U1(k, a), U1(d, d))
26.81/8.77	   A^2 -> H(U1(c, d), U1(c, b))
26.81/8.77	   A^2 -> H(U1(c, d), U1(d, b))
26.81/8.77	   A^2 -> H(U1(c, d), U1(b, c))
26.81/8.77	   A^2 -> H(U1(c, d), U1(b, d))
26.81/8.77	   A^2 -> H(U1(c, d), U1(c, c))
26.81/8.77	   A^2 -> H(U1(c, d), f(e))
26.81/8.77	   A^2 -> H(U1(c, d), f(k))
26.81/8.77	   A^2 -> H(U1(c, d), U1(d, d))
26.81/8.77	   A^2 -> H(U1(c, a), U1(e, b))
26.81/8.77	   A^2 -> H(U1(c, a), U1(k, b))
26.81/8.77	   A^2 -> H(U1(c, a), U1(c, d))
26.81/8.77	   A^2 -> H(U1(c, a), U1(d, c))
26.81/8.77	   A^2 -> H(U1(c, a), U1(b, e))
26.81/8.77	   A^2 -> H(U1(c, a), U1(b, k))
26.81/8.77	   A^2 -> H(U1(c, a), U1(e, c))
26.81/8.77	   A^2 -> H(U1(c, a), U1(k, c))
26.81/8.77	   A^2 -> H(U1(c, a), U1(c, e))
26.81/8.77	   A^2 -> H(U1(c, a), U1(c, k))
26.81/8.77	   A^2 -> H(U1(c, a), U1(e, e))
26.81/8.77	   A^2 -> H(U1(c, a), U1(k, k))
26.81/8.77	   A^2 -> H(U1(c, a), U1(k, d))
26.81/8.77	   A^2 -> H(U1(c, a), U1(d, k))
26.81/8.77	   A^2 -> H(U1(d, e), U1(b, b))
26.81/8.77	   A^2 -> H(U1(d, e), f(c))
26.81/8.77	   A^2 -> H(U1(d, e), f(d))
26.81/8.77	   A^2 -> H(U1(d, c), U1(c, b))
26.81/8.77	   A^2 -> H(U1(d, c), U1(d, b))
26.81/8.77	   A^2 -> H(U1(d, c), U1(b, c))
26.81/8.77	   A^2 -> H(U1(d, c), U1(b, d))
26.81/8.77	   A^2 -> H(U1(d, c), U1(c, c))
26.81/8.77	   A^2 -> H(U1(d, c), f(e))
26.81/8.77	   A^2 -> H(U1(d, c), f(k))
26.81/8.77	   A^2 -> H(U1(d, c), U1(d, d))
26.81/8.77	   A^2 -> H(U1(d, a), U1(e, b))
26.81/8.77	   A^2 -> H(U1(d, a), U1(k, b))
26.81/8.77	   A^2 -> H(U1(d, a), U1(c, d))
26.81/8.77	   A^2 -> H(U1(d, a), U1(d, c))
26.81/8.77	   A^2 -> H(U1(d, a), U1(b, e))
26.81/8.77	   A^2 -> H(U1(d, a), U1(b, k))
26.81/8.77	   A^2 -> H(U1(d, a), U1(e, c))
26.81/8.77	   A^2 -> H(U1(d, a), U1(k, c))
26.81/8.77	   A^2 -> H(U1(d, a), U1(c, e))
26.81/8.77	   A^2 -> H(U1(d, a), U1(c, k))
26.81/8.77	   A^2 -> H(U1(d, a), U1(e, e))
26.81/8.77	   A^2 -> H(U1(d, a), U1(k, k))
26.81/8.77	   A^2 -> H(U1(d, a), U1(k, d))
26.81/8.77	   A^2 -> H(U1(d, a), U1(d, k))
26.81/8.77	   A^2 -> H(U1(a, e), U1(c, b))
26.81/8.77	   A^2 -> H(U1(a, e), U1(d, b))
26.81/8.77	   A^2 -> H(U1(a, e), U1(b, c))
26.81/8.77	   A^2 -> H(U1(a, e), U1(b, d))
26.81/8.77	   A^2 -> H(U1(a, e), U1(c, c))
26.81/8.77	   A^2 -> H(U1(a, e), f(e))
26.81/8.77	   A^2 -> H(U1(a, e), f(k))
26.81/8.77	   A^2 -> H(U1(a, e), U1(d, d))
26.81/8.77	   A^2 -> H(U1(a, k), U1(c, b))
26.81/8.77	   A^2 -> H(U1(a, k), U1(d, b))
26.81/8.77	   A^2 -> H(U1(a, k), U1(b, c))
26.81/8.77	   A^2 -> H(U1(a, k), U1(b, d))
26.81/8.77	   A^2 -> H(U1(a, k), U1(c, c))
26.81/8.77	   A^2 -> H(U1(a, k), f(e))
26.81/8.77	   A^2 -> H(U1(a, k), f(k))
26.81/8.77	   A^2 -> H(U1(a, k), U1(d, d))
26.81/8.77	   A^2 -> H(U1(a, c), U1(e, b))
26.81/8.77	   A^2 -> H(U1(a, c), U1(k, b))
26.81/8.77	   A^2 -> H(U1(a, c), U1(c, d))
26.81/8.77	   A^2 -> H(U1(a, c), U1(d, c))
26.81/8.77	   A^2 -> H(U1(a, c), U1(b, e))
26.81/8.77	   A^2 -> H(U1(a, c), U1(b, k))
26.81/8.77	   A^2 -> H(U1(a, c), U1(e, c))
26.81/8.77	   A^2 -> H(U1(a, c), U1(k, c))
26.81/8.77	   A^2 -> H(U1(a, c), U1(c, e))
26.81/8.77	   A^2 -> H(U1(a, c), U1(c, k))
26.81/8.77	   A^2 -> H(U1(a, c), U1(e, e))
26.81/8.77	   A^2 -> H(U1(a, c), U1(k, k))
26.81/8.77	   A^2 -> H(U1(a, c), U1(k, d))
26.81/8.77	   A^2 -> H(U1(a, c), U1(d, k))
26.81/8.77	   A^2 -> H(U1(a, d), U1(e, b))
26.81/8.77	   A^2 -> H(U1(a, d), U1(k, b))
26.81/8.77	   A^2 -> H(U1(a, d), U1(c, d))
26.81/8.77	   A^2 -> H(U1(a, d), U1(d, c))
26.81/8.77	   A^2 -> H(U1(a, d), U1(b, e))
26.81/8.77	   A^2 -> H(U1(a, d), U1(b, k))
26.81/8.77	   A^2 -> H(U1(a, d), U1(e, c))
26.81/8.77	   A^2 -> H(U1(a, d), U1(k, c))
26.81/8.77	   A^2 -> H(U1(a, d), U1(c, e))
26.81/8.77	   A^2 -> H(U1(a, d), U1(c, k))
26.81/8.77	   A^2 -> H(U1(a, d), U1(e, e))
26.81/8.77	   A^2 -> H(U1(a, d), U1(k, k))
26.81/8.77	   A^2 -> H(U1(a, d), U1(k, d))
26.81/8.77	   A^2 -> H(U1(a, d), U1(d, k))
26.81/8.77	   A^2 -> H(U1(a, a), b)
26.81/8.77	   A^2 -> H(U1(a, a), U1(e, d))
26.81/8.77	   A^2 -> H(U1(a, a), U1(d, e))
26.81/8.77	   A^2 -> H(U1(a, a), c)
26.81/8.77	   A^2 -> H(U1(a, a), U1(e, k))
26.81/8.77	   A^2 -> H(U1(a, a), U1(k, e))
26.81/8.77	   A^2 -> H(U1(a, a), e)
26.81/8.77	   A^2 -> H(U1(a, a), U1(k, k))
26.81/8.77	   A^2 -> H(k, f(b))
26.81/8.77	   A^2 -> H(c, U1(b, b))
26.81/8.77	   A^2 -> H(c, f(c))
26.81/8.77	   A^2 -> H(c, f(d))
26.81/8.77	   A^2 -> H(U1(e, k), U1(b, b))
26.81/8.77	   A^2 -> H(U1(e, k), f(c))
26.81/8.77	   A^2 -> H(U1(e, k), f(d))
26.81/8.77	   A^2 -> H(U1(e, c), U1(c, b))
26.81/8.77	   A^2 -> H(U1(e, c), U1(d, b))
26.81/8.77	   A^2 -> H(U1(e, c), U1(b, c))
26.81/8.77	   A^2 -> H(U1(e, c), U1(b, d))
26.81/8.77	   A^2 -> H(U1(e, c), U1(c, c))
26.81/8.77	   A^2 -> H(U1(e, c), f(e))
26.81/8.77	   A^2 -> H(U1(e, c), f(k))
26.81/8.77	   A^2 -> H(U1(e, c), U1(d, d))
26.81/8.77	   A^2 -> H(U1(k, e), U1(b, b))
26.81/8.77	   A^2 -> H(U1(k, e), f(c))
26.81/8.77	   A^2 -> H(U1(k, e), f(d))
26.81/8.77	   A^2 -> H(U1(k, c), U1(c, b))
26.81/8.77	   A^2 -> H(U1(k, c), U1(d, b))
26.81/8.77	   A^2 -> H(U1(k, c), U1(b, c))
26.81/8.77	   A^2 -> H(U1(k, c), U1(b, d))
26.81/8.77	   A^2 -> H(U1(k, c), U1(c, c))
26.81/8.77	   A^2 -> H(U1(k, c), f(e))
26.81/8.77	   A^2 -> H(U1(k, c), f(k))
26.81/8.77	   A^2 -> H(U1(k, c), U1(d, d))
26.81/8.77	   A^2 -> H(U1(c, e), U1(c, b))
26.81/8.77	   A^2 -> H(U1(c, e), U1(d, b))
26.81/8.77	   A^2 -> H(U1(c, e), U1(b, c))
26.81/8.77	   A^2 -> H(U1(c, e), U1(b, d))
26.81/8.77	   A^2 -> H(U1(c, e), U1(c, c))
26.81/8.77	   A^2 -> H(U1(c, e), f(e))
26.81/8.77	   A^2 -> H(U1(c, e), f(k))
26.81/8.77	   A^2 -> H(U1(c, e), U1(d, d))
26.81/8.77	   A^2 -> H(U1(c, k), U1(c, b))
26.81/8.77	   A^2 -> H(U1(c, k), U1(d, b))
26.81/8.77	   A^2 -> H(U1(c, k), U1(b, c))
26.81/8.77	   A^2 -> H(U1(c, k), U1(b, d))
26.81/8.77	   A^2 -> H(U1(c, k), U1(c, c))
26.81/8.77	   A^2 -> H(U1(c, k), f(e))
26.81/8.77	   A^2 -> H(U1(c, k), f(k))
26.81/8.77	   A^2 -> H(U1(c, k), U1(d, d))
26.81/8.77	   A^2 -> H(U1(c, c), U1(e, b))
26.81/8.77	   A^2 -> H(U1(c, c), U1(k, b))
26.81/8.77	   A^2 -> H(U1(c, c), U1(c, d))
26.81/8.77	   A^2 -> H(U1(c, c), U1(d, c))
26.81/8.77	   A^2 -> H(U1(c, c), U1(b, e))
26.81/8.77	   A^2 -> H(U1(c, c), U1(b, k))
26.81/8.77	   A^2 -> H(U1(c, c), U1(e, e))
26.81/8.77	   A^2 -> H(U1(c, c), U1(k, k))
26.81/8.77	   A^2 -> H(U1(c, c), U1(k, d))
26.81/8.77	   A^2 -> H(U1(c, c), U1(d, k))
26.81/8.77	   A^2 -> H(e, U1(b, b))
26.81/8.77	   A^2 -> H(e, f(c))
26.81/8.77	   A^2 -> H(e, f(d))
26.81/8.77	   A^2 -> H(U1(e, e), U1(c, b))
26.81/8.77	   A^2 -> H(U1(e, e), U1(d, b))
26.81/8.77	   A^2 -> H(U1(e, e), U1(b, c))
26.81/8.77	   A^2 -> H(U1(e, e), U1(b, d))
26.81/8.77	   A^2 -> H(U1(e, e), U1(c, c))
26.81/8.77	   A^2 -> H(U1(e, e), f(e))
26.81/8.77	   A^2 -> H(U1(e, e), f(k))
26.81/8.77	   A^2 -> H(U1(e, e), U1(d, d))
26.81/8.77	   A^2 -> H(f(e), U1(e, b))
26.81/8.77	   A^2 -> H(f(e), U1(k, b))
26.81/8.77	   A^2 -> H(f(e), U1(c, d))
26.81/8.77	   A^2 -> H(f(e), U1(d, c))
26.81/8.77	   A^2 -> H(f(e), U1(b, e))
26.81/8.77	   A^2 -> H(f(e), U1(b, k))
26.81/8.77	   A^2 -> H(f(e), U1(e, c))
26.81/8.77	   A^2 -> H(f(e), U1(k, c))
26.81/8.77	   A^2 -> H(f(e), U1(c, e))
26.81/8.77	   A^2 -> H(f(e), U1(c, k))
26.81/8.77	   A^2 -> H(f(e), U1(k, k))
26.81/8.77	   A^2 -> H(f(e), U1(k, d))
26.81/8.77	   A^2 -> H(f(e), U1(d, k))
26.81/8.77	   A^2 -> H(U1(k, k), U1(c, b))
26.81/8.77	   A^2 -> H(U1(k, k), U1(d, b))
26.81/8.77	   A^2 -> H(U1(k, k), U1(b, c))
26.81/8.77	   A^2 -> H(U1(k, k), U1(b, d))
26.81/8.77	   A^2 -> H(U1(k, k), U1(c, c))
26.81/8.77	   A^2 -> H(U1(k, k), f(e))
26.81/8.77	   A^2 -> H(U1(k, k), f(k))
26.81/8.77	   A^2 -> H(U1(k, k), U1(d, d))
26.81/8.77	   A^2 -> H(f(k), U1(e, b))
26.81/8.77	   A^2 -> H(f(k), U1(k, b))
26.81/8.77	   A^2 -> H(f(k), U1(c, d))
26.81/8.77	   A^2 -> H(f(k), U1(d, c))
26.81/8.77	   A^2 -> H(f(k), U1(b, e))
26.81/8.77	   A^2 -> H(f(k), U1(b, k))
26.81/8.77	   A^2 -> H(f(k), U1(e, c))
26.81/8.77	   A^2 -> H(f(k), U1(k, c))
26.81/8.77	   A^2 -> H(f(k), U1(c, e))
26.81/8.77	   A^2 -> H(f(k), U1(c, k))
26.81/8.77	   A^2 -> H(f(k), U1(e, e))
26.81/8.77	   A^2 -> H(f(k), U1(k, d))
26.81/8.77	   A^2 -> H(f(k), U1(d, k))
26.81/8.77	   A^2 -> H(f(c), b)
26.81/8.77	   A^2 -> H(f(c), U1(e, d))
26.81/8.77	   A^2 -> H(f(c), U1(d, e))
26.81/8.77	   A^2 -> H(f(k), U1(k, k))
26.81/8.77	   A^2 -> H(U1(k, k), U1(b, b))
26.81/8.77	   A^2 -> H(U1(k, k), f(c))
26.81/8.77	   A^2 -> H(U1(k, k), f(d))
26.81/8.77	   A^2 -> H(U1(k, d), U1(c, b))
26.81/8.77	   A^2 -> H(U1(k, d), U1(d, b))
26.81/8.77	   A^2 -> H(U1(k, d), U1(b, c))
26.81/8.77	   A^2 -> H(U1(k, d), U1(b, d))
26.81/8.77	   A^2 -> H(U1(k, d), U1(c, c))
26.81/8.77	   A^2 -> H(U1(k, d), f(e))
26.81/8.77	   A^2 -> H(U1(k, d), f(k))
26.81/8.77	   A^2 -> H(U1(k, d), U1(d, d))
26.81/8.77	   A^2 -> H(U1(d, k), U1(c, b))
26.81/8.77	   A^2 -> H(U1(d, k), U1(d, b))
26.81/8.77	   A^2 -> H(U1(d, k), U1(b, c))
26.81/8.77	   A^2 -> H(U1(d, k), U1(b, d))
26.81/8.77	   A^2 -> H(U1(d, k), U1(c, c))
26.81/8.77	   A^2 -> H(U1(d, k), f(e))
26.81/8.77	   A^2 -> H(U1(d, k), f(k))
26.81/8.77	   A^2 -> H(U1(d, k), U1(d, d))
26.81/8.77	   A^2 -> H(U1(d, d), U1(e, b))
26.81/8.77	   A^2 -> H(U1(d, d), U1(k, b))
26.81/8.77	   A^2 -> H(U1(d, d), U1(c, d))
26.81/8.77	   A^2 -> H(U1(d, d), U1(d, c))
26.81/8.77	   A^2 -> H(U1(d, d), U1(b, e))
26.81/8.77	   A^2 -> H(U1(d, d), U1(b, k))
26.81/8.77	   A^2 -> H(U1(d, d), U1(e, c))
26.81/8.77	   A^2 -> H(U1(d, d), U1(k, c))
26.81/8.77	   A^2 -> H(U1(d, d), U1(c, e))
26.81/8.77	   A^2 -> H(U1(d, d), U1(c, k))
26.81/8.77	   A^2 -> H(U1(d, d), U1(e, e))
26.81/8.77	   A^2 -> H(U1(d, d), U1(k, k))
26.81/8.77	   A^2 -> H(f(d), b)
26.81/8.77	   A^2 -> H(f(d), U1(e, d))
26.81/8.77	   A^2 -> H(f(d), U1(d, e))
26.81/8.77	   A^2 -> H(f(d), c)
26.81/8.77	   A^2 -> H(f(d), U1(e, k))
26.81/8.77	   A^2 -> H(f(d), U1(k, e))
26.81/8.77	   A^2 -> H(f(d), e)
26.81/8.77	   A^2 -> H(f(a), d)
26.81/8.77	   A^2 -> H(U1(c, c), U1(e, c))
26.81/8.77	   A^2 -> H(f(c), c)
26.81/8.77	   A^2 -> H(f(c), U1(e, k))
26.81/8.77	   A^2 -> H(U1(c, c), U1(k, c))
26.81/8.77	   A^2 -> H(f(c), U1(k, e))
26.81/8.77	   A^2 -> H(f(c), U1(k, k))
26.81/8.77	   A^2 -> H(U1(c, c), U1(c, e))
26.81/8.77	   A^2 -> H(U1(c, c), U1(c, k))
26.81/8.77	   A^2 -> H(f(a), k)
26.81/8.77	   A^2 -> H(f(e), U1(e, e))
26.81/8.77	   A^2 -> H(f(c), e)
26.81/8.77	   A^2 -> H(U1(d, d), U1(k, d))
26.81/8.77	   A^2 -> H(f(d), U1(k, k))
26.81/8.77	   A^2 -> H(U1(d, d), U1(d, k))
26.81/8.77	
26.81/8.77	The TRS R consists of the following rules:
26.81/8.77	
26.81/8.77	   f(x) -> U1(x, x)
26.81/8.77	   U1(e, x) -> x
26.81/8.77	   a -> c
26.81/8.77	   a -> d
26.81/8.77	   b -> c
26.81/8.77	   b -> d
26.81/8.77	   d -> k
26.81/8.77	   c -> e
26.81/8.77	   c -> k
26.81/8.77	
26.81/8.77	Q is empty.
26.81/8.77	We have to consider all minimal (P,Q,R)-chains.
26.81/8.77	----------------------------------------
26.81/8.77	
26.81/8.77	(541) TransformationProof (EQUIVALENT)
26.81/8.77	By narrowing [LPAR04] the rule A^2 -> H(d, f(b)) at position [] we obtained the following new rules [LPAR04]:
26.81/8.77	
26.81/8.77	   (A^2 -> H(k, f(b)),A^2 -> H(k, f(b)))
26.81/8.77	   (A^2 -> H(d, U1(b, b)),A^2 -> H(d, U1(b, b)))
26.81/8.77	   (A^2 -> H(d, f(c)),A^2 -> H(d, f(c)))
26.81/8.77	   (A^2 -> H(d, f(d)),A^2 -> H(d, f(d)))
26.81/8.77	
26.81/8.77	
26.81/8.77	----------------------------------------
26.81/8.77	
26.81/8.77	(542)
26.81/8.77	Obligation:
26.81/8.77	Q DP problem:
26.81/8.77	The TRS P consists of the following rules:
26.81/8.77	
26.81/8.77	   H(x, x) -> G(x, x, f(k))
26.81/8.77	   G(d, x, x) -> A^2
26.81/8.77	   A^2 -> H(f(c), f(c))
26.81/8.77	   A^2 -> H(f(d), f(d))
26.81/8.77	   A^2 -> H(U1(c, c), U1(c, c))
26.81/8.77	   A^2 -> H(f(e), f(e))
26.81/8.77	   A^2 -> H(f(k), f(k))
26.81/8.77	   A^2 -> H(U1(d, d), U1(d, d))
26.81/8.77	   A^2 -> H(a, U1(b, b))
26.81/8.77	   A^2 -> H(a, f(c))
26.81/8.77	   A^2 -> H(a, f(d))
26.81/8.77	   A^2 -> H(U1(e, d), U1(b, b))
26.81/8.77	   A^2 -> H(U1(e, d), f(c))
26.81/8.77	   A^2 -> H(U1(e, d), f(d))
26.81/8.77	   A^2 -> H(U1(e, a), U1(c, b))
26.81/8.77	   A^2 -> H(U1(e, a), U1(d, b))
26.81/8.77	   A^2 -> H(U1(e, a), U1(b, c))
26.81/8.77	   A^2 -> H(U1(e, a), U1(b, d))
26.81/8.77	   A^2 -> H(U1(e, a), U1(c, c))
26.81/8.77	   A^2 -> H(U1(e, a), f(e))
26.81/8.77	   A^2 -> H(U1(e, a), f(k))
26.81/8.77	   A^2 -> H(U1(e, a), U1(d, d))
26.81/8.77	   A^2 -> H(U1(k, a), U1(c, b))
26.81/8.77	   A^2 -> H(U1(k, a), U1(d, b))
26.81/8.77	   A^2 -> H(U1(k, a), U1(b, c))
26.81/8.77	   A^2 -> H(U1(k, a), U1(b, d))
26.81/8.77	   A^2 -> H(U1(k, a), U1(c, c))
26.81/8.77	   A^2 -> H(U1(k, a), f(e))
26.81/8.77	   A^2 -> H(U1(k, a), f(k))
26.81/8.77	   A^2 -> H(U1(k, a), U1(d, d))
26.81/8.77	   A^2 -> H(U1(c, d), U1(c, b))
26.81/8.77	   A^2 -> H(U1(c, d), U1(d, b))
26.81/8.77	   A^2 -> H(U1(c, d), U1(b, c))
26.81/8.77	   A^2 -> H(U1(c, d), U1(b, d))
26.81/8.77	   A^2 -> H(U1(c, d), U1(c, c))
26.81/8.77	   A^2 -> H(U1(c, d), f(e))
26.81/8.77	   A^2 -> H(U1(c, d), f(k))
26.81/8.77	   A^2 -> H(U1(c, d), U1(d, d))
26.81/8.77	   A^2 -> H(U1(c, a), U1(e, b))
26.81/8.77	   A^2 -> H(U1(c, a), U1(k, b))
26.81/8.77	   A^2 -> H(U1(c, a), U1(c, d))
26.81/8.77	   A^2 -> H(U1(c, a), U1(d, c))
26.81/8.77	   A^2 -> H(U1(c, a), U1(b, e))
26.81/8.77	   A^2 -> H(U1(c, a), U1(b, k))
26.81/8.77	   A^2 -> H(U1(c, a), U1(e, c))
26.81/8.77	   A^2 -> H(U1(c, a), U1(k, c))
26.81/8.77	   A^2 -> H(U1(c, a), U1(c, e))
26.81/8.77	   A^2 -> H(U1(c, a), U1(c, k))
26.81/8.77	   A^2 -> H(U1(c, a), U1(e, e))
26.81/8.77	   A^2 -> H(U1(c, a), U1(k, k))
26.81/8.77	   A^2 -> H(U1(c, a), U1(k, d))
26.81/8.77	   A^2 -> H(U1(c, a), U1(d, k))
26.81/8.77	   A^2 -> H(U1(d, e), U1(b, b))
26.81/8.77	   A^2 -> H(U1(d, e), f(c))
26.81/8.77	   A^2 -> H(U1(d, e), f(d))
26.81/8.77	   A^2 -> H(U1(d, c), U1(c, b))
26.81/8.77	   A^2 -> H(U1(d, c), U1(d, b))
26.81/8.77	   A^2 -> H(U1(d, c), U1(b, c))
26.81/8.77	   A^2 -> H(U1(d, c), U1(b, d))
26.81/8.77	   A^2 -> H(U1(d, c), U1(c, c))
26.81/8.77	   A^2 -> H(U1(d, c), f(e))
26.81/8.77	   A^2 -> H(U1(d, c), f(k))
26.81/8.77	   A^2 -> H(U1(d, c), U1(d, d))
26.81/8.77	   A^2 -> H(U1(d, a), U1(e, b))
26.81/8.77	   A^2 -> H(U1(d, a), U1(k, b))
26.81/8.77	   A^2 -> H(U1(d, a), U1(c, d))
26.81/8.77	   A^2 -> H(U1(d, a), U1(d, c))
26.81/8.77	   A^2 -> H(U1(d, a), U1(b, e))
26.81/8.77	   A^2 -> H(U1(d, a), U1(b, k))
26.81/8.77	   A^2 -> H(U1(d, a), U1(e, c))
26.81/8.77	   A^2 -> H(U1(d, a), U1(k, c))
26.81/8.77	   A^2 -> H(U1(d, a), U1(c, e))
26.81/8.77	   A^2 -> H(U1(d, a), U1(c, k))
26.81/8.77	   A^2 -> H(U1(d, a), U1(e, e))
26.81/8.77	   A^2 -> H(U1(d, a), U1(k, k))
26.81/8.77	   A^2 -> H(U1(d, a), U1(k, d))
26.81/8.77	   A^2 -> H(U1(d, a), U1(d, k))
26.81/8.77	   A^2 -> H(U1(a, e), U1(c, b))
26.81/8.77	   A^2 -> H(U1(a, e), U1(d, b))
26.81/8.77	   A^2 -> H(U1(a, e), U1(b, c))
26.81/8.77	   A^2 -> H(U1(a, e), U1(b, d))
26.81/8.77	   A^2 -> H(U1(a, e), U1(c, c))
26.81/8.77	   A^2 -> H(U1(a, e), f(e))
26.81/8.77	   A^2 -> H(U1(a, e), f(k))
26.81/8.77	   A^2 -> H(U1(a, e), U1(d, d))
26.81/8.77	   A^2 -> H(U1(a, k), U1(c, b))
26.81/8.77	   A^2 -> H(U1(a, k), U1(d, b))
26.81/8.77	   A^2 -> H(U1(a, k), U1(b, c))
26.81/8.77	   A^2 -> H(U1(a, k), U1(b, d))
26.81/8.77	   A^2 -> H(U1(a, k), U1(c, c))
26.81/8.77	   A^2 -> H(U1(a, k), f(e))
26.81/8.77	   A^2 -> H(U1(a, k), f(k))
26.81/8.77	   A^2 -> H(U1(a, k), U1(d, d))
26.81/8.77	   A^2 -> H(U1(a, c), U1(e, b))
26.81/8.77	   A^2 -> H(U1(a, c), U1(k, b))
26.81/8.77	   A^2 -> H(U1(a, c), U1(c, d))
26.81/8.77	   A^2 -> H(U1(a, c), U1(d, c))
26.81/8.77	   A^2 -> H(U1(a, c), U1(b, e))
26.81/8.77	   A^2 -> H(U1(a, c), U1(b, k))
26.81/8.77	   A^2 -> H(U1(a, c), U1(e, c))
26.81/8.77	   A^2 -> H(U1(a, c), U1(k, c))
26.81/8.77	   A^2 -> H(U1(a, c), U1(c, e))
26.81/8.77	   A^2 -> H(U1(a, c), U1(c, k))
26.81/8.77	   A^2 -> H(U1(a, c), U1(e, e))
26.81/8.77	   A^2 -> H(U1(a, c), U1(k, k))
26.81/8.77	   A^2 -> H(U1(a, c), U1(k, d))
26.81/8.77	   A^2 -> H(U1(a, c), U1(d, k))
26.81/8.77	   A^2 -> H(U1(a, d), U1(e, b))
26.81/8.77	   A^2 -> H(U1(a, d), U1(k, b))
26.81/8.77	   A^2 -> H(U1(a, d), U1(c, d))
26.81/8.77	   A^2 -> H(U1(a, d), U1(d, c))
26.81/8.77	   A^2 -> H(U1(a, d), U1(b, e))
26.81/8.77	   A^2 -> H(U1(a, d), U1(b, k))
26.81/8.77	   A^2 -> H(U1(a, d), U1(e, c))
26.81/8.77	   A^2 -> H(U1(a, d), U1(k, c))
26.81/8.77	   A^2 -> H(U1(a, d), U1(c, e))
26.81/8.77	   A^2 -> H(U1(a, d), U1(c, k))
26.81/8.77	   A^2 -> H(U1(a, d), U1(e, e))
26.81/8.77	   A^2 -> H(U1(a, d), U1(k, k))
26.81/8.77	   A^2 -> H(U1(a, d), U1(k, d))
26.81/8.77	   A^2 -> H(U1(a, d), U1(d, k))
26.81/8.77	   A^2 -> H(U1(a, a), b)
26.81/8.77	   A^2 -> H(U1(a, a), U1(e, d))
26.81/8.77	   A^2 -> H(U1(a, a), U1(d, e))
26.81/8.77	   A^2 -> H(U1(a, a), c)
26.81/8.77	   A^2 -> H(U1(a, a), U1(e, k))
26.81/8.77	   A^2 -> H(U1(a, a), U1(k, e))
26.81/8.77	   A^2 -> H(U1(a, a), e)
26.81/8.77	   A^2 -> H(U1(a, a), U1(k, k))
26.81/8.77	   A^2 -> H(k, f(b))
26.81/8.77	   A^2 -> H(c, U1(b, b))
26.81/8.77	   A^2 -> H(c, f(c))
26.81/8.77	   A^2 -> H(c, f(d))
26.81/8.77	   A^2 -> H(U1(e, k), U1(b, b))
26.81/8.77	   A^2 -> H(U1(e, k), f(c))
26.81/8.77	   A^2 -> H(U1(e, k), f(d))
26.81/8.78	   A^2 -> H(U1(e, c), U1(c, b))
26.81/8.78	   A^2 -> H(U1(e, c), U1(d, b))
26.81/8.78	   A^2 -> H(U1(e, c), U1(b, c))
26.81/8.78	   A^2 -> H(U1(e, c), U1(b, d))
26.81/8.78	   A^2 -> H(U1(e, c), U1(c, c))
26.81/8.78	   A^2 -> H(U1(e, c), f(e))
26.81/8.78	   A^2 -> H(U1(e, c), f(k))
26.81/8.78	   A^2 -> H(U1(e, c), U1(d, d))
26.81/8.78	   A^2 -> H(U1(k, e), U1(b, b))
26.81/8.78	   A^2 -> H(U1(k, e), f(c))
26.81/8.78	   A^2 -> H(U1(k, e), f(d))
26.81/8.78	   A^2 -> H(U1(k, c), U1(c, b))
26.81/8.78	   A^2 -> H(U1(k, c), U1(d, b))
26.81/8.78	   A^2 -> H(U1(k, c), U1(b, c))
26.81/8.78	   A^2 -> H(U1(k, c), U1(b, d))
26.81/8.78	   A^2 -> H(U1(k, c), U1(c, c))
26.81/8.78	   A^2 -> H(U1(k, c), f(e))
26.81/8.78	   A^2 -> H(U1(k, c), f(k))
26.81/8.78	   A^2 -> H(U1(k, c), U1(d, d))
26.81/8.78	   A^2 -> H(U1(c, e), U1(c, b))
26.81/8.78	   A^2 -> H(U1(c, e), U1(d, b))
26.81/8.78	   A^2 -> H(U1(c, e), U1(b, c))
26.81/8.78	   A^2 -> H(U1(c, e), U1(b, d))
26.81/8.78	   A^2 -> H(U1(c, e), U1(c, c))
26.81/8.78	   A^2 -> H(U1(c, e), f(e))
26.81/8.78	   A^2 -> H(U1(c, e), f(k))
26.81/8.78	   A^2 -> H(U1(c, e), U1(d, d))
26.81/8.78	   A^2 -> H(U1(c, k), U1(c, b))
26.81/8.78	   A^2 -> H(U1(c, k), U1(d, b))
26.81/8.78	   A^2 -> H(U1(c, k), U1(b, c))
26.81/8.78	   A^2 -> H(U1(c, k), U1(b, d))
26.81/8.78	   A^2 -> H(U1(c, k), U1(c, c))
26.81/8.78	   A^2 -> H(U1(c, k), f(e))
26.81/8.78	   A^2 -> H(U1(c, k), f(k))
26.81/8.78	   A^2 -> H(U1(c, k), U1(d, d))
26.81/8.78	   A^2 -> H(U1(c, c), U1(e, b))
26.81/8.78	   A^2 -> H(U1(c, c), U1(k, b))
26.81/8.78	   A^2 -> H(U1(c, c), U1(c, d))
26.81/8.78	   A^2 -> H(U1(c, c), U1(d, c))
26.81/8.78	   A^2 -> H(U1(c, c), U1(b, e))
26.81/8.78	   A^2 -> H(U1(c, c), U1(b, k))
26.81/8.78	   A^2 -> H(U1(c, c), U1(e, e))
26.81/8.78	   A^2 -> H(U1(c, c), U1(k, k))
26.81/8.78	   A^2 -> H(U1(c, c), U1(k, d))
26.81/8.78	   A^2 -> H(U1(c, c), U1(d, k))
26.81/8.78	   A^2 -> H(e, U1(b, b))
26.81/8.78	   A^2 -> H(e, f(c))
26.81/8.78	   A^2 -> H(e, f(d))
26.81/8.78	   A^2 -> H(U1(e, e), U1(c, b))
26.81/8.78	   A^2 -> H(U1(e, e), U1(d, b))
26.81/8.78	   A^2 -> H(U1(e, e), U1(b, c))
26.81/8.78	   A^2 -> H(U1(e, e), U1(b, d))
26.81/8.78	   A^2 -> H(U1(e, e), U1(c, c))
26.81/8.78	   A^2 -> H(U1(e, e), f(e))
26.81/8.78	   A^2 -> H(U1(e, e), f(k))
26.81/8.78	   A^2 -> H(U1(e, e), U1(d, d))
26.81/8.78	   A^2 -> H(f(e), U1(e, b))
26.81/8.78	   A^2 -> H(f(e), U1(k, b))
26.81/8.78	   A^2 -> H(f(e), U1(c, d))
26.81/8.78	   A^2 -> H(f(e), U1(d, c))
26.81/8.78	   A^2 -> H(f(e), U1(b, e))
26.81/8.78	   A^2 -> H(f(e), U1(b, k))
26.81/8.78	   A^2 -> H(f(e), U1(e, c))
26.81/8.78	   A^2 -> H(f(e), U1(k, c))
26.81/8.78	   A^2 -> H(f(e), U1(c, e))
26.81/8.78	   A^2 -> H(f(e), U1(c, k))
26.81/8.78	   A^2 -> H(f(e), U1(k, k))
26.81/8.78	   A^2 -> H(f(e), U1(k, d))
26.81/8.78	   A^2 -> H(f(e), U1(d, k))
26.81/8.78	   A^2 -> H(U1(k, k), U1(c, b))
26.81/8.78	   A^2 -> H(U1(k, k), U1(d, b))
26.81/8.78	   A^2 -> H(U1(k, k), U1(b, c))
26.81/8.78	   A^2 -> H(U1(k, k), U1(b, d))
26.81/8.78	   A^2 -> H(U1(k, k), U1(c, c))
26.81/8.78	   A^2 -> H(U1(k, k), f(e))
26.81/8.78	   A^2 -> H(U1(k, k), f(k))
26.81/8.78	   A^2 -> H(U1(k, k), U1(d, d))
26.81/8.78	   A^2 -> H(f(k), U1(e, b))
26.81/8.78	   A^2 -> H(f(k), U1(k, b))
26.81/8.78	   A^2 -> H(f(k), U1(c, d))
26.81/8.78	   A^2 -> H(f(k), U1(d, c))
26.81/8.78	   A^2 -> H(f(k), U1(b, e))
26.81/8.78	   A^2 -> H(f(k), U1(b, k))
26.81/8.78	   A^2 -> H(f(k), U1(e, c))
26.81/8.78	   A^2 -> H(f(k), U1(k, c))
26.81/8.78	   A^2 -> H(f(k), U1(c, e))
26.81/8.78	   A^2 -> H(f(k), U1(c, k))
26.81/8.78	   A^2 -> H(f(k), U1(e, e))
26.81/8.78	   A^2 -> H(f(k), U1(k, d))
26.81/8.78	   A^2 -> H(f(k), U1(d, k))
26.81/8.78	   A^2 -> H(f(c), b)
26.81/8.78	   A^2 -> H(f(c), U1(e, d))
26.81/8.78	   A^2 -> H(f(c), U1(d, e))
26.81/8.78	   A^2 -> H(f(k), U1(k, k))
26.81/8.78	   A^2 -> H(U1(k, k), U1(b, b))
26.81/8.78	   A^2 -> H(U1(k, k), f(c))
26.81/8.78	   A^2 -> H(U1(k, k), f(d))
26.81/8.78	   A^2 -> H(U1(k, d), U1(c, b))
26.81/8.78	   A^2 -> H(U1(k, d), U1(d, b))
26.81/8.78	   A^2 -> H(U1(k, d), U1(b, c))
26.81/8.78	   A^2 -> H(U1(k, d), U1(b, d))
26.81/8.78	   A^2 -> H(U1(k, d), U1(c, c))
26.81/8.78	   A^2 -> H(U1(k, d), f(e))
26.81/8.78	   A^2 -> H(U1(k, d), f(k))
26.81/8.78	   A^2 -> H(U1(k, d), U1(d, d))
26.81/8.78	   A^2 -> H(U1(d, k), U1(c, b))
26.81/8.78	   A^2 -> H(U1(d, k), U1(d, b))
26.81/8.78	   A^2 -> H(U1(d, k), U1(b, c))
26.81/8.78	   A^2 -> H(U1(d, k), U1(b, d))
26.81/8.78	   A^2 -> H(U1(d, k), U1(c, c))
26.81/8.78	   A^2 -> H(U1(d, k), f(e))
26.81/8.78	   A^2 -> H(U1(d, k), f(k))
26.81/8.78	   A^2 -> H(U1(d, k), U1(d, d))
26.81/8.78	   A^2 -> H(U1(d, d), U1(e, b))
26.81/8.78	   A^2 -> H(U1(d, d), U1(k, b))
26.81/8.78	   A^2 -> H(U1(d, d), U1(c, d))
26.81/8.78	   A^2 -> H(U1(d, d), U1(d, c))
26.81/8.78	   A^2 -> H(U1(d, d), U1(b, e))
26.81/8.78	   A^2 -> H(U1(d, d), U1(b, k))
26.81/8.78	   A^2 -> H(U1(d, d), U1(e, c))
26.81/8.78	   A^2 -> H(U1(d, d), U1(k, c))
26.81/8.78	   A^2 -> H(U1(d, d), U1(c, e))
26.81/8.78	   A^2 -> H(U1(d, d), U1(c, k))
26.81/8.78	   A^2 -> H(U1(d, d), U1(e, e))
26.81/8.78	   A^2 -> H(U1(d, d), U1(k, k))
26.81/8.78	   A^2 -> H(f(d), b)
26.81/8.78	   A^2 -> H(f(d), U1(e, d))
26.81/8.78	   A^2 -> H(f(d), U1(d, e))
26.81/8.78	   A^2 -> H(f(d), c)
26.81/8.78	   A^2 -> H(f(d), U1(e, k))
26.81/8.78	   A^2 -> H(f(d), U1(k, e))
26.81/8.78	   A^2 -> H(f(d), e)
26.81/8.78	   A^2 -> H(f(a), d)
26.81/8.78	   A^2 -> H(U1(c, c), U1(e, c))
26.81/8.78	   A^2 -> H(f(c), c)
26.81/8.78	   A^2 -> H(f(c), U1(e, k))
26.81/8.78	   A^2 -> H(U1(c, c), U1(k, c))
26.81/8.78	   A^2 -> H(f(c), U1(k, e))
26.81/8.78	   A^2 -> H(f(c), U1(k, k))
26.81/8.78	   A^2 -> H(U1(c, c), U1(c, e))
26.81/8.78	   A^2 -> H(U1(c, c), U1(c, k))
26.81/8.78	   A^2 -> H(f(a), k)
26.81/8.78	   A^2 -> H(f(e), U1(e, e))
26.81/8.78	   A^2 -> H(f(c), e)
26.81/8.78	   A^2 -> H(U1(d, d), U1(k, d))
26.81/8.78	   A^2 -> H(f(d), U1(k, k))
26.81/8.78	   A^2 -> H(U1(d, d), U1(d, k))
26.81/8.78	   A^2 -> H(d, U1(b, b))
26.81/8.78	   A^2 -> H(d, f(c))
26.81/8.78	   A^2 -> H(d, f(d))
26.81/8.78	
26.81/8.78	The TRS R consists of the following rules:
26.81/8.78	
26.81/8.78	   f(x) -> U1(x, x)
26.81/8.78	   U1(e, x) -> x
26.81/8.78	   a -> c
26.81/8.78	   a -> d
26.81/8.78	   b -> c
26.81/8.78	   b -> d
26.81/8.78	   d -> k
26.81/8.78	   c -> e
26.81/8.78	   c -> k
26.81/8.78	
26.81/8.78	Q is empty.
26.81/8.78	We have to consider all minimal (P,Q,R)-chains.
26.81/8.78	----------------------------------------
26.81/8.78	
26.81/8.78	(543) TransformationProof (EQUIVALENT)
26.81/8.78	By narrowing [LPAR04] the rule A^2 -> H(a, U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
26.81/8.78	
26.81/8.78	   (A^2 -> H(c, U1(b, b)),A^2 -> H(c, U1(b, b)))
26.81/8.78	   (A^2 -> H(d, U1(b, b)),A^2 -> H(d, U1(b, b)))
26.81/8.78	   (A^2 -> H(a, U1(c, b)),A^2 -> H(a, U1(c, b)))
26.81/8.78	   (A^2 -> H(a, U1(d, b)),A^2 -> H(a, U1(d, b)))
26.81/8.78	   (A^2 -> H(a, U1(b, c)),A^2 -> H(a, U1(b, c)))
26.81/8.78	   (A^2 -> H(a, U1(b, d)),A^2 -> H(a, U1(b, d)))
26.81/8.78	
26.81/8.78	
26.81/8.78	----------------------------------------
26.81/8.78	
26.81/8.78	(544)
26.81/8.78	Obligation:
26.81/8.78	Q DP problem:
26.81/8.78	The TRS P consists of the following rules:
26.81/8.78	
26.81/8.78	   H(x, x) -> G(x, x, f(k))
26.81/8.78	   G(d, x, x) -> A^2
26.81/8.78	   A^2 -> H(f(c), f(c))
26.81/8.78	   A^2 -> H(f(d), f(d))
26.81/8.78	   A^2 -> H(U1(c, c), U1(c, c))
26.81/8.78	   A^2 -> H(f(e), f(e))
26.81/8.78	   A^2 -> H(f(k), f(k))
26.81/8.78	   A^2 -> H(U1(d, d), U1(d, d))
26.81/8.78	   A^2 -> H(a, f(c))
26.81/8.78	   A^2 -> H(a, f(d))
26.81/8.78	   A^2 -> H(U1(e, d), U1(b, b))
26.81/8.78	   A^2 -> H(U1(e, d), f(c))
26.81/8.78	   A^2 -> H(U1(e, d), f(d))
26.81/8.78	   A^2 -> H(U1(e, a), U1(c, b))
26.81/8.78	   A^2 -> H(U1(e, a), U1(d, b))
26.81/8.78	   A^2 -> H(U1(e, a), U1(b, c))
26.81/8.78	   A^2 -> H(U1(e, a), U1(b, d))
26.81/8.78	   A^2 -> H(U1(e, a), U1(c, c))
26.81/8.78	   A^2 -> H(U1(e, a), f(e))
26.81/8.78	   A^2 -> H(U1(e, a), f(k))
26.81/8.78	   A^2 -> H(U1(e, a), U1(d, d))
26.81/8.78	   A^2 -> H(U1(k, a), U1(c, b))
26.81/8.78	   A^2 -> H(U1(k, a), U1(d, b))
26.81/8.78	   A^2 -> H(U1(k, a), U1(b, c))
26.81/8.78	   A^2 -> H(U1(k, a), U1(b, d))
26.81/8.78	   A^2 -> H(U1(k, a), U1(c, c))
26.81/8.78	   A^2 -> H(U1(k, a), f(e))
26.81/8.78	   A^2 -> H(U1(k, a), f(k))
26.81/8.78	   A^2 -> H(U1(k, a), U1(d, d))
26.81/8.78	   A^2 -> H(U1(c, d), U1(c, b))
26.81/8.78	   A^2 -> H(U1(c, d), U1(d, b))
26.81/8.78	   A^2 -> H(U1(c, d), U1(b, c))
26.81/8.78	   A^2 -> H(U1(c, d), U1(b, d))
26.81/8.78	   A^2 -> H(U1(c, d), U1(c, c))
26.81/8.78	   A^2 -> H(U1(c, d), f(e))
26.81/8.78	   A^2 -> H(U1(c, d), f(k))
26.81/8.78	   A^2 -> H(U1(c, d), U1(d, d))
26.81/8.78	   A^2 -> H(U1(c, a), U1(e, b))
26.81/8.78	   A^2 -> H(U1(c, a), U1(k, b))
26.81/8.78	   A^2 -> H(U1(c, a), U1(c, d))
26.81/8.78	   A^2 -> H(U1(c, a), U1(d, c))
26.81/8.78	   A^2 -> H(U1(c, a), U1(b, e))
26.81/8.78	   A^2 -> H(U1(c, a), U1(b, k))
26.81/8.78	   A^2 -> H(U1(c, a), U1(e, c))
26.81/8.78	   A^2 -> H(U1(c, a), U1(k, c))
26.81/8.78	   A^2 -> H(U1(c, a), U1(c, e))
26.81/8.78	   A^2 -> H(U1(c, a), U1(c, k))
26.81/8.78	   A^2 -> H(U1(c, a), U1(e, e))
26.81/8.78	   A^2 -> H(U1(c, a), U1(k, k))
26.81/8.78	   A^2 -> H(U1(c, a), U1(k, d))
26.81/8.78	   A^2 -> H(U1(c, a), U1(d, k))
26.81/8.78	   A^2 -> H(U1(d, e), U1(b, b))
26.81/8.78	   A^2 -> H(U1(d, e), f(c))
26.81/8.78	   A^2 -> H(U1(d, e), f(d))
26.81/8.78	   A^2 -> H(U1(d, c), U1(c, b))
26.81/8.78	   A^2 -> H(U1(d, c), U1(d, b))
26.81/8.78	   A^2 -> H(U1(d, c), U1(b, c))
26.81/8.78	   A^2 -> H(U1(d, c), U1(b, d))
26.81/8.78	   A^2 -> H(U1(d, c), U1(c, c))
26.81/8.78	   A^2 -> H(U1(d, c), f(e))
26.81/8.78	   A^2 -> H(U1(d, c), f(k))
26.81/8.78	   A^2 -> H(U1(d, c), U1(d, d))
26.81/8.78	   A^2 -> H(U1(d, a), U1(e, b))
26.81/8.78	   A^2 -> H(U1(d, a), U1(k, b))
26.81/8.78	   A^2 -> H(U1(d, a), U1(c, d))
26.81/8.78	   A^2 -> H(U1(d, a), U1(d, c))
26.81/8.78	   A^2 -> H(U1(d, a), U1(b, e))
26.81/8.78	   A^2 -> H(U1(d, a), U1(b, k))
26.81/8.78	   A^2 -> H(U1(d, a), U1(e, c))
26.81/8.78	   A^2 -> H(U1(d, a), U1(k, c))
26.81/8.78	   A^2 -> H(U1(d, a), U1(c, e))
26.81/8.78	   A^2 -> H(U1(d, a), U1(c, k))
26.81/8.78	   A^2 -> H(U1(d, a), U1(e, e))
26.81/8.78	   A^2 -> H(U1(d, a), U1(k, k))
26.81/8.78	   A^2 -> H(U1(d, a), U1(k, d))
26.81/8.78	   A^2 -> H(U1(d, a), U1(d, k))
26.81/8.78	   A^2 -> H(U1(a, e), U1(c, b))
26.81/8.78	   A^2 -> H(U1(a, e), U1(d, b))
26.81/8.78	   A^2 -> H(U1(a, e), U1(b, c))
26.81/8.78	   A^2 -> H(U1(a, e), U1(b, d))
26.81/8.78	   A^2 -> H(U1(a, e), U1(c, c))
26.81/8.78	   A^2 -> H(U1(a, e), f(e))
26.81/8.78	   A^2 -> H(U1(a, e), f(k))
26.81/8.78	   A^2 -> H(U1(a, e), U1(d, d))
26.81/8.78	   A^2 -> H(U1(a, k), U1(c, b))
26.81/8.78	   A^2 -> H(U1(a, k), U1(d, b))
26.81/8.78	   A^2 -> H(U1(a, k), U1(b, c))
26.81/8.78	   A^2 -> H(U1(a, k), U1(b, d))
26.81/8.78	   A^2 -> H(U1(a, k), U1(c, c))
26.81/8.78	   A^2 -> H(U1(a, k), f(e))
26.81/8.78	   A^2 -> H(U1(a, k), f(k))
26.81/8.78	   A^2 -> H(U1(a, k), U1(d, d))
26.81/8.78	   A^2 -> H(U1(a, c), U1(e, b))
26.81/8.78	   A^2 -> H(U1(a, c), U1(k, b))
26.81/8.78	   A^2 -> H(U1(a, c), U1(c, d))
26.81/8.78	   A^2 -> H(U1(a, c), U1(d, c))
26.81/8.78	   A^2 -> H(U1(a, c), U1(b, e))
26.81/8.78	   A^2 -> H(U1(a, c), U1(b, k))
26.81/8.78	   A^2 -> H(U1(a, c), U1(e, c))
26.81/8.78	   A^2 -> H(U1(a, c), U1(k, c))
26.81/8.78	   A^2 -> H(U1(a, c), U1(c, e))
26.81/8.78	   A^2 -> H(U1(a, c), U1(c, k))
26.81/8.78	   A^2 -> H(U1(a, c), U1(e, e))
26.81/8.78	   A^2 -> H(U1(a, c), U1(k, k))
26.81/8.78	   A^2 -> H(U1(a, c), U1(k, d))
26.81/8.78	   A^2 -> H(U1(a, c), U1(d, k))
26.81/8.78	   A^2 -> H(U1(a, d), U1(e, b))
26.81/8.78	   A^2 -> H(U1(a, d), U1(k, b))
26.81/8.78	   A^2 -> H(U1(a, d), U1(c, d))
26.81/8.78	   A^2 -> H(U1(a, d), U1(d, c))
26.81/8.78	   A^2 -> H(U1(a, d), U1(b, e))
26.81/8.78	   A^2 -> H(U1(a, d), U1(b, k))
26.81/8.78	   A^2 -> H(U1(a, d), U1(e, c))
26.81/8.78	   A^2 -> H(U1(a, d), U1(k, c))
26.81/8.78	   A^2 -> H(U1(a, d), U1(c, e))
26.81/8.78	   A^2 -> H(U1(a, d), U1(c, k))
26.81/8.78	   A^2 -> H(U1(a, d), U1(e, e))
26.81/8.78	   A^2 -> H(U1(a, d), U1(k, k))
26.81/8.78	   A^2 -> H(U1(a, d), U1(k, d))
26.81/8.78	   A^2 -> H(U1(a, d), U1(d, k))
26.81/8.78	   A^2 -> H(U1(a, a), b)
26.81/8.78	   A^2 -> H(U1(a, a), U1(e, d))
26.81/8.78	   A^2 -> H(U1(a, a), U1(d, e))
26.81/8.78	   A^2 -> H(U1(a, a), c)
26.81/8.78	   A^2 -> H(U1(a, a), U1(e, k))
26.81/8.78	   A^2 -> H(U1(a, a), U1(k, e))
26.81/8.78	   A^2 -> H(U1(a, a), e)
26.81/8.78	   A^2 -> H(U1(a, a), U1(k, k))
26.81/8.78	   A^2 -> H(k, f(b))
26.81/8.78	   A^2 -> H(c, U1(b, b))
26.81/8.78	   A^2 -> H(c, f(c))
26.81/8.78	   A^2 -> H(c, f(d))
26.81/8.78	   A^2 -> H(U1(e, k), U1(b, b))
26.81/8.78	   A^2 -> H(U1(e, k), f(c))
26.81/8.78	   A^2 -> H(U1(e, k), f(d))
26.81/8.78	   A^2 -> H(U1(e, c), U1(c, b))
26.81/8.78	   A^2 -> H(U1(e, c), U1(d, b))
26.81/8.78	   A^2 -> H(U1(e, c), U1(b, c))
26.81/8.78	   A^2 -> H(U1(e, c), U1(b, d))
26.81/8.78	   A^2 -> H(U1(e, c), U1(c, c))
26.81/8.78	   A^2 -> H(U1(e, c), f(e))
26.81/8.78	   A^2 -> H(U1(e, c), f(k))
26.81/8.78	   A^2 -> H(U1(e, c), U1(d, d))
26.81/8.78	   A^2 -> H(U1(k, e), U1(b, b))
26.81/8.78	   A^2 -> H(U1(k, e), f(c))
26.81/8.78	   A^2 -> H(U1(k, e), f(d))
26.81/8.78	   A^2 -> H(U1(k, c), U1(c, b))
26.81/8.78	   A^2 -> H(U1(k, c), U1(d, b))
26.81/8.78	   A^2 -> H(U1(k, c), U1(b, c))
26.81/8.78	   A^2 -> H(U1(k, c), U1(b, d))
26.81/8.78	   A^2 -> H(U1(k, c), U1(c, c))
26.81/8.78	   A^2 -> H(U1(k, c), f(e))
26.81/8.78	   A^2 -> H(U1(k, c), f(k))
26.81/8.78	   A^2 -> H(U1(k, c), U1(d, d))
26.81/8.78	   A^2 -> H(U1(c, e), U1(c, b))
26.81/8.78	   A^2 -> H(U1(c, e), U1(d, b))
26.81/8.78	   A^2 -> H(U1(c, e), U1(b, c))
26.81/8.78	   A^2 -> H(U1(c, e), U1(b, d))
26.81/8.78	   A^2 -> H(U1(c, e), U1(c, c))
26.81/8.78	   A^2 -> H(U1(c, e), f(e))
26.81/8.78	   A^2 -> H(U1(c, e), f(k))
26.81/8.78	   A^2 -> H(U1(c, e), U1(d, d))
26.81/8.78	   A^2 -> H(U1(c, k), U1(c, b))
26.81/8.78	   A^2 -> H(U1(c, k), U1(d, b))
26.81/8.78	   A^2 -> H(U1(c, k), U1(b, c))
26.81/8.78	   A^2 -> H(U1(c, k), U1(b, d))
26.81/8.78	   A^2 -> H(U1(c, k), U1(c, c))
26.81/8.78	   A^2 -> H(U1(c, k), f(e))
26.81/8.78	   A^2 -> H(U1(c, k), f(k))
26.81/8.78	   A^2 -> H(U1(c, k), U1(d, d))
26.81/8.78	   A^2 -> H(U1(c, c), U1(e, b))
26.81/8.78	   A^2 -> H(U1(c, c), U1(k, b))
26.81/8.78	   A^2 -> H(U1(c, c), U1(c, d))
26.81/8.78	   A^2 -> H(U1(c, c), U1(d, c))
26.81/8.78	   A^2 -> H(U1(c, c), U1(b, e))
26.81/8.78	   A^2 -> H(U1(c, c), U1(b, k))
26.81/8.78	   A^2 -> H(U1(c, c), U1(e, e))
26.81/8.78	   A^2 -> H(U1(c, c), U1(k, k))
26.81/8.78	   A^2 -> H(U1(c, c), U1(k, d))
26.81/8.78	   A^2 -> H(U1(c, c), U1(d, k))
26.81/8.78	   A^2 -> H(e, U1(b, b))
26.81/8.78	   A^2 -> H(e, f(c))
26.81/8.78	   A^2 -> H(e, f(d))
26.81/8.78	   A^2 -> H(U1(e, e), U1(c, b))
26.81/8.78	   A^2 -> H(U1(e, e), U1(d, b))
26.81/8.78	   A^2 -> H(U1(e, e), U1(b, c))
26.81/8.78	   A^2 -> H(U1(e, e), U1(b, d))
26.81/8.78	   A^2 -> H(U1(e, e), U1(c, c))
26.81/8.78	   A^2 -> H(U1(e, e), f(e))
26.81/8.78	   A^2 -> H(U1(e, e), f(k))
26.81/8.78	   A^2 -> H(U1(e, e), U1(d, d))
26.81/8.78	   A^2 -> H(f(e), U1(e, b))
26.81/8.78	   A^2 -> H(f(e), U1(k, b))
26.81/8.78	   A^2 -> H(f(e), U1(c, d))
26.81/8.78	   A^2 -> H(f(e), U1(d, c))
26.81/8.78	   A^2 -> H(f(e), U1(b, e))
26.81/8.78	   A^2 -> H(f(e), U1(b, k))
26.81/8.78	   A^2 -> H(f(e), U1(e, c))
26.81/8.78	   A^2 -> H(f(e), U1(k, c))
26.81/8.78	   A^2 -> H(f(e), U1(c, e))
26.81/8.78	   A^2 -> H(f(e), U1(c, k))
26.81/8.78	   A^2 -> H(f(e), U1(k, k))
26.81/8.78	   A^2 -> H(f(e), U1(k, d))
26.81/8.78	   A^2 -> H(f(e), U1(d, k))
26.81/8.78	   A^2 -> H(U1(k, k), U1(c, b))
26.81/8.78	   A^2 -> H(U1(k, k), U1(d, b))
26.81/8.78	   A^2 -> H(U1(k, k), U1(b, c))
26.81/8.78	   A^2 -> H(U1(k, k), U1(b, d))
26.81/8.78	   A^2 -> H(U1(k, k), U1(c, c))
26.81/8.78	   A^2 -> H(U1(k, k), f(e))
26.81/8.78	   A^2 -> H(U1(k, k), f(k))
26.81/8.78	   A^2 -> H(U1(k, k), U1(d, d))
26.81/8.78	   A^2 -> H(f(k), U1(e, b))
26.81/8.78	   A^2 -> H(f(k), U1(k, b))
26.81/8.78	   A^2 -> H(f(k), U1(c, d))
26.81/8.78	   A^2 -> H(f(k), U1(d, c))
26.81/8.78	   A^2 -> H(f(k), U1(b, e))
26.81/8.78	   A^2 -> H(f(k), U1(b, k))
26.81/8.78	   A^2 -> H(f(k), U1(e, c))
26.81/8.78	   A^2 -> H(f(k), U1(k, c))
26.81/8.78	   A^2 -> H(f(k), U1(c, e))
26.81/8.78	   A^2 -> H(f(k), U1(c, k))
26.81/8.78	   A^2 -> H(f(k), U1(e, e))
26.81/8.78	   A^2 -> H(f(k), U1(k, d))
26.81/8.78	   A^2 -> H(f(k), U1(d, k))
26.81/8.78	   A^2 -> H(f(c), b)
26.81/8.78	   A^2 -> H(f(c), U1(e, d))
26.81/8.78	   A^2 -> H(f(c), U1(d, e))
26.81/8.78	   A^2 -> H(f(k), U1(k, k))
26.81/8.78	   A^2 -> H(U1(k, k), U1(b, b))
26.81/8.78	   A^2 -> H(U1(k, k), f(c))
26.81/8.78	   A^2 -> H(U1(k, k), f(d))
26.81/8.78	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.78	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.78	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.78	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.78	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.78	   A^2 -> H(U1(k, d), f(e))
26.98/8.78	   A^2 -> H(U1(k, d), f(k))
26.98/8.78	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.78	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.78	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.78	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.78	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.78	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.78	   A^2 -> H(U1(d, k), f(e))
26.98/8.78	   A^2 -> H(U1(d, k), f(k))
26.98/8.78	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.78	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.78	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.78	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.78	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.78	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.78	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.78	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.78	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.78	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.78	   A^2 -> H(f(d), b)
26.98/8.78	   A^2 -> H(f(d), U1(e, d))
26.98/8.78	   A^2 -> H(f(d), U1(d, e))
26.98/8.78	   A^2 -> H(f(d), c)
26.98/8.78	   A^2 -> H(f(d), U1(e, k))
26.98/8.78	   A^2 -> H(f(d), U1(k, e))
26.98/8.78	   A^2 -> H(f(d), e)
26.98/8.78	   A^2 -> H(f(a), d)
26.98/8.78	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.78	   A^2 -> H(f(c), c)
26.98/8.78	   A^2 -> H(f(c), U1(e, k))
26.98/8.78	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.78	   A^2 -> H(f(c), U1(k, e))
26.98/8.78	   A^2 -> H(f(c), U1(k, k))
26.98/8.78	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.78	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.78	   A^2 -> H(f(a), k)
26.98/8.78	   A^2 -> H(f(e), U1(e, e))
26.98/8.78	   A^2 -> H(f(c), e)
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.78	   A^2 -> H(f(d), U1(k, k))
26.98/8.78	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.78	   A^2 -> H(d, U1(b, b))
26.98/8.78	   A^2 -> H(d, f(c))
26.98/8.78	   A^2 -> H(d, f(d))
26.98/8.78	   A^2 -> H(a, U1(c, b))
26.98/8.78	   A^2 -> H(a, U1(d, b))
26.98/8.78	   A^2 -> H(a, U1(b, c))
26.98/8.78	   A^2 -> H(a, U1(b, d))
26.98/8.78	
26.98/8.78	The TRS R consists of the following rules:
26.98/8.78	
26.98/8.78	   f(x) -> U1(x, x)
26.98/8.78	   U1(e, x) -> x
26.98/8.78	   a -> c
26.98/8.78	   a -> d
26.98/8.78	   b -> c
26.98/8.78	   b -> d
26.98/8.78	   d -> k
26.98/8.78	   c -> e
26.98/8.78	   c -> k
26.98/8.78	
26.98/8.78	Q is empty.
26.98/8.78	We have to consider all minimal (P,Q,R)-chains.
26.98/8.78	----------------------------------------
26.98/8.78	
26.98/8.78	(545) TransformationProof (EQUIVALENT)
26.98/8.78	By narrowing [LPAR04] the rule A^2 -> H(a, f(c)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.78	
26.98/8.78	   (A^2 -> H(c, f(c)),A^2 -> H(c, f(c)))
26.98/8.78	   (A^2 -> H(d, f(c)),A^2 -> H(d, f(c)))
26.98/8.78	   (A^2 -> H(a, U1(c, c)),A^2 -> H(a, U1(c, c)))
26.98/8.78	   (A^2 -> H(a, f(e)),A^2 -> H(a, f(e)))
26.98/8.78	   (A^2 -> H(a, f(k)),A^2 -> H(a, f(k)))
26.98/8.78	
26.98/8.78	
26.98/8.78	----------------------------------------
26.98/8.78	
26.98/8.78	(546)
26.98/8.78	Obligation:
26.98/8.78	Q DP problem:
26.98/8.78	The TRS P consists of the following rules:
26.98/8.78	
26.98/8.78	   H(x, x) -> G(x, x, f(k))
26.98/8.78	   G(d, x, x) -> A^2
26.98/8.78	   A^2 -> H(f(c), f(c))
26.98/8.78	   A^2 -> H(f(d), f(d))
26.98/8.78	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.78	   A^2 -> H(f(e), f(e))
26.98/8.78	   A^2 -> H(f(k), f(k))
26.98/8.78	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.78	   A^2 -> H(a, f(d))
26.98/8.78	   A^2 -> H(U1(e, d), U1(b, b))
26.98/8.78	   A^2 -> H(U1(e, d), f(c))
26.98/8.78	   A^2 -> H(U1(e, d), f(d))
26.98/8.78	   A^2 -> H(U1(e, a), U1(c, b))
26.98/8.78	   A^2 -> H(U1(e, a), U1(d, b))
26.98/8.78	   A^2 -> H(U1(e, a), U1(b, c))
26.98/8.78	   A^2 -> H(U1(e, a), U1(b, d))
26.98/8.78	   A^2 -> H(U1(e, a), U1(c, c))
26.98/8.78	   A^2 -> H(U1(e, a), f(e))
26.98/8.78	   A^2 -> H(U1(e, a), f(k))
26.98/8.78	   A^2 -> H(U1(e, a), U1(d, d))
26.98/8.78	   A^2 -> H(U1(k, a), U1(c, b))
26.98/8.78	   A^2 -> H(U1(k, a), U1(d, b))
26.98/8.78	   A^2 -> H(U1(k, a), U1(b, c))
26.98/8.78	   A^2 -> H(U1(k, a), U1(b, d))
26.98/8.78	   A^2 -> H(U1(k, a), U1(c, c))
26.98/8.78	   A^2 -> H(U1(k, a), f(e))
26.98/8.78	   A^2 -> H(U1(k, a), f(k))
26.98/8.78	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.78	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.78	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.78	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.78	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.78	   A^2 -> H(U1(c, d), f(e))
26.98/8.78	   A^2 -> H(U1(c, d), f(k))
26.98/8.78	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.78	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.78	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.78	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.78	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.78	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.78	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.78	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.78	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.78	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.78	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.78	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.78	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.78	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.78	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.78	   A^2 -> H(U1(d, e), f(c))
26.98/8.78	   A^2 -> H(U1(d, e), f(d))
26.98/8.78	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.78	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.78	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.78	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.78	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.78	   A^2 -> H(U1(d, c), f(e))
26.98/8.78	   A^2 -> H(U1(d, c), f(k))
26.98/8.78	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.78	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.78	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.78	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.78	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.78	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.78	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.78	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.78	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.78	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.78	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.78	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.78	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.78	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.78	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.78	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.78	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.78	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.78	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.78	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.78	   A^2 -> H(U1(a, e), f(e))
26.98/8.78	   A^2 -> H(U1(a, e), f(k))
26.98/8.78	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.78	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.78	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.78	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.78	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.78	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.78	   A^2 -> H(U1(a, k), f(e))
26.98/8.78	   A^2 -> H(U1(a, k), f(k))
26.98/8.78	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.78	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.78	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.78	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.78	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.78	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.78	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.78	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.78	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.78	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.78	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.78	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.78	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.78	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.78	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.78	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.78	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.78	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.78	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.78	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.78	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.78	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.78	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.78	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.78	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.78	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.78	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.78	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.78	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.78	   A^2 -> H(U1(a, a), b)
26.98/8.78	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.78	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.78	   A^2 -> H(U1(a, a), c)
26.98/8.78	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.78	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.78	   A^2 -> H(U1(a, a), e)
26.98/8.78	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.78	   A^2 -> H(k, f(b))
26.98/8.78	   A^2 -> H(c, U1(b, b))
26.98/8.78	   A^2 -> H(c, f(c))
26.98/8.78	   A^2 -> H(c, f(d))
26.98/8.78	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.78	   A^2 -> H(U1(e, k), f(c))
26.98/8.78	   A^2 -> H(U1(e, k), f(d))
26.98/8.78	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.78	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.78	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.78	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.78	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.78	   A^2 -> H(U1(e, c), f(e))
26.98/8.78	   A^2 -> H(U1(e, c), f(k))
26.98/8.78	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.78	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.78	   A^2 -> H(U1(k, e), f(c))
26.98/8.78	   A^2 -> H(U1(k, e), f(d))
26.98/8.78	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.78	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.78	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.78	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.78	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.78	   A^2 -> H(U1(k, c), f(e))
26.98/8.78	   A^2 -> H(U1(k, c), f(k))
26.98/8.78	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.78	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.78	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.78	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.78	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.78	   A^2 -> H(U1(c, e), f(e))
26.98/8.78	   A^2 -> H(U1(c, e), f(k))
26.98/8.78	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.78	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.78	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.78	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.78	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.78	   A^2 -> H(U1(c, k), f(e))
26.98/8.78	   A^2 -> H(U1(c, k), f(k))
26.98/8.78	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.78	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.78	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.78	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.78	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.78	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.78	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.78	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.78	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.78	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.78	   A^2 -> H(e, U1(b, b))
26.98/8.78	   A^2 -> H(e, f(c))
26.98/8.78	   A^2 -> H(e, f(d))
26.98/8.78	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.78	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.78	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.78	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.78	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.78	   A^2 -> H(U1(e, e), f(e))
26.98/8.78	   A^2 -> H(U1(e, e), f(k))
26.98/8.78	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.78	   A^2 -> H(f(e), U1(e, b))
26.98/8.78	   A^2 -> H(f(e), U1(k, b))
26.98/8.78	   A^2 -> H(f(e), U1(c, d))
26.98/8.78	   A^2 -> H(f(e), U1(d, c))
26.98/8.78	   A^2 -> H(f(e), U1(b, e))
26.98/8.78	   A^2 -> H(f(e), U1(b, k))
26.98/8.78	   A^2 -> H(f(e), U1(e, c))
26.98/8.78	   A^2 -> H(f(e), U1(k, c))
26.98/8.78	   A^2 -> H(f(e), U1(c, e))
26.98/8.78	   A^2 -> H(f(e), U1(c, k))
26.98/8.78	   A^2 -> H(f(e), U1(k, k))
26.98/8.78	   A^2 -> H(f(e), U1(k, d))
26.98/8.78	   A^2 -> H(f(e), U1(d, k))
26.98/8.78	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.78	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.78	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.78	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.78	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.78	   A^2 -> H(U1(k, k), f(e))
26.98/8.78	   A^2 -> H(U1(k, k), f(k))
26.98/8.78	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.78	   A^2 -> H(f(k), U1(e, b))
26.98/8.78	   A^2 -> H(f(k), U1(k, b))
26.98/8.78	   A^2 -> H(f(k), U1(c, d))
26.98/8.78	   A^2 -> H(f(k), U1(d, c))
26.98/8.78	   A^2 -> H(f(k), U1(b, e))
26.98/8.78	   A^2 -> H(f(k), U1(b, k))
26.98/8.78	   A^2 -> H(f(k), U1(e, c))
26.98/8.78	   A^2 -> H(f(k), U1(k, c))
26.98/8.78	   A^2 -> H(f(k), U1(c, e))
26.98/8.78	   A^2 -> H(f(k), U1(c, k))
26.98/8.78	   A^2 -> H(f(k), U1(e, e))
26.98/8.78	   A^2 -> H(f(k), U1(k, d))
26.98/8.78	   A^2 -> H(f(k), U1(d, k))
26.98/8.78	   A^2 -> H(f(c), b)
26.98/8.78	   A^2 -> H(f(c), U1(e, d))
26.98/8.78	   A^2 -> H(f(c), U1(d, e))
26.98/8.78	   A^2 -> H(f(k), U1(k, k))
26.98/8.78	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.78	   A^2 -> H(U1(k, k), f(c))
26.98/8.78	   A^2 -> H(U1(k, k), f(d))
26.98/8.78	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.78	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.78	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.78	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.78	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.78	   A^2 -> H(U1(k, d), f(e))
26.98/8.78	   A^2 -> H(U1(k, d), f(k))
26.98/8.78	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.78	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.78	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.78	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.78	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.78	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.78	   A^2 -> H(U1(d, k), f(e))
26.98/8.78	   A^2 -> H(U1(d, k), f(k))
26.98/8.78	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.78	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.78	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.78	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.78	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.78	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.78	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.78	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.78	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.78	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.78	   A^2 -> H(f(d), b)
26.98/8.78	   A^2 -> H(f(d), U1(e, d))
26.98/8.78	   A^2 -> H(f(d), U1(d, e))
26.98/8.78	   A^2 -> H(f(d), c)
26.98/8.78	   A^2 -> H(f(d), U1(e, k))
26.98/8.78	   A^2 -> H(f(d), U1(k, e))
26.98/8.78	   A^2 -> H(f(d), e)
26.98/8.78	   A^2 -> H(f(a), d)
26.98/8.78	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.78	   A^2 -> H(f(c), c)
26.98/8.78	   A^2 -> H(f(c), U1(e, k))
26.98/8.78	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.78	   A^2 -> H(f(c), U1(k, e))
26.98/8.78	   A^2 -> H(f(c), U1(k, k))
26.98/8.78	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.78	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.78	   A^2 -> H(f(a), k)
26.98/8.78	   A^2 -> H(f(e), U1(e, e))
26.98/8.78	   A^2 -> H(f(c), e)
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.78	   A^2 -> H(f(d), U1(k, k))
26.98/8.78	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.78	   A^2 -> H(d, U1(b, b))
26.98/8.78	   A^2 -> H(d, f(c))
26.98/8.78	   A^2 -> H(d, f(d))
26.98/8.78	   A^2 -> H(a, U1(c, b))
26.98/8.78	   A^2 -> H(a, U1(d, b))
26.98/8.78	   A^2 -> H(a, U1(b, c))
26.98/8.78	   A^2 -> H(a, U1(b, d))
26.98/8.78	   A^2 -> H(a, U1(c, c))
26.98/8.78	   A^2 -> H(a, f(e))
26.98/8.78	   A^2 -> H(a, f(k))
26.98/8.78	
26.98/8.78	The TRS R consists of the following rules:
26.98/8.78	
26.98/8.78	   f(x) -> U1(x, x)
26.98/8.78	   U1(e, x) -> x
26.98/8.78	   a -> c
26.98/8.78	   a -> d
26.98/8.78	   b -> c
26.98/8.78	   b -> d
26.98/8.78	   d -> k
26.98/8.78	   c -> e
26.98/8.78	   c -> k
26.98/8.78	
26.98/8.78	Q is empty.
26.98/8.78	We have to consider all minimal (P,Q,R)-chains.
26.98/8.78	----------------------------------------
26.98/8.78	
26.98/8.78	(547) TransformationProof (EQUIVALENT)
26.98/8.78	By narrowing [LPAR04] the rule A^2 -> H(a, f(d)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.78	
26.98/8.78	   (A^2 -> H(c, f(d)),A^2 -> H(c, f(d)))
26.98/8.78	   (A^2 -> H(d, f(d)),A^2 -> H(d, f(d)))
26.98/8.78	   (A^2 -> H(a, U1(d, d)),A^2 -> H(a, U1(d, d)))
26.98/8.78	   (A^2 -> H(a, f(k)),A^2 -> H(a, f(k)))
26.98/8.78	
26.98/8.78	
26.98/8.78	----------------------------------------
26.98/8.78	
26.98/8.78	(548)
26.98/8.78	Obligation:
26.98/8.78	Q DP problem:
26.98/8.78	The TRS P consists of the following rules:
26.98/8.78	
26.98/8.78	   H(x, x) -> G(x, x, f(k))
26.98/8.78	   G(d, x, x) -> A^2
26.98/8.78	   A^2 -> H(f(c), f(c))
26.98/8.78	   A^2 -> H(f(d), f(d))
26.98/8.78	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.78	   A^2 -> H(f(e), f(e))
26.98/8.78	   A^2 -> H(f(k), f(k))
26.98/8.78	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.78	   A^2 -> H(U1(e, d), U1(b, b))
26.98/8.78	   A^2 -> H(U1(e, d), f(c))
26.98/8.78	   A^2 -> H(U1(e, d), f(d))
26.98/8.78	   A^2 -> H(U1(e, a), U1(c, b))
26.98/8.78	   A^2 -> H(U1(e, a), U1(d, b))
26.98/8.78	   A^2 -> H(U1(e, a), U1(b, c))
26.98/8.78	   A^2 -> H(U1(e, a), U1(b, d))
26.98/8.78	   A^2 -> H(U1(e, a), U1(c, c))
26.98/8.78	   A^2 -> H(U1(e, a), f(e))
26.98/8.78	   A^2 -> H(U1(e, a), f(k))
26.98/8.78	   A^2 -> H(U1(e, a), U1(d, d))
26.98/8.78	   A^2 -> H(U1(k, a), U1(c, b))
26.98/8.78	   A^2 -> H(U1(k, a), U1(d, b))
26.98/8.78	   A^2 -> H(U1(k, a), U1(b, c))
26.98/8.78	   A^2 -> H(U1(k, a), U1(b, d))
26.98/8.78	   A^2 -> H(U1(k, a), U1(c, c))
26.98/8.78	   A^2 -> H(U1(k, a), f(e))
26.98/8.78	   A^2 -> H(U1(k, a), f(k))
26.98/8.78	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.78	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.78	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.78	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.78	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.78	   A^2 -> H(U1(c, d), f(e))
26.98/8.78	   A^2 -> H(U1(c, d), f(k))
26.98/8.78	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.78	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.78	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.78	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.78	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.78	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.78	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.78	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.78	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.78	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.78	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.78	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.78	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.78	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.78	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.78	   A^2 -> H(U1(d, e), f(c))
26.98/8.78	   A^2 -> H(U1(d, e), f(d))
26.98/8.78	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.78	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.78	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.78	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.78	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.78	   A^2 -> H(U1(d, c), f(e))
26.98/8.78	   A^2 -> H(U1(d, c), f(k))
26.98/8.78	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.78	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.78	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.78	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.78	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.78	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.78	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.78	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.78	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.78	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.78	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.78	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.78	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.78	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.78	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.78	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.78	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.78	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.78	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.78	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.78	   A^2 -> H(U1(a, e), f(e))
26.98/8.78	   A^2 -> H(U1(a, e), f(k))
26.98/8.78	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.78	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.78	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.78	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.78	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.78	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.78	   A^2 -> H(U1(a, k), f(e))
26.98/8.78	   A^2 -> H(U1(a, k), f(k))
26.98/8.78	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.78	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.78	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.78	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.78	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.78	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.78	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.78	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.78	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.78	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.78	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.78	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.78	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.78	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.78	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.78	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.78	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.78	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.78	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.78	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.78	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.78	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.78	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.78	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.78	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.78	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.78	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.78	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.78	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.78	   A^2 -> H(U1(a, a), b)
26.98/8.78	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.78	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.78	   A^2 -> H(U1(a, a), c)
26.98/8.78	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.78	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.78	   A^2 -> H(U1(a, a), e)
26.98/8.78	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.78	   A^2 -> H(k, f(b))
26.98/8.78	   A^2 -> H(c, U1(b, b))
26.98/8.78	   A^2 -> H(c, f(c))
26.98/8.78	   A^2 -> H(c, f(d))
26.98/8.78	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.78	   A^2 -> H(U1(e, k), f(c))
26.98/8.78	   A^2 -> H(U1(e, k), f(d))
26.98/8.78	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.78	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.78	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.78	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.78	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.78	   A^2 -> H(U1(e, c), f(e))
26.98/8.78	   A^2 -> H(U1(e, c), f(k))
26.98/8.78	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.78	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.78	   A^2 -> H(U1(k, e), f(c))
26.98/8.78	   A^2 -> H(U1(k, e), f(d))
26.98/8.78	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.78	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.78	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.78	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.78	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.78	   A^2 -> H(U1(k, c), f(e))
26.98/8.78	   A^2 -> H(U1(k, c), f(k))
26.98/8.78	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.78	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.78	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.78	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.78	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.78	   A^2 -> H(U1(c, e), f(e))
26.98/8.78	   A^2 -> H(U1(c, e), f(k))
26.98/8.78	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.78	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.78	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.78	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.78	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.78	   A^2 -> H(U1(c, k), f(e))
26.98/8.78	   A^2 -> H(U1(c, k), f(k))
26.98/8.78	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.78	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.78	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.78	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.78	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.78	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.78	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.78	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.78	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.78	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.78	   A^2 -> H(e, U1(b, b))
26.98/8.78	   A^2 -> H(e, f(c))
26.98/8.78	   A^2 -> H(e, f(d))
26.98/8.78	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.78	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.78	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.78	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.78	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.78	   A^2 -> H(U1(e, e), f(e))
26.98/8.78	   A^2 -> H(U1(e, e), f(k))
26.98/8.78	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.78	   A^2 -> H(f(e), U1(e, b))
26.98/8.78	   A^2 -> H(f(e), U1(k, b))
26.98/8.78	   A^2 -> H(f(e), U1(c, d))
26.98/8.78	   A^2 -> H(f(e), U1(d, c))
26.98/8.78	   A^2 -> H(f(e), U1(b, e))
26.98/8.78	   A^2 -> H(f(e), U1(b, k))
26.98/8.78	   A^2 -> H(f(e), U1(e, c))
26.98/8.78	   A^2 -> H(f(e), U1(k, c))
26.98/8.78	   A^2 -> H(f(e), U1(c, e))
26.98/8.78	   A^2 -> H(f(e), U1(c, k))
26.98/8.78	   A^2 -> H(f(e), U1(k, k))
26.98/8.78	   A^2 -> H(f(e), U1(k, d))
26.98/8.78	   A^2 -> H(f(e), U1(d, k))
26.98/8.78	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.78	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.78	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.78	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.78	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.78	   A^2 -> H(U1(k, k), f(e))
26.98/8.78	   A^2 -> H(U1(k, k), f(k))
26.98/8.78	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.78	   A^2 -> H(f(k), U1(e, b))
26.98/8.78	   A^2 -> H(f(k), U1(k, b))
26.98/8.78	   A^2 -> H(f(k), U1(c, d))
26.98/8.78	   A^2 -> H(f(k), U1(d, c))
26.98/8.78	   A^2 -> H(f(k), U1(b, e))
26.98/8.78	   A^2 -> H(f(k), U1(b, k))
26.98/8.78	   A^2 -> H(f(k), U1(e, c))
26.98/8.78	   A^2 -> H(f(k), U1(k, c))
26.98/8.78	   A^2 -> H(f(k), U1(c, e))
26.98/8.78	   A^2 -> H(f(k), U1(c, k))
26.98/8.78	   A^2 -> H(f(k), U1(e, e))
26.98/8.78	   A^2 -> H(f(k), U1(k, d))
26.98/8.78	   A^2 -> H(f(k), U1(d, k))
26.98/8.78	   A^2 -> H(f(c), b)
26.98/8.78	   A^2 -> H(f(c), U1(e, d))
26.98/8.78	   A^2 -> H(f(c), U1(d, e))
26.98/8.78	   A^2 -> H(f(k), U1(k, k))
26.98/8.78	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.78	   A^2 -> H(U1(k, k), f(c))
26.98/8.78	   A^2 -> H(U1(k, k), f(d))
26.98/8.78	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.78	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.78	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.78	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.78	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.78	   A^2 -> H(U1(k, d), f(e))
26.98/8.78	   A^2 -> H(U1(k, d), f(k))
26.98/8.78	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.78	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.78	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.78	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.78	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.78	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.78	   A^2 -> H(U1(d, k), f(e))
26.98/8.78	   A^2 -> H(U1(d, k), f(k))
26.98/8.78	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.78	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.78	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.78	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.78	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.78	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.78	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.78	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.78	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.78	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.78	   A^2 -> H(f(d), b)
26.98/8.78	   A^2 -> H(f(d), U1(e, d))
26.98/8.78	   A^2 -> H(f(d), U1(d, e))
26.98/8.78	   A^2 -> H(f(d), c)
26.98/8.78	   A^2 -> H(f(d), U1(e, k))
26.98/8.78	   A^2 -> H(f(d), U1(k, e))
26.98/8.78	   A^2 -> H(f(d), e)
26.98/8.78	   A^2 -> H(f(a), d)
26.98/8.78	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.78	   A^2 -> H(f(c), c)
26.98/8.78	   A^2 -> H(f(c), U1(e, k))
26.98/8.78	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.78	   A^2 -> H(f(c), U1(k, e))
26.98/8.78	   A^2 -> H(f(c), U1(k, k))
26.98/8.78	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.78	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.78	   A^2 -> H(f(a), k)
26.98/8.78	   A^2 -> H(f(e), U1(e, e))
26.98/8.78	   A^2 -> H(f(c), e)
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.78	   A^2 -> H(f(d), U1(k, k))
26.98/8.78	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.78	   A^2 -> H(d, U1(b, b))
26.98/8.78	   A^2 -> H(d, f(c))
26.98/8.78	   A^2 -> H(d, f(d))
26.98/8.78	   A^2 -> H(a, U1(c, b))
26.98/8.78	   A^2 -> H(a, U1(d, b))
26.98/8.78	   A^2 -> H(a, U1(b, c))
26.98/8.78	   A^2 -> H(a, U1(b, d))
26.98/8.78	   A^2 -> H(a, U1(c, c))
26.98/8.78	   A^2 -> H(a, f(e))
26.98/8.78	   A^2 -> H(a, f(k))
26.98/8.78	   A^2 -> H(a, U1(d, d))
26.98/8.78	
26.98/8.78	The TRS R consists of the following rules:
26.98/8.78	
26.98/8.78	   f(x) -> U1(x, x)
26.98/8.78	   U1(e, x) -> x
26.98/8.78	   a -> c
26.98/8.78	   a -> d
26.98/8.78	   b -> c
26.98/8.78	   b -> d
26.98/8.78	   d -> k
26.98/8.78	   c -> e
26.98/8.78	   c -> k
26.98/8.78	
26.98/8.78	Q is empty.
26.98/8.78	We have to consider all minimal (P,Q,R)-chains.
26.98/8.78	----------------------------------------
26.98/8.78	
26.98/8.78	(549) TransformationProof (EQUIVALENT)
26.98/8.78	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.78	
26.98/8.78	   (A^2 -> H(d, U1(b, b)),A^2 -> H(d, U1(b, b)))
26.98/8.78	   (A^2 -> H(U1(e, k), U1(b, b)),A^2 -> H(U1(e, k), U1(b, b)))
26.98/8.78	   (A^2 -> H(U1(e, d), U1(c, b)),A^2 -> H(U1(e, d), U1(c, b)))
26.98/8.78	   (A^2 -> H(U1(e, d), U1(d, b)),A^2 -> H(U1(e, d), U1(d, b)))
26.98/8.78	   (A^2 -> H(U1(e, d), U1(b, c)),A^2 -> H(U1(e, d), U1(b, c)))
26.98/8.78	   (A^2 -> H(U1(e, d), U1(b, d)),A^2 -> H(U1(e, d), U1(b, d)))
26.98/8.78	
26.98/8.78	
26.98/8.78	----------------------------------------
26.98/8.78	
26.98/8.78	(550)
26.98/8.78	Obligation:
26.98/8.78	Q DP problem:
26.98/8.78	The TRS P consists of the following rules:
26.98/8.78	
26.98/8.78	   H(x, x) -> G(x, x, f(k))
26.98/8.78	   G(d, x, x) -> A^2
26.98/8.78	   A^2 -> H(f(c), f(c))
26.98/8.78	   A^2 -> H(f(d), f(d))
26.98/8.78	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.78	   A^2 -> H(f(e), f(e))
26.98/8.78	   A^2 -> H(f(k), f(k))
26.98/8.78	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.78	   A^2 -> H(U1(e, d), f(c))
26.98/8.78	   A^2 -> H(U1(e, d), f(d))
26.98/8.78	   A^2 -> H(U1(e, a), U1(c, b))
26.98/8.78	   A^2 -> H(U1(e, a), U1(d, b))
26.98/8.78	   A^2 -> H(U1(e, a), U1(b, c))
26.98/8.78	   A^2 -> H(U1(e, a), U1(b, d))
26.98/8.78	   A^2 -> H(U1(e, a), U1(c, c))
26.98/8.78	   A^2 -> H(U1(e, a), f(e))
26.98/8.78	   A^2 -> H(U1(e, a), f(k))
26.98/8.78	   A^2 -> H(U1(e, a), U1(d, d))
26.98/8.78	   A^2 -> H(U1(k, a), U1(c, b))
26.98/8.78	   A^2 -> H(U1(k, a), U1(d, b))
26.98/8.78	   A^2 -> H(U1(k, a), U1(b, c))
26.98/8.78	   A^2 -> H(U1(k, a), U1(b, d))
26.98/8.78	   A^2 -> H(U1(k, a), U1(c, c))
26.98/8.78	   A^2 -> H(U1(k, a), f(e))
26.98/8.78	   A^2 -> H(U1(k, a), f(k))
26.98/8.78	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.78	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.78	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.78	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.78	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.78	   A^2 -> H(U1(c, d), f(e))
26.98/8.78	   A^2 -> H(U1(c, d), f(k))
26.98/8.78	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.78	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.78	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.78	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.78	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.78	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.78	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.78	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.78	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.78	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.78	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.78	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.78	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.78	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.78	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.78	   A^2 -> H(U1(d, e), f(c))
26.98/8.78	   A^2 -> H(U1(d, e), f(d))
26.98/8.78	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.78	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.78	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.78	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.78	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.78	   A^2 -> H(U1(d, c), f(e))
26.98/8.78	   A^2 -> H(U1(d, c), f(k))
26.98/8.78	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.78	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.78	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.78	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.78	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.78	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.78	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.78	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.78	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.78	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.78	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.78	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.78	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.78	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.78	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.78	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.78	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.78	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.78	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.78	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.78	   A^2 -> H(U1(a, e), f(e))
26.98/8.78	   A^2 -> H(U1(a, e), f(k))
26.98/8.78	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.78	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.78	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.78	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.78	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.78	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.78	   A^2 -> H(U1(a, k), f(e))
26.98/8.78	   A^2 -> H(U1(a, k), f(k))
26.98/8.78	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.78	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.78	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.78	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.78	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.78	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.78	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.78	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.78	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.78	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.78	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.78	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.78	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.78	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.78	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.78	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.78	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.78	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.78	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.78	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.78	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.78	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.78	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.78	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.78	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.78	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.78	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.78	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.78	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.78	   A^2 -> H(U1(a, a), b)
26.98/8.78	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.78	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.78	   A^2 -> H(U1(a, a), c)
26.98/8.78	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.78	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.78	   A^2 -> H(U1(a, a), e)
26.98/8.78	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.78	   A^2 -> H(k, f(b))
26.98/8.78	   A^2 -> H(c, U1(b, b))
26.98/8.78	   A^2 -> H(c, f(c))
26.98/8.78	   A^2 -> H(c, f(d))
26.98/8.78	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.78	   A^2 -> H(U1(e, k), f(c))
26.98/8.78	   A^2 -> H(U1(e, k), f(d))
26.98/8.78	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.78	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.78	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.78	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.78	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.78	   A^2 -> H(U1(e, c), f(e))
26.98/8.78	   A^2 -> H(U1(e, c), f(k))
26.98/8.78	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.78	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.78	   A^2 -> H(U1(k, e), f(c))
26.98/8.78	   A^2 -> H(U1(k, e), f(d))
26.98/8.78	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.78	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.78	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.78	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.78	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.78	   A^2 -> H(U1(k, c), f(e))
26.98/8.78	   A^2 -> H(U1(k, c), f(k))
26.98/8.78	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.78	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.78	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.78	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.78	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.78	   A^2 -> H(U1(c, e), f(e))
26.98/8.78	   A^2 -> H(U1(c, e), f(k))
26.98/8.78	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.78	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.78	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.78	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.78	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.78	   A^2 -> H(U1(c, k), f(e))
26.98/8.78	   A^2 -> H(U1(c, k), f(k))
26.98/8.78	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.78	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.78	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.78	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.78	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.78	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.78	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.78	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.78	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.78	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.78	   A^2 -> H(e, U1(b, b))
26.98/8.78	   A^2 -> H(e, f(c))
26.98/8.78	   A^2 -> H(e, f(d))
26.98/8.78	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.78	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.78	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.78	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.78	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.78	   A^2 -> H(U1(e, e), f(e))
26.98/8.78	   A^2 -> H(U1(e, e), f(k))
26.98/8.78	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.78	   A^2 -> H(f(e), U1(e, b))
26.98/8.78	   A^2 -> H(f(e), U1(k, b))
26.98/8.78	   A^2 -> H(f(e), U1(c, d))
26.98/8.78	   A^2 -> H(f(e), U1(d, c))
26.98/8.78	   A^2 -> H(f(e), U1(b, e))
26.98/8.78	   A^2 -> H(f(e), U1(b, k))
26.98/8.78	   A^2 -> H(f(e), U1(e, c))
26.98/8.78	   A^2 -> H(f(e), U1(k, c))
26.98/8.78	   A^2 -> H(f(e), U1(c, e))
26.98/8.78	   A^2 -> H(f(e), U1(c, k))
26.98/8.78	   A^2 -> H(f(e), U1(k, k))
26.98/8.78	   A^2 -> H(f(e), U1(k, d))
26.98/8.78	   A^2 -> H(f(e), U1(d, k))
26.98/8.78	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.78	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.78	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.78	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.78	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.78	   A^2 -> H(U1(k, k), f(e))
26.98/8.78	   A^2 -> H(U1(k, k), f(k))
26.98/8.78	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.78	   A^2 -> H(f(k), U1(e, b))
26.98/8.78	   A^2 -> H(f(k), U1(k, b))
26.98/8.78	   A^2 -> H(f(k), U1(c, d))
26.98/8.78	   A^2 -> H(f(k), U1(d, c))
26.98/8.78	   A^2 -> H(f(k), U1(b, e))
26.98/8.78	   A^2 -> H(f(k), U1(b, k))
26.98/8.78	   A^2 -> H(f(k), U1(e, c))
26.98/8.78	   A^2 -> H(f(k), U1(k, c))
26.98/8.78	   A^2 -> H(f(k), U1(c, e))
26.98/8.78	   A^2 -> H(f(k), U1(c, k))
26.98/8.78	   A^2 -> H(f(k), U1(e, e))
26.98/8.78	   A^2 -> H(f(k), U1(k, d))
26.98/8.78	   A^2 -> H(f(k), U1(d, k))
26.98/8.78	   A^2 -> H(f(c), b)
26.98/8.78	   A^2 -> H(f(c), U1(e, d))
26.98/8.78	   A^2 -> H(f(c), U1(d, e))
26.98/8.78	   A^2 -> H(f(k), U1(k, k))
26.98/8.78	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.78	   A^2 -> H(U1(k, k), f(c))
26.98/8.78	   A^2 -> H(U1(k, k), f(d))
26.98/8.78	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.78	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.78	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.78	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.78	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.78	   A^2 -> H(U1(k, d), f(e))
26.98/8.78	   A^2 -> H(U1(k, d), f(k))
26.98/8.78	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.78	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.78	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.78	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.78	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.78	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.78	   A^2 -> H(U1(d, k), f(e))
26.98/8.78	   A^2 -> H(U1(d, k), f(k))
26.98/8.78	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.78	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.78	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.78	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.78	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.78	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.78	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.78	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.78	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.78	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.78	   A^2 -> H(f(d), b)
26.98/8.78	   A^2 -> H(f(d), U1(e, d))
26.98/8.78	   A^2 -> H(f(d), U1(d, e))
26.98/8.78	   A^2 -> H(f(d), c)
26.98/8.78	   A^2 -> H(f(d), U1(e, k))
26.98/8.78	   A^2 -> H(f(d), U1(k, e))
26.98/8.78	   A^2 -> H(f(d), e)
26.98/8.78	   A^2 -> H(f(a), d)
26.98/8.78	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.78	   A^2 -> H(f(c), c)
26.98/8.78	   A^2 -> H(f(c), U1(e, k))
26.98/8.78	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.78	   A^2 -> H(f(c), U1(k, e))
26.98/8.78	   A^2 -> H(f(c), U1(k, k))
26.98/8.78	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.78	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.78	   A^2 -> H(f(a), k)
26.98/8.78	   A^2 -> H(f(e), U1(e, e))
26.98/8.78	   A^2 -> H(f(c), e)
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.78	   A^2 -> H(f(d), U1(k, k))
26.98/8.78	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.78	   A^2 -> H(d, U1(b, b))
26.98/8.78	   A^2 -> H(d, f(c))
26.98/8.78	   A^2 -> H(d, f(d))
26.98/8.78	   A^2 -> H(a, U1(c, b))
26.98/8.78	   A^2 -> H(a, U1(d, b))
26.98/8.78	   A^2 -> H(a, U1(b, c))
26.98/8.78	   A^2 -> H(a, U1(b, d))
26.98/8.78	   A^2 -> H(a, U1(c, c))
26.98/8.78	   A^2 -> H(a, f(e))
26.98/8.78	   A^2 -> H(a, f(k))
26.98/8.78	   A^2 -> H(a, U1(d, d))
26.98/8.78	   A^2 -> H(U1(e, d), U1(c, b))
26.98/8.78	   A^2 -> H(U1(e, d), U1(d, b))
26.98/8.78	   A^2 -> H(U1(e, d), U1(b, c))
26.98/8.78	   A^2 -> H(U1(e, d), U1(b, d))
26.98/8.78	
26.98/8.78	The TRS R consists of the following rules:
26.98/8.78	
26.98/8.78	   f(x) -> U1(x, x)
26.98/8.78	   U1(e, x) -> x
26.98/8.78	   a -> c
26.98/8.78	   a -> d
26.98/8.78	   b -> c
26.98/8.78	   b -> d
26.98/8.78	   d -> k
26.98/8.78	   c -> e
26.98/8.78	   c -> k
26.98/8.78	
26.98/8.78	Q is empty.
26.98/8.78	We have to consider all minimal (P,Q,R)-chains.
26.98/8.78	----------------------------------------
26.98/8.78	
26.98/8.78	(551) TransformationProof (EQUIVALENT)
26.98/8.78	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), f(c)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.78	
26.98/8.78	   (A^2 -> H(d, f(c)),A^2 -> H(d, f(c)))
26.98/8.78	   (A^2 -> H(U1(e, k), f(c)),A^2 -> H(U1(e, k), f(c)))
26.98/8.78	   (A^2 -> H(U1(e, d), U1(c, c)),A^2 -> H(U1(e, d), U1(c, c)))
26.98/8.78	   (A^2 -> H(U1(e, d), f(e)),A^2 -> H(U1(e, d), f(e)))
26.98/8.78	   (A^2 -> H(U1(e, d), f(k)),A^2 -> H(U1(e, d), f(k)))
26.98/8.78	
26.98/8.78	
26.98/8.78	----------------------------------------
26.98/8.78	
26.98/8.78	(552)
26.98/8.78	Obligation:
26.98/8.78	Q DP problem:
26.98/8.78	The TRS P consists of the following rules:
26.98/8.78	
26.98/8.78	   H(x, x) -> G(x, x, f(k))
26.98/8.78	   G(d, x, x) -> A^2
26.98/8.78	   A^2 -> H(f(c), f(c))
26.98/8.78	   A^2 -> H(f(d), f(d))
26.98/8.78	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.78	   A^2 -> H(f(e), f(e))
26.98/8.78	   A^2 -> H(f(k), f(k))
26.98/8.78	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.78	   A^2 -> H(U1(e, d), f(d))
26.98/8.78	   A^2 -> H(U1(e, a), U1(c, b))
26.98/8.78	   A^2 -> H(U1(e, a), U1(d, b))
26.98/8.78	   A^2 -> H(U1(e, a), U1(b, c))
26.98/8.78	   A^2 -> H(U1(e, a), U1(b, d))
26.98/8.78	   A^2 -> H(U1(e, a), U1(c, c))
26.98/8.78	   A^2 -> H(U1(e, a), f(e))
26.98/8.78	   A^2 -> H(U1(e, a), f(k))
26.98/8.78	   A^2 -> H(U1(e, a), U1(d, d))
26.98/8.78	   A^2 -> H(U1(k, a), U1(c, b))
26.98/8.78	   A^2 -> H(U1(k, a), U1(d, b))
26.98/8.78	   A^2 -> H(U1(k, a), U1(b, c))
26.98/8.78	   A^2 -> H(U1(k, a), U1(b, d))
26.98/8.78	   A^2 -> H(U1(k, a), U1(c, c))
26.98/8.78	   A^2 -> H(U1(k, a), f(e))
26.98/8.78	   A^2 -> H(U1(k, a), f(k))
26.98/8.78	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.78	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.78	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.78	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.78	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.78	   A^2 -> H(U1(c, d), f(e))
26.98/8.78	   A^2 -> H(U1(c, d), f(k))
26.98/8.78	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.78	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.78	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.78	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.78	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.78	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.78	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.78	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.78	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.78	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.78	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.78	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.78	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.78	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.78	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.78	   A^2 -> H(U1(d, e), f(c))
26.98/8.78	   A^2 -> H(U1(d, e), f(d))
26.98/8.78	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.78	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.78	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.78	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.78	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.78	   A^2 -> H(U1(d, c), f(e))
26.98/8.78	   A^2 -> H(U1(d, c), f(k))
26.98/8.78	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.78	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.78	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.78	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.78	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.78	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.78	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.78	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.78	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.78	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.78	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.78	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.78	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.78	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.78	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.78	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.78	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.78	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.78	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.78	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.78	   A^2 -> H(U1(a, e), f(e))
26.98/8.78	   A^2 -> H(U1(a, e), f(k))
26.98/8.78	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.78	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.78	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.78	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.78	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.78	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.78	   A^2 -> H(U1(a, k), f(e))
26.98/8.78	   A^2 -> H(U1(a, k), f(k))
26.98/8.78	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.78	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.78	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.78	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.78	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.78	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.78	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.78	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.78	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.78	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.78	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.78	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.78	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.78	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.78	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.78	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.78	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.78	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.78	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.78	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.78	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.78	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.78	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.78	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.78	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.78	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.78	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.78	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.78	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.78	   A^2 -> H(U1(a, a), b)
26.98/8.78	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.78	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.78	   A^2 -> H(U1(a, a), c)
26.98/8.78	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.78	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.78	   A^2 -> H(U1(a, a), e)
26.98/8.78	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.78	   A^2 -> H(k, f(b))
26.98/8.78	   A^2 -> H(c, U1(b, b))
26.98/8.78	   A^2 -> H(c, f(c))
26.98/8.78	   A^2 -> H(c, f(d))
26.98/8.78	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.78	   A^2 -> H(U1(e, k), f(c))
26.98/8.78	   A^2 -> H(U1(e, k), f(d))
26.98/8.78	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.78	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.78	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.78	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.78	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.78	   A^2 -> H(U1(e, c), f(e))
26.98/8.78	   A^2 -> H(U1(e, c), f(k))
26.98/8.78	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.78	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.78	   A^2 -> H(U1(k, e), f(c))
26.98/8.78	   A^2 -> H(U1(k, e), f(d))
26.98/8.78	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.78	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.78	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.78	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.78	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.78	   A^2 -> H(U1(k, c), f(e))
26.98/8.78	   A^2 -> H(U1(k, c), f(k))
26.98/8.78	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.78	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.78	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.78	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.78	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.78	   A^2 -> H(U1(c, e), f(e))
26.98/8.78	   A^2 -> H(U1(c, e), f(k))
26.98/8.78	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.78	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.78	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.78	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.78	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.78	   A^2 -> H(U1(c, k), f(e))
26.98/8.78	   A^2 -> H(U1(c, k), f(k))
26.98/8.78	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.78	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.78	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.78	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.78	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.78	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.78	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.78	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.78	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.78	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.78	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.78	   A^2 -> H(e, U1(b, b))
26.98/8.78	   A^2 -> H(e, f(c))
26.98/8.78	   A^2 -> H(e, f(d))
26.98/8.78	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.78	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.78	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.78	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.78	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.78	   A^2 -> H(U1(e, e), f(e))
26.98/8.78	   A^2 -> H(U1(e, e), f(k))
26.98/8.78	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.78	   A^2 -> H(f(e), U1(e, b))
26.98/8.78	   A^2 -> H(f(e), U1(k, b))
26.98/8.78	   A^2 -> H(f(e), U1(c, d))
26.98/8.78	   A^2 -> H(f(e), U1(d, c))
26.98/8.78	   A^2 -> H(f(e), U1(b, e))
26.98/8.78	   A^2 -> H(f(e), U1(b, k))
26.98/8.78	   A^2 -> H(f(e), U1(e, c))
26.98/8.78	   A^2 -> H(f(e), U1(k, c))
26.98/8.78	   A^2 -> H(f(e), U1(c, e))
26.98/8.78	   A^2 -> H(f(e), U1(c, k))
26.98/8.78	   A^2 -> H(f(e), U1(k, k))
26.98/8.78	   A^2 -> H(f(e), U1(k, d))
26.98/8.78	   A^2 -> H(f(e), U1(d, k))
26.98/8.78	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.78	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.78	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.78	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.78	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.78	   A^2 -> H(U1(k, k), f(e))
26.98/8.78	   A^2 -> H(U1(k, k), f(k))
26.98/8.78	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.78	   A^2 -> H(f(k), U1(e, b))
26.98/8.78	   A^2 -> H(f(k), U1(k, b))
26.98/8.78	   A^2 -> H(f(k), U1(c, d))
26.98/8.78	   A^2 -> H(f(k), U1(d, c))
26.98/8.78	   A^2 -> H(f(k), U1(b, e))
26.98/8.78	   A^2 -> H(f(k), U1(b, k))
26.98/8.78	   A^2 -> H(f(k), U1(e, c))
26.98/8.78	   A^2 -> H(f(k), U1(k, c))
26.98/8.78	   A^2 -> H(f(k), U1(c, e))
26.98/8.78	   A^2 -> H(f(k), U1(c, k))
26.98/8.78	   A^2 -> H(f(k), U1(e, e))
26.98/8.78	   A^2 -> H(f(k), U1(k, d))
26.98/8.78	   A^2 -> H(f(k), U1(d, k))
26.98/8.78	   A^2 -> H(f(c), b)
26.98/8.78	   A^2 -> H(f(c), U1(e, d))
26.98/8.78	   A^2 -> H(f(c), U1(d, e))
26.98/8.78	   A^2 -> H(f(k), U1(k, k))
26.98/8.78	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.78	   A^2 -> H(U1(k, k), f(c))
26.98/8.78	   A^2 -> H(U1(k, k), f(d))
26.98/8.78	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.78	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.78	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.78	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.78	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.78	   A^2 -> H(U1(k, d), f(e))
26.98/8.78	   A^2 -> H(U1(k, d), f(k))
26.98/8.78	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.78	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.78	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.78	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.78	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.78	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.78	   A^2 -> H(U1(d, k), f(e))
26.98/8.78	   A^2 -> H(U1(d, k), f(k))
26.98/8.78	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.78	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.78	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.78	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.78	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.78	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.78	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.78	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.78	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.78	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.78	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.78	   A^2 -> H(f(d), b)
26.98/8.78	   A^2 -> H(f(d), U1(e, d))
26.98/8.78	   A^2 -> H(f(d), U1(d, e))
26.98/8.78	   A^2 -> H(f(d), c)
26.98/8.78	   A^2 -> H(f(d), U1(e, k))
26.98/8.78	   A^2 -> H(f(d), U1(k, e))
26.98/8.78	   A^2 -> H(f(d), e)
26.98/8.78	   A^2 -> H(f(a), d)
26.98/8.78	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.79	   A^2 -> H(f(c), c)
26.98/8.79	   A^2 -> H(f(c), U1(e, k))
26.98/8.79	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.79	   A^2 -> H(f(c), U1(k, e))
26.98/8.79	   A^2 -> H(f(c), U1(k, k))
26.98/8.79	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.79	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.79	   A^2 -> H(f(a), k)
26.98/8.79	   A^2 -> H(f(e), U1(e, e))
26.98/8.79	   A^2 -> H(f(c), e)
26.98/8.79	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.79	   A^2 -> H(f(d), U1(k, k))
26.98/8.79	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.79	   A^2 -> H(d, U1(b, b))
26.98/8.79	   A^2 -> H(d, f(c))
26.98/8.79	   A^2 -> H(d, f(d))
26.98/8.79	   A^2 -> H(a, U1(c, b))
26.98/8.79	   A^2 -> H(a, U1(d, b))
26.98/8.79	   A^2 -> H(a, U1(b, c))
26.98/8.79	   A^2 -> H(a, U1(b, d))
26.98/8.79	   A^2 -> H(a, U1(c, c))
26.98/8.79	   A^2 -> H(a, f(e))
26.98/8.79	   A^2 -> H(a, f(k))
26.98/8.79	   A^2 -> H(a, U1(d, d))
26.98/8.79	   A^2 -> H(U1(e, d), U1(c, b))
26.98/8.79	   A^2 -> H(U1(e, d), U1(d, b))
26.98/8.79	   A^2 -> H(U1(e, d), U1(b, c))
26.98/8.79	   A^2 -> H(U1(e, d), U1(b, d))
26.98/8.79	   A^2 -> H(U1(e, d), U1(c, c))
26.98/8.79	   A^2 -> H(U1(e, d), f(e))
26.98/8.79	   A^2 -> H(U1(e, d), f(k))
26.98/8.79	
26.98/8.79	The TRS R consists of the following rules:
26.98/8.79	
26.98/8.79	   f(x) -> U1(x, x)
26.98/8.79	   U1(e, x) -> x
26.98/8.79	   a -> c
26.98/8.79	   a -> d
26.98/8.79	   b -> c
26.98/8.79	   b -> d
26.98/8.79	   d -> k
26.98/8.79	   c -> e
26.98/8.79	   c -> k
26.98/8.79	
26.98/8.79	Q is empty.
26.98/8.79	We have to consider all minimal (P,Q,R)-chains.
26.98/8.79	----------------------------------------
26.98/8.79	
26.98/8.79	(553) TransformationProof (EQUIVALENT)
26.98/8.79	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), f(d)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.79	
26.98/8.79	   (A^2 -> H(d, f(d)),A^2 -> H(d, f(d)))
26.98/8.79	   (A^2 -> H(U1(e, k), f(d)),A^2 -> H(U1(e, k), f(d)))
26.98/8.79	   (A^2 -> H(U1(e, d), U1(d, d)),A^2 -> H(U1(e, d), U1(d, d)))
26.98/8.79	   (A^2 -> H(U1(e, d), f(k)),A^2 -> H(U1(e, d), f(k)))
26.98/8.79	
26.98/8.79	
26.98/8.79	----------------------------------------
26.98/8.79	
26.98/8.79	(554)
26.98/8.79	Obligation:
26.98/8.79	Q DP problem:
26.98/8.79	The TRS P consists of the following rules:
26.98/8.79	
26.98/8.79	   H(x, x) -> G(x, x, f(k))
26.98/8.79	   G(d, x, x) -> A^2
26.98/8.79	   A^2 -> H(f(c), f(c))
26.98/8.79	   A^2 -> H(f(d), f(d))
26.98/8.79	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.79	   A^2 -> H(f(e), f(e))
26.98/8.79	   A^2 -> H(f(k), f(k))
26.98/8.79	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.79	   A^2 -> H(U1(e, a), U1(c, b))
26.98/8.79	   A^2 -> H(U1(e, a), U1(d, b))
26.98/8.79	   A^2 -> H(U1(e, a), U1(b, c))
26.98/8.79	   A^2 -> H(U1(e, a), U1(b, d))
26.98/8.79	   A^2 -> H(U1(e, a), U1(c, c))
26.98/8.79	   A^2 -> H(U1(e, a), f(e))
26.98/8.79	   A^2 -> H(U1(e, a), f(k))
26.98/8.79	   A^2 -> H(U1(e, a), U1(d, d))
26.98/8.79	   A^2 -> H(U1(k, a), U1(c, b))
26.98/8.79	   A^2 -> H(U1(k, a), U1(d, b))
26.98/8.79	   A^2 -> H(U1(k, a), U1(b, c))
26.98/8.79	   A^2 -> H(U1(k, a), U1(b, d))
26.98/8.79	   A^2 -> H(U1(k, a), U1(c, c))
26.98/8.79	   A^2 -> H(U1(k, a), f(e))
26.98/8.79	   A^2 -> H(U1(k, a), f(k))
26.98/8.79	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.79	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.79	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.79	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.79	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.79	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.79	   A^2 -> H(U1(c, d), f(e))
26.98/8.79	   A^2 -> H(U1(c, d), f(k))
26.98/8.79	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.79	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.79	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.79	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.79	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.79	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.79	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.79	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.79	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.79	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.79	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.79	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.79	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.79	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.79	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.79	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.79	   A^2 -> H(U1(d, e), f(c))
26.98/8.79	   A^2 -> H(U1(d, e), f(d))
26.98/8.79	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.79	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.79	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.79	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.79	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.79	   A^2 -> H(U1(d, c), f(e))
26.98/8.79	   A^2 -> H(U1(d, c), f(k))
26.98/8.79	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.79	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.79	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.79	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.79	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.79	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.79	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.79	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.79	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.79	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.79	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.79	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.79	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.79	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.79	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.79	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.79	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.79	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.79	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.79	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.79	   A^2 -> H(U1(a, e), f(e))
26.98/8.79	   A^2 -> H(U1(a, e), f(k))
26.98/8.79	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.79	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.79	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.79	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.79	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.79	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.79	   A^2 -> H(U1(a, k), f(e))
26.98/8.79	   A^2 -> H(U1(a, k), f(k))
26.98/8.79	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.79	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.79	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.79	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.79	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.79	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.79	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.79	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.79	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.79	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.79	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.79	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.79	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.79	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.79	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.79	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.79	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.79	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.79	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.79	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.79	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.79	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.79	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.79	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.79	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.79	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.79	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.79	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.79	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.79	   A^2 -> H(U1(a, a), b)
26.98/8.79	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.79	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.79	   A^2 -> H(U1(a, a), c)
26.98/8.79	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.79	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.79	   A^2 -> H(U1(a, a), e)
26.98/8.79	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.79	   A^2 -> H(k, f(b))
26.98/8.79	   A^2 -> H(c, U1(b, b))
26.98/8.79	   A^2 -> H(c, f(c))
26.98/8.79	   A^2 -> H(c, f(d))
26.98/8.79	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.79	   A^2 -> H(U1(e, k), f(c))
26.98/8.79	   A^2 -> H(U1(e, k), f(d))
26.98/8.79	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.79	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.79	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.79	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.79	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.79	   A^2 -> H(U1(e, c), f(e))
26.98/8.79	   A^2 -> H(U1(e, c), f(k))
26.98/8.79	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.79	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.79	   A^2 -> H(U1(k, e), f(c))
26.98/8.79	   A^2 -> H(U1(k, e), f(d))
26.98/8.79	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.79	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.79	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.79	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.79	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.79	   A^2 -> H(U1(k, c), f(e))
26.98/8.79	   A^2 -> H(U1(k, c), f(k))
26.98/8.79	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.79	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.79	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.79	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.79	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.79	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.79	   A^2 -> H(U1(c, e), f(e))
26.98/8.79	   A^2 -> H(U1(c, e), f(k))
26.98/8.79	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.79	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.79	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.79	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.79	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.79	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.79	   A^2 -> H(U1(c, k), f(e))
26.98/8.79	   A^2 -> H(U1(c, k), f(k))
26.98/8.79	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.79	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.79	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.79	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.79	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.79	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.79	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.79	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.79	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.79	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.79	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.79	   A^2 -> H(e, U1(b, b))
26.98/8.79	   A^2 -> H(e, f(c))
26.98/8.79	   A^2 -> H(e, f(d))
26.98/8.79	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.79	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.79	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.79	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.79	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.79	   A^2 -> H(U1(e, e), f(e))
26.98/8.79	   A^2 -> H(U1(e, e), f(k))
26.98/8.79	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.79	   A^2 -> H(f(e), U1(e, b))
26.98/8.79	   A^2 -> H(f(e), U1(k, b))
26.98/8.79	   A^2 -> H(f(e), U1(c, d))
26.98/8.79	   A^2 -> H(f(e), U1(d, c))
26.98/8.79	   A^2 -> H(f(e), U1(b, e))
26.98/8.79	   A^2 -> H(f(e), U1(b, k))
26.98/8.79	   A^2 -> H(f(e), U1(e, c))
26.98/8.79	   A^2 -> H(f(e), U1(k, c))
26.98/8.79	   A^2 -> H(f(e), U1(c, e))
26.98/8.79	   A^2 -> H(f(e), U1(c, k))
26.98/8.79	   A^2 -> H(f(e), U1(k, k))
26.98/8.79	   A^2 -> H(f(e), U1(k, d))
26.98/8.79	   A^2 -> H(f(e), U1(d, k))
26.98/8.79	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.79	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.79	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.79	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.79	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.79	   A^2 -> H(U1(k, k), f(e))
26.98/8.79	   A^2 -> H(U1(k, k), f(k))
26.98/8.79	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.79	   A^2 -> H(f(k), U1(e, b))
26.98/8.79	   A^2 -> H(f(k), U1(k, b))
26.98/8.79	   A^2 -> H(f(k), U1(c, d))
26.98/8.79	   A^2 -> H(f(k), U1(d, c))
26.98/8.79	   A^2 -> H(f(k), U1(b, e))
26.98/8.79	   A^2 -> H(f(k), U1(b, k))
26.98/8.79	   A^2 -> H(f(k), U1(e, c))
26.98/8.79	   A^2 -> H(f(k), U1(k, c))
26.98/8.79	   A^2 -> H(f(k), U1(c, e))
26.98/8.79	   A^2 -> H(f(k), U1(c, k))
26.98/8.79	   A^2 -> H(f(k), U1(e, e))
26.98/8.79	   A^2 -> H(f(k), U1(k, d))
26.98/8.79	   A^2 -> H(f(k), U1(d, k))
26.98/8.79	   A^2 -> H(f(c), b)
26.98/8.79	   A^2 -> H(f(c), U1(e, d))
26.98/8.79	   A^2 -> H(f(c), U1(d, e))
26.98/8.79	   A^2 -> H(f(k), U1(k, k))
26.98/8.79	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.79	   A^2 -> H(U1(k, k), f(c))
26.98/8.79	   A^2 -> H(U1(k, k), f(d))
26.98/8.79	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.79	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.79	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.79	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.79	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.79	   A^2 -> H(U1(k, d), f(e))
26.98/8.79	   A^2 -> H(U1(k, d), f(k))
26.98/8.79	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.79	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.79	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.79	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.79	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.79	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.79	   A^2 -> H(U1(d, k), f(e))
26.98/8.79	   A^2 -> H(U1(d, k), f(k))
26.98/8.79	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.79	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.79	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.79	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.79	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.79	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.79	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.79	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.79	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.79	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.79	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.79	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.79	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.79	   A^2 -> H(f(d), b)
26.98/8.79	   A^2 -> H(f(d), U1(e, d))
26.98/8.79	   A^2 -> H(f(d), U1(d, e))
26.98/8.79	   A^2 -> H(f(d), c)
26.98/8.79	   A^2 -> H(f(d), U1(e, k))
26.98/8.79	   A^2 -> H(f(d), U1(k, e))
26.98/8.79	   A^2 -> H(f(d), e)
26.98/8.79	   A^2 -> H(f(a), d)
26.98/8.79	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.79	   A^2 -> H(f(c), c)
26.98/8.79	   A^2 -> H(f(c), U1(e, k))
26.98/8.79	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.79	   A^2 -> H(f(c), U1(k, e))
26.98/8.79	   A^2 -> H(f(c), U1(k, k))
26.98/8.79	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.79	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.79	   A^2 -> H(f(a), k)
26.98/8.79	   A^2 -> H(f(e), U1(e, e))
26.98/8.79	   A^2 -> H(f(c), e)
26.98/8.79	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.79	   A^2 -> H(f(d), U1(k, k))
26.98/8.79	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.79	   A^2 -> H(d, U1(b, b))
26.98/8.79	   A^2 -> H(d, f(c))
26.98/8.79	   A^2 -> H(d, f(d))
26.98/8.79	   A^2 -> H(a, U1(c, b))
26.98/8.79	   A^2 -> H(a, U1(d, b))
26.98/8.79	   A^2 -> H(a, U1(b, c))
26.98/8.79	   A^2 -> H(a, U1(b, d))
26.98/8.79	   A^2 -> H(a, U1(c, c))
26.98/8.79	   A^2 -> H(a, f(e))
26.98/8.79	   A^2 -> H(a, f(k))
26.98/8.79	   A^2 -> H(a, U1(d, d))
26.98/8.79	   A^2 -> H(U1(e, d), U1(c, b))
26.98/8.79	   A^2 -> H(U1(e, d), U1(d, b))
26.98/8.79	   A^2 -> H(U1(e, d), U1(b, c))
26.98/8.79	   A^2 -> H(U1(e, d), U1(b, d))
26.98/8.79	   A^2 -> H(U1(e, d), U1(c, c))
26.98/8.79	   A^2 -> H(U1(e, d), f(e))
26.98/8.79	   A^2 -> H(U1(e, d), f(k))
26.98/8.79	   A^2 -> H(U1(e, d), U1(d, d))
26.98/8.79	
26.98/8.79	The TRS R consists of the following rules:
26.98/8.79	
26.98/8.79	   f(x) -> U1(x, x)
26.98/8.79	   U1(e, x) -> x
26.98/8.79	   a -> c
26.98/8.79	   a -> d
26.98/8.79	   b -> c
26.98/8.79	   b -> d
26.98/8.79	   d -> k
26.98/8.79	   c -> e
26.98/8.79	   c -> k
26.98/8.79	
26.98/8.79	Q is empty.
26.98/8.79	We have to consider all minimal (P,Q,R)-chains.
26.98/8.79	----------------------------------------
26.98/8.79	
26.98/8.79	(555) TransformationProof (EQUIVALENT)
26.98/8.79	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.79	
26.98/8.79	   (A^2 -> H(a, U1(c, b)),A^2 -> H(a, U1(c, b)))
26.98/8.79	   (A^2 -> H(U1(e, c), U1(c, b)),A^2 -> H(U1(e, c), U1(c, b)))
26.98/8.79	   (A^2 -> H(U1(e, d), U1(c, b)),A^2 -> H(U1(e, d), U1(c, b)))
26.98/8.79	   (A^2 -> H(U1(e, a), U1(e, b)),A^2 -> H(U1(e, a), U1(e, b)))
26.98/8.79	   (A^2 -> H(U1(e, a), U1(k, b)),A^2 -> H(U1(e, a), U1(k, b)))
26.98/8.79	   (A^2 -> H(U1(e, a), U1(c, c)),A^2 -> H(U1(e, a), U1(c, c)))
26.98/8.79	   (A^2 -> H(U1(e, a), U1(c, d)),A^2 -> H(U1(e, a), U1(c, d)))
26.98/8.79	
26.98/8.79	
26.98/8.79	----------------------------------------
26.98/8.79	
26.98/8.79	(556)
26.98/8.79	Obligation:
26.98/8.79	Q DP problem:
26.98/8.79	The TRS P consists of the following rules:
26.98/8.79	
26.98/8.79	   H(x, x) -> G(x, x, f(k))
26.98/8.79	   G(d, x, x) -> A^2
26.98/8.79	   A^2 -> H(f(c), f(c))
26.98/8.79	   A^2 -> H(f(d), f(d))
26.98/8.79	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.79	   A^2 -> H(f(e), f(e))
26.98/8.79	   A^2 -> H(f(k), f(k))
26.98/8.79	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.79	   A^2 -> H(U1(e, a), U1(d, b))
26.98/8.79	   A^2 -> H(U1(e, a), U1(b, c))
26.98/8.79	   A^2 -> H(U1(e, a), U1(b, d))
26.98/8.79	   A^2 -> H(U1(e, a), U1(c, c))
26.98/8.79	   A^2 -> H(U1(e, a), f(e))
26.98/8.79	   A^2 -> H(U1(e, a), f(k))
26.98/8.79	   A^2 -> H(U1(e, a), U1(d, d))
26.98/8.79	   A^2 -> H(U1(k, a), U1(c, b))
26.98/8.79	   A^2 -> H(U1(k, a), U1(d, b))
26.98/8.79	   A^2 -> H(U1(k, a), U1(b, c))
26.98/8.79	   A^2 -> H(U1(k, a), U1(b, d))
26.98/8.79	   A^2 -> H(U1(k, a), U1(c, c))
26.98/8.79	   A^2 -> H(U1(k, a), f(e))
26.98/8.79	   A^2 -> H(U1(k, a), f(k))
26.98/8.79	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.79	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.79	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.79	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.79	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.79	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.79	   A^2 -> H(U1(c, d), f(e))
26.98/8.79	   A^2 -> H(U1(c, d), f(k))
26.98/8.79	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.79	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.79	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.79	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.79	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.79	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.79	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.79	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.79	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.79	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.79	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.79	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.79	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.79	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.79	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.79	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.79	   A^2 -> H(U1(d, e), f(c))
26.98/8.79	   A^2 -> H(U1(d, e), f(d))
26.98/8.79	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.79	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.79	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.79	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.79	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.79	   A^2 -> H(U1(d, c), f(e))
26.98/8.79	   A^2 -> H(U1(d, c), f(k))
26.98/8.79	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.79	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.79	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.79	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.79	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.79	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.79	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.79	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.79	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.79	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.79	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.79	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.79	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.79	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.79	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.79	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.79	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.79	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.79	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.79	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.79	   A^2 -> H(U1(a, e), f(e))
26.98/8.79	   A^2 -> H(U1(a, e), f(k))
26.98/8.79	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.79	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.79	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.79	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.79	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.79	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.79	   A^2 -> H(U1(a, k), f(e))
26.98/8.79	   A^2 -> H(U1(a, k), f(k))
26.98/8.79	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.79	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.79	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.79	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.79	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.79	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.79	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.79	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.79	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.79	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.79	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.79	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.79	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.79	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.79	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.79	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.79	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.79	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.79	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.79	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.79	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.79	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.79	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.79	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.79	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.79	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.79	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.79	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.79	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.79	   A^2 -> H(U1(a, a), b)
26.98/8.79	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.79	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.79	   A^2 -> H(U1(a, a), c)
26.98/8.79	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.79	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.79	   A^2 -> H(U1(a, a), e)
26.98/8.79	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.79	   A^2 -> H(k, f(b))
26.98/8.79	   A^2 -> H(c, U1(b, b))
26.98/8.79	   A^2 -> H(c, f(c))
26.98/8.79	   A^2 -> H(c, f(d))
26.98/8.79	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.79	   A^2 -> H(U1(e, k), f(c))
26.98/8.79	   A^2 -> H(U1(e, k), f(d))
26.98/8.79	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.80	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.80	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.80	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.80	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.80	   A^2 -> H(U1(e, c), f(e))
26.98/8.80	   A^2 -> H(U1(e, c), f(k))
26.98/8.80	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.80	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.80	   A^2 -> H(U1(k, e), f(c))
26.98/8.80	   A^2 -> H(U1(k, e), f(d))
26.98/8.80	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.80	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.80	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.80	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.80	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.80	   A^2 -> H(U1(k, c), f(e))
26.98/8.80	   A^2 -> H(U1(k, c), f(k))
26.98/8.80	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.80	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.80	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.80	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.80	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.80	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.80	   A^2 -> H(U1(c, e), f(e))
26.98/8.80	   A^2 -> H(U1(c, e), f(k))
26.98/8.80	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.80	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.80	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.80	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.80	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.80	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.80	   A^2 -> H(U1(c, k), f(e))
26.98/8.80	   A^2 -> H(U1(c, k), f(k))
26.98/8.80	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.80	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.80	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.80	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.80	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.80	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.80	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.80	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.80	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.80	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.80	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.80	   A^2 -> H(e, U1(b, b))
26.98/8.80	   A^2 -> H(e, f(c))
26.98/8.80	   A^2 -> H(e, f(d))
26.98/8.80	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.80	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.80	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.80	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.80	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.80	   A^2 -> H(U1(e, e), f(e))
26.98/8.80	   A^2 -> H(U1(e, e), f(k))
26.98/8.80	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.80	   A^2 -> H(f(e), U1(e, b))
26.98/8.80	   A^2 -> H(f(e), U1(k, b))
26.98/8.80	   A^2 -> H(f(e), U1(c, d))
26.98/8.80	   A^2 -> H(f(e), U1(d, c))
26.98/8.80	   A^2 -> H(f(e), U1(b, e))
26.98/8.80	   A^2 -> H(f(e), U1(b, k))
26.98/8.80	   A^2 -> H(f(e), U1(e, c))
26.98/8.80	   A^2 -> H(f(e), U1(k, c))
26.98/8.80	   A^2 -> H(f(e), U1(c, e))
26.98/8.80	   A^2 -> H(f(e), U1(c, k))
26.98/8.80	   A^2 -> H(f(e), U1(k, k))
26.98/8.80	   A^2 -> H(f(e), U1(k, d))
26.98/8.80	   A^2 -> H(f(e), U1(d, k))
26.98/8.80	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.80	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.80	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.80	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.80	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.80	   A^2 -> H(U1(k, k), f(e))
26.98/8.80	   A^2 -> H(U1(k, k), f(k))
26.98/8.80	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.80	   A^2 -> H(f(k), U1(e, b))
26.98/8.80	   A^2 -> H(f(k), U1(k, b))
26.98/8.80	   A^2 -> H(f(k), U1(c, d))
26.98/8.80	   A^2 -> H(f(k), U1(d, c))
26.98/8.80	   A^2 -> H(f(k), U1(b, e))
26.98/8.80	   A^2 -> H(f(k), U1(b, k))
26.98/8.80	   A^2 -> H(f(k), U1(e, c))
26.98/8.80	   A^2 -> H(f(k), U1(k, c))
26.98/8.80	   A^2 -> H(f(k), U1(c, e))
26.98/8.80	   A^2 -> H(f(k), U1(c, k))
26.98/8.80	   A^2 -> H(f(k), U1(e, e))
26.98/8.80	   A^2 -> H(f(k), U1(k, d))
26.98/8.80	   A^2 -> H(f(k), U1(d, k))
26.98/8.80	   A^2 -> H(f(c), b)
26.98/8.80	   A^2 -> H(f(c), U1(e, d))
26.98/8.80	   A^2 -> H(f(c), U1(d, e))
26.98/8.80	   A^2 -> H(f(k), U1(k, k))
26.98/8.80	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.80	   A^2 -> H(U1(k, k), f(c))
26.98/8.80	   A^2 -> H(U1(k, k), f(d))
26.98/8.80	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.80	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.80	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.80	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.80	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.80	   A^2 -> H(U1(k, d), f(e))
26.98/8.80	   A^2 -> H(U1(k, d), f(k))
26.98/8.80	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.80	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.80	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.80	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.80	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.80	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.80	   A^2 -> H(U1(d, k), f(e))
26.98/8.80	   A^2 -> H(U1(d, k), f(k))
26.98/8.80	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.80	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.80	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.80	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.80	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.80	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.80	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.80	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.80	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.80	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.80	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.80	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.80	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.80	   A^2 -> H(f(d), b)
26.98/8.80	   A^2 -> H(f(d), U1(e, d))
26.98/8.80	   A^2 -> H(f(d), U1(d, e))
26.98/8.80	   A^2 -> H(f(d), c)
26.98/8.80	   A^2 -> H(f(d), U1(e, k))
26.98/8.80	   A^2 -> H(f(d), U1(k, e))
26.98/8.80	   A^2 -> H(f(d), e)
26.98/8.80	   A^2 -> H(f(a), d)
26.98/8.80	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.80	   A^2 -> H(f(c), c)
26.98/8.80	   A^2 -> H(f(c), U1(e, k))
26.98/8.80	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.80	   A^2 -> H(f(c), U1(k, e))
26.98/8.80	   A^2 -> H(f(c), U1(k, k))
26.98/8.80	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.80	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.80	   A^2 -> H(f(a), k)
26.98/8.80	   A^2 -> H(f(e), U1(e, e))
26.98/8.80	   A^2 -> H(f(c), e)
26.98/8.80	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.80	   A^2 -> H(f(d), U1(k, k))
26.98/8.80	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.80	   A^2 -> H(d, U1(b, b))
26.98/8.80	   A^2 -> H(d, f(c))
26.98/8.80	   A^2 -> H(d, f(d))
26.98/8.80	   A^2 -> H(a, U1(c, b))
26.98/8.80	   A^2 -> H(a, U1(d, b))
26.98/8.80	   A^2 -> H(a, U1(b, c))
26.98/8.80	   A^2 -> H(a, U1(b, d))
26.98/8.80	   A^2 -> H(a, U1(c, c))
26.98/8.80	   A^2 -> H(a, f(e))
26.98/8.80	   A^2 -> H(a, f(k))
26.98/8.80	   A^2 -> H(a, U1(d, d))
26.98/8.80	   A^2 -> H(U1(e, d), U1(c, b))
26.98/8.80	   A^2 -> H(U1(e, d), U1(d, b))
26.98/8.80	   A^2 -> H(U1(e, d), U1(b, c))
26.98/8.80	   A^2 -> H(U1(e, d), U1(b, d))
26.98/8.80	   A^2 -> H(U1(e, d), U1(c, c))
26.98/8.80	   A^2 -> H(U1(e, d), f(e))
26.98/8.80	   A^2 -> H(U1(e, d), f(k))
26.98/8.80	   A^2 -> H(U1(e, d), U1(d, d))
26.98/8.80	   A^2 -> H(U1(e, a), U1(e, b))
26.98/8.80	   A^2 -> H(U1(e, a), U1(k, b))
26.98/8.80	   A^2 -> H(U1(e, a), U1(c, d))
26.98/8.80	
26.98/8.80	The TRS R consists of the following rules:
26.98/8.80	
26.98/8.80	   f(x) -> U1(x, x)
26.98/8.80	   U1(e, x) -> x
26.98/8.80	   a -> c
26.98/8.80	   a -> d
26.98/8.80	   b -> c
26.98/8.80	   b -> d
26.98/8.80	   d -> k
26.98/8.80	   c -> e
26.98/8.80	   c -> k
26.98/8.80	
26.98/8.80	Q is empty.
26.98/8.80	We have to consider all minimal (P,Q,R)-chains.
26.98/8.80	----------------------------------------
26.98/8.80	
26.98/8.80	(557) TransformationProof (EQUIVALENT)
26.98/8.80	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.80	
26.98/8.80	   (A^2 -> H(a, U1(d, b)),A^2 -> H(a, U1(d, b)))
26.98/8.80	   (A^2 -> H(U1(e, c), U1(d, b)),A^2 -> H(U1(e, c), U1(d, b)))
26.98/8.80	   (A^2 -> H(U1(e, d), U1(d, b)),A^2 -> H(U1(e, d), U1(d, b)))
26.98/8.80	   (A^2 -> H(U1(e, a), U1(k, b)),A^2 -> H(U1(e, a), U1(k, b)))
26.98/8.80	   (A^2 -> H(U1(e, a), U1(d, c)),A^2 -> H(U1(e, a), U1(d, c)))
26.98/8.80	   (A^2 -> H(U1(e, a), U1(d, d)),A^2 -> H(U1(e, a), U1(d, d)))
26.98/8.80	
26.98/8.80	
26.98/8.80	----------------------------------------
26.98/8.80	
26.98/8.80	(558)
26.98/8.80	Obligation:
26.98/8.80	Q DP problem:
26.98/8.80	The TRS P consists of the following rules:
26.98/8.80	
26.98/8.80	   H(x, x) -> G(x, x, f(k))
26.98/8.80	   G(d, x, x) -> A^2
26.98/8.80	   A^2 -> H(f(c), f(c))
26.98/8.80	   A^2 -> H(f(d), f(d))
26.98/8.80	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.80	   A^2 -> H(f(e), f(e))
26.98/8.80	   A^2 -> H(f(k), f(k))
26.98/8.80	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.80	   A^2 -> H(U1(e, a), U1(b, c))
26.98/8.80	   A^2 -> H(U1(e, a), U1(b, d))
26.98/8.80	   A^2 -> H(U1(e, a), U1(c, c))
26.98/8.80	   A^2 -> H(U1(e, a), f(e))
26.98/8.80	   A^2 -> H(U1(e, a), f(k))
26.98/8.80	   A^2 -> H(U1(e, a), U1(d, d))
26.98/8.80	   A^2 -> H(U1(k, a), U1(c, b))
26.98/8.80	   A^2 -> H(U1(k, a), U1(d, b))
26.98/8.80	   A^2 -> H(U1(k, a), U1(b, c))
26.98/8.80	   A^2 -> H(U1(k, a), U1(b, d))
26.98/8.80	   A^2 -> H(U1(k, a), U1(c, c))
26.98/8.80	   A^2 -> H(U1(k, a), f(e))
26.98/8.80	   A^2 -> H(U1(k, a), f(k))
26.98/8.80	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.80	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.80	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.80	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.80	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.80	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.80	   A^2 -> H(U1(c, d), f(e))
26.98/8.80	   A^2 -> H(U1(c, d), f(k))
26.98/8.80	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.80	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.80	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.80	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.80	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.80	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.80	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.80	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.80	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.80	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.80	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.80	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.80	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.80	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.80	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.80	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.80	   A^2 -> H(U1(d, e), f(c))
26.98/8.80	   A^2 -> H(U1(d, e), f(d))
26.98/8.80	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.80	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.80	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.80	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.80	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.80	   A^2 -> H(U1(d, c), f(e))
26.98/8.80	   A^2 -> H(U1(d, c), f(k))
26.98/8.80	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.80	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.80	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.80	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.80	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.80	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.80	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.80	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.80	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.80	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.80	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.80	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.80	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.80	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.80	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.80	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.80	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.80	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.80	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.80	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.80	   A^2 -> H(U1(a, e), f(e))
26.98/8.80	   A^2 -> H(U1(a, e), f(k))
26.98/8.80	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.80	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.80	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.80	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.80	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.80	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.80	   A^2 -> H(U1(a, k), f(e))
26.98/8.80	   A^2 -> H(U1(a, k), f(k))
26.98/8.80	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.80	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.80	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.80	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.80	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.80	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.80	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.80	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.80	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.80	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.80	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.80	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.80	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.80	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.80	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.80	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.80	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.80	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.80	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.80	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.80	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.80	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.80	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.80	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.80	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.80	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.80	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.80	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.80	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.80	   A^2 -> H(U1(a, a), b)
26.98/8.80	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.80	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.80	   A^2 -> H(U1(a, a), c)
26.98/8.80	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.80	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.80	   A^2 -> H(U1(a, a), e)
26.98/8.80	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.80	   A^2 -> H(k, f(b))
26.98/8.80	   A^2 -> H(c, U1(b, b))
26.98/8.80	   A^2 -> H(c, f(c))
26.98/8.80	   A^2 -> H(c, f(d))
26.98/8.80	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.80	   A^2 -> H(U1(e, k), f(c))
26.98/8.80	   A^2 -> H(U1(e, k), f(d))
26.98/8.80	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.80	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.80	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.80	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.80	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.80	   A^2 -> H(U1(e, c), f(e))
26.98/8.80	   A^2 -> H(U1(e, c), f(k))
26.98/8.80	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.80	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.80	   A^2 -> H(U1(k, e), f(c))
26.98/8.80	   A^2 -> H(U1(k, e), f(d))
26.98/8.80	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.80	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.80	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.80	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.80	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.80	   A^2 -> H(U1(k, c), f(e))
26.98/8.80	   A^2 -> H(U1(k, c), f(k))
26.98/8.80	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.80	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.80	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.80	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.80	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.80	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.80	   A^2 -> H(U1(c, e), f(e))
26.98/8.80	   A^2 -> H(U1(c, e), f(k))
26.98/8.80	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.80	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.80	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.80	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.80	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.80	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.80	   A^2 -> H(U1(c, k), f(e))
26.98/8.80	   A^2 -> H(U1(c, k), f(k))
26.98/8.80	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.80	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.80	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.80	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.80	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.80	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.80	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.80	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.80	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.80	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.80	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.80	   A^2 -> H(e, U1(b, b))
26.98/8.80	   A^2 -> H(e, f(c))
26.98/8.80	   A^2 -> H(e, f(d))
26.98/8.80	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.80	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.80	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.80	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.80	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.80	   A^2 -> H(U1(e, e), f(e))
26.98/8.80	   A^2 -> H(U1(e, e), f(k))
26.98/8.80	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.80	   A^2 -> H(f(e), U1(e, b))
26.98/8.80	   A^2 -> H(f(e), U1(k, b))
26.98/8.80	   A^2 -> H(f(e), U1(c, d))
26.98/8.80	   A^2 -> H(f(e), U1(d, c))
26.98/8.80	   A^2 -> H(f(e), U1(b, e))
26.98/8.80	   A^2 -> H(f(e), U1(b, k))
26.98/8.80	   A^2 -> H(f(e), U1(e, c))
26.98/8.80	   A^2 -> H(f(e), U1(k, c))
26.98/8.80	   A^2 -> H(f(e), U1(c, e))
26.98/8.80	   A^2 -> H(f(e), U1(c, k))
26.98/8.80	   A^2 -> H(f(e), U1(k, k))
26.98/8.80	   A^2 -> H(f(e), U1(k, d))
26.98/8.80	   A^2 -> H(f(e), U1(d, k))
26.98/8.80	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.80	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.80	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.80	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.80	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.80	   A^2 -> H(U1(k, k), f(e))
26.98/8.80	   A^2 -> H(U1(k, k), f(k))
26.98/8.80	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.80	   A^2 -> H(f(k), U1(e, b))
26.98/8.80	   A^2 -> H(f(k), U1(k, b))
26.98/8.80	   A^2 -> H(f(k), U1(c, d))
26.98/8.80	   A^2 -> H(f(k), U1(d, c))
26.98/8.80	   A^2 -> H(f(k), U1(b, e))
26.98/8.80	   A^2 -> H(f(k), U1(b, k))
26.98/8.80	   A^2 -> H(f(k), U1(e, c))
26.98/8.80	   A^2 -> H(f(k), U1(k, c))
26.98/8.80	   A^2 -> H(f(k), U1(c, e))
26.98/8.80	   A^2 -> H(f(k), U1(c, k))
26.98/8.80	   A^2 -> H(f(k), U1(e, e))
26.98/8.80	   A^2 -> H(f(k), U1(k, d))
26.98/8.80	   A^2 -> H(f(k), U1(d, k))
26.98/8.80	   A^2 -> H(f(c), b)
26.98/8.80	   A^2 -> H(f(c), U1(e, d))
26.98/8.80	   A^2 -> H(f(c), U1(d, e))
26.98/8.80	   A^2 -> H(f(k), U1(k, k))
26.98/8.80	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.80	   A^2 -> H(U1(k, k), f(c))
26.98/8.80	   A^2 -> H(U1(k, k), f(d))
26.98/8.80	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.80	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.80	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.80	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.80	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.80	   A^2 -> H(U1(k, d), f(e))
26.98/8.80	   A^2 -> H(U1(k, d), f(k))
26.98/8.80	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.80	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.80	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.80	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.80	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.80	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.80	   A^2 -> H(U1(d, k), f(e))
26.98/8.80	   A^2 -> H(U1(d, k), f(k))
26.98/8.80	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.80	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.80	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.80	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.80	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.80	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.80	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.80	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.80	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.80	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.80	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.80	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.80	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.80	   A^2 -> H(f(d), b)
26.98/8.80	   A^2 -> H(f(d), U1(e, d))
26.98/8.80	   A^2 -> H(f(d), U1(d, e))
26.98/8.80	   A^2 -> H(f(d), c)
26.98/8.80	   A^2 -> H(f(d), U1(e, k))
26.98/8.80	   A^2 -> H(f(d), U1(k, e))
26.98/8.80	   A^2 -> H(f(d), e)
26.98/8.80	   A^2 -> H(f(a), d)
26.98/8.80	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.80	   A^2 -> H(f(c), c)
26.98/8.80	   A^2 -> H(f(c), U1(e, k))
26.98/8.80	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.80	   A^2 -> H(f(c), U1(k, e))
26.98/8.80	   A^2 -> H(f(c), U1(k, k))
26.98/8.80	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.80	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.80	   A^2 -> H(f(a), k)
26.98/8.80	   A^2 -> H(f(e), U1(e, e))
26.98/8.80	   A^2 -> H(f(c), e)
26.98/8.80	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.80	   A^2 -> H(f(d), U1(k, k))
26.98/8.80	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.80	   A^2 -> H(d, U1(b, b))
26.98/8.80	   A^2 -> H(d, f(c))
26.98/8.80	   A^2 -> H(d, f(d))
26.98/8.80	   A^2 -> H(a, U1(c, b))
26.98/8.80	   A^2 -> H(a, U1(d, b))
26.98/8.80	   A^2 -> H(a, U1(b, c))
26.98/8.80	   A^2 -> H(a, U1(b, d))
26.98/8.80	   A^2 -> H(a, U1(c, c))
26.98/8.80	   A^2 -> H(a, f(e))
26.98/8.80	   A^2 -> H(a, f(k))
26.98/8.80	   A^2 -> H(a, U1(d, d))
26.98/8.80	   A^2 -> H(U1(e, d), U1(c, b))
26.98/8.80	   A^2 -> H(U1(e, d), U1(d, b))
26.98/8.80	   A^2 -> H(U1(e, d), U1(b, c))
26.98/8.80	   A^2 -> H(U1(e, d), U1(b, d))
26.98/8.80	   A^2 -> H(U1(e, d), U1(c, c))
26.98/8.80	   A^2 -> H(U1(e, d), f(e))
26.98/8.80	   A^2 -> H(U1(e, d), f(k))
26.98/8.80	   A^2 -> H(U1(e, d), U1(d, d))
26.98/8.80	   A^2 -> H(U1(e, a), U1(e, b))
26.98/8.80	   A^2 -> H(U1(e, a), U1(k, b))
26.98/8.80	   A^2 -> H(U1(e, a), U1(c, d))
26.98/8.80	   A^2 -> H(U1(e, a), U1(d, c))
26.98/8.80	
26.98/8.80	The TRS R consists of the following rules:
26.98/8.80	
26.98/8.80	   f(x) -> U1(x, x)
26.98/8.80	   U1(e, x) -> x
26.98/8.80	   a -> c
26.98/8.80	   a -> d
26.98/8.80	   b -> c
26.98/8.80	   b -> d
26.98/8.80	   d -> k
26.98/8.80	   c -> e
26.98/8.80	   c -> k
26.98/8.80	
26.98/8.80	Q is empty.
26.98/8.80	We have to consider all minimal (P,Q,R)-chains.
26.98/8.80	----------------------------------------
26.98/8.80	
26.98/8.80	(559) TransformationProof (EQUIVALENT)
26.98/8.80	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.80	
26.98/8.80	   (A^2 -> H(a, U1(b, c)),A^2 -> H(a, U1(b, c)))
26.98/8.80	   (A^2 -> H(U1(e, c), U1(b, c)),A^2 -> H(U1(e, c), U1(b, c)))
26.98/8.80	   (A^2 -> H(U1(e, d), U1(b, c)),A^2 -> H(U1(e, d), U1(b, c)))
26.98/8.80	   (A^2 -> H(U1(e, a), U1(c, c)),A^2 -> H(U1(e, a), U1(c, c)))
26.98/8.80	   (A^2 -> H(U1(e, a), U1(d, c)),A^2 -> H(U1(e, a), U1(d, c)))
26.98/8.80	   (A^2 -> H(U1(e, a), U1(b, e)),A^2 -> H(U1(e, a), U1(b, e)))
26.98/8.80	   (A^2 -> H(U1(e, a), U1(b, k)),A^2 -> H(U1(e, a), U1(b, k)))
26.98/8.80	
26.98/8.80	
26.98/8.80	----------------------------------------
26.98/8.80	
26.98/8.80	(560)
26.98/8.80	Obligation:
26.98/8.80	Q DP problem:
26.98/8.80	The TRS P consists of the following rules:
26.98/8.80	
26.98/8.80	   H(x, x) -> G(x, x, f(k))
26.98/8.80	   G(d, x, x) -> A^2
26.98/8.80	   A^2 -> H(f(c), f(c))
26.98/8.80	   A^2 -> H(f(d), f(d))
26.98/8.80	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.80	   A^2 -> H(f(e), f(e))
26.98/8.80	   A^2 -> H(f(k), f(k))
26.98/8.80	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.80	   A^2 -> H(U1(e, a), U1(b, d))
26.98/8.80	   A^2 -> H(U1(e, a), U1(c, c))
26.98/8.80	   A^2 -> H(U1(e, a), f(e))
26.98/8.80	   A^2 -> H(U1(e, a), f(k))
26.98/8.80	   A^2 -> H(U1(e, a), U1(d, d))
26.98/8.80	   A^2 -> H(U1(k, a), U1(c, b))
26.98/8.80	   A^2 -> H(U1(k, a), U1(d, b))
26.98/8.80	   A^2 -> H(U1(k, a), U1(b, c))
26.98/8.80	   A^2 -> H(U1(k, a), U1(b, d))
26.98/8.80	   A^2 -> H(U1(k, a), U1(c, c))
26.98/8.80	   A^2 -> H(U1(k, a), f(e))
26.98/8.80	   A^2 -> H(U1(k, a), f(k))
26.98/8.80	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.80	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.80	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.80	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.80	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.80	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.80	   A^2 -> H(U1(c, d), f(e))
26.98/8.80	   A^2 -> H(U1(c, d), f(k))
26.98/8.80	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.80	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.80	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.80	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.80	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.80	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.80	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.80	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.80	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.80	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.80	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.80	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.80	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.80	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.80	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.80	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.80	   A^2 -> H(U1(d, e), f(c))
26.98/8.80	   A^2 -> H(U1(d, e), f(d))
26.98/8.80	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.80	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.80	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.80	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.80	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.80	   A^2 -> H(U1(d, c), f(e))
26.98/8.80	   A^2 -> H(U1(d, c), f(k))
26.98/8.80	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.80	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.80	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.80	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.80	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.80	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.80	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.80	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.80	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.80	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.80	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.80	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.80	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.80	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.80	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.80	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.80	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.80	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.80	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.80	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.80	   A^2 -> H(U1(a, e), f(e))
26.98/8.80	   A^2 -> H(U1(a, e), f(k))
26.98/8.80	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.80	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.80	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.80	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.80	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.80	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.80	   A^2 -> H(U1(a, k), f(e))
26.98/8.80	   A^2 -> H(U1(a, k), f(k))
26.98/8.80	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.80	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.80	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.80	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.80	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.80	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.80	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.80	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.80	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.80	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.80	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.80	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.80	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.80	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.80	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.80	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.80	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.80	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.80	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.80	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.80	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.80	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.80	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.80	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.80	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.80	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.80	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.80	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.80	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.80	   A^2 -> H(U1(a, a), b)
26.98/8.80	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.80	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.80	   A^2 -> H(U1(a, a), c)
26.98/8.80	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.80	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.80	   A^2 -> H(U1(a, a), e)
26.98/8.80	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.80	   A^2 -> H(k, f(b))
26.98/8.80	   A^2 -> H(c, U1(b, b))
26.98/8.80	   A^2 -> H(c, f(c))
26.98/8.80	   A^2 -> H(c, f(d))
26.98/8.80	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.80	   A^2 -> H(U1(e, k), f(c))
26.98/8.80	   A^2 -> H(U1(e, k), f(d))
26.98/8.80	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.80	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.80	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.80	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.80	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.80	   A^2 -> H(U1(e, c), f(e))
26.98/8.80	   A^2 -> H(U1(e, c), f(k))
26.98/8.80	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.80	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.80	   A^2 -> H(U1(k, e), f(c))
26.98/8.80	   A^2 -> H(U1(k, e), f(d))
26.98/8.80	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.80	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.80	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.80	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.80	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.80	   A^2 -> H(U1(k, c), f(e))
26.98/8.80	   A^2 -> H(U1(k, c), f(k))
26.98/8.80	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.80	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.80	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.80	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.80	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.80	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.80	   A^2 -> H(U1(c, e), f(e))
26.98/8.80	   A^2 -> H(U1(c, e), f(k))
26.98/8.80	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.80	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(c, k), f(e))
26.98/8.81	   A^2 -> H(U1(c, k), f(k))
26.98/8.81	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.81	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.81	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.81	   A^2 -> H(e, U1(b, b))
26.98/8.81	   A^2 -> H(e, f(c))
26.98/8.81	   A^2 -> H(e, f(d))
26.98/8.81	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.81	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.81	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.81	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.81	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, e), f(e))
26.98/8.81	   A^2 -> H(U1(e, e), f(k))
26.98/8.81	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.81	   A^2 -> H(f(e), U1(e, b))
26.98/8.81	   A^2 -> H(f(e), U1(k, b))
26.98/8.81	   A^2 -> H(f(e), U1(c, d))
26.98/8.81	   A^2 -> H(f(e), U1(d, c))
26.98/8.81	   A^2 -> H(f(e), U1(b, e))
26.98/8.81	   A^2 -> H(f(e), U1(b, k))
26.98/8.81	   A^2 -> H(f(e), U1(e, c))
26.98/8.81	   A^2 -> H(f(e), U1(k, c))
26.98/8.81	   A^2 -> H(f(e), U1(c, e))
26.98/8.81	   A^2 -> H(f(e), U1(c, k))
26.98/8.81	   A^2 -> H(f(e), U1(k, k))
26.98/8.81	   A^2 -> H(f(e), U1(k, d))
26.98/8.81	   A^2 -> H(f(e), U1(d, k))
26.98/8.81	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, k), f(e))
26.98/8.81	   A^2 -> H(U1(k, k), f(k))
26.98/8.81	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.81	   A^2 -> H(f(k), U1(e, b))
26.98/8.81	   A^2 -> H(f(k), U1(k, b))
26.98/8.81	   A^2 -> H(f(k), U1(c, d))
26.98/8.81	   A^2 -> H(f(k), U1(d, c))
26.98/8.81	   A^2 -> H(f(k), U1(b, e))
26.98/8.81	   A^2 -> H(f(k), U1(b, k))
26.98/8.81	   A^2 -> H(f(k), U1(e, c))
26.98/8.81	   A^2 -> H(f(k), U1(k, c))
26.98/8.81	   A^2 -> H(f(k), U1(c, e))
26.98/8.81	   A^2 -> H(f(k), U1(c, k))
26.98/8.81	   A^2 -> H(f(k), U1(e, e))
26.98/8.81	   A^2 -> H(f(k), U1(k, d))
26.98/8.81	   A^2 -> H(f(k), U1(d, k))
26.98/8.81	   A^2 -> H(f(c), b)
26.98/8.81	   A^2 -> H(f(c), U1(e, d))
26.98/8.81	   A^2 -> H(f(c), U1(d, e))
26.98/8.81	   A^2 -> H(f(k), U1(k, k))
26.98/8.81	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.81	   A^2 -> H(U1(k, k), f(c))
26.98/8.81	   A^2 -> H(U1(k, k), f(d))
26.98/8.81	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, d), f(e))
26.98/8.81	   A^2 -> H(U1(k, d), f(k))
26.98/8.81	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(d, k), f(e))
26.98/8.81	   A^2 -> H(U1(d, k), f(k))
26.98/8.81	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.81	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.81	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.81	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.81	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.81	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.81	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.81	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.81	   A^2 -> H(f(d), b)
26.98/8.81	   A^2 -> H(f(d), U1(e, d))
26.98/8.81	   A^2 -> H(f(d), U1(d, e))
26.98/8.81	   A^2 -> H(f(d), c)
26.98/8.81	   A^2 -> H(f(d), U1(e, k))
26.98/8.81	   A^2 -> H(f(d), U1(k, e))
26.98/8.81	   A^2 -> H(f(d), e)
26.98/8.81	   A^2 -> H(f(a), d)
26.98/8.81	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.81	   A^2 -> H(f(c), c)
26.98/8.81	   A^2 -> H(f(c), U1(e, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.81	   A^2 -> H(f(c), U1(k, e))
26.98/8.81	   A^2 -> H(f(c), U1(k, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.81	   A^2 -> H(f(a), k)
26.98/8.81	   A^2 -> H(f(e), U1(e, e))
26.98/8.81	   A^2 -> H(f(c), e)
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.81	   A^2 -> H(f(d), U1(k, k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.81	   A^2 -> H(d, U1(b, b))
26.98/8.81	   A^2 -> H(d, f(c))
26.98/8.81	   A^2 -> H(d, f(d))
26.98/8.81	   A^2 -> H(a, U1(c, b))
26.98/8.81	   A^2 -> H(a, U1(d, b))
26.98/8.81	   A^2 -> H(a, U1(b, c))
26.98/8.81	   A^2 -> H(a, U1(b, d))
26.98/8.81	   A^2 -> H(a, U1(c, c))
26.98/8.81	   A^2 -> H(a, f(e))
26.98/8.81	   A^2 -> H(a, f(k))
26.98/8.81	   A^2 -> H(a, U1(d, d))
26.98/8.81	   A^2 -> H(U1(e, d), U1(c, b))
26.98/8.81	   A^2 -> H(U1(e, d), U1(d, b))
26.98/8.81	   A^2 -> H(U1(e, d), U1(b, c))
26.98/8.81	   A^2 -> H(U1(e, d), U1(b, d))
26.98/8.81	   A^2 -> H(U1(e, d), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, d), f(e))
26.98/8.81	   A^2 -> H(U1(e, d), f(k))
26.98/8.81	   A^2 -> H(U1(e, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(e, a), U1(e, b))
26.98/8.81	   A^2 -> H(U1(e, a), U1(k, b))
26.98/8.81	   A^2 -> H(U1(e, a), U1(c, d))
26.98/8.81	   A^2 -> H(U1(e, a), U1(d, c))
26.98/8.81	   A^2 -> H(U1(e, a), U1(b, e))
26.98/8.81	   A^2 -> H(U1(e, a), U1(b, k))
26.98/8.81	
26.98/8.81	The TRS R consists of the following rules:
26.98/8.81	
26.98/8.81	   f(x) -> U1(x, x)
26.98/8.81	   U1(e, x) -> x
26.98/8.81	   a -> c
26.98/8.81	   a -> d
26.98/8.81	   b -> c
26.98/8.81	   b -> d
26.98/8.81	   d -> k
26.98/8.81	   c -> e
26.98/8.81	   c -> k
26.98/8.81	
26.98/8.81	Q is empty.
26.98/8.81	We have to consider all minimal (P,Q,R)-chains.
26.98/8.81	----------------------------------------
26.98/8.81	
26.98/8.81	(561) TransformationProof (EQUIVALENT)
26.98/8.81	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.81	
26.98/8.81	   (A^2 -> H(a, U1(b, d)),A^2 -> H(a, U1(b, d)))
26.98/8.81	   (A^2 -> H(U1(e, c), U1(b, d)),A^2 -> H(U1(e, c), U1(b, d)))
26.98/8.81	   (A^2 -> H(U1(e, d), U1(b, d)),A^2 -> H(U1(e, d), U1(b, d)))
26.98/8.81	   (A^2 -> H(U1(e, a), U1(c, d)),A^2 -> H(U1(e, a), U1(c, d)))
26.98/8.81	   (A^2 -> H(U1(e, a), U1(d, d)),A^2 -> H(U1(e, a), U1(d, d)))
26.98/8.81	   (A^2 -> H(U1(e, a), U1(b, k)),A^2 -> H(U1(e, a), U1(b, k)))
26.98/8.81	
26.98/8.81	
26.98/8.81	----------------------------------------
26.98/8.81	
26.98/8.81	(562)
26.98/8.81	Obligation:
26.98/8.81	Q DP problem:
26.98/8.81	The TRS P consists of the following rules:
26.98/8.81	
26.98/8.81	   H(x, x) -> G(x, x, f(k))
26.98/8.81	   G(d, x, x) -> A^2
26.98/8.81	   A^2 -> H(f(c), f(c))
26.98/8.81	   A^2 -> H(f(d), f(d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.81	   A^2 -> H(f(e), f(e))
26.98/8.81	   A^2 -> H(f(k), f(k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(e, a), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, a), f(e))
26.98/8.81	   A^2 -> H(U1(e, a), f(k))
26.98/8.81	   A^2 -> H(U1(e, a), U1(d, d))
26.98/8.81	   A^2 -> H(U1(k, a), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, a), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, a), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, a), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, a), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, a), f(e))
26.98/8.81	   A^2 -> H(U1(k, a), f(k))
26.98/8.81	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.81	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.81	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.81	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.81	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.81	   A^2 -> H(U1(c, d), f(e))
26.98/8.81	   A^2 -> H(U1(c, d), f(k))
26.98/8.81	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.81	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.81	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.81	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.81	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.81	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.81	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.81	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.81	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.81	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.81	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.81	   A^2 -> H(U1(d, e), f(c))
26.98/8.81	   A^2 -> H(U1(d, e), f(d))
26.98/8.81	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.81	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.81	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.81	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.81	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.81	   A^2 -> H(U1(d, c), f(e))
26.98/8.81	   A^2 -> H(U1(d, c), f(k))
26.98/8.81	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.81	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.81	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.81	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.81	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.81	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.81	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.81	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.81	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.81	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.81	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.81	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.81	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.81	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.81	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.81	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.81	   A^2 -> H(U1(a, e), f(e))
26.98/8.81	   A^2 -> H(U1(a, e), f(k))
26.98/8.81	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.81	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(a, k), f(e))
26.98/8.81	   A^2 -> H(U1(a, k), f(k))
26.98/8.81	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.81	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.81	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.81	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.81	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.81	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.81	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.81	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.81	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.81	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.81	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.81	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.81	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.81	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.81	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.81	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.81	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.81	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.81	   A^2 -> H(U1(a, a), b)
26.98/8.81	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.81	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.81	   A^2 -> H(U1(a, a), c)
26.98/8.81	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.81	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.81	   A^2 -> H(U1(a, a), e)
26.98/8.81	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.81	   A^2 -> H(k, f(b))
26.98/8.81	   A^2 -> H(c, U1(b, b))
26.98/8.81	   A^2 -> H(c, f(c))
26.98/8.81	   A^2 -> H(c, f(d))
26.98/8.81	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.81	   A^2 -> H(U1(e, k), f(c))
26.98/8.81	   A^2 -> H(U1(e, k), f(d))
26.98/8.81	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.81	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.81	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.81	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.81	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, c), f(e))
26.98/8.81	   A^2 -> H(U1(e, c), f(k))
26.98/8.81	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.81	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.81	   A^2 -> H(U1(k, e), f(c))
26.98/8.81	   A^2 -> H(U1(k, e), f(d))
26.98/8.81	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, c), f(e))
26.98/8.81	   A^2 -> H(U1(k, c), f(k))
26.98/8.81	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.81	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.81	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.81	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.81	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.81	   A^2 -> H(U1(c, e), f(e))
26.98/8.81	   A^2 -> H(U1(c, e), f(k))
26.98/8.81	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(c, k), f(e))
26.98/8.81	   A^2 -> H(U1(c, k), f(k))
26.98/8.81	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.81	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.81	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.81	   A^2 -> H(e, U1(b, b))
26.98/8.81	   A^2 -> H(e, f(c))
26.98/8.81	   A^2 -> H(e, f(d))
26.98/8.81	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.81	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.81	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.81	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.81	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, e), f(e))
26.98/8.81	   A^2 -> H(U1(e, e), f(k))
26.98/8.81	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.81	   A^2 -> H(f(e), U1(e, b))
26.98/8.81	   A^2 -> H(f(e), U1(k, b))
26.98/8.81	   A^2 -> H(f(e), U1(c, d))
26.98/8.81	   A^2 -> H(f(e), U1(d, c))
26.98/8.81	   A^2 -> H(f(e), U1(b, e))
26.98/8.81	   A^2 -> H(f(e), U1(b, k))
26.98/8.81	   A^2 -> H(f(e), U1(e, c))
26.98/8.81	   A^2 -> H(f(e), U1(k, c))
26.98/8.81	   A^2 -> H(f(e), U1(c, e))
26.98/8.81	   A^2 -> H(f(e), U1(c, k))
26.98/8.81	   A^2 -> H(f(e), U1(k, k))
26.98/8.81	   A^2 -> H(f(e), U1(k, d))
26.98/8.81	   A^2 -> H(f(e), U1(d, k))
26.98/8.81	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, k), f(e))
26.98/8.81	   A^2 -> H(U1(k, k), f(k))
26.98/8.81	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.81	   A^2 -> H(f(k), U1(e, b))
26.98/8.81	   A^2 -> H(f(k), U1(k, b))
26.98/8.81	   A^2 -> H(f(k), U1(c, d))
26.98/8.81	   A^2 -> H(f(k), U1(d, c))
26.98/8.81	   A^2 -> H(f(k), U1(b, e))
26.98/8.81	   A^2 -> H(f(k), U1(b, k))
26.98/8.81	   A^2 -> H(f(k), U1(e, c))
26.98/8.81	   A^2 -> H(f(k), U1(k, c))
26.98/8.81	   A^2 -> H(f(k), U1(c, e))
26.98/8.81	   A^2 -> H(f(k), U1(c, k))
26.98/8.81	   A^2 -> H(f(k), U1(e, e))
26.98/8.81	   A^2 -> H(f(k), U1(k, d))
26.98/8.81	   A^2 -> H(f(k), U1(d, k))
26.98/8.81	   A^2 -> H(f(c), b)
26.98/8.81	   A^2 -> H(f(c), U1(e, d))
26.98/8.81	   A^2 -> H(f(c), U1(d, e))
26.98/8.81	   A^2 -> H(f(k), U1(k, k))
26.98/8.81	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.81	   A^2 -> H(U1(k, k), f(c))
26.98/8.81	   A^2 -> H(U1(k, k), f(d))
26.98/8.81	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, d), f(e))
26.98/8.81	   A^2 -> H(U1(k, d), f(k))
26.98/8.81	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(d, k), f(e))
26.98/8.81	   A^2 -> H(U1(d, k), f(k))
26.98/8.81	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.81	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.81	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.81	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.81	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.81	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.81	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.81	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.81	   A^2 -> H(f(d), b)
26.98/8.81	   A^2 -> H(f(d), U1(e, d))
26.98/8.81	   A^2 -> H(f(d), U1(d, e))
26.98/8.81	   A^2 -> H(f(d), c)
26.98/8.81	   A^2 -> H(f(d), U1(e, k))
26.98/8.81	   A^2 -> H(f(d), U1(k, e))
26.98/8.81	   A^2 -> H(f(d), e)
26.98/8.81	   A^2 -> H(f(a), d)
26.98/8.81	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.81	   A^2 -> H(f(c), c)
26.98/8.81	   A^2 -> H(f(c), U1(e, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.81	   A^2 -> H(f(c), U1(k, e))
26.98/8.81	   A^2 -> H(f(c), U1(k, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.81	   A^2 -> H(f(a), k)
26.98/8.81	   A^2 -> H(f(e), U1(e, e))
26.98/8.81	   A^2 -> H(f(c), e)
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.81	   A^2 -> H(f(d), U1(k, k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.81	   A^2 -> H(d, U1(b, b))
26.98/8.81	   A^2 -> H(d, f(c))
26.98/8.81	   A^2 -> H(d, f(d))
26.98/8.81	   A^2 -> H(a, U1(c, b))
26.98/8.81	   A^2 -> H(a, U1(d, b))
26.98/8.81	   A^2 -> H(a, U1(b, c))
26.98/8.81	   A^2 -> H(a, U1(b, d))
26.98/8.81	   A^2 -> H(a, U1(c, c))
26.98/8.81	   A^2 -> H(a, f(e))
26.98/8.81	   A^2 -> H(a, f(k))
26.98/8.81	   A^2 -> H(a, U1(d, d))
26.98/8.81	   A^2 -> H(U1(e, d), U1(c, b))
26.98/8.81	   A^2 -> H(U1(e, d), U1(d, b))
26.98/8.81	   A^2 -> H(U1(e, d), U1(b, c))
26.98/8.81	   A^2 -> H(U1(e, d), U1(b, d))
26.98/8.81	   A^2 -> H(U1(e, d), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, d), f(e))
26.98/8.81	   A^2 -> H(U1(e, d), f(k))
26.98/8.81	   A^2 -> H(U1(e, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(e, a), U1(e, b))
26.98/8.81	   A^2 -> H(U1(e, a), U1(k, b))
26.98/8.81	   A^2 -> H(U1(e, a), U1(c, d))
26.98/8.81	   A^2 -> H(U1(e, a), U1(d, c))
26.98/8.81	   A^2 -> H(U1(e, a), U1(b, e))
26.98/8.81	   A^2 -> H(U1(e, a), U1(b, k))
26.98/8.81	
26.98/8.81	The TRS R consists of the following rules:
26.98/8.81	
26.98/8.81	   f(x) -> U1(x, x)
26.98/8.81	   U1(e, x) -> x
26.98/8.81	   a -> c
26.98/8.81	   a -> d
26.98/8.81	   b -> c
26.98/8.81	   b -> d
26.98/8.81	   d -> k
26.98/8.81	   c -> e
26.98/8.81	   c -> k
26.98/8.81	
26.98/8.81	Q is empty.
26.98/8.81	We have to consider all minimal (P,Q,R)-chains.
26.98/8.81	----------------------------------------
26.98/8.81	
26.98/8.81	(563) TransformationProof (EQUIVALENT)
26.98/8.81	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.81	
26.98/8.81	   (A^2 -> H(a, U1(c, c)),A^2 -> H(a, U1(c, c)))
26.98/8.81	   (A^2 -> H(U1(e, c), U1(c, c)),A^2 -> H(U1(e, c), U1(c, c)))
26.98/8.81	   (A^2 -> H(U1(e, d), U1(c, c)),A^2 -> H(U1(e, d), U1(c, c)))
26.98/8.81	   (A^2 -> H(U1(e, a), U1(e, c)),A^2 -> H(U1(e, a), U1(e, c)))
26.98/8.81	   (A^2 -> H(U1(e, a), U1(k, c)),A^2 -> H(U1(e, a), U1(k, c)))
26.98/8.81	   (A^2 -> H(U1(e, a), U1(c, e)),A^2 -> H(U1(e, a), U1(c, e)))
26.98/8.81	   (A^2 -> H(U1(e, a), U1(c, k)),A^2 -> H(U1(e, a), U1(c, k)))
26.98/8.81	
26.98/8.81	
26.98/8.81	----------------------------------------
26.98/8.81	
26.98/8.81	(564)
26.98/8.81	Obligation:
26.98/8.81	Q DP problem:
26.98/8.81	The TRS P consists of the following rules:
26.98/8.81	
26.98/8.81	   H(x, x) -> G(x, x, f(k))
26.98/8.81	   G(d, x, x) -> A^2
26.98/8.81	   A^2 -> H(f(c), f(c))
26.98/8.81	   A^2 -> H(f(d), f(d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.81	   A^2 -> H(f(e), f(e))
26.98/8.81	   A^2 -> H(f(k), f(k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(e, a), f(e))
26.98/8.81	   A^2 -> H(U1(e, a), f(k))
26.98/8.81	   A^2 -> H(U1(e, a), U1(d, d))
26.98/8.81	   A^2 -> H(U1(k, a), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, a), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, a), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, a), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, a), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, a), f(e))
26.98/8.81	   A^2 -> H(U1(k, a), f(k))
26.98/8.81	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.81	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.81	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.81	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.81	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.81	   A^2 -> H(U1(c, d), f(e))
26.98/8.81	   A^2 -> H(U1(c, d), f(k))
26.98/8.81	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.81	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.81	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.81	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.81	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.81	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.81	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.81	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.81	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.81	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.81	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.81	   A^2 -> H(U1(d, e), f(c))
26.98/8.81	   A^2 -> H(U1(d, e), f(d))
26.98/8.81	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.81	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.81	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.81	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.81	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.81	   A^2 -> H(U1(d, c), f(e))
26.98/8.81	   A^2 -> H(U1(d, c), f(k))
26.98/8.81	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.81	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.81	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.81	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.81	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.81	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.81	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.81	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.81	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.81	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.81	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.81	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.81	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.81	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.81	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.81	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.81	   A^2 -> H(U1(a, e), f(e))
26.98/8.81	   A^2 -> H(U1(a, e), f(k))
26.98/8.81	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.81	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(a, k), f(e))
26.98/8.81	   A^2 -> H(U1(a, k), f(k))
26.98/8.81	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.81	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.81	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.81	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.81	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.81	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.81	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.81	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.81	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.81	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.81	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.81	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.81	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.81	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.81	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.81	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.81	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.81	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.81	   A^2 -> H(U1(a, a), b)
26.98/8.81	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.81	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.81	   A^2 -> H(U1(a, a), c)
26.98/8.81	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.81	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.81	   A^2 -> H(U1(a, a), e)
26.98/8.81	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.81	   A^2 -> H(k, f(b))
26.98/8.81	   A^2 -> H(c, U1(b, b))
26.98/8.81	   A^2 -> H(c, f(c))
26.98/8.81	   A^2 -> H(c, f(d))
26.98/8.81	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.81	   A^2 -> H(U1(e, k), f(c))
26.98/8.81	   A^2 -> H(U1(e, k), f(d))
26.98/8.81	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.81	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.81	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.81	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.81	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, c), f(e))
26.98/8.81	   A^2 -> H(U1(e, c), f(k))
26.98/8.81	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.81	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.81	   A^2 -> H(U1(k, e), f(c))
26.98/8.81	   A^2 -> H(U1(k, e), f(d))
26.98/8.81	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, c), f(e))
26.98/8.81	   A^2 -> H(U1(k, c), f(k))
26.98/8.81	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.81	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.81	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.81	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.81	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.81	   A^2 -> H(U1(c, e), f(e))
26.98/8.81	   A^2 -> H(U1(c, e), f(k))
26.98/8.81	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(c, k), f(e))
26.98/8.81	   A^2 -> H(U1(c, k), f(k))
26.98/8.81	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.81	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.81	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.81	   A^2 -> H(e, U1(b, b))
26.98/8.81	   A^2 -> H(e, f(c))
26.98/8.81	   A^2 -> H(e, f(d))
26.98/8.81	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.81	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.81	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.81	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.81	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, e), f(e))
26.98/8.81	   A^2 -> H(U1(e, e), f(k))
26.98/8.81	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.81	   A^2 -> H(f(e), U1(e, b))
26.98/8.81	   A^2 -> H(f(e), U1(k, b))
26.98/8.81	   A^2 -> H(f(e), U1(c, d))
26.98/8.81	   A^2 -> H(f(e), U1(d, c))
26.98/8.81	   A^2 -> H(f(e), U1(b, e))
26.98/8.81	   A^2 -> H(f(e), U1(b, k))
26.98/8.81	   A^2 -> H(f(e), U1(e, c))
26.98/8.81	   A^2 -> H(f(e), U1(k, c))
26.98/8.81	   A^2 -> H(f(e), U1(c, e))
26.98/8.81	   A^2 -> H(f(e), U1(c, k))
26.98/8.81	   A^2 -> H(f(e), U1(k, k))
26.98/8.81	   A^2 -> H(f(e), U1(k, d))
26.98/8.81	   A^2 -> H(f(e), U1(d, k))
26.98/8.81	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, k), f(e))
26.98/8.81	   A^2 -> H(U1(k, k), f(k))
26.98/8.81	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.81	   A^2 -> H(f(k), U1(e, b))
26.98/8.81	   A^2 -> H(f(k), U1(k, b))
26.98/8.81	   A^2 -> H(f(k), U1(c, d))
26.98/8.81	   A^2 -> H(f(k), U1(d, c))
26.98/8.81	   A^2 -> H(f(k), U1(b, e))
26.98/8.81	   A^2 -> H(f(k), U1(b, k))
26.98/8.81	   A^2 -> H(f(k), U1(e, c))
26.98/8.81	   A^2 -> H(f(k), U1(k, c))
26.98/8.81	   A^2 -> H(f(k), U1(c, e))
26.98/8.81	   A^2 -> H(f(k), U1(c, k))
26.98/8.81	   A^2 -> H(f(k), U1(e, e))
26.98/8.81	   A^2 -> H(f(k), U1(k, d))
26.98/8.81	   A^2 -> H(f(k), U1(d, k))
26.98/8.81	   A^2 -> H(f(c), b)
26.98/8.81	   A^2 -> H(f(c), U1(e, d))
26.98/8.81	   A^2 -> H(f(c), U1(d, e))
26.98/8.81	   A^2 -> H(f(k), U1(k, k))
26.98/8.81	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.81	   A^2 -> H(U1(k, k), f(c))
26.98/8.81	   A^2 -> H(U1(k, k), f(d))
26.98/8.81	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, d), f(e))
26.98/8.81	   A^2 -> H(U1(k, d), f(k))
26.98/8.81	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(d, k), f(e))
26.98/8.81	   A^2 -> H(U1(d, k), f(k))
26.98/8.81	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.81	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.81	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.81	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.81	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.81	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.81	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.81	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.81	   A^2 -> H(f(d), b)
26.98/8.81	   A^2 -> H(f(d), U1(e, d))
26.98/8.81	   A^2 -> H(f(d), U1(d, e))
26.98/8.81	   A^2 -> H(f(d), c)
26.98/8.81	   A^2 -> H(f(d), U1(e, k))
26.98/8.81	   A^2 -> H(f(d), U1(k, e))
26.98/8.81	   A^2 -> H(f(d), e)
26.98/8.81	   A^2 -> H(f(a), d)
26.98/8.81	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.81	   A^2 -> H(f(c), c)
26.98/8.81	   A^2 -> H(f(c), U1(e, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.81	   A^2 -> H(f(c), U1(k, e))
26.98/8.81	   A^2 -> H(f(c), U1(k, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.81	   A^2 -> H(f(a), k)
26.98/8.81	   A^2 -> H(f(e), U1(e, e))
26.98/8.81	   A^2 -> H(f(c), e)
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.81	   A^2 -> H(f(d), U1(k, k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.81	   A^2 -> H(d, U1(b, b))
26.98/8.81	   A^2 -> H(d, f(c))
26.98/8.81	   A^2 -> H(d, f(d))
26.98/8.81	   A^2 -> H(a, U1(c, b))
26.98/8.81	   A^2 -> H(a, U1(d, b))
26.98/8.81	   A^2 -> H(a, U1(b, c))
26.98/8.81	   A^2 -> H(a, U1(b, d))
26.98/8.81	   A^2 -> H(a, U1(c, c))
26.98/8.81	   A^2 -> H(a, f(e))
26.98/8.81	   A^2 -> H(a, f(k))
26.98/8.81	   A^2 -> H(a, U1(d, d))
26.98/8.81	   A^2 -> H(U1(e, d), U1(c, b))
26.98/8.81	   A^2 -> H(U1(e, d), U1(d, b))
26.98/8.81	   A^2 -> H(U1(e, d), U1(b, c))
26.98/8.81	   A^2 -> H(U1(e, d), U1(b, d))
26.98/8.81	   A^2 -> H(U1(e, d), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, d), f(e))
26.98/8.81	   A^2 -> H(U1(e, d), f(k))
26.98/8.81	   A^2 -> H(U1(e, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(e, a), U1(e, b))
26.98/8.81	   A^2 -> H(U1(e, a), U1(k, b))
26.98/8.81	   A^2 -> H(U1(e, a), U1(c, d))
26.98/8.81	   A^2 -> H(U1(e, a), U1(d, c))
26.98/8.81	   A^2 -> H(U1(e, a), U1(b, e))
26.98/8.81	   A^2 -> H(U1(e, a), U1(b, k))
26.98/8.81	   A^2 -> H(U1(e, a), U1(e, c))
26.98/8.81	   A^2 -> H(U1(e, a), U1(k, c))
26.98/8.81	   A^2 -> H(U1(e, a), U1(c, e))
26.98/8.81	   A^2 -> H(U1(e, a), U1(c, k))
26.98/8.81	
26.98/8.81	The TRS R consists of the following rules:
26.98/8.81	
26.98/8.81	   f(x) -> U1(x, x)
26.98/8.81	   U1(e, x) -> x
26.98/8.81	   a -> c
26.98/8.81	   a -> d
26.98/8.81	   b -> c
26.98/8.81	   b -> d
26.98/8.81	   d -> k
26.98/8.81	   c -> e
26.98/8.81	   c -> k
26.98/8.81	
26.98/8.81	Q is empty.
26.98/8.81	We have to consider all minimal (P,Q,R)-chains.
26.98/8.81	----------------------------------------
26.98/8.81	
26.98/8.81	(565) TransformationProof (EQUIVALENT)
26.98/8.81	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), f(e)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.81	
26.98/8.81	   (A^2 -> H(a, f(e)),A^2 -> H(a, f(e)))
26.98/8.81	   (A^2 -> H(U1(e, c), f(e)),A^2 -> H(U1(e, c), f(e)))
26.98/8.81	   (A^2 -> H(U1(e, d), f(e)),A^2 -> H(U1(e, d), f(e)))
26.98/8.81	   (A^2 -> H(U1(e, a), U1(e, e)),A^2 -> H(U1(e, a), U1(e, e)))
26.98/8.81	
26.98/8.81	
26.98/8.81	----------------------------------------
26.98/8.81	
26.98/8.81	(566)
26.98/8.81	Obligation:
26.98/8.81	Q DP problem:
26.98/8.81	The TRS P consists of the following rules:
26.98/8.81	
26.98/8.81	   H(x, x) -> G(x, x, f(k))
26.98/8.81	   G(d, x, x) -> A^2
26.98/8.81	   A^2 -> H(f(c), f(c))
26.98/8.81	   A^2 -> H(f(d), f(d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.81	   A^2 -> H(f(e), f(e))
26.98/8.81	   A^2 -> H(f(k), f(k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(e, a), f(k))
26.98/8.81	   A^2 -> H(U1(e, a), U1(d, d))
26.98/8.81	   A^2 -> H(U1(k, a), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, a), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, a), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, a), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, a), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, a), f(e))
26.98/8.81	   A^2 -> H(U1(k, a), f(k))
26.98/8.81	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.81	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.81	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.81	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.81	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.81	   A^2 -> H(U1(c, d), f(e))
26.98/8.81	   A^2 -> H(U1(c, d), f(k))
26.98/8.81	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.81	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.81	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.81	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.81	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.81	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.81	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.81	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.81	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.81	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.81	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.81	   A^2 -> H(U1(d, e), f(c))
26.98/8.81	   A^2 -> H(U1(d, e), f(d))
26.98/8.81	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.81	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.81	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.81	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.81	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.81	   A^2 -> H(U1(d, c), f(e))
26.98/8.81	   A^2 -> H(U1(d, c), f(k))
26.98/8.81	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.81	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.81	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.81	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.81	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.81	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.81	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.81	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.81	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.81	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.81	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.81	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.81	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.81	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.81	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.81	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.81	   A^2 -> H(U1(a, e), f(e))
26.98/8.81	   A^2 -> H(U1(a, e), f(k))
26.98/8.81	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.81	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(a, k), f(e))
26.98/8.81	   A^2 -> H(U1(a, k), f(k))
26.98/8.81	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.81	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.81	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.81	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.81	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.81	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.81	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.81	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.81	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.81	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.81	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.81	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.81	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.81	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.81	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.81	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.81	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.81	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.81	   A^2 -> H(U1(a, a), b)
26.98/8.81	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.81	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.81	   A^2 -> H(U1(a, a), c)
26.98/8.81	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.81	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.81	   A^2 -> H(U1(a, a), e)
26.98/8.81	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.81	   A^2 -> H(k, f(b))
26.98/8.81	   A^2 -> H(c, U1(b, b))
26.98/8.81	   A^2 -> H(c, f(c))
26.98/8.81	   A^2 -> H(c, f(d))
26.98/8.81	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.81	   A^2 -> H(U1(e, k), f(c))
26.98/8.81	   A^2 -> H(U1(e, k), f(d))
26.98/8.81	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.81	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.81	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.81	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.81	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, c), f(e))
26.98/8.81	   A^2 -> H(U1(e, c), f(k))
26.98/8.81	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.81	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.81	   A^2 -> H(U1(k, e), f(c))
26.98/8.81	   A^2 -> H(U1(k, e), f(d))
26.98/8.81	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, c), f(e))
26.98/8.81	   A^2 -> H(U1(k, c), f(k))
26.98/8.81	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.81	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.81	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.81	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.81	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.81	   A^2 -> H(U1(c, e), f(e))
26.98/8.81	   A^2 -> H(U1(c, e), f(k))
26.98/8.81	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(c, k), f(e))
26.98/8.81	   A^2 -> H(U1(c, k), f(k))
26.98/8.81	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.81	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.81	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.81	   A^2 -> H(e, U1(b, b))
26.98/8.81	   A^2 -> H(e, f(c))
26.98/8.81	   A^2 -> H(e, f(d))
26.98/8.81	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.81	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.81	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.81	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.81	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, e), f(e))
26.98/8.81	   A^2 -> H(U1(e, e), f(k))
26.98/8.81	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.81	   A^2 -> H(f(e), U1(e, b))
26.98/8.81	   A^2 -> H(f(e), U1(k, b))
26.98/8.81	   A^2 -> H(f(e), U1(c, d))
26.98/8.81	   A^2 -> H(f(e), U1(d, c))
26.98/8.81	   A^2 -> H(f(e), U1(b, e))
26.98/8.81	   A^2 -> H(f(e), U1(b, k))
26.98/8.81	   A^2 -> H(f(e), U1(e, c))
26.98/8.81	   A^2 -> H(f(e), U1(k, c))
26.98/8.81	   A^2 -> H(f(e), U1(c, e))
26.98/8.81	   A^2 -> H(f(e), U1(c, k))
26.98/8.81	   A^2 -> H(f(e), U1(k, k))
26.98/8.81	   A^2 -> H(f(e), U1(k, d))
26.98/8.81	   A^2 -> H(f(e), U1(d, k))
26.98/8.81	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, k), f(e))
26.98/8.81	   A^2 -> H(U1(k, k), f(k))
26.98/8.81	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.81	   A^2 -> H(f(k), U1(e, b))
26.98/8.81	   A^2 -> H(f(k), U1(k, b))
26.98/8.81	   A^2 -> H(f(k), U1(c, d))
26.98/8.81	   A^2 -> H(f(k), U1(d, c))
26.98/8.81	   A^2 -> H(f(k), U1(b, e))
26.98/8.81	   A^2 -> H(f(k), U1(b, k))
26.98/8.81	   A^2 -> H(f(k), U1(e, c))
26.98/8.81	   A^2 -> H(f(k), U1(k, c))
26.98/8.81	   A^2 -> H(f(k), U1(c, e))
26.98/8.81	   A^2 -> H(f(k), U1(c, k))
26.98/8.81	   A^2 -> H(f(k), U1(e, e))
26.98/8.81	   A^2 -> H(f(k), U1(k, d))
26.98/8.81	   A^2 -> H(f(k), U1(d, k))
26.98/8.81	   A^2 -> H(f(c), b)
26.98/8.81	   A^2 -> H(f(c), U1(e, d))
26.98/8.81	   A^2 -> H(f(c), U1(d, e))
26.98/8.81	   A^2 -> H(f(k), U1(k, k))
26.98/8.81	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.81	   A^2 -> H(U1(k, k), f(c))
26.98/8.81	   A^2 -> H(U1(k, k), f(d))
26.98/8.81	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, d), f(e))
26.98/8.81	   A^2 -> H(U1(k, d), f(k))
26.98/8.81	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(d, k), f(e))
26.98/8.81	   A^2 -> H(U1(d, k), f(k))
26.98/8.81	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.81	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.81	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.81	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.81	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.81	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.81	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.81	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.81	   A^2 -> H(f(d), b)
26.98/8.81	   A^2 -> H(f(d), U1(e, d))
26.98/8.81	   A^2 -> H(f(d), U1(d, e))
26.98/8.81	   A^2 -> H(f(d), c)
26.98/8.81	   A^2 -> H(f(d), U1(e, k))
26.98/8.81	   A^2 -> H(f(d), U1(k, e))
26.98/8.81	   A^2 -> H(f(d), e)
26.98/8.81	   A^2 -> H(f(a), d)
26.98/8.81	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.81	   A^2 -> H(f(c), c)
26.98/8.81	   A^2 -> H(f(c), U1(e, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.81	   A^2 -> H(f(c), U1(k, e))
26.98/8.81	   A^2 -> H(f(c), U1(k, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.81	   A^2 -> H(f(a), k)
26.98/8.81	   A^2 -> H(f(e), U1(e, e))
26.98/8.81	   A^2 -> H(f(c), e)
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.81	   A^2 -> H(f(d), U1(k, k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.81	   A^2 -> H(d, U1(b, b))
26.98/8.81	   A^2 -> H(d, f(c))
26.98/8.81	   A^2 -> H(d, f(d))
26.98/8.81	   A^2 -> H(a, U1(c, b))
26.98/8.81	   A^2 -> H(a, U1(d, b))
26.98/8.81	   A^2 -> H(a, U1(b, c))
26.98/8.81	   A^2 -> H(a, U1(b, d))
26.98/8.81	   A^2 -> H(a, U1(c, c))
26.98/8.81	   A^2 -> H(a, f(e))
26.98/8.81	   A^2 -> H(a, f(k))
26.98/8.81	   A^2 -> H(a, U1(d, d))
26.98/8.81	   A^2 -> H(U1(e, d), U1(c, b))
26.98/8.81	   A^2 -> H(U1(e, d), U1(d, b))
26.98/8.81	   A^2 -> H(U1(e, d), U1(b, c))
26.98/8.81	   A^2 -> H(U1(e, d), U1(b, d))
26.98/8.81	   A^2 -> H(U1(e, d), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, d), f(e))
26.98/8.81	   A^2 -> H(U1(e, d), f(k))
26.98/8.81	   A^2 -> H(U1(e, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(e, a), U1(e, b))
26.98/8.81	   A^2 -> H(U1(e, a), U1(k, b))
26.98/8.81	   A^2 -> H(U1(e, a), U1(c, d))
26.98/8.81	   A^2 -> H(U1(e, a), U1(d, c))
26.98/8.81	   A^2 -> H(U1(e, a), U1(b, e))
26.98/8.81	   A^2 -> H(U1(e, a), U1(b, k))
26.98/8.81	   A^2 -> H(U1(e, a), U1(e, c))
26.98/8.81	   A^2 -> H(U1(e, a), U1(k, c))
26.98/8.81	   A^2 -> H(U1(e, a), U1(c, e))
26.98/8.81	   A^2 -> H(U1(e, a), U1(c, k))
26.98/8.81	   A^2 -> H(U1(e, a), U1(e, e))
26.98/8.81	
26.98/8.81	The TRS R consists of the following rules:
26.98/8.81	
26.98/8.81	   f(x) -> U1(x, x)
26.98/8.81	   U1(e, x) -> x
26.98/8.81	   a -> c
26.98/8.81	   a -> d
26.98/8.81	   b -> c
26.98/8.81	   b -> d
26.98/8.81	   d -> k
26.98/8.81	   c -> e
26.98/8.81	   c -> k
26.98/8.81	
26.98/8.81	Q is empty.
26.98/8.81	We have to consider all minimal (P,Q,R)-chains.
26.98/8.81	----------------------------------------
26.98/8.81	
26.98/8.81	(567) TransformationProof (EQUIVALENT)
26.98/8.81	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), f(k)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.81	
26.98/8.81	   (A^2 -> H(a, f(k)),A^2 -> H(a, f(k)))
26.98/8.81	   (A^2 -> H(U1(e, c), f(k)),A^2 -> H(U1(e, c), f(k)))
26.98/8.81	   (A^2 -> H(U1(e, d), f(k)),A^2 -> H(U1(e, d), f(k)))
26.98/8.81	   (A^2 -> H(U1(e, a), U1(k, k)),A^2 -> H(U1(e, a), U1(k, k)))
26.98/8.81	
26.98/8.81	
26.98/8.81	----------------------------------------
26.98/8.81	
26.98/8.81	(568)
26.98/8.81	Obligation:
26.98/8.81	Q DP problem:
26.98/8.81	The TRS P consists of the following rules:
26.98/8.81	
26.98/8.81	   H(x, x) -> G(x, x, f(k))
26.98/8.81	   G(d, x, x) -> A^2
26.98/8.81	   A^2 -> H(f(c), f(c))
26.98/8.81	   A^2 -> H(f(d), f(d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.81	   A^2 -> H(f(e), f(e))
26.98/8.81	   A^2 -> H(f(k), f(k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(e, a), U1(d, d))
26.98/8.81	   A^2 -> H(U1(k, a), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, a), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, a), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, a), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, a), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, a), f(e))
26.98/8.81	   A^2 -> H(U1(k, a), f(k))
26.98/8.81	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.81	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.81	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.81	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.81	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.81	   A^2 -> H(U1(c, d), f(e))
26.98/8.81	   A^2 -> H(U1(c, d), f(k))
26.98/8.81	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.81	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.81	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.81	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.81	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.81	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.81	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.81	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.81	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.81	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.81	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.81	   A^2 -> H(U1(d, e), f(c))
26.98/8.81	   A^2 -> H(U1(d, e), f(d))
26.98/8.81	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.81	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.81	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.81	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.81	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.81	   A^2 -> H(U1(d, c), f(e))
26.98/8.81	   A^2 -> H(U1(d, c), f(k))
26.98/8.81	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.81	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.81	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.81	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.81	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.81	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.81	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.81	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.81	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.81	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.81	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.81	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.81	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.81	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.81	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.81	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.81	   A^2 -> H(U1(a, e), f(e))
26.98/8.81	   A^2 -> H(U1(a, e), f(k))
26.98/8.81	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.81	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(a, k), f(e))
26.98/8.81	   A^2 -> H(U1(a, k), f(k))
26.98/8.81	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.81	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.81	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.81	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.81	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.81	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.81	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.81	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.81	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.81	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.81	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.81	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.81	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.81	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.81	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.81	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.81	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.81	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.81	   A^2 -> H(U1(a, a), b)
26.98/8.81	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.81	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.81	   A^2 -> H(U1(a, a), c)
26.98/8.81	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.81	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.81	   A^2 -> H(U1(a, a), e)
26.98/8.81	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.81	   A^2 -> H(k, f(b))
26.98/8.81	   A^2 -> H(c, U1(b, b))
26.98/8.81	   A^2 -> H(c, f(c))
26.98/8.81	   A^2 -> H(c, f(d))
26.98/8.81	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.81	   A^2 -> H(U1(e, k), f(c))
26.98/8.81	   A^2 -> H(U1(e, k), f(d))
26.98/8.81	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.81	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.81	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.81	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.81	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, c), f(e))
26.98/8.81	   A^2 -> H(U1(e, c), f(k))
26.98/8.81	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.81	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.81	   A^2 -> H(U1(k, e), f(c))
26.98/8.81	   A^2 -> H(U1(k, e), f(d))
26.98/8.81	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, c), f(e))
26.98/8.81	   A^2 -> H(U1(k, c), f(k))
26.98/8.81	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.81	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.81	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.81	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.81	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.81	   A^2 -> H(U1(c, e), f(e))
26.98/8.81	   A^2 -> H(U1(c, e), f(k))
26.98/8.81	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(c, k), f(e))
26.98/8.81	   A^2 -> H(U1(c, k), f(k))
26.98/8.81	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.81	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.81	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.81	   A^2 -> H(e, U1(b, b))
26.98/8.81	   A^2 -> H(e, f(c))
26.98/8.81	   A^2 -> H(e, f(d))
26.98/8.81	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.81	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.81	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.81	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.81	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, e), f(e))
26.98/8.81	   A^2 -> H(U1(e, e), f(k))
26.98/8.81	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.81	   A^2 -> H(f(e), U1(e, b))
26.98/8.81	   A^2 -> H(f(e), U1(k, b))
26.98/8.81	   A^2 -> H(f(e), U1(c, d))
26.98/8.81	   A^2 -> H(f(e), U1(d, c))
26.98/8.81	   A^2 -> H(f(e), U1(b, e))
26.98/8.81	   A^2 -> H(f(e), U1(b, k))
26.98/8.81	   A^2 -> H(f(e), U1(e, c))
26.98/8.81	   A^2 -> H(f(e), U1(k, c))
26.98/8.81	   A^2 -> H(f(e), U1(c, e))
26.98/8.81	   A^2 -> H(f(e), U1(c, k))
26.98/8.81	   A^2 -> H(f(e), U1(k, k))
26.98/8.81	   A^2 -> H(f(e), U1(k, d))
26.98/8.81	   A^2 -> H(f(e), U1(d, k))
26.98/8.81	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, k), f(e))
26.98/8.81	   A^2 -> H(U1(k, k), f(k))
26.98/8.81	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.81	   A^2 -> H(f(k), U1(e, b))
26.98/8.81	   A^2 -> H(f(k), U1(k, b))
26.98/8.81	   A^2 -> H(f(k), U1(c, d))
26.98/8.81	   A^2 -> H(f(k), U1(d, c))
26.98/8.81	   A^2 -> H(f(k), U1(b, e))
26.98/8.81	   A^2 -> H(f(k), U1(b, k))
26.98/8.81	   A^2 -> H(f(k), U1(e, c))
26.98/8.81	   A^2 -> H(f(k), U1(k, c))
26.98/8.81	   A^2 -> H(f(k), U1(c, e))
26.98/8.81	   A^2 -> H(f(k), U1(c, k))
26.98/8.81	   A^2 -> H(f(k), U1(e, e))
26.98/8.81	   A^2 -> H(f(k), U1(k, d))
26.98/8.81	   A^2 -> H(f(k), U1(d, k))
26.98/8.81	   A^2 -> H(f(c), b)
26.98/8.81	   A^2 -> H(f(c), U1(e, d))
26.98/8.81	   A^2 -> H(f(c), U1(d, e))
26.98/8.81	   A^2 -> H(f(k), U1(k, k))
26.98/8.81	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.81	   A^2 -> H(U1(k, k), f(c))
26.98/8.81	   A^2 -> H(U1(k, k), f(d))
26.98/8.81	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, d), f(e))
26.98/8.81	   A^2 -> H(U1(k, d), f(k))
26.98/8.81	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(d, k), f(e))
26.98/8.81	   A^2 -> H(U1(d, k), f(k))
26.98/8.81	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.81	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.81	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.81	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.81	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.81	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.81	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.81	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.81	   A^2 -> H(f(d), b)
26.98/8.81	   A^2 -> H(f(d), U1(e, d))
26.98/8.81	   A^2 -> H(f(d), U1(d, e))
26.98/8.81	   A^2 -> H(f(d), c)
26.98/8.81	   A^2 -> H(f(d), U1(e, k))
26.98/8.81	   A^2 -> H(f(d), U1(k, e))
26.98/8.81	   A^2 -> H(f(d), e)
26.98/8.81	   A^2 -> H(f(a), d)
26.98/8.81	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.81	   A^2 -> H(f(c), c)
26.98/8.81	   A^2 -> H(f(c), U1(e, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.81	   A^2 -> H(f(c), U1(k, e))
26.98/8.81	   A^2 -> H(f(c), U1(k, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.81	   A^2 -> H(f(a), k)
26.98/8.81	   A^2 -> H(f(e), U1(e, e))
26.98/8.81	   A^2 -> H(f(c), e)
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.81	   A^2 -> H(f(d), U1(k, k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.81	   A^2 -> H(d, U1(b, b))
26.98/8.81	   A^2 -> H(d, f(c))
26.98/8.81	   A^2 -> H(d, f(d))
26.98/8.81	   A^2 -> H(a, U1(c, b))
26.98/8.81	   A^2 -> H(a, U1(d, b))
26.98/8.81	   A^2 -> H(a, U1(b, c))
26.98/8.81	   A^2 -> H(a, U1(b, d))
26.98/8.81	   A^2 -> H(a, U1(c, c))
26.98/8.81	   A^2 -> H(a, f(e))
26.98/8.81	   A^2 -> H(a, f(k))
26.98/8.81	   A^2 -> H(a, U1(d, d))
26.98/8.81	   A^2 -> H(U1(e, d), U1(c, b))
26.98/8.81	   A^2 -> H(U1(e, d), U1(d, b))
26.98/8.81	   A^2 -> H(U1(e, d), U1(b, c))
26.98/8.81	   A^2 -> H(U1(e, d), U1(b, d))
26.98/8.81	   A^2 -> H(U1(e, d), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, d), f(e))
26.98/8.81	   A^2 -> H(U1(e, d), f(k))
26.98/8.81	   A^2 -> H(U1(e, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(e, a), U1(e, b))
26.98/8.81	   A^2 -> H(U1(e, a), U1(k, b))
26.98/8.81	   A^2 -> H(U1(e, a), U1(c, d))
26.98/8.81	   A^2 -> H(U1(e, a), U1(d, c))
26.98/8.81	   A^2 -> H(U1(e, a), U1(b, e))
26.98/8.81	   A^2 -> H(U1(e, a), U1(b, k))
26.98/8.81	   A^2 -> H(U1(e, a), U1(e, c))
26.98/8.81	   A^2 -> H(U1(e, a), U1(k, c))
26.98/8.81	   A^2 -> H(U1(e, a), U1(c, e))
26.98/8.81	   A^2 -> H(U1(e, a), U1(c, k))
26.98/8.81	   A^2 -> H(U1(e, a), U1(e, e))
26.98/8.81	   A^2 -> H(U1(e, a), U1(k, k))
26.98/8.81	
26.98/8.81	The TRS R consists of the following rules:
26.98/8.81	
26.98/8.81	   f(x) -> U1(x, x)
26.98/8.81	   U1(e, x) -> x
26.98/8.81	   a -> c
26.98/8.81	   a -> d
26.98/8.81	   b -> c
26.98/8.81	   b -> d
26.98/8.81	   d -> k
26.98/8.81	   c -> e
26.98/8.81	   c -> k
26.98/8.81	
26.98/8.81	Q is empty.
26.98/8.81	We have to consider all minimal (P,Q,R)-chains.
26.98/8.81	----------------------------------------
26.98/8.81	
26.98/8.81	(569) TransformationProof (EQUIVALENT)
26.98/8.81	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.81	
26.98/8.81	   (A^2 -> H(a, U1(d, d)),A^2 -> H(a, U1(d, d)))
26.98/8.81	   (A^2 -> H(U1(e, c), U1(d, d)),A^2 -> H(U1(e, c), U1(d, d)))
26.98/8.81	   (A^2 -> H(U1(e, d), U1(d, d)),A^2 -> H(U1(e, d), U1(d, d)))
26.98/8.81	   (A^2 -> H(U1(e, a), U1(k, d)),A^2 -> H(U1(e, a), U1(k, d)))
26.98/8.81	   (A^2 -> H(U1(e, a), U1(d, k)),A^2 -> H(U1(e, a), U1(d, k)))
26.98/8.81	
26.98/8.81	
26.98/8.81	----------------------------------------
26.98/8.81	
26.98/8.81	(570)
26.98/8.81	Obligation:
26.98/8.81	Q DP problem:
26.98/8.81	The TRS P consists of the following rules:
26.98/8.81	
26.98/8.81	   H(x, x) -> G(x, x, f(k))
26.98/8.81	   G(d, x, x) -> A^2
26.98/8.81	   A^2 -> H(f(c), f(c))
26.98/8.81	   A^2 -> H(f(d), f(d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.81	   A^2 -> H(f(e), f(e))
26.98/8.81	   A^2 -> H(f(k), f(k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(k, a), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, a), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, a), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, a), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, a), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, a), f(e))
26.98/8.81	   A^2 -> H(U1(k, a), f(k))
26.98/8.81	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.81	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.81	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.81	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.81	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.81	   A^2 -> H(U1(c, d), f(e))
26.98/8.81	   A^2 -> H(U1(c, d), f(k))
26.98/8.81	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.81	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.81	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.81	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.81	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.81	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.81	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.81	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.81	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.81	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.81	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.81	   A^2 -> H(U1(d, e), f(c))
26.98/8.81	   A^2 -> H(U1(d, e), f(d))
26.98/8.81	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.81	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.81	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.81	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.81	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.81	   A^2 -> H(U1(d, c), f(e))
26.98/8.81	   A^2 -> H(U1(d, c), f(k))
26.98/8.81	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.81	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.81	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.81	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.81	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.81	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.81	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.81	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.81	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.81	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.81	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.81	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.81	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.81	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.81	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.81	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.81	   A^2 -> H(U1(a, e), f(e))
26.98/8.81	   A^2 -> H(U1(a, e), f(k))
26.98/8.81	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.81	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(a, k), f(e))
26.98/8.81	   A^2 -> H(U1(a, k), f(k))
26.98/8.81	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.81	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.81	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.81	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.81	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.81	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.81	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.81	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.81	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.81	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.81	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.81	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.81	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.81	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.81	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.81	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.81	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.81	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.81	   A^2 -> H(U1(a, a), b)
26.98/8.81	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.81	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.81	   A^2 -> H(U1(a, a), c)
26.98/8.81	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.81	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.81	   A^2 -> H(U1(a, a), e)
26.98/8.81	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.81	   A^2 -> H(k, f(b))
26.98/8.81	   A^2 -> H(c, U1(b, b))
26.98/8.81	   A^2 -> H(c, f(c))
26.98/8.81	   A^2 -> H(c, f(d))
26.98/8.81	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.81	   A^2 -> H(U1(e, k), f(c))
26.98/8.81	   A^2 -> H(U1(e, k), f(d))
26.98/8.81	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.81	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.81	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.81	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.81	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, c), f(e))
26.98/8.81	   A^2 -> H(U1(e, c), f(k))
26.98/8.81	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.81	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.81	   A^2 -> H(U1(k, e), f(c))
26.98/8.81	   A^2 -> H(U1(k, e), f(d))
26.98/8.81	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, c), f(e))
26.98/8.81	   A^2 -> H(U1(k, c), f(k))
26.98/8.81	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.81	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.81	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.81	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.81	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.81	   A^2 -> H(U1(c, e), f(e))
26.98/8.81	   A^2 -> H(U1(c, e), f(k))
26.98/8.81	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(c, k), f(e))
26.98/8.81	   A^2 -> H(U1(c, k), f(k))
26.98/8.81	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.81	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.81	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.81	   A^2 -> H(e, U1(b, b))
26.98/8.81	   A^2 -> H(e, f(c))
26.98/8.81	   A^2 -> H(e, f(d))
26.98/8.81	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.81	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.81	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.81	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.81	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, e), f(e))
26.98/8.81	   A^2 -> H(U1(e, e), f(k))
26.98/8.81	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.81	   A^2 -> H(f(e), U1(e, b))
26.98/8.81	   A^2 -> H(f(e), U1(k, b))
26.98/8.81	   A^2 -> H(f(e), U1(c, d))
26.98/8.81	   A^2 -> H(f(e), U1(d, c))
26.98/8.81	   A^2 -> H(f(e), U1(b, e))
26.98/8.81	   A^2 -> H(f(e), U1(b, k))
26.98/8.81	   A^2 -> H(f(e), U1(e, c))
26.98/8.81	   A^2 -> H(f(e), U1(k, c))
26.98/8.81	   A^2 -> H(f(e), U1(c, e))
26.98/8.81	   A^2 -> H(f(e), U1(c, k))
26.98/8.81	   A^2 -> H(f(e), U1(k, k))
26.98/8.81	   A^2 -> H(f(e), U1(k, d))
26.98/8.81	   A^2 -> H(f(e), U1(d, k))
26.98/8.81	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, k), f(e))
26.98/8.81	   A^2 -> H(U1(k, k), f(k))
26.98/8.81	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.81	   A^2 -> H(f(k), U1(e, b))
26.98/8.81	   A^2 -> H(f(k), U1(k, b))
26.98/8.81	   A^2 -> H(f(k), U1(c, d))
26.98/8.81	   A^2 -> H(f(k), U1(d, c))
26.98/8.81	   A^2 -> H(f(k), U1(b, e))
26.98/8.81	   A^2 -> H(f(k), U1(b, k))
26.98/8.81	   A^2 -> H(f(k), U1(e, c))
26.98/8.81	   A^2 -> H(f(k), U1(k, c))
26.98/8.81	   A^2 -> H(f(k), U1(c, e))
26.98/8.81	   A^2 -> H(f(k), U1(c, k))
26.98/8.81	   A^2 -> H(f(k), U1(e, e))
26.98/8.81	   A^2 -> H(f(k), U1(k, d))
26.98/8.81	   A^2 -> H(f(k), U1(d, k))
26.98/8.81	   A^2 -> H(f(c), b)
26.98/8.81	   A^2 -> H(f(c), U1(e, d))
26.98/8.81	   A^2 -> H(f(c), U1(d, e))
26.98/8.81	   A^2 -> H(f(k), U1(k, k))
26.98/8.81	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.81	   A^2 -> H(U1(k, k), f(c))
26.98/8.81	   A^2 -> H(U1(k, k), f(d))
26.98/8.81	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.81	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, d), f(e))
26.98/8.81	   A^2 -> H(U1(k, d), f(k))
26.98/8.81	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(d, k), f(e))
26.98/8.81	   A^2 -> H(U1(d, k), f(k))
26.98/8.81	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.81	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.81	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.81	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.81	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.81	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.81	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.81	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.81	   A^2 -> H(f(d), b)
26.98/8.81	   A^2 -> H(f(d), U1(e, d))
26.98/8.81	   A^2 -> H(f(d), U1(d, e))
26.98/8.81	   A^2 -> H(f(d), c)
26.98/8.81	   A^2 -> H(f(d), U1(e, k))
26.98/8.81	   A^2 -> H(f(d), U1(k, e))
26.98/8.81	   A^2 -> H(f(d), e)
26.98/8.81	   A^2 -> H(f(a), d)
26.98/8.81	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.81	   A^2 -> H(f(c), c)
26.98/8.81	   A^2 -> H(f(c), U1(e, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.81	   A^2 -> H(f(c), U1(k, e))
26.98/8.81	   A^2 -> H(f(c), U1(k, k))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.81	   A^2 -> H(f(a), k)
26.98/8.81	   A^2 -> H(f(e), U1(e, e))
26.98/8.81	   A^2 -> H(f(c), e)
26.98/8.81	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.81	   A^2 -> H(f(d), U1(k, k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.81	   A^2 -> H(d, U1(b, b))
26.98/8.81	   A^2 -> H(d, f(c))
26.98/8.81	   A^2 -> H(d, f(d))
26.98/8.81	   A^2 -> H(a, U1(c, b))
26.98/8.81	   A^2 -> H(a, U1(d, b))
26.98/8.81	   A^2 -> H(a, U1(b, c))
26.98/8.81	   A^2 -> H(a, U1(b, d))
26.98/8.81	   A^2 -> H(a, U1(c, c))
26.98/8.81	   A^2 -> H(a, f(e))
26.98/8.81	   A^2 -> H(a, f(k))
26.98/8.81	   A^2 -> H(a, U1(d, d))
26.98/8.81	   A^2 -> H(U1(e, d), U1(c, b))
26.98/8.81	   A^2 -> H(U1(e, d), U1(d, b))
26.98/8.81	   A^2 -> H(U1(e, d), U1(b, c))
26.98/8.81	   A^2 -> H(U1(e, d), U1(b, d))
26.98/8.81	   A^2 -> H(U1(e, d), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, d), f(e))
26.98/8.81	   A^2 -> H(U1(e, d), f(k))
26.98/8.81	   A^2 -> H(U1(e, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(e, a), U1(e, b))
26.98/8.81	   A^2 -> H(U1(e, a), U1(k, b))
26.98/8.81	   A^2 -> H(U1(e, a), U1(c, d))
26.98/8.81	   A^2 -> H(U1(e, a), U1(d, c))
26.98/8.81	   A^2 -> H(U1(e, a), U1(b, e))
26.98/8.81	   A^2 -> H(U1(e, a), U1(b, k))
26.98/8.81	   A^2 -> H(U1(e, a), U1(e, c))
26.98/8.81	   A^2 -> H(U1(e, a), U1(k, c))
26.98/8.81	   A^2 -> H(U1(e, a), U1(c, e))
26.98/8.81	   A^2 -> H(U1(e, a), U1(c, k))
26.98/8.81	   A^2 -> H(U1(e, a), U1(e, e))
26.98/8.81	   A^2 -> H(U1(e, a), U1(k, k))
26.98/8.81	   A^2 -> H(U1(e, a), U1(k, d))
26.98/8.81	   A^2 -> H(U1(e, a), U1(d, k))
26.98/8.81	
26.98/8.81	The TRS R consists of the following rules:
26.98/8.81	
26.98/8.81	   f(x) -> U1(x, x)
26.98/8.81	   U1(e, x) -> x
26.98/8.81	   a -> c
26.98/8.81	   a -> d
26.98/8.81	   b -> c
26.98/8.81	   b -> d
26.98/8.81	   d -> k
26.98/8.81	   c -> e
26.98/8.81	   c -> k
26.98/8.81	
26.98/8.81	Q is empty.
26.98/8.81	We have to consider all minimal (P,Q,R)-chains.
26.98/8.81	----------------------------------------
26.98/8.81	
26.98/8.81	(571) TransformationProof (EQUIVALENT)
26.98/8.81	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.81	
26.98/8.81	   (A^2 -> H(U1(k, c), U1(c, b)),A^2 -> H(U1(k, c), U1(c, b)))
26.98/8.81	   (A^2 -> H(U1(k, d), U1(c, b)),A^2 -> H(U1(k, d), U1(c, b)))
26.98/8.81	   (A^2 -> H(U1(k, a), U1(e, b)),A^2 -> H(U1(k, a), U1(e, b)))
26.98/8.81	   (A^2 -> H(U1(k, a), U1(k, b)),A^2 -> H(U1(k, a), U1(k, b)))
26.98/8.81	   (A^2 -> H(U1(k, a), U1(c, c)),A^2 -> H(U1(k, a), U1(c, c)))
26.98/8.81	   (A^2 -> H(U1(k, a), U1(c, d)),A^2 -> H(U1(k, a), U1(c, d)))
26.98/8.81	
26.98/8.81	
26.98/8.81	----------------------------------------
26.98/8.81	
26.98/8.81	(572)
26.98/8.81	Obligation:
26.98/8.81	Q DP problem:
26.98/8.81	The TRS P consists of the following rules:
26.98/8.81	
26.98/8.81	   H(x, x) -> G(x, x, f(k))
26.98/8.81	   G(d, x, x) -> A^2
26.98/8.81	   A^2 -> H(f(c), f(c))
26.98/8.81	   A^2 -> H(f(d), f(d))
26.98/8.81	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.81	   A^2 -> H(f(e), f(e))
26.98/8.81	   A^2 -> H(f(k), f(k))
26.98/8.81	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(k, a), U1(d, b))
26.98/8.81	   A^2 -> H(U1(k, a), U1(b, c))
26.98/8.81	   A^2 -> H(U1(k, a), U1(b, d))
26.98/8.81	   A^2 -> H(U1(k, a), U1(c, c))
26.98/8.81	   A^2 -> H(U1(k, a), f(e))
26.98/8.81	   A^2 -> H(U1(k, a), f(k))
26.98/8.81	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.81	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.81	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.81	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.81	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.81	   A^2 -> H(U1(c, d), f(e))
26.98/8.81	   A^2 -> H(U1(c, d), f(k))
26.98/8.81	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.81	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.81	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.81	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.81	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.81	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.81	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.81	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.81	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.81	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.81	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.81	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.81	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.81	   A^2 -> H(U1(d, e), f(c))
26.98/8.81	   A^2 -> H(U1(d, e), f(d))
26.98/8.81	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.81	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.81	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.81	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.81	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.81	   A^2 -> H(U1(d, c), f(e))
26.98/8.81	   A^2 -> H(U1(d, c), f(k))
26.98/8.81	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.81	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.81	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.81	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.81	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.81	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.81	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.81	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.81	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.81	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.81	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.81	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.81	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.81	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.81	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.81	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.81	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.81	   A^2 -> H(U1(a, e), f(e))
26.98/8.81	   A^2 -> H(U1(a, e), f(k))
26.98/8.81	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.81	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.81	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.81	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.81	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.81	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.81	   A^2 -> H(U1(a, k), f(e))
26.98/8.81	   A^2 -> H(U1(a, k), f(k))
26.98/8.81	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.81	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.81	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.81	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.81	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.81	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.81	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.81	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.81	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.81	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.81	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.81	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.81	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.81	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.81	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.81	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.81	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.81	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.81	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.81	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.81	   A^2 -> H(U1(a, a), b)
26.98/8.81	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.81	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.81	   A^2 -> H(U1(a, a), c)
26.98/8.81	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.81	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.81	   A^2 -> H(U1(a, a), e)
26.98/8.81	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.81	   A^2 -> H(k, f(b))
26.98/8.81	   A^2 -> H(c, U1(b, b))
26.98/8.81	   A^2 -> H(c, f(c))
26.98/8.81	   A^2 -> H(c, f(d))
26.98/8.81	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.81	   A^2 -> H(U1(e, k), f(c))
26.98/8.81	   A^2 -> H(U1(e, k), f(d))
26.98/8.81	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.81	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.81	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.81	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.81	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.81	   A^2 -> H(U1(e, c), f(e))
26.98/8.81	   A^2 -> H(U1(e, c), f(k))
26.98/8.81	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.81	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.81	   A^2 -> H(U1(k, e), f(c))
26.98/8.81	   A^2 -> H(U1(k, e), f(d))
26.98/8.81	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.83	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.83	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.83	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.83	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.83	   A^2 -> H(U1(k, c), f(e))
26.98/8.83	   A^2 -> H(U1(k, c), f(k))
26.98/8.83	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.83	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.83	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.83	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.83	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.83	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.83	   A^2 -> H(U1(c, e), f(e))
26.98/8.83	   A^2 -> H(U1(c, e), f(k))
26.98/8.83	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.83	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.83	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.83	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.83	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.83	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.83	   A^2 -> H(U1(c, k), f(e))
26.98/8.83	   A^2 -> H(U1(c, k), f(k))
26.98/8.83	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.83	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.83	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.83	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.83	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.83	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.83	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.83	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.83	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.83	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.83	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.83	   A^2 -> H(e, U1(b, b))
26.98/8.83	   A^2 -> H(e, f(c))
26.98/8.83	   A^2 -> H(e, f(d))
26.98/8.83	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.83	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.83	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.83	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.83	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.83	   A^2 -> H(U1(e, e), f(e))
26.98/8.83	   A^2 -> H(U1(e, e), f(k))
26.98/8.83	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.83	   A^2 -> H(f(e), U1(e, b))
26.98/8.83	   A^2 -> H(f(e), U1(k, b))
26.98/8.83	   A^2 -> H(f(e), U1(c, d))
26.98/8.83	   A^2 -> H(f(e), U1(d, c))
26.98/8.83	   A^2 -> H(f(e), U1(b, e))
26.98/8.83	   A^2 -> H(f(e), U1(b, k))
26.98/8.83	   A^2 -> H(f(e), U1(e, c))
26.98/8.83	   A^2 -> H(f(e), U1(k, c))
26.98/8.83	   A^2 -> H(f(e), U1(c, e))
26.98/8.83	   A^2 -> H(f(e), U1(c, k))
26.98/8.83	   A^2 -> H(f(e), U1(k, k))
26.98/8.83	   A^2 -> H(f(e), U1(k, d))
26.98/8.83	   A^2 -> H(f(e), U1(d, k))
26.98/8.83	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.83	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.83	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.83	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.83	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.83	   A^2 -> H(U1(k, k), f(e))
26.98/8.83	   A^2 -> H(U1(k, k), f(k))
26.98/8.83	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.83	   A^2 -> H(f(k), U1(e, b))
26.98/8.83	   A^2 -> H(f(k), U1(k, b))
26.98/8.83	   A^2 -> H(f(k), U1(c, d))
26.98/8.83	   A^2 -> H(f(k), U1(d, c))
26.98/8.83	   A^2 -> H(f(k), U1(b, e))
26.98/8.83	   A^2 -> H(f(k), U1(b, k))
26.98/8.83	   A^2 -> H(f(k), U1(e, c))
26.98/8.83	   A^2 -> H(f(k), U1(k, c))
26.98/8.83	   A^2 -> H(f(k), U1(c, e))
26.98/8.83	   A^2 -> H(f(k), U1(c, k))
26.98/8.83	   A^2 -> H(f(k), U1(e, e))
26.98/8.83	   A^2 -> H(f(k), U1(k, d))
26.98/8.83	   A^2 -> H(f(k), U1(d, k))
26.98/8.83	   A^2 -> H(f(c), b)
26.98/8.83	   A^2 -> H(f(c), U1(e, d))
26.98/8.83	   A^2 -> H(f(c), U1(d, e))
26.98/8.83	   A^2 -> H(f(k), U1(k, k))
26.98/8.83	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.83	   A^2 -> H(U1(k, k), f(c))
26.98/8.83	   A^2 -> H(U1(k, k), f(d))
26.98/8.83	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.83	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.83	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.83	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.83	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.83	   A^2 -> H(U1(k, d), f(e))
26.98/8.83	   A^2 -> H(U1(k, d), f(k))
26.98/8.83	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.83	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.83	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.83	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.83	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.83	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.83	   A^2 -> H(U1(d, k), f(e))
26.98/8.83	   A^2 -> H(U1(d, k), f(k))
26.98/8.83	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.83	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.83	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.83	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.83	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.83	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.83	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.83	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.83	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.83	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.83	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.83	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.83	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.83	   A^2 -> H(f(d), b)
26.98/8.83	   A^2 -> H(f(d), U1(e, d))
26.98/8.83	   A^2 -> H(f(d), U1(d, e))
26.98/8.83	   A^2 -> H(f(d), c)
26.98/8.83	   A^2 -> H(f(d), U1(e, k))
26.98/8.83	   A^2 -> H(f(d), U1(k, e))
26.98/8.83	   A^2 -> H(f(d), e)
26.98/8.83	   A^2 -> H(f(a), d)
26.98/8.83	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.83	   A^2 -> H(f(c), c)
26.98/8.83	   A^2 -> H(f(c), U1(e, k))
26.98/8.83	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.83	   A^2 -> H(f(c), U1(k, e))
26.98/8.83	   A^2 -> H(f(c), U1(k, k))
26.98/8.83	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.83	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.83	   A^2 -> H(f(a), k)
26.98/8.83	   A^2 -> H(f(e), U1(e, e))
26.98/8.83	   A^2 -> H(f(c), e)
26.98/8.83	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.83	   A^2 -> H(f(d), U1(k, k))
26.98/8.83	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.83	   A^2 -> H(d, U1(b, b))
26.98/8.83	   A^2 -> H(d, f(c))
26.98/8.83	   A^2 -> H(d, f(d))
26.98/8.83	   A^2 -> H(a, U1(c, b))
26.98/8.83	   A^2 -> H(a, U1(d, b))
26.98/8.83	   A^2 -> H(a, U1(b, c))
26.98/8.83	   A^2 -> H(a, U1(b, d))
26.98/8.83	   A^2 -> H(a, U1(c, c))
26.98/8.83	   A^2 -> H(a, f(e))
26.98/8.83	   A^2 -> H(a, f(k))
26.98/8.83	   A^2 -> H(a, U1(d, d))
26.98/8.83	   A^2 -> H(U1(e, d), U1(c, b))
26.98/8.83	   A^2 -> H(U1(e, d), U1(d, b))
26.98/8.83	   A^2 -> H(U1(e, d), U1(b, c))
26.98/8.83	   A^2 -> H(U1(e, d), U1(b, d))
26.98/8.83	   A^2 -> H(U1(e, d), U1(c, c))
26.98/8.83	   A^2 -> H(U1(e, d), f(e))
26.98/8.83	   A^2 -> H(U1(e, d), f(k))
26.98/8.83	   A^2 -> H(U1(e, d), U1(d, d))
26.98/8.83	   A^2 -> H(U1(e, a), U1(e, b))
26.98/8.83	   A^2 -> H(U1(e, a), U1(k, b))
26.98/8.83	   A^2 -> H(U1(e, a), U1(c, d))
26.98/8.83	   A^2 -> H(U1(e, a), U1(d, c))
26.98/8.83	   A^2 -> H(U1(e, a), U1(b, e))
26.98/8.83	   A^2 -> H(U1(e, a), U1(b, k))
26.98/8.83	   A^2 -> H(U1(e, a), U1(e, c))
26.98/8.83	   A^2 -> H(U1(e, a), U1(k, c))
26.98/8.83	   A^2 -> H(U1(e, a), U1(c, e))
26.98/8.83	   A^2 -> H(U1(e, a), U1(c, k))
26.98/8.83	   A^2 -> H(U1(e, a), U1(e, e))
26.98/8.83	   A^2 -> H(U1(e, a), U1(k, k))
26.98/8.83	   A^2 -> H(U1(e, a), U1(k, d))
26.98/8.83	   A^2 -> H(U1(e, a), U1(d, k))
26.98/8.83	   A^2 -> H(U1(k, a), U1(e, b))
26.98/8.83	   A^2 -> H(U1(k, a), U1(k, b))
26.98/8.83	   A^2 -> H(U1(k, a), U1(c, d))
26.98/8.83	
26.98/8.83	The TRS R consists of the following rules:
26.98/8.83	
26.98/8.83	   f(x) -> U1(x, x)
26.98/8.83	   U1(e, x) -> x
26.98/8.83	   a -> c
26.98/8.83	   a -> d
26.98/8.83	   b -> c
26.98/8.83	   b -> d
26.98/8.83	   d -> k
26.98/8.83	   c -> e
26.98/8.83	   c -> k
26.98/8.83	
26.98/8.83	Q is empty.
26.98/8.83	We have to consider all minimal (P,Q,R)-chains.
26.98/8.83	----------------------------------------
26.98/8.83	
26.98/8.83	(573) TransformationProof (EQUIVALENT)
26.98/8.83	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.83	
26.98/8.83	   (A^2 -> H(U1(k, c), U1(d, b)),A^2 -> H(U1(k, c), U1(d, b)))
26.98/8.83	   (A^2 -> H(U1(k, d), U1(d, b)),A^2 -> H(U1(k, d), U1(d, b)))
26.98/8.83	   (A^2 -> H(U1(k, a), U1(k, b)),A^2 -> H(U1(k, a), U1(k, b)))
26.98/8.83	   (A^2 -> H(U1(k, a), U1(d, c)),A^2 -> H(U1(k, a), U1(d, c)))
26.98/8.83	   (A^2 -> H(U1(k, a), U1(d, d)),A^2 -> H(U1(k, a), U1(d, d)))
26.98/8.83	
26.98/8.83	
26.98/8.83	----------------------------------------
26.98/8.83	
26.98/8.83	(574)
26.98/8.83	Obligation:
26.98/8.83	Q DP problem:
26.98/8.83	The TRS P consists of the following rules:
26.98/8.83	
26.98/8.83	   H(x, x) -> G(x, x, f(k))
26.98/8.83	   G(d, x, x) -> A^2
26.98/8.83	   A^2 -> H(f(c), f(c))
26.98/8.83	   A^2 -> H(f(d), f(d))
26.98/8.83	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.83	   A^2 -> H(f(e), f(e))
26.98/8.83	   A^2 -> H(f(k), f(k))
26.98/8.83	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.83	   A^2 -> H(U1(k, a), U1(b, c))
26.98/8.83	   A^2 -> H(U1(k, a), U1(b, d))
26.98/8.83	   A^2 -> H(U1(k, a), U1(c, c))
26.98/8.83	   A^2 -> H(U1(k, a), f(e))
26.98/8.83	   A^2 -> H(U1(k, a), f(k))
26.98/8.83	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.83	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.83	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.83	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.83	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.83	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.83	   A^2 -> H(U1(c, d), f(e))
26.98/8.83	   A^2 -> H(U1(c, d), f(k))
26.98/8.83	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.83	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.83	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.83	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.83	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.83	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.83	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.83	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.83	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.83	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.83	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.83	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.83	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.83	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.83	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.83	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.83	   A^2 -> H(U1(d, e), f(c))
26.98/8.83	   A^2 -> H(U1(d, e), f(d))
26.98/8.83	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.83	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.83	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.83	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.83	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.83	   A^2 -> H(U1(d, c), f(e))
26.98/8.83	   A^2 -> H(U1(d, c), f(k))
26.98/8.83	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.83	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.83	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.83	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.83	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.83	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.83	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.83	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.83	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.83	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.83	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.83	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.83	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.83	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.83	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.83	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.83	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.83	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.83	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.83	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.83	   A^2 -> H(U1(a, e), f(e))
26.98/8.83	   A^2 -> H(U1(a, e), f(k))
26.98/8.83	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.83	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.83	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.83	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.83	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.83	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.83	   A^2 -> H(U1(a, k), f(e))
26.98/8.83	   A^2 -> H(U1(a, k), f(k))
26.98/8.83	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.83	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.83	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.83	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.83	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.83	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.83	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.83	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.83	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.83	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.83	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.83	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.83	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.83	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.83	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.83	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.83	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.83	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.83	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.83	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.83	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.83	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.83	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.83	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.83	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.83	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.83	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.83	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.83	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.83	   A^2 -> H(U1(a, a), b)
26.98/8.83	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.83	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.83	   A^2 -> H(U1(a, a), c)
26.98/8.83	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.83	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.83	   A^2 -> H(U1(a, a), e)
26.98/8.83	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.83	   A^2 -> H(k, f(b))
26.98/8.83	   A^2 -> H(c, U1(b, b))
26.98/8.83	   A^2 -> H(c, f(c))
26.98/8.83	   A^2 -> H(c, f(d))
26.98/8.83	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.83	   A^2 -> H(U1(e, k), f(c))
26.98/8.83	   A^2 -> H(U1(e, k), f(d))
26.98/8.83	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.83	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.83	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.83	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.83	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.83	   A^2 -> H(U1(e, c), f(e))
26.98/8.83	   A^2 -> H(U1(e, c), f(k))
26.98/8.83	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.83	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.83	   A^2 -> H(U1(k, e), f(c))
26.98/8.83	   A^2 -> H(U1(k, e), f(d))
26.98/8.83	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.83	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.83	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.83	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.83	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.83	   A^2 -> H(U1(k, c), f(e))
26.98/8.83	   A^2 -> H(U1(k, c), f(k))
26.98/8.83	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.83	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.83	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.83	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.83	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.83	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.83	   A^2 -> H(U1(c, e), f(e))
26.98/8.83	   A^2 -> H(U1(c, e), f(k))
26.98/8.83	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.83	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.83	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.83	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.83	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.83	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.83	   A^2 -> H(U1(c, k), f(e))
26.98/8.83	   A^2 -> H(U1(c, k), f(k))
26.98/8.83	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.83	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.83	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.83	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.83	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.83	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.83	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.83	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.83	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.83	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.83	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.83	   A^2 -> H(e, U1(b, b))
26.98/8.83	   A^2 -> H(e, f(c))
26.98/8.83	   A^2 -> H(e, f(d))
26.98/8.83	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.83	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.83	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.83	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.83	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.83	   A^2 -> H(U1(e, e), f(e))
26.98/8.83	   A^2 -> H(U1(e, e), f(k))
26.98/8.83	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.83	   A^2 -> H(f(e), U1(e, b))
26.98/8.83	   A^2 -> H(f(e), U1(k, b))
26.98/8.83	   A^2 -> H(f(e), U1(c, d))
26.98/8.83	   A^2 -> H(f(e), U1(d, c))
26.98/8.83	   A^2 -> H(f(e), U1(b, e))
26.98/8.83	   A^2 -> H(f(e), U1(b, k))
26.98/8.83	   A^2 -> H(f(e), U1(e, c))
26.98/8.83	   A^2 -> H(f(e), U1(k, c))
26.98/8.83	   A^2 -> H(f(e), U1(c, e))
26.98/8.83	   A^2 -> H(f(e), U1(c, k))
26.98/8.83	   A^2 -> H(f(e), U1(k, k))
26.98/8.83	   A^2 -> H(f(e), U1(k, d))
26.98/8.83	   A^2 -> H(f(e), U1(d, k))
26.98/8.83	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.83	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.83	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.83	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.83	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.83	   A^2 -> H(U1(k, k), f(e))
26.98/8.83	   A^2 -> H(U1(k, k), f(k))
26.98/8.83	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.83	   A^2 -> H(f(k), U1(e, b))
26.98/8.83	   A^2 -> H(f(k), U1(k, b))
26.98/8.83	   A^2 -> H(f(k), U1(c, d))
26.98/8.83	   A^2 -> H(f(k), U1(d, c))
26.98/8.83	   A^2 -> H(f(k), U1(b, e))
26.98/8.83	   A^2 -> H(f(k), U1(b, k))
26.98/8.83	   A^2 -> H(f(k), U1(e, c))
26.98/8.83	   A^2 -> H(f(k), U1(k, c))
26.98/8.83	   A^2 -> H(f(k), U1(c, e))
26.98/8.83	   A^2 -> H(f(k), U1(c, k))
26.98/8.83	   A^2 -> H(f(k), U1(e, e))
26.98/8.83	   A^2 -> H(f(k), U1(k, d))
26.98/8.83	   A^2 -> H(f(k), U1(d, k))
26.98/8.83	   A^2 -> H(f(c), b)
26.98/8.83	   A^2 -> H(f(c), U1(e, d))
26.98/8.83	   A^2 -> H(f(c), U1(d, e))
26.98/8.83	   A^2 -> H(f(k), U1(k, k))
26.98/8.83	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.83	   A^2 -> H(U1(k, k), f(c))
26.98/8.83	   A^2 -> H(U1(k, k), f(d))
26.98/8.83	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.83	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.83	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.83	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.83	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.83	   A^2 -> H(U1(k, d), f(e))
26.98/8.83	   A^2 -> H(U1(k, d), f(k))
26.98/8.83	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.83	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.83	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.83	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.83	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.83	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.83	   A^2 -> H(U1(d, k), f(e))
26.98/8.83	   A^2 -> H(U1(d, k), f(k))
26.98/8.83	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.83	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.83	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.83	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.83	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.83	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.83	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.83	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.83	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.83	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.83	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.83	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.83	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.83	   A^2 -> H(f(d), b)
26.98/8.83	   A^2 -> H(f(d), U1(e, d))
26.98/8.83	   A^2 -> H(f(d), U1(d, e))
26.98/8.83	   A^2 -> H(f(d), c)
26.98/8.83	   A^2 -> H(f(d), U1(e, k))
26.98/8.83	   A^2 -> H(f(d), U1(k, e))
26.98/8.83	   A^2 -> H(f(d), e)
26.98/8.83	   A^2 -> H(f(a), d)
26.98/8.83	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.83	   A^2 -> H(f(c), c)
26.98/8.83	   A^2 -> H(f(c), U1(e, k))
26.98/8.83	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.83	   A^2 -> H(f(c), U1(k, e))
26.98/8.83	   A^2 -> H(f(c), U1(k, k))
26.98/8.83	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.83	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.83	   A^2 -> H(f(a), k)
26.98/8.83	   A^2 -> H(f(e), U1(e, e))
26.98/8.83	   A^2 -> H(f(c), e)
26.98/8.83	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.83	   A^2 -> H(f(d), U1(k, k))
26.98/8.83	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.83	   A^2 -> H(d, U1(b, b))
26.98/8.83	   A^2 -> H(d, f(c))
26.98/8.83	   A^2 -> H(d, f(d))
26.98/8.83	   A^2 -> H(a, U1(c, b))
26.98/8.83	   A^2 -> H(a, U1(d, b))
26.98/8.83	   A^2 -> H(a, U1(b, c))
26.98/8.83	   A^2 -> H(a, U1(b, d))
26.98/8.83	   A^2 -> H(a, U1(c, c))
26.98/8.83	   A^2 -> H(a, f(e))
26.98/8.83	   A^2 -> H(a, f(k))
26.98/8.83	   A^2 -> H(a, U1(d, d))
26.98/8.83	   A^2 -> H(U1(e, d), U1(c, b))
26.98/8.83	   A^2 -> H(U1(e, d), U1(d, b))
26.98/8.83	   A^2 -> H(U1(e, d), U1(b, c))
26.98/8.83	   A^2 -> H(U1(e, d), U1(b, d))
26.98/8.83	   A^2 -> H(U1(e, d), U1(c, c))
26.98/8.83	   A^2 -> H(U1(e, d), f(e))
26.98/8.83	   A^2 -> H(U1(e, d), f(k))
26.98/8.83	   A^2 -> H(U1(e, d), U1(d, d))
26.98/8.83	   A^2 -> H(U1(e, a), U1(e, b))
26.98/8.83	   A^2 -> H(U1(e, a), U1(k, b))
26.98/8.83	   A^2 -> H(U1(e, a), U1(c, d))
26.98/8.83	   A^2 -> H(U1(e, a), U1(d, c))
26.98/8.83	   A^2 -> H(U1(e, a), U1(b, e))
26.98/8.83	   A^2 -> H(U1(e, a), U1(b, k))
26.98/8.83	   A^2 -> H(U1(e, a), U1(e, c))
26.98/8.83	   A^2 -> H(U1(e, a), U1(k, c))
26.98/8.83	   A^2 -> H(U1(e, a), U1(c, e))
26.98/8.83	   A^2 -> H(U1(e, a), U1(c, k))
26.98/8.83	   A^2 -> H(U1(e, a), U1(e, e))
26.98/8.83	   A^2 -> H(U1(e, a), U1(k, k))
26.98/8.83	   A^2 -> H(U1(e, a), U1(k, d))
26.98/8.83	   A^2 -> H(U1(e, a), U1(d, k))
26.98/8.83	   A^2 -> H(U1(k, a), U1(e, b))
26.98/8.83	   A^2 -> H(U1(k, a), U1(k, b))
26.98/8.83	   A^2 -> H(U1(k, a), U1(c, d))
26.98/8.83	   A^2 -> H(U1(k, a), U1(d, c))
26.98/8.83	
26.98/8.83	The TRS R consists of the following rules:
26.98/8.83	
26.98/8.83	   f(x) -> U1(x, x)
26.98/8.83	   U1(e, x) -> x
26.98/8.83	   a -> c
26.98/8.83	   a -> d
26.98/8.83	   b -> c
26.98/8.83	   b -> d
26.98/8.83	   d -> k
26.98/8.83	   c -> e
26.98/8.83	   c -> k
26.98/8.83	
26.98/8.83	Q is empty.
26.98/8.83	We have to consider all minimal (P,Q,R)-chains.
26.98/8.83	----------------------------------------
26.98/8.83	
26.98/8.83	(575) TransformationProof (EQUIVALENT)
26.98/8.83	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.83	
26.98/8.83	   (A^2 -> H(U1(k, c), U1(b, c)),A^2 -> H(U1(k, c), U1(b, c)))
26.98/8.83	   (A^2 -> H(U1(k, d), U1(b, c)),A^2 -> H(U1(k, d), U1(b, c)))
26.98/8.83	   (A^2 -> H(U1(k, a), U1(c, c)),A^2 -> H(U1(k, a), U1(c, c)))
26.98/8.83	   (A^2 -> H(U1(k, a), U1(d, c)),A^2 -> H(U1(k, a), U1(d, c)))
26.98/8.83	   (A^2 -> H(U1(k, a), U1(b, e)),A^2 -> H(U1(k, a), U1(b, e)))
26.98/8.83	   (A^2 -> H(U1(k, a), U1(b, k)),A^2 -> H(U1(k, a), U1(b, k)))
26.98/8.83	
26.98/8.83	
26.98/8.83	----------------------------------------
26.98/8.83	
26.98/8.83	(576)
26.98/8.83	Obligation:
26.98/8.83	Q DP problem:
26.98/8.83	The TRS P consists of the following rules:
26.98/8.83	
26.98/8.83	   H(x, x) -> G(x, x, f(k))
26.98/8.83	   G(d, x, x) -> A^2
26.98/8.83	   A^2 -> H(f(c), f(c))
26.98/8.83	   A^2 -> H(f(d), f(d))
26.98/8.83	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.83	   A^2 -> H(f(e), f(e))
26.98/8.83	   A^2 -> H(f(k), f(k))
26.98/8.83	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.83	   A^2 -> H(U1(k, a), U1(b, d))
26.98/8.83	   A^2 -> H(U1(k, a), U1(c, c))
26.98/8.83	   A^2 -> H(U1(k, a), f(e))
26.98/8.83	   A^2 -> H(U1(k, a), f(k))
26.98/8.83	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.83	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.83	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.83	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.83	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.83	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.83	   A^2 -> H(U1(c, d), f(e))
26.98/8.83	   A^2 -> H(U1(c, d), f(k))
26.98/8.83	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.83	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.83	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.83	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.83	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.83	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.83	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.83	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.83	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.83	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.83	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.83	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.83	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.83	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.83	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.83	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.83	   A^2 -> H(U1(d, e), f(c))
26.98/8.83	   A^2 -> H(U1(d, e), f(d))
26.98/8.83	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.83	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.83	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.83	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.83	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.83	   A^2 -> H(U1(d, c), f(e))
26.98/8.83	   A^2 -> H(U1(d, c), f(k))
26.98/8.83	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.83	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.83	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.83	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.83	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.83	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.83	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.83	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.83	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.83	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.83	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.83	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.83	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.83	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.83	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.83	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.83	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.83	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.83	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.83	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.83	   A^2 -> H(U1(a, e), f(e))
26.98/8.83	   A^2 -> H(U1(a, e), f(k))
26.98/8.83	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.83	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.83	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.83	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.83	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.83	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.83	   A^2 -> H(U1(a, k), f(e))
26.98/8.83	   A^2 -> H(U1(a, k), f(k))
26.98/8.83	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.83	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.83	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.83	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.83	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.83	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.83	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.83	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.83	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.83	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.83	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.83	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.83	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.83	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.83	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.83	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.83	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.83	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.83	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.83	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.83	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.83	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.83	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.83	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.83	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.83	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.83	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.83	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.83	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.83	   A^2 -> H(U1(a, a), b)
26.98/8.83	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.83	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.83	   A^2 -> H(U1(a, a), c)
26.98/8.83	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.83	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.83	   A^2 -> H(U1(a, a), e)
26.98/8.83	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.83	   A^2 -> H(k, f(b))
26.98/8.83	   A^2 -> H(c, U1(b, b))
26.98/8.83	   A^2 -> H(c, f(c))
26.98/8.83	   A^2 -> H(c, f(d))
26.98/8.83	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.83	   A^2 -> H(U1(e, k), f(c))
26.98/8.83	   A^2 -> H(U1(e, k), f(d))
26.98/8.83	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.83	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.83	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.83	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.83	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.83	   A^2 -> H(U1(e, c), f(e))
26.98/8.83	   A^2 -> H(U1(e, c), f(k))
26.98/8.83	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.83	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.83	   A^2 -> H(U1(k, e), f(c))
26.98/8.83	   A^2 -> H(U1(k, e), f(d))
26.98/8.83	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.83	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.83	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.83	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.83	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.83	   A^2 -> H(U1(k, c), f(e))
26.98/8.83	   A^2 -> H(U1(k, c), f(k))
26.98/8.83	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.83	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.83	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.83	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.83	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.83	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.83	   A^2 -> H(U1(c, e), f(e))
26.98/8.83	   A^2 -> H(U1(c, e), f(k))
26.98/8.83	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.83	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.83	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.83	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.83	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.83	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.83	   A^2 -> H(U1(c, k), f(e))
26.98/8.83	   A^2 -> H(U1(c, k), f(k))
26.98/8.83	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.83	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.83	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.83	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.83	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.83	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.83	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.83	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.83	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.83	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.83	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.83	   A^2 -> H(e, U1(b, b))
26.98/8.83	   A^2 -> H(e, f(c))
26.98/8.83	   A^2 -> H(e, f(d))
26.98/8.83	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.83	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.83	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.83	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.83	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.83	   A^2 -> H(U1(e, e), f(e))
26.98/8.83	   A^2 -> H(U1(e, e), f(k))
26.98/8.83	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.83	   A^2 -> H(f(e), U1(e, b))
26.98/8.83	   A^2 -> H(f(e), U1(k, b))
26.98/8.83	   A^2 -> H(f(e), U1(c, d))
26.98/8.83	   A^2 -> H(f(e), U1(d, c))
26.98/8.83	   A^2 -> H(f(e), U1(b, e))
26.98/8.83	   A^2 -> H(f(e), U1(b, k))
26.98/8.83	   A^2 -> H(f(e), U1(e, c))
26.98/8.83	   A^2 -> H(f(e), U1(k, c))
26.98/8.83	   A^2 -> H(f(e), U1(c, e))
26.98/8.83	   A^2 -> H(f(e), U1(c, k))
26.98/8.83	   A^2 -> H(f(e), U1(k, k))
26.98/8.83	   A^2 -> H(f(e), U1(k, d))
26.98/8.83	   A^2 -> H(f(e), U1(d, k))
26.98/8.83	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.83	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.83	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.83	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.83	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.83	   A^2 -> H(U1(k, k), f(e))
26.98/8.83	   A^2 -> H(U1(k, k), f(k))
26.98/8.83	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.83	   A^2 -> H(f(k), U1(e, b))
26.98/8.83	   A^2 -> H(f(k), U1(k, b))
26.98/8.83	   A^2 -> H(f(k), U1(c, d))
26.98/8.83	   A^2 -> H(f(k), U1(d, c))
26.98/8.83	   A^2 -> H(f(k), U1(b, e))
26.98/8.83	   A^2 -> H(f(k), U1(b, k))
26.98/8.83	   A^2 -> H(f(k), U1(e, c))
26.98/8.83	   A^2 -> H(f(k), U1(k, c))
26.98/8.83	   A^2 -> H(f(k), U1(c, e))
26.98/8.83	   A^2 -> H(f(k), U1(c, k))
26.98/8.83	   A^2 -> H(f(k), U1(e, e))
26.98/8.83	   A^2 -> H(f(k), U1(k, d))
26.98/8.83	   A^2 -> H(f(k), U1(d, k))
26.98/8.83	   A^2 -> H(f(c), b)
26.98/8.83	   A^2 -> H(f(c), U1(e, d))
26.98/8.83	   A^2 -> H(f(c), U1(d, e))
26.98/8.83	   A^2 -> H(f(k), U1(k, k))
26.98/8.83	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.83	   A^2 -> H(U1(k, k), f(c))
26.98/8.83	   A^2 -> H(U1(k, k), f(d))
26.98/8.83	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.83	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.83	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.83	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.83	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.83	   A^2 -> H(U1(k, d), f(e))
26.98/8.83	   A^2 -> H(U1(k, d), f(k))
26.98/8.83	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.83	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.83	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.83	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.83	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.83	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.83	   A^2 -> H(U1(d, k), f(e))
26.98/8.83	   A^2 -> H(U1(d, k), f(k))
26.98/8.83	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.83	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.83	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.83	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.83	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.83	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.83	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.83	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.83	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.83	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.83	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.83	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.83	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.83	   A^2 -> H(f(d), b)
26.98/8.83	   A^2 -> H(f(d), U1(e, d))
26.98/8.83	   A^2 -> H(f(d), U1(d, e))
26.98/8.83	   A^2 -> H(f(d), c)
26.98/8.83	   A^2 -> H(f(d), U1(e, k))
26.98/8.83	   A^2 -> H(f(d), U1(k, e))
26.98/8.83	   A^2 -> H(f(d), e)
26.98/8.83	   A^2 -> H(f(a), d)
26.98/8.83	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.83	   A^2 -> H(f(c), c)
26.98/8.83	   A^2 -> H(f(c), U1(e, k))
26.98/8.83	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.83	   A^2 -> H(f(c), U1(k, e))
26.98/8.83	   A^2 -> H(f(c), U1(k, k))
26.98/8.83	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.83	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.83	   A^2 -> H(f(a), k)
26.98/8.83	   A^2 -> H(f(e), U1(e, e))
26.98/8.83	   A^2 -> H(f(c), e)
26.98/8.83	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.83	   A^2 -> H(f(d), U1(k, k))
26.98/8.83	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.83	   A^2 -> H(d, U1(b, b))
26.98/8.83	   A^2 -> H(d, f(c))
26.98/8.83	   A^2 -> H(d, f(d))
26.98/8.83	   A^2 -> H(a, U1(c, b))
26.98/8.83	   A^2 -> H(a, U1(d, b))
26.98/8.83	   A^2 -> H(a, U1(b, c))
26.98/8.83	   A^2 -> H(a, U1(b, d))
26.98/8.83	   A^2 -> H(a, U1(c, c))
26.98/8.83	   A^2 -> H(a, f(e))
26.98/8.83	   A^2 -> H(a, f(k))
26.98/8.83	   A^2 -> H(a, U1(d, d))
26.98/8.83	   A^2 -> H(U1(e, d), U1(c, b))
26.98/8.83	   A^2 -> H(U1(e, d), U1(d, b))
26.98/8.83	   A^2 -> H(U1(e, d), U1(b, c))
26.98/8.83	   A^2 -> H(U1(e, d), U1(b, d))
26.98/8.83	   A^2 -> H(U1(e, d), U1(c, c))
26.98/8.83	   A^2 -> H(U1(e, d), f(e))
26.98/8.83	   A^2 -> H(U1(e, d), f(k))
26.98/8.83	   A^2 -> H(U1(e, d), U1(d, d))
26.98/8.83	   A^2 -> H(U1(e, a), U1(e, b))
26.98/8.83	   A^2 -> H(U1(e, a), U1(k, b))
26.98/8.83	   A^2 -> H(U1(e, a), U1(c, d))
26.98/8.83	   A^2 -> H(U1(e, a), U1(d, c))
26.98/8.83	   A^2 -> H(U1(e, a), U1(b, e))
26.98/8.83	   A^2 -> H(U1(e, a), U1(b, k))
26.98/8.83	   A^2 -> H(U1(e, a), U1(e, c))
26.98/8.83	   A^2 -> H(U1(e, a), U1(k, c))
26.98/8.83	   A^2 -> H(U1(e, a), U1(c, e))
26.98/8.83	   A^2 -> H(U1(e, a), U1(c, k))
26.98/8.83	   A^2 -> H(U1(e, a), U1(e, e))
26.98/8.83	   A^2 -> H(U1(e, a), U1(k, k))
26.98/8.83	   A^2 -> H(U1(e, a), U1(k, d))
26.98/8.83	   A^2 -> H(U1(e, a), U1(d, k))
26.98/8.83	   A^2 -> H(U1(k, a), U1(e, b))
26.98/8.83	   A^2 -> H(U1(k, a), U1(k, b))
26.98/8.83	   A^2 -> H(U1(k, a), U1(c, d))
26.98/8.83	   A^2 -> H(U1(k, a), U1(d, c))
26.98/8.83	   A^2 -> H(U1(k, a), U1(b, e))
26.98/8.83	   A^2 -> H(U1(k, a), U1(b, k))
26.98/8.83	
26.98/8.83	The TRS R consists of the following rules:
26.98/8.83	
26.98/8.83	   f(x) -> U1(x, x)
26.98/8.83	   U1(e, x) -> x
26.98/8.83	   a -> c
26.98/8.83	   a -> d
26.98/8.83	   b -> c
26.98/8.83	   b -> d
26.98/8.83	   d -> k
26.98/8.83	   c -> e
26.98/8.83	   c -> k
26.98/8.83	
26.98/8.83	Q is empty.
26.98/8.83	We have to consider all minimal (P,Q,R)-chains.
26.98/8.83	----------------------------------------
26.98/8.83	
26.98/8.83	(577) TransformationProof (EQUIVALENT)
26.98/8.83	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.83	
26.98/8.83	   (A^2 -> H(U1(k, c), U1(b, d)),A^2 -> H(U1(k, c), U1(b, d)))
26.98/8.83	   (A^2 -> H(U1(k, d), U1(b, d)),A^2 -> H(U1(k, d), U1(b, d)))
26.98/8.83	   (A^2 -> H(U1(k, a), U1(c, d)),A^2 -> H(U1(k, a), U1(c, d)))
26.98/8.83	   (A^2 -> H(U1(k, a), U1(d, d)),A^2 -> H(U1(k, a), U1(d, d)))
26.98/8.83	   (A^2 -> H(U1(k, a), U1(b, k)),A^2 -> H(U1(k, a), U1(b, k)))
26.98/8.83	
26.98/8.83	
26.98/8.83	----------------------------------------
26.98/8.83	
26.98/8.83	(578)
26.98/8.83	Obligation:
26.98/8.83	Q DP problem:
26.98/8.83	The TRS P consists of the following rules:
26.98/8.83	
26.98/8.83	   H(x, x) -> G(x, x, f(k))
26.98/8.83	   G(d, x, x) -> A^2
26.98/8.83	   A^2 -> H(f(c), f(c))
26.98/8.83	   A^2 -> H(f(d), f(d))
26.98/8.83	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.83	   A^2 -> H(f(e), f(e))
26.98/8.83	   A^2 -> H(f(k), f(k))
26.98/8.83	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.83	   A^2 -> H(U1(k, a), U1(c, c))
26.98/8.83	   A^2 -> H(U1(k, a), f(e))
26.98/8.83	   A^2 -> H(U1(k, a), f(k))
26.98/8.83	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.83	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.83	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.83	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.83	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.83	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.83	   A^2 -> H(U1(c, d), f(e))
26.98/8.83	   A^2 -> H(U1(c, d), f(k))
26.98/8.83	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.83	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.83	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.83	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.83	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.83	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.83	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.83	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.83	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.83	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.83	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.83	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.83	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.83	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.83	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.83	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.83	   A^2 -> H(U1(d, e), f(c))
26.98/8.83	   A^2 -> H(U1(d, e), f(d))
26.98/8.83	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.83	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.83	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.83	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.83	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.83	   A^2 -> H(U1(d, c), f(e))
26.98/8.83	   A^2 -> H(U1(d, c), f(k))
26.98/8.83	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.83	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.83	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.83	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.83	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.83	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.83	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.83	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.83	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.83	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.83	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.83	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.83	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.83	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.83	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.83	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.83	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.83	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.83	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.83	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.83	   A^2 -> H(U1(a, e), f(e))
26.98/8.83	   A^2 -> H(U1(a, e), f(k))
26.98/8.83	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.83	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.83	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.83	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.83	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.83	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.83	   A^2 -> H(U1(a, k), f(e))
26.98/8.83	   A^2 -> H(U1(a, k), f(k))
26.98/8.83	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.83	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.83	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.83	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.83	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.83	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.83	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.83	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.83	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.83	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.83	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.83	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.83	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.83	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.83	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.83	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.83	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.83	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.83	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.83	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.83	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.83	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.83	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.83	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.83	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.83	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.83	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.83	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.83	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.83	   A^2 -> H(U1(a, a), b)
26.98/8.83	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.83	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.83	   A^2 -> H(U1(a, a), c)
26.98/8.83	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.83	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.83	   A^2 -> H(U1(a, a), e)
26.98/8.83	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.83	   A^2 -> H(k, f(b))
26.98/8.83	   A^2 -> H(c, U1(b, b))
26.98/8.83	   A^2 -> H(c, f(c))
26.98/8.83	   A^2 -> H(c, f(d))
26.98/8.83	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.83	   A^2 -> H(U1(e, k), f(c))
26.98/8.83	   A^2 -> H(U1(e, k), f(d))
26.98/8.83	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.83	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.83	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.83	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.83	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.83	   A^2 -> H(U1(e, c), f(e))
26.98/8.83	   A^2 -> H(U1(e, c), f(k))
26.98/8.83	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.83	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.83	   A^2 -> H(U1(k, e), f(c))
26.98/8.83	   A^2 -> H(U1(k, e), f(d))
26.98/8.83	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.83	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.83	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.83	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.83	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.83	   A^2 -> H(U1(k, c), f(e))
26.98/8.83	   A^2 -> H(U1(k, c), f(k))
26.98/8.83	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.83	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.83	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.83	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.83	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.83	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.83	   A^2 -> H(U1(c, e), f(e))
26.98/8.83	   A^2 -> H(U1(c, e), f(k))
26.98/8.83	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.83	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.83	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.83	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.83	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.83	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.83	   A^2 -> H(U1(c, k), f(e))
26.98/8.83	   A^2 -> H(U1(c, k), f(k))
26.98/8.83	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.83	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.83	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.83	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.83	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.83	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.83	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.83	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.83	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.83	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.83	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.83	   A^2 -> H(e, U1(b, b))
26.98/8.83	   A^2 -> H(e, f(c))
26.98/8.83	   A^2 -> H(e, f(d))
26.98/8.83	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.83	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.83	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.83	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.83	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.83	   A^2 -> H(U1(e, e), f(e))
26.98/8.83	   A^2 -> H(U1(e, e), f(k))
26.98/8.83	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.83	   A^2 -> H(f(e), U1(e, b))
26.98/8.83	   A^2 -> H(f(e), U1(k, b))
26.98/8.83	   A^2 -> H(f(e), U1(c, d))
26.98/8.83	   A^2 -> H(f(e), U1(d, c))
26.98/8.83	   A^2 -> H(f(e), U1(b, e))
26.98/8.83	   A^2 -> H(f(e), U1(b, k))
26.98/8.83	   A^2 -> H(f(e), U1(e, c))
26.98/8.83	   A^2 -> H(f(e), U1(k, c))
26.98/8.83	   A^2 -> H(f(e), U1(c, e))
26.98/8.83	   A^2 -> H(f(e), U1(c, k))
26.98/8.83	   A^2 -> H(f(e), U1(k, k))
26.98/8.83	   A^2 -> H(f(e), U1(k, d))
26.98/8.83	   A^2 -> H(f(e), U1(d, k))
26.98/8.83	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.83	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.83	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.83	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.83	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.83	   A^2 -> H(U1(k, k), f(e))
26.98/8.83	   A^2 -> H(U1(k, k), f(k))
26.98/8.83	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.83	   A^2 -> H(f(k), U1(e, b))
26.98/8.83	   A^2 -> H(f(k), U1(k, b))
26.98/8.83	   A^2 -> H(f(k), U1(c, d))
26.98/8.83	   A^2 -> H(f(k), U1(d, c))
26.98/8.83	   A^2 -> H(f(k), U1(b, e))
26.98/8.83	   A^2 -> H(f(k), U1(b, k))
26.98/8.83	   A^2 -> H(f(k), U1(e, c))
26.98/8.83	   A^2 -> H(f(k), U1(k, c))
26.98/8.83	   A^2 -> H(f(k), U1(c, e))
26.98/8.83	   A^2 -> H(f(k), U1(c, k))
26.98/8.83	   A^2 -> H(f(k), U1(e, e))
26.98/8.83	   A^2 -> H(f(k), U1(k, d))
26.98/8.83	   A^2 -> H(f(k), U1(d, k))
26.98/8.83	   A^2 -> H(f(c), b)
26.98/8.83	   A^2 -> H(f(c), U1(e, d))
26.98/8.83	   A^2 -> H(f(c), U1(d, e))
26.98/8.83	   A^2 -> H(f(k), U1(k, k))
26.98/8.83	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.83	   A^2 -> H(U1(k, k), f(c))
26.98/8.83	   A^2 -> H(U1(k, k), f(d))
26.98/8.83	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.83	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.83	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.83	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.83	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.83	   A^2 -> H(U1(k, d), f(e))
26.98/8.83	   A^2 -> H(U1(k, d), f(k))
26.98/8.83	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.83	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.83	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.83	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.84	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.84	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.84	   A^2 -> H(U1(d, k), f(e))
26.98/8.84	   A^2 -> H(U1(d, k), f(k))
26.98/8.84	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.84	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.84	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.84	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.84	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.84	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.84	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.84	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.84	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.84	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.84	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.84	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.84	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.84	   A^2 -> H(f(d), b)
26.98/8.84	   A^2 -> H(f(d), U1(e, d))
26.98/8.84	   A^2 -> H(f(d), U1(d, e))
26.98/8.84	   A^2 -> H(f(d), c)
26.98/8.84	   A^2 -> H(f(d), U1(e, k))
26.98/8.84	   A^2 -> H(f(d), U1(k, e))
26.98/8.84	   A^2 -> H(f(d), e)
26.98/8.84	   A^2 -> H(f(a), d)
26.98/8.84	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.84	   A^2 -> H(f(c), c)
26.98/8.84	   A^2 -> H(f(c), U1(e, k))
26.98/8.84	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.84	   A^2 -> H(f(c), U1(k, e))
26.98/8.84	   A^2 -> H(f(c), U1(k, k))
26.98/8.84	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.84	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.84	   A^2 -> H(f(a), k)
26.98/8.84	   A^2 -> H(f(e), U1(e, e))
26.98/8.84	   A^2 -> H(f(c), e)
26.98/8.84	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.84	   A^2 -> H(f(d), U1(k, k))
26.98/8.84	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.84	   A^2 -> H(d, U1(b, b))
26.98/8.84	   A^2 -> H(d, f(c))
26.98/8.84	   A^2 -> H(d, f(d))
26.98/8.84	   A^2 -> H(a, U1(c, b))
26.98/8.84	   A^2 -> H(a, U1(d, b))
26.98/8.84	   A^2 -> H(a, U1(b, c))
26.98/8.84	   A^2 -> H(a, U1(b, d))
26.98/8.84	   A^2 -> H(a, U1(c, c))
26.98/8.84	   A^2 -> H(a, f(e))
26.98/8.84	   A^2 -> H(a, f(k))
26.98/8.84	   A^2 -> H(a, U1(d, d))
26.98/8.84	   A^2 -> H(U1(e, d), U1(c, b))
26.98/8.84	   A^2 -> H(U1(e, d), U1(d, b))
26.98/8.84	   A^2 -> H(U1(e, d), U1(b, c))
26.98/8.84	   A^2 -> H(U1(e, d), U1(b, d))
26.98/8.84	   A^2 -> H(U1(e, d), U1(c, c))
26.98/8.84	   A^2 -> H(U1(e, d), f(e))
26.98/8.84	   A^2 -> H(U1(e, d), f(k))
26.98/8.84	   A^2 -> H(U1(e, d), U1(d, d))
26.98/8.84	   A^2 -> H(U1(e, a), U1(e, b))
26.98/8.84	   A^2 -> H(U1(e, a), U1(k, b))
26.98/8.84	   A^2 -> H(U1(e, a), U1(c, d))
26.98/8.84	   A^2 -> H(U1(e, a), U1(d, c))
26.98/8.84	   A^2 -> H(U1(e, a), U1(b, e))
26.98/8.84	   A^2 -> H(U1(e, a), U1(b, k))
26.98/8.84	   A^2 -> H(U1(e, a), U1(e, c))
26.98/8.84	   A^2 -> H(U1(e, a), U1(k, c))
26.98/8.84	   A^2 -> H(U1(e, a), U1(c, e))
26.98/8.84	   A^2 -> H(U1(e, a), U1(c, k))
26.98/8.84	   A^2 -> H(U1(e, a), U1(e, e))
26.98/8.84	   A^2 -> H(U1(e, a), U1(k, k))
26.98/8.84	   A^2 -> H(U1(e, a), U1(k, d))
26.98/8.84	   A^2 -> H(U1(e, a), U1(d, k))
26.98/8.84	   A^2 -> H(U1(k, a), U1(e, b))
26.98/8.84	   A^2 -> H(U1(k, a), U1(k, b))
26.98/8.84	   A^2 -> H(U1(k, a), U1(c, d))
26.98/8.84	   A^2 -> H(U1(k, a), U1(d, c))
26.98/8.84	   A^2 -> H(U1(k, a), U1(b, e))
26.98/8.84	   A^2 -> H(U1(k, a), U1(b, k))
26.98/8.84	
26.98/8.84	The TRS R consists of the following rules:
26.98/8.84	
26.98/8.84	   f(x) -> U1(x, x)
26.98/8.84	   U1(e, x) -> x
26.98/8.84	   a -> c
26.98/8.84	   a -> d
26.98/8.84	   b -> c
26.98/8.84	   b -> d
26.98/8.84	   d -> k
26.98/8.84	   c -> e
26.98/8.84	   c -> k
26.98/8.84	
26.98/8.84	Q is empty.
26.98/8.84	We have to consider all minimal (P,Q,R)-chains.
26.98/8.84	----------------------------------------
26.98/8.84	
26.98/8.84	(579) TransformationProof (EQUIVALENT)
26.98/8.84	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.84	
26.98/8.84	   (A^2 -> H(U1(k, c), U1(c, c)),A^2 -> H(U1(k, c), U1(c, c)))
26.98/8.84	   (A^2 -> H(U1(k, d), U1(c, c)),A^2 -> H(U1(k, d), U1(c, c)))
26.98/8.84	   (A^2 -> H(U1(k, a), U1(e, c)),A^2 -> H(U1(k, a), U1(e, c)))
26.98/8.84	   (A^2 -> H(U1(k, a), U1(k, c)),A^2 -> H(U1(k, a), U1(k, c)))
26.98/8.84	   (A^2 -> H(U1(k, a), U1(c, e)),A^2 -> H(U1(k, a), U1(c, e)))
26.98/8.84	   (A^2 -> H(U1(k, a), U1(c, k)),A^2 -> H(U1(k, a), U1(c, k)))
26.98/8.84	
26.98/8.84	
26.98/8.84	----------------------------------------
26.98/8.84	
26.98/8.84	(580)
26.98/8.84	Obligation:
26.98/8.84	Q DP problem:
26.98/8.84	The TRS P consists of the following rules:
26.98/8.84	
26.98/8.84	   H(x, x) -> G(x, x, f(k))
26.98/8.84	   G(d, x, x) -> A^2
26.98/8.84	   A^2 -> H(f(c), f(c))
26.98/8.84	   A^2 -> H(f(d), f(d))
26.98/8.84	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.84	   A^2 -> H(f(e), f(e))
26.98/8.84	   A^2 -> H(f(k), f(k))
26.98/8.84	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.84	   A^2 -> H(U1(k, a), f(e))
26.98/8.84	   A^2 -> H(U1(k, a), f(k))
26.98/8.84	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.84	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.84	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.84	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.84	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.84	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.84	   A^2 -> H(U1(c, d), f(e))
26.98/8.84	   A^2 -> H(U1(c, d), f(k))
26.98/8.84	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.84	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.84	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.84	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.84	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.84	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.84	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.84	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.84	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.84	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.84	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.84	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.84	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.84	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.84	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.84	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.84	   A^2 -> H(U1(d, e), f(c))
26.98/8.84	   A^2 -> H(U1(d, e), f(d))
26.98/8.84	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.84	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.84	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.84	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.84	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.84	   A^2 -> H(U1(d, c), f(e))
26.98/8.84	   A^2 -> H(U1(d, c), f(k))
26.98/8.84	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.84	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.84	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.84	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.84	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.84	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.84	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.84	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.84	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.84	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.84	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.84	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.84	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.84	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.84	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.84	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.84	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.84	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.84	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.84	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.84	   A^2 -> H(U1(a, e), f(e))
26.98/8.84	   A^2 -> H(U1(a, e), f(k))
26.98/8.84	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.84	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.84	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.84	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.84	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.84	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.84	   A^2 -> H(U1(a, k), f(e))
26.98/8.84	   A^2 -> H(U1(a, k), f(k))
26.98/8.84	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.84	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.84	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.84	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.84	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.84	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.84	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.84	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.84	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.84	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.84	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.84	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.84	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.84	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.84	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.84	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.84	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.84	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.84	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.84	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.84	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.84	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.84	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.84	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.84	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.84	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.84	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.84	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.84	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.84	   A^2 -> H(U1(a, a), b)
26.98/8.84	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.84	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.84	   A^2 -> H(U1(a, a), c)
26.98/8.84	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.84	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.84	   A^2 -> H(U1(a, a), e)
26.98/8.84	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.84	   A^2 -> H(k, f(b))
26.98/8.84	   A^2 -> H(c, U1(b, b))
26.98/8.84	   A^2 -> H(c, f(c))
26.98/8.84	   A^2 -> H(c, f(d))
26.98/8.84	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.84	   A^2 -> H(U1(e, k), f(c))
26.98/8.84	   A^2 -> H(U1(e, k), f(d))
26.98/8.84	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.84	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.84	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.84	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.84	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.84	   A^2 -> H(U1(e, c), f(e))
26.98/8.84	   A^2 -> H(U1(e, c), f(k))
26.98/8.84	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.84	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.84	   A^2 -> H(U1(k, e), f(c))
26.98/8.84	   A^2 -> H(U1(k, e), f(d))
26.98/8.84	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.84	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.84	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.84	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.84	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.84	   A^2 -> H(U1(k, c), f(e))
26.98/8.84	   A^2 -> H(U1(k, c), f(k))
26.98/8.84	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.84	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.84	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.84	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.84	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.84	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.84	   A^2 -> H(U1(c, e), f(e))
26.98/8.84	   A^2 -> H(U1(c, e), f(k))
26.98/8.84	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.84	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.84	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.84	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.84	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.84	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.84	   A^2 -> H(U1(c, k), f(e))
26.98/8.84	   A^2 -> H(U1(c, k), f(k))
26.98/8.84	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.84	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.84	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.84	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.84	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.84	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.84	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.84	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.84	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.84	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.84	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.84	   A^2 -> H(e, U1(b, b))
26.98/8.84	   A^2 -> H(e, f(c))
26.98/8.84	   A^2 -> H(e, f(d))
26.98/8.84	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.84	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.84	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.84	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.84	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.84	   A^2 -> H(U1(e, e), f(e))
26.98/8.84	   A^2 -> H(U1(e, e), f(k))
26.98/8.84	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.84	   A^2 -> H(f(e), U1(e, b))
26.98/8.84	   A^2 -> H(f(e), U1(k, b))
26.98/8.84	   A^2 -> H(f(e), U1(c, d))
26.98/8.84	   A^2 -> H(f(e), U1(d, c))
26.98/8.84	   A^2 -> H(f(e), U1(b, e))
26.98/8.84	   A^2 -> H(f(e), U1(b, k))
26.98/8.84	   A^2 -> H(f(e), U1(e, c))
26.98/8.84	   A^2 -> H(f(e), U1(k, c))
26.98/8.84	   A^2 -> H(f(e), U1(c, e))
26.98/8.84	   A^2 -> H(f(e), U1(c, k))
26.98/8.84	   A^2 -> H(f(e), U1(k, k))
26.98/8.84	   A^2 -> H(f(e), U1(k, d))
26.98/8.84	   A^2 -> H(f(e), U1(d, k))
26.98/8.84	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.84	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.84	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.84	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.84	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.84	   A^2 -> H(U1(k, k), f(e))
26.98/8.84	   A^2 -> H(U1(k, k), f(k))
26.98/8.84	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.84	   A^2 -> H(f(k), U1(e, b))
26.98/8.84	   A^2 -> H(f(k), U1(k, b))
26.98/8.84	   A^2 -> H(f(k), U1(c, d))
26.98/8.84	   A^2 -> H(f(k), U1(d, c))
26.98/8.84	   A^2 -> H(f(k), U1(b, e))
26.98/8.84	   A^2 -> H(f(k), U1(b, k))
26.98/8.84	   A^2 -> H(f(k), U1(e, c))
26.98/8.84	   A^2 -> H(f(k), U1(k, c))
26.98/8.84	   A^2 -> H(f(k), U1(c, e))
26.98/8.84	   A^2 -> H(f(k), U1(c, k))
26.98/8.84	   A^2 -> H(f(k), U1(e, e))
26.98/8.84	   A^2 -> H(f(k), U1(k, d))
26.98/8.84	   A^2 -> H(f(k), U1(d, k))
26.98/8.84	   A^2 -> H(f(c), b)
26.98/8.84	   A^2 -> H(f(c), U1(e, d))
26.98/8.84	   A^2 -> H(f(c), U1(d, e))
26.98/8.84	   A^2 -> H(f(k), U1(k, k))
26.98/8.84	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.84	   A^2 -> H(U1(k, k), f(c))
26.98/8.84	   A^2 -> H(U1(k, k), f(d))
26.98/8.84	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.84	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.84	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.84	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.84	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.84	   A^2 -> H(U1(k, d), f(e))
26.98/8.84	   A^2 -> H(U1(k, d), f(k))
26.98/8.84	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.84	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.84	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.84	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.84	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.84	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.84	   A^2 -> H(U1(d, k), f(e))
26.98/8.84	   A^2 -> H(U1(d, k), f(k))
26.98/8.84	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.84	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.84	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.84	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.84	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.84	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.84	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.84	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.84	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.84	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.84	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.84	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.84	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.84	   A^2 -> H(f(d), b)
26.98/8.84	   A^2 -> H(f(d), U1(e, d))
26.98/8.84	   A^2 -> H(f(d), U1(d, e))
26.98/8.84	   A^2 -> H(f(d), c)
26.98/8.84	   A^2 -> H(f(d), U1(e, k))
26.98/8.84	   A^2 -> H(f(d), U1(k, e))
26.98/8.84	   A^2 -> H(f(d), e)
26.98/8.84	   A^2 -> H(f(a), d)
26.98/8.84	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.84	   A^2 -> H(f(c), c)
26.98/8.84	   A^2 -> H(f(c), U1(e, k))
26.98/8.84	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.84	   A^2 -> H(f(c), U1(k, e))
26.98/8.84	   A^2 -> H(f(c), U1(k, k))
26.98/8.84	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.84	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.84	   A^2 -> H(f(a), k)
26.98/8.84	   A^2 -> H(f(e), U1(e, e))
26.98/8.84	   A^2 -> H(f(c), e)
26.98/8.84	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.84	   A^2 -> H(f(d), U1(k, k))
26.98/8.84	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.84	   A^2 -> H(d, U1(b, b))
26.98/8.84	   A^2 -> H(d, f(c))
26.98/8.84	   A^2 -> H(d, f(d))
26.98/8.84	   A^2 -> H(a, U1(c, b))
26.98/8.84	   A^2 -> H(a, U1(d, b))
26.98/8.84	   A^2 -> H(a, U1(b, c))
26.98/8.84	   A^2 -> H(a, U1(b, d))
26.98/8.84	   A^2 -> H(a, U1(c, c))
26.98/8.84	   A^2 -> H(a, f(e))
26.98/8.84	   A^2 -> H(a, f(k))
26.98/8.84	   A^2 -> H(a, U1(d, d))
26.98/8.84	   A^2 -> H(U1(e, d), U1(c, b))
26.98/8.84	   A^2 -> H(U1(e, d), U1(d, b))
26.98/8.84	   A^2 -> H(U1(e, d), U1(b, c))
26.98/8.84	   A^2 -> H(U1(e, d), U1(b, d))
26.98/8.84	   A^2 -> H(U1(e, d), U1(c, c))
26.98/8.84	   A^2 -> H(U1(e, d), f(e))
26.98/8.84	   A^2 -> H(U1(e, d), f(k))
26.98/8.84	   A^2 -> H(U1(e, d), U1(d, d))
26.98/8.84	   A^2 -> H(U1(e, a), U1(e, b))
26.98/8.84	   A^2 -> H(U1(e, a), U1(k, b))
26.98/8.84	   A^2 -> H(U1(e, a), U1(c, d))
26.98/8.84	   A^2 -> H(U1(e, a), U1(d, c))
26.98/8.84	   A^2 -> H(U1(e, a), U1(b, e))
26.98/8.84	   A^2 -> H(U1(e, a), U1(b, k))
26.98/8.84	   A^2 -> H(U1(e, a), U1(e, c))
26.98/8.84	   A^2 -> H(U1(e, a), U1(k, c))
26.98/8.84	   A^2 -> H(U1(e, a), U1(c, e))
26.98/8.84	   A^2 -> H(U1(e, a), U1(c, k))
26.98/8.84	   A^2 -> H(U1(e, a), U1(e, e))
26.98/8.84	   A^2 -> H(U1(e, a), U1(k, k))
26.98/8.84	   A^2 -> H(U1(e, a), U1(k, d))
26.98/8.84	   A^2 -> H(U1(e, a), U1(d, k))
26.98/8.84	   A^2 -> H(U1(k, a), U1(e, b))
26.98/8.84	   A^2 -> H(U1(k, a), U1(k, b))
26.98/8.84	   A^2 -> H(U1(k, a), U1(c, d))
26.98/8.84	   A^2 -> H(U1(k, a), U1(d, c))
26.98/8.84	   A^2 -> H(U1(k, a), U1(b, e))
26.98/8.84	   A^2 -> H(U1(k, a), U1(b, k))
26.98/8.84	   A^2 -> H(U1(k, a), U1(e, c))
26.98/8.84	   A^2 -> H(U1(k, a), U1(k, c))
26.98/8.84	   A^2 -> H(U1(k, a), U1(c, e))
26.98/8.84	   A^2 -> H(U1(k, a), U1(c, k))
26.98/8.84	
26.98/8.84	The TRS R consists of the following rules:
26.98/8.84	
26.98/8.84	   f(x) -> U1(x, x)
26.98/8.84	   U1(e, x) -> x
26.98/8.84	   a -> c
26.98/8.84	   a -> d
26.98/8.84	   b -> c
26.98/8.84	   b -> d
26.98/8.84	   d -> k
26.98/8.84	   c -> e
26.98/8.84	   c -> k
26.98/8.84	
26.98/8.84	Q is empty.
26.98/8.84	We have to consider all minimal (P,Q,R)-chains.
26.98/8.84	----------------------------------------
26.98/8.84	
26.98/8.84	(581) TransformationProof (EQUIVALENT)
26.98/8.84	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), f(e)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.84	
26.98/8.84	   (A^2 -> H(U1(k, c), f(e)),A^2 -> H(U1(k, c), f(e)))
26.98/8.84	   (A^2 -> H(U1(k, d), f(e)),A^2 -> H(U1(k, d), f(e)))
26.98/8.84	   (A^2 -> H(U1(k, a), U1(e, e)),A^2 -> H(U1(k, a), U1(e, e)))
26.98/8.84	
26.98/8.84	
26.98/8.84	----------------------------------------
26.98/8.84	
26.98/8.84	(582)
26.98/8.84	Obligation:
26.98/8.84	Q DP problem:
26.98/8.84	The TRS P consists of the following rules:
26.98/8.84	
26.98/8.84	   H(x, x) -> G(x, x, f(k))
26.98/8.84	   G(d, x, x) -> A^2
26.98/8.84	   A^2 -> H(f(c), f(c))
26.98/8.84	   A^2 -> H(f(d), f(d))
26.98/8.84	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.84	   A^2 -> H(f(e), f(e))
26.98/8.84	   A^2 -> H(f(k), f(k))
26.98/8.84	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.84	   A^2 -> H(U1(k, a), f(k))
26.98/8.84	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.84	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.84	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.84	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.84	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.84	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.84	   A^2 -> H(U1(c, d), f(e))
26.98/8.84	   A^2 -> H(U1(c, d), f(k))
26.98/8.84	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.84	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.84	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.84	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.84	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.84	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.84	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.84	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.84	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.84	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.84	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.84	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.84	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.84	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.84	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.84	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.84	   A^2 -> H(U1(d, e), f(c))
26.98/8.84	   A^2 -> H(U1(d, e), f(d))
26.98/8.84	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.84	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.84	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.84	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.84	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.84	   A^2 -> H(U1(d, c), f(e))
26.98/8.84	   A^2 -> H(U1(d, c), f(k))
26.98/8.84	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.84	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.84	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.84	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.84	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.84	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.84	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.84	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.84	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.84	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.84	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.84	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.84	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.84	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.84	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.84	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.84	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.84	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.84	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.84	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.84	   A^2 -> H(U1(a, e), f(e))
26.98/8.84	   A^2 -> H(U1(a, e), f(k))
26.98/8.84	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.84	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.84	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.84	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.84	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.84	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.84	   A^2 -> H(U1(a, k), f(e))
26.98/8.84	   A^2 -> H(U1(a, k), f(k))
26.98/8.84	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.84	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.84	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.84	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.84	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.84	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.84	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.84	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.84	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.84	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.84	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.84	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.84	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.84	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.84	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.84	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.84	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.84	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.84	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.84	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.84	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.84	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.84	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.84	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.84	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.84	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.84	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.84	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.84	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.84	   A^2 -> H(U1(a, a), b)
26.98/8.84	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.84	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.84	   A^2 -> H(U1(a, a), c)
26.98/8.84	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.84	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.84	   A^2 -> H(U1(a, a), e)
26.98/8.84	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.84	   A^2 -> H(k, f(b))
26.98/8.84	   A^2 -> H(c, U1(b, b))
26.98/8.84	   A^2 -> H(c, f(c))
26.98/8.84	   A^2 -> H(c, f(d))
26.98/8.84	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.84	   A^2 -> H(U1(e, k), f(c))
26.98/8.84	   A^2 -> H(U1(e, k), f(d))
26.98/8.84	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.84	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.84	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.84	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.84	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.84	   A^2 -> H(U1(e, c), f(e))
26.98/8.84	   A^2 -> H(U1(e, c), f(k))
26.98/8.84	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.84	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.84	   A^2 -> H(U1(k, e), f(c))
26.98/8.84	   A^2 -> H(U1(k, e), f(d))
26.98/8.84	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.84	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.84	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.84	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.84	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.84	   A^2 -> H(U1(k, c), f(e))
26.98/8.84	   A^2 -> H(U1(k, c), f(k))
26.98/8.84	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.84	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.84	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.84	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.84	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.84	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.84	   A^2 -> H(U1(c, e), f(e))
26.98/8.84	   A^2 -> H(U1(c, e), f(k))
26.98/8.84	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.84	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.84	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.84	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.84	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.84	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.84	   A^2 -> H(U1(c, k), f(e))
26.98/8.84	   A^2 -> H(U1(c, k), f(k))
26.98/8.84	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.84	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.84	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.84	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.84	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.84	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.84	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.84	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.84	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.84	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.84	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.84	   A^2 -> H(e, U1(b, b))
26.98/8.84	   A^2 -> H(e, f(c))
26.98/8.84	   A^2 -> H(e, f(d))
26.98/8.84	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.84	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.84	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.84	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.84	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.84	   A^2 -> H(U1(e, e), f(e))
26.98/8.84	   A^2 -> H(U1(e, e), f(k))
26.98/8.84	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.84	   A^2 -> H(f(e), U1(e, b))
26.98/8.84	   A^2 -> H(f(e), U1(k, b))
26.98/8.84	   A^2 -> H(f(e), U1(c, d))
26.98/8.84	   A^2 -> H(f(e), U1(d, c))
26.98/8.84	   A^2 -> H(f(e), U1(b, e))
26.98/8.84	   A^2 -> H(f(e), U1(b, k))
26.98/8.84	   A^2 -> H(f(e), U1(e, c))
26.98/8.84	   A^2 -> H(f(e), U1(k, c))
26.98/8.84	   A^2 -> H(f(e), U1(c, e))
26.98/8.84	   A^2 -> H(f(e), U1(c, k))
26.98/8.84	   A^2 -> H(f(e), U1(k, k))
26.98/8.84	   A^2 -> H(f(e), U1(k, d))
26.98/8.84	   A^2 -> H(f(e), U1(d, k))
26.98/8.84	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.84	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.84	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.84	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.84	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.84	   A^2 -> H(U1(k, k), f(e))
26.98/8.84	   A^2 -> H(U1(k, k), f(k))
26.98/8.84	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.84	   A^2 -> H(f(k), U1(e, b))
26.98/8.84	   A^2 -> H(f(k), U1(k, b))
26.98/8.84	   A^2 -> H(f(k), U1(c, d))
26.98/8.84	   A^2 -> H(f(k), U1(d, c))
26.98/8.84	   A^2 -> H(f(k), U1(b, e))
26.98/8.84	   A^2 -> H(f(k), U1(b, k))
26.98/8.84	   A^2 -> H(f(k), U1(e, c))
26.98/8.84	   A^2 -> H(f(k), U1(k, c))
26.98/8.84	   A^2 -> H(f(k), U1(c, e))
26.98/8.84	   A^2 -> H(f(k), U1(c, k))
26.98/8.84	   A^2 -> H(f(k), U1(e, e))
26.98/8.84	   A^2 -> H(f(k), U1(k, d))
26.98/8.84	   A^2 -> H(f(k), U1(d, k))
26.98/8.84	   A^2 -> H(f(c), b)
26.98/8.84	   A^2 -> H(f(c), U1(e, d))
26.98/8.84	   A^2 -> H(f(c), U1(d, e))
26.98/8.84	   A^2 -> H(f(k), U1(k, k))
26.98/8.84	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.84	   A^2 -> H(U1(k, k), f(c))
26.98/8.84	   A^2 -> H(U1(k, k), f(d))
26.98/8.84	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.84	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.84	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.84	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.84	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.84	   A^2 -> H(U1(k, d), f(e))
26.98/8.84	   A^2 -> H(U1(k, d), f(k))
26.98/8.84	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.84	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.84	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.84	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.84	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.84	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.84	   A^2 -> H(U1(d, k), f(e))
26.98/8.84	   A^2 -> H(U1(d, k), f(k))
26.98/8.84	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.84	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.84	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.84	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.84	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.84	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.84	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.84	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.84	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.84	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.84	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.84	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.84	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.84	   A^2 -> H(f(d), b)
26.98/8.84	   A^2 -> H(f(d), U1(e, d))
26.98/8.84	   A^2 -> H(f(d), U1(d, e))
26.98/8.84	   A^2 -> H(f(d), c)
26.98/8.84	   A^2 -> H(f(d), U1(e, k))
26.98/8.84	   A^2 -> H(f(d), U1(k, e))
26.98/8.84	   A^2 -> H(f(d), e)
26.98/8.84	   A^2 -> H(f(a), d)
26.98/8.84	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.84	   A^2 -> H(f(c), c)
26.98/8.84	   A^2 -> H(f(c), U1(e, k))
26.98/8.84	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.84	   A^2 -> H(f(c), U1(k, e))
26.98/8.84	   A^2 -> H(f(c), U1(k, k))
26.98/8.84	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.84	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.84	   A^2 -> H(f(a), k)
26.98/8.84	   A^2 -> H(f(e), U1(e, e))
26.98/8.84	   A^2 -> H(f(c), e)
26.98/8.84	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.84	   A^2 -> H(f(d), U1(k, k))
26.98/8.84	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.84	   A^2 -> H(d, U1(b, b))
26.98/8.84	   A^2 -> H(d, f(c))
26.98/8.84	   A^2 -> H(d, f(d))
26.98/8.84	   A^2 -> H(a, U1(c, b))
26.98/8.84	   A^2 -> H(a, U1(d, b))
26.98/8.84	   A^2 -> H(a, U1(b, c))
26.98/8.84	   A^2 -> H(a, U1(b, d))
26.98/8.84	   A^2 -> H(a, U1(c, c))
26.98/8.84	   A^2 -> H(a, f(e))
26.98/8.84	   A^2 -> H(a, f(k))
26.98/8.84	   A^2 -> H(a, U1(d, d))
26.98/8.84	   A^2 -> H(U1(e, d), U1(c, b))
26.98/8.84	   A^2 -> H(U1(e, d), U1(d, b))
26.98/8.84	   A^2 -> H(U1(e, d), U1(b, c))
26.98/8.84	   A^2 -> H(U1(e, d), U1(b, d))
26.98/8.84	   A^2 -> H(U1(e, d), U1(c, c))
26.98/8.84	   A^2 -> H(U1(e, d), f(e))
26.98/8.84	   A^2 -> H(U1(e, d), f(k))
26.98/8.84	   A^2 -> H(U1(e, d), U1(d, d))
26.98/8.84	   A^2 -> H(U1(e, a), U1(e, b))
26.98/8.84	   A^2 -> H(U1(e, a), U1(k, b))
26.98/8.84	   A^2 -> H(U1(e, a), U1(c, d))
26.98/8.84	   A^2 -> H(U1(e, a), U1(d, c))
26.98/8.84	   A^2 -> H(U1(e, a), U1(b, e))
26.98/8.84	   A^2 -> H(U1(e, a), U1(b, k))
26.98/8.84	   A^2 -> H(U1(e, a), U1(e, c))
26.98/8.84	   A^2 -> H(U1(e, a), U1(k, c))
26.98/8.84	   A^2 -> H(U1(e, a), U1(c, e))
26.98/8.84	   A^2 -> H(U1(e, a), U1(c, k))
26.98/8.84	   A^2 -> H(U1(e, a), U1(e, e))
26.98/8.84	   A^2 -> H(U1(e, a), U1(k, k))
26.98/8.84	   A^2 -> H(U1(e, a), U1(k, d))
26.98/8.84	   A^2 -> H(U1(e, a), U1(d, k))
26.98/8.84	   A^2 -> H(U1(k, a), U1(e, b))
26.98/8.84	   A^2 -> H(U1(k, a), U1(k, b))
26.98/8.84	   A^2 -> H(U1(k, a), U1(c, d))
26.98/8.84	   A^2 -> H(U1(k, a), U1(d, c))
26.98/8.84	   A^2 -> H(U1(k, a), U1(b, e))
26.98/8.84	   A^2 -> H(U1(k, a), U1(b, k))
26.98/8.84	   A^2 -> H(U1(k, a), U1(e, c))
26.98/8.84	   A^2 -> H(U1(k, a), U1(k, c))
26.98/8.84	   A^2 -> H(U1(k, a), U1(c, e))
26.98/8.84	   A^2 -> H(U1(k, a), U1(c, k))
26.98/8.84	   A^2 -> H(U1(k, a), U1(e, e))
26.98/8.84	
26.98/8.84	The TRS R consists of the following rules:
26.98/8.84	
26.98/8.84	   f(x) -> U1(x, x)
26.98/8.84	   U1(e, x) -> x
26.98/8.84	   a -> c
26.98/8.84	   a -> d
26.98/8.84	   b -> c
26.98/8.84	   b -> d
26.98/8.84	   d -> k
26.98/8.84	   c -> e
26.98/8.84	   c -> k
26.98/8.84	
26.98/8.84	Q is empty.
26.98/8.84	We have to consider all minimal (P,Q,R)-chains.
26.98/8.84	----------------------------------------
26.98/8.84	
26.98/8.84	(583) TransformationProof (EQUIVALENT)
26.98/8.84	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), f(k)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.84	
26.98/8.84	   (A^2 -> H(U1(k, c), f(k)),A^2 -> H(U1(k, c), f(k)))
26.98/8.84	   (A^2 -> H(U1(k, d), f(k)),A^2 -> H(U1(k, d), f(k)))
26.98/8.84	   (A^2 -> H(U1(k, a), U1(k, k)),A^2 -> H(U1(k, a), U1(k, k)))
26.98/8.84	
26.98/8.84	
26.98/8.84	----------------------------------------
26.98/8.84	
26.98/8.84	(584)
26.98/8.84	Obligation:
26.98/8.84	Q DP problem:
26.98/8.84	The TRS P consists of the following rules:
26.98/8.84	
26.98/8.84	   H(x, x) -> G(x, x, f(k))
26.98/8.84	   G(d, x, x) -> A^2
26.98/8.84	   A^2 -> H(f(c), f(c))
26.98/8.84	   A^2 -> H(f(d), f(d))
26.98/8.84	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.84	   A^2 -> H(f(e), f(e))
26.98/8.84	   A^2 -> H(f(k), f(k))
26.98/8.84	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.84	   A^2 -> H(U1(k, a), U1(d, d))
26.98/8.84	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.84	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.84	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.84	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.84	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.84	   A^2 -> H(U1(c, d), f(e))
26.98/8.84	   A^2 -> H(U1(c, d), f(k))
26.98/8.84	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.84	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.84	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.84	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.84	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.84	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.84	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.84	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.84	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.84	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.84	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.84	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.84	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.84	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.84	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.84	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.84	   A^2 -> H(U1(d, e), f(c))
26.98/8.84	   A^2 -> H(U1(d, e), f(d))
26.98/8.84	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.84	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.84	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.84	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.84	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.84	   A^2 -> H(U1(d, c), f(e))
26.98/8.84	   A^2 -> H(U1(d, c), f(k))
26.98/8.84	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.84	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.84	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.84	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.84	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.84	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.84	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.84	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.84	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.84	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.84	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.84	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.84	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.84	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.84	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.84	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.84	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.84	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.84	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.84	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.84	   A^2 -> H(U1(a, e), f(e))
26.98/8.84	   A^2 -> H(U1(a, e), f(k))
26.98/8.84	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.84	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.84	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.84	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.84	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.84	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.84	   A^2 -> H(U1(a, k), f(e))
26.98/8.84	   A^2 -> H(U1(a, k), f(k))
26.98/8.84	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.84	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.84	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.84	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.84	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.84	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.84	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.84	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.84	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.84	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.84	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.84	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.84	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.84	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.84	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.84	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.84	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.84	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.84	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.84	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.84	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.84	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.84	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.84	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.84	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.84	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.84	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.84	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.84	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.84	   A^2 -> H(U1(a, a), b)
26.98/8.84	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.84	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.84	   A^2 -> H(U1(a, a), c)
26.98/8.84	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.84	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.84	   A^2 -> H(U1(a, a), e)
26.98/8.84	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.84	   A^2 -> H(k, f(b))
26.98/8.84	   A^2 -> H(c, U1(b, b))
26.98/8.84	   A^2 -> H(c, f(c))
26.98/8.84	   A^2 -> H(c, f(d))
26.98/8.84	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.84	   A^2 -> H(U1(e, k), f(c))
26.98/8.84	   A^2 -> H(U1(e, k), f(d))
26.98/8.84	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.84	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.84	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.84	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.84	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.84	   A^2 -> H(U1(e, c), f(e))
26.98/8.84	   A^2 -> H(U1(e, c), f(k))
26.98/8.84	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.84	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.84	   A^2 -> H(U1(k, e), f(c))
26.98/8.84	   A^2 -> H(U1(k, e), f(d))
26.98/8.84	   A^2 -> H(U1(k, c), U1(c, b))
26.98/8.84	   A^2 -> H(U1(k, c), U1(d, b))
26.98/8.84	   A^2 -> H(U1(k, c), U1(b, c))
26.98/8.84	   A^2 -> H(U1(k, c), U1(b, d))
26.98/8.84	   A^2 -> H(U1(k, c), U1(c, c))
26.98/8.84	   A^2 -> H(U1(k, c), f(e))
26.98/8.84	   A^2 -> H(U1(k, c), f(k))
26.98/8.84	   A^2 -> H(U1(k, c), U1(d, d))
26.98/8.84	   A^2 -> H(U1(c, e), U1(c, b))
26.98/8.84	   A^2 -> H(U1(c, e), U1(d, b))
26.98/8.84	   A^2 -> H(U1(c, e), U1(b, c))
26.98/8.84	   A^2 -> H(U1(c, e), U1(b, d))
26.98/8.84	   A^2 -> H(U1(c, e), U1(c, c))
26.98/8.84	   A^2 -> H(U1(c, e), f(e))
26.98/8.84	   A^2 -> H(U1(c, e), f(k))
26.98/8.84	   A^2 -> H(U1(c, e), U1(d, d))
26.98/8.84	   A^2 -> H(U1(c, k), U1(c, b))
26.98/8.84	   A^2 -> H(U1(c, k), U1(d, b))
26.98/8.84	   A^2 -> H(U1(c, k), U1(b, c))
26.98/8.84	   A^2 -> H(U1(c, k), U1(b, d))
26.98/8.84	   A^2 -> H(U1(c, k), U1(c, c))
26.98/8.84	   A^2 -> H(U1(c, k), f(e))
26.98/8.84	   A^2 -> H(U1(c, k), f(k))
26.98/8.84	   A^2 -> H(U1(c, k), U1(d, d))
26.98/8.84	   A^2 -> H(U1(c, c), U1(e, b))
26.98/8.84	   A^2 -> H(U1(c, c), U1(k, b))
26.98/8.84	   A^2 -> H(U1(c, c), U1(c, d))
26.98/8.84	   A^2 -> H(U1(c, c), U1(d, c))
26.98/8.84	   A^2 -> H(U1(c, c), U1(b, e))
26.98/8.84	   A^2 -> H(U1(c, c), U1(b, k))
26.98/8.84	   A^2 -> H(U1(c, c), U1(e, e))
26.98/8.84	   A^2 -> H(U1(c, c), U1(k, k))
26.98/8.84	   A^2 -> H(U1(c, c), U1(k, d))
26.98/8.84	   A^2 -> H(U1(c, c), U1(d, k))
26.98/8.84	   A^2 -> H(e, U1(b, b))
26.98/8.84	   A^2 -> H(e, f(c))
26.98/8.84	   A^2 -> H(e, f(d))
26.98/8.84	   A^2 -> H(U1(e, e), U1(c, b))
26.98/8.84	   A^2 -> H(U1(e, e), U1(d, b))
26.98/8.84	   A^2 -> H(U1(e, e), U1(b, c))
26.98/8.84	   A^2 -> H(U1(e, e), U1(b, d))
26.98/8.84	   A^2 -> H(U1(e, e), U1(c, c))
26.98/8.84	   A^2 -> H(U1(e, e), f(e))
26.98/8.84	   A^2 -> H(U1(e, e), f(k))
26.98/8.84	   A^2 -> H(U1(e, e), U1(d, d))
26.98/8.84	   A^2 -> H(f(e), U1(e, b))
26.98/8.84	   A^2 -> H(f(e), U1(k, b))
26.98/8.84	   A^2 -> H(f(e), U1(c, d))
26.98/8.84	   A^2 -> H(f(e), U1(d, c))
26.98/8.84	   A^2 -> H(f(e), U1(b, e))
26.98/8.84	   A^2 -> H(f(e), U1(b, k))
26.98/8.84	   A^2 -> H(f(e), U1(e, c))
26.98/8.84	   A^2 -> H(f(e), U1(k, c))
26.98/8.84	   A^2 -> H(f(e), U1(c, e))
26.98/8.84	   A^2 -> H(f(e), U1(c, k))
26.98/8.84	   A^2 -> H(f(e), U1(k, k))
26.98/8.84	   A^2 -> H(f(e), U1(k, d))
26.98/8.84	   A^2 -> H(f(e), U1(d, k))
26.98/8.84	   A^2 -> H(U1(k, k), U1(c, b))
26.98/8.84	   A^2 -> H(U1(k, k), U1(d, b))
26.98/8.84	   A^2 -> H(U1(k, k), U1(b, c))
26.98/8.84	   A^2 -> H(U1(k, k), U1(b, d))
26.98/8.84	   A^2 -> H(U1(k, k), U1(c, c))
26.98/8.84	   A^2 -> H(U1(k, k), f(e))
26.98/8.84	   A^2 -> H(U1(k, k), f(k))
26.98/8.84	   A^2 -> H(U1(k, k), U1(d, d))
26.98/8.84	   A^2 -> H(f(k), U1(e, b))
26.98/8.84	   A^2 -> H(f(k), U1(k, b))
26.98/8.84	   A^2 -> H(f(k), U1(c, d))
26.98/8.84	   A^2 -> H(f(k), U1(d, c))
26.98/8.84	   A^2 -> H(f(k), U1(b, e))
26.98/8.84	   A^2 -> H(f(k), U1(b, k))
26.98/8.84	   A^2 -> H(f(k), U1(e, c))
26.98/8.84	   A^2 -> H(f(k), U1(k, c))
26.98/8.84	   A^2 -> H(f(k), U1(c, e))
26.98/8.84	   A^2 -> H(f(k), U1(c, k))
26.98/8.84	   A^2 -> H(f(k), U1(e, e))
26.98/8.84	   A^2 -> H(f(k), U1(k, d))
26.98/8.84	   A^2 -> H(f(k), U1(d, k))
26.98/8.84	   A^2 -> H(f(c), b)
26.98/8.84	   A^2 -> H(f(c), U1(e, d))
26.98/8.84	   A^2 -> H(f(c), U1(d, e))
26.98/8.84	   A^2 -> H(f(k), U1(k, k))
26.98/8.84	   A^2 -> H(U1(k, k), U1(b, b))
26.98/8.84	   A^2 -> H(U1(k, k), f(c))
26.98/8.84	   A^2 -> H(U1(k, k), f(d))
26.98/8.84	   A^2 -> H(U1(k, d), U1(c, b))
26.98/8.84	   A^2 -> H(U1(k, d), U1(d, b))
26.98/8.84	   A^2 -> H(U1(k, d), U1(b, c))
26.98/8.84	   A^2 -> H(U1(k, d), U1(b, d))
26.98/8.84	   A^2 -> H(U1(k, d), U1(c, c))
26.98/8.84	   A^2 -> H(U1(k, d), f(e))
26.98/8.84	   A^2 -> H(U1(k, d), f(k))
26.98/8.84	   A^2 -> H(U1(k, d), U1(d, d))
26.98/8.84	   A^2 -> H(U1(d, k), U1(c, b))
26.98/8.84	   A^2 -> H(U1(d, k), U1(d, b))
26.98/8.84	   A^2 -> H(U1(d, k), U1(b, c))
26.98/8.84	   A^2 -> H(U1(d, k), U1(b, d))
26.98/8.84	   A^2 -> H(U1(d, k), U1(c, c))
26.98/8.84	   A^2 -> H(U1(d, k), f(e))
26.98/8.84	   A^2 -> H(U1(d, k), f(k))
26.98/8.84	   A^2 -> H(U1(d, k), U1(d, d))
26.98/8.84	   A^2 -> H(U1(d, d), U1(e, b))
26.98/8.84	   A^2 -> H(U1(d, d), U1(k, b))
26.98/8.84	   A^2 -> H(U1(d, d), U1(c, d))
26.98/8.84	   A^2 -> H(U1(d, d), U1(d, c))
26.98/8.84	   A^2 -> H(U1(d, d), U1(b, e))
26.98/8.84	   A^2 -> H(U1(d, d), U1(b, k))
26.98/8.84	   A^2 -> H(U1(d, d), U1(e, c))
26.98/8.84	   A^2 -> H(U1(d, d), U1(k, c))
26.98/8.84	   A^2 -> H(U1(d, d), U1(c, e))
26.98/8.84	   A^2 -> H(U1(d, d), U1(c, k))
26.98/8.84	   A^2 -> H(U1(d, d), U1(e, e))
26.98/8.84	   A^2 -> H(U1(d, d), U1(k, k))
26.98/8.84	   A^2 -> H(f(d), b)
26.98/8.84	   A^2 -> H(f(d), U1(e, d))
26.98/8.84	   A^2 -> H(f(d), U1(d, e))
26.98/8.84	   A^2 -> H(f(d), c)
26.98/8.84	   A^2 -> H(f(d), U1(e, k))
26.98/8.84	   A^2 -> H(f(d), U1(k, e))
26.98/8.84	   A^2 -> H(f(d), e)
26.98/8.84	   A^2 -> H(f(a), d)
26.98/8.84	   A^2 -> H(U1(c, c), U1(e, c))
26.98/8.84	   A^2 -> H(f(c), c)
26.98/8.84	   A^2 -> H(f(c), U1(e, k))
26.98/8.84	   A^2 -> H(U1(c, c), U1(k, c))
26.98/8.84	   A^2 -> H(f(c), U1(k, e))
26.98/8.84	   A^2 -> H(f(c), U1(k, k))
26.98/8.84	   A^2 -> H(U1(c, c), U1(c, e))
26.98/8.84	   A^2 -> H(U1(c, c), U1(c, k))
26.98/8.84	   A^2 -> H(f(a), k)
26.98/8.84	   A^2 -> H(f(e), U1(e, e))
26.98/8.84	   A^2 -> H(f(c), e)
26.98/8.84	   A^2 -> H(U1(d, d), U1(k, d))
26.98/8.84	   A^2 -> H(f(d), U1(k, k))
26.98/8.84	   A^2 -> H(U1(d, d), U1(d, k))
26.98/8.84	   A^2 -> H(d, U1(b, b))
26.98/8.84	   A^2 -> H(d, f(c))
26.98/8.84	   A^2 -> H(d, f(d))
26.98/8.84	   A^2 -> H(a, U1(c, b))
26.98/8.84	   A^2 -> H(a, U1(d, b))
26.98/8.84	   A^2 -> H(a, U1(b, c))
26.98/8.84	   A^2 -> H(a, U1(b, d))
26.98/8.84	   A^2 -> H(a, U1(c, c))
26.98/8.84	   A^2 -> H(a, f(e))
26.98/8.84	   A^2 -> H(a, f(k))
26.98/8.84	   A^2 -> H(a, U1(d, d))
26.98/8.84	   A^2 -> H(U1(e, d), U1(c, b))
26.98/8.84	   A^2 -> H(U1(e, d), U1(d, b))
26.98/8.84	   A^2 -> H(U1(e, d), U1(b, c))
26.98/8.84	   A^2 -> H(U1(e, d), U1(b, d))
26.98/8.84	   A^2 -> H(U1(e, d), U1(c, c))
26.98/8.84	   A^2 -> H(U1(e, d), f(e))
26.98/8.84	   A^2 -> H(U1(e, d), f(k))
26.98/8.84	   A^2 -> H(U1(e, d), U1(d, d))
26.98/8.84	   A^2 -> H(U1(e, a), U1(e, b))
26.98/8.84	   A^2 -> H(U1(e, a), U1(k, b))
26.98/8.84	   A^2 -> H(U1(e, a), U1(c, d))
26.98/8.84	   A^2 -> H(U1(e, a), U1(d, c))
26.98/8.84	   A^2 -> H(U1(e, a), U1(b, e))
26.98/8.84	   A^2 -> H(U1(e, a), U1(b, k))
26.98/8.84	   A^2 -> H(U1(e, a), U1(e, c))
26.98/8.84	   A^2 -> H(U1(e, a), U1(k, c))
26.98/8.84	   A^2 -> H(U1(e, a), U1(c, e))
26.98/8.84	   A^2 -> H(U1(e, a), U1(c, k))
26.98/8.84	   A^2 -> H(U1(e, a), U1(e, e))
26.98/8.84	   A^2 -> H(U1(e, a), U1(k, k))
26.98/8.84	   A^2 -> H(U1(e, a), U1(k, d))
26.98/8.84	   A^2 -> H(U1(e, a), U1(d, k))
26.98/8.84	   A^2 -> H(U1(k, a), U1(e, b))
26.98/8.84	   A^2 -> H(U1(k, a), U1(k, b))
26.98/8.84	   A^2 -> H(U1(k, a), U1(c, d))
26.98/8.84	   A^2 -> H(U1(k, a), U1(d, c))
26.98/8.84	   A^2 -> H(U1(k, a), U1(b, e))
26.98/8.84	   A^2 -> H(U1(k, a), U1(b, k))
26.98/8.84	   A^2 -> H(U1(k, a), U1(e, c))
26.98/8.84	   A^2 -> H(U1(k, a), U1(k, c))
26.98/8.84	   A^2 -> H(U1(k, a), U1(c, e))
26.98/8.84	   A^2 -> H(U1(k, a), U1(c, k))
26.98/8.84	   A^2 -> H(U1(k, a), U1(e, e))
26.98/8.84	   A^2 -> H(U1(k, a), U1(k, k))
26.98/8.84	
26.98/8.84	The TRS R consists of the following rules:
26.98/8.84	
26.98/8.84	   f(x) -> U1(x, x)
26.98/8.84	   U1(e, x) -> x
26.98/8.84	   a -> c
26.98/8.84	   a -> d
26.98/8.84	   b -> c
26.98/8.84	   b -> d
26.98/8.84	   d -> k
26.98/8.84	   c -> e
26.98/8.84	   c -> k
26.98/8.84	
26.98/8.84	Q is empty.
26.98/8.84	We have to consider all minimal (P,Q,R)-chains.
26.98/8.84	----------------------------------------
26.98/8.84	
26.98/8.84	(585) TransformationProof (EQUIVALENT)
26.98/8.84	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
26.98/8.84	
26.98/8.84	   (A^2 -> H(U1(k, c), U1(d, d)),A^2 -> H(U1(k, c), U1(d, d)))
26.98/8.84	   (A^2 -> H(U1(k, d), U1(d, d)),A^2 -> H(U1(k, d), U1(d, d)))
26.98/8.84	   (A^2 -> H(U1(k, a), U1(k, d)),A^2 -> H(U1(k, a), U1(k, d)))
26.98/8.84	   (A^2 -> H(U1(k, a), U1(d, k)),A^2 -> H(U1(k, a), U1(d, k)))
26.98/8.84	
26.98/8.84	
26.98/8.84	----------------------------------------
26.98/8.84	
26.98/8.84	(586)
26.98/8.84	Obligation:
26.98/8.84	Q DP problem:
26.98/8.84	The TRS P consists of the following rules:
26.98/8.84	
26.98/8.84	   H(x, x) -> G(x, x, f(k))
26.98/8.84	   G(d, x, x) -> A^2
26.98/8.84	   A^2 -> H(f(c), f(c))
26.98/8.84	   A^2 -> H(f(d), f(d))
26.98/8.84	   A^2 -> H(U1(c, c), U1(c, c))
26.98/8.84	   A^2 -> H(f(e), f(e))
26.98/8.84	   A^2 -> H(f(k), f(k))
26.98/8.84	   A^2 -> H(U1(d, d), U1(d, d))
26.98/8.84	   A^2 -> H(U1(c, d), U1(c, b))
26.98/8.84	   A^2 -> H(U1(c, d), U1(d, b))
26.98/8.84	   A^2 -> H(U1(c, d), U1(b, c))
26.98/8.84	   A^2 -> H(U1(c, d), U1(b, d))
26.98/8.84	   A^2 -> H(U1(c, d), U1(c, c))
26.98/8.84	   A^2 -> H(U1(c, d), f(e))
26.98/8.84	   A^2 -> H(U1(c, d), f(k))
26.98/8.84	   A^2 -> H(U1(c, d), U1(d, d))
26.98/8.84	   A^2 -> H(U1(c, a), U1(e, b))
26.98/8.84	   A^2 -> H(U1(c, a), U1(k, b))
26.98/8.84	   A^2 -> H(U1(c, a), U1(c, d))
26.98/8.84	   A^2 -> H(U1(c, a), U1(d, c))
26.98/8.84	   A^2 -> H(U1(c, a), U1(b, e))
26.98/8.84	   A^2 -> H(U1(c, a), U1(b, k))
26.98/8.84	   A^2 -> H(U1(c, a), U1(e, c))
26.98/8.84	   A^2 -> H(U1(c, a), U1(k, c))
26.98/8.84	   A^2 -> H(U1(c, a), U1(c, e))
26.98/8.84	   A^2 -> H(U1(c, a), U1(c, k))
26.98/8.84	   A^2 -> H(U1(c, a), U1(e, e))
26.98/8.84	   A^2 -> H(U1(c, a), U1(k, k))
26.98/8.84	   A^2 -> H(U1(c, a), U1(k, d))
26.98/8.84	   A^2 -> H(U1(c, a), U1(d, k))
26.98/8.84	   A^2 -> H(U1(d, e), U1(b, b))
26.98/8.84	   A^2 -> H(U1(d, e), f(c))
26.98/8.84	   A^2 -> H(U1(d, e), f(d))
26.98/8.84	   A^2 -> H(U1(d, c), U1(c, b))
26.98/8.84	   A^2 -> H(U1(d, c), U1(d, b))
26.98/8.84	   A^2 -> H(U1(d, c), U1(b, c))
26.98/8.84	   A^2 -> H(U1(d, c), U1(b, d))
26.98/8.84	   A^2 -> H(U1(d, c), U1(c, c))
26.98/8.84	   A^2 -> H(U1(d, c), f(e))
26.98/8.84	   A^2 -> H(U1(d, c), f(k))
26.98/8.84	   A^2 -> H(U1(d, c), U1(d, d))
26.98/8.84	   A^2 -> H(U1(d, a), U1(e, b))
26.98/8.84	   A^2 -> H(U1(d, a), U1(k, b))
26.98/8.84	   A^2 -> H(U1(d, a), U1(c, d))
26.98/8.84	   A^2 -> H(U1(d, a), U1(d, c))
26.98/8.84	   A^2 -> H(U1(d, a), U1(b, e))
26.98/8.84	   A^2 -> H(U1(d, a), U1(b, k))
26.98/8.84	   A^2 -> H(U1(d, a), U1(e, c))
26.98/8.84	   A^2 -> H(U1(d, a), U1(k, c))
26.98/8.84	   A^2 -> H(U1(d, a), U1(c, e))
26.98/8.84	   A^2 -> H(U1(d, a), U1(c, k))
26.98/8.84	   A^2 -> H(U1(d, a), U1(e, e))
26.98/8.84	   A^2 -> H(U1(d, a), U1(k, k))
26.98/8.84	   A^2 -> H(U1(d, a), U1(k, d))
26.98/8.84	   A^2 -> H(U1(d, a), U1(d, k))
26.98/8.84	   A^2 -> H(U1(a, e), U1(c, b))
26.98/8.84	   A^2 -> H(U1(a, e), U1(d, b))
26.98/8.84	   A^2 -> H(U1(a, e), U1(b, c))
26.98/8.84	   A^2 -> H(U1(a, e), U1(b, d))
26.98/8.84	   A^2 -> H(U1(a, e), U1(c, c))
26.98/8.84	   A^2 -> H(U1(a, e), f(e))
26.98/8.84	   A^2 -> H(U1(a, e), f(k))
26.98/8.84	   A^2 -> H(U1(a, e), U1(d, d))
26.98/8.84	   A^2 -> H(U1(a, k), U1(c, b))
26.98/8.84	   A^2 -> H(U1(a, k), U1(d, b))
26.98/8.84	   A^2 -> H(U1(a, k), U1(b, c))
26.98/8.84	   A^2 -> H(U1(a, k), U1(b, d))
26.98/8.84	   A^2 -> H(U1(a, k), U1(c, c))
26.98/8.84	   A^2 -> H(U1(a, k), f(e))
26.98/8.84	   A^2 -> H(U1(a, k), f(k))
26.98/8.84	   A^2 -> H(U1(a, k), U1(d, d))
26.98/8.84	   A^2 -> H(U1(a, c), U1(e, b))
26.98/8.84	   A^2 -> H(U1(a, c), U1(k, b))
26.98/8.84	   A^2 -> H(U1(a, c), U1(c, d))
26.98/8.84	   A^2 -> H(U1(a, c), U1(d, c))
26.98/8.84	   A^2 -> H(U1(a, c), U1(b, e))
26.98/8.84	   A^2 -> H(U1(a, c), U1(b, k))
26.98/8.84	   A^2 -> H(U1(a, c), U1(e, c))
26.98/8.84	   A^2 -> H(U1(a, c), U1(k, c))
26.98/8.84	   A^2 -> H(U1(a, c), U1(c, e))
26.98/8.84	   A^2 -> H(U1(a, c), U1(c, k))
26.98/8.84	   A^2 -> H(U1(a, c), U1(e, e))
26.98/8.84	   A^2 -> H(U1(a, c), U1(k, k))
26.98/8.84	   A^2 -> H(U1(a, c), U1(k, d))
26.98/8.84	   A^2 -> H(U1(a, c), U1(d, k))
26.98/8.84	   A^2 -> H(U1(a, d), U1(e, b))
26.98/8.84	   A^2 -> H(U1(a, d), U1(k, b))
26.98/8.84	   A^2 -> H(U1(a, d), U1(c, d))
26.98/8.84	   A^2 -> H(U1(a, d), U1(d, c))
26.98/8.84	   A^2 -> H(U1(a, d), U1(b, e))
26.98/8.84	   A^2 -> H(U1(a, d), U1(b, k))
26.98/8.84	   A^2 -> H(U1(a, d), U1(e, c))
26.98/8.84	   A^2 -> H(U1(a, d), U1(k, c))
26.98/8.84	   A^2 -> H(U1(a, d), U1(c, e))
26.98/8.84	   A^2 -> H(U1(a, d), U1(c, k))
26.98/8.84	   A^2 -> H(U1(a, d), U1(e, e))
26.98/8.84	   A^2 -> H(U1(a, d), U1(k, k))
26.98/8.84	   A^2 -> H(U1(a, d), U1(k, d))
26.98/8.84	   A^2 -> H(U1(a, d), U1(d, k))
26.98/8.84	   A^2 -> H(U1(a, a), b)
26.98/8.84	   A^2 -> H(U1(a, a), U1(e, d))
26.98/8.84	   A^2 -> H(U1(a, a), U1(d, e))
26.98/8.84	   A^2 -> H(U1(a, a), c)
26.98/8.84	   A^2 -> H(U1(a, a), U1(e, k))
26.98/8.84	   A^2 -> H(U1(a, a), U1(k, e))
26.98/8.84	   A^2 -> H(U1(a, a), e)
26.98/8.84	   A^2 -> H(U1(a, a), U1(k, k))
26.98/8.84	   A^2 -> H(k, f(b))
26.98/8.84	   A^2 -> H(c, U1(b, b))
26.98/8.84	   A^2 -> H(c, f(c))
26.98/8.84	   A^2 -> H(c, f(d))
26.98/8.84	   A^2 -> H(U1(e, k), U1(b, b))
26.98/8.84	   A^2 -> H(U1(e, k), f(c))
26.98/8.84	   A^2 -> H(U1(e, k), f(d))
26.98/8.84	   A^2 -> H(U1(e, c), U1(c, b))
26.98/8.84	   A^2 -> H(U1(e, c), U1(d, b))
26.98/8.84	   A^2 -> H(U1(e, c), U1(b, c))
26.98/8.84	   A^2 -> H(U1(e, c), U1(b, d))
26.98/8.84	   A^2 -> H(U1(e, c), U1(c, c))
26.98/8.84	   A^2 -> H(U1(e, c), f(e))
26.98/8.84	   A^2 -> H(U1(e, c), f(k))
26.98/8.84	   A^2 -> H(U1(e, c), U1(d, d))
26.98/8.84	   A^2 -> H(U1(k, e), U1(b, b))
26.98/8.84	   A^2 -> H(U1(k, e), f(c))
26.98/8.84	   A^2 -> H(U1(k, e), f(d))
26.98/8.84	   A^2 -> H(U1(k, c), U1(c, b))
27.25/8.85	   A^2 -> H(U1(k, c), U1(d, b))
27.25/8.85	   A^2 -> H(U1(k, c), U1(b, c))
27.25/8.85	   A^2 -> H(U1(k, c), U1(b, d))
27.25/8.85	   A^2 -> H(U1(k, c), U1(c, c))
27.25/8.85	   A^2 -> H(U1(k, c), f(e))
27.25/8.85	   A^2 -> H(U1(k, c), f(k))
27.25/8.85	   A^2 -> H(U1(k, c), U1(d, d))
27.25/8.85	   A^2 -> H(U1(c, e), U1(c, b))
27.25/8.85	   A^2 -> H(U1(c, e), U1(d, b))
27.25/8.85	   A^2 -> H(U1(c, e), U1(b, c))
27.25/8.85	   A^2 -> H(U1(c, e), U1(b, d))
27.25/8.85	   A^2 -> H(U1(c, e), U1(c, c))
27.25/8.85	   A^2 -> H(U1(c, e), f(e))
27.25/8.85	   A^2 -> H(U1(c, e), f(k))
27.25/8.85	   A^2 -> H(U1(c, e), U1(d, d))
27.25/8.85	   A^2 -> H(U1(c, k), U1(c, b))
27.25/8.85	   A^2 -> H(U1(c, k), U1(d, b))
27.25/8.85	   A^2 -> H(U1(c, k), U1(b, c))
27.25/8.85	   A^2 -> H(U1(c, k), U1(b, d))
27.25/8.85	   A^2 -> H(U1(c, k), U1(c, c))
27.25/8.85	   A^2 -> H(U1(c, k), f(e))
27.25/8.85	   A^2 -> H(U1(c, k), f(k))
27.25/8.85	   A^2 -> H(U1(c, k), U1(d, d))
27.25/8.85	   A^2 -> H(U1(c, c), U1(e, b))
27.25/8.85	   A^2 -> H(U1(c, c), U1(k, b))
27.25/8.85	   A^2 -> H(U1(c, c), U1(c, d))
27.25/8.85	   A^2 -> H(U1(c, c), U1(d, c))
27.25/8.85	   A^2 -> H(U1(c, c), U1(b, e))
27.25/8.85	   A^2 -> H(U1(c, c), U1(b, k))
27.25/8.85	   A^2 -> H(U1(c, c), U1(e, e))
27.25/8.85	   A^2 -> H(U1(c, c), U1(k, k))
27.25/8.85	   A^2 -> H(U1(c, c), U1(k, d))
27.25/8.85	   A^2 -> H(U1(c, c), U1(d, k))
27.25/8.85	   A^2 -> H(e, U1(b, b))
27.25/8.85	   A^2 -> H(e, f(c))
27.25/8.85	   A^2 -> H(e, f(d))
27.25/8.85	   A^2 -> H(U1(e, e), U1(c, b))
27.25/8.85	   A^2 -> H(U1(e, e), U1(d, b))
27.25/8.85	   A^2 -> H(U1(e, e), U1(b, c))
27.25/8.85	   A^2 -> H(U1(e, e), U1(b, d))
27.25/8.85	   A^2 -> H(U1(e, e), U1(c, c))
27.25/8.85	   A^2 -> H(U1(e, e), f(e))
27.25/8.85	   A^2 -> H(U1(e, e), f(k))
27.25/8.85	   A^2 -> H(U1(e, e), U1(d, d))
27.25/8.85	   A^2 -> H(f(e), U1(e, b))
27.25/8.85	   A^2 -> H(f(e), U1(k, b))
27.25/8.85	   A^2 -> H(f(e), U1(c, d))
27.25/8.85	   A^2 -> H(f(e), U1(d, c))
27.25/8.85	   A^2 -> H(f(e), U1(b, e))
27.25/8.85	   A^2 -> H(f(e), U1(b, k))
27.25/8.85	   A^2 -> H(f(e), U1(e, c))
27.25/8.85	   A^2 -> H(f(e), U1(k, c))
27.25/8.85	   A^2 -> H(f(e), U1(c, e))
27.25/8.85	   A^2 -> H(f(e), U1(c, k))
27.25/8.85	   A^2 -> H(f(e), U1(k, k))
27.25/8.85	   A^2 -> H(f(e), U1(k, d))
27.25/8.85	   A^2 -> H(f(e), U1(d, k))
27.25/8.85	   A^2 -> H(U1(k, k), U1(c, b))
27.25/8.85	   A^2 -> H(U1(k, k), U1(d, b))
27.25/8.85	   A^2 -> H(U1(k, k), U1(b, c))
27.25/8.85	   A^2 -> H(U1(k, k), U1(b, d))
27.25/8.85	   A^2 -> H(U1(k, k), U1(c, c))
27.25/8.85	   A^2 -> H(U1(k, k), f(e))
27.25/8.85	   A^2 -> H(U1(k, k), f(k))
27.25/8.85	   A^2 -> H(U1(k, k), U1(d, d))
27.25/8.85	   A^2 -> H(f(k), U1(e, b))
27.25/8.85	   A^2 -> H(f(k), U1(k, b))
27.25/8.85	   A^2 -> H(f(k), U1(c, d))
27.25/8.85	   A^2 -> H(f(k), U1(d, c))
27.25/8.85	   A^2 -> H(f(k), U1(b, e))
27.25/8.85	   A^2 -> H(f(k), U1(b, k))
27.25/8.85	   A^2 -> H(f(k), U1(e, c))
27.25/8.85	   A^2 -> H(f(k), U1(k, c))
27.25/8.85	   A^2 -> H(f(k), U1(c, e))
27.25/8.85	   A^2 -> H(f(k), U1(c, k))
27.25/8.85	   A^2 -> H(f(k), U1(e, e))
27.25/8.85	   A^2 -> H(f(k), U1(k, d))
27.25/8.85	   A^2 -> H(f(k), U1(d, k))
27.25/8.85	   A^2 -> H(f(c), b)
27.25/8.85	   A^2 -> H(f(c), U1(e, d))
27.25/8.85	   A^2 -> H(f(c), U1(d, e))
27.25/8.85	   A^2 -> H(f(k), U1(k, k))
27.25/8.85	   A^2 -> H(U1(k, k), U1(b, b))
27.25/8.85	   A^2 -> H(U1(k, k), f(c))
27.25/8.85	   A^2 -> H(U1(k, k), f(d))
27.25/8.85	   A^2 -> H(U1(k, d), U1(c, b))
27.25/8.85	   A^2 -> H(U1(k, d), U1(d, b))
27.25/8.85	   A^2 -> H(U1(k, d), U1(b, c))
27.25/8.85	   A^2 -> H(U1(k, d), U1(b, d))
27.25/8.85	   A^2 -> H(U1(k, d), U1(c, c))
27.25/8.85	   A^2 -> H(U1(k, d), f(e))
27.25/8.85	   A^2 -> H(U1(k, d), f(k))
27.25/8.85	   A^2 -> H(U1(k, d), U1(d, d))
27.25/8.85	   A^2 -> H(U1(d, k), U1(c, b))
27.25/8.85	   A^2 -> H(U1(d, k), U1(d, b))
27.25/8.85	   A^2 -> H(U1(d, k), U1(b, c))
27.25/8.85	   A^2 -> H(U1(d, k), U1(b, d))
27.25/8.85	   A^2 -> H(U1(d, k), U1(c, c))
27.25/8.85	   A^2 -> H(U1(d, k), f(e))
27.25/8.85	   A^2 -> H(U1(d, k), f(k))
27.25/8.85	   A^2 -> H(U1(d, k), U1(d, d))
27.25/8.85	   A^2 -> H(U1(d, d), U1(e, b))
27.25/8.85	   A^2 -> H(U1(d, d), U1(k, b))
27.25/8.85	   A^2 -> H(U1(d, d), U1(c, d))
27.25/8.85	   A^2 -> H(U1(d, d), U1(d, c))
27.25/8.85	   A^2 -> H(U1(d, d), U1(b, e))
27.25/8.85	   A^2 -> H(U1(d, d), U1(b, k))
27.25/8.85	   A^2 -> H(U1(d, d), U1(e, c))
27.25/8.85	   A^2 -> H(U1(d, d), U1(k, c))
27.25/8.85	   A^2 -> H(U1(d, d), U1(c, e))
27.25/8.85	   A^2 -> H(U1(d, d), U1(c, k))
27.25/8.85	   A^2 -> H(U1(d, d), U1(e, e))
27.25/8.85	   A^2 -> H(U1(d, d), U1(k, k))
27.25/8.85	   A^2 -> H(f(d), b)
27.25/8.85	   A^2 -> H(f(d), U1(e, d))
27.25/8.85	   A^2 -> H(f(d), U1(d, e))
27.25/8.85	   A^2 -> H(f(d), c)
27.25/8.85	   A^2 -> H(f(d), U1(e, k))
27.25/8.85	   A^2 -> H(f(d), U1(k, e))
27.25/8.85	   A^2 -> H(f(d), e)
27.25/8.85	   A^2 -> H(f(a), d)
27.25/8.85	   A^2 -> H(U1(c, c), U1(e, c))
27.25/8.85	   A^2 -> H(f(c), c)
27.25/8.85	   A^2 -> H(f(c), U1(e, k))
27.25/8.85	   A^2 -> H(U1(c, c), U1(k, c))
27.25/8.85	   A^2 -> H(f(c), U1(k, e))
27.25/8.85	   A^2 -> H(f(c), U1(k, k))
27.25/8.85	   A^2 -> H(U1(c, c), U1(c, e))
27.25/8.85	   A^2 -> H(U1(c, c), U1(c, k))
27.25/8.85	   A^2 -> H(f(a), k)
27.25/8.85	   A^2 -> H(f(e), U1(e, e))
27.25/8.85	   A^2 -> H(f(c), e)
27.25/8.85	   A^2 -> H(U1(d, d), U1(k, d))
27.25/8.85	   A^2 -> H(f(d), U1(k, k))
27.25/8.85	   A^2 -> H(U1(d, d), U1(d, k))
27.25/8.85	   A^2 -> H(d, U1(b, b))
27.25/8.85	   A^2 -> H(d, f(c))
27.25/8.85	   A^2 -> H(d, f(d))
27.25/8.85	   A^2 -> H(a, U1(c, b))
27.25/8.85	   A^2 -> H(a, U1(d, b))
27.25/8.85	   A^2 -> H(a, U1(b, c))
27.25/8.85	   A^2 -> H(a, U1(b, d))
27.25/8.85	   A^2 -> H(a, U1(c, c))
27.25/8.85	   A^2 -> H(a, f(e))
27.25/8.85	   A^2 -> H(a, f(k))
27.25/8.85	   A^2 -> H(a, U1(d, d))
27.25/8.85	   A^2 -> H(U1(e, d), U1(c, b))
27.25/8.85	   A^2 -> H(U1(e, d), U1(d, b))
27.25/8.85	   A^2 -> H(U1(e, d), U1(b, c))
27.25/8.85	   A^2 -> H(U1(e, d), U1(b, d))
27.25/8.85	   A^2 -> H(U1(e, d), U1(c, c))
27.25/8.85	   A^2 -> H(U1(e, d), f(e))
27.25/8.85	   A^2 -> H(U1(e, d), f(k))
27.25/8.85	   A^2 -> H(U1(e, d), U1(d, d))
27.25/8.85	   A^2 -> H(U1(e, a), U1(e, b))
27.25/8.85	   A^2 -> H(U1(e, a), U1(k, b))
27.25/8.85	   A^2 -> H(U1(e, a), U1(c, d))
27.25/8.85	   A^2 -> H(U1(e, a), U1(d, c))
27.25/8.85	   A^2 -> H(U1(e, a), U1(b, e))
27.25/8.85	   A^2 -> H(U1(e, a), U1(b, k))
27.25/8.85	   A^2 -> H(U1(e, a), U1(e, c))
27.25/8.85	   A^2 -> H(U1(e, a), U1(k, c))
27.25/8.85	   A^2 -> H(U1(e, a), U1(c, e))
27.25/8.85	   A^2 -> H(U1(e, a), U1(c, k))
27.25/8.85	   A^2 -> H(U1(e, a), U1(e, e))
27.25/8.85	   A^2 -> H(U1(e, a), U1(k, k))
27.25/8.85	   A^2 -> H(U1(e, a), U1(k, d))
27.25/8.85	   A^2 -> H(U1(e, a), U1(d, k))
27.25/8.85	   A^2 -> H(U1(k, a), U1(e, b))
27.25/8.85	   A^2 -> H(U1(k, a), U1(k, b))
27.25/8.85	   A^2 -> H(U1(k, a), U1(c, d))
27.25/8.85	   A^2 -> H(U1(k, a), U1(d, c))
27.25/8.85	   A^2 -> H(U1(k, a), U1(b, e))
27.25/8.85	   A^2 -> H(U1(k, a), U1(b, k))
27.25/8.85	   A^2 -> H(U1(k, a), U1(e, c))
27.25/8.85	   A^2 -> H(U1(k, a), U1(k, c))
27.25/8.85	   A^2 -> H(U1(k, a), U1(c, e))
27.25/8.85	   A^2 -> H(U1(k, a), U1(c, k))
27.25/8.85	   A^2 -> H(U1(k, a), U1(e, e))
27.25/8.85	   A^2 -> H(U1(k, a), U1(k, k))
27.25/8.85	   A^2 -> H(U1(k, a), U1(k, d))
27.25/8.85	   A^2 -> H(U1(k, a), U1(d, k))
27.25/8.85	
27.25/8.85	The TRS R consists of the following rules:
27.25/8.85	
27.25/8.85	   f(x) -> U1(x, x)
27.25/8.85	   U1(e, x) -> x
27.25/8.85	   a -> c
27.25/8.85	   a -> d
27.25/8.85	   b -> c
27.25/8.85	   b -> d
27.25/8.85	   d -> k
27.25/8.85	   c -> e
27.25/8.85	   c -> k
27.25/8.85	
27.25/8.85	Q is empty.
27.25/8.85	We have to consider all minimal (P,Q,R)-chains.
27.25/8.85	----------------------------------------
27.25/8.85	
27.25/8.85	(587) TransformationProof (EQUIVALENT)
27.25/8.85	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
27.25/8.85	
27.25/8.85	   (A^2 -> H(U1(e, d), U1(c, b)),A^2 -> H(U1(e, d), U1(c, b)))
27.25/8.85	   (A^2 -> H(U1(k, d), U1(c, b)),A^2 -> H(U1(k, d), U1(c, b)))
27.25/8.85	   (A^2 -> H(U1(c, k), U1(c, b)),A^2 -> H(U1(c, k), U1(c, b)))
27.25/8.85	   (A^2 -> H(U1(c, d), U1(e, b)),A^2 -> H(U1(c, d), U1(e, b)))
27.25/8.85	   (A^2 -> H(U1(c, d), U1(k, b)),A^2 -> H(U1(c, d), U1(k, b)))
27.25/8.85	   (A^2 -> H(U1(c, d), U1(c, c)),A^2 -> H(U1(c, d), U1(c, c)))
27.25/8.85	   (A^2 -> H(U1(c, d), U1(c, d)),A^2 -> H(U1(c, d), U1(c, d)))
27.25/8.85	
27.25/8.85	
27.25/8.85	----------------------------------------
27.25/8.85	
27.25/8.85	(588)
27.25/8.85	Obligation:
27.25/8.85	Q DP problem:
27.25/8.85	The TRS P consists of the following rules:
27.25/8.85	
27.25/8.85	   H(x, x) -> G(x, x, f(k))
27.25/8.85	   G(d, x, x) -> A^2
27.25/8.85	   A^2 -> H(f(c), f(c))
27.25/8.85	   A^2 -> H(f(d), f(d))
27.25/8.85	   A^2 -> H(U1(c, c), U1(c, c))
27.25/8.85	   A^2 -> H(f(e), f(e))
27.25/8.85	   A^2 -> H(f(k), f(k))
27.25/8.85	   A^2 -> H(U1(d, d), U1(d, d))
27.25/8.85	   A^2 -> H(U1(c, d), U1(d, b))
27.25/8.85	   A^2 -> H(U1(c, d), U1(b, c))
27.25/8.85	   A^2 -> H(U1(c, d), U1(b, d))
27.25/8.85	   A^2 -> H(U1(c, d), U1(c, c))
27.25/8.85	   A^2 -> H(U1(c, d), f(e))
27.25/8.85	   A^2 -> H(U1(c, d), f(k))
27.25/8.85	   A^2 -> H(U1(c, d), U1(d, d))
27.25/8.85	   A^2 -> H(U1(c, a), U1(e, b))
27.25/8.85	   A^2 -> H(U1(c, a), U1(k, b))
27.25/8.85	   A^2 -> H(U1(c, a), U1(c, d))
27.25/8.85	   A^2 -> H(U1(c, a), U1(d, c))
27.25/8.85	   A^2 -> H(U1(c, a), U1(b, e))
27.25/8.85	   A^2 -> H(U1(c, a), U1(b, k))
27.25/8.85	   A^2 -> H(U1(c, a), U1(e, c))
27.25/8.85	   A^2 -> H(U1(c, a), U1(k, c))
27.25/8.85	   A^2 -> H(U1(c, a), U1(c, e))
27.25/8.85	   A^2 -> H(U1(c, a), U1(c, k))
27.25/8.85	   A^2 -> H(U1(c, a), U1(e, e))
27.25/8.85	   A^2 -> H(U1(c, a), U1(k, k))
27.25/8.85	   A^2 -> H(U1(c, a), U1(k, d))
27.25/8.85	   A^2 -> H(U1(c, a), U1(d, k))
27.25/8.85	   A^2 -> H(U1(d, e), U1(b, b))
27.25/8.85	   A^2 -> H(U1(d, e), f(c))
27.25/8.85	   A^2 -> H(U1(d, e), f(d))
27.25/8.85	   A^2 -> H(U1(d, c), U1(c, b))
27.25/8.85	   A^2 -> H(U1(d, c), U1(d, b))
27.25/8.85	   A^2 -> H(U1(d, c), U1(b, c))
27.25/8.85	   A^2 -> H(U1(d, c), U1(b, d))
27.25/8.85	   A^2 -> H(U1(d, c), U1(c, c))
27.25/8.85	   A^2 -> H(U1(d, c), f(e))
27.25/8.85	   A^2 -> H(U1(d, c), f(k))
27.25/8.85	   A^2 -> H(U1(d, c), U1(d, d))
27.25/8.85	   A^2 -> H(U1(d, a), U1(e, b))
27.25/8.85	   A^2 -> H(U1(d, a), U1(k, b))
27.25/8.85	   A^2 -> H(U1(d, a), U1(c, d))
27.25/8.85	   A^2 -> H(U1(d, a), U1(d, c))
27.25/8.85	   A^2 -> H(U1(d, a), U1(b, e))
27.25/8.85	   A^2 -> H(U1(d, a), U1(b, k))
27.25/8.85	   A^2 -> H(U1(d, a), U1(e, c))
27.25/8.85	   A^2 -> H(U1(d, a), U1(k, c))
27.25/8.85	   A^2 -> H(U1(d, a), U1(c, e))
27.25/8.85	   A^2 -> H(U1(d, a), U1(c, k))
27.25/8.85	   A^2 -> H(U1(d, a), U1(e, e))
27.25/8.85	   A^2 -> H(U1(d, a), U1(k, k))
27.25/8.85	   A^2 -> H(U1(d, a), U1(k, d))
27.25/8.85	   A^2 -> H(U1(d, a), U1(d, k))
27.25/8.85	   A^2 -> H(U1(a, e), U1(c, b))
27.25/8.85	   A^2 -> H(U1(a, e), U1(d, b))
27.25/8.85	   A^2 -> H(U1(a, e), U1(b, c))
27.25/8.85	   A^2 -> H(U1(a, e), U1(b, d))
27.25/8.85	   A^2 -> H(U1(a, e), U1(c, c))
27.25/8.85	   A^2 -> H(U1(a, e), f(e))
27.25/8.85	   A^2 -> H(U1(a, e), f(k))
27.25/8.85	   A^2 -> H(U1(a, e), U1(d, d))
27.25/8.85	   A^2 -> H(U1(a, k), U1(c, b))
27.25/8.85	   A^2 -> H(U1(a, k), U1(d, b))
27.25/8.85	   A^2 -> H(U1(a, k), U1(b, c))
27.25/8.85	   A^2 -> H(U1(a, k), U1(b, d))
27.25/8.85	   A^2 -> H(U1(a, k), U1(c, c))
27.25/8.85	   A^2 -> H(U1(a, k), f(e))
27.25/8.85	   A^2 -> H(U1(a, k), f(k))
27.25/8.85	   A^2 -> H(U1(a, k), U1(d, d))
27.25/8.85	   A^2 -> H(U1(a, c), U1(e, b))
27.25/8.85	   A^2 -> H(U1(a, c), U1(k, b))
27.25/8.85	   A^2 -> H(U1(a, c), U1(c, d))
27.25/8.85	   A^2 -> H(U1(a, c), U1(d, c))
27.25/8.85	   A^2 -> H(U1(a, c), U1(b, e))
27.25/8.85	   A^2 -> H(U1(a, c), U1(b, k))
27.25/8.85	   A^2 -> H(U1(a, c), U1(e, c))
27.25/8.85	   A^2 -> H(U1(a, c), U1(k, c))
27.25/8.85	   A^2 -> H(U1(a, c), U1(c, e))
27.25/8.85	   A^2 -> H(U1(a, c), U1(c, k))
27.25/8.85	   A^2 -> H(U1(a, c), U1(e, e))
27.25/8.85	   A^2 -> H(U1(a, c), U1(k, k))
27.25/8.85	   A^2 -> H(U1(a, c), U1(k, d))
27.25/8.85	   A^2 -> H(U1(a, c), U1(d, k))
27.25/8.85	   A^2 -> H(U1(a, d), U1(e, b))
27.25/8.85	   A^2 -> H(U1(a, d), U1(k, b))
27.25/8.85	   A^2 -> H(U1(a, d), U1(c, d))
27.25/8.85	   A^2 -> H(U1(a, d), U1(d, c))
27.25/8.85	   A^2 -> H(U1(a, d), U1(b, e))
27.25/8.85	   A^2 -> H(U1(a, d), U1(b, k))
27.25/8.85	   A^2 -> H(U1(a, d), U1(e, c))
27.25/8.85	   A^2 -> H(U1(a, d), U1(k, c))
27.25/8.85	   A^2 -> H(U1(a, d), U1(c, e))
27.25/8.85	   A^2 -> H(U1(a, d), U1(c, k))
27.25/8.85	   A^2 -> H(U1(a, d), U1(e, e))
27.25/8.85	   A^2 -> H(U1(a, d), U1(k, k))
27.25/8.85	   A^2 -> H(U1(a, d), U1(k, d))
27.25/8.85	   A^2 -> H(U1(a, d), U1(d, k))
27.25/8.85	   A^2 -> H(U1(a, a), b)
27.25/8.85	   A^2 -> H(U1(a, a), U1(e, d))
27.25/8.85	   A^2 -> H(U1(a, a), U1(d, e))
27.25/8.85	   A^2 -> H(U1(a, a), c)
27.25/8.85	   A^2 -> H(U1(a, a), U1(e, k))
27.25/8.85	   A^2 -> H(U1(a, a), U1(k, e))
27.25/8.85	   A^2 -> H(U1(a, a), e)
27.25/8.85	   A^2 -> H(U1(a, a), U1(k, k))
27.25/8.85	   A^2 -> H(k, f(b))
27.25/8.85	   A^2 -> H(c, U1(b, b))
27.25/8.85	   A^2 -> H(c, f(c))
27.25/8.85	   A^2 -> H(c, f(d))
27.25/8.85	   A^2 -> H(U1(e, k), U1(b, b))
27.25/8.85	   A^2 -> H(U1(e, k), f(c))
27.25/8.85	   A^2 -> H(U1(e, k), f(d))
27.25/8.85	   A^2 -> H(U1(e, c), U1(c, b))
27.25/8.85	   A^2 -> H(U1(e, c), U1(d, b))
27.25/8.85	   A^2 -> H(U1(e, c), U1(b, c))
27.25/8.85	   A^2 -> H(U1(e, c), U1(b, d))
27.25/8.85	   A^2 -> H(U1(e, c), U1(c, c))
27.25/8.85	   A^2 -> H(U1(e, c), f(e))
27.25/8.85	   A^2 -> H(U1(e, c), f(k))
27.25/8.85	   A^2 -> H(U1(e, c), U1(d, d))
27.25/8.85	   A^2 -> H(U1(k, e), U1(b, b))
27.25/8.85	   A^2 -> H(U1(k, e), f(c))
27.25/8.85	   A^2 -> H(U1(k, e), f(d))
27.25/8.85	   A^2 -> H(U1(k, c), U1(c, b))
27.25/8.85	   A^2 -> H(U1(k, c), U1(d, b))
27.25/8.85	   A^2 -> H(U1(k, c), U1(b, c))
27.25/8.85	   A^2 -> H(U1(k, c), U1(b, d))
27.25/8.85	   A^2 -> H(U1(k, c), U1(c, c))
27.25/8.85	   A^2 -> H(U1(k, c), f(e))
27.25/8.85	   A^2 -> H(U1(k, c), f(k))
27.25/8.85	   A^2 -> H(U1(k, c), U1(d, d))
27.25/8.85	   A^2 -> H(U1(c, e), U1(c, b))
27.25/8.85	   A^2 -> H(U1(c, e), U1(d, b))
27.25/8.85	   A^2 -> H(U1(c, e), U1(b, c))
27.25/8.85	   A^2 -> H(U1(c, e), U1(b, d))
27.25/8.85	   A^2 -> H(U1(c, e), U1(c, c))
27.25/8.85	   A^2 -> H(U1(c, e), f(e))
27.25/8.85	   A^2 -> H(U1(c, e), f(k))
27.25/8.85	   A^2 -> H(U1(c, e), U1(d, d))
27.25/8.85	   A^2 -> H(U1(c, k), U1(c, b))
27.25/8.85	   A^2 -> H(U1(c, k), U1(d, b))
27.25/8.85	   A^2 -> H(U1(c, k), U1(b, c))
27.25/8.85	   A^2 -> H(U1(c, k), U1(b, d))
27.25/8.85	   A^2 -> H(U1(c, k), U1(c, c))
27.25/8.85	   A^2 -> H(U1(c, k), f(e))
27.25/8.85	   A^2 -> H(U1(c, k), f(k))
27.25/8.85	   A^2 -> H(U1(c, k), U1(d, d))
27.25/8.85	   A^2 -> H(U1(c, c), U1(e, b))
27.25/8.85	   A^2 -> H(U1(c, c), U1(k, b))
27.25/8.85	   A^2 -> H(U1(c, c), U1(c, d))
27.25/8.85	   A^2 -> H(U1(c, c), U1(d, c))
27.25/8.85	   A^2 -> H(U1(c, c), U1(b, e))
27.25/8.85	   A^2 -> H(U1(c, c), U1(b, k))
27.25/8.85	   A^2 -> H(U1(c, c), U1(e, e))
27.25/8.85	   A^2 -> H(U1(c, c), U1(k, k))
27.25/8.85	   A^2 -> H(U1(c, c), U1(k, d))
27.25/8.85	   A^2 -> H(U1(c, c), U1(d, k))
27.25/8.85	   A^2 -> H(e, U1(b, b))
27.25/8.86	   A^2 -> H(e, f(c))
27.25/8.86	   A^2 -> H(e, f(d))
27.25/8.86	   A^2 -> H(U1(e, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, e), U1(c, c))
27.25/8.86	   A^2 -> H(U1(e, e), f(e))
27.25/8.86	   A^2 -> H(U1(e, e), f(k))
27.25/8.86	   A^2 -> H(U1(e, e), U1(d, d))
27.25/8.86	   A^2 -> H(f(e), U1(e, b))
27.25/8.86	   A^2 -> H(f(e), U1(k, b))
27.25/8.86	   A^2 -> H(f(e), U1(c, d))
27.25/8.86	   A^2 -> H(f(e), U1(d, c))
27.25/8.86	   A^2 -> H(f(e), U1(b, e))
27.25/8.86	   A^2 -> H(f(e), U1(b, k))
27.25/8.86	   A^2 -> H(f(e), U1(e, c))
27.25/8.86	   A^2 -> H(f(e), U1(k, c))
27.25/8.86	   A^2 -> H(f(e), U1(c, e))
27.25/8.86	   A^2 -> H(f(e), U1(c, k))
27.25/8.86	   A^2 -> H(f(e), U1(k, k))
27.25/8.86	   A^2 -> H(f(e), U1(k, d))
27.25/8.86	   A^2 -> H(f(e), U1(d, k))
27.25/8.86	   A^2 -> H(U1(k, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(k, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(k, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(k, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(k, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(k, k), f(e))
27.25/8.86	   A^2 -> H(U1(k, k), f(k))
27.25/8.86	   A^2 -> H(U1(k, k), U1(d, d))
27.25/8.86	   A^2 -> H(f(k), U1(e, b))
27.25/8.86	   A^2 -> H(f(k), U1(k, b))
27.25/8.86	   A^2 -> H(f(k), U1(c, d))
27.25/8.86	   A^2 -> H(f(k), U1(d, c))
27.25/8.86	   A^2 -> H(f(k), U1(b, e))
27.25/8.86	   A^2 -> H(f(k), U1(b, k))
27.25/8.86	   A^2 -> H(f(k), U1(e, c))
27.25/8.86	   A^2 -> H(f(k), U1(k, c))
27.25/8.86	   A^2 -> H(f(k), U1(c, e))
27.25/8.86	   A^2 -> H(f(k), U1(c, k))
27.25/8.86	   A^2 -> H(f(k), U1(e, e))
27.25/8.86	   A^2 -> H(f(k), U1(k, d))
27.25/8.86	   A^2 -> H(f(k), U1(d, k))
27.25/8.86	   A^2 -> H(f(c), b)
27.25/8.86	   A^2 -> H(f(c), U1(e, d))
27.25/8.86	   A^2 -> H(f(c), U1(d, e))
27.25/8.86	   A^2 -> H(f(k), U1(k, k))
27.25/8.86	   A^2 -> H(U1(k, k), U1(b, b))
27.25/8.86	   A^2 -> H(U1(k, k), f(c))
27.25/8.86	   A^2 -> H(U1(k, k), f(d))
27.25/8.86	   A^2 -> H(U1(k, d), U1(c, b))
27.25/8.86	   A^2 -> H(U1(k, d), U1(d, b))
27.25/8.86	   A^2 -> H(U1(k, d), U1(b, c))
27.25/8.86	   A^2 -> H(U1(k, d), U1(b, d))
27.25/8.86	   A^2 -> H(U1(k, d), U1(c, c))
27.25/8.86	   A^2 -> H(U1(k, d), f(e))
27.25/8.86	   A^2 -> H(U1(k, d), f(k))
27.25/8.86	   A^2 -> H(U1(k, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(d, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(d, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(d, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(d, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(d, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(d, k), f(e))
27.25/8.86	   A^2 -> H(U1(d, k), f(k))
27.25/8.86	   A^2 -> H(U1(d, k), U1(d, d))
27.25/8.86	   A^2 -> H(U1(d, d), U1(e, b))
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, b))
27.25/8.86	   A^2 -> H(U1(d, d), U1(c, d))
27.25/8.86	   A^2 -> H(U1(d, d), U1(d, c))
27.25/8.86	   A^2 -> H(U1(d, d), U1(b, e))
27.25/8.86	   A^2 -> H(U1(d, d), U1(b, k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(e, c))
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, c))
27.25/8.86	   A^2 -> H(U1(d, d), U1(c, e))
27.25/8.86	   A^2 -> H(U1(d, d), U1(c, k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(e, e))
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, k))
27.25/8.86	   A^2 -> H(f(d), b)
27.25/8.86	   A^2 -> H(f(d), U1(e, d))
27.25/8.86	   A^2 -> H(f(d), U1(d, e))
27.25/8.86	   A^2 -> H(f(d), c)
27.25/8.86	   A^2 -> H(f(d), U1(e, k))
27.25/8.86	   A^2 -> H(f(d), U1(k, e))
27.25/8.86	   A^2 -> H(f(d), e)
27.25/8.86	   A^2 -> H(f(a), d)
27.25/8.86	   A^2 -> H(U1(c, c), U1(e, c))
27.25/8.86	   A^2 -> H(f(c), c)
27.25/8.86	   A^2 -> H(f(c), U1(e, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, c))
27.25/8.86	   A^2 -> H(f(c), U1(k, e))
27.25/8.86	   A^2 -> H(f(c), U1(k, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, e))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, k))
27.25/8.86	   A^2 -> H(f(a), k)
27.25/8.86	   A^2 -> H(f(e), U1(e, e))
27.25/8.86	   A^2 -> H(f(c), e)
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, d))
27.25/8.86	   A^2 -> H(f(d), U1(k, k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(d, k))
27.25/8.86	   A^2 -> H(d, U1(b, b))
27.25/8.86	   A^2 -> H(d, f(c))
27.25/8.86	   A^2 -> H(d, f(d))
27.25/8.86	   A^2 -> H(a, U1(c, b))
27.25/8.86	   A^2 -> H(a, U1(d, b))
27.25/8.86	   A^2 -> H(a, U1(b, c))
27.25/8.86	   A^2 -> H(a, U1(b, d))
27.25/8.86	   A^2 -> H(a, U1(c, c))
27.25/8.86	   A^2 -> H(a, f(e))
27.25/8.86	   A^2 -> H(a, f(k))
27.25/8.86	   A^2 -> H(a, U1(d, d))
27.25/8.86	   A^2 -> H(U1(e, d), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, d), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, d), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, d), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, d), U1(c, c))
27.25/8.86	   A^2 -> H(U1(e, d), f(e))
27.25/8.86	   A^2 -> H(U1(e, d), f(k))
27.25/8.86	   A^2 -> H(U1(e, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(e, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(e, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(e, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(e, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(e, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(e, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(e, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(e, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(e, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(e, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(k, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(k, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(k, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(k, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(k, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(k, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(k, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(c, d), U1(e, b))
27.25/8.86	   A^2 -> H(U1(c, d), U1(k, b))
27.25/8.86	   A^2 -> H(U1(c, d), U1(c, d))
27.25/8.86	
27.25/8.86	The TRS R consists of the following rules:
27.25/8.86	
27.25/8.86	   f(x) -> U1(x, x)
27.25/8.86	   U1(e, x) -> x
27.25/8.86	   a -> c
27.25/8.86	   a -> d
27.25/8.86	   b -> c
27.25/8.86	   b -> d
27.25/8.86	   d -> k
27.25/8.86	   c -> e
27.25/8.86	   c -> k
27.25/8.86	
27.25/8.86	Q is empty.
27.25/8.86	We have to consider all minimal (P,Q,R)-chains.
27.25/8.86	----------------------------------------
27.25/8.86	
27.25/8.86	(589) TransformationProof (EQUIVALENT)
27.25/8.86	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
27.25/8.86	
27.25/8.86	   (A^2 -> H(U1(e, d), U1(d, b)),A^2 -> H(U1(e, d), U1(d, b)))
27.25/8.86	   (A^2 -> H(U1(k, d), U1(d, b)),A^2 -> H(U1(k, d), U1(d, b)))
27.25/8.86	   (A^2 -> H(U1(c, k), U1(d, b)),A^2 -> H(U1(c, k), U1(d, b)))
27.25/8.86	   (A^2 -> H(U1(c, d), U1(k, b)),A^2 -> H(U1(c, d), U1(k, b)))
27.25/8.86	   (A^2 -> H(U1(c, d), U1(d, c)),A^2 -> H(U1(c, d), U1(d, c)))
27.25/8.86	   (A^2 -> H(U1(c, d), U1(d, d)),A^2 -> H(U1(c, d), U1(d, d)))
27.25/8.86	
27.25/8.86	
27.25/8.86	----------------------------------------
27.25/8.86	
27.25/8.86	(590)
27.25/8.86	Obligation:
27.25/8.86	Q DP problem:
27.25/8.86	The TRS P consists of the following rules:
27.25/8.86	
27.25/8.86	   H(x, x) -> G(x, x, f(k))
27.25/8.86	   G(d, x, x) -> A^2
27.25/8.86	   A^2 -> H(f(c), f(c))
27.25/8.86	   A^2 -> H(f(d), f(d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, c))
27.25/8.86	   A^2 -> H(f(e), f(e))
27.25/8.86	   A^2 -> H(f(k), f(k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, d), U1(b, c))
27.25/8.86	   A^2 -> H(U1(c, d), U1(b, d))
27.25/8.86	   A^2 -> H(U1(c, d), U1(c, c))
27.25/8.86	   A^2 -> H(U1(c, d), f(e))
27.25/8.86	   A^2 -> H(U1(c, d), f(k))
27.25/8.86	   A^2 -> H(U1(c, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(c, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(c, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(c, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(c, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(c, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(c, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(c, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(c, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(c, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(d, e), U1(b, b))
27.25/8.86	   A^2 -> H(U1(d, e), f(c))
27.25/8.86	   A^2 -> H(U1(d, e), f(d))
27.25/8.86	   A^2 -> H(U1(d, c), U1(c, b))
27.25/8.86	   A^2 -> H(U1(d, c), U1(d, b))
27.25/8.86	   A^2 -> H(U1(d, c), U1(b, c))
27.25/8.86	   A^2 -> H(U1(d, c), U1(b, d))
27.25/8.86	   A^2 -> H(U1(d, c), U1(c, c))
27.25/8.86	   A^2 -> H(U1(d, c), f(e))
27.25/8.86	   A^2 -> H(U1(d, c), f(k))
27.25/8.86	   A^2 -> H(U1(d, c), U1(d, d))
27.25/8.86	   A^2 -> H(U1(d, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(d, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(d, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(d, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(d, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(d, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(d, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(d, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(d, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(d, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(a, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(a, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(a, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(a, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(a, e), U1(c, c))
27.25/8.86	   A^2 -> H(U1(a, e), f(e))
27.25/8.86	   A^2 -> H(U1(a, e), f(k))
27.25/8.86	   A^2 -> H(U1(a, e), U1(d, d))
27.25/8.86	   A^2 -> H(U1(a, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(a, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(a, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(a, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(a, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(a, k), f(e))
27.25/8.86	   A^2 -> H(U1(a, k), f(k))
27.25/8.86	   A^2 -> H(U1(a, k), U1(d, d))
27.25/8.86	   A^2 -> H(U1(a, c), U1(e, b))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, b))
27.25/8.86	   A^2 -> H(U1(a, c), U1(c, d))
27.25/8.86	   A^2 -> H(U1(a, c), U1(d, c))
27.25/8.86	   A^2 -> H(U1(a, c), U1(b, e))
27.25/8.86	   A^2 -> H(U1(a, c), U1(b, k))
27.25/8.86	   A^2 -> H(U1(a, c), U1(e, c))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, c))
27.25/8.86	   A^2 -> H(U1(a, c), U1(c, e))
27.25/8.86	   A^2 -> H(U1(a, c), U1(c, k))
27.25/8.86	   A^2 -> H(U1(a, c), U1(e, e))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, k))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, d))
27.25/8.86	   A^2 -> H(U1(a, c), U1(d, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(e, b))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, b))
27.25/8.86	   A^2 -> H(U1(a, d), U1(c, d))
27.25/8.86	   A^2 -> H(U1(a, d), U1(d, c))
27.25/8.86	   A^2 -> H(U1(a, d), U1(b, e))
27.25/8.86	   A^2 -> H(U1(a, d), U1(b, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(e, c))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, c))
27.25/8.86	   A^2 -> H(U1(a, d), U1(c, e))
27.25/8.86	   A^2 -> H(U1(a, d), U1(c, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(e, e))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, d))
27.25/8.86	   A^2 -> H(U1(a, d), U1(d, k))
27.25/8.86	   A^2 -> H(U1(a, a), b)
27.25/8.86	   A^2 -> H(U1(a, a), U1(e, d))
27.25/8.86	   A^2 -> H(U1(a, a), U1(d, e))
27.25/8.86	   A^2 -> H(U1(a, a), c)
27.25/8.86	   A^2 -> H(U1(a, a), U1(e, k))
27.25/8.86	   A^2 -> H(U1(a, a), U1(k, e))
27.25/8.86	   A^2 -> H(U1(a, a), e)
27.25/8.86	   A^2 -> H(U1(a, a), U1(k, k))
27.25/8.86	   A^2 -> H(k, f(b))
27.25/8.86	   A^2 -> H(c, U1(b, b))
27.25/8.86	   A^2 -> H(c, f(c))
27.25/8.86	   A^2 -> H(c, f(d))
27.25/8.86	   A^2 -> H(U1(e, k), U1(b, b))
27.25/8.86	   A^2 -> H(U1(e, k), f(c))
27.25/8.86	   A^2 -> H(U1(e, k), f(d))
27.25/8.86	   A^2 -> H(U1(e, c), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, c), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, c), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, c), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, c), U1(c, c))
27.25/8.86	   A^2 -> H(U1(e, c), f(e))
27.25/8.86	   A^2 -> H(U1(e, c), f(k))
27.25/8.86	   A^2 -> H(U1(e, c), U1(d, d))
27.25/8.86	   A^2 -> H(U1(k, e), U1(b, b))
27.25/8.86	   A^2 -> H(U1(k, e), f(c))
27.25/8.86	   A^2 -> H(U1(k, e), f(d))
27.25/8.86	   A^2 -> H(U1(k, c), U1(c, b))
27.25/8.86	   A^2 -> H(U1(k, c), U1(d, b))
27.25/8.86	   A^2 -> H(U1(k, c), U1(b, c))
27.25/8.86	   A^2 -> H(U1(k, c), U1(b, d))
27.25/8.86	   A^2 -> H(U1(k, c), U1(c, c))
27.25/8.86	   A^2 -> H(U1(k, c), f(e))
27.25/8.86	   A^2 -> H(U1(k, c), f(k))
27.25/8.86	   A^2 -> H(U1(k, c), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(c, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(c, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(c, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(c, e), U1(c, c))
27.25/8.86	   A^2 -> H(U1(c, e), f(e))
27.25/8.86	   A^2 -> H(U1(c, e), f(k))
27.25/8.86	   A^2 -> H(U1(c, e), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(c, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(c, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(c, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(c, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(c, k), f(e))
27.25/8.86	   A^2 -> H(U1(c, k), f(k))
27.25/8.86	   A^2 -> H(U1(c, k), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(e, b))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, b))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(d, c))
27.25/8.86	   A^2 -> H(U1(c, c), U1(b, e))
27.25/8.86	   A^2 -> H(U1(c, c), U1(b, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(e, e))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(d, k))
27.25/8.86	   A^2 -> H(e, U1(b, b))
27.25/8.86	   A^2 -> H(e, f(c))
27.25/8.86	   A^2 -> H(e, f(d))
27.25/8.86	   A^2 -> H(U1(e, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, e), U1(c, c))
27.25/8.86	   A^2 -> H(U1(e, e), f(e))
27.25/8.86	   A^2 -> H(U1(e, e), f(k))
27.25/8.86	   A^2 -> H(U1(e, e), U1(d, d))
27.25/8.86	   A^2 -> H(f(e), U1(e, b))
27.25/8.86	   A^2 -> H(f(e), U1(k, b))
27.25/8.86	   A^2 -> H(f(e), U1(c, d))
27.25/8.86	   A^2 -> H(f(e), U1(d, c))
27.25/8.86	   A^2 -> H(f(e), U1(b, e))
27.25/8.86	   A^2 -> H(f(e), U1(b, k))
27.25/8.86	   A^2 -> H(f(e), U1(e, c))
27.25/8.86	   A^2 -> H(f(e), U1(k, c))
27.25/8.86	   A^2 -> H(f(e), U1(c, e))
27.25/8.86	   A^2 -> H(f(e), U1(c, k))
27.25/8.86	   A^2 -> H(f(e), U1(k, k))
27.25/8.86	   A^2 -> H(f(e), U1(k, d))
27.25/8.86	   A^2 -> H(f(e), U1(d, k))
27.25/8.86	   A^2 -> H(U1(k, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(k, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(k, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(k, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(k, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(k, k), f(e))
27.25/8.86	   A^2 -> H(U1(k, k), f(k))
27.25/8.86	   A^2 -> H(U1(k, k), U1(d, d))
27.25/8.86	   A^2 -> H(f(k), U1(e, b))
27.25/8.86	   A^2 -> H(f(k), U1(k, b))
27.25/8.86	   A^2 -> H(f(k), U1(c, d))
27.25/8.86	   A^2 -> H(f(k), U1(d, c))
27.25/8.86	   A^2 -> H(f(k), U1(b, e))
27.25/8.86	   A^2 -> H(f(k), U1(b, k))
27.25/8.86	   A^2 -> H(f(k), U1(e, c))
27.25/8.86	   A^2 -> H(f(k), U1(k, c))
27.25/8.86	   A^2 -> H(f(k), U1(c, e))
27.25/8.86	   A^2 -> H(f(k), U1(c, k))
27.25/8.86	   A^2 -> H(f(k), U1(e, e))
27.25/8.86	   A^2 -> H(f(k), U1(k, d))
27.25/8.86	   A^2 -> H(f(k), U1(d, k))
27.25/8.86	   A^2 -> H(f(c), b)
27.25/8.86	   A^2 -> H(f(c), U1(e, d))
27.25/8.86	   A^2 -> H(f(c), U1(d, e))
27.25/8.86	   A^2 -> H(f(k), U1(k, k))
27.25/8.86	   A^2 -> H(U1(k, k), U1(b, b))
27.25/8.86	   A^2 -> H(U1(k, k), f(c))
27.25/8.86	   A^2 -> H(U1(k, k), f(d))
27.25/8.86	   A^2 -> H(U1(k, d), U1(c, b))
27.25/8.86	   A^2 -> H(U1(k, d), U1(d, b))
27.25/8.86	   A^2 -> H(U1(k, d), U1(b, c))
27.25/8.86	   A^2 -> H(U1(k, d), U1(b, d))
27.25/8.86	   A^2 -> H(U1(k, d), U1(c, c))
27.25/8.86	   A^2 -> H(U1(k, d), f(e))
27.25/8.86	   A^2 -> H(U1(k, d), f(k))
27.25/8.86	   A^2 -> H(U1(k, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(d, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(d, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(d, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(d, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(d, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(d, k), f(e))
27.25/8.86	   A^2 -> H(U1(d, k), f(k))
27.25/8.86	   A^2 -> H(U1(d, k), U1(d, d))
27.25/8.86	   A^2 -> H(U1(d, d), U1(e, b))
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, b))
27.25/8.86	   A^2 -> H(U1(d, d), U1(c, d))
27.25/8.86	   A^2 -> H(U1(d, d), U1(d, c))
27.25/8.86	   A^2 -> H(U1(d, d), U1(b, e))
27.25/8.86	   A^2 -> H(U1(d, d), U1(b, k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(e, c))
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, c))
27.25/8.86	   A^2 -> H(U1(d, d), U1(c, e))
27.25/8.86	   A^2 -> H(U1(d, d), U1(c, k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(e, e))
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, k))
27.25/8.86	   A^2 -> H(f(d), b)
27.25/8.86	   A^2 -> H(f(d), U1(e, d))
27.25/8.86	   A^2 -> H(f(d), U1(d, e))
27.25/8.86	   A^2 -> H(f(d), c)
27.25/8.86	   A^2 -> H(f(d), U1(e, k))
27.25/8.86	   A^2 -> H(f(d), U1(k, e))
27.25/8.86	   A^2 -> H(f(d), e)
27.25/8.86	   A^2 -> H(f(a), d)
27.25/8.86	   A^2 -> H(U1(c, c), U1(e, c))
27.25/8.86	   A^2 -> H(f(c), c)
27.25/8.86	   A^2 -> H(f(c), U1(e, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, c))
27.25/8.86	   A^2 -> H(f(c), U1(k, e))
27.25/8.86	   A^2 -> H(f(c), U1(k, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, e))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, k))
27.25/8.86	   A^2 -> H(f(a), k)
27.25/8.86	   A^2 -> H(f(e), U1(e, e))
27.25/8.86	   A^2 -> H(f(c), e)
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, d))
27.25/8.86	   A^2 -> H(f(d), U1(k, k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(d, k))
27.25/8.86	   A^2 -> H(d, U1(b, b))
27.25/8.86	   A^2 -> H(d, f(c))
27.25/8.86	   A^2 -> H(d, f(d))
27.25/8.86	   A^2 -> H(a, U1(c, b))
27.25/8.86	   A^2 -> H(a, U1(d, b))
27.25/8.86	   A^2 -> H(a, U1(b, c))
27.25/8.86	   A^2 -> H(a, U1(b, d))
27.25/8.86	   A^2 -> H(a, U1(c, c))
27.25/8.86	   A^2 -> H(a, f(e))
27.25/8.86	   A^2 -> H(a, f(k))
27.25/8.86	   A^2 -> H(a, U1(d, d))
27.25/8.86	   A^2 -> H(U1(e, d), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, d), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, d), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, d), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, d), U1(c, c))
27.25/8.86	   A^2 -> H(U1(e, d), f(e))
27.25/8.86	   A^2 -> H(U1(e, d), f(k))
27.25/8.86	   A^2 -> H(U1(e, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(e, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(e, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(e, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(e, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(e, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(e, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(e, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(e, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(e, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(e, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(k, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(k, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(k, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(k, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(k, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(k, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(k, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(c, d), U1(e, b))
27.25/8.86	   A^2 -> H(U1(c, d), U1(k, b))
27.25/8.86	   A^2 -> H(U1(c, d), U1(c, d))
27.25/8.86	   A^2 -> H(U1(c, d), U1(d, c))
27.25/8.86	
27.25/8.86	The TRS R consists of the following rules:
27.25/8.86	
27.25/8.86	   f(x) -> U1(x, x)
27.25/8.86	   U1(e, x) -> x
27.25/8.86	   a -> c
27.25/8.86	   a -> d
27.25/8.86	   b -> c
27.25/8.86	   b -> d
27.25/8.86	   d -> k
27.25/8.86	   c -> e
27.25/8.86	   c -> k
27.25/8.86	
27.25/8.86	Q is empty.
27.25/8.86	We have to consider all minimal (P,Q,R)-chains.
27.25/8.86	----------------------------------------
27.25/8.86	
27.25/8.86	(591) TransformationProof (EQUIVALENT)
27.25/8.86	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
27.25/8.86	
27.25/8.86	   (A^2 -> H(U1(e, d), U1(b, c)),A^2 -> H(U1(e, d), U1(b, c)))
27.25/8.86	   (A^2 -> H(U1(k, d), U1(b, c)),A^2 -> H(U1(k, d), U1(b, c)))
27.25/8.86	   (A^2 -> H(U1(c, k), U1(b, c)),A^2 -> H(U1(c, k), U1(b, c)))
27.25/8.86	   (A^2 -> H(U1(c, d), U1(c, c)),A^2 -> H(U1(c, d), U1(c, c)))
27.25/8.86	   (A^2 -> H(U1(c, d), U1(d, c)),A^2 -> H(U1(c, d), U1(d, c)))
27.25/8.86	   (A^2 -> H(U1(c, d), U1(b, e)),A^2 -> H(U1(c, d), U1(b, e)))
27.25/8.86	   (A^2 -> H(U1(c, d), U1(b, k)),A^2 -> H(U1(c, d), U1(b, k)))
27.25/8.86	
27.25/8.86	
27.25/8.86	----------------------------------------
27.25/8.86	
27.25/8.86	(592)
27.25/8.86	Obligation:
27.25/8.86	Q DP problem:
27.25/8.86	The TRS P consists of the following rules:
27.25/8.86	
27.25/8.86	   H(x, x) -> G(x, x, f(k))
27.25/8.86	   G(d, x, x) -> A^2
27.25/8.86	   A^2 -> H(f(c), f(c))
27.25/8.86	   A^2 -> H(f(d), f(d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, c))
27.25/8.86	   A^2 -> H(f(e), f(e))
27.25/8.86	   A^2 -> H(f(k), f(k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, d), U1(b, d))
27.25/8.86	   A^2 -> H(U1(c, d), U1(c, c))
27.25/8.86	   A^2 -> H(U1(c, d), f(e))
27.25/8.86	   A^2 -> H(U1(c, d), f(k))
27.25/8.86	   A^2 -> H(U1(c, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(c, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(c, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(c, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(c, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(c, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(c, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(c, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(c, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(c, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(d, e), U1(b, b))
27.25/8.86	   A^2 -> H(U1(d, e), f(c))
27.25/8.86	   A^2 -> H(U1(d, e), f(d))
27.25/8.86	   A^2 -> H(U1(d, c), U1(c, b))
27.25/8.86	   A^2 -> H(U1(d, c), U1(d, b))
27.25/8.86	   A^2 -> H(U1(d, c), U1(b, c))
27.25/8.86	   A^2 -> H(U1(d, c), U1(b, d))
27.25/8.86	   A^2 -> H(U1(d, c), U1(c, c))
27.25/8.86	   A^2 -> H(U1(d, c), f(e))
27.25/8.86	   A^2 -> H(U1(d, c), f(k))
27.25/8.86	   A^2 -> H(U1(d, c), U1(d, d))
27.25/8.86	   A^2 -> H(U1(d, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(d, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(d, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(d, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(d, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(d, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(d, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(d, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(d, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(d, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(a, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(a, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(a, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(a, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(a, e), U1(c, c))
27.25/8.86	   A^2 -> H(U1(a, e), f(e))
27.25/8.86	   A^2 -> H(U1(a, e), f(k))
27.25/8.86	   A^2 -> H(U1(a, e), U1(d, d))
27.25/8.86	   A^2 -> H(U1(a, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(a, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(a, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(a, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(a, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(a, k), f(e))
27.25/8.86	   A^2 -> H(U1(a, k), f(k))
27.25/8.86	   A^2 -> H(U1(a, k), U1(d, d))
27.25/8.86	   A^2 -> H(U1(a, c), U1(e, b))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, b))
27.25/8.86	   A^2 -> H(U1(a, c), U1(c, d))
27.25/8.86	   A^2 -> H(U1(a, c), U1(d, c))
27.25/8.86	   A^2 -> H(U1(a, c), U1(b, e))
27.25/8.86	   A^2 -> H(U1(a, c), U1(b, k))
27.25/8.86	   A^2 -> H(U1(a, c), U1(e, c))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, c))
27.25/8.86	   A^2 -> H(U1(a, c), U1(c, e))
27.25/8.86	   A^2 -> H(U1(a, c), U1(c, k))
27.25/8.86	   A^2 -> H(U1(a, c), U1(e, e))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, k))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, d))
27.25/8.86	   A^2 -> H(U1(a, c), U1(d, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(e, b))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, b))
27.25/8.86	   A^2 -> H(U1(a, d), U1(c, d))
27.25/8.86	   A^2 -> H(U1(a, d), U1(d, c))
27.25/8.86	   A^2 -> H(U1(a, d), U1(b, e))
27.25/8.86	   A^2 -> H(U1(a, d), U1(b, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(e, c))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, c))
27.25/8.86	   A^2 -> H(U1(a, d), U1(c, e))
27.25/8.86	   A^2 -> H(U1(a, d), U1(c, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(e, e))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, d))
27.25/8.86	   A^2 -> H(U1(a, d), U1(d, k))
27.25/8.86	   A^2 -> H(U1(a, a), b)
27.25/8.86	   A^2 -> H(U1(a, a), U1(e, d))
27.25/8.86	   A^2 -> H(U1(a, a), U1(d, e))
27.25/8.86	   A^2 -> H(U1(a, a), c)
27.25/8.86	   A^2 -> H(U1(a, a), U1(e, k))
27.25/8.86	   A^2 -> H(U1(a, a), U1(k, e))
27.25/8.86	   A^2 -> H(U1(a, a), e)
27.25/8.86	   A^2 -> H(U1(a, a), U1(k, k))
27.25/8.86	   A^2 -> H(k, f(b))
27.25/8.86	   A^2 -> H(c, U1(b, b))
27.25/8.86	   A^2 -> H(c, f(c))
27.25/8.86	   A^2 -> H(c, f(d))
27.25/8.86	   A^2 -> H(U1(e, k), U1(b, b))
27.25/8.86	   A^2 -> H(U1(e, k), f(c))
27.25/8.86	   A^2 -> H(U1(e, k), f(d))
27.25/8.86	   A^2 -> H(U1(e, c), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, c), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, c), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, c), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, c), U1(c, c))
27.25/8.86	   A^2 -> H(U1(e, c), f(e))
27.25/8.86	   A^2 -> H(U1(e, c), f(k))
27.25/8.86	   A^2 -> H(U1(e, c), U1(d, d))
27.25/8.86	   A^2 -> H(U1(k, e), U1(b, b))
27.25/8.86	   A^2 -> H(U1(k, e), f(c))
27.25/8.86	   A^2 -> H(U1(k, e), f(d))
27.25/8.86	   A^2 -> H(U1(k, c), U1(c, b))
27.25/8.86	   A^2 -> H(U1(k, c), U1(d, b))
27.25/8.86	   A^2 -> H(U1(k, c), U1(b, c))
27.25/8.86	   A^2 -> H(U1(k, c), U1(b, d))
27.25/8.86	   A^2 -> H(U1(k, c), U1(c, c))
27.25/8.86	   A^2 -> H(U1(k, c), f(e))
27.25/8.86	   A^2 -> H(U1(k, c), f(k))
27.25/8.86	   A^2 -> H(U1(k, c), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(c, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(c, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(c, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(c, e), U1(c, c))
27.25/8.86	   A^2 -> H(U1(c, e), f(e))
27.25/8.86	   A^2 -> H(U1(c, e), f(k))
27.25/8.86	   A^2 -> H(U1(c, e), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(c, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(c, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(c, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(c, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(c, k), f(e))
27.25/8.86	   A^2 -> H(U1(c, k), f(k))
27.25/8.86	   A^2 -> H(U1(c, k), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(e, b))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, b))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(d, c))
27.25/8.86	   A^2 -> H(U1(c, c), U1(b, e))
27.25/8.86	   A^2 -> H(U1(c, c), U1(b, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(e, e))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(d, k))
27.25/8.86	   A^2 -> H(e, U1(b, b))
27.25/8.86	   A^2 -> H(e, f(c))
27.25/8.86	   A^2 -> H(e, f(d))
27.25/8.86	   A^2 -> H(U1(e, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, e), U1(c, c))
27.25/8.86	   A^2 -> H(U1(e, e), f(e))
27.25/8.86	   A^2 -> H(U1(e, e), f(k))
27.25/8.86	   A^2 -> H(U1(e, e), U1(d, d))
27.25/8.86	   A^2 -> H(f(e), U1(e, b))
27.25/8.86	   A^2 -> H(f(e), U1(k, b))
27.25/8.86	   A^2 -> H(f(e), U1(c, d))
27.25/8.86	   A^2 -> H(f(e), U1(d, c))
27.25/8.86	   A^2 -> H(f(e), U1(b, e))
27.25/8.86	   A^2 -> H(f(e), U1(b, k))
27.25/8.86	   A^2 -> H(f(e), U1(e, c))
27.25/8.86	   A^2 -> H(f(e), U1(k, c))
27.25/8.86	   A^2 -> H(f(e), U1(c, e))
27.25/8.86	   A^2 -> H(f(e), U1(c, k))
27.25/8.86	   A^2 -> H(f(e), U1(k, k))
27.25/8.86	   A^2 -> H(f(e), U1(k, d))
27.25/8.86	   A^2 -> H(f(e), U1(d, k))
27.25/8.86	   A^2 -> H(U1(k, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(k, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(k, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(k, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(k, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(k, k), f(e))
27.25/8.86	   A^2 -> H(U1(k, k), f(k))
27.25/8.86	   A^2 -> H(U1(k, k), U1(d, d))
27.25/8.86	   A^2 -> H(f(k), U1(e, b))
27.25/8.86	   A^2 -> H(f(k), U1(k, b))
27.25/8.86	   A^2 -> H(f(k), U1(c, d))
27.25/8.86	   A^2 -> H(f(k), U1(d, c))
27.25/8.86	   A^2 -> H(f(k), U1(b, e))
27.25/8.86	   A^2 -> H(f(k), U1(b, k))
27.25/8.86	   A^2 -> H(f(k), U1(e, c))
27.25/8.86	   A^2 -> H(f(k), U1(k, c))
27.25/8.86	   A^2 -> H(f(k), U1(c, e))
27.25/8.86	   A^2 -> H(f(k), U1(c, k))
27.25/8.86	   A^2 -> H(f(k), U1(e, e))
27.25/8.86	   A^2 -> H(f(k), U1(k, d))
27.25/8.86	   A^2 -> H(f(k), U1(d, k))
27.25/8.86	   A^2 -> H(f(c), b)
27.25/8.86	   A^2 -> H(f(c), U1(e, d))
27.25/8.86	   A^2 -> H(f(c), U1(d, e))
27.25/8.86	   A^2 -> H(f(k), U1(k, k))
27.25/8.86	   A^2 -> H(U1(k, k), U1(b, b))
27.25/8.86	   A^2 -> H(U1(k, k), f(c))
27.25/8.86	   A^2 -> H(U1(k, k), f(d))
27.25/8.86	   A^2 -> H(U1(k, d), U1(c, b))
27.25/8.86	   A^2 -> H(U1(k, d), U1(d, b))
27.25/8.86	   A^2 -> H(U1(k, d), U1(b, c))
27.25/8.86	   A^2 -> H(U1(k, d), U1(b, d))
27.25/8.86	   A^2 -> H(U1(k, d), U1(c, c))
27.25/8.86	   A^2 -> H(U1(k, d), f(e))
27.25/8.86	   A^2 -> H(U1(k, d), f(k))
27.25/8.86	   A^2 -> H(U1(k, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(d, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(d, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(d, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(d, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(d, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(d, k), f(e))
27.25/8.86	   A^2 -> H(U1(d, k), f(k))
27.25/8.86	   A^2 -> H(U1(d, k), U1(d, d))
27.25/8.86	   A^2 -> H(U1(d, d), U1(e, b))
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, b))
27.25/8.86	   A^2 -> H(U1(d, d), U1(c, d))
27.25/8.86	   A^2 -> H(U1(d, d), U1(d, c))
27.25/8.86	   A^2 -> H(U1(d, d), U1(b, e))
27.25/8.86	   A^2 -> H(U1(d, d), U1(b, k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(e, c))
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, c))
27.25/8.86	   A^2 -> H(U1(d, d), U1(c, e))
27.25/8.86	   A^2 -> H(U1(d, d), U1(c, k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(e, e))
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, k))
27.25/8.86	   A^2 -> H(f(d), b)
27.25/8.86	   A^2 -> H(f(d), U1(e, d))
27.25/8.86	   A^2 -> H(f(d), U1(d, e))
27.25/8.86	   A^2 -> H(f(d), c)
27.25/8.86	   A^2 -> H(f(d), U1(e, k))
27.25/8.86	   A^2 -> H(f(d), U1(k, e))
27.25/8.86	   A^2 -> H(f(d), e)
27.25/8.86	   A^2 -> H(f(a), d)
27.25/8.86	   A^2 -> H(U1(c, c), U1(e, c))
27.25/8.86	   A^2 -> H(f(c), c)
27.25/8.86	   A^2 -> H(f(c), U1(e, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, c))
27.25/8.86	   A^2 -> H(f(c), U1(k, e))
27.25/8.86	   A^2 -> H(f(c), U1(k, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, e))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, k))
27.25/8.86	   A^2 -> H(f(a), k)
27.25/8.86	   A^2 -> H(f(e), U1(e, e))
27.25/8.86	   A^2 -> H(f(c), e)
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, d))
27.25/8.86	   A^2 -> H(f(d), U1(k, k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(d, k))
27.25/8.86	   A^2 -> H(d, U1(b, b))
27.25/8.86	   A^2 -> H(d, f(c))
27.25/8.86	   A^2 -> H(d, f(d))
27.25/8.86	   A^2 -> H(a, U1(c, b))
27.25/8.86	   A^2 -> H(a, U1(d, b))
27.25/8.86	   A^2 -> H(a, U1(b, c))
27.25/8.86	   A^2 -> H(a, U1(b, d))
27.25/8.86	   A^2 -> H(a, U1(c, c))
27.25/8.86	   A^2 -> H(a, f(e))
27.25/8.86	   A^2 -> H(a, f(k))
27.25/8.86	   A^2 -> H(a, U1(d, d))
27.25/8.86	   A^2 -> H(U1(e, d), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, d), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, d), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, d), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, d), U1(c, c))
27.25/8.86	   A^2 -> H(U1(e, d), f(e))
27.25/8.86	   A^2 -> H(U1(e, d), f(k))
27.25/8.86	   A^2 -> H(U1(e, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(e, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(e, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(e, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(e, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(e, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(e, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(e, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(e, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(e, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(e, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(k, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(k, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(k, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(k, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(k, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(k, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(k, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(c, d), U1(e, b))
27.25/8.86	   A^2 -> H(U1(c, d), U1(k, b))
27.25/8.86	   A^2 -> H(U1(c, d), U1(c, d))
27.25/8.86	   A^2 -> H(U1(c, d), U1(d, c))
27.25/8.86	   A^2 -> H(U1(c, d), U1(b, e))
27.25/8.86	   A^2 -> H(U1(c, d), U1(b, k))
27.25/8.86	
27.25/8.86	The TRS R consists of the following rules:
27.25/8.86	
27.25/8.86	   f(x) -> U1(x, x)
27.25/8.86	   U1(e, x) -> x
27.25/8.86	   a -> c
27.25/8.86	   a -> d
27.25/8.86	   b -> c
27.25/8.86	   b -> d
27.25/8.86	   d -> k
27.25/8.86	   c -> e
27.25/8.86	   c -> k
27.25/8.86	
27.25/8.86	Q is empty.
27.25/8.86	We have to consider all minimal (P,Q,R)-chains.
27.25/8.86	----------------------------------------
27.25/8.86	
27.25/8.86	(593) TransformationProof (EQUIVALENT)
27.25/8.86	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
27.25/8.86	
27.25/8.86	   (A^2 -> H(U1(e, d), U1(b, d)),A^2 -> H(U1(e, d), U1(b, d)))
27.25/8.86	   (A^2 -> H(U1(k, d), U1(b, d)),A^2 -> H(U1(k, d), U1(b, d)))
27.25/8.86	   (A^2 -> H(U1(c, k), U1(b, d)),A^2 -> H(U1(c, k), U1(b, d)))
27.25/8.86	   (A^2 -> H(U1(c, d), U1(c, d)),A^2 -> H(U1(c, d), U1(c, d)))
27.25/8.86	   (A^2 -> H(U1(c, d), U1(d, d)),A^2 -> H(U1(c, d), U1(d, d)))
27.25/8.86	   (A^2 -> H(U1(c, d), U1(b, k)),A^2 -> H(U1(c, d), U1(b, k)))
27.25/8.86	
27.25/8.86	
27.25/8.86	----------------------------------------
27.25/8.86	
27.25/8.86	(594)
27.25/8.86	Obligation:
27.25/8.86	Q DP problem:
27.25/8.86	The TRS P consists of the following rules:
27.25/8.86	
27.25/8.86	   H(x, x) -> G(x, x, f(k))
27.25/8.86	   G(d, x, x) -> A^2
27.25/8.86	   A^2 -> H(f(c), f(c))
27.25/8.86	   A^2 -> H(f(d), f(d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, c))
27.25/8.86	   A^2 -> H(f(e), f(e))
27.25/8.86	   A^2 -> H(f(k), f(k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, d), U1(c, c))
27.25/8.86	   A^2 -> H(U1(c, d), f(e))
27.25/8.86	   A^2 -> H(U1(c, d), f(k))
27.25/8.86	   A^2 -> H(U1(c, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(c, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(c, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(c, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(c, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(c, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(c, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(c, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(c, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(c, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(d, e), U1(b, b))
27.25/8.86	   A^2 -> H(U1(d, e), f(c))
27.25/8.86	   A^2 -> H(U1(d, e), f(d))
27.25/8.86	   A^2 -> H(U1(d, c), U1(c, b))
27.25/8.86	   A^2 -> H(U1(d, c), U1(d, b))
27.25/8.86	   A^2 -> H(U1(d, c), U1(b, c))
27.25/8.86	   A^2 -> H(U1(d, c), U1(b, d))
27.25/8.86	   A^2 -> H(U1(d, c), U1(c, c))
27.25/8.86	   A^2 -> H(U1(d, c), f(e))
27.25/8.86	   A^2 -> H(U1(d, c), f(k))
27.25/8.86	   A^2 -> H(U1(d, c), U1(d, d))
27.25/8.86	   A^2 -> H(U1(d, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(d, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(d, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(d, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(d, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(d, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(d, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(d, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(d, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(d, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(a, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(a, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(a, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(a, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(a, e), U1(c, c))
27.25/8.86	   A^2 -> H(U1(a, e), f(e))
27.25/8.86	   A^2 -> H(U1(a, e), f(k))
27.25/8.86	   A^2 -> H(U1(a, e), U1(d, d))
27.25/8.86	   A^2 -> H(U1(a, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(a, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(a, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(a, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(a, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(a, k), f(e))
27.25/8.86	   A^2 -> H(U1(a, k), f(k))
27.25/8.86	   A^2 -> H(U1(a, k), U1(d, d))
27.25/8.86	   A^2 -> H(U1(a, c), U1(e, b))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, b))
27.25/8.86	   A^2 -> H(U1(a, c), U1(c, d))
27.25/8.86	   A^2 -> H(U1(a, c), U1(d, c))
27.25/8.86	   A^2 -> H(U1(a, c), U1(b, e))
27.25/8.86	   A^2 -> H(U1(a, c), U1(b, k))
27.25/8.86	   A^2 -> H(U1(a, c), U1(e, c))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, c))
27.25/8.86	   A^2 -> H(U1(a, c), U1(c, e))
27.25/8.86	   A^2 -> H(U1(a, c), U1(c, k))
27.25/8.86	   A^2 -> H(U1(a, c), U1(e, e))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, k))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, d))
27.25/8.86	   A^2 -> H(U1(a, c), U1(d, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(e, b))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, b))
27.25/8.86	   A^2 -> H(U1(a, d), U1(c, d))
27.25/8.86	   A^2 -> H(U1(a, d), U1(d, c))
27.25/8.86	   A^2 -> H(U1(a, d), U1(b, e))
27.25/8.86	   A^2 -> H(U1(a, d), U1(b, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(e, c))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, c))
27.25/8.86	   A^2 -> H(U1(a, d), U1(c, e))
27.25/8.86	   A^2 -> H(U1(a, d), U1(c, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(e, e))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, d))
27.25/8.86	   A^2 -> H(U1(a, d), U1(d, k))
27.25/8.86	   A^2 -> H(U1(a, a), b)
27.25/8.86	   A^2 -> H(U1(a, a), U1(e, d))
27.25/8.86	   A^2 -> H(U1(a, a), U1(d, e))
27.25/8.86	   A^2 -> H(U1(a, a), c)
27.25/8.86	   A^2 -> H(U1(a, a), U1(e, k))
27.25/8.86	   A^2 -> H(U1(a, a), U1(k, e))
27.25/8.86	   A^2 -> H(U1(a, a), e)
27.25/8.86	   A^2 -> H(U1(a, a), U1(k, k))
27.25/8.86	   A^2 -> H(k, f(b))
27.25/8.86	   A^2 -> H(c, U1(b, b))
27.25/8.86	   A^2 -> H(c, f(c))
27.25/8.86	   A^2 -> H(c, f(d))
27.25/8.86	   A^2 -> H(U1(e, k), U1(b, b))
27.25/8.86	   A^2 -> H(U1(e, k), f(c))
27.25/8.86	   A^2 -> H(U1(e, k), f(d))
27.25/8.86	   A^2 -> H(U1(e, c), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, c), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, c), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, c), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, c), U1(c, c))
27.25/8.86	   A^2 -> H(U1(e, c), f(e))
27.25/8.86	   A^2 -> H(U1(e, c), f(k))
27.25/8.86	   A^2 -> H(U1(e, c), U1(d, d))
27.25/8.86	   A^2 -> H(U1(k, e), U1(b, b))
27.25/8.86	   A^2 -> H(U1(k, e), f(c))
27.25/8.86	   A^2 -> H(U1(k, e), f(d))
27.25/8.86	   A^2 -> H(U1(k, c), U1(c, b))
27.25/8.86	   A^2 -> H(U1(k, c), U1(d, b))
27.25/8.86	   A^2 -> H(U1(k, c), U1(b, c))
27.25/8.86	   A^2 -> H(U1(k, c), U1(b, d))
27.25/8.86	   A^2 -> H(U1(k, c), U1(c, c))
27.25/8.86	   A^2 -> H(U1(k, c), f(e))
27.25/8.86	   A^2 -> H(U1(k, c), f(k))
27.25/8.86	   A^2 -> H(U1(k, c), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(c, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(c, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(c, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(c, e), U1(c, c))
27.25/8.86	   A^2 -> H(U1(c, e), f(e))
27.25/8.86	   A^2 -> H(U1(c, e), f(k))
27.25/8.86	   A^2 -> H(U1(c, e), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(c, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(c, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(c, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(c, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(c, k), f(e))
27.25/8.86	   A^2 -> H(U1(c, k), f(k))
27.25/8.86	   A^2 -> H(U1(c, k), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(e, b))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, b))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(d, c))
27.25/8.86	   A^2 -> H(U1(c, c), U1(b, e))
27.25/8.86	   A^2 -> H(U1(c, c), U1(b, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(e, e))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(d, k))
27.25/8.86	   A^2 -> H(e, U1(b, b))
27.25/8.86	   A^2 -> H(e, f(c))
27.25/8.86	   A^2 -> H(e, f(d))
27.25/8.86	   A^2 -> H(U1(e, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, e), U1(c, c))
27.25/8.86	   A^2 -> H(U1(e, e), f(e))
27.25/8.86	   A^2 -> H(U1(e, e), f(k))
27.25/8.86	   A^2 -> H(U1(e, e), U1(d, d))
27.25/8.86	   A^2 -> H(f(e), U1(e, b))
27.25/8.86	   A^2 -> H(f(e), U1(k, b))
27.25/8.86	   A^2 -> H(f(e), U1(c, d))
27.25/8.86	   A^2 -> H(f(e), U1(d, c))
27.25/8.86	   A^2 -> H(f(e), U1(b, e))
27.25/8.86	   A^2 -> H(f(e), U1(b, k))
27.25/8.86	   A^2 -> H(f(e), U1(e, c))
27.25/8.86	   A^2 -> H(f(e), U1(k, c))
27.25/8.86	   A^2 -> H(f(e), U1(c, e))
27.25/8.86	   A^2 -> H(f(e), U1(c, k))
27.25/8.86	   A^2 -> H(f(e), U1(k, k))
27.25/8.86	   A^2 -> H(f(e), U1(k, d))
27.25/8.86	   A^2 -> H(f(e), U1(d, k))
27.25/8.86	   A^2 -> H(U1(k, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(k, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(k, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(k, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(k, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(k, k), f(e))
27.25/8.86	   A^2 -> H(U1(k, k), f(k))
27.25/8.86	   A^2 -> H(U1(k, k), U1(d, d))
27.25/8.86	   A^2 -> H(f(k), U1(e, b))
27.25/8.86	   A^2 -> H(f(k), U1(k, b))
27.25/8.86	   A^2 -> H(f(k), U1(c, d))
27.25/8.86	   A^2 -> H(f(k), U1(d, c))
27.25/8.86	   A^2 -> H(f(k), U1(b, e))
27.25/8.86	   A^2 -> H(f(k), U1(b, k))
27.25/8.86	   A^2 -> H(f(k), U1(e, c))
27.25/8.86	   A^2 -> H(f(k), U1(k, c))
27.25/8.86	   A^2 -> H(f(k), U1(c, e))
27.25/8.86	   A^2 -> H(f(k), U1(c, k))
27.25/8.86	   A^2 -> H(f(k), U1(e, e))
27.25/8.86	   A^2 -> H(f(k), U1(k, d))
27.25/8.86	   A^2 -> H(f(k), U1(d, k))
27.25/8.86	   A^2 -> H(f(c), b)
27.25/8.86	   A^2 -> H(f(c), U1(e, d))
27.25/8.86	   A^2 -> H(f(c), U1(d, e))
27.25/8.86	   A^2 -> H(f(k), U1(k, k))
27.25/8.86	   A^2 -> H(U1(k, k), U1(b, b))
27.25/8.86	   A^2 -> H(U1(k, k), f(c))
27.25/8.86	   A^2 -> H(U1(k, k), f(d))
27.25/8.86	   A^2 -> H(U1(k, d), U1(c, b))
27.25/8.86	   A^2 -> H(U1(k, d), U1(d, b))
27.25/8.86	   A^2 -> H(U1(k, d), U1(b, c))
27.25/8.86	   A^2 -> H(U1(k, d), U1(b, d))
27.25/8.86	   A^2 -> H(U1(k, d), U1(c, c))
27.25/8.86	   A^2 -> H(U1(k, d), f(e))
27.25/8.86	   A^2 -> H(U1(k, d), f(k))
27.25/8.86	   A^2 -> H(U1(k, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(d, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(d, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(d, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(d, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(d, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(d, k), f(e))
27.25/8.86	   A^2 -> H(U1(d, k), f(k))
27.25/8.86	   A^2 -> H(U1(d, k), U1(d, d))
27.25/8.86	   A^2 -> H(U1(d, d), U1(e, b))
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, b))
27.25/8.86	   A^2 -> H(U1(d, d), U1(c, d))
27.25/8.86	   A^2 -> H(U1(d, d), U1(d, c))
27.25/8.86	   A^2 -> H(U1(d, d), U1(b, e))
27.25/8.86	   A^2 -> H(U1(d, d), U1(b, k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(e, c))
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, c))
27.25/8.86	   A^2 -> H(U1(d, d), U1(c, e))
27.25/8.86	   A^2 -> H(U1(d, d), U1(c, k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(e, e))
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, k))
27.25/8.86	   A^2 -> H(f(d), b)
27.25/8.86	   A^2 -> H(f(d), U1(e, d))
27.25/8.86	   A^2 -> H(f(d), U1(d, e))
27.25/8.86	   A^2 -> H(f(d), c)
27.25/8.86	   A^2 -> H(f(d), U1(e, k))
27.25/8.86	   A^2 -> H(f(d), U1(k, e))
27.25/8.86	   A^2 -> H(f(d), e)
27.25/8.86	   A^2 -> H(f(a), d)
27.25/8.86	   A^2 -> H(U1(c, c), U1(e, c))
27.25/8.86	   A^2 -> H(f(c), c)
27.25/8.86	   A^2 -> H(f(c), U1(e, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, c))
27.25/8.86	   A^2 -> H(f(c), U1(k, e))
27.25/8.86	   A^2 -> H(f(c), U1(k, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, e))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, k))
27.25/8.86	   A^2 -> H(f(a), k)
27.25/8.86	   A^2 -> H(f(e), U1(e, e))
27.25/8.86	   A^2 -> H(f(c), e)
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, d))
27.25/8.86	   A^2 -> H(f(d), U1(k, k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(d, k))
27.25/8.86	   A^2 -> H(d, U1(b, b))
27.25/8.86	   A^2 -> H(d, f(c))
27.25/8.86	   A^2 -> H(d, f(d))
27.25/8.86	   A^2 -> H(a, U1(c, b))
27.25/8.86	   A^2 -> H(a, U1(d, b))
27.25/8.86	   A^2 -> H(a, U1(b, c))
27.25/8.86	   A^2 -> H(a, U1(b, d))
27.25/8.86	   A^2 -> H(a, U1(c, c))
27.25/8.86	   A^2 -> H(a, f(e))
27.25/8.86	   A^2 -> H(a, f(k))
27.25/8.86	   A^2 -> H(a, U1(d, d))
27.25/8.86	   A^2 -> H(U1(e, d), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, d), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, d), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, d), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, d), U1(c, c))
27.25/8.86	   A^2 -> H(U1(e, d), f(e))
27.25/8.86	   A^2 -> H(U1(e, d), f(k))
27.25/8.86	   A^2 -> H(U1(e, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(e, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(e, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(e, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(e, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(e, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(e, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(e, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(e, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(e, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(e, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(k, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(k, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(k, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(k, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(k, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(k, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(k, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(c, d), U1(e, b))
27.25/8.86	   A^2 -> H(U1(c, d), U1(k, b))
27.25/8.86	   A^2 -> H(U1(c, d), U1(c, d))
27.25/8.86	   A^2 -> H(U1(c, d), U1(d, c))
27.25/8.86	   A^2 -> H(U1(c, d), U1(b, e))
27.25/8.86	   A^2 -> H(U1(c, d), U1(b, k))
27.25/8.86	
27.25/8.86	The TRS R consists of the following rules:
27.25/8.86	
27.25/8.86	   f(x) -> U1(x, x)
27.25/8.86	   U1(e, x) -> x
27.25/8.86	   a -> c
27.25/8.86	   a -> d
27.25/8.86	   b -> c
27.25/8.86	   b -> d
27.25/8.86	   d -> k
27.25/8.86	   c -> e
27.25/8.86	   c -> k
27.25/8.86	
27.25/8.86	Q is empty.
27.25/8.86	We have to consider all minimal (P,Q,R)-chains.
27.25/8.86	----------------------------------------
27.25/8.86	
27.25/8.86	(595) TransformationProof (EQUIVALENT)
27.25/8.86	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
27.25/8.86	
27.25/8.86	   (A^2 -> H(U1(e, d), U1(c, c)),A^2 -> H(U1(e, d), U1(c, c)))
27.25/8.86	   (A^2 -> H(U1(k, d), U1(c, c)),A^2 -> H(U1(k, d), U1(c, c)))
27.25/8.86	   (A^2 -> H(U1(c, k), U1(c, c)),A^2 -> H(U1(c, k), U1(c, c)))
27.25/8.86	   (A^2 -> H(U1(c, d), U1(e, c)),A^2 -> H(U1(c, d), U1(e, c)))
27.25/8.86	   (A^2 -> H(U1(c, d), U1(k, c)),A^2 -> H(U1(c, d), U1(k, c)))
27.25/8.86	   (A^2 -> H(U1(c, d), U1(c, e)),A^2 -> H(U1(c, d), U1(c, e)))
27.25/8.86	   (A^2 -> H(U1(c, d), U1(c, k)),A^2 -> H(U1(c, d), U1(c, k)))
27.25/8.86	
27.25/8.86	
27.25/8.86	----------------------------------------
27.25/8.86	
27.25/8.86	(596)
27.25/8.86	Obligation:
27.25/8.86	Q DP problem:
27.25/8.86	The TRS P consists of the following rules:
27.25/8.86	
27.25/8.86	   H(x, x) -> G(x, x, f(k))
27.25/8.86	   G(d, x, x) -> A^2
27.25/8.86	   A^2 -> H(f(c), f(c))
27.25/8.86	   A^2 -> H(f(d), f(d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, c))
27.25/8.86	   A^2 -> H(f(e), f(e))
27.25/8.86	   A^2 -> H(f(k), f(k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, d), f(e))
27.25/8.86	   A^2 -> H(U1(c, d), f(k))
27.25/8.86	   A^2 -> H(U1(c, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(c, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(c, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(c, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(c, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(c, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(c, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(c, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(c, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(c, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(d, e), U1(b, b))
27.25/8.86	   A^2 -> H(U1(d, e), f(c))
27.25/8.86	   A^2 -> H(U1(d, e), f(d))
27.25/8.86	   A^2 -> H(U1(d, c), U1(c, b))
27.25/8.86	   A^2 -> H(U1(d, c), U1(d, b))
27.25/8.86	   A^2 -> H(U1(d, c), U1(b, c))
27.25/8.86	   A^2 -> H(U1(d, c), U1(b, d))
27.25/8.86	   A^2 -> H(U1(d, c), U1(c, c))
27.25/8.86	   A^2 -> H(U1(d, c), f(e))
27.25/8.86	   A^2 -> H(U1(d, c), f(k))
27.25/8.86	   A^2 -> H(U1(d, c), U1(d, d))
27.25/8.86	   A^2 -> H(U1(d, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(d, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(d, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(d, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(d, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(d, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(d, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(d, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(d, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(d, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(a, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(a, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(a, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(a, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(a, e), U1(c, c))
27.25/8.86	   A^2 -> H(U1(a, e), f(e))
27.25/8.86	   A^2 -> H(U1(a, e), f(k))
27.25/8.86	   A^2 -> H(U1(a, e), U1(d, d))
27.25/8.86	   A^2 -> H(U1(a, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(a, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(a, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(a, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(a, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(a, k), f(e))
27.25/8.86	   A^2 -> H(U1(a, k), f(k))
27.25/8.86	   A^2 -> H(U1(a, k), U1(d, d))
27.25/8.86	   A^2 -> H(U1(a, c), U1(e, b))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, b))
27.25/8.86	   A^2 -> H(U1(a, c), U1(c, d))
27.25/8.86	   A^2 -> H(U1(a, c), U1(d, c))
27.25/8.86	   A^2 -> H(U1(a, c), U1(b, e))
27.25/8.86	   A^2 -> H(U1(a, c), U1(b, k))
27.25/8.86	   A^2 -> H(U1(a, c), U1(e, c))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, c))
27.25/8.86	   A^2 -> H(U1(a, c), U1(c, e))
27.25/8.86	   A^2 -> H(U1(a, c), U1(c, k))
27.25/8.86	   A^2 -> H(U1(a, c), U1(e, e))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, k))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, d))
27.25/8.86	   A^2 -> H(U1(a, c), U1(d, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(e, b))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, b))
27.25/8.86	   A^2 -> H(U1(a, d), U1(c, d))
27.25/8.86	   A^2 -> H(U1(a, d), U1(d, c))
27.25/8.86	   A^2 -> H(U1(a, d), U1(b, e))
27.25/8.86	   A^2 -> H(U1(a, d), U1(b, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(e, c))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, c))
27.25/8.86	   A^2 -> H(U1(a, d), U1(c, e))
27.25/8.86	   A^2 -> H(U1(a, d), U1(c, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(e, e))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, d))
27.25/8.86	   A^2 -> H(U1(a, d), U1(d, k))
27.25/8.86	   A^2 -> H(U1(a, a), b)
27.25/8.86	   A^2 -> H(U1(a, a), U1(e, d))
27.25/8.86	   A^2 -> H(U1(a, a), U1(d, e))
27.25/8.86	   A^2 -> H(U1(a, a), c)
27.25/8.86	   A^2 -> H(U1(a, a), U1(e, k))
27.25/8.86	   A^2 -> H(U1(a, a), U1(k, e))
27.25/8.86	   A^2 -> H(U1(a, a), e)
27.25/8.86	   A^2 -> H(U1(a, a), U1(k, k))
27.25/8.86	   A^2 -> H(k, f(b))
27.25/8.86	   A^2 -> H(c, U1(b, b))
27.25/8.86	   A^2 -> H(c, f(c))
27.25/8.86	   A^2 -> H(c, f(d))
27.25/8.86	   A^2 -> H(U1(e, k), U1(b, b))
27.25/8.86	   A^2 -> H(U1(e, k), f(c))
27.25/8.86	   A^2 -> H(U1(e, k), f(d))
27.25/8.86	   A^2 -> H(U1(e, c), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, c), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, c), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, c), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, c), U1(c, c))
27.25/8.86	   A^2 -> H(U1(e, c), f(e))
27.25/8.86	   A^2 -> H(U1(e, c), f(k))
27.25/8.86	   A^2 -> H(U1(e, c), U1(d, d))
27.25/8.86	   A^2 -> H(U1(k, e), U1(b, b))
27.25/8.86	   A^2 -> H(U1(k, e), f(c))
27.25/8.86	   A^2 -> H(U1(k, e), f(d))
27.25/8.86	   A^2 -> H(U1(k, c), U1(c, b))
27.25/8.86	   A^2 -> H(U1(k, c), U1(d, b))
27.25/8.86	   A^2 -> H(U1(k, c), U1(b, c))
27.25/8.86	   A^2 -> H(U1(k, c), U1(b, d))
27.25/8.86	   A^2 -> H(U1(k, c), U1(c, c))
27.25/8.86	   A^2 -> H(U1(k, c), f(e))
27.25/8.86	   A^2 -> H(U1(k, c), f(k))
27.25/8.86	   A^2 -> H(U1(k, c), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(c, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(c, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(c, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(c, e), U1(c, c))
27.25/8.86	   A^2 -> H(U1(c, e), f(e))
27.25/8.86	   A^2 -> H(U1(c, e), f(k))
27.25/8.86	   A^2 -> H(U1(c, e), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(c, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(c, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(c, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(c, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(c, k), f(e))
27.25/8.86	   A^2 -> H(U1(c, k), f(k))
27.25/8.86	   A^2 -> H(U1(c, k), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(e, b))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, b))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(d, c))
27.25/8.86	   A^2 -> H(U1(c, c), U1(b, e))
27.25/8.86	   A^2 -> H(U1(c, c), U1(b, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(e, e))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(d, k))
27.25/8.86	   A^2 -> H(e, U1(b, b))
27.25/8.86	   A^2 -> H(e, f(c))
27.25/8.86	   A^2 -> H(e, f(d))
27.25/8.86	   A^2 -> H(U1(e, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, e), U1(c, c))
27.25/8.86	   A^2 -> H(U1(e, e), f(e))
27.25/8.86	   A^2 -> H(U1(e, e), f(k))
27.25/8.86	   A^2 -> H(U1(e, e), U1(d, d))
27.25/8.86	   A^2 -> H(f(e), U1(e, b))
27.25/8.86	   A^2 -> H(f(e), U1(k, b))
27.25/8.86	   A^2 -> H(f(e), U1(c, d))
27.25/8.86	   A^2 -> H(f(e), U1(d, c))
27.25/8.86	   A^2 -> H(f(e), U1(b, e))
27.25/8.86	   A^2 -> H(f(e), U1(b, k))
27.25/8.86	   A^2 -> H(f(e), U1(e, c))
27.25/8.86	   A^2 -> H(f(e), U1(k, c))
27.25/8.86	   A^2 -> H(f(e), U1(c, e))
27.25/8.86	   A^2 -> H(f(e), U1(c, k))
27.25/8.86	   A^2 -> H(f(e), U1(k, k))
27.25/8.86	   A^2 -> H(f(e), U1(k, d))
27.25/8.86	   A^2 -> H(f(e), U1(d, k))
27.25/8.86	   A^2 -> H(U1(k, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(k, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(k, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(k, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(k, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(k, k), f(e))
27.25/8.86	   A^2 -> H(U1(k, k), f(k))
27.25/8.86	   A^2 -> H(U1(k, k), U1(d, d))
27.25/8.86	   A^2 -> H(f(k), U1(e, b))
27.25/8.86	   A^2 -> H(f(k), U1(k, b))
27.25/8.86	   A^2 -> H(f(k), U1(c, d))
27.25/8.86	   A^2 -> H(f(k), U1(d, c))
27.25/8.86	   A^2 -> H(f(k), U1(b, e))
27.25/8.86	   A^2 -> H(f(k), U1(b, k))
27.25/8.86	   A^2 -> H(f(k), U1(e, c))
27.25/8.86	   A^2 -> H(f(k), U1(k, c))
27.25/8.86	   A^2 -> H(f(k), U1(c, e))
27.25/8.86	   A^2 -> H(f(k), U1(c, k))
27.25/8.86	   A^2 -> H(f(k), U1(e, e))
27.25/8.86	   A^2 -> H(f(k), U1(k, d))
27.25/8.86	   A^2 -> H(f(k), U1(d, k))
27.25/8.86	   A^2 -> H(f(c), b)
27.25/8.86	   A^2 -> H(f(c), U1(e, d))
27.25/8.86	   A^2 -> H(f(c), U1(d, e))
27.25/8.86	   A^2 -> H(f(k), U1(k, k))
27.25/8.86	   A^2 -> H(U1(k, k), U1(b, b))
27.25/8.86	   A^2 -> H(U1(k, k), f(c))
27.25/8.86	   A^2 -> H(U1(k, k), f(d))
27.25/8.86	   A^2 -> H(U1(k, d), U1(c, b))
27.25/8.86	   A^2 -> H(U1(k, d), U1(d, b))
27.25/8.86	   A^2 -> H(U1(k, d), U1(b, c))
27.25/8.86	   A^2 -> H(U1(k, d), U1(b, d))
27.25/8.86	   A^2 -> H(U1(k, d), U1(c, c))
27.25/8.86	   A^2 -> H(U1(k, d), f(e))
27.25/8.86	   A^2 -> H(U1(k, d), f(k))
27.25/8.86	   A^2 -> H(U1(k, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(d, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(d, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(d, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(d, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(d, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(d, k), f(e))
27.25/8.86	   A^2 -> H(U1(d, k), f(k))
27.25/8.86	   A^2 -> H(U1(d, k), U1(d, d))
27.25/8.86	   A^2 -> H(U1(d, d), U1(e, b))
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, b))
27.25/8.86	   A^2 -> H(U1(d, d), U1(c, d))
27.25/8.86	   A^2 -> H(U1(d, d), U1(d, c))
27.25/8.86	   A^2 -> H(U1(d, d), U1(b, e))
27.25/8.86	   A^2 -> H(U1(d, d), U1(b, k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(e, c))
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, c))
27.25/8.86	   A^2 -> H(U1(d, d), U1(c, e))
27.25/8.86	   A^2 -> H(U1(d, d), U1(c, k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(e, e))
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, k))
27.25/8.86	   A^2 -> H(f(d), b)
27.25/8.86	   A^2 -> H(f(d), U1(e, d))
27.25/8.86	   A^2 -> H(f(d), U1(d, e))
27.25/8.86	   A^2 -> H(f(d), c)
27.25/8.86	   A^2 -> H(f(d), U1(e, k))
27.25/8.86	   A^2 -> H(f(d), U1(k, e))
27.25/8.86	   A^2 -> H(f(d), e)
27.25/8.86	   A^2 -> H(f(a), d)
27.25/8.86	   A^2 -> H(U1(c, c), U1(e, c))
27.25/8.86	   A^2 -> H(f(c), c)
27.25/8.86	   A^2 -> H(f(c), U1(e, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, c))
27.25/8.86	   A^2 -> H(f(c), U1(k, e))
27.25/8.86	   A^2 -> H(f(c), U1(k, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, e))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, k))
27.25/8.86	   A^2 -> H(f(a), k)
27.25/8.86	   A^2 -> H(f(e), U1(e, e))
27.25/8.86	   A^2 -> H(f(c), e)
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, d))
27.25/8.86	   A^2 -> H(f(d), U1(k, k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(d, k))
27.25/8.86	   A^2 -> H(d, U1(b, b))
27.25/8.86	   A^2 -> H(d, f(c))
27.25/8.86	   A^2 -> H(d, f(d))
27.25/8.86	   A^2 -> H(a, U1(c, b))
27.25/8.86	   A^2 -> H(a, U1(d, b))
27.25/8.86	   A^2 -> H(a, U1(b, c))
27.25/8.86	   A^2 -> H(a, U1(b, d))
27.25/8.86	   A^2 -> H(a, U1(c, c))
27.25/8.86	   A^2 -> H(a, f(e))
27.25/8.86	   A^2 -> H(a, f(k))
27.25/8.86	   A^2 -> H(a, U1(d, d))
27.25/8.86	   A^2 -> H(U1(e, d), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, d), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, d), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, d), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, d), U1(c, c))
27.25/8.86	   A^2 -> H(U1(e, d), f(e))
27.25/8.86	   A^2 -> H(U1(e, d), f(k))
27.25/8.86	   A^2 -> H(U1(e, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(e, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(e, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(e, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(e, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(e, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(e, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(e, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(e, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(e, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(e, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(k, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(k, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(k, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(k, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(k, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(k, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(k, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(c, d), U1(e, b))
27.25/8.86	   A^2 -> H(U1(c, d), U1(k, b))
27.25/8.86	   A^2 -> H(U1(c, d), U1(c, d))
27.25/8.86	   A^2 -> H(U1(c, d), U1(d, c))
27.25/8.86	   A^2 -> H(U1(c, d), U1(b, e))
27.25/8.86	   A^2 -> H(U1(c, d), U1(b, k))
27.25/8.86	   A^2 -> H(U1(c, d), U1(e, c))
27.25/8.86	   A^2 -> H(U1(c, d), U1(k, c))
27.25/8.86	   A^2 -> H(U1(c, d), U1(c, e))
27.25/8.86	   A^2 -> H(U1(c, d), U1(c, k))
27.25/8.86	
27.25/8.86	The TRS R consists of the following rules:
27.25/8.86	
27.25/8.86	   f(x) -> U1(x, x)
27.25/8.86	   U1(e, x) -> x
27.25/8.86	   a -> c
27.25/8.86	   a -> d
27.25/8.86	   b -> c
27.25/8.86	   b -> d
27.25/8.86	   d -> k
27.25/8.86	   c -> e
27.25/8.86	   c -> k
27.25/8.86	
27.25/8.86	Q is empty.
27.25/8.86	We have to consider all minimal (P,Q,R)-chains.
27.25/8.86	----------------------------------------
27.25/8.86	
27.25/8.86	(597) TransformationProof (EQUIVALENT)
27.25/8.86	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), f(e)) at position [] we obtained the following new rules [LPAR04]:
27.25/8.86	
27.25/8.86	   (A^2 -> H(U1(e, d), f(e)),A^2 -> H(U1(e, d), f(e)))
27.25/8.86	   (A^2 -> H(U1(k, d), f(e)),A^2 -> H(U1(k, d), f(e)))
27.25/8.86	   (A^2 -> H(U1(c, k), f(e)),A^2 -> H(U1(c, k), f(e)))
27.25/8.86	   (A^2 -> H(U1(c, d), U1(e, e)),A^2 -> H(U1(c, d), U1(e, e)))
27.25/8.86	
27.25/8.86	
27.25/8.86	----------------------------------------
27.25/8.86	
27.25/8.86	(598)
27.25/8.86	Obligation:
27.25/8.86	Q DP problem:
27.25/8.86	The TRS P consists of the following rules:
27.25/8.86	
27.25/8.86	   H(x, x) -> G(x, x, f(k))
27.25/8.86	   G(d, x, x) -> A^2
27.25/8.86	   A^2 -> H(f(c), f(c))
27.25/8.86	   A^2 -> H(f(d), f(d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, c))
27.25/8.86	   A^2 -> H(f(e), f(e))
27.25/8.86	   A^2 -> H(f(k), f(k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, d), f(k))
27.25/8.86	   A^2 -> H(U1(c, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(c, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(c, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(c, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(c, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(c, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(c, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(c, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(c, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(c, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(d, e), U1(b, b))
27.25/8.86	   A^2 -> H(U1(d, e), f(c))
27.25/8.86	   A^2 -> H(U1(d, e), f(d))
27.25/8.86	   A^2 -> H(U1(d, c), U1(c, b))
27.25/8.86	   A^2 -> H(U1(d, c), U1(d, b))
27.25/8.86	   A^2 -> H(U1(d, c), U1(b, c))
27.25/8.86	   A^2 -> H(U1(d, c), U1(b, d))
27.25/8.86	   A^2 -> H(U1(d, c), U1(c, c))
27.25/8.86	   A^2 -> H(U1(d, c), f(e))
27.25/8.86	   A^2 -> H(U1(d, c), f(k))
27.25/8.86	   A^2 -> H(U1(d, c), U1(d, d))
27.25/8.86	   A^2 -> H(U1(d, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(d, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(d, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(d, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(d, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(d, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(d, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(d, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(d, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(d, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(a, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(a, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(a, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(a, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(a, e), U1(c, c))
27.25/8.86	   A^2 -> H(U1(a, e), f(e))
27.25/8.86	   A^2 -> H(U1(a, e), f(k))
27.25/8.86	   A^2 -> H(U1(a, e), U1(d, d))
27.25/8.86	   A^2 -> H(U1(a, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(a, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(a, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(a, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(a, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(a, k), f(e))
27.25/8.86	   A^2 -> H(U1(a, k), f(k))
27.25/8.86	   A^2 -> H(U1(a, k), U1(d, d))
27.25/8.86	   A^2 -> H(U1(a, c), U1(e, b))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, b))
27.25/8.86	   A^2 -> H(U1(a, c), U1(c, d))
27.25/8.86	   A^2 -> H(U1(a, c), U1(d, c))
27.25/8.86	   A^2 -> H(U1(a, c), U1(b, e))
27.25/8.86	   A^2 -> H(U1(a, c), U1(b, k))
27.25/8.86	   A^2 -> H(U1(a, c), U1(e, c))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, c))
27.25/8.86	   A^2 -> H(U1(a, c), U1(c, e))
27.25/8.86	   A^2 -> H(U1(a, c), U1(c, k))
27.25/8.86	   A^2 -> H(U1(a, c), U1(e, e))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, k))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, d))
27.25/8.86	   A^2 -> H(U1(a, c), U1(d, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(e, b))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, b))
27.25/8.86	   A^2 -> H(U1(a, d), U1(c, d))
27.25/8.86	   A^2 -> H(U1(a, d), U1(d, c))
27.25/8.86	   A^2 -> H(U1(a, d), U1(b, e))
27.25/8.86	   A^2 -> H(U1(a, d), U1(b, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(e, c))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, c))
27.25/8.86	   A^2 -> H(U1(a, d), U1(c, e))
27.25/8.86	   A^2 -> H(U1(a, d), U1(c, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(e, e))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, d))
27.25/8.86	   A^2 -> H(U1(a, d), U1(d, k))
27.25/8.86	   A^2 -> H(U1(a, a), b)
27.25/8.86	   A^2 -> H(U1(a, a), U1(e, d))
27.25/8.86	   A^2 -> H(U1(a, a), U1(d, e))
27.25/8.86	   A^2 -> H(U1(a, a), c)
27.25/8.86	   A^2 -> H(U1(a, a), U1(e, k))
27.25/8.86	   A^2 -> H(U1(a, a), U1(k, e))
27.25/8.86	   A^2 -> H(U1(a, a), e)
27.25/8.86	   A^2 -> H(U1(a, a), U1(k, k))
27.25/8.86	   A^2 -> H(k, f(b))
27.25/8.86	   A^2 -> H(c, U1(b, b))
27.25/8.86	   A^2 -> H(c, f(c))
27.25/8.86	   A^2 -> H(c, f(d))
27.25/8.86	   A^2 -> H(U1(e, k), U1(b, b))
27.25/8.86	   A^2 -> H(U1(e, k), f(c))
27.25/8.86	   A^2 -> H(U1(e, k), f(d))
27.25/8.86	   A^2 -> H(U1(e, c), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, c), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, c), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, c), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, c), U1(c, c))
27.25/8.86	   A^2 -> H(U1(e, c), f(e))
27.25/8.86	   A^2 -> H(U1(e, c), f(k))
27.25/8.86	   A^2 -> H(U1(e, c), U1(d, d))
27.25/8.86	   A^2 -> H(U1(k, e), U1(b, b))
27.25/8.86	   A^2 -> H(U1(k, e), f(c))
27.25/8.86	   A^2 -> H(U1(k, e), f(d))
27.25/8.86	   A^2 -> H(U1(k, c), U1(c, b))
27.25/8.86	   A^2 -> H(U1(k, c), U1(d, b))
27.25/8.86	   A^2 -> H(U1(k, c), U1(b, c))
27.25/8.86	   A^2 -> H(U1(k, c), U1(b, d))
27.25/8.86	   A^2 -> H(U1(k, c), U1(c, c))
27.25/8.86	   A^2 -> H(U1(k, c), f(e))
27.25/8.86	   A^2 -> H(U1(k, c), f(k))
27.25/8.86	   A^2 -> H(U1(k, c), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(c, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(c, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(c, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(c, e), U1(c, c))
27.25/8.86	   A^2 -> H(U1(c, e), f(e))
27.25/8.86	   A^2 -> H(U1(c, e), f(k))
27.25/8.86	   A^2 -> H(U1(c, e), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(c, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(c, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(c, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(c, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(c, k), f(e))
27.25/8.86	   A^2 -> H(U1(c, k), f(k))
27.25/8.86	   A^2 -> H(U1(c, k), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(e, b))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, b))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(d, c))
27.25/8.86	   A^2 -> H(U1(c, c), U1(b, e))
27.25/8.86	   A^2 -> H(U1(c, c), U1(b, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(e, e))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(d, k))
27.25/8.86	   A^2 -> H(e, U1(b, b))
27.25/8.86	   A^2 -> H(e, f(c))
27.25/8.86	   A^2 -> H(e, f(d))
27.25/8.86	   A^2 -> H(U1(e, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, e), U1(c, c))
27.25/8.86	   A^2 -> H(U1(e, e), f(e))
27.25/8.86	   A^2 -> H(U1(e, e), f(k))
27.25/8.86	   A^2 -> H(U1(e, e), U1(d, d))
27.25/8.86	   A^2 -> H(f(e), U1(e, b))
27.25/8.86	   A^2 -> H(f(e), U1(k, b))
27.25/8.86	   A^2 -> H(f(e), U1(c, d))
27.25/8.86	   A^2 -> H(f(e), U1(d, c))
27.25/8.86	   A^2 -> H(f(e), U1(b, e))
27.25/8.86	   A^2 -> H(f(e), U1(b, k))
27.25/8.86	   A^2 -> H(f(e), U1(e, c))
27.25/8.86	   A^2 -> H(f(e), U1(k, c))
27.25/8.86	   A^2 -> H(f(e), U1(c, e))
27.25/8.86	   A^2 -> H(f(e), U1(c, k))
27.25/8.86	   A^2 -> H(f(e), U1(k, k))
27.25/8.86	   A^2 -> H(f(e), U1(k, d))
27.25/8.86	   A^2 -> H(f(e), U1(d, k))
27.25/8.86	   A^2 -> H(U1(k, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(k, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(k, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(k, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(k, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(k, k), f(e))
27.25/8.86	   A^2 -> H(U1(k, k), f(k))
27.25/8.86	   A^2 -> H(U1(k, k), U1(d, d))
27.25/8.86	   A^2 -> H(f(k), U1(e, b))
27.25/8.86	   A^2 -> H(f(k), U1(k, b))
27.25/8.86	   A^2 -> H(f(k), U1(c, d))
27.25/8.86	   A^2 -> H(f(k), U1(d, c))
27.25/8.86	   A^2 -> H(f(k), U1(b, e))
27.25/8.86	   A^2 -> H(f(k), U1(b, k))
27.25/8.86	   A^2 -> H(f(k), U1(e, c))
27.25/8.86	   A^2 -> H(f(k), U1(k, c))
27.25/8.86	   A^2 -> H(f(k), U1(c, e))
27.25/8.86	   A^2 -> H(f(k), U1(c, k))
27.25/8.86	   A^2 -> H(f(k), U1(e, e))
27.25/8.86	   A^2 -> H(f(k), U1(k, d))
27.25/8.86	   A^2 -> H(f(k), U1(d, k))
27.25/8.86	   A^2 -> H(f(c), b)
27.25/8.86	   A^2 -> H(f(c), U1(e, d))
27.25/8.86	   A^2 -> H(f(c), U1(d, e))
27.25/8.86	   A^2 -> H(f(k), U1(k, k))
27.25/8.86	   A^2 -> H(U1(k, k), U1(b, b))
27.25/8.86	   A^2 -> H(U1(k, k), f(c))
27.25/8.86	   A^2 -> H(U1(k, k), f(d))
27.25/8.86	   A^2 -> H(U1(k, d), U1(c, b))
27.25/8.86	   A^2 -> H(U1(k, d), U1(d, b))
27.25/8.86	   A^2 -> H(U1(k, d), U1(b, c))
27.25/8.86	   A^2 -> H(U1(k, d), U1(b, d))
27.25/8.86	   A^2 -> H(U1(k, d), U1(c, c))
27.25/8.86	   A^2 -> H(U1(k, d), f(e))
27.25/8.86	   A^2 -> H(U1(k, d), f(k))
27.25/8.86	   A^2 -> H(U1(k, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(d, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(d, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(d, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(d, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(d, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(d, k), f(e))
27.25/8.86	   A^2 -> H(U1(d, k), f(k))
27.25/8.86	   A^2 -> H(U1(d, k), U1(d, d))
27.25/8.86	   A^2 -> H(U1(d, d), U1(e, b))
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, b))
27.25/8.86	   A^2 -> H(U1(d, d), U1(c, d))
27.25/8.86	   A^2 -> H(U1(d, d), U1(d, c))
27.25/8.86	   A^2 -> H(U1(d, d), U1(b, e))
27.25/8.86	   A^2 -> H(U1(d, d), U1(b, k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(e, c))
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, c))
27.25/8.86	   A^2 -> H(U1(d, d), U1(c, e))
27.25/8.86	   A^2 -> H(U1(d, d), U1(c, k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(e, e))
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, k))
27.25/8.86	   A^2 -> H(f(d), b)
27.25/8.86	   A^2 -> H(f(d), U1(e, d))
27.25/8.86	   A^2 -> H(f(d), U1(d, e))
27.25/8.86	   A^2 -> H(f(d), c)
27.25/8.86	   A^2 -> H(f(d), U1(e, k))
27.25/8.86	   A^2 -> H(f(d), U1(k, e))
27.25/8.86	   A^2 -> H(f(d), e)
27.25/8.86	   A^2 -> H(f(a), d)
27.25/8.86	   A^2 -> H(U1(c, c), U1(e, c))
27.25/8.86	   A^2 -> H(f(c), c)
27.25/8.86	   A^2 -> H(f(c), U1(e, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, c))
27.25/8.86	   A^2 -> H(f(c), U1(k, e))
27.25/8.86	   A^2 -> H(f(c), U1(k, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, e))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, k))
27.25/8.86	   A^2 -> H(f(a), k)
27.25/8.86	   A^2 -> H(f(e), U1(e, e))
27.25/8.86	   A^2 -> H(f(c), e)
27.25/8.86	   A^2 -> H(U1(d, d), U1(k, d))
27.25/8.86	   A^2 -> H(f(d), U1(k, k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(d, k))
27.25/8.86	   A^2 -> H(d, U1(b, b))
27.25/8.86	   A^2 -> H(d, f(c))
27.25/8.86	   A^2 -> H(d, f(d))
27.25/8.86	   A^2 -> H(a, U1(c, b))
27.25/8.86	   A^2 -> H(a, U1(d, b))
27.25/8.86	   A^2 -> H(a, U1(b, c))
27.25/8.86	   A^2 -> H(a, U1(b, d))
27.25/8.86	   A^2 -> H(a, U1(c, c))
27.25/8.86	   A^2 -> H(a, f(e))
27.25/8.86	   A^2 -> H(a, f(k))
27.25/8.86	   A^2 -> H(a, U1(d, d))
27.25/8.86	   A^2 -> H(U1(e, d), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, d), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, d), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, d), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, d), U1(c, c))
27.25/8.86	   A^2 -> H(U1(e, d), f(e))
27.25/8.86	   A^2 -> H(U1(e, d), f(k))
27.25/8.86	   A^2 -> H(U1(e, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(e, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(e, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(e, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(e, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(e, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(e, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(e, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(e, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(e, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(e, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(e, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(k, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(k, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(k, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(k, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(k, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(k, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(k, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(k, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(c, d), U1(e, b))
27.25/8.86	   A^2 -> H(U1(c, d), U1(k, b))
27.25/8.86	   A^2 -> H(U1(c, d), U1(c, d))
27.25/8.86	   A^2 -> H(U1(c, d), U1(d, c))
27.25/8.86	   A^2 -> H(U1(c, d), U1(b, e))
27.25/8.86	   A^2 -> H(U1(c, d), U1(b, k))
27.25/8.86	   A^2 -> H(U1(c, d), U1(e, c))
27.25/8.86	   A^2 -> H(U1(c, d), U1(k, c))
27.25/8.86	   A^2 -> H(U1(c, d), U1(c, e))
27.25/8.86	   A^2 -> H(U1(c, d), U1(c, k))
27.25/8.86	   A^2 -> H(U1(c, d), U1(e, e))
27.25/8.86	
27.25/8.86	The TRS R consists of the following rules:
27.25/8.86	
27.25/8.86	   f(x) -> U1(x, x)
27.25/8.86	   U1(e, x) -> x
27.25/8.86	   a -> c
27.25/8.86	   a -> d
27.25/8.86	   b -> c
27.25/8.86	   b -> d
27.25/8.86	   d -> k
27.25/8.86	   c -> e
27.25/8.86	   c -> k
27.25/8.86	
27.25/8.86	Q is empty.
27.25/8.86	We have to consider all minimal (P,Q,R)-chains.
27.25/8.86	----------------------------------------
27.25/8.86	
27.25/8.86	(599) TransformationProof (EQUIVALENT)
27.25/8.86	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), f(k)) at position [] we obtained the following new rules [LPAR04]:
27.25/8.86	
27.25/8.86	   (A^2 -> H(U1(e, d), f(k)),A^2 -> H(U1(e, d), f(k)))
27.25/8.86	   (A^2 -> H(U1(k, d), f(k)),A^2 -> H(U1(k, d), f(k)))
27.25/8.86	   (A^2 -> H(U1(c, k), f(k)),A^2 -> H(U1(c, k), f(k)))
27.25/8.86	   (A^2 -> H(U1(c, d), U1(k, k)),A^2 -> H(U1(c, d), U1(k, k)))
27.25/8.86	
27.25/8.86	
27.25/8.86	----------------------------------------
27.25/8.86	
27.25/8.86	(600)
27.25/8.86	Obligation:
27.25/8.86	Q DP problem:
27.25/8.86	The TRS P consists of the following rules:
27.25/8.86	
27.25/8.86	   H(x, x) -> G(x, x, f(k))
27.25/8.86	   G(d, x, x) -> A^2
27.25/8.86	   A^2 -> H(f(c), f(c))
27.25/8.86	   A^2 -> H(f(d), f(d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, c))
27.25/8.86	   A^2 -> H(f(e), f(e))
27.25/8.86	   A^2 -> H(f(k), f(k))
27.25/8.86	   A^2 -> H(U1(d, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, d), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(c, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(c, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(c, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(c, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(c, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(c, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(c, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(c, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(c, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(c, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(d, e), U1(b, b))
27.25/8.86	   A^2 -> H(U1(d, e), f(c))
27.25/8.86	   A^2 -> H(U1(d, e), f(d))
27.25/8.86	   A^2 -> H(U1(d, c), U1(c, b))
27.25/8.86	   A^2 -> H(U1(d, c), U1(d, b))
27.25/8.86	   A^2 -> H(U1(d, c), U1(b, c))
27.25/8.86	   A^2 -> H(U1(d, c), U1(b, d))
27.25/8.86	   A^2 -> H(U1(d, c), U1(c, c))
27.25/8.86	   A^2 -> H(U1(d, c), f(e))
27.25/8.86	   A^2 -> H(U1(d, c), f(k))
27.25/8.86	   A^2 -> H(U1(d, c), U1(d, d))
27.25/8.86	   A^2 -> H(U1(d, a), U1(e, b))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, b))
27.25/8.86	   A^2 -> H(U1(d, a), U1(c, d))
27.25/8.86	   A^2 -> H(U1(d, a), U1(d, c))
27.25/8.86	   A^2 -> H(U1(d, a), U1(b, e))
27.25/8.86	   A^2 -> H(U1(d, a), U1(b, k))
27.25/8.86	   A^2 -> H(U1(d, a), U1(e, c))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, c))
27.25/8.86	   A^2 -> H(U1(d, a), U1(c, e))
27.25/8.86	   A^2 -> H(U1(d, a), U1(c, k))
27.25/8.86	   A^2 -> H(U1(d, a), U1(e, e))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, k))
27.25/8.86	   A^2 -> H(U1(d, a), U1(k, d))
27.25/8.86	   A^2 -> H(U1(d, a), U1(d, k))
27.25/8.86	   A^2 -> H(U1(a, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(a, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(a, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(a, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(a, e), U1(c, c))
27.25/8.86	   A^2 -> H(U1(a, e), f(e))
27.25/8.86	   A^2 -> H(U1(a, e), f(k))
27.25/8.86	   A^2 -> H(U1(a, e), U1(d, d))
27.25/8.86	   A^2 -> H(U1(a, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(a, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(a, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(a, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(a, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(a, k), f(e))
27.25/8.86	   A^2 -> H(U1(a, k), f(k))
27.25/8.86	   A^2 -> H(U1(a, k), U1(d, d))
27.25/8.86	   A^2 -> H(U1(a, c), U1(e, b))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, b))
27.25/8.86	   A^2 -> H(U1(a, c), U1(c, d))
27.25/8.86	   A^2 -> H(U1(a, c), U1(d, c))
27.25/8.86	   A^2 -> H(U1(a, c), U1(b, e))
27.25/8.86	   A^2 -> H(U1(a, c), U1(b, k))
27.25/8.86	   A^2 -> H(U1(a, c), U1(e, c))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, c))
27.25/8.86	   A^2 -> H(U1(a, c), U1(c, e))
27.25/8.86	   A^2 -> H(U1(a, c), U1(c, k))
27.25/8.86	   A^2 -> H(U1(a, c), U1(e, e))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, k))
27.25/8.86	   A^2 -> H(U1(a, c), U1(k, d))
27.25/8.86	   A^2 -> H(U1(a, c), U1(d, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(e, b))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, b))
27.25/8.86	   A^2 -> H(U1(a, d), U1(c, d))
27.25/8.86	   A^2 -> H(U1(a, d), U1(d, c))
27.25/8.86	   A^2 -> H(U1(a, d), U1(b, e))
27.25/8.86	   A^2 -> H(U1(a, d), U1(b, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(e, c))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, c))
27.25/8.86	   A^2 -> H(U1(a, d), U1(c, e))
27.25/8.86	   A^2 -> H(U1(a, d), U1(c, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(e, e))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, k))
27.25/8.86	   A^2 -> H(U1(a, d), U1(k, d))
27.25/8.86	   A^2 -> H(U1(a, d), U1(d, k))
27.25/8.86	   A^2 -> H(U1(a, a), b)
27.25/8.86	   A^2 -> H(U1(a, a), U1(e, d))
27.25/8.86	   A^2 -> H(U1(a, a), U1(d, e))
27.25/8.86	   A^2 -> H(U1(a, a), c)
27.25/8.86	   A^2 -> H(U1(a, a), U1(e, k))
27.25/8.86	   A^2 -> H(U1(a, a), U1(k, e))
27.25/8.86	   A^2 -> H(U1(a, a), e)
27.25/8.86	   A^2 -> H(U1(a, a), U1(k, k))
27.25/8.86	   A^2 -> H(k, f(b))
27.25/8.86	   A^2 -> H(c, U1(b, b))
27.25/8.86	   A^2 -> H(c, f(c))
27.25/8.86	   A^2 -> H(c, f(d))
27.25/8.86	   A^2 -> H(U1(e, k), U1(b, b))
27.25/8.86	   A^2 -> H(U1(e, k), f(c))
27.25/8.86	   A^2 -> H(U1(e, k), f(d))
27.25/8.86	   A^2 -> H(U1(e, c), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, c), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, c), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, c), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, c), U1(c, c))
27.25/8.86	   A^2 -> H(U1(e, c), f(e))
27.25/8.86	   A^2 -> H(U1(e, c), f(k))
27.25/8.86	   A^2 -> H(U1(e, c), U1(d, d))
27.25/8.86	   A^2 -> H(U1(k, e), U1(b, b))
27.25/8.86	   A^2 -> H(U1(k, e), f(c))
27.25/8.86	   A^2 -> H(U1(k, e), f(d))
27.25/8.86	   A^2 -> H(U1(k, c), U1(c, b))
27.25/8.86	   A^2 -> H(U1(k, c), U1(d, b))
27.25/8.86	   A^2 -> H(U1(k, c), U1(b, c))
27.25/8.86	   A^2 -> H(U1(k, c), U1(b, d))
27.25/8.86	   A^2 -> H(U1(k, c), U1(c, c))
27.25/8.86	   A^2 -> H(U1(k, c), f(e))
27.25/8.86	   A^2 -> H(U1(k, c), f(k))
27.25/8.86	   A^2 -> H(U1(k, c), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(c, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(c, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(c, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(c, e), U1(c, c))
27.25/8.86	   A^2 -> H(U1(c, e), f(e))
27.25/8.86	   A^2 -> H(U1(c, e), f(k))
27.25/8.86	   A^2 -> H(U1(c, e), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, k), U1(c, b))
27.25/8.86	   A^2 -> H(U1(c, k), U1(d, b))
27.25/8.86	   A^2 -> H(U1(c, k), U1(b, c))
27.25/8.86	   A^2 -> H(U1(c, k), U1(b, d))
27.25/8.86	   A^2 -> H(U1(c, k), U1(c, c))
27.25/8.86	   A^2 -> H(U1(c, k), f(e))
27.25/8.86	   A^2 -> H(U1(c, k), f(k))
27.25/8.86	   A^2 -> H(U1(c, k), U1(d, d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(e, b))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, b))
27.25/8.86	   A^2 -> H(U1(c, c), U1(c, d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(d, c))
27.25/8.86	   A^2 -> H(U1(c, c), U1(b, e))
27.25/8.86	   A^2 -> H(U1(c, c), U1(b, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(e, e))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, k))
27.25/8.86	   A^2 -> H(U1(c, c), U1(k, d))
27.25/8.86	   A^2 -> H(U1(c, c), U1(d, k))
27.25/8.86	   A^2 -> H(e, U1(b, b))
27.25/8.86	   A^2 -> H(e, f(c))
27.25/8.86	   A^2 -> H(e, f(d))
27.25/8.86	   A^2 -> H(U1(e, e), U1(c, b))
27.25/8.86	   A^2 -> H(U1(e, e), U1(d, b))
27.25/8.86	   A^2 -> H(U1(e, e), U1(b, c))
27.25/8.86	   A^2 -> H(U1(e, e), U1(b, d))
27.25/8.86	   A^2 -> H(U1(e, e), U1(c, c))
27.25/8.87	   A^2 -> H(U1(e, e), f(e))
27.25/8.87	   A^2 -> H(U1(e, e), f(k))
27.25/8.87	   A^2 -> H(U1(e, e), U1(d, d))
27.25/8.87	   A^2 -> H(f(e), U1(e, b))
27.25/8.87	   A^2 -> H(f(e), U1(k, b))
27.25/8.87	   A^2 -> H(f(e), U1(c, d))
27.25/8.87	   A^2 -> H(f(e), U1(d, c))
27.25/8.87	   A^2 -> H(f(e), U1(b, e))
27.25/8.87	   A^2 -> H(f(e), U1(b, k))
27.25/8.87	   A^2 -> H(f(e), U1(e, c))
27.25/8.87	   A^2 -> H(f(e), U1(k, c))
27.25/8.87	   A^2 -> H(f(e), U1(c, e))
27.25/8.87	   A^2 -> H(f(e), U1(c, k))
27.25/8.87	   A^2 -> H(f(e), U1(k, k))
27.25/8.87	   A^2 -> H(f(e), U1(k, d))
27.25/8.87	   A^2 -> H(f(e), U1(d, k))
27.25/8.87	   A^2 -> H(U1(k, k), U1(c, b))
27.25/8.87	   A^2 -> H(U1(k, k), U1(d, b))
27.25/8.87	   A^2 -> H(U1(k, k), U1(b, c))
27.25/8.87	   A^2 -> H(U1(k, k), U1(b, d))
27.25/8.87	   A^2 -> H(U1(k, k), U1(c, c))
27.25/8.87	   A^2 -> H(U1(k, k), f(e))
27.25/8.87	   A^2 -> H(U1(k, k), f(k))
27.25/8.87	   A^2 -> H(U1(k, k), U1(d, d))
27.25/8.87	   A^2 -> H(f(k), U1(e, b))
27.25/8.87	   A^2 -> H(f(k), U1(k, b))
27.25/8.87	   A^2 -> H(f(k), U1(c, d))
27.25/8.87	   A^2 -> H(f(k), U1(d, c))
27.25/8.87	   A^2 -> H(f(k), U1(b, e))
27.25/8.87	   A^2 -> H(f(k), U1(b, k))
27.25/8.87	   A^2 -> H(f(k), U1(e, c))
27.25/8.87	   A^2 -> H(f(k), U1(k, c))
27.25/8.87	   A^2 -> H(f(k), U1(c, e))
27.25/8.87	   A^2 -> H(f(k), U1(c, k))
27.25/8.87	   A^2 -> H(f(k), U1(e, e))
27.25/8.87	   A^2 -> H(f(k), U1(k, d))
27.25/8.87	   A^2 -> H(f(k), U1(d, k))
27.25/8.87	   A^2 -> H(f(c), b)
27.25/8.87	   A^2 -> H(f(c), U1(e, d))
27.25/8.87	   A^2 -> H(f(c), U1(d, e))
27.25/8.87	   A^2 -> H(f(k), U1(k, k))
27.25/8.87	   A^2 -> H(U1(k, k), U1(b, b))
27.25/8.87	   A^2 -> H(U1(k, k), f(c))
27.25/8.87	   A^2 -> H(U1(k, k), f(d))
27.25/8.87	   A^2 -> H(U1(k, d), U1(c, b))
27.25/8.87	   A^2 -> H(U1(k, d), U1(d, b))
27.25/8.87	   A^2 -> H(U1(k, d), U1(b, c))
27.25/8.87	   A^2 -> H(U1(k, d), U1(b, d))
27.25/8.87	   A^2 -> H(U1(k, d), U1(c, c))
27.25/8.87	   A^2 -> H(U1(k, d), f(e))
27.25/8.87	   A^2 -> H(U1(k, d), f(k))
27.25/8.87	   A^2 -> H(U1(k, d), U1(d, d))
27.25/8.87	   A^2 -> H(U1(d, k), U1(c, b))
27.25/8.87	   A^2 -> H(U1(d, k), U1(d, b))
27.25/8.87	   A^2 -> H(U1(d, k), U1(b, c))
27.25/8.87	   A^2 -> H(U1(d, k), U1(b, d))
27.25/8.87	   A^2 -> H(U1(d, k), U1(c, c))
27.25/8.87	   A^2 -> H(U1(d, k), f(e))
27.25/8.87	   A^2 -> H(U1(d, k), f(k))
27.25/8.87	   A^2 -> H(U1(d, k), U1(d, d))
27.25/8.87	   A^2 -> H(U1(d, d), U1(e, b))
27.25/8.87	   A^2 -> H(U1(d, d), U1(k, b))
27.25/8.87	   A^2 -> H(U1(d, d), U1(c, d))
27.25/8.87	   A^2 -> H(U1(d, d), U1(d, c))
27.25/8.87	   A^2 -> H(U1(d, d), U1(b, e))
27.25/8.87	   A^2 -> H(U1(d, d), U1(b, k))
27.25/8.87	   A^2 -> H(U1(d, d), U1(e, c))
27.25/8.87	   A^2 -> H(U1(d, d), U1(k, c))
27.25/8.87	   A^2 -> H(U1(d, d), U1(c, e))
27.25/8.87	   A^2 -> H(U1(d, d), U1(c, k))
27.25/8.87	   A^2 -> H(U1(d, d), U1(e, e))
27.25/8.87	   A^2 -> H(U1(d, d), U1(k, k))
27.25/8.87	   A^2 -> H(f(d), b)
27.25/8.87	   A^2 -> H(f(d), U1(e, d))
27.25/8.87	   A^2 -> H(f(d), U1(d, e))
27.25/8.87	   A^2 -> H(f(d), c)
27.25/8.87	   A^2 -> H(f(d), U1(e, k))
27.25/8.87	   A^2 -> H(f(d), U1(k, e))
27.25/8.87	   A^2 -> H(f(d), e)
27.25/8.87	   A^2 -> H(f(a), d)
27.25/8.87	   A^2 -> H(U1(c, c), U1(e, c))
27.25/8.87	   A^2 -> H(f(c), c)
27.25/8.87	   A^2 -> H(f(c), U1(e, k))
27.25/8.87	   A^2 -> H(U1(c, c), U1(k, c))
27.25/8.87	   A^2 -> H(f(c), U1(k, e))
27.25/8.87	   A^2 -> H(f(c), U1(k, k))
27.25/8.87	   A^2 -> H(U1(c, c), U1(c, e))
27.25/8.87	   A^2 -> H(U1(c, c), U1(c, k))
27.25/8.87	   A^2 -> H(f(a), k)
27.25/8.87	   A^2 -> H(f(e), U1(e, e))
27.25/8.87	   A^2 -> H(f(c), e)
27.25/8.87	   A^2 -> H(U1(d, d), U1(k, d))
27.25/8.87	   A^2 -> H(f(d), U1(k, k))
27.25/8.87	   A^2 -> H(U1(d, d), U1(d, k))
27.25/8.87	   A^2 -> H(d, U1(b, b))
27.25/8.87	   A^2 -> H(d, f(c))
27.25/8.87	   A^2 -> H(d, f(d))
27.25/8.87	   A^2 -> H(a, U1(c, b))
27.25/8.87	   A^2 -> H(a, U1(d, b))
27.25/8.87	   A^2 -> H(a, U1(b, c))
27.25/8.87	   A^2 -> H(a, U1(b, d))
27.25/8.87	   A^2 -> H(a, U1(c, c))
27.25/8.87	   A^2 -> H(a, f(e))
27.25/8.87	   A^2 -> H(a, f(k))
27.25/8.87	   A^2 -> H(a, U1(d, d))
27.25/8.87	   A^2 -> H(U1(e, d), U1(c, b))
27.25/8.87	   A^2 -> H(U1(e, d), U1(d, b))
27.25/8.87	   A^2 -> H(U1(e, d), U1(b, c))
27.25/8.87	   A^2 -> H(U1(e, d), U1(b, d))
27.25/8.87	   A^2 -> H(U1(e, d), U1(c, c))
27.25/8.87	   A^2 -> H(U1(e, d), f(e))
27.25/8.87	   A^2 -> H(U1(e, d), f(k))
27.25/8.87	   A^2 -> H(U1(e, d), U1(d, d))
27.25/8.87	   A^2 -> H(U1(e, a), U1(e, b))
27.25/8.87	   A^2 -> H(U1(e, a), U1(k, b))
27.25/8.87	   A^2 -> H(U1(e, a), U1(c, d))
27.25/8.87	   A^2 -> H(U1(e, a), U1(d, c))
27.25/8.87	   A^2 -> H(U1(e, a), U1(b, e))
27.25/8.87	   A^2 -> H(U1(e, a), U1(b, k))
27.25/8.87	   A^2 -> H(U1(e, a), U1(e, c))
27.25/8.87	   A^2 -> H(U1(e, a), U1(k, c))
27.25/8.87	   A^2 -> H(U1(e, a), U1(c, e))
27.25/8.87	   A^2 -> H(U1(e, a), U1(c, k))
27.25/8.87	   A^2 -> H(U1(e, a), U1(e, e))
27.25/8.87	   A^2 -> H(U1(e, a), U1(k, k))
27.25/8.87	   A^2 -> H(U1(e, a), U1(k, d))
27.25/8.87	   A^2 -> H(U1(e, a), U1(d, k))
27.25/8.87	   A^2 -> H(U1(k, a), U1(e, b))
27.25/8.87	   A^2 -> H(U1(k, a), U1(k, b))
27.25/8.87	   A^2 -> H(U1(k, a), U1(c, d))
27.25/8.87	   A^2 -> H(U1(k, a), U1(d, c))
27.25/8.87	   A^2 -> H(U1(k, a), U1(b, e))
27.25/8.87	   A^2 -> H(U1(k, a), U1(b, k))
27.25/8.87	   A^2 -> H(U1(k, a), U1(e, c))
27.25/8.87	   A^2 -> H(U1(k, a), U1(k, c))
27.25/8.87	   A^2 -> H(U1(k, a), U1(c, e))
27.25/8.87	   A^2 -> H(U1(k, a), U1(c, k))
27.25/8.87	   A^2 -> H(U1(k, a), U1(e, e))
27.25/8.87	   A^2 -> H(U1(k, a), U1(k, k))
27.25/8.87	   A^2 -> H(U1(k, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(k, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(e, b))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, b))
27.32/8.89	   A^2 -> H(U1(c, d), U1(c, d))
27.32/8.89	   A^2 -> H(U1(c, d), U1(d, c))
27.32/8.89	   A^2 -> H(U1(c, d), U1(b, e))
27.32/8.89	   A^2 -> H(U1(c, d), U1(b, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(e, c))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, c))
27.32/8.89	   A^2 -> H(U1(c, d), U1(c, e))
27.32/8.89	   A^2 -> H(U1(c, d), U1(c, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(e, e))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, k))
27.32/8.89	
27.32/8.89	The TRS R consists of the following rules:
27.32/8.89	
27.32/8.89	   f(x) -> U1(x, x)
27.32/8.89	   U1(e, x) -> x
27.32/8.89	   a -> c
27.32/8.89	   a -> d
27.32/8.89	   b -> c
27.32/8.89	   b -> d
27.32/8.89	   d -> k
27.32/8.89	   c -> e
27.32/8.89	   c -> k
27.32/8.89	
27.32/8.89	Q is empty.
27.32/8.89	We have to consider all minimal (P,Q,R)-chains.
27.32/8.89	----------------------------------------
27.32/8.89	
27.32/8.89	(601) TransformationProof (EQUIVALENT)
27.32/8.89	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
27.32/8.89	
27.32/8.89	   (A^2 -> H(U1(e, d), U1(d, d)),A^2 -> H(U1(e, d), U1(d, d)))
27.32/8.89	   (A^2 -> H(U1(k, d), U1(d, d)),A^2 -> H(U1(k, d), U1(d, d)))
27.32/8.89	   (A^2 -> H(U1(c, k), U1(d, d)),A^2 -> H(U1(c, k), U1(d, d)))
27.32/8.89	   (A^2 -> H(U1(c, d), U1(k, d)),A^2 -> H(U1(c, d), U1(k, d)))
27.32/8.89	   (A^2 -> H(U1(c, d), U1(d, k)),A^2 -> H(U1(c, d), U1(d, k)))
27.32/8.89	
27.32/8.89	
27.32/8.89	----------------------------------------
27.32/8.89	
27.32/8.89	(602)
27.32/8.89	Obligation:
27.32/8.89	Q DP problem:
27.32/8.89	The TRS P consists of the following rules:
27.32/8.89	
27.32/8.89	   H(x, x) -> G(x, x, f(k))
27.32/8.89	   G(d, x, x) -> A^2
27.32/8.89	   A^2 -> H(f(c), f(c))
27.32/8.89	   A^2 -> H(f(d), f(d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, c))
27.32/8.89	   A^2 -> H(f(e), f(e))
27.32/8.89	   A^2 -> H(f(k), f(k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, a), U1(e, b))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(c, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(c, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(c, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(c, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(c, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(c, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(c, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(c, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(c, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(d, e), U1(b, b))
27.32/8.89	   A^2 -> H(U1(d, e), f(c))
27.32/8.89	   A^2 -> H(U1(d, e), f(d))
27.32/8.89	   A^2 -> H(U1(d, c), U1(c, b))
27.32/8.89	   A^2 -> H(U1(d, c), U1(d, b))
27.32/8.89	   A^2 -> H(U1(d, c), U1(b, c))
27.32/8.89	   A^2 -> H(U1(d, c), U1(b, d))
27.32/8.89	   A^2 -> H(U1(d, c), U1(c, c))
27.32/8.89	   A^2 -> H(U1(d, c), f(e))
27.32/8.89	   A^2 -> H(U1(d, c), f(k))
27.32/8.89	   A^2 -> H(U1(d, c), U1(d, d))
27.32/8.89	   A^2 -> H(U1(d, a), U1(e, b))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(d, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(d, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(d, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(d, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(d, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(d, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(d, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(d, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(d, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(a, e), U1(c, b))
27.32/8.89	   A^2 -> H(U1(a, e), U1(d, b))
27.32/8.89	   A^2 -> H(U1(a, e), U1(b, c))
27.32/8.89	   A^2 -> H(U1(a, e), U1(b, d))
27.32/8.89	   A^2 -> H(U1(a, e), U1(c, c))
27.32/8.89	   A^2 -> H(U1(a, e), f(e))
27.32/8.89	   A^2 -> H(U1(a, e), f(k))
27.32/8.89	   A^2 -> H(U1(a, e), U1(d, d))
27.32/8.89	   A^2 -> H(U1(a, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(a, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(a, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(a, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(a, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(a, k), f(e))
27.32/8.89	   A^2 -> H(U1(a, k), f(k))
27.32/8.89	   A^2 -> H(U1(a, k), U1(d, d))
27.32/8.89	   A^2 -> H(U1(a, c), U1(e, b))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, b))
27.32/8.89	   A^2 -> H(U1(a, c), U1(c, d))
27.32/8.89	   A^2 -> H(U1(a, c), U1(d, c))
27.32/8.89	   A^2 -> H(U1(a, c), U1(b, e))
27.32/8.89	   A^2 -> H(U1(a, c), U1(b, k))
27.32/8.89	   A^2 -> H(U1(a, c), U1(e, c))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, c))
27.32/8.89	   A^2 -> H(U1(a, c), U1(c, e))
27.32/8.89	   A^2 -> H(U1(a, c), U1(c, k))
27.32/8.89	   A^2 -> H(U1(a, c), U1(e, e))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, k))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, d))
27.32/8.89	   A^2 -> H(U1(a, c), U1(d, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(e, b))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, b))
27.32/8.89	   A^2 -> H(U1(a, d), U1(c, d))
27.32/8.89	   A^2 -> H(U1(a, d), U1(d, c))
27.32/8.89	   A^2 -> H(U1(a, d), U1(b, e))
27.32/8.89	   A^2 -> H(U1(a, d), U1(b, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(e, c))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, c))
27.32/8.89	   A^2 -> H(U1(a, d), U1(c, e))
27.32/8.89	   A^2 -> H(U1(a, d), U1(c, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(e, e))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, d))
27.32/8.89	   A^2 -> H(U1(a, d), U1(d, k))
27.32/8.89	   A^2 -> H(U1(a, a), b)
27.32/8.89	   A^2 -> H(U1(a, a), U1(e, d))
27.32/8.89	   A^2 -> H(U1(a, a), U1(d, e))
27.32/8.89	   A^2 -> H(U1(a, a), c)
27.32/8.89	   A^2 -> H(U1(a, a), U1(e, k))
27.32/8.89	   A^2 -> H(U1(a, a), U1(k, e))
27.32/8.89	   A^2 -> H(U1(a, a), e)
27.32/8.89	   A^2 -> H(U1(a, a), U1(k, k))
27.32/8.89	   A^2 -> H(k, f(b))
27.32/8.89	   A^2 -> H(c, U1(b, b))
27.32/8.89	   A^2 -> H(c, f(c))
27.32/8.89	   A^2 -> H(c, f(d))
27.32/8.89	   A^2 -> H(U1(e, k), U1(b, b))
27.32/8.89	   A^2 -> H(U1(e, k), f(c))
27.32/8.89	   A^2 -> H(U1(e, k), f(d))
27.32/8.89	   A^2 -> H(U1(e, c), U1(c, b))
27.32/8.89	   A^2 -> H(U1(e, c), U1(d, b))
27.32/8.89	   A^2 -> H(U1(e, c), U1(b, c))
27.32/8.89	   A^2 -> H(U1(e, c), U1(b, d))
27.32/8.89	   A^2 -> H(U1(e, c), U1(c, c))
27.32/8.89	   A^2 -> H(U1(e, c), f(e))
27.32/8.89	   A^2 -> H(U1(e, c), f(k))
27.32/8.89	   A^2 -> H(U1(e, c), U1(d, d))
27.32/8.89	   A^2 -> H(U1(k, e), U1(b, b))
27.32/8.89	   A^2 -> H(U1(k, e), f(c))
27.32/8.89	   A^2 -> H(U1(k, e), f(d))
27.32/8.89	   A^2 -> H(U1(k, c), U1(c, b))
27.32/8.89	   A^2 -> H(U1(k, c), U1(d, b))
27.32/8.89	   A^2 -> H(U1(k, c), U1(b, c))
27.32/8.89	   A^2 -> H(U1(k, c), U1(b, d))
27.32/8.89	   A^2 -> H(U1(k, c), U1(c, c))
27.32/8.89	   A^2 -> H(U1(k, c), f(e))
27.32/8.89	   A^2 -> H(U1(k, c), f(k))
27.32/8.89	   A^2 -> H(U1(k, c), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, e), U1(c, b))
27.32/8.89	   A^2 -> H(U1(c, e), U1(d, b))
27.32/8.89	   A^2 -> H(U1(c, e), U1(b, c))
27.32/8.89	   A^2 -> H(U1(c, e), U1(b, d))
27.32/8.89	   A^2 -> H(U1(c, e), U1(c, c))
27.32/8.89	   A^2 -> H(U1(c, e), f(e))
27.32/8.89	   A^2 -> H(U1(c, e), f(k))
27.32/8.89	   A^2 -> H(U1(c, e), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(c, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(c, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(c, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(c, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(c, k), f(e))
27.32/8.89	   A^2 -> H(U1(c, k), f(k))
27.32/8.89	   A^2 -> H(U1(c, k), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(e, b))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, b))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(d, c))
27.32/8.89	   A^2 -> H(U1(c, c), U1(b, e))
27.32/8.89	   A^2 -> H(U1(c, c), U1(b, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(e, e))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(d, k))
27.32/8.89	   A^2 -> H(e, U1(b, b))
27.32/8.89	   A^2 -> H(e, f(c))
27.32/8.89	   A^2 -> H(e, f(d))
27.32/8.89	   A^2 -> H(U1(e, e), U1(c, b))
27.32/8.89	   A^2 -> H(U1(e, e), U1(d, b))
27.32/8.89	   A^2 -> H(U1(e, e), U1(b, c))
27.32/8.89	   A^2 -> H(U1(e, e), U1(b, d))
27.32/8.89	   A^2 -> H(U1(e, e), U1(c, c))
27.32/8.89	   A^2 -> H(U1(e, e), f(e))
27.32/8.89	   A^2 -> H(U1(e, e), f(k))
27.32/8.89	   A^2 -> H(U1(e, e), U1(d, d))
27.32/8.89	   A^2 -> H(f(e), U1(e, b))
27.32/8.89	   A^2 -> H(f(e), U1(k, b))
27.32/8.89	   A^2 -> H(f(e), U1(c, d))
27.32/8.89	   A^2 -> H(f(e), U1(d, c))
27.32/8.89	   A^2 -> H(f(e), U1(b, e))
27.32/8.89	   A^2 -> H(f(e), U1(b, k))
27.32/8.89	   A^2 -> H(f(e), U1(e, c))
27.32/8.89	   A^2 -> H(f(e), U1(k, c))
27.32/8.89	   A^2 -> H(f(e), U1(c, e))
27.32/8.89	   A^2 -> H(f(e), U1(c, k))
27.32/8.89	   A^2 -> H(f(e), U1(k, k))
27.32/8.89	   A^2 -> H(f(e), U1(k, d))
27.32/8.89	   A^2 -> H(f(e), U1(d, k))
27.32/8.89	   A^2 -> H(U1(k, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(k, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(k, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(k, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(k, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(k, k), f(e))
27.32/8.89	   A^2 -> H(U1(k, k), f(k))
27.32/8.89	   A^2 -> H(U1(k, k), U1(d, d))
27.32/8.89	   A^2 -> H(f(k), U1(e, b))
27.32/8.89	   A^2 -> H(f(k), U1(k, b))
27.32/8.89	   A^2 -> H(f(k), U1(c, d))
27.32/8.89	   A^2 -> H(f(k), U1(d, c))
27.32/8.89	   A^2 -> H(f(k), U1(b, e))
27.32/8.89	   A^2 -> H(f(k), U1(b, k))
27.32/8.89	   A^2 -> H(f(k), U1(e, c))
27.32/8.89	   A^2 -> H(f(k), U1(k, c))
27.32/8.89	   A^2 -> H(f(k), U1(c, e))
27.32/8.89	   A^2 -> H(f(k), U1(c, k))
27.32/8.89	   A^2 -> H(f(k), U1(e, e))
27.32/8.89	   A^2 -> H(f(k), U1(k, d))
27.32/8.89	   A^2 -> H(f(k), U1(d, k))
27.32/8.89	   A^2 -> H(f(c), b)
27.32/8.89	   A^2 -> H(f(c), U1(e, d))
27.32/8.89	   A^2 -> H(f(c), U1(d, e))
27.32/8.89	   A^2 -> H(f(k), U1(k, k))
27.32/8.89	   A^2 -> H(U1(k, k), U1(b, b))
27.32/8.89	   A^2 -> H(U1(k, k), f(c))
27.32/8.89	   A^2 -> H(U1(k, k), f(d))
27.32/8.89	   A^2 -> H(U1(k, d), U1(c, b))
27.32/8.89	   A^2 -> H(U1(k, d), U1(d, b))
27.32/8.89	   A^2 -> H(U1(k, d), U1(b, c))
27.32/8.89	   A^2 -> H(U1(k, d), U1(b, d))
27.32/8.89	   A^2 -> H(U1(k, d), U1(c, c))
27.32/8.89	   A^2 -> H(U1(k, d), f(e))
27.32/8.89	   A^2 -> H(U1(k, d), f(k))
27.32/8.89	   A^2 -> H(U1(k, d), U1(d, d))
27.32/8.89	   A^2 -> H(U1(d, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(d, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(d, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(d, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(d, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(d, k), f(e))
27.32/8.89	   A^2 -> H(U1(d, k), f(k))
27.32/8.89	   A^2 -> H(U1(d, k), U1(d, d))
27.32/8.89	   A^2 -> H(U1(d, d), U1(e, b))
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, b))
27.32/8.89	   A^2 -> H(U1(d, d), U1(c, d))
27.32/8.89	   A^2 -> H(U1(d, d), U1(d, c))
27.32/8.89	   A^2 -> H(U1(d, d), U1(b, e))
27.32/8.89	   A^2 -> H(U1(d, d), U1(b, k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(e, c))
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, c))
27.32/8.89	   A^2 -> H(U1(d, d), U1(c, e))
27.32/8.89	   A^2 -> H(U1(d, d), U1(c, k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(e, e))
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, k))
27.32/8.89	   A^2 -> H(f(d), b)
27.32/8.89	   A^2 -> H(f(d), U1(e, d))
27.32/8.89	   A^2 -> H(f(d), U1(d, e))
27.32/8.89	   A^2 -> H(f(d), c)
27.32/8.89	   A^2 -> H(f(d), U1(e, k))
27.32/8.89	   A^2 -> H(f(d), U1(k, e))
27.32/8.89	   A^2 -> H(f(d), e)
27.32/8.89	   A^2 -> H(f(a), d)
27.32/8.89	   A^2 -> H(U1(c, c), U1(e, c))
27.32/8.89	   A^2 -> H(f(c), c)
27.32/8.89	   A^2 -> H(f(c), U1(e, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, c))
27.32/8.89	   A^2 -> H(f(c), U1(k, e))
27.32/8.89	   A^2 -> H(f(c), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, e))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, k))
27.32/8.89	   A^2 -> H(f(a), k)
27.32/8.89	   A^2 -> H(f(e), U1(e, e))
27.32/8.89	   A^2 -> H(f(c), e)
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, d))
27.32/8.89	   A^2 -> H(f(d), U1(k, k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(d, k))
27.32/8.89	   A^2 -> H(d, U1(b, b))
27.32/8.89	   A^2 -> H(d, f(c))
27.32/8.89	   A^2 -> H(d, f(d))
27.32/8.89	   A^2 -> H(a, U1(c, b))
27.32/8.89	   A^2 -> H(a, U1(d, b))
27.32/8.89	   A^2 -> H(a, U1(b, c))
27.32/8.89	   A^2 -> H(a, U1(b, d))
27.32/8.89	   A^2 -> H(a, U1(c, c))
27.32/8.89	   A^2 -> H(a, f(e))
27.32/8.89	   A^2 -> H(a, f(k))
27.32/8.89	   A^2 -> H(a, U1(d, d))
27.32/8.89	   A^2 -> H(U1(e, d), U1(c, b))
27.32/8.89	   A^2 -> H(U1(e, d), U1(d, b))
27.32/8.89	   A^2 -> H(U1(e, d), U1(b, c))
27.32/8.89	   A^2 -> H(U1(e, d), U1(b, d))
27.32/8.89	   A^2 -> H(U1(e, d), U1(c, c))
27.32/8.89	   A^2 -> H(U1(e, d), f(e))
27.32/8.89	   A^2 -> H(U1(e, d), f(k))
27.32/8.89	   A^2 -> H(U1(e, d), U1(d, d))
27.32/8.89	   A^2 -> H(U1(e, a), U1(e, b))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(e, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(e, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(e, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(e, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(e, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(e, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(e, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(e, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(e, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(e, b))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(k, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(k, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(k, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(k, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(k, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(k, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(k, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(e, b))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, b))
27.32/8.89	   A^2 -> H(U1(c, d), U1(c, d))
27.32/8.89	   A^2 -> H(U1(c, d), U1(d, c))
27.32/8.89	   A^2 -> H(U1(c, d), U1(b, e))
27.32/8.89	   A^2 -> H(U1(c, d), U1(b, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(e, c))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, c))
27.32/8.89	   A^2 -> H(U1(c, d), U1(c, e))
27.32/8.89	   A^2 -> H(U1(c, d), U1(c, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(e, e))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, d))
27.32/8.89	   A^2 -> H(U1(c, d), U1(d, k))
27.32/8.89	
27.32/8.89	The TRS R consists of the following rules:
27.32/8.89	
27.32/8.89	   f(x) -> U1(x, x)
27.32/8.89	   U1(e, x) -> x
27.32/8.89	   a -> c
27.32/8.89	   a -> d
27.32/8.89	   b -> c
27.32/8.89	   b -> d
27.32/8.89	   d -> k
27.32/8.89	   c -> e
27.32/8.89	   c -> k
27.32/8.89	
27.32/8.89	Q is empty.
27.32/8.89	We have to consider all minimal (P,Q,R)-chains.
27.32/8.89	----------------------------------------
27.32/8.89	
27.32/8.89	(603) TransformationProof (EQUIVALENT)
27.32/8.89	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
27.32/8.89	
27.32/8.89	   (A^2 -> H(U1(e, a), U1(e, b)),A^2 -> H(U1(e, a), U1(e, b)))
27.32/8.89	   (A^2 -> H(U1(k, a), U1(e, b)),A^2 -> H(U1(k, a), U1(e, b)))
27.32/8.89	   (A^2 -> H(U1(c, c), U1(e, b)),A^2 -> H(U1(c, c), U1(e, b)))
27.32/8.89	   (A^2 -> H(U1(c, d), U1(e, b)),A^2 -> H(U1(c, d), U1(e, b)))
27.32/8.89	   (A^2 -> H(U1(c, a), b),A^2 -> H(U1(c, a), b))
27.32/8.89	   (A^2 -> H(U1(c, a), U1(e, c)),A^2 -> H(U1(c, a), U1(e, c)))
27.32/8.89	   (A^2 -> H(U1(c, a), U1(e, d)),A^2 -> H(U1(c, a), U1(e, d)))
27.32/8.89	
27.32/8.89	
27.32/8.89	----------------------------------------
27.32/8.89	
27.32/8.89	(604)
27.32/8.89	Obligation:
27.32/8.89	Q DP problem:
27.32/8.89	The TRS P consists of the following rules:
27.32/8.89	
27.32/8.89	   H(x, x) -> G(x, x, f(k))
27.32/8.89	   G(d, x, x) -> A^2
27.32/8.89	   A^2 -> H(f(c), f(c))
27.32/8.89	   A^2 -> H(f(d), f(d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, c))
27.32/8.89	   A^2 -> H(f(e), f(e))
27.32/8.89	   A^2 -> H(f(k), f(k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(c, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(c, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(c, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(c, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(c, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(c, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(c, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(c, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(c, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(d, e), U1(b, b))
27.32/8.89	   A^2 -> H(U1(d, e), f(c))
27.32/8.89	   A^2 -> H(U1(d, e), f(d))
27.32/8.89	   A^2 -> H(U1(d, c), U1(c, b))
27.32/8.89	   A^2 -> H(U1(d, c), U1(d, b))
27.32/8.89	   A^2 -> H(U1(d, c), U1(b, c))
27.32/8.89	   A^2 -> H(U1(d, c), U1(b, d))
27.32/8.89	   A^2 -> H(U1(d, c), U1(c, c))
27.32/8.89	   A^2 -> H(U1(d, c), f(e))
27.32/8.89	   A^2 -> H(U1(d, c), f(k))
27.32/8.89	   A^2 -> H(U1(d, c), U1(d, d))
27.32/8.89	   A^2 -> H(U1(d, a), U1(e, b))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(d, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(d, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(d, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(d, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(d, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(d, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(d, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(d, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(d, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(a, e), U1(c, b))
27.32/8.89	   A^2 -> H(U1(a, e), U1(d, b))
27.32/8.89	   A^2 -> H(U1(a, e), U1(b, c))
27.32/8.89	   A^2 -> H(U1(a, e), U1(b, d))
27.32/8.89	   A^2 -> H(U1(a, e), U1(c, c))
27.32/8.89	   A^2 -> H(U1(a, e), f(e))
27.32/8.89	   A^2 -> H(U1(a, e), f(k))
27.32/8.89	   A^2 -> H(U1(a, e), U1(d, d))
27.32/8.89	   A^2 -> H(U1(a, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(a, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(a, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(a, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(a, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(a, k), f(e))
27.32/8.89	   A^2 -> H(U1(a, k), f(k))
27.32/8.89	   A^2 -> H(U1(a, k), U1(d, d))
27.32/8.89	   A^2 -> H(U1(a, c), U1(e, b))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, b))
27.32/8.89	   A^2 -> H(U1(a, c), U1(c, d))
27.32/8.89	   A^2 -> H(U1(a, c), U1(d, c))
27.32/8.89	   A^2 -> H(U1(a, c), U1(b, e))
27.32/8.89	   A^2 -> H(U1(a, c), U1(b, k))
27.32/8.89	   A^2 -> H(U1(a, c), U1(e, c))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, c))
27.32/8.89	   A^2 -> H(U1(a, c), U1(c, e))
27.32/8.89	   A^2 -> H(U1(a, c), U1(c, k))
27.32/8.89	   A^2 -> H(U1(a, c), U1(e, e))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, k))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, d))
27.32/8.89	   A^2 -> H(U1(a, c), U1(d, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(e, b))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, b))
27.32/8.89	   A^2 -> H(U1(a, d), U1(c, d))
27.32/8.89	   A^2 -> H(U1(a, d), U1(d, c))
27.32/8.89	   A^2 -> H(U1(a, d), U1(b, e))
27.32/8.89	   A^2 -> H(U1(a, d), U1(b, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(e, c))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, c))
27.32/8.89	   A^2 -> H(U1(a, d), U1(c, e))
27.32/8.89	   A^2 -> H(U1(a, d), U1(c, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(e, e))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, d))
27.32/8.89	   A^2 -> H(U1(a, d), U1(d, k))
27.32/8.89	   A^2 -> H(U1(a, a), b)
27.32/8.89	   A^2 -> H(U1(a, a), U1(e, d))
27.32/8.89	   A^2 -> H(U1(a, a), U1(d, e))
27.32/8.89	   A^2 -> H(U1(a, a), c)
27.32/8.89	   A^2 -> H(U1(a, a), U1(e, k))
27.32/8.89	   A^2 -> H(U1(a, a), U1(k, e))
27.32/8.89	   A^2 -> H(U1(a, a), e)
27.32/8.89	   A^2 -> H(U1(a, a), U1(k, k))
27.32/8.89	   A^2 -> H(k, f(b))
27.32/8.89	   A^2 -> H(c, U1(b, b))
27.32/8.89	   A^2 -> H(c, f(c))
27.32/8.89	   A^2 -> H(c, f(d))
27.32/8.89	   A^2 -> H(U1(e, k), U1(b, b))
27.32/8.89	   A^2 -> H(U1(e, k), f(c))
27.32/8.89	   A^2 -> H(U1(e, k), f(d))
27.32/8.89	   A^2 -> H(U1(e, c), U1(c, b))
27.32/8.89	   A^2 -> H(U1(e, c), U1(d, b))
27.32/8.89	   A^2 -> H(U1(e, c), U1(b, c))
27.32/8.89	   A^2 -> H(U1(e, c), U1(b, d))
27.32/8.89	   A^2 -> H(U1(e, c), U1(c, c))
27.32/8.89	   A^2 -> H(U1(e, c), f(e))
27.32/8.89	   A^2 -> H(U1(e, c), f(k))
27.32/8.89	   A^2 -> H(U1(e, c), U1(d, d))
27.32/8.89	   A^2 -> H(U1(k, e), U1(b, b))
27.32/8.89	   A^2 -> H(U1(k, e), f(c))
27.32/8.89	   A^2 -> H(U1(k, e), f(d))
27.32/8.89	   A^2 -> H(U1(k, c), U1(c, b))
27.32/8.89	   A^2 -> H(U1(k, c), U1(d, b))
27.32/8.89	   A^2 -> H(U1(k, c), U1(b, c))
27.32/8.89	   A^2 -> H(U1(k, c), U1(b, d))
27.32/8.89	   A^2 -> H(U1(k, c), U1(c, c))
27.32/8.89	   A^2 -> H(U1(k, c), f(e))
27.32/8.89	   A^2 -> H(U1(k, c), f(k))
27.32/8.89	   A^2 -> H(U1(k, c), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, e), U1(c, b))
27.32/8.89	   A^2 -> H(U1(c, e), U1(d, b))
27.32/8.89	   A^2 -> H(U1(c, e), U1(b, c))
27.32/8.89	   A^2 -> H(U1(c, e), U1(b, d))
27.32/8.89	   A^2 -> H(U1(c, e), U1(c, c))
27.32/8.89	   A^2 -> H(U1(c, e), f(e))
27.32/8.89	   A^2 -> H(U1(c, e), f(k))
27.32/8.89	   A^2 -> H(U1(c, e), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(c, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(c, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(c, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(c, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(c, k), f(e))
27.32/8.89	   A^2 -> H(U1(c, k), f(k))
27.32/8.89	   A^2 -> H(U1(c, k), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(e, b))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, b))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(d, c))
27.32/8.89	   A^2 -> H(U1(c, c), U1(b, e))
27.32/8.89	   A^2 -> H(U1(c, c), U1(b, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(e, e))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(d, k))
27.32/8.89	   A^2 -> H(e, U1(b, b))
27.32/8.89	   A^2 -> H(e, f(c))
27.32/8.89	   A^2 -> H(e, f(d))
27.32/8.89	   A^2 -> H(U1(e, e), U1(c, b))
27.32/8.89	   A^2 -> H(U1(e, e), U1(d, b))
27.32/8.89	   A^2 -> H(U1(e, e), U1(b, c))
27.32/8.89	   A^2 -> H(U1(e, e), U1(b, d))
27.32/8.89	   A^2 -> H(U1(e, e), U1(c, c))
27.32/8.89	   A^2 -> H(U1(e, e), f(e))
27.32/8.89	   A^2 -> H(U1(e, e), f(k))
27.32/8.89	   A^2 -> H(U1(e, e), U1(d, d))
27.32/8.89	   A^2 -> H(f(e), U1(e, b))
27.32/8.89	   A^2 -> H(f(e), U1(k, b))
27.32/8.89	   A^2 -> H(f(e), U1(c, d))
27.32/8.89	   A^2 -> H(f(e), U1(d, c))
27.32/8.89	   A^2 -> H(f(e), U1(b, e))
27.32/8.89	   A^2 -> H(f(e), U1(b, k))
27.32/8.89	   A^2 -> H(f(e), U1(e, c))
27.32/8.89	   A^2 -> H(f(e), U1(k, c))
27.32/8.89	   A^2 -> H(f(e), U1(c, e))
27.32/8.89	   A^2 -> H(f(e), U1(c, k))
27.32/8.89	   A^2 -> H(f(e), U1(k, k))
27.32/8.89	   A^2 -> H(f(e), U1(k, d))
27.32/8.89	   A^2 -> H(f(e), U1(d, k))
27.32/8.89	   A^2 -> H(U1(k, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(k, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(k, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(k, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(k, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(k, k), f(e))
27.32/8.89	   A^2 -> H(U1(k, k), f(k))
27.32/8.89	   A^2 -> H(U1(k, k), U1(d, d))
27.32/8.89	   A^2 -> H(f(k), U1(e, b))
27.32/8.89	   A^2 -> H(f(k), U1(k, b))
27.32/8.89	   A^2 -> H(f(k), U1(c, d))
27.32/8.89	   A^2 -> H(f(k), U1(d, c))
27.32/8.89	   A^2 -> H(f(k), U1(b, e))
27.32/8.89	   A^2 -> H(f(k), U1(b, k))
27.32/8.89	   A^2 -> H(f(k), U1(e, c))
27.32/8.89	   A^2 -> H(f(k), U1(k, c))
27.32/8.89	   A^2 -> H(f(k), U1(c, e))
27.32/8.89	   A^2 -> H(f(k), U1(c, k))
27.32/8.89	   A^2 -> H(f(k), U1(e, e))
27.32/8.89	   A^2 -> H(f(k), U1(k, d))
27.32/8.89	   A^2 -> H(f(k), U1(d, k))
27.32/8.89	   A^2 -> H(f(c), b)
27.32/8.89	   A^2 -> H(f(c), U1(e, d))
27.32/8.89	   A^2 -> H(f(c), U1(d, e))
27.32/8.89	   A^2 -> H(f(k), U1(k, k))
27.32/8.89	   A^2 -> H(U1(k, k), U1(b, b))
27.32/8.89	   A^2 -> H(U1(k, k), f(c))
27.32/8.89	   A^2 -> H(U1(k, k), f(d))
27.32/8.89	   A^2 -> H(U1(k, d), U1(c, b))
27.32/8.89	   A^2 -> H(U1(k, d), U1(d, b))
27.32/8.89	   A^2 -> H(U1(k, d), U1(b, c))
27.32/8.89	   A^2 -> H(U1(k, d), U1(b, d))
27.32/8.89	   A^2 -> H(U1(k, d), U1(c, c))
27.32/8.89	   A^2 -> H(U1(k, d), f(e))
27.32/8.89	   A^2 -> H(U1(k, d), f(k))
27.32/8.89	   A^2 -> H(U1(k, d), U1(d, d))
27.32/8.89	   A^2 -> H(U1(d, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(d, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(d, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(d, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(d, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(d, k), f(e))
27.32/8.89	   A^2 -> H(U1(d, k), f(k))
27.32/8.89	   A^2 -> H(U1(d, k), U1(d, d))
27.32/8.89	   A^2 -> H(U1(d, d), U1(e, b))
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, b))
27.32/8.89	   A^2 -> H(U1(d, d), U1(c, d))
27.32/8.89	   A^2 -> H(U1(d, d), U1(d, c))
27.32/8.89	   A^2 -> H(U1(d, d), U1(b, e))
27.32/8.89	   A^2 -> H(U1(d, d), U1(b, k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(e, c))
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, c))
27.32/8.89	   A^2 -> H(U1(d, d), U1(c, e))
27.32/8.89	   A^2 -> H(U1(d, d), U1(c, k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(e, e))
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, k))
27.32/8.89	   A^2 -> H(f(d), b)
27.32/8.89	   A^2 -> H(f(d), U1(e, d))
27.32/8.89	   A^2 -> H(f(d), U1(d, e))
27.32/8.89	   A^2 -> H(f(d), c)
27.32/8.89	   A^2 -> H(f(d), U1(e, k))
27.32/8.89	   A^2 -> H(f(d), U1(k, e))
27.32/8.89	   A^2 -> H(f(d), e)
27.32/8.89	   A^2 -> H(f(a), d)
27.32/8.89	   A^2 -> H(U1(c, c), U1(e, c))
27.32/8.89	   A^2 -> H(f(c), c)
27.32/8.89	   A^2 -> H(f(c), U1(e, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, c))
27.32/8.89	   A^2 -> H(f(c), U1(k, e))
27.32/8.89	   A^2 -> H(f(c), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, e))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, k))
27.32/8.89	   A^2 -> H(f(a), k)
27.32/8.89	   A^2 -> H(f(e), U1(e, e))
27.32/8.89	   A^2 -> H(f(c), e)
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, d))
27.32/8.89	   A^2 -> H(f(d), U1(k, k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(d, k))
27.32/8.89	   A^2 -> H(d, U1(b, b))
27.32/8.89	   A^2 -> H(d, f(c))
27.32/8.89	   A^2 -> H(d, f(d))
27.32/8.89	   A^2 -> H(a, U1(c, b))
27.32/8.89	   A^2 -> H(a, U1(d, b))
27.32/8.89	   A^2 -> H(a, U1(b, c))
27.32/8.89	   A^2 -> H(a, U1(b, d))
27.32/8.89	   A^2 -> H(a, U1(c, c))
27.32/8.89	   A^2 -> H(a, f(e))
27.32/8.89	   A^2 -> H(a, f(k))
27.32/8.89	   A^2 -> H(a, U1(d, d))
27.32/8.89	   A^2 -> H(U1(e, d), U1(c, b))
27.32/8.89	   A^2 -> H(U1(e, d), U1(d, b))
27.32/8.89	   A^2 -> H(U1(e, d), U1(b, c))
27.32/8.89	   A^2 -> H(U1(e, d), U1(b, d))
27.32/8.89	   A^2 -> H(U1(e, d), U1(c, c))
27.32/8.89	   A^2 -> H(U1(e, d), f(e))
27.32/8.89	   A^2 -> H(U1(e, d), f(k))
27.32/8.89	   A^2 -> H(U1(e, d), U1(d, d))
27.32/8.89	   A^2 -> H(U1(e, a), U1(e, b))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(e, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(e, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(e, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(e, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(e, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(e, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(e, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(e, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(e, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(e, b))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(k, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(k, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(k, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(k, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(k, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(k, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(k, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(e, b))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, b))
27.32/8.89	   A^2 -> H(U1(c, d), U1(c, d))
27.32/8.89	   A^2 -> H(U1(c, d), U1(d, c))
27.32/8.89	   A^2 -> H(U1(c, d), U1(b, e))
27.32/8.89	   A^2 -> H(U1(c, d), U1(b, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(e, c))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, c))
27.32/8.89	   A^2 -> H(U1(c, d), U1(c, e))
27.32/8.89	   A^2 -> H(U1(c, d), U1(c, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(e, e))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, d))
27.32/8.89	   A^2 -> H(U1(c, d), U1(d, k))
27.32/8.89	   A^2 -> H(U1(c, a), b)
27.32/8.89	   A^2 -> H(U1(c, a), U1(e, d))
27.32/8.89	
27.32/8.89	The TRS R consists of the following rules:
27.32/8.89	
27.32/8.89	   f(x) -> U1(x, x)
27.32/8.89	   U1(e, x) -> x
27.32/8.89	   a -> c
27.32/8.89	   a -> d
27.32/8.89	   b -> c
27.32/8.89	   b -> d
27.32/8.89	   d -> k
27.32/8.89	   c -> e
27.32/8.89	   c -> k
27.32/8.89	
27.32/8.89	Q is empty.
27.32/8.89	We have to consider all minimal (P,Q,R)-chains.
27.32/8.89	----------------------------------------
27.32/8.89	
27.32/8.89	(605) TransformationProof (EQUIVALENT)
27.32/8.89	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
27.32/8.89	
27.32/8.89	   (A^2 -> H(U1(e, a), U1(k, b)),A^2 -> H(U1(e, a), U1(k, b)))
27.32/8.89	   (A^2 -> H(U1(k, a), U1(k, b)),A^2 -> H(U1(k, a), U1(k, b)))
27.32/8.89	   (A^2 -> H(U1(c, c), U1(k, b)),A^2 -> H(U1(c, c), U1(k, b)))
27.32/8.89	   (A^2 -> H(U1(c, d), U1(k, b)),A^2 -> H(U1(c, d), U1(k, b)))
27.32/8.89	   (A^2 -> H(U1(c, a), U1(k, c)),A^2 -> H(U1(c, a), U1(k, c)))
27.32/8.89	   (A^2 -> H(U1(c, a), U1(k, d)),A^2 -> H(U1(c, a), U1(k, d)))
27.32/8.89	
27.32/8.89	
27.32/8.89	----------------------------------------
27.32/8.89	
27.32/8.89	(606)
27.32/8.89	Obligation:
27.32/8.89	Q DP problem:
27.32/8.89	The TRS P consists of the following rules:
27.32/8.89	
27.32/8.89	   H(x, x) -> G(x, x, f(k))
27.32/8.89	   G(d, x, x) -> A^2
27.32/8.89	   A^2 -> H(f(c), f(c))
27.32/8.89	   A^2 -> H(f(d), f(d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, c))
27.32/8.89	   A^2 -> H(f(e), f(e))
27.32/8.89	   A^2 -> H(f(k), f(k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(c, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(c, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(c, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(c, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(c, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(c, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(c, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(c, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(d, e), U1(b, b))
27.32/8.89	   A^2 -> H(U1(d, e), f(c))
27.32/8.89	   A^2 -> H(U1(d, e), f(d))
27.32/8.89	   A^2 -> H(U1(d, c), U1(c, b))
27.32/8.89	   A^2 -> H(U1(d, c), U1(d, b))
27.32/8.89	   A^2 -> H(U1(d, c), U1(b, c))
27.32/8.89	   A^2 -> H(U1(d, c), U1(b, d))
27.32/8.89	   A^2 -> H(U1(d, c), U1(c, c))
27.32/8.89	   A^2 -> H(U1(d, c), f(e))
27.32/8.89	   A^2 -> H(U1(d, c), f(k))
27.32/8.89	   A^2 -> H(U1(d, c), U1(d, d))
27.32/8.89	   A^2 -> H(U1(d, a), U1(e, b))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(d, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(d, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(d, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(d, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(d, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(d, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(d, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(d, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(d, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(a, e), U1(c, b))
27.32/8.89	   A^2 -> H(U1(a, e), U1(d, b))
27.32/8.89	   A^2 -> H(U1(a, e), U1(b, c))
27.32/8.89	   A^2 -> H(U1(a, e), U1(b, d))
27.32/8.89	   A^2 -> H(U1(a, e), U1(c, c))
27.32/8.89	   A^2 -> H(U1(a, e), f(e))
27.32/8.89	   A^2 -> H(U1(a, e), f(k))
27.32/8.89	   A^2 -> H(U1(a, e), U1(d, d))
27.32/8.89	   A^2 -> H(U1(a, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(a, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(a, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(a, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(a, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(a, k), f(e))
27.32/8.89	   A^2 -> H(U1(a, k), f(k))
27.32/8.89	   A^2 -> H(U1(a, k), U1(d, d))
27.32/8.89	   A^2 -> H(U1(a, c), U1(e, b))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, b))
27.32/8.89	   A^2 -> H(U1(a, c), U1(c, d))
27.32/8.89	   A^2 -> H(U1(a, c), U1(d, c))
27.32/8.89	   A^2 -> H(U1(a, c), U1(b, e))
27.32/8.89	   A^2 -> H(U1(a, c), U1(b, k))
27.32/8.89	   A^2 -> H(U1(a, c), U1(e, c))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, c))
27.32/8.89	   A^2 -> H(U1(a, c), U1(c, e))
27.32/8.89	   A^2 -> H(U1(a, c), U1(c, k))
27.32/8.89	   A^2 -> H(U1(a, c), U1(e, e))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, k))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, d))
27.32/8.89	   A^2 -> H(U1(a, c), U1(d, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(e, b))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, b))
27.32/8.89	   A^2 -> H(U1(a, d), U1(c, d))
27.32/8.89	   A^2 -> H(U1(a, d), U1(d, c))
27.32/8.89	   A^2 -> H(U1(a, d), U1(b, e))
27.32/8.89	   A^2 -> H(U1(a, d), U1(b, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(e, c))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, c))
27.32/8.89	   A^2 -> H(U1(a, d), U1(c, e))
27.32/8.89	   A^2 -> H(U1(a, d), U1(c, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(e, e))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, d))
27.32/8.89	   A^2 -> H(U1(a, d), U1(d, k))
27.32/8.89	   A^2 -> H(U1(a, a), b)
27.32/8.89	   A^2 -> H(U1(a, a), U1(e, d))
27.32/8.89	   A^2 -> H(U1(a, a), U1(d, e))
27.32/8.89	   A^2 -> H(U1(a, a), c)
27.32/8.89	   A^2 -> H(U1(a, a), U1(e, k))
27.32/8.89	   A^2 -> H(U1(a, a), U1(k, e))
27.32/8.89	   A^2 -> H(U1(a, a), e)
27.32/8.89	   A^2 -> H(U1(a, a), U1(k, k))
27.32/8.89	   A^2 -> H(k, f(b))
27.32/8.89	   A^2 -> H(c, U1(b, b))
27.32/8.89	   A^2 -> H(c, f(c))
27.32/8.89	   A^2 -> H(c, f(d))
27.32/8.89	   A^2 -> H(U1(e, k), U1(b, b))
27.32/8.89	   A^2 -> H(U1(e, k), f(c))
27.32/8.89	   A^2 -> H(U1(e, k), f(d))
27.32/8.89	   A^2 -> H(U1(e, c), U1(c, b))
27.32/8.89	   A^2 -> H(U1(e, c), U1(d, b))
27.32/8.89	   A^2 -> H(U1(e, c), U1(b, c))
27.32/8.89	   A^2 -> H(U1(e, c), U1(b, d))
27.32/8.89	   A^2 -> H(U1(e, c), U1(c, c))
27.32/8.89	   A^2 -> H(U1(e, c), f(e))
27.32/8.89	   A^2 -> H(U1(e, c), f(k))
27.32/8.89	   A^2 -> H(U1(e, c), U1(d, d))
27.32/8.89	   A^2 -> H(U1(k, e), U1(b, b))
27.32/8.89	   A^2 -> H(U1(k, e), f(c))
27.32/8.89	   A^2 -> H(U1(k, e), f(d))
27.32/8.89	   A^2 -> H(U1(k, c), U1(c, b))
27.32/8.89	   A^2 -> H(U1(k, c), U1(d, b))
27.32/8.89	   A^2 -> H(U1(k, c), U1(b, c))
27.32/8.89	   A^2 -> H(U1(k, c), U1(b, d))
27.32/8.89	   A^2 -> H(U1(k, c), U1(c, c))
27.32/8.89	   A^2 -> H(U1(k, c), f(e))
27.32/8.89	   A^2 -> H(U1(k, c), f(k))
27.32/8.89	   A^2 -> H(U1(k, c), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, e), U1(c, b))
27.32/8.89	   A^2 -> H(U1(c, e), U1(d, b))
27.32/8.89	   A^2 -> H(U1(c, e), U1(b, c))
27.32/8.89	   A^2 -> H(U1(c, e), U1(b, d))
27.32/8.89	   A^2 -> H(U1(c, e), U1(c, c))
27.32/8.89	   A^2 -> H(U1(c, e), f(e))
27.32/8.89	   A^2 -> H(U1(c, e), f(k))
27.32/8.89	   A^2 -> H(U1(c, e), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(c, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(c, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(c, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(c, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(c, k), f(e))
27.32/8.89	   A^2 -> H(U1(c, k), f(k))
27.32/8.89	   A^2 -> H(U1(c, k), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(e, b))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, b))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(d, c))
27.32/8.89	   A^2 -> H(U1(c, c), U1(b, e))
27.32/8.89	   A^2 -> H(U1(c, c), U1(b, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(e, e))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(d, k))
27.32/8.89	   A^2 -> H(e, U1(b, b))
27.32/8.89	   A^2 -> H(e, f(c))
27.32/8.89	   A^2 -> H(e, f(d))
27.32/8.89	   A^2 -> H(U1(e, e), U1(c, b))
27.32/8.89	   A^2 -> H(U1(e, e), U1(d, b))
27.32/8.89	   A^2 -> H(U1(e, e), U1(b, c))
27.32/8.89	   A^2 -> H(U1(e, e), U1(b, d))
27.32/8.89	   A^2 -> H(U1(e, e), U1(c, c))
27.32/8.89	   A^2 -> H(U1(e, e), f(e))
27.32/8.89	   A^2 -> H(U1(e, e), f(k))
27.32/8.89	   A^2 -> H(U1(e, e), U1(d, d))
27.32/8.89	   A^2 -> H(f(e), U1(e, b))
27.32/8.89	   A^2 -> H(f(e), U1(k, b))
27.32/8.89	   A^2 -> H(f(e), U1(c, d))
27.32/8.89	   A^2 -> H(f(e), U1(d, c))
27.32/8.89	   A^2 -> H(f(e), U1(b, e))
27.32/8.89	   A^2 -> H(f(e), U1(b, k))
27.32/8.89	   A^2 -> H(f(e), U1(e, c))
27.32/8.89	   A^2 -> H(f(e), U1(k, c))
27.32/8.89	   A^2 -> H(f(e), U1(c, e))
27.32/8.89	   A^2 -> H(f(e), U1(c, k))
27.32/8.89	   A^2 -> H(f(e), U1(k, k))
27.32/8.89	   A^2 -> H(f(e), U1(k, d))
27.32/8.89	   A^2 -> H(f(e), U1(d, k))
27.32/8.89	   A^2 -> H(U1(k, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(k, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(k, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(k, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(k, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(k, k), f(e))
27.32/8.89	   A^2 -> H(U1(k, k), f(k))
27.32/8.89	   A^2 -> H(U1(k, k), U1(d, d))
27.32/8.89	   A^2 -> H(f(k), U1(e, b))
27.32/8.89	   A^2 -> H(f(k), U1(k, b))
27.32/8.89	   A^2 -> H(f(k), U1(c, d))
27.32/8.89	   A^2 -> H(f(k), U1(d, c))
27.32/8.89	   A^2 -> H(f(k), U1(b, e))
27.32/8.89	   A^2 -> H(f(k), U1(b, k))
27.32/8.89	   A^2 -> H(f(k), U1(e, c))
27.32/8.89	   A^2 -> H(f(k), U1(k, c))
27.32/8.89	   A^2 -> H(f(k), U1(c, e))
27.32/8.89	   A^2 -> H(f(k), U1(c, k))
27.32/8.89	   A^2 -> H(f(k), U1(e, e))
27.32/8.89	   A^2 -> H(f(k), U1(k, d))
27.32/8.89	   A^2 -> H(f(k), U1(d, k))
27.32/8.89	   A^2 -> H(f(c), b)
27.32/8.89	   A^2 -> H(f(c), U1(e, d))
27.32/8.89	   A^2 -> H(f(c), U1(d, e))
27.32/8.89	   A^2 -> H(f(k), U1(k, k))
27.32/8.89	   A^2 -> H(U1(k, k), U1(b, b))
27.32/8.89	   A^2 -> H(U1(k, k), f(c))
27.32/8.89	   A^2 -> H(U1(k, k), f(d))
27.32/8.89	   A^2 -> H(U1(k, d), U1(c, b))
27.32/8.89	   A^2 -> H(U1(k, d), U1(d, b))
27.32/8.89	   A^2 -> H(U1(k, d), U1(b, c))
27.32/8.89	   A^2 -> H(U1(k, d), U1(b, d))
27.32/8.89	   A^2 -> H(U1(k, d), U1(c, c))
27.32/8.89	   A^2 -> H(U1(k, d), f(e))
27.32/8.89	   A^2 -> H(U1(k, d), f(k))
27.32/8.89	   A^2 -> H(U1(k, d), U1(d, d))
27.32/8.89	   A^2 -> H(U1(d, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(d, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(d, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(d, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(d, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(d, k), f(e))
27.32/8.89	   A^2 -> H(U1(d, k), f(k))
27.32/8.89	   A^2 -> H(U1(d, k), U1(d, d))
27.32/8.89	   A^2 -> H(U1(d, d), U1(e, b))
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, b))
27.32/8.89	   A^2 -> H(U1(d, d), U1(c, d))
27.32/8.89	   A^2 -> H(U1(d, d), U1(d, c))
27.32/8.89	   A^2 -> H(U1(d, d), U1(b, e))
27.32/8.89	   A^2 -> H(U1(d, d), U1(b, k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(e, c))
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, c))
27.32/8.89	   A^2 -> H(U1(d, d), U1(c, e))
27.32/8.89	   A^2 -> H(U1(d, d), U1(c, k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(e, e))
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, k))
27.32/8.89	   A^2 -> H(f(d), b)
27.32/8.89	   A^2 -> H(f(d), U1(e, d))
27.32/8.89	   A^2 -> H(f(d), U1(d, e))
27.32/8.89	   A^2 -> H(f(d), c)
27.32/8.89	   A^2 -> H(f(d), U1(e, k))
27.32/8.89	   A^2 -> H(f(d), U1(k, e))
27.32/8.89	   A^2 -> H(f(d), e)
27.32/8.89	   A^2 -> H(f(a), d)
27.32/8.89	   A^2 -> H(U1(c, c), U1(e, c))
27.32/8.89	   A^2 -> H(f(c), c)
27.32/8.89	   A^2 -> H(f(c), U1(e, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, c))
27.32/8.89	   A^2 -> H(f(c), U1(k, e))
27.32/8.89	   A^2 -> H(f(c), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, e))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, k))
27.32/8.89	   A^2 -> H(f(a), k)
27.32/8.89	   A^2 -> H(f(e), U1(e, e))
27.32/8.89	   A^2 -> H(f(c), e)
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, d))
27.32/8.89	   A^2 -> H(f(d), U1(k, k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(d, k))
27.32/8.89	   A^2 -> H(d, U1(b, b))
27.32/8.89	   A^2 -> H(d, f(c))
27.32/8.89	   A^2 -> H(d, f(d))
27.32/8.89	   A^2 -> H(a, U1(c, b))
27.32/8.89	   A^2 -> H(a, U1(d, b))
27.32/8.89	   A^2 -> H(a, U1(b, c))
27.32/8.89	   A^2 -> H(a, U1(b, d))
27.32/8.89	   A^2 -> H(a, U1(c, c))
27.32/8.89	   A^2 -> H(a, f(e))
27.32/8.89	   A^2 -> H(a, f(k))
27.32/8.89	   A^2 -> H(a, U1(d, d))
27.32/8.89	   A^2 -> H(U1(e, d), U1(c, b))
27.32/8.89	   A^2 -> H(U1(e, d), U1(d, b))
27.32/8.89	   A^2 -> H(U1(e, d), U1(b, c))
27.32/8.89	   A^2 -> H(U1(e, d), U1(b, d))
27.32/8.89	   A^2 -> H(U1(e, d), U1(c, c))
27.32/8.89	   A^2 -> H(U1(e, d), f(e))
27.32/8.89	   A^2 -> H(U1(e, d), f(k))
27.32/8.89	   A^2 -> H(U1(e, d), U1(d, d))
27.32/8.89	   A^2 -> H(U1(e, a), U1(e, b))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(e, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(e, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(e, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(e, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(e, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(e, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(e, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(e, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(e, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(e, b))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(k, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(k, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(k, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(k, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(k, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(k, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(k, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(e, b))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, b))
27.32/8.89	   A^2 -> H(U1(c, d), U1(c, d))
27.32/8.89	   A^2 -> H(U1(c, d), U1(d, c))
27.32/8.89	   A^2 -> H(U1(c, d), U1(b, e))
27.32/8.89	   A^2 -> H(U1(c, d), U1(b, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(e, c))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, c))
27.32/8.89	   A^2 -> H(U1(c, d), U1(c, e))
27.32/8.89	   A^2 -> H(U1(c, d), U1(c, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(e, e))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, d))
27.32/8.89	   A^2 -> H(U1(c, d), U1(d, k))
27.32/8.89	   A^2 -> H(U1(c, a), b)
27.32/8.89	   A^2 -> H(U1(c, a), U1(e, d))
27.32/8.89	
27.32/8.89	The TRS R consists of the following rules:
27.32/8.89	
27.32/8.89	   f(x) -> U1(x, x)
27.32/8.89	   U1(e, x) -> x
27.32/8.89	   a -> c
27.32/8.89	   a -> d
27.32/8.89	   b -> c
27.32/8.89	   b -> d
27.32/8.89	   d -> k
27.32/8.89	   c -> e
27.32/8.89	   c -> k
27.32/8.89	
27.32/8.89	Q is empty.
27.32/8.89	We have to consider all minimal (P,Q,R)-chains.
27.32/8.89	----------------------------------------
27.32/8.89	
27.32/8.89	(607) TransformationProof (EQUIVALENT)
27.32/8.89	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
27.32/8.89	
27.32/8.89	   (A^2 -> H(U1(e, a), U1(c, d)),A^2 -> H(U1(e, a), U1(c, d)))
27.32/8.89	   (A^2 -> H(U1(k, a), U1(c, d)),A^2 -> H(U1(k, a), U1(c, d)))
27.32/8.89	   (A^2 -> H(U1(c, c), U1(c, d)),A^2 -> H(U1(c, c), U1(c, d)))
27.32/8.89	   (A^2 -> H(U1(c, d), U1(c, d)),A^2 -> H(U1(c, d), U1(c, d)))
27.32/8.89	   (A^2 -> H(U1(c, a), U1(e, d)),A^2 -> H(U1(c, a), U1(e, d)))
27.32/8.89	   (A^2 -> H(U1(c, a), U1(k, d)),A^2 -> H(U1(c, a), U1(k, d)))
27.32/8.89	   (A^2 -> H(U1(c, a), U1(c, k)),A^2 -> H(U1(c, a), U1(c, k)))
27.32/8.89	
27.32/8.89	
27.32/8.89	----------------------------------------
27.32/8.89	
27.32/8.89	(608)
27.32/8.89	Obligation:
27.32/8.89	Q DP problem:
27.32/8.89	The TRS P consists of the following rules:
27.32/8.89	
27.32/8.89	   H(x, x) -> G(x, x, f(k))
27.32/8.89	   G(d, x, x) -> A^2
27.32/8.89	   A^2 -> H(f(c), f(c))
27.32/8.89	   A^2 -> H(f(d), f(d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, c))
27.32/8.89	   A^2 -> H(f(e), f(e))
27.32/8.89	   A^2 -> H(f(k), f(k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(c, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(c, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(c, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(c, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(c, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(c, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(c, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(d, e), U1(b, b))
27.32/8.89	   A^2 -> H(U1(d, e), f(c))
27.32/8.89	   A^2 -> H(U1(d, e), f(d))
27.32/8.89	   A^2 -> H(U1(d, c), U1(c, b))
27.32/8.89	   A^2 -> H(U1(d, c), U1(d, b))
27.32/8.89	   A^2 -> H(U1(d, c), U1(b, c))
27.32/8.89	   A^2 -> H(U1(d, c), U1(b, d))
27.32/8.89	   A^2 -> H(U1(d, c), U1(c, c))
27.32/8.89	   A^2 -> H(U1(d, c), f(e))
27.32/8.89	   A^2 -> H(U1(d, c), f(k))
27.32/8.89	   A^2 -> H(U1(d, c), U1(d, d))
27.32/8.89	   A^2 -> H(U1(d, a), U1(e, b))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(d, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(d, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(d, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(d, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(d, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(d, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(d, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(d, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(d, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(a, e), U1(c, b))
27.32/8.89	   A^2 -> H(U1(a, e), U1(d, b))
27.32/8.89	   A^2 -> H(U1(a, e), U1(b, c))
27.32/8.89	   A^2 -> H(U1(a, e), U1(b, d))
27.32/8.89	   A^2 -> H(U1(a, e), U1(c, c))
27.32/8.89	   A^2 -> H(U1(a, e), f(e))
27.32/8.89	   A^2 -> H(U1(a, e), f(k))
27.32/8.89	   A^2 -> H(U1(a, e), U1(d, d))
27.32/8.89	   A^2 -> H(U1(a, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(a, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(a, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(a, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(a, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(a, k), f(e))
27.32/8.89	   A^2 -> H(U1(a, k), f(k))
27.32/8.89	   A^2 -> H(U1(a, k), U1(d, d))
27.32/8.89	   A^2 -> H(U1(a, c), U1(e, b))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, b))
27.32/8.89	   A^2 -> H(U1(a, c), U1(c, d))
27.32/8.89	   A^2 -> H(U1(a, c), U1(d, c))
27.32/8.89	   A^2 -> H(U1(a, c), U1(b, e))
27.32/8.89	   A^2 -> H(U1(a, c), U1(b, k))
27.32/8.89	   A^2 -> H(U1(a, c), U1(e, c))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, c))
27.32/8.89	   A^2 -> H(U1(a, c), U1(c, e))
27.32/8.89	   A^2 -> H(U1(a, c), U1(c, k))
27.32/8.89	   A^2 -> H(U1(a, c), U1(e, e))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, k))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, d))
27.32/8.89	   A^2 -> H(U1(a, c), U1(d, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(e, b))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, b))
27.32/8.89	   A^2 -> H(U1(a, d), U1(c, d))
27.32/8.89	   A^2 -> H(U1(a, d), U1(d, c))
27.32/8.89	   A^2 -> H(U1(a, d), U1(b, e))
27.32/8.89	   A^2 -> H(U1(a, d), U1(b, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(e, c))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, c))
27.32/8.89	   A^2 -> H(U1(a, d), U1(c, e))
27.32/8.89	   A^2 -> H(U1(a, d), U1(c, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(e, e))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, d))
27.32/8.89	   A^2 -> H(U1(a, d), U1(d, k))
27.32/8.89	   A^2 -> H(U1(a, a), b)
27.32/8.89	   A^2 -> H(U1(a, a), U1(e, d))
27.32/8.89	   A^2 -> H(U1(a, a), U1(d, e))
27.32/8.89	   A^2 -> H(U1(a, a), c)
27.32/8.89	   A^2 -> H(U1(a, a), U1(e, k))
27.32/8.89	   A^2 -> H(U1(a, a), U1(k, e))
27.32/8.89	   A^2 -> H(U1(a, a), e)
27.32/8.89	   A^2 -> H(U1(a, a), U1(k, k))
27.32/8.89	   A^2 -> H(k, f(b))
27.32/8.89	   A^2 -> H(c, U1(b, b))
27.32/8.89	   A^2 -> H(c, f(c))
27.32/8.89	   A^2 -> H(c, f(d))
27.32/8.89	   A^2 -> H(U1(e, k), U1(b, b))
27.32/8.89	   A^2 -> H(U1(e, k), f(c))
27.32/8.89	   A^2 -> H(U1(e, k), f(d))
27.32/8.89	   A^2 -> H(U1(e, c), U1(c, b))
27.32/8.89	   A^2 -> H(U1(e, c), U1(d, b))
27.32/8.89	   A^2 -> H(U1(e, c), U1(b, c))
27.32/8.89	   A^2 -> H(U1(e, c), U1(b, d))
27.32/8.89	   A^2 -> H(U1(e, c), U1(c, c))
27.32/8.89	   A^2 -> H(U1(e, c), f(e))
27.32/8.89	   A^2 -> H(U1(e, c), f(k))
27.32/8.89	   A^2 -> H(U1(e, c), U1(d, d))
27.32/8.89	   A^2 -> H(U1(k, e), U1(b, b))
27.32/8.89	   A^2 -> H(U1(k, e), f(c))
27.32/8.89	   A^2 -> H(U1(k, e), f(d))
27.32/8.89	   A^2 -> H(U1(k, c), U1(c, b))
27.32/8.89	   A^2 -> H(U1(k, c), U1(d, b))
27.32/8.89	   A^2 -> H(U1(k, c), U1(b, c))
27.32/8.89	   A^2 -> H(U1(k, c), U1(b, d))
27.32/8.89	   A^2 -> H(U1(k, c), U1(c, c))
27.32/8.89	   A^2 -> H(U1(k, c), f(e))
27.32/8.89	   A^2 -> H(U1(k, c), f(k))
27.32/8.89	   A^2 -> H(U1(k, c), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, e), U1(c, b))
27.32/8.89	   A^2 -> H(U1(c, e), U1(d, b))
27.32/8.89	   A^2 -> H(U1(c, e), U1(b, c))
27.32/8.89	   A^2 -> H(U1(c, e), U1(b, d))
27.32/8.89	   A^2 -> H(U1(c, e), U1(c, c))
27.32/8.89	   A^2 -> H(U1(c, e), f(e))
27.32/8.89	   A^2 -> H(U1(c, e), f(k))
27.32/8.89	   A^2 -> H(U1(c, e), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(c, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(c, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(c, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(c, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(c, k), f(e))
27.32/8.89	   A^2 -> H(U1(c, k), f(k))
27.32/8.89	   A^2 -> H(U1(c, k), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(e, b))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, b))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(d, c))
27.32/8.89	   A^2 -> H(U1(c, c), U1(b, e))
27.32/8.89	   A^2 -> H(U1(c, c), U1(b, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(e, e))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(d, k))
27.32/8.89	   A^2 -> H(e, U1(b, b))
27.32/8.89	   A^2 -> H(e, f(c))
27.32/8.89	   A^2 -> H(e, f(d))
27.32/8.89	   A^2 -> H(U1(e, e), U1(c, b))
27.32/8.89	   A^2 -> H(U1(e, e), U1(d, b))
27.32/8.89	   A^2 -> H(U1(e, e), U1(b, c))
27.32/8.89	   A^2 -> H(U1(e, e), U1(b, d))
27.32/8.89	   A^2 -> H(U1(e, e), U1(c, c))
27.32/8.89	   A^2 -> H(U1(e, e), f(e))
27.32/8.89	   A^2 -> H(U1(e, e), f(k))
27.32/8.89	   A^2 -> H(U1(e, e), U1(d, d))
27.32/8.89	   A^2 -> H(f(e), U1(e, b))
27.32/8.89	   A^2 -> H(f(e), U1(k, b))
27.32/8.89	   A^2 -> H(f(e), U1(c, d))
27.32/8.89	   A^2 -> H(f(e), U1(d, c))
27.32/8.89	   A^2 -> H(f(e), U1(b, e))
27.32/8.89	   A^2 -> H(f(e), U1(b, k))
27.32/8.89	   A^2 -> H(f(e), U1(e, c))
27.32/8.89	   A^2 -> H(f(e), U1(k, c))
27.32/8.89	   A^2 -> H(f(e), U1(c, e))
27.32/8.89	   A^2 -> H(f(e), U1(c, k))
27.32/8.89	   A^2 -> H(f(e), U1(k, k))
27.32/8.89	   A^2 -> H(f(e), U1(k, d))
27.32/8.89	   A^2 -> H(f(e), U1(d, k))
27.32/8.89	   A^2 -> H(U1(k, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(k, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(k, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(k, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(k, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(k, k), f(e))
27.32/8.89	   A^2 -> H(U1(k, k), f(k))
27.32/8.89	   A^2 -> H(U1(k, k), U1(d, d))
27.32/8.89	   A^2 -> H(f(k), U1(e, b))
27.32/8.89	   A^2 -> H(f(k), U1(k, b))
27.32/8.89	   A^2 -> H(f(k), U1(c, d))
27.32/8.89	   A^2 -> H(f(k), U1(d, c))
27.32/8.89	   A^2 -> H(f(k), U1(b, e))
27.32/8.89	   A^2 -> H(f(k), U1(b, k))
27.32/8.89	   A^2 -> H(f(k), U1(e, c))
27.32/8.89	   A^2 -> H(f(k), U1(k, c))
27.32/8.89	   A^2 -> H(f(k), U1(c, e))
27.32/8.89	   A^2 -> H(f(k), U1(c, k))
27.32/8.89	   A^2 -> H(f(k), U1(e, e))
27.32/8.89	   A^2 -> H(f(k), U1(k, d))
27.32/8.89	   A^2 -> H(f(k), U1(d, k))
27.32/8.89	   A^2 -> H(f(c), b)
27.32/8.89	   A^2 -> H(f(c), U1(e, d))
27.32/8.89	   A^2 -> H(f(c), U1(d, e))
27.32/8.89	   A^2 -> H(f(k), U1(k, k))
27.32/8.89	   A^2 -> H(U1(k, k), U1(b, b))
27.32/8.89	   A^2 -> H(U1(k, k), f(c))
27.32/8.89	   A^2 -> H(U1(k, k), f(d))
27.32/8.89	   A^2 -> H(U1(k, d), U1(c, b))
27.32/8.89	   A^2 -> H(U1(k, d), U1(d, b))
27.32/8.89	   A^2 -> H(U1(k, d), U1(b, c))
27.32/8.89	   A^2 -> H(U1(k, d), U1(b, d))
27.32/8.89	   A^2 -> H(U1(k, d), U1(c, c))
27.32/8.89	   A^2 -> H(U1(k, d), f(e))
27.32/8.89	   A^2 -> H(U1(k, d), f(k))
27.32/8.89	   A^2 -> H(U1(k, d), U1(d, d))
27.32/8.89	   A^2 -> H(U1(d, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(d, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(d, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(d, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(d, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(d, k), f(e))
27.32/8.89	   A^2 -> H(U1(d, k), f(k))
27.32/8.89	   A^2 -> H(U1(d, k), U1(d, d))
27.32/8.89	   A^2 -> H(U1(d, d), U1(e, b))
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, b))
27.32/8.89	   A^2 -> H(U1(d, d), U1(c, d))
27.32/8.89	   A^2 -> H(U1(d, d), U1(d, c))
27.32/8.89	   A^2 -> H(U1(d, d), U1(b, e))
27.32/8.89	   A^2 -> H(U1(d, d), U1(b, k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(e, c))
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, c))
27.32/8.89	   A^2 -> H(U1(d, d), U1(c, e))
27.32/8.89	   A^2 -> H(U1(d, d), U1(c, k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(e, e))
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, k))
27.32/8.89	   A^2 -> H(f(d), b)
27.32/8.89	   A^2 -> H(f(d), U1(e, d))
27.32/8.89	   A^2 -> H(f(d), U1(d, e))
27.32/8.89	   A^2 -> H(f(d), c)
27.32/8.89	   A^2 -> H(f(d), U1(e, k))
27.32/8.89	   A^2 -> H(f(d), U1(k, e))
27.32/8.89	   A^2 -> H(f(d), e)
27.32/8.89	   A^2 -> H(f(a), d)
27.32/8.89	   A^2 -> H(U1(c, c), U1(e, c))
27.32/8.89	   A^2 -> H(f(c), c)
27.32/8.89	   A^2 -> H(f(c), U1(e, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, c))
27.32/8.89	   A^2 -> H(f(c), U1(k, e))
27.32/8.89	   A^2 -> H(f(c), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, e))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, k))
27.32/8.89	   A^2 -> H(f(a), k)
27.32/8.89	   A^2 -> H(f(e), U1(e, e))
27.32/8.89	   A^2 -> H(f(c), e)
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, d))
27.32/8.89	   A^2 -> H(f(d), U1(k, k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(d, k))
27.32/8.89	   A^2 -> H(d, U1(b, b))
27.32/8.89	   A^2 -> H(d, f(c))
27.32/8.89	   A^2 -> H(d, f(d))
27.32/8.89	   A^2 -> H(a, U1(c, b))
27.32/8.89	   A^2 -> H(a, U1(d, b))
27.32/8.89	   A^2 -> H(a, U1(b, c))
27.32/8.89	   A^2 -> H(a, U1(b, d))
27.32/8.89	   A^2 -> H(a, U1(c, c))
27.32/8.89	   A^2 -> H(a, f(e))
27.32/8.89	   A^2 -> H(a, f(k))
27.32/8.89	   A^2 -> H(a, U1(d, d))
27.32/8.89	   A^2 -> H(U1(e, d), U1(c, b))
27.32/8.89	   A^2 -> H(U1(e, d), U1(d, b))
27.32/8.89	   A^2 -> H(U1(e, d), U1(b, c))
27.32/8.89	   A^2 -> H(U1(e, d), U1(b, d))
27.32/8.89	   A^2 -> H(U1(e, d), U1(c, c))
27.32/8.89	   A^2 -> H(U1(e, d), f(e))
27.32/8.89	   A^2 -> H(U1(e, d), f(k))
27.32/8.89	   A^2 -> H(U1(e, d), U1(d, d))
27.32/8.89	   A^2 -> H(U1(e, a), U1(e, b))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(e, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(e, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(e, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(e, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(e, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(e, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(e, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(e, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(e, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(e, b))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(k, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(k, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(k, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(k, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(k, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(k, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(k, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(e, b))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, b))
27.32/8.89	   A^2 -> H(U1(c, d), U1(c, d))
27.32/8.89	   A^2 -> H(U1(c, d), U1(d, c))
27.32/8.89	   A^2 -> H(U1(c, d), U1(b, e))
27.32/8.89	   A^2 -> H(U1(c, d), U1(b, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(e, c))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, c))
27.32/8.89	   A^2 -> H(U1(c, d), U1(c, e))
27.32/8.89	   A^2 -> H(U1(c, d), U1(c, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(e, e))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, d))
27.32/8.89	   A^2 -> H(U1(c, d), U1(d, k))
27.32/8.89	   A^2 -> H(U1(c, a), b)
27.32/8.89	   A^2 -> H(U1(c, a), U1(e, d))
27.32/8.89	
27.32/8.89	The TRS R consists of the following rules:
27.32/8.89	
27.32/8.89	   f(x) -> U1(x, x)
27.32/8.89	   U1(e, x) -> x
27.32/8.89	   a -> c
27.32/8.89	   a -> d
27.32/8.89	   b -> c
27.32/8.89	   b -> d
27.32/8.89	   d -> k
27.32/8.89	   c -> e
27.32/8.89	   c -> k
27.32/8.89	
27.32/8.89	Q is empty.
27.32/8.89	We have to consider all minimal (P,Q,R)-chains.
27.32/8.89	----------------------------------------
27.32/8.89	
27.32/8.89	(609) TransformationProof (EQUIVALENT)
27.32/8.89	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
27.32/8.89	
27.32/8.89	   (A^2 -> H(U1(e, a), U1(d, c)),A^2 -> H(U1(e, a), U1(d, c)))
27.32/8.89	   (A^2 -> H(U1(k, a), U1(d, c)),A^2 -> H(U1(k, a), U1(d, c)))
27.32/8.89	   (A^2 -> H(U1(c, c), U1(d, c)),A^2 -> H(U1(c, c), U1(d, c)))
27.32/8.89	   (A^2 -> H(U1(c, d), U1(d, c)),A^2 -> H(U1(c, d), U1(d, c)))
27.32/8.89	   (A^2 -> H(U1(c, a), U1(k, c)),A^2 -> H(U1(c, a), U1(k, c)))
27.32/8.89	   (A^2 -> H(U1(c, a), U1(d, e)),A^2 -> H(U1(c, a), U1(d, e)))
27.32/8.89	   (A^2 -> H(U1(c, a), U1(d, k)),A^2 -> H(U1(c, a), U1(d, k)))
27.32/8.89	
27.32/8.89	
27.32/8.89	----------------------------------------
27.32/8.89	
27.32/8.89	(610)
27.32/8.89	Obligation:
27.32/8.89	Q DP problem:
27.32/8.89	The TRS P consists of the following rules:
27.32/8.89	
27.32/8.89	   H(x, x) -> G(x, x, f(k))
27.32/8.89	   G(d, x, x) -> A^2
27.32/8.89	   A^2 -> H(f(c), f(c))
27.32/8.89	   A^2 -> H(f(d), f(d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, c))
27.32/8.89	   A^2 -> H(f(e), f(e))
27.32/8.89	   A^2 -> H(f(k), f(k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(c, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(c, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(c, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(c, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(c, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(c, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(d, e), U1(b, b))
27.32/8.89	   A^2 -> H(U1(d, e), f(c))
27.32/8.89	   A^2 -> H(U1(d, e), f(d))
27.32/8.89	   A^2 -> H(U1(d, c), U1(c, b))
27.32/8.89	   A^2 -> H(U1(d, c), U1(d, b))
27.32/8.89	   A^2 -> H(U1(d, c), U1(b, c))
27.32/8.89	   A^2 -> H(U1(d, c), U1(b, d))
27.32/8.89	   A^2 -> H(U1(d, c), U1(c, c))
27.32/8.89	   A^2 -> H(U1(d, c), f(e))
27.32/8.89	   A^2 -> H(U1(d, c), f(k))
27.32/8.89	   A^2 -> H(U1(d, c), U1(d, d))
27.32/8.89	   A^2 -> H(U1(d, a), U1(e, b))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(d, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(d, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(d, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(d, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(d, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(d, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(d, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(d, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(d, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(a, e), U1(c, b))
27.32/8.89	   A^2 -> H(U1(a, e), U1(d, b))
27.32/8.89	   A^2 -> H(U1(a, e), U1(b, c))
27.32/8.89	   A^2 -> H(U1(a, e), U1(b, d))
27.32/8.89	   A^2 -> H(U1(a, e), U1(c, c))
27.32/8.89	   A^2 -> H(U1(a, e), f(e))
27.32/8.89	   A^2 -> H(U1(a, e), f(k))
27.32/8.89	   A^2 -> H(U1(a, e), U1(d, d))
27.32/8.89	   A^2 -> H(U1(a, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(a, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(a, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(a, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(a, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(a, k), f(e))
27.32/8.89	   A^2 -> H(U1(a, k), f(k))
27.32/8.89	   A^2 -> H(U1(a, k), U1(d, d))
27.32/8.89	   A^2 -> H(U1(a, c), U1(e, b))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, b))
27.32/8.89	   A^2 -> H(U1(a, c), U1(c, d))
27.32/8.89	   A^2 -> H(U1(a, c), U1(d, c))
27.32/8.89	   A^2 -> H(U1(a, c), U1(b, e))
27.32/8.89	   A^2 -> H(U1(a, c), U1(b, k))
27.32/8.89	   A^2 -> H(U1(a, c), U1(e, c))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, c))
27.32/8.89	   A^2 -> H(U1(a, c), U1(c, e))
27.32/8.89	   A^2 -> H(U1(a, c), U1(c, k))
27.32/8.89	   A^2 -> H(U1(a, c), U1(e, e))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, k))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, d))
27.32/8.89	   A^2 -> H(U1(a, c), U1(d, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(e, b))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, b))
27.32/8.89	   A^2 -> H(U1(a, d), U1(c, d))
27.32/8.89	   A^2 -> H(U1(a, d), U1(d, c))
27.32/8.89	   A^2 -> H(U1(a, d), U1(b, e))
27.32/8.89	   A^2 -> H(U1(a, d), U1(b, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(e, c))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, c))
27.32/8.89	   A^2 -> H(U1(a, d), U1(c, e))
27.32/8.89	   A^2 -> H(U1(a, d), U1(c, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(e, e))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, d))
27.32/8.89	   A^2 -> H(U1(a, d), U1(d, k))
27.32/8.89	   A^2 -> H(U1(a, a), b)
27.32/8.89	   A^2 -> H(U1(a, a), U1(e, d))
27.32/8.89	   A^2 -> H(U1(a, a), U1(d, e))
27.32/8.89	   A^2 -> H(U1(a, a), c)
27.32/8.89	   A^2 -> H(U1(a, a), U1(e, k))
27.32/8.89	   A^2 -> H(U1(a, a), U1(k, e))
27.32/8.89	   A^2 -> H(U1(a, a), e)
27.32/8.89	   A^2 -> H(U1(a, a), U1(k, k))
27.32/8.89	   A^2 -> H(k, f(b))
27.32/8.89	   A^2 -> H(c, U1(b, b))
27.32/8.89	   A^2 -> H(c, f(c))
27.32/8.89	   A^2 -> H(c, f(d))
27.32/8.89	   A^2 -> H(U1(e, k), U1(b, b))
27.32/8.89	   A^2 -> H(U1(e, k), f(c))
27.32/8.89	   A^2 -> H(U1(e, k), f(d))
27.32/8.89	   A^2 -> H(U1(e, c), U1(c, b))
27.32/8.89	   A^2 -> H(U1(e, c), U1(d, b))
27.32/8.89	   A^2 -> H(U1(e, c), U1(b, c))
27.32/8.89	   A^2 -> H(U1(e, c), U1(b, d))
27.32/8.89	   A^2 -> H(U1(e, c), U1(c, c))
27.32/8.89	   A^2 -> H(U1(e, c), f(e))
27.32/8.89	   A^2 -> H(U1(e, c), f(k))
27.32/8.89	   A^2 -> H(U1(e, c), U1(d, d))
27.32/8.89	   A^2 -> H(U1(k, e), U1(b, b))
27.32/8.89	   A^2 -> H(U1(k, e), f(c))
27.32/8.89	   A^2 -> H(U1(k, e), f(d))
27.32/8.89	   A^2 -> H(U1(k, c), U1(c, b))
27.32/8.89	   A^2 -> H(U1(k, c), U1(d, b))
27.32/8.89	   A^2 -> H(U1(k, c), U1(b, c))
27.32/8.89	   A^2 -> H(U1(k, c), U1(b, d))
27.32/8.89	   A^2 -> H(U1(k, c), U1(c, c))
27.32/8.89	   A^2 -> H(U1(k, c), f(e))
27.32/8.89	   A^2 -> H(U1(k, c), f(k))
27.32/8.89	   A^2 -> H(U1(k, c), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, e), U1(c, b))
27.32/8.89	   A^2 -> H(U1(c, e), U1(d, b))
27.32/8.89	   A^2 -> H(U1(c, e), U1(b, c))
27.32/8.89	   A^2 -> H(U1(c, e), U1(b, d))
27.32/8.89	   A^2 -> H(U1(c, e), U1(c, c))
27.32/8.89	   A^2 -> H(U1(c, e), f(e))
27.32/8.89	   A^2 -> H(U1(c, e), f(k))
27.32/8.89	   A^2 -> H(U1(c, e), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(c, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(c, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(c, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(c, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(c, k), f(e))
27.32/8.89	   A^2 -> H(U1(c, k), f(k))
27.32/8.89	   A^2 -> H(U1(c, k), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(e, b))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, b))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(d, c))
27.32/8.89	   A^2 -> H(U1(c, c), U1(b, e))
27.32/8.89	   A^2 -> H(U1(c, c), U1(b, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(e, e))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(d, k))
27.32/8.89	   A^2 -> H(e, U1(b, b))
27.32/8.89	   A^2 -> H(e, f(c))
27.32/8.89	   A^2 -> H(e, f(d))
27.32/8.89	   A^2 -> H(U1(e, e), U1(c, b))
27.32/8.89	   A^2 -> H(U1(e, e), U1(d, b))
27.32/8.89	   A^2 -> H(U1(e, e), U1(b, c))
27.32/8.89	   A^2 -> H(U1(e, e), U1(b, d))
27.32/8.89	   A^2 -> H(U1(e, e), U1(c, c))
27.32/8.89	   A^2 -> H(U1(e, e), f(e))
27.32/8.89	   A^2 -> H(U1(e, e), f(k))
27.32/8.89	   A^2 -> H(U1(e, e), U1(d, d))
27.32/8.89	   A^2 -> H(f(e), U1(e, b))
27.32/8.89	   A^2 -> H(f(e), U1(k, b))
27.32/8.89	   A^2 -> H(f(e), U1(c, d))
27.32/8.89	   A^2 -> H(f(e), U1(d, c))
27.32/8.89	   A^2 -> H(f(e), U1(b, e))
27.32/8.89	   A^2 -> H(f(e), U1(b, k))
27.32/8.89	   A^2 -> H(f(e), U1(e, c))
27.32/8.89	   A^2 -> H(f(e), U1(k, c))
27.32/8.89	   A^2 -> H(f(e), U1(c, e))
27.32/8.89	   A^2 -> H(f(e), U1(c, k))
27.32/8.89	   A^2 -> H(f(e), U1(k, k))
27.32/8.89	   A^2 -> H(f(e), U1(k, d))
27.32/8.89	   A^2 -> H(f(e), U1(d, k))
27.32/8.89	   A^2 -> H(U1(k, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(k, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(k, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(k, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(k, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(k, k), f(e))
27.32/8.89	   A^2 -> H(U1(k, k), f(k))
27.32/8.89	   A^2 -> H(U1(k, k), U1(d, d))
27.32/8.89	   A^2 -> H(f(k), U1(e, b))
27.32/8.89	   A^2 -> H(f(k), U1(k, b))
27.32/8.89	   A^2 -> H(f(k), U1(c, d))
27.32/8.89	   A^2 -> H(f(k), U1(d, c))
27.32/8.89	   A^2 -> H(f(k), U1(b, e))
27.32/8.89	   A^2 -> H(f(k), U1(b, k))
27.32/8.89	   A^2 -> H(f(k), U1(e, c))
27.32/8.89	   A^2 -> H(f(k), U1(k, c))
27.32/8.89	   A^2 -> H(f(k), U1(c, e))
27.32/8.89	   A^2 -> H(f(k), U1(c, k))
27.32/8.89	   A^2 -> H(f(k), U1(e, e))
27.32/8.89	   A^2 -> H(f(k), U1(k, d))
27.32/8.89	   A^2 -> H(f(k), U1(d, k))
27.32/8.89	   A^2 -> H(f(c), b)
27.32/8.89	   A^2 -> H(f(c), U1(e, d))
27.32/8.89	   A^2 -> H(f(c), U1(d, e))
27.32/8.89	   A^2 -> H(f(k), U1(k, k))
27.32/8.89	   A^2 -> H(U1(k, k), U1(b, b))
27.32/8.89	   A^2 -> H(U1(k, k), f(c))
27.32/8.89	   A^2 -> H(U1(k, k), f(d))
27.32/8.89	   A^2 -> H(U1(k, d), U1(c, b))
27.32/8.89	   A^2 -> H(U1(k, d), U1(d, b))
27.32/8.89	   A^2 -> H(U1(k, d), U1(b, c))
27.32/8.89	   A^2 -> H(U1(k, d), U1(b, d))
27.32/8.89	   A^2 -> H(U1(k, d), U1(c, c))
27.32/8.89	   A^2 -> H(U1(k, d), f(e))
27.32/8.89	   A^2 -> H(U1(k, d), f(k))
27.32/8.89	   A^2 -> H(U1(k, d), U1(d, d))
27.32/8.89	   A^2 -> H(U1(d, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(d, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(d, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(d, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(d, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(d, k), f(e))
27.32/8.89	   A^2 -> H(U1(d, k), f(k))
27.32/8.89	   A^2 -> H(U1(d, k), U1(d, d))
27.32/8.89	   A^2 -> H(U1(d, d), U1(e, b))
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, b))
27.32/8.89	   A^2 -> H(U1(d, d), U1(c, d))
27.32/8.89	   A^2 -> H(U1(d, d), U1(d, c))
27.32/8.89	   A^2 -> H(U1(d, d), U1(b, e))
27.32/8.89	   A^2 -> H(U1(d, d), U1(b, k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(e, c))
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, c))
27.32/8.89	   A^2 -> H(U1(d, d), U1(c, e))
27.32/8.89	   A^2 -> H(U1(d, d), U1(c, k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(e, e))
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, k))
27.32/8.89	   A^2 -> H(f(d), b)
27.32/8.89	   A^2 -> H(f(d), U1(e, d))
27.32/8.89	   A^2 -> H(f(d), U1(d, e))
27.32/8.89	   A^2 -> H(f(d), c)
27.32/8.89	   A^2 -> H(f(d), U1(e, k))
27.32/8.89	   A^2 -> H(f(d), U1(k, e))
27.32/8.89	   A^2 -> H(f(d), e)
27.32/8.89	   A^2 -> H(f(a), d)
27.32/8.89	   A^2 -> H(U1(c, c), U1(e, c))
27.32/8.89	   A^2 -> H(f(c), c)
27.32/8.89	   A^2 -> H(f(c), U1(e, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, c))
27.32/8.89	   A^2 -> H(f(c), U1(k, e))
27.32/8.89	   A^2 -> H(f(c), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, e))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, k))
27.32/8.89	   A^2 -> H(f(a), k)
27.32/8.89	   A^2 -> H(f(e), U1(e, e))
27.32/8.89	   A^2 -> H(f(c), e)
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, d))
27.32/8.89	   A^2 -> H(f(d), U1(k, k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(d, k))
27.32/8.89	   A^2 -> H(d, U1(b, b))
27.32/8.89	   A^2 -> H(d, f(c))
27.32/8.89	   A^2 -> H(d, f(d))
27.32/8.89	   A^2 -> H(a, U1(c, b))
27.32/8.89	   A^2 -> H(a, U1(d, b))
27.32/8.89	   A^2 -> H(a, U1(b, c))
27.32/8.89	   A^2 -> H(a, U1(b, d))
27.32/8.89	   A^2 -> H(a, U1(c, c))
27.32/8.89	   A^2 -> H(a, f(e))
27.32/8.89	   A^2 -> H(a, f(k))
27.32/8.89	   A^2 -> H(a, U1(d, d))
27.32/8.89	   A^2 -> H(U1(e, d), U1(c, b))
27.32/8.89	   A^2 -> H(U1(e, d), U1(d, b))
27.32/8.89	   A^2 -> H(U1(e, d), U1(b, c))
27.32/8.89	   A^2 -> H(U1(e, d), U1(b, d))
27.32/8.89	   A^2 -> H(U1(e, d), U1(c, c))
27.32/8.89	   A^2 -> H(U1(e, d), f(e))
27.32/8.89	   A^2 -> H(U1(e, d), f(k))
27.32/8.89	   A^2 -> H(U1(e, d), U1(d, d))
27.32/8.89	   A^2 -> H(U1(e, a), U1(e, b))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(e, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(e, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(e, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(e, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(e, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(e, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(e, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(e, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(e, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(e, b))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(k, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(k, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(k, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(k, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(k, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(k, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(k, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(k, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(e, b))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, b))
27.32/8.89	   A^2 -> H(U1(c, d), U1(c, d))
27.32/8.89	   A^2 -> H(U1(c, d), U1(d, c))
27.32/8.89	   A^2 -> H(U1(c, d), U1(b, e))
27.32/8.89	   A^2 -> H(U1(c, d), U1(b, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(e, c))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, c))
27.32/8.89	   A^2 -> H(U1(c, d), U1(c, e))
27.32/8.89	   A^2 -> H(U1(c, d), U1(c, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(e, e))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, d), U1(k, d))
27.32/8.89	   A^2 -> H(U1(c, d), U1(d, k))
27.32/8.89	   A^2 -> H(U1(c, a), b)
27.32/8.89	   A^2 -> H(U1(c, a), U1(e, d))
27.32/8.89	   A^2 -> H(U1(c, a), U1(d, e))
27.32/8.89	
27.32/8.89	The TRS R consists of the following rules:
27.32/8.89	
27.32/8.89	   f(x) -> U1(x, x)
27.32/8.89	   U1(e, x) -> x
27.32/8.89	   a -> c
27.32/8.89	   a -> d
27.32/8.89	   b -> c
27.32/8.89	   b -> d
27.32/8.89	   d -> k
27.32/8.89	   c -> e
27.32/8.89	   c -> k
27.32/8.89	
27.32/8.89	Q is empty.
27.32/8.89	We have to consider all minimal (P,Q,R)-chains.
27.32/8.89	----------------------------------------
27.32/8.89	
27.32/8.89	(611) TransformationProof (EQUIVALENT)
27.32/8.89	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
27.32/8.89	
27.32/8.89	   (A^2 -> H(U1(e, a), U1(b, e)),A^2 -> H(U1(e, a), U1(b, e)))
27.32/8.89	   (A^2 -> H(U1(k, a), U1(b, e)),A^2 -> H(U1(k, a), U1(b, e)))
27.32/8.89	   (A^2 -> H(U1(c, c), U1(b, e)),A^2 -> H(U1(c, c), U1(b, e)))
27.32/8.89	   (A^2 -> H(U1(c, d), U1(b, e)),A^2 -> H(U1(c, d), U1(b, e)))
27.32/8.89	   (A^2 -> H(U1(c, a), U1(c, e)),A^2 -> H(U1(c, a), U1(c, e)))
27.32/8.89	   (A^2 -> H(U1(c, a), U1(d, e)),A^2 -> H(U1(c, a), U1(d, e)))
27.32/8.89	
27.32/8.89	
27.32/8.89	----------------------------------------
27.32/8.89	
27.32/8.89	(612)
27.32/8.89	Obligation:
27.32/8.89	Q DP problem:
27.32/8.89	The TRS P consists of the following rules:
27.32/8.89	
27.32/8.89	   H(x, x) -> G(x, x, f(k))
27.32/8.89	   G(d, x, x) -> A^2
27.32/8.89	   A^2 -> H(f(c), f(c))
27.32/8.89	   A^2 -> H(f(d), f(d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, c))
27.32/8.89	   A^2 -> H(f(e), f(e))
27.32/8.89	   A^2 -> H(f(k), f(k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(c, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(c, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(c, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(c, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(c, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(d, e), U1(b, b))
27.32/8.89	   A^2 -> H(U1(d, e), f(c))
27.32/8.89	   A^2 -> H(U1(d, e), f(d))
27.32/8.89	   A^2 -> H(U1(d, c), U1(c, b))
27.32/8.89	   A^2 -> H(U1(d, c), U1(d, b))
27.32/8.89	   A^2 -> H(U1(d, c), U1(b, c))
27.32/8.89	   A^2 -> H(U1(d, c), U1(b, d))
27.32/8.89	   A^2 -> H(U1(d, c), U1(c, c))
27.32/8.89	   A^2 -> H(U1(d, c), f(e))
27.32/8.89	   A^2 -> H(U1(d, c), f(k))
27.32/8.89	   A^2 -> H(U1(d, c), U1(d, d))
27.32/8.89	   A^2 -> H(U1(d, a), U1(e, b))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(d, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(d, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(d, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(d, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(d, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(d, a), U1(c, e))
27.32/8.89	   A^2 -> H(U1(d, a), U1(c, k))
27.32/8.89	   A^2 -> H(U1(d, a), U1(e, e))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, k))
27.32/8.89	   A^2 -> H(U1(d, a), U1(k, d))
27.32/8.89	   A^2 -> H(U1(d, a), U1(d, k))
27.32/8.89	   A^2 -> H(U1(a, e), U1(c, b))
27.32/8.89	   A^2 -> H(U1(a, e), U1(d, b))
27.32/8.89	   A^2 -> H(U1(a, e), U1(b, c))
27.32/8.89	   A^2 -> H(U1(a, e), U1(b, d))
27.32/8.89	   A^2 -> H(U1(a, e), U1(c, c))
27.32/8.89	   A^2 -> H(U1(a, e), f(e))
27.32/8.89	   A^2 -> H(U1(a, e), f(k))
27.32/8.89	   A^2 -> H(U1(a, e), U1(d, d))
27.32/8.89	   A^2 -> H(U1(a, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(a, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(a, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(a, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(a, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(a, k), f(e))
27.32/8.89	   A^2 -> H(U1(a, k), f(k))
27.32/8.89	   A^2 -> H(U1(a, k), U1(d, d))
27.32/8.89	   A^2 -> H(U1(a, c), U1(e, b))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, b))
27.32/8.89	   A^2 -> H(U1(a, c), U1(c, d))
27.32/8.89	   A^2 -> H(U1(a, c), U1(d, c))
27.32/8.89	   A^2 -> H(U1(a, c), U1(b, e))
27.32/8.89	   A^2 -> H(U1(a, c), U1(b, k))
27.32/8.89	   A^2 -> H(U1(a, c), U1(e, c))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, c))
27.32/8.89	   A^2 -> H(U1(a, c), U1(c, e))
27.32/8.89	   A^2 -> H(U1(a, c), U1(c, k))
27.32/8.89	   A^2 -> H(U1(a, c), U1(e, e))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, k))
27.32/8.89	   A^2 -> H(U1(a, c), U1(k, d))
27.32/8.89	   A^2 -> H(U1(a, c), U1(d, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(e, b))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, b))
27.32/8.89	   A^2 -> H(U1(a, d), U1(c, d))
27.32/8.89	   A^2 -> H(U1(a, d), U1(d, c))
27.32/8.89	   A^2 -> H(U1(a, d), U1(b, e))
27.32/8.89	   A^2 -> H(U1(a, d), U1(b, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(e, c))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, c))
27.32/8.89	   A^2 -> H(U1(a, d), U1(c, e))
27.32/8.89	   A^2 -> H(U1(a, d), U1(c, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(e, e))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, k))
27.32/8.89	   A^2 -> H(U1(a, d), U1(k, d))
27.32/8.89	   A^2 -> H(U1(a, d), U1(d, k))
27.32/8.89	   A^2 -> H(U1(a, a), b)
27.32/8.89	   A^2 -> H(U1(a, a), U1(e, d))
27.32/8.89	   A^2 -> H(U1(a, a), U1(d, e))
27.32/8.89	   A^2 -> H(U1(a, a), c)
27.32/8.89	   A^2 -> H(U1(a, a), U1(e, k))
27.32/8.89	   A^2 -> H(U1(a, a), U1(k, e))
27.32/8.89	   A^2 -> H(U1(a, a), e)
27.32/8.89	   A^2 -> H(U1(a, a), U1(k, k))
27.32/8.89	   A^2 -> H(k, f(b))
27.32/8.89	   A^2 -> H(c, U1(b, b))
27.32/8.89	   A^2 -> H(c, f(c))
27.32/8.89	   A^2 -> H(c, f(d))
27.32/8.89	   A^2 -> H(U1(e, k), U1(b, b))
27.32/8.89	   A^2 -> H(U1(e, k), f(c))
27.32/8.89	   A^2 -> H(U1(e, k), f(d))
27.32/8.89	   A^2 -> H(U1(e, c), U1(c, b))
27.32/8.89	   A^2 -> H(U1(e, c), U1(d, b))
27.32/8.89	   A^2 -> H(U1(e, c), U1(b, c))
27.32/8.89	   A^2 -> H(U1(e, c), U1(b, d))
27.32/8.89	   A^2 -> H(U1(e, c), U1(c, c))
27.32/8.89	   A^2 -> H(U1(e, c), f(e))
27.32/8.89	   A^2 -> H(U1(e, c), f(k))
27.32/8.89	   A^2 -> H(U1(e, c), U1(d, d))
27.32/8.89	   A^2 -> H(U1(k, e), U1(b, b))
27.32/8.89	   A^2 -> H(U1(k, e), f(c))
27.32/8.89	   A^2 -> H(U1(k, e), f(d))
27.32/8.89	   A^2 -> H(U1(k, c), U1(c, b))
27.32/8.89	   A^2 -> H(U1(k, c), U1(d, b))
27.32/8.89	   A^2 -> H(U1(k, c), U1(b, c))
27.32/8.89	   A^2 -> H(U1(k, c), U1(b, d))
27.32/8.89	   A^2 -> H(U1(k, c), U1(c, c))
27.32/8.89	   A^2 -> H(U1(k, c), f(e))
27.32/8.89	   A^2 -> H(U1(k, c), f(k))
27.32/8.89	   A^2 -> H(U1(k, c), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, e), U1(c, b))
27.32/8.89	   A^2 -> H(U1(c, e), U1(d, b))
27.32/8.89	   A^2 -> H(U1(c, e), U1(b, c))
27.32/8.89	   A^2 -> H(U1(c, e), U1(b, d))
27.32/8.89	   A^2 -> H(U1(c, e), U1(c, c))
27.32/8.89	   A^2 -> H(U1(c, e), f(e))
27.32/8.89	   A^2 -> H(U1(c, e), f(k))
27.32/8.89	   A^2 -> H(U1(c, e), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(c, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(c, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(c, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(c, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(c, k), f(e))
27.32/8.89	   A^2 -> H(U1(c, k), f(k))
27.32/8.89	   A^2 -> H(U1(c, k), U1(d, d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(e, b))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, b))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(d, c))
27.32/8.89	   A^2 -> H(U1(c, c), U1(b, e))
27.32/8.89	   A^2 -> H(U1(c, c), U1(b, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(e, e))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, d))
27.32/8.89	   A^2 -> H(U1(c, c), U1(d, k))
27.32/8.89	   A^2 -> H(e, U1(b, b))
27.32/8.89	   A^2 -> H(e, f(c))
27.32/8.89	   A^2 -> H(e, f(d))
27.32/8.89	   A^2 -> H(U1(e, e), U1(c, b))
27.32/8.89	   A^2 -> H(U1(e, e), U1(d, b))
27.32/8.89	   A^2 -> H(U1(e, e), U1(b, c))
27.32/8.89	   A^2 -> H(U1(e, e), U1(b, d))
27.32/8.89	   A^2 -> H(U1(e, e), U1(c, c))
27.32/8.89	   A^2 -> H(U1(e, e), f(e))
27.32/8.89	   A^2 -> H(U1(e, e), f(k))
27.32/8.89	   A^2 -> H(U1(e, e), U1(d, d))
27.32/8.89	   A^2 -> H(f(e), U1(e, b))
27.32/8.89	   A^2 -> H(f(e), U1(k, b))
27.32/8.89	   A^2 -> H(f(e), U1(c, d))
27.32/8.89	   A^2 -> H(f(e), U1(d, c))
27.32/8.89	   A^2 -> H(f(e), U1(b, e))
27.32/8.89	   A^2 -> H(f(e), U1(b, k))
27.32/8.89	   A^2 -> H(f(e), U1(e, c))
27.32/8.89	   A^2 -> H(f(e), U1(k, c))
27.32/8.89	   A^2 -> H(f(e), U1(c, e))
27.32/8.89	   A^2 -> H(f(e), U1(c, k))
27.32/8.89	   A^2 -> H(f(e), U1(k, k))
27.32/8.89	   A^2 -> H(f(e), U1(k, d))
27.32/8.89	   A^2 -> H(f(e), U1(d, k))
27.32/8.89	   A^2 -> H(U1(k, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(k, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(k, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(k, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(k, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(k, k), f(e))
27.32/8.89	   A^2 -> H(U1(k, k), f(k))
27.32/8.89	   A^2 -> H(U1(k, k), U1(d, d))
27.32/8.89	   A^2 -> H(f(k), U1(e, b))
27.32/8.89	   A^2 -> H(f(k), U1(k, b))
27.32/8.89	   A^2 -> H(f(k), U1(c, d))
27.32/8.89	   A^2 -> H(f(k), U1(d, c))
27.32/8.89	   A^2 -> H(f(k), U1(b, e))
27.32/8.89	   A^2 -> H(f(k), U1(b, k))
27.32/8.89	   A^2 -> H(f(k), U1(e, c))
27.32/8.89	   A^2 -> H(f(k), U1(k, c))
27.32/8.89	   A^2 -> H(f(k), U1(c, e))
27.32/8.89	   A^2 -> H(f(k), U1(c, k))
27.32/8.89	   A^2 -> H(f(k), U1(e, e))
27.32/8.89	   A^2 -> H(f(k), U1(k, d))
27.32/8.89	   A^2 -> H(f(k), U1(d, k))
27.32/8.89	   A^2 -> H(f(c), b)
27.32/8.89	   A^2 -> H(f(c), U1(e, d))
27.32/8.89	   A^2 -> H(f(c), U1(d, e))
27.32/8.89	   A^2 -> H(f(k), U1(k, k))
27.32/8.89	   A^2 -> H(U1(k, k), U1(b, b))
27.32/8.89	   A^2 -> H(U1(k, k), f(c))
27.32/8.89	   A^2 -> H(U1(k, k), f(d))
27.32/8.89	   A^2 -> H(U1(k, d), U1(c, b))
27.32/8.89	   A^2 -> H(U1(k, d), U1(d, b))
27.32/8.89	   A^2 -> H(U1(k, d), U1(b, c))
27.32/8.89	   A^2 -> H(U1(k, d), U1(b, d))
27.32/8.89	   A^2 -> H(U1(k, d), U1(c, c))
27.32/8.89	   A^2 -> H(U1(k, d), f(e))
27.32/8.89	   A^2 -> H(U1(k, d), f(k))
27.32/8.89	   A^2 -> H(U1(k, d), U1(d, d))
27.32/8.89	   A^2 -> H(U1(d, k), U1(c, b))
27.32/8.89	   A^2 -> H(U1(d, k), U1(d, b))
27.32/8.89	   A^2 -> H(U1(d, k), U1(b, c))
27.32/8.89	   A^2 -> H(U1(d, k), U1(b, d))
27.32/8.89	   A^2 -> H(U1(d, k), U1(c, c))
27.32/8.89	   A^2 -> H(U1(d, k), f(e))
27.32/8.89	   A^2 -> H(U1(d, k), f(k))
27.32/8.89	   A^2 -> H(U1(d, k), U1(d, d))
27.32/8.89	   A^2 -> H(U1(d, d), U1(e, b))
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, b))
27.32/8.89	   A^2 -> H(U1(d, d), U1(c, d))
27.32/8.89	   A^2 -> H(U1(d, d), U1(d, c))
27.32/8.89	   A^2 -> H(U1(d, d), U1(b, e))
27.32/8.89	   A^2 -> H(U1(d, d), U1(b, k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(e, c))
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, c))
27.32/8.89	   A^2 -> H(U1(d, d), U1(c, e))
27.32/8.89	   A^2 -> H(U1(d, d), U1(c, k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(e, e))
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, k))
27.32/8.89	   A^2 -> H(f(d), b)
27.32/8.89	   A^2 -> H(f(d), U1(e, d))
27.32/8.89	   A^2 -> H(f(d), U1(d, e))
27.32/8.89	   A^2 -> H(f(d), c)
27.32/8.89	   A^2 -> H(f(d), U1(e, k))
27.32/8.89	   A^2 -> H(f(d), U1(k, e))
27.32/8.89	   A^2 -> H(f(d), e)
27.32/8.89	   A^2 -> H(f(a), d)
27.32/8.89	   A^2 -> H(U1(c, c), U1(e, c))
27.32/8.89	   A^2 -> H(f(c), c)
27.32/8.89	   A^2 -> H(f(c), U1(e, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(k, c))
27.32/8.89	   A^2 -> H(f(c), U1(k, e))
27.32/8.89	   A^2 -> H(f(c), U1(k, k))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, e))
27.32/8.89	   A^2 -> H(U1(c, c), U1(c, k))
27.32/8.89	   A^2 -> H(f(a), k)
27.32/8.89	   A^2 -> H(f(e), U1(e, e))
27.32/8.89	   A^2 -> H(f(c), e)
27.32/8.89	   A^2 -> H(U1(d, d), U1(k, d))
27.32/8.89	   A^2 -> H(f(d), U1(k, k))
27.32/8.89	   A^2 -> H(U1(d, d), U1(d, k))
27.32/8.89	   A^2 -> H(d, U1(b, b))
27.32/8.89	   A^2 -> H(d, f(c))
27.32/8.89	   A^2 -> H(d, f(d))
27.32/8.89	   A^2 -> H(a, U1(c, b))
27.32/8.89	   A^2 -> H(a, U1(d, b))
27.32/8.89	   A^2 -> H(a, U1(b, c))
27.32/8.89	   A^2 -> H(a, U1(b, d))
27.32/8.89	   A^2 -> H(a, U1(c, c))
27.32/8.89	   A^2 -> H(a, f(e))
27.32/8.89	   A^2 -> H(a, f(k))
27.32/8.89	   A^2 -> H(a, U1(d, d))
27.32/8.89	   A^2 -> H(U1(e, d), U1(c, b))
27.32/8.89	   A^2 -> H(U1(e, d), U1(d, b))
27.32/8.89	   A^2 -> H(U1(e, d), U1(b, c))
27.32/8.89	   A^2 -> H(U1(e, d), U1(b, d))
27.32/8.89	   A^2 -> H(U1(e, d), U1(c, c))
27.32/8.89	   A^2 -> H(U1(e, d), f(e))
27.32/8.89	   A^2 -> H(U1(e, d), f(k))
27.32/8.89	   A^2 -> H(U1(e, d), U1(d, d))
27.32/8.89	   A^2 -> H(U1(e, a), U1(e, b))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, b))
27.32/8.89	   A^2 -> H(U1(e, a), U1(c, d))
27.32/8.89	   A^2 -> H(U1(e, a), U1(d, c))
27.32/8.89	   A^2 -> H(U1(e, a), U1(b, e))
27.32/8.89	   A^2 -> H(U1(e, a), U1(b, k))
27.32/8.89	   A^2 -> H(U1(e, a), U1(e, c))
27.32/8.89	   A^2 -> H(U1(e, a), U1(k, c))
27.32/8.89	   A^2 -> H(U1(e, a), U1(c, e))
27.32/8.90	   A^2 -> H(U1(e, a), U1(c, k))
27.32/8.90	   A^2 -> H(U1(e, a), U1(e, e))
27.32/8.90	   A^2 -> H(U1(e, a), U1(k, k))
27.32/8.90	   A^2 -> H(U1(e, a), U1(k, d))
27.32/8.90	   A^2 -> H(U1(e, a), U1(d, k))
27.32/8.90	   A^2 -> H(U1(k, a), U1(e, b))
27.32/8.90	   A^2 -> H(U1(k, a), U1(k, b))
27.32/8.90	   A^2 -> H(U1(k, a), U1(c, d))
27.32/8.90	   A^2 -> H(U1(k, a), U1(d, c))
27.32/8.90	   A^2 -> H(U1(k, a), U1(b, e))
27.32/8.90	   A^2 -> H(U1(k, a), U1(b, k))
27.32/8.90	   A^2 -> H(U1(k, a), U1(e, c))
27.32/8.90	   A^2 -> H(U1(k, a), U1(k, c))
27.32/8.90	   A^2 -> H(U1(k, a), U1(c, e))
27.32/8.90	   A^2 -> H(U1(k, a), U1(c, k))
27.32/8.90	   A^2 -> H(U1(k, a), U1(e, e))
27.32/8.90	   A^2 -> H(U1(k, a), U1(k, k))
27.32/8.90	   A^2 -> H(U1(k, a), U1(k, d))
27.32/8.90	   A^2 -> H(U1(k, a), U1(d, k))
27.32/8.90	   A^2 -> H(U1(c, d), U1(e, b))
27.32/8.90	   A^2 -> H(U1(c, d), U1(k, b))
27.32/8.90	   A^2 -> H(U1(c, d), U1(c, d))
27.32/8.90	   A^2 -> H(U1(c, d), U1(d, c))
27.32/8.90	   A^2 -> H(U1(c, d), U1(b, e))
27.32/8.90	   A^2 -> H(U1(c, d), U1(b, k))
27.32/8.90	   A^2 -> H(U1(c, d), U1(e, c))
27.32/8.90	   A^2 -> H(U1(c, d), U1(k, c))
27.32/8.90	   A^2 -> H(U1(c, d), U1(c, e))
27.32/8.90	   A^2 -> H(U1(c, d), U1(c, k))
27.32/8.90	   A^2 -> H(U1(c, d), U1(e, e))
27.32/8.90	   A^2 -> H(U1(c, d), U1(k, k))
27.32/8.90	   A^2 -> H(U1(c, d), U1(k, d))
27.32/8.90	   A^2 -> H(U1(c, d), U1(d, k))
27.32/8.90	   A^2 -> H(U1(c, a), b)
27.32/8.90	   A^2 -> H(U1(c, a), U1(e, d))
27.32/8.90	   A^2 -> H(U1(c, a), U1(d, e))
27.32/8.90	
27.32/8.90	The TRS R consists of the following rules:
27.32/8.90	
27.32/8.90	   f(x) -> U1(x, x)
27.32/8.90	   U1(e, x) -> x
27.32/8.90	   a -> c
27.32/8.90	   a -> d
27.32/8.90	   b -> c
27.32/8.90	   b -> d
27.32/8.90	   d -> k
27.32/8.90	   c -> e
27.32/8.90	   c -> k
27.32/8.90	
27.32/8.90	Q is empty.
27.32/8.90	We have to consider all minimal (P,Q,R)-chains.
27.32/8.90	----------------------------------------
27.32/8.90	
27.32/8.90	(613) TransformationProof (EQUIVALENT)
27.32/8.90	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
27.32/8.90	
27.32/8.90	   (A^2 -> H(U1(e, a), U1(b, k)),A^2 -> H(U1(e, a), U1(b, k)))
27.32/8.90	   (A^2 -> H(U1(k, a), U1(b, k)),A^2 -> H(U1(k, a), U1(b, k)))
27.32/8.90	   (A^2 -> H(U1(c, c), U1(b, k)),A^2 -> H(U1(c, c), U1(b, k)))
27.32/8.90	   (A^2 -> H(U1(c, d), U1(b, k)),A^2 -> H(U1(c, d), U1(b, k)))
27.32/8.90	   (A^2 -> H(U1(c, a), U1(c, k)),A^2 -> H(U1(c, a), U1(c, k)))
27.32/8.90	   (A^2 -> H(U1(c, a), U1(d, k)),A^2 -> H(U1(c, a), U1(d, k)))
27.32/8.90	
27.32/8.90	
27.32/8.90	----------------------------------------
27.32/8.90	
27.32/8.90	(614)
27.32/8.90	Obligation:
27.32/8.90	Q DP problem:
27.32/8.90	The TRS P consists of the following rules:
27.32/8.90	
27.32/8.90	   H(x, x) -> G(x, x, f(k))
27.32/8.90	   G(d, x, x) -> A^2
27.32/8.90	   A^2 -> H(f(c), f(c))
27.32/8.90	   A^2 -> H(f(d), f(d))
27.32/8.90	   A^2 -> H(U1(c, c), U1(c, c))
27.32/8.90	   A^2 -> H(f(e), f(e))
27.32/8.90	   A^2 -> H(f(k), f(k))
27.32/8.90	   A^2 -> H(U1(d, d), U1(d, d))
27.32/8.90	   A^2 -> H(U1(c, a), U1(e, c))
27.32/8.90	   A^2 -> H(U1(c, a), U1(k, c))
27.32/8.90	   A^2 -> H(U1(c, a), U1(c, e))
27.32/8.90	   A^2 -> H(U1(c, a), U1(c, k))
27.32/8.90	   A^2 -> H(U1(c, a), U1(e, e))
27.32/8.90	   A^2 -> H(U1(c, a), U1(k, k))
27.32/8.90	   A^2 -> H(U1(c, a), U1(k, d))
27.32/8.90	   A^2 -> H(U1(c, a), U1(d, k))
27.32/8.90	   A^2 -> H(U1(d, e), U1(b, b))
27.32/8.90	   A^2 -> H(U1(d, e), f(c))
27.32/8.90	   A^2 -> H(U1(d, e), f(d))
27.32/8.90	   A^2 -> H(U1(d, c), U1(c, b))
27.32/8.90	   A^2 -> H(U1(d, c), U1(d, b))
27.32/8.90	   A^2 -> H(U1(d, c), U1(b, c))
27.32/8.90	   A^2 -> H(U1(d, c), U1(b, d))
27.32/8.90	   A^2 -> H(U1(d, c), U1(c, c))
27.32/8.90	   A^2 -> H(U1(d, c), f(e))
27.32/8.90	   A^2 -> H(U1(d, c), f(k))
27.32/8.90	   A^2 -> H(U1(d, c), U1(d, d))
27.32/8.90	   A^2 -> H(U1(d, a), U1(e, b))
27.32/8.90	   A^2 -> H(U1(d, a), U1(k, b))
27.32/8.90	   A^2 -> H(U1(d, a), U1(c, d))
27.32/8.90	   A^2 -> H(U1(d, a), U1(d, c))
27.32/8.90	   A^2 -> H(U1(d, a), U1(b, e))
27.32/8.90	   A^2 -> H(U1(d, a), U1(b, k))
27.32/8.90	   A^2 -> H(U1(d, a), U1(e, c))
27.32/8.90	   A^2 -> H(U1(d, a), U1(k, c))
27.32/8.90	   A^2 -> H(U1(d, a), U1(c, e))
27.32/8.90	   A^2 -> H(U1(d, a), U1(c, k))
27.32/8.90	   A^2 -> H(U1(d, a), U1(e, e))
27.32/8.90	   A^2 -> H(U1(d, a), U1(k, k))
27.32/8.90	   A^2 -> H(U1(d, a), U1(k, d))
27.32/8.90	   A^2 -> H(U1(d, a), U1(d, k))
27.32/8.90	   A^2 -> H(U1(a, e), U1(c, b))
27.32/8.90	   A^2 -> H(U1(a, e), U1(d, b))
27.32/8.90	   A^2 -> H(U1(a, e), U1(b, c))
27.32/8.90	   A^2 -> H(U1(a, e), U1(b, d))
27.32/8.90	   A^2 -> H(U1(a, e), U1(c, c))
27.32/8.90	   A^2 -> H(U1(a, e), f(e))
27.32/8.90	   A^2 -> H(U1(a, e), f(k))
27.32/8.90	   A^2 -> H(U1(a, e), U1(d, d))
27.32/8.90	   A^2 -> H(U1(a, k), U1(c, b))
27.32/8.90	   A^2 -> H(U1(a, k), U1(d, b))
27.32/8.90	   A^2 -> H(U1(a, k), U1(b, c))
27.32/8.90	   A^2 -> H(U1(a, k), U1(b, d))
27.32/8.90	   A^2 -> H(U1(a, k), U1(c, c))
27.32/8.90	   A^2 -> H(U1(a, k), f(e))
27.32/8.90	   A^2 -> H(U1(a, k), f(k))
27.32/8.90	   A^2 -> H(U1(a, k), U1(d, d))
27.32/8.90	   A^2 -> H(U1(a, c), U1(e, b))
27.32/8.90	   A^2 -> H(U1(a, c), U1(k, b))
27.32/8.90	   A^2 -> H(U1(a, c), U1(c, d))
27.32/8.90	   A^2 -> H(U1(a, c), U1(d, c))
27.32/8.90	   A^2 -> H(U1(a, c), U1(b, e))
27.32/8.90	   A^2 -> H(U1(a, c), U1(b, k))
27.32/8.90	   A^2 -> H(U1(a, c), U1(e, c))
27.32/8.90	   A^2 -> H(U1(a, c), U1(k, c))
27.32/8.90	   A^2 -> H(U1(a, c), U1(c, e))
27.32/8.90	   A^2 -> H(U1(a, c), U1(c, k))
27.32/8.90	   A^2 -> H(U1(a, c), U1(e, e))
27.32/8.90	   A^2 -> H(U1(a, c), U1(k, k))
27.32/8.90	   A^2 -> H(U1(a, c), U1(k, d))
27.32/8.90	   A^2 -> H(U1(a, c), U1(d, k))
27.32/8.90	   A^2 -> H(U1(a, d), U1(e, b))
27.32/8.90	   A^2 -> H(U1(a, d), U1(k, b))
27.32/8.90	   A^2 -> H(U1(a, d), U1(c, d))
27.32/8.90	   A^2 -> H(U1(a, d), U1(d, c))
27.32/8.90	   A^2 -> H(U1(a, d), U1(b, e))
27.32/8.90	   A^2 -> H(U1(a, d), U1(b, k))
27.32/8.90	   A^2 -> H(U1(a, d), U1(e, c))
27.32/8.90	   A^2 -> H(U1(a, d), U1(k, c))
27.32/8.90	   A^2 -> H(U1(a, d), U1(c, e))
27.32/8.90	   A^2 -> H(U1(a, d), U1(c, k))
27.32/8.90	   A^2 -> H(U1(a, d), U1(e, e))
27.32/8.90	   A^2 -> H(U1(a, d), U1(k, k))
27.32/8.90	   A^2 -> H(U1(a, d), U1(k, d))
27.32/8.90	   A^2 -> H(U1(a, d), U1(d, k))
27.32/8.90	   A^2 -> H(U1(a, a), b)
27.32/8.90	   A^2 -> H(U1(a, a), U1(e, d))
27.32/8.90	   A^2 -> H(U1(a, a), U1(d, e))
27.32/8.90	   A^2 -> H(U1(a, a), c)
27.32/8.90	   A^2 -> H(U1(a, a), U1(e, k))
27.32/8.90	   A^2 -> H(U1(a, a), U1(k, e))
27.32/8.90	   A^2 -> H(U1(a, a), e)
27.32/8.90	   A^2 -> H(U1(a, a), U1(k, k))
27.32/8.90	   A^2 -> H(k, f(b))
27.32/8.90	   A^2 -> H(c, U1(b, b))
27.32/8.90	   A^2 -> H(c, f(c))
27.32/8.90	   A^2 -> H(c, f(d))
27.32/8.90	   A^2 -> H(U1(e, k), U1(b, b))
27.32/8.90	   A^2 -> H(U1(e, k), f(c))
27.32/8.90	   A^2 -> H(U1(e, k), f(d))
27.32/8.90	   A^2 -> H(U1(e, c), U1(c, b))
27.32/8.91	   A^2 -> H(U1(e, c), U1(d, b))
27.32/8.91	   A^2 -> H(U1(e, c), U1(b, c))
27.32/8.91	   A^2 -> H(U1(e, c), U1(b, d))
27.32/8.91	   A^2 -> H(U1(e, c), U1(c, c))
27.32/8.91	   A^2 -> H(U1(e, c), f(e))
27.32/8.91	   A^2 -> H(U1(e, c), f(k))
27.32/8.91	   A^2 -> H(U1(e, c), U1(d, d))
27.32/8.91	   A^2 -> H(U1(k, e), U1(b, b))
27.32/8.91	   A^2 -> H(U1(k, e), f(c))
27.32/8.91	   A^2 -> H(U1(k, e), f(d))
27.32/8.91	   A^2 -> H(U1(k, c), U1(c, b))
27.32/8.91	   A^2 -> H(U1(k, c), U1(d, b))
27.32/8.91	   A^2 -> H(U1(k, c), U1(b, c))
27.32/8.91	   A^2 -> H(U1(k, c), U1(b, d))
27.32/8.91	   A^2 -> H(U1(k, c), U1(c, c))
27.32/8.91	   A^2 -> H(U1(k, c), f(e))
27.32/8.91	   A^2 -> H(U1(k, c), f(k))
27.32/8.91	   A^2 -> H(U1(k, c), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, e), U1(c, b))
27.32/8.91	   A^2 -> H(U1(c, e), U1(d, b))
27.32/8.91	   A^2 -> H(U1(c, e), U1(b, c))
27.32/8.91	   A^2 -> H(U1(c, e), U1(b, d))
27.32/8.91	   A^2 -> H(U1(c, e), U1(c, c))
27.32/8.91	   A^2 -> H(U1(c, e), f(e))
27.32/8.91	   A^2 -> H(U1(c, e), f(k))
27.32/8.91	   A^2 -> H(U1(c, e), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(c, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(c, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(c, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(c, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(c, k), f(e))
27.32/8.91	   A^2 -> H(U1(c, k), f(k))
27.32/8.91	   A^2 -> H(U1(c, k), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(e, b))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, b))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(d, c))
27.32/8.91	   A^2 -> H(U1(c, c), U1(b, e))
27.32/8.91	   A^2 -> H(U1(c, c), U1(b, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(e, e))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(d, k))
27.32/8.91	   A^2 -> H(e, U1(b, b))
27.32/8.91	   A^2 -> H(e, f(c))
27.32/8.91	   A^2 -> H(e, f(d))
27.32/8.91	   A^2 -> H(U1(e, e), U1(c, b))
27.32/8.91	   A^2 -> H(U1(e, e), U1(d, b))
27.32/8.91	   A^2 -> H(U1(e, e), U1(b, c))
27.32/8.91	   A^2 -> H(U1(e, e), U1(b, d))
27.32/8.91	   A^2 -> H(U1(e, e), U1(c, c))
27.32/8.91	   A^2 -> H(U1(e, e), f(e))
27.32/8.91	   A^2 -> H(U1(e, e), f(k))
27.32/8.91	   A^2 -> H(U1(e, e), U1(d, d))
27.32/8.91	   A^2 -> H(f(e), U1(e, b))
27.32/8.91	   A^2 -> H(f(e), U1(k, b))
27.32/8.91	   A^2 -> H(f(e), U1(c, d))
27.32/8.91	   A^2 -> H(f(e), U1(d, c))
27.32/8.91	   A^2 -> H(f(e), U1(b, e))
27.32/8.91	   A^2 -> H(f(e), U1(b, k))
27.32/8.91	   A^2 -> H(f(e), U1(e, c))
27.32/8.91	   A^2 -> H(f(e), U1(k, c))
27.32/8.91	   A^2 -> H(f(e), U1(c, e))
27.32/8.91	   A^2 -> H(f(e), U1(c, k))
27.32/8.91	   A^2 -> H(f(e), U1(k, k))
27.32/8.91	   A^2 -> H(f(e), U1(k, d))
27.32/8.91	   A^2 -> H(f(e), U1(d, k))
27.32/8.91	   A^2 -> H(U1(k, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(k, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(k, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(k, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(k, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(k, k), f(e))
27.32/8.91	   A^2 -> H(U1(k, k), f(k))
27.32/8.91	   A^2 -> H(U1(k, k), U1(d, d))
27.32/8.91	   A^2 -> H(f(k), U1(e, b))
27.32/8.91	   A^2 -> H(f(k), U1(k, b))
27.32/8.91	   A^2 -> H(f(k), U1(c, d))
27.32/8.91	   A^2 -> H(f(k), U1(d, c))
27.32/8.91	   A^2 -> H(f(k), U1(b, e))
27.32/8.91	   A^2 -> H(f(k), U1(b, k))
27.32/8.91	   A^2 -> H(f(k), U1(e, c))
27.32/8.91	   A^2 -> H(f(k), U1(k, c))
27.32/8.91	   A^2 -> H(f(k), U1(c, e))
27.32/8.91	   A^2 -> H(f(k), U1(c, k))
27.32/8.91	   A^2 -> H(f(k), U1(e, e))
27.32/8.91	   A^2 -> H(f(k), U1(k, d))
27.32/8.91	   A^2 -> H(f(k), U1(d, k))
27.32/8.91	   A^2 -> H(f(c), b)
27.32/8.91	   A^2 -> H(f(c), U1(e, d))
27.32/8.91	   A^2 -> H(f(c), U1(d, e))
27.32/8.91	   A^2 -> H(f(k), U1(k, k))
27.32/8.91	   A^2 -> H(U1(k, k), U1(b, b))
27.32/8.91	   A^2 -> H(U1(k, k), f(c))
27.32/8.91	   A^2 -> H(U1(k, k), f(d))
27.32/8.91	   A^2 -> H(U1(k, d), U1(c, b))
27.32/8.91	   A^2 -> H(U1(k, d), U1(d, b))
27.32/8.91	   A^2 -> H(U1(k, d), U1(b, c))
27.32/8.91	   A^2 -> H(U1(k, d), U1(b, d))
27.32/8.91	   A^2 -> H(U1(k, d), U1(c, c))
27.32/8.91	   A^2 -> H(U1(k, d), f(e))
27.32/8.91	   A^2 -> H(U1(k, d), f(k))
27.32/8.91	   A^2 -> H(U1(k, d), U1(d, d))
27.32/8.91	   A^2 -> H(U1(d, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(d, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(d, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(d, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(d, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(d, k), f(e))
27.32/8.91	   A^2 -> H(U1(d, k), f(k))
27.32/8.91	   A^2 -> H(U1(d, k), U1(d, d))
27.32/8.91	   A^2 -> H(U1(d, d), U1(e, b))
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, b))
27.32/8.91	   A^2 -> H(U1(d, d), U1(c, d))
27.32/8.91	   A^2 -> H(U1(d, d), U1(d, c))
27.32/8.91	   A^2 -> H(U1(d, d), U1(b, e))
27.32/8.91	   A^2 -> H(U1(d, d), U1(b, k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(e, c))
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, c))
27.32/8.91	   A^2 -> H(U1(d, d), U1(c, e))
27.32/8.91	   A^2 -> H(U1(d, d), U1(c, k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(e, e))
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, k))
27.32/8.91	   A^2 -> H(f(d), b)
27.32/8.91	   A^2 -> H(f(d), U1(e, d))
27.32/8.91	   A^2 -> H(f(d), U1(d, e))
27.32/8.91	   A^2 -> H(f(d), c)
27.32/8.91	   A^2 -> H(f(d), U1(e, k))
27.32/8.91	   A^2 -> H(f(d), U1(k, e))
27.32/8.91	   A^2 -> H(f(d), e)
27.32/8.91	   A^2 -> H(f(a), d)
27.32/8.91	   A^2 -> H(U1(c, c), U1(e, c))
27.32/8.91	   A^2 -> H(f(c), c)
27.32/8.91	   A^2 -> H(f(c), U1(e, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, c))
27.32/8.91	   A^2 -> H(f(c), U1(k, e))
27.32/8.91	   A^2 -> H(f(c), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, e))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, k))
27.32/8.91	   A^2 -> H(f(a), k)
27.32/8.91	   A^2 -> H(f(e), U1(e, e))
27.32/8.91	   A^2 -> H(f(c), e)
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, d))
27.32/8.91	   A^2 -> H(f(d), U1(k, k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(d, k))
27.32/8.91	   A^2 -> H(d, U1(b, b))
27.32/8.91	   A^2 -> H(d, f(c))
27.32/8.91	   A^2 -> H(d, f(d))
27.32/8.91	   A^2 -> H(a, U1(c, b))
27.32/8.91	   A^2 -> H(a, U1(d, b))
27.32/8.91	   A^2 -> H(a, U1(b, c))
27.32/8.91	   A^2 -> H(a, U1(b, d))
27.32/8.91	   A^2 -> H(a, U1(c, c))
27.32/8.91	   A^2 -> H(a, f(e))
27.32/8.91	   A^2 -> H(a, f(k))
27.32/8.91	   A^2 -> H(a, U1(d, d))
27.32/8.91	   A^2 -> H(U1(e, d), U1(c, b))
27.32/8.91	   A^2 -> H(U1(e, d), U1(d, b))
27.32/8.91	   A^2 -> H(U1(e, d), U1(b, c))
27.32/8.91	   A^2 -> H(U1(e, d), U1(b, d))
27.32/8.91	   A^2 -> H(U1(e, d), U1(c, c))
27.32/8.91	   A^2 -> H(U1(e, d), f(e))
27.32/8.91	   A^2 -> H(U1(e, d), f(k))
27.32/8.91	   A^2 -> H(U1(e, d), U1(d, d))
27.32/8.91	   A^2 -> H(U1(e, a), U1(e, b))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, b))
27.32/8.91	   A^2 -> H(U1(e, a), U1(c, d))
27.32/8.91	   A^2 -> H(U1(e, a), U1(d, c))
27.32/8.91	   A^2 -> H(U1(e, a), U1(b, e))
27.32/8.91	   A^2 -> H(U1(e, a), U1(b, k))
27.32/8.91	   A^2 -> H(U1(e, a), U1(e, c))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, c))
27.32/8.91	   A^2 -> H(U1(e, a), U1(c, e))
27.32/8.91	   A^2 -> H(U1(e, a), U1(c, k))
27.32/8.91	   A^2 -> H(U1(e, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(e, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(e, b))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, b))
27.32/8.91	   A^2 -> H(U1(k, a), U1(c, d))
27.32/8.91	   A^2 -> H(U1(k, a), U1(d, c))
27.32/8.91	   A^2 -> H(U1(k, a), U1(b, e))
27.32/8.91	   A^2 -> H(U1(k, a), U1(b, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(e, c))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, c))
27.32/8.91	   A^2 -> H(U1(k, a), U1(c, e))
27.32/8.91	   A^2 -> H(U1(k, a), U1(c, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(k, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(e, b))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, b))
27.32/8.91	   A^2 -> H(U1(c, d), U1(c, d))
27.32/8.91	   A^2 -> H(U1(c, d), U1(d, c))
27.32/8.91	   A^2 -> H(U1(c, d), U1(b, e))
27.32/8.91	   A^2 -> H(U1(c, d), U1(b, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(e, c))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, c))
27.32/8.91	   A^2 -> H(U1(c, d), U1(c, e))
27.32/8.91	   A^2 -> H(U1(c, d), U1(c, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(e, e))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, d))
27.32/8.91	   A^2 -> H(U1(c, d), U1(d, k))
27.32/8.91	   A^2 -> H(U1(c, a), b)
27.32/8.91	   A^2 -> H(U1(c, a), U1(e, d))
27.32/8.91	   A^2 -> H(U1(c, a), U1(d, e))
27.32/8.91	
27.32/8.91	The TRS R consists of the following rules:
27.32/8.91	
27.32/8.91	   f(x) -> U1(x, x)
27.32/8.91	   U1(e, x) -> x
27.32/8.91	   a -> c
27.32/8.91	   a -> d
27.32/8.91	   b -> c
27.32/8.91	   b -> d
27.32/8.91	   d -> k
27.32/8.91	   c -> e
27.32/8.91	   c -> k
27.32/8.91	
27.32/8.91	Q is empty.
27.32/8.91	We have to consider all minimal (P,Q,R)-chains.
27.32/8.91	----------------------------------------
27.32/8.91	
27.32/8.91	(615) TransformationProof (EQUIVALENT)
27.32/8.91	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
27.32/8.91	
27.32/8.91	   (A^2 -> H(U1(e, a), U1(e, c)),A^2 -> H(U1(e, a), U1(e, c)))
27.32/8.91	   (A^2 -> H(U1(k, a), U1(e, c)),A^2 -> H(U1(k, a), U1(e, c)))
27.32/8.91	   (A^2 -> H(U1(c, c), U1(e, c)),A^2 -> H(U1(c, c), U1(e, c)))
27.32/8.91	   (A^2 -> H(U1(c, d), U1(e, c)),A^2 -> H(U1(c, d), U1(e, c)))
27.32/8.91	   (A^2 -> H(U1(c, a), c),A^2 -> H(U1(c, a), c))
27.32/8.91	   (A^2 -> H(U1(c, a), U1(e, e)),A^2 -> H(U1(c, a), U1(e, e)))
27.32/8.91	   (A^2 -> H(U1(c, a), U1(e, k)),A^2 -> H(U1(c, a), U1(e, k)))
27.32/8.91	
27.32/8.91	
27.32/8.91	----------------------------------------
27.32/8.91	
27.32/8.91	(616)
27.32/8.91	Obligation:
27.32/8.91	Q DP problem:
27.32/8.91	The TRS P consists of the following rules:
27.32/8.91	
27.32/8.91	   H(x, x) -> G(x, x, f(k))
27.32/8.91	   G(d, x, x) -> A^2
27.32/8.91	   A^2 -> H(f(c), f(c))
27.32/8.91	   A^2 -> H(f(d), f(d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, c))
27.32/8.91	   A^2 -> H(f(e), f(e))
27.32/8.91	   A^2 -> H(f(k), f(k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, a), U1(k, c))
27.32/8.91	   A^2 -> H(U1(c, a), U1(c, e))
27.32/8.91	   A^2 -> H(U1(c, a), U1(c, k))
27.32/8.91	   A^2 -> H(U1(c, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(c, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(c, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(d, e), U1(b, b))
27.32/8.91	   A^2 -> H(U1(d, e), f(c))
27.32/8.91	   A^2 -> H(U1(d, e), f(d))
27.32/8.91	   A^2 -> H(U1(d, c), U1(c, b))
27.32/8.91	   A^2 -> H(U1(d, c), U1(d, b))
27.32/8.91	   A^2 -> H(U1(d, c), U1(b, c))
27.32/8.91	   A^2 -> H(U1(d, c), U1(b, d))
27.32/8.91	   A^2 -> H(U1(d, c), U1(c, c))
27.32/8.91	   A^2 -> H(U1(d, c), f(e))
27.32/8.91	   A^2 -> H(U1(d, c), f(k))
27.32/8.91	   A^2 -> H(U1(d, c), U1(d, d))
27.32/8.91	   A^2 -> H(U1(d, a), U1(e, b))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, b))
27.32/8.91	   A^2 -> H(U1(d, a), U1(c, d))
27.32/8.91	   A^2 -> H(U1(d, a), U1(d, c))
27.32/8.91	   A^2 -> H(U1(d, a), U1(b, e))
27.32/8.91	   A^2 -> H(U1(d, a), U1(b, k))
27.32/8.91	   A^2 -> H(U1(d, a), U1(e, c))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, c))
27.32/8.91	   A^2 -> H(U1(d, a), U1(c, e))
27.32/8.91	   A^2 -> H(U1(d, a), U1(c, k))
27.32/8.91	   A^2 -> H(U1(d, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(d, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(a, e), U1(c, b))
27.32/8.91	   A^2 -> H(U1(a, e), U1(d, b))
27.32/8.91	   A^2 -> H(U1(a, e), U1(b, c))
27.32/8.91	   A^2 -> H(U1(a, e), U1(b, d))
27.32/8.91	   A^2 -> H(U1(a, e), U1(c, c))
27.32/8.91	   A^2 -> H(U1(a, e), f(e))
27.32/8.91	   A^2 -> H(U1(a, e), f(k))
27.32/8.91	   A^2 -> H(U1(a, e), U1(d, d))
27.32/8.91	   A^2 -> H(U1(a, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(a, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(a, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(a, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(a, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(a, k), f(e))
27.32/8.91	   A^2 -> H(U1(a, k), f(k))
27.32/8.91	   A^2 -> H(U1(a, k), U1(d, d))
27.32/8.91	   A^2 -> H(U1(a, c), U1(e, b))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, b))
27.32/8.91	   A^2 -> H(U1(a, c), U1(c, d))
27.32/8.91	   A^2 -> H(U1(a, c), U1(d, c))
27.32/8.91	   A^2 -> H(U1(a, c), U1(b, e))
27.32/8.91	   A^2 -> H(U1(a, c), U1(b, k))
27.32/8.91	   A^2 -> H(U1(a, c), U1(e, c))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, c))
27.32/8.91	   A^2 -> H(U1(a, c), U1(c, e))
27.32/8.91	   A^2 -> H(U1(a, c), U1(c, k))
27.32/8.91	   A^2 -> H(U1(a, c), U1(e, e))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, k))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, d))
27.32/8.91	   A^2 -> H(U1(a, c), U1(d, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(e, b))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, b))
27.32/8.91	   A^2 -> H(U1(a, d), U1(c, d))
27.32/8.91	   A^2 -> H(U1(a, d), U1(d, c))
27.32/8.91	   A^2 -> H(U1(a, d), U1(b, e))
27.32/8.91	   A^2 -> H(U1(a, d), U1(b, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(e, c))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, c))
27.32/8.91	   A^2 -> H(U1(a, d), U1(c, e))
27.32/8.91	   A^2 -> H(U1(a, d), U1(c, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(e, e))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, d))
27.32/8.91	   A^2 -> H(U1(a, d), U1(d, k))
27.32/8.91	   A^2 -> H(U1(a, a), b)
27.32/8.91	   A^2 -> H(U1(a, a), U1(e, d))
27.32/8.91	   A^2 -> H(U1(a, a), U1(d, e))
27.32/8.91	   A^2 -> H(U1(a, a), c)
27.32/8.91	   A^2 -> H(U1(a, a), U1(e, k))
27.32/8.91	   A^2 -> H(U1(a, a), U1(k, e))
27.32/8.91	   A^2 -> H(U1(a, a), e)
27.32/8.91	   A^2 -> H(U1(a, a), U1(k, k))
27.32/8.91	   A^2 -> H(k, f(b))
27.32/8.91	   A^2 -> H(c, U1(b, b))
27.32/8.91	   A^2 -> H(c, f(c))
27.32/8.91	   A^2 -> H(c, f(d))
27.32/8.91	   A^2 -> H(U1(e, k), U1(b, b))
27.32/8.91	   A^2 -> H(U1(e, k), f(c))
27.32/8.91	   A^2 -> H(U1(e, k), f(d))
27.32/8.91	   A^2 -> H(U1(e, c), U1(c, b))
27.32/8.91	   A^2 -> H(U1(e, c), U1(d, b))
27.32/8.91	   A^2 -> H(U1(e, c), U1(b, c))
27.32/8.91	   A^2 -> H(U1(e, c), U1(b, d))
27.32/8.91	   A^2 -> H(U1(e, c), U1(c, c))
27.32/8.91	   A^2 -> H(U1(e, c), f(e))
27.32/8.91	   A^2 -> H(U1(e, c), f(k))
27.32/8.91	   A^2 -> H(U1(e, c), U1(d, d))
27.32/8.91	   A^2 -> H(U1(k, e), U1(b, b))
27.32/8.91	   A^2 -> H(U1(k, e), f(c))
27.32/8.91	   A^2 -> H(U1(k, e), f(d))
27.32/8.91	   A^2 -> H(U1(k, c), U1(c, b))
27.32/8.91	   A^2 -> H(U1(k, c), U1(d, b))
27.32/8.91	   A^2 -> H(U1(k, c), U1(b, c))
27.32/8.91	   A^2 -> H(U1(k, c), U1(b, d))
27.32/8.91	   A^2 -> H(U1(k, c), U1(c, c))
27.32/8.91	   A^2 -> H(U1(k, c), f(e))
27.32/8.91	   A^2 -> H(U1(k, c), f(k))
27.32/8.91	   A^2 -> H(U1(k, c), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, e), U1(c, b))
27.32/8.91	   A^2 -> H(U1(c, e), U1(d, b))
27.32/8.91	   A^2 -> H(U1(c, e), U1(b, c))
27.32/8.91	   A^2 -> H(U1(c, e), U1(b, d))
27.32/8.91	   A^2 -> H(U1(c, e), U1(c, c))
27.32/8.91	   A^2 -> H(U1(c, e), f(e))
27.32/8.91	   A^2 -> H(U1(c, e), f(k))
27.32/8.91	   A^2 -> H(U1(c, e), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(c, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(c, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(c, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(c, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(c, k), f(e))
27.32/8.91	   A^2 -> H(U1(c, k), f(k))
27.32/8.91	   A^2 -> H(U1(c, k), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(e, b))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, b))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(d, c))
27.32/8.91	   A^2 -> H(U1(c, c), U1(b, e))
27.32/8.91	   A^2 -> H(U1(c, c), U1(b, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(e, e))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(d, k))
27.32/8.91	   A^2 -> H(e, U1(b, b))
27.32/8.91	   A^2 -> H(e, f(c))
27.32/8.91	   A^2 -> H(e, f(d))
27.32/8.91	   A^2 -> H(U1(e, e), U1(c, b))
27.32/8.91	   A^2 -> H(U1(e, e), U1(d, b))
27.32/8.91	   A^2 -> H(U1(e, e), U1(b, c))
27.32/8.91	   A^2 -> H(U1(e, e), U1(b, d))
27.32/8.91	   A^2 -> H(U1(e, e), U1(c, c))
27.32/8.91	   A^2 -> H(U1(e, e), f(e))
27.32/8.91	   A^2 -> H(U1(e, e), f(k))
27.32/8.91	   A^2 -> H(U1(e, e), U1(d, d))
27.32/8.91	   A^2 -> H(f(e), U1(e, b))
27.32/8.91	   A^2 -> H(f(e), U1(k, b))
27.32/8.91	   A^2 -> H(f(e), U1(c, d))
27.32/8.91	   A^2 -> H(f(e), U1(d, c))
27.32/8.91	   A^2 -> H(f(e), U1(b, e))
27.32/8.91	   A^2 -> H(f(e), U1(b, k))
27.32/8.91	   A^2 -> H(f(e), U1(e, c))
27.32/8.91	   A^2 -> H(f(e), U1(k, c))
27.32/8.91	   A^2 -> H(f(e), U1(c, e))
27.32/8.91	   A^2 -> H(f(e), U1(c, k))
27.32/8.91	   A^2 -> H(f(e), U1(k, k))
27.32/8.91	   A^2 -> H(f(e), U1(k, d))
27.32/8.91	   A^2 -> H(f(e), U1(d, k))
27.32/8.91	   A^2 -> H(U1(k, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(k, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(k, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(k, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(k, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(k, k), f(e))
27.32/8.91	   A^2 -> H(U1(k, k), f(k))
27.32/8.91	   A^2 -> H(U1(k, k), U1(d, d))
27.32/8.91	   A^2 -> H(f(k), U1(e, b))
27.32/8.91	   A^2 -> H(f(k), U1(k, b))
27.32/8.91	   A^2 -> H(f(k), U1(c, d))
27.32/8.91	   A^2 -> H(f(k), U1(d, c))
27.32/8.91	   A^2 -> H(f(k), U1(b, e))
27.32/8.91	   A^2 -> H(f(k), U1(b, k))
27.32/8.91	   A^2 -> H(f(k), U1(e, c))
27.32/8.91	   A^2 -> H(f(k), U1(k, c))
27.32/8.91	   A^2 -> H(f(k), U1(c, e))
27.32/8.91	   A^2 -> H(f(k), U1(c, k))
27.32/8.91	   A^2 -> H(f(k), U1(e, e))
27.32/8.91	   A^2 -> H(f(k), U1(k, d))
27.32/8.91	   A^2 -> H(f(k), U1(d, k))
27.32/8.91	   A^2 -> H(f(c), b)
27.32/8.91	   A^2 -> H(f(c), U1(e, d))
27.32/8.91	   A^2 -> H(f(c), U1(d, e))
27.32/8.91	   A^2 -> H(f(k), U1(k, k))
27.32/8.91	   A^2 -> H(U1(k, k), U1(b, b))
27.32/8.91	   A^2 -> H(U1(k, k), f(c))
27.32/8.91	   A^2 -> H(U1(k, k), f(d))
27.32/8.91	   A^2 -> H(U1(k, d), U1(c, b))
27.32/8.91	   A^2 -> H(U1(k, d), U1(d, b))
27.32/8.91	   A^2 -> H(U1(k, d), U1(b, c))
27.32/8.91	   A^2 -> H(U1(k, d), U1(b, d))
27.32/8.91	   A^2 -> H(U1(k, d), U1(c, c))
27.32/8.91	   A^2 -> H(U1(k, d), f(e))
27.32/8.91	   A^2 -> H(U1(k, d), f(k))
27.32/8.91	   A^2 -> H(U1(k, d), U1(d, d))
27.32/8.91	   A^2 -> H(U1(d, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(d, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(d, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(d, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(d, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(d, k), f(e))
27.32/8.91	   A^2 -> H(U1(d, k), f(k))
27.32/8.91	   A^2 -> H(U1(d, k), U1(d, d))
27.32/8.91	   A^2 -> H(U1(d, d), U1(e, b))
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, b))
27.32/8.91	   A^2 -> H(U1(d, d), U1(c, d))
27.32/8.91	   A^2 -> H(U1(d, d), U1(d, c))
27.32/8.91	   A^2 -> H(U1(d, d), U1(b, e))
27.32/8.91	   A^2 -> H(U1(d, d), U1(b, k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(e, c))
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, c))
27.32/8.91	   A^2 -> H(U1(d, d), U1(c, e))
27.32/8.91	   A^2 -> H(U1(d, d), U1(c, k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(e, e))
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, k))
27.32/8.91	   A^2 -> H(f(d), b)
27.32/8.91	   A^2 -> H(f(d), U1(e, d))
27.32/8.91	   A^2 -> H(f(d), U1(d, e))
27.32/8.91	   A^2 -> H(f(d), c)
27.32/8.91	   A^2 -> H(f(d), U1(e, k))
27.32/8.91	   A^2 -> H(f(d), U1(k, e))
27.32/8.91	   A^2 -> H(f(d), e)
27.32/8.91	   A^2 -> H(f(a), d)
27.32/8.91	   A^2 -> H(U1(c, c), U1(e, c))
27.32/8.91	   A^2 -> H(f(c), c)
27.32/8.91	   A^2 -> H(f(c), U1(e, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, c))
27.32/8.91	   A^2 -> H(f(c), U1(k, e))
27.32/8.91	   A^2 -> H(f(c), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, e))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, k))
27.32/8.91	   A^2 -> H(f(a), k)
27.32/8.91	   A^2 -> H(f(e), U1(e, e))
27.32/8.91	   A^2 -> H(f(c), e)
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, d))
27.32/8.91	   A^2 -> H(f(d), U1(k, k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(d, k))
27.32/8.91	   A^2 -> H(d, U1(b, b))
27.32/8.91	   A^2 -> H(d, f(c))
27.32/8.91	   A^2 -> H(d, f(d))
27.32/8.91	   A^2 -> H(a, U1(c, b))
27.32/8.91	   A^2 -> H(a, U1(d, b))
27.32/8.91	   A^2 -> H(a, U1(b, c))
27.32/8.91	   A^2 -> H(a, U1(b, d))
27.32/8.91	   A^2 -> H(a, U1(c, c))
27.32/8.91	   A^2 -> H(a, f(e))
27.32/8.91	   A^2 -> H(a, f(k))
27.32/8.91	   A^2 -> H(a, U1(d, d))
27.32/8.91	   A^2 -> H(U1(e, d), U1(c, b))
27.32/8.91	   A^2 -> H(U1(e, d), U1(d, b))
27.32/8.91	   A^2 -> H(U1(e, d), U1(b, c))
27.32/8.91	   A^2 -> H(U1(e, d), U1(b, d))
27.32/8.91	   A^2 -> H(U1(e, d), U1(c, c))
27.32/8.91	   A^2 -> H(U1(e, d), f(e))
27.32/8.91	   A^2 -> H(U1(e, d), f(k))
27.32/8.91	   A^2 -> H(U1(e, d), U1(d, d))
27.32/8.91	   A^2 -> H(U1(e, a), U1(e, b))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, b))
27.32/8.91	   A^2 -> H(U1(e, a), U1(c, d))
27.32/8.91	   A^2 -> H(U1(e, a), U1(d, c))
27.32/8.91	   A^2 -> H(U1(e, a), U1(b, e))
27.32/8.91	   A^2 -> H(U1(e, a), U1(b, k))
27.32/8.91	   A^2 -> H(U1(e, a), U1(e, c))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, c))
27.32/8.91	   A^2 -> H(U1(e, a), U1(c, e))
27.32/8.91	   A^2 -> H(U1(e, a), U1(c, k))
27.32/8.91	   A^2 -> H(U1(e, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(e, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(e, b))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, b))
27.32/8.91	   A^2 -> H(U1(k, a), U1(c, d))
27.32/8.91	   A^2 -> H(U1(k, a), U1(d, c))
27.32/8.91	   A^2 -> H(U1(k, a), U1(b, e))
27.32/8.91	   A^2 -> H(U1(k, a), U1(b, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(e, c))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, c))
27.32/8.91	   A^2 -> H(U1(k, a), U1(c, e))
27.32/8.91	   A^2 -> H(U1(k, a), U1(c, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(k, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(e, b))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, b))
27.32/8.91	   A^2 -> H(U1(c, d), U1(c, d))
27.32/8.91	   A^2 -> H(U1(c, d), U1(d, c))
27.32/8.91	   A^2 -> H(U1(c, d), U1(b, e))
27.32/8.91	   A^2 -> H(U1(c, d), U1(b, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(e, c))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, c))
27.32/8.91	   A^2 -> H(U1(c, d), U1(c, e))
27.32/8.91	   A^2 -> H(U1(c, d), U1(c, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(e, e))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, d))
27.32/8.91	   A^2 -> H(U1(c, d), U1(d, k))
27.32/8.91	   A^2 -> H(U1(c, a), b)
27.32/8.91	   A^2 -> H(U1(c, a), U1(e, d))
27.32/8.91	   A^2 -> H(U1(c, a), U1(d, e))
27.32/8.91	   A^2 -> H(U1(c, a), c)
27.32/8.91	   A^2 -> H(U1(c, a), U1(e, k))
27.32/8.91	
27.32/8.91	The TRS R consists of the following rules:
27.32/8.91	
27.32/8.91	   f(x) -> U1(x, x)
27.32/8.91	   U1(e, x) -> x
27.32/8.91	   a -> c
27.32/8.91	   a -> d
27.32/8.91	   b -> c
27.32/8.91	   b -> d
27.32/8.91	   d -> k
27.32/8.91	   c -> e
27.32/8.91	   c -> k
27.32/8.91	
27.32/8.91	Q is empty.
27.32/8.91	We have to consider all minimal (P,Q,R)-chains.
27.32/8.91	----------------------------------------
27.32/8.91	
27.32/8.91	(617) TransformationProof (EQUIVALENT)
27.32/8.91	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
27.32/8.91	
27.32/8.91	   (A^2 -> H(U1(e, a), U1(k, c)),A^2 -> H(U1(e, a), U1(k, c)))
27.32/8.91	   (A^2 -> H(U1(k, a), U1(k, c)),A^2 -> H(U1(k, a), U1(k, c)))
27.32/8.91	   (A^2 -> H(U1(c, c), U1(k, c)),A^2 -> H(U1(c, c), U1(k, c)))
27.32/8.91	   (A^2 -> H(U1(c, d), U1(k, c)),A^2 -> H(U1(c, d), U1(k, c)))
27.32/8.91	   (A^2 -> H(U1(c, a), U1(k, e)),A^2 -> H(U1(c, a), U1(k, e)))
27.32/8.91	   (A^2 -> H(U1(c, a), U1(k, k)),A^2 -> H(U1(c, a), U1(k, k)))
27.32/8.91	
27.32/8.91	
27.32/8.91	----------------------------------------
27.32/8.91	
27.32/8.91	(618)
27.32/8.91	Obligation:
27.32/8.91	Q DP problem:
27.32/8.91	The TRS P consists of the following rules:
27.32/8.91	
27.32/8.91	   H(x, x) -> G(x, x, f(k))
27.32/8.91	   G(d, x, x) -> A^2
27.32/8.91	   A^2 -> H(f(c), f(c))
27.32/8.91	   A^2 -> H(f(d), f(d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, c))
27.32/8.91	   A^2 -> H(f(e), f(e))
27.32/8.91	   A^2 -> H(f(k), f(k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, a), U1(c, e))
27.32/8.91	   A^2 -> H(U1(c, a), U1(c, k))
27.32/8.91	   A^2 -> H(U1(c, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(c, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(c, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(d, e), U1(b, b))
27.32/8.91	   A^2 -> H(U1(d, e), f(c))
27.32/8.91	   A^2 -> H(U1(d, e), f(d))
27.32/8.91	   A^2 -> H(U1(d, c), U1(c, b))
27.32/8.91	   A^2 -> H(U1(d, c), U1(d, b))
27.32/8.91	   A^2 -> H(U1(d, c), U1(b, c))
27.32/8.91	   A^2 -> H(U1(d, c), U1(b, d))
27.32/8.91	   A^2 -> H(U1(d, c), U1(c, c))
27.32/8.91	   A^2 -> H(U1(d, c), f(e))
27.32/8.91	   A^2 -> H(U1(d, c), f(k))
27.32/8.91	   A^2 -> H(U1(d, c), U1(d, d))
27.32/8.91	   A^2 -> H(U1(d, a), U1(e, b))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, b))
27.32/8.91	   A^2 -> H(U1(d, a), U1(c, d))
27.32/8.91	   A^2 -> H(U1(d, a), U1(d, c))
27.32/8.91	   A^2 -> H(U1(d, a), U1(b, e))
27.32/8.91	   A^2 -> H(U1(d, a), U1(b, k))
27.32/8.91	   A^2 -> H(U1(d, a), U1(e, c))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, c))
27.32/8.91	   A^2 -> H(U1(d, a), U1(c, e))
27.32/8.91	   A^2 -> H(U1(d, a), U1(c, k))
27.32/8.91	   A^2 -> H(U1(d, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(d, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(a, e), U1(c, b))
27.32/8.91	   A^2 -> H(U1(a, e), U1(d, b))
27.32/8.91	   A^2 -> H(U1(a, e), U1(b, c))
27.32/8.91	   A^2 -> H(U1(a, e), U1(b, d))
27.32/8.91	   A^2 -> H(U1(a, e), U1(c, c))
27.32/8.91	   A^2 -> H(U1(a, e), f(e))
27.32/8.91	   A^2 -> H(U1(a, e), f(k))
27.32/8.91	   A^2 -> H(U1(a, e), U1(d, d))
27.32/8.91	   A^2 -> H(U1(a, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(a, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(a, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(a, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(a, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(a, k), f(e))
27.32/8.91	   A^2 -> H(U1(a, k), f(k))
27.32/8.91	   A^2 -> H(U1(a, k), U1(d, d))
27.32/8.91	   A^2 -> H(U1(a, c), U1(e, b))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, b))
27.32/8.91	   A^2 -> H(U1(a, c), U1(c, d))
27.32/8.91	   A^2 -> H(U1(a, c), U1(d, c))
27.32/8.91	   A^2 -> H(U1(a, c), U1(b, e))
27.32/8.91	   A^2 -> H(U1(a, c), U1(b, k))
27.32/8.91	   A^2 -> H(U1(a, c), U1(e, c))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, c))
27.32/8.91	   A^2 -> H(U1(a, c), U1(c, e))
27.32/8.91	   A^2 -> H(U1(a, c), U1(c, k))
27.32/8.91	   A^2 -> H(U1(a, c), U1(e, e))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, k))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, d))
27.32/8.91	   A^2 -> H(U1(a, c), U1(d, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(e, b))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, b))
27.32/8.91	   A^2 -> H(U1(a, d), U1(c, d))
27.32/8.91	   A^2 -> H(U1(a, d), U1(d, c))
27.32/8.91	   A^2 -> H(U1(a, d), U1(b, e))
27.32/8.91	   A^2 -> H(U1(a, d), U1(b, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(e, c))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, c))
27.32/8.91	   A^2 -> H(U1(a, d), U1(c, e))
27.32/8.91	   A^2 -> H(U1(a, d), U1(c, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(e, e))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, d))
27.32/8.91	   A^2 -> H(U1(a, d), U1(d, k))
27.32/8.91	   A^2 -> H(U1(a, a), b)
27.32/8.91	   A^2 -> H(U1(a, a), U1(e, d))
27.32/8.91	   A^2 -> H(U1(a, a), U1(d, e))
27.32/8.91	   A^2 -> H(U1(a, a), c)
27.32/8.91	   A^2 -> H(U1(a, a), U1(e, k))
27.32/8.91	   A^2 -> H(U1(a, a), U1(k, e))
27.32/8.91	   A^2 -> H(U1(a, a), e)
27.32/8.91	   A^2 -> H(U1(a, a), U1(k, k))
27.32/8.91	   A^2 -> H(k, f(b))
27.32/8.91	   A^2 -> H(c, U1(b, b))
27.32/8.91	   A^2 -> H(c, f(c))
27.32/8.91	   A^2 -> H(c, f(d))
27.32/8.91	   A^2 -> H(U1(e, k), U1(b, b))
27.32/8.91	   A^2 -> H(U1(e, k), f(c))
27.32/8.91	   A^2 -> H(U1(e, k), f(d))
27.32/8.91	   A^2 -> H(U1(e, c), U1(c, b))
27.32/8.91	   A^2 -> H(U1(e, c), U1(d, b))
27.32/8.91	   A^2 -> H(U1(e, c), U1(b, c))
27.32/8.91	   A^2 -> H(U1(e, c), U1(b, d))
27.32/8.91	   A^2 -> H(U1(e, c), U1(c, c))
27.32/8.91	   A^2 -> H(U1(e, c), f(e))
27.32/8.91	   A^2 -> H(U1(e, c), f(k))
27.32/8.91	   A^2 -> H(U1(e, c), U1(d, d))
27.32/8.91	   A^2 -> H(U1(k, e), U1(b, b))
27.32/8.91	   A^2 -> H(U1(k, e), f(c))
27.32/8.91	   A^2 -> H(U1(k, e), f(d))
27.32/8.91	   A^2 -> H(U1(k, c), U1(c, b))
27.32/8.91	   A^2 -> H(U1(k, c), U1(d, b))
27.32/8.91	   A^2 -> H(U1(k, c), U1(b, c))
27.32/8.91	   A^2 -> H(U1(k, c), U1(b, d))
27.32/8.91	   A^2 -> H(U1(k, c), U1(c, c))
27.32/8.91	   A^2 -> H(U1(k, c), f(e))
27.32/8.91	   A^2 -> H(U1(k, c), f(k))
27.32/8.91	   A^2 -> H(U1(k, c), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, e), U1(c, b))
27.32/8.91	   A^2 -> H(U1(c, e), U1(d, b))
27.32/8.91	   A^2 -> H(U1(c, e), U1(b, c))
27.32/8.91	   A^2 -> H(U1(c, e), U1(b, d))
27.32/8.91	   A^2 -> H(U1(c, e), U1(c, c))
27.32/8.91	   A^2 -> H(U1(c, e), f(e))
27.32/8.91	   A^2 -> H(U1(c, e), f(k))
27.32/8.91	   A^2 -> H(U1(c, e), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(c, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(c, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(c, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(c, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(c, k), f(e))
27.32/8.91	   A^2 -> H(U1(c, k), f(k))
27.32/8.91	   A^2 -> H(U1(c, k), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(e, b))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, b))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(d, c))
27.32/8.91	   A^2 -> H(U1(c, c), U1(b, e))
27.32/8.91	   A^2 -> H(U1(c, c), U1(b, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(e, e))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(d, k))
27.32/8.91	   A^2 -> H(e, U1(b, b))
27.32/8.91	   A^2 -> H(e, f(c))
27.32/8.91	   A^2 -> H(e, f(d))
27.32/8.91	   A^2 -> H(U1(e, e), U1(c, b))
27.32/8.91	   A^2 -> H(U1(e, e), U1(d, b))
27.32/8.91	   A^2 -> H(U1(e, e), U1(b, c))
27.32/8.91	   A^2 -> H(U1(e, e), U1(b, d))
27.32/8.91	   A^2 -> H(U1(e, e), U1(c, c))
27.32/8.91	   A^2 -> H(U1(e, e), f(e))
27.32/8.91	   A^2 -> H(U1(e, e), f(k))
27.32/8.91	   A^2 -> H(U1(e, e), U1(d, d))
27.32/8.91	   A^2 -> H(f(e), U1(e, b))
27.32/8.91	   A^2 -> H(f(e), U1(k, b))
27.32/8.91	   A^2 -> H(f(e), U1(c, d))
27.32/8.91	   A^2 -> H(f(e), U1(d, c))
27.32/8.91	   A^2 -> H(f(e), U1(b, e))
27.32/8.91	   A^2 -> H(f(e), U1(b, k))
27.32/8.91	   A^2 -> H(f(e), U1(e, c))
27.32/8.91	   A^2 -> H(f(e), U1(k, c))
27.32/8.91	   A^2 -> H(f(e), U1(c, e))
27.32/8.91	   A^2 -> H(f(e), U1(c, k))
27.32/8.91	   A^2 -> H(f(e), U1(k, k))
27.32/8.91	   A^2 -> H(f(e), U1(k, d))
27.32/8.91	   A^2 -> H(f(e), U1(d, k))
27.32/8.91	   A^2 -> H(U1(k, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(k, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(k, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(k, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(k, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(k, k), f(e))
27.32/8.91	   A^2 -> H(U1(k, k), f(k))
27.32/8.91	   A^2 -> H(U1(k, k), U1(d, d))
27.32/8.91	   A^2 -> H(f(k), U1(e, b))
27.32/8.91	   A^2 -> H(f(k), U1(k, b))
27.32/8.91	   A^2 -> H(f(k), U1(c, d))
27.32/8.91	   A^2 -> H(f(k), U1(d, c))
27.32/8.91	   A^2 -> H(f(k), U1(b, e))
27.32/8.91	   A^2 -> H(f(k), U1(b, k))
27.32/8.91	   A^2 -> H(f(k), U1(e, c))
27.32/8.91	   A^2 -> H(f(k), U1(k, c))
27.32/8.91	   A^2 -> H(f(k), U1(c, e))
27.32/8.91	   A^2 -> H(f(k), U1(c, k))
27.32/8.91	   A^2 -> H(f(k), U1(e, e))
27.32/8.91	   A^2 -> H(f(k), U1(k, d))
27.32/8.91	   A^2 -> H(f(k), U1(d, k))
27.32/8.91	   A^2 -> H(f(c), b)
27.32/8.91	   A^2 -> H(f(c), U1(e, d))
27.32/8.91	   A^2 -> H(f(c), U1(d, e))
27.32/8.91	   A^2 -> H(f(k), U1(k, k))
27.32/8.91	   A^2 -> H(U1(k, k), U1(b, b))
27.32/8.91	   A^2 -> H(U1(k, k), f(c))
27.32/8.91	   A^2 -> H(U1(k, k), f(d))
27.32/8.91	   A^2 -> H(U1(k, d), U1(c, b))
27.32/8.91	   A^2 -> H(U1(k, d), U1(d, b))
27.32/8.91	   A^2 -> H(U1(k, d), U1(b, c))
27.32/8.91	   A^2 -> H(U1(k, d), U1(b, d))
27.32/8.91	   A^2 -> H(U1(k, d), U1(c, c))
27.32/8.91	   A^2 -> H(U1(k, d), f(e))
27.32/8.91	   A^2 -> H(U1(k, d), f(k))
27.32/8.91	   A^2 -> H(U1(k, d), U1(d, d))
27.32/8.91	   A^2 -> H(U1(d, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(d, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(d, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(d, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(d, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(d, k), f(e))
27.32/8.91	   A^2 -> H(U1(d, k), f(k))
27.32/8.91	   A^2 -> H(U1(d, k), U1(d, d))
27.32/8.91	   A^2 -> H(U1(d, d), U1(e, b))
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, b))
27.32/8.91	   A^2 -> H(U1(d, d), U1(c, d))
27.32/8.91	   A^2 -> H(U1(d, d), U1(d, c))
27.32/8.91	   A^2 -> H(U1(d, d), U1(b, e))
27.32/8.91	   A^2 -> H(U1(d, d), U1(b, k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(e, c))
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, c))
27.32/8.91	   A^2 -> H(U1(d, d), U1(c, e))
27.32/8.91	   A^2 -> H(U1(d, d), U1(c, k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(e, e))
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, k))
27.32/8.91	   A^2 -> H(f(d), b)
27.32/8.91	   A^2 -> H(f(d), U1(e, d))
27.32/8.91	   A^2 -> H(f(d), U1(d, e))
27.32/8.91	   A^2 -> H(f(d), c)
27.32/8.91	   A^2 -> H(f(d), U1(e, k))
27.32/8.91	   A^2 -> H(f(d), U1(k, e))
27.32/8.91	   A^2 -> H(f(d), e)
27.32/8.91	   A^2 -> H(f(a), d)
27.32/8.91	   A^2 -> H(U1(c, c), U1(e, c))
27.32/8.91	   A^2 -> H(f(c), c)
27.32/8.91	   A^2 -> H(f(c), U1(e, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, c))
27.32/8.91	   A^2 -> H(f(c), U1(k, e))
27.32/8.91	   A^2 -> H(f(c), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, e))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, k))
27.32/8.91	   A^2 -> H(f(a), k)
27.32/8.91	   A^2 -> H(f(e), U1(e, e))
27.32/8.91	   A^2 -> H(f(c), e)
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, d))
27.32/8.91	   A^2 -> H(f(d), U1(k, k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(d, k))
27.32/8.91	   A^2 -> H(d, U1(b, b))
27.32/8.91	   A^2 -> H(d, f(c))
27.32/8.91	   A^2 -> H(d, f(d))
27.32/8.91	   A^2 -> H(a, U1(c, b))
27.32/8.91	   A^2 -> H(a, U1(d, b))
27.32/8.91	   A^2 -> H(a, U1(b, c))
27.32/8.91	   A^2 -> H(a, U1(b, d))
27.32/8.91	   A^2 -> H(a, U1(c, c))
27.32/8.91	   A^2 -> H(a, f(e))
27.32/8.91	   A^2 -> H(a, f(k))
27.32/8.91	   A^2 -> H(a, U1(d, d))
27.32/8.91	   A^2 -> H(U1(e, d), U1(c, b))
27.32/8.91	   A^2 -> H(U1(e, d), U1(d, b))
27.32/8.91	   A^2 -> H(U1(e, d), U1(b, c))
27.32/8.91	   A^2 -> H(U1(e, d), U1(b, d))
27.32/8.91	   A^2 -> H(U1(e, d), U1(c, c))
27.32/8.91	   A^2 -> H(U1(e, d), f(e))
27.32/8.91	   A^2 -> H(U1(e, d), f(k))
27.32/8.91	   A^2 -> H(U1(e, d), U1(d, d))
27.32/8.91	   A^2 -> H(U1(e, a), U1(e, b))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, b))
27.32/8.91	   A^2 -> H(U1(e, a), U1(c, d))
27.32/8.91	   A^2 -> H(U1(e, a), U1(d, c))
27.32/8.91	   A^2 -> H(U1(e, a), U1(b, e))
27.32/8.91	   A^2 -> H(U1(e, a), U1(b, k))
27.32/8.91	   A^2 -> H(U1(e, a), U1(e, c))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, c))
27.32/8.91	   A^2 -> H(U1(e, a), U1(c, e))
27.32/8.91	   A^2 -> H(U1(e, a), U1(c, k))
27.32/8.91	   A^2 -> H(U1(e, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(e, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(e, b))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, b))
27.32/8.91	   A^2 -> H(U1(k, a), U1(c, d))
27.32/8.91	   A^2 -> H(U1(k, a), U1(d, c))
27.32/8.91	   A^2 -> H(U1(k, a), U1(b, e))
27.32/8.91	   A^2 -> H(U1(k, a), U1(b, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(e, c))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, c))
27.32/8.91	   A^2 -> H(U1(k, a), U1(c, e))
27.32/8.91	   A^2 -> H(U1(k, a), U1(c, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(k, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(e, b))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, b))
27.32/8.91	   A^2 -> H(U1(c, d), U1(c, d))
27.32/8.91	   A^2 -> H(U1(c, d), U1(d, c))
27.32/8.91	   A^2 -> H(U1(c, d), U1(b, e))
27.32/8.91	   A^2 -> H(U1(c, d), U1(b, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(e, c))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, c))
27.32/8.91	   A^2 -> H(U1(c, d), U1(c, e))
27.32/8.91	   A^2 -> H(U1(c, d), U1(c, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(e, e))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, d))
27.32/8.91	   A^2 -> H(U1(c, d), U1(d, k))
27.32/8.91	   A^2 -> H(U1(c, a), b)
27.32/8.91	   A^2 -> H(U1(c, a), U1(e, d))
27.32/8.91	   A^2 -> H(U1(c, a), U1(d, e))
27.32/8.91	   A^2 -> H(U1(c, a), c)
27.32/8.91	   A^2 -> H(U1(c, a), U1(e, k))
27.32/8.91	   A^2 -> H(U1(c, a), U1(k, e))
27.32/8.91	
27.32/8.91	The TRS R consists of the following rules:
27.32/8.91	
27.32/8.91	   f(x) -> U1(x, x)
27.32/8.91	   U1(e, x) -> x
27.32/8.91	   a -> c
27.32/8.91	   a -> d
27.32/8.91	   b -> c
27.32/8.91	   b -> d
27.32/8.91	   d -> k
27.32/8.91	   c -> e
27.32/8.91	   c -> k
27.32/8.91	
27.32/8.91	Q is empty.
27.32/8.91	We have to consider all minimal (P,Q,R)-chains.
27.32/8.91	----------------------------------------
27.32/8.91	
27.32/8.91	(619) TransformationProof (EQUIVALENT)
27.32/8.91	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
27.32/8.91	
27.32/8.91	   (A^2 -> H(U1(e, a), U1(c, e)),A^2 -> H(U1(e, a), U1(c, e)))
27.32/8.91	   (A^2 -> H(U1(k, a), U1(c, e)),A^2 -> H(U1(k, a), U1(c, e)))
27.32/8.91	   (A^2 -> H(U1(c, c), U1(c, e)),A^2 -> H(U1(c, c), U1(c, e)))
27.32/8.91	   (A^2 -> H(U1(c, d), U1(c, e)),A^2 -> H(U1(c, d), U1(c, e)))
27.32/8.91	   (A^2 -> H(U1(c, a), U1(e, e)),A^2 -> H(U1(c, a), U1(e, e)))
27.32/8.91	   (A^2 -> H(U1(c, a), U1(k, e)),A^2 -> H(U1(c, a), U1(k, e)))
27.32/8.91	
27.32/8.91	
27.32/8.91	----------------------------------------
27.32/8.91	
27.32/8.91	(620)
27.32/8.91	Obligation:
27.32/8.91	Q DP problem:
27.32/8.91	The TRS P consists of the following rules:
27.32/8.91	
27.32/8.91	   H(x, x) -> G(x, x, f(k))
27.32/8.91	   G(d, x, x) -> A^2
27.32/8.91	   A^2 -> H(f(c), f(c))
27.32/8.91	   A^2 -> H(f(d), f(d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, c))
27.32/8.91	   A^2 -> H(f(e), f(e))
27.32/8.91	   A^2 -> H(f(k), f(k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, a), U1(c, k))
27.32/8.91	   A^2 -> H(U1(c, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(c, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(c, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(d, e), U1(b, b))
27.32/8.91	   A^2 -> H(U1(d, e), f(c))
27.32/8.91	   A^2 -> H(U1(d, e), f(d))
27.32/8.91	   A^2 -> H(U1(d, c), U1(c, b))
27.32/8.91	   A^2 -> H(U1(d, c), U1(d, b))
27.32/8.91	   A^2 -> H(U1(d, c), U1(b, c))
27.32/8.91	   A^2 -> H(U1(d, c), U1(b, d))
27.32/8.91	   A^2 -> H(U1(d, c), U1(c, c))
27.32/8.91	   A^2 -> H(U1(d, c), f(e))
27.32/8.91	   A^2 -> H(U1(d, c), f(k))
27.32/8.91	   A^2 -> H(U1(d, c), U1(d, d))
27.32/8.91	   A^2 -> H(U1(d, a), U1(e, b))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, b))
27.32/8.91	   A^2 -> H(U1(d, a), U1(c, d))
27.32/8.91	   A^2 -> H(U1(d, a), U1(d, c))
27.32/8.91	   A^2 -> H(U1(d, a), U1(b, e))
27.32/8.91	   A^2 -> H(U1(d, a), U1(b, k))
27.32/8.91	   A^2 -> H(U1(d, a), U1(e, c))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, c))
27.32/8.91	   A^2 -> H(U1(d, a), U1(c, e))
27.32/8.91	   A^2 -> H(U1(d, a), U1(c, k))
27.32/8.91	   A^2 -> H(U1(d, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(d, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(a, e), U1(c, b))
27.32/8.91	   A^2 -> H(U1(a, e), U1(d, b))
27.32/8.91	   A^2 -> H(U1(a, e), U1(b, c))
27.32/8.91	   A^2 -> H(U1(a, e), U1(b, d))
27.32/8.91	   A^2 -> H(U1(a, e), U1(c, c))
27.32/8.91	   A^2 -> H(U1(a, e), f(e))
27.32/8.91	   A^2 -> H(U1(a, e), f(k))
27.32/8.91	   A^2 -> H(U1(a, e), U1(d, d))
27.32/8.91	   A^2 -> H(U1(a, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(a, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(a, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(a, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(a, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(a, k), f(e))
27.32/8.91	   A^2 -> H(U1(a, k), f(k))
27.32/8.91	   A^2 -> H(U1(a, k), U1(d, d))
27.32/8.91	   A^2 -> H(U1(a, c), U1(e, b))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, b))
27.32/8.91	   A^2 -> H(U1(a, c), U1(c, d))
27.32/8.91	   A^2 -> H(U1(a, c), U1(d, c))
27.32/8.91	   A^2 -> H(U1(a, c), U1(b, e))
27.32/8.91	   A^2 -> H(U1(a, c), U1(b, k))
27.32/8.91	   A^2 -> H(U1(a, c), U1(e, c))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, c))
27.32/8.91	   A^2 -> H(U1(a, c), U1(c, e))
27.32/8.91	   A^2 -> H(U1(a, c), U1(c, k))
27.32/8.91	   A^2 -> H(U1(a, c), U1(e, e))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, k))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, d))
27.32/8.91	   A^2 -> H(U1(a, c), U1(d, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(e, b))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, b))
27.32/8.91	   A^2 -> H(U1(a, d), U1(c, d))
27.32/8.91	   A^2 -> H(U1(a, d), U1(d, c))
27.32/8.91	   A^2 -> H(U1(a, d), U1(b, e))
27.32/8.91	   A^2 -> H(U1(a, d), U1(b, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(e, c))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, c))
27.32/8.91	   A^2 -> H(U1(a, d), U1(c, e))
27.32/8.91	   A^2 -> H(U1(a, d), U1(c, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(e, e))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, d))
27.32/8.91	   A^2 -> H(U1(a, d), U1(d, k))
27.32/8.91	   A^2 -> H(U1(a, a), b)
27.32/8.91	   A^2 -> H(U1(a, a), U1(e, d))
27.32/8.91	   A^2 -> H(U1(a, a), U1(d, e))
27.32/8.91	   A^2 -> H(U1(a, a), c)
27.32/8.91	   A^2 -> H(U1(a, a), U1(e, k))
27.32/8.91	   A^2 -> H(U1(a, a), U1(k, e))
27.32/8.91	   A^2 -> H(U1(a, a), e)
27.32/8.91	   A^2 -> H(U1(a, a), U1(k, k))
27.32/8.91	   A^2 -> H(k, f(b))
27.32/8.91	   A^2 -> H(c, U1(b, b))
27.32/8.91	   A^2 -> H(c, f(c))
27.32/8.91	   A^2 -> H(c, f(d))
27.32/8.91	   A^2 -> H(U1(e, k), U1(b, b))
27.32/8.91	   A^2 -> H(U1(e, k), f(c))
27.32/8.91	   A^2 -> H(U1(e, k), f(d))
27.32/8.91	   A^2 -> H(U1(e, c), U1(c, b))
27.32/8.91	   A^2 -> H(U1(e, c), U1(d, b))
27.32/8.91	   A^2 -> H(U1(e, c), U1(b, c))
27.32/8.91	   A^2 -> H(U1(e, c), U1(b, d))
27.32/8.91	   A^2 -> H(U1(e, c), U1(c, c))
27.32/8.91	   A^2 -> H(U1(e, c), f(e))
27.32/8.91	   A^2 -> H(U1(e, c), f(k))
27.32/8.91	   A^2 -> H(U1(e, c), U1(d, d))
27.32/8.91	   A^2 -> H(U1(k, e), U1(b, b))
27.32/8.91	   A^2 -> H(U1(k, e), f(c))
27.32/8.91	   A^2 -> H(U1(k, e), f(d))
27.32/8.91	   A^2 -> H(U1(k, c), U1(c, b))
27.32/8.91	   A^2 -> H(U1(k, c), U1(d, b))
27.32/8.91	   A^2 -> H(U1(k, c), U1(b, c))
27.32/8.91	   A^2 -> H(U1(k, c), U1(b, d))
27.32/8.91	   A^2 -> H(U1(k, c), U1(c, c))
27.32/8.91	   A^2 -> H(U1(k, c), f(e))
27.32/8.91	   A^2 -> H(U1(k, c), f(k))
27.32/8.91	   A^2 -> H(U1(k, c), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, e), U1(c, b))
27.32/8.91	   A^2 -> H(U1(c, e), U1(d, b))
27.32/8.91	   A^2 -> H(U1(c, e), U1(b, c))
27.32/8.91	   A^2 -> H(U1(c, e), U1(b, d))
27.32/8.91	   A^2 -> H(U1(c, e), U1(c, c))
27.32/8.91	   A^2 -> H(U1(c, e), f(e))
27.32/8.91	   A^2 -> H(U1(c, e), f(k))
27.32/8.91	   A^2 -> H(U1(c, e), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(c, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(c, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(c, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(c, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(c, k), f(e))
27.32/8.91	   A^2 -> H(U1(c, k), f(k))
27.32/8.91	   A^2 -> H(U1(c, k), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(e, b))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, b))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(d, c))
27.32/8.91	   A^2 -> H(U1(c, c), U1(b, e))
27.32/8.91	   A^2 -> H(U1(c, c), U1(b, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(e, e))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(d, k))
27.32/8.91	   A^2 -> H(e, U1(b, b))
27.32/8.91	   A^2 -> H(e, f(c))
27.32/8.91	   A^2 -> H(e, f(d))
27.32/8.91	   A^2 -> H(U1(e, e), U1(c, b))
27.32/8.91	   A^2 -> H(U1(e, e), U1(d, b))
27.32/8.91	   A^2 -> H(U1(e, e), U1(b, c))
27.32/8.91	   A^2 -> H(U1(e, e), U1(b, d))
27.32/8.91	   A^2 -> H(U1(e, e), U1(c, c))
27.32/8.91	   A^2 -> H(U1(e, e), f(e))
27.32/8.91	   A^2 -> H(U1(e, e), f(k))
27.32/8.91	   A^2 -> H(U1(e, e), U1(d, d))
27.32/8.91	   A^2 -> H(f(e), U1(e, b))
27.32/8.91	   A^2 -> H(f(e), U1(k, b))
27.32/8.91	   A^2 -> H(f(e), U1(c, d))
27.32/8.91	   A^2 -> H(f(e), U1(d, c))
27.32/8.91	   A^2 -> H(f(e), U1(b, e))
27.32/8.91	   A^2 -> H(f(e), U1(b, k))
27.32/8.91	   A^2 -> H(f(e), U1(e, c))
27.32/8.91	   A^2 -> H(f(e), U1(k, c))
27.32/8.91	   A^2 -> H(f(e), U1(c, e))
27.32/8.91	   A^2 -> H(f(e), U1(c, k))
27.32/8.91	   A^2 -> H(f(e), U1(k, k))
27.32/8.91	   A^2 -> H(f(e), U1(k, d))
27.32/8.91	   A^2 -> H(f(e), U1(d, k))
27.32/8.91	   A^2 -> H(U1(k, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(k, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(k, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(k, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(k, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(k, k), f(e))
27.32/8.91	   A^2 -> H(U1(k, k), f(k))
27.32/8.91	   A^2 -> H(U1(k, k), U1(d, d))
27.32/8.91	   A^2 -> H(f(k), U1(e, b))
27.32/8.91	   A^2 -> H(f(k), U1(k, b))
27.32/8.91	   A^2 -> H(f(k), U1(c, d))
27.32/8.91	   A^2 -> H(f(k), U1(d, c))
27.32/8.91	   A^2 -> H(f(k), U1(b, e))
27.32/8.91	   A^2 -> H(f(k), U1(b, k))
27.32/8.91	   A^2 -> H(f(k), U1(e, c))
27.32/8.91	   A^2 -> H(f(k), U1(k, c))
27.32/8.91	   A^2 -> H(f(k), U1(c, e))
27.32/8.91	   A^2 -> H(f(k), U1(c, k))
27.32/8.91	   A^2 -> H(f(k), U1(e, e))
27.32/8.91	   A^2 -> H(f(k), U1(k, d))
27.32/8.91	   A^2 -> H(f(k), U1(d, k))
27.32/8.91	   A^2 -> H(f(c), b)
27.32/8.91	   A^2 -> H(f(c), U1(e, d))
27.32/8.91	   A^2 -> H(f(c), U1(d, e))
27.32/8.91	   A^2 -> H(f(k), U1(k, k))
27.32/8.91	   A^2 -> H(U1(k, k), U1(b, b))
27.32/8.91	   A^2 -> H(U1(k, k), f(c))
27.32/8.91	   A^2 -> H(U1(k, k), f(d))
27.32/8.91	   A^2 -> H(U1(k, d), U1(c, b))
27.32/8.91	   A^2 -> H(U1(k, d), U1(d, b))
27.32/8.91	   A^2 -> H(U1(k, d), U1(b, c))
27.32/8.91	   A^2 -> H(U1(k, d), U1(b, d))
27.32/8.91	   A^2 -> H(U1(k, d), U1(c, c))
27.32/8.91	   A^2 -> H(U1(k, d), f(e))
27.32/8.91	   A^2 -> H(U1(k, d), f(k))
27.32/8.91	   A^2 -> H(U1(k, d), U1(d, d))
27.32/8.91	   A^2 -> H(U1(d, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(d, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(d, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(d, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(d, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(d, k), f(e))
27.32/8.91	   A^2 -> H(U1(d, k), f(k))
27.32/8.91	   A^2 -> H(U1(d, k), U1(d, d))
27.32/8.91	   A^2 -> H(U1(d, d), U1(e, b))
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, b))
27.32/8.91	   A^2 -> H(U1(d, d), U1(c, d))
27.32/8.91	   A^2 -> H(U1(d, d), U1(d, c))
27.32/8.91	   A^2 -> H(U1(d, d), U1(b, e))
27.32/8.91	   A^2 -> H(U1(d, d), U1(b, k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(e, c))
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, c))
27.32/8.91	   A^2 -> H(U1(d, d), U1(c, e))
27.32/8.91	   A^2 -> H(U1(d, d), U1(c, k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(e, e))
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, k))
27.32/8.91	   A^2 -> H(f(d), b)
27.32/8.91	   A^2 -> H(f(d), U1(e, d))
27.32/8.91	   A^2 -> H(f(d), U1(d, e))
27.32/8.91	   A^2 -> H(f(d), c)
27.32/8.91	   A^2 -> H(f(d), U1(e, k))
27.32/8.91	   A^2 -> H(f(d), U1(k, e))
27.32/8.91	   A^2 -> H(f(d), e)
27.32/8.91	   A^2 -> H(f(a), d)
27.32/8.91	   A^2 -> H(U1(c, c), U1(e, c))
27.32/8.91	   A^2 -> H(f(c), c)
27.32/8.91	   A^2 -> H(f(c), U1(e, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, c))
27.32/8.91	   A^2 -> H(f(c), U1(k, e))
27.32/8.91	   A^2 -> H(f(c), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, e))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, k))
27.32/8.91	   A^2 -> H(f(a), k)
27.32/8.91	   A^2 -> H(f(e), U1(e, e))
27.32/8.91	   A^2 -> H(f(c), e)
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, d))
27.32/8.91	   A^2 -> H(f(d), U1(k, k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(d, k))
27.32/8.91	   A^2 -> H(d, U1(b, b))
27.32/8.91	   A^2 -> H(d, f(c))
27.32/8.91	   A^2 -> H(d, f(d))
27.32/8.91	   A^2 -> H(a, U1(c, b))
27.32/8.91	   A^2 -> H(a, U1(d, b))
27.32/8.91	   A^2 -> H(a, U1(b, c))
27.32/8.91	   A^2 -> H(a, U1(b, d))
27.32/8.91	   A^2 -> H(a, U1(c, c))
27.32/8.91	   A^2 -> H(a, f(e))
27.32/8.91	   A^2 -> H(a, f(k))
27.32/8.91	   A^2 -> H(a, U1(d, d))
27.32/8.91	   A^2 -> H(U1(e, d), U1(c, b))
27.32/8.91	   A^2 -> H(U1(e, d), U1(d, b))
27.32/8.91	   A^2 -> H(U1(e, d), U1(b, c))
27.32/8.91	   A^2 -> H(U1(e, d), U1(b, d))
27.32/8.91	   A^2 -> H(U1(e, d), U1(c, c))
27.32/8.91	   A^2 -> H(U1(e, d), f(e))
27.32/8.91	   A^2 -> H(U1(e, d), f(k))
27.32/8.91	   A^2 -> H(U1(e, d), U1(d, d))
27.32/8.91	   A^2 -> H(U1(e, a), U1(e, b))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, b))
27.32/8.91	   A^2 -> H(U1(e, a), U1(c, d))
27.32/8.91	   A^2 -> H(U1(e, a), U1(d, c))
27.32/8.91	   A^2 -> H(U1(e, a), U1(b, e))
27.32/8.91	   A^2 -> H(U1(e, a), U1(b, k))
27.32/8.91	   A^2 -> H(U1(e, a), U1(e, c))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, c))
27.32/8.91	   A^2 -> H(U1(e, a), U1(c, e))
27.32/8.91	   A^2 -> H(U1(e, a), U1(c, k))
27.32/8.91	   A^2 -> H(U1(e, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(e, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(e, b))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, b))
27.32/8.91	   A^2 -> H(U1(k, a), U1(c, d))
27.32/8.91	   A^2 -> H(U1(k, a), U1(d, c))
27.32/8.91	   A^2 -> H(U1(k, a), U1(b, e))
27.32/8.91	   A^2 -> H(U1(k, a), U1(b, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(e, c))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, c))
27.32/8.91	   A^2 -> H(U1(k, a), U1(c, e))
27.32/8.91	   A^2 -> H(U1(k, a), U1(c, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(k, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(e, b))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, b))
27.32/8.91	   A^2 -> H(U1(c, d), U1(c, d))
27.32/8.91	   A^2 -> H(U1(c, d), U1(d, c))
27.32/8.91	   A^2 -> H(U1(c, d), U1(b, e))
27.32/8.91	   A^2 -> H(U1(c, d), U1(b, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(e, c))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, c))
27.32/8.91	   A^2 -> H(U1(c, d), U1(c, e))
27.32/8.91	   A^2 -> H(U1(c, d), U1(c, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(e, e))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, d))
27.32/8.91	   A^2 -> H(U1(c, d), U1(d, k))
27.32/8.91	   A^2 -> H(U1(c, a), b)
27.32/8.91	   A^2 -> H(U1(c, a), U1(e, d))
27.32/8.91	   A^2 -> H(U1(c, a), U1(d, e))
27.32/8.91	   A^2 -> H(U1(c, a), c)
27.32/8.91	   A^2 -> H(U1(c, a), U1(e, k))
27.32/8.91	   A^2 -> H(U1(c, a), U1(k, e))
27.32/8.91	
27.32/8.91	The TRS R consists of the following rules:
27.32/8.91	
27.32/8.91	   f(x) -> U1(x, x)
27.32/8.91	   U1(e, x) -> x
27.32/8.91	   a -> c
27.32/8.91	   a -> d
27.32/8.91	   b -> c
27.32/8.91	   b -> d
27.32/8.91	   d -> k
27.32/8.91	   c -> e
27.32/8.91	   c -> k
27.32/8.91	
27.32/8.91	Q is empty.
27.32/8.91	We have to consider all minimal (P,Q,R)-chains.
27.32/8.91	----------------------------------------
27.32/8.91	
27.32/8.91	(621) TransformationProof (EQUIVALENT)
27.32/8.91	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
27.32/8.91	
27.32/8.91	   (A^2 -> H(U1(e, a), U1(c, k)),A^2 -> H(U1(e, a), U1(c, k)))
27.32/8.91	   (A^2 -> H(U1(k, a), U1(c, k)),A^2 -> H(U1(k, a), U1(c, k)))
27.32/8.91	   (A^2 -> H(U1(c, c), U1(c, k)),A^2 -> H(U1(c, c), U1(c, k)))
27.32/8.91	   (A^2 -> H(U1(c, d), U1(c, k)),A^2 -> H(U1(c, d), U1(c, k)))
27.32/8.91	   (A^2 -> H(U1(c, a), U1(e, k)),A^2 -> H(U1(c, a), U1(e, k)))
27.32/8.91	   (A^2 -> H(U1(c, a), U1(k, k)),A^2 -> H(U1(c, a), U1(k, k)))
27.32/8.91	
27.32/8.91	
27.32/8.91	----------------------------------------
27.32/8.91	
27.32/8.91	(622)
27.32/8.91	Obligation:
27.32/8.91	Q DP problem:
27.32/8.91	The TRS P consists of the following rules:
27.32/8.91	
27.32/8.91	   H(x, x) -> G(x, x, f(k))
27.32/8.91	   G(d, x, x) -> A^2
27.32/8.91	   A^2 -> H(f(c), f(c))
27.32/8.91	   A^2 -> H(f(d), f(d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, c))
27.32/8.91	   A^2 -> H(f(e), f(e))
27.32/8.91	   A^2 -> H(f(k), f(k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(c, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(c, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(d, e), U1(b, b))
27.32/8.91	   A^2 -> H(U1(d, e), f(c))
27.32/8.91	   A^2 -> H(U1(d, e), f(d))
27.32/8.91	   A^2 -> H(U1(d, c), U1(c, b))
27.32/8.91	   A^2 -> H(U1(d, c), U1(d, b))
27.32/8.91	   A^2 -> H(U1(d, c), U1(b, c))
27.32/8.91	   A^2 -> H(U1(d, c), U1(b, d))
27.32/8.91	   A^2 -> H(U1(d, c), U1(c, c))
27.32/8.91	   A^2 -> H(U1(d, c), f(e))
27.32/8.91	   A^2 -> H(U1(d, c), f(k))
27.32/8.91	   A^2 -> H(U1(d, c), U1(d, d))
27.32/8.91	   A^2 -> H(U1(d, a), U1(e, b))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, b))
27.32/8.91	   A^2 -> H(U1(d, a), U1(c, d))
27.32/8.91	   A^2 -> H(U1(d, a), U1(d, c))
27.32/8.91	   A^2 -> H(U1(d, a), U1(b, e))
27.32/8.91	   A^2 -> H(U1(d, a), U1(b, k))
27.32/8.91	   A^2 -> H(U1(d, a), U1(e, c))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, c))
27.32/8.91	   A^2 -> H(U1(d, a), U1(c, e))
27.32/8.91	   A^2 -> H(U1(d, a), U1(c, k))
27.32/8.91	   A^2 -> H(U1(d, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(d, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(a, e), U1(c, b))
27.32/8.91	   A^2 -> H(U1(a, e), U1(d, b))
27.32/8.91	   A^2 -> H(U1(a, e), U1(b, c))
27.32/8.91	   A^2 -> H(U1(a, e), U1(b, d))
27.32/8.91	   A^2 -> H(U1(a, e), U1(c, c))
27.32/8.91	   A^2 -> H(U1(a, e), f(e))
27.32/8.91	   A^2 -> H(U1(a, e), f(k))
27.32/8.91	   A^2 -> H(U1(a, e), U1(d, d))
27.32/8.91	   A^2 -> H(U1(a, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(a, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(a, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(a, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(a, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(a, k), f(e))
27.32/8.91	   A^2 -> H(U1(a, k), f(k))
27.32/8.91	   A^2 -> H(U1(a, k), U1(d, d))
27.32/8.91	   A^2 -> H(U1(a, c), U1(e, b))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, b))
27.32/8.91	   A^2 -> H(U1(a, c), U1(c, d))
27.32/8.91	   A^2 -> H(U1(a, c), U1(d, c))
27.32/8.91	   A^2 -> H(U1(a, c), U1(b, e))
27.32/8.91	   A^2 -> H(U1(a, c), U1(b, k))
27.32/8.91	   A^2 -> H(U1(a, c), U1(e, c))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, c))
27.32/8.91	   A^2 -> H(U1(a, c), U1(c, e))
27.32/8.91	   A^2 -> H(U1(a, c), U1(c, k))
27.32/8.91	   A^2 -> H(U1(a, c), U1(e, e))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, k))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, d))
27.32/8.91	   A^2 -> H(U1(a, c), U1(d, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(e, b))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, b))
27.32/8.91	   A^2 -> H(U1(a, d), U1(c, d))
27.32/8.91	   A^2 -> H(U1(a, d), U1(d, c))
27.32/8.91	   A^2 -> H(U1(a, d), U1(b, e))
27.32/8.91	   A^2 -> H(U1(a, d), U1(b, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(e, c))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, c))
27.32/8.91	   A^2 -> H(U1(a, d), U1(c, e))
27.32/8.91	   A^2 -> H(U1(a, d), U1(c, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(e, e))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, d))
27.32/8.91	   A^2 -> H(U1(a, d), U1(d, k))
27.32/8.91	   A^2 -> H(U1(a, a), b)
27.32/8.91	   A^2 -> H(U1(a, a), U1(e, d))
27.32/8.91	   A^2 -> H(U1(a, a), U1(d, e))
27.32/8.91	   A^2 -> H(U1(a, a), c)
27.32/8.91	   A^2 -> H(U1(a, a), U1(e, k))
27.32/8.91	   A^2 -> H(U1(a, a), U1(k, e))
27.32/8.91	   A^2 -> H(U1(a, a), e)
27.32/8.91	   A^2 -> H(U1(a, a), U1(k, k))
27.32/8.91	   A^2 -> H(k, f(b))
27.32/8.91	   A^2 -> H(c, U1(b, b))
27.32/8.91	   A^2 -> H(c, f(c))
27.32/8.91	   A^2 -> H(c, f(d))
27.32/8.91	   A^2 -> H(U1(e, k), U1(b, b))
27.32/8.91	   A^2 -> H(U1(e, k), f(c))
27.32/8.91	   A^2 -> H(U1(e, k), f(d))
27.32/8.91	   A^2 -> H(U1(e, c), U1(c, b))
27.32/8.91	   A^2 -> H(U1(e, c), U1(d, b))
27.32/8.91	   A^2 -> H(U1(e, c), U1(b, c))
27.32/8.91	   A^2 -> H(U1(e, c), U1(b, d))
27.32/8.91	   A^2 -> H(U1(e, c), U1(c, c))
27.32/8.91	   A^2 -> H(U1(e, c), f(e))
27.32/8.91	   A^2 -> H(U1(e, c), f(k))
27.32/8.91	   A^2 -> H(U1(e, c), U1(d, d))
27.32/8.91	   A^2 -> H(U1(k, e), U1(b, b))
27.32/8.91	   A^2 -> H(U1(k, e), f(c))
27.32/8.91	   A^2 -> H(U1(k, e), f(d))
27.32/8.91	   A^2 -> H(U1(k, c), U1(c, b))
27.32/8.91	   A^2 -> H(U1(k, c), U1(d, b))
27.32/8.91	   A^2 -> H(U1(k, c), U1(b, c))
27.32/8.91	   A^2 -> H(U1(k, c), U1(b, d))
27.32/8.91	   A^2 -> H(U1(k, c), U1(c, c))
27.32/8.91	   A^2 -> H(U1(k, c), f(e))
27.32/8.91	   A^2 -> H(U1(k, c), f(k))
27.32/8.91	   A^2 -> H(U1(k, c), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, e), U1(c, b))
27.32/8.91	   A^2 -> H(U1(c, e), U1(d, b))
27.32/8.91	   A^2 -> H(U1(c, e), U1(b, c))
27.32/8.91	   A^2 -> H(U1(c, e), U1(b, d))
27.32/8.91	   A^2 -> H(U1(c, e), U1(c, c))
27.32/8.91	   A^2 -> H(U1(c, e), f(e))
27.32/8.91	   A^2 -> H(U1(c, e), f(k))
27.32/8.91	   A^2 -> H(U1(c, e), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(c, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(c, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(c, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(c, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(c, k), f(e))
27.32/8.91	   A^2 -> H(U1(c, k), f(k))
27.32/8.91	   A^2 -> H(U1(c, k), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(e, b))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, b))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(d, c))
27.32/8.91	   A^2 -> H(U1(c, c), U1(b, e))
27.32/8.91	   A^2 -> H(U1(c, c), U1(b, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(e, e))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(d, k))
27.32/8.91	   A^2 -> H(e, U1(b, b))
27.32/8.91	   A^2 -> H(e, f(c))
27.32/8.91	   A^2 -> H(e, f(d))
27.32/8.91	   A^2 -> H(U1(e, e), U1(c, b))
27.32/8.91	   A^2 -> H(U1(e, e), U1(d, b))
27.32/8.91	   A^2 -> H(U1(e, e), U1(b, c))
27.32/8.91	   A^2 -> H(U1(e, e), U1(b, d))
27.32/8.91	   A^2 -> H(U1(e, e), U1(c, c))
27.32/8.91	   A^2 -> H(U1(e, e), f(e))
27.32/8.91	   A^2 -> H(U1(e, e), f(k))
27.32/8.91	   A^2 -> H(U1(e, e), U1(d, d))
27.32/8.91	   A^2 -> H(f(e), U1(e, b))
27.32/8.91	   A^2 -> H(f(e), U1(k, b))
27.32/8.91	   A^2 -> H(f(e), U1(c, d))
27.32/8.91	   A^2 -> H(f(e), U1(d, c))
27.32/8.91	   A^2 -> H(f(e), U1(b, e))
27.32/8.91	   A^2 -> H(f(e), U1(b, k))
27.32/8.91	   A^2 -> H(f(e), U1(e, c))
27.32/8.91	   A^2 -> H(f(e), U1(k, c))
27.32/8.91	   A^2 -> H(f(e), U1(c, e))
27.32/8.91	   A^2 -> H(f(e), U1(c, k))
27.32/8.91	   A^2 -> H(f(e), U1(k, k))
27.32/8.91	   A^2 -> H(f(e), U1(k, d))
27.32/8.91	   A^2 -> H(f(e), U1(d, k))
27.32/8.91	   A^2 -> H(U1(k, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(k, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(k, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(k, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(k, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(k, k), f(e))
27.32/8.91	   A^2 -> H(U1(k, k), f(k))
27.32/8.91	   A^2 -> H(U1(k, k), U1(d, d))
27.32/8.91	   A^2 -> H(f(k), U1(e, b))
27.32/8.91	   A^2 -> H(f(k), U1(k, b))
27.32/8.91	   A^2 -> H(f(k), U1(c, d))
27.32/8.91	   A^2 -> H(f(k), U1(d, c))
27.32/8.91	   A^2 -> H(f(k), U1(b, e))
27.32/8.91	   A^2 -> H(f(k), U1(b, k))
27.32/8.91	   A^2 -> H(f(k), U1(e, c))
27.32/8.91	   A^2 -> H(f(k), U1(k, c))
27.32/8.91	   A^2 -> H(f(k), U1(c, e))
27.32/8.91	   A^2 -> H(f(k), U1(c, k))
27.32/8.91	   A^2 -> H(f(k), U1(e, e))
27.32/8.91	   A^2 -> H(f(k), U1(k, d))
27.32/8.91	   A^2 -> H(f(k), U1(d, k))
27.32/8.91	   A^2 -> H(f(c), b)
27.32/8.91	   A^2 -> H(f(c), U1(e, d))
27.32/8.91	   A^2 -> H(f(c), U1(d, e))
27.32/8.91	   A^2 -> H(f(k), U1(k, k))
27.32/8.91	   A^2 -> H(U1(k, k), U1(b, b))
27.32/8.91	   A^2 -> H(U1(k, k), f(c))
27.32/8.91	   A^2 -> H(U1(k, k), f(d))
27.32/8.91	   A^2 -> H(U1(k, d), U1(c, b))
27.32/8.91	   A^2 -> H(U1(k, d), U1(d, b))
27.32/8.91	   A^2 -> H(U1(k, d), U1(b, c))
27.32/8.91	   A^2 -> H(U1(k, d), U1(b, d))
27.32/8.91	   A^2 -> H(U1(k, d), U1(c, c))
27.32/8.91	   A^2 -> H(U1(k, d), f(e))
27.32/8.91	   A^2 -> H(U1(k, d), f(k))
27.32/8.91	   A^2 -> H(U1(k, d), U1(d, d))
27.32/8.91	   A^2 -> H(U1(d, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(d, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(d, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(d, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(d, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(d, k), f(e))
27.32/8.91	   A^2 -> H(U1(d, k), f(k))
27.32/8.91	   A^2 -> H(U1(d, k), U1(d, d))
27.32/8.91	   A^2 -> H(U1(d, d), U1(e, b))
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, b))
27.32/8.91	   A^2 -> H(U1(d, d), U1(c, d))
27.32/8.91	   A^2 -> H(U1(d, d), U1(d, c))
27.32/8.91	   A^2 -> H(U1(d, d), U1(b, e))
27.32/8.91	   A^2 -> H(U1(d, d), U1(b, k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(e, c))
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, c))
27.32/8.91	   A^2 -> H(U1(d, d), U1(c, e))
27.32/8.91	   A^2 -> H(U1(d, d), U1(c, k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(e, e))
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, k))
27.32/8.91	   A^2 -> H(f(d), b)
27.32/8.91	   A^2 -> H(f(d), U1(e, d))
27.32/8.91	   A^2 -> H(f(d), U1(d, e))
27.32/8.91	   A^2 -> H(f(d), c)
27.32/8.91	   A^2 -> H(f(d), U1(e, k))
27.32/8.91	   A^2 -> H(f(d), U1(k, e))
27.32/8.91	   A^2 -> H(f(d), e)
27.32/8.91	   A^2 -> H(f(a), d)
27.32/8.91	   A^2 -> H(U1(c, c), U1(e, c))
27.32/8.91	   A^2 -> H(f(c), c)
27.32/8.91	   A^2 -> H(f(c), U1(e, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(k, c))
27.32/8.91	   A^2 -> H(f(c), U1(k, e))
27.32/8.91	   A^2 -> H(f(c), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, e))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, k))
27.32/8.91	   A^2 -> H(f(a), k)
27.32/8.91	   A^2 -> H(f(e), U1(e, e))
27.32/8.91	   A^2 -> H(f(c), e)
27.32/8.91	   A^2 -> H(U1(d, d), U1(k, d))
27.32/8.91	   A^2 -> H(f(d), U1(k, k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(d, k))
27.32/8.91	   A^2 -> H(d, U1(b, b))
27.32/8.91	   A^2 -> H(d, f(c))
27.32/8.91	   A^2 -> H(d, f(d))
27.32/8.91	   A^2 -> H(a, U1(c, b))
27.32/8.91	   A^2 -> H(a, U1(d, b))
27.32/8.91	   A^2 -> H(a, U1(b, c))
27.32/8.91	   A^2 -> H(a, U1(b, d))
27.32/8.91	   A^2 -> H(a, U1(c, c))
27.32/8.91	   A^2 -> H(a, f(e))
27.32/8.91	   A^2 -> H(a, f(k))
27.32/8.91	   A^2 -> H(a, U1(d, d))
27.32/8.91	   A^2 -> H(U1(e, d), U1(c, b))
27.32/8.91	   A^2 -> H(U1(e, d), U1(d, b))
27.32/8.91	   A^2 -> H(U1(e, d), U1(b, c))
27.32/8.91	   A^2 -> H(U1(e, d), U1(b, d))
27.32/8.91	   A^2 -> H(U1(e, d), U1(c, c))
27.32/8.91	   A^2 -> H(U1(e, d), f(e))
27.32/8.91	   A^2 -> H(U1(e, d), f(k))
27.32/8.91	   A^2 -> H(U1(e, d), U1(d, d))
27.32/8.91	   A^2 -> H(U1(e, a), U1(e, b))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, b))
27.32/8.91	   A^2 -> H(U1(e, a), U1(c, d))
27.32/8.91	   A^2 -> H(U1(e, a), U1(d, c))
27.32/8.91	   A^2 -> H(U1(e, a), U1(b, e))
27.32/8.91	   A^2 -> H(U1(e, a), U1(b, k))
27.32/8.91	   A^2 -> H(U1(e, a), U1(e, c))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, c))
27.32/8.91	   A^2 -> H(U1(e, a), U1(c, e))
27.32/8.91	   A^2 -> H(U1(e, a), U1(c, k))
27.32/8.91	   A^2 -> H(U1(e, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(e, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(e, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(e, b))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, b))
27.32/8.91	   A^2 -> H(U1(k, a), U1(c, d))
27.32/8.91	   A^2 -> H(U1(k, a), U1(d, c))
27.32/8.91	   A^2 -> H(U1(k, a), U1(b, e))
27.32/8.91	   A^2 -> H(U1(k, a), U1(b, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(e, c))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, c))
27.32/8.91	   A^2 -> H(U1(k, a), U1(c, e))
27.32/8.91	   A^2 -> H(U1(k, a), U1(c, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(k, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(k, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(e, b))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, b))
27.32/8.91	   A^2 -> H(U1(c, d), U1(c, d))
27.32/8.91	   A^2 -> H(U1(c, d), U1(d, c))
27.32/8.91	   A^2 -> H(U1(c, d), U1(b, e))
27.32/8.91	   A^2 -> H(U1(c, d), U1(b, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(e, c))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, c))
27.32/8.91	   A^2 -> H(U1(c, d), U1(c, e))
27.32/8.91	   A^2 -> H(U1(c, d), U1(c, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(e, e))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, d), U1(k, d))
27.32/8.91	   A^2 -> H(U1(c, d), U1(d, k))
27.32/8.91	   A^2 -> H(U1(c, a), b)
27.32/8.91	   A^2 -> H(U1(c, a), U1(e, d))
27.32/8.91	   A^2 -> H(U1(c, a), U1(d, e))
27.32/8.91	   A^2 -> H(U1(c, a), c)
27.32/8.91	   A^2 -> H(U1(c, a), U1(e, k))
27.32/8.91	   A^2 -> H(U1(c, a), U1(k, e))
27.32/8.91	
27.32/8.91	The TRS R consists of the following rules:
27.32/8.91	
27.32/8.91	   f(x) -> U1(x, x)
27.32/8.91	   U1(e, x) -> x
27.32/8.91	   a -> c
27.32/8.91	   a -> d
27.32/8.91	   b -> c
27.32/8.91	   b -> d
27.32/8.91	   d -> k
27.32/8.91	   c -> e
27.32/8.91	   c -> k
27.32/8.91	
27.32/8.91	Q is empty.
27.32/8.91	We have to consider all minimal (P,Q,R)-chains.
27.32/8.91	----------------------------------------
27.32/8.91	
27.32/8.91	(623) TransformationProof (EQUIVALENT)
27.32/8.91	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
27.32/8.91	
27.32/8.91	   (A^2 -> H(U1(e, a), U1(e, e)),A^2 -> H(U1(e, a), U1(e, e)))
27.32/8.91	   (A^2 -> H(U1(k, a), U1(e, e)),A^2 -> H(U1(k, a), U1(e, e)))
27.32/8.91	   (A^2 -> H(U1(c, c), U1(e, e)),A^2 -> H(U1(c, c), U1(e, e)))
27.32/8.91	   (A^2 -> H(U1(c, d), U1(e, e)),A^2 -> H(U1(c, d), U1(e, e)))
27.32/8.91	   (A^2 -> H(U1(c, a), e),A^2 -> H(U1(c, a), e))
27.32/8.91	
27.32/8.91	
27.32/8.91	----------------------------------------
27.32/8.91	
27.32/8.91	(624)
27.32/8.91	Obligation:
27.32/8.91	Q DP problem:
27.32/8.91	The TRS P consists of the following rules:
27.32/8.91	
27.32/8.91	   H(x, x) -> G(x, x, f(k))
27.32/8.91	   G(d, x, x) -> A^2
27.32/8.91	   A^2 -> H(f(c), f(c))
27.32/8.91	   A^2 -> H(f(d), f(d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(c, c))
27.32/8.91	   A^2 -> H(f(e), f(e))
27.32/8.91	   A^2 -> H(f(k), f(k))
27.32/8.91	   A^2 -> H(U1(d, d), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(c, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(c, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(d, e), U1(b, b))
27.32/8.91	   A^2 -> H(U1(d, e), f(c))
27.32/8.91	   A^2 -> H(U1(d, e), f(d))
27.32/8.91	   A^2 -> H(U1(d, c), U1(c, b))
27.32/8.91	   A^2 -> H(U1(d, c), U1(d, b))
27.32/8.91	   A^2 -> H(U1(d, c), U1(b, c))
27.32/8.91	   A^2 -> H(U1(d, c), U1(b, d))
27.32/8.91	   A^2 -> H(U1(d, c), U1(c, c))
27.32/8.91	   A^2 -> H(U1(d, c), f(e))
27.32/8.91	   A^2 -> H(U1(d, c), f(k))
27.32/8.91	   A^2 -> H(U1(d, c), U1(d, d))
27.32/8.91	   A^2 -> H(U1(d, a), U1(e, b))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, b))
27.32/8.91	   A^2 -> H(U1(d, a), U1(c, d))
27.32/8.91	   A^2 -> H(U1(d, a), U1(d, c))
27.32/8.91	   A^2 -> H(U1(d, a), U1(b, e))
27.32/8.91	   A^2 -> H(U1(d, a), U1(b, k))
27.32/8.91	   A^2 -> H(U1(d, a), U1(e, c))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, c))
27.32/8.91	   A^2 -> H(U1(d, a), U1(c, e))
27.32/8.91	   A^2 -> H(U1(d, a), U1(c, k))
27.32/8.91	   A^2 -> H(U1(d, a), U1(e, e))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, k))
27.32/8.91	   A^2 -> H(U1(d, a), U1(k, d))
27.32/8.91	   A^2 -> H(U1(d, a), U1(d, k))
27.32/8.91	   A^2 -> H(U1(a, e), U1(c, b))
27.32/8.91	   A^2 -> H(U1(a, e), U1(d, b))
27.32/8.91	   A^2 -> H(U1(a, e), U1(b, c))
27.32/8.91	   A^2 -> H(U1(a, e), U1(b, d))
27.32/8.91	   A^2 -> H(U1(a, e), U1(c, c))
27.32/8.91	   A^2 -> H(U1(a, e), f(e))
27.32/8.91	   A^2 -> H(U1(a, e), f(k))
27.32/8.91	   A^2 -> H(U1(a, e), U1(d, d))
27.32/8.91	   A^2 -> H(U1(a, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(a, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(a, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(a, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(a, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(a, k), f(e))
27.32/8.91	   A^2 -> H(U1(a, k), f(k))
27.32/8.91	   A^2 -> H(U1(a, k), U1(d, d))
27.32/8.91	   A^2 -> H(U1(a, c), U1(e, b))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, b))
27.32/8.91	   A^2 -> H(U1(a, c), U1(c, d))
27.32/8.91	   A^2 -> H(U1(a, c), U1(d, c))
27.32/8.91	   A^2 -> H(U1(a, c), U1(b, e))
27.32/8.91	   A^2 -> H(U1(a, c), U1(b, k))
27.32/8.91	   A^2 -> H(U1(a, c), U1(e, c))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, c))
27.32/8.91	   A^2 -> H(U1(a, c), U1(c, e))
27.32/8.91	   A^2 -> H(U1(a, c), U1(c, k))
27.32/8.91	   A^2 -> H(U1(a, c), U1(e, e))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, k))
27.32/8.91	   A^2 -> H(U1(a, c), U1(k, d))
27.32/8.91	   A^2 -> H(U1(a, c), U1(d, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(e, b))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, b))
27.32/8.91	   A^2 -> H(U1(a, d), U1(c, d))
27.32/8.91	   A^2 -> H(U1(a, d), U1(d, c))
27.32/8.91	   A^2 -> H(U1(a, d), U1(b, e))
27.32/8.91	   A^2 -> H(U1(a, d), U1(b, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(e, c))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, c))
27.32/8.91	   A^2 -> H(U1(a, d), U1(c, e))
27.32/8.91	   A^2 -> H(U1(a, d), U1(c, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(e, e))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, k))
27.32/8.91	   A^2 -> H(U1(a, d), U1(k, d))
27.32/8.91	   A^2 -> H(U1(a, d), U1(d, k))
27.32/8.91	   A^2 -> H(U1(a, a), b)
27.32/8.91	   A^2 -> H(U1(a, a), U1(e, d))
27.32/8.91	   A^2 -> H(U1(a, a), U1(d, e))
27.32/8.91	   A^2 -> H(U1(a, a), c)
27.32/8.91	   A^2 -> H(U1(a, a), U1(e, k))
27.32/8.91	   A^2 -> H(U1(a, a), U1(k, e))
27.32/8.91	   A^2 -> H(U1(a, a), e)
27.32/8.91	   A^2 -> H(U1(a, a), U1(k, k))
27.32/8.91	   A^2 -> H(k, f(b))
27.32/8.91	   A^2 -> H(c, U1(b, b))
27.32/8.91	   A^2 -> H(c, f(c))
27.32/8.91	   A^2 -> H(c, f(d))
27.32/8.91	   A^2 -> H(U1(e, k), U1(b, b))
27.32/8.91	   A^2 -> H(U1(e, k), f(c))
27.32/8.91	   A^2 -> H(U1(e, k), f(d))
27.32/8.91	   A^2 -> H(U1(e, c), U1(c, b))
27.32/8.91	   A^2 -> H(U1(e, c), U1(d, b))
27.32/8.91	   A^2 -> H(U1(e, c), U1(b, c))
27.32/8.91	   A^2 -> H(U1(e, c), U1(b, d))
27.32/8.91	   A^2 -> H(U1(e, c), U1(c, c))
27.32/8.91	   A^2 -> H(U1(e, c), f(e))
27.32/8.91	   A^2 -> H(U1(e, c), f(k))
27.32/8.91	   A^2 -> H(U1(e, c), U1(d, d))
27.32/8.91	   A^2 -> H(U1(k, e), U1(b, b))
27.32/8.91	   A^2 -> H(U1(k, e), f(c))
27.32/8.91	   A^2 -> H(U1(k, e), f(d))
27.32/8.91	   A^2 -> H(U1(k, c), U1(c, b))
27.32/8.91	   A^2 -> H(U1(k, c), U1(d, b))
27.32/8.91	   A^2 -> H(U1(k, c), U1(b, c))
27.32/8.91	   A^2 -> H(U1(k, c), U1(b, d))
27.32/8.91	   A^2 -> H(U1(k, c), U1(c, c))
27.32/8.91	   A^2 -> H(U1(k, c), f(e))
27.32/8.91	   A^2 -> H(U1(k, c), f(k))
27.32/8.91	   A^2 -> H(U1(k, c), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, e), U1(c, b))
27.32/8.91	   A^2 -> H(U1(c, e), U1(d, b))
27.32/8.91	   A^2 -> H(U1(c, e), U1(b, c))
27.32/8.91	   A^2 -> H(U1(c, e), U1(b, d))
27.32/8.91	   A^2 -> H(U1(c, e), U1(c, c))
27.32/8.91	   A^2 -> H(U1(c, e), f(e))
27.32/8.91	   A^2 -> H(U1(c, e), f(k))
27.32/8.91	   A^2 -> H(U1(c, e), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, k), U1(c, b))
27.32/8.91	   A^2 -> H(U1(c, k), U1(d, b))
27.32/8.91	   A^2 -> H(U1(c, k), U1(b, c))
27.32/8.91	   A^2 -> H(U1(c, k), U1(b, d))
27.32/8.91	   A^2 -> H(U1(c, k), U1(c, c))
27.32/8.91	   A^2 -> H(U1(c, k), f(e))
27.32/8.91	   A^2 -> H(U1(c, k), f(k))
27.32/8.91	   A^2 -> H(U1(c, k), U1(d, d))
27.32/8.91	   A^2 -> H(U1(c, c), U1(e, b))
27.32/8.92	   A^2 -> H(U1(c, c), U1(k, b))
27.32/8.92	   A^2 -> H(U1(c, c), U1(c, d))
27.32/8.92	   A^2 -> H(U1(c, c), U1(d, c))
27.32/8.92	   A^2 -> H(U1(c, c), U1(b, e))
27.32/8.92	   A^2 -> H(U1(c, c), U1(b, k))
27.32/8.92	   A^2 -> H(U1(c, c), U1(e, e))
27.32/8.92	   A^2 -> H(U1(c, c), U1(k, k))
27.32/8.92	   A^2 -> H(U1(c, c), U1(k, d))
27.32/8.92	   A^2 -> H(U1(c, c), U1(d, k))
27.32/8.92	   A^2 -> H(e, U1(b, b))
27.32/8.92	   A^2 -> H(e, f(c))
27.32/8.92	   A^2 -> H(e, f(d))
27.32/8.92	   A^2 -> H(U1(e, e), U1(c, b))
27.32/8.92	   A^2 -> H(U1(e, e), U1(d, b))
27.32/8.92	   A^2 -> H(U1(e, e), U1(b, c))
27.32/8.92	   A^2 -> H(U1(e, e), U1(b, d))
27.32/8.92	   A^2 -> H(U1(e, e), U1(c, c))
27.32/8.92	   A^2 -> H(U1(e, e), f(e))
27.32/8.92	   A^2 -> H(U1(e, e), f(k))
27.32/8.92	   A^2 -> H(U1(e, e), U1(d, d))
27.32/8.92	   A^2 -> H(f(e), U1(e, b))
27.32/8.92	   A^2 -> H(f(e), U1(k, b))
27.32/8.92	   A^2 -> H(f(e), U1(c, d))
27.32/8.92	   A^2 -> H(f(e), U1(d, c))
27.32/8.92	   A^2 -> H(f(e), U1(b, e))
27.32/8.92	   A^2 -> H(f(e), U1(b, k))
27.32/8.92	   A^2 -> H(f(e), U1(e, c))
27.32/8.92	   A^2 -> H(f(e), U1(k, c))
27.32/8.92	   A^2 -> H(f(e), U1(c, e))
27.32/8.92	   A^2 -> H(f(e), U1(c, k))
27.32/8.92	   A^2 -> H(f(e), U1(k, k))
27.32/8.92	   A^2 -> H(f(e), U1(k, d))
27.32/8.92	   A^2 -> H(f(e), U1(d, k))
27.32/8.92	   A^2 -> H(U1(k, k), U1(c, b))
27.32/8.92	   A^2 -> H(U1(k, k), U1(d, b))
27.32/8.92	   A^2 -> H(U1(k, k), U1(b, c))
27.32/8.92	   A^2 -> H(U1(k, k), U1(b, d))
27.32/8.92	   A^2 -> H(U1(k, k), U1(c, c))
27.32/8.92	   A^2 -> H(U1(k, k), f(e))
27.32/8.92	   A^2 -> H(U1(k, k), f(k))
27.32/8.92	   A^2 -> H(U1(k, k), U1(d, d))
27.32/8.92	   A^2 -> H(f(k), U1(e, b))
27.32/8.92	   A^2 -> H(f(k), U1(k, b))
27.32/8.92	   A^2 -> H(f(k), U1(c, d))
27.32/8.92	   A^2 -> H(f(k), U1(d, c))
27.32/8.92	   A^2 -> H(f(k), U1(b, e))
27.32/8.92	   A^2 -> H(f(k), U1(b, k))
27.32/8.92	   A^2 -> H(f(k), U1(e, c))
27.32/8.92	   A^2 -> H(f(k), U1(k, c))
27.32/8.92	   A^2 -> H(f(k), U1(c, e))
27.32/8.92	   A^2 -> H(f(k), U1(c, k))
27.32/8.92	   A^2 -> H(f(k), U1(e, e))
27.32/8.92	   A^2 -> H(f(k), U1(k, d))
27.32/8.92	   A^2 -> H(f(k), U1(d, k))
27.32/8.92	   A^2 -> H(f(c), b)
27.32/8.92	   A^2 -> H(f(c), U1(e, d))
27.32/8.92	   A^2 -> H(f(c), U1(d, e))
27.32/8.92	   A^2 -> H(f(k), U1(k, k))
27.32/8.92	   A^2 -> H(U1(k, k), U1(b, b))
27.32/8.92	   A^2 -> H(U1(k, k), f(c))
27.32/8.92	   A^2 -> H(U1(k, k), f(d))
27.32/8.92	   A^2 -> H(U1(k, d), U1(c, b))
27.32/8.92	   A^2 -> H(U1(k, d), U1(d, b))
27.32/8.92	   A^2 -> H(U1(k, d), U1(b, c))
27.32/8.92	   A^2 -> H(U1(k, d), U1(b, d))
27.32/8.92	   A^2 -> H(U1(k, d), U1(c, c))
27.32/8.92	   A^2 -> H(U1(k, d), f(e))
27.32/8.92	   A^2 -> H(U1(k, d), f(k))
27.32/8.92	   A^2 -> H(U1(k, d), U1(d, d))
27.32/8.92	   A^2 -> H(U1(d, k), U1(c, b))
27.32/8.92	   A^2 -> H(U1(d, k), U1(d, b))
27.32/8.92	   A^2 -> H(U1(d, k), U1(b, c))
27.32/8.92	   A^2 -> H(U1(d, k), U1(b, d))
27.32/8.92	   A^2 -> H(U1(d, k), U1(c, c))
27.32/8.92	   A^2 -> H(U1(d, k), f(e))
27.32/8.92	   A^2 -> H(U1(d, k), f(k))
27.32/8.92	   A^2 -> H(U1(d, k), U1(d, d))
27.32/8.92	   A^2 -> H(U1(d, d), U1(e, b))
27.32/8.92	   A^2 -> H(U1(d, d), U1(k, b))
27.32/8.92	   A^2 -> H(U1(d, d), U1(c, d))
27.32/8.92	   A^2 -> H(U1(d, d), U1(d, c))
27.32/8.92	   A^2 -> H(U1(d, d), U1(b, e))
27.32/8.92	   A^2 -> H(U1(d, d), U1(b, k))
27.32/8.92	   A^2 -> H(U1(d, d), U1(e, c))
27.32/8.92	   A^2 -> H(U1(d, d), U1(k, c))
27.32/8.92	   A^2 -> H(U1(d, d), U1(c, e))
27.32/8.92	   A^2 -> H(U1(d, d), U1(c, k))
27.32/8.92	   A^2 -> H(U1(d, d), U1(e, e))
27.32/8.92	   A^2 -> H(U1(d, d), U1(k, k))
27.32/8.92	   A^2 -> H(f(d), b)
27.32/8.92	   A^2 -> H(f(d), U1(e, d))
27.32/8.92	   A^2 -> H(f(d), U1(d, e))
27.32/8.92	   A^2 -> H(f(d), c)
27.32/8.92	   A^2 -> H(f(d), U1(e, k))
27.32/8.92	   A^2 -> H(f(d), U1(k, e))
27.32/8.92	   A^2 -> H(f(d), e)
27.32/8.92	   A^2 -> H(f(a), d)
27.32/8.92	   A^2 -> H(U1(c, c), U1(e, c))
27.32/8.92	   A^2 -> H(f(c), c)
27.32/8.92	   A^2 -> H(f(c), U1(e, k))
27.32/8.92	   A^2 -> H(U1(c, c), U1(k, c))
27.32/8.92	   A^2 -> H(f(c), U1(k, e))
27.32/8.92	   A^2 -> H(f(c), U1(k, k))
27.32/8.92	   A^2 -> H(U1(c, c), U1(c, e))
27.32/8.92	   A^2 -> H(U1(c, c), U1(c, k))
27.47/8.92	   A^2 -> H(f(a), k)
27.47/8.92	   A^2 -> H(f(e), U1(e, e))
27.47/8.92	   A^2 -> H(f(c), e)
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, d))
27.47/8.92	   A^2 -> H(f(d), U1(k, k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(d, k))
27.47/8.92	   A^2 -> H(d, U1(b, b))
27.47/8.92	   A^2 -> H(d, f(c))
27.47/8.92	   A^2 -> H(d, f(d))
27.47/8.92	   A^2 -> H(a, U1(c, b))
27.47/8.92	   A^2 -> H(a, U1(d, b))
27.47/8.92	   A^2 -> H(a, U1(b, c))
27.47/8.92	   A^2 -> H(a, U1(b, d))
27.47/8.92	   A^2 -> H(a, U1(c, c))
27.47/8.92	   A^2 -> H(a, f(e))
27.47/8.92	   A^2 -> H(a, f(k))
27.47/8.92	   A^2 -> H(a, U1(d, d))
27.47/8.92	   A^2 -> H(U1(e, d), U1(c, b))
27.47/8.92	   A^2 -> H(U1(e, d), U1(d, b))
27.47/8.92	   A^2 -> H(U1(e, d), U1(b, c))
27.47/8.92	   A^2 -> H(U1(e, d), U1(b, d))
27.47/8.92	   A^2 -> H(U1(e, d), U1(c, c))
27.47/8.92	   A^2 -> H(U1(e, d), f(e))
27.47/8.92	   A^2 -> H(U1(e, d), f(k))
27.47/8.92	   A^2 -> H(U1(e, d), U1(d, d))
27.47/8.92	   A^2 -> H(U1(e, a), U1(e, b))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, b))
27.47/8.92	   A^2 -> H(U1(e, a), U1(c, d))
27.47/8.92	   A^2 -> H(U1(e, a), U1(d, c))
27.47/8.92	   A^2 -> H(U1(e, a), U1(b, e))
27.47/8.92	   A^2 -> H(U1(e, a), U1(b, k))
27.47/8.92	   A^2 -> H(U1(e, a), U1(e, c))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, c))
27.47/8.92	   A^2 -> H(U1(e, a), U1(c, e))
27.47/8.92	   A^2 -> H(U1(e, a), U1(c, k))
27.47/8.92	   A^2 -> H(U1(e, a), U1(e, e))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, k))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, d))
27.47/8.92	   A^2 -> H(U1(e, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(e, b))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, b))
27.47/8.92	   A^2 -> H(U1(k, a), U1(c, d))
27.47/8.92	   A^2 -> H(U1(k, a), U1(d, c))
27.47/8.92	   A^2 -> H(U1(k, a), U1(b, e))
27.47/8.92	   A^2 -> H(U1(k, a), U1(b, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(e, c))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, c))
27.47/8.92	   A^2 -> H(U1(k, a), U1(c, e))
27.47/8.92	   A^2 -> H(U1(k, a), U1(c, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(e, e))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, d))
27.47/8.92	   A^2 -> H(U1(k, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(e, b))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, b))
27.47/8.92	   A^2 -> H(U1(c, d), U1(c, d))
27.47/8.92	   A^2 -> H(U1(c, d), U1(d, c))
27.47/8.92	   A^2 -> H(U1(c, d), U1(b, e))
27.47/8.92	   A^2 -> H(U1(c, d), U1(b, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(e, c))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, c))
27.47/8.92	   A^2 -> H(U1(c, d), U1(c, e))
27.47/8.92	   A^2 -> H(U1(c, d), U1(c, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(e, e))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, d))
27.47/8.92	   A^2 -> H(U1(c, d), U1(d, k))
27.47/8.92	   A^2 -> H(U1(c, a), b)
27.47/8.92	   A^2 -> H(U1(c, a), U1(e, d))
27.47/8.92	   A^2 -> H(U1(c, a), U1(d, e))
27.47/8.92	   A^2 -> H(U1(c, a), c)
27.47/8.92	   A^2 -> H(U1(c, a), U1(e, k))
27.47/8.92	   A^2 -> H(U1(c, a), U1(k, e))
27.47/8.92	   A^2 -> H(U1(c, a), e)
27.47/8.92	
27.47/8.92	The TRS R consists of the following rules:
27.47/8.92	
27.47/8.92	   f(x) -> U1(x, x)
27.47/8.92	   U1(e, x) -> x
27.47/8.92	   a -> c
27.47/8.92	   a -> d
27.47/8.92	   b -> c
27.47/8.92	   b -> d
27.47/8.92	   d -> k
27.47/8.92	   c -> e
27.47/8.92	   c -> k
27.47/8.92	
27.47/8.92	Q is empty.
27.47/8.92	We have to consider all minimal (P,Q,R)-chains.
27.47/8.92	----------------------------------------
27.47/8.92	
27.47/8.92	(625) TransformationProof (EQUIVALENT)
27.47/8.92	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
27.47/8.92	
27.47/8.92	   (A^2 -> H(U1(e, a), U1(k, k)),A^2 -> H(U1(e, a), U1(k, k)))
27.47/8.92	   (A^2 -> H(U1(k, a), U1(k, k)),A^2 -> H(U1(k, a), U1(k, k)))
27.47/8.92	   (A^2 -> H(U1(c, c), U1(k, k)),A^2 -> H(U1(c, c), U1(k, k)))
27.47/8.92	   (A^2 -> H(U1(c, d), U1(k, k)),A^2 -> H(U1(c, d), U1(k, k)))
27.47/8.92	
27.47/8.92	
27.47/8.92	----------------------------------------
27.47/8.92	
27.47/8.92	(626)
27.47/8.92	Obligation:
27.47/8.92	Q DP problem:
27.47/8.92	The TRS P consists of the following rules:
27.47/8.92	
27.47/8.92	   H(x, x) -> G(x, x, f(k))
27.47/8.92	   G(d, x, x) -> A^2
27.47/8.92	   A^2 -> H(f(c), f(c))
27.47/8.92	   A^2 -> H(f(d), f(d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, c))
27.47/8.92	   A^2 -> H(f(e), f(e))
27.47/8.92	   A^2 -> H(f(k), f(k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(d, d))
27.47/8.92	   A^2 -> H(U1(c, a), U1(k, d))
27.47/8.92	   A^2 -> H(U1(c, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(d, e), U1(b, b))
27.47/8.92	   A^2 -> H(U1(d, e), f(c))
27.47/8.92	   A^2 -> H(U1(d, e), f(d))
27.47/8.92	   A^2 -> H(U1(d, c), U1(c, b))
27.47/8.92	   A^2 -> H(U1(d, c), U1(d, b))
27.47/8.92	   A^2 -> H(U1(d, c), U1(b, c))
27.47/8.92	   A^2 -> H(U1(d, c), U1(b, d))
27.47/8.92	   A^2 -> H(U1(d, c), U1(c, c))
27.47/8.92	   A^2 -> H(U1(d, c), f(e))
27.47/8.92	   A^2 -> H(U1(d, c), f(k))
27.47/8.92	   A^2 -> H(U1(d, c), U1(d, d))
27.47/8.92	   A^2 -> H(U1(d, a), U1(e, b))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, b))
27.47/8.92	   A^2 -> H(U1(d, a), U1(c, d))
27.47/8.92	   A^2 -> H(U1(d, a), U1(d, c))
27.47/8.92	   A^2 -> H(U1(d, a), U1(b, e))
27.47/8.92	   A^2 -> H(U1(d, a), U1(b, k))
27.47/8.92	   A^2 -> H(U1(d, a), U1(e, c))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, c))
27.47/8.92	   A^2 -> H(U1(d, a), U1(c, e))
27.47/8.92	   A^2 -> H(U1(d, a), U1(c, k))
27.47/8.92	   A^2 -> H(U1(d, a), U1(e, e))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, k))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, d))
27.47/8.92	   A^2 -> H(U1(d, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(a, e), U1(c, b))
27.47/8.92	   A^2 -> H(U1(a, e), U1(d, b))
27.47/8.92	   A^2 -> H(U1(a, e), U1(b, c))
27.47/8.92	   A^2 -> H(U1(a, e), U1(b, d))
27.47/8.92	   A^2 -> H(U1(a, e), U1(c, c))
27.47/8.92	   A^2 -> H(U1(a, e), f(e))
27.47/8.92	   A^2 -> H(U1(a, e), f(k))
27.47/8.92	   A^2 -> H(U1(a, e), U1(d, d))
27.47/8.92	   A^2 -> H(U1(a, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(a, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(a, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(a, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(a, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(a, k), f(e))
27.47/8.92	   A^2 -> H(U1(a, k), f(k))
27.47/8.92	   A^2 -> H(U1(a, k), U1(d, d))
27.47/8.92	   A^2 -> H(U1(a, c), U1(e, b))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, b))
27.47/8.92	   A^2 -> H(U1(a, c), U1(c, d))
27.47/8.92	   A^2 -> H(U1(a, c), U1(d, c))
27.47/8.92	   A^2 -> H(U1(a, c), U1(b, e))
27.47/8.92	   A^2 -> H(U1(a, c), U1(b, k))
27.47/8.92	   A^2 -> H(U1(a, c), U1(e, c))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, c))
27.47/8.92	   A^2 -> H(U1(a, c), U1(c, e))
27.47/8.92	   A^2 -> H(U1(a, c), U1(c, k))
27.47/8.92	   A^2 -> H(U1(a, c), U1(e, e))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, k))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, d))
27.47/8.92	   A^2 -> H(U1(a, c), U1(d, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(e, b))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, b))
27.47/8.92	   A^2 -> H(U1(a, d), U1(c, d))
27.47/8.92	   A^2 -> H(U1(a, d), U1(d, c))
27.47/8.92	   A^2 -> H(U1(a, d), U1(b, e))
27.47/8.92	   A^2 -> H(U1(a, d), U1(b, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(e, c))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, c))
27.47/8.92	   A^2 -> H(U1(a, d), U1(c, e))
27.47/8.92	   A^2 -> H(U1(a, d), U1(c, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(e, e))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, d))
27.47/8.92	   A^2 -> H(U1(a, d), U1(d, k))
27.47/8.92	   A^2 -> H(U1(a, a), b)
27.47/8.92	   A^2 -> H(U1(a, a), U1(e, d))
27.47/8.92	   A^2 -> H(U1(a, a), U1(d, e))
27.47/8.92	   A^2 -> H(U1(a, a), c)
27.47/8.92	   A^2 -> H(U1(a, a), U1(e, k))
27.47/8.92	   A^2 -> H(U1(a, a), U1(k, e))
27.47/8.92	   A^2 -> H(U1(a, a), e)
27.47/8.92	   A^2 -> H(U1(a, a), U1(k, k))
27.47/8.92	   A^2 -> H(k, f(b))
27.47/8.92	   A^2 -> H(c, U1(b, b))
27.47/8.92	   A^2 -> H(c, f(c))
27.47/8.92	   A^2 -> H(c, f(d))
27.47/8.92	   A^2 -> H(U1(e, k), U1(b, b))
27.47/8.92	   A^2 -> H(U1(e, k), f(c))
27.47/8.92	   A^2 -> H(U1(e, k), f(d))
27.47/8.92	   A^2 -> H(U1(e, c), U1(c, b))
27.47/8.92	   A^2 -> H(U1(e, c), U1(d, b))
27.47/8.92	   A^2 -> H(U1(e, c), U1(b, c))
27.47/8.92	   A^2 -> H(U1(e, c), U1(b, d))
27.47/8.92	   A^2 -> H(U1(e, c), U1(c, c))
27.47/8.92	   A^2 -> H(U1(e, c), f(e))
27.47/8.92	   A^2 -> H(U1(e, c), f(k))
27.47/8.92	   A^2 -> H(U1(e, c), U1(d, d))
27.47/8.92	   A^2 -> H(U1(k, e), U1(b, b))
27.47/8.92	   A^2 -> H(U1(k, e), f(c))
27.47/8.92	   A^2 -> H(U1(k, e), f(d))
27.47/8.92	   A^2 -> H(U1(k, c), U1(c, b))
27.47/8.92	   A^2 -> H(U1(k, c), U1(d, b))
27.47/8.92	   A^2 -> H(U1(k, c), U1(b, c))
27.47/8.92	   A^2 -> H(U1(k, c), U1(b, d))
27.47/8.92	   A^2 -> H(U1(k, c), U1(c, c))
27.47/8.92	   A^2 -> H(U1(k, c), f(e))
27.47/8.92	   A^2 -> H(U1(k, c), f(k))
27.47/8.92	   A^2 -> H(U1(k, c), U1(d, d))
27.47/8.92	   A^2 -> H(U1(c, e), U1(c, b))
27.47/8.92	   A^2 -> H(U1(c, e), U1(d, b))
27.47/8.92	   A^2 -> H(U1(c, e), U1(b, c))
27.47/8.92	   A^2 -> H(U1(c, e), U1(b, d))
27.47/8.92	   A^2 -> H(U1(c, e), U1(c, c))
27.47/8.92	   A^2 -> H(U1(c, e), f(e))
27.47/8.92	   A^2 -> H(U1(c, e), f(k))
27.47/8.92	   A^2 -> H(U1(c, e), U1(d, d))
27.47/8.92	   A^2 -> H(U1(c, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(c, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(c, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(c, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(c, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(c, k), f(e))
27.47/8.92	   A^2 -> H(U1(c, k), f(k))
27.47/8.92	   A^2 -> H(U1(c, k), U1(d, d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(e, b))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, b))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(d, c))
27.47/8.92	   A^2 -> H(U1(c, c), U1(b, e))
27.47/8.92	   A^2 -> H(U1(c, c), U1(b, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(e, e))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(d, k))
27.47/8.92	   A^2 -> H(e, U1(b, b))
27.47/8.92	   A^2 -> H(e, f(c))
27.47/8.92	   A^2 -> H(e, f(d))
27.47/8.92	   A^2 -> H(U1(e, e), U1(c, b))
27.47/8.92	   A^2 -> H(U1(e, e), U1(d, b))
27.47/8.92	   A^2 -> H(U1(e, e), U1(b, c))
27.47/8.92	   A^2 -> H(U1(e, e), U1(b, d))
27.47/8.92	   A^2 -> H(U1(e, e), U1(c, c))
27.47/8.92	   A^2 -> H(U1(e, e), f(e))
27.47/8.92	   A^2 -> H(U1(e, e), f(k))
27.47/8.92	   A^2 -> H(U1(e, e), U1(d, d))
27.47/8.92	   A^2 -> H(f(e), U1(e, b))
27.47/8.92	   A^2 -> H(f(e), U1(k, b))
27.47/8.92	   A^2 -> H(f(e), U1(c, d))
27.47/8.92	   A^2 -> H(f(e), U1(d, c))
27.47/8.92	   A^2 -> H(f(e), U1(b, e))
27.47/8.92	   A^2 -> H(f(e), U1(b, k))
27.47/8.92	   A^2 -> H(f(e), U1(e, c))
27.47/8.92	   A^2 -> H(f(e), U1(k, c))
27.47/8.92	   A^2 -> H(f(e), U1(c, e))
27.47/8.92	   A^2 -> H(f(e), U1(c, k))
27.47/8.92	   A^2 -> H(f(e), U1(k, k))
27.47/8.92	   A^2 -> H(f(e), U1(k, d))
27.47/8.92	   A^2 -> H(f(e), U1(d, k))
27.47/8.92	   A^2 -> H(U1(k, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(k, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(k, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(k, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(k, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(k, k), f(e))
27.47/8.92	   A^2 -> H(U1(k, k), f(k))
27.47/8.92	   A^2 -> H(U1(k, k), U1(d, d))
27.47/8.92	   A^2 -> H(f(k), U1(e, b))
27.47/8.92	   A^2 -> H(f(k), U1(k, b))
27.47/8.92	   A^2 -> H(f(k), U1(c, d))
27.47/8.92	   A^2 -> H(f(k), U1(d, c))
27.47/8.92	   A^2 -> H(f(k), U1(b, e))
27.47/8.92	   A^2 -> H(f(k), U1(b, k))
27.47/8.92	   A^2 -> H(f(k), U1(e, c))
27.47/8.92	   A^2 -> H(f(k), U1(k, c))
27.47/8.92	   A^2 -> H(f(k), U1(c, e))
27.47/8.92	   A^2 -> H(f(k), U1(c, k))
27.47/8.92	   A^2 -> H(f(k), U1(e, e))
27.47/8.92	   A^2 -> H(f(k), U1(k, d))
27.47/8.92	   A^2 -> H(f(k), U1(d, k))
27.47/8.92	   A^2 -> H(f(c), b)
27.47/8.92	   A^2 -> H(f(c), U1(e, d))
27.47/8.92	   A^2 -> H(f(c), U1(d, e))
27.47/8.92	   A^2 -> H(f(k), U1(k, k))
27.47/8.92	   A^2 -> H(U1(k, k), U1(b, b))
27.47/8.92	   A^2 -> H(U1(k, k), f(c))
27.47/8.92	   A^2 -> H(U1(k, k), f(d))
27.47/8.92	   A^2 -> H(U1(k, d), U1(c, b))
27.47/8.92	   A^2 -> H(U1(k, d), U1(d, b))
27.47/8.92	   A^2 -> H(U1(k, d), U1(b, c))
27.47/8.92	   A^2 -> H(U1(k, d), U1(b, d))
27.47/8.92	   A^2 -> H(U1(k, d), U1(c, c))
27.47/8.92	   A^2 -> H(U1(k, d), f(e))
27.47/8.92	   A^2 -> H(U1(k, d), f(k))
27.47/8.92	   A^2 -> H(U1(k, d), U1(d, d))
27.47/8.92	   A^2 -> H(U1(d, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(d, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(d, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(d, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(d, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(d, k), f(e))
27.47/8.92	   A^2 -> H(U1(d, k), f(k))
27.47/8.92	   A^2 -> H(U1(d, k), U1(d, d))
27.47/8.92	   A^2 -> H(U1(d, d), U1(e, b))
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, b))
27.47/8.92	   A^2 -> H(U1(d, d), U1(c, d))
27.47/8.92	   A^2 -> H(U1(d, d), U1(d, c))
27.47/8.92	   A^2 -> H(U1(d, d), U1(b, e))
27.47/8.92	   A^2 -> H(U1(d, d), U1(b, k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(e, c))
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, c))
27.47/8.92	   A^2 -> H(U1(d, d), U1(c, e))
27.47/8.92	   A^2 -> H(U1(d, d), U1(c, k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(e, e))
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, k))
27.47/8.92	   A^2 -> H(f(d), b)
27.47/8.92	   A^2 -> H(f(d), U1(e, d))
27.47/8.92	   A^2 -> H(f(d), U1(d, e))
27.47/8.92	   A^2 -> H(f(d), c)
27.47/8.92	   A^2 -> H(f(d), U1(e, k))
27.47/8.92	   A^2 -> H(f(d), U1(k, e))
27.47/8.92	   A^2 -> H(f(d), e)
27.47/8.92	   A^2 -> H(f(a), d)
27.47/8.92	   A^2 -> H(U1(c, c), U1(e, c))
27.47/8.92	   A^2 -> H(f(c), c)
27.47/8.92	   A^2 -> H(f(c), U1(e, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, c))
27.47/8.92	   A^2 -> H(f(c), U1(k, e))
27.47/8.92	   A^2 -> H(f(c), U1(k, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, e))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, k))
27.47/8.92	   A^2 -> H(f(a), k)
27.47/8.92	   A^2 -> H(f(e), U1(e, e))
27.47/8.92	   A^2 -> H(f(c), e)
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, d))
27.47/8.92	   A^2 -> H(f(d), U1(k, k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(d, k))
27.47/8.92	   A^2 -> H(d, U1(b, b))
27.47/8.92	   A^2 -> H(d, f(c))
27.47/8.92	   A^2 -> H(d, f(d))
27.47/8.92	   A^2 -> H(a, U1(c, b))
27.47/8.92	   A^2 -> H(a, U1(d, b))
27.47/8.92	   A^2 -> H(a, U1(b, c))
27.47/8.92	   A^2 -> H(a, U1(b, d))
27.47/8.92	   A^2 -> H(a, U1(c, c))
27.47/8.92	   A^2 -> H(a, f(e))
27.47/8.92	   A^2 -> H(a, f(k))
27.47/8.92	   A^2 -> H(a, U1(d, d))
27.47/8.92	   A^2 -> H(U1(e, d), U1(c, b))
27.47/8.92	   A^2 -> H(U1(e, d), U1(d, b))
27.47/8.92	   A^2 -> H(U1(e, d), U1(b, c))
27.47/8.92	   A^2 -> H(U1(e, d), U1(b, d))
27.47/8.92	   A^2 -> H(U1(e, d), U1(c, c))
27.47/8.92	   A^2 -> H(U1(e, d), f(e))
27.47/8.92	   A^2 -> H(U1(e, d), f(k))
27.47/8.92	   A^2 -> H(U1(e, d), U1(d, d))
27.47/8.92	   A^2 -> H(U1(e, a), U1(e, b))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, b))
27.47/8.92	   A^2 -> H(U1(e, a), U1(c, d))
27.47/8.92	   A^2 -> H(U1(e, a), U1(d, c))
27.47/8.92	   A^2 -> H(U1(e, a), U1(b, e))
27.47/8.92	   A^2 -> H(U1(e, a), U1(b, k))
27.47/8.92	   A^2 -> H(U1(e, a), U1(e, c))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, c))
27.47/8.92	   A^2 -> H(U1(e, a), U1(c, e))
27.47/8.92	   A^2 -> H(U1(e, a), U1(c, k))
27.47/8.92	   A^2 -> H(U1(e, a), U1(e, e))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, k))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, d))
27.47/8.92	   A^2 -> H(U1(e, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(e, b))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, b))
27.47/8.92	   A^2 -> H(U1(k, a), U1(c, d))
27.47/8.92	   A^2 -> H(U1(k, a), U1(d, c))
27.47/8.92	   A^2 -> H(U1(k, a), U1(b, e))
27.47/8.92	   A^2 -> H(U1(k, a), U1(b, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(e, c))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, c))
27.47/8.92	   A^2 -> H(U1(k, a), U1(c, e))
27.47/8.92	   A^2 -> H(U1(k, a), U1(c, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(e, e))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, d))
27.47/8.92	   A^2 -> H(U1(k, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(e, b))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, b))
27.47/8.92	   A^2 -> H(U1(c, d), U1(c, d))
27.47/8.92	   A^2 -> H(U1(c, d), U1(d, c))
27.47/8.92	   A^2 -> H(U1(c, d), U1(b, e))
27.47/8.92	   A^2 -> H(U1(c, d), U1(b, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(e, c))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, c))
27.47/8.92	   A^2 -> H(U1(c, d), U1(c, e))
27.47/8.92	   A^2 -> H(U1(c, d), U1(c, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(e, e))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, d))
27.47/8.92	   A^2 -> H(U1(c, d), U1(d, k))
27.47/8.92	   A^2 -> H(U1(c, a), b)
27.47/8.92	   A^2 -> H(U1(c, a), U1(e, d))
27.47/8.92	   A^2 -> H(U1(c, a), U1(d, e))
27.47/8.92	   A^2 -> H(U1(c, a), c)
27.47/8.92	   A^2 -> H(U1(c, a), U1(e, k))
27.47/8.92	   A^2 -> H(U1(c, a), U1(k, e))
27.47/8.92	   A^2 -> H(U1(c, a), e)
27.47/8.92	
27.47/8.92	The TRS R consists of the following rules:
27.47/8.92	
27.47/8.92	   f(x) -> U1(x, x)
27.47/8.92	   U1(e, x) -> x
27.47/8.92	   a -> c
27.47/8.92	   a -> d
27.47/8.92	   b -> c
27.47/8.92	   b -> d
27.47/8.92	   d -> k
27.47/8.92	   c -> e
27.47/8.92	   c -> k
27.47/8.92	
27.47/8.92	Q is empty.
27.47/8.92	We have to consider all minimal (P,Q,R)-chains.
27.47/8.92	----------------------------------------
27.47/8.92	
27.47/8.92	(627) TransformationProof (EQUIVALENT)
27.47/8.92	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
27.47/8.92	
27.47/8.92	   (A^2 -> H(U1(e, a), U1(k, d)),A^2 -> H(U1(e, a), U1(k, d)))
27.47/8.92	   (A^2 -> H(U1(k, a), U1(k, d)),A^2 -> H(U1(k, a), U1(k, d)))
27.47/8.92	   (A^2 -> H(U1(c, c), U1(k, d)),A^2 -> H(U1(c, c), U1(k, d)))
27.47/8.92	   (A^2 -> H(U1(c, d), U1(k, d)),A^2 -> H(U1(c, d), U1(k, d)))
27.47/8.92	   (A^2 -> H(U1(c, a), U1(k, k)),A^2 -> H(U1(c, a), U1(k, k)))
27.47/8.92	
27.47/8.92	
27.47/8.92	----------------------------------------
27.47/8.92	
27.47/8.92	(628)
27.47/8.92	Obligation:
27.47/8.92	Q DP problem:
27.47/8.92	The TRS P consists of the following rules:
27.47/8.92	
27.47/8.92	   H(x, x) -> G(x, x, f(k))
27.47/8.92	   G(d, x, x) -> A^2
27.47/8.92	   A^2 -> H(f(c), f(c))
27.47/8.92	   A^2 -> H(f(d), f(d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, c))
27.47/8.92	   A^2 -> H(f(e), f(e))
27.47/8.92	   A^2 -> H(f(k), f(k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(d, d))
27.47/8.92	   A^2 -> H(U1(c, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(d, e), U1(b, b))
27.47/8.92	   A^2 -> H(U1(d, e), f(c))
27.47/8.92	   A^2 -> H(U1(d, e), f(d))
27.47/8.92	   A^2 -> H(U1(d, c), U1(c, b))
27.47/8.92	   A^2 -> H(U1(d, c), U1(d, b))
27.47/8.92	   A^2 -> H(U1(d, c), U1(b, c))
27.47/8.92	   A^2 -> H(U1(d, c), U1(b, d))
27.47/8.92	   A^2 -> H(U1(d, c), U1(c, c))
27.47/8.92	   A^2 -> H(U1(d, c), f(e))
27.47/8.92	   A^2 -> H(U1(d, c), f(k))
27.47/8.92	   A^2 -> H(U1(d, c), U1(d, d))
27.47/8.92	   A^2 -> H(U1(d, a), U1(e, b))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, b))
27.47/8.92	   A^2 -> H(U1(d, a), U1(c, d))
27.47/8.92	   A^2 -> H(U1(d, a), U1(d, c))
27.47/8.92	   A^2 -> H(U1(d, a), U1(b, e))
27.47/8.92	   A^2 -> H(U1(d, a), U1(b, k))
27.47/8.92	   A^2 -> H(U1(d, a), U1(e, c))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, c))
27.47/8.92	   A^2 -> H(U1(d, a), U1(c, e))
27.47/8.92	   A^2 -> H(U1(d, a), U1(c, k))
27.47/8.92	   A^2 -> H(U1(d, a), U1(e, e))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, k))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, d))
27.47/8.92	   A^2 -> H(U1(d, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(a, e), U1(c, b))
27.47/8.92	   A^2 -> H(U1(a, e), U1(d, b))
27.47/8.92	   A^2 -> H(U1(a, e), U1(b, c))
27.47/8.92	   A^2 -> H(U1(a, e), U1(b, d))
27.47/8.92	   A^2 -> H(U1(a, e), U1(c, c))
27.47/8.92	   A^2 -> H(U1(a, e), f(e))
27.47/8.92	   A^2 -> H(U1(a, e), f(k))
27.47/8.92	   A^2 -> H(U1(a, e), U1(d, d))
27.47/8.92	   A^2 -> H(U1(a, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(a, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(a, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(a, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(a, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(a, k), f(e))
27.47/8.92	   A^2 -> H(U1(a, k), f(k))
27.47/8.92	   A^2 -> H(U1(a, k), U1(d, d))
27.47/8.92	   A^2 -> H(U1(a, c), U1(e, b))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, b))
27.47/8.92	   A^2 -> H(U1(a, c), U1(c, d))
27.47/8.92	   A^2 -> H(U1(a, c), U1(d, c))
27.47/8.92	   A^2 -> H(U1(a, c), U1(b, e))
27.47/8.92	   A^2 -> H(U1(a, c), U1(b, k))
27.47/8.92	   A^2 -> H(U1(a, c), U1(e, c))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, c))
27.47/8.92	   A^2 -> H(U1(a, c), U1(c, e))
27.47/8.92	   A^2 -> H(U1(a, c), U1(c, k))
27.47/8.92	   A^2 -> H(U1(a, c), U1(e, e))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, k))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, d))
27.47/8.92	   A^2 -> H(U1(a, c), U1(d, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(e, b))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, b))
27.47/8.92	   A^2 -> H(U1(a, d), U1(c, d))
27.47/8.92	   A^2 -> H(U1(a, d), U1(d, c))
27.47/8.92	   A^2 -> H(U1(a, d), U1(b, e))
27.47/8.92	   A^2 -> H(U1(a, d), U1(b, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(e, c))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, c))
27.47/8.92	   A^2 -> H(U1(a, d), U1(c, e))
27.47/8.92	   A^2 -> H(U1(a, d), U1(c, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(e, e))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, d))
27.47/8.92	   A^2 -> H(U1(a, d), U1(d, k))
27.47/8.92	   A^2 -> H(U1(a, a), b)
27.47/8.92	   A^2 -> H(U1(a, a), U1(e, d))
27.47/8.92	   A^2 -> H(U1(a, a), U1(d, e))
27.47/8.92	   A^2 -> H(U1(a, a), c)
27.47/8.92	   A^2 -> H(U1(a, a), U1(e, k))
27.47/8.92	   A^2 -> H(U1(a, a), U1(k, e))
27.47/8.92	   A^2 -> H(U1(a, a), e)
27.47/8.92	   A^2 -> H(U1(a, a), U1(k, k))
27.47/8.92	   A^2 -> H(k, f(b))
27.47/8.92	   A^2 -> H(c, U1(b, b))
27.47/8.92	   A^2 -> H(c, f(c))
27.47/8.92	   A^2 -> H(c, f(d))
27.47/8.92	   A^2 -> H(U1(e, k), U1(b, b))
27.47/8.92	   A^2 -> H(U1(e, k), f(c))
27.47/8.92	   A^2 -> H(U1(e, k), f(d))
27.47/8.92	   A^2 -> H(U1(e, c), U1(c, b))
27.47/8.92	   A^2 -> H(U1(e, c), U1(d, b))
27.47/8.92	   A^2 -> H(U1(e, c), U1(b, c))
27.47/8.92	   A^2 -> H(U1(e, c), U1(b, d))
27.47/8.92	   A^2 -> H(U1(e, c), U1(c, c))
27.47/8.92	   A^2 -> H(U1(e, c), f(e))
27.47/8.92	   A^2 -> H(U1(e, c), f(k))
27.47/8.92	   A^2 -> H(U1(e, c), U1(d, d))
27.47/8.92	   A^2 -> H(U1(k, e), U1(b, b))
27.47/8.92	   A^2 -> H(U1(k, e), f(c))
27.47/8.92	   A^2 -> H(U1(k, e), f(d))
27.47/8.92	   A^2 -> H(U1(k, c), U1(c, b))
27.47/8.92	   A^2 -> H(U1(k, c), U1(d, b))
27.47/8.92	   A^2 -> H(U1(k, c), U1(b, c))
27.47/8.92	   A^2 -> H(U1(k, c), U1(b, d))
27.47/8.92	   A^2 -> H(U1(k, c), U1(c, c))
27.47/8.92	   A^2 -> H(U1(k, c), f(e))
27.47/8.92	   A^2 -> H(U1(k, c), f(k))
27.47/8.92	   A^2 -> H(U1(k, c), U1(d, d))
27.47/8.92	   A^2 -> H(U1(c, e), U1(c, b))
27.47/8.92	   A^2 -> H(U1(c, e), U1(d, b))
27.47/8.92	   A^2 -> H(U1(c, e), U1(b, c))
27.47/8.92	   A^2 -> H(U1(c, e), U1(b, d))
27.47/8.92	   A^2 -> H(U1(c, e), U1(c, c))
27.47/8.92	   A^2 -> H(U1(c, e), f(e))
27.47/8.92	   A^2 -> H(U1(c, e), f(k))
27.47/8.92	   A^2 -> H(U1(c, e), U1(d, d))
27.47/8.92	   A^2 -> H(U1(c, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(c, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(c, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(c, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(c, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(c, k), f(e))
27.47/8.92	   A^2 -> H(U1(c, k), f(k))
27.47/8.92	   A^2 -> H(U1(c, k), U1(d, d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(e, b))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, b))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(d, c))
27.47/8.92	   A^2 -> H(U1(c, c), U1(b, e))
27.47/8.92	   A^2 -> H(U1(c, c), U1(b, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(e, e))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(d, k))
27.47/8.92	   A^2 -> H(e, U1(b, b))
27.47/8.92	   A^2 -> H(e, f(c))
27.47/8.92	   A^2 -> H(e, f(d))
27.47/8.92	   A^2 -> H(U1(e, e), U1(c, b))
27.47/8.92	   A^2 -> H(U1(e, e), U1(d, b))
27.47/8.92	   A^2 -> H(U1(e, e), U1(b, c))
27.47/8.92	   A^2 -> H(U1(e, e), U1(b, d))
27.47/8.92	   A^2 -> H(U1(e, e), U1(c, c))
27.47/8.92	   A^2 -> H(U1(e, e), f(e))
27.47/8.92	   A^2 -> H(U1(e, e), f(k))
27.47/8.92	   A^2 -> H(U1(e, e), U1(d, d))
27.47/8.92	   A^2 -> H(f(e), U1(e, b))
27.47/8.92	   A^2 -> H(f(e), U1(k, b))
27.47/8.92	   A^2 -> H(f(e), U1(c, d))
27.47/8.92	   A^2 -> H(f(e), U1(d, c))
27.47/8.92	   A^2 -> H(f(e), U1(b, e))
27.47/8.92	   A^2 -> H(f(e), U1(b, k))
27.47/8.92	   A^2 -> H(f(e), U1(e, c))
27.47/8.92	   A^2 -> H(f(e), U1(k, c))
27.47/8.92	   A^2 -> H(f(e), U1(c, e))
27.47/8.92	   A^2 -> H(f(e), U1(c, k))
27.47/8.92	   A^2 -> H(f(e), U1(k, k))
27.47/8.92	   A^2 -> H(f(e), U1(k, d))
27.47/8.92	   A^2 -> H(f(e), U1(d, k))
27.47/8.92	   A^2 -> H(U1(k, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(k, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(k, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(k, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(k, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(k, k), f(e))
27.47/8.92	   A^2 -> H(U1(k, k), f(k))
27.47/8.92	   A^2 -> H(U1(k, k), U1(d, d))
27.47/8.92	   A^2 -> H(f(k), U1(e, b))
27.47/8.92	   A^2 -> H(f(k), U1(k, b))
27.47/8.92	   A^2 -> H(f(k), U1(c, d))
27.47/8.92	   A^2 -> H(f(k), U1(d, c))
27.47/8.92	   A^2 -> H(f(k), U1(b, e))
27.47/8.92	   A^2 -> H(f(k), U1(b, k))
27.47/8.92	   A^2 -> H(f(k), U1(e, c))
27.47/8.92	   A^2 -> H(f(k), U1(k, c))
27.47/8.92	   A^2 -> H(f(k), U1(c, e))
27.47/8.92	   A^2 -> H(f(k), U1(c, k))
27.47/8.92	   A^2 -> H(f(k), U1(e, e))
27.47/8.92	   A^2 -> H(f(k), U1(k, d))
27.47/8.92	   A^2 -> H(f(k), U1(d, k))
27.47/8.92	   A^2 -> H(f(c), b)
27.47/8.92	   A^2 -> H(f(c), U1(e, d))
27.47/8.92	   A^2 -> H(f(c), U1(d, e))
27.47/8.92	   A^2 -> H(f(k), U1(k, k))
27.47/8.92	   A^2 -> H(U1(k, k), U1(b, b))
27.47/8.92	   A^2 -> H(U1(k, k), f(c))
27.47/8.92	   A^2 -> H(U1(k, k), f(d))
27.47/8.92	   A^2 -> H(U1(k, d), U1(c, b))
27.47/8.92	   A^2 -> H(U1(k, d), U1(d, b))
27.47/8.92	   A^2 -> H(U1(k, d), U1(b, c))
27.47/8.92	   A^2 -> H(U1(k, d), U1(b, d))
27.47/8.92	   A^2 -> H(U1(k, d), U1(c, c))
27.47/8.92	   A^2 -> H(U1(k, d), f(e))
27.47/8.92	   A^2 -> H(U1(k, d), f(k))
27.47/8.92	   A^2 -> H(U1(k, d), U1(d, d))
27.47/8.92	   A^2 -> H(U1(d, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(d, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(d, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(d, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(d, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(d, k), f(e))
27.47/8.92	   A^2 -> H(U1(d, k), f(k))
27.47/8.92	   A^2 -> H(U1(d, k), U1(d, d))
27.47/8.92	   A^2 -> H(U1(d, d), U1(e, b))
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, b))
27.47/8.92	   A^2 -> H(U1(d, d), U1(c, d))
27.47/8.92	   A^2 -> H(U1(d, d), U1(d, c))
27.47/8.92	   A^2 -> H(U1(d, d), U1(b, e))
27.47/8.92	   A^2 -> H(U1(d, d), U1(b, k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(e, c))
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, c))
27.47/8.92	   A^2 -> H(U1(d, d), U1(c, e))
27.47/8.92	   A^2 -> H(U1(d, d), U1(c, k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(e, e))
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, k))
27.47/8.92	   A^2 -> H(f(d), b)
27.47/8.92	   A^2 -> H(f(d), U1(e, d))
27.47/8.92	   A^2 -> H(f(d), U1(d, e))
27.47/8.92	   A^2 -> H(f(d), c)
27.47/8.92	   A^2 -> H(f(d), U1(e, k))
27.47/8.92	   A^2 -> H(f(d), U1(k, e))
27.47/8.92	   A^2 -> H(f(d), e)
27.47/8.92	   A^2 -> H(f(a), d)
27.47/8.92	   A^2 -> H(U1(c, c), U1(e, c))
27.47/8.92	   A^2 -> H(f(c), c)
27.47/8.92	   A^2 -> H(f(c), U1(e, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, c))
27.47/8.92	   A^2 -> H(f(c), U1(k, e))
27.47/8.92	   A^2 -> H(f(c), U1(k, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, e))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, k))
27.47/8.92	   A^2 -> H(f(a), k)
27.47/8.92	   A^2 -> H(f(e), U1(e, e))
27.47/8.92	   A^2 -> H(f(c), e)
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, d))
27.47/8.92	   A^2 -> H(f(d), U1(k, k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(d, k))
27.47/8.92	   A^2 -> H(d, U1(b, b))
27.47/8.92	   A^2 -> H(d, f(c))
27.47/8.92	   A^2 -> H(d, f(d))
27.47/8.92	   A^2 -> H(a, U1(c, b))
27.47/8.92	   A^2 -> H(a, U1(d, b))
27.47/8.92	   A^2 -> H(a, U1(b, c))
27.47/8.92	   A^2 -> H(a, U1(b, d))
27.47/8.92	   A^2 -> H(a, U1(c, c))
27.47/8.92	   A^2 -> H(a, f(e))
27.47/8.92	   A^2 -> H(a, f(k))
27.47/8.92	   A^2 -> H(a, U1(d, d))
27.47/8.92	   A^2 -> H(U1(e, d), U1(c, b))
27.47/8.92	   A^2 -> H(U1(e, d), U1(d, b))
27.47/8.92	   A^2 -> H(U1(e, d), U1(b, c))
27.47/8.92	   A^2 -> H(U1(e, d), U1(b, d))
27.47/8.92	   A^2 -> H(U1(e, d), U1(c, c))
27.47/8.92	   A^2 -> H(U1(e, d), f(e))
27.47/8.92	   A^2 -> H(U1(e, d), f(k))
27.47/8.92	   A^2 -> H(U1(e, d), U1(d, d))
27.47/8.92	   A^2 -> H(U1(e, a), U1(e, b))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, b))
27.47/8.92	   A^2 -> H(U1(e, a), U1(c, d))
27.47/8.92	   A^2 -> H(U1(e, a), U1(d, c))
27.47/8.92	   A^2 -> H(U1(e, a), U1(b, e))
27.47/8.92	   A^2 -> H(U1(e, a), U1(b, k))
27.47/8.92	   A^2 -> H(U1(e, a), U1(e, c))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, c))
27.47/8.92	   A^2 -> H(U1(e, a), U1(c, e))
27.47/8.92	   A^2 -> H(U1(e, a), U1(c, k))
27.47/8.92	   A^2 -> H(U1(e, a), U1(e, e))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, k))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, d))
27.47/8.92	   A^2 -> H(U1(e, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(e, b))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, b))
27.47/8.92	   A^2 -> H(U1(k, a), U1(c, d))
27.47/8.92	   A^2 -> H(U1(k, a), U1(d, c))
27.47/8.92	   A^2 -> H(U1(k, a), U1(b, e))
27.47/8.92	   A^2 -> H(U1(k, a), U1(b, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(e, c))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, c))
27.47/8.92	   A^2 -> H(U1(k, a), U1(c, e))
27.47/8.92	   A^2 -> H(U1(k, a), U1(c, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(e, e))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, d))
27.47/8.92	   A^2 -> H(U1(k, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(e, b))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, b))
27.47/8.92	   A^2 -> H(U1(c, d), U1(c, d))
27.47/8.92	   A^2 -> H(U1(c, d), U1(d, c))
27.47/8.92	   A^2 -> H(U1(c, d), U1(b, e))
27.47/8.92	   A^2 -> H(U1(c, d), U1(b, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(e, c))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, c))
27.47/8.92	   A^2 -> H(U1(c, d), U1(c, e))
27.47/8.92	   A^2 -> H(U1(c, d), U1(c, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(e, e))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, d))
27.47/8.92	   A^2 -> H(U1(c, d), U1(d, k))
27.47/8.92	   A^2 -> H(U1(c, a), b)
27.47/8.92	   A^2 -> H(U1(c, a), U1(e, d))
27.47/8.92	   A^2 -> H(U1(c, a), U1(d, e))
27.47/8.92	   A^2 -> H(U1(c, a), c)
27.47/8.92	   A^2 -> H(U1(c, a), U1(e, k))
27.47/8.92	   A^2 -> H(U1(c, a), U1(k, e))
27.47/8.92	   A^2 -> H(U1(c, a), e)
27.47/8.92	   A^2 -> H(U1(c, a), U1(k, k))
27.47/8.92	
27.47/8.92	The TRS R consists of the following rules:
27.47/8.92	
27.47/8.92	   f(x) -> U1(x, x)
27.47/8.92	   U1(e, x) -> x
27.47/8.92	   a -> c
27.47/8.92	   a -> d
27.47/8.92	   b -> c
27.47/8.92	   b -> d
27.47/8.92	   d -> k
27.47/8.92	   c -> e
27.47/8.92	   c -> k
27.47/8.92	
27.47/8.92	Q is empty.
27.47/8.92	We have to consider all minimal (P,Q,R)-chains.
27.47/8.92	----------------------------------------
27.47/8.92	
27.47/8.92	(629) TransformationProof (EQUIVALENT)
27.47/8.92	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
27.47/8.92	
27.47/8.92	   (A^2 -> H(U1(e, a), U1(d, k)),A^2 -> H(U1(e, a), U1(d, k)))
27.47/8.92	   (A^2 -> H(U1(k, a), U1(d, k)),A^2 -> H(U1(k, a), U1(d, k)))
27.47/8.92	   (A^2 -> H(U1(c, c), U1(d, k)),A^2 -> H(U1(c, c), U1(d, k)))
27.47/8.92	   (A^2 -> H(U1(c, d), U1(d, k)),A^2 -> H(U1(c, d), U1(d, k)))
27.47/8.92	   (A^2 -> H(U1(c, a), U1(k, k)),A^2 -> H(U1(c, a), U1(k, k)))
27.47/8.92	
27.47/8.92	
27.47/8.92	----------------------------------------
27.47/8.92	
27.47/8.92	(630)
27.47/8.92	Obligation:
27.47/8.92	Q DP problem:
27.47/8.92	The TRS P consists of the following rules:
27.47/8.92	
27.47/8.92	   H(x, x) -> G(x, x, f(k))
27.47/8.92	   G(d, x, x) -> A^2
27.47/8.92	   A^2 -> H(f(c), f(c))
27.47/8.92	   A^2 -> H(f(d), f(d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, c))
27.47/8.92	   A^2 -> H(f(e), f(e))
27.47/8.92	   A^2 -> H(f(k), f(k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(d, d))
27.47/8.92	   A^2 -> H(U1(d, e), U1(b, b))
27.47/8.92	   A^2 -> H(U1(d, e), f(c))
27.47/8.92	   A^2 -> H(U1(d, e), f(d))
27.47/8.92	   A^2 -> H(U1(d, c), U1(c, b))
27.47/8.92	   A^2 -> H(U1(d, c), U1(d, b))
27.47/8.92	   A^2 -> H(U1(d, c), U1(b, c))
27.47/8.92	   A^2 -> H(U1(d, c), U1(b, d))
27.47/8.92	   A^2 -> H(U1(d, c), U1(c, c))
27.47/8.92	   A^2 -> H(U1(d, c), f(e))
27.47/8.92	   A^2 -> H(U1(d, c), f(k))
27.47/8.92	   A^2 -> H(U1(d, c), U1(d, d))
27.47/8.92	   A^2 -> H(U1(d, a), U1(e, b))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, b))
27.47/8.92	   A^2 -> H(U1(d, a), U1(c, d))
27.47/8.92	   A^2 -> H(U1(d, a), U1(d, c))
27.47/8.92	   A^2 -> H(U1(d, a), U1(b, e))
27.47/8.92	   A^2 -> H(U1(d, a), U1(b, k))
27.47/8.92	   A^2 -> H(U1(d, a), U1(e, c))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, c))
27.47/8.92	   A^2 -> H(U1(d, a), U1(c, e))
27.47/8.92	   A^2 -> H(U1(d, a), U1(c, k))
27.47/8.92	   A^2 -> H(U1(d, a), U1(e, e))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, k))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, d))
27.47/8.92	   A^2 -> H(U1(d, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(a, e), U1(c, b))
27.47/8.92	   A^2 -> H(U1(a, e), U1(d, b))
27.47/8.92	   A^2 -> H(U1(a, e), U1(b, c))
27.47/8.92	   A^2 -> H(U1(a, e), U1(b, d))
27.47/8.92	   A^2 -> H(U1(a, e), U1(c, c))
27.47/8.92	   A^2 -> H(U1(a, e), f(e))
27.47/8.92	   A^2 -> H(U1(a, e), f(k))
27.47/8.92	   A^2 -> H(U1(a, e), U1(d, d))
27.47/8.92	   A^2 -> H(U1(a, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(a, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(a, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(a, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(a, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(a, k), f(e))
27.47/8.92	   A^2 -> H(U1(a, k), f(k))
27.47/8.92	   A^2 -> H(U1(a, k), U1(d, d))
27.47/8.92	   A^2 -> H(U1(a, c), U1(e, b))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, b))
27.47/8.92	   A^2 -> H(U1(a, c), U1(c, d))
27.47/8.92	   A^2 -> H(U1(a, c), U1(d, c))
27.47/8.92	   A^2 -> H(U1(a, c), U1(b, e))
27.47/8.92	   A^2 -> H(U1(a, c), U1(b, k))
27.47/8.92	   A^2 -> H(U1(a, c), U1(e, c))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, c))
27.47/8.92	   A^2 -> H(U1(a, c), U1(c, e))
27.47/8.92	   A^2 -> H(U1(a, c), U1(c, k))
27.47/8.92	   A^2 -> H(U1(a, c), U1(e, e))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, k))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, d))
27.47/8.92	   A^2 -> H(U1(a, c), U1(d, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(e, b))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, b))
27.47/8.92	   A^2 -> H(U1(a, d), U1(c, d))
27.47/8.92	   A^2 -> H(U1(a, d), U1(d, c))
27.47/8.92	   A^2 -> H(U1(a, d), U1(b, e))
27.47/8.92	   A^2 -> H(U1(a, d), U1(b, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(e, c))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, c))
27.47/8.92	   A^2 -> H(U1(a, d), U1(c, e))
27.47/8.92	   A^2 -> H(U1(a, d), U1(c, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(e, e))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, d))
27.47/8.92	   A^2 -> H(U1(a, d), U1(d, k))
27.47/8.92	   A^2 -> H(U1(a, a), b)
27.47/8.92	   A^2 -> H(U1(a, a), U1(e, d))
27.47/8.92	   A^2 -> H(U1(a, a), U1(d, e))
27.47/8.92	   A^2 -> H(U1(a, a), c)
27.47/8.92	   A^2 -> H(U1(a, a), U1(e, k))
27.47/8.92	   A^2 -> H(U1(a, a), U1(k, e))
27.47/8.92	   A^2 -> H(U1(a, a), e)
27.47/8.92	   A^2 -> H(U1(a, a), U1(k, k))
27.47/8.92	   A^2 -> H(k, f(b))
27.47/8.92	   A^2 -> H(c, U1(b, b))
27.47/8.92	   A^2 -> H(c, f(c))
27.47/8.92	   A^2 -> H(c, f(d))
27.47/8.92	   A^2 -> H(U1(e, k), U1(b, b))
27.47/8.92	   A^2 -> H(U1(e, k), f(c))
27.47/8.92	   A^2 -> H(U1(e, k), f(d))
27.47/8.92	   A^2 -> H(U1(e, c), U1(c, b))
27.47/8.92	   A^2 -> H(U1(e, c), U1(d, b))
27.47/8.92	   A^2 -> H(U1(e, c), U1(b, c))
27.47/8.92	   A^2 -> H(U1(e, c), U1(b, d))
27.47/8.92	   A^2 -> H(U1(e, c), U1(c, c))
27.47/8.92	   A^2 -> H(U1(e, c), f(e))
27.47/8.92	   A^2 -> H(U1(e, c), f(k))
27.47/8.92	   A^2 -> H(U1(e, c), U1(d, d))
27.47/8.92	   A^2 -> H(U1(k, e), U1(b, b))
27.47/8.92	   A^2 -> H(U1(k, e), f(c))
27.47/8.92	   A^2 -> H(U1(k, e), f(d))
27.47/8.92	   A^2 -> H(U1(k, c), U1(c, b))
27.47/8.92	   A^2 -> H(U1(k, c), U1(d, b))
27.47/8.92	   A^2 -> H(U1(k, c), U1(b, c))
27.47/8.92	   A^2 -> H(U1(k, c), U1(b, d))
27.47/8.92	   A^2 -> H(U1(k, c), U1(c, c))
27.47/8.92	   A^2 -> H(U1(k, c), f(e))
27.47/8.92	   A^2 -> H(U1(k, c), f(k))
27.47/8.92	   A^2 -> H(U1(k, c), U1(d, d))
27.47/8.92	   A^2 -> H(U1(c, e), U1(c, b))
27.47/8.92	   A^2 -> H(U1(c, e), U1(d, b))
27.47/8.92	   A^2 -> H(U1(c, e), U1(b, c))
27.47/8.92	   A^2 -> H(U1(c, e), U1(b, d))
27.47/8.92	   A^2 -> H(U1(c, e), U1(c, c))
27.47/8.92	   A^2 -> H(U1(c, e), f(e))
27.47/8.92	   A^2 -> H(U1(c, e), f(k))
27.47/8.92	   A^2 -> H(U1(c, e), U1(d, d))
27.47/8.92	   A^2 -> H(U1(c, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(c, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(c, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(c, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(c, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(c, k), f(e))
27.47/8.92	   A^2 -> H(U1(c, k), f(k))
27.47/8.92	   A^2 -> H(U1(c, k), U1(d, d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(e, b))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, b))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(d, c))
27.47/8.92	   A^2 -> H(U1(c, c), U1(b, e))
27.47/8.92	   A^2 -> H(U1(c, c), U1(b, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(e, e))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(d, k))
27.47/8.92	   A^2 -> H(e, U1(b, b))
27.47/8.92	   A^2 -> H(e, f(c))
27.47/8.92	   A^2 -> H(e, f(d))
27.47/8.92	   A^2 -> H(U1(e, e), U1(c, b))
27.47/8.92	   A^2 -> H(U1(e, e), U1(d, b))
27.47/8.92	   A^2 -> H(U1(e, e), U1(b, c))
27.47/8.92	   A^2 -> H(U1(e, e), U1(b, d))
27.47/8.92	   A^2 -> H(U1(e, e), U1(c, c))
27.47/8.92	   A^2 -> H(U1(e, e), f(e))
27.47/8.92	   A^2 -> H(U1(e, e), f(k))
27.47/8.92	   A^2 -> H(U1(e, e), U1(d, d))
27.47/8.92	   A^2 -> H(f(e), U1(e, b))
27.47/8.92	   A^2 -> H(f(e), U1(k, b))
27.47/8.92	   A^2 -> H(f(e), U1(c, d))
27.47/8.92	   A^2 -> H(f(e), U1(d, c))
27.47/8.92	   A^2 -> H(f(e), U1(b, e))
27.47/8.92	   A^2 -> H(f(e), U1(b, k))
27.47/8.92	   A^2 -> H(f(e), U1(e, c))
27.47/8.92	   A^2 -> H(f(e), U1(k, c))
27.47/8.92	   A^2 -> H(f(e), U1(c, e))
27.47/8.92	   A^2 -> H(f(e), U1(c, k))
27.47/8.92	   A^2 -> H(f(e), U1(k, k))
27.47/8.92	   A^2 -> H(f(e), U1(k, d))
27.47/8.92	   A^2 -> H(f(e), U1(d, k))
27.47/8.92	   A^2 -> H(U1(k, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(k, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(k, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(k, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(k, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(k, k), f(e))
27.47/8.92	   A^2 -> H(U1(k, k), f(k))
27.47/8.92	   A^2 -> H(U1(k, k), U1(d, d))
27.47/8.92	   A^2 -> H(f(k), U1(e, b))
27.47/8.92	   A^2 -> H(f(k), U1(k, b))
27.47/8.92	   A^2 -> H(f(k), U1(c, d))
27.47/8.92	   A^2 -> H(f(k), U1(d, c))
27.47/8.92	   A^2 -> H(f(k), U1(b, e))
27.47/8.92	   A^2 -> H(f(k), U1(b, k))
27.47/8.92	   A^2 -> H(f(k), U1(e, c))
27.47/8.92	   A^2 -> H(f(k), U1(k, c))
27.47/8.92	   A^2 -> H(f(k), U1(c, e))
27.47/8.92	   A^2 -> H(f(k), U1(c, k))
27.47/8.92	   A^2 -> H(f(k), U1(e, e))
27.47/8.92	   A^2 -> H(f(k), U1(k, d))
27.47/8.92	   A^2 -> H(f(k), U1(d, k))
27.47/8.92	   A^2 -> H(f(c), b)
27.47/8.92	   A^2 -> H(f(c), U1(e, d))
27.47/8.92	   A^2 -> H(f(c), U1(d, e))
27.47/8.92	   A^2 -> H(f(k), U1(k, k))
27.47/8.92	   A^2 -> H(U1(k, k), U1(b, b))
27.47/8.92	   A^2 -> H(U1(k, k), f(c))
27.47/8.92	   A^2 -> H(U1(k, k), f(d))
27.47/8.92	   A^2 -> H(U1(k, d), U1(c, b))
27.47/8.92	   A^2 -> H(U1(k, d), U1(d, b))
27.47/8.92	   A^2 -> H(U1(k, d), U1(b, c))
27.47/8.92	   A^2 -> H(U1(k, d), U1(b, d))
27.47/8.92	   A^2 -> H(U1(k, d), U1(c, c))
27.47/8.92	   A^2 -> H(U1(k, d), f(e))
27.47/8.92	   A^2 -> H(U1(k, d), f(k))
27.47/8.92	   A^2 -> H(U1(k, d), U1(d, d))
27.47/8.92	   A^2 -> H(U1(d, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(d, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(d, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(d, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(d, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(d, k), f(e))
27.47/8.92	   A^2 -> H(U1(d, k), f(k))
27.47/8.92	   A^2 -> H(U1(d, k), U1(d, d))
27.47/8.92	   A^2 -> H(U1(d, d), U1(e, b))
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, b))
27.47/8.92	   A^2 -> H(U1(d, d), U1(c, d))
27.47/8.92	   A^2 -> H(U1(d, d), U1(d, c))
27.47/8.92	   A^2 -> H(U1(d, d), U1(b, e))
27.47/8.92	   A^2 -> H(U1(d, d), U1(b, k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(e, c))
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, c))
27.47/8.92	   A^2 -> H(U1(d, d), U1(c, e))
27.47/8.92	   A^2 -> H(U1(d, d), U1(c, k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(e, e))
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, k))
27.47/8.92	   A^2 -> H(f(d), b)
27.47/8.92	   A^2 -> H(f(d), U1(e, d))
27.47/8.92	   A^2 -> H(f(d), U1(d, e))
27.47/8.92	   A^2 -> H(f(d), c)
27.47/8.92	   A^2 -> H(f(d), U1(e, k))
27.47/8.92	   A^2 -> H(f(d), U1(k, e))
27.47/8.92	   A^2 -> H(f(d), e)
27.47/8.92	   A^2 -> H(f(a), d)
27.47/8.92	   A^2 -> H(U1(c, c), U1(e, c))
27.47/8.92	   A^2 -> H(f(c), c)
27.47/8.92	   A^2 -> H(f(c), U1(e, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, c))
27.47/8.92	   A^2 -> H(f(c), U1(k, e))
27.47/8.92	   A^2 -> H(f(c), U1(k, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, e))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, k))
27.47/8.92	   A^2 -> H(f(a), k)
27.47/8.92	   A^2 -> H(f(e), U1(e, e))
27.47/8.92	   A^2 -> H(f(c), e)
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, d))
27.47/8.92	   A^2 -> H(f(d), U1(k, k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(d, k))
27.47/8.92	   A^2 -> H(d, U1(b, b))
27.47/8.92	   A^2 -> H(d, f(c))
27.47/8.92	   A^2 -> H(d, f(d))
27.47/8.92	   A^2 -> H(a, U1(c, b))
27.47/8.92	   A^2 -> H(a, U1(d, b))
27.47/8.92	   A^2 -> H(a, U1(b, c))
27.47/8.92	   A^2 -> H(a, U1(b, d))
27.47/8.92	   A^2 -> H(a, U1(c, c))
27.47/8.92	   A^2 -> H(a, f(e))
27.47/8.92	   A^2 -> H(a, f(k))
27.47/8.92	   A^2 -> H(a, U1(d, d))
27.47/8.92	   A^2 -> H(U1(e, d), U1(c, b))
27.47/8.92	   A^2 -> H(U1(e, d), U1(d, b))
27.47/8.92	   A^2 -> H(U1(e, d), U1(b, c))
27.47/8.92	   A^2 -> H(U1(e, d), U1(b, d))
27.47/8.92	   A^2 -> H(U1(e, d), U1(c, c))
27.47/8.92	   A^2 -> H(U1(e, d), f(e))
27.47/8.92	   A^2 -> H(U1(e, d), f(k))
27.47/8.92	   A^2 -> H(U1(e, d), U1(d, d))
27.47/8.92	   A^2 -> H(U1(e, a), U1(e, b))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, b))
27.47/8.92	   A^2 -> H(U1(e, a), U1(c, d))
27.47/8.92	   A^2 -> H(U1(e, a), U1(d, c))
27.47/8.92	   A^2 -> H(U1(e, a), U1(b, e))
27.47/8.92	   A^2 -> H(U1(e, a), U1(b, k))
27.47/8.92	   A^2 -> H(U1(e, a), U1(e, c))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, c))
27.47/8.92	   A^2 -> H(U1(e, a), U1(c, e))
27.47/8.92	   A^2 -> H(U1(e, a), U1(c, k))
27.47/8.92	   A^2 -> H(U1(e, a), U1(e, e))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, k))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, d))
27.47/8.92	   A^2 -> H(U1(e, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(e, b))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, b))
27.47/8.92	   A^2 -> H(U1(k, a), U1(c, d))
27.47/8.92	   A^2 -> H(U1(k, a), U1(d, c))
27.47/8.92	   A^2 -> H(U1(k, a), U1(b, e))
27.47/8.92	   A^2 -> H(U1(k, a), U1(b, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(e, c))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, c))
27.47/8.92	   A^2 -> H(U1(k, a), U1(c, e))
27.47/8.92	   A^2 -> H(U1(k, a), U1(c, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(e, e))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, d))
27.47/8.92	   A^2 -> H(U1(k, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(e, b))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, b))
27.47/8.92	   A^2 -> H(U1(c, d), U1(c, d))
27.47/8.92	   A^2 -> H(U1(c, d), U1(d, c))
27.47/8.92	   A^2 -> H(U1(c, d), U1(b, e))
27.47/8.92	   A^2 -> H(U1(c, d), U1(b, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(e, c))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, c))
27.47/8.92	   A^2 -> H(U1(c, d), U1(c, e))
27.47/8.92	   A^2 -> H(U1(c, d), U1(c, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(e, e))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, d))
27.47/8.92	   A^2 -> H(U1(c, d), U1(d, k))
27.47/8.92	   A^2 -> H(U1(c, a), b)
27.47/8.92	   A^2 -> H(U1(c, a), U1(e, d))
27.47/8.92	   A^2 -> H(U1(c, a), U1(d, e))
27.47/8.92	   A^2 -> H(U1(c, a), c)
27.47/8.92	   A^2 -> H(U1(c, a), U1(e, k))
27.47/8.92	   A^2 -> H(U1(c, a), U1(k, e))
27.47/8.92	   A^2 -> H(U1(c, a), e)
27.47/8.92	   A^2 -> H(U1(c, a), U1(k, k))
27.47/8.92	
27.47/8.92	The TRS R consists of the following rules:
27.47/8.92	
27.47/8.92	   f(x) -> U1(x, x)
27.47/8.92	   U1(e, x) -> x
27.47/8.92	   a -> c
27.47/8.92	   a -> d
27.47/8.92	   b -> c
27.47/8.92	   b -> d
27.47/8.92	   d -> k
27.47/8.92	   c -> e
27.47/8.92	   c -> k
27.47/8.92	
27.47/8.92	Q is empty.
27.47/8.92	We have to consider all minimal (P,Q,R)-chains.
27.47/8.92	----------------------------------------
27.47/8.92	
27.47/8.92	(631) TransformationProof (EQUIVALENT)
27.47/8.92	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
27.47/8.92	
27.47/8.92	   (A^2 -> H(U1(k, e), U1(b, b)),A^2 -> H(U1(k, e), U1(b, b)))
27.47/8.92	   (A^2 -> H(U1(d, e), U1(c, b)),A^2 -> H(U1(d, e), U1(c, b)))
27.47/8.92	   (A^2 -> H(U1(d, e), U1(d, b)),A^2 -> H(U1(d, e), U1(d, b)))
27.47/8.92	   (A^2 -> H(U1(d, e), U1(b, c)),A^2 -> H(U1(d, e), U1(b, c)))
27.47/8.92	   (A^2 -> H(U1(d, e), U1(b, d)),A^2 -> H(U1(d, e), U1(b, d)))
27.47/8.92	
27.47/8.92	
27.47/8.92	----------------------------------------
27.47/8.92	
27.47/8.92	(632)
27.47/8.92	Obligation:
27.47/8.92	Q DP problem:
27.47/8.92	The TRS P consists of the following rules:
27.47/8.92	
27.47/8.92	   H(x, x) -> G(x, x, f(k))
27.47/8.92	   G(d, x, x) -> A^2
27.47/8.92	   A^2 -> H(f(c), f(c))
27.47/8.92	   A^2 -> H(f(d), f(d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, c))
27.47/8.92	   A^2 -> H(f(e), f(e))
27.47/8.92	   A^2 -> H(f(k), f(k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(d, d))
27.47/8.92	   A^2 -> H(U1(d, e), f(c))
27.47/8.92	   A^2 -> H(U1(d, e), f(d))
27.47/8.92	   A^2 -> H(U1(d, c), U1(c, b))
27.47/8.92	   A^2 -> H(U1(d, c), U1(d, b))
27.47/8.92	   A^2 -> H(U1(d, c), U1(b, c))
27.47/8.92	   A^2 -> H(U1(d, c), U1(b, d))
27.47/8.92	   A^2 -> H(U1(d, c), U1(c, c))
27.47/8.92	   A^2 -> H(U1(d, c), f(e))
27.47/8.92	   A^2 -> H(U1(d, c), f(k))
27.47/8.92	   A^2 -> H(U1(d, c), U1(d, d))
27.47/8.92	   A^2 -> H(U1(d, a), U1(e, b))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, b))
27.47/8.92	   A^2 -> H(U1(d, a), U1(c, d))
27.47/8.92	   A^2 -> H(U1(d, a), U1(d, c))
27.47/8.92	   A^2 -> H(U1(d, a), U1(b, e))
27.47/8.92	   A^2 -> H(U1(d, a), U1(b, k))
27.47/8.92	   A^2 -> H(U1(d, a), U1(e, c))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, c))
27.47/8.92	   A^2 -> H(U1(d, a), U1(c, e))
27.47/8.92	   A^2 -> H(U1(d, a), U1(c, k))
27.47/8.92	   A^2 -> H(U1(d, a), U1(e, e))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, k))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, d))
27.47/8.92	   A^2 -> H(U1(d, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(a, e), U1(c, b))
27.47/8.92	   A^2 -> H(U1(a, e), U1(d, b))
27.47/8.92	   A^2 -> H(U1(a, e), U1(b, c))
27.47/8.92	   A^2 -> H(U1(a, e), U1(b, d))
27.47/8.92	   A^2 -> H(U1(a, e), U1(c, c))
27.47/8.92	   A^2 -> H(U1(a, e), f(e))
27.47/8.92	   A^2 -> H(U1(a, e), f(k))
27.47/8.92	   A^2 -> H(U1(a, e), U1(d, d))
27.47/8.92	   A^2 -> H(U1(a, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(a, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(a, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(a, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(a, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(a, k), f(e))
27.47/8.92	   A^2 -> H(U1(a, k), f(k))
27.47/8.92	   A^2 -> H(U1(a, k), U1(d, d))
27.47/8.92	   A^2 -> H(U1(a, c), U1(e, b))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, b))
27.47/8.92	   A^2 -> H(U1(a, c), U1(c, d))
27.47/8.92	   A^2 -> H(U1(a, c), U1(d, c))
27.47/8.92	   A^2 -> H(U1(a, c), U1(b, e))
27.47/8.92	   A^2 -> H(U1(a, c), U1(b, k))
27.47/8.92	   A^2 -> H(U1(a, c), U1(e, c))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, c))
27.47/8.92	   A^2 -> H(U1(a, c), U1(c, e))
27.47/8.92	   A^2 -> H(U1(a, c), U1(c, k))
27.47/8.92	   A^2 -> H(U1(a, c), U1(e, e))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, k))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, d))
27.47/8.92	   A^2 -> H(U1(a, c), U1(d, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(e, b))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, b))
27.47/8.92	   A^2 -> H(U1(a, d), U1(c, d))
27.47/8.92	   A^2 -> H(U1(a, d), U1(d, c))
27.47/8.92	   A^2 -> H(U1(a, d), U1(b, e))
27.47/8.92	   A^2 -> H(U1(a, d), U1(b, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(e, c))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, c))
27.47/8.92	   A^2 -> H(U1(a, d), U1(c, e))
27.47/8.92	   A^2 -> H(U1(a, d), U1(c, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(e, e))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, d))
27.47/8.92	   A^2 -> H(U1(a, d), U1(d, k))
27.47/8.92	   A^2 -> H(U1(a, a), b)
27.47/8.92	   A^2 -> H(U1(a, a), U1(e, d))
27.47/8.92	   A^2 -> H(U1(a, a), U1(d, e))
27.47/8.92	   A^2 -> H(U1(a, a), c)
27.47/8.92	   A^2 -> H(U1(a, a), U1(e, k))
27.47/8.92	   A^2 -> H(U1(a, a), U1(k, e))
27.47/8.92	   A^2 -> H(U1(a, a), e)
27.47/8.92	   A^2 -> H(U1(a, a), U1(k, k))
27.47/8.92	   A^2 -> H(k, f(b))
27.47/8.92	   A^2 -> H(c, U1(b, b))
27.47/8.92	   A^2 -> H(c, f(c))
27.47/8.92	   A^2 -> H(c, f(d))
27.47/8.92	   A^2 -> H(U1(e, k), U1(b, b))
27.47/8.92	   A^2 -> H(U1(e, k), f(c))
27.47/8.92	   A^2 -> H(U1(e, k), f(d))
27.47/8.92	   A^2 -> H(U1(e, c), U1(c, b))
27.47/8.92	   A^2 -> H(U1(e, c), U1(d, b))
27.47/8.92	   A^2 -> H(U1(e, c), U1(b, c))
27.47/8.92	   A^2 -> H(U1(e, c), U1(b, d))
27.47/8.92	   A^2 -> H(U1(e, c), U1(c, c))
27.47/8.92	   A^2 -> H(U1(e, c), f(e))
27.47/8.92	   A^2 -> H(U1(e, c), f(k))
27.47/8.92	   A^2 -> H(U1(e, c), U1(d, d))
27.47/8.92	   A^2 -> H(U1(k, e), U1(b, b))
27.47/8.92	   A^2 -> H(U1(k, e), f(c))
27.47/8.92	   A^2 -> H(U1(k, e), f(d))
27.47/8.92	   A^2 -> H(U1(k, c), U1(c, b))
27.47/8.92	   A^2 -> H(U1(k, c), U1(d, b))
27.47/8.92	   A^2 -> H(U1(k, c), U1(b, c))
27.47/8.92	   A^2 -> H(U1(k, c), U1(b, d))
27.47/8.92	   A^2 -> H(U1(k, c), U1(c, c))
27.47/8.92	   A^2 -> H(U1(k, c), f(e))
27.47/8.92	   A^2 -> H(U1(k, c), f(k))
27.47/8.92	   A^2 -> H(U1(k, c), U1(d, d))
27.47/8.92	   A^2 -> H(U1(c, e), U1(c, b))
27.47/8.92	   A^2 -> H(U1(c, e), U1(d, b))
27.47/8.92	   A^2 -> H(U1(c, e), U1(b, c))
27.47/8.92	   A^2 -> H(U1(c, e), U1(b, d))
27.47/8.92	   A^2 -> H(U1(c, e), U1(c, c))
27.47/8.92	   A^2 -> H(U1(c, e), f(e))
27.47/8.92	   A^2 -> H(U1(c, e), f(k))
27.47/8.92	   A^2 -> H(U1(c, e), U1(d, d))
27.47/8.92	   A^2 -> H(U1(c, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(c, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(c, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(c, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(c, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(c, k), f(e))
27.47/8.92	   A^2 -> H(U1(c, k), f(k))
27.47/8.92	   A^2 -> H(U1(c, k), U1(d, d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(e, b))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, b))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(d, c))
27.47/8.92	   A^2 -> H(U1(c, c), U1(b, e))
27.47/8.92	   A^2 -> H(U1(c, c), U1(b, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(e, e))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(d, k))
27.47/8.92	   A^2 -> H(e, U1(b, b))
27.47/8.92	   A^2 -> H(e, f(c))
27.47/8.92	   A^2 -> H(e, f(d))
27.47/8.92	   A^2 -> H(U1(e, e), U1(c, b))
27.47/8.92	   A^2 -> H(U1(e, e), U1(d, b))
27.47/8.92	   A^2 -> H(U1(e, e), U1(b, c))
27.47/8.92	   A^2 -> H(U1(e, e), U1(b, d))
27.47/8.92	   A^2 -> H(U1(e, e), U1(c, c))
27.47/8.92	   A^2 -> H(U1(e, e), f(e))
27.47/8.92	   A^2 -> H(U1(e, e), f(k))
27.47/8.92	   A^2 -> H(U1(e, e), U1(d, d))
27.47/8.92	   A^2 -> H(f(e), U1(e, b))
27.47/8.92	   A^2 -> H(f(e), U1(k, b))
27.47/8.92	   A^2 -> H(f(e), U1(c, d))
27.47/8.92	   A^2 -> H(f(e), U1(d, c))
27.47/8.92	   A^2 -> H(f(e), U1(b, e))
27.47/8.92	   A^2 -> H(f(e), U1(b, k))
27.47/8.92	   A^2 -> H(f(e), U1(e, c))
27.47/8.92	   A^2 -> H(f(e), U1(k, c))
27.47/8.92	   A^2 -> H(f(e), U1(c, e))
27.47/8.92	   A^2 -> H(f(e), U1(c, k))
27.47/8.92	   A^2 -> H(f(e), U1(k, k))
27.47/8.92	   A^2 -> H(f(e), U1(k, d))
27.47/8.92	   A^2 -> H(f(e), U1(d, k))
27.47/8.92	   A^2 -> H(U1(k, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(k, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(k, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(k, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(k, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(k, k), f(e))
27.47/8.92	   A^2 -> H(U1(k, k), f(k))
27.47/8.92	   A^2 -> H(U1(k, k), U1(d, d))
27.47/8.92	   A^2 -> H(f(k), U1(e, b))
27.47/8.92	   A^2 -> H(f(k), U1(k, b))
27.47/8.92	   A^2 -> H(f(k), U1(c, d))
27.47/8.92	   A^2 -> H(f(k), U1(d, c))
27.47/8.92	   A^2 -> H(f(k), U1(b, e))
27.47/8.92	   A^2 -> H(f(k), U1(b, k))
27.47/8.92	   A^2 -> H(f(k), U1(e, c))
27.47/8.92	   A^2 -> H(f(k), U1(k, c))
27.47/8.92	   A^2 -> H(f(k), U1(c, e))
27.47/8.92	   A^2 -> H(f(k), U1(c, k))
27.47/8.92	   A^2 -> H(f(k), U1(e, e))
27.47/8.92	   A^2 -> H(f(k), U1(k, d))
27.47/8.92	   A^2 -> H(f(k), U1(d, k))
27.47/8.92	   A^2 -> H(f(c), b)
27.47/8.92	   A^2 -> H(f(c), U1(e, d))
27.47/8.92	   A^2 -> H(f(c), U1(d, e))
27.47/8.92	   A^2 -> H(f(k), U1(k, k))
27.47/8.92	   A^2 -> H(U1(k, k), U1(b, b))
27.47/8.92	   A^2 -> H(U1(k, k), f(c))
27.47/8.92	   A^2 -> H(U1(k, k), f(d))
27.47/8.92	   A^2 -> H(U1(k, d), U1(c, b))
27.47/8.92	   A^2 -> H(U1(k, d), U1(d, b))
27.47/8.92	   A^2 -> H(U1(k, d), U1(b, c))
27.47/8.92	   A^2 -> H(U1(k, d), U1(b, d))
27.47/8.92	   A^2 -> H(U1(k, d), U1(c, c))
27.47/8.92	   A^2 -> H(U1(k, d), f(e))
27.47/8.92	   A^2 -> H(U1(k, d), f(k))
27.47/8.92	   A^2 -> H(U1(k, d), U1(d, d))
27.47/8.92	   A^2 -> H(U1(d, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(d, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(d, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(d, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(d, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(d, k), f(e))
27.47/8.92	   A^2 -> H(U1(d, k), f(k))
27.47/8.92	   A^2 -> H(U1(d, k), U1(d, d))
27.47/8.92	   A^2 -> H(U1(d, d), U1(e, b))
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, b))
27.47/8.92	   A^2 -> H(U1(d, d), U1(c, d))
27.47/8.92	   A^2 -> H(U1(d, d), U1(d, c))
27.47/8.92	   A^2 -> H(U1(d, d), U1(b, e))
27.47/8.92	   A^2 -> H(U1(d, d), U1(b, k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(e, c))
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, c))
27.47/8.92	   A^2 -> H(U1(d, d), U1(c, e))
27.47/8.92	   A^2 -> H(U1(d, d), U1(c, k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(e, e))
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, k))
27.47/8.92	   A^2 -> H(f(d), b)
27.47/8.92	   A^2 -> H(f(d), U1(e, d))
27.47/8.92	   A^2 -> H(f(d), U1(d, e))
27.47/8.92	   A^2 -> H(f(d), c)
27.47/8.92	   A^2 -> H(f(d), U1(e, k))
27.47/8.92	   A^2 -> H(f(d), U1(k, e))
27.47/8.92	   A^2 -> H(f(d), e)
27.47/8.92	   A^2 -> H(f(a), d)
27.47/8.92	   A^2 -> H(U1(c, c), U1(e, c))
27.47/8.92	   A^2 -> H(f(c), c)
27.47/8.92	   A^2 -> H(f(c), U1(e, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, c))
27.47/8.92	   A^2 -> H(f(c), U1(k, e))
27.47/8.92	   A^2 -> H(f(c), U1(k, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, e))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, k))
27.47/8.92	   A^2 -> H(f(a), k)
27.47/8.92	   A^2 -> H(f(e), U1(e, e))
27.47/8.92	   A^2 -> H(f(c), e)
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, d))
27.47/8.92	   A^2 -> H(f(d), U1(k, k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(d, k))
27.47/8.92	   A^2 -> H(d, U1(b, b))
27.47/8.92	   A^2 -> H(d, f(c))
27.47/8.92	   A^2 -> H(d, f(d))
27.47/8.92	   A^2 -> H(a, U1(c, b))
27.47/8.92	   A^2 -> H(a, U1(d, b))
27.47/8.92	   A^2 -> H(a, U1(b, c))
27.47/8.92	   A^2 -> H(a, U1(b, d))
27.47/8.92	   A^2 -> H(a, U1(c, c))
27.47/8.92	   A^2 -> H(a, f(e))
27.47/8.92	   A^2 -> H(a, f(k))
27.47/8.92	   A^2 -> H(a, U1(d, d))
27.47/8.92	   A^2 -> H(U1(e, d), U1(c, b))
27.47/8.92	   A^2 -> H(U1(e, d), U1(d, b))
27.47/8.92	   A^2 -> H(U1(e, d), U1(b, c))
27.47/8.92	   A^2 -> H(U1(e, d), U1(b, d))
27.47/8.92	   A^2 -> H(U1(e, d), U1(c, c))
27.47/8.92	   A^2 -> H(U1(e, d), f(e))
27.47/8.92	   A^2 -> H(U1(e, d), f(k))
27.47/8.92	   A^2 -> H(U1(e, d), U1(d, d))
27.47/8.92	   A^2 -> H(U1(e, a), U1(e, b))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, b))
27.47/8.92	   A^2 -> H(U1(e, a), U1(c, d))
27.47/8.92	   A^2 -> H(U1(e, a), U1(d, c))
27.47/8.92	   A^2 -> H(U1(e, a), U1(b, e))
27.47/8.92	   A^2 -> H(U1(e, a), U1(b, k))
27.47/8.92	   A^2 -> H(U1(e, a), U1(e, c))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, c))
27.47/8.92	   A^2 -> H(U1(e, a), U1(c, e))
27.47/8.92	   A^2 -> H(U1(e, a), U1(c, k))
27.47/8.92	   A^2 -> H(U1(e, a), U1(e, e))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, k))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, d))
27.47/8.92	   A^2 -> H(U1(e, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(e, b))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, b))
27.47/8.92	   A^2 -> H(U1(k, a), U1(c, d))
27.47/8.92	   A^2 -> H(U1(k, a), U1(d, c))
27.47/8.92	   A^2 -> H(U1(k, a), U1(b, e))
27.47/8.92	   A^2 -> H(U1(k, a), U1(b, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(e, c))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, c))
27.47/8.92	   A^2 -> H(U1(k, a), U1(c, e))
27.47/8.92	   A^2 -> H(U1(k, a), U1(c, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(e, e))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, d))
27.47/8.92	   A^2 -> H(U1(k, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(e, b))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, b))
27.47/8.92	   A^2 -> H(U1(c, d), U1(c, d))
27.47/8.92	   A^2 -> H(U1(c, d), U1(d, c))
27.47/8.92	   A^2 -> H(U1(c, d), U1(b, e))
27.47/8.92	   A^2 -> H(U1(c, d), U1(b, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(e, c))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, c))
27.47/8.92	   A^2 -> H(U1(c, d), U1(c, e))
27.47/8.92	   A^2 -> H(U1(c, d), U1(c, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(e, e))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, d))
27.47/8.92	   A^2 -> H(U1(c, d), U1(d, k))
27.47/8.92	   A^2 -> H(U1(c, a), b)
27.47/8.92	   A^2 -> H(U1(c, a), U1(e, d))
27.47/8.92	   A^2 -> H(U1(c, a), U1(d, e))
27.47/8.92	   A^2 -> H(U1(c, a), c)
27.47/8.92	   A^2 -> H(U1(c, a), U1(e, k))
27.47/8.92	   A^2 -> H(U1(c, a), U1(k, e))
27.47/8.92	   A^2 -> H(U1(c, a), e)
27.47/8.92	   A^2 -> H(U1(c, a), U1(k, k))
27.47/8.92	   A^2 -> H(U1(d, e), U1(c, b))
27.47/8.92	   A^2 -> H(U1(d, e), U1(d, b))
27.47/8.92	   A^2 -> H(U1(d, e), U1(b, c))
27.47/8.92	   A^2 -> H(U1(d, e), U1(b, d))
27.47/8.92	
27.47/8.92	The TRS R consists of the following rules:
27.47/8.92	
27.47/8.92	   f(x) -> U1(x, x)
27.47/8.92	   U1(e, x) -> x
27.47/8.92	   a -> c
27.47/8.92	   a -> d
27.47/8.92	   b -> c
27.47/8.92	   b -> d
27.47/8.92	   d -> k
27.47/8.92	   c -> e
27.47/8.92	   c -> k
27.47/8.92	
27.47/8.92	Q is empty.
27.47/8.92	We have to consider all minimal (P,Q,R)-chains.
27.47/8.92	----------------------------------------
27.47/8.92	
27.47/8.92	(633) TransformationProof (EQUIVALENT)
27.47/8.92	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), f(c)) at position [] we obtained the following new rules [LPAR04]:
27.47/8.92	
27.47/8.92	   (A^2 -> H(U1(k, e), f(c)),A^2 -> H(U1(k, e), f(c)))
27.47/8.92	   (A^2 -> H(U1(d, e), U1(c, c)),A^2 -> H(U1(d, e), U1(c, c)))
27.47/8.92	   (A^2 -> H(U1(d, e), f(e)),A^2 -> H(U1(d, e), f(e)))
27.47/8.92	   (A^2 -> H(U1(d, e), f(k)),A^2 -> H(U1(d, e), f(k)))
27.47/8.92	
27.47/8.92	
27.47/8.92	----------------------------------------
27.47/8.92	
27.47/8.92	(634)
27.47/8.92	Obligation:
27.47/8.92	Q DP problem:
27.47/8.92	The TRS P consists of the following rules:
27.47/8.92	
27.47/8.92	   H(x, x) -> G(x, x, f(k))
27.47/8.92	   G(d, x, x) -> A^2
27.47/8.92	   A^2 -> H(f(c), f(c))
27.47/8.92	   A^2 -> H(f(d), f(d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, c))
27.47/8.92	   A^2 -> H(f(e), f(e))
27.47/8.92	   A^2 -> H(f(k), f(k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(d, d))
27.47/8.92	   A^2 -> H(U1(d, e), f(d))
27.47/8.92	   A^2 -> H(U1(d, c), U1(c, b))
27.47/8.92	   A^2 -> H(U1(d, c), U1(d, b))
27.47/8.92	   A^2 -> H(U1(d, c), U1(b, c))
27.47/8.92	   A^2 -> H(U1(d, c), U1(b, d))
27.47/8.92	   A^2 -> H(U1(d, c), U1(c, c))
27.47/8.92	   A^2 -> H(U1(d, c), f(e))
27.47/8.92	   A^2 -> H(U1(d, c), f(k))
27.47/8.92	   A^2 -> H(U1(d, c), U1(d, d))
27.47/8.92	   A^2 -> H(U1(d, a), U1(e, b))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, b))
27.47/8.92	   A^2 -> H(U1(d, a), U1(c, d))
27.47/8.92	   A^2 -> H(U1(d, a), U1(d, c))
27.47/8.92	   A^2 -> H(U1(d, a), U1(b, e))
27.47/8.92	   A^2 -> H(U1(d, a), U1(b, k))
27.47/8.92	   A^2 -> H(U1(d, a), U1(e, c))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, c))
27.47/8.92	   A^2 -> H(U1(d, a), U1(c, e))
27.47/8.92	   A^2 -> H(U1(d, a), U1(c, k))
27.47/8.92	   A^2 -> H(U1(d, a), U1(e, e))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, k))
27.47/8.92	   A^2 -> H(U1(d, a), U1(k, d))
27.47/8.92	   A^2 -> H(U1(d, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(a, e), U1(c, b))
27.47/8.92	   A^2 -> H(U1(a, e), U1(d, b))
27.47/8.92	   A^2 -> H(U1(a, e), U1(b, c))
27.47/8.92	   A^2 -> H(U1(a, e), U1(b, d))
27.47/8.92	   A^2 -> H(U1(a, e), U1(c, c))
27.47/8.92	   A^2 -> H(U1(a, e), f(e))
27.47/8.92	   A^2 -> H(U1(a, e), f(k))
27.47/8.92	   A^2 -> H(U1(a, e), U1(d, d))
27.47/8.92	   A^2 -> H(U1(a, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(a, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(a, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(a, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(a, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(a, k), f(e))
27.47/8.92	   A^2 -> H(U1(a, k), f(k))
27.47/8.92	   A^2 -> H(U1(a, k), U1(d, d))
27.47/8.92	   A^2 -> H(U1(a, c), U1(e, b))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, b))
27.47/8.92	   A^2 -> H(U1(a, c), U1(c, d))
27.47/8.92	   A^2 -> H(U1(a, c), U1(d, c))
27.47/8.92	   A^2 -> H(U1(a, c), U1(b, e))
27.47/8.92	   A^2 -> H(U1(a, c), U1(b, k))
27.47/8.92	   A^2 -> H(U1(a, c), U1(e, c))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, c))
27.47/8.92	   A^2 -> H(U1(a, c), U1(c, e))
27.47/8.92	   A^2 -> H(U1(a, c), U1(c, k))
27.47/8.92	   A^2 -> H(U1(a, c), U1(e, e))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, k))
27.47/8.92	   A^2 -> H(U1(a, c), U1(k, d))
27.47/8.92	   A^2 -> H(U1(a, c), U1(d, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(e, b))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, b))
27.47/8.92	   A^2 -> H(U1(a, d), U1(c, d))
27.47/8.92	   A^2 -> H(U1(a, d), U1(d, c))
27.47/8.92	   A^2 -> H(U1(a, d), U1(b, e))
27.47/8.92	   A^2 -> H(U1(a, d), U1(b, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(e, c))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, c))
27.47/8.92	   A^2 -> H(U1(a, d), U1(c, e))
27.47/8.92	   A^2 -> H(U1(a, d), U1(c, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(e, e))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, k))
27.47/8.92	   A^2 -> H(U1(a, d), U1(k, d))
27.47/8.92	   A^2 -> H(U1(a, d), U1(d, k))
27.47/8.92	   A^2 -> H(U1(a, a), b)
27.47/8.92	   A^2 -> H(U1(a, a), U1(e, d))
27.47/8.92	   A^2 -> H(U1(a, a), U1(d, e))
27.47/8.92	   A^2 -> H(U1(a, a), c)
27.47/8.92	   A^2 -> H(U1(a, a), U1(e, k))
27.47/8.92	   A^2 -> H(U1(a, a), U1(k, e))
27.47/8.92	   A^2 -> H(U1(a, a), e)
27.47/8.92	   A^2 -> H(U1(a, a), U1(k, k))
27.47/8.92	   A^2 -> H(k, f(b))
27.47/8.92	   A^2 -> H(c, U1(b, b))
27.47/8.92	   A^2 -> H(c, f(c))
27.47/8.92	   A^2 -> H(c, f(d))
27.47/8.92	   A^2 -> H(U1(e, k), U1(b, b))
27.47/8.92	   A^2 -> H(U1(e, k), f(c))
27.47/8.92	   A^2 -> H(U1(e, k), f(d))
27.47/8.92	   A^2 -> H(U1(e, c), U1(c, b))
27.47/8.92	   A^2 -> H(U1(e, c), U1(d, b))
27.47/8.92	   A^2 -> H(U1(e, c), U1(b, c))
27.47/8.92	   A^2 -> H(U1(e, c), U1(b, d))
27.47/8.92	   A^2 -> H(U1(e, c), U1(c, c))
27.47/8.92	   A^2 -> H(U1(e, c), f(e))
27.47/8.92	   A^2 -> H(U1(e, c), f(k))
27.47/8.92	   A^2 -> H(U1(e, c), U1(d, d))
27.47/8.92	   A^2 -> H(U1(k, e), U1(b, b))
27.47/8.92	   A^2 -> H(U1(k, e), f(c))
27.47/8.92	   A^2 -> H(U1(k, e), f(d))
27.47/8.92	   A^2 -> H(U1(k, c), U1(c, b))
27.47/8.92	   A^2 -> H(U1(k, c), U1(d, b))
27.47/8.92	   A^2 -> H(U1(k, c), U1(b, c))
27.47/8.92	   A^2 -> H(U1(k, c), U1(b, d))
27.47/8.92	   A^2 -> H(U1(k, c), U1(c, c))
27.47/8.92	   A^2 -> H(U1(k, c), f(e))
27.47/8.92	   A^2 -> H(U1(k, c), f(k))
27.47/8.92	   A^2 -> H(U1(k, c), U1(d, d))
27.47/8.92	   A^2 -> H(U1(c, e), U1(c, b))
27.47/8.92	   A^2 -> H(U1(c, e), U1(d, b))
27.47/8.92	   A^2 -> H(U1(c, e), U1(b, c))
27.47/8.92	   A^2 -> H(U1(c, e), U1(b, d))
27.47/8.92	   A^2 -> H(U1(c, e), U1(c, c))
27.47/8.92	   A^2 -> H(U1(c, e), f(e))
27.47/8.92	   A^2 -> H(U1(c, e), f(k))
27.47/8.92	   A^2 -> H(U1(c, e), U1(d, d))
27.47/8.92	   A^2 -> H(U1(c, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(c, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(c, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(c, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(c, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(c, k), f(e))
27.47/8.92	   A^2 -> H(U1(c, k), f(k))
27.47/8.92	   A^2 -> H(U1(c, k), U1(d, d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(e, b))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, b))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(d, c))
27.47/8.92	   A^2 -> H(U1(c, c), U1(b, e))
27.47/8.92	   A^2 -> H(U1(c, c), U1(b, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(e, e))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, d))
27.47/8.92	   A^2 -> H(U1(c, c), U1(d, k))
27.47/8.92	   A^2 -> H(e, U1(b, b))
27.47/8.92	   A^2 -> H(e, f(c))
27.47/8.92	   A^2 -> H(e, f(d))
27.47/8.92	   A^2 -> H(U1(e, e), U1(c, b))
27.47/8.92	   A^2 -> H(U1(e, e), U1(d, b))
27.47/8.92	   A^2 -> H(U1(e, e), U1(b, c))
27.47/8.92	   A^2 -> H(U1(e, e), U1(b, d))
27.47/8.92	   A^2 -> H(U1(e, e), U1(c, c))
27.47/8.92	   A^2 -> H(U1(e, e), f(e))
27.47/8.92	   A^2 -> H(U1(e, e), f(k))
27.47/8.92	   A^2 -> H(U1(e, e), U1(d, d))
27.47/8.92	   A^2 -> H(f(e), U1(e, b))
27.47/8.92	   A^2 -> H(f(e), U1(k, b))
27.47/8.92	   A^2 -> H(f(e), U1(c, d))
27.47/8.92	   A^2 -> H(f(e), U1(d, c))
27.47/8.92	   A^2 -> H(f(e), U1(b, e))
27.47/8.92	   A^2 -> H(f(e), U1(b, k))
27.47/8.92	   A^2 -> H(f(e), U1(e, c))
27.47/8.92	   A^2 -> H(f(e), U1(k, c))
27.47/8.92	   A^2 -> H(f(e), U1(c, e))
27.47/8.92	   A^2 -> H(f(e), U1(c, k))
27.47/8.92	   A^2 -> H(f(e), U1(k, k))
27.47/8.92	   A^2 -> H(f(e), U1(k, d))
27.47/8.92	   A^2 -> H(f(e), U1(d, k))
27.47/8.92	   A^2 -> H(U1(k, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(k, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(k, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(k, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(k, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(k, k), f(e))
27.47/8.92	   A^2 -> H(U1(k, k), f(k))
27.47/8.92	   A^2 -> H(U1(k, k), U1(d, d))
27.47/8.92	   A^2 -> H(f(k), U1(e, b))
27.47/8.92	   A^2 -> H(f(k), U1(k, b))
27.47/8.92	   A^2 -> H(f(k), U1(c, d))
27.47/8.92	   A^2 -> H(f(k), U1(d, c))
27.47/8.92	   A^2 -> H(f(k), U1(b, e))
27.47/8.92	   A^2 -> H(f(k), U1(b, k))
27.47/8.92	   A^2 -> H(f(k), U1(e, c))
27.47/8.92	   A^2 -> H(f(k), U1(k, c))
27.47/8.92	   A^2 -> H(f(k), U1(c, e))
27.47/8.92	   A^2 -> H(f(k), U1(c, k))
27.47/8.92	   A^2 -> H(f(k), U1(e, e))
27.47/8.92	   A^2 -> H(f(k), U1(k, d))
27.47/8.92	   A^2 -> H(f(k), U1(d, k))
27.47/8.92	   A^2 -> H(f(c), b)
27.47/8.92	   A^2 -> H(f(c), U1(e, d))
27.47/8.92	   A^2 -> H(f(c), U1(d, e))
27.47/8.92	   A^2 -> H(f(k), U1(k, k))
27.47/8.92	   A^2 -> H(U1(k, k), U1(b, b))
27.47/8.92	   A^2 -> H(U1(k, k), f(c))
27.47/8.92	   A^2 -> H(U1(k, k), f(d))
27.47/8.92	   A^2 -> H(U1(k, d), U1(c, b))
27.47/8.92	   A^2 -> H(U1(k, d), U1(d, b))
27.47/8.92	   A^2 -> H(U1(k, d), U1(b, c))
27.47/8.92	   A^2 -> H(U1(k, d), U1(b, d))
27.47/8.92	   A^2 -> H(U1(k, d), U1(c, c))
27.47/8.92	   A^2 -> H(U1(k, d), f(e))
27.47/8.92	   A^2 -> H(U1(k, d), f(k))
27.47/8.92	   A^2 -> H(U1(k, d), U1(d, d))
27.47/8.92	   A^2 -> H(U1(d, k), U1(c, b))
27.47/8.92	   A^2 -> H(U1(d, k), U1(d, b))
27.47/8.92	   A^2 -> H(U1(d, k), U1(b, c))
27.47/8.92	   A^2 -> H(U1(d, k), U1(b, d))
27.47/8.92	   A^2 -> H(U1(d, k), U1(c, c))
27.47/8.92	   A^2 -> H(U1(d, k), f(e))
27.47/8.92	   A^2 -> H(U1(d, k), f(k))
27.47/8.92	   A^2 -> H(U1(d, k), U1(d, d))
27.47/8.92	   A^2 -> H(U1(d, d), U1(e, b))
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, b))
27.47/8.92	   A^2 -> H(U1(d, d), U1(c, d))
27.47/8.92	   A^2 -> H(U1(d, d), U1(d, c))
27.47/8.92	   A^2 -> H(U1(d, d), U1(b, e))
27.47/8.92	   A^2 -> H(U1(d, d), U1(b, k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(e, c))
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, c))
27.47/8.92	   A^2 -> H(U1(d, d), U1(c, e))
27.47/8.92	   A^2 -> H(U1(d, d), U1(c, k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(e, e))
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, k))
27.47/8.92	   A^2 -> H(f(d), b)
27.47/8.92	   A^2 -> H(f(d), U1(e, d))
27.47/8.92	   A^2 -> H(f(d), U1(d, e))
27.47/8.92	   A^2 -> H(f(d), c)
27.47/8.92	   A^2 -> H(f(d), U1(e, k))
27.47/8.92	   A^2 -> H(f(d), U1(k, e))
27.47/8.92	   A^2 -> H(f(d), e)
27.47/8.92	   A^2 -> H(f(a), d)
27.47/8.92	   A^2 -> H(U1(c, c), U1(e, c))
27.47/8.92	   A^2 -> H(f(c), c)
27.47/8.92	   A^2 -> H(f(c), U1(e, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(k, c))
27.47/8.92	   A^2 -> H(f(c), U1(k, e))
27.47/8.92	   A^2 -> H(f(c), U1(k, k))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, e))
27.47/8.92	   A^2 -> H(U1(c, c), U1(c, k))
27.47/8.92	   A^2 -> H(f(a), k)
27.47/8.92	   A^2 -> H(f(e), U1(e, e))
27.47/8.92	   A^2 -> H(f(c), e)
27.47/8.92	   A^2 -> H(U1(d, d), U1(k, d))
27.47/8.92	   A^2 -> H(f(d), U1(k, k))
27.47/8.92	   A^2 -> H(U1(d, d), U1(d, k))
27.47/8.92	   A^2 -> H(d, U1(b, b))
27.47/8.92	   A^2 -> H(d, f(c))
27.47/8.92	   A^2 -> H(d, f(d))
27.47/8.92	   A^2 -> H(a, U1(c, b))
27.47/8.92	   A^2 -> H(a, U1(d, b))
27.47/8.92	   A^2 -> H(a, U1(b, c))
27.47/8.92	   A^2 -> H(a, U1(b, d))
27.47/8.92	   A^2 -> H(a, U1(c, c))
27.47/8.92	   A^2 -> H(a, f(e))
27.47/8.92	   A^2 -> H(a, f(k))
27.47/8.92	   A^2 -> H(a, U1(d, d))
27.47/8.92	   A^2 -> H(U1(e, d), U1(c, b))
27.47/8.92	   A^2 -> H(U1(e, d), U1(d, b))
27.47/8.92	   A^2 -> H(U1(e, d), U1(b, c))
27.47/8.92	   A^2 -> H(U1(e, d), U1(b, d))
27.47/8.92	   A^2 -> H(U1(e, d), U1(c, c))
27.47/8.92	   A^2 -> H(U1(e, d), f(e))
27.47/8.92	   A^2 -> H(U1(e, d), f(k))
27.47/8.92	   A^2 -> H(U1(e, d), U1(d, d))
27.47/8.92	   A^2 -> H(U1(e, a), U1(e, b))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, b))
27.47/8.92	   A^2 -> H(U1(e, a), U1(c, d))
27.47/8.92	   A^2 -> H(U1(e, a), U1(d, c))
27.47/8.92	   A^2 -> H(U1(e, a), U1(b, e))
27.47/8.92	   A^2 -> H(U1(e, a), U1(b, k))
27.47/8.92	   A^2 -> H(U1(e, a), U1(e, c))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, c))
27.47/8.92	   A^2 -> H(U1(e, a), U1(c, e))
27.47/8.92	   A^2 -> H(U1(e, a), U1(c, k))
27.47/8.92	   A^2 -> H(U1(e, a), U1(e, e))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, k))
27.47/8.92	   A^2 -> H(U1(e, a), U1(k, d))
27.47/8.92	   A^2 -> H(U1(e, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(e, b))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, b))
27.47/8.92	   A^2 -> H(U1(k, a), U1(c, d))
27.47/8.92	   A^2 -> H(U1(k, a), U1(d, c))
27.47/8.92	   A^2 -> H(U1(k, a), U1(b, e))
27.47/8.92	   A^2 -> H(U1(k, a), U1(b, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(e, c))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, c))
27.47/8.92	   A^2 -> H(U1(k, a), U1(c, e))
27.47/8.92	   A^2 -> H(U1(k, a), U1(c, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(e, e))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, k))
27.47/8.92	   A^2 -> H(U1(k, a), U1(k, d))
27.47/8.92	   A^2 -> H(U1(k, a), U1(d, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(e, b))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, b))
27.47/8.92	   A^2 -> H(U1(c, d), U1(c, d))
27.47/8.92	   A^2 -> H(U1(c, d), U1(d, c))
27.47/8.92	   A^2 -> H(U1(c, d), U1(b, e))
27.47/8.92	   A^2 -> H(U1(c, d), U1(b, k))
27.47/8.92	   A^2 -> H(U1(c, d), U1(e, c))
27.47/8.92	   A^2 -> H(U1(c, d), U1(k, c))
27.47/8.92	   A^2 -> H(U1(c, d), U1(c, e))
27.47/8.93	   A^2 -> H(U1(c, d), U1(c, k))
27.47/8.93	   A^2 -> H(U1(c, d), U1(e, e))
27.47/8.93	   A^2 -> H(U1(c, d), U1(k, k))
27.47/8.93	   A^2 -> H(U1(c, d), U1(k, d))
27.47/8.93	   A^2 -> H(U1(c, d), U1(d, k))
27.47/8.93	   A^2 -> H(U1(c, a), b)
27.47/8.93	   A^2 -> H(U1(c, a), U1(e, d))
27.47/8.93	   A^2 -> H(U1(c, a), U1(d, e))
27.47/8.93	   A^2 -> H(U1(c, a), c)
27.47/8.93	   A^2 -> H(U1(c, a), U1(e, k))
27.47/8.93	   A^2 -> H(U1(c, a), U1(k, e))
27.47/8.93	   A^2 -> H(U1(c, a), e)
27.47/8.93	   A^2 -> H(U1(c, a), U1(k, k))
27.47/8.93	   A^2 -> H(U1(d, e), U1(c, b))
27.47/8.93	   A^2 -> H(U1(d, e), U1(d, b))
27.47/8.93	   A^2 -> H(U1(d, e), U1(b, c))
27.47/8.93	   A^2 -> H(U1(d, e), U1(b, d))
27.47/8.93	   A^2 -> H(U1(d, e), U1(c, c))
27.47/8.93	   A^2 -> H(U1(d, e), f(e))
27.47/8.93	   A^2 -> H(U1(d, e), f(k))
27.47/8.93	
27.47/8.93	The TRS R consists of the following rules:
27.47/8.93	
27.47/8.93	   f(x) -> U1(x, x)
27.47/8.93	   U1(e, x) -> x
27.47/8.93	   a -> c
27.47/8.93	   a -> d
27.47/8.93	   b -> c
27.47/8.93	   b -> d
27.47/8.93	   d -> k
27.47/8.93	   c -> e
27.47/8.93	   c -> k
27.47/8.93	
27.47/8.93	Q is empty.
27.47/8.93	We have to consider all minimal (P,Q,R)-chains.
27.47/8.93	----------------------------------------
27.47/8.93	
27.47/8.93	(635) TransformationProof (EQUIVALENT)
27.47/8.93	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), f(d)) at position [] we obtained the following new rules [LPAR04]:
27.47/8.93	
27.47/8.93	   (A^2 -> H(U1(k, e), f(d)),A^2 -> H(U1(k, e), f(d)))
27.47/8.93	   (A^2 -> H(U1(d, e), U1(d, d)),A^2 -> H(U1(d, e), U1(d, d)))
27.47/8.93	   (A^2 -> H(U1(d, e), f(k)),A^2 -> H(U1(d, e), f(k)))
27.47/8.93	
27.47/8.93	
27.47/8.93	----------------------------------------
27.47/8.93	
27.47/8.93	(636)
27.47/8.93	Obligation:
27.47/8.93	Q DP problem:
27.47/8.93	The TRS P consists of the following rules:
27.47/8.93	
27.47/8.93	   H(x, x) -> G(x, x, f(k))
27.47/8.93	   G(d, x, x) -> A^2
27.47/8.93	   A^2 -> H(f(c), f(c))
27.47/8.93	   A^2 -> H(f(d), f(d))
27.47/8.93	   A^2 -> H(U1(c, c), U1(c, c))
27.47/8.93	   A^2 -> H(f(e), f(e))
27.47/8.93	   A^2 -> H(f(k), f(k))
27.47/8.93	   A^2 -> H(U1(d, d), U1(d, d))
27.47/8.93	   A^2 -> H(U1(d, c), U1(c, b))
27.47/8.93	   A^2 -> H(U1(d, c), U1(d, b))
27.47/8.93	   A^2 -> H(U1(d, c), U1(b, c))
27.47/8.93	   A^2 -> H(U1(d, c), U1(b, d))
27.47/8.93	   A^2 -> H(U1(d, c), U1(c, c))
27.47/8.93	   A^2 -> H(U1(d, c), f(e))
27.47/8.93	   A^2 -> H(U1(d, c), f(k))
27.47/8.93	   A^2 -> H(U1(d, c), U1(d, d))
27.47/8.93	   A^2 -> H(U1(d, a), U1(e, b))
27.47/8.93	   A^2 -> H(U1(d, a), U1(k, b))
27.47/8.93	   A^2 -> H(U1(d, a), U1(c, d))
27.47/8.93	   A^2 -> H(U1(d, a), U1(d, c))
27.47/8.93	   A^2 -> H(U1(d, a), U1(b, e))
27.47/8.93	   A^2 -> H(U1(d, a), U1(b, k))
27.47/8.93	   A^2 -> H(U1(d, a), U1(e, c))
27.47/8.93	   A^2 -> H(U1(d, a), U1(k, c))
27.47/8.93	   A^2 -> H(U1(d, a), U1(c, e))
27.47/8.93	   A^2 -> H(U1(d, a), U1(c, k))
27.47/8.93	   A^2 -> H(U1(d, a), U1(e, e))
27.47/8.93	   A^2 -> H(U1(d, a), U1(k, k))
27.47/8.93	   A^2 -> H(U1(d, a), U1(k, d))
27.47/8.93	   A^2 -> H(U1(d, a), U1(d, k))
27.47/8.93	   A^2 -> H(U1(a, e), U1(c, b))
27.47/8.93	   A^2 -> H(U1(a, e), U1(d, b))
27.47/8.93	   A^2 -> H(U1(a, e), U1(b, c))
27.47/8.93	   A^2 -> H(U1(a, e), U1(b, d))
27.47/8.93	   A^2 -> H(U1(a, e), U1(c, c))
27.47/8.93	   A^2 -> H(U1(a, e), f(e))
27.47/8.93	   A^2 -> H(U1(a, e), f(k))
27.47/8.93	   A^2 -> H(U1(a, e), U1(d, d))
27.47/8.93	   A^2 -> H(U1(a, k), U1(c, b))
27.47/8.93	   A^2 -> H(U1(a, k), U1(d, b))
27.47/8.93	   A^2 -> H(U1(a, k), U1(b, c))
27.47/8.93	   A^2 -> H(U1(a, k), U1(b, d))
27.47/8.93	   A^2 -> H(U1(a, k), U1(c, c))
27.47/8.93	   A^2 -> H(U1(a, k), f(e))
27.47/8.93	   A^2 -> H(U1(a, k), f(k))
27.47/8.93	   A^2 -> H(U1(a, k), U1(d, d))
27.47/8.93	   A^2 -> H(U1(a, c), U1(e, b))
27.47/8.93	   A^2 -> H(U1(a, c), U1(k, b))
27.47/8.93	   A^2 -> H(U1(a, c), U1(c, d))
27.47/8.93	   A^2 -> H(U1(a, c), U1(d, c))
27.47/8.93	   A^2 -> H(U1(a, c), U1(b, e))
27.47/8.93	   A^2 -> H(U1(a, c), U1(b, k))
27.47/8.93	   A^2 -> H(U1(a, c), U1(e, c))
27.47/8.93	   A^2 -> H(U1(a, c), U1(k, c))
27.47/8.93	   A^2 -> H(U1(a, c), U1(c, e))
27.47/8.93	   A^2 -> H(U1(a, c), U1(c, k))
27.47/8.93	   A^2 -> H(U1(a, c), U1(e, e))
27.47/8.93	   A^2 -> H(U1(a, c), U1(k, k))
27.47/8.93	   A^2 -> H(U1(a, c), U1(k, d))
27.47/8.93	   A^2 -> H(U1(a, c), U1(d, k))
27.47/8.93	   A^2 -> H(U1(a, d), U1(e, b))
27.47/8.93	   A^2 -> H(U1(a, d), U1(k, b))
27.47/8.93	   A^2 -> H(U1(a, d), U1(c, d))
27.47/8.93	   A^2 -> H(U1(a, d), U1(d, c))
27.47/8.93	   A^2 -> H(U1(a, d), U1(b, e))
27.47/8.93	   A^2 -> H(U1(a, d), U1(b, k))
27.47/8.93	   A^2 -> H(U1(a, d), U1(e, c))
27.47/8.93	   A^2 -> H(U1(a, d), U1(k, c))
27.47/8.93	   A^2 -> H(U1(a, d), U1(c, e))
27.47/8.93	   A^2 -> H(U1(a, d), U1(c, k))
27.47/8.93	   A^2 -> H(U1(a, d), U1(e, e))
27.47/8.93	   A^2 -> H(U1(a, d), U1(k, k))
27.47/8.93	   A^2 -> H(U1(a, d), U1(k, d))
27.47/8.93	   A^2 -> H(U1(a, d), U1(d, k))
27.47/8.93	   A^2 -> H(U1(a, a), b)
27.47/8.93	   A^2 -> H(U1(a, a), U1(e, d))
27.47/8.93	   A^2 -> H(U1(a, a), U1(d, e))
27.47/8.93	   A^2 -> H(U1(a, a), c)
27.47/8.93	   A^2 -> H(U1(a, a), U1(e, k))
27.47/8.93	   A^2 -> H(U1(a, a), U1(k, e))
27.47/8.93	   A^2 -> H(U1(a, a), e)
27.47/8.93	   A^2 -> H(U1(a, a), U1(k, k))
27.47/8.93	   A^2 -> H(k, f(b))
27.47/8.93	   A^2 -> H(c, U1(b, b))
27.47/8.93	   A^2 -> H(c, f(c))
27.47/8.93	   A^2 -> H(c, f(d))
27.47/8.93	   A^2 -> H(U1(e, k), U1(b, b))
27.47/8.93	   A^2 -> H(U1(e, k), f(c))
27.47/8.93	   A^2 -> H(U1(e, k), f(d))
27.47/8.93	   A^2 -> H(U1(e, c), U1(c, b))
27.47/8.93	   A^2 -> H(U1(e, c), U1(d, b))
27.47/8.93	   A^2 -> H(U1(e, c), U1(b, c))
27.47/8.93	   A^2 -> H(U1(e, c), U1(b, d))
27.47/8.93	   A^2 -> H(U1(e, c), U1(c, c))
27.47/8.93	   A^2 -> H(U1(e, c), f(e))
27.47/8.93	   A^2 -> H(U1(e, c), f(k))
27.47/8.93	   A^2 -> H(U1(e, c), U1(d, d))
27.47/8.93	   A^2 -> H(U1(k, e), U1(b, b))
27.47/8.93	   A^2 -> H(U1(k, e), f(c))
27.47/8.93	   A^2 -> H(U1(k, e), f(d))
27.47/8.93	   A^2 -> H(U1(k, c), U1(c, b))
27.47/8.93	   A^2 -> H(U1(k, c), U1(d, b))
27.47/8.93	   A^2 -> H(U1(k, c), U1(b, c))
27.47/8.93	   A^2 -> H(U1(k, c), U1(b, d))
27.47/8.93	   A^2 -> H(U1(k, c), U1(c, c))
27.47/8.93	   A^2 -> H(U1(k, c), f(e))
27.47/8.93	   A^2 -> H(U1(k, c), f(k))
27.47/8.93	   A^2 -> H(U1(k, c), U1(d, d))
27.47/8.93	   A^2 -> H(U1(c, e), U1(c, b))
27.47/8.93	   A^2 -> H(U1(c, e), U1(d, b))
27.47/8.93	   A^2 -> H(U1(c, e), U1(b, c))
27.47/8.93	   A^2 -> H(U1(c, e), U1(b, d))
27.47/8.93	   A^2 -> H(U1(c, e), U1(c, c))
27.47/8.93	   A^2 -> H(U1(c, e), f(e))
27.47/8.93	   A^2 -> H(U1(c, e), f(k))
27.47/8.93	   A^2 -> H(U1(c, e), U1(d, d))
27.47/8.93	   A^2 -> H(U1(c, k), U1(c, b))
27.47/8.93	   A^2 -> H(U1(c, k), U1(d, b))
27.47/8.93	   A^2 -> H(U1(c, k), U1(b, c))
27.47/8.93	   A^2 -> H(U1(c, k), U1(b, d))
27.47/8.93	   A^2 -> H(U1(c, k), U1(c, c))
27.47/8.93	   A^2 -> H(U1(c, k), f(e))
27.47/8.93	   A^2 -> H(U1(c, k), f(k))
27.47/8.93	   A^2 -> H(U1(c, k), U1(d, d))
27.47/8.93	   A^2 -> H(U1(c, c), U1(e, b))
27.47/8.93	   A^2 -> H(U1(c, c), U1(k, b))
27.47/8.93	   A^2 -> H(U1(c, c), U1(c, d))
27.47/8.93	   A^2 -> H(U1(c, c), U1(d, c))
27.47/8.93	   A^2 -> H(U1(c, c), U1(b, e))
27.47/8.93	   A^2 -> H(U1(c, c), U1(b, k))
27.47/8.93	   A^2 -> H(U1(c, c), U1(e, e))
27.47/8.93	   A^2 -> H(U1(c, c), U1(k, k))
27.47/8.93	   A^2 -> H(U1(c, c), U1(k, d))
27.47/8.93	   A^2 -> H(U1(c, c), U1(d, k))
27.47/8.93	   A^2 -> H(e, U1(b, b))
27.47/8.93	   A^2 -> H(e, f(c))
27.47/8.93	   A^2 -> H(e, f(d))
27.47/8.93	   A^2 -> H(U1(e, e), U1(c, b))
27.47/8.93	   A^2 -> H(U1(e, e), U1(d, b))
27.47/8.93	   A^2 -> H(U1(e, e), U1(b, c))
27.47/8.93	   A^2 -> H(U1(e, e), U1(b, d))
27.47/8.93	   A^2 -> H(U1(e, e), U1(c, c))
27.47/8.93	   A^2 -> H(U1(e, e), f(e))
27.47/8.93	   A^2 -> H(U1(e, e), f(k))
27.47/8.93	   A^2 -> H(U1(e, e), U1(d, d))
27.47/8.93	   A^2 -> H(f(e), U1(e, b))
27.47/8.93	   A^2 -> H(f(e), U1(k, b))
27.47/8.93	   A^2 -> H(f(e), U1(c, d))
27.47/8.93	   A^2 -> H(f(e), U1(d, c))
27.47/8.93	   A^2 -> H(f(e), U1(b, e))
27.47/8.93	   A^2 -> H(f(e), U1(b, k))
27.47/8.93	   A^2 -> H(f(e), U1(e, c))
27.47/8.93	   A^2 -> H(f(e), U1(k, c))
27.47/8.93	   A^2 -> H(f(e), U1(c, e))
27.47/8.93	   A^2 -> H(f(e), U1(c, k))
27.47/8.93	   A^2 -> H(f(e), U1(k, k))
27.47/8.93	   A^2 -> H(f(e), U1(k, d))
27.47/8.93	   A^2 -> H(f(e), U1(d, k))
27.47/8.93	   A^2 -> H(U1(k, k), U1(c, b))
27.47/8.93	   A^2 -> H(U1(k, k), U1(d, b))
27.47/8.93	   A^2 -> H(U1(k, k), U1(b, c))
27.47/8.93	   A^2 -> H(U1(k, k), U1(b, d))
27.47/8.93	   A^2 -> H(U1(k, k), U1(c, c))
27.47/8.93	   A^2 -> H(U1(k, k), f(e))
27.47/8.93	   A^2 -> H(U1(k, k), f(k))
27.47/8.93	   A^2 -> H(U1(k, k), U1(d, d))
27.47/8.93	   A^2 -> H(f(k), U1(e, b))
27.47/8.93	   A^2 -> H(f(k), U1(k, b))
27.47/8.93	   A^2 -> H(f(k), U1(c, d))
27.47/8.93	   A^2 -> H(f(k), U1(d, c))
27.47/8.93	   A^2 -> H(f(k), U1(b, e))
27.47/8.93	   A^2 -> H(f(k), U1(b, k))
27.47/8.93	   A^2 -> H(f(k), U1(e, c))
27.47/8.93	   A^2 -> H(f(k), U1(k, c))
27.47/8.93	   A^2 -> H(f(k), U1(c, e))
27.47/8.93	   A^2 -> H(f(k), U1(c, k))
27.47/8.93	   A^2 -> H(f(k), U1(e, e))
27.47/8.93	   A^2 -> H(f(k), U1(k, d))
27.47/8.93	   A^2 -> H(f(k), U1(d, k))
27.47/8.93	   A^2 -> H(f(c), b)
27.47/8.93	   A^2 -> H(f(c), U1(e, d))
27.47/8.93	   A^2 -> H(f(c), U1(d, e))
27.47/8.93	   A^2 -> H(f(k), U1(k, k))
27.47/8.93	   A^2 -> H(U1(k, k), U1(b, b))
27.47/8.93	   A^2 -> H(U1(k, k), f(c))
27.47/8.93	   A^2 -> H(U1(k, k), f(d))
27.47/8.93	   A^2 -> H(U1(k, d), U1(c, b))
27.47/8.93	   A^2 -> H(U1(k, d), U1(d, b))
27.47/8.93	   A^2 -> H(U1(k, d), U1(b, c))
27.47/8.93	   A^2 -> H(U1(k, d), U1(b, d))
27.47/8.93	   A^2 -> H(U1(k, d), U1(c, c))
27.47/8.93	   A^2 -> H(U1(k, d), f(e))
27.47/8.93	   A^2 -> H(U1(k, d), f(k))
27.47/8.93	   A^2 -> H(U1(k, d), U1(d, d))
27.47/8.93	   A^2 -> H(U1(d, k), U1(c, b))
27.47/8.93	   A^2 -> H(U1(d, k), U1(d, b))
27.47/8.93	   A^2 -> H(U1(d, k), U1(b, c))
27.47/8.93	   A^2 -> H(U1(d, k), U1(b, d))
27.47/8.93	   A^2 -> H(U1(d, k), U1(c, c))
27.47/8.93	   A^2 -> H(U1(d, k), f(e))
27.47/8.93	   A^2 -> H(U1(d, k), f(k))
27.47/8.93	   A^2 -> H(U1(d, k), U1(d, d))
27.47/8.93	   A^2 -> H(U1(d, d), U1(e, b))
27.47/8.93	   A^2 -> H(U1(d, d), U1(k, b))
27.47/8.93	   A^2 -> H(U1(d, d), U1(c, d))
27.47/8.93	   A^2 -> H(U1(d, d), U1(d, c))
27.47/8.93	   A^2 -> H(U1(d, d), U1(b, e))
27.47/8.93	   A^2 -> H(U1(d, d), U1(b, k))
27.47/8.93	   A^2 -> H(U1(d, d), U1(e, c))
27.47/8.93	   A^2 -> H(U1(d, d), U1(k, c))
27.47/8.93	   A^2 -> H(U1(d, d), U1(c, e))
27.47/8.93	   A^2 -> H(U1(d, d), U1(c, k))
27.47/8.93	   A^2 -> H(U1(d, d), U1(e, e))
27.47/8.93	   A^2 -> H(U1(d, d), U1(k, k))
27.47/8.93	   A^2 -> H(f(d), b)
27.47/8.93	   A^2 -> H(f(d), U1(e, d))
27.47/8.93	   A^2 -> H(f(d), U1(d, e))
27.47/8.93	   A^2 -> H(f(d), c)
27.47/8.93	   A^2 -> H(f(d), U1(e, k))
27.47/8.93	   A^2 -> H(f(d), U1(k, e))
27.47/8.93	   A^2 -> H(f(d), e)
27.47/8.93	   A^2 -> H(f(a), d)
27.47/8.93	   A^2 -> H(U1(c, c), U1(e, c))
27.47/8.93	   A^2 -> H(f(c), c)
27.47/8.93	   A^2 -> H(f(c), U1(e, k))
27.47/8.93	   A^2 -> H(U1(c, c), U1(k, c))
27.47/8.93	   A^2 -> H(f(c), U1(k, e))
27.47/8.93	   A^2 -> H(f(c), U1(k, k))
27.47/8.93	   A^2 -> H(U1(c, c), U1(c, e))
27.47/8.93	   A^2 -> H(U1(c, c), U1(c, k))
27.47/8.93	   A^2 -> H(f(a), k)
27.47/8.93	   A^2 -> H(f(e), U1(e, e))
27.47/8.93	   A^2 -> H(f(c), e)
27.47/8.93	   A^2 -> H(U1(d, d), U1(k, d))
27.47/8.93	   A^2 -> H(f(d), U1(k, k))
27.47/8.93	   A^2 -> H(U1(d, d), U1(d, k))
27.47/8.93	   A^2 -> H(d, U1(b, b))
27.47/8.93	   A^2 -> H(d, f(c))
27.47/8.93	   A^2 -> H(d, f(d))
27.47/8.93	   A^2 -> H(a, U1(c, b))
27.47/8.93	   A^2 -> H(a, U1(d, b))
27.47/8.93	   A^2 -> H(a, U1(b, c))
27.47/8.93	   A^2 -> H(a, U1(b, d))
27.47/8.93	   A^2 -> H(a, U1(c, c))
27.47/8.93	   A^2 -> H(a, f(e))
27.47/8.93	   A^2 -> H(a, f(k))
27.47/8.93	   A^2 -> H(a, U1(d, d))
27.47/8.93	   A^2 -> H(U1(e, d), U1(c, b))
27.47/8.93	   A^2 -> H(U1(e, d), U1(d, b))
27.47/8.93	   A^2 -> H(U1(e, d), U1(b, c))
27.47/8.93	   A^2 -> H(U1(e, d), U1(b, d))
27.47/8.93	   A^2 -> H(U1(e, d), U1(c, c))
27.47/8.93	   A^2 -> H(U1(e, d), f(e))
27.47/8.93	   A^2 -> H(U1(e, d), f(k))
27.47/8.93	   A^2 -> H(U1(e, d), U1(d, d))
27.47/8.93	   A^2 -> H(U1(e, a), U1(e, b))
27.47/8.93	   A^2 -> H(U1(e, a), U1(k, b))
27.47/8.93	   A^2 -> H(U1(e, a), U1(c, d))
27.47/8.93	   A^2 -> H(U1(e, a), U1(d, c))
27.47/8.93	   A^2 -> H(U1(e, a), U1(b, e))
27.47/8.93	   A^2 -> H(U1(e, a), U1(b, k))
27.47/8.93	   A^2 -> H(U1(e, a), U1(e, c))
27.47/8.93	   A^2 -> H(U1(e, a), U1(k, c))
27.47/8.93	   A^2 -> H(U1(e, a), U1(c, e))
27.47/8.93	   A^2 -> H(U1(e, a), U1(c, k))
27.47/8.93	   A^2 -> H(U1(e, a), U1(e, e))
27.47/8.93	   A^2 -> H(U1(e, a), U1(k, k))
27.47/8.93	   A^2 -> H(U1(e, a), U1(k, d))
27.47/8.93	   A^2 -> H(U1(e, a), U1(d, k))
27.47/8.93	   A^2 -> H(U1(k, a), U1(e, b))
27.47/8.93	   A^2 -> H(U1(k, a), U1(k, b))
27.47/8.93	   A^2 -> H(U1(k, a), U1(c, d))
27.47/8.93	   A^2 -> H(U1(k, a), U1(d, c))
27.47/8.93	   A^2 -> H(U1(k, a), U1(b, e))
27.47/8.93	   A^2 -> H(U1(k, a), U1(b, k))
27.47/8.93	   A^2 -> H(U1(k, a), U1(e, c))
27.47/8.93	   A^2 -> H(U1(k, a), U1(k, c))
27.47/8.93	   A^2 -> H(U1(k, a), U1(c, e))
27.47/8.93	   A^2 -> H(U1(k, a), U1(c, k))
27.47/8.93	   A^2 -> H(U1(k, a), U1(e, e))
27.47/8.93	   A^2 -> H(U1(k, a), U1(k, k))
27.47/8.93	   A^2 -> H(U1(k, a), U1(k, d))
27.47/8.93	   A^2 -> H(U1(k, a), U1(d, k))
27.47/8.93	   A^2 -> H(U1(c, d), U1(e, b))
27.47/8.93	   A^2 -> H(U1(c, d), U1(k, b))
27.47/8.93	   A^2 -> H(U1(c, d), U1(c, d))
27.47/8.93	   A^2 -> H(U1(c, d), U1(d, c))
27.47/8.93	   A^2 -> H(U1(c, d), U1(b, e))
27.47/8.93	   A^2 -> H(U1(c, d), U1(b, k))
27.47/8.93	   A^2 -> H(U1(c, d), U1(e, c))
27.47/8.93	   A^2 -> H(U1(c, d), U1(k, c))
27.47/8.93	   A^2 -> H(U1(c, d), U1(c, e))
27.47/8.93	   A^2 -> H(U1(c, d), U1(c, k))
27.47/8.93	   A^2 -> H(U1(c, d), U1(e, e))
27.47/8.93	   A^2 -> H(U1(c, d), U1(k, k))
27.47/8.93	   A^2 -> H(U1(c, d), U1(k, d))
27.47/8.93	   A^2 -> H(U1(c, d), U1(d, k))
27.47/8.93	   A^2 -> H(U1(c, a), b)
27.47/8.93	   A^2 -> H(U1(c, a), U1(e, d))
27.47/8.93	   A^2 -> H(U1(c, a), U1(d, e))
27.47/8.93	   A^2 -> H(U1(c, a), c)
27.47/8.93	   A^2 -> H(U1(c, a), U1(e, k))
27.47/8.93	   A^2 -> H(U1(c, a), U1(k, e))
27.47/8.93	   A^2 -> H(U1(c, a), e)
27.47/8.93	   A^2 -> H(U1(c, a), U1(k, k))
27.47/8.93	   A^2 -> H(U1(d, e), U1(c, b))
27.47/8.93	   A^2 -> H(U1(d, e), U1(d, b))
27.47/8.93	   A^2 -> H(U1(d, e), U1(b, c))
27.47/8.93	   A^2 -> H(U1(d, e), U1(b, d))
27.47/8.93	   A^2 -> H(U1(d, e), U1(c, c))
27.47/8.93	   A^2 -> H(U1(d, e), f(e))
27.47/8.93	   A^2 -> H(U1(d, e), f(k))
27.47/8.93	   A^2 -> H(U1(d, e), U1(d, d))
27.47/8.93	
27.47/8.93	The TRS R consists of the following rules:
27.47/8.93	
27.47/8.93	   f(x) -> U1(x, x)
27.47/8.93	   U1(e, x) -> x
27.47/8.93	   a -> c
27.47/8.93	   a -> d
27.47/8.93	   b -> c
27.47/8.93	   b -> d
27.47/8.93	   d -> k
27.47/8.93	   c -> e
27.47/8.93	   c -> k
27.47/8.93	
27.47/8.93	Q is empty.
27.47/8.93	We have to consider all minimal (P,Q,R)-chains.
27.47/8.93	----------------------------------------
27.47/8.93	
27.47/8.93	(637) TransformationProof (EQUIVALENT)
27.47/8.93	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
27.47/8.93	
27.47/8.93	   (A^2 -> H(U1(k, c), U1(c, b)),A^2 -> H(U1(k, c), U1(c, b)))
27.47/8.93	   (A^2 -> H(U1(d, e), U1(c, b)),A^2 -> H(U1(d, e), U1(c, b)))
27.47/8.93	   (A^2 -> H(U1(d, k), U1(c, b)),A^2 -> H(U1(d, k), U1(c, b)))
27.47/8.93	   (A^2 -> H(U1(d, c), U1(e, b)),A^2 -> H(U1(d, c), U1(e, b)))
27.47/8.93	   (A^2 -> H(U1(d, c), U1(k, b)),A^2 -> H(U1(d, c), U1(k, b)))
27.47/8.93	   (A^2 -> H(U1(d, c), U1(c, c)),A^2 -> H(U1(d, c), U1(c, c)))
27.47/8.93	   (A^2 -> H(U1(d, c), U1(c, d)),A^2 -> H(U1(d, c), U1(c, d)))
27.47/8.93	
27.47/8.93	
27.47/8.93	----------------------------------------
27.47/8.93	
27.47/8.93	(638)
27.47/8.93	Obligation:
27.47/8.93	Q DP problem:
27.47/8.93	The TRS P consists of the following rules:
27.47/8.93	
27.47/8.93	   H(x, x) -> G(x, x, f(k))
27.47/8.93	   G(d, x, x) -> A^2
27.47/8.93	   A^2 -> H(f(c), f(c))
27.47/8.93	   A^2 -> H(f(d), f(d))
27.47/8.93	   A^2 -> H(U1(c, c), U1(c, c))
27.47/8.93	   A^2 -> H(f(e), f(e))
27.47/8.93	   A^2 -> H(f(k), f(k))
27.47/8.93	   A^2 -> H(U1(d, d), U1(d, d))
27.47/8.93	   A^2 -> H(U1(d, c), U1(d, b))
27.47/8.93	   A^2 -> H(U1(d, c), U1(b, c))
27.47/8.93	   A^2 -> H(U1(d, c), U1(b, d))
27.47/8.93	   A^2 -> H(U1(d, c), U1(c, c))
27.47/8.93	   A^2 -> H(U1(d, c), f(e))
27.47/8.93	   A^2 -> H(U1(d, c), f(k))
27.47/8.93	   A^2 -> H(U1(d, c), U1(d, d))
27.47/8.93	   A^2 -> H(U1(d, a), U1(e, b))
27.47/8.93	   A^2 -> H(U1(d, a), U1(k, b))
27.47/8.93	   A^2 -> H(U1(d, a), U1(c, d))
27.47/8.93	   A^2 -> H(U1(d, a), U1(d, c))
27.47/8.93	   A^2 -> H(U1(d, a), U1(b, e))
27.47/8.93	   A^2 -> H(U1(d, a), U1(b, k))
27.47/8.93	   A^2 -> H(U1(d, a), U1(e, c))
27.47/8.93	   A^2 -> H(U1(d, a), U1(k, c))
27.47/8.93	   A^2 -> H(U1(d, a), U1(c, e))
27.47/8.93	   A^2 -> H(U1(d, a), U1(c, k))
27.47/8.93	   A^2 -> H(U1(d, a), U1(e, e))
27.47/8.93	   A^2 -> H(U1(d, a), U1(k, k))
27.47/8.93	   A^2 -> H(U1(d, a), U1(k, d))
27.47/8.93	   A^2 -> H(U1(d, a), U1(d, k))
27.47/8.93	   A^2 -> H(U1(a, e), U1(c, b))
27.47/8.93	   A^2 -> H(U1(a, e), U1(d, b))
27.47/8.93	   A^2 -> H(U1(a, e), U1(b, c))
27.47/8.93	   A^2 -> H(U1(a, e), U1(b, d))
27.47/8.93	   A^2 -> H(U1(a, e), U1(c, c))
27.47/8.93	   A^2 -> H(U1(a, e), f(e))
27.47/8.93	   A^2 -> H(U1(a, e), f(k))
27.47/8.93	   A^2 -> H(U1(a, e), U1(d, d))
27.47/8.93	   A^2 -> H(U1(a, k), U1(c, b))
27.47/8.93	   A^2 -> H(U1(a, k), U1(d, b))
27.47/8.93	   A^2 -> H(U1(a, k), U1(b, c))
27.47/8.93	   A^2 -> H(U1(a, k), U1(b, d))
27.47/8.93	   A^2 -> H(U1(a, k), U1(c, c))
27.47/8.93	   A^2 -> H(U1(a, k), f(e))
27.47/8.93	   A^2 -> H(U1(a, k), f(k))
27.47/8.93	   A^2 -> H(U1(a, k), U1(d, d))
27.47/8.93	   A^2 -> H(U1(a, c), U1(e, b))
27.47/8.93	   A^2 -> H(U1(a, c), U1(k, b))
27.47/8.93	   A^2 -> H(U1(a, c), U1(c, d))
27.47/8.93	   A^2 -> H(U1(a, c), U1(d, c))
27.47/8.93	   A^2 -> H(U1(a, c), U1(b, e))
27.47/8.93	   A^2 -> H(U1(a, c), U1(b, k))
27.47/8.93	   A^2 -> H(U1(a, c), U1(e, c))
27.47/8.93	   A^2 -> H(U1(a, c), U1(k, c))
27.47/8.93	   A^2 -> H(U1(a, c), U1(c, e))
27.47/8.93	   A^2 -> H(U1(a, c), U1(c, k))
27.47/8.93	   A^2 -> H(U1(a, c), U1(e, e))
27.47/8.93	   A^2 -> H(U1(a, c), U1(k, k))
27.47/8.93	   A^2 -> H(U1(a, c), U1(k, d))
27.47/8.93	   A^2 -> H(U1(a, c), U1(d, k))
27.47/8.93	   A^2 -> H(U1(a, d), U1(e, b))
27.47/8.93	   A^2 -> H(U1(a, d), U1(k, b))
27.47/8.93	   A^2 -> H(U1(a, d), U1(c, d))
27.47/8.93	   A^2 -> H(U1(a, d), U1(d, c))
27.47/8.93	   A^2 -> H(U1(a, d), U1(b, e))
27.47/8.93	   A^2 -> H(U1(a, d), U1(b, k))
27.47/8.93	   A^2 -> H(U1(a, d), U1(e, c))
27.47/8.93	   A^2 -> H(U1(a, d), U1(k, c))
27.47/8.93	   A^2 -> H(U1(a, d), U1(c, e))
27.47/8.93	   A^2 -> H(U1(a, d), U1(c, k))
27.47/8.93	   A^2 -> H(U1(a, d), U1(e, e))
27.47/8.93	   A^2 -> H(U1(a, d), U1(k, k))
27.47/8.93	   A^2 -> H(U1(a, d), U1(k, d))
27.47/8.93	   A^2 -> H(U1(a, d), U1(d, k))
27.47/8.93	   A^2 -> H(U1(a, a), b)
27.47/8.93	   A^2 -> H(U1(a, a), U1(e, d))
27.47/8.93	   A^2 -> H(U1(a, a), U1(d, e))
27.47/8.93	   A^2 -> H(U1(a, a), c)
27.47/8.93	   A^2 -> H(U1(a, a), U1(e, k))
27.47/8.93	   A^2 -> H(U1(a, a), U1(k, e))
27.47/8.93	   A^2 -> H(U1(a, a), e)
27.47/8.93	   A^2 -> H(U1(a, a), U1(k, k))
27.47/8.93	   A^2 -> H(k, f(b))
27.47/8.93	   A^2 -> H(c, U1(b, b))
27.47/8.93	   A^2 -> H(c, f(c))
27.47/8.93	   A^2 -> H(c, f(d))
27.47/8.93	   A^2 -> H(U1(e, k), U1(b, b))
27.47/8.93	   A^2 -> H(U1(e, k), f(c))
27.47/8.93	   A^2 -> H(U1(e, k), f(d))
27.47/8.93	   A^2 -> H(U1(e, c), U1(c, b))
27.47/8.93	   A^2 -> H(U1(e, c), U1(d, b))
27.47/8.93	   A^2 -> H(U1(e, c), U1(b, c))
27.47/8.93	   A^2 -> H(U1(e, c), U1(b, d))
27.47/8.93	   A^2 -> H(U1(e, c), U1(c, c))
27.47/8.93	   A^2 -> H(U1(e, c), f(e))
27.47/8.93	   A^2 -> H(U1(e, c), f(k))
27.47/8.93	   A^2 -> H(U1(e, c), U1(d, d))
27.47/8.93	   A^2 -> H(U1(k, e), U1(b, b))
27.47/8.93	   A^2 -> H(U1(k, e), f(c))
27.47/8.93	   A^2 -> H(U1(k, e), f(d))
27.47/8.93	   A^2 -> H(U1(k, c), U1(c, b))
27.47/8.93	   A^2 -> H(U1(k, c), U1(d, b))
27.47/8.93	   A^2 -> H(U1(k, c), U1(b, c))
27.47/8.93	   A^2 -> H(U1(k, c), U1(b, d))
27.47/8.93	   A^2 -> H(U1(k, c), U1(c, c))
27.47/8.93	   A^2 -> H(U1(k, c), f(e))
27.47/8.93	   A^2 -> H(U1(k, c), f(k))
27.47/8.93	   A^2 -> H(U1(k, c), U1(d, d))
27.47/8.93	   A^2 -> H(U1(c, e), U1(c, b))
27.47/8.93	   A^2 -> H(U1(c, e), U1(d, b))
27.47/8.93	   A^2 -> H(U1(c, e), U1(b, c))
27.47/8.93	   A^2 -> H(U1(c, e), U1(b, d))
27.47/8.93	   A^2 -> H(U1(c, e), U1(c, c))
27.47/8.93	   A^2 -> H(U1(c, e), f(e))
27.47/8.93	   A^2 -> H(U1(c, e), f(k))
27.47/8.93	   A^2 -> H(U1(c, e), U1(d, d))
27.47/8.93	   A^2 -> H(U1(c, k), U1(c, b))
27.47/8.93	   A^2 -> H(U1(c, k), U1(d, b))
27.47/8.93	   A^2 -> H(U1(c, k), U1(b, c))
27.47/8.93	   A^2 -> H(U1(c, k), U1(b, d))
27.47/8.93	   A^2 -> H(U1(c, k), U1(c, c))
27.47/8.93	   A^2 -> H(U1(c, k), f(e))
27.47/8.93	   A^2 -> H(U1(c, k), f(k))
27.47/8.93	   A^2 -> H(U1(c, k), U1(d, d))
27.47/8.93	   A^2 -> H(U1(c, c), U1(e, b))
27.47/8.93	   A^2 -> H(U1(c, c), U1(k, b))
27.47/8.93	   A^2 -> H(U1(c, c), U1(c, d))
27.47/8.93	   A^2 -> H(U1(c, c), U1(d, c))
27.47/8.93	   A^2 -> H(U1(c, c), U1(b, e))
27.47/8.93	   A^2 -> H(U1(c, c), U1(b, k))
27.47/8.93	   A^2 -> H(U1(c, c), U1(e, e))
27.47/8.93	   A^2 -> H(U1(c, c), U1(k, k))
27.47/8.93	   A^2 -> H(U1(c, c), U1(k, d))
27.47/8.93	   A^2 -> H(U1(c, c), U1(d, k))
27.47/8.93	   A^2 -> H(e, U1(b, b))
27.47/8.93	   A^2 -> H(e, f(c))
27.47/8.93	   A^2 -> H(e, f(d))
27.47/8.93	   A^2 -> H(U1(e, e), U1(c, b))
27.47/8.93	   A^2 -> H(U1(e, e), U1(d, b))
27.47/8.93	   A^2 -> H(U1(e, e), U1(b, c))
27.47/8.93	   A^2 -> H(U1(e, e), U1(b, d))
27.47/8.93	   A^2 -> H(U1(e, e), U1(c, c))
27.47/8.93	   A^2 -> H(U1(e, e), f(e))
27.47/8.93	   A^2 -> H(U1(e, e), f(k))
27.47/8.93	   A^2 -> H(U1(e, e), U1(d, d))
27.47/8.93	   A^2 -> H(f(e), U1(e, b))
27.47/8.93	   A^2 -> H(f(e), U1(k, b))
27.47/8.93	   A^2 -> H(f(e), U1(c, d))
27.47/8.93	   A^2 -> H(f(e), U1(d, c))
27.47/8.93	   A^2 -> H(f(e), U1(b, e))
27.47/8.93	   A^2 -> H(f(e), U1(b, k))
27.47/8.93	   A^2 -> H(f(e), U1(e, c))
27.47/8.93	   A^2 -> H(f(e), U1(k, c))
27.47/8.93	   A^2 -> H(f(e), U1(c, e))
27.47/8.93	   A^2 -> H(f(e), U1(c, k))
27.47/8.93	   A^2 -> H(f(e), U1(k, k))
27.47/8.93	   A^2 -> H(f(e), U1(k, d))
27.47/8.93	   A^2 -> H(f(e), U1(d, k))
27.47/8.93	   A^2 -> H(U1(k, k), U1(c, b))
27.47/8.93	   A^2 -> H(U1(k, k), U1(d, b))
27.47/8.93	   A^2 -> H(U1(k, k), U1(b, c))
27.47/8.93	   A^2 -> H(U1(k, k), U1(b, d))
27.47/8.93	   A^2 -> H(U1(k, k), U1(c, c))
27.47/8.93	   A^2 -> H(U1(k, k), f(e))
27.47/8.93	   A^2 -> H(U1(k, k), f(k))
27.47/8.93	   A^2 -> H(U1(k, k), U1(d, d))
27.47/8.93	   A^2 -> H(f(k), U1(e, b))
27.47/8.93	   A^2 -> H(f(k), U1(k, b))
27.47/8.93	   A^2 -> H(f(k), U1(c, d))
27.47/8.93	   A^2 -> H(f(k), U1(d, c))
27.47/8.93	   A^2 -> H(f(k), U1(b, e))
27.47/8.93	   A^2 -> H(f(k), U1(b, k))
27.47/8.93	   A^2 -> H(f(k), U1(e, c))
27.47/8.93	   A^2 -> H(f(k), U1(k, c))
27.47/8.93	   A^2 -> H(f(k), U1(c, e))
27.47/8.93	   A^2 -> H(f(k), U1(c, k))
27.47/8.93	   A^2 -> H(f(k), U1(e, e))
27.47/8.93	   A^2 -> H(f(k), U1(k, d))
27.47/8.93	   A^2 -> H(f(k), U1(d, k))
27.47/8.93	   A^2 -> H(f(c), b)
27.47/8.93	   A^2 -> H(f(c), U1(e, d))
27.47/8.93	   A^2 -> H(f(c), U1(d, e))
27.47/8.93	   A^2 -> H(f(k), U1(k, k))
27.47/8.93	   A^2 -> H(U1(k, k), U1(b, b))
27.47/8.93	   A^2 -> H(U1(k, k), f(c))
27.47/8.93	   A^2 -> H(U1(k, k), f(d))
27.47/8.93	   A^2 -> H(U1(k, d), U1(c, b))
27.47/8.93	   A^2 -> H(U1(k, d), U1(d, b))
27.47/8.93	   A^2 -> H(U1(k, d), U1(b, c))
27.47/8.93	   A^2 -> H(U1(k, d), U1(b, d))
27.47/8.93	   A^2 -> H(U1(k, d), U1(c, c))
27.47/8.93	   A^2 -> H(U1(k, d), f(e))
27.47/8.93	   A^2 -> H(U1(k, d), f(k))
27.47/8.93	   A^2 -> H(U1(k, d), U1(d, d))
27.47/8.93	   A^2 -> H(U1(d, k), U1(c, b))
27.47/8.93	   A^2 -> H(U1(d, k), U1(d, b))
27.47/8.93	   A^2 -> H(U1(d, k), U1(b, c))
27.47/8.93	   A^2 -> H(U1(d, k), U1(b, d))
27.47/8.93	   A^2 -> H(U1(d, k), U1(c, c))
27.47/8.93	   A^2 -> H(U1(d, k), f(e))
27.47/8.93	   A^2 -> H(U1(d, k), f(k))
27.47/8.93	   A^2 -> H(U1(d, k), U1(d, d))
27.47/8.93	   A^2 -> H(U1(d, d), U1(e, b))
27.47/8.93	   A^2 -> H(U1(d, d), U1(k, b))
27.47/8.93	   A^2 -> H(U1(d, d), U1(c, d))
27.47/8.93	   A^2 -> H(U1(d, d), U1(d, c))
27.47/8.93	   A^2 -> H(U1(d, d), U1(b, e))
27.47/8.93	   A^2 -> H(U1(d, d), U1(b, k))
27.47/8.93	   A^2 -> H(U1(d, d), U1(e, c))
27.47/8.93	   A^2 -> H(U1(d, d), U1(k, c))
27.47/8.93	   A^2 -> H(U1(d, d), U1(c, e))
27.47/8.93	   A^2 -> H(U1(d, d), U1(c, k))
27.47/8.93	   A^2 -> H(U1(d, d), U1(e, e))
27.47/8.93	   A^2 -> H(U1(d, d), U1(k, k))
27.47/8.93	   A^2 -> H(f(d), b)
27.47/8.93	   A^2 -> H(f(d), U1(e, d))
27.47/8.93	   A^2 -> H(f(d), U1(d, e))
27.47/8.93	   A^2 -> H(f(d), c)
27.47/8.93	   A^2 -> H(f(d), U1(e, k))
27.47/8.93	   A^2 -> H(f(d), U1(k, e))
27.47/8.93	   A^2 -> H(f(d), e)
27.47/8.93	   A^2 -> H(f(a), d)
27.47/8.93	   A^2 -> H(U1(c, c), U1(e, c))
27.47/8.93	   A^2 -> H(f(c), c)
27.47/8.93	   A^2 -> H(f(c), U1(e, k))
27.47/8.93	   A^2 -> H(U1(c, c), U1(k, c))
27.47/8.93	   A^2 -> H(f(c), U1(k, e))
27.47/8.93	   A^2 -> H(f(c), U1(k, k))
27.47/8.93	   A^2 -> H(U1(c, c), U1(c, e))
27.47/8.93	   A^2 -> H(U1(c, c), U1(c, k))
27.47/8.93	   A^2 -> H(f(a), k)
27.47/8.93	   A^2 -> H(f(e), U1(e, e))
27.47/8.93	   A^2 -> H(f(c), e)
27.47/8.93	   A^2 -> H(U1(d, d), U1(k, d))
27.47/8.93	   A^2 -> H(f(d), U1(k, k))
27.47/8.93	   A^2 -> H(U1(d, d), U1(d, k))
27.47/8.93	   A^2 -> H(d, U1(b, b))
27.47/8.93	   A^2 -> H(d, f(c))
27.47/8.93	   A^2 -> H(d, f(d))
27.47/8.93	   A^2 -> H(a, U1(c, b))
27.47/8.93	   A^2 -> H(a, U1(d, b))
27.47/8.93	   A^2 -> H(a, U1(b, c))
27.47/8.93	   A^2 -> H(a, U1(b, d))
27.47/8.93	   A^2 -> H(a, U1(c, c))
27.47/8.93	   A^2 -> H(a, f(e))
27.47/8.93	   A^2 -> H(a, f(k))
27.47/8.93	   A^2 -> H(a, U1(d, d))
27.47/8.93	   A^2 -> H(U1(e, d), U1(c, b))
27.47/8.93	   A^2 -> H(U1(e, d), U1(d, b))
27.47/8.93	   A^2 -> H(U1(e, d), U1(b, c))
27.47/8.93	   A^2 -> H(U1(e, d), U1(b, d))
27.47/8.93	   A^2 -> H(U1(e, d), U1(c, c))
27.47/8.93	   A^2 -> H(U1(e, d), f(e))
27.47/8.93	   A^2 -> H(U1(e, d), f(k))
27.47/8.93	   A^2 -> H(U1(e, d), U1(d, d))
27.47/8.93	   A^2 -> H(U1(e, a), U1(e, b))
27.47/8.93	   A^2 -> H(U1(e, a), U1(k, b))
27.47/8.93	   A^2 -> H(U1(e, a), U1(c, d))
27.47/8.93	   A^2 -> H(U1(e, a), U1(d, c))
27.47/8.93	   A^2 -> H(U1(e, a), U1(b, e))
27.47/8.93	   A^2 -> H(U1(e, a), U1(b, k))
27.47/8.93	   A^2 -> H(U1(e, a), U1(e, c))
27.47/8.93	   A^2 -> H(U1(e, a), U1(k, c))
27.47/8.93	   A^2 -> H(U1(e, a), U1(c, e))
27.47/8.93	   A^2 -> H(U1(e, a), U1(c, k))
27.47/8.93	   A^2 -> H(U1(e, a), U1(e, e))
27.47/8.93	   A^2 -> H(U1(e, a), U1(k, k))
27.47/8.93	   A^2 -> H(U1(e, a), U1(k, d))
27.47/8.93	   A^2 -> H(U1(e, a), U1(d, k))
27.47/8.93	   A^2 -> H(U1(k, a), U1(e, b))
27.47/8.93	   A^2 -> H(U1(k, a), U1(k, b))
27.47/8.93	   A^2 -> H(U1(k, a), U1(c, d))
27.47/8.93	   A^2 -> H(U1(k, a), U1(d, c))
27.47/8.93	   A^2 -> H(U1(k, a), U1(b, e))
27.47/8.93	   A^2 -> H(U1(k, a), U1(b, k))
27.47/8.93	   A^2 -> H(U1(k, a), U1(e, c))
27.47/8.93	   A^2 -> H(U1(k, a), U1(k, c))
27.47/8.93	   A^2 -> H(U1(k, a), U1(c, e))
27.47/8.93	   A^2 -> H(U1(k, a), U1(c, k))
27.47/8.93	   A^2 -> H(U1(k, a), U1(e, e))
27.47/8.93	   A^2 -> H(U1(k, a), U1(k, k))
27.47/8.93	   A^2 -> H(U1(k, a), U1(k, d))
27.47/8.93	   A^2 -> H(U1(k, a), U1(d, k))
27.47/8.93	   A^2 -> H(U1(c, d), U1(e, b))
27.47/8.93	   A^2 -> H(U1(c, d), U1(k, b))
27.47/8.93	   A^2 -> H(U1(c, d), U1(c, d))
27.47/8.93	   A^2 -> H(U1(c, d), U1(d, c))
27.47/8.93	   A^2 -> H(U1(c, d), U1(b, e))
27.47/8.93	   A^2 -> H(U1(c, d), U1(b, k))
27.47/8.93	   A^2 -> H(U1(c, d), U1(e, c))
27.47/8.93	   A^2 -> H(U1(c, d), U1(k, c))
27.47/8.93	   A^2 -> H(U1(c, d), U1(c, e))
27.47/8.93	   A^2 -> H(U1(c, d), U1(c, k))
27.47/8.93	   A^2 -> H(U1(c, d), U1(e, e))
27.47/8.93	   A^2 -> H(U1(c, d), U1(k, k))
27.47/8.93	   A^2 -> H(U1(c, d), U1(k, d))
27.47/8.93	   A^2 -> H(U1(c, d), U1(d, k))
27.47/8.93	   A^2 -> H(U1(c, a), b)
27.47/8.93	   A^2 -> H(U1(c, a), U1(e, d))
27.47/8.93	   A^2 -> H(U1(c, a), U1(d, e))
27.47/8.93	   A^2 -> H(U1(c, a), c)
27.47/8.93	   A^2 -> H(U1(c, a), U1(e, k))
27.47/8.93	   A^2 -> H(U1(c, a), U1(k, e))
27.47/8.93	   A^2 -> H(U1(c, a), e)
27.47/8.93	   A^2 -> H(U1(c, a), U1(k, k))
27.47/8.93	   A^2 -> H(U1(d, e), U1(c, b))
27.47/8.93	   A^2 -> H(U1(d, e), U1(d, b))
27.47/8.93	   A^2 -> H(U1(d, e), U1(b, c))
27.47/8.93	   A^2 -> H(U1(d, e), U1(b, d))
27.47/8.93	   A^2 -> H(U1(d, e), U1(c, c))
27.47/8.93	   A^2 -> H(U1(d, e), f(e))
27.47/8.93	   A^2 -> H(U1(d, e), f(k))
27.47/8.93	   A^2 -> H(U1(d, e), U1(d, d))
27.47/8.93	   A^2 -> H(U1(d, c), U1(e, b))
27.47/8.93	   A^2 -> H(U1(d, c), U1(k, b))
27.47/8.93	   A^2 -> H(U1(d, c), U1(c, d))
27.47/8.93	
27.47/8.93	The TRS R consists of the following rules:
27.47/8.93	
27.47/8.93	   f(x) -> U1(x, x)
27.47/8.93	   U1(e, x) -> x
27.47/8.93	   a -> c
27.47/8.93	   a -> d
27.47/8.93	   b -> c
27.47/8.93	   b -> d
27.47/8.93	   d -> k
27.47/8.93	   c -> e
27.47/8.93	   c -> k
27.47/8.93	
27.47/8.93	Q is empty.
27.47/8.93	We have to consider all minimal (P,Q,R)-chains.
27.47/8.93	----------------------------------------
27.47/8.93	
27.47/8.93	(639) TransformationProof (EQUIVALENT)
27.47/8.93	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
27.56/8.95	
27.56/8.95	   (A^2 -> H(U1(k, c), U1(d, b)),A^2 -> H(U1(k, c), U1(d, b)))
27.56/8.95	   (A^2 -> H(U1(d, e), U1(d, b)),A^2 -> H(U1(d, e), U1(d, b)))
27.56/8.95	   (A^2 -> H(U1(d, k), U1(d, b)),A^2 -> H(U1(d, k), U1(d, b)))
27.56/8.95	   (A^2 -> H(U1(d, c), U1(k, b)),A^2 -> H(U1(d, c), U1(k, b)))
27.56/8.95	   (A^2 -> H(U1(d, c), U1(d, c)),A^2 -> H(U1(d, c), U1(d, c)))
27.56/8.95	   (A^2 -> H(U1(d, c), U1(d, d)),A^2 -> H(U1(d, c), U1(d, d)))
27.56/8.95	
27.56/8.95	
27.56/8.95	----------------------------------------
27.56/8.95	
27.56/8.95	(640)
27.56/8.95	Obligation:
27.56/8.95	Q DP problem:
27.56/8.95	The TRS P consists of the following rules:
27.56/8.95	
27.56/8.95	   H(x, x) -> G(x, x, f(k))
27.56/8.95	   G(d, x, x) -> A^2
27.56/8.95	   A^2 -> H(f(c), f(c))
27.56/8.95	   A^2 -> H(f(d), f(d))
27.56/8.95	   A^2 -> H(U1(c, c), U1(c, c))
27.56/8.95	   A^2 -> H(f(e), f(e))
27.56/8.95	   A^2 -> H(f(k), f(k))
27.56/8.95	   A^2 -> H(U1(d, d), U1(d, d))
27.56/8.95	   A^2 -> H(U1(d, c), U1(b, c))
27.56/8.95	   A^2 -> H(U1(d, c), U1(b, d))
27.56/8.95	   A^2 -> H(U1(d, c), U1(c, c))
27.56/8.95	   A^2 -> H(U1(d, c), f(e))
27.56/8.95	   A^2 -> H(U1(d, c), f(k))
27.56/8.95	   A^2 -> H(U1(d, c), U1(d, d))
27.56/8.95	   A^2 -> H(U1(d, a), U1(e, b))
27.56/8.95	   A^2 -> H(U1(d, a), U1(k, b))
27.56/8.95	   A^2 -> H(U1(d, a), U1(c, d))
27.56/8.95	   A^2 -> H(U1(d, a), U1(d, c))
27.56/8.95	   A^2 -> H(U1(d, a), U1(b, e))
27.56/8.95	   A^2 -> H(U1(d, a), U1(b, k))
27.56/8.95	   A^2 -> H(U1(d, a), U1(e, c))
27.56/8.95	   A^2 -> H(U1(d, a), U1(k, c))
27.56/8.95	   A^2 -> H(U1(d, a), U1(c, e))
27.56/8.95	   A^2 -> H(U1(d, a), U1(c, k))
27.56/8.95	   A^2 -> H(U1(d, a), U1(e, e))
27.56/8.95	   A^2 -> H(U1(d, a), U1(k, k))
27.56/8.95	   A^2 -> H(U1(d, a), U1(k, d))
27.56/8.95	   A^2 -> H(U1(d, a), U1(d, k))
27.56/8.95	   A^2 -> H(U1(a, e), U1(c, b))
27.56/8.95	   A^2 -> H(U1(a, e), U1(d, b))
27.56/8.95	   A^2 -> H(U1(a, e), U1(b, c))
27.56/8.95	   A^2 -> H(U1(a, e), U1(b, d))
27.56/8.95	   A^2 -> H(U1(a, e), U1(c, c))
27.56/8.95	   A^2 -> H(U1(a, e), f(e))
27.56/8.95	   A^2 -> H(U1(a, e), f(k))
27.56/8.95	   A^2 -> H(U1(a, e), U1(d, d))
27.56/8.95	   A^2 -> H(U1(a, k), U1(c, b))
27.56/8.95	   A^2 -> H(U1(a, k), U1(d, b))
27.56/8.95	   A^2 -> H(U1(a, k), U1(b, c))
27.56/8.95	   A^2 -> H(U1(a, k), U1(b, d))
27.56/8.95	   A^2 -> H(U1(a, k), U1(c, c))
27.56/8.95	   A^2 -> H(U1(a, k), f(e))
27.56/8.95	   A^2 -> H(U1(a, k), f(k))
27.56/8.95	   A^2 -> H(U1(a, k), U1(d, d))
27.56/8.95	   A^2 -> H(U1(a, c), U1(e, b))
27.56/8.95	   A^2 -> H(U1(a, c), U1(k, b))
27.56/8.95	   A^2 -> H(U1(a, c), U1(c, d))
27.56/8.95	   A^2 -> H(U1(a, c), U1(d, c))
27.56/8.95	   A^2 -> H(U1(a, c), U1(b, e))
27.56/8.95	   A^2 -> H(U1(a, c), U1(b, k))
27.56/8.95	   A^2 -> H(U1(a, c), U1(e, c))
27.56/8.95	   A^2 -> H(U1(a, c), U1(k, c))
27.56/8.95	   A^2 -> H(U1(a, c), U1(c, e))
27.56/8.95	   A^2 -> H(U1(a, c), U1(c, k))
27.56/8.95	   A^2 -> H(U1(a, c), U1(e, e))
27.56/8.95	   A^2 -> H(U1(a, c), U1(k, k))
27.56/8.95	   A^2 -> H(U1(a, c), U1(k, d))
27.56/8.95	   A^2 -> H(U1(a, c), U1(d, k))
27.56/8.95	   A^2 -> H(U1(a, d), U1(e, b))
27.56/8.95	   A^2 -> H(U1(a, d), U1(k, b))
27.56/8.95	   A^2 -> H(U1(a, d), U1(c, d))
27.56/8.95	   A^2 -> H(U1(a, d), U1(d, c))
27.56/8.95	   A^2 -> H(U1(a, d), U1(b, e))
27.56/8.95	   A^2 -> H(U1(a, d), U1(b, k))
27.56/8.95	   A^2 -> H(U1(a, d), U1(e, c))
27.56/8.95	   A^2 -> H(U1(a, d), U1(k, c))
27.56/8.95	   A^2 -> H(U1(a, d), U1(c, e))
27.56/8.95	   A^2 -> H(U1(a, d), U1(c, k))
27.56/8.95	   A^2 -> H(U1(a, d), U1(e, e))
27.56/8.95	   A^2 -> H(U1(a, d), U1(k, k))
27.56/8.95	   A^2 -> H(U1(a, d), U1(k, d))
27.56/8.95	   A^2 -> H(U1(a, d), U1(d, k))
27.56/8.95	   A^2 -> H(U1(a, a), b)
27.56/8.95	   A^2 -> H(U1(a, a), U1(e, d))
27.56/8.95	   A^2 -> H(U1(a, a), U1(d, e))
27.56/8.95	   A^2 -> H(U1(a, a), c)
27.56/8.95	   A^2 -> H(U1(a, a), U1(e, k))
27.56/8.95	   A^2 -> H(U1(a, a), U1(k, e))
27.56/8.95	   A^2 -> H(U1(a, a), e)
27.56/8.95	   A^2 -> H(U1(a, a), U1(k, k))
27.56/8.95	   A^2 -> H(k, f(b))
27.56/8.95	   A^2 -> H(c, U1(b, b))
27.56/8.95	   A^2 -> H(c, f(c))
27.56/8.95	   A^2 -> H(c, f(d))
27.56/8.95	   A^2 -> H(U1(e, k), U1(b, b))
27.56/8.95	   A^2 -> H(U1(e, k), f(c))
27.56/8.95	   A^2 -> H(U1(e, k), f(d))
27.56/8.95	   A^2 -> H(U1(e, c), U1(c, b))
27.56/8.95	   A^2 -> H(U1(e, c), U1(d, b))
27.56/8.95	   A^2 -> H(U1(e, c), U1(b, c))
27.56/8.95	   A^2 -> H(U1(e, c), U1(b, d))
27.56/8.95	   A^2 -> H(U1(e, c), U1(c, c))
27.56/8.95	   A^2 -> H(U1(e, c), f(e))
27.56/8.95	   A^2 -> H(U1(e, c), f(k))
27.56/8.95	   A^2 -> H(U1(e, c), U1(d, d))
27.56/8.95	   A^2 -> H(U1(k, e), U1(b, b))
27.56/8.95	   A^2 -> H(U1(k, e), f(c))
27.56/8.95	   A^2 -> H(U1(k, e), f(d))
27.56/8.95	   A^2 -> H(U1(k, c), U1(c, b))
27.56/8.95	   A^2 -> H(U1(k, c), U1(d, b))
27.56/8.95	   A^2 -> H(U1(k, c), U1(b, c))
27.56/8.95	   A^2 -> H(U1(k, c), U1(b, d))
27.56/8.95	   A^2 -> H(U1(k, c), U1(c, c))
27.56/8.95	   A^2 -> H(U1(k, c), f(e))
27.56/8.95	   A^2 -> H(U1(k, c), f(k))
27.56/8.95	   A^2 -> H(U1(k, c), U1(d, d))
27.56/8.95	   A^2 -> H(U1(c, e), U1(c, b))
27.56/8.95	   A^2 -> H(U1(c, e), U1(d, b))
27.56/8.95	   A^2 -> H(U1(c, e), U1(b, c))
27.56/8.95	   A^2 -> H(U1(c, e), U1(b, d))
27.56/8.95	   A^2 -> H(U1(c, e), U1(c, c))
27.56/8.95	   A^2 -> H(U1(c, e), f(e))
27.56/8.95	   A^2 -> H(U1(c, e), f(k))
27.56/8.95	   A^2 -> H(U1(c, e), U1(d, d))
27.56/8.95	   A^2 -> H(U1(c, k), U1(c, b))
27.56/8.95	   A^2 -> H(U1(c, k), U1(d, b))
27.56/8.95	   A^2 -> H(U1(c, k), U1(b, c))
27.56/8.95	   A^2 -> H(U1(c, k), U1(b, d))
27.56/8.95	   A^2 -> H(U1(c, k), U1(c, c))
27.56/8.95	   A^2 -> H(U1(c, k), f(e))
27.56/8.95	   A^2 -> H(U1(c, k), f(k))
27.56/8.95	   A^2 -> H(U1(c, k), U1(d, d))
27.56/8.95	   A^2 -> H(U1(c, c), U1(e, b))
27.56/8.95	   A^2 -> H(U1(c, c), U1(k, b))
27.56/8.95	   A^2 -> H(U1(c, c), U1(c, d))
27.56/8.95	   A^2 -> H(U1(c, c), U1(d, c))
27.56/8.95	   A^2 -> H(U1(c, c), U1(b, e))
27.56/8.95	   A^2 -> H(U1(c, c), U1(b, k))
27.56/8.95	   A^2 -> H(U1(c, c), U1(e, e))
27.56/8.95	   A^2 -> H(U1(c, c), U1(k, k))
27.56/8.95	   A^2 -> H(U1(c, c), U1(k, d))
27.56/8.95	   A^2 -> H(U1(c, c), U1(d, k))
27.56/8.95	   A^2 -> H(e, U1(b, b))
27.56/8.95	   A^2 -> H(e, f(c))
27.56/8.95	   A^2 -> H(e, f(d))
27.56/8.95	   A^2 -> H(U1(e, e), U1(c, b))
27.56/8.95	   A^2 -> H(U1(e, e), U1(d, b))
27.56/8.95	   A^2 -> H(U1(e, e), U1(b, c))
27.56/8.95	   A^2 -> H(U1(e, e), U1(b, d))
27.56/8.95	   A^2 -> H(U1(e, e), U1(c, c))
27.56/8.95	   A^2 -> H(U1(e, e), f(e))
27.56/8.95	   A^2 -> H(U1(e, e), f(k))
27.56/8.95	   A^2 -> H(U1(e, e), U1(d, d))
27.56/8.95	   A^2 -> H(f(e), U1(e, b))
27.56/8.95	   A^2 -> H(f(e), U1(k, b))
27.56/8.95	   A^2 -> H(f(e), U1(c, d))
27.56/8.95	   A^2 -> H(f(e), U1(d, c))
27.56/8.95	   A^2 -> H(f(e), U1(b, e))
27.56/8.95	   A^2 -> H(f(e), U1(b, k))
27.56/8.95	   A^2 -> H(f(e), U1(e, c))
27.56/8.95	   A^2 -> H(f(e), U1(k, c))
27.56/8.95	   A^2 -> H(f(e), U1(c, e))
27.56/8.95	   A^2 -> H(f(e), U1(c, k))
27.56/8.95	   A^2 -> H(f(e), U1(k, k))
27.56/8.95	   A^2 -> H(f(e), U1(k, d))
27.56/8.95	   A^2 -> H(f(e), U1(d, k))
27.56/8.95	   A^2 -> H(U1(k, k), U1(c, b))
27.56/8.95	   A^2 -> H(U1(k, k), U1(d, b))
27.56/8.95	   A^2 -> H(U1(k, k), U1(b, c))
27.56/8.95	   A^2 -> H(U1(k, k), U1(b, d))
27.56/8.95	   A^2 -> H(U1(k, k), U1(c, c))
27.56/8.95	   A^2 -> H(U1(k, k), f(e))
27.56/8.95	   A^2 -> H(U1(k, k), f(k))
27.56/8.95	   A^2 -> H(U1(k, k), U1(d, d))
27.56/8.95	   A^2 -> H(f(k), U1(e, b))
27.56/8.95	   A^2 -> H(f(k), U1(k, b))
27.56/8.95	   A^2 -> H(f(k), U1(c, d))
27.56/8.95	   A^2 -> H(f(k), U1(d, c))
27.56/8.95	   A^2 -> H(f(k), U1(b, e))
27.56/8.95	   A^2 -> H(f(k), U1(b, k))
27.56/8.95	   A^2 -> H(f(k), U1(e, c))
27.56/8.95	   A^2 -> H(f(k), U1(k, c))
27.56/8.95	   A^2 -> H(f(k), U1(c, e))
27.56/8.95	   A^2 -> H(f(k), U1(c, k))
27.56/8.95	   A^2 -> H(f(k), U1(e, e))
27.56/8.95	   A^2 -> H(f(k), U1(k, d))
27.56/8.95	   A^2 -> H(f(k), U1(d, k))
27.56/8.95	   A^2 -> H(f(c), b)
27.56/8.95	   A^2 -> H(f(c), U1(e, d))
27.56/8.95	   A^2 -> H(f(c), U1(d, e))
27.56/8.95	   A^2 -> H(f(k), U1(k, k))
27.56/8.95	   A^2 -> H(U1(k, k), U1(b, b))
27.56/8.95	   A^2 -> H(U1(k, k), f(c))
27.56/8.95	   A^2 -> H(U1(k, k), f(d))
27.56/8.95	   A^2 -> H(U1(k, d), U1(c, b))
27.56/8.95	   A^2 -> H(U1(k, d), U1(d, b))
27.56/8.95	   A^2 -> H(U1(k, d), U1(b, c))
27.56/8.95	   A^2 -> H(U1(k, d), U1(b, d))
27.56/8.95	   A^2 -> H(U1(k, d), U1(c, c))
27.56/8.95	   A^2 -> H(U1(k, d), f(e))
27.56/8.95	   A^2 -> H(U1(k, d), f(k))
27.56/8.95	   A^2 -> H(U1(k, d), U1(d, d))
27.56/8.95	   A^2 -> H(U1(d, k), U1(c, b))
27.56/8.95	   A^2 -> H(U1(d, k), U1(d, b))
27.56/8.95	   A^2 -> H(U1(d, k), U1(b, c))
27.56/8.95	   A^2 -> H(U1(d, k), U1(b, d))
27.56/8.95	   A^2 -> H(U1(d, k), U1(c, c))
27.56/8.95	   A^2 -> H(U1(d, k), f(e))
27.56/8.95	   A^2 -> H(U1(d, k), f(k))
27.56/8.95	   A^2 -> H(U1(d, k), U1(d, d))
27.56/8.95	   A^2 -> H(U1(d, d), U1(e, b))
27.56/8.95	   A^2 -> H(U1(d, d), U1(k, b))
27.56/8.95	   A^2 -> H(U1(d, d), U1(c, d))
27.56/8.95	   A^2 -> H(U1(d, d), U1(d, c))
27.56/8.95	   A^2 -> H(U1(d, d), U1(b, e))
27.56/8.95	   A^2 -> H(U1(d, d), U1(b, k))
27.56/8.95	   A^2 -> H(U1(d, d), U1(e, c))
27.56/8.95	   A^2 -> H(U1(d, d), U1(k, c))
27.56/8.95	   A^2 -> H(U1(d, d), U1(c, e))
27.56/8.95	   A^2 -> H(U1(d, d), U1(c, k))
27.56/8.95	   A^2 -> H(U1(d, d), U1(e, e))
27.56/8.95	   A^2 -> H(U1(d, d), U1(k, k))
27.56/8.95	   A^2 -> H(f(d), b)
27.56/8.95	   A^2 -> H(f(d), U1(e, d))
27.56/8.95	   A^2 -> H(f(d), U1(d, e))
27.56/8.95	   A^2 -> H(f(d), c)
27.56/8.95	   A^2 -> H(f(d), U1(e, k))
27.56/8.95	   A^2 -> H(f(d), U1(k, e))
27.56/8.95	   A^2 -> H(f(d), e)
27.56/8.95	   A^2 -> H(f(a), d)
27.56/8.95	   A^2 -> H(U1(c, c), U1(e, c))
27.56/8.95	   A^2 -> H(f(c), c)
27.56/8.95	   A^2 -> H(f(c), U1(e, k))
27.56/8.95	   A^2 -> H(U1(c, c), U1(k, c))
27.56/8.95	   A^2 -> H(f(c), U1(k, e))
27.56/8.95	   A^2 -> H(f(c), U1(k, k))
27.56/8.95	   A^2 -> H(U1(c, c), U1(c, e))
27.56/8.95	   A^2 -> H(U1(c, c), U1(c, k))
27.56/8.95	   A^2 -> H(f(a), k)
27.56/8.95	   A^2 -> H(f(e), U1(e, e))
27.56/8.95	   A^2 -> H(f(c), e)
27.56/8.95	   A^2 -> H(U1(d, d), U1(k, d))
27.56/8.95	   A^2 -> H(f(d), U1(k, k))
27.56/8.95	   A^2 -> H(U1(d, d), U1(d, k))
27.56/8.95	   A^2 -> H(d, U1(b, b))
27.56/8.95	   A^2 -> H(d, f(c))
27.56/8.95	   A^2 -> H(d, f(d))
27.56/8.95	   A^2 -> H(a, U1(c, b))
27.56/8.95	   A^2 -> H(a, U1(d, b))
27.56/8.95	   A^2 -> H(a, U1(b, c))
27.56/8.95	   A^2 -> H(a, U1(b, d))
27.56/8.95	   A^2 -> H(a, U1(c, c))
27.56/8.95	   A^2 -> H(a, f(e))
27.56/8.95	   A^2 -> H(a, f(k))
27.56/8.95	   A^2 -> H(a, U1(d, d))
27.56/8.95	   A^2 -> H(U1(e, d), U1(c, b))
27.56/8.95	   A^2 -> H(U1(e, d), U1(d, b))
27.56/8.95	   A^2 -> H(U1(e, d), U1(b, c))
27.56/8.95	   A^2 -> H(U1(e, d), U1(b, d))
27.56/8.95	   A^2 -> H(U1(e, d), U1(c, c))
27.56/8.95	   A^2 -> H(U1(e, d), f(e))
27.56/8.95	   A^2 -> H(U1(e, d), f(k))
27.56/8.95	   A^2 -> H(U1(e, d), U1(d, d))
27.56/8.95	   A^2 -> H(U1(e, a), U1(e, b))
27.56/8.95	   A^2 -> H(U1(e, a), U1(k, b))
27.56/8.95	   A^2 -> H(U1(e, a), U1(c, d))
27.56/8.95	   A^2 -> H(U1(e, a), U1(d, c))
27.56/8.95	   A^2 -> H(U1(e, a), U1(b, e))
27.56/8.95	   A^2 -> H(U1(e, a), U1(b, k))
27.56/8.95	   A^2 -> H(U1(e, a), U1(e, c))
27.56/8.95	   A^2 -> H(U1(e, a), U1(k, c))
27.56/8.95	   A^2 -> H(U1(e, a), U1(c, e))
27.56/8.95	   A^2 -> H(U1(e, a), U1(c, k))
27.56/8.95	   A^2 -> H(U1(e, a), U1(e, e))
27.56/8.95	   A^2 -> H(U1(e, a), U1(k, k))
27.56/8.95	   A^2 -> H(U1(e, a), U1(k, d))
27.56/8.95	   A^2 -> H(U1(e, a), U1(d, k))
27.56/8.95	   A^2 -> H(U1(k, a), U1(e, b))
27.56/8.95	   A^2 -> H(U1(k, a), U1(k, b))
27.56/8.95	   A^2 -> H(U1(k, a), U1(c, d))
27.56/8.95	   A^2 -> H(U1(k, a), U1(d, c))
27.56/8.95	   A^2 -> H(U1(k, a), U1(b, e))
27.56/8.95	   A^2 -> H(U1(k, a), U1(b, k))
27.56/8.95	   A^2 -> H(U1(k, a), U1(e, c))
27.56/8.95	   A^2 -> H(U1(k, a), U1(k, c))
27.56/8.95	   A^2 -> H(U1(k, a), U1(c, e))
27.56/8.95	   A^2 -> H(U1(k, a), U1(c, k))
27.56/8.95	   A^2 -> H(U1(k, a), U1(e, e))
27.56/8.95	   A^2 -> H(U1(k, a), U1(k, k))
27.56/8.95	   A^2 -> H(U1(k, a), U1(k, d))
27.56/8.95	   A^2 -> H(U1(k, a), U1(d, k))
27.56/8.95	   A^2 -> H(U1(c, d), U1(e, b))
27.56/8.95	   A^2 -> H(U1(c, d), U1(k, b))
27.56/8.95	   A^2 -> H(U1(c, d), U1(c, d))
27.56/8.95	   A^2 -> H(U1(c, d), U1(d, c))
27.56/8.95	   A^2 -> H(U1(c, d), U1(b, e))
27.56/8.95	   A^2 -> H(U1(c, d), U1(b, k))
27.56/8.95	   A^2 -> H(U1(c, d), U1(e, c))
27.56/8.95	   A^2 -> H(U1(c, d), U1(k, c))
27.56/8.95	   A^2 -> H(U1(c, d), U1(c, e))
27.56/8.95	   A^2 -> H(U1(c, d), U1(c, k))
27.56/8.95	   A^2 -> H(U1(c, d), U1(e, e))
27.56/8.95	   A^2 -> H(U1(c, d), U1(k, k))
27.56/8.95	   A^2 -> H(U1(c, d), U1(k, d))
27.56/8.95	   A^2 -> H(U1(c, d), U1(d, k))
27.56/8.95	   A^2 -> H(U1(c, a), b)
27.56/8.95	   A^2 -> H(U1(c, a), U1(e, d))
27.56/8.95	   A^2 -> H(U1(c, a), U1(d, e))
27.56/8.95	   A^2 -> H(U1(c, a), c)
27.56/8.95	   A^2 -> H(U1(c, a), U1(e, k))
27.56/8.95	   A^2 -> H(U1(c, a), U1(k, e))
27.56/8.95	   A^2 -> H(U1(c, a), e)
27.56/8.95	   A^2 -> H(U1(c, a), U1(k, k))
27.56/8.95	   A^2 -> H(U1(d, e), U1(c, b))
27.56/8.95	   A^2 -> H(U1(d, e), U1(d, b))
27.56/8.95	   A^2 -> H(U1(d, e), U1(b, c))
27.56/8.95	   A^2 -> H(U1(d, e), U1(b, d))
27.56/8.95	   A^2 -> H(U1(d, e), U1(c, c))
27.56/8.95	   A^2 -> H(U1(d, e), f(e))
27.56/8.95	   A^2 -> H(U1(d, e), f(k))
27.56/8.95	   A^2 -> H(U1(d, e), U1(d, d))
27.56/8.95	   A^2 -> H(U1(d, c), U1(e, b))
27.56/8.95	   A^2 -> H(U1(d, c), U1(k, b))
27.56/8.95	   A^2 -> H(U1(d, c), U1(c, d))
27.56/8.95	   A^2 -> H(U1(d, c), U1(d, c))
27.56/8.95	
27.56/8.95	The TRS R consists of the following rules:
27.56/8.95	
27.56/8.95	   f(x) -> U1(x, x)
27.56/8.95	   U1(e, x) -> x
27.56/8.95	   a -> c
27.56/8.95	   a -> d
27.56/8.95	   b -> c
27.56/8.95	   b -> d
27.56/8.95	   d -> k
27.56/8.95	   c -> e
27.56/8.95	   c -> k
27.56/8.95	
27.56/8.95	Q is empty.
27.56/8.95	We have to consider all minimal (P,Q,R)-chains.
27.56/8.95	----------------------------------------
27.56/8.95	
27.56/8.95	(641) TransformationProof (EQUIVALENT)
27.56/8.95	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
27.56/8.95	
27.56/8.95	   (A^2 -> H(U1(k, c), U1(b, c)),A^2 -> H(U1(k, c), U1(b, c)))
27.56/8.95	   (A^2 -> H(U1(d, e), U1(b, c)),A^2 -> H(U1(d, e), U1(b, c)))
27.56/8.95	   (A^2 -> H(U1(d, k), U1(b, c)),A^2 -> H(U1(d, k), U1(b, c)))
27.56/8.95	   (A^2 -> H(U1(d, c), U1(c, c)),A^2 -> H(U1(d, c), U1(c, c)))
27.56/8.95	   (A^2 -> H(U1(d, c), U1(d, c)),A^2 -> H(U1(d, c), U1(d, c)))
27.56/8.95	   (A^2 -> H(U1(d, c), U1(b, e)),A^2 -> H(U1(d, c), U1(b, e)))
27.56/8.95	   (A^2 -> H(U1(d, c), U1(b, k)),A^2 -> H(U1(d, c), U1(b, k)))
27.56/8.95	
27.56/8.95	
27.56/8.95	----------------------------------------
27.56/8.95	
27.56/8.95	(642)
27.56/8.95	Obligation:
27.56/8.95	Q DP problem:
27.56/8.95	The TRS P consists of the following rules:
27.56/8.95	
27.56/8.95	   H(x, x) -> G(x, x, f(k))
27.56/8.95	   G(d, x, x) -> A^2
27.56/8.95	   A^2 -> H(f(c), f(c))
27.56/8.95	   A^2 -> H(f(d), f(d))
27.56/8.95	   A^2 -> H(U1(c, c), U1(c, c))
27.56/8.95	   A^2 -> H(f(e), f(e))
27.56/8.95	   A^2 -> H(f(k), f(k))
27.56/8.95	   A^2 -> H(U1(d, d), U1(d, d))
27.56/8.95	   A^2 -> H(U1(d, c), U1(b, d))
27.56/8.95	   A^2 -> H(U1(d, c), U1(c, c))
27.56/8.95	   A^2 -> H(U1(d, c), f(e))
27.56/8.95	   A^2 -> H(U1(d, c), f(k))
27.56/8.95	   A^2 -> H(U1(d, c), U1(d, d))
27.56/8.95	   A^2 -> H(U1(d, a), U1(e, b))
27.56/8.95	   A^2 -> H(U1(d, a), U1(k, b))
27.56/8.95	   A^2 -> H(U1(d, a), U1(c, d))
27.56/8.95	   A^2 -> H(U1(d, a), U1(d, c))
27.56/8.95	   A^2 -> H(U1(d, a), U1(b, e))
27.56/8.95	   A^2 -> H(U1(d, a), U1(b, k))
27.56/8.95	   A^2 -> H(U1(d, a), U1(e, c))
27.56/8.95	   A^2 -> H(U1(d, a), U1(k, c))
27.56/8.95	   A^2 -> H(U1(d, a), U1(c, e))
27.56/8.95	   A^2 -> H(U1(d, a), U1(c, k))
27.56/8.95	   A^2 -> H(U1(d, a), U1(e, e))
27.56/8.95	   A^2 -> H(U1(d, a), U1(k, k))
27.56/8.95	   A^2 -> H(U1(d, a), U1(k, d))
27.56/8.95	   A^2 -> H(U1(d, a), U1(d, k))
27.56/8.95	   A^2 -> H(U1(a, e), U1(c, b))
27.56/8.95	   A^2 -> H(U1(a, e), U1(d, b))
27.56/8.95	   A^2 -> H(U1(a, e), U1(b, c))
27.56/8.95	   A^2 -> H(U1(a, e), U1(b, d))
27.56/8.95	   A^2 -> H(U1(a, e), U1(c, c))
27.56/8.95	   A^2 -> H(U1(a, e), f(e))
27.56/8.95	   A^2 -> H(U1(a, e), f(k))
27.56/8.95	   A^2 -> H(U1(a, e), U1(d, d))
27.56/8.95	   A^2 -> H(U1(a, k), U1(c, b))
27.56/8.95	   A^2 -> H(U1(a, k), U1(d, b))
27.56/8.95	   A^2 -> H(U1(a, k), U1(b, c))
27.56/8.95	   A^2 -> H(U1(a, k), U1(b, d))
27.56/8.95	   A^2 -> H(U1(a, k), U1(c, c))
27.56/8.95	   A^2 -> H(U1(a, k), f(e))
27.56/8.95	   A^2 -> H(U1(a, k), f(k))
27.56/8.95	   A^2 -> H(U1(a, k), U1(d, d))
27.56/8.95	   A^2 -> H(U1(a, c), U1(e, b))
27.56/8.95	   A^2 -> H(U1(a, c), U1(k, b))
27.56/8.95	   A^2 -> H(U1(a, c), U1(c, d))
27.56/8.95	   A^2 -> H(U1(a, c), U1(d, c))
27.56/8.95	   A^2 -> H(U1(a, c), U1(b, e))
27.56/8.95	   A^2 -> H(U1(a, c), U1(b, k))
27.56/8.95	   A^2 -> H(U1(a, c), U1(e, c))
27.56/8.95	   A^2 -> H(U1(a, c), U1(k, c))
27.56/8.95	   A^2 -> H(U1(a, c), U1(c, e))
27.56/8.95	   A^2 -> H(U1(a, c), U1(c, k))
27.56/8.95	   A^2 -> H(U1(a, c), U1(e, e))
27.56/8.95	   A^2 -> H(U1(a, c), U1(k, k))
27.56/8.95	   A^2 -> H(U1(a, c), U1(k, d))
27.56/8.95	   A^2 -> H(U1(a, c), U1(d, k))
27.56/8.95	   A^2 -> H(U1(a, d), U1(e, b))
27.56/8.95	   A^2 -> H(U1(a, d), U1(k, b))
27.56/8.95	   A^2 -> H(U1(a, d), U1(c, d))
27.56/8.95	   A^2 -> H(U1(a, d), U1(d, c))
27.56/8.95	   A^2 -> H(U1(a, d), U1(b, e))
27.56/8.95	   A^2 -> H(U1(a, d), U1(b, k))
27.56/8.95	   A^2 -> H(U1(a, d), U1(e, c))
27.56/8.95	   A^2 -> H(U1(a, d), U1(k, c))
27.56/8.95	   A^2 -> H(U1(a, d), U1(c, e))
27.56/8.95	   A^2 -> H(U1(a, d), U1(c, k))
27.56/8.95	   A^2 -> H(U1(a, d), U1(e, e))
27.56/8.95	   A^2 -> H(U1(a, d), U1(k, k))
27.56/8.95	   A^2 -> H(U1(a, d), U1(k, d))
27.56/8.95	   A^2 -> H(U1(a, d), U1(d, k))
27.56/8.95	   A^2 -> H(U1(a, a), b)
27.56/8.95	   A^2 -> H(U1(a, a), U1(e, d))
27.56/8.95	   A^2 -> H(U1(a, a), U1(d, e))
27.56/8.95	   A^2 -> H(U1(a, a), c)
27.56/8.95	   A^2 -> H(U1(a, a), U1(e, k))
27.56/8.95	   A^2 -> H(U1(a, a), U1(k, e))
27.56/8.95	   A^2 -> H(U1(a, a), e)
27.56/8.95	   A^2 -> H(U1(a, a), U1(k, k))
27.56/8.95	   A^2 -> H(k, f(b))
27.56/8.95	   A^2 -> H(c, U1(b, b))
27.56/8.95	   A^2 -> H(c, f(c))
27.56/8.95	   A^2 -> H(c, f(d))
27.56/8.95	   A^2 -> H(U1(e, k), U1(b, b))
27.56/8.95	   A^2 -> H(U1(e, k), f(c))
27.56/8.95	   A^2 -> H(U1(e, k), f(d))
27.56/8.95	   A^2 -> H(U1(e, c), U1(c, b))
27.56/8.95	   A^2 -> H(U1(e, c), U1(d, b))
27.56/8.95	   A^2 -> H(U1(e, c), U1(b, c))
27.56/8.95	   A^2 -> H(U1(e, c), U1(b, d))
27.56/8.95	   A^2 -> H(U1(e, c), U1(c, c))
27.56/8.95	   A^2 -> H(U1(e, c), f(e))
27.56/8.95	   A^2 -> H(U1(e, c), f(k))
27.56/8.95	   A^2 -> H(U1(e, c), U1(d, d))
27.56/8.95	   A^2 -> H(U1(k, e), U1(b, b))
27.56/8.95	   A^2 -> H(U1(k, e), f(c))
27.56/8.95	   A^2 -> H(U1(k, e), f(d))
27.56/8.95	   A^2 -> H(U1(k, c), U1(c, b))
27.56/8.95	   A^2 -> H(U1(k, c), U1(d, b))
27.56/8.95	   A^2 -> H(U1(k, c), U1(b, c))
27.56/8.95	   A^2 -> H(U1(k, c), U1(b, d))
27.56/8.95	   A^2 -> H(U1(k, c), U1(c, c))
27.56/8.95	   A^2 -> H(U1(k, c), f(e))
27.56/8.95	   A^2 -> H(U1(k, c), f(k))
27.56/8.95	   A^2 -> H(U1(k, c), U1(d, d))
27.56/8.95	   A^2 -> H(U1(c, e), U1(c, b))
27.56/8.95	   A^2 -> H(U1(c, e), U1(d, b))
27.56/8.95	   A^2 -> H(U1(c, e), U1(b, c))
27.56/8.95	   A^2 -> H(U1(c, e), U1(b, d))
27.56/8.95	   A^2 -> H(U1(c, e), U1(c, c))
27.56/8.95	   A^2 -> H(U1(c, e), f(e))
27.56/8.95	   A^2 -> H(U1(c, e), f(k))
27.56/8.95	   A^2 -> H(U1(c, e), U1(d, d))
27.56/8.95	   A^2 -> H(U1(c, k), U1(c, b))
27.56/8.95	   A^2 -> H(U1(c, k), U1(d, b))
27.56/8.95	   A^2 -> H(U1(c, k), U1(b, c))
27.56/8.95	   A^2 -> H(U1(c, k), U1(b, d))
27.56/8.95	   A^2 -> H(U1(c, k), U1(c, c))
27.56/8.95	   A^2 -> H(U1(c, k), f(e))
27.56/8.95	   A^2 -> H(U1(c, k), f(k))
27.56/8.95	   A^2 -> H(U1(c, k), U1(d, d))
27.56/8.95	   A^2 -> H(U1(c, c), U1(e, b))
27.56/8.95	   A^2 -> H(U1(c, c), U1(k, b))
27.56/8.95	   A^2 -> H(U1(c, c), U1(c, d))
27.56/8.95	   A^2 -> H(U1(c, c), U1(d, c))
27.56/8.95	   A^2 -> H(U1(c, c), U1(b, e))
27.56/8.95	   A^2 -> H(U1(c, c), U1(b, k))
27.56/8.95	   A^2 -> H(U1(c, c), U1(e, e))
27.56/8.95	   A^2 -> H(U1(c, c), U1(k, k))
27.56/8.95	   A^2 -> H(U1(c, c), U1(k, d))
27.56/8.95	   A^2 -> H(U1(c, c), U1(d, k))
27.56/8.95	   A^2 -> H(e, U1(b, b))
27.56/8.95	   A^2 -> H(e, f(c))
27.56/8.95	   A^2 -> H(e, f(d))
27.56/8.95	   A^2 -> H(U1(e, e), U1(c, b))
27.56/8.95	   A^2 -> H(U1(e, e), U1(d, b))
27.56/8.95	   A^2 -> H(U1(e, e), U1(b, c))
27.56/8.95	   A^2 -> H(U1(e, e), U1(b, d))
27.56/8.95	   A^2 -> H(U1(e, e), U1(c, c))
27.56/8.95	   A^2 -> H(U1(e, e), f(e))
27.56/8.95	   A^2 -> H(U1(e, e), f(k))
27.56/8.95	   A^2 -> H(U1(e, e), U1(d, d))
27.56/8.95	   A^2 -> H(f(e), U1(e, b))
27.56/8.95	   A^2 -> H(f(e), U1(k, b))
27.56/8.95	   A^2 -> H(f(e), U1(c, d))
27.56/8.95	   A^2 -> H(f(e), U1(d, c))
27.56/8.95	   A^2 -> H(f(e), U1(b, e))
27.56/8.95	   A^2 -> H(f(e), U1(b, k))
27.56/8.95	   A^2 -> H(f(e), U1(e, c))
27.56/8.95	   A^2 -> H(f(e), U1(k, c))
27.56/8.95	   A^2 -> H(f(e), U1(c, e))
27.56/8.95	   A^2 -> H(f(e), U1(c, k))
27.56/8.95	   A^2 -> H(f(e), U1(k, k))
27.56/8.95	   A^2 -> H(f(e), U1(k, d))
27.56/8.95	   A^2 -> H(f(e), U1(d, k))
27.56/8.95	   A^2 -> H(U1(k, k), U1(c, b))
27.56/8.95	   A^2 -> H(U1(k, k), U1(d, b))
27.56/8.95	   A^2 -> H(U1(k, k), U1(b, c))
27.56/8.95	   A^2 -> H(U1(k, k), U1(b, d))
27.56/8.95	   A^2 -> H(U1(k, k), U1(c, c))
27.56/8.95	   A^2 -> H(U1(k, k), f(e))
27.56/8.95	   A^2 -> H(U1(k, k), f(k))
27.56/8.95	   A^2 -> H(U1(k, k), U1(d, d))
27.56/8.95	   A^2 -> H(f(k), U1(e, b))
27.56/8.95	   A^2 -> H(f(k), U1(k, b))
27.56/8.95	   A^2 -> H(f(k), U1(c, d))
27.56/8.95	   A^2 -> H(f(k), U1(d, c))
27.56/8.95	   A^2 -> H(f(k), U1(b, e))
27.56/8.95	   A^2 -> H(f(k), U1(b, k))
27.56/8.95	   A^2 -> H(f(k), U1(e, c))
27.56/8.95	   A^2 -> H(f(k), U1(k, c))
27.56/8.95	   A^2 -> H(f(k), U1(c, e))
27.56/8.95	   A^2 -> H(f(k), U1(c, k))
27.56/8.95	   A^2 -> H(f(k), U1(e, e))
27.56/8.95	   A^2 -> H(f(k), U1(k, d))
27.56/8.95	   A^2 -> H(f(k), U1(d, k))
27.56/8.95	   A^2 -> H(f(c), b)
27.56/8.95	   A^2 -> H(f(c), U1(e, d))
27.56/8.95	   A^2 -> H(f(c), U1(d, e))
27.56/8.95	   A^2 -> H(f(k), U1(k, k))
27.56/8.95	   A^2 -> H(U1(k, k), U1(b, b))
27.56/8.95	   A^2 -> H(U1(k, k), f(c))
27.56/8.95	   A^2 -> H(U1(k, k), f(d))
27.56/8.95	   A^2 -> H(U1(k, d), U1(c, b))
27.56/8.95	   A^2 -> H(U1(k, d), U1(d, b))
27.56/8.95	   A^2 -> H(U1(k, d), U1(b, c))
27.56/8.95	   A^2 -> H(U1(k, d), U1(b, d))
27.56/8.95	   A^2 -> H(U1(k, d), U1(c, c))
27.56/8.95	   A^2 -> H(U1(k, d), f(e))
27.56/8.95	   A^2 -> H(U1(k, d), f(k))
27.56/8.95	   A^2 -> H(U1(k, d), U1(d, d))
27.56/8.95	   A^2 -> H(U1(d, k), U1(c, b))
27.56/8.95	   A^2 -> H(U1(d, k), U1(d, b))
27.56/8.95	   A^2 -> H(U1(d, k), U1(b, c))
27.56/8.95	   A^2 -> H(U1(d, k), U1(b, d))
27.56/8.95	   A^2 -> H(U1(d, k), U1(c, c))
27.56/8.95	   A^2 -> H(U1(d, k), f(e))
27.56/8.95	   A^2 -> H(U1(d, k), f(k))
27.56/8.95	   A^2 -> H(U1(d, k), U1(d, d))
27.56/8.95	   A^2 -> H(U1(d, d), U1(e, b))
27.56/8.95	   A^2 -> H(U1(d, d), U1(k, b))
27.56/8.95	   A^2 -> H(U1(d, d), U1(c, d))
27.56/8.95	   A^2 -> H(U1(d, d), U1(d, c))
27.56/8.95	   A^2 -> H(U1(d, d), U1(b, e))
27.56/8.95	   A^2 -> H(U1(d, d), U1(b, k))
27.56/8.95	   A^2 -> H(U1(d, d), U1(e, c))
27.56/8.95	   A^2 -> H(U1(d, d), U1(k, c))
27.56/8.95	   A^2 -> H(U1(d, d), U1(c, e))
27.56/8.95	   A^2 -> H(U1(d, d), U1(c, k))
27.56/8.95	   A^2 -> H(U1(d, d), U1(e, e))
27.56/8.95	   A^2 -> H(U1(d, d), U1(k, k))
27.56/8.95	   A^2 -> H(f(d), b)
27.56/8.95	   A^2 -> H(f(d), U1(e, d))
27.56/8.95	   A^2 -> H(f(d), U1(d, e))
27.56/8.95	   A^2 -> H(f(d), c)
27.56/8.95	   A^2 -> H(f(d), U1(e, k))
27.56/8.95	   A^2 -> H(f(d), U1(k, e))
27.56/8.95	   A^2 -> H(f(d), e)
27.56/8.95	   A^2 -> H(f(a), d)
27.56/8.95	   A^2 -> H(U1(c, c), U1(e, c))
27.56/8.95	   A^2 -> H(f(c), c)
27.56/8.95	   A^2 -> H(f(c), U1(e, k))
27.56/8.95	   A^2 -> H(U1(c, c), U1(k, c))
27.56/8.95	   A^2 -> H(f(c), U1(k, e))
27.56/8.95	   A^2 -> H(f(c), U1(k, k))
27.56/8.95	   A^2 -> H(U1(c, c), U1(c, e))
27.56/8.95	   A^2 -> H(U1(c, c), U1(c, k))
27.56/8.95	   A^2 -> H(f(a), k)
27.56/8.95	   A^2 -> H(f(e), U1(e, e))
27.56/8.95	   A^2 -> H(f(c), e)
27.56/8.95	   A^2 -> H(U1(d, d), U1(k, d))
27.56/8.95	   A^2 -> H(f(d), U1(k, k))
27.56/8.95	   A^2 -> H(U1(d, d), U1(d, k))
27.56/8.95	   A^2 -> H(d, U1(b, b))
27.56/8.95	   A^2 -> H(d, f(c))
27.56/8.95	   A^2 -> H(d, f(d))
27.56/8.95	   A^2 -> H(a, U1(c, b))
27.56/8.95	   A^2 -> H(a, U1(d, b))
27.56/8.95	   A^2 -> H(a, U1(b, c))
27.56/8.95	   A^2 -> H(a, U1(b, d))
27.56/8.95	   A^2 -> H(a, U1(c, c))
27.56/8.95	   A^2 -> H(a, f(e))
27.56/8.95	   A^2 -> H(a, f(k))
27.56/8.95	   A^2 -> H(a, U1(d, d))
27.56/8.95	   A^2 -> H(U1(e, d), U1(c, b))
27.56/8.95	   A^2 -> H(U1(e, d), U1(d, b))
27.56/8.95	   A^2 -> H(U1(e, d), U1(b, c))
27.56/8.95	   A^2 -> H(U1(e, d), U1(b, d))
27.56/8.95	   A^2 -> H(U1(e, d), U1(c, c))
27.56/8.95	   A^2 -> H(U1(e, d), f(e))
27.56/8.95	   A^2 -> H(U1(e, d), f(k))
27.56/8.95	   A^2 -> H(U1(e, d), U1(d, d))
27.56/8.95	   A^2 -> H(U1(e, a), U1(e, b))
27.56/8.95	   A^2 -> H(U1(e, a), U1(k, b))
27.56/8.95	   A^2 -> H(U1(e, a), U1(c, d))
27.56/8.95	   A^2 -> H(U1(e, a), U1(d, c))
27.56/8.95	   A^2 -> H(U1(e, a), U1(b, e))
27.56/8.95	   A^2 -> H(U1(e, a), U1(b, k))
27.56/8.95	   A^2 -> H(U1(e, a), U1(e, c))
27.56/8.95	   A^2 -> H(U1(e, a), U1(k, c))
27.56/8.95	   A^2 -> H(U1(e, a), U1(c, e))
27.56/8.95	   A^2 -> H(U1(e, a), U1(c, k))
27.56/8.95	   A^2 -> H(U1(e, a), U1(e, e))
27.56/8.95	   A^2 -> H(U1(e, a), U1(k, k))
27.56/8.95	   A^2 -> H(U1(e, a), U1(k, d))
27.56/8.95	   A^2 -> H(U1(e, a), U1(d, k))
27.56/8.95	   A^2 -> H(U1(k, a), U1(e, b))
27.56/8.95	   A^2 -> H(U1(k, a), U1(k, b))
27.56/8.95	   A^2 -> H(U1(k, a), U1(c, d))
27.56/8.95	   A^2 -> H(U1(k, a), U1(d, c))
27.56/8.95	   A^2 -> H(U1(k, a), U1(b, e))
27.56/8.95	   A^2 -> H(U1(k, a), U1(b, k))
27.56/8.95	   A^2 -> H(U1(k, a), U1(e, c))
27.56/8.95	   A^2 -> H(U1(k, a), U1(k, c))
27.56/8.95	   A^2 -> H(U1(k, a), U1(c, e))
27.56/8.95	   A^2 -> H(U1(k, a), U1(c, k))
27.56/8.95	   A^2 -> H(U1(k, a), U1(e, e))
27.56/8.95	   A^2 -> H(U1(k, a), U1(k, k))
27.56/8.95	   A^2 -> H(U1(k, a), U1(k, d))
27.56/8.95	   A^2 -> H(U1(k, a), U1(d, k))
27.56/8.95	   A^2 -> H(U1(c, d), U1(e, b))
27.56/8.95	   A^2 -> H(U1(c, d), U1(k, b))
27.56/8.95	   A^2 -> H(U1(c, d), U1(c, d))
27.56/8.95	   A^2 -> H(U1(c, d), U1(d, c))
27.56/8.95	   A^2 -> H(U1(c, d), U1(b, e))
27.56/8.95	   A^2 -> H(U1(c, d), U1(b, k))
27.56/8.95	   A^2 -> H(U1(c, d), U1(e, c))
27.56/8.95	   A^2 -> H(U1(c, d), U1(k, c))
27.56/8.95	   A^2 -> H(U1(c, d), U1(c, e))
27.56/8.95	   A^2 -> H(U1(c, d), U1(c, k))
27.56/8.95	   A^2 -> H(U1(c, d), U1(e, e))
27.56/8.95	   A^2 -> H(U1(c, d), U1(k, k))
27.56/8.95	   A^2 -> H(U1(c, d), U1(k, d))
27.56/8.95	   A^2 -> H(U1(c, d), U1(d, k))
27.56/8.95	   A^2 -> H(U1(c, a), b)
27.56/8.95	   A^2 -> H(U1(c, a), U1(e, d))
27.56/8.95	   A^2 -> H(U1(c, a), U1(d, e))
27.56/8.95	   A^2 -> H(U1(c, a), c)
27.56/8.95	   A^2 -> H(U1(c, a), U1(e, k))
27.56/8.95	   A^2 -> H(U1(c, a), U1(k, e))
27.56/8.95	   A^2 -> H(U1(c, a), e)
27.56/8.95	   A^2 -> H(U1(c, a), U1(k, k))
27.56/8.95	   A^2 -> H(U1(d, e), U1(c, b))
27.56/8.95	   A^2 -> H(U1(d, e), U1(d, b))
27.56/8.95	   A^2 -> H(U1(d, e), U1(b, c))
27.56/8.95	   A^2 -> H(U1(d, e), U1(b, d))
27.56/8.95	   A^2 -> H(U1(d, e), U1(c, c))
27.56/8.95	   A^2 -> H(U1(d, e), f(e))
27.56/8.95	   A^2 -> H(U1(d, e), f(k))
27.56/8.95	   A^2 -> H(U1(d, e), U1(d, d))
27.56/8.95	   A^2 -> H(U1(d, c), U1(e, b))
27.56/8.95	   A^2 -> H(U1(d, c), U1(k, b))
27.56/8.95	   A^2 -> H(U1(d, c), U1(c, d))
27.56/8.95	   A^2 -> H(U1(d, c), U1(d, c))
27.56/8.95	   A^2 -> H(U1(d, c), U1(b, e))
27.56/8.95	   A^2 -> H(U1(d, c), U1(b, k))
27.56/8.96	
27.56/8.96	The TRS R consists of the following rules:
27.56/8.96	
27.56/8.96	   f(x) -> U1(x, x)
27.56/8.96	   U1(e, x) -> x
27.56/8.96	   a -> c
27.56/8.96	   a -> d
27.56/8.96	   b -> c
27.56/8.96	   b -> d
27.56/8.96	   d -> k
27.56/8.96	   c -> e
27.56/8.96	   c -> k
27.56/8.96	
27.56/8.96	Q is empty.
27.56/8.96	We have to consider all minimal (P,Q,R)-chains.
27.56/8.96	----------------------------------------
27.56/8.96	
27.56/8.96	(643) TransformationProof (EQUIVALENT)
27.56/8.96	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
27.56/8.96	
27.56/8.96	   (A^2 -> H(U1(k, c), U1(b, d)),A^2 -> H(U1(k, c), U1(b, d)))
27.56/8.96	   (A^2 -> H(U1(d, e), U1(b, d)),A^2 -> H(U1(d, e), U1(b, d)))
27.56/8.96	   (A^2 -> H(U1(d, k), U1(b, d)),A^2 -> H(U1(d, k), U1(b, d)))
27.56/8.96	   (A^2 -> H(U1(d, c), U1(c, d)),A^2 -> H(U1(d, c), U1(c, d)))
27.56/8.96	   (A^2 -> H(U1(d, c), U1(d, d)),A^2 -> H(U1(d, c), U1(d, d)))
27.56/8.96	   (A^2 -> H(U1(d, c), U1(b, k)),A^2 -> H(U1(d, c), U1(b, k)))
27.56/8.96	
27.56/8.96	
27.56/8.96	----------------------------------------
27.56/8.96	
27.56/8.96	(644)
27.56/8.96	Obligation:
27.56/8.96	Q DP problem:
27.56/8.96	The TRS P consists of the following rules:
27.56/8.96	
27.56/8.96	   H(x, x) -> G(x, x, f(k))
27.56/8.96	   G(d, x, x) -> A^2
27.56/8.96	   A^2 -> H(f(c), f(c))
27.56/8.96	   A^2 -> H(f(d), f(d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(c, c))
27.56/8.96	   A^2 -> H(f(e), f(e))
27.56/8.96	   A^2 -> H(f(k), f(k))
27.56/8.96	   A^2 -> H(U1(d, d), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, c), U1(c, c))
27.56/8.96	   A^2 -> H(U1(d, c), f(e))
27.56/8.96	   A^2 -> H(U1(d, c), f(k))
27.56/8.96	   A^2 -> H(U1(d, c), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, a), U1(e, b))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, b))
27.56/8.96	   A^2 -> H(U1(d, a), U1(c, d))
27.56/8.96	   A^2 -> H(U1(d, a), U1(d, c))
27.56/8.96	   A^2 -> H(U1(d, a), U1(b, e))
27.56/8.96	   A^2 -> H(U1(d, a), U1(b, k))
27.56/8.96	   A^2 -> H(U1(d, a), U1(e, c))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, c))
27.56/8.96	   A^2 -> H(U1(d, a), U1(c, e))
27.56/8.96	   A^2 -> H(U1(d, a), U1(c, k))
27.56/8.96	   A^2 -> H(U1(d, a), U1(e, e))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, k))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, d))
27.56/8.96	   A^2 -> H(U1(d, a), U1(d, k))
27.56/8.96	   A^2 -> H(U1(a, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(a, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(a, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(a, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(a, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(a, e), f(e))
27.56/8.96	   A^2 -> H(U1(a, e), f(k))
27.56/8.96	   A^2 -> H(U1(a, e), U1(d, d))
27.56/8.96	   A^2 -> H(U1(a, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(a, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(a, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(a, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(a, k), U1(c, c))
27.56/8.96	   A^2 -> H(U1(a, k), f(e))
27.56/8.96	   A^2 -> H(U1(a, k), f(k))
27.56/8.96	   A^2 -> H(U1(a, k), U1(d, d))
27.56/8.96	   A^2 -> H(U1(a, c), U1(e, b))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, b))
27.56/8.96	   A^2 -> H(U1(a, c), U1(c, d))
27.56/8.96	   A^2 -> H(U1(a, c), U1(d, c))
27.56/8.96	   A^2 -> H(U1(a, c), U1(b, e))
27.56/8.96	   A^2 -> H(U1(a, c), U1(b, k))
27.56/8.96	   A^2 -> H(U1(a, c), U1(e, c))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, c))
27.56/8.96	   A^2 -> H(U1(a, c), U1(c, e))
27.56/8.96	   A^2 -> H(U1(a, c), U1(c, k))
27.56/8.96	   A^2 -> H(U1(a, c), U1(e, e))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, k))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, d))
27.56/8.96	   A^2 -> H(U1(a, c), U1(d, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(e, b))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, b))
27.56/8.96	   A^2 -> H(U1(a, d), U1(c, d))
27.56/8.96	   A^2 -> H(U1(a, d), U1(d, c))
27.56/8.96	   A^2 -> H(U1(a, d), U1(b, e))
27.56/8.96	   A^2 -> H(U1(a, d), U1(b, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(e, c))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, c))
27.56/8.96	   A^2 -> H(U1(a, d), U1(c, e))
27.56/8.96	   A^2 -> H(U1(a, d), U1(c, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(e, e))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, d))
27.56/8.96	   A^2 -> H(U1(a, d), U1(d, k))
27.56/8.96	   A^2 -> H(U1(a, a), b)
27.56/8.96	   A^2 -> H(U1(a, a), U1(e, d))
27.56/8.96	   A^2 -> H(U1(a, a), U1(d, e))
27.56/8.96	   A^2 -> H(U1(a, a), c)
27.56/8.96	   A^2 -> H(U1(a, a), U1(e, k))
27.56/8.96	   A^2 -> H(U1(a, a), U1(k, e))
27.56/8.96	   A^2 -> H(U1(a, a), e)
27.56/8.96	   A^2 -> H(U1(a, a), U1(k, k))
27.56/8.96	   A^2 -> H(k, f(b))
27.56/8.96	   A^2 -> H(c, U1(b, b))
27.56/8.96	   A^2 -> H(c, f(c))
27.56/8.96	   A^2 -> H(c, f(d))
27.56/8.96	   A^2 -> H(U1(e, k), U1(b, b))
27.56/8.96	   A^2 -> H(U1(e, k), f(c))
27.56/8.96	   A^2 -> H(U1(e, k), f(d))
27.56/8.96	   A^2 -> H(U1(e, c), U1(c, b))
27.56/8.96	   A^2 -> H(U1(e, c), U1(d, b))
27.56/8.96	   A^2 -> H(U1(e, c), U1(b, c))
27.56/8.96	   A^2 -> H(U1(e, c), U1(b, d))
27.56/8.96	   A^2 -> H(U1(e, c), U1(c, c))
27.56/8.96	   A^2 -> H(U1(e, c), f(e))
27.56/8.96	   A^2 -> H(U1(e, c), f(k))
27.56/8.96	   A^2 -> H(U1(e, c), U1(d, d))
27.56/8.96	   A^2 -> H(U1(k, e), U1(b, b))
27.56/8.96	   A^2 -> H(U1(k, e), f(c))
27.56/8.96	   A^2 -> H(U1(k, e), f(d))
27.56/8.96	   A^2 -> H(U1(k, c), U1(c, b))
27.56/8.96	   A^2 -> H(U1(k, c), U1(d, b))
27.56/8.96	   A^2 -> H(U1(k, c), U1(b, c))
27.56/8.96	   A^2 -> H(U1(k, c), U1(b, d))
27.56/8.96	   A^2 -> H(U1(k, c), U1(c, c))
27.56/8.96	   A^2 -> H(U1(k, c), f(e))
27.56/8.96	   A^2 -> H(U1(k, c), f(k))
27.56/8.96	   A^2 -> H(U1(k, c), U1(d, d))
27.56/8.96	   A^2 -> H(U1(c, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(c, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(c, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(c, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(c, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(c, e), f(e))
27.56/8.96	   A^2 -> H(U1(c, e), f(k))
27.56/8.96	   A^2 -> H(U1(c, e), U1(d, d))
27.56/8.96	   A^2 -> H(U1(c, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(c, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(c, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(c, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(c, k), U1(c, c))
27.56/8.96	   A^2 -> H(U1(c, k), f(e))
27.56/8.96	   A^2 -> H(U1(c, k), f(k))
27.56/8.96	   A^2 -> H(U1(c, k), U1(d, d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(e, b))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, b))
27.56/8.96	   A^2 -> H(U1(c, c), U1(c, d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(d, c))
27.56/8.96	   A^2 -> H(U1(c, c), U1(b, e))
27.56/8.96	   A^2 -> H(U1(c, c), U1(b, k))
27.56/8.96	   A^2 -> H(U1(c, c), U1(e, e))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, k))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(d, k))
27.56/8.96	   A^2 -> H(e, U1(b, b))
27.56/8.96	   A^2 -> H(e, f(c))
27.56/8.96	   A^2 -> H(e, f(d))
27.56/8.96	   A^2 -> H(U1(e, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(e, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(e, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(e, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(e, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(e, e), f(e))
27.56/8.96	   A^2 -> H(U1(e, e), f(k))
27.56/8.96	   A^2 -> H(U1(e, e), U1(d, d))
27.56/8.96	   A^2 -> H(f(e), U1(e, b))
27.56/8.96	   A^2 -> H(f(e), U1(k, b))
27.56/8.96	   A^2 -> H(f(e), U1(c, d))
27.56/8.96	   A^2 -> H(f(e), U1(d, c))
27.56/8.96	   A^2 -> H(f(e), U1(b, e))
27.56/8.96	   A^2 -> H(f(e), U1(b, k))
27.56/8.96	   A^2 -> H(f(e), U1(e, c))
27.56/8.96	   A^2 -> H(f(e), U1(k, c))
27.56/8.96	   A^2 -> H(f(e), U1(c, e))
27.56/8.96	   A^2 -> H(f(e), U1(c, k))
27.56/8.96	   A^2 -> H(f(e), U1(k, k))
27.56/8.96	   A^2 -> H(f(e), U1(k, d))
27.56/8.96	   A^2 -> H(f(e), U1(d, k))
27.56/8.96	   A^2 -> H(U1(k, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(k, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(k, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(k, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(k, k), U1(c, c))
27.56/8.96	   A^2 -> H(U1(k, k), f(e))
27.56/8.96	   A^2 -> H(U1(k, k), f(k))
27.56/8.96	   A^2 -> H(U1(k, k), U1(d, d))
27.56/8.96	   A^2 -> H(f(k), U1(e, b))
27.56/8.96	   A^2 -> H(f(k), U1(k, b))
27.56/8.96	   A^2 -> H(f(k), U1(c, d))
27.56/8.96	   A^2 -> H(f(k), U1(d, c))
27.56/8.96	   A^2 -> H(f(k), U1(b, e))
27.56/8.96	   A^2 -> H(f(k), U1(b, k))
27.56/8.96	   A^2 -> H(f(k), U1(e, c))
27.56/8.96	   A^2 -> H(f(k), U1(k, c))
27.56/8.96	   A^2 -> H(f(k), U1(c, e))
27.56/8.96	   A^2 -> H(f(k), U1(c, k))
27.56/8.96	   A^2 -> H(f(k), U1(e, e))
27.56/8.96	   A^2 -> H(f(k), U1(k, d))
27.56/8.96	   A^2 -> H(f(k), U1(d, k))
27.56/8.96	   A^2 -> H(f(c), b)
27.56/8.96	   A^2 -> H(f(c), U1(e, d))
27.56/8.96	   A^2 -> H(f(c), U1(d, e))
27.56/8.96	   A^2 -> H(f(k), U1(k, k))
27.56/8.96	   A^2 -> H(U1(k, k), U1(b, b))
27.56/8.96	   A^2 -> H(U1(k, k), f(c))
27.56/8.96	   A^2 -> H(U1(k, k), f(d))
27.56/8.96	   A^2 -> H(U1(k, d), U1(c, b))
27.56/8.96	   A^2 -> H(U1(k, d), U1(d, b))
27.56/8.96	   A^2 -> H(U1(k, d), U1(b, c))
27.56/8.96	   A^2 -> H(U1(k, d), U1(b, d))
27.56/8.96	   A^2 -> H(U1(k, d), U1(c, c))
27.56/8.96	   A^2 -> H(U1(k, d), f(e))
27.56/8.96	   A^2 -> H(U1(k, d), f(k))
27.56/8.96	   A^2 -> H(U1(k, d), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(d, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(d, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(d, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(d, k), U1(c, c))
27.56/8.96	   A^2 -> H(U1(d, k), f(e))
27.56/8.96	   A^2 -> H(U1(d, k), f(k))
27.56/8.96	   A^2 -> H(U1(d, k), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, d), U1(e, b))
27.56/8.96	   A^2 -> H(U1(d, d), U1(k, b))
27.56/8.96	   A^2 -> H(U1(d, d), U1(c, d))
27.56/8.96	   A^2 -> H(U1(d, d), U1(d, c))
27.56/8.96	   A^2 -> H(U1(d, d), U1(b, e))
27.56/8.96	   A^2 -> H(U1(d, d), U1(b, k))
27.56/8.96	   A^2 -> H(U1(d, d), U1(e, c))
27.56/8.96	   A^2 -> H(U1(d, d), U1(k, c))
27.56/8.96	   A^2 -> H(U1(d, d), U1(c, e))
27.56/8.96	   A^2 -> H(U1(d, d), U1(c, k))
27.56/8.96	   A^2 -> H(U1(d, d), U1(e, e))
27.56/8.96	   A^2 -> H(U1(d, d), U1(k, k))
27.56/8.96	   A^2 -> H(f(d), b)
27.56/8.96	   A^2 -> H(f(d), U1(e, d))
27.56/8.96	   A^2 -> H(f(d), U1(d, e))
27.56/8.96	   A^2 -> H(f(d), c)
27.56/8.96	   A^2 -> H(f(d), U1(e, k))
27.56/8.96	   A^2 -> H(f(d), U1(k, e))
27.56/8.96	   A^2 -> H(f(d), e)
27.56/8.96	   A^2 -> H(f(a), d)
27.56/8.96	   A^2 -> H(U1(c, c), U1(e, c))
27.56/8.96	   A^2 -> H(f(c), c)
27.56/8.96	   A^2 -> H(f(c), U1(e, k))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, c))
27.56/8.96	   A^2 -> H(f(c), U1(k, e))
27.56/8.96	   A^2 -> H(f(c), U1(k, k))
27.56/8.96	   A^2 -> H(U1(c, c), U1(c, e))
27.56/8.96	   A^2 -> H(U1(c, c), U1(c, k))
27.56/8.96	   A^2 -> H(f(a), k)
27.56/8.96	   A^2 -> H(f(e), U1(e, e))
27.56/8.96	   A^2 -> H(f(c), e)
27.56/8.96	   A^2 -> H(U1(d, d), U1(k, d))
27.56/8.96	   A^2 -> H(f(d), U1(k, k))
27.56/8.96	   A^2 -> H(U1(d, d), U1(d, k))
27.56/8.96	   A^2 -> H(d, U1(b, b))
27.56/8.96	   A^2 -> H(d, f(c))
27.56/8.96	   A^2 -> H(d, f(d))
27.56/8.96	   A^2 -> H(a, U1(c, b))
27.56/8.96	   A^2 -> H(a, U1(d, b))
27.56/8.96	   A^2 -> H(a, U1(b, c))
27.56/8.96	   A^2 -> H(a, U1(b, d))
27.56/8.96	   A^2 -> H(a, U1(c, c))
27.56/8.96	   A^2 -> H(a, f(e))
27.56/8.96	   A^2 -> H(a, f(k))
27.56/8.96	   A^2 -> H(a, U1(d, d))
27.56/8.96	   A^2 -> H(U1(e, d), U1(c, b))
27.56/8.96	   A^2 -> H(U1(e, d), U1(d, b))
27.56/8.96	   A^2 -> H(U1(e, d), U1(b, c))
27.56/8.96	   A^2 -> H(U1(e, d), U1(b, d))
27.56/8.96	   A^2 -> H(U1(e, d), U1(c, c))
27.56/8.96	   A^2 -> H(U1(e, d), f(e))
27.56/8.96	   A^2 -> H(U1(e, d), f(k))
27.56/8.96	   A^2 -> H(U1(e, d), U1(d, d))
27.56/8.96	   A^2 -> H(U1(e, a), U1(e, b))
27.56/8.96	   A^2 -> H(U1(e, a), U1(k, b))
27.56/8.96	   A^2 -> H(U1(e, a), U1(c, d))
27.56/8.96	   A^2 -> H(U1(e, a), U1(d, c))
27.56/8.96	   A^2 -> H(U1(e, a), U1(b, e))
27.56/8.96	   A^2 -> H(U1(e, a), U1(b, k))
27.56/8.96	   A^2 -> H(U1(e, a), U1(e, c))
27.56/8.96	   A^2 -> H(U1(e, a), U1(k, c))
27.56/8.96	   A^2 -> H(U1(e, a), U1(c, e))
27.56/8.96	   A^2 -> H(U1(e, a), U1(c, k))
27.56/8.96	   A^2 -> H(U1(e, a), U1(e, e))
27.56/8.96	   A^2 -> H(U1(e, a), U1(k, k))
27.56/8.96	   A^2 -> H(U1(e, a), U1(k, d))
27.56/8.96	   A^2 -> H(U1(e, a), U1(d, k))
27.56/8.96	   A^2 -> H(U1(k, a), U1(e, b))
27.56/8.96	   A^2 -> H(U1(k, a), U1(k, b))
27.56/8.96	   A^2 -> H(U1(k, a), U1(c, d))
27.56/8.96	   A^2 -> H(U1(k, a), U1(d, c))
27.56/8.96	   A^2 -> H(U1(k, a), U1(b, e))
27.56/8.96	   A^2 -> H(U1(k, a), U1(b, k))
27.56/8.96	   A^2 -> H(U1(k, a), U1(e, c))
27.56/8.96	   A^2 -> H(U1(k, a), U1(k, c))
27.56/8.96	   A^2 -> H(U1(k, a), U1(c, e))
27.56/8.96	   A^2 -> H(U1(k, a), U1(c, k))
27.56/8.96	   A^2 -> H(U1(k, a), U1(e, e))
27.56/8.96	   A^2 -> H(U1(k, a), U1(k, k))
27.56/8.96	   A^2 -> H(U1(k, a), U1(k, d))
27.56/8.96	   A^2 -> H(U1(k, a), U1(d, k))
27.56/8.96	   A^2 -> H(U1(c, d), U1(e, b))
27.56/8.96	   A^2 -> H(U1(c, d), U1(k, b))
27.56/8.96	   A^2 -> H(U1(c, d), U1(c, d))
27.56/8.96	   A^2 -> H(U1(c, d), U1(d, c))
27.56/8.96	   A^2 -> H(U1(c, d), U1(b, e))
27.56/8.96	   A^2 -> H(U1(c, d), U1(b, k))
27.56/8.96	   A^2 -> H(U1(c, d), U1(e, c))
27.56/8.96	   A^2 -> H(U1(c, d), U1(k, c))
27.56/8.96	   A^2 -> H(U1(c, d), U1(c, e))
27.56/8.96	   A^2 -> H(U1(c, d), U1(c, k))
27.56/8.96	   A^2 -> H(U1(c, d), U1(e, e))
27.56/8.96	   A^2 -> H(U1(c, d), U1(k, k))
27.56/8.96	   A^2 -> H(U1(c, d), U1(k, d))
27.56/8.96	   A^2 -> H(U1(c, d), U1(d, k))
27.56/8.96	   A^2 -> H(U1(c, a), b)
27.56/8.96	   A^2 -> H(U1(c, a), U1(e, d))
27.56/8.96	   A^2 -> H(U1(c, a), U1(d, e))
27.56/8.96	   A^2 -> H(U1(c, a), c)
27.56/8.96	   A^2 -> H(U1(c, a), U1(e, k))
27.56/8.96	   A^2 -> H(U1(c, a), U1(k, e))
27.56/8.96	   A^2 -> H(U1(c, a), e)
27.56/8.96	   A^2 -> H(U1(c, a), U1(k, k))
27.56/8.96	   A^2 -> H(U1(d, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(d, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(d, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(d, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(d, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(d, e), f(e))
27.56/8.96	   A^2 -> H(U1(d, e), f(k))
27.56/8.96	   A^2 -> H(U1(d, e), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, c), U1(e, b))
27.56/8.96	   A^2 -> H(U1(d, c), U1(k, b))
27.56/8.96	   A^2 -> H(U1(d, c), U1(c, d))
27.56/8.96	   A^2 -> H(U1(d, c), U1(d, c))
27.56/8.96	   A^2 -> H(U1(d, c), U1(b, e))
27.56/8.96	   A^2 -> H(U1(d, c), U1(b, k))
27.56/8.96	
27.56/8.96	The TRS R consists of the following rules:
27.56/8.96	
27.56/8.96	   f(x) -> U1(x, x)
27.56/8.96	   U1(e, x) -> x
27.56/8.96	   a -> c
27.56/8.96	   a -> d
27.56/8.96	   b -> c
27.56/8.96	   b -> d
27.56/8.96	   d -> k
27.56/8.96	   c -> e
27.56/8.96	   c -> k
27.56/8.96	
27.56/8.96	Q is empty.
27.56/8.96	We have to consider all minimal (P,Q,R)-chains.
27.56/8.96	----------------------------------------
27.56/8.96	
27.56/8.96	(645) TransformationProof (EQUIVALENT)
27.56/8.96	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
27.56/8.96	
27.56/8.96	   (A^2 -> H(U1(k, c), U1(c, c)),A^2 -> H(U1(k, c), U1(c, c)))
27.56/8.96	   (A^2 -> H(U1(d, e), U1(c, c)),A^2 -> H(U1(d, e), U1(c, c)))
27.56/8.96	   (A^2 -> H(U1(d, k), U1(c, c)),A^2 -> H(U1(d, k), U1(c, c)))
27.56/8.96	   (A^2 -> H(U1(d, c), U1(e, c)),A^2 -> H(U1(d, c), U1(e, c)))
27.56/8.96	   (A^2 -> H(U1(d, c), U1(k, c)),A^2 -> H(U1(d, c), U1(k, c)))
27.56/8.96	   (A^2 -> H(U1(d, c), U1(c, e)),A^2 -> H(U1(d, c), U1(c, e)))
27.56/8.96	   (A^2 -> H(U1(d, c), U1(c, k)),A^2 -> H(U1(d, c), U1(c, k)))
27.56/8.96	
27.56/8.96	
27.56/8.96	----------------------------------------
27.56/8.96	
27.56/8.96	(646)
27.56/8.96	Obligation:
27.56/8.96	Q DP problem:
27.56/8.96	The TRS P consists of the following rules:
27.56/8.96	
27.56/8.96	   H(x, x) -> G(x, x, f(k))
27.56/8.96	   G(d, x, x) -> A^2
27.56/8.96	   A^2 -> H(f(c), f(c))
27.56/8.96	   A^2 -> H(f(d), f(d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(c, c))
27.56/8.96	   A^2 -> H(f(e), f(e))
27.56/8.96	   A^2 -> H(f(k), f(k))
27.56/8.96	   A^2 -> H(U1(d, d), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, c), f(e))
27.56/8.96	   A^2 -> H(U1(d, c), f(k))
27.56/8.96	   A^2 -> H(U1(d, c), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, a), U1(e, b))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, b))
27.56/8.96	   A^2 -> H(U1(d, a), U1(c, d))
27.56/8.96	   A^2 -> H(U1(d, a), U1(d, c))
27.56/8.96	   A^2 -> H(U1(d, a), U1(b, e))
27.56/8.96	   A^2 -> H(U1(d, a), U1(b, k))
27.56/8.96	   A^2 -> H(U1(d, a), U1(e, c))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, c))
27.56/8.96	   A^2 -> H(U1(d, a), U1(c, e))
27.56/8.96	   A^2 -> H(U1(d, a), U1(c, k))
27.56/8.96	   A^2 -> H(U1(d, a), U1(e, e))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, k))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, d))
27.56/8.96	   A^2 -> H(U1(d, a), U1(d, k))
27.56/8.96	   A^2 -> H(U1(a, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(a, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(a, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(a, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(a, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(a, e), f(e))
27.56/8.96	   A^2 -> H(U1(a, e), f(k))
27.56/8.96	   A^2 -> H(U1(a, e), U1(d, d))
27.56/8.96	   A^2 -> H(U1(a, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(a, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(a, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(a, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(a, k), U1(c, c))
27.56/8.96	   A^2 -> H(U1(a, k), f(e))
27.56/8.96	   A^2 -> H(U1(a, k), f(k))
27.56/8.96	   A^2 -> H(U1(a, k), U1(d, d))
27.56/8.96	   A^2 -> H(U1(a, c), U1(e, b))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, b))
27.56/8.96	   A^2 -> H(U1(a, c), U1(c, d))
27.56/8.96	   A^2 -> H(U1(a, c), U1(d, c))
27.56/8.96	   A^2 -> H(U1(a, c), U1(b, e))
27.56/8.96	   A^2 -> H(U1(a, c), U1(b, k))
27.56/8.96	   A^2 -> H(U1(a, c), U1(e, c))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, c))
27.56/8.96	   A^2 -> H(U1(a, c), U1(c, e))
27.56/8.96	   A^2 -> H(U1(a, c), U1(c, k))
27.56/8.96	   A^2 -> H(U1(a, c), U1(e, e))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, k))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, d))
27.56/8.96	   A^2 -> H(U1(a, c), U1(d, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(e, b))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, b))
27.56/8.96	   A^2 -> H(U1(a, d), U1(c, d))
27.56/8.96	   A^2 -> H(U1(a, d), U1(d, c))
27.56/8.96	   A^2 -> H(U1(a, d), U1(b, e))
27.56/8.96	   A^2 -> H(U1(a, d), U1(b, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(e, c))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, c))
27.56/8.96	   A^2 -> H(U1(a, d), U1(c, e))
27.56/8.96	   A^2 -> H(U1(a, d), U1(c, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(e, e))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, d))
27.56/8.96	   A^2 -> H(U1(a, d), U1(d, k))
27.56/8.96	   A^2 -> H(U1(a, a), b)
27.56/8.96	   A^2 -> H(U1(a, a), U1(e, d))
27.56/8.96	   A^2 -> H(U1(a, a), U1(d, e))
27.56/8.96	   A^2 -> H(U1(a, a), c)
27.56/8.96	   A^2 -> H(U1(a, a), U1(e, k))
27.56/8.96	   A^2 -> H(U1(a, a), U1(k, e))
27.56/8.96	   A^2 -> H(U1(a, a), e)
27.56/8.96	   A^2 -> H(U1(a, a), U1(k, k))
27.56/8.96	   A^2 -> H(k, f(b))
27.56/8.96	   A^2 -> H(c, U1(b, b))
27.56/8.96	   A^2 -> H(c, f(c))
27.56/8.96	   A^2 -> H(c, f(d))
27.56/8.96	   A^2 -> H(U1(e, k), U1(b, b))
27.56/8.96	   A^2 -> H(U1(e, k), f(c))
27.56/8.96	   A^2 -> H(U1(e, k), f(d))
27.56/8.96	   A^2 -> H(U1(e, c), U1(c, b))
27.56/8.96	   A^2 -> H(U1(e, c), U1(d, b))
27.56/8.96	   A^2 -> H(U1(e, c), U1(b, c))
27.56/8.96	   A^2 -> H(U1(e, c), U1(b, d))
27.56/8.96	   A^2 -> H(U1(e, c), U1(c, c))
27.56/8.96	   A^2 -> H(U1(e, c), f(e))
27.56/8.96	   A^2 -> H(U1(e, c), f(k))
27.56/8.96	   A^2 -> H(U1(e, c), U1(d, d))
27.56/8.96	   A^2 -> H(U1(k, e), U1(b, b))
27.56/8.96	   A^2 -> H(U1(k, e), f(c))
27.56/8.96	   A^2 -> H(U1(k, e), f(d))
27.56/8.96	   A^2 -> H(U1(k, c), U1(c, b))
27.56/8.96	   A^2 -> H(U1(k, c), U1(d, b))
27.56/8.96	   A^2 -> H(U1(k, c), U1(b, c))
27.56/8.96	   A^2 -> H(U1(k, c), U1(b, d))
27.56/8.96	   A^2 -> H(U1(k, c), U1(c, c))
27.56/8.96	   A^2 -> H(U1(k, c), f(e))
27.56/8.96	   A^2 -> H(U1(k, c), f(k))
27.56/8.96	   A^2 -> H(U1(k, c), U1(d, d))
27.56/8.96	   A^2 -> H(U1(c, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(c, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(c, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(c, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(c, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(c, e), f(e))
27.56/8.96	   A^2 -> H(U1(c, e), f(k))
27.56/8.96	   A^2 -> H(U1(c, e), U1(d, d))
27.56/8.96	   A^2 -> H(U1(c, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(c, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(c, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(c, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(c, k), U1(c, c))
27.56/8.96	   A^2 -> H(U1(c, k), f(e))
27.56/8.96	   A^2 -> H(U1(c, k), f(k))
27.56/8.96	   A^2 -> H(U1(c, k), U1(d, d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(e, b))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, b))
27.56/8.96	   A^2 -> H(U1(c, c), U1(c, d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(d, c))
27.56/8.96	   A^2 -> H(U1(c, c), U1(b, e))
27.56/8.96	   A^2 -> H(U1(c, c), U1(b, k))
27.56/8.96	   A^2 -> H(U1(c, c), U1(e, e))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, k))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(d, k))
27.56/8.96	   A^2 -> H(e, U1(b, b))
27.56/8.96	   A^2 -> H(e, f(c))
27.56/8.96	   A^2 -> H(e, f(d))
27.56/8.96	   A^2 -> H(U1(e, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(e, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(e, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(e, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(e, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(e, e), f(e))
27.56/8.96	   A^2 -> H(U1(e, e), f(k))
27.56/8.96	   A^2 -> H(U1(e, e), U1(d, d))
27.56/8.96	   A^2 -> H(f(e), U1(e, b))
27.56/8.96	   A^2 -> H(f(e), U1(k, b))
27.56/8.96	   A^2 -> H(f(e), U1(c, d))
27.56/8.96	   A^2 -> H(f(e), U1(d, c))
27.56/8.96	   A^2 -> H(f(e), U1(b, e))
27.56/8.96	   A^2 -> H(f(e), U1(b, k))
27.56/8.96	   A^2 -> H(f(e), U1(e, c))
27.56/8.96	   A^2 -> H(f(e), U1(k, c))
27.56/8.96	   A^2 -> H(f(e), U1(c, e))
27.56/8.96	   A^2 -> H(f(e), U1(c, k))
27.56/8.96	   A^2 -> H(f(e), U1(k, k))
27.56/8.96	   A^2 -> H(f(e), U1(k, d))
27.56/8.96	   A^2 -> H(f(e), U1(d, k))
27.56/8.96	   A^2 -> H(U1(k, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(k, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(k, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(k, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(k, k), U1(c, c))
27.56/8.96	   A^2 -> H(U1(k, k), f(e))
27.56/8.96	   A^2 -> H(U1(k, k), f(k))
27.56/8.96	   A^2 -> H(U1(k, k), U1(d, d))
27.56/8.96	   A^2 -> H(f(k), U1(e, b))
27.56/8.96	   A^2 -> H(f(k), U1(k, b))
27.56/8.96	   A^2 -> H(f(k), U1(c, d))
27.56/8.96	   A^2 -> H(f(k), U1(d, c))
27.56/8.96	   A^2 -> H(f(k), U1(b, e))
27.56/8.96	   A^2 -> H(f(k), U1(b, k))
27.56/8.96	   A^2 -> H(f(k), U1(e, c))
27.56/8.96	   A^2 -> H(f(k), U1(k, c))
27.56/8.96	   A^2 -> H(f(k), U1(c, e))
27.56/8.96	   A^2 -> H(f(k), U1(c, k))
27.56/8.96	   A^2 -> H(f(k), U1(e, e))
27.56/8.96	   A^2 -> H(f(k), U1(k, d))
27.56/8.96	   A^2 -> H(f(k), U1(d, k))
27.56/8.96	   A^2 -> H(f(c), b)
27.56/8.96	   A^2 -> H(f(c), U1(e, d))
27.56/8.96	   A^2 -> H(f(c), U1(d, e))
27.56/8.96	   A^2 -> H(f(k), U1(k, k))
27.56/8.96	   A^2 -> H(U1(k, k), U1(b, b))
27.56/8.96	   A^2 -> H(U1(k, k), f(c))
27.56/8.96	   A^2 -> H(U1(k, k), f(d))
27.56/8.96	   A^2 -> H(U1(k, d), U1(c, b))
27.56/8.96	   A^2 -> H(U1(k, d), U1(d, b))
27.56/8.96	   A^2 -> H(U1(k, d), U1(b, c))
27.56/8.96	   A^2 -> H(U1(k, d), U1(b, d))
27.56/8.96	   A^2 -> H(U1(k, d), U1(c, c))
27.56/8.96	   A^2 -> H(U1(k, d), f(e))
27.56/8.96	   A^2 -> H(U1(k, d), f(k))
27.56/8.96	   A^2 -> H(U1(k, d), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(d, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(d, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(d, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(d, k), U1(c, c))
27.56/8.96	   A^2 -> H(U1(d, k), f(e))
27.56/8.96	   A^2 -> H(U1(d, k), f(k))
27.56/8.96	   A^2 -> H(U1(d, k), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, d), U1(e, b))
27.56/8.96	   A^2 -> H(U1(d, d), U1(k, b))
27.56/8.96	   A^2 -> H(U1(d, d), U1(c, d))
27.56/8.96	   A^2 -> H(U1(d, d), U1(d, c))
27.56/8.96	   A^2 -> H(U1(d, d), U1(b, e))
27.56/8.96	   A^2 -> H(U1(d, d), U1(b, k))
27.56/8.96	   A^2 -> H(U1(d, d), U1(e, c))
27.56/8.96	   A^2 -> H(U1(d, d), U1(k, c))
27.56/8.96	   A^2 -> H(U1(d, d), U1(c, e))
27.56/8.96	   A^2 -> H(U1(d, d), U1(c, k))
27.56/8.96	   A^2 -> H(U1(d, d), U1(e, e))
27.56/8.96	   A^2 -> H(U1(d, d), U1(k, k))
27.56/8.96	   A^2 -> H(f(d), b)
27.56/8.96	   A^2 -> H(f(d), U1(e, d))
27.56/8.96	   A^2 -> H(f(d), U1(d, e))
27.56/8.96	   A^2 -> H(f(d), c)
27.56/8.96	   A^2 -> H(f(d), U1(e, k))
27.56/8.96	   A^2 -> H(f(d), U1(k, e))
27.56/8.96	   A^2 -> H(f(d), e)
27.56/8.96	   A^2 -> H(f(a), d)
27.56/8.96	   A^2 -> H(U1(c, c), U1(e, c))
27.56/8.96	   A^2 -> H(f(c), c)
27.56/8.96	   A^2 -> H(f(c), U1(e, k))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, c))
27.56/8.96	   A^2 -> H(f(c), U1(k, e))
27.56/8.96	   A^2 -> H(f(c), U1(k, k))
27.56/8.96	   A^2 -> H(U1(c, c), U1(c, e))
27.56/8.96	   A^2 -> H(U1(c, c), U1(c, k))
27.56/8.96	   A^2 -> H(f(a), k)
27.56/8.96	   A^2 -> H(f(e), U1(e, e))
27.56/8.96	   A^2 -> H(f(c), e)
27.56/8.96	   A^2 -> H(U1(d, d), U1(k, d))
27.56/8.96	   A^2 -> H(f(d), U1(k, k))
27.56/8.96	   A^2 -> H(U1(d, d), U1(d, k))
27.56/8.96	   A^2 -> H(d, U1(b, b))
27.56/8.96	   A^2 -> H(d, f(c))
27.56/8.96	   A^2 -> H(d, f(d))
27.56/8.96	   A^2 -> H(a, U1(c, b))
27.56/8.96	   A^2 -> H(a, U1(d, b))
27.56/8.96	   A^2 -> H(a, U1(b, c))
27.56/8.96	   A^2 -> H(a, U1(b, d))
27.56/8.96	   A^2 -> H(a, U1(c, c))
27.56/8.96	   A^2 -> H(a, f(e))
27.56/8.96	   A^2 -> H(a, f(k))
27.56/8.96	   A^2 -> H(a, U1(d, d))
27.56/8.96	   A^2 -> H(U1(e, d), U1(c, b))
27.56/8.96	   A^2 -> H(U1(e, d), U1(d, b))
27.56/8.96	   A^2 -> H(U1(e, d), U1(b, c))
27.56/8.96	   A^2 -> H(U1(e, d), U1(b, d))
27.56/8.96	   A^2 -> H(U1(e, d), U1(c, c))
27.56/8.96	   A^2 -> H(U1(e, d), f(e))
27.56/8.96	   A^2 -> H(U1(e, d), f(k))
27.56/8.96	   A^2 -> H(U1(e, d), U1(d, d))
27.56/8.96	   A^2 -> H(U1(e, a), U1(e, b))
27.56/8.96	   A^2 -> H(U1(e, a), U1(k, b))
27.56/8.96	   A^2 -> H(U1(e, a), U1(c, d))
27.56/8.96	   A^2 -> H(U1(e, a), U1(d, c))
27.56/8.96	   A^2 -> H(U1(e, a), U1(b, e))
27.56/8.96	   A^2 -> H(U1(e, a), U1(b, k))
27.56/8.96	   A^2 -> H(U1(e, a), U1(e, c))
27.56/8.96	   A^2 -> H(U1(e, a), U1(k, c))
27.56/8.96	   A^2 -> H(U1(e, a), U1(c, e))
27.56/8.96	   A^2 -> H(U1(e, a), U1(c, k))
27.56/8.96	   A^2 -> H(U1(e, a), U1(e, e))
27.56/8.96	   A^2 -> H(U1(e, a), U1(k, k))
27.56/8.96	   A^2 -> H(U1(e, a), U1(k, d))
27.56/8.96	   A^2 -> H(U1(e, a), U1(d, k))
27.56/8.96	   A^2 -> H(U1(k, a), U1(e, b))
27.56/8.96	   A^2 -> H(U1(k, a), U1(k, b))
27.56/8.96	   A^2 -> H(U1(k, a), U1(c, d))
27.56/8.96	   A^2 -> H(U1(k, a), U1(d, c))
27.56/8.96	   A^2 -> H(U1(k, a), U1(b, e))
27.56/8.96	   A^2 -> H(U1(k, a), U1(b, k))
27.56/8.96	   A^2 -> H(U1(k, a), U1(e, c))
27.56/8.96	   A^2 -> H(U1(k, a), U1(k, c))
27.56/8.96	   A^2 -> H(U1(k, a), U1(c, e))
27.56/8.96	   A^2 -> H(U1(k, a), U1(c, k))
27.56/8.96	   A^2 -> H(U1(k, a), U1(e, e))
27.56/8.96	   A^2 -> H(U1(k, a), U1(k, k))
27.56/8.96	   A^2 -> H(U1(k, a), U1(k, d))
27.56/8.96	   A^2 -> H(U1(k, a), U1(d, k))
27.56/8.96	   A^2 -> H(U1(c, d), U1(e, b))
27.56/8.96	   A^2 -> H(U1(c, d), U1(k, b))
27.56/8.96	   A^2 -> H(U1(c, d), U1(c, d))
27.56/8.96	   A^2 -> H(U1(c, d), U1(d, c))
27.56/8.96	   A^2 -> H(U1(c, d), U1(b, e))
27.56/8.96	   A^2 -> H(U1(c, d), U1(b, k))
27.56/8.96	   A^2 -> H(U1(c, d), U1(e, c))
27.56/8.96	   A^2 -> H(U1(c, d), U1(k, c))
27.56/8.96	   A^2 -> H(U1(c, d), U1(c, e))
27.56/8.96	   A^2 -> H(U1(c, d), U1(c, k))
27.56/8.96	   A^2 -> H(U1(c, d), U1(e, e))
27.56/8.96	   A^2 -> H(U1(c, d), U1(k, k))
27.56/8.96	   A^2 -> H(U1(c, d), U1(k, d))
27.56/8.96	   A^2 -> H(U1(c, d), U1(d, k))
27.56/8.96	   A^2 -> H(U1(c, a), b)
27.56/8.96	   A^2 -> H(U1(c, a), U1(e, d))
27.56/8.96	   A^2 -> H(U1(c, a), U1(d, e))
27.56/8.96	   A^2 -> H(U1(c, a), c)
27.56/8.96	   A^2 -> H(U1(c, a), U1(e, k))
27.56/8.96	   A^2 -> H(U1(c, a), U1(k, e))
27.56/8.96	   A^2 -> H(U1(c, a), e)
27.56/8.96	   A^2 -> H(U1(c, a), U1(k, k))
27.56/8.96	   A^2 -> H(U1(d, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(d, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(d, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(d, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(d, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(d, e), f(e))
27.56/8.96	   A^2 -> H(U1(d, e), f(k))
27.56/8.96	   A^2 -> H(U1(d, e), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, c), U1(e, b))
27.56/8.96	   A^2 -> H(U1(d, c), U1(k, b))
27.56/8.96	   A^2 -> H(U1(d, c), U1(c, d))
27.56/8.96	   A^2 -> H(U1(d, c), U1(d, c))
27.56/8.96	   A^2 -> H(U1(d, c), U1(b, e))
27.56/8.96	   A^2 -> H(U1(d, c), U1(b, k))
27.56/8.96	   A^2 -> H(U1(d, c), U1(e, c))
27.56/8.96	   A^2 -> H(U1(d, c), U1(k, c))
27.56/8.96	   A^2 -> H(U1(d, c), U1(c, e))
27.56/8.96	   A^2 -> H(U1(d, c), U1(c, k))
27.56/8.96	
27.56/8.96	The TRS R consists of the following rules:
27.56/8.96	
27.56/8.96	   f(x) -> U1(x, x)
27.56/8.96	   U1(e, x) -> x
27.56/8.96	   a -> c
27.56/8.96	   a -> d
27.56/8.96	   b -> c
27.56/8.96	   b -> d
27.56/8.96	   d -> k
27.56/8.96	   c -> e
27.56/8.96	   c -> k
27.56/8.96	
27.56/8.96	Q is empty.
27.56/8.96	We have to consider all minimal (P,Q,R)-chains.
27.56/8.96	----------------------------------------
27.56/8.96	
27.56/8.96	(647) TransformationProof (EQUIVALENT)
27.56/8.96	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), f(e)) at position [] we obtained the following new rules [LPAR04]:
27.56/8.96	
27.56/8.96	   (A^2 -> H(U1(k, c), f(e)),A^2 -> H(U1(k, c), f(e)))
27.56/8.96	   (A^2 -> H(U1(d, e), f(e)),A^2 -> H(U1(d, e), f(e)))
27.56/8.96	   (A^2 -> H(U1(d, k), f(e)),A^2 -> H(U1(d, k), f(e)))
27.56/8.96	   (A^2 -> H(U1(d, c), U1(e, e)),A^2 -> H(U1(d, c), U1(e, e)))
27.56/8.96	
27.56/8.96	
27.56/8.96	----------------------------------------
27.56/8.96	
27.56/8.96	(648)
27.56/8.96	Obligation:
27.56/8.96	Q DP problem:
27.56/8.96	The TRS P consists of the following rules:
27.56/8.96	
27.56/8.96	   H(x, x) -> G(x, x, f(k))
27.56/8.96	   G(d, x, x) -> A^2
27.56/8.96	   A^2 -> H(f(c), f(c))
27.56/8.96	   A^2 -> H(f(d), f(d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(c, c))
27.56/8.96	   A^2 -> H(f(e), f(e))
27.56/8.96	   A^2 -> H(f(k), f(k))
27.56/8.96	   A^2 -> H(U1(d, d), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, c), f(k))
27.56/8.96	   A^2 -> H(U1(d, c), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, a), U1(e, b))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, b))
27.56/8.96	   A^2 -> H(U1(d, a), U1(c, d))
27.56/8.96	   A^2 -> H(U1(d, a), U1(d, c))
27.56/8.96	   A^2 -> H(U1(d, a), U1(b, e))
27.56/8.96	   A^2 -> H(U1(d, a), U1(b, k))
27.56/8.96	   A^2 -> H(U1(d, a), U1(e, c))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, c))
27.56/8.96	   A^2 -> H(U1(d, a), U1(c, e))
27.56/8.96	   A^2 -> H(U1(d, a), U1(c, k))
27.56/8.96	   A^2 -> H(U1(d, a), U1(e, e))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, k))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, d))
27.56/8.96	   A^2 -> H(U1(d, a), U1(d, k))
27.56/8.96	   A^2 -> H(U1(a, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(a, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(a, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(a, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(a, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(a, e), f(e))
27.56/8.96	   A^2 -> H(U1(a, e), f(k))
27.56/8.96	   A^2 -> H(U1(a, e), U1(d, d))
27.56/8.96	   A^2 -> H(U1(a, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(a, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(a, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(a, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(a, k), U1(c, c))
27.56/8.96	   A^2 -> H(U1(a, k), f(e))
27.56/8.96	   A^2 -> H(U1(a, k), f(k))
27.56/8.96	   A^2 -> H(U1(a, k), U1(d, d))
27.56/8.96	   A^2 -> H(U1(a, c), U1(e, b))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, b))
27.56/8.96	   A^2 -> H(U1(a, c), U1(c, d))
27.56/8.96	   A^2 -> H(U1(a, c), U1(d, c))
27.56/8.96	   A^2 -> H(U1(a, c), U1(b, e))
27.56/8.96	   A^2 -> H(U1(a, c), U1(b, k))
27.56/8.96	   A^2 -> H(U1(a, c), U1(e, c))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, c))
27.56/8.96	   A^2 -> H(U1(a, c), U1(c, e))
27.56/8.96	   A^2 -> H(U1(a, c), U1(c, k))
27.56/8.96	   A^2 -> H(U1(a, c), U1(e, e))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, k))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, d))
27.56/8.96	   A^2 -> H(U1(a, c), U1(d, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(e, b))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, b))
27.56/8.96	   A^2 -> H(U1(a, d), U1(c, d))
27.56/8.96	   A^2 -> H(U1(a, d), U1(d, c))
27.56/8.96	   A^2 -> H(U1(a, d), U1(b, e))
27.56/8.96	   A^2 -> H(U1(a, d), U1(b, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(e, c))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, c))
27.56/8.96	   A^2 -> H(U1(a, d), U1(c, e))
27.56/8.96	   A^2 -> H(U1(a, d), U1(c, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(e, e))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, d))
27.56/8.96	   A^2 -> H(U1(a, d), U1(d, k))
27.56/8.96	   A^2 -> H(U1(a, a), b)
27.56/8.96	   A^2 -> H(U1(a, a), U1(e, d))
27.56/8.96	   A^2 -> H(U1(a, a), U1(d, e))
27.56/8.96	   A^2 -> H(U1(a, a), c)
27.56/8.96	   A^2 -> H(U1(a, a), U1(e, k))
27.56/8.96	   A^2 -> H(U1(a, a), U1(k, e))
27.56/8.96	   A^2 -> H(U1(a, a), e)
27.56/8.96	   A^2 -> H(U1(a, a), U1(k, k))
27.56/8.96	   A^2 -> H(k, f(b))
27.56/8.96	   A^2 -> H(c, U1(b, b))
27.56/8.96	   A^2 -> H(c, f(c))
27.56/8.96	   A^2 -> H(c, f(d))
27.56/8.96	   A^2 -> H(U1(e, k), U1(b, b))
27.56/8.96	   A^2 -> H(U1(e, k), f(c))
27.56/8.96	   A^2 -> H(U1(e, k), f(d))
27.56/8.96	   A^2 -> H(U1(e, c), U1(c, b))
27.56/8.96	   A^2 -> H(U1(e, c), U1(d, b))
27.56/8.96	   A^2 -> H(U1(e, c), U1(b, c))
27.56/8.96	   A^2 -> H(U1(e, c), U1(b, d))
27.56/8.96	   A^2 -> H(U1(e, c), U1(c, c))
27.56/8.96	   A^2 -> H(U1(e, c), f(e))
27.56/8.96	   A^2 -> H(U1(e, c), f(k))
27.56/8.96	   A^2 -> H(U1(e, c), U1(d, d))
27.56/8.96	   A^2 -> H(U1(k, e), U1(b, b))
27.56/8.96	   A^2 -> H(U1(k, e), f(c))
27.56/8.96	   A^2 -> H(U1(k, e), f(d))
27.56/8.96	   A^2 -> H(U1(k, c), U1(c, b))
27.56/8.96	   A^2 -> H(U1(k, c), U1(d, b))
27.56/8.96	   A^2 -> H(U1(k, c), U1(b, c))
27.56/8.96	   A^2 -> H(U1(k, c), U1(b, d))
27.56/8.96	   A^2 -> H(U1(k, c), U1(c, c))
27.56/8.96	   A^2 -> H(U1(k, c), f(e))
27.56/8.96	   A^2 -> H(U1(k, c), f(k))
27.56/8.96	   A^2 -> H(U1(k, c), U1(d, d))
27.56/8.96	   A^2 -> H(U1(c, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(c, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(c, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(c, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(c, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(c, e), f(e))
27.56/8.96	   A^2 -> H(U1(c, e), f(k))
27.56/8.96	   A^2 -> H(U1(c, e), U1(d, d))
27.56/8.96	   A^2 -> H(U1(c, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(c, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(c, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(c, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(c, k), U1(c, c))
27.56/8.96	   A^2 -> H(U1(c, k), f(e))
27.56/8.96	   A^2 -> H(U1(c, k), f(k))
27.56/8.96	   A^2 -> H(U1(c, k), U1(d, d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(e, b))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, b))
27.56/8.96	   A^2 -> H(U1(c, c), U1(c, d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(d, c))
27.56/8.96	   A^2 -> H(U1(c, c), U1(b, e))
27.56/8.96	   A^2 -> H(U1(c, c), U1(b, k))
27.56/8.96	   A^2 -> H(U1(c, c), U1(e, e))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, k))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(d, k))
27.56/8.96	   A^2 -> H(e, U1(b, b))
27.56/8.96	   A^2 -> H(e, f(c))
27.56/8.96	   A^2 -> H(e, f(d))
27.56/8.96	   A^2 -> H(U1(e, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(e, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(e, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(e, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(e, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(e, e), f(e))
27.56/8.96	   A^2 -> H(U1(e, e), f(k))
27.56/8.96	   A^2 -> H(U1(e, e), U1(d, d))
27.56/8.96	   A^2 -> H(f(e), U1(e, b))
27.56/8.96	   A^2 -> H(f(e), U1(k, b))
27.56/8.96	   A^2 -> H(f(e), U1(c, d))
27.56/8.96	   A^2 -> H(f(e), U1(d, c))
27.56/8.96	   A^2 -> H(f(e), U1(b, e))
27.56/8.96	   A^2 -> H(f(e), U1(b, k))
27.56/8.96	   A^2 -> H(f(e), U1(e, c))
27.56/8.96	   A^2 -> H(f(e), U1(k, c))
27.56/8.96	   A^2 -> H(f(e), U1(c, e))
27.56/8.96	   A^2 -> H(f(e), U1(c, k))
27.56/8.96	   A^2 -> H(f(e), U1(k, k))
27.56/8.96	   A^2 -> H(f(e), U1(k, d))
27.56/8.96	   A^2 -> H(f(e), U1(d, k))
27.56/8.96	   A^2 -> H(U1(k, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(k, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(k, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(k, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(k, k), U1(c, c))
27.56/8.96	   A^2 -> H(U1(k, k), f(e))
27.56/8.96	   A^2 -> H(U1(k, k), f(k))
27.56/8.96	   A^2 -> H(U1(k, k), U1(d, d))
27.56/8.96	   A^2 -> H(f(k), U1(e, b))
27.56/8.96	   A^2 -> H(f(k), U1(k, b))
27.56/8.96	   A^2 -> H(f(k), U1(c, d))
27.56/8.96	   A^2 -> H(f(k), U1(d, c))
27.56/8.96	   A^2 -> H(f(k), U1(b, e))
27.56/8.96	   A^2 -> H(f(k), U1(b, k))
27.56/8.96	   A^2 -> H(f(k), U1(e, c))
27.56/8.96	   A^2 -> H(f(k), U1(k, c))
27.56/8.96	   A^2 -> H(f(k), U1(c, e))
27.56/8.96	   A^2 -> H(f(k), U1(c, k))
27.56/8.96	   A^2 -> H(f(k), U1(e, e))
27.56/8.96	   A^2 -> H(f(k), U1(k, d))
27.56/8.96	   A^2 -> H(f(k), U1(d, k))
27.56/8.96	   A^2 -> H(f(c), b)
27.56/8.96	   A^2 -> H(f(c), U1(e, d))
27.56/8.96	   A^2 -> H(f(c), U1(d, e))
27.56/8.96	   A^2 -> H(f(k), U1(k, k))
27.56/8.96	   A^2 -> H(U1(k, k), U1(b, b))
27.56/8.96	   A^2 -> H(U1(k, k), f(c))
27.56/8.96	   A^2 -> H(U1(k, k), f(d))
27.56/8.96	   A^2 -> H(U1(k, d), U1(c, b))
27.56/8.96	   A^2 -> H(U1(k, d), U1(d, b))
27.56/8.96	   A^2 -> H(U1(k, d), U1(b, c))
27.56/8.96	   A^2 -> H(U1(k, d), U1(b, d))
27.56/8.96	   A^2 -> H(U1(k, d), U1(c, c))
27.56/8.96	   A^2 -> H(U1(k, d), f(e))
27.56/8.96	   A^2 -> H(U1(k, d), f(k))
27.56/8.96	   A^2 -> H(U1(k, d), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(d, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(d, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(d, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(d, k), U1(c, c))
27.56/8.96	   A^2 -> H(U1(d, k), f(e))
27.56/8.96	   A^2 -> H(U1(d, k), f(k))
27.56/8.96	   A^2 -> H(U1(d, k), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, d), U1(e, b))
27.56/8.96	   A^2 -> H(U1(d, d), U1(k, b))
27.56/8.96	   A^2 -> H(U1(d, d), U1(c, d))
27.56/8.96	   A^2 -> H(U1(d, d), U1(d, c))
27.56/8.96	   A^2 -> H(U1(d, d), U1(b, e))
27.56/8.96	   A^2 -> H(U1(d, d), U1(b, k))
27.56/8.96	   A^2 -> H(U1(d, d), U1(e, c))
27.56/8.96	   A^2 -> H(U1(d, d), U1(k, c))
27.56/8.96	   A^2 -> H(U1(d, d), U1(c, e))
27.56/8.96	   A^2 -> H(U1(d, d), U1(c, k))
27.56/8.96	   A^2 -> H(U1(d, d), U1(e, e))
27.56/8.96	   A^2 -> H(U1(d, d), U1(k, k))
27.56/8.96	   A^2 -> H(f(d), b)
27.56/8.96	   A^2 -> H(f(d), U1(e, d))
27.56/8.96	   A^2 -> H(f(d), U1(d, e))
27.56/8.96	   A^2 -> H(f(d), c)
27.56/8.96	   A^2 -> H(f(d), U1(e, k))
27.56/8.96	   A^2 -> H(f(d), U1(k, e))
27.56/8.96	   A^2 -> H(f(d), e)
27.56/8.96	   A^2 -> H(f(a), d)
27.56/8.96	   A^2 -> H(U1(c, c), U1(e, c))
27.56/8.96	   A^2 -> H(f(c), c)
27.56/8.96	   A^2 -> H(f(c), U1(e, k))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, c))
27.56/8.96	   A^2 -> H(f(c), U1(k, e))
27.56/8.96	   A^2 -> H(f(c), U1(k, k))
27.56/8.96	   A^2 -> H(U1(c, c), U1(c, e))
27.56/8.96	   A^2 -> H(U1(c, c), U1(c, k))
27.56/8.96	   A^2 -> H(f(a), k)
27.56/8.96	   A^2 -> H(f(e), U1(e, e))
27.56/8.96	   A^2 -> H(f(c), e)
27.56/8.96	   A^2 -> H(U1(d, d), U1(k, d))
27.56/8.96	   A^2 -> H(f(d), U1(k, k))
27.56/8.96	   A^2 -> H(U1(d, d), U1(d, k))
27.56/8.96	   A^2 -> H(d, U1(b, b))
27.56/8.96	   A^2 -> H(d, f(c))
27.56/8.96	   A^2 -> H(d, f(d))
27.56/8.96	   A^2 -> H(a, U1(c, b))
27.56/8.96	   A^2 -> H(a, U1(d, b))
27.56/8.96	   A^2 -> H(a, U1(b, c))
27.56/8.96	   A^2 -> H(a, U1(b, d))
27.56/8.96	   A^2 -> H(a, U1(c, c))
27.56/8.96	   A^2 -> H(a, f(e))
27.56/8.96	   A^2 -> H(a, f(k))
27.56/8.96	   A^2 -> H(a, U1(d, d))
27.56/8.96	   A^2 -> H(U1(e, d), U1(c, b))
27.56/8.96	   A^2 -> H(U1(e, d), U1(d, b))
27.56/8.96	   A^2 -> H(U1(e, d), U1(b, c))
27.56/8.96	   A^2 -> H(U1(e, d), U1(b, d))
27.56/8.96	   A^2 -> H(U1(e, d), U1(c, c))
27.56/8.96	   A^2 -> H(U1(e, d), f(e))
27.56/8.96	   A^2 -> H(U1(e, d), f(k))
27.56/8.96	   A^2 -> H(U1(e, d), U1(d, d))
27.56/8.96	   A^2 -> H(U1(e, a), U1(e, b))
27.56/8.96	   A^2 -> H(U1(e, a), U1(k, b))
27.56/8.96	   A^2 -> H(U1(e, a), U1(c, d))
27.56/8.96	   A^2 -> H(U1(e, a), U1(d, c))
27.56/8.96	   A^2 -> H(U1(e, a), U1(b, e))
27.56/8.96	   A^2 -> H(U1(e, a), U1(b, k))
27.56/8.96	   A^2 -> H(U1(e, a), U1(e, c))
27.56/8.96	   A^2 -> H(U1(e, a), U1(k, c))
27.56/8.96	   A^2 -> H(U1(e, a), U1(c, e))
27.56/8.96	   A^2 -> H(U1(e, a), U1(c, k))
27.56/8.96	   A^2 -> H(U1(e, a), U1(e, e))
27.56/8.96	   A^2 -> H(U1(e, a), U1(k, k))
27.56/8.96	   A^2 -> H(U1(e, a), U1(k, d))
27.56/8.96	   A^2 -> H(U1(e, a), U1(d, k))
27.56/8.96	   A^2 -> H(U1(k, a), U1(e, b))
27.56/8.96	   A^2 -> H(U1(k, a), U1(k, b))
27.56/8.96	   A^2 -> H(U1(k, a), U1(c, d))
27.56/8.96	   A^2 -> H(U1(k, a), U1(d, c))
27.56/8.96	   A^2 -> H(U1(k, a), U1(b, e))
27.56/8.96	   A^2 -> H(U1(k, a), U1(b, k))
27.56/8.96	   A^2 -> H(U1(k, a), U1(e, c))
27.56/8.96	   A^2 -> H(U1(k, a), U1(k, c))
27.56/8.96	   A^2 -> H(U1(k, a), U1(c, e))
27.56/8.96	   A^2 -> H(U1(k, a), U1(c, k))
27.56/8.96	   A^2 -> H(U1(k, a), U1(e, e))
27.56/8.96	   A^2 -> H(U1(k, a), U1(k, k))
27.56/8.96	   A^2 -> H(U1(k, a), U1(k, d))
27.56/8.96	   A^2 -> H(U1(k, a), U1(d, k))
27.56/8.96	   A^2 -> H(U1(c, d), U1(e, b))
27.56/8.96	   A^2 -> H(U1(c, d), U1(k, b))
27.56/8.96	   A^2 -> H(U1(c, d), U1(c, d))
27.56/8.96	   A^2 -> H(U1(c, d), U1(d, c))
27.56/8.96	   A^2 -> H(U1(c, d), U1(b, e))
27.56/8.96	   A^2 -> H(U1(c, d), U1(b, k))
27.56/8.96	   A^2 -> H(U1(c, d), U1(e, c))
27.56/8.96	   A^2 -> H(U1(c, d), U1(k, c))
27.56/8.96	   A^2 -> H(U1(c, d), U1(c, e))
27.56/8.96	   A^2 -> H(U1(c, d), U1(c, k))
27.56/8.96	   A^2 -> H(U1(c, d), U1(e, e))
27.56/8.96	   A^2 -> H(U1(c, d), U1(k, k))
27.56/8.96	   A^2 -> H(U1(c, d), U1(k, d))
27.56/8.96	   A^2 -> H(U1(c, d), U1(d, k))
27.56/8.96	   A^2 -> H(U1(c, a), b)
27.56/8.96	   A^2 -> H(U1(c, a), U1(e, d))
27.56/8.96	   A^2 -> H(U1(c, a), U1(d, e))
27.56/8.96	   A^2 -> H(U1(c, a), c)
27.56/8.96	   A^2 -> H(U1(c, a), U1(e, k))
27.56/8.96	   A^2 -> H(U1(c, a), U1(k, e))
27.56/8.96	   A^2 -> H(U1(c, a), e)
27.56/8.96	   A^2 -> H(U1(c, a), U1(k, k))
27.56/8.96	   A^2 -> H(U1(d, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(d, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(d, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(d, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(d, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(d, e), f(e))
27.56/8.96	   A^2 -> H(U1(d, e), f(k))
27.56/8.96	   A^2 -> H(U1(d, e), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, c), U1(e, b))
27.56/8.96	   A^2 -> H(U1(d, c), U1(k, b))
27.56/8.96	   A^2 -> H(U1(d, c), U1(c, d))
27.56/8.96	   A^2 -> H(U1(d, c), U1(d, c))
27.56/8.96	   A^2 -> H(U1(d, c), U1(b, e))
27.56/8.96	   A^2 -> H(U1(d, c), U1(b, k))
27.56/8.96	   A^2 -> H(U1(d, c), U1(e, c))
27.56/8.96	   A^2 -> H(U1(d, c), U1(k, c))
27.56/8.96	   A^2 -> H(U1(d, c), U1(c, e))
27.56/8.96	   A^2 -> H(U1(d, c), U1(c, k))
27.56/8.96	   A^2 -> H(U1(d, c), U1(e, e))
27.56/8.96	
27.56/8.96	The TRS R consists of the following rules:
27.56/8.96	
27.56/8.96	   f(x) -> U1(x, x)
27.56/8.96	   U1(e, x) -> x
27.56/8.96	   a -> c
27.56/8.96	   a -> d
27.56/8.96	   b -> c
27.56/8.96	   b -> d
27.56/8.96	   d -> k
27.56/8.96	   c -> e
27.56/8.96	   c -> k
27.56/8.96	
27.56/8.96	Q is empty.
27.56/8.96	We have to consider all minimal (P,Q,R)-chains.
27.56/8.96	----------------------------------------
27.56/8.96	
27.56/8.96	(649) TransformationProof (EQUIVALENT)
27.56/8.96	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), f(k)) at position [] we obtained the following new rules [LPAR04]:
27.56/8.96	
27.56/8.96	   (A^2 -> H(U1(k, c), f(k)),A^2 -> H(U1(k, c), f(k)))
27.56/8.96	   (A^2 -> H(U1(d, e), f(k)),A^2 -> H(U1(d, e), f(k)))
27.56/8.96	   (A^2 -> H(U1(d, k), f(k)),A^2 -> H(U1(d, k), f(k)))
27.56/8.96	   (A^2 -> H(U1(d, c), U1(k, k)),A^2 -> H(U1(d, c), U1(k, k)))
27.56/8.96	
27.56/8.96	
27.56/8.96	----------------------------------------
27.56/8.96	
27.56/8.96	(650)
27.56/8.96	Obligation:
27.56/8.96	Q DP problem:
27.56/8.96	The TRS P consists of the following rules:
27.56/8.96	
27.56/8.96	   H(x, x) -> G(x, x, f(k))
27.56/8.96	   G(d, x, x) -> A^2
27.56/8.96	   A^2 -> H(f(c), f(c))
27.56/8.96	   A^2 -> H(f(d), f(d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(c, c))
27.56/8.96	   A^2 -> H(f(e), f(e))
27.56/8.96	   A^2 -> H(f(k), f(k))
27.56/8.96	   A^2 -> H(U1(d, d), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, c), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, a), U1(e, b))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, b))
27.56/8.96	   A^2 -> H(U1(d, a), U1(c, d))
27.56/8.96	   A^2 -> H(U1(d, a), U1(d, c))
27.56/8.96	   A^2 -> H(U1(d, a), U1(b, e))
27.56/8.96	   A^2 -> H(U1(d, a), U1(b, k))
27.56/8.96	   A^2 -> H(U1(d, a), U1(e, c))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, c))
27.56/8.96	   A^2 -> H(U1(d, a), U1(c, e))
27.56/8.96	   A^2 -> H(U1(d, a), U1(c, k))
27.56/8.96	   A^2 -> H(U1(d, a), U1(e, e))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, k))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, d))
27.56/8.96	   A^2 -> H(U1(d, a), U1(d, k))
27.56/8.96	   A^2 -> H(U1(a, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(a, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(a, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(a, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(a, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(a, e), f(e))
27.56/8.96	   A^2 -> H(U1(a, e), f(k))
27.56/8.96	   A^2 -> H(U1(a, e), U1(d, d))
27.56/8.96	   A^2 -> H(U1(a, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(a, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(a, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(a, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(a, k), U1(c, c))
27.56/8.96	   A^2 -> H(U1(a, k), f(e))
27.56/8.96	   A^2 -> H(U1(a, k), f(k))
27.56/8.96	   A^2 -> H(U1(a, k), U1(d, d))
27.56/8.96	   A^2 -> H(U1(a, c), U1(e, b))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, b))
27.56/8.96	   A^2 -> H(U1(a, c), U1(c, d))
27.56/8.96	   A^2 -> H(U1(a, c), U1(d, c))
27.56/8.96	   A^2 -> H(U1(a, c), U1(b, e))
27.56/8.96	   A^2 -> H(U1(a, c), U1(b, k))
27.56/8.96	   A^2 -> H(U1(a, c), U1(e, c))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, c))
27.56/8.96	   A^2 -> H(U1(a, c), U1(c, e))
27.56/8.96	   A^2 -> H(U1(a, c), U1(c, k))
27.56/8.96	   A^2 -> H(U1(a, c), U1(e, e))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, k))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, d))
27.56/8.96	   A^2 -> H(U1(a, c), U1(d, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(e, b))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, b))
27.56/8.96	   A^2 -> H(U1(a, d), U1(c, d))
27.56/8.96	   A^2 -> H(U1(a, d), U1(d, c))
27.56/8.96	   A^2 -> H(U1(a, d), U1(b, e))
27.56/8.96	   A^2 -> H(U1(a, d), U1(b, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(e, c))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, c))
27.56/8.96	   A^2 -> H(U1(a, d), U1(c, e))
27.56/8.96	   A^2 -> H(U1(a, d), U1(c, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(e, e))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, d))
27.56/8.96	   A^2 -> H(U1(a, d), U1(d, k))
27.56/8.96	   A^2 -> H(U1(a, a), b)
27.56/8.96	   A^2 -> H(U1(a, a), U1(e, d))
27.56/8.96	   A^2 -> H(U1(a, a), U1(d, e))
27.56/8.96	   A^2 -> H(U1(a, a), c)
27.56/8.96	   A^2 -> H(U1(a, a), U1(e, k))
27.56/8.96	   A^2 -> H(U1(a, a), U1(k, e))
27.56/8.96	   A^2 -> H(U1(a, a), e)
27.56/8.96	   A^2 -> H(U1(a, a), U1(k, k))
27.56/8.96	   A^2 -> H(k, f(b))
27.56/8.96	   A^2 -> H(c, U1(b, b))
27.56/8.96	   A^2 -> H(c, f(c))
27.56/8.96	   A^2 -> H(c, f(d))
27.56/8.96	   A^2 -> H(U1(e, k), U1(b, b))
27.56/8.96	   A^2 -> H(U1(e, k), f(c))
27.56/8.96	   A^2 -> H(U1(e, k), f(d))
27.56/8.96	   A^2 -> H(U1(e, c), U1(c, b))
27.56/8.96	   A^2 -> H(U1(e, c), U1(d, b))
27.56/8.96	   A^2 -> H(U1(e, c), U1(b, c))
27.56/8.96	   A^2 -> H(U1(e, c), U1(b, d))
27.56/8.96	   A^2 -> H(U1(e, c), U1(c, c))
27.56/8.96	   A^2 -> H(U1(e, c), f(e))
27.56/8.96	   A^2 -> H(U1(e, c), f(k))
27.56/8.96	   A^2 -> H(U1(e, c), U1(d, d))
27.56/8.96	   A^2 -> H(U1(k, e), U1(b, b))
27.56/8.96	   A^2 -> H(U1(k, e), f(c))
27.56/8.96	   A^2 -> H(U1(k, e), f(d))
27.56/8.96	   A^2 -> H(U1(k, c), U1(c, b))
27.56/8.96	   A^2 -> H(U1(k, c), U1(d, b))
27.56/8.96	   A^2 -> H(U1(k, c), U1(b, c))
27.56/8.96	   A^2 -> H(U1(k, c), U1(b, d))
27.56/8.96	   A^2 -> H(U1(k, c), U1(c, c))
27.56/8.96	   A^2 -> H(U1(k, c), f(e))
27.56/8.96	   A^2 -> H(U1(k, c), f(k))
27.56/8.96	   A^2 -> H(U1(k, c), U1(d, d))
27.56/8.96	   A^2 -> H(U1(c, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(c, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(c, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(c, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(c, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(c, e), f(e))
27.56/8.96	   A^2 -> H(U1(c, e), f(k))
27.56/8.96	   A^2 -> H(U1(c, e), U1(d, d))
27.56/8.96	   A^2 -> H(U1(c, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(c, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(c, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(c, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(c, k), U1(c, c))
27.56/8.96	   A^2 -> H(U1(c, k), f(e))
27.56/8.96	   A^2 -> H(U1(c, k), f(k))
27.56/8.96	   A^2 -> H(U1(c, k), U1(d, d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(e, b))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, b))
27.56/8.96	   A^2 -> H(U1(c, c), U1(c, d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(d, c))
27.56/8.96	   A^2 -> H(U1(c, c), U1(b, e))
27.56/8.96	   A^2 -> H(U1(c, c), U1(b, k))
27.56/8.96	   A^2 -> H(U1(c, c), U1(e, e))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, k))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(d, k))
27.56/8.96	   A^2 -> H(e, U1(b, b))
27.56/8.96	   A^2 -> H(e, f(c))
27.56/8.96	   A^2 -> H(e, f(d))
27.56/8.96	   A^2 -> H(U1(e, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(e, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(e, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(e, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(e, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(e, e), f(e))
27.56/8.96	   A^2 -> H(U1(e, e), f(k))
27.56/8.96	   A^2 -> H(U1(e, e), U1(d, d))
27.56/8.96	   A^2 -> H(f(e), U1(e, b))
27.56/8.96	   A^2 -> H(f(e), U1(k, b))
27.56/8.96	   A^2 -> H(f(e), U1(c, d))
27.56/8.96	   A^2 -> H(f(e), U1(d, c))
27.56/8.96	   A^2 -> H(f(e), U1(b, e))
27.56/8.96	   A^2 -> H(f(e), U1(b, k))
27.56/8.96	   A^2 -> H(f(e), U1(e, c))
27.56/8.96	   A^2 -> H(f(e), U1(k, c))
27.56/8.96	   A^2 -> H(f(e), U1(c, e))
27.56/8.96	   A^2 -> H(f(e), U1(c, k))
27.56/8.96	   A^2 -> H(f(e), U1(k, k))
27.56/8.96	   A^2 -> H(f(e), U1(k, d))
27.56/8.96	   A^2 -> H(f(e), U1(d, k))
27.56/8.96	   A^2 -> H(U1(k, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(k, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(k, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(k, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(k, k), U1(c, c))
27.56/8.96	   A^2 -> H(U1(k, k), f(e))
27.56/8.96	   A^2 -> H(U1(k, k), f(k))
27.56/8.96	   A^2 -> H(U1(k, k), U1(d, d))
27.56/8.96	   A^2 -> H(f(k), U1(e, b))
27.56/8.96	   A^2 -> H(f(k), U1(k, b))
27.56/8.96	   A^2 -> H(f(k), U1(c, d))
27.56/8.96	   A^2 -> H(f(k), U1(d, c))
27.56/8.96	   A^2 -> H(f(k), U1(b, e))
27.56/8.96	   A^2 -> H(f(k), U1(b, k))
27.56/8.96	   A^2 -> H(f(k), U1(e, c))
27.56/8.96	   A^2 -> H(f(k), U1(k, c))
27.56/8.96	   A^2 -> H(f(k), U1(c, e))
27.56/8.96	   A^2 -> H(f(k), U1(c, k))
27.56/8.96	   A^2 -> H(f(k), U1(e, e))
27.56/8.96	   A^2 -> H(f(k), U1(k, d))
27.56/8.96	   A^2 -> H(f(k), U1(d, k))
27.56/8.96	   A^2 -> H(f(c), b)
27.56/8.96	   A^2 -> H(f(c), U1(e, d))
27.56/8.96	   A^2 -> H(f(c), U1(d, e))
27.56/8.96	   A^2 -> H(f(k), U1(k, k))
27.56/8.96	   A^2 -> H(U1(k, k), U1(b, b))
27.56/8.96	   A^2 -> H(U1(k, k), f(c))
27.56/8.96	   A^2 -> H(U1(k, k), f(d))
27.56/8.96	   A^2 -> H(U1(k, d), U1(c, b))
27.56/8.96	   A^2 -> H(U1(k, d), U1(d, b))
27.56/8.96	   A^2 -> H(U1(k, d), U1(b, c))
27.56/8.96	   A^2 -> H(U1(k, d), U1(b, d))
27.56/8.96	   A^2 -> H(U1(k, d), U1(c, c))
27.56/8.96	   A^2 -> H(U1(k, d), f(e))
27.56/8.96	   A^2 -> H(U1(k, d), f(k))
27.56/8.96	   A^2 -> H(U1(k, d), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(d, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(d, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(d, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(d, k), U1(c, c))
27.56/8.96	   A^2 -> H(U1(d, k), f(e))
27.56/8.96	   A^2 -> H(U1(d, k), f(k))
27.56/8.96	   A^2 -> H(U1(d, k), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, d), U1(e, b))
27.56/8.96	   A^2 -> H(U1(d, d), U1(k, b))
27.56/8.96	   A^2 -> H(U1(d, d), U1(c, d))
27.56/8.96	   A^2 -> H(U1(d, d), U1(d, c))
27.56/8.96	   A^2 -> H(U1(d, d), U1(b, e))
27.56/8.96	   A^2 -> H(U1(d, d), U1(b, k))
27.56/8.96	   A^2 -> H(U1(d, d), U1(e, c))
27.56/8.96	   A^2 -> H(U1(d, d), U1(k, c))
27.56/8.96	   A^2 -> H(U1(d, d), U1(c, e))
27.56/8.96	   A^2 -> H(U1(d, d), U1(c, k))
27.56/8.96	   A^2 -> H(U1(d, d), U1(e, e))
27.56/8.96	   A^2 -> H(U1(d, d), U1(k, k))
27.56/8.96	   A^2 -> H(f(d), b)
27.56/8.96	   A^2 -> H(f(d), U1(e, d))
27.56/8.96	   A^2 -> H(f(d), U1(d, e))
27.56/8.96	   A^2 -> H(f(d), c)
27.56/8.96	   A^2 -> H(f(d), U1(e, k))
27.56/8.96	   A^2 -> H(f(d), U1(k, e))
27.56/8.96	   A^2 -> H(f(d), e)
27.56/8.96	   A^2 -> H(f(a), d)
27.56/8.96	   A^2 -> H(U1(c, c), U1(e, c))
27.56/8.96	   A^2 -> H(f(c), c)
27.56/8.96	   A^2 -> H(f(c), U1(e, k))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, c))
27.56/8.96	   A^2 -> H(f(c), U1(k, e))
27.56/8.96	   A^2 -> H(f(c), U1(k, k))
27.56/8.96	   A^2 -> H(U1(c, c), U1(c, e))
27.56/8.96	   A^2 -> H(U1(c, c), U1(c, k))
27.56/8.96	   A^2 -> H(f(a), k)
27.56/8.96	   A^2 -> H(f(e), U1(e, e))
27.56/8.96	   A^2 -> H(f(c), e)
27.56/8.96	   A^2 -> H(U1(d, d), U1(k, d))
27.56/8.96	   A^2 -> H(f(d), U1(k, k))
27.56/8.96	   A^2 -> H(U1(d, d), U1(d, k))
27.56/8.96	   A^2 -> H(d, U1(b, b))
27.56/8.96	   A^2 -> H(d, f(c))
27.56/8.96	   A^2 -> H(d, f(d))
27.56/8.96	   A^2 -> H(a, U1(c, b))
27.56/8.96	   A^2 -> H(a, U1(d, b))
27.56/8.96	   A^2 -> H(a, U1(b, c))
27.56/8.96	   A^2 -> H(a, U1(b, d))
27.56/8.96	   A^2 -> H(a, U1(c, c))
27.56/8.96	   A^2 -> H(a, f(e))
27.56/8.96	   A^2 -> H(a, f(k))
27.56/8.96	   A^2 -> H(a, U1(d, d))
27.56/8.96	   A^2 -> H(U1(e, d), U1(c, b))
27.56/8.96	   A^2 -> H(U1(e, d), U1(d, b))
27.56/8.96	   A^2 -> H(U1(e, d), U1(b, c))
27.56/8.96	   A^2 -> H(U1(e, d), U1(b, d))
27.56/8.96	   A^2 -> H(U1(e, d), U1(c, c))
27.56/8.96	   A^2 -> H(U1(e, d), f(e))
27.56/8.96	   A^2 -> H(U1(e, d), f(k))
27.56/8.96	   A^2 -> H(U1(e, d), U1(d, d))
27.56/8.96	   A^2 -> H(U1(e, a), U1(e, b))
27.56/8.96	   A^2 -> H(U1(e, a), U1(k, b))
27.56/8.96	   A^2 -> H(U1(e, a), U1(c, d))
27.56/8.96	   A^2 -> H(U1(e, a), U1(d, c))
27.56/8.96	   A^2 -> H(U1(e, a), U1(b, e))
27.56/8.96	   A^2 -> H(U1(e, a), U1(b, k))
27.56/8.96	   A^2 -> H(U1(e, a), U1(e, c))
27.56/8.96	   A^2 -> H(U1(e, a), U1(k, c))
27.56/8.96	   A^2 -> H(U1(e, a), U1(c, e))
27.56/8.96	   A^2 -> H(U1(e, a), U1(c, k))
27.56/8.96	   A^2 -> H(U1(e, a), U1(e, e))
27.56/8.96	   A^2 -> H(U1(e, a), U1(k, k))
27.56/8.96	   A^2 -> H(U1(e, a), U1(k, d))
27.56/8.96	   A^2 -> H(U1(e, a), U1(d, k))
27.56/8.96	   A^2 -> H(U1(k, a), U1(e, b))
27.56/8.96	   A^2 -> H(U1(k, a), U1(k, b))
27.56/8.96	   A^2 -> H(U1(k, a), U1(c, d))
27.56/8.96	   A^2 -> H(U1(k, a), U1(d, c))
27.56/8.96	   A^2 -> H(U1(k, a), U1(b, e))
27.56/8.96	   A^2 -> H(U1(k, a), U1(b, k))
27.56/8.96	   A^2 -> H(U1(k, a), U1(e, c))
27.56/8.96	   A^2 -> H(U1(k, a), U1(k, c))
27.56/8.96	   A^2 -> H(U1(k, a), U1(c, e))
27.56/8.96	   A^2 -> H(U1(k, a), U1(c, k))
27.56/8.96	   A^2 -> H(U1(k, a), U1(e, e))
27.56/8.96	   A^2 -> H(U1(k, a), U1(k, k))
27.56/8.96	   A^2 -> H(U1(k, a), U1(k, d))
27.56/8.96	   A^2 -> H(U1(k, a), U1(d, k))
27.56/8.96	   A^2 -> H(U1(c, d), U1(e, b))
27.56/8.96	   A^2 -> H(U1(c, d), U1(k, b))
27.56/8.96	   A^2 -> H(U1(c, d), U1(c, d))
27.56/8.96	   A^2 -> H(U1(c, d), U1(d, c))
27.56/8.96	   A^2 -> H(U1(c, d), U1(b, e))
27.56/8.96	   A^2 -> H(U1(c, d), U1(b, k))
27.56/8.96	   A^2 -> H(U1(c, d), U1(e, c))
27.56/8.96	   A^2 -> H(U1(c, d), U1(k, c))
27.56/8.96	   A^2 -> H(U1(c, d), U1(c, e))
27.56/8.96	   A^2 -> H(U1(c, d), U1(c, k))
27.56/8.96	   A^2 -> H(U1(c, d), U1(e, e))
27.56/8.96	   A^2 -> H(U1(c, d), U1(k, k))
27.56/8.96	   A^2 -> H(U1(c, d), U1(k, d))
27.56/8.96	   A^2 -> H(U1(c, d), U1(d, k))
27.56/8.96	   A^2 -> H(U1(c, a), b)
27.56/8.96	   A^2 -> H(U1(c, a), U1(e, d))
27.56/8.96	   A^2 -> H(U1(c, a), U1(d, e))
27.56/8.96	   A^2 -> H(U1(c, a), c)
27.56/8.96	   A^2 -> H(U1(c, a), U1(e, k))
27.56/8.96	   A^2 -> H(U1(c, a), U1(k, e))
27.56/8.96	   A^2 -> H(U1(c, a), e)
27.56/8.96	   A^2 -> H(U1(c, a), U1(k, k))
27.56/8.96	   A^2 -> H(U1(d, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(d, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(d, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(d, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(d, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(d, e), f(e))
27.56/8.96	   A^2 -> H(U1(d, e), f(k))
27.56/8.96	   A^2 -> H(U1(d, e), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, c), U1(e, b))
27.56/8.96	   A^2 -> H(U1(d, c), U1(k, b))
27.56/8.96	   A^2 -> H(U1(d, c), U1(c, d))
27.56/8.96	   A^2 -> H(U1(d, c), U1(d, c))
27.56/8.96	   A^2 -> H(U1(d, c), U1(b, e))
27.56/8.96	   A^2 -> H(U1(d, c), U1(b, k))
27.56/8.96	   A^2 -> H(U1(d, c), U1(e, c))
27.56/8.96	   A^2 -> H(U1(d, c), U1(k, c))
27.56/8.96	   A^2 -> H(U1(d, c), U1(c, e))
27.56/8.96	   A^2 -> H(U1(d, c), U1(c, k))
27.56/8.96	   A^2 -> H(U1(d, c), U1(e, e))
27.56/8.96	   A^2 -> H(U1(d, c), U1(k, k))
27.56/8.96	
27.56/8.96	The TRS R consists of the following rules:
27.56/8.96	
27.56/8.96	   f(x) -> U1(x, x)
27.56/8.96	   U1(e, x) -> x
27.56/8.96	   a -> c
27.56/8.96	   a -> d
27.56/8.96	   b -> c
27.56/8.96	   b -> d
27.56/8.96	   d -> k
27.56/8.96	   c -> e
27.56/8.96	   c -> k
27.56/8.96	
27.56/8.96	Q is empty.
27.56/8.96	We have to consider all minimal (P,Q,R)-chains.
27.56/8.96	----------------------------------------
27.56/8.96	
27.56/8.96	(651) TransformationProof (EQUIVALENT)
27.56/8.96	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
27.56/8.96	
27.56/8.96	   (A^2 -> H(U1(k, c), U1(d, d)),A^2 -> H(U1(k, c), U1(d, d)))
27.56/8.96	   (A^2 -> H(U1(d, e), U1(d, d)),A^2 -> H(U1(d, e), U1(d, d)))
27.56/8.96	   (A^2 -> H(U1(d, k), U1(d, d)),A^2 -> H(U1(d, k), U1(d, d)))
27.56/8.96	   (A^2 -> H(U1(d, c), U1(k, d)),A^2 -> H(U1(d, c), U1(k, d)))
27.56/8.96	   (A^2 -> H(U1(d, c), U1(d, k)),A^2 -> H(U1(d, c), U1(d, k)))
27.56/8.96	
27.56/8.96	
27.56/8.96	----------------------------------------
27.56/8.96	
27.56/8.96	(652)
27.56/8.96	Obligation:
27.56/8.96	Q DP problem:
27.56/8.96	The TRS P consists of the following rules:
27.56/8.96	
27.56/8.96	   H(x, x) -> G(x, x, f(k))
27.56/8.96	   G(d, x, x) -> A^2
27.56/8.96	   A^2 -> H(f(c), f(c))
27.56/8.96	   A^2 -> H(f(d), f(d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(c, c))
27.56/8.96	   A^2 -> H(f(e), f(e))
27.56/8.96	   A^2 -> H(f(k), f(k))
27.56/8.96	   A^2 -> H(U1(d, d), U1(d, d))
27.56/8.96	   A^2 -> H(U1(d, a), U1(e, b))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, b))
27.56/8.96	   A^2 -> H(U1(d, a), U1(c, d))
27.56/8.96	   A^2 -> H(U1(d, a), U1(d, c))
27.56/8.96	   A^2 -> H(U1(d, a), U1(b, e))
27.56/8.96	   A^2 -> H(U1(d, a), U1(b, k))
27.56/8.96	   A^2 -> H(U1(d, a), U1(e, c))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, c))
27.56/8.96	   A^2 -> H(U1(d, a), U1(c, e))
27.56/8.96	   A^2 -> H(U1(d, a), U1(c, k))
27.56/8.96	   A^2 -> H(U1(d, a), U1(e, e))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, k))
27.56/8.96	   A^2 -> H(U1(d, a), U1(k, d))
27.56/8.96	   A^2 -> H(U1(d, a), U1(d, k))
27.56/8.96	   A^2 -> H(U1(a, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(a, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(a, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(a, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(a, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(a, e), f(e))
27.56/8.96	   A^2 -> H(U1(a, e), f(k))
27.56/8.96	   A^2 -> H(U1(a, e), U1(d, d))
27.56/8.96	   A^2 -> H(U1(a, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(a, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(a, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(a, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(a, k), U1(c, c))
27.56/8.96	   A^2 -> H(U1(a, k), f(e))
27.56/8.96	   A^2 -> H(U1(a, k), f(k))
27.56/8.96	   A^2 -> H(U1(a, k), U1(d, d))
27.56/8.96	   A^2 -> H(U1(a, c), U1(e, b))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, b))
27.56/8.96	   A^2 -> H(U1(a, c), U1(c, d))
27.56/8.96	   A^2 -> H(U1(a, c), U1(d, c))
27.56/8.96	   A^2 -> H(U1(a, c), U1(b, e))
27.56/8.96	   A^2 -> H(U1(a, c), U1(b, k))
27.56/8.96	   A^2 -> H(U1(a, c), U1(e, c))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, c))
27.56/8.96	   A^2 -> H(U1(a, c), U1(c, e))
27.56/8.96	   A^2 -> H(U1(a, c), U1(c, k))
27.56/8.96	   A^2 -> H(U1(a, c), U1(e, e))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, k))
27.56/8.96	   A^2 -> H(U1(a, c), U1(k, d))
27.56/8.96	   A^2 -> H(U1(a, c), U1(d, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(e, b))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, b))
27.56/8.96	   A^2 -> H(U1(a, d), U1(c, d))
27.56/8.96	   A^2 -> H(U1(a, d), U1(d, c))
27.56/8.96	   A^2 -> H(U1(a, d), U1(b, e))
27.56/8.96	   A^2 -> H(U1(a, d), U1(b, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(e, c))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, c))
27.56/8.96	   A^2 -> H(U1(a, d), U1(c, e))
27.56/8.96	   A^2 -> H(U1(a, d), U1(c, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(e, e))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, k))
27.56/8.96	   A^2 -> H(U1(a, d), U1(k, d))
27.56/8.96	   A^2 -> H(U1(a, d), U1(d, k))
27.56/8.96	   A^2 -> H(U1(a, a), b)
27.56/8.96	   A^2 -> H(U1(a, a), U1(e, d))
27.56/8.96	   A^2 -> H(U1(a, a), U1(d, e))
27.56/8.96	   A^2 -> H(U1(a, a), c)
27.56/8.96	   A^2 -> H(U1(a, a), U1(e, k))
27.56/8.96	   A^2 -> H(U1(a, a), U1(k, e))
27.56/8.96	   A^2 -> H(U1(a, a), e)
27.56/8.96	   A^2 -> H(U1(a, a), U1(k, k))
27.56/8.96	   A^2 -> H(k, f(b))
27.56/8.96	   A^2 -> H(c, U1(b, b))
27.56/8.96	   A^2 -> H(c, f(c))
27.56/8.96	   A^2 -> H(c, f(d))
27.56/8.96	   A^2 -> H(U1(e, k), U1(b, b))
27.56/8.96	   A^2 -> H(U1(e, k), f(c))
27.56/8.96	   A^2 -> H(U1(e, k), f(d))
27.56/8.96	   A^2 -> H(U1(e, c), U1(c, b))
27.56/8.96	   A^2 -> H(U1(e, c), U1(d, b))
27.56/8.96	   A^2 -> H(U1(e, c), U1(b, c))
27.56/8.96	   A^2 -> H(U1(e, c), U1(b, d))
27.56/8.96	   A^2 -> H(U1(e, c), U1(c, c))
27.56/8.96	   A^2 -> H(U1(e, c), f(e))
27.56/8.96	   A^2 -> H(U1(e, c), f(k))
27.56/8.96	   A^2 -> H(U1(e, c), U1(d, d))
27.56/8.96	   A^2 -> H(U1(k, e), U1(b, b))
27.56/8.96	   A^2 -> H(U1(k, e), f(c))
27.56/8.96	   A^2 -> H(U1(k, e), f(d))
27.56/8.96	   A^2 -> H(U1(k, c), U1(c, b))
27.56/8.96	   A^2 -> H(U1(k, c), U1(d, b))
27.56/8.96	   A^2 -> H(U1(k, c), U1(b, c))
27.56/8.96	   A^2 -> H(U1(k, c), U1(b, d))
27.56/8.96	   A^2 -> H(U1(k, c), U1(c, c))
27.56/8.96	   A^2 -> H(U1(k, c), f(e))
27.56/8.96	   A^2 -> H(U1(k, c), f(k))
27.56/8.96	   A^2 -> H(U1(k, c), U1(d, d))
27.56/8.96	   A^2 -> H(U1(c, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(c, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(c, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(c, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(c, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(c, e), f(e))
27.56/8.96	   A^2 -> H(U1(c, e), f(k))
27.56/8.96	   A^2 -> H(U1(c, e), U1(d, d))
27.56/8.96	   A^2 -> H(U1(c, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(c, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(c, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(c, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(c, k), U1(c, c))
27.56/8.96	   A^2 -> H(U1(c, k), f(e))
27.56/8.96	   A^2 -> H(U1(c, k), f(k))
27.56/8.96	   A^2 -> H(U1(c, k), U1(d, d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(e, b))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, b))
27.56/8.96	   A^2 -> H(U1(c, c), U1(c, d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(d, c))
27.56/8.96	   A^2 -> H(U1(c, c), U1(b, e))
27.56/8.96	   A^2 -> H(U1(c, c), U1(b, k))
27.56/8.96	   A^2 -> H(U1(c, c), U1(e, e))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, k))
27.56/8.96	   A^2 -> H(U1(c, c), U1(k, d))
27.56/8.96	   A^2 -> H(U1(c, c), U1(d, k))
27.56/8.96	   A^2 -> H(e, U1(b, b))
27.56/8.96	   A^2 -> H(e, f(c))
27.56/8.96	   A^2 -> H(e, f(d))
27.56/8.96	   A^2 -> H(U1(e, e), U1(c, b))
27.56/8.96	   A^2 -> H(U1(e, e), U1(d, b))
27.56/8.96	   A^2 -> H(U1(e, e), U1(b, c))
27.56/8.96	   A^2 -> H(U1(e, e), U1(b, d))
27.56/8.96	   A^2 -> H(U1(e, e), U1(c, c))
27.56/8.96	   A^2 -> H(U1(e, e), f(e))
27.56/8.96	   A^2 -> H(U1(e, e), f(k))
27.56/8.96	   A^2 -> H(U1(e, e), U1(d, d))
27.56/8.96	   A^2 -> H(f(e), U1(e, b))
27.56/8.96	   A^2 -> H(f(e), U1(k, b))
27.56/8.96	   A^2 -> H(f(e), U1(c, d))
27.56/8.96	   A^2 -> H(f(e), U1(d, c))
27.56/8.96	   A^2 -> H(f(e), U1(b, e))
27.56/8.96	   A^2 -> H(f(e), U1(b, k))
27.56/8.96	   A^2 -> H(f(e), U1(e, c))
27.56/8.96	   A^2 -> H(f(e), U1(k, c))
27.56/8.96	   A^2 -> H(f(e), U1(c, e))
27.56/8.96	   A^2 -> H(f(e), U1(c, k))
27.56/8.96	   A^2 -> H(f(e), U1(k, k))
27.56/8.96	   A^2 -> H(f(e), U1(k, d))
27.56/8.96	   A^2 -> H(f(e), U1(d, k))
27.56/8.96	   A^2 -> H(U1(k, k), U1(c, b))
27.56/8.96	   A^2 -> H(U1(k, k), U1(d, b))
27.56/8.96	   A^2 -> H(U1(k, k), U1(b, c))
27.56/8.96	   A^2 -> H(U1(k, k), U1(b, d))
27.56/8.96	   A^2 -> H(U1(k, k), U1(c, c))
27.56/8.97	   A^2 -> H(U1(k, k), f(e))
27.56/8.97	   A^2 -> H(U1(k, k), f(k))
27.56/8.97	   A^2 -> H(U1(k, k), U1(d, d))
27.56/8.97	   A^2 -> H(f(k), U1(e, b))
27.56/8.97	   A^2 -> H(f(k), U1(k, b))
27.56/8.97	   A^2 -> H(f(k), U1(c, d))
27.56/8.97	   A^2 -> H(f(k), U1(d, c))
27.56/8.97	   A^2 -> H(f(k), U1(b, e))
27.56/8.97	   A^2 -> H(f(k), U1(b, k))
27.56/8.97	   A^2 -> H(f(k), U1(e, c))
27.56/8.97	   A^2 -> H(f(k), U1(k, c))
27.56/8.97	   A^2 -> H(f(k), U1(c, e))
27.56/8.97	   A^2 -> H(f(k), U1(c, k))
27.56/8.97	   A^2 -> H(f(k), U1(e, e))
27.56/8.97	   A^2 -> H(f(k), U1(k, d))
27.56/8.97	   A^2 -> H(f(k), U1(d, k))
27.56/8.97	   A^2 -> H(f(c), b)
27.56/8.97	   A^2 -> H(f(c), U1(e, d))
27.56/8.97	   A^2 -> H(f(c), U1(d, e))
27.56/8.97	   A^2 -> H(f(k), U1(k, k))
27.56/8.97	   A^2 -> H(U1(k, k), U1(b, b))
27.56/8.97	   A^2 -> H(U1(k, k), f(c))
27.56/8.97	   A^2 -> H(U1(k, k), f(d))
27.56/8.97	   A^2 -> H(U1(k, d), U1(c, b))
27.56/8.97	   A^2 -> H(U1(k, d), U1(d, b))
27.56/8.97	   A^2 -> H(U1(k, d), U1(b, c))
27.56/8.97	   A^2 -> H(U1(k, d), U1(b, d))
27.56/8.97	   A^2 -> H(U1(k, d), U1(c, c))
27.56/8.97	   A^2 -> H(U1(k, d), f(e))
27.56/8.97	   A^2 -> H(U1(k, d), f(k))
27.56/8.97	   A^2 -> H(U1(k, d), U1(d, d))
27.56/8.97	   A^2 -> H(U1(d, k), U1(c, b))
27.56/8.97	   A^2 -> H(U1(d, k), U1(d, b))
27.56/8.97	   A^2 -> H(U1(d, k), U1(b, c))
27.56/8.97	   A^2 -> H(U1(d, k), U1(b, d))
27.56/8.97	   A^2 -> H(U1(d, k), U1(c, c))
27.56/8.97	   A^2 -> H(U1(d, k), f(e))
27.56/8.97	   A^2 -> H(U1(d, k), f(k))
27.56/8.97	   A^2 -> H(U1(d, k), U1(d, d))
27.56/8.97	   A^2 -> H(U1(d, d), U1(e, b))
27.56/8.97	   A^2 -> H(U1(d, d), U1(k, b))
27.56/8.97	   A^2 -> H(U1(d, d), U1(c, d))
27.56/8.97	   A^2 -> H(U1(d, d), U1(d, c))
27.56/8.97	   A^2 -> H(U1(d, d), U1(b, e))
27.56/8.97	   A^2 -> H(U1(d, d), U1(b, k))
27.56/8.97	   A^2 -> H(U1(d, d), U1(e, c))
27.56/8.97	   A^2 -> H(U1(d, d), U1(k, c))
27.56/8.97	   A^2 -> H(U1(d, d), U1(c, e))
27.56/8.97	   A^2 -> H(U1(d, d), U1(c, k))
27.56/8.97	   A^2 -> H(U1(d, d), U1(e, e))
27.56/8.97	   A^2 -> H(U1(d, d), U1(k, k))
27.56/8.97	   A^2 -> H(f(d), b)
27.56/8.97	   A^2 -> H(f(d), U1(e, d))
27.56/8.97	   A^2 -> H(f(d), U1(d, e))
27.56/8.97	   A^2 -> H(f(d), c)
27.56/8.97	   A^2 -> H(f(d), U1(e, k))
27.56/8.97	   A^2 -> H(f(d), U1(k, e))
27.56/8.97	   A^2 -> H(f(d), e)
27.56/8.97	   A^2 -> H(f(a), d)
27.56/8.97	   A^2 -> H(U1(c, c), U1(e, c))
27.56/8.97	   A^2 -> H(f(c), c)
27.56/8.97	   A^2 -> H(f(c), U1(e, k))
27.56/8.97	   A^2 -> H(U1(c, c), U1(k, c))
27.56/8.97	   A^2 -> H(f(c), U1(k, e))
27.56/8.97	   A^2 -> H(f(c), U1(k, k))
27.56/8.97	   A^2 -> H(U1(c, c), U1(c, e))
27.56/8.97	   A^2 -> H(U1(c, c), U1(c, k))
27.56/8.97	   A^2 -> H(f(a), k)
27.56/8.97	   A^2 -> H(f(e), U1(e, e))
27.56/8.97	   A^2 -> H(f(c), e)
27.56/8.97	   A^2 -> H(U1(d, d), U1(k, d))
27.56/8.97	   A^2 -> H(f(d), U1(k, k))
27.56/8.97	   A^2 -> H(U1(d, d), U1(d, k))
27.56/8.97	   A^2 -> H(d, U1(b, b))
27.56/8.97	   A^2 -> H(d, f(c))
27.56/8.97	   A^2 -> H(d, f(d))
27.56/8.97	   A^2 -> H(a, U1(c, b))
27.56/8.97	   A^2 -> H(a, U1(d, b))
27.56/8.97	   A^2 -> H(a, U1(b, c))
27.56/8.97	   A^2 -> H(a, U1(b, d))
27.56/8.97	   A^2 -> H(a, U1(c, c))
27.56/8.97	   A^2 -> H(a, f(e))
27.56/8.97	   A^2 -> H(a, f(k))
27.56/8.97	   A^2 -> H(a, U1(d, d))
27.56/8.97	   A^2 -> H(U1(e, d), U1(c, b))
27.56/8.97	   A^2 -> H(U1(e, d), U1(d, b))
27.56/8.97	   A^2 -> H(U1(e, d), U1(b, c))
27.56/8.97	   A^2 -> H(U1(e, d), U1(b, d))
27.56/8.97	   A^2 -> H(U1(e, d), U1(c, c))
27.56/8.97	   A^2 -> H(U1(e, d), f(e))
27.56/8.97	   A^2 -> H(U1(e, d), f(k))
27.56/8.97	   A^2 -> H(U1(e, d), U1(d, d))
27.56/8.97	   A^2 -> H(U1(e, a), U1(e, b))
27.56/8.97	   A^2 -> H(U1(e, a), U1(k, b))
27.56/8.97	   A^2 -> H(U1(e, a), U1(c, d))
27.56/8.97	   A^2 -> H(U1(e, a), U1(d, c))
27.56/8.97	   A^2 -> H(U1(e, a), U1(b, e))
27.56/8.97	   A^2 -> H(U1(e, a), U1(b, k))
27.56/8.97	   A^2 -> H(U1(e, a), U1(e, c))
27.56/8.97	   A^2 -> H(U1(e, a), U1(k, c))
27.56/8.97	   A^2 -> H(U1(e, a), U1(c, e))
27.56/8.97	   A^2 -> H(U1(e, a), U1(c, k))
27.56/8.97	   A^2 -> H(U1(e, a), U1(e, e))
27.56/8.97	   A^2 -> H(U1(e, a), U1(k, k))
27.56/8.97	   A^2 -> H(U1(e, a), U1(k, d))
27.56/8.97	   A^2 -> H(U1(e, a), U1(d, k))
27.56/8.97	   A^2 -> H(U1(k, a), U1(e, b))
27.56/8.97	   A^2 -> H(U1(k, a), U1(k, b))
27.56/8.97	   A^2 -> H(U1(k, a), U1(c, d))
27.56/8.97	   A^2 -> H(U1(k, a), U1(d, c))
27.56/8.97	   A^2 -> H(U1(k, a), U1(b, e))
27.56/8.97	   A^2 -> H(U1(k, a), U1(b, k))
27.56/8.97	   A^2 -> H(U1(k, a), U1(e, c))
27.56/8.97	   A^2 -> H(U1(k, a), U1(k, c))
27.56/8.97	   A^2 -> H(U1(k, a), U1(c, e))
27.56/8.97	   A^2 -> H(U1(k, a), U1(c, k))
27.56/8.97	   A^2 -> H(U1(k, a), U1(e, e))
27.56/8.97	   A^2 -> H(U1(k, a), U1(k, k))
27.56/8.97	   A^2 -> H(U1(k, a), U1(k, d))
27.56/8.97	   A^2 -> H(U1(k, a), U1(d, k))
27.56/8.97	   A^2 -> H(U1(c, d), U1(e, b))
27.56/8.97	   A^2 -> H(U1(c, d), U1(k, b))
27.56/8.97	   A^2 -> H(U1(c, d), U1(c, d))
27.56/8.97	   A^2 -> H(U1(c, d), U1(d, c))
27.56/8.97	   A^2 -> H(U1(c, d), U1(b, e))
27.56/8.97	   A^2 -> H(U1(c, d), U1(b, k))
27.56/8.97	   A^2 -> H(U1(c, d), U1(e, c))
27.56/8.97	   A^2 -> H(U1(c, d), U1(k, c))
27.56/8.97	   A^2 -> H(U1(c, d), U1(c, e))
27.56/8.97	   A^2 -> H(U1(c, d), U1(c, k))
27.56/8.97	   A^2 -> H(U1(c, d), U1(e, e))
27.56/8.97	   A^2 -> H(U1(c, d), U1(k, k))
27.56/8.97	   A^2 -> H(U1(c, d), U1(k, d))
27.56/8.97	   A^2 -> H(U1(c, d), U1(d, k))
27.56/8.97	   A^2 -> H(U1(c, a), b)
27.56/8.97	   A^2 -> H(U1(c, a), U1(e, d))
27.56/8.97	   A^2 -> H(U1(c, a), U1(d, e))
27.56/8.97	   A^2 -> H(U1(c, a), c)
27.56/8.97	   A^2 -> H(U1(c, a), U1(e, k))
27.56/8.97	   A^2 -> H(U1(c, a), U1(k, e))
27.56/8.97	   A^2 -> H(U1(c, a), e)
27.56/8.97	   A^2 -> H(U1(c, a), U1(k, k))
27.56/8.97	   A^2 -> H(U1(d, e), U1(c, b))
27.56/8.97	   A^2 -> H(U1(d, e), U1(d, b))
27.56/8.97	   A^2 -> H(U1(d, e), U1(b, c))
27.56/8.97	   A^2 -> H(U1(d, e), U1(b, d))
27.56/8.97	   A^2 -> H(U1(d, e), U1(c, c))
27.56/8.97	   A^2 -> H(U1(d, e), f(e))
27.56/8.97	   A^2 -> H(U1(d, e), f(k))
27.56/8.97	   A^2 -> H(U1(d, e), U1(d, d))
27.56/8.97	   A^2 -> H(U1(d, c), U1(e, b))
27.56/8.97	   A^2 -> H(U1(d, c), U1(k, b))
27.56/8.97	   A^2 -> H(U1(d, c), U1(c, d))
27.56/8.97	   A^2 -> H(U1(d, c), U1(d, c))
27.56/8.97	   A^2 -> H(U1(d, c), U1(b, e))
27.56/8.97	   A^2 -> H(U1(d, c), U1(b, k))
27.56/8.97	   A^2 -> H(U1(d, c), U1(e, c))
27.56/8.97	   A^2 -> H(U1(d, c), U1(k, c))
27.56/8.97	   A^2 -> H(U1(d, c), U1(c, e))
27.56/8.97	   A^2 -> H(U1(d, c), U1(c, k))
27.56/8.97	   A^2 -> H(U1(d, c), U1(e, e))
27.56/8.97	   A^2 -> H(U1(d, c), U1(k, k))
27.56/8.97	   A^2 -> H(U1(d, c), U1(k, d))
27.56/8.97	   A^2 -> H(U1(d, c), U1(d, k))
27.56/8.97	
27.56/8.97	The TRS R consists of the following rules:
27.56/8.97	
27.56/8.97	   f(x) -> U1(x, x)
27.56/8.97	   U1(e, x) -> x
27.56/8.97	   a -> c
27.56/8.97	   a -> d
27.56/8.97	   b -> c
27.56/8.97	   b -> d
27.56/8.97	   d -> k
27.56/8.97	   c -> e
27.56/8.97	   c -> k
27.56/8.97	
27.56/8.97	Q is empty.
27.56/8.97	We have to consider all minimal (P,Q,R)-chains.
27.56/8.97	----------------------------------------
27.56/8.97	
27.56/8.97	(653) TransformationProof (EQUIVALENT)
27.56/8.97	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
27.56/8.97	
27.56/8.97	   (A^2 -> H(U1(k, a), U1(e, b)),A^2 -> H(U1(k, a), U1(e, b)))
27.56/8.97	   (A^2 -> H(U1(d, c), U1(e, b)),A^2 -> H(U1(d, c), U1(e, b)))
27.56/8.97	   (A^2 -> H(U1(d, d), U1(e, b)),A^2 -> H(U1(d, d), U1(e, b)))
27.56/8.97	   (A^2 -> H(U1(d, a), b),A^2 -> H(U1(d, a), b))
27.56/8.97	   (A^2 -> H(U1(d, a), U1(e, c)),A^2 -> H(U1(d, a), U1(e, c)))
27.56/8.97	   (A^2 -> H(U1(d, a), U1(e, d)),A^2 -> H(U1(d, a), U1(e, d)))
27.56/8.97	
27.56/8.97	
27.56/8.97	----------------------------------------
27.56/8.97	
27.56/8.97	(654)
27.56/8.97	Obligation:
27.56/8.97	Q DP problem:
27.56/8.97	The TRS P consists of the following rules:
27.56/8.97	
27.56/8.97	   H(x, x) -> G(x, x, f(k))
27.56/8.97	   G(d, x, x) -> A^2
27.56/8.97	   A^2 -> H(f(c), f(c))
27.56/8.97	   A^2 -> H(f(d), f(d))
27.56/8.97	   A^2 -> H(U1(c, c), U1(c, c))
27.56/8.97	   A^2 -> H(f(e), f(e))
27.56/8.97	   A^2 -> H(f(k), f(k))
27.56/8.97	   A^2 -> H(U1(d, d), U1(d, d))
27.56/8.97	   A^2 -> H(U1(d, a), U1(k, b))
27.56/8.97	   A^2 -> H(U1(d, a), U1(c, d))
27.56/8.97	   A^2 -> H(U1(d, a), U1(d, c))
27.56/8.97	   A^2 -> H(U1(d, a), U1(b, e))
27.56/8.97	   A^2 -> H(U1(d, a), U1(b, k))
27.56/8.97	   A^2 -> H(U1(d, a), U1(e, c))
27.56/8.97	   A^2 -> H(U1(d, a), U1(k, c))
27.56/8.97	   A^2 -> H(U1(d, a), U1(c, e))
27.56/8.97	   A^2 -> H(U1(d, a), U1(c, k))
27.56/8.97	   A^2 -> H(U1(d, a), U1(e, e))
27.56/8.97	   A^2 -> H(U1(d, a), U1(k, k))
27.56/8.97	   A^2 -> H(U1(d, a), U1(k, d))
27.56/8.97	   A^2 -> H(U1(d, a), U1(d, k))
27.56/8.97	   A^2 -> H(U1(a, e), U1(c, b))
27.56/8.97	   A^2 -> H(U1(a, e), U1(d, b))
27.56/8.97	   A^2 -> H(U1(a, e), U1(b, c))
27.56/8.97	   A^2 -> H(U1(a, e), U1(b, d))
27.56/8.97	   A^2 -> H(U1(a, e), U1(c, c))
27.56/8.97	   A^2 -> H(U1(a, e), f(e))
27.56/8.97	   A^2 -> H(U1(a, e), f(k))
27.56/8.97	   A^2 -> H(U1(a, e), U1(d, d))
27.56/8.97	   A^2 -> H(U1(a, k), U1(c, b))
27.56/8.97	   A^2 -> H(U1(a, k), U1(d, b))
27.56/8.97	   A^2 -> H(U1(a, k), U1(b, c))
27.56/8.97	   A^2 -> H(U1(a, k), U1(b, d))
27.56/8.97	   A^2 -> H(U1(a, k), U1(c, c))
27.56/8.97	   A^2 -> H(U1(a, k), f(e))
27.56/8.97	   A^2 -> H(U1(a, k), f(k))
27.56/8.97	   A^2 -> H(U1(a, k), U1(d, d))
27.56/8.97	   A^2 -> H(U1(a, c), U1(e, b))
27.56/8.97	   A^2 -> H(U1(a, c), U1(k, b))
27.56/8.97	   A^2 -> H(U1(a, c), U1(c, d))
27.56/8.97	   A^2 -> H(U1(a, c), U1(d, c))
27.56/8.97	   A^2 -> H(U1(a, c), U1(b, e))
27.56/8.97	   A^2 -> H(U1(a, c), U1(b, k))
27.56/8.97	   A^2 -> H(U1(a, c), U1(e, c))
27.56/8.97	   A^2 -> H(U1(a, c), U1(k, c))
27.56/8.97	   A^2 -> H(U1(a, c), U1(c, e))
27.56/8.97	   A^2 -> H(U1(a, c), U1(c, k))
27.56/8.97	   A^2 -> H(U1(a, c), U1(e, e))
27.56/8.97	   A^2 -> H(U1(a, c), U1(k, k))
27.56/8.97	   A^2 -> H(U1(a, c), U1(k, d))
27.56/8.97	   A^2 -> H(U1(a, c), U1(d, k))
27.56/8.97	   A^2 -> H(U1(a, d), U1(e, b))
27.56/8.97	   A^2 -> H(U1(a, d), U1(k, b))
27.56/8.97	   A^2 -> H(U1(a, d), U1(c, d))
27.56/8.97	   A^2 -> H(U1(a, d), U1(d, c))
27.56/8.97	   A^2 -> H(U1(a, d), U1(b, e))
27.56/8.97	   A^2 -> H(U1(a, d), U1(b, k))
27.56/8.97	   A^2 -> H(U1(a, d), U1(e, c))
27.56/8.97	   A^2 -> H(U1(a, d), U1(k, c))
27.56/8.97	   A^2 -> H(U1(a, d), U1(c, e))
27.56/8.97	   A^2 -> H(U1(a, d), U1(c, k))
27.56/8.97	   A^2 -> H(U1(a, d), U1(e, e))
27.56/8.97	   A^2 -> H(U1(a, d), U1(k, k))
27.56/8.97	   A^2 -> H(U1(a, d), U1(k, d))
27.56/8.97	   A^2 -> H(U1(a, d), U1(d, k))
27.56/8.97	   A^2 -> H(U1(a, a), b)
27.56/8.97	   A^2 -> H(U1(a, a), U1(e, d))
27.56/8.97	   A^2 -> H(U1(a, a), U1(d, e))
27.56/8.97	   A^2 -> H(U1(a, a), c)
27.56/8.97	   A^2 -> H(U1(a, a), U1(e, k))
27.56/8.97	   A^2 -> H(U1(a, a), U1(k, e))
27.56/8.97	   A^2 -> H(U1(a, a), e)
27.56/8.97	   A^2 -> H(U1(a, a), U1(k, k))
27.56/8.97	   A^2 -> H(k, f(b))
27.56/8.97	   A^2 -> H(c, U1(b, b))
27.56/8.97	   A^2 -> H(c, f(c))
27.56/8.97	   A^2 -> H(c, f(d))
27.56/8.97	   A^2 -> H(U1(e, k), U1(b, b))
27.56/8.97	   A^2 -> H(U1(e, k), f(c))
27.56/8.97	   A^2 -> H(U1(e, k), f(d))
27.56/8.97	   A^2 -> H(U1(e, c), U1(c, b))
27.56/8.97	   A^2 -> H(U1(e, c), U1(d, b))
27.56/8.97	   A^2 -> H(U1(e, c), U1(b, c))
27.56/8.97	   A^2 -> H(U1(e, c), U1(b, d))
27.56/8.97	   A^2 -> H(U1(e, c), U1(c, c))
27.56/8.97	   A^2 -> H(U1(e, c), f(e))
27.56/8.97	   A^2 -> H(U1(e, c), f(k))
27.56/8.97	   A^2 -> H(U1(e, c), U1(d, d))
27.56/8.97	   A^2 -> H(U1(k, e), U1(b, b))
27.56/8.97	   A^2 -> H(U1(k, e), f(c))
27.56/8.97	   A^2 -> H(U1(k, e), f(d))
27.56/8.97	   A^2 -> H(U1(k, c), U1(c, b))
27.56/8.97	   A^2 -> H(U1(k, c), U1(d, b))
27.56/8.97	   A^2 -> H(U1(k, c), U1(b, c))
27.56/8.97	   A^2 -> H(U1(k, c), U1(b, d))
27.56/8.97	   A^2 -> H(U1(k, c), U1(c, c))
27.56/8.97	   A^2 -> H(U1(k, c), f(e))
27.56/8.97	   A^2 -> H(U1(k, c), f(k))
27.56/8.97	   A^2 -> H(U1(k, c), U1(d, d))
27.56/8.97	   A^2 -> H(U1(c, e), U1(c, b))
27.56/8.97	   A^2 -> H(U1(c, e), U1(d, b))
27.56/8.97	   A^2 -> H(U1(c, e), U1(b, c))
27.56/8.97	   A^2 -> H(U1(c, e), U1(b, d))
27.56/8.97	   A^2 -> H(U1(c, e), U1(c, c))
27.56/8.97	   A^2 -> H(U1(c, e), f(e))
27.56/8.97	   A^2 -> H(U1(c, e), f(k))
27.56/8.97	   A^2 -> H(U1(c, e), U1(d, d))
27.56/8.97	   A^2 -> H(U1(c, k), U1(c, b))
27.56/8.97	   A^2 -> H(U1(c, k), U1(d, b))
27.56/8.97	   A^2 -> H(U1(c, k), U1(b, c))
27.56/8.97	   A^2 -> H(U1(c, k), U1(b, d))
27.56/8.97	   A^2 -> H(U1(c, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(c, k), f(e))
27.56/8.98	   A^2 -> H(U1(c, k), f(k))
27.56/8.98	   A^2 -> H(U1(c, k), U1(d, d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(e, b))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, b))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(d, c))
27.56/8.98	   A^2 -> H(U1(c, c), U1(b, e))
27.56/8.98	   A^2 -> H(U1(c, c), U1(b, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(e, e))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(d, k))
27.56/8.98	   A^2 -> H(e, U1(b, b))
27.56/8.98	   A^2 -> H(e, f(c))
27.56/8.98	   A^2 -> H(e, f(d))
27.56/8.98	   A^2 -> H(U1(e, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(e, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(e, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(e, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(e, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(e, e), f(e))
27.56/8.98	   A^2 -> H(U1(e, e), f(k))
27.56/8.98	   A^2 -> H(U1(e, e), U1(d, d))
27.56/8.98	   A^2 -> H(f(e), U1(e, b))
27.56/8.98	   A^2 -> H(f(e), U1(k, b))
27.56/8.98	   A^2 -> H(f(e), U1(c, d))
27.56/8.98	   A^2 -> H(f(e), U1(d, c))
27.56/8.98	   A^2 -> H(f(e), U1(b, e))
27.56/8.98	   A^2 -> H(f(e), U1(b, k))
27.56/8.98	   A^2 -> H(f(e), U1(e, c))
27.56/8.98	   A^2 -> H(f(e), U1(k, c))
27.56/8.98	   A^2 -> H(f(e), U1(c, e))
27.56/8.98	   A^2 -> H(f(e), U1(c, k))
27.56/8.98	   A^2 -> H(f(e), U1(k, k))
27.56/8.98	   A^2 -> H(f(e), U1(k, d))
27.56/8.98	   A^2 -> H(f(e), U1(d, k))
27.56/8.98	   A^2 -> H(U1(k, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(k, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(k, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(k, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(k, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(k, k), f(e))
27.56/8.98	   A^2 -> H(U1(k, k), f(k))
27.56/8.98	   A^2 -> H(U1(k, k), U1(d, d))
27.56/8.98	   A^2 -> H(f(k), U1(e, b))
27.56/8.98	   A^2 -> H(f(k), U1(k, b))
27.56/8.98	   A^2 -> H(f(k), U1(c, d))
27.56/8.98	   A^2 -> H(f(k), U1(d, c))
27.56/8.98	   A^2 -> H(f(k), U1(b, e))
27.56/8.98	   A^2 -> H(f(k), U1(b, k))
27.56/8.98	   A^2 -> H(f(k), U1(e, c))
27.56/8.98	   A^2 -> H(f(k), U1(k, c))
27.56/8.98	   A^2 -> H(f(k), U1(c, e))
27.56/8.98	   A^2 -> H(f(k), U1(c, k))
27.56/8.98	   A^2 -> H(f(k), U1(e, e))
27.56/8.98	   A^2 -> H(f(k), U1(k, d))
27.56/8.98	   A^2 -> H(f(k), U1(d, k))
27.56/8.98	   A^2 -> H(f(c), b)
27.56/8.98	   A^2 -> H(f(c), U1(e, d))
27.56/8.98	   A^2 -> H(f(c), U1(d, e))
27.56/8.98	   A^2 -> H(f(k), U1(k, k))
27.56/8.98	   A^2 -> H(U1(k, k), U1(b, b))
27.56/8.98	   A^2 -> H(U1(k, k), f(c))
27.56/8.98	   A^2 -> H(U1(k, k), f(d))
27.56/8.98	   A^2 -> H(U1(k, d), U1(c, b))
27.56/8.98	   A^2 -> H(U1(k, d), U1(d, b))
27.56/8.98	   A^2 -> H(U1(k, d), U1(b, c))
27.56/8.98	   A^2 -> H(U1(k, d), U1(b, d))
27.56/8.98	   A^2 -> H(U1(k, d), U1(c, c))
27.56/8.98	   A^2 -> H(U1(k, d), f(e))
27.56/8.98	   A^2 -> H(U1(k, d), f(k))
27.56/8.98	   A^2 -> H(U1(k, d), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(d, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(d, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(d, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(d, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(d, k), f(e))
27.56/8.98	   A^2 -> H(U1(d, k), f(k))
27.56/8.98	   A^2 -> H(U1(d, k), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, d), U1(e, b))
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, b))
27.56/8.98	   A^2 -> H(U1(d, d), U1(c, d))
27.56/8.98	   A^2 -> H(U1(d, d), U1(d, c))
27.56/8.98	   A^2 -> H(U1(d, d), U1(b, e))
27.56/8.98	   A^2 -> H(U1(d, d), U1(b, k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(e, c))
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, c))
27.56/8.98	   A^2 -> H(U1(d, d), U1(c, e))
27.56/8.98	   A^2 -> H(U1(d, d), U1(c, k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(e, e))
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, k))
27.56/8.98	   A^2 -> H(f(d), b)
27.56/8.98	   A^2 -> H(f(d), U1(e, d))
27.56/8.98	   A^2 -> H(f(d), U1(d, e))
27.56/8.98	   A^2 -> H(f(d), c)
27.56/8.98	   A^2 -> H(f(d), U1(e, k))
27.56/8.98	   A^2 -> H(f(d), U1(k, e))
27.56/8.98	   A^2 -> H(f(d), e)
27.56/8.98	   A^2 -> H(f(a), d)
27.56/8.98	   A^2 -> H(U1(c, c), U1(e, c))
27.56/8.98	   A^2 -> H(f(c), c)
27.56/8.98	   A^2 -> H(f(c), U1(e, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, c))
27.56/8.98	   A^2 -> H(f(c), U1(k, e))
27.56/8.98	   A^2 -> H(f(c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, e))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, k))
27.56/8.98	   A^2 -> H(f(a), k)
27.56/8.98	   A^2 -> H(f(e), U1(e, e))
27.56/8.98	   A^2 -> H(f(c), e)
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, d))
27.56/8.98	   A^2 -> H(f(d), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(d, k))
27.56/8.98	   A^2 -> H(d, U1(b, b))
27.56/8.98	   A^2 -> H(d, f(c))
27.56/8.98	   A^2 -> H(d, f(d))
27.56/8.98	   A^2 -> H(a, U1(c, b))
27.56/8.98	   A^2 -> H(a, U1(d, b))
27.56/8.98	   A^2 -> H(a, U1(b, c))
27.56/8.98	   A^2 -> H(a, U1(b, d))
27.56/8.98	   A^2 -> H(a, U1(c, c))
27.56/8.98	   A^2 -> H(a, f(e))
27.56/8.98	   A^2 -> H(a, f(k))
27.56/8.98	   A^2 -> H(a, U1(d, d))
27.56/8.98	   A^2 -> H(U1(e, d), U1(c, b))
27.56/8.98	   A^2 -> H(U1(e, d), U1(d, b))
27.56/8.98	   A^2 -> H(U1(e, d), U1(b, c))
27.56/8.98	   A^2 -> H(U1(e, d), U1(b, d))
27.56/8.98	   A^2 -> H(U1(e, d), U1(c, c))
27.56/8.98	   A^2 -> H(U1(e, d), f(e))
27.56/8.98	   A^2 -> H(U1(e, d), f(k))
27.56/8.98	   A^2 -> H(U1(e, d), U1(d, d))
27.56/8.98	   A^2 -> H(U1(e, a), U1(e, b))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, b))
27.56/8.98	   A^2 -> H(U1(e, a), U1(c, d))
27.56/8.98	   A^2 -> H(U1(e, a), U1(d, c))
27.56/8.98	   A^2 -> H(U1(e, a), U1(b, e))
27.56/8.98	   A^2 -> H(U1(e, a), U1(b, k))
27.56/8.98	   A^2 -> H(U1(e, a), U1(e, c))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, c))
27.56/8.98	   A^2 -> H(U1(e, a), U1(c, e))
27.56/8.98	   A^2 -> H(U1(e, a), U1(c, k))
27.56/8.98	   A^2 -> H(U1(e, a), U1(e, e))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, d))
27.56/8.98	   A^2 -> H(U1(e, a), U1(d, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(e, b))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, b))
27.56/8.98	   A^2 -> H(U1(k, a), U1(c, d))
27.56/8.98	   A^2 -> H(U1(k, a), U1(d, c))
27.56/8.98	   A^2 -> H(U1(k, a), U1(b, e))
27.56/8.98	   A^2 -> H(U1(k, a), U1(b, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(e, c))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, c))
27.56/8.98	   A^2 -> H(U1(k, a), U1(c, e))
27.56/8.98	   A^2 -> H(U1(k, a), U1(c, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(e, e))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, d))
27.56/8.98	   A^2 -> H(U1(k, a), U1(d, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(e, b))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, b))
27.56/8.98	   A^2 -> H(U1(c, d), U1(c, d))
27.56/8.98	   A^2 -> H(U1(c, d), U1(d, c))
27.56/8.98	   A^2 -> H(U1(c, d), U1(b, e))
27.56/8.98	   A^2 -> H(U1(c, d), U1(b, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(e, c))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, c))
27.56/8.98	   A^2 -> H(U1(c, d), U1(c, e))
27.56/8.98	   A^2 -> H(U1(c, d), U1(c, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(e, e))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, d))
27.56/8.98	   A^2 -> H(U1(c, d), U1(d, k))
27.56/8.98	   A^2 -> H(U1(c, a), b)
27.56/8.98	   A^2 -> H(U1(c, a), U1(e, d))
27.56/8.98	   A^2 -> H(U1(c, a), U1(d, e))
27.56/8.98	   A^2 -> H(U1(c, a), c)
27.56/8.98	   A^2 -> H(U1(c, a), U1(e, k))
27.56/8.98	   A^2 -> H(U1(c, a), U1(k, e))
27.56/8.98	   A^2 -> H(U1(c, a), e)
27.56/8.98	   A^2 -> H(U1(c, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(d, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(d, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(d, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(d, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(d, e), f(e))
27.56/8.98	   A^2 -> H(U1(d, e), f(k))
27.56/8.98	   A^2 -> H(U1(d, e), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, c), U1(e, b))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, b))
27.56/8.98	   A^2 -> H(U1(d, c), U1(c, d))
27.56/8.98	   A^2 -> H(U1(d, c), U1(d, c))
27.56/8.98	   A^2 -> H(U1(d, c), U1(b, e))
27.56/8.98	   A^2 -> H(U1(d, c), U1(b, k))
27.56/8.98	   A^2 -> H(U1(d, c), U1(e, c))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, c))
27.56/8.98	   A^2 -> H(U1(d, c), U1(c, e))
27.56/8.98	   A^2 -> H(U1(d, c), U1(c, k))
27.56/8.98	   A^2 -> H(U1(d, c), U1(e, e))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, d))
27.56/8.98	   A^2 -> H(U1(d, c), U1(d, k))
27.56/8.98	   A^2 -> H(U1(d, a), b)
27.56/8.98	   A^2 -> H(U1(d, a), U1(e, d))
27.56/8.98	
27.56/8.98	The TRS R consists of the following rules:
27.56/8.98	
27.56/8.98	   f(x) -> U1(x, x)
27.56/8.98	   U1(e, x) -> x
27.56/8.98	   a -> c
27.56/8.98	   a -> d
27.56/8.98	   b -> c
27.56/8.98	   b -> d
27.56/8.98	   d -> k
27.56/8.98	   c -> e
27.56/8.98	   c -> k
27.56/8.98	
27.56/8.98	Q is empty.
27.56/8.98	We have to consider all minimal (P,Q,R)-chains.
27.56/8.98	----------------------------------------
27.56/8.98	
27.56/8.98	(655) TransformationProof (EQUIVALENT)
27.56/8.98	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
27.56/8.98	
27.56/8.98	   (A^2 -> H(U1(k, a), U1(k, b)),A^2 -> H(U1(k, a), U1(k, b)))
27.56/8.98	   (A^2 -> H(U1(d, c), U1(k, b)),A^2 -> H(U1(d, c), U1(k, b)))
27.56/8.98	   (A^2 -> H(U1(d, d), U1(k, b)),A^2 -> H(U1(d, d), U1(k, b)))
27.56/8.98	   (A^2 -> H(U1(d, a), U1(k, c)),A^2 -> H(U1(d, a), U1(k, c)))
27.56/8.98	   (A^2 -> H(U1(d, a), U1(k, d)),A^2 -> H(U1(d, a), U1(k, d)))
27.56/8.98	
27.56/8.98	
27.56/8.98	----------------------------------------
27.56/8.98	
27.56/8.98	(656)
27.56/8.98	Obligation:
27.56/8.98	Q DP problem:
27.56/8.98	The TRS P consists of the following rules:
27.56/8.98	
27.56/8.98	   H(x, x) -> G(x, x, f(k))
27.56/8.98	   G(d, x, x) -> A^2
27.56/8.98	   A^2 -> H(f(c), f(c))
27.56/8.98	   A^2 -> H(f(d), f(d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, c))
27.56/8.98	   A^2 -> H(f(e), f(e))
27.56/8.98	   A^2 -> H(f(k), f(k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, a), U1(c, d))
27.56/8.98	   A^2 -> H(U1(d, a), U1(d, c))
27.56/8.98	   A^2 -> H(U1(d, a), U1(b, e))
27.56/8.98	   A^2 -> H(U1(d, a), U1(b, k))
27.56/8.98	   A^2 -> H(U1(d, a), U1(e, c))
27.56/8.98	   A^2 -> H(U1(d, a), U1(k, c))
27.56/8.98	   A^2 -> H(U1(d, a), U1(c, e))
27.56/8.98	   A^2 -> H(U1(d, a), U1(c, k))
27.56/8.98	   A^2 -> H(U1(d, a), U1(e, e))
27.56/8.98	   A^2 -> H(U1(d, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, a), U1(k, d))
27.56/8.98	   A^2 -> H(U1(d, a), U1(d, k))
27.56/8.98	   A^2 -> H(U1(a, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(a, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(a, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(a, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(a, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(a, e), f(e))
27.56/8.98	   A^2 -> H(U1(a, e), f(k))
27.56/8.98	   A^2 -> H(U1(a, e), U1(d, d))
27.56/8.98	   A^2 -> H(U1(a, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(a, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(a, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(a, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(a, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(a, k), f(e))
27.56/8.98	   A^2 -> H(U1(a, k), f(k))
27.56/8.98	   A^2 -> H(U1(a, k), U1(d, d))
27.56/8.98	   A^2 -> H(U1(a, c), U1(e, b))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, b))
27.56/8.98	   A^2 -> H(U1(a, c), U1(c, d))
27.56/8.98	   A^2 -> H(U1(a, c), U1(d, c))
27.56/8.98	   A^2 -> H(U1(a, c), U1(b, e))
27.56/8.98	   A^2 -> H(U1(a, c), U1(b, k))
27.56/8.98	   A^2 -> H(U1(a, c), U1(e, c))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, c))
27.56/8.98	   A^2 -> H(U1(a, c), U1(c, e))
27.56/8.98	   A^2 -> H(U1(a, c), U1(c, k))
27.56/8.98	   A^2 -> H(U1(a, c), U1(e, e))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, d))
27.56/8.98	   A^2 -> H(U1(a, c), U1(d, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(e, b))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, b))
27.56/8.98	   A^2 -> H(U1(a, d), U1(c, d))
27.56/8.98	   A^2 -> H(U1(a, d), U1(d, c))
27.56/8.98	   A^2 -> H(U1(a, d), U1(b, e))
27.56/8.98	   A^2 -> H(U1(a, d), U1(b, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(e, c))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, c))
27.56/8.98	   A^2 -> H(U1(a, d), U1(c, e))
27.56/8.98	   A^2 -> H(U1(a, d), U1(c, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(e, e))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, d))
27.56/8.98	   A^2 -> H(U1(a, d), U1(d, k))
27.56/8.98	   A^2 -> H(U1(a, a), b)
27.56/8.98	   A^2 -> H(U1(a, a), U1(e, d))
27.56/8.98	   A^2 -> H(U1(a, a), U1(d, e))
27.56/8.98	   A^2 -> H(U1(a, a), c)
27.56/8.98	   A^2 -> H(U1(a, a), U1(e, k))
27.56/8.98	   A^2 -> H(U1(a, a), U1(k, e))
27.56/8.98	   A^2 -> H(U1(a, a), e)
27.56/8.98	   A^2 -> H(U1(a, a), U1(k, k))
27.56/8.98	   A^2 -> H(k, f(b))
27.56/8.98	   A^2 -> H(c, U1(b, b))
27.56/8.98	   A^2 -> H(c, f(c))
27.56/8.98	   A^2 -> H(c, f(d))
27.56/8.98	   A^2 -> H(U1(e, k), U1(b, b))
27.56/8.98	   A^2 -> H(U1(e, k), f(c))
27.56/8.98	   A^2 -> H(U1(e, k), f(d))
27.56/8.98	   A^2 -> H(U1(e, c), U1(c, b))
27.56/8.98	   A^2 -> H(U1(e, c), U1(d, b))
27.56/8.98	   A^2 -> H(U1(e, c), U1(b, c))
27.56/8.98	   A^2 -> H(U1(e, c), U1(b, d))
27.56/8.98	   A^2 -> H(U1(e, c), U1(c, c))
27.56/8.98	   A^2 -> H(U1(e, c), f(e))
27.56/8.98	   A^2 -> H(U1(e, c), f(k))
27.56/8.98	   A^2 -> H(U1(e, c), U1(d, d))
27.56/8.98	   A^2 -> H(U1(k, e), U1(b, b))
27.56/8.98	   A^2 -> H(U1(k, e), f(c))
27.56/8.98	   A^2 -> H(U1(k, e), f(d))
27.56/8.98	   A^2 -> H(U1(k, c), U1(c, b))
27.56/8.98	   A^2 -> H(U1(k, c), U1(d, b))
27.56/8.98	   A^2 -> H(U1(k, c), U1(b, c))
27.56/8.98	   A^2 -> H(U1(k, c), U1(b, d))
27.56/8.98	   A^2 -> H(U1(k, c), U1(c, c))
27.56/8.98	   A^2 -> H(U1(k, c), f(e))
27.56/8.98	   A^2 -> H(U1(k, c), f(k))
27.56/8.98	   A^2 -> H(U1(k, c), U1(d, d))
27.56/8.98	   A^2 -> H(U1(c, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(c, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(c, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(c, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(c, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(c, e), f(e))
27.56/8.98	   A^2 -> H(U1(c, e), f(k))
27.56/8.98	   A^2 -> H(U1(c, e), U1(d, d))
27.56/8.98	   A^2 -> H(U1(c, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(c, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(c, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(c, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(c, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(c, k), f(e))
27.56/8.98	   A^2 -> H(U1(c, k), f(k))
27.56/8.98	   A^2 -> H(U1(c, k), U1(d, d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(e, b))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, b))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(d, c))
27.56/8.98	   A^2 -> H(U1(c, c), U1(b, e))
27.56/8.98	   A^2 -> H(U1(c, c), U1(b, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(e, e))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(d, k))
27.56/8.98	   A^2 -> H(e, U1(b, b))
27.56/8.98	   A^2 -> H(e, f(c))
27.56/8.98	   A^2 -> H(e, f(d))
27.56/8.98	   A^2 -> H(U1(e, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(e, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(e, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(e, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(e, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(e, e), f(e))
27.56/8.98	   A^2 -> H(U1(e, e), f(k))
27.56/8.98	   A^2 -> H(U1(e, e), U1(d, d))
27.56/8.98	   A^2 -> H(f(e), U1(e, b))
27.56/8.98	   A^2 -> H(f(e), U1(k, b))
27.56/8.98	   A^2 -> H(f(e), U1(c, d))
27.56/8.98	   A^2 -> H(f(e), U1(d, c))
27.56/8.98	   A^2 -> H(f(e), U1(b, e))
27.56/8.98	   A^2 -> H(f(e), U1(b, k))
27.56/8.98	   A^2 -> H(f(e), U1(e, c))
27.56/8.98	   A^2 -> H(f(e), U1(k, c))
27.56/8.98	   A^2 -> H(f(e), U1(c, e))
27.56/8.98	   A^2 -> H(f(e), U1(c, k))
27.56/8.98	   A^2 -> H(f(e), U1(k, k))
27.56/8.98	   A^2 -> H(f(e), U1(k, d))
27.56/8.98	   A^2 -> H(f(e), U1(d, k))
27.56/8.98	   A^2 -> H(U1(k, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(k, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(k, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(k, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(k, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(k, k), f(e))
27.56/8.98	   A^2 -> H(U1(k, k), f(k))
27.56/8.98	   A^2 -> H(U1(k, k), U1(d, d))
27.56/8.98	   A^2 -> H(f(k), U1(e, b))
27.56/8.98	   A^2 -> H(f(k), U1(k, b))
27.56/8.98	   A^2 -> H(f(k), U1(c, d))
27.56/8.98	   A^2 -> H(f(k), U1(d, c))
27.56/8.98	   A^2 -> H(f(k), U1(b, e))
27.56/8.98	   A^2 -> H(f(k), U1(b, k))
27.56/8.98	   A^2 -> H(f(k), U1(e, c))
27.56/8.98	   A^2 -> H(f(k), U1(k, c))
27.56/8.98	   A^2 -> H(f(k), U1(c, e))
27.56/8.98	   A^2 -> H(f(k), U1(c, k))
27.56/8.98	   A^2 -> H(f(k), U1(e, e))
27.56/8.98	   A^2 -> H(f(k), U1(k, d))
27.56/8.98	   A^2 -> H(f(k), U1(d, k))
27.56/8.98	   A^2 -> H(f(c), b)
27.56/8.98	   A^2 -> H(f(c), U1(e, d))
27.56/8.98	   A^2 -> H(f(c), U1(d, e))
27.56/8.98	   A^2 -> H(f(k), U1(k, k))
27.56/8.98	   A^2 -> H(U1(k, k), U1(b, b))
27.56/8.98	   A^2 -> H(U1(k, k), f(c))
27.56/8.98	   A^2 -> H(U1(k, k), f(d))
27.56/8.98	   A^2 -> H(U1(k, d), U1(c, b))
27.56/8.98	   A^2 -> H(U1(k, d), U1(d, b))
27.56/8.98	   A^2 -> H(U1(k, d), U1(b, c))
27.56/8.98	   A^2 -> H(U1(k, d), U1(b, d))
27.56/8.98	   A^2 -> H(U1(k, d), U1(c, c))
27.56/8.98	   A^2 -> H(U1(k, d), f(e))
27.56/8.98	   A^2 -> H(U1(k, d), f(k))
27.56/8.98	   A^2 -> H(U1(k, d), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(d, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(d, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(d, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(d, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(d, k), f(e))
27.56/8.98	   A^2 -> H(U1(d, k), f(k))
27.56/8.98	   A^2 -> H(U1(d, k), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, d), U1(e, b))
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, b))
27.56/8.98	   A^2 -> H(U1(d, d), U1(c, d))
27.56/8.98	   A^2 -> H(U1(d, d), U1(d, c))
27.56/8.98	   A^2 -> H(U1(d, d), U1(b, e))
27.56/8.98	   A^2 -> H(U1(d, d), U1(b, k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(e, c))
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, c))
27.56/8.98	   A^2 -> H(U1(d, d), U1(c, e))
27.56/8.98	   A^2 -> H(U1(d, d), U1(c, k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(e, e))
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, k))
27.56/8.98	   A^2 -> H(f(d), b)
27.56/8.98	   A^2 -> H(f(d), U1(e, d))
27.56/8.98	   A^2 -> H(f(d), U1(d, e))
27.56/8.98	   A^2 -> H(f(d), c)
27.56/8.98	   A^2 -> H(f(d), U1(e, k))
27.56/8.98	   A^2 -> H(f(d), U1(k, e))
27.56/8.98	   A^2 -> H(f(d), e)
27.56/8.98	   A^2 -> H(f(a), d)
27.56/8.98	   A^2 -> H(U1(c, c), U1(e, c))
27.56/8.98	   A^2 -> H(f(c), c)
27.56/8.98	   A^2 -> H(f(c), U1(e, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, c))
27.56/8.98	   A^2 -> H(f(c), U1(k, e))
27.56/8.98	   A^2 -> H(f(c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, e))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, k))
27.56/8.98	   A^2 -> H(f(a), k)
27.56/8.98	   A^2 -> H(f(e), U1(e, e))
27.56/8.98	   A^2 -> H(f(c), e)
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, d))
27.56/8.98	   A^2 -> H(f(d), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(d, k))
27.56/8.98	   A^2 -> H(d, U1(b, b))
27.56/8.98	   A^2 -> H(d, f(c))
27.56/8.98	   A^2 -> H(d, f(d))
27.56/8.98	   A^2 -> H(a, U1(c, b))
27.56/8.98	   A^2 -> H(a, U1(d, b))
27.56/8.98	   A^2 -> H(a, U1(b, c))
27.56/8.98	   A^2 -> H(a, U1(b, d))
27.56/8.98	   A^2 -> H(a, U1(c, c))
27.56/8.98	   A^2 -> H(a, f(e))
27.56/8.98	   A^2 -> H(a, f(k))
27.56/8.98	   A^2 -> H(a, U1(d, d))
27.56/8.98	   A^2 -> H(U1(e, d), U1(c, b))
27.56/8.98	   A^2 -> H(U1(e, d), U1(d, b))
27.56/8.98	   A^2 -> H(U1(e, d), U1(b, c))
27.56/8.98	   A^2 -> H(U1(e, d), U1(b, d))
27.56/8.98	   A^2 -> H(U1(e, d), U1(c, c))
27.56/8.98	   A^2 -> H(U1(e, d), f(e))
27.56/8.98	   A^2 -> H(U1(e, d), f(k))
27.56/8.98	   A^2 -> H(U1(e, d), U1(d, d))
27.56/8.98	   A^2 -> H(U1(e, a), U1(e, b))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, b))
27.56/8.98	   A^2 -> H(U1(e, a), U1(c, d))
27.56/8.98	   A^2 -> H(U1(e, a), U1(d, c))
27.56/8.98	   A^2 -> H(U1(e, a), U1(b, e))
27.56/8.98	   A^2 -> H(U1(e, a), U1(b, k))
27.56/8.98	   A^2 -> H(U1(e, a), U1(e, c))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, c))
27.56/8.98	   A^2 -> H(U1(e, a), U1(c, e))
27.56/8.98	   A^2 -> H(U1(e, a), U1(c, k))
27.56/8.98	   A^2 -> H(U1(e, a), U1(e, e))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, d))
27.56/8.98	   A^2 -> H(U1(e, a), U1(d, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(e, b))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, b))
27.56/8.98	   A^2 -> H(U1(k, a), U1(c, d))
27.56/8.98	   A^2 -> H(U1(k, a), U1(d, c))
27.56/8.98	   A^2 -> H(U1(k, a), U1(b, e))
27.56/8.98	   A^2 -> H(U1(k, a), U1(b, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(e, c))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, c))
27.56/8.98	   A^2 -> H(U1(k, a), U1(c, e))
27.56/8.98	   A^2 -> H(U1(k, a), U1(c, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(e, e))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, d))
27.56/8.98	   A^2 -> H(U1(k, a), U1(d, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(e, b))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, b))
27.56/8.98	   A^2 -> H(U1(c, d), U1(c, d))
27.56/8.98	   A^2 -> H(U1(c, d), U1(d, c))
27.56/8.98	   A^2 -> H(U1(c, d), U1(b, e))
27.56/8.98	   A^2 -> H(U1(c, d), U1(b, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(e, c))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, c))
27.56/8.98	   A^2 -> H(U1(c, d), U1(c, e))
27.56/8.98	   A^2 -> H(U1(c, d), U1(c, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(e, e))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, d))
27.56/8.98	   A^2 -> H(U1(c, d), U1(d, k))
27.56/8.98	   A^2 -> H(U1(c, a), b)
27.56/8.98	   A^2 -> H(U1(c, a), U1(e, d))
27.56/8.98	   A^2 -> H(U1(c, a), U1(d, e))
27.56/8.98	   A^2 -> H(U1(c, a), c)
27.56/8.98	   A^2 -> H(U1(c, a), U1(e, k))
27.56/8.98	   A^2 -> H(U1(c, a), U1(k, e))
27.56/8.98	   A^2 -> H(U1(c, a), e)
27.56/8.98	   A^2 -> H(U1(c, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(d, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(d, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(d, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(d, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(d, e), f(e))
27.56/8.98	   A^2 -> H(U1(d, e), f(k))
27.56/8.98	   A^2 -> H(U1(d, e), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, c), U1(e, b))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, b))
27.56/8.98	   A^2 -> H(U1(d, c), U1(c, d))
27.56/8.98	   A^2 -> H(U1(d, c), U1(d, c))
27.56/8.98	   A^2 -> H(U1(d, c), U1(b, e))
27.56/8.98	   A^2 -> H(U1(d, c), U1(b, k))
27.56/8.98	   A^2 -> H(U1(d, c), U1(e, c))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, c))
27.56/8.98	   A^2 -> H(U1(d, c), U1(c, e))
27.56/8.98	   A^2 -> H(U1(d, c), U1(c, k))
27.56/8.98	   A^2 -> H(U1(d, c), U1(e, e))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, d))
27.56/8.98	   A^2 -> H(U1(d, c), U1(d, k))
27.56/8.98	   A^2 -> H(U1(d, a), b)
27.56/8.98	   A^2 -> H(U1(d, a), U1(e, d))
27.56/8.98	
27.56/8.98	The TRS R consists of the following rules:
27.56/8.98	
27.56/8.98	   f(x) -> U1(x, x)
27.56/8.98	   U1(e, x) -> x
27.56/8.98	   a -> c
27.56/8.98	   a -> d
27.56/8.98	   b -> c
27.56/8.98	   b -> d
27.56/8.98	   d -> k
27.56/8.98	   c -> e
27.56/8.98	   c -> k
27.56/8.98	
27.56/8.98	Q is empty.
27.56/8.98	We have to consider all minimal (P,Q,R)-chains.
27.56/8.98	----------------------------------------
27.56/8.98	
27.56/8.98	(657) TransformationProof (EQUIVALENT)
27.56/8.98	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
27.56/8.98	
27.56/8.98	   (A^2 -> H(U1(k, a), U1(c, d)),A^2 -> H(U1(k, a), U1(c, d)))
27.56/8.98	   (A^2 -> H(U1(d, c), U1(c, d)),A^2 -> H(U1(d, c), U1(c, d)))
27.56/8.98	   (A^2 -> H(U1(d, d), U1(c, d)),A^2 -> H(U1(d, d), U1(c, d)))
27.56/8.98	   (A^2 -> H(U1(d, a), U1(e, d)),A^2 -> H(U1(d, a), U1(e, d)))
27.56/8.98	   (A^2 -> H(U1(d, a), U1(k, d)),A^2 -> H(U1(d, a), U1(k, d)))
27.56/8.98	   (A^2 -> H(U1(d, a), U1(c, k)),A^2 -> H(U1(d, a), U1(c, k)))
27.56/8.98	
27.56/8.98	
27.56/8.98	----------------------------------------
27.56/8.98	
27.56/8.98	(658)
27.56/8.98	Obligation:
27.56/8.98	Q DP problem:
27.56/8.98	The TRS P consists of the following rules:
27.56/8.98	
27.56/8.98	   H(x, x) -> G(x, x, f(k))
27.56/8.98	   G(d, x, x) -> A^2
27.56/8.98	   A^2 -> H(f(c), f(c))
27.56/8.98	   A^2 -> H(f(d), f(d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, c))
27.56/8.98	   A^2 -> H(f(e), f(e))
27.56/8.98	   A^2 -> H(f(k), f(k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, a), U1(d, c))
27.56/8.98	   A^2 -> H(U1(d, a), U1(b, e))
27.56/8.98	   A^2 -> H(U1(d, a), U1(b, k))
27.56/8.98	   A^2 -> H(U1(d, a), U1(e, c))
27.56/8.98	   A^2 -> H(U1(d, a), U1(k, c))
27.56/8.98	   A^2 -> H(U1(d, a), U1(c, e))
27.56/8.98	   A^2 -> H(U1(d, a), U1(c, k))
27.56/8.98	   A^2 -> H(U1(d, a), U1(e, e))
27.56/8.98	   A^2 -> H(U1(d, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, a), U1(k, d))
27.56/8.98	   A^2 -> H(U1(d, a), U1(d, k))
27.56/8.98	   A^2 -> H(U1(a, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(a, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(a, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(a, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(a, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(a, e), f(e))
27.56/8.98	   A^2 -> H(U1(a, e), f(k))
27.56/8.98	   A^2 -> H(U1(a, e), U1(d, d))
27.56/8.98	   A^2 -> H(U1(a, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(a, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(a, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(a, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(a, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(a, k), f(e))
27.56/8.98	   A^2 -> H(U1(a, k), f(k))
27.56/8.98	   A^2 -> H(U1(a, k), U1(d, d))
27.56/8.98	   A^2 -> H(U1(a, c), U1(e, b))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, b))
27.56/8.98	   A^2 -> H(U1(a, c), U1(c, d))
27.56/8.98	   A^2 -> H(U1(a, c), U1(d, c))
27.56/8.98	   A^2 -> H(U1(a, c), U1(b, e))
27.56/8.98	   A^2 -> H(U1(a, c), U1(b, k))
27.56/8.98	   A^2 -> H(U1(a, c), U1(e, c))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, c))
27.56/8.98	   A^2 -> H(U1(a, c), U1(c, e))
27.56/8.98	   A^2 -> H(U1(a, c), U1(c, k))
27.56/8.98	   A^2 -> H(U1(a, c), U1(e, e))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, d))
27.56/8.98	   A^2 -> H(U1(a, c), U1(d, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(e, b))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, b))
27.56/8.98	   A^2 -> H(U1(a, d), U1(c, d))
27.56/8.98	   A^2 -> H(U1(a, d), U1(d, c))
27.56/8.98	   A^2 -> H(U1(a, d), U1(b, e))
27.56/8.98	   A^2 -> H(U1(a, d), U1(b, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(e, c))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, c))
27.56/8.98	   A^2 -> H(U1(a, d), U1(c, e))
27.56/8.98	   A^2 -> H(U1(a, d), U1(c, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(e, e))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, d))
27.56/8.98	   A^2 -> H(U1(a, d), U1(d, k))
27.56/8.98	   A^2 -> H(U1(a, a), b)
27.56/8.98	   A^2 -> H(U1(a, a), U1(e, d))
27.56/8.98	   A^2 -> H(U1(a, a), U1(d, e))
27.56/8.98	   A^2 -> H(U1(a, a), c)
27.56/8.98	   A^2 -> H(U1(a, a), U1(e, k))
27.56/8.98	   A^2 -> H(U1(a, a), U1(k, e))
27.56/8.98	   A^2 -> H(U1(a, a), e)
27.56/8.98	   A^2 -> H(U1(a, a), U1(k, k))
27.56/8.98	   A^2 -> H(k, f(b))
27.56/8.98	   A^2 -> H(c, U1(b, b))
27.56/8.98	   A^2 -> H(c, f(c))
27.56/8.98	   A^2 -> H(c, f(d))
27.56/8.98	   A^2 -> H(U1(e, k), U1(b, b))
27.56/8.98	   A^2 -> H(U1(e, k), f(c))
27.56/8.98	   A^2 -> H(U1(e, k), f(d))
27.56/8.98	   A^2 -> H(U1(e, c), U1(c, b))
27.56/8.98	   A^2 -> H(U1(e, c), U1(d, b))
27.56/8.98	   A^2 -> H(U1(e, c), U1(b, c))
27.56/8.98	   A^2 -> H(U1(e, c), U1(b, d))
27.56/8.98	   A^2 -> H(U1(e, c), U1(c, c))
27.56/8.98	   A^2 -> H(U1(e, c), f(e))
27.56/8.98	   A^2 -> H(U1(e, c), f(k))
27.56/8.98	   A^2 -> H(U1(e, c), U1(d, d))
27.56/8.98	   A^2 -> H(U1(k, e), U1(b, b))
27.56/8.98	   A^2 -> H(U1(k, e), f(c))
27.56/8.98	   A^2 -> H(U1(k, e), f(d))
27.56/8.98	   A^2 -> H(U1(k, c), U1(c, b))
27.56/8.98	   A^2 -> H(U1(k, c), U1(d, b))
27.56/8.98	   A^2 -> H(U1(k, c), U1(b, c))
27.56/8.98	   A^2 -> H(U1(k, c), U1(b, d))
27.56/8.98	   A^2 -> H(U1(k, c), U1(c, c))
27.56/8.98	   A^2 -> H(U1(k, c), f(e))
27.56/8.98	   A^2 -> H(U1(k, c), f(k))
27.56/8.98	   A^2 -> H(U1(k, c), U1(d, d))
27.56/8.98	   A^2 -> H(U1(c, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(c, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(c, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(c, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(c, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(c, e), f(e))
27.56/8.98	   A^2 -> H(U1(c, e), f(k))
27.56/8.98	   A^2 -> H(U1(c, e), U1(d, d))
27.56/8.98	   A^2 -> H(U1(c, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(c, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(c, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(c, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(c, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(c, k), f(e))
27.56/8.98	   A^2 -> H(U1(c, k), f(k))
27.56/8.98	   A^2 -> H(U1(c, k), U1(d, d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(e, b))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, b))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(d, c))
27.56/8.98	   A^2 -> H(U1(c, c), U1(b, e))
27.56/8.98	   A^2 -> H(U1(c, c), U1(b, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(e, e))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(d, k))
27.56/8.98	   A^2 -> H(e, U1(b, b))
27.56/8.98	   A^2 -> H(e, f(c))
27.56/8.98	   A^2 -> H(e, f(d))
27.56/8.98	   A^2 -> H(U1(e, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(e, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(e, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(e, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(e, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(e, e), f(e))
27.56/8.98	   A^2 -> H(U1(e, e), f(k))
27.56/8.98	   A^2 -> H(U1(e, e), U1(d, d))
27.56/8.98	   A^2 -> H(f(e), U1(e, b))
27.56/8.98	   A^2 -> H(f(e), U1(k, b))
27.56/8.98	   A^2 -> H(f(e), U1(c, d))
27.56/8.98	   A^2 -> H(f(e), U1(d, c))
27.56/8.98	   A^2 -> H(f(e), U1(b, e))
27.56/8.98	   A^2 -> H(f(e), U1(b, k))
27.56/8.98	   A^2 -> H(f(e), U1(e, c))
27.56/8.98	   A^2 -> H(f(e), U1(k, c))
27.56/8.98	   A^2 -> H(f(e), U1(c, e))
27.56/8.98	   A^2 -> H(f(e), U1(c, k))
27.56/8.98	   A^2 -> H(f(e), U1(k, k))
27.56/8.98	   A^2 -> H(f(e), U1(k, d))
27.56/8.98	   A^2 -> H(f(e), U1(d, k))
27.56/8.98	   A^2 -> H(U1(k, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(k, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(k, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(k, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(k, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(k, k), f(e))
27.56/8.98	   A^2 -> H(U1(k, k), f(k))
27.56/8.98	   A^2 -> H(U1(k, k), U1(d, d))
27.56/8.98	   A^2 -> H(f(k), U1(e, b))
27.56/8.98	   A^2 -> H(f(k), U1(k, b))
27.56/8.98	   A^2 -> H(f(k), U1(c, d))
27.56/8.98	   A^2 -> H(f(k), U1(d, c))
27.56/8.98	   A^2 -> H(f(k), U1(b, e))
27.56/8.98	   A^2 -> H(f(k), U1(b, k))
27.56/8.98	   A^2 -> H(f(k), U1(e, c))
27.56/8.98	   A^2 -> H(f(k), U1(k, c))
27.56/8.98	   A^2 -> H(f(k), U1(c, e))
27.56/8.98	   A^2 -> H(f(k), U1(c, k))
27.56/8.98	   A^2 -> H(f(k), U1(e, e))
27.56/8.98	   A^2 -> H(f(k), U1(k, d))
27.56/8.98	   A^2 -> H(f(k), U1(d, k))
27.56/8.98	   A^2 -> H(f(c), b)
27.56/8.98	   A^2 -> H(f(c), U1(e, d))
27.56/8.98	   A^2 -> H(f(c), U1(d, e))
27.56/8.98	   A^2 -> H(f(k), U1(k, k))
27.56/8.98	   A^2 -> H(U1(k, k), U1(b, b))
27.56/8.98	   A^2 -> H(U1(k, k), f(c))
27.56/8.98	   A^2 -> H(U1(k, k), f(d))
27.56/8.98	   A^2 -> H(U1(k, d), U1(c, b))
27.56/8.98	   A^2 -> H(U1(k, d), U1(d, b))
27.56/8.98	   A^2 -> H(U1(k, d), U1(b, c))
27.56/8.98	   A^2 -> H(U1(k, d), U1(b, d))
27.56/8.98	   A^2 -> H(U1(k, d), U1(c, c))
27.56/8.98	   A^2 -> H(U1(k, d), f(e))
27.56/8.98	   A^2 -> H(U1(k, d), f(k))
27.56/8.98	   A^2 -> H(U1(k, d), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(d, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(d, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(d, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(d, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(d, k), f(e))
27.56/8.98	   A^2 -> H(U1(d, k), f(k))
27.56/8.98	   A^2 -> H(U1(d, k), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, d), U1(e, b))
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, b))
27.56/8.98	   A^2 -> H(U1(d, d), U1(c, d))
27.56/8.98	   A^2 -> H(U1(d, d), U1(d, c))
27.56/8.98	   A^2 -> H(U1(d, d), U1(b, e))
27.56/8.98	   A^2 -> H(U1(d, d), U1(b, k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(e, c))
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, c))
27.56/8.98	   A^2 -> H(U1(d, d), U1(c, e))
27.56/8.98	   A^2 -> H(U1(d, d), U1(c, k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(e, e))
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, k))
27.56/8.98	   A^2 -> H(f(d), b)
27.56/8.98	   A^2 -> H(f(d), U1(e, d))
27.56/8.98	   A^2 -> H(f(d), U1(d, e))
27.56/8.98	   A^2 -> H(f(d), c)
27.56/8.98	   A^2 -> H(f(d), U1(e, k))
27.56/8.98	   A^2 -> H(f(d), U1(k, e))
27.56/8.98	   A^2 -> H(f(d), e)
27.56/8.98	   A^2 -> H(f(a), d)
27.56/8.98	   A^2 -> H(U1(c, c), U1(e, c))
27.56/8.98	   A^2 -> H(f(c), c)
27.56/8.98	   A^2 -> H(f(c), U1(e, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, c))
27.56/8.98	   A^2 -> H(f(c), U1(k, e))
27.56/8.98	   A^2 -> H(f(c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, e))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, k))
27.56/8.98	   A^2 -> H(f(a), k)
27.56/8.98	   A^2 -> H(f(e), U1(e, e))
27.56/8.98	   A^2 -> H(f(c), e)
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, d))
27.56/8.98	   A^2 -> H(f(d), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(d, k))
27.56/8.98	   A^2 -> H(d, U1(b, b))
27.56/8.98	   A^2 -> H(d, f(c))
27.56/8.98	   A^2 -> H(d, f(d))
27.56/8.98	   A^2 -> H(a, U1(c, b))
27.56/8.98	   A^2 -> H(a, U1(d, b))
27.56/8.98	   A^2 -> H(a, U1(b, c))
27.56/8.98	   A^2 -> H(a, U1(b, d))
27.56/8.98	   A^2 -> H(a, U1(c, c))
27.56/8.98	   A^2 -> H(a, f(e))
27.56/8.98	   A^2 -> H(a, f(k))
27.56/8.98	   A^2 -> H(a, U1(d, d))
27.56/8.98	   A^2 -> H(U1(e, d), U1(c, b))
27.56/8.98	   A^2 -> H(U1(e, d), U1(d, b))
27.56/8.98	   A^2 -> H(U1(e, d), U1(b, c))
27.56/8.98	   A^2 -> H(U1(e, d), U1(b, d))
27.56/8.98	   A^2 -> H(U1(e, d), U1(c, c))
27.56/8.98	   A^2 -> H(U1(e, d), f(e))
27.56/8.98	   A^2 -> H(U1(e, d), f(k))
27.56/8.98	   A^2 -> H(U1(e, d), U1(d, d))
27.56/8.98	   A^2 -> H(U1(e, a), U1(e, b))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, b))
27.56/8.98	   A^2 -> H(U1(e, a), U1(c, d))
27.56/8.98	   A^2 -> H(U1(e, a), U1(d, c))
27.56/8.98	   A^2 -> H(U1(e, a), U1(b, e))
27.56/8.98	   A^2 -> H(U1(e, a), U1(b, k))
27.56/8.98	   A^2 -> H(U1(e, a), U1(e, c))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, c))
27.56/8.98	   A^2 -> H(U1(e, a), U1(c, e))
27.56/8.98	   A^2 -> H(U1(e, a), U1(c, k))
27.56/8.98	   A^2 -> H(U1(e, a), U1(e, e))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, d))
27.56/8.98	   A^2 -> H(U1(e, a), U1(d, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(e, b))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, b))
27.56/8.98	   A^2 -> H(U1(k, a), U1(c, d))
27.56/8.98	   A^2 -> H(U1(k, a), U1(d, c))
27.56/8.98	   A^2 -> H(U1(k, a), U1(b, e))
27.56/8.98	   A^2 -> H(U1(k, a), U1(b, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(e, c))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, c))
27.56/8.98	   A^2 -> H(U1(k, a), U1(c, e))
27.56/8.98	   A^2 -> H(U1(k, a), U1(c, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(e, e))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, d))
27.56/8.98	   A^2 -> H(U1(k, a), U1(d, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(e, b))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, b))
27.56/8.98	   A^2 -> H(U1(c, d), U1(c, d))
27.56/8.98	   A^2 -> H(U1(c, d), U1(d, c))
27.56/8.98	   A^2 -> H(U1(c, d), U1(b, e))
27.56/8.98	   A^2 -> H(U1(c, d), U1(b, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(e, c))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, c))
27.56/8.98	   A^2 -> H(U1(c, d), U1(c, e))
27.56/8.98	   A^2 -> H(U1(c, d), U1(c, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(e, e))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, d))
27.56/8.98	   A^2 -> H(U1(c, d), U1(d, k))
27.56/8.98	   A^2 -> H(U1(c, a), b)
27.56/8.98	   A^2 -> H(U1(c, a), U1(e, d))
27.56/8.98	   A^2 -> H(U1(c, a), U1(d, e))
27.56/8.98	   A^2 -> H(U1(c, a), c)
27.56/8.98	   A^2 -> H(U1(c, a), U1(e, k))
27.56/8.98	   A^2 -> H(U1(c, a), U1(k, e))
27.56/8.98	   A^2 -> H(U1(c, a), e)
27.56/8.98	   A^2 -> H(U1(c, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(d, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(d, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(d, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(d, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(d, e), f(e))
27.56/8.98	   A^2 -> H(U1(d, e), f(k))
27.56/8.98	   A^2 -> H(U1(d, e), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, c), U1(e, b))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, b))
27.56/8.98	   A^2 -> H(U1(d, c), U1(c, d))
27.56/8.98	   A^2 -> H(U1(d, c), U1(d, c))
27.56/8.98	   A^2 -> H(U1(d, c), U1(b, e))
27.56/8.98	   A^2 -> H(U1(d, c), U1(b, k))
27.56/8.98	   A^2 -> H(U1(d, c), U1(e, c))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, c))
27.56/8.98	   A^2 -> H(U1(d, c), U1(c, e))
27.56/8.98	   A^2 -> H(U1(d, c), U1(c, k))
27.56/8.98	   A^2 -> H(U1(d, c), U1(e, e))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, d))
27.56/8.98	   A^2 -> H(U1(d, c), U1(d, k))
27.56/8.98	   A^2 -> H(U1(d, a), b)
27.56/8.98	   A^2 -> H(U1(d, a), U1(e, d))
27.56/8.98	
27.56/8.98	The TRS R consists of the following rules:
27.56/8.98	
27.56/8.98	   f(x) -> U1(x, x)
27.56/8.98	   U1(e, x) -> x
27.56/8.98	   a -> c
27.56/8.98	   a -> d
27.56/8.98	   b -> c
27.56/8.98	   b -> d
27.56/8.98	   d -> k
27.56/8.98	   c -> e
27.56/8.98	   c -> k
27.56/8.98	
27.56/8.98	Q is empty.
27.56/8.98	We have to consider all minimal (P,Q,R)-chains.
27.56/8.98	----------------------------------------
27.56/8.98	
27.56/8.98	(659) TransformationProof (EQUIVALENT)
27.56/8.98	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
27.56/8.98	
27.56/8.98	   (A^2 -> H(U1(k, a), U1(d, c)),A^2 -> H(U1(k, a), U1(d, c)))
27.56/8.98	   (A^2 -> H(U1(d, c), U1(d, c)),A^2 -> H(U1(d, c), U1(d, c)))
27.56/8.98	   (A^2 -> H(U1(d, d), U1(d, c)),A^2 -> H(U1(d, d), U1(d, c)))
27.56/8.98	   (A^2 -> H(U1(d, a), U1(k, c)),A^2 -> H(U1(d, a), U1(k, c)))
27.56/8.98	   (A^2 -> H(U1(d, a), U1(d, e)),A^2 -> H(U1(d, a), U1(d, e)))
27.56/8.98	   (A^2 -> H(U1(d, a), U1(d, k)),A^2 -> H(U1(d, a), U1(d, k)))
27.56/8.98	
27.56/8.98	
27.56/8.98	----------------------------------------
27.56/8.98	
27.56/8.98	(660)
27.56/8.98	Obligation:
27.56/8.98	Q DP problem:
27.56/8.98	The TRS P consists of the following rules:
27.56/8.98	
27.56/8.98	   H(x, x) -> G(x, x, f(k))
27.56/8.98	   G(d, x, x) -> A^2
27.56/8.98	   A^2 -> H(f(c), f(c))
27.56/8.98	   A^2 -> H(f(d), f(d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, c))
27.56/8.98	   A^2 -> H(f(e), f(e))
27.56/8.98	   A^2 -> H(f(k), f(k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, a), U1(b, e))
27.56/8.98	   A^2 -> H(U1(d, a), U1(b, k))
27.56/8.98	   A^2 -> H(U1(d, a), U1(e, c))
27.56/8.98	   A^2 -> H(U1(d, a), U1(k, c))
27.56/8.98	   A^2 -> H(U1(d, a), U1(c, e))
27.56/8.98	   A^2 -> H(U1(d, a), U1(c, k))
27.56/8.98	   A^2 -> H(U1(d, a), U1(e, e))
27.56/8.98	   A^2 -> H(U1(d, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, a), U1(k, d))
27.56/8.98	   A^2 -> H(U1(d, a), U1(d, k))
27.56/8.98	   A^2 -> H(U1(a, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(a, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(a, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(a, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(a, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(a, e), f(e))
27.56/8.98	   A^2 -> H(U1(a, e), f(k))
27.56/8.98	   A^2 -> H(U1(a, e), U1(d, d))
27.56/8.98	   A^2 -> H(U1(a, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(a, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(a, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(a, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(a, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(a, k), f(e))
27.56/8.98	   A^2 -> H(U1(a, k), f(k))
27.56/8.98	   A^2 -> H(U1(a, k), U1(d, d))
27.56/8.98	   A^2 -> H(U1(a, c), U1(e, b))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, b))
27.56/8.98	   A^2 -> H(U1(a, c), U1(c, d))
27.56/8.98	   A^2 -> H(U1(a, c), U1(d, c))
27.56/8.98	   A^2 -> H(U1(a, c), U1(b, e))
27.56/8.98	   A^2 -> H(U1(a, c), U1(b, k))
27.56/8.98	   A^2 -> H(U1(a, c), U1(e, c))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, c))
27.56/8.98	   A^2 -> H(U1(a, c), U1(c, e))
27.56/8.98	   A^2 -> H(U1(a, c), U1(c, k))
27.56/8.98	   A^2 -> H(U1(a, c), U1(e, e))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, d))
27.56/8.98	   A^2 -> H(U1(a, c), U1(d, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(e, b))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, b))
27.56/8.98	   A^2 -> H(U1(a, d), U1(c, d))
27.56/8.98	   A^2 -> H(U1(a, d), U1(d, c))
27.56/8.98	   A^2 -> H(U1(a, d), U1(b, e))
27.56/8.98	   A^2 -> H(U1(a, d), U1(b, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(e, c))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, c))
27.56/8.98	   A^2 -> H(U1(a, d), U1(c, e))
27.56/8.98	   A^2 -> H(U1(a, d), U1(c, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(e, e))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, d))
27.56/8.98	   A^2 -> H(U1(a, d), U1(d, k))
27.56/8.98	   A^2 -> H(U1(a, a), b)
27.56/8.98	   A^2 -> H(U1(a, a), U1(e, d))
27.56/8.98	   A^2 -> H(U1(a, a), U1(d, e))
27.56/8.98	   A^2 -> H(U1(a, a), c)
27.56/8.98	   A^2 -> H(U1(a, a), U1(e, k))
27.56/8.98	   A^2 -> H(U1(a, a), U1(k, e))
27.56/8.98	   A^2 -> H(U1(a, a), e)
27.56/8.98	   A^2 -> H(U1(a, a), U1(k, k))
27.56/8.98	   A^2 -> H(k, f(b))
27.56/8.98	   A^2 -> H(c, U1(b, b))
27.56/8.98	   A^2 -> H(c, f(c))
27.56/8.98	   A^2 -> H(c, f(d))
27.56/8.98	   A^2 -> H(U1(e, k), U1(b, b))
27.56/8.98	   A^2 -> H(U1(e, k), f(c))
27.56/8.98	   A^2 -> H(U1(e, k), f(d))
27.56/8.98	   A^2 -> H(U1(e, c), U1(c, b))
27.56/8.98	   A^2 -> H(U1(e, c), U1(d, b))
27.56/8.98	   A^2 -> H(U1(e, c), U1(b, c))
27.56/8.98	   A^2 -> H(U1(e, c), U1(b, d))
27.56/8.98	   A^2 -> H(U1(e, c), U1(c, c))
27.56/8.98	   A^2 -> H(U1(e, c), f(e))
27.56/8.98	   A^2 -> H(U1(e, c), f(k))
27.56/8.98	   A^2 -> H(U1(e, c), U1(d, d))
27.56/8.98	   A^2 -> H(U1(k, e), U1(b, b))
27.56/8.98	   A^2 -> H(U1(k, e), f(c))
27.56/8.98	   A^2 -> H(U1(k, e), f(d))
27.56/8.98	   A^2 -> H(U1(k, c), U1(c, b))
27.56/8.98	   A^2 -> H(U1(k, c), U1(d, b))
27.56/8.98	   A^2 -> H(U1(k, c), U1(b, c))
27.56/8.98	   A^2 -> H(U1(k, c), U1(b, d))
27.56/8.98	   A^2 -> H(U1(k, c), U1(c, c))
27.56/8.98	   A^2 -> H(U1(k, c), f(e))
27.56/8.98	   A^2 -> H(U1(k, c), f(k))
27.56/8.98	   A^2 -> H(U1(k, c), U1(d, d))
27.56/8.98	   A^2 -> H(U1(c, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(c, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(c, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(c, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(c, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(c, e), f(e))
27.56/8.98	   A^2 -> H(U1(c, e), f(k))
27.56/8.98	   A^2 -> H(U1(c, e), U1(d, d))
27.56/8.98	   A^2 -> H(U1(c, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(c, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(c, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(c, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(c, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(c, k), f(e))
27.56/8.98	   A^2 -> H(U1(c, k), f(k))
27.56/8.98	   A^2 -> H(U1(c, k), U1(d, d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(e, b))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, b))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(d, c))
27.56/8.98	   A^2 -> H(U1(c, c), U1(b, e))
27.56/8.98	   A^2 -> H(U1(c, c), U1(b, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(e, e))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(d, k))
27.56/8.98	   A^2 -> H(e, U1(b, b))
27.56/8.98	   A^2 -> H(e, f(c))
27.56/8.98	   A^2 -> H(e, f(d))
27.56/8.98	   A^2 -> H(U1(e, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(e, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(e, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(e, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(e, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(e, e), f(e))
27.56/8.98	   A^2 -> H(U1(e, e), f(k))
27.56/8.98	   A^2 -> H(U1(e, e), U1(d, d))
27.56/8.98	   A^2 -> H(f(e), U1(e, b))
27.56/8.98	   A^2 -> H(f(e), U1(k, b))
27.56/8.98	   A^2 -> H(f(e), U1(c, d))
27.56/8.98	   A^2 -> H(f(e), U1(d, c))
27.56/8.98	   A^2 -> H(f(e), U1(b, e))
27.56/8.98	   A^2 -> H(f(e), U1(b, k))
27.56/8.98	   A^2 -> H(f(e), U1(e, c))
27.56/8.98	   A^2 -> H(f(e), U1(k, c))
27.56/8.98	   A^2 -> H(f(e), U1(c, e))
27.56/8.98	   A^2 -> H(f(e), U1(c, k))
27.56/8.98	   A^2 -> H(f(e), U1(k, k))
27.56/8.98	   A^2 -> H(f(e), U1(k, d))
27.56/8.98	   A^2 -> H(f(e), U1(d, k))
27.56/8.98	   A^2 -> H(U1(k, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(k, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(k, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(k, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(k, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(k, k), f(e))
27.56/8.98	   A^2 -> H(U1(k, k), f(k))
27.56/8.98	   A^2 -> H(U1(k, k), U1(d, d))
27.56/8.98	   A^2 -> H(f(k), U1(e, b))
27.56/8.98	   A^2 -> H(f(k), U1(k, b))
27.56/8.98	   A^2 -> H(f(k), U1(c, d))
27.56/8.98	   A^2 -> H(f(k), U1(d, c))
27.56/8.98	   A^2 -> H(f(k), U1(b, e))
27.56/8.98	   A^2 -> H(f(k), U1(b, k))
27.56/8.98	   A^2 -> H(f(k), U1(e, c))
27.56/8.98	   A^2 -> H(f(k), U1(k, c))
27.56/8.98	   A^2 -> H(f(k), U1(c, e))
27.56/8.98	   A^2 -> H(f(k), U1(c, k))
27.56/8.98	   A^2 -> H(f(k), U1(e, e))
27.56/8.98	   A^2 -> H(f(k), U1(k, d))
27.56/8.98	   A^2 -> H(f(k), U1(d, k))
27.56/8.98	   A^2 -> H(f(c), b)
27.56/8.98	   A^2 -> H(f(c), U1(e, d))
27.56/8.98	   A^2 -> H(f(c), U1(d, e))
27.56/8.98	   A^2 -> H(f(k), U1(k, k))
27.56/8.98	   A^2 -> H(U1(k, k), U1(b, b))
27.56/8.98	   A^2 -> H(U1(k, k), f(c))
27.56/8.98	   A^2 -> H(U1(k, k), f(d))
27.56/8.98	   A^2 -> H(U1(k, d), U1(c, b))
27.56/8.98	   A^2 -> H(U1(k, d), U1(d, b))
27.56/8.98	   A^2 -> H(U1(k, d), U1(b, c))
27.56/8.98	   A^2 -> H(U1(k, d), U1(b, d))
27.56/8.98	   A^2 -> H(U1(k, d), U1(c, c))
27.56/8.98	   A^2 -> H(U1(k, d), f(e))
27.56/8.98	   A^2 -> H(U1(k, d), f(k))
27.56/8.98	   A^2 -> H(U1(k, d), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(d, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(d, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(d, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(d, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(d, k), f(e))
27.56/8.98	   A^2 -> H(U1(d, k), f(k))
27.56/8.98	   A^2 -> H(U1(d, k), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, d), U1(e, b))
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, b))
27.56/8.98	   A^2 -> H(U1(d, d), U1(c, d))
27.56/8.98	   A^2 -> H(U1(d, d), U1(d, c))
27.56/8.98	   A^2 -> H(U1(d, d), U1(b, e))
27.56/8.98	   A^2 -> H(U1(d, d), U1(b, k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(e, c))
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, c))
27.56/8.98	   A^2 -> H(U1(d, d), U1(c, e))
27.56/8.98	   A^2 -> H(U1(d, d), U1(c, k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(e, e))
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, k))
27.56/8.98	   A^2 -> H(f(d), b)
27.56/8.98	   A^2 -> H(f(d), U1(e, d))
27.56/8.98	   A^2 -> H(f(d), U1(d, e))
27.56/8.98	   A^2 -> H(f(d), c)
27.56/8.98	   A^2 -> H(f(d), U1(e, k))
27.56/8.98	   A^2 -> H(f(d), U1(k, e))
27.56/8.98	   A^2 -> H(f(d), e)
27.56/8.98	   A^2 -> H(f(a), d)
27.56/8.98	   A^2 -> H(U1(c, c), U1(e, c))
27.56/8.98	   A^2 -> H(f(c), c)
27.56/8.98	   A^2 -> H(f(c), U1(e, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, c))
27.56/8.98	   A^2 -> H(f(c), U1(k, e))
27.56/8.98	   A^2 -> H(f(c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, e))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, k))
27.56/8.98	   A^2 -> H(f(a), k)
27.56/8.98	   A^2 -> H(f(e), U1(e, e))
27.56/8.98	   A^2 -> H(f(c), e)
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, d))
27.56/8.98	   A^2 -> H(f(d), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(d, k))
27.56/8.98	   A^2 -> H(d, U1(b, b))
27.56/8.98	   A^2 -> H(d, f(c))
27.56/8.98	   A^2 -> H(d, f(d))
27.56/8.98	   A^2 -> H(a, U1(c, b))
27.56/8.98	   A^2 -> H(a, U1(d, b))
27.56/8.98	   A^2 -> H(a, U1(b, c))
27.56/8.98	   A^2 -> H(a, U1(b, d))
27.56/8.98	   A^2 -> H(a, U1(c, c))
27.56/8.98	   A^2 -> H(a, f(e))
27.56/8.98	   A^2 -> H(a, f(k))
27.56/8.98	   A^2 -> H(a, U1(d, d))
27.56/8.98	   A^2 -> H(U1(e, d), U1(c, b))
27.56/8.98	   A^2 -> H(U1(e, d), U1(d, b))
27.56/8.98	   A^2 -> H(U1(e, d), U1(b, c))
27.56/8.98	   A^2 -> H(U1(e, d), U1(b, d))
27.56/8.98	   A^2 -> H(U1(e, d), U1(c, c))
27.56/8.98	   A^2 -> H(U1(e, d), f(e))
27.56/8.98	   A^2 -> H(U1(e, d), f(k))
27.56/8.98	   A^2 -> H(U1(e, d), U1(d, d))
27.56/8.98	   A^2 -> H(U1(e, a), U1(e, b))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, b))
27.56/8.98	   A^2 -> H(U1(e, a), U1(c, d))
27.56/8.98	   A^2 -> H(U1(e, a), U1(d, c))
27.56/8.98	   A^2 -> H(U1(e, a), U1(b, e))
27.56/8.98	   A^2 -> H(U1(e, a), U1(b, k))
27.56/8.98	   A^2 -> H(U1(e, a), U1(e, c))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, c))
27.56/8.98	   A^2 -> H(U1(e, a), U1(c, e))
27.56/8.98	   A^2 -> H(U1(e, a), U1(c, k))
27.56/8.98	   A^2 -> H(U1(e, a), U1(e, e))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, d))
27.56/8.98	   A^2 -> H(U1(e, a), U1(d, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(e, b))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, b))
27.56/8.98	   A^2 -> H(U1(k, a), U1(c, d))
27.56/8.98	   A^2 -> H(U1(k, a), U1(d, c))
27.56/8.98	   A^2 -> H(U1(k, a), U1(b, e))
27.56/8.98	   A^2 -> H(U1(k, a), U1(b, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(e, c))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, c))
27.56/8.98	   A^2 -> H(U1(k, a), U1(c, e))
27.56/8.98	   A^2 -> H(U1(k, a), U1(c, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(e, e))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, d))
27.56/8.98	   A^2 -> H(U1(k, a), U1(d, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(e, b))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, b))
27.56/8.98	   A^2 -> H(U1(c, d), U1(c, d))
27.56/8.98	   A^2 -> H(U1(c, d), U1(d, c))
27.56/8.98	   A^2 -> H(U1(c, d), U1(b, e))
27.56/8.98	   A^2 -> H(U1(c, d), U1(b, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(e, c))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, c))
27.56/8.98	   A^2 -> H(U1(c, d), U1(c, e))
27.56/8.98	   A^2 -> H(U1(c, d), U1(c, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(e, e))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, d))
27.56/8.98	   A^2 -> H(U1(c, d), U1(d, k))
27.56/8.98	   A^2 -> H(U1(c, a), b)
27.56/8.98	   A^2 -> H(U1(c, a), U1(e, d))
27.56/8.98	   A^2 -> H(U1(c, a), U1(d, e))
27.56/8.98	   A^2 -> H(U1(c, a), c)
27.56/8.98	   A^2 -> H(U1(c, a), U1(e, k))
27.56/8.98	   A^2 -> H(U1(c, a), U1(k, e))
27.56/8.98	   A^2 -> H(U1(c, a), e)
27.56/8.98	   A^2 -> H(U1(c, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(d, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(d, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(d, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(d, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(d, e), f(e))
27.56/8.98	   A^2 -> H(U1(d, e), f(k))
27.56/8.98	   A^2 -> H(U1(d, e), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, c), U1(e, b))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, b))
27.56/8.98	   A^2 -> H(U1(d, c), U1(c, d))
27.56/8.98	   A^2 -> H(U1(d, c), U1(d, c))
27.56/8.98	   A^2 -> H(U1(d, c), U1(b, e))
27.56/8.98	   A^2 -> H(U1(d, c), U1(b, k))
27.56/8.98	   A^2 -> H(U1(d, c), U1(e, c))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, c))
27.56/8.98	   A^2 -> H(U1(d, c), U1(c, e))
27.56/8.98	   A^2 -> H(U1(d, c), U1(c, k))
27.56/8.98	   A^2 -> H(U1(d, c), U1(e, e))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, d))
27.56/8.98	   A^2 -> H(U1(d, c), U1(d, k))
27.56/8.98	   A^2 -> H(U1(d, a), b)
27.56/8.98	   A^2 -> H(U1(d, a), U1(e, d))
27.56/8.98	   A^2 -> H(U1(d, a), U1(d, e))
27.56/8.98	
27.56/8.98	The TRS R consists of the following rules:
27.56/8.98	
27.56/8.98	   f(x) -> U1(x, x)
27.56/8.98	   U1(e, x) -> x
27.56/8.98	   a -> c
27.56/8.98	   a -> d
27.56/8.98	   b -> c
27.56/8.98	   b -> d
27.56/8.98	   d -> k
27.56/8.98	   c -> e
27.56/8.98	   c -> k
27.56/8.98	
27.56/8.98	Q is empty.
27.56/8.98	We have to consider all minimal (P,Q,R)-chains.
27.56/8.98	----------------------------------------
27.56/8.98	
27.56/8.98	(661) TransformationProof (EQUIVALENT)
27.56/8.98	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
27.56/8.98	
27.56/8.98	   (A^2 -> H(U1(k, a), U1(b, e)),A^2 -> H(U1(k, a), U1(b, e)))
27.56/8.98	   (A^2 -> H(U1(d, c), U1(b, e)),A^2 -> H(U1(d, c), U1(b, e)))
27.56/8.98	   (A^2 -> H(U1(d, d), U1(b, e)),A^2 -> H(U1(d, d), U1(b, e)))
27.56/8.98	   (A^2 -> H(U1(d, a), U1(c, e)),A^2 -> H(U1(d, a), U1(c, e)))
27.56/8.98	   (A^2 -> H(U1(d, a), U1(d, e)),A^2 -> H(U1(d, a), U1(d, e)))
27.56/8.98	
27.56/8.98	
27.56/8.98	----------------------------------------
27.56/8.98	
27.56/8.98	(662)
27.56/8.98	Obligation:
27.56/8.98	Q DP problem:
27.56/8.98	The TRS P consists of the following rules:
27.56/8.98	
27.56/8.98	   H(x, x) -> G(x, x, f(k))
27.56/8.98	   G(d, x, x) -> A^2
27.56/8.98	   A^2 -> H(f(c), f(c))
27.56/8.98	   A^2 -> H(f(d), f(d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, c))
27.56/8.98	   A^2 -> H(f(e), f(e))
27.56/8.98	   A^2 -> H(f(k), f(k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, a), U1(b, k))
27.56/8.98	   A^2 -> H(U1(d, a), U1(e, c))
27.56/8.98	   A^2 -> H(U1(d, a), U1(k, c))
27.56/8.98	   A^2 -> H(U1(d, a), U1(c, e))
27.56/8.98	   A^2 -> H(U1(d, a), U1(c, k))
27.56/8.98	   A^2 -> H(U1(d, a), U1(e, e))
27.56/8.98	   A^2 -> H(U1(d, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, a), U1(k, d))
27.56/8.98	   A^2 -> H(U1(d, a), U1(d, k))
27.56/8.98	   A^2 -> H(U1(a, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(a, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(a, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(a, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(a, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(a, e), f(e))
27.56/8.98	   A^2 -> H(U1(a, e), f(k))
27.56/8.98	   A^2 -> H(U1(a, e), U1(d, d))
27.56/8.98	   A^2 -> H(U1(a, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(a, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(a, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(a, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(a, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(a, k), f(e))
27.56/8.98	   A^2 -> H(U1(a, k), f(k))
27.56/8.98	   A^2 -> H(U1(a, k), U1(d, d))
27.56/8.98	   A^2 -> H(U1(a, c), U1(e, b))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, b))
27.56/8.98	   A^2 -> H(U1(a, c), U1(c, d))
27.56/8.98	   A^2 -> H(U1(a, c), U1(d, c))
27.56/8.98	   A^2 -> H(U1(a, c), U1(b, e))
27.56/8.98	   A^2 -> H(U1(a, c), U1(b, k))
27.56/8.98	   A^2 -> H(U1(a, c), U1(e, c))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, c))
27.56/8.98	   A^2 -> H(U1(a, c), U1(c, e))
27.56/8.98	   A^2 -> H(U1(a, c), U1(c, k))
27.56/8.98	   A^2 -> H(U1(a, c), U1(e, e))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, d))
27.56/8.98	   A^2 -> H(U1(a, c), U1(d, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(e, b))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, b))
27.56/8.98	   A^2 -> H(U1(a, d), U1(c, d))
27.56/8.98	   A^2 -> H(U1(a, d), U1(d, c))
27.56/8.98	   A^2 -> H(U1(a, d), U1(b, e))
27.56/8.98	   A^2 -> H(U1(a, d), U1(b, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(e, c))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, c))
27.56/8.98	   A^2 -> H(U1(a, d), U1(c, e))
27.56/8.98	   A^2 -> H(U1(a, d), U1(c, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(e, e))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, d))
27.56/8.98	   A^2 -> H(U1(a, d), U1(d, k))
27.56/8.98	   A^2 -> H(U1(a, a), b)
27.56/8.98	   A^2 -> H(U1(a, a), U1(e, d))
27.56/8.98	   A^2 -> H(U1(a, a), U1(d, e))
27.56/8.98	   A^2 -> H(U1(a, a), c)
27.56/8.98	   A^2 -> H(U1(a, a), U1(e, k))
27.56/8.98	   A^2 -> H(U1(a, a), U1(k, e))
27.56/8.98	   A^2 -> H(U1(a, a), e)
27.56/8.98	   A^2 -> H(U1(a, a), U1(k, k))
27.56/8.98	   A^2 -> H(k, f(b))
27.56/8.98	   A^2 -> H(c, U1(b, b))
27.56/8.98	   A^2 -> H(c, f(c))
27.56/8.98	   A^2 -> H(c, f(d))
27.56/8.98	   A^2 -> H(U1(e, k), U1(b, b))
27.56/8.98	   A^2 -> H(U1(e, k), f(c))
27.56/8.98	   A^2 -> H(U1(e, k), f(d))
27.56/8.98	   A^2 -> H(U1(e, c), U1(c, b))
27.56/8.98	   A^2 -> H(U1(e, c), U1(d, b))
27.56/8.98	   A^2 -> H(U1(e, c), U1(b, c))
27.56/8.98	   A^2 -> H(U1(e, c), U1(b, d))
27.56/8.98	   A^2 -> H(U1(e, c), U1(c, c))
27.56/8.98	   A^2 -> H(U1(e, c), f(e))
27.56/8.98	   A^2 -> H(U1(e, c), f(k))
27.56/8.98	   A^2 -> H(U1(e, c), U1(d, d))
27.56/8.98	   A^2 -> H(U1(k, e), U1(b, b))
27.56/8.98	   A^2 -> H(U1(k, e), f(c))
27.56/8.98	   A^2 -> H(U1(k, e), f(d))
27.56/8.98	   A^2 -> H(U1(k, c), U1(c, b))
27.56/8.98	   A^2 -> H(U1(k, c), U1(d, b))
27.56/8.98	   A^2 -> H(U1(k, c), U1(b, c))
27.56/8.98	   A^2 -> H(U1(k, c), U1(b, d))
27.56/8.98	   A^2 -> H(U1(k, c), U1(c, c))
27.56/8.98	   A^2 -> H(U1(k, c), f(e))
27.56/8.98	   A^2 -> H(U1(k, c), f(k))
27.56/8.98	   A^2 -> H(U1(k, c), U1(d, d))
27.56/8.98	   A^2 -> H(U1(c, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(c, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(c, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(c, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(c, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(c, e), f(e))
27.56/8.98	   A^2 -> H(U1(c, e), f(k))
27.56/8.98	   A^2 -> H(U1(c, e), U1(d, d))
27.56/8.98	   A^2 -> H(U1(c, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(c, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(c, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(c, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(c, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(c, k), f(e))
27.56/8.98	   A^2 -> H(U1(c, k), f(k))
27.56/8.98	   A^2 -> H(U1(c, k), U1(d, d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(e, b))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, b))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(d, c))
27.56/8.98	   A^2 -> H(U1(c, c), U1(b, e))
27.56/8.98	   A^2 -> H(U1(c, c), U1(b, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(e, e))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(d, k))
27.56/8.98	   A^2 -> H(e, U1(b, b))
27.56/8.98	   A^2 -> H(e, f(c))
27.56/8.98	   A^2 -> H(e, f(d))
27.56/8.98	   A^2 -> H(U1(e, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(e, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(e, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(e, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(e, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(e, e), f(e))
27.56/8.98	   A^2 -> H(U1(e, e), f(k))
27.56/8.98	   A^2 -> H(U1(e, e), U1(d, d))
27.56/8.98	   A^2 -> H(f(e), U1(e, b))
27.56/8.98	   A^2 -> H(f(e), U1(k, b))
27.56/8.98	   A^2 -> H(f(e), U1(c, d))
27.56/8.98	   A^2 -> H(f(e), U1(d, c))
27.56/8.98	   A^2 -> H(f(e), U1(b, e))
27.56/8.98	   A^2 -> H(f(e), U1(b, k))
27.56/8.98	   A^2 -> H(f(e), U1(e, c))
27.56/8.98	   A^2 -> H(f(e), U1(k, c))
27.56/8.98	   A^2 -> H(f(e), U1(c, e))
27.56/8.98	   A^2 -> H(f(e), U1(c, k))
27.56/8.98	   A^2 -> H(f(e), U1(k, k))
27.56/8.98	   A^2 -> H(f(e), U1(k, d))
27.56/8.98	   A^2 -> H(f(e), U1(d, k))
27.56/8.98	   A^2 -> H(U1(k, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(k, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(k, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(k, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(k, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(k, k), f(e))
27.56/8.98	   A^2 -> H(U1(k, k), f(k))
27.56/8.98	   A^2 -> H(U1(k, k), U1(d, d))
27.56/8.98	   A^2 -> H(f(k), U1(e, b))
27.56/8.98	   A^2 -> H(f(k), U1(k, b))
27.56/8.98	   A^2 -> H(f(k), U1(c, d))
27.56/8.98	   A^2 -> H(f(k), U1(d, c))
27.56/8.98	   A^2 -> H(f(k), U1(b, e))
27.56/8.98	   A^2 -> H(f(k), U1(b, k))
27.56/8.98	   A^2 -> H(f(k), U1(e, c))
27.56/8.98	   A^2 -> H(f(k), U1(k, c))
27.56/8.98	   A^2 -> H(f(k), U1(c, e))
27.56/8.98	   A^2 -> H(f(k), U1(c, k))
27.56/8.98	   A^2 -> H(f(k), U1(e, e))
27.56/8.98	   A^2 -> H(f(k), U1(k, d))
27.56/8.98	   A^2 -> H(f(k), U1(d, k))
27.56/8.98	   A^2 -> H(f(c), b)
27.56/8.98	   A^2 -> H(f(c), U1(e, d))
27.56/8.98	   A^2 -> H(f(c), U1(d, e))
27.56/8.98	   A^2 -> H(f(k), U1(k, k))
27.56/8.98	   A^2 -> H(U1(k, k), U1(b, b))
27.56/8.98	   A^2 -> H(U1(k, k), f(c))
27.56/8.98	   A^2 -> H(U1(k, k), f(d))
27.56/8.98	   A^2 -> H(U1(k, d), U1(c, b))
27.56/8.98	   A^2 -> H(U1(k, d), U1(d, b))
27.56/8.98	   A^2 -> H(U1(k, d), U1(b, c))
27.56/8.98	   A^2 -> H(U1(k, d), U1(b, d))
27.56/8.98	   A^2 -> H(U1(k, d), U1(c, c))
27.56/8.98	   A^2 -> H(U1(k, d), f(e))
27.56/8.98	   A^2 -> H(U1(k, d), f(k))
27.56/8.98	   A^2 -> H(U1(k, d), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(d, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(d, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(d, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(d, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(d, k), f(e))
27.56/8.98	   A^2 -> H(U1(d, k), f(k))
27.56/8.98	   A^2 -> H(U1(d, k), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, d), U1(e, b))
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, b))
27.56/8.98	   A^2 -> H(U1(d, d), U1(c, d))
27.56/8.98	   A^2 -> H(U1(d, d), U1(d, c))
27.56/8.98	   A^2 -> H(U1(d, d), U1(b, e))
27.56/8.98	   A^2 -> H(U1(d, d), U1(b, k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(e, c))
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, c))
27.56/8.98	   A^2 -> H(U1(d, d), U1(c, e))
27.56/8.98	   A^2 -> H(U1(d, d), U1(c, k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(e, e))
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, k))
27.56/8.98	   A^2 -> H(f(d), b)
27.56/8.98	   A^2 -> H(f(d), U1(e, d))
27.56/8.98	   A^2 -> H(f(d), U1(d, e))
27.56/8.98	   A^2 -> H(f(d), c)
27.56/8.98	   A^2 -> H(f(d), U1(e, k))
27.56/8.98	   A^2 -> H(f(d), U1(k, e))
27.56/8.98	   A^2 -> H(f(d), e)
27.56/8.98	   A^2 -> H(f(a), d)
27.56/8.98	   A^2 -> H(U1(c, c), U1(e, c))
27.56/8.98	   A^2 -> H(f(c), c)
27.56/8.98	   A^2 -> H(f(c), U1(e, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, c))
27.56/8.98	   A^2 -> H(f(c), U1(k, e))
27.56/8.98	   A^2 -> H(f(c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, e))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, k))
27.56/8.98	   A^2 -> H(f(a), k)
27.56/8.98	   A^2 -> H(f(e), U1(e, e))
27.56/8.98	   A^2 -> H(f(c), e)
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, d))
27.56/8.98	   A^2 -> H(f(d), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(d, k))
27.56/8.98	   A^2 -> H(d, U1(b, b))
27.56/8.98	   A^2 -> H(d, f(c))
27.56/8.98	   A^2 -> H(d, f(d))
27.56/8.98	   A^2 -> H(a, U1(c, b))
27.56/8.98	   A^2 -> H(a, U1(d, b))
27.56/8.98	   A^2 -> H(a, U1(b, c))
27.56/8.98	   A^2 -> H(a, U1(b, d))
27.56/8.98	   A^2 -> H(a, U1(c, c))
27.56/8.98	   A^2 -> H(a, f(e))
27.56/8.98	   A^2 -> H(a, f(k))
27.56/8.98	   A^2 -> H(a, U1(d, d))
27.56/8.98	   A^2 -> H(U1(e, d), U1(c, b))
27.56/8.98	   A^2 -> H(U1(e, d), U1(d, b))
27.56/8.98	   A^2 -> H(U1(e, d), U1(b, c))
27.56/8.98	   A^2 -> H(U1(e, d), U1(b, d))
27.56/8.98	   A^2 -> H(U1(e, d), U1(c, c))
27.56/8.98	   A^2 -> H(U1(e, d), f(e))
27.56/8.98	   A^2 -> H(U1(e, d), f(k))
27.56/8.98	   A^2 -> H(U1(e, d), U1(d, d))
27.56/8.98	   A^2 -> H(U1(e, a), U1(e, b))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, b))
27.56/8.98	   A^2 -> H(U1(e, a), U1(c, d))
27.56/8.98	   A^2 -> H(U1(e, a), U1(d, c))
27.56/8.98	   A^2 -> H(U1(e, a), U1(b, e))
27.56/8.98	   A^2 -> H(U1(e, a), U1(b, k))
27.56/8.98	   A^2 -> H(U1(e, a), U1(e, c))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, c))
27.56/8.98	   A^2 -> H(U1(e, a), U1(c, e))
27.56/8.98	   A^2 -> H(U1(e, a), U1(c, k))
27.56/8.98	   A^2 -> H(U1(e, a), U1(e, e))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, d))
27.56/8.98	   A^2 -> H(U1(e, a), U1(d, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(e, b))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, b))
27.56/8.98	   A^2 -> H(U1(k, a), U1(c, d))
27.56/8.98	   A^2 -> H(U1(k, a), U1(d, c))
27.56/8.98	   A^2 -> H(U1(k, a), U1(b, e))
27.56/8.98	   A^2 -> H(U1(k, a), U1(b, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(e, c))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, c))
27.56/8.98	   A^2 -> H(U1(k, a), U1(c, e))
27.56/8.98	   A^2 -> H(U1(k, a), U1(c, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(e, e))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, d))
27.56/8.98	   A^2 -> H(U1(k, a), U1(d, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(e, b))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, b))
27.56/8.98	   A^2 -> H(U1(c, d), U1(c, d))
27.56/8.98	   A^2 -> H(U1(c, d), U1(d, c))
27.56/8.98	   A^2 -> H(U1(c, d), U1(b, e))
27.56/8.98	   A^2 -> H(U1(c, d), U1(b, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(e, c))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, c))
27.56/8.98	   A^2 -> H(U1(c, d), U1(c, e))
27.56/8.98	   A^2 -> H(U1(c, d), U1(c, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(e, e))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, d))
27.56/8.98	   A^2 -> H(U1(c, d), U1(d, k))
27.56/8.98	   A^2 -> H(U1(c, a), b)
27.56/8.98	   A^2 -> H(U1(c, a), U1(e, d))
27.56/8.98	   A^2 -> H(U1(c, a), U1(d, e))
27.56/8.98	   A^2 -> H(U1(c, a), c)
27.56/8.98	   A^2 -> H(U1(c, a), U1(e, k))
27.56/8.98	   A^2 -> H(U1(c, a), U1(k, e))
27.56/8.98	   A^2 -> H(U1(c, a), e)
27.56/8.98	   A^2 -> H(U1(c, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(d, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(d, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(d, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(d, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(d, e), f(e))
27.56/8.98	   A^2 -> H(U1(d, e), f(k))
27.56/8.98	   A^2 -> H(U1(d, e), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, c), U1(e, b))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, b))
27.56/8.98	   A^2 -> H(U1(d, c), U1(c, d))
27.56/8.98	   A^2 -> H(U1(d, c), U1(d, c))
27.56/8.98	   A^2 -> H(U1(d, c), U1(b, e))
27.56/8.98	   A^2 -> H(U1(d, c), U1(b, k))
27.56/8.98	   A^2 -> H(U1(d, c), U1(e, c))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, c))
27.56/8.98	   A^2 -> H(U1(d, c), U1(c, e))
27.56/8.98	   A^2 -> H(U1(d, c), U1(c, k))
27.56/8.98	   A^2 -> H(U1(d, c), U1(e, e))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, d))
27.56/8.98	   A^2 -> H(U1(d, c), U1(d, k))
27.56/8.98	   A^2 -> H(U1(d, a), b)
27.56/8.98	   A^2 -> H(U1(d, a), U1(e, d))
27.56/8.98	   A^2 -> H(U1(d, a), U1(d, e))
27.56/8.98	
27.56/8.98	The TRS R consists of the following rules:
27.56/8.98	
27.56/8.98	   f(x) -> U1(x, x)
27.56/8.98	   U1(e, x) -> x
27.56/8.98	   a -> c
27.56/8.98	   a -> d
27.56/8.98	   b -> c
27.56/8.98	   b -> d
27.56/8.98	   d -> k
27.56/8.98	   c -> e
27.56/8.98	   c -> k
27.56/8.98	
27.56/8.98	Q is empty.
27.56/8.98	We have to consider all minimal (P,Q,R)-chains.
27.56/8.98	----------------------------------------
27.56/8.98	
27.56/8.98	(663) TransformationProof (EQUIVALENT)
27.56/8.98	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
27.56/8.98	
27.56/8.98	   (A^2 -> H(U1(k, a), U1(b, k)),A^2 -> H(U1(k, a), U1(b, k)))
27.56/8.98	   (A^2 -> H(U1(d, c), U1(b, k)),A^2 -> H(U1(d, c), U1(b, k)))
27.56/8.98	   (A^2 -> H(U1(d, d), U1(b, k)),A^2 -> H(U1(d, d), U1(b, k)))
27.56/8.98	   (A^2 -> H(U1(d, a), U1(c, k)),A^2 -> H(U1(d, a), U1(c, k)))
27.56/8.98	   (A^2 -> H(U1(d, a), U1(d, k)),A^2 -> H(U1(d, a), U1(d, k)))
27.56/8.98	
27.56/8.98	
27.56/8.98	----------------------------------------
27.56/8.98	
27.56/8.98	(664)
27.56/8.98	Obligation:
27.56/8.98	Q DP problem:
27.56/8.98	The TRS P consists of the following rules:
27.56/8.98	
27.56/8.98	   H(x, x) -> G(x, x, f(k))
27.56/8.98	   G(d, x, x) -> A^2
27.56/8.98	   A^2 -> H(f(c), f(c))
27.56/8.98	   A^2 -> H(f(d), f(d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, c))
27.56/8.98	   A^2 -> H(f(e), f(e))
27.56/8.98	   A^2 -> H(f(k), f(k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, a), U1(e, c))
27.56/8.98	   A^2 -> H(U1(d, a), U1(k, c))
27.56/8.98	   A^2 -> H(U1(d, a), U1(c, e))
27.56/8.98	   A^2 -> H(U1(d, a), U1(c, k))
27.56/8.98	   A^2 -> H(U1(d, a), U1(e, e))
27.56/8.98	   A^2 -> H(U1(d, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, a), U1(k, d))
27.56/8.98	   A^2 -> H(U1(d, a), U1(d, k))
27.56/8.98	   A^2 -> H(U1(a, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(a, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(a, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(a, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(a, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(a, e), f(e))
27.56/8.98	   A^2 -> H(U1(a, e), f(k))
27.56/8.98	   A^2 -> H(U1(a, e), U1(d, d))
27.56/8.98	   A^2 -> H(U1(a, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(a, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(a, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(a, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(a, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(a, k), f(e))
27.56/8.98	   A^2 -> H(U1(a, k), f(k))
27.56/8.98	   A^2 -> H(U1(a, k), U1(d, d))
27.56/8.98	   A^2 -> H(U1(a, c), U1(e, b))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, b))
27.56/8.98	   A^2 -> H(U1(a, c), U1(c, d))
27.56/8.98	   A^2 -> H(U1(a, c), U1(d, c))
27.56/8.98	   A^2 -> H(U1(a, c), U1(b, e))
27.56/8.98	   A^2 -> H(U1(a, c), U1(b, k))
27.56/8.98	   A^2 -> H(U1(a, c), U1(e, c))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, c))
27.56/8.98	   A^2 -> H(U1(a, c), U1(c, e))
27.56/8.98	   A^2 -> H(U1(a, c), U1(c, k))
27.56/8.98	   A^2 -> H(U1(a, c), U1(e, e))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, d))
27.56/8.98	   A^2 -> H(U1(a, c), U1(d, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(e, b))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, b))
27.56/8.98	   A^2 -> H(U1(a, d), U1(c, d))
27.56/8.98	   A^2 -> H(U1(a, d), U1(d, c))
27.56/8.98	   A^2 -> H(U1(a, d), U1(b, e))
27.56/8.98	   A^2 -> H(U1(a, d), U1(b, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(e, c))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, c))
27.56/8.98	   A^2 -> H(U1(a, d), U1(c, e))
27.56/8.98	   A^2 -> H(U1(a, d), U1(c, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(e, e))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, k))
27.56/8.98	   A^2 -> H(U1(a, d), U1(k, d))
27.56/8.98	   A^2 -> H(U1(a, d), U1(d, k))
27.56/8.98	   A^2 -> H(U1(a, a), b)
27.56/8.98	   A^2 -> H(U1(a, a), U1(e, d))
27.56/8.98	   A^2 -> H(U1(a, a), U1(d, e))
27.56/8.98	   A^2 -> H(U1(a, a), c)
27.56/8.98	   A^2 -> H(U1(a, a), U1(e, k))
27.56/8.98	   A^2 -> H(U1(a, a), U1(k, e))
27.56/8.98	   A^2 -> H(U1(a, a), e)
27.56/8.98	   A^2 -> H(U1(a, a), U1(k, k))
27.56/8.98	   A^2 -> H(k, f(b))
27.56/8.98	   A^2 -> H(c, U1(b, b))
27.56/8.98	   A^2 -> H(c, f(c))
27.56/8.98	   A^2 -> H(c, f(d))
27.56/8.98	   A^2 -> H(U1(e, k), U1(b, b))
27.56/8.98	   A^2 -> H(U1(e, k), f(c))
27.56/8.98	   A^2 -> H(U1(e, k), f(d))
27.56/8.98	   A^2 -> H(U1(e, c), U1(c, b))
27.56/8.98	   A^2 -> H(U1(e, c), U1(d, b))
27.56/8.98	   A^2 -> H(U1(e, c), U1(b, c))
27.56/8.98	   A^2 -> H(U1(e, c), U1(b, d))
27.56/8.98	   A^2 -> H(U1(e, c), U1(c, c))
27.56/8.98	   A^2 -> H(U1(e, c), f(e))
27.56/8.98	   A^2 -> H(U1(e, c), f(k))
27.56/8.98	   A^2 -> H(U1(e, c), U1(d, d))
27.56/8.98	   A^2 -> H(U1(k, e), U1(b, b))
27.56/8.98	   A^2 -> H(U1(k, e), f(c))
27.56/8.98	   A^2 -> H(U1(k, e), f(d))
27.56/8.98	   A^2 -> H(U1(k, c), U1(c, b))
27.56/8.98	   A^2 -> H(U1(k, c), U1(d, b))
27.56/8.98	   A^2 -> H(U1(k, c), U1(b, c))
27.56/8.98	   A^2 -> H(U1(k, c), U1(b, d))
27.56/8.98	   A^2 -> H(U1(k, c), U1(c, c))
27.56/8.98	   A^2 -> H(U1(k, c), f(e))
27.56/8.98	   A^2 -> H(U1(k, c), f(k))
27.56/8.98	   A^2 -> H(U1(k, c), U1(d, d))
27.56/8.98	   A^2 -> H(U1(c, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(c, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(c, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(c, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(c, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(c, e), f(e))
27.56/8.98	   A^2 -> H(U1(c, e), f(k))
27.56/8.98	   A^2 -> H(U1(c, e), U1(d, d))
27.56/8.98	   A^2 -> H(U1(c, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(c, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(c, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(c, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(c, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(c, k), f(e))
27.56/8.98	   A^2 -> H(U1(c, k), f(k))
27.56/8.98	   A^2 -> H(U1(c, k), U1(d, d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(e, b))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, b))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(d, c))
27.56/8.98	   A^2 -> H(U1(c, c), U1(b, e))
27.56/8.98	   A^2 -> H(U1(c, c), U1(b, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(e, e))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(d, k))
27.56/8.98	   A^2 -> H(e, U1(b, b))
27.56/8.98	   A^2 -> H(e, f(c))
27.56/8.98	   A^2 -> H(e, f(d))
27.56/8.98	   A^2 -> H(U1(e, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(e, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(e, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(e, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(e, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(e, e), f(e))
27.56/8.98	   A^2 -> H(U1(e, e), f(k))
27.56/8.98	   A^2 -> H(U1(e, e), U1(d, d))
27.56/8.98	   A^2 -> H(f(e), U1(e, b))
27.56/8.98	   A^2 -> H(f(e), U1(k, b))
27.56/8.98	   A^2 -> H(f(e), U1(c, d))
27.56/8.98	   A^2 -> H(f(e), U1(d, c))
27.56/8.98	   A^2 -> H(f(e), U1(b, e))
27.56/8.98	   A^2 -> H(f(e), U1(b, k))
27.56/8.98	   A^2 -> H(f(e), U1(e, c))
27.56/8.98	   A^2 -> H(f(e), U1(k, c))
27.56/8.98	   A^2 -> H(f(e), U1(c, e))
27.56/8.98	   A^2 -> H(f(e), U1(c, k))
27.56/8.98	   A^2 -> H(f(e), U1(k, k))
27.56/8.98	   A^2 -> H(f(e), U1(k, d))
27.56/8.98	   A^2 -> H(f(e), U1(d, k))
27.56/8.98	   A^2 -> H(U1(k, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(k, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(k, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(k, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(k, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(k, k), f(e))
27.56/8.98	   A^2 -> H(U1(k, k), f(k))
27.56/8.98	   A^2 -> H(U1(k, k), U1(d, d))
27.56/8.98	   A^2 -> H(f(k), U1(e, b))
27.56/8.98	   A^2 -> H(f(k), U1(k, b))
27.56/8.98	   A^2 -> H(f(k), U1(c, d))
27.56/8.98	   A^2 -> H(f(k), U1(d, c))
27.56/8.98	   A^2 -> H(f(k), U1(b, e))
27.56/8.98	   A^2 -> H(f(k), U1(b, k))
27.56/8.98	   A^2 -> H(f(k), U1(e, c))
27.56/8.98	   A^2 -> H(f(k), U1(k, c))
27.56/8.98	   A^2 -> H(f(k), U1(c, e))
27.56/8.98	   A^2 -> H(f(k), U1(c, k))
27.56/8.98	   A^2 -> H(f(k), U1(e, e))
27.56/8.98	   A^2 -> H(f(k), U1(k, d))
27.56/8.98	   A^2 -> H(f(k), U1(d, k))
27.56/8.98	   A^2 -> H(f(c), b)
27.56/8.98	   A^2 -> H(f(c), U1(e, d))
27.56/8.98	   A^2 -> H(f(c), U1(d, e))
27.56/8.98	   A^2 -> H(f(k), U1(k, k))
27.56/8.98	   A^2 -> H(U1(k, k), U1(b, b))
27.56/8.98	   A^2 -> H(U1(k, k), f(c))
27.56/8.98	   A^2 -> H(U1(k, k), f(d))
27.56/8.98	   A^2 -> H(U1(k, d), U1(c, b))
27.56/8.98	   A^2 -> H(U1(k, d), U1(d, b))
27.56/8.98	   A^2 -> H(U1(k, d), U1(b, c))
27.56/8.98	   A^2 -> H(U1(k, d), U1(b, d))
27.56/8.98	   A^2 -> H(U1(k, d), U1(c, c))
27.56/8.98	   A^2 -> H(U1(k, d), f(e))
27.56/8.98	   A^2 -> H(U1(k, d), f(k))
27.56/8.98	   A^2 -> H(U1(k, d), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(d, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(d, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(d, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(d, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(d, k), f(e))
27.56/8.98	   A^2 -> H(U1(d, k), f(k))
27.56/8.98	   A^2 -> H(U1(d, k), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, d), U1(e, b))
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, b))
27.56/8.98	   A^2 -> H(U1(d, d), U1(c, d))
27.56/8.98	   A^2 -> H(U1(d, d), U1(d, c))
27.56/8.98	   A^2 -> H(U1(d, d), U1(b, e))
27.56/8.98	   A^2 -> H(U1(d, d), U1(b, k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(e, c))
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, c))
27.56/8.98	   A^2 -> H(U1(d, d), U1(c, e))
27.56/8.98	   A^2 -> H(U1(d, d), U1(c, k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(e, e))
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, k))
27.56/8.98	   A^2 -> H(f(d), b)
27.56/8.98	   A^2 -> H(f(d), U1(e, d))
27.56/8.98	   A^2 -> H(f(d), U1(d, e))
27.56/8.98	   A^2 -> H(f(d), c)
27.56/8.98	   A^2 -> H(f(d), U1(e, k))
27.56/8.98	   A^2 -> H(f(d), U1(k, e))
27.56/8.98	   A^2 -> H(f(d), e)
27.56/8.98	   A^2 -> H(f(a), d)
27.56/8.98	   A^2 -> H(U1(c, c), U1(e, c))
27.56/8.98	   A^2 -> H(f(c), c)
27.56/8.98	   A^2 -> H(f(c), U1(e, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(k, c))
27.56/8.98	   A^2 -> H(f(c), U1(k, e))
27.56/8.98	   A^2 -> H(f(c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, e))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, k))
27.56/8.98	   A^2 -> H(f(a), k)
27.56/8.98	   A^2 -> H(f(e), U1(e, e))
27.56/8.98	   A^2 -> H(f(c), e)
27.56/8.98	   A^2 -> H(U1(d, d), U1(k, d))
27.56/8.98	   A^2 -> H(f(d), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(d, k))
27.56/8.98	   A^2 -> H(d, U1(b, b))
27.56/8.98	   A^2 -> H(d, f(c))
27.56/8.98	   A^2 -> H(d, f(d))
27.56/8.98	   A^2 -> H(a, U1(c, b))
27.56/8.98	   A^2 -> H(a, U1(d, b))
27.56/8.98	   A^2 -> H(a, U1(b, c))
27.56/8.98	   A^2 -> H(a, U1(b, d))
27.56/8.98	   A^2 -> H(a, U1(c, c))
27.56/8.98	   A^2 -> H(a, f(e))
27.56/8.98	   A^2 -> H(a, f(k))
27.56/8.98	   A^2 -> H(a, U1(d, d))
27.56/8.98	   A^2 -> H(U1(e, d), U1(c, b))
27.56/8.98	   A^2 -> H(U1(e, d), U1(d, b))
27.56/8.98	   A^2 -> H(U1(e, d), U1(b, c))
27.56/8.98	   A^2 -> H(U1(e, d), U1(b, d))
27.56/8.98	   A^2 -> H(U1(e, d), U1(c, c))
27.56/8.98	   A^2 -> H(U1(e, d), f(e))
27.56/8.98	   A^2 -> H(U1(e, d), f(k))
27.56/8.98	   A^2 -> H(U1(e, d), U1(d, d))
27.56/8.98	   A^2 -> H(U1(e, a), U1(e, b))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, b))
27.56/8.98	   A^2 -> H(U1(e, a), U1(c, d))
27.56/8.98	   A^2 -> H(U1(e, a), U1(d, c))
27.56/8.98	   A^2 -> H(U1(e, a), U1(b, e))
27.56/8.98	   A^2 -> H(U1(e, a), U1(b, k))
27.56/8.98	   A^2 -> H(U1(e, a), U1(e, c))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, c))
27.56/8.98	   A^2 -> H(U1(e, a), U1(c, e))
27.56/8.98	   A^2 -> H(U1(e, a), U1(c, k))
27.56/8.98	   A^2 -> H(U1(e, a), U1(e, e))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(e, a), U1(k, d))
27.56/8.98	   A^2 -> H(U1(e, a), U1(d, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(e, b))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, b))
27.56/8.98	   A^2 -> H(U1(k, a), U1(c, d))
27.56/8.98	   A^2 -> H(U1(k, a), U1(d, c))
27.56/8.98	   A^2 -> H(U1(k, a), U1(b, e))
27.56/8.98	   A^2 -> H(U1(k, a), U1(b, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(e, c))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, c))
27.56/8.98	   A^2 -> H(U1(k, a), U1(c, e))
27.56/8.98	   A^2 -> H(U1(k, a), U1(c, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(e, e))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(k, a), U1(k, d))
27.56/8.98	   A^2 -> H(U1(k, a), U1(d, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(e, b))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, b))
27.56/8.98	   A^2 -> H(U1(c, d), U1(c, d))
27.56/8.98	   A^2 -> H(U1(c, d), U1(d, c))
27.56/8.98	   A^2 -> H(U1(c, d), U1(b, e))
27.56/8.98	   A^2 -> H(U1(c, d), U1(b, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(e, c))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, c))
27.56/8.98	   A^2 -> H(U1(c, d), U1(c, e))
27.56/8.98	   A^2 -> H(U1(c, d), U1(c, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(e, e))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, k))
27.56/8.98	   A^2 -> H(U1(c, d), U1(k, d))
27.56/8.98	   A^2 -> H(U1(c, d), U1(d, k))
27.56/8.98	   A^2 -> H(U1(c, a), b)
27.56/8.98	   A^2 -> H(U1(c, a), U1(e, d))
27.56/8.98	   A^2 -> H(U1(c, a), U1(d, e))
27.56/8.98	   A^2 -> H(U1(c, a), c)
27.56/8.98	   A^2 -> H(U1(c, a), U1(e, k))
27.56/8.98	   A^2 -> H(U1(c, a), U1(k, e))
27.56/8.98	   A^2 -> H(U1(c, a), e)
27.56/8.98	   A^2 -> H(U1(c, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(d, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(d, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(d, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(d, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(d, e), f(e))
27.56/8.98	   A^2 -> H(U1(d, e), f(k))
27.56/8.98	   A^2 -> H(U1(d, e), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, c), U1(e, b))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, b))
27.56/8.98	   A^2 -> H(U1(d, c), U1(c, d))
27.56/8.98	   A^2 -> H(U1(d, c), U1(d, c))
27.56/8.98	   A^2 -> H(U1(d, c), U1(b, e))
27.56/8.98	   A^2 -> H(U1(d, c), U1(b, k))
27.56/8.98	   A^2 -> H(U1(d, c), U1(e, c))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, c))
27.56/8.98	   A^2 -> H(U1(d, c), U1(c, e))
27.56/8.98	   A^2 -> H(U1(d, c), U1(c, k))
27.56/8.98	   A^2 -> H(U1(d, c), U1(e, e))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, c), U1(k, d))
27.56/8.98	   A^2 -> H(U1(d, c), U1(d, k))
27.56/8.98	   A^2 -> H(U1(d, a), b)
27.56/8.98	   A^2 -> H(U1(d, a), U1(e, d))
27.56/8.98	   A^2 -> H(U1(d, a), U1(d, e))
27.56/8.98	
27.56/8.98	The TRS R consists of the following rules:
27.56/8.98	
27.56/8.98	   f(x) -> U1(x, x)
27.56/8.98	   U1(e, x) -> x
27.56/8.98	   a -> c
27.56/8.98	   a -> d
27.56/8.98	   b -> c
27.56/8.98	   b -> d
27.56/8.98	   d -> k
27.56/8.98	   c -> e
27.56/8.98	   c -> k
27.56/8.98	
27.56/8.98	Q is empty.
27.56/8.98	We have to consider all minimal (P,Q,R)-chains.
27.56/8.98	----------------------------------------
27.56/8.98	
27.56/8.98	(665) TransformationProof (EQUIVALENT)
27.56/8.98	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
27.56/8.98	
27.56/8.98	   (A^2 -> H(U1(k, a), U1(e, c)),A^2 -> H(U1(k, a), U1(e, c)))
27.56/8.98	   (A^2 -> H(U1(d, c), U1(e, c)),A^2 -> H(U1(d, c), U1(e, c)))
27.56/8.98	   (A^2 -> H(U1(d, d), U1(e, c)),A^2 -> H(U1(d, d), U1(e, c)))
27.56/8.98	   (A^2 -> H(U1(d, a), c),A^2 -> H(U1(d, a), c))
27.56/8.98	   (A^2 -> H(U1(d, a), U1(e, e)),A^2 -> H(U1(d, a), U1(e, e)))
27.56/8.98	   (A^2 -> H(U1(d, a), U1(e, k)),A^2 -> H(U1(d, a), U1(e, k)))
27.56/8.98	
27.56/8.98	
27.56/8.98	----------------------------------------
27.56/8.98	
27.56/8.98	(666)
27.56/8.98	Obligation:
27.56/8.98	Q DP problem:
27.56/8.98	The TRS P consists of the following rules:
27.56/8.98	
27.56/8.98	   H(x, x) -> G(x, x, f(k))
27.56/8.98	   G(d, x, x) -> A^2
27.56/8.98	   A^2 -> H(f(c), f(c))
27.56/8.98	   A^2 -> H(f(d), f(d))
27.56/8.98	   A^2 -> H(U1(c, c), U1(c, c))
27.56/8.98	   A^2 -> H(f(e), f(e))
27.56/8.98	   A^2 -> H(f(k), f(k))
27.56/8.98	   A^2 -> H(U1(d, d), U1(d, d))
27.56/8.98	   A^2 -> H(U1(d, a), U1(k, c))
27.56/8.98	   A^2 -> H(U1(d, a), U1(c, e))
27.56/8.98	   A^2 -> H(U1(d, a), U1(c, k))
27.56/8.98	   A^2 -> H(U1(d, a), U1(e, e))
27.56/8.98	   A^2 -> H(U1(d, a), U1(k, k))
27.56/8.98	   A^2 -> H(U1(d, a), U1(k, d))
27.56/8.98	   A^2 -> H(U1(d, a), U1(d, k))
27.56/8.98	   A^2 -> H(U1(a, e), U1(c, b))
27.56/8.98	   A^2 -> H(U1(a, e), U1(d, b))
27.56/8.98	   A^2 -> H(U1(a, e), U1(b, c))
27.56/8.98	   A^2 -> H(U1(a, e), U1(b, d))
27.56/8.98	   A^2 -> H(U1(a, e), U1(c, c))
27.56/8.98	   A^2 -> H(U1(a, e), f(e))
27.56/8.98	   A^2 -> H(U1(a, e), f(k))
27.56/8.98	   A^2 -> H(U1(a, e), U1(d, d))
27.56/8.98	   A^2 -> H(U1(a, k), U1(c, b))
27.56/8.98	   A^2 -> H(U1(a, k), U1(d, b))
27.56/8.98	   A^2 -> H(U1(a, k), U1(b, c))
27.56/8.98	   A^2 -> H(U1(a, k), U1(b, d))
27.56/8.98	   A^2 -> H(U1(a, k), U1(c, c))
27.56/8.98	   A^2 -> H(U1(a, k), f(e))
27.56/8.98	   A^2 -> H(U1(a, k), f(k))
27.56/8.98	   A^2 -> H(U1(a, k), U1(d, d))
27.56/8.98	   A^2 -> H(U1(a, c), U1(e, b))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, b))
27.56/8.98	   A^2 -> H(U1(a, c), U1(c, d))
27.56/8.98	   A^2 -> H(U1(a, c), U1(d, c))
27.56/8.98	   A^2 -> H(U1(a, c), U1(b, e))
27.56/8.98	   A^2 -> H(U1(a, c), U1(b, k))
27.56/8.98	   A^2 -> H(U1(a, c), U1(e, c))
27.56/8.98	   A^2 -> H(U1(a, c), U1(k, c))
27.56/8.98	   A^2 -> H(U1(a, c), U1(c, e))
27.56/9.00	   A^2 -> H(U1(a, c), U1(c, k))
27.56/9.00	   A^2 -> H(U1(a, c), U1(e, e))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, d))
27.56/9.00	   A^2 -> H(U1(a, c), U1(d, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(e, b))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, b))
27.56/9.00	   A^2 -> H(U1(a, d), U1(c, d))
27.56/9.00	   A^2 -> H(U1(a, d), U1(d, c))
27.56/9.00	   A^2 -> H(U1(a, d), U1(b, e))
27.56/9.00	   A^2 -> H(U1(a, d), U1(b, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(e, c))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, c))
27.56/9.00	   A^2 -> H(U1(a, d), U1(c, e))
27.56/9.00	   A^2 -> H(U1(a, d), U1(c, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(e, e))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, d))
27.56/9.00	   A^2 -> H(U1(a, d), U1(d, k))
27.56/9.00	   A^2 -> H(U1(a, a), b)
27.56/9.00	   A^2 -> H(U1(a, a), U1(e, d))
27.56/9.00	   A^2 -> H(U1(a, a), U1(d, e))
27.56/9.00	   A^2 -> H(U1(a, a), c)
27.56/9.00	   A^2 -> H(U1(a, a), U1(e, k))
27.56/9.00	   A^2 -> H(U1(a, a), U1(k, e))
27.56/9.00	   A^2 -> H(U1(a, a), e)
27.56/9.00	   A^2 -> H(U1(a, a), U1(k, k))
27.56/9.00	   A^2 -> H(k, f(b))
27.56/9.00	   A^2 -> H(c, U1(b, b))
27.56/9.00	   A^2 -> H(c, f(c))
27.56/9.00	   A^2 -> H(c, f(d))
27.56/9.00	   A^2 -> H(U1(e, k), U1(b, b))
27.56/9.00	   A^2 -> H(U1(e, k), f(c))
27.56/9.00	   A^2 -> H(U1(e, k), f(d))
27.56/9.00	   A^2 -> H(U1(e, c), U1(c, b))
27.56/9.00	   A^2 -> H(U1(e, c), U1(d, b))
27.56/9.00	   A^2 -> H(U1(e, c), U1(b, c))
27.56/9.00	   A^2 -> H(U1(e, c), U1(b, d))
27.56/9.00	   A^2 -> H(U1(e, c), U1(c, c))
27.56/9.00	   A^2 -> H(U1(e, c), f(e))
27.56/9.00	   A^2 -> H(U1(e, c), f(k))
27.56/9.00	   A^2 -> H(U1(e, c), U1(d, d))
27.56/9.00	   A^2 -> H(U1(k, e), U1(b, b))
27.56/9.00	   A^2 -> H(U1(k, e), f(c))
27.56/9.00	   A^2 -> H(U1(k, e), f(d))
27.56/9.00	   A^2 -> H(U1(k, c), U1(c, b))
27.56/9.00	   A^2 -> H(U1(k, c), U1(d, b))
27.56/9.00	   A^2 -> H(U1(k, c), U1(b, c))
27.56/9.00	   A^2 -> H(U1(k, c), U1(b, d))
27.56/9.00	   A^2 -> H(U1(k, c), U1(c, c))
27.56/9.00	   A^2 -> H(U1(k, c), f(e))
27.56/9.00	   A^2 -> H(U1(k, c), f(k))
27.56/9.00	   A^2 -> H(U1(k, c), U1(d, d))
27.56/9.00	   A^2 -> H(U1(c, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(c, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(c, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(c, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(c, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(c, e), f(e))
27.56/9.00	   A^2 -> H(U1(c, e), f(k))
27.56/9.00	   A^2 -> H(U1(c, e), U1(d, d))
27.56/9.00	   A^2 -> H(U1(c, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(c, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(c, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(c, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(c, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(c, k), f(e))
27.56/9.00	   A^2 -> H(U1(c, k), f(k))
27.56/9.00	   A^2 -> H(U1(c, k), U1(d, d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(e, b))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, b))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(d, c))
27.56/9.00	   A^2 -> H(U1(c, c), U1(b, e))
27.56/9.00	   A^2 -> H(U1(c, c), U1(b, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(e, e))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(d, k))
27.56/9.00	   A^2 -> H(e, U1(b, b))
27.56/9.00	   A^2 -> H(e, f(c))
27.56/9.00	   A^2 -> H(e, f(d))
27.56/9.00	   A^2 -> H(U1(e, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(e, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(e, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(e, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(e, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(e, e), f(e))
27.56/9.00	   A^2 -> H(U1(e, e), f(k))
27.56/9.00	   A^2 -> H(U1(e, e), U1(d, d))
27.56/9.00	   A^2 -> H(f(e), U1(e, b))
27.56/9.00	   A^2 -> H(f(e), U1(k, b))
27.56/9.00	   A^2 -> H(f(e), U1(c, d))
27.56/9.00	   A^2 -> H(f(e), U1(d, c))
27.56/9.00	   A^2 -> H(f(e), U1(b, e))
27.56/9.00	   A^2 -> H(f(e), U1(b, k))
27.56/9.00	   A^2 -> H(f(e), U1(e, c))
27.56/9.00	   A^2 -> H(f(e), U1(k, c))
27.56/9.00	   A^2 -> H(f(e), U1(c, e))
27.56/9.00	   A^2 -> H(f(e), U1(c, k))
27.56/9.00	   A^2 -> H(f(e), U1(k, k))
27.56/9.00	   A^2 -> H(f(e), U1(k, d))
27.56/9.00	   A^2 -> H(f(e), U1(d, k))
27.56/9.00	   A^2 -> H(U1(k, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(k, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(k, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(k, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(k, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(k, k), f(e))
27.56/9.00	   A^2 -> H(U1(k, k), f(k))
27.56/9.00	   A^2 -> H(U1(k, k), U1(d, d))
27.56/9.00	   A^2 -> H(f(k), U1(e, b))
27.56/9.00	   A^2 -> H(f(k), U1(k, b))
27.56/9.00	   A^2 -> H(f(k), U1(c, d))
27.56/9.00	   A^2 -> H(f(k), U1(d, c))
27.56/9.00	   A^2 -> H(f(k), U1(b, e))
27.56/9.00	   A^2 -> H(f(k), U1(b, k))
27.56/9.00	   A^2 -> H(f(k), U1(e, c))
27.56/9.00	   A^2 -> H(f(k), U1(k, c))
27.56/9.00	   A^2 -> H(f(k), U1(c, e))
27.56/9.00	   A^2 -> H(f(k), U1(c, k))
27.56/9.00	   A^2 -> H(f(k), U1(e, e))
27.56/9.00	   A^2 -> H(f(k), U1(k, d))
27.56/9.00	   A^2 -> H(f(k), U1(d, k))
27.56/9.00	   A^2 -> H(f(c), b)
27.56/9.00	   A^2 -> H(f(c), U1(e, d))
27.56/9.00	   A^2 -> H(f(c), U1(d, e))
27.56/9.00	   A^2 -> H(f(k), U1(k, k))
27.56/9.00	   A^2 -> H(U1(k, k), U1(b, b))
27.56/9.00	   A^2 -> H(U1(k, k), f(c))
27.56/9.00	   A^2 -> H(U1(k, k), f(d))
27.56/9.00	   A^2 -> H(U1(k, d), U1(c, b))
27.56/9.00	   A^2 -> H(U1(k, d), U1(d, b))
27.56/9.00	   A^2 -> H(U1(k, d), U1(b, c))
27.56/9.00	   A^2 -> H(U1(k, d), U1(b, d))
27.56/9.00	   A^2 -> H(U1(k, d), U1(c, c))
27.56/9.00	   A^2 -> H(U1(k, d), f(e))
27.56/9.00	   A^2 -> H(U1(k, d), f(k))
27.56/9.00	   A^2 -> H(U1(k, d), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(d, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(d, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(d, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(d, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(d, k), f(e))
27.56/9.00	   A^2 -> H(U1(d, k), f(k))
27.56/9.00	   A^2 -> H(U1(d, k), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, d), U1(e, b))
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, b))
27.56/9.00	   A^2 -> H(U1(d, d), U1(c, d))
27.56/9.00	   A^2 -> H(U1(d, d), U1(d, c))
27.56/9.00	   A^2 -> H(U1(d, d), U1(b, e))
27.56/9.00	   A^2 -> H(U1(d, d), U1(b, k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(e, c))
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, c))
27.56/9.00	   A^2 -> H(U1(d, d), U1(c, e))
27.56/9.00	   A^2 -> H(U1(d, d), U1(c, k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(e, e))
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, k))
27.56/9.00	   A^2 -> H(f(d), b)
27.56/9.00	   A^2 -> H(f(d), U1(e, d))
27.56/9.00	   A^2 -> H(f(d), U1(d, e))
27.56/9.00	   A^2 -> H(f(d), c)
27.56/9.00	   A^2 -> H(f(d), U1(e, k))
27.56/9.00	   A^2 -> H(f(d), U1(k, e))
27.56/9.00	   A^2 -> H(f(d), e)
27.56/9.00	   A^2 -> H(f(a), d)
27.56/9.00	   A^2 -> H(U1(c, c), U1(e, c))
27.56/9.00	   A^2 -> H(f(c), c)
27.56/9.00	   A^2 -> H(f(c), U1(e, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, c))
27.56/9.00	   A^2 -> H(f(c), U1(k, e))
27.56/9.00	   A^2 -> H(f(c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, e))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, k))
27.56/9.00	   A^2 -> H(f(a), k)
27.56/9.00	   A^2 -> H(f(e), U1(e, e))
27.56/9.00	   A^2 -> H(f(c), e)
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, d))
27.56/9.00	   A^2 -> H(f(d), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(d, k))
27.56/9.00	   A^2 -> H(d, U1(b, b))
27.56/9.00	   A^2 -> H(d, f(c))
27.56/9.00	   A^2 -> H(d, f(d))
27.56/9.00	   A^2 -> H(a, U1(c, b))
27.56/9.00	   A^2 -> H(a, U1(d, b))
27.56/9.00	   A^2 -> H(a, U1(b, c))
27.56/9.00	   A^2 -> H(a, U1(b, d))
27.56/9.00	   A^2 -> H(a, U1(c, c))
27.56/9.00	   A^2 -> H(a, f(e))
27.56/9.00	   A^2 -> H(a, f(k))
27.56/9.00	   A^2 -> H(a, U1(d, d))
27.56/9.00	   A^2 -> H(U1(e, d), U1(c, b))
27.56/9.00	   A^2 -> H(U1(e, d), U1(d, b))
27.56/9.00	   A^2 -> H(U1(e, d), U1(b, c))
27.56/9.00	   A^2 -> H(U1(e, d), U1(b, d))
27.56/9.00	   A^2 -> H(U1(e, d), U1(c, c))
27.56/9.00	   A^2 -> H(U1(e, d), f(e))
27.56/9.00	   A^2 -> H(U1(e, d), f(k))
27.56/9.00	   A^2 -> H(U1(e, d), U1(d, d))
27.56/9.00	   A^2 -> H(U1(e, a), U1(e, b))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, b))
27.56/9.00	   A^2 -> H(U1(e, a), U1(c, d))
27.56/9.00	   A^2 -> H(U1(e, a), U1(d, c))
27.56/9.00	   A^2 -> H(U1(e, a), U1(b, e))
27.56/9.00	   A^2 -> H(U1(e, a), U1(b, k))
27.56/9.00	   A^2 -> H(U1(e, a), U1(e, c))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, c))
27.56/9.00	   A^2 -> H(U1(e, a), U1(c, e))
27.56/9.00	   A^2 -> H(U1(e, a), U1(c, k))
27.56/9.00	   A^2 -> H(U1(e, a), U1(e, e))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, d))
27.56/9.00	   A^2 -> H(U1(e, a), U1(d, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(e, b))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, b))
27.56/9.00	   A^2 -> H(U1(k, a), U1(c, d))
27.56/9.00	   A^2 -> H(U1(k, a), U1(d, c))
27.56/9.00	   A^2 -> H(U1(k, a), U1(b, e))
27.56/9.00	   A^2 -> H(U1(k, a), U1(b, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(e, c))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, c))
27.56/9.00	   A^2 -> H(U1(k, a), U1(c, e))
27.56/9.00	   A^2 -> H(U1(k, a), U1(c, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(e, e))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, d))
27.56/9.00	   A^2 -> H(U1(k, a), U1(d, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(e, b))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, b))
27.56/9.00	   A^2 -> H(U1(c, d), U1(c, d))
27.56/9.00	   A^2 -> H(U1(c, d), U1(d, c))
27.56/9.00	   A^2 -> H(U1(c, d), U1(b, e))
27.56/9.00	   A^2 -> H(U1(c, d), U1(b, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(e, c))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, c))
27.56/9.00	   A^2 -> H(U1(c, d), U1(c, e))
27.56/9.00	   A^2 -> H(U1(c, d), U1(c, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(e, e))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, d))
27.56/9.00	   A^2 -> H(U1(c, d), U1(d, k))
27.56/9.00	   A^2 -> H(U1(c, a), b)
27.56/9.00	   A^2 -> H(U1(c, a), U1(e, d))
27.56/9.00	   A^2 -> H(U1(c, a), U1(d, e))
27.56/9.00	   A^2 -> H(U1(c, a), c)
27.56/9.00	   A^2 -> H(U1(c, a), U1(e, k))
27.56/9.00	   A^2 -> H(U1(c, a), U1(k, e))
27.56/9.00	   A^2 -> H(U1(c, a), e)
27.56/9.00	   A^2 -> H(U1(c, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(d, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(d, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(d, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(d, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(d, e), f(e))
27.56/9.00	   A^2 -> H(U1(d, e), f(k))
27.56/9.00	   A^2 -> H(U1(d, e), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, c), U1(e, b))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, b))
27.56/9.00	   A^2 -> H(U1(d, c), U1(c, d))
27.56/9.00	   A^2 -> H(U1(d, c), U1(d, c))
27.56/9.00	   A^2 -> H(U1(d, c), U1(b, e))
27.56/9.00	   A^2 -> H(U1(d, c), U1(b, k))
27.56/9.00	   A^2 -> H(U1(d, c), U1(e, c))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, c))
27.56/9.00	   A^2 -> H(U1(d, c), U1(c, e))
27.56/9.00	   A^2 -> H(U1(d, c), U1(c, k))
27.56/9.00	   A^2 -> H(U1(d, c), U1(e, e))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, d))
27.56/9.00	   A^2 -> H(U1(d, c), U1(d, k))
27.56/9.00	   A^2 -> H(U1(d, a), b)
27.56/9.00	   A^2 -> H(U1(d, a), U1(e, d))
27.56/9.00	   A^2 -> H(U1(d, a), U1(d, e))
27.56/9.00	   A^2 -> H(U1(d, a), c)
27.56/9.00	   A^2 -> H(U1(d, a), U1(e, k))
27.56/9.00	
27.56/9.00	The TRS R consists of the following rules:
27.56/9.00	
27.56/9.00	   f(x) -> U1(x, x)
27.56/9.00	   U1(e, x) -> x
27.56/9.00	   a -> c
27.56/9.00	   a -> d
27.56/9.00	   b -> c
27.56/9.00	   b -> d
27.56/9.00	   d -> k
27.56/9.00	   c -> e
27.56/9.00	   c -> k
27.56/9.00	
27.56/9.00	Q is empty.
27.56/9.00	We have to consider all minimal (P,Q,R)-chains.
27.56/9.00	----------------------------------------
27.56/9.00	
27.56/9.00	(667) TransformationProof (EQUIVALENT)
27.56/9.00	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
27.56/9.00	
27.56/9.00	   (A^2 -> H(U1(k, a), U1(k, c)),A^2 -> H(U1(k, a), U1(k, c)))
27.56/9.00	   (A^2 -> H(U1(d, c), U1(k, c)),A^2 -> H(U1(d, c), U1(k, c)))
27.56/9.00	   (A^2 -> H(U1(d, d), U1(k, c)),A^2 -> H(U1(d, d), U1(k, c)))
27.56/9.00	   (A^2 -> H(U1(d, a), U1(k, e)),A^2 -> H(U1(d, a), U1(k, e)))
27.56/9.00	   (A^2 -> H(U1(d, a), U1(k, k)),A^2 -> H(U1(d, a), U1(k, k)))
27.56/9.00	
27.56/9.00	
27.56/9.00	----------------------------------------
27.56/9.00	
27.56/9.00	(668)
27.56/9.00	Obligation:
27.56/9.00	Q DP problem:
27.56/9.00	The TRS P consists of the following rules:
27.56/9.00	
27.56/9.00	   H(x, x) -> G(x, x, f(k))
27.56/9.00	   G(d, x, x) -> A^2
27.56/9.00	   A^2 -> H(f(c), f(c))
27.56/9.00	   A^2 -> H(f(d), f(d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, c))
27.56/9.00	   A^2 -> H(f(e), f(e))
27.56/9.00	   A^2 -> H(f(k), f(k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, a), U1(c, e))
27.56/9.00	   A^2 -> H(U1(d, a), U1(c, k))
27.56/9.00	   A^2 -> H(U1(d, a), U1(e, e))
27.56/9.00	   A^2 -> H(U1(d, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, a), U1(k, d))
27.56/9.00	   A^2 -> H(U1(d, a), U1(d, k))
27.56/9.00	   A^2 -> H(U1(a, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(a, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(a, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(a, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(a, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(a, e), f(e))
27.56/9.00	   A^2 -> H(U1(a, e), f(k))
27.56/9.00	   A^2 -> H(U1(a, e), U1(d, d))
27.56/9.00	   A^2 -> H(U1(a, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(a, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(a, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(a, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(a, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(a, k), f(e))
27.56/9.00	   A^2 -> H(U1(a, k), f(k))
27.56/9.00	   A^2 -> H(U1(a, k), U1(d, d))
27.56/9.00	   A^2 -> H(U1(a, c), U1(e, b))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, b))
27.56/9.00	   A^2 -> H(U1(a, c), U1(c, d))
27.56/9.00	   A^2 -> H(U1(a, c), U1(d, c))
27.56/9.00	   A^2 -> H(U1(a, c), U1(b, e))
27.56/9.00	   A^2 -> H(U1(a, c), U1(b, k))
27.56/9.00	   A^2 -> H(U1(a, c), U1(e, c))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, c))
27.56/9.00	   A^2 -> H(U1(a, c), U1(c, e))
27.56/9.00	   A^2 -> H(U1(a, c), U1(c, k))
27.56/9.00	   A^2 -> H(U1(a, c), U1(e, e))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, d))
27.56/9.00	   A^2 -> H(U1(a, c), U1(d, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(e, b))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, b))
27.56/9.00	   A^2 -> H(U1(a, d), U1(c, d))
27.56/9.00	   A^2 -> H(U1(a, d), U1(d, c))
27.56/9.00	   A^2 -> H(U1(a, d), U1(b, e))
27.56/9.00	   A^2 -> H(U1(a, d), U1(b, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(e, c))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, c))
27.56/9.00	   A^2 -> H(U1(a, d), U1(c, e))
27.56/9.00	   A^2 -> H(U1(a, d), U1(c, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(e, e))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, d))
27.56/9.00	   A^2 -> H(U1(a, d), U1(d, k))
27.56/9.00	   A^2 -> H(U1(a, a), b)
27.56/9.00	   A^2 -> H(U1(a, a), U1(e, d))
27.56/9.00	   A^2 -> H(U1(a, a), U1(d, e))
27.56/9.00	   A^2 -> H(U1(a, a), c)
27.56/9.00	   A^2 -> H(U1(a, a), U1(e, k))
27.56/9.00	   A^2 -> H(U1(a, a), U1(k, e))
27.56/9.00	   A^2 -> H(U1(a, a), e)
27.56/9.00	   A^2 -> H(U1(a, a), U1(k, k))
27.56/9.00	   A^2 -> H(k, f(b))
27.56/9.00	   A^2 -> H(c, U1(b, b))
27.56/9.00	   A^2 -> H(c, f(c))
27.56/9.00	   A^2 -> H(c, f(d))
27.56/9.00	   A^2 -> H(U1(e, k), U1(b, b))
27.56/9.00	   A^2 -> H(U1(e, k), f(c))
27.56/9.00	   A^2 -> H(U1(e, k), f(d))
27.56/9.00	   A^2 -> H(U1(e, c), U1(c, b))
27.56/9.00	   A^2 -> H(U1(e, c), U1(d, b))
27.56/9.00	   A^2 -> H(U1(e, c), U1(b, c))
27.56/9.00	   A^2 -> H(U1(e, c), U1(b, d))
27.56/9.00	   A^2 -> H(U1(e, c), U1(c, c))
27.56/9.00	   A^2 -> H(U1(e, c), f(e))
27.56/9.00	   A^2 -> H(U1(e, c), f(k))
27.56/9.00	   A^2 -> H(U1(e, c), U1(d, d))
27.56/9.00	   A^2 -> H(U1(k, e), U1(b, b))
27.56/9.00	   A^2 -> H(U1(k, e), f(c))
27.56/9.00	   A^2 -> H(U1(k, e), f(d))
27.56/9.00	   A^2 -> H(U1(k, c), U1(c, b))
27.56/9.00	   A^2 -> H(U1(k, c), U1(d, b))
27.56/9.00	   A^2 -> H(U1(k, c), U1(b, c))
27.56/9.00	   A^2 -> H(U1(k, c), U1(b, d))
27.56/9.00	   A^2 -> H(U1(k, c), U1(c, c))
27.56/9.00	   A^2 -> H(U1(k, c), f(e))
27.56/9.00	   A^2 -> H(U1(k, c), f(k))
27.56/9.00	   A^2 -> H(U1(k, c), U1(d, d))
27.56/9.00	   A^2 -> H(U1(c, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(c, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(c, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(c, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(c, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(c, e), f(e))
27.56/9.00	   A^2 -> H(U1(c, e), f(k))
27.56/9.00	   A^2 -> H(U1(c, e), U1(d, d))
27.56/9.00	   A^2 -> H(U1(c, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(c, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(c, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(c, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(c, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(c, k), f(e))
27.56/9.00	   A^2 -> H(U1(c, k), f(k))
27.56/9.00	   A^2 -> H(U1(c, k), U1(d, d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(e, b))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, b))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(d, c))
27.56/9.00	   A^2 -> H(U1(c, c), U1(b, e))
27.56/9.00	   A^2 -> H(U1(c, c), U1(b, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(e, e))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(d, k))
27.56/9.00	   A^2 -> H(e, U1(b, b))
27.56/9.00	   A^2 -> H(e, f(c))
27.56/9.00	   A^2 -> H(e, f(d))
27.56/9.00	   A^2 -> H(U1(e, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(e, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(e, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(e, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(e, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(e, e), f(e))
27.56/9.00	   A^2 -> H(U1(e, e), f(k))
27.56/9.00	   A^2 -> H(U1(e, e), U1(d, d))
27.56/9.00	   A^2 -> H(f(e), U1(e, b))
27.56/9.00	   A^2 -> H(f(e), U1(k, b))
27.56/9.00	   A^2 -> H(f(e), U1(c, d))
27.56/9.00	   A^2 -> H(f(e), U1(d, c))
27.56/9.00	   A^2 -> H(f(e), U1(b, e))
27.56/9.00	   A^2 -> H(f(e), U1(b, k))
27.56/9.00	   A^2 -> H(f(e), U1(e, c))
27.56/9.00	   A^2 -> H(f(e), U1(k, c))
27.56/9.00	   A^2 -> H(f(e), U1(c, e))
27.56/9.00	   A^2 -> H(f(e), U1(c, k))
27.56/9.00	   A^2 -> H(f(e), U1(k, k))
27.56/9.00	   A^2 -> H(f(e), U1(k, d))
27.56/9.00	   A^2 -> H(f(e), U1(d, k))
27.56/9.00	   A^2 -> H(U1(k, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(k, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(k, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(k, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(k, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(k, k), f(e))
27.56/9.00	   A^2 -> H(U1(k, k), f(k))
27.56/9.00	   A^2 -> H(U1(k, k), U1(d, d))
27.56/9.00	   A^2 -> H(f(k), U1(e, b))
27.56/9.00	   A^2 -> H(f(k), U1(k, b))
27.56/9.00	   A^2 -> H(f(k), U1(c, d))
27.56/9.00	   A^2 -> H(f(k), U1(d, c))
27.56/9.00	   A^2 -> H(f(k), U1(b, e))
27.56/9.00	   A^2 -> H(f(k), U1(b, k))
27.56/9.00	   A^2 -> H(f(k), U1(e, c))
27.56/9.00	   A^2 -> H(f(k), U1(k, c))
27.56/9.00	   A^2 -> H(f(k), U1(c, e))
27.56/9.00	   A^2 -> H(f(k), U1(c, k))
27.56/9.00	   A^2 -> H(f(k), U1(e, e))
27.56/9.00	   A^2 -> H(f(k), U1(k, d))
27.56/9.00	   A^2 -> H(f(k), U1(d, k))
27.56/9.00	   A^2 -> H(f(c), b)
27.56/9.00	   A^2 -> H(f(c), U1(e, d))
27.56/9.00	   A^2 -> H(f(c), U1(d, e))
27.56/9.00	   A^2 -> H(f(k), U1(k, k))
27.56/9.00	   A^2 -> H(U1(k, k), U1(b, b))
27.56/9.00	   A^2 -> H(U1(k, k), f(c))
27.56/9.00	   A^2 -> H(U1(k, k), f(d))
27.56/9.00	   A^2 -> H(U1(k, d), U1(c, b))
27.56/9.00	   A^2 -> H(U1(k, d), U1(d, b))
27.56/9.00	   A^2 -> H(U1(k, d), U1(b, c))
27.56/9.00	   A^2 -> H(U1(k, d), U1(b, d))
27.56/9.00	   A^2 -> H(U1(k, d), U1(c, c))
27.56/9.00	   A^2 -> H(U1(k, d), f(e))
27.56/9.00	   A^2 -> H(U1(k, d), f(k))
27.56/9.00	   A^2 -> H(U1(k, d), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(d, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(d, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(d, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(d, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(d, k), f(e))
27.56/9.00	   A^2 -> H(U1(d, k), f(k))
27.56/9.00	   A^2 -> H(U1(d, k), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, d), U1(e, b))
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, b))
27.56/9.00	   A^2 -> H(U1(d, d), U1(c, d))
27.56/9.00	   A^2 -> H(U1(d, d), U1(d, c))
27.56/9.00	   A^2 -> H(U1(d, d), U1(b, e))
27.56/9.00	   A^2 -> H(U1(d, d), U1(b, k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(e, c))
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, c))
27.56/9.00	   A^2 -> H(U1(d, d), U1(c, e))
27.56/9.00	   A^2 -> H(U1(d, d), U1(c, k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(e, e))
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, k))
27.56/9.00	   A^2 -> H(f(d), b)
27.56/9.00	   A^2 -> H(f(d), U1(e, d))
27.56/9.00	   A^2 -> H(f(d), U1(d, e))
27.56/9.00	   A^2 -> H(f(d), c)
27.56/9.00	   A^2 -> H(f(d), U1(e, k))
27.56/9.00	   A^2 -> H(f(d), U1(k, e))
27.56/9.00	   A^2 -> H(f(d), e)
27.56/9.00	   A^2 -> H(f(a), d)
27.56/9.00	   A^2 -> H(U1(c, c), U1(e, c))
27.56/9.00	   A^2 -> H(f(c), c)
27.56/9.00	   A^2 -> H(f(c), U1(e, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, c))
27.56/9.00	   A^2 -> H(f(c), U1(k, e))
27.56/9.00	   A^2 -> H(f(c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, e))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, k))
27.56/9.00	   A^2 -> H(f(a), k)
27.56/9.00	   A^2 -> H(f(e), U1(e, e))
27.56/9.00	   A^2 -> H(f(c), e)
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, d))
27.56/9.00	   A^2 -> H(f(d), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(d, k))
27.56/9.00	   A^2 -> H(d, U1(b, b))
27.56/9.00	   A^2 -> H(d, f(c))
27.56/9.00	   A^2 -> H(d, f(d))
27.56/9.00	   A^2 -> H(a, U1(c, b))
27.56/9.00	   A^2 -> H(a, U1(d, b))
27.56/9.00	   A^2 -> H(a, U1(b, c))
27.56/9.00	   A^2 -> H(a, U1(b, d))
27.56/9.00	   A^2 -> H(a, U1(c, c))
27.56/9.00	   A^2 -> H(a, f(e))
27.56/9.00	   A^2 -> H(a, f(k))
27.56/9.00	   A^2 -> H(a, U1(d, d))
27.56/9.00	   A^2 -> H(U1(e, d), U1(c, b))
27.56/9.00	   A^2 -> H(U1(e, d), U1(d, b))
27.56/9.00	   A^2 -> H(U1(e, d), U1(b, c))
27.56/9.00	   A^2 -> H(U1(e, d), U1(b, d))
27.56/9.00	   A^2 -> H(U1(e, d), U1(c, c))
27.56/9.00	   A^2 -> H(U1(e, d), f(e))
27.56/9.00	   A^2 -> H(U1(e, d), f(k))
27.56/9.00	   A^2 -> H(U1(e, d), U1(d, d))
27.56/9.00	   A^2 -> H(U1(e, a), U1(e, b))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, b))
27.56/9.00	   A^2 -> H(U1(e, a), U1(c, d))
27.56/9.00	   A^2 -> H(U1(e, a), U1(d, c))
27.56/9.00	   A^2 -> H(U1(e, a), U1(b, e))
27.56/9.00	   A^2 -> H(U1(e, a), U1(b, k))
27.56/9.00	   A^2 -> H(U1(e, a), U1(e, c))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, c))
27.56/9.00	   A^2 -> H(U1(e, a), U1(c, e))
27.56/9.00	   A^2 -> H(U1(e, a), U1(c, k))
27.56/9.00	   A^2 -> H(U1(e, a), U1(e, e))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, d))
27.56/9.00	   A^2 -> H(U1(e, a), U1(d, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(e, b))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, b))
27.56/9.00	   A^2 -> H(U1(k, a), U1(c, d))
27.56/9.00	   A^2 -> H(U1(k, a), U1(d, c))
27.56/9.00	   A^2 -> H(U1(k, a), U1(b, e))
27.56/9.00	   A^2 -> H(U1(k, a), U1(b, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(e, c))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, c))
27.56/9.00	   A^2 -> H(U1(k, a), U1(c, e))
27.56/9.00	   A^2 -> H(U1(k, a), U1(c, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(e, e))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, d))
27.56/9.00	   A^2 -> H(U1(k, a), U1(d, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(e, b))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, b))
27.56/9.00	   A^2 -> H(U1(c, d), U1(c, d))
27.56/9.00	   A^2 -> H(U1(c, d), U1(d, c))
27.56/9.00	   A^2 -> H(U1(c, d), U1(b, e))
27.56/9.00	   A^2 -> H(U1(c, d), U1(b, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(e, c))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, c))
27.56/9.00	   A^2 -> H(U1(c, d), U1(c, e))
27.56/9.00	   A^2 -> H(U1(c, d), U1(c, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(e, e))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, d))
27.56/9.00	   A^2 -> H(U1(c, d), U1(d, k))
27.56/9.00	   A^2 -> H(U1(c, a), b)
27.56/9.00	   A^2 -> H(U1(c, a), U1(e, d))
27.56/9.00	   A^2 -> H(U1(c, a), U1(d, e))
27.56/9.00	   A^2 -> H(U1(c, a), c)
27.56/9.00	   A^2 -> H(U1(c, a), U1(e, k))
27.56/9.00	   A^2 -> H(U1(c, a), U1(k, e))
27.56/9.00	   A^2 -> H(U1(c, a), e)
27.56/9.00	   A^2 -> H(U1(c, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(d, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(d, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(d, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(d, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(d, e), f(e))
27.56/9.00	   A^2 -> H(U1(d, e), f(k))
27.56/9.00	   A^2 -> H(U1(d, e), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, c), U1(e, b))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, b))
27.56/9.00	   A^2 -> H(U1(d, c), U1(c, d))
27.56/9.00	   A^2 -> H(U1(d, c), U1(d, c))
27.56/9.00	   A^2 -> H(U1(d, c), U1(b, e))
27.56/9.00	   A^2 -> H(U1(d, c), U1(b, k))
27.56/9.00	   A^2 -> H(U1(d, c), U1(e, c))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, c))
27.56/9.00	   A^2 -> H(U1(d, c), U1(c, e))
27.56/9.00	   A^2 -> H(U1(d, c), U1(c, k))
27.56/9.00	   A^2 -> H(U1(d, c), U1(e, e))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, d))
27.56/9.00	   A^2 -> H(U1(d, c), U1(d, k))
27.56/9.00	   A^2 -> H(U1(d, a), b)
27.56/9.00	   A^2 -> H(U1(d, a), U1(e, d))
27.56/9.00	   A^2 -> H(U1(d, a), U1(d, e))
27.56/9.00	   A^2 -> H(U1(d, a), c)
27.56/9.00	   A^2 -> H(U1(d, a), U1(e, k))
27.56/9.00	   A^2 -> H(U1(d, a), U1(k, e))
27.56/9.00	
27.56/9.00	The TRS R consists of the following rules:
27.56/9.00	
27.56/9.00	   f(x) -> U1(x, x)
27.56/9.00	   U1(e, x) -> x
27.56/9.00	   a -> c
27.56/9.00	   a -> d
27.56/9.00	   b -> c
27.56/9.00	   b -> d
27.56/9.00	   d -> k
27.56/9.00	   c -> e
27.56/9.00	   c -> k
27.56/9.00	
27.56/9.00	Q is empty.
27.56/9.00	We have to consider all minimal (P,Q,R)-chains.
27.56/9.00	----------------------------------------
27.56/9.00	
27.56/9.00	(669) TransformationProof (EQUIVALENT)
27.56/9.00	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
27.56/9.00	
27.56/9.00	   (A^2 -> H(U1(k, a), U1(c, e)),A^2 -> H(U1(k, a), U1(c, e)))
27.56/9.00	   (A^2 -> H(U1(d, c), U1(c, e)),A^2 -> H(U1(d, c), U1(c, e)))
27.56/9.00	   (A^2 -> H(U1(d, d), U1(c, e)),A^2 -> H(U1(d, d), U1(c, e)))
27.56/9.00	   (A^2 -> H(U1(d, a), U1(e, e)),A^2 -> H(U1(d, a), U1(e, e)))
27.56/9.00	   (A^2 -> H(U1(d, a), U1(k, e)),A^2 -> H(U1(d, a), U1(k, e)))
27.56/9.00	
27.56/9.00	
27.56/9.00	----------------------------------------
27.56/9.00	
27.56/9.00	(670)
27.56/9.00	Obligation:
27.56/9.00	Q DP problem:
27.56/9.00	The TRS P consists of the following rules:
27.56/9.00	
27.56/9.00	   H(x, x) -> G(x, x, f(k))
27.56/9.00	   G(d, x, x) -> A^2
27.56/9.00	   A^2 -> H(f(c), f(c))
27.56/9.00	   A^2 -> H(f(d), f(d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, c))
27.56/9.00	   A^2 -> H(f(e), f(e))
27.56/9.00	   A^2 -> H(f(k), f(k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, a), U1(c, k))
27.56/9.00	   A^2 -> H(U1(d, a), U1(e, e))
27.56/9.00	   A^2 -> H(U1(d, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, a), U1(k, d))
27.56/9.00	   A^2 -> H(U1(d, a), U1(d, k))
27.56/9.00	   A^2 -> H(U1(a, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(a, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(a, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(a, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(a, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(a, e), f(e))
27.56/9.00	   A^2 -> H(U1(a, e), f(k))
27.56/9.00	   A^2 -> H(U1(a, e), U1(d, d))
27.56/9.00	   A^2 -> H(U1(a, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(a, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(a, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(a, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(a, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(a, k), f(e))
27.56/9.00	   A^2 -> H(U1(a, k), f(k))
27.56/9.00	   A^2 -> H(U1(a, k), U1(d, d))
27.56/9.00	   A^2 -> H(U1(a, c), U1(e, b))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, b))
27.56/9.00	   A^2 -> H(U1(a, c), U1(c, d))
27.56/9.00	   A^2 -> H(U1(a, c), U1(d, c))
27.56/9.00	   A^2 -> H(U1(a, c), U1(b, e))
27.56/9.00	   A^2 -> H(U1(a, c), U1(b, k))
27.56/9.00	   A^2 -> H(U1(a, c), U1(e, c))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, c))
27.56/9.00	   A^2 -> H(U1(a, c), U1(c, e))
27.56/9.00	   A^2 -> H(U1(a, c), U1(c, k))
27.56/9.00	   A^2 -> H(U1(a, c), U1(e, e))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, d))
27.56/9.00	   A^2 -> H(U1(a, c), U1(d, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(e, b))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, b))
27.56/9.00	   A^2 -> H(U1(a, d), U1(c, d))
27.56/9.00	   A^2 -> H(U1(a, d), U1(d, c))
27.56/9.00	   A^2 -> H(U1(a, d), U1(b, e))
27.56/9.00	   A^2 -> H(U1(a, d), U1(b, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(e, c))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, c))
27.56/9.00	   A^2 -> H(U1(a, d), U1(c, e))
27.56/9.00	   A^2 -> H(U1(a, d), U1(c, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(e, e))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, d))
27.56/9.00	   A^2 -> H(U1(a, d), U1(d, k))
27.56/9.00	   A^2 -> H(U1(a, a), b)
27.56/9.00	   A^2 -> H(U1(a, a), U1(e, d))
27.56/9.00	   A^2 -> H(U1(a, a), U1(d, e))
27.56/9.00	   A^2 -> H(U1(a, a), c)
27.56/9.00	   A^2 -> H(U1(a, a), U1(e, k))
27.56/9.00	   A^2 -> H(U1(a, a), U1(k, e))
27.56/9.00	   A^2 -> H(U1(a, a), e)
27.56/9.00	   A^2 -> H(U1(a, a), U1(k, k))
27.56/9.00	   A^2 -> H(k, f(b))
27.56/9.00	   A^2 -> H(c, U1(b, b))
27.56/9.00	   A^2 -> H(c, f(c))
27.56/9.00	   A^2 -> H(c, f(d))
27.56/9.00	   A^2 -> H(U1(e, k), U1(b, b))
27.56/9.00	   A^2 -> H(U1(e, k), f(c))
27.56/9.00	   A^2 -> H(U1(e, k), f(d))
27.56/9.00	   A^2 -> H(U1(e, c), U1(c, b))
27.56/9.00	   A^2 -> H(U1(e, c), U1(d, b))
27.56/9.00	   A^2 -> H(U1(e, c), U1(b, c))
27.56/9.00	   A^2 -> H(U1(e, c), U1(b, d))
27.56/9.00	   A^2 -> H(U1(e, c), U1(c, c))
27.56/9.00	   A^2 -> H(U1(e, c), f(e))
27.56/9.00	   A^2 -> H(U1(e, c), f(k))
27.56/9.00	   A^2 -> H(U1(e, c), U1(d, d))
27.56/9.00	   A^2 -> H(U1(k, e), U1(b, b))
27.56/9.00	   A^2 -> H(U1(k, e), f(c))
27.56/9.00	   A^2 -> H(U1(k, e), f(d))
27.56/9.00	   A^2 -> H(U1(k, c), U1(c, b))
27.56/9.00	   A^2 -> H(U1(k, c), U1(d, b))
27.56/9.00	   A^2 -> H(U1(k, c), U1(b, c))
27.56/9.00	   A^2 -> H(U1(k, c), U1(b, d))
27.56/9.00	   A^2 -> H(U1(k, c), U1(c, c))
27.56/9.00	   A^2 -> H(U1(k, c), f(e))
27.56/9.00	   A^2 -> H(U1(k, c), f(k))
27.56/9.00	   A^2 -> H(U1(k, c), U1(d, d))
27.56/9.00	   A^2 -> H(U1(c, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(c, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(c, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(c, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(c, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(c, e), f(e))
27.56/9.00	   A^2 -> H(U1(c, e), f(k))
27.56/9.00	   A^2 -> H(U1(c, e), U1(d, d))
27.56/9.00	   A^2 -> H(U1(c, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(c, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(c, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(c, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(c, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(c, k), f(e))
27.56/9.00	   A^2 -> H(U1(c, k), f(k))
27.56/9.00	   A^2 -> H(U1(c, k), U1(d, d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(e, b))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, b))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(d, c))
27.56/9.00	   A^2 -> H(U1(c, c), U1(b, e))
27.56/9.00	   A^2 -> H(U1(c, c), U1(b, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(e, e))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(d, k))
27.56/9.00	   A^2 -> H(e, U1(b, b))
27.56/9.00	   A^2 -> H(e, f(c))
27.56/9.00	   A^2 -> H(e, f(d))
27.56/9.00	   A^2 -> H(U1(e, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(e, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(e, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(e, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(e, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(e, e), f(e))
27.56/9.00	   A^2 -> H(U1(e, e), f(k))
27.56/9.00	   A^2 -> H(U1(e, e), U1(d, d))
27.56/9.00	   A^2 -> H(f(e), U1(e, b))
27.56/9.00	   A^2 -> H(f(e), U1(k, b))
27.56/9.00	   A^2 -> H(f(e), U1(c, d))
27.56/9.00	   A^2 -> H(f(e), U1(d, c))
27.56/9.00	   A^2 -> H(f(e), U1(b, e))
27.56/9.00	   A^2 -> H(f(e), U1(b, k))
27.56/9.00	   A^2 -> H(f(e), U1(e, c))
27.56/9.00	   A^2 -> H(f(e), U1(k, c))
27.56/9.00	   A^2 -> H(f(e), U1(c, e))
27.56/9.00	   A^2 -> H(f(e), U1(c, k))
27.56/9.00	   A^2 -> H(f(e), U1(k, k))
27.56/9.00	   A^2 -> H(f(e), U1(k, d))
27.56/9.00	   A^2 -> H(f(e), U1(d, k))
27.56/9.00	   A^2 -> H(U1(k, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(k, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(k, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(k, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(k, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(k, k), f(e))
27.56/9.00	   A^2 -> H(U1(k, k), f(k))
27.56/9.00	   A^2 -> H(U1(k, k), U1(d, d))
27.56/9.00	   A^2 -> H(f(k), U1(e, b))
27.56/9.00	   A^2 -> H(f(k), U1(k, b))
27.56/9.00	   A^2 -> H(f(k), U1(c, d))
27.56/9.00	   A^2 -> H(f(k), U1(d, c))
27.56/9.00	   A^2 -> H(f(k), U1(b, e))
27.56/9.00	   A^2 -> H(f(k), U1(b, k))
27.56/9.00	   A^2 -> H(f(k), U1(e, c))
27.56/9.00	   A^2 -> H(f(k), U1(k, c))
27.56/9.00	   A^2 -> H(f(k), U1(c, e))
27.56/9.00	   A^2 -> H(f(k), U1(c, k))
27.56/9.00	   A^2 -> H(f(k), U1(e, e))
27.56/9.00	   A^2 -> H(f(k), U1(k, d))
27.56/9.00	   A^2 -> H(f(k), U1(d, k))
27.56/9.00	   A^2 -> H(f(c), b)
27.56/9.00	   A^2 -> H(f(c), U1(e, d))
27.56/9.00	   A^2 -> H(f(c), U1(d, e))
27.56/9.00	   A^2 -> H(f(k), U1(k, k))
27.56/9.00	   A^2 -> H(U1(k, k), U1(b, b))
27.56/9.00	   A^2 -> H(U1(k, k), f(c))
27.56/9.00	   A^2 -> H(U1(k, k), f(d))
27.56/9.00	   A^2 -> H(U1(k, d), U1(c, b))
27.56/9.00	   A^2 -> H(U1(k, d), U1(d, b))
27.56/9.00	   A^2 -> H(U1(k, d), U1(b, c))
27.56/9.00	   A^2 -> H(U1(k, d), U1(b, d))
27.56/9.00	   A^2 -> H(U1(k, d), U1(c, c))
27.56/9.00	   A^2 -> H(U1(k, d), f(e))
27.56/9.00	   A^2 -> H(U1(k, d), f(k))
27.56/9.00	   A^2 -> H(U1(k, d), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(d, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(d, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(d, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(d, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(d, k), f(e))
27.56/9.00	   A^2 -> H(U1(d, k), f(k))
27.56/9.00	   A^2 -> H(U1(d, k), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, d), U1(e, b))
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, b))
27.56/9.00	   A^2 -> H(U1(d, d), U1(c, d))
27.56/9.00	   A^2 -> H(U1(d, d), U1(d, c))
27.56/9.00	   A^2 -> H(U1(d, d), U1(b, e))
27.56/9.00	   A^2 -> H(U1(d, d), U1(b, k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(e, c))
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, c))
27.56/9.00	   A^2 -> H(U1(d, d), U1(c, e))
27.56/9.00	   A^2 -> H(U1(d, d), U1(c, k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(e, e))
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, k))
27.56/9.00	   A^2 -> H(f(d), b)
27.56/9.00	   A^2 -> H(f(d), U1(e, d))
27.56/9.00	   A^2 -> H(f(d), U1(d, e))
27.56/9.00	   A^2 -> H(f(d), c)
27.56/9.00	   A^2 -> H(f(d), U1(e, k))
27.56/9.00	   A^2 -> H(f(d), U1(k, e))
27.56/9.00	   A^2 -> H(f(d), e)
27.56/9.00	   A^2 -> H(f(a), d)
27.56/9.00	   A^2 -> H(U1(c, c), U1(e, c))
27.56/9.00	   A^2 -> H(f(c), c)
27.56/9.00	   A^2 -> H(f(c), U1(e, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, c))
27.56/9.00	   A^2 -> H(f(c), U1(k, e))
27.56/9.00	   A^2 -> H(f(c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, e))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, k))
27.56/9.00	   A^2 -> H(f(a), k)
27.56/9.00	   A^2 -> H(f(e), U1(e, e))
27.56/9.00	   A^2 -> H(f(c), e)
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, d))
27.56/9.00	   A^2 -> H(f(d), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(d, k))
27.56/9.00	   A^2 -> H(d, U1(b, b))
27.56/9.00	   A^2 -> H(d, f(c))
27.56/9.00	   A^2 -> H(d, f(d))
27.56/9.00	   A^2 -> H(a, U1(c, b))
27.56/9.00	   A^2 -> H(a, U1(d, b))
27.56/9.00	   A^2 -> H(a, U1(b, c))
27.56/9.00	   A^2 -> H(a, U1(b, d))
27.56/9.00	   A^2 -> H(a, U1(c, c))
27.56/9.00	   A^2 -> H(a, f(e))
27.56/9.00	   A^2 -> H(a, f(k))
27.56/9.00	   A^2 -> H(a, U1(d, d))
27.56/9.00	   A^2 -> H(U1(e, d), U1(c, b))
27.56/9.00	   A^2 -> H(U1(e, d), U1(d, b))
27.56/9.00	   A^2 -> H(U1(e, d), U1(b, c))
27.56/9.00	   A^2 -> H(U1(e, d), U1(b, d))
27.56/9.00	   A^2 -> H(U1(e, d), U1(c, c))
27.56/9.00	   A^2 -> H(U1(e, d), f(e))
27.56/9.00	   A^2 -> H(U1(e, d), f(k))
27.56/9.00	   A^2 -> H(U1(e, d), U1(d, d))
27.56/9.00	   A^2 -> H(U1(e, a), U1(e, b))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, b))
27.56/9.00	   A^2 -> H(U1(e, a), U1(c, d))
27.56/9.00	   A^2 -> H(U1(e, a), U1(d, c))
27.56/9.00	   A^2 -> H(U1(e, a), U1(b, e))
27.56/9.00	   A^2 -> H(U1(e, a), U1(b, k))
27.56/9.00	   A^2 -> H(U1(e, a), U1(e, c))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, c))
27.56/9.00	   A^2 -> H(U1(e, a), U1(c, e))
27.56/9.00	   A^2 -> H(U1(e, a), U1(c, k))
27.56/9.00	   A^2 -> H(U1(e, a), U1(e, e))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, d))
27.56/9.00	   A^2 -> H(U1(e, a), U1(d, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(e, b))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, b))
27.56/9.00	   A^2 -> H(U1(k, a), U1(c, d))
27.56/9.00	   A^2 -> H(U1(k, a), U1(d, c))
27.56/9.00	   A^2 -> H(U1(k, a), U1(b, e))
27.56/9.00	   A^2 -> H(U1(k, a), U1(b, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(e, c))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, c))
27.56/9.00	   A^2 -> H(U1(k, a), U1(c, e))
27.56/9.00	   A^2 -> H(U1(k, a), U1(c, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(e, e))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, d))
27.56/9.00	   A^2 -> H(U1(k, a), U1(d, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(e, b))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, b))
27.56/9.00	   A^2 -> H(U1(c, d), U1(c, d))
27.56/9.00	   A^2 -> H(U1(c, d), U1(d, c))
27.56/9.00	   A^2 -> H(U1(c, d), U1(b, e))
27.56/9.00	   A^2 -> H(U1(c, d), U1(b, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(e, c))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, c))
27.56/9.00	   A^2 -> H(U1(c, d), U1(c, e))
27.56/9.00	   A^2 -> H(U1(c, d), U1(c, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(e, e))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, d))
27.56/9.00	   A^2 -> H(U1(c, d), U1(d, k))
27.56/9.00	   A^2 -> H(U1(c, a), b)
27.56/9.00	   A^2 -> H(U1(c, a), U1(e, d))
27.56/9.00	   A^2 -> H(U1(c, a), U1(d, e))
27.56/9.00	   A^2 -> H(U1(c, a), c)
27.56/9.00	   A^2 -> H(U1(c, a), U1(e, k))
27.56/9.00	   A^2 -> H(U1(c, a), U1(k, e))
27.56/9.00	   A^2 -> H(U1(c, a), e)
27.56/9.00	   A^2 -> H(U1(c, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(d, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(d, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(d, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(d, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(d, e), f(e))
27.56/9.00	   A^2 -> H(U1(d, e), f(k))
27.56/9.00	   A^2 -> H(U1(d, e), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, c), U1(e, b))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, b))
27.56/9.00	   A^2 -> H(U1(d, c), U1(c, d))
27.56/9.00	   A^2 -> H(U1(d, c), U1(d, c))
27.56/9.00	   A^2 -> H(U1(d, c), U1(b, e))
27.56/9.00	   A^2 -> H(U1(d, c), U1(b, k))
27.56/9.00	   A^2 -> H(U1(d, c), U1(e, c))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, c))
27.56/9.00	   A^2 -> H(U1(d, c), U1(c, e))
27.56/9.00	   A^2 -> H(U1(d, c), U1(c, k))
27.56/9.00	   A^2 -> H(U1(d, c), U1(e, e))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, d))
27.56/9.00	   A^2 -> H(U1(d, c), U1(d, k))
27.56/9.00	   A^2 -> H(U1(d, a), b)
27.56/9.00	   A^2 -> H(U1(d, a), U1(e, d))
27.56/9.00	   A^2 -> H(U1(d, a), U1(d, e))
27.56/9.00	   A^2 -> H(U1(d, a), c)
27.56/9.00	   A^2 -> H(U1(d, a), U1(e, k))
27.56/9.00	   A^2 -> H(U1(d, a), U1(k, e))
27.56/9.00	
27.56/9.00	The TRS R consists of the following rules:
27.56/9.00	
27.56/9.00	   f(x) -> U1(x, x)
27.56/9.00	   U1(e, x) -> x
27.56/9.00	   a -> c
27.56/9.00	   a -> d
27.56/9.00	   b -> c
27.56/9.00	   b -> d
27.56/9.00	   d -> k
27.56/9.00	   c -> e
27.56/9.00	   c -> k
27.56/9.00	
27.56/9.00	Q is empty.
27.56/9.00	We have to consider all minimal (P,Q,R)-chains.
27.56/9.00	----------------------------------------
27.56/9.00	
27.56/9.00	(671) TransformationProof (EQUIVALENT)
27.56/9.00	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
27.56/9.00	
27.56/9.00	   (A^2 -> H(U1(k, a), U1(c, k)),A^2 -> H(U1(k, a), U1(c, k)))
27.56/9.00	   (A^2 -> H(U1(d, c), U1(c, k)),A^2 -> H(U1(d, c), U1(c, k)))
27.56/9.00	   (A^2 -> H(U1(d, d), U1(c, k)),A^2 -> H(U1(d, d), U1(c, k)))
27.56/9.00	   (A^2 -> H(U1(d, a), U1(e, k)),A^2 -> H(U1(d, a), U1(e, k)))
27.56/9.00	   (A^2 -> H(U1(d, a), U1(k, k)),A^2 -> H(U1(d, a), U1(k, k)))
27.56/9.00	
27.56/9.00	
27.56/9.00	----------------------------------------
27.56/9.00	
27.56/9.00	(672)
27.56/9.00	Obligation:
27.56/9.00	Q DP problem:
27.56/9.00	The TRS P consists of the following rules:
27.56/9.00	
27.56/9.00	   H(x, x) -> G(x, x, f(k))
27.56/9.00	   G(d, x, x) -> A^2
27.56/9.00	   A^2 -> H(f(c), f(c))
27.56/9.00	   A^2 -> H(f(d), f(d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, c))
27.56/9.00	   A^2 -> H(f(e), f(e))
27.56/9.00	   A^2 -> H(f(k), f(k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, a), U1(e, e))
27.56/9.00	   A^2 -> H(U1(d, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, a), U1(k, d))
27.56/9.00	   A^2 -> H(U1(d, a), U1(d, k))
27.56/9.00	   A^2 -> H(U1(a, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(a, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(a, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(a, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(a, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(a, e), f(e))
27.56/9.00	   A^2 -> H(U1(a, e), f(k))
27.56/9.00	   A^2 -> H(U1(a, e), U1(d, d))
27.56/9.00	   A^2 -> H(U1(a, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(a, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(a, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(a, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(a, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(a, k), f(e))
27.56/9.00	   A^2 -> H(U1(a, k), f(k))
27.56/9.00	   A^2 -> H(U1(a, k), U1(d, d))
27.56/9.00	   A^2 -> H(U1(a, c), U1(e, b))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, b))
27.56/9.00	   A^2 -> H(U1(a, c), U1(c, d))
27.56/9.00	   A^2 -> H(U1(a, c), U1(d, c))
27.56/9.00	   A^2 -> H(U1(a, c), U1(b, e))
27.56/9.00	   A^2 -> H(U1(a, c), U1(b, k))
27.56/9.00	   A^2 -> H(U1(a, c), U1(e, c))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, c))
27.56/9.00	   A^2 -> H(U1(a, c), U1(c, e))
27.56/9.00	   A^2 -> H(U1(a, c), U1(c, k))
27.56/9.00	   A^2 -> H(U1(a, c), U1(e, e))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, d))
27.56/9.00	   A^2 -> H(U1(a, c), U1(d, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(e, b))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, b))
27.56/9.00	   A^2 -> H(U1(a, d), U1(c, d))
27.56/9.00	   A^2 -> H(U1(a, d), U1(d, c))
27.56/9.00	   A^2 -> H(U1(a, d), U1(b, e))
27.56/9.00	   A^2 -> H(U1(a, d), U1(b, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(e, c))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, c))
27.56/9.00	   A^2 -> H(U1(a, d), U1(c, e))
27.56/9.00	   A^2 -> H(U1(a, d), U1(c, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(e, e))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, d))
27.56/9.00	   A^2 -> H(U1(a, d), U1(d, k))
27.56/9.00	   A^2 -> H(U1(a, a), b)
27.56/9.00	   A^2 -> H(U1(a, a), U1(e, d))
27.56/9.00	   A^2 -> H(U1(a, a), U1(d, e))
27.56/9.00	   A^2 -> H(U1(a, a), c)
27.56/9.00	   A^2 -> H(U1(a, a), U1(e, k))
27.56/9.00	   A^2 -> H(U1(a, a), U1(k, e))
27.56/9.00	   A^2 -> H(U1(a, a), e)
27.56/9.00	   A^2 -> H(U1(a, a), U1(k, k))
27.56/9.00	   A^2 -> H(k, f(b))
27.56/9.00	   A^2 -> H(c, U1(b, b))
27.56/9.00	   A^2 -> H(c, f(c))
27.56/9.00	   A^2 -> H(c, f(d))
27.56/9.00	   A^2 -> H(U1(e, k), U1(b, b))
27.56/9.00	   A^2 -> H(U1(e, k), f(c))
27.56/9.00	   A^2 -> H(U1(e, k), f(d))
27.56/9.00	   A^2 -> H(U1(e, c), U1(c, b))
27.56/9.00	   A^2 -> H(U1(e, c), U1(d, b))
27.56/9.00	   A^2 -> H(U1(e, c), U1(b, c))
27.56/9.00	   A^2 -> H(U1(e, c), U1(b, d))
27.56/9.00	   A^2 -> H(U1(e, c), U1(c, c))
27.56/9.00	   A^2 -> H(U1(e, c), f(e))
27.56/9.00	   A^2 -> H(U1(e, c), f(k))
27.56/9.00	   A^2 -> H(U1(e, c), U1(d, d))
27.56/9.00	   A^2 -> H(U1(k, e), U1(b, b))
27.56/9.00	   A^2 -> H(U1(k, e), f(c))
27.56/9.00	   A^2 -> H(U1(k, e), f(d))
27.56/9.00	   A^2 -> H(U1(k, c), U1(c, b))
27.56/9.00	   A^2 -> H(U1(k, c), U1(d, b))
27.56/9.00	   A^2 -> H(U1(k, c), U1(b, c))
27.56/9.00	   A^2 -> H(U1(k, c), U1(b, d))
27.56/9.00	   A^2 -> H(U1(k, c), U1(c, c))
27.56/9.00	   A^2 -> H(U1(k, c), f(e))
27.56/9.00	   A^2 -> H(U1(k, c), f(k))
27.56/9.00	   A^2 -> H(U1(k, c), U1(d, d))
27.56/9.00	   A^2 -> H(U1(c, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(c, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(c, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(c, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(c, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(c, e), f(e))
27.56/9.00	   A^2 -> H(U1(c, e), f(k))
27.56/9.00	   A^2 -> H(U1(c, e), U1(d, d))
27.56/9.00	   A^2 -> H(U1(c, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(c, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(c, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(c, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(c, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(c, k), f(e))
27.56/9.00	   A^2 -> H(U1(c, k), f(k))
27.56/9.00	   A^2 -> H(U1(c, k), U1(d, d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(e, b))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, b))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(d, c))
27.56/9.00	   A^2 -> H(U1(c, c), U1(b, e))
27.56/9.00	   A^2 -> H(U1(c, c), U1(b, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(e, e))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(d, k))
27.56/9.00	   A^2 -> H(e, U1(b, b))
27.56/9.00	   A^2 -> H(e, f(c))
27.56/9.00	   A^2 -> H(e, f(d))
27.56/9.00	   A^2 -> H(U1(e, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(e, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(e, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(e, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(e, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(e, e), f(e))
27.56/9.00	   A^2 -> H(U1(e, e), f(k))
27.56/9.00	   A^2 -> H(U1(e, e), U1(d, d))
27.56/9.00	   A^2 -> H(f(e), U1(e, b))
27.56/9.00	   A^2 -> H(f(e), U1(k, b))
27.56/9.00	   A^2 -> H(f(e), U1(c, d))
27.56/9.00	   A^2 -> H(f(e), U1(d, c))
27.56/9.00	   A^2 -> H(f(e), U1(b, e))
27.56/9.00	   A^2 -> H(f(e), U1(b, k))
27.56/9.00	   A^2 -> H(f(e), U1(e, c))
27.56/9.00	   A^2 -> H(f(e), U1(k, c))
27.56/9.00	   A^2 -> H(f(e), U1(c, e))
27.56/9.00	   A^2 -> H(f(e), U1(c, k))
27.56/9.00	   A^2 -> H(f(e), U1(k, k))
27.56/9.00	   A^2 -> H(f(e), U1(k, d))
27.56/9.00	   A^2 -> H(f(e), U1(d, k))
27.56/9.00	   A^2 -> H(U1(k, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(k, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(k, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(k, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(k, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(k, k), f(e))
27.56/9.00	   A^2 -> H(U1(k, k), f(k))
27.56/9.00	   A^2 -> H(U1(k, k), U1(d, d))
27.56/9.00	   A^2 -> H(f(k), U1(e, b))
27.56/9.00	   A^2 -> H(f(k), U1(k, b))
27.56/9.00	   A^2 -> H(f(k), U1(c, d))
27.56/9.00	   A^2 -> H(f(k), U1(d, c))
27.56/9.00	   A^2 -> H(f(k), U1(b, e))
27.56/9.00	   A^2 -> H(f(k), U1(b, k))
27.56/9.00	   A^2 -> H(f(k), U1(e, c))
27.56/9.00	   A^2 -> H(f(k), U1(k, c))
27.56/9.00	   A^2 -> H(f(k), U1(c, e))
27.56/9.00	   A^2 -> H(f(k), U1(c, k))
27.56/9.00	   A^2 -> H(f(k), U1(e, e))
27.56/9.00	   A^2 -> H(f(k), U1(k, d))
27.56/9.00	   A^2 -> H(f(k), U1(d, k))
27.56/9.00	   A^2 -> H(f(c), b)
27.56/9.00	   A^2 -> H(f(c), U1(e, d))
27.56/9.00	   A^2 -> H(f(c), U1(d, e))
27.56/9.00	   A^2 -> H(f(k), U1(k, k))
27.56/9.00	   A^2 -> H(U1(k, k), U1(b, b))
27.56/9.00	   A^2 -> H(U1(k, k), f(c))
27.56/9.00	   A^2 -> H(U1(k, k), f(d))
27.56/9.00	   A^2 -> H(U1(k, d), U1(c, b))
27.56/9.00	   A^2 -> H(U1(k, d), U1(d, b))
27.56/9.00	   A^2 -> H(U1(k, d), U1(b, c))
27.56/9.00	   A^2 -> H(U1(k, d), U1(b, d))
27.56/9.00	   A^2 -> H(U1(k, d), U1(c, c))
27.56/9.00	   A^2 -> H(U1(k, d), f(e))
27.56/9.00	   A^2 -> H(U1(k, d), f(k))
27.56/9.00	   A^2 -> H(U1(k, d), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(d, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(d, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(d, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(d, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(d, k), f(e))
27.56/9.00	   A^2 -> H(U1(d, k), f(k))
27.56/9.00	   A^2 -> H(U1(d, k), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, d), U1(e, b))
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, b))
27.56/9.00	   A^2 -> H(U1(d, d), U1(c, d))
27.56/9.00	   A^2 -> H(U1(d, d), U1(d, c))
27.56/9.00	   A^2 -> H(U1(d, d), U1(b, e))
27.56/9.00	   A^2 -> H(U1(d, d), U1(b, k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(e, c))
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, c))
27.56/9.00	   A^2 -> H(U1(d, d), U1(c, e))
27.56/9.00	   A^2 -> H(U1(d, d), U1(c, k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(e, e))
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, k))
27.56/9.00	   A^2 -> H(f(d), b)
27.56/9.00	   A^2 -> H(f(d), U1(e, d))
27.56/9.00	   A^2 -> H(f(d), U1(d, e))
27.56/9.00	   A^2 -> H(f(d), c)
27.56/9.00	   A^2 -> H(f(d), U1(e, k))
27.56/9.00	   A^2 -> H(f(d), U1(k, e))
27.56/9.00	   A^2 -> H(f(d), e)
27.56/9.00	   A^2 -> H(f(a), d)
27.56/9.00	   A^2 -> H(U1(c, c), U1(e, c))
27.56/9.00	   A^2 -> H(f(c), c)
27.56/9.00	   A^2 -> H(f(c), U1(e, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, c))
27.56/9.00	   A^2 -> H(f(c), U1(k, e))
27.56/9.00	   A^2 -> H(f(c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, e))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, k))
27.56/9.00	   A^2 -> H(f(a), k)
27.56/9.00	   A^2 -> H(f(e), U1(e, e))
27.56/9.00	   A^2 -> H(f(c), e)
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, d))
27.56/9.00	   A^2 -> H(f(d), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(d, k))
27.56/9.00	   A^2 -> H(d, U1(b, b))
27.56/9.00	   A^2 -> H(d, f(c))
27.56/9.00	   A^2 -> H(d, f(d))
27.56/9.00	   A^2 -> H(a, U1(c, b))
27.56/9.00	   A^2 -> H(a, U1(d, b))
27.56/9.00	   A^2 -> H(a, U1(b, c))
27.56/9.00	   A^2 -> H(a, U1(b, d))
27.56/9.00	   A^2 -> H(a, U1(c, c))
27.56/9.00	   A^2 -> H(a, f(e))
27.56/9.00	   A^2 -> H(a, f(k))
27.56/9.00	   A^2 -> H(a, U1(d, d))
27.56/9.00	   A^2 -> H(U1(e, d), U1(c, b))
27.56/9.00	   A^2 -> H(U1(e, d), U1(d, b))
27.56/9.00	   A^2 -> H(U1(e, d), U1(b, c))
27.56/9.00	   A^2 -> H(U1(e, d), U1(b, d))
27.56/9.00	   A^2 -> H(U1(e, d), U1(c, c))
27.56/9.00	   A^2 -> H(U1(e, d), f(e))
27.56/9.00	   A^2 -> H(U1(e, d), f(k))
27.56/9.00	   A^2 -> H(U1(e, d), U1(d, d))
27.56/9.00	   A^2 -> H(U1(e, a), U1(e, b))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, b))
27.56/9.00	   A^2 -> H(U1(e, a), U1(c, d))
27.56/9.00	   A^2 -> H(U1(e, a), U1(d, c))
27.56/9.00	   A^2 -> H(U1(e, a), U1(b, e))
27.56/9.00	   A^2 -> H(U1(e, a), U1(b, k))
27.56/9.00	   A^2 -> H(U1(e, a), U1(e, c))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, c))
27.56/9.00	   A^2 -> H(U1(e, a), U1(c, e))
27.56/9.00	   A^2 -> H(U1(e, a), U1(c, k))
27.56/9.00	   A^2 -> H(U1(e, a), U1(e, e))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, d))
27.56/9.00	   A^2 -> H(U1(e, a), U1(d, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(e, b))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, b))
27.56/9.00	   A^2 -> H(U1(k, a), U1(c, d))
27.56/9.00	   A^2 -> H(U1(k, a), U1(d, c))
27.56/9.00	   A^2 -> H(U1(k, a), U1(b, e))
27.56/9.00	   A^2 -> H(U1(k, a), U1(b, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(e, c))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, c))
27.56/9.00	   A^2 -> H(U1(k, a), U1(c, e))
27.56/9.00	   A^2 -> H(U1(k, a), U1(c, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(e, e))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, d))
27.56/9.00	   A^2 -> H(U1(k, a), U1(d, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(e, b))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, b))
27.56/9.00	   A^2 -> H(U1(c, d), U1(c, d))
27.56/9.00	   A^2 -> H(U1(c, d), U1(d, c))
27.56/9.00	   A^2 -> H(U1(c, d), U1(b, e))
27.56/9.00	   A^2 -> H(U1(c, d), U1(b, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(e, c))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, c))
27.56/9.00	   A^2 -> H(U1(c, d), U1(c, e))
27.56/9.00	   A^2 -> H(U1(c, d), U1(c, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(e, e))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, d))
27.56/9.00	   A^2 -> H(U1(c, d), U1(d, k))
27.56/9.00	   A^2 -> H(U1(c, a), b)
27.56/9.00	   A^2 -> H(U1(c, a), U1(e, d))
27.56/9.00	   A^2 -> H(U1(c, a), U1(d, e))
27.56/9.00	   A^2 -> H(U1(c, a), c)
27.56/9.00	   A^2 -> H(U1(c, a), U1(e, k))
27.56/9.00	   A^2 -> H(U1(c, a), U1(k, e))
27.56/9.00	   A^2 -> H(U1(c, a), e)
27.56/9.00	   A^2 -> H(U1(c, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(d, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(d, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(d, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(d, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(d, e), f(e))
27.56/9.00	   A^2 -> H(U1(d, e), f(k))
27.56/9.00	   A^2 -> H(U1(d, e), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, c), U1(e, b))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, b))
27.56/9.00	   A^2 -> H(U1(d, c), U1(c, d))
27.56/9.00	   A^2 -> H(U1(d, c), U1(d, c))
27.56/9.00	   A^2 -> H(U1(d, c), U1(b, e))
27.56/9.00	   A^2 -> H(U1(d, c), U1(b, k))
27.56/9.00	   A^2 -> H(U1(d, c), U1(e, c))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, c))
27.56/9.00	   A^2 -> H(U1(d, c), U1(c, e))
27.56/9.00	   A^2 -> H(U1(d, c), U1(c, k))
27.56/9.00	   A^2 -> H(U1(d, c), U1(e, e))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, d))
27.56/9.00	   A^2 -> H(U1(d, c), U1(d, k))
27.56/9.00	   A^2 -> H(U1(d, a), b)
27.56/9.00	   A^2 -> H(U1(d, a), U1(e, d))
27.56/9.00	   A^2 -> H(U1(d, a), U1(d, e))
27.56/9.00	   A^2 -> H(U1(d, a), c)
27.56/9.00	   A^2 -> H(U1(d, a), U1(e, k))
27.56/9.00	   A^2 -> H(U1(d, a), U1(k, e))
27.56/9.00	
27.56/9.00	The TRS R consists of the following rules:
27.56/9.00	
27.56/9.00	   f(x) -> U1(x, x)
27.56/9.00	   U1(e, x) -> x
27.56/9.00	   a -> c
27.56/9.00	   a -> d
27.56/9.00	   b -> c
27.56/9.00	   b -> d
27.56/9.00	   d -> k
27.56/9.00	   c -> e
27.56/9.00	   c -> k
27.56/9.00	
27.56/9.00	Q is empty.
27.56/9.00	We have to consider all minimal (P,Q,R)-chains.
27.56/9.00	----------------------------------------
27.56/9.00	
27.56/9.00	(673) TransformationProof (EQUIVALENT)
27.56/9.00	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
27.56/9.00	
27.56/9.00	   (A^2 -> H(U1(k, a), U1(e, e)),A^2 -> H(U1(k, a), U1(e, e)))
27.56/9.00	   (A^2 -> H(U1(d, c), U1(e, e)),A^2 -> H(U1(d, c), U1(e, e)))
27.56/9.00	   (A^2 -> H(U1(d, d), U1(e, e)),A^2 -> H(U1(d, d), U1(e, e)))
27.56/9.00	   (A^2 -> H(U1(d, a), e),A^2 -> H(U1(d, a), e))
27.56/9.00	
27.56/9.00	
27.56/9.00	----------------------------------------
27.56/9.00	
27.56/9.00	(674)
27.56/9.00	Obligation:
27.56/9.00	Q DP problem:
27.56/9.00	The TRS P consists of the following rules:
27.56/9.00	
27.56/9.00	   H(x, x) -> G(x, x, f(k))
27.56/9.00	   G(d, x, x) -> A^2
27.56/9.00	   A^2 -> H(f(c), f(c))
27.56/9.00	   A^2 -> H(f(d), f(d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, c))
27.56/9.00	   A^2 -> H(f(e), f(e))
27.56/9.00	   A^2 -> H(f(k), f(k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, a), U1(k, d))
27.56/9.00	   A^2 -> H(U1(d, a), U1(d, k))
27.56/9.00	   A^2 -> H(U1(a, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(a, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(a, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(a, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(a, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(a, e), f(e))
27.56/9.00	   A^2 -> H(U1(a, e), f(k))
27.56/9.00	   A^2 -> H(U1(a, e), U1(d, d))
27.56/9.00	   A^2 -> H(U1(a, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(a, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(a, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(a, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(a, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(a, k), f(e))
27.56/9.00	   A^2 -> H(U1(a, k), f(k))
27.56/9.00	   A^2 -> H(U1(a, k), U1(d, d))
27.56/9.00	   A^2 -> H(U1(a, c), U1(e, b))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, b))
27.56/9.00	   A^2 -> H(U1(a, c), U1(c, d))
27.56/9.00	   A^2 -> H(U1(a, c), U1(d, c))
27.56/9.00	   A^2 -> H(U1(a, c), U1(b, e))
27.56/9.00	   A^2 -> H(U1(a, c), U1(b, k))
27.56/9.00	   A^2 -> H(U1(a, c), U1(e, c))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, c))
27.56/9.00	   A^2 -> H(U1(a, c), U1(c, e))
27.56/9.00	   A^2 -> H(U1(a, c), U1(c, k))
27.56/9.00	   A^2 -> H(U1(a, c), U1(e, e))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, d))
27.56/9.00	   A^2 -> H(U1(a, c), U1(d, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(e, b))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, b))
27.56/9.00	   A^2 -> H(U1(a, d), U1(c, d))
27.56/9.00	   A^2 -> H(U1(a, d), U1(d, c))
27.56/9.00	   A^2 -> H(U1(a, d), U1(b, e))
27.56/9.00	   A^2 -> H(U1(a, d), U1(b, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(e, c))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, c))
27.56/9.00	   A^2 -> H(U1(a, d), U1(c, e))
27.56/9.00	   A^2 -> H(U1(a, d), U1(c, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(e, e))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, d))
27.56/9.00	   A^2 -> H(U1(a, d), U1(d, k))
27.56/9.00	   A^2 -> H(U1(a, a), b)
27.56/9.00	   A^2 -> H(U1(a, a), U1(e, d))
27.56/9.00	   A^2 -> H(U1(a, a), U1(d, e))
27.56/9.00	   A^2 -> H(U1(a, a), c)
27.56/9.00	   A^2 -> H(U1(a, a), U1(e, k))
27.56/9.00	   A^2 -> H(U1(a, a), U1(k, e))
27.56/9.00	   A^2 -> H(U1(a, a), e)
27.56/9.00	   A^2 -> H(U1(a, a), U1(k, k))
27.56/9.00	   A^2 -> H(k, f(b))
27.56/9.00	   A^2 -> H(c, U1(b, b))
27.56/9.00	   A^2 -> H(c, f(c))
27.56/9.00	   A^2 -> H(c, f(d))
27.56/9.00	   A^2 -> H(U1(e, k), U1(b, b))
27.56/9.00	   A^2 -> H(U1(e, k), f(c))
27.56/9.00	   A^2 -> H(U1(e, k), f(d))
27.56/9.00	   A^2 -> H(U1(e, c), U1(c, b))
27.56/9.00	   A^2 -> H(U1(e, c), U1(d, b))
27.56/9.00	   A^2 -> H(U1(e, c), U1(b, c))
27.56/9.00	   A^2 -> H(U1(e, c), U1(b, d))
27.56/9.00	   A^2 -> H(U1(e, c), U1(c, c))
27.56/9.00	   A^2 -> H(U1(e, c), f(e))
27.56/9.00	   A^2 -> H(U1(e, c), f(k))
27.56/9.00	   A^2 -> H(U1(e, c), U1(d, d))
27.56/9.00	   A^2 -> H(U1(k, e), U1(b, b))
27.56/9.00	   A^2 -> H(U1(k, e), f(c))
27.56/9.00	   A^2 -> H(U1(k, e), f(d))
27.56/9.00	   A^2 -> H(U1(k, c), U1(c, b))
27.56/9.00	   A^2 -> H(U1(k, c), U1(d, b))
27.56/9.00	   A^2 -> H(U1(k, c), U1(b, c))
27.56/9.00	   A^2 -> H(U1(k, c), U1(b, d))
27.56/9.00	   A^2 -> H(U1(k, c), U1(c, c))
27.56/9.00	   A^2 -> H(U1(k, c), f(e))
27.56/9.00	   A^2 -> H(U1(k, c), f(k))
27.56/9.00	   A^2 -> H(U1(k, c), U1(d, d))
27.56/9.00	   A^2 -> H(U1(c, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(c, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(c, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(c, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(c, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(c, e), f(e))
27.56/9.00	   A^2 -> H(U1(c, e), f(k))
27.56/9.00	   A^2 -> H(U1(c, e), U1(d, d))
27.56/9.00	   A^2 -> H(U1(c, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(c, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(c, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(c, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(c, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(c, k), f(e))
27.56/9.00	   A^2 -> H(U1(c, k), f(k))
27.56/9.00	   A^2 -> H(U1(c, k), U1(d, d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(e, b))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, b))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(d, c))
27.56/9.00	   A^2 -> H(U1(c, c), U1(b, e))
27.56/9.00	   A^2 -> H(U1(c, c), U1(b, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(e, e))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(d, k))
27.56/9.00	   A^2 -> H(e, U1(b, b))
27.56/9.00	   A^2 -> H(e, f(c))
27.56/9.00	   A^2 -> H(e, f(d))
27.56/9.00	   A^2 -> H(U1(e, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(e, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(e, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(e, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(e, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(e, e), f(e))
27.56/9.00	   A^2 -> H(U1(e, e), f(k))
27.56/9.00	   A^2 -> H(U1(e, e), U1(d, d))
27.56/9.00	   A^2 -> H(f(e), U1(e, b))
27.56/9.00	   A^2 -> H(f(e), U1(k, b))
27.56/9.00	   A^2 -> H(f(e), U1(c, d))
27.56/9.00	   A^2 -> H(f(e), U1(d, c))
27.56/9.00	   A^2 -> H(f(e), U1(b, e))
27.56/9.00	   A^2 -> H(f(e), U1(b, k))
27.56/9.00	   A^2 -> H(f(e), U1(e, c))
27.56/9.00	   A^2 -> H(f(e), U1(k, c))
27.56/9.00	   A^2 -> H(f(e), U1(c, e))
27.56/9.00	   A^2 -> H(f(e), U1(c, k))
27.56/9.00	   A^2 -> H(f(e), U1(k, k))
27.56/9.00	   A^2 -> H(f(e), U1(k, d))
27.56/9.00	   A^2 -> H(f(e), U1(d, k))
27.56/9.00	   A^2 -> H(U1(k, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(k, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(k, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(k, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(k, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(k, k), f(e))
27.56/9.00	   A^2 -> H(U1(k, k), f(k))
27.56/9.00	   A^2 -> H(U1(k, k), U1(d, d))
27.56/9.00	   A^2 -> H(f(k), U1(e, b))
27.56/9.00	   A^2 -> H(f(k), U1(k, b))
27.56/9.00	   A^2 -> H(f(k), U1(c, d))
27.56/9.00	   A^2 -> H(f(k), U1(d, c))
27.56/9.00	   A^2 -> H(f(k), U1(b, e))
27.56/9.00	   A^2 -> H(f(k), U1(b, k))
27.56/9.00	   A^2 -> H(f(k), U1(e, c))
27.56/9.00	   A^2 -> H(f(k), U1(k, c))
27.56/9.00	   A^2 -> H(f(k), U1(c, e))
27.56/9.00	   A^2 -> H(f(k), U1(c, k))
27.56/9.00	   A^2 -> H(f(k), U1(e, e))
27.56/9.00	   A^2 -> H(f(k), U1(k, d))
27.56/9.00	   A^2 -> H(f(k), U1(d, k))
27.56/9.00	   A^2 -> H(f(c), b)
27.56/9.00	   A^2 -> H(f(c), U1(e, d))
27.56/9.00	   A^2 -> H(f(c), U1(d, e))
27.56/9.00	   A^2 -> H(f(k), U1(k, k))
27.56/9.00	   A^2 -> H(U1(k, k), U1(b, b))
27.56/9.00	   A^2 -> H(U1(k, k), f(c))
27.56/9.00	   A^2 -> H(U1(k, k), f(d))
27.56/9.00	   A^2 -> H(U1(k, d), U1(c, b))
27.56/9.00	   A^2 -> H(U1(k, d), U1(d, b))
27.56/9.00	   A^2 -> H(U1(k, d), U1(b, c))
27.56/9.00	   A^2 -> H(U1(k, d), U1(b, d))
27.56/9.00	   A^2 -> H(U1(k, d), U1(c, c))
27.56/9.00	   A^2 -> H(U1(k, d), f(e))
27.56/9.00	   A^2 -> H(U1(k, d), f(k))
27.56/9.00	   A^2 -> H(U1(k, d), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(d, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(d, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(d, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(d, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(d, k), f(e))
27.56/9.00	   A^2 -> H(U1(d, k), f(k))
27.56/9.00	   A^2 -> H(U1(d, k), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, d), U1(e, b))
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, b))
27.56/9.00	   A^2 -> H(U1(d, d), U1(c, d))
27.56/9.00	   A^2 -> H(U1(d, d), U1(d, c))
27.56/9.00	   A^2 -> H(U1(d, d), U1(b, e))
27.56/9.00	   A^2 -> H(U1(d, d), U1(b, k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(e, c))
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, c))
27.56/9.00	   A^2 -> H(U1(d, d), U1(c, e))
27.56/9.00	   A^2 -> H(U1(d, d), U1(c, k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(e, e))
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, k))
27.56/9.00	   A^2 -> H(f(d), b)
27.56/9.00	   A^2 -> H(f(d), U1(e, d))
27.56/9.00	   A^2 -> H(f(d), U1(d, e))
27.56/9.00	   A^2 -> H(f(d), c)
27.56/9.00	   A^2 -> H(f(d), U1(e, k))
27.56/9.00	   A^2 -> H(f(d), U1(k, e))
27.56/9.00	   A^2 -> H(f(d), e)
27.56/9.00	   A^2 -> H(f(a), d)
27.56/9.00	   A^2 -> H(U1(c, c), U1(e, c))
27.56/9.00	   A^2 -> H(f(c), c)
27.56/9.00	   A^2 -> H(f(c), U1(e, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, c))
27.56/9.00	   A^2 -> H(f(c), U1(k, e))
27.56/9.00	   A^2 -> H(f(c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, e))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, k))
27.56/9.00	   A^2 -> H(f(a), k)
27.56/9.00	   A^2 -> H(f(e), U1(e, e))
27.56/9.00	   A^2 -> H(f(c), e)
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, d))
27.56/9.00	   A^2 -> H(f(d), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(d, k))
27.56/9.00	   A^2 -> H(d, U1(b, b))
27.56/9.00	   A^2 -> H(d, f(c))
27.56/9.00	   A^2 -> H(d, f(d))
27.56/9.00	   A^2 -> H(a, U1(c, b))
27.56/9.00	   A^2 -> H(a, U1(d, b))
27.56/9.00	   A^2 -> H(a, U1(b, c))
27.56/9.00	   A^2 -> H(a, U1(b, d))
27.56/9.00	   A^2 -> H(a, U1(c, c))
27.56/9.00	   A^2 -> H(a, f(e))
27.56/9.00	   A^2 -> H(a, f(k))
27.56/9.00	   A^2 -> H(a, U1(d, d))
27.56/9.00	   A^2 -> H(U1(e, d), U1(c, b))
27.56/9.00	   A^2 -> H(U1(e, d), U1(d, b))
27.56/9.00	   A^2 -> H(U1(e, d), U1(b, c))
27.56/9.00	   A^2 -> H(U1(e, d), U1(b, d))
27.56/9.00	   A^2 -> H(U1(e, d), U1(c, c))
27.56/9.00	   A^2 -> H(U1(e, d), f(e))
27.56/9.00	   A^2 -> H(U1(e, d), f(k))
27.56/9.00	   A^2 -> H(U1(e, d), U1(d, d))
27.56/9.00	   A^2 -> H(U1(e, a), U1(e, b))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, b))
27.56/9.00	   A^2 -> H(U1(e, a), U1(c, d))
27.56/9.00	   A^2 -> H(U1(e, a), U1(d, c))
27.56/9.00	   A^2 -> H(U1(e, a), U1(b, e))
27.56/9.00	   A^2 -> H(U1(e, a), U1(b, k))
27.56/9.00	   A^2 -> H(U1(e, a), U1(e, c))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, c))
27.56/9.00	   A^2 -> H(U1(e, a), U1(c, e))
27.56/9.00	   A^2 -> H(U1(e, a), U1(c, k))
27.56/9.00	   A^2 -> H(U1(e, a), U1(e, e))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, d))
27.56/9.00	   A^2 -> H(U1(e, a), U1(d, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(e, b))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, b))
27.56/9.00	   A^2 -> H(U1(k, a), U1(c, d))
27.56/9.00	   A^2 -> H(U1(k, a), U1(d, c))
27.56/9.00	   A^2 -> H(U1(k, a), U1(b, e))
27.56/9.00	   A^2 -> H(U1(k, a), U1(b, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(e, c))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, c))
27.56/9.00	   A^2 -> H(U1(k, a), U1(c, e))
27.56/9.00	   A^2 -> H(U1(k, a), U1(c, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(e, e))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(k, a), U1(k, d))
27.56/9.00	   A^2 -> H(U1(k, a), U1(d, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(e, b))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, b))
27.56/9.00	   A^2 -> H(U1(c, d), U1(c, d))
27.56/9.00	   A^2 -> H(U1(c, d), U1(d, c))
27.56/9.00	   A^2 -> H(U1(c, d), U1(b, e))
27.56/9.00	   A^2 -> H(U1(c, d), U1(b, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(e, c))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, c))
27.56/9.00	   A^2 -> H(U1(c, d), U1(c, e))
27.56/9.00	   A^2 -> H(U1(c, d), U1(c, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(e, e))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, k))
27.56/9.00	   A^2 -> H(U1(c, d), U1(k, d))
27.56/9.00	   A^2 -> H(U1(c, d), U1(d, k))
27.56/9.00	   A^2 -> H(U1(c, a), b)
27.56/9.00	   A^2 -> H(U1(c, a), U1(e, d))
27.56/9.00	   A^2 -> H(U1(c, a), U1(d, e))
27.56/9.00	   A^2 -> H(U1(c, a), c)
27.56/9.00	   A^2 -> H(U1(c, a), U1(e, k))
27.56/9.00	   A^2 -> H(U1(c, a), U1(k, e))
27.56/9.00	   A^2 -> H(U1(c, a), e)
27.56/9.00	   A^2 -> H(U1(c, a), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(d, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(d, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(d, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(d, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(d, e), f(e))
27.56/9.00	   A^2 -> H(U1(d, e), f(k))
27.56/9.00	   A^2 -> H(U1(d, e), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, c), U1(e, b))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, b))
27.56/9.00	   A^2 -> H(U1(d, c), U1(c, d))
27.56/9.00	   A^2 -> H(U1(d, c), U1(d, c))
27.56/9.00	   A^2 -> H(U1(d, c), U1(b, e))
27.56/9.00	   A^2 -> H(U1(d, c), U1(b, k))
27.56/9.00	   A^2 -> H(U1(d, c), U1(e, c))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, c))
27.56/9.00	   A^2 -> H(U1(d, c), U1(c, e))
27.56/9.00	   A^2 -> H(U1(d, c), U1(c, k))
27.56/9.00	   A^2 -> H(U1(d, c), U1(e, e))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, c), U1(k, d))
27.56/9.00	   A^2 -> H(U1(d, c), U1(d, k))
27.56/9.00	   A^2 -> H(U1(d, a), b)
27.56/9.00	   A^2 -> H(U1(d, a), U1(e, d))
27.56/9.00	   A^2 -> H(U1(d, a), U1(d, e))
27.56/9.00	   A^2 -> H(U1(d, a), c)
27.56/9.00	   A^2 -> H(U1(d, a), U1(e, k))
27.56/9.00	   A^2 -> H(U1(d, a), U1(k, e))
27.56/9.00	   A^2 -> H(U1(d, a), e)
27.56/9.00	
27.56/9.00	The TRS R consists of the following rules:
27.56/9.00	
27.56/9.00	   f(x) -> U1(x, x)
27.56/9.00	   U1(e, x) -> x
27.56/9.00	   a -> c
27.56/9.00	   a -> d
27.56/9.00	   b -> c
27.56/9.00	   b -> d
27.56/9.00	   d -> k
27.56/9.00	   c -> e
27.56/9.00	   c -> k
27.56/9.00	
27.56/9.00	Q is empty.
27.56/9.00	We have to consider all minimal (P,Q,R)-chains.
27.56/9.00	----------------------------------------
27.56/9.00	
27.56/9.00	(675) TransformationProof (EQUIVALENT)
27.56/9.00	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
27.56/9.00	
27.56/9.00	   (A^2 -> H(U1(k, a), U1(k, k)),A^2 -> H(U1(k, a), U1(k, k)))
27.56/9.00	   (A^2 -> H(U1(d, c), U1(k, k)),A^2 -> H(U1(d, c), U1(k, k)))
27.56/9.00	   (A^2 -> H(U1(d, d), U1(k, k)),A^2 -> H(U1(d, d), U1(k, k)))
27.56/9.00	
27.56/9.00	
27.56/9.00	----------------------------------------
27.56/9.00	
27.56/9.00	(676)
27.56/9.00	Obligation:
27.56/9.00	Q DP problem:
27.56/9.00	The TRS P consists of the following rules:
27.56/9.00	
27.56/9.00	   H(x, x) -> G(x, x, f(k))
27.56/9.00	   G(d, x, x) -> A^2
27.56/9.00	   A^2 -> H(f(c), f(c))
27.56/9.00	   A^2 -> H(f(d), f(d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, c))
27.56/9.00	   A^2 -> H(f(e), f(e))
27.56/9.00	   A^2 -> H(f(k), f(k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, a), U1(k, d))
27.56/9.00	   A^2 -> H(U1(d, a), U1(d, k))
27.56/9.00	   A^2 -> H(U1(a, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(a, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(a, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(a, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(a, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(a, e), f(e))
27.56/9.00	   A^2 -> H(U1(a, e), f(k))
27.56/9.00	   A^2 -> H(U1(a, e), U1(d, d))
27.56/9.00	   A^2 -> H(U1(a, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(a, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(a, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(a, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(a, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(a, k), f(e))
27.56/9.00	   A^2 -> H(U1(a, k), f(k))
27.56/9.00	   A^2 -> H(U1(a, k), U1(d, d))
27.56/9.00	   A^2 -> H(U1(a, c), U1(e, b))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, b))
27.56/9.00	   A^2 -> H(U1(a, c), U1(c, d))
27.56/9.00	   A^2 -> H(U1(a, c), U1(d, c))
27.56/9.00	   A^2 -> H(U1(a, c), U1(b, e))
27.56/9.00	   A^2 -> H(U1(a, c), U1(b, k))
27.56/9.00	   A^2 -> H(U1(a, c), U1(e, c))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, c))
27.56/9.00	   A^2 -> H(U1(a, c), U1(c, e))
27.56/9.00	   A^2 -> H(U1(a, c), U1(c, k))
27.56/9.00	   A^2 -> H(U1(a, c), U1(e, e))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(a, c), U1(k, d))
27.56/9.00	   A^2 -> H(U1(a, c), U1(d, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(e, b))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, b))
27.56/9.00	   A^2 -> H(U1(a, d), U1(c, d))
27.56/9.00	   A^2 -> H(U1(a, d), U1(d, c))
27.56/9.00	   A^2 -> H(U1(a, d), U1(b, e))
27.56/9.00	   A^2 -> H(U1(a, d), U1(b, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(e, c))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, c))
27.56/9.00	   A^2 -> H(U1(a, d), U1(c, e))
27.56/9.00	   A^2 -> H(U1(a, d), U1(c, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(e, e))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, k))
27.56/9.00	   A^2 -> H(U1(a, d), U1(k, d))
27.56/9.00	   A^2 -> H(U1(a, d), U1(d, k))
27.56/9.00	   A^2 -> H(U1(a, a), b)
27.56/9.00	   A^2 -> H(U1(a, a), U1(e, d))
27.56/9.00	   A^2 -> H(U1(a, a), U1(d, e))
27.56/9.00	   A^2 -> H(U1(a, a), c)
27.56/9.00	   A^2 -> H(U1(a, a), U1(e, k))
27.56/9.00	   A^2 -> H(U1(a, a), U1(k, e))
27.56/9.00	   A^2 -> H(U1(a, a), e)
27.56/9.00	   A^2 -> H(U1(a, a), U1(k, k))
27.56/9.00	   A^2 -> H(k, f(b))
27.56/9.00	   A^2 -> H(c, U1(b, b))
27.56/9.00	   A^2 -> H(c, f(c))
27.56/9.00	   A^2 -> H(c, f(d))
27.56/9.00	   A^2 -> H(U1(e, k), U1(b, b))
27.56/9.00	   A^2 -> H(U1(e, k), f(c))
27.56/9.00	   A^2 -> H(U1(e, k), f(d))
27.56/9.00	   A^2 -> H(U1(e, c), U1(c, b))
27.56/9.00	   A^2 -> H(U1(e, c), U1(d, b))
27.56/9.00	   A^2 -> H(U1(e, c), U1(b, c))
27.56/9.00	   A^2 -> H(U1(e, c), U1(b, d))
27.56/9.00	   A^2 -> H(U1(e, c), U1(c, c))
27.56/9.00	   A^2 -> H(U1(e, c), f(e))
27.56/9.00	   A^2 -> H(U1(e, c), f(k))
27.56/9.00	   A^2 -> H(U1(e, c), U1(d, d))
27.56/9.00	   A^2 -> H(U1(k, e), U1(b, b))
27.56/9.00	   A^2 -> H(U1(k, e), f(c))
27.56/9.00	   A^2 -> H(U1(k, e), f(d))
27.56/9.00	   A^2 -> H(U1(k, c), U1(c, b))
27.56/9.00	   A^2 -> H(U1(k, c), U1(d, b))
27.56/9.00	   A^2 -> H(U1(k, c), U1(b, c))
27.56/9.00	   A^2 -> H(U1(k, c), U1(b, d))
27.56/9.00	   A^2 -> H(U1(k, c), U1(c, c))
27.56/9.00	   A^2 -> H(U1(k, c), f(e))
27.56/9.00	   A^2 -> H(U1(k, c), f(k))
27.56/9.00	   A^2 -> H(U1(k, c), U1(d, d))
27.56/9.00	   A^2 -> H(U1(c, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(c, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(c, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(c, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(c, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(c, e), f(e))
27.56/9.00	   A^2 -> H(U1(c, e), f(k))
27.56/9.00	   A^2 -> H(U1(c, e), U1(d, d))
27.56/9.00	   A^2 -> H(U1(c, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(c, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(c, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(c, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(c, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(c, k), f(e))
27.56/9.00	   A^2 -> H(U1(c, k), f(k))
27.56/9.00	   A^2 -> H(U1(c, k), U1(d, d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(e, b))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, b))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(d, c))
27.56/9.00	   A^2 -> H(U1(c, c), U1(b, e))
27.56/9.00	   A^2 -> H(U1(c, c), U1(b, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(e, e))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, d))
27.56/9.00	   A^2 -> H(U1(c, c), U1(d, k))
27.56/9.00	   A^2 -> H(e, U1(b, b))
27.56/9.00	   A^2 -> H(e, f(c))
27.56/9.00	   A^2 -> H(e, f(d))
27.56/9.00	   A^2 -> H(U1(e, e), U1(c, b))
27.56/9.00	   A^2 -> H(U1(e, e), U1(d, b))
27.56/9.00	   A^2 -> H(U1(e, e), U1(b, c))
27.56/9.00	   A^2 -> H(U1(e, e), U1(b, d))
27.56/9.00	   A^2 -> H(U1(e, e), U1(c, c))
27.56/9.00	   A^2 -> H(U1(e, e), f(e))
27.56/9.00	   A^2 -> H(U1(e, e), f(k))
27.56/9.00	   A^2 -> H(U1(e, e), U1(d, d))
27.56/9.00	   A^2 -> H(f(e), U1(e, b))
27.56/9.00	   A^2 -> H(f(e), U1(k, b))
27.56/9.00	   A^2 -> H(f(e), U1(c, d))
27.56/9.00	   A^2 -> H(f(e), U1(d, c))
27.56/9.00	   A^2 -> H(f(e), U1(b, e))
27.56/9.00	   A^2 -> H(f(e), U1(b, k))
27.56/9.00	   A^2 -> H(f(e), U1(e, c))
27.56/9.00	   A^2 -> H(f(e), U1(k, c))
27.56/9.00	   A^2 -> H(f(e), U1(c, e))
27.56/9.00	   A^2 -> H(f(e), U1(c, k))
27.56/9.00	   A^2 -> H(f(e), U1(k, k))
27.56/9.00	   A^2 -> H(f(e), U1(k, d))
27.56/9.00	   A^2 -> H(f(e), U1(d, k))
27.56/9.00	   A^2 -> H(U1(k, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(k, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(k, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(k, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(k, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(k, k), f(e))
27.56/9.00	   A^2 -> H(U1(k, k), f(k))
27.56/9.00	   A^2 -> H(U1(k, k), U1(d, d))
27.56/9.00	   A^2 -> H(f(k), U1(e, b))
27.56/9.00	   A^2 -> H(f(k), U1(k, b))
27.56/9.00	   A^2 -> H(f(k), U1(c, d))
27.56/9.00	   A^2 -> H(f(k), U1(d, c))
27.56/9.00	   A^2 -> H(f(k), U1(b, e))
27.56/9.00	   A^2 -> H(f(k), U1(b, k))
27.56/9.00	   A^2 -> H(f(k), U1(e, c))
27.56/9.00	   A^2 -> H(f(k), U1(k, c))
27.56/9.00	   A^2 -> H(f(k), U1(c, e))
27.56/9.00	   A^2 -> H(f(k), U1(c, k))
27.56/9.00	   A^2 -> H(f(k), U1(e, e))
27.56/9.00	   A^2 -> H(f(k), U1(k, d))
27.56/9.00	   A^2 -> H(f(k), U1(d, k))
27.56/9.00	   A^2 -> H(f(c), b)
27.56/9.00	   A^2 -> H(f(c), U1(e, d))
27.56/9.00	   A^2 -> H(f(c), U1(d, e))
27.56/9.00	   A^2 -> H(f(k), U1(k, k))
27.56/9.00	   A^2 -> H(U1(k, k), U1(b, b))
27.56/9.00	   A^2 -> H(U1(k, k), f(c))
27.56/9.00	   A^2 -> H(U1(k, k), f(d))
27.56/9.00	   A^2 -> H(U1(k, d), U1(c, b))
27.56/9.00	   A^2 -> H(U1(k, d), U1(d, b))
27.56/9.00	   A^2 -> H(U1(k, d), U1(b, c))
27.56/9.00	   A^2 -> H(U1(k, d), U1(b, d))
27.56/9.00	   A^2 -> H(U1(k, d), U1(c, c))
27.56/9.00	   A^2 -> H(U1(k, d), f(e))
27.56/9.00	   A^2 -> H(U1(k, d), f(k))
27.56/9.00	   A^2 -> H(U1(k, d), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, k), U1(c, b))
27.56/9.00	   A^2 -> H(U1(d, k), U1(d, b))
27.56/9.00	   A^2 -> H(U1(d, k), U1(b, c))
27.56/9.00	   A^2 -> H(U1(d, k), U1(b, d))
27.56/9.00	   A^2 -> H(U1(d, k), U1(c, c))
27.56/9.00	   A^2 -> H(U1(d, k), f(e))
27.56/9.00	   A^2 -> H(U1(d, k), f(k))
27.56/9.00	   A^2 -> H(U1(d, k), U1(d, d))
27.56/9.00	   A^2 -> H(U1(d, d), U1(e, b))
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, b))
27.56/9.00	   A^2 -> H(U1(d, d), U1(c, d))
27.56/9.00	   A^2 -> H(U1(d, d), U1(d, c))
27.56/9.00	   A^2 -> H(U1(d, d), U1(b, e))
27.56/9.00	   A^2 -> H(U1(d, d), U1(b, k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(e, c))
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, c))
27.56/9.00	   A^2 -> H(U1(d, d), U1(c, e))
27.56/9.00	   A^2 -> H(U1(d, d), U1(c, k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(e, e))
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, k))
27.56/9.00	   A^2 -> H(f(d), b)
27.56/9.00	   A^2 -> H(f(d), U1(e, d))
27.56/9.00	   A^2 -> H(f(d), U1(d, e))
27.56/9.00	   A^2 -> H(f(d), c)
27.56/9.00	   A^2 -> H(f(d), U1(e, k))
27.56/9.00	   A^2 -> H(f(d), U1(k, e))
27.56/9.00	   A^2 -> H(f(d), e)
27.56/9.00	   A^2 -> H(f(a), d)
27.56/9.00	   A^2 -> H(U1(c, c), U1(e, c))
27.56/9.00	   A^2 -> H(f(c), c)
27.56/9.00	   A^2 -> H(f(c), U1(e, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(k, c))
27.56/9.00	   A^2 -> H(f(c), U1(k, e))
27.56/9.00	   A^2 -> H(f(c), U1(k, k))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, e))
27.56/9.00	   A^2 -> H(U1(c, c), U1(c, k))
27.56/9.00	   A^2 -> H(f(a), k)
27.56/9.00	   A^2 -> H(f(e), U1(e, e))
27.56/9.00	   A^2 -> H(f(c), e)
27.56/9.00	   A^2 -> H(U1(d, d), U1(k, d))
27.56/9.00	   A^2 -> H(f(d), U1(k, k))
27.56/9.00	   A^2 -> H(U1(d, d), U1(d, k))
27.56/9.00	   A^2 -> H(d, U1(b, b))
27.56/9.00	   A^2 -> H(d, f(c))
27.56/9.00	   A^2 -> H(d, f(d))
27.56/9.00	   A^2 -> H(a, U1(c, b))
27.56/9.00	   A^2 -> H(a, U1(d, b))
27.56/9.00	   A^2 -> H(a, U1(b, c))
27.56/9.00	   A^2 -> H(a, U1(b, d))
27.56/9.00	   A^2 -> H(a, U1(c, c))
27.56/9.00	   A^2 -> H(a, f(e))
27.56/9.00	   A^2 -> H(a, f(k))
27.56/9.00	   A^2 -> H(a, U1(d, d))
27.56/9.00	   A^2 -> H(U1(e, d), U1(c, b))
27.56/9.00	   A^2 -> H(U1(e, d), U1(d, b))
27.56/9.00	   A^2 -> H(U1(e, d), U1(b, c))
27.56/9.00	   A^2 -> H(U1(e, d), U1(b, d))
27.56/9.00	   A^2 -> H(U1(e, d), U1(c, c))
27.56/9.00	   A^2 -> H(U1(e, d), f(e))
27.56/9.00	   A^2 -> H(U1(e, d), f(k))
27.56/9.00	   A^2 -> H(U1(e, d), U1(d, d))
27.56/9.00	   A^2 -> H(U1(e, a), U1(e, b))
27.56/9.00	   A^2 -> H(U1(e, a), U1(k, b))
27.56/9.00	   A^2 -> H(U1(e, a), U1(c, d))
27.56/9.00	   A^2 -> H(U1(e, a), U1(d, c))
27.56/9.01	   A^2 -> H(U1(e, a), U1(b, e))
27.56/9.01	   A^2 -> H(U1(e, a), U1(b, k))
27.56/9.01	   A^2 -> H(U1(e, a), U1(e, c))
27.56/9.01	   A^2 -> H(U1(e, a), U1(k, c))
27.56/9.01	   A^2 -> H(U1(e, a), U1(c, e))
27.56/9.01	   A^2 -> H(U1(e, a), U1(c, k))
27.56/9.01	   A^2 -> H(U1(e, a), U1(e, e))
27.56/9.01	   A^2 -> H(U1(e, a), U1(k, k))
27.56/9.01	   A^2 -> H(U1(e, a), U1(k, d))
27.56/9.01	   A^2 -> H(U1(e, a), U1(d, k))
27.56/9.01	   A^2 -> H(U1(k, a), U1(e, b))
27.56/9.01	   A^2 -> H(U1(k, a), U1(k, b))
27.56/9.01	   A^2 -> H(U1(k, a), U1(c, d))
27.56/9.01	   A^2 -> H(U1(k, a), U1(d, c))
27.56/9.01	   A^2 -> H(U1(k, a), U1(b, e))
27.56/9.01	   A^2 -> H(U1(k, a), U1(b, k))
27.56/9.01	   A^2 -> H(U1(k, a), U1(e, c))
27.56/9.01	   A^2 -> H(U1(k, a), U1(k, c))
27.56/9.01	   A^2 -> H(U1(k, a), U1(c, e))
27.56/9.01	   A^2 -> H(U1(k, a), U1(c, k))
27.56/9.01	   A^2 -> H(U1(k, a), U1(e, e))
27.56/9.01	   A^2 -> H(U1(k, a), U1(k, k))
27.56/9.01	   A^2 -> H(U1(k, a), U1(k, d))
27.56/9.01	   A^2 -> H(U1(k, a), U1(d, k))
27.56/9.01	   A^2 -> H(U1(c, d), U1(e, b))
27.56/9.01	   A^2 -> H(U1(c, d), U1(k, b))
27.56/9.01	   A^2 -> H(U1(c, d), U1(c, d))
27.56/9.01	   A^2 -> H(U1(c, d), U1(d, c))
27.56/9.01	   A^2 -> H(U1(c, d), U1(b, e))
27.56/9.01	   A^2 -> H(U1(c, d), U1(b, k))
27.56/9.01	   A^2 -> H(U1(c, d), U1(e, c))
27.56/9.01	   A^2 -> H(U1(c, d), U1(k, c))
27.56/9.01	   A^2 -> H(U1(c, d), U1(c, e))
27.56/9.01	   A^2 -> H(U1(c, d), U1(c, k))
27.56/9.01	   A^2 -> H(U1(c, d), U1(e, e))
27.56/9.01	   A^2 -> H(U1(c, d), U1(k, k))
27.56/9.01	   A^2 -> H(U1(c, d), U1(k, d))
27.56/9.01	   A^2 -> H(U1(c, d), U1(d, k))
27.56/9.01	   A^2 -> H(U1(c, a), b)
27.56/9.01	   A^2 -> H(U1(c, a), U1(e, d))
27.56/9.01	   A^2 -> H(U1(c, a), U1(d, e))
27.56/9.01	   A^2 -> H(U1(c, a), c)
27.56/9.01	   A^2 -> H(U1(c, a), U1(e, k))
27.56/9.01	   A^2 -> H(U1(c, a), U1(k, e))
27.56/9.01	   A^2 -> H(U1(c, a), e)
27.56/9.01	   A^2 -> H(U1(c, a), U1(k, k))
27.56/9.01	   A^2 -> H(U1(d, e), U1(c, b))
27.56/9.01	   A^2 -> H(U1(d, e), U1(d, b))
27.56/9.01	   A^2 -> H(U1(d, e), U1(b, c))
27.56/9.01	   A^2 -> H(U1(d, e), U1(b, d))
27.56/9.01	   A^2 -> H(U1(d, e), U1(c, c))
27.56/9.01	   A^2 -> H(U1(d, e), f(e))
27.56/9.01	   A^2 -> H(U1(d, e), f(k))
27.56/9.01	   A^2 -> H(U1(d, e), U1(d, d))
27.56/9.01	   A^2 -> H(U1(d, c), U1(e, b))
27.56/9.01	   A^2 -> H(U1(d, c), U1(k, b))
27.56/9.01	   A^2 -> H(U1(d, c), U1(c, d))
27.56/9.01	   A^2 -> H(U1(d, c), U1(d, c))
27.56/9.01	   A^2 -> H(U1(d, c), U1(b, e))
27.56/9.01	   A^2 -> H(U1(d, c), U1(b, k))
27.56/9.01	   A^2 -> H(U1(d, c), U1(e, c))
27.56/9.01	   A^2 -> H(U1(d, c), U1(k, c))
27.56/9.01	   A^2 -> H(U1(d, c), U1(c, e))
27.56/9.01	   A^2 -> H(U1(d, c), U1(c, k))
27.56/9.01	   A^2 -> H(U1(d, c), U1(e, e))
27.56/9.01	   A^2 -> H(U1(d, c), U1(k, k))
27.56/9.01	   A^2 -> H(U1(d, c), U1(k, d))
27.56/9.01	   A^2 -> H(U1(d, c), U1(d, k))
27.56/9.01	   A^2 -> H(U1(d, a), b)
27.56/9.01	   A^2 -> H(U1(d, a), U1(e, d))
27.56/9.01	   A^2 -> H(U1(d, a), U1(d, e))
27.56/9.01	   A^2 -> H(U1(d, a), c)
27.56/9.01	   A^2 -> H(U1(d, a), U1(e, k))
27.56/9.01	   A^2 -> H(U1(d, a), U1(k, e))
27.56/9.01	   A^2 -> H(U1(d, a), e)
27.56/9.01	
27.56/9.01	The TRS R consists of the following rules:
27.56/9.01	
27.56/9.01	   f(x) -> U1(x, x)
27.56/9.01	   U1(e, x) -> x
27.56/9.01	   a -> c
27.56/9.01	   a -> d
27.56/9.01	   b -> c
27.56/9.01	   b -> d
27.56/9.01	   d -> k
27.56/9.01	   c -> e
27.56/9.01	   c -> k
27.56/9.01	
27.56/9.01	Q is empty.
27.56/9.01	We have to consider all minimal (P,Q,R)-chains.
27.56/9.01	----------------------------------------
27.56/9.01	
27.56/9.01	(677) TransformationProof (EQUIVALENT)
27.56/9.01	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
27.56/9.01	
27.56/9.01	   (A^2 -> H(U1(k, a), U1(k, d)),A^2 -> H(U1(k, a), U1(k, d)))
27.56/9.01	   (A^2 -> H(U1(d, c), U1(k, d)),A^2 -> H(U1(d, c), U1(k, d)))
27.56/9.01	   (A^2 -> H(U1(d, d), U1(k, d)),A^2 -> H(U1(d, d), U1(k, d)))
27.56/9.01	   (A^2 -> H(U1(d, a), U1(k, k)),A^2 -> H(U1(d, a), U1(k, k)))
27.56/9.01	
27.56/9.01	
27.56/9.01	----------------------------------------
27.56/9.01	
27.56/9.01	(678)
27.56/9.01	Obligation:
27.56/9.01	Q DP problem:
27.56/9.01	The TRS P consists of the following rules:
27.56/9.01	
27.56/9.01	   H(x, x) -> G(x, x, f(k))
27.56/9.01	   G(d, x, x) -> A^2
27.56/9.01	   A^2 -> H(f(c), f(c))
27.56/9.01	   A^2 -> H(f(d), f(d))
27.56/9.01	   A^2 -> H(U1(c, c), U1(c, c))
27.56/9.01	   A^2 -> H(f(e), f(e))
27.56/9.01	   A^2 -> H(f(k), f(k))
27.56/9.01	   A^2 -> H(U1(d, d), U1(d, d))
27.56/9.01	   A^2 -> H(U1(d, a), U1(d, k))
27.56/9.01	   A^2 -> H(U1(a, e), U1(c, b))
27.56/9.01	   A^2 -> H(U1(a, e), U1(d, b))
27.56/9.01	   A^2 -> H(U1(a, e), U1(b, c))
27.56/9.01	   A^2 -> H(U1(a, e), U1(b, d))
27.56/9.01	   A^2 -> H(U1(a, e), U1(c, c))
27.56/9.01	   A^2 -> H(U1(a, e), f(e))
27.56/9.01	   A^2 -> H(U1(a, e), f(k))
27.56/9.01	   A^2 -> H(U1(a, e), U1(d, d))
27.56/9.01	   A^2 -> H(U1(a, k), U1(c, b))
27.56/9.01	   A^2 -> H(U1(a, k), U1(d, b))
27.56/9.01	   A^2 -> H(U1(a, k), U1(b, c))
27.56/9.01	   A^2 -> H(U1(a, k), U1(b, d))
27.56/9.01	   A^2 -> H(U1(a, k), U1(c, c))
27.56/9.01	   A^2 -> H(U1(a, k), f(e))
27.56/9.01	   A^2 -> H(U1(a, k), f(k))
27.56/9.01	   A^2 -> H(U1(a, k), U1(d, d))
27.56/9.01	   A^2 -> H(U1(a, c), U1(e, b))
27.56/9.01	   A^2 -> H(U1(a, c), U1(k, b))
27.56/9.01	   A^2 -> H(U1(a, c), U1(c, d))
27.56/9.01	   A^2 -> H(U1(a, c), U1(d, c))
27.56/9.01	   A^2 -> H(U1(a, c), U1(b, e))
27.56/9.01	   A^2 -> H(U1(a, c), U1(b, k))
27.56/9.01	   A^2 -> H(U1(a, c), U1(e, c))
27.56/9.01	   A^2 -> H(U1(a, c), U1(k, c))
27.56/9.01	   A^2 -> H(U1(a, c), U1(c, e))
27.56/9.01	   A^2 -> H(U1(a, c), U1(c, k))
27.56/9.01	   A^2 -> H(U1(a, c), U1(e, e))
27.56/9.01	   A^2 -> H(U1(a, c), U1(k, k))
27.56/9.01	   A^2 -> H(U1(a, c), U1(k, d))
27.56/9.01	   A^2 -> H(U1(a, c), U1(d, k))
27.56/9.01	   A^2 -> H(U1(a, d), U1(e, b))
27.56/9.01	   A^2 -> H(U1(a, d), U1(k, b))
27.56/9.01	   A^2 -> H(U1(a, d), U1(c, d))
27.56/9.01	   A^2 -> H(U1(a, d), U1(d, c))
27.56/9.01	   A^2 -> H(U1(a, d), U1(b, e))
27.56/9.01	   A^2 -> H(U1(a, d), U1(b, k))
27.56/9.01	   A^2 -> H(U1(a, d), U1(e, c))
27.56/9.01	   A^2 -> H(U1(a, d), U1(k, c))
27.56/9.01	   A^2 -> H(U1(a, d), U1(c, e))
27.56/9.01	   A^2 -> H(U1(a, d), U1(c, k))
27.56/9.01	   A^2 -> H(U1(a, d), U1(e, e))
27.56/9.01	   A^2 -> H(U1(a, d), U1(k, k))
27.56/9.01	   A^2 -> H(U1(a, d), U1(k, d))
27.56/9.01	   A^2 -> H(U1(a, d), U1(d, k))
27.56/9.01	   A^2 -> H(U1(a, a), b)
27.56/9.01	   A^2 -> H(U1(a, a), U1(e, d))
27.56/9.01	   A^2 -> H(U1(a, a), U1(d, e))
27.56/9.01	   A^2 -> H(U1(a, a), c)
27.56/9.01	   A^2 -> H(U1(a, a), U1(e, k))
27.56/9.01	   A^2 -> H(U1(a, a), U1(k, e))
27.56/9.01	   A^2 -> H(U1(a, a), e)
27.56/9.01	   A^2 -> H(U1(a, a), U1(k, k))
27.56/9.01	   A^2 -> H(k, f(b))
27.56/9.01	   A^2 -> H(c, U1(b, b))
27.56/9.01	   A^2 -> H(c, f(c))
27.56/9.01	   A^2 -> H(c, f(d))
27.56/9.01	   A^2 -> H(U1(e, k), U1(b, b))
27.56/9.01	   A^2 -> H(U1(e, k), f(c))
27.56/9.01	   A^2 -> H(U1(e, k), f(d))
27.56/9.01	   A^2 -> H(U1(e, c), U1(c, b))
27.56/9.01	   A^2 -> H(U1(e, c), U1(d, b))
27.56/9.01	   A^2 -> H(U1(e, c), U1(b, c))
27.56/9.01	   A^2 -> H(U1(e, c), U1(b, d))
27.56/9.01	   A^2 -> H(U1(e, c), U1(c, c))
27.56/9.01	   A^2 -> H(U1(e, c), f(e))
27.56/9.01	   A^2 -> H(U1(e, c), f(k))
27.56/9.01	   A^2 -> H(U1(e, c), U1(d, d))
27.56/9.01	   A^2 -> H(U1(k, e), U1(b, b))
27.56/9.01	   A^2 -> H(U1(k, e), f(c))
27.56/9.01	   A^2 -> H(U1(k, e), f(d))
27.56/9.01	   A^2 -> H(U1(k, c), U1(c, b))
27.56/9.01	   A^2 -> H(U1(k, c), U1(d, b))
27.56/9.01	   A^2 -> H(U1(k, c), U1(b, c))
27.56/9.01	   A^2 -> H(U1(k, c), U1(b, d))
27.56/9.01	   A^2 -> H(U1(k, c), U1(c, c))
27.56/9.01	   A^2 -> H(U1(k, c), f(e))
27.56/9.01	   A^2 -> H(U1(k, c), f(k))
27.56/9.01	   A^2 -> H(U1(k, c), U1(d, d))
27.56/9.01	   A^2 -> H(U1(c, e), U1(c, b))
27.56/9.01	   A^2 -> H(U1(c, e), U1(d, b))
27.56/9.01	   A^2 -> H(U1(c, e), U1(b, c))
27.56/9.01	   A^2 -> H(U1(c, e), U1(b, d))
27.56/9.01	   A^2 -> H(U1(c, e), U1(c, c))
27.56/9.01	   A^2 -> H(U1(c, e), f(e))
27.56/9.01	   A^2 -> H(U1(c, e), f(k))
27.56/9.01	   A^2 -> H(U1(c, e), U1(d, d))
27.56/9.01	   A^2 -> H(U1(c, k), U1(c, b))
27.56/9.01	   A^2 -> H(U1(c, k), U1(d, b))
27.56/9.01	   A^2 -> H(U1(c, k), U1(b, c))
27.56/9.01	   A^2 -> H(U1(c, k), U1(b, d))
27.56/9.01	   A^2 -> H(U1(c, k), U1(c, c))
27.56/9.01	   A^2 -> H(U1(c, k), f(e))
27.56/9.01	   A^2 -> H(U1(c, k), f(k))
27.56/9.01	   A^2 -> H(U1(c, k), U1(d, d))
27.56/9.01	   A^2 -> H(U1(c, c), U1(e, b))
27.56/9.01	   A^2 -> H(U1(c, c), U1(k, b))
27.56/9.01	   A^2 -> H(U1(c, c), U1(c, d))
27.56/9.01	   A^2 -> H(U1(c, c), U1(d, c))
27.56/9.01	   A^2 -> H(U1(c, c), U1(b, e))
27.56/9.01	   A^2 -> H(U1(c, c), U1(b, k))
27.56/9.01	   A^2 -> H(U1(c, c), U1(e, e))
27.56/9.01	   A^2 -> H(U1(c, c), U1(k, k))
27.56/9.01	   A^2 -> H(U1(c, c), U1(k, d))
27.56/9.01	   A^2 -> H(U1(c, c), U1(d, k))
27.56/9.01	   A^2 -> H(e, U1(b, b))
27.56/9.01	   A^2 -> H(e, f(c))
27.56/9.01	   A^2 -> H(e, f(d))
27.56/9.01	   A^2 -> H(U1(e, e), U1(c, b))
27.56/9.01	   A^2 -> H(U1(e, e), U1(d, b))
27.56/9.01	   A^2 -> H(U1(e, e), U1(b, c))
27.56/9.01	   A^2 -> H(U1(e, e), U1(b, d))
27.56/9.01	   A^2 -> H(U1(e, e), U1(c, c))
27.56/9.01	   A^2 -> H(U1(e, e), f(e))
27.56/9.01	   A^2 -> H(U1(e, e), f(k))
27.56/9.01	   A^2 -> H(U1(e, e), U1(d, d))
27.56/9.01	   A^2 -> H(f(e), U1(e, b))
27.56/9.01	   A^2 -> H(f(e), U1(k, b))
27.56/9.01	   A^2 -> H(f(e), U1(c, d))
27.56/9.01	   A^2 -> H(f(e), U1(d, c))
27.56/9.01	   A^2 -> H(f(e), U1(b, e))
27.56/9.01	   A^2 -> H(f(e), U1(b, k))
27.56/9.01	   A^2 -> H(f(e), U1(e, c))
27.56/9.01	   A^2 -> H(f(e), U1(k, c))
27.56/9.01	   A^2 -> H(f(e), U1(c, e))
27.56/9.01	   A^2 -> H(f(e), U1(c, k))
27.56/9.01	   A^2 -> H(f(e), U1(k, k))
27.56/9.01	   A^2 -> H(f(e), U1(k, d))
27.56/9.01	   A^2 -> H(f(e), U1(d, k))
27.56/9.01	   A^2 -> H(U1(k, k), U1(c, b))
27.56/9.01	   A^2 -> H(U1(k, k), U1(d, b))
27.56/9.01	   A^2 -> H(U1(k, k), U1(b, c))
27.56/9.01	   A^2 -> H(U1(k, k), U1(b, d))
27.56/9.01	   A^2 -> H(U1(k, k), U1(c, c))
27.56/9.01	   A^2 -> H(U1(k, k), f(e))
27.56/9.01	   A^2 -> H(U1(k, k), f(k))
27.56/9.01	   A^2 -> H(U1(k, k), U1(d, d))
27.56/9.01	   A^2 -> H(f(k), U1(e, b))
27.56/9.01	   A^2 -> H(f(k), U1(k, b))
27.56/9.01	   A^2 -> H(f(k), U1(c, d))
27.56/9.01	   A^2 -> H(f(k), U1(d, c))
27.56/9.01	   A^2 -> H(f(k), U1(b, e))
27.56/9.01	   A^2 -> H(f(k), U1(b, k))
27.56/9.01	   A^2 -> H(f(k), U1(e, c))
27.56/9.01	   A^2 -> H(f(k), U1(k, c))
27.56/9.01	   A^2 -> H(f(k), U1(c, e))
27.56/9.01	   A^2 -> H(f(k), U1(c, k))
27.56/9.01	   A^2 -> H(f(k), U1(e, e))
27.56/9.01	   A^2 -> H(f(k), U1(k, d))
27.56/9.01	   A^2 -> H(f(k), U1(d, k))
27.56/9.01	   A^2 -> H(f(c), b)
27.56/9.01	   A^2 -> H(f(c), U1(e, d))
27.56/9.01	   A^2 -> H(f(c), U1(d, e))
27.56/9.01	   A^2 -> H(f(k), U1(k, k))
27.56/9.01	   A^2 -> H(U1(k, k), U1(b, b))
27.56/9.01	   A^2 -> H(U1(k, k), f(c))
27.56/9.01	   A^2 -> H(U1(k, k), f(d))
27.56/9.01	   A^2 -> H(U1(k, d), U1(c, b))
27.56/9.01	   A^2 -> H(U1(k, d), U1(d, b))
27.56/9.01	   A^2 -> H(U1(k, d), U1(b, c))
27.56/9.01	   A^2 -> H(U1(k, d), U1(b, d))
27.56/9.01	   A^2 -> H(U1(k, d), U1(c, c))
27.56/9.01	   A^2 -> H(U1(k, d), f(e))
27.56/9.01	   A^2 -> H(U1(k, d), f(k))
27.56/9.01	   A^2 -> H(U1(k, d), U1(d, d))
27.56/9.01	   A^2 -> H(U1(d, k), U1(c, b))
27.56/9.01	   A^2 -> H(U1(d, k), U1(d, b))
27.56/9.01	   A^2 -> H(U1(d, k), U1(b, c))
27.56/9.01	   A^2 -> H(U1(d, k), U1(b, d))
27.56/9.01	   A^2 -> H(U1(d, k), U1(c, c))
27.56/9.01	   A^2 -> H(U1(d, k), f(e))
27.56/9.01	   A^2 -> H(U1(d, k), f(k))
27.56/9.01	   A^2 -> H(U1(d, k), U1(d, d))
27.56/9.01	   A^2 -> H(U1(d, d), U1(e, b))
27.56/9.01	   A^2 -> H(U1(d, d), U1(k, b))
27.56/9.01	   A^2 -> H(U1(d, d), U1(c, d))
27.56/9.01	   A^2 -> H(U1(d, d), U1(d, c))
27.56/9.01	   A^2 -> H(U1(d, d), U1(b, e))
27.56/9.01	   A^2 -> H(U1(d, d), U1(b, k))
27.56/9.01	   A^2 -> H(U1(d, d), U1(e, c))
27.56/9.01	   A^2 -> H(U1(d, d), U1(k, c))
27.56/9.01	   A^2 -> H(U1(d, d), U1(c, e))
27.56/9.01	   A^2 -> H(U1(d, d), U1(c, k))
27.56/9.01	   A^2 -> H(U1(d, d), U1(e, e))
27.56/9.01	   A^2 -> H(U1(d, d), U1(k, k))
27.56/9.01	   A^2 -> H(f(d), b)
27.56/9.01	   A^2 -> H(f(d), U1(e, d))
27.56/9.01	   A^2 -> H(f(d), U1(d, e))
27.56/9.01	   A^2 -> H(f(d), c)
27.56/9.01	   A^2 -> H(f(d), U1(e, k))
27.56/9.01	   A^2 -> H(f(d), U1(k, e))
27.56/9.01	   A^2 -> H(f(d), e)
27.56/9.01	   A^2 -> H(f(a), d)
27.56/9.01	   A^2 -> H(U1(c, c), U1(e, c))
27.56/9.01	   A^2 -> H(f(c), c)
27.56/9.01	   A^2 -> H(f(c), U1(e, k))
27.56/9.01	   A^2 -> H(U1(c, c), U1(k, c))
27.56/9.01	   A^2 -> H(f(c), U1(k, e))
27.56/9.01	   A^2 -> H(f(c), U1(k, k))
27.56/9.01	   A^2 -> H(U1(c, c), U1(c, e))
27.56/9.01	   A^2 -> H(U1(c, c), U1(c, k))
27.56/9.01	   A^2 -> H(f(a), k)
27.56/9.01	   A^2 -> H(f(e), U1(e, e))
27.56/9.01	   A^2 -> H(f(c), e)
27.56/9.01	   A^2 -> H(U1(d, d), U1(k, d))
27.56/9.01	   A^2 -> H(f(d), U1(k, k))
27.56/9.01	   A^2 -> H(U1(d, d), U1(d, k))
27.56/9.01	   A^2 -> H(d, U1(b, b))
27.56/9.01	   A^2 -> H(d, f(c))
27.56/9.01	   A^2 -> H(d, f(d))
27.56/9.01	   A^2 -> H(a, U1(c, b))
27.56/9.01	   A^2 -> H(a, U1(d, b))
27.56/9.01	   A^2 -> H(a, U1(b, c))
27.56/9.01	   A^2 -> H(a, U1(b, d))
27.56/9.01	   A^2 -> H(a, U1(c, c))
27.56/9.01	   A^2 -> H(a, f(e))
27.56/9.01	   A^2 -> H(a, f(k))
27.56/9.01	   A^2 -> H(a, U1(d, d))
27.56/9.01	   A^2 -> H(U1(e, d), U1(c, b))
27.56/9.01	   A^2 -> H(U1(e, d), U1(d, b))
27.56/9.01	   A^2 -> H(U1(e, d), U1(b, c))
27.56/9.01	   A^2 -> H(U1(e, d), U1(b, d))
27.56/9.01	   A^2 -> H(U1(e, d), U1(c, c))
27.56/9.01	   A^2 -> H(U1(e, d), f(e))
27.56/9.01	   A^2 -> H(U1(e, d), f(k))
27.56/9.01	   A^2 -> H(U1(e, d), U1(d, d))
27.56/9.01	   A^2 -> H(U1(e, a), U1(e, b))
27.56/9.01	   A^2 -> H(U1(e, a), U1(k, b))
27.56/9.01	   A^2 -> H(U1(e, a), U1(c, d))
27.56/9.01	   A^2 -> H(U1(e, a), U1(d, c))
27.56/9.01	   A^2 -> H(U1(e, a), U1(b, e))
27.56/9.01	   A^2 -> H(U1(e, a), U1(b, k))
27.56/9.01	   A^2 -> H(U1(e, a), U1(e, c))
27.56/9.01	   A^2 -> H(U1(e, a), U1(k, c))
27.56/9.01	   A^2 -> H(U1(e, a), U1(c, e))
27.56/9.01	   A^2 -> H(U1(e, a), U1(c, k))
27.56/9.01	   A^2 -> H(U1(e, a), U1(e, e))
27.56/9.01	   A^2 -> H(U1(e, a), U1(k, k))
27.56/9.01	   A^2 -> H(U1(e, a), U1(k, d))
27.56/9.01	   A^2 -> H(U1(e, a), U1(d, k))
27.56/9.01	   A^2 -> H(U1(k, a), U1(e, b))
27.56/9.01	   A^2 -> H(U1(k, a), U1(k, b))
27.56/9.01	   A^2 -> H(U1(k, a), U1(c, d))
27.56/9.01	   A^2 -> H(U1(k, a), U1(d, c))
27.56/9.01	   A^2 -> H(U1(k, a), U1(b, e))
27.56/9.01	   A^2 -> H(U1(k, a), U1(b, k))
27.56/9.01	   A^2 -> H(U1(k, a), U1(e, c))
27.56/9.01	   A^2 -> H(U1(k, a), U1(k, c))
27.56/9.01	   A^2 -> H(U1(k, a), U1(c, e))
27.56/9.01	   A^2 -> H(U1(k, a), U1(c, k))
27.56/9.01	   A^2 -> H(U1(k, a), U1(e, e))
27.56/9.01	   A^2 -> H(U1(k, a), U1(k, k))
27.56/9.01	   A^2 -> H(U1(k, a), U1(k, d))
27.56/9.01	   A^2 -> H(U1(k, a), U1(d, k))
27.56/9.01	   A^2 -> H(U1(c, d), U1(e, b))
27.56/9.01	   A^2 -> H(U1(c, d), U1(k, b))
27.56/9.01	   A^2 -> H(U1(c, d), U1(c, d))
27.56/9.01	   A^2 -> H(U1(c, d), U1(d, c))
27.56/9.01	   A^2 -> H(U1(c, d), U1(b, e))
27.56/9.01	   A^2 -> H(U1(c, d), U1(b, k))
27.56/9.01	   A^2 -> H(U1(c, d), U1(e, c))
27.56/9.01	   A^2 -> H(U1(c, d), U1(k, c))
27.56/9.01	   A^2 -> H(U1(c, d), U1(c, e))
27.56/9.01	   A^2 -> H(U1(c, d), U1(c, k))
27.56/9.01	   A^2 -> H(U1(c, d), U1(e, e))
27.56/9.01	   A^2 -> H(U1(c, d), U1(k, k))
27.56/9.01	   A^2 -> H(U1(c, d), U1(k, d))
27.56/9.01	   A^2 -> H(U1(c, d), U1(d, k))
27.56/9.01	   A^2 -> H(U1(c, a), b)
27.56/9.01	   A^2 -> H(U1(c, a), U1(e, d))
27.56/9.01	   A^2 -> H(U1(c, a), U1(d, e))
27.56/9.01	   A^2 -> H(U1(c, a), c)
27.56/9.01	   A^2 -> H(U1(c, a), U1(e, k))
27.56/9.01	   A^2 -> H(U1(c, a), U1(k, e))
27.56/9.01	   A^2 -> H(U1(c, a), e)
27.56/9.01	   A^2 -> H(U1(c, a), U1(k, k))
27.56/9.01	   A^2 -> H(U1(d, e), U1(c, b))
27.56/9.01	   A^2 -> H(U1(d, e), U1(d, b))
27.56/9.01	   A^2 -> H(U1(d, e), U1(b, c))
27.56/9.01	   A^2 -> H(U1(d, e), U1(b, d))
27.56/9.01	   A^2 -> H(U1(d, e), U1(c, c))
27.56/9.01	   A^2 -> H(U1(d, e), f(e))
27.56/9.01	   A^2 -> H(U1(d, e), f(k))
27.56/9.01	   A^2 -> H(U1(d, e), U1(d, d))
27.56/9.01	   A^2 -> H(U1(d, c), U1(e, b))
27.56/9.01	   A^2 -> H(U1(d, c), U1(k, b))
27.56/9.01	   A^2 -> H(U1(d, c), U1(c, d))
27.56/9.01	   A^2 -> H(U1(d, c), U1(d, c))
27.56/9.01	   A^2 -> H(U1(d, c), U1(b, e))
27.56/9.01	   A^2 -> H(U1(d, c), U1(b, k))
27.56/9.01	   A^2 -> H(U1(d, c), U1(e, c))
27.56/9.01	   A^2 -> H(U1(d, c), U1(k, c))
27.56/9.01	   A^2 -> H(U1(d, c), U1(c, e))
27.56/9.01	   A^2 -> H(U1(d, c), U1(c, k))
27.56/9.01	   A^2 -> H(U1(d, c), U1(e, e))
27.56/9.01	   A^2 -> H(U1(d, c), U1(k, k))
27.56/9.01	   A^2 -> H(U1(d, c), U1(k, d))
27.56/9.02	   A^2 -> H(U1(d, c), U1(d, k))
27.56/9.02	   A^2 -> H(U1(d, a), b)
27.56/9.02	   A^2 -> H(U1(d, a), U1(e, d))
27.56/9.02	   A^2 -> H(U1(d, a), U1(d, e))
27.56/9.02	   A^2 -> H(U1(d, a), c)
27.56/9.02	   A^2 -> H(U1(d, a), U1(e, k))
27.56/9.02	   A^2 -> H(U1(d, a), U1(k, e))
27.56/9.02	   A^2 -> H(U1(d, a), e)
27.56/9.02	   A^2 -> H(U1(d, a), U1(k, k))
27.56/9.02	
27.56/9.02	The TRS R consists of the following rules:
27.56/9.02	
27.56/9.02	   f(x) -> U1(x, x)
27.56/9.02	   U1(e, x) -> x
27.56/9.02	   a -> c
27.56/9.02	   a -> d
27.56/9.02	   b -> c
27.56/9.02	   b -> d
27.56/9.02	   d -> k
27.56/9.02	   c -> e
27.56/9.02	   c -> k
27.56/9.02	
27.56/9.02	Q is empty.
27.56/9.02	We have to consider all minimal (P,Q,R)-chains.
27.56/9.02	----------------------------------------
27.56/9.02	
27.56/9.02	(679) TransformationProof (EQUIVALENT)
27.56/9.02	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
27.56/9.02	
27.56/9.02	   (A^2 -> H(U1(k, a), U1(d, k)),A^2 -> H(U1(k, a), U1(d, k)))
27.56/9.02	   (A^2 -> H(U1(d, c), U1(d, k)),A^2 -> H(U1(d, c), U1(d, k)))
27.56/9.02	   (A^2 -> H(U1(d, d), U1(d, k)),A^2 -> H(U1(d, d), U1(d, k)))
27.56/9.02	   (A^2 -> H(U1(d, a), U1(k, k)),A^2 -> H(U1(d, a), U1(k, k)))
27.56/9.02	
27.56/9.02	
27.56/9.02	----------------------------------------
27.56/9.02	
27.56/9.02	(680)
27.56/9.02	Obligation:
27.56/9.02	Q DP problem:
27.56/9.02	The TRS P consists of the following rules:
27.56/9.02	
27.56/9.02	   H(x, x) -> G(x, x, f(k))
27.56/9.02	   G(d, x, x) -> A^2
27.56/9.02	   A^2 -> H(f(c), f(c))
27.56/9.02	   A^2 -> H(f(d), f(d))
27.56/9.02	   A^2 -> H(U1(c, c), U1(c, c))
27.56/9.02	   A^2 -> H(f(e), f(e))
27.56/9.02	   A^2 -> H(f(k), f(k))
27.56/9.02	   A^2 -> H(U1(d, d), U1(d, d))
27.56/9.02	   A^2 -> H(U1(a, e), U1(c, b))
27.56/9.02	   A^2 -> H(U1(a, e), U1(d, b))
27.56/9.02	   A^2 -> H(U1(a, e), U1(b, c))
27.56/9.02	   A^2 -> H(U1(a, e), U1(b, d))
27.56/9.02	   A^2 -> H(U1(a, e), U1(c, c))
27.56/9.02	   A^2 -> H(U1(a, e), f(e))
27.56/9.02	   A^2 -> H(U1(a, e), f(k))
27.56/9.02	   A^2 -> H(U1(a, e), U1(d, d))
27.56/9.02	   A^2 -> H(U1(a, k), U1(c, b))
27.56/9.02	   A^2 -> H(U1(a, k), U1(d, b))
27.56/9.02	   A^2 -> H(U1(a, k), U1(b, c))
27.56/9.02	   A^2 -> H(U1(a, k), U1(b, d))
27.56/9.02	   A^2 -> H(U1(a, k), U1(c, c))
27.56/9.02	   A^2 -> H(U1(a, k), f(e))
27.56/9.02	   A^2 -> H(U1(a, k), f(k))
27.56/9.02	   A^2 -> H(U1(a, k), U1(d, d))
27.56/9.02	   A^2 -> H(U1(a, c), U1(e, b))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, b))
27.56/9.02	   A^2 -> H(U1(a, c), U1(c, d))
27.56/9.02	   A^2 -> H(U1(a, c), U1(d, c))
27.56/9.02	   A^2 -> H(U1(a, c), U1(b, e))
27.56/9.02	   A^2 -> H(U1(a, c), U1(b, k))
27.56/9.02	   A^2 -> H(U1(a, c), U1(e, c))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, c))
27.56/9.02	   A^2 -> H(U1(a, c), U1(c, e))
27.56/9.02	   A^2 -> H(U1(a, c), U1(c, k))
27.56/9.02	   A^2 -> H(U1(a, c), U1(e, e))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, k))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, d))
27.56/9.02	   A^2 -> H(U1(a, c), U1(d, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(e, b))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, b))
27.56/9.02	   A^2 -> H(U1(a, d), U1(c, d))
27.56/9.02	   A^2 -> H(U1(a, d), U1(d, c))
27.56/9.02	   A^2 -> H(U1(a, d), U1(b, e))
27.56/9.02	   A^2 -> H(U1(a, d), U1(b, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(e, c))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, c))
27.56/9.02	   A^2 -> H(U1(a, d), U1(c, e))
27.56/9.02	   A^2 -> H(U1(a, d), U1(c, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(e, e))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, d))
27.56/9.02	   A^2 -> H(U1(a, d), U1(d, k))
27.56/9.02	   A^2 -> H(U1(a, a), b)
27.56/9.02	   A^2 -> H(U1(a, a), U1(e, d))
27.56/9.02	   A^2 -> H(U1(a, a), U1(d, e))
27.56/9.02	   A^2 -> H(U1(a, a), c)
27.56/9.02	   A^2 -> H(U1(a, a), U1(e, k))
27.56/9.02	   A^2 -> H(U1(a, a), U1(k, e))
27.56/9.02	   A^2 -> H(U1(a, a), e)
27.56/9.02	   A^2 -> H(U1(a, a), U1(k, k))
27.56/9.02	   A^2 -> H(k, f(b))
27.56/9.02	   A^2 -> H(c, U1(b, b))
27.56/9.02	   A^2 -> H(c, f(c))
27.56/9.02	   A^2 -> H(c, f(d))
27.56/9.02	   A^2 -> H(U1(e, k), U1(b, b))
27.56/9.02	   A^2 -> H(U1(e, k), f(c))
27.56/9.02	   A^2 -> H(U1(e, k), f(d))
27.56/9.02	   A^2 -> H(U1(e, c), U1(c, b))
27.56/9.02	   A^2 -> H(U1(e, c), U1(d, b))
27.56/9.02	   A^2 -> H(U1(e, c), U1(b, c))
27.56/9.02	   A^2 -> H(U1(e, c), U1(b, d))
27.56/9.02	   A^2 -> H(U1(e, c), U1(c, c))
27.56/9.02	   A^2 -> H(U1(e, c), f(e))
27.56/9.02	   A^2 -> H(U1(e, c), f(k))
27.56/9.02	   A^2 -> H(U1(e, c), U1(d, d))
27.56/9.02	   A^2 -> H(U1(k, e), U1(b, b))
27.56/9.02	   A^2 -> H(U1(k, e), f(c))
27.56/9.02	   A^2 -> H(U1(k, e), f(d))
27.56/9.02	   A^2 -> H(U1(k, c), U1(c, b))
27.56/9.02	   A^2 -> H(U1(k, c), U1(d, b))
27.56/9.02	   A^2 -> H(U1(k, c), U1(b, c))
27.56/9.02	   A^2 -> H(U1(k, c), U1(b, d))
27.56/9.02	   A^2 -> H(U1(k, c), U1(c, c))
27.56/9.02	   A^2 -> H(U1(k, c), f(e))
27.56/9.02	   A^2 -> H(U1(k, c), f(k))
27.56/9.02	   A^2 -> H(U1(k, c), U1(d, d))
27.56/9.02	   A^2 -> H(U1(c, e), U1(c, b))
27.56/9.02	   A^2 -> H(U1(c, e), U1(d, b))
27.56/9.02	   A^2 -> H(U1(c, e), U1(b, c))
27.56/9.02	   A^2 -> H(U1(c, e), U1(b, d))
27.56/9.02	   A^2 -> H(U1(c, e), U1(c, c))
27.56/9.02	   A^2 -> H(U1(c, e), f(e))
27.56/9.02	   A^2 -> H(U1(c, e), f(k))
27.56/9.02	   A^2 -> H(U1(c, e), U1(d, d))
27.56/9.02	   A^2 -> H(U1(c, k), U1(c, b))
27.56/9.02	   A^2 -> H(U1(c, k), U1(d, b))
27.56/9.02	   A^2 -> H(U1(c, k), U1(b, c))
27.56/9.02	   A^2 -> H(U1(c, k), U1(b, d))
27.56/9.02	   A^2 -> H(U1(c, k), U1(c, c))
27.56/9.02	   A^2 -> H(U1(c, k), f(e))
27.56/9.02	   A^2 -> H(U1(c, k), f(k))
27.56/9.02	   A^2 -> H(U1(c, k), U1(d, d))
27.56/9.02	   A^2 -> H(U1(c, c), U1(e, b))
27.56/9.02	   A^2 -> H(U1(c, c), U1(k, b))
27.56/9.02	   A^2 -> H(U1(c, c), U1(c, d))
27.56/9.02	   A^2 -> H(U1(c, c), U1(d, c))
27.56/9.02	   A^2 -> H(U1(c, c), U1(b, e))
27.56/9.02	   A^2 -> H(U1(c, c), U1(b, k))
27.56/9.02	   A^2 -> H(U1(c, c), U1(e, e))
27.56/9.02	   A^2 -> H(U1(c, c), U1(k, k))
27.56/9.02	   A^2 -> H(U1(c, c), U1(k, d))
27.56/9.02	   A^2 -> H(U1(c, c), U1(d, k))
27.56/9.02	   A^2 -> H(e, U1(b, b))
27.56/9.02	   A^2 -> H(e, f(c))
27.56/9.02	   A^2 -> H(e, f(d))
27.56/9.02	   A^2 -> H(U1(e, e), U1(c, b))
27.56/9.02	   A^2 -> H(U1(e, e), U1(d, b))
27.56/9.02	   A^2 -> H(U1(e, e), U1(b, c))
27.56/9.02	   A^2 -> H(U1(e, e), U1(b, d))
27.56/9.02	   A^2 -> H(U1(e, e), U1(c, c))
27.56/9.02	   A^2 -> H(U1(e, e), f(e))
27.56/9.02	   A^2 -> H(U1(e, e), f(k))
27.56/9.02	   A^2 -> H(U1(e, e), U1(d, d))
27.56/9.02	   A^2 -> H(f(e), U1(e, b))
27.56/9.02	   A^2 -> H(f(e), U1(k, b))
27.56/9.02	   A^2 -> H(f(e), U1(c, d))
27.56/9.02	   A^2 -> H(f(e), U1(d, c))
27.56/9.02	   A^2 -> H(f(e), U1(b, e))
27.56/9.02	   A^2 -> H(f(e), U1(b, k))
27.56/9.02	   A^2 -> H(f(e), U1(e, c))
27.56/9.02	   A^2 -> H(f(e), U1(k, c))
27.56/9.02	   A^2 -> H(f(e), U1(c, e))
27.56/9.02	   A^2 -> H(f(e), U1(c, k))
27.56/9.02	   A^2 -> H(f(e), U1(k, k))
27.56/9.02	   A^2 -> H(f(e), U1(k, d))
27.56/9.02	   A^2 -> H(f(e), U1(d, k))
27.56/9.02	   A^2 -> H(U1(k, k), U1(c, b))
27.56/9.02	   A^2 -> H(U1(k, k), U1(d, b))
27.56/9.02	   A^2 -> H(U1(k, k), U1(b, c))
27.56/9.02	   A^2 -> H(U1(k, k), U1(b, d))
27.56/9.02	   A^2 -> H(U1(k, k), U1(c, c))
27.56/9.02	   A^2 -> H(U1(k, k), f(e))
27.56/9.02	   A^2 -> H(U1(k, k), f(k))
27.56/9.02	   A^2 -> H(U1(k, k), U1(d, d))
27.56/9.02	   A^2 -> H(f(k), U1(e, b))
27.56/9.02	   A^2 -> H(f(k), U1(k, b))
27.56/9.02	   A^2 -> H(f(k), U1(c, d))
27.56/9.02	   A^2 -> H(f(k), U1(d, c))
27.56/9.02	   A^2 -> H(f(k), U1(b, e))
27.56/9.02	   A^2 -> H(f(k), U1(b, k))
27.56/9.02	   A^2 -> H(f(k), U1(e, c))
27.56/9.02	   A^2 -> H(f(k), U1(k, c))
27.56/9.02	   A^2 -> H(f(k), U1(c, e))
27.56/9.02	   A^2 -> H(f(k), U1(c, k))
27.56/9.02	   A^2 -> H(f(k), U1(e, e))
27.56/9.02	   A^2 -> H(f(k), U1(k, d))
27.56/9.02	   A^2 -> H(f(k), U1(d, k))
27.56/9.02	   A^2 -> H(f(c), b)
27.56/9.02	   A^2 -> H(f(c), U1(e, d))
27.56/9.02	   A^2 -> H(f(c), U1(d, e))
27.56/9.02	   A^2 -> H(f(k), U1(k, k))
27.56/9.02	   A^2 -> H(U1(k, k), U1(b, b))
27.56/9.02	   A^2 -> H(U1(k, k), f(c))
27.56/9.02	   A^2 -> H(U1(k, k), f(d))
27.56/9.02	   A^2 -> H(U1(k, d), U1(c, b))
27.56/9.02	   A^2 -> H(U1(k, d), U1(d, b))
27.56/9.02	   A^2 -> H(U1(k, d), U1(b, c))
27.56/9.02	   A^2 -> H(U1(k, d), U1(b, d))
27.56/9.02	   A^2 -> H(U1(k, d), U1(c, c))
27.56/9.02	   A^2 -> H(U1(k, d), f(e))
27.56/9.02	   A^2 -> H(U1(k, d), f(k))
27.56/9.02	   A^2 -> H(U1(k, d), U1(d, d))
27.56/9.02	   A^2 -> H(U1(d, k), U1(c, b))
27.56/9.02	   A^2 -> H(U1(d, k), U1(d, b))
27.56/9.02	   A^2 -> H(U1(d, k), U1(b, c))
27.56/9.02	   A^2 -> H(U1(d, k), U1(b, d))
27.56/9.02	   A^2 -> H(U1(d, k), U1(c, c))
27.56/9.02	   A^2 -> H(U1(d, k), f(e))
27.56/9.02	   A^2 -> H(U1(d, k), f(k))
27.56/9.02	   A^2 -> H(U1(d, k), U1(d, d))
27.56/9.02	   A^2 -> H(U1(d, d), U1(e, b))
27.56/9.02	   A^2 -> H(U1(d, d), U1(k, b))
27.56/9.02	   A^2 -> H(U1(d, d), U1(c, d))
27.56/9.02	   A^2 -> H(U1(d, d), U1(d, c))
27.56/9.02	   A^2 -> H(U1(d, d), U1(b, e))
27.56/9.02	   A^2 -> H(U1(d, d), U1(b, k))
27.56/9.02	   A^2 -> H(U1(d, d), U1(e, c))
27.56/9.02	   A^2 -> H(U1(d, d), U1(k, c))
27.56/9.02	   A^2 -> H(U1(d, d), U1(c, e))
27.56/9.02	   A^2 -> H(U1(d, d), U1(c, k))
27.56/9.02	   A^2 -> H(U1(d, d), U1(e, e))
27.56/9.02	   A^2 -> H(U1(d, d), U1(k, k))
27.56/9.02	   A^2 -> H(f(d), b)
27.56/9.02	   A^2 -> H(f(d), U1(e, d))
27.56/9.02	   A^2 -> H(f(d), U1(d, e))
27.56/9.02	   A^2 -> H(f(d), c)
27.56/9.02	   A^2 -> H(f(d), U1(e, k))
27.56/9.02	   A^2 -> H(f(d), U1(k, e))
27.56/9.02	   A^2 -> H(f(d), e)
27.56/9.02	   A^2 -> H(f(a), d)
27.56/9.02	   A^2 -> H(U1(c, c), U1(e, c))
27.56/9.02	   A^2 -> H(f(c), c)
27.56/9.02	   A^2 -> H(f(c), U1(e, k))
27.56/9.02	   A^2 -> H(U1(c, c), U1(k, c))
27.56/9.02	   A^2 -> H(f(c), U1(k, e))
27.56/9.02	   A^2 -> H(f(c), U1(k, k))
27.56/9.02	   A^2 -> H(U1(c, c), U1(c, e))
27.56/9.02	   A^2 -> H(U1(c, c), U1(c, k))
27.56/9.02	   A^2 -> H(f(a), k)
27.56/9.02	   A^2 -> H(f(e), U1(e, e))
27.56/9.02	   A^2 -> H(f(c), e)
27.56/9.02	   A^2 -> H(U1(d, d), U1(k, d))
27.56/9.02	   A^2 -> H(f(d), U1(k, k))
27.56/9.02	   A^2 -> H(U1(d, d), U1(d, k))
27.56/9.02	   A^2 -> H(d, U1(b, b))
27.56/9.02	   A^2 -> H(d, f(c))
27.56/9.02	   A^2 -> H(d, f(d))
27.56/9.02	   A^2 -> H(a, U1(c, b))
27.56/9.02	   A^2 -> H(a, U1(d, b))
27.56/9.02	   A^2 -> H(a, U1(b, c))
27.56/9.02	   A^2 -> H(a, U1(b, d))
27.56/9.02	   A^2 -> H(a, U1(c, c))
27.56/9.02	   A^2 -> H(a, f(e))
27.56/9.02	   A^2 -> H(a, f(k))
27.56/9.02	   A^2 -> H(a, U1(d, d))
27.56/9.02	   A^2 -> H(U1(e, d), U1(c, b))
27.56/9.02	   A^2 -> H(U1(e, d), U1(d, b))
27.56/9.02	   A^2 -> H(U1(e, d), U1(b, c))
27.56/9.02	   A^2 -> H(U1(e, d), U1(b, d))
27.56/9.02	   A^2 -> H(U1(e, d), U1(c, c))
27.56/9.02	   A^2 -> H(U1(e, d), f(e))
27.56/9.02	   A^2 -> H(U1(e, d), f(k))
27.56/9.02	   A^2 -> H(U1(e, d), U1(d, d))
27.56/9.02	   A^2 -> H(U1(e, a), U1(e, b))
27.56/9.02	   A^2 -> H(U1(e, a), U1(k, b))
27.56/9.02	   A^2 -> H(U1(e, a), U1(c, d))
27.56/9.02	   A^2 -> H(U1(e, a), U1(d, c))
27.56/9.02	   A^2 -> H(U1(e, a), U1(b, e))
27.56/9.02	   A^2 -> H(U1(e, a), U1(b, k))
27.56/9.02	   A^2 -> H(U1(e, a), U1(e, c))
27.56/9.02	   A^2 -> H(U1(e, a), U1(k, c))
27.56/9.02	   A^2 -> H(U1(e, a), U1(c, e))
27.56/9.02	   A^2 -> H(U1(e, a), U1(c, k))
27.56/9.02	   A^2 -> H(U1(e, a), U1(e, e))
27.56/9.02	   A^2 -> H(U1(e, a), U1(k, k))
27.56/9.02	   A^2 -> H(U1(e, a), U1(k, d))
27.56/9.02	   A^2 -> H(U1(e, a), U1(d, k))
27.56/9.02	   A^2 -> H(U1(k, a), U1(e, b))
27.56/9.02	   A^2 -> H(U1(k, a), U1(k, b))
27.56/9.02	   A^2 -> H(U1(k, a), U1(c, d))
27.56/9.02	   A^2 -> H(U1(k, a), U1(d, c))
27.56/9.02	   A^2 -> H(U1(k, a), U1(b, e))
27.56/9.02	   A^2 -> H(U1(k, a), U1(b, k))
27.56/9.02	   A^2 -> H(U1(k, a), U1(e, c))
27.56/9.02	   A^2 -> H(U1(k, a), U1(k, c))
27.56/9.02	   A^2 -> H(U1(k, a), U1(c, e))
27.56/9.02	   A^2 -> H(U1(k, a), U1(c, k))
27.56/9.02	   A^2 -> H(U1(k, a), U1(e, e))
27.56/9.02	   A^2 -> H(U1(k, a), U1(k, k))
27.56/9.02	   A^2 -> H(U1(k, a), U1(k, d))
27.56/9.02	   A^2 -> H(U1(k, a), U1(d, k))
27.56/9.02	   A^2 -> H(U1(c, d), U1(e, b))
27.56/9.02	   A^2 -> H(U1(c, d), U1(k, b))
27.56/9.02	   A^2 -> H(U1(c, d), U1(c, d))
27.56/9.02	   A^2 -> H(U1(c, d), U1(d, c))
27.56/9.02	   A^2 -> H(U1(c, d), U1(b, e))
27.56/9.02	   A^2 -> H(U1(c, d), U1(b, k))
27.56/9.02	   A^2 -> H(U1(c, d), U1(e, c))
27.56/9.02	   A^2 -> H(U1(c, d), U1(k, c))
27.56/9.02	   A^2 -> H(U1(c, d), U1(c, e))
27.56/9.02	   A^2 -> H(U1(c, d), U1(c, k))
27.56/9.02	   A^2 -> H(U1(c, d), U1(e, e))
27.56/9.02	   A^2 -> H(U1(c, d), U1(k, k))
27.56/9.02	   A^2 -> H(U1(c, d), U1(k, d))
27.56/9.02	   A^2 -> H(U1(c, d), U1(d, k))
27.56/9.02	   A^2 -> H(U1(c, a), b)
27.56/9.02	   A^2 -> H(U1(c, a), U1(e, d))
27.56/9.02	   A^2 -> H(U1(c, a), U1(d, e))
27.56/9.02	   A^2 -> H(U1(c, a), c)
27.56/9.02	   A^2 -> H(U1(c, a), U1(e, k))
27.56/9.02	   A^2 -> H(U1(c, a), U1(k, e))
27.56/9.02	   A^2 -> H(U1(c, a), e)
27.56/9.02	   A^2 -> H(U1(c, a), U1(k, k))
27.56/9.02	   A^2 -> H(U1(d, e), U1(c, b))
27.56/9.02	   A^2 -> H(U1(d, e), U1(d, b))
27.56/9.02	   A^2 -> H(U1(d, e), U1(b, c))
27.56/9.02	   A^2 -> H(U1(d, e), U1(b, d))
27.56/9.02	   A^2 -> H(U1(d, e), U1(c, c))
27.56/9.02	   A^2 -> H(U1(d, e), f(e))
27.56/9.02	   A^2 -> H(U1(d, e), f(k))
27.56/9.02	   A^2 -> H(U1(d, e), U1(d, d))
27.56/9.02	   A^2 -> H(U1(d, c), U1(e, b))
27.56/9.02	   A^2 -> H(U1(d, c), U1(k, b))
27.56/9.02	   A^2 -> H(U1(d, c), U1(c, d))
27.56/9.02	   A^2 -> H(U1(d, c), U1(d, c))
27.56/9.02	   A^2 -> H(U1(d, c), U1(b, e))
27.56/9.02	   A^2 -> H(U1(d, c), U1(b, k))
27.56/9.02	   A^2 -> H(U1(d, c), U1(e, c))
27.56/9.02	   A^2 -> H(U1(d, c), U1(k, c))
27.56/9.02	   A^2 -> H(U1(d, c), U1(c, e))
27.56/9.02	   A^2 -> H(U1(d, c), U1(c, k))
27.56/9.02	   A^2 -> H(U1(d, c), U1(e, e))
27.56/9.02	   A^2 -> H(U1(d, c), U1(k, k))
27.56/9.02	   A^2 -> H(U1(d, c), U1(k, d))
27.56/9.02	   A^2 -> H(U1(d, c), U1(d, k))
27.56/9.02	   A^2 -> H(U1(d, a), b)
27.56/9.02	   A^2 -> H(U1(d, a), U1(e, d))
27.56/9.02	   A^2 -> H(U1(d, a), U1(d, e))
27.56/9.02	   A^2 -> H(U1(d, a), c)
27.56/9.02	   A^2 -> H(U1(d, a), U1(e, k))
27.56/9.02	   A^2 -> H(U1(d, a), U1(k, e))
27.56/9.02	   A^2 -> H(U1(d, a), e)
27.56/9.02	   A^2 -> H(U1(d, a), U1(k, k))
27.56/9.02	
27.56/9.02	The TRS R consists of the following rules:
27.56/9.02	
27.56/9.02	   f(x) -> U1(x, x)
27.56/9.02	   U1(e, x) -> x
27.56/9.02	   a -> c
27.56/9.02	   a -> d
27.56/9.02	   b -> c
27.56/9.02	   b -> d
27.56/9.02	   d -> k
27.56/9.02	   c -> e
27.56/9.02	   c -> k
27.56/9.02	
27.56/9.02	Q is empty.
27.56/9.02	We have to consider all minimal (P,Q,R)-chains.
27.56/9.02	----------------------------------------
27.56/9.02	
27.56/9.02	(681) TransformationProof (EQUIVALENT)
27.56/9.02	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
27.56/9.02	
27.56/9.02	   (A^2 -> H(U1(c, e), U1(c, b)),A^2 -> H(U1(c, e), U1(c, b)))
27.56/9.02	   (A^2 -> H(U1(d, e), U1(c, b)),A^2 -> H(U1(d, e), U1(c, b)))
27.56/9.02	   (A^2 -> H(U1(a, e), U1(e, b)),A^2 -> H(U1(a, e), U1(e, b)))
27.56/9.02	   (A^2 -> H(U1(a, e), U1(k, b)),A^2 -> H(U1(a, e), U1(k, b)))
27.56/9.02	   (A^2 -> H(U1(a, e), U1(c, c)),A^2 -> H(U1(a, e), U1(c, c)))
27.56/9.02	   (A^2 -> H(U1(a, e), U1(c, d)),A^2 -> H(U1(a, e), U1(c, d)))
27.56/9.02	
27.56/9.02	
27.56/9.02	----------------------------------------
27.56/9.02	
27.56/9.02	(682)
27.56/9.02	Obligation:
27.56/9.02	Q DP problem:
27.56/9.02	The TRS P consists of the following rules:
27.56/9.02	
27.56/9.02	   H(x, x) -> G(x, x, f(k))
27.56/9.02	   G(d, x, x) -> A^2
27.56/9.02	   A^2 -> H(f(c), f(c))
27.56/9.02	   A^2 -> H(f(d), f(d))
27.56/9.02	   A^2 -> H(U1(c, c), U1(c, c))
27.56/9.02	   A^2 -> H(f(e), f(e))
27.56/9.02	   A^2 -> H(f(k), f(k))
27.56/9.02	   A^2 -> H(U1(d, d), U1(d, d))
27.56/9.02	   A^2 -> H(U1(a, e), U1(d, b))
27.56/9.02	   A^2 -> H(U1(a, e), U1(b, c))
27.56/9.02	   A^2 -> H(U1(a, e), U1(b, d))
27.56/9.02	   A^2 -> H(U1(a, e), U1(c, c))
27.56/9.02	   A^2 -> H(U1(a, e), f(e))
27.56/9.02	   A^2 -> H(U1(a, e), f(k))
27.56/9.02	   A^2 -> H(U1(a, e), U1(d, d))
27.56/9.02	   A^2 -> H(U1(a, k), U1(c, b))
27.56/9.02	   A^2 -> H(U1(a, k), U1(d, b))
27.56/9.02	   A^2 -> H(U1(a, k), U1(b, c))
27.56/9.02	   A^2 -> H(U1(a, k), U1(b, d))
27.56/9.02	   A^2 -> H(U1(a, k), U1(c, c))
27.56/9.02	   A^2 -> H(U1(a, k), f(e))
27.56/9.02	   A^2 -> H(U1(a, k), f(k))
27.56/9.02	   A^2 -> H(U1(a, k), U1(d, d))
27.56/9.02	   A^2 -> H(U1(a, c), U1(e, b))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, b))
27.56/9.02	   A^2 -> H(U1(a, c), U1(c, d))
27.56/9.02	   A^2 -> H(U1(a, c), U1(d, c))
27.56/9.02	   A^2 -> H(U1(a, c), U1(b, e))
27.56/9.02	   A^2 -> H(U1(a, c), U1(b, k))
27.56/9.02	   A^2 -> H(U1(a, c), U1(e, c))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, c))
27.56/9.02	   A^2 -> H(U1(a, c), U1(c, e))
27.56/9.02	   A^2 -> H(U1(a, c), U1(c, k))
27.56/9.02	   A^2 -> H(U1(a, c), U1(e, e))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, k))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, d))
27.56/9.02	   A^2 -> H(U1(a, c), U1(d, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(e, b))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, b))
27.56/9.02	   A^2 -> H(U1(a, d), U1(c, d))
27.56/9.02	   A^2 -> H(U1(a, d), U1(d, c))
27.56/9.02	   A^2 -> H(U1(a, d), U1(b, e))
27.56/9.02	   A^2 -> H(U1(a, d), U1(b, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(e, c))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, c))
27.56/9.02	   A^2 -> H(U1(a, d), U1(c, e))
27.56/9.02	   A^2 -> H(U1(a, d), U1(c, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(e, e))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, d))
27.56/9.02	   A^2 -> H(U1(a, d), U1(d, k))
27.56/9.02	   A^2 -> H(U1(a, a), b)
27.56/9.02	   A^2 -> H(U1(a, a), U1(e, d))
27.56/9.02	   A^2 -> H(U1(a, a), U1(d, e))
27.56/9.02	   A^2 -> H(U1(a, a), c)
27.56/9.02	   A^2 -> H(U1(a, a), U1(e, k))
27.56/9.02	   A^2 -> H(U1(a, a), U1(k, e))
27.56/9.02	   A^2 -> H(U1(a, a), e)
27.56/9.02	   A^2 -> H(U1(a, a), U1(k, k))
27.56/9.02	   A^2 -> H(k, f(b))
27.56/9.02	   A^2 -> H(c, U1(b, b))
27.56/9.02	   A^2 -> H(c, f(c))
27.56/9.02	   A^2 -> H(c, f(d))
27.56/9.02	   A^2 -> H(U1(e, k), U1(b, b))
27.56/9.02	   A^2 -> H(U1(e, k), f(c))
27.56/9.02	   A^2 -> H(U1(e, k), f(d))
27.56/9.02	   A^2 -> H(U1(e, c), U1(c, b))
27.56/9.02	   A^2 -> H(U1(e, c), U1(d, b))
27.56/9.02	   A^2 -> H(U1(e, c), U1(b, c))
27.56/9.02	   A^2 -> H(U1(e, c), U1(b, d))
27.56/9.02	   A^2 -> H(U1(e, c), U1(c, c))
27.56/9.02	   A^2 -> H(U1(e, c), f(e))
27.56/9.02	   A^2 -> H(U1(e, c), f(k))
27.56/9.02	   A^2 -> H(U1(e, c), U1(d, d))
27.56/9.02	   A^2 -> H(U1(k, e), U1(b, b))
27.56/9.02	   A^2 -> H(U1(k, e), f(c))
27.56/9.02	   A^2 -> H(U1(k, e), f(d))
27.56/9.02	   A^2 -> H(U1(k, c), U1(c, b))
27.56/9.02	   A^2 -> H(U1(k, c), U1(d, b))
27.56/9.02	   A^2 -> H(U1(k, c), U1(b, c))
27.56/9.02	   A^2 -> H(U1(k, c), U1(b, d))
27.56/9.02	   A^2 -> H(U1(k, c), U1(c, c))
27.56/9.02	   A^2 -> H(U1(k, c), f(e))
27.56/9.02	   A^2 -> H(U1(k, c), f(k))
27.56/9.02	   A^2 -> H(U1(k, c), U1(d, d))
27.56/9.02	   A^2 -> H(U1(c, e), U1(c, b))
27.56/9.02	   A^2 -> H(U1(c, e), U1(d, b))
27.56/9.02	   A^2 -> H(U1(c, e), U1(b, c))
27.56/9.02	   A^2 -> H(U1(c, e), U1(b, d))
27.56/9.02	   A^2 -> H(U1(c, e), U1(c, c))
27.56/9.02	   A^2 -> H(U1(c, e), f(e))
27.56/9.02	   A^2 -> H(U1(c, e), f(k))
27.56/9.02	   A^2 -> H(U1(c, e), U1(d, d))
27.56/9.02	   A^2 -> H(U1(c, k), U1(c, b))
27.56/9.02	   A^2 -> H(U1(c, k), U1(d, b))
27.56/9.02	   A^2 -> H(U1(c, k), U1(b, c))
27.56/9.02	   A^2 -> H(U1(c, k), U1(b, d))
27.56/9.02	   A^2 -> H(U1(c, k), U1(c, c))
27.56/9.02	   A^2 -> H(U1(c, k), f(e))
27.56/9.02	   A^2 -> H(U1(c, k), f(k))
27.56/9.02	   A^2 -> H(U1(c, k), U1(d, d))
27.56/9.02	   A^2 -> H(U1(c, c), U1(e, b))
27.56/9.02	   A^2 -> H(U1(c, c), U1(k, b))
27.56/9.02	   A^2 -> H(U1(c, c), U1(c, d))
27.56/9.02	   A^2 -> H(U1(c, c), U1(d, c))
27.56/9.02	   A^2 -> H(U1(c, c), U1(b, e))
27.56/9.02	   A^2 -> H(U1(c, c), U1(b, k))
27.56/9.02	   A^2 -> H(U1(c, c), U1(e, e))
27.56/9.02	   A^2 -> H(U1(c, c), U1(k, k))
27.56/9.02	   A^2 -> H(U1(c, c), U1(k, d))
27.56/9.02	   A^2 -> H(U1(c, c), U1(d, k))
27.56/9.02	   A^2 -> H(e, U1(b, b))
27.56/9.02	   A^2 -> H(e, f(c))
27.56/9.02	   A^2 -> H(e, f(d))
27.56/9.02	   A^2 -> H(U1(e, e), U1(c, b))
27.56/9.02	   A^2 -> H(U1(e, e), U1(d, b))
27.56/9.02	   A^2 -> H(U1(e, e), U1(b, c))
27.56/9.02	   A^2 -> H(U1(e, e), U1(b, d))
27.56/9.02	   A^2 -> H(U1(e, e), U1(c, c))
27.56/9.02	   A^2 -> H(U1(e, e), f(e))
27.56/9.02	   A^2 -> H(U1(e, e), f(k))
27.56/9.02	   A^2 -> H(U1(e, e), U1(d, d))
27.56/9.02	   A^2 -> H(f(e), U1(e, b))
27.56/9.02	   A^2 -> H(f(e), U1(k, b))
27.56/9.02	   A^2 -> H(f(e), U1(c, d))
27.56/9.02	   A^2 -> H(f(e), U1(d, c))
27.56/9.02	   A^2 -> H(f(e), U1(b, e))
27.56/9.02	   A^2 -> H(f(e), U1(b, k))
27.56/9.02	   A^2 -> H(f(e), U1(e, c))
27.56/9.02	   A^2 -> H(f(e), U1(k, c))
27.56/9.02	   A^2 -> H(f(e), U1(c, e))
27.56/9.02	   A^2 -> H(f(e), U1(c, k))
27.56/9.02	   A^2 -> H(f(e), U1(k, k))
27.56/9.02	   A^2 -> H(f(e), U1(k, d))
27.56/9.02	   A^2 -> H(f(e), U1(d, k))
27.56/9.02	   A^2 -> H(U1(k, k), U1(c, b))
27.56/9.02	   A^2 -> H(U1(k, k), U1(d, b))
27.56/9.02	   A^2 -> H(U1(k, k), U1(b, c))
27.56/9.02	   A^2 -> H(U1(k, k), U1(b, d))
27.56/9.02	   A^2 -> H(U1(k, k), U1(c, c))
27.56/9.02	   A^2 -> H(U1(k, k), f(e))
27.56/9.02	   A^2 -> H(U1(k, k), f(k))
27.56/9.02	   A^2 -> H(U1(k, k), U1(d, d))
27.56/9.02	   A^2 -> H(f(k), U1(e, b))
27.56/9.02	   A^2 -> H(f(k), U1(k, b))
27.56/9.02	   A^2 -> H(f(k), U1(c, d))
27.56/9.02	   A^2 -> H(f(k), U1(d, c))
27.56/9.02	   A^2 -> H(f(k), U1(b, e))
27.56/9.02	   A^2 -> H(f(k), U1(b, k))
27.56/9.02	   A^2 -> H(f(k), U1(e, c))
27.56/9.02	   A^2 -> H(f(k), U1(k, c))
27.56/9.02	   A^2 -> H(f(k), U1(c, e))
27.56/9.02	   A^2 -> H(f(k), U1(c, k))
27.56/9.02	   A^2 -> H(f(k), U1(e, e))
27.56/9.02	   A^2 -> H(f(k), U1(k, d))
27.56/9.02	   A^2 -> H(f(k), U1(d, k))
27.56/9.02	   A^2 -> H(f(c), b)
27.56/9.02	   A^2 -> H(f(c), U1(e, d))
27.56/9.02	   A^2 -> H(f(c), U1(d, e))
27.56/9.02	   A^2 -> H(f(k), U1(k, k))
27.56/9.02	   A^2 -> H(U1(k, k), U1(b, b))
27.56/9.02	   A^2 -> H(U1(k, k), f(c))
27.56/9.02	   A^2 -> H(U1(k, k), f(d))
27.56/9.02	   A^2 -> H(U1(k, d), U1(c, b))
27.56/9.02	   A^2 -> H(U1(k, d), U1(d, b))
27.56/9.02	   A^2 -> H(U1(k, d), U1(b, c))
27.56/9.02	   A^2 -> H(U1(k, d), U1(b, d))
27.56/9.02	   A^2 -> H(U1(k, d), U1(c, c))
27.56/9.02	   A^2 -> H(U1(k, d), f(e))
27.56/9.02	   A^2 -> H(U1(k, d), f(k))
27.56/9.02	   A^2 -> H(U1(k, d), U1(d, d))
27.56/9.02	   A^2 -> H(U1(d, k), U1(c, b))
27.56/9.02	   A^2 -> H(U1(d, k), U1(d, b))
27.56/9.02	   A^2 -> H(U1(d, k), U1(b, c))
27.56/9.02	   A^2 -> H(U1(d, k), U1(b, d))
27.56/9.02	   A^2 -> H(U1(d, k), U1(c, c))
27.56/9.02	   A^2 -> H(U1(d, k), f(e))
27.56/9.02	   A^2 -> H(U1(d, k), f(k))
27.56/9.02	   A^2 -> H(U1(d, k), U1(d, d))
27.56/9.02	   A^2 -> H(U1(d, d), U1(e, b))
27.56/9.02	   A^2 -> H(U1(d, d), U1(k, b))
27.56/9.02	   A^2 -> H(U1(d, d), U1(c, d))
27.56/9.02	   A^2 -> H(U1(d, d), U1(d, c))
27.56/9.02	   A^2 -> H(U1(d, d), U1(b, e))
27.56/9.02	   A^2 -> H(U1(d, d), U1(b, k))
27.56/9.02	   A^2 -> H(U1(d, d), U1(e, c))
27.56/9.02	   A^2 -> H(U1(d, d), U1(k, c))
27.56/9.02	   A^2 -> H(U1(d, d), U1(c, e))
27.56/9.02	   A^2 -> H(U1(d, d), U1(c, k))
27.56/9.02	   A^2 -> H(U1(d, d), U1(e, e))
27.56/9.02	   A^2 -> H(U1(d, d), U1(k, k))
27.56/9.02	   A^2 -> H(f(d), b)
27.56/9.02	   A^2 -> H(f(d), U1(e, d))
27.56/9.02	   A^2 -> H(f(d), U1(d, e))
27.56/9.02	   A^2 -> H(f(d), c)
27.56/9.02	   A^2 -> H(f(d), U1(e, k))
27.56/9.02	   A^2 -> H(f(d), U1(k, e))
27.56/9.02	   A^2 -> H(f(d), e)
27.56/9.02	   A^2 -> H(f(a), d)
27.56/9.02	   A^2 -> H(U1(c, c), U1(e, c))
27.56/9.02	   A^2 -> H(f(c), c)
27.56/9.02	   A^2 -> H(f(c), U1(e, k))
27.56/9.02	   A^2 -> H(U1(c, c), U1(k, c))
27.56/9.02	   A^2 -> H(f(c), U1(k, e))
27.56/9.02	   A^2 -> H(f(c), U1(k, k))
27.56/9.02	   A^2 -> H(U1(c, c), U1(c, e))
27.56/9.02	   A^2 -> H(U1(c, c), U1(c, k))
27.56/9.02	   A^2 -> H(f(a), k)
27.56/9.02	   A^2 -> H(f(e), U1(e, e))
27.56/9.02	   A^2 -> H(f(c), e)
27.56/9.02	   A^2 -> H(U1(d, d), U1(k, d))
27.56/9.02	   A^2 -> H(f(d), U1(k, k))
27.56/9.02	   A^2 -> H(U1(d, d), U1(d, k))
27.56/9.02	   A^2 -> H(d, U1(b, b))
27.56/9.02	   A^2 -> H(d, f(c))
27.56/9.02	   A^2 -> H(d, f(d))
27.56/9.02	   A^2 -> H(a, U1(c, b))
27.56/9.02	   A^2 -> H(a, U1(d, b))
27.56/9.02	   A^2 -> H(a, U1(b, c))
27.56/9.02	   A^2 -> H(a, U1(b, d))
27.56/9.02	   A^2 -> H(a, U1(c, c))
27.56/9.02	   A^2 -> H(a, f(e))
27.56/9.02	   A^2 -> H(a, f(k))
27.56/9.02	   A^2 -> H(a, U1(d, d))
27.56/9.02	   A^2 -> H(U1(e, d), U1(c, b))
27.56/9.02	   A^2 -> H(U1(e, d), U1(d, b))
27.56/9.02	   A^2 -> H(U1(e, d), U1(b, c))
27.56/9.02	   A^2 -> H(U1(e, d), U1(b, d))
27.56/9.02	   A^2 -> H(U1(e, d), U1(c, c))
27.56/9.02	   A^2 -> H(U1(e, d), f(e))
27.56/9.02	   A^2 -> H(U1(e, d), f(k))
27.56/9.02	   A^2 -> H(U1(e, d), U1(d, d))
27.56/9.02	   A^2 -> H(U1(e, a), U1(e, b))
27.56/9.02	   A^2 -> H(U1(e, a), U1(k, b))
27.56/9.02	   A^2 -> H(U1(e, a), U1(c, d))
27.56/9.02	   A^2 -> H(U1(e, a), U1(d, c))
27.56/9.02	   A^2 -> H(U1(e, a), U1(b, e))
27.56/9.02	   A^2 -> H(U1(e, a), U1(b, k))
27.56/9.02	   A^2 -> H(U1(e, a), U1(e, c))
27.56/9.02	   A^2 -> H(U1(e, a), U1(k, c))
27.56/9.02	   A^2 -> H(U1(e, a), U1(c, e))
27.56/9.02	   A^2 -> H(U1(e, a), U1(c, k))
27.56/9.02	   A^2 -> H(U1(e, a), U1(e, e))
27.56/9.02	   A^2 -> H(U1(e, a), U1(k, k))
27.56/9.02	   A^2 -> H(U1(e, a), U1(k, d))
27.56/9.02	   A^2 -> H(U1(e, a), U1(d, k))
27.56/9.02	   A^2 -> H(U1(k, a), U1(e, b))
27.56/9.02	   A^2 -> H(U1(k, a), U1(k, b))
27.56/9.02	   A^2 -> H(U1(k, a), U1(c, d))
27.56/9.02	   A^2 -> H(U1(k, a), U1(d, c))
27.56/9.02	   A^2 -> H(U1(k, a), U1(b, e))
27.56/9.02	   A^2 -> H(U1(k, a), U1(b, k))
27.56/9.02	   A^2 -> H(U1(k, a), U1(e, c))
27.56/9.02	   A^2 -> H(U1(k, a), U1(k, c))
27.56/9.02	   A^2 -> H(U1(k, a), U1(c, e))
27.56/9.02	   A^2 -> H(U1(k, a), U1(c, k))
27.56/9.02	   A^2 -> H(U1(k, a), U1(e, e))
27.56/9.02	   A^2 -> H(U1(k, a), U1(k, k))
27.56/9.02	   A^2 -> H(U1(k, a), U1(k, d))
27.56/9.02	   A^2 -> H(U1(k, a), U1(d, k))
27.56/9.02	   A^2 -> H(U1(c, d), U1(e, b))
27.56/9.02	   A^2 -> H(U1(c, d), U1(k, b))
27.56/9.02	   A^2 -> H(U1(c, d), U1(c, d))
27.56/9.02	   A^2 -> H(U1(c, d), U1(d, c))
27.56/9.02	   A^2 -> H(U1(c, d), U1(b, e))
27.56/9.02	   A^2 -> H(U1(c, d), U1(b, k))
27.56/9.02	   A^2 -> H(U1(c, d), U1(e, c))
27.56/9.02	   A^2 -> H(U1(c, d), U1(k, c))
27.56/9.02	   A^2 -> H(U1(c, d), U1(c, e))
27.56/9.02	   A^2 -> H(U1(c, d), U1(c, k))
27.56/9.02	   A^2 -> H(U1(c, d), U1(e, e))
27.56/9.02	   A^2 -> H(U1(c, d), U1(k, k))
27.56/9.02	   A^2 -> H(U1(c, d), U1(k, d))
27.56/9.02	   A^2 -> H(U1(c, d), U1(d, k))
27.56/9.02	   A^2 -> H(U1(c, a), b)
27.56/9.02	   A^2 -> H(U1(c, a), U1(e, d))
27.56/9.02	   A^2 -> H(U1(c, a), U1(d, e))
27.56/9.02	   A^2 -> H(U1(c, a), c)
27.56/9.02	   A^2 -> H(U1(c, a), U1(e, k))
27.56/9.02	   A^2 -> H(U1(c, a), U1(k, e))
27.56/9.02	   A^2 -> H(U1(c, a), e)
27.56/9.02	   A^2 -> H(U1(c, a), U1(k, k))
27.56/9.02	   A^2 -> H(U1(d, e), U1(c, b))
27.56/9.02	   A^2 -> H(U1(d, e), U1(d, b))
27.56/9.02	   A^2 -> H(U1(d, e), U1(b, c))
27.56/9.02	   A^2 -> H(U1(d, e), U1(b, d))
27.56/9.02	   A^2 -> H(U1(d, e), U1(c, c))
27.56/9.02	   A^2 -> H(U1(d, e), f(e))
27.56/9.02	   A^2 -> H(U1(d, e), f(k))
27.56/9.02	   A^2 -> H(U1(d, e), U1(d, d))
27.56/9.02	   A^2 -> H(U1(d, c), U1(e, b))
27.56/9.02	   A^2 -> H(U1(d, c), U1(k, b))
27.56/9.02	   A^2 -> H(U1(d, c), U1(c, d))
27.56/9.02	   A^2 -> H(U1(d, c), U1(d, c))
27.56/9.02	   A^2 -> H(U1(d, c), U1(b, e))
27.56/9.02	   A^2 -> H(U1(d, c), U1(b, k))
27.56/9.02	   A^2 -> H(U1(d, c), U1(e, c))
27.56/9.02	   A^2 -> H(U1(d, c), U1(k, c))
27.56/9.02	   A^2 -> H(U1(d, c), U1(c, e))
27.56/9.02	   A^2 -> H(U1(d, c), U1(c, k))
27.56/9.02	   A^2 -> H(U1(d, c), U1(e, e))
27.56/9.02	   A^2 -> H(U1(d, c), U1(k, k))
27.56/9.02	   A^2 -> H(U1(d, c), U1(k, d))
27.56/9.02	   A^2 -> H(U1(d, c), U1(d, k))
27.56/9.02	   A^2 -> H(U1(d, a), b)
27.56/9.02	   A^2 -> H(U1(d, a), U1(e, d))
27.56/9.02	   A^2 -> H(U1(d, a), U1(d, e))
27.56/9.02	   A^2 -> H(U1(d, a), c)
27.56/9.02	   A^2 -> H(U1(d, a), U1(e, k))
27.56/9.02	   A^2 -> H(U1(d, a), U1(k, e))
27.56/9.02	   A^2 -> H(U1(d, a), e)
27.56/9.02	   A^2 -> H(U1(d, a), U1(k, k))
27.56/9.02	   A^2 -> H(U1(a, e), U1(e, b))
27.56/9.02	   A^2 -> H(U1(a, e), U1(k, b))
27.56/9.02	   A^2 -> H(U1(a, e), U1(c, d))
27.56/9.02	
27.56/9.02	The TRS R consists of the following rules:
27.56/9.02	
27.56/9.02	   f(x) -> U1(x, x)
27.56/9.02	   U1(e, x) -> x
27.56/9.02	   a -> c
27.56/9.02	   a -> d
27.56/9.02	   b -> c
27.56/9.02	   b -> d
27.56/9.02	   d -> k
27.56/9.02	   c -> e
27.56/9.02	   c -> k
27.56/9.02	
27.56/9.02	Q is empty.
27.56/9.02	We have to consider all minimal (P,Q,R)-chains.
27.56/9.02	----------------------------------------
27.56/9.02	
27.56/9.02	(683) TransformationProof (EQUIVALENT)
27.56/9.02	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
27.56/9.02	
27.56/9.02	   (A^2 -> H(U1(c, e), U1(d, b)),A^2 -> H(U1(c, e), U1(d, b)))
27.56/9.02	   (A^2 -> H(U1(d, e), U1(d, b)),A^2 -> H(U1(d, e), U1(d, b)))
27.56/9.02	   (A^2 -> H(U1(a, e), U1(k, b)),A^2 -> H(U1(a, e), U1(k, b)))
27.56/9.02	   (A^2 -> H(U1(a, e), U1(d, c)),A^2 -> H(U1(a, e), U1(d, c)))
27.56/9.02	   (A^2 -> H(U1(a, e), U1(d, d)),A^2 -> H(U1(a, e), U1(d, d)))
27.56/9.02	
27.56/9.02	
27.56/9.02	----------------------------------------
27.56/9.02	
27.56/9.02	(684)
27.56/9.02	Obligation:
27.56/9.02	Q DP problem:
27.56/9.02	The TRS P consists of the following rules:
27.56/9.02	
27.56/9.02	   H(x, x) -> G(x, x, f(k))
27.56/9.02	   G(d, x, x) -> A^2
27.56/9.02	   A^2 -> H(f(c), f(c))
27.56/9.02	   A^2 -> H(f(d), f(d))
27.56/9.02	   A^2 -> H(U1(c, c), U1(c, c))
27.56/9.02	   A^2 -> H(f(e), f(e))
27.56/9.02	   A^2 -> H(f(k), f(k))
27.56/9.02	   A^2 -> H(U1(d, d), U1(d, d))
27.56/9.02	   A^2 -> H(U1(a, e), U1(b, c))
27.56/9.02	   A^2 -> H(U1(a, e), U1(b, d))
27.56/9.02	   A^2 -> H(U1(a, e), U1(c, c))
27.56/9.02	   A^2 -> H(U1(a, e), f(e))
27.56/9.02	   A^2 -> H(U1(a, e), f(k))
27.56/9.02	   A^2 -> H(U1(a, e), U1(d, d))
27.56/9.02	   A^2 -> H(U1(a, k), U1(c, b))
27.56/9.02	   A^2 -> H(U1(a, k), U1(d, b))
27.56/9.02	   A^2 -> H(U1(a, k), U1(b, c))
27.56/9.02	   A^2 -> H(U1(a, k), U1(b, d))
27.56/9.02	   A^2 -> H(U1(a, k), U1(c, c))
27.56/9.02	   A^2 -> H(U1(a, k), f(e))
27.56/9.02	   A^2 -> H(U1(a, k), f(k))
27.56/9.02	   A^2 -> H(U1(a, k), U1(d, d))
27.56/9.02	   A^2 -> H(U1(a, c), U1(e, b))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, b))
27.56/9.02	   A^2 -> H(U1(a, c), U1(c, d))
27.56/9.02	   A^2 -> H(U1(a, c), U1(d, c))
27.56/9.02	   A^2 -> H(U1(a, c), U1(b, e))
27.56/9.02	   A^2 -> H(U1(a, c), U1(b, k))
27.56/9.02	   A^2 -> H(U1(a, c), U1(e, c))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, c))
27.56/9.02	   A^2 -> H(U1(a, c), U1(c, e))
27.56/9.02	   A^2 -> H(U1(a, c), U1(c, k))
27.56/9.02	   A^2 -> H(U1(a, c), U1(e, e))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, k))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, d))
27.56/9.02	   A^2 -> H(U1(a, c), U1(d, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(e, b))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, b))
27.56/9.02	   A^2 -> H(U1(a, d), U1(c, d))
27.56/9.02	   A^2 -> H(U1(a, d), U1(d, c))
27.56/9.02	   A^2 -> H(U1(a, d), U1(b, e))
27.56/9.02	   A^2 -> H(U1(a, d), U1(b, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(e, c))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, c))
27.56/9.02	   A^2 -> H(U1(a, d), U1(c, e))
27.56/9.02	   A^2 -> H(U1(a, d), U1(c, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(e, e))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, d))
27.56/9.02	   A^2 -> H(U1(a, d), U1(d, k))
27.56/9.02	   A^2 -> H(U1(a, a), b)
27.56/9.02	   A^2 -> H(U1(a, a), U1(e, d))
27.56/9.02	   A^2 -> H(U1(a, a), U1(d, e))
27.56/9.02	   A^2 -> H(U1(a, a), c)
27.56/9.02	   A^2 -> H(U1(a, a), U1(e, k))
27.56/9.02	   A^2 -> H(U1(a, a), U1(k, e))
27.56/9.02	   A^2 -> H(U1(a, a), e)
27.56/9.02	   A^2 -> H(U1(a, a), U1(k, k))
27.56/9.02	   A^2 -> H(k, f(b))
27.56/9.02	   A^2 -> H(c, U1(b, b))
27.56/9.02	   A^2 -> H(c, f(c))
27.56/9.02	   A^2 -> H(c, f(d))
27.56/9.02	   A^2 -> H(U1(e, k), U1(b, b))
27.56/9.02	   A^2 -> H(U1(e, k), f(c))
27.56/9.02	   A^2 -> H(U1(e, k), f(d))
27.56/9.02	   A^2 -> H(U1(e, c), U1(c, b))
27.56/9.02	   A^2 -> H(U1(e, c), U1(d, b))
27.56/9.02	   A^2 -> H(U1(e, c), U1(b, c))
27.56/9.02	   A^2 -> H(U1(e, c), U1(b, d))
27.56/9.02	   A^2 -> H(U1(e, c), U1(c, c))
27.56/9.02	   A^2 -> H(U1(e, c), f(e))
27.56/9.02	   A^2 -> H(U1(e, c), f(k))
27.56/9.02	   A^2 -> H(U1(e, c), U1(d, d))
27.56/9.02	   A^2 -> H(U1(k, e), U1(b, b))
27.56/9.02	   A^2 -> H(U1(k, e), f(c))
27.56/9.02	   A^2 -> H(U1(k, e), f(d))
27.56/9.02	   A^2 -> H(U1(k, c), U1(c, b))
27.56/9.02	   A^2 -> H(U1(k, c), U1(d, b))
27.56/9.02	   A^2 -> H(U1(k, c), U1(b, c))
27.56/9.02	   A^2 -> H(U1(k, c), U1(b, d))
27.56/9.02	   A^2 -> H(U1(k, c), U1(c, c))
27.56/9.02	   A^2 -> H(U1(k, c), f(e))
27.56/9.02	   A^2 -> H(U1(k, c), f(k))
27.56/9.02	   A^2 -> H(U1(k, c), U1(d, d))
27.56/9.02	   A^2 -> H(U1(c, e), U1(c, b))
27.56/9.02	   A^2 -> H(U1(c, e), U1(d, b))
27.56/9.02	   A^2 -> H(U1(c, e), U1(b, c))
27.56/9.02	   A^2 -> H(U1(c, e), U1(b, d))
27.56/9.02	   A^2 -> H(U1(c, e), U1(c, c))
27.56/9.02	   A^2 -> H(U1(c, e), f(e))
27.56/9.02	   A^2 -> H(U1(c, e), f(k))
27.56/9.02	   A^2 -> H(U1(c, e), U1(d, d))
27.56/9.02	   A^2 -> H(U1(c, k), U1(c, b))
27.56/9.02	   A^2 -> H(U1(c, k), U1(d, b))
27.56/9.02	   A^2 -> H(U1(c, k), U1(b, c))
27.56/9.02	   A^2 -> H(U1(c, k), U1(b, d))
27.56/9.02	   A^2 -> H(U1(c, k), U1(c, c))
27.56/9.02	   A^2 -> H(U1(c, k), f(e))
27.56/9.02	   A^2 -> H(U1(c, k), f(k))
27.56/9.02	   A^2 -> H(U1(c, k), U1(d, d))
27.56/9.02	   A^2 -> H(U1(c, c), U1(e, b))
27.56/9.02	   A^2 -> H(U1(c, c), U1(k, b))
27.56/9.02	   A^2 -> H(U1(c, c), U1(c, d))
27.56/9.02	   A^2 -> H(U1(c, c), U1(d, c))
27.56/9.02	   A^2 -> H(U1(c, c), U1(b, e))
27.56/9.02	   A^2 -> H(U1(c, c), U1(b, k))
27.56/9.02	   A^2 -> H(U1(c, c), U1(e, e))
27.56/9.02	   A^2 -> H(U1(c, c), U1(k, k))
27.56/9.02	   A^2 -> H(U1(c, c), U1(k, d))
27.56/9.02	   A^2 -> H(U1(c, c), U1(d, k))
27.56/9.02	   A^2 -> H(e, U1(b, b))
27.56/9.02	   A^2 -> H(e, f(c))
27.56/9.02	   A^2 -> H(e, f(d))
27.56/9.02	   A^2 -> H(U1(e, e), U1(c, b))
27.56/9.02	   A^2 -> H(U1(e, e), U1(d, b))
27.56/9.02	   A^2 -> H(U1(e, e), U1(b, c))
27.56/9.02	   A^2 -> H(U1(e, e), U1(b, d))
27.56/9.02	   A^2 -> H(U1(e, e), U1(c, c))
27.56/9.02	   A^2 -> H(U1(e, e), f(e))
27.56/9.02	   A^2 -> H(U1(e, e), f(k))
27.56/9.02	   A^2 -> H(U1(e, e), U1(d, d))
27.56/9.02	   A^2 -> H(f(e), U1(e, b))
27.56/9.02	   A^2 -> H(f(e), U1(k, b))
27.56/9.02	   A^2 -> H(f(e), U1(c, d))
27.56/9.02	   A^2 -> H(f(e), U1(d, c))
27.56/9.02	   A^2 -> H(f(e), U1(b, e))
27.56/9.02	   A^2 -> H(f(e), U1(b, k))
27.56/9.02	   A^2 -> H(f(e), U1(e, c))
27.56/9.02	   A^2 -> H(f(e), U1(k, c))
27.56/9.02	   A^2 -> H(f(e), U1(c, e))
27.56/9.02	   A^2 -> H(f(e), U1(c, k))
27.56/9.02	   A^2 -> H(f(e), U1(k, k))
27.56/9.02	   A^2 -> H(f(e), U1(k, d))
27.56/9.02	   A^2 -> H(f(e), U1(d, k))
27.56/9.02	   A^2 -> H(U1(k, k), U1(c, b))
27.56/9.02	   A^2 -> H(U1(k, k), U1(d, b))
27.56/9.02	   A^2 -> H(U1(k, k), U1(b, c))
27.56/9.02	   A^2 -> H(U1(k, k), U1(b, d))
27.56/9.02	   A^2 -> H(U1(k, k), U1(c, c))
27.56/9.02	   A^2 -> H(U1(k, k), f(e))
27.56/9.02	   A^2 -> H(U1(k, k), f(k))
27.56/9.02	   A^2 -> H(U1(k, k), U1(d, d))
27.56/9.02	   A^2 -> H(f(k), U1(e, b))
27.56/9.02	   A^2 -> H(f(k), U1(k, b))
27.56/9.02	   A^2 -> H(f(k), U1(c, d))
27.56/9.02	   A^2 -> H(f(k), U1(d, c))
27.56/9.02	   A^2 -> H(f(k), U1(b, e))
27.56/9.02	   A^2 -> H(f(k), U1(b, k))
27.56/9.02	   A^2 -> H(f(k), U1(e, c))
27.56/9.02	   A^2 -> H(f(k), U1(k, c))
27.56/9.02	   A^2 -> H(f(k), U1(c, e))
27.56/9.02	   A^2 -> H(f(k), U1(c, k))
27.56/9.02	   A^2 -> H(f(k), U1(e, e))
27.56/9.02	   A^2 -> H(f(k), U1(k, d))
27.56/9.02	   A^2 -> H(f(k), U1(d, k))
27.56/9.02	   A^2 -> H(f(c), b)
27.56/9.02	   A^2 -> H(f(c), U1(e, d))
27.56/9.02	   A^2 -> H(f(c), U1(d, e))
27.56/9.02	   A^2 -> H(f(k), U1(k, k))
27.56/9.02	   A^2 -> H(U1(k, k), U1(b, b))
27.56/9.02	   A^2 -> H(U1(k, k), f(c))
27.56/9.02	   A^2 -> H(U1(k, k), f(d))
27.56/9.02	   A^2 -> H(U1(k, d), U1(c, b))
27.56/9.02	   A^2 -> H(U1(k, d), U1(d, b))
27.56/9.02	   A^2 -> H(U1(k, d), U1(b, c))
27.56/9.02	   A^2 -> H(U1(k, d), U1(b, d))
27.56/9.02	   A^2 -> H(U1(k, d), U1(c, c))
27.56/9.02	   A^2 -> H(U1(k, d), f(e))
27.56/9.02	   A^2 -> H(U1(k, d), f(k))
27.56/9.02	   A^2 -> H(U1(k, d), U1(d, d))
27.56/9.02	   A^2 -> H(U1(d, k), U1(c, b))
27.56/9.02	   A^2 -> H(U1(d, k), U1(d, b))
27.56/9.02	   A^2 -> H(U1(d, k), U1(b, c))
27.56/9.02	   A^2 -> H(U1(d, k), U1(b, d))
27.56/9.02	   A^2 -> H(U1(d, k), U1(c, c))
27.56/9.02	   A^2 -> H(U1(d, k), f(e))
27.56/9.02	   A^2 -> H(U1(d, k), f(k))
27.56/9.02	   A^2 -> H(U1(d, k), U1(d, d))
27.56/9.02	   A^2 -> H(U1(d, d), U1(e, b))
27.56/9.02	   A^2 -> H(U1(d, d), U1(k, b))
27.56/9.02	   A^2 -> H(U1(d, d), U1(c, d))
27.56/9.02	   A^2 -> H(U1(d, d), U1(d, c))
27.56/9.02	   A^2 -> H(U1(d, d), U1(b, e))
27.56/9.02	   A^2 -> H(U1(d, d), U1(b, k))
27.56/9.02	   A^2 -> H(U1(d, d), U1(e, c))
27.56/9.02	   A^2 -> H(U1(d, d), U1(k, c))
27.56/9.02	   A^2 -> H(U1(d, d), U1(c, e))
27.56/9.02	   A^2 -> H(U1(d, d), U1(c, k))
27.56/9.02	   A^2 -> H(U1(d, d), U1(e, e))
27.56/9.02	   A^2 -> H(U1(d, d), U1(k, k))
27.56/9.02	   A^2 -> H(f(d), b)
27.56/9.02	   A^2 -> H(f(d), U1(e, d))
27.56/9.02	   A^2 -> H(f(d), U1(d, e))
27.56/9.02	   A^2 -> H(f(d), c)
27.56/9.02	   A^2 -> H(f(d), U1(e, k))
27.56/9.02	   A^2 -> H(f(d), U1(k, e))
27.56/9.02	   A^2 -> H(f(d), e)
27.56/9.02	   A^2 -> H(f(a), d)
27.56/9.02	   A^2 -> H(U1(c, c), U1(e, c))
27.56/9.02	   A^2 -> H(f(c), c)
27.56/9.02	   A^2 -> H(f(c), U1(e, k))
27.56/9.02	   A^2 -> H(U1(c, c), U1(k, c))
27.56/9.02	   A^2 -> H(f(c), U1(k, e))
27.56/9.02	   A^2 -> H(f(c), U1(k, k))
27.56/9.02	   A^2 -> H(U1(c, c), U1(c, e))
27.56/9.02	   A^2 -> H(U1(c, c), U1(c, k))
27.56/9.02	   A^2 -> H(f(a), k)
27.56/9.02	   A^2 -> H(f(e), U1(e, e))
27.56/9.02	   A^2 -> H(f(c), e)
27.56/9.02	   A^2 -> H(U1(d, d), U1(k, d))
27.56/9.02	   A^2 -> H(f(d), U1(k, k))
27.56/9.02	   A^2 -> H(U1(d, d), U1(d, k))
27.56/9.02	   A^2 -> H(d, U1(b, b))
27.56/9.02	   A^2 -> H(d, f(c))
27.56/9.02	   A^2 -> H(d, f(d))
27.56/9.02	   A^2 -> H(a, U1(c, b))
27.56/9.02	   A^2 -> H(a, U1(d, b))
27.56/9.02	   A^2 -> H(a, U1(b, c))
27.56/9.02	   A^2 -> H(a, U1(b, d))
27.56/9.02	   A^2 -> H(a, U1(c, c))
27.56/9.02	   A^2 -> H(a, f(e))
27.56/9.02	   A^2 -> H(a, f(k))
27.56/9.02	   A^2 -> H(a, U1(d, d))
27.56/9.02	   A^2 -> H(U1(e, d), U1(c, b))
27.56/9.02	   A^2 -> H(U1(e, d), U1(d, b))
27.56/9.02	   A^2 -> H(U1(e, d), U1(b, c))
27.56/9.02	   A^2 -> H(U1(e, d), U1(b, d))
27.56/9.02	   A^2 -> H(U1(e, d), U1(c, c))
27.56/9.02	   A^2 -> H(U1(e, d), f(e))
27.56/9.02	   A^2 -> H(U1(e, d), f(k))
27.56/9.02	   A^2 -> H(U1(e, d), U1(d, d))
27.56/9.02	   A^2 -> H(U1(e, a), U1(e, b))
27.56/9.02	   A^2 -> H(U1(e, a), U1(k, b))
27.56/9.02	   A^2 -> H(U1(e, a), U1(c, d))
27.56/9.02	   A^2 -> H(U1(e, a), U1(d, c))
27.56/9.02	   A^2 -> H(U1(e, a), U1(b, e))
27.56/9.02	   A^2 -> H(U1(e, a), U1(b, k))
27.56/9.02	   A^2 -> H(U1(e, a), U1(e, c))
27.56/9.02	   A^2 -> H(U1(e, a), U1(k, c))
27.56/9.02	   A^2 -> H(U1(e, a), U1(c, e))
27.56/9.02	   A^2 -> H(U1(e, a), U1(c, k))
27.56/9.02	   A^2 -> H(U1(e, a), U1(e, e))
27.56/9.02	   A^2 -> H(U1(e, a), U1(k, k))
27.56/9.02	   A^2 -> H(U1(e, a), U1(k, d))
27.56/9.02	   A^2 -> H(U1(e, a), U1(d, k))
27.56/9.02	   A^2 -> H(U1(k, a), U1(e, b))
27.56/9.02	   A^2 -> H(U1(k, a), U1(k, b))
27.56/9.02	   A^2 -> H(U1(k, a), U1(c, d))
27.56/9.02	   A^2 -> H(U1(k, a), U1(d, c))
27.56/9.02	   A^2 -> H(U1(k, a), U1(b, e))
27.56/9.02	   A^2 -> H(U1(k, a), U1(b, k))
27.56/9.02	   A^2 -> H(U1(k, a), U1(e, c))
27.56/9.02	   A^2 -> H(U1(k, a), U1(k, c))
27.56/9.02	   A^2 -> H(U1(k, a), U1(c, e))
27.56/9.02	   A^2 -> H(U1(k, a), U1(c, k))
27.56/9.02	   A^2 -> H(U1(k, a), U1(e, e))
27.56/9.02	   A^2 -> H(U1(k, a), U1(k, k))
27.56/9.02	   A^2 -> H(U1(k, a), U1(k, d))
27.56/9.02	   A^2 -> H(U1(k, a), U1(d, k))
27.56/9.02	   A^2 -> H(U1(c, d), U1(e, b))
27.56/9.02	   A^2 -> H(U1(c, d), U1(k, b))
27.56/9.02	   A^2 -> H(U1(c, d), U1(c, d))
27.56/9.02	   A^2 -> H(U1(c, d), U1(d, c))
27.56/9.02	   A^2 -> H(U1(c, d), U1(b, e))
27.56/9.02	   A^2 -> H(U1(c, d), U1(b, k))
27.56/9.02	   A^2 -> H(U1(c, d), U1(e, c))
27.56/9.02	   A^2 -> H(U1(c, d), U1(k, c))
27.56/9.02	   A^2 -> H(U1(c, d), U1(c, e))
27.56/9.02	   A^2 -> H(U1(c, d), U1(c, k))
27.56/9.02	   A^2 -> H(U1(c, d), U1(e, e))
27.56/9.02	   A^2 -> H(U1(c, d), U1(k, k))
27.56/9.02	   A^2 -> H(U1(c, d), U1(k, d))
27.56/9.02	   A^2 -> H(U1(c, d), U1(d, k))
27.56/9.02	   A^2 -> H(U1(c, a), b)
27.56/9.02	   A^2 -> H(U1(c, a), U1(e, d))
27.56/9.02	   A^2 -> H(U1(c, a), U1(d, e))
27.56/9.02	   A^2 -> H(U1(c, a), c)
27.56/9.02	   A^2 -> H(U1(c, a), U1(e, k))
27.56/9.02	   A^2 -> H(U1(c, a), U1(k, e))
27.56/9.02	   A^2 -> H(U1(c, a), e)
27.56/9.02	   A^2 -> H(U1(c, a), U1(k, k))
27.56/9.02	   A^2 -> H(U1(d, e), U1(c, b))
27.56/9.02	   A^2 -> H(U1(d, e), U1(d, b))
27.56/9.02	   A^2 -> H(U1(d, e), U1(b, c))
27.56/9.02	   A^2 -> H(U1(d, e), U1(b, d))
27.56/9.02	   A^2 -> H(U1(d, e), U1(c, c))
27.56/9.02	   A^2 -> H(U1(d, e), f(e))
27.56/9.02	   A^2 -> H(U1(d, e), f(k))
27.56/9.02	   A^2 -> H(U1(d, e), U1(d, d))
27.56/9.02	   A^2 -> H(U1(d, c), U1(e, b))
27.56/9.02	   A^2 -> H(U1(d, c), U1(k, b))
27.56/9.02	   A^2 -> H(U1(d, c), U1(c, d))
27.56/9.02	   A^2 -> H(U1(d, c), U1(d, c))
27.56/9.02	   A^2 -> H(U1(d, c), U1(b, e))
27.56/9.02	   A^2 -> H(U1(d, c), U1(b, k))
27.56/9.02	   A^2 -> H(U1(d, c), U1(e, c))
27.56/9.02	   A^2 -> H(U1(d, c), U1(k, c))
27.56/9.02	   A^2 -> H(U1(d, c), U1(c, e))
27.56/9.02	   A^2 -> H(U1(d, c), U1(c, k))
27.56/9.02	   A^2 -> H(U1(d, c), U1(e, e))
27.56/9.02	   A^2 -> H(U1(d, c), U1(k, k))
27.56/9.02	   A^2 -> H(U1(d, c), U1(k, d))
27.56/9.02	   A^2 -> H(U1(d, c), U1(d, k))
27.56/9.02	   A^2 -> H(U1(d, a), b)
27.56/9.02	   A^2 -> H(U1(d, a), U1(e, d))
27.56/9.02	   A^2 -> H(U1(d, a), U1(d, e))
27.56/9.02	   A^2 -> H(U1(d, a), c)
27.56/9.02	   A^2 -> H(U1(d, a), U1(e, k))
27.56/9.02	   A^2 -> H(U1(d, a), U1(k, e))
27.56/9.02	   A^2 -> H(U1(d, a), e)
27.56/9.02	   A^2 -> H(U1(d, a), U1(k, k))
27.56/9.02	   A^2 -> H(U1(a, e), U1(e, b))
27.56/9.02	   A^2 -> H(U1(a, e), U1(k, b))
27.56/9.02	   A^2 -> H(U1(a, e), U1(c, d))
27.56/9.02	   A^2 -> H(U1(a, e), U1(d, c))
27.56/9.02	
27.56/9.02	The TRS R consists of the following rules:
27.56/9.02	
27.56/9.02	   f(x) -> U1(x, x)
27.56/9.02	   U1(e, x) -> x
27.56/9.02	   a -> c
27.56/9.02	   a -> d
27.56/9.02	   b -> c
27.56/9.02	   b -> d
27.56/9.02	   d -> k
27.56/9.02	   c -> e
27.56/9.02	   c -> k
27.56/9.02	
27.56/9.02	Q is empty.
27.56/9.02	We have to consider all minimal (P,Q,R)-chains.
27.56/9.02	----------------------------------------
27.56/9.02	
27.56/9.02	(685) TransformationProof (EQUIVALENT)
27.56/9.02	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
27.56/9.02	
27.56/9.02	   (A^2 -> H(U1(c, e), U1(b, c)),A^2 -> H(U1(c, e), U1(b, c)))
27.56/9.02	   (A^2 -> H(U1(d, e), U1(b, c)),A^2 -> H(U1(d, e), U1(b, c)))
27.56/9.02	   (A^2 -> H(U1(a, e), U1(c, c)),A^2 -> H(U1(a, e), U1(c, c)))
27.56/9.02	   (A^2 -> H(U1(a, e), U1(d, c)),A^2 -> H(U1(a, e), U1(d, c)))
27.56/9.02	   (A^2 -> H(U1(a, e), U1(b, e)),A^2 -> H(U1(a, e), U1(b, e)))
27.56/9.02	   (A^2 -> H(U1(a, e), U1(b, k)),A^2 -> H(U1(a, e), U1(b, k)))
27.56/9.02	
27.56/9.02	
27.56/9.02	----------------------------------------
27.56/9.02	
27.56/9.02	(686)
27.56/9.02	Obligation:
27.56/9.02	Q DP problem:
27.56/9.02	The TRS P consists of the following rules:
27.56/9.02	
27.56/9.02	   H(x, x) -> G(x, x, f(k))
27.56/9.02	   G(d, x, x) -> A^2
27.56/9.02	   A^2 -> H(f(c), f(c))
27.56/9.02	   A^2 -> H(f(d), f(d))
27.56/9.02	   A^2 -> H(U1(c, c), U1(c, c))
27.56/9.02	   A^2 -> H(f(e), f(e))
27.56/9.02	   A^2 -> H(f(k), f(k))
27.56/9.02	   A^2 -> H(U1(d, d), U1(d, d))
27.56/9.02	   A^2 -> H(U1(a, e), U1(b, d))
27.56/9.02	   A^2 -> H(U1(a, e), U1(c, c))
27.56/9.02	   A^2 -> H(U1(a, e), f(e))
27.56/9.02	   A^2 -> H(U1(a, e), f(k))
27.56/9.02	   A^2 -> H(U1(a, e), U1(d, d))
27.56/9.02	   A^2 -> H(U1(a, k), U1(c, b))
27.56/9.02	   A^2 -> H(U1(a, k), U1(d, b))
27.56/9.02	   A^2 -> H(U1(a, k), U1(b, c))
27.56/9.02	   A^2 -> H(U1(a, k), U1(b, d))
27.56/9.02	   A^2 -> H(U1(a, k), U1(c, c))
27.56/9.02	   A^2 -> H(U1(a, k), f(e))
27.56/9.02	   A^2 -> H(U1(a, k), f(k))
27.56/9.02	   A^2 -> H(U1(a, k), U1(d, d))
27.56/9.02	   A^2 -> H(U1(a, c), U1(e, b))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, b))
27.56/9.02	   A^2 -> H(U1(a, c), U1(c, d))
27.56/9.02	   A^2 -> H(U1(a, c), U1(d, c))
27.56/9.02	   A^2 -> H(U1(a, c), U1(b, e))
27.56/9.02	   A^2 -> H(U1(a, c), U1(b, k))
27.56/9.02	   A^2 -> H(U1(a, c), U1(e, c))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, c))
27.56/9.02	   A^2 -> H(U1(a, c), U1(c, e))
27.56/9.02	   A^2 -> H(U1(a, c), U1(c, k))
27.56/9.02	   A^2 -> H(U1(a, c), U1(e, e))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, k))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, d))
27.56/9.02	   A^2 -> H(U1(a, c), U1(d, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(e, b))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, b))
27.56/9.02	   A^2 -> H(U1(a, d), U1(c, d))
27.56/9.02	   A^2 -> H(U1(a, d), U1(d, c))
27.56/9.02	   A^2 -> H(U1(a, d), U1(b, e))
27.56/9.02	   A^2 -> H(U1(a, d), U1(b, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(e, c))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, c))
27.56/9.02	   A^2 -> H(U1(a, d), U1(c, e))
27.56/9.02	   A^2 -> H(U1(a, d), U1(c, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(e, e))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, d))
27.56/9.02	   A^2 -> H(U1(a, d), U1(d, k))
27.56/9.02	   A^2 -> H(U1(a, a), b)
27.56/9.02	   A^2 -> H(U1(a, a), U1(e, d))
27.56/9.02	   A^2 -> H(U1(a, a), U1(d, e))
27.56/9.02	   A^2 -> H(U1(a, a), c)
27.56/9.02	   A^2 -> H(U1(a, a), U1(e, k))
27.56/9.02	   A^2 -> H(U1(a, a), U1(k, e))
27.56/9.02	   A^2 -> H(U1(a, a), e)
27.56/9.02	   A^2 -> H(U1(a, a), U1(k, k))
27.56/9.02	   A^2 -> H(k, f(b))
27.56/9.02	   A^2 -> H(c, U1(b, b))
27.56/9.02	   A^2 -> H(c, f(c))
27.56/9.02	   A^2 -> H(c, f(d))
27.56/9.02	   A^2 -> H(U1(e, k), U1(b, b))
27.56/9.02	   A^2 -> H(U1(e, k), f(c))
27.56/9.02	   A^2 -> H(U1(e, k), f(d))
27.56/9.02	   A^2 -> H(U1(e, c), U1(c, b))
27.56/9.02	   A^2 -> H(U1(e, c), U1(d, b))
27.56/9.02	   A^2 -> H(U1(e, c), U1(b, c))
27.56/9.02	   A^2 -> H(U1(e, c), U1(b, d))
27.56/9.02	   A^2 -> H(U1(e, c), U1(c, c))
27.56/9.02	   A^2 -> H(U1(e, c), f(e))
27.56/9.02	   A^2 -> H(U1(e, c), f(k))
27.56/9.02	   A^2 -> H(U1(e, c), U1(d, d))
27.56/9.02	   A^2 -> H(U1(k, e), U1(b, b))
27.56/9.02	   A^2 -> H(U1(k, e), f(c))
27.56/9.02	   A^2 -> H(U1(k, e), f(d))
27.56/9.02	   A^2 -> H(U1(k, c), U1(c, b))
27.56/9.02	   A^2 -> H(U1(k, c), U1(d, b))
27.56/9.02	   A^2 -> H(U1(k, c), U1(b, c))
27.56/9.02	   A^2 -> H(U1(k, c), U1(b, d))
27.56/9.02	   A^2 -> H(U1(k, c), U1(c, c))
27.56/9.02	   A^2 -> H(U1(k, c), f(e))
27.56/9.02	   A^2 -> H(U1(k, c), f(k))
27.56/9.02	   A^2 -> H(U1(k, c), U1(d, d))
27.56/9.02	   A^2 -> H(U1(c, e), U1(c, b))
27.56/9.02	   A^2 -> H(U1(c, e), U1(d, b))
27.56/9.02	   A^2 -> H(U1(c, e), U1(b, c))
27.56/9.02	   A^2 -> H(U1(c, e), U1(b, d))
27.56/9.02	   A^2 -> H(U1(c, e), U1(c, c))
27.56/9.02	   A^2 -> H(U1(c, e), f(e))
27.56/9.02	   A^2 -> H(U1(c, e), f(k))
27.56/9.02	   A^2 -> H(U1(c, e), U1(d, d))
27.56/9.02	   A^2 -> H(U1(c, k), U1(c, b))
27.56/9.02	   A^2 -> H(U1(c, k), U1(d, b))
27.56/9.02	   A^2 -> H(U1(c, k), U1(b, c))
27.56/9.02	   A^2 -> H(U1(c, k), U1(b, d))
27.56/9.02	   A^2 -> H(U1(c, k), U1(c, c))
27.56/9.02	   A^2 -> H(U1(c, k), f(e))
27.56/9.02	   A^2 -> H(U1(c, k), f(k))
27.56/9.02	   A^2 -> H(U1(c, k), U1(d, d))
27.56/9.02	   A^2 -> H(U1(c, c), U1(e, b))
27.56/9.02	   A^2 -> H(U1(c, c), U1(k, b))
27.56/9.02	   A^2 -> H(U1(c, c), U1(c, d))
27.56/9.02	   A^2 -> H(U1(c, c), U1(d, c))
27.56/9.02	   A^2 -> H(U1(c, c), U1(b, e))
27.56/9.02	   A^2 -> H(U1(c, c), U1(b, k))
27.56/9.02	   A^2 -> H(U1(c, c), U1(e, e))
27.56/9.02	   A^2 -> H(U1(c, c), U1(k, k))
27.56/9.02	   A^2 -> H(U1(c, c), U1(k, d))
27.56/9.02	   A^2 -> H(U1(c, c), U1(d, k))
27.56/9.02	   A^2 -> H(e, U1(b, b))
27.56/9.02	   A^2 -> H(e, f(c))
27.56/9.02	   A^2 -> H(e, f(d))
27.56/9.02	   A^2 -> H(U1(e, e), U1(c, b))
27.56/9.02	   A^2 -> H(U1(e, e), U1(d, b))
27.56/9.02	   A^2 -> H(U1(e, e), U1(b, c))
27.56/9.02	   A^2 -> H(U1(e, e), U1(b, d))
27.56/9.02	   A^2 -> H(U1(e, e), U1(c, c))
27.56/9.02	   A^2 -> H(U1(e, e), f(e))
27.56/9.02	   A^2 -> H(U1(e, e), f(k))
27.56/9.02	   A^2 -> H(U1(e, e), U1(d, d))
27.56/9.02	   A^2 -> H(f(e), U1(e, b))
27.56/9.02	   A^2 -> H(f(e), U1(k, b))
27.56/9.02	   A^2 -> H(f(e), U1(c, d))
27.56/9.02	   A^2 -> H(f(e), U1(d, c))
27.56/9.02	   A^2 -> H(f(e), U1(b, e))
27.56/9.02	   A^2 -> H(f(e), U1(b, k))
27.56/9.02	   A^2 -> H(f(e), U1(e, c))
27.56/9.02	   A^2 -> H(f(e), U1(k, c))
27.56/9.02	   A^2 -> H(f(e), U1(c, e))
27.56/9.02	   A^2 -> H(f(e), U1(c, k))
27.56/9.02	   A^2 -> H(f(e), U1(k, k))
27.56/9.02	   A^2 -> H(f(e), U1(k, d))
27.56/9.02	   A^2 -> H(f(e), U1(d, k))
27.56/9.02	   A^2 -> H(U1(k, k), U1(c, b))
27.56/9.02	   A^2 -> H(U1(k, k), U1(d, b))
27.56/9.02	   A^2 -> H(U1(k, k), U1(b, c))
27.56/9.02	   A^2 -> H(U1(k, k), U1(b, d))
27.56/9.02	   A^2 -> H(U1(k, k), U1(c, c))
27.56/9.02	   A^2 -> H(U1(k, k), f(e))
27.56/9.02	   A^2 -> H(U1(k, k), f(k))
27.56/9.02	   A^2 -> H(U1(k, k), U1(d, d))
27.56/9.02	   A^2 -> H(f(k), U1(e, b))
27.56/9.02	   A^2 -> H(f(k), U1(k, b))
27.56/9.02	   A^2 -> H(f(k), U1(c, d))
27.56/9.02	   A^2 -> H(f(k), U1(d, c))
27.56/9.02	   A^2 -> H(f(k), U1(b, e))
27.56/9.02	   A^2 -> H(f(k), U1(b, k))
27.56/9.02	   A^2 -> H(f(k), U1(e, c))
27.56/9.02	   A^2 -> H(f(k), U1(k, c))
27.56/9.02	   A^2 -> H(f(k), U1(c, e))
27.56/9.02	   A^2 -> H(f(k), U1(c, k))
27.56/9.02	   A^2 -> H(f(k), U1(e, e))
27.56/9.02	   A^2 -> H(f(k), U1(k, d))
27.56/9.02	   A^2 -> H(f(k), U1(d, k))
27.56/9.02	   A^2 -> H(f(c), b)
27.56/9.02	   A^2 -> H(f(c), U1(e, d))
27.56/9.02	   A^2 -> H(f(c), U1(d, e))
27.56/9.02	   A^2 -> H(f(k), U1(k, k))
27.56/9.02	   A^2 -> H(U1(k, k), U1(b, b))
27.56/9.02	   A^2 -> H(U1(k, k), f(c))
27.56/9.02	   A^2 -> H(U1(k, k), f(d))
27.56/9.02	   A^2 -> H(U1(k, d), U1(c, b))
27.56/9.02	   A^2 -> H(U1(k, d), U1(d, b))
27.56/9.02	   A^2 -> H(U1(k, d), U1(b, c))
27.56/9.02	   A^2 -> H(U1(k, d), U1(b, d))
27.56/9.02	   A^2 -> H(U1(k, d), U1(c, c))
27.56/9.02	   A^2 -> H(U1(k, d), f(e))
27.56/9.02	   A^2 -> H(U1(k, d), f(k))
27.56/9.02	   A^2 -> H(U1(k, d), U1(d, d))
27.56/9.02	   A^2 -> H(U1(d, k), U1(c, b))
27.56/9.02	   A^2 -> H(U1(d, k), U1(d, b))
27.56/9.02	   A^2 -> H(U1(d, k), U1(b, c))
27.56/9.02	   A^2 -> H(U1(d, k), U1(b, d))
27.56/9.02	   A^2 -> H(U1(d, k), U1(c, c))
27.56/9.02	   A^2 -> H(U1(d, k), f(e))
27.56/9.02	   A^2 -> H(U1(d, k), f(k))
27.56/9.02	   A^2 -> H(U1(d, k), U1(d, d))
27.56/9.02	   A^2 -> H(U1(d, d), U1(e, b))
27.56/9.02	   A^2 -> H(U1(d, d), U1(k, b))
27.56/9.02	   A^2 -> H(U1(d, d), U1(c, d))
27.56/9.02	   A^2 -> H(U1(d, d), U1(d, c))
27.56/9.02	   A^2 -> H(U1(d, d), U1(b, e))
27.56/9.02	   A^2 -> H(U1(d, d), U1(b, k))
27.56/9.02	   A^2 -> H(U1(d, d), U1(e, c))
27.56/9.02	   A^2 -> H(U1(d, d), U1(k, c))
27.56/9.02	   A^2 -> H(U1(d, d), U1(c, e))
27.56/9.02	   A^2 -> H(U1(d, d), U1(c, k))
27.56/9.02	   A^2 -> H(U1(d, d), U1(e, e))
27.56/9.02	   A^2 -> H(U1(d, d), U1(k, k))
27.56/9.02	   A^2 -> H(f(d), b)
27.56/9.02	   A^2 -> H(f(d), U1(e, d))
27.56/9.02	   A^2 -> H(f(d), U1(d, e))
27.56/9.02	   A^2 -> H(f(d), c)
27.56/9.02	   A^2 -> H(f(d), U1(e, k))
27.56/9.02	   A^2 -> H(f(d), U1(k, e))
27.56/9.02	   A^2 -> H(f(d), e)
27.56/9.02	   A^2 -> H(f(a), d)
27.56/9.02	   A^2 -> H(U1(c, c), U1(e, c))
27.56/9.02	   A^2 -> H(f(c), c)
27.56/9.02	   A^2 -> H(f(c), U1(e, k))
27.56/9.02	   A^2 -> H(U1(c, c), U1(k, c))
27.56/9.02	   A^2 -> H(f(c), U1(k, e))
27.56/9.02	   A^2 -> H(f(c), U1(k, k))
27.56/9.02	   A^2 -> H(U1(c, c), U1(c, e))
27.56/9.02	   A^2 -> H(U1(c, c), U1(c, k))
27.56/9.02	   A^2 -> H(f(a), k)
27.56/9.02	   A^2 -> H(f(e), U1(e, e))
27.56/9.02	   A^2 -> H(f(c), e)
27.56/9.02	   A^2 -> H(U1(d, d), U1(k, d))
27.56/9.02	   A^2 -> H(f(d), U1(k, k))
27.56/9.02	   A^2 -> H(U1(d, d), U1(d, k))
27.56/9.02	   A^2 -> H(d, U1(b, b))
27.56/9.02	   A^2 -> H(d, f(c))
27.56/9.02	   A^2 -> H(d, f(d))
27.56/9.02	   A^2 -> H(a, U1(c, b))
27.56/9.02	   A^2 -> H(a, U1(d, b))
27.56/9.02	   A^2 -> H(a, U1(b, c))
27.56/9.02	   A^2 -> H(a, U1(b, d))
27.56/9.02	   A^2 -> H(a, U1(c, c))
27.56/9.02	   A^2 -> H(a, f(e))
27.56/9.02	   A^2 -> H(a, f(k))
27.56/9.02	   A^2 -> H(a, U1(d, d))
27.56/9.02	   A^2 -> H(U1(e, d), U1(c, b))
27.56/9.02	   A^2 -> H(U1(e, d), U1(d, b))
27.56/9.02	   A^2 -> H(U1(e, d), U1(b, c))
27.56/9.02	   A^2 -> H(U1(e, d), U1(b, d))
27.56/9.02	   A^2 -> H(U1(e, d), U1(c, c))
27.56/9.02	   A^2 -> H(U1(e, d), f(e))
27.56/9.02	   A^2 -> H(U1(e, d), f(k))
27.56/9.02	   A^2 -> H(U1(e, d), U1(d, d))
27.56/9.02	   A^2 -> H(U1(e, a), U1(e, b))
27.56/9.02	   A^2 -> H(U1(e, a), U1(k, b))
27.56/9.02	   A^2 -> H(U1(e, a), U1(c, d))
27.56/9.02	   A^2 -> H(U1(e, a), U1(d, c))
27.56/9.02	   A^2 -> H(U1(e, a), U1(b, e))
27.56/9.02	   A^2 -> H(U1(e, a), U1(b, k))
27.56/9.02	   A^2 -> H(U1(e, a), U1(e, c))
27.56/9.02	   A^2 -> H(U1(e, a), U1(k, c))
27.56/9.02	   A^2 -> H(U1(e, a), U1(c, e))
27.56/9.02	   A^2 -> H(U1(e, a), U1(c, k))
27.56/9.02	   A^2 -> H(U1(e, a), U1(e, e))
27.56/9.02	   A^2 -> H(U1(e, a), U1(k, k))
27.56/9.02	   A^2 -> H(U1(e, a), U1(k, d))
27.56/9.02	   A^2 -> H(U1(e, a), U1(d, k))
27.56/9.02	   A^2 -> H(U1(k, a), U1(e, b))
27.56/9.02	   A^2 -> H(U1(k, a), U1(k, b))
27.56/9.02	   A^2 -> H(U1(k, a), U1(c, d))
27.56/9.02	   A^2 -> H(U1(k, a), U1(d, c))
27.56/9.02	   A^2 -> H(U1(k, a), U1(b, e))
27.56/9.02	   A^2 -> H(U1(k, a), U1(b, k))
27.56/9.02	   A^2 -> H(U1(k, a), U1(e, c))
27.56/9.02	   A^2 -> H(U1(k, a), U1(k, c))
27.56/9.02	   A^2 -> H(U1(k, a), U1(c, e))
27.56/9.02	   A^2 -> H(U1(k, a), U1(c, k))
27.56/9.02	   A^2 -> H(U1(k, a), U1(e, e))
27.56/9.02	   A^2 -> H(U1(k, a), U1(k, k))
27.56/9.02	   A^2 -> H(U1(k, a), U1(k, d))
27.56/9.02	   A^2 -> H(U1(k, a), U1(d, k))
27.56/9.02	   A^2 -> H(U1(c, d), U1(e, b))
27.56/9.02	   A^2 -> H(U1(c, d), U1(k, b))
27.56/9.02	   A^2 -> H(U1(c, d), U1(c, d))
27.56/9.02	   A^2 -> H(U1(c, d), U1(d, c))
27.56/9.02	   A^2 -> H(U1(c, d), U1(b, e))
27.56/9.02	   A^2 -> H(U1(c, d), U1(b, k))
27.56/9.02	   A^2 -> H(U1(c, d), U1(e, c))
27.56/9.02	   A^2 -> H(U1(c, d), U1(k, c))
27.56/9.02	   A^2 -> H(U1(c, d), U1(c, e))
27.56/9.02	   A^2 -> H(U1(c, d), U1(c, k))
27.56/9.02	   A^2 -> H(U1(c, d), U1(e, e))
27.56/9.02	   A^2 -> H(U1(c, d), U1(k, k))
27.56/9.02	   A^2 -> H(U1(c, d), U1(k, d))
27.56/9.02	   A^2 -> H(U1(c, d), U1(d, k))
27.56/9.02	   A^2 -> H(U1(c, a), b)
27.56/9.02	   A^2 -> H(U1(c, a), U1(e, d))
27.56/9.02	   A^2 -> H(U1(c, a), U1(d, e))
27.56/9.02	   A^2 -> H(U1(c, a), c)
27.56/9.02	   A^2 -> H(U1(c, a), U1(e, k))
27.56/9.02	   A^2 -> H(U1(c, a), U1(k, e))
27.56/9.02	   A^2 -> H(U1(c, a), e)
27.56/9.02	   A^2 -> H(U1(c, a), U1(k, k))
27.56/9.02	   A^2 -> H(U1(d, e), U1(c, b))
27.56/9.02	   A^2 -> H(U1(d, e), U1(d, b))
27.56/9.02	   A^2 -> H(U1(d, e), U1(b, c))
27.56/9.02	   A^2 -> H(U1(d, e), U1(b, d))
27.56/9.02	   A^2 -> H(U1(d, e), U1(c, c))
27.56/9.02	   A^2 -> H(U1(d, e), f(e))
27.56/9.02	   A^2 -> H(U1(d, e), f(k))
27.56/9.02	   A^2 -> H(U1(d, e), U1(d, d))
27.56/9.02	   A^2 -> H(U1(d, c), U1(e, b))
27.56/9.02	   A^2 -> H(U1(d, c), U1(k, b))
27.56/9.02	   A^2 -> H(U1(d, c), U1(c, d))
27.56/9.02	   A^2 -> H(U1(d, c), U1(d, c))
27.56/9.02	   A^2 -> H(U1(d, c), U1(b, e))
27.56/9.02	   A^2 -> H(U1(d, c), U1(b, k))
27.56/9.02	   A^2 -> H(U1(d, c), U1(e, c))
27.56/9.02	   A^2 -> H(U1(d, c), U1(k, c))
27.56/9.02	   A^2 -> H(U1(d, c), U1(c, e))
27.56/9.02	   A^2 -> H(U1(d, c), U1(c, k))
27.56/9.02	   A^2 -> H(U1(d, c), U1(e, e))
27.56/9.02	   A^2 -> H(U1(d, c), U1(k, k))
27.56/9.02	   A^2 -> H(U1(d, c), U1(k, d))
27.56/9.02	   A^2 -> H(U1(d, c), U1(d, k))
27.56/9.02	   A^2 -> H(U1(d, a), b)
27.56/9.02	   A^2 -> H(U1(d, a), U1(e, d))
27.56/9.02	   A^2 -> H(U1(d, a), U1(d, e))
27.56/9.02	   A^2 -> H(U1(d, a), c)
27.56/9.02	   A^2 -> H(U1(d, a), U1(e, k))
27.56/9.02	   A^2 -> H(U1(d, a), U1(k, e))
27.56/9.02	   A^2 -> H(U1(d, a), e)
27.56/9.02	   A^2 -> H(U1(d, a), U1(k, k))
27.56/9.02	   A^2 -> H(U1(a, e), U1(e, b))
27.56/9.02	   A^2 -> H(U1(a, e), U1(k, b))
27.56/9.02	   A^2 -> H(U1(a, e), U1(c, d))
27.56/9.02	   A^2 -> H(U1(a, e), U1(d, c))
27.56/9.02	   A^2 -> H(U1(a, e), U1(b, e))
27.56/9.02	   A^2 -> H(U1(a, e), U1(b, k))
27.56/9.02	
27.56/9.02	The TRS R consists of the following rules:
27.56/9.02	
27.56/9.02	   f(x) -> U1(x, x)
27.56/9.02	   U1(e, x) -> x
27.56/9.02	   a -> c
27.56/9.02	   a -> d
27.56/9.02	   b -> c
27.56/9.02	   b -> d
27.56/9.02	   d -> k
27.56/9.02	   c -> e
27.56/9.02	   c -> k
27.56/9.02	
27.56/9.02	Q is empty.
27.56/9.02	We have to consider all minimal (P,Q,R)-chains.
27.56/9.02	----------------------------------------
27.56/9.02	
27.56/9.02	(687) TransformationProof (EQUIVALENT)
27.56/9.02	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
27.56/9.02	
27.56/9.02	   (A^2 -> H(U1(c, e), U1(b, d)),A^2 -> H(U1(c, e), U1(b, d)))
27.56/9.02	   (A^2 -> H(U1(d, e), U1(b, d)),A^2 -> H(U1(d, e), U1(b, d)))
27.56/9.02	   (A^2 -> H(U1(a, e), U1(c, d)),A^2 -> H(U1(a, e), U1(c, d)))
27.56/9.02	   (A^2 -> H(U1(a, e), U1(d, d)),A^2 -> H(U1(a, e), U1(d, d)))
27.56/9.02	   (A^2 -> H(U1(a, e), U1(b, k)),A^2 -> H(U1(a, e), U1(b, k)))
27.56/9.02	
27.56/9.02	
27.56/9.02	----------------------------------------
27.56/9.02	
27.56/9.02	(688)
27.56/9.02	Obligation:
27.56/9.02	Q DP problem:
27.56/9.02	The TRS P consists of the following rules:
27.56/9.02	
27.56/9.02	   H(x, x) -> G(x, x, f(k))
27.56/9.02	   G(d, x, x) -> A^2
27.56/9.02	   A^2 -> H(f(c), f(c))
27.56/9.02	   A^2 -> H(f(d), f(d))
27.56/9.02	   A^2 -> H(U1(c, c), U1(c, c))
27.56/9.02	   A^2 -> H(f(e), f(e))
27.56/9.02	   A^2 -> H(f(k), f(k))
27.56/9.02	   A^2 -> H(U1(d, d), U1(d, d))
27.56/9.02	   A^2 -> H(U1(a, e), U1(c, c))
27.56/9.02	   A^2 -> H(U1(a, e), f(e))
27.56/9.02	   A^2 -> H(U1(a, e), f(k))
27.56/9.02	   A^2 -> H(U1(a, e), U1(d, d))
27.56/9.02	   A^2 -> H(U1(a, k), U1(c, b))
27.56/9.02	   A^2 -> H(U1(a, k), U1(d, b))
27.56/9.02	   A^2 -> H(U1(a, k), U1(b, c))
27.56/9.02	   A^2 -> H(U1(a, k), U1(b, d))
27.56/9.02	   A^2 -> H(U1(a, k), U1(c, c))
27.56/9.02	   A^2 -> H(U1(a, k), f(e))
27.56/9.02	   A^2 -> H(U1(a, k), f(k))
27.56/9.02	   A^2 -> H(U1(a, k), U1(d, d))
27.56/9.02	   A^2 -> H(U1(a, c), U1(e, b))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, b))
27.56/9.02	   A^2 -> H(U1(a, c), U1(c, d))
27.56/9.02	   A^2 -> H(U1(a, c), U1(d, c))
27.56/9.02	   A^2 -> H(U1(a, c), U1(b, e))
27.56/9.02	   A^2 -> H(U1(a, c), U1(b, k))
27.56/9.02	   A^2 -> H(U1(a, c), U1(e, c))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, c))
27.56/9.02	   A^2 -> H(U1(a, c), U1(c, e))
27.56/9.02	   A^2 -> H(U1(a, c), U1(c, k))
27.56/9.02	   A^2 -> H(U1(a, c), U1(e, e))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, k))
27.56/9.02	   A^2 -> H(U1(a, c), U1(k, d))
27.56/9.02	   A^2 -> H(U1(a, c), U1(d, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(e, b))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, b))
27.56/9.02	   A^2 -> H(U1(a, d), U1(c, d))
27.56/9.02	   A^2 -> H(U1(a, d), U1(d, c))
27.56/9.02	   A^2 -> H(U1(a, d), U1(b, e))
27.56/9.02	   A^2 -> H(U1(a, d), U1(b, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(e, c))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, c))
27.56/9.02	   A^2 -> H(U1(a, d), U1(c, e))
27.56/9.02	   A^2 -> H(U1(a, d), U1(c, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(e, e))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, k))
27.56/9.02	   A^2 -> H(U1(a, d), U1(k, d))
27.56/9.02	   A^2 -> H(U1(a, d), U1(d, k))
27.56/9.02	   A^2 -> H(U1(a, a), b)
27.56/9.02	   A^2 -> H(U1(a, a), U1(e, d))
27.56/9.02	   A^2 -> H(U1(a, a), U1(d, e))
27.56/9.02	   A^2 -> H(U1(a, a), c)
27.56/9.02	   A^2 -> H(U1(a, a), U1(e, k))
27.56/9.02	   A^2 -> H(U1(a, a), U1(k, e))
27.56/9.02	   A^2 -> H(U1(a, a), e)
27.56/9.02	   A^2 -> H(U1(a, a), U1(k, k))
27.56/9.02	   A^2 -> H(k, f(b))
27.56/9.02	   A^2 -> H(c, U1(b, b))
27.56/9.02	   A^2 -> H(c, f(c))
27.56/9.02	   A^2 -> H(c, f(d))
27.56/9.02	   A^2 -> H(U1(e, k), U1(b, b))
27.56/9.02	   A^2 -> H(U1(e, k), f(c))
27.56/9.02	   A^2 -> H(U1(e, k), f(d))
27.56/9.02	   A^2 -> H(U1(e, c), U1(c, b))
27.56/9.02	   A^2 -> H(U1(e, c), U1(d, b))
27.56/9.02	   A^2 -> H(U1(e, c), U1(b, c))
27.56/9.02	   A^2 -> H(U1(e, c), U1(b, d))
27.56/9.02	   A^2 -> H(U1(e, c), U1(c, c))
27.56/9.02	   A^2 -> H(U1(e, c), f(e))
27.56/9.02	   A^2 -> H(U1(e, c), f(k))
27.56/9.02	   A^2 -> H(U1(e, c), U1(d, d))
27.56/9.02	   A^2 -> H(U1(k, e), U1(b, b))
27.56/9.02	   A^2 -> H(U1(k, e), f(c))
27.56/9.02	   A^2 -> H(U1(k, e), f(d))
27.56/9.02	   A^2 -> H(U1(k, c), U1(c, b))
27.56/9.02	   A^2 -> H(U1(k, c), U1(d, b))
27.56/9.02	   A^2 -> H(U1(k, c), U1(b, c))
27.56/9.02	   A^2 -> H(U1(k, c), U1(b, d))
27.56/9.02	   A^2 -> H(U1(k, c), U1(c, c))
27.56/9.02	   A^2 -> H(U1(k, c), f(e))
27.56/9.02	   A^2 -> H(U1(k, c), f(k))
27.56/9.02	   A^2 -> H(U1(k, c), U1(d, d))
27.56/9.02	   A^2 -> H(U1(c, e), U1(c, b))
27.56/9.02	   A^2 -> H(U1(c, e), U1(d, b))
27.56/9.02	   A^2 -> H(U1(c, e), U1(b, c))
27.56/9.02	   A^2 -> H(U1(c, e), U1(b, d))
27.56/9.02	   A^2 -> H(U1(c, e), U1(c, c))
27.56/9.02	   A^2 -> H(U1(c, e), f(e))
27.56/9.02	   A^2 -> H(U1(c, e), f(k))
27.56/9.02	   A^2 -> H(U1(c, e), U1(d, d))
27.56/9.03	   A^2 -> H(U1(c, k), U1(c, b))
27.56/9.03	   A^2 -> H(U1(c, k), U1(d, b))
27.56/9.03	   A^2 -> H(U1(c, k), U1(b, c))
27.56/9.03	   A^2 -> H(U1(c, k), U1(b, d))
27.56/9.03	   A^2 -> H(U1(c, k), U1(c, c))
27.56/9.03	   A^2 -> H(U1(c, k), f(e))
27.56/9.03	   A^2 -> H(U1(c, k), f(k))
27.56/9.03	   A^2 -> H(U1(c, k), U1(d, d))
27.56/9.03	   A^2 -> H(U1(c, c), U1(e, b))
27.56/9.03	   A^2 -> H(U1(c, c), U1(k, b))
27.56/9.03	   A^2 -> H(U1(c, c), U1(c, d))
27.56/9.03	   A^2 -> H(U1(c, c), U1(d, c))
27.56/9.03	   A^2 -> H(U1(c, c), U1(b, e))
27.56/9.03	   A^2 -> H(U1(c, c), U1(b, k))
27.56/9.03	   A^2 -> H(U1(c, c), U1(e, e))
27.56/9.03	   A^2 -> H(U1(c, c), U1(k, k))
27.56/9.03	   A^2 -> H(U1(c, c), U1(k, d))
27.56/9.03	   A^2 -> H(U1(c, c), U1(d, k))
27.56/9.03	   A^2 -> H(e, U1(b, b))
27.56/9.03	   A^2 -> H(e, f(c))
27.56/9.03	   A^2 -> H(e, f(d))
27.56/9.03	   A^2 -> H(U1(e, e), U1(c, b))
27.56/9.03	   A^2 -> H(U1(e, e), U1(d, b))
27.56/9.03	   A^2 -> H(U1(e, e), U1(b, c))
27.56/9.03	   A^2 -> H(U1(e, e), U1(b, d))
27.56/9.03	   A^2 -> H(U1(e, e), U1(c, c))
27.56/9.03	   A^2 -> H(U1(e, e), f(e))
27.56/9.03	   A^2 -> H(U1(e, e), f(k))
27.56/9.03	   A^2 -> H(U1(e, e), U1(d, d))
27.56/9.03	   A^2 -> H(f(e), U1(e, b))
27.56/9.03	   A^2 -> H(f(e), U1(k, b))
27.56/9.03	   A^2 -> H(f(e), U1(c, d))
27.56/9.03	   A^2 -> H(f(e), U1(d, c))
27.56/9.03	   A^2 -> H(f(e), U1(b, e))
27.56/9.03	   A^2 -> H(f(e), U1(b, k))
27.56/9.03	   A^2 -> H(f(e), U1(e, c))
27.56/9.03	   A^2 -> H(f(e), U1(k, c))
27.56/9.03	   A^2 -> H(f(e), U1(c, e))
27.56/9.03	   A^2 -> H(f(e), U1(c, k))
27.56/9.03	   A^2 -> H(f(e), U1(k, k))
27.56/9.03	   A^2 -> H(f(e), U1(k, d))
27.56/9.03	   A^2 -> H(f(e), U1(d, k))
27.56/9.03	   A^2 -> H(U1(k, k), U1(c, b))
27.56/9.03	   A^2 -> H(U1(k, k), U1(d, b))
27.56/9.03	   A^2 -> H(U1(k, k), U1(b, c))
27.56/9.03	   A^2 -> H(U1(k, k), U1(b, d))
27.56/9.03	   A^2 -> H(U1(k, k), U1(c, c))
27.56/9.03	   A^2 -> H(U1(k, k), f(e))
27.56/9.03	   A^2 -> H(U1(k, k), f(k))
27.56/9.03	   A^2 -> H(U1(k, k), U1(d, d))
27.56/9.03	   A^2 -> H(f(k), U1(e, b))
27.56/9.03	   A^2 -> H(f(k), U1(k, b))
27.56/9.03	   A^2 -> H(f(k), U1(c, d))
27.56/9.03	   A^2 -> H(f(k), U1(d, c))
27.56/9.03	   A^2 -> H(f(k), U1(b, e))
27.56/9.03	   A^2 -> H(f(k), U1(b, k))
27.56/9.03	   A^2 -> H(f(k), U1(e, c))
27.56/9.03	   A^2 -> H(f(k), U1(k, c))
27.56/9.03	   A^2 -> H(f(k), U1(c, e))
27.56/9.03	   A^2 -> H(f(k), U1(c, k))
27.56/9.03	   A^2 -> H(f(k), U1(e, e))
27.56/9.03	   A^2 -> H(f(k), U1(k, d))
27.56/9.03	   A^2 -> H(f(k), U1(d, k))
27.56/9.03	   A^2 -> H(f(c), b)
27.56/9.03	   A^2 -> H(f(c), U1(e, d))
27.56/9.03	   A^2 -> H(f(c), U1(d, e))
27.56/9.03	   A^2 -> H(f(k), U1(k, k))
27.56/9.03	   A^2 -> H(U1(k, k), U1(b, b))
27.56/9.03	   A^2 -> H(U1(k, k), f(c))
27.56/9.03	   A^2 -> H(U1(k, k), f(d))
27.56/9.03	   A^2 -> H(U1(k, d), U1(c, b))
27.56/9.03	   A^2 -> H(U1(k, d), U1(d, b))
27.56/9.03	   A^2 -> H(U1(k, d), U1(b, c))
27.56/9.03	   A^2 -> H(U1(k, d), U1(b, d))
27.56/9.03	   A^2 -> H(U1(k, d), U1(c, c))
27.56/9.03	   A^2 -> H(U1(k, d), f(e))
27.56/9.03	   A^2 -> H(U1(k, d), f(k))
27.56/9.03	   A^2 -> H(U1(k, d), U1(d, d))
27.56/9.03	   A^2 -> H(U1(d, k), U1(c, b))
27.56/9.03	   A^2 -> H(U1(d, k), U1(d, b))
27.56/9.03	   A^2 -> H(U1(d, k), U1(b, c))
27.56/9.03	   A^2 -> H(U1(d, k), U1(b, d))
27.56/9.03	   A^2 -> H(U1(d, k), U1(c, c))
27.56/9.03	   A^2 -> H(U1(d, k), f(e))
27.56/9.03	   A^2 -> H(U1(d, k), f(k))
27.56/9.03	   A^2 -> H(U1(d, k), U1(d, d))
27.56/9.03	   A^2 -> H(U1(d, d), U1(e, b))
27.56/9.03	   A^2 -> H(U1(d, d), U1(k, b))
27.56/9.03	   A^2 -> H(U1(d, d), U1(c, d))
27.56/9.03	   A^2 -> H(U1(d, d), U1(d, c))
27.56/9.03	   A^2 -> H(U1(d, d), U1(b, e))
27.56/9.03	   A^2 -> H(U1(d, d), U1(b, k))
27.56/9.03	   A^2 -> H(U1(d, d), U1(e, c))
27.56/9.03	   A^2 -> H(U1(d, d), U1(k, c))
27.56/9.03	   A^2 -> H(U1(d, d), U1(c, e))
27.56/9.03	   A^2 -> H(U1(d, d), U1(c, k))
27.56/9.03	   A^2 -> H(U1(d, d), U1(e, e))
27.56/9.03	   A^2 -> H(U1(d, d), U1(k, k))
27.56/9.03	   A^2 -> H(f(d), b)
27.56/9.03	   A^2 -> H(f(d), U1(e, d))
27.56/9.03	   A^2 -> H(f(d), U1(d, e))
27.56/9.03	   A^2 -> H(f(d), c)
27.56/9.03	   A^2 -> H(f(d), U1(e, k))
27.56/9.03	   A^2 -> H(f(d), U1(k, e))
27.56/9.03	   A^2 -> H(f(d), e)
27.56/9.03	   A^2 -> H(f(a), d)
27.56/9.03	   A^2 -> H(U1(c, c), U1(e, c))
27.56/9.03	   A^2 -> H(f(c), c)
27.56/9.03	   A^2 -> H(f(c), U1(e, k))
27.56/9.03	   A^2 -> H(U1(c, c), U1(k, c))
27.56/9.03	   A^2 -> H(f(c), U1(k, e))
27.56/9.03	   A^2 -> H(f(c), U1(k, k))
27.56/9.03	   A^2 -> H(U1(c, c), U1(c, e))
27.56/9.03	   A^2 -> H(U1(c, c), U1(c, k))
27.56/9.03	   A^2 -> H(f(a), k)
27.56/9.03	   A^2 -> H(f(e), U1(e, e))
27.56/9.03	   A^2 -> H(f(c), e)
27.56/9.03	   A^2 -> H(U1(d, d), U1(k, d))
27.56/9.03	   A^2 -> H(f(d), U1(k, k))
27.56/9.03	   A^2 -> H(U1(d, d), U1(d, k))
27.56/9.03	   A^2 -> H(d, U1(b, b))
27.56/9.03	   A^2 -> H(d, f(c))
27.56/9.03	   A^2 -> H(d, f(d))
27.56/9.03	   A^2 -> H(a, U1(c, b))
27.56/9.03	   A^2 -> H(a, U1(d, b))
27.56/9.03	   A^2 -> H(a, U1(b, c))
27.56/9.03	   A^2 -> H(a, U1(b, d))
27.56/9.03	   A^2 -> H(a, U1(c, c))
27.56/9.03	   A^2 -> H(a, f(e))
27.56/9.03	   A^2 -> H(a, f(k))
27.56/9.03	   A^2 -> H(a, U1(d, d))
27.56/9.03	   A^2 -> H(U1(e, d), U1(c, b))
27.56/9.03	   A^2 -> H(U1(e, d), U1(d, b))
27.56/9.03	   A^2 -> H(U1(e, d), U1(b, c))
27.56/9.03	   A^2 -> H(U1(e, d), U1(b, d))
27.56/9.03	   A^2 -> H(U1(e, d), U1(c, c))
27.56/9.03	   A^2 -> H(U1(e, d), f(e))
27.56/9.03	   A^2 -> H(U1(e, d), f(k))
27.56/9.03	   A^2 -> H(U1(e, d), U1(d, d))
27.56/9.03	   A^2 -> H(U1(e, a), U1(e, b))
27.56/9.03	   A^2 -> H(U1(e, a), U1(k, b))
27.56/9.03	   A^2 -> H(U1(e, a), U1(c, d))
27.56/9.03	   A^2 -> H(U1(e, a), U1(d, c))
27.56/9.03	   A^2 -> H(U1(e, a), U1(b, e))
27.56/9.03	   A^2 -> H(U1(e, a), U1(b, k))
27.56/9.03	   A^2 -> H(U1(e, a), U1(e, c))
27.56/9.03	   A^2 -> H(U1(e, a), U1(k, c))
27.56/9.03	   A^2 -> H(U1(e, a), U1(c, e))
27.56/9.03	   A^2 -> H(U1(e, a), U1(c, k))
27.56/9.03	   A^2 -> H(U1(e, a), U1(e, e))
27.56/9.03	   A^2 -> H(U1(e, a), U1(k, k))
27.56/9.03	   A^2 -> H(U1(e, a), U1(k, d))
27.56/9.03	   A^2 -> H(U1(e, a), U1(d, k))
27.56/9.03	   A^2 -> H(U1(k, a), U1(e, b))
27.56/9.03	   A^2 -> H(U1(k, a), U1(k, b))
27.56/9.03	   A^2 -> H(U1(k, a), U1(c, d))
27.56/9.03	   A^2 -> H(U1(k, a), U1(d, c))
27.56/9.03	   A^2 -> H(U1(k, a), U1(b, e))
27.56/9.03	   A^2 -> H(U1(k, a), U1(b, k))
27.56/9.03	   A^2 -> H(U1(k, a), U1(e, c))
27.56/9.03	   A^2 -> H(U1(k, a), U1(k, c))
27.56/9.03	   A^2 -> H(U1(k, a), U1(c, e))
27.56/9.03	   A^2 -> H(U1(k, a), U1(c, k))
27.56/9.03	   A^2 -> H(U1(k, a), U1(e, e))
27.56/9.03	   A^2 -> H(U1(k, a), U1(k, k))
27.56/9.03	   A^2 -> H(U1(k, a), U1(k, d))
27.56/9.03	   A^2 -> H(U1(k, a), U1(d, k))
27.56/9.03	   A^2 -> H(U1(c, d), U1(e, b))
27.56/9.03	   A^2 -> H(U1(c, d), U1(k, b))
27.56/9.03	   A^2 -> H(U1(c, d), U1(c, d))
27.56/9.03	   A^2 -> H(U1(c, d), U1(d, c))
27.56/9.03	   A^2 -> H(U1(c, d), U1(b, e))
27.56/9.03	   A^2 -> H(U1(c, d), U1(b, k))
27.56/9.03	   A^2 -> H(U1(c, d), U1(e, c))
27.56/9.03	   A^2 -> H(U1(c, d), U1(k, c))
27.56/9.03	   A^2 -> H(U1(c, d), U1(c, e))
27.56/9.03	   A^2 -> H(U1(c, d), U1(c, k))
27.56/9.03	   A^2 -> H(U1(c, d), U1(e, e))
27.56/9.03	   A^2 -> H(U1(c, d), U1(k, k))
27.56/9.03	   A^2 -> H(U1(c, d), U1(k, d))
27.56/9.03	   A^2 -> H(U1(c, d), U1(d, k))
27.56/9.03	   A^2 -> H(U1(c, a), b)
27.56/9.03	   A^2 -> H(U1(c, a), U1(e, d))
27.56/9.03	   A^2 -> H(U1(c, a), U1(d, e))
27.56/9.03	   A^2 -> H(U1(c, a), c)
27.56/9.03	   A^2 -> H(U1(c, a), U1(e, k))
27.56/9.03	   A^2 -> H(U1(c, a), U1(k, e))
27.56/9.03	   A^2 -> H(U1(c, a), e)
27.56/9.03	   A^2 -> H(U1(c, a), U1(k, k))
27.56/9.03	   A^2 -> H(U1(d, e), U1(c, b))
27.56/9.03	   A^2 -> H(U1(d, e), U1(d, b))
27.56/9.03	   A^2 -> H(U1(d, e), U1(b, c))
27.56/9.03	   A^2 -> H(U1(d, e), U1(b, d))
27.56/9.03	   A^2 -> H(U1(d, e), U1(c, c))
27.56/9.03	   A^2 -> H(U1(d, e), f(e))
27.56/9.03	   A^2 -> H(U1(d, e), f(k))
27.56/9.03	   A^2 -> H(U1(d, e), U1(d, d))
27.56/9.03	   A^2 -> H(U1(d, c), U1(e, b))
27.56/9.03	   A^2 -> H(U1(d, c), U1(k, b))
27.56/9.03	   A^2 -> H(U1(d, c), U1(c, d))
27.56/9.03	   A^2 -> H(U1(d, c), U1(d, c))
27.56/9.03	   A^2 -> H(U1(d, c), U1(b, e))
27.56/9.03	   A^2 -> H(U1(d, c), U1(b, k))
27.56/9.03	   A^2 -> H(U1(d, c), U1(e, c))
27.56/9.03	   A^2 -> H(U1(d, c), U1(k, c))
27.56/9.03	   A^2 -> H(U1(d, c), U1(c, e))
27.56/9.03	   A^2 -> H(U1(d, c), U1(c, k))
27.56/9.03	   A^2 -> H(U1(d, c), U1(e, e))
27.56/9.03	   A^2 -> H(U1(d, c), U1(k, k))
27.56/9.03	   A^2 -> H(U1(d, c), U1(k, d))
27.56/9.03	   A^2 -> H(U1(d, c), U1(d, k))
27.56/9.03	   A^2 -> H(U1(d, a), b)
27.56/9.03	   A^2 -> H(U1(d, a), U1(e, d))
27.56/9.03	   A^2 -> H(U1(d, a), U1(d, e))
27.56/9.03	   A^2 -> H(U1(d, a), c)
27.56/9.03	   A^2 -> H(U1(d, a), U1(e, k))
27.56/9.03	   A^2 -> H(U1(d, a), U1(k, e))
27.56/9.03	   A^2 -> H(U1(d, a), e)
27.56/9.03	   A^2 -> H(U1(d, a), U1(k, k))
27.56/9.03	   A^2 -> H(U1(a, e), U1(e, b))
27.56/9.03	   A^2 -> H(U1(a, e), U1(k, b))
27.56/9.03	   A^2 -> H(U1(a, e), U1(c, d))
27.56/9.03	   A^2 -> H(U1(a, e), U1(d, c))
27.56/9.03	   A^2 -> H(U1(a, e), U1(b, e))
27.56/9.03	   A^2 -> H(U1(a, e), U1(b, k))
27.56/9.03	
27.56/9.03	The TRS R consists of the following rules:
27.56/9.03	
27.56/9.03	   f(x) -> U1(x, x)
27.56/9.03	   U1(e, x) -> x
27.56/9.03	   a -> c
27.56/9.03	   a -> d
27.56/9.03	   b -> c
27.56/9.03	   b -> d
27.56/9.03	   d -> k
27.56/9.03	   c -> e
27.56/9.03	   c -> k
27.56/9.03	
27.56/9.03	Q is empty.
27.56/9.03	We have to consider all minimal (P,Q,R)-chains.
27.56/9.03	----------------------------------------
27.56/9.03	
27.56/9.03	(689) TransformationProof (EQUIVALENT)
27.56/9.03	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
27.56/9.03	
27.56/9.03	   (A^2 -> H(U1(c, e), U1(c, c)),A^2 -> H(U1(c, e), U1(c, c)))
27.56/9.03	   (A^2 -> H(U1(d, e), U1(c, c)),A^2 -> H(U1(d, e), U1(c, c)))
27.56/9.03	   (A^2 -> H(U1(a, e), U1(e, c)),A^2 -> H(U1(a, e), U1(e, c)))
27.56/9.03	   (A^2 -> H(U1(a, e), U1(k, c)),A^2 -> H(U1(a, e), U1(k, c)))
27.56/9.03	   (A^2 -> H(U1(a, e), U1(c, e)),A^2 -> H(U1(a, e), U1(c, e)))
27.56/9.03	   (A^2 -> H(U1(a, e), U1(c, k)),A^2 -> H(U1(a, e), U1(c, k)))
27.56/9.03	
27.56/9.03	
27.56/9.03	----------------------------------------
27.56/9.03	
27.56/9.03	(690)
27.56/9.03	Obligation:
27.56/9.03	Q DP problem:
27.56/9.03	The TRS P consists of the following rules:
27.56/9.03	
27.56/9.03	   H(x, x) -> G(x, x, f(k))
27.56/9.03	   G(d, x, x) -> A^2
27.56/9.03	   A^2 -> H(f(c), f(c))
27.56/9.03	   A^2 -> H(f(d), f(d))
27.56/9.03	   A^2 -> H(U1(c, c), U1(c, c))
27.56/9.03	   A^2 -> H(f(e), f(e))
27.56/9.03	   A^2 -> H(f(k), f(k))
27.56/9.03	   A^2 -> H(U1(d, d), U1(d, d))
27.56/9.03	   A^2 -> H(U1(a, e), f(e))
27.56/9.03	   A^2 -> H(U1(a, e), f(k))
27.56/9.03	   A^2 -> H(U1(a, e), U1(d, d))
27.56/9.03	   A^2 -> H(U1(a, k), U1(c, b))
27.56/9.03	   A^2 -> H(U1(a, k), U1(d, b))
27.56/9.03	   A^2 -> H(U1(a, k), U1(b, c))
27.56/9.03	   A^2 -> H(U1(a, k), U1(b, d))
27.56/9.03	   A^2 -> H(U1(a, k), U1(c, c))
27.56/9.03	   A^2 -> H(U1(a, k), f(e))
27.56/9.03	   A^2 -> H(U1(a, k), f(k))
27.56/9.03	   A^2 -> H(U1(a, k), U1(d, d))
27.56/9.03	   A^2 -> H(U1(a, c), U1(e, b))
27.56/9.03	   A^2 -> H(U1(a, c), U1(k, b))
27.56/9.03	   A^2 -> H(U1(a, c), U1(c, d))
27.56/9.03	   A^2 -> H(U1(a, c), U1(d, c))
27.56/9.03	   A^2 -> H(U1(a, c), U1(b, e))
27.56/9.03	   A^2 -> H(U1(a, c), U1(b, k))
27.56/9.03	   A^2 -> H(U1(a, c), U1(e, c))
27.56/9.03	   A^2 -> H(U1(a, c), U1(k, c))
27.56/9.03	   A^2 -> H(U1(a, c), U1(c, e))
27.56/9.03	   A^2 -> H(U1(a, c), U1(c, k))
27.56/9.03	   A^2 -> H(U1(a, c), U1(e, e))
27.56/9.03	   A^2 -> H(U1(a, c), U1(k, k))
27.56/9.03	   A^2 -> H(U1(a, c), U1(k, d))
27.56/9.03	   A^2 -> H(U1(a, c), U1(d, k))
27.56/9.03	   A^2 -> H(U1(a, d), U1(e, b))
27.56/9.03	   A^2 -> H(U1(a, d), U1(k, b))
27.56/9.03	   A^2 -> H(U1(a, d), U1(c, d))
27.56/9.03	   A^2 -> H(U1(a, d), U1(d, c))
27.56/9.03	   A^2 -> H(U1(a, d), U1(b, e))
27.56/9.03	   A^2 -> H(U1(a, d), U1(b, k))
27.56/9.03	   A^2 -> H(U1(a, d), U1(e, c))
27.56/9.03	   A^2 -> H(U1(a, d), U1(k, c))
27.56/9.03	   A^2 -> H(U1(a, d), U1(c, e))
27.56/9.03	   A^2 -> H(U1(a, d), U1(c, k))
27.56/9.03	   A^2 -> H(U1(a, d), U1(e, e))
27.56/9.03	   A^2 -> H(U1(a, d), U1(k, k))
27.56/9.03	   A^2 -> H(U1(a, d), U1(k, d))
27.56/9.03	   A^2 -> H(U1(a, d), U1(d, k))
27.56/9.03	   A^2 -> H(U1(a, a), b)
27.56/9.03	   A^2 -> H(U1(a, a), U1(e, d))
27.56/9.03	   A^2 -> H(U1(a, a), U1(d, e))
27.56/9.03	   A^2 -> H(U1(a, a), c)
27.56/9.03	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.03	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.03	   A^2 -> H(U1(a, a), e)
27.86/9.03	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.03	   A^2 -> H(k, f(b))
27.86/9.03	   A^2 -> H(c, U1(b, b))
27.86/9.03	   A^2 -> H(c, f(c))
27.86/9.03	   A^2 -> H(c, f(d))
27.86/9.03	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.03	   A^2 -> H(U1(e, k), f(c))
27.86/9.03	   A^2 -> H(U1(e, k), f(d))
27.86/9.03	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.03	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.03	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.03	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.03	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.03	   A^2 -> H(U1(e, c), f(e))
27.86/9.03	   A^2 -> H(U1(e, c), f(k))
27.86/9.03	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.03	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.03	   A^2 -> H(U1(k, e), f(c))
27.86/9.03	   A^2 -> H(U1(k, e), f(d))
27.86/9.03	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.03	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.03	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.03	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.03	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.03	   A^2 -> H(U1(k, c), f(e))
27.86/9.03	   A^2 -> H(U1(k, c), f(k))
27.86/9.03	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.03	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.03	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.03	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.03	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.03	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.03	   A^2 -> H(U1(c, e), f(e))
27.86/9.03	   A^2 -> H(U1(c, e), f(k))
27.86/9.03	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.03	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.03	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(c, k), f(e))
27.86/9.03	   A^2 -> H(U1(c, k), f(k))
27.86/9.03	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.03	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.03	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.03	   A^2 -> H(e, U1(b, b))
27.86/9.03	   A^2 -> H(e, f(c))
27.86/9.03	   A^2 -> H(e, f(d))
27.86/9.03	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.03	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.03	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.03	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.03	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.03	   A^2 -> H(U1(e, e), f(e))
27.86/9.03	   A^2 -> H(U1(e, e), f(k))
27.86/9.03	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.03	   A^2 -> H(f(e), U1(e, b))
27.86/9.03	   A^2 -> H(f(e), U1(k, b))
27.86/9.03	   A^2 -> H(f(e), U1(c, d))
27.86/9.03	   A^2 -> H(f(e), U1(d, c))
27.86/9.03	   A^2 -> H(f(e), U1(b, e))
27.86/9.03	   A^2 -> H(f(e), U1(b, k))
27.86/9.03	   A^2 -> H(f(e), U1(e, c))
27.86/9.03	   A^2 -> H(f(e), U1(k, c))
27.86/9.03	   A^2 -> H(f(e), U1(c, e))
27.86/9.03	   A^2 -> H(f(e), U1(c, k))
27.86/9.03	   A^2 -> H(f(e), U1(k, k))
27.86/9.03	   A^2 -> H(f(e), U1(k, d))
27.86/9.03	   A^2 -> H(f(e), U1(d, k))
27.86/9.03	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.03	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(k, k), f(e))
27.86/9.03	   A^2 -> H(U1(k, k), f(k))
27.86/9.03	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.03	   A^2 -> H(f(k), U1(e, b))
27.86/9.03	   A^2 -> H(f(k), U1(k, b))
27.86/9.03	   A^2 -> H(f(k), U1(c, d))
27.86/9.03	   A^2 -> H(f(k), U1(d, c))
27.86/9.03	   A^2 -> H(f(k), U1(b, e))
27.86/9.03	   A^2 -> H(f(k), U1(b, k))
27.86/9.03	   A^2 -> H(f(k), U1(e, c))
27.86/9.03	   A^2 -> H(f(k), U1(k, c))
27.86/9.03	   A^2 -> H(f(k), U1(c, e))
27.86/9.03	   A^2 -> H(f(k), U1(c, k))
27.86/9.03	   A^2 -> H(f(k), U1(e, e))
27.86/9.03	   A^2 -> H(f(k), U1(k, d))
27.86/9.03	   A^2 -> H(f(k), U1(d, k))
27.86/9.03	   A^2 -> H(f(c), b)
27.86/9.03	   A^2 -> H(f(c), U1(e, d))
27.86/9.03	   A^2 -> H(f(c), U1(d, e))
27.86/9.03	   A^2 -> H(f(k), U1(k, k))
27.86/9.03	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.03	   A^2 -> H(U1(k, k), f(c))
27.86/9.03	   A^2 -> H(U1(k, k), f(d))
27.86/9.03	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.03	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.03	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.03	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.03	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.03	   A^2 -> H(U1(k, d), f(e))
27.86/9.03	   A^2 -> H(U1(k, d), f(k))
27.86/9.03	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.03	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.03	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(d, k), f(e))
27.86/9.03	   A^2 -> H(U1(d, k), f(k))
27.86/9.03	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.03	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.03	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.03	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.03	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.03	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.03	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.03	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.03	   A^2 -> H(f(d), b)
27.86/9.03	   A^2 -> H(f(d), U1(e, d))
27.86/9.03	   A^2 -> H(f(d), U1(d, e))
27.86/9.03	   A^2 -> H(f(d), c)
27.86/9.03	   A^2 -> H(f(d), U1(e, k))
27.86/9.03	   A^2 -> H(f(d), U1(k, e))
27.86/9.03	   A^2 -> H(f(d), e)
27.86/9.03	   A^2 -> H(f(a), d)
27.86/9.03	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.03	   A^2 -> H(f(c), c)
27.86/9.03	   A^2 -> H(f(c), U1(e, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.03	   A^2 -> H(f(c), U1(k, e))
27.86/9.03	   A^2 -> H(f(c), U1(k, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.03	   A^2 -> H(f(a), k)
27.86/9.03	   A^2 -> H(f(e), U1(e, e))
27.86/9.03	   A^2 -> H(f(c), e)
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.03	   A^2 -> H(f(d), U1(k, k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.03	   A^2 -> H(d, U1(b, b))
27.86/9.03	   A^2 -> H(d, f(c))
27.86/9.03	   A^2 -> H(d, f(d))
27.86/9.03	   A^2 -> H(a, U1(c, b))
27.86/9.03	   A^2 -> H(a, U1(d, b))
27.86/9.03	   A^2 -> H(a, U1(b, c))
27.86/9.03	   A^2 -> H(a, U1(b, d))
27.86/9.03	   A^2 -> H(a, U1(c, c))
27.86/9.03	   A^2 -> H(a, f(e))
27.86/9.03	   A^2 -> H(a, f(k))
27.86/9.03	   A^2 -> H(a, U1(d, d))
27.86/9.03	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.03	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.03	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.03	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.03	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.03	   A^2 -> H(U1(e, d), f(e))
27.86/9.03	   A^2 -> H(U1(e, d), f(k))
27.86/9.03	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.03	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.03	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.03	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.03	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.03	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.03	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.03	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.03	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.03	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.03	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.03	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.03	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.03	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.03	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.03	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.03	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.03	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.03	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.03	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.03	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.03	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.03	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.03	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.03	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.03	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.03	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.03	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.03	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.03	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.03	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.03	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.03	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.03	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.03	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.03	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.03	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.03	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.03	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.03	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.03	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.03	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.03	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.03	   A^2 -> H(U1(c, a), b)
27.86/9.03	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.03	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.03	   A^2 -> H(U1(c, a), c)
27.86/9.03	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.03	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.03	   A^2 -> H(U1(c, a), e)
27.86/9.03	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.03	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.03	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.03	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.03	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.03	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.03	   A^2 -> H(U1(d, e), f(e))
27.86/9.03	   A^2 -> H(U1(d, e), f(k))
27.86/9.03	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.03	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.03	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.03	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.03	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.03	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.03	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.03	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.03	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.03	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.03	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.03	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.03	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.03	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.03	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.03	   A^2 -> H(U1(d, a), b)
27.86/9.03	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.03	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.03	   A^2 -> H(U1(d, a), c)
27.86/9.03	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.03	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.03	   A^2 -> H(U1(d, a), e)
27.86/9.03	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.03	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.03	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.03	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.03	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.03	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.03	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.03	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.03	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.03	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.03	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.03	
27.86/9.03	The TRS R consists of the following rules:
27.86/9.03	
27.86/9.03	   f(x) -> U1(x, x)
27.86/9.03	   U1(e, x) -> x
27.86/9.03	   a -> c
27.86/9.03	   a -> d
27.86/9.03	   b -> c
27.86/9.03	   b -> d
27.86/9.03	   d -> k
27.86/9.03	   c -> e
27.86/9.03	   c -> k
27.86/9.03	
27.86/9.03	Q is empty.
27.86/9.03	We have to consider all minimal (P,Q,R)-chains.
27.86/9.03	----------------------------------------
27.86/9.03	
27.86/9.03	(691) TransformationProof (EQUIVALENT)
27.86/9.03	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), f(e)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.03	
27.86/9.03	   (A^2 -> H(U1(c, e), f(e)),A^2 -> H(U1(c, e), f(e)))
27.86/9.03	   (A^2 -> H(U1(d, e), f(e)),A^2 -> H(U1(d, e), f(e)))
27.86/9.03	   (A^2 -> H(U1(a, e), U1(e, e)),A^2 -> H(U1(a, e), U1(e, e)))
27.86/9.03	
27.86/9.03	
27.86/9.03	----------------------------------------
27.86/9.03	
27.86/9.03	(692)
27.86/9.03	Obligation:
27.86/9.03	Q DP problem:
27.86/9.03	The TRS P consists of the following rules:
27.86/9.03	
27.86/9.03	   H(x, x) -> G(x, x, f(k))
27.86/9.03	   G(d, x, x) -> A^2
27.86/9.03	   A^2 -> H(f(c), f(c))
27.86/9.03	   A^2 -> H(f(d), f(d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.03	   A^2 -> H(f(e), f(e))
27.86/9.03	   A^2 -> H(f(k), f(k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.03	   A^2 -> H(U1(a, e), f(k))
27.86/9.03	   A^2 -> H(U1(a, e), U1(d, d))
27.86/9.03	   A^2 -> H(U1(a, k), U1(c, b))
27.86/9.03	   A^2 -> H(U1(a, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(a, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(a, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(a, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(a, k), f(e))
27.86/9.03	   A^2 -> H(U1(a, k), f(k))
27.86/9.03	   A^2 -> H(U1(a, k), U1(d, d))
27.86/9.03	   A^2 -> H(U1(a, c), U1(e, b))
27.86/9.03	   A^2 -> H(U1(a, c), U1(k, b))
27.86/9.03	   A^2 -> H(U1(a, c), U1(c, d))
27.86/9.03	   A^2 -> H(U1(a, c), U1(d, c))
27.86/9.03	   A^2 -> H(U1(a, c), U1(b, e))
27.86/9.03	   A^2 -> H(U1(a, c), U1(b, k))
27.86/9.03	   A^2 -> H(U1(a, c), U1(e, c))
27.86/9.03	   A^2 -> H(U1(a, c), U1(k, c))
27.86/9.03	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.03	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.03	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.03	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.03	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.03	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.03	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.03	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.03	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.03	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.03	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.03	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.03	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.03	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.03	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.03	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.03	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.03	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.03	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.03	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.03	   A^2 -> H(U1(a, a), b)
27.86/9.03	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.03	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.03	   A^2 -> H(U1(a, a), c)
27.86/9.03	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.03	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.03	   A^2 -> H(U1(a, a), e)
27.86/9.03	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.03	   A^2 -> H(k, f(b))
27.86/9.03	   A^2 -> H(c, U1(b, b))
27.86/9.03	   A^2 -> H(c, f(c))
27.86/9.03	   A^2 -> H(c, f(d))
27.86/9.03	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.03	   A^2 -> H(U1(e, k), f(c))
27.86/9.03	   A^2 -> H(U1(e, k), f(d))
27.86/9.03	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.03	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.03	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.03	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.03	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.03	   A^2 -> H(U1(e, c), f(e))
27.86/9.03	   A^2 -> H(U1(e, c), f(k))
27.86/9.03	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.03	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.03	   A^2 -> H(U1(k, e), f(c))
27.86/9.03	   A^2 -> H(U1(k, e), f(d))
27.86/9.03	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.03	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.03	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.03	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.03	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.03	   A^2 -> H(U1(k, c), f(e))
27.86/9.03	   A^2 -> H(U1(k, c), f(k))
27.86/9.03	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.03	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.03	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.03	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.03	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.03	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.03	   A^2 -> H(U1(c, e), f(e))
27.86/9.03	   A^2 -> H(U1(c, e), f(k))
27.86/9.03	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.03	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.03	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(c, k), f(e))
27.86/9.03	   A^2 -> H(U1(c, k), f(k))
27.86/9.03	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.03	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.03	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.03	   A^2 -> H(e, U1(b, b))
27.86/9.03	   A^2 -> H(e, f(c))
27.86/9.03	   A^2 -> H(e, f(d))
27.86/9.03	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.03	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.03	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.03	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.03	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.03	   A^2 -> H(U1(e, e), f(e))
27.86/9.03	   A^2 -> H(U1(e, e), f(k))
27.86/9.03	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.03	   A^2 -> H(f(e), U1(e, b))
27.86/9.03	   A^2 -> H(f(e), U1(k, b))
27.86/9.03	   A^2 -> H(f(e), U1(c, d))
27.86/9.03	   A^2 -> H(f(e), U1(d, c))
27.86/9.03	   A^2 -> H(f(e), U1(b, e))
27.86/9.03	   A^2 -> H(f(e), U1(b, k))
27.86/9.03	   A^2 -> H(f(e), U1(e, c))
27.86/9.03	   A^2 -> H(f(e), U1(k, c))
27.86/9.03	   A^2 -> H(f(e), U1(c, e))
27.86/9.03	   A^2 -> H(f(e), U1(c, k))
27.86/9.03	   A^2 -> H(f(e), U1(k, k))
27.86/9.03	   A^2 -> H(f(e), U1(k, d))
27.86/9.03	   A^2 -> H(f(e), U1(d, k))
27.86/9.03	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.03	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(k, k), f(e))
27.86/9.03	   A^2 -> H(U1(k, k), f(k))
27.86/9.03	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.03	   A^2 -> H(f(k), U1(e, b))
27.86/9.03	   A^2 -> H(f(k), U1(k, b))
27.86/9.03	   A^2 -> H(f(k), U1(c, d))
27.86/9.03	   A^2 -> H(f(k), U1(d, c))
27.86/9.03	   A^2 -> H(f(k), U1(b, e))
27.86/9.03	   A^2 -> H(f(k), U1(b, k))
27.86/9.03	   A^2 -> H(f(k), U1(e, c))
27.86/9.03	   A^2 -> H(f(k), U1(k, c))
27.86/9.03	   A^2 -> H(f(k), U1(c, e))
27.86/9.03	   A^2 -> H(f(k), U1(c, k))
27.86/9.03	   A^2 -> H(f(k), U1(e, e))
27.86/9.03	   A^2 -> H(f(k), U1(k, d))
27.86/9.03	   A^2 -> H(f(k), U1(d, k))
27.86/9.03	   A^2 -> H(f(c), b)
27.86/9.03	   A^2 -> H(f(c), U1(e, d))
27.86/9.03	   A^2 -> H(f(c), U1(d, e))
27.86/9.03	   A^2 -> H(f(k), U1(k, k))
27.86/9.03	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.03	   A^2 -> H(U1(k, k), f(c))
27.86/9.03	   A^2 -> H(U1(k, k), f(d))
27.86/9.03	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.03	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.03	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.03	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.03	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.03	   A^2 -> H(U1(k, d), f(e))
27.86/9.03	   A^2 -> H(U1(k, d), f(k))
27.86/9.03	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.03	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.03	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(d, k), f(e))
27.86/9.03	   A^2 -> H(U1(d, k), f(k))
27.86/9.03	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.03	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.03	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.03	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.03	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.03	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.03	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.03	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.03	   A^2 -> H(f(d), b)
27.86/9.03	   A^2 -> H(f(d), U1(e, d))
27.86/9.03	   A^2 -> H(f(d), U1(d, e))
27.86/9.03	   A^2 -> H(f(d), c)
27.86/9.03	   A^2 -> H(f(d), U1(e, k))
27.86/9.03	   A^2 -> H(f(d), U1(k, e))
27.86/9.03	   A^2 -> H(f(d), e)
27.86/9.03	   A^2 -> H(f(a), d)
27.86/9.03	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.03	   A^2 -> H(f(c), c)
27.86/9.03	   A^2 -> H(f(c), U1(e, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.03	   A^2 -> H(f(c), U1(k, e))
27.86/9.03	   A^2 -> H(f(c), U1(k, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.03	   A^2 -> H(f(a), k)
27.86/9.03	   A^2 -> H(f(e), U1(e, e))
27.86/9.03	   A^2 -> H(f(c), e)
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.03	   A^2 -> H(f(d), U1(k, k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.03	   A^2 -> H(d, U1(b, b))
27.86/9.03	   A^2 -> H(d, f(c))
27.86/9.03	   A^2 -> H(d, f(d))
27.86/9.03	   A^2 -> H(a, U1(c, b))
27.86/9.03	   A^2 -> H(a, U1(d, b))
27.86/9.03	   A^2 -> H(a, U1(b, c))
27.86/9.03	   A^2 -> H(a, U1(b, d))
27.86/9.03	   A^2 -> H(a, U1(c, c))
27.86/9.03	   A^2 -> H(a, f(e))
27.86/9.03	   A^2 -> H(a, f(k))
27.86/9.03	   A^2 -> H(a, U1(d, d))
27.86/9.03	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.03	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.03	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.03	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.03	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.03	   A^2 -> H(U1(e, d), f(e))
27.86/9.03	   A^2 -> H(U1(e, d), f(k))
27.86/9.03	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.03	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.03	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.03	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.03	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.03	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.03	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.03	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.03	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.03	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.03	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.03	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.03	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.03	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.03	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.03	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.03	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.03	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.03	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.03	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.03	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.03	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.03	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.03	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.03	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.03	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.03	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.03	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.03	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.03	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.03	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.03	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.03	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.03	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.03	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.03	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.03	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.03	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.03	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.03	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.03	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.03	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.03	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.03	   A^2 -> H(U1(c, a), b)
27.86/9.03	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.03	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.03	   A^2 -> H(U1(c, a), c)
27.86/9.03	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.03	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.03	   A^2 -> H(U1(c, a), e)
27.86/9.03	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.03	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.03	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.03	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.03	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.03	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.03	   A^2 -> H(U1(d, e), f(e))
27.86/9.03	   A^2 -> H(U1(d, e), f(k))
27.86/9.03	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.03	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.03	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.03	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.03	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.03	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.03	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.03	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.03	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.03	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.03	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.03	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.03	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.03	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.03	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.03	   A^2 -> H(U1(d, a), b)
27.86/9.03	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.03	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.03	   A^2 -> H(U1(d, a), c)
27.86/9.03	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.03	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.03	   A^2 -> H(U1(d, a), e)
27.86/9.03	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.03	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.03	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.03	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.03	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.03	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.03	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.03	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.03	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.03	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.03	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.03	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.03	
27.86/9.03	The TRS R consists of the following rules:
27.86/9.03	
27.86/9.03	   f(x) -> U1(x, x)
27.86/9.03	   U1(e, x) -> x
27.86/9.03	   a -> c
27.86/9.03	   a -> d
27.86/9.03	   b -> c
27.86/9.03	   b -> d
27.86/9.03	   d -> k
27.86/9.03	   c -> e
27.86/9.03	   c -> k
27.86/9.03	
27.86/9.03	Q is empty.
27.86/9.03	We have to consider all minimal (P,Q,R)-chains.
27.86/9.03	----------------------------------------
27.86/9.03	
27.86/9.03	(693) TransformationProof (EQUIVALENT)
27.86/9.03	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), f(k)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.03	
27.86/9.03	   (A^2 -> H(U1(c, e), f(k)),A^2 -> H(U1(c, e), f(k)))
27.86/9.03	   (A^2 -> H(U1(d, e), f(k)),A^2 -> H(U1(d, e), f(k)))
27.86/9.03	   (A^2 -> H(U1(a, e), U1(k, k)),A^2 -> H(U1(a, e), U1(k, k)))
27.86/9.03	
27.86/9.03	
27.86/9.03	----------------------------------------
27.86/9.03	
27.86/9.03	(694)
27.86/9.03	Obligation:
27.86/9.03	Q DP problem:
27.86/9.03	The TRS P consists of the following rules:
27.86/9.03	
27.86/9.03	   H(x, x) -> G(x, x, f(k))
27.86/9.03	   G(d, x, x) -> A^2
27.86/9.03	   A^2 -> H(f(c), f(c))
27.86/9.03	   A^2 -> H(f(d), f(d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.03	   A^2 -> H(f(e), f(e))
27.86/9.03	   A^2 -> H(f(k), f(k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.03	   A^2 -> H(U1(a, e), U1(d, d))
27.86/9.03	   A^2 -> H(U1(a, k), U1(c, b))
27.86/9.03	   A^2 -> H(U1(a, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(a, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(a, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(a, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(a, k), f(e))
27.86/9.03	   A^2 -> H(U1(a, k), f(k))
27.86/9.03	   A^2 -> H(U1(a, k), U1(d, d))
27.86/9.03	   A^2 -> H(U1(a, c), U1(e, b))
27.86/9.03	   A^2 -> H(U1(a, c), U1(k, b))
27.86/9.03	   A^2 -> H(U1(a, c), U1(c, d))
27.86/9.03	   A^2 -> H(U1(a, c), U1(d, c))
27.86/9.03	   A^2 -> H(U1(a, c), U1(b, e))
27.86/9.03	   A^2 -> H(U1(a, c), U1(b, k))
27.86/9.03	   A^2 -> H(U1(a, c), U1(e, c))
27.86/9.03	   A^2 -> H(U1(a, c), U1(k, c))
27.86/9.03	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.03	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.03	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.03	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.03	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.03	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.03	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.03	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.03	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.03	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.03	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.03	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.03	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.03	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.03	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.03	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.03	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.03	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.03	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.03	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.03	   A^2 -> H(U1(a, a), b)
27.86/9.03	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.03	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.03	   A^2 -> H(U1(a, a), c)
27.86/9.03	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.03	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.03	   A^2 -> H(U1(a, a), e)
27.86/9.03	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.03	   A^2 -> H(k, f(b))
27.86/9.03	   A^2 -> H(c, U1(b, b))
27.86/9.03	   A^2 -> H(c, f(c))
27.86/9.03	   A^2 -> H(c, f(d))
27.86/9.03	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.03	   A^2 -> H(U1(e, k), f(c))
27.86/9.03	   A^2 -> H(U1(e, k), f(d))
27.86/9.03	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.03	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.03	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.03	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.03	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.03	   A^2 -> H(U1(e, c), f(e))
27.86/9.03	   A^2 -> H(U1(e, c), f(k))
27.86/9.03	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.03	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.03	   A^2 -> H(U1(k, e), f(c))
27.86/9.03	   A^2 -> H(U1(k, e), f(d))
27.86/9.03	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.03	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.03	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.03	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.03	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.03	   A^2 -> H(U1(k, c), f(e))
27.86/9.03	   A^2 -> H(U1(k, c), f(k))
27.86/9.03	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.03	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.03	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.03	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.03	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.03	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.03	   A^2 -> H(U1(c, e), f(e))
27.86/9.03	   A^2 -> H(U1(c, e), f(k))
27.86/9.03	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.03	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.03	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(c, k), f(e))
27.86/9.03	   A^2 -> H(U1(c, k), f(k))
27.86/9.03	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.03	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.03	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.03	   A^2 -> H(e, U1(b, b))
27.86/9.03	   A^2 -> H(e, f(c))
27.86/9.03	   A^2 -> H(e, f(d))
27.86/9.03	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.03	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.03	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.03	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.03	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.03	   A^2 -> H(U1(e, e), f(e))
27.86/9.03	   A^2 -> H(U1(e, e), f(k))
27.86/9.03	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.03	   A^2 -> H(f(e), U1(e, b))
27.86/9.03	   A^2 -> H(f(e), U1(k, b))
27.86/9.03	   A^2 -> H(f(e), U1(c, d))
27.86/9.03	   A^2 -> H(f(e), U1(d, c))
27.86/9.03	   A^2 -> H(f(e), U1(b, e))
27.86/9.03	   A^2 -> H(f(e), U1(b, k))
27.86/9.03	   A^2 -> H(f(e), U1(e, c))
27.86/9.03	   A^2 -> H(f(e), U1(k, c))
27.86/9.03	   A^2 -> H(f(e), U1(c, e))
27.86/9.03	   A^2 -> H(f(e), U1(c, k))
27.86/9.03	   A^2 -> H(f(e), U1(k, k))
27.86/9.03	   A^2 -> H(f(e), U1(k, d))
27.86/9.03	   A^2 -> H(f(e), U1(d, k))
27.86/9.03	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.03	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(k, k), f(e))
27.86/9.03	   A^2 -> H(U1(k, k), f(k))
27.86/9.03	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.03	   A^2 -> H(f(k), U1(e, b))
27.86/9.03	   A^2 -> H(f(k), U1(k, b))
27.86/9.03	   A^2 -> H(f(k), U1(c, d))
27.86/9.03	   A^2 -> H(f(k), U1(d, c))
27.86/9.03	   A^2 -> H(f(k), U1(b, e))
27.86/9.03	   A^2 -> H(f(k), U1(b, k))
27.86/9.03	   A^2 -> H(f(k), U1(e, c))
27.86/9.03	   A^2 -> H(f(k), U1(k, c))
27.86/9.03	   A^2 -> H(f(k), U1(c, e))
27.86/9.03	   A^2 -> H(f(k), U1(c, k))
27.86/9.03	   A^2 -> H(f(k), U1(e, e))
27.86/9.03	   A^2 -> H(f(k), U1(k, d))
27.86/9.03	   A^2 -> H(f(k), U1(d, k))
27.86/9.03	   A^2 -> H(f(c), b)
27.86/9.03	   A^2 -> H(f(c), U1(e, d))
27.86/9.03	   A^2 -> H(f(c), U1(d, e))
27.86/9.03	   A^2 -> H(f(k), U1(k, k))
27.86/9.03	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.03	   A^2 -> H(U1(k, k), f(c))
27.86/9.03	   A^2 -> H(U1(k, k), f(d))
27.86/9.03	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.03	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.03	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.03	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.03	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.03	   A^2 -> H(U1(k, d), f(e))
27.86/9.03	   A^2 -> H(U1(k, d), f(k))
27.86/9.03	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.03	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.03	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(d, k), f(e))
27.86/9.03	   A^2 -> H(U1(d, k), f(k))
27.86/9.03	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.03	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.03	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.03	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.03	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.03	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.03	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.03	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.03	   A^2 -> H(f(d), b)
27.86/9.03	   A^2 -> H(f(d), U1(e, d))
27.86/9.03	   A^2 -> H(f(d), U1(d, e))
27.86/9.03	   A^2 -> H(f(d), c)
27.86/9.03	   A^2 -> H(f(d), U1(e, k))
27.86/9.03	   A^2 -> H(f(d), U1(k, e))
27.86/9.03	   A^2 -> H(f(d), e)
27.86/9.03	   A^2 -> H(f(a), d)
27.86/9.03	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.03	   A^2 -> H(f(c), c)
27.86/9.03	   A^2 -> H(f(c), U1(e, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.03	   A^2 -> H(f(c), U1(k, e))
27.86/9.03	   A^2 -> H(f(c), U1(k, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.03	   A^2 -> H(f(a), k)
27.86/9.03	   A^2 -> H(f(e), U1(e, e))
27.86/9.03	   A^2 -> H(f(c), e)
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.03	   A^2 -> H(f(d), U1(k, k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.03	   A^2 -> H(d, U1(b, b))
27.86/9.03	   A^2 -> H(d, f(c))
27.86/9.03	   A^2 -> H(d, f(d))
27.86/9.03	   A^2 -> H(a, U1(c, b))
27.86/9.03	   A^2 -> H(a, U1(d, b))
27.86/9.03	   A^2 -> H(a, U1(b, c))
27.86/9.03	   A^2 -> H(a, U1(b, d))
27.86/9.03	   A^2 -> H(a, U1(c, c))
27.86/9.03	   A^2 -> H(a, f(e))
27.86/9.03	   A^2 -> H(a, f(k))
27.86/9.03	   A^2 -> H(a, U1(d, d))
27.86/9.03	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.03	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.03	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.03	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.03	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.03	   A^2 -> H(U1(e, d), f(e))
27.86/9.03	   A^2 -> H(U1(e, d), f(k))
27.86/9.03	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.03	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.03	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.03	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.03	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.03	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.03	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.03	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.03	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.03	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.03	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.03	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.03	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.03	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.03	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.03	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.03	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.03	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.03	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.03	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.03	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.03	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.03	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.03	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.03	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.03	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.03	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.03	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.03	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.03	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.03	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.03	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.03	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.03	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.03	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.03	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.03	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.03	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.03	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.03	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.03	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.03	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.03	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.03	   A^2 -> H(U1(c, a), b)
27.86/9.03	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.03	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.03	   A^2 -> H(U1(c, a), c)
27.86/9.03	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.03	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.03	   A^2 -> H(U1(c, a), e)
27.86/9.03	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.03	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.03	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.03	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.03	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.03	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.03	   A^2 -> H(U1(d, e), f(e))
27.86/9.03	   A^2 -> H(U1(d, e), f(k))
27.86/9.03	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.03	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.03	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.03	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.03	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.03	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.03	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.03	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.03	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.03	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.03	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.03	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.03	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.03	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.03	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.03	   A^2 -> H(U1(d, a), b)
27.86/9.03	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.03	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.03	   A^2 -> H(U1(d, a), c)
27.86/9.03	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.03	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.03	   A^2 -> H(U1(d, a), e)
27.86/9.03	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.03	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.03	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.03	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.03	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.03	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.03	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.03	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.03	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.03	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.03	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.03	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.03	   A^2 -> H(U1(a, e), U1(k, k))
27.86/9.03	
27.86/9.03	The TRS R consists of the following rules:
27.86/9.03	
27.86/9.03	   f(x) -> U1(x, x)
27.86/9.03	   U1(e, x) -> x
27.86/9.03	   a -> c
27.86/9.03	   a -> d
27.86/9.03	   b -> c
27.86/9.03	   b -> d
27.86/9.03	   d -> k
27.86/9.03	   c -> e
27.86/9.03	   c -> k
27.86/9.03	
27.86/9.03	Q is empty.
27.86/9.03	We have to consider all minimal (P,Q,R)-chains.
27.86/9.03	----------------------------------------
27.86/9.03	
27.86/9.03	(695) TransformationProof (EQUIVALENT)
27.86/9.03	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.03	
27.86/9.03	   (A^2 -> H(U1(c, e), U1(d, d)),A^2 -> H(U1(c, e), U1(d, d)))
27.86/9.03	   (A^2 -> H(U1(d, e), U1(d, d)),A^2 -> H(U1(d, e), U1(d, d)))
27.86/9.03	   (A^2 -> H(U1(a, e), U1(k, d)),A^2 -> H(U1(a, e), U1(k, d)))
27.86/9.03	   (A^2 -> H(U1(a, e), U1(d, k)),A^2 -> H(U1(a, e), U1(d, k)))
27.86/9.03	
27.86/9.03	
27.86/9.03	----------------------------------------
27.86/9.03	
27.86/9.03	(696)
27.86/9.03	Obligation:
27.86/9.03	Q DP problem:
27.86/9.03	The TRS P consists of the following rules:
27.86/9.03	
27.86/9.03	   H(x, x) -> G(x, x, f(k))
27.86/9.03	   G(d, x, x) -> A^2
27.86/9.03	   A^2 -> H(f(c), f(c))
27.86/9.03	   A^2 -> H(f(d), f(d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.03	   A^2 -> H(f(e), f(e))
27.86/9.03	   A^2 -> H(f(k), f(k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.03	   A^2 -> H(U1(a, k), U1(c, b))
27.86/9.03	   A^2 -> H(U1(a, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(a, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(a, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(a, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(a, k), f(e))
27.86/9.03	   A^2 -> H(U1(a, k), f(k))
27.86/9.03	   A^2 -> H(U1(a, k), U1(d, d))
27.86/9.03	   A^2 -> H(U1(a, c), U1(e, b))
27.86/9.03	   A^2 -> H(U1(a, c), U1(k, b))
27.86/9.03	   A^2 -> H(U1(a, c), U1(c, d))
27.86/9.03	   A^2 -> H(U1(a, c), U1(d, c))
27.86/9.03	   A^2 -> H(U1(a, c), U1(b, e))
27.86/9.03	   A^2 -> H(U1(a, c), U1(b, k))
27.86/9.03	   A^2 -> H(U1(a, c), U1(e, c))
27.86/9.03	   A^2 -> H(U1(a, c), U1(k, c))
27.86/9.03	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.03	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.03	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.03	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.03	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.03	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.03	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.03	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.03	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.03	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.03	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.03	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.03	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.03	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.03	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.03	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.03	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.03	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.03	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.03	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.03	   A^2 -> H(U1(a, a), b)
27.86/9.03	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.03	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.03	   A^2 -> H(U1(a, a), c)
27.86/9.03	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.03	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.03	   A^2 -> H(U1(a, a), e)
27.86/9.03	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.03	   A^2 -> H(k, f(b))
27.86/9.03	   A^2 -> H(c, U1(b, b))
27.86/9.03	   A^2 -> H(c, f(c))
27.86/9.03	   A^2 -> H(c, f(d))
27.86/9.03	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.03	   A^2 -> H(U1(e, k), f(c))
27.86/9.03	   A^2 -> H(U1(e, k), f(d))
27.86/9.03	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.03	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.03	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.03	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.03	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.03	   A^2 -> H(U1(e, c), f(e))
27.86/9.03	   A^2 -> H(U1(e, c), f(k))
27.86/9.03	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.03	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.03	   A^2 -> H(U1(k, e), f(c))
27.86/9.03	   A^2 -> H(U1(k, e), f(d))
27.86/9.03	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.03	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.03	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.03	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.03	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.03	   A^2 -> H(U1(k, c), f(e))
27.86/9.03	   A^2 -> H(U1(k, c), f(k))
27.86/9.03	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.03	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.03	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.03	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.03	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.03	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.03	   A^2 -> H(U1(c, e), f(e))
27.86/9.03	   A^2 -> H(U1(c, e), f(k))
27.86/9.03	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.03	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.03	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(c, k), f(e))
27.86/9.03	   A^2 -> H(U1(c, k), f(k))
27.86/9.03	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.03	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.03	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.03	   A^2 -> H(e, U1(b, b))
27.86/9.03	   A^2 -> H(e, f(c))
27.86/9.03	   A^2 -> H(e, f(d))
27.86/9.03	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.03	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.03	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.03	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.03	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.03	   A^2 -> H(U1(e, e), f(e))
27.86/9.03	   A^2 -> H(U1(e, e), f(k))
27.86/9.03	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.03	   A^2 -> H(f(e), U1(e, b))
27.86/9.03	   A^2 -> H(f(e), U1(k, b))
27.86/9.03	   A^2 -> H(f(e), U1(c, d))
27.86/9.03	   A^2 -> H(f(e), U1(d, c))
27.86/9.03	   A^2 -> H(f(e), U1(b, e))
27.86/9.03	   A^2 -> H(f(e), U1(b, k))
27.86/9.03	   A^2 -> H(f(e), U1(e, c))
27.86/9.03	   A^2 -> H(f(e), U1(k, c))
27.86/9.03	   A^2 -> H(f(e), U1(c, e))
27.86/9.03	   A^2 -> H(f(e), U1(c, k))
27.86/9.03	   A^2 -> H(f(e), U1(k, k))
27.86/9.03	   A^2 -> H(f(e), U1(k, d))
27.86/9.03	   A^2 -> H(f(e), U1(d, k))
27.86/9.03	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.03	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(k, k), f(e))
27.86/9.03	   A^2 -> H(U1(k, k), f(k))
27.86/9.03	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.03	   A^2 -> H(f(k), U1(e, b))
27.86/9.03	   A^2 -> H(f(k), U1(k, b))
27.86/9.03	   A^2 -> H(f(k), U1(c, d))
27.86/9.03	   A^2 -> H(f(k), U1(d, c))
27.86/9.03	   A^2 -> H(f(k), U1(b, e))
27.86/9.03	   A^2 -> H(f(k), U1(b, k))
27.86/9.03	   A^2 -> H(f(k), U1(e, c))
27.86/9.03	   A^2 -> H(f(k), U1(k, c))
27.86/9.03	   A^2 -> H(f(k), U1(c, e))
27.86/9.03	   A^2 -> H(f(k), U1(c, k))
27.86/9.03	   A^2 -> H(f(k), U1(e, e))
27.86/9.03	   A^2 -> H(f(k), U1(k, d))
27.86/9.03	   A^2 -> H(f(k), U1(d, k))
27.86/9.03	   A^2 -> H(f(c), b)
27.86/9.03	   A^2 -> H(f(c), U1(e, d))
27.86/9.03	   A^2 -> H(f(c), U1(d, e))
27.86/9.03	   A^2 -> H(f(k), U1(k, k))
27.86/9.03	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.03	   A^2 -> H(U1(k, k), f(c))
27.86/9.03	   A^2 -> H(U1(k, k), f(d))
27.86/9.03	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.03	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.03	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.03	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.03	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.03	   A^2 -> H(U1(k, d), f(e))
27.86/9.03	   A^2 -> H(U1(k, d), f(k))
27.86/9.03	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.03	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.03	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(d, k), f(e))
27.86/9.03	   A^2 -> H(U1(d, k), f(k))
27.86/9.03	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.03	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.03	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.03	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.03	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.03	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.03	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.03	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.03	   A^2 -> H(f(d), b)
27.86/9.03	   A^2 -> H(f(d), U1(e, d))
27.86/9.03	   A^2 -> H(f(d), U1(d, e))
27.86/9.03	   A^2 -> H(f(d), c)
27.86/9.03	   A^2 -> H(f(d), U1(e, k))
27.86/9.03	   A^2 -> H(f(d), U1(k, e))
27.86/9.03	   A^2 -> H(f(d), e)
27.86/9.03	   A^2 -> H(f(a), d)
27.86/9.03	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.03	   A^2 -> H(f(c), c)
27.86/9.03	   A^2 -> H(f(c), U1(e, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.03	   A^2 -> H(f(c), U1(k, e))
27.86/9.03	   A^2 -> H(f(c), U1(k, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.03	   A^2 -> H(f(a), k)
27.86/9.03	   A^2 -> H(f(e), U1(e, e))
27.86/9.03	   A^2 -> H(f(c), e)
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.03	   A^2 -> H(f(d), U1(k, k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.03	   A^2 -> H(d, U1(b, b))
27.86/9.03	   A^2 -> H(d, f(c))
27.86/9.03	   A^2 -> H(d, f(d))
27.86/9.03	   A^2 -> H(a, U1(c, b))
27.86/9.03	   A^2 -> H(a, U1(d, b))
27.86/9.03	   A^2 -> H(a, U1(b, c))
27.86/9.03	   A^2 -> H(a, U1(b, d))
27.86/9.03	   A^2 -> H(a, U1(c, c))
27.86/9.03	   A^2 -> H(a, f(e))
27.86/9.03	   A^2 -> H(a, f(k))
27.86/9.03	   A^2 -> H(a, U1(d, d))
27.86/9.03	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.03	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.03	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.03	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.03	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.03	   A^2 -> H(U1(e, d), f(e))
27.86/9.03	   A^2 -> H(U1(e, d), f(k))
27.86/9.03	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.03	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.03	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.03	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.03	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.03	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.03	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.03	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.03	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.03	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.03	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.03	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.03	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.03	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.03	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.03	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.03	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.03	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.03	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.03	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.03	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.03	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.03	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.03	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.03	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.03	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.03	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.03	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.03	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.03	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.03	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.03	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.03	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.03	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.03	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.03	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.03	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.03	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.03	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.03	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.03	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.03	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.03	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.03	   A^2 -> H(U1(c, a), b)
27.86/9.03	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.03	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.03	   A^2 -> H(U1(c, a), c)
27.86/9.03	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.03	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.03	   A^2 -> H(U1(c, a), e)
27.86/9.03	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.03	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.03	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.03	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.03	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.03	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.03	   A^2 -> H(U1(d, e), f(e))
27.86/9.03	   A^2 -> H(U1(d, e), f(k))
27.86/9.03	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.03	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.03	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.03	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.03	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.03	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.03	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.03	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.03	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.03	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.03	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.03	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.03	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.03	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.03	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.03	   A^2 -> H(U1(d, a), b)
27.86/9.03	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.03	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.03	   A^2 -> H(U1(d, a), c)
27.86/9.03	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.03	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.03	   A^2 -> H(U1(d, a), e)
27.86/9.03	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.03	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.03	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.03	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.03	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.03	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.03	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.03	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.03	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.03	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.03	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.03	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.03	   A^2 -> H(U1(a, e), U1(k, k))
27.86/9.03	   A^2 -> H(U1(a, e), U1(k, d))
27.86/9.03	   A^2 -> H(U1(a, e), U1(d, k))
27.86/9.03	
27.86/9.03	The TRS R consists of the following rules:
27.86/9.03	
27.86/9.03	   f(x) -> U1(x, x)
27.86/9.03	   U1(e, x) -> x
27.86/9.03	   a -> c
27.86/9.03	   a -> d
27.86/9.03	   b -> c
27.86/9.03	   b -> d
27.86/9.03	   d -> k
27.86/9.03	   c -> e
27.86/9.03	   c -> k
27.86/9.03	
27.86/9.03	Q is empty.
27.86/9.03	We have to consider all minimal (P,Q,R)-chains.
27.86/9.03	----------------------------------------
27.86/9.03	
27.86/9.03	(697) TransformationProof (EQUIVALENT)
27.86/9.03	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.03	
27.86/9.03	   (A^2 -> H(U1(c, k), U1(c, b)),A^2 -> H(U1(c, k), U1(c, b)))
27.86/9.03	   (A^2 -> H(U1(d, k), U1(c, b)),A^2 -> H(U1(d, k), U1(c, b)))
27.86/9.03	   (A^2 -> H(U1(a, k), U1(e, b)),A^2 -> H(U1(a, k), U1(e, b)))
27.86/9.03	   (A^2 -> H(U1(a, k), U1(k, b)),A^2 -> H(U1(a, k), U1(k, b)))
27.86/9.03	   (A^2 -> H(U1(a, k), U1(c, c)),A^2 -> H(U1(a, k), U1(c, c)))
27.86/9.03	   (A^2 -> H(U1(a, k), U1(c, d)),A^2 -> H(U1(a, k), U1(c, d)))
27.86/9.03	
27.86/9.03	
27.86/9.03	----------------------------------------
27.86/9.03	
27.86/9.03	(698)
27.86/9.03	Obligation:
27.86/9.03	Q DP problem:
27.86/9.03	The TRS P consists of the following rules:
27.86/9.03	
27.86/9.03	   H(x, x) -> G(x, x, f(k))
27.86/9.03	   G(d, x, x) -> A^2
27.86/9.03	   A^2 -> H(f(c), f(c))
27.86/9.03	   A^2 -> H(f(d), f(d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.03	   A^2 -> H(f(e), f(e))
27.86/9.03	   A^2 -> H(f(k), f(k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.03	   A^2 -> H(U1(a, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(a, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(a, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(a, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(a, k), f(e))
27.86/9.03	   A^2 -> H(U1(a, k), f(k))
27.86/9.03	   A^2 -> H(U1(a, k), U1(d, d))
27.86/9.03	   A^2 -> H(U1(a, c), U1(e, b))
27.86/9.03	   A^2 -> H(U1(a, c), U1(k, b))
27.86/9.03	   A^2 -> H(U1(a, c), U1(c, d))
27.86/9.03	   A^2 -> H(U1(a, c), U1(d, c))
27.86/9.03	   A^2 -> H(U1(a, c), U1(b, e))
27.86/9.03	   A^2 -> H(U1(a, c), U1(b, k))
27.86/9.03	   A^2 -> H(U1(a, c), U1(e, c))
27.86/9.03	   A^2 -> H(U1(a, c), U1(k, c))
27.86/9.03	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.03	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.03	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.03	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.03	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.03	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.03	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.03	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.03	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.03	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.03	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.03	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.03	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.03	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.03	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.03	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.03	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.03	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.03	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.03	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.03	   A^2 -> H(U1(a, a), b)
27.86/9.03	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.03	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.03	   A^2 -> H(U1(a, a), c)
27.86/9.03	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.03	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.03	   A^2 -> H(U1(a, a), e)
27.86/9.03	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.03	   A^2 -> H(k, f(b))
27.86/9.03	   A^2 -> H(c, U1(b, b))
27.86/9.03	   A^2 -> H(c, f(c))
27.86/9.03	   A^2 -> H(c, f(d))
27.86/9.03	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.03	   A^2 -> H(U1(e, k), f(c))
27.86/9.03	   A^2 -> H(U1(e, k), f(d))
27.86/9.03	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.03	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.03	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.03	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.03	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.03	   A^2 -> H(U1(e, c), f(e))
27.86/9.03	   A^2 -> H(U1(e, c), f(k))
27.86/9.03	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.03	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.03	   A^2 -> H(U1(k, e), f(c))
27.86/9.03	   A^2 -> H(U1(k, e), f(d))
27.86/9.03	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.03	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.03	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.03	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.03	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.03	   A^2 -> H(U1(k, c), f(e))
27.86/9.03	   A^2 -> H(U1(k, c), f(k))
27.86/9.03	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.03	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.03	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.03	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.03	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.03	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.03	   A^2 -> H(U1(c, e), f(e))
27.86/9.03	   A^2 -> H(U1(c, e), f(k))
27.86/9.03	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.03	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.03	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(c, k), f(e))
27.86/9.03	   A^2 -> H(U1(c, k), f(k))
27.86/9.03	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.03	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.03	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.03	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.03	   A^2 -> H(e, U1(b, b))
27.86/9.03	   A^2 -> H(e, f(c))
27.86/9.03	   A^2 -> H(e, f(d))
27.86/9.03	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.03	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.03	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.03	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.03	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.03	   A^2 -> H(U1(e, e), f(e))
27.86/9.03	   A^2 -> H(U1(e, e), f(k))
27.86/9.03	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.03	   A^2 -> H(f(e), U1(e, b))
27.86/9.03	   A^2 -> H(f(e), U1(k, b))
27.86/9.03	   A^2 -> H(f(e), U1(c, d))
27.86/9.03	   A^2 -> H(f(e), U1(d, c))
27.86/9.03	   A^2 -> H(f(e), U1(b, e))
27.86/9.03	   A^2 -> H(f(e), U1(b, k))
27.86/9.03	   A^2 -> H(f(e), U1(e, c))
27.86/9.03	   A^2 -> H(f(e), U1(k, c))
27.86/9.03	   A^2 -> H(f(e), U1(c, e))
27.86/9.03	   A^2 -> H(f(e), U1(c, k))
27.86/9.03	   A^2 -> H(f(e), U1(k, k))
27.86/9.03	   A^2 -> H(f(e), U1(k, d))
27.86/9.03	   A^2 -> H(f(e), U1(d, k))
27.86/9.03	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.03	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(k, k), f(e))
27.86/9.03	   A^2 -> H(U1(k, k), f(k))
27.86/9.03	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.03	   A^2 -> H(f(k), U1(e, b))
27.86/9.03	   A^2 -> H(f(k), U1(k, b))
27.86/9.03	   A^2 -> H(f(k), U1(c, d))
27.86/9.03	   A^2 -> H(f(k), U1(d, c))
27.86/9.03	   A^2 -> H(f(k), U1(b, e))
27.86/9.03	   A^2 -> H(f(k), U1(b, k))
27.86/9.03	   A^2 -> H(f(k), U1(e, c))
27.86/9.03	   A^2 -> H(f(k), U1(k, c))
27.86/9.03	   A^2 -> H(f(k), U1(c, e))
27.86/9.03	   A^2 -> H(f(k), U1(c, k))
27.86/9.03	   A^2 -> H(f(k), U1(e, e))
27.86/9.03	   A^2 -> H(f(k), U1(k, d))
27.86/9.03	   A^2 -> H(f(k), U1(d, k))
27.86/9.03	   A^2 -> H(f(c), b)
27.86/9.03	   A^2 -> H(f(c), U1(e, d))
27.86/9.03	   A^2 -> H(f(c), U1(d, e))
27.86/9.03	   A^2 -> H(f(k), U1(k, k))
27.86/9.03	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.03	   A^2 -> H(U1(k, k), f(c))
27.86/9.03	   A^2 -> H(U1(k, k), f(d))
27.86/9.03	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.03	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.03	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.03	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.03	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.03	   A^2 -> H(U1(k, d), f(e))
27.86/9.03	   A^2 -> H(U1(k, d), f(k))
27.86/9.03	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.03	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.03	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.03	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.03	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.03	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.03	   A^2 -> H(U1(d, k), f(e))
27.86/9.03	   A^2 -> H(U1(d, k), f(k))
27.86/9.03	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.03	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.03	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.03	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.03	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.03	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.03	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.03	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.03	   A^2 -> H(f(d), b)
27.86/9.03	   A^2 -> H(f(d), U1(e, d))
27.86/9.03	   A^2 -> H(f(d), U1(d, e))
27.86/9.03	   A^2 -> H(f(d), c)
27.86/9.03	   A^2 -> H(f(d), U1(e, k))
27.86/9.03	   A^2 -> H(f(d), U1(k, e))
27.86/9.03	   A^2 -> H(f(d), e)
27.86/9.03	   A^2 -> H(f(a), d)
27.86/9.03	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.03	   A^2 -> H(f(c), c)
27.86/9.03	   A^2 -> H(f(c), U1(e, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.03	   A^2 -> H(f(c), U1(k, e))
27.86/9.03	   A^2 -> H(f(c), U1(k, k))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.03	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.03	   A^2 -> H(f(a), k)
27.86/9.03	   A^2 -> H(f(e), U1(e, e))
27.86/9.03	   A^2 -> H(f(c), e)
27.86/9.03	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.03	   A^2 -> H(f(d), U1(k, k))
27.86/9.03	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.03	   A^2 -> H(d, U1(b, b))
27.86/9.03	   A^2 -> H(d, f(c))
27.86/9.03	   A^2 -> H(d, f(d))
27.86/9.03	   A^2 -> H(a, U1(c, b))
27.86/9.03	   A^2 -> H(a, U1(d, b))
27.86/9.03	   A^2 -> H(a, U1(b, c))
27.86/9.03	   A^2 -> H(a, U1(b, d))
27.86/9.03	   A^2 -> H(a, U1(c, c))
27.86/9.03	   A^2 -> H(a, f(e))
27.86/9.04	   A^2 -> H(a, f(k))
27.86/9.04	   A^2 -> H(a, U1(d, d))
27.86/9.04	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.04	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.04	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.04	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.04	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.04	   A^2 -> H(U1(e, d), f(e))
27.86/9.04	   A^2 -> H(U1(e, d), f(k))
27.86/9.04	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.04	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.04	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.04	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.04	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.04	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.04	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.04	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.04	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.04	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.04	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.04	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.04	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.04	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.04	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.04	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.04	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.04	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.04	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.04	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.04	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.04	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.04	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.04	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.04	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.04	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.04	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.04	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.04	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.04	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.04	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.04	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.04	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.04	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.04	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.04	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.04	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.04	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.04	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.04	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.04	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.04	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.04	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.04	   A^2 -> H(U1(c, a), b)
27.86/9.04	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.04	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.04	   A^2 -> H(U1(c, a), c)
27.86/9.04	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.04	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.04	   A^2 -> H(U1(c, a), e)
27.86/9.04	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.04	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.04	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.04	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.04	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.04	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.04	   A^2 -> H(U1(d, e), f(e))
27.86/9.04	   A^2 -> H(U1(d, e), f(k))
27.86/9.04	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.04	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.04	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.04	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.04	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.04	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.04	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.04	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.04	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.04	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.04	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.04	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.04	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.04	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.04	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.04	   A^2 -> H(U1(d, a), b)
27.86/9.04	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.04	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.04	   A^2 -> H(U1(d, a), c)
27.86/9.04	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.04	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.04	   A^2 -> H(U1(d, a), e)
27.86/9.04	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.04	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.04	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.04	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.04	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.04	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.04	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.04	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.04	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.04	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.04	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.04	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.04	   A^2 -> H(U1(a, e), U1(k, k))
27.86/9.04	   A^2 -> H(U1(a, e), U1(k, d))
27.86/9.04	   A^2 -> H(U1(a, e), U1(d, k))
27.86/9.04	   A^2 -> H(U1(a, k), U1(e, b))
27.86/9.04	   A^2 -> H(U1(a, k), U1(k, b))
27.86/9.04	   A^2 -> H(U1(a, k), U1(c, d))
27.86/9.04	
27.86/9.04	The TRS R consists of the following rules:
27.86/9.04	
27.86/9.04	   f(x) -> U1(x, x)
27.86/9.04	   U1(e, x) -> x
27.86/9.04	   a -> c
27.86/9.04	   a -> d
27.86/9.04	   b -> c
27.86/9.04	   b -> d
27.86/9.04	   d -> k
27.86/9.04	   c -> e
27.86/9.04	   c -> k
27.86/9.04	
27.86/9.04	Q is empty.
27.86/9.04	We have to consider all minimal (P,Q,R)-chains.
27.86/9.04	----------------------------------------
27.86/9.04	
27.86/9.04	(699) TransformationProof (EQUIVALENT)
27.86/9.04	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.04	
27.86/9.04	   (A^2 -> H(U1(c, k), U1(d, b)),A^2 -> H(U1(c, k), U1(d, b)))
27.86/9.04	   (A^2 -> H(U1(d, k), U1(d, b)),A^2 -> H(U1(d, k), U1(d, b)))
27.86/9.04	   (A^2 -> H(U1(a, k), U1(k, b)),A^2 -> H(U1(a, k), U1(k, b)))
27.86/9.04	   (A^2 -> H(U1(a, k), U1(d, c)),A^2 -> H(U1(a, k), U1(d, c)))
27.86/9.04	   (A^2 -> H(U1(a, k), U1(d, d)),A^2 -> H(U1(a, k), U1(d, d)))
27.86/9.04	
27.86/9.04	
27.86/9.04	----------------------------------------
27.86/9.04	
27.86/9.04	(700)
27.86/9.04	Obligation:
27.86/9.04	Q DP problem:
27.86/9.04	The TRS P consists of the following rules:
27.86/9.04	
27.86/9.04	   H(x, x) -> G(x, x, f(k))
27.86/9.04	   G(d, x, x) -> A^2
27.86/9.04	   A^2 -> H(f(c), f(c))
27.86/9.04	   A^2 -> H(f(d), f(d))
27.86/9.04	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.04	   A^2 -> H(f(e), f(e))
27.86/9.04	   A^2 -> H(f(k), f(k))
27.86/9.04	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.04	   A^2 -> H(U1(a, k), U1(b, c))
27.86/9.04	   A^2 -> H(U1(a, k), U1(b, d))
27.86/9.04	   A^2 -> H(U1(a, k), U1(c, c))
27.86/9.04	   A^2 -> H(U1(a, k), f(e))
27.86/9.04	   A^2 -> H(U1(a, k), f(k))
27.86/9.04	   A^2 -> H(U1(a, k), U1(d, d))
27.86/9.04	   A^2 -> H(U1(a, c), U1(e, b))
27.86/9.04	   A^2 -> H(U1(a, c), U1(k, b))
27.86/9.04	   A^2 -> H(U1(a, c), U1(c, d))
27.86/9.04	   A^2 -> H(U1(a, c), U1(d, c))
27.86/9.04	   A^2 -> H(U1(a, c), U1(b, e))
27.86/9.04	   A^2 -> H(U1(a, c), U1(b, k))
27.86/9.04	   A^2 -> H(U1(a, c), U1(e, c))
27.86/9.04	   A^2 -> H(U1(a, c), U1(k, c))
27.86/9.04	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.04	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.04	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.04	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.04	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.04	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.04	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.04	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.04	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.04	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.04	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.04	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.04	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.04	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.04	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.04	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.04	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.04	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.04	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.04	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.04	   A^2 -> H(U1(a, a), b)
27.86/9.04	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.04	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.04	   A^2 -> H(U1(a, a), c)
27.86/9.04	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.04	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.04	   A^2 -> H(U1(a, a), e)
27.86/9.04	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.04	   A^2 -> H(k, f(b))
27.86/9.04	   A^2 -> H(c, U1(b, b))
27.86/9.04	   A^2 -> H(c, f(c))
27.86/9.04	   A^2 -> H(c, f(d))
27.86/9.04	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.04	   A^2 -> H(U1(e, k), f(c))
27.86/9.04	   A^2 -> H(U1(e, k), f(d))
27.86/9.04	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.04	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.04	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.04	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.04	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.04	   A^2 -> H(U1(e, c), f(e))
27.86/9.04	   A^2 -> H(U1(e, c), f(k))
27.86/9.04	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.04	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.04	   A^2 -> H(U1(k, e), f(c))
27.86/9.04	   A^2 -> H(U1(k, e), f(d))
27.86/9.04	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.04	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.04	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.04	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.04	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.04	   A^2 -> H(U1(k, c), f(e))
27.86/9.04	   A^2 -> H(U1(k, c), f(k))
27.86/9.04	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.04	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.04	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.04	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.04	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.04	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.04	   A^2 -> H(U1(c, e), f(e))
27.86/9.04	   A^2 -> H(U1(c, e), f(k))
27.86/9.04	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.04	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.04	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.04	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.04	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.04	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.04	   A^2 -> H(U1(c, k), f(e))
27.86/9.04	   A^2 -> H(U1(c, k), f(k))
27.86/9.04	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.04	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.04	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.04	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.04	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.04	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.04	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.04	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.04	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.04	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.04	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.04	   A^2 -> H(e, U1(b, b))
27.86/9.04	   A^2 -> H(e, f(c))
27.86/9.04	   A^2 -> H(e, f(d))
27.86/9.04	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.04	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.04	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.04	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.04	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.04	   A^2 -> H(U1(e, e), f(e))
27.86/9.04	   A^2 -> H(U1(e, e), f(k))
27.86/9.04	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.04	   A^2 -> H(f(e), U1(e, b))
27.86/9.04	   A^2 -> H(f(e), U1(k, b))
27.86/9.04	   A^2 -> H(f(e), U1(c, d))
27.86/9.04	   A^2 -> H(f(e), U1(d, c))
27.86/9.04	   A^2 -> H(f(e), U1(b, e))
27.86/9.04	   A^2 -> H(f(e), U1(b, k))
27.86/9.04	   A^2 -> H(f(e), U1(e, c))
27.86/9.04	   A^2 -> H(f(e), U1(k, c))
27.86/9.04	   A^2 -> H(f(e), U1(c, e))
27.86/9.04	   A^2 -> H(f(e), U1(c, k))
27.86/9.04	   A^2 -> H(f(e), U1(k, k))
27.86/9.04	   A^2 -> H(f(e), U1(k, d))
27.86/9.04	   A^2 -> H(f(e), U1(d, k))
27.86/9.04	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.04	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.04	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.04	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.04	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.04	   A^2 -> H(U1(k, k), f(e))
27.86/9.04	   A^2 -> H(U1(k, k), f(k))
27.86/9.04	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.04	   A^2 -> H(f(k), U1(e, b))
27.86/9.04	   A^2 -> H(f(k), U1(k, b))
27.86/9.04	   A^2 -> H(f(k), U1(c, d))
27.86/9.04	   A^2 -> H(f(k), U1(d, c))
27.86/9.04	   A^2 -> H(f(k), U1(b, e))
27.86/9.04	   A^2 -> H(f(k), U1(b, k))
27.86/9.04	   A^2 -> H(f(k), U1(e, c))
27.86/9.04	   A^2 -> H(f(k), U1(k, c))
27.86/9.04	   A^2 -> H(f(k), U1(c, e))
27.86/9.04	   A^2 -> H(f(k), U1(c, k))
27.86/9.04	   A^2 -> H(f(k), U1(e, e))
27.86/9.04	   A^2 -> H(f(k), U1(k, d))
27.86/9.04	   A^2 -> H(f(k), U1(d, k))
27.86/9.04	   A^2 -> H(f(c), b)
27.86/9.04	   A^2 -> H(f(c), U1(e, d))
27.86/9.04	   A^2 -> H(f(c), U1(d, e))
27.86/9.04	   A^2 -> H(f(k), U1(k, k))
27.86/9.04	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.04	   A^2 -> H(U1(k, k), f(c))
27.86/9.04	   A^2 -> H(U1(k, k), f(d))
27.86/9.04	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.04	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.04	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.04	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.04	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.04	   A^2 -> H(U1(k, d), f(e))
27.86/9.04	   A^2 -> H(U1(k, d), f(k))
27.86/9.04	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.04	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.04	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.04	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.04	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.04	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.04	   A^2 -> H(U1(d, k), f(e))
27.86/9.04	   A^2 -> H(U1(d, k), f(k))
27.86/9.04	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.04	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.04	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.04	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.04	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.04	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.04	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.04	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.04	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.04	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.04	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.04	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.04	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.04	   A^2 -> H(f(d), b)
27.86/9.04	   A^2 -> H(f(d), U1(e, d))
27.86/9.04	   A^2 -> H(f(d), U1(d, e))
27.86/9.04	   A^2 -> H(f(d), c)
27.86/9.04	   A^2 -> H(f(d), U1(e, k))
27.86/9.04	   A^2 -> H(f(d), U1(k, e))
27.86/9.04	   A^2 -> H(f(d), e)
27.86/9.04	   A^2 -> H(f(a), d)
27.86/9.04	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.04	   A^2 -> H(f(c), c)
27.86/9.04	   A^2 -> H(f(c), U1(e, k))
27.86/9.04	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.04	   A^2 -> H(f(c), U1(k, e))
27.86/9.04	   A^2 -> H(f(c), U1(k, k))
27.86/9.04	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.04	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.04	   A^2 -> H(f(a), k)
27.86/9.04	   A^2 -> H(f(e), U1(e, e))
27.86/9.04	   A^2 -> H(f(c), e)
27.86/9.04	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.04	   A^2 -> H(f(d), U1(k, k))
27.86/9.04	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.04	   A^2 -> H(d, U1(b, b))
27.86/9.04	   A^2 -> H(d, f(c))
27.86/9.04	   A^2 -> H(d, f(d))
27.86/9.04	   A^2 -> H(a, U1(c, b))
27.86/9.04	   A^2 -> H(a, U1(d, b))
27.86/9.04	   A^2 -> H(a, U1(b, c))
27.86/9.04	   A^2 -> H(a, U1(b, d))
27.86/9.04	   A^2 -> H(a, U1(c, c))
27.86/9.04	   A^2 -> H(a, f(e))
27.86/9.04	   A^2 -> H(a, f(k))
27.86/9.04	   A^2 -> H(a, U1(d, d))
27.86/9.04	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.04	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.04	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.04	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.04	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.04	   A^2 -> H(U1(e, d), f(e))
27.86/9.04	   A^2 -> H(U1(e, d), f(k))
27.86/9.04	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.04	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.04	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.04	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.04	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.04	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.04	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.04	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.04	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.04	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.04	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.04	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.04	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.04	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.04	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.04	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.04	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.04	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.04	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.04	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.04	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.04	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.04	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.04	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.04	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.04	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.04	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.04	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.04	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.04	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.04	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.04	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.04	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.04	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.04	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.04	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.04	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.04	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.04	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.04	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.04	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.04	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.04	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.04	   A^2 -> H(U1(c, a), b)
27.86/9.04	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.04	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.04	   A^2 -> H(U1(c, a), c)
27.86/9.04	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.04	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.04	   A^2 -> H(U1(c, a), e)
27.86/9.04	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.04	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.04	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.04	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.04	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.04	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.04	   A^2 -> H(U1(d, e), f(e))
27.86/9.04	   A^2 -> H(U1(d, e), f(k))
27.86/9.04	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.04	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.04	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.04	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.04	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.04	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.04	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.04	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.04	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.04	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.04	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.04	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.04	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.04	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.04	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.04	   A^2 -> H(U1(d, a), b)
27.86/9.04	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.04	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.04	   A^2 -> H(U1(d, a), c)
27.86/9.04	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.04	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.04	   A^2 -> H(U1(d, a), e)
27.86/9.04	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.04	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.04	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.04	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.04	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.04	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.04	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.04	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.04	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.04	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.04	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.04	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.04	   A^2 -> H(U1(a, e), U1(k, k))
27.86/9.04	   A^2 -> H(U1(a, e), U1(k, d))
27.86/9.04	   A^2 -> H(U1(a, e), U1(d, k))
27.86/9.04	   A^2 -> H(U1(a, k), U1(e, b))
27.86/9.04	   A^2 -> H(U1(a, k), U1(k, b))
27.86/9.04	   A^2 -> H(U1(a, k), U1(c, d))
27.86/9.04	   A^2 -> H(U1(a, k), U1(d, c))
27.86/9.04	
27.86/9.04	The TRS R consists of the following rules:
27.86/9.04	
27.86/9.04	   f(x) -> U1(x, x)
27.86/9.04	   U1(e, x) -> x
27.86/9.04	   a -> c
27.86/9.04	   a -> d
27.86/9.04	   b -> c
27.86/9.04	   b -> d
27.86/9.04	   d -> k
27.86/9.04	   c -> e
27.86/9.04	   c -> k
27.86/9.04	
27.86/9.04	Q is empty.
27.86/9.04	We have to consider all minimal (P,Q,R)-chains.
27.86/9.04	----------------------------------------
27.86/9.04	
27.86/9.04	(701) TransformationProof (EQUIVALENT)
27.86/9.04	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.04	
27.86/9.04	   (A^2 -> H(U1(c, k), U1(b, c)),A^2 -> H(U1(c, k), U1(b, c)))
27.86/9.04	   (A^2 -> H(U1(d, k), U1(b, c)),A^2 -> H(U1(d, k), U1(b, c)))
27.86/9.04	   (A^2 -> H(U1(a, k), U1(c, c)),A^2 -> H(U1(a, k), U1(c, c)))
27.86/9.04	   (A^2 -> H(U1(a, k), U1(d, c)),A^2 -> H(U1(a, k), U1(d, c)))
27.86/9.04	   (A^2 -> H(U1(a, k), U1(b, e)),A^2 -> H(U1(a, k), U1(b, e)))
27.86/9.04	   (A^2 -> H(U1(a, k), U1(b, k)),A^2 -> H(U1(a, k), U1(b, k)))
27.86/9.04	
27.86/9.04	
27.86/9.04	----------------------------------------
27.86/9.04	
27.86/9.04	(702)
27.86/9.04	Obligation:
27.86/9.04	Q DP problem:
27.86/9.04	The TRS P consists of the following rules:
27.86/9.04	
27.86/9.04	   H(x, x) -> G(x, x, f(k))
27.86/9.04	   G(d, x, x) -> A^2
27.86/9.04	   A^2 -> H(f(c), f(c))
27.86/9.04	   A^2 -> H(f(d), f(d))
27.86/9.04	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.04	   A^2 -> H(f(e), f(e))
27.86/9.04	   A^2 -> H(f(k), f(k))
27.86/9.04	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.04	   A^2 -> H(U1(a, k), U1(b, d))
27.86/9.04	   A^2 -> H(U1(a, k), U1(c, c))
27.86/9.04	   A^2 -> H(U1(a, k), f(e))
27.86/9.04	   A^2 -> H(U1(a, k), f(k))
27.86/9.04	   A^2 -> H(U1(a, k), U1(d, d))
27.86/9.04	   A^2 -> H(U1(a, c), U1(e, b))
27.86/9.04	   A^2 -> H(U1(a, c), U1(k, b))
27.86/9.04	   A^2 -> H(U1(a, c), U1(c, d))
27.86/9.04	   A^2 -> H(U1(a, c), U1(d, c))
27.86/9.04	   A^2 -> H(U1(a, c), U1(b, e))
27.86/9.04	   A^2 -> H(U1(a, c), U1(b, k))
27.86/9.04	   A^2 -> H(U1(a, c), U1(e, c))
27.86/9.04	   A^2 -> H(U1(a, c), U1(k, c))
27.86/9.04	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.04	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.04	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.04	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.04	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.04	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.04	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.04	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.04	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.04	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.04	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.04	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.04	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.04	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.04	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.04	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.04	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.04	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.04	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.04	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.04	   A^2 -> H(U1(a, a), b)
27.86/9.04	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.04	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.04	   A^2 -> H(U1(a, a), c)
27.86/9.04	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.04	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.04	   A^2 -> H(U1(a, a), e)
27.86/9.04	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.04	   A^2 -> H(k, f(b))
27.86/9.04	   A^2 -> H(c, U1(b, b))
27.86/9.04	   A^2 -> H(c, f(c))
27.86/9.04	   A^2 -> H(c, f(d))
27.86/9.04	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.04	   A^2 -> H(U1(e, k), f(c))
27.86/9.04	   A^2 -> H(U1(e, k), f(d))
27.86/9.04	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.04	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.04	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.04	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.04	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.04	   A^2 -> H(U1(e, c), f(e))
27.86/9.04	   A^2 -> H(U1(e, c), f(k))
27.86/9.04	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.04	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.04	   A^2 -> H(U1(k, e), f(c))
27.86/9.04	   A^2 -> H(U1(k, e), f(d))
27.86/9.04	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.04	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.04	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.04	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.04	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.04	   A^2 -> H(U1(k, c), f(e))
27.86/9.04	   A^2 -> H(U1(k, c), f(k))
27.86/9.04	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.04	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.04	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.04	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.04	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.04	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.04	   A^2 -> H(U1(c, e), f(e))
27.86/9.04	   A^2 -> H(U1(c, e), f(k))
27.86/9.04	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.04	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.04	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.04	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.04	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.04	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.04	   A^2 -> H(U1(c, k), f(e))
27.86/9.04	   A^2 -> H(U1(c, k), f(k))
27.86/9.04	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.04	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.04	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.04	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.04	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.04	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.04	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.04	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.04	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.04	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.04	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.04	   A^2 -> H(e, U1(b, b))
27.86/9.04	   A^2 -> H(e, f(c))
27.86/9.04	   A^2 -> H(e, f(d))
27.86/9.04	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.04	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.04	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.04	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.04	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.04	   A^2 -> H(U1(e, e), f(e))
27.86/9.04	   A^2 -> H(U1(e, e), f(k))
27.86/9.04	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.04	   A^2 -> H(f(e), U1(e, b))
27.86/9.04	   A^2 -> H(f(e), U1(k, b))
27.86/9.04	   A^2 -> H(f(e), U1(c, d))
27.86/9.04	   A^2 -> H(f(e), U1(d, c))
27.86/9.04	   A^2 -> H(f(e), U1(b, e))
27.86/9.04	   A^2 -> H(f(e), U1(b, k))
27.86/9.04	   A^2 -> H(f(e), U1(e, c))
27.86/9.04	   A^2 -> H(f(e), U1(k, c))
27.86/9.04	   A^2 -> H(f(e), U1(c, e))
27.86/9.04	   A^2 -> H(f(e), U1(c, k))
27.86/9.04	   A^2 -> H(f(e), U1(k, k))
27.86/9.04	   A^2 -> H(f(e), U1(k, d))
27.86/9.04	   A^2 -> H(f(e), U1(d, k))
27.86/9.04	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.04	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.04	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.04	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.04	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.04	   A^2 -> H(U1(k, k), f(e))
27.86/9.04	   A^2 -> H(U1(k, k), f(k))
27.86/9.04	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.04	   A^2 -> H(f(k), U1(e, b))
27.86/9.04	   A^2 -> H(f(k), U1(k, b))
27.86/9.04	   A^2 -> H(f(k), U1(c, d))
27.86/9.04	   A^2 -> H(f(k), U1(d, c))
27.86/9.04	   A^2 -> H(f(k), U1(b, e))
27.86/9.04	   A^2 -> H(f(k), U1(b, k))
27.86/9.04	   A^2 -> H(f(k), U1(e, c))
27.86/9.04	   A^2 -> H(f(k), U1(k, c))
27.86/9.04	   A^2 -> H(f(k), U1(c, e))
27.86/9.04	   A^2 -> H(f(k), U1(c, k))
27.86/9.04	   A^2 -> H(f(k), U1(e, e))
27.86/9.04	   A^2 -> H(f(k), U1(k, d))
27.86/9.04	   A^2 -> H(f(k), U1(d, k))
27.86/9.04	   A^2 -> H(f(c), b)
27.86/9.04	   A^2 -> H(f(c), U1(e, d))
27.86/9.04	   A^2 -> H(f(c), U1(d, e))
27.86/9.04	   A^2 -> H(f(k), U1(k, k))
27.86/9.04	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.04	   A^2 -> H(U1(k, k), f(c))
27.86/9.04	   A^2 -> H(U1(k, k), f(d))
27.86/9.04	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.04	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.04	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.04	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.04	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.04	   A^2 -> H(U1(k, d), f(e))
27.86/9.04	   A^2 -> H(U1(k, d), f(k))
27.86/9.04	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.04	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.04	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.04	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.04	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.04	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.04	   A^2 -> H(U1(d, k), f(e))
27.86/9.04	   A^2 -> H(U1(d, k), f(k))
27.86/9.04	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.04	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.04	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.04	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.04	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.04	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.04	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.04	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.04	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.04	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.04	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.04	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.04	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.04	   A^2 -> H(f(d), b)
27.86/9.04	   A^2 -> H(f(d), U1(e, d))
27.86/9.04	   A^2 -> H(f(d), U1(d, e))
27.86/9.04	   A^2 -> H(f(d), c)
27.86/9.04	   A^2 -> H(f(d), U1(e, k))
27.86/9.04	   A^2 -> H(f(d), U1(k, e))
27.86/9.04	   A^2 -> H(f(d), e)
27.86/9.04	   A^2 -> H(f(a), d)
27.86/9.04	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.04	   A^2 -> H(f(c), c)
27.86/9.04	   A^2 -> H(f(c), U1(e, k))
27.86/9.04	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.04	   A^2 -> H(f(c), U1(k, e))
27.86/9.04	   A^2 -> H(f(c), U1(k, k))
27.86/9.04	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.04	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.04	   A^2 -> H(f(a), k)
27.86/9.04	   A^2 -> H(f(e), U1(e, e))
27.86/9.04	   A^2 -> H(f(c), e)
27.86/9.04	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.04	   A^2 -> H(f(d), U1(k, k))
27.86/9.04	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.04	   A^2 -> H(d, U1(b, b))
27.86/9.04	   A^2 -> H(d, f(c))
27.86/9.04	   A^2 -> H(d, f(d))
27.86/9.04	   A^2 -> H(a, U1(c, b))
27.86/9.04	   A^2 -> H(a, U1(d, b))
27.86/9.04	   A^2 -> H(a, U1(b, c))
27.86/9.04	   A^2 -> H(a, U1(b, d))
27.86/9.04	   A^2 -> H(a, U1(c, c))
27.86/9.04	   A^2 -> H(a, f(e))
27.86/9.04	   A^2 -> H(a, f(k))
27.86/9.04	   A^2 -> H(a, U1(d, d))
27.86/9.04	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.04	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.04	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.04	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.04	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.04	   A^2 -> H(U1(e, d), f(e))
27.86/9.04	   A^2 -> H(U1(e, d), f(k))
27.86/9.04	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.04	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.04	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.04	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.04	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.04	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.04	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.04	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.04	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.04	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.04	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.04	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.04	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.04	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.04	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.04	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.04	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.04	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.04	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.04	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.04	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.04	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.04	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.04	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.04	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.04	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.04	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.04	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.04	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.04	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.04	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.04	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.04	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.04	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.04	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.04	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.04	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.04	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.04	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.04	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.04	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.04	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.04	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.04	   A^2 -> H(U1(c, a), b)
27.86/9.04	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.04	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.04	   A^2 -> H(U1(c, a), c)
27.86/9.04	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.04	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.04	   A^2 -> H(U1(c, a), e)
27.86/9.04	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.04	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.04	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.04	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.04	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.04	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.04	   A^2 -> H(U1(d, e), f(e))
27.86/9.04	   A^2 -> H(U1(d, e), f(k))
27.86/9.04	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.04	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.04	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.04	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.04	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.04	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.04	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.04	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.04	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.04	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.04	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.04	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.04	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.04	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.04	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.04	   A^2 -> H(U1(d, a), b)
27.86/9.04	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.04	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.04	   A^2 -> H(U1(d, a), c)
27.86/9.04	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.04	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.04	   A^2 -> H(U1(d, a), e)
27.86/9.04	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.04	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.04	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.04	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.04	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.04	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.04	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.04	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.04	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.04	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.04	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.04	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.04	   A^2 -> H(U1(a, e), U1(k, k))
27.86/9.04	   A^2 -> H(U1(a, e), U1(k, d))
27.86/9.04	   A^2 -> H(U1(a, e), U1(d, k))
27.86/9.04	   A^2 -> H(U1(a, k), U1(e, b))
27.86/9.04	   A^2 -> H(U1(a, k), U1(k, b))
27.86/9.04	   A^2 -> H(U1(a, k), U1(c, d))
27.86/9.04	   A^2 -> H(U1(a, k), U1(d, c))
27.86/9.04	   A^2 -> H(U1(a, k), U1(b, e))
27.86/9.04	   A^2 -> H(U1(a, k), U1(b, k))
27.86/9.04	
27.86/9.04	The TRS R consists of the following rules:
27.86/9.04	
27.86/9.04	   f(x) -> U1(x, x)
27.86/9.04	   U1(e, x) -> x
27.86/9.04	   a -> c
27.86/9.04	   a -> d
27.86/9.04	   b -> c
27.86/9.04	   b -> d
27.86/9.04	   d -> k
27.86/9.04	   c -> e
27.86/9.04	   c -> k
27.86/9.04	
27.86/9.04	Q is empty.
27.86/9.04	We have to consider all minimal (P,Q,R)-chains.
27.86/9.04	----------------------------------------
27.86/9.04	
27.86/9.04	(703) TransformationProof (EQUIVALENT)
27.86/9.04	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.04	
27.86/9.04	   (A^2 -> H(U1(c, k), U1(b, d)),A^2 -> H(U1(c, k), U1(b, d)))
27.86/9.04	   (A^2 -> H(U1(d, k), U1(b, d)),A^2 -> H(U1(d, k), U1(b, d)))
27.86/9.04	   (A^2 -> H(U1(a, k), U1(c, d)),A^2 -> H(U1(a, k), U1(c, d)))
27.86/9.04	   (A^2 -> H(U1(a, k), U1(d, d)),A^2 -> H(U1(a, k), U1(d, d)))
27.86/9.04	   (A^2 -> H(U1(a, k), U1(b, k)),A^2 -> H(U1(a, k), U1(b, k)))
27.86/9.04	
27.86/9.04	
27.86/9.04	----------------------------------------
27.86/9.04	
27.86/9.04	(704)
27.86/9.04	Obligation:
27.86/9.04	Q DP problem:
27.86/9.04	The TRS P consists of the following rules:
27.86/9.04	
27.86/9.04	   H(x, x) -> G(x, x, f(k))
27.86/9.04	   G(d, x, x) -> A^2
27.86/9.04	   A^2 -> H(f(c), f(c))
27.86/9.04	   A^2 -> H(f(d), f(d))
27.86/9.04	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.04	   A^2 -> H(f(e), f(e))
27.86/9.04	   A^2 -> H(f(k), f(k))
27.86/9.04	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.04	   A^2 -> H(U1(a, k), U1(c, c))
27.86/9.04	   A^2 -> H(U1(a, k), f(e))
27.86/9.04	   A^2 -> H(U1(a, k), f(k))
27.86/9.04	   A^2 -> H(U1(a, k), U1(d, d))
27.86/9.04	   A^2 -> H(U1(a, c), U1(e, b))
27.86/9.04	   A^2 -> H(U1(a, c), U1(k, b))
27.86/9.04	   A^2 -> H(U1(a, c), U1(c, d))
27.86/9.04	   A^2 -> H(U1(a, c), U1(d, c))
27.86/9.04	   A^2 -> H(U1(a, c), U1(b, e))
27.86/9.04	   A^2 -> H(U1(a, c), U1(b, k))
27.86/9.04	   A^2 -> H(U1(a, c), U1(e, c))
27.86/9.04	   A^2 -> H(U1(a, c), U1(k, c))
27.86/9.04	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.04	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.04	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.04	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.04	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.04	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.04	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.04	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.04	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.04	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.04	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.04	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.04	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.04	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.04	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.04	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.04	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.04	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.04	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.04	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.04	   A^2 -> H(U1(a, a), b)
27.86/9.04	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.04	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.04	   A^2 -> H(U1(a, a), c)
27.86/9.04	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.04	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.04	   A^2 -> H(U1(a, a), e)
27.86/9.04	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.04	   A^2 -> H(k, f(b))
27.86/9.04	   A^2 -> H(c, U1(b, b))
27.86/9.04	   A^2 -> H(c, f(c))
27.86/9.04	   A^2 -> H(c, f(d))
27.86/9.04	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.04	   A^2 -> H(U1(e, k), f(c))
27.86/9.04	   A^2 -> H(U1(e, k), f(d))
27.86/9.04	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.04	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.04	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.04	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.04	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.04	   A^2 -> H(U1(e, c), f(e))
27.86/9.04	   A^2 -> H(U1(e, c), f(k))
27.86/9.04	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.04	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.04	   A^2 -> H(U1(k, e), f(c))
27.86/9.04	   A^2 -> H(U1(k, e), f(d))
27.86/9.04	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.04	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.04	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.04	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.04	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.04	   A^2 -> H(U1(k, c), f(e))
27.86/9.04	   A^2 -> H(U1(k, c), f(k))
27.86/9.04	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.04	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.04	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.04	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.04	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.04	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.04	   A^2 -> H(U1(c, e), f(e))
27.86/9.04	   A^2 -> H(U1(c, e), f(k))
27.86/9.04	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.04	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.04	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.04	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.04	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.04	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.04	   A^2 -> H(U1(c, k), f(e))
27.86/9.04	   A^2 -> H(U1(c, k), f(k))
27.86/9.04	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.04	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.04	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.04	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.04	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.04	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.04	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.04	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.04	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.04	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.04	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.04	   A^2 -> H(e, U1(b, b))
27.86/9.04	   A^2 -> H(e, f(c))
27.86/9.04	   A^2 -> H(e, f(d))
27.86/9.04	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.04	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.04	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.04	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.04	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.04	   A^2 -> H(U1(e, e), f(e))
27.86/9.04	   A^2 -> H(U1(e, e), f(k))
27.86/9.04	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.04	   A^2 -> H(f(e), U1(e, b))
27.86/9.04	   A^2 -> H(f(e), U1(k, b))
27.86/9.04	   A^2 -> H(f(e), U1(c, d))
27.86/9.04	   A^2 -> H(f(e), U1(d, c))
27.86/9.04	   A^2 -> H(f(e), U1(b, e))
27.86/9.04	   A^2 -> H(f(e), U1(b, k))
27.86/9.04	   A^2 -> H(f(e), U1(e, c))
27.86/9.04	   A^2 -> H(f(e), U1(k, c))
27.86/9.04	   A^2 -> H(f(e), U1(c, e))
27.86/9.04	   A^2 -> H(f(e), U1(c, k))
27.86/9.04	   A^2 -> H(f(e), U1(k, k))
27.86/9.04	   A^2 -> H(f(e), U1(k, d))
27.86/9.04	   A^2 -> H(f(e), U1(d, k))
27.86/9.04	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.04	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.04	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.04	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.04	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.04	   A^2 -> H(U1(k, k), f(e))
27.86/9.04	   A^2 -> H(U1(k, k), f(k))
27.86/9.04	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.04	   A^2 -> H(f(k), U1(e, b))
27.86/9.04	   A^2 -> H(f(k), U1(k, b))
27.86/9.04	   A^2 -> H(f(k), U1(c, d))
27.86/9.04	   A^2 -> H(f(k), U1(d, c))
27.86/9.04	   A^2 -> H(f(k), U1(b, e))
27.86/9.04	   A^2 -> H(f(k), U1(b, k))
27.86/9.04	   A^2 -> H(f(k), U1(e, c))
27.86/9.04	   A^2 -> H(f(k), U1(k, c))
27.86/9.04	   A^2 -> H(f(k), U1(c, e))
27.86/9.04	   A^2 -> H(f(k), U1(c, k))
27.86/9.04	   A^2 -> H(f(k), U1(e, e))
27.86/9.04	   A^2 -> H(f(k), U1(k, d))
27.86/9.04	   A^2 -> H(f(k), U1(d, k))
27.86/9.04	   A^2 -> H(f(c), b)
27.86/9.04	   A^2 -> H(f(c), U1(e, d))
27.86/9.04	   A^2 -> H(f(c), U1(d, e))
27.86/9.05	   A^2 -> H(f(k), U1(k, k))
27.86/9.05	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.05	   A^2 -> H(U1(k, k), f(c))
27.86/9.05	   A^2 -> H(U1(k, k), f(d))
27.86/9.05	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.05	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.05	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.05	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.05	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.05	   A^2 -> H(U1(k, d), f(e))
27.86/9.05	   A^2 -> H(U1(k, d), f(k))
27.86/9.05	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.05	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.05	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.05	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.05	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.05	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.05	   A^2 -> H(U1(d, k), f(e))
27.86/9.05	   A^2 -> H(U1(d, k), f(k))
27.86/9.05	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.05	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.05	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.05	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.05	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.05	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.05	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.05	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.05	   A^2 -> H(f(d), b)
27.86/9.05	   A^2 -> H(f(d), U1(e, d))
27.86/9.05	   A^2 -> H(f(d), U1(d, e))
27.86/9.05	   A^2 -> H(f(d), c)
27.86/9.05	   A^2 -> H(f(d), U1(e, k))
27.86/9.05	   A^2 -> H(f(d), U1(k, e))
27.86/9.05	   A^2 -> H(f(d), e)
27.86/9.05	   A^2 -> H(f(a), d)
27.86/9.05	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.05	   A^2 -> H(f(c), c)
27.86/9.05	   A^2 -> H(f(c), U1(e, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.05	   A^2 -> H(f(c), U1(k, e))
27.86/9.05	   A^2 -> H(f(c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.05	   A^2 -> H(f(a), k)
27.86/9.05	   A^2 -> H(f(e), U1(e, e))
27.86/9.05	   A^2 -> H(f(c), e)
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.05	   A^2 -> H(f(d), U1(k, k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.05	   A^2 -> H(d, U1(b, b))
27.86/9.05	   A^2 -> H(d, f(c))
27.86/9.05	   A^2 -> H(d, f(d))
27.86/9.05	   A^2 -> H(a, U1(c, b))
27.86/9.05	   A^2 -> H(a, U1(d, b))
27.86/9.05	   A^2 -> H(a, U1(b, c))
27.86/9.05	   A^2 -> H(a, U1(b, d))
27.86/9.05	   A^2 -> H(a, U1(c, c))
27.86/9.05	   A^2 -> H(a, f(e))
27.86/9.05	   A^2 -> H(a, f(k))
27.86/9.05	   A^2 -> H(a, U1(d, d))
27.86/9.05	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.05	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.05	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.05	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.05	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.05	   A^2 -> H(U1(e, d), f(e))
27.86/9.05	   A^2 -> H(U1(e, d), f(k))
27.86/9.05	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.05	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.05	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.05	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.05	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.05	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.05	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.05	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.05	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.05	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.05	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.05	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.05	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.05	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.05	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.05	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.05	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.05	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.05	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.05	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.05	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.05	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.05	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.05	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.05	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.05	   A^2 -> H(U1(c, a), b)
27.86/9.05	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.05	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.05	   A^2 -> H(U1(c, a), c)
27.86/9.05	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.05	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.05	   A^2 -> H(U1(c, a), e)
27.86/9.05	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.05	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.05	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.05	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.05	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.05	   A^2 -> H(U1(d, e), f(e))
27.86/9.05	   A^2 -> H(U1(d, e), f(k))
27.86/9.05	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.05	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.05	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.05	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.05	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.05	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.05	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.05	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.05	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.05	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.05	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.05	   A^2 -> H(U1(d, a), b)
27.86/9.05	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.05	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.05	   A^2 -> H(U1(d, a), c)
27.86/9.05	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.05	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.05	   A^2 -> H(U1(d, a), e)
27.86/9.05	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, d))
27.86/9.05	   A^2 -> H(U1(a, e), U1(d, k))
27.86/9.05	   A^2 -> H(U1(a, k), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, k), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, k), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, k), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, k), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, k), U1(b, k))
27.86/9.05	
27.86/9.05	The TRS R consists of the following rules:
27.86/9.05	
27.86/9.05	   f(x) -> U1(x, x)
27.86/9.05	   U1(e, x) -> x
27.86/9.05	   a -> c
27.86/9.05	   a -> d
27.86/9.05	   b -> c
27.86/9.05	   b -> d
27.86/9.05	   d -> k
27.86/9.05	   c -> e
27.86/9.05	   c -> k
27.86/9.05	
27.86/9.05	Q is empty.
27.86/9.05	We have to consider all minimal (P,Q,R)-chains.
27.86/9.05	----------------------------------------
27.86/9.05	
27.86/9.05	(705) TransformationProof (EQUIVALENT)
27.86/9.05	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.05	
27.86/9.05	   (A^2 -> H(U1(c, k), U1(c, c)),A^2 -> H(U1(c, k), U1(c, c)))
27.86/9.05	   (A^2 -> H(U1(d, k), U1(c, c)),A^2 -> H(U1(d, k), U1(c, c)))
27.86/9.05	   (A^2 -> H(U1(a, k), U1(e, c)),A^2 -> H(U1(a, k), U1(e, c)))
27.86/9.05	   (A^2 -> H(U1(a, k), U1(k, c)),A^2 -> H(U1(a, k), U1(k, c)))
27.86/9.05	   (A^2 -> H(U1(a, k), U1(c, e)),A^2 -> H(U1(a, k), U1(c, e)))
27.86/9.05	   (A^2 -> H(U1(a, k), U1(c, k)),A^2 -> H(U1(a, k), U1(c, k)))
27.86/9.05	
27.86/9.05	
27.86/9.05	----------------------------------------
27.86/9.05	
27.86/9.05	(706)
27.86/9.05	Obligation:
27.86/9.05	Q DP problem:
27.86/9.05	The TRS P consists of the following rules:
27.86/9.05	
27.86/9.05	   H(x, x) -> G(x, x, f(k))
27.86/9.05	   G(d, x, x) -> A^2
27.86/9.05	   A^2 -> H(f(c), f(c))
27.86/9.05	   A^2 -> H(f(d), f(d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.05	   A^2 -> H(f(e), f(e))
27.86/9.05	   A^2 -> H(f(k), f(k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.05	   A^2 -> H(U1(a, k), f(e))
27.86/9.05	   A^2 -> H(U1(a, k), f(k))
27.86/9.05	   A^2 -> H(U1(a, k), U1(d, d))
27.86/9.05	   A^2 -> H(U1(a, c), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, c), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, c), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, c), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, c), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, c), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.05	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.05	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.05	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.05	   A^2 -> H(U1(a, a), b)
27.86/9.05	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.05	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.05	   A^2 -> H(U1(a, a), c)
27.86/9.05	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.05	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.05	   A^2 -> H(U1(a, a), e)
27.86/9.05	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.05	   A^2 -> H(k, f(b))
27.86/9.05	   A^2 -> H(c, U1(b, b))
27.86/9.05	   A^2 -> H(c, f(c))
27.86/9.05	   A^2 -> H(c, f(d))
27.86/9.05	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.05	   A^2 -> H(U1(e, k), f(c))
27.86/9.05	   A^2 -> H(U1(e, k), f(d))
27.86/9.05	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.05	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.05	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.05	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.05	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.05	   A^2 -> H(U1(e, c), f(e))
27.86/9.05	   A^2 -> H(U1(e, c), f(k))
27.86/9.05	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.05	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.05	   A^2 -> H(U1(k, e), f(c))
27.86/9.05	   A^2 -> H(U1(k, e), f(d))
27.86/9.05	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.05	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.05	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.05	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.05	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.05	   A^2 -> H(U1(k, c), f(e))
27.86/9.05	   A^2 -> H(U1(k, c), f(k))
27.86/9.05	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.05	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.05	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.05	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.05	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.05	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.05	   A^2 -> H(U1(c, e), f(e))
27.86/9.05	   A^2 -> H(U1(c, e), f(k))
27.86/9.05	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.05	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.05	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.05	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.05	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.05	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.05	   A^2 -> H(U1(c, k), f(e))
27.86/9.05	   A^2 -> H(U1(c, k), f(k))
27.86/9.05	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.05	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.05	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.05	   A^2 -> H(e, U1(b, b))
27.86/9.05	   A^2 -> H(e, f(c))
27.86/9.05	   A^2 -> H(e, f(d))
27.86/9.05	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.05	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.05	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.05	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.05	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.05	   A^2 -> H(U1(e, e), f(e))
27.86/9.05	   A^2 -> H(U1(e, e), f(k))
27.86/9.05	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.05	   A^2 -> H(f(e), U1(e, b))
27.86/9.05	   A^2 -> H(f(e), U1(k, b))
27.86/9.05	   A^2 -> H(f(e), U1(c, d))
27.86/9.05	   A^2 -> H(f(e), U1(d, c))
27.86/9.05	   A^2 -> H(f(e), U1(b, e))
27.86/9.05	   A^2 -> H(f(e), U1(b, k))
27.86/9.05	   A^2 -> H(f(e), U1(e, c))
27.86/9.05	   A^2 -> H(f(e), U1(k, c))
27.86/9.05	   A^2 -> H(f(e), U1(c, e))
27.86/9.05	   A^2 -> H(f(e), U1(c, k))
27.86/9.05	   A^2 -> H(f(e), U1(k, k))
27.86/9.05	   A^2 -> H(f(e), U1(k, d))
27.86/9.05	   A^2 -> H(f(e), U1(d, k))
27.86/9.05	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.05	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.05	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.05	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.05	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.05	   A^2 -> H(U1(k, k), f(e))
27.86/9.05	   A^2 -> H(U1(k, k), f(k))
27.86/9.05	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.05	   A^2 -> H(f(k), U1(e, b))
27.86/9.05	   A^2 -> H(f(k), U1(k, b))
27.86/9.05	   A^2 -> H(f(k), U1(c, d))
27.86/9.05	   A^2 -> H(f(k), U1(d, c))
27.86/9.05	   A^2 -> H(f(k), U1(b, e))
27.86/9.05	   A^2 -> H(f(k), U1(b, k))
27.86/9.05	   A^2 -> H(f(k), U1(e, c))
27.86/9.05	   A^2 -> H(f(k), U1(k, c))
27.86/9.05	   A^2 -> H(f(k), U1(c, e))
27.86/9.05	   A^2 -> H(f(k), U1(c, k))
27.86/9.05	   A^2 -> H(f(k), U1(e, e))
27.86/9.05	   A^2 -> H(f(k), U1(k, d))
27.86/9.05	   A^2 -> H(f(k), U1(d, k))
27.86/9.05	   A^2 -> H(f(c), b)
27.86/9.05	   A^2 -> H(f(c), U1(e, d))
27.86/9.05	   A^2 -> H(f(c), U1(d, e))
27.86/9.05	   A^2 -> H(f(k), U1(k, k))
27.86/9.05	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.05	   A^2 -> H(U1(k, k), f(c))
27.86/9.05	   A^2 -> H(U1(k, k), f(d))
27.86/9.05	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.05	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.05	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.05	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.05	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.05	   A^2 -> H(U1(k, d), f(e))
27.86/9.05	   A^2 -> H(U1(k, d), f(k))
27.86/9.05	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.05	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.05	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.05	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.05	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.05	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.05	   A^2 -> H(U1(d, k), f(e))
27.86/9.05	   A^2 -> H(U1(d, k), f(k))
27.86/9.05	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.05	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.05	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.05	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.05	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.05	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.05	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.05	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.05	   A^2 -> H(f(d), b)
27.86/9.05	   A^2 -> H(f(d), U1(e, d))
27.86/9.05	   A^2 -> H(f(d), U1(d, e))
27.86/9.05	   A^2 -> H(f(d), c)
27.86/9.05	   A^2 -> H(f(d), U1(e, k))
27.86/9.05	   A^2 -> H(f(d), U1(k, e))
27.86/9.05	   A^2 -> H(f(d), e)
27.86/9.05	   A^2 -> H(f(a), d)
27.86/9.05	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.05	   A^2 -> H(f(c), c)
27.86/9.05	   A^2 -> H(f(c), U1(e, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.05	   A^2 -> H(f(c), U1(k, e))
27.86/9.05	   A^2 -> H(f(c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.05	   A^2 -> H(f(a), k)
27.86/9.05	   A^2 -> H(f(e), U1(e, e))
27.86/9.05	   A^2 -> H(f(c), e)
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.05	   A^2 -> H(f(d), U1(k, k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.05	   A^2 -> H(d, U1(b, b))
27.86/9.05	   A^2 -> H(d, f(c))
27.86/9.05	   A^2 -> H(d, f(d))
27.86/9.05	   A^2 -> H(a, U1(c, b))
27.86/9.05	   A^2 -> H(a, U1(d, b))
27.86/9.05	   A^2 -> H(a, U1(b, c))
27.86/9.05	   A^2 -> H(a, U1(b, d))
27.86/9.05	   A^2 -> H(a, U1(c, c))
27.86/9.05	   A^2 -> H(a, f(e))
27.86/9.05	   A^2 -> H(a, f(k))
27.86/9.05	   A^2 -> H(a, U1(d, d))
27.86/9.05	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.05	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.05	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.05	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.05	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.05	   A^2 -> H(U1(e, d), f(e))
27.86/9.05	   A^2 -> H(U1(e, d), f(k))
27.86/9.05	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.05	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.05	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.05	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.05	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.05	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.05	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.05	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.05	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.05	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.05	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.05	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.05	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.05	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.05	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.05	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.05	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.05	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.05	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.05	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.05	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.05	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.05	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.05	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.05	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.05	   A^2 -> H(U1(c, a), b)
27.86/9.05	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.05	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.05	   A^2 -> H(U1(c, a), c)
27.86/9.05	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.05	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.05	   A^2 -> H(U1(c, a), e)
27.86/9.05	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.05	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.05	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.05	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.05	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.05	   A^2 -> H(U1(d, e), f(e))
27.86/9.05	   A^2 -> H(U1(d, e), f(k))
27.86/9.05	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.05	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.05	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.05	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.05	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.05	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.05	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.05	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.05	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.05	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.05	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.05	   A^2 -> H(U1(d, a), b)
27.86/9.05	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.05	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.05	   A^2 -> H(U1(d, a), c)
27.86/9.05	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.05	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.05	   A^2 -> H(U1(d, a), e)
27.86/9.05	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, d))
27.86/9.05	   A^2 -> H(U1(a, e), U1(d, k))
27.86/9.05	   A^2 -> H(U1(a, k), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, k), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, k), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, k), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, k), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, k), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, k), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, k), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, k), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, k), U1(c, k))
27.86/9.05	
27.86/9.05	The TRS R consists of the following rules:
27.86/9.05	
27.86/9.05	   f(x) -> U1(x, x)
27.86/9.05	   U1(e, x) -> x
27.86/9.05	   a -> c
27.86/9.05	   a -> d
27.86/9.05	   b -> c
27.86/9.05	   b -> d
27.86/9.05	   d -> k
27.86/9.05	   c -> e
27.86/9.05	   c -> k
27.86/9.05	
27.86/9.05	Q is empty.
27.86/9.05	We have to consider all minimal (P,Q,R)-chains.
27.86/9.05	----------------------------------------
27.86/9.05	
27.86/9.05	(707) TransformationProof (EQUIVALENT)
27.86/9.05	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), f(e)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.05	
27.86/9.05	   (A^2 -> H(U1(c, k), f(e)),A^2 -> H(U1(c, k), f(e)))
27.86/9.05	   (A^2 -> H(U1(d, k), f(e)),A^2 -> H(U1(d, k), f(e)))
27.86/9.05	   (A^2 -> H(U1(a, k), U1(e, e)),A^2 -> H(U1(a, k), U1(e, e)))
27.86/9.05	
27.86/9.05	
27.86/9.05	----------------------------------------
27.86/9.05	
27.86/9.05	(708)
27.86/9.05	Obligation:
27.86/9.05	Q DP problem:
27.86/9.05	The TRS P consists of the following rules:
27.86/9.05	
27.86/9.05	   H(x, x) -> G(x, x, f(k))
27.86/9.05	   G(d, x, x) -> A^2
27.86/9.05	   A^2 -> H(f(c), f(c))
27.86/9.05	   A^2 -> H(f(d), f(d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.05	   A^2 -> H(f(e), f(e))
27.86/9.05	   A^2 -> H(f(k), f(k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.05	   A^2 -> H(U1(a, k), f(k))
27.86/9.05	   A^2 -> H(U1(a, k), U1(d, d))
27.86/9.05	   A^2 -> H(U1(a, c), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, c), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, c), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, c), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, c), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, c), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.05	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.05	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.05	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.05	   A^2 -> H(U1(a, a), b)
27.86/9.05	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.05	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.05	   A^2 -> H(U1(a, a), c)
27.86/9.05	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.05	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.05	   A^2 -> H(U1(a, a), e)
27.86/9.05	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.05	   A^2 -> H(k, f(b))
27.86/9.05	   A^2 -> H(c, U1(b, b))
27.86/9.05	   A^2 -> H(c, f(c))
27.86/9.05	   A^2 -> H(c, f(d))
27.86/9.05	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.05	   A^2 -> H(U1(e, k), f(c))
27.86/9.05	   A^2 -> H(U1(e, k), f(d))
27.86/9.05	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.05	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.05	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.05	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.05	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.05	   A^2 -> H(U1(e, c), f(e))
27.86/9.05	   A^2 -> H(U1(e, c), f(k))
27.86/9.05	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.05	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.05	   A^2 -> H(U1(k, e), f(c))
27.86/9.05	   A^2 -> H(U1(k, e), f(d))
27.86/9.05	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.05	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.05	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.05	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.05	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.05	   A^2 -> H(U1(k, c), f(e))
27.86/9.05	   A^2 -> H(U1(k, c), f(k))
27.86/9.05	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.05	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.05	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.05	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.05	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.05	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.05	   A^2 -> H(U1(c, e), f(e))
27.86/9.05	   A^2 -> H(U1(c, e), f(k))
27.86/9.05	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.05	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.05	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.05	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.05	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.05	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.05	   A^2 -> H(U1(c, k), f(e))
27.86/9.05	   A^2 -> H(U1(c, k), f(k))
27.86/9.05	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.05	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.05	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.05	   A^2 -> H(e, U1(b, b))
27.86/9.05	   A^2 -> H(e, f(c))
27.86/9.05	   A^2 -> H(e, f(d))
27.86/9.05	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.05	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.05	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.05	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.05	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.05	   A^2 -> H(U1(e, e), f(e))
27.86/9.05	   A^2 -> H(U1(e, e), f(k))
27.86/9.05	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.05	   A^2 -> H(f(e), U1(e, b))
27.86/9.05	   A^2 -> H(f(e), U1(k, b))
27.86/9.05	   A^2 -> H(f(e), U1(c, d))
27.86/9.05	   A^2 -> H(f(e), U1(d, c))
27.86/9.05	   A^2 -> H(f(e), U1(b, e))
27.86/9.05	   A^2 -> H(f(e), U1(b, k))
27.86/9.05	   A^2 -> H(f(e), U1(e, c))
27.86/9.05	   A^2 -> H(f(e), U1(k, c))
27.86/9.05	   A^2 -> H(f(e), U1(c, e))
27.86/9.05	   A^2 -> H(f(e), U1(c, k))
27.86/9.05	   A^2 -> H(f(e), U1(k, k))
27.86/9.05	   A^2 -> H(f(e), U1(k, d))
27.86/9.05	   A^2 -> H(f(e), U1(d, k))
27.86/9.05	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.05	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.05	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.05	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.05	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.05	   A^2 -> H(U1(k, k), f(e))
27.86/9.05	   A^2 -> H(U1(k, k), f(k))
27.86/9.05	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.05	   A^2 -> H(f(k), U1(e, b))
27.86/9.05	   A^2 -> H(f(k), U1(k, b))
27.86/9.05	   A^2 -> H(f(k), U1(c, d))
27.86/9.05	   A^2 -> H(f(k), U1(d, c))
27.86/9.05	   A^2 -> H(f(k), U1(b, e))
27.86/9.05	   A^2 -> H(f(k), U1(b, k))
27.86/9.05	   A^2 -> H(f(k), U1(e, c))
27.86/9.05	   A^2 -> H(f(k), U1(k, c))
27.86/9.05	   A^2 -> H(f(k), U1(c, e))
27.86/9.05	   A^2 -> H(f(k), U1(c, k))
27.86/9.05	   A^2 -> H(f(k), U1(e, e))
27.86/9.05	   A^2 -> H(f(k), U1(k, d))
27.86/9.05	   A^2 -> H(f(k), U1(d, k))
27.86/9.05	   A^2 -> H(f(c), b)
27.86/9.05	   A^2 -> H(f(c), U1(e, d))
27.86/9.05	   A^2 -> H(f(c), U1(d, e))
27.86/9.05	   A^2 -> H(f(k), U1(k, k))
27.86/9.05	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.05	   A^2 -> H(U1(k, k), f(c))
27.86/9.05	   A^2 -> H(U1(k, k), f(d))
27.86/9.05	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.05	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.05	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.05	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.05	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.05	   A^2 -> H(U1(k, d), f(e))
27.86/9.05	   A^2 -> H(U1(k, d), f(k))
27.86/9.05	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.05	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.05	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.05	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.05	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.05	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.05	   A^2 -> H(U1(d, k), f(e))
27.86/9.05	   A^2 -> H(U1(d, k), f(k))
27.86/9.05	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.05	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.05	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.05	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.05	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.05	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.05	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.05	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.05	   A^2 -> H(f(d), b)
27.86/9.05	   A^2 -> H(f(d), U1(e, d))
27.86/9.05	   A^2 -> H(f(d), U1(d, e))
27.86/9.05	   A^2 -> H(f(d), c)
27.86/9.05	   A^2 -> H(f(d), U1(e, k))
27.86/9.05	   A^2 -> H(f(d), U1(k, e))
27.86/9.05	   A^2 -> H(f(d), e)
27.86/9.05	   A^2 -> H(f(a), d)
27.86/9.05	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.05	   A^2 -> H(f(c), c)
27.86/9.05	   A^2 -> H(f(c), U1(e, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.05	   A^2 -> H(f(c), U1(k, e))
27.86/9.05	   A^2 -> H(f(c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.05	   A^2 -> H(f(a), k)
27.86/9.05	   A^2 -> H(f(e), U1(e, e))
27.86/9.05	   A^2 -> H(f(c), e)
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.05	   A^2 -> H(f(d), U1(k, k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.05	   A^2 -> H(d, U1(b, b))
27.86/9.05	   A^2 -> H(d, f(c))
27.86/9.05	   A^2 -> H(d, f(d))
27.86/9.05	   A^2 -> H(a, U1(c, b))
27.86/9.05	   A^2 -> H(a, U1(d, b))
27.86/9.05	   A^2 -> H(a, U1(b, c))
27.86/9.05	   A^2 -> H(a, U1(b, d))
27.86/9.05	   A^2 -> H(a, U1(c, c))
27.86/9.05	   A^2 -> H(a, f(e))
27.86/9.05	   A^2 -> H(a, f(k))
27.86/9.05	   A^2 -> H(a, U1(d, d))
27.86/9.05	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.05	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.05	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.05	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.05	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.05	   A^2 -> H(U1(e, d), f(e))
27.86/9.05	   A^2 -> H(U1(e, d), f(k))
27.86/9.05	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.05	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.05	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.05	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.05	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.05	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.05	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.05	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.05	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.05	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.05	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.05	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.05	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.05	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.05	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.05	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.05	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.05	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.05	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.05	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.05	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.05	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.05	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.05	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.05	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.05	   A^2 -> H(U1(c, a), b)
27.86/9.05	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.05	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.05	   A^2 -> H(U1(c, a), c)
27.86/9.05	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.05	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.05	   A^2 -> H(U1(c, a), e)
27.86/9.05	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.05	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.05	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.05	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.05	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.05	   A^2 -> H(U1(d, e), f(e))
27.86/9.05	   A^2 -> H(U1(d, e), f(k))
27.86/9.05	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.05	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.05	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.05	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.05	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.05	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.05	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.05	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.05	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.05	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.05	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.05	   A^2 -> H(U1(d, a), b)
27.86/9.05	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.05	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.05	   A^2 -> H(U1(d, a), c)
27.86/9.05	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.05	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.05	   A^2 -> H(U1(d, a), e)
27.86/9.05	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, d))
27.86/9.05	   A^2 -> H(U1(a, e), U1(d, k))
27.86/9.05	   A^2 -> H(U1(a, k), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, k), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, k), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, k), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, k), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, k), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, k), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, k), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, k), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, k), U1(c, k))
27.86/9.05	   A^2 -> H(U1(a, k), U1(e, e))
27.86/9.05	
27.86/9.05	The TRS R consists of the following rules:
27.86/9.05	
27.86/9.05	   f(x) -> U1(x, x)
27.86/9.05	   U1(e, x) -> x
27.86/9.05	   a -> c
27.86/9.05	   a -> d
27.86/9.05	   b -> c
27.86/9.05	   b -> d
27.86/9.05	   d -> k
27.86/9.05	   c -> e
27.86/9.05	   c -> k
27.86/9.05	
27.86/9.05	Q is empty.
27.86/9.05	We have to consider all minimal (P,Q,R)-chains.
27.86/9.05	----------------------------------------
27.86/9.05	
27.86/9.05	(709) TransformationProof (EQUIVALENT)
27.86/9.05	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), f(k)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.05	
27.86/9.05	   (A^2 -> H(U1(c, k), f(k)),A^2 -> H(U1(c, k), f(k)))
27.86/9.05	   (A^2 -> H(U1(d, k), f(k)),A^2 -> H(U1(d, k), f(k)))
27.86/9.05	   (A^2 -> H(U1(a, k), U1(k, k)),A^2 -> H(U1(a, k), U1(k, k)))
27.86/9.05	
27.86/9.05	
27.86/9.05	----------------------------------------
27.86/9.05	
27.86/9.05	(710)
27.86/9.05	Obligation:
27.86/9.05	Q DP problem:
27.86/9.05	The TRS P consists of the following rules:
27.86/9.05	
27.86/9.05	   H(x, x) -> G(x, x, f(k))
27.86/9.05	   G(d, x, x) -> A^2
27.86/9.05	   A^2 -> H(f(c), f(c))
27.86/9.05	   A^2 -> H(f(d), f(d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.05	   A^2 -> H(f(e), f(e))
27.86/9.05	   A^2 -> H(f(k), f(k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.05	   A^2 -> H(U1(a, k), U1(d, d))
27.86/9.05	   A^2 -> H(U1(a, c), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, c), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, c), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, c), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, c), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, c), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.05	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.05	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.05	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.05	   A^2 -> H(U1(a, a), b)
27.86/9.05	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.05	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.05	   A^2 -> H(U1(a, a), c)
27.86/9.05	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.05	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.05	   A^2 -> H(U1(a, a), e)
27.86/9.05	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.05	   A^2 -> H(k, f(b))
27.86/9.05	   A^2 -> H(c, U1(b, b))
27.86/9.05	   A^2 -> H(c, f(c))
27.86/9.05	   A^2 -> H(c, f(d))
27.86/9.05	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.05	   A^2 -> H(U1(e, k), f(c))
27.86/9.05	   A^2 -> H(U1(e, k), f(d))
27.86/9.05	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.05	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.05	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.05	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.05	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.05	   A^2 -> H(U1(e, c), f(e))
27.86/9.05	   A^2 -> H(U1(e, c), f(k))
27.86/9.05	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.05	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.05	   A^2 -> H(U1(k, e), f(c))
27.86/9.05	   A^2 -> H(U1(k, e), f(d))
27.86/9.05	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.05	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.05	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.05	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.05	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.05	   A^2 -> H(U1(k, c), f(e))
27.86/9.05	   A^2 -> H(U1(k, c), f(k))
27.86/9.05	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.05	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.05	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.05	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.05	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.05	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.05	   A^2 -> H(U1(c, e), f(e))
27.86/9.05	   A^2 -> H(U1(c, e), f(k))
27.86/9.05	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.05	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.05	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.05	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.05	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.05	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.05	   A^2 -> H(U1(c, k), f(e))
27.86/9.05	   A^2 -> H(U1(c, k), f(k))
27.86/9.05	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.05	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.05	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.05	   A^2 -> H(e, U1(b, b))
27.86/9.05	   A^2 -> H(e, f(c))
27.86/9.05	   A^2 -> H(e, f(d))
27.86/9.05	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.05	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.05	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.05	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.05	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.05	   A^2 -> H(U1(e, e), f(e))
27.86/9.05	   A^2 -> H(U1(e, e), f(k))
27.86/9.05	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.05	   A^2 -> H(f(e), U1(e, b))
27.86/9.05	   A^2 -> H(f(e), U1(k, b))
27.86/9.05	   A^2 -> H(f(e), U1(c, d))
27.86/9.05	   A^2 -> H(f(e), U1(d, c))
27.86/9.05	   A^2 -> H(f(e), U1(b, e))
27.86/9.05	   A^2 -> H(f(e), U1(b, k))
27.86/9.05	   A^2 -> H(f(e), U1(e, c))
27.86/9.05	   A^2 -> H(f(e), U1(k, c))
27.86/9.05	   A^2 -> H(f(e), U1(c, e))
27.86/9.05	   A^2 -> H(f(e), U1(c, k))
27.86/9.05	   A^2 -> H(f(e), U1(k, k))
27.86/9.05	   A^2 -> H(f(e), U1(k, d))
27.86/9.05	   A^2 -> H(f(e), U1(d, k))
27.86/9.05	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.05	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.05	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.05	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.05	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.05	   A^2 -> H(U1(k, k), f(e))
27.86/9.05	   A^2 -> H(U1(k, k), f(k))
27.86/9.05	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.05	   A^2 -> H(f(k), U1(e, b))
27.86/9.05	   A^2 -> H(f(k), U1(k, b))
27.86/9.05	   A^2 -> H(f(k), U1(c, d))
27.86/9.05	   A^2 -> H(f(k), U1(d, c))
27.86/9.05	   A^2 -> H(f(k), U1(b, e))
27.86/9.05	   A^2 -> H(f(k), U1(b, k))
27.86/9.05	   A^2 -> H(f(k), U1(e, c))
27.86/9.05	   A^2 -> H(f(k), U1(k, c))
27.86/9.05	   A^2 -> H(f(k), U1(c, e))
27.86/9.05	   A^2 -> H(f(k), U1(c, k))
27.86/9.05	   A^2 -> H(f(k), U1(e, e))
27.86/9.05	   A^2 -> H(f(k), U1(k, d))
27.86/9.05	   A^2 -> H(f(k), U1(d, k))
27.86/9.05	   A^2 -> H(f(c), b)
27.86/9.05	   A^2 -> H(f(c), U1(e, d))
27.86/9.05	   A^2 -> H(f(c), U1(d, e))
27.86/9.05	   A^2 -> H(f(k), U1(k, k))
27.86/9.05	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.05	   A^2 -> H(U1(k, k), f(c))
27.86/9.05	   A^2 -> H(U1(k, k), f(d))
27.86/9.05	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.05	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.05	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.05	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.05	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.05	   A^2 -> H(U1(k, d), f(e))
27.86/9.05	   A^2 -> H(U1(k, d), f(k))
27.86/9.05	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.05	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.05	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.05	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.05	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.05	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.05	   A^2 -> H(U1(d, k), f(e))
27.86/9.05	   A^2 -> H(U1(d, k), f(k))
27.86/9.05	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.05	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.05	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.05	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.05	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.05	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.05	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.05	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.05	   A^2 -> H(f(d), b)
27.86/9.05	   A^2 -> H(f(d), U1(e, d))
27.86/9.05	   A^2 -> H(f(d), U1(d, e))
27.86/9.05	   A^2 -> H(f(d), c)
27.86/9.05	   A^2 -> H(f(d), U1(e, k))
27.86/9.05	   A^2 -> H(f(d), U1(k, e))
27.86/9.05	   A^2 -> H(f(d), e)
27.86/9.05	   A^2 -> H(f(a), d)
27.86/9.05	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.05	   A^2 -> H(f(c), c)
27.86/9.05	   A^2 -> H(f(c), U1(e, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.05	   A^2 -> H(f(c), U1(k, e))
27.86/9.05	   A^2 -> H(f(c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.05	   A^2 -> H(f(a), k)
27.86/9.05	   A^2 -> H(f(e), U1(e, e))
27.86/9.05	   A^2 -> H(f(c), e)
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.05	   A^2 -> H(f(d), U1(k, k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.05	   A^2 -> H(d, U1(b, b))
27.86/9.05	   A^2 -> H(d, f(c))
27.86/9.05	   A^2 -> H(d, f(d))
27.86/9.05	   A^2 -> H(a, U1(c, b))
27.86/9.05	   A^2 -> H(a, U1(d, b))
27.86/9.05	   A^2 -> H(a, U1(b, c))
27.86/9.05	   A^2 -> H(a, U1(b, d))
27.86/9.05	   A^2 -> H(a, U1(c, c))
27.86/9.05	   A^2 -> H(a, f(e))
27.86/9.05	   A^2 -> H(a, f(k))
27.86/9.05	   A^2 -> H(a, U1(d, d))
27.86/9.05	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.05	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.05	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.05	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.05	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.05	   A^2 -> H(U1(e, d), f(e))
27.86/9.05	   A^2 -> H(U1(e, d), f(k))
27.86/9.05	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.05	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.05	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.05	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.05	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.05	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.05	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.05	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.05	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.05	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.05	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.05	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.05	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.05	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.05	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.05	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.05	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.05	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.05	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.05	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.05	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.05	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.05	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.05	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.05	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.05	   A^2 -> H(U1(c, a), b)
27.86/9.05	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.05	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.05	   A^2 -> H(U1(c, a), c)
27.86/9.05	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.05	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.05	   A^2 -> H(U1(c, a), e)
27.86/9.05	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.05	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.05	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.05	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.05	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.05	   A^2 -> H(U1(d, e), f(e))
27.86/9.05	   A^2 -> H(U1(d, e), f(k))
27.86/9.05	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.05	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.05	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.05	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.05	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.05	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.05	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.05	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.05	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.05	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.05	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.05	   A^2 -> H(U1(d, a), b)
27.86/9.05	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.05	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.05	   A^2 -> H(U1(d, a), c)
27.86/9.05	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.05	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.05	   A^2 -> H(U1(d, a), e)
27.86/9.05	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, d))
27.86/9.05	   A^2 -> H(U1(a, e), U1(d, k))
27.86/9.05	   A^2 -> H(U1(a, k), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, k), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, k), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, k), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, k), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, k), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, k), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, k), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, k), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, k), U1(c, k))
27.86/9.05	   A^2 -> H(U1(a, k), U1(e, e))
27.86/9.05	   A^2 -> H(U1(a, k), U1(k, k))
27.86/9.05	
27.86/9.05	The TRS R consists of the following rules:
27.86/9.05	
27.86/9.05	   f(x) -> U1(x, x)
27.86/9.05	   U1(e, x) -> x
27.86/9.05	   a -> c
27.86/9.05	   a -> d
27.86/9.05	   b -> c
27.86/9.05	   b -> d
27.86/9.05	   d -> k
27.86/9.05	   c -> e
27.86/9.05	   c -> k
27.86/9.05	
27.86/9.05	Q is empty.
27.86/9.05	We have to consider all minimal (P,Q,R)-chains.
27.86/9.05	----------------------------------------
27.86/9.05	
27.86/9.05	(711) TransformationProof (EQUIVALENT)
27.86/9.05	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.05	
27.86/9.05	   (A^2 -> H(U1(c, k), U1(d, d)),A^2 -> H(U1(c, k), U1(d, d)))
27.86/9.05	   (A^2 -> H(U1(d, k), U1(d, d)),A^2 -> H(U1(d, k), U1(d, d)))
27.86/9.05	   (A^2 -> H(U1(a, k), U1(k, d)),A^2 -> H(U1(a, k), U1(k, d)))
27.86/9.05	   (A^2 -> H(U1(a, k), U1(d, k)),A^2 -> H(U1(a, k), U1(d, k)))
27.86/9.05	
27.86/9.05	
27.86/9.05	----------------------------------------
27.86/9.05	
27.86/9.05	(712)
27.86/9.05	Obligation:
27.86/9.05	Q DP problem:
27.86/9.05	The TRS P consists of the following rules:
27.86/9.05	
27.86/9.05	   H(x, x) -> G(x, x, f(k))
27.86/9.05	   G(d, x, x) -> A^2
27.86/9.05	   A^2 -> H(f(c), f(c))
27.86/9.05	   A^2 -> H(f(d), f(d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.05	   A^2 -> H(f(e), f(e))
27.86/9.05	   A^2 -> H(f(k), f(k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.05	   A^2 -> H(U1(a, c), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, c), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, c), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, c), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, c), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, c), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.05	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.05	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.05	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.05	   A^2 -> H(U1(a, a), b)
27.86/9.05	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.05	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.05	   A^2 -> H(U1(a, a), c)
27.86/9.05	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.05	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.05	   A^2 -> H(U1(a, a), e)
27.86/9.05	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.05	   A^2 -> H(k, f(b))
27.86/9.05	   A^2 -> H(c, U1(b, b))
27.86/9.05	   A^2 -> H(c, f(c))
27.86/9.05	   A^2 -> H(c, f(d))
27.86/9.05	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.05	   A^2 -> H(U1(e, k), f(c))
27.86/9.05	   A^2 -> H(U1(e, k), f(d))
27.86/9.05	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.05	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.05	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.05	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.05	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.05	   A^2 -> H(U1(e, c), f(e))
27.86/9.05	   A^2 -> H(U1(e, c), f(k))
27.86/9.05	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.05	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.05	   A^2 -> H(U1(k, e), f(c))
27.86/9.05	   A^2 -> H(U1(k, e), f(d))
27.86/9.05	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.05	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.05	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.05	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.05	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.05	   A^2 -> H(U1(k, c), f(e))
27.86/9.05	   A^2 -> H(U1(k, c), f(k))
27.86/9.05	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.05	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.05	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.05	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.05	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.05	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.05	   A^2 -> H(U1(c, e), f(e))
27.86/9.05	   A^2 -> H(U1(c, e), f(k))
27.86/9.05	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.05	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.05	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.05	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.05	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.05	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.05	   A^2 -> H(U1(c, k), f(e))
27.86/9.05	   A^2 -> H(U1(c, k), f(k))
27.86/9.05	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.05	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.05	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.05	   A^2 -> H(e, U1(b, b))
27.86/9.05	   A^2 -> H(e, f(c))
27.86/9.05	   A^2 -> H(e, f(d))
27.86/9.05	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.05	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.05	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.05	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.05	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.05	   A^2 -> H(U1(e, e), f(e))
27.86/9.05	   A^2 -> H(U1(e, e), f(k))
27.86/9.05	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.05	   A^2 -> H(f(e), U1(e, b))
27.86/9.05	   A^2 -> H(f(e), U1(k, b))
27.86/9.05	   A^2 -> H(f(e), U1(c, d))
27.86/9.05	   A^2 -> H(f(e), U1(d, c))
27.86/9.05	   A^2 -> H(f(e), U1(b, e))
27.86/9.05	   A^2 -> H(f(e), U1(b, k))
27.86/9.05	   A^2 -> H(f(e), U1(e, c))
27.86/9.05	   A^2 -> H(f(e), U1(k, c))
27.86/9.05	   A^2 -> H(f(e), U1(c, e))
27.86/9.05	   A^2 -> H(f(e), U1(c, k))
27.86/9.05	   A^2 -> H(f(e), U1(k, k))
27.86/9.05	   A^2 -> H(f(e), U1(k, d))
27.86/9.05	   A^2 -> H(f(e), U1(d, k))
27.86/9.05	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.05	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.05	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.05	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.05	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.05	   A^2 -> H(U1(k, k), f(e))
27.86/9.05	   A^2 -> H(U1(k, k), f(k))
27.86/9.05	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.05	   A^2 -> H(f(k), U1(e, b))
27.86/9.05	   A^2 -> H(f(k), U1(k, b))
27.86/9.05	   A^2 -> H(f(k), U1(c, d))
27.86/9.05	   A^2 -> H(f(k), U1(d, c))
27.86/9.05	   A^2 -> H(f(k), U1(b, e))
27.86/9.05	   A^2 -> H(f(k), U1(b, k))
27.86/9.05	   A^2 -> H(f(k), U1(e, c))
27.86/9.05	   A^2 -> H(f(k), U1(k, c))
27.86/9.05	   A^2 -> H(f(k), U1(c, e))
27.86/9.05	   A^2 -> H(f(k), U1(c, k))
27.86/9.05	   A^2 -> H(f(k), U1(e, e))
27.86/9.05	   A^2 -> H(f(k), U1(k, d))
27.86/9.05	   A^2 -> H(f(k), U1(d, k))
27.86/9.05	   A^2 -> H(f(c), b)
27.86/9.05	   A^2 -> H(f(c), U1(e, d))
27.86/9.05	   A^2 -> H(f(c), U1(d, e))
27.86/9.05	   A^2 -> H(f(k), U1(k, k))
27.86/9.05	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.05	   A^2 -> H(U1(k, k), f(c))
27.86/9.05	   A^2 -> H(U1(k, k), f(d))
27.86/9.05	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.05	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.05	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.05	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.05	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.05	   A^2 -> H(U1(k, d), f(e))
27.86/9.05	   A^2 -> H(U1(k, d), f(k))
27.86/9.05	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.05	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.05	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.05	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.05	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.05	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.05	   A^2 -> H(U1(d, k), f(e))
27.86/9.05	   A^2 -> H(U1(d, k), f(k))
27.86/9.05	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.05	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.05	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.05	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.05	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.05	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.05	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.05	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.05	   A^2 -> H(f(d), b)
27.86/9.05	   A^2 -> H(f(d), U1(e, d))
27.86/9.05	   A^2 -> H(f(d), U1(d, e))
27.86/9.05	   A^2 -> H(f(d), c)
27.86/9.05	   A^2 -> H(f(d), U1(e, k))
27.86/9.05	   A^2 -> H(f(d), U1(k, e))
27.86/9.05	   A^2 -> H(f(d), e)
27.86/9.05	   A^2 -> H(f(a), d)
27.86/9.05	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.05	   A^2 -> H(f(c), c)
27.86/9.05	   A^2 -> H(f(c), U1(e, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.05	   A^2 -> H(f(c), U1(k, e))
27.86/9.05	   A^2 -> H(f(c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.05	   A^2 -> H(f(a), k)
27.86/9.05	   A^2 -> H(f(e), U1(e, e))
27.86/9.05	   A^2 -> H(f(c), e)
27.86/9.05	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.05	   A^2 -> H(f(d), U1(k, k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.05	   A^2 -> H(d, U1(b, b))
27.86/9.05	   A^2 -> H(d, f(c))
27.86/9.05	   A^2 -> H(d, f(d))
27.86/9.05	   A^2 -> H(a, U1(c, b))
27.86/9.05	   A^2 -> H(a, U1(d, b))
27.86/9.05	   A^2 -> H(a, U1(b, c))
27.86/9.05	   A^2 -> H(a, U1(b, d))
27.86/9.05	   A^2 -> H(a, U1(c, c))
27.86/9.05	   A^2 -> H(a, f(e))
27.86/9.05	   A^2 -> H(a, f(k))
27.86/9.05	   A^2 -> H(a, U1(d, d))
27.86/9.05	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.05	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.05	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.05	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.05	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.05	   A^2 -> H(U1(e, d), f(e))
27.86/9.05	   A^2 -> H(U1(e, d), f(k))
27.86/9.05	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.05	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.05	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.05	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.05	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.05	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.05	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.05	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.05	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.05	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.05	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.05	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.05	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.05	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.05	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.05	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.05	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.05	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.05	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.05	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.05	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.05	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.05	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.05	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.05	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.05	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.05	   A^2 -> H(U1(c, a), b)
27.86/9.05	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.05	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.05	   A^2 -> H(U1(c, a), c)
27.86/9.05	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.05	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.05	   A^2 -> H(U1(c, a), e)
27.86/9.05	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.05	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.05	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.05	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.05	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.05	   A^2 -> H(U1(d, e), f(e))
27.86/9.05	   A^2 -> H(U1(d, e), f(k))
27.86/9.05	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.05	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.05	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.05	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.05	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.05	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.05	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.05	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.05	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.05	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.05	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.05	   A^2 -> H(U1(d, a), b)
27.86/9.05	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.05	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.05	   A^2 -> H(U1(d, a), c)
27.86/9.05	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.05	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.05	   A^2 -> H(U1(d, a), e)
27.86/9.05	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, e), U1(k, d))
27.86/9.05	   A^2 -> H(U1(a, e), U1(d, k))
27.86/9.05	   A^2 -> H(U1(a, k), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, k), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, k), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, k), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, k), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, k), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, k), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, k), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, k), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, k), U1(c, k))
27.86/9.05	   A^2 -> H(U1(a, k), U1(e, e))
27.86/9.05	   A^2 -> H(U1(a, k), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, k), U1(k, d))
27.86/9.05	   A^2 -> H(U1(a, k), U1(d, k))
27.86/9.05	
27.86/9.05	The TRS R consists of the following rules:
27.86/9.05	
27.86/9.05	   f(x) -> U1(x, x)
27.86/9.05	   U1(e, x) -> x
27.86/9.05	   a -> c
27.86/9.05	   a -> d
27.86/9.05	   b -> c
27.86/9.05	   b -> d
27.86/9.05	   d -> k
27.86/9.05	   c -> e
27.86/9.05	   c -> k
27.86/9.05	
27.86/9.05	Q is empty.
27.86/9.05	We have to consider all minimal (P,Q,R)-chains.
27.86/9.05	----------------------------------------
27.86/9.05	
27.86/9.05	(713) TransformationProof (EQUIVALENT)
27.86/9.05	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.05	
27.86/9.05	   (A^2 -> H(U1(c, c), U1(e, b)),A^2 -> H(U1(c, c), U1(e, b)))
27.86/9.05	   (A^2 -> H(U1(d, c), U1(e, b)),A^2 -> H(U1(d, c), U1(e, b)))
27.86/9.05	   (A^2 -> H(U1(a, e), U1(e, b)),A^2 -> H(U1(a, e), U1(e, b)))
27.86/9.05	   (A^2 -> H(U1(a, k), U1(e, b)),A^2 -> H(U1(a, k), U1(e, b)))
27.86/9.05	   (A^2 -> H(U1(a, c), b),A^2 -> H(U1(a, c), b))
27.86/9.05	   (A^2 -> H(U1(a, c), U1(e, c)),A^2 -> H(U1(a, c), U1(e, c)))
27.86/9.05	   (A^2 -> H(U1(a, c), U1(e, d)),A^2 -> H(U1(a, c), U1(e, d)))
27.86/9.05	
27.86/9.05	
27.86/9.05	----------------------------------------
27.86/9.05	
27.86/9.05	(714)
27.86/9.05	Obligation:
27.86/9.05	Q DP problem:
27.86/9.05	The TRS P consists of the following rules:
27.86/9.05	
27.86/9.05	   H(x, x) -> G(x, x, f(k))
27.86/9.05	   G(d, x, x) -> A^2
27.86/9.05	   A^2 -> H(f(c), f(c))
27.86/9.05	   A^2 -> H(f(d), f(d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.05	   A^2 -> H(f(e), f(e))
27.86/9.05	   A^2 -> H(f(k), f(k))
27.86/9.05	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, c), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, c), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, c), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, c), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, c), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.05	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.05	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.05	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.05	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.05	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.05	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.05	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.05	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.05	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.05	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.05	   A^2 -> H(U1(a, a), b)
27.86/9.05	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.05	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.05	   A^2 -> H(U1(a, a), c)
27.86/9.05	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.05	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.05	   A^2 -> H(U1(a, a), e)
27.86/9.05	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.05	   A^2 -> H(k, f(b))
27.86/9.05	   A^2 -> H(c, U1(b, b))
27.86/9.05	   A^2 -> H(c, f(c))
27.86/9.05	   A^2 -> H(c, f(d))
27.86/9.05	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.05	   A^2 -> H(U1(e, k), f(c))
27.86/9.05	   A^2 -> H(U1(e, k), f(d))
27.86/9.05	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.05	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.05	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.05	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.05	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.05	   A^2 -> H(U1(e, c), f(e))
27.86/9.05	   A^2 -> H(U1(e, c), f(k))
27.86/9.05	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.05	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.05	   A^2 -> H(U1(k, e), f(c))
27.86/9.05	   A^2 -> H(U1(k, e), f(d))
27.86/9.05	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.05	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.05	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.05	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.05	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.05	   A^2 -> H(U1(k, c), f(e))
27.86/9.05	   A^2 -> H(U1(k, c), f(k))
27.86/9.05	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.05	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.05	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.05	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.05	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.05	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.05	   A^2 -> H(U1(c, e), f(e))
27.86/9.05	   A^2 -> H(U1(c, e), f(k))
27.86/9.05	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.05	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.05	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.05	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.05	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.05	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.05	   A^2 -> H(U1(c, k), f(e))
27.86/9.05	   A^2 -> H(U1(c, k), f(k))
27.86/9.05	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.05	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.05	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.05	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.05	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.05	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.05	   A^2 -> H(e, U1(b, b))
27.86/9.05	   A^2 -> H(e, f(c))
27.86/9.05	   A^2 -> H(e, f(d))
27.86/9.05	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.05	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.05	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.05	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.05	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.05	   A^2 -> H(U1(e, e), f(e))
27.86/9.05	   A^2 -> H(U1(e, e), f(k))
27.86/9.05	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.05	   A^2 -> H(f(e), U1(e, b))
27.86/9.05	   A^2 -> H(f(e), U1(k, b))
27.86/9.05	   A^2 -> H(f(e), U1(c, d))
27.86/9.05	   A^2 -> H(f(e), U1(d, c))
27.86/9.05	   A^2 -> H(f(e), U1(b, e))
27.86/9.05	   A^2 -> H(f(e), U1(b, k))
27.86/9.05	   A^2 -> H(f(e), U1(e, c))
27.86/9.05	   A^2 -> H(f(e), U1(k, c))
27.86/9.05	   A^2 -> H(f(e), U1(c, e))
27.86/9.05	   A^2 -> H(f(e), U1(c, k))
27.86/9.05	   A^2 -> H(f(e), U1(k, k))
27.86/9.05	   A^2 -> H(f(e), U1(k, d))
27.86/9.05	   A^2 -> H(f(e), U1(d, k))
27.86/9.05	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.05	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.05	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.05	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.05	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.05	   A^2 -> H(U1(k, k), f(e))
27.86/9.05	   A^2 -> H(U1(k, k), f(k))
27.86/9.05	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.05	   A^2 -> H(f(k), U1(e, b))
27.86/9.05	   A^2 -> H(f(k), U1(k, b))
27.86/9.05	   A^2 -> H(f(k), U1(c, d))
27.86/9.07	   A^2 -> H(f(k), U1(d, c))
27.86/9.07	   A^2 -> H(f(k), U1(b, e))
27.86/9.07	   A^2 -> H(f(k), U1(b, k))
27.86/9.07	   A^2 -> H(f(k), U1(e, c))
27.86/9.07	   A^2 -> H(f(k), U1(k, c))
27.86/9.07	   A^2 -> H(f(k), U1(c, e))
27.86/9.07	   A^2 -> H(f(k), U1(c, k))
27.86/9.07	   A^2 -> H(f(k), U1(e, e))
27.86/9.07	   A^2 -> H(f(k), U1(k, d))
27.86/9.07	   A^2 -> H(f(k), U1(d, k))
27.86/9.07	   A^2 -> H(f(c), b)
27.86/9.07	   A^2 -> H(f(c), U1(e, d))
27.86/9.07	   A^2 -> H(f(c), U1(d, e))
27.86/9.07	   A^2 -> H(f(k), U1(k, k))
27.86/9.07	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.07	   A^2 -> H(U1(k, k), f(c))
27.86/9.07	   A^2 -> H(U1(k, k), f(d))
27.86/9.07	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.07	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.07	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.07	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.07	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.07	   A^2 -> H(U1(k, d), f(e))
27.86/9.07	   A^2 -> H(U1(k, d), f(k))
27.86/9.07	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.07	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.07	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.07	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.07	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.07	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.07	   A^2 -> H(U1(d, k), f(e))
27.86/9.07	   A^2 -> H(U1(d, k), f(k))
27.86/9.07	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.07	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.07	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.07	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.07	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.07	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.07	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.07	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.07	   A^2 -> H(f(d), b)
27.86/9.07	   A^2 -> H(f(d), U1(e, d))
27.86/9.07	   A^2 -> H(f(d), U1(d, e))
27.86/9.07	   A^2 -> H(f(d), c)
27.86/9.07	   A^2 -> H(f(d), U1(e, k))
27.86/9.07	   A^2 -> H(f(d), U1(k, e))
27.86/9.07	   A^2 -> H(f(d), e)
27.86/9.07	   A^2 -> H(f(a), d)
27.86/9.07	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.07	   A^2 -> H(f(c), c)
27.86/9.07	   A^2 -> H(f(c), U1(e, k))
27.86/9.07	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.07	   A^2 -> H(f(c), U1(k, e))
27.86/9.07	   A^2 -> H(f(c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.07	   A^2 -> H(f(a), k)
27.86/9.07	   A^2 -> H(f(e), U1(e, e))
27.86/9.07	   A^2 -> H(f(c), e)
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.07	   A^2 -> H(f(d), U1(k, k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.07	   A^2 -> H(d, U1(b, b))
27.86/9.07	   A^2 -> H(d, f(c))
27.86/9.07	   A^2 -> H(d, f(d))
27.86/9.07	   A^2 -> H(a, U1(c, b))
27.86/9.07	   A^2 -> H(a, U1(d, b))
27.86/9.07	   A^2 -> H(a, U1(b, c))
27.86/9.07	   A^2 -> H(a, U1(b, d))
27.86/9.07	   A^2 -> H(a, U1(c, c))
27.86/9.07	   A^2 -> H(a, f(e))
27.86/9.07	   A^2 -> H(a, f(k))
27.86/9.07	   A^2 -> H(a, U1(d, d))
27.86/9.07	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.07	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.07	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.07	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.07	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.07	   A^2 -> H(U1(e, d), f(e))
27.86/9.07	   A^2 -> H(U1(e, d), f(k))
27.86/9.07	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.07	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.07	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.07	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.07	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.07	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.07	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.07	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.07	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.07	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.07	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.07	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.07	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.07	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.07	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.07	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.07	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.07	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.07	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.07	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.07	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.07	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.07	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.07	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.07	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.07	   A^2 -> H(U1(c, a), b)
27.86/9.07	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.07	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.07	   A^2 -> H(U1(c, a), c)
27.86/9.07	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.07	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.07	   A^2 -> H(U1(c, a), e)
27.86/9.07	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.07	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.07	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.07	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.07	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.07	   A^2 -> H(U1(d, e), f(e))
27.86/9.07	   A^2 -> H(U1(d, e), f(k))
27.86/9.07	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.07	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.07	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.07	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.07	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.07	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.07	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.07	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.07	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.07	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.07	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.07	   A^2 -> H(U1(d, a), b)
27.86/9.07	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.07	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.07	   A^2 -> H(U1(d, a), c)
27.86/9.07	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.07	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.07	   A^2 -> H(U1(d, a), e)
27.86/9.07	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.07	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.07	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.07	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.07	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, e), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(e, b))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, b))
27.86/9.07	   A^2 -> H(U1(a, k), U1(c, d))
27.86/9.07	   A^2 -> H(U1(a, k), U1(d, c))
27.86/9.07	   A^2 -> H(U1(a, k), U1(b, e))
27.86/9.07	   A^2 -> H(U1(a, k), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, k), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, k), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, k), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, c), b)
27.86/9.07	   A^2 -> H(U1(a, c), U1(e, d))
27.86/9.07	
27.86/9.07	The TRS R consists of the following rules:
27.86/9.07	
27.86/9.07	   f(x) -> U1(x, x)
27.86/9.07	   U1(e, x) -> x
27.86/9.07	   a -> c
27.86/9.07	   a -> d
27.86/9.07	   b -> c
27.86/9.07	   b -> d
27.86/9.07	   d -> k
27.86/9.07	   c -> e
27.86/9.07	   c -> k
27.86/9.07	
27.86/9.07	Q is empty.
27.86/9.07	We have to consider all minimal (P,Q,R)-chains.
27.86/9.07	----------------------------------------
27.86/9.07	
27.86/9.07	(715) TransformationProof (EQUIVALENT)
27.86/9.07	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.07	
27.86/9.07	   (A^2 -> H(U1(c, c), U1(k, b)),A^2 -> H(U1(c, c), U1(k, b)))
27.86/9.07	   (A^2 -> H(U1(d, c), U1(k, b)),A^2 -> H(U1(d, c), U1(k, b)))
27.86/9.07	   (A^2 -> H(U1(a, e), U1(k, b)),A^2 -> H(U1(a, e), U1(k, b)))
27.86/9.07	   (A^2 -> H(U1(a, k), U1(k, b)),A^2 -> H(U1(a, k), U1(k, b)))
27.86/9.07	   (A^2 -> H(U1(a, c), U1(k, c)),A^2 -> H(U1(a, c), U1(k, c)))
27.86/9.07	   (A^2 -> H(U1(a, c), U1(k, d)),A^2 -> H(U1(a, c), U1(k, d)))
27.86/9.07	
27.86/9.07	
27.86/9.07	----------------------------------------
27.86/9.07	
27.86/9.07	(716)
27.86/9.07	Obligation:
27.86/9.07	Q DP problem:
27.86/9.07	The TRS P consists of the following rules:
27.86/9.07	
27.86/9.07	   H(x, x) -> G(x, x, f(k))
27.86/9.07	   G(d, x, x) -> A^2
27.86/9.07	   A^2 -> H(f(c), f(c))
27.86/9.07	   A^2 -> H(f(d), f(d))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.07	   A^2 -> H(f(e), f(e))
27.86/9.07	   A^2 -> H(f(k), f(k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.07	   A^2 -> H(U1(a, c), U1(c, d))
27.86/9.07	   A^2 -> H(U1(a, c), U1(d, c))
27.86/9.07	   A^2 -> H(U1(a, c), U1(b, e))
27.86/9.07	   A^2 -> H(U1(a, c), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, c), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, c), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.07	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.07	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.07	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.07	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, a), b)
27.86/9.07	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.07	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.07	   A^2 -> H(U1(a, a), c)
27.86/9.07	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.07	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.07	   A^2 -> H(U1(a, a), e)
27.86/9.07	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.07	   A^2 -> H(k, f(b))
27.86/9.07	   A^2 -> H(c, U1(b, b))
27.86/9.07	   A^2 -> H(c, f(c))
27.86/9.07	   A^2 -> H(c, f(d))
27.86/9.07	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.07	   A^2 -> H(U1(e, k), f(c))
27.86/9.07	   A^2 -> H(U1(e, k), f(d))
27.86/9.07	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.07	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.07	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.07	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.07	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.07	   A^2 -> H(U1(e, c), f(e))
27.86/9.07	   A^2 -> H(U1(e, c), f(k))
27.86/9.07	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.07	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.07	   A^2 -> H(U1(k, e), f(c))
27.86/9.07	   A^2 -> H(U1(k, e), f(d))
27.86/9.07	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.07	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.07	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.07	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.07	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.07	   A^2 -> H(U1(k, c), f(e))
27.86/9.07	   A^2 -> H(U1(k, c), f(k))
27.86/9.07	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.07	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.07	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.07	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.07	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.07	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.07	   A^2 -> H(U1(c, e), f(e))
27.86/9.07	   A^2 -> H(U1(c, e), f(k))
27.86/9.07	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.07	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.07	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.07	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.07	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.07	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.07	   A^2 -> H(U1(c, k), f(e))
27.86/9.07	   A^2 -> H(U1(c, k), f(k))
27.86/9.07	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.07	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.07	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.07	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.07	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.07	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.07	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.07	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.07	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.07	   A^2 -> H(e, U1(b, b))
27.86/9.07	   A^2 -> H(e, f(c))
27.86/9.07	   A^2 -> H(e, f(d))
27.86/9.07	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.07	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.07	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.07	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.07	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.07	   A^2 -> H(U1(e, e), f(e))
27.86/9.07	   A^2 -> H(U1(e, e), f(k))
27.86/9.07	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.07	   A^2 -> H(f(e), U1(e, b))
27.86/9.07	   A^2 -> H(f(e), U1(k, b))
27.86/9.07	   A^2 -> H(f(e), U1(c, d))
27.86/9.07	   A^2 -> H(f(e), U1(d, c))
27.86/9.07	   A^2 -> H(f(e), U1(b, e))
27.86/9.07	   A^2 -> H(f(e), U1(b, k))
27.86/9.07	   A^2 -> H(f(e), U1(e, c))
27.86/9.07	   A^2 -> H(f(e), U1(k, c))
27.86/9.07	   A^2 -> H(f(e), U1(c, e))
27.86/9.07	   A^2 -> H(f(e), U1(c, k))
27.86/9.07	   A^2 -> H(f(e), U1(k, k))
27.86/9.07	   A^2 -> H(f(e), U1(k, d))
27.86/9.07	   A^2 -> H(f(e), U1(d, k))
27.86/9.07	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.07	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.07	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.07	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.07	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.07	   A^2 -> H(U1(k, k), f(e))
27.86/9.07	   A^2 -> H(U1(k, k), f(k))
27.86/9.07	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.07	   A^2 -> H(f(k), U1(e, b))
27.86/9.07	   A^2 -> H(f(k), U1(k, b))
27.86/9.07	   A^2 -> H(f(k), U1(c, d))
27.86/9.07	   A^2 -> H(f(k), U1(d, c))
27.86/9.07	   A^2 -> H(f(k), U1(b, e))
27.86/9.07	   A^2 -> H(f(k), U1(b, k))
27.86/9.07	   A^2 -> H(f(k), U1(e, c))
27.86/9.07	   A^2 -> H(f(k), U1(k, c))
27.86/9.07	   A^2 -> H(f(k), U1(c, e))
27.86/9.07	   A^2 -> H(f(k), U1(c, k))
27.86/9.07	   A^2 -> H(f(k), U1(e, e))
27.86/9.07	   A^2 -> H(f(k), U1(k, d))
27.86/9.07	   A^2 -> H(f(k), U1(d, k))
27.86/9.07	   A^2 -> H(f(c), b)
27.86/9.07	   A^2 -> H(f(c), U1(e, d))
27.86/9.07	   A^2 -> H(f(c), U1(d, e))
27.86/9.07	   A^2 -> H(f(k), U1(k, k))
27.86/9.07	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.07	   A^2 -> H(U1(k, k), f(c))
27.86/9.07	   A^2 -> H(U1(k, k), f(d))
27.86/9.07	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.07	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.07	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.07	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.07	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.07	   A^2 -> H(U1(k, d), f(e))
27.86/9.07	   A^2 -> H(U1(k, d), f(k))
27.86/9.07	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.07	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.07	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.07	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.07	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.07	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.07	   A^2 -> H(U1(d, k), f(e))
27.86/9.07	   A^2 -> H(U1(d, k), f(k))
27.86/9.07	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.07	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.07	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.07	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.07	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.07	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.07	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.07	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.07	   A^2 -> H(f(d), b)
27.86/9.07	   A^2 -> H(f(d), U1(e, d))
27.86/9.07	   A^2 -> H(f(d), U1(d, e))
27.86/9.07	   A^2 -> H(f(d), c)
27.86/9.07	   A^2 -> H(f(d), U1(e, k))
27.86/9.07	   A^2 -> H(f(d), U1(k, e))
27.86/9.07	   A^2 -> H(f(d), e)
27.86/9.07	   A^2 -> H(f(a), d)
27.86/9.07	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.07	   A^2 -> H(f(c), c)
27.86/9.07	   A^2 -> H(f(c), U1(e, k))
27.86/9.07	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.07	   A^2 -> H(f(c), U1(k, e))
27.86/9.07	   A^2 -> H(f(c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.07	   A^2 -> H(f(a), k)
27.86/9.07	   A^2 -> H(f(e), U1(e, e))
27.86/9.07	   A^2 -> H(f(c), e)
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.07	   A^2 -> H(f(d), U1(k, k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.07	   A^2 -> H(d, U1(b, b))
27.86/9.07	   A^2 -> H(d, f(c))
27.86/9.07	   A^2 -> H(d, f(d))
27.86/9.07	   A^2 -> H(a, U1(c, b))
27.86/9.07	   A^2 -> H(a, U1(d, b))
27.86/9.07	   A^2 -> H(a, U1(b, c))
27.86/9.07	   A^2 -> H(a, U1(b, d))
27.86/9.07	   A^2 -> H(a, U1(c, c))
27.86/9.07	   A^2 -> H(a, f(e))
27.86/9.07	   A^2 -> H(a, f(k))
27.86/9.07	   A^2 -> H(a, U1(d, d))
27.86/9.07	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.07	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.07	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.07	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.07	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.07	   A^2 -> H(U1(e, d), f(e))
27.86/9.07	   A^2 -> H(U1(e, d), f(k))
27.86/9.07	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.07	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.07	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.07	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.07	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.07	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.07	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.07	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.07	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.07	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.07	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.07	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.07	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.07	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.07	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.07	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.07	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.07	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.07	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.07	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.07	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.07	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.07	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.07	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.07	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.07	   A^2 -> H(U1(c, a), b)
27.86/9.07	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.07	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.07	   A^2 -> H(U1(c, a), c)
27.86/9.07	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.07	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.07	   A^2 -> H(U1(c, a), e)
27.86/9.07	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.07	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.07	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.07	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.07	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.07	   A^2 -> H(U1(d, e), f(e))
27.86/9.07	   A^2 -> H(U1(d, e), f(k))
27.86/9.07	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.07	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.07	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.07	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.07	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.07	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.07	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.07	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.07	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.07	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.07	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.07	   A^2 -> H(U1(d, a), b)
27.86/9.07	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.07	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.07	   A^2 -> H(U1(d, a), c)
27.86/9.07	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.07	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.07	   A^2 -> H(U1(d, a), e)
27.86/9.07	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.07	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.07	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.07	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.07	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, e), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(e, b))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, b))
27.86/9.07	   A^2 -> H(U1(a, k), U1(c, d))
27.86/9.07	   A^2 -> H(U1(a, k), U1(d, c))
27.86/9.07	   A^2 -> H(U1(a, k), U1(b, e))
27.86/9.07	   A^2 -> H(U1(a, k), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, k), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, k), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, k), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, c), b)
27.86/9.07	   A^2 -> H(U1(a, c), U1(e, d))
27.86/9.07	
27.86/9.07	The TRS R consists of the following rules:
27.86/9.07	
27.86/9.07	   f(x) -> U1(x, x)
27.86/9.07	   U1(e, x) -> x
27.86/9.07	   a -> c
27.86/9.07	   a -> d
27.86/9.07	   b -> c
27.86/9.07	   b -> d
27.86/9.07	   d -> k
27.86/9.07	   c -> e
27.86/9.07	   c -> k
27.86/9.07	
27.86/9.07	Q is empty.
27.86/9.07	We have to consider all minimal (P,Q,R)-chains.
27.86/9.07	----------------------------------------
27.86/9.07	
27.86/9.07	(717) TransformationProof (EQUIVALENT)
27.86/9.07	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.07	
27.86/9.07	   (A^2 -> H(U1(c, c), U1(c, d)),A^2 -> H(U1(c, c), U1(c, d)))
27.86/9.07	   (A^2 -> H(U1(d, c), U1(c, d)),A^2 -> H(U1(d, c), U1(c, d)))
27.86/9.07	   (A^2 -> H(U1(a, e), U1(c, d)),A^2 -> H(U1(a, e), U1(c, d)))
27.86/9.07	   (A^2 -> H(U1(a, k), U1(c, d)),A^2 -> H(U1(a, k), U1(c, d)))
27.86/9.07	   (A^2 -> H(U1(a, c), U1(e, d)),A^2 -> H(U1(a, c), U1(e, d)))
27.86/9.07	   (A^2 -> H(U1(a, c), U1(k, d)),A^2 -> H(U1(a, c), U1(k, d)))
27.86/9.07	   (A^2 -> H(U1(a, c), U1(c, k)),A^2 -> H(U1(a, c), U1(c, k)))
27.86/9.07	
27.86/9.07	
27.86/9.07	----------------------------------------
27.86/9.07	
27.86/9.07	(718)
27.86/9.07	Obligation:
27.86/9.07	Q DP problem:
27.86/9.07	The TRS P consists of the following rules:
27.86/9.07	
27.86/9.07	   H(x, x) -> G(x, x, f(k))
27.86/9.07	   G(d, x, x) -> A^2
27.86/9.07	   A^2 -> H(f(c), f(c))
27.86/9.07	   A^2 -> H(f(d), f(d))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.07	   A^2 -> H(f(e), f(e))
27.86/9.07	   A^2 -> H(f(k), f(k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.07	   A^2 -> H(U1(a, c), U1(d, c))
27.86/9.07	   A^2 -> H(U1(a, c), U1(b, e))
27.86/9.07	   A^2 -> H(U1(a, c), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, c), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, c), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.07	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.07	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.07	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.07	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, a), b)
27.86/9.07	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.07	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.07	   A^2 -> H(U1(a, a), c)
27.86/9.07	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.07	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.07	   A^2 -> H(U1(a, a), e)
27.86/9.07	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.07	   A^2 -> H(k, f(b))
27.86/9.07	   A^2 -> H(c, U1(b, b))
27.86/9.07	   A^2 -> H(c, f(c))
27.86/9.07	   A^2 -> H(c, f(d))
27.86/9.07	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.07	   A^2 -> H(U1(e, k), f(c))
27.86/9.07	   A^2 -> H(U1(e, k), f(d))
27.86/9.07	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.07	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.07	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.07	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.07	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.07	   A^2 -> H(U1(e, c), f(e))
27.86/9.07	   A^2 -> H(U1(e, c), f(k))
27.86/9.07	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.07	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.07	   A^2 -> H(U1(k, e), f(c))
27.86/9.07	   A^2 -> H(U1(k, e), f(d))
27.86/9.07	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.07	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.07	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.07	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.07	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.07	   A^2 -> H(U1(k, c), f(e))
27.86/9.07	   A^2 -> H(U1(k, c), f(k))
27.86/9.07	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.07	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.07	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.07	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.07	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.07	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.07	   A^2 -> H(U1(c, e), f(e))
27.86/9.07	   A^2 -> H(U1(c, e), f(k))
27.86/9.07	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.07	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.07	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.07	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.07	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.07	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.07	   A^2 -> H(U1(c, k), f(e))
27.86/9.07	   A^2 -> H(U1(c, k), f(k))
27.86/9.07	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.07	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.07	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.07	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.07	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.07	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.07	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.07	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.07	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.07	   A^2 -> H(e, U1(b, b))
27.86/9.07	   A^2 -> H(e, f(c))
27.86/9.07	   A^2 -> H(e, f(d))
27.86/9.07	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.07	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.07	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.07	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.07	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.07	   A^2 -> H(U1(e, e), f(e))
27.86/9.07	   A^2 -> H(U1(e, e), f(k))
27.86/9.07	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.07	   A^2 -> H(f(e), U1(e, b))
27.86/9.07	   A^2 -> H(f(e), U1(k, b))
27.86/9.07	   A^2 -> H(f(e), U1(c, d))
27.86/9.07	   A^2 -> H(f(e), U1(d, c))
27.86/9.07	   A^2 -> H(f(e), U1(b, e))
27.86/9.07	   A^2 -> H(f(e), U1(b, k))
27.86/9.07	   A^2 -> H(f(e), U1(e, c))
27.86/9.07	   A^2 -> H(f(e), U1(k, c))
27.86/9.07	   A^2 -> H(f(e), U1(c, e))
27.86/9.07	   A^2 -> H(f(e), U1(c, k))
27.86/9.07	   A^2 -> H(f(e), U1(k, k))
27.86/9.07	   A^2 -> H(f(e), U1(k, d))
27.86/9.07	   A^2 -> H(f(e), U1(d, k))
27.86/9.07	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.07	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.07	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.07	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.07	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.07	   A^2 -> H(U1(k, k), f(e))
27.86/9.07	   A^2 -> H(U1(k, k), f(k))
27.86/9.07	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.07	   A^2 -> H(f(k), U1(e, b))
27.86/9.07	   A^2 -> H(f(k), U1(k, b))
27.86/9.07	   A^2 -> H(f(k), U1(c, d))
27.86/9.07	   A^2 -> H(f(k), U1(d, c))
27.86/9.07	   A^2 -> H(f(k), U1(b, e))
27.86/9.07	   A^2 -> H(f(k), U1(b, k))
27.86/9.07	   A^2 -> H(f(k), U1(e, c))
27.86/9.07	   A^2 -> H(f(k), U1(k, c))
27.86/9.07	   A^2 -> H(f(k), U1(c, e))
27.86/9.07	   A^2 -> H(f(k), U1(c, k))
27.86/9.07	   A^2 -> H(f(k), U1(e, e))
27.86/9.07	   A^2 -> H(f(k), U1(k, d))
27.86/9.07	   A^2 -> H(f(k), U1(d, k))
27.86/9.07	   A^2 -> H(f(c), b)
27.86/9.07	   A^2 -> H(f(c), U1(e, d))
27.86/9.07	   A^2 -> H(f(c), U1(d, e))
27.86/9.07	   A^2 -> H(f(k), U1(k, k))
27.86/9.07	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.07	   A^2 -> H(U1(k, k), f(c))
27.86/9.07	   A^2 -> H(U1(k, k), f(d))
27.86/9.07	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.07	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.07	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.07	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.07	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.07	   A^2 -> H(U1(k, d), f(e))
27.86/9.07	   A^2 -> H(U1(k, d), f(k))
27.86/9.07	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.07	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.07	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.07	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.07	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.07	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.07	   A^2 -> H(U1(d, k), f(e))
27.86/9.07	   A^2 -> H(U1(d, k), f(k))
27.86/9.07	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.07	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.07	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.07	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.07	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.07	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.07	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.07	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.07	   A^2 -> H(f(d), b)
27.86/9.07	   A^2 -> H(f(d), U1(e, d))
27.86/9.07	   A^2 -> H(f(d), U1(d, e))
27.86/9.07	   A^2 -> H(f(d), c)
27.86/9.07	   A^2 -> H(f(d), U1(e, k))
27.86/9.07	   A^2 -> H(f(d), U1(k, e))
27.86/9.07	   A^2 -> H(f(d), e)
27.86/9.07	   A^2 -> H(f(a), d)
27.86/9.07	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.07	   A^2 -> H(f(c), c)
27.86/9.07	   A^2 -> H(f(c), U1(e, k))
27.86/9.07	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.07	   A^2 -> H(f(c), U1(k, e))
27.86/9.07	   A^2 -> H(f(c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.07	   A^2 -> H(f(a), k)
27.86/9.07	   A^2 -> H(f(e), U1(e, e))
27.86/9.07	   A^2 -> H(f(c), e)
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.07	   A^2 -> H(f(d), U1(k, k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.07	   A^2 -> H(d, U1(b, b))
27.86/9.07	   A^2 -> H(d, f(c))
27.86/9.07	   A^2 -> H(d, f(d))
27.86/9.07	   A^2 -> H(a, U1(c, b))
27.86/9.07	   A^2 -> H(a, U1(d, b))
27.86/9.07	   A^2 -> H(a, U1(b, c))
27.86/9.07	   A^2 -> H(a, U1(b, d))
27.86/9.07	   A^2 -> H(a, U1(c, c))
27.86/9.07	   A^2 -> H(a, f(e))
27.86/9.07	   A^2 -> H(a, f(k))
27.86/9.07	   A^2 -> H(a, U1(d, d))
27.86/9.07	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.07	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.07	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.07	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.07	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.07	   A^2 -> H(U1(e, d), f(e))
27.86/9.07	   A^2 -> H(U1(e, d), f(k))
27.86/9.07	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.07	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.07	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.07	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.07	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.07	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.07	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.07	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.07	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.07	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.07	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.07	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.07	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.07	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.07	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.07	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.07	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.07	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.07	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.07	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.07	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.07	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.07	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.07	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.07	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.07	   A^2 -> H(U1(c, a), b)
27.86/9.07	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.07	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.07	   A^2 -> H(U1(c, a), c)
27.86/9.07	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.07	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.07	   A^2 -> H(U1(c, a), e)
27.86/9.07	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.07	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.07	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.07	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.07	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.07	   A^2 -> H(U1(d, e), f(e))
27.86/9.07	   A^2 -> H(U1(d, e), f(k))
27.86/9.07	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.07	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.07	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.07	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.07	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.07	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.07	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.07	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.07	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.07	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.07	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.07	   A^2 -> H(U1(d, a), b)
27.86/9.07	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.07	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.07	   A^2 -> H(U1(d, a), c)
27.86/9.07	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.07	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.07	   A^2 -> H(U1(d, a), e)
27.86/9.07	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.07	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.07	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.07	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.07	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, e), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(e, b))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, b))
27.86/9.07	   A^2 -> H(U1(a, k), U1(c, d))
27.86/9.07	   A^2 -> H(U1(a, k), U1(d, c))
27.86/9.07	   A^2 -> H(U1(a, k), U1(b, e))
27.86/9.07	   A^2 -> H(U1(a, k), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, k), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, k), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, k), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, c), b)
27.86/9.07	   A^2 -> H(U1(a, c), U1(e, d))
27.86/9.07	
27.86/9.07	The TRS R consists of the following rules:
27.86/9.07	
27.86/9.07	   f(x) -> U1(x, x)
27.86/9.07	   U1(e, x) -> x
27.86/9.07	   a -> c
27.86/9.07	   a -> d
27.86/9.07	   b -> c
27.86/9.07	   b -> d
27.86/9.07	   d -> k
27.86/9.07	   c -> e
27.86/9.07	   c -> k
27.86/9.07	
27.86/9.07	Q is empty.
27.86/9.07	We have to consider all minimal (P,Q,R)-chains.
27.86/9.07	----------------------------------------
27.86/9.07	
27.86/9.07	(719) TransformationProof (EQUIVALENT)
27.86/9.07	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.07	
27.86/9.07	   (A^2 -> H(U1(c, c), U1(d, c)),A^2 -> H(U1(c, c), U1(d, c)))
27.86/9.07	   (A^2 -> H(U1(d, c), U1(d, c)),A^2 -> H(U1(d, c), U1(d, c)))
27.86/9.07	   (A^2 -> H(U1(a, e), U1(d, c)),A^2 -> H(U1(a, e), U1(d, c)))
27.86/9.07	   (A^2 -> H(U1(a, k), U1(d, c)),A^2 -> H(U1(a, k), U1(d, c)))
27.86/9.07	   (A^2 -> H(U1(a, c), U1(k, c)),A^2 -> H(U1(a, c), U1(k, c)))
27.86/9.07	   (A^2 -> H(U1(a, c), U1(d, e)),A^2 -> H(U1(a, c), U1(d, e)))
27.86/9.07	   (A^2 -> H(U1(a, c), U1(d, k)),A^2 -> H(U1(a, c), U1(d, k)))
27.86/9.07	
27.86/9.07	
27.86/9.07	----------------------------------------
27.86/9.07	
27.86/9.07	(720)
27.86/9.07	Obligation:
27.86/9.07	Q DP problem:
27.86/9.07	The TRS P consists of the following rules:
27.86/9.07	
27.86/9.07	   H(x, x) -> G(x, x, f(k))
27.86/9.07	   G(d, x, x) -> A^2
27.86/9.07	   A^2 -> H(f(c), f(c))
27.86/9.07	   A^2 -> H(f(d), f(d))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.07	   A^2 -> H(f(e), f(e))
27.86/9.07	   A^2 -> H(f(k), f(k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.07	   A^2 -> H(U1(a, c), U1(b, e))
27.86/9.07	   A^2 -> H(U1(a, c), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, c), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, c), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.07	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.07	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.07	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.07	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, a), b)
27.86/9.07	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.07	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.07	   A^2 -> H(U1(a, a), c)
27.86/9.07	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.07	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.07	   A^2 -> H(U1(a, a), e)
27.86/9.07	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.07	   A^2 -> H(k, f(b))
27.86/9.07	   A^2 -> H(c, U1(b, b))
27.86/9.07	   A^2 -> H(c, f(c))
27.86/9.07	   A^2 -> H(c, f(d))
27.86/9.07	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.07	   A^2 -> H(U1(e, k), f(c))
27.86/9.07	   A^2 -> H(U1(e, k), f(d))
27.86/9.07	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.07	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.07	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.07	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.07	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.07	   A^2 -> H(U1(e, c), f(e))
27.86/9.07	   A^2 -> H(U1(e, c), f(k))
27.86/9.07	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.07	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.07	   A^2 -> H(U1(k, e), f(c))
27.86/9.07	   A^2 -> H(U1(k, e), f(d))
27.86/9.07	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.07	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.07	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.07	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.07	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.07	   A^2 -> H(U1(k, c), f(e))
27.86/9.07	   A^2 -> H(U1(k, c), f(k))
27.86/9.07	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.07	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.07	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.07	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.07	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.07	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.07	   A^2 -> H(U1(c, e), f(e))
27.86/9.07	   A^2 -> H(U1(c, e), f(k))
27.86/9.07	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.07	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.07	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.07	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.07	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.07	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.07	   A^2 -> H(U1(c, k), f(e))
27.86/9.07	   A^2 -> H(U1(c, k), f(k))
27.86/9.07	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.07	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.07	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.07	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.07	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.07	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.07	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.07	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.07	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.07	   A^2 -> H(e, U1(b, b))
27.86/9.07	   A^2 -> H(e, f(c))
27.86/9.07	   A^2 -> H(e, f(d))
27.86/9.07	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.07	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.07	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.07	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.07	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.07	   A^2 -> H(U1(e, e), f(e))
27.86/9.07	   A^2 -> H(U1(e, e), f(k))
27.86/9.07	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.07	   A^2 -> H(f(e), U1(e, b))
27.86/9.07	   A^2 -> H(f(e), U1(k, b))
27.86/9.07	   A^2 -> H(f(e), U1(c, d))
27.86/9.07	   A^2 -> H(f(e), U1(d, c))
27.86/9.07	   A^2 -> H(f(e), U1(b, e))
27.86/9.07	   A^2 -> H(f(e), U1(b, k))
27.86/9.07	   A^2 -> H(f(e), U1(e, c))
27.86/9.07	   A^2 -> H(f(e), U1(k, c))
27.86/9.07	   A^2 -> H(f(e), U1(c, e))
27.86/9.07	   A^2 -> H(f(e), U1(c, k))
27.86/9.07	   A^2 -> H(f(e), U1(k, k))
27.86/9.07	   A^2 -> H(f(e), U1(k, d))
27.86/9.07	   A^2 -> H(f(e), U1(d, k))
27.86/9.07	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.07	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.07	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.07	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.07	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.07	   A^2 -> H(U1(k, k), f(e))
27.86/9.07	   A^2 -> H(U1(k, k), f(k))
27.86/9.07	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.07	   A^2 -> H(f(k), U1(e, b))
27.86/9.07	   A^2 -> H(f(k), U1(k, b))
27.86/9.07	   A^2 -> H(f(k), U1(c, d))
27.86/9.07	   A^2 -> H(f(k), U1(d, c))
27.86/9.07	   A^2 -> H(f(k), U1(b, e))
27.86/9.07	   A^2 -> H(f(k), U1(b, k))
27.86/9.07	   A^2 -> H(f(k), U1(e, c))
27.86/9.07	   A^2 -> H(f(k), U1(k, c))
27.86/9.07	   A^2 -> H(f(k), U1(c, e))
27.86/9.07	   A^2 -> H(f(k), U1(c, k))
27.86/9.07	   A^2 -> H(f(k), U1(e, e))
27.86/9.07	   A^2 -> H(f(k), U1(k, d))
27.86/9.07	   A^2 -> H(f(k), U1(d, k))
27.86/9.07	   A^2 -> H(f(c), b)
27.86/9.07	   A^2 -> H(f(c), U1(e, d))
27.86/9.07	   A^2 -> H(f(c), U1(d, e))
27.86/9.07	   A^2 -> H(f(k), U1(k, k))
27.86/9.07	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.07	   A^2 -> H(U1(k, k), f(c))
27.86/9.07	   A^2 -> H(U1(k, k), f(d))
27.86/9.07	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.07	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.07	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.07	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.07	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.07	   A^2 -> H(U1(k, d), f(e))
27.86/9.07	   A^2 -> H(U1(k, d), f(k))
27.86/9.07	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.07	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.07	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.07	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.07	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.07	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.07	   A^2 -> H(U1(d, k), f(e))
27.86/9.07	   A^2 -> H(U1(d, k), f(k))
27.86/9.07	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.07	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.07	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.07	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.07	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.07	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.07	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.07	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.07	   A^2 -> H(f(d), b)
27.86/9.07	   A^2 -> H(f(d), U1(e, d))
27.86/9.07	   A^2 -> H(f(d), U1(d, e))
27.86/9.07	   A^2 -> H(f(d), c)
27.86/9.07	   A^2 -> H(f(d), U1(e, k))
27.86/9.07	   A^2 -> H(f(d), U1(k, e))
27.86/9.07	   A^2 -> H(f(d), e)
27.86/9.07	   A^2 -> H(f(a), d)
27.86/9.07	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.07	   A^2 -> H(f(c), c)
27.86/9.07	   A^2 -> H(f(c), U1(e, k))
27.86/9.07	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.07	   A^2 -> H(f(c), U1(k, e))
27.86/9.07	   A^2 -> H(f(c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.07	   A^2 -> H(f(a), k)
27.86/9.07	   A^2 -> H(f(e), U1(e, e))
27.86/9.07	   A^2 -> H(f(c), e)
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.07	   A^2 -> H(f(d), U1(k, k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.07	   A^2 -> H(d, U1(b, b))
27.86/9.07	   A^2 -> H(d, f(c))
27.86/9.07	   A^2 -> H(d, f(d))
27.86/9.07	   A^2 -> H(a, U1(c, b))
27.86/9.07	   A^2 -> H(a, U1(d, b))
27.86/9.07	   A^2 -> H(a, U1(b, c))
27.86/9.07	   A^2 -> H(a, U1(b, d))
27.86/9.07	   A^2 -> H(a, U1(c, c))
27.86/9.07	   A^2 -> H(a, f(e))
27.86/9.07	   A^2 -> H(a, f(k))
27.86/9.07	   A^2 -> H(a, U1(d, d))
27.86/9.07	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.07	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.07	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.07	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.07	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.07	   A^2 -> H(U1(e, d), f(e))
27.86/9.07	   A^2 -> H(U1(e, d), f(k))
27.86/9.07	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.07	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.07	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.07	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.07	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.07	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.07	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.07	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.07	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.07	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.07	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.07	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.07	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.07	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.07	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.07	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.07	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.07	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.07	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.07	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.07	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.07	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.07	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.07	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.07	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.07	   A^2 -> H(U1(c, a), b)
27.86/9.07	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.07	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.07	   A^2 -> H(U1(c, a), c)
27.86/9.07	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.07	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.07	   A^2 -> H(U1(c, a), e)
27.86/9.07	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.07	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.07	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.07	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.07	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.07	   A^2 -> H(U1(d, e), f(e))
27.86/9.07	   A^2 -> H(U1(d, e), f(k))
27.86/9.07	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.07	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.07	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.07	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.07	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.07	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.07	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.07	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.07	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.07	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.07	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.07	   A^2 -> H(U1(d, a), b)
27.86/9.07	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.07	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.07	   A^2 -> H(U1(d, a), c)
27.86/9.07	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.07	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.07	   A^2 -> H(U1(d, a), e)
27.86/9.07	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.07	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.07	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.07	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.07	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, e), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(e, b))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, b))
27.86/9.07	   A^2 -> H(U1(a, k), U1(c, d))
27.86/9.07	   A^2 -> H(U1(a, k), U1(d, c))
27.86/9.07	   A^2 -> H(U1(a, k), U1(b, e))
27.86/9.07	   A^2 -> H(U1(a, k), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, k), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, k), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, k), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, c), b)
27.86/9.07	   A^2 -> H(U1(a, c), U1(e, d))
27.86/9.07	   A^2 -> H(U1(a, c), U1(d, e))
27.86/9.07	
27.86/9.07	The TRS R consists of the following rules:
27.86/9.07	
27.86/9.07	   f(x) -> U1(x, x)
27.86/9.07	   U1(e, x) -> x
27.86/9.07	   a -> c
27.86/9.07	   a -> d
27.86/9.07	   b -> c
27.86/9.07	   b -> d
27.86/9.07	   d -> k
27.86/9.07	   c -> e
27.86/9.07	   c -> k
27.86/9.07	
27.86/9.07	Q is empty.
27.86/9.07	We have to consider all minimal (P,Q,R)-chains.
27.86/9.07	----------------------------------------
27.86/9.07	
27.86/9.07	(721) TransformationProof (EQUIVALENT)
27.86/9.07	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.07	
27.86/9.07	   (A^2 -> H(U1(c, c), U1(b, e)),A^2 -> H(U1(c, c), U1(b, e)))
27.86/9.07	   (A^2 -> H(U1(d, c), U1(b, e)),A^2 -> H(U1(d, c), U1(b, e)))
27.86/9.07	   (A^2 -> H(U1(a, e), U1(b, e)),A^2 -> H(U1(a, e), U1(b, e)))
27.86/9.07	   (A^2 -> H(U1(a, k), U1(b, e)),A^2 -> H(U1(a, k), U1(b, e)))
27.86/9.07	   (A^2 -> H(U1(a, c), U1(c, e)),A^2 -> H(U1(a, c), U1(c, e)))
27.86/9.07	   (A^2 -> H(U1(a, c), U1(d, e)),A^2 -> H(U1(a, c), U1(d, e)))
27.86/9.07	
27.86/9.07	
27.86/9.07	----------------------------------------
27.86/9.07	
27.86/9.07	(722)
27.86/9.07	Obligation:
27.86/9.07	Q DP problem:
27.86/9.07	The TRS P consists of the following rules:
27.86/9.07	
27.86/9.07	   H(x, x) -> G(x, x, f(k))
27.86/9.07	   G(d, x, x) -> A^2
27.86/9.07	   A^2 -> H(f(c), f(c))
27.86/9.07	   A^2 -> H(f(d), f(d))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.07	   A^2 -> H(f(e), f(e))
27.86/9.07	   A^2 -> H(f(k), f(k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.07	   A^2 -> H(U1(a, c), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, c), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, c), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.07	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.07	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.07	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.07	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, a), b)
27.86/9.07	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.07	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.07	   A^2 -> H(U1(a, a), c)
27.86/9.07	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.07	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.07	   A^2 -> H(U1(a, a), e)
27.86/9.07	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.07	   A^2 -> H(k, f(b))
27.86/9.07	   A^2 -> H(c, U1(b, b))
27.86/9.07	   A^2 -> H(c, f(c))
27.86/9.07	   A^2 -> H(c, f(d))
27.86/9.07	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.07	   A^2 -> H(U1(e, k), f(c))
27.86/9.07	   A^2 -> H(U1(e, k), f(d))
27.86/9.07	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.07	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.07	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.07	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.07	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.07	   A^2 -> H(U1(e, c), f(e))
27.86/9.07	   A^2 -> H(U1(e, c), f(k))
27.86/9.07	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.07	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.07	   A^2 -> H(U1(k, e), f(c))
27.86/9.07	   A^2 -> H(U1(k, e), f(d))
27.86/9.07	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.07	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.07	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.07	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.07	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.07	   A^2 -> H(U1(k, c), f(e))
27.86/9.07	   A^2 -> H(U1(k, c), f(k))
27.86/9.07	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.07	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.07	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.07	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.07	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.07	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.07	   A^2 -> H(U1(c, e), f(e))
27.86/9.07	   A^2 -> H(U1(c, e), f(k))
27.86/9.07	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.07	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.07	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.07	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.07	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.07	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.07	   A^2 -> H(U1(c, k), f(e))
27.86/9.07	   A^2 -> H(U1(c, k), f(k))
27.86/9.07	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.07	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.07	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.07	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.07	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.07	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.07	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.07	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.07	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.07	   A^2 -> H(e, U1(b, b))
27.86/9.07	   A^2 -> H(e, f(c))
27.86/9.07	   A^2 -> H(e, f(d))
27.86/9.07	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.07	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.07	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.07	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.07	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.07	   A^2 -> H(U1(e, e), f(e))
27.86/9.07	   A^2 -> H(U1(e, e), f(k))
27.86/9.07	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.07	   A^2 -> H(f(e), U1(e, b))
27.86/9.07	   A^2 -> H(f(e), U1(k, b))
27.86/9.07	   A^2 -> H(f(e), U1(c, d))
27.86/9.07	   A^2 -> H(f(e), U1(d, c))
27.86/9.07	   A^2 -> H(f(e), U1(b, e))
27.86/9.07	   A^2 -> H(f(e), U1(b, k))
27.86/9.07	   A^2 -> H(f(e), U1(e, c))
27.86/9.07	   A^2 -> H(f(e), U1(k, c))
27.86/9.07	   A^2 -> H(f(e), U1(c, e))
27.86/9.07	   A^2 -> H(f(e), U1(c, k))
27.86/9.07	   A^2 -> H(f(e), U1(k, k))
27.86/9.07	   A^2 -> H(f(e), U1(k, d))
27.86/9.07	   A^2 -> H(f(e), U1(d, k))
27.86/9.07	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.07	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.07	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.07	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.07	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.07	   A^2 -> H(U1(k, k), f(e))
27.86/9.07	   A^2 -> H(U1(k, k), f(k))
27.86/9.07	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.07	   A^2 -> H(f(k), U1(e, b))
27.86/9.07	   A^2 -> H(f(k), U1(k, b))
27.86/9.07	   A^2 -> H(f(k), U1(c, d))
27.86/9.07	   A^2 -> H(f(k), U1(d, c))
27.86/9.07	   A^2 -> H(f(k), U1(b, e))
27.86/9.07	   A^2 -> H(f(k), U1(b, k))
27.86/9.07	   A^2 -> H(f(k), U1(e, c))
27.86/9.07	   A^2 -> H(f(k), U1(k, c))
27.86/9.07	   A^2 -> H(f(k), U1(c, e))
27.86/9.07	   A^2 -> H(f(k), U1(c, k))
27.86/9.07	   A^2 -> H(f(k), U1(e, e))
27.86/9.07	   A^2 -> H(f(k), U1(k, d))
27.86/9.07	   A^2 -> H(f(k), U1(d, k))
27.86/9.07	   A^2 -> H(f(c), b)
27.86/9.07	   A^2 -> H(f(c), U1(e, d))
27.86/9.07	   A^2 -> H(f(c), U1(d, e))
27.86/9.07	   A^2 -> H(f(k), U1(k, k))
27.86/9.07	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.07	   A^2 -> H(U1(k, k), f(c))
27.86/9.07	   A^2 -> H(U1(k, k), f(d))
27.86/9.07	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.07	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.07	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.07	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.07	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.07	   A^2 -> H(U1(k, d), f(e))
27.86/9.07	   A^2 -> H(U1(k, d), f(k))
27.86/9.07	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.07	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.07	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.07	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.07	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.07	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.07	   A^2 -> H(U1(d, k), f(e))
27.86/9.07	   A^2 -> H(U1(d, k), f(k))
27.86/9.07	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.07	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.07	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.07	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.07	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.07	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.07	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.07	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.07	   A^2 -> H(f(d), b)
27.86/9.07	   A^2 -> H(f(d), U1(e, d))
27.86/9.07	   A^2 -> H(f(d), U1(d, e))
27.86/9.07	   A^2 -> H(f(d), c)
27.86/9.07	   A^2 -> H(f(d), U1(e, k))
27.86/9.07	   A^2 -> H(f(d), U1(k, e))
27.86/9.07	   A^2 -> H(f(d), e)
27.86/9.07	   A^2 -> H(f(a), d)
27.86/9.07	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.07	   A^2 -> H(f(c), c)
27.86/9.07	   A^2 -> H(f(c), U1(e, k))
27.86/9.07	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.07	   A^2 -> H(f(c), U1(k, e))
27.86/9.07	   A^2 -> H(f(c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.07	   A^2 -> H(f(a), k)
27.86/9.07	   A^2 -> H(f(e), U1(e, e))
27.86/9.07	   A^2 -> H(f(c), e)
27.86/9.07	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.07	   A^2 -> H(f(d), U1(k, k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.07	   A^2 -> H(d, U1(b, b))
27.86/9.07	   A^2 -> H(d, f(c))
27.86/9.07	   A^2 -> H(d, f(d))
27.86/9.07	   A^2 -> H(a, U1(c, b))
27.86/9.07	   A^2 -> H(a, U1(d, b))
27.86/9.07	   A^2 -> H(a, U1(b, c))
27.86/9.07	   A^2 -> H(a, U1(b, d))
27.86/9.07	   A^2 -> H(a, U1(c, c))
27.86/9.07	   A^2 -> H(a, f(e))
27.86/9.07	   A^2 -> H(a, f(k))
27.86/9.07	   A^2 -> H(a, U1(d, d))
27.86/9.07	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.07	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.07	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.07	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.07	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.07	   A^2 -> H(U1(e, d), f(e))
27.86/9.07	   A^2 -> H(U1(e, d), f(k))
27.86/9.07	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.07	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.07	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.07	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.07	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.07	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.07	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.07	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.07	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.07	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.07	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.07	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.07	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.07	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.07	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.07	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.07	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.07	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.07	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.07	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.07	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.07	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.07	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.07	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.07	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.07	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.07	   A^2 -> H(U1(c, a), b)
27.86/9.07	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.07	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.07	   A^2 -> H(U1(c, a), c)
27.86/9.07	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.07	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.07	   A^2 -> H(U1(c, a), e)
27.86/9.07	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.07	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.07	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.07	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.07	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.07	   A^2 -> H(U1(d, e), f(e))
27.86/9.07	   A^2 -> H(U1(d, e), f(k))
27.86/9.07	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.07	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.07	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.07	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.07	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.07	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.07	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.07	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.07	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.07	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.07	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.07	   A^2 -> H(U1(d, a), b)
27.86/9.07	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.07	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.07	   A^2 -> H(U1(d, a), c)
27.86/9.07	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.07	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.07	   A^2 -> H(U1(d, a), e)
27.86/9.07	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.07	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.07	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.07	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.07	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, e), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, e), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(e, b))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, b))
27.86/9.07	   A^2 -> H(U1(a, k), U1(c, d))
27.86/9.07	   A^2 -> H(U1(a, k), U1(d, c))
27.86/9.07	   A^2 -> H(U1(a, k), U1(b, e))
27.86/9.07	   A^2 -> H(U1(a, k), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, k), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, k), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, k), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, k), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, c), b)
27.86/9.07	   A^2 -> H(U1(a, c), U1(e, d))
27.86/9.07	   A^2 -> H(U1(a, c), U1(d, e))
27.86/9.07	
27.86/9.07	The TRS R consists of the following rules:
27.86/9.07	
27.86/9.07	   f(x) -> U1(x, x)
27.86/9.07	   U1(e, x) -> x
27.86/9.07	   a -> c
27.86/9.07	   a -> d
27.86/9.07	   b -> c
27.86/9.07	   b -> d
27.86/9.07	   d -> k
27.86/9.07	   c -> e
27.86/9.07	   c -> k
27.86/9.07	
27.86/9.07	Q is empty.
27.86/9.07	We have to consider all minimal (P,Q,R)-chains.
27.86/9.07	----------------------------------------
27.86/9.07	
27.86/9.07	(723) TransformationProof (EQUIVALENT)
27.86/9.07	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.07	
27.86/9.07	   (A^2 -> H(U1(c, c), U1(b, k)),A^2 -> H(U1(c, c), U1(b, k)))
27.86/9.07	   (A^2 -> H(U1(d, c), U1(b, k)),A^2 -> H(U1(d, c), U1(b, k)))
27.86/9.07	   (A^2 -> H(U1(a, e), U1(b, k)),A^2 -> H(U1(a, e), U1(b, k)))
27.86/9.07	   (A^2 -> H(U1(a, k), U1(b, k)),A^2 -> H(U1(a, k), U1(b, k)))
27.86/9.07	   (A^2 -> H(U1(a, c), U1(c, k)),A^2 -> H(U1(a, c), U1(c, k)))
27.86/9.07	   (A^2 -> H(U1(a, c), U1(d, k)),A^2 -> H(U1(a, c), U1(d, k)))
27.86/9.07	
27.86/9.07	
27.86/9.07	----------------------------------------
27.86/9.07	
27.86/9.07	(724)
27.86/9.07	Obligation:
27.86/9.07	Q DP problem:
27.86/9.07	The TRS P consists of the following rules:
27.86/9.07	
27.86/9.07	   H(x, x) -> G(x, x, f(k))
27.86/9.07	   G(d, x, x) -> A^2
27.86/9.07	   A^2 -> H(f(c), f(c))
27.86/9.07	   A^2 -> H(f(d), f(d))
27.86/9.07	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.07	   A^2 -> H(f(e), f(e))
27.86/9.07	   A^2 -> H(f(k), f(k))
27.86/9.07	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.07	   A^2 -> H(U1(a, c), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, c), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.07	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.07	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.07	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.07	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.07	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.07	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.07	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.07	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.07	   A^2 -> H(U1(a, a), b)
27.86/9.07	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.07	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.07	   A^2 -> H(U1(a, a), c)
27.86/9.07	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.07	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.07	   A^2 -> H(U1(a, a), e)
27.86/9.07	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.07	   A^2 -> H(k, f(b))
27.86/9.07	   A^2 -> H(c, U1(b, b))
27.86/9.07	   A^2 -> H(c, f(c))
27.86/9.07	   A^2 -> H(c, f(d))
27.86/9.07	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.07	   A^2 -> H(U1(e, k), f(c))
27.86/9.07	   A^2 -> H(U1(e, k), f(d))
27.86/9.07	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.07	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.07	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.07	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.07	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.07	   A^2 -> H(U1(e, c), f(e))
27.86/9.07	   A^2 -> H(U1(e, c), f(k))
27.86/9.07	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.07	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.08	   A^2 -> H(U1(k, e), f(c))
27.86/9.08	   A^2 -> H(U1(k, e), f(d))
27.86/9.08	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.08	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.08	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.08	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.08	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.08	   A^2 -> H(U1(k, c), f(e))
27.86/9.08	   A^2 -> H(U1(k, c), f(k))
27.86/9.08	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.08	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.08	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.08	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.08	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.08	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.08	   A^2 -> H(U1(c, e), f(e))
27.86/9.08	   A^2 -> H(U1(c, e), f(k))
27.86/9.08	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.08	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.08	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.08	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.08	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.08	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.08	   A^2 -> H(U1(c, k), f(e))
27.86/9.08	   A^2 -> H(U1(c, k), f(k))
27.86/9.08	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.08	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.08	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.08	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.08	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.08	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.08	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.08	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.08	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.08	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.08	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.08	   A^2 -> H(e, U1(b, b))
27.86/9.08	   A^2 -> H(e, f(c))
27.86/9.08	   A^2 -> H(e, f(d))
27.86/9.08	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.08	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.08	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.08	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.08	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.08	   A^2 -> H(U1(e, e), f(e))
27.86/9.08	   A^2 -> H(U1(e, e), f(k))
27.86/9.08	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.08	   A^2 -> H(f(e), U1(e, b))
27.86/9.08	   A^2 -> H(f(e), U1(k, b))
27.86/9.08	   A^2 -> H(f(e), U1(c, d))
27.86/9.08	   A^2 -> H(f(e), U1(d, c))
27.86/9.08	   A^2 -> H(f(e), U1(b, e))
27.86/9.08	   A^2 -> H(f(e), U1(b, k))
27.86/9.08	   A^2 -> H(f(e), U1(e, c))
27.86/9.08	   A^2 -> H(f(e), U1(k, c))
27.86/9.08	   A^2 -> H(f(e), U1(c, e))
27.86/9.08	   A^2 -> H(f(e), U1(c, k))
27.86/9.08	   A^2 -> H(f(e), U1(k, k))
27.86/9.08	   A^2 -> H(f(e), U1(k, d))
27.86/9.08	   A^2 -> H(f(e), U1(d, k))
27.86/9.08	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.08	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.08	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.08	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.08	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.08	   A^2 -> H(U1(k, k), f(e))
27.86/9.08	   A^2 -> H(U1(k, k), f(k))
27.86/9.08	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.08	   A^2 -> H(f(k), U1(e, b))
27.86/9.08	   A^2 -> H(f(k), U1(k, b))
27.86/9.08	   A^2 -> H(f(k), U1(c, d))
27.86/9.08	   A^2 -> H(f(k), U1(d, c))
27.86/9.08	   A^2 -> H(f(k), U1(b, e))
27.86/9.08	   A^2 -> H(f(k), U1(b, k))
27.86/9.08	   A^2 -> H(f(k), U1(e, c))
27.86/9.08	   A^2 -> H(f(k), U1(k, c))
27.86/9.08	   A^2 -> H(f(k), U1(c, e))
27.86/9.08	   A^2 -> H(f(k), U1(c, k))
27.86/9.08	   A^2 -> H(f(k), U1(e, e))
27.86/9.08	   A^2 -> H(f(k), U1(k, d))
27.86/9.08	   A^2 -> H(f(k), U1(d, k))
27.86/9.08	   A^2 -> H(f(c), b)
27.86/9.08	   A^2 -> H(f(c), U1(e, d))
27.86/9.08	   A^2 -> H(f(c), U1(d, e))
27.86/9.08	   A^2 -> H(f(k), U1(k, k))
27.86/9.08	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.08	   A^2 -> H(U1(k, k), f(c))
27.86/9.08	   A^2 -> H(U1(k, k), f(d))
27.86/9.08	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.08	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.08	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.08	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.08	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.08	   A^2 -> H(U1(k, d), f(e))
27.86/9.08	   A^2 -> H(U1(k, d), f(k))
27.86/9.08	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.08	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.08	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.08	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.08	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.08	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.08	   A^2 -> H(U1(d, k), f(e))
27.86/9.08	   A^2 -> H(U1(d, k), f(k))
27.86/9.08	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.08	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.08	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.08	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.08	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.08	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.08	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.08	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.08	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.08	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.08	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.08	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.08	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.08	   A^2 -> H(f(d), b)
27.86/9.08	   A^2 -> H(f(d), U1(e, d))
27.86/9.08	   A^2 -> H(f(d), U1(d, e))
27.86/9.08	   A^2 -> H(f(d), c)
27.86/9.08	   A^2 -> H(f(d), U1(e, k))
27.86/9.08	   A^2 -> H(f(d), U1(k, e))
27.86/9.08	   A^2 -> H(f(d), e)
27.86/9.08	   A^2 -> H(f(a), d)
27.86/9.08	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.08	   A^2 -> H(f(c), c)
27.86/9.08	   A^2 -> H(f(c), U1(e, k))
27.86/9.08	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.08	   A^2 -> H(f(c), U1(k, e))
27.86/9.08	   A^2 -> H(f(c), U1(k, k))
27.86/9.08	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.08	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.08	   A^2 -> H(f(a), k)
27.86/9.08	   A^2 -> H(f(e), U1(e, e))
27.86/9.08	   A^2 -> H(f(c), e)
27.86/9.08	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.08	   A^2 -> H(f(d), U1(k, k))
27.86/9.08	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.08	   A^2 -> H(d, U1(b, b))
27.86/9.08	   A^2 -> H(d, f(c))
27.86/9.08	   A^2 -> H(d, f(d))
27.86/9.08	   A^2 -> H(a, U1(c, b))
27.86/9.08	   A^2 -> H(a, U1(d, b))
27.86/9.08	   A^2 -> H(a, U1(b, c))
27.86/9.08	   A^2 -> H(a, U1(b, d))
27.86/9.08	   A^2 -> H(a, U1(c, c))
27.86/9.08	   A^2 -> H(a, f(e))
27.86/9.08	   A^2 -> H(a, f(k))
27.86/9.08	   A^2 -> H(a, U1(d, d))
27.86/9.08	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.08	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.08	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.08	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.08	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.08	   A^2 -> H(U1(e, d), f(e))
27.86/9.08	   A^2 -> H(U1(e, d), f(k))
27.86/9.08	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.08	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.08	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.08	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.08	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.08	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.08	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.08	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.08	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.08	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.08	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.08	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.08	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.08	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.08	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.08	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.08	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.08	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.08	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.08	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.08	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.08	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.08	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.08	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.08	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.08	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.08	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.08	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.08	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.08	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.08	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.08	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.08	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.08	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.08	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.08	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.08	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.08	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.08	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.08	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.08	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.08	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.08	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.08	   A^2 -> H(U1(c, a), b)
27.86/9.08	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.08	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.08	   A^2 -> H(U1(c, a), c)
27.86/9.08	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.08	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.08	   A^2 -> H(U1(c, a), e)
27.86/9.08	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.08	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.08	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.08	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.08	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.08	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.08	   A^2 -> H(U1(d, e), f(e))
27.86/9.08	   A^2 -> H(U1(d, e), f(k))
27.86/9.08	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.08	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.08	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.08	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.08	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.08	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.08	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.08	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.08	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.08	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.08	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.08	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.08	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.08	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.08	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.08	   A^2 -> H(U1(d, a), b)
27.86/9.08	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.08	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.08	   A^2 -> H(U1(d, a), c)
27.86/9.08	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.08	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.08	   A^2 -> H(U1(d, a), e)
27.86/9.08	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.08	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.08	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.08	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.08	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.08	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.08	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.08	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.08	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.08	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.08	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.08	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.08	   A^2 -> H(U1(a, e), U1(k, k))
27.86/9.08	   A^2 -> H(U1(a, e), U1(k, d))
27.86/9.08	   A^2 -> H(U1(a, e), U1(d, k))
27.86/9.08	   A^2 -> H(U1(a, k), U1(e, b))
27.86/9.08	   A^2 -> H(U1(a, k), U1(k, b))
27.86/9.08	   A^2 -> H(U1(a, k), U1(c, d))
27.86/9.08	   A^2 -> H(U1(a, k), U1(d, c))
27.86/9.08	   A^2 -> H(U1(a, k), U1(b, e))
27.86/9.08	   A^2 -> H(U1(a, k), U1(b, k))
27.86/9.08	   A^2 -> H(U1(a, k), U1(e, c))
27.86/9.08	   A^2 -> H(U1(a, k), U1(k, c))
27.86/9.08	   A^2 -> H(U1(a, k), U1(c, e))
27.86/9.08	   A^2 -> H(U1(a, k), U1(c, k))
27.86/9.08	   A^2 -> H(U1(a, k), U1(e, e))
27.86/9.08	   A^2 -> H(U1(a, k), U1(k, k))
27.86/9.08	   A^2 -> H(U1(a, k), U1(k, d))
27.86/9.08	   A^2 -> H(U1(a, k), U1(d, k))
27.86/9.08	   A^2 -> H(U1(a, c), b)
27.86/9.08	   A^2 -> H(U1(a, c), U1(e, d))
27.86/9.08	   A^2 -> H(U1(a, c), U1(d, e))
27.86/9.08	
27.86/9.08	The TRS R consists of the following rules:
27.86/9.08	
27.86/9.08	   f(x) -> U1(x, x)
27.86/9.08	   U1(e, x) -> x
27.86/9.08	   a -> c
27.86/9.08	   a -> d
27.86/9.08	   b -> c
27.86/9.08	   b -> d
27.86/9.08	   d -> k
27.86/9.08	   c -> e
27.86/9.08	   c -> k
27.86/9.08	
27.86/9.08	Q is empty.
27.86/9.08	We have to consider all minimal (P,Q,R)-chains.
27.86/9.08	----------------------------------------
27.86/9.08	
27.86/9.08	(725) TransformationProof (EQUIVALENT)
27.86/9.08	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.08	
27.86/9.08	   (A^2 -> H(U1(c, c), U1(e, c)),A^2 -> H(U1(c, c), U1(e, c)))
27.86/9.08	   (A^2 -> H(U1(d, c), U1(e, c)),A^2 -> H(U1(d, c), U1(e, c)))
27.86/9.08	   (A^2 -> H(U1(a, e), U1(e, c)),A^2 -> H(U1(a, e), U1(e, c)))
27.86/9.08	   (A^2 -> H(U1(a, k), U1(e, c)),A^2 -> H(U1(a, k), U1(e, c)))
27.86/9.08	   (A^2 -> H(U1(a, c), c),A^2 -> H(U1(a, c), c))
27.86/9.08	   (A^2 -> H(U1(a, c), U1(e, e)),A^2 -> H(U1(a, c), U1(e, e)))
27.86/9.08	   (A^2 -> H(U1(a, c), U1(e, k)),A^2 -> H(U1(a, c), U1(e, k)))
27.86/9.08	
27.86/9.08	
27.86/9.08	----------------------------------------
27.86/9.08	
27.86/9.08	(726)
27.86/9.08	Obligation:
27.86/9.08	Q DP problem:
27.86/9.08	The TRS P consists of the following rules:
27.86/9.08	
27.86/9.08	   H(x, x) -> G(x, x, f(k))
27.86/9.08	   G(d, x, x) -> A^2
27.86/9.08	   A^2 -> H(f(c), f(c))
27.86/9.08	   A^2 -> H(f(d), f(d))
27.86/9.08	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.08	   A^2 -> H(f(e), f(e))
27.86/9.08	   A^2 -> H(f(k), f(k))
27.86/9.08	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.08	   A^2 -> H(U1(a, c), U1(k, c))
27.86/9.08	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.08	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.08	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.08	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.08	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.08	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.08	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.08	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.08	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.08	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.08	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.08	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.08	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.08	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.08	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.08	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.08	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.08	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.08	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.08	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.08	   A^2 -> H(U1(a, a), b)
27.86/9.08	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.08	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.08	   A^2 -> H(U1(a, a), c)
27.86/9.08	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.08	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.08	   A^2 -> H(U1(a, a), e)
27.86/9.08	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.08	   A^2 -> H(k, f(b))
27.86/9.08	   A^2 -> H(c, U1(b, b))
27.86/9.08	   A^2 -> H(c, f(c))
27.86/9.08	   A^2 -> H(c, f(d))
27.86/9.08	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.08	   A^2 -> H(U1(e, k), f(c))
27.86/9.08	   A^2 -> H(U1(e, k), f(d))
27.86/9.08	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.08	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.08	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.08	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.08	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.08	   A^2 -> H(U1(e, c), f(e))
27.86/9.08	   A^2 -> H(U1(e, c), f(k))
27.86/9.08	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.08	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.08	   A^2 -> H(U1(k, e), f(c))
27.86/9.08	   A^2 -> H(U1(k, e), f(d))
27.86/9.08	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.08	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.08	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.08	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.08	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.08	   A^2 -> H(U1(k, c), f(e))
27.86/9.08	   A^2 -> H(U1(k, c), f(k))
27.86/9.08	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.08	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.08	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.08	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.08	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.08	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.08	   A^2 -> H(U1(c, e), f(e))
27.86/9.08	   A^2 -> H(U1(c, e), f(k))
27.86/9.08	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.08	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.08	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.08	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.08	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.08	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.08	   A^2 -> H(U1(c, k), f(e))
27.86/9.08	   A^2 -> H(U1(c, k), f(k))
27.86/9.08	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.08	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.08	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.08	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.08	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.08	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.08	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.08	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.08	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.08	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.08	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.08	   A^2 -> H(e, U1(b, b))
27.86/9.08	   A^2 -> H(e, f(c))
27.86/9.08	   A^2 -> H(e, f(d))
27.86/9.08	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.08	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.08	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.08	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.08	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.08	   A^2 -> H(U1(e, e), f(e))
27.86/9.08	   A^2 -> H(U1(e, e), f(k))
27.86/9.08	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.08	   A^2 -> H(f(e), U1(e, b))
27.86/9.08	   A^2 -> H(f(e), U1(k, b))
27.86/9.08	   A^2 -> H(f(e), U1(c, d))
27.86/9.08	   A^2 -> H(f(e), U1(d, c))
27.86/9.08	   A^2 -> H(f(e), U1(b, e))
27.86/9.08	   A^2 -> H(f(e), U1(b, k))
27.86/9.08	   A^2 -> H(f(e), U1(e, c))
27.86/9.08	   A^2 -> H(f(e), U1(k, c))
27.86/9.08	   A^2 -> H(f(e), U1(c, e))
27.86/9.08	   A^2 -> H(f(e), U1(c, k))
27.86/9.08	   A^2 -> H(f(e), U1(k, k))
27.86/9.08	   A^2 -> H(f(e), U1(k, d))
27.86/9.08	   A^2 -> H(f(e), U1(d, k))
27.86/9.08	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.08	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.08	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.08	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.08	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.08	   A^2 -> H(U1(k, k), f(e))
27.86/9.08	   A^2 -> H(U1(k, k), f(k))
27.86/9.08	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.08	   A^2 -> H(f(k), U1(e, b))
27.86/9.08	   A^2 -> H(f(k), U1(k, b))
27.86/9.08	   A^2 -> H(f(k), U1(c, d))
27.86/9.08	   A^2 -> H(f(k), U1(d, c))
27.86/9.08	   A^2 -> H(f(k), U1(b, e))
27.86/9.08	   A^2 -> H(f(k), U1(b, k))
27.86/9.08	   A^2 -> H(f(k), U1(e, c))
27.86/9.08	   A^2 -> H(f(k), U1(k, c))
27.86/9.08	   A^2 -> H(f(k), U1(c, e))
27.86/9.08	   A^2 -> H(f(k), U1(c, k))
27.86/9.08	   A^2 -> H(f(k), U1(e, e))
27.86/9.08	   A^2 -> H(f(k), U1(k, d))
27.86/9.08	   A^2 -> H(f(k), U1(d, k))
27.86/9.08	   A^2 -> H(f(c), b)
27.86/9.08	   A^2 -> H(f(c), U1(e, d))
27.86/9.08	   A^2 -> H(f(c), U1(d, e))
27.86/9.08	   A^2 -> H(f(k), U1(k, k))
27.86/9.08	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.08	   A^2 -> H(U1(k, k), f(c))
27.86/9.08	   A^2 -> H(U1(k, k), f(d))
27.86/9.08	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.08	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.08	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.08	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.08	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.08	   A^2 -> H(U1(k, d), f(e))
27.86/9.08	   A^2 -> H(U1(k, d), f(k))
27.86/9.08	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.08	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.08	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.08	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.08	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.08	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.08	   A^2 -> H(U1(d, k), f(e))
27.86/9.08	   A^2 -> H(U1(d, k), f(k))
27.86/9.08	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.08	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.08	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.08	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.08	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.08	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.08	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.08	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.08	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.08	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.08	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.08	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.08	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.08	   A^2 -> H(f(d), b)
27.86/9.08	   A^2 -> H(f(d), U1(e, d))
27.86/9.08	   A^2 -> H(f(d), U1(d, e))
27.86/9.08	   A^2 -> H(f(d), c)
27.86/9.08	   A^2 -> H(f(d), U1(e, k))
27.86/9.08	   A^2 -> H(f(d), U1(k, e))
27.86/9.08	   A^2 -> H(f(d), e)
27.86/9.08	   A^2 -> H(f(a), d)
27.86/9.08	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.08	   A^2 -> H(f(c), c)
27.86/9.08	   A^2 -> H(f(c), U1(e, k))
27.86/9.08	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.08	   A^2 -> H(f(c), U1(k, e))
27.86/9.08	   A^2 -> H(f(c), U1(k, k))
27.86/9.08	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.08	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.08	   A^2 -> H(f(a), k)
27.86/9.08	   A^2 -> H(f(e), U1(e, e))
27.86/9.08	   A^2 -> H(f(c), e)
27.86/9.08	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.08	   A^2 -> H(f(d), U1(k, k))
27.86/9.08	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.08	   A^2 -> H(d, U1(b, b))
27.86/9.08	   A^2 -> H(d, f(c))
27.86/9.08	   A^2 -> H(d, f(d))
27.86/9.08	   A^2 -> H(a, U1(c, b))
27.86/9.08	   A^2 -> H(a, U1(d, b))
27.86/9.08	   A^2 -> H(a, U1(b, c))
27.86/9.08	   A^2 -> H(a, U1(b, d))
27.86/9.08	   A^2 -> H(a, U1(c, c))
27.86/9.08	   A^2 -> H(a, f(e))
27.86/9.08	   A^2 -> H(a, f(k))
27.86/9.08	   A^2 -> H(a, U1(d, d))
27.86/9.08	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.08	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.08	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.08	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.08	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.08	   A^2 -> H(U1(e, d), f(e))
27.86/9.08	   A^2 -> H(U1(e, d), f(k))
27.86/9.08	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.08	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.08	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.08	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.08	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.08	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.08	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.08	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.08	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.08	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.08	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.08	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.08	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.08	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.08	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.08	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.08	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.08	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.08	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.08	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.08	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.08	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.08	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.08	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.08	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.08	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.08	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.08	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.08	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.08	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.08	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.08	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.08	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.08	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.08	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.08	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.08	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.08	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.08	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.08	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.08	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.08	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.08	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.08	   A^2 -> H(U1(c, a), b)
27.86/9.08	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.08	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.08	   A^2 -> H(U1(c, a), c)
27.86/9.08	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.08	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.08	   A^2 -> H(U1(c, a), e)
27.86/9.08	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.08	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.08	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.08	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.08	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.08	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.08	   A^2 -> H(U1(d, e), f(e))
27.86/9.08	   A^2 -> H(U1(d, e), f(k))
27.86/9.08	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.08	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.08	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.08	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.08	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.08	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.08	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.08	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.08	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.08	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.08	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.08	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.08	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.08	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.08	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.08	   A^2 -> H(U1(d, a), b)
27.86/9.08	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.08	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.08	   A^2 -> H(U1(d, a), c)
27.86/9.08	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.08	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.08	   A^2 -> H(U1(d, a), e)
27.86/9.08	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.08	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.08	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.08	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.08	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.08	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.08	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.08	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.08	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.08	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.08	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.08	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.08	   A^2 -> H(U1(a, e), U1(k, k))
27.86/9.08	   A^2 -> H(U1(a, e), U1(k, d))
27.86/9.08	   A^2 -> H(U1(a, e), U1(d, k))
27.86/9.08	   A^2 -> H(U1(a, k), U1(e, b))
27.86/9.08	   A^2 -> H(U1(a, k), U1(k, b))
27.86/9.08	   A^2 -> H(U1(a, k), U1(c, d))
27.86/9.08	   A^2 -> H(U1(a, k), U1(d, c))
27.86/9.08	   A^2 -> H(U1(a, k), U1(b, e))
27.86/9.08	   A^2 -> H(U1(a, k), U1(b, k))
27.86/9.08	   A^2 -> H(U1(a, k), U1(e, c))
27.86/9.08	   A^2 -> H(U1(a, k), U1(k, c))
27.86/9.08	   A^2 -> H(U1(a, k), U1(c, e))
27.86/9.08	   A^2 -> H(U1(a, k), U1(c, k))
27.86/9.08	   A^2 -> H(U1(a, k), U1(e, e))
27.86/9.08	   A^2 -> H(U1(a, k), U1(k, k))
27.86/9.08	   A^2 -> H(U1(a, k), U1(k, d))
27.86/9.08	   A^2 -> H(U1(a, k), U1(d, k))
27.86/9.08	   A^2 -> H(U1(a, c), b)
27.86/9.08	   A^2 -> H(U1(a, c), U1(e, d))
27.86/9.08	   A^2 -> H(U1(a, c), U1(d, e))
27.86/9.08	   A^2 -> H(U1(a, c), c)
27.86/9.08	   A^2 -> H(U1(a, c), U1(e, k))
27.86/9.08	
27.86/9.08	The TRS R consists of the following rules:
27.86/9.08	
27.86/9.08	   f(x) -> U1(x, x)
27.86/9.08	   U1(e, x) -> x
27.86/9.08	   a -> c
27.86/9.08	   a -> d
27.86/9.08	   b -> c
27.86/9.08	   b -> d
27.86/9.08	   d -> k
27.86/9.08	   c -> e
27.86/9.08	   c -> k
27.86/9.08	
27.86/9.08	Q is empty.
27.86/9.08	We have to consider all minimal (P,Q,R)-chains.
27.86/9.08	----------------------------------------
27.86/9.08	
27.86/9.08	(727) TransformationProof (EQUIVALENT)
27.86/9.08	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
27.86/9.08	
27.86/9.08	   (A^2 -> H(U1(c, c), U1(k, c)),A^2 -> H(U1(c, c), U1(k, c)))
27.86/9.08	   (A^2 -> H(U1(d, c), U1(k, c)),A^2 -> H(U1(d, c), U1(k, c)))
27.86/9.08	   (A^2 -> H(U1(a, e), U1(k, c)),A^2 -> H(U1(a, e), U1(k, c)))
27.86/9.08	   (A^2 -> H(U1(a, k), U1(k, c)),A^2 -> H(U1(a, k), U1(k, c)))
27.86/9.08	   (A^2 -> H(U1(a, c), U1(k, e)),A^2 -> H(U1(a, c), U1(k, e)))
27.86/9.08	   (A^2 -> H(U1(a, c), U1(k, k)),A^2 -> H(U1(a, c), U1(k, k)))
27.86/9.08	
27.86/9.08	
27.86/9.08	----------------------------------------
27.86/9.08	
27.86/9.08	(728)
27.86/9.08	Obligation:
27.86/9.08	Q DP problem:
27.86/9.08	The TRS P consists of the following rules:
27.86/9.08	
27.86/9.08	   H(x, x) -> G(x, x, f(k))
27.86/9.08	   G(d, x, x) -> A^2
27.86/9.08	   A^2 -> H(f(c), f(c))
27.86/9.08	   A^2 -> H(f(d), f(d))
27.86/9.08	   A^2 -> H(U1(c, c), U1(c, c))
27.86/9.08	   A^2 -> H(f(e), f(e))
27.86/9.08	   A^2 -> H(f(k), f(k))
27.86/9.08	   A^2 -> H(U1(d, d), U1(d, d))
27.86/9.08	   A^2 -> H(U1(a, c), U1(c, e))
27.86/9.08	   A^2 -> H(U1(a, c), U1(c, k))
27.86/9.08	   A^2 -> H(U1(a, c), U1(e, e))
27.86/9.08	   A^2 -> H(U1(a, c), U1(k, k))
27.86/9.08	   A^2 -> H(U1(a, c), U1(k, d))
27.86/9.08	   A^2 -> H(U1(a, c), U1(d, k))
27.86/9.08	   A^2 -> H(U1(a, d), U1(e, b))
27.86/9.08	   A^2 -> H(U1(a, d), U1(k, b))
27.86/9.08	   A^2 -> H(U1(a, d), U1(c, d))
27.86/9.08	   A^2 -> H(U1(a, d), U1(d, c))
27.86/9.08	   A^2 -> H(U1(a, d), U1(b, e))
27.86/9.08	   A^2 -> H(U1(a, d), U1(b, k))
27.86/9.08	   A^2 -> H(U1(a, d), U1(e, c))
27.86/9.08	   A^2 -> H(U1(a, d), U1(k, c))
27.86/9.08	   A^2 -> H(U1(a, d), U1(c, e))
27.86/9.08	   A^2 -> H(U1(a, d), U1(c, k))
27.86/9.08	   A^2 -> H(U1(a, d), U1(e, e))
27.86/9.08	   A^2 -> H(U1(a, d), U1(k, k))
27.86/9.08	   A^2 -> H(U1(a, d), U1(k, d))
27.86/9.08	   A^2 -> H(U1(a, d), U1(d, k))
27.86/9.08	   A^2 -> H(U1(a, a), b)
27.86/9.08	   A^2 -> H(U1(a, a), U1(e, d))
27.86/9.08	   A^2 -> H(U1(a, a), U1(d, e))
27.86/9.08	   A^2 -> H(U1(a, a), c)
27.86/9.08	   A^2 -> H(U1(a, a), U1(e, k))
27.86/9.08	   A^2 -> H(U1(a, a), U1(k, e))
27.86/9.08	   A^2 -> H(U1(a, a), e)
27.86/9.08	   A^2 -> H(U1(a, a), U1(k, k))
27.86/9.08	   A^2 -> H(k, f(b))
27.86/9.08	   A^2 -> H(c, U1(b, b))
27.86/9.08	   A^2 -> H(c, f(c))
27.86/9.08	   A^2 -> H(c, f(d))
27.86/9.08	   A^2 -> H(U1(e, k), U1(b, b))
27.86/9.08	   A^2 -> H(U1(e, k), f(c))
27.86/9.08	   A^2 -> H(U1(e, k), f(d))
27.86/9.08	   A^2 -> H(U1(e, c), U1(c, b))
27.86/9.08	   A^2 -> H(U1(e, c), U1(d, b))
27.86/9.08	   A^2 -> H(U1(e, c), U1(b, c))
27.86/9.08	   A^2 -> H(U1(e, c), U1(b, d))
27.86/9.08	   A^2 -> H(U1(e, c), U1(c, c))
27.86/9.08	   A^2 -> H(U1(e, c), f(e))
27.86/9.08	   A^2 -> H(U1(e, c), f(k))
27.86/9.08	   A^2 -> H(U1(e, c), U1(d, d))
27.86/9.08	   A^2 -> H(U1(k, e), U1(b, b))
27.86/9.08	   A^2 -> H(U1(k, e), f(c))
27.86/9.08	   A^2 -> H(U1(k, e), f(d))
27.86/9.08	   A^2 -> H(U1(k, c), U1(c, b))
27.86/9.08	   A^2 -> H(U1(k, c), U1(d, b))
27.86/9.08	   A^2 -> H(U1(k, c), U1(b, c))
27.86/9.08	   A^2 -> H(U1(k, c), U1(b, d))
27.86/9.08	   A^2 -> H(U1(k, c), U1(c, c))
27.86/9.08	   A^2 -> H(U1(k, c), f(e))
27.86/9.08	   A^2 -> H(U1(k, c), f(k))
27.86/9.08	   A^2 -> H(U1(k, c), U1(d, d))
27.86/9.08	   A^2 -> H(U1(c, e), U1(c, b))
27.86/9.08	   A^2 -> H(U1(c, e), U1(d, b))
27.86/9.08	   A^2 -> H(U1(c, e), U1(b, c))
27.86/9.08	   A^2 -> H(U1(c, e), U1(b, d))
27.86/9.08	   A^2 -> H(U1(c, e), U1(c, c))
27.86/9.08	   A^2 -> H(U1(c, e), f(e))
27.86/9.08	   A^2 -> H(U1(c, e), f(k))
27.86/9.08	   A^2 -> H(U1(c, e), U1(d, d))
27.86/9.08	   A^2 -> H(U1(c, k), U1(c, b))
27.86/9.08	   A^2 -> H(U1(c, k), U1(d, b))
27.86/9.08	   A^2 -> H(U1(c, k), U1(b, c))
27.86/9.08	   A^2 -> H(U1(c, k), U1(b, d))
27.86/9.08	   A^2 -> H(U1(c, k), U1(c, c))
27.86/9.08	   A^2 -> H(U1(c, k), f(e))
27.86/9.08	   A^2 -> H(U1(c, k), f(k))
27.86/9.08	   A^2 -> H(U1(c, k), U1(d, d))
27.86/9.08	   A^2 -> H(U1(c, c), U1(e, b))
27.86/9.08	   A^2 -> H(U1(c, c), U1(k, b))
27.86/9.08	   A^2 -> H(U1(c, c), U1(c, d))
27.86/9.08	   A^2 -> H(U1(c, c), U1(d, c))
27.86/9.08	   A^2 -> H(U1(c, c), U1(b, e))
27.86/9.08	   A^2 -> H(U1(c, c), U1(b, k))
27.86/9.08	   A^2 -> H(U1(c, c), U1(e, e))
27.86/9.08	   A^2 -> H(U1(c, c), U1(k, k))
27.86/9.08	   A^2 -> H(U1(c, c), U1(k, d))
27.86/9.08	   A^2 -> H(U1(c, c), U1(d, k))
27.86/9.08	   A^2 -> H(e, U1(b, b))
27.86/9.08	   A^2 -> H(e, f(c))
27.86/9.08	   A^2 -> H(e, f(d))
27.86/9.08	   A^2 -> H(U1(e, e), U1(c, b))
27.86/9.08	   A^2 -> H(U1(e, e), U1(d, b))
27.86/9.08	   A^2 -> H(U1(e, e), U1(b, c))
27.86/9.08	   A^2 -> H(U1(e, e), U1(b, d))
27.86/9.08	   A^2 -> H(U1(e, e), U1(c, c))
27.86/9.08	   A^2 -> H(U1(e, e), f(e))
27.86/9.08	   A^2 -> H(U1(e, e), f(k))
27.86/9.08	   A^2 -> H(U1(e, e), U1(d, d))
27.86/9.08	   A^2 -> H(f(e), U1(e, b))
27.86/9.08	   A^2 -> H(f(e), U1(k, b))
27.86/9.08	   A^2 -> H(f(e), U1(c, d))
27.86/9.08	   A^2 -> H(f(e), U1(d, c))
27.86/9.08	   A^2 -> H(f(e), U1(b, e))
27.86/9.08	   A^2 -> H(f(e), U1(b, k))
27.86/9.08	   A^2 -> H(f(e), U1(e, c))
27.86/9.08	   A^2 -> H(f(e), U1(k, c))
27.86/9.08	   A^2 -> H(f(e), U1(c, e))
27.86/9.08	   A^2 -> H(f(e), U1(c, k))
27.86/9.08	   A^2 -> H(f(e), U1(k, k))
27.86/9.08	   A^2 -> H(f(e), U1(k, d))
27.86/9.08	   A^2 -> H(f(e), U1(d, k))
27.86/9.08	   A^2 -> H(U1(k, k), U1(c, b))
27.86/9.08	   A^2 -> H(U1(k, k), U1(d, b))
27.86/9.08	   A^2 -> H(U1(k, k), U1(b, c))
27.86/9.08	   A^2 -> H(U1(k, k), U1(b, d))
27.86/9.08	   A^2 -> H(U1(k, k), U1(c, c))
27.86/9.08	   A^2 -> H(U1(k, k), f(e))
27.86/9.08	   A^2 -> H(U1(k, k), f(k))
27.86/9.08	   A^2 -> H(U1(k, k), U1(d, d))
27.86/9.08	   A^2 -> H(f(k), U1(e, b))
27.86/9.08	   A^2 -> H(f(k), U1(k, b))
27.86/9.08	   A^2 -> H(f(k), U1(c, d))
27.86/9.08	   A^2 -> H(f(k), U1(d, c))
27.86/9.08	   A^2 -> H(f(k), U1(b, e))
27.86/9.08	   A^2 -> H(f(k), U1(b, k))
27.86/9.08	   A^2 -> H(f(k), U1(e, c))
27.86/9.08	   A^2 -> H(f(k), U1(k, c))
27.86/9.08	   A^2 -> H(f(k), U1(c, e))
27.86/9.08	   A^2 -> H(f(k), U1(c, k))
27.86/9.08	   A^2 -> H(f(k), U1(e, e))
27.86/9.08	   A^2 -> H(f(k), U1(k, d))
27.86/9.08	   A^2 -> H(f(k), U1(d, k))
27.86/9.08	   A^2 -> H(f(c), b)
27.86/9.08	   A^2 -> H(f(c), U1(e, d))
27.86/9.08	   A^2 -> H(f(c), U1(d, e))
27.86/9.08	   A^2 -> H(f(k), U1(k, k))
27.86/9.08	   A^2 -> H(U1(k, k), U1(b, b))
27.86/9.08	   A^2 -> H(U1(k, k), f(c))
27.86/9.08	   A^2 -> H(U1(k, k), f(d))
27.86/9.08	   A^2 -> H(U1(k, d), U1(c, b))
27.86/9.08	   A^2 -> H(U1(k, d), U1(d, b))
27.86/9.08	   A^2 -> H(U1(k, d), U1(b, c))
27.86/9.08	   A^2 -> H(U1(k, d), U1(b, d))
27.86/9.08	   A^2 -> H(U1(k, d), U1(c, c))
27.86/9.08	   A^2 -> H(U1(k, d), f(e))
27.86/9.08	   A^2 -> H(U1(k, d), f(k))
27.86/9.08	   A^2 -> H(U1(k, d), U1(d, d))
27.86/9.08	   A^2 -> H(U1(d, k), U1(c, b))
27.86/9.08	   A^2 -> H(U1(d, k), U1(d, b))
27.86/9.08	   A^2 -> H(U1(d, k), U1(b, c))
27.86/9.08	   A^2 -> H(U1(d, k), U1(b, d))
27.86/9.08	   A^2 -> H(U1(d, k), U1(c, c))
27.86/9.08	   A^2 -> H(U1(d, k), f(e))
27.86/9.08	   A^2 -> H(U1(d, k), f(k))
27.86/9.08	   A^2 -> H(U1(d, k), U1(d, d))
27.86/9.08	   A^2 -> H(U1(d, d), U1(e, b))
27.86/9.08	   A^2 -> H(U1(d, d), U1(k, b))
27.86/9.08	   A^2 -> H(U1(d, d), U1(c, d))
27.86/9.08	   A^2 -> H(U1(d, d), U1(d, c))
27.86/9.08	   A^2 -> H(U1(d, d), U1(b, e))
27.86/9.08	   A^2 -> H(U1(d, d), U1(b, k))
27.86/9.08	   A^2 -> H(U1(d, d), U1(e, c))
27.86/9.08	   A^2 -> H(U1(d, d), U1(k, c))
27.86/9.08	   A^2 -> H(U1(d, d), U1(c, e))
27.86/9.08	   A^2 -> H(U1(d, d), U1(c, k))
27.86/9.08	   A^2 -> H(U1(d, d), U1(e, e))
27.86/9.08	   A^2 -> H(U1(d, d), U1(k, k))
27.86/9.08	   A^2 -> H(f(d), b)
27.86/9.08	   A^2 -> H(f(d), U1(e, d))
27.86/9.08	   A^2 -> H(f(d), U1(d, e))
27.86/9.08	   A^2 -> H(f(d), c)
27.86/9.08	   A^2 -> H(f(d), U1(e, k))
27.86/9.08	   A^2 -> H(f(d), U1(k, e))
27.86/9.08	   A^2 -> H(f(d), e)
27.86/9.08	   A^2 -> H(f(a), d)
27.86/9.08	   A^2 -> H(U1(c, c), U1(e, c))
27.86/9.08	   A^2 -> H(f(c), c)
27.86/9.08	   A^2 -> H(f(c), U1(e, k))
27.86/9.08	   A^2 -> H(U1(c, c), U1(k, c))
27.86/9.08	   A^2 -> H(f(c), U1(k, e))
27.86/9.08	   A^2 -> H(f(c), U1(k, k))
27.86/9.08	   A^2 -> H(U1(c, c), U1(c, e))
27.86/9.08	   A^2 -> H(U1(c, c), U1(c, k))
27.86/9.08	   A^2 -> H(f(a), k)
27.86/9.08	   A^2 -> H(f(e), U1(e, e))
27.86/9.08	   A^2 -> H(f(c), e)
27.86/9.08	   A^2 -> H(U1(d, d), U1(k, d))
27.86/9.08	   A^2 -> H(f(d), U1(k, k))
27.86/9.08	   A^2 -> H(U1(d, d), U1(d, k))
27.86/9.08	   A^2 -> H(d, U1(b, b))
27.86/9.08	   A^2 -> H(d, f(c))
27.86/9.08	   A^2 -> H(d, f(d))
27.86/9.08	   A^2 -> H(a, U1(c, b))
27.86/9.08	   A^2 -> H(a, U1(d, b))
27.86/9.08	   A^2 -> H(a, U1(b, c))
27.86/9.08	   A^2 -> H(a, U1(b, d))
27.86/9.08	   A^2 -> H(a, U1(c, c))
27.86/9.08	   A^2 -> H(a, f(e))
27.86/9.08	   A^2 -> H(a, f(k))
27.86/9.08	   A^2 -> H(a, U1(d, d))
27.86/9.08	   A^2 -> H(U1(e, d), U1(c, b))
27.86/9.08	   A^2 -> H(U1(e, d), U1(d, b))
27.86/9.08	   A^2 -> H(U1(e, d), U1(b, c))
27.86/9.08	   A^2 -> H(U1(e, d), U1(b, d))
27.86/9.08	   A^2 -> H(U1(e, d), U1(c, c))
27.86/9.08	   A^2 -> H(U1(e, d), f(e))
27.86/9.08	   A^2 -> H(U1(e, d), f(k))
27.86/9.08	   A^2 -> H(U1(e, d), U1(d, d))
27.86/9.08	   A^2 -> H(U1(e, a), U1(e, b))
27.86/9.08	   A^2 -> H(U1(e, a), U1(k, b))
27.86/9.08	   A^2 -> H(U1(e, a), U1(c, d))
27.86/9.08	   A^2 -> H(U1(e, a), U1(d, c))
27.86/9.08	   A^2 -> H(U1(e, a), U1(b, e))
27.86/9.08	   A^2 -> H(U1(e, a), U1(b, k))
27.86/9.08	   A^2 -> H(U1(e, a), U1(e, c))
27.86/9.08	   A^2 -> H(U1(e, a), U1(k, c))
27.86/9.08	   A^2 -> H(U1(e, a), U1(c, e))
27.86/9.08	   A^2 -> H(U1(e, a), U1(c, k))
27.86/9.08	   A^2 -> H(U1(e, a), U1(e, e))
27.86/9.08	   A^2 -> H(U1(e, a), U1(k, k))
27.86/9.08	   A^2 -> H(U1(e, a), U1(k, d))
27.86/9.08	   A^2 -> H(U1(e, a), U1(d, k))
27.86/9.08	   A^2 -> H(U1(k, a), U1(e, b))
27.86/9.08	   A^2 -> H(U1(k, a), U1(k, b))
27.86/9.08	   A^2 -> H(U1(k, a), U1(c, d))
27.86/9.08	   A^2 -> H(U1(k, a), U1(d, c))
27.86/9.08	   A^2 -> H(U1(k, a), U1(b, e))
27.86/9.08	   A^2 -> H(U1(k, a), U1(b, k))
27.86/9.08	   A^2 -> H(U1(k, a), U1(e, c))
27.86/9.08	   A^2 -> H(U1(k, a), U1(k, c))
27.86/9.08	   A^2 -> H(U1(k, a), U1(c, e))
27.86/9.08	   A^2 -> H(U1(k, a), U1(c, k))
27.86/9.08	   A^2 -> H(U1(k, a), U1(e, e))
27.86/9.08	   A^2 -> H(U1(k, a), U1(k, k))
27.86/9.08	   A^2 -> H(U1(k, a), U1(k, d))
27.86/9.08	   A^2 -> H(U1(k, a), U1(d, k))
27.86/9.08	   A^2 -> H(U1(c, d), U1(e, b))
27.86/9.08	   A^2 -> H(U1(c, d), U1(k, b))
27.86/9.08	   A^2 -> H(U1(c, d), U1(c, d))
27.86/9.08	   A^2 -> H(U1(c, d), U1(d, c))
27.86/9.08	   A^2 -> H(U1(c, d), U1(b, e))
27.86/9.08	   A^2 -> H(U1(c, d), U1(b, k))
27.86/9.08	   A^2 -> H(U1(c, d), U1(e, c))
27.86/9.08	   A^2 -> H(U1(c, d), U1(k, c))
27.86/9.08	   A^2 -> H(U1(c, d), U1(c, e))
27.86/9.08	   A^2 -> H(U1(c, d), U1(c, k))
27.86/9.08	   A^2 -> H(U1(c, d), U1(e, e))
27.86/9.08	   A^2 -> H(U1(c, d), U1(k, k))
27.86/9.08	   A^2 -> H(U1(c, d), U1(k, d))
27.86/9.08	   A^2 -> H(U1(c, d), U1(d, k))
27.86/9.08	   A^2 -> H(U1(c, a), b)
27.86/9.08	   A^2 -> H(U1(c, a), U1(e, d))
27.86/9.08	   A^2 -> H(U1(c, a), U1(d, e))
27.86/9.08	   A^2 -> H(U1(c, a), c)
27.86/9.08	   A^2 -> H(U1(c, a), U1(e, k))
27.86/9.08	   A^2 -> H(U1(c, a), U1(k, e))
27.86/9.08	   A^2 -> H(U1(c, a), e)
27.86/9.08	   A^2 -> H(U1(c, a), U1(k, k))
27.86/9.08	   A^2 -> H(U1(d, e), U1(c, b))
27.86/9.08	   A^2 -> H(U1(d, e), U1(d, b))
27.86/9.08	   A^2 -> H(U1(d, e), U1(b, c))
27.86/9.08	   A^2 -> H(U1(d, e), U1(b, d))
27.86/9.08	   A^2 -> H(U1(d, e), U1(c, c))
27.86/9.08	   A^2 -> H(U1(d, e), f(e))
27.86/9.08	   A^2 -> H(U1(d, e), f(k))
27.86/9.08	   A^2 -> H(U1(d, e), U1(d, d))
27.86/9.08	   A^2 -> H(U1(d, c), U1(e, b))
27.86/9.08	   A^2 -> H(U1(d, c), U1(k, b))
27.86/9.08	   A^2 -> H(U1(d, c), U1(c, d))
27.86/9.08	   A^2 -> H(U1(d, c), U1(d, c))
27.86/9.08	   A^2 -> H(U1(d, c), U1(b, e))
27.86/9.08	   A^2 -> H(U1(d, c), U1(b, k))
27.86/9.08	   A^2 -> H(U1(d, c), U1(e, c))
27.86/9.08	   A^2 -> H(U1(d, c), U1(k, c))
27.86/9.08	   A^2 -> H(U1(d, c), U1(c, e))
27.86/9.08	   A^2 -> H(U1(d, c), U1(c, k))
27.86/9.08	   A^2 -> H(U1(d, c), U1(e, e))
27.86/9.08	   A^2 -> H(U1(d, c), U1(k, k))
27.86/9.08	   A^2 -> H(U1(d, c), U1(k, d))
27.86/9.08	   A^2 -> H(U1(d, c), U1(d, k))
27.86/9.08	   A^2 -> H(U1(d, a), b)
27.86/9.08	   A^2 -> H(U1(d, a), U1(e, d))
27.86/9.08	   A^2 -> H(U1(d, a), U1(d, e))
27.86/9.08	   A^2 -> H(U1(d, a), c)
27.86/9.08	   A^2 -> H(U1(d, a), U1(e, k))
27.86/9.08	   A^2 -> H(U1(d, a), U1(k, e))
27.86/9.08	   A^2 -> H(U1(d, a), e)
27.86/9.08	   A^2 -> H(U1(d, a), U1(k, k))
27.86/9.08	   A^2 -> H(U1(a, e), U1(e, b))
27.86/9.08	   A^2 -> H(U1(a, e), U1(k, b))
27.86/9.08	   A^2 -> H(U1(a, e), U1(c, d))
27.86/9.08	   A^2 -> H(U1(a, e), U1(d, c))
27.86/9.08	   A^2 -> H(U1(a, e), U1(b, e))
27.86/9.08	   A^2 -> H(U1(a, e), U1(b, k))
27.86/9.08	   A^2 -> H(U1(a, e), U1(e, c))
27.86/9.08	   A^2 -> H(U1(a, e), U1(k, c))
27.86/9.08	   A^2 -> H(U1(a, e), U1(c, e))
27.86/9.08	   A^2 -> H(U1(a, e), U1(c, k))
27.86/9.08	   A^2 -> H(U1(a, e), U1(e, e))
27.86/9.08	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.10	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.10	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.10	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.10	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.10	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.10	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.10	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.10	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.10	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.10	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.10	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.10	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.10	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.10	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.10	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.10	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.10	   A^2 -> H(U1(a, c), b)
28.11/9.10	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.10	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.10	   A^2 -> H(U1(a, c), c)
28.11/9.10	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.10	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.10	
28.11/9.10	The TRS R consists of the following rules:
28.11/9.10	
28.11/9.10	   f(x) -> U1(x, x)
28.11/9.10	   U1(e, x) -> x
28.11/9.10	   a -> c
28.11/9.10	   a -> d
28.11/9.10	   b -> c
28.11/9.10	   b -> d
28.11/9.10	   d -> k
28.11/9.10	   c -> e
28.11/9.10	   c -> k
28.11/9.10	
28.11/9.10	Q is empty.
28.11/9.10	We have to consider all minimal (P,Q,R)-chains.
28.11/9.10	----------------------------------------
28.11/9.10	
28.11/9.10	(729) TransformationProof (EQUIVALENT)
28.11/9.10	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.10	
28.11/9.10	   (A^2 -> H(U1(c, c), U1(c, e)),A^2 -> H(U1(c, c), U1(c, e)))
28.11/9.10	   (A^2 -> H(U1(d, c), U1(c, e)),A^2 -> H(U1(d, c), U1(c, e)))
28.11/9.10	   (A^2 -> H(U1(a, e), U1(c, e)),A^2 -> H(U1(a, e), U1(c, e)))
28.11/9.10	   (A^2 -> H(U1(a, k), U1(c, e)),A^2 -> H(U1(a, k), U1(c, e)))
28.11/9.10	   (A^2 -> H(U1(a, c), U1(e, e)),A^2 -> H(U1(a, c), U1(e, e)))
28.11/9.10	   (A^2 -> H(U1(a, c), U1(k, e)),A^2 -> H(U1(a, c), U1(k, e)))
28.11/9.10	
28.11/9.10	
28.11/9.10	----------------------------------------
28.11/9.10	
28.11/9.10	(730)
28.11/9.10	Obligation:
28.11/9.10	Q DP problem:
28.11/9.10	The TRS P consists of the following rules:
28.11/9.10	
28.11/9.10	   H(x, x) -> G(x, x, f(k))
28.11/9.10	   G(d, x, x) -> A^2
28.11/9.10	   A^2 -> H(f(c), f(c))
28.11/9.10	   A^2 -> H(f(d), f(d))
28.11/9.10	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.10	   A^2 -> H(f(e), f(e))
28.11/9.10	   A^2 -> H(f(k), f(k))
28.11/9.10	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.10	   A^2 -> H(U1(a, c), U1(c, k))
28.11/9.10	   A^2 -> H(U1(a, c), U1(e, e))
28.11/9.10	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.10	   A^2 -> H(U1(a, c), U1(k, d))
28.11/9.10	   A^2 -> H(U1(a, c), U1(d, k))
28.11/9.10	   A^2 -> H(U1(a, d), U1(e, b))
28.11/9.10	   A^2 -> H(U1(a, d), U1(k, b))
28.11/9.10	   A^2 -> H(U1(a, d), U1(c, d))
28.11/9.10	   A^2 -> H(U1(a, d), U1(d, c))
28.11/9.10	   A^2 -> H(U1(a, d), U1(b, e))
28.11/9.10	   A^2 -> H(U1(a, d), U1(b, k))
28.11/9.10	   A^2 -> H(U1(a, d), U1(e, c))
28.11/9.10	   A^2 -> H(U1(a, d), U1(k, c))
28.11/9.10	   A^2 -> H(U1(a, d), U1(c, e))
28.11/9.10	   A^2 -> H(U1(a, d), U1(c, k))
28.11/9.10	   A^2 -> H(U1(a, d), U1(e, e))
28.11/9.10	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.10	   A^2 -> H(U1(a, d), U1(k, d))
28.11/9.10	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.10	   A^2 -> H(U1(a, a), b)
28.11/9.10	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.10	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.10	   A^2 -> H(U1(a, a), c)
28.11/9.10	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.10	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.10	   A^2 -> H(U1(a, a), e)
28.11/9.10	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.10	   A^2 -> H(k, f(b))
28.11/9.10	   A^2 -> H(c, U1(b, b))
28.11/9.10	   A^2 -> H(c, f(c))
28.11/9.10	   A^2 -> H(c, f(d))
28.11/9.10	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.10	   A^2 -> H(U1(e, k), f(c))
28.11/9.10	   A^2 -> H(U1(e, k), f(d))
28.11/9.10	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.10	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.10	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.10	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.10	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.10	   A^2 -> H(U1(e, c), f(e))
28.11/9.10	   A^2 -> H(U1(e, c), f(k))
28.11/9.10	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.10	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.10	   A^2 -> H(U1(k, e), f(c))
28.11/9.10	   A^2 -> H(U1(k, e), f(d))
28.11/9.10	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.10	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.10	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.10	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.10	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.10	   A^2 -> H(U1(k, c), f(e))
28.11/9.10	   A^2 -> H(U1(k, c), f(k))
28.11/9.10	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.10	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.10	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.10	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.10	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.10	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.10	   A^2 -> H(U1(c, e), f(e))
28.11/9.10	   A^2 -> H(U1(c, e), f(k))
28.11/9.10	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.10	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.10	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.10	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.10	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.10	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.10	   A^2 -> H(U1(c, k), f(e))
28.11/9.10	   A^2 -> H(U1(c, k), f(k))
28.11/9.10	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.10	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.10	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.10	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.10	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.10	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.10	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.10	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.10	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.10	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.10	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.10	   A^2 -> H(e, U1(b, b))
28.11/9.10	   A^2 -> H(e, f(c))
28.11/9.10	   A^2 -> H(e, f(d))
28.11/9.10	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.10	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.10	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.10	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.10	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.10	   A^2 -> H(U1(e, e), f(e))
28.11/9.10	   A^2 -> H(U1(e, e), f(k))
28.11/9.10	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.10	   A^2 -> H(f(e), U1(e, b))
28.11/9.10	   A^2 -> H(f(e), U1(k, b))
28.11/9.10	   A^2 -> H(f(e), U1(c, d))
28.11/9.10	   A^2 -> H(f(e), U1(d, c))
28.11/9.10	   A^2 -> H(f(e), U1(b, e))
28.11/9.10	   A^2 -> H(f(e), U1(b, k))
28.11/9.10	   A^2 -> H(f(e), U1(e, c))
28.11/9.10	   A^2 -> H(f(e), U1(k, c))
28.11/9.10	   A^2 -> H(f(e), U1(c, e))
28.11/9.10	   A^2 -> H(f(e), U1(c, k))
28.11/9.10	   A^2 -> H(f(e), U1(k, k))
28.11/9.10	   A^2 -> H(f(e), U1(k, d))
28.11/9.10	   A^2 -> H(f(e), U1(d, k))
28.11/9.10	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.10	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.10	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.10	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.10	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.10	   A^2 -> H(U1(k, k), f(e))
28.11/9.10	   A^2 -> H(U1(k, k), f(k))
28.11/9.10	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.10	   A^2 -> H(f(k), U1(e, b))
28.11/9.10	   A^2 -> H(f(k), U1(k, b))
28.11/9.10	   A^2 -> H(f(k), U1(c, d))
28.11/9.10	   A^2 -> H(f(k), U1(d, c))
28.11/9.10	   A^2 -> H(f(k), U1(b, e))
28.11/9.10	   A^2 -> H(f(k), U1(b, k))
28.11/9.10	   A^2 -> H(f(k), U1(e, c))
28.11/9.10	   A^2 -> H(f(k), U1(k, c))
28.11/9.10	   A^2 -> H(f(k), U1(c, e))
28.11/9.10	   A^2 -> H(f(k), U1(c, k))
28.11/9.10	   A^2 -> H(f(k), U1(e, e))
28.11/9.10	   A^2 -> H(f(k), U1(k, d))
28.11/9.10	   A^2 -> H(f(k), U1(d, k))
28.11/9.10	   A^2 -> H(f(c), b)
28.11/9.10	   A^2 -> H(f(c), U1(e, d))
28.11/9.10	   A^2 -> H(f(c), U1(d, e))
28.11/9.10	   A^2 -> H(f(k), U1(k, k))
28.11/9.10	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.10	   A^2 -> H(U1(k, k), f(c))
28.11/9.10	   A^2 -> H(U1(k, k), f(d))
28.11/9.10	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.10	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.10	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.10	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.10	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.10	   A^2 -> H(U1(k, d), f(e))
28.11/9.10	   A^2 -> H(U1(k, d), f(k))
28.11/9.10	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.10	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.10	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.10	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.10	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.10	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.10	   A^2 -> H(U1(d, k), f(e))
28.11/9.10	   A^2 -> H(U1(d, k), f(k))
28.11/9.10	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.10	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.10	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.10	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.10	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.10	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.10	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.10	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.10	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.10	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.10	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.10	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.10	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.10	   A^2 -> H(f(d), b)
28.11/9.10	   A^2 -> H(f(d), U1(e, d))
28.11/9.10	   A^2 -> H(f(d), U1(d, e))
28.11/9.10	   A^2 -> H(f(d), c)
28.11/9.10	   A^2 -> H(f(d), U1(e, k))
28.11/9.10	   A^2 -> H(f(d), U1(k, e))
28.11/9.10	   A^2 -> H(f(d), e)
28.11/9.10	   A^2 -> H(f(a), d)
28.11/9.10	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.10	   A^2 -> H(f(c), c)
28.11/9.10	   A^2 -> H(f(c), U1(e, k))
28.11/9.10	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.10	   A^2 -> H(f(c), U1(k, e))
28.11/9.10	   A^2 -> H(f(c), U1(k, k))
28.11/9.10	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.10	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.10	   A^2 -> H(f(a), k)
28.11/9.10	   A^2 -> H(f(e), U1(e, e))
28.11/9.10	   A^2 -> H(f(c), e)
28.11/9.10	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.10	   A^2 -> H(f(d), U1(k, k))
28.11/9.10	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.10	   A^2 -> H(d, U1(b, b))
28.11/9.10	   A^2 -> H(d, f(c))
28.11/9.10	   A^2 -> H(d, f(d))
28.11/9.10	   A^2 -> H(a, U1(c, b))
28.11/9.10	   A^2 -> H(a, U1(d, b))
28.11/9.10	   A^2 -> H(a, U1(b, c))
28.11/9.10	   A^2 -> H(a, U1(b, d))
28.11/9.10	   A^2 -> H(a, U1(c, c))
28.11/9.10	   A^2 -> H(a, f(e))
28.11/9.10	   A^2 -> H(a, f(k))
28.11/9.10	   A^2 -> H(a, U1(d, d))
28.11/9.10	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.10	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.10	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.10	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.10	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.10	   A^2 -> H(U1(e, d), f(e))
28.11/9.10	   A^2 -> H(U1(e, d), f(k))
28.11/9.10	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.10	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.10	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.10	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.10	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.10	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.10	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.10	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.10	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.10	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.10	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.10	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.10	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.10	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.10	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.10	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.10	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.10	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.10	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.10	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.10	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.10	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.10	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.10	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.10	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.10	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.10	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.10	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.10	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.10	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.10	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.10	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.10	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.10	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.10	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.10	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.10	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.10	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.10	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.10	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.10	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.10	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.10	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.10	   A^2 -> H(U1(c, a), b)
28.11/9.10	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.10	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.10	   A^2 -> H(U1(c, a), c)
28.11/9.10	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.10	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.10	   A^2 -> H(U1(c, a), e)
28.11/9.10	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.10	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.10	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.10	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.10	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.10	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.10	   A^2 -> H(U1(d, e), f(e))
28.11/9.10	   A^2 -> H(U1(d, e), f(k))
28.11/9.10	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.10	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.10	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.10	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.10	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.10	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.10	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.10	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.10	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.10	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.10	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.10	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.10	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.10	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.10	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.10	   A^2 -> H(U1(d, a), b)
28.11/9.10	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.10	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.10	   A^2 -> H(U1(d, a), c)
28.11/9.10	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.10	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.10	   A^2 -> H(U1(d, a), e)
28.11/9.10	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.10	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.10	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.10	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.10	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.10	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.10	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.10	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.10	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.10	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.10	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.10	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.10	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.10	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.10	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.10	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.10	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.10	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.10	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.10	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.10	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.10	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.10	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.10	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.10	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.10	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.10	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.10	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.10	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.10	   A^2 -> H(U1(a, c), b)
28.11/9.10	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.10	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.10	   A^2 -> H(U1(a, c), c)
28.11/9.10	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.10	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.10	
28.11/9.10	The TRS R consists of the following rules:
28.11/9.10	
28.11/9.10	   f(x) -> U1(x, x)
28.11/9.10	   U1(e, x) -> x
28.11/9.10	   a -> c
28.11/9.10	   a -> d
28.11/9.10	   b -> c
28.11/9.10	   b -> d
28.11/9.10	   d -> k
28.11/9.10	   c -> e
28.11/9.10	   c -> k
28.11/9.10	
28.11/9.10	Q is empty.
28.11/9.10	We have to consider all minimal (P,Q,R)-chains.
28.11/9.10	----------------------------------------
28.11/9.10	
28.11/9.10	(731) TransformationProof (EQUIVALENT)
28.11/9.10	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.10	
28.11/9.10	   (A^2 -> H(U1(c, c), U1(c, k)),A^2 -> H(U1(c, c), U1(c, k)))
28.11/9.10	   (A^2 -> H(U1(d, c), U1(c, k)),A^2 -> H(U1(d, c), U1(c, k)))
28.11/9.10	   (A^2 -> H(U1(a, e), U1(c, k)),A^2 -> H(U1(a, e), U1(c, k)))
28.11/9.10	   (A^2 -> H(U1(a, k), U1(c, k)),A^2 -> H(U1(a, k), U1(c, k)))
28.11/9.10	   (A^2 -> H(U1(a, c), U1(e, k)),A^2 -> H(U1(a, c), U1(e, k)))
28.11/9.10	   (A^2 -> H(U1(a, c), U1(k, k)),A^2 -> H(U1(a, c), U1(k, k)))
28.11/9.10	
28.11/9.10	
28.11/9.10	----------------------------------------
28.11/9.10	
28.11/9.10	(732)
28.11/9.10	Obligation:
28.11/9.10	Q DP problem:
28.11/9.10	The TRS P consists of the following rules:
28.11/9.10	
28.11/9.10	   H(x, x) -> G(x, x, f(k))
28.11/9.10	   G(d, x, x) -> A^2
28.11/9.10	   A^2 -> H(f(c), f(c))
28.11/9.10	   A^2 -> H(f(d), f(d))
28.11/9.10	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.10	   A^2 -> H(f(e), f(e))
28.11/9.10	   A^2 -> H(f(k), f(k))
28.11/9.10	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.10	   A^2 -> H(U1(a, c), U1(e, e))
28.11/9.10	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.10	   A^2 -> H(U1(a, c), U1(k, d))
28.11/9.10	   A^2 -> H(U1(a, c), U1(d, k))
28.11/9.10	   A^2 -> H(U1(a, d), U1(e, b))
28.11/9.10	   A^2 -> H(U1(a, d), U1(k, b))
28.11/9.10	   A^2 -> H(U1(a, d), U1(c, d))
28.11/9.10	   A^2 -> H(U1(a, d), U1(d, c))
28.11/9.10	   A^2 -> H(U1(a, d), U1(b, e))
28.11/9.10	   A^2 -> H(U1(a, d), U1(b, k))
28.11/9.10	   A^2 -> H(U1(a, d), U1(e, c))
28.11/9.10	   A^2 -> H(U1(a, d), U1(k, c))
28.11/9.10	   A^2 -> H(U1(a, d), U1(c, e))
28.11/9.10	   A^2 -> H(U1(a, d), U1(c, k))
28.11/9.10	   A^2 -> H(U1(a, d), U1(e, e))
28.11/9.10	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.10	   A^2 -> H(U1(a, d), U1(k, d))
28.11/9.10	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.10	   A^2 -> H(U1(a, a), b)
28.11/9.10	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.10	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.10	   A^2 -> H(U1(a, a), c)
28.11/9.10	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.10	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.10	   A^2 -> H(U1(a, a), e)
28.11/9.10	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.10	   A^2 -> H(k, f(b))
28.11/9.10	   A^2 -> H(c, U1(b, b))
28.11/9.10	   A^2 -> H(c, f(c))
28.11/9.10	   A^2 -> H(c, f(d))
28.11/9.10	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.10	   A^2 -> H(U1(e, k), f(c))
28.11/9.10	   A^2 -> H(U1(e, k), f(d))
28.11/9.10	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.10	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.10	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.10	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.10	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.10	   A^2 -> H(U1(e, c), f(e))
28.11/9.10	   A^2 -> H(U1(e, c), f(k))
28.11/9.10	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.10	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.10	   A^2 -> H(U1(k, e), f(c))
28.11/9.10	   A^2 -> H(U1(k, e), f(d))
28.11/9.10	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.10	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.10	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.10	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.10	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.10	   A^2 -> H(U1(k, c), f(e))
28.11/9.10	   A^2 -> H(U1(k, c), f(k))
28.11/9.10	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.10	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.10	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.10	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.10	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.10	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.10	   A^2 -> H(U1(c, e), f(e))
28.11/9.10	   A^2 -> H(U1(c, e), f(k))
28.11/9.10	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.10	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.10	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.10	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.10	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.10	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.10	   A^2 -> H(U1(c, k), f(e))
28.11/9.10	   A^2 -> H(U1(c, k), f(k))
28.11/9.10	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.10	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.10	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.10	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.10	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.10	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.10	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.10	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.10	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.10	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.10	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.10	   A^2 -> H(e, U1(b, b))
28.11/9.10	   A^2 -> H(e, f(c))
28.11/9.10	   A^2 -> H(e, f(d))
28.11/9.10	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.10	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.10	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.10	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.10	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.10	   A^2 -> H(U1(e, e), f(e))
28.11/9.10	   A^2 -> H(U1(e, e), f(k))
28.11/9.10	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.10	   A^2 -> H(f(e), U1(e, b))
28.11/9.10	   A^2 -> H(f(e), U1(k, b))
28.11/9.10	   A^2 -> H(f(e), U1(c, d))
28.11/9.10	   A^2 -> H(f(e), U1(d, c))
28.11/9.10	   A^2 -> H(f(e), U1(b, e))
28.11/9.10	   A^2 -> H(f(e), U1(b, k))
28.11/9.10	   A^2 -> H(f(e), U1(e, c))
28.11/9.10	   A^2 -> H(f(e), U1(k, c))
28.11/9.10	   A^2 -> H(f(e), U1(c, e))
28.11/9.10	   A^2 -> H(f(e), U1(c, k))
28.11/9.10	   A^2 -> H(f(e), U1(k, k))
28.11/9.10	   A^2 -> H(f(e), U1(k, d))
28.11/9.10	   A^2 -> H(f(e), U1(d, k))
28.11/9.10	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.10	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.10	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.10	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.10	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.10	   A^2 -> H(U1(k, k), f(e))
28.11/9.10	   A^2 -> H(U1(k, k), f(k))
28.11/9.10	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.10	   A^2 -> H(f(k), U1(e, b))
28.11/9.10	   A^2 -> H(f(k), U1(k, b))
28.11/9.10	   A^2 -> H(f(k), U1(c, d))
28.11/9.10	   A^2 -> H(f(k), U1(d, c))
28.11/9.10	   A^2 -> H(f(k), U1(b, e))
28.11/9.10	   A^2 -> H(f(k), U1(b, k))
28.11/9.10	   A^2 -> H(f(k), U1(e, c))
28.11/9.10	   A^2 -> H(f(k), U1(k, c))
28.11/9.10	   A^2 -> H(f(k), U1(c, e))
28.11/9.10	   A^2 -> H(f(k), U1(c, k))
28.11/9.10	   A^2 -> H(f(k), U1(e, e))
28.11/9.10	   A^2 -> H(f(k), U1(k, d))
28.11/9.10	   A^2 -> H(f(k), U1(d, k))
28.11/9.10	   A^2 -> H(f(c), b)
28.11/9.10	   A^2 -> H(f(c), U1(e, d))
28.11/9.10	   A^2 -> H(f(c), U1(d, e))
28.11/9.10	   A^2 -> H(f(k), U1(k, k))
28.11/9.10	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.10	   A^2 -> H(U1(k, k), f(c))
28.11/9.10	   A^2 -> H(U1(k, k), f(d))
28.11/9.10	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.10	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.10	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.10	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.10	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.10	   A^2 -> H(U1(k, d), f(e))
28.11/9.10	   A^2 -> H(U1(k, d), f(k))
28.11/9.10	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.10	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.10	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.10	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.10	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.10	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.10	   A^2 -> H(U1(d, k), f(e))
28.11/9.10	   A^2 -> H(U1(d, k), f(k))
28.11/9.10	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.10	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.10	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.10	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.10	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.10	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.10	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.10	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.10	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.10	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.10	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.10	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.10	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.10	   A^2 -> H(f(d), b)
28.11/9.10	   A^2 -> H(f(d), U1(e, d))
28.11/9.10	   A^2 -> H(f(d), U1(d, e))
28.11/9.10	   A^2 -> H(f(d), c)
28.11/9.10	   A^2 -> H(f(d), U1(e, k))
28.11/9.10	   A^2 -> H(f(d), U1(k, e))
28.11/9.10	   A^2 -> H(f(d), e)
28.11/9.10	   A^2 -> H(f(a), d)
28.11/9.10	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.10	   A^2 -> H(f(c), c)
28.11/9.10	   A^2 -> H(f(c), U1(e, k))
28.11/9.10	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.10	   A^2 -> H(f(c), U1(k, e))
28.11/9.10	   A^2 -> H(f(c), U1(k, k))
28.11/9.10	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.10	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.10	   A^2 -> H(f(a), k)
28.11/9.10	   A^2 -> H(f(e), U1(e, e))
28.11/9.10	   A^2 -> H(f(c), e)
28.11/9.10	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.10	   A^2 -> H(f(d), U1(k, k))
28.11/9.10	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.10	   A^2 -> H(d, U1(b, b))
28.11/9.10	   A^2 -> H(d, f(c))
28.11/9.10	   A^2 -> H(d, f(d))
28.11/9.10	   A^2 -> H(a, U1(c, b))
28.11/9.10	   A^2 -> H(a, U1(d, b))
28.11/9.10	   A^2 -> H(a, U1(b, c))
28.11/9.10	   A^2 -> H(a, U1(b, d))
28.11/9.10	   A^2 -> H(a, U1(c, c))
28.11/9.10	   A^2 -> H(a, f(e))
28.11/9.10	   A^2 -> H(a, f(k))
28.11/9.10	   A^2 -> H(a, U1(d, d))
28.11/9.10	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.10	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.10	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.10	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.10	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.10	   A^2 -> H(U1(e, d), f(e))
28.11/9.10	   A^2 -> H(U1(e, d), f(k))
28.11/9.10	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.10	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.10	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.10	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.10	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.10	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.10	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.10	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.10	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.10	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.10	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.10	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.10	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.10	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.10	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.10	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.10	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.10	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.10	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.10	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.10	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.10	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.10	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.10	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.10	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.10	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.10	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.10	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.10	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.10	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.10	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.10	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.10	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.10	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.10	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.10	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.10	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.10	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.10	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.11	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.11	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.11	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.11	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.11	   A^2 -> H(U1(c, a), b)
28.11/9.11	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.11	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.11	   A^2 -> H(U1(c, a), c)
28.11/9.11	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.11	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.11	   A^2 -> H(U1(c, a), e)
28.11/9.11	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.11	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.11	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.11	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.11	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.11	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.11	   A^2 -> H(U1(d, e), f(e))
28.11/9.11	   A^2 -> H(U1(d, e), f(k))
28.11/9.11	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.11	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.11	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.11	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.11	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.11	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.11	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.11	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.11	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.11	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.11	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.11	   A^2 -> H(U1(d, a), b)
28.11/9.11	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.11	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.11	   A^2 -> H(U1(d, a), c)
28.11/9.11	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.11	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.11	   A^2 -> H(U1(d, a), e)
28.11/9.11	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.11	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.11	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.11	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.11	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.11	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.11	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.11	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.11	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.11	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.11	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.11	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.11	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.11	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.11	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.11	   A^2 -> H(U1(a, c), b)
28.11/9.11	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.11	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.11	   A^2 -> H(U1(a, c), c)
28.11/9.11	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.11	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.11	
28.11/9.11	The TRS R consists of the following rules:
28.11/9.11	
28.11/9.11	   f(x) -> U1(x, x)
28.11/9.11	   U1(e, x) -> x
28.11/9.11	   a -> c
28.11/9.11	   a -> d
28.11/9.11	   b -> c
28.11/9.11	   b -> d
28.11/9.11	   d -> k
28.11/9.11	   c -> e
28.11/9.11	   c -> k
28.11/9.11	
28.11/9.11	Q is empty.
28.11/9.11	We have to consider all minimal (P,Q,R)-chains.
28.11/9.11	----------------------------------------
28.11/9.11	
28.11/9.11	(733) TransformationProof (EQUIVALENT)
28.11/9.11	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.11	
28.11/9.11	   (A^2 -> H(U1(c, c), U1(e, e)),A^2 -> H(U1(c, c), U1(e, e)))
28.11/9.11	   (A^2 -> H(U1(d, c), U1(e, e)),A^2 -> H(U1(d, c), U1(e, e)))
28.11/9.11	   (A^2 -> H(U1(a, e), U1(e, e)),A^2 -> H(U1(a, e), U1(e, e)))
28.11/9.11	   (A^2 -> H(U1(a, k), U1(e, e)),A^2 -> H(U1(a, k), U1(e, e)))
28.11/9.11	   (A^2 -> H(U1(a, c), e),A^2 -> H(U1(a, c), e))
28.11/9.11	
28.11/9.11	
28.11/9.11	----------------------------------------
28.11/9.11	
28.11/9.11	(734)
28.11/9.11	Obligation:
28.11/9.11	Q DP problem:
28.11/9.11	The TRS P consists of the following rules:
28.11/9.11	
28.11/9.11	   H(x, x) -> G(x, x, f(k))
28.11/9.11	   G(d, x, x) -> A^2
28.11/9.11	   A^2 -> H(f(c), f(c))
28.11/9.11	   A^2 -> H(f(d), f(d))
28.11/9.11	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.11	   A^2 -> H(f(e), f(e))
28.11/9.11	   A^2 -> H(f(k), f(k))
28.11/9.11	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.11	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, c), U1(k, d))
28.11/9.11	   A^2 -> H(U1(a, c), U1(d, k))
28.11/9.11	   A^2 -> H(U1(a, d), U1(e, b))
28.11/9.11	   A^2 -> H(U1(a, d), U1(k, b))
28.11/9.11	   A^2 -> H(U1(a, d), U1(c, d))
28.11/9.11	   A^2 -> H(U1(a, d), U1(d, c))
28.11/9.11	   A^2 -> H(U1(a, d), U1(b, e))
28.11/9.11	   A^2 -> H(U1(a, d), U1(b, k))
28.11/9.11	   A^2 -> H(U1(a, d), U1(e, c))
28.11/9.11	   A^2 -> H(U1(a, d), U1(k, c))
28.11/9.11	   A^2 -> H(U1(a, d), U1(c, e))
28.11/9.11	   A^2 -> H(U1(a, d), U1(c, k))
28.11/9.11	   A^2 -> H(U1(a, d), U1(e, e))
28.11/9.11	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, d), U1(k, d))
28.11/9.11	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.11	   A^2 -> H(U1(a, a), b)
28.11/9.11	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.11	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.11	   A^2 -> H(U1(a, a), c)
28.11/9.11	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.11	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.11	   A^2 -> H(U1(a, a), e)
28.11/9.11	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.11	   A^2 -> H(k, f(b))
28.11/9.11	   A^2 -> H(c, U1(b, b))
28.11/9.11	   A^2 -> H(c, f(c))
28.11/9.11	   A^2 -> H(c, f(d))
28.11/9.11	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.11	   A^2 -> H(U1(e, k), f(c))
28.11/9.11	   A^2 -> H(U1(e, k), f(d))
28.11/9.11	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.11	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.11	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.11	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.11	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.11	   A^2 -> H(U1(e, c), f(e))
28.11/9.11	   A^2 -> H(U1(e, c), f(k))
28.11/9.11	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.11	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.11	   A^2 -> H(U1(k, e), f(c))
28.11/9.11	   A^2 -> H(U1(k, e), f(d))
28.11/9.11	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.11	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.11	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.11	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.11	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.11	   A^2 -> H(U1(k, c), f(e))
28.11/9.11	   A^2 -> H(U1(k, c), f(k))
28.11/9.11	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.11	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.11	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.11	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.11	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.11	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.11	   A^2 -> H(U1(c, e), f(e))
28.11/9.11	   A^2 -> H(U1(c, e), f(k))
28.11/9.11	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.11	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.11	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.11	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.11	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.11	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.11	   A^2 -> H(U1(c, k), f(e))
28.11/9.11	   A^2 -> H(U1(c, k), f(k))
28.11/9.11	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.11	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.11	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.11	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.11	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.11	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.11	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.11	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.11	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.11	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.11	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.11	   A^2 -> H(e, U1(b, b))
28.11/9.11	   A^2 -> H(e, f(c))
28.11/9.11	   A^2 -> H(e, f(d))
28.11/9.11	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.11	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.11	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.11	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.11	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.11	   A^2 -> H(U1(e, e), f(e))
28.11/9.11	   A^2 -> H(U1(e, e), f(k))
28.11/9.11	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.11	   A^2 -> H(f(e), U1(e, b))
28.11/9.11	   A^2 -> H(f(e), U1(k, b))
28.11/9.11	   A^2 -> H(f(e), U1(c, d))
28.11/9.11	   A^2 -> H(f(e), U1(d, c))
28.11/9.11	   A^2 -> H(f(e), U1(b, e))
28.11/9.11	   A^2 -> H(f(e), U1(b, k))
28.11/9.11	   A^2 -> H(f(e), U1(e, c))
28.11/9.11	   A^2 -> H(f(e), U1(k, c))
28.11/9.11	   A^2 -> H(f(e), U1(c, e))
28.11/9.11	   A^2 -> H(f(e), U1(c, k))
28.11/9.11	   A^2 -> H(f(e), U1(k, k))
28.11/9.11	   A^2 -> H(f(e), U1(k, d))
28.11/9.11	   A^2 -> H(f(e), U1(d, k))
28.11/9.11	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.11	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.11	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.11	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.11	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.11	   A^2 -> H(U1(k, k), f(e))
28.11/9.11	   A^2 -> H(U1(k, k), f(k))
28.11/9.11	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.11	   A^2 -> H(f(k), U1(e, b))
28.11/9.11	   A^2 -> H(f(k), U1(k, b))
28.11/9.11	   A^2 -> H(f(k), U1(c, d))
28.11/9.11	   A^2 -> H(f(k), U1(d, c))
28.11/9.11	   A^2 -> H(f(k), U1(b, e))
28.11/9.11	   A^2 -> H(f(k), U1(b, k))
28.11/9.11	   A^2 -> H(f(k), U1(e, c))
28.11/9.11	   A^2 -> H(f(k), U1(k, c))
28.11/9.11	   A^2 -> H(f(k), U1(c, e))
28.11/9.11	   A^2 -> H(f(k), U1(c, k))
28.11/9.11	   A^2 -> H(f(k), U1(e, e))
28.11/9.11	   A^2 -> H(f(k), U1(k, d))
28.11/9.11	   A^2 -> H(f(k), U1(d, k))
28.11/9.11	   A^2 -> H(f(c), b)
28.11/9.11	   A^2 -> H(f(c), U1(e, d))
28.11/9.11	   A^2 -> H(f(c), U1(d, e))
28.11/9.11	   A^2 -> H(f(k), U1(k, k))
28.11/9.11	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.11	   A^2 -> H(U1(k, k), f(c))
28.11/9.11	   A^2 -> H(U1(k, k), f(d))
28.11/9.11	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.11	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.11	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.11	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.11	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.11	   A^2 -> H(U1(k, d), f(e))
28.11/9.11	   A^2 -> H(U1(k, d), f(k))
28.11/9.11	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.11	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.11	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.11	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.11	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.11	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.11	   A^2 -> H(U1(d, k), f(e))
28.11/9.11	   A^2 -> H(U1(d, k), f(k))
28.11/9.11	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.11	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.11	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.11	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.11	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.11	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.11	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.11	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.11	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.11	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.11	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.11	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.11	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.11	   A^2 -> H(f(d), b)
28.11/9.11	   A^2 -> H(f(d), U1(e, d))
28.11/9.11	   A^2 -> H(f(d), U1(d, e))
28.11/9.11	   A^2 -> H(f(d), c)
28.11/9.11	   A^2 -> H(f(d), U1(e, k))
28.11/9.11	   A^2 -> H(f(d), U1(k, e))
28.11/9.11	   A^2 -> H(f(d), e)
28.11/9.11	   A^2 -> H(f(a), d)
28.11/9.11	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.11	   A^2 -> H(f(c), c)
28.11/9.11	   A^2 -> H(f(c), U1(e, k))
28.11/9.11	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.11	   A^2 -> H(f(c), U1(k, e))
28.11/9.11	   A^2 -> H(f(c), U1(k, k))
28.11/9.11	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.11	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.11	   A^2 -> H(f(a), k)
28.11/9.11	   A^2 -> H(f(e), U1(e, e))
28.11/9.11	   A^2 -> H(f(c), e)
28.11/9.11	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.11	   A^2 -> H(f(d), U1(k, k))
28.11/9.11	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.11	   A^2 -> H(d, U1(b, b))
28.11/9.11	   A^2 -> H(d, f(c))
28.11/9.11	   A^2 -> H(d, f(d))
28.11/9.11	   A^2 -> H(a, U1(c, b))
28.11/9.11	   A^2 -> H(a, U1(d, b))
28.11/9.11	   A^2 -> H(a, U1(b, c))
28.11/9.11	   A^2 -> H(a, U1(b, d))
28.11/9.11	   A^2 -> H(a, U1(c, c))
28.11/9.11	   A^2 -> H(a, f(e))
28.11/9.11	   A^2 -> H(a, f(k))
28.11/9.11	   A^2 -> H(a, U1(d, d))
28.11/9.11	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.11	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.11	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.11	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.11	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.11	   A^2 -> H(U1(e, d), f(e))
28.11/9.11	   A^2 -> H(U1(e, d), f(k))
28.11/9.11	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.11	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.11	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.11	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.11	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.11	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.11	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.11	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.11	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.11	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.11	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.11	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.11	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.11	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.11	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.11	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.11	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.11	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.11	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.11	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.11	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.11	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.11	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.11	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.11	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.11	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.11	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.11	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.11	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.11	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.11	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.11	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.11	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.11	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.11	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.11	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.11	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.11	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.11	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.11	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.11	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.11	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.11	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.11	   A^2 -> H(U1(c, a), b)
28.11/9.11	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.11	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.11	   A^2 -> H(U1(c, a), c)
28.11/9.11	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.11	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.11	   A^2 -> H(U1(c, a), e)
28.11/9.11	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.11	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.11	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.11	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.11	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.11	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.11	   A^2 -> H(U1(d, e), f(e))
28.11/9.11	   A^2 -> H(U1(d, e), f(k))
28.11/9.11	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.11	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.11	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.11	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.11	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.11	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.11	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.11	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.11	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.11	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.11	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.11	   A^2 -> H(U1(d, a), b)
28.11/9.11	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.11	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.11	   A^2 -> H(U1(d, a), c)
28.11/9.11	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.11	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.11	   A^2 -> H(U1(d, a), e)
28.11/9.11	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.11	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.11	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.11	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.11	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.11	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.11	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.11	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.11	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.11	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.11	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.11	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.11	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.11	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.11	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.11	   A^2 -> H(U1(a, c), b)
28.11/9.11	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.11	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.11	   A^2 -> H(U1(a, c), c)
28.11/9.11	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.11	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.11	   A^2 -> H(U1(a, c), e)
28.11/9.11	
28.11/9.11	The TRS R consists of the following rules:
28.11/9.11	
28.11/9.11	   f(x) -> U1(x, x)
28.11/9.11	   U1(e, x) -> x
28.11/9.11	   a -> c
28.11/9.11	   a -> d
28.11/9.11	   b -> c
28.11/9.11	   b -> d
28.11/9.11	   d -> k
28.11/9.11	   c -> e
28.11/9.11	   c -> k
28.11/9.11	
28.11/9.11	Q is empty.
28.11/9.11	We have to consider all minimal (P,Q,R)-chains.
28.11/9.11	----------------------------------------
28.11/9.11	
28.11/9.11	(735) TransformationProof (EQUIVALENT)
28.11/9.11	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.11	
28.11/9.11	   (A^2 -> H(U1(c, c), U1(k, k)),A^2 -> H(U1(c, c), U1(k, k)))
28.11/9.11	   (A^2 -> H(U1(d, c), U1(k, k)),A^2 -> H(U1(d, c), U1(k, k)))
28.11/9.11	   (A^2 -> H(U1(a, e), U1(k, k)),A^2 -> H(U1(a, e), U1(k, k)))
28.11/9.11	   (A^2 -> H(U1(a, k), U1(k, k)),A^2 -> H(U1(a, k), U1(k, k)))
28.11/9.11	
28.11/9.11	
28.11/9.11	----------------------------------------
28.11/9.11	
28.11/9.11	(736)
28.11/9.11	Obligation:
28.11/9.11	Q DP problem:
28.11/9.11	The TRS P consists of the following rules:
28.11/9.11	
28.11/9.11	   H(x, x) -> G(x, x, f(k))
28.11/9.11	   G(d, x, x) -> A^2
28.11/9.11	   A^2 -> H(f(c), f(c))
28.11/9.11	   A^2 -> H(f(d), f(d))
28.11/9.11	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.11	   A^2 -> H(f(e), f(e))
28.11/9.11	   A^2 -> H(f(k), f(k))
28.11/9.11	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.11	   A^2 -> H(U1(a, c), U1(k, d))
28.11/9.11	   A^2 -> H(U1(a, c), U1(d, k))
28.11/9.11	   A^2 -> H(U1(a, d), U1(e, b))
28.11/9.11	   A^2 -> H(U1(a, d), U1(k, b))
28.11/9.11	   A^2 -> H(U1(a, d), U1(c, d))
28.11/9.11	   A^2 -> H(U1(a, d), U1(d, c))
28.11/9.11	   A^2 -> H(U1(a, d), U1(b, e))
28.11/9.11	   A^2 -> H(U1(a, d), U1(b, k))
28.11/9.11	   A^2 -> H(U1(a, d), U1(e, c))
28.11/9.11	   A^2 -> H(U1(a, d), U1(k, c))
28.11/9.11	   A^2 -> H(U1(a, d), U1(c, e))
28.11/9.11	   A^2 -> H(U1(a, d), U1(c, k))
28.11/9.11	   A^2 -> H(U1(a, d), U1(e, e))
28.11/9.11	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, d), U1(k, d))
28.11/9.11	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.11	   A^2 -> H(U1(a, a), b)
28.11/9.11	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.11	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.11	   A^2 -> H(U1(a, a), c)
28.11/9.11	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.11	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.11	   A^2 -> H(U1(a, a), e)
28.11/9.11	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.11	   A^2 -> H(k, f(b))
28.11/9.11	   A^2 -> H(c, U1(b, b))
28.11/9.11	   A^2 -> H(c, f(c))
28.11/9.11	   A^2 -> H(c, f(d))
28.11/9.11	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.11	   A^2 -> H(U1(e, k), f(c))
28.11/9.11	   A^2 -> H(U1(e, k), f(d))
28.11/9.11	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.11	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.11	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.11	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.11	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.11	   A^2 -> H(U1(e, c), f(e))
28.11/9.11	   A^2 -> H(U1(e, c), f(k))
28.11/9.11	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.11	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.11	   A^2 -> H(U1(k, e), f(c))
28.11/9.11	   A^2 -> H(U1(k, e), f(d))
28.11/9.11	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.11	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.11	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.11	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.11	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.11	   A^2 -> H(U1(k, c), f(e))
28.11/9.11	   A^2 -> H(U1(k, c), f(k))
28.11/9.11	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.11	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.11	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.11	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.11	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.11	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.11	   A^2 -> H(U1(c, e), f(e))
28.11/9.11	   A^2 -> H(U1(c, e), f(k))
28.11/9.11	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.11	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.11	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.11	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.11	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.11	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.11	   A^2 -> H(U1(c, k), f(e))
28.11/9.11	   A^2 -> H(U1(c, k), f(k))
28.11/9.11	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.11	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.11	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.11	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.11	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.11	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.11	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.11	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.11	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.11	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.11	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.11	   A^2 -> H(e, U1(b, b))
28.11/9.11	   A^2 -> H(e, f(c))
28.11/9.11	   A^2 -> H(e, f(d))
28.11/9.11	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.11	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.11	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.11	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.11	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.11	   A^2 -> H(U1(e, e), f(e))
28.11/9.11	   A^2 -> H(U1(e, e), f(k))
28.11/9.11	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.11	   A^2 -> H(f(e), U1(e, b))
28.11/9.11	   A^2 -> H(f(e), U1(k, b))
28.11/9.11	   A^2 -> H(f(e), U1(c, d))
28.11/9.11	   A^2 -> H(f(e), U1(d, c))
28.11/9.11	   A^2 -> H(f(e), U1(b, e))
28.11/9.11	   A^2 -> H(f(e), U1(b, k))
28.11/9.11	   A^2 -> H(f(e), U1(e, c))
28.11/9.11	   A^2 -> H(f(e), U1(k, c))
28.11/9.11	   A^2 -> H(f(e), U1(c, e))
28.11/9.11	   A^2 -> H(f(e), U1(c, k))
28.11/9.11	   A^2 -> H(f(e), U1(k, k))
28.11/9.11	   A^2 -> H(f(e), U1(k, d))
28.11/9.11	   A^2 -> H(f(e), U1(d, k))
28.11/9.11	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.11	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.11	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.11	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.11	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.11	   A^2 -> H(U1(k, k), f(e))
28.11/9.11	   A^2 -> H(U1(k, k), f(k))
28.11/9.11	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.11	   A^2 -> H(f(k), U1(e, b))
28.11/9.11	   A^2 -> H(f(k), U1(k, b))
28.11/9.11	   A^2 -> H(f(k), U1(c, d))
28.11/9.11	   A^2 -> H(f(k), U1(d, c))
28.11/9.11	   A^2 -> H(f(k), U1(b, e))
28.11/9.11	   A^2 -> H(f(k), U1(b, k))
28.11/9.11	   A^2 -> H(f(k), U1(e, c))
28.11/9.11	   A^2 -> H(f(k), U1(k, c))
28.11/9.11	   A^2 -> H(f(k), U1(c, e))
28.11/9.11	   A^2 -> H(f(k), U1(c, k))
28.11/9.11	   A^2 -> H(f(k), U1(e, e))
28.11/9.11	   A^2 -> H(f(k), U1(k, d))
28.11/9.11	   A^2 -> H(f(k), U1(d, k))
28.11/9.11	   A^2 -> H(f(c), b)
28.11/9.11	   A^2 -> H(f(c), U1(e, d))
28.11/9.11	   A^2 -> H(f(c), U1(d, e))
28.11/9.11	   A^2 -> H(f(k), U1(k, k))
28.11/9.11	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.11	   A^2 -> H(U1(k, k), f(c))
28.11/9.11	   A^2 -> H(U1(k, k), f(d))
28.11/9.11	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.11	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.11	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.11	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.11	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.11	   A^2 -> H(U1(k, d), f(e))
28.11/9.11	   A^2 -> H(U1(k, d), f(k))
28.11/9.11	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.11	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.11	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.11	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.11	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.11	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.11	   A^2 -> H(U1(d, k), f(e))
28.11/9.11	   A^2 -> H(U1(d, k), f(k))
28.11/9.11	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.11	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.11	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.11	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.11	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.11	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.11	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.11	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.11	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.11	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.11	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.11	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.11	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.11	   A^2 -> H(f(d), b)
28.11/9.11	   A^2 -> H(f(d), U1(e, d))
28.11/9.11	   A^2 -> H(f(d), U1(d, e))
28.11/9.11	   A^2 -> H(f(d), c)
28.11/9.11	   A^2 -> H(f(d), U1(e, k))
28.11/9.11	   A^2 -> H(f(d), U1(k, e))
28.11/9.11	   A^2 -> H(f(d), e)
28.11/9.11	   A^2 -> H(f(a), d)
28.11/9.11	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.11	   A^2 -> H(f(c), c)
28.11/9.11	   A^2 -> H(f(c), U1(e, k))
28.11/9.11	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.11	   A^2 -> H(f(c), U1(k, e))
28.11/9.11	   A^2 -> H(f(c), U1(k, k))
28.11/9.11	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.11	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.11	   A^2 -> H(f(a), k)
28.11/9.11	   A^2 -> H(f(e), U1(e, e))
28.11/9.11	   A^2 -> H(f(c), e)
28.11/9.11	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.11	   A^2 -> H(f(d), U1(k, k))
28.11/9.11	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.11	   A^2 -> H(d, U1(b, b))
28.11/9.11	   A^2 -> H(d, f(c))
28.11/9.11	   A^2 -> H(d, f(d))
28.11/9.11	   A^2 -> H(a, U1(c, b))
28.11/9.11	   A^2 -> H(a, U1(d, b))
28.11/9.11	   A^2 -> H(a, U1(b, c))
28.11/9.11	   A^2 -> H(a, U1(b, d))
28.11/9.11	   A^2 -> H(a, U1(c, c))
28.11/9.11	   A^2 -> H(a, f(e))
28.11/9.11	   A^2 -> H(a, f(k))
28.11/9.11	   A^2 -> H(a, U1(d, d))
28.11/9.11	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.11	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.11	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.11	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.11	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.11	   A^2 -> H(U1(e, d), f(e))
28.11/9.11	   A^2 -> H(U1(e, d), f(k))
28.11/9.11	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.11	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.11	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.11	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.11	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.11	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.11	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.11	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.11	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.11	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.11	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.11	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.11	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.11	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.11	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.11	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.11	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.11	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.11	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.11	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.11	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.11	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.11	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.11	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.11	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.11	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.11	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.11	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.11	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.11	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.11	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.11	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.11	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.11	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.11	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.11	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.11	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.11	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.11	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.11	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.11	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.11	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.11	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.11	   A^2 -> H(U1(c, a), b)
28.11/9.11	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.11	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.11	   A^2 -> H(U1(c, a), c)
28.11/9.11	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.11	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.11	   A^2 -> H(U1(c, a), e)
28.11/9.11	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.11	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.11	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.11	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.11	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.11	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.11	   A^2 -> H(U1(d, e), f(e))
28.11/9.11	   A^2 -> H(U1(d, e), f(k))
28.11/9.11	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.11	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.11	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.11	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.11	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.11	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.11	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.11	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.11	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.11	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.11	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.11	   A^2 -> H(U1(d, a), b)
28.11/9.11	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.11	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.11	   A^2 -> H(U1(d, a), c)
28.11/9.11	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.11	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.11	   A^2 -> H(U1(d, a), e)
28.11/9.11	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.11	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.11	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.11	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.11	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.11	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.11	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.11	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.11	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.11	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.11	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.11	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.11	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.11	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.11	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.11	   A^2 -> H(U1(a, c), b)
28.11/9.11	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.11	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.11	   A^2 -> H(U1(a, c), c)
28.11/9.11	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.11	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.11	   A^2 -> H(U1(a, c), e)
28.11/9.11	
28.11/9.11	The TRS R consists of the following rules:
28.11/9.11	
28.11/9.11	   f(x) -> U1(x, x)
28.11/9.11	   U1(e, x) -> x
28.11/9.11	   a -> c
28.11/9.11	   a -> d
28.11/9.11	   b -> c
28.11/9.11	   b -> d
28.11/9.11	   d -> k
28.11/9.11	   c -> e
28.11/9.11	   c -> k
28.11/9.11	
28.11/9.11	Q is empty.
28.11/9.11	We have to consider all minimal (P,Q,R)-chains.
28.11/9.11	----------------------------------------
28.11/9.11	
28.11/9.11	(737) TransformationProof (EQUIVALENT)
28.11/9.11	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.11	
28.11/9.11	   (A^2 -> H(U1(c, c), U1(k, d)),A^2 -> H(U1(c, c), U1(k, d)))
28.11/9.11	   (A^2 -> H(U1(d, c), U1(k, d)),A^2 -> H(U1(d, c), U1(k, d)))
28.11/9.11	   (A^2 -> H(U1(a, e), U1(k, d)),A^2 -> H(U1(a, e), U1(k, d)))
28.11/9.11	   (A^2 -> H(U1(a, k), U1(k, d)),A^2 -> H(U1(a, k), U1(k, d)))
28.11/9.11	   (A^2 -> H(U1(a, c), U1(k, k)),A^2 -> H(U1(a, c), U1(k, k)))
28.11/9.11	
28.11/9.11	
28.11/9.11	----------------------------------------
28.11/9.11	
28.11/9.11	(738)
28.11/9.11	Obligation:
28.11/9.11	Q DP problem:
28.11/9.11	The TRS P consists of the following rules:
28.11/9.11	
28.11/9.11	   H(x, x) -> G(x, x, f(k))
28.11/9.11	   G(d, x, x) -> A^2
28.11/9.11	   A^2 -> H(f(c), f(c))
28.11/9.11	   A^2 -> H(f(d), f(d))
28.11/9.11	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.11	   A^2 -> H(f(e), f(e))
28.11/9.11	   A^2 -> H(f(k), f(k))
28.11/9.11	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.11	   A^2 -> H(U1(a, c), U1(d, k))
28.11/9.11	   A^2 -> H(U1(a, d), U1(e, b))
28.11/9.11	   A^2 -> H(U1(a, d), U1(k, b))
28.11/9.11	   A^2 -> H(U1(a, d), U1(c, d))
28.11/9.11	   A^2 -> H(U1(a, d), U1(d, c))
28.11/9.11	   A^2 -> H(U1(a, d), U1(b, e))
28.11/9.11	   A^2 -> H(U1(a, d), U1(b, k))
28.11/9.11	   A^2 -> H(U1(a, d), U1(e, c))
28.11/9.11	   A^2 -> H(U1(a, d), U1(k, c))
28.11/9.11	   A^2 -> H(U1(a, d), U1(c, e))
28.11/9.11	   A^2 -> H(U1(a, d), U1(c, k))
28.11/9.11	   A^2 -> H(U1(a, d), U1(e, e))
28.11/9.11	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, d), U1(k, d))
28.11/9.11	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.11	   A^2 -> H(U1(a, a), b)
28.11/9.11	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.11	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.11	   A^2 -> H(U1(a, a), c)
28.11/9.11	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.11	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.11	   A^2 -> H(U1(a, a), e)
28.11/9.11	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.11	   A^2 -> H(k, f(b))
28.11/9.11	   A^2 -> H(c, U1(b, b))
28.11/9.11	   A^2 -> H(c, f(c))
28.11/9.11	   A^2 -> H(c, f(d))
28.11/9.11	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.11	   A^2 -> H(U1(e, k), f(c))
28.11/9.11	   A^2 -> H(U1(e, k), f(d))
28.11/9.11	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.11	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.11	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.11	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.11	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.11	   A^2 -> H(U1(e, c), f(e))
28.11/9.11	   A^2 -> H(U1(e, c), f(k))
28.11/9.11	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.11	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.11	   A^2 -> H(U1(k, e), f(c))
28.11/9.11	   A^2 -> H(U1(k, e), f(d))
28.11/9.11	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.11	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.11	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.11	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.11	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.11	   A^2 -> H(U1(k, c), f(e))
28.11/9.11	   A^2 -> H(U1(k, c), f(k))
28.11/9.11	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.11	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.11	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.11	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.11	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.11	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.11	   A^2 -> H(U1(c, e), f(e))
28.11/9.11	   A^2 -> H(U1(c, e), f(k))
28.11/9.11	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.11	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.11	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.11	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.11	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.11	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.11	   A^2 -> H(U1(c, k), f(e))
28.11/9.11	   A^2 -> H(U1(c, k), f(k))
28.11/9.11	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.11	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.11	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.11	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.11	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.11	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.11	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.11	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.11	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.11	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.11	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.11	   A^2 -> H(e, U1(b, b))
28.11/9.11	   A^2 -> H(e, f(c))
28.11/9.11	   A^2 -> H(e, f(d))
28.11/9.11	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.11	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.11	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.11	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.11	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.11	   A^2 -> H(U1(e, e), f(e))
28.11/9.11	   A^2 -> H(U1(e, e), f(k))
28.11/9.11	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.11	   A^2 -> H(f(e), U1(e, b))
28.11/9.11	   A^2 -> H(f(e), U1(k, b))
28.11/9.11	   A^2 -> H(f(e), U1(c, d))
28.11/9.11	   A^2 -> H(f(e), U1(d, c))
28.11/9.11	   A^2 -> H(f(e), U1(b, e))
28.11/9.11	   A^2 -> H(f(e), U1(b, k))
28.11/9.11	   A^2 -> H(f(e), U1(e, c))
28.11/9.11	   A^2 -> H(f(e), U1(k, c))
28.11/9.11	   A^2 -> H(f(e), U1(c, e))
28.11/9.11	   A^2 -> H(f(e), U1(c, k))
28.11/9.11	   A^2 -> H(f(e), U1(k, k))
28.11/9.11	   A^2 -> H(f(e), U1(k, d))
28.11/9.11	   A^2 -> H(f(e), U1(d, k))
28.11/9.11	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.11	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.11	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.11	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.11	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.11	   A^2 -> H(U1(k, k), f(e))
28.11/9.11	   A^2 -> H(U1(k, k), f(k))
28.11/9.11	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.11	   A^2 -> H(f(k), U1(e, b))
28.11/9.11	   A^2 -> H(f(k), U1(k, b))
28.11/9.11	   A^2 -> H(f(k), U1(c, d))
28.11/9.11	   A^2 -> H(f(k), U1(d, c))
28.11/9.11	   A^2 -> H(f(k), U1(b, e))
28.11/9.11	   A^2 -> H(f(k), U1(b, k))
28.11/9.11	   A^2 -> H(f(k), U1(e, c))
28.11/9.11	   A^2 -> H(f(k), U1(k, c))
28.11/9.11	   A^2 -> H(f(k), U1(c, e))
28.11/9.11	   A^2 -> H(f(k), U1(c, k))
28.11/9.11	   A^2 -> H(f(k), U1(e, e))
28.11/9.11	   A^2 -> H(f(k), U1(k, d))
28.11/9.11	   A^2 -> H(f(k), U1(d, k))
28.11/9.11	   A^2 -> H(f(c), b)
28.11/9.11	   A^2 -> H(f(c), U1(e, d))
28.11/9.11	   A^2 -> H(f(c), U1(d, e))
28.11/9.11	   A^2 -> H(f(k), U1(k, k))
28.11/9.11	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.11	   A^2 -> H(U1(k, k), f(c))
28.11/9.11	   A^2 -> H(U1(k, k), f(d))
28.11/9.11	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.11	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.11	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.11	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.11	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.11	   A^2 -> H(U1(k, d), f(e))
28.11/9.11	   A^2 -> H(U1(k, d), f(k))
28.11/9.11	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.11	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.11	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.11	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.11	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.11	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.11	   A^2 -> H(U1(d, k), f(e))
28.11/9.11	   A^2 -> H(U1(d, k), f(k))
28.11/9.11	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.11	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.11	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.11	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.11	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.11	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.11	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.11	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.11	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.11	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.11	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.11	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.11	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.11	   A^2 -> H(f(d), b)
28.11/9.11	   A^2 -> H(f(d), U1(e, d))
28.11/9.11	   A^2 -> H(f(d), U1(d, e))
28.11/9.11	   A^2 -> H(f(d), c)
28.11/9.11	   A^2 -> H(f(d), U1(e, k))
28.11/9.11	   A^2 -> H(f(d), U1(k, e))
28.11/9.11	   A^2 -> H(f(d), e)
28.11/9.11	   A^2 -> H(f(a), d)
28.11/9.11	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.11	   A^2 -> H(f(c), c)
28.11/9.11	   A^2 -> H(f(c), U1(e, k))
28.11/9.11	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.11	   A^2 -> H(f(c), U1(k, e))
28.11/9.11	   A^2 -> H(f(c), U1(k, k))
28.11/9.11	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.11	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.11	   A^2 -> H(f(a), k)
28.11/9.11	   A^2 -> H(f(e), U1(e, e))
28.11/9.11	   A^2 -> H(f(c), e)
28.11/9.11	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.11	   A^2 -> H(f(d), U1(k, k))
28.11/9.11	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.11	   A^2 -> H(d, U1(b, b))
28.11/9.11	   A^2 -> H(d, f(c))
28.11/9.11	   A^2 -> H(d, f(d))
28.11/9.11	   A^2 -> H(a, U1(c, b))
28.11/9.11	   A^2 -> H(a, U1(d, b))
28.11/9.11	   A^2 -> H(a, U1(b, c))
28.11/9.11	   A^2 -> H(a, U1(b, d))
28.11/9.11	   A^2 -> H(a, U1(c, c))
28.11/9.11	   A^2 -> H(a, f(e))
28.11/9.11	   A^2 -> H(a, f(k))
28.11/9.11	   A^2 -> H(a, U1(d, d))
28.11/9.11	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.11	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.11	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.11	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.11	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.11	   A^2 -> H(U1(e, d), f(e))
28.11/9.11	   A^2 -> H(U1(e, d), f(k))
28.11/9.11	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.11	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.11	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.11	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.11	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.11	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.11	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.11	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.11	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.11	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.11	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.11	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.11	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.11	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.11	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.11	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.11	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.11	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.11	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.11	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.11	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.11	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.11	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.11	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.11	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.11	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.11	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.11	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.11	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.11	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.11	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.11	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.11	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.11	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.11	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.11	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.11	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.11	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.11	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.11	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.11	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.11	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.11	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.11	   A^2 -> H(U1(c, a), b)
28.11/9.11	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.11	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.11	   A^2 -> H(U1(c, a), c)
28.11/9.11	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.11	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.11	   A^2 -> H(U1(c, a), e)
28.11/9.11	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.11	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.11	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.11	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.11	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.11	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.11	   A^2 -> H(U1(d, e), f(e))
28.11/9.11	   A^2 -> H(U1(d, e), f(k))
28.11/9.11	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.11	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.11	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.11	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.11	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.11	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.11	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.11	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.11	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.11	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.11	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.11	   A^2 -> H(U1(d, a), b)
28.11/9.11	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.11	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.11	   A^2 -> H(U1(d, a), c)
28.11/9.11	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.11	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.11	   A^2 -> H(U1(d, a), e)
28.11/9.11	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.11	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.11	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.11	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.11	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.11	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.11	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.11	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.11	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.11	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.11	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.11	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.11	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.11	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.11	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.11	   A^2 -> H(U1(a, c), b)
28.11/9.11	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.11	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.11	   A^2 -> H(U1(a, c), c)
28.11/9.11	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.11	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.11	   A^2 -> H(U1(a, c), e)
28.11/9.11	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.11	
28.11/9.11	The TRS R consists of the following rules:
28.11/9.11	
28.11/9.11	   f(x) -> U1(x, x)
28.11/9.11	   U1(e, x) -> x
28.11/9.11	   a -> c
28.11/9.11	   a -> d
28.11/9.11	   b -> c
28.11/9.11	   b -> d
28.11/9.11	   d -> k
28.11/9.11	   c -> e
28.11/9.11	   c -> k
28.11/9.11	
28.11/9.11	Q is empty.
28.11/9.11	We have to consider all minimal (P,Q,R)-chains.
28.11/9.11	----------------------------------------
28.11/9.11	
28.11/9.11	(739) TransformationProof (EQUIVALENT)
28.11/9.11	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.11	
28.11/9.11	   (A^2 -> H(U1(c, c), U1(d, k)),A^2 -> H(U1(c, c), U1(d, k)))
28.11/9.11	   (A^2 -> H(U1(d, c), U1(d, k)),A^2 -> H(U1(d, c), U1(d, k)))
28.11/9.11	   (A^2 -> H(U1(a, e), U1(d, k)),A^2 -> H(U1(a, e), U1(d, k)))
28.11/9.11	   (A^2 -> H(U1(a, k), U1(d, k)),A^2 -> H(U1(a, k), U1(d, k)))
28.11/9.11	   (A^2 -> H(U1(a, c), U1(k, k)),A^2 -> H(U1(a, c), U1(k, k)))
28.11/9.11	
28.11/9.11	
28.11/9.11	----------------------------------------
28.11/9.11	
28.11/9.11	(740)
28.11/9.11	Obligation:
28.11/9.11	Q DP problem:
28.11/9.11	The TRS P consists of the following rules:
28.11/9.11	
28.11/9.11	   H(x, x) -> G(x, x, f(k))
28.11/9.11	   G(d, x, x) -> A^2
28.11/9.11	   A^2 -> H(f(c), f(c))
28.11/9.11	   A^2 -> H(f(d), f(d))
28.11/9.11	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.11	   A^2 -> H(f(e), f(e))
28.11/9.11	   A^2 -> H(f(k), f(k))
28.11/9.11	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.11	   A^2 -> H(U1(a, d), U1(e, b))
28.11/9.11	   A^2 -> H(U1(a, d), U1(k, b))
28.11/9.11	   A^2 -> H(U1(a, d), U1(c, d))
28.11/9.11	   A^2 -> H(U1(a, d), U1(d, c))
28.11/9.11	   A^2 -> H(U1(a, d), U1(b, e))
28.11/9.11	   A^2 -> H(U1(a, d), U1(b, k))
28.11/9.11	   A^2 -> H(U1(a, d), U1(e, c))
28.11/9.11	   A^2 -> H(U1(a, d), U1(k, c))
28.11/9.11	   A^2 -> H(U1(a, d), U1(c, e))
28.11/9.11	   A^2 -> H(U1(a, d), U1(c, k))
28.11/9.11	   A^2 -> H(U1(a, d), U1(e, e))
28.11/9.11	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, d), U1(k, d))
28.11/9.11	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.11	   A^2 -> H(U1(a, a), b)
28.11/9.11	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.11	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.11	   A^2 -> H(U1(a, a), c)
28.11/9.11	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.11	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.11	   A^2 -> H(U1(a, a), e)
28.11/9.11	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.11	   A^2 -> H(k, f(b))
28.11/9.11	   A^2 -> H(c, U1(b, b))
28.11/9.11	   A^2 -> H(c, f(c))
28.11/9.11	   A^2 -> H(c, f(d))
28.11/9.11	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.11	   A^2 -> H(U1(e, k), f(c))
28.11/9.11	   A^2 -> H(U1(e, k), f(d))
28.11/9.11	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.11	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.11	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.11	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.11	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.11	   A^2 -> H(U1(e, c), f(e))
28.11/9.11	   A^2 -> H(U1(e, c), f(k))
28.11/9.11	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.11	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.11	   A^2 -> H(U1(k, e), f(c))
28.11/9.11	   A^2 -> H(U1(k, e), f(d))
28.11/9.11	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.11	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.11	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.11	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.11	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.11	   A^2 -> H(U1(k, c), f(e))
28.11/9.11	   A^2 -> H(U1(k, c), f(k))
28.11/9.11	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.11	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.11	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.11	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.11	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.11	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.11	   A^2 -> H(U1(c, e), f(e))
28.11/9.11	   A^2 -> H(U1(c, e), f(k))
28.11/9.11	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.11	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.11	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.11	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.11	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.11	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.11	   A^2 -> H(U1(c, k), f(e))
28.11/9.11	   A^2 -> H(U1(c, k), f(k))
28.11/9.11	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.11	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.11	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.11	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.11	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.11	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.11	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.11	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.11	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.11	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.11	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.11	   A^2 -> H(e, U1(b, b))
28.11/9.11	   A^2 -> H(e, f(c))
28.11/9.11	   A^2 -> H(e, f(d))
28.11/9.11	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.11	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.11	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.11	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.11	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.11	   A^2 -> H(U1(e, e), f(e))
28.11/9.11	   A^2 -> H(U1(e, e), f(k))
28.11/9.11	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.11	   A^2 -> H(f(e), U1(e, b))
28.11/9.11	   A^2 -> H(f(e), U1(k, b))
28.11/9.11	   A^2 -> H(f(e), U1(c, d))
28.11/9.11	   A^2 -> H(f(e), U1(d, c))
28.11/9.11	   A^2 -> H(f(e), U1(b, e))
28.11/9.11	   A^2 -> H(f(e), U1(b, k))
28.11/9.11	   A^2 -> H(f(e), U1(e, c))
28.11/9.11	   A^2 -> H(f(e), U1(k, c))
28.11/9.11	   A^2 -> H(f(e), U1(c, e))
28.11/9.11	   A^2 -> H(f(e), U1(c, k))
28.11/9.11	   A^2 -> H(f(e), U1(k, k))
28.11/9.11	   A^2 -> H(f(e), U1(k, d))
28.11/9.11	   A^2 -> H(f(e), U1(d, k))
28.11/9.11	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.11	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.11	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.11	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.11	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.11	   A^2 -> H(U1(k, k), f(e))
28.11/9.11	   A^2 -> H(U1(k, k), f(k))
28.11/9.11	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.11	   A^2 -> H(f(k), U1(e, b))
28.11/9.11	   A^2 -> H(f(k), U1(k, b))
28.11/9.11	   A^2 -> H(f(k), U1(c, d))
28.11/9.11	   A^2 -> H(f(k), U1(d, c))
28.11/9.11	   A^2 -> H(f(k), U1(b, e))
28.11/9.11	   A^2 -> H(f(k), U1(b, k))
28.11/9.11	   A^2 -> H(f(k), U1(e, c))
28.11/9.11	   A^2 -> H(f(k), U1(k, c))
28.11/9.11	   A^2 -> H(f(k), U1(c, e))
28.11/9.11	   A^2 -> H(f(k), U1(c, k))
28.11/9.11	   A^2 -> H(f(k), U1(e, e))
28.11/9.11	   A^2 -> H(f(k), U1(k, d))
28.11/9.11	   A^2 -> H(f(k), U1(d, k))
28.11/9.11	   A^2 -> H(f(c), b)
28.11/9.11	   A^2 -> H(f(c), U1(e, d))
28.11/9.11	   A^2 -> H(f(c), U1(d, e))
28.11/9.11	   A^2 -> H(f(k), U1(k, k))
28.11/9.11	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.11	   A^2 -> H(U1(k, k), f(c))
28.11/9.11	   A^2 -> H(U1(k, k), f(d))
28.11/9.11	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.11	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.11	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.11	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.11	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.11	   A^2 -> H(U1(k, d), f(e))
28.11/9.11	   A^2 -> H(U1(k, d), f(k))
28.11/9.11	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.11	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.11	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.11	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.11	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.11	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.11	   A^2 -> H(U1(d, k), f(e))
28.11/9.11	   A^2 -> H(U1(d, k), f(k))
28.11/9.11	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.11	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.11	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.11	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.11	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.11	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.11	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.11	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.11	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.11	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.11	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.11	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.11	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.11	   A^2 -> H(f(d), b)
28.11/9.11	   A^2 -> H(f(d), U1(e, d))
28.11/9.11	   A^2 -> H(f(d), U1(d, e))
28.11/9.11	   A^2 -> H(f(d), c)
28.11/9.11	   A^2 -> H(f(d), U1(e, k))
28.11/9.11	   A^2 -> H(f(d), U1(k, e))
28.11/9.11	   A^2 -> H(f(d), e)
28.11/9.11	   A^2 -> H(f(a), d)
28.11/9.11	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.11	   A^2 -> H(f(c), c)
28.11/9.11	   A^2 -> H(f(c), U1(e, k))
28.11/9.11	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.11	   A^2 -> H(f(c), U1(k, e))
28.11/9.11	   A^2 -> H(f(c), U1(k, k))
28.11/9.11	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.11	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.11	   A^2 -> H(f(a), k)
28.11/9.11	   A^2 -> H(f(e), U1(e, e))
28.11/9.11	   A^2 -> H(f(c), e)
28.11/9.11	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.11	   A^2 -> H(f(d), U1(k, k))
28.11/9.11	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.11	   A^2 -> H(d, U1(b, b))
28.11/9.11	   A^2 -> H(d, f(c))
28.11/9.11	   A^2 -> H(d, f(d))
28.11/9.11	   A^2 -> H(a, U1(c, b))
28.11/9.11	   A^2 -> H(a, U1(d, b))
28.11/9.11	   A^2 -> H(a, U1(b, c))
28.11/9.11	   A^2 -> H(a, U1(b, d))
28.11/9.11	   A^2 -> H(a, U1(c, c))
28.11/9.11	   A^2 -> H(a, f(e))
28.11/9.11	   A^2 -> H(a, f(k))
28.11/9.11	   A^2 -> H(a, U1(d, d))
28.11/9.11	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.11	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.11	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.11	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.11	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.11	   A^2 -> H(U1(e, d), f(e))
28.11/9.11	   A^2 -> H(U1(e, d), f(k))
28.11/9.11	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.11	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.11	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.11	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.11	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.11	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.11	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.11	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.11	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.11	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.11	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.11	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.11	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.11	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.11	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.11	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.11	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.11	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.11	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.11	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.11	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.11	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.11	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.11	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.11	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.11	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.11	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.11	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.11	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.11	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.11	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.11	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.11	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.11	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.11	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.11	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.11	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.11	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.11	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.11	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.11	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.11	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.11	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.11	   A^2 -> H(U1(c, a), b)
28.11/9.11	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.11	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.11	   A^2 -> H(U1(c, a), c)
28.11/9.11	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.11	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.11	   A^2 -> H(U1(c, a), e)
28.11/9.11	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.11	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.11	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.11	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.11	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.11	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.11	   A^2 -> H(U1(d, e), f(e))
28.11/9.11	   A^2 -> H(U1(d, e), f(k))
28.11/9.11	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.11	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.11	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.11	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.11	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.11	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.11	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.11	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.11	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.11	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.11	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.11	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.11	   A^2 -> H(U1(d, a), b)
28.11/9.11	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.11	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.11	   A^2 -> H(U1(d, a), c)
28.11/9.11	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.11	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.11	   A^2 -> H(U1(d, a), e)
28.11/9.11	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.11	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.11	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.11	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.11	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.11	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.11	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.11	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.11	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.11	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.11	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.11	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.11	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.11	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.11	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.11	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.11	   A^2 -> H(U1(a, c), b)
28.11/9.11	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.11	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.11	   A^2 -> H(U1(a, c), c)
28.11/9.11	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.11	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.11	   A^2 -> H(U1(a, c), e)
28.11/9.11	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.11	
28.11/9.11	The TRS R consists of the following rules:
28.11/9.11	
28.11/9.11	   f(x) -> U1(x, x)
28.11/9.11	   U1(e, x) -> x
28.11/9.11	   a -> c
28.11/9.11	   a -> d
28.11/9.11	   b -> c
28.11/9.11	   b -> d
28.11/9.11	   d -> k
28.11/9.11	   c -> e
28.11/9.11	   c -> k
28.11/9.11	
28.11/9.11	Q is empty.
28.11/9.11	We have to consider all minimal (P,Q,R)-chains.
28.11/9.11	----------------------------------------
28.11/9.11	
28.11/9.11	(741) TransformationProof (EQUIVALENT)
28.11/9.11	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.11	
28.11/9.11	   (A^2 -> H(U1(c, d), U1(e, b)),A^2 -> H(U1(c, d), U1(e, b)))
28.11/9.11	   (A^2 -> H(U1(d, d), U1(e, b)),A^2 -> H(U1(d, d), U1(e, b)))
28.11/9.11	   (A^2 -> H(U1(a, k), U1(e, b)),A^2 -> H(U1(a, k), U1(e, b)))
28.11/9.11	   (A^2 -> H(U1(a, d), b),A^2 -> H(U1(a, d), b))
28.11/9.11	   (A^2 -> H(U1(a, d), U1(e, c)),A^2 -> H(U1(a, d), U1(e, c)))
28.11/9.11	   (A^2 -> H(U1(a, d), U1(e, d)),A^2 -> H(U1(a, d), U1(e, d)))
28.11/9.11	
28.11/9.11	
28.11/9.11	----------------------------------------
28.11/9.11	
28.11/9.11	(742)
28.11/9.11	Obligation:
28.11/9.11	Q DP problem:
28.11/9.11	The TRS P consists of the following rules:
28.11/9.11	
28.11/9.11	   H(x, x) -> G(x, x, f(k))
28.11/9.12	   G(d, x, x) -> A^2
28.11/9.12	   A^2 -> H(f(c), f(c))
28.11/9.12	   A^2 -> H(f(d), f(d))
28.11/9.12	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.12	   A^2 -> H(f(e), f(e))
28.11/9.12	   A^2 -> H(f(k), f(k))
28.11/9.12	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.12	   A^2 -> H(U1(a, d), U1(k, b))
28.11/9.12	   A^2 -> H(U1(a, d), U1(c, d))
28.11/9.12	   A^2 -> H(U1(a, d), U1(d, c))
28.11/9.12	   A^2 -> H(U1(a, d), U1(b, e))
28.11/9.12	   A^2 -> H(U1(a, d), U1(b, k))
28.11/9.12	   A^2 -> H(U1(a, d), U1(e, c))
28.11/9.12	   A^2 -> H(U1(a, d), U1(k, c))
28.11/9.12	   A^2 -> H(U1(a, d), U1(c, e))
28.11/9.12	   A^2 -> H(U1(a, d), U1(c, k))
28.11/9.12	   A^2 -> H(U1(a, d), U1(e, e))
28.11/9.12	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.12	   A^2 -> H(U1(a, d), U1(k, d))
28.11/9.12	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.12	   A^2 -> H(U1(a, a), b)
28.11/9.12	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.12	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.12	   A^2 -> H(U1(a, a), c)
28.11/9.12	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.12	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.12	   A^2 -> H(U1(a, a), e)
28.11/9.12	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.12	   A^2 -> H(k, f(b))
28.11/9.12	   A^2 -> H(c, U1(b, b))
28.11/9.12	   A^2 -> H(c, f(c))
28.11/9.12	   A^2 -> H(c, f(d))
28.11/9.12	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.12	   A^2 -> H(U1(e, k), f(c))
28.11/9.12	   A^2 -> H(U1(e, k), f(d))
28.11/9.12	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.12	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.12	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.12	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.12	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.12	   A^2 -> H(U1(e, c), f(e))
28.11/9.12	   A^2 -> H(U1(e, c), f(k))
28.11/9.12	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.12	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.12	   A^2 -> H(U1(k, e), f(c))
28.11/9.12	   A^2 -> H(U1(k, e), f(d))
28.11/9.12	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.12	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.12	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.12	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.12	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.12	   A^2 -> H(U1(k, c), f(e))
28.11/9.12	   A^2 -> H(U1(k, c), f(k))
28.11/9.12	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.12	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.12	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.12	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.12	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.12	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.12	   A^2 -> H(U1(c, e), f(e))
28.11/9.12	   A^2 -> H(U1(c, e), f(k))
28.11/9.12	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.12	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.12	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.12	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.12	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.12	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.12	   A^2 -> H(U1(c, k), f(e))
28.11/9.12	   A^2 -> H(U1(c, k), f(k))
28.11/9.12	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.12	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.12	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.12	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.12	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.12	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.12	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.12	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.12	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.12	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.12	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.12	   A^2 -> H(e, U1(b, b))
28.11/9.12	   A^2 -> H(e, f(c))
28.11/9.12	   A^2 -> H(e, f(d))
28.11/9.12	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.12	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.12	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.12	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.12	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.12	   A^2 -> H(U1(e, e), f(e))
28.11/9.12	   A^2 -> H(U1(e, e), f(k))
28.11/9.12	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.12	   A^2 -> H(f(e), U1(e, b))
28.11/9.12	   A^2 -> H(f(e), U1(k, b))
28.11/9.12	   A^2 -> H(f(e), U1(c, d))
28.11/9.12	   A^2 -> H(f(e), U1(d, c))
28.11/9.12	   A^2 -> H(f(e), U1(b, e))
28.11/9.12	   A^2 -> H(f(e), U1(b, k))
28.11/9.12	   A^2 -> H(f(e), U1(e, c))
28.11/9.12	   A^2 -> H(f(e), U1(k, c))
28.11/9.12	   A^2 -> H(f(e), U1(c, e))
28.11/9.12	   A^2 -> H(f(e), U1(c, k))
28.11/9.12	   A^2 -> H(f(e), U1(k, k))
28.11/9.12	   A^2 -> H(f(e), U1(k, d))
28.11/9.12	   A^2 -> H(f(e), U1(d, k))
28.11/9.13	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.13	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.13	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.13	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.13	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.13	   A^2 -> H(U1(k, k), f(e))
28.11/9.13	   A^2 -> H(U1(k, k), f(k))
28.11/9.13	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.13	   A^2 -> H(f(k), U1(e, b))
28.11/9.13	   A^2 -> H(f(k), U1(k, b))
28.11/9.13	   A^2 -> H(f(k), U1(c, d))
28.11/9.13	   A^2 -> H(f(k), U1(d, c))
28.11/9.13	   A^2 -> H(f(k), U1(b, e))
28.11/9.13	   A^2 -> H(f(k), U1(b, k))
28.11/9.13	   A^2 -> H(f(k), U1(e, c))
28.11/9.13	   A^2 -> H(f(k), U1(k, c))
28.11/9.13	   A^2 -> H(f(k), U1(c, e))
28.11/9.13	   A^2 -> H(f(k), U1(c, k))
28.11/9.13	   A^2 -> H(f(k), U1(e, e))
28.11/9.13	   A^2 -> H(f(k), U1(k, d))
28.11/9.13	   A^2 -> H(f(k), U1(d, k))
28.11/9.13	   A^2 -> H(f(c), b)
28.11/9.13	   A^2 -> H(f(c), U1(e, d))
28.11/9.13	   A^2 -> H(f(c), U1(d, e))
28.11/9.13	   A^2 -> H(f(k), U1(k, k))
28.11/9.13	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.13	   A^2 -> H(U1(k, k), f(c))
28.11/9.13	   A^2 -> H(U1(k, k), f(d))
28.11/9.13	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.13	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.13	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.13	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.13	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.13	   A^2 -> H(U1(k, d), f(e))
28.11/9.13	   A^2 -> H(U1(k, d), f(k))
28.11/9.13	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.13	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.13	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.13	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.13	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.13	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.13	   A^2 -> H(U1(d, k), f(e))
28.11/9.13	   A^2 -> H(U1(d, k), f(k))
28.11/9.13	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.13	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.13	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.13	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.13	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.13	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.13	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.13	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.13	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.13	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.13	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.13	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.13	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.13	   A^2 -> H(f(d), b)
28.11/9.13	   A^2 -> H(f(d), U1(e, d))
28.11/9.13	   A^2 -> H(f(d), U1(d, e))
28.11/9.13	   A^2 -> H(f(d), c)
28.11/9.13	   A^2 -> H(f(d), U1(e, k))
28.11/9.13	   A^2 -> H(f(d), U1(k, e))
28.11/9.13	   A^2 -> H(f(d), e)
28.11/9.13	   A^2 -> H(f(a), d)
28.11/9.13	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.13	   A^2 -> H(f(c), c)
28.11/9.13	   A^2 -> H(f(c), U1(e, k))
28.11/9.13	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.13	   A^2 -> H(f(c), U1(k, e))
28.11/9.13	   A^2 -> H(f(c), U1(k, k))
28.11/9.13	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.13	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.13	   A^2 -> H(f(a), k)
28.11/9.13	   A^2 -> H(f(e), U1(e, e))
28.11/9.13	   A^2 -> H(f(c), e)
28.11/9.13	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.13	   A^2 -> H(f(d), U1(k, k))
28.11/9.13	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.13	   A^2 -> H(d, U1(b, b))
28.11/9.13	   A^2 -> H(d, f(c))
28.11/9.13	   A^2 -> H(d, f(d))
28.11/9.13	   A^2 -> H(a, U1(c, b))
28.11/9.13	   A^2 -> H(a, U1(d, b))
28.11/9.13	   A^2 -> H(a, U1(b, c))
28.11/9.13	   A^2 -> H(a, U1(b, d))
28.11/9.13	   A^2 -> H(a, U1(c, c))
28.11/9.13	   A^2 -> H(a, f(e))
28.11/9.13	   A^2 -> H(a, f(k))
28.11/9.13	   A^2 -> H(a, U1(d, d))
28.11/9.13	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.13	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.13	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.13	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.13	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.13	   A^2 -> H(U1(e, d), f(e))
28.11/9.13	   A^2 -> H(U1(e, d), f(k))
28.11/9.13	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.13	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.13	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.13	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.13	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.13	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.13	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.13	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.13	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.13	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.13	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.13	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.13	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.13	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.13	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.13	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.13	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.13	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.13	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.13	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.13	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.13	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.13	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.13	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.13	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.13	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.13	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.13	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.13	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.13	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.13	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.13	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.13	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.13	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.13	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.13	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.13	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.13	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.13	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.13	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.13	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.13	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.13	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.13	   A^2 -> H(U1(c, a), b)
28.11/9.13	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.13	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.13	   A^2 -> H(U1(c, a), c)
28.11/9.13	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.13	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.13	   A^2 -> H(U1(c, a), e)
28.11/9.13	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.13	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.13	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.13	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.13	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.13	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.13	   A^2 -> H(U1(d, e), f(e))
28.11/9.13	   A^2 -> H(U1(d, e), f(k))
28.11/9.13	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.13	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.13	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.13	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.13	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.13	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.13	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.13	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.13	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.13	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.13	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.13	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.13	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.13	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.13	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.13	   A^2 -> H(U1(d, a), b)
28.11/9.13	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.13	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.13	   A^2 -> H(U1(d, a), c)
28.11/9.13	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.13	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.13	   A^2 -> H(U1(d, a), e)
28.11/9.13	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.13	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.13	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.13	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.13	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.13	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.13	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.13	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.13	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.13	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.13	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.13	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.13	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.13	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.13	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.13	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.13	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.13	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.13	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.13	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.13	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.13	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.13	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.13	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.13	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.13	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.13	   A^2 -> H(U1(a, c), b)
28.11/9.13	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.13	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.13	   A^2 -> H(U1(a, c), c)
28.11/9.13	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.13	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.13	   A^2 -> H(U1(a, c), e)
28.11/9.13	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, d), b)
28.11/9.13	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.13	
28.11/9.13	The TRS R consists of the following rules:
28.11/9.13	
28.11/9.13	   f(x) -> U1(x, x)
28.11/9.13	   U1(e, x) -> x
28.11/9.13	   a -> c
28.11/9.13	   a -> d
28.11/9.13	   b -> c
28.11/9.13	   b -> d
28.11/9.13	   d -> k
28.11/9.13	   c -> e
28.11/9.13	   c -> k
28.11/9.13	
28.11/9.13	Q is empty.
28.11/9.13	We have to consider all minimal (P,Q,R)-chains.
28.11/9.13	----------------------------------------
28.11/9.13	
28.11/9.13	(743) TransformationProof (EQUIVALENT)
28.11/9.13	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.13	
28.11/9.13	   (A^2 -> H(U1(c, d), U1(k, b)),A^2 -> H(U1(c, d), U1(k, b)))
28.11/9.13	   (A^2 -> H(U1(d, d), U1(k, b)),A^2 -> H(U1(d, d), U1(k, b)))
28.11/9.13	   (A^2 -> H(U1(a, k), U1(k, b)),A^2 -> H(U1(a, k), U1(k, b)))
28.11/9.13	   (A^2 -> H(U1(a, d), U1(k, c)),A^2 -> H(U1(a, d), U1(k, c)))
28.11/9.13	   (A^2 -> H(U1(a, d), U1(k, d)),A^2 -> H(U1(a, d), U1(k, d)))
28.11/9.13	
28.11/9.13	
28.11/9.13	----------------------------------------
28.11/9.13	
28.11/9.13	(744)
28.11/9.13	Obligation:
28.11/9.13	Q DP problem:
28.11/9.13	The TRS P consists of the following rules:
28.11/9.13	
28.11/9.13	   H(x, x) -> G(x, x, f(k))
28.11/9.13	   G(d, x, x) -> A^2
28.11/9.13	   A^2 -> H(f(c), f(c))
28.11/9.13	   A^2 -> H(f(d), f(d))
28.11/9.13	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.13	   A^2 -> H(f(e), f(e))
28.11/9.13	   A^2 -> H(f(k), f(k))
28.11/9.13	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.13	   A^2 -> H(U1(a, d), U1(c, d))
28.11/9.13	   A^2 -> H(U1(a, d), U1(d, c))
28.11/9.13	   A^2 -> H(U1(a, d), U1(b, e))
28.11/9.13	   A^2 -> H(U1(a, d), U1(b, k))
28.11/9.13	   A^2 -> H(U1(a, d), U1(e, c))
28.11/9.13	   A^2 -> H(U1(a, d), U1(k, c))
28.11/9.13	   A^2 -> H(U1(a, d), U1(c, e))
28.11/9.13	   A^2 -> H(U1(a, d), U1(c, k))
28.11/9.13	   A^2 -> H(U1(a, d), U1(e, e))
28.11/9.13	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, d), U1(k, d))
28.11/9.13	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.13	   A^2 -> H(U1(a, a), b)
28.11/9.13	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.13	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.13	   A^2 -> H(U1(a, a), c)
28.11/9.13	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.13	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.13	   A^2 -> H(U1(a, a), e)
28.11/9.13	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.13	   A^2 -> H(k, f(b))
28.11/9.13	   A^2 -> H(c, U1(b, b))
28.11/9.13	   A^2 -> H(c, f(c))
28.11/9.13	   A^2 -> H(c, f(d))
28.11/9.13	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.13	   A^2 -> H(U1(e, k), f(c))
28.11/9.13	   A^2 -> H(U1(e, k), f(d))
28.11/9.13	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.13	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.13	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.13	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.13	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.13	   A^2 -> H(U1(e, c), f(e))
28.11/9.13	   A^2 -> H(U1(e, c), f(k))
28.11/9.13	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.13	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.13	   A^2 -> H(U1(k, e), f(c))
28.11/9.13	   A^2 -> H(U1(k, e), f(d))
28.11/9.13	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.13	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.13	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.13	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.13	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.13	   A^2 -> H(U1(k, c), f(e))
28.11/9.13	   A^2 -> H(U1(k, c), f(k))
28.11/9.13	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.13	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.13	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.13	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.13	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.13	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.13	   A^2 -> H(U1(c, e), f(e))
28.11/9.13	   A^2 -> H(U1(c, e), f(k))
28.11/9.13	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.13	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.13	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.13	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.13	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.13	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.13	   A^2 -> H(U1(c, k), f(e))
28.11/9.13	   A^2 -> H(U1(c, k), f(k))
28.11/9.13	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.13	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.13	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.13	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.13	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.13	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.13	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.13	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.13	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.13	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.13	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.13	   A^2 -> H(e, U1(b, b))
28.11/9.13	   A^2 -> H(e, f(c))
28.11/9.13	   A^2 -> H(e, f(d))
28.11/9.13	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.13	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.13	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.13	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.13	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.13	   A^2 -> H(U1(e, e), f(e))
28.11/9.13	   A^2 -> H(U1(e, e), f(k))
28.11/9.13	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.13	   A^2 -> H(f(e), U1(e, b))
28.11/9.13	   A^2 -> H(f(e), U1(k, b))
28.11/9.13	   A^2 -> H(f(e), U1(c, d))
28.11/9.13	   A^2 -> H(f(e), U1(d, c))
28.11/9.13	   A^2 -> H(f(e), U1(b, e))
28.11/9.13	   A^2 -> H(f(e), U1(b, k))
28.11/9.13	   A^2 -> H(f(e), U1(e, c))
28.11/9.13	   A^2 -> H(f(e), U1(k, c))
28.11/9.13	   A^2 -> H(f(e), U1(c, e))
28.11/9.13	   A^2 -> H(f(e), U1(c, k))
28.11/9.13	   A^2 -> H(f(e), U1(k, k))
28.11/9.13	   A^2 -> H(f(e), U1(k, d))
28.11/9.13	   A^2 -> H(f(e), U1(d, k))
28.11/9.13	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.13	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.13	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.13	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.13	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.13	   A^2 -> H(U1(k, k), f(e))
28.11/9.13	   A^2 -> H(U1(k, k), f(k))
28.11/9.13	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.13	   A^2 -> H(f(k), U1(e, b))
28.11/9.13	   A^2 -> H(f(k), U1(k, b))
28.11/9.13	   A^2 -> H(f(k), U1(c, d))
28.11/9.13	   A^2 -> H(f(k), U1(d, c))
28.11/9.13	   A^2 -> H(f(k), U1(b, e))
28.11/9.13	   A^2 -> H(f(k), U1(b, k))
28.11/9.13	   A^2 -> H(f(k), U1(e, c))
28.11/9.13	   A^2 -> H(f(k), U1(k, c))
28.11/9.13	   A^2 -> H(f(k), U1(c, e))
28.11/9.13	   A^2 -> H(f(k), U1(c, k))
28.11/9.13	   A^2 -> H(f(k), U1(e, e))
28.11/9.13	   A^2 -> H(f(k), U1(k, d))
28.11/9.13	   A^2 -> H(f(k), U1(d, k))
28.11/9.13	   A^2 -> H(f(c), b)
28.11/9.13	   A^2 -> H(f(c), U1(e, d))
28.11/9.13	   A^2 -> H(f(c), U1(d, e))
28.11/9.13	   A^2 -> H(f(k), U1(k, k))
28.11/9.13	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.13	   A^2 -> H(U1(k, k), f(c))
28.11/9.13	   A^2 -> H(U1(k, k), f(d))
28.11/9.13	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.13	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.13	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.13	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.13	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.13	   A^2 -> H(U1(k, d), f(e))
28.11/9.13	   A^2 -> H(U1(k, d), f(k))
28.11/9.13	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.13	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.13	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.13	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.13	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.13	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.13	   A^2 -> H(U1(d, k), f(e))
28.11/9.13	   A^2 -> H(U1(d, k), f(k))
28.11/9.13	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.13	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.13	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.13	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.13	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.13	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.13	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.13	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.13	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.13	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.13	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.13	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.13	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.13	   A^2 -> H(f(d), b)
28.11/9.13	   A^2 -> H(f(d), U1(e, d))
28.11/9.13	   A^2 -> H(f(d), U1(d, e))
28.11/9.13	   A^2 -> H(f(d), c)
28.11/9.13	   A^2 -> H(f(d), U1(e, k))
28.11/9.13	   A^2 -> H(f(d), U1(k, e))
28.11/9.13	   A^2 -> H(f(d), e)
28.11/9.13	   A^2 -> H(f(a), d)
28.11/9.13	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.13	   A^2 -> H(f(c), c)
28.11/9.13	   A^2 -> H(f(c), U1(e, k))
28.11/9.13	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.13	   A^2 -> H(f(c), U1(k, e))
28.11/9.13	   A^2 -> H(f(c), U1(k, k))
28.11/9.13	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.13	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.13	   A^2 -> H(f(a), k)
28.11/9.13	   A^2 -> H(f(e), U1(e, e))
28.11/9.13	   A^2 -> H(f(c), e)
28.11/9.13	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.13	   A^2 -> H(f(d), U1(k, k))
28.11/9.13	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.13	   A^2 -> H(d, U1(b, b))
28.11/9.13	   A^2 -> H(d, f(c))
28.11/9.13	   A^2 -> H(d, f(d))
28.11/9.13	   A^2 -> H(a, U1(c, b))
28.11/9.13	   A^2 -> H(a, U1(d, b))
28.11/9.13	   A^2 -> H(a, U1(b, c))
28.11/9.13	   A^2 -> H(a, U1(b, d))
28.11/9.13	   A^2 -> H(a, U1(c, c))
28.11/9.13	   A^2 -> H(a, f(e))
28.11/9.13	   A^2 -> H(a, f(k))
28.11/9.13	   A^2 -> H(a, U1(d, d))
28.11/9.13	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.13	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.13	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.13	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.13	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.13	   A^2 -> H(U1(e, d), f(e))
28.11/9.13	   A^2 -> H(U1(e, d), f(k))
28.11/9.13	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.13	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.13	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.13	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.13	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.13	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.13	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.13	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.13	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.13	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.13	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.13	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.13	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.13	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.13	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.13	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.13	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.13	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.13	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.13	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.13	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.13	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.13	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.13	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.13	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.13	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.13	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.13	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.13	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.13	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.13	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.13	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.13	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.13	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.13	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.13	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.13	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.13	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.13	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.13	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.13	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.13	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.13	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.13	   A^2 -> H(U1(c, a), b)
28.11/9.13	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.13	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.13	   A^2 -> H(U1(c, a), c)
28.11/9.13	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.13	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.13	   A^2 -> H(U1(c, a), e)
28.11/9.13	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.13	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.13	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.13	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.13	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.13	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.13	   A^2 -> H(U1(d, e), f(e))
28.11/9.13	   A^2 -> H(U1(d, e), f(k))
28.11/9.13	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.13	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.13	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.13	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.13	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.13	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.13	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.13	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.13	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.13	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.13	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.13	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.13	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.13	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.13	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.13	   A^2 -> H(U1(d, a), b)
28.11/9.13	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.13	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.13	   A^2 -> H(U1(d, a), c)
28.11/9.13	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.13	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.13	   A^2 -> H(U1(d, a), e)
28.11/9.13	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.13	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.13	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.13	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.13	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.13	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.13	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.13	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.13	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.13	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.13	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.13	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.13	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.13	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.13	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.13	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.13	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.13	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.13	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.13	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.13	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.13	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.13	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.13	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.13	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.13	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.13	   A^2 -> H(U1(a, c), b)
28.11/9.13	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.13	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.13	   A^2 -> H(U1(a, c), c)
28.11/9.13	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.13	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.13	   A^2 -> H(U1(a, c), e)
28.11/9.13	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, d), b)
28.11/9.13	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.13	
28.11/9.13	The TRS R consists of the following rules:
28.11/9.13	
28.11/9.13	   f(x) -> U1(x, x)
28.11/9.13	   U1(e, x) -> x
28.11/9.13	   a -> c
28.11/9.13	   a -> d
28.11/9.13	   b -> c
28.11/9.13	   b -> d
28.11/9.13	   d -> k
28.11/9.13	   c -> e
28.11/9.13	   c -> k
28.11/9.13	
28.11/9.13	Q is empty.
28.11/9.13	We have to consider all minimal (P,Q,R)-chains.
28.11/9.13	----------------------------------------
28.11/9.13	
28.11/9.13	(745) TransformationProof (EQUIVALENT)
28.11/9.13	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.13	
28.11/9.13	   (A^2 -> H(U1(c, d), U1(c, d)),A^2 -> H(U1(c, d), U1(c, d)))
28.11/9.13	   (A^2 -> H(U1(d, d), U1(c, d)),A^2 -> H(U1(d, d), U1(c, d)))
28.11/9.13	   (A^2 -> H(U1(a, k), U1(c, d)),A^2 -> H(U1(a, k), U1(c, d)))
28.11/9.13	   (A^2 -> H(U1(a, d), U1(e, d)),A^2 -> H(U1(a, d), U1(e, d)))
28.11/9.13	   (A^2 -> H(U1(a, d), U1(k, d)),A^2 -> H(U1(a, d), U1(k, d)))
28.11/9.13	   (A^2 -> H(U1(a, d), U1(c, k)),A^2 -> H(U1(a, d), U1(c, k)))
28.11/9.13	
28.11/9.13	
28.11/9.13	----------------------------------------
28.11/9.13	
28.11/9.13	(746)
28.11/9.13	Obligation:
28.11/9.13	Q DP problem:
28.11/9.13	The TRS P consists of the following rules:
28.11/9.13	
28.11/9.13	   H(x, x) -> G(x, x, f(k))
28.11/9.13	   G(d, x, x) -> A^2
28.11/9.13	   A^2 -> H(f(c), f(c))
28.11/9.13	   A^2 -> H(f(d), f(d))
28.11/9.13	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.13	   A^2 -> H(f(e), f(e))
28.11/9.13	   A^2 -> H(f(k), f(k))
28.11/9.13	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.13	   A^2 -> H(U1(a, d), U1(d, c))
28.11/9.13	   A^2 -> H(U1(a, d), U1(b, e))
28.11/9.13	   A^2 -> H(U1(a, d), U1(b, k))
28.11/9.13	   A^2 -> H(U1(a, d), U1(e, c))
28.11/9.13	   A^2 -> H(U1(a, d), U1(k, c))
28.11/9.13	   A^2 -> H(U1(a, d), U1(c, e))
28.11/9.13	   A^2 -> H(U1(a, d), U1(c, k))
28.11/9.13	   A^2 -> H(U1(a, d), U1(e, e))
28.11/9.13	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, d), U1(k, d))
28.11/9.13	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.13	   A^2 -> H(U1(a, a), b)
28.11/9.13	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.13	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.13	   A^2 -> H(U1(a, a), c)
28.11/9.13	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.13	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.13	   A^2 -> H(U1(a, a), e)
28.11/9.13	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.13	   A^2 -> H(k, f(b))
28.11/9.13	   A^2 -> H(c, U1(b, b))
28.11/9.13	   A^2 -> H(c, f(c))
28.11/9.13	   A^2 -> H(c, f(d))
28.11/9.13	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.13	   A^2 -> H(U1(e, k), f(c))
28.11/9.13	   A^2 -> H(U1(e, k), f(d))
28.11/9.13	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.13	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.13	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.13	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.13	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.13	   A^2 -> H(U1(e, c), f(e))
28.11/9.13	   A^2 -> H(U1(e, c), f(k))
28.11/9.13	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.13	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.13	   A^2 -> H(U1(k, e), f(c))
28.11/9.13	   A^2 -> H(U1(k, e), f(d))
28.11/9.13	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.13	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.13	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.13	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.13	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.13	   A^2 -> H(U1(k, c), f(e))
28.11/9.13	   A^2 -> H(U1(k, c), f(k))
28.11/9.13	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.13	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.13	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.13	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.13	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.13	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.13	   A^2 -> H(U1(c, e), f(e))
28.11/9.13	   A^2 -> H(U1(c, e), f(k))
28.11/9.13	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.13	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.13	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.13	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.13	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.13	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.13	   A^2 -> H(U1(c, k), f(e))
28.11/9.13	   A^2 -> H(U1(c, k), f(k))
28.11/9.13	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.13	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.13	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.13	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.13	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.13	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.13	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.13	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.13	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.13	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.13	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.13	   A^2 -> H(e, U1(b, b))
28.11/9.13	   A^2 -> H(e, f(c))
28.11/9.13	   A^2 -> H(e, f(d))
28.11/9.13	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.13	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.13	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.13	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.13	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.13	   A^2 -> H(U1(e, e), f(e))
28.11/9.13	   A^2 -> H(U1(e, e), f(k))
28.11/9.13	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.13	   A^2 -> H(f(e), U1(e, b))
28.11/9.13	   A^2 -> H(f(e), U1(k, b))
28.11/9.13	   A^2 -> H(f(e), U1(c, d))
28.11/9.13	   A^2 -> H(f(e), U1(d, c))
28.11/9.13	   A^2 -> H(f(e), U1(b, e))
28.11/9.13	   A^2 -> H(f(e), U1(b, k))
28.11/9.13	   A^2 -> H(f(e), U1(e, c))
28.11/9.13	   A^2 -> H(f(e), U1(k, c))
28.11/9.13	   A^2 -> H(f(e), U1(c, e))
28.11/9.13	   A^2 -> H(f(e), U1(c, k))
28.11/9.13	   A^2 -> H(f(e), U1(k, k))
28.11/9.13	   A^2 -> H(f(e), U1(k, d))
28.11/9.13	   A^2 -> H(f(e), U1(d, k))
28.11/9.13	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.13	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.13	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.13	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.13	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.13	   A^2 -> H(U1(k, k), f(e))
28.11/9.13	   A^2 -> H(U1(k, k), f(k))
28.11/9.13	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.13	   A^2 -> H(f(k), U1(e, b))
28.11/9.13	   A^2 -> H(f(k), U1(k, b))
28.11/9.13	   A^2 -> H(f(k), U1(c, d))
28.11/9.13	   A^2 -> H(f(k), U1(d, c))
28.11/9.13	   A^2 -> H(f(k), U1(b, e))
28.11/9.13	   A^2 -> H(f(k), U1(b, k))
28.11/9.13	   A^2 -> H(f(k), U1(e, c))
28.11/9.13	   A^2 -> H(f(k), U1(k, c))
28.11/9.13	   A^2 -> H(f(k), U1(c, e))
28.11/9.13	   A^2 -> H(f(k), U1(c, k))
28.11/9.13	   A^2 -> H(f(k), U1(e, e))
28.11/9.13	   A^2 -> H(f(k), U1(k, d))
28.11/9.13	   A^2 -> H(f(k), U1(d, k))
28.11/9.13	   A^2 -> H(f(c), b)
28.11/9.13	   A^2 -> H(f(c), U1(e, d))
28.11/9.13	   A^2 -> H(f(c), U1(d, e))
28.11/9.13	   A^2 -> H(f(k), U1(k, k))
28.11/9.13	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.13	   A^2 -> H(U1(k, k), f(c))
28.11/9.13	   A^2 -> H(U1(k, k), f(d))
28.11/9.13	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.13	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.13	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.13	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.13	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.13	   A^2 -> H(U1(k, d), f(e))
28.11/9.13	   A^2 -> H(U1(k, d), f(k))
28.11/9.13	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.13	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.13	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.13	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.13	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.13	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.13	   A^2 -> H(U1(d, k), f(e))
28.11/9.13	   A^2 -> H(U1(d, k), f(k))
28.11/9.13	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.13	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.13	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.13	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.13	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.13	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.13	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.13	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.13	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.13	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.13	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.13	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.13	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.13	   A^2 -> H(f(d), b)
28.11/9.13	   A^2 -> H(f(d), U1(e, d))
28.11/9.13	   A^2 -> H(f(d), U1(d, e))
28.11/9.13	   A^2 -> H(f(d), c)
28.11/9.13	   A^2 -> H(f(d), U1(e, k))
28.11/9.13	   A^2 -> H(f(d), U1(k, e))
28.11/9.13	   A^2 -> H(f(d), e)
28.11/9.13	   A^2 -> H(f(a), d)
28.11/9.13	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.13	   A^2 -> H(f(c), c)
28.11/9.13	   A^2 -> H(f(c), U1(e, k))
28.11/9.13	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.13	   A^2 -> H(f(c), U1(k, e))
28.11/9.13	   A^2 -> H(f(c), U1(k, k))
28.11/9.13	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.13	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.13	   A^2 -> H(f(a), k)
28.11/9.13	   A^2 -> H(f(e), U1(e, e))
28.11/9.13	   A^2 -> H(f(c), e)
28.11/9.13	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.13	   A^2 -> H(f(d), U1(k, k))
28.11/9.13	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.13	   A^2 -> H(d, U1(b, b))
28.11/9.13	   A^2 -> H(d, f(c))
28.11/9.13	   A^2 -> H(d, f(d))
28.11/9.13	   A^2 -> H(a, U1(c, b))
28.11/9.13	   A^2 -> H(a, U1(d, b))
28.11/9.13	   A^2 -> H(a, U1(b, c))
28.11/9.13	   A^2 -> H(a, U1(b, d))
28.11/9.13	   A^2 -> H(a, U1(c, c))
28.11/9.13	   A^2 -> H(a, f(e))
28.11/9.13	   A^2 -> H(a, f(k))
28.11/9.13	   A^2 -> H(a, U1(d, d))
28.11/9.13	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.13	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.13	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.13	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.13	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.13	   A^2 -> H(U1(e, d), f(e))
28.11/9.13	   A^2 -> H(U1(e, d), f(k))
28.11/9.13	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.13	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.13	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.13	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.13	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.13	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.13	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.13	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.13	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.13	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.13	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.13	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.13	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.13	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.13	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.13	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.13	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.13	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.13	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.13	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.13	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.13	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.13	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.13	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.13	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.13	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.13	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.13	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.13	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.13	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.13	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.13	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.13	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.13	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.13	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.13	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.13	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.13	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.13	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.13	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.13	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.13	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.13	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.13	   A^2 -> H(U1(c, a), b)
28.11/9.13	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.13	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.13	   A^2 -> H(U1(c, a), c)
28.11/9.13	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.13	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.13	   A^2 -> H(U1(c, a), e)
28.11/9.13	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.13	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.13	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.13	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.13	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.13	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.13	   A^2 -> H(U1(d, e), f(e))
28.11/9.13	   A^2 -> H(U1(d, e), f(k))
28.11/9.13	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.13	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.13	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.13	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.13	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.13	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.13	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.13	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.13	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.13	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.13	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.13	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.13	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.13	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.13	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.13	   A^2 -> H(U1(d, a), b)
28.11/9.13	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.13	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.13	   A^2 -> H(U1(d, a), c)
28.11/9.13	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.13	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.13	   A^2 -> H(U1(d, a), e)
28.11/9.13	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.13	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.13	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.13	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.13	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.13	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.13	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.13	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.13	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.13	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.13	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.13	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.13	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.13	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.13	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.13	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.13	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.13	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.13	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.13	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.13	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.13	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.13	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.13	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.13	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.13	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.13	   A^2 -> H(U1(a, c), b)
28.11/9.13	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.13	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.13	   A^2 -> H(U1(a, c), c)
28.11/9.13	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.13	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.13	   A^2 -> H(U1(a, c), e)
28.11/9.13	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, d), b)
28.11/9.13	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.13	
28.11/9.13	The TRS R consists of the following rules:
28.11/9.13	
28.11/9.13	   f(x) -> U1(x, x)
28.11/9.13	   U1(e, x) -> x
28.11/9.13	   a -> c
28.11/9.13	   a -> d
28.11/9.13	   b -> c
28.11/9.13	   b -> d
28.11/9.13	   d -> k
28.11/9.13	   c -> e
28.11/9.13	   c -> k
28.11/9.13	
28.11/9.13	Q is empty.
28.11/9.13	We have to consider all minimal (P,Q,R)-chains.
28.11/9.13	----------------------------------------
28.11/9.13	
28.11/9.13	(747) TransformationProof (EQUIVALENT)
28.11/9.13	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.13	
28.11/9.13	   (A^2 -> H(U1(c, d), U1(d, c)),A^2 -> H(U1(c, d), U1(d, c)))
28.11/9.13	   (A^2 -> H(U1(d, d), U1(d, c)),A^2 -> H(U1(d, d), U1(d, c)))
28.11/9.13	   (A^2 -> H(U1(a, k), U1(d, c)),A^2 -> H(U1(a, k), U1(d, c)))
28.11/9.13	   (A^2 -> H(U1(a, d), U1(k, c)),A^2 -> H(U1(a, d), U1(k, c)))
28.11/9.13	   (A^2 -> H(U1(a, d), U1(d, e)),A^2 -> H(U1(a, d), U1(d, e)))
28.11/9.13	   (A^2 -> H(U1(a, d), U1(d, k)),A^2 -> H(U1(a, d), U1(d, k)))
28.11/9.13	
28.11/9.13	
28.11/9.13	----------------------------------------
28.11/9.13	
28.11/9.13	(748)
28.11/9.13	Obligation:
28.11/9.13	Q DP problem:
28.11/9.13	The TRS P consists of the following rules:
28.11/9.13	
28.11/9.13	   H(x, x) -> G(x, x, f(k))
28.11/9.13	   G(d, x, x) -> A^2
28.11/9.13	   A^2 -> H(f(c), f(c))
28.11/9.13	   A^2 -> H(f(d), f(d))
28.11/9.13	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.13	   A^2 -> H(f(e), f(e))
28.11/9.13	   A^2 -> H(f(k), f(k))
28.11/9.13	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.13	   A^2 -> H(U1(a, d), U1(b, e))
28.11/9.13	   A^2 -> H(U1(a, d), U1(b, k))
28.11/9.13	   A^2 -> H(U1(a, d), U1(e, c))
28.11/9.13	   A^2 -> H(U1(a, d), U1(k, c))
28.11/9.13	   A^2 -> H(U1(a, d), U1(c, e))
28.11/9.13	   A^2 -> H(U1(a, d), U1(c, k))
28.11/9.13	   A^2 -> H(U1(a, d), U1(e, e))
28.11/9.13	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, d), U1(k, d))
28.11/9.13	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.13	   A^2 -> H(U1(a, a), b)
28.11/9.13	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.13	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.13	   A^2 -> H(U1(a, a), c)
28.11/9.13	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.13	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.13	   A^2 -> H(U1(a, a), e)
28.11/9.13	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.13	   A^2 -> H(k, f(b))
28.11/9.13	   A^2 -> H(c, U1(b, b))
28.11/9.13	   A^2 -> H(c, f(c))
28.11/9.13	   A^2 -> H(c, f(d))
28.11/9.13	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.13	   A^2 -> H(U1(e, k), f(c))
28.11/9.13	   A^2 -> H(U1(e, k), f(d))
28.11/9.13	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.13	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.13	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.13	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.13	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.13	   A^2 -> H(U1(e, c), f(e))
28.11/9.13	   A^2 -> H(U1(e, c), f(k))
28.11/9.13	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.13	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.13	   A^2 -> H(U1(k, e), f(c))
28.11/9.13	   A^2 -> H(U1(k, e), f(d))
28.11/9.13	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.13	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.13	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.13	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.13	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.13	   A^2 -> H(U1(k, c), f(e))
28.11/9.13	   A^2 -> H(U1(k, c), f(k))
28.11/9.13	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.13	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.13	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.13	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.13	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.13	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.13	   A^2 -> H(U1(c, e), f(e))
28.11/9.13	   A^2 -> H(U1(c, e), f(k))
28.11/9.13	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.13	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.13	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.13	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.13	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.13	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.13	   A^2 -> H(U1(c, k), f(e))
28.11/9.13	   A^2 -> H(U1(c, k), f(k))
28.11/9.13	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.13	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.13	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.13	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.13	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.13	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.13	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.13	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.13	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.13	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.13	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.13	   A^2 -> H(e, U1(b, b))
28.11/9.13	   A^2 -> H(e, f(c))
28.11/9.13	   A^2 -> H(e, f(d))
28.11/9.13	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.13	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.13	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.13	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.13	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.13	   A^2 -> H(U1(e, e), f(e))
28.11/9.13	   A^2 -> H(U1(e, e), f(k))
28.11/9.13	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.13	   A^2 -> H(f(e), U1(e, b))
28.11/9.13	   A^2 -> H(f(e), U1(k, b))
28.11/9.13	   A^2 -> H(f(e), U1(c, d))
28.11/9.13	   A^2 -> H(f(e), U1(d, c))
28.11/9.13	   A^2 -> H(f(e), U1(b, e))
28.11/9.13	   A^2 -> H(f(e), U1(b, k))
28.11/9.13	   A^2 -> H(f(e), U1(e, c))
28.11/9.13	   A^2 -> H(f(e), U1(k, c))
28.11/9.13	   A^2 -> H(f(e), U1(c, e))
28.11/9.13	   A^2 -> H(f(e), U1(c, k))
28.11/9.13	   A^2 -> H(f(e), U1(k, k))
28.11/9.13	   A^2 -> H(f(e), U1(k, d))
28.11/9.13	   A^2 -> H(f(e), U1(d, k))
28.11/9.13	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.13	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.13	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.13	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.13	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.13	   A^2 -> H(U1(k, k), f(e))
28.11/9.13	   A^2 -> H(U1(k, k), f(k))
28.11/9.13	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.13	   A^2 -> H(f(k), U1(e, b))
28.11/9.13	   A^2 -> H(f(k), U1(k, b))
28.11/9.13	   A^2 -> H(f(k), U1(c, d))
28.11/9.13	   A^2 -> H(f(k), U1(d, c))
28.11/9.13	   A^2 -> H(f(k), U1(b, e))
28.11/9.13	   A^2 -> H(f(k), U1(b, k))
28.11/9.13	   A^2 -> H(f(k), U1(e, c))
28.11/9.13	   A^2 -> H(f(k), U1(k, c))
28.11/9.13	   A^2 -> H(f(k), U1(c, e))
28.11/9.13	   A^2 -> H(f(k), U1(c, k))
28.11/9.13	   A^2 -> H(f(k), U1(e, e))
28.11/9.13	   A^2 -> H(f(k), U1(k, d))
28.11/9.13	   A^2 -> H(f(k), U1(d, k))
28.11/9.13	   A^2 -> H(f(c), b)
28.11/9.13	   A^2 -> H(f(c), U1(e, d))
28.11/9.13	   A^2 -> H(f(c), U1(d, e))
28.11/9.13	   A^2 -> H(f(k), U1(k, k))
28.11/9.13	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.13	   A^2 -> H(U1(k, k), f(c))
28.11/9.13	   A^2 -> H(U1(k, k), f(d))
28.11/9.13	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.13	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.13	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.13	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.13	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.13	   A^2 -> H(U1(k, d), f(e))
28.11/9.13	   A^2 -> H(U1(k, d), f(k))
28.11/9.13	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.13	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.13	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.13	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.13	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.13	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.13	   A^2 -> H(U1(d, k), f(e))
28.11/9.13	   A^2 -> H(U1(d, k), f(k))
28.11/9.13	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.13	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.13	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.13	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.13	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.13	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.13	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.13	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.13	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.13	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.13	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.13	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.13	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.13	   A^2 -> H(f(d), b)
28.11/9.13	   A^2 -> H(f(d), U1(e, d))
28.11/9.13	   A^2 -> H(f(d), U1(d, e))
28.11/9.13	   A^2 -> H(f(d), c)
28.11/9.13	   A^2 -> H(f(d), U1(e, k))
28.11/9.13	   A^2 -> H(f(d), U1(k, e))
28.11/9.13	   A^2 -> H(f(d), e)
28.11/9.13	   A^2 -> H(f(a), d)
28.11/9.13	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.13	   A^2 -> H(f(c), c)
28.11/9.13	   A^2 -> H(f(c), U1(e, k))
28.11/9.13	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.13	   A^2 -> H(f(c), U1(k, e))
28.11/9.13	   A^2 -> H(f(c), U1(k, k))
28.11/9.13	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.13	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.13	   A^2 -> H(f(a), k)
28.11/9.13	   A^2 -> H(f(e), U1(e, e))
28.11/9.13	   A^2 -> H(f(c), e)
28.11/9.13	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.13	   A^2 -> H(f(d), U1(k, k))
28.11/9.13	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.13	   A^2 -> H(d, U1(b, b))
28.11/9.13	   A^2 -> H(d, f(c))
28.11/9.13	   A^2 -> H(d, f(d))
28.11/9.13	   A^2 -> H(a, U1(c, b))
28.11/9.13	   A^2 -> H(a, U1(d, b))
28.11/9.13	   A^2 -> H(a, U1(b, c))
28.11/9.13	   A^2 -> H(a, U1(b, d))
28.11/9.13	   A^2 -> H(a, U1(c, c))
28.11/9.13	   A^2 -> H(a, f(e))
28.11/9.13	   A^2 -> H(a, f(k))
28.11/9.13	   A^2 -> H(a, U1(d, d))
28.11/9.13	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.13	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.13	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.13	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.13	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.13	   A^2 -> H(U1(e, d), f(e))
28.11/9.13	   A^2 -> H(U1(e, d), f(k))
28.11/9.13	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.13	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.13	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.13	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.13	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.13	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.13	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.13	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.13	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.13	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.13	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.13	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.13	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.13	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.13	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.13	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.13	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.13	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.13	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.13	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.13	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.13	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.13	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.13	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.13	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.13	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.13	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.13	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.13	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.13	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.13	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.13	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.13	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.13	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.13	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.13	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.13	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.13	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.13	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.13	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.13	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.13	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.13	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.13	   A^2 -> H(U1(c, a), b)
28.11/9.13	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.13	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.13	   A^2 -> H(U1(c, a), c)
28.11/9.13	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.13	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.13	   A^2 -> H(U1(c, a), e)
28.11/9.13	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.13	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.13	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.13	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.13	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.13	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.13	   A^2 -> H(U1(d, e), f(e))
28.11/9.13	   A^2 -> H(U1(d, e), f(k))
28.11/9.13	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.13	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.13	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.13	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.13	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.13	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.13	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.13	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.13	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.13	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.13	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.13	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.13	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.13	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.13	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.13	   A^2 -> H(U1(d, a), b)
28.11/9.13	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.13	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.13	   A^2 -> H(U1(d, a), c)
28.11/9.13	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.13	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.13	   A^2 -> H(U1(d, a), e)
28.11/9.13	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.13	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.13	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.13	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.13	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.13	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.13	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.13	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.13	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.13	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.13	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.13	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.13	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.13	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.13	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.13	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.13	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.13	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.13	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.13	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.13	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.13	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.13	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.13	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.13	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.13	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.13	   A^2 -> H(U1(a, c), b)
28.11/9.13	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.13	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.13	   A^2 -> H(U1(a, c), c)
28.11/9.13	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.13	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.13	   A^2 -> H(U1(a, c), e)
28.11/9.13	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.13	   A^2 -> H(U1(a, d), b)
28.11/9.13	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.13	   A^2 -> H(U1(a, d), U1(d, e))
28.11/9.13	
28.11/9.13	The TRS R consists of the following rules:
28.11/9.13	
28.11/9.13	   f(x) -> U1(x, x)
28.11/9.13	   U1(e, x) -> x
28.11/9.13	   a -> c
28.11/9.13	   a -> d
28.11/9.13	   b -> c
28.11/9.13	   b -> d
28.11/9.13	   d -> k
28.11/9.13	   c -> e
28.11/9.13	   c -> k
28.11/9.13	
28.11/9.13	Q is empty.
28.11/9.13	We have to consider all minimal (P,Q,R)-chains.
28.11/9.13	----------------------------------------
28.11/9.13	
28.11/9.13	(749) TransformationProof (EQUIVALENT)
28.11/9.13	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.13	
28.11/9.13	   (A^2 -> H(U1(c, d), U1(b, e)),A^2 -> H(U1(c, d), U1(b, e)))
28.11/9.13	   (A^2 -> H(U1(d, d), U1(b, e)),A^2 -> H(U1(d, d), U1(b, e)))
28.11/9.13	   (A^2 -> H(U1(a, k), U1(b, e)),A^2 -> H(U1(a, k), U1(b, e)))
28.11/9.13	   (A^2 -> H(U1(a, d), U1(c, e)),A^2 -> H(U1(a, d), U1(c, e)))
28.11/9.13	   (A^2 -> H(U1(a, d), U1(d, e)),A^2 -> H(U1(a, d), U1(d, e)))
28.11/9.13	
28.11/9.13	
28.11/9.13	----------------------------------------
28.11/9.13	
28.11/9.13	(750)
28.11/9.13	Obligation:
28.11/9.13	Q DP problem:
28.11/9.13	The TRS P consists of the following rules:
28.11/9.13	
28.11/9.13	   H(x, x) -> G(x, x, f(k))
28.11/9.13	   G(d, x, x) -> A^2
28.11/9.13	   A^2 -> H(f(c), f(c))
28.11/9.13	   A^2 -> H(f(d), f(d))
28.11/9.13	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.13	   A^2 -> H(f(e), f(e))
28.11/9.13	   A^2 -> H(f(k), f(k))
28.11/9.13	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.13	   A^2 -> H(U1(a, d), U1(b, k))
28.11/9.13	   A^2 -> H(U1(a, d), U1(e, c))
28.11/9.14	   A^2 -> H(U1(a, d), U1(k, c))
28.11/9.14	   A^2 -> H(U1(a, d), U1(c, e))
28.11/9.14	   A^2 -> H(U1(a, d), U1(c, k))
28.11/9.14	   A^2 -> H(U1(a, d), U1(e, e))
28.11/9.14	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, d), U1(k, d))
28.11/9.14	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.14	   A^2 -> H(U1(a, a), b)
28.11/9.14	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.14	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.14	   A^2 -> H(U1(a, a), c)
28.11/9.14	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.14	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.14	   A^2 -> H(U1(a, a), e)
28.11/9.14	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.14	   A^2 -> H(k, f(b))
28.11/9.14	   A^2 -> H(c, U1(b, b))
28.11/9.14	   A^2 -> H(c, f(c))
28.11/9.14	   A^2 -> H(c, f(d))
28.11/9.14	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.14	   A^2 -> H(U1(e, k), f(c))
28.11/9.14	   A^2 -> H(U1(e, k), f(d))
28.11/9.14	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.14	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.14	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.14	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.14	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.14	   A^2 -> H(U1(e, c), f(e))
28.11/9.14	   A^2 -> H(U1(e, c), f(k))
28.11/9.14	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.14	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.14	   A^2 -> H(U1(k, e), f(c))
28.11/9.14	   A^2 -> H(U1(k, e), f(d))
28.11/9.14	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.14	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.14	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.14	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.14	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.14	   A^2 -> H(U1(k, c), f(e))
28.11/9.14	   A^2 -> H(U1(k, c), f(k))
28.11/9.14	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.14	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.14	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.14	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.14	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.14	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.14	   A^2 -> H(U1(c, e), f(e))
28.11/9.14	   A^2 -> H(U1(c, e), f(k))
28.11/9.14	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.14	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.14	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.14	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.14	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.14	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.14	   A^2 -> H(U1(c, k), f(e))
28.11/9.14	   A^2 -> H(U1(c, k), f(k))
28.11/9.14	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.14	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.14	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.14	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.14	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.14	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.14	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.14	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.14	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.14	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.14	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.14	   A^2 -> H(e, U1(b, b))
28.11/9.14	   A^2 -> H(e, f(c))
28.11/9.14	   A^2 -> H(e, f(d))
28.11/9.14	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.14	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.14	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.14	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.14	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.14	   A^2 -> H(U1(e, e), f(e))
28.11/9.14	   A^2 -> H(U1(e, e), f(k))
28.11/9.14	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.14	   A^2 -> H(f(e), U1(e, b))
28.11/9.14	   A^2 -> H(f(e), U1(k, b))
28.11/9.14	   A^2 -> H(f(e), U1(c, d))
28.11/9.14	   A^2 -> H(f(e), U1(d, c))
28.11/9.14	   A^2 -> H(f(e), U1(b, e))
28.11/9.14	   A^2 -> H(f(e), U1(b, k))
28.11/9.14	   A^2 -> H(f(e), U1(e, c))
28.11/9.14	   A^2 -> H(f(e), U1(k, c))
28.11/9.14	   A^2 -> H(f(e), U1(c, e))
28.11/9.14	   A^2 -> H(f(e), U1(c, k))
28.11/9.14	   A^2 -> H(f(e), U1(k, k))
28.11/9.14	   A^2 -> H(f(e), U1(k, d))
28.11/9.14	   A^2 -> H(f(e), U1(d, k))
28.11/9.14	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.14	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.14	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.14	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.14	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.14	   A^2 -> H(U1(k, k), f(e))
28.11/9.14	   A^2 -> H(U1(k, k), f(k))
28.11/9.14	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.14	   A^2 -> H(f(k), U1(e, b))
28.11/9.14	   A^2 -> H(f(k), U1(k, b))
28.11/9.14	   A^2 -> H(f(k), U1(c, d))
28.11/9.14	   A^2 -> H(f(k), U1(d, c))
28.11/9.14	   A^2 -> H(f(k), U1(b, e))
28.11/9.14	   A^2 -> H(f(k), U1(b, k))
28.11/9.14	   A^2 -> H(f(k), U1(e, c))
28.11/9.14	   A^2 -> H(f(k), U1(k, c))
28.11/9.14	   A^2 -> H(f(k), U1(c, e))
28.11/9.14	   A^2 -> H(f(k), U1(c, k))
28.11/9.14	   A^2 -> H(f(k), U1(e, e))
28.11/9.14	   A^2 -> H(f(k), U1(k, d))
28.11/9.14	   A^2 -> H(f(k), U1(d, k))
28.11/9.14	   A^2 -> H(f(c), b)
28.11/9.14	   A^2 -> H(f(c), U1(e, d))
28.11/9.14	   A^2 -> H(f(c), U1(d, e))
28.11/9.14	   A^2 -> H(f(k), U1(k, k))
28.11/9.14	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.14	   A^2 -> H(U1(k, k), f(c))
28.11/9.14	   A^2 -> H(U1(k, k), f(d))
28.11/9.14	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.14	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.14	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.14	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.14	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.14	   A^2 -> H(U1(k, d), f(e))
28.11/9.14	   A^2 -> H(U1(k, d), f(k))
28.11/9.14	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.14	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.14	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.14	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.14	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.14	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.14	   A^2 -> H(U1(d, k), f(e))
28.11/9.14	   A^2 -> H(U1(d, k), f(k))
28.11/9.14	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.14	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.14	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.14	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.14	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.14	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.14	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.14	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.14	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.14	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.14	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.14	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.14	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.14	   A^2 -> H(f(d), b)
28.11/9.14	   A^2 -> H(f(d), U1(e, d))
28.11/9.14	   A^2 -> H(f(d), U1(d, e))
28.11/9.14	   A^2 -> H(f(d), c)
28.11/9.14	   A^2 -> H(f(d), U1(e, k))
28.11/9.14	   A^2 -> H(f(d), U1(k, e))
28.11/9.14	   A^2 -> H(f(d), e)
28.11/9.14	   A^2 -> H(f(a), d)
28.11/9.14	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.14	   A^2 -> H(f(c), c)
28.11/9.14	   A^2 -> H(f(c), U1(e, k))
28.11/9.14	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.14	   A^2 -> H(f(c), U1(k, e))
28.11/9.14	   A^2 -> H(f(c), U1(k, k))
28.11/9.14	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.14	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.14	   A^2 -> H(f(a), k)
28.11/9.14	   A^2 -> H(f(e), U1(e, e))
28.11/9.14	   A^2 -> H(f(c), e)
28.11/9.14	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.14	   A^2 -> H(f(d), U1(k, k))
28.11/9.14	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.14	   A^2 -> H(d, U1(b, b))
28.11/9.14	   A^2 -> H(d, f(c))
28.11/9.14	   A^2 -> H(d, f(d))
28.11/9.14	   A^2 -> H(a, U1(c, b))
28.11/9.14	   A^2 -> H(a, U1(d, b))
28.11/9.14	   A^2 -> H(a, U1(b, c))
28.11/9.14	   A^2 -> H(a, U1(b, d))
28.11/9.14	   A^2 -> H(a, U1(c, c))
28.11/9.14	   A^2 -> H(a, f(e))
28.11/9.14	   A^2 -> H(a, f(k))
28.11/9.14	   A^2 -> H(a, U1(d, d))
28.11/9.14	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.14	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.14	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.14	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.14	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.14	   A^2 -> H(U1(e, d), f(e))
28.11/9.14	   A^2 -> H(U1(e, d), f(k))
28.11/9.14	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.14	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.14	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.14	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.14	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.14	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.14	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.14	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.14	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.14	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.14	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.14	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.14	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.14	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.14	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.14	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.14	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.14	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.14	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.14	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.14	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.14	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.14	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.14	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.14	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.14	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.14	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.14	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.14	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.14	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.14	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.14	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.14	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.14	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.14	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.14	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.14	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.14	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.14	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.14	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.14	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.14	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.14	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.14	   A^2 -> H(U1(c, a), b)
28.11/9.14	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.14	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.14	   A^2 -> H(U1(c, a), c)
28.11/9.14	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.14	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.14	   A^2 -> H(U1(c, a), e)
28.11/9.14	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.14	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.14	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.14	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.14	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.14	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.14	   A^2 -> H(U1(d, e), f(e))
28.11/9.14	   A^2 -> H(U1(d, e), f(k))
28.11/9.14	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.14	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.14	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.14	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.14	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.14	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.14	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.14	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.14	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.14	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.14	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.14	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.14	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.14	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.14	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.14	   A^2 -> H(U1(d, a), b)
28.11/9.14	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.14	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.14	   A^2 -> H(U1(d, a), c)
28.11/9.14	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.14	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.14	   A^2 -> H(U1(d, a), e)
28.11/9.14	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.14	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.14	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.14	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.14	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.14	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.14	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.14	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.14	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.14	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.14	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.14	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.14	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.14	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.14	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.14	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.14	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.14	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.14	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.14	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.14	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.14	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.14	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.14	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.14	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.14	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.14	   A^2 -> H(U1(a, c), b)
28.11/9.14	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.14	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.14	   A^2 -> H(U1(a, c), c)
28.11/9.14	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.14	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.14	   A^2 -> H(U1(a, c), e)
28.11/9.14	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, d), b)
28.11/9.14	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.14	   A^2 -> H(U1(a, d), U1(d, e))
28.11/9.14	
28.11/9.14	The TRS R consists of the following rules:
28.11/9.14	
28.11/9.14	   f(x) -> U1(x, x)
28.11/9.14	   U1(e, x) -> x
28.11/9.14	   a -> c
28.11/9.14	   a -> d
28.11/9.14	   b -> c
28.11/9.14	   b -> d
28.11/9.14	   d -> k
28.11/9.14	   c -> e
28.11/9.14	   c -> k
28.11/9.14	
28.11/9.14	Q is empty.
28.11/9.14	We have to consider all minimal (P,Q,R)-chains.
28.11/9.14	----------------------------------------
28.11/9.14	
28.11/9.14	(751) TransformationProof (EQUIVALENT)
28.11/9.14	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.14	
28.11/9.14	   (A^2 -> H(U1(c, d), U1(b, k)),A^2 -> H(U1(c, d), U1(b, k)))
28.11/9.14	   (A^2 -> H(U1(d, d), U1(b, k)),A^2 -> H(U1(d, d), U1(b, k)))
28.11/9.14	   (A^2 -> H(U1(a, k), U1(b, k)),A^2 -> H(U1(a, k), U1(b, k)))
28.11/9.14	   (A^2 -> H(U1(a, d), U1(c, k)),A^2 -> H(U1(a, d), U1(c, k)))
28.11/9.14	   (A^2 -> H(U1(a, d), U1(d, k)),A^2 -> H(U1(a, d), U1(d, k)))
28.11/9.14	
28.11/9.14	
28.11/9.14	----------------------------------------
28.11/9.14	
28.11/9.14	(752)
28.11/9.14	Obligation:
28.11/9.14	Q DP problem:
28.11/9.14	The TRS P consists of the following rules:
28.11/9.14	
28.11/9.14	   H(x, x) -> G(x, x, f(k))
28.11/9.14	   G(d, x, x) -> A^2
28.11/9.14	   A^2 -> H(f(c), f(c))
28.11/9.14	   A^2 -> H(f(d), f(d))
28.11/9.14	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.14	   A^2 -> H(f(e), f(e))
28.11/9.14	   A^2 -> H(f(k), f(k))
28.11/9.14	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.14	   A^2 -> H(U1(a, d), U1(e, c))
28.11/9.14	   A^2 -> H(U1(a, d), U1(k, c))
28.11/9.14	   A^2 -> H(U1(a, d), U1(c, e))
28.11/9.14	   A^2 -> H(U1(a, d), U1(c, k))
28.11/9.14	   A^2 -> H(U1(a, d), U1(e, e))
28.11/9.14	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, d), U1(k, d))
28.11/9.14	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.14	   A^2 -> H(U1(a, a), b)
28.11/9.14	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.14	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.14	   A^2 -> H(U1(a, a), c)
28.11/9.14	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.14	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.14	   A^2 -> H(U1(a, a), e)
28.11/9.14	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.14	   A^2 -> H(k, f(b))
28.11/9.14	   A^2 -> H(c, U1(b, b))
28.11/9.14	   A^2 -> H(c, f(c))
28.11/9.14	   A^2 -> H(c, f(d))
28.11/9.14	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.14	   A^2 -> H(U1(e, k), f(c))
28.11/9.14	   A^2 -> H(U1(e, k), f(d))
28.11/9.14	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.14	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.14	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.14	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.14	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.14	   A^2 -> H(U1(e, c), f(e))
28.11/9.14	   A^2 -> H(U1(e, c), f(k))
28.11/9.14	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.14	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.14	   A^2 -> H(U1(k, e), f(c))
28.11/9.14	   A^2 -> H(U1(k, e), f(d))
28.11/9.14	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.14	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.14	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.14	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.14	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.14	   A^2 -> H(U1(k, c), f(e))
28.11/9.14	   A^2 -> H(U1(k, c), f(k))
28.11/9.14	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.14	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.14	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.14	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.14	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.14	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.14	   A^2 -> H(U1(c, e), f(e))
28.11/9.14	   A^2 -> H(U1(c, e), f(k))
28.11/9.14	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.14	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.14	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.14	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.14	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.14	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.14	   A^2 -> H(U1(c, k), f(e))
28.11/9.14	   A^2 -> H(U1(c, k), f(k))
28.11/9.14	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.14	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.14	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.14	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.14	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.14	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.14	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.14	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.14	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.14	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.14	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.14	   A^2 -> H(e, U1(b, b))
28.11/9.14	   A^2 -> H(e, f(c))
28.11/9.14	   A^2 -> H(e, f(d))
28.11/9.14	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.14	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.14	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.14	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.14	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.14	   A^2 -> H(U1(e, e), f(e))
28.11/9.14	   A^2 -> H(U1(e, e), f(k))
28.11/9.14	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.14	   A^2 -> H(f(e), U1(e, b))
28.11/9.14	   A^2 -> H(f(e), U1(k, b))
28.11/9.14	   A^2 -> H(f(e), U1(c, d))
28.11/9.14	   A^2 -> H(f(e), U1(d, c))
28.11/9.14	   A^2 -> H(f(e), U1(b, e))
28.11/9.14	   A^2 -> H(f(e), U1(b, k))
28.11/9.14	   A^2 -> H(f(e), U1(e, c))
28.11/9.14	   A^2 -> H(f(e), U1(k, c))
28.11/9.14	   A^2 -> H(f(e), U1(c, e))
28.11/9.14	   A^2 -> H(f(e), U1(c, k))
28.11/9.14	   A^2 -> H(f(e), U1(k, k))
28.11/9.14	   A^2 -> H(f(e), U1(k, d))
28.11/9.14	   A^2 -> H(f(e), U1(d, k))
28.11/9.14	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.14	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.14	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.14	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.14	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.14	   A^2 -> H(U1(k, k), f(e))
28.11/9.14	   A^2 -> H(U1(k, k), f(k))
28.11/9.14	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.14	   A^2 -> H(f(k), U1(e, b))
28.11/9.14	   A^2 -> H(f(k), U1(k, b))
28.11/9.14	   A^2 -> H(f(k), U1(c, d))
28.11/9.14	   A^2 -> H(f(k), U1(d, c))
28.11/9.14	   A^2 -> H(f(k), U1(b, e))
28.11/9.14	   A^2 -> H(f(k), U1(b, k))
28.11/9.14	   A^2 -> H(f(k), U1(e, c))
28.11/9.14	   A^2 -> H(f(k), U1(k, c))
28.11/9.14	   A^2 -> H(f(k), U1(c, e))
28.11/9.14	   A^2 -> H(f(k), U1(c, k))
28.11/9.14	   A^2 -> H(f(k), U1(e, e))
28.11/9.14	   A^2 -> H(f(k), U1(k, d))
28.11/9.14	   A^2 -> H(f(k), U1(d, k))
28.11/9.14	   A^2 -> H(f(c), b)
28.11/9.14	   A^2 -> H(f(c), U1(e, d))
28.11/9.14	   A^2 -> H(f(c), U1(d, e))
28.11/9.14	   A^2 -> H(f(k), U1(k, k))
28.11/9.14	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.14	   A^2 -> H(U1(k, k), f(c))
28.11/9.14	   A^2 -> H(U1(k, k), f(d))
28.11/9.14	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.14	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.14	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.14	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.14	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.14	   A^2 -> H(U1(k, d), f(e))
28.11/9.14	   A^2 -> H(U1(k, d), f(k))
28.11/9.14	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.14	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.14	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.14	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.14	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.14	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.14	   A^2 -> H(U1(d, k), f(e))
28.11/9.14	   A^2 -> H(U1(d, k), f(k))
28.11/9.14	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.14	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.14	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.14	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.14	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.14	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.14	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.14	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.14	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.14	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.14	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.14	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.14	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.14	   A^2 -> H(f(d), b)
28.11/9.14	   A^2 -> H(f(d), U1(e, d))
28.11/9.14	   A^2 -> H(f(d), U1(d, e))
28.11/9.14	   A^2 -> H(f(d), c)
28.11/9.14	   A^2 -> H(f(d), U1(e, k))
28.11/9.14	   A^2 -> H(f(d), U1(k, e))
28.11/9.14	   A^2 -> H(f(d), e)
28.11/9.14	   A^2 -> H(f(a), d)
28.11/9.14	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.14	   A^2 -> H(f(c), c)
28.11/9.14	   A^2 -> H(f(c), U1(e, k))
28.11/9.14	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.14	   A^2 -> H(f(c), U1(k, e))
28.11/9.14	   A^2 -> H(f(c), U1(k, k))
28.11/9.14	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.14	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.14	   A^2 -> H(f(a), k)
28.11/9.14	   A^2 -> H(f(e), U1(e, e))
28.11/9.14	   A^2 -> H(f(c), e)
28.11/9.14	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.14	   A^2 -> H(f(d), U1(k, k))
28.11/9.14	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.14	   A^2 -> H(d, U1(b, b))
28.11/9.14	   A^2 -> H(d, f(c))
28.11/9.14	   A^2 -> H(d, f(d))
28.11/9.14	   A^2 -> H(a, U1(c, b))
28.11/9.14	   A^2 -> H(a, U1(d, b))
28.11/9.14	   A^2 -> H(a, U1(b, c))
28.11/9.14	   A^2 -> H(a, U1(b, d))
28.11/9.14	   A^2 -> H(a, U1(c, c))
28.11/9.14	   A^2 -> H(a, f(e))
28.11/9.14	   A^2 -> H(a, f(k))
28.11/9.14	   A^2 -> H(a, U1(d, d))
28.11/9.14	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.14	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.14	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.14	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.14	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.14	   A^2 -> H(U1(e, d), f(e))
28.11/9.14	   A^2 -> H(U1(e, d), f(k))
28.11/9.14	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.14	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.14	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.14	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.14	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.14	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.14	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.14	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.14	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.14	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.14	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.14	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.14	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.14	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.14	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.14	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.14	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.14	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.14	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.14	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.14	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.14	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.14	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.14	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.14	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.14	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.14	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.14	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.14	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.14	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.14	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.14	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.14	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.14	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.14	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.14	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.14	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.14	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.14	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.14	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.14	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.14	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.14	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.14	   A^2 -> H(U1(c, a), b)
28.11/9.14	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.14	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.14	   A^2 -> H(U1(c, a), c)
28.11/9.14	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.14	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.14	   A^2 -> H(U1(c, a), e)
28.11/9.14	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.14	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.14	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.14	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.14	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.14	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.14	   A^2 -> H(U1(d, e), f(e))
28.11/9.14	   A^2 -> H(U1(d, e), f(k))
28.11/9.14	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.14	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.14	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.14	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.14	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.14	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.14	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.14	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.14	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.14	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.14	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.14	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.14	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.14	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.14	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.14	   A^2 -> H(U1(d, a), b)
28.11/9.14	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.14	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.14	   A^2 -> H(U1(d, a), c)
28.11/9.14	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.14	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.14	   A^2 -> H(U1(d, a), e)
28.11/9.14	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.14	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.14	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.14	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.14	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.14	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.14	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.14	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.14	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.14	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.14	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.14	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.14	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.14	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.14	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.14	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.14	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.14	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.14	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.14	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.14	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.14	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.14	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.14	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.14	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.14	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.14	   A^2 -> H(U1(a, c), b)
28.11/9.14	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.14	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.14	   A^2 -> H(U1(a, c), c)
28.11/9.14	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.14	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.14	   A^2 -> H(U1(a, c), e)
28.11/9.14	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, d), b)
28.11/9.14	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.14	   A^2 -> H(U1(a, d), U1(d, e))
28.11/9.14	
28.11/9.14	The TRS R consists of the following rules:
28.11/9.14	
28.11/9.14	   f(x) -> U1(x, x)
28.11/9.14	   U1(e, x) -> x
28.11/9.14	   a -> c
28.11/9.14	   a -> d
28.11/9.14	   b -> c
28.11/9.14	   b -> d
28.11/9.14	   d -> k
28.11/9.14	   c -> e
28.11/9.14	   c -> k
28.11/9.14	
28.11/9.14	Q is empty.
28.11/9.14	We have to consider all minimal (P,Q,R)-chains.
28.11/9.14	----------------------------------------
28.11/9.14	
28.11/9.14	(753) TransformationProof (EQUIVALENT)
28.11/9.14	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.14	
28.11/9.14	   (A^2 -> H(U1(c, d), U1(e, c)),A^2 -> H(U1(c, d), U1(e, c)))
28.11/9.14	   (A^2 -> H(U1(d, d), U1(e, c)),A^2 -> H(U1(d, d), U1(e, c)))
28.11/9.14	   (A^2 -> H(U1(a, k), U1(e, c)),A^2 -> H(U1(a, k), U1(e, c)))
28.11/9.14	   (A^2 -> H(U1(a, d), c),A^2 -> H(U1(a, d), c))
28.11/9.14	   (A^2 -> H(U1(a, d), U1(e, e)),A^2 -> H(U1(a, d), U1(e, e)))
28.11/9.14	   (A^2 -> H(U1(a, d), U1(e, k)),A^2 -> H(U1(a, d), U1(e, k)))
28.11/9.14	
28.11/9.14	
28.11/9.14	----------------------------------------
28.11/9.14	
28.11/9.14	(754)
28.11/9.14	Obligation:
28.11/9.14	Q DP problem:
28.11/9.14	The TRS P consists of the following rules:
28.11/9.14	
28.11/9.14	   H(x, x) -> G(x, x, f(k))
28.11/9.14	   G(d, x, x) -> A^2
28.11/9.14	   A^2 -> H(f(c), f(c))
28.11/9.14	   A^2 -> H(f(d), f(d))
28.11/9.14	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.14	   A^2 -> H(f(e), f(e))
28.11/9.14	   A^2 -> H(f(k), f(k))
28.11/9.14	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.14	   A^2 -> H(U1(a, d), U1(k, c))
28.11/9.14	   A^2 -> H(U1(a, d), U1(c, e))
28.11/9.14	   A^2 -> H(U1(a, d), U1(c, k))
28.11/9.14	   A^2 -> H(U1(a, d), U1(e, e))
28.11/9.14	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, d), U1(k, d))
28.11/9.14	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.14	   A^2 -> H(U1(a, a), b)
28.11/9.14	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.14	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.14	   A^2 -> H(U1(a, a), c)
28.11/9.14	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.14	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.14	   A^2 -> H(U1(a, a), e)
28.11/9.14	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.14	   A^2 -> H(k, f(b))
28.11/9.14	   A^2 -> H(c, U1(b, b))
28.11/9.14	   A^2 -> H(c, f(c))
28.11/9.14	   A^2 -> H(c, f(d))
28.11/9.14	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.14	   A^2 -> H(U1(e, k), f(c))
28.11/9.14	   A^2 -> H(U1(e, k), f(d))
28.11/9.14	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.14	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.14	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.14	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.14	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.14	   A^2 -> H(U1(e, c), f(e))
28.11/9.14	   A^2 -> H(U1(e, c), f(k))
28.11/9.14	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.14	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.14	   A^2 -> H(U1(k, e), f(c))
28.11/9.14	   A^2 -> H(U1(k, e), f(d))
28.11/9.14	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.14	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.14	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.14	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.14	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.14	   A^2 -> H(U1(k, c), f(e))
28.11/9.14	   A^2 -> H(U1(k, c), f(k))
28.11/9.14	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.14	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.14	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.14	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.14	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.14	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.14	   A^2 -> H(U1(c, e), f(e))
28.11/9.14	   A^2 -> H(U1(c, e), f(k))
28.11/9.14	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.14	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.14	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.14	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.14	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.14	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.14	   A^2 -> H(U1(c, k), f(e))
28.11/9.14	   A^2 -> H(U1(c, k), f(k))
28.11/9.14	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.14	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.14	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.14	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.14	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.14	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.14	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.14	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.14	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.14	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.14	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.14	   A^2 -> H(e, U1(b, b))
28.11/9.14	   A^2 -> H(e, f(c))
28.11/9.14	   A^2 -> H(e, f(d))
28.11/9.14	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.14	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.14	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.14	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.14	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.14	   A^2 -> H(U1(e, e), f(e))
28.11/9.14	   A^2 -> H(U1(e, e), f(k))
28.11/9.14	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.14	   A^2 -> H(f(e), U1(e, b))
28.11/9.14	   A^2 -> H(f(e), U1(k, b))
28.11/9.14	   A^2 -> H(f(e), U1(c, d))
28.11/9.14	   A^2 -> H(f(e), U1(d, c))
28.11/9.14	   A^2 -> H(f(e), U1(b, e))
28.11/9.14	   A^2 -> H(f(e), U1(b, k))
28.11/9.14	   A^2 -> H(f(e), U1(e, c))
28.11/9.14	   A^2 -> H(f(e), U1(k, c))
28.11/9.14	   A^2 -> H(f(e), U1(c, e))
28.11/9.14	   A^2 -> H(f(e), U1(c, k))
28.11/9.14	   A^2 -> H(f(e), U1(k, k))
28.11/9.14	   A^2 -> H(f(e), U1(k, d))
28.11/9.14	   A^2 -> H(f(e), U1(d, k))
28.11/9.14	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.14	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.14	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.14	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.14	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.14	   A^2 -> H(U1(k, k), f(e))
28.11/9.14	   A^2 -> H(U1(k, k), f(k))
28.11/9.14	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.14	   A^2 -> H(f(k), U1(e, b))
28.11/9.14	   A^2 -> H(f(k), U1(k, b))
28.11/9.14	   A^2 -> H(f(k), U1(c, d))
28.11/9.14	   A^2 -> H(f(k), U1(d, c))
28.11/9.14	   A^2 -> H(f(k), U1(b, e))
28.11/9.14	   A^2 -> H(f(k), U1(b, k))
28.11/9.14	   A^2 -> H(f(k), U1(e, c))
28.11/9.14	   A^2 -> H(f(k), U1(k, c))
28.11/9.14	   A^2 -> H(f(k), U1(c, e))
28.11/9.14	   A^2 -> H(f(k), U1(c, k))
28.11/9.14	   A^2 -> H(f(k), U1(e, e))
28.11/9.14	   A^2 -> H(f(k), U1(k, d))
28.11/9.14	   A^2 -> H(f(k), U1(d, k))
28.11/9.14	   A^2 -> H(f(c), b)
28.11/9.14	   A^2 -> H(f(c), U1(e, d))
28.11/9.14	   A^2 -> H(f(c), U1(d, e))
28.11/9.14	   A^2 -> H(f(k), U1(k, k))
28.11/9.14	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.14	   A^2 -> H(U1(k, k), f(c))
28.11/9.14	   A^2 -> H(U1(k, k), f(d))
28.11/9.14	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.14	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.14	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.14	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.14	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.14	   A^2 -> H(U1(k, d), f(e))
28.11/9.14	   A^2 -> H(U1(k, d), f(k))
28.11/9.14	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.14	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.14	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.14	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.14	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.14	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.14	   A^2 -> H(U1(d, k), f(e))
28.11/9.14	   A^2 -> H(U1(d, k), f(k))
28.11/9.14	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.14	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.14	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.14	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.14	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.14	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.14	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.14	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.14	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.14	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.14	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.14	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.14	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.14	   A^2 -> H(f(d), b)
28.11/9.14	   A^2 -> H(f(d), U1(e, d))
28.11/9.14	   A^2 -> H(f(d), U1(d, e))
28.11/9.14	   A^2 -> H(f(d), c)
28.11/9.14	   A^2 -> H(f(d), U1(e, k))
28.11/9.14	   A^2 -> H(f(d), U1(k, e))
28.11/9.14	   A^2 -> H(f(d), e)
28.11/9.14	   A^2 -> H(f(a), d)
28.11/9.14	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.14	   A^2 -> H(f(c), c)
28.11/9.14	   A^2 -> H(f(c), U1(e, k))
28.11/9.14	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.14	   A^2 -> H(f(c), U1(k, e))
28.11/9.14	   A^2 -> H(f(c), U1(k, k))
28.11/9.14	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.14	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.14	   A^2 -> H(f(a), k)
28.11/9.14	   A^2 -> H(f(e), U1(e, e))
28.11/9.14	   A^2 -> H(f(c), e)
28.11/9.14	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.14	   A^2 -> H(f(d), U1(k, k))
28.11/9.14	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.14	   A^2 -> H(d, U1(b, b))
28.11/9.14	   A^2 -> H(d, f(c))
28.11/9.14	   A^2 -> H(d, f(d))
28.11/9.14	   A^2 -> H(a, U1(c, b))
28.11/9.14	   A^2 -> H(a, U1(d, b))
28.11/9.14	   A^2 -> H(a, U1(b, c))
28.11/9.14	   A^2 -> H(a, U1(b, d))
28.11/9.14	   A^2 -> H(a, U1(c, c))
28.11/9.14	   A^2 -> H(a, f(e))
28.11/9.14	   A^2 -> H(a, f(k))
28.11/9.14	   A^2 -> H(a, U1(d, d))
28.11/9.14	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.14	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.14	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.14	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.14	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.14	   A^2 -> H(U1(e, d), f(e))
28.11/9.14	   A^2 -> H(U1(e, d), f(k))
28.11/9.14	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.14	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.14	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.14	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.14	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.14	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.14	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.14	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.14	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.14	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.14	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.14	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.14	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.14	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.14	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.14	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.14	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.14	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.14	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.14	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.14	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.14	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.14	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.14	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.14	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.14	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.14	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.14	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.14	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.14	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.14	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.14	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.14	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.14	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.14	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.14	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.14	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.14	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.14	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.14	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.14	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.14	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.14	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.14	   A^2 -> H(U1(c, a), b)
28.11/9.14	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.14	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.14	   A^2 -> H(U1(c, a), c)
28.11/9.14	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.14	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.14	   A^2 -> H(U1(c, a), e)
28.11/9.14	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.14	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.14	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.14	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.14	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.14	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.14	   A^2 -> H(U1(d, e), f(e))
28.11/9.14	   A^2 -> H(U1(d, e), f(k))
28.11/9.14	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.14	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.14	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.14	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.14	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.14	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.14	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.14	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.14	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.14	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.14	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.14	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.14	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.14	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.14	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.14	   A^2 -> H(U1(d, a), b)
28.11/9.14	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.14	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.14	   A^2 -> H(U1(d, a), c)
28.11/9.14	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.14	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.14	   A^2 -> H(U1(d, a), e)
28.11/9.14	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.14	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.14	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.14	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.14	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.14	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.14	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.14	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.14	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.14	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.14	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.14	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.14	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.14	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.14	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.14	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.14	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.14	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.14	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.14	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.14	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.14	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.14	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.14	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.14	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.14	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.14	   A^2 -> H(U1(a, c), b)
28.11/9.14	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.14	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.14	   A^2 -> H(U1(a, c), c)
28.11/9.14	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.14	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.14	   A^2 -> H(U1(a, c), e)
28.11/9.14	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, d), b)
28.11/9.14	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.14	   A^2 -> H(U1(a, d), U1(d, e))
28.11/9.14	   A^2 -> H(U1(a, d), c)
28.11/9.14	   A^2 -> H(U1(a, d), U1(e, k))
28.11/9.14	
28.11/9.14	The TRS R consists of the following rules:
28.11/9.14	
28.11/9.14	   f(x) -> U1(x, x)
28.11/9.14	   U1(e, x) -> x
28.11/9.14	   a -> c
28.11/9.14	   a -> d
28.11/9.14	   b -> c
28.11/9.14	   b -> d
28.11/9.14	   d -> k
28.11/9.14	   c -> e
28.11/9.14	   c -> k
28.11/9.14	
28.11/9.14	Q is empty.
28.11/9.14	We have to consider all minimal (P,Q,R)-chains.
28.11/9.14	----------------------------------------
28.11/9.14	
28.11/9.14	(755) TransformationProof (EQUIVALENT)
28.11/9.14	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.14	
28.11/9.14	   (A^2 -> H(U1(c, d), U1(k, c)),A^2 -> H(U1(c, d), U1(k, c)))
28.11/9.14	   (A^2 -> H(U1(d, d), U1(k, c)),A^2 -> H(U1(d, d), U1(k, c)))
28.11/9.14	   (A^2 -> H(U1(a, k), U1(k, c)),A^2 -> H(U1(a, k), U1(k, c)))
28.11/9.14	   (A^2 -> H(U1(a, d), U1(k, e)),A^2 -> H(U1(a, d), U1(k, e)))
28.11/9.14	   (A^2 -> H(U1(a, d), U1(k, k)),A^2 -> H(U1(a, d), U1(k, k)))
28.11/9.14	
28.11/9.14	
28.11/9.14	----------------------------------------
28.11/9.14	
28.11/9.14	(756)
28.11/9.14	Obligation:
28.11/9.14	Q DP problem:
28.11/9.14	The TRS P consists of the following rules:
28.11/9.14	
28.11/9.14	   H(x, x) -> G(x, x, f(k))
28.11/9.14	   G(d, x, x) -> A^2
28.11/9.14	   A^2 -> H(f(c), f(c))
28.11/9.14	   A^2 -> H(f(d), f(d))
28.11/9.14	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.14	   A^2 -> H(f(e), f(e))
28.11/9.14	   A^2 -> H(f(k), f(k))
28.11/9.14	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.14	   A^2 -> H(U1(a, d), U1(c, e))
28.11/9.14	   A^2 -> H(U1(a, d), U1(c, k))
28.11/9.14	   A^2 -> H(U1(a, d), U1(e, e))
28.11/9.14	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, d), U1(k, d))
28.11/9.14	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.14	   A^2 -> H(U1(a, a), b)
28.11/9.14	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.14	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.14	   A^2 -> H(U1(a, a), c)
28.11/9.14	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.14	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.14	   A^2 -> H(U1(a, a), e)
28.11/9.14	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.14	   A^2 -> H(k, f(b))
28.11/9.14	   A^2 -> H(c, U1(b, b))
28.11/9.14	   A^2 -> H(c, f(c))
28.11/9.14	   A^2 -> H(c, f(d))
28.11/9.14	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.14	   A^2 -> H(U1(e, k), f(c))
28.11/9.14	   A^2 -> H(U1(e, k), f(d))
28.11/9.14	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.14	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.14	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.14	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.14	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.14	   A^2 -> H(U1(e, c), f(e))
28.11/9.14	   A^2 -> H(U1(e, c), f(k))
28.11/9.14	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.14	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.14	   A^2 -> H(U1(k, e), f(c))
28.11/9.14	   A^2 -> H(U1(k, e), f(d))
28.11/9.14	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.14	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.14	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.14	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.14	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.14	   A^2 -> H(U1(k, c), f(e))
28.11/9.14	   A^2 -> H(U1(k, c), f(k))
28.11/9.14	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.14	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.14	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.14	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.14	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.14	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.14	   A^2 -> H(U1(c, e), f(e))
28.11/9.14	   A^2 -> H(U1(c, e), f(k))
28.11/9.14	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.14	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.14	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.14	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.14	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.14	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.14	   A^2 -> H(U1(c, k), f(e))
28.11/9.14	   A^2 -> H(U1(c, k), f(k))
28.11/9.14	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.14	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.14	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.14	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.14	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.14	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.14	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.14	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.14	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.14	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.14	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.14	   A^2 -> H(e, U1(b, b))
28.11/9.14	   A^2 -> H(e, f(c))
28.11/9.14	   A^2 -> H(e, f(d))
28.11/9.14	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.14	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.14	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.14	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.14	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.14	   A^2 -> H(U1(e, e), f(e))
28.11/9.14	   A^2 -> H(U1(e, e), f(k))
28.11/9.14	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.14	   A^2 -> H(f(e), U1(e, b))
28.11/9.14	   A^2 -> H(f(e), U1(k, b))
28.11/9.14	   A^2 -> H(f(e), U1(c, d))
28.11/9.14	   A^2 -> H(f(e), U1(d, c))
28.11/9.14	   A^2 -> H(f(e), U1(b, e))
28.11/9.14	   A^2 -> H(f(e), U1(b, k))
28.11/9.14	   A^2 -> H(f(e), U1(e, c))
28.11/9.14	   A^2 -> H(f(e), U1(k, c))
28.11/9.14	   A^2 -> H(f(e), U1(c, e))
28.11/9.14	   A^2 -> H(f(e), U1(c, k))
28.11/9.14	   A^2 -> H(f(e), U1(k, k))
28.11/9.14	   A^2 -> H(f(e), U1(k, d))
28.11/9.14	   A^2 -> H(f(e), U1(d, k))
28.11/9.14	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.14	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.14	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.14	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.14	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.14	   A^2 -> H(U1(k, k), f(e))
28.11/9.14	   A^2 -> H(U1(k, k), f(k))
28.11/9.14	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.14	   A^2 -> H(f(k), U1(e, b))
28.11/9.14	   A^2 -> H(f(k), U1(k, b))
28.11/9.14	   A^2 -> H(f(k), U1(c, d))
28.11/9.14	   A^2 -> H(f(k), U1(d, c))
28.11/9.14	   A^2 -> H(f(k), U1(b, e))
28.11/9.14	   A^2 -> H(f(k), U1(b, k))
28.11/9.14	   A^2 -> H(f(k), U1(e, c))
28.11/9.14	   A^2 -> H(f(k), U1(k, c))
28.11/9.14	   A^2 -> H(f(k), U1(c, e))
28.11/9.14	   A^2 -> H(f(k), U1(c, k))
28.11/9.14	   A^2 -> H(f(k), U1(e, e))
28.11/9.14	   A^2 -> H(f(k), U1(k, d))
28.11/9.14	   A^2 -> H(f(k), U1(d, k))
28.11/9.14	   A^2 -> H(f(c), b)
28.11/9.14	   A^2 -> H(f(c), U1(e, d))
28.11/9.14	   A^2 -> H(f(c), U1(d, e))
28.11/9.14	   A^2 -> H(f(k), U1(k, k))
28.11/9.14	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.14	   A^2 -> H(U1(k, k), f(c))
28.11/9.14	   A^2 -> H(U1(k, k), f(d))
28.11/9.14	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.14	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.14	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.14	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.14	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.14	   A^2 -> H(U1(k, d), f(e))
28.11/9.14	   A^2 -> H(U1(k, d), f(k))
28.11/9.14	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.14	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.14	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.14	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.14	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.14	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.14	   A^2 -> H(U1(d, k), f(e))
28.11/9.14	   A^2 -> H(U1(d, k), f(k))
28.11/9.14	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.14	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.14	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.14	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.14	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.14	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.14	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.14	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.14	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.14	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.14	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.14	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.14	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.14	   A^2 -> H(f(d), b)
28.11/9.14	   A^2 -> H(f(d), U1(e, d))
28.11/9.14	   A^2 -> H(f(d), U1(d, e))
28.11/9.14	   A^2 -> H(f(d), c)
28.11/9.14	   A^2 -> H(f(d), U1(e, k))
28.11/9.14	   A^2 -> H(f(d), U1(k, e))
28.11/9.14	   A^2 -> H(f(d), e)
28.11/9.14	   A^2 -> H(f(a), d)
28.11/9.14	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.14	   A^2 -> H(f(c), c)
28.11/9.14	   A^2 -> H(f(c), U1(e, k))
28.11/9.14	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.14	   A^2 -> H(f(c), U1(k, e))
28.11/9.14	   A^2 -> H(f(c), U1(k, k))
28.11/9.14	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.14	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.14	   A^2 -> H(f(a), k)
28.11/9.14	   A^2 -> H(f(e), U1(e, e))
28.11/9.14	   A^2 -> H(f(c), e)
28.11/9.14	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.14	   A^2 -> H(f(d), U1(k, k))
28.11/9.14	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.14	   A^2 -> H(d, U1(b, b))
28.11/9.14	   A^2 -> H(d, f(c))
28.11/9.14	   A^2 -> H(d, f(d))
28.11/9.14	   A^2 -> H(a, U1(c, b))
28.11/9.14	   A^2 -> H(a, U1(d, b))
28.11/9.14	   A^2 -> H(a, U1(b, c))
28.11/9.14	   A^2 -> H(a, U1(b, d))
28.11/9.14	   A^2 -> H(a, U1(c, c))
28.11/9.14	   A^2 -> H(a, f(e))
28.11/9.14	   A^2 -> H(a, f(k))
28.11/9.14	   A^2 -> H(a, U1(d, d))
28.11/9.14	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.14	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.14	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.14	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.14	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.14	   A^2 -> H(U1(e, d), f(e))
28.11/9.14	   A^2 -> H(U1(e, d), f(k))
28.11/9.14	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.14	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.14	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.14	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.14	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.14	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.14	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.14	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.14	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.14	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.14	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.14	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.14	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.14	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.14	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.14	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.14	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.14	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.14	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.14	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.14	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.14	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.14	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.14	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.14	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.14	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.14	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.14	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.14	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.14	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.14	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.14	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.14	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.14	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.14	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.14	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.14	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.14	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.14	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.14	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.14	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.14	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.14	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.14	   A^2 -> H(U1(c, a), b)
28.11/9.14	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.14	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.14	   A^2 -> H(U1(c, a), c)
28.11/9.14	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.14	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.14	   A^2 -> H(U1(c, a), e)
28.11/9.14	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.14	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.14	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.14	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.14	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.14	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.14	   A^2 -> H(U1(d, e), f(e))
28.11/9.14	   A^2 -> H(U1(d, e), f(k))
28.11/9.14	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.14	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.14	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.14	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.14	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.14	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.14	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.14	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.14	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.14	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.14	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.14	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.14	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.14	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.14	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.14	   A^2 -> H(U1(d, a), b)
28.11/9.14	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.14	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.14	   A^2 -> H(U1(d, a), c)
28.11/9.14	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.14	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.14	   A^2 -> H(U1(d, a), e)
28.11/9.14	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.14	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.14	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.14	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.14	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.14	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.14	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.14	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.14	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.14	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.14	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.14	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.14	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.14	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.14	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.14	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.14	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.14	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.14	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.14	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.14	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.14	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.14	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.14	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.14	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.14	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.14	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.14	   A^2 -> H(U1(a, c), b)
28.11/9.14	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.15	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.15	   A^2 -> H(U1(a, c), c)
28.11/9.15	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.15	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.15	   A^2 -> H(U1(a, c), e)
28.11/9.15	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.15	   A^2 -> H(U1(a, d), b)
28.11/9.15	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.15	   A^2 -> H(U1(a, d), U1(d, e))
28.11/9.15	   A^2 -> H(U1(a, d), c)
28.11/9.15	   A^2 -> H(U1(a, d), U1(e, k))
28.11/9.15	   A^2 -> H(U1(a, d), U1(k, e))
28.11/9.15	
28.11/9.15	The TRS R consists of the following rules:
28.11/9.15	
28.11/9.15	   f(x) -> U1(x, x)
28.11/9.15	   U1(e, x) -> x
28.11/9.15	   a -> c
28.11/9.15	   a -> d
28.11/9.15	   b -> c
28.11/9.15	   b -> d
28.11/9.15	   d -> k
28.11/9.15	   c -> e
28.11/9.15	   c -> k
28.11/9.15	
28.11/9.15	Q is empty.
28.11/9.15	We have to consider all minimal (P,Q,R)-chains.
28.11/9.15	----------------------------------------
28.11/9.15	
28.11/9.15	(757) TransformationProof (EQUIVALENT)
28.11/9.15	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.15	
28.11/9.15	   (A^2 -> H(U1(c, d), U1(c, e)),A^2 -> H(U1(c, d), U1(c, e)))
28.11/9.15	   (A^2 -> H(U1(d, d), U1(c, e)),A^2 -> H(U1(d, d), U1(c, e)))
28.11/9.15	   (A^2 -> H(U1(a, k), U1(c, e)),A^2 -> H(U1(a, k), U1(c, e)))
28.11/9.15	   (A^2 -> H(U1(a, d), U1(e, e)),A^2 -> H(U1(a, d), U1(e, e)))
28.11/9.15	   (A^2 -> H(U1(a, d), U1(k, e)),A^2 -> H(U1(a, d), U1(k, e)))
28.11/9.15	
28.11/9.15	
28.11/9.15	----------------------------------------
28.11/9.15	
28.11/9.15	(758)
28.11/9.15	Obligation:
28.11/9.15	Q DP problem:
28.11/9.15	The TRS P consists of the following rules:
28.11/9.15	
28.11/9.15	   H(x, x) -> G(x, x, f(k))
28.11/9.15	   G(d, x, x) -> A^2
28.11/9.15	   A^2 -> H(f(c), f(c))
28.11/9.15	   A^2 -> H(f(d), f(d))
28.11/9.15	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.15	   A^2 -> H(f(e), f(e))
28.11/9.15	   A^2 -> H(f(k), f(k))
28.11/9.15	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.15	   A^2 -> H(U1(a, d), U1(c, k))
28.11/9.15	   A^2 -> H(U1(a, d), U1(e, e))
28.11/9.15	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.15	   A^2 -> H(U1(a, d), U1(k, d))
28.11/9.15	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.15	   A^2 -> H(U1(a, a), b)
28.11/9.15	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.15	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.15	   A^2 -> H(U1(a, a), c)
28.11/9.15	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.15	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.15	   A^2 -> H(U1(a, a), e)
28.11/9.15	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.15	   A^2 -> H(k, f(b))
28.11/9.15	   A^2 -> H(c, U1(b, b))
28.11/9.15	   A^2 -> H(c, f(c))
28.11/9.15	   A^2 -> H(c, f(d))
28.11/9.15	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.15	   A^2 -> H(U1(e, k), f(c))
28.11/9.15	   A^2 -> H(U1(e, k), f(d))
28.11/9.15	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.15	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.15	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.15	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.15	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.15	   A^2 -> H(U1(e, c), f(e))
28.11/9.15	   A^2 -> H(U1(e, c), f(k))
28.11/9.15	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.15	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.15	   A^2 -> H(U1(k, e), f(c))
28.11/9.15	   A^2 -> H(U1(k, e), f(d))
28.11/9.15	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.15	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.15	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.15	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.15	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.15	   A^2 -> H(U1(k, c), f(e))
28.11/9.15	   A^2 -> H(U1(k, c), f(k))
28.11/9.15	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.15	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.15	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.15	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.15	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.15	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.15	   A^2 -> H(U1(c, e), f(e))
28.11/9.15	   A^2 -> H(U1(c, e), f(k))
28.11/9.15	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.15	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.15	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.15	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.15	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.15	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.15	   A^2 -> H(U1(c, k), f(e))
28.11/9.15	   A^2 -> H(U1(c, k), f(k))
28.11/9.15	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.15	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.15	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.15	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.15	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.15	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.15	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.15	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.15	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.15	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.15	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.15	   A^2 -> H(e, U1(b, b))
28.11/9.15	   A^2 -> H(e, f(c))
28.11/9.15	   A^2 -> H(e, f(d))
28.11/9.15	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.15	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.15	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.15	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.15	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.15	   A^2 -> H(U1(e, e), f(e))
28.11/9.15	   A^2 -> H(U1(e, e), f(k))
28.11/9.15	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.15	   A^2 -> H(f(e), U1(e, b))
28.11/9.15	   A^2 -> H(f(e), U1(k, b))
28.11/9.15	   A^2 -> H(f(e), U1(c, d))
28.11/9.15	   A^2 -> H(f(e), U1(d, c))
28.11/9.15	   A^2 -> H(f(e), U1(b, e))
28.11/9.15	   A^2 -> H(f(e), U1(b, k))
28.11/9.15	   A^2 -> H(f(e), U1(e, c))
28.11/9.15	   A^2 -> H(f(e), U1(k, c))
28.11/9.15	   A^2 -> H(f(e), U1(c, e))
28.11/9.15	   A^2 -> H(f(e), U1(c, k))
28.11/9.15	   A^2 -> H(f(e), U1(k, k))
28.11/9.15	   A^2 -> H(f(e), U1(k, d))
28.11/9.15	   A^2 -> H(f(e), U1(d, k))
28.11/9.15	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.15	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.15	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.15	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.15	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.15	   A^2 -> H(U1(k, k), f(e))
28.11/9.15	   A^2 -> H(U1(k, k), f(k))
28.11/9.15	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.15	   A^2 -> H(f(k), U1(e, b))
28.11/9.15	   A^2 -> H(f(k), U1(k, b))
28.11/9.15	   A^2 -> H(f(k), U1(c, d))
28.11/9.15	   A^2 -> H(f(k), U1(d, c))
28.11/9.15	   A^2 -> H(f(k), U1(b, e))
28.11/9.15	   A^2 -> H(f(k), U1(b, k))
28.11/9.15	   A^2 -> H(f(k), U1(e, c))
28.11/9.15	   A^2 -> H(f(k), U1(k, c))
28.11/9.15	   A^2 -> H(f(k), U1(c, e))
28.11/9.15	   A^2 -> H(f(k), U1(c, k))
28.11/9.15	   A^2 -> H(f(k), U1(e, e))
28.11/9.15	   A^2 -> H(f(k), U1(k, d))
28.11/9.15	   A^2 -> H(f(k), U1(d, k))
28.11/9.15	   A^2 -> H(f(c), b)
28.11/9.15	   A^2 -> H(f(c), U1(e, d))
28.11/9.15	   A^2 -> H(f(c), U1(d, e))
28.11/9.15	   A^2 -> H(f(k), U1(k, k))
28.11/9.15	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.15	   A^2 -> H(U1(k, k), f(c))
28.11/9.15	   A^2 -> H(U1(k, k), f(d))
28.11/9.15	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.15	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.15	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.15	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.15	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.15	   A^2 -> H(U1(k, d), f(e))
28.11/9.15	   A^2 -> H(U1(k, d), f(k))
28.11/9.15	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.15	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.15	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.15	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.15	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.15	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.15	   A^2 -> H(U1(d, k), f(e))
28.11/9.15	   A^2 -> H(U1(d, k), f(k))
28.11/9.15	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.15	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.15	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.15	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.15	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.15	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.15	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.15	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.15	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.15	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.15	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.15	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.15	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.15	   A^2 -> H(f(d), b)
28.11/9.15	   A^2 -> H(f(d), U1(e, d))
28.11/9.15	   A^2 -> H(f(d), U1(d, e))
28.11/9.15	   A^2 -> H(f(d), c)
28.11/9.15	   A^2 -> H(f(d), U1(e, k))
28.11/9.15	   A^2 -> H(f(d), U1(k, e))
28.11/9.15	   A^2 -> H(f(d), e)
28.11/9.15	   A^2 -> H(f(a), d)
28.11/9.15	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.15	   A^2 -> H(f(c), c)
28.11/9.15	   A^2 -> H(f(c), U1(e, k))
28.11/9.15	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.15	   A^2 -> H(f(c), U1(k, e))
28.11/9.15	   A^2 -> H(f(c), U1(k, k))
28.11/9.15	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.15	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.15	   A^2 -> H(f(a), k)
28.11/9.15	   A^2 -> H(f(e), U1(e, e))
28.11/9.15	   A^2 -> H(f(c), e)
28.11/9.15	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.15	   A^2 -> H(f(d), U1(k, k))
28.11/9.15	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.15	   A^2 -> H(d, U1(b, b))
28.11/9.15	   A^2 -> H(d, f(c))
28.11/9.15	   A^2 -> H(d, f(d))
28.11/9.15	   A^2 -> H(a, U1(c, b))
28.11/9.15	   A^2 -> H(a, U1(d, b))
28.11/9.15	   A^2 -> H(a, U1(b, c))
28.11/9.15	   A^2 -> H(a, U1(b, d))
28.11/9.15	   A^2 -> H(a, U1(c, c))
28.11/9.15	   A^2 -> H(a, f(e))
28.11/9.15	   A^2 -> H(a, f(k))
28.11/9.15	   A^2 -> H(a, U1(d, d))
28.11/9.15	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.15	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.15	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.15	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.15	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.15	   A^2 -> H(U1(e, d), f(e))
28.11/9.15	   A^2 -> H(U1(e, d), f(k))
28.11/9.15	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.15	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.15	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.15	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.15	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.15	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.15	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.15	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.15	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.15	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.15	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.15	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.15	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.15	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.15	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.15	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.15	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.15	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.15	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.15	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.15	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.15	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.15	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.15	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.15	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.15	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.15	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.15	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.15	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.15	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.15	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.15	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.15	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.15	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.15	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.15	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.15	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.15	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.15	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.15	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.15	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.15	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.15	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.15	   A^2 -> H(U1(c, a), b)
28.11/9.15	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.15	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.15	   A^2 -> H(U1(c, a), c)
28.11/9.15	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.15	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.15	   A^2 -> H(U1(c, a), e)
28.11/9.15	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.15	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.15	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.15	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.15	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.15	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.15	   A^2 -> H(U1(d, e), f(e))
28.11/9.15	   A^2 -> H(U1(d, e), f(k))
28.11/9.15	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.15	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.15	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.15	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.15	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.15	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.15	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.15	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.15	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.15	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.15	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.15	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.15	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.15	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.15	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.15	   A^2 -> H(U1(d, a), b)
28.11/9.15	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.15	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.15	   A^2 -> H(U1(d, a), c)
28.11/9.15	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.15	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.15	   A^2 -> H(U1(d, a), e)
28.11/9.15	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.15	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.15	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.15	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.15	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.15	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.15	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.15	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.15	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.15	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.15	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.15	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.15	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.15	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.15	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.15	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.15	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.15	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.15	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.15	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.15	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.15	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.15	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.15	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.15	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.15	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.15	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.15	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.15	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.15	   A^2 -> H(U1(a, c), b)
28.11/9.15	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.15	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.15	   A^2 -> H(U1(a, c), c)
28.11/9.15	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.15	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.15	   A^2 -> H(U1(a, c), e)
28.11/9.15	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.15	   A^2 -> H(U1(a, d), b)
28.11/9.15	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.15	   A^2 -> H(U1(a, d), U1(d, e))
28.11/9.15	   A^2 -> H(U1(a, d), c)
28.11/9.15	   A^2 -> H(U1(a, d), U1(e, k))
28.11/9.15	   A^2 -> H(U1(a, d), U1(k, e))
28.11/9.15	
28.11/9.15	The TRS R consists of the following rules:
28.11/9.15	
28.11/9.15	   f(x) -> U1(x, x)
28.11/9.15	   U1(e, x) -> x
28.11/9.15	   a -> c
28.11/9.15	   a -> d
28.11/9.15	   b -> c
28.11/9.15	   b -> d
28.11/9.15	   d -> k
28.11/9.15	   c -> e
28.11/9.15	   c -> k
28.11/9.15	
28.11/9.15	Q is empty.
28.11/9.15	We have to consider all minimal (P,Q,R)-chains.
28.11/9.15	----------------------------------------
28.11/9.15	
28.11/9.15	(759) TransformationProof (EQUIVALENT)
28.11/9.15	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.15	
28.11/9.15	   (A^2 -> H(U1(c, d), U1(c, k)),A^2 -> H(U1(c, d), U1(c, k)))
28.11/9.15	   (A^2 -> H(U1(d, d), U1(c, k)),A^2 -> H(U1(d, d), U1(c, k)))
28.11/9.15	   (A^2 -> H(U1(a, k), U1(c, k)),A^2 -> H(U1(a, k), U1(c, k)))
28.11/9.15	   (A^2 -> H(U1(a, d), U1(e, k)),A^2 -> H(U1(a, d), U1(e, k)))
28.11/9.15	   (A^2 -> H(U1(a, d), U1(k, k)),A^2 -> H(U1(a, d), U1(k, k)))
28.11/9.15	
28.11/9.15	
28.11/9.15	----------------------------------------
28.11/9.15	
28.11/9.15	(760)
28.11/9.15	Obligation:
28.11/9.15	Q DP problem:
28.11/9.15	The TRS P consists of the following rules:
28.11/9.15	
28.11/9.15	   H(x, x) -> G(x, x, f(k))
28.11/9.15	   G(d, x, x) -> A^2
28.11/9.15	   A^2 -> H(f(c), f(c))
28.11/9.15	   A^2 -> H(f(d), f(d))
28.11/9.15	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.15	   A^2 -> H(f(e), f(e))
28.11/9.15	   A^2 -> H(f(k), f(k))
28.11/9.15	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.15	   A^2 -> H(U1(a, d), U1(e, e))
28.11/9.15	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.15	   A^2 -> H(U1(a, d), U1(k, d))
28.11/9.15	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.15	   A^2 -> H(U1(a, a), b)
28.11/9.15	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.15	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.15	   A^2 -> H(U1(a, a), c)
28.11/9.15	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.15	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.15	   A^2 -> H(U1(a, a), e)
28.11/9.15	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.15	   A^2 -> H(k, f(b))
28.11/9.15	   A^2 -> H(c, U1(b, b))
28.11/9.15	   A^2 -> H(c, f(c))
28.11/9.15	   A^2 -> H(c, f(d))
28.11/9.15	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.15	   A^2 -> H(U1(e, k), f(c))
28.11/9.15	   A^2 -> H(U1(e, k), f(d))
28.11/9.15	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.15	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.15	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.15	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.15	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.15	   A^2 -> H(U1(e, c), f(e))
28.11/9.15	   A^2 -> H(U1(e, c), f(k))
28.11/9.15	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.15	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.15	   A^2 -> H(U1(k, e), f(c))
28.11/9.15	   A^2 -> H(U1(k, e), f(d))
28.11/9.15	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.15	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.15	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.15	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.15	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.15	   A^2 -> H(U1(k, c), f(e))
28.11/9.15	   A^2 -> H(U1(k, c), f(k))
28.11/9.15	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.15	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.15	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.15	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.15	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.15	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.15	   A^2 -> H(U1(c, e), f(e))
28.11/9.15	   A^2 -> H(U1(c, e), f(k))
28.11/9.15	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.15	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.15	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.15	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.15	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.15	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.15	   A^2 -> H(U1(c, k), f(e))
28.11/9.15	   A^2 -> H(U1(c, k), f(k))
28.11/9.15	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.15	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.15	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.15	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.15	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.15	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.15	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.15	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.15	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.15	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.15	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.15	   A^2 -> H(e, U1(b, b))
28.11/9.15	   A^2 -> H(e, f(c))
28.11/9.15	   A^2 -> H(e, f(d))
28.11/9.15	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.15	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.15	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.15	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.15	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.15	   A^2 -> H(U1(e, e), f(e))
28.11/9.15	   A^2 -> H(U1(e, e), f(k))
28.11/9.15	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.15	   A^2 -> H(f(e), U1(e, b))
28.11/9.15	   A^2 -> H(f(e), U1(k, b))
28.11/9.15	   A^2 -> H(f(e), U1(c, d))
28.11/9.15	   A^2 -> H(f(e), U1(d, c))
28.11/9.15	   A^2 -> H(f(e), U1(b, e))
28.11/9.15	   A^2 -> H(f(e), U1(b, k))
28.11/9.15	   A^2 -> H(f(e), U1(e, c))
28.11/9.15	   A^2 -> H(f(e), U1(k, c))
28.11/9.15	   A^2 -> H(f(e), U1(c, e))
28.11/9.15	   A^2 -> H(f(e), U1(c, k))
28.11/9.15	   A^2 -> H(f(e), U1(k, k))
28.11/9.15	   A^2 -> H(f(e), U1(k, d))
28.11/9.15	   A^2 -> H(f(e), U1(d, k))
28.11/9.15	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.15	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.15	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.15	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.15	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.15	   A^2 -> H(U1(k, k), f(e))
28.11/9.15	   A^2 -> H(U1(k, k), f(k))
28.11/9.15	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.15	   A^2 -> H(f(k), U1(e, b))
28.11/9.15	   A^2 -> H(f(k), U1(k, b))
28.11/9.15	   A^2 -> H(f(k), U1(c, d))
28.11/9.15	   A^2 -> H(f(k), U1(d, c))
28.11/9.15	   A^2 -> H(f(k), U1(b, e))
28.11/9.15	   A^2 -> H(f(k), U1(b, k))
28.11/9.15	   A^2 -> H(f(k), U1(e, c))
28.11/9.15	   A^2 -> H(f(k), U1(k, c))
28.11/9.15	   A^2 -> H(f(k), U1(c, e))
28.11/9.15	   A^2 -> H(f(k), U1(c, k))
28.11/9.15	   A^2 -> H(f(k), U1(e, e))
28.11/9.15	   A^2 -> H(f(k), U1(k, d))
28.11/9.15	   A^2 -> H(f(k), U1(d, k))
28.11/9.15	   A^2 -> H(f(c), b)
28.11/9.15	   A^2 -> H(f(c), U1(e, d))
28.11/9.15	   A^2 -> H(f(c), U1(d, e))
28.11/9.15	   A^2 -> H(f(k), U1(k, k))
28.11/9.15	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.15	   A^2 -> H(U1(k, k), f(c))
28.11/9.15	   A^2 -> H(U1(k, k), f(d))
28.11/9.15	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.15	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.15	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.15	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.15	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.15	   A^2 -> H(U1(k, d), f(e))
28.11/9.15	   A^2 -> H(U1(k, d), f(k))
28.11/9.15	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.15	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.15	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.15	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.15	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.15	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.15	   A^2 -> H(U1(d, k), f(e))
28.11/9.15	   A^2 -> H(U1(d, k), f(k))
28.11/9.15	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.15	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.15	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.15	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.15	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.15	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.15	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.15	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.15	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.15	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.15	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.15	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.15	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.15	   A^2 -> H(f(d), b)
28.11/9.15	   A^2 -> H(f(d), U1(e, d))
28.11/9.15	   A^2 -> H(f(d), U1(d, e))
28.11/9.15	   A^2 -> H(f(d), c)
28.11/9.15	   A^2 -> H(f(d), U1(e, k))
28.11/9.15	   A^2 -> H(f(d), U1(k, e))
28.11/9.15	   A^2 -> H(f(d), e)
28.11/9.15	   A^2 -> H(f(a), d)
28.11/9.15	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.15	   A^2 -> H(f(c), c)
28.11/9.15	   A^2 -> H(f(c), U1(e, k))
28.11/9.15	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.15	   A^2 -> H(f(c), U1(k, e))
28.11/9.15	   A^2 -> H(f(c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.16	   A^2 -> H(f(a), k)
28.11/9.16	   A^2 -> H(f(e), U1(e, e))
28.11/9.16	   A^2 -> H(f(c), e)
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.16	   A^2 -> H(f(d), U1(k, k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.16	   A^2 -> H(d, U1(b, b))
28.11/9.16	   A^2 -> H(d, f(c))
28.11/9.16	   A^2 -> H(d, f(d))
28.11/9.16	   A^2 -> H(a, U1(c, b))
28.11/9.16	   A^2 -> H(a, U1(d, b))
28.11/9.16	   A^2 -> H(a, U1(b, c))
28.11/9.16	   A^2 -> H(a, U1(b, d))
28.11/9.16	   A^2 -> H(a, U1(c, c))
28.11/9.16	   A^2 -> H(a, f(e))
28.11/9.16	   A^2 -> H(a, f(k))
28.11/9.16	   A^2 -> H(a, U1(d, d))
28.11/9.16	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.16	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.16	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.16	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.16	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.16	   A^2 -> H(U1(e, d), f(e))
28.11/9.16	   A^2 -> H(U1(e, d), f(k))
28.11/9.16	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.16	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.16	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.16	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.16	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.16	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.16	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.16	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.16	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.16	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.16	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.16	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.16	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.16	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.16	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.16	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.16	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.16	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.16	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.16	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.16	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.16	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.16	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.16	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.16	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.16	   A^2 -> H(U1(c, a), b)
28.11/9.16	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.16	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.16	   A^2 -> H(U1(c, a), c)
28.11/9.16	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.16	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.16	   A^2 -> H(U1(c, a), e)
28.11/9.16	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.16	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.16	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.16	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.16	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.16	   A^2 -> H(U1(d, e), f(e))
28.11/9.16	   A^2 -> H(U1(d, e), f(k))
28.11/9.16	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.16	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.16	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.16	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.16	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.16	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.16	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.16	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.16	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.16	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.16	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.16	   A^2 -> H(U1(d, a), b)
28.11/9.16	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.16	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.16	   A^2 -> H(U1(d, a), c)
28.11/9.16	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.16	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.16	   A^2 -> H(U1(d, a), e)
28.11/9.16	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.16	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.16	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.16	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.16	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.16	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.16	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.16	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.16	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.16	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.16	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.16	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.16	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.16	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.16	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.16	   A^2 -> H(U1(a, c), b)
28.11/9.16	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.16	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.16	   A^2 -> H(U1(a, c), c)
28.11/9.16	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.16	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.16	   A^2 -> H(U1(a, c), e)
28.11/9.16	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, d), b)
28.11/9.16	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.16	   A^2 -> H(U1(a, d), U1(d, e))
28.11/9.16	   A^2 -> H(U1(a, d), c)
28.11/9.16	   A^2 -> H(U1(a, d), U1(e, k))
28.11/9.16	   A^2 -> H(U1(a, d), U1(k, e))
28.11/9.16	
28.11/9.16	The TRS R consists of the following rules:
28.11/9.16	
28.11/9.16	   f(x) -> U1(x, x)
28.11/9.16	   U1(e, x) -> x
28.11/9.16	   a -> c
28.11/9.16	   a -> d
28.11/9.16	   b -> c
28.11/9.16	   b -> d
28.11/9.16	   d -> k
28.11/9.16	   c -> e
28.11/9.16	   c -> k
28.11/9.16	
28.11/9.16	Q is empty.
28.11/9.16	We have to consider all minimal (P,Q,R)-chains.
28.11/9.16	----------------------------------------
28.11/9.16	
28.11/9.16	(761) TransformationProof (EQUIVALENT)
28.11/9.16	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.16	
28.11/9.16	   (A^2 -> H(U1(c, d), U1(e, e)),A^2 -> H(U1(c, d), U1(e, e)))
28.11/9.16	   (A^2 -> H(U1(d, d), U1(e, e)),A^2 -> H(U1(d, d), U1(e, e)))
28.11/9.16	   (A^2 -> H(U1(a, k), U1(e, e)),A^2 -> H(U1(a, k), U1(e, e)))
28.11/9.16	   (A^2 -> H(U1(a, d), e),A^2 -> H(U1(a, d), e))
28.11/9.16	
28.11/9.16	
28.11/9.16	----------------------------------------
28.11/9.16	
28.11/9.16	(762)
28.11/9.16	Obligation:
28.11/9.16	Q DP problem:
28.11/9.16	The TRS P consists of the following rules:
28.11/9.16	
28.11/9.16	   H(x, x) -> G(x, x, f(k))
28.11/9.16	   G(d, x, x) -> A^2
28.11/9.16	   A^2 -> H(f(c), f(c))
28.11/9.16	   A^2 -> H(f(d), f(d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.16	   A^2 -> H(f(e), f(e))
28.11/9.16	   A^2 -> H(f(k), f(k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.16	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, d), U1(k, d))
28.11/9.16	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.16	   A^2 -> H(U1(a, a), b)
28.11/9.16	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.16	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.16	   A^2 -> H(U1(a, a), c)
28.11/9.16	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.16	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.16	   A^2 -> H(U1(a, a), e)
28.11/9.16	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.16	   A^2 -> H(k, f(b))
28.11/9.16	   A^2 -> H(c, U1(b, b))
28.11/9.16	   A^2 -> H(c, f(c))
28.11/9.16	   A^2 -> H(c, f(d))
28.11/9.16	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.16	   A^2 -> H(U1(e, k), f(c))
28.11/9.16	   A^2 -> H(U1(e, k), f(d))
28.11/9.16	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.16	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.16	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.16	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.16	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.16	   A^2 -> H(U1(e, c), f(e))
28.11/9.16	   A^2 -> H(U1(e, c), f(k))
28.11/9.16	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.16	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.16	   A^2 -> H(U1(k, e), f(c))
28.11/9.16	   A^2 -> H(U1(k, e), f(d))
28.11/9.16	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.16	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.16	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.16	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.16	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.16	   A^2 -> H(U1(k, c), f(e))
28.11/9.16	   A^2 -> H(U1(k, c), f(k))
28.11/9.16	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.16	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.16	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.16	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.16	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.16	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.16	   A^2 -> H(U1(c, e), f(e))
28.11/9.16	   A^2 -> H(U1(c, e), f(k))
28.11/9.16	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.16	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.16	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.16	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.16	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.16	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.16	   A^2 -> H(U1(c, k), f(e))
28.11/9.16	   A^2 -> H(U1(c, k), f(k))
28.11/9.16	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.16	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.16	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.16	   A^2 -> H(e, U1(b, b))
28.11/9.16	   A^2 -> H(e, f(c))
28.11/9.16	   A^2 -> H(e, f(d))
28.11/9.16	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.16	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.16	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.16	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.16	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.16	   A^2 -> H(U1(e, e), f(e))
28.11/9.16	   A^2 -> H(U1(e, e), f(k))
28.11/9.16	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.16	   A^2 -> H(f(e), U1(e, b))
28.11/9.16	   A^2 -> H(f(e), U1(k, b))
28.11/9.16	   A^2 -> H(f(e), U1(c, d))
28.11/9.16	   A^2 -> H(f(e), U1(d, c))
28.11/9.16	   A^2 -> H(f(e), U1(b, e))
28.11/9.16	   A^2 -> H(f(e), U1(b, k))
28.11/9.16	   A^2 -> H(f(e), U1(e, c))
28.11/9.16	   A^2 -> H(f(e), U1(k, c))
28.11/9.16	   A^2 -> H(f(e), U1(c, e))
28.11/9.16	   A^2 -> H(f(e), U1(c, k))
28.11/9.16	   A^2 -> H(f(e), U1(k, k))
28.11/9.16	   A^2 -> H(f(e), U1(k, d))
28.11/9.16	   A^2 -> H(f(e), U1(d, k))
28.11/9.16	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.16	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.16	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.16	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.16	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.16	   A^2 -> H(U1(k, k), f(e))
28.11/9.16	   A^2 -> H(U1(k, k), f(k))
28.11/9.16	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.16	   A^2 -> H(f(k), U1(e, b))
28.11/9.16	   A^2 -> H(f(k), U1(k, b))
28.11/9.16	   A^2 -> H(f(k), U1(c, d))
28.11/9.16	   A^2 -> H(f(k), U1(d, c))
28.11/9.16	   A^2 -> H(f(k), U1(b, e))
28.11/9.16	   A^2 -> H(f(k), U1(b, k))
28.11/9.16	   A^2 -> H(f(k), U1(e, c))
28.11/9.16	   A^2 -> H(f(k), U1(k, c))
28.11/9.16	   A^2 -> H(f(k), U1(c, e))
28.11/9.16	   A^2 -> H(f(k), U1(c, k))
28.11/9.16	   A^2 -> H(f(k), U1(e, e))
28.11/9.16	   A^2 -> H(f(k), U1(k, d))
28.11/9.16	   A^2 -> H(f(k), U1(d, k))
28.11/9.16	   A^2 -> H(f(c), b)
28.11/9.16	   A^2 -> H(f(c), U1(e, d))
28.11/9.16	   A^2 -> H(f(c), U1(d, e))
28.11/9.16	   A^2 -> H(f(k), U1(k, k))
28.11/9.16	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.16	   A^2 -> H(U1(k, k), f(c))
28.11/9.16	   A^2 -> H(U1(k, k), f(d))
28.11/9.16	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.16	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.16	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.16	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.16	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.16	   A^2 -> H(U1(k, d), f(e))
28.11/9.16	   A^2 -> H(U1(k, d), f(k))
28.11/9.16	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.16	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.16	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.16	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.16	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.16	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.16	   A^2 -> H(U1(d, k), f(e))
28.11/9.16	   A^2 -> H(U1(d, k), f(k))
28.11/9.16	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.16	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.16	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.16	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.16	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.16	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.16	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.16	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.16	   A^2 -> H(f(d), b)
28.11/9.16	   A^2 -> H(f(d), U1(e, d))
28.11/9.16	   A^2 -> H(f(d), U1(d, e))
28.11/9.16	   A^2 -> H(f(d), c)
28.11/9.16	   A^2 -> H(f(d), U1(e, k))
28.11/9.16	   A^2 -> H(f(d), U1(k, e))
28.11/9.16	   A^2 -> H(f(d), e)
28.11/9.16	   A^2 -> H(f(a), d)
28.11/9.16	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.16	   A^2 -> H(f(c), c)
28.11/9.16	   A^2 -> H(f(c), U1(e, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.16	   A^2 -> H(f(c), U1(k, e))
28.11/9.16	   A^2 -> H(f(c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.16	   A^2 -> H(f(a), k)
28.11/9.16	   A^2 -> H(f(e), U1(e, e))
28.11/9.16	   A^2 -> H(f(c), e)
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.16	   A^2 -> H(f(d), U1(k, k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.16	   A^2 -> H(d, U1(b, b))
28.11/9.16	   A^2 -> H(d, f(c))
28.11/9.16	   A^2 -> H(d, f(d))
28.11/9.16	   A^2 -> H(a, U1(c, b))
28.11/9.16	   A^2 -> H(a, U1(d, b))
28.11/9.16	   A^2 -> H(a, U1(b, c))
28.11/9.16	   A^2 -> H(a, U1(b, d))
28.11/9.16	   A^2 -> H(a, U1(c, c))
28.11/9.16	   A^2 -> H(a, f(e))
28.11/9.16	   A^2 -> H(a, f(k))
28.11/9.16	   A^2 -> H(a, U1(d, d))
28.11/9.16	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.16	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.16	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.16	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.16	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.16	   A^2 -> H(U1(e, d), f(e))
28.11/9.16	   A^2 -> H(U1(e, d), f(k))
28.11/9.16	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.16	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.16	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.16	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.16	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.16	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.16	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.16	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.16	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.16	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.16	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.16	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.16	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.16	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.16	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.16	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.16	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.16	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.16	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.16	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.16	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.16	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.16	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.16	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.16	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.16	   A^2 -> H(U1(c, a), b)
28.11/9.16	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.16	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.16	   A^2 -> H(U1(c, a), c)
28.11/9.16	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.16	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.16	   A^2 -> H(U1(c, a), e)
28.11/9.16	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.16	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.16	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.16	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.16	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.16	   A^2 -> H(U1(d, e), f(e))
28.11/9.16	   A^2 -> H(U1(d, e), f(k))
28.11/9.16	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.16	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.16	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.16	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.16	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.16	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.16	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.16	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.16	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.16	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.16	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.16	   A^2 -> H(U1(d, a), b)
28.11/9.16	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.16	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.16	   A^2 -> H(U1(d, a), c)
28.11/9.16	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.16	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.16	   A^2 -> H(U1(d, a), e)
28.11/9.16	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.16	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.16	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.16	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.16	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.16	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.16	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.16	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.16	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.16	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.16	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.16	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.16	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.16	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.16	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.16	   A^2 -> H(U1(a, c), b)
28.11/9.16	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.16	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.16	   A^2 -> H(U1(a, c), c)
28.11/9.16	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.16	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.16	   A^2 -> H(U1(a, c), e)
28.11/9.16	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, d), b)
28.11/9.16	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.16	   A^2 -> H(U1(a, d), U1(d, e))
28.11/9.16	   A^2 -> H(U1(a, d), c)
28.11/9.16	   A^2 -> H(U1(a, d), U1(e, k))
28.11/9.16	   A^2 -> H(U1(a, d), U1(k, e))
28.11/9.16	   A^2 -> H(U1(a, d), e)
28.11/9.16	
28.11/9.16	The TRS R consists of the following rules:
28.11/9.16	
28.11/9.16	   f(x) -> U1(x, x)
28.11/9.16	   U1(e, x) -> x
28.11/9.16	   a -> c
28.11/9.16	   a -> d
28.11/9.16	   b -> c
28.11/9.16	   b -> d
28.11/9.16	   d -> k
28.11/9.16	   c -> e
28.11/9.16	   c -> k
28.11/9.16	
28.11/9.16	Q is empty.
28.11/9.16	We have to consider all minimal (P,Q,R)-chains.
28.11/9.16	----------------------------------------
28.11/9.16	
28.11/9.16	(763) TransformationProof (EQUIVALENT)
28.11/9.16	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.16	
28.11/9.16	   (A^2 -> H(U1(c, d), U1(k, k)),A^2 -> H(U1(c, d), U1(k, k)))
28.11/9.16	   (A^2 -> H(U1(d, d), U1(k, k)),A^2 -> H(U1(d, d), U1(k, k)))
28.11/9.16	   (A^2 -> H(U1(a, k), U1(k, k)),A^2 -> H(U1(a, k), U1(k, k)))
28.11/9.16	
28.11/9.16	
28.11/9.16	----------------------------------------
28.11/9.16	
28.11/9.16	(764)
28.11/9.16	Obligation:
28.11/9.16	Q DP problem:
28.11/9.16	The TRS P consists of the following rules:
28.11/9.16	
28.11/9.16	   H(x, x) -> G(x, x, f(k))
28.11/9.16	   G(d, x, x) -> A^2
28.11/9.16	   A^2 -> H(f(c), f(c))
28.11/9.16	   A^2 -> H(f(d), f(d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.16	   A^2 -> H(f(e), f(e))
28.11/9.16	   A^2 -> H(f(k), f(k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.16	   A^2 -> H(U1(a, d), U1(k, d))
28.11/9.16	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.16	   A^2 -> H(U1(a, a), b)
28.11/9.16	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.16	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.16	   A^2 -> H(U1(a, a), c)
28.11/9.16	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.16	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.16	   A^2 -> H(U1(a, a), e)
28.11/9.16	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.16	   A^2 -> H(k, f(b))
28.11/9.16	   A^2 -> H(c, U1(b, b))
28.11/9.16	   A^2 -> H(c, f(c))
28.11/9.16	   A^2 -> H(c, f(d))
28.11/9.16	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.16	   A^2 -> H(U1(e, k), f(c))
28.11/9.16	   A^2 -> H(U1(e, k), f(d))
28.11/9.16	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.16	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.16	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.16	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.16	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.16	   A^2 -> H(U1(e, c), f(e))
28.11/9.16	   A^2 -> H(U1(e, c), f(k))
28.11/9.16	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.16	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.16	   A^2 -> H(U1(k, e), f(c))
28.11/9.16	   A^2 -> H(U1(k, e), f(d))
28.11/9.16	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.16	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.16	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.16	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.16	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.16	   A^2 -> H(U1(k, c), f(e))
28.11/9.16	   A^2 -> H(U1(k, c), f(k))
28.11/9.16	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.16	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.16	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.16	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.16	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.16	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.16	   A^2 -> H(U1(c, e), f(e))
28.11/9.16	   A^2 -> H(U1(c, e), f(k))
28.11/9.16	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.16	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.16	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.16	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.16	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.16	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.16	   A^2 -> H(U1(c, k), f(e))
28.11/9.16	   A^2 -> H(U1(c, k), f(k))
28.11/9.16	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.16	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.16	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.16	   A^2 -> H(e, U1(b, b))
28.11/9.16	   A^2 -> H(e, f(c))
28.11/9.16	   A^2 -> H(e, f(d))
28.11/9.16	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.16	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.16	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.16	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.16	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.16	   A^2 -> H(U1(e, e), f(e))
28.11/9.16	   A^2 -> H(U1(e, e), f(k))
28.11/9.16	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.16	   A^2 -> H(f(e), U1(e, b))
28.11/9.16	   A^2 -> H(f(e), U1(k, b))
28.11/9.16	   A^2 -> H(f(e), U1(c, d))
28.11/9.16	   A^2 -> H(f(e), U1(d, c))
28.11/9.16	   A^2 -> H(f(e), U1(b, e))
28.11/9.16	   A^2 -> H(f(e), U1(b, k))
28.11/9.16	   A^2 -> H(f(e), U1(e, c))
28.11/9.16	   A^2 -> H(f(e), U1(k, c))
28.11/9.16	   A^2 -> H(f(e), U1(c, e))
28.11/9.16	   A^2 -> H(f(e), U1(c, k))
28.11/9.16	   A^2 -> H(f(e), U1(k, k))
28.11/9.16	   A^2 -> H(f(e), U1(k, d))
28.11/9.16	   A^2 -> H(f(e), U1(d, k))
28.11/9.16	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.16	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.16	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.16	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.16	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.16	   A^2 -> H(U1(k, k), f(e))
28.11/9.16	   A^2 -> H(U1(k, k), f(k))
28.11/9.16	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.16	   A^2 -> H(f(k), U1(e, b))
28.11/9.16	   A^2 -> H(f(k), U1(k, b))
28.11/9.16	   A^2 -> H(f(k), U1(c, d))
28.11/9.16	   A^2 -> H(f(k), U1(d, c))
28.11/9.16	   A^2 -> H(f(k), U1(b, e))
28.11/9.16	   A^2 -> H(f(k), U1(b, k))
28.11/9.16	   A^2 -> H(f(k), U1(e, c))
28.11/9.16	   A^2 -> H(f(k), U1(k, c))
28.11/9.16	   A^2 -> H(f(k), U1(c, e))
28.11/9.16	   A^2 -> H(f(k), U1(c, k))
28.11/9.16	   A^2 -> H(f(k), U1(e, e))
28.11/9.16	   A^2 -> H(f(k), U1(k, d))
28.11/9.16	   A^2 -> H(f(k), U1(d, k))
28.11/9.16	   A^2 -> H(f(c), b)
28.11/9.16	   A^2 -> H(f(c), U1(e, d))
28.11/9.16	   A^2 -> H(f(c), U1(d, e))
28.11/9.16	   A^2 -> H(f(k), U1(k, k))
28.11/9.16	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.16	   A^2 -> H(U1(k, k), f(c))
28.11/9.16	   A^2 -> H(U1(k, k), f(d))
28.11/9.16	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.16	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.16	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.16	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.16	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.16	   A^2 -> H(U1(k, d), f(e))
28.11/9.16	   A^2 -> H(U1(k, d), f(k))
28.11/9.16	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.16	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.16	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.16	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.16	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.16	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.16	   A^2 -> H(U1(d, k), f(e))
28.11/9.16	   A^2 -> H(U1(d, k), f(k))
28.11/9.16	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.16	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.16	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.16	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.16	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.16	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.16	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.16	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.16	   A^2 -> H(f(d), b)
28.11/9.16	   A^2 -> H(f(d), U1(e, d))
28.11/9.16	   A^2 -> H(f(d), U1(d, e))
28.11/9.16	   A^2 -> H(f(d), c)
28.11/9.16	   A^2 -> H(f(d), U1(e, k))
28.11/9.16	   A^2 -> H(f(d), U1(k, e))
28.11/9.16	   A^2 -> H(f(d), e)
28.11/9.16	   A^2 -> H(f(a), d)
28.11/9.16	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.16	   A^2 -> H(f(c), c)
28.11/9.16	   A^2 -> H(f(c), U1(e, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.16	   A^2 -> H(f(c), U1(k, e))
28.11/9.16	   A^2 -> H(f(c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.16	   A^2 -> H(f(a), k)
28.11/9.16	   A^2 -> H(f(e), U1(e, e))
28.11/9.16	   A^2 -> H(f(c), e)
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.16	   A^2 -> H(f(d), U1(k, k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.16	   A^2 -> H(d, U1(b, b))
28.11/9.16	   A^2 -> H(d, f(c))
28.11/9.16	   A^2 -> H(d, f(d))
28.11/9.16	   A^2 -> H(a, U1(c, b))
28.11/9.16	   A^2 -> H(a, U1(d, b))
28.11/9.16	   A^2 -> H(a, U1(b, c))
28.11/9.16	   A^2 -> H(a, U1(b, d))
28.11/9.16	   A^2 -> H(a, U1(c, c))
28.11/9.16	   A^2 -> H(a, f(e))
28.11/9.16	   A^2 -> H(a, f(k))
28.11/9.16	   A^2 -> H(a, U1(d, d))
28.11/9.16	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.16	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.16	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.16	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.16	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.16	   A^2 -> H(U1(e, d), f(e))
28.11/9.16	   A^2 -> H(U1(e, d), f(k))
28.11/9.16	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.16	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.16	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.16	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.16	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.16	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.16	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.16	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.16	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.16	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.16	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.16	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.16	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.16	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.16	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.16	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.16	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.16	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.16	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.16	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.16	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.16	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.16	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.16	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.16	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.16	   A^2 -> H(U1(c, a), b)
28.11/9.16	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.16	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.16	   A^2 -> H(U1(c, a), c)
28.11/9.16	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.16	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.16	   A^2 -> H(U1(c, a), e)
28.11/9.16	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.16	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.16	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.16	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.16	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.16	   A^2 -> H(U1(d, e), f(e))
28.11/9.16	   A^2 -> H(U1(d, e), f(k))
28.11/9.16	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.16	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.16	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.16	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.16	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.16	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.16	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.16	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.16	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.16	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.16	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.16	   A^2 -> H(U1(d, a), b)
28.11/9.16	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.16	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.16	   A^2 -> H(U1(d, a), c)
28.11/9.16	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.16	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.16	   A^2 -> H(U1(d, a), e)
28.11/9.16	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.16	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.16	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.16	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.16	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.16	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.16	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.16	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.16	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.16	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.16	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.16	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.16	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.16	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.16	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.16	   A^2 -> H(U1(a, c), b)
28.11/9.16	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.16	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.16	   A^2 -> H(U1(a, c), c)
28.11/9.16	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.16	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.16	   A^2 -> H(U1(a, c), e)
28.11/9.16	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, d), b)
28.11/9.16	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.16	   A^2 -> H(U1(a, d), U1(d, e))
28.11/9.16	   A^2 -> H(U1(a, d), c)
28.11/9.16	   A^2 -> H(U1(a, d), U1(e, k))
28.11/9.16	   A^2 -> H(U1(a, d), U1(k, e))
28.11/9.16	   A^2 -> H(U1(a, d), e)
28.11/9.16	
28.11/9.16	The TRS R consists of the following rules:
28.11/9.16	
28.11/9.16	   f(x) -> U1(x, x)
28.11/9.16	   U1(e, x) -> x
28.11/9.16	   a -> c
28.11/9.16	   a -> d
28.11/9.16	   b -> c
28.11/9.16	   b -> d
28.11/9.16	   d -> k
28.11/9.16	   c -> e
28.11/9.16	   c -> k
28.11/9.16	
28.11/9.16	Q is empty.
28.11/9.16	We have to consider all minimal (P,Q,R)-chains.
28.11/9.16	----------------------------------------
28.11/9.16	
28.11/9.16	(765) TransformationProof (EQUIVALENT)
28.11/9.16	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.16	
28.11/9.16	   (A^2 -> H(U1(c, d), U1(k, d)),A^2 -> H(U1(c, d), U1(k, d)))
28.11/9.16	   (A^2 -> H(U1(d, d), U1(k, d)),A^2 -> H(U1(d, d), U1(k, d)))
28.11/9.16	   (A^2 -> H(U1(a, k), U1(k, d)),A^2 -> H(U1(a, k), U1(k, d)))
28.11/9.16	   (A^2 -> H(U1(a, d), U1(k, k)),A^2 -> H(U1(a, d), U1(k, k)))
28.11/9.16	
28.11/9.16	
28.11/9.16	----------------------------------------
28.11/9.16	
28.11/9.16	(766)
28.11/9.16	Obligation:
28.11/9.16	Q DP problem:
28.11/9.16	The TRS P consists of the following rules:
28.11/9.16	
28.11/9.16	   H(x, x) -> G(x, x, f(k))
28.11/9.16	   G(d, x, x) -> A^2
28.11/9.16	   A^2 -> H(f(c), f(c))
28.11/9.16	   A^2 -> H(f(d), f(d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.16	   A^2 -> H(f(e), f(e))
28.11/9.16	   A^2 -> H(f(k), f(k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.16	   A^2 -> H(U1(a, d), U1(d, k))
28.11/9.16	   A^2 -> H(U1(a, a), b)
28.11/9.16	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.16	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.16	   A^2 -> H(U1(a, a), c)
28.11/9.16	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.16	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.16	   A^2 -> H(U1(a, a), e)
28.11/9.16	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.16	   A^2 -> H(k, f(b))
28.11/9.16	   A^2 -> H(c, U1(b, b))
28.11/9.16	   A^2 -> H(c, f(c))
28.11/9.16	   A^2 -> H(c, f(d))
28.11/9.16	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.16	   A^2 -> H(U1(e, k), f(c))
28.11/9.16	   A^2 -> H(U1(e, k), f(d))
28.11/9.16	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.16	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.16	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.16	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.16	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.16	   A^2 -> H(U1(e, c), f(e))
28.11/9.16	   A^2 -> H(U1(e, c), f(k))
28.11/9.16	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.16	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.16	   A^2 -> H(U1(k, e), f(c))
28.11/9.16	   A^2 -> H(U1(k, e), f(d))
28.11/9.16	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.16	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.16	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.16	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.16	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.16	   A^2 -> H(U1(k, c), f(e))
28.11/9.16	   A^2 -> H(U1(k, c), f(k))
28.11/9.16	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.16	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.16	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.16	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.16	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.16	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.16	   A^2 -> H(U1(c, e), f(e))
28.11/9.16	   A^2 -> H(U1(c, e), f(k))
28.11/9.16	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.16	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.16	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.16	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.16	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.16	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.16	   A^2 -> H(U1(c, k), f(e))
28.11/9.16	   A^2 -> H(U1(c, k), f(k))
28.11/9.16	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.16	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.16	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.16	   A^2 -> H(e, U1(b, b))
28.11/9.16	   A^2 -> H(e, f(c))
28.11/9.16	   A^2 -> H(e, f(d))
28.11/9.16	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.16	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.16	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.16	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.16	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.16	   A^2 -> H(U1(e, e), f(e))
28.11/9.16	   A^2 -> H(U1(e, e), f(k))
28.11/9.16	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.16	   A^2 -> H(f(e), U1(e, b))
28.11/9.16	   A^2 -> H(f(e), U1(k, b))
28.11/9.16	   A^2 -> H(f(e), U1(c, d))
28.11/9.16	   A^2 -> H(f(e), U1(d, c))
28.11/9.16	   A^2 -> H(f(e), U1(b, e))
28.11/9.16	   A^2 -> H(f(e), U1(b, k))
28.11/9.16	   A^2 -> H(f(e), U1(e, c))
28.11/9.16	   A^2 -> H(f(e), U1(k, c))
28.11/9.16	   A^2 -> H(f(e), U1(c, e))
28.11/9.16	   A^2 -> H(f(e), U1(c, k))
28.11/9.16	   A^2 -> H(f(e), U1(k, k))
28.11/9.16	   A^2 -> H(f(e), U1(k, d))
28.11/9.16	   A^2 -> H(f(e), U1(d, k))
28.11/9.16	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.16	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.16	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.16	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.16	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.16	   A^2 -> H(U1(k, k), f(e))
28.11/9.16	   A^2 -> H(U1(k, k), f(k))
28.11/9.16	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.16	   A^2 -> H(f(k), U1(e, b))
28.11/9.16	   A^2 -> H(f(k), U1(k, b))
28.11/9.16	   A^2 -> H(f(k), U1(c, d))
28.11/9.16	   A^2 -> H(f(k), U1(d, c))
28.11/9.16	   A^2 -> H(f(k), U1(b, e))
28.11/9.16	   A^2 -> H(f(k), U1(b, k))
28.11/9.16	   A^2 -> H(f(k), U1(e, c))
28.11/9.16	   A^2 -> H(f(k), U1(k, c))
28.11/9.16	   A^2 -> H(f(k), U1(c, e))
28.11/9.16	   A^2 -> H(f(k), U1(c, k))
28.11/9.16	   A^2 -> H(f(k), U1(e, e))
28.11/9.16	   A^2 -> H(f(k), U1(k, d))
28.11/9.16	   A^2 -> H(f(k), U1(d, k))
28.11/9.16	   A^2 -> H(f(c), b)
28.11/9.16	   A^2 -> H(f(c), U1(e, d))
28.11/9.16	   A^2 -> H(f(c), U1(d, e))
28.11/9.16	   A^2 -> H(f(k), U1(k, k))
28.11/9.16	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.16	   A^2 -> H(U1(k, k), f(c))
28.11/9.16	   A^2 -> H(U1(k, k), f(d))
28.11/9.16	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.16	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.16	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.16	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.16	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.16	   A^2 -> H(U1(k, d), f(e))
28.11/9.16	   A^2 -> H(U1(k, d), f(k))
28.11/9.16	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.16	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.16	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.16	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.16	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.16	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.16	   A^2 -> H(U1(d, k), f(e))
28.11/9.16	   A^2 -> H(U1(d, k), f(k))
28.11/9.16	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.16	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.16	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.16	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.16	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.16	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.16	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.16	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.16	   A^2 -> H(f(d), b)
28.11/9.16	   A^2 -> H(f(d), U1(e, d))
28.11/9.16	   A^2 -> H(f(d), U1(d, e))
28.11/9.16	   A^2 -> H(f(d), c)
28.11/9.16	   A^2 -> H(f(d), U1(e, k))
28.11/9.16	   A^2 -> H(f(d), U1(k, e))
28.11/9.16	   A^2 -> H(f(d), e)
28.11/9.16	   A^2 -> H(f(a), d)
28.11/9.16	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.16	   A^2 -> H(f(c), c)
28.11/9.16	   A^2 -> H(f(c), U1(e, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.16	   A^2 -> H(f(c), U1(k, e))
28.11/9.16	   A^2 -> H(f(c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.16	   A^2 -> H(f(a), k)
28.11/9.16	   A^2 -> H(f(e), U1(e, e))
28.11/9.16	   A^2 -> H(f(c), e)
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.16	   A^2 -> H(f(d), U1(k, k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.16	   A^2 -> H(d, U1(b, b))
28.11/9.16	   A^2 -> H(d, f(c))
28.11/9.16	   A^2 -> H(d, f(d))
28.11/9.16	   A^2 -> H(a, U1(c, b))
28.11/9.16	   A^2 -> H(a, U1(d, b))
28.11/9.16	   A^2 -> H(a, U1(b, c))
28.11/9.16	   A^2 -> H(a, U1(b, d))
28.11/9.16	   A^2 -> H(a, U1(c, c))
28.11/9.16	   A^2 -> H(a, f(e))
28.11/9.16	   A^2 -> H(a, f(k))
28.11/9.16	   A^2 -> H(a, U1(d, d))
28.11/9.16	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.16	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.16	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.16	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.16	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.16	   A^2 -> H(U1(e, d), f(e))
28.11/9.16	   A^2 -> H(U1(e, d), f(k))
28.11/9.16	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.16	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.16	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.16	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.16	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.16	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.16	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.16	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.16	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.16	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.16	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.16	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.16	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.16	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.16	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.16	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.16	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.16	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.16	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.16	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.16	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.16	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.16	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.16	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.16	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.16	   A^2 -> H(U1(c, a), b)
28.11/9.16	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.16	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.16	   A^2 -> H(U1(c, a), c)
28.11/9.16	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.16	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.16	   A^2 -> H(U1(c, a), e)
28.11/9.16	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.16	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.16	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.16	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.16	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.16	   A^2 -> H(U1(d, e), f(e))
28.11/9.16	   A^2 -> H(U1(d, e), f(k))
28.11/9.16	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.16	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.16	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.16	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.16	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.16	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.16	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.16	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.16	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.16	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.16	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.16	   A^2 -> H(U1(d, a), b)
28.11/9.16	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.16	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.16	   A^2 -> H(U1(d, a), c)
28.11/9.16	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.16	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.16	   A^2 -> H(U1(d, a), e)
28.11/9.16	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.16	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.16	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.16	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.16	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.16	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.16	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.16	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.16	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.16	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.16	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.16	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.16	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.16	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.16	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.16	   A^2 -> H(U1(a, c), b)
28.11/9.16	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.16	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.16	   A^2 -> H(U1(a, c), c)
28.11/9.16	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.16	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.16	   A^2 -> H(U1(a, c), e)
28.11/9.16	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, d), b)
28.11/9.16	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.16	   A^2 -> H(U1(a, d), U1(d, e))
28.11/9.16	   A^2 -> H(U1(a, d), c)
28.11/9.16	   A^2 -> H(U1(a, d), U1(e, k))
28.11/9.16	   A^2 -> H(U1(a, d), U1(k, e))
28.11/9.16	   A^2 -> H(U1(a, d), e)
28.11/9.16	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.16	
28.11/9.16	The TRS R consists of the following rules:
28.11/9.16	
28.11/9.16	   f(x) -> U1(x, x)
28.11/9.16	   U1(e, x) -> x
28.11/9.16	   a -> c
28.11/9.16	   a -> d
28.11/9.16	   b -> c
28.11/9.16	   b -> d
28.11/9.16	   d -> k
28.11/9.16	   c -> e
28.11/9.16	   c -> k
28.11/9.16	
28.11/9.16	Q is empty.
28.11/9.16	We have to consider all minimal (P,Q,R)-chains.
28.11/9.16	----------------------------------------
28.11/9.16	
28.11/9.16	(767) TransformationProof (EQUIVALENT)
28.11/9.16	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.16	
28.11/9.16	   (A^2 -> H(U1(c, d), U1(d, k)),A^2 -> H(U1(c, d), U1(d, k)))
28.11/9.16	   (A^2 -> H(U1(d, d), U1(d, k)),A^2 -> H(U1(d, d), U1(d, k)))
28.11/9.16	   (A^2 -> H(U1(a, k), U1(d, k)),A^2 -> H(U1(a, k), U1(d, k)))
28.11/9.16	   (A^2 -> H(U1(a, d), U1(k, k)),A^2 -> H(U1(a, d), U1(k, k)))
28.11/9.16	
28.11/9.16	
28.11/9.16	----------------------------------------
28.11/9.16	
28.11/9.16	(768)
28.11/9.16	Obligation:
28.11/9.16	Q DP problem:
28.11/9.16	The TRS P consists of the following rules:
28.11/9.16	
28.11/9.16	   H(x, x) -> G(x, x, f(k))
28.11/9.16	   G(d, x, x) -> A^2
28.11/9.16	   A^2 -> H(f(c), f(c))
28.11/9.16	   A^2 -> H(f(d), f(d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.16	   A^2 -> H(f(e), f(e))
28.11/9.16	   A^2 -> H(f(k), f(k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.16	   A^2 -> H(U1(a, a), b)
28.11/9.16	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.16	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.16	   A^2 -> H(U1(a, a), c)
28.11/9.16	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.16	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.16	   A^2 -> H(U1(a, a), e)
28.11/9.16	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.16	   A^2 -> H(k, f(b))
28.11/9.16	   A^2 -> H(c, U1(b, b))
28.11/9.16	   A^2 -> H(c, f(c))
28.11/9.16	   A^2 -> H(c, f(d))
28.11/9.16	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.16	   A^2 -> H(U1(e, k), f(c))
28.11/9.16	   A^2 -> H(U1(e, k), f(d))
28.11/9.16	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.16	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.16	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.16	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.16	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.16	   A^2 -> H(U1(e, c), f(e))
28.11/9.16	   A^2 -> H(U1(e, c), f(k))
28.11/9.16	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.16	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.16	   A^2 -> H(U1(k, e), f(c))
28.11/9.16	   A^2 -> H(U1(k, e), f(d))
28.11/9.16	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.16	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.16	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.16	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.16	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.16	   A^2 -> H(U1(k, c), f(e))
28.11/9.16	   A^2 -> H(U1(k, c), f(k))
28.11/9.16	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.16	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.16	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.16	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.16	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.16	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.16	   A^2 -> H(U1(c, e), f(e))
28.11/9.16	   A^2 -> H(U1(c, e), f(k))
28.11/9.16	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.16	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.16	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.16	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.16	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.16	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.16	   A^2 -> H(U1(c, k), f(e))
28.11/9.16	   A^2 -> H(U1(c, k), f(k))
28.11/9.16	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.16	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.16	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.16	   A^2 -> H(e, U1(b, b))
28.11/9.16	   A^2 -> H(e, f(c))
28.11/9.16	   A^2 -> H(e, f(d))
28.11/9.16	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.16	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.16	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.16	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.16	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.16	   A^2 -> H(U1(e, e), f(e))
28.11/9.16	   A^2 -> H(U1(e, e), f(k))
28.11/9.16	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.16	   A^2 -> H(f(e), U1(e, b))
28.11/9.16	   A^2 -> H(f(e), U1(k, b))
28.11/9.16	   A^2 -> H(f(e), U1(c, d))
28.11/9.16	   A^2 -> H(f(e), U1(d, c))
28.11/9.16	   A^2 -> H(f(e), U1(b, e))
28.11/9.16	   A^2 -> H(f(e), U1(b, k))
28.11/9.16	   A^2 -> H(f(e), U1(e, c))
28.11/9.16	   A^2 -> H(f(e), U1(k, c))
28.11/9.16	   A^2 -> H(f(e), U1(c, e))
28.11/9.16	   A^2 -> H(f(e), U1(c, k))
28.11/9.16	   A^2 -> H(f(e), U1(k, k))
28.11/9.16	   A^2 -> H(f(e), U1(k, d))
28.11/9.16	   A^2 -> H(f(e), U1(d, k))
28.11/9.16	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.16	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.16	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.16	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.16	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.16	   A^2 -> H(U1(k, k), f(e))
28.11/9.16	   A^2 -> H(U1(k, k), f(k))
28.11/9.16	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.16	   A^2 -> H(f(k), U1(e, b))
28.11/9.16	   A^2 -> H(f(k), U1(k, b))
28.11/9.16	   A^2 -> H(f(k), U1(c, d))
28.11/9.16	   A^2 -> H(f(k), U1(d, c))
28.11/9.16	   A^2 -> H(f(k), U1(b, e))
28.11/9.16	   A^2 -> H(f(k), U1(b, k))
28.11/9.16	   A^2 -> H(f(k), U1(e, c))
28.11/9.16	   A^2 -> H(f(k), U1(k, c))
28.11/9.16	   A^2 -> H(f(k), U1(c, e))
28.11/9.16	   A^2 -> H(f(k), U1(c, k))
28.11/9.16	   A^2 -> H(f(k), U1(e, e))
28.11/9.16	   A^2 -> H(f(k), U1(k, d))
28.11/9.16	   A^2 -> H(f(k), U1(d, k))
28.11/9.16	   A^2 -> H(f(c), b)
28.11/9.16	   A^2 -> H(f(c), U1(e, d))
28.11/9.16	   A^2 -> H(f(c), U1(d, e))
28.11/9.16	   A^2 -> H(f(k), U1(k, k))
28.11/9.16	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.16	   A^2 -> H(U1(k, k), f(c))
28.11/9.16	   A^2 -> H(U1(k, k), f(d))
28.11/9.16	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.16	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.16	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.16	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.16	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.16	   A^2 -> H(U1(k, d), f(e))
28.11/9.16	   A^2 -> H(U1(k, d), f(k))
28.11/9.16	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.16	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.16	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.16	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.16	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.16	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.16	   A^2 -> H(U1(d, k), f(e))
28.11/9.16	   A^2 -> H(U1(d, k), f(k))
28.11/9.16	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.16	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.16	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.16	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.16	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.16	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.16	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.16	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.16	   A^2 -> H(f(d), b)
28.11/9.16	   A^2 -> H(f(d), U1(e, d))
28.11/9.16	   A^2 -> H(f(d), U1(d, e))
28.11/9.16	   A^2 -> H(f(d), c)
28.11/9.16	   A^2 -> H(f(d), U1(e, k))
28.11/9.16	   A^2 -> H(f(d), U1(k, e))
28.11/9.16	   A^2 -> H(f(d), e)
28.11/9.16	   A^2 -> H(f(a), d)
28.11/9.16	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.16	   A^2 -> H(f(c), c)
28.11/9.16	   A^2 -> H(f(c), U1(e, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.16	   A^2 -> H(f(c), U1(k, e))
28.11/9.16	   A^2 -> H(f(c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.16	   A^2 -> H(f(a), k)
28.11/9.16	   A^2 -> H(f(e), U1(e, e))
28.11/9.16	   A^2 -> H(f(c), e)
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.16	   A^2 -> H(f(d), U1(k, k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.16	   A^2 -> H(d, U1(b, b))
28.11/9.16	   A^2 -> H(d, f(c))
28.11/9.16	   A^2 -> H(d, f(d))
28.11/9.16	   A^2 -> H(a, U1(c, b))
28.11/9.16	   A^2 -> H(a, U1(d, b))
28.11/9.16	   A^2 -> H(a, U1(b, c))
28.11/9.16	   A^2 -> H(a, U1(b, d))
28.11/9.16	   A^2 -> H(a, U1(c, c))
28.11/9.16	   A^2 -> H(a, f(e))
28.11/9.16	   A^2 -> H(a, f(k))
28.11/9.16	   A^2 -> H(a, U1(d, d))
28.11/9.16	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.16	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.16	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.16	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.16	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.16	   A^2 -> H(U1(e, d), f(e))
28.11/9.16	   A^2 -> H(U1(e, d), f(k))
28.11/9.16	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.16	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.16	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.16	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.16	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.16	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.16	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.16	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.16	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.16	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.16	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.16	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.16	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.16	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.16	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.16	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.16	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.16	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.16	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.16	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.16	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.16	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.16	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.16	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.16	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.16	   A^2 -> H(U1(c, a), b)
28.11/9.16	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.16	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.16	   A^2 -> H(U1(c, a), c)
28.11/9.16	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.16	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.16	   A^2 -> H(U1(c, a), e)
28.11/9.16	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.16	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.16	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.16	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.16	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.16	   A^2 -> H(U1(d, e), f(e))
28.11/9.16	   A^2 -> H(U1(d, e), f(k))
28.11/9.16	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.16	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.16	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.16	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.16	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.16	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.16	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.16	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.16	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.16	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.16	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.16	   A^2 -> H(U1(d, a), b)
28.11/9.16	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.16	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.16	   A^2 -> H(U1(d, a), c)
28.11/9.16	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.16	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.16	   A^2 -> H(U1(d, a), e)
28.11/9.16	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.16	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.16	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.16	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.16	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.16	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.16	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.16	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.16	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.16	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.16	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.16	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.16	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.16	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.16	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.16	   A^2 -> H(U1(a, c), b)
28.11/9.16	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.16	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.16	   A^2 -> H(U1(a, c), c)
28.11/9.16	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.16	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.16	   A^2 -> H(U1(a, c), e)
28.11/9.16	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(a, d), b)
28.11/9.16	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.16	   A^2 -> H(U1(a, d), U1(d, e))
28.11/9.16	   A^2 -> H(U1(a, d), c)
28.11/9.16	   A^2 -> H(U1(a, d), U1(e, k))
28.11/9.16	   A^2 -> H(U1(a, d), U1(k, e))
28.11/9.16	   A^2 -> H(U1(a, d), e)
28.11/9.16	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.16	
28.11/9.16	The TRS R consists of the following rules:
28.11/9.16	
28.11/9.16	   f(x) -> U1(x, x)
28.11/9.16	   U1(e, x) -> x
28.11/9.16	   a -> c
28.11/9.16	   a -> d
28.11/9.16	   b -> c
28.11/9.16	   b -> d
28.11/9.16	   d -> k
28.11/9.16	   c -> e
28.11/9.16	   c -> k
28.11/9.16	
28.11/9.16	Q is empty.
28.11/9.16	We have to consider all minimal (P,Q,R)-chains.
28.11/9.16	----------------------------------------
28.11/9.16	
28.11/9.16	(769) TransformationProof (EQUIVALENT)
28.11/9.16	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), b) at position [] we obtained the following new rules [LPAR04]:
28.11/9.16	
28.11/9.16	   (A^2 -> H(U1(c, a), b),A^2 -> H(U1(c, a), b))
28.11/9.16	   (A^2 -> H(U1(d, a), b),A^2 -> H(U1(d, a), b))
28.11/9.16	   (A^2 -> H(U1(a, c), b),A^2 -> H(U1(a, c), b))
28.11/9.16	   (A^2 -> H(U1(a, d), b),A^2 -> H(U1(a, d), b))
28.11/9.16	   (A^2 -> H(U1(a, a), c),A^2 -> H(U1(a, a), c))
28.11/9.16	   (A^2 -> H(U1(a, a), d),A^2 -> H(U1(a, a), d))
28.11/9.16	
28.11/9.16	
28.11/9.16	----------------------------------------
28.11/9.16	
28.11/9.16	(770)
28.11/9.16	Obligation:
28.11/9.16	Q DP problem:
28.11/9.16	The TRS P consists of the following rules:
28.11/9.16	
28.11/9.16	   H(x, x) -> G(x, x, f(k))
28.11/9.16	   G(d, x, x) -> A^2
28.11/9.16	   A^2 -> H(f(c), f(c))
28.11/9.16	   A^2 -> H(f(d), f(d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.16	   A^2 -> H(f(e), f(e))
28.11/9.16	   A^2 -> H(f(k), f(k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.16	   A^2 -> H(U1(a, a), U1(e, d))
28.11/9.16	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.16	   A^2 -> H(U1(a, a), c)
28.11/9.16	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.16	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.16	   A^2 -> H(U1(a, a), e)
28.11/9.16	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.16	   A^2 -> H(k, f(b))
28.11/9.16	   A^2 -> H(c, U1(b, b))
28.11/9.16	   A^2 -> H(c, f(c))
28.11/9.16	   A^2 -> H(c, f(d))
28.11/9.16	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.16	   A^2 -> H(U1(e, k), f(c))
28.11/9.16	   A^2 -> H(U1(e, k), f(d))
28.11/9.16	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.16	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.16	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.16	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.16	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.16	   A^2 -> H(U1(e, c), f(e))
28.11/9.16	   A^2 -> H(U1(e, c), f(k))
28.11/9.16	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.16	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.16	   A^2 -> H(U1(k, e), f(c))
28.11/9.16	   A^2 -> H(U1(k, e), f(d))
28.11/9.16	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.16	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.16	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.16	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.16	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.16	   A^2 -> H(U1(k, c), f(e))
28.11/9.16	   A^2 -> H(U1(k, c), f(k))
28.11/9.16	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.16	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.16	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.16	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.16	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.16	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.16	   A^2 -> H(U1(c, e), f(e))
28.11/9.16	   A^2 -> H(U1(c, e), f(k))
28.11/9.16	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.16	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.16	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.16	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.16	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.16	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.16	   A^2 -> H(U1(c, k), f(e))
28.11/9.16	   A^2 -> H(U1(c, k), f(k))
28.11/9.16	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.16	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.16	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.16	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.16	   A^2 -> H(e, U1(b, b))
28.11/9.16	   A^2 -> H(e, f(c))
28.11/9.16	   A^2 -> H(e, f(d))
28.11/9.16	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.16	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.16	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.16	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.16	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.16	   A^2 -> H(U1(e, e), f(e))
28.11/9.16	   A^2 -> H(U1(e, e), f(k))
28.11/9.16	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.16	   A^2 -> H(f(e), U1(e, b))
28.11/9.16	   A^2 -> H(f(e), U1(k, b))
28.11/9.16	   A^2 -> H(f(e), U1(c, d))
28.11/9.16	   A^2 -> H(f(e), U1(d, c))
28.11/9.16	   A^2 -> H(f(e), U1(b, e))
28.11/9.16	   A^2 -> H(f(e), U1(b, k))
28.11/9.16	   A^2 -> H(f(e), U1(e, c))
28.11/9.16	   A^2 -> H(f(e), U1(k, c))
28.11/9.16	   A^2 -> H(f(e), U1(c, e))
28.11/9.16	   A^2 -> H(f(e), U1(c, k))
28.11/9.16	   A^2 -> H(f(e), U1(k, k))
28.11/9.16	   A^2 -> H(f(e), U1(k, d))
28.11/9.16	   A^2 -> H(f(e), U1(d, k))
28.11/9.16	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.16	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.16	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.16	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.16	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.16	   A^2 -> H(U1(k, k), f(e))
28.11/9.16	   A^2 -> H(U1(k, k), f(k))
28.11/9.16	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.16	   A^2 -> H(f(k), U1(e, b))
28.11/9.16	   A^2 -> H(f(k), U1(k, b))
28.11/9.16	   A^2 -> H(f(k), U1(c, d))
28.11/9.16	   A^2 -> H(f(k), U1(d, c))
28.11/9.16	   A^2 -> H(f(k), U1(b, e))
28.11/9.16	   A^2 -> H(f(k), U1(b, k))
28.11/9.16	   A^2 -> H(f(k), U1(e, c))
28.11/9.16	   A^2 -> H(f(k), U1(k, c))
28.11/9.16	   A^2 -> H(f(k), U1(c, e))
28.11/9.16	   A^2 -> H(f(k), U1(c, k))
28.11/9.16	   A^2 -> H(f(k), U1(e, e))
28.11/9.16	   A^2 -> H(f(k), U1(k, d))
28.11/9.16	   A^2 -> H(f(k), U1(d, k))
28.11/9.16	   A^2 -> H(f(c), b)
28.11/9.16	   A^2 -> H(f(c), U1(e, d))
28.11/9.16	   A^2 -> H(f(c), U1(d, e))
28.11/9.16	   A^2 -> H(f(k), U1(k, k))
28.11/9.16	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.16	   A^2 -> H(U1(k, k), f(c))
28.11/9.16	   A^2 -> H(U1(k, k), f(d))
28.11/9.16	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.16	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.16	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.16	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.16	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.16	   A^2 -> H(U1(k, d), f(e))
28.11/9.16	   A^2 -> H(U1(k, d), f(k))
28.11/9.16	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.16	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.16	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.16	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.16	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.16	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.16	   A^2 -> H(U1(d, k), f(e))
28.11/9.16	   A^2 -> H(U1(d, k), f(k))
28.11/9.16	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.16	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.16	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.16	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.16	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.16	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.16	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.16	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.16	   A^2 -> H(f(d), b)
28.11/9.16	   A^2 -> H(f(d), U1(e, d))
28.11/9.16	   A^2 -> H(f(d), U1(d, e))
28.11/9.16	   A^2 -> H(f(d), c)
28.11/9.16	   A^2 -> H(f(d), U1(e, k))
28.11/9.16	   A^2 -> H(f(d), U1(k, e))
28.11/9.16	   A^2 -> H(f(d), e)
28.11/9.16	   A^2 -> H(f(a), d)
28.11/9.16	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.16	   A^2 -> H(f(c), c)
28.11/9.16	   A^2 -> H(f(c), U1(e, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.16	   A^2 -> H(f(c), U1(k, e))
28.11/9.16	   A^2 -> H(f(c), U1(k, k))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.16	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.16	   A^2 -> H(f(a), k)
28.11/9.16	   A^2 -> H(f(e), U1(e, e))
28.11/9.16	   A^2 -> H(f(c), e)
28.11/9.16	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.16	   A^2 -> H(f(d), U1(k, k))
28.11/9.16	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.16	   A^2 -> H(d, U1(b, b))
28.11/9.16	   A^2 -> H(d, f(c))
28.11/9.16	   A^2 -> H(d, f(d))
28.11/9.16	   A^2 -> H(a, U1(c, b))
28.11/9.16	   A^2 -> H(a, U1(d, b))
28.11/9.16	   A^2 -> H(a, U1(b, c))
28.11/9.16	   A^2 -> H(a, U1(b, d))
28.11/9.16	   A^2 -> H(a, U1(c, c))
28.11/9.16	   A^2 -> H(a, f(e))
28.11/9.16	   A^2 -> H(a, f(k))
28.11/9.16	   A^2 -> H(a, U1(d, d))
28.11/9.16	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.16	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.16	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.16	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.16	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.16	   A^2 -> H(U1(e, d), f(e))
28.11/9.16	   A^2 -> H(U1(e, d), f(k))
28.11/9.16	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.16	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.16	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.16	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.16	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.16	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.16	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.16	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.16	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.16	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.16	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.16	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.16	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.16	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.16	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.16	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.16	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.16	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.16	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.16	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.16	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.16	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.16	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.16	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.16	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.16	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.16	   A^2 -> H(U1(c, a), b)
28.11/9.16	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.16	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.16	   A^2 -> H(U1(c, a), c)
28.11/9.16	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.16	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.16	   A^2 -> H(U1(c, a), e)
28.11/9.16	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.16	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.16	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.16	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.16	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.16	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.16	   A^2 -> H(U1(d, e), f(e))
28.11/9.17	   A^2 -> H(U1(d, e), f(k))
28.11/9.17	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.17	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.17	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.17	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.17	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.17	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.17	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.17	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.17	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.17	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.17	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.17	   A^2 -> H(U1(d, a), b)
28.11/9.17	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.17	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.17	   A^2 -> H(U1(d, a), c)
28.11/9.17	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.17	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.17	   A^2 -> H(U1(d, a), e)
28.11/9.17	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.17	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.17	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.17	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.17	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.17	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.17	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.17	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.17	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.17	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.17	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.17	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.17	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.17	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.17	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.17	   A^2 -> H(U1(a, c), b)
28.11/9.17	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.17	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.17	   A^2 -> H(U1(a, c), c)
28.11/9.17	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.17	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.17	   A^2 -> H(U1(a, c), e)
28.11/9.17	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, d), b)
28.11/9.17	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.17	   A^2 -> H(U1(a, d), U1(d, e))
28.11/9.17	   A^2 -> H(U1(a, d), c)
28.11/9.17	   A^2 -> H(U1(a, d), U1(e, k))
28.11/9.17	   A^2 -> H(U1(a, d), U1(k, e))
28.11/9.17	   A^2 -> H(U1(a, d), e)
28.11/9.17	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, a), d)
28.11/9.17	
28.11/9.17	The TRS R consists of the following rules:
28.11/9.17	
28.11/9.17	   f(x) -> U1(x, x)
28.11/9.17	   U1(e, x) -> x
28.11/9.17	   a -> c
28.11/9.17	   a -> d
28.11/9.17	   b -> c
28.11/9.17	   b -> d
28.11/9.17	   d -> k
28.11/9.17	   c -> e
28.11/9.17	   c -> k
28.11/9.17	
28.11/9.17	Q is empty.
28.11/9.17	We have to consider all minimal (P,Q,R)-chains.
28.11/9.17	----------------------------------------
28.11/9.17	
28.11/9.17	(771) TransformationProof (EQUIVALENT)
28.11/9.17	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.17	
28.11/9.17	   (A^2 -> H(U1(c, a), U1(e, d)),A^2 -> H(U1(c, a), U1(e, d)))
28.11/9.17	   (A^2 -> H(U1(d, a), U1(e, d)),A^2 -> H(U1(d, a), U1(e, d)))
28.11/9.17	   (A^2 -> H(U1(a, c), U1(e, d)),A^2 -> H(U1(a, c), U1(e, d)))
28.11/9.17	   (A^2 -> H(U1(a, d), U1(e, d)),A^2 -> H(U1(a, d), U1(e, d)))
28.11/9.17	   (A^2 -> H(U1(a, a), d),A^2 -> H(U1(a, a), d))
28.11/9.17	   (A^2 -> H(U1(a, a), U1(e, k)),A^2 -> H(U1(a, a), U1(e, k)))
28.11/9.17	
28.11/9.17	
28.11/9.17	----------------------------------------
28.11/9.17	
28.11/9.17	(772)
28.11/9.17	Obligation:
28.11/9.17	Q DP problem:
28.11/9.17	The TRS P consists of the following rules:
28.11/9.17	
28.11/9.17	   H(x, x) -> G(x, x, f(k))
28.11/9.17	   G(d, x, x) -> A^2
28.11/9.17	   A^2 -> H(f(c), f(c))
28.11/9.17	   A^2 -> H(f(d), f(d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.17	   A^2 -> H(f(e), f(e))
28.11/9.17	   A^2 -> H(f(k), f(k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.17	   A^2 -> H(U1(a, a), U1(d, e))
28.11/9.17	   A^2 -> H(U1(a, a), c)
28.11/9.17	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.17	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.17	   A^2 -> H(U1(a, a), e)
28.11/9.17	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.17	   A^2 -> H(k, f(b))
28.11/9.17	   A^2 -> H(c, U1(b, b))
28.11/9.17	   A^2 -> H(c, f(c))
28.11/9.17	   A^2 -> H(c, f(d))
28.11/9.17	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.17	   A^2 -> H(U1(e, k), f(c))
28.11/9.17	   A^2 -> H(U1(e, k), f(d))
28.11/9.17	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.17	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.17	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.17	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.17	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.17	   A^2 -> H(U1(e, c), f(e))
28.11/9.17	   A^2 -> H(U1(e, c), f(k))
28.11/9.17	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.17	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.17	   A^2 -> H(U1(k, e), f(c))
28.11/9.17	   A^2 -> H(U1(k, e), f(d))
28.11/9.17	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.17	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.17	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.17	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.17	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.17	   A^2 -> H(U1(k, c), f(e))
28.11/9.17	   A^2 -> H(U1(k, c), f(k))
28.11/9.17	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.17	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.17	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.17	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.17	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.17	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.17	   A^2 -> H(U1(c, e), f(e))
28.11/9.17	   A^2 -> H(U1(c, e), f(k))
28.11/9.17	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.17	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.17	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.17	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.17	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.17	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.17	   A^2 -> H(U1(c, k), f(e))
28.11/9.17	   A^2 -> H(U1(c, k), f(k))
28.11/9.17	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.17	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.17	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.17	   A^2 -> H(e, U1(b, b))
28.11/9.17	   A^2 -> H(e, f(c))
28.11/9.17	   A^2 -> H(e, f(d))
28.11/9.17	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.17	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.17	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.17	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.17	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.17	   A^2 -> H(U1(e, e), f(e))
28.11/9.17	   A^2 -> H(U1(e, e), f(k))
28.11/9.17	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.17	   A^2 -> H(f(e), U1(e, b))
28.11/9.17	   A^2 -> H(f(e), U1(k, b))
28.11/9.17	   A^2 -> H(f(e), U1(c, d))
28.11/9.17	   A^2 -> H(f(e), U1(d, c))
28.11/9.17	   A^2 -> H(f(e), U1(b, e))
28.11/9.17	   A^2 -> H(f(e), U1(b, k))
28.11/9.17	   A^2 -> H(f(e), U1(e, c))
28.11/9.17	   A^2 -> H(f(e), U1(k, c))
28.11/9.17	   A^2 -> H(f(e), U1(c, e))
28.11/9.17	   A^2 -> H(f(e), U1(c, k))
28.11/9.17	   A^2 -> H(f(e), U1(k, k))
28.11/9.17	   A^2 -> H(f(e), U1(k, d))
28.11/9.17	   A^2 -> H(f(e), U1(d, k))
28.11/9.17	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.17	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.17	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.17	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.17	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.17	   A^2 -> H(U1(k, k), f(e))
28.11/9.17	   A^2 -> H(U1(k, k), f(k))
28.11/9.17	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.17	   A^2 -> H(f(k), U1(e, b))
28.11/9.17	   A^2 -> H(f(k), U1(k, b))
28.11/9.17	   A^2 -> H(f(k), U1(c, d))
28.11/9.17	   A^2 -> H(f(k), U1(d, c))
28.11/9.17	   A^2 -> H(f(k), U1(b, e))
28.11/9.17	   A^2 -> H(f(k), U1(b, k))
28.11/9.17	   A^2 -> H(f(k), U1(e, c))
28.11/9.17	   A^2 -> H(f(k), U1(k, c))
28.11/9.17	   A^2 -> H(f(k), U1(c, e))
28.11/9.17	   A^2 -> H(f(k), U1(c, k))
28.11/9.17	   A^2 -> H(f(k), U1(e, e))
28.11/9.17	   A^2 -> H(f(k), U1(k, d))
28.11/9.17	   A^2 -> H(f(k), U1(d, k))
28.11/9.17	   A^2 -> H(f(c), b)
28.11/9.17	   A^2 -> H(f(c), U1(e, d))
28.11/9.17	   A^2 -> H(f(c), U1(d, e))
28.11/9.17	   A^2 -> H(f(k), U1(k, k))
28.11/9.17	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.17	   A^2 -> H(U1(k, k), f(c))
28.11/9.17	   A^2 -> H(U1(k, k), f(d))
28.11/9.17	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.17	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.17	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.17	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.17	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.17	   A^2 -> H(U1(k, d), f(e))
28.11/9.17	   A^2 -> H(U1(k, d), f(k))
28.11/9.17	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.17	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.17	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.17	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.17	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.17	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.17	   A^2 -> H(U1(d, k), f(e))
28.11/9.17	   A^2 -> H(U1(d, k), f(k))
28.11/9.17	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.17	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.17	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.17	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.17	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.17	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.17	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.17	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.17	   A^2 -> H(f(d), b)
28.11/9.17	   A^2 -> H(f(d), U1(e, d))
28.11/9.17	   A^2 -> H(f(d), U1(d, e))
28.11/9.17	   A^2 -> H(f(d), c)
28.11/9.17	   A^2 -> H(f(d), U1(e, k))
28.11/9.17	   A^2 -> H(f(d), U1(k, e))
28.11/9.17	   A^2 -> H(f(d), e)
28.11/9.17	   A^2 -> H(f(a), d)
28.11/9.17	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.17	   A^2 -> H(f(c), c)
28.11/9.17	   A^2 -> H(f(c), U1(e, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.17	   A^2 -> H(f(c), U1(k, e))
28.11/9.17	   A^2 -> H(f(c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.17	   A^2 -> H(f(a), k)
28.11/9.17	   A^2 -> H(f(e), U1(e, e))
28.11/9.17	   A^2 -> H(f(c), e)
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.17	   A^2 -> H(f(d), U1(k, k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.17	   A^2 -> H(d, U1(b, b))
28.11/9.17	   A^2 -> H(d, f(c))
28.11/9.17	   A^2 -> H(d, f(d))
28.11/9.17	   A^2 -> H(a, U1(c, b))
28.11/9.17	   A^2 -> H(a, U1(d, b))
28.11/9.17	   A^2 -> H(a, U1(b, c))
28.11/9.17	   A^2 -> H(a, U1(b, d))
28.11/9.17	   A^2 -> H(a, U1(c, c))
28.11/9.17	   A^2 -> H(a, f(e))
28.11/9.17	   A^2 -> H(a, f(k))
28.11/9.17	   A^2 -> H(a, U1(d, d))
28.11/9.17	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.17	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.17	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.17	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.17	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.17	   A^2 -> H(U1(e, d), f(e))
28.11/9.17	   A^2 -> H(U1(e, d), f(k))
28.11/9.17	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.17	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.17	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.17	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.17	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.17	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.17	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.17	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.17	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.17	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.17	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.17	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.17	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.17	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.17	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.17	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.17	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.17	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.17	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.17	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.17	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.17	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.17	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.17	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.17	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.17	   A^2 -> H(U1(c, a), b)
28.11/9.17	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.17	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.17	   A^2 -> H(U1(c, a), c)
28.11/9.17	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.17	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.17	   A^2 -> H(U1(c, a), e)
28.11/9.17	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.17	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.17	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.17	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.17	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.17	   A^2 -> H(U1(d, e), f(e))
28.11/9.17	   A^2 -> H(U1(d, e), f(k))
28.11/9.17	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.17	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.17	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.17	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.17	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.17	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.17	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.17	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.17	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.17	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.17	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.17	   A^2 -> H(U1(d, a), b)
28.11/9.17	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.17	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.17	   A^2 -> H(U1(d, a), c)
28.11/9.17	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.17	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.17	   A^2 -> H(U1(d, a), e)
28.11/9.17	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.17	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.17	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.17	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.17	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.17	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.17	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.17	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.17	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.17	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.17	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.17	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.17	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.17	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.17	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.17	   A^2 -> H(U1(a, c), b)
28.11/9.17	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.17	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.17	   A^2 -> H(U1(a, c), c)
28.11/9.17	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.17	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.17	   A^2 -> H(U1(a, c), e)
28.11/9.17	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, d), b)
28.11/9.17	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.17	   A^2 -> H(U1(a, d), U1(d, e))
28.11/9.17	   A^2 -> H(U1(a, d), c)
28.11/9.17	   A^2 -> H(U1(a, d), U1(e, k))
28.11/9.17	   A^2 -> H(U1(a, d), U1(k, e))
28.11/9.17	   A^2 -> H(U1(a, d), e)
28.11/9.17	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, a), d)
28.11/9.17	
28.11/9.17	The TRS R consists of the following rules:
28.11/9.17	
28.11/9.17	   f(x) -> U1(x, x)
28.11/9.17	   U1(e, x) -> x
28.11/9.17	   a -> c
28.11/9.17	   a -> d
28.11/9.17	   b -> c
28.11/9.17	   b -> d
28.11/9.17	   d -> k
28.11/9.17	   c -> e
28.11/9.17	   c -> k
28.11/9.17	
28.11/9.17	Q is empty.
28.11/9.17	We have to consider all minimal (P,Q,R)-chains.
28.11/9.17	----------------------------------------
28.11/9.17	
28.11/9.17	(773) TransformationProof (EQUIVALENT)
28.11/9.17	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.17	
28.11/9.17	   (A^2 -> H(U1(c, a), U1(d, e)),A^2 -> H(U1(c, a), U1(d, e)))
28.11/9.17	   (A^2 -> H(U1(d, a), U1(d, e)),A^2 -> H(U1(d, a), U1(d, e)))
28.11/9.17	   (A^2 -> H(U1(a, c), U1(d, e)),A^2 -> H(U1(a, c), U1(d, e)))
28.11/9.17	   (A^2 -> H(U1(a, d), U1(d, e)),A^2 -> H(U1(a, d), U1(d, e)))
28.11/9.17	   (A^2 -> H(U1(a, a), U1(k, e)),A^2 -> H(U1(a, a), U1(k, e)))
28.11/9.17	
28.11/9.17	
28.11/9.17	----------------------------------------
28.11/9.17	
28.11/9.17	(774)
28.11/9.17	Obligation:
28.11/9.17	Q DP problem:
28.11/9.17	The TRS P consists of the following rules:
28.11/9.17	
28.11/9.17	   H(x, x) -> G(x, x, f(k))
28.11/9.17	   G(d, x, x) -> A^2
28.11/9.17	   A^2 -> H(f(c), f(c))
28.11/9.17	   A^2 -> H(f(d), f(d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.17	   A^2 -> H(f(e), f(e))
28.11/9.17	   A^2 -> H(f(k), f(k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.17	   A^2 -> H(U1(a, a), c)
28.11/9.17	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.17	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.17	   A^2 -> H(U1(a, a), e)
28.11/9.17	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.17	   A^2 -> H(k, f(b))
28.11/9.17	   A^2 -> H(c, U1(b, b))
28.11/9.17	   A^2 -> H(c, f(c))
28.11/9.17	   A^2 -> H(c, f(d))
28.11/9.17	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.17	   A^2 -> H(U1(e, k), f(c))
28.11/9.17	   A^2 -> H(U1(e, k), f(d))
28.11/9.17	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.17	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.17	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.17	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.17	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.17	   A^2 -> H(U1(e, c), f(e))
28.11/9.17	   A^2 -> H(U1(e, c), f(k))
28.11/9.17	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.17	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.17	   A^2 -> H(U1(k, e), f(c))
28.11/9.17	   A^2 -> H(U1(k, e), f(d))
28.11/9.17	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.17	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.17	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.17	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.17	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.17	   A^2 -> H(U1(k, c), f(e))
28.11/9.17	   A^2 -> H(U1(k, c), f(k))
28.11/9.17	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.17	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.17	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.17	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.17	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.17	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.17	   A^2 -> H(U1(c, e), f(e))
28.11/9.17	   A^2 -> H(U1(c, e), f(k))
28.11/9.17	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.17	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.17	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.17	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.17	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.17	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.17	   A^2 -> H(U1(c, k), f(e))
28.11/9.17	   A^2 -> H(U1(c, k), f(k))
28.11/9.17	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.17	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.17	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.17	   A^2 -> H(e, U1(b, b))
28.11/9.17	   A^2 -> H(e, f(c))
28.11/9.17	   A^2 -> H(e, f(d))
28.11/9.17	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.17	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.17	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.17	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.17	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.17	   A^2 -> H(U1(e, e), f(e))
28.11/9.17	   A^2 -> H(U1(e, e), f(k))
28.11/9.17	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.17	   A^2 -> H(f(e), U1(e, b))
28.11/9.17	   A^2 -> H(f(e), U1(k, b))
28.11/9.17	   A^2 -> H(f(e), U1(c, d))
28.11/9.17	   A^2 -> H(f(e), U1(d, c))
28.11/9.17	   A^2 -> H(f(e), U1(b, e))
28.11/9.17	   A^2 -> H(f(e), U1(b, k))
28.11/9.17	   A^2 -> H(f(e), U1(e, c))
28.11/9.17	   A^2 -> H(f(e), U1(k, c))
28.11/9.17	   A^2 -> H(f(e), U1(c, e))
28.11/9.17	   A^2 -> H(f(e), U1(c, k))
28.11/9.17	   A^2 -> H(f(e), U1(k, k))
28.11/9.17	   A^2 -> H(f(e), U1(k, d))
28.11/9.17	   A^2 -> H(f(e), U1(d, k))
28.11/9.17	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.17	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.17	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.17	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.17	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.17	   A^2 -> H(U1(k, k), f(e))
28.11/9.17	   A^2 -> H(U1(k, k), f(k))
28.11/9.17	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.17	   A^2 -> H(f(k), U1(e, b))
28.11/9.17	   A^2 -> H(f(k), U1(k, b))
28.11/9.17	   A^2 -> H(f(k), U1(c, d))
28.11/9.17	   A^2 -> H(f(k), U1(d, c))
28.11/9.17	   A^2 -> H(f(k), U1(b, e))
28.11/9.17	   A^2 -> H(f(k), U1(b, k))
28.11/9.17	   A^2 -> H(f(k), U1(e, c))
28.11/9.17	   A^2 -> H(f(k), U1(k, c))
28.11/9.17	   A^2 -> H(f(k), U1(c, e))
28.11/9.17	   A^2 -> H(f(k), U1(c, k))
28.11/9.17	   A^2 -> H(f(k), U1(e, e))
28.11/9.17	   A^2 -> H(f(k), U1(k, d))
28.11/9.17	   A^2 -> H(f(k), U1(d, k))
28.11/9.17	   A^2 -> H(f(c), b)
28.11/9.17	   A^2 -> H(f(c), U1(e, d))
28.11/9.17	   A^2 -> H(f(c), U1(d, e))
28.11/9.17	   A^2 -> H(f(k), U1(k, k))
28.11/9.17	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.17	   A^2 -> H(U1(k, k), f(c))
28.11/9.17	   A^2 -> H(U1(k, k), f(d))
28.11/9.17	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.17	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.17	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.17	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.17	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.17	   A^2 -> H(U1(k, d), f(e))
28.11/9.17	   A^2 -> H(U1(k, d), f(k))
28.11/9.17	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.17	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.17	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.17	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.17	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.17	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.17	   A^2 -> H(U1(d, k), f(e))
28.11/9.17	   A^2 -> H(U1(d, k), f(k))
28.11/9.17	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.17	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.17	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.17	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.17	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.17	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.17	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.17	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.17	   A^2 -> H(f(d), b)
28.11/9.17	   A^2 -> H(f(d), U1(e, d))
28.11/9.17	   A^2 -> H(f(d), U1(d, e))
28.11/9.17	   A^2 -> H(f(d), c)
28.11/9.17	   A^2 -> H(f(d), U1(e, k))
28.11/9.17	   A^2 -> H(f(d), U1(k, e))
28.11/9.17	   A^2 -> H(f(d), e)
28.11/9.17	   A^2 -> H(f(a), d)
28.11/9.17	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.17	   A^2 -> H(f(c), c)
28.11/9.17	   A^2 -> H(f(c), U1(e, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.17	   A^2 -> H(f(c), U1(k, e))
28.11/9.17	   A^2 -> H(f(c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.17	   A^2 -> H(f(a), k)
28.11/9.17	   A^2 -> H(f(e), U1(e, e))
28.11/9.17	   A^2 -> H(f(c), e)
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.17	   A^2 -> H(f(d), U1(k, k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.17	   A^2 -> H(d, U1(b, b))
28.11/9.17	   A^2 -> H(d, f(c))
28.11/9.17	   A^2 -> H(d, f(d))
28.11/9.17	   A^2 -> H(a, U1(c, b))
28.11/9.17	   A^2 -> H(a, U1(d, b))
28.11/9.17	   A^2 -> H(a, U1(b, c))
28.11/9.17	   A^2 -> H(a, U1(b, d))
28.11/9.17	   A^2 -> H(a, U1(c, c))
28.11/9.17	   A^2 -> H(a, f(e))
28.11/9.17	   A^2 -> H(a, f(k))
28.11/9.17	   A^2 -> H(a, U1(d, d))
28.11/9.17	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.17	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.17	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.17	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.17	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.17	   A^2 -> H(U1(e, d), f(e))
28.11/9.17	   A^2 -> H(U1(e, d), f(k))
28.11/9.17	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.17	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.17	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.17	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.17	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.17	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.17	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.17	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.17	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.17	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.17	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.17	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.17	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.17	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.17	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.17	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.17	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.17	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.17	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.17	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.17	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.17	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.17	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.17	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.17	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.17	   A^2 -> H(U1(c, a), b)
28.11/9.17	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.17	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.17	   A^2 -> H(U1(c, a), c)
28.11/9.17	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.17	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.17	   A^2 -> H(U1(c, a), e)
28.11/9.17	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.17	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.17	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.17	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.17	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.17	   A^2 -> H(U1(d, e), f(e))
28.11/9.17	   A^2 -> H(U1(d, e), f(k))
28.11/9.17	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.17	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.17	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.17	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.17	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.17	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.17	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.17	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.17	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.17	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.17	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.17	   A^2 -> H(U1(d, a), b)
28.11/9.17	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.17	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.17	   A^2 -> H(U1(d, a), c)
28.11/9.17	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.17	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.17	   A^2 -> H(U1(d, a), e)
28.11/9.17	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.17	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.17	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.17	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.17	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.17	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.17	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.17	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.17	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.17	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.17	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.17	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.17	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.17	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.17	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.17	   A^2 -> H(U1(a, c), b)
28.11/9.17	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.17	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.17	   A^2 -> H(U1(a, c), c)
28.11/9.17	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.17	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.17	   A^2 -> H(U1(a, c), e)
28.11/9.17	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, d), b)
28.11/9.17	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.17	   A^2 -> H(U1(a, d), U1(d, e))
28.11/9.17	   A^2 -> H(U1(a, d), c)
28.11/9.17	   A^2 -> H(U1(a, d), U1(e, k))
28.11/9.17	   A^2 -> H(U1(a, d), U1(k, e))
28.11/9.17	   A^2 -> H(U1(a, d), e)
28.11/9.17	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, a), d)
28.11/9.17	
28.11/9.17	The TRS R consists of the following rules:
28.11/9.17	
28.11/9.17	   f(x) -> U1(x, x)
28.11/9.17	   U1(e, x) -> x
28.11/9.17	   a -> c
28.11/9.17	   a -> d
28.11/9.17	   b -> c
28.11/9.17	   b -> d
28.11/9.17	   d -> k
28.11/9.17	   c -> e
28.11/9.17	   c -> k
28.11/9.17	
28.11/9.17	Q is empty.
28.11/9.17	We have to consider all minimal (P,Q,R)-chains.
28.11/9.17	----------------------------------------
28.11/9.17	
28.11/9.17	(775) TransformationProof (EQUIVALENT)
28.11/9.17	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), c) at position [] we obtained the following new rules [LPAR04]:
28.11/9.17	
28.11/9.17	   (A^2 -> H(U1(c, a), c),A^2 -> H(U1(c, a), c))
28.11/9.17	   (A^2 -> H(U1(d, a), c),A^2 -> H(U1(d, a), c))
28.11/9.17	   (A^2 -> H(U1(a, c), c),A^2 -> H(U1(a, c), c))
28.11/9.17	   (A^2 -> H(U1(a, d), c),A^2 -> H(U1(a, d), c))
28.11/9.17	   (A^2 -> H(U1(a, a), e),A^2 -> H(U1(a, a), e))
28.11/9.17	   (A^2 -> H(U1(a, a), k),A^2 -> H(U1(a, a), k))
28.11/9.17	
28.11/9.17	
28.11/9.17	----------------------------------------
28.11/9.17	
28.11/9.17	(776)
28.11/9.17	Obligation:
28.11/9.17	Q DP problem:
28.11/9.17	The TRS P consists of the following rules:
28.11/9.17	
28.11/9.17	   H(x, x) -> G(x, x, f(k))
28.11/9.17	   G(d, x, x) -> A^2
28.11/9.17	   A^2 -> H(f(c), f(c))
28.11/9.17	   A^2 -> H(f(d), f(d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.17	   A^2 -> H(f(e), f(e))
28.11/9.17	   A^2 -> H(f(k), f(k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.17	   A^2 -> H(U1(a, a), U1(e, k))
28.11/9.17	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.17	   A^2 -> H(U1(a, a), e)
28.11/9.17	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.17	   A^2 -> H(k, f(b))
28.11/9.17	   A^2 -> H(c, U1(b, b))
28.11/9.17	   A^2 -> H(c, f(c))
28.11/9.17	   A^2 -> H(c, f(d))
28.11/9.17	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.17	   A^2 -> H(U1(e, k), f(c))
28.11/9.17	   A^2 -> H(U1(e, k), f(d))
28.11/9.17	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.17	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.17	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.17	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.17	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.17	   A^2 -> H(U1(e, c), f(e))
28.11/9.17	   A^2 -> H(U1(e, c), f(k))
28.11/9.17	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.17	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.17	   A^2 -> H(U1(k, e), f(c))
28.11/9.17	   A^2 -> H(U1(k, e), f(d))
28.11/9.17	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.17	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.17	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.17	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.17	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.17	   A^2 -> H(U1(k, c), f(e))
28.11/9.17	   A^2 -> H(U1(k, c), f(k))
28.11/9.17	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.17	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.17	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.17	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.17	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.17	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.17	   A^2 -> H(U1(c, e), f(e))
28.11/9.17	   A^2 -> H(U1(c, e), f(k))
28.11/9.17	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.17	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.17	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.17	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.17	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.17	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.17	   A^2 -> H(U1(c, k), f(e))
28.11/9.17	   A^2 -> H(U1(c, k), f(k))
28.11/9.17	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.17	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.17	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.17	   A^2 -> H(e, U1(b, b))
28.11/9.17	   A^2 -> H(e, f(c))
28.11/9.17	   A^2 -> H(e, f(d))
28.11/9.17	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.17	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.17	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.17	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.17	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.17	   A^2 -> H(U1(e, e), f(e))
28.11/9.17	   A^2 -> H(U1(e, e), f(k))
28.11/9.17	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.17	   A^2 -> H(f(e), U1(e, b))
28.11/9.17	   A^2 -> H(f(e), U1(k, b))
28.11/9.17	   A^2 -> H(f(e), U1(c, d))
28.11/9.17	   A^2 -> H(f(e), U1(d, c))
28.11/9.17	   A^2 -> H(f(e), U1(b, e))
28.11/9.17	   A^2 -> H(f(e), U1(b, k))
28.11/9.17	   A^2 -> H(f(e), U1(e, c))
28.11/9.17	   A^2 -> H(f(e), U1(k, c))
28.11/9.17	   A^2 -> H(f(e), U1(c, e))
28.11/9.17	   A^2 -> H(f(e), U1(c, k))
28.11/9.17	   A^2 -> H(f(e), U1(k, k))
28.11/9.17	   A^2 -> H(f(e), U1(k, d))
28.11/9.17	   A^2 -> H(f(e), U1(d, k))
28.11/9.17	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.17	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.17	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.17	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.17	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.17	   A^2 -> H(U1(k, k), f(e))
28.11/9.17	   A^2 -> H(U1(k, k), f(k))
28.11/9.17	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.17	   A^2 -> H(f(k), U1(e, b))
28.11/9.17	   A^2 -> H(f(k), U1(k, b))
28.11/9.17	   A^2 -> H(f(k), U1(c, d))
28.11/9.17	   A^2 -> H(f(k), U1(d, c))
28.11/9.17	   A^2 -> H(f(k), U1(b, e))
28.11/9.17	   A^2 -> H(f(k), U1(b, k))
28.11/9.17	   A^2 -> H(f(k), U1(e, c))
28.11/9.17	   A^2 -> H(f(k), U1(k, c))
28.11/9.17	   A^2 -> H(f(k), U1(c, e))
28.11/9.17	   A^2 -> H(f(k), U1(c, k))
28.11/9.17	   A^2 -> H(f(k), U1(e, e))
28.11/9.17	   A^2 -> H(f(k), U1(k, d))
28.11/9.17	   A^2 -> H(f(k), U1(d, k))
28.11/9.17	   A^2 -> H(f(c), b)
28.11/9.17	   A^2 -> H(f(c), U1(e, d))
28.11/9.17	   A^2 -> H(f(c), U1(d, e))
28.11/9.17	   A^2 -> H(f(k), U1(k, k))
28.11/9.17	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.17	   A^2 -> H(U1(k, k), f(c))
28.11/9.17	   A^2 -> H(U1(k, k), f(d))
28.11/9.17	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.17	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.17	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.17	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.17	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.17	   A^2 -> H(U1(k, d), f(e))
28.11/9.17	   A^2 -> H(U1(k, d), f(k))
28.11/9.17	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.17	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.17	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.17	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.17	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.17	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.17	   A^2 -> H(U1(d, k), f(e))
28.11/9.17	   A^2 -> H(U1(d, k), f(k))
28.11/9.17	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.17	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.17	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.17	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.17	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.17	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.17	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.17	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.17	   A^2 -> H(f(d), b)
28.11/9.17	   A^2 -> H(f(d), U1(e, d))
28.11/9.17	   A^2 -> H(f(d), U1(d, e))
28.11/9.17	   A^2 -> H(f(d), c)
28.11/9.17	   A^2 -> H(f(d), U1(e, k))
28.11/9.17	   A^2 -> H(f(d), U1(k, e))
28.11/9.17	   A^2 -> H(f(d), e)
28.11/9.17	   A^2 -> H(f(a), d)
28.11/9.17	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.17	   A^2 -> H(f(c), c)
28.11/9.17	   A^2 -> H(f(c), U1(e, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.17	   A^2 -> H(f(c), U1(k, e))
28.11/9.17	   A^2 -> H(f(c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.17	   A^2 -> H(f(a), k)
28.11/9.17	   A^2 -> H(f(e), U1(e, e))
28.11/9.17	   A^2 -> H(f(c), e)
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.17	   A^2 -> H(f(d), U1(k, k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.17	   A^2 -> H(d, U1(b, b))
28.11/9.17	   A^2 -> H(d, f(c))
28.11/9.17	   A^2 -> H(d, f(d))
28.11/9.17	   A^2 -> H(a, U1(c, b))
28.11/9.17	   A^2 -> H(a, U1(d, b))
28.11/9.17	   A^2 -> H(a, U1(b, c))
28.11/9.17	   A^2 -> H(a, U1(b, d))
28.11/9.17	   A^2 -> H(a, U1(c, c))
28.11/9.17	   A^2 -> H(a, f(e))
28.11/9.17	   A^2 -> H(a, f(k))
28.11/9.17	   A^2 -> H(a, U1(d, d))
28.11/9.17	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.17	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.17	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.17	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.17	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.17	   A^2 -> H(U1(e, d), f(e))
28.11/9.17	   A^2 -> H(U1(e, d), f(k))
28.11/9.17	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.17	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.17	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.17	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.17	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.17	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.17	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.17	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.17	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.17	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.17	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.17	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.17	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.17	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.17	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.17	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.17	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.17	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.17	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.17	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.17	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.17	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.17	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.17	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.17	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.17	   A^2 -> H(U1(c, a), b)
28.11/9.17	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.17	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.17	   A^2 -> H(U1(c, a), c)
28.11/9.17	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.17	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.17	   A^2 -> H(U1(c, a), e)
28.11/9.17	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.17	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.17	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.17	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.17	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.17	   A^2 -> H(U1(d, e), f(e))
28.11/9.17	   A^2 -> H(U1(d, e), f(k))
28.11/9.17	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.17	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.17	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.17	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.17	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.17	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.17	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.17	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.17	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.17	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.17	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.17	   A^2 -> H(U1(d, a), b)
28.11/9.17	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.17	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.17	   A^2 -> H(U1(d, a), c)
28.11/9.17	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.17	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.17	   A^2 -> H(U1(d, a), e)
28.11/9.17	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.17	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.17	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.17	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.17	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.17	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.17	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.17	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.17	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.17	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.17	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.17	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.17	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.17	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.17	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.17	   A^2 -> H(U1(a, c), b)
28.11/9.17	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.17	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.17	   A^2 -> H(U1(a, c), c)
28.11/9.17	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.17	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.17	   A^2 -> H(U1(a, c), e)
28.11/9.17	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, d), b)
28.11/9.17	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.17	   A^2 -> H(U1(a, d), U1(d, e))
28.11/9.17	   A^2 -> H(U1(a, d), c)
28.11/9.17	   A^2 -> H(U1(a, d), U1(e, k))
28.11/9.17	   A^2 -> H(U1(a, d), U1(k, e))
28.11/9.17	   A^2 -> H(U1(a, d), e)
28.11/9.17	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, a), d)
28.11/9.17	   A^2 -> H(U1(a, a), k)
28.11/9.17	
28.11/9.17	The TRS R consists of the following rules:
28.11/9.17	
28.11/9.17	   f(x) -> U1(x, x)
28.11/9.17	   U1(e, x) -> x
28.11/9.17	   a -> c
28.11/9.17	   a -> d
28.11/9.17	   b -> c
28.11/9.17	   b -> d
28.11/9.17	   d -> k
28.11/9.17	   c -> e
28.11/9.17	   c -> k
28.11/9.17	
28.11/9.17	Q is empty.
28.11/9.17	We have to consider all minimal (P,Q,R)-chains.
28.11/9.17	----------------------------------------
28.11/9.17	
28.11/9.17	(777) TransformationProof (EQUIVALENT)
28.11/9.17	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.17	
28.11/9.17	   (A^2 -> H(U1(c, a), U1(e, k)),A^2 -> H(U1(c, a), U1(e, k)))
28.11/9.17	   (A^2 -> H(U1(d, a), U1(e, k)),A^2 -> H(U1(d, a), U1(e, k)))
28.11/9.17	   (A^2 -> H(U1(a, c), U1(e, k)),A^2 -> H(U1(a, c), U1(e, k)))
28.11/9.17	   (A^2 -> H(U1(a, d), U1(e, k)),A^2 -> H(U1(a, d), U1(e, k)))
28.11/9.17	   (A^2 -> H(U1(a, a), k),A^2 -> H(U1(a, a), k))
28.11/9.17	
28.11/9.17	
28.11/9.17	----------------------------------------
28.11/9.17	
28.11/9.17	(778)
28.11/9.17	Obligation:
28.11/9.17	Q DP problem:
28.11/9.17	The TRS P consists of the following rules:
28.11/9.17	
28.11/9.17	   H(x, x) -> G(x, x, f(k))
28.11/9.17	   G(d, x, x) -> A^2
28.11/9.17	   A^2 -> H(f(c), f(c))
28.11/9.17	   A^2 -> H(f(d), f(d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.17	   A^2 -> H(f(e), f(e))
28.11/9.17	   A^2 -> H(f(k), f(k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.17	   A^2 -> H(U1(a, a), U1(k, e))
28.11/9.17	   A^2 -> H(U1(a, a), e)
28.11/9.17	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.17	   A^2 -> H(k, f(b))
28.11/9.17	   A^2 -> H(c, U1(b, b))
28.11/9.17	   A^2 -> H(c, f(c))
28.11/9.17	   A^2 -> H(c, f(d))
28.11/9.17	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.17	   A^2 -> H(U1(e, k), f(c))
28.11/9.17	   A^2 -> H(U1(e, k), f(d))
28.11/9.17	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.17	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.17	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.17	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.17	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.17	   A^2 -> H(U1(e, c), f(e))
28.11/9.17	   A^2 -> H(U1(e, c), f(k))
28.11/9.17	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.17	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.17	   A^2 -> H(U1(k, e), f(c))
28.11/9.17	   A^2 -> H(U1(k, e), f(d))
28.11/9.17	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.17	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.17	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.17	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.17	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.17	   A^2 -> H(U1(k, c), f(e))
28.11/9.17	   A^2 -> H(U1(k, c), f(k))
28.11/9.17	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.17	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.17	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.17	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.17	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.17	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.17	   A^2 -> H(U1(c, e), f(e))
28.11/9.17	   A^2 -> H(U1(c, e), f(k))
28.11/9.17	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.17	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.17	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.17	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.17	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.17	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.17	   A^2 -> H(U1(c, k), f(e))
28.11/9.17	   A^2 -> H(U1(c, k), f(k))
28.11/9.17	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.17	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.17	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.17	   A^2 -> H(e, U1(b, b))
28.11/9.17	   A^2 -> H(e, f(c))
28.11/9.17	   A^2 -> H(e, f(d))
28.11/9.17	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.17	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.17	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.17	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.17	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.17	   A^2 -> H(U1(e, e), f(e))
28.11/9.17	   A^2 -> H(U1(e, e), f(k))
28.11/9.17	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.17	   A^2 -> H(f(e), U1(e, b))
28.11/9.17	   A^2 -> H(f(e), U1(k, b))
28.11/9.17	   A^2 -> H(f(e), U1(c, d))
28.11/9.17	   A^2 -> H(f(e), U1(d, c))
28.11/9.17	   A^2 -> H(f(e), U1(b, e))
28.11/9.17	   A^2 -> H(f(e), U1(b, k))
28.11/9.17	   A^2 -> H(f(e), U1(e, c))
28.11/9.17	   A^2 -> H(f(e), U1(k, c))
28.11/9.17	   A^2 -> H(f(e), U1(c, e))
28.11/9.17	   A^2 -> H(f(e), U1(c, k))
28.11/9.17	   A^2 -> H(f(e), U1(k, k))
28.11/9.17	   A^2 -> H(f(e), U1(k, d))
28.11/9.17	   A^2 -> H(f(e), U1(d, k))
28.11/9.17	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.17	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.17	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.17	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.17	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.17	   A^2 -> H(U1(k, k), f(e))
28.11/9.17	   A^2 -> H(U1(k, k), f(k))
28.11/9.17	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.17	   A^2 -> H(f(k), U1(e, b))
28.11/9.17	   A^2 -> H(f(k), U1(k, b))
28.11/9.17	   A^2 -> H(f(k), U1(c, d))
28.11/9.17	   A^2 -> H(f(k), U1(d, c))
28.11/9.17	   A^2 -> H(f(k), U1(b, e))
28.11/9.17	   A^2 -> H(f(k), U1(b, k))
28.11/9.17	   A^2 -> H(f(k), U1(e, c))
28.11/9.17	   A^2 -> H(f(k), U1(k, c))
28.11/9.17	   A^2 -> H(f(k), U1(c, e))
28.11/9.17	   A^2 -> H(f(k), U1(c, k))
28.11/9.17	   A^2 -> H(f(k), U1(e, e))
28.11/9.17	   A^2 -> H(f(k), U1(k, d))
28.11/9.17	   A^2 -> H(f(k), U1(d, k))
28.11/9.17	   A^2 -> H(f(c), b)
28.11/9.17	   A^2 -> H(f(c), U1(e, d))
28.11/9.17	   A^2 -> H(f(c), U1(d, e))
28.11/9.17	   A^2 -> H(f(k), U1(k, k))
28.11/9.17	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.17	   A^2 -> H(U1(k, k), f(c))
28.11/9.17	   A^2 -> H(U1(k, k), f(d))
28.11/9.17	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.17	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.17	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.17	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.17	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.17	   A^2 -> H(U1(k, d), f(e))
28.11/9.17	   A^2 -> H(U1(k, d), f(k))
28.11/9.17	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.17	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.17	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.17	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.17	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.17	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.17	   A^2 -> H(U1(d, k), f(e))
28.11/9.17	   A^2 -> H(U1(d, k), f(k))
28.11/9.17	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.17	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.17	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.17	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.17	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.17	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.17	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.17	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.17	   A^2 -> H(f(d), b)
28.11/9.17	   A^2 -> H(f(d), U1(e, d))
28.11/9.17	   A^2 -> H(f(d), U1(d, e))
28.11/9.17	   A^2 -> H(f(d), c)
28.11/9.17	   A^2 -> H(f(d), U1(e, k))
28.11/9.17	   A^2 -> H(f(d), U1(k, e))
28.11/9.17	   A^2 -> H(f(d), e)
28.11/9.17	   A^2 -> H(f(a), d)
28.11/9.17	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.17	   A^2 -> H(f(c), c)
28.11/9.17	   A^2 -> H(f(c), U1(e, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.17	   A^2 -> H(f(c), U1(k, e))
28.11/9.17	   A^2 -> H(f(c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.17	   A^2 -> H(f(a), k)
28.11/9.17	   A^2 -> H(f(e), U1(e, e))
28.11/9.17	   A^2 -> H(f(c), e)
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.17	   A^2 -> H(f(d), U1(k, k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.17	   A^2 -> H(d, U1(b, b))
28.11/9.17	   A^2 -> H(d, f(c))
28.11/9.17	   A^2 -> H(d, f(d))
28.11/9.17	   A^2 -> H(a, U1(c, b))
28.11/9.17	   A^2 -> H(a, U1(d, b))
28.11/9.17	   A^2 -> H(a, U1(b, c))
28.11/9.17	   A^2 -> H(a, U1(b, d))
28.11/9.17	   A^2 -> H(a, U1(c, c))
28.11/9.17	   A^2 -> H(a, f(e))
28.11/9.17	   A^2 -> H(a, f(k))
28.11/9.17	   A^2 -> H(a, U1(d, d))
28.11/9.17	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.17	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.17	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.17	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.17	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.17	   A^2 -> H(U1(e, d), f(e))
28.11/9.17	   A^2 -> H(U1(e, d), f(k))
28.11/9.17	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.17	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.17	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.17	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.17	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.17	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.17	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.17	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.17	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.17	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.17	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.17	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.17	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.17	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.17	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.17	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.17	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.17	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.17	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.17	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.17	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.17	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.17	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.17	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.17	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.17	   A^2 -> H(U1(c, a), b)
28.11/9.17	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.17	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.17	   A^2 -> H(U1(c, a), c)
28.11/9.17	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.17	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.17	   A^2 -> H(U1(c, a), e)
28.11/9.17	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.17	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.17	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.17	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.17	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.17	   A^2 -> H(U1(d, e), f(e))
28.11/9.17	   A^2 -> H(U1(d, e), f(k))
28.11/9.17	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.17	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.17	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.17	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.17	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.17	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.17	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.17	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.17	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.17	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.17	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.17	   A^2 -> H(U1(d, a), b)
28.11/9.17	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.17	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.17	   A^2 -> H(U1(d, a), c)
28.11/9.17	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.17	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.17	   A^2 -> H(U1(d, a), e)
28.11/9.17	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.17	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.17	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.17	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.17	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.17	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.17	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.17	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.17	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.17	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.17	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.17	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.17	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.17	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.17	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.17	   A^2 -> H(U1(a, c), b)
28.11/9.17	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.17	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.17	   A^2 -> H(U1(a, c), c)
28.11/9.17	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.17	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.17	   A^2 -> H(U1(a, c), e)
28.11/9.17	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, d), b)
28.11/9.17	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.17	   A^2 -> H(U1(a, d), U1(d, e))
28.11/9.17	   A^2 -> H(U1(a, d), c)
28.11/9.17	   A^2 -> H(U1(a, d), U1(e, k))
28.11/9.17	   A^2 -> H(U1(a, d), U1(k, e))
28.11/9.17	   A^2 -> H(U1(a, d), e)
28.11/9.17	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, a), d)
28.11/9.17	   A^2 -> H(U1(a, a), k)
28.11/9.17	
28.11/9.17	The TRS R consists of the following rules:
28.11/9.17	
28.11/9.17	   f(x) -> U1(x, x)
28.11/9.17	   U1(e, x) -> x
28.11/9.17	   a -> c
28.11/9.17	   a -> d
28.11/9.17	   b -> c
28.11/9.17	   b -> d
28.11/9.17	   d -> k
28.11/9.17	   c -> e
28.11/9.17	   c -> k
28.11/9.17	
28.11/9.17	Q is empty.
28.11/9.17	We have to consider all minimal (P,Q,R)-chains.
28.11/9.17	----------------------------------------
28.11/9.17	
28.11/9.17	(779) TransformationProof (EQUIVALENT)
28.11/9.17	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.11/9.17	
28.11/9.17	   (A^2 -> H(U1(c, a), U1(k, e)),A^2 -> H(U1(c, a), U1(k, e)))
28.11/9.17	   (A^2 -> H(U1(d, a), U1(k, e)),A^2 -> H(U1(d, a), U1(k, e)))
28.11/9.17	   (A^2 -> H(U1(a, c), U1(k, e)),A^2 -> H(U1(a, c), U1(k, e)))
28.11/9.17	   (A^2 -> H(U1(a, d), U1(k, e)),A^2 -> H(U1(a, d), U1(k, e)))
28.11/9.17	
28.11/9.17	
28.11/9.17	----------------------------------------
28.11/9.17	
28.11/9.17	(780)
28.11/9.17	Obligation:
28.11/9.17	Q DP problem:
28.11/9.17	The TRS P consists of the following rules:
28.11/9.17	
28.11/9.17	   H(x, x) -> G(x, x, f(k))
28.11/9.17	   G(d, x, x) -> A^2
28.11/9.17	   A^2 -> H(f(c), f(c))
28.11/9.17	   A^2 -> H(f(d), f(d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.17	   A^2 -> H(f(e), f(e))
28.11/9.17	   A^2 -> H(f(k), f(k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.17	   A^2 -> H(U1(a, a), e)
28.11/9.17	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.17	   A^2 -> H(k, f(b))
28.11/9.17	   A^2 -> H(c, U1(b, b))
28.11/9.17	   A^2 -> H(c, f(c))
28.11/9.17	   A^2 -> H(c, f(d))
28.11/9.17	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.17	   A^2 -> H(U1(e, k), f(c))
28.11/9.17	   A^2 -> H(U1(e, k), f(d))
28.11/9.17	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.17	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.17	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.17	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.17	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.17	   A^2 -> H(U1(e, c), f(e))
28.11/9.17	   A^2 -> H(U1(e, c), f(k))
28.11/9.17	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.17	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.17	   A^2 -> H(U1(k, e), f(c))
28.11/9.17	   A^2 -> H(U1(k, e), f(d))
28.11/9.17	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.17	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.17	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.17	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.17	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.17	   A^2 -> H(U1(k, c), f(e))
28.11/9.17	   A^2 -> H(U1(k, c), f(k))
28.11/9.17	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.17	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.17	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.17	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.17	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.17	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.17	   A^2 -> H(U1(c, e), f(e))
28.11/9.17	   A^2 -> H(U1(c, e), f(k))
28.11/9.17	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.17	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.17	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.17	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.17	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.17	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.17	   A^2 -> H(U1(c, k), f(e))
28.11/9.17	   A^2 -> H(U1(c, k), f(k))
28.11/9.17	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.17	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.17	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.17	   A^2 -> H(e, U1(b, b))
28.11/9.17	   A^2 -> H(e, f(c))
28.11/9.17	   A^2 -> H(e, f(d))
28.11/9.17	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.17	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.17	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.17	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.17	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.17	   A^2 -> H(U1(e, e), f(e))
28.11/9.17	   A^2 -> H(U1(e, e), f(k))
28.11/9.17	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.17	   A^2 -> H(f(e), U1(e, b))
28.11/9.17	   A^2 -> H(f(e), U1(k, b))
28.11/9.17	   A^2 -> H(f(e), U1(c, d))
28.11/9.17	   A^2 -> H(f(e), U1(d, c))
28.11/9.17	   A^2 -> H(f(e), U1(b, e))
28.11/9.17	   A^2 -> H(f(e), U1(b, k))
28.11/9.17	   A^2 -> H(f(e), U1(e, c))
28.11/9.17	   A^2 -> H(f(e), U1(k, c))
28.11/9.17	   A^2 -> H(f(e), U1(c, e))
28.11/9.17	   A^2 -> H(f(e), U1(c, k))
28.11/9.17	   A^2 -> H(f(e), U1(k, k))
28.11/9.17	   A^2 -> H(f(e), U1(k, d))
28.11/9.17	   A^2 -> H(f(e), U1(d, k))
28.11/9.17	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.17	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.17	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.17	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.17	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.17	   A^2 -> H(U1(k, k), f(e))
28.11/9.17	   A^2 -> H(U1(k, k), f(k))
28.11/9.17	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.17	   A^2 -> H(f(k), U1(e, b))
28.11/9.17	   A^2 -> H(f(k), U1(k, b))
28.11/9.17	   A^2 -> H(f(k), U1(c, d))
28.11/9.17	   A^2 -> H(f(k), U1(d, c))
28.11/9.17	   A^2 -> H(f(k), U1(b, e))
28.11/9.17	   A^2 -> H(f(k), U1(b, k))
28.11/9.17	   A^2 -> H(f(k), U1(e, c))
28.11/9.17	   A^2 -> H(f(k), U1(k, c))
28.11/9.17	   A^2 -> H(f(k), U1(c, e))
28.11/9.17	   A^2 -> H(f(k), U1(c, k))
28.11/9.17	   A^2 -> H(f(k), U1(e, e))
28.11/9.17	   A^2 -> H(f(k), U1(k, d))
28.11/9.17	   A^2 -> H(f(k), U1(d, k))
28.11/9.17	   A^2 -> H(f(c), b)
28.11/9.17	   A^2 -> H(f(c), U1(e, d))
28.11/9.17	   A^2 -> H(f(c), U1(d, e))
28.11/9.17	   A^2 -> H(f(k), U1(k, k))
28.11/9.17	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.17	   A^2 -> H(U1(k, k), f(c))
28.11/9.17	   A^2 -> H(U1(k, k), f(d))
28.11/9.17	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.17	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.17	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.17	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.17	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.17	   A^2 -> H(U1(k, d), f(e))
28.11/9.17	   A^2 -> H(U1(k, d), f(k))
28.11/9.17	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.17	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.17	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.17	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.17	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.17	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.17	   A^2 -> H(U1(d, k), f(e))
28.11/9.17	   A^2 -> H(U1(d, k), f(k))
28.11/9.17	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.17	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.17	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.17	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.17	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.17	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.17	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.17	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.17	   A^2 -> H(f(d), b)
28.11/9.17	   A^2 -> H(f(d), U1(e, d))
28.11/9.17	   A^2 -> H(f(d), U1(d, e))
28.11/9.17	   A^2 -> H(f(d), c)
28.11/9.17	   A^2 -> H(f(d), U1(e, k))
28.11/9.17	   A^2 -> H(f(d), U1(k, e))
28.11/9.17	   A^2 -> H(f(d), e)
28.11/9.17	   A^2 -> H(f(a), d)
28.11/9.17	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.17	   A^2 -> H(f(c), c)
28.11/9.17	   A^2 -> H(f(c), U1(e, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.17	   A^2 -> H(f(c), U1(k, e))
28.11/9.17	   A^2 -> H(f(c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.17	   A^2 -> H(f(a), k)
28.11/9.17	   A^2 -> H(f(e), U1(e, e))
28.11/9.17	   A^2 -> H(f(c), e)
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.17	   A^2 -> H(f(d), U1(k, k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.17	   A^2 -> H(d, U1(b, b))
28.11/9.17	   A^2 -> H(d, f(c))
28.11/9.17	   A^2 -> H(d, f(d))
28.11/9.17	   A^2 -> H(a, U1(c, b))
28.11/9.17	   A^2 -> H(a, U1(d, b))
28.11/9.17	   A^2 -> H(a, U1(b, c))
28.11/9.17	   A^2 -> H(a, U1(b, d))
28.11/9.17	   A^2 -> H(a, U1(c, c))
28.11/9.17	   A^2 -> H(a, f(e))
28.11/9.17	   A^2 -> H(a, f(k))
28.11/9.17	   A^2 -> H(a, U1(d, d))
28.11/9.17	   A^2 -> H(U1(e, d), U1(c, b))
28.11/9.17	   A^2 -> H(U1(e, d), U1(d, b))
28.11/9.17	   A^2 -> H(U1(e, d), U1(b, c))
28.11/9.17	   A^2 -> H(U1(e, d), U1(b, d))
28.11/9.17	   A^2 -> H(U1(e, d), U1(c, c))
28.11/9.17	   A^2 -> H(U1(e, d), f(e))
28.11/9.17	   A^2 -> H(U1(e, d), f(k))
28.11/9.17	   A^2 -> H(U1(e, d), U1(d, d))
28.11/9.17	   A^2 -> H(U1(e, a), U1(e, b))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, b))
28.11/9.17	   A^2 -> H(U1(e, a), U1(c, d))
28.11/9.17	   A^2 -> H(U1(e, a), U1(d, c))
28.11/9.17	   A^2 -> H(U1(e, a), U1(b, e))
28.11/9.17	   A^2 -> H(U1(e, a), U1(b, k))
28.11/9.17	   A^2 -> H(U1(e, a), U1(e, c))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, c))
28.11/9.17	   A^2 -> H(U1(e, a), U1(c, e))
28.11/9.17	   A^2 -> H(U1(e, a), U1(c, k))
28.11/9.17	   A^2 -> H(U1(e, a), U1(e, e))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(e, a), U1(k, d))
28.11/9.17	   A^2 -> H(U1(e, a), U1(d, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(e, b))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, b))
28.11/9.17	   A^2 -> H(U1(k, a), U1(c, d))
28.11/9.17	   A^2 -> H(U1(k, a), U1(d, c))
28.11/9.17	   A^2 -> H(U1(k, a), U1(b, e))
28.11/9.17	   A^2 -> H(U1(k, a), U1(b, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(e, c))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, c))
28.11/9.17	   A^2 -> H(U1(k, a), U1(c, e))
28.11/9.17	   A^2 -> H(U1(k, a), U1(c, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(e, e))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(k, a), U1(k, d))
28.11/9.17	   A^2 -> H(U1(k, a), U1(d, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(e, b))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, b))
28.11/9.17	   A^2 -> H(U1(c, d), U1(c, d))
28.11/9.17	   A^2 -> H(U1(c, d), U1(d, c))
28.11/9.17	   A^2 -> H(U1(c, d), U1(b, e))
28.11/9.17	   A^2 -> H(U1(c, d), U1(b, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(e, c))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, c))
28.11/9.17	   A^2 -> H(U1(c, d), U1(c, e))
28.11/9.17	   A^2 -> H(U1(c, d), U1(c, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(e, e))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, k))
28.11/9.17	   A^2 -> H(U1(c, d), U1(k, d))
28.11/9.17	   A^2 -> H(U1(c, d), U1(d, k))
28.11/9.17	   A^2 -> H(U1(c, a), b)
28.11/9.17	   A^2 -> H(U1(c, a), U1(e, d))
28.11/9.17	   A^2 -> H(U1(c, a), U1(d, e))
28.11/9.17	   A^2 -> H(U1(c, a), c)
28.11/9.17	   A^2 -> H(U1(c, a), U1(e, k))
28.11/9.17	   A^2 -> H(U1(c, a), U1(k, e))
28.11/9.17	   A^2 -> H(U1(c, a), e)
28.11/9.17	   A^2 -> H(U1(c, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(d, e), U1(c, b))
28.11/9.17	   A^2 -> H(U1(d, e), U1(d, b))
28.11/9.17	   A^2 -> H(U1(d, e), U1(b, c))
28.11/9.17	   A^2 -> H(U1(d, e), U1(b, d))
28.11/9.17	   A^2 -> H(U1(d, e), U1(c, c))
28.11/9.17	   A^2 -> H(U1(d, e), f(e))
28.11/9.17	   A^2 -> H(U1(d, e), f(k))
28.11/9.17	   A^2 -> H(U1(d, e), U1(d, d))
28.11/9.17	   A^2 -> H(U1(d, c), U1(e, b))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, b))
28.11/9.17	   A^2 -> H(U1(d, c), U1(c, d))
28.11/9.17	   A^2 -> H(U1(d, c), U1(d, c))
28.11/9.17	   A^2 -> H(U1(d, c), U1(b, e))
28.11/9.17	   A^2 -> H(U1(d, c), U1(b, k))
28.11/9.17	   A^2 -> H(U1(d, c), U1(e, c))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, c))
28.11/9.17	   A^2 -> H(U1(d, c), U1(c, e))
28.11/9.17	   A^2 -> H(U1(d, c), U1(c, k))
28.11/9.17	   A^2 -> H(U1(d, c), U1(e, e))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(d, c), U1(k, d))
28.11/9.17	   A^2 -> H(U1(d, c), U1(d, k))
28.11/9.17	   A^2 -> H(U1(d, a), b)
28.11/9.17	   A^2 -> H(U1(d, a), U1(e, d))
28.11/9.17	   A^2 -> H(U1(d, a), U1(d, e))
28.11/9.17	   A^2 -> H(U1(d, a), c)
28.11/9.17	   A^2 -> H(U1(d, a), U1(e, k))
28.11/9.17	   A^2 -> H(U1(d, a), U1(k, e))
28.11/9.17	   A^2 -> H(U1(d, a), e)
28.11/9.17	   A^2 -> H(U1(d, a), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(e, b))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, b))
28.11/9.17	   A^2 -> H(U1(a, e), U1(c, d))
28.11/9.17	   A^2 -> H(U1(a, e), U1(d, c))
28.11/9.17	   A^2 -> H(U1(a, e), U1(b, e))
28.11/9.17	   A^2 -> H(U1(a, e), U1(b, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(e, c))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, c))
28.11/9.17	   A^2 -> H(U1(a, e), U1(c, e))
28.11/9.17	   A^2 -> H(U1(a, e), U1(c, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(e, e))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, e), U1(k, d))
28.11/9.17	   A^2 -> H(U1(a, e), U1(d, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(e, b))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, b))
28.11/9.17	   A^2 -> H(U1(a, k), U1(c, d))
28.11/9.17	   A^2 -> H(U1(a, k), U1(d, c))
28.11/9.17	   A^2 -> H(U1(a, k), U1(b, e))
28.11/9.17	   A^2 -> H(U1(a, k), U1(b, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(e, c))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, c))
28.11/9.17	   A^2 -> H(U1(a, k), U1(c, e))
28.11/9.17	   A^2 -> H(U1(a, k), U1(c, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(e, e))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, k), U1(k, d))
28.11/9.17	   A^2 -> H(U1(a, k), U1(d, k))
28.11/9.17	   A^2 -> H(U1(a, c), b)
28.11/9.17	   A^2 -> H(U1(a, c), U1(e, d))
28.11/9.17	   A^2 -> H(U1(a, c), U1(d, e))
28.11/9.17	   A^2 -> H(U1(a, c), c)
28.11/9.17	   A^2 -> H(U1(a, c), U1(e, k))
28.11/9.17	   A^2 -> H(U1(a, c), U1(k, e))
28.11/9.17	   A^2 -> H(U1(a, c), e)
28.11/9.17	   A^2 -> H(U1(a, c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, d), b)
28.11/9.17	   A^2 -> H(U1(a, d), U1(e, d))
28.11/9.17	   A^2 -> H(U1(a, d), U1(d, e))
28.11/9.17	   A^2 -> H(U1(a, d), c)
28.11/9.17	   A^2 -> H(U1(a, d), U1(e, k))
28.11/9.17	   A^2 -> H(U1(a, d), U1(k, e))
28.11/9.17	   A^2 -> H(U1(a, d), e)
28.11/9.17	   A^2 -> H(U1(a, d), U1(k, k))
28.11/9.17	   A^2 -> H(U1(a, a), d)
28.11/9.17	   A^2 -> H(U1(a, a), k)
28.11/9.17	
28.11/9.17	The TRS R consists of the following rules:
28.11/9.17	
28.11/9.17	   f(x) -> U1(x, x)
28.11/9.17	   U1(e, x) -> x
28.11/9.17	   a -> c
28.11/9.17	   a -> d
28.11/9.17	   b -> c
28.11/9.17	   b -> d
28.11/9.17	   d -> k
28.11/9.17	   c -> e
28.11/9.17	   c -> k
28.11/9.17	
28.11/9.17	Q is empty.
28.11/9.17	We have to consider all minimal (P,Q,R)-chains.
28.11/9.17	----------------------------------------
28.11/9.17	
28.11/9.17	(781) TransformationProof (EQUIVALENT)
28.11/9.17	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), e) at position [] we obtained the following new rules [LPAR04]:
28.11/9.17	
28.11/9.17	   (A^2 -> H(U1(c, a), e),A^2 -> H(U1(c, a), e))
28.11/9.17	   (A^2 -> H(U1(d, a), e),A^2 -> H(U1(d, a), e))
28.11/9.17	   (A^2 -> H(U1(a, c), e),A^2 -> H(U1(a, c), e))
28.11/9.17	   (A^2 -> H(U1(a, d), e),A^2 -> H(U1(a, d), e))
28.11/9.17	
28.11/9.17	
28.11/9.17	----------------------------------------
28.11/9.17	
28.11/9.17	(782)
28.11/9.17	Obligation:
28.11/9.17	Q DP problem:
28.11/9.17	The TRS P consists of the following rules:
28.11/9.17	
28.11/9.17	   H(x, x) -> G(x, x, f(k))
28.11/9.17	   G(d, x, x) -> A^2
28.11/9.17	   A^2 -> H(f(c), f(c))
28.11/9.17	   A^2 -> H(f(d), f(d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, c))
28.11/9.17	   A^2 -> H(f(e), f(e))
28.11/9.17	   A^2 -> H(f(k), f(k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(d, d))
28.11/9.17	   A^2 -> H(U1(a, a), U1(k, k))
28.11/9.17	   A^2 -> H(k, f(b))
28.11/9.17	   A^2 -> H(c, U1(b, b))
28.11/9.17	   A^2 -> H(c, f(c))
28.11/9.17	   A^2 -> H(c, f(d))
28.11/9.17	   A^2 -> H(U1(e, k), U1(b, b))
28.11/9.17	   A^2 -> H(U1(e, k), f(c))
28.11/9.17	   A^2 -> H(U1(e, k), f(d))
28.11/9.17	   A^2 -> H(U1(e, c), U1(c, b))
28.11/9.17	   A^2 -> H(U1(e, c), U1(d, b))
28.11/9.17	   A^2 -> H(U1(e, c), U1(b, c))
28.11/9.17	   A^2 -> H(U1(e, c), U1(b, d))
28.11/9.17	   A^2 -> H(U1(e, c), U1(c, c))
28.11/9.17	   A^2 -> H(U1(e, c), f(e))
28.11/9.17	   A^2 -> H(U1(e, c), f(k))
28.11/9.17	   A^2 -> H(U1(e, c), U1(d, d))
28.11/9.17	   A^2 -> H(U1(k, e), U1(b, b))
28.11/9.17	   A^2 -> H(U1(k, e), f(c))
28.11/9.17	   A^2 -> H(U1(k, e), f(d))
28.11/9.17	   A^2 -> H(U1(k, c), U1(c, b))
28.11/9.17	   A^2 -> H(U1(k, c), U1(d, b))
28.11/9.17	   A^2 -> H(U1(k, c), U1(b, c))
28.11/9.17	   A^2 -> H(U1(k, c), U1(b, d))
28.11/9.17	   A^2 -> H(U1(k, c), U1(c, c))
28.11/9.17	   A^2 -> H(U1(k, c), f(e))
28.11/9.17	   A^2 -> H(U1(k, c), f(k))
28.11/9.17	   A^2 -> H(U1(k, c), U1(d, d))
28.11/9.17	   A^2 -> H(U1(c, e), U1(c, b))
28.11/9.17	   A^2 -> H(U1(c, e), U1(d, b))
28.11/9.17	   A^2 -> H(U1(c, e), U1(b, c))
28.11/9.17	   A^2 -> H(U1(c, e), U1(b, d))
28.11/9.17	   A^2 -> H(U1(c, e), U1(c, c))
28.11/9.17	   A^2 -> H(U1(c, e), f(e))
28.11/9.17	   A^2 -> H(U1(c, e), f(k))
28.11/9.17	   A^2 -> H(U1(c, e), U1(d, d))
28.11/9.17	   A^2 -> H(U1(c, k), U1(c, b))
28.11/9.17	   A^2 -> H(U1(c, k), U1(d, b))
28.11/9.17	   A^2 -> H(U1(c, k), U1(b, c))
28.11/9.17	   A^2 -> H(U1(c, k), U1(b, d))
28.11/9.17	   A^2 -> H(U1(c, k), U1(c, c))
28.11/9.17	   A^2 -> H(U1(c, k), f(e))
28.11/9.17	   A^2 -> H(U1(c, k), f(k))
28.11/9.17	   A^2 -> H(U1(c, k), U1(d, d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(e, b))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, b))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(d, c))
28.11/9.17	   A^2 -> H(U1(c, c), U1(b, e))
28.11/9.17	   A^2 -> H(U1(c, c), U1(b, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(e, e))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, d))
28.11/9.17	   A^2 -> H(U1(c, c), U1(d, k))
28.11/9.17	   A^2 -> H(e, U1(b, b))
28.11/9.17	   A^2 -> H(e, f(c))
28.11/9.17	   A^2 -> H(e, f(d))
28.11/9.17	   A^2 -> H(U1(e, e), U1(c, b))
28.11/9.17	   A^2 -> H(U1(e, e), U1(d, b))
28.11/9.17	   A^2 -> H(U1(e, e), U1(b, c))
28.11/9.17	   A^2 -> H(U1(e, e), U1(b, d))
28.11/9.17	   A^2 -> H(U1(e, e), U1(c, c))
28.11/9.17	   A^2 -> H(U1(e, e), f(e))
28.11/9.17	   A^2 -> H(U1(e, e), f(k))
28.11/9.17	   A^2 -> H(U1(e, e), U1(d, d))
28.11/9.17	   A^2 -> H(f(e), U1(e, b))
28.11/9.17	   A^2 -> H(f(e), U1(k, b))
28.11/9.17	   A^2 -> H(f(e), U1(c, d))
28.11/9.17	   A^2 -> H(f(e), U1(d, c))
28.11/9.17	   A^2 -> H(f(e), U1(b, e))
28.11/9.17	   A^2 -> H(f(e), U1(b, k))
28.11/9.17	   A^2 -> H(f(e), U1(e, c))
28.11/9.17	   A^2 -> H(f(e), U1(k, c))
28.11/9.17	   A^2 -> H(f(e), U1(c, e))
28.11/9.17	   A^2 -> H(f(e), U1(c, k))
28.11/9.17	   A^2 -> H(f(e), U1(k, k))
28.11/9.17	   A^2 -> H(f(e), U1(k, d))
28.11/9.17	   A^2 -> H(f(e), U1(d, k))
28.11/9.17	   A^2 -> H(U1(k, k), U1(c, b))
28.11/9.17	   A^2 -> H(U1(k, k), U1(d, b))
28.11/9.17	   A^2 -> H(U1(k, k), U1(b, c))
28.11/9.17	   A^2 -> H(U1(k, k), U1(b, d))
28.11/9.17	   A^2 -> H(U1(k, k), U1(c, c))
28.11/9.17	   A^2 -> H(U1(k, k), f(e))
28.11/9.17	   A^2 -> H(U1(k, k), f(k))
28.11/9.17	   A^2 -> H(U1(k, k), U1(d, d))
28.11/9.17	   A^2 -> H(f(k), U1(e, b))
28.11/9.17	   A^2 -> H(f(k), U1(k, b))
28.11/9.17	   A^2 -> H(f(k), U1(c, d))
28.11/9.17	   A^2 -> H(f(k), U1(d, c))
28.11/9.17	   A^2 -> H(f(k), U1(b, e))
28.11/9.17	   A^2 -> H(f(k), U1(b, k))
28.11/9.17	   A^2 -> H(f(k), U1(e, c))
28.11/9.17	   A^2 -> H(f(k), U1(k, c))
28.11/9.17	   A^2 -> H(f(k), U1(c, e))
28.11/9.17	   A^2 -> H(f(k), U1(c, k))
28.11/9.17	   A^2 -> H(f(k), U1(e, e))
28.11/9.17	   A^2 -> H(f(k), U1(k, d))
28.11/9.17	   A^2 -> H(f(k), U1(d, k))
28.11/9.17	   A^2 -> H(f(c), b)
28.11/9.17	   A^2 -> H(f(c), U1(e, d))
28.11/9.17	   A^2 -> H(f(c), U1(d, e))
28.11/9.17	   A^2 -> H(f(k), U1(k, k))
28.11/9.17	   A^2 -> H(U1(k, k), U1(b, b))
28.11/9.17	   A^2 -> H(U1(k, k), f(c))
28.11/9.17	   A^2 -> H(U1(k, k), f(d))
28.11/9.17	   A^2 -> H(U1(k, d), U1(c, b))
28.11/9.17	   A^2 -> H(U1(k, d), U1(d, b))
28.11/9.17	   A^2 -> H(U1(k, d), U1(b, c))
28.11/9.17	   A^2 -> H(U1(k, d), U1(b, d))
28.11/9.17	   A^2 -> H(U1(k, d), U1(c, c))
28.11/9.17	   A^2 -> H(U1(k, d), f(e))
28.11/9.17	   A^2 -> H(U1(k, d), f(k))
28.11/9.17	   A^2 -> H(U1(k, d), U1(d, d))
28.11/9.17	   A^2 -> H(U1(d, k), U1(c, b))
28.11/9.17	   A^2 -> H(U1(d, k), U1(d, b))
28.11/9.17	   A^2 -> H(U1(d, k), U1(b, c))
28.11/9.17	   A^2 -> H(U1(d, k), U1(b, d))
28.11/9.17	   A^2 -> H(U1(d, k), U1(c, c))
28.11/9.17	   A^2 -> H(U1(d, k), f(e))
28.11/9.17	   A^2 -> H(U1(d, k), f(k))
28.11/9.17	   A^2 -> H(U1(d, k), U1(d, d))
28.11/9.17	   A^2 -> H(U1(d, d), U1(e, b))
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, b))
28.11/9.17	   A^2 -> H(U1(d, d), U1(c, d))
28.11/9.17	   A^2 -> H(U1(d, d), U1(d, c))
28.11/9.17	   A^2 -> H(U1(d, d), U1(b, e))
28.11/9.17	   A^2 -> H(U1(d, d), U1(b, k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(e, c))
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, c))
28.11/9.17	   A^2 -> H(U1(d, d), U1(c, e))
28.11/9.17	   A^2 -> H(U1(d, d), U1(c, k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(e, e))
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, k))
28.11/9.17	   A^2 -> H(f(d), b)
28.11/9.17	   A^2 -> H(f(d), U1(e, d))
28.11/9.17	   A^2 -> H(f(d), U1(d, e))
28.11/9.17	   A^2 -> H(f(d), c)
28.11/9.17	   A^2 -> H(f(d), U1(e, k))
28.11/9.17	   A^2 -> H(f(d), U1(k, e))
28.11/9.17	   A^2 -> H(f(d), e)
28.11/9.17	   A^2 -> H(f(a), d)
28.11/9.17	   A^2 -> H(U1(c, c), U1(e, c))
28.11/9.17	   A^2 -> H(f(c), c)
28.11/9.17	   A^2 -> H(f(c), U1(e, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(k, c))
28.11/9.17	   A^2 -> H(f(c), U1(k, e))
28.11/9.17	   A^2 -> H(f(c), U1(k, k))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, e))
28.11/9.17	   A^2 -> H(U1(c, c), U1(c, k))
28.11/9.17	   A^2 -> H(f(a), k)
28.11/9.17	   A^2 -> H(f(e), U1(e, e))
28.11/9.17	   A^2 -> H(f(c), e)
28.11/9.17	   A^2 -> H(U1(d, d), U1(k, d))
28.11/9.17	   A^2 -> H(f(d), U1(k, k))
28.11/9.17	   A^2 -> H(U1(d, d), U1(d, k))
28.11/9.17	   A^2 -> H(d, U1(b, b))
28.11/9.17	   A^2 -> H(d, f(c))
28.11/9.17	   A^2 -> H(d, f(d))
28.11/9.17	   A^2 -> H(a, U1(c, b))
28.11/9.17	   A^2 -> H(a, U1(d, b))
28.11/9.17	   A^2 -> H(a, U1(b, c))
28.36/9.18	   A^2 -> H(a, U1(b, d))
28.36/9.18	   A^2 -> H(a, U1(c, c))
28.36/9.18	   A^2 -> H(a, f(e))
28.36/9.18	   A^2 -> H(a, f(k))
28.36/9.18	   A^2 -> H(a, U1(d, d))
28.36/9.18	   A^2 -> H(U1(e, d), U1(c, b))
28.36/9.18	   A^2 -> H(U1(e, d), U1(d, b))
28.36/9.18	   A^2 -> H(U1(e, d), U1(b, c))
28.36/9.18	   A^2 -> H(U1(e, d), U1(b, d))
28.36/9.18	   A^2 -> H(U1(e, d), U1(c, c))
28.36/9.18	   A^2 -> H(U1(e, d), f(e))
28.36/9.18	   A^2 -> H(U1(e, d), f(k))
28.36/9.18	   A^2 -> H(U1(e, d), U1(d, d))
28.36/9.18	   A^2 -> H(U1(e, a), U1(e, b))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, b))
28.36/9.18	   A^2 -> H(U1(e, a), U1(c, d))
28.36/9.18	   A^2 -> H(U1(e, a), U1(d, c))
28.36/9.18	   A^2 -> H(U1(e, a), U1(b, e))
28.36/9.18	   A^2 -> H(U1(e, a), U1(b, k))
28.36/9.18	   A^2 -> H(U1(e, a), U1(e, c))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, c))
28.36/9.18	   A^2 -> H(U1(e, a), U1(c, e))
28.36/9.18	   A^2 -> H(U1(e, a), U1(c, k))
28.36/9.18	   A^2 -> H(U1(e, a), U1(e, e))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, d))
28.36/9.18	   A^2 -> H(U1(e, a), U1(d, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(e, b))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, b))
28.36/9.18	   A^2 -> H(U1(k, a), U1(c, d))
28.36/9.18	   A^2 -> H(U1(k, a), U1(d, c))
28.36/9.18	   A^2 -> H(U1(k, a), U1(b, e))
28.36/9.18	   A^2 -> H(U1(k, a), U1(b, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(e, c))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, c))
28.36/9.18	   A^2 -> H(U1(k, a), U1(c, e))
28.36/9.18	   A^2 -> H(U1(k, a), U1(c, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(e, e))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, d))
28.36/9.18	   A^2 -> H(U1(k, a), U1(d, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(e, b))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, b))
28.36/9.18	   A^2 -> H(U1(c, d), U1(c, d))
28.36/9.18	   A^2 -> H(U1(c, d), U1(d, c))
28.36/9.18	   A^2 -> H(U1(c, d), U1(b, e))
28.36/9.18	   A^2 -> H(U1(c, d), U1(b, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(e, c))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, c))
28.36/9.18	   A^2 -> H(U1(c, d), U1(c, e))
28.36/9.18	   A^2 -> H(U1(c, d), U1(c, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(e, e))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, d))
28.36/9.18	   A^2 -> H(U1(c, d), U1(d, k))
28.36/9.18	   A^2 -> H(U1(c, a), b)
28.36/9.18	   A^2 -> H(U1(c, a), U1(e, d))
28.36/9.18	   A^2 -> H(U1(c, a), U1(d, e))
28.36/9.18	   A^2 -> H(U1(c, a), c)
28.36/9.18	   A^2 -> H(U1(c, a), U1(e, k))
28.36/9.18	   A^2 -> H(U1(c, a), U1(k, e))
28.36/9.18	   A^2 -> H(U1(c, a), e)
28.36/9.18	   A^2 -> H(U1(c, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(d, e), U1(c, b))
28.36/9.18	   A^2 -> H(U1(d, e), U1(d, b))
28.36/9.18	   A^2 -> H(U1(d, e), U1(b, c))
28.36/9.18	   A^2 -> H(U1(d, e), U1(b, d))
28.36/9.18	   A^2 -> H(U1(d, e), U1(c, c))
28.36/9.18	   A^2 -> H(U1(d, e), f(e))
28.36/9.18	   A^2 -> H(U1(d, e), f(k))
28.36/9.18	   A^2 -> H(U1(d, e), U1(d, d))
28.36/9.18	   A^2 -> H(U1(d, c), U1(e, b))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, b))
28.36/9.18	   A^2 -> H(U1(d, c), U1(c, d))
28.36/9.18	   A^2 -> H(U1(d, c), U1(d, c))
28.36/9.18	   A^2 -> H(U1(d, c), U1(b, e))
28.36/9.18	   A^2 -> H(U1(d, c), U1(b, k))
28.36/9.18	   A^2 -> H(U1(d, c), U1(e, c))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, c))
28.36/9.18	   A^2 -> H(U1(d, c), U1(c, e))
28.36/9.18	   A^2 -> H(U1(d, c), U1(c, k))
28.36/9.18	   A^2 -> H(U1(d, c), U1(e, e))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, d))
28.36/9.18	   A^2 -> H(U1(d, c), U1(d, k))
28.36/9.18	   A^2 -> H(U1(d, a), b)
28.36/9.18	   A^2 -> H(U1(d, a), U1(e, d))
28.36/9.18	   A^2 -> H(U1(d, a), U1(d, e))
28.36/9.18	   A^2 -> H(U1(d, a), c)
28.36/9.18	   A^2 -> H(U1(d, a), U1(e, k))
28.36/9.18	   A^2 -> H(U1(d, a), U1(k, e))
28.36/9.18	   A^2 -> H(U1(d, a), e)
28.36/9.18	   A^2 -> H(U1(d, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(e, b))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, b))
28.36/9.18	   A^2 -> H(U1(a, e), U1(c, d))
28.36/9.18	   A^2 -> H(U1(a, e), U1(d, c))
28.36/9.18	   A^2 -> H(U1(a, e), U1(b, e))
28.36/9.18	   A^2 -> H(U1(a, e), U1(b, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(e, c))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, c))
28.36/9.18	   A^2 -> H(U1(a, e), U1(c, e))
28.36/9.18	   A^2 -> H(U1(a, e), U1(c, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(e, e))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, d))
28.36/9.18	   A^2 -> H(U1(a, e), U1(d, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(e, b))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, b))
28.36/9.18	   A^2 -> H(U1(a, k), U1(c, d))
28.36/9.18	   A^2 -> H(U1(a, k), U1(d, c))
28.36/9.18	   A^2 -> H(U1(a, k), U1(b, e))
28.36/9.18	   A^2 -> H(U1(a, k), U1(b, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(e, c))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, c))
28.36/9.18	   A^2 -> H(U1(a, k), U1(c, e))
28.36/9.18	   A^2 -> H(U1(a, k), U1(c, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(e, e))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, d))
28.36/9.18	   A^2 -> H(U1(a, k), U1(d, k))
28.36/9.18	   A^2 -> H(U1(a, c), b)
28.36/9.18	   A^2 -> H(U1(a, c), U1(e, d))
28.36/9.18	   A^2 -> H(U1(a, c), U1(d, e))
28.36/9.18	   A^2 -> H(U1(a, c), c)
28.36/9.18	   A^2 -> H(U1(a, c), U1(e, k))
28.36/9.18	   A^2 -> H(U1(a, c), U1(k, e))
28.36/9.18	   A^2 -> H(U1(a, c), e)
28.36/9.18	   A^2 -> H(U1(a, c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, d), b)
28.36/9.18	   A^2 -> H(U1(a, d), U1(e, d))
28.36/9.18	   A^2 -> H(U1(a, d), U1(d, e))
28.36/9.18	   A^2 -> H(U1(a, d), c)
28.36/9.18	   A^2 -> H(U1(a, d), U1(e, k))
28.36/9.18	   A^2 -> H(U1(a, d), U1(k, e))
28.36/9.18	   A^2 -> H(U1(a, d), e)
28.36/9.18	   A^2 -> H(U1(a, d), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, a), d)
28.36/9.18	   A^2 -> H(U1(a, a), k)
28.36/9.18	
28.36/9.18	The TRS R consists of the following rules:
28.36/9.18	
28.36/9.18	   f(x) -> U1(x, x)
28.36/9.18	   U1(e, x) -> x
28.36/9.18	   a -> c
28.36/9.18	   a -> d
28.36/9.18	   b -> c
28.36/9.18	   b -> d
28.36/9.18	   d -> k
28.36/9.18	   c -> e
28.36/9.18	   c -> k
28.36/9.18	
28.36/9.18	Q is empty.
28.36/9.18	We have to consider all minimal (P,Q,R)-chains.
28.36/9.18	----------------------------------------
28.36/9.18	
28.36/9.18	(783) TransformationProof (EQUIVALENT)
28.36/9.18	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.36/9.18	
28.36/9.18	   (A^2 -> H(U1(c, a), U1(k, k)),A^2 -> H(U1(c, a), U1(k, k)))
28.36/9.18	   (A^2 -> H(U1(d, a), U1(k, k)),A^2 -> H(U1(d, a), U1(k, k)))
28.36/9.18	   (A^2 -> H(U1(a, c), U1(k, k)),A^2 -> H(U1(a, c), U1(k, k)))
28.36/9.18	   (A^2 -> H(U1(a, d), U1(k, k)),A^2 -> H(U1(a, d), U1(k, k)))
28.36/9.18	
28.36/9.18	
28.36/9.18	----------------------------------------
28.36/9.18	
28.36/9.18	(784)
28.36/9.18	Obligation:
28.36/9.18	Q DP problem:
28.36/9.18	The TRS P consists of the following rules:
28.36/9.18	
28.36/9.18	   H(x, x) -> G(x, x, f(k))
28.36/9.18	   G(d, x, x) -> A^2
28.36/9.18	   A^2 -> H(f(c), f(c))
28.36/9.18	   A^2 -> H(f(d), f(d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, c))
28.36/9.18	   A^2 -> H(f(e), f(e))
28.36/9.18	   A^2 -> H(f(k), f(k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(d, d))
28.36/9.18	   A^2 -> H(k, f(b))
28.36/9.18	   A^2 -> H(c, U1(b, b))
28.36/9.18	   A^2 -> H(c, f(c))
28.36/9.18	   A^2 -> H(c, f(d))
28.36/9.18	   A^2 -> H(U1(e, k), U1(b, b))
28.36/9.18	   A^2 -> H(U1(e, k), f(c))
28.36/9.18	   A^2 -> H(U1(e, k), f(d))
28.36/9.18	   A^2 -> H(U1(e, c), U1(c, b))
28.36/9.18	   A^2 -> H(U1(e, c), U1(d, b))
28.36/9.18	   A^2 -> H(U1(e, c), U1(b, c))
28.36/9.18	   A^2 -> H(U1(e, c), U1(b, d))
28.36/9.18	   A^2 -> H(U1(e, c), U1(c, c))
28.36/9.18	   A^2 -> H(U1(e, c), f(e))
28.36/9.18	   A^2 -> H(U1(e, c), f(k))
28.36/9.18	   A^2 -> H(U1(e, c), U1(d, d))
28.36/9.18	   A^2 -> H(U1(k, e), U1(b, b))
28.36/9.18	   A^2 -> H(U1(k, e), f(c))
28.36/9.18	   A^2 -> H(U1(k, e), f(d))
28.36/9.18	   A^2 -> H(U1(k, c), U1(c, b))
28.36/9.18	   A^2 -> H(U1(k, c), U1(d, b))
28.36/9.18	   A^2 -> H(U1(k, c), U1(b, c))
28.36/9.18	   A^2 -> H(U1(k, c), U1(b, d))
28.36/9.18	   A^2 -> H(U1(k, c), U1(c, c))
28.36/9.18	   A^2 -> H(U1(k, c), f(e))
28.36/9.18	   A^2 -> H(U1(k, c), f(k))
28.36/9.18	   A^2 -> H(U1(k, c), U1(d, d))
28.36/9.18	   A^2 -> H(U1(c, e), U1(c, b))
28.36/9.18	   A^2 -> H(U1(c, e), U1(d, b))
28.36/9.18	   A^2 -> H(U1(c, e), U1(b, c))
28.36/9.18	   A^2 -> H(U1(c, e), U1(b, d))
28.36/9.18	   A^2 -> H(U1(c, e), U1(c, c))
28.36/9.18	   A^2 -> H(U1(c, e), f(e))
28.36/9.18	   A^2 -> H(U1(c, e), f(k))
28.36/9.18	   A^2 -> H(U1(c, e), U1(d, d))
28.36/9.18	   A^2 -> H(U1(c, k), U1(c, b))
28.36/9.18	   A^2 -> H(U1(c, k), U1(d, b))
28.36/9.18	   A^2 -> H(U1(c, k), U1(b, c))
28.36/9.18	   A^2 -> H(U1(c, k), U1(b, d))
28.36/9.18	   A^2 -> H(U1(c, k), U1(c, c))
28.36/9.18	   A^2 -> H(U1(c, k), f(e))
28.36/9.18	   A^2 -> H(U1(c, k), f(k))
28.36/9.18	   A^2 -> H(U1(c, k), U1(d, d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(e, b))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, b))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(d, c))
28.36/9.18	   A^2 -> H(U1(c, c), U1(b, e))
28.36/9.18	   A^2 -> H(U1(c, c), U1(b, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(e, e))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(d, k))
28.36/9.18	   A^2 -> H(e, U1(b, b))
28.36/9.18	   A^2 -> H(e, f(c))
28.36/9.18	   A^2 -> H(e, f(d))
28.36/9.18	   A^2 -> H(U1(e, e), U1(c, b))
28.36/9.18	   A^2 -> H(U1(e, e), U1(d, b))
28.36/9.18	   A^2 -> H(U1(e, e), U1(b, c))
28.36/9.18	   A^2 -> H(U1(e, e), U1(b, d))
28.36/9.18	   A^2 -> H(U1(e, e), U1(c, c))
28.36/9.18	   A^2 -> H(U1(e, e), f(e))
28.36/9.18	   A^2 -> H(U1(e, e), f(k))
28.36/9.18	   A^2 -> H(U1(e, e), U1(d, d))
28.36/9.18	   A^2 -> H(f(e), U1(e, b))
28.36/9.18	   A^2 -> H(f(e), U1(k, b))
28.36/9.18	   A^2 -> H(f(e), U1(c, d))
28.36/9.18	   A^2 -> H(f(e), U1(d, c))
28.36/9.18	   A^2 -> H(f(e), U1(b, e))
28.36/9.18	   A^2 -> H(f(e), U1(b, k))
28.36/9.18	   A^2 -> H(f(e), U1(e, c))
28.36/9.18	   A^2 -> H(f(e), U1(k, c))
28.36/9.18	   A^2 -> H(f(e), U1(c, e))
28.36/9.18	   A^2 -> H(f(e), U1(c, k))
28.36/9.18	   A^2 -> H(f(e), U1(k, k))
28.36/9.18	   A^2 -> H(f(e), U1(k, d))
28.36/9.18	   A^2 -> H(f(e), U1(d, k))
28.36/9.18	   A^2 -> H(U1(k, k), U1(c, b))
28.36/9.18	   A^2 -> H(U1(k, k), U1(d, b))
28.36/9.18	   A^2 -> H(U1(k, k), U1(b, c))
28.36/9.18	   A^2 -> H(U1(k, k), U1(b, d))
28.36/9.18	   A^2 -> H(U1(k, k), U1(c, c))
28.36/9.18	   A^2 -> H(U1(k, k), f(e))
28.36/9.18	   A^2 -> H(U1(k, k), f(k))
28.36/9.18	   A^2 -> H(U1(k, k), U1(d, d))
28.36/9.18	   A^2 -> H(f(k), U1(e, b))
28.36/9.18	   A^2 -> H(f(k), U1(k, b))
28.36/9.18	   A^2 -> H(f(k), U1(c, d))
28.36/9.18	   A^2 -> H(f(k), U1(d, c))
28.36/9.18	   A^2 -> H(f(k), U1(b, e))
28.36/9.18	   A^2 -> H(f(k), U1(b, k))
28.36/9.18	   A^2 -> H(f(k), U1(e, c))
28.36/9.18	   A^2 -> H(f(k), U1(k, c))
28.36/9.18	   A^2 -> H(f(k), U1(c, e))
28.36/9.18	   A^2 -> H(f(k), U1(c, k))
28.36/9.18	   A^2 -> H(f(k), U1(e, e))
28.36/9.18	   A^2 -> H(f(k), U1(k, d))
28.36/9.18	   A^2 -> H(f(k), U1(d, k))
28.36/9.18	   A^2 -> H(f(c), b)
28.36/9.18	   A^2 -> H(f(c), U1(e, d))
28.36/9.18	   A^2 -> H(f(c), U1(d, e))
28.36/9.18	   A^2 -> H(f(k), U1(k, k))
28.36/9.18	   A^2 -> H(U1(k, k), U1(b, b))
28.36/9.18	   A^2 -> H(U1(k, k), f(c))
28.36/9.18	   A^2 -> H(U1(k, k), f(d))
28.36/9.18	   A^2 -> H(U1(k, d), U1(c, b))
28.36/9.18	   A^2 -> H(U1(k, d), U1(d, b))
28.36/9.18	   A^2 -> H(U1(k, d), U1(b, c))
28.36/9.18	   A^2 -> H(U1(k, d), U1(b, d))
28.36/9.18	   A^2 -> H(U1(k, d), U1(c, c))
28.36/9.18	   A^2 -> H(U1(k, d), f(e))
28.36/9.18	   A^2 -> H(U1(k, d), f(k))
28.36/9.18	   A^2 -> H(U1(k, d), U1(d, d))
28.36/9.18	   A^2 -> H(U1(d, k), U1(c, b))
28.36/9.18	   A^2 -> H(U1(d, k), U1(d, b))
28.36/9.18	   A^2 -> H(U1(d, k), U1(b, c))
28.36/9.18	   A^2 -> H(U1(d, k), U1(b, d))
28.36/9.18	   A^2 -> H(U1(d, k), U1(c, c))
28.36/9.18	   A^2 -> H(U1(d, k), f(e))
28.36/9.18	   A^2 -> H(U1(d, k), f(k))
28.36/9.18	   A^2 -> H(U1(d, k), U1(d, d))
28.36/9.18	   A^2 -> H(U1(d, d), U1(e, b))
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, b))
28.36/9.18	   A^2 -> H(U1(d, d), U1(c, d))
28.36/9.18	   A^2 -> H(U1(d, d), U1(d, c))
28.36/9.18	   A^2 -> H(U1(d, d), U1(b, e))
28.36/9.18	   A^2 -> H(U1(d, d), U1(b, k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(e, c))
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, c))
28.36/9.18	   A^2 -> H(U1(d, d), U1(c, e))
28.36/9.18	   A^2 -> H(U1(d, d), U1(c, k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(e, e))
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, k))
28.36/9.18	   A^2 -> H(f(d), b)
28.36/9.18	   A^2 -> H(f(d), U1(e, d))
28.36/9.18	   A^2 -> H(f(d), U1(d, e))
28.36/9.18	   A^2 -> H(f(d), c)
28.36/9.18	   A^2 -> H(f(d), U1(e, k))
28.36/9.18	   A^2 -> H(f(d), U1(k, e))
28.36/9.18	   A^2 -> H(f(d), e)
28.36/9.18	   A^2 -> H(f(a), d)
28.36/9.18	   A^2 -> H(U1(c, c), U1(e, c))
28.36/9.18	   A^2 -> H(f(c), c)
28.36/9.18	   A^2 -> H(f(c), U1(e, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, c))
28.36/9.18	   A^2 -> H(f(c), U1(k, e))
28.36/9.18	   A^2 -> H(f(c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, e))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, k))
28.36/9.18	   A^2 -> H(f(a), k)
28.36/9.18	   A^2 -> H(f(e), U1(e, e))
28.36/9.18	   A^2 -> H(f(c), e)
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, d))
28.36/9.18	   A^2 -> H(f(d), U1(k, k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(d, k))
28.36/9.18	   A^2 -> H(d, U1(b, b))
28.36/9.18	   A^2 -> H(d, f(c))
28.36/9.18	   A^2 -> H(d, f(d))
28.36/9.18	   A^2 -> H(a, U1(c, b))
28.36/9.18	   A^2 -> H(a, U1(d, b))
28.36/9.18	   A^2 -> H(a, U1(b, c))
28.36/9.18	   A^2 -> H(a, U1(b, d))
28.36/9.18	   A^2 -> H(a, U1(c, c))
28.36/9.18	   A^2 -> H(a, f(e))
28.36/9.18	   A^2 -> H(a, f(k))
28.36/9.18	   A^2 -> H(a, U1(d, d))
28.36/9.18	   A^2 -> H(U1(e, d), U1(c, b))
28.36/9.18	   A^2 -> H(U1(e, d), U1(d, b))
28.36/9.18	   A^2 -> H(U1(e, d), U1(b, c))
28.36/9.18	   A^2 -> H(U1(e, d), U1(b, d))
28.36/9.18	   A^2 -> H(U1(e, d), U1(c, c))
28.36/9.18	   A^2 -> H(U1(e, d), f(e))
28.36/9.18	   A^2 -> H(U1(e, d), f(k))
28.36/9.18	   A^2 -> H(U1(e, d), U1(d, d))
28.36/9.18	   A^2 -> H(U1(e, a), U1(e, b))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, b))
28.36/9.18	   A^2 -> H(U1(e, a), U1(c, d))
28.36/9.18	   A^2 -> H(U1(e, a), U1(d, c))
28.36/9.18	   A^2 -> H(U1(e, a), U1(b, e))
28.36/9.18	   A^2 -> H(U1(e, a), U1(b, k))
28.36/9.18	   A^2 -> H(U1(e, a), U1(e, c))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, c))
28.36/9.18	   A^2 -> H(U1(e, a), U1(c, e))
28.36/9.18	   A^2 -> H(U1(e, a), U1(c, k))
28.36/9.18	   A^2 -> H(U1(e, a), U1(e, e))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, d))
28.36/9.18	   A^2 -> H(U1(e, a), U1(d, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(e, b))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, b))
28.36/9.18	   A^2 -> H(U1(k, a), U1(c, d))
28.36/9.18	   A^2 -> H(U1(k, a), U1(d, c))
28.36/9.18	   A^2 -> H(U1(k, a), U1(b, e))
28.36/9.18	   A^2 -> H(U1(k, a), U1(b, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(e, c))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, c))
28.36/9.18	   A^2 -> H(U1(k, a), U1(c, e))
28.36/9.18	   A^2 -> H(U1(k, a), U1(c, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(e, e))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, d))
28.36/9.18	   A^2 -> H(U1(k, a), U1(d, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(e, b))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, b))
28.36/9.18	   A^2 -> H(U1(c, d), U1(c, d))
28.36/9.18	   A^2 -> H(U1(c, d), U1(d, c))
28.36/9.18	   A^2 -> H(U1(c, d), U1(b, e))
28.36/9.18	   A^2 -> H(U1(c, d), U1(b, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(e, c))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, c))
28.36/9.18	   A^2 -> H(U1(c, d), U1(c, e))
28.36/9.18	   A^2 -> H(U1(c, d), U1(c, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(e, e))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, d))
28.36/9.18	   A^2 -> H(U1(c, d), U1(d, k))
28.36/9.18	   A^2 -> H(U1(c, a), b)
28.36/9.18	   A^2 -> H(U1(c, a), U1(e, d))
28.36/9.18	   A^2 -> H(U1(c, a), U1(d, e))
28.36/9.18	   A^2 -> H(U1(c, a), c)
28.36/9.18	   A^2 -> H(U1(c, a), U1(e, k))
28.36/9.18	   A^2 -> H(U1(c, a), U1(k, e))
28.36/9.18	   A^2 -> H(U1(c, a), e)
28.36/9.18	   A^2 -> H(U1(c, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(d, e), U1(c, b))
28.36/9.18	   A^2 -> H(U1(d, e), U1(d, b))
28.36/9.18	   A^2 -> H(U1(d, e), U1(b, c))
28.36/9.18	   A^2 -> H(U1(d, e), U1(b, d))
28.36/9.18	   A^2 -> H(U1(d, e), U1(c, c))
28.36/9.18	   A^2 -> H(U1(d, e), f(e))
28.36/9.18	   A^2 -> H(U1(d, e), f(k))
28.36/9.18	   A^2 -> H(U1(d, e), U1(d, d))
28.36/9.18	   A^2 -> H(U1(d, c), U1(e, b))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, b))
28.36/9.18	   A^2 -> H(U1(d, c), U1(c, d))
28.36/9.18	   A^2 -> H(U1(d, c), U1(d, c))
28.36/9.18	   A^2 -> H(U1(d, c), U1(b, e))
28.36/9.18	   A^2 -> H(U1(d, c), U1(b, k))
28.36/9.18	   A^2 -> H(U1(d, c), U1(e, c))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, c))
28.36/9.18	   A^2 -> H(U1(d, c), U1(c, e))
28.36/9.18	   A^2 -> H(U1(d, c), U1(c, k))
28.36/9.18	   A^2 -> H(U1(d, c), U1(e, e))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, d))
28.36/9.18	   A^2 -> H(U1(d, c), U1(d, k))
28.36/9.18	   A^2 -> H(U1(d, a), b)
28.36/9.18	   A^2 -> H(U1(d, a), U1(e, d))
28.36/9.18	   A^2 -> H(U1(d, a), U1(d, e))
28.36/9.18	   A^2 -> H(U1(d, a), c)
28.36/9.18	   A^2 -> H(U1(d, a), U1(e, k))
28.36/9.18	   A^2 -> H(U1(d, a), U1(k, e))
28.36/9.18	   A^2 -> H(U1(d, a), e)
28.36/9.18	   A^2 -> H(U1(d, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(e, b))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, b))
28.36/9.18	   A^2 -> H(U1(a, e), U1(c, d))
28.36/9.18	   A^2 -> H(U1(a, e), U1(d, c))
28.36/9.18	   A^2 -> H(U1(a, e), U1(b, e))
28.36/9.18	   A^2 -> H(U1(a, e), U1(b, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(e, c))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, c))
28.36/9.18	   A^2 -> H(U1(a, e), U1(c, e))
28.36/9.18	   A^2 -> H(U1(a, e), U1(c, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(e, e))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, d))
28.36/9.18	   A^2 -> H(U1(a, e), U1(d, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(e, b))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, b))
28.36/9.18	   A^2 -> H(U1(a, k), U1(c, d))
28.36/9.18	   A^2 -> H(U1(a, k), U1(d, c))
28.36/9.18	   A^2 -> H(U1(a, k), U1(b, e))
28.36/9.18	   A^2 -> H(U1(a, k), U1(b, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(e, c))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, c))
28.36/9.18	   A^2 -> H(U1(a, k), U1(c, e))
28.36/9.18	   A^2 -> H(U1(a, k), U1(c, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(e, e))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, d))
28.36/9.18	   A^2 -> H(U1(a, k), U1(d, k))
28.36/9.18	   A^2 -> H(U1(a, c), b)
28.36/9.18	   A^2 -> H(U1(a, c), U1(e, d))
28.36/9.18	   A^2 -> H(U1(a, c), U1(d, e))
28.36/9.18	   A^2 -> H(U1(a, c), c)
28.36/9.18	   A^2 -> H(U1(a, c), U1(e, k))
28.36/9.18	   A^2 -> H(U1(a, c), U1(k, e))
28.36/9.18	   A^2 -> H(U1(a, c), e)
28.36/9.18	   A^2 -> H(U1(a, c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, d), b)
28.36/9.18	   A^2 -> H(U1(a, d), U1(e, d))
28.36/9.18	   A^2 -> H(U1(a, d), U1(d, e))
28.36/9.18	   A^2 -> H(U1(a, d), c)
28.36/9.18	   A^2 -> H(U1(a, d), U1(e, k))
28.36/9.18	   A^2 -> H(U1(a, d), U1(k, e))
28.36/9.18	   A^2 -> H(U1(a, d), e)
28.36/9.18	   A^2 -> H(U1(a, d), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, a), d)
28.36/9.18	   A^2 -> H(U1(a, a), k)
28.36/9.18	
28.36/9.18	The TRS R consists of the following rules:
28.36/9.18	
28.36/9.18	   f(x) -> U1(x, x)
28.36/9.18	   U1(e, x) -> x
28.36/9.18	   a -> c
28.36/9.18	   a -> d
28.36/9.18	   b -> c
28.36/9.18	   b -> d
28.36/9.18	   d -> k
28.36/9.18	   c -> e
28.36/9.18	   c -> k
28.36/9.18	
28.36/9.18	Q is empty.
28.36/9.18	We have to consider all minimal (P,Q,R)-chains.
28.36/9.18	----------------------------------------
28.36/9.18	
28.36/9.18	(785) TransformationProof (EQUIVALENT)
28.36/9.18	By narrowing [LPAR04] the rule A^2 -> H(k, f(b)) at position [] we obtained the following new rules [LPAR04]:
28.36/9.18	
28.36/9.18	   (A^2 -> H(k, U1(b, b)),A^2 -> H(k, U1(b, b)))
28.36/9.18	   (A^2 -> H(k, f(c)),A^2 -> H(k, f(c)))
28.36/9.18	   (A^2 -> H(k, f(d)),A^2 -> H(k, f(d)))
28.36/9.18	
28.36/9.18	
28.36/9.18	----------------------------------------
28.36/9.18	
28.36/9.18	(786)
28.36/9.18	Obligation:
28.36/9.18	Q DP problem:
28.36/9.18	The TRS P consists of the following rules:
28.36/9.18	
28.36/9.18	   H(x, x) -> G(x, x, f(k))
28.36/9.18	   G(d, x, x) -> A^2
28.36/9.18	   A^2 -> H(f(c), f(c))
28.36/9.18	   A^2 -> H(f(d), f(d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, c))
28.36/9.18	   A^2 -> H(f(e), f(e))
28.36/9.18	   A^2 -> H(f(k), f(k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(d, d))
28.36/9.18	   A^2 -> H(c, U1(b, b))
28.36/9.18	   A^2 -> H(c, f(c))
28.36/9.18	   A^2 -> H(c, f(d))
28.36/9.18	   A^2 -> H(U1(e, k), U1(b, b))
28.36/9.18	   A^2 -> H(U1(e, k), f(c))
28.36/9.18	   A^2 -> H(U1(e, k), f(d))
28.36/9.18	   A^2 -> H(U1(e, c), U1(c, b))
28.36/9.18	   A^2 -> H(U1(e, c), U1(d, b))
28.36/9.18	   A^2 -> H(U1(e, c), U1(b, c))
28.36/9.18	   A^2 -> H(U1(e, c), U1(b, d))
28.36/9.18	   A^2 -> H(U1(e, c), U1(c, c))
28.36/9.18	   A^2 -> H(U1(e, c), f(e))
28.36/9.18	   A^2 -> H(U1(e, c), f(k))
28.36/9.18	   A^2 -> H(U1(e, c), U1(d, d))
28.36/9.18	   A^2 -> H(U1(k, e), U1(b, b))
28.36/9.18	   A^2 -> H(U1(k, e), f(c))
28.36/9.18	   A^2 -> H(U1(k, e), f(d))
28.36/9.18	   A^2 -> H(U1(k, c), U1(c, b))
28.36/9.18	   A^2 -> H(U1(k, c), U1(d, b))
28.36/9.18	   A^2 -> H(U1(k, c), U1(b, c))
28.36/9.18	   A^2 -> H(U1(k, c), U1(b, d))
28.36/9.18	   A^2 -> H(U1(k, c), U1(c, c))
28.36/9.18	   A^2 -> H(U1(k, c), f(e))
28.36/9.18	   A^2 -> H(U1(k, c), f(k))
28.36/9.18	   A^2 -> H(U1(k, c), U1(d, d))
28.36/9.18	   A^2 -> H(U1(c, e), U1(c, b))
28.36/9.18	   A^2 -> H(U1(c, e), U1(d, b))
28.36/9.18	   A^2 -> H(U1(c, e), U1(b, c))
28.36/9.18	   A^2 -> H(U1(c, e), U1(b, d))
28.36/9.18	   A^2 -> H(U1(c, e), U1(c, c))
28.36/9.18	   A^2 -> H(U1(c, e), f(e))
28.36/9.18	   A^2 -> H(U1(c, e), f(k))
28.36/9.18	   A^2 -> H(U1(c, e), U1(d, d))
28.36/9.18	   A^2 -> H(U1(c, k), U1(c, b))
28.36/9.18	   A^2 -> H(U1(c, k), U1(d, b))
28.36/9.18	   A^2 -> H(U1(c, k), U1(b, c))
28.36/9.18	   A^2 -> H(U1(c, k), U1(b, d))
28.36/9.18	   A^2 -> H(U1(c, k), U1(c, c))
28.36/9.18	   A^2 -> H(U1(c, k), f(e))
28.36/9.18	   A^2 -> H(U1(c, k), f(k))
28.36/9.18	   A^2 -> H(U1(c, k), U1(d, d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(e, b))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, b))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(d, c))
28.36/9.18	   A^2 -> H(U1(c, c), U1(b, e))
28.36/9.18	   A^2 -> H(U1(c, c), U1(b, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(e, e))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(d, k))
28.36/9.18	   A^2 -> H(e, U1(b, b))
28.36/9.18	   A^2 -> H(e, f(c))
28.36/9.18	   A^2 -> H(e, f(d))
28.36/9.18	   A^2 -> H(U1(e, e), U1(c, b))
28.36/9.18	   A^2 -> H(U1(e, e), U1(d, b))
28.36/9.18	   A^2 -> H(U1(e, e), U1(b, c))
28.36/9.18	   A^2 -> H(U1(e, e), U1(b, d))
28.36/9.18	   A^2 -> H(U1(e, e), U1(c, c))
28.36/9.18	   A^2 -> H(U1(e, e), f(e))
28.36/9.18	   A^2 -> H(U1(e, e), f(k))
28.36/9.18	   A^2 -> H(U1(e, e), U1(d, d))
28.36/9.18	   A^2 -> H(f(e), U1(e, b))
28.36/9.18	   A^2 -> H(f(e), U1(k, b))
28.36/9.18	   A^2 -> H(f(e), U1(c, d))
28.36/9.18	   A^2 -> H(f(e), U1(d, c))
28.36/9.18	   A^2 -> H(f(e), U1(b, e))
28.36/9.18	   A^2 -> H(f(e), U1(b, k))
28.36/9.18	   A^2 -> H(f(e), U1(e, c))
28.36/9.18	   A^2 -> H(f(e), U1(k, c))
28.36/9.18	   A^2 -> H(f(e), U1(c, e))
28.36/9.18	   A^2 -> H(f(e), U1(c, k))
28.36/9.18	   A^2 -> H(f(e), U1(k, k))
28.36/9.18	   A^2 -> H(f(e), U1(k, d))
28.36/9.18	   A^2 -> H(f(e), U1(d, k))
28.36/9.18	   A^2 -> H(U1(k, k), U1(c, b))
28.36/9.18	   A^2 -> H(U1(k, k), U1(d, b))
28.36/9.18	   A^2 -> H(U1(k, k), U1(b, c))
28.36/9.18	   A^2 -> H(U1(k, k), U1(b, d))
28.36/9.18	   A^2 -> H(U1(k, k), U1(c, c))
28.36/9.18	   A^2 -> H(U1(k, k), f(e))
28.36/9.18	   A^2 -> H(U1(k, k), f(k))
28.36/9.18	   A^2 -> H(U1(k, k), U1(d, d))
28.36/9.18	   A^2 -> H(f(k), U1(e, b))
28.36/9.18	   A^2 -> H(f(k), U1(k, b))
28.36/9.18	   A^2 -> H(f(k), U1(c, d))
28.36/9.18	   A^2 -> H(f(k), U1(d, c))
28.36/9.18	   A^2 -> H(f(k), U1(b, e))
28.36/9.18	   A^2 -> H(f(k), U1(b, k))
28.36/9.18	   A^2 -> H(f(k), U1(e, c))
28.36/9.18	   A^2 -> H(f(k), U1(k, c))
28.36/9.18	   A^2 -> H(f(k), U1(c, e))
28.36/9.18	   A^2 -> H(f(k), U1(c, k))
28.36/9.18	   A^2 -> H(f(k), U1(e, e))
28.36/9.18	   A^2 -> H(f(k), U1(k, d))
28.36/9.18	   A^2 -> H(f(k), U1(d, k))
28.36/9.18	   A^2 -> H(f(c), b)
28.36/9.18	   A^2 -> H(f(c), U1(e, d))
28.36/9.18	   A^2 -> H(f(c), U1(d, e))
28.36/9.18	   A^2 -> H(f(k), U1(k, k))
28.36/9.18	   A^2 -> H(U1(k, k), U1(b, b))
28.36/9.18	   A^2 -> H(U1(k, k), f(c))
28.36/9.18	   A^2 -> H(U1(k, k), f(d))
28.36/9.18	   A^2 -> H(U1(k, d), U1(c, b))
28.36/9.18	   A^2 -> H(U1(k, d), U1(d, b))
28.36/9.18	   A^2 -> H(U1(k, d), U1(b, c))
28.36/9.18	   A^2 -> H(U1(k, d), U1(b, d))
28.36/9.18	   A^2 -> H(U1(k, d), U1(c, c))
28.36/9.18	   A^2 -> H(U1(k, d), f(e))
28.36/9.18	   A^2 -> H(U1(k, d), f(k))
28.36/9.18	   A^2 -> H(U1(k, d), U1(d, d))
28.36/9.18	   A^2 -> H(U1(d, k), U1(c, b))
28.36/9.18	   A^2 -> H(U1(d, k), U1(d, b))
28.36/9.18	   A^2 -> H(U1(d, k), U1(b, c))
28.36/9.18	   A^2 -> H(U1(d, k), U1(b, d))
28.36/9.18	   A^2 -> H(U1(d, k), U1(c, c))
28.36/9.18	   A^2 -> H(U1(d, k), f(e))
28.36/9.18	   A^2 -> H(U1(d, k), f(k))
28.36/9.18	   A^2 -> H(U1(d, k), U1(d, d))
28.36/9.18	   A^2 -> H(U1(d, d), U1(e, b))
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, b))
28.36/9.18	   A^2 -> H(U1(d, d), U1(c, d))
28.36/9.18	   A^2 -> H(U1(d, d), U1(d, c))
28.36/9.18	   A^2 -> H(U1(d, d), U1(b, e))
28.36/9.18	   A^2 -> H(U1(d, d), U1(b, k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(e, c))
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, c))
28.36/9.18	   A^2 -> H(U1(d, d), U1(c, e))
28.36/9.18	   A^2 -> H(U1(d, d), U1(c, k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(e, e))
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, k))
28.36/9.18	   A^2 -> H(f(d), b)
28.36/9.18	   A^2 -> H(f(d), U1(e, d))
28.36/9.18	   A^2 -> H(f(d), U1(d, e))
28.36/9.18	   A^2 -> H(f(d), c)
28.36/9.18	   A^2 -> H(f(d), U1(e, k))
28.36/9.18	   A^2 -> H(f(d), U1(k, e))
28.36/9.18	   A^2 -> H(f(d), e)
28.36/9.18	   A^2 -> H(f(a), d)
28.36/9.18	   A^2 -> H(U1(c, c), U1(e, c))
28.36/9.18	   A^2 -> H(f(c), c)
28.36/9.18	   A^2 -> H(f(c), U1(e, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, c))
28.36/9.18	   A^2 -> H(f(c), U1(k, e))
28.36/9.18	   A^2 -> H(f(c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, e))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, k))
28.36/9.18	   A^2 -> H(f(a), k)
28.36/9.18	   A^2 -> H(f(e), U1(e, e))
28.36/9.18	   A^2 -> H(f(c), e)
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, d))
28.36/9.18	   A^2 -> H(f(d), U1(k, k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(d, k))
28.36/9.18	   A^2 -> H(d, U1(b, b))
28.36/9.18	   A^2 -> H(d, f(c))
28.36/9.18	   A^2 -> H(d, f(d))
28.36/9.18	   A^2 -> H(a, U1(c, b))
28.36/9.18	   A^2 -> H(a, U1(d, b))
28.36/9.18	   A^2 -> H(a, U1(b, c))
28.36/9.18	   A^2 -> H(a, U1(b, d))
28.36/9.18	   A^2 -> H(a, U1(c, c))
28.36/9.18	   A^2 -> H(a, f(e))
28.36/9.18	   A^2 -> H(a, f(k))
28.36/9.18	   A^2 -> H(a, U1(d, d))
28.36/9.18	   A^2 -> H(U1(e, d), U1(c, b))
28.36/9.18	   A^2 -> H(U1(e, d), U1(d, b))
28.36/9.18	   A^2 -> H(U1(e, d), U1(b, c))
28.36/9.18	   A^2 -> H(U1(e, d), U1(b, d))
28.36/9.18	   A^2 -> H(U1(e, d), U1(c, c))
28.36/9.18	   A^2 -> H(U1(e, d), f(e))
28.36/9.18	   A^2 -> H(U1(e, d), f(k))
28.36/9.18	   A^2 -> H(U1(e, d), U1(d, d))
28.36/9.18	   A^2 -> H(U1(e, a), U1(e, b))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, b))
28.36/9.18	   A^2 -> H(U1(e, a), U1(c, d))
28.36/9.18	   A^2 -> H(U1(e, a), U1(d, c))
28.36/9.18	   A^2 -> H(U1(e, a), U1(b, e))
28.36/9.18	   A^2 -> H(U1(e, a), U1(b, k))
28.36/9.18	   A^2 -> H(U1(e, a), U1(e, c))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, c))
28.36/9.18	   A^2 -> H(U1(e, a), U1(c, e))
28.36/9.18	   A^2 -> H(U1(e, a), U1(c, k))
28.36/9.18	   A^2 -> H(U1(e, a), U1(e, e))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, d))
28.36/9.18	   A^2 -> H(U1(e, a), U1(d, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(e, b))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, b))
28.36/9.18	   A^2 -> H(U1(k, a), U1(c, d))
28.36/9.18	   A^2 -> H(U1(k, a), U1(d, c))
28.36/9.18	   A^2 -> H(U1(k, a), U1(b, e))
28.36/9.18	   A^2 -> H(U1(k, a), U1(b, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(e, c))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, c))
28.36/9.18	   A^2 -> H(U1(k, a), U1(c, e))
28.36/9.18	   A^2 -> H(U1(k, a), U1(c, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(e, e))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, d))
28.36/9.18	   A^2 -> H(U1(k, a), U1(d, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(e, b))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, b))
28.36/9.18	   A^2 -> H(U1(c, d), U1(c, d))
28.36/9.18	   A^2 -> H(U1(c, d), U1(d, c))
28.36/9.18	   A^2 -> H(U1(c, d), U1(b, e))
28.36/9.18	   A^2 -> H(U1(c, d), U1(b, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(e, c))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, c))
28.36/9.18	   A^2 -> H(U1(c, d), U1(c, e))
28.36/9.18	   A^2 -> H(U1(c, d), U1(c, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(e, e))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, d))
28.36/9.18	   A^2 -> H(U1(c, d), U1(d, k))
28.36/9.18	   A^2 -> H(U1(c, a), b)
28.36/9.18	   A^2 -> H(U1(c, a), U1(e, d))
28.36/9.18	   A^2 -> H(U1(c, a), U1(d, e))
28.36/9.18	   A^2 -> H(U1(c, a), c)
28.36/9.18	   A^2 -> H(U1(c, a), U1(e, k))
28.36/9.18	   A^2 -> H(U1(c, a), U1(k, e))
28.36/9.18	   A^2 -> H(U1(c, a), e)
28.36/9.18	   A^2 -> H(U1(c, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(d, e), U1(c, b))
28.36/9.18	   A^2 -> H(U1(d, e), U1(d, b))
28.36/9.18	   A^2 -> H(U1(d, e), U1(b, c))
28.36/9.18	   A^2 -> H(U1(d, e), U1(b, d))
28.36/9.18	   A^2 -> H(U1(d, e), U1(c, c))
28.36/9.18	   A^2 -> H(U1(d, e), f(e))
28.36/9.18	   A^2 -> H(U1(d, e), f(k))
28.36/9.18	   A^2 -> H(U1(d, e), U1(d, d))
28.36/9.18	   A^2 -> H(U1(d, c), U1(e, b))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, b))
28.36/9.18	   A^2 -> H(U1(d, c), U1(c, d))
28.36/9.18	   A^2 -> H(U1(d, c), U1(d, c))
28.36/9.18	   A^2 -> H(U1(d, c), U1(b, e))
28.36/9.18	   A^2 -> H(U1(d, c), U1(b, k))
28.36/9.18	   A^2 -> H(U1(d, c), U1(e, c))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, c))
28.36/9.18	   A^2 -> H(U1(d, c), U1(c, e))
28.36/9.18	   A^2 -> H(U1(d, c), U1(c, k))
28.36/9.18	   A^2 -> H(U1(d, c), U1(e, e))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, d))
28.36/9.18	   A^2 -> H(U1(d, c), U1(d, k))
28.36/9.18	   A^2 -> H(U1(d, a), b)
28.36/9.18	   A^2 -> H(U1(d, a), U1(e, d))
28.36/9.18	   A^2 -> H(U1(d, a), U1(d, e))
28.36/9.18	   A^2 -> H(U1(d, a), c)
28.36/9.18	   A^2 -> H(U1(d, a), U1(e, k))
28.36/9.18	   A^2 -> H(U1(d, a), U1(k, e))
28.36/9.18	   A^2 -> H(U1(d, a), e)
28.36/9.18	   A^2 -> H(U1(d, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(e, b))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, b))
28.36/9.18	   A^2 -> H(U1(a, e), U1(c, d))
28.36/9.18	   A^2 -> H(U1(a, e), U1(d, c))
28.36/9.18	   A^2 -> H(U1(a, e), U1(b, e))
28.36/9.18	   A^2 -> H(U1(a, e), U1(b, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(e, c))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, c))
28.36/9.18	   A^2 -> H(U1(a, e), U1(c, e))
28.36/9.18	   A^2 -> H(U1(a, e), U1(c, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(e, e))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, d))
28.36/9.18	   A^2 -> H(U1(a, e), U1(d, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(e, b))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, b))
28.36/9.18	   A^2 -> H(U1(a, k), U1(c, d))
28.36/9.18	   A^2 -> H(U1(a, k), U1(d, c))
28.36/9.18	   A^2 -> H(U1(a, k), U1(b, e))
28.36/9.18	   A^2 -> H(U1(a, k), U1(b, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(e, c))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, c))
28.36/9.18	   A^2 -> H(U1(a, k), U1(c, e))
28.36/9.18	   A^2 -> H(U1(a, k), U1(c, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(e, e))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, d))
28.36/9.18	   A^2 -> H(U1(a, k), U1(d, k))
28.36/9.18	   A^2 -> H(U1(a, c), b)
28.36/9.18	   A^2 -> H(U1(a, c), U1(e, d))
28.36/9.18	   A^2 -> H(U1(a, c), U1(d, e))
28.36/9.18	   A^2 -> H(U1(a, c), c)
28.36/9.18	   A^2 -> H(U1(a, c), U1(e, k))
28.36/9.18	   A^2 -> H(U1(a, c), U1(k, e))
28.36/9.18	   A^2 -> H(U1(a, c), e)
28.36/9.18	   A^2 -> H(U1(a, c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, d), b)
28.36/9.18	   A^2 -> H(U1(a, d), U1(e, d))
28.36/9.18	   A^2 -> H(U1(a, d), U1(d, e))
28.36/9.18	   A^2 -> H(U1(a, d), c)
28.36/9.18	   A^2 -> H(U1(a, d), U1(e, k))
28.36/9.18	   A^2 -> H(U1(a, d), U1(k, e))
28.36/9.18	   A^2 -> H(U1(a, d), e)
28.36/9.18	   A^2 -> H(U1(a, d), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, a), d)
28.36/9.18	   A^2 -> H(U1(a, a), k)
28.36/9.18	   A^2 -> H(k, U1(b, b))
28.36/9.18	   A^2 -> H(k, f(c))
28.36/9.18	   A^2 -> H(k, f(d))
28.36/9.18	
28.36/9.18	The TRS R consists of the following rules:
28.36/9.18	
28.36/9.18	   f(x) -> U1(x, x)
28.36/9.18	   U1(e, x) -> x
28.36/9.18	   a -> c
28.36/9.18	   a -> d
28.36/9.18	   b -> c
28.36/9.18	   b -> d
28.36/9.18	   d -> k
28.36/9.18	   c -> e
28.36/9.18	   c -> k
28.36/9.18	
28.36/9.18	Q is empty.
28.36/9.18	We have to consider all minimal (P,Q,R)-chains.
28.36/9.18	----------------------------------------
28.36/9.18	
28.36/9.18	(787) TransformationProof (EQUIVALENT)
28.36/9.18	By narrowing [LPAR04] the rule A^2 -> H(c, U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
28.36/9.18	
28.36/9.18	   (A^2 -> H(e, U1(b, b)),A^2 -> H(e, U1(b, b)))
28.36/9.18	   (A^2 -> H(k, U1(b, b)),A^2 -> H(k, U1(b, b)))
28.36/9.18	   (A^2 -> H(c, U1(c, b)),A^2 -> H(c, U1(c, b)))
28.36/9.18	   (A^2 -> H(c, U1(d, b)),A^2 -> H(c, U1(d, b)))
28.36/9.18	   (A^2 -> H(c, U1(b, c)),A^2 -> H(c, U1(b, c)))
28.36/9.18	   (A^2 -> H(c, U1(b, d)),A^2 -> H(c, U1(b, d)))
28.36/9.18	
28.36/9.18	
28.36/9.18	----------------------------------------
28.36/9.18	
28.36/9.18	(788)
28.36/9.18	Obligation:
28.36/9.18	Q DP problem:
28.36/9.18	The TRS P consists of the following rules:
28.36/9.18	
28.36/9.18	   H(x, x) -> G(x, x, f(k))
28.36/9.18	   G(d, x, x) -> A^2
28.36/9.18	   A^2 -> H(f(c), f(c))
28.36/9.18	   A^2 -> H(f(d), f(d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, c))
28.36/9.18	   A^2 -> H(f(e), f(e))
28.36/9.18	   A^2 -> H(f(k), f(k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(d, d))
28.36/9.18	   A^2 -> H(c, f(c))
28.36/9.18	   A^2 -> H(c, f(d))
28.36/9.18	   A^2 -> H(U1(e, k), U1(b, b))
28.36/9.18	   A^2 -> H(U1(e, k), f(c))
28.36/9.18	   A^2 -> H(U1(e, k), f(d))
28.36/9.18	   A^2 -> H(U1(e, c), U1(c, b))
28.36/9.18	   A^2 -> H(U1(e, c), U1(d, b))
28.36/9.18	   A^2 -> H(U1(e, c), U1(b, c))
28.36/9.18	   A^2 -> H(U1(e, c), U1(b, d))
28.36/9.18	   A^2 -> H(U1(e, c), U1(c, c))
28.36/9.18	   A^2 -> H(U1(e, c), f(e))
28.36/9.18	   A^2 -> H(U1(e, c), f(k))
28.36/9.18	   A^2 -> H(U1(e, c), U1(d, d))
28.36/9.18	   A^2 -> H(U1(k, e), U1(b, b))
28.36/9.18	   A^2 -> H(U1(k, e), f(c))
28.36/9.18	   A^2 -> H(U1(k, e), f(d))
28.36/9.18	   A^2 -> H(U1(k, c), U1(c, b))
28.36/9.18	   A^2 -> H(U1(k, c), U1(d, b))
28.36/9.18	   A^2 -> H(U1(k, c), U1(b, c))
28.36/9.18	   A^2 -> H(U1(k, c), U1(b, d))
28.36/9.18	   A^2 -> H(U1(k, c), U1(c, c))
28.36/9.18	   A^2 -> H(U1(k, c), f(e))
28.36/9.18	   A^2 -> H(U1(k, c), f(k))
28.36/9.18	   A^2 -> H(U1(k, c), U1(d, d))
28.36/9.18	   A^2 -> H(U1(c, e), U1(c, b))
28.36/9.18	   A^2 -> H(U1(c, e), U1(d, b))
28.36/9.18	   A^2 -> H(U1(c, e), U1(b, c))
28.36/9.18	   A^2 -> H(U1(c, e), U1(b, d))
28.36/9.18	   A^2 -> H(U1(c, e), U1(c, c))
28.36/9.18	   A^2 -> H(U1(c, e), f(e))
28.36/9.18	   A^2 -> H(U1(c, e), f(k))
28.36/9.18	   A^2 -> H(U1(c, e), U1(d, d))
28.36/9.18	   A^2 -> H(U1(c, k), U1(c, b))
28.36/9.18	   A^2 -> H(U1(c, k), U1(d, b))
28.36/9.18	   A^2 -> H(U1(c, k), U1(b, c))
28.36/9.18	   A^2 -> H(U1(c, k), U1(b, d))
28.36/9.18	   A^2 -> H(U1(c, k), U1(c, c))
28.36/9.18	   A^2 -> H(U1(c, k), f(e))
28.36/9.18	   A^2 -> H(U1(c, k), f(k))
28.36/9.18	   A^2 -> H(U1(c, k), U1(d, d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(e, b))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, b))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(d, c))
28.36/9.18	   A^2 -> H(U1(c, c), U1(b, e))
28.36/9.18	   A^2 -> H(U1(c, c), U1(b, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(e, e))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(d, k))
28.36/9.18	   A^2 -> H(e, U1(b, b))
28.36/9.18	   A^2 -> H(e, f(c))
28.36/9.18	   A^2 -> H(e, f(d))
28.36/9.18	   A^2 -> H(U1(e, e), U1(c, b))
28.36/9.18	   A^2 -> H(U1(e, e), U1(d, b))
28.36/9.18	   A^2 -> H(U1(e, e), U1(b, c))
28.36/9.18	   A^2 -> H(U1(e, e), U1(b, d))
28.36/9.18	   A^2 -> H(U1(e, e), U1(c, c))
28.36/9.18	   A^2 -> H(U1(e, e), f(e))
28.36/9.18	   A^2 -> H(U1(e, e), f(k))
28.36/9.18	   A^2 -> H(U1(e, e), U1(d, d))
28.36/9.18	   A^2 -> H(f(e), U1(e, b))
28.36/9.18	   A^2 -> H(f(e), U1(k, b))
28.36/9.18	   A^2 -> H(f(e), U1(c, d))
28.36/9.18	   A^2 -> H(f(e), U1(d, c))
28.36/9.18	   A^2 -> H(f(e), U1(b, e))
28.36/9.18	   A^2 -> H(f(e), U1(b, k))
28.36/9.18	   A^2 -> H(f(e), U1(e, c))
28.36/9.18	   A^2 -> H(f(e), U1(k, c))
28.36/9.18	   A^2 -> H(f(e), U1(c, e))
28.36/9.18	   A^2 -> H(f(e), U1(c, k))
28.36/9.18	   A^2 -> H(f(e), U1(k, k))
28.36/9.18	   A^2 -> H(f(e), U1(k, d))
28.36/9.18	   A^2 -> H(f(e), U1(d, k))
28.36/9.18	   A^2 -> H(U1(k, k), U1(c, b))
28.36/9.18	   A^2 -> H(U1(k, k), U1(d, b))
28.36/9.18	   A^2 -> H(U1(k, k), U1(b, c))
28.36/9.18	   A^2 -> H(U1(k, k), U1(b, d))
28.36/9.18	   A^2 -> H(U1(k, k), U1(c, c))
28.36/9.18	   A^2 -> H(U1(k, k), f(e))
28.36/9.18	   A^2 -> H(U1(k, k), f(k))
28.36/9.18	   A^2 -> H(U1(k, k), U1(d, d))
28.36/9.18	   A^2 -> H(f(k), U1(e, b))
28.36/9.18	   A^2 -> H(f(k), U1(k, b))
28.36/9.18	   A^2 -> H(f(k), U1(c, d))
28.36/9.18	   A^2 -> H(f(k), U1(d, c))
28.36/9.18	   A^2 -> H(f(k), U1(b, e))
28.36/9.18	   A^2 -> H(f(k), U1(b, k))
28.36/9.18	   A^2 -> H(f(k), U1(e, c))
28.36/9.18	   A^2 -> H(f(k), U1(k, c))
28.36/9.18	   A^2 -> H(f(k), U1(c, e))
28.36/9.18	   A^2 -> H(f(k), U1(c, k))
28.36/9.18	   A^2 -> H(f(k), U1(e, e))
28.36/9.18	   A^2 -> H(f(k), U1(k, d))
28.36/9.18	   A^2 -> H(f(k), U1(d, k))
28.36/9.18	   A^2 -> H(f(c), b)
28.36/9.18	   A^2 -> H(f(c), U1(e, d))
28.36/9.18	   A^2 -> H(f(c), U1(d, e))
28.36/9.18	   A^2 -> H(f(k), U1(k, k))
28.36/9.18	   A^2 -> H(U1(k, k), U1(b, b))
28.36/9.18	   A^2 -> H(U1(k, k), f(c))
28.36/9.18	   A^2 -> H(U1(k, k), f(d))
28.36/9.18	   A^2 -> H(U1(k, d), U1(c, b))
28.36/9.18	   A^2 -> H(U1(k, d), U1(d, b))
28.36/9.18	   A^2 -> H(U1(k, d), U1(b, c))
28.36/9.18	   A^2 -> H(U1(k, d), U1(b, d))
28.36/9.18	   A^2 -> H(U1(k, d), U1(c, c))
28.36/9.18	   A^2 -> H(U1(k, d), f(e))
28.36/9.18	   A^2 -> H(U1(k, d), f(k))
28.36/9.18	   A^2 -> H(U1(k, d), U1(d, d))
28.36/9.18	   A^2 -> H(U1(d, k), U1(c, b))
28.36/9.18	   A^2 -> H(U1(d, k), U1(d, b))
28.36/9.18	   A^2 -> H(U1(d, k), U1(b, c))
28.36/9.18	   A^2 -> H(U1(d, k), U1(b, d))
28.36/9.18	   A^2 -> H(U1(d, k), U1(c, c))
28.36/9.18	   A^2 -> H(U1(d, k), f(e))
28.36/9.18	   A^2 -> H(U1(d, k), f(k))
28.36/9.18	   A^2 -> H(U1(d, k), U1(d, d))
28.36/9.18	   A^2 -> H(U1(d, d), U1(e, b))
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, b))
28.36/9.18	   A^2 -> H(U1(d, d), U1(c, d))
28.36/9.18	   A^2 -> H(U1(d, d), U1(d, c))
28.36/9.18	   A^2 -> H(U1(d, d), U1(b, e))
28.36/9.18	   A^2 -> H(U1(d, d), U1(b, k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(e, c))
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, c))
28.36/9.18	   A^2 -> H(U1(d, d), U1(c, e))
28.36/9.18	   A^2 -> H(U1(d, d), U1(c, k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(e, e))
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, k))
28.36/9.18	   A^2 -> H(f(d), b)
28.36/9.18	   A^2 -> H(f(d), U1(e, d))
28.36/9.18	   A^2 -> H(f(d), U1(d, e))
28.36/9.18	   A^2 -> H(f(d), c)
28.36/9.18	   A^2 -> H(f(d), U1(e, k))
28.36/9.18	   A^2 -> H(f(d), U1(k, e))
28.36/9.18	   A^2 -> H(f(d), e)
28.36/9.18	   A^2 -> H(f(a), d)
28.36/9.18	   A^2 -> H(U1(c, c), U1(e, c))
28.36/9.18	   A^2 -> H(f(c), c)
28.36/9.18	   A^2 -> H(f(c), U1(e, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, c))
28.36/9.18	   A^2 -> H(f(c), U1(k, e))
28.36/9.18	   A^2 -> H(f(c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, e))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, k))
28.36/9.18	   A^2 -> H(f(a), k)
28.36/9.18	   A^2 -> H(f(e), U1(e, e))
28.36/9.18	   A^2 -> H(f(c), e)
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, d))
28.36/9.18	   A^2 -> H(f(d), U1(k, k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(d, k))
28.36/9.18	   A^2 -> H(d, U1(b, b))
28.36/9.18	   A^2 -> H(d, f(c))
28.36/9.18	   A^2 -> H(d, f(d))
28.36/9.18	   A^2 -> H(a, U1(c, b))
28.36/9.18	   A^2 -> H(a, U1(d, b))
28.36/9.18	   A^2 -> H(a, U1(b, c))
28.36/9.18	   A^2 -> H(a, U1(b, d))
28.36/9.18	   A^2 -> H(a, U1(c, c))
28.36/9.18	   A^2 -> H(a, f(e))
28.36/9.18	   A^2 -> H(a, f(k))
28.36/9.18	   A^2 -> H(a, U1(d, d))
28.36/9.18	   A^2 -> H(U1(e, d), U1(c, b))
28.36/9.18	   A^2 -> H(U1(e, d), U1(d, b))
28.36/9.18	   A^2 -> H(U1(e, d), U1(b, c))
28.36/9.18	   A^2 -> H(U1(e, d), U1(b, d))
28.36/9.18	   A^2 -> H(U1(e, d), U1(c, c))
28.36/9.18	   A^2 -> H(U1(e, d), f(e))
28.36/9.18	   A^2 -> H(U1(e, d), f(k))
28.36/9.18	   A^2 -> H(U1(e, d), U1(d, d))
28.36/9.18	   A^2 -> H(U1(e, a), U1(e, b))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, b))
28.36/9.18	   A^2 -> H(U1(e, a), U1(c, d))
28.36/9.18	   A^2 -> H(U1(e, a), U1(d, c))
28.36/9.18	   A^2 -> H(U1(e, a), U1(b, e))
28.36/9.18	   A^2 -> H(U1(e, a), U1(b, k))
28.36/9.18	   A^2 -> H(U1(e, a), U1(e, c))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, c))
28.36/9.18	   A^2 -> H(U1(e, a), U1(c, e))
28.36/9.18	   A^2 -> H(U1(e, a), U1(c, k))
28.36/9.18	   A^2 -> H(U1(e, a), U1(e, e))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, d))
28.36/9.18	   A^2 -> H(U1(e, a), U1(d, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(e, b))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, b))
28.36/9.18	   A^2 -> H(U1(k, a), U1(c, d))
28.36/9.18	   A^2 -> H(U1(k, a), U1(d, c))
28.36/9.18	   A^2 -> H(U1(k, a), U1(b, e))
28.36/9.18	   A^2 -> H(U1(k, a), U1(b, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(e, c))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, c))
28.36/9.18	   A^2 -> H(U1(k, a), U1(c, e))
28.36/9.18	   A^2 -> H(U1(k, a), U1(c, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(e, e))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, d))
28.36/9.18	   A^2 -> H(U1(k, a), U1(d, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(e, b))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, b))
28.36/9.18	   A^2 -> H(U1(c, d), U1(c, d))
28.36/9.18	   A^2 -> H(U1(c, d), U1(d, c))
28.36/9.18	   A^2 -> H(U1(c, d), U1(b, e))
28.36/9.18	   A^2 -> H(U1(c, d), U1(b, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(e, c))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, c))
28.36/9.18	   A^2 -> H(U1(c, d), U1(c, e))
28.36/9.18	   A^2 -> H(U1(c, d), U1(c, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(e, e))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, d))
28.36/9.18	   A^2 -> H(U1(c, d), U1(d, k))
28.36/9.18	   A^2 -> H(U1(c, a), b)
28.36/9.18	   A^2 -> H(U1(c, a), U1(e, d))
28.36/9.18	   A^2 -> H(U1(c, a), U1(d, e))
28.36/9.18	   A^2 -> H(U1(c, a), c)
28.36/9.18	   A^2 -> H(U1(c, a), U1(e, k))
28.36/9.18	   A^2 -> H(U1(c, a), U1(k, e))
28.36/9.18	   A^2 -> H(U1(c, a), e)
28.36/9.18	   A^2 -> H(U1(c, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(d, e), U1(c, b))
28.36/9.18	   A^2 -> H(U1(d, e), U1(d, b))
28.36/9.18	   A^2 -> H(U1(d, e), U1(b, c))
28.36/9.18	   A^2 -> H(U1(d, e), U1(b, d))
28.36/9.18	   A^2 -> H(U1(d, e), U1(c, c))
28.36/9.18	   A^2 -> H(U1(d, e), f(e))
28.36/9.18	   A^2 -> H(U1(d, e), f(k))
28.36/9.18	   A^2 -> H(U1(d, e), U1(d, d))
28.36/9.18	   A^2 -> H(U1(d, c), U1(e, b))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, b))
28.36/9.18	   A^2 -> H(U1(d, c), U1(c, d))
28.36/9.18	   A^2 -> H(U1(d, c), U1(d, c))
28.36/9.18	   A^2 -> H(U1(d, c), U1(b, e))
28.36/9.18	   A^2 -> H(U1(d, c), U1(b, k))
28.36/9.18	   A^2 -> H(U1(d, c), U1(e, c))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, c))
28.36/9.18	   A^2 -> H(U1(d, c), U1(c, e))
28.36/9.18	   A^2 -> H(U1(d, c), U1(c, k))
28.36/9.18	   A^2 -> H(U1(d, c), U1(e, e))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, d))
28.36/9.18	   A^2 -> H(U1(d, c), U1(d, k))
28.36/9.18	   A^2 -> H(U1(d, a), b)
28.36/9.18	   A^2 -> H(U1(d, a), U1(e, d))
28.36/9.18	   A^2 -> H(U1(d, a), U1(d, e))
28.36/9.18	   A^2 -> H(U1(d, a), c)
28.36/9.18	   A^2 -> H(U1(d, a), U1(e, k))
28.36/9.18	   A^2 -> H(U1(d, a), U1(k, e))
28.36/9.18	   A^2 -> H(U1(d, a), e)
28.36/9.18	   A^2 -> H(U1(d, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(e, b))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, b))
28.36/9.18	   A^2 -> H(U1(a, e), U1(c, d))
28.36/9.18	   A^2 -> H(U1(a, e), U1(d, c))
28.36/9.18	   A^2 -> H(U1(a, e), U1(b, e))
28.36/9.18	   A^2 -> H(U1(a, e), U1(b, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(e, c))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, c))
28.36/9.18	   A^2 -> H(U1(a, e), U1(c, e))
28.36/9.18	   A^2 -> H(U1(a, e), U1(c, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(e, e))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, d))
28.36/9.18	   A^2 -> H(U1(a, e), U1(d, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(e, b))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, b))
28.36/9.18	   A^2 -> H(U1(a, k), U1(c, d))
28.36/9.18	   A^2 -> H(U1(a, k), U1(d, c))
28.36/9.18	   A^2 -> H(U1(a, k), U1(b, e))
28.36/9.18	   A^2 -> H(U1(a, k), U1(b, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(e, c))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, c))
28.36/9.18	   A^2 -> H(U1(a, k), U1(c, e))
28.36/9.18	   A^2 -> H(U1(a, k), U1(c, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(e, e))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, d))
28.36/9.18	   A^2 -> H(U1(a, k), U1(d, k))
28.36/9.18	   A^2 -> H(U1(a, c), b)
28.36/9.18	   A^2 -> H(U1(a, c), U1(e, d))
28.36/9.18	   A^2 -> H(U1(a, c), U1(d, e))
28.36/9.18	   A^2 -> H(U1(a, c), c)
28.36/9.18	   A^2 -> H(U1(a, c), U1(e, k))
28.36/9.18	   A^2 -> H(U1(a, c), U1(k, e))
28.36/9.18	   A^2 -> H(U1(a, c), e)
28.36/9.18	   A^2 -> H(U1(a, c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, d), b)
28.36/9.18	   A^2 -> H(U1(a, d), U1(e, d))
28.36/9.18	   A^2 -> H(U1(a, d), U1(d, e))
28.36/9.18	   A^2 -> H(U1(a, d), c)
28.36/9.18	   A^2 -> H(U1(a, d), U1(e, k))
28.36/9.18	   A^2 -> H(U1(a, d), U1(k, e))
28.36/9.18	   A^2 -> H(U1(a, d), e)
28.36/9.18	   A^2 -> H(U1(a, d), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, a), d)
28.36/9.18	   A^2 -> H(U1(a, a), k)
28.36/9.18	   A^2 -> H(k, U1(b, b))
28.36/9.18	   A^2 -> H(k, f(c))
28.36/9.18	   A^2 -> H(k, f(d))
28.36/9.18	   A^2 -> H(c, U1(c, b))
28.36/9.18	   A^2 -> H(c, U1(d, b))
28.36/9.18	   A^2 -> H(c, U1(b, c))
28.36/9.18	   A^2 -> H(c, U1(b, d))
28.36/9.18	
28.36/9.18	The TRS R consists of the following rules:
28.36/9.18	
28.36/9.18	   f(x) -> U1(x, x)
28.36/9.18	   U1(e, x) -> x
28.36/9.18	   a -> c
28.36/9.18	   a -> d
28.36/9.18	   b -> c
28.36/9.18	   b -> d
28.36/9.18	   d -> k
28.36/9.18	   c -> e
28.36/9.18	   c -> k
28.36/9.18	
28.36/9.18	Q is empty.
28.36/9.18	We have to consider all minimal (P,Q,R)-chains.
28.36/9.18	----------------------------------------
28.36/9.18	
28.36/9.18	(789) TransformationProof (EQUIVALENT)
28.36/9.18	By narrowing [LPAR04] the rule A^2 -> H(c, f(c)) at position [] we obtained the following new rules [LPAR04]:
28.36/9.18	
28.36/9.18	   (A^2 -> H(e, f(c)),A^2 -> H(e, f(c)))
28.36/9.18	   (A^2 -> H(k, f(c)),A^2 -> H(k, f(c)))
28.36/9.18	   (A^2 -> H(c, U1(c, c)),A^2 -> H(c, U1(c, c)))
28.36/9.18	   (A^2 -> H(c, f(e)),A^2 -> H(c, f(e)))
28.36/9.18	   (A^2 -> H(c, f(k)),A^2 -> H(c, f(k)))
28.36/9.18	
28.36/9.18	
28.36/9.18	----------------------------------------
28.36/9.18	
28.36/9.18	(790)
28.36/9.18	Obligation:
28.36/9.18	Q DP problem:
28.36/9.18	The TRS P consists of the following rules:
28.36/9.18	
28.36/9.18	   H(x, x) -> G(x, x, f(k))
28.36/9.18	   G(d, x, x) -> A^2
28.36/9.18	   A^2 -> H(f(c), f(c))
28.36/9.18	   A^2 -> H(f(d), f(d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, c))
28.36/9.18	   A^2 -> H(f(e), f(e))
28.36/9.18	   A^2 -> H(f(k), f(k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(d, d))
28.36/9.18	   A^2 -> H(c, f(d))
28.36/9.18	   A^2 -> H(U1(e, k), U1(b, b))
28.36/9.18	   A^2 -> H(U1(e, k), f(c))
28.36/9.18	   A^2 -> H(U1(e, k), f(d))
28.36/9.18	   A^2 -> H(U1(e, c), U1(c, b))
28.36/9.18	   A^2 -> H(U1(e, c), U1(d, b))
28.36/9.18	   A^2 -> H(U1(e, c), U1(b, c))
28.36/9.18	   A^2 -> H(U1(e, c), U1(b, d))
28.36/9.18	   A^2 -> H(U1(e, c), U1(c, c))
28.36/9.18	   A^2 -> H(U1(e, c), f(e))
28.36/9.18	   A^2 -> H(U1(e, c), f(k))
28.36/9.18	   A^2 -> H(U1(e, c), U1(d, d))
28.36/9.18	   A^2 -> H(U1(k, e), U1(b, b))
28.36/9.18	   A^2 -> H(U1(k, e), f(c))
28.36/9.18	   A^2 -> H(U1(k, e), f(d))
28.36/9.18	   A^2 -> H(U1(k, c), U1(c, b))
28.36/9.18	   A^2 -> H(U1(k, c), U1(d, b))
28.36/9.18	   A^2 -> H(U1(k, c), U1(b, c))
28.36/9.18	   A^2 -> H(U1(k, c), U1(b, d))
28.36/9.18	   A^2 -> H(U1(k, c), U1(c, c))
28.36/9.18	   A^2 -> H(U1(k, c), f(e))
28.36/9.18	   A^2 -> H(U1(k, c), f(k))
28.36/9.18	   A^2 -> H(U1(k, c), U1(d, d))
28.36/9.18	   A^2 -> H(U1(c, e), U1(c, b))
28.36/9.18	   A^2 -> H(U1(c, e), U1(d, b))
28.36/9.18	   A^2 -> H(U1(c, e), U1(b, c))
28.36/9.18	   A^2 -> H(U1(c, e), U1(b, d))
28.36/9.18	   A^2 -> H(U1(c, e), U1(c, c))
28.36/9.18	   A^2 -> H(U1(c, e), f(e))
28.36/9.18	   A^2 -> H(U1(c, e), f(k))
28.36/9.18	   A^2 -> H(U1(c, e), U1(d, d))
28.36/9.18	   A^2 -> H(U1(c, k), U1(c, b))
28.36/9.18	   A^2 -> H(U1(c, k), U1(d, b))
28.36/9.18	   A^2 -> H(U1(c, k), U1(b, c))
28.36/9.18	   A^2 -> H(U1(c, k), U1(b, d))
28.36/9.18	   A^2 -> H(U1(c, k), U1(c, c))
28.36/9.18	   A^2 -> H(U1(c, k), f(e))
28.36/9.18	   A^2 -> H(U1(c, k), f(k))
28.36/9.18	   A^2 -> H(U1(c, k), U1(d, d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(e, b))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, b))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(d, c))
28.36/9.18	   A^2 -> H(U1(c, c), U1(b, e))
28.36/9.18	   A^2 -> H(U1(c, c), U1(b, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(e, e))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(d, k))
28.36/9.18	   A^2 -> H(e, U1(b, b))
28.36/9.18	   A^2 -> H(e, f(c))
28.36/9.18	   A^2 -> H(e, f(d))
28.36/9.18	   A^2 -> H(U1(e, e), U1(c, b))
28.36/9.18	   A^2 -> H(U1(e, e), U1(d, b))
28.36/9.18	   A^2 -> H(U1(e, e), U1(b, c))
28.36/9.18	   A^2 -> H(U1(e, e), U1(b, d))
28.36/9.18	   A^2 -> H(U1(e, e), U1(c, c))
28.36/9.18	   A^2 -> H(U1(e, e), f(e))
28.36/9.18	   A^2 -> H(U1(e, e), f(k))
28.36/9.18	   A^2 -> H(U1(e, e), U1(d, d))
28.36/9.18	   A^2 -> H(f(e), U1(e, b))
28.36/9.18	   A^2 -> H(f(e), U1(k, b))
28.36/9.18	   A^2 -> H(f(e), U1(c, d))
28.36/9.18	   A^2 -> H(f(e), U1(d, c))
28.36/9.18	   A^2 -> H(f(e), U1(b, e))
28.36/9.18	   A^2 -> H(f(e), U1(b, k))
28.36/9.18	   A^2 -> H(f(e), U1(e, c))
28.36/9.18	   A^2 -> H(f(e), U1(k, c))
28.36/9.18	   A^2 -> H(f(e), U1(c, e))
28.36/9.18	   A^2 -> H(f(e), U1(c, k))
28.36/9.18	   A^2 -> H(f(e), U1(k, k))
28.36/9.18	   A^2 -> H(f(e), U1(k, d))
28.36/9.18	   A^2 -> H(f(e), U1(d, k))
28.36/9.18	   A^2 -> H(U1(k, k), U1(c, b))
28.36/9.18	   A^2 -> H(U1(k, k), U1(d, b))
28.36/9.18	   A^2 -> H(U1(k, k), U1(b, c))
28.36/9.18	   A^2 -> H(U1(k, k), U1(b, d))
28.36/9.18	   A^2 -> H(U1(k, k), U1(c, c))
28.36/9.18	   A^2 -> H(U1(k, k), f(e))
28.36/9.18	   A^2 -> H(U1(k, k), f(k))
28.36/9.18	   A^2 -> H(U1(k, k), U1(d, d))
28.36/9.18	   A^2 -> H(f(k), U1(e, b))
28.36/9.18	   A^2 -> H(f(k), U1(k, b))
28.36/9.18	   A^2 -> H(f(k), U1(c, d))
28.36/9.18	   A^2 -> H(f(k), U1(d, c))
28.36/9.18	   A^2 -> H(f(k), U1(b, e))
28.36/9.18	   A^2 -> H(f(k), U1(b, k))
28.36/9.18	   A^2 -> H(f(k), U1(e, c))
28.36/9.18	   A^2 -> H(f(k), U1(k, c))
28.36/9.18	   A^2 -> H(f(k), U1(c, e))
28.36/9.18	   A^2 -> H(f(k), U1(c, k))
28.36/9.18	   A^2 -> H(f(k), U1(e, e))
28.36/9.18	   A^2 -> H(f(k), U1(k, d))
28.36/9.18	   A^2 -> H(f(k), U1(d, k))
28.36/9.18	   A^2 -> H(f(c), b)
28.36/9.18	   A^2 -> H(f(c), U1(e, d))
28.36/9.18	   A^2 -> H(f(c), U1(d, e))
28.36/9.18	   A^2 -> H(f(k), U1(k, k))
28.36/9.18	   A^2 -> H(U1(k, k), U1(b, b))
28.36/9.18	   A^2 -> H(U1(k, k), f(c))
28.36/9.18	   A^2 -> H(U1(k, k), f(d))
28.36/9.18	   A^2 -> H(U1(k, d), U1(c, b))
28.36/9.18	   A^2 -> H(U1(k, d), U1(d, b))
28.36/9.18	   A^2 -> H(U1(k, d), U1(b, c))
28.36/9.18	   A^2 -> H(U1(k, d), U1(b, d))
28.36/9.18	   A^2 -> H(U1(k, d), U1(c, c))
28.36/9.18	   A^2 -> H(U1(k, d), f(e))
28.36/9.18	   A^2 -> H(U1(k, d), f(k))
28.36/9.18	   A^2 -> H(U1(k, d), U1(d, d))
28.36/9.18	   A^2 -> H(U1(d, k), U1(c, b))
28.36/9.18	   A^2 -> H(U1(d, k), U1(d, b))
28.36/9.18	   A^2 -> H(U1(d, k), U1(b, c))
28.36/9.18	   A^2 -> H(U1(d, k), U1(b, d))
28.36/9.18	   A^2 -> H(U1(d, k), U1(c, c))
28.36/9.18	   A^2 -> H(U1(d, k), f(e))
28.36/9.18	   A^2 -> H(U1(d, k), f(k))
28.36/9.18	   A^2 -> H(U1(d, k), U1(d, d))
28.36/9.18	   A^2 -> H(U1(d, d), U1(e, b))
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, b))
28.36/9.18	   A^2 -> H(U1(d, d), U1(c, d))
28.36/9.18	   A^2 -> H(U1(d, d), U1(d, c))
28.36/9.18	   A^2 -> H(U1(d, d), U1(b, e))
28.36/9.18	   A^2 -> H(U1(d, d), U1(b, k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(e, c))
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, c))
28.36/9.18	   A^2 -> H(U1(d, d), U1(c, e))
28.36/9.18	   A^2 -> H(U1(d, d), U1(c, k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(e, e))
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, k))
28.36/9.18	   A^2 -> H(f(d), b)
28.36/9.18	   A^2 -> H(f(d), U1(e, d))
28.36/9.18	   A^2 -> H(f(d), U1(d, e))
28.36/9.18	   A^2 -> H(f(d), c)
28.36/9.18	   A^2 -> H(f(d), U1(e, k))
28.36/9.18	   A^2 -> H(f(d), U1(k, e))
28.36/9.18	   A^2 -> H(f(d), e)
28.36/9.18	   A^2 -> H(f(a), d)
28.36/9.18	   A^2 -> H(U1(c, c), U1(e, c))
28.36/9.18	   A^2 -> H(f(c), c)
28.36/9.18	   A^2 -> H(f(c), U1(e, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, c))
28.36/9.18	   A^2 -> H(f(c), U1(k, e))
28.36/9.18	   A^2 -> H(f(c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, e))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, k))
28.36/9.18	   A^2 -> H(f(a), k)
28.36/9.18	   A^2 -> H(f(e), U1(e, e))
28.36/9.18	   A^2 -> H(f(c), e)
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, d))
28.36/9.18	   A^2 -> H(f(d), U1(k, k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(d, k))
28.36/9.18	   A^2 -> H(d, U1(b, b))
28.36/9.18	   A^2 -> H(d, f(c))
28.36/9.18	   A^2 -> H(d, f(d))
28.36/9.18	   A^2 -> H(a, U1(c, b))
28.36/9.18	   A^2 -> H(a, U1(d, b))
28.36/9.18	   A^2 -> H(a, U1(b, c))
28.36/9.18	   A^2 -> H(a, U1(b, d))
28.36/9.18	   A^2 -> H(a, U1(c, c))
28.36/9.18	   A^2 -> H(a, f(e))
28.36/9.18	   A^2 -> H(a, f(k))
28.36/9.18	   A^2 -> H(a, U1(d, d))
28.36/9.18	   A^2 -> H(U1(e, d), U1(c, b))
28.36/9.18	   A^2 -> H(U1(e, d), U1(d, b))
28.36/9.18	   A^2 -> H(U1(e, d), U1(b, c))
28.36/9.18	   A^2 -> H(U1(e, d), U1(b, d))
28.36/9.18	   A^2 -> H(U1(e, d), U1(c, c))
28.36/9.18	   A^2 -> H(U1(e, d), f(e))
28.36/9.18	   A^2 -> H(U1(e, d), f(k))
28.36/9.18	   A^2 -> H(U1(e, d), U1(d, d))
28.36/9.18	   A^2 -> H(U1(e, a), U1(e, b))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, b))
28.36/9.18	   A^2 -> H(U1(e, a), U1(c, d))
28.36/9.18	   A^2 -> H(U1(e, a), U1(d, c))
28.36/9.18	   A^2 -> H(U1(e, a), U1(b, e))
28.36/9.18	   A^2 -> H(U1(e, a), U1(b, k))
28.36/9.18	   A^2 -> H(U1(e, a), U1(e, c))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, c))
28.36/9.18	   A^2 -> H(U1(e, a), U1(c, e))
28.36/9.18	   A^2 -> H(U1(e, a), U1(c, k))
28.36/9.18	   A^2 -> H(U1(e, a), U1(e, e))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, d))
28.36/9.18	   A^2 -> H(U1(e, a), U1(d, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(e, b))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, b))
28.36/9.18	   A^2 -> H(U1(k, a), U1(c, d))
28.36/9.18	   A^2 -> H(U1(k, a), U1(d, c))
28.36/9.18	   A^2 -> H(U1(k, a), U1(b, e))
28.36/9.18	   A^2 -> H(U1(k, a), U1(b, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(e, c))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, c))
28.36/9.18	   A^2 -> H(U1(k, a), U1(c, e))
28.36/9.18	   A^2 -> H(U1(k, a), U1(c, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(e, e))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, d))
28.36/9.18	   A^2 -> H(U1(k, a), U1(d, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(e, b))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, b))
28.36/9.18	   A^2 -> H(U1(c, d), U1(c, d))
28.36/9.18	   A^2 -> H(U1(c, d), U1(d, c))
28.36/9.18	   A^2 -> H(U1(c, d), U1(b, e))
28.36/9.18	   A^2 -> H(U1(c, d), U1(b, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(e, c))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, c))
28.36/9.18	   A^2 -> H(U1(c, d), U1(c, e))
28.36/9.18	   A^2 -> H(U1(c, d), U1(c, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(e, e))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, d))
28.36/9.18	   A^2 -> H(U1(c, d), U1(d, k))
28.36/9.18	   A^2 -> H(U1(c, a), b)
28.36/9.18	   A^2 -> H(U1(c, a), U1(e, d))
28.36/9.18	   A^2 -> H(U1(c, a), U1(d, e))
28.36/9.18	   A^2 -> H(U1(c, a), c)
28.36/9.18	   A^2 -> H(U1(c, a), U1(e, k))
28.36/9.18	   A^2 -> H(U1(c, a), U1(k, e))
28.36/9.18	   A^2 -> H(U1(c, a), e)
28.36/9.18	   A^2 -> H(U1(c, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(d, e), U1(c, b))
28.36/9.18	   A^2 -> H(U1(d, e), U1(d, b))
28.36/9.18	   A^2 -> H(U1(d, e), U1(b, c))
28.36/9.18	   A^2 -> H(U1(d, e), U1(b, d))
28.36/9.18	   A^2 -> H(U1(d, e), U1(c, c))
28.36/9.18	   A^2 -> H(U1(d, e), f(e))
28.36/9.18	   A^2 -> H(U1(d, e), f(k))
28.36/9.18	   A^2 -> H(U1(d, e), U1(d, d))
28.36/9.18	   A^2 -> H(U1(d, c), U1(e, b))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, b))
28.36/9.18	   A^2 -> H(U1(d, c), U1(c, d))
28.36/9.18	   A^2 -> H(U1(d, c), U1(d, c))
28.36/9.18	   A^2 -> H(U1(d, c), U1(b, e))
28.36/9.18	   A^2 -> H(U1(d, c), U1(b, k))
28.36/9.18	   A^2 -> H(U1(d, c), U1(e, c))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, c))
28.36/9.18	   A^2 -> H(U1(d, c), U1(c, e))
28.36/9.18	   A^2 -> H(U1(d, c), U1(c, k))
28.36/9.18	   A^2 -> H(U1(d, c), U1(e, e))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, d))
28.36/9.18	   A^2 -> H(U1(d, c), U1(d, k))
28.36/9.18	   A^2 -> H(U1(d, a), b)
28.36/9.18	   A^2 -> H(U1(d, a), U1(e, d))
28.36/9.18	   A^2 -> H(U1(d, a), U1(d, e))
28.36/9.18	   A^2 -> H(U1(d, a), c)
28.36/9.18	   A^2 -> H(U1(d, a), U1(e, k))
28.36/9.18	   A^2 -> H(U1(d, a), U1(k, e))
28.36/9.18	   A^2 -> H(U1(d, a), e)
28.36/9.18	   A^2 -> H(U1(d, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(e, b))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, b))
28.36/9.18	   A^2 -> H(U1(a, e), U1(c, d))
28.36/9.18	   A^2 -> H(U1(a, e), U1(d, c))
28.36/9.18	   A^2 -> H(U1(a, e), U1(b, e))
28.36/9.18	   A^2 -> H(U1(a, e), U1(b, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(e, c))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, c))
28.36/9.18	   A^2 -> H(U1(a, e), U1(c, e))
28.36/9.18	   A^2 -> H(U1(a, e), U1(c, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(e, e))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, d))
28.36/9.18	   A^2 -> H(U1(a, e), U1(d, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(e, b))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, b))
28.36/9.18	   A^2 -> H(U1(a, k), U1(c, d))
28.36/9.18	   A^2 -> H(U1(a, k), U1(d, c))
28.36/9.18	   A^2 -> H(U1(a, k), U1(b, e))
28.36/9.18	   A^2 -> H(U1(a, k), U1(b, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(e, c))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, c))
28.36/9.18	   A^2 -> H(U1(a, k), U1(c, e))
28.36/9.18	   A^2 -> H(U1(a, k), U1(c, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(e, e))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, d))
28.36/9.18	   A^2 -> H(U1(a, k), U1(d, k))
28.36/9.18	   A^2 -> H(U1(a, c), b)
28.36/9.18	   A^2 -> H(U1(a, c), U1(e, d))
28.36/9.18	   A^2 -> H(U1(a, c), U1(d, e))
28.36/9.18	   A^2 -> H(U1(a, c), c)
28.36/9.18	   A^2 -> H(U1(a, c), U1(e, k))
28.36/9.18	   A^2 -> H(U1(a, c), U1(k, e))
28.36/9.18	   A^2 -> H(U1(a, c), e)
28.36/9.18	   A^2 -> H(U1(a, c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, d), b)
28.36/9.18	   A^2 -> H(U1(a, d), U1(e, d))
28.36/9.18	   A^2 -> H(U1(a, d), U1(d, e))
28.36/9.18	   A^2 -> H(U1(a, d), c)
28.36/9.18	   A^2 -> H(U1(a, d), U1(e, k))
28.36/9.18	   A^2 -> H(U1(a, d), U1(k, e))
28.36/9.18	   A^2 -> H(U1(a, d), e)
28.36/9.18	   A^2 -> H(U1(a, d), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, a), d)
28.36/9.18	   A^2 -> H(U1(a, a), k)
28.36/9.18	   A^2 -> H(k, U1(b, b))
28.36/9.18	   A^2 -> H(k, f(c))
28.36/9.18	   A^2 -> H(k, f(d))
28.36/9.18	   A^2 -> H(c, U1(c, b))
28.36/9.18	   A^2 -> H(c, U1(d, b))
28.36/9.18	   A^2 -> H(c, U1(b, c))
28.36/9.18	   A^2 -> H(c, U1(b, d))
28.36/9.18	   A^2 -> H(c, U1(c, c))
28.36/9.18	   A^2 -> H(c, f(e))
28.36/9.18	   A^2 -> H(c, f(k))
28.36/9.18	
28.36/9.18	The TRS R consists of the following rules:
28.36/9.18	
28.36/9.18	   f(x) -> U1(x, x)
28.36/9.18	   U1(e, x) -> x
28.36/9.18	   a -> c
28.36/9.18	   a -> d
28.36/9.18	   b -> c
28.36/9.18	   b -> d
28.36/9.18	   d -> k
28.36/9.18	   c -> e
28.36/9.18	   c -> k
28.36/9.18	
28.36/9.18	Q is empty.
28.36/9.18	We have to consider all minimal (P,Q,R)-chains.
28.36/9.18	----------------------------------------
28.36/9.18	
28.36/9.18	(791) TransformationProof (EQUIVALENT)
28.36/9.18	By narrowing [LPAR04] the rule A^2 -> H(c, f(d)) at position [] we obtained the following new rules [LPAR04]:
28.36/9.18	
28.36/9.18	   (A^2 -> H(e, f(d)),A^2 -> H(e, f(d)))
28.36/9.18	   (A^2 -> H(k, f(d)),A^2 -> H(k, f(d)))
28.36/9.18	   (A^2 -> H(c, U1(d, d)),A^2 -> H(c, U1(d, d)))
28.36/9.18	   (A^2 -> H(c, f(k)),A^2 -> H(c, f(k)))
28.36/9.18	
28.36/9.18	
28.36/9.18	----------------------------------------
28.36/9.18	
28.36/9.18	(792)
28.36/9.18	Obligation:
28.36/9.18	Q DP problem:
28.36/9.18	The TRS P consists of the following rules:
28.36/9.18	
28.36/9.18	   H(x, x) -> G(x, x, f(k))
28.36/9.18	   G(d, x, x) -> A^2
28.36/9.18	   A^2 -> H(f(c), f(c))
28.36/9.18	   A^2 -> H(f(d), f(d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, c))
28.36/9.18	   A^2 -> H(f(e), f(e))
28.36/9.18	   A^2 -> H(f(k), f(k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(d, d))
28.36/9.18	   A^2 -> H(U1(e, k), U1(b, b))
28.36/9.18	   A^2 -> H(U1(e, k), f(c))
28.36/9.18	   A^2 -> H(U1(e, k), f(d))
28.36/9.18	   A^2 -> H(U1(e, c), U1(c, b))
28.36/9.18	   A^2 -> H(U1(e, c), U1(d, b))
28.36/9.18	   A^2 -> H(U1(e, c), U1(b, c))
28.36/9.18	   A^2 -> H(U1(e, c), U1(b, d))
28.36/9.18	   A^2 -> H(U1(e, c), U1(c, c))
28.36/9.18	   A^2 -> H(U1(e, c), f(e))
28.36/9.18	   A^2 -> H(U1(e, c), f(k))
28.36/9.18	   A^2 -> H(U1(e, c), U1(d, d))
28.36/9.18	   A^2 -> H(U1(k, e), U1(b, b))
28.36/9.18	   A^2 -> H(U1(k, e), f(c))
28.36/9.18	   A^2 -> H(U1(k, e), f(d))
28.36/9.18	   A^2 -> H(U1(k, c), U1(c, b))
28.36/9.18	   A^2 -> H(U1(k, c), U1(d, b))
28.36/9.18	   A^2 -> H(U1(k, c), U1(b, c))
28.36/9.18	   A^2 -> H(U1(k, c), U1(b, d))
28.36/9.18	   A^2 -> H(U1(k, c), U1(c, c))
28.36/9.18	   A^2 -> H(U1(k, c), f(e))
28.36/9.18	   A^2 -> H(U1(k, c), f(k))
28.36/9.18	   A^2 -> H(U1(k, c), U1(d, d))
28.36/9.18	   A^2 -> H(U1(c, e), U1(c, b))
28.36/9.18	   A^2 -> H(U1(c, e), U1(d, b))
28.36/9.18	   A^2 -> H(U1(c, e), U1(b, c))
28.36/9.18	   A^2 -> H(U1(c, e), U1(b, d))
28.36/9.18	   A^2 -> H(U1(c, e), U1(c, c))
28.36/9.18	   A^2 -> H(U1(c, e), f(e))
28.36/9.18	   A^2 -> H(U1(c, e), f(k))
28.36/9.18	   A^2 -> H(U1(c, e), U1(d, d))
28.36/9.18	   A^2 -> H(U1(c, k), U1(c, b))
28.36/9.18	   A^2 -> H(U1(c, k), U1(d, b))
28.36/9.18	   A^2 -> H(U1(c, k), U1(b, c))
28.36/9.18	   A^2 -> H(U1(c, k), U1(b, d))
28.36/9.18	   A^2 -> H(U1(c, k), U1(c, c))
28.36/9.18	   A^2 -> H(U1(c, k), f(e))
28.36/9.18	   A^2 -> H(U1(c, k), f(k))
28.36/9.18	   A^2 -> H(U1(c, k), U1(d, d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(e, b))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, b))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(d, c))
28.36/9.18	   A^2 -> H(U1(c, c), U1(b, e))
28.36/9.18	   A^2 -> H(U1(c, c), U1(b, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(e, e))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(d, k))
28.36/9.18	   A^2 -> H(e, U1(b, b))
28.36/9.18	   A^2 -> H(e, f(c))
28.36/9.18	   A^2 -> H(e, f(d))
28.36/9.18	   A^2 -> H(U1(e, e), U1(c, b))
28.36/9.18	   A^2 -> H(U1(e, e), U1(d, b))
28.36/9.18	   A^2 -> H(U1(e, e), U1(b, c))
28.36/9.18	   A^2 -> H(U1(e, e), U1(b, d))
28.36/9.18	   A^2 -> H(U1(e, e), U1(c, c))
28.36/9.18	   A^2 -> H(U1(e, e), f(e))
28.36/9.18	   A^2 -> H(U1(e, e), f(k))
28.36/9.18	   A^2 -> H(U1(e, e), U1(d, d))
28.36/9.18	   A^2 -> H(f(e), U1(e, b))
28.36/9.18	   A^2 -> H(f(e), U1(k, b))
28.36/9.18	   A^2 -> H(f(e), U1(c, d))
28.36/9.18	   A^2 -> H(f(e), U1(d, c))
28.36/9.18	   A^2 -> H(f(e), U1(b, e))
28.36/9.18	   A^2 -> H(f(e), U1(b, k))
28.36/9.18	   A^2 -> H(f(e), U1(e, c))
28.36/9.18	   A^2 -> H(f(e), U1(k, c))
28.36/9.18	   A^2 -> H(f(e), U1(c, e))
28.36/9.18	   A^2 -> H(f(e), U1(c, k))
28.36/9.18	   A^2 -> H(f(e), U1(k, k))
28.36/9.18	   A^2 -> H(f(e), U1(k, d))
28.36/9.18	   A^2 -> H(f(e), U1(d, k))
28.36/9.18	   A^2 -> H(U1(k, k), U1(c, b))
28.36/9.18	   A^2 -> H(U1(k, k), U1(d, b))
28.36/9.18	   A^2 -> H(U1(k, k), U1(b, c))
28.36/9.18	   A^2 -> H(U1(k, k), U1(b, d))
28.36/9.18	   A^2 -> H(U1(k, k), U1(c, c))
28.36/9.18	   A^2 -> H(U1(k, k), f(e))
28.36/9.18	   A^2 -> H(U1(k, k), f(k))
28.36/9.18	   A^2 -> H(U1(k, k), U1(d, d))
28.36/9.18	   A^2 -> H(f(k), U1(e, b))
28.36/9.18	   A^2 -> H(f(k), U1(k, b))
28.36/9.18	   A^2 -> H(f(k), U1(c, d))
28.36/9.18	   A^2 -> H(f(k), U1(d, c))
28.36/9.18	   A^2 -> H(f(k), U1(b, e))
28.36/9.18	   A^2 -> H(f(k), U1(b, k))
28.36/9.18	   A^2 -> H(f(k), U1(e, c))
28.36/9.18	   A^2 -> H(f(k), U1(k, c))
28.36/9.18	   A^2 -> H(f(k), U1(c, e))
28.36/9.18	   A^2 -> H(f(k), U1(c, k))
28.36/9.18	   A^2 -> H(f(k), U1(e, e))
28.36/9.18	   A^2 -> H(f(k), U1(k, d))
28.36/9.18	   A^2 -> H(f(k), U1(d, k))
28.36/9.18	   A^2 -> H(f(c), b)
28.36/9.18	   A^2 -> H(f(c), U1(e, d))
28.36/9.18	   A^2 -> H(f(c), U1(d, e))
28.36/9.18	   A^2 -> H(f(k), U1(k, k))
28.36/9.18	   A^2 -> H(U1(k, k), U1(b, b))
28.36/9.18	   A^2 -> H(U1(k, k), f(c))
28.36/9.18	   A^2 -> H(U1(k, k), f(d))
28.36/9.18	   A^2 -> H(U1(k, d), U1(c, b))
28.36/9.18	   A^2 -> H(U1(k, d), U1(d, b))
28.36/9.18	   A^2 -> H(U1(k, d), U1(b, c))
28.36/9.18	   A^2 -> H(U1(k, d), U1(b, d))
28.36/9.18	   A^2 -> H(U1(k, d), U1(c, c))
28.36/9.18	   A^2 -> H(U1(k, d), f(e))
28.36/9.18	   A^2 -> H(U1(k, d), f(k))
28.36/9.18	   A^2 -> H(U1(k, d), U1(d, d))
28.36/9.18	   A^2 -> H(U1(d, k), U1(c, b))
28.36/9.18	   A^2 -> H(U1(d, k), U1(d, b))
28.36/9.18	   A^2 -> H(U1(d, k), U1(b, c))
28.36/9.18	   A^2 -> H(U1(d, k), U1(b, d))
28.36/9.18	   A^2 -> H(U1(d, k), U1(c, c))
28.36/9.18	   A^2 -> H(U1(d, k), f(e))
28.36/9.18	   A^2 -> H(U1(d, k), f(k))
28.36/9.18	   A^2 -> H(U1(d, k), U1(d, d))
28.36/9.18	   A^2 -> H(U1(d, d), U1(e, b))
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, b))
28.36/9.18	   A^2 -> H(U1(d, d), U1(c, d))
28.36/9.18	   A^2 -> H(U1(d, d), U1(d, c))
28.36/9.18	   A^2 -> H(U1(d, d), U1(b, e))
28.36/9.18	   A^2 -> H(U1(d, d), U1(b, k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(e, c))
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, c))
28.36/9.18	   A^2 -> H(U1(d, d), U1(c, e))
28.36/9.18	   A^2 -> H(U1(d, d), U1(c, k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(e, e))
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, k))
28.36/9.18	   A^2 -> H(f(d), b)
28.36/9.18	   A^2 -> H(f(d), U1(e, d))
28.36/9.18	   A^2 -> H(f(d), U1(d, e))
28.36/9.18	   A^2 -> H(f(d), c)
28.36/9.18	   A^2 -> H(f(d), U1(e, k))
28.36/9.18	   A^2 -> H(f(d), U1(k, e))
28.36/9.18	   A^2 -> H(f(d), e)
28.36/9.18	   A^2 -> H(f(a), d)
28.36/9.18	   A^2 -> H(U1(c, c), U1(e, c))
28.36/9.18	   A^2 -> H(f(c), c)
28.36/9.18	   A^2 -> H(f(c), U1(e, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, c))
28.36/9.18	   A^2 -> H(f(c), U1(k, e))
28.36/9.18	   A^2 -> H(f(c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, e))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, k))
28.36/9.18	   A^2 -> H(f(a), k)
28.36/9.18	   A^2 -> H(f(e), U1(e, e))
28.36/9.18	   A^2 -> H(f(c), e)
28.36/9.18	   A^2 -> H(U1(d, d), U1(k, d))
28.36/9.18	   A^2 -> H(f(d), U1(k, k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(d, k))
28.36/9.18	   A^2 -> H(d, U1(b, b))
28.36/9.18	   A^2 -> H(d, f(c))
28.36/9.18	   A^2 -> H(d, f(d))
28.36/9.18	   A^2 -> H(a, U1(c, b))
28.36/9.18	   A^2 -> H(a, U1(d, b))
28.36/9.18	   A^2 -> H(a, U1(b, c))
28.36/9.18	   A^2 -> H(a, U1(b, d))
28.36/9.18	   A^2 -> H(a, U1(c, c))
28.36/9.18	   A^2 -> H(a, f(e))
28.36/9.18	   A^2 -> H(a, f(k))
28.36/9.18	   A^2 -> H(a, U1(d, d))
28.36/9.18	   A^2 -> H(U1(e, d), U1(c, b))
28.36/9.18	   A^2 -> H(U1(e, d), U1(d, b))
28.36/9.18	   A^2 -> H(U1(e, d), U1(b, c))
28.36/9.18	   A^2 -> H(U1(e, d), U1(b, d))
28.36/9.18	   A^2 -> H(U1(e, d), U1(c, c))
28.36/9.18	   A^2 -> H(U1(e, d), f(e))
28.36/9.18	   A^2 -> H(U1(e, d), f(k))
28.36/9.18	   A^2 -> H(U1(e, d), U1(d, d))
28.36/9.18	   A^2 -> H(U1(e, a), U1(e, b))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, b))
28.36/9.18	   A^2 -> H(U1(e, a), U1(c, d))
28.36/9.18	   A^2 -> H(U1(e, a), U1(d, c))
28.36/9.18	   A^2 -> H(U1(e, a), U1(b, e))
28.36/9.18	   A^2 -> H(U1(e, a), U1(b, k))
28.36/9.18	   A^2 -> H(U1(e, a), U1(e, c))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, c))
28.36/9.18	   A^2 -> H(U1(e, a), U1(c, e))
28.36/9.18	   A^2 -> H(U1(e, a), U1(c, k))
28.36/9.18	   A^2 -> H(U1(e, a), U1(e, e))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(e, a), U1(k, d))
28.36/9.18	   A^2 -> H(U1(e, a), U1(d, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(e, b))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, b))
28.36/9.18	   A^2 -> H(U1(k, a), U1(c, d))
28.36/9.18	   A^2 -> H(U1(k, a), U1(d, c))
28.36/9.18	   A^2 -> H(U1(k, a), U1(b, e))
28.36/9.18	   A^2 -> H(U1(k, a), U1(b, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(e, c))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, c))
28.36/9.18	   A^2 -> H(U1(k, a), U1(c, e))
28.36/9.18	   A^2 -> H(U1(k, a), U1(c, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(e, e))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(k, a), U1(k, d))
28.36/9.18	   A^2 -> H(U1(k, a), U1(d, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(e, b))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, b))
28.36/9.18	   A^2 -> H(U1(c, d), U1(c, d))
28.36/9.18	   A^2 -> H(U1(c, d), U1(d, c))
28.36/9.18	   A^2 -> H(U1(c, d), U1(b, e))
28.36/9.18	   A^2 -> H(U1(c, d), U1(b, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(e, c))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, c))
28.36/9.18	   A^2 -> H(U1(c, d), U1(c, e))
28.36/9.18	   A^2 -> H(U1(c, d), U1(c, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(e, e))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, k))
28.36/9.18	   A^2 -> H(U1(c, d), U1(k, d))
28.36/9.18	   A^2 -> H(U1(c, d), U1(d, k))
28.36/9.18	   A^2 -> H(U1(c, a), b)
28.36/9.18	   A^2 -> H(U1(c, a), U1(e, d))
28.36/9.18	   A^2 -> H(U1(c, a), U1(d, e))
28.36/9.18	   A^2 -> H(U1(c, a), c)
28.36/9.18	   A^2 -> H(U1(c, a), U1(e, k))
28.36/9.18	   A^2 -> H(U1(c, a), U1(k, e))
28.36/9.18	   A^2 -> H(U1(c, a), e)
28.36/9.18	   A^2 -> H(U1(c, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(d, e), U1(c, b))
28.36/9.18	   A^2 -> H(U1(d, e), U1(d, b))
28.36/9.18	   A^2 -> H(U1(d, e), U1(b, c))
28.36/9.18	   A^2 -> H(U1(d, e), U1(b, d))
28.36/9.18	   A^2 -> H(U1(d, e), U1(c, c))
28.36/9.18	   A^2 -> H(U1(d, e), f(e))
28.36/9.18	   A^2 -> H(U1(d, e), f(k))
28.36/9.18	   A^2 -> H(U1(d, e), U1(d, d))
28.36/9.18	   A^2 -> H(U1(d, c), U1(e, b))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, b))
28.36/9.18	   A^2 -> H(U1(d, c), U1(c, d))
28.36/9.18	   A^2 -> H(U1(d, c), U1(d, c))
28.36/9.18	   A^2 -> H(U1(d, c), U1(b, e))
28.36/9.18	   A^2 -> H(U1(d, c), U1(b, k))
28.36/9.18	   A^2 -> H(U1(d, c), U1(e, c))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, c))
28.36/9.18	   A^2 -> H(U1(d, c), U1(c, e))
28.36/9.18	   A^2 -> H(U1(d, c), U1(c, k))
28.36/9.18	   A^2 -> H(U1(d, c), U1(e, e))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(d, c), U1(k, d))
28.36/9.18	   A^2 -> H(U1(d, c), U1(d, k))
28.36/9.18	   A^2 -> H(U1(d, a), b)
28.36/9.18	   A^2 -> H(U1(d, a), U1(e, d))
28.36/9.18	   A^2 -> H(U1(d, a), U1(d, e))
28.36/9.18	   A^2 -> H(U1(d, a), c)
28.36/9.18	   A^2 -> H(U1(d, a), U1(e, k))
28.36/9.18	   A^2 -> H(U1(d, a), U1(k, e))
28.36/9.18	   A^2 -> H(U1(d, a), e)
28.36/9.18	   A^2 -> H(U1(d, a), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(e, b))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, b))
28.36/9.18	   A^2 -> H(U1(a, e), U1(c, d))
28.36/9.18	   A^2 -> H(U1(a, e), U1(d, c))
28.36/9.18	   A^2 -> H(U1(a, e), U1(b, e))
28.36/9.18	   A^2 -> H(U1(a, e), U1(b, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(e, c))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, c))
28.36/9.18	   A^2 -> H(U1(a, e), U1(c, e))
28.36/9.18	   A^2 -> H(U1(a, e), U1(c, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(e, e))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, e), U1(k, d))
28.36/9.18	   A^2 -> H(U1(a, e), U1(d, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(e, b))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, b))
28.36/9.18	   A^2 -> H(U1(a, k), U1(c, d))
28.36/9.18	   A^2 -> H(U1(a, k), U1(d, c))
28.36/9.18	   A^2 -> H(U1(a, k), U1(b, e))
28.36/9.18	   A^2 -> H(U1(a, k), U1(b, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(e, c))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, c))
28.36/9.18	   A^2 -> H(U1(a, k), U1(c, e))
28.36/9.18	   A^2 -> H(U1(a, k), U1(c, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(e, e))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, k), U1(k, d))
28.36/9.18	   A^2 -> H(U1(a, k), U1(d, k))
28.36/9.18	   A^2 -> H(U1(a, c), b)
28.36/9.18	   A^2 -> H(U1(a, c), U1(e, d))
28.36/9.18	   A^2 -> H(U1(a, c), U1(d, e))
28.36/9.18	   A^2 -> H(U1(a, c), c)
28.36/9.18	   A^2 -> H(U1(a, c), U1(e, k))
28.36/9.18	   A^2 -> H(U1(a, c), U1(k, e))
28.36/9.18	   A^2 -> H(U1(a, c), e)
28.36/9.18	   A^2 -> H(U1(a, c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, d), b)
28.36/9.18	   A^2 -> H(U1(a, d), U1(e, d))
28.36/9.18	   A^2 -> H(U1(a, d), U1(d, e))
28.36/9.18	   A^2 -> H(U1(a, d), c)
28.36/9.18	   A^2 -> H(U1(a, d), U1(e, k))
28.36/9.18	   A^2 -> H(U1(a, d), U1(k, e))
28.36/9.18	   A^2 -> H(U1(a, d), e)
28.36/9.18	   A^2 -> H(U1(a, d), U1(k, k))
28.36/9.18	   A^2 -> H(U1(a, a), d)
28.36/9.18	   A^2 -> H(U1(a, a), k)
28.36/9.18	   A^2 -> H(k, U1(b, b))
28.36/9.18	   A^2 -> H(k, f(c))
28.36/9.18	   A^2 -> H(k, f(d))
28.36/9.18	   A^2 -> H(c, U1(c, b))
28.36/9.18	   A^2 -> H(c, U1(d, b))
28.36/9.18	   A^2 -> H(c, U1(b, c))
28.36/9.18	   A^2 -> H(c, U1(b, d))
28.36/9.18	   A^2 -> H(c, U1(c, c))
28.36/9.18	   A^2 -> H(c, f(e))
28.36/9.18	   A^2 -> H(c, f(k))
28.36/9.18	   A^2 -> H(c, U1(d, d))
28.36/9.18	
28.36/9.18	The TRS R consists of the following rules:
28.36/9.18	
28.36/9.18	   f(x) -> U1(x, x)
28.36/9.18	   U1(e, x) -> x
28.36/9.18	   a -> c
28.36/9.18	   a -> d
28.36/9.18	   b -> c
28.36/9.18	   b -> d
28.36/9.18	   d -> k
28.36/9.18	   c -> e
28.36/9.18	   c -> k
28.36/9.18	
28.36/9.18	Q is empty.
28.36/9.18	We have to consider all minimal (P,Q,R)-chains.
28.36/9.18	----------------------------------------
28.36/9.18	
28.36/9.18	(793) TransformationProof (EQUIVALENT)
28.36/9.18	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
28.36/9.18	
28.36/9.18	   (A^2 -> H(k, U1(b, b)),A^2 -> H(k, U1(b, b)))
28.36/9.18	   (A^2 -> H(U1(e, k), U1(c, b)),A^2 -> H(U1(e, k), U1(c, b)))
28.36/9.18	   (A^2 -> H(U1(e, k), U1(d, b)),A^2 -> H(U1(e, k), U1(d, b)))
28.36/9.18	   (A^2 -> H(U1(e, k), U1(b, c)),A^2 -> H(U1(e, k), U1(b, c)))
28.36/9.18	   (A^2 -> H(U1(e, k), U1(b, d)),A^2 -> H(U1(e, k), U1(b, d)))
28.36/9.18	
28.36/9.18	
28.36/9.18	----------------------------------------
28.36/9.18	
28.36/9.18	(794)
28.36/9.18	Obligation:
28.36/9.18	Q DP problem:
28.36/9.18	The TRS P consists of the following rules:
28.36/9.18	
28.36/9.18	   H(x, x) -> G(x, x, f(k))
28.36/9.18	   G(d, x, x) -> A^2
28.36/9.18	   A^2 -> H(f(c), f(c))
28.36/9.18	   A^2 -> H(f(d), f(d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, c))
28.36/9.18	   A^2 -> H(f(e), f(e))
28.36/9.18	   A^2 -> H(f(k), f(k))
28.36/9.18	   A^2 -> H(U1(d, d), U1(d, d))
28.36/9.18	   A^2 -> H(U1(e, k), f(c))
28.36/9.18	   A^2 -> H(U1(e, k), f(d))
28.36/9.18	   A^2 -> H(U1(e, c), U1(c, b))
28.36/9.18	   A^2 -> H(U1(e, c), U1(d, b))
28.36/9.18	   A^2 -> H(U1(e, c), U1(b, c))
28.36/9.18	   A^2 -> H(U1(e, c), U1(b, d))
28.36/9.18	   A^2 -> H(U1(e, c), U1(c, c))
28.36/9.18	   A^2 -> H(U1(e, c), f(e))
28.36/9.18	   A^2 -> H(U1(e, c), f(k))
28.36/9.18	   A^2 -> H(U1(e, c), U1(d, d))
28.36/9.18	   A^2 -> H(U1(k, e), U1(b, b))
28.36/9.18	   A^2 -> H(U1(k, e), f(c))
28.36/9.18	   A^2 -> H(U1(k, e), f(d))
28.36/9.18	   A^2 -> H(U1(k, c), U1(c, b))
28.36/9.18	   A^2 -> H(U1(k, c), U1(d, b))
28.36/9.18	   A^2 -> H(U1(k, c), U1(b, c))
28.36/9.18	   A^2 -> H(U1(k, c), U1(b, d))
28.36/9.18	   A^2 -> H(U1(k, c), U1(c, c))
28.36/9.18	   A^2 -> H(U1(k, c), f(e))
28.36/9.18	   A^2 -> H(U1(k, c), f(k))
28.36/9.18	   A^2 -> H(U1(k, c), U1(d, d))
28.36/9.18	   A^2 -> H(U1(c, e), U1(c, b))
28.36/9.18	   A^2 -> H(U1(c, e), U1(d, b))
28.36/9.18	   A^2 -> H(U1(c, e), U1(b, c))
28.36/9.18	   A^2 -> H(U1(c, e), U1(b, d))
28.36/9.18	   A^2 -> H(U1(c, e), U1(c, c))
28.36/9.18	   A^2 -> H(U1(c, e), f(e))
28.36/9.18	   A^2 -> H(U1(c, e), f(k))
28.36/9.18	   A^2 -> H(U1(c, e), U1(d, d))
28.36/9.18	   A^2 -> H(U1(c, k), U1(c, b))
28.36/9.18	   A^2 -> H(U1(c, k), U1(d, b))
28.36/9.18	   A^2 -> H(U1(c, k), U1(b, c))
28.36/9.18	   A^2 -> H(U1(c, k), U1(b, d))
28.36/9.18	   A^2 -> H(U1(c, k), U1(c, c))
28.36/9.18	   A^2 -> H(U1(c, k), f(e))
28.36/9.18	   A^2 -> H(U1(c, k), f(k))
28.36/9.18	   A^2 -> H(U1(c, k), U1(d, d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(e, b))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, b))
28.36/9.18	   A^2 -> H(U1(c, c), U1(c, d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(d, c))
28.36/9.18	   A^2 -> H(U1(c, c), U1(b, e))
28.36/9.18	   A^2 -> H(U1(c, c), U1(b, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(e, e))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, k))
28.36/9.18	   A^2 -> H(U1(c, c), U1(k, d))
28.36/9.18	   A^2 -> H(U1(c, c), U1(d, k))
28.36/9.18	   A^2 -> H(e, U1(b, b))
28.36/9.18	   A^2 -> H(e, f(c))
28.36/9.18	   A^2 -> H(e, f(d))
28.36/9.18	   A^2 -> H(U1(e, e), U1(c, b))
28.36/9.18	   A^2 -> H(U1(e, e), U1(d, b))
28.36/9.18	   A^2 -> H(U1(e, e), U1(b, c))
28.36/9.18	   A^2 -> H(U1(e, e), U1(b, d))
28.36/9.18	   A^2 -> H(U1(e, e), U1(c, c))
28.36/9.18	   A^2 -> H(U1(e, e), f(e))
28.36/9.18	   A^2 -> H(U1(e, e), f(k))
28.36/9.18	   A^2 -> H(U1(e, e), U1(d, d))
28.36/9.18	   A^2 -> H(f(e), U1(e, b))
28.36/9.18	   A^2 -> H(f(e), U1(k, b))
28.36/9.18	   A^2 -> H(f(e), U1(c, d))
28.36/9.18	   A^2 -> H(f(e), U1(d, c))
28.36/9.18	   A^2 -> H(f(e), U1(b, e))
28.36/9.18	   A^2 -> H(f(e), U1(b, k))
28.36/9.19	   A^2 -> H(f(e), U1(e, c))
28.36/9.19	   A^2 -> H(f(e), U1(k, c))
28.36/9.19	   A^2 -> H(f(e), U1(c, e))
28.36/9.19	   A^2 -> H(f(e), U1(c, k))
28.36/9.19	   A^2 -> H(f(e), U1(k, k))
28.36/9.19	   A^2 -> H(f(e), U1(k, d))
28.36/9.19	   A^2 -> H(f(e), U1(d, k))
28.36/9.19	   A^2 -> H(U1(k, k), U1(c, b))
28.36/9.19	   A^2 -> H(U1(k, k), U1(d, b))
28.36/9.19	   A^2 -> H(U1(k, k), U1(b, c))
28.36/9.19	   A^2 -> H(U1(k, k), U1(b, d))
28.36/9.19	   A^2 -> H(U1(k, k), U1(c, c))
28.36/9.19	   A^2 -> H(U1(k, k), f(e))
28.36/9.19	   A^2 -> H(U1(k, k), f(k))
28.36/9.19	   A^2 -> H(U1(k, k), U1(d, d))
28.36/9.19	   A^2 -> H(f(k), U1(e, b))
28.36/9.19	   A^2 -> H(f(k), U1(k, b))
28.36/9.19	   A^2 -> H(f(k), U1(c, d))
28.36/9.19	   A^2 -> H(f(k), U1(d, c))
28.36/9.19	   A^2 -> H(f(k), U1(b, e))
28.36/9.19	   A^2 -> H(f(k), U1(b, k))
28.36/9.19	   A^2 -> H(f(k), U1(e, c))
28.36/9.19	   A^2 -> H(f(k), U1(k, c))
28.36/9.19	   A^2 -> H(f(k), U1(c, e))
28.36/9.19	   A^2 -> H(f(k), U1(c, k))
28.36/9.19	   A^2 -> H(f(k), U1(e, e))
28.36/9.19	   A^2 -> H(f(k), U1(k, d))
28.36/9.19	   A^2 -> H(f(k), U1(d, k))
28.36/9.19	   A^2 -> H(f(c), b)
28.36/9.19	   A^2 -> H(f(c), U1(e, d))
28.36/9.19	   A^2 -> H(f(c), U1(d, e))
28.36/9.19	   A^2 -> H(f(k), U1(k, k))
28.36/9.19	   A^2 -> H(U1(k, k), U1(b, b))
28.36/9.19	   A^2 -> H(U1(k, k), f(c))
28.36/9.19	   A^2 -> H(U1(k, k), f(d))
28.36/9.19	   A^2 -> H(U1(k, d), U1(c, b))
28.36/9.19	   A^2 -> H(U1(k, d), U1(d, b))
28.36/9.19	   A^2 -> H(U1(k, d), U1(b, c))
28.36/9.19	   A^2 -> H(U1(k, d), U1(b, d))
28.36/9.19	   A^2 -> H(U1(k, d), U1(c, c))
28.36/9.19	   A^2 -> H(U1(k, d), f(e))
28.36/9.19	   A^2 -> H(U1(k, d), f(k))
28.36/9.19	   A^2 -> H(U1(k, d), U1(d, d))
28.36/9.19	   A^2 -> H(U1(d, k), U1(c, b))
28.36/9.19	   A^2 -> H(U1(d, k), U1(d, b))
28.36/9.19	   A^2 -> H(U1(d, k), U1(b, c))
28.36/9.19	   A^2 -> H(U1(d, k), U1(b, d))
28.36/9.19	   A^2 -> H(U1(d, k), U1(c, c))
28.36/9.19	   A^2 -> H(U1(d, k), f(e))
28.36/9.19	   A^2 -> H(U1(d, k), f(k))
28.36/9.19	   A^2 -> H(U1(d, k), U1(d, d))
28.36/9.19	   A^2 -> H(U1(d, d), U1(e, b))
28.36/9.19	   A^2 -> H(U1(d, d), U1(k, b))
28.36/9.19	   A^2 -> H(U1(d, d), U1(c, d))
28.36/9.19	   A^2 -> H(U1(d, d), U1(d, c))
28.36/9.19	   A^2 -> H(U1(d, d), U1(b, e))
28.36/9.19	   A^2 -> H(U1(d, d), U1(b, k))
28.36/9.19	   A^2 -> H(U1(d, d), U1(e, c))
28.36/9.19	   A^2 -> H(U1(d, d), U1(k, c))
28.36/9.19	   A^2 -> H(U1(d, d), U1(c, e))
28.36/9.19	   A^2 -> H(U1(d, d), U1(c, k))
28.36/9.19	   A^2 -> H(U1(d, d), U1(e, e))
28.36/9.19	   A^2 -> H(U1(d, d), U1(k, k))
28.36/9.19	   A^2 -> H(f(d), b)
28.36/9.19	   A^2 -> H(f(d), U1(e, d))
28.36/9.19	   A^2 -> H(f(d), U1(d, e))
28.36/9.19	   A^2 -> H(f(d), c)
28.36/9.19	   A^2 -> H(f(d), U1(e, k))
28.36/9.19	   A^2 -> H(f(d), U1(k, e))
28.36/9.19	   A^2 -> H(f(d), e)
28.36/9.19	   A^2 -> H(f(a), d)
28.36/9.19	   A^2 -> H(U1(c, c), U1(e, c))
28.36/9.19	   A^2 -> H(f(c), c)
28.36/9.19	   A^2 -> H(f(c), U1(e, k))
28.36/9.19	   A^2 -> H(U1(c, c), U1(k, c))
28.36/9.19	   A^2 -> H(f(c), U1(k, e))
28.36/9.19	   A^2 -> H(f(c), U1(k, k))
28.36/9.19	   A^2 -> H(U1(c, c), U1(c, e))
28.36/9.19	   A^2 -> H(U1(c, c), U1(c, k))
28.36/9.19	   A^2 -> H(f(a), k)
28.36/9.19	   A^2 -> H(f(e), U1(e, e))
28.36/9.19	   A^2 -> H(f(c), e)
28.36/9.19	   A^2 -> H(U1(d, d), U1(k, d))
28.36/9.19	   A^2 -> H(f(d), U1(k, k))
28.36/9.19	   A^2 -> H(U1(d, d), U1(d, k))
28.36/9.19	   A^2 -> H(d, U1(b, b))
28.36/9.19	   A^2 -> H(d, f(c))
28.36/9.19	   A^2 -> H(d, f(d))
28.36/9.19	   A^2 -> H(a, U1(c, b))
28.36/9.19	   A^2 -> H(a, U1(d, b))
28.36/9.19	   A^2 -> H(a, U1(b, c))
28.36/9.19	   A^2 -> H(a, U1(b, d))
28.36/9.19	   A^2 -> H(a, U1(c, c))
28.36/9.19	   A^2 -> H(a, f(e))
28.36/9.19	   A^2 -> H(a, f(k))
28.36/9.19	   A^2 -> H(a, U1(d, d))
28.36/9.19	   A^2 -> H(U1(e, d), U1(c, b))
28.36/9.19	   A^2 -> H(U1(e, d), U1(d, b))
28.36/9.19	   A^2 -> H(U1(e, d), U1(b, c))
28.36/9.19	   A^2 -> H(U1(e, d), U1(b, d))
28.36/9.19	   A^2 -> H(U1(e, d), U1(c, c))
28.36/9.19	   A^2 -> H(U1(e, d), f(e))
28.36/9.19	   A^2 -> H(U1(e, d), f(k))
28.36/9.19	   A^2 -> H(U1(e, d), U1(d, d))
28.36/9.19	   A^2 -> H(U1(e, a), U1(e, b))
28.36/9.19	   A^2 -> H(U1(e, a), U1(k, b))
28.36/9.19	   A^2 -> H(U1(e, a), U1(c, d))
28.38/9.19	   A^2 -> H(U1(e, a), U1(d, c))
28.38/9.19	   A^2 -> H(U1(e, a), U1(b, e))
28.38/9.19	   A^2 -> H(U1(e, a), U1(b, k))
28.38/9.19	   A^2 -> H(U1(e, a), U1(e, c))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, c))
28.38/9.19	   A^2 -> H(U1(e, a), U1(c, e))
28.38/9.19	   A^2 -> H(U1(e, a), U1(c, k))
28.38/9.19	   A^2 -> H(U1(e, a), U1(e, e))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, d))
28.38/9.19	   A^2 -> H(U1(e, a), U1(d, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(e, b))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, b))
28.38/9.19	   A^2 -> H(U1(k, a), U1(c, d))
28.38/9.19	   A^2 -> H(U1(k, a), U1(d, c))
28.38/9.19	   A^2 -> H(U1(k, a), U1(b, e))
28.38/9.19	   A^2 -> H(U1(k, a), U1(b, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(e, c))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, c))
28.38/9.19	   A^2 -> H(U1(k, a), U1(c, e))
28.38/9.19	   A^2 -> H(U1(k, a), U1(c, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(e, e))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, d))
28.38/9.19	   A^2 -> H(U1(k, a), U1(d, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(e, b))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, b))
28.38/9.19	   A^2 -> H(U1(c, d), U1(c, d))
28.38/9.19	   A^2 -> H(U1(c, d), U1(d, c))
28.38/9.19	   A^2 -> H(U1(c, d), U1(b, e))
28.38/9.19	   A^2 -> H(U1(c, d), U1(b, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(e, c))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, c))
28.38/9.19	   A^2 -> H(U1(c, d), U1(c, e))
28.38/9.19	   A^2 -> H(U1(c, d), U1(c, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(e, e))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, d))
28.38/9.19	   A^2 -> H(U1(c, d), U1(d, k))
28.38/9.19	   A^2 -> H(U1(c, a), b)
28.38/9.19	   A^2 -> H(U1(c, a), U1(e, d))
28.38/9.19	   A^2 -> H(U1(c, a), U1(d, e))
28.38/9.19	   A^2 -> H(U1(c, a), c)
28.38/9.19	   A^2 -> H(U1(c, a), U1(e, k))
28.38/9.19	   A^2 -> H(U1(c, a), U1(k, e))
28.38/9.19	   A^2 -> H(U1(c, a), e)
28.38/9.19	   A^2 -> H(U1(c, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(d, e), U1(c, b))
28.38/9.19	   A^2 -> H(U1(d, e), U1(d, b))
28.38/9.19	   A^2 -> H(U1(d, e), U1(b, c))
28.38/9.19	   A^2 -> H(U1(d, e), U1(b, d))
28.38/9.19	   A^2 -> H(U1(d, e), U1(c, c))
28.38/9.19	   A^2 -> H(U1(d, e), f(e))
28.38/9.19	   A^2 -> H(U1(d, e), f(k))
28.38/9.19	   A^2 -> H(U1(d, e), U1(d, d))
28.38/9.19	   A^2 -> H(U1(d, c), U1(e, b))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, b))
28.38/9.19	   A^2 -> H(U1(d, c), U1(c, d))
28.38/9.19	   A^2 -> H(U1(d, c), U1(d, c))
28.38/9.19	   A^2 -> H(U1(d, c), U1(b, e))
28.38/9.19	   A^2 -> H(U1(d, c), U1(b, k))
28.38/9.19	   A^2 -> H(U1(d, c), U1(e, c))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, c))
28.38/9.19	   A^2 -> H(U1(d, c), U1(c, e))
28.38/9.19	   A^2 -> H(U1(d, c), U1(c, k))
28.38/9.19	   A^2 -> H(U1(d, c), U1(e, e))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, d))
28.38/9.19	   A^2 -> H(U1(d, c), U1(d, k))
28.38/9.19	   A^2 -> H(U1(d, a), b)
28.38/9.19	   A^2 -> H(U1(d, a), U1(e, d))
28.38/9.19	   A^2 -> H(U1(d, a), U1(d, e))
28.38/9.19	   A^2 -> H(U1(d, a), c)
28.38/9.19	   A^2 -> H(U1(d, a), U1(e, k))
28.38/9.19	   A^2 -> H(U1(d, a), U1(k, e))
28.38/9.19	   A^2 -> H(U1(d, a), e)
28.38/9.19	   A^2 -> H(U1(d, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(e, b))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, b))
28.38/9.19	   A^2 -> H(U1(a, e), U1(c, d))
28.38/9.19	   A^2 -> H(U1(a, e), U1(d, c))
28.38/9.19	   A^2 -> H(U1(a, e), U1(b, e))
28.38/9.19	   A^2 -> H(U1(a, e), U1(b, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(e, c))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, c))
28.38/9.19	   A^2 -> H(U1(a, e), U1(c, e))
28.38/9.19	   A^2 -> H(U1(a, e), U1(c, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(e, e))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, d))
28.38/9.19	   A^2 -> H(U1(a, e), U1(d, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(e, b))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, b))
28.38/9.19	   A^2 -> H(U1(a, k), U1(c, d))
28.38/9.19	   A^2 -> H(U1(a, k), U1(d, c))
28.38/9.19	   A^2 -> H(U1(a, k), U1(b, e))
28.38/9.19	   A^2 -> H(U1(a, k), U1(b, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(e, c))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, c))
28.38/9.19	   A^2 -> H(U1(a, k), U1(c, e))
28.38/9.19	   A^2 -> H(U1(a, k), U1(c, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(e, e))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, d))
28.38/9.19	   A^2 -> H(U1(a, k), U1(d, k))
28.38/9.19	   A^2 -> H(U1(a, c), b)
28.38/9.19	   A^2 -> H(U1(a, c), U1(e, d))
28.38/9.19	   A^2 -> H(U1(a, c), U1(d, e))
28.38/9.19	   A^2 -> H(U1(a, c), c)
28.38/9.19	   A^2 -> H(U1(a, c), U1(e, k))
28.38/9.19	   A^2 -> H(U1(a, c), U1(k, e))
28.38/9.19	   A^2 -> H(U1(a, c), e)
28.38/9.19	   A^2 -> H(U1(a, c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, d), b)
28.38/9.19	   A^2 -> H(U1(a, d), U1(e, d))
28.38/9.19	   A^2 -> H(U1(a, d), U1(d, e))
28.38/9.19	   A^2 -> H(U1(a, d), c)
28.38/9.19	   A^2 -> H(U1(a, d), U1(e, k))
28.38/9.19	   A^2 -> H(U1(a, d), U1(k, e))
28.38/9.19	   A^2 -> H(U1(a, d), e)
28.38/9.19	   A^2 -> H(U1(a, d), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, a), d)
28.38/9.19	   A^2 -> H(U1(a, a), k)
28.38/9.19	   A^2 -> H(k, U1(b, b))
28.38/9.19	   A^2 -> H(k, f(c))
28.38/9.19	   A^2 -> H(k, f(d))
28.38/9.19	   A^2 -> H(c, U1(c, b))
28.38/9.19	   A^2 -> H(c, U1(d, b))
28.38/9.19	   A^2 -> H(c, U1(b, c))
28.38/9.19	   A^2 -> H(c, U1(b, d))
28.38/9.19	   A^2 -> H(c, U1(c, c))
28.38/9.19	   A^2 -> H(c, f(e))
28.38/9.19	   A^2 -> H(c, f(k))
28.38/9.19	   A^2 -> H(c, U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(e, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(e, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, k), U1(b, d))
28.38/9.19	
28.38/9.19	The TRS R consists of the following rules:
28.38/9.19	
28.38/9.19	   f(x) -> U1(x, x)
28.38/9.19	   U1(e, x) -> x
28.38/9.19	   a -> c
28.38/9.19	   a -> d
28.38/9.19	   b -> c
28.38/9.19	   b -> d
28.38/9.19	   d -> k
28.38/9.19	   c -> e
28.38/9.19	   c -> k
28.38/9.19	
28.38/9.19	Q is empty.
28.38/9.19	We have to consider all minimal (P,Q,R)-chains.
28.38/9.19	----------------------------------------
28.38/9.19	
28.38/9.19	(795) TransformationProof (EQUIVALENT)
28.38/9.19	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), f(c)) at position [] we obtained the following new rules [LPAR04]:
28.38/9.19	
28.38/9.19	   (A^2 -> H(k, f(c)),A^2 -> H(k, f(c)))
28.38/9.19	   (A^2 -> H(U1(e, k), U1(c, c)),A^2 -> H(U1(e, k), U1(c, c)))
28.38/9.19	   (A^2 -> H(U1(e, k), f(e)),A^2 -> H(U1(e, k), f(e)))
28.38/9.19	   (A^2 -> H(U1(e, k), f(k)),A^2 -> H(U1(e, k), f(k)))
28.38/9.19	
28.38/9.19	
28.38/9.19	----------------------------------------
28.38/9.19	
28.38/9.19	(796)
28.38/9.19	Obligation:
28.38/9.19	Q DP problem:
28.38/9.19	The TRS P consists of the following rules:
28.38/9.19	
28.38/9.19	   H(x, x) -> G(x, x, f(k))
28.38/9.19	   G(d, x, x) -> A^2
28.38/9.19	   A^2 -> H(f(c), f(c))
28.38/9.19	   A^2 -> H(f(d), f(d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, c))
28.38/9.19	   A^2 -> H(f(e), f(e))
28.38/9.19	   A^2 -> H(f(k), f(k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, k), f(d))
28.38/9.19	   A^2 -> H(U1(e, c), U1(c, b))
28.38/9.19	   A^2 -> H(U1(e, c), U1(d, b))
28.38/9.19	   A^2 -> H(U1(e, c), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, c), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, c), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, c), f(e))
28.38/9.19	   A^2 -> H(U1(e, c), f(k))
28.38/9.19	   A^2 -> H(U1(e, c), U1(d, d))
28.38/9.19	   A^2 -> H(U1(k, e), U1(b, b))
28.38/9.19	   A^2 -> H(U1(k, e), f(c))
28.38/9.19	   A^2 -> H(U1(k, e), f(d))
28.38/9.19	   A^2 -> H(U1(k, c), U1(c, b))
28.38/9.19	   A^2 -> H(U1(k, c), U1(d, b))
28.38/9.19	   A^2 -> H(U1(k, c), U1(b, c))
28.38/9.19	   A^2 -> H(U1(k, c), U1(b, d))
28.38/9.19	   A^2 -> H(U1(k, c), U1(c, c))
28.38/9.19	   A^2 -> H(U1(k, c), f(e))
28.38/9.19	   A^2 -> H(U1(k, c), f(k))
28.38/9.19	   A^2 -> H(U1(k, c), U1(d, d))
28.38/9.19	   A^2 -> H(U1(c, e), U1(c, b))
28.38/9.19	   A^2 -> H(U1(c, e), U1(d, b))
28.38/9.19	   A^2 -> H(U1(c, e), U1(b, c))
28.38/9.19	   A^2 -> H(U1(c, e), U1(b, d))
28.38/9.19	   A^2 -> H(U1(c, e), U1(c, c))
28.38/9.19	   A^2 -> H(U1(c, e), f(e))
28.38/9.19	   A^2 -> H(U1(c, e), f(k))
28.38/9.19	   A^2 -> H(U1(c, e), U1(d, d))
28.38/9.19	   A^2 -> H(U1(c, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(c, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(c, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(c, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(c, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(c, k), f(e))
28.38/9.19	   A^2 -> H(U1(c, k), f(k))
28.38/9.19	   A^2 -> H(U1(c, k), U1(d, d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(e, b))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, b))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(d, c))
28.38/9.19	   A^2 -> H(U1(c, c), U1(b, e))
28.38/9.19	   A^2 -> H(U1(c, c), U1(b, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(e, e))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(d, k))
28.38/9.19	   A^2 -> H(e, U1(b, b))
28.38/9.19	   A^2 -> H(e, f(c))
28.38/9.19	   A^2 -> H(e, f(d))
28.38/9.19	   A^2 -> H(U1(e, e), U1(c, b))
28.38/9.19	   A^2 -> H(U1(e, e), U1(d, b))
28.38/9.19	   A^2 -> H(U1(e, e), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, e), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, e), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, e), f(e))
28.38/9.19	   A^2 -> H(U1(e, e), f(k))
28.38/9.19	   A^2 -> H(U1(e, e), U1(d, d))
28.38/9.19	   A^2 -> H(f(e), U1(e, b))
28.38/9.19	   A^2 -> H(f(e), U1(k, b))
28.38/9.19	   A^2 -> H(f(e), U1(c, d))
28.38/9.19	   A^2 -> H(f(e), U1(d, c))
28.38/9.19	   A^2 -> H(f(e), U1(b, e))
28.38/9.19	   A^2 -> H(f(e), U1(b, k))
28.38/9.19	   A^2 -> H(f(e), U1(e, c))
28.38/9.19	   A^2 -> H(f(e), U1(k, c))
28.38/9.19	   A^2 -> H(f(e), U1(c, e))
28.38/9.19	   A^2 -> H(f(e), U1(c, k))
28.38/9.19	   A^2 -> H(f(e), U1(k, k))
28.38/9.19	   A^2 -> H(f(e), U1(k, d))
28.38/9.19	   A^2 -> H(f(e), U1(d, k))
28.38/9.19	   A^2 -> H(U1(k, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(k, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(k, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(k, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(k, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(k, k), f(e))
28.38/9.19	   A^2 -> H(U1(k, k), f(k))
28.38/9.19	   A^2 -> H(U1(k, k), U1(d, d))
28.38/9.19	   A^2 -> H(f(k), U1(e, b))
28.38/9.19	   A^2 -> H(f(k), U1(k, b))
28.38/9.19	   A^2 -> H(f(k), U1(c, d))
28.38/9.19	   A^2 -> H(f(k), U1(d, c))
28.38/9.19	   A^2 -> H(f(k), U1(b, e))
28.38/9.19	   A^2 -> H(f(k), U1(b, k))
28.38/9.19	   A^2 -> H(f(k), U1(e, c))
28.38/9.19	   A^2 -> H(f(k), U1(k, c))
28.38/9.19	   A^2 -> H(f(k), U1(c, e))
28.38/9.19	   A^2 -> H(f(k), U1(c, k))
28.38/9.19	   A^2 -> H(f(k), U1(e, e))
28.38/9.19	   A^2 -> H(f(k), U1(k, d))
28.38/9.19	   A^2 -> H(f(k), U1(d, k))
28.38/9.19	   A^2 -> H(f(c), b)
28.38/9.19	   A^2 -> H(f(c), U1(e, d))
28.38/9.19	   A^2 -> H(f(c), U1(d, e))
28.38/9.19	   A^2 -> H(f(k), U1(k, k))
28.38/9.19	   A^2 -> H(U1(k, k), U1(b, b))
28.38/9.19	   A^2 -> H(U1(k, k), f(c))
28.38/9.19	   A^2 -> H(U1(k, k), f(d))
28.38/9.19	   A^2 -> H(U1(k, d), U1(c, b))
28.38/9.19	   A^2 -> H(U1(k, d), U1(d, b))
28.38/9.19	   A^2 -> H(U1(k, d), U1(b, c))
28.38/9.19	   A^2 -> H(U1(k, d), U1(b, d))
28.38/9.19	   A^2 -> H(U1(k, d), U1(c, c))
28.38/9.19	   A^2 -> H(U1(k, d), f(e))
28.38/9.19	   A^2 -> H(U1(k, d), f(k))
28.38/9.19	   A^2 -> H(U1(k, d), U1(d, d))
28.38/9.19	   A^2 -> H(U1(d, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(d, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(d, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(d, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(d, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(d, k), f(e))
28.38/9.19	   A^2 -> H(U1(d, k), f(k))
28.38/9.19	   A^2 -> H(U1(d, k), U1(d, d))
28.38/9.19	   A^2 -> H(U1(d, d), U1(e, b))
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, b))
28.38/9.19	   A^2 -> H(U1(d, d), U1(c, d))
28.38/9.19	   A^2 -> H(U1(d, d), U1(d, c))
28.38/9.19	   A^2 -> H(U1(d, d), U1(b, e))
28.38/9.19	   A^2 -> H(U1(d, d), U1(b, k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(e, c))
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, c))
28.38/9.19	   A^2 -> H(U1(d, d), U1(c, e))
28.38/9.19	   A^2 -> H(U1(d, d), U1(c, k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(e, e))
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, k))
28.38/9.19	   A^2 -> H(f(d), b)
28.38/9.19	   A^2 -> H(f(d), U1(e, d))
28.38/9.19	   A^2 -> H(f(d), U1(d, e))
28.38/9.19	   A^2 -> H(f(d), c)
28.38/9.19	   A^2 -> H(f(d), U1(e, k))
28.38/9.19	   A^2 -> H(f(d), U1(k, e))
28.38/9.19	   A^2 -> H(f(d), e)
28.38/9.19	   A^2 -> H(f(a), d)
28.38/9.19	   A^2 -> H(U1(c, c), U1(e, c))
28.38/9.19	   A^2 -> H(f(c), c)
28.38/9.19	   A^2 -> H(f(c), U1(e, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, c))
28.38/9.19	   A^2 -> H(f(c), U1(k, e))
28.38/9.19	   A^2 -> H(f(c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, e))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, k))
28.38/9.19	   A^2 -> H(f(a), k)
28.38/9.19	   A^2 -> H(f(e), U1(e, e))
28.38/9.19	   A^2 -> H(f(c), e)
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, d))
28.38/9.19	   A^2 -> H(f(d), U1(k, k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(d, k))
28.38/9.19	   A^2 -> H(d, U1(b, b))
28.38/9.19	   A^2 -> H(d, f(c))
28.38/9.19	   A^2 -> H(d, f(d))
28.38/9.19	   A^2 -> H(a, U1(c, b))
28.38/9.19	   A^2 -> H(a, U1(d, b))
28.38/9.19	   A^2 -> H(a, U1(b, c))
28.38/9.19	   A^2 -> H(a, U1(b, d))
28.38/9.19	   A^2 -> H(a, U1(c, c))
28.38/9.19	   A^2 -> H(a, f(e))
28.38/9.19	   A^2 -> H(a, f(k))
28.38/9.19	   A^2 -> H(a, U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, d), U1(c, b))
28.38/9.19	   A^2 -> H(U1(e, d), U1(d, b))
28.38/9.19	   A^2 -> H(U1(e, d), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, d), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, d), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, d), f(e))
28.38/9.19	   A^2 -> H(U1(e, d), f(k))
28.38/9.19	   A^2 -> H(U1(e, d), U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, a), U1(e, b))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, b))
28.38/9.19	   A^2 -> H(U1(e, a), U1(c, d))
28.38/9.19	   A^2 -> H(U1(e, a), U1(d, c))
28.38/9.19	   A^2 -> H(U1(e, a), U1(b, e))
28.38/9.19	   A^2 -> H(U1(e, a), U1(b, k))
28.38/9.19	   A^2 -> H(U1(e, a), U1(e, c))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, c))
28.38/9.19	   A^2 -> H(U1(e, a), U1(c, e))
28.38/9.19	   A^2 -> H(U1(e, a), U1(c, k))
28.38/9.19	   A^2 -> H(U1(e, a), U1(e, e))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, d))
28.38/9.19	   A^2 -> H(U1(e, a), U1(d, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(e, b))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, b))
28.38/9.19	   A^2 -> H(U1(k, a), U1(c, d))
28.38/9.19	   A^2 -> H(U1(k, a), U1(d, c))
28.38/9.19	   A^2 -> H(U1(k, a), U1(b, e))
28.38/9.19	   A^2 -> H(U1(k, a), U1(b, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(e, c))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, c))
28.38/9.19	   A^2 -> H(U1(k, a), U1(c, e))
28.38/9.19	   A^2 -> H(U1(k, a), U1(c, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(e, e))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, d))
28.38/9.19	   A^2 -> H(U1(k, a), U1(d, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(e, b))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, b))
28.38/9.19	   A^2 -> H(U1(c, d), U1(c, d))
28.38/9.19	   A^2 -> H(U1(c, d), U1(d, c))
28.38/9.19	   A^2 -> H(U1(c, d), U1(b, e))
28.38/9.19	   A^2 -> H(U1(c, d), U1(b, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(e, c))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, c))
28.38/9.19	   A^2 -> H(U1(c, d), U1(c, e))
28.38/9.19	   A^2 -> H(U1(c, d), U1(c, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(e, e))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, d))
28.38/9.19	   A^2 -> H(U1(c, d), U1(d, k))
28.38/9.19	   A^2 -> H(U1(c, a), b)
28.38/9.19	   A^2 -> H(U1(c, a), U1(e, d))
28.38/9.19	   A^2 -> H(U1(c, a), U1(d, e))
28.38/9.19	   A^2 -> H(U1(c, a), c)
28.38/9.19	   A^2 -> H(U1(c, a), U1(e, k))
28.38/9.19	   A^2 -> H(U1(c, a), U1(k, e))
28.38/9.19	   A^2 -> H(U1(c, a), e)
28.38/9.19	   A^2 -> H(U1(c, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(d, e), U1(c, b))
28.38/9.19	   A^2 -> H(U1(d, e), U1(d, b))
28.38/9.19	   A^2 -> H(U1(d, e), U1(b, c))
28.38/9.19	   A^2 -> H(U1(d, e), U1(b, d))
28.38/9.19	   A^2 -> H(U1(d, e), U1(c, c))
28.38/9.19	   A^2 -> H(U1(d, e), f(e))
28.38/9.19	   A^2 -> H(U1(d, e), f(k))
28.38/9.19	   A^2 -> H(U1(d, e), U1(d, d))
28.38/9.19	   A^2 -> H(U1(d, c), U1(e, b))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, b))
28.38/9.19	   A^2 -> H(U1(d, c), U1(c, d))
28.38/9.19	   A^2 -> H(U1(d, c), U1(d, c))
28.38/9.19	   A^2 -> H(U1(d, c), U1(b, e))
28.38/9.19	   A^2 -> H(U1(d, c), U1(b, k))
28.38/9.19	   A^2 -> H(U1(d, c), U1(e, c))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, c))
28.38/9.19	   A^2 -> H(U1(d, c), U1(c, e))
28.38/9.19	   A^2 -> H(U1(d, c), U1(c, k))
28.38/9.19	   A^2 -> H(U1(d, c), U1(e, e))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, d))
28.38/9.19	   A^2 -> H(U1(d, c), U1(d, k))
28.38/9.19	   A^2 -> H(U1(d, a), b)
28.38/9.19	   A^2 -> H(U1(d, a), U1(e, d))
28.38/9.19	   A^2 -> H(U1(d, a), U1(d, e))
28.38/9.19	   A^2 -> H(U1(d, a), c)
28.38/9.19	   A^2 -> H(U1(d, a), U1(e, k))
28.38/9.19	   A^2 -> H(U1(d, a), U1(k, e))
28.38/9.19	   A^2 -> H(U1(d, a), e)
28.38/9.19	   A^2 -> H(U1(d, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(e, b))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, b))
28.38/9.19	   A^2 -> H(U1(a, e), U1(c, d))
28.38/9.19	   A^2 -> H(U1(a, e), U1(d, c))
28.38/9.19	   A^2 -> H(U1(a, e), U1(b, e))
28.38/9.19	   A^2 -> H(U1(a, e), U1(b, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(e, c))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, c))
28.38/9.19	   A^2 -> H(U1(a, e), U1(c, e))
28.38/9.19	   A^2 -> H(U1(a, e), U1(c, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(e, e))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, d))
28.38/9.19	   A^2 -> H(U1(a, e), U1(d, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(e, b))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, b))
28.38/9.19	   A^2 -> H(U1(a, k), U1(c, d))
28.38/9.19	   A^2 -> H(U1(a, k), U1(d, c))
28.38/9.19	   A^2 -> H(U1(a, k), U1(b, e))
28.38/9.19	   A^2 -> H(U1(a, k), U1(b, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(e, c))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, c))
28.38/9.19	   A^2 -> H(U1(a, k), U1(c, e))
28.38/9.19	   A^2 -> H(U1(a, k), U1(c, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(e, e))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, d))
28.38/9.19	   A^2 -> H(U1(a, k), U1(d, k))
28.38/9.19	   A^2 -> H(U1(a, c), b)
28.38/9.19	   A^2 -> H(U1(a, c), U1(e, d))
28.38/9.19	   A^2 -> H(U1(a, c), U1(d, e))
28.38/9.19	   A^2 -> H(U1(a, c), c)
28.38/9.19	   A^2 -> H(U1(a, c), U1(e, k))
28.38/9.19	   A^2 -> H(U1(a, c), U1(k, e))
28.38/9.19	   A^2 -> H(U1(a, c), e)
28.38/9.19	   A^2 -> H(U1(a, c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, d), b)
28.38/9.19	   A^2 -> H(U1(a, d), U1(e, d))
28.38/9.19	   A^2 -> H(U1(a, d), U1(d, e))
28.38/9.19	   A^2 -> H(U1(a, d), c)
28.38/9.19	   A^2 -> H(U1(a, d), U1(e, k))
28.38/9.19	   A^2 -> H(U1(a, d), U1(k, e))
28.38/9.19	   A^2 -> H(U1(a, d), e)
28.38/9.19	   A^2 -> H(U1(a, d), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, a), d)
28.38/9.19	   A^2 -> H(U1(a, a), k)
28.38/9.19	   A^2 -> H(k, U1(b, b))
28.38/9.19	   A^2 -> H(k, f(c))
28.38/9.19	   A^2 -> H(k, f(d))
28.38/9.19	   A^2 -> H(c, U1(c, b))
28.38/9.19	   A^2 -> H(c, U1(d, b))
28.38/9.19	   A^2 -> H(c, U1(b, c))
28.38/9.19	   A^2 -> H(c, U1(b, d))
28.38/9.19	   A^2 -> H(c, U1(c, c))
28.38/9.19	   A^2 -> H(c, f(e))
28.38/9.19	   A^2 -> H(c, f(k))
28.38/9.19	   A^2 -> H(c, U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(e, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(e, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, k), f(e))
28.38/9.19	   A^2 -> H(U1(e, k), f(k))
28.38/9.19	
28.38/9.19	The TRS R consists of the following rules:
28.38/9.19	
28.38/9.19	   f(x) -> U1(x, x)
28.38/9.19	   U1(e, x) -> x
28.38/9.19	   a -> c
28.38/9.19	   a -> d
28.38/9.19	   b -> c
28.38/9.19	   b -> d
28.38/9.19	   d -> k
28.38/9.19	   c -> e
28.38/9.19	   c -> k
28.38/9.19	
28.38/9.19	Q is empty.
28.38/9.19	We have to consider all minimal (P,Q,R)-chains.
28.38/9.19	----------------------------------------
28.38/9.19	
28.38/9.19	(797) TransformationProof (EQUIVALENT)
28.38/9.19	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), f(d)) at position [] we obtained the following new rules [LPAR04]:
28.38/9.19	
28.38/9.19	   (A^2 -> H(k, f(d)),A^2 -> H(k, f(d)))
28.38/9.19	   (A^2 -> H(U1(e, k), U1(d, d)),A^2 -> H(U1(e, k), U1(d, d)))
28.38/9.19	   (A^2 -> H(U1(e, k), f(k)),A^2 -> H(U1(e, k), f(k)))
28.38/9.19	
28.38/9.19	
28.38/9.19	----------------------------------------
28.38/9.19	
28.38/9.19	(798)
28.38/9.19	Obligation:
28.38/9.19	Q DP problem:
28.38/9.19	The TRS P consists of the following rules:
28.38/9.19	
28.38/9.19	   H(x, x) -> G(x, x, f(k))
28.38/9.19	   G(d, x, x) -> A^2
28.38/9.19	   A^2 -> H(f(c), f(c))
28.38/9.19	   A^2 -> H(f(d), f(d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, c))
28.38/9.19	   A^2 -> H(f(e), f(e))
28.38/9.19	   A^2 -> H(f(k), f(k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, c), U1(c, b))
28.38/9.19	   A^2 -> H(U1(e, c), U1(d, b))
28.38/9.19	   A^2 -> H(U1(e, c), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, c), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, c), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, c), f(e))
28.38/9.19	   A^2 -> H(U1(e, c), f(k))
28.38/9.19	   A^2 -> H(U1(e, c), U1(d, d))
28.38/9.19	   A^2 -> H(U1(k, e), U1(b, b))
28.38/9.19	   A^2 -> H(U1(k, e), f(c))
28.38/9.19	   A^2 -> H(U1(k, e), f(d))
28.38/9.19	   A^2 -> H(U1(k, c), U1(c, b))
28.38/9.19	   A^2 -> H(U1(k, c), U1(d, b))
28.38/9.19	   A^2 -> H(U1(k, c), U1(b, c))
28.38/9.19	   A^2 -> H(U1(k, c), U1(b, d))
28.38/9.19	   A^2 -> H(U1(k, c), U1(c, c))
28.38/9.19	   A^2 -> H(U1(k, c), f(e))
28.38/9.19	   A^2 -> H(U1(k, c), f(k))
28.38/9.19	   A^2 -> H(U1(k, c), U1(d, d))
28.38/9.19	   A^2 -> H(U1(c, e), U1(c, b))
28.38/9.19	   A^2 -> H(U1(c, e), U1(d, b))
28.38/9.19	   A^2 -> H(U1(c, e), U1(b, c))
28.38/9.19	   A^2 -> H(U1(c, e), U1(b, d))
28.38/9.19	   A^2 -> H(U1(c, e), U1(c, c))
28.38/9.19	   A^2 -> H(U1(c, e), f(e))
28.38/9.19	   A^2 -> H(U1(c, e), f(k))
28.38/9.19	   A^2 -> H(U1(c, e), U1(d, d))
28.38/9.19	   A^2 -> H(U1(c, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(c, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(c, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(c, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(c, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(c, k), f(e))
28.38/9.19	   A^2 -> H(U1(c, k), f(k))
28.38/9.19	   A^2 -> H(U1(c, k), U1(d, d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(e, b))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, b))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(d, c))
28.38/9.19	   A^2 -> H(U1(c, c), U1(b, e))
28.38/9.19	   A^2 -> H(U1(c, c), U1(b, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(e, e))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(d, k))
28.38/9.19	   A^2 -> H(e, U1(b, b))
28.38/9.19	   A^2 -> H(e, f(c))
28.38/9.19	   A^2 -> H(e, f(d))
28.38/9.19	   A^2 -> H(U1(e, e), U1(c, b))
28.38/9.19	   A^2 -> H(U1(e, e), U1(d, b))
28.38/9.19	   A^2 -> H(U1(e, e), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, e), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, e), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, e), f(e))
28.38/9.19	   A^2 -> H(U1(e, e), f(k))
28.38/9.19	   A^2 -> H(U1(e, e), U1(d, d))
28.38/9.19	   A^2 -> H(f(e), U1(e, b))
28.38/9.19	   A^2 -> H(f(e), U1(k, b))
28.38/9.19	   A^2 -> H(f(e), U1(c, d))
28.38/9.19	   A^2 -> H(f(e), U1(d, c))
28.38/9.19	   A^2 -> H(f(e), U1(b, e))
28.38/9.19	   A^2 -> H(f(e), U1(b, k))
28.38/9.19	   A^2 -> H(f(e), U1(e, c))
28.38/9.19	   A^2 -> H(f(e), U1(k, c))
28.38/9.19	   A^2 -> H(f(e), U1(c, e))
28.38/9.19	   A^2 -> H(f(e), U1(c, k))
28.38/9.19	   A^2 -> H(f(e), U1(k, k))
28.38/9.19	   A^2 -> H(f(e), U1(k, d))
28.38/9.19	   A^2 -> H(f(e), U1(d, k))
28.38/9.19	   A^2 -> H(U1(k, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(k, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(k, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(k, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(k, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(k, k), f(e))
28.38/9.19	   A^2 -> H(U1(k, k), f(k))
28.38/9.19	   A^2 -> H(U1(k, k), U1(d, d))
28.38/9.19	   A^2 -> H(f(k), U1(e, b))
28.38/9.19	   A^2 -> H(f(k), U1(k, b))
28.38/9.19	   A^2 -> H(f(k), U1(c, d))
28.38/9.19	   A^2 -> H(f(k), U1(d, c))
28.38/9.19	   A^2 -> H(f(k), U1(b, e))
28.38/9.19	   A^2 -> H(f(k), U1(b, k))
28.38/9.19	   A^2 -> H(f(k), U1(e, c))
28.38/9.19	   A^2 -> H(f(k), U1(k, c))
28.38/9.19	   A^2 -> H(f(k), U1(c, e))
28.38/9.19	   A^2 -> H(f(k), U1(c, k))
28.38/9.19	   A^2 -> H(f(k), U1(e, e))
28.38/9.19	   A^2 -> H(f(k), U1(k, d))
28.38/9.19	   A^2 -> H(f(k), U1(d, k))
28.38/9.19	   A^2 -> H(f(c), b)
28.38/9.19	   A^2 -> H(f(c), U1(e, d))
28.38/9.19	   A^2 -> H(f(c), U1(d, e))
28.38/9.19	   A^2 -> H(f(k), U1(k, k))
28.38/9.19	   A^2 -> H(U1(k, k), U1(b, b))
28.38/9.19	   A^2 -> H(U1(k, k), f(c))
28.38/9.19	   A^2 -> H(U1(k, k), f(d))
28.38/9.19	   A^2 -> H(U1(k, d), U1(c, b))
28.38/9.19	   A^2 -> H(U1(k, d), U1(d, b))
28.38/9.19	   A^2 -> H(U1(k, d), U1(b, c))
28.38/9.19	   A^2 -> H(U1(k, d), U1(b, d))
28.38/9.19	   A^2 -> H(U1(k, d), U1(c, c))
28.38/9.19	   A^2 -> H(U1(k, d), f(e))
28.38/9.19	   A^2 -> H(U1(k, d), f(k))
28.38/9.19	   A^2 -> H(U1(k, d), U1(d, d))
28.38/9.19	   A^2 -> H(U1(d, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(d, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(d, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(d, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(d, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(d, k), f(e))
28.38/9.19	   A^2 -> H(U1(d, k), f(k))
28.38/9.19	   A^2 -> H(U1(d, k), U1(d, d))
28.38/9.19	   A^2 -> H(U1(d, d), U1(e, b))
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, b))
28.38/9.19	   A^2 -> H(U1(d, d), U1(c, d))
28.38/9.19	   A^2 -> H(U1(d, d), U1(d, c))
28.38/9.19	   A^2 -> H(U1(d, d), U1(b, e))
28.38/9.19	   A^2 -> H(U1(d, d), U1(b, k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(e, c))
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, c))
28.38/9.19	   A^2 -> H(U1(d, d), U1(c, e))
28.38/9.19	   A^2 -> H(U1(d, d), U1(c, k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(e, e))
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, k))
28.38/9.19	   A^2 -> H(f(d), b)
28.38/9.19	   A^2 -> H(f(d), U1(e, d))
28.38/9.19	   A^2 -> H(f(d), U1(d, e))
28.38/9.19	   A^2 -> H(f(d), c)
28.38/9.19	   A^2 -> H(f(d), U1(e, k))
28.38/9.19	   A^2 -> H(f(d), U1(k, e))
28.38/9.19	   A^2 -> H(f(d), e)
28.38/9.19	   A^2 -> H(f(a), d)
28.38/9.19	   A^2 -> H(U1(c, c), U1(e, c))
28.38/9.19	   A^2 -> H(f(c), c)
28.38/9.19	   A^2 -> H(f(c), U1(e, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, c))
28.38/9.19	   A^2 -> H(f(c), U1(k, e))
28.38/9.19	   A^2 -> H(f(c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, e))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, k))
28.38/9.19	   A^2 -> H(f(a), k)
28.38/9.19	   A^2 -> H(f(e), U1(e, e))
28.38/9.19	   A^2 -> H(f(c), e)
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, d))
28.38/9.19	   A^2 -> H(f(d), U1(k, k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(d, k))
28.38/9.19	   A^2 -> H(d, U1(b, b))
28.38/9.19	   A^2 -> H(d, f(c))
28.38/9.19	   A^2 -> H(d, f(d))
28.38/9.19	   A^2 -> H(a, U1(c, b))
28.38/9.19	   A^2 -> H(a, U1(d, b))
28.38/9.19	   A^2 -> H(a, U1(b, c))
28.38/9.19	   A^2 -> H(a, U1(b, d))
28.38/9.19	   A^2 -> H(a, U1(c, c))
28.38/9.19	   A^2 -> H(a, f(e))
28.38/9.19	   A^2 -> H(a, f(k))
28.38/9.19	   A^2 -> H(a, U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, d), U1(c, b))
28.38/9.19	   A^2 -> H(U1(e, d), U1(d, b))
28.38/9.19	   A^2 -> H(U1(e, d), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, d), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, d), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, d), f(e))
28.38/9.19	   A^2 -> H(U1(e, d), f(k))
28.38/9.19	   A^2 -> H(U1(e, d), U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, a), U1(e, b))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, b))
28.38/9.19	   A^2 -> H(U1(e, a), U1(c, d))
28.38/9.19	   A^2 -> H(U1(e, a), U1(d, c))
28.38/9.19	   A^2 -> H(U1(e, a), U1(b, e))
28.38/9.19	   A^2 -> H(U1(e, a), U1(b, k))
28.38/9.19	   A^2 -> H(U1(e, a), U1(e, c))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, c))
28.38/9.19	   A^2 -> H(U1(e, a), U1(c, e))
28.38/9.19	   A^2 -> H(U1(e, a), U1(c, k))
28.38/9.19	   A^2 -> H(U1(e, a), U1(e, e))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, d))
28.38/9.19	   A^2 -> H(U1(e, a), U1(d, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(e, b))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, b))
28.38/9.19	   A^2 -> H(U1(k, a), U1(c, d))
28.38/9.19	   A^2 -> H(U1(k, a), U1(d, c))
28.38/9.19	   A^2 -> H(U1(k, a), U1(b, e))
28.38/9.19	   A^2 -> H(U1(k, a), U1(b, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(e, c))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, c))
28.38/9.19	   A^2 -> H(U1(k, a), U1(c, e))
28.38/9.19	   A^2 -> H(U1(k, a), U1(c, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(e, e))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, d))
28.38/9.19	   A^2 -> H(U1(k, a), U1(d, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(e, b))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, b))
28.38/9.19	   A^2 -> H(U1(c, d), U1(c, d))
28.38/9.19	   A^2 -> H(U1(c, d), U1(d, c))
28.38/9.19	   A^2 -> H(U1(c, d), U1(b, e))
28.38/9.19	   A^2 -> H(U1(c, d), U1(b, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(e, c))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, c))
28.38/9.19	   A^2 -> H(U1(c, d), U1(c, e))
28.38/9.19	   A^2 -> H(U1(c, d), U1(c, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(e, e))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, d))
28.38/9.19	   A^2 -> H(U1(c, d), U1(d, k))
28.38/9.19	   A^2 -> H(U1(c, a), b)
28.38/9.19	   A^2 -> H(U1(c, a), U1(e, d))
28.38/9.19	   A^2 -> H(U1(c, a), U1(d, e))
28.38/9.19	   A^2 -> H(U1(c, a), c)
28.38/9.19	   A^2 -> H(U1(c, a), U1(e, k))
28.38/9.19	   A^2 -> H(U1(c, a), U1(k, e))
28.38/9.19	   A^2 -> H(U1(c, a), e)
28.38/9.19	   A^2 -> H(U1(c, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(d, e), U1(c, b))
28.38/9.19	   A^2 -> H(U1(d, e), U1(d, b))
28.38/9.19	   A^2 -> H(U1(d, e), U1(b, c))
28.38/9.19	   A^2 -> H(U1(d, e), U1(b, d))
28.38/9.19	   A^2 -> H(U1(d, e), U1(c, c))
28.38/9.19	   A^2 -> H(U1(d, e), f(e))
28.38/9.19	   A^2 -> H(U1(d, e), f(k))
28.38/9.19	   A^2 -> H(U1(d, e), U1(d, d))
28.38/9.19	   A^2 -> H(U1(d, c), U1(e, b))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, b))
28.38/9.19	   A^2 -> H(U1(d, c), U1(c, d))
28.38/9.19	   A^2 -> H(U1(d, c), U1(d, c))
28.38/9.19	   A^2 -> H(U1(d, c), U1(b, e))
28.38/9.19	   A^2 -> H(U1(d, c), U1(b, k))
28.38/9.19	   A^2 -> H(U1(d, c), U1(e, c))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, c))
28.38/9.19	   A^2 -> H(U1(d, c), U1(c, e))
28.38/9.19	   A^2 -> H(U1(d, c), U1(c, k))
28.38/9.19	   A^2 -> H(U1(d, c), U1(e, e))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, d))
28.38/9.19	   A^2 -> H(U1(d, c), U1(d, k))
28.38/9.19	   A^2 -> H(U1(d, a), b)
28.38/9.19	   A^2 -> H(U1(d, a), U1(e, d))
28.38/9.19	   A^2 -> H(U1(d, a), U1(d, e))
28.38/9.19	   A^2 -> H(U1(d, a), c)
28.38/9.19	   A^2 -> H(U1(d, a), U1(e, k))
28.38/9.19	   A^2 -> H(U1(d, a), U1(k, e))
28.38/9.19	   A^2 -> H(U1(d, a), e)
28.38/9.19	   A^2 -> H(U1(d, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(e, b))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, b))
28.38/9.19	   A^2 -> H(U1(a, e), U1(c, d))
28.38/9.19	   A^2 -> H(U1(a, e), U1(d, c))
28.38/9.19	   A^2 -> H(U1(a, e), U1(b, e))
28.38/9.19	   A^2 -> H(U1(a, e), U1(b, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(e, c))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, c))
28.38/9.19	   A^2 -> H(U1(a, e), U1(c, e))
28.38/9.19	   A^2 -> H(U1(a, e), U1(c, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(e, e))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, d))
28.38/9.19	   A^2 -> H(U1(a, e), U1(d, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(e, b))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, b))
28.38/9.19	   A^2 -> H(U1(a, k), U1(c, d))
28.38/9.19	   A^2 -> H(U1(a, k), U1(d, c))
28.38/9.19	   A^2 -> H(U1(a, k), U1(b, e))
28.38/9.19	   A^2 -> H(U1(a, k), U1(b, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(e, c))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, c))
28.38/9.19	   A^2 -> H(U1(a, k), U1(c, e))
28.38/9.19	   A^2 -> H(U1(a, k), U1(c, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(e, e))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, d))
28.38/9.19	   A^2 -> H(U1(a, k), U1(d, k))
28.38/9.19	   A^2 -> H(U1(a, c), b)
28.38/9.19	   A^2 -> H(U1(a, c), U1(e, d))
28.38/9.19	   A^2 -> H(U1(a, c), U1(d, e))
28.38/9.19	   A^2 -> H(U1(a, c), c)
28.38/9.19	   A^2 -> H(U1(a, c), U1(e, k))
28.38/9.19	   A^2 -> H(U1(a, c), U1(k, e))
28.38/9.19	   A^2 -> H(U1(a, c), e)
28.38/9.19	   A^2 -> H(U1(a, c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, d), b)
28.38/9.19	   A^2 -> H(U1(a, d), U1(e, d))
28.38/9.19	   A^2 -> H(U1(a, d), U1(d, e))
28.38/9.19	   A^2 -> H(U1(a, d), c)
28.38/9.19	   A^2 -> H(U1(a, d), U1(e, k))
28.38/9.19	   A^2 -> H(U1(a, d), U1(k, e))
28.38/9.19	   A^2 -> H(U1(a, d), e)
28.38/9.19	   A^2 -> H(U1(a, d), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, a), d)
28.38/9.19	   A^2 -> H(U1(a, a), k)
28.38/9.19	   A^2 -> H(k, U1(b, b))
28.38/9.19	   A^2 -> H(k, f(c))
28.38/9.19	   A^2 -> H(k, f(d))
28.38/9.19	   A^2 -> H(c, U1(c, b))
28.38/9.19	   A^2 -> H(c, U1(d, b))
28.38/9.19	   A^2 -> H(c, U1(b, c))
28.38/9.19	   A^2 -> H(c, U1(b, d))
28.38/9.19	   A^2 -> H(c, U1(c, c))
28.38/9.19	   A^2 -> H(c, f(e))
28.38/9.19	   A^2 -> H(c, f(k))
28.38/9.19	   A^2 -> H(c, U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(e, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(e, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, k), f(e))
28.38/9.19	   A^2 -> H(U1(e, k), f(k))
28.38/9.19	   A^2 -> H(U1(e, k), U1(d, d))
28.38/9.19	
28.38/9.19	The TRS R consists of the following rules:
28.38/9.19	
28.38/9.19	   f(x) -> U1(x, x)
28.38/9.19	   U1(e, x) -> x
28.38/9.19	   a -> c
28.38/9.19	   a -> d
28.38/9.19	   b -> c
28.38/9.19	   b -> d
28.38/9.19	   d -> k
28.38/9.19	   c -> e
28.38/9.19	   c -> k
28.38/9.19	
28.38/9.19	Q is empty.
28.38/9.19	We have to consider all minimal (P,Q,R)-chains.
28.38/9.19	----------------------------------------
28.38/9.19	
28.38/9.19	(799) TransformationProof (EQUIVALENT)
28.38/9.19	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
28.38/9.19	
28.38/9.19	   (A^2 -> H(c, U1(c, b)),A^2 -> H(c, U1(c, b)))
28.38/9.19	   (A^2 -> H(U1(e, e), U1(c, b)),A^2 -> H(U1(e, e), U1(c, b)))
28.38/9.19	   (A^2 -> H(U1(e, k), U1(c, b)),A^2 -> H(U1(e, k), U1(c, b)))
28.38/9.19	   (A^2 -> H(U1(e, c), U1(e, b)),A^2 -> H(U1(e, c), U1(e, b)))
28.38/9.19	   (A^2 -> H(U1(e, c), U1(k, b)),A^2 -> H(U1(e, c), U1(k, b)))
28.38/9.19	   (A^2 -> H(U1(e, c), U1(c, c)),A^2 -> H(U1(e, c), U1(c, c)))
28.38/9.19	   (A^2 -> H(U1(e, c), U1(c, d)),A^2 -> H(U1(e, c), U1(c, d)))
28.38/9.19	
28.38/9.19	
28.38/9.19	----------------------------------------
28.38/9.19	
28.38/9.19	(800)
28.38/9.19	Obligation:
28.38/9.19	Q DP problem:
28.38/9.19	The TRS P consists of the following rules:
28.38/9.19	
28.38/9.19	   H(x, x) -> G(x, x, f(k))
28.38/9.19	   G(d, x, x) -> A^2
28.38/9.19	   A^2 -> H(f(c), f(c))
28.38/9.19	   A^2 -> H(f(d), f(d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, c))
28.38/9.19	   A^2 -> H(f(e), f(e))
28.38/9.19	   A^2 -> H(f(k), f(k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, c), U1(d, b))
28.38/9.19	   A^2 -> H(U1(e, c), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, c), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, c), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, c), f(e))
28.38/9.19	   A^2 -> H(U1(e, c), f(k))
28.38/9.19	   A^2 -> H(U1(e, c), U1(d, d))
28.38/9.19	   A^2 -> H(U1(k, e), U1(b, b))
28.38/9.19	   A^2 -> H(U1(k, e), f(c))
28.38/9.19	   A^2 -> H(U1(k, e), f(d))
28.38/9.19	   A^2 -> H(U1(k, c), U1(c, b))
28.38/9.19	   A^2 -> H(U1(k, c), U1(d, b))
28.38/9.19	   A^2 -> H(U1(k, c), U1(b, c))
28.38/9.19	   A^2 -> H(U1(k, c), U1(b, d))
28.38/9.19	   A^2 -> H(U1(k, c), U1(c, c))
28.38/9.19	   A^2 -> H(U1(k, c), f(e))
28.38/9.19	   A^2 -> H(U1(k, c), f(k))
28.38/9.19	   A^2 -> H(U1(k, c), U1(d, d))
28.38/9.19	   A^2 -> H(U1(c, e), U1(c, b))
28.38/9.19	   A^2 -> H(U1(c, e), U1(d, b))
28.38/9.19	   A^2 -> H(U1(c, e), U1(b, c))
28.38/9.19	   A^2 -> H(U1(c, e), U1(b, d))
28.38/9.19	   A^2 -> H(U1(c, e), U1(c, c))
28.38/9.19	   A^2 -> H(U1(c, e), f(e))
28.38/9.19	   A^2 -> H(U1(c, e), f(k))
28.38/9.19	   A^2 -> H(U1(c, e), U1(d, d))
28.38/9.19	   A^2 -> H(U1(c, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(c, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(c, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(c, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(c, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(c, k), f(e))
28.38/9.19	   A^2 -> H(U1(c, k), f(k))
28.38/9.19	   A^2 -> H(U1(c, k), U1(d, d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(e, b))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, b))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(d, c))
28.38/9.19	   A^2 -> H(U1(c, c), U1(b, e))
28.38/9.19	   A^2 -> H(U1(c, c), U1(b, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(e, e))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(d, k))
28.38/9.19	   A^2 -> H(e, U1(b, b))
28.38/9.19	   A^2 -> H(e, f(c))
28.38/9.19	   A^2 -> H(e, f(d))
28.38/9.19	   A^2 -> H(U1(e, e), U1(c, b))
28.38/9.19	   A^2 -> H(U1(e, e), U1(d, b))
28.38/9.19	   A^2 -> H(U1(e, e), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, e), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, e), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, e), f(e))
28.38/9.19	   A^2 -> H(U1(e, e), f(k))
28.38/9.19	   A^2 -> H(U1(e, e), U1(d, d))
28.38/9.19	   A^2 -> H(f(e), U1(e, b))
28.38/9.19	   A^2 -> H(f(e), U1(k, b))
28.38/9.19	   A^2 -> H(f(e), U1(c, d))
28.38/9.19	   A^2 -> H(f(e), U1(d, c))
28.38/9.19	   A^2 -> H(f(e), U1(b, e))
28.38/9.19	   A^2 -> H(f(e), U1(b, k))
28.38/9.19	   A^2 -> H(f(e), U1(e, c))
28.38/9.19	   A^2 -> H(f(e), U1(k, c))
28.38/9.19	   A^2 -> H(f(e), U1(c, e))
28.38/9.19	   A^2 -> H(f(e), U1(c, k))
28.38/9.19	   A^2 -> H(f(e), U1(k, k))
28.38/9.19	   A^2 -> H(f(e), U1(k, d))
28.38/9.19	   A^2 -> H(f(e), U1(d, k))
28.38/9.19	   A^2 -> H(U1(k, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(k, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(k, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(k, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(k, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(k, k), f(e))
28.38/9.19	   A^2 -> H(U1(k, k), f(k))
28.38/9.19	   A^2 -> H(U1(k, k), U1(d, d))
28.38/9.19	   A^2 -> H(f(k), U1(e, b))
28.38/9.19	   A^2 -> H(f(k), U1(k, b))
28.38/9.19	   A^2 -> H(f(k), U1(c, d))
28.38/9.19	   A^2 -> H(f(k), U1(d, c))
28.38/9.19	   A^2 -> H(f(k), U1(b, e))
28.38/9.19	   A^2 -> H(f(k), U1(b, k))
28.38/9.19	   A^2 -> H(f(k), U1(e, c))
28.38/9.19	   A^2 -> H(f(k), U1(k, c))
28.38/9.19	   A^2 -> H(f(k), U1(c, e))
28.38/9.19	   A^2 -> H(f(k), U1(c, k))
28.38/9.19	   A^2 -> H(f(k), U1(e, e))
28.38/9.19	   A^2 -> H(f(k), U1(k, d))
28.38/9.19	   A^2 -> H(f(k), U1(d, k))
28.38/9.19	   A^2 -> H(f(c), b)
28.38/9.19	   A^2 -> H(f(c), U1(e, d))
28.38/9.19	   A^2 -> H(f(c), U1(d, e))
28.38/9.19	   A^2 -> H(f(k), U1(k, k))
28.38/9.19	   A^2 -> H(U1(k, k), U1(b, b))
28.38/9.19	   A^2 -> H(U1(k, k), f(c))
28.38/9.19	   A^2 -> H(U1(k, k), f(d))
28.38/9.19	   A^2 -> H(U1(k, d), U1(c, b))
28.38/9.19	   A^2 -> H(U1(k, d), U1(d, b))
28.38/9.19	   A^2 -> H(U1(k, d), U1(b, c))
28.38/9.19	   A^2 -> H(U1(k, d), U1(b, d))
28.38/9.19	   A^2 -> H(U1(k, d), U1(c, c))
28.38/9.19	   A^2 -> H(U1(k, d), f(e))
28.38/9.19	   A^2 -> H(U1(k, d), f(k))
28.38/9.19	   A^2 -> H(U1(k, d), U1(d, d))
28.38/9.19	   A^2 -> H(U1(d, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(d, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(d, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(d, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(d, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(d, k), f(e))
28.38/9.19	   A^2 -> H(U1(d, k), f(k))
28.38/9.19	   A^2 -> H(U1(d, k), U1(d, d))
28.38/9.19	   A^2 -> H(U1(d, d), U1(e, b))
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, b))
28.38/9.19	   A^2 -> H(U1(d, d), U1(c, d))
28.38/9.19	   A^2 -> H(U1(d, d), U1(d, c))
28.38/9.19	   A^2 -> H(U1(d, d), U1(b, e))
28.38/9.19	   A^2 -> H(U1(d, d), U1(b, k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(e, c))
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, c))
28.38/9.19	   A^2 -> H(U1(d, d), U1(c, e))
28.38/9.19	   A^2 -> H(U1(d, d), U1(c, k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(e, e))
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, k))
28.38/9.19	   A^2 -> H(f(d), b)
28.38/9.19	   A^2 -> H(f(d), U1(e, d))
28.38/9.19	   A^2 -> H(f(d), U1(d, e))
28.38/9.19	   A^2 -> H(f(d), c)
28.38/9.19	   A^2 -> H(f(d), U1(e, k))
28.38/9.19	   A^2 -> H(f(d), U1(k, e))
28.38/9.19	   A^2 -> H(f(d), e)
28.38/9.19	   A^2 -> H(f(a), d)
28.38/9.19	   A^2 -> H(U1(c, c), U1(e, c))
28.38/9.19	   A^2 -> H(f(c), c)
28.38/9.19	   A^2 -> H(f(c), U1(e, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, c))
28.38/9.19	   A^2 -> H(f(c), U1(k, e))
28.38/9.19	   A^2 -> H(f(c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, e))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, k))
28.38/9.19	   A^2 -> H(f(a), k)
28.38/9.19	   A^2 -> H(f(e), U1(e, e))
28.38/9.19	   A^2 -> H(f(c), e)
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, d))
28.38/9.19	   A^2 -> H(f(d), U1(k, k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(d, k))
28.38/9.19	   A^2 -> H(d, U1(b, b))
28.38/9.19	   A^2 -> H(d, f(c))
28.38/9.19	   A^2 -> H(d, f(d))
28.38/9.19	   A^2 -> H(a, U1(c, b))
28.38/9.19	   A^2 -> H(a, U1(d, b))
28.38/9.19	   A^2 -> H(a, U1(b, c))
28.38/9.19	   A^2 -> H(a, U1(b, d))
28.38/9.19	   A^2 -> H(a, U1(c, c))
28.38/9.19	   A^2 -> H(a, f(e))
28.38/9.19	   A^2 -> H(a, f(k))
28.38/9.19	   A^2 -> H(a, U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, d), U1(c, b))
28.38/9.19	   A^2 -> H(U1(e, d), U1(d, b))
28.38/9.19	   A^2 -> H(U1(e, d), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, d), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, d), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, d), f(e))
28.38/9.19	   A^2 -> H(U1(e, d), f(k))
28.38/9.19	   A^2 -> H(U1(e, d), U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, a), U1(e, b))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, b))
28.38/9.19	   A^2 -> H(U1(e, a), U1(c, d))
28.38/9.19	   A^2 -> H(U1(e, a), U1(d, c))
28.38/9.19	   A^2 -> H(U1(e, a), U1(b, e))
28.38/9.19	   A^2 -> H(U1(e, a), U1(b, k))
28.38/9.19	   A^2 -> H(U1(e, a), U1(e, c))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, c))
28.38/9.19	   A^2 -> H(U1(e, a), U1(c, e))
28.38/9.19	   A^2 -> H(U1(e, a), U1(c, k))
28.38/9.19	   A^2 -> H(U1(e, a), U1(e, e))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, d))
28.38/9.19	   A^2 -> H(U1(e, a), U1(d, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(e, b))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, b))
28.38/9.19	   A^2 -> H(U1(k, a), U1(c, d))
28.38/9.19	   A^2 -> H(U1(k, a), U1(d, c))
28.38/9.19	   A^2 -> H(U1(k, a), U1(b, e))
28.38/9.19	   A^2 -> H(U1(k, a), U1(b, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(e, c))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, c))
28.38/9.19	   A^2 -> H(U1(k, a), U1(c, e))
28.38/9.19	   A^2 -> H(U1(k, a), U1(c, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(e, e))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, d))
28.38/9.19	   A^2 -> H(U1(k, a), U1(d, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(e, b))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, b))
28.38/9.19	   A^2 -> H(U1(c, d), U1(c, d))
28.38/9.19	   A^2 -> H(U1(c, d), U1(d, c))
28.38/9.19	   A^2 -> H(U1(c, d), U1(b, e))
28.38/9.19	   A^2 -> H(U1(c, d), U1(b, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(e, c))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, c))
28.38/9.19	   A^2 -> H(U1(c, d), U1(c, e))
28.38/9.19	   A^2 -> H(U1(c, d), U1(c, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(e, e))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, d))
28.38/9.19	   A^2 -> H(U1(c, d), U1(d, k))
28.38/9.19	   A^2 -> H(U1(c, a), b)
28.38/9.19	   A^2 -> H(U1(c, a), U1(e, d))
28.38/9.19	   A^2 -> H(U1(c, a), U1(d, e))
28.38/9.19	   A^2 -> H(U1(c, a), c)
28.38/9.19	   A^2 -> H(U1(c, a), U1(e, k))
28.38/9.19	   A^2 -> H(U1(c, a), U1(k, e))
28.38/9.19	   A^2 -> H(U1(c, a), e)
28.38/9.19	   A^2 -> H(U1(c, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(d, e), U1(c, b))
28.38/9.19	   A^2 -> H(U1(d, e), U1(d, b))
28.38/9.19	   A^2 -> H(U1(d, e), U1(b, c))
28.38/9.19	   A^2 -> H(U1(d, e), U1(b, d))
28.38/9.19	   A^2 -> H(U1(d, e), U1(c, c))
28.38/9.19	   A^2 -> H(U1(d, e), f(e))
28.38/9.19	   A^2 -> H(U1(d, e), f(k))
28.38/9.19	   A^2 -> H(U1(d, e), U1(d, d))
28.38/9.19	   A^2 -> H(U1(d, c), U1(e, b))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, b))
28.38/9.19	   A^2 -> H(U1(d, c), U1(c, d))
28.38/9.19	   A^2 -> H(U1(d, c), U1(d, c))
28.38/9.19	   A^2 -> H(U1(d, c), U1(b, e))
28.38/9.19	   A^2 -> H(U1(d, c), U1(b, k))
28.38/9.19	   A^2 -> H(U1(d, c), U1(e, c))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, c))
28.38/9.19	   A^2 -> H(U1(d, c), U1(c, e))
28.38/9.19	   A^2 -> H(U1(d, c), U1(c, k))
28.38/9.19	   A^2 -> H(U1(d, c), U1(e, e))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, d))
28.38/9.19	   A^2 -> H(U1(d, c), U1(d, k))
28.38/9.19	   A^2 -> H(U1(d, a), b)
28.38/9.19	   A^2 -> H(U1(d, a), U1(e, d))
28.38/9.19	   A^2 -> H(U1(d, a), U1(d, e))
28.38/9.19	   A^2 -> H(U1(d, a), c)
28.38/9.19	   A^2 -> H(U1(d, a), U1(e, k))
28.38/9.19	   A^2 -> H(U1(d, a), U1(k, e))
28.38/9.19	   A^2 -> H(U1(d, a), e)
28.38/9.19	   A^2 -> H(U1(d, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(e, b))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, b))
28.38/9.19	   A^2 -> H(U1(a, e), U1(c, d))
28.38/9.19	   A^2 -> H(U1(a, e), U1(d, c))
28.38/9.19	   A^2 -> H(U1(a, e), U1(b, e))
28.38/9.19	   A^2 -> H(U1(a, e), U1(b, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(e, c))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, c))
28.38/9.19	   A^2 -> H(U1(a, e), U1(c, e))
28.38/9.19	   A^2 -> H(U1(a, e), U1(c, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(e, e))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, d))
28.38/9.19	   A^2 -> H(U1(a, e), U1(d, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(e, b))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, b))
28.38/9.19	   A^2 -> H(U1(a, k), U1(c, d))
28.38/9.19	   A^2 -> H(U1(a, k), U1(d, c))
28.38/9.19	   A^2 -> H(U1(a, k), U1(b, e))
28.38/9.19	   A^2 -> H(U1(a, k), U1(b, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(e, c))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, c))
28.38/9.19	   A^2 -> H(U1(a, k), U1(c, e))
28.38/9.19	   A^2 -> H(U1(a, k), U1(c, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(e, e))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, d))
28.38/9.19	   A^2 -> H(U1(a, k), U1(d, k))
28.38/9.19	   A^2 -> H(U1(a, c), b)
28.38/9.19	   A^2 -> H(U1(a, c), U1(e, d))
28.38/9.19	   A^2 -> H(U1(a, c), U1(d, e))
28.38/9.19	   A^2 -> H(U1(a, c), c)
28.38/9.19	   A^2 -> H(U1(a, c), U1(e, k))
28.38/9.19	   A^2 -> H(U1(a, c), U1(k, e))
28.38/9.19	   A^2 -> H(U1(a, c), e)
28.38/9.19	   A^2 -> H(U1(a, c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, d), b)
28.38/9.19	   A^2 -> H(U1(a, d), U1(e, d))
28.38/9.19	   A^2 -> H(U1(a, d), U1(d, e))
28.38/9.19	   A^2 -> H(U1(a, d), c)
28.38/9.19	   A^2 -> H(U1(a, d), U1(e, k))
28.38/9.19	   A^2 -> H(U1(a, d), U1(k, e))
28.38/9.19	   A^2 -> H(U1(a, d), e)
28.38/9.19	   A^2 -> H(U1(a, d), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, a), d)
28.38/9.19	   A^2 -> H(U1(a, a), k)
28.38/9.19	   A^2 -> H(k, U1(b, b))
28.38/9.19	   A^2 -> H(k, f(c))
28.38/9.19	   A^2 -> H(k, f(d))
28.38/9.19	   A^2 -> H(c, U1(c, b))
28.38/9.19	   A^2 -> H(c, U1(d, b))
28.38/9.19	   A^2 -> H(c, U1(b, c))
28.38/9.19	   A^2 -> H(c, U1(b, d))
28.38/9.19	   A^2 -> H(c, U1(c, c))
28.38/9.19	   A^2 -> H(c, f(e))
28.38/9.19	   A^2 -> H(c, f(k))
28.38/9.19	   A^2 -> H(c, U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(e, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(e, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, k), f(e))
28.38/9.19	   A^2 -> H(U1(e, k), f(k))
28.38/9.19	   A^2 -> H(U1(e, k), U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, c), U1(e, b))
28.38/9.19	   A^2 -> H(U1(e, c), U1(k, b))
28.38/9.19	   A^2 -> H(U1(e, c), U1(c, d))
28.38/9.19	
28.38/9.19	The TRS R consists of the following rules:
28.38/9.19	
28.38/9.19	   f(x) -> U1(x, x)
28.38/9.19	   U1(e, x) -> x
28.38/9.19	   a -> c
28.38/9.19	   a -> d
28.38/9.19	   b -> c
28.38/9.19	   b -> d
28.38/9.19	   d -> k
28.38/9.19	   c -> e
28.38/9.19	   c -> k
28.38/9.19	
28.38/9.19	Q is empty.
28.38/9.19	We have to consider all minimal (P,Q,R)-chains.
28.38/9.19	----------------------------------------
28.38/9.19	
28.38/9.19	(801) TransformationProof (EQUIVALENT)
28.38/9.19	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
28.38/9.19	
28.38/9.19	   (A^2 -> H(c, U1(d, b)),A^2 -> H(c, U1(d, b)))
28.38/9.19	   (A^2 -> H(U1(e, e), U1(d, b)),A^2 -> H(U1(e, e), U1(d, b)))
28.38/9.19	   (A^2 -> H(U1(e, k), U1(d, b)),A^2 -> H(U1(e, k), U1(d, b)))
28.38/9.19	   (A^2 -> H(U1(e, c), U1(k, b)),A^2 -> H(U1(e, c), U1(k, b)))
28.38/9.19	   (A^2 -> H(U1(e, c), U1(d, c)),A^2 -> H(U1(e, c), U1(d, c)))
28.38/9.19	   (A^2 -> H(U1(e, c), U1(d, d)),A^2 -> H(U1(e, c), U1(d, d)))
28.38/9.19	
28.38/9.19	
28.38/9.19	----------------------------------------
28.38/9.19	
28.38/9.19	(802)
28.38/9.19	Obligation:
28.38/9.19	Q DP problem:
28.38/9.19	The TRS P consists of the following rules:
28.38/9.19	
28.38/9.19	   H(x, x) -> G(x, x, f(k))
28.38/9.19	   G(d, x, x) -> A^2
28.38/9.19	   A^2 -> H(f(c), f(c))
28.38/9.19	   A^2 -> H(f(d), f(d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, c))
28.38/9.19	   A^2 -> H(f(e), f(e))
28.38/9.19	   A^2 -> H(f(k), f(k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, c), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, c), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, c), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, c), f(e))
28.38/9.19	   A^2 -> H(U1(e, c), f(k))
28.38/9.19	   A^2 -> H(U1(e, c), U1(d, d))
28.38/9.19	   A^2 -> H(U1(k, e), U1(b, b))
28.38/9.19	   A^2 -> H(U1(k, e), f(c))
28.38/9.19	   A^2 -> H(U1(k, e), f(d))
28.38/9.19	   A^2 -> H(U1(k, c), U1(c, b))
28.38/9.19	   A^2 -> H(U1(k, c), U1(d, b))
28.38/9.19	   A^2 -> H(U1(k, c), U1(b, c))
28.38/9.19	   A^2 -> H(U1(k, c), U1(b, d))
28.38/9.19	   A^2 -> H(U1(k, c), U1(c, c))
28.38/9.19	   A^2 -> H(U1(k, c), f(e))
28.38/9.19	   A^2 -> H(U1(k, c), f(k))
28.38/9.19	   A^2 -> H(U1(k, c), U1(d, d))
28.38/9.19	   A^2 -> H(U1(c, e), U1(c, b))
28.38/9.19	   A^2 -> H(U1(c, e), U1(d, b))
28.38/9.19	   A^2 -> H(U1(c, e), U1(b, c))
28.38/9.19	   A^2 -> H(U1(c, e), U1(b, d))
28.38/9.19	   A^2 -> H(U1(c, e), U1(c, c))
28.38/9.19	   A^2 -> H(U1(c, e), f(e))
28.38/9.19	   A^2 -> H(U1(c, e), f(k))
28.38/9.19	   A^2 -> H(U1(c, e), U1(d, d))
28.38/9.19	   A^2 -> H(U1(c, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(c, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(c, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(c, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(c, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(c, k), f(e))
28.38/9.19	   A^2 -> H(U1(c, k), f(k))
28.38/9.19	   A^2 -> H(U1(c, k), U1(d, d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(e, b))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, b))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(d, c))
28.38/9.19	   A^2 -> H(U1(c, c), U1(b, e))
28.38/9.19	   A^2 -> H(U1(c, c), U1(b, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(e, e))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(d, k))
28.38/9.19	   A^2 -> H(e, U1(b, b))
28.38/9.19	   A^2 -> H(e, f(c))
28.38/9.19	   A^2 -> H(e, f(d))
28.38/9.19	   A^2 -> H(U1(e, e), U1(c, b))
28.38/9.19	   A^2 -> H(U1(e, e), U1(d, b))
28.38/9.19	   A^2 -> H(U1(e, e), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, e), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, e), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, e), f(e))
28.38/9.19	   A^2 -> H(U1(e, e), f(k))
28.38/9.19	   A^2 -> H(U1(e, e), U1(d, d))
28.38/9.19	   A^2 -> H(f(e), U1(e, b))
28.38/9.19	   A^2 -> H(f(e), U1(k, b))
28.38/9.19	   A^2 -> H(f(e), U1(c, d))
28.38/9.19	   A^2 -> H(f(e), U1(d, c))
28.38/9.19	   A^2 -> H(f(e), U1(b, e))
28.38/9.19	   A^2 -> H(f(e), U1(b, k))
28.38/9.19	   A^2 -> H(f(e), U1(e, c))
28.38/9.19	   A^2 -> H(f(e), U1(k, c))
28.38/9.19	   A^2 -> H(f(e), U1(c, e))
28.38/9.19	   A^2 -> H(f(e), U1(c, k))
28.38/9.19	   A^2 -> H(f(e), U1(k, k))
28.38/9.19	   A^2 -> H(f(e), U1(k, d))
28.38/9.19	   A^2 -> H(f(e), U1(d, k))
28.38/9.19	   A^2 -> H(U1(k, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(k, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(k, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(k, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(k, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(k, k), f(e))
28.38/9.19	   A^2 -> H(U1(k, k), f(k))
28.38/9.19	   A^2 -> H(U1(k, k), U1(d, d))
28.38/9.19	   A^2 -> H(f(k), U1(e, b))
28.38/9.19	   A^2 -> H(f(k), U1(k, b))
28.38/9.19	   A^2 -> H(f(k), U1(c, d))
28.38/9.19	   A^2 -> H(f(k), U1(d, c))
28.38/9.19	   A^2 -> H(f(k), U1(b, e))
28.38/9.19	   A^2 -> H(f(k), U1(b, k))
28.38/9.19	   A^2 -> H(f(k), U1(e, c))
28.38/9.19	   A^2 -> H(f(k), U1(k, c))
28.38/9.19	   A^2 -> H(f(k), U1(c, e))
28.38/9.19	   A^2 -> H(f(k), U1(c, k))
28.38/9.19	   A^2 -> H(f(k), U1(e, e))
28.38/9.19	   A^2 -> H(f(k), U1(k, d))
28.38/9.19	   A^2 -> H(f(k), U1(d, k))
28.38/9.19	   A^2 -> H(f(c), b)
28.38/9.19	   A^2 -> H(f(c), U1(e, d))
28.38/9.19	   A^2 -> H(f(c), U1(d, e))
28.38/9.19	   A^2 -> H(f(k), U1(k, k))
28.38/9.19	   A^2 -> H(U1(k, k), U1(b, b))
28.38/9.19	   A^2 -> H(U1(k, k), f(c))
28.38/9.19	   A^2 -> H(U1(k, k), f(d))
28.38/9.19	   A^2 -> H(U1(k, d), U1(c, b))
28.38/9.19	   A^2 -> H(U1(k, d), U1(d, b))
28.38/9.19	   A^2 -> H(U1(k, d), U1(b, c))
28.38/9.19	   A^2 -> H(U1(k, d), U1(b, d))
28.38/9.19	   A^2 -> H(U1(k, d), U1(c, c))
28.38/9.19	   A^2 -> H(U1(k, d), f(e))
28.38/9.19	   A^2 -> H(U1(k, d), f(k))
28.38/9.19	   A^2 -> H(U1(k, d), U1(d, d))
28.38/9.19	   A^2 -> H(U1(d, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(d, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(d, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(d, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(d, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(d, k), f(e))
28.38/9.19	   A^2 -> H(U1(d, k), f(k))
28.38/9.19	   A^2 -> H(U1(d, k), U1(d, d))
28.38/9.19	   A^2 -> H(U1(d, d), U1(e, b))
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, b))
28.38/9.19	   A^2 -> H(U1(d, d), U1(c, d))
28.38/9.19	   A^2 -> H(U1(d, d), U1(d, c))
28.38/9.19	   A^2 -> H(U1(d, d), U1(b, e))
28.38/9.19	   A^2 -> H(U1(d, d), U1(b, k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(e, c))
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, c))
28.38/9.19	   A^2 -> H(U1(d, d), U1(c, e))
28.38/9.19	   A^2 -> H(U1(d, d), U1(c, k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(e, e))
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, k))
28.38/9.19	   A^2 -> H(f(d), b)
28.38/9.19	   A^2 -> H(f(d), U1(e, d))
28.38/9.19	   A^2 -> H(f(d), U1(d, e))
28.38/9.19	   A^2 -> H(f(d), c)
28.38/9.19	   A^2 -> H(f(d), U1(e, k))
28.38/9.19	   A^2 -> H(f(d), U1(k, e))
28.38/9.19	   A^2 -> H(f(d), e)
28.38/9.19	   A^2 -> H(f(a), d)
28.38/9.19	   A^2 -> H(U1(c, c), U1(e, c))
28.38/9.19	   A^2 -> H(f(c), c)
28.38/9.19	   A^2 -> H(f(c), U1(e, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, c))
28.38/9.19	   A^2 -> H(f(c), U1(k, e))
28.38/9.19	   A^2 -> H(f(c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, e))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, k))
28.38/9.19	   A^2 -> H(f(a), k)
28.38/9.19	   A^2 -> H(f(e), U1(e, e))
28.38/9.19	   A^2 -> H(f(c), e)
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, d))
28.38/9.19	   A^2 -> H(f(d), U1(k, k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(d, k))
28.38/9.19	   A^2 -> H(d, U1(b, b))
28.38/9.19	   A^2 -> H(d, f(c))
28.38/9.19	   A^2 -> H(d, f(d))
28.38/9.19	   A^2 -> H(a, U1(c, b))
28.38/9.19	   A^2 -> H(a, U1(d, b))
28.38/9.19	   A^2 -> H(a, U1(b, c))
28.38/9.19	   A^2 -> H(a, U1(b, d))
28.38/9.19	   A^2 -> H(a, U1(c, c))
28.38/9.19	   A^2 -> H(a, f(e))
28.38/9.19	   A^2 -> H(a, f(k))
28.38/9.19	   A^2 -> H(a, U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, d), U1(c, b))
28.38/9.19	   A^2 -> H(U1(e, d), U1(d, b))
28.38/9.19	   A^2 -> H(U1(e, d), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, d), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, d), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, d), f(e))
28.38/9.19	   A^2 -> H(U1(e, d), f(k))
28.38/9.19	   A^2 -> H(U1(e, d), U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, a), U1(e, b))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, b))
28.38/9.19	   A^2 -> H(U1(e, a), U1(c, d))
28.38/9.19	   A^2 -> H(U1(e, a), U1(d, c))
28.38/9.19	   A^2 -> H(U1(e, a), U1(b, e))
28.38/9.19	   A^2 -> H(U1(e, a), U1(b, k))
28.38/9.19	   A^2 -> H(U1(e, a), U1(e, c))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, c))
28.38/9.19	   A^2 -> H(U1(e, a), U1(c, e))
28.38/9.19	   A^2 -> H(U1(e, a), U1(c, k))
28.38/9.19	   A^2 -> H(U1(e, a), U1(e, e))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, d))
28.38/9.19	   A^2 -> H(U1(e, a), U1(d, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(e, b))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, b))
28.38/9.19	   A^2 -> H(U1(k, a), U1(c, d))
28.38/9.19	   A^2 -> H(U1(k, a), U1(d, c))
28.38/9.19	   A^2 -> H(U1(k, a), U1(b, e))
28.38/9.19	   A^2 -> H(U1(k, a), U1(b, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(e, c))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, c))
28.38/9.19	   A^2 -> H(U1(k, a), U1(c, e))
28.38/9.19	   A^2 -> H(U1(k, a), U1(c, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(e, e))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, d))
28.38/9.19	   A^2 -> H(U1(k, a), U1(d, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(e, b))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, b))
28.38/9.19	   A^2 -> H(U1(c, d), U1(c, d))
28.38/9.19	   A^2 -> H(U1(c, d), U1(d, c))
28.38/9.19	   A^2 -> H(U1(c, d), U1(b, e))
28.38/9.19	   A^2 -> H(U1(c, d), U1(b, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(e, c))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, c))
28.38/9.19	   A^2 -> H(U1(c, d), U1(c, e))
28.38/9.19	   A^2 -> H(U1(c, d), U1(c, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(e, e))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, d))
28.38/9.19	   A^2 -> H(U1(c, d), U1(d, k))
28.38/9.19	   A^2 -> H(U1(c, a), b)
28.38/9.19	   A^2 -> H(U1(c, a), U1(e, d))
28.38/9.19	   A^2 -> H(U1(c, a), U1(d, e))
28.38/9.19	   A^2 -> H(U1(c, a), c)
28.38/9.19	   A^2 -> H(U1(c, a), U1(e, k))
28.38/9.19	   A^2 -> H(U1(c, a), U1(k, e))
28.38/9.19	   A^2 -> H(U1(c, a), e)
28.38/9.19	   A^2 -> H(U1(c, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(d, e), U1(c, b))
28.38/9.19	   A^2 -> H(U1(d, e), U1(d, b))
28.38/9.19	   A^2 -> H(U1(d, e), U1(b, c))
28.38/9.19	   A^2 -> H(U1(d, e), U1(b, d))
28.38/9.19	   A^2 -> H(U1(d, e), U1(c, c))
28.38/9.19	   A^2 -> H(U1(d, e), f(e))
28.38/9.19	   A^2 -> H(U1(d, e), f(k))
28.38/9.19	   A^2 -> H(U1(d, e), U1(d, d))
28.38/9.19	   A^2 -> H(U1(d, c), U1(e, b))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, b))
28.38/9.19	   A^2 -> H(U1(d, c), U1(c, d))
28.38/9.19	   A^2 -> H(U1(d, c), U1(d, c))
28.38/9.19	   A^2 -> H(U1(d, c), U1(b, e))
28.38/9.19	   A^2 -> H(U1(d, c), U1(b, k))
28.38/9.19	   A^2 -> H(U1(d, c), U1(e, c))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, c))
28.38/9.19	   A^2 -> H(U1(d, c), U1(c, e))
28.38/9.19	   A^2 -> H(U1(d, c), U1(c, k))
28.38/9.19	   A^2 -> H(U1(d, c), U1(e, e))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(d, c), U1(k, d))
28.38/9.19	   A^2 -> H(U1(d, c), U1(d, k))
28.38/9.19	   A^2 -> H(U1(d, a), b)
28.38/9.19	   A^2 -> H(U1(d, a), U1(e, d))
28.38/9.19	   A^2 -> H(U1(d, a), U1(d, e))
28.38/9.19	   A^2 -> H(U1(d, a), c)
28.38/9.19	   A^2 -> H(U1(d, a), U1(e, k))
28.38/9.19	   A^2 -> H(U1(d, a), U1(k, e))
28.38/9.19	   A^2 -> H(U1(d, a), e)
28.38/9.19	   A^2 -> H(U1(d, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(e, b))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, b))
28.38/9.19	   A^2 -> H(U1(a, e), U1(c, d))
28.38/9.19	   A^2 -> H(U1(a, e), U1(d, c))
28.38/9.19	   A^2 -> H(U1(a, e), U1(b, e))
28.38/9.19	   A^2 -> H(U1(a, e), U1(b, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(e, c))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, c))
28.38/9.19	   A^2 -> H(U1(a, e), U1(c, e))
28.38/9.19	   A^2 -> H(U1(a, e), U1(c, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(e, e))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, e), U1(k, d))
28.38/9.19	   A^2 -> H(U1(a, e), U1(d, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(e, b))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, b))
28.38/9.19	   A^2 -> H(U1(a, k), U1(c, d))
28.38/9.19	   A^2 -> H(U1(a, k), U1(d, c))
28.38/9.19	   A^2 -> H(U1(a, k), U1(b, e))
28.38/9.19	   A^2 -> H(U1(a, k), U1(b, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(e, c))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, c))
28.38/9.19	   A^2 -> H(U1(a, k), U1(c, e))
28.38/9.19	   A^2 -> H(U1(a, k), U1(c, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(e, e))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, k), U1(k, d))
28.38/9.19	   A^2 -> H(U1(a, k), U1(d, k))
28.38/9.19	   A^2 -> H(U1(a, c), b)
28.38/9.19	   A^2 -> H(U1(a, c), U1(e, d))
28.38/9.19	   A^2 -> H(U1(a, c), U1(d, e))
28.38/9.19	   A^2 -> H(U1(a, c), c)
28.38/9.19	   A^2 -> H(U1(a, c), U1(e, k))
28.38/9.19	   A^2 -> H(U1(a, c), U1(k, e))
28.38/9.19	   A^2 -> H(U1(a, c), e)
28.38/9.19	   A^2 -> H(U1(a, c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, d), b)
28.38/9.19	   A^2 -> H(U1(a, d), U1(e, d))
28.38/9.19	   A^2 -> H(U1(a, d), U1(d, e))
28.38/9.19	   A^2 -> H(U1(a, d), c)
28.38/9.19	   A^2 -> H(U1(a, d), U1(e, k))
28.38/9.19	   A^2 -> H(U1(a, d), U1(k, e))
28.38/9.19	   A^2 -> H(U1(a, d), e)
28.38/9.19	   A^2 -> H(U1(a, d), U1(k, k))
28.38/9.19	   A^2 -> H(U1(a, a), d)
28.38/9.19	   A^2 -> H(U1(a, a), k)
28.38/9.19	   A^2 -> H(k, U1(b, b))
28.38/9.19	   A^2 -> H(k, f(c))
28.38/9.19	   A^2 -> H(k, f(d))
28.38/9.19	   A^2 -> H(c, U1(c, b))
28.38/9.19	   A^2 -> H(c, U1(d, b))
28.38/9.19	   A^2 -> H(c, U1(b, c))
28.38/9.19	   A^2 -> H(c, U1(b, d))
28.38/9.19	   A^2 -> H(c, U1(c, c))
28.38/9.19	   A^2 -> H(c, f(e))
28.38/9.19	   A^2 -> H(c, f(k))
28.38/9.19	   A^2 -> H(c, U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(e, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(e, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, k), f(e))
28.38/9.19	   A^2 -> H(U1(e, k), f(k))
28.38/9.19	   A^2 -> H(U1(e, k), U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, c), U1(e, b))
28.38/9.19	   A^2 -> H(U1(e, c), U1(k, b))
28.38/9.19	   A^2 -> H(U1(e, c), U1(c, d))
28.38/9.19	   A^2 -> H(U1(e, c), U1(d, c))
28.38/9.19	
28.38/9.19	The TRS R consists of the following rules:
28.38/9.19	
28.38/9.19	   f(x) -> U1(x, x)
28.38/9.19	   U1(e, x) -> x
28.38/9.19	   a -> c
28.38/9.19	   a -> d
28.38/9.19	   b -> c
28.38/9.19	   b -> d
28.38/9.19	   d -> k
28.38/9.19	   c -> e
28.38/9.19	   c -> k
28.38/9.19	
28.38/9.19	Q is empty.
28.38/9.19	We have to consider all minimal (P,Q,R)-chains.
28.38/9.19	----------------------------------------
28.38/9.19	
28.38/9.19	(803) TransformationProof (EQUIVALENT)
28.38/9.19	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
28.38/9.19	
28.38/9.19	   (A^2 -> H(c, U1(b, c)),A^2 -> H(c, U1(b, c)))
28.38/9.19	   (A^2 -> H(U1(e, e), U1(b, c)),A^2 -> H(U1(e, e), U1(b, c)))
28.38/9.19	   (A^2 -> H(U1(e, k), U1(b, c)),A^2 -> H(U1(e, k), U1(b, c)))
28.38/9.19	   (A^2 -> H(U1(e, c), U1(c, c)),A^2 -> H(U1(e, c), U1(c, c)))
28.38/9.19	   (A^2 -> H(U1(e, c), U1(d, c)),A^2 -> H(U1(e, c), U1(d, c)))
28.38/9.19	   (A^2 -> H(U1(e, c), U1(b, e)),A^2 -> H(U1(e, c), U1(b, e)))
28.38/9.19	   (A^2 -> H(U1(e, c), U1(b, k)),A^2 -> H(U1(e, c), U1(b, k)))
28.38/9.19	
28.38/9.19	
28.38/9.19	----------------------------------------
28.38/9.19	
28.38/9.19	(804)
28.38/9.19	Obligation:
28.38/9.19	Q DP problem:
28.38/9.19	The TRS P consists of the following rules:
28.38/9.19	
28.38/9.19	   H(x, x) -> G(x, x, f(k))
28.38/9.19	   G(d, x, x) -> A^2
28.38/9.19	   A^2 -> H(f(c), f(c))
28.38/9.19	   A^2 -> H(f(d), f(d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, c))
28.38/9.19	   A^2 -> H(f(e), f(e))
28.38/9.19	   A^2 -> H(f(k), f(k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, c), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, c), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, c), f(e))
28.38/9.19	   A^2 -> H(U1(e, c), f(k))
28.38/9.19	   A^2 -> H(U1(e, c), U1(d, d))
28.38/9.19	   A^2 -> H(U1(k, e), U1(b, b))
28.38/9.19	   A^2 -> H(U1(k, e), f(c))
28.38/9.19	   A^2 -> H(U1(k, e), f(d))
28.38/9.19	   A^2 -> H(U1(k, c), U1(c, b))
28.38/9.19	   A^2 -> H(U1(k, c), U1(d, b))
28.38/9.19	   A^2 -> H(U1(k, c), U1(b, c))
28.38/9.19	   A^2 -> H(U1(k, c), U1(b, d))
28.38/9.19	   A^2 -> H(U1(k, c), U1(c, c))
28.38/9.19	   A^2 -> H(U1(k, c), f(e))
28.38/9.19	   A^2 -> H(U1(k, c), f(k))
28.38/9.19	   A^2 -> H(U1(k, c), U1(d, d))
28.38/9.19	   A^2 -> H(U1(c, e), U1(c, b))
28.38/9.19	   A^2 -> H(U1(c, e), U1(d, b))
28.38/9.19	   A^2 -> H(U1(c, e), U1(b, c))
28.38/9.19	   A^2 -> H(U1(c, e), U1(b, d))
28.38/9.19	   A^2 -> H(U1(c, e), U1(c, c))
28.38/9.19	   A^2 -> H(U1(c, e), f(e))
28.38/9.19	   A^2 -> H(U1(c, e), f(k))
28.38/9.19	   A^2 -> H(U1(c, e), U1(d, d))
28.38/9.19	   A^2 -> H(U1(c, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(c, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(c, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(c, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(c, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(c, k), f(e))
28.38/9.19	   A^2 -> H(U1(c, k), f(k))
28.38/9.19	   A^2 -> H(U1(c, k), U1(d, d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(e, b))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, b))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(d, c))
28.38/9.19	   A^2 -> H(U1(c, c), U1(b, e))
28.38/9.19	   A^2 -> H(U1(c, c), U1(b, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(e, e))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, d))
28.38/9.19	   A^2 -> H(U1(c, c), U1(d, k))
28.38/9.19	   A^2 -> H(e, U1(b, b))
28.38/9.19	   A^2 -> H(e, f(c))
28.38/9.19	   A^2 -> H(e, f(d))
28.38/9.19	   A^2 -> H(U1(e, e), U1(c, b))
28.38/9.19	   A^2 -> H(U1(e, e), U1(d, b))
28.38/9.19	   A^2 -> H(U1(e, e), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, e), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, e), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, e), f(e))
28.38/9.19	   A^2 -> H(U1(e, e), f(k))
28.38/9.19	   A^2 -> H(U1(e, e), U1(d, d))
28.38/9.19	   A^2 -> H(f(e), U1(e, b))
28.38/9.19	   A^2 -> H(f(e), U1(k, b))
28.38/9.19	   A^2 -> H(f(e), U1(c, d))
28.38/9.19	   A^2 -> H(f(e), U1(d, c))
28.38/9.19	   A^2 -> H(f(e), U1(b, e))
28.38/9.19	   A^2 -> H(f(e), U1(b, k))
28.38/9.19	   A^2 -> H(f(e), U1(e, c))
28.38/9.19	   A^2 -> H(f(e), U1(k, c))
28.38/9.19	   A^2 -> H(f(e), U1(c, e))
28.38/9.19	   A^2 -> H(f(e), U1(c, k))
28.38/9.19	   A^2 -> H(f(e), U1(k, k))
28.38/9.19	   A^2 -> H(f(e), U1(k, d))
28.38/9.19	   A^2 -> H(f(e), U1(d, k))
28.38/9.19	   A^2 -> H(U1(k, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(k, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(k, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(k, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(k, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(k, k), f(e))
28.38/9.19	   A^2 -> H(U1(k, k), f(k))
28.38/9.19	   A^2 -> H(U1(k, k), U1(d, d))
28.38/9.19	   A^2 -> H(f(k), U1(e, b))
28.38/9.19	   A^2 -> H(f(k), U1(k, b))
28.38/9.19	   A^2 -> H(f(k), U1(c, d))
28.38/9.19	   A^2 -> H(f(k), U1(d, c))
28.38/9.19	   A^2 -> H(f(k), U1(b, e))
28.38/9.19	   A^2 -> H(f(k), U1(b, k))
28.38/9.19	   A^2 -> H(f(k), U1(e, c))
28.38/9.19	   A^2 -> H(f(k), U1(k, c))
28.38/9.19	   A^2 -> H(f(k), U1(c, e))
28.38/9.19	   A^2 -> H(f(k), U1(c, k))
28.38/9.19	   A^2 -> H(f(k), U1(e, e))
28.38/9.19	   A^2 -> H(f(k), U1(k, d))
28.38/9.19	   A^2 -> H(f(k), U1(d, k))
28.38/9.19	   A^2 -> H(f(c), b)
28.38/9.19	   A^2 -> H(f(c), U1(e, d))
28.38/9.19	   A^2 -> H(f(c), U1(d, e))
28.38/9.19	   A^2 -> H(f(k), U1(k, k))
28.38/9.19	   A^2 -> H(U1(k, k), U1(b, b))
28.38/9.19	   A^2 -> H(U1(k, k), f(c))
28.38/9.19	   A^2 -> H(U1(k, k), f(d))
28.38/9.19	   A^2 -> H(U1(k, d), U1(c, b))
28.38/9.19	   A^2 -> H(U1(k, d), U1(d, b))
28.38/9.19	   A^2 -> H(U1(k, d), U1(b, c))
28.38/9.19	   A^2 -> H(U1(k, d), U1(b, d))
28.38/9.19	   A^2 -> H(U1(k, d), U1(c, c))
28.38/9.19	   A^2 -> H(U1(k, d), f(e))
28.38/9.19	   A^2 -> H(U1(k, d), f(k))
28.38/9.19	   A^2 -> H(U1(k, d), U1(d, d))
28.38/9.19	   A^2 -> H(U1(d, k), U1(c, b))
28.38/9.19	   A^2 -> H(U1(d, k), U1(d, b))
28.38/9.19	   A^2 -> H(U1(d, k), U1(b, c))
28.38/9.19	   A^2 -> H(U1(d, k), U1(b, d))
28.38/9.19	   A^2 -> H(U1(d, k), U1(c, c))
28.38/9.19	   A^2 -> H(U1(d, k), f(e))
28.38/9.19	   A^2 -> H(U1(d, k), f(k))
28.38/9.19	   A^2 -> H(U1(d, k), U1(d, d))
28.38/9.19	   A^2 -> H(U1(d, d), U1(e, b))
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, b))
28.38/9.19	   A^2 -> H(U1(d, d), U1(c, d))
28.38/9.19	   A^2 -> H(U1(d, d), U1(d, c))
28.38/9.19	   A^2 -> H(U1(d, d), U1(b, e))
28.38/9.19	   A^2 -> H(U1(d, d), U1(b, k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(e, c))
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, c))
28.38/9.19	   A^2 -> H(U1(d, d), U1(c, e))
28.38/9.19	   A^2 -> H(U1(d, d), U1(c, k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(e, e))
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, k))
28.38/9.19	   A^2 -> H(f(d), b)
28.38/9.19	   A^2 -> H(f(d), U1(e, d))
28.38/9.19	   A^2 -> H(f(d), U1(d, e))
28.38/9.19	   A^2 -> H(f(d), c)
28.38/9.19	   A^2 -> H(f(d), U1(e, k))
28.38/9.19	   A^2 -> H(f(d), U1(k, e))
28.38/9.19	   A^2 -> H(f(d), e)
28.38/9.19	   A^2 -> H(f(a), d)
28.38/9.19	   A^2 -> H(U1(c, c), U1(e, c))
28.38/9.19	   A^2 -> H(f(c), c)
28.38/9.19	   A^2 -> H(f(c), U1(e, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(k, c))
28.38/9.19	   A^2 -> H(f(c), U1(k, e))
28.38/9.19	   A^2 -> H(f(c), U1(k, k))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, e))
28.38/9.19	   A^2 -> H(U1(c, c), U1(c, k))
28.38/9.19	   A^2 -> H(f(a), k)
28.38/9.19	   A^2 -> H(f(e), U1(e, e))
28.38/9.19	   A^2 -> H(f(c), e)
28.38/9.19	   A^2 -> H(U1(d, d), U1(k, d))
28.38/9.19	   A^2 -> H(f(d), U1(k, k))
28.38/9.19	   A^2 -> H(U1(d, d), U1(d, k))
28.38/9.19	   A^2 -> H(d, U1(b, b))
28.38/9.19	   A^2 -> H(d, f(c))
28.38/9.19	   A^2 -> H(d, f(d))
28.38/9.19	   A^2 -> H(a, U1(c, b))
28.38/9.19	   A^2 -> H(a, U1(d, b))
28.38/9.19	   A^2 -> H(a, U1(b, c))
28.38/9.19	   A^2 -> H(a, U1(b, d))
28.38/9.19	   A^2 -> H(a, U1(c, c))
28.38/9.19	   A^2 -> H(a, f(e))
28.38/9.19	   A^2 -> H(a, f(k))
28.38/9.19	   A^2 -> H(a, U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, d), U1(c, b))
28.38/9.19	   A^2 -> H(U1(e, d), U1(d, b))
28.38/9.19	   A^2 -> H(U1(e, d), U1(b, c))
28.38/9.19	   A^2 -> H(U1(e, d), U1(b, d))
28.38/9.19	   A^2 -> H(U1(e, d), U1(c, c))
28.38/9.19	   A^2 -> H(U1(e, d), f(e))
28.38/9.19	   A^2 -> H(U1(e, d), f(k))
28.38/9.19	   A^2 -> H(U1(e, d), U1(d, d))
28.38/9.19	   A^2 -> H(U1(e, a), U1(e, b))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, b))
28.38/9.19	   A^2 -> H(U1(e, a), U1(c, d))
28.38/9.19	   A^2 -> H(U1(e, a), U1(d, c))
28.38/9.19	   A^2 -> H(U1(e, a), U1(b, e))
28.38/9.19	   A^2 -> H(U1(e, a), U1(b, k))
28.38/9.19	   A^2 -> H(U1(e, a), U1(e, c))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, c))
28.38/9.19	   A^2 -> H(U1(e, a), U1(c, e))
28.38/9.19	   A^2 -> H(U1(e, a), U1(c, k))
28.38/9.19	   A^2 -> H(U1(e, a), U1(e, e))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(e, a), U1(k, d))
28.38/9.19	   A^2 -> H(U1(e, a), U1(d, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(e, b))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, b))
28.38/9.19	   A^2 -> H(U1(k, a), U1(c, d))
28.38/9.19	   A^2 -> H(U1(k, a), U1(d, c))
28.38/9.19	   A^2 -> H(U1(k, a), U1(b, e))
28.38/9.19	   A^2 -> H(U1(k, a), U1(b, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(e, c))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, c))
28.38/9.19	   A^2 -> H(U1(k, a), U1(c, e))
28.38/9.19	   A^2 -> H(U1(k, a), U1(c, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(e, e))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(k, a), U1(k, d))
28.38/9.19	   A^2 -> H(U1(k, a), U1(d, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(e, b))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, b))
28.38/9.19	   A^2 -> H(U1(c, d), U1(c, d))
28.38/9.19	   A^2 -> H(U1(c, d), U1(d, c))
28.38/9.19	   A^2 -> H(U1(c, d), U1(b, e))
28.38/9.19	   A^2 -> H(U1(c, d), U1(b, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(e, c))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, c))
28.38/9.19	   A^2 -> H(U1(c, d), U1(c, e))
28.38/9.19	   A^2 -> H(U1(c, d), U1(c, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(e, e))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, k))
28.38/9.19	   A^2 -> H(U1(c, d), U1(k, d))
28.38/9.19	   A^2 -> H(U1(c, d), U1(d, k))
28.38/9.19	   A^2 -> H(U1(c, a), b)
28.38/9.19	   A^2 -> H(U1(c, a), U1(e, d))
28.38/9.19	   A^2 -> H(U1(c, a), U1(d, e))
28.38/9.19	   A^2 -> H(U1(c, a), c)
28.38/9.19	   A^2 -> H(U1(c, a), U1(e, k))
28.38/9.19	   A^2 -> H(U1(c, a), U1(k, e))
28.38/9.19	   A^2 -> H(U1(c, a), e)
28.38/9.19	   A^2 -> H(U1(c, a), U1(k, k))
28.38/9.19	   A^2 -> H(U1(d, e), U1(c, b))
28.38/9.19	   A^2 -> H(U1(d, e), U1(d, b))
28.38/9.20	   A^2 -> H(U1(d, e), U1(b, c))
28.38/9.20	   A^2 -> H(U1(d, e), U1(b, d))
28.38/9.20	   A^2 -> H(U1(d, e), U1(c, c))
28.38/9.20	   A^2 -> H(U1(d, e), f(e))
28.38/9.20	   A^2 -> H(U1(d, e), f(k))
28.38/9.20	   A^2 -> H(U1(d, e), U1(d, d))
28.38/9.20	   A^2 -> H(U1(d, c), U1(e, b))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, b))
28.38/9.20	   A^2 -> H(U1(d, c), U1(c, d))
28.38/9.20	   A^2 -> H(U1(d, c), U1(d, c))
28.38/9.20	   A^2 -> H(U1(d, c), U1(b, e))
28.38/9.20	   A^2 -> H(U1(d, c), U1(b, k))
28.38/9.20	   A^2 -> H(U1(d, c), U1(e, c))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, c))
28.38/9.20	   A^2 -> H(U1(d, c), U1(c, e))
28.38/9.20	   A^2 -> H(U1(d, c), U1(c, k))
28.38/9.20	   A^2 -> H(U1(d, c), U1(e, e))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, d))
28.38/9.20	   A^2 -> H(U1(d, c), U1(d, k))
28.38/9.20	   A^2 -> H(U1(d, a), b)
28.38/9.20	   A^2 -> H(U1(d, a), U1(e, d))
28.38/9.20	   A^2 -> H(U1(d, a), U1(d, e))
28.38/9.20	   A^2 -> H(U1(d, a), c)
28.38/9.20	   A^2 -> H(U1(d, a), U1(e, k))
28.38/9.20	   A^2 -> H(U1(d, a), U1(k, e))
28.38/9.20	   A^2 -> H(U1(d, a), e)
28.38/9.20	   A^2 -> H(U1(d, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(e, b))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, b))
28.38/9.20	   A^2 -> H(U1(a, e), U1(c, d))
28.38/9.20	   A^2 -> H(U1(a, e), U1(d, c))
28.38/9.20	   A^2 -> H(U1(a, e), U1(b, e))
28.38/9.20	   A^2 -> H(U1(a, e), U1(b, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(e, c))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, c))
28.38/9.20	   A^2 -> H(U1(a, e), U1(c, e))
28.38/9.20	   A^2 -> H(U1(a, e), U1(c, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(e, e))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, d))
28.38/9.20	   A^2 -> H(U1(a, e), U1(d, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(e, b))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, b))
28.38/9.20	   A^2 -> H(U1(a, k), U1(c, d))
28.38/9.20	   A^2 -> H(U1(a, k), U1(d, c))
28.38/9.20	   A^2 -> H(U1(a, k), U1(b, e))
28.38/9.20	   A^2 -> H(U1(a, k), U1(b, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(e, c))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, c))
28.38/9.20	   A^2 -> H(U1(a, k), U1(c, e))
28.38/9.20	   A^2 -> H(U1(a, k), U1(c, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(e, e))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, d))
28.38/9.20	   A^2 -> H(U1(a, k), U1(d, k))
28.38/9.20	   A^2 -> H(U1(a, c), b)
28.38/9.20	   A^2 -> H(U1(a, c), U1(e, d))
28.38/9.20	   A^2 -> H(U1(a, c), U1(d, e))
28.38/9.20	   A^2 -> H(U1(a, c), c)
28.38/9.20	   A^2 -> H(U1(a, c), U1(e, k))
28.38/9.20	   A^2 -> H(U1(a, c), U1(k, e))
28.38/9.20	   A^2 -> H(U1(a, c), e)
28.38/9.20	   A^2 -> H(U1(a, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, d), b)
28.38/9.20	   A^2 -> H(U1(a, d), U1(e, d))
28.38/9.20	   A^2 -> H(U1(a, d), U1(d, e))
28.38/9.20	   A^2 -> H(U1(a, d), c)
28.38/9.20	   A^2 -> H(U1(a, d), U1(e, k))
28.38/9.20	   A^2 -> H(U1(a, d), U1(k, e))
28.38/9.20	   A^2 -> H(U1(a, d), e)
28.38/9.20	   A^2 -> H(U1(a, d), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, a), d)
28.38/9.20	   A^2 -> H(U1(a, a), k)
28.38/9.20	   A^2 -> H(k, U1(b, b))
28.38/9.20	   A^2 -> H(k, f(c))
28.38/9.20	   A^2 -> H(k, f(d))
28.38/9.20	   A^2 -> H(c, U1(c, b))
28.38/9.20	   A^2 -> H(c, U1(d, b))
28.38/9.20	   A^2 -> H(c, U1(b, c))
28.38/9.20	   A^2 -> H(c, U1(b, d))
28.38/9.20	   A^2 -> H(c, U1(c, c))
28.38/9.20	   A^2 -> H(c, f(e))
28.38/9.20	   A^2 -> H(c, f(k))
28.38/9.20	   A^2 -> H(c, U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(e, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(e, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(e, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(e, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, k), f(e))
28.38/9.20	   A^2 -> H(U1(e, k), f(k))
28.38/9.20	   A^2 -> H(U1(e, k), U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, c), U1(e, b))
28.38/9.20	   A^2 -> H(U1(e, c), U1(k, b))
28.38/9.20	   A^2 -> H(U1(e, c), U1(c, d))
28.38/9.20	   A^2 -> H(U1(e, c), U1(d, c))
28.38/9.20	   A^2 -> H(U1(e, c), U1(b, e))
28.38/9.20	   A^2 -> H(U1(e, c), U1(b, k))
28.38/9.20	
28.38/9.20	The TRS R consists of the following rules:
28.38/9.20	
28.38/9.20	   f(x) -> U1(x, x)
28.38/9.20	   U1(e, x) -> x
28.38/9.20	   a -> c
28.38/9.20	   a -> d
28.38/9.20	   b -> c
28.38/9.20	   b -> d
28.38/9.20	   d -> k
28.38/9.20	   c -> e
28.38/9.20	   c -> k
28.38/9.20	
28.38/9.20	Q is empty.
28.38/9.20	We have to consider all minimal (P,Q,R)-chains.
28.38/9.20	----------------------------------------
28.38/9.20	
28.38/9.20	(805) TransformationProof (EQUIVALENT)
28.38/9.20	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
28.38/9.20	
28.38/9.20	   (A^2 -> H(c, U1(b, d)),A^2 -> H(c, U1(b, d)))
28.38/9.20	   (A^2 -> H(U1(e, e), U1(b, d)),A^2 -> H(U1(e, e), U1(b, d)))
28.38/9.20	   (A^2 -> H(U1(e, k), U1(b, d)),A^2 -> H(U1(e, k), U1(b, d)))
28.38/9.20	   (A^2 -> H(U1(e, c), U1(c, d)),A^2 -> H(U1(e, c), U1(c, d)))
28.38/9.20	   (A^2 -> H(U1(e, c), U1(d, d)),A^2 -> H(U1(e, c), U1(d, d)))
28.38/9.20	   (A^2 -> H(U1(e, c), U1(b, k)),A^2 -> H(U1(e, c), U1(b, k)))
28.38/9.20	
28.38/9.20	
28.38/9.20	----------------------------------------
28.38/9.20	
28.38/9.20	(806)
28.38/9.20	Obligation:
28.38/9.20	Q DP problem:
28.38/9.20	The TRS P consists of the following rules:
28.38/9.20	
28.38/9.20	   H(x, x) -> G(x, x, f(k))
28.38/9.20	   G(d, x, x) -> A^2
28.38/9.20	   A^2 -> H(f(c), f(c))
28.38/9.20	   A^2 -> H(f(d), f(d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, c))
28.38/9.20	   A^2 -> H(f(e), f(e))
28.38/9.20	   A^2 -> H(f(k), f(k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, c), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, c), f(e))
28.38/9.20	   A^2 -> H(U1(e, c), f(k))
28.38/9.20	   A^2 -> H(U1(e, c), U1(d, d))
28.38/9.20	   A^2 -> H(U1(k, e), U1(b, b))
28.38/9.20	   A^2 -> H(U1(k, e), f(c))
28.38/9.20	   A^2 -> H(U1(k, e), f(d))
28.38/9.20	   A^2 -> H(U1(k, c), U1(c, b))
28.38/9.20	   A^2 -> H(U1(k, c), U1(d, b))
28.38/9.20	   A^2 -> H(U1(k, c), U1(b, c))
28.38/9.20	   A^2 -> H(U1(k, c), U1(b, d))
28.38/9.20	   A^2 -> H(U1(k, c), U1(c, c))
28.38/9.20	   A^2 -> H(U1(k, c), f(e))
28.38/9.20	   A^2 -> H(U1(k, c), f(k))
28.38/9.20	   A^2 -> H(U1(k, c), U1(d, d))
28.38/9.20	   A^2 -> H(U1(c, e), U1(c, b))
28.38/9.20	   A^2 -> H(U1(c, e), U1(d, b))
28.38/9.20	   A^2 -> H(U1(c, e), U1(b, c))
28.38/9.20	   A^2 -> H(U1(c, e), U1(b, d))
28.38/9.20	   A^2 -> H(U1(c, e), U1(c, c))
28.38/9.20	   A^2 -> H(U1(c, e), f(e))
28.38/9.20	   A^2 -> H(U1(c, e), f(k))
28.38/9.20	   A^2 -> H(U1(c, e), U1(d, d))
28.38/9.20	   A^2 -> H(U1(c, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(c, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(c, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(c, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(c, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(c, k), f(e))
28.38/9.20	   A^2 -> H(U1(c, k), f(k))
28.38/9.20	   A^2 -> H(U1(c, k), U1(d, d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(e, b))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, b))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(d, c))
28.38/9.20	   A^2 -> H(U1(c, c), U1(b, e))
28.38/9.20	   A^2 -> H(U1(c, c), U1(b, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(e, e))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(d, k))
28.38/9.20	   A^2 -> H(e, U1(b, b))
28.38/9.20	   A^2 -> H(e, f(c))
28.38/9.20	   A^2 -> H(e, f(d))
28.38/9.20	   A^2 -> H(U1(e, e), U1(c, b))
28.38/9.20	   A^2 -> H(U1(e, e), U1(d, b))
28.38/9.20	   A^2 -> H(U1(e, e), U1(b, c))
28.38/9.20	   A^2 -> H(U1(e, e), U1(b, d))
28.38/9.20	   A^2 -> H(U1(e, e), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, e), f(e))
28.38/9.20	   A^2 -> H(U1(e, e), f(k))
28.38/9.20	   A^2 -> H(U1(e, e), U1(d, d))
28.38/9.20	   A^2 -> H(f(e), U1(e, b))
28.38/9.20	   A^2 -> H(f(e), U1(k, b))
28.38/9.20	   A^2 -> H(f(e), U1(c, d))
28.38/9.20	   A^2 -> H(f(e), U1(d, c))
28.38/9.20	   A^2 -> H(f(e), U1(b, e))
28.38/9.20	   A^2 -> H(f(e), U1(b, k))
28.38/9.20	   A^2 -> H(f(e), U1(e, c))
28.38/9.20	   A^2 -> H(f(e), U1(k, c))
28.38/9.20	   A^2 -> H(f(e), U1(c, e))
28.38/9.20	   A^2 -> H(f(e), U1(c, k))
28.38/9.20	   A^2 -> H(f(e), U1(k, k))
28.38/9.20	   A^2 -> H(f(e), U1(k, d))
28.38/9.20	   A^2 -> H(f(e), U1(d, k))
28.38/9.20	   A^2 -> H(U1(k, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(k, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(k, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(k, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(k, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(k, k), f(e))
28.38/9.20	   A^2 -> H(U1(k, k), f(k))
28.38/9.20	   A^2 -> H(U1(k, k), U1(d, d))
28.38/9.20	   A^2 -> H(f(k), U1(e, b))
28.38/9.20	   A^2 -> H(f(k), U1(k, b))
28.38/9.20	   A^2 -> H(f(k), U1(c, d))
28.38/9.20	   A^2 -> H(f(k), U1(d, c))
28.38/9.20	   A^2 -> H(f(k), U1(b, e))
28.38/9.20	   A^2 -> H(f(k), U1(b, k))
28.38/9.20	   A^2 -> H(f(k), U1(e, c))
28.38/9.20	   A^2 -> H(f(k), U1(k, c))
28.38/9.20	   A^2 -> H(f(k), U1(c, e))
28.38/9.20	   A^2 -> H(f(k), U1(c, k))
28.38/9.20	   A^2 -> H(f(k), U1(e, e))
28.38/9.20	   A^2 -> H(f(k), U1(k, d))
28.38/9.20	   A^2 -> H(f(k), U1(d, k))
28.38/9.20	   A^2 -> H(f(c), b)
28.38/9.20	   A^2 -> H(f(c), U1(e, d))
28.38/9.20	   A^2 -> H(f(c), U1(d, e))
28.38/9.20	   A^2 -> H(f(k), U1(k, k))
28.38/9.20	   A^2 -> H(U1(k, k), U1(b, b))
28.38/9.20	   A^2 -> H(U1(k, k), f(c))
28.38/9.20	   A^2 -> H(U1(k, k), f(d))
28.38/9.20	   A^2 -> H(U1(k, d), U1(c, b))
28.38/9.20	   A^2 -> H(U1(k, d), U1(d, b))
28.38/9.20	   A^2 -> H(U1(k, d), U1(b, c))
28.38/9.20	   A^2 -> H(U1(k, d), U1(b, d))
28.38/9.20	   A^2 -> H(U1(k, d), U1(c, c))
28.38/9.20	   A^2 -> H(U1(k, d), f(e))
28.38/9.20	   A^2 -> H(U1(k, d), f(k))
28.38/9.20	   A^2 -> H(U1(k, d), U1(d, d))
28.38/9.20	   A^2 -> H(U1(d, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(d, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(d, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(d, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(d, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(d, k), f(e))
28.38/9.20	   A^2 -> H(U1(d, k), f(k))
28.38/9.20	   A^2 -> H(U1(d, k), U1(d, d))
28.38/9.20	   A^2 -> H(U1(d, d), U1(e, b))
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, b))
28.38/9.20	   A^2 -> H(U1(d, d), U1(c, d))
28.38/9.20	   A^2 -> H(U1(d, d), U1(d, c))
28.38/9.20	   A^2 -> H(U1(d, d), U1(b, e))
28.38/9.20	   A^2 -> H(U1(d, d), U1(b, k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(e, c))
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, c))
28.38/9.20	   A^2 -> H(U1(d, d), U1(c, e))
28.38/9.20	   A^2 -> H(U1(d, d), U1(c, k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(e, e))
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, k))
28.38/9.20	   A^2 -> H(f(d), b)
28.38/9.20	   A^2 -> H(f(d), U1(e, d))
28.38/9.20	   A^2 -> H(f(d), U1(d, e))
28.38/9.20	   A^2 -> H(f(d), c)
28.38/9.20	   A^2 -> H(f(d), U1(e, k))
28.38/9.20	   A^2 -> H(f(d), U1(k, e))
28.38/9.20	   A^2 -> H(f(d), e)
28.38/9.20	   A^2 -> H(f(a), d)
28.38/9.20	   A^2 -> H(U1(c, c), U1(e, c))
28.38/9.20	   A^2 -> H(f(c), c)
28.38/9.20	   A^2 -> H(f(c), U1(e, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, c))
28.38/9.20	   A^2 -> H(f(c), U1(k, e))
28.38/9.20	   A^2 -> H(f(c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, e))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, k))
28.38/9.20	   A^2 -> H(f(a), k)
28.38/9.20	   A^2 -> H(f(e), U1(e, e))
28.38/9.20	   A^2 -> H(f(c), e)
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, d))
28.38/9.20	   A^2 -> H(f(d), U1(k, k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(d, k))
28.38/9.20	   A^2 -> H(d, U1(b, b))
28.38/9.20	   A^2 -> H(d, f(c))
28.38/9.20	   A^2 -> H(d, f(d))
28.38/9.20	   A^2 -> H(a, U1(c, b))
28.38/9.20	   A^2 -> H(a, U1(d, b))
28.38/9.20	   A^2 -> H(a, U1(b, c))
28.38/9.20	   A^2 -> H(a, U1(b, d))
28.38/9.20	   A^2 -> H(a, U1(c, c))
28.38/9.20	   A^2 -> H(a, f(e))
28.38/9.20	   A^2 -> H(a, f(k))
28.38/9.20	   A^2 -> H(a, U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, d), U1(c, b))
28.38/9.20	   A^2 -> H(U1(e, d), U1(d, b))
28.38/9.20	   A^2 -> H(U1(e, d), U1(b, c))
28.38/9.20	   A^2 -> H(U1(e, d), U1(b, d))
28.38/9.20	   A^2 -> H(U1(e, d), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, d), f(e))
28.38/9.20	   A^2 -> H(U1(e, d), f(k))
28.38/9.20	   A^2 -> H(U1(e, d), U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, a), U1(e, b))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, b))
28.38/9.20	   A^2 -> H(U1(e, a), U1(c, d))
28.38/9.20	   A^2 -> H(U1(e, a), U1(d, c))
28.38/9.20	   A^2 -> H(U1(e, a), U1(b, e))
28.38/9.20	   A^2 -> H(U1(e, a), U1(b, k))
28.38/9.20	   A^2 -> H(U1(e, a), U1(e, c))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, c))
28.38/9.20	   A^2 -> H(U1(e, a), U1(c, e))
28.38/9.20	   A^2 -> H(U1(e, a), U1(c, k))
28.38/9.20	   A^2 -> H(U1(e, a), U1(e, e))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, d))
28.38/9.20	   A^2 -> H(U1(e, a), U1(d, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(e, b))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, b))
28.38/9.20	   A^2 -> H(U1(k, a), U1(c, d))
28.38/9.20	   A^2 -> H(U1(k, a), U1(d, c))
28.38/9.20	   A^2 -> H(U1(k, a), U1(b, e))
28.38/9.20	   A^2 -> H(U1(k, a), U1(b, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(e, c))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, c))
28.38/9.20	   A^2 -> H(U1(k, a), U1(c, e))
28.38/9.20	   A^2 -> H(U1(k, a), U1(c, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(e, e))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, d))
28.38/9.20	   A^2 -> H(U1(k, a), U1(d, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(e, b))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, b))
28.38/9.20	   A^2 -> H(U1(c, d), U1(c, d))
28.38/9.20	   A^2 -> H(U1(c, d), U1(d, c))
28.38/9.20	   A^2 -> H(U1(c, d), U1(b, e))
28.38/9.20	   A^2 -> H(U1(c, d), U1(b, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(e, c))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, c))
28.38/9.20	   A^2 -> H(U1(c, d), U1(c, e))
28.38/9.20	   A^2 -> H(U1(c, d), U1(c, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(e, e))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, d))
28.38/9.20	   A^2 -> H(U1(c, d), U1(d, k))
28.38/9.20	   A^2 -> H(U1(c, a), b)
28.38/9.20	   A^2 -> H(U1(c, a), U1(e, d))
28.38/9.20	   A^2 -> H(U1(c, a), U1(d, e))
28.38/9.20	   A^2 -> H(U1(c, a), c)
28.38/9.20	   A^2 -> H(U1(c, a), U1(e, k))
28.38/9.20	   A^2 -> H(U1(c, a), U1(k, e))
28.38/9.20	   A^2 -> H(U1(c, a), e)
28.38/9.20	   A^2 -> H(U1(c, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(d, e), U1(c, b))
28.38/9.20	   A^2 -> H(U1(d, e), U1(d, b))
28.38/9.20	   A^2 -> H(U1(d, e), U1(b, c))
28.38/9.20	   A^2 -> H(U1(d, e), U1(b, d))
28.38/9.20	   A^2 -> H(U1(d, e), U1(c, c))
28.38/9.20	   A^2 -> H(U1(d, e), f(e))
28.38/9.20	   A^2 -> H(U1(d, e), f(k))
28.38/9.20	   A^2 -> H(U1(d, e), U1(d, d))
28.38/9.20	   A^2 -> H(U1(d, c), U1(e, b))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, b))
28.38/9.20	   A^2 -> H(U1(d, c), U1(c, d))
28.38/9.20	   A^2 -> H(U1(d, c), U1(d, c))
28.38/9.20	   A^2 -> H(U1(d, c), U1(b, e))
28.38/9.20	   A^2 -> H(U1(d, c), U1(b, k))
28.38/9.20	   A^2 -> H(U1(d, c), U1(e, c))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, c))
28.38/9.20	   A^2 -> H(U1(d, c), U1(c, e))
28.38/9.20	   A^2 -> H(U1(d, c), U1(c, k))
28.38/9.20	   A^2 -> H(U1(d, c), U1(e, e))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, d))
28.38/9.20	   A^2 -> H(U1(d, c), U1(d, k))
28.38/9.20	   A^2 -> H(U1(d, a), b)
28.38/9.20	   A^2 -> H(U1(d, a), U1(e, d))
28.38/9.20	   A^2 -> H(U1(d, a), U1(d, e))
28.38/9.20	   A^2 -> H(U1(d, a), c)
28.38/9.20	   A^2 -> H(U1(d, a), U1(e, k))
28.38/9.20	   A^2 -> H(U1(d, a), U1(k, e))
28.38/9.20	   A^2 -> H(U1(d, a), e)
28.38/9.20	   A^2 -> H(U1(d, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(e, b))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, b))
28.38/9.20	   A^2 -> H(U1(a, e), U1(c, d))
28.38/9.20	   A^2 -> H(U1(a, e), U1(d, c))
28.38/9.20	   A^2 -> H(U1(a, e), U1(b, e))
28.38/9.20	   A^2 -> H(U1(a, e), U1(b, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(e, c))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, c))
28.38/9.20	   A^2 -> H(U1(a, e), U1(c, e))
28.38/9.20	   A^2 -> H(U1(a, e), U1(c, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(e, e))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, d))
28.38/9.20	   A^2 -> H(U1(a, e), U1(d, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(e, b))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, b))
28.38/9.20	   A^2 -> H(U1(a, k), U1(c, d))
28.38/9.20	   A^2 -> H(U1(a, k), U1(d, c))
28.38/9.20	   A^2 -> H(U1(a, k), U1(b, e))
28.38/9.20	   A^2 -> H(U1(a, k), U1(b, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(e, c))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, c))
28.38/9.20	   A^2 -> H(U1(a, k), U1(c, e))
28.38/9.20	   A^2 -> H(U1(a, k), U1(c, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(e, e))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, d))
28.38/9.20	   A^2 -> H(U1(a, k), U1(d, k))
28.38/9.20	   A^2 -> H(U1(a, c), b)
28.38/9.20	   A^2 -> H(U1(a, c), U1(e, d))
28.38/9.20	   A^2 -> H(U1(a, c), U1(d, e))
28.38/9.20	   A^2 -> H(U1(a, c), c)
28.38/9.20	   A^2 -> H(U1(a, c), U1(e, k))
28.38/9.20	   A^2 -> H(U1(a, c), U1(k, e))
28.38/9.20	   A^2 -> H(U1(a, c), e)
28.38/9.20	   A^2 -> H(U1(a, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, d), b)
28.38/9.20	   A^2 -> H(U1(a, d), U1(e, d))
28.38/9.20	   A^2 -> H(U1(a, d), U1(d, e))
28.38/9.20	   A^2 -> H(U1(a, d), c)
28.38/9.20	   A^2 -> H(U1(a, d), U1(e, k))
28.38/9.20	   A^2 -> H(U1(a, d), U1(k, e))
28.38/9.20	   A^2 -> H(U1(a, d), e)
28.38/9.20	   A^2 -> H(U1(a, d), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, a), d)
28.38/9.20	   A^2 -> H(U1(a, a), k)
28.38/9.20	   A^2 -> H(k, U1(b, b))
28.38/9.20	   A^2 -> H(k, f(c))
28.38/9.20	   A^2 -> H(k, f(d))
28.38/9.20	   A^2 -> H(c, U1(c, b))
28.38/9.20	   A^2 -> H(c, U1(d, b))
28.38/9.20	   A^2 -> H(c, U1(b, c))
28.38/9.20	   A^2 -> H(c, U1(b, d))
28.38/9.20	   A^2 -> H(c, U1(c, c))
28.38/9.20	   A^2 -> H(c, f(e))
28.38/9.20	   A^2 -> H(c, f(k))
28.38/9.20	   A^2 -> H(c, U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(e, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(e, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(e, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(e, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, k), f(e))
28.38/9.20	   A^2 -> H(U1(e, k), f(k))
28.38/9.20	   A^2 -> H(U1(e, k), U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, c), U1(e, b))
28.38/9.20	   A^2 -> H(U1(e, c), U1(k, b))
28.38/9.20	   A^2 -> H(U1(e, c), U1(c, d))
28.38/9.20	   A^2 -> H(U1(e, c), U1(d, c))
28.38/9.20	   A^2 -> H(U1(e, c), U1(b, e))
28.38/9.20	   A^2 -> H(U1(e, c), U1(b, k))
28.38/9.20	
28.38/9.20	The TRS R consists of the following rules:
28.38/9.20	
28.38/9.20	   f(x) -> U1(x, x)
28.38/9.20	   U1(e, x) -> x
28.38/9.20	   a -> c
28.38/9.20	   a -> d
28.38/9.20	   b -> c
28.38/9.20	   b -> d
28.38/9.20	   d -> k
28.38/9.20	   c -> e
28.38/9.20	   c -> k
28.38/9.20	
28.38/9.20	Q is empty.
28.38/9.20	We have to consider all minimal (P,Q,R)-chains.
28.38/9.20	----------------------------------------
28.38/9.20	
28.38/9.20	(807) TransformationProof (EQUIVALENT)
28.38/9.20	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
28.38/9.20	
28.38/9.20	   (A^2 -> H(c, U1(c, c)),A^2 -> H(c, U1(c, c)))
28.38/9.20	   (A^2 -> H(U1(e, e), U1(c, c)),A^2 -> H(U1(e, e), U1(c, c)))
28.38/9.20	   (A^2 -> H(U1(e, k), U1(c, c)),A^2 -> H(U1(e, k), U1(c, c)))
28.38/9.20	   (A^2 -> H(U1(e, c), U1(e, c)),A^2 -> H(U1(e, c), U1(e, c)))
28.38/9.20	   (A^2 -> H(U1(e, c), U1(k, c)),A^2 -> H(U1(e, c), U1(k, c)))
28.38/9.20	   (A^2 -> H(U1(e, c), U1(c, e)),A^2 -> H(U1(e, c), U1(c, e)))
28.38/9.20	   (A^2 -> H(U1(e, c), U1(c, k)),A^2 -> H(U1(e, c), U1(c, k)))
28.38/9.20	
28.38/9.20	
28.38/9.20	----------------------------------------
28.38/9.20	
28.38/9.20	(808)
28.38/9.20	Obligation:
28.38/9.20	Q DP problem:
28.38/9.20	The TRS P consists of the following rules:
28.38/9.20	
28.38/9.20	   H(x, x) -> G(x, x, f(k))
28.38/9.20	   G(d, x, x) -> A^2
28.38/9.20	   A^2 -> H(f(c), f(c))
28.38/9.20	   A^2 -> H(f(d), f(d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, c))
28.38/9.20	   A^2 -> H(f(e), f(e))
28.38/9.20	   A^2 -> H(f(k), f(k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, c), f(e))
28.38/9.20	   A^2 -> H(U1(e, c), f(k))
28.38/9.20	   A^2 -> H(U1(e, c), U1(d, d))
28.38/9.20	   A^2 -> H(U1(k, e), U1(b, b))
28.38/9.20	   A^2 -> H(U1(k, e), f(c))
28.38/9.20	   A^2 -> H(U1(k, e), f(d))
28.38/9.20	   A^2 -> H(U1(k, c), U1(c, b))
28.38/9.20	   A^2 -> H(U1(k, c), U1(d, b))
28.38/9.20	   A^2 -> H(U1(k, c), U1(b, c))
28.38/9.20	   A^2 -> H(U1(k, c), U1(b, d))
28.38/9.20	   A^2 -> H(U1(k, c), U1(c, c))
28.38/9.20	   A^2 -> H(U1(k, c), f(e))
28.38/9.20	   A^2 -> H(U1(k, c), f(k))
28.38/9.20	   A^2 -> H(U1(k, c), U1(d, d))
28.38/9.20	   A^2 -> H(U1(c, e), U1(c, b))
28.38/9.20	   A^2 -> H(U1(c, e), U1(d, b))
28.38/9.20	   A^2 -> H(U1(c, e), U1(b, c))
28.38/9.20	   A^2 -> H(U1(c, e), U1(b, d))
28.38/9.20	   A^2 -> H(U1(c, e), U1(c, c))
28.38/9.20	   A^2 -> H(U1(c, e), f(e))
28.38/9.20	   A^2 -> H(U1(c, e), f(k))
28.38/9.20	   A^2 -> H(U1(c, e), U1(d, d))
28.38/9.20	   A^2 -> H(U1(c, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(c, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(c, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(c, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(c, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(c, k), f(e))
28.38/9.20	   A^2 -> H(U1(c, k), f(k))
28.38/9.20	   A^2 -> H(U1(c, k), U1(d, d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(e, b))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, b))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(d, c))
28.38/9.20	   A^2 -> H(U1(c, c), U1(b, e))
28.38/9.20	   A^2 -> H(U1(c, c), U1(b, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(e, e))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(d, k))
28.38/9.20	   A^2 -> H(e, U1(b, b))
28.38/9.20	   A^2 -> H(e, f(c))
28.38/9.20	   A^2 -> H(e, f(d))
28.38/9.20	   A^2 -> H(U1(e, e), U1(c, b))
28.38/9.20	   A^2 -> H(U1(e, e), U1(d, b))
28.38/9.20	   A^2 -> H(U1(e, e), U1(b, c))
28.38/9.20	   A^2 -> H(U1(e, e), U1(b, d))
28.38/9.20	   A^2 -> H(U1(e, e), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, e), f(e))
28.38/9.20	   A^2 -> H(U1(e, e), f(k))
28.38/9.20	   A^2 -> H(U1(e, e), U1(d, d))
28.38/9.20	   A^2 -> H(f(e), U1(e, b))
28.38/9.20	   A^2 -> H(f(e), U1(k, b))
28.38/9.20	   A^2 -> H(f(e), U1(c, d))
28.38/9.20	   A^2 -> H(f(e), U1(d, c))
28.38/9.20	   A^2 -> H(f(e), U1(b, e))
28.38/9.20	   A^2 -> H(f(e), U1(b, k))
28.38/9.20	   A^2 -> H(f(e), U1(e, c))
28.38/9.20	   A^2 -> H(f(e), U1(k, c))
28.38/9.20	   A^2 -> H(f(e), U1(c, e))
28.38/9.20	   A^2 -> H(f(e), U1(c, k))
28.38/9.20	   A^2 -> H(f(e), U1(k, k))
28.38/9.20	   A^2 -> H(f(e), U1(k, d))
28.38/9.20	   A^2 -> H(f(e), U1(d, k))
28.38/9.20	   A^2 -> H(U1(k, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(k, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(k, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(k, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(k, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(k, k), f(e))
28.38/9.20	   A^2 -> H(U1(k, k), f(k))
28.38/9.20	   A^2 -> H(U1(k, k), U1(d, d))
28.38/9.20	   A^2 -> H(f(k), U1(e, b))
28.38/9.20	   A^2 -> H(f(k), U1(k, b))
28.38/9.20	   A^2 -> H(f(k), U1(c, d))
28.38/9.20	   A^2 -> H(f(k), U1(d, c))
28.38/9.20	   A^2 -> H(f(k), U1(b, e))
28.38/9.20	   A^2 -> H(f(k), U1(b, k))
28.38/9.20	   A^2 -> H(f(k), U1(e, c))
28.38/9.20	   A^2 -> H(f(k), U1(k, c))
28.38/9.20	   A^2 -> H(f(k), U1(c, e))
28.38/9.20	   A^2 -> H(f(k), U1(c, k))
28.38/9.20	   A^2 -> H(f(k), U1(e, e))
28.38/9.20	   A^2 -> H(f(k), U1(k, d))
28.38/9.20	   A^2 -> H(f(k), U1(d, k))
28.38/9.20	   A^2 -> H(f(c), b)
28.38/9.20	   A^2 -> H(f(c), U1(e, d))
28.38/9.20	   A^2 -> H(f(c), U1(d, e))
28.38/9.20	   A^2 -> H(f(k), U1(k, k))
28.38/9.20	   A^2 -> H(U1(k, k), U1(b, b))
28.38/9.20	   A^2 -> H(U1(k, k), f(c))
28.38/9.20	   A^2 -> H(U1(k, k), f(d))
28.38/9.20	   A^2 -> H(U1(k, d), U1(c, b))
28.38/9.20	   A^2 -> H(U1(k, d), U1(d, b))
28.38/9.20	   A^2 -> H(U1(k, d), U1(b, c))
28.38/9.20	   A^2 -> H(U1(k, d), U1(b, d))
28.38/9.20	   A^2 -> H(U1(k, d), U1(c, c))
28.38/9.20	   A^2 -> H(U1(k, d), f(e))
28.38/9.20	   A^2 -> H(U1(k, d), f(k))
28.38/9.20	   A^2 -> H(U1(k, d), U1(d, d))
28.38/9.20	   A^2 -> H(U1(d, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(d, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(d, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(d, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(d, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(d, k), f(e))
28.38/9.20	   A^2 -> H(U1(d, k), f(k))
28.38/9.20	   A^2 -> H(U1(d, k), U1(d, d))
28.38/9.20	   A^2 -> H(U1(d, d), U1(e, b))
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, b))
28.38/9.20	   A^2 -> H(U1(d, d), U1(c, d))
28.38/9.20	   A^2 -> H(U1(d, d), U1(d, c))
28.38/9.20	   A^2 -> H(U1(d, d), U1(b, e))
28.38/9.20	   A^2 -> H(U1(d, d), U1(b, k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(e, c))
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, c))
28.38/9.20	   A^2 -> H(U1(d, d), U1(c, e))
28.38/9.20	   A^2 -> H(U1(d, d), U1(c, k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(e, e))
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, k))
28.38/9.20	   A^2 -> H(f(d), b)
28.38/9.20	   A^2 -> H(f(d), U1(e, d))
28.38/9.20	   A^2 -> H(f(d), U1(d, e))
28.38/9.20	   A^2 -> H(f(d), c)
28.38/9.20	   A^2 -> H(f(d), U1(e, k))
28.38/9.20	   A^2 -> H(f(d), U1(k, e))
28.38/9.20	   A^2 -> H(f(d), e)
28.38/9.20	   A^2 -> H(f(a), d)
28.38/9.20	   A^2 -> H(U1(c, c), U1(e, c))
28.38/9.20	   A^2 -> H(f(c), c)
28.38/9.20	   A^2 -> H(f(c), U1(e, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, c))
28.38/9.20	   A^2 -> H(f(c), U1(k, e))
28.38/9.20	   A^2 -> H(f(c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, e))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, k))
28.38/9.20	   A^2 -> H(f(a), k)
28.38/9.20	   A^2 -> H(f(e), U1(e, e))
28.38/9.20	   A^2 -> H(f(c), e)
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, d))
28.38/9.20	   A^2 -> H(f(d), U1(k, k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(d, k))
28.38/9.20	   A^2 -> H(d, U1(b, b))
28.38/9.20	   A^2 -> H(d, f(c))
28.38/9.20	   A^2 -> H(d, f(d))
28.38/9.20	   A^2 -> H(a, U1(c, b))
28.38/9.20	   A^2 -> H(a, U1(d, b))
28.38/9.20	   A^2 -> H(a, U1(b, c))
28.38/9.20	   A^2 -> H(a, U1(b, d))
28.38/9.20	   A^2 -> H(a, U1(c, c))
28.38/9.20	   A^2 -> H(a, f(e))
28.38/9.20	   A^2 -> H(a, f(k))
28.38/9.20	   A^2 -> H(a, U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, d), U1(c, b))
28.38/9.20	   A^2 -> H(U1(e, d), U1(d, b))
28.38/9.20	   A^2 -> H(U1(e, d), U1(b, c))
28.38/9.20	   A^2 -> H(U1(e, d), U1(b, d))
28.38/9.20	   A^2 -> H(U1(e, d), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, d), f(e))
28.38/9.20	   A^2 -> H(U1(e, d), f(k))
28.38/9.20	   A^2 -> H(U1(e, d), U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, a), U1(e, b))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, b))
28.38/9.20	   A^2 -> H(U1(e, a), U1(c, d))
28.38/9.20	   A^2 -> H(U1(e, a), U1(d, c))
28.38/9.20	   A^2 -> H(U1(e, a), U1(b, e))
28.38/9.20	   A^2 -> H(U1(e, a), U1(b, k))
28.38/9.20	   A^2 -> H(U1(e, a), U1(e, c))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, c))
28.38/9.20	   A^2 -> H(U1(e, a), U1(c, e))
28.38/9.20	   A^2 -> H(U1(e, a), U1(c, k))
28.38/9.20	   A^2 -> H(U1(e, a), U1(e, e))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, d))
28.38/9.20	   A^2 -> H(U1(e, a), U1(d, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(e, b))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, b))
28.38/9.20	   A^2 -> H(U1(k, a), U1(c, d))
28.38/9.20	   A^2 -> H(U1(k, a), U1(d, c))
28.38/9.20	   A^2 -> H(U1(k, a), U1(b, e))
28.38/9.20	   A^2 -> H(U1(k, a), U1(b, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(e, c))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, c))
28.38/9.20	   A^2 -> H(U1(k, a), U1(c, e))
28.38/9.20	   A^2 -> H(U1(k, a), U1(c, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(e, e))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, d))
28.38/9.20	   A^2 -> H(U1(k, a), U1(d, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(e, b))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, b))
28.38/9.20	   A^2 -> H(U1(c, d), U1(c, d))
28.38/9.20	   A^2 -> H(U1(c, d), U1(d, c))
28.38/9.20	   A^2 -> H(U1(c, d), U1(b, e))
28.38/9.20	   A^2 -> H(U1(c, d), U1(b, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(e, c))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, c))
28.38/9.20	   A^2 -> H(U1(c, d), U1(c, e))
28.38/9.20	   A^2 -> H(U1(c, d), U1(c, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(e, e))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, d))
28.38/9.20	   A^2 -> H(U1(c, d), U1(d, k))
28.38/9.20	   A^2 -> H(U1(c, a), b)
28.38/9.20	   A^2 -> H(U1(c, a), U1(e, d))
28.38/9.20	   A^2 -> H(U1(c, a), U1(d, e))
28.38/9.20	   A^2 -> H(U1(c, a), c)
28.38/9.20	   A^2 -> H(U1(c, a), U1(e, k))
28.38/9.20	   A^2 -> H(U1(c, a), U1(k, e))
28.38/9.20	   A^2 -> H(U1(c, a), e)
28.38/9.20	   A^2 -> H(U1(c, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(d, e), U1(c, b))
28.38/9.20	   A^2 -> H(U1(d, e), U1(d, b))
28.38/9.20	   A^2 -> H(U1(d, e), U1(b, c))
28.38/9.20	   A^2 -> H(U1(d, e), U1(b, d))
28.38/9.20	   A^2 -> H(U1(d, e), U1(c, c))
28.38/9.20	   A^2 -> H(U1(d, e), f(e))
28.38/9.20	   A^2 -> H(U1(d, e), f(k))
28.38/9.20	   A^2 -> H(U1(d, e), U1(d, d))
28.38/9.20	   A^2 -> H(U1(d, c), U1(e, b))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, b))
28.38/9.20	   A^2 -> H(U1(d, c), U1(c, d))
28.38/9.20	   A^2 -> H(U1(d, c), U1(d, c))
28.38/9.20	   A^2 -> H(U1(d, c), U1(b, e))
28.38/9.20	   A^2 -> H(U1(d, c), U1(b, k))
28.38/9.20	   A^2 -> H(U1(d, c), U1(e, c))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, c))
28.38/9.20	   A^2 -> H(U1(d, c), U1(c, e))
28.38/9.20	   A^2 -> H(U1(d, c), U1(c, k))
28.38/9.20	   A^2 -> H(U1(d, c), U1(e, e))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, d))
28.38/9.20	   A^2 -> H(U1(d, c), U1(d, k))
28.38/9.20	   A^2 -> H(U1(d, a), b)
28.38/9.20	   A^2 -> H(U1(d, a), U1(e, d))
28.38/9.20	   A^2 -> H(U1(d, a), U1(d, e))
28.38/9.20	   A^2 -> H(U1(d, a), c)
28.38/9.20	   A^2 -> H(U1(d, a), U1(e, k))
28.38/9.20	   A^2 -> H(U1(d, a), U1(k, e))
28.38/9.20	   A^2 -> H(U1(d, a), e)
28.38/9.20	   A^2 -> H(U1(d, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(e, b))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, b))
28.38/9.20	   A^2 -> H(U1(a, e), U1(c, d))
28.38/9.20	   A^2 -> H(U1(a, e), U1(d, c))
28.38/9.20	   A^2 -> H(U1(a, e), U1(b, e))
28.38/9.20	   A^2 -> H(U1(a, e), U1(b, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(e, c))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, c))
28.38/9.20	   A^2 -> H(U1(a, e), U1(c, e))
28.38/9.20	   A^2 -> H(U1(a, e), U1(c, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(e, e))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, d))
28.38/9.20	   A^2 -> H(U1(a, e), U1(d, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(e, b))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, b))
28.38/9.20	   A^2 -> H(U1(a, k), U1(c, d))
28.38/9.20	   A^2 -> H(U1(a, k), U1(d, c))
28.38/9.20	   A^2 -> H(U1(a, k), U1(b, e))
28.38/9.20	   A^2 -> H(U1(a, k), U1(b, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(e, c))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, c))
28.38/9.20	   A^2 -> H(U1(a, k), U1(c, e))
28.38/9.20	   A^2 -> H(U1(a, k), U1(c, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(e, e))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, d))
28.38/9.20	   A^2 -> H(U1(a, k), U1(d, k))
28.38/9.20	   A^2 -> H(U1(a, c), b)
28.38/9.20	   A^2 -> H(U1(a, c), U1(e, d))
28.38/9.20	   A^2 -> H(U1(a, c), U1(d, e))
28.38/9.20	   A^2 -> H(U1(a, c), c)
28.38/9.20	   A^2 -> H(U1(a, c), U1(e, k))
28.38/9.20	   A^2 -> H(U1(a, c), U1(k, e))
28.38/9.20	   A^2 -> H(U1(a, c), e)
28.38/9.20	   A^2 -> H(U1(a, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, d), b)
28.38/9.20	   A^2 -> H(U1(a, d), U1(e, d))
28.38/9.20	   A^2 -> H(U1(a, d), U1(d, e))
28.38/9.20	   A^2 -> H(U1(a, d), c)
28.38/9.20	   A^2 -> H(U1(a, d), U1(e, k))
28.38/9.20	   A^2 -> H(U1(a, d), U1(k, e))
28.38/9.20	   A^2 -> H(U1(a, d), e)
28.38/9.20	   A^2 -> H(U1(a, d), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, a), d)
28.38/9.20	   A^2 -> H(U1(a, a), k)
28.38/9.20	   A^2 -> H(k, U1(b, b))
28.38/9.20	   A^2 -> H(k, f(c))
28.38/9.20	   A^2 -> H(k, f(d))
28.38/9.20	   A^2 -> H(c, U1(c, b))
28.38/9.20	   A^2 -> H(c, U1(d, b))
28.38/9.20	   A^2 -> H(c, U1(b, c))
28.38/9.20	   A^2 -> H(c, U1(b, d))
28.38/9.20	   A^2 -> H(c, U1(c, c))
28.38/9.20	   A^2 -> H(c, f(e))
28.38/9.20	   A^2 -> H(c, f(k))
28.38/9.20	   A^2 -> H(c, U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(e, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(e, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(e, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(e, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, k), f(e))
28.38/9.20	   A^2 -> H(U1(e, k), f(k))
28.38/9.20	   A^2 -> H(U1(e, k), U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, c), U1(e, b))
28.38/9.20	   A^2 -> H(U1(e, c), U1(k, b))
28.38/9.20	   A^2 -> H(U1(e, c), U1(c, d))
28.38/9.20	   A^2 -> H(U1(e, c), U1(d, c))
28.38/9.20	   A^2 -> H(U1(e, c), U1(b, e))
28.38/9.20	   A^2 -> H(U1(e, c), U1(b, k))
28.38/9.20	   A^2 -> H(U1(e, c), U1(e, c))
28.38/9.20	   A^2 -> H(U1(e, c), U1(k, c))
28.38/9.20	   A^2 -> H(U1(e, c), U1(c, e))
28.38/9.20	   A^2 -> H(U1(e, c), U1(c, k))
28.38/9.20	
28.38/9.20	The TRS R consists of the following rules:
28.38/9.20	
28.38/9.20	   f(x) -> U1(x, x)
28.38/9.20	   U1(e, x) -> x
28.38/9.20	   a -> c
28.38/9.20	   a -> d
28.38/9.20	   b -> c
28.38/9.20	   b -> d
28.38/9.20	   d -> k
28.38/9.20	   c -> e
28.38/9.20	   c -> k
28.38/9.20	
28.38/9.20	Q is empty.
28.38/9.20	We have to consider all minimal (P,Q,R)-chains.
28.38/9.20	----------------------------------------
28.38/9.20	
28.38/9.20	(809) TransformationProof (EQUIVALENT)
28.38/9.20	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), f(e)) at position [] we obtained the following new rules [LPAR04]:
28.38/9.20	
28.38/9.20	   (A^2 -> H(c, f(e)),A^2 -> H(c, f(e)))
28.38/9.20	   (A^2 -> H(U1(e, e), f(e)),A^2 -> H(U1(e, e), f(e)))
28.38/9.20	   (A^2 -> H(U1(e, k), f(e)),A^2 -> H(U1(e, k), f(e)))
28.38/9.20	   (A^2 -> H(U1(e, c), U1(e, e)),A^2 -> H(U1(e, c), U1(e, e)))
28.38/9.20	
28.38/9.20	
28.38/9.20	----------------------------------------
28.38/9.20	
28.38/9.20	(810)
28.38/9.20	Obligation:
28.38/9.20	Q DP problem:
28.38/9.20	The TRS P consists of the following rules:
28.38/9.20	
28.38/9.20	   H(x, x) -> G(x, x, f(k))
28.38/9.20	   G(d, x, x) -> A^2
28.38/9.20	   A^2 -> H(f(c), f(c))
28.38/9.20	   A^2 -> H(f(d), f(d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, c))
28.38/9.20	   A^2 -> H(f(e), f(e))
28.38/9.20	   A^2 -> H(f(k), f(k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, c), f(k))
28.38/9.20	   A^2 -> H(U1(e, c), U1(d, d))
28.38/9.20	   A^2 -> H(U1(k, e), U1(b, b))
28.38/9.20	   A^2 -> H(U1(k, e), f(c))
28.38/9.20	   A^2 -> H(U1(k, e), f(d))
28.38/9.20	   A^2 -> H(U1(k, c), U1(c, b))
28.38/9.20	   A^2 -> H(U1(k, c), U1(d, b))
28.38/9.20	   A^2 -> H(U1(k, c), U1(b, c))
28.38/9.20	   A^2 -> H(U1(k, c), U1(b, d))
28.38/9.20	   A^2 -> H(U1(k, c), U1(c, c))
28.38/9.20	   A^2 -> H(U1(k, c), f(e))
28.38/9.20	   A^2 -> H(U1(k, c), f(k))
28.38/9.20	   A^2 -> H(U1(k, c), U1(d, d))
28.38/9.20	   A^2 -> H(U1(c, e), U1(c, b))
28.38/9.20	   A^2 -> H(U1(c, e), U1(d, b))
28.38/9.20	   A^2 -> H(U1(c, e), U1(b, c))
28.38/9.20	   A^2 -> H(U1(c, e), U1(b, d))
28.38/9.20	   A^2 -> H(U1(c, e), U1(c, c))
28.38/9.20	   A^2 -> H(U1(c, e), f(e))
28.38/9.20	   A^2 -> H(U1(c, e), f(k))
28.38/9.20	   A^2 -> H(U1(c, e), U1(d, d))
28.38/9.20	   A^2 -> H(U1(c, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(c, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(c, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(c, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(c, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(c, k), f(e))
28.38/9.20	   A^2 -> H(U1(c, k), f(k))
28.38/9.20	   A^2 -> H(U1(c, k), U1(d, d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(e, b))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, b))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(d, c))
28.38/9.20	   A^2 -> H(U1(c, c), U1(b, e))
28.38/9.20	   A^2 -> H(U1(c, c), U1(b, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(e, e))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(d, k))
28.38/9.20	   A^2 -> H(e, U1(b, b))
28.38/9.20	   A^2 -> H(e, f(c))
28.38/9.20	   A^2 -> H(e, f(d))
28.38/9.20	   A^2 -> H(U1(e, e), U1(c, b))
28.38/9.20	   A^2 -> H(U1(e, e), U1(d, b))
28.38/9.20	   A^2 -> H(U1(e, e), U1(b, c))
28.38/9.20	   A^2 -> H(U1(e, e), U1(b, d))
28.38/9.20	   A^2 -> H(U1(e, e), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, e), f(e))
28.38/9.20	   A^2 -> H(U1(e, e), f(k))
28.38/9.20	   A^2 -> H(U1(e, e), U1(d, d))
28.38/9.20	   A^2 -> H(f(e), U1(e, b))
28.38/9.20	   A^2 -> H(f(e), U1(k, b))
28.38/9.20	   A^2 -> H(f(e), U1(c, d))
28.38/9.20	   A^2 -> H(f(e), U1(d, c))
28.38/9.20	   A^2 -> H(f(e), U1(b, e))
28.38/9.20	   A^2 -> H(f(e), U1(b, k))
28.38/9.20	   A^2 -> H(f(e), U1(e, c))
28.38/9.20	   A^2 -> H(f(e), U1(k, c))
28.38/9.20	   A^2 -> H(f(e), U1(c, e))
28.38/9.20	   A^2 -> H(f(e), U1(c, k))
28.38/9.20	   A^2 -> H(f(e), U1(k, k))
28.38/9.20	   A^2 -> H(f(e), U1(k, d))
28.38/9.20	   A^2 -> H(f(e), U1(d, k))
28.38/9.20	   A^2 -> H(U1(k, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(k, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(k, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(k, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(k, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(k, k), f(e))
28.38/9.20	   A^2 -> H(U1(k, k), f(k))
28.38/9.20	   A^2 -> H(U1(k, k), U1(d, d))
28.38/9.20	   A^2 -> H(f(k), U1(e, b))
28.38/9.20	   A^2 -> H(f(k), U1(k, b))
28.38/9.20	   A^2 -> H(f(k), U1(c, d))
28.38/9.20	   A^2 -> H(f(k), U1(d, c))
28.38/9.20	   A^2 -> H(f(k), U1(b, e))
28.38/9.20	   A^2 -> H(f(k), U1(b, k))
28.38/9.20	   A^2 -> H(f(k), U1(e, c))
28.38/9.20	   A^2 -> H(f(k), U1(k, c))
28.38/9.20	   A^2 -> H(f(k), U1(c, e))
28.38/9.20	   A^2 -> H(f(k), U1(c, k))
28.38/9.20	   A^2 -> H(f(k), U1(e, e))
28.38/9.20	   A^2 -> H(f(k), U1(k, d))
28.38/9.20	   A^2 -> H(f(k), U1(d, k))
28.38/9.20	   A^2 -> H(f(c), b)
28.38/9.20	   A^2 -> H(f(c), U1(e, d))
28.38/9.20	   A^2 -> H(f(c), U1(d, e))
28.38/9.20	   A^2 -> H(f(k), U1(k, k))
28.38/9.20	   A^2 -> H(U1(k, k), U1(b, b))
28.38/9.20	   A^2 -> H(U1(k, k), f(c))
28.38/9.20	   A^2 -> H(U1(k, k), f(d))
28.38/9.20	   A^2 -> H(U1(k, d), U1(c, b))
28.38/9.20	   A^2 -> H(U1(k, d), U1(d, b))
28.38/9.20	   A^2 -> H(U1(k, d), U1(b, c))
28.38/9.20	   A^2 -> H(U1(k, d), U1(b, d))
28.38/9.20	   A^2 -> H(U1(k, d), U1(c, c))
28.38/9.20	   A^2 -> H(U1(k, d), f(e))
28.38/9.20	   A^2 -> H(U1(k, d), f(k))
28.38/9.20	   A^2 -> H(U1(k, d), U1(d, d))
28.38/9.20	   A^2 -> H(U1(d, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(d, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(d, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(d, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(d, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(d, k), f(e))
28.38/9.20	   A^2 -> H(U1(d, k), f(k))
28.38/9.20	   A^2 -> H(U1(d, k), U1(d, d))
28.38/9.20	   A^2 -> H(U1(d, d), U1(e, b))
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, b))
28.38/9.20	   A^2 -> H(U1(d, d), U1(c, d))
28.38/9.20	   A^2 -> H(U1(d, d), U1(d, c))
28.38/9.20	   A^2 -> H(U1(d, d), U1(b, e))
28.38/9.20	   A^2 -> H(U1(d, d), U1(b, k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(e, c))
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, c))
28.38/9.20	   A^2 -> H(U1(d, d), U1(c, e))
28.38/9.20	   A^2 -> H(U1(d, d), U1(c, k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(e, e))
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, k))
28.38/9.20	   A^2 -> H(f(d), b)
28.38/9.20	   A^2 -> H(f(d), U1(e, d))
28.38/9.20	   A^2 -> H(f(d), U1(d, e))
28.38/9.20	   A^2 -> H(f(d), c)
28.38/9.20	   A^2 -> H(f(d), U1(e, k))
28.38/9.20	   A^2 -> H(f(d), U1(k, e))
28.38/9.20	   A^2 -> H(f(d), e)
28.38/9.20	   A^2 -> H(f(a), d)
28.38/9.20	   A^2 -> H(U1(c, c), U1(e, c))
28.38/9.20	   A^2 -> H(f(c), c)
28.38/9.20	   A^2 -> H(f(c), U1(e, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, c))
28.38/9.20	   A^2 -> H(f(c), U1(k, e))
28.38/9.20	   A^2 -> H(f(c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, e))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, k))
28.38/9.20	   A^2 -> H(f(a), k)
28.38/9.20	   A^2 -> H(f(e), U1(e, e))
28.38/9.20	   A^2 -> H(f(c), e)
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, d))
28.38/9.20	   A^2 -> H(f(d), U1(k, k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(d, k))
28.38/9.20	   A^2 -> H(d, U1(b, b))
28.38/9.20	   A^2 -> H(d, f(c))
28.38/9.20	   A^2 -> H(d, f(d))
28.38/9.20	   A^2 -> H(a, U1(c, b))
28.38/9.20	   A^2 -> H(a, U1(d, b))
28.38/9.20	   A^2 -> H(a, U1(b, c))
28.38/9.20	   A^2 -> H(a, U1(b, d))
28.38/9.20	   A^2 -> H(a, U1(c, c))
28.38/9.20	   A^2 -> H(a, f(e))
28.38/9.20	   A^2 -> H(a, f(k))
28.38/9.20	   A^2 -> H(a, U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, d), U1(c, b))
28.38/9.20	   A^2 -> H(U1(e, d), U1(d, b))
28.38/9.20	   A^2 -> H(U1(e, d), U1(b, c))
28.38/9.20	   A^2 -> H(U1(e, d), U1(b, d))
28.38/9.20	   A^2 -> H(U1(e, d), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, d), f(e))
28.38/9.20	   A^2 -> H(U1(e, d), f(k))
28.38/9.20	   A^2 -> H(U1(e, d), U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, a), U1(e, b))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, b))
28.38/9.20	   A^2 -> H(U1(e, a), U1(c, d))
28.38/9.20	   A^2 -> H(U1(e, a), U1(d, c))
28.38/9.20	   A^2 -> H(U1(e, a), U1(b, e))
28.38/9.20	   A^2 -> H(U1(e, a), U1(b, k))
28.38/9.20	   A^2 -> H(U1(e, a), U1(e, c))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, c))
28.38/9.20	   A^2 -> H(U1(e, a), U1(c, e))
28.38/9.20	   A^2 -> H(U1(e, a), U1(c, k))
28.38/9.20	   A^2 -> H(U1(e, a), U1(e, e))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, d))
28.38/9.20	   A^2 -> H(U1(e, a), U1(d, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(e, b))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, b))
28.38/9.20	   A^2 -> H(U1(k, a), U1(c, d))
28.38/9.20	   A^2 -> H(U1(k, a), U1(d, c))
28.38/9.20	   A^2 -> H(U1(k, a), U1(b, e))
28.38/9.20	   A^2 -> H(U1(k, a), U1(b, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(e, c))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, c))
28.38/9.20	   A^2 -> H(U1(k, a), U1(c, e))
28.38/9.20	   A^2 -> H(U1(k, a), U1(c, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(e, e))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, d))
28.38/9.20	   A^2 -> H(U1(k, a), U1(d, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(e, b))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, b))
28.38/9.20	   A^2 -> H(U1(c, d), U1(c, d))
28.38/9.20	   A^2 -> H(U1(c, d), U1(d, c))
28.38/9.20	   A^2 -> H(U1(c, d), U1(b, e))
28.38/9.20	   A^2 -> H(U1(c, d), U1(b, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(e, c))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, c))
28.38/9.20	   A^2 -> H(U1(c, d), U1(c, e))
28.38/9.20	   A^2 -> H(U1(c, d), U1(c, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(e, e))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, d))
28.38/9.20	   A^2 -> H(U1(c, d), U1(d, k))
28.38/9.20	   A^2 -> H(U1(c, a), b)
28.38/9.20	   A^2 -> H(U1(c, a), U1(e, d))
28.38/9.20	   A^2 -> H(U1(c, a), U1(d, e))
28.38/9.20	   A^2 -> H(U1(c, a), c)
28.38/9.20	   A^2 -> H(U1(c, a), U1(e, k))
28.38/9.20	   A^2 -> H(U1(c, a), U1(k, e))
28.38/9.20	   A^2 -> H(U1(c, a), e)
28.38/9.20	   A^2 -> H(U1(c, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(d, e), U1(c, b))
28.38/9.20	   A^2 -> H(U1(d, e), U1(d, b))
28.38/9.20	   A^2 -> H(U1(d, e), U1(b, c))
28.38/9.20	   A^2 -> H(U1(d, e), U1(b, d))
28.38/9.20	   A^2 -> H(U1(d, e), U1(c, c))
28.38/9.20	   A^2 -> H(U1(d, e), f(e))
28.38/9.20	   A^2 -> H(U1(d, e), f(k))
28.38/9.20	   A^2 -> H(U1(d, e), U1(d, d))
28.38/9.20	   A^2 -> H(U1(d, c), U1(e, b))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, b))
28.38/9.20	   A^2 -> H(U1(d, c), U1(c, d))
28.38/9.20	   A^2 -> H(U1(d, c), U1(d, c))
28.38/9.20	   A^2 -> H(U1(d, c), U1(b, e))
28.38/9.20	   A^2 -> H(U1(d, c), U1(b, k))
28.38/9.20	   A^2 -> H(U1(d, c), U1(e, c))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, c))
28.38/9.20	   A^2 -> H(U1(d, c), U1(c, e))
28.38/9.20	   A^2 -> H(U1(d, c), U1(c, k))
28.38/9.20	   A^2 -> H(U1(d, c), U1(e, e))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, d))
28.38/9.20	   A^2 -> H(U1(d, c), U1(d, k))
28.38/9.20	   A^2 -> H(U1(d, a), b)
28.38/9.20	   A^2 -> H(U1(d, a), U1(e, d))
28.38/9.20	   A^2 -> H(U1(d, a), U1(d, e))
28.38/9.20	   A^2 -> H(U1(d, a), c)
28.38/9.20	   A^2 -> H(U1(d, a), U1(e, k))
28.38/9.20	   A^2 -> H(U1(d, a), U1(k, e))
28.38/9.20	   A^2 -> H(U1(d, a), e)
28.38/9.20	   A^2 -> H(U1(d, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(e, b))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, b))
28.38/9.20	   A^2 -> H(U1(a, e), U1(c, d))
28.38/9.20	   A^2 -> H(U1(a, e), U1(d, c))
28.38/9.20	   A^2 -> H(U1(a, e), U1(b, e))
28.38/9.20	   A^2 -> H(U1(a, e), U1(b, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(e, c))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, c))
28.38/9.20	   A^2 -> H(U1(a, e), U1(c, e))
28.38/9.20	   A^2 -> H(U1(a, e), U1(c, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(e, e))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, d))
28.38/9.20	   A^2 -> H(U1(a, e), U1(d, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(e, b))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, b))
28.38/9.20	   A^2 -> H(U1(a, k), U1(c, d))
28.38/9.20	   A^2 -> H(U1(a, k), U1(d, c))
28.38/9.20	   A^2 -> H(U1(a, k), U1(b, e))
28.38/9.20	   A^2 -> H(U1(a, k), U1(b, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(e, c))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, c))
28.38/9.20	   A^2 -> H(U1(a, k), U1(c, e))
28.38/9.20	   A^2 -> H(U1(a, k), U1(c, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(e, e))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, d))
28.38/9.20	   A^2 -> H(U1(a, k), U1(d, k))
28.38/9.20	   A^2 -> H(U1(a, c), b)
28.38/9.20	   A^2 -> H(U1(a, c), U1(e, d))
28.38/9.20	   A^2 -> H(U1(a, c), U1(d, e))
28.38/9.20	   A^2 -> H(U1(a, c), c)
28.38/9.20	   A^2 -> H(U1(a, c), U1(e, k))
28.38/9.20	   A^2 -> H(U1(a, c), U1(k, e))
28.38/9.20	   A^2 -> H(U1(a, c), e)
28.38/9.20	   A^2 -> H(U1(a, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, d), b)
28.38/9.20	   A^2 -> H(U1(a, d), U1(e, d))
28.38/9.20	   A^2 -> H(U1(a, d), U1(d, e))
28.38/9.20	   A^2 -> H(U1(a, d), c)
28.38/9.20	   A^2 -> H(U1(a, d), U1(e, k))
28.38/9.20	   A^2 -> H(U1(a, d), U1(k, e))
28.38/9.20	   A^2 -> H(U1(a, d), e)
28.38/9.20	   A^2 -> H(U1(a, d), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, a), d)
28.38/9.20	   A^2 -> H(U1(a, a), k)
28.38/9.20	   A^2 -> H(k, U1(b, b))
28.38/9.20	   A^2 -> H(k, f(c))
28.38/9.20	   A^2 -> H(k, f(d))
28.38/9.20	   A^2 -> H(c, U1(c, b))
28.38/9.20	   A^2 -> H(c, U1(d, b))
28.38/9.20	   A^2 -> H(c, U1(b, c))
28.38/9.20	   A^2 -> H(c, U1(b, d))
28.38/9.20	   A^2 -> H(c, U1(c, c))
28.38/9.20	   A^2 -> H(c, f(e))
28.38/9.20	   A^2 -> H(c, f(k))
28.38/9.20	   A^2 -> H(c, U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(e, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(e, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(e, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(e, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, k), f(e))
28.38/9.20	   A^2 -> H(U1(e, k), f(k))
28.38/9.20	   A^2 -> H(U1(e, k), U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, c), U1(e, b))
28.38/9.20	   A^2 -> H(U1(e, c), U1(k, b))
28.38/9.20	   A^2 -> H(U1(e, c), U1(c, d))
28.38/9.20	   A^2 -> H(U1(e, c), U1(d, c))
28.38/9.20	   A^2 -> H(U1(e, c), U1(b, e))
28.38/9.20	   A^2 -> H(U1(e, c), U1(b, k))
28.38/9.20	   A^2 -> H(U1(e, c), U1(e, c))
28.38/9.20	   A^2 -> H(U1(e, c), U1(k, c))
28.38/9.20	   A^2 -> H(U1(e, c), U1(c, e))
28.38/9.20	   A^2 -> H(U1(e, c), U1(c, k))
28.38/9.20	   A^2 -> H(U1(e, c), U1(e, e))
28.38/9.20	
28.38/9.20	The TRS R consists of the following rules:
28.38/9.20	
28.38/9.20	   f(x) -> U1(x, x)
28.38/9.20	   U1(e, x) -> x
28.38/9.20	   a -> c
28.38/9.20	   a -> d
28.38/9.20	   b -> c
28.38/9.20	   b -> d
28.38/9.20	   d -> k
28.38/9.20	   c -> e
28.38/9.20	   c -> k
28.38/9.20	
28.38/9.20	Q is empty.
28.38/9.20	We have to consider all minimal (P,Q,R)-chains.
28.38/9.20	----------------------------------------
28.38/9.20	
28.38/9.20	(811) TransformationProof (EQUIVALENT)
28.38/9.20	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), f(k)) at position [] we obtained the following new rules [LPAR04]:
28.38/9.20	
28.38/9.20	   (A^2 -> H(c, f(k)),A^2 -> H(c, f(k)))
28.38/9.20	   (A^2 -> H(U1(e, e), f(k)),A^2 -> H(U1(e, e), f(k)))
28.38/9.20	   (A^2 -> H(U1(e, k), f(k)),A^2 -> H(U1(e, k), f(k)))
28.38/9.20	   (A^2 -> H(U1(e, c), U1(k, k)),A^2 -> H(U1(e, c), U1(k, k)))
28.38/9.20	
28.38/9.20	
28.38/9.20	----------------------------------------
28.38/9.20	
28.38/9.20	(812)
28.38/9.20	Obligation:
28.38/9.20	Q DP problem:
28.38/9.20	The TRS P consists of the following rules:
28.38/9.20	
28.38/9.20	   H(x, x) -> G(x, x, f(k))
28.38/9.20	   G(d, x, x) -> A^2
28.38/9.20	   A^2 -> H(f(c), f(c))
28.38/9.20	   A^2 -> H(f(d), f(d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, c))
28.38/9.20	   A^2 -> H(f(e), f(e))
28.38/9.20	   A^2 -> H(f(k), f(k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, c), U1(d, d))
28.38/9.20	   A^2 -> H(U1(k, e), U1(b, b))
28.38/9.20	   A^2 -> H(U1(k, e), f(c))
28.38/9.20	   A^2 -> H(U1(k, e), f(d))
28.38/9.20	   A^2 -> H(U1(k, c), U1(c, b))
28.38/9.20	   A^2 -> H(U1(k, c), U1(d, b))
28.38/9.20	   A^2 -> H(U1(k, c), U1(b, c))
28.38/9.20	   A^2 -> H(U1(k, c), U1(b, d))
28.38/9.20	   A^2 -> H(U1(k, c), U1(c, c))
28.38/9.20	   A^2 -> H(U1(k, c), f(e))
28.38/9.20	   A^2 -> H(U1(k, c), f(k))
28.38/9.20	   A^2 -> H(U1(k, c), U1(d, d))
28.38/9.20	   A^2 -> H(U1(c, e), U1(c, b))
28.38/9.20	   A^2 -> H(U1(c, e), U1(d, b))
28.38/9.20	   A^2 -> H(U1(c, e), U1(b, c))
28.38/9.20	   A^2 -> H(U1(c, e), U1(b, d))
28.38/9.20	   A^2 -> H(U1(c, e), U1(c, c))
28.38/9.20	   A^2 -> H(U1(c, e), f(e))
28.38/9.20	   A^2 -> H(U1(c, e), f(k))
28.38/9.20	   A^2 -> H(U1(c, e), U1(d, d))
28.38/9.20	   A^2 -> H(U1(c, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(c, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(c, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(c, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(c, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(c, k), f(e))
28.38/9.20	   A^2 -> H(U1(c, k), f(k))
28.38/9.20	   A^2 -> H(U1(c, k), U1(d, d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(e, b))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, b))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(d, c))
28.38/9.20	   A^2 -> H(U1(c, c), U1(b, e))
28.38/9.20	   A^2 -> H(U1(c, c), U1(b, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(e, e))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(d, k))
28.38/9.20	   A^2 -> H(e, U1(b, b))
28.38/9.20	   A^2 -> H(e, f(c))
28.38/9.20	   A^2 -> H(e, f(d))
28.38/9.20	   A^2 -> H(U1(e, e), U1(c, b))
28.38/9.20	   A^2 -> H(U1(e, e), U1(d, b))
28.38/9.20	   A^2 -> H(U1(e, e), U1(b, c))
28.38/9.20	   A^2 -> H(U1(e, e), U1(b, d))
28.38/9.20	   A^2 -> H(U1(e, e), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, e), f(e))
28.38/9.20	   A^2 -> H(U1(e, e), f(k))
28.38/9.20	   A^2 -> H(U1(e, e), U1(d, d))
28.38/9.20	   A^2 -> H(f(e), U1(e, b))
28.38/9.20	   A^2 -> H(f(e), U1(k, b))
28.38/9.20	   A^2 -> H(f(e), U1(c, d))
28.38/9.20	   A^2 -> H(f(e), U1(d, c))
28.38/9.20	   A^2 -> H(f(e), U1(b, e))
28.38/9.20	   A^2 -> H(f(e), U1(b, k))
28.38/9.20	   A^2 -> H(f(e), U1(e, c))
28.38/9.20	   A^2 -> H(f(e), U1(k, c))
28.38/9.20	   A^2 -> H(f(e), U1(c, e))
28.38/9.20	   A^2 -> H(f(e), U1(c, k))
28.38/9.20	   A^2 -> H(f(e), U1(k, k))
28.38/9.20	   A^2 -> H(f(e), U1(k, d))
28.38/9.20	   A^2 -> H(f(e), U1(d, k))
28.38/9.20	   A^2 -> H(U1(k, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(k, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(k, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(k, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(k, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(k, k), f(e))
28.38/9.20	   A^2 -> H(U1(k, k), f(k))
28.38/9.20	   A^2 -> H(U1(k, k), U1(d, d))
28.38/9.20	   A^2 -> H(f(k), U1(e, b))
28.38/9.20	   A^2 -> H(f(k), U1(k, b))
28.38/9.20	   A^2 -> H(f(k), U1(c, d))
28.38/9.20	   A^2 -> H(f(k), U1(d, c))
28.38/9.20	   A^2 -> H(f(k), U1(b, e))
28.38/9.20	   A^2 -> H(f(k), U1(b, k))
28.38/9.20	   A^2 -> H(f(k), U1(e, c))
28.38/9.20	   A^2 -> H(f(k), U1(k, c))
28.38/9.20	   A^2 -> H(f(k), U1(c, e))
28.38/9.20	   A^2 -> H(f(k), U1(c, k))
28.38/9.20	   A^2 -> H(f(k), U1(e, e))
28.38/9.20	   A^2 -> H(f(k), U1(k, d))
28.38/9.20	   A^2 -> H(f(k), U1(d, k))
28.38/9.20	   A^2 -> H(f(c), b)
28.38/9.20	   A^2 -> H(f(c), U1(e, d))
28.38/9.20	   A^2 -> H(f(c), U1(d, e))
28.38/9.20	   A^2 -> H(f(k), U1(k, k))
28.38/9.20	   A^2 -> H(U1(k, k), U1(b, b))
28.38/9.20	   A^2 -> H(U1(k, k), f(c))
28.38/9.20	   A^2 -> H(U1(k, k), f(d))
28.38/9.20	   A^2 -> H(U1(k, d), U1(c, b))
28.38/9.20	   A^2 -> H(U1(k, d), U1(d, b))
28.38/9.20	   A^2 -> H(U1(k, d), U1(b, c))
28.38/9.20	   A^2 -> H(U1(k, d), U1(b, d))
28.38/9.20	   A^2 -> H(U1(k, d), U1(c, c))
28.38/9.20	   A^2 -> H(U1(k, d), f(e))
28.38/9.20	   A^2 -> H(U1(k, d), f(k))
28.38/9.20	   A^2 -> H(U1(k, d), U1(d, d))
28.38/9.20	   A^2 -> H(U1(d, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(d, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(d, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(d, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(d, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(d, k), f(e))
28.38/9.20	   A^2 -> H(U1(d, k), f(k))
28.38/9.20	   A^2 -> H(U1(d, k), U1(d, d))
28.38/9.20	   A^2 -> H(U1(d, d), U1(e, b))
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, b))
28.38/9.20	   A^2 -> H(U1(d, d), U1(c, d))
28.38/9.20	   A^2 -> H(U1(d, d), U1(d, c))
28.38/9.20	   A^2 -> H(U1(d, d), U1(b, e))
28.38/9.20	   A^2 -> H(U1(d, d), U1(b, k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(e, c))
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, c))
28.38/9.20	   A^2 -> H(U1(d, d), U1(c, e))
28.38/9.20	   A^2 -> H(U1(d, d), U1(c, k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(e, e))
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, k))
28.38/9.20	   A^2 -> H(f(d), b)
28.38/9.20	   A^2 -> H(f(d), U1(e, d))
28.38/9.20	   A^2 -> H(f(d), U1(d, e))
28.38/9.20	   A^2 -> H(f(d), c)
28.38/9.20	   A^2 -> H(f(d), U1(e, k))
28.38/9.20	   A^2 -> H(f(d), U1(k, e))
28.38/9.20	   A^2 -> H(f(d), e)
28.38/9.20	   A^2 -> H(f(a), d)
28.38/9.20	   A^2 -> H(U1(c, c), U1(e, c))
28.38/9.20	   A^2 -> H(f(c), c)
28.38/9.20	   A^2 -> H(f(c), U1(e, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, c))
28.38/9.20	   A^2 -> H(f(c), U1(k, e))
28.38/9.20	   A^2 -> H(f(c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, e))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, k))
28.38/9.20	   A^2 -> H(f(a), k)
28.38/9.20	   A^2 -> H(f(e), U1(e, e))
28.38/9.20	   A^2 -> H(f(c), e)
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, d))
28.38/9.20	   A^2 -> H(f(d), U1(k, k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(d, k))
28.38/9.20	   A^2 -> H(d, U1(b, b))
28.38/9.20	   A^2 -> H(d, f(c))
28.38/9.20	   A^2 -> H(d, f(d))
28.38/9.20	   A^2 -> H(a, U1(c, b))
28.38/9.20	   A^2 -> H(a, U1(d, b))
28.38/9.20	   A^2 -> H(a, U1(b, c))
28.38/9.20	   A^2 -> H(a, U1(b, d))
28.38/9.20	   A^2 -> H(a, U1(c, c))
28.38/9.20	   A^2 -> H(a, f(e))
28.38/9.20	   A^2 -> H(a, f(k))
28.38/9.20	   A^2 -> H(a, U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, d), U1(c, b))
28.38/9.20	   A^2 -> H(U1(e, d), U1(d, b))
28.38/9.20	   A^2 -> H(U1(e, d), U1(b, c))
28.38/9.20	   A^2 -> H(U1(e, d), U1(b, d))
28.38/9.20	   A^2 -> H(U1(e, d), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, d), f(e))
28.38/9.20	   A^2 -> H(U1(e, d), f(k))
28.38/9.20	   A^2 -> H(U1(e, d), U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, a), U1(e, b))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, b))
28.38/9.20	   A^2 -> H(U1(e, a), U1(c, d))
28.38/9.20	   A^2 -> H(U1(e, a), U1(d, c))
28.38/9.20	   A^2 -> H(U1(e, a), U1(b, e))
28.38/9.20	   A^2 -> H(U1(e, a), U1(b, k))
28.38/9.20	   A^2 -> H(U1(e, a), U1(e, c))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, c))
28.38/9.20	   A^2 -> H(U1(e, a), U1(c, e))
28.38/9.20	   A^2 -> H(U1(e, a), U1(c, k))
28.38/9.20	   A^2 -> H(U1(e, a), U1(e, e))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, d))
28.38/9.20	   A^2 -> H(U1(e, a), U1(d, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(e, b))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, b))
28.38/9.20	   A^2 -> H(U1(k, a), U1(c, d))
28.38/9.20	   A^2 -> H(U1(k, a), U1(d, c))
28.38/9.20	   A^2 -> H(U1(k, a), U1(b, e))
28.38/9.20	   A^2 -> H(U1(k, a), U1(b, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(e, c))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, c))
28.38/9.20	   A^2 -> H(U1(k, a), U1(c, e))
28.38/9.20	   A^2 -> H(U1(k, a), U1(c, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(e, e))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, d))
28.38/9.20	   A^2 -> H(U1(k, a), U1(d, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(e, b))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, b))
28.38/9.20	   A^2 -> H(U1(c, d), U1(c, d))
28.38/9.20	   A^2 -> H(U1(c, d), U1(d, c))
28.38/9.20	   A^2 -> H(U1(c, d), U1(b, e))
28.38/9.20	   A^2 -> H(U1(c, d), U1(b, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(e, c))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, c))
28.38/9.20	   A^2 -> H(U1(c, d), U1(c, e))
28.38/9.20	   A^2 -> H(U1(c, d), U1(c, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(e, e))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, d))
28.38/9.20	   A^2 -> H(U1(c, d), U1(d, k))
28.38/9.20	   A^2 -> H(U1(c, a), b)
28.38/9.20	   A^2 -> H(U1(c, a), U1(e, d))
28.38/9.20	   A^2 -> H(U1(c, a), U1(d, e))
28.38/9.20	   A^2 -> H(U1(c, a), c)
28.38/9.20	   A^2 -> H(U1(c, a), U1(e, k))
28.38/9.20	   A^2 -> H(U1(c, a), U1(k, e))
28.38/9.20	   A^2 -> H(U1(c, a), e)
28.38/9.20	   A^2 -> H(U1(c, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(d, e), U1(c, b))
28.38/9.20	   A^2 -> H(U1(d, e), U1(d, b))
28.38/9.20	   A^2 -> H(U1(d, e), U1(b, c))
28.38/9.20	   A^2 -> H(U1(d, e), U1(b, d))
28.38/9.20	   A^2 -> H(U1(d, e), U1(c, c))
28.38/9.20	   A^2 -> H(U1(d, e), f(e))
28.38/9.20	   A^2 -> H(U1(d, e), f(k))
28.38/9.20	   A^2 -> H(U1(d, e), U1(d, d))
28.38/9.20	   A^2 -> H(U1(d, c), U1(e, b))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, b))
28.38/9.20	   A^2 -> H(U1(d, c), U1(c, d))
28.38/9.20	   A^2 -> H(U1(d, c), U1(d, c))
28.38/9.20	   A^2 -> H(U1(d, c), U1(b, e))
28.38/9.20	   A^2 -> H(U1(d, c), U1(b, k))
28.38/9.20	   A^2 -> H(U1(d, c), U1(e, c))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, c))
28.38/9.20	   A^2 -> H(U1(d, c), U1(c, e))
28.38/9.20	   A^2 -> H(U1(d, c), U1(c, k))
28.38/9.20	   A^2 -> H(U1(d, c), U1(e, e))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, d))
28.38/9.20	   A^2 -> H(U1(d, c), U1(d, k))
28.38/9.20	   A^2 -> H(U1(d, a), b)
28.38/9.20	   A^2 -> H(U1(d, a), U1(e, d))
28.38/9.20	   A^2 -> H(U1(d, a), U1(d, e))
28.38/9.20	   A^2 -> H(U1(d, a), c)
28.38/9.20	   A^2 -> H(U1(d, a), U1(e, k))
28.38/9.20	   A^2 -> H(U1(d, a), U1(k, e))
28.38/9.20	   A^2 -> H(U1(d, a), e)
28.38/9.20	   A^2 -> H(U1(d, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(e, b))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, b))
28.38/9.20	   A^2 -> H(U1(a, e), U1(c, d))
28.38/9.20	   A^2 -> H(U1(a, e), U1(d, c))
28.38/9.20	   A^2 -> H(U1(a, e), U1(b, e))
28.38/9.20	   A^2 -> H(U1(a, e), U1(b, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(e, c))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, c))
28.38/9.20	   A^2 -> H(U1(a, e), U1(c, e))
28.38/9.20	   A^2 -> H(U1(a, e), U1(c, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(e, e))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, d))
28.38/9.20	   A^2 -> H(U1(a, e), U1(d, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(e, b))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, b))
28.38/9.20	   A^2 -> H(U1(a, k), U1(c, d))
28.38/9.20	   A^2 -> H(U1(a, k), U1(d, c))
28.38/9.20	   A^2 -> H(U1(a, k), U1(b, e))
28.38/9.20	   A^2 -> H(U1(a, k), U1(b, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(e, c))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, c))
28.38/9.20	   A^2 -> H(U1(a, k), U1(c, e))
28.38/9.20	   A^2 -> H(U1(a, k), U1(c, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(e, e))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, d))
28.38/9.20	   A^2 -> H(U1(a, k), U1(d, k))
28.38/9.20	   A^2 -> H(U1(a, c), b)
28.38/9.20	   A^2 -> H(U1(a, c), U1(e, d))
28.38/9.20	   A^2 -> H(U1(a, c), U1(d, e))
28.38/9.20	   A^2 -> H(U1(a, c), c)
28.38/9.20	   A^2 -> H(U1(a, c), U1(e, k))
28.38/9.20	   A^2 -> H(U1(a, c), U1(k, e))
28.38/9.20	   A^2 -> H(U1(a, c), e)
28.38/9.20	   A^2 -> H(U1(a, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, d), b)
28.38/9.20	   A^2 -> H(U1(a, d), U1(e, d))
28.38/9.20	   A^2 -> H(U1(a, d), U1(d, e))
28.38/9.20	   A^2 -> H(U1(a, d), c)
28.38/9.20	   A^2 -> H(U1(a, d), U1(e, k))
28.38/9.20	   A^2 -> H(U1(a, d), U1(k, e))
28.38/9.20	   A^2 -> H(U1(a, d), e)
28.38/9.20	   A^2 -> H(U1(a, d), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, a), d)
28.38/9.20	   A^2 -> H(U1(a, a), k)
28.38/9.20	   A^2 -> H(k, U1(b, b))
28.38/9.20	   A^2 -> H(k, f(c))
28.38/9.20	   A^2 -> H(k, f(d))
28.38/9.20	   A^2 -> H(c, U1(c, b))
28.38/9.20	   A^2 -> H(c, U1(d, b))
28.38/9.20	   A^2 -> H(c, U1(b, c))
28.38/9.20	   A^2 -> H(c, U1(b, d))
28.38/9.20	   A^2 -> H(c, U1(c, c))
28.38/9.20	   A^2 -> H(c, f(e))
28.38/9.20	   A^2 -> H(c, f(k))
28.38/9.20	   A^2 -> H(c, U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(e, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(e, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(e, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(e, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, k), f(e))
28.38/9.20	   A^2 -> H(U1(e, k), f(k))
28.38/9.20	   A^2 -> H(U1(e, k), U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, c), U1(e, b))
28.38/9.20	   A^2 -> H(U1(e, c), U1(k, b))
28.38/9.20	   A^2 -> H(U1(e, c), U1(c, d))
28.38/9.20	   A^2 -> H(U1(e, c), U1(d, c))
28.38/9.20	   A^2 -> H(U1(e, c), U1(b, e))
28.38/9.20	   A^2 -> H(U1(e, c), U1(b, k))
28.38/9.20	   A^2 -> H(U1(e, c), U1(e, c))
28.38/9.20	   A^2 -> H(U1(e, c), U1(k, c))
28.38/9.20	   A^2 -> H(U1(e, c), U1(c, e))
28.38/9.20	   A^2 -> H(U1(e, c), U1(c, k))
28.38/9.20	   A^2 -> H(U1(e, c), U1(e, e))
28.38/9.20	   A^2 -> H(U1(e, c), U1(k, k))
28.38/9.20	
28.38/9.20	The TRS R consists of the following rules:
28.38/9.20	
28.38/9.20	   f(x) -> U1(x, x)
28.38/9.20	   U1(e, x) -> x
28.38/9.20	   a -> c
28.38/9.20	   a -> d
28.38/9.20	   b -> c
28.38/9.20	   b -> d
28.38/9.20	   d -> k
28.38/9.20	   c -> e
28.38/9.20	   c -> k
28.38/9.20	
28.38/9.20	Q is empty.
28.38/9.20	We have to consider all minimal (P,Q,R)-chains.
28.38/9.20	----------------------------------------
28.38/9.20	
28.38/9.20	(813) TransformationProof (EQUIVALENT)
28.38/9.20	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
28.38/9.20	
28.38/9.20	   (A^2 -> H(c, U1(d, d)),A^2 -> H(c, U1(d, d)))
28.38/9.20	   (A^2 -> H(U1(e, e), U1(d, d)),A^2 -> H(U1(e, e), U1(d, d)))
28.38/9.20	   (A^2 -> H(U1(e, k), U1(d, d)),A^2 -> H(U1(e, k), U1(d, d)))
28.38/9.20	   (A^2 -> H(U1(e, c), U1(k, d)),A^2 -> H(U1(e, c), U1(k, d)))
28.38/9.20	   (A^2 -> H(U1(e, c), U1(d, k)),A^2 -> H(U1(e, c), U1(d, k)))
28.38/9.20	
28.38/9.20	
28.38/9.20	----------------------------------------
28.38/9.20	
28.38/9.20	(814)
28.38/9.20	Obligation:
28.38/9.20	Q DP problem:
28.38/9.20	The TRS P consists of the following rules:
28.38/9.20	
28.38/9.20	   H(x, x) -> G(x, x, f(k))
28.38/9.20	   G(d, x, x) -> A^2
28.38/9.20	   A^2 -> H(f(c), f(c))
28.38/9.20	   A^2 -> H(f(d), f(d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, c))
28.38/9.20	   A^2 -> H(f(e), f(e))
28.38/9.20	   A^2 -> H(f(k), f(k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(d, d))
28.38/9.20	   A^2 -> H(U1(k, e), U1(b, b))
28.38/9.20	   A^2 -> H(U1(k, e), f(c))
28.38/9.20	   A^2 -> H(U1(k, e), f(d))
28.38/9.20	   A^2 -> H(U1(k, c), U1(c, b))
28.38/9.20	   A^2 -> H(U1(k, c), U1(d, b))
28.38/9.20	   A^2 -> H(U1(k, c), U1(b, c))
28.38/9.20	   A^2 -> H(U1(k, c), U1(b, d))
28.38/9.20	   A^2 -> H(U1(k, c), U1(c, c))
28.38/9.20	   A^2 -> H(U1(k, c), f(e))
28.38/9.20	   A^2 -> H(U1(k, c), f(k))
28.38/9.20	   A^2 -> H(U1(k, c), U1(d, d))
28.38/9.20	   A^2 -> H(U1(c, e), U1(c, b))
28.38/9.20	   A^2 -> H(U1(c, e), U1(d, b))
28.38/9.20	   A^2 -> H(U1(c, e), U1(b, c))
28.38/9.20	   A^2 -> H(U1(c, e), U1(b, d))
28.38/9.20	   A^2 -> H(U1(c, e), U1(c, c))
28.38/9.20	   A^2 -> H(U1(c, e), f(e))
28.38/9.20	   A^2 -> H(U1(c, e), f(k))
28.38/9.20	   A^2 -> H(U1(c, e), U1(d, d))
28.38/9.20	   A^2 -> H(U1(c, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(c, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(c, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(c, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(c, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(c, k), f(e))
28.38/9.20	   A^2 -> H(U1(c, k), f(k))
28.38/9.20	   A^2 -> H(U1(c, k), U1(d, d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(e, b))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, b))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(d, c))
28.38/9.20	   A^2 -> H(U1(c, c), U1(b, e))
28.38/9.20	   A^2 -> H(U1(c, c), U1(b, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(e, e))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(d, k))
28.38/9.20	   A^2 -> H(e, U1(b, b))
28.38/9.20	   A^2 -> H(e, f(c))
28.38/9.20	   A^2 -> H(e, f(d))
28.38/9.20	   A^2 -> H(U1(e, e), U1(c, b))
28.38/9.20	   A^2 -> H(U1(e, e), U1(d, b))
28.38/9.20	   A^2 -> H(U1(e, e), U1(b, c))
28.38/9.20	   A^2 -> H(U1(e, e), U1(b, d))
28.38/9.20	   A^2 -> H(U1(e, e), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, e), f(e))
28.38/9.20	   A^2 -> H(U1(e, e), f(k))
28.38/9.20	   A^2 -> H(U1(e, e), U1(d, d))
28.38/9.20	   A^2 -> H(f(e), U1(e, b))
28.38/9.20	   A^2 -> H(f(e), U1(k, b))
28.38/9.20	   A^2 -> H(f(e), U1(c, d))
28.38/9.20	   A^2 -> H(f(e), U1(d, c))
28.38/9.20	   A^2 -> H(f(e), U1(b, e))
28.38/9.20	   A^2 -> H(f(e), U1(b, k))
28.38/9.20	   A^2 -> H(f(e), U1(e, c))
28.38/9.20	   A^2 -> H(f(e), U1(k, c))
28.38/9.20	   A^2 -> H(f(e), U1(c, e))
28.38/9.20	   A^2 -> H(f(e), U1(c, k))
28.38/9.20	   A^2 -> H(f(e), U1(k, k))
28.38/9.20	   A^2 -> H(f(e), U1(k, d))
28.38/9.20	   A^2 -> H(f(e), U1(d, k))
28.38/9.20	   A^2 -> H(U1(k, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(k, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(k, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(k, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(k, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(k, k), f(e))
28.38/9.20	   A^2 -> H(U1(k, k), f(k))
28.38/9.20	   A^2 -> H(U1(k, k), U1(d, d))
28.38/9.20	   A^2 -> H(f(k), U1(e, b))
28.38/9.20	   A^2 -> H(f(k), U1(k, b))
28.38/9.20	   A^2 -> H(f(k), U1(c, d))
28.38/9.20	   A^2 -> H(f(k), U1(d, c))
28.38/9.20	   A^2 -> H(f(k), U1(b, e))
28.38/9.20	   A^2 -> H(f(k), U1(b, k))
28.38/9.20	   A^2 -> H(f(k), U1(e, c))
28.38/9.20	   A^2 -> H(f(k), U1(k, c))
28.38/9.20	   A^2 -> H(f(k), U1(c, e))
28.38/9.20	   A^2 -> H(f(k), U1(c, k))
28.38/9.20	   A^2 -> H(f(k), U1(e, e))
28.38/9.20	   A^2 -> H(f(k), U1(k, d))
28.38/9.20	   A^2 -> H(f(k), U1(d, k))
28.38/9.20	   A^2 -> H(f(c), b)
28.38/9.20	   A^2 -> H(f(c), U1(e, d))
28.38/9.20	   A^2 -> H(f(c), U1(d, e))
28.38/9.20	   A^2 -> H(f(k), U1(k, k))
28.38/9.20	   A^2 -> H(U1(k, k), U1(b, b))
28.38/9.20	   A^2 -> H(U1(k, k), f(c))
28.38/9.20	   A^2 -> H(U1(k, k), f(d))
28.38/9.20	   A^2 -> H(U1(k, d), U1(c, b))
28.38/9.20	   A^2 -> H(U1(k, d), U1(d, b))
28.38/9.20	   A^2 -> H(U1(k, d), U1(b, c))
28.38/9.20	   A^2 -> H(U1(k, d), U1(b, d))
28.38/9.20	   A^2 -> H(U1(k, d), U1(c, c))
28.38/9.20	   A^2 -> H(U1(k, d), f(e))
28.38/9.20	   A^2 -> H(U1(k, d), f(k))
28.38/9.20	   A^2 -> H(U1(k, d), U1(d, d))
28.38/9.20	   A^2 -> H(U1(d, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(d, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(d, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(d, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(d, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(d, k), f(e))
28.38/9.20	   A^2 -> H(U1(d, k), f(k))
28.38/9.20	   A^2 -> H(U1(d, k), U1(d, d))
28.38/9.20	   A^2 -> H(U1(d, d), U1(e, b))
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, b))
28.38/9.20	   A^2 -> H(U1(d, d), U1(c, d))
28.38/9.20	   A^2 -> H(U1(d, d), U1(d, c))
28.38/9.20	   A^2 -> H(U1(d, d), U1(b, e))
28.38/9.20	   A^2 -> H(U1(d, d), U1(b, k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(e, c))
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, c))
28.38/9.20	   A^2 -> H(U1(d, d), U1(c, e))
28.38/9.20	   A^2 -> H(U1(d, d), U1(c, k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(e, e))
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, k))
28.38/9.20	   A^2 -> H(f(d), b)
28.38/9.20	   A^2 -> H(f(d), U1(e, d))
28.38/9.20	   A^2 -> H(f(d), U1(d, e))
28.38/9.20	   A^2 -> H(f(d), c)
28.38/9.20	   A^2 -> H(f(d), U1(e, k))
28.38/9.20	   A^2 -> H(f(d), U1(k, e))
28.38/9.20	   A^2 -> H(f(d), e)
28.38/9.20	   A^2 -> H(f(a), d)
28.38/9.20	   A^2 -> H(U1(c, c), U1(e, c))
28.38/9.20	   A^2 -> H(f(c), c)
28.38/9.20	   A^2 -> H(f(c), U1(e, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, c))
28.38/9.20	   A^2 -> H(f(c), U1(k, e))
28.38/9.20	   A^2 -> H(f(c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, e))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, k))
28.38/9.20	   A^2 -> H(f(a), k)
28.38/9.20	   A^2 -> H(f(e), U1(e, e))
28.38/9.20	   A^2 -> H(f(c), e)
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, d))
28.38/9.20	   A^2 -> H(f(d), U1(k, k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(d, k))
28.38/9.20	   A^2 -> H(d, U1(b, b))
28.38/9.20	   A^2 -> H(d, f(c))
28.38/9.20	   A^2 -> H(d, f(d))
28.38/9.20	   A^2 -> H(a, U1(c, b))
28.38/9.20	   A^2 -> H(a, U1(d, b))
28.38/9.20	   A^2 -> H(a, U1(b, c))
28.38/9.20	   A^2 -> H(a, U1(b, d))
28.38/9.20	   A^2 -> H(a, U1(c, c))
28.38/9.20	   A^2 -> H(a, f(e))
28.38/9.20	   A^2 -> H(a, f(k))
28.38/9.20	   A^2 -> H(a, U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, d), U1(c, b))
28.38/9.20	   A^2 -> H(U1(e, d), U1(d, b))
28.38/9.20	   A^2 -> H(U1(e, d), U1(b, c))
28.38/9.20	   A^2 -> H(U1(e, d), U1(b, d))
28.38/9.20	   A^2 -> H(U1(e, d), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, d), f(e))
28.38/9.20	   A^2 -> H(U1(e, d), f(k))
28.38/9.20	   A^2 -> H(U1(e, d), U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, a), U1(e, b))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, b))
28.38/9.20	   A^2 -> H(U1(e, a), U1(c, d))
28.38/9.20	   A^2 -> H(U1(e, a), U1(d, c))
28.38/9.20	   A^2 -> H(U1(e, a), U1(b, e))
28.38/9.20	   A^2 -> H(U1(e, a), U1(b, k))
28.38/9.20	   A^2 -> H(U1(e, a), U1(e, c))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, c))
28.38/9.20	   A^2 -> H(U1(e, a), U1(c, e))
28.38/9.20	   A^2 -> H(U1(e, a), U1(c, k))
28.38/9.20	   A^2 -> H(U1(e, a), U1(e, e))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, d))
28.38/9.20	   A^2 -> H(U1(e, a), U1(d, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(e, b))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, b))
28.38/9.20	   A^2 -> H(U1(k, a), U1(c, d))
28.38/9.20	   A^2 -> H(U1(k, a), U1(d, c))
28.38/9.20	   A^2 -> H(U1(k, a), U1(b, e))
28.38/9.20	   A^2 -> H(U1(k, a), U1(b, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(e, c))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, c))
28.38/9.20	   A^2 -> H(U1(k, a), U1(c, e))
28.38/9.20	   A^2 -> H(U1(k, a), U1(c, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(e, e))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(k, a), U1(k, d))
28.38/9.20	   A^2 -> H(U1(k, a), U1(d, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(e, b))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, b))
28.38/9.20	   A^2 -> H(U1(c, d), U1(c, d))
28.38/9.20	   A^2 -> H(U1(c, d), U1(d, c))
28.38/9.20	   A^2 -> H(U1(c, d), U1(b, e))
28.38/9.20	   A^2 -> H(U1(c, d), U1(b, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(e, c))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, c))
28.38/9.20	   A^2 -> H(U1(c, d), U1(c, e))
28.38/9.20	   A^2 -> H(U1(c, d), U1(c, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(e, e))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, k))
28.38/9.20	   A^2 -> H(U1(c, d), U1(k, d))
28.38/9.20	   A^2 -> H(U1(c, d), U1(d, k))
28.38/9.20	   A^2 -> H(U1(c, a), b)
28.38/9.20	   A^2 -> H(U1(c, a), U1(e, d))
28.38/9.20	   A^2 -> H(U1(c, a), U1(d, e))
28.38/9.20	   A^2 -> H(U1(c, a), c)
28.38/9.20	   A^2 -> H(U1(c, a), U1(e, k))
28.38/9.20	   A^2 -> H(U1(c, a), U1(k, e))
28.38/9.20	   A^2 -> H(U1(c, a), e)
28.38/9.20	   A^2 -> H(U1(c, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(d, e), U1(c, b))
28.38/9.20	   A^2 -> H(U1(d, e), U1(d, b))
28.38/9.20	   A^2 -> H(U1(d, e), U1(b, c))
28.38/9.20	   A^2 -> H(U1(d, e), U1(b, d))
28.38/9.20	   A^2 -> H(U1(d, e), U1(c, c))
28.38/9.20	   A^2 -> H(U1(d, e), f(e))
28.38/9.20	   A^2 -> H(U1(d, e), f(k))
28.38/9.20	   A^2 -> H(U1(d, e), U1(d, d))
28.38/9.20	   A^2 -> H(U1(d, c), U1(e, b))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, b))
28.38/9.20	   A^2 -> H(U1(d, c), U1(c, d))
28.38/9.20	   A^2 -> H(U1(d, c), U1(d, c))
28.38/9.20	   A^2 -> H(U1(d, c), U1(b, e))
28.38/9.20	   A^2 -> H(U1(d, c), U1(b, k))
28.38/9.20	   A^2 -> H(U1(d, c), U1(e, c))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, c))
28.38/9.20	   A^2 -> H(U1(d, c), U1(c, e))
28.38/9.20	   A^2 -> H(U1(d, c), U1(c, k))
28.38/9.20	   A^2 -> H(U1(d, c), U1(e, e))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(d, c), U1(k, d))
28.38/9.20	   A^2 -> H(U1(d, c), U1(d, k))
28.38/9.20	   A^2 -> H(U1(d, a), b)
28.38/9.20	   A^2 -> H(U1(d, a), U1(e, d))
28.38/9.20	   A^2 -> H(U1(d, a), U1(d, e))
28.38/9.20	   A^2 -> H(U1(d, a), c)
28.38/9.20	   A^2 -> H(U1(d, a), U1(e, k))
28.38/9.20	   A^2 -> H(U1(d, a), U1(k, e))
28.38/9.20	   A^2 -> H(U1(d, a), e)
28.38/9.20	   A^2 -> H(U1(d, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(e, b))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, b))
28.38/9.20	   A^2 -> H(U1(a, e), U1(c, d))
28.38/9.20	   A^2 -> H(U1(a, e), U1(d, c))
28.38/9.20	   A^2 -> H(U1(a, e), U1(b, e))
28.38/9.20	   A^2 -> H(U1(a, e), U1(b, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(e, c))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, c))
28.38/9.20	   A^2 -> H(U1(a, e), U1(c, e))
28.38/9.20	   A^2 -> H(U1(a, e), U1(c, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(e, e))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, e), U1(k, d))
28.38/9.20	   A^2 -> H(U1(a, e), U1(d, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(e, b))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, b))
28.38/9.20	   A^2 -> H(U1(a, k), U1(c, d))
28.38/9.20	   A^2 -> H(U1(a, k), U1(d, c))
28.38/9.20	   A^2 -> H(U1(a, k), U1(b, e))
28.38/9.20	   A^2 -> H(U1(a, k), U1(b, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(e, c))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, c))
28.38/9.20	   A^2 -> H(U1(a, k), U1(c, e))
28.38/9.20	   A^2 -> H(U1(a, k), U1(c, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(e, e))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, k), U1(k, d))
28.38/9.20	   A^2 -> H(U1(a, k), U1(d, k))
28.38/9.20	   A^2 -> H(U1(a, c), b)
28.38/9.20	   A^2 -> H(U1(a, c), U1(e, d))
28.38/9.20	   A^2 -> H(U1(a, c), U1(d, e))
28.38/9.20	   A^2 -> H(U1(a, c), c)
28.38/9.20	   A^2 -> H(U1(a, c), U1(e, k))
28.38/9.20	   A^2 -> H(U1(a, c), U1(k, e))
28.38/9.20	   A^2 -> H(U1(a, c), e)
28.38/9.20	   A^2 -> H(U1(a, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, d), b)
28.38/9.20	   A^2 -> H(U1(a, d), U1(e, d))
28.38/9.20	   A^2 -> H(U1(a, d), U1(d, e))
28.38/9.20	   A^2 -> H(U1(a, d), c)
28.38/9.20	   A^2 -> H(U1(a, d), U1(e, k))
28.38/9.20	   A^2 -> H(U1(a, d), U1(k, e))
28.38/9.20	   A^2 -> H(U1(a, d), e)
28.38/9.20	   A^2 -> H(U1(a, d), U1(k, k))
28.38/9.20	   A^2 -> H(U1(a, a), d)
28.38/9.20	   A^2 -> H(U1(a, a), k)
28.38/9.20	   A^2 -> H(k, U1(b, b))
28.38/9.20	   A^2 -> H(k, f(c))
28.38/9.20	   A^2 -> H(k, f(d))
28.38/9.20	   A^2 -> H(c, U1(c, b))
28.38/9.20	   A^2 -> H(c, U1(d, b))
28.38/9.20	   A^2 -> H(c, U1(b, c))
28.38/9.20	   A^2 -> H(c, U1(b, d))
28.38/9.20	   A^2 -> H(c, U1(c, c))
28.38/9.20	   A^2 -> H(c, f(e))
28.38/9.20	   A^2 -> H(c, f(k))
28.38/9.20	   A^2 -> H(c, U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(e, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(e, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(e, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(e, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, k), f(e))
28.38/9.20	   A^2 -> H(U1(e, k), f(k))
28.38/9.20	   A^2 -> H(U1(e, k), U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, c), U1(e, b))
28.38/9.20	   A^2 -> H(U1(e, c), U1(k, b))
28.38/9.20	   A^2 -> H(U1(e, c), U1(c, d))
28.38/9.20	   A^2 -> H(U1(e, c), U1(d, c))
28.38/9.20	   A^2 -> H(U1(e, c), U1(b, e))
28.38/9.20	   A^2 -> H(U1(e, c), U1(b, k))
28.38/9.20	   A^2 -> H(U1(e, c), U1(e, c))
28.38/9.20	   A^2 -> H(U1(e, c), U1(k, c))
28.38/9.20	   A^2 -> H(U1(e, c), U1(c, e))
28.38/9.20	   A^2 -> H(U1(e, c), U1(c, k))
28.38/9.20	   A^2 -> H(U1(e, c), U1(e, e))
28.38/9.20	   A^2 -> H(U1(e, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(e, c), U1(k, d))
28.38/9.20	   A^2 -> H(U1(e, c), U1(d, k))
28.38/9.20	
28.38/9.20	The TRS R consists of the following rules:
28.38/9.20	
28.38/9.20	   f(x) -> U1(x, x)
28.38/9.20	   U1(e, x) -> x
28.38/9.20	   a -> c
28.38/9.20	   a -> d
28.38/9.20	   b -> c
28.38/9.20	   b -> d
28.38/9.20	   d -> k
28.38/9.20	   c -> e
28.38/9.20	   c -> k
28.38/9.20	
28.38/9.20	Q is empty.
28.38/9.20	We have to consider all minimal (P,Q,R)-chains.
28.38/9.20	----------------------------------------
28.38/9.20	
28.38/9.20	(815) TransformationProof (EQUIVALENT)
28.38/9.20	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
28.38/9.20	
28.38/9.20	   (A^2 -> H(U1(k, e), U1(c, b)),A^2 -> H(U1(k, e), U1(c, b)))
28.38/9.20	   (A^2 -> H(U1(k, e), U1(d, b)),A^2 -> H(U1(k, e), U1(d, b)))
28.38/9.20	   (A^2 -> H(U1(k, e), U1(b, c)),A^2 -> H(U1(k, e), U1(b, c)))
28.38/9.20	   (A^2 -> H(U1(k, e), U1(b, d)),A^2 -> H(U1(k, e), U1(b, d)))
28.38/9.20	
28.38/9.20	
28.38/9.20	----------------------------------------
28.38/9.20	
28.38/9.20	(816)
28.38/9.20	Obligation:
28.38/9.20	Q DP problem:
28.38/9.20	The TRS P consists of the following rules:
28.38/9.20	
28.38/9.20	   H(x, x) -> G(x, x, f(k))
28.38/9.20	   G(d, x, x) -> A^2
28.38/9.20	   A^2 -> H(f(c), f(c))
28.38/9.20	   A^2 -> H(f(d), f(d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, c))
28.38/9.20	   A^2 -> H(f(e), f(e))
28.38/9.20	   A^2 -> H(f(k), f(k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(d, d))
28.38/9.20	   A^2 -> H(U1(k, e), f(c))
28.38/9.20	   A^2 -> H(U1(k, e), f(d))
28.38/9.20	   A^2 -> H(U1(k, c), U1(c, b))
28.38/9.20	   A^2 -> H(U1(k, c), U1(d, b))
28.38/9.20	   A^2 -> H(U1(k, c), U1(b, c))
28.38/9.20	   A^2 -> H(U1(k, c), U1(b, d))
28.38/9.20	   A^2 -> H(U1(k, c), U1(c, c))
28.38/9.20	   A^2 -> H(U1(k, c), f(e))
28.38/9.20	   A^2 -> H(U1(k, c), f(k))
28.38/9.20	   A^2 -> H(U1(k, c), U1(d, d))
28.38/9.20	   A^2 -> H(U1(c, e), U1(c, b))
28.38/9.20	   A^2 -> H(U1(c, e), U1(d, b))
28.38/9.20	   A^2 -> H(U1(c, e), U1(b, c))
28.38/9.20	   A^2 -> H(U1(c, e), U1(b, d))
28.38/9.20	   A^2 -> H(U1(c, e), U1(c, c))
28.38/9.20	   A^2 -> H(U1(c, e), f(e))
28.38/9.20	   A^2 -> H(U1(c, e), f(k))
28.38/9.20	   A^2 -> H(U1(c, e), U1(d, d))
28.38/9.20	   A^2 -> H(U1(c, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(c, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(c, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(c, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(c, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(c, k), f(e))
28.38/9.20	   A^2 -> H(U1(c, k), f(k))
28.38/9.20	   A^2 -> H(U1(c, k), U1(d, d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(e, b))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, b))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(d, c))
28.38/9.20	   A^2 -> H(U1(c, c), U1(b, e))
28.38/9.20	   A^2 -> H(U1(c, c), U1(b, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(e, e))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, d))
28.38/9.20	   A^2 -> H(U1(c, c), U1(d, k))
28.38/9.20	   A^2 -> H(e, U1(b, b))
28.38/9.20	   A^2 -> H(e, f(c))
28.38/9.20	   A^2 -> H(e, f(d))
28.38/9.20	   A^2 -> H(U1(e, e), U1(c, b))
28.38/9.20	   A^2 -> H(U1(e, e), U1(d, b))
28.38/9.20	   A^2 -> H(U1(e, e), U1(b, c))
28.38/9.20	   A^2 -> H(U1(e, e), U1(b, d))
28.38/9.20	   A^2 -> H(U1(e, e), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, e), f(e))
28.38/9.20	   A^2 -> H(U1(e, e), f(k))
28.38/9.20	   A^2 -> H(U1(e, e), U1(d, d))
28.38/9.20	   A^2 -> H(f(e), U1(e, b))
28.38/9.20	   A^2 -> H(f(e), U1(k, b))
28.38/9.20	   A^2 -> H(f(e), U1(c, d))
28.38/9.20	   A^2 -> H(f(e), U1(d, c))
28.38/9.20	   A^2 -> H(f(e), U1(b, e))
28.38/9.20	   A^2 -> H(f(e), U1(b, k))
28.38/9.20	   A^2 -> H(f(e), U1(e, c))
28.38/9.20	   A^2 -> H(f(e), U1(k, c))
28.38/9.20	   A^2 -> H(f(e), U1(c, e))
28.38/9.20	   A^2 -> H(f(e), U1(c, k))
28.38/9.20	   A^2 -> H(f(e), U1(k, k))
28.38/9.20	   A^2 -> H(f(e), U1(k, d))
28.38/9.20	   A^2 -> H(f(e), U1(d, k))
28.38/9.20	   A^2 -> H(U1(k, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(k, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(k, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(k, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(k, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(k, k), f(e))
28.38/9.20	   A^2 -> H(U1(k, k), f(k))
28.38/9.20	   A^2 -> H(U1(k, k), U1(d, d))
28.38/9.20	   A^2 -> H(f(k), U1(e, b))
28.38/9.20	   A^2 -> H(f(k), U1(k, b))
28.38/9.20	   A^2 -> H(f(k), U1(c, d))
28.38/9.20	   A^2 -> H(f(k), U1(d, c))
28.38/9.20	   A^2 -> H(f(k), U1(b, e))
28.38/9.20	   A^2 -> H(f(k), U1(b, k))
28.38/9.20	   A^2 -> H(f(k), U1(e, c))
28.38/9.20	   A^2 -> H(f(k), U1(k, c))
28.38/9.20	   A^2 -> H(f(k), U1(c, e))
28.38/9.20	   A^2 -> H(f(k), U1(c, k))
28.38/9.20	   A^2 -> H(f(k), U1(e, e))
28.38/9.20	   A^2 -> H(f(k), U1(k, d))
28.38/9.20	   A^2 -> H(f(k), U1(d, k))
28.38/9.20	   A^2 -> H(f(c), b)
28.38/9.20	   A^2 -> H(f(c), U1(e, d))
28.38/9.20	   A^2 -> H(f(c), U1(d, e))
28.38/9.20	   A^2 -> H(f(k), U1(k, k))
28.38/9.20	   A^2 -> H(U1(k, k), U1(b, b))
28.38/9.20	   A^2 -> H(U1(k, k), f(c))
28.38/9.20	   A^2 -> H(U1(k, k), f(d))
28.38/9.20	   A^2 -> H(U1(k, d), U1(c, b))
28.38/9.20	   A^2 -> H(U1(k, d), U1(d, b))
28.38/9.20	   A^2 -> H(U1(k, d), U1(b, c))
28.38/9.20	   A^2 -> H(U1(k, d), U1(b, d))
28.38/9.20	   A^2 -> H(U1(k, d), U1(c, c))
28.38/9.20	   A^2 -> H(U1(k, d), f(e))
28.38/9.20	   A^2 -> H(U1(k, d), f(k))
28.38/9.20	   A^2 -> H(U1(k, d), U1(d, d))
28.38/9.20	   A^2 -> H(U1(d, k), U1(c, b))
28.38/9.20	   A^2 -> H(U1(d, k), U1(d, b))
28.38/9.20	   A^2 -> H(U1(d, k), U1(b, c))
28.38/9.20	   A^2 -> H(U1(d, k), U1(b, d))
28.38/9.20	   A^2 -> H(U1(d, k), U1(c, c))
28.38/9.20	   A^2 -> H(U1(d, k), f(e))
28.38/9.20	   A^2 -> H(U1(d, k), f(k))
28.38/9.20	   A^2 -> H(U1(d, k), U1(d, d))
28.38/9.20	   A^2 -> H(U1(d, d), U1(e, b))
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, b))
28.38/9.20	   A^2 -> H(U1(d, d), U1(c, d))
28.38/9.20	   A^2 -> H(U1(d, d), U1(d, c))
28.38/9.20	   A^2 -> H(U1(d, d), U1(b, e))
28.38/9.20	   A^2 -> H(U1(d, d), U1(b, k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(e, c))
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, c))
28.38/9.20	   A^2 -> H(U1(d, d), U1(c, e))
28.38/9.20	   A^2 -> H(U1(d, d), U1(c, k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(e, e))
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, k))
28.38/9.20	   A^2 -> H(f(d), b)
28.38/9.20	   A^2 -> H(f(d), U1(e, d))
28.38/9.20	   A^2 -> H(f(d), U1(d, e))
28.38/9.20	   A^2 -> H(f(d), c)
28.38/9.20	   A^2 -> H(f(d), U1(e, k))
28.38/9.20	   A^2 -> H(f(d), U1(k, e))
28.38/9.20	   A^2 -> H(f(d), e)
28.38/9.20	   A^2 -> H(f(a), d)
28.38/9.20	   A^2 -> H(U1(c, c), U1(e, c))
28.38/9.20	   A^2 -> H(f(c), c)
28.38/9.20	   A^2 -> H(f(c), U1(e, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(k, c))
28.38/9.20	   A^2 -> H(f(c), U1(k, e))
28.38/9.20	   A^2 -> H(f(c), U1(k, k))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, e))
28.38/9.20	   A^2 -> H(U1(c, c), U1(c, k))
28.38/9.20	   A^2 -> H(f(a), k)
28.38/9.20	   A^2 -> H(f(e), U1(e, e))
28.38/9.20	   A^2 -> H(f(c), e)
28.38/9.20	   A^2 -> H(U1(d, d), U1(k, d))
28.38/9.20	   A^2 -> H(f(d), U1(k, k))
28.38/9.20	   A^2 -> H(U1(d, d), U1(d, k))
28.38/9.20	   A^2 -> H(d, U1(b, b))
28.38/9.20	   A^2 -> H(d, f(c))
28.38/9.20	   A^2 -> H(d, f(d))
28.38/9.20	   A^2 -> H(a, U1(c, b))
28.38/9.20	   A^2 -> H(a, U1(d, b))
28.38/9.20	   A^2 -> H(a, U1(b, c))
28.38/9.20	   A^2 -> H(a, U1(b, d))
28.38/9.20	   A^2 -> H(a, U1(c, c))
28.38/9.20	   A^2 -> H(a, f(e))
28.38/9.20	   A^2 -> H(a, f(k))
28.38/9.20	   A^2 -> H(a, U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, d), U1(c, b))
28.38/9.20	   A^2 -> H(U1(e, d), U1(d, b))
28.38/9.20	   A^2 -> H(U1(e, d), U1(b, c))
28.38/9.20	   A^2 -> H(U1(e, d), U1(b, d))
28.38/9.20	   A^2 -> H(U1(e, d), U1(c, c))
28.38/9.20	   A^2 -> H(U1(e, d), f(e))
28.38/9.20	   A^2 -> H(U1(e, d), f(k))
28.38/9.20	   A^2 -> H(U1(e, d), U1(d, d))
28.38/9.20	   A^2 -> H(U1(e, a), U1(e, b))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, b))
28.38/9.20	   A^2 -> H(U1(e, a), U1(c, d))
28.38/9.20	   A^2 -> H(U1(e, a), U1(d, c))
28.38/9.20	   A^2 -> H(U1(e, a), U1(b, e))
28.38/9.20	   A^2 -> H(U1(e, a), U1(b, k))
28.38/9.20	   A^2 -> H(U1(e, a), U1(e, c))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, c))
28.38/9.20	   A^2 -> H(U1(e, a), U1(c, e))
28.38/9.20	   A^2 -> H(U1(e, a), U1(c, k))
28.38/9.20	   A^2 -> H(U1(e, a), U1(e, e))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, k))
28.38/9.20	   A^2 -> H(U1(e, a), U1(k, d))
28.38/9.21	   A^2 -> H(U1(e, a), U1(d, k))
28.38/9.21	   A^2 -> H(U1(k, a), U1(e, b))
28.38/9.21	   A^2 -> H(U1(k, a), U1(k, b))
28.38/9.21	   A^2 -> H(U1(k, a), U1(c, d))
28.38/9.21	   A^2 -> H(U1(k, a), U1(d, c))
28.38/9.21	   A^2 -> H(U1(k, a), U1(b, e))
28.38/9.21	   A^2 -> H(U1(k, a), U1(b, k))
28.38/9.21	   A^2 -> H(U1(k, a), U1(e, c))
28.38/9.21	   A^2 -> H(U1(k, a), U1(k, c))
28.38/9.21	   A^2 -> H(U1(k, a), U1(c, e))
28.38/9.21	   A^2 -> H(U1(k, a), U1(c, k))
28.38/9.21	   A^2 -> H(U1(k, a), U1(e, e))
28.38/9.21	   A^2 -> H(U1(k, a), U1(k, k))
28.38/9.21	   A^2 -> H(U1(k, a), U1(k, d))
28.38/9.21	   A^2 -> H(U1(k, a), U1(d, k))
28.38/9.21	   A^2 -> H(U1(c, d), U1(e, b))
28.38/9.21	   A^2 -> H(U1(c, d), U1(k, b))
28.38/9.21	   A^2 -> H(U1(c, d), U1(c, d))
28.38/9.21	   A^2 -> H(U1(c, d), U1(d, c))
28.38/9.21	   A^2 -> H(U1(c, d), U1(b, e))
28.38/9.21	   A^2 -> H(U1(c, d), U1(b, k))
28.38/9.21	   A^2 -> H(U1(c, d), U1(e, c))
28.38/9.21	   A^2 -> H(U1(c, d), U1(k, c))
28.38/9.21	   A^2 -> H(U1(c, d), U1(c, e))
28.38/9.21	   A^2 -> H(U1(c, d), U1(c, k))
28.38/9.21	   A^2 -> H(U1(c, d), U1(e, e))
28.38/9.21	   A^2 -> H(U1(c, d), U1(k, k))
28.38/9.21	   A^2 -> H(U1(c, d), U1(k, d))
28.38/9.21	   A^2 -> H(U1(c, d), U1(d, k))
28.38/9.21	   A^2 -> H(U1(c, a), b)
28.38/9.21	   A^2 -> H(U1(c, a), U1(e, d))
28.38/9.21	   A^2 -> H(U1(c, a), U1(d, e))
28.38/9.21	   A^2 -> H(U1(c, a), c)
28.38/9.21	   A^2 -> H(U1(c, a), U1(e, k))
28.38/9.21	   A^2 -> H(U1(c, a), U1(k, e))
28.38/9.21	   A^2 -> H(U1(c, a), e)
28.38/9.21	   A^2 -> H(U1(c, a), U1(k, k))
28.38/9.21	   A^2 -> H(U1(d, e), U1(c, b))
28.38/9.21	   A^2 -> H(U1(d, e), U1(d, b))
28.38/9.21	   A^2 -> H(U1(d, e), U1(b, c))
28.38/9.21	   A^2 -> H(U1(d, e), U1(b, d))
28.38/9.21	   A^2 -> H(U1(d, e), U1(c, c))
28.38/9.21	   A^2 -> H(U1(d, e), f(e))
28.38/9.21	   A^2 -> H(U1(d, e), f(k))
28.38/9.21	   A^2 -> H(U1(d, e), U1(d, d))
28.38/9.21	   A^2 -> H(U1(d, c), U1(e, b))
28.38/9.21	   A^2 -> H(U1(d, c), U1(k, b))
28.38/9.21	   A^2 -> H(U1(d, c), U1(c, d))
28.38/9.21	   A^2 -> H(U1(d, c), U1(d, c))
28.38/9.21	   A^2 -> H(U1(d, c), U1(b, e))
28.38/9.21	   A^2 -> H(U1(d, c), U1(b, k))
28.38/9.21	   A^2 -> H(U1(d, c), U1(e, c))
28.38/9.21	   A^2 -> H(U1(d, c), U1(k, c))
28.38/9.21	   A^2 -> H(U1(d, c), U1(c, e))
28.38/9.21	   A^2 -> H(U1(d, c), U1(c, k))
28.38/9.21	   A^2 -> H(U1(d, c), U1(e, e))
28.38/9.21	   A^2 -> H(U1(d, c), U1(k, k))
28.38/9.21	   A^2 -> H(U1(d, c), U1(k, d))
28.38/9.21	   A^2 -> H(U1(d, c), U1(d, k))
28.38/9.21	   A^2 -> H(U1(d, a), b)
28.38/9.21	   A^2 -> H(U1(d, a), U1(e, d))
28.38/9.21	   A^2 -> H(U1(d, a), U1(d, e))
28.38/9.21	   A^2 -> H(U1(d, a), c)
28.38/9.21	   A^2 -> H(U1(d, a), U1(e, k))
28.38/9.21	   A^2 -> H(U1(d, a), U1(k, e))
28.38/9.21	   A^2 -> H(U1(d, a), e)
28.38/9.21	   A^2 -> H(U1(d, a), U1(k, k))
28.38/9.21	   A^2 -> H(U1(a, e), U1(e, b))
28.38/9.21	   A^2 -> H(U1(a, e), U1(k, b))
28.38/9.21	   A^2 -> H(U1(a, e), U1(c, d))
28.38/9.21	   A^2 -> H(U1(a, e), U1(d, c))
28.38/9.21	   A^2 -> H(U1(a, e), U1(b, e))
28.38/9.21	   A^2 -> H(U1(a, e), U1(b, k))
28.38/9.21	   A^2 -> H(U1(a, e), U1(e, c))
28.38/9.21	   A^2 -> H(U1(a, e), U1(k, c))
28.38/9.21	   A^2 -> H(U1(a, e), U1(c, e))
28.38/9.21	   A^2 -> H(U1(a, e), U1(c, k))
28.38/9.21	   A^2 -> H(U1(a, e), U1(e, e))
28.38/9.21	   A^2 -> H(U1(a, e), U1(k, k))
28.38/9.21	   A^2 -> H(U1(a, e), U1(k, d))
28.38/9.21	   A^2 -> H(U1(a, e), U1(d, k))
28.38/9.21	   A^2 -> H(U1(a, k), U1(e, b))
28.38/9.21	   A^2 -> H(U1(a, k), U1(k, b))
28.38/9.21	   A^2 -> H(U1(a, k), U1(c, d))
28.38/9.21	   A^2 -> H(U1(a, k), U1(d, c))
28.38/9.21	   A^2 -> H(U1(a, k), U1(b, e))
28.38/9.21	   A^2 -> H(U1(a, k), U1(b, k))
28.38/9.21	   A^2 -> H(U1(a, k), U1(e, c))
28.38/9.21	   A^2 -> H(U1(a, k), U1(k, c))
28.38/9.21	   A^2 -> H(U1(a, k), U1(c, e))
28.38/9.21	   A^2 -> H(U1(a, k), U1(c, k))
28.38/9.21	   A^2 -> H(U1(a, k), U1(e, e))
28.38/9.21	   A^2 -> H(U1(a, k), U1(k, k))
28.38/9.21	   A^2 -> H(U1(a, k), U1(k, d))
28.38/9.21	   A^2 -> H(U1(a, k), U1(d, k))
28.38/9.21	   A^2 -> H(U1(a, c), b)
28.38/9.21	   A^2 -> H(U1(a, c), U1(e, d))
28.38/9.21	   A^2 -> H(U1(a, c), U1(d, e))
28.38/9.21	   A^2 -> H(U1(a, c), c)
28.38/9.21	   A^2 -> H(U1(a, c), U1(e, k))
28.38/9.21	   A^2 -> H(U1(a, c), U1(k, e))
28.38/9.21	   A^2 -> H(U1(a, c), e)
28.38/9.21	   A^2 -> H(U1(a, c), U1(k, k))
28.38/9.21	   A^2 -> H(U1(a, d), b)
28.38/9.21	   A^2 -> H(U1(a, d), U1(e, d))
28.38/9.21	   A^2 -> H(U1(a, d), U1(d, e))
28.38/9.21	   A^2 -> H(U1(a, d), c)
28.38/9.21	   A^2 -> H(U1(a, d), U1(e, k))
28.38/9.21	   A^2 -> H(U1(a, d), U1(k, e))
28.38/9.21	   A^2 -> H(U1(a, d), e)
28.38/9.21	   A^2 -> H(U1(a, d), U1(k, k))
28.38/9.21	   A^2 -> H(U1(a, a), d)
28.38/9.21	   A^2 -> H(U1(a, a), k)
28.38/9.21	   A^2 -> H(k, U1(b, b))
28.38/9.21	   A^2 -> H(k, f(c))
28.38/9.21	   A^2 -> H(k, f(d))
28.38/9.21	   A^2 -> H(c, U1(c, b))
28.38/9.21	   A^2 -> H(c, U1(d, b))
28.38/9.21	   A^2 -> H(c, U1(b, c))
28.38/9.21	   A^2 -> H(c, U1(b, d))
28.38/9.21	   A^2 -> H(c, U1(c, c))
28.38/9.21	   A^2 -> H(c, f(e))
28.38/9.21	   A^2 -> H(c, f(k))
28.38/9.21	   A^2 -> H(c, U1(d, d))
28.38/9.21	   A^2 -> H(U1(e, k), U1(c, b))
28.38/9.21	   A^2 -> H(U1(e, k), U1(d, b))
28.38/9.21	   A^2 -> H(U1(e, k), U1(b, c))
28.38/9.21	   A^2 -> H(U1(e, k), U1(b, d))
28.38/9.21	   A^2 -> H(U1(e, k), U1(c, c))
28.38/9.21	   A^2 -> H(U1(e, k), f(e))
28.38/9.21	   A^2 -> H(U1(e, k), f(k))
28.38/9.21	   A^2 -> H(U1(e, k), U1(d, d))
28.38/9.21	   A^2 -> H(U1(e, c), U1(e, b))
28.38/9.21	   A^2 -> H(U1(e, c), U1(k, b))
28.38/9.21	   A^2 -> H(U1(e, c), U1(c, d))
28.38/9.21	   A^2 -> H(U1(e, c), U1(d, c))
28.38/9.21	   A^2 -> H(U1(e, c), U1(b, e))
28.38/9.21	   A^2 -> H(U1(e, c), U1(b, k))
28.38/9.21	   A^2 -> H(U1(e, c), U1(e, c))
28.38/9.21	   A^2 -> H(U1(e, c), U1(k, c))
28.38/9.21	   A^2 -> H(U1(e, c), U1(c, e))
28.38/9.21	   A^2 -> H(U1(e, c), U1(c, k))
28.38/9.21	   A^2 -> H(U1(e, c), U1(e, e))
28.38/9.21	   A^2 -> H(U1(e, c), U1(k, k))
28.38/9.21	   A^2 -> H(U1(e, c), U1(k, d))
28.38/9.21	   A^2 -> H(U1(e, c), U1(d, k))
28.38/9.21	   A^2 -> H(U1(k, e), U1(c, b))
28.38/9.21	   A^2 -> H(U1(k, e), U1(d, b))
28.38/9.21	   A^2 -> H(U1(k, e), U1(b, c))
28.38/9.21	   A^2 -> H(U1(k, e), U1(b, d))
28.38/9.21	
28.38/9.21	The TRS R consists of the following rules:
28.38/9.21	
28.38/9.21	   f(x) -> U1(x, x)
28.38/9.21	   U1(e, x) -> x
28.38/9.21	   a -> c
28.38/9.21	   a -> d
28.38/9.21	   b -> c
28.38/9.21	   b -> d
28.38/9.21	   d -> k
28.38/9.21	   c -> e
28.38/9.21	   c -> k
28.38/9.21	
28.38/9.21	Q is empty.
28.38/9.21	We have to consider all minimal (P,Q,R)-chains.
28.38/9.21	----------------------------------------
28.38/9.21	
28.38/9.21	(817) TransformationProof (EQUIVALENT)
28.38/9.21	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), f(c)) at position [] we obtained the following new rules [LPAR04]:
28.38/9.21	
28.38/9.21	   (A^2 -> H(U1(k, e), U1(c, c)),A^2 -> H(U1(k, e), U1(c, c)))
28.38/9.21	   (A^2 -> H(U1(k, e), f(e)),A^2 -> H(U1(k, e), f(e)))
28.38/9.21	   (A^2 -> H(U1(k, e), f(k)),A^2 -> H(U1(k, e), f(k)))
28.38/9.21	
28.38/9.21	
28.38/9.21	----------------------------------------
28.38/9.21	
28.38/9.21	(818)
28.38/9.21	Obligation:
28.38/9.21	Q DP problem:
28.38/9.21	The TRS P consists of the following rules:
28.38/9.21	
28.38/9.21	   H(x, x) -> G(x, x, f(k))
28.38/9.21	   G(d, x, x) -> A^2
28.38/9.21	   A^2 -> H(f(c), f(c))
28.38/9.21	   A^2 -> H(f(d), f(d))
28.38/9.21	   A^2 -> H(U1(c, c), U1(c, c))
28.38/9.21	   A^2 -> H(f(e), f(e))
28.38/9.21	   A^2 -> H(f(k), f(k))
28.38/9.21	   A^2 -> H(U1(d, d), U1(d, d))
28.38/9.21	   A^2 -> H(U1(k, e), f(d))
28.38/9.21	   A^2 -> H(U1(k, c), U1(c, b))
28.38/9.21	   A^2 -> H(U1(k, c), U1(d, b))
28.38/9.21	   A^2 -> H(U1(k, c), U1(b, c))
28.38/9.21	   A^2 -> H(U1(k, c), U1(b, d))
28.38/9.21	   A^2 -> H(U1(k, c), U1(c, c))
28.38/9.21	   A^2 -> H(U1(k, c), f(e))
28.38/9.21	   A^2 -> H(U1(k, c), f(k))
28.38/9.21	   A^2 -> H(U1(k, c), U1(d, d))
28.38/9.21	   A^2 -> H(U1(c, e), U1(c, b))
28.38/9.21	   A^2 -> H(U1(c, e), U1(d, b))
28.38/9.21	   A^2 -> H(U1(c, e), U1(b, c))
28.38/9.21	   A^2 -> H(U1(c, e), U1(b, d))
28.38/9.21	   A^2 -> H(U1(c, e), U1(c, c))
28.38/9.21	   A^2 -> H(U1(c, e), f(e))
28.38/9.21	   A^2 -> H(U1(c, e), f(k))
28.38/9.21	   A^2 -> H(U1(c, e), U1(d, d))
28.38/9.21	   A^2 -> H(U1(c, k), U1(c, b))
28.38/9.21	   A^2 -> H(U1(c, k), U1(d, b))
28.38/9.21	   A^2 -> H(U1(c, k), U1(b, c))
28.38/9.21	   A^2 -> H(U1(c, k), U1(b, d))
28.38/9.21	   A^2 -> H(U1(c, k), U1(c, c))
28.38/9.21	   A^2 -> H(U1(c, k), f(e))
28.38/9.21	   A^2 -> H(U1(c, k), f(k))
28.38/9.21	   A^2 -> H(U1(c, k), U1(d, d))
28.38/9.21	   A^2 -> H(U1(c, c), U1(e, b))
28.38/9.21	   A^2 -> H(U1(c, c), U1(k, b))
28.38/9.21	   A^2 -> H(U1(c, c), U1(c, d))
28.38/9.21	   A^2 -> H(U1(c, c), U1(d, c))
28.38/9.21	   A^2 -> H(U1(c, c), U1(b, e))
28.38/9.21	   A^2 -> H(U1(c, c), U1(b, k))
28.38/9.21	   A^2 -> H(U1(c, c), U1(e, e))
28.38/9.21	   A^2 -> H(U1(c, c), U1(k, k))
28.38/9.21	   A^2 -> H(U1(c, c), U1(k, d))
28.38/9.21	   A^2 -> H(U1(c, c), U1(d, k))
28.38/9.21	   A^2 -> H(e, U1(b, b))
28.38/9.21	   A^2 -> H(e, f(c))
28.38/9.21	   A^2 -> H(e, f(d))
28.38/9.21	   A^2 -> H(U1(e, e), U1(c, b))
28.38/9.21	   A^2 -> H(U1(e, e), U1(d, b))
28.38/9.21	   A^2 -> H(U1(e, e), U1(b, c))
28.38/9.21	   A^2 -> H(U1(e, e), U1(b, d))
28.38/9.21	   A^2 -> H(U1(e, e), U1(c, c))
28.38/9.21	   A^2 -> H(U1(e, e), f(e))
28.38/9.21	   A^2 -> H(U1(e, e), f(k))
28.38/9.21	   A^2 -> H(U1(e, e), U1(d, d))
28.38/9.21	   A^2 -> H(f(e), U1(e, b))
28.38/9.21	   A^2 -> H(f(e), U1(k, b))
28.38/9.21	   A^2 -> H(f(e), U1(c, d))
28.38/9.21	   A^2 -> H(f(e), U1(d, c))
28.38/9.21	   A^2 -> H(f(e), U1(b, e))
28.38/9.21	   A^2 -> H(f(e), U1(b, k))
28.38/9.21	   A^2 -> H(f(e), U1(e, c))
28.38/9.21	   A^2 -> H(f(e), U1(k, c))
28.38/9.21	   A^2 -> H(f(e), U1(c, e))
28.38/9.21	   A^2 -> H(f(e), U1(c, k))
28.38/9.21	   A^2 -> H(f(e), U1(k, k))
28.38/9.21	   A^2 -> H(f(e), U1(k, d))
28.38/9.21	   A^2 -> H(f(e), U1(d, k))
28.38/9.21	   A^2 -> H(U1(k, k), U1(c, b))
28.38/9.21	   A^2 -> H(U1(k, k), U1(d, b))
28.38/9.21	   A^2 -> H(U1(k, k), U1(b, c))
28.38/9.21	   A^2 -> H(U1(k, k), U1(b, d))
28.38/9.21	   A^2 -> H(U1(k, k), U1(c, c))
28.38/9.21	   A^2 -> H(U1(k, k), f(e))
28.38/9.21	   A^2 -> H(U1(k, k), f(k))
28.38/9.21	   A^2 -> H(U1(k, k), U1(d, d))
28.38/9.21	   A^2 -> H(f(k), U1(e, b))
28.38/9.21	   A^2 -> H(f(k), U1(k, b))
28.38/9.21	   A^2 -> H(f(k), U1(c, d))
28.38/9.21	   A^2 -> H(f(k), U1(d, c))
28.38/9.21	   A^2 -> H(f(k), U1(b, e))
28.38/9.21	   A^2 -> H(f(k), U1(b, k))
28.38/9.21	   A^2 -> H(f(k), U1(e, c))
28.38/9.21	   A^2 -> H(f(k), U1(k, c))
28.38/9.21	   A^2 -> H(f(k), U1(c, e))
28.38/9.21	   A^2 -> H(f(k), U1(c, k))
28.38/9.21	   A^2 -> H(f(k), U1(e, e))
28.38/9.21	   A^2 -> H(f(k), U1(k, d))
28.38/9.21	   A^2 -> H(f(k), U1(d, k))
28.38/9.21	   A^2 -> H(f(c), b)
28.38/9.21	   A^2 -> H(f(c), U1(e, d))
28.38/9.21	   A^2 -> H(f(c), U1(d, e))
28.38/9.21	   A^2 -> H(f(k), U1(k, k))
28.38/9.21	   A^2 -> H(U1(k, k), U1(b, b))
28.38/9.21	   A^2 -> H(U1(k, k), f(c))
28.38/9.21	   A^2 -> H(U1(k, k), f(d))
28.38/9.21	   A^2 -> H(U1(k, d), U1(c, b))
28.38/9.21	   A^2 -> H(U1(k, d), U1(d, b))
28.38/9.21	   A^2 -> H(U1(k, d), U1(b, c))
28.38/9.21	   A^2 -> H(U1(k, d), U1(b, d))
28.38/9.21	   A^2 -> H(U1(k, d), U1(c, c))
28.38/9.21	   A^2 -> H(U1(k, d), f(e))
28.38/9.21	   A^2 -> H(U1(k, d), f(k))
28.38/9.21	   A^2 -> H(U1(k, d), U1(d, d))
28.38/9.21	   A^2 -> H(U1(d, k), U1(c, b))
28.38/9.21	   A^2 -> H(U1(d, k), U1(d, b))
28.38/9.21	   A^2 -> H(U1(d, k), U1(b, c))
28.38/9.21	   A^2 -> H(U1(d, k), U1(b, d))
28.38/9.21	   A^2 -> H(U1(d, k), U1(c, c))
28.38/9.21	   A^2 -> H(U1(d, k), f(e))
28.38/9.21	   A^2 -> H(U1(d, k), f(k))
28.38/9.21	   A^2 -> H(U1(d, k), U1(d, d))
28.38/9.21	   A^2 -> H(U1(d, d), U1(e, b))
28.38/9.21	   A^2 -> H(U1(d, d), U1(k, b))
28.38/9.21	   A^2 -> H(U1(d, d), U1(c, d))
28.38/9.21	   A^2 -> H(U1(d, d), U1(d, c))
28.38/9.21	   A^2 -> H(U1(d, d), U1(b, e))
28.38/9.21	   A^2 -> H(U1(d, d), U1(b, k))
28.38/9.21	   A^2 -> H(U1(d, d), U1(e, c))
28.38/9.21	   A^2 -> H(U1(d, d), U1(k, c))
28.38/9.21	   A^2 -> H(U1(d, d), U1(c, e))
28.38/9.21	   A^2 -> H(U1(d, d), U1(c, k))
28.38/9.21	   A^2 -> H(U1(d, d), U1(e, e))
28.38/9.21	   A^2 -> H(U1(d, d), U1(k, k))
28.38/9.21	   A^2 -> H(f(d), b)
28.38/9.21	   A^2 -> H(f(d), U1(e, d))
28.38/9.21	   A^2 -> H(f(d), U1(d, e))
28.38/9.21	   A^2 -> H(f(d), c)
28.38/9.21	   A^2 -> H(f(d), U1(e, k))
28.38/9.21	   A^2 -> H(f(d), U1(k, e))
28.38/9.21	   A^2 -> H(f(d), e)
28.38/9.21	   A^2 -> H(f(a), d)
28.38/9.21	   A^2 -> H(U1(c, c), U1(e, c))
28.38/9.21	   A^2 -> H(f(c), c)
28.38/9.21	   A^2 -> H(f(c), U1(e, k))
28.38/9.21	   A^2 -> H(U1(c, c), U1(k, c))
28.38/9.21	   A^2 -> H(f(c), U1(k, e))
28.38/9.21	   A^2 -> H(f(c), U1(k, k))
28.38/9.21	   A^2 -> H(U1(c, c), U1(c, e))
28.38/9.21	   A^2 -> H(U1(c, c), U1(c, k))
28.38/9.21	   A^2 -> H(f(a), k)
28.38/9.21	   A^2 -> H(f(e), U1(e, e))
28.38/9.21	   A^2 -> H(f(c), e)
28.38/9.21	   A^2 -> H(U1(d, d), U1(k, d))
28.38/9.21	   A^2 -> H(f(d), U1(k, k))
28.38/9.21	   A^2 -> H(U1(d, d), U1(d, k))
28.38/9.21	   A^2 -> H(d, U1(b, b))
28.38/9.21	   A^2 -> H(d, f(c))
28.38/9.21	   A^2 -> H(d, f(d))
28.38/9.21	   A^2 -> H(a, U1(c, b))
28.38/9.21	   A^2 -> H(a, U1(d, b))
28.38/9.21	   A^2 -> H(a, U1(b, c))
28.38/9.21	   A^2 -> H(a, U1(b, d))
28.38/9.21	   A^2 -> H(a, U1(c, c))
28.38/9.21	   A^2 -> H(a, f(e))
28.38/9.21	   A^2 -> H(a, f(k))
28.38/9.21	   A^2 -> H(a, U1(d, d))
28.38/9.21	   A^2 -> H(U1(e, d), U1(c, b))
28.38/9.21	   A^2 -> H(U1(e, d), U1(d, b))
28.38/9.21	   A^2 -> H(U1(e, d), U1(b, c))
28.38/9.21	   A^2 -> H(U1(e, d), U1(b, d))
28.38/9.21	   A^2 -> H(U1(e, d), U1(c, c))
28.38/9.21	   A^2 -> H(U1(e, d), f(e))
28.38/9.21	   A^2 -> H(U1(e, d), f(k))
28.38/9.21	   A^2 -> H(U1(e, d), U1(d, d))
28.38/9.21	   A^2 -> H(U1(e, a), U1(e, b))
28.38/9.21	   A^2 -> H(U1(e, a), U1(k, b))
28.38/9.21	   A^2 -> H(U1(e, a), U1(c, d))
28.38/9.21	   A^2 -> H(U1(e, a), U1(d, c))
28.38/9.21	   A^2 -> H(U1(e, a), U1(b, e))
28.38/9.21	   A^2 -> H(U1(e, a), U1(b, k))
28.38/9.21	   A^2 -> H(U1(e, a), U1(e, c))
28.38/9.21	   A^2 -> H(U1(e, a), U1(k, c))
28.38/9.21	   A^2 -> H(U1(e, a), U1(c, e))
28.38/9.21	   A^2 -> H(U1(e, a), U1(c, k))
28.38/9.21	   A^2 -> H(U1(e, a), U1(e, e))
28.38/9.21	   A^2 -> H(U1(e, a), U1(k, k))
28.38/9.21	   A^2 -> H(U1(e, a), U1(k, d))
28.38/9.21	   A^2 -> H(U1(e, a), U1(d, k))
28.38/9.21	   A^2 -> H(U1(k, a), U1(e, b))
28.38/9.21	   A^2 -> H(U1(k, a), U1(k, b))
28.38/9.21	   A^2 -> H(U1(k, a), U1(c, d))
28.38/9.21	   A^2 -> H(U1(k, a), U1(d, c))
28.38/9.21	   A^2 -> H(U1(k, a), U1(b, e))
28.38/9.21	   A^2 -> H(U1(k, a), U1(b, k))
28.38/9.21	   A^2 -> H(U1(k, a), U1(e, c))
28.38/9.21	   A^2 -> H(U1(k, a), U1(k, c))
28.38/9.21	   A^2 -> H(U1(k, a), U1(c, e))
28.38/9.21	   A^2 -> H(U1(k, a), U1(c, k))
28.38/9.21	   A^2 -> H(U1(k, a), U1(e, e))
28.38/9.21	   A^2 -> H(U1(k, a), U1(k, k))
28.38/9.21	   A^2 -> H(U1(k, a), U1(k, d))
28.38/9.21	   A^2 -> H(U1(k, a), U1(d, k))
28.38/9.21	   A^2 -> H(U1(c, d), U1(e, b))
28.38/9.21	   A^2 -> H(U1(c, d), U1(k, b))
28.38/9.21	   A^2 -> H(U1(c, d), U1(c, d))
28.38/9.21	   A^2 -> H(U1(c, d), U1(d, c))
28.38/9.21	   A^2 -> H(U1(c, d), U1(b, e))
28.38/9.21	   A^2 -> H(U1(c, d), U1(b, k))
28.38/9.21	   A^2 -> H(U1(c, d), U1(e, c))
28.38/9.21	   A^2 -> H(U1(c, d), U1(k, c))
28.38/9.21	   A^2 -> H(U1(c, d), U1(c, e))
28.38/9.21	   A^2 -> H(U1(c, d), U1(c, k))
28.38/9.21	   A^2 -> H(U1(c, d), U1(e, e))
28.38/9.21	   A^2 -> H(U1(c, d), U1(k, k))
28.38/9.21	   A^2 -> H(U1(c, d), U1(k, d))
28.38/9.21	   A^2 -> H(U1(c, d), U1(d, k))
28.38/9.21	   A^2 -> H(U1(c, a), b)
28.38/9.21	   A^2 -> H(U1(c, a), U1(e, d))
28.38/9.21	   A^2 -> H(U1(c, a), U1(d, e))
28.38/9.21	   A^2 -> H(U1(c, a), c)
28.38/9.21	   A^2 -> H(U1(c, a), U1(e, k))
28.38/9.21	   A^2 -> H(U1(c, a), U1(k, e))
28.38/9.21	   A^2 -> H(U1(c, a), e)
28.38/9.21	   A^2 -> H(U1(c, a), U1(k, k))
28.38/9.21	   A^2 -> H(U1(d, e), U1(c, b))
28.38/9.21	   A^2 -> H(U1(d, e), U1(d, b))
28.38/9.21	   A^2 -> H(U1(d, e), U1(b, c))
28.38/9.21	   A^2 -> H(U1(d, e), U1(b, d))
28.38/9.21	   A^2 -> H(U1(d, e), U1(c, c))
28.38/9.21	   A^2 -> H(U1(d, e), f(e))
28.38/9.21	   A^2 -> H(U1(d, e), f(k))
28.38/9.21	   A^2 -> H(U1(d, e), U1(d, d))
28.38/9.21	   A^2 -> H(U1(d, c), U1(e, b))
28.38/9.21	   A^2 -> H(U1(d, c), U1(k, b))
28.38/9.21	   A^2 -> H(U1(d, c), U1(c, d))
28.38/9.21	   A^2 -> H(U1(d, c), U1(d, c))
28.38/9.21	   A^2 -> H(U1(d, c), U1(b, e))
28.38/9.21	   A^2 -> H(U1(d, c), U1(b, k))
28.38/9.21	   A^2 -> H(U1(d, c), U1(e, c))
28.38/9.21	   A^2 -> H(U1(d, c), U1(k, c))
28.38/9.21	   A^2 -> H(U1(d, c), U1(c, e))
28.38/9.21	   A^2 -> H(U1(d, c), U1(c, k))
28.38/9.21	   A^2 -> H(U1(d, c), U1(e, e))
28.38/9.21	   A^2 -> H(U1(d, c), U1(k, k))
28.38/9.21	   A^2 -> H(U1(d, c), U1(k, d))
28.38/9.21	   A^2 -> H(U1(d, c), U1(d, k))
28.38/9.21	   A^2 -> H(U1(d, a), b)
28.38/9.21	   A^2 -> H(U1(d, a), U1(e, d))
28.38/9.21	   A^2 -> H(U1(d, a), U1(d, e))
28.38/9.21	   A^2 -> H(U1(d, a), c)
28.38/9.21	   A^2 -> H(U1(d, a), U1(e, k))
28.38/9.21	   A^2 -> H(U1(d, a), U1(k, e))
28.38/9.21	   A^2 -> H(U1(d, a), e)
28.38/9.21	   A^2 -> H(U1(d, a), U1(k, k))
28.38/9.21	   A^2 -> H(U1(a, e), U1(e, b))
28.38/9.21	   A^2 -> H(U1(a, e), U1(k, b))
28.38/9.21	   A^2 -> H(U1(a, e), U1(c, d))
28.38/9.21	   A^2 -> H(U1(a, e), U1(d, c))
28.38/9.21	   A^2 -> H(U1(a, e), U1(b, e))
28.38/9.21	   A^2 -> H(U1(a, e), U1(b, k))
28.38/9.21	   A^2 -> H(U1(a, e), U1(e, c))
28.38/9.21	   A^2 -> H(U1(a, e), U1(k, c))
28.38/9.21	   A^2 -> H(U1(a, e), U1(c, e))
28.38/9.21	   A^2 -> H(U1(a, e), U1(c, k))
28.38/9.21	   A^2 -> H(U1(a, e), U1(e, e))
28.38/9.21	   A^2 -> H(U1(a, e), U1(k, k))
28.38/9.21	   A^2 -> H(U1(a, e), U1(k, d))
28.38/9.21	   A^2 -> H(U1(a, e), U1(d, k))
28.38/9.21	   A^2 -> H(U1(a, k), U1(e, b))
28.38/9.21	   A^2 -> H(U1(a, k), U1(k, b))
28.38/9.21	   A^2 -> H(U1(a, k), U1(c, d))
28.38/9.21	   A^2 -> H(U1(a, k), U1(d, c))
28.38/9.21	   A^2 -> H(U1(a, k), U1(b, e))
28.38/9.21	   A^2 -> H(U1(a, k), U1(b, k))
28.38/9.21	   A^2 -> H(U1(a, k), U1(e, c))
28.38/9.21	   A^2 -> H(U1(a, k), U1(k, c))
28.38/9.21	   A^2 -> H(U1(a, k), U1(c, e))
28.38/9.21	   A^2 -> H(U1(a, k), U1(c, k))
28.38/9.21	   A^2 -> H(U1(a, k), U1(e, e))
28.38/9.21	   A^2 -> H(U1(a, k), U1(k, k))
28.38/9.21	   A^2 -> H(U1(a, k), U1(k, d))
28.38/9.21	   A^2 -> H(U1(a, k), U1(d, k))
28.38/9.21	   A^2 -> H(U1(a, c), b)
28.38/9.21	   A^2 -> H(U1(a, c), U1(e, d))
28.38/9.21	   A^2 -> H(U1(a, c), U1(d, e))
28.38/9.21	   A^2 -> H(U1(a, c), c)
28.38/9.21	   A^2 -> H(U1(a, c), U1(e, k))
28.38/9.21	   A^2 -> H(U1(a, c), U1(k, e))
28.38/9.21	   A^2 -> H(U1(a, c), e)
28.38/9.21	   A^2 -> H(U1(a, c), U1(k, k))
28.38/9.21	   A^2 -> H(U1(a, d), b)
28.38/9.21	   A^2 -> H(U1(a, d), U1(e, d))
28.38/9.21	   A^2 -> H(U1(a, d), U1(d, e))
28.38/9.21	   A^2 -> H(U1(a, d), c)
28.38/9.21	   A^2 -> H(U1(a, d), U1(e, k))
28.38/9.21	   A^2 -> H(U1(a, d), U1(k, e))
28.38/9.21	   A^2 -> H(U1(a, d), e)
28.38/9.21	   A^2 -> H(U1(a, d), U1(k, k))
28.38/9.21	   A^2 -> H(U1(a, a), d)
28.38/9.21	   A^2 -> H(U1(a, a), k)
28.38/9.21	   A^2 -> H(k, U1(b, b))
28.38/9.21	   A^2 -> H(k, f(c))
28.38/9.21	   A^2 -> H(k, f(d))
28.38/9.21	   A^2 -> H(c, U1(c, b))
28.38/9.21	   A^2 -> H(c, U1(d, b))
28.38/9.21	   A^2 -> H(c, U1(b, c))
28.38/9.21	   A^2 -> H(c, U1(b, d))
28.38/9.21	   A^2 -> H(c, U1(c, c))
28.38/9.21	   A^2 -> H(c, f(e))
28.38/9.21	   A^2 -> H(c, f(k))
28.38/9.21	   A^2 -> H(c, U1(d, d))
28.38/9.21	   A^2 -> H(U1(e, k), U1(c, b))
28.38/9.21	   A^2 -> H(U1(e, k), U1(d, b))
28.38/9.21	   A^2 -> H(U1(e, k), U1(b, c))
28.38/9.21	   A^2 -> H(U1(e, k), U1(b, d))
28.38/9.21	   A^2 -> H(U1(e, k), U1(c, c))
28.38/9.21	   A^2 -> H(U1(e, k), f(e))
28.38/9.21	   A^2 -> H(U1(e, k), f(k))
28.38/9.21	   A^2 -> H(U1(e, k), U1(d, d))
28.38/9.21	   A^2 -> H(U1(e, c), U1(e, b))
28.38/9.21	   A^2 -> H(U1(e, c), U1(k, b))
28.38/9.21	   A^2 -> H(U1(e, c), U1(c, d))
28.38/9.21	   A^2 -> H(U1(e, c), U1(d, c))
28.38/9.21	   A^2 -> H(U1(e, c), U1(b, e))
28.38/9.21	   A^2 -> H(U1(e, c), U1(b, k))
28.38/9.21	   A^2 -> H(U1(e, c), U1(e, c))
28.38/9.21	   A^2 -> H(U1(e, c), U1(k, c))
28.38/9.21	   A^2 -> H(U1(e, c), U1(c, e))
28.38/9.21	   A^2 -> H(U1(e, c), U1(c, k))
28.38/9.21	   A^2 -> H(U1(e, c), U1(e, e))
28.38/9.21	   A^2 -> H(U1(e, c), U1(k, k))
28.38/9.21	   A^2 -> H(U1(e, c), U1(k, d))
28.38/9.21	   A^2 -> H(U1(e, c), U1(d, k))
28.38/9.21	   A^2 -> H(U1(k, e), U1(c, b))
28.38/9.21	   A^2 -> H(U1(k, e), U1(d, b))
28.38/9.21	   A^2 -> H(U1(k, e), U1(b, c))
28.38/9.21	   A^2 -> H(U1(k, e), U1(b, d))
28.38/9.21	   A^2 -> H(U1(k, e), U1(c, c))
28.38/9.21	   A^2 -> H(U1(k, e), f(e))
28.38/9.21	   A^2 -> H(U1(k, e), f(k))
28.38/9.21	
28.38/9.21	The TRS R consists of the following rules:
28.38/9.21	
28.38/9.21	   f(x) -> U1(x, x)
28.38/9.21	   U1(e, x) -> x
28.38/9.21	   a -> c
28.38/9.21	   a -> d
28.38/9.21	   b -> c
28.38/9.21	   b -> d
28.38/9.21	   d -> k
28.38/9.21	   c -> e
28.38/9.21	   c -> k
28.38/9.21	
28.38/9.21	Q is empty.
28.38/9.21	We have to consider all minimal (P,Q,R)-chains.
28.38/9.21	----------------------------------------
28.38/9.21	
28.38/9.21	(819) TransformationProof (EQUIVALENT)
28.38/9.21	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), f(d)) at position [] we obtained the following new rules [LPAR04]:
28.38/9.21	
28.38/9.21	   (A^2 -> H(U1(k, e), U1(d, d)),A^2 -> H(U1(k, e), U1(d, d)))
28.38/9.21	   (A^2 -> H(U1(k, e), f(k)),A^2 -> H(U1(k, e), f(k)))
28.38/9.21	
28.38/9.21	
28.38/9.21	----------------------------------------
28.38/9.21	
28.38/9.21	(820)
28.38/9.21	Obligation:
28.38/9.21	Q DP problem:
28.38/9.21	The TRS P consists of the following rules:
28.38/9.21	
28.38/9.21	   H(x, x) -> G(x, x, f(k))
28.38/9.21	   G(d, x, x) -> A^2
28.38/9.21	   A^2 -> H(f(c), f(c))
28.38/9.21	   A^2 -> H(f(d), f(d))
28.38/9.21	   A^2 -> H(U1(c, c), U1(c, c))
28.38/9.21	   A^2 -> H(f(e), f(e))
28.38/9.21	   A^2 -> H(f(k), f(k))
28.38/9.21	   A^2 -> H(U1(d, d), U1(d, d))
28.38/9.21	   A^2 -> H(U1(k, c), U1(c, b))
28.38/9.21	   A^2 -> H(U1(k, c), U1(d, b))
28.38/9.21	   A^2 -> H(U1(k, c), U1(b, c))
28.38/9.21	   A^2 -> H(U1(k, c), U1(b, d))
28.38/9.21	   A^2 -> H(U1(k, c), U1(c, c))
28.38/9.21	   A^2 -> H(U1(k, c), f(e))
28.38/9.21	   A^2 -> H(U1(k, c), f(k))
28.38/9.21	   A^2 -> H(U1(k, c), U1(d, d))
28.38/9.21	   A^2 -> H(U1(c, e), U1(c, b))
28.38/9.21	   A^2 -> H(U1(c, e), U1(d, b))
28.38/9.21	   A^2 -> H(U1(c, e), U1(b, c))
28.38/9.21	   A^2 -> H(U1(c, e), U1(b, d))
28.38/9.21	   A^2 -> H(U1(c, e), U1(c, c))
28.38/9.21	   A^2 -> H(U1(c, e), f(e))
28.38/9.21	   A^2 -> H(U1(c, e), f(k))
28.38/9.21	   A^2 -> H(U1(c, e), U1(d, d))
28.38/9.21	   A^2 -> H(U1(c, k), U1(c, b))
28.38/9.21	   A^2 -> H(U1(c, k), U1(d, b))
28.38/9.21	   A^2 -> H(U1(c, k), U1(b, c))
28.38/9.21	   A^2 -> H(U1(c, k), U1(b, d))
28.38/9.21	   A^2 -> H(U1(c, k), U1(c, c))
28.38/9.21	   A^2 -> H(U1(c, k), f(e))
28.38/9.21	   A^2 -> H(U1(c, k), f(k))
28.38/9.21	   A^2 -> H(U1(c, k), U1(d, d))
28.38/9.21	   A^2 -> H(U1(c, c), U1(e, b))
28.38/9.21	   A^2 -> H(U1(c, c), U1(k, b))
28.38/9.21	   A^2 -> H(U1(c, c), U1(c, d))
28.38/9.21	   A^2 -> H(U1(c, c), U1(d, c))
28.38/9.21	   A^2 -> H(U1(c, c), U1(b, e))
28.38/9.21	   A^2 -> H(U1(c, c), U1(b, k))
28.38/9.21	   A^2 -> H(U1(c, c), U1(e, e))
28.38/9.21	   A^2 -> H(U1(c, c), U1(k, k))
28.38/9.21	   A^2 -> H(U1(c, c), U1(k, d))
28.38/9.21	   A^2 -> H(U1(c, c), U1(d, k))
28.38/9.21	   A^2 -> H(e, U1(b, b))
28.38/9.21	   A^2 -> H(e, f(c))
28.38/9.21	   A^2 -> H(e, f(d))
28.38/9.21	   A^2 -> H(U1(e, e), U1(c, b))
28.38/9.21	   A^2 -> H(U1(e, e), U1(d, b))
28.38/9.21	   A^2 -> H(U1(e, e), U1(b, c))
28.38/9.21	   A^2 -> H(U1(e, e), U1(b, d))
28.38/9.21	   A^2 -> H(U1(e, e), U1(c, c))
28.38/9.21	   A^2 -> H(U1(e, e), f(e))
28.38/9.21	   A^2 -> H(U1(e, e), f(k))
28.38/9.21	   A^2 -> H(U1(e, e), U1(d, d))
28.38/9.21	   A^2 -> H(f(e), U1(e, b))
28.38/9.21	   A^2 -> H(f(e), U1(k, b))
28.38/9.21	   A^2 -> H(f(e), U1(c, d))
28.38/9.21	   A^2 -> H(f(e), U1(d, c))
28.38/9.21	   A^2 -> H(f(e), U1(b, e))
28.38/9.21	   A^2 -> H(f(e), U1(b, k))
28.38/9.21	   A^2 -> H(f(e), U1(e, c))
28.38/9.21	   A^2 -> H(f(e), U1(k, c))
28.38/9.21	   A^2 -> H(f(e), U1(c, e))
28.38/9.21	   A^2 -> H(f(e), U1(c, k))
28.38/9.21	   A^2 -> H(f(e), U1(k, k))
28.38/9.21	   A^2 -> H(f(e), U1(k, d))
28.38/9.21	   A^2 -> H(f(e), U1(d, k))
28.38/9.21	   A^2 -> H(U1(k, k), U1(c, b))
28.38/9.21	   A^2 -> H(U1(k, k), U1(d, b))
28.38/9.21	   A^2 -> H(U1(k, k), U1(b, c))
28.38/9.21	   A^2 -> H(U1(k, k), U1(b, d))
28.38/9.21	   A^2 -> H(U1(k, k), U1(c, c))
28.38/9.21	   A^2 -> H(U1(k, k), f(e))
28.38/9.21	   A^2 -> H(U1(k, k), f(k))
28.38/9.21	   A^2 -> H(U1(k, k), U1(d, d))
28.38/9.21	   A^2 -> H(f(k), U1(e, b))
28.38/9.21	   A^2 -> H(f(k), U1(k, b))
28.38/9.21	   A^2 -> H(f(k), U1(c, d))
28.38/9.21	   A^2 -> H(f(k), U1(d, c))
28.38/9.21	   A^2 -> H(f(k), U1(b, e))
28.38/9.21	   A^2 -> H(f(k), U1(b, k))
28.38/9.21	   A^2 -> H(f(k), U1(e, c))
28.38/9.21	   A^2 -> H(f(k), U1(k, c))
28.38/9.21	   A^2 -> H(f(k), U1(c, e))
28.38/9.21	   A^2 -> H(f(k), U1(c, k))
28.38/9.21	   A^2 -> H(f(k), U1(e, e))
28.38/9.21	   A^2 -> H(f(k), U1(k, d))
28.38/9.21	   A^2 -> H(f(k), U1(d, k))
28.38/9.21	   A^2 -> H(f(c), b)
28.38/9.21	   A^2 -> H(f(c), U1(e, d))
28.38/9.21	   A^2 -> H(f(c), U1(d, e))
28.38/9.21	   A^2 -> H(f(k), U1(k, k))
28.38/9.21	   A^2 -> H(U1(k, k), U1(b, b))
28.38/9.21	   A^2 -> H(U1(k, k), f(c))
28.38/9.21	   A^2 -> H(U1(k, k), f(d))
28.38/9.21	   A^2 -> H(U1(k, d), U1(c, b))
28.38/9.21	   A^2 -> H(U1(k, d), U1(d, b))
28.38/9.21	   A^2 -> H(U1(k, d), U1(b, c))
28.38/9.21	   A^2 -> H(U1(k, d), U1(b, d))
28.38/9.21	   A^2 -> H(U1(k, d), U1(c, c))
28.38/9.21	   A^2 -> H(U1(k, d), f(e))
28.38/9.21	   A^2 -> H(U1(k, d), f(k))
28.38/9.21	   A^2 -> H(U1(k, d), U1(d, d))
28.38/9.21	   A^2 -> H(U1(d, k), U1(c, b))
28.38/9.21	   A^2 -> H(U1(d, k), U1(d, b))
28.38/9.21	   A^2 -> H(U1(d, k), U1(b, c))
28.38/9.21	   A^2 -> H(U1(d, k), U1(b, d))
28.38/9.21	   A^2 -> H(U1(d, k), U1(c, c))
28.38/9.21	   A^2 -> H(U1(d, k), f(e))
28.38/9.21	   A^2 -> H(U1(d, k), f(k))
28.38/9.21	   A^2 -> H(U1(d, k), U1(d, d))
28.38/9.21	   A^2 -> H(U1(d, d), U1(e, b))
28.38/9.21	   A^2 -> H(U1(d, d), U1(k, b))
28.38/9.21	   A^2 -> H(U1(d, d), U1(c, d))
28.38/9.21	   A^2 -> H(U1(d, d), U1(d, c))
28.38/9.21	   A^2 -> H(U1(d, d), U1(b, e))
28.38/9.21	   A^2 -> H(U1(d, d), U1(b, k))
28.38/9.21	   A^2 -> H(U1(d, d), U1(e, c))
28.38/9.21	   A^2 -> H(U1(d, d), U1(k, c))
28.38/9.21	   A^2 -> H(U1(d, d), U1(c, e))
28.38/9.21	   A^2 -> H(U1(d, d), U1(c, k))
28.38/9.21	   A^2 -> H(U1(d, d), U1(e, e))
28.38/9.21	   A^2 -> H(U1(d, d), U1(k, k))
28.38/9.21	   A^2 -> H(f(d), b)
28.38/9.21	   A^2 -> H(f(d), U1(e, d))
28.38/9.21	   A^2 -> H(f(d), U1(d, e))
28.38/9.21	   A^2 -> H(f(d), c)
28.38/9.21	   A^2 -> H(f(d), U1(e, k))
28.38/9.21	   A^2 -> H(f(d), U1(k, e))
28.38/9.21	   A^2 -> H(f(d), e)
28.38/9.21	   A^2 -> H(f(a), d)
28.38/9.21	   A^2 -> H(U1(c, c), U1(e, c))
28.38/9.21	   A^2 -> H(f(c), c)
28.38/9.21	   A^2 -> H(f(c), U1(e, k))
28.38/9.21	   A^2 -> H(U1(c, c), U1(k, c))
28.38/9.21	   A^2 -> H(f(c), U1(k, e))
28.38/9.21	   A^2 -> H(f(c), U1(k, k))
28.38/9.21	   A^2 -> H(U1(c, c), U1(c, e))
28.38/9.21	   A^2 -> H(U1(c, c), U1(c, k))
28.38/9.21	   A^2 -> H(f(a), k)
28.38/9.21	   A^2 -> H(f(e), U1(e, e))
28.38/9.21	   A^2 -> H(f(c), e)
28.38/9.21	   A^2 -> H(U1(d, d), U1(k, d))
28.38/9.21	   A^2 -> H(f(d), U1(k, k))
28.38/9.21	   A^2 -> H(U1(d, d), U1(d, k))
28.38/9.21	   A^2 -> H(d, U1(b, b))
28.38/9.21	   A^2 -> H(d, f(c))
28.38/9.21	   A^2 -> H(d, f(d))
28.38/9.21	   A^2 -> H(a, U1(c, b))
28.38/9.21	   A^2 -> H(a, U1(d, b))
28.38/9.21	   A^2 -> H(a, U1(b, c))
28.38/9.21	   A^2 -> H(a, U1(b, d))
28.38/9.21	   A^2 -> H(a, U1(c, c))
28.38/9.21	   A^2 -> H(a, f(e))
28.38/9.21	   A^2 -> H(a, f(k))
28.38/9.21	   A^2 -> H(a, U1(d, d))
28.38/9.21	   A^2 -> H(U1(e, d), U1(c, b))
28.38/9.21	   A^2 -> H(U1(e, d), U1(d, b))
28.38/9.21	   A^2 -> H(U1(e, d), U1(b, c))
28.38/9.21	   A^2 -> H(U1(e, d), U1(b, d))
28.38/9.21	   A^2 -> H(U1(e, d), U1(c, c))
28.38/9.21	   A^2 -> H(U1(e, d), f(e))
28.38/9.21	   A^2 -> H(U1(e, d), f(k))
28.38/9.21	   A^2 -> H(U1(e, d), U1(d, d))
28.38/9.21	   A^2 -> H(U1(e, a), U1(e, b))
28.38/9.21	   A^2 -> H(U1(e, a), U1(k, b))
28.38/9.21	   A^2 -> H(U1(e, a), U1(c, d))
28.38/9.21	   A^2 -> H(U1(e, a), U1(d, c))
28.38/9.21	   A^2 -> H(U1(e, a), U1(b, e))
28.38/9.21	   A^2 -> H(U1(e, a), U1(b, k))
28.38/9.21	   A^2 -> H(U1(e, a), U1(e, c))
28.38/9.21	   A^2 -> H(U1(e, a), U1(k, c))
28.38/9.21	   A^2 -> H(U1(e, a), U1(c, e))
28.38/9.21	   A^2 -> H(U1(e, a), U1(c, k))
28.38/9.21	   A^2 -> H(U1(e, a), U1(e, e))
28.38/9.21	   A^2 -> H(U1(e, a), U1(k, k))
28.38/9.21	   A^2 -> H(U1(e, a), U1(k, d))
28.38/9.21	   A^2 -> H(U1(e, a), U1(d, k))
28.38/9.21	   A^2 -> H(U1(k, a), U1(e, b))
28.38/9.21	   A^2 -> H(U1(k, a), U1(k, b))
28.38/9.21	   A^2 -> H(U1(k, a), U1(c, d))
28.38/9.21	   A^2 -> H(U1(k, a), U1(d, c))
28.38/9.21	   A^2 -> H(U1(k, a), U1(b, e))
28.38/9.21	   A^2 -> H(U1(k, a), U1(b, k))
28.38/9.21	   A^2 -> H(U1(k, a), U1(e, c))
28.38/9.21	   A^2 -> H(U1(k, a), U1(k, c))
28.38/9.21	   A^2 -> H(U1(k, a), U1(c, e))
28.38/9.21	   A^2 -> H(U1(k, a), U1(c, k))
28.38/9.21	   A^2 -> H(U1(k, a), U1(e, e))
28.38/9.21	   A^2 -> H(U1(k, a), U1(k, k))
28.38/9.21	   A^2 -> H(U1(k, a), U1(k, d))
28.38/9.21	   A^2 -> H(U1(k, a), U1(d, k))
28.38/9.21	   A^2 -> H(U1(c, d), U1(e, b))
28.38/9.21	   A^2 -> H(U1(c, d), U1(k, b))
28.38/9.21	   A^2 -> H(U1(c, d), U1(c, d))
28.38/9.21	   A^2 -> H(U1(c, d), U1(d, c))
28.38/9.21	   A^2 -> H(U1(c, d), U1(b, e))
28.38/9.21	   A^2 -> H(U1(c, d), U1(b, k))
28.38/9.21	   A^2 -> H(U1(c, d), U1(e, c))
28.38/9.21	   A^2 -> H(U1(c, d), U1(k, c))
28.38/9.21	   A^2 -> H(U1(c, d), U1(c, e))
28.38/9.21	   A^2 -> H(U1(c, d), U1(c, k))
28.38/9.21	   A^2 -> H(U1(c, d), U1(e, e))
28.38/9.21	   A^2 -> H(U1(c, d), U1(k, k))
28.38/9.21	   A^2 -> H(U1(c, d), U1(k, d))
28.38/9.21	   A^2 -> H(U1(c, d), U1(d, k))
28.38/9.21	   A^2 -> H(U1(c, a), b)
28.38/9.21	   A^2 -> H(U1(c, a), U1(e, d))
28.38/9.21	   A^2 -> H(U1(c, a), U1(d, e))
28.38/9.21	   A^2 -> H(U1(c, a), c)
28.38/9.21	   A^2 -> H(U1(c, a), U1(e, k))
28.38/9.21	   A^2 -> H(U1(c, a), U1(k, e))
28.38/9.21	   A^2 -> H(U1(c, a), e)
28.38/9.21	   A^2 -> H(U1(c, a), U1(k, k))
28.38/9.21	   A^2 -> H(U1(d, e), U1(c, b))
28.38/9.21	   A^2 -> H(U1(d, e), U1(d, b))
28.38/9.21	   A^2 -> H(U1(d, e), U1(b, c))
28.38/9.21	   A^2 -> H(U1(d, e), U1(b, d))
28.38/9.21	   A^2 -> H(U1(d, e), U1(c, c))
28.38/9.21	   A^2 -> H(U1(d, e), f(e))
28.38/9.21	   A^2 -> H(U1(d, e), f(k))
28.38/9.21	   A^2 -> H(U1(d, e), U1(d, d))
28.38/9.21	   A^2 -> H(U1(d, c), U1(e, b))
28.38/9.21	   A^2 -> H(U1(d, c), U1(k, b))
28.38/9.21	   A^2 -> H(U1(d, c), U1(c, d))
28.38/9.21	   A^2 -> H(U1(d, c), U1(d, c))
28.38/9.21	   A^2 -> H(U1(d, c), U1(b, e))
28.38/9.21	   A^2 -> H(U1(d, c), U1(b, k))
28.38/9.21	   A^2 -> H(U1(d, c), U1(e, c))
28.38/9.21	   A^2 -> H(U1(d, c), U1(k, c))
28.38/9.21	   A^2 -> H(U1(d, c), U1(c, e))
28.38/9.21	   A^2 -> H(U1(d, c), U1(c, k))
28.38/9.21	   A^2 -> H(U1(d, c), U1(e, e))
28.38/9.21	   A^2 -> H(U1(d, c), U1(k, k))
28.38/9.21	   A^2 -> H(U1(d, c), U1(k, d))
28.38/9.21	   A^2 -> H(U1(d, c), U1(d, k))
28.38/9.21	   A^2 -> H(U1(d, a), b)
28.38/9.21	   A^2 -> H(U1(d, a), U1(e, d))
28.38/9.21	   A^2 -> H(U1(d, a), U1(d, e))
28.38/9.21	   A^2 -> H(U1(d, a), c)
28.38/9.21	   A^2 -> H(U1(d, a), U1(e, k))
28.38/9.21	   A^2 -> H(U1(d, a), U1(k, e))
28.38/9.21	   A^2 -> H(U1(d, a), e)
28.38/9.21	   A^2 -> H(U1(d, a), U1(k, k))
28.38/9.21	   A^2 -> H(U1(a, e), U1(e, b))
28.38/9.21	   A^2 -> H(U1(a, e), U1(k, b))
28.38/9.21	   A^2 -> H(U1(a, e), U1(c, d))
28.38/9.21	   A^2 -> H(U1(a, e), U1(d, c))
28.38/9.21	   A^2 -> H(U1(a, e), U1(b, e))
28.38/9.21	   A^2 -> H(U1(a, e), U1(b, k))
28.38/9.21	   A^2 -> H(U1(a, e), U1(e, c))
28.38/9.21	   A^2 -> H(U1(a, e), U1(k, c))
28.38/9.21	   A^2 -> H(U1(a, e), U1(c, e))
28.38/9.21	   A^2 -> H(U1(a, e), U1(c, k))
28.38/9.21	   A^2 -> H(U1(a, e), U1(e, e))
28.38/9.21	   A^2 -> H(U1(a, e), U1(k, k))
28.38/9.21	   A^2 -> H(U1(a, e), U1(k, d))
28.38/9.21	   A^2 -> H(U1(a, e), U1(d, k))
28.38/9.21	   A^2 -> H(U1(a, k), U1(e, b))
28.38/9.21	   A^2 -> H(U1(a, k), U1(k, b))
28.38/9.21	   A^2 -> H(U1(a, k), U1(c, d))
28.38/9.21	   A^2 -> H(U1(a, k), U1(d, c))
28.38/9.21	   A^2 -> H(U1(a, k), U1(b, e))
28.38/9.21	   A^2 -> H(U1(a, k), U1(b, k))
28.38/9.21	   A^2 -> H(U1(a, k), U1(e, c))
28.38/9.21	   A^2 -> H(U1(a, k), U1(k, c))
28.38/9.21	   A^2 -> H(U1(a, k), U1(c, e))
28.38/9.21	   A^2 -> H(U1(a, k), U1(c, k))
28.38/9.21	   A^2 -> H(U1(a, k), U1(e, e))
28.38/9.21	   A^2 -> H(U1(a, k), U1(k, k))
28.38/9.21	   A^2 -> H(U1(a, k), U1(k, d))
28.38/9.21	   A^2 -> H(U1(a, k), U1(d, k))
28.38/9.21	   A^2 -> H(U1(a, c), b)
28.38/9.21	   A^2 -> H(U1(a, c), U1(e, d))
28.38/9.21	   A^2 -> H(U1(a, c), U1(d, e))
28.38/9.21	   A^2 -> H(U1(a, c), c)
28.38/9.21	   A^2 -> H(U1(a, c), U1(e, k))
28.38/9.21	   A^2 -> H(U1(a, c), U1(k, e))
28.38/9.21	   A^2 -> H(U1(a, c), e)
28.38/9.21	   A^2 -> H(U1(a, c), U1(k, k))
28.38/9.21	   A^2 -> H(U1(a, d), b)
28.38/9.21	   A^2 -> H(U1(a, d), U1(e, d))
28.38/9.21	   A^2 -> H(U1(a, d), U1(d, e))
28.38/9.21	   A^2 -> H(U1(a, d), c)
28.38/9.21	   A^2 -> H(U1(a, d), U1(e, k))
28.38/9.21	   A^2 -> H(U1(a, d), U1(k, e))
28.38/9.21	   A^2 -> H(U1(a, d), e)
28.38/9.21	   A^2 -> H(U1(a, d), U1(k, k))
28.38/9.21	   A^2 -> H(U1(a, a), d)
28.38/9.21	   A^2 -> H(U1(a, a), k)
28.38/9.21	   A^2 -> H(k, U1(b, b))
28.38/9.21	   A^2 -> H(k, f(c))
28.38/9.21	   A^2 -> H(k, f(d))
28.38/9.21	   A^2 -> H(c, U1(c, b))
28.38/9.21	   A^2 -> H(c, U1(d, b))
28.38/9.21	   A^2 -> H(c, U1(b, c))
28.38/9.21	   A^2 -> H(c, U1(b, d))
28.38/9.21	   A^2 -> H(c, U1(c, c))
28.38/9.21	   A^2 -> H(c, f(e))
28.38/9.21	   A^2 -> H(c, f(k))
28.38/9.21	   A^2 -> H(c, U1(d, d))
28.38/9.21	   A^2 -> H(U1(e, k), U1(c, b))
28.38/9.21	   A^2 -> H(U1(e, k), U1(d, b))
28.38/9.21	   A^2 -> H(U1(e, k), U1(b, c))
28.38/9.21	   A^2 -> H(U1(e, k), U1(b, d))
28.38/9.21	   A^2 -> H(U1(e, k), U1(c, c))
28.38/9.21	   A^2 -> H(U1(e, k), f(e))
28.38/9.21	   A^2 -> H(U1(e, k), f(k))
28.38/9.21	   A^2 -> H(U1(e, k), U1(d, d))
28.38/9.21	   A^2 -> H(U1(e, c), U1(e, b))
28.38/9.21	   A^2 -> H(U1(e, c), U1(k, b))
28.38/9.21	   A^2 -> H(U1(e, c), U1(c, d))
28.38/9.21	   A^2 -> H(U1(e, c), U1(d, c))
28.38/9.21	   A^2 -> H(U1(e, c), U1(b, e))
28.38/9.21	   A^2 -> H(U1(e, c), U1(b, k))
28.38/9.21	   A^2 -> H(U1(e, c), U1(e, c))
28.38/9.21	   A^2 -> H(U1(e, c), U1(k, c))
28.38/9.21	   A^2 -> H(U1(e, c), U1(c, e))
28.38/9.21	   A^2 -> H(U1(e, c), U1(c, k))
28.38/9.21	   A^2 -> H(U1(e, c), U1(e, e))
28.38/9.21	   A^2 -> H(U1(e, c), U1(k, k))
28.38/9.21	   A^2 -> H(U1(e, c), U1(k, d))
28.38/9.21	   A^2 -> H(U1(e, c), U1(d, k))
28.38/9.21	   A^2 -> H(U1(k, e), U1(c, b))
28.38/9.21	   A^2 -> H(U1(k, e), U1(d, b))
28.38/9.21	   A^2 -> H(U1(k, e), U1(b, c))
28.38/9.21	   A^2 -> H(U1(k, e), U1(b, d))
28.38/9.21	   A^2 -> H(U1(k, e), U1(c, c))
28.38/9.21	   A^2 -> H(U1(k, e), f(e))
28.38/9.21	   A^2 -> H(U1(k, e), f(k))
28.38/9.21	   A^2 -> H(U1(k, e), U1(d, d))
28.38/9.21	
28.38/9.21	The TRS R consists of the following rules:
28.38/9.21	
28.38/9.21	   f(x) -> U1(x, x)
28.38/9.21	   U1(e, x) -> x
28.38/9.21	   a -> c
28.38/9.21	   a -> d
28.38/9.21	   b -> c
28.38/9.21	   b -> d
28.38/9.21	   d -> k
28.38/9.21	   c -> e
28.38/9.21	   c -> k
28.38/9.21	
28.38/9.21	Q is empty.
28.38/9.21	We have to consider all minimal (P,Q,R)-chains.
28.38/9.21	----------------------------------------
28.38/9.21	
28.38/9.21	(821) TransformationProof (EQUIVALENT)
28.38/9.21	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
28.38/9.21	
28.38/9.21	   (A^2 -> H(U1(k, e), U1(c, b)),A^2 -> H(U1(k, e), U1(c, b)))
28.38/9.21	   (A^2 -> H(U1(k, k), U1(c, b)),A^2 -> H(U1(k, k), U1(c, b)))
28.38/9.21	   (A^2 -> H(U1(k, c), U1(e, b)),A^2 -> H(U1(k, c), U1(e, b)))
28.38/9.21	   (A^2 -> H(U1(k, c), U1(k, b)),A^2 -> H(U1(k, c), U1(k, b)))
28.38/9.21	   (A^2 -> H(U1(k, c), U1(c, c)),A^2 -> H(U1(k, c), U1(c, c)))
28.38/9.21	   (A^2 -> H(U1(k, c), U1(c, d)),A^2 -> H(U1(k, c), U1(c, d)))
28.38/9.21	
28.38/9.21	
28.38/9.21	----------------------------------------
28.38/9.21	
28.38/9.21	(822)
28.38/9.21	Obligation:
28.38/9.21	Q DP problem:
28.38/9.21	The TRS P consists of the following rules:
28.38/9.21	
28.38/9.21	   H(x, x) -> G(x, x, f(k))
28.38/9.21	   G(d, x, x) -> A^2
28.38/9.21	   A^2 -> H(f(c), f(c))
28.38/9.21	   A^2 -> H(f(d), f(d))
28.38/9.21	   A^2 -> H(U1(c, c), U1(c, c))
28.38/9.21	   A^2 -> H(f(e), f(e))
28.38/9.21	   A^2 -> H(f(k), f(k))
28.38/9.21	   A^2 -> H(U1(d, d), U1(d, d))
28.38/9.21	   A^2 -> H(U1(k, c), U1(d, b))
28.38/9.21	   A^2 -> H(U1(k, c), U1(b, c))
28.38/9.21	   A^2 -> H(U1(k, c), U1(b, d))
28.38/9.21	   A^2 -> H(U1(k, c), U1(c, c))
28.38/9.21	   A^2 -> H(U1(k, c), f(e))
28.38/9.21	   A^2 -> H(U1(k, c), f(k))
28.38/9.21	   A^2 -> H(U1(k, c), U1(d, d))
28.38/9.21	   A^2 -> H(U1(c, e), U1(c, b))
28.38/9.21	   A^2 -> H(U1(c, e), U1(d, b))
28.38/9.21	   A^2 -> H(U1(c, e), U1(b, c))
28.38/9.21	   A^2 -> H(U1(c, e), U1(b, d))
28.38/9.21	   A^2 -> H(U1(c, e), U1(c, c))
28.38/9.21	   A^2 -> H(U1(c, e), f(e))
28.38/9.21	   A^2 -> H(U1(c, e), f(k))
28.38/9.21	   A^2 -> H(U1(c, e), U1(d, d))
28.38/9.21	   A^2 -> H(U1(c, k), U1(c, b))
28.38/9.21	   A^2 -> H(U1(c, k), U1(d, b))
28.38/9.21	   A^2 -> H(U1(c, k), U1(b, c))
28.38/9.21	   A^2 -> H(U1(c, k), U1(b, d))
28.38/9.21	   A^2 -> H(U1(c, k), U1(c, c))
28.38/9.21	   A^2 -> H(U1(c, k), f(e))
28.38/9.21	   A^2 -> H(U1(c, k), f(k))
28.38/9.21	   A^2 -> H(U1(c, k), U1(d, d))
28.38/9.21	   A^2 -> H(U1(c, c), U1(e, b))
28.38/9.21	   A^2 -> H(U1(c, c), U1(k, b))
28.38/9.21	   A^2 -> H(U1(c, c), U1(c, d))
28.38/9.21	   A^2 -> H(U1(c, c), U1(d, c))
28.43/9.21	   A^2 -> H(U1(c, c), U1(b, e))
28.43/9.21	   A^2 -> H(U1(c, c), U1(b, k))
28.43/9.21	   A^2 -> H(U1(c, c), U1(e, e))
28.43/9.21	   A^2 -> H(U1(c, c), U1(k, k))
28.43/9.21	   A^2 -> H(U1(c, c), U1(k, d))
28.43/9.21	   A^2 -> H(U1(c, c), U1(d, k))
28.43/9.21	   A^2 -> H(e, U1(b, b))
28.43/9.21	   A^2 -> H(e, f(c))
28.43/9.21	   A^2 -> H(e, f(d))
28.43/9.21	   A^2 -> H(U1(e, e), U1(c, b))
28.43/9.21	   A^2 -> H(U1(e, e), U1(d, b))
28.43/9.21	   A^2 -> H(U1(e, e), U1(b, c))
28.43/9.21	   A^2 -> H(U1(e, e), U1(b, d))
28.43/9.21	   A^2 -> H(U1(e, e), U1(c, c))
28.43/9.21	   A^2 -> H(U1(e, e), f(e))
28.43/9.21	   A^2 -> H(U1(e, e), f(k))
28.43/9.21	   A^2 -> H(U1(e, e), U1(d, d))
28.43/9.21	   A^2 -> H(f(e), U1(e, b))
28.43/9.21	   A^2 -> H(f(e), U1(k, b))
28.43/9.21	   A^2 -> H(f(e), U1(c, d))
28.43/9.21	   A^2 -> H(f(e), U1(d, c))
28.43/9.21	   A^2 -> H(f(e), U1(b, e))
28.43/9.21	   A^2 -> H(f(e), U1(b, k))
28.43/9.21	   A^2 -> H(f(e), U1(e, c))
28.43/9.21	   A^2 -> H(f(e), U1(k, c))
28.43/9.21	   A^2 -> H(f(e), U1(c, e))
28.43/9.21	   A^2 -> H(f(e), U1(c, k))
28.43/9.21	   A^2 -> H(f(e), U1(k, k))
28.43/9.21	   A^2 -> H(f(e), U1(k, d))
28.43/9.21	   A^2 -> H(f(e), U1(d, k))
28.43/9.21	   A^2 -> H(U1(k, k), U1(c, b))
28.43/9.21	   A^2 -> H(U1(k, k), U1(d, b))
28.43/9.21	   A^2 -> H(U1(k, k), U1(b, c))
28.43/9.21	   A^2 -> H(U1(k, k), U1(b, d))
28.43/9.21	   A^2 -> H(U1(k, k), U1(c, c))
28.43/9.21	   A^2 -> H(U1(k, k), f(e))
28.43/9.21	   A^2 -> H(U1(k, k), f(k))
28.43/9.21	   A^2 -> H(U1(k, k), U1(d, d))
28.43/9.21	   A^2 -> H(f(k), U1(e, b))
28.43/9.21	   A^2 -> H(f(k), U1(k, b))
28.43/9.21	   A^2 -> H(f(k), U1(c, d))
28.43/9.21	   A^2 -> H(f(k), U1(d, c))
28.43/9.21	   A^2 -> H(f(k), U1(b, e))
28.43/9.21	   A^2 -> H(f(k), U1(b, k))
28.43/9.21	   A^2 -> H(f(k), U1(e, c))
28.43/9.21	   A^2 -> H(f(k), U1(k, c))
28.43/9.21	   A^2 -> H(f(k), U1(c, e))
28.43/9.21	   A^2 -> H(f(k), U1(c, k))
28.43/9.21	   A^2 -> H(f(k), U1(e, e))
28.43/9.21	   A^2 -> H(f(k), U1(k, d))
28.43/9.21	   A^2 -> H(f(k), U1(d, k))
28.43/9.21	   A^2 -> H(f(c), b)
28.43/9.21	   A^2 -> H(f(c), U1(e, d))
28.43/9.21	   A^2 -> H(f(c), U1(d, e))
28.43/9.21	   A^2 -> H(f(k), U1(k, k))
28.43/9.21	   A^2 -> H(U1(k, k), U1(b, b))
28.43/9.21	   A^2 -> H(U1(k, k), f(c))
28.43/9.21	   A^2 -> H(U1(k, k), f(d))
28.43/9.21	   A^2 -> H(U1(k, d), U1(c, b))
28.43/9.21	   A^2 -> H(U1(k, d), U1(d, b))
28.43/9.21	   A^2 -> H(U1(k, d), U1(b, c))
28.43/9.21	   A^2 -> H(U1(k, d), U1(b, d))
28.43/9.21	   A^2 -> H(U1(k, d), U1(c, c))
28.43/9.21	   A^2 -> H(U1(k, d), f(e))
28.43/9.21	   A^2 -> H(U1(k, d), f(k))
28.43/9.21	   A^2 -> H(U1(k, d), U1(d, d))
28.43/9.21	   A^2 -> H(U1(d, k), U1(c, b))
28.43/9.21	   A^2 -> H(U1(d, k), U1(d, b))
28.43/9.21	   A^2 -> H(U1(d, k), U1(b, c))
28.43/9.21	   A^2 -> H(U1(d, k), U1(b, d))
28.43/9.21	   A^2 -> H(U1(d, k), U1(c, c))
28.43/9.21	   A^2 -> H(U1(d, k), f(e))
28.43/9.21	   A^2 -> H(U1(d, k), f(k))
28.43/9.21	   A^2 -> H(U1(d, k), U1(d, d))
28.43/9.21	   A^2 -> H(U1(d, d), U1(e, b))
28.43/9.21	   A^2 -> H(U1(d, d), U1(k, b))
28.43/9.21	   A^2 -> H(U1(d, d), U1(c, d))
28.43/9.21	   A^2 -> H(U1(d, d), U1(d, c))
28.43/9.21	   A^2 -> H(U1(d, d), U1(b, e))
28.43/9.21	   A^2 -> H(U1(d, d), U1(b, k))
28.43/9.21	   A^2 -> H(U1(d, d), U1(e, c))
28.43/9.21	   A^2 -> H(U1(d, d), U1(k, c))
28.43/9.21	   A^2 -> H(U1(d, d), U1(c, e))
28.43/9.21	   A^2 -> H(U1(d, d), U1(c, k))
28.43/9.21	   A^2 -> H(U1(d, d), U1(e, e))
28.43/9.21	   A^2 -> H(U1(d, d), U1(k, k))
28.43/9.21	   A^2 -> H(f(d), b)
28.43/9.21	   A^2 -> H(f(d), U1(e, d))
28.43/9.21	   A^2 -> H(f(d), U1(d, e))
28.43/9.21	   A^2 -> H(f(d), c)
28.43/9.21	   A^2 -> H(f(d), U1(e, k))
28.43/9.21	   A^2 -> H(f(d), U1(k, e))
28.43/9.21	   A^2 -> H(f(d), e)
28.43/9.21	   A^2 -> H(f(a), d)
28.43/9.21	   A^2 -> H(U1(c, c), U1(e, c))
28.43/9.21	   A^2 -> H(f(c), c)
28.43/9.21	   A^2 -> H(f(c), U1(e, k))
28.43/9.21	   A^2 -> H(U1(c, c), U1(k, c))
28.43/9.21	   A^2 -> H(f(c), U1(k, e))
28.43/9.21	   A^2 -> H(f(c), U1(k, k))
28.43/9.21	   A^2 -> H(U1(c, c), U1(c, e))
28.43/9.21	   A^2 -> H(U1(c, c), U1(c, k))
28.43/9.21	   A^2 -> H(f(a), k)
28.43/9.21	   A^2 -> H(f(e), U1(e, e))
28.43/9.21	   A^2 -> H(f(c), e)
28.43/9.21	   A^2 -> H(U1(d, d), U1(k, d))
28.43/9.21	   A^2 -> H(f(d), U1(k, k))
28.43/9.21	   A^2 -> H(U1(d, d), U1(d, k))
28.43/9.21	   A^2 -> H(d, U1(b, b))
28.43/9.21	   A^2 -> H(d, f(c))
28.43/9.21	   A^2 -> H(d, f(d))
28.43/9.21	   A^2 -> H(a, U1(c, b))
28.43/9.21	   A^2 -> H(a, U1(d, b))
28.43/9.21	   A^2 -> H(a, U1(b, c))
28.43/9.21	   A^2 -> H(a, U1(b, d))
28.43/9.21	   A^2 -> H(a, U1(c, c))
28.43/9.21	   A^2 -> H(a, f(e))
28.43/9.21	   A^2 -> H(a, f(k))
28.43/9.21	   A^2 -> H(a, U1(d, d))
28.43/9.21	   A^2 -> H(U1(e, d), U1(c, b))
28.43/9.21	   A^2 -> H(U1(e, d), U1(d, b))
28.43/9.21	   A^2 -> H(U1(e, d), U1(b, c))
28.43/9.21	   A^2 -> H(U1(e, d), U1(b, d))
28.43/9.21	   A^2 -> H(U1(e, d), U1(c, c))
28.43/9.21	   A^2 -> H(U1(e, d), f(e))
28.43/9.21	   A^2 -> H(U1(e, d), f(k))
28.43/9.21	   A^2 -> H(U1(e, d), U1(d, d))
28.43/9.21	   A^2 -> H(U1(e, a), U1(e, b))
28.43/9.21	   A^2 -> H(U1(e, a), U1(k, b))
28.43/9.21	   A^2 -> H(U1(e, a), U1(c, d))
28.43/9.21	   A^2 -> H(U1(e, a), U1(d, c))
28.43/9.21	   A^2 -> H(U1(e, a), U1(b, e))
28.43/9.21	   A^2 -> H(U1(e, a), U1(b, k))
28.43/9.21	   A^2 -> H(U1(e, a), U1(e, c))
28.43/9.21	   A^2 -> H(U1(e, a), U1(k, c))
28.43/9.21	   A^2 -> H(U1(e, a), U1(c, e))
28.43/9.21	   A^2 -> H(U1(e, a), U1(c, k))
28.43/9.21	   A^2 -> H(U1(e, a), U1(e, e))
28.43/9.21	   A^2 -> H(U1(e, a), U1(k, k))
28.43/9.21	   A^2 -> H(U1(e, a), U1(k, d))
28.43/9.21	   A^2 -> H(U1(e, a), U1(d, k))
28.43/9.21	   A^2 -> H(U1(k, a), U1(e, b))
28.43/9.21	   A^2 -> H(U1(k, a), U1(k, b))
28.43/9.21	   A^2 -> H(U1(k, a), U1(c, d))
28.43/9.21	   A^2 -> H(U1(k, a), U1(d, c))
28.43/9.21	   A^2 -> H(U1(k, a), U1(b, e))
28.43/9.21	   A^2 -> H(U1(k, a), U1(b, k))
28.43/9.21	   A^2 -> H(U1(k, a), U1(e, c))
28.43/9.21	   A^2 -> H(U1(k, a), U1(k, c))
28.43/9.21	   A^2 -> H(U1(k, a), U1(c, e))
28.43/9.21	   A^2 -> H(U1(k, a), U1(c, k))
28.43/9.21	   A^2 -> H(U1(k, a), U1(e, e))
28.43/9.21	   A^2 -> H(U1(k, a), U1(k, k))
28.43/9.21	   A^2 -> H(U1(k, a), U1(k, d))
28.43/9.21	   A^2 -> H(U1(k, a), U1(d, k))
28.43/9.21	   A^2 -> H(U1(c, d), U1(e, b))
28.43/9.21	   A^2 -> H(U1(c, d), U1(k, b))
28.43/9.21	   A^2 -> H(U1(c, d), U1(c, d))
28.43/9.21	   A^2 -> H(U1(c, d), U1(d, c))
28.43/9.21	   A^2 -> H(U1(c, d), U1(b, e))
28.43/9.21	   A^2 -> H(U1(c, d), U1(b, k))
28.43/9.21	   A^2 -> H(U1(c, d), U1(e, c))
28.43/9.21	   A^2 -> H(U1(c, d), U1(k, c))
28.43/9.21	   A^2 -> H(U1(c, d), U1(c, e))
28.43/9.21	   A^2 -> H(U1(c, d), U1(c, k))
28.43/9.21	   A^2 -> H(U1(c, d), U1(e, e))
28.43/9.21	   A^2 -> H(U1(c, d), U1(k, k))
28.43/9.21	   A^2 -> H(U1(c, d), U1(k, d))
28.43/9.21	   A^2 -> H(U1(c, d), U1(d, k))
28.43/9.21	   A^2 -> H(U1(c, a), b)
28.43/9.21	   A^2 -> H(U1(c, a), U1(e, d))
28.43/9.21	   A^2 -> H(U1(c, a), U1(d, e))
28.43/9.21	   A^2 -> H(U1(c, a), c)
28.43/9.21	   A^2 -> H(U1(c, a), U1(e, k))
28.43/9.21	   A^2 -> H(U1(c, a), U1(k, e))
28.43/9.21	   A^2 -> H(U1(c, a), e)
28.43/9.21	   A^2 -> H(U1(c, a), U1(k, k))
28.43/9.21	   A^2 -> H(U1(d, e), U1(c, b))
28.43/9.21	   A^2 -> H(U1(d, e), U1(d, b))
28.43/9.21	   A^2 -> H(U1(d, e), U1(b, c))
28.43/9.21	   A^2 -> H(U1(d, e), U1(b, d))
28.43/9.21	   A^2 -> H(U1(d, e), U1(c, c))
28.43/9.21	   A^2 -> H(U1(d, e), f(e))
28.43/9.21	   A^2 -> H(U1(d, e), f(k))
28.43/9.21	   A^2 -> H(U1(d, e), U1(d, d))
28.43/9.21	   A^2 -> H(U1(d, c), U1(e, b))
28.43/9.21	   A^2 -> H(U1(d, c), U1(k, b))
28.43/9.21	   A^2 -> H(U1(d, c), U1(c, d))
28.43/9.21	   A^2 -> H(U1(d, c), U1(d, c))
28.43/9.21	   A^2 -> H(U1(d, c), U1(b, e))
28.43/9.21	   A^2 -> H(U1(d, c), U1(b, k))
28.43/9.21	   A^2 -> H(U1(d, c), U1(e, c))
28.43/9.21	   A^2 -> H(U1(d, c), U1(k, c))
28.43/9.21	   A^2 -> H(U1(d, c), U1(c, e))
28.43/9.21	   A^2 -> H(U1(d, c), U1(c, k))
28.43/9.21	   A^2 -> H(U1(d, c), U1(e, e))
28.43/9.21	   A^2 -> H(U1(d, c), U1(k, k))
28.43/9.21	   A^2 -> H(U1(d, c), U1(k, d))
28.43/9.21	   A^2 -> H(U1(d, c), U1(d, k))
28.43/9.21	   A^2 -> H(U1(d, a), b)
28.43/9.21	   A^2 -> H(U1(d, a), U1(e, d))
28.43/9.21	   A^2 -> H(U1(d, a), U1(d, e))
28.43/9.21	   A^2 -> H(U1(d, a), c)
28.43/9.21	   A^2 -> H(U1(d, a), U1(e, k))
28.43/9.21	   A^2 -> H(U1(d, a), U1(k, e))
28.43/9.21	   A^2 -> H(U1(d, a), e)
28.43/9.21	   A^2 -> H(U1(d, a), U1(k, k))
28.43/9.21	   A^2 -> H(U1(a, e), U1(e, b))
28.43/9.21	   A^2 -> H(U1(a, e), U1(k, b))
28.43/9.21	   A^2 -> H(U1(a, e), U1(c, d))
28.43/9.21	   A^2 -> H(U1(a, e), U1(d, c))
28.43/9.21	   A^2 -> H(U1(a, e), U1(b, e))
28.43/9.21	   A^2 -> H(U1(a, e), U1(b, k))
28.43/9.21	   A^2 -> H(U1(a, e), U1(e, c))
28.43/9.21	   A^2 -> H(U1(a, e), U1(k, c))
28.43/9.21	   A^2 -> H(U1(a, e), U1(c, e))
28.43/9.21	   A^2 -> H(U1(a, e), U1(c, k))
28.43/9.21	   A^2 -> H(U1(a, e), U1(e, e))
28.43/9.21	   A^2 -> H(U1(a, e), U1(k, k))
28.43/9.21	   A^2 -> H(U1(a, e), U1(k, d))
28.43/9.21	   A^2 -> H(U1(a, e), U1(d, k))
28.43/9.21	   A^2 -> H(U1(a, k), U1(e, b))
28.43/9.21	   A^2 -> H(U1(a, k), U1(k, b))
28.43/9.21	   A^2 -> H(U1(a, k), U1(c, d))
28.43/9.21	   A^2 -> H(U1(a, k), U1(d, c))
28.43/9.21	   A^2 -> H(U1(a, k), U1(b, e))
28.43/9.21	   A^2 -> H(U1(a, k), U1(b, k))
28.43/9.21	   A^2 -> H(U1(a, k), U1(e, c))
28.43/9.21	   A^2 -> H(U1(a, k), U1(k, c))
28.43/9.21	   A^2 -> H(U1(a, k), U1(c, e))
28.43/9.21	   A^2 -> H(U1(a, k), U1(c, k))
28.43/9.21	   A^2 -> H(U1(a, k), U1(e, e))
28.43/9.21	   A^2 -> H(U1(a, k), U1(k, k))
28.43/9.21	   A^2 -> H(U1(a, k), U1(k, d))
28.43/9.21	   A^2 -> H(U1(a, k), U1(d, k))
28.43/9.21	   A^2 -> H(U1(a, c), b)
28.43/9.21	   A^2 -> H(U1(a, c), U1(e, d))
28.43/9.21	   A^2 -> H(U1(a, c), U1(d, e))
28.43/9.21	   A^2 -> H(U1(a, c), c)
28.43/9.21	   A^2 -> H(U1(a, c), U1(e, k))
28.43/9.21	   A^2 -> H(U1(a, c), U1(k, e))
28.43/9.21	   A^2 -> H(U1(a, c), e)
28.43/9.21	   A^2 -> H(U1(a, c), U1(k, k))
28.43/9.21	   A^2 -> H(U1(a, d), b)
28.43/9.21	   A^2 -> H(U1(a, d), U1(e, d))
28.43/9.21	   A^2 -> H(U1(a, d), U1(d, e))
28.43/9.21	   A^2 -> H(U1(a, d), c)
28.43/9.21	   A^2 -> H(U1(a, d), U1(e, k))
28.43/9.21	   A^2 -> H(U1(a, d), U1(k, e))
28.43/9.21	   A^2 -> H(U1(a, d), e)
28.43/9.21	   A^2 -> H(U1(a, d), U1(k, k))
28.43/9.21	   A^2 -> H(U1(a, a), d)
28.43/9.21	   A^2 -> H(U1(a, a), k)
28.43/9.21	   A^2 -> H(k, U1(b, b))
28.43/9.21	   A^2 -> H(k, f(c))
28.43/9.21	   A^2 -> H(k, f(d))
28.43/9.21	   A^2 -> H(c, U1(c, b))
28.43/9.21	   A^2 -> H(c, U1(d, b))
28.43/9.21	   A^2 -> H(c, U1(b, c))
28.43/9.21	   A^2 -> H(c, U1(b, d))
28.43/9.21	   A^2 -> H(c, U1(c, c))
28.43/9.21	   A^2 -> H(c, f(e))
28.43/9.21	   A^2 -> H(c, f(k))
28.43/9.21	   A^2 -> H(c, U1(d, d))
28.43/9.21	   A^2 -> H(U1(e, k), U1(c, b))
28.43/9.21	   A^2 -> H(U1(e, k), U1(d, b))
28.43/9.21	   A^2 -> H(U1(e, k), U1(b, c))
28.43/9.21	   A^2 -> H(U1(e, k), U1(b, d))
28.43/9.21	   A^2 -> H(U1(e, k), U1(c, c))
28.43/9.21	   A^2 -> H(U1(e, k), f(e))
28.43/9.21	   A^2 -> H(U1(e, k), f(k))
28.43/9.21	   A^2 -> H(U1(e, k), U1(d, d))
28.43/9.21	   A^2 -> H(U1(e, c), U1(e, b))
28.43/9.21	   A^2 -> H(U1(e, c), U1(k, b))
28.43/9.21	   A^2 -> H(U1(e, c), U1(c, d))
28.43/9.21	   A^2 -> H(U1(e, c), U1(d, c))
28.43/9.21	   A^2 -> H(U1(e, c), U1(b, e))
28.43/9.21	   A^2 -> H(U1(e, c), U1(b, k))
28.43/9.21	   A^2 -> H(U1(e, c), U1(e, c))
28.43/9.21	   A^2 -> H(U1(e, c), U1(k, c))
28.43/9.21	   A^2 -> H(U1(e, c), U1(c, e))
28.43/9.21	   A^2 -> H(U1(e, c), U1(c, k))
28.43/9.21	   A^2 -> H(U1(e, c), U1(e, e))
28.43/9.21	   A^2 -> H(U1(e, c), U1(k, k))
28.43/9.21	   A^2 -> H(U1(e, c), U1(k, d))
28.43/9.21	   A^2 -> H(U1(e, c), U1(d, k))
28.43/9.21	   A^2 -> H(U1(k, e), U1(c, b))
28.43/9.21	   A^2 -> H(U1(k, e), U1(d, b))
28.43/9.21	   A^2 -> H(U1(k, e), U1(b, c))
28.43/9.21	   A^2 -> H(U1(k, e), U1(b, d))
28.43/9.21	   A^2 -> H(U1(k, e), U1(c, c))
28.43/9.21	   A^2 -> H(U1(k, e), f(e))
28.43/9.21	   A^2 -> H(U1(k, e), f(k))
28.43/9.21	   A^2 -> H(U1(k, e), U1(d, d))
28.43/9.21	   A^2 -> H(U1(k, c), U1(e, b))
28.43/9.21	   A^2 -> H(U1(k, c), U1(k, b))
28.43/9.21	   A^2 -> H(U1(k, c), U1(c, d))
28.43/9.21	
28.43/9.21	The TRS R consists of the following rules:
28.43/9.21	
28.43/9.21	   f(x) -> U1(x, x)
28.43/9.21	   U1(e, x) -> x
28.43/9.21	   a -> c
28.43/9.21	   a -> d
28.43/9.21	   b -> c
28.43/9.21	   b -> d
28.43/9.21	   d -> k
28.43/9.21	   c -> e
28.43/9.21	   c -> k
28.43/9.21	
28.43/9.21	Q is empty.
28.43/9.21	We have to consider all minimal (P,Q,R)-chains.
28.43/9.21	----------------------------------------
28.43/9.21	
28.43/9.21	(823) TransformationProof (EQUIVALENT)
28.43/9.21	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
28.43/9.21	
28.43/9.21	   (A^2 -> H(U1(k, e), U1(d, b)),A^2 -> H(U1(k, e), U1(d, b)))
28.43/9.21	   (A^2 -> H(U1(k, k), U1(d, b)),A^2 -> H(U1(k, k), U1(d, b)))
28.43/9.21	   (A^2 -> H(U1(k, c), U1(k, b)),A^2 -> H(U1(k, c), U1(k, b)))
28.43/9.21	   (A^2 -> H(U1(k, c), U1(d, c)),A^2 -> H(U1(k, c), U1(d, c)))
28.43/9.21	   (A^2 -> H(U1(k, c), U1(d, d)),A^2 -> H(U1(k, c), U1(d, d)))
28.43/9.21	
28.43/9.21	
28.43/9.21	----------------------------------------
28.43/9.21	
28.43/9.21	(824)
28.43/9.21	Obligation:
28.43/9.21	Q DP problem:
28.43/9.21	The TRS P consists of the following rules:
28.43/9.21	
28.43/9.21	   H(x, x) -> G(x, x, f(k))
28.43/9.21	   G(d, x, x) -> A^2
28.43/9.21	   A^2 -> H(f(c), f(c))
28.43/9.21	   A^2 -> H(f(d), f(d))
28.43/9.21	   A^2 -> H(U1(c, c), U1(c, c))
28.43/9.21	   A^2 -> H(f(e), f(e))
28.43/9.21	   A^2 -> H(f(k), f(k))
28.43/9.21	   A^2 -> H(U1(d, d), U1(d, d))
28.43/9.21	   A^2 -> H(U1(k, c), U1(b, c))
28.43/9.21	   A^2 -> H(U1(k, c), U1(b, d))
28.43/9.21	   A^2 -> H(U1(k, c), U1(c, c))
28.43/9.21	   A^2 -> H(U1(k, c), f(e))
28.43/9.21	   A^2 -> H(U1(k, c), f(k))
28.43/9.21	   A^2 -> H(U1(k, c), U1(d, d))
28.43/9.21	   A^2 -> H(U1(c, e), U1(c, b))
28.43/9.21	   A^2 -> H(U1(c, e), U1(d, b))
28.43/9.21	   A^2 -> H(U1(c, e), U1(b, c))
28.43/9.21	   A^2 -> H(U1(c, e), U1(b, d))
28.43/9.21	   A^2 -> H(U1(c, e), U1(c, c))
28.43/9.21	   A^2 -> H(U1(c, e), f(e))
28.43/9.21	   A^2 -> H(U1(c, e), f(k))
28.43/9.21	   A^2 -> H(U1(c, e), U1(d, d))
28.43/9.21	   A^2 -> H(U1(c, k), U1(c, b))
28.43/9.21	   A^2 -> H(U1(c, k), U1(d, b))
28.43/9.21	   A^2 -> H(U1(c, k), U1(b, c))
28.43/9.21	   A^2 -> H(U1(c, k), U1(b, d))
28.43/9.21	   A^2 -> H(U1(c, k), U1(c, c))
28.43/9.21	   A^2 -> H(U1(c, k), f(e))
28.43/9.21	   A^2 -> H(U1(c, k), f(k))
28.43/9.21	   A^2 -> H(U1(c, k), U1(d, d))
28.43/9.21	   A^2 -> H(U1(c, c), U1(e, b))
28.43/9.21	   A^2 -> H(U1(c, c), U1(k, b))
28.43/9.21	   A^2 -> H(U1(c, c), U1(c, d))
28.43/9.21	   A^2 -> H(U1(c, c), U1(d, c))
28.43/9.21	   A^2 -> H(U1(c, c), U1(b, e))
28.43/9.21	   A^2 -> H(U1(c, c), U1(b, k))
28.43/9.21	   A^2 -> H(U1(c, c), U1(e, e))
28.43/9.21	   A^2 -> H(U1(c, c), U1(k, k))
28.43/9.21	   A^2 -> H(U1(c, c), U1(k, d))
28.43/9.21	   A^2 -> H(U1(c, c), U1(d, k))
28.43/9.21	   A^2 -> H(e, U1(b, b))
28.43/9.21	   A^2 -> H(e, f(c))
28.43/9.21	   A^2 -> H(e, f(d))
28.43/9.21	   A^2 -> H(U1(e, e), U1(c, b))
28.43/9.21	   A^2 -> H(U1(e, e), U1(d, b))
28.43/9.21	   A^2 -> H(U1(e, e), U1(b, c))
28.43/9.21	   A^2 -> H(U1(e, e), U1(b, d))
28.43/9.21	   A^2 -> H(U1(e, e), U1(c, c))
28.43/9.21	   A^2 -> H(U1(e, e), f(e))
28.43/9.21	   A^2 -> H(U1(e, e), f(k))
28.43/9.21	   A^2 -> H(U1(e, e), U1(d, d))
28.43/9.21	   A^2 -> H(f(e), U1(e, b))
28.43/9.21	   A^2 -> H(f(e), U1(k, b))
28.43/9.21	   A^2 -> H(f(e), U1(c, d))
28.43/9.21	   A^2 -> H(f(e), U1(d, c))
28.43/9.21	   A^2 -> H(f(e), U1(b, e))
28.43/9.21	   A^2 -> H(f(e), U1(b, k))
28.43/9.21	   A^2 -> H(f(e), U1(e, c))
28.43/9.21	   A^2 -> H(f(e), U1(k, c))
28.43/9.21	   A^2 -> H(f(e), U1(c, e))
28.43/9.21	   A^2 -> H(f(e), U1(c, k))
28.43/9.21	   A^2 -> H(f(e), U1(k, k))
28.43/9.21	   A^2 -> H(f(e), U1(k, d))
28.43/9.21	   A^2 -> H(f(e), U1(d, k))
28.43/9.21	   A^2 -> H(U1(k, k), U1(c, b))
28.43/9.21	   A^2 -> H(U1(k, k), U1(d, b))
28.43/9.21	   A^2 -> H(U1(k, k), U1(b, c))
28.43/9.21	   A^2 -> H(U1(k, k), U1(b, d))
28.43/9.21	   A^2 -> H(U1(k, k), U1(c, c))
28.43/9.21	   A^2 -> H(U1(k, k), f(e))
28.43/9.21	   A^2 -> H(U1(k, k), f(k))
28.43/9.21	   A^2 -> H(U1(k, k), U1(d, d))
28.43/9.21	   A^2 -> H(f(k), U1(e, b))
28.43/9.21	   A^2 -> H(f(k), U1(k, b))
28.43/9.21	   A^2 -> H(f(k), U1(c, d))
28.43/9.21	   A^2 -> H(f(k), U1(d, c))
28.43/9.21	   A^2 -> H(f(k), U1(b, e))
28.43/9.21	   A^2 -> H(f(k), U1(b, k))
28.43/9.21	   A^2 -> H(f(k), U1(e, c))
28.43/9.21	   A^2 -> H(f(k), U1(k, c))
28.43/9.21	   A^2 -> H(f(k), U1(c, e))
28.43/9.21	   A^2 -> H(f(k), U1(c, k))
28.43/9.21	   A^2 -> H(f(k), U1(e, e))
28.43/9.21	   A^2 -> H(f(k), U1(k, d))
28.43/9.21	   A^2 -> H(f(k), U1(d, k))
28.43/9.21	   A^2 -> H(f(c), b)
28.43/9.21	   A^2 -> H(f(c), U1(e, d))
28.43/9.21	   A^2 -> H(f(c), U1(d, e))
28.43/9.21	   A^2 -> H(f(k), U1(k, k))
28.43/9.21	   A^2 -> H(U1(k, k), U1(b, b))
28.43/9.21	   A^2 -> H(U1(k, k), f(c))
28.43/9.21	   A^2 -> H(U1(k, k), f(d))
28.43/9.21	   A^2 -> H(U1(k, d), U1(c, b))
28.43/9.21	   A^2 -> H(U1(k, d), U1(d, b))
28.43/9.21	   A^2 -> H(U1(k, d), U1(b, c))
28.43/9.21	   A^2 -> H(U1(k, d), U1(b, d))
28.43/9.21	   A^2 -> H(U1(k, d), U1(c, c))
28.43/9.21	   A^2 -> H(U1(k, d), f(e))
28.43/9.21	   A^2 -> H(U1(k, d), f(k))
28.43/9.21	   A^2 -> H(U1(k, d), U1(d, d))
28.43/9.21	   A^2 -> H(U1(d, k), U1(c, b))
28.43/9.21	   A^2 -> H(U1(d, k), U1(d, b))
28.43/9.21	   A^2 -> H(U1(d, k), U1(b, c))
28.43/9.21	   A^2 -> H(U1(d, k), U1(b, d))
28.43/9.21	   A^2 -> H(U1(d, k), U1(c, c))
28.43/9.21	   A^2 -> H(U1(d, k), f(e))
28.43/9.21	   A^2 -> H(U1(d, k), f(k))
28.43/9.21	   A^2 -> H(U1(d, k), U1(d, d))
28.43/9.21	   A^2 -> H(U1(d, d), U1(e, b))
28.43/9.21	   A^2 -> H(U1(d, d), U1(k, b))
28.43/9.21	   A^2 -> H(U1(d, d), U1(c, d))
28.43/9.21	   A^2 -> H(U1(d, d), U1(d, c))
28.43/9.21	   A^2 -> H(U1(d, d), U1(b, e))
28.43/9.21	   A^2 -> H(U1(d, d), U1(b, k))
28.43/9.21	   A^2 -> H(U1(d, d), U1(e, c))
28.43/9.21	   A^2 -> H(U1(d, d), U1(k, c))
28.43/9.21	   A^2 -> H(U1(d, d), U1(c, e))
28.43/9.21	   A^2 -> H(U1(d, d), U1(c, k))
28.43/9.21	   A^2 -> H(U1(d, d), U1(e, e))
28.43/9.21	   A^2 -> H(U1(d, d), U1(k, k))
28.43/9.21	   A^2 -> H(f(d), b)
28.43/9.21	   A^2 -> H(f(d), U1(e, d))
28.43/9.21	   A^2 -> H(f(d), U1(d, e))
28.43/9.21	   A^2 -> H(f(d), c)
28.43/9.21	   A^2 -> H(f(d), U1(e, k))
28.43/9.21	   A^2 -> H(f(d), U1(k, e))
28.43/9.21	   A^2 -> H(f(d), e)
28.43/9.21	   A^2 -> H(f(a), d)
28.43/9.21	   A^2 -> H(U1(c, c), U1(e, c))
28.43/9.21	   A^2 -> H(f(c), c)
28.43/9.21	   A^2 -> H(f(c), U1(e, k))
28.43/9.21	   A^2 -> H(U1(c, c), U1(k, c))
28.43/9.21	   A^2 -> H(f(c), U1(k, e))
28.43/9.21	   A^2 -> H(f(c), U1(k, k))
28.43/9.21	   A^2 -> H(U1(c, c), U1(c, e))
28.43/9.21	   A^2 -> H(U1(c, c), U1(c, k))
28.43/9.21	   A^2 -> H(f(a), k)
28.43/9.21	   A^2 -> H(f(e), U1(e, e))
28.43/9.21	   A^2 -> H(f(c), e)
28.43/9.21	   A^2 -> H(U1(d, d), U1(k, d))
28.43/9.21	   A^2 -> H(f(d), U1(k, k))
28.43/9.21	   A^2 -> H(U1(d, d), U1(d, k))
28.43/9.21	   A^2 -> H(d, U1(b, b))
28.43/9.21	   A^2 -> H(d, f(c))
28.43/9.21	   A^2 -> H(d, f(d))
28.43/9.21	   A^2 -> H(a, U1(c, b))
28.43/9.21	   A^2 -> H(a, U1(d, b))
28.43/9.21	   A^2 -> H(a, U1(b, c))
28.43/9.21	   A^2 -> H(a, U1(b, d))
28.43/9.21	   A^2 -> H(a, U1(c, c))
28.43/9.21	   A^2 -> H(a, f(e))
28.43/9.21	   A^2 -> H(a, f(k))
28.43/9.21	   A^2 -> H(a, U1(d, d))
28.43/9.21	   A^2 -> H(U1(e, d), U1(c, b))
28.43/9.21	   A^2 -> H(U1(e, d), U1(d, b))
28.43/9.21	   A^2 -> H(U1(e, d), U1(b, c))
28.43/9.21	   A^2 -> H(U1(e, d), U1(b, d))
28.43/9.21	   A^2 -> H(U1(e, d), U1(c, c))
28.43/9.21	   A^2 -> H(U1(e, d), f(e))
28.43/9.21	   A^2 -> H(U1(e, d), f(k))
28.43/9.21	   A^2 -> H(U1(e, d), U1(d, d))
28.43/9.21	   A^2 -> H(U1(e, a), U1(e, b))
28.43/9.21	   A^2 -> H(U1(e, a), U1(k, b))
28.43/9.21	   A^2 -> H(U1(e, a), U1(c, d))
28.43/9.21	   A^2 -> H(U1(e, a), U1(d, c))
28.43/9.21	   A^2 -> H(U1(e, a), U1(b, e))
28.43/9.21	   A^2 -> H(U1(e, a), U1(b, k))
28.43/9.21	   A^2 -> H(U1(e, a), U1(e, c))
28.43/9.21	   A^2 -> H(U1(e, a), U1(k, c))
28.43/9.21	   A^2 -> H(U1(e, a), U1(c, e))
28.43/9.21	   A^2 -> H(U1(e, a), U1(c, k))
28.43/9.21	   A^2 -> H(U1(e, a), U1(e, e))
28.43/9.21	   A^2 -> H(U1(e, a), U1(k, k))
28.43/9.21	   A^2 -> H(U1(e, a), U1(k, d))
28.43/9.21	   A^2 -> H(U1(e, a), U1(d, k))
28.43/9.21	   A^2 -> H(U1(k, a), U1(e, b))
28.43/9.21	   A^2 -> H(U1(k, a), U1(k, b))
28.43/9.21	   A^2 -> H(U1(k, a), U1(c, d))
28.43/9.21	   A^2 -> H(U1(k, a), U1(d, c))
28.43/9.21	   A^2 -> H(U1(k, a), U1(b, e))
28.43/9.21	   A^2 -> H(U1(k, a), U1(b, k))
28.43/9.21	   A^2 -> H(U1(k, a), U1(e, c))
28.43/9.21	   A^2 -> H(U1(k, a), U1(k, c))
28.43/9.21	   A^2 -> H(U1(k, a), U1(c, e))
28.43/9.21	   A^2 -> H(U1(k, a), U1(c, k))
28.43/9.21	   A^2 -> H(U1(k, a), U1(e, e))
28.43/9.21	   A^2 -> H(U1(k, a), U1(k, k))
28.43/9.21	   A^2 -> H(U1(k, a), U1(k, d))
28.43/9.21	   A^2 -> H(U1(k, a), U1(d, k))
28.43/9.21	   A^2 -> H(U1(c, d), U1(e, b))
28.43/9.21	   A^2 -> H(U1(c, d), U1(k, b))
28.43/9.21	   A^2 -> H(U1(c, d), U1(c, d))
28.43/9.21	   A^2 -> H(U1(c, d), U1(d, c))
28.43/9.21	   A^2 -> H(U1(c, d), U1(b, e))
28.43/9.21	   A^2 -> H(U1(c, d), U1(b, k))
28.43/9.21	   A^2 -> H(U1(c, d), U1(e, c))
28.43/9.21	   A^2 -> H(U1(c, d), U1(k, c))
28.43/9.21	   A^2 -> H(U1(c, d), U1(c, e))
28.43/9.21	   A^2 -> H(U1(c, d), U1(c, k))
28.43/9.21	   A^2 -> H(U1(c, d), U1(e, e))
28.43/9.21	   A^2 -> H(U1(c, d), U1(k, k))
28.43/9.21	   A^2 -> H(U1(c, d), U1(k, d))
28.43/9.21	   A^2 -> H(U1(c, d), U1(d, k))
28.43/9.21	   A^2 -> H(U1(c, a), b)
28.43/9.21	   A^2 -> H(U1(c, a), U1(e, d))
28.43/9.21	   A^2 -> H(U1(c, a), U1(d, e))
28.43/9.21	   A^2 -> H(U1(c, a), c)
28.43/9.21	   A^2 -> H(U1(c, a), U1(e, k))
28.43/9.21	   A^2 -> H(U1(c, a), U1(k, e))
28.43/9.21	   A^2 -> H(U1(c, a), e)
28.43/9.21	   A^2 -> H(U1(c, a), U1(k, k))
28.43/9.21	   A^2 -> H(U1(d, e), U1(c, b))
28.43/9.21	   A^2 -> H(U1(d, e), U1(d, b))
28.43/9.21	   A^2 -> H(U1(d, e), U1(b, c))
28.43/9.21	   A^2 -> H(U1(d, e), U1(b, d))
28.43/9.21	   A^2 -> H(U1(d, e), U1(c, c))
28.43/9.21	   A^2 -> H(U1(d, e), f(e))
28.43/9.21	   A^2 -> H(U1(d, e), f(k))
28.43/9.21	   A^2 -> H(U1(d, e), U1(d, d))
28.43/9.21	   A^2 -> H(U1(d, c), U1(e, b))
28.43/9.21	   A^2 -> H(U1(d, c), U1(k, b))
28.43/9.21	   A^2 -> H(U1(d, c), U1(c, d))
28.43/9.21	   A^2 -> H(U1(d, c), U1(d, c))
28.43/9.21	   A^2 -> H(U1(d, c), U1(b, e))
28.43/9.21	   A^2 -> H(U1(d, c), U1(b, k))
28.43/9.21	   A^2 -> H(U1(d, c), U1(e, c))
28.43/9.21	   A^2 -> H(U1(d, c), U1(k, c))
28.43/9.21	   A^2 -> H(U1(d, c), U1(c, e))
28.43/9.21	   A^2 -> H(U1(d, c), U1(c, k))
28.43/9.21	   A^2 -> H(U1(d, c), U1(e, e))
28.43/9.21	   A^2 -> H(U1(d, c), U1(k, k))
28.43/9.21	   A^2 -> H(U1(d, c), U1(k, d))
28.43/9.21	   A^2 -> H(U1(d, c), U1(d, k))
28.43/9.21	   A^2 -> H(U1(d, a), b)
28.43/9.21	   A^2 -> H(U1(d, a), U1(e, d))
28.43/9.21	   A^2 -> H(U1(d, a), U1(d, e))
28.43/9.21	   A^2 -> H(U1(d, a), c)
28.43/9.21	   A^2 -> H(U1(d, a), U1(e, k))
28.43/9.21	   A^2 -> H(U1(d, a), U1(k, e))
28.43/9.21	   A^2 -> H(U1(d, a), e)
28.43/9.21	   A^2 -> H(U1(d, a), U1(k, k))
28.43/9.21	   A^2 -> H(U1(a, e), U1(e, b))
28.43/9.21	   A^2 -> H(U1(a, e), U1(k, b))
28.43/9.21	   A^2 -> H(U1(a, e), U1(c, d))
28.43/9.21	   A^2 -> H(U1(a, e), U1(d, c))
28.43/9.21	   A^2 -> H(U1(a, e), U1(b, e))
28.43/9.21	   A^2 -> H(U1(a, e), U1(b, k))
28.43/9.21	   A^2 -> H(U1(a, e), U1(e, c))
28.43/9.21	   A^2 -> H(U1(a, e), U1(k, c))
28.43/9.21	   A^2 -> H(U1(a, e), U1(c, e))
28.43/9.21	   A^2 -> H(U1(a, e), U1(c, k))
28.43/9.21	   A^2 -> H(U1(a, e), U1(e, e))
28.43/9.21	   A^2 -> H(U1(a, e), U1(k, k))
28.43/9.21	   A^2 -> H(U1(a, e), U1(k, d))
28.43/9.21	   A^2 -> H(U1(a, e), U1(d, k))
28.43/9.21	   A^2 -> H(U1(a, k), U1(e, b))
28.43/9.21	   A^2 -> H(U1(a, k), U1(k, b))
28.43/9.21	   A^2 -> H(U1(a, k), U1(c, d))
28.43/9.21	   A^2 -> H(U1(a, k), U1(d, c))
28.43/9.21	   A^2 -> H(U1(a, k), U1(b, e))
28.43/9.21	   A^2 -> H(U1(a, k), U1(b, k))
28.43/9.21	   A^2 -> H(U1(a, k), U1(e, c))
28.43/9.21	   A^2 -> H(U1(a, k), U1(k, c))
28.43/9.21	   A^2 -> H(U1(a, k), U1(c, e))
28.43/9.21	   A^2 -> H(U1(a, k), U1(c, k))
28.43/9.21	   A^2 -> H(U1(a, k), U1(e, e))
28.43/9.21	   A^2 -> H(U1(a, k), U1(k, k))
28.43/9.21	   A^2 -> H(U1(a, k), U1(k, d))
28.43/9.21	   A^2 -> H(U1(a, k), U1(d, k))
28.43/9.21	   A^2 -> H(U1(a, c), b)
28.43/9.21	   A^2 -> H(U1(a, c), U1(e, d))
28.43/9.21	   A^2 -> H(U1(a, c), U1(d, e))
28.43/9.21	   A^2 -> H(U1(a, c), c)
28.43/9.21	   A^2 -> H(U1(a, c), U1(e, k))
28.43/9.21	   A^2 -> H(U1(a, c), U1(k, e))
28.43/9.21	   A^2 -> H(U1(a, c), e)
28.43/9.21	   A^2 -> H(U1(a, c), U1(k, k))
28.43/9.21	   A^2 -> H(U1(a, d), b)
28.43/9.21	   A^2 -> H(U1(a, d), U1(e, d))
28.43/9.21	   A^2 -> H(U1(a, d), U1(d, e))
28.43/9.21	   A^2 -> H(U1(a, d), c)
28.43/9.21	   A^2 -> H(U1(a, d), U1(e, k))
28.43/9.21	   A^2 -> H(U1(a, d), U1(k, e))
28.43/9.21	   A^2 -> H(U1(a, d), e)
28.43/9.21	   A^2 -> H(U1(a, d), U1(k, k))
28.43/9.21	   A^2 -> H(U1(a, a), d)
28.43/9.21	   A^2 -> H(U1(a, a), k)
28.43/9.21	   A^2 -> H(k, U1(b, b))
28.43/9.21	   A^2 -> H(k, f(c))
28.43/9.21	   A^2 -> H(k, f(d))
28.43/9.21	   A^2 -> H(c, U1(c, b))
28.43/9.21	   A^2 -> H(c, U1(d, b))
28.43/9.21	   A^2 -> H(c, U1(b, c))
28.43/9.21	   A^2 -> H(c, U1(b, d))
28.43/9.21	   A^2 -> H(c, U1(c, c))
28.43/9.21	   A^2 -> H(c, f(e))
28.43/9.21	   A^2 -> H(c, f(k))
28.43/9.21	   A^2 -> H(c, U1(d, d))
28.43/9.21	   A^2 -> H(U1(e, k), U1(c, b))
28.43/9.21	   A^2 -> H(U1(e, k), U1(d, b))
28.43/9.21	   A^2 -> H(U1(e, k), U1(b, c))
28.43/9.21	   A^2 -> H(U1(e, k), U1(b, d))
28.43/9.21	   A^2 -> H(U1(e, k), U1(c, c))
28.43/9.21	   A^2 -> H(U1(e, k), f(e))
28.43/9.21	   A^2 -> H(U1(e, k), f(k))
28.43/9.21	   A^2 -> H(U1(e, k), U1(d, d))
28.43/9.21	   A^2 -> H(U1(e, c), U1(e, b))
28.43/9.21	   A^2 -> H(U1(e, c), U1(k, b))
28.43/9.21	   A^2 -> H(U1(e, c), U1(c, d))
28.43/9.21	   A^2 -> H(U1(e, c), U1(d, c))
28.43/9.21	   A^2 -> H(U1(e, c), U1(b, e))
28.43/9.21	   A^2 -> H(U1(e, c), U1(b, k))
28.43/9.21	   A^2 -> H(U1(e, c), U1(e, c))
28.43/9.21	   A^2 -> H(U1(e, c), U1(k, c))
28.43/9.21	   A^2 -> H(U1(e, c), U1(c, e))
28.43/9.21	   A^2 -> H(U1(e, c), U1(c, k))
28.43/9.21	   A^2 -> H(U1(e, c), U1(e, e))
28.43/9.21	   A^2 -> H(U1(e, c), U1(k, k))
28.43/9.21	   A^2 -> H(U1(e, c), U1(k, d))
28.43/9.21	   A^2 -> H(U1(e, c), U1(d, k))
28.43/9.21	   A^2 -> H(U1(k, e), U1(c, b))
28.43/9.21	   A^2 -> H(U1(k, e), U1(d, b))
28.43/9.21	   A^2 -> H(U1(k, e), U1(b, c))
28.43/9.21	   A^2 -> H(U1(k, e), U1(b, d))
28.43/9.21	   A^2 -> H(U1(k, e), U1(c, c))
28.43/9.21	   A^2 -> H(U1(k, e), f(e))
28.43/9.21	   A^2 -> H(U1(k, e), f(k))
28.43/9.21	   A^2 -> H(U1(k, e), U1(d, d))
28.43/9.21	   A^2 -> H(U1(k, c), U1(e, b))
28.43/9.21	   A^2 -> H(U1(k, c), U1(k, b))
28.43/9.21	   A^2 -> H(U1(k, c), U1(c, d))
28.43/9.21	   A^2 -> H(U1(k, c), U1(d, c))
28.43/9.21	
28.43/9.21	The TRS R consists of the following rules:
28.43/9.21	
28.43/9.21	   f(x) -> U1(x, x)
28.43/9.21	   U1(e, x) -> x
28.43/9.21	   a -> c
28.43/9.21	   a -> d
28.43/9.21	   b -> c
28.43/9.21	   b -> d
28.43/9.21	   d -> k
28.43/9.21	   c -> e
28.43/9.21	   c -> k
28.43/9.21	
28.43/9.21	Q is empty.
28.43/9.21	We have to consider all minimal (P,Q,R)-chains.
28.43/9.21	----------------------------------------
28.43/9.21	
28.43/9.21	(825) TransformationProof (EQUIVALENT)
28.43/9.21	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
28.43/9.21	
28.43/9.21	   (A^2 -> H(U1(k, e), U1(b, c)),A^2 -> H(U1(k, e), U1(b, c)))
28.43/9.21	   (A^2 -> H(U1(k, k), U1(b, c)),A^2 -> H(U1(k, k), U1(b, c)))
28.43/9.21	   (A^2 -> H(U1(k, c), U1(c, c)),A^2 -> H(U1(k, c), U1(c, c)))
28.43/9.21	   (A^2 -> H(U1(k, c), U1(d, c)),A^2 -> H(U1(k, c), U1(d, c)))
28.43/9.21	   (A^2 -> H(U1(k, c), U1(b, e)),A^2 -> H(U1(k, c), U1(b, e)))
28.43/9.21	   (A^2 -> H(U1(k, c), U1(b, k)),A^2 -> H(U1(k, c), U1(b, k)))
28.43/9.21	
28.43/9.21	
28.43/9.21	----------------------------------------
28.43/9.21	
28.43/9.21	(826)
28.43/9.21	Obligation:
28.43/9.21	Q DP problem:
28.43/9.21	The TRS P consists of the following rules:
28.43/9.21	
28.43/9.21	   H(x, x) -> G(x, x, f(k))
28.43/9.21	   G(d, x, x) -> A^2
28.43/9.21	   A^2 -> H(f(c), f(c))
28.43/9.21	   A^2 -> H(f(d), f(d))
28.43/9.21	   A^2 -> H(U1(c, c), U1(c, c))
28.43/9.21	   A^2 -> H(f(e), f(e))
28.43/9.21	   A^2 -> H(f(k), f(k))
28.43/9.21	   A^2 -> H(U1(d, d), U1(d, d))
28.43/9.21	   A^2 -> H(U1(k, c), U1(b, d))
28.43/9.21	   A^2 -> H(U1(k, c), U1(c, c))
28.43/9.21	   A^2 -> H(U1(k, c), f(e))
28.43/9.21	   A^2 -> H(U1(k, c), f(k))
28.43/9.21	   A^2 -> H(U1(k, c), U1(d, d))
28.43/9.21	   A^2 -> H(U1(c, e), U1(c, b))
28.43/9.21	   A^2 -> H(U1(c, e), U1(d, b))
28.43/9.21	   A^2 -> H(U1(c, e), U1(b, c))
28.43/9.21	   A^2 -> H(U1(c, e), U1(b, d))
28.43/9.21	   A^2 -> H(U1(c, e), U1(c, c))
28.43/9.21	   A^2 -> H(U1(c, e), f(e))
28.43/9.21	   A^2 -> H(U1(c, e), f(k))
28.43/9.21	   A^2 -> H(U1(c, e), U1(d, d))
28.43/9.21	   A^2 -> H(U1(c, k), U1(c, b))
28.43/9.21	   A^2 -> H(U1(c, k), U1(d, b))
28.43/9.21	   A^2 -> H(U1(c, k), U1(b, c))
28.43/9.21	   A^2 -> H(U1(c, k), U1(b, d))
28.43/9.21	   A^2 -> H(U1(c, k), U1(c, c))
28.43/9.21	   A^2 -> H(U1(c, k), f(e))
28.43/9.21	   A^2 -> H(U1(c, k), f(k))
28.43/9.21	   A^2 -> H(U1(c, k), U1(d, d))
28.43/9.21	   A^2 -> H(U1(c, c), U1(e, b))
28.43/9.21	   A^2 -> H(U1(c, c), U1(k, b))
28.43/9.21	   A^2 -> H(U1(c, c), U1(c, d))
28.43/9.21	   A^2 -> H(U1(c, c), U1(d, c))
28.43/9.21	   A^2 -> H(U1(c, c), U1(b, e))
28.43/9.21	   A^2 -> H(U1(c, c), U1(b, k))
28.43/9.21	   A^2 -> H(U1(c, c), U1(e, e))
28.43/9.21	   A^2 -> H(U1(c, c), U1(k, k))
28.43/9.21	   A^2 -> H(U1(c, c), U1(k, d))
28.43/9.21	   A^2 -> H(U1(c, c), U1(d, k))
28.43/9.21	   A^2 -> H(e, U1(b, b))
28.43/9.21	   A^2 -> H(e, f(c))
28.43/9.21	   A^2 -> H(e, f(d))
28.43/9.21	   A^2 -> H(U1(e, e), U1(c, b))
28.43/9.21	   A^2 -> H(U1(e, e), U1(d, b))
28.43/9.21	   A^2 -> H(U1(e, e), U1(b, c))
28.43/9.21	   A^2 -> H(U1(e, e), U1(b, d))
28.43/9.21	   A^2 -> H(U1(e, e), U1(c, c))
28.43/9.21	   A^2 -> H(U1(e, e), f(e))
28.43/9.21	   A^2 -> H(U1(e, e), f(k))
28.43/9.21	   A^2 -> H(U1(e, e), U1(d, d))
28.43/9.21	   A^2 -> H(f(e), U1(e, b))
28.43/9.21	   A^2 -> H(f(e), U1(k, b))
28.43/9.21	   A^2 -> H(f(e), U1(c, d))
28.43/9.21	   A^2 -> H(f(e), U1(d, c))
28.43/9.21	   A^2 -> H(f(e), U1(b, e))
28.43/9.21	   A^2 -> H(f(e), U1(b, k))
28.43/9.21	   A^2 -> H(f(e), U1(e, c))
28.43/9.21	   A^2 -> H(f(e), U1(k, c))
28.43/9.21	   A^2 -> H(f(e), U1(c, e))
28.43/9.21	   A^2 -> H(f(e), U1(c, k))
28.43/9.21	   A^2 -> H(f(e), U1(k, k))
28.43/9.21	   A^2 -> H(f(e), U1(k, d))
28.43/9.21	   A^2 -> H(f(e), U1(d, k))
28.43/9.21	   A^2 -> H(U1(k, k), U1(c, b))
28.43/9.21	   A^2 -> H(U1(k, k), U1(d, b))
28.43/9.21	   A^2 -> H(U1(k, k), U1(b, c))
28.43/9.21	   A^2 -> H(U1(k, k), U1(b, d))
28.43/9.21	   A^2 -> H(U1(k, k), U1(c, c))
28.43/9.21	   A^2 -> H(U1(k, k), f(e))
28.43/9.21	   A^2 -> H(U1(k, k), f(k))
28.43/9.21	   A^2 -> H(U1(k, k), U1(d, d))
28.43/9.21	   A^2 -> H(f(k), U1(e, b))
28.43/9.21	   A^2 -> H(f(k), U1(k, b))
28.43/9.21	   A^2 -> H(f(k), U1(c, d))
28.43/9.21	   A^2 -> H(f(k), U1(d, c))
28.43/9.21	   A^2 -> H(f(k), U1(b, e))
28.43/9.21	   A^2 -> H(f(k), U1(b, k))
28.43/9.21	   A^2 -> H(f(k), U1(e, c))
28.43/9.21	   A^2 -> H(f(k), U1(k, c))
28.43/9.21	   A^2 -> H(f(k), U1(c, e))
28.43/9.21	   A^2 -> H(f(k), U1(c, k))
28.43/9.21	   A^2 -> H(f(k), U1(e, e))
28.43/9.21	   A^2 -> H(f(k), U1(k, d))
28.43/9.21	   A^2 -> H(f(k), U1(d, k))
28.43/9.21	   A^2 -> H(f(c), b)
28.43/9.21	   A^2 -> H(f(c), U1(e, d))
28.43/9.21	   A^2 -> H(f(c), U1(d, e))
28.43/9.21	   A^2 -> H(f(k), U1(k, k))
28.43/9.21	   A^2 -> H(U1(k, k), U1(b, b))
28.43/9.21	   A^2 -> H(U1(k, k), f(c))
28.43/9.21	   A^2 -> H(U1(k, k), f(d))
28.43/9.21	   A^2 -> H(U1(k, d), U1(c, b))
28.43/9.21	   A^2 -> H(U1(k, d), U1(d, b))
28.43/9.21	   A^2 -> H(U1(k, d), U1(b, c))
28.43/9.21	   A^2 -> H(U1(k, d), U1(b, d))
28.43/9.21	   A^2 -> H(U1(k, d), U1(c, c))
28.43/9.21	   A^2 -> H(U1(k, d), f(e))
28.43/9.21	   A^2 -> H(U1(k, d), f(k))
28.43/9.21	   A^2 -> H(U1(k, d), U1(d, d))
28.43/9.21	   A^2 -> H(U1(d, k), U1(c, b))
28.43/9.21	   A^2 -> H(U1(d, k), U1(d, b))
28.43/9.21	   A^2 -> H(U1(d, k), U1(b, c))
28.43/9.21	   A^2 -> H(U1(d, k), U1(b, d))
28.43/9.21	   A^2 -> H(U1(d, k), U1(c, c))
28.43/9.21	   A^2 -> H(U1(d, k), f(e))
28.43/9.21	   A^2 -> H(U1(d, k), f(k))
28.43/9.21	   A^2 -> H(U1(d, k), U1(d, d))
28.43/9.21	   A^2 -> H(U1(d, d), U1(e, b))
28.43/9.21	   A^2 -> H(U1(d, d), U1(k, b))
28.43/9.21	   A^2 -> H(U1(d, d), U1(c, d))
28.43/9.21	   A^2 -> H(U1(d, d), U1(d, c))
28.43/9.21	   A^2 -> H(U1(d, d), U1(b, e))
28.43/9.21	   A^2 -> H(U1(d, d), U1(b, k))
28.43/9.21	   A^2 -> H(U1(d, d), U1(e, c))
28.43/9.21	   A^2 -> H(U1(d, d), U1(k, c))
28.43/9.21	   A^2 -> H(U1(d, d), U1(c, e))
28.43/9.21	   A^2 -> H(U1(d, d), U1(c, k))
28.43/9.21	   A^2 -> H(U1(d, d), U1(e, e))
28.43/9.21	   A^2 -> H(U1(d, d), U1(k, k))
28.43/9.21	   A^2 -> H(f(d), b)
28.43/9.21	   A^2 -> H(f(d), U1(e, d))
28.43/9.21	   A^2 -> H(f(d), U1(d, e))
28.43/9.21	   A^2 -> H(f(d), c)
28.43/9.21	   A^2 -> H(f(d), U1(e, k))
28.43/9.21	   A^2 -> H(f(d), U1(k, e))
28.43/9.21	   A^2 -> H(f(d), e)
28.43/9.21	   A^2 -> H(f(a), d)
28.43/9.21	   A^2 -> H(U1(c, c), U1(e, c))
28.43/9.21	   A^2 -> H(f(c), c)
28.43/9.21	   A^2 -> H(f(c), U1(e, k))
28.43/9.21	   A^2 -> H(U1(c, c), U1(k, c))
28.43/9.21	   A^2 -> H(f(c), U1(k, e))
28.43/9.21	   A^2 -> H(f(c), U1(k, k))
28.43/9.21	   A^2 -> H(U1(c, c), U1(c, e))
28.43/9.21	   A^2 -> H(U1(c, c), U1(c, k))
28.43/9.21	   A^2 -> H(f(a), k)
28.43/9.21	   A^2 -> H(f(e), U1(e, e))
28.43/9.21	   A^2 -> H(f(c), e)
28.43/9.21	   A^2 -> H(U1(d, d), U1(k, d))
28.43/9.21	   A^2 -> H(f(d), U1(k, k))
28.43/9.21	   A^2 -> H(U1(d, d), U1(d, k))
28.43/9.21	   A^2 -> H(d, U1(b, b))
28.43/9.21	   A^2 -> H(d, f(c))
28.43/9.21	   A^2 -> H(d, f(d))
28.43/9.21	   A^2 -> H(a, U1(c, b))
28.43/9.21	   A^2 -> H(a, U1(d, b))
28.43/9.21	   A^2 -> H(a, U1(b, c))
28.43/9.21	   A^2 -> H(a, U1(b, d))
28.43/9.21	   A^2 -> H(a, U1(c, c))
28.43/9.21	   A^2 -> H(a, f(e))
28.43/9.21	   A^2 -> H(a, f(k))
28.43/9.21	   A^2 -> H(a, U1(d, d))
28.43/9.21	   A^2 -> H(U1(e, d), U1(c, b))
28.43/9.21	   A^2 -> H(U1(e, d), U1(d, b))
28.43/9.21	   A^2 -> H(U1(e, d), U1(b, c))
28.43/9.21	   A^2 -> H(U1(e, d), U1(b, d))
28.43/9.21	   A^2 -> H(U1(e, d), U1(c, c))
28.43/9.21	   A^2 -> H(U1(e, d), f(e))
28.43/9.21	   A^2 -> H(U1(e, d), f(k))
28.43/9.21	   A^2 -> H(U1(e, d), U1(d, d))
28.43/9.21	   A^2 -> H(U1(e, a), U1(e, b))
28.43/9.21	   A^2 -> H(U1(e, a), U1(k, b))
28.43/9.21	   A^2 -> H(U1(e, a), U1(c, d))
28.43/9.21	   A^2 -> H(U1(e, a), U1(d, c))
28.43/9.21	   A^2 -> H(U1(e, a), U1(b, e))
28.43/9.21	   A^2 -> H(U1(e, a), U1(b, k))
28.43/9.21	   A^2 -> H(U1(e, a), U1(e, c))
28.43/9.21	   A^2 -> H(U1(e, a), U1(k, c))
28.43/9.21	   A^2 -> H(U1(e, a), U1(c, e))
28.43/9.21	   A^2 -> H(U1(e, a), U1(c, k))
28.43/9.21	   A^2 -> H(U1(e, a), U1(e, e))
28.43/9.21	   A^2 -> H(U1(e, a), U1(k, k))
28.43/9.21	   A^2 -> H(U1(e, a), U1(k, d))
28.43/9.21	   A^2 -> H(U1(e, a), U1(d, k))
28.43/9.21	   A^2 -> H(U1(k, a), U1(e, b))
28.43/9.21	   A^2 -> H(U1(k, a), U1(k, b))
28.43/9.21	   A^2 -> H(U1(k, a), U1(c, d))
28.43/9.21	   A^2 -> H(U1(k, a), U1(d, c))
28.43/9.21	   A^2 -> H(U1(k, a), U1(b, e))
28.43/9.21	   A^2 -> H(U1(k, a), U1(b, k))
28.43/9.21	   A^2 -> H(U1(k, a), U1(e, c))
28.43/9.21	   A^2 -> H(U1(k, a), U1(k, c))
28.43/9.21	   A^2 -> H(U1(k, a), U1(c, e))
28.43/9.21	   A^2 -> H(U1(k, a), U1(c, k))
28.43/9.21	   A^2 -> H(U1(k, a), U1(e, e))
28.43/9.21	   A^2 -> H(U1(k, a), U1(k, k))
28.43/9.21	   A^2 -> H(U1(k, a), U1(k, d))
28.43/9.21	   A^2 -> H(U1(k, a), U1(d, k))
28.43/9.21	   A^2 -> H(U1(c, d), U1(e, b))
28.43/9.21	   A^2 -> H(U1(c, d), U1(k, b))
28.43/9.21	   A^2 -> H(U1(c, d), U1(c, d))
28.43/9.21	   A^2 -> H(U1(c, d), U1(d, c))
28.43/9.21	   A^2 -> H(U1(c, d), U1(b, e))
28.43/9.21	   A^2 -> H(U1(c, d), U1(b, k))
28.43/9.21	   A^2 -> H(U1(c, d), U1(e, c))
28.43/9.21	   A^2 -> H(U1(c, d), U1(k, c))
28.43/9.21	   A^2 -> H(U1(c, d), U1(c, e))
28.43/9.21	   A^2 -> H(U1(c, d), U1(c, k))
28.43/9.21	   A^2 -> H(U1(c, d), U1(e, e))
28.43/9.21	   A^2 -> H(U1(c, d), U1(k, k))
28.43/9.21	   A^2 -> H(U1(c, d), U1(k, d))
28.43/9.21	   A^2 -> H(U1(c, d), U1(d, k))
28.43/9.21	   A^2 -> H(U1(c, a), b)
28.43/9.21	   A^2 -> H(U1(c, a), U1(e, d))
28.43/9.21	   A^2 -> H(U1(c, a), U1(d, e))
28.43/9.21	   A^2 -> H(U1(c, a), c)
28.43/9.21	   A^2 -> H(U1(c, a), U1(e, k))
28.43/9.21	   A^2 -> H(U1(c, a), U1(k, e))
28.43/9.21	   A^2 -> H(U1(c, a), e)
28.43/9.21	   A^2 -> H(U1(c, a), U1(k, k))
28.43/9.21	   A^2 -> H(U1(d, e), U1(c, b))
28.43/9.21	   A^2 -> H(U1(d, e), U1(d, b))
28.43/9.21	   A^2 -> H(U1(d, e), U1(b, c))
28.43/9.21	   A^2 -> H(U1(d, e), U1(b, d))
28.43/9.21	   A^2 -> H(U1(d, e), U1(c, c))
28.43/9.21	   A^2 -> H(U1(d, e), f(e))
28.43/9.21	   A^2 -> H(U1(d, e), f(k))
28.43/9.21	   A^2 -> H(U1(d, e), U1(d, d))
28.43/9.21	   A^2 -> H(U1(d, c), U1(e, b))
28.43/9.21	   A^2 -> H(U1(d, c), U1(k, b))
28.43/9.21	   A^2 -> H(U1(d, c), U1(c, d))
28.43/9.21	   A^2 -> H(U1(d, c), U1(d, c))
28.43/9.21	   A^2 -> H(U1(d, c), U1(b, e))
28.43/9.21	   A^2 -> H(U1(d, c), U1(b, k))
28.43/9.21	   A^2 -> H(U1(d, c), U1(e, c))
28.43/9.21	   A^2 -> H(U1(d, c), U1(k, c))
28.43/9.21	   A^2 -> H(U1(d, c), U1(c, e))
28.43/9.21	   A^2 -> H(U1(d, c), U1(c, k))
28.43/9.21	   A^2 -> H(U1(d, c), U1(e, e))
28.43/9.21	   A^2 -> H(U1(d, c), U1(k, k))
28.43/9.21	   A^2 -> H(U1(d, c), U1(k, d))
28.43/9.21	   A^2 -> H(U1(d, c), U1(d, k))
28.43/9.21	   A^2 -> H(U1(d, a), b)
28.43/9.21	   A^2 -> H(U1(d, a), U1(e, d))
28.43/9.21	   A^2 -> H(U1(d, a), U1(d, e))
28.43/9.21	   A^2 -> H(U1(d, a), c)
28.43/9.21	   A^2 -> H(U1(d, a), U1(e, k))
28.43/9.21	   A^2 -> H(U1(d, a), U1(k, e))
28.43/9.22	   A^2 -> H(U1(d, a), e)
28.43/9.22	   A^2 -> H(U1(d, a), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, e), U1(e, b))
28.43/9.22	   A^2 -> H(U1(a, e), U1(k, b))
28.43/9.22	   A^2 -> H(U1(a, e), U1(c, d))
28.43/9.22	   A^2 -> H(U1(a, e), U1(d, c))
28.43/9.22	   A^2 -> H(U1(a, e), U1(b, e))
28.43/9.22	   A^2 -> H(U1(a, e), U1(b, k))
28.43/9.22	   A^2 -> H(U1(a, e), U1(e, c))
28.43/9.22	   A^2 -> H(U1(a, e), U1(k, c))
28.43/9.22	   A^2 -> H(U1(a, e), U1(c, e))
28.43/9.22	   A^2 -> H(U1(a, e), U1(c, k))
28.43/9.22	   A^2 -> H(U1(a, e), U1(e, e))
28.43/9.22	   A^2 -> H(U1(a, e), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, e), U1(k, d))
28.43/9.22	   A^2 -> H(U1(a, e), U1(d, k))
28.43/9.22	   A^2 -> H(U1(a, k), U1(e, b))
28.43/9.22	   A^2 -> H(U1(a, k), U1(k, b))
28.43/9.22	   A^2 -> H(U1(a, k), U1(c, d))
28.43/9.22	   A^2 -> H(U1(a, k), U1(d, c))
28.43/9.22	   A^2 -> H(U1(a, k), U1(b, e))
28.43/9.22	   A^2 -> H(U1(a, k), U1(b, k))
28.43/9.22	   A^2 -> H(U1(a, k), U1(e, c))
28.43/9.22	   A^2 -> H(U1(a, k), U1(k, c))
28.43/9.22	   A^2 -> H(U1(a, k), U1(c, e))
28.43/9.22	   A^2 -> H(U1(a, k), U1(c, k))
28.43/9.22	   A^2 -> H(U1(a, k), U1(e, e))
28.43/9.22	   A^2 -> H(U1(a, k), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, k), U1(k, d))
28.43/9.22	   A^2 -> H(U1(a, k), U1(d, k))
28.43/9.22	   A^2 -> H(U1(a, c), b)
28.43/9.22	   A^2 -> H(U1(a, c), U1(e, d))
28.43/9.22	   A^2 -> H(U1(a, c), U1(d, e))
28.43/9.22	   A^2 -> H(U1(a, c), c)
28.43/9.22	   A^2 -> H(U1(a, c), U1(e, k))
28.43/9.22	   A^2 -> H(U1(a, c), U1(k, e))
28.43/9.22	   A^2 -> H(U1(a, c), e)
28.43/9.22	   A^2 -> H(U1(a, c), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, d), b)
28.43/9.22	   A^2 -> H(U1(a, d), U1(e, d))
28.43/9.22	   A^2 -> H(U1(a, d), U1(d, e))
28.43/9.22	   A^2 -> H(U1(a, d), c)
28.43/9.22	   A^2 -> H(U1(a, d), U1(e, k))
28.43/9.22	   A^2 -> H(U1(a, d), U1(k, e))
28.43/9.22	   A^2 -> H(U1(a, d), e)
28.43/9.22	   A^2 -> H(U1(a, d), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, a), d)
28.43/9.22	   A^2 -> H(U1(a, a), k)
28.43/9.22	   A^2 -> H(k, U1(b, b))
28.43/9.22	   A^2 -> H(k, f(c))
28.43/9.22	   A^2 -> H(k, f(d))
28.43/9.22	   A^2 -> H(c, U1(c, b))
28.43/9.22	   A^2 -> H(c, U1(d, b))
28.43/9.22	   A^2 -> H(c, U1(b, c))
28.43/9.22	   A^2 -> H(c, U1(b, d))
28.43/9.22	   A^2 -> H(c, U1(c, c))
28.43/9.22	   A^2 -> H(c, f(e))
28.43/9.22	   A^2 -> H(c, f(k))
28.43/9.22	   A^2 -> H(c, U1(d, d))
28.43/9.22	   A^2 -> H(U1(e, k), U1(c, b))
28.43/9.22	   A^2 -> H(U1(e, k), U1(d, b))
28.43/9.22	   A^2 -> H(U1(e, k), U1(b, c))
28.43/9.22	   A^2 -> H(U1(e, k), U1(b, d))
28.43/9.22	   A^2 -> H(U1(e, k), U1(c, c))
28.43/9.22	   A^2 -> H(U1(e, k), f(e))
28.43/9.22	   A^2 -> H(U1(e, k), f(k))
28.43/9.22	   A^2 -> H(U1(e, k), U1(d, d))
28.43/9.22	   A^2 -> H(U1(e, c), U1(e, b))
28.43/9.22	   A^2 -> H(U1(e, c), U1(k, b))
28.43/9.22	   A^2 -> H(U1(e, c), U1(c, d))
28.43/9.22	   A^2 -> H(U1(e, c), U1(d, c))
28.43/9.22	   A^2 -> H(U1(e, c), U1(b, e))
28.43/9.22	   A^2 -> H(U1(e, c), U1(b, k))
28.43/9.22	   A^2 -> H(U1(e, c), U1(e, c))
28.43/9.22	   A^2 -> H(U1(e, c), U1(k, c))
28.43/9.22	   A^2 -> H(U1(e, c), U1(c, e))
28.43/9.22	   A^2 -> H(U1(e, c), U1(c, k))
28.43/9.22	   A^2 -> H(U1(e, c), U1(e, e))
28.43/9.22	   A^2 -> H(U1(e, c), U1(k, k))
28.43/9.22	   A^2 -> H(U1(e, c), U1(k, d))
28.43/9.22	   A^2 -> H(U1(e, c), U1(d, k))
28.43/9.22	   A^2 -> H(U1(k, e), U1(c, b))
28.43/9.22	   A^2 -> H(U1(k, e), U1(d, b))
28.43/9.22	   A^2 -> H(U1(k, e), U1(b, c))
28.43/9.22	   A^2 -> H(U1(k, e), U1(b, d))
28.43/9.22	   A^2 -> H(U1(k, e), U1(c, c))
28.43/9.22	   A^2 -> H(U1(k, e), f(e))
28.43/9.22	   A^2 -> H(U1(k, e), f(k))
28.43/9.22	   A^2 -> H(U1(k, e), U1(d, d))
28.43/9.22	   A^2 -> H(U1(k, c), U1(e, b))
28.43/9.22	   A^2 -> H(U1(k, c), U1(k, b))
28.43/9.22	   A^2 -> H(U1(k, c), U1(c, d))
28.43/9.22	   A^2 -> H(U1(k, c), U1(d, c))
28.43/9.22	   A^2 -> H(U1(k, c), U1(b, e))
28.43/9.22	   A^2 -> H(U1(k, c), U1(b, k))
28.43/9.22	
28.43/9.22	The TRS R consists of the following rules:
28.43/9.22	
28.43/9.22	   f(x) -> U1(x, x)
28.43/9.22	   U1(e, x) -> x
28.43/9.22	   a -> c
28.43/9.22	   a -> d
28.43/9.22	   b -> c
28.43/9.22	   b -> d
28.43/9.22	   d -> k
28.43/9.22	   c -> e
28.43/9.22	   c -> k
28.43/9.22	
28.43/9.22	Q is empty.
28.43/9.22	We have to consider all minimal (P,Q,R)-chains.
28.43/9.22	----------------------------------------
28.43/9.22	
28.43/9.22	(827) TransformationProof (EQUIVALENT)
28.43/9.22	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
28.43/9.22	
28.43/9.22	   (A^2 -> H(U1(k, e), U1(b, d)),A^2 -> H(U1(k, e), U1(b, d)))
28.43/9.22	   (A^2 -> H(U1(k, k), U1(b, d)),A^2 -> H(U1(k, k), U1(b, d)))
28.43/9.22	   (A^2 -> H(U1(k, c), U1(c, d)),A^2 -> H(U1(k, c), U1(c, d)))
28.43/9.22	   (A^2 -> H(U1(k, c), U1(d, d)),A^2 -> H(U1(k, c), U1(d, d)))
28.43/9.22	   (A^2 -> H(U1(k, c), U1(b, k)),A^2 -> H(U1(k, c), U1(b, k)))
28.43/9.22	
28.43/9.22	
28.43/9.22	----------------------------------------
28.43/9.22	
28.43/9.22	(828)
28.43/9.22	Obligation:
28.43/9.22	Q DP problem:
28.43/9.22	The TRS P consists of the following rules:
28.43/9.22	
28.43/9.22	   H(x, x) -> G(x, x, f(k))
28.43/9.22	   G(d, x, x) -> A^2
28.43/9.22	   A^2 -> H(f(c), f(c))
28.43/9.22	   A^2 -> H(f(d), f(d))
28.43/9.22	   A^2 -> H(U1(c, c), U1(c, c))
28.43/9.22	   A^2 -> H(f(e), f(e))
28.43/9.22	   A^2 -> H(f(k), f(k))
28.43/9.22	   A^2 -> H(U1(d, d), U1(d, d))
28.43/9.22	   A^2 -> H(U1(k, c), U1(c, c))
28.43/9.22	   A^2 -> H(U1(k, c), f(e))
28.43/9.22	   A^2 -> H(U1(k, c), f(k))
28.43/9.22	   A^2 -> H(U1(k, c), U1(d, d))
28.43/9.22	   A^2 -> H(U1(c, e), U1(c, b))
28.43/9.22	   A^2 -> H(U1(c, e), U1(d, b))
28.43/9.22	   A^2 -> H(U1(c, e), U1(b, c))
28.43/9.22	   A^2 -> H(U1(c, e), U1(b, d))
28.43/9.22	   A^2 -> H(U1(c, e), U1(c, c))
28.43/9.22	   A^2 -> H(U1(c, e), f(e))
28.43/9.22	   A^2 -> H(U1(c, e), f(k))
28.43/9.22	   A^2 -> H(U1(c, e), U1(d, d))
28.43/9.22	   A^2 -> H(U1(c, k), U1(c, b))
28.43/9.22	   A^2 -> H(U1(c, k), U1(d, b))
28.43/9.22	   A^2 -> H(U1(c, k), U1(b, c))
28.43/9.22	   A^2 -> H(U1(c, k), U1(b, d))
28.43/9.22	   A^2 -> H(U1(c, k), U1(c, c))
28.43/9.22	   A^2 -> H(U1(c, k), f(e))
28.43/9.22	   A^2 -> H(U1(c, k), f(k))
28.43/9.22	   A^2 -> H(U1(c, k), U1(d, d))
28.43/9.22	   A^2 -> H(U1(c, c), U1(e, b))
28.43/9.22	   A^2 -> H(U1(c, c), U1(k, b))
28.43/9.22	   A^2 -> H(U1(c, c), U1(c, d))
28.43/9.22	   A^2 -> H(U1(c, c), U1(d, c))
28.43/9.22	   A^2 -> H(U1(c, c), U1(b, e))
28.43/9.22	   A^2 -> H(U1(c, c), U1(b, k))
28.43/9.22	   A^2 -> H(U1(c, c), U1(e, e))
28.43/9.22	   A^2 -> H(U1(c, c), U1(k, k))
28.43/9.22	   A^2 -> H(U1(c, c), U1(k, d))
28.43/9.22	   A^2 -> H(U1(c, c), U1(d, k))
28.43/9.22	   A^2 -> H(e, U1(b, b))
28.43/9.22	   A^2 -> H(e, f(c))
28.43/9.22	   A^2 -> H(e, f(d))
28.43/9.22	   A^2 -> H(U1(e, e), U1(c, b))
28.43/9.22	   A^2 -> H(U1(e, e), U1(d, b))
28.43/9.22	   A^2 -> H(U1(e, e), U1(b, c))
28.43/9.22	   A^2 -> H(U1(e, e), U1(b, d))
28.43/9.22	   A^2 -> H(U1(e, e), U1(c, c))
28.43/9.22	   A^2 -> H(U1(e, e), f(e))
28.43/9.22	   A^2 -> H(U1(e, e), f(k))
28.43/9.22	   A^2 -> H(U1(e, e), U1(d, d))
28.43/9.22	   A^2 -> H(f(e), U1(e, b))
28.43/9.22	   A^2 -> H(f(e), U1(k, b))
28.43/9.22	   A^2 -> H(f(e), U1(c, d))
28.43/9.22	   A^2 -> H(f(e), U1(d, c))
28.43/9.22	   A^2 -> H(f(e), U1(b, e))
28.43/9.22	   A^2 -> H(f(e), U1(b, k))
28.43/9.22	   A^2 -> H(f(e), U1(e, c))
28.43/9.22	   A^2 -> H(f(e), U1(k, c))
28.43/9.22	   A^2 -> H(f(e), U1(c, e))
28.43/9.22	   A^2 -> H(f(e), U1(c, k))
28.43/9.22	   A^2 -> H(f(e), U1(k, k))
28.43/9.22	   A^2 -> H(f(e), U1(k, d))
28.43/9.22	   A^2 -> H(f(e), U1(d, k))
28.43/9.22	   A^2 -> H(U1(k, k), U1(c, b))
28.43/9.22	   A^2 -> H(U1(k, k), U1(d, b))
28.43/9.22	   A^2 -> H(U1(k, k), U1(b, c))
28.43/9.22	   A^2 -> H(U1(k, k), U1(b, d))
28.43/9.22	   A^2 -> H(U1(k, k), U1(c, c))
28.43/9.22	   A^2 -> H(U1(k, k), f(e))
28.43/9.22	   A^2 -> H(U1(k, k), f(k))
28.43/9.22	   A^2 -> H(U1(k, k), U1(d, d))
28.43/9.22	   A^2 -> H(f(k), U1(e, b))
28.43/9.22	   A^2 -> H(f(k), U1(k, b))
28.43/9.22	   A^2 -> H(f(k), U1(c, d))
28.43/9.22	   A^2 -> H(f(k), U1(d, c))
28.43/9.22	   A^2 -> H(f(k), U1(b, e))
28.43/9.22	   A^2 -> H(f(k), U1(b, k))
28.43/9.22	   A^2 -> H(f(k), U1(e, c))
28.43/9.22	   A^2 -> H(f(k), U1(k, c))
28.43/9.22	   A^2 -> H(f(k), U1(c, e))
28.43/9.22	   A^2 -> H(f(k), U1(c, k))
28.43/9.22	   A^2 -> H(f(k), U1(e, e))
28.43/9.22	   A^2 -> H(f(k), U1(k, d))
28.43/9.22	   A^2 -> H(f(k), U1(d, k))
28.43/9.22	   A^2 -> H(f(c), b)
28.43/9.22	   A^2 -> H(f(c), U1(e, d))
28.43/9.22	   A^2 -> H(f(c), U1(d, e))
28.43/9.22	   A^2 -> H(f(k), U1(k, k))
28.43/9.22	   A^2 -> H(U1(k, k), U1(b, b))
28.43/9.22	   A^2 -> H(U1(k, k), f(c))
28.43/9.22	   A^2 -> H(U1(k, k), f(d))
28.43/9.22	   A^2 -> H(U1(k, d), U1(c, b))
28.43/9.22	   A^2 -> H(U1(k, d), U1(d, b))
28.43/9.22	   A^2 -> H(U1(k, d), U1(b, c))
28.43/9.22	   A^2 -> H(U1(k, d), U1(b, d))
28.43/9.22	   A^2 -> H(U1(k, d), U1(c, c))
28.43/9.22	   A^2 -> H(U1(k, d), f(e))
28.43/9.22	   A^2 -> H(U1(k, d), f(k))
28.43/9.22	   A^2 -> H(U1(k, d), U1(d, d))
28.43/9.22	   A^2 -> H(U1(d, k), U1(c, b))
28.43/9.22	   A^2 -> H(U1(d, k), U1(d, b))
28.43/9.22	   A^2 -> H(U1(d, k), U1(b, c))
28.43/9.22	   A^2 -> H(U1(d, k), U1(b, d))
28.43/9.22	   A^2 -> H(U1(d, k), U1(c, c))
28.43/9.22	   A^2 -> H(U1(d, k), f(e))
28.43/9.22	   A^2 -> H(U1(d, k), f(k))
28.43/9.22	   A^2 -> H(U1(d, k), U1(d, d))
28.43/9.22	   A^2 -> H(U1(d, d), U1(e, b))
28.43/9.22	   A^2 -> H(U1(d, d), U1(k, b))
28.43/9.22	   A^2 -> H(U1(d, d), U1(c, d))
28.43/9.22	   A^2 -> H(U1(d, d), U1(d, c))
28.43/9.22	   A^2 -> H(U1(d, d), U1(b, e))
28.43/9.22	   A^2 -> H(U1(d, d), U1(b, k))
28.43/9.22	   A^2 -> H(U1(d, d), U1(e, c))
28.43/9.22	   A^2 -> H(U1(d, d), U1(k, c))
28.43/9.22	   A^2 -> H(U1(d, d), U1(c, e))
28.43/9.22	   A^2 -> H(U1(d, d), U1(c, k))
28.43/9.22	   A^2 -> H(U1(d, d), U1(e, e))
28.43/9.22	   A^2 -> H(U1(d, d), U1(k, k))
28.43/9.22	   A^2 -> H(f(d), b)
28.43/9.22	   A^2 -> H(f(d), U1(e, d))
28.43/9.22	   A^2 -> H(f(d), U1(d, e))
28.43/9.22	   A^2 -> H(f(d), c)
28.43/9.22	   A^2 -> H(f(d), U1(e, k))
28.43/9.22	   A^2 -> H(f(d), U1(k, e))
28.43/9.22	   A^2 -> H(f(d), e)
28.43/9.22	   A^2 -> H(f(a), d)
28.43/9.22	   A^2 -> H(U1(c, c), U1(e, c))
28.43/9.22	   A^2 -> H(f(c), c)
28.43/9.22	   A^2 -> H(f(c), U1(e, k))
28.43/9.22	   A^2 -> H(U1(c, c), U1(k, c))
28.43/9.22	   A^2 -> H(f(c), U1(k, e))
28.43/9.22	   A^2 -> H(f(c), U1(k, k))
28.43/9.22	   A^2 -> H(U1(c, c), U1(c, e))
28.43/9.22	   A^2 -> H(U1(c, c), U1(c, k))
28.43/9.22	   A^2 -> H(f(a), k)
28.43/9.22	   A^2 -> H(f(e), U1(e, e))
28.43/9.22	   A^2 -> H(f(c), e)
28.43/9.22	   A^2 -> H(U1(d, d), U1(k, d))
28.43/9.22	   A^2 -> H(f(d), U1(k, k))
28.43/9.22	   A^2 -> H(U1(d, d), U1(d, k))
28.43/9.22	   A^2 -> H(d, U1(b, b))
28.43/9.22	   A^2 -> H(d, f(c))
28.43/9.22	   A^2 -> H(d, f(d))
28.43/9.22	   A^2 -> H(a, U1(c, b))
28.43/9.22	   A^2 -> H(a, U1(d, b))
28.43/9.22	   A^2 -> H(a, U1(b, c))
28.43/9.22	   A^2 -> H(a, U1(b, d))
28.43/9.22	   A^2 -> H(a, U1(c, c))
28.43/9.22	   A^2 -> H(a, f(e))
28.43/9.22	   A^2 -> H(a, f(k))
28.43/9.22	   A^2 -> H(a, U1(d, d))
28.43/9.22	   A^2 -> H(U1(e, d), U1(c, b))
28.43/9.22	   A^2 -> H(U1(e, d), U1(d, b))
28.43/9.22	   A^2 -> H(U1(e, d), U1(b, c))
28.43/9.22	   A^2 -> H(U1(e, d), U1(b, d))
28.43/9.22	   A^2 -> H(U1(e, d), U1(c, c))
28.43/9.22	   A^2 -> H(U1(e, d), f(e))
28.43/9.22	   A^2 -> H(U1(e, d), f(k))
28.43/9.22	   A^2 -> H(U1(e, d), U1(d, d))
28.43/9.22	   A^2 -> H(U1(e, a), U1(e, b))
28.43/9.22	   A^2 -> H(U1(e, a), U1(k, b))
28.43/9.22	   A^2 -> H(U1(e, a), U1(c, d))
28.43/9.22	   A^2 -> H(U1(e, a), U1(d, c))
28.43/9.22	   A^2 -> H(U1(e, a), U1(b, e))
28.43/9.22	   A^2 -> H(U1(e, a), U1(b, k))
28.43/9.22	   A^2 -> H(U1(e, a), U1(e, c))
28.43/9.22	   A^2 -> H(U1(e, a), U1(k, c))
28.43/9.22	   A^2 -> H(U1(e, a), U1(c, e))
28.43/9.22	   A^2 -> H(U1(e, a), U1(c, k))
28.43/9.22	   A^2 -> H(U1(e, a), U1(e, e))
28.43/9.22	   A^2 -> H(U1(e, a), U1(k, k))
28.43/9.22	   A^2 -> H(U1(e, a), U1(k, d))
28.43/9.22	   A^2 -> H(U1(e, a), U1(d, k))
28.43/9.22	   A^2 -> H(U1(k, a), U1(e, b))
28.43/9.22	   A^2 -> H(U1(k, a), U1(k, b))
28.43/9.22	   A^2 -> H(U1(k, a), U1(c, d))
28.43/9.22	   A^2 -> H(U1(k, a), U1(d, c))
28.43/9.22	   A^2 -> H(U1(k, a), U1(b, e))
28.43/9.22	   A^2 -> H(U1(k, a), U1(b, k))
28.43/9.22	   A^2 -> H(U1(k, a), U1(e, c))
28.43/9.22	   A^2 -> H(U1(k, a), U1(k, c))
28.43/9.22	   A^2 -> H(U1(k, a), U1(c, e))
28.43/9.22	   A^2 -> H(U1(k, a), U1(c, k))
28.43/9.22	   A^2 -> H(U1(k, a), U1(e, e))
28.43/9.22	   A^2 -> H(U1(k, a), U1(k, k))
28.43/9.22	   A^2 -> H(U1(k, a), U1(k, d))
28.43/9.22	   A^2 -> H(U1(k, a), U1(d, k))
28.43/9.22	   A^2 -> H(U1(c, d), U1(e, b))
28.43/9.22	   A^2 -> H(U1(c, d), U1(k, b))
28.43/9.22	   A^2 -> H(U1(c, d), U1(c, d))
28.43/9.22	   A^2 -> H(U1(c, d), U1(d, c))
28.43/9.22	   A^2 -> H(U1(c, d), U1(b, e))
28.43/9.22	   A^2 -> H(U1(c, d), U1(b, k))
28.43/9.22	   A^2 -> H(U1(c, d), U1(e, c))
28.43/9.22	   A^2 -> H(U1(c, d), U1(k, c))
28.43/9.22	   A^2 -> H(U1(c, d), U1(c, e))
28.43/9.22	   A^2 -> H(U1(c, d), U1(c, k))
28.43/9.22	   A^2 -> H(U1(c, d), U1(e, e))
28.43/9.22	   A^2 -> H(U1(c, d), U1(k, k))
28.43/9.22	   A^2 -> H(U1(c, d), U1(k, d))
28.43/9.22	   A^2 -> H(U1(c, d), U1(d, k))
28.43/9.22	   A^2 -> H(U1(c, a), b)
28.43/9.22	   A^2 -> H(U1(c, a), U1(e, d))
28.43/9.22	   A^2 -> H(U1(c, a), U1(d, e))
28.43/9.22	   A^2 -> H(U1(c, a), c)
28.43/9.22	   A^2 -> H(U1(c, a), U1(e, k))
28.43/9.22	   A^2 -> H(U1(c, a), U1(k, e))
28.43/9.22	   A^2 -> H(U1(c, a), e)
28.43/9.22	   A^2 -> H(U1(c, a), U1(k, k))
28.43/9.22	   A^2 -> H(U1(d, e), U1(c, b))
28.43/9.22	   A^2 -> H(U1(d, e), U1(d, b))
28.43/9.22	   A^2 -> H(U1(d, e), U1(b, c))
28.43/9.22	   A^2 -> H(U1(d, e), U1(b, d))
28.43/9.22	   A^2 -> H(U1(d, e), U1(c, c))
28.43/9.22	   A^2 -> H(U1(d, e), f(e))
28.43/9.22	   A^2 -> H(U1(d, e), f(k))
28.43/9.22	   A^2 -> H(U1(d, e), U1(d, d))
28.43/9.22	   A^2 -> H(U1(d, c), U1(e, b))
28.43/9.22	   A^2 -> H(U1(d, c), U1(k, b))
28.43/9.22	   A^2 -> H(U1(d, c), U1(c, d))
28.43/9.22	   A^2 -> H(U1(d, c), U1(d, c))
28.43/9.22	   A^2 -> H(U1(d, c), U1(b, e))
28.43/9.22	   A^2 -> H(U1(d, c), U1(b, k))
28.43/9.22	   A^2 -> H(U1(d, c), U1(e, c))
28.43/9.22	   A^2 -> H(U1(d, c), U1(k, c))
28.43/9.22	   A^2 -> H(U1(d, c), U1(c, e))
28.43/9.22	   A^2 -> H(U1(d, c), U1(c, k))
28.43/9.22	   A^2 -> H(U1(d, c), U1(e, e))
28.43/9.22	   A^2 -> H(U1(d, c), U1(k, k))
28.43/9.22	   A^2 -> H(U1(d, c), U1(k, d))
28.43/9.22	   A^2 -> H(U1(d, c), U1(d, k))
28.43/9.22	   A^2 -> H(U1(d, a), b)
28.43/9.22	   A^2 -> H(U1(d, a), U1(e, d))
28.43/9.22	   A^2 -> H(U1(d, a), U1(d, e))
28.43/9.22	   A^2 -> H(U1(d, a), c)
28.43/9.22	   A^2 -> H(U1(d, a), U1(e, k))
28.43/9.22	   A^2 -> H(U1(d, a), U1(k, e))
28.43/9.22	   A^2 -> H(U1(d, a), e)
28.43/9.22	   A^2 -> H(U1(d, a), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, e), U1(e, b))
28.43/9.22	   A^2 -> H(U1(a, e), U1(k, b))
28.43/9.22	   A^2 -> H(U1(a, e), U1(c, d))
28.43/9.22	   A^2 -> H(U1(a, e), U1(d, c))
28.43/9.22	   A^2 -> H(U1(a, e), U1(b, e))
28.43/9.22	   A^2 -> H(U1(a, e), U1(b, k))
28.43/9.22	   A^2 -> H(U1(a, e), U1(e, c))
28.43/9.22	   A^2 -> H(U1(a, e), U1(k, c))
28.43/9.22	   A^2 -> H(U1(a, e), U1(c, e))
28.43/9.22	   A^2 -> H(U1(a, e), U1(c, k))
28.43/9.22	   A^2 -> H(U1(a, e), U1(e, e))
28.43/9.22	   A^2 -> H(U1(a, e), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, e), U1(k, d))
28.43/9.22	   A^2 -> H(U1(a, e), U1(d, k))
28.43/9.22	   A^2 -> H(U1(a, k), U1(e, b))
28.43/9.22	   A^2 -> H(U1(a, k), U1(k, b))
28.43/9.22	   A^2 -> H(U1(a, k), U1(c, d))
28.43/9.22	   A^2 -> H(U1(a, k), U1(d, c))
28.43/9.22	   A^2 -> H(U1(a, k), U1(b, e))
28.43/9.22	   A^2 -> H(U1(a, k), U1(b, k))
28.43/9.22	   A^2 -> H(U1(a, k), U1(e, c))
28.43/9.22	   A^2 -> H(U1(a, k), U1(k, c))
28.43/9.22	   A^2 -> H(U1(a, k), U1(c, e))
28.43/9.22	   A^2 -> H(U1(a, k), U1(c, k))
28.43/9.22	   A^2 -> H(U1(a, k), U1(e, e))
28.43/9.22	   A^2 -> H(U1(a, k), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, k), U1(k, d))
28.43/9.22	   A^2 -> H(U1(a, k), U1(d, k))
28.43/9.22	   A^2 -> H(U1(a, c), b)
28.43/9.22	   A^2 -> H(U1(a, c), U1(e, d))
28.43/9.22	   A^2 -> H(U1(a, c), U1(d, e))
28.43/9.22	   A^2 -> H(U1(a, c), c)
28.43/9.22	   A^2 -> H(U1(a, c), U1(e, k))
28.43/9.22	   A^2 -> H(U1(a, c), U1(k, e))
28.43/9.22	   A^2 -> H(U1(a, c), e)
28.43/9.22	   A^2 -> H(U1(a, c), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, d), b)
28.43/9.22	   A^2 -> H(U1(a, d), U1(e, d))
28.43/9.22	   A^2 -> H(U1(a, d), U1(d, e))
28.43/9.22	   A^2 -> H(U1(a, d), c)
28.43/9.22	   A^2 -> H(U1(a, d), U1(e, k))
28.43/9.22	   A^2 -> H(U1(a, d), U1(k, e))
28.43/9.22	   A^2 -> H(U1(a, d), e)
28.43/9.22	   A^2 -> H(U1(a, d), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, a), d)
28.43/9.22	   A^2 -> H(U1(a, a), k)
28.43/9.22	   A^2 -> H(k, U1(b, b))
28.43/9.22	   A^2 -> H(k, f(c))
28.43/9.22	   A^2 -> H(k, f(d))
28.43/9.22	   A^2 -> H(c, U1(c, b))
28.43/9.22	   A^2 -> H(c, U1(d, b))
28.43/9.22	   A^2 -> H(c, U1(b, c))
28.43/9.22	   A^2 -> H(c, U1(b, d))
28.43/9.22	   A^2 -> H(c, U1(c, c))
28.43/9.22	   A^2 -> H(c, f(e))
28.43/9.22	   A^2 -> H(c, f(k))
28.43/9.22	   A^2 -> H(c, U1(d, d))
28.43/9.22	   A^2 -> H(U1(e, k), U1(c, b))
28.43/9.22	   A^2 -> H(U1(e, k), U1(d, b))
28.43/9.22	   A^2 -> H(U1(e, k), U1(b, c))
28.43/9.22	   A^2 -> H(U1(e, k), U1(b, d))
28.43/9.22	   A^2 -> H(U1(e, k), U1(c, c))
28.43/9.22	   A^2 -> H(U1(e, k), f(e))
28.43/9.22	   A^2 -> H(U1(e, k), f(k))
28.43/9.22	   A^2 -> H(U1(e, k), U1(d, d))
28.43/9.22	   A^2 -> H(U1(e, c), U1(e, b))
28.43/9.22	   A^2 -> H(U1(e, c), U1(k, b))
28.43/9.22	   A^2 -> H(U1(e, c), U1(c, d))
28.43/9.22	   A^2 -> H(U1(e, c), U1(d, c))
28.43/9.22	   A^2 -> H(U1(e, c), U1(b, e))
28.43/9.22	   A^2 -> H(U1(e, c), U1(b, k))
28.43/9.22	   A^2 -> H(U1(e, c), U1(e, c))
28.43/9.22	   A^2 -> H(U1(e, c), U1(k, c))
28.43/9.22	   A^2 -> H(U1(e, c), U1(c, e))
28.43/9.22	   A^2 -> H(U1(e, c), U1(c, k))
28.43/9.22	   A^2 -> H(U1(e, c), U1(e, e))
28.43/9.22	   A^2 -> H(U1(e, c), U1(k, k))
28.43/9.22	   A^2 -> H(U1(e, c), U1(k, d))
28.43/9.22	   A^2 -> H(U1(e, c), U1(d, k))
28.43/9.22	   A^2 -> H(U1(k, e), U1(c, b))
28.43/9.22	   A^2 -> H(U1(k, e), U1(d, b))
28.43/9.22	   A^2 -> H(U1(k, e), U1(b, c))
28.43/9.22	   A^2 -> H(U1(k, e), U1(b, d))
28.43/9.22	   A^2 -> H(U1(k, e), U1(c, c))
28.43/9.22	   A^2 -> H(U1(k, e), f(e))
28.43/9.22	   A^2 -> H(U1(k, e), f(k))
28.43/9.22	   A^2 -> H(U1(k, e), U1(d, d))
28.43/9.22	   A^2 -> H(U1(k, c), U1(e, b))
28.43/9.22	   A^2 -> H(U1(k, c), U1(k, b))
28.43/9.22	   A^2 -> H(U1(k, c), U1(c, d))
28.43/9.22	   A^2 -> H(U1(k, c), U1(d, c))
28.43/9.22	   A^2 -> H(U1(k, c), U1(b, e))
28.43/9.22	   A^2 -> H(U1(k, c), U1(b, k))
28.43/9.22	
28.43/9.22	The TRS R consists of the following rules:
28.43/9.22	
28.43/9.22	   f(x) -> U1(x, x)
28.43/9.22	   U1(e, x) -> x
28.43/9.22	   a -> c
28.43/9.22	   a -> d
28.43/9.22	   b -> c
28.43/9.22	   b -> d
28.43/9.22	   d -> k
28.43/9.22	   c -> e
28.43/9.22	   c -> k
28.43/9.22	
28.43/9.22	Q is empty.
28.43/9.22	We have to consider all minimal (P,Q,R)-chains.
28.43/9.22	----------------------------------------
28.43/9.22	
28.43/9.22	(829) TransformationProof (EQUIVALENT)
28.43/9.22	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
28.43/9.22	
28.43/9.22	   (A^2 -> H(U1(k, e), U1(c, c)),A^2 -> H(U1(k, e), U1(c, c)))
28.43/9.22	   (A^2 -> H(U1(k, k), U1(c, c)),A^2 -> H(U1(k, k), U1(c, c)))
28.43/9.22	   (A^2 -> H(U1(k, c), U1(e, c)),A^2 -> H(U1(k, c), U1(e, c)))
28.43/9.22	   (A^2 -> H(U1(k, c), U1(k, c)),A^2 -> H(U1(k, c), U1(k, c)))
28.43/9.22	   (A^2 -> H(U1(k, c), U1(c, e)),A^2 -> H(U1(k, c), U1(c, e)))
28.43/9.22	   (A^2 -> H(U1(k, c), U1(c, k)),A^2 -> H(U1(k, c), U1(c, k)))
28.43/9.22	
28.43/9.22	
28.43/9.22	----------------------------------------
28.43/9.22	
28.43/9.22	(830)
28.43/9.22	Obligation:
28.43/9.22	Q DP problem:
28.43/9.22	The TRS P consists of the following rules:
28.43/9.22	
28.43/9.22	   H(x, x) -> G(x, x, f(k))
28.43/9.22	   G(d, x, x) -> A^2
28.43/9.22	   A^2 -> H(f(c), f(c))
28.43/9.22	   A^2 -> H(f(d), f(d))
28.43/9.22	   A^2 -> H(U1(c, c), U1(c, c))
28.43/9.22	   A^2 -> H(f(e), f(e))
28.43/9.22	   A^2 -> H(f(k), f(k))
28.43/9.22	   A^2 -> H(U1(d, d), U1(d, d))
28.43/9.22	   A^2 -> H(U1(k, c), f(e))
28.43/9.22	   A^2 -> H(U1(k, c), f(k))
28.43/9.22	   A^2 -> H(U1(k, c), U1(d, d))
28.43/9.22	   A^2 -> H(U1(c, e), U1(c, b))
28.43/9.22	   A^2 -> H(U1(c, e), U1(d, b))
28.43/9.22	   A^2 -> H(U1(c, e), U1(b, c))
28.43/9.22	   A^2 -> H(U1(c, e), U1(b, d))
28.43/9.22	   A^2 -> H(U1(c, e), U1(c, c))
28.43/9.22	   A^2 -> H(U1(c, e), f(e))
28.43/9.22	   A^2 -> H(U1(c, e), f(k))
28.43/9.22	   A^2 -> H(U1(c, e), U1(d, d))
28.43/9.22	   A^2 -> H(U1(c, k), U1(c, b))
28.43/9.22	   A^2 -> H(U1(c, k), U1(d, b))
28.43/9.22	   A^2 -> H(U1(c, k), U1(b, c))
28.43/9.22	   A^2 -> H(U1(c, k), U1(b, d))
28.43/9.22	   A^2 -> H(U1(c, k), U1(c, c))
28.43/9.22	   A^2 -> H(U1(c, k), f(e))
28.43/9.22	   A^2 -> H(U1(c, k), f(k))
28.43/9.22	   A^2 -> H(U1(c, k), U1(d, d))
28.43/9.22	   A^2 -> H(U1(c, c), U1(e, b))
28.43/9.22	   A^2 -> H(U1(c, c), U1(k, b))
28.43/9.22	   A^2 -> H(U1(c, c), U1(c, d))
28.43/9.22	   A^2 -> H(U1(c, c), U1(d, c))
28.43/9.22	   A^2 -> H(U1(c, c), U1(b, e))
28.43/9.22	   A^2 -> H(U1(c, c), U1(b, k))
28.43/9.22	   A^2 -> H(U1(c, c), U1(e, e))
28.43/9.22	   A^2 -> H(U1(c, c), U1(k, k))
28.43/9.22	   A^2 -> H(U1(c, c), U1(k, d))
28.43/9.22	   A^2 -> H(U1(c, c), U1(d, k))
28.43/9.22	   A^2 -> H(e, U1(b, b))
28.43/9.22	   A^2 -> H(e, f(c))
28.43/9.22	   A^2 -> H(e, f(d))
28.43/9.22	   A^2 -> H(U1(e, e), U1(c, b))
28.43/9.22	   A^2 -> H(U1(e, e), U1(d, b))
28.43/9.22	   A^2 -> H(U1(e, e), U1(b, c))
28.43/9.22	   A^2 -> H(U1(e, e), U1(b, d))
28.43/9.22	   A^2 -> H(U1(e, e), U1(c, c))
28.43/9.22	   A^2 -> H(U1(e, e), f(e))
28.43/9.22	   A^2 -> H(U1(e, e), f(k))
28.43/9.22	   A^2 -> H(U1(e, e), U1(d, d))
28.43/9.22	   A^2 -> H(f(e), U1(e, b))
28.43/9.22	   A^2 -> H(f(e), U1(k, b))
28.43/9.22	   A^2 -> H(f(e), U1(c, d))
28.43/9.22	   A^2 -> H(f(e), U1(d, c))
28.43/9.22	   A^2 -> H(f(e), U1(b, e))
28.43/9.22	   A^2 -> H(f(e), U1(b, k))
28.43/9.22	   A^2 -> H(f(e), U1(e, c))
28.43/9.22	   A^2 -> H(f(e), U1(k, c))
28.43/9.22	   A^2 -> H(f(e), U1(c, e))
28.43/9.22	   A^2 -> H(f(e), U1(c, k))
28.43/9.22	   A^2 -> H(f(e), U1(k, k))
28.43/9.22	   A^2 -> H(f(e), U1(k, d))
28.43/9.22	   A^2 -> H(f(e), U1(d, k))
28.43/9.22	   A^2 -> H(U1(k, k), U1(c, b))
28.43/9.22	   A^2 -> H(U1(k, k), U1(d, b))
28.43/9.22	   A^2 -> H(U1(k, k), U1(b, c))
28.43/9.22	   A^2 -> H(U1(k, k), U1(b, d))
28.43/9.22	   A^2 -> H(U1(k, k), U1(c, c))
28.43/9.22	   A^2 -> H(U1(k, k), f(e))
28.43/9.22	   A^2 -> H(U1(k, k), f(k))
28.43/9.22	   A^2 -> H(U1(k, k), U1(d, d))
28.43/9.22	   A^2 -> H(f(k), U1(e, b))
28.43/9.22	   A^2 -> H(f(k), U1(k, b))
28.43/9.22	   A^2 -> H(f(k), U1(c, d))
28.43/9.22	   A^2 -> H(f(k), U1(d, c))
28.43/9.22	   A^2 -> H(f(k), U1(b, e))
28.43/9.22	   A^2 -> H(f(k), U1(b, k))
28.43/9.22	   A^2 -> H(f(k), U1(e, c))
28.43/9.22	   A^2 -> H(f(k), U1(k, c))
28.43/9.22	   A^2 -> H(f(k), U1(c, e))
28.43/9.22	   A^2 -> H(f(k), U1(c, k))
28.43/9.22	   A^2 -> H(f(k), U1(e, e))
28.43/9.22	   A^2 -> H(f(k), U1(k, d))
28.43/9.22	   A^2 -> H(f(k), U1(d, k))
28.43/9.22	   A^2 -> H(f(c), b)
28.43/9.22	   A^2 -> H(f(c), U1(e, d))
28.43/9.22	   A^2 -> H(f(c), U1(d, e))
28.43/9.22	   A^2 -> H(f(k), U1(k, k))
28.43/9.22	   A^2 -> H(U1(k, k), U1(b, b))
28.43/9.22	   A^2 -> H(U1(k, k), f(c))
28.43/9.22	   A^2 -> H(U1(k, k), f(d))
28.43/9.22	   A^2 -> H(U1(k, d), U1(c, b))
28.43/9.22	   A^2 -> H(U1(k, d), U1(d, b))
28.43/9.22	   A^2 -> H(U1(k, d), U1(b, c))
28.43/9.22	   A^2 -> H(U1(k, d), U1(b, d))
28.43/9.22	   A^2 -> H(U1(k, d), U1(c, c))
28.43/9.22	   A^2 -> H(U1(k, d), f(e))
28.43/9.22	   A^2 -> H(U1(k, d), f(k))
28.43/9.22	   A^2 -> H(U1(k, d), U1(d, d))
28.43/9.22	   A^2 -> H(U1(d, k), U1(c, b))
28.43/9.22	   A^2 -> H(U1(d, k), U1(d, b))
28.43/9.22	   A^2 -> H(U1(d, k), U1(b, c))
28.43/9.22	   A^2 -> H(U1(d, k), U1(b, d))
28.43/9.22	   A^2 -> H(U1(d, k), U1(c, c))
28.43/9.22	   A^2 -> H(U1(d, k), f(e))
28.43/9.22	   A^2 -> H(U1(d, k), f(k))
28.43/9.22	   A^2 -> H(U1(d, k), U1(d, d))
28.43/9.22	   A^2 -> H(U1(d, d), U1(e, b))
28.43/9.22	   A^2 -> H(U1(d, d), U1(k, b))
28.43/9.22	   A^2 -> H(U1(d, d), U1(c, d))
28.43/9.22	   A^2 -> H(U1(d, d), U1(d, c))
28.43/9.22	   A^2 -> H(U1(d, d), U1(b, e))
28.43/9.22	   A^2 -> H(U1(d, d), U1(b, k))
28.43/9.22	   A^2 -> H(U1(d, d), U1(e, c))
28.43/9.22	   A^2 -> H(U1(d, d), U1(k, c))
28.43/9.22	   A^2 -> H(U1(d, d), U1(c, e))
28.43/9.22	   A^2 -> H(U1(d, d), U1(c, k))
28.43/9.22	   A^2 -> H(U1(d, d), U1(e, e))
28.43/9.22	   A^2 -> H(U1(d, d), U1(k, k))
28.43/9.22	   A^2 -> H(f(d), b)
28.43/9.22	   A^2 -> H(f(d), U1(e, d))
28.43/9.22	   A^2 -> H(f(d), U1(d, e))
28.43/9.22	   A^2 -> H(f(d), c)
28.43/9.22	   A^2 -> H(f(d), U1(e, k))
28.43/9.22	   A^2 -> H(f(d), U1(k, e))
28.43/9.22	   A^2 -> H(f(d), e)
28.43/9.22	   A^2 -> H(f(a), d)
28.43/9.22	   A^2 -> H(U1(c, c), U1(e, c))
28.43/9.22	   A^2 -> H(f(c), c)
28.43/9.22	   A^2 -> H(f(c), U1(e, k))
28.43/9.22	   A^2 -> H(U1(c, c), U1(k, c))
28.43/9.22	   A^2 -> H(f(c), U1(k, e))
28.43/9.22	   A^2 -> H(f(c), U1(k, k))
28.43/9.22	   A^2 -> H(U1(c, c), U1(c, e))
28.43/9.22	   A^2 -> H(U1(c, c), U1(c, k))
28.43/9.22	   A^2 -> H(f(a), k)
28.43/9.22	   A^2 -> H(f(e), U1(e, e))
28.43/9.22	   A^2 -> H(f(c), e)
28.43/9.22	   A^2 -> H(U1(d, d), U1(k, d))
28.43/9.22	   A^2 -> H(f(d), U1(k, k))
28.43/9.22	   A^2 -> H(U1(d, d), U1(d, k))
28.43/9.22	   A^2 -> H(d, U1(b, b))
28.43/9.22	   A^2 -> H(d, f(c))
28.43/9.22	   A^2 -> H(d, f(d))
28.43/9.22	   A^2 -> H(a, U1(c, b))
28.43/9.22	   A^2 -> H(a, U1(d, b))
28.43/9.22	   A^2 -> H(a, U1(b, c))
28.43/9.22	   A^2 -> H(a, U1(b, d))
28.43/9.22	   A^2 -> H(a, U1(c, c))
28.43/9.22	   A^2 -> H(a, f(e))
28.43/9.22	   A^2 -> H(a, f(k))
28.43/9.22	   A^2 -> H(a, U1(d, d))
28.43/9.22	   A^2 -> H(U1(e, d), U1(c, b))
28.43/9.22	   A^2 -> H(U1(e, d), U1(d, b))
28.43/9.22	   A^2 -> H(U1(e, d), U1(b, c))
28.43/9.22	   A^2 -> H(U1(e, d), U1(b, d))
28.43/9.22	   A^2 -> H(U1(e, d), U1(c, c))
28.43/9.22	   A^2 -> H(U1(e, d), f(e))
28.43/9.22	   A^2 -> H(U1(e, d), f(k))
28.43/9.22	   A^2 -> H(U1(e, d), U1(d, d))
28.43/9.22	   A^2 -> H(U1(e, a), U1(e, b))
28.43/9.22	   A^2 -> H(U1(e, a), U1(k, b))
28.43/9.22	   A^2 -> H(U1(e, a), U1(c, d))
28.43/9.22	   A^2 -> H(U1(e, a), U1(d, c))
28.43/9.22	   A^2 -> H(U1(e, a), U1(b, e))
28.43/9.22	   A^2 -> H(U1(e, a), U1(b, k))
28.43/9.22	   A^2 -> H(U1(e, a), U1(e, c))
28.43/9.22	   A^2 -> H(U1(e, a), U1(k, c))
28.43/9.22	   A^2 -> H(U1(e, a), U1(c, e))
28.43/9.22	   A^2 -> H(U1(e, a), U1(c, k))
28.43/9.22	   A^2 -> H(U1(e, a), U1(e, e))
28.43/9.22	   A^2 -> H(U1(e, a), U1(k, k))
28.43/9.22	   A^2 -> H(U1(e, a), U1(k, d))
28.43/9.22	   A^2 -> H(U1(e, a), U1(d, k))
28.43/9.22	   A^2 -> H(U1(k, a), U1(e, b))
28.43/9.22	   A^2 -> H(U1(k, a), U1(k, b))
28.43/9.22	   A^2 -> H(U1(k, a), U1(c, d))
28.43/9.22	   A^2 -> H(U1(k, a), U1(d, c))
28.43/9.22	   A^2 -> H(U1(k, a), U1(b, e))
28.43/9.22	   A^2 -> H(U1(k, a), U1(b, k))
28.43/9.22	   A^2 -> H(U1(k, a), U1(e, c))
28.43/9.22	   A^2 -> H(U1(k, a), U1(k, c))
28.43/9.22	   A^2 -> H(U1(k, a), U1(c, e))
28.43/9.22	   A^2 -> H(U1(k, a), U1(c, k))
28.43/9.22	   A^2 -> H(U1(k, a), U1(e, e))
28.43/9.22	   A^2 -> H(U1(k, a), U1(k, k))
28.43/9.22	   A^2 -> H(U1(k, a), U1(k, d))
28.43/9.22	   A^2 -> H(U1(k, a), U1(d, k))
28.43/9.22	   A^2 -> H(U1(c, d), U1(e, b))
28.43/9.22	   A^2 -> H(U1(c, d), U1(k, b))
28.43/9.22	   A^2 -> H(U1(c, d), U1(c, d))
28.43/9.22	   A^2 -> H(U1(c, d), U1(d, c))
28.43/9.22	   A^2 -> H(U1(c, d), U1(b, e))
28.43/9.22	   A^2 -> H(U1(c, d), U1(b, k))
28.43/9.22	   A^2 -> H(U1(c, d), U1(e, c))
28.43/9.22	   A^2 -> H(U1(c, d), U1(k, c))
28.43/9.22	   A^2 -> H(U1(c, d), U1(c, e))
28.43/9.22	   A^2 -> H(U1(c, d), U1(c, k))
28.43/9.22	   A^2 -> H(U1(c, d), U1(e, e))
28.43/9.22	   A^2 -> H(U1(c, d), U1(k, k))
28.43/9.22	   A^2 -> H(U1(c, d), U1(k, d))
28.43/9.22	   A^2 -> H(U1(c, d), U1(d, k))
28.43/9.22	   A^2 -> H(U1(c, a), b)
28.43/9.22	   A^2 -> H(U1(c, a), U1(e, d))
28.43/9.22	   A^2 -> H(U1(c, a), U1(d, e))
28.43/9.22	   A^2 -> H(U1(c, a), c)
28.43/9.22	   A^2 -> H(U1(c, a), U1(e, k))
28.43/9.22	   A^2 -> H(U1(c, a), U1(k, e))
28.43/9.22	   A^2 -> H(U1(c, a), e)
28.43/9.22	   A^2 -> H(U1(c, a), U1(k, k))
28.43/9.22	   A^2 -> H(U1(d, e), U1(c, b))
28.43/9.22	   A^2 -> H(U1(d, e), U1(d, b))
28.43/9.22	   A^2 -> H(U1(d, e), U1(b, c))
28.43/9.22	   A^2 -> H(U1(d, e), U1(b, d))
28.43/9.22	   A^2 -> H(U1(d, e), U1(c, c))
28.43/9.22	   A^2 -> H(U1(d, e), f(e))
28.43/9.22	   A^2 -> H(U1(d, e), f(k))
28.43/9.22	   A^2 -> H(U1(d, e), U1(d, d))
28.43/9.22	   A^2 -> H(U1(d, c), U1(e, b))
28.43/9.22	   A^2 -> H(U1(d, c), U1(k, b))
28.43/9.22	   A^2 -> H(U1(d, c), U1(c, d))
28.43/9.22	   A^2 -> H(U1(d, c), U1(d, c))
28.43/9.22	   A^2 -> H(U1(d, c), U1(b, e))
28.43/9.22	   A^2 -> H(U1(d, c), U1(b, k))
28.43/9.22	   A^2 -> H(U1(d, c), U1(e, c))
28.43/9.22	   A^2 -> H(U1(d, c), U1(k, c))
28.43/9.22	   A^2 -> H(U1(d, c), U1(c, e))
28.43/9.22	   A^2 -> H(U1(d, c), U1(c, k))
28.43/9.22	   A^2 -> H(U1(d, c), U1(e, e))
28.43/9.22	   A^2 -> H(U1(d, c), U1(k, k))
28.43/9.22	   A^2 -> H(U1(d, c), U1(k, d))
28.43/9.22	   A^2 -> H(U1(d, c), U1(d, k))
28.43/9.22	   A^2 -> H(U1(d, a), b)
28.43/9.22	   A^2 -> H(U1(d, a), U1(e, d))
28.43/9.22	   A^2 -> H(U1(d, a), U1(d, e))
28.43/9.22	   A^2 -> H(U1(d, a), c)
28.43/9.22	   A^2 -> H(U1(d, a), U1(e, k))
28.43/9.22	   A^2 -> H(U1(d, a), U1(k, e))
28.43/9.22	   A^2 -> H(U1(d, a), e)
28.43/9.22	   A^2 -> H(U1(d, a), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, e), U1(e, b))
28.43/9.22	   A^2 -> H(U1(a, e), U1(k, b))
28.43/9.22	   A^2 -> H(U1(a, e), U1(c, d))
28.43/9.22	   A^2 -> H(U1(a, e), U1(d, c))
28.43/9.22	   A^2 -> H(U1(a, e), U1(b, e))
28.43/9.22	   A^2 -> H(U1(a, e), U1(b, k))
28.43/9.22	   A^2 -> H(U1(a, e), U1(e, c))
28.43/9.22	   A^2 -> H(U1(a, e), U1(k, c))
28.43/9.22	   A^2 -> H(U1(a, e), U1(c, e))
28.43/9.22	   A^2 -> H(U1(a, e), U1(c, k))
28.43/9.22	   A^2 -> H(U1(a, e), U1(e, e))
28.43/9.22	   A^2 -> H(U1(a, e), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, e), U1(k, d))
28.43/9.22	   A^2 -> H(U1(a, e), U1(d, k))
28.43/9.22	   A^2 -> H(U1(a, k), U1(e, b))
28.43/9.22	   A^2 -> H(U1(a, k), U1(k, b))
28.43/9.22	   A^2 -> H(U1(a, k), U1(c, d))
28.43/9.22	   A^2 -> H(U1(a, k), U1(d, c))
28.43/9.22	   A^2 -> H(U1(a, k), U1(b, e))
28.43/9.22	   A^2 -> H(U1(a, k), U1(b, k))
28.43/9.22	   A^2 -> H(U1(a, k), U1(e, c))
28.43/9.22	   A^2 -> H(U1(a, k), U1(k, c))
28.43/9.22	   A^2 -> H(U1(a, k), U1(c, e))
28.43/9.22	   A^2 -> H(U1(a, k), U1(c, k))
28.43/9.22	   A^2 -> H(U1(a, k), U1(e, e))
28.43/9.22	   A^2 -> H(U1(a, k), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, k), U1(k, d))
28.43/9.22	   A^2 -> H(U1(a, k), U1(d, k))
28.43/9.22	   A^2 -> H(U1(a, c), b)
28.43/9.22	   A^2 -> H(U1(a, c), U1(e, d))
28.43/9.22	   A^2 -> H(U1(a, c), U1(d, e))
28.43/9.22	   A^2 -> H(U1(a, c), c)
28.43/9.22	   A^2 -> H(U1(a, c), U1(e, k))
28.43/9.22	   A^2 -> H(U1(a, c), U1(k, e))
28.43/9.22	   A^2 -> H(U1(a, c), e)
28.43/9.22	   A^2 -> H(U1(a, c), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, d), b)
28.43/9.22	   A^2 -> H(U1(a, d), U1(e, d))
28.43/9.22	   A^2 -> H(U1(a, d), U1(d, e))
28.43/9.22	   A^2 -> H(U1(a, d), c)
28.43/9.22	   A^2 -> H(U1(a, d), U1(e, k))
28.43/9.22	   A^2 -> H(U1(a, d), U1(k, e))
28.43/9.22	   A^2 -> H(U1(a, d), e)
28.43/9.22	   A^2 -> H(U1(a, d), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, a), d)
28.43/9.22	   A^2 -> H(U1(a, a), k)
28.43/9.22	   A^2 -> H(k, U1(b, b))
28.43/9.22	   A^2 -> H(k, f(c))
28.43/9.22	   A^2 -> H(k, f(d))
28.43/9.22	   A^2 -> H(c, U1(c, b))
28.43/9.22	   A^2 -> H(c, U1(d, b))
28.43/9.22	   A^2 -> H(c, U1(b, c))
28.43/9.22	   A^2 -> H(c, U1(b, d))
28.43/9.22	   A^2 -> H(c, U1(c, c))
28.43/9.22	   A^2 -> H(c, f(e))
28.43/9.22	   A^2 -> H(c, f(k))
28.43/9.22	   A^2 -> H(c, U1(d, d))
28.43/9.22	   A^2 -> H(U1(e, k), U1(c, b))
28.43/9.22	   A^2 -> H(U1(e, k), U1(d, b))
28.43/9.22	   A^2 -> H(U1(e, k), U1(b, c))
28.43/9.22	   A^2 -> H(U1(e, k), U1(b, d))
28.43/9.22	   A^2 -> H(U1(e, k), U1(c, c))
28.43/9.22	   A^2 -> H(U1(e, k), f(e))
28.43/9.22	   A^2 -> H(U1(e, k), f(k))
28.43/9.22	   A^2 -> H(U1(e, k), U1(d, d))
28.43/9.22	   A^2 -> H(U1(e, c), U1(e, b))
28.43/9.22	   A^2 -> H(U1(e, c), U1(k, b))
28.43/9.22	   A^2 -> H(U1(e, c), U1(c, d))
28.43/9.22	   A^2 -> H(U1(e, c), U1(d, c))
28.43/9.22	   A^2 -> H(U1(e, c), U1(b, e))
28.43/9.22	   A^2 -> H(U1(e, c), U1(b, k))
28.43/9.22	   A^2 -> H(U1(e, c), U1(e, c))
28.43/9.22	   A^2 -> H(U1(e, c), U1(k, c))
28.43/9.22	   A^2 -> H(U1(e, c), U1(c, e))
28.43/9.22	   A^2 -> H(U1(e, c), U1(c, k))
28.43/9.22	   A^2 -> H(U1(e, c), U1(e, e))
28.43/9.22	   A^2 -> H(U1(e, c), U1(k, k))
28.43/9.22	   A^2 -> H(U1(e, c), U1(k, d))
28.43/9.22	   A^2 -> H(U1(e, c), U1(d, k))
28.43/9.22	   A^2 -> H(U1(k, e), U1(c, b))
28.43/9.22	   A^2 -> H(U1(k, e), U1(d, b))
28.43/9.22	   A^2 -> H(U1(k, e), U1(b, c))
28.43/9.22	   A^2 -> H(U1(k, e), U1(b, d))
28.43/9.22	   A^2 -> H(U1(k, e), U1(c, c))
28.43/9.22	   A^2 -> H(U1(k, e), f(e))
28.43/9.22	   A^2 -> H(U1(k, e), f(k))
28.43/9.22	   A^2 -> H(U1(k, e), U1(d, d))
28.43/9.22	   A^2 -> H(U1(k, c), U1(e, b))
28.43/9.22	   A^2 -> H(U1(k, c), U1(k, b))
28.43/9.22	   A^2 -> H(U1(k, c), U1(c, d))
28.43/9.22	   A^2 -> H(U1(k, c), U1(d, c))
28.43/9.22	   A^2 -> H(U1(k, c), U1(b, e))
28.43/9.22	   A^2 -> H(U1(k, c), U1(b, k))
28.43/9.22	   A^2 -> H(U1(k, c), U1(e, c))
28.43/9.22	   A^2 -> H(U1(k, c), U1(k, c))
28.43/9.22	   A^2 -> H(U1(k, c), U1(c, e))
28.43/9.22	   A^2 -> H(U1(k, c), U1(c, k))
28.43/9.22	
28.43/9.22	The TRS R consists of the following rules:
28.43/9.22	
28.43/9.22	   f(x) -> U1(x, x)
28.43/9.22	   U1(e, x) -> x
28.43/9.22	   a -> c
28.43/9.22	   a -> d
28.43/9.22	   b -> c
28.43/9.22	   b -> d
28.43/9.22	   d -> k
28.43/9.22	   c -> e
28.43/9.22	   c -> k
28.43/9.22	
28.43/9.22	Q is empty.
28.43/9.22	We have to consider all minimal (P,Q,R)-chains.
28.43/9.22	----------------------------------------
28.43/9.22	
28.43/9.22	(831) TransformationProof (EQUIVALENT)
28.43/9.22	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), f(e)) at position [] we obtained the following new rules [LPAR04]:
28.43/9.22	
28.43/9.22	   (A^2 -> H(U1(k, e), f(e)),A^2 -> H(U1(k, e), f(e)))
28.43/9.22	   (A^2 -> H(U1(k, k), f(e)),A^2 -> H(U1(k, k), f(e)))
28.43/9.22	   (A^2 -> H(U1(k, c), U1(e, e)),A^2 -> H(U1(k, c), U1(e, e)))
28.43/9.22	
28.43/9.22	
28.43/9.22	----------------------------------------
28.43/9.22	
28.43/9.22	(832)
28.43/9.22	Obligation:
28.43/9.22	Q DP problem:
28.43/9.22	The TRS P consists of the following rules:
28.43/9.22	
28.43/9.22	   H(x, x) -> G(x, x, f(k))
28.43/9.22	   G(d, x, x) -> A^2
28.43/9.22	   A^2 -> H(f(c), f(c))
28.43/9.22	   A^2 -> H(f(d), f(d))
28.43/9.22	   A^2 -> H(U1(c, c), U1(c, c))
28.43/9.22	   A^2 -> H(f(e), f(e))
28.43/9.22	   A^2 -> H(f(k), f(k))
28.43/9.22	   A^2 -> H(U1(d, d), U1(d, d))
28.43/9.22	   A^2 -> H(U1(k, c), f(k))
28.43/9.22	   A^2 -> H(U1(k, c), U1(d, d))
28.43/9.22	   A^2 -> H(U1(c, e), U1(c, b))
28.43/9.22	   A^2 -> H(U1(c, e), U1(d, b))
28.43/9.22	   A^2 -> H(U1(c, e), U1(b, c))
28.43/9.22	   A^2 -> H(U1(c, e), U1(b, d))
28.43/9.22	   A^2 -> H(U1(c, e), U1(c, c))
28.43/9.22	   A^2 -> H(U1(c, e), f(e))
28.43/9.22	   A^2 -> H(U1(c, e), f(k))
28.43/9.22	   A^2 -> H(U1(c, e), U1(d, d))
28.43/9.22	   A^2 -> H(U1(c, k), U1(c, b))
28.43/9.22	   A^2 -> H(U1(c, k), U1(d, b))
28.43/9.22	   A^2 -> H(U1(c, k), U1(b, c))
28.43/9.22	   A^2 -> H(U1(c, k), U1(b, d))
28.43/9.22	   A^2 -> H(U1(c, k), U1(c, c))
28.43/9.22	   A^2 -> H(U1(c, k), f(e))
28.43/9.22	   A^2 -> H(U1(c, k), f(k))
28.43/9.22	   A^2 -> H(U1(c, k), U1(d, d))
28.43/9.22	   A^2 -> H(U1(c, c), U1(e, b))
28.43/9.22	   A^2 -> H(U1(c, c), U1(k, b))
28.43/9.22	   A^2 -> H(U1(c, c), U1(c, d))
28.43/9.22	   A^2 -> H(U1(c, c), U1(d, c))
28.43/9.22	   A^2 -> H(U1(c, c), U1(b, e))
28.43/9.22	   A^2 -> H(U1(c, c), U1(b, k))
28.43/9.22	   A^2 -> H(U1(c, c), U1(e, e))
28.43/9.22	   A^2 -> H(U1(c, c), U1(k, k))
28.43/9.22	   A^2 -> H(U1(c, c), U1(k, d))
28.43/9.22	   A^2 -> H(U1(c, c), U1(d, k))
28.43/9.22	   A^2 -> H(e, U1(b, b))
28.43/9.22	   A^2 -> H(e, f(c))
28.43/9.22	   A^2 -> H(e, f(d))
28.43/9.22	   A^2 -> H(U1(e, e), U1(c, b))
28.43/9.22	   A^2 -> H(U1(e, e), U1(d, b))
28.43/9.22	   A^2 -> H(U1(e, e), U1(b, c))
28.43/9.22	   A^2 -> H(U1(e, e), U1(b, d))
28.43/9.22	   A^2 -> H(U1(e, e), U1(c, c))
28.43/9.22	   A^2 -> H(U1(e, e), f(e))
28.43/9.22	   A^2 -> H(U1(e, e), f(k))
28.43/9.22	   A^2 -> H(U1(e, e), U1(d, d))
28.43/9.22	   A^2 -> H(f(e), U1(e, b))
28.43/9.22	   A^2 -> H(f(e), U1(k, b))
28.43/9.22	   A^2 -> H(f(e), U1(c, d))
28.43/9.22	   A^2 -> H(f(e), U1(d, c))
28.43/9.22	   A^2 -> H(f(e), U1(b, e))
28.43/9.22	   A^2 -> H(f(e), U1(b, k))
28.43/9.22	   A^2 -> H(f(e), U1(e, c))
28.43/9.22	   A^2 -> H(f(e), U1(k, c))
28.43/9.22	   A^2 -> H(f(e), U1(c, e))
28.43/9.22	   A^2 -> H(f(e), U1(c, k))
28.43/9.22	   A^2 -> H(f(e), U1(k, k))
28.43/9.22	   A^2 -> H(f(e), U1(k, d))
28.43/9.22	   A^2 -> H(f(e), U1(d, k))
28.43/9.22	   A^2 -> H(U1(k, k), U1(c, b))
28.43/9.22	   A^2 -> H(U1(k, k), U1(d, b))
28.43/9.22	   A^2 -> H(U1(k, k), U1(b, c))
28.43/9.22	   A^2 -> H(U1(k, k), U1(b, d))
28.43/9.22	   A^2 -> H(U1(k, k), U1(c, c))
28.43/9.22	   A^2 -> H(U1(k, k), f(e))
28.43/9.22	   A^2 -> H(U1(k, k), f(k))
28.43/9.22	   A^2 -> H(U1(k, k), U1(d, d))
28.43/9.22	   A^2 -> H(f(k), U1(e, b))
28.43/9.22	   A^2 -> H(f(k), U1(k, b))
28.43/9.22	   A^2 -> H(f(k), U1(c, d))
28.43/9.22	   A^2 -> H(f(k), U1(d, c))
28.43/9.22	   A^2 -> H(f(k), U1(b, e))
28.43/9.22	   A^2 -> H(f(k), U1(b, k))
28.43/9.22	   A^2 -> H(f(k), U1(e, c))
28.43/9.22	   A^2 -> H(f(k), U1(k, c))
28.43/9.22	   A^2 -> H(f(k), U1(c, e))
28.43/9.22	   A^2 -> H(f(k), U1(c, k))
28.43/9.22	   A^2 -> H(f(k), U1(e, e))
28.43/9.22	   A^2 -> H(f(k), U1(k, d))
28.43/9.22	   A^2 -> H(f(k), U1(d, k))
28.43/9.22	   A^2 -> H(f(c), b)
28.43/9.22	   A^2 -> H(f(c), U1(e, d))
28.43/9.22	   A^2 -> H(f(c), U1(d, e))
28.43/9.22	   A^2 -> H(f(k), U1(k, k))
28.43/9.22	   A^2 -> H(U1(k, k), U1(b, b))
28.43/9.22	   A^2 -> H(U1(k, k), f(c))
28.43/9.22	   A^2 -> H(U1(k, k), f(d))
28.43/9.22	   A^2 -> H(U1(k, d), U1(c, b))
28.43/9.22	   A^2 -> H(U1(k, d), U1(d, b))
28.43/9.22	   A^2 -> H(U1(k, d), U1(b, c))
28.43/9.22	   A^2 -> H(U1(k, d), U1(b, d))
28.43/9.22	   A^2 -> H(U1(k, d), U1(c, c))
28.43/9.22	   A^2 -> H(U1(k, d), f(e))
28.43/9.22	   A^2 -> H(U1(k, d), f(k))
28.43/9.22	   A^2 -> H(U1(k, d), U1(d, d))
28.43/9.22	   A^2 -> H(U1(d, k), U1(c, b))
28.43/9.22	   A^2 -> H(U1(d, k), U1(d, b))
28.43/9.22	   A^2 -> H(U1(d, k), U1(b, c))
28.43/9.22	   A^2 -> H(U1(d, k), U1(b, d))
28.43/9.22	   A^2 -> H(U1(d, k), U1(c, c))
28.43/9.22	   A^2 -> H(U1(d, k), f(e))
28.43/9.22	   A^2 -> H(U1(d, k), f(k))
28.43/9.22	   A^2 -> H(U1(d, k), U1(d, d))
28.43/9.22	   A^2 -> H(U1(d, d), U1(e, b))
28.43/9.22	   A^2 -> H(U1(d, d), U1(k, b))
28.43/9.22	   A^2 -> H(U1(d, d), U1(c, d))
28.43/9.22	   A^2 -> H(U1(d, d), U1(d, c))
28.43/9.22	   A^2 -> H(U1(d, d), U1(b, e))
28.43/9.22	   A^2 -> H(U1(d, d), U1(b, k))
28.43/9.22	   A^2 -> H(U1(d, d), U1(e, c))
28.43/9.22	   A^2 -> H(U1(d, d), U1(k, c))
28.43/9.22	   A^2 -> H(U1(d, d), U1(c, e))
28.43/9.22	   A^2 -> H(U1(d, d), U1(c, k))
28.43/9.22	   A^2 -> H(U1(d, d), U1(e, e))
28.43/9.22	   A^2 -> H(U1(d, d), U1(k, k))
28.43/9.22	   A^2 -> H(f(d), b)
28.43/9.22	   A^2 -> H(f(d), U1(e, d))
28.43/9.22	   A^2 -> H(f(d), U1(d, e))
28.43/9.22	   A^2 -> H(f(d), c)
28.43/9.22	   A^2 -> H(f(d), U1(e, k))
28.43/9.22	   A^2 -> H(f(d), U1(k, e))
28.43/9.22	   A^2 -> H(f(d), e)
28.43/9.22	   A^2 -> H(f(a), d)
28.43/9.22	   A^2 -> H(U1(c, c), U1(e, c))
28.43/9.22	   A^2 -> H(f(c), c)
28.43/9.22	   A^2 -> H(f(c), U1(e, k))
28.43/9.22	   A^2 -> H(U1(c, c), U1(k, c))
28.43/9.22	   A^2 -> H(f(c), U1(k, e))
28.43/9.22	   A^2 -> H(f(c), U1(k, k))
28.43/9.22	   A^2 -> H(U1(c, c), U1(c, e))
28.43/9.22	   A^2 -> H(U1(c, c), U1(c, k))
28.43/9.22	   A^2 -> H(f(a), k)
28.43/9.22	   A^2 -> H(f(e), U1(e, e))
28.43/9.22	   A^2 -> H(f(c), e)
28.43/9.22	   A^2 -> H(U1(d, d), U1(k, d))
28.43/9.22	   A^2 -> H(f(d), U1(k, k))
28.43/9.22	   A^2 -> H(U1(d, d), U1(d, k))
28.43/9.22	   A^2 -> H(d, U1(b, b))
28.43/9.22	   A^2 -> H(d, f(c))
28.43/9.22	   A^2 -> H(d, f(d))
28.43/9.22	   A^2 -> H(a, U1(c, b))
28.43/9.22	   A^2 -> H(a, U1(d, b))
28.43/9.22	   A^2 -> H(a, U1(b, c))
28.43/9.22	   A^2 -> H(a, U1(b, d))
28.43/9.22	   A^2 -> H(a, U1(c, c))
28.43/9.22	   A^2 -> H(a, f(e))
28.43/9.22	   A^2 -> H(a, f(k))
28.43/9.22	   A^2 -> H(a, U1(d, d))
28.43/9.22	   A^2 -> H(U1(e, d), U1(c, b))
28.43/9.22	   A^2 -> H(U1(e, d), U1(d, b))
28.43/9.22	   A^2 -> H(U1(e, d), U1(b, c))
28.43/9.22	   A^2 -> H(U1(e, d), U1(b, d))
28.43/9.22	   A^2 -> H(U1(e, d), U1(c, c))
28.43/9.22	   A^2 -> H(U1(e, d), f(e))
28.43/9.22	   A^2 -> H(U1(e, d), f(k))
28.43/9.22	   A^2 -> H(U1(e, d), U1(d, d))
28.43/9.22	   A^2 -> H(U1(e, a), U1(e, b))
28.43/9.22	   A^2 -> H(U1(e, a), U1(k, b))
28.43/9.22	   A^2 -> H(U1(e, a), U1(c, d))
28.43/9.22	   A^2 -> H(U1(e, a), U1(d, c))
28.43/9.22	   A^2 -> H(U1(e, a), U1(b, e))
28.43/9.22	   A^2 -> H(U1(e, a), U1(b, k))
28.43/9.22	   A^2 -> H(U1(e, a), U1(e, c))
28.43/9.22	   A^2 -> H(U1(e, a), U1(k, c))
28.43/9.22	   A^2 -> H(U1(e, a), U1(c, e))
28.43/9.22	   A^2 -> H(U1(e, a), U1(c, k))
28.43/9.22	   A^2 -> H(U1(e, a), U1(e, e))
28.43/9.22	   A^2 -> H(U1(e, a), U1(k, k))
28.43/9.22	   A^2 -> H(U1(e, a), U1(k, d))
28.43/9.22	   A^2 -> H(U1(e, a), U1(d, k))
28.43/9.22	   A^2 -> H(U1(k, a), U1(e, b))
28.43/9.22	   A^2 -> H(U1(k, a), U1(k, b))
28.43/9.22	   A^2 -> H(U1(k, a), U1(c, d))
28.43/9.22	   A^2 -> H(U1(k, a), U1(d, c))
28.43/9.22	   A^2 -> H(U1(k, a), U1(b, e))
28.43/9.22	   A^2 -> H(U1(k, a), U1(b, k))
28.43/9.22	   A^2 -> H(U1(k, a), U1(e, c))
28.43/9.22	   A^2 -> H(U1(k, a), U1(k, c))
28.43/9.22	   A^2 -> H(U1(k, a), U1(c, e))
28.43/9.22	   A^2 -> H(U1(k, a), U1(c, k))
28.43/9.22	   A^2 -> H(U1(k, a), U1(e, e))
28.43/9.22	   A^2 -> H(U1(k, a), U1(k, k))
28.43/9.22	   A^2 -> H(U1(k, a), U1(k, d))
28.43/9.22	   A^2 -> H(U1(k, a), U1(d, k))
28.43/9.22	   A^2 -> H(U1(c, d), U1(e, b))
28.43/9.22	   A^2 -> H(U1(c, d), U1(k, b))
28.43/9.22	   A^2 -> H(U1(c, d), U1(c, d))
28.43/9.22	   A^2 -> H(U1(c, d), U1(d, c))
28.43/9.22	   A^2 -> H(U1(c, d), U1(b, e))
28.43/9.22	   A^2 -> H(U1(c, d), U1(b, k))
28.43/9.22	   A^2 -> H(U1(c, d), U1(e, c))
28.43/9.22	   A^2 -> H(U1(c, d), U1(k, c))
28.43/9.22	   A^2 -> H(U1(c, d), U1(c, e))
28.43/9.22	   A^2 -> H(U1(c, d), U1(c, k))
28.43/9.22	   A^2 -> H(U1(c, d), U1(e, e))
28.43/9.22	   A^2 -> H(U1(c, d), U1(k, k))
28.43/9.22	   A^2 -> H(U1(c, d), U1(k, d))
28.43/9.22	   A^2 -> H(U1(c, d), U1(d, k))
28.43/9.22	   A^2 -> H(U1(c, a), b)
28.43/9.22	   A^2 -> H(U1(c, a), U1(e, d))
28.43/9.22	   A^2 -> H(U1(c, a), U1(d, e))
28.43/9.22	   A^2 -> H(U1(c, a), c)
28.43/9.22	   A^2 -> H(U1(c, a), U1(e, k))
28.43/9.22	   A^2 -> H(U1(c, a), U1(k, e))
28.43/9.22	   A^2 -> H(U1(c, a), e)
28.43/9.22	   A^2 -> H(U1(c, a), U1(k, k))
28.43/9.22	   A^2 -> H(U1(d, e), U1(c, b))
28.43/9.22	   A^2 -> H(U1(d, e), U1(d, b))
28.43/9.22	   A^2 -> H(U1(d, e), U1(b, c))
28.43/9.22	   A^2 -> H(U1(d, e), U1(b, d))
28.43/9.22	   A^2 -> H(U1(d, e), U1(c, c))
28.43/9.22	   A^2 -> H(U1(d, e), f(e))
28.43/9.22	   A^2 -> H(U1(d, e), f(k))
28.43/9.22	   A^2 -> H(U1(d, e), U1(d, d))
28.43/9.22	   A^2 -> H(U1(d, c), U1(e, b))
28.43/9.22	   A^2 -> H(U1(d, c), U1(k, b))
28.43/9.22	   A^2 -> H(U1(d, c), U1(c, d))
28.43/9.22	   A^2 -> H(U1(d, c), U1(d, c))
28.43/9.22	   A^2 -> H(U1(d, c), U1(b, e))
28.43/9.22	   A^2 -> H(U1(d, c), U1(b, k))
28.43/9.22	   A^2 -> H(U1(d, c), U1(e, c))
28.43/9.22	   A^2 -> H(U1(d, c), U1(k, c))
28.43/9.22	   A^2 -> H(U1(d, c), U1(c, e))
28.43/9.22	   A^2 -> H(U1(d, c), U1(c, k))
28.43/9.22	   A^2 -> H(U1(d, c), U1(e, e))
28.43/9.22	   A^2 -> H(U1(d, c), U1(k, k))
28.43/9.22	   A^2 -> H(U1(d, c), U1(k, d))
28.43/9.22	   A^2 -> H(U1(d, c), U1(d, k))
28.43/9.22	   A^2 -> H(U1(d, a), b)
28.43/9.22	   A^2 -> H(U1(d, a), U1(e, d))
28.43/9.22	   A^2 -> H(U1(d, a), U1(d, e))
28.43/9.22	   A^2 -> H(U1(d, a), c)
28.43/9.22	   A^2 -> H(U1(d, a), U1(e, k))
28.43/9.22	   A^2 -> H(U1(d, a), U1(k, e))
28.43/9.22	   A^2 -> H(U1(d, a), e)
28.43/9.22	   A^2 -> H(U1(d, a), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, e), U1(e, b))
28.43/9.22	   A^2 -> H(U1(a, e), U1(k, b))
28.43/9.22	   A^2 -> H(U1(a, e), U1(c, d))
28.43/9.22	   A^2 -> H(U1(a, e), U1(d, c))
28.43/9.22	   A^2 -> H(U1(a, e), U1(b, e))
28.43/9.22	   A^2 -> H(U1(a, e), U1(b, k))
28.43/9.22	   A^2 -> H(U1(a, e), U1(e, c))
28.43/9.22	   A^2 -> H(U1(a, e), U1(k, c))
28.43/9.22	   A^2 -> H(U1(a, e), U1(c, e))
28.43/9.22	   A^2 -> H(U1(a, e), U1(c, k))
28.43/9.22	   A^2 -> H(U1(a, e), U1(e, e))
28.43/9.22	   A^2 -> H(U1(a, e), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, e), U1(k, d))
28.43/9.22	   A^2 -> H(U1(a, e), U1(d, k))
28.43/9.22	   A^2 -> H(U1(a, k), U1(e, b))
28.43/9.22	   A^2 -> H(U1(a, k), U1(k, b))
28.43/9.22	   A^2 -> H(U1(a, k), U1(c, d))
28.43/9.22	   A^2 -> H(U1(a, k), U1(d, c))
28.43/9.22	   A^2 -> H(U1(a, k), U1(b, e))
28.43/9.22	   A^2 -> H(U1(a, k), U1(b, k))
28.43/9.22	   A^2 -> H(U1(a, k), U1(e, c))
28.43/9.22	   A^2 -> H(U1(a, k), U1(k, c))
28.43/9.22	   A^2 -> H(U1(a, k), U1(c, e))
28.43/9.22	   A^2 -> H(U1(a, k), U1(c, k))
28.43/9.22	   A^2 -> H(U1(a, k), U1(e, e))
28.43/9.22	   A^2 -> H(U1(a, k), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, k), U1(k, d))
28.43/9.22	   A^2 -> H(U1(a, k), U1(d, k))
28.43/9.22	   A^2 -> H(U1(a, c), b)
28.43/9.22	   A^2 -> H(U1(a, c), U1(e, d))
28.43/9.22	   A^2 -> H(U1(a, c), U1(d, e))
28.43/9.22	   A^2 -> H(U1(a, c), c)
28.43/9.22	   A^2 -> H(U1(a, c), U1(e, k))
28.43/9.22	   A^2 -> H(U1(a, c), U1(k, e))
28.43/9.22	   A^2 -> H(U1(a, c), e)
28.43/9.22	   A^2 -> H(U1(a, c), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, d), b)
28.43/9.22	   A^2 -> H(U1(a, d), U1(e, d))
28.43/9.22	   A^2 -> H(U1(a, d), U1(d, e))
28.43/9.22	   A^2 -> H(U1(a, d), c)
28.43/9.22	   A^2 -> H(U1(a, d), U1(e, k))
28.43/9.22	   A^2 -> H(U1(a, d), U1(k, e))
28.43/9.22	   A^2 -> H(U1(a, d), e)
28.43/9.22	   A^2 -> H(U1(a, d), U1(k, k))
28.43/9.22	   A^2 -> H(U1(a, a), d)
28.43/9.22	   A^2 -> H(U1(a, a), k)
28.43/9.22	   A^2 -> H(k, U1(b, b))
28.43/9.22	   A^2 -> H(k, f(c))
28.43/9.22	   A^2 -> H(k, f(d))
28.43/9.22	   A^2 -> H(c, U1(c, b))
28.43/9.22	   A^2 -> H(c, U1(d, b))
28.43/9.22	   A^2 -> H(c, U1(b, c))
28.43/9.22	   A^2 -> H(c, U1(b, d))
28.43/9.22	   A^2 -> H(c, U1(c, c))
28.43/9.22	   A^2 -> H(c, f(e))
28.43/9.22	   A^2 -> H(c, f(k))
28.43/9.22	   A^2 -> H(c, U1(d, d))
28.43/9.22	   A^2 -> H(U1(e, k), U1(c, b))
28.43/9.22	   A^2 -> H(U1(e, k), U1(d, b))
28.43/9.22	   A^2 -> H(U1(e, k), U1(b, c))
28.43/9.22	   A^2 -> H(U1(e, k), U1(b, d))
28.43/9.22	   A^2 -> H(U1(e, k), U1(c, c))
28.43/9.22	   A^2 -> H(U1(e, k), f(e))
28.43/9.22	   A^2 -> H(U1(e, k), f(k))
28.43/9.22	   A^2 -> H(U1(e, k), U1(d, d))
28.43/9.22	   A^2 -> H(U1(e, c), U1(e, b))
28.43/9.22	   A^2 -> H(U1(e, c), U1(k, b))
28.43/9.22	   A^2 -> H(U1(e, c), U1(c, d))
28.43/9.22	   A^2 -> H(U1(e, c), U1(d, c))
28.43/9.22	   A^2 -> H(U1(e, c), U1(b, e))
28.43/9.22	   A^2 -> H(U1(e, c), U1(b, k))
28.43/9.22	   A^2 -> H(U1(e, c), U1(e, c))
28.43/9.22	   A^2 -> H(U1(e, c), U1(k, c))
28.43/9.22	   A^2 -> H(U1(e, c), U1(c, e))
28.43/9.22	   A^2 -> H(U1(e, c), U1(c, k))
28.43/9.22	   A^2 -> H(U1(e, c), U1(e, e))
28.43/9.22	   A^2 -> H(U1(e, c), U1(k, k))
28.43/9.22	   A^2 -> H(U1(e, c), U1(k, d))
28.43/9.22	   A^2 -> H(U1(e, c), U1(d, k))
28.43/9.22	   A^2 -> H(U1(k, e), U1(c, b))
28.43/9.22	   A^2 -> H(U1(k, e), U1(d, b))
28.43/9.22	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.22	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.22	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.22	   A^2 -> H(U1(k, e), f(e))
28.45/9.22	   A^2 -> H(U1(k, e), f(k))
28.45/9.22	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.22	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.22	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.22	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.22	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.22	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.22	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.22	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.22	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.22	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.22	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.22	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.22	
28.45/9.22	The TRS R consists of the following rules:
28.45/9.22	
28.45/9.22	   f(x) -> U1(x, x)
28.45/9.22	   U1(e, x) -> x
28.45/9.22	   a -> c
28.45/9.22	   a -> d
28.45/9.22	   b -> c
28.45/9.22	   b -> d
28.45/9.22	   d -> k
28.45/9.22	   c -> e
28.45/9.22	   c -> k
28.45/9.22	
28.45/9.22	Q is empty.
28.45/9.22	We have to consider all minimal (P,Q,R)-chains.
28.45/9.22	----------------------------------------
28.45/9.22	
28.45/9.22	(833) TransformationProof (EQUIVALENT)
28.45/9.22	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), f(k)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.22	
28.45/9.22	   (A^2 -> H(U1(k, e), f(k)),A^2 -> H(U1(k, e), f(k)))
28.45/9.22	   (A^2 -> H(U1(k, k), f(k)),A^2 -> H(U1(k, k), f(k)))
28.45/9.22	   (A^2 -> H(U1(k, c), U1(k, k)),A^2 -> H(U1(k, c), U1(k, k)))
28.45/9.22	
28.45/9.22	
28.45/9.22	----------------------------------------
28.45/9.22	
28.45/9.22	(834)
28.45/9.22	Obligation:
28.45/9.22	Q DP problem:
28.45/9.22	The TRS P consists of the following rules:
28.45/9.22	
28.45/9.22	   H(x, x) -> G(x, x, f(k))
28.45/9.22	   G(d, x, x) -> A^2
28.45/9.22	   A^2 -> H(f(c), f(c))
28.45/9.22	   A^2 -> H(f(d), f(d))
28.45/9.22	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.22	   A^2 -> H(f(e), f(e))
28.45/9.22	   A^2 -> H(f(k), f(k))
28.45/9.22	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.22	   A^2 -> H(U1(k, c), U1(d, d))
28.45/9.22	   A^2 -> H(U1(c, e), U1(c, b))
28.45/9.22	   A^2 -> H(U1(c, e), U1(d, b))
28.45/9.22	   A^2 -> H(U1(c, e), U1(b, c))
28.45/9.22	   A^2 -> H(U1(c, e), U1(b, d))
28.45/9.22	   A^2 -> H(U1(c, e), U1(c, c))
28.45/9.22	   A^2 -> H(U1(c, e), f(e))
28.45/9.22	   A^2 -> H(U1(c, e), f(k))
28.45/9.22	   A^2 -> H(U1(c, e), U1(d, d))
28.45/9.22	   A^2 -> H(U1(c, k), U1(c, b))
28.45/9.22	   A^2 -> H(U1(c, k), U1(d, b))
28.45/9.22	   A^2 -> H(U1(c, k), U1(b, c))
28.45/9.22	   A^2 -> H(U1(c, k), U1(b, d))
28.45/9.22	   A^2 -> H(U1(c, k), U1(c, c))
28.45/9.22	   A^2 -> H(U1(c, k), f(e))
28.45/9.22	   A^2 -> H(U1(c, k), f(k))
28.45/9.22	   A^2 -> H(U1(c, k), U1(d, d))
28.45/9.22	   A^2 -> H(U1(c, c), U1(e, b))
28.45/9.22	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.22	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.22	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.22	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.22	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.22	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.22	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.22	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.22	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.22	   A^2 -> H(e, U1(b, b))
28.45/9.22	   A^2 -> H(e, f(c))
28.45/9.22	   A^2 -> H(e, f(d))
28.45/9.22	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.22	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.22	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.22	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.22	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.22	   A^2 -> H(U1(e, e), f(e))
28.45/9.22	   A^2 -> H(U1(e, e), f(k))
28.45/9.22	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.22	   A^2 -> H(f(e), U1(e, b))
28.45/9.22	   A^2 -> H(f(e), U1(k, b))
28.45/9.22	   A^2 -> H(f(e), U1(c, d))
28.45/9.22	   A^2 -> H(f(e), U1(d, c))
28.45/9.22	   A^2 -> H(f(e), U1(b, e))
28.45/9.22	   A^2 -> H(f(e), U1(b, k))
28.45/9.22	   A^2 -> H(f(e), U1(e, c))
28.45/9.22	   A^2 -> H(f(e), U1(k, c))
28.45/9.22	   A^2 -> H(f(e), U1(c, e))
28.45/9.22	   A^2 -> H(f(e), U1(c, k))
28.45/9.22	   A^2 -> H(f(e), U1(k, k))
28.45/9.22	   A^2 -> H(f(e), U1(k, d))
28.45/9.22	   A^2 -> H(f(e), U1(d, k))
28.45/9.22	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.22	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.22	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.22	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.22	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.22	   A^2 -> H(U1(k, k), f(e))
28.45/9.22	   A^2 -> H(U1(k, k), f(k))
28.45/9.22	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.22	   A^2 -> H(f(k), U1(e, b))
28.45/9.22	   A^2 -> H(f(k), U1(k, b))
28.45/9.22	   A^2 -> H(f(k), U1(c, d))
28.45/9.22	   A^2 -> H(f(k), U1(d, c))
28.45/9.22	   A^2 -> H(f(k), U1(b, e))
28.45/9.22	   A^2 -> H(f(k), U1(b, k))
28.45/9.22	   A^2 -> H(f(k), U1(e, c))
28.45/9.22	   A^2 -> H(f(k), U1(k, c))
28.45/9.22	   A^2 -> H(f(k), U1(c, e))
28.45/9.22	   A^2 -> H(f(k), U1(c, k))
28.45/9.22	   A^2 -> H(f(k), U1(e, e))
28.45/9.22	   A^2 -> H(f(k), U1(k, d))
28.45/9.22	   A^2 -> H(f(k), U1(d, k))
28.45/9.22	   A^2 -> H(f(c), b)
28.45/9.22	   A^2 -> H(f(c), U1(e, d))
28.45/9.22	   A^2 -> H(f(c), U1(d, e))
28.45/9.22	   A^2 -> H(f(k), U1(k, k))
28.45/9.22	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.22	   A^2 -> H(U1(k, k), f(c))
28.45/9.22	   A^2 -> H(U1(k, k), f(d))
28.45/9.22	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.22	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.22	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.22	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.22	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.22	   A^2 -> H(U1(k, d), f(e))
28.45/9.22	   A^2 -> H(U1(k, d), f(k))
28.45/9.22	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.22	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.22	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.22	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.22	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.22	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.22	   A^2 -> H(U1(d, k), f(e))
28.45/9.22	   A^2 -> H(U1(d, k), f(k))
28.45/9.22	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.22	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.22	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.22	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.22	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.22	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.22	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.22	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.22	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.22	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.22	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.22	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.22	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.22	   A^2 -> H(f(d), b)
28.45/9.22	   A^2 -> H(f(d), U1(e, d))
28.45/9.22	   A^2 -> H(f(d), U1(d, e))
28.45/9.22	   A^2 -> H(f(d), c)
28.45/9.22	   A^2 -> H(f(d), U1(e, k))
28.45/9.22	   A^2 -> H(f(d), U1(k, e))
28.45/9.22	   A^2 -> H(f(d), e)
28.45/9.22	   A^2 -> H(f(a), d)
28.45/9.22	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.22	   A^2 -> H(f(c), c)
28.45/9.22	   A^2 -> H(f(c), U1(e, k))
28.45/9.22	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.22	   A^2 -> H(f(c), U1(k, e))
28.45/9.22	   A^2 -> H(f(c), U1(k, k))
28.45/9.22	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.22	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.22	   A^2 -> H(f(a), k)
28.45/9.22	   A^2 -> H(f(e), U1(e, e))
28.45/9.22	   A^2 -> H(f(c), e)
28.45/9.22	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.22	   A^2 -> H(f(d), U1(k, k))
28.45/9.22	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.22	   A^2 -> H(d, U1(b, b))
28.45/9.22	   A^2 -> H(d, f(c))
28.45/9.22	   A^2 -> H(d, f(d))
28.45/9.22	   A^2 -> H(a, U1(c, b))
28.45/9.22	   A^2 -> H(a, U1(d, b))
28.45/9.22	   A^2 -> H(a, U1(b, c))
28.45/9.22	   A^2 -> H(a, U1(b, d))
28.45/9.22	   A^2 -> H(a, U1(c, c))
28.45/9.22	   A^2 -> H(a, f(e))
28.45/9.22	   A^2 -> H(a, f(k))
28.45/9.22	   A^2 -> H(a, U1(d, d))
28.45/9.22	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.22	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.22	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.22	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.22	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.22	   A^2 -> H(U1(e, d), f(e))
28.45/9.22	   A^2 -> H(U1(e, d), f(k))
28.45/9.22	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.22	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.22	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.22	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.22	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.22	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.22	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.22	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.22	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.22	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.22	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.22	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.22	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.22	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.22	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.22	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.22	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.22	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.22	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.22	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.22	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.22	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.22	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.22	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.22	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.22	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.22	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.22	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.22	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.22	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.22	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.22	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.22	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.22	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.22	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.22	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.22	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.22	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.22	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.22	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.22	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.22	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.22	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.22	   A^2 -> H(U1(c, a), b)
28.45/9.22	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.22	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.22	   A^2 -> H(U1(c, a), c)
28.45/9.22	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.22	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.22	   A^2 -> H(U1(c, a), e)
28.45/9.22	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.22	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.22	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.22	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.22	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.22	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.22	   A^2 -> H(U1(d, e), f(e))
28.45/9.22	   A^2 -> H(U1(d, e), f(k))
28.45/9.22	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.22	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.22	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.22	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.22	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.22	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.22	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.22	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.22	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.22	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.22	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.22	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.22	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.22	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.22	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.22	   A^2 -> H(U1(d, a), b)
28.45/9.22	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.22	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.22	   A^2 -> H(U1(d, a), c)
28.45/9.22	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.22	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.22	   A^2 -> H(U1(d, a), e)
28.45/9.22	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.22	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.22	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.22	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.22	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.22	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.22	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.22	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.22	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.22	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.22	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.22	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.22	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.22	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.22	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.22	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.22	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.22	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.22	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.22	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.22	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.22	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.22	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.22	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.22	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.22	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.22	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.22	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.22	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.22	   A^2 -> H(U1(a, c), b)
28.45/9.22	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.22	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.22	   A^2 -> H(U1(a, c), c)
28.45/9.22	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.22	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.22	   A^2 -> H(U1(a, c), e)
28.45/9.22	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.22	   A^2 -> H(U1(a, d), b)
28.45/9.22	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.22	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.22	   A^2 -> H(U1(a, d), c)
28.45/9.22	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.22	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.22	   A^2 -> H(U1(a, d), e)
28.45/9.22	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.22	   A^2 -> H(U1(a, a), d)
28.45/9.22	   A^2 -> H(U1(a, a), k)
28.45/9.22	   A^2 -> H(k, U1(b, b))
28.45/9.22	   A^2 -> H(k, f(c))
28.45/9.22	   A^2 -> H(k, f(d))
28.45/9.22	   A^2 -> H(c, U1(c, b))
28.45/9.22	   A^2 -> H(c, U1(d, b))
28.45/9.22	   A^2 -> H(c, U1(b, c))
28.45/9.22	   A^2 -> H(c, U1(b, d))
28.45/9.22	   A^2 -> H(c, U1(c, c))
28.45/9.22	   A^2 -> H(c, f(e))
28.45/9.22	   A^2 -> H(c, f(k))
28.45/9.22	   A^2 -> H(c, U1(d, d))
28.45/9.22	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.22	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.22	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.22	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.22	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.22	   A^2 -> H(U1(e, k), f(e))
28.45/9.22	   A^2 -> H(U1(e, k), f(k))
28.45/9.22	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.22	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.22	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.22	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.22	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.22	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.22	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.22	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.22	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.22	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.22	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.22	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.22	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.22	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.22	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.22	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.22	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.22	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.22	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.22	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.22	   A^2 -> H(U1(k, e), f(e))
28.45/9.22	   A^2 -> H(U1(k, e), f(k))
28.45/9.22	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.22	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.22	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.22	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.22	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.22	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.22	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.22	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.22	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.22	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.22	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.22	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.22	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.22	
28.45/9.22	The TRS R consists of the following rules:
28.45/9.22	
28.45/9.22	   f(x) -> U1(x, x)
28.45/9.22	   U1(e, x) -> x
28.45/9.22	   a -> c
28.45/9.22	   a -> d
28.45/9.22	   b -> c
28.45/9.22	   b -> d
28.45/9.22	   d -> k
28.45/9.22	   c -> e
28.45/9.22	   c -> k
28.45/9.22	
28.45/9.22	Q is empty.
28.45/9.22	We have to consider all minimal (P,Q,R)-chains.
28.45/9.22	----------------------------------------
28.45/9.22	
28.45/9.22	(835) TransformationProof (EQUIVALENT)
28.45/9.22	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.22	
28.45/9.22	   (A^2 -> H(U1(k, e), U1(d, d)),A^2 -> H(U1(k, e), U1(d, d)))
28.45/9.22	   (A^2 -> H(U1(k, k), U1(d, d)),A^2 -> H(U1(k, k), U1(d, d)))
28.45/9.22	   (A^2 -> H(U1(k, c), U1(k, d)),A^2 -> H(U1(k, c), U1(k, d)))
28.45/9.22	   (A^2 -> H(U1(k, c), U1(d, k)),A^2 -> H(U1(k, c), U1(d, k)))
28.45/9.22	
28.45/9.22	
28.45/9.22	----------------------------------------
28.45/9.22	
28.45/9.22	(836)
28.45/9.22	Obligation:
28.45/9.22	Q DP problem:
28.45/9.22	The TRS P consists of the following rules:
28.45/9.22	
28.45/9.22	   H(x, x) -> G(x, x, f(k))
28.45/9.22	   G(d, x, x) -> A^2
28.45/9.22	   A^2 -> H(f(c), f(c))
28.45/9.22	   A^2 -> H(f(d), f(d))
28.45/9.22	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.22	   A^2 -> H(f(e), f(e))
28.45/9.22	   A^2 -> H(f(k), f(k))
28.45/9.22	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.22	   A^2 -> H(U1(c, e), U1(c, b))
28.45/9.22	   A^2 -> H(U1(c, e), U1(d, b))
28.45/9.22	   A^2 -> H(U1(c, e), U1(b, c))
28.45/9.22	   A^2 -> H(U1(c, e), U1(b, d))
28.45/9.22	   A^2 -> H(U1(c, e), U1(c, c))
28.45/9.22	   A^2 -> H(U1(c, e), f(e))
28.45/9.22	   A^2 -> H(U1(c, e), f(k))
28.45/9.22	   A^2 -> H(U1(c, e), U1(d, d))
28.45/9.22	   A^2 -> H(U1(c, k), U1(c, b))
28.45/9.22	   A^2 -> H(U1(c, k), U1(d, b))
28.45/9.22	   A^2 -> H(U1(c, k), U1(b, c))
28.45/9.22	   A^2 -> H(U1(c, k), U1(b, d))
28.45/9.22	   A^2 -> H(U1(c, k), U1(c, c))
28.45/9.22	   A^2 -> H(U1(c, k), f(e))
28.45/9.22	   A^2 -> H(U1(c, k), f(k))
28.45/9.22	   A^2 -> H(U1(c, k), U1(d, d))
28.45/9.22	   A^2 -> H(U1(c, c), U1(e, b))
28.45/9.22	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.22	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.22	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.22	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.22	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.22	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.22	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.22	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.22	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.22	   A^2 -> H(e, U1(b, b))
28.45/9.22	   A^2 -> H(e, f(c))
28.45/9.22	   A^2 -> H(e, f(d))
28.45/9.22	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.22	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.22	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.22	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.22	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.22	   A^2 -> H(U1(e, e), f(e))
28.45/9.22	   A^2 -> H(U1(e, e), f(k))
28.45/9.22	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.22	   A^2 -> H(f(e), U1(e, b))
28.45/9.22	   A^2 -> H(f(e), U1(k, b))
28.45/9.22	   A^2 -> H(f(e), U1(c, d))
28.45/9.22	   A^2 -> H(f(e), U1(d, c))
28.45/9.22	   A^2 -> H(f(e), U1(b, e))
28.45/9.22	   A^2 -> H(f(e), U1(b, k))
28.45/9.22	   A^2 -> H(f(e), U1(e, c))
28.45/9.22	   A^2 -> H(f(e), U1(k, c))
28.45/9.22	   A^2 -> H(f(e), U1(c, e))
28.45/9.22	   A^2 -> H(f(e), U1(c, k))
28.45/9.22	   A^2 -> H(f(e), U1(k, k))
28.45/9.22	   A^2 -> H(f(e), U1(k, d))
28.45/9.22	   A^2 -> H(f(e), U1(d, k))
28.45/9.22	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.22	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.22	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.22	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.22	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.22	   A^2 -> H(U1(k, k), f(e))
28.45/9.22	   A^2 -> H(U1(k, k), f(k))
28.45/9.22	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.22	   A^2 -> H(f(k), U1(e, b))
28.45/9.22	   A^2 -> H(f(k), U1(k, b))
28.45/9.22	   A^2 -> H(f(k), U1(c, d))
28.45/9.22	   A^2 -> H(f(k), U1(d, c))
28.45/9.22	   A^2 -> H(f(k), U1(b, e))
28.45/9.22	   A^2 -> H(f(k), U1(b, k))
28.45/9.22	   A^2 -> H(f(k), U1(e, c))
28.45/9.22	   A^2 -> H(f(k), U1(k, c))
28.45/9.22	   A^2 -> H(f(k), U1(c, e))
28.45/9.22	   A^2 -> H(f(k), U1(c, k))
28.45/9.22	   A^2 -> H(f(k), U1(e, e))
28.45/9.22	   A^2 -> H(f(k), U1(k, d))
28.45/9.22	   A^2 -> H(f(k), U1(d, k))
28.45/9.22	   A^2 -> H(f(c), b)
28.45/9.22	   A^2 -> H(f(c), U1(e, d))
28.45/9.22	   A^2 -> H(f(c), U1(d, e))
28.45/9.22	   A^2 -> H(f(k), U1(k, k))
28.45/9.22	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.22	   A^2 -> H(U1(k, k), f(c))
28.45/9.22	   A^2 -> H(U1(k, k), f(d))
28.45/9.22	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.22	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.22	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.22	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.22	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.22	   A^2 -> H(U1(k, d), f(e))
28.45/9.22	   A^2 -> H(U1(k, d), f(k))
28.45/9.22	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.22	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.22	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.22	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.22	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.22	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.22	   A^2 -> H(U1(d, k), f(e))
28.45/9.22	   A^2 -> H(U1(d, k), f(k))
28.45/9.22	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.22	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.22	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.22	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.22	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.22	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.22	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.22	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.22	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.22	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.22	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.22	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.22	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.22	   A^2 -> H(f(d), b)
28.45/9.22	   A^2 -> H(f(d), U1(e, d))
28.45/9.22	   A^2 -> H(f(d), U1(d, e))
28.45/9.22	   A^2 -> H(f(d), c)
28.45/9.22	   A^2 -> H(f(d), U1(e, k))
28.45/9.22	   A^2 -> H(f(d), U1(k, e))
28.45/9.22	   A^2 -> H(f(d), e)
28.45/9.22	   A^2 -> H(f(a), d)
28.45/9.22	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.22	   A^2 -> H(f(c), c)
28.45/9.22	   A^2 -> H(f(c), U1(e, k))
28.45/9.22	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.22	   A^2 -> H(f(c), U1(k, e))
28.45/9.22	   A^2 -> H(f(c), U1(k, k))
28.45/9.22	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.22	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.22	   A^2 -> H(f(a), k)
28.45/9.22	   A^2 -> H(f(e), U1(e, e))
28.45/9.22	   A^2 -> H(f(c), e)
28.45/9.22	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.22	   A^2 -> H(f(d), U1(k, k))
28.45/9.22	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.22	   A^2 -> H(d, U1(b, b))
28.45/9.22	   A^2 -> H(d, f(c))
28.45/9.22	   A^2 -> H(d, f(d))
28.45/9.22	   A^2 -> H(a, U1(c, b))
28.45/9.22	   A^2 -> H(a, U1(d, b))
28.45/9.22	   A^2 -> H(a, U1(b, c))
28.45/9.22	   A^2 -> H(a, U1(b, d))
28.45/9.22	   A^2 -> H(a, U1(c, c))
28.45/9.22	   A^2 -> H(a, f(e))
28.45/9.22	   A^2 -> H(a, f(k))
28.45/9.22	   A^2 -> H(a, U1(d, d))
28.45/9.22	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.22	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.22	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.22	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.22	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.22	   A^2 -> H(U1(e, d), f(e))
28.45/9.22	   A^2 -> H(U1(e, d), f(k))
28.45/9.22	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.22	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.22	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.22	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.22	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.22	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.22	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.22	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.22	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.22	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.22	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.22	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.22	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.22	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.22	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.22	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.22	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.22	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.22	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.22	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.22	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.22	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.22	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.22	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.22	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.22	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.22	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.22	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.22	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.22	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.22	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.22	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.22	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.22	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.22	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.22	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.22	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.22	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.22	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.22	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.22	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.22	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.22	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.22	   A^2 -> H(U1(c, a), b)
28.45/9.22	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.22	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.22	   A^2 -> H(U1(c, a), c)
28.45/9.22	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.22	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.22	   A^2 -> H(U1(c, a), e)
28.45/9.22	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.22	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.22	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.22	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.22	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.22	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.22	   A^2 -> H(U1(d, e), f(e))
28.45/9.22	   A^2 -> H(U1(d, e), f(k))
28.45/9.22	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.22	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.22	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.22	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.22	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.22	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.22	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.22	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.22	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.22	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.22	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.22	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.22	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.22	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.22	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.22	   A^2 -> H(U1(d, a), b)
28.45/9.22	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.22	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.22	   A^2 -> H(U1(d, a), c)
28.45/9.22	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.22	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.22	   A^2 -> H(U1(d, a), e)
28.45/9.22	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.22	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.22	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.22	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.22	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.22	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.22	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.22	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.22	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.22	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.22	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.22	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.22	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.22	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.22	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.22	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.22	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.22	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.22	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.22	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.22	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.22	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.22	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.22	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.22	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.22	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.22	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.22	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.22	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.22	   A^2 -> H(U1(a, c), b)
28.45/9.22	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.22	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.22	   A^2 -> H(U1(a, c), c)
28.45/9.22	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.22	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.22	   A^2 -> H(U1(a, c), e)
28.45/9.22	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.22	   A^2 -> H(U1(a, d), b)
28.45/9.22	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.22	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.22	   A^2 -> H(U1(a, d), c)
28.45/9.22	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.22	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.22	   A^2 -> H(U1(a, d), e)
28.45/9.22	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.22	   A^2 -> H(U1(a, a), d)
28.45/9.22	   A^2 -> H(U1(a, a), k)
28.45/9.22	   A^2 -> H(k, U1(b, b))
28.45/9.22	   A^2 -> H(k, f(c))
28.45/9.22	   A^2 -> H(k, f(d))
28.45/9.22	   A^2 -> H(c, U1(c, b))
28.45/9.22	   A^2 -> H(c, U1(d, b))
28.45/9.22	   A^2 -> H(c, U1(b, c))
28.45/9.22	   A^2 -> H(c, U1(b, d))
28.45/9.22	   A^2 -> H(c, U1(c, c))
28.45/9.22	   A^2 -> H(c, f(e))
28.45/9.22	   A^2 -> H(c, f(k))
28.45/9.22	   A^2 -> H(c, U1(d, d))
28.45/9.22	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.22	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.22	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.22	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.22	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.22	   A^2 -> H(U1(e, k), f(e))
28.45/9.22	   A^2 -> H(U1(e, k), f(k))
28.45/9.22	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.22	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.22	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.22	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.22	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.22	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.22	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.22	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.22	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.22	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.22	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.22	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.22	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.22	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.22	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.22	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.22	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.22	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(k, e), f(e))
28.45/9.23	   A^2 -> H(U1(k, e), f(k))
28.45/9.23	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.23	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.23	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.23	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.23	
28.45/9.23	The TRS R consists of the following rules:
28.45/9.23	
28.45/9.23	   f(x) -> U1(x, x)
28.45/9.23	   U1(e, x) -> x
28.45/9.23	   a -> c
28.45/9.23	   a -> d
28.45/9.23	   b -> c
28.45/9.23	   b -> d
28.45/9.23	   d -> k
28.45/9.23	   c -> e
28.45/9.23	   c -> k
28.45/9.23	
28.45/9.23	Q is empty.
28.45/9.23	We have to consider all minimal (P,Q,R)-chains.
28.45/9.23	----------------------------------------
28.45/9.23	
28.45/9.23	(837) TransformationProof (EQUIVALENT)
28.45/9.23	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.23	
28.45/9.23	   (A^2 -> H(U1(e, e), U1(c, b)),A^2 -> H(U1(e, e), U1(c, b)))
28.45/9.23	   (A^2 -> H(U1(k, e), U1(c, b)),A^2 -> H(U1(k, e), U1(c, b)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(e, b)),A^2 -> H(U1(c, e), U1(e, b)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(k, b)),A^2 -> H(U1(c, e), U1(k, b)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(c, c)),A^2 -> H(U1(c, e), U1(c, c)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(c, d)),A^2 -> H(U1(c, e), U1(c, d)))
28.45/9.23	
28.45/9.23	
28.45/9.23	----------------------------------------
28.45/9.23	
28.45/9.23	(838)
28.45/9.23	Obligation:
28.45/9.23	Q DP problem:
28.45/9.23	The TRS P consists of the following rules:
28.45/9.23	
28.45/9.23	   H(x, x) -> G(x, x, f(k))
28.45/9.23	   G(d, x, x) -> A^2
28.45/9.23	   A^2 -> H(f(c), f(c))
28.45/9.23	   A^2 -> H(f(d), f(d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.23	   A^2 -> H(f(e), f(e))
28.45/9.23	   A^2 -> H(f(k), f(k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.23	   A^2 -> H(U1(c, e), U1(d, b))
28.45/9.23	   A^2 -> H(U1(c, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(c, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(c, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(c, e), f(e))
28.45/9.23	   A^2 -> H(U1(c, e), f(k))
28.45/9.23	   A^2 -> H(U1(c, e), U1(d, d))
28.45/9.23	   A^2 -> H(U1(c, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(c, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(c, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(c, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(c, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(c, k), f(e))
28.45/9.23	   A^2 -> H(U1(c, k), f(k))
28.45/9.23	   A^2 -> H(U1(c, k), U1(d, d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.23	   A^2 -> H(e, U1(b, b))
28.45/9.23	   A^2 -> H(e, f(c))
28.45/9.23	   A^2 -> H(e, f(d))
28.45/9.23	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.23	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.23	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(e, e), f(e))
28.45/9.23	   A^2 -> H(U1(e, e), f(k))
28.45/9.23	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.23	   A^2 -> H(f(e), U1(e, b))
28.45/9.23	   A^2 -> H(f(e), U1(k, b))
28.45/9.23	   A^2 -> H(f(e), U1(c, d))
28.45/9.23	   A^2 -> H(f(e), U1(d, c))
28.45/9.23	   A^2 -> H(f(e), U1(b, e))
28.45/9.23	   A^2 -> H(f(e), U1(b, k))
28.45/9.23	   A^2 -> H(f(e), U1(e, c))
28.45/9.23	   A^2 -> H(f(e), U1(k, c))
28.45/9.23	   A^2 -> H(f(e), U1(c, e))
28.45/9.23	   A^2 -> H(f(e), U1(c, k))
28.45/9.23	   A^2 -> H(f(e), U1(k, k))
28.45/9.23	   A^2 -> H(f(e), U1(k, d))
28.45/9.23	   A^2 -> H(f(e), U1(d, k))
28.45/9.23	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(k, k), f(e))
28.45/9.23	   A^2 -> H(U1(k, k), f(k))
28.45/9.23	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.23	   A^2 -> H(f(k), U1(e, b))
28.45/9.23	   A^2 -> H(f(k), U1(k, b))
28.45/9.23	   A^2 -> H(f(k), U1(c, d))
28.45/9.23	   A^2 -> H(f(k), U1(d, c))
28.45/9.23	   A^2 -> H(f(k), U1(b, e))
28.45/9.23	   A^2 -> H(f(k), U1(b, k))
28.45/9.23	   A^2 -> H(f(k), U1(e, c))
28.45/9.23	   A^2 -> H(f(k), U1(k, c))
28.45/9.23	   A^2 -> H(f(k), U1(c, e))
28.45/9.23	   A^2 -> H(f(k), U1(c, k))
28.45/9.23	   A^2 -> H(f(k), U1(e, e))
28.45/9.23	   A^2 -> H(f(k), U1(k, d))
28.45/9.23	   A^2 -> H(f(k), U1(d, k))
28.45/9.23	   A^2 -> H(f(c), b)
28.45/9.23	   A^2 -> H(f(c), U1(e, d))
28.45/9.23	   A^2 -> H(f(c), U1(d, e))
28.45/9.23	   A^2 -> H(f(k), U1(k, k))
28.45/9.23	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.23	   A^2 -> H(U1(k, k), f(c))
28.45/9.23	   A^2 -> H(U1(k, k), f(d))
28.45/9.23	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.23	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.23	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.23	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.23	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.23	   A^2 -> H(U1(k, d), f(e))
28.45/9.23	   A^2 -> H(U1(k, d), f(k))
28.45/9.23	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.23	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(d, k), f(e))
28.45/9.23	   A^2 -> H(U1(d, k), f(k))
28.45/9.23	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.23	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.23	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.23	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.23	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.23	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.23	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.23	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.23	   A^2 -> H(f(d), b)
28.45/9.23	   A^2 -> H(f(d), U1(e, d))
28.45/9.23	   A^2 -> H(f(d), U1(d, e))
28.45/9.23	   A^2 -> H(f(d), c)
28.45/9.23	   A^2 -> H(f(d), U1(e, k))
28.45/9.23	   A^2 -> H(f(d), U1(k, e))
28.45/9.23	   A^2 -> H(f(d), e)
28.45/9.23	   A^2 -> H(f(a), d)
28.45/9.23	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.23	   A^2 -> H(f(c), c)
28.45/9.23	   A^2 -> H(f(c), U1(e, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.23	   A^2 -> H(f(c), U1(k, e))
28.45/9.23	   A^2 -> H(f(c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.23	   A^2 -> H(f(a), k)
28.45/9.23	   A^2 -> H(f(e), U1(e, e))
28.45/9.23	   A^2 -> H(f(c), e)
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.23	   A^2 -> H(f(d), U1(k, k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.23	   A^2 -> H(d, U1(b, b))
28.45/9.23	   A^2 -> H(d, f(c))
28.45/9.23	   A^2 -> H(d, f(d))
28.45/9.23	   A^2 -> H(a, U1(c, b))
28.45/9.23	   A^2 -> H(a, U1(d, b))
28.45/9.23	   A^2 -> H(a, U1(b, c))
28.45/9.23	   A^2 -> H(a, U1(b, d))
28.45/9.23	   A^2 -> H(a, U1(c, c))
28.45/9.23	   A^2 -> H(a, f(e))
28.45/9.23	   A^2 -> H(a, f(k))
28.45/9.23	   A^2 -> H(a, U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.23	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.23	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.23	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.23	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.23	   A^2 -> H(U1(e, d), f(e))
28.45/9.23	   A^2 -> H(U1(e, d), f(k))
28.45/9.23	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.23	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.23	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.23	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.23	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.23	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.23	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.23	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.23	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.23	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.23	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.23	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.23	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.23	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.23	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.23	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.23	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.23	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.23	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.23	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.23	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.23	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.23	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.23	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.23	   A^2 -> H(U1(c, a), b)
28.45/9.23	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.23	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.23	   A^2 -> H(U1(c, a), c)
28.45/9.23	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.23	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.23	   A^2 -> H(U1(c, a), e)
28.45/9.23	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.23	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.23	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(d, e), f(e))
28.45/9.23	   A^2 -> H(U1(d, e), f(k))
28.45/9.23	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.23	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.23	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.23	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.23	   A^2 -> H(U1(d, a), b)
28.45/9.23	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.23	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.23	   A^2 -> H(U1(d, a), c)
28.45/9.23	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.23	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.23	   A^2 -> H(U1(d, a), e)
28.45/9.23	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.23	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.23	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.23	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.23	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.23	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.23	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.23	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.23	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.23	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.23	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.23	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.23	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.23	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.23	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.23	   A^2 -> H(U1(a, c), b)
28.45/9.23	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.23	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.23	   A^2 -> H(U1(a, c), c)
28.45/9.23	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.23	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.23	   A^2 -> H(U1(a, c), e)
28.45/9.23	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, d), b)
28.45/9.23	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.23	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.23	   A^2 -> H(U1(a, d), c)
28.45/9.23	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.23	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.23	   A^2 -> H(U1(a, d), e)
28.45/9.23	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, a), d)
28.45/9.23	   A^2 -> H(U1(a, a), k)
28.45/9.23	   A^2 -> H(k, U1(b, b))
28.45/9.23	   A^2 -> H(k, f(c))
28.45/9.23	   A^2 -> H(k, f(d))
28.45/9.23	   A^2 -> H(c, U1(c, b))
28.45/9.23	   A^2 -> H(c, U1(d, b))
28.45/9.23	   A^2 -> H(c, U1(b, c))
28.45/9.23	   A^2 -> H(c, U1(b, d))
28.45/9.23	   A^2 -> H(c, U1(c, c))
28.45/9.23	   A^2 -> H(c, f(e))
28.45/9.23	   A^2 -> H(c, f(k))
28.45/9.23	   A^2 -> H(c, U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(e, k), f(e))
28.45/9.23	   A^2 -> H(U1(e, k), f(k))
28.45/9.23	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.23	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.23	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.23	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.23	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.23	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(k, e), f(e))
28.45/9.23	   A^2 -> H(U1(k, e), f(k))
28.45/9.23	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.23	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.23	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.23	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.23	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.23	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.23	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.23	
28.45/9.23	The TRS R consists of the following rules:
28.45/9.23	
28.45/9.23	   f(x) -> U1(x, x)
28.45/9.23	   U1(e, x) -> x
28.45/9.23	   a -> c
28.45/9.23	   a -> d
28.45/9.23	   b -> c
28.45/9.23	   b -> d
28.45/9.23	   d -> k
28.45/9.23	   c -> e
28.45/9.23	   c -> k
28.45/9.23	
28.45/9.23	Q is empty.
28.45/9.23	We have to consider all minimal (P,Q,R)-chains.
28.45/9.23	----------------------------------------
28.45/9.23	
28.45/9.23	(839) TransformationProof (EQUIVALENT)
28.45/9.23	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.23	
28.45/9.23	   (A^2 -> H(U1(e, e), U1(d, b)),A^2 -> H(U1(e, e), U1(d, b)))
28.45/9.23	   (A^2 -> H(U1(k, e), U1(d, b)),A^2 -> H(U1(k, e), U1(d, b)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(k, b)),A^2 -> H(U1(c, e), U1(k, b)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(d, c)),A^2 -> H(U1(c, e), U1(d, c)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(d, d)),A^2 -> H(U1(c, e), U1(d, d)))
28.45/9.23	
28.45/9.23	
28.45/9.23	----------------------------------------
28.45/9.23	
28.45/9.23	(840)
28.45/9.23	Obligation:
28.45/9.23	Q DP problem:
28.45/9.23	The TRS P consists of the following rules:
28.45/9.23	
28.45/9.23	   H(x, x) -> G(x, x, f(k))
28.45/9.23	   G(d, x, x) -> A^2
28.45/9.23	   A^2 -> H(f(c), f(c))
28.45/9.23	   A^2 -> H(f(d), f(d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.23	   A^2 -> H(f(e), f(e))
28.45/9.23	   A^2 -> H(f(k), f(k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.23	   A^2 -> H(U1(c, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(c, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(c, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(c, e), f(e))
28.45/9.23	   A^2 -> H(U1(c, e), f(k))
28.45/9.23	   A^2 -> H(U1(c, e), U1(d, d))
28.45/9.23	   A^2 -> H(U1(c, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(c, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(c, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(c, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(c, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(c, k), f(e))
28.45/9.23	   A^2 -> H(U1(c, k), f(k))
28.45/9.23	   A^2 -> H(U1(c, k), U1(d, d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.23	   A^2 -> H(e, U1(b, b))
28.45/9.23	   A^2 -> H(e, f(c))
28.45/9.23	   A^2 -> H(e, f(d))
28.45/9.23	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.23	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.23	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(e, e), f(e))
28.45/9.23	   A^2 -> H(U1(e, e), f(k))
28.45/9.23	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.23	   A^2 -> H(f(e), U1(e, b))
28.45/9.23	   A^2 -> H(f(e), U1(k, b))
28.45/9.23	   A^2 -> H(f(e), U1(c, d))
28.45/9.23	   A^2 -> H(f(e), U1(d, c))
28.45/9.23	   A^2 -> H(f(e), U1(b, e))
28.45/9.23	   A^2 -> H(f(e), U1(b, k))
28.45/9.23	   A^2 -> H(f(e), U1(e, c))
28.45/9.23	   A^2 -> H(f(e), U1(k, c))
28.45/9.23	   A^2 -> H(f(e), U1(c, e))
28.45/9.23	   A^2 -> H(f(e), U1(c, k))
28.45/9.23	   A^2 -> H(f(e), U1(k, k))
28.45/9.23	   A^2 -> H(f(e), U1(k, d))
28.45/9.23	   A^2 -> H(f(e), U1(d, k))
28.45/9.23	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(k, k), f(e))
28.45/9.23	   A^2 -> H(U1(k, k), f(k))
28.45/9.23	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.23	   A^2 -> H(f(k), U1(e, b))
28.45/9.23	   A^2 -> H(f(k), U1(k, b))
28.45/9.23	   A^2 -> H(f(k), U1(c, d))
28.45/9.23	   A^2 -> H(f(k), U1(d, c))
28.45/9.23	   A^2 -> H(f(k), U1(b, e))
28.45/9.23	   A^2 -> H(f(k), U1(b, k))
28.45/9.23	   A^2 -> H(f(k), U1(e, c))
28.45/9.23	   A^2 -> H(f(k), U1(k, c))
28.45/9.23	   A^2 -> H(f(k), U1(c, e))
28.45/9.23	   A^2 -> H(f(k), U1(c, k))
28.45/9.23	   A^2 -> H(f(k), U1(e, e))
28.45/9.23	   A^2 -> H(f(k), U1(k, d))
28.45/9.23	   A^2 -> H(f(k), U1(d, k))
28.45/9.23	   A^2 -> H(f(c), b)
28.45/9.23	   A^2 -> H(f(c), U1(e, d))
28.45/9.23	   A^2 -> H(f(c), U1(d, e))
28.45/9.23	   A^2 -> H(f(k), U1(k, k))
28.45/9.23	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.23	   A^2 -> H(U1(k, k), f(c))
28.45/9.23	   A^2 -> H(U1(k, k), f(d))
28.45/9.23	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.23	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.23	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.23	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.23	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.23	   A^2 -> H(U1(k, d), f(e))
28.45/9.23	   A^2 -> H(U1(k, d), f(k))
28.45/9.23	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.23	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(d, k), f(e))
28.45/9.23	   A^2 -> H(U1(d, k), f(k))
28.45/9.23	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.23	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.23	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.23	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.23	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.23	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.23	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.23	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.23	   A^2 -> H(f(d), b)
28.45/9.23	   A^2 -> H(f(d), U1(e, d))
28.45/9.23	   A^2 -> H(f(d), U1(d, e))
28.45/9.23	   A^2 -> H(f(d), c)
28.45/9.23	   A^2 -> H(f(d), U1(e, k))
28.45/9.23	   A^2 -> H(f(d), U1(k, e))
28.45/9.23	   A^2 -> H(f(d), e)
28.45/9.23	   A^2 -> H(f(a), d)
28.45/9.23	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.23	   A^2 -> H(f(c), c)
28.45/9.23	   A^2 -> H(f(c), U1(e, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.23	   A^2 -> H(f(c), U1(k, e))
28.45/9.23	   A^2 -> H(f(c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.23	   A^2 -> H(f(a), k)
28.45/9.23	   A^2 -> H(f(e), U1(e, e))
28.45/9.23	   A^2 -> H(f(c), e)
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.23	   A^2 -> H(f(d), U1(k, k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.23	   A^2 -> H(d, U1(b, b))
28.45/9.23	   A^2 -> H(d, f(c))
28.45/9.23	   A^2 -> H(d, f(d))
28.45/9.23	   A^2 -> H(a, U1(c, b))
28.45/9.23	   A^2 -> H(a, U1(d, b))
28.45/9.23	   A^2 -> H(a, U1(b, c))
28.45/9.23	   A^2 -> H(a, U1(b, d))
28.45/9.23	   A^2 -> H(a, U1(c, c))
28.45/9.23	   A^2 -> H(a, f(e))
28.45/9.23	   A^2 -> H(a, f(k))
28.45/9.23	   A^2 -> H(a, U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.23	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.23	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.23	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.23	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.23	   A^2 -> H(U1(e, d), f(e))
28.45/9.23	   A^2 -> H(U1(e, d), f(k))
28.45/9.23	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.23	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.23	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.23	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.23	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.23	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.23	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.23	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.23	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.23	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.23	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.23	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.23	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.23	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.23	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.23	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.23	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.23	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.23	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.23	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.23	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.23	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.23	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.23	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.23	   A^2 -> H(U1(c, a), b)
28.45/9.23	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.23	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.23	   A^2 -> H(U1(c, a), c)
28.45/9.23	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.23	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.23	   A^2 -> H(U1(c, a), e)
28.45/9.23	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.23	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.23	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(d, e), f(e))
28.45/9.23	   A^2 -> H(U1(d, e), f(k))
28.45/9.23	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.23	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.23	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.23	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.23	   A^2 -> H(U1(d, a), b)
28.45/9.23	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.23	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.23	   A^2 -> H(U1(d, a), c)
28.45/9.23	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.23	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.23	   A^2 -> H(U1(d, a), e)
28.45/9.23	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.23	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.23	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.23	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.23	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.23	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.23	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.23	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.23	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.23	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.23	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.23	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.23	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.23	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.23	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.23	   A^2 -> H(U1(a, c), b)
28.45/9.23	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.23	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.23	   A^2 -> H(U1(a, c), c)
28.45/9.23	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.23	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.23	   A^2 -> H(U1(a, c), e)
28.45/9.23	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, d), b)
28.45/9.23	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.23	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.23	   A^2 -> H(U1(a, d), c)
28.45/9.23	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.23	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.23	   A^2 -> H(U1(a, d), e)
28.45/9.23	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, a), d)
28.45/9.23	   A^2 -> H(U1(a, a), k)
28.45/9.23	   A^2 -> H(k, U1(b, b))
28.45/9.23	   A^2 -> H(k, f(c))
28.45/9.23	   A^2 -> H(k, f(d))
28.45/9.23	   A^2 -> H(c, U1(c, b))
28.45/9.23	   A^2 -> H(c, U1(d, b))
28.45/9.23	   A^2 -> H(c, U1(b, c))
28.45/9.23	   A^2 -> H(c, U1(b, d))
28.45/9.23	   A^2 -> H(c, U1(c, c))
28.45/9.23	   A^2 -> H(c, f(e))
28.45/9.23	   A^2 -> H(c, f(k))
28.45/9.23	   A^2 -> H(c, U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(e, k), f(e))
28.45/9.23	   A^2 -> H(U1(e, k), f(k))
28.45/9.23	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.23	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.23	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.23	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.23	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.23	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(k, e), f(e))
28.45/9.23	   A^2 -> H(U1(k, e), f(k))
28.45/9.23	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.23	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.23	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.23	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.23	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.23	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.23	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.23	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.23	
28.45/9.23	The TRS R consists of the following rules:
28.45/9.23	
28.45/9.23	   f(x) -> U1(x, x)
28.45/9.23	   U1(e, x) -> x
28.45/9.23	   a -> c
28.45/9.23	   a -> d
28.45/9.23	   b -> c
28.45/9.23	   b -> d
28.45/9.23	   d -> k
28.45/9.23	   c -> e
28.45/9.23	   c -> k
28.45/9.23	
28.45/9.23	Q is empty.
28.45/9.23	We have to consider all minimal (P,Q,R)-chains.
28.45/9.23	----------------------------------------
28.45/9.23	
28.45/9.23	(841) TransformationProof (EQUIVALENT)
28.45/9.23	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.23	
28.45/9.23	   (A^2 -> H(U1(e, e), U1(b, c)),A^2 -> H(U1(e, e), U1(b, c)))
28.45/9.23	   (A^2 -> H(U1(k, e), U1(b, c)),A^2 -> H(U1(k, e), U1(b, c)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(c, c)),A^2 -> H(U1(c, e), U1(c, c)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(d, c)),A^2 -> H(U1(c, e), U1(d, c)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(b, e)),A^2 -> H(U1(c, e), U1(b, e)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(b, k)),A^2 -> H(U1(c, e), U1(b, k)))
28.45/9.23	
28.45/9.23	
28.45/9.23	----------------------------------------
28.45/9.23	
28.45/9.23	(842)
28.45/9.23	Obligation:
28.45/9.23	Q DP problem:
28.45/9.23	The TRS P consists of the following rules:
28.45/9.23	
28.45/9.23	   H(x, x) -> G(x, x, f(k))
28.45/9.23	   G(d, x, x) -> A^2
28.45/9.23	   A^2 -> H(f(c), f(c))
28.45/9.23	   A^2 -> H(f(d), f(d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.23	   A^2 -> H(f(e), f(e))
28.45/9.23	   A^2 -> H(f(k), f(k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.23	   A^2 -> H(U1(c, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(c, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(c, e), f(e))
28.45/9.23	   A^2 -> H(U1(c, e), f(k))
28.45/9.23	   A^2 -> H(U1(c, e), U1(d, d))
28.45/9.23	   A^2 -> H(U1(c, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(c, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(c, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(c, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(c, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(c, k), f(e))
28.45/9.23	   A^2 -> H(U1(c, k), f(k))
28.45/9.23	   A^2 -> H(U1(c, k), U1(d, d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.23	   A^2 -> H(e, U1(b, b))
28.45/9.23	   A^2 -> H(e, f(c))
28.45/9.23	   A^2 -> H(e, f(d))
28.45/9.23	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.23	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.23	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(e, e), f(e))
28.45/9.23	   A^2 -> H(U1(e, e), f(k))
28.45/9.23	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.23	   A^2 -> H(f(e), U1(e, b))
28.45/9.23	   A^2 -> H(f(e), U1(k, b))
28.45/9.23	   A^2 -> H(f(e), U1(c, d))
28.45/9.23	   A^2 -> H(f(e), U1(d, c))
28.45/9.23	   A^2 -> H(f(e), U1(b, e))
28.45/9.23	   A^2 -> H(f(e), U1(b, k))
28.45/9.23	   A^2 -> H(f(e), U1(e, c))
28.45/9.23	   A^2 -> H(f(e), U1(k, c))
28.45/9.23	   A^2 -> H(f(e), U1(c, e))
28.45/9.23	   A^2 -> H(f(e), U1(c, k))
28.45/9.23	   A^2 -> H(f(e), U1(k, k))
28.45/9.23	   A^2 -> H(f(e), U1(k, d))
28.45/9.23	   A^2 -> H(f(e), U1(d, k))
28.45/9.23	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(k, k), f(e))
28.45/9.23	   A^2 -> H(U1(k, k), f(k))
28.45/9.23	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.23	   A^2 -> H(f(k), U1(e, b))
28.45/9.23	   A^2 -> H(f(k), U1(k, b))
28.45/9.23	   A^2 -> H(f(k), U1(c, d))
28.45/9.23	   A^2 -> H(f(k), U1(d, c))
28.45/9.23	   A^2 -> H(f(k), U1(b, e))
28.45/9.23	   A^2 -> H(f(k), U1(b, k))
28.45/9.23	   A^2 -> H(f(k), U1(e, c))
28.45/9.23	   A^2 -> H(f(k), U1(k, c))
28.45/9.23	   A^2 -> H(f(k), U1(c, e))
28.45/9.23	   A^2 -> H(f(k), U1(c, k))
28.45/9.23	   A^2 -> H(f(k), U1(e, e))
28.45/9.23	   A^2 -> H(f(k), U1(k, d))
28.45/9.23	   A^2 -> H(f(k), U1(d, k))
28.45/9.23	   A^2 -> H(f(c), b)
28.45/9.23	   A^2 -> H(f(c), U1(e, d))
28.45/9.23	   A^2 -> H(f(c), U1(d, e))
28.45/9.23	   A^2 -> H(f(k), U1(k, k))
28.45/9.23	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.23	   A^2 -> H(U1(k, k), f(c))
28.45/9.23	   A^2 -> H(U1(k, k), f(d))
28.45/9.23	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.23	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.23	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.23	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.23	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.23	   A^2 -> H(U1(k, d), f(e))
28.45/9.23	   A^2 -> H(U1(k, d), f(k))
28.45/9.23	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.23	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(d, k), f(e))
28.45/9.23	   A^2 -> H(U1(d, k), f(k))
28.45/9.23	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.23	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.23	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.23	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.23	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.23	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.23	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.23	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.23	   A^2 -> H(f(d), b)
28.45/9.23	   A^2 -> H(f(d), U1(e, d))
28.45/9.23	   A^2 -> H(f(d), U1(d, e))
28.45/9.23	   A^2 -> H(f(d), c)
28.45/9.23	   A^2 -> H(f(d), U1(e, k))
28.45/9.23	   A^2 -> H(f(d), U1(k, e))
28.45/9.23	   A^2 -> H(f(d), e)
28.45/9.23	   A^2 -> H(f(a), d)
28.45/9.23	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.23	   A^2 -> H(f(c), c)
28.45/9.23	   A^2 -> H(f(c), U1(e, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.23	   A^2 -> H(f(c), U1(k, e))
28.45/9.23	   A^2 -> H(f(c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.23	   A^2 -> H(f(a), k)
28.45/9.23	   A^2 -> H(f(e), U1(e, e))
28.45/9.23	   A^2 -> H(f(c), e)
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.23	   A^2 -> H(f(d), U1(k, k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.23	   A^2 -> H(d, U1(b, b))
28.45/9.23	   A^2 -> H(d, f(c))
28.45/9.23	   A^2 -> H(d, f(d))
28.45/9.23	   A^2 -> H(a, U1(c, b))
28.45/9.23	   A^2 -> H(a, U1(d, b))
28.45/9.23	   A^2 -> H(a, U1(b, c))
28.45/9.23	   A^2 -> H(a, U1(b, d))
28.45/9.23	   A^2 -> H(a, U1(c, c))
28.45/9.23	   A^2 -> H(a, f(e))
28.45/9.23	   A^2 -> H(a, f(k))
28.45/9.23	   A^2 -> H(a, U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.23	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.23	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.23	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.23	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.23	   A^2 -> H(U1(e, d), f(e))
28.45/9.23	   A^2 -> H(U1(e, d), f(k))
28.45/9.23	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.23	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.23	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.23	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.23	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.23	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.23	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.23	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.23	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.23	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.23	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.23	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.23	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.23	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.23	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.23	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.23	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.23	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.23	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.23	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.23	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.23	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.23	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.23	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.23	   A^2 -> H(U1(c, a), b)
28.45/9.23	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.23	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.23	   A^2 -> H(U1(c, a), c)
28.45/9.23	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.23	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.23	   A^2 -> H(U1(c, a), e)
28.45/9.23	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.23	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.23	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(d, e), f(e))
28.45/9.23	   A^2 -> H(U1(d, e), f(k))
28.45/9.23	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.23	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.23	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.23	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.23	   A^2 -> H(U1(d, a), b)
28.45/9.23	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.23	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.23	   A^2 -> H(U1(d, a), c)
28.45/9.23	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.23	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.23	   A^2 -> H(U1(d, a), e)
28.45/9.23	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.23	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.23	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.23	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.23	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.23	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.23	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.23	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.23	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.23	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.23	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.23	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.23	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.23	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.23	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.23	   A^2 -> H(U1(a, c), b)
28.45/9.23	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.23	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.23	   A^2 -> H(U1(a, c), c)
28.45/9.23	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.23	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.23	   A^2 -> H(U1(a, c), e)
28.45/9.23	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, d), b)
28.45/9.23	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.23	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.23	   A^2 -> H(U1(a, d), c)
28.45/9.23	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.23	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.23	   A^2 -> H(U1(a, d), e)
28.45/9.23	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, a), d)
28.45/9.23	   A^2 -> H(U1(a, a), k)
28.45/9.23	   A^2 -> H(k, U1(b, b))
28.45/9.23	   A^2 -> H(k, f(c))
28.45/9.23	   A^2 -> H(k, f(d))
28.45/9.23	   A^2 -> H(c, U1(c, b))
28.45/9.23	   A^2 -> H(c, U1(d, b))
28.45/9.23	   A^2 -> H(c, U1(b, c))
28.45/9.23	   A^2 -> H(c, U1(b, d))
28.45/9.23	   A^2 -> H(c, U1(c, c))
28.45/9.23	   A^2 -> H(c, f(e))
28.45/9.23	   A^2 -> H(c, f(k))
28.45/9.23	   A^2 -> H(c, U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(e, k), f(e))
28.45/9.23	   A^2 -> H(U1(e, k), f(k))
28.45/9.23	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.23	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.23	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.23	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.23	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.23	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(k, e), f(e))
28.45/9.23	   A^2 -> H(U1(k, e), f(k))
28.45/9.23	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.23	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.23	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.23	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.23	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.23	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.23	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.23	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.23	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.23	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.23	
28.45/9.23	The TRS R consists of the following rules:
28.45/9.23	
28.45/9.23	   f(x) -> U1(x, x)
28.45/9.23	   U1(e, x) -> x
28.45/9.23	   a -> c
28.45/9.23	   a -> d
28.45/9.23	   b -> c
28.45/9.23	   b -> d
28.45/9.23	   d -> k
28.45/9.23	   c -> e
28.45/9.23	   c -> k
28.45/9.23	
28.45/9.23	Q is empty.
28.45/9.23	We have to consider all minimal (P,Q,R)-chains.
28.45/9.23	----------------------------------------
28.45/9.23	
28.45/9.23	(843) TransformationProof (EQUIVALENT)
28.45/9.23	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.23	
28.45/9.23	   (A^2 -> H(U1(e, e), U1(b, d)),A^2 -> H(U1(e, e), U1(b, d)))
28.45/9.23	   (A^2 -> H(U1(k, e), U1(b, d)),A^2 -> H(U1(k, e), U1(b, d)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(c, d)),A^2 -> H(U1(c, e), U1(c, d)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(d, d)),A^2 -> H(U1(c, e), U1(d, d)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(b, k)),A^2 -> H(U1(c, e), U1(b, k)))
28.45/9.23	
28.45/9.23	
28.45/9.23	----------------------------------------
28.45/9.23	
28.45/9.23	(844)
28.45/9.23	Obligation:
28.45/9.23	Q DP problem:
28.45/9.23	The TRS P consists of the following rules:
28.45/9.23	
28.45/9.23	   H(x, x) -> G(x, x, f(k))
28.45/9.23	   G(d, x, x) -> A^2
28.45/9.23	   A^2 -> H(f(c), f(c))
28.45/9.23	   A^2 -> H(f(d), f(d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.23	   A^2 -> H(f(e), f(e))
28.45/9.23	   A^2 -> H(f(k), f(k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.23	   A^2 -> H(U1(c, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(c, e), f(e))
28.45/9.23	   A^2 -> H(U1(c, e), f(k))
28.45/9.23	   A^2 -> H(U1(c, e), U1(d, d))
28.45/9.23	   A^2 -> H(U1(c, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(c, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(c, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(c, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(c, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(c, k), f(e))
28.45/9.23	   A^2 -> H(U1(c, k), f(k))
28.45/9.23	   A^2 -> H(U1(c, k), U1(d, d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.23	   A^2 -> H(e, U1(b, b))
28.45/9.23	   A^2 -> H(e, f(c))
28.45/9.23	   A^2 -> H(e, f(d))
28.45/9.23	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.23	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.23	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(e, e), f(e))
28.45/9.23	   A^2 -> H(U1(e, e), f(k))
28.45/9.23	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.23	   A^2 -> H(f(e), U1(e, b))
28.45/9.23	   A^2 -> H(f(e), U1(k, b))
28.45/9.23	   A^2 -> H(f(e), U1(c, d))
28.45/9.23	   A^2 -> H(f(e), U1(d, c))
28.45/9.23	   A^2 -> H(f(e), U1(b, e))
28.45/9.23	   A^2 -> H(f(e), U1(b, k))
28.45/9.23	   A^2 -> H(f(e), U1(e, c))
28.45/9.23	   A^2 -> H(f(e), U1(k, c))
28.45/9.23	   A^2 -> H(f(e), U1(c, e))
28.45/9.23	   A^2 -> H(f(e), U1(c, k))
28.45/9.23	   A^2 -> H(f(e), U1(k, k))
28.45/9.23	   A^2 -> H(f(e), U1(k, d))
28.45/9.23	   A^2 -> H(f(e), U1(d, k))
28.45/9.23	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(k, k), f(e))
28.45/9.23	   A^2 -> H(U1(k, k), f(k))
28.45/9.23	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.23	   A^2 -> H(f(k), U1(e, b))
28.45/9.23	   A^2 -> H(f(k), U1(k, b))
28.45/9.23	   A^2 -> H(f(k), U1(c, d))
28.45/9.23	   A^2 -> H(f(k), U1(d, c))
28.45/9.23	   A^2 -> H(f(k), U1(b, e))
28.45/9.23	   A^2 -> H(f(k), U1(b, k))
28.45/9.23	   A^2 -> H(f(k), U1(e, c))
28.45/9.23	   A^2 -> H(f(k), U1(k, c))
28.45/9.23	   A^2 -> H(f(k), U1(c, e))
28.45/9.23	   A^2 -> H(f(k), U1(c, k))
28.45/9.23	   A^2 -> H(f(k), U1(e, e))
28.45/9.23	   A^2 -> H(f(k), U1(k, d))
28.45/9.23	   A^2 -> H(f(k), U1(d, k))
28.45/9.23	   A^2 -> H(f(c), b)
28.45/9.23	   A^2 -> H(f(c), U1(e, d))
28.45/9.23	   A^2 -> H(f(c), U1(d, e))
28.45/9.23	   A^2 -> H(f(k), U1(k, k))
28.45/9.23	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.23	   A^2 -> H(U1(k, k), f(c))
28.45/9.23	   A^2 -> H(U1(k, k), f(d))
28.45/9.23	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.23	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.23	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.23	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.23	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.23	   A^2 -> H(U1(k, d), f(e))
28.45/9.23	   A^2 -> H(U1(k, d), f(k))
28.45/9.23	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.23	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(d, k), f(e))
28.45/9.23	   A^2 -> H(U1(d, k), f(k))
28.45/9.23	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.23	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.23	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.23	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.23	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.23	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.23	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.23	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.23	   A^2 -> H(f(d), b)
28.45/9.23	   A^2 -> H(f(d), U1(e, d))
28.45/9.23	   A^2 -> H(f(d), U1(d, e))
28.45/9.23	   A^2 -> H(f(d), c)
28.45/9.23	   A^2 -> H(f(d), U1(e, k))
28.45/9.23	   A^2 -> H(f(d), U1(k, e))
28.45/9.23	   A^2 -> H(f(d), e)
28.45/9.23	   A^2 -> H(f(a), d)
28.45/9.23	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.23	   A^2 -> H(f(c), c)
28.45/9.23	   A^2 -> H(f(c), U1(e, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.23	   A^2 -> H(f(c), U1(k, e))
28.45/9.23	   A^2 -> H(f(c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.23	   A^2 -> H(f(a), k)
28.45/9.23	   A^2 -> H(f(e), U1(e, e))
28.45/9.23	   A^2 -> H(f(c), e)
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.23	   A^2 -> H(f(d), U1(k, k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.23	   A^2 -> H(d, U1(b, b))
28.45/9.23	   A^2 -> H(d, f(c))
28.45/9.23	   A^2 -> H(d, f(d))
28.45/9.23	   A^2 -> H(a, U1(c, b))
28.45/9.23	   A^2 -> H(a, U1(d, b))
28.45/9.23	   A^2 -> H(a, U1(b, c))
28.45/9.23	   A^2 -> H(a, U1(b, d))
28.45/9.23	   A^2 -> H(a, U1(c, c))
28.45/9.23	   A^2 -> H(a, f(e))
28.45/9.23	   A^2 -> H(a, f(k))
28.45/9.23	   A^2 -> H(a, U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.23	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.23	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.23	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.23	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.23	   A^2 -> H(U1(e, d), f(e))
28.45/9.23	   A^2 -> H(U1(e, d), f(k))
28.45/9.23	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.23	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.23	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.23	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.23	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.23	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.23	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.23	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.23	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.23	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.23	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.23	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.23	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.23	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.23	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.23	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.23	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.23	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.23	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.23	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.23	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.23	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.23	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.23	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.23	   A^2 -> H(U1(c, a), b)
28.45/9.23	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.23	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.23	   A^2 -> H(U1(c, a), c)
28.45/9.23	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.23	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.23	   A^2 -> H(U1(c, a), e)
28.45/9.23	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.23	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.23	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(d, e), f(e))
28.45/9.23	   A^2 -> H(U1(d, e), f(k))
28.45/9.23	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.23	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.23	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.23	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.23	   A^2 -> H(U1(d, a), b)
28.45/9.23	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.23	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.23	   A^2 -> H(U1(d, a), c)
28.45/9.23	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.23	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.23	   A^2 -> H(U1(d, a), e)
28.45/9.23	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.23	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.23	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.23	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.23	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.23	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.23	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.23	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.23	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.23	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.23	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.23	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.23	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.23	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.23	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.23	   A^2 -> H(U1(a, c), b)
28.45/9.23	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.23	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.23	   A^2 -> H(U1(a, c), c)
28.45/9.23	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.23	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.23	   A^2 -> H(U1(a, c), e)
28.45/9.23	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, d), b)
28.45/9.23	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.23	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.23	   A^2 -> H(U1(a, d), c)
28.45/9.23	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.23	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.23	   A^2 -> H(U1(a, d), e)
28.45/9.23	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, a), d)
28.45/9.23	   A^2 -> H(U1(a, a), k)
28.45/9.23	   A^2 -> H(k, U1(b, b))
28.45/9.23	   A^2 -> H(k, f(c))
28.45/9.23	   A^2 -> H(k, f(d))
28.45/9.23	   A^2 -> H(c, U1(c, b))
28.45/9.23	   A^2 -> H(c, U1(d, b))
28.45/9.23	   A^2 -> H(c, U1(b, c))
28.45/9.23	   A^2 -> H(c, U1(b, d))
28.45/9.23	   A^2 -> H(c, U1(c, c))
28.45/9.23	   A^2 -> H(c, f(e))
28.45/9.23	   A^2 -> H(c, f(k))
28.45/9.23	   A^2 -> H(c, U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(e, k), f(e))
28.45/9.23	   A^2 -> H(U1(e, k), f(k))
28.45/9.23	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.23	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.23	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.23	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.23	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.23	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(k, e), f(e))
28.45/9.23	   A^2 -> H(U1(k, e), f(k))
28.45/9.23	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.23	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.23	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.23	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.23	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.23	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.23	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.23	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.23	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.23	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.23	
28.45/9.23	The TRS R consists of the following rules:
28.45/9.23	
28.45/9.23	   f(x) -> U1(x, x)
28.45/9.23	   U1(e, x) -> x
28.45/9.23	   a -> c
28.45/9.23	   a -> d
28.45/9.23	   b -> c
28.45/9.23	   b -> d
28.45/9.23	   d -> k
28.45/9.23	   c -> e
28.45/9.23	   c -> k
28.45/9.23	
28.45/9.23	Q is empty.
28.45/9.23	We have to consider all minimal (P,Q,R)-chains.
28.45/9.23	----------------------------------------
28.45/9.23	
28.45/9.23	(845) TransformationProof (EQUIVALENT)
28.45/9.23	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.23	
28.45/9.23	   (A^2 -> H(U1(e, e), U1(c, c)),A^2 -> H(U1(e, e), U1(c, c)))
28.45/9.23	   (A^2 -> H(U1(k, e), U1(c, c)),A^2 -> H(U1(k, e), U1(c, c)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(e, c)),A^2 -> H(U1(c, e), U1(e, c)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(k, c)),A^2 -> H(U1(c, e), U1(k, c)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(c, e)),A^2 -> H(U1(c, e), U1(c, e)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(c, k)),A^2 -> H(U1(c, e), U1(c, k)))
28.45/9.23	
28.45/9.23	
28.45/9.23	----------------------------------------
28.45/9.23	
28.45/9.23	(846)
28.45/9.23	Obligation:
28.45/9.23	Q DP problem:
28.45/9.23	The TRS P consists of the following rules:
28.45/9.23	
28.45/9.23	   H(x, x) -> G(x, x, f(k))
28.45/9.23	   G(d, x, x) -> A^2
28.45/9.23	   A^2 -> H(f(c), f(c))
28.45/9.23	   A^2 -> H(f(d), f(d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.23	   A^2 -> H(f(e), f(e))
28.45/9.23	   A^2 -> H(f(k), f(k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.23	   A^2 -> H(U1(c, e), f(e))
28.45/9.23	   A^2 -> H(U1(c, e), f(k))
28.45/9.23	   A^2 -> H(U1(c, e), U1(d, d))
28.45/9.23	   A^2 -> H(U1(c, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(c, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(c, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(c, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(c, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(c, k), f(e))
28.45/9.23	   A^2 -> H(U1(c, k), f(k))
28.45/9.23	   A^2 -> H(U1(c, k), U1(d, d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.23	   A^2 -> H(e, U1(b, b))
28.45/9.23	   A^2 -> H(e, f(c))
28.45/9.23	   A^2 -> H(e, f(d))
28.45/9.23	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.23	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.23	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(e, e), f(e))
28.45/9.23	   A^2 -> H(U1(e, e), f(k))
28.45/9.23	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.23	   A^2 -> H(f(e), U1(e, b))
28.45/9.23	   A^2 -> H(f(e), U1(k, b))
28.45/9.23	   A^2 -> H(f(e), U1(c, d))
28.45/9.23	   A^2 -> H(f(e), U1(d, c))
28.45/9.23	   A^2 -> H(f(e), U1(b, e))
28.45/9.23	   A^2 -> H(f(e), U1(b, k))
28.45/9.23	   A^2 -> H(f(e), U1(e, c))
28.45/9.23	   A^2 -> H(f(e), U1(k, c))
28.45/9.23	   A^2 -> H(f(e), U1(c, e))
28.45/9.23	   A^2 -> H(f(e), U1(c, k))
28.45/9.23	   A^2 -> H(f(e), U1(k, k))
28.45/9.23	   A^2 -> H(f(e), U1(k, d))
28.45/9.23	   A^2 -> H(f(e), U1(d, k))
28.45/9.23	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(k, k), f(e))
28.45/9.23	   A^2 -> H(U1(k, k), f(k))
28.45/9.23	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.23	   A^2 -> H(f(k), U1(e, b))
28.45/9.23	   A^2 -> H(f(k), U1(k, b))
28.45/9.23	   A^2 -> H(f(k), U1(c, d))
28.45/9.23	   A^2 -> H(f(k), U1(d, c))
28.45/9.23	   A^2 -> H(f(k), U1(b, e))
28.45/9.23	   A^2 -> H(f(k), U1(b, k))
28.45/9.23	   A^2 -> H(f(k), U1(e, c))
28.45/9.23	   A^2 -> H(f(k), U1(k, c))
28.45/9.23	   A^2 -> H(f(k), U1(c, e))
28.45/9.23	   A^2 -> H(f(k), U1(c, k))
28.45/9.23	   A^2 -> H(f(k), U1(e, e))
28.45/9.23	   A^2 -> H(f(k), U1(k, d))
28.45/9.23	   A^2 -> H(f(k), U1(d, k))
28.45/9.23	   A^2 -> H(f(c), b)
28.45/9.23	   A^2 -> H(f(c), U1(e, d))
28.45/9.23	   A^2 -> H(f(c), U1(d, e))
28.45/9.23	   A^2 -> H(f(k), U1(k, k))
28.45/9.23	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.23	   A^2 -> H(U1(k, k), f(c))
28.45/9.23	   A^2 -> H(U1(k, k), f(d))
28.45/9.23	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.23	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.23	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.23	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.23	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.23	   A^2 -> H(U1(k, d), f(e))
28.45/9.23	   A^2 -> H(U1(k, d), f(k))
28.45/9.23	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.23	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(d, k), f(e))
28.45/9.23	   A^2 -> H(U1(d, k), f(k))
28.45/9.23	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.23	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.23	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.23	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.23	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.23	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.23	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.23	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.23	   A^2 -> H(f(d), b)
28.45/9.23	   A^2 -> H(f(d), U1(e, d))
28.45/9.23	   A^2 -> H(f(d), U1(d, e))
28.45/9.23	   A^2 -> H(f(d), c)
28.45/9.23	   A^2 -> H(f(d), U1(e, k))
28.45/9.23	   A^2 -> H(f(d), U1(k, e))
28.45/9.23	   A^2 -> H(f(d), e)
28.45/9.23	   A^2 -> H(f(a), d)
28.45/9.23	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.23	   A^2 -> H(f(c), c)
28.45/9.23	   A^2 -> H(f(c), U1(e, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.23	   A^2 -> H(f(c), U1(k, e))
28.45/9.23	   A^2 -> H(f(c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.23	   A^2 -> H(f(a), k)
28.45/9.23	   A^2 -> H(f(e), U1(e, e))
28.45/9.23	   A^2 -> H(f(c), e)
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.23	   A^2 -> H(f(d), U1(k, k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.23	   A^2 -> H(d, U1(b, b))
28.45/9.23	   A^2 -> H(d, f(c))
28.45/9.23	   A^2 -> H(d, f(d))
28.45/9.23	   A^2 -> H(a, U1(c, b))
28.45/9.23	   A^2 -> H(a, U1(d, b))
28.45/9.23	   A^2 -> H(a, U1(b, c))
28.45/9.23	   A^2 -> H(a, U1(b, d))
28.45/9.23	   A^2 -> H(a, U1(c, c))
28.45/9.23	   A^2 -> H(a, f(e))
28.45/9.23	   A^2 -> H(a, f(k))
28.45/9.23	   A^2 -> H(a, U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.23	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.23	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.23	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.23	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.23	   A^2 -> H(U1(e, d), f(e))
28.45/9.23	   A^2 -> H(U1(e, d), f(k))
28.45/9.23	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.23	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.23	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.23	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.23	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.23	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.23	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.23	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.23	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.23	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.23	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.23	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.23	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.23	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.23	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.23	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.23	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.23	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.23	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.23	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.23	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.23	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.23	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.23	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.23	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.23	   A^2 -> H(U1(c, a), b)
28.45/9.23	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.23	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.23	   A^2 -> H(U1(c, a), c)
28.45/9.23	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.23	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.23	   A^2 -> H(U1(c, a), e)
28.45/9.23	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.23	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.23	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(d, e), f(e))
28.45/9.23	   A^2 -> H(U1(d, e), f(k))
28.45/9.23	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.23	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.23	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.23	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.23	   A^2 -> H(U1(d, a), b)
28.45/9.23	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.23	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.23	   A^2 -> H(U1(d, a), c)
28.45/9.23	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.23	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.23	   A^2 -> H(U1(d, a), e)
28.45/9.23	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.23	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.23	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.23	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.23	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.23	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.23	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.23	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.23	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.23	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.23	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.23	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.23	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.23	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.23	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.23	   A^2 -> H(U1(a, c), b)
28.45/9.23	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.23	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.23	   A^2 -> H(U1(a, c), c)
28.45/9.23	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.23	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.23	   A^2 -> H(U1(a, c), e)
28.45/9.23	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, d), b)
28.45/9.23	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.23	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.23	   A^2 -> H(U1(a, d), c)
28.45/9.23	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.23	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.23	   A^2 -> H(U1(a, d), e)
28.45/9.23	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.23	   A^2 -> H(U1(a, a), d)
28.45/9.23	   A^2 -> H(U1(a, a), k)
28.45/9.23	   A^2 -> H(k, U1(b, b))
28.45/9.23	   A^2 -> H(k, f(c))
28.45/9.23	   A^2 -> H(k, f(d))
28.45/9.23	   A^2 -> H(c, U1(c, b))
28.45/9.23	   A^2 -> H(c, U1(d, b))
28.45/9.23	   A^2 -> H(c, U1(b, c))
28.45/9.23	   A^2 -> H(c, U1(b, d))
28.45/9.23	   A^2 -> H(c, U1(c, c))
28.45/9.23	   A^2 -> H(c, f(e))
28.45/9.23	   A^2 -> H(c, f(k))
28.45/9.23	   A^2 -> H(c, U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(e, k), f(e))
28.45/9.23	   A^2 -> H(U1(e, k), f(k))
28.45/9.23	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.23	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.23	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.23	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.23	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.23	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(k, e), f(e))
28.45/9.23	   A^2 -> H(U1(k, e), f(k))
28.45/9.23	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.23	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.23	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.23	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.23	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.23	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.23	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.23	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.23	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.23	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.23	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.23	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.23	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.23	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.23	
28.45/9.23	The TRS R consists of the following rules:
28.45/9.23	
28.45/9.23	   f(x) -> U1(x, x)
28.45/9.23	   U1(e, x) -> x
28.45/9.23	   a -> c
28.45/9.23	   a -> d
28.45/9.23	   b -> c
28.45/9.23	   b -> d
28.45/9.23	   d -> k
28.45/9.23	   c -> e
28.45/9.23	   c -> k
28.45/9.23	
28.45/9.23	Q is empty.
28.45/9.23	We have to consider all minimal (P,Q,R)-chains.
28.45/9.23	----------------------------------------
28.45/9.23	
28.45/9.23	(847) TransformationProof (EQUIVALENT)
28.45/9.23	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), f(e)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.23	
28.45/9.23	   (A^2 -> H(U1(e, e), f(e)),A^2 -> H(U1(e, e), f(e)))
28.45/9.23	   (A^2 -> H(U1(k, e), f(e)),A^2 -> H(U1(k, e), f(e)))
28.45/9.23	   (A^2 -> H(U1(c, e), U1(e, e)),A^2 -> H(U1(c, e), U1(e, e)))
28.45/9.23	
28.45/9.23	
28.45/9.23	----------------------------------------
28.45/9.23	
28.45/9.23	(848)
28.45/9.23	Obligation:
28.45/9.23	Q DP problem:
28.45/9.23	The TRS P consists of the following rules:
28.45/9.23	
28.45/9.23	   H(x, x) -> G(x, x, f(k))
28.45/9.23	   G(d, x, x) -> A^2
28.45/9.23	   A^2 -> H(f(c), f(c))
28.45/9.23	   A^2 -> H(f(d), f(d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.23	   A^2 -> H(f(e), f(e))
28.45/9.23	   A^2 -> H(f(k), f(k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.23	   A^2 -> H(U1(c, e), f(k))
28.45/9.23	   A^2 -> H(U1(c, e), U1(d, d))
28.45/9.23	   A^2 -> H(U1(c, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(c, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(c, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(c, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(c, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(c, k), f(e))
28.45/9.23	   A^2 -> H(U1(c, k), f(k))
28.45/9.23	   A^2 -> H(U1(c, k), U1(d, d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(e, b))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.23	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.23	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.23	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.23	   A^2 -> H(e, U1(b, b))
28.45/9.23	   A^2 -> H(e, f(c))
28.45/9.23	   A^2 -> H(e, f(d))
28.45/9.23	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.23	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.23	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.23	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.23	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.23	   A^2 -> H(U1(e, e), f(e))
28.45/9.23	   A^2 -> H(U1(e, e), f(k))
28.45/9.23	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.23	   A^2 -> H(f(e), U1(e, b))
28.45/9.23	   A^2 -> H(f(e), U1(k, b))
28.45/9.23	   A^2 -> H(f(e), U1(c, d))
28.45/9.23	   A^2 -> H(f(e), U1(d, c))
28.45/9.23	   A^2 -> H(f(e), U1(b, e))
28.45/9.23	   A^2 -> H(f(e), U1(b, k))
28.45/9.23	   A^2 -> H(f(e), U1(e, c))
28.45/9.23	   A^2 -> H(f(e), U1(k, c))
28.45/9.23	   A^2 -> H(f(e), U1(c, e))
28.45/9.23	   A^2 -> H(f(e), U1(c, k))
28.45/9.23	   A^2 -> H(f(e), U1(k, k))
28.45/9.23	   A^2 -> H(f(e), U1(k, d))
28.45/9.23	   A^2 -> H(f(e), U1(d, k))
28.45/9.23	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(k, k), f(e))
28.45/9.23	   A^2 -> H(U1(k, k), f(k))
28.45/9.23	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.23	   A^2 -> H(f(k), U1(e, b))
28.45/9.23	   A^2 -> H(f(k), U1(k, b))
28.45/9.23	   A^2 -> H(f(k), U1(c, d))
28.45/9.23	   A^2 -> H(f(k), U1(d, c))
28.45/9.23	   A^2 -> H(f(k), U1(b, e))
28.45/9.23	   A^2 -> H(f(k), U1(b, k))
28.45/9.23	   A^2 -> H(f(k), U1(e, c))
28.45/9.23	   A^2 -> H(f(k), U1(k, c))
28.45/9.23	   A^2 -> H(f(k), U1(c, e))
28.45/9.23	   A^2 -> H(f(k), U1(c, k))
28.45/9.23	   A^2 -> H(f(k), U1(e, e))
28.45/9.23	   A^2 -> H(f(k), U1(k, d))
28.45/9.23	   A^2 -> H(f(k), U1(d, k))
28.45/9.23	   A^2 -> H(f(c), b)
28.45/9.23	   A^2 -> H(f(c), U1(e, d))
28.45/9.23	   A^2 -> H(f(c), U1(d, e))
28.45/9.23	   A^2 -> H(f(k), U1(k, k))
28.45/9.23	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.23	   A^2 -> H(U1(k, k), f(c))
28.45/9.23	   A^2 -> H(U1(k, k), f(d))
28.45/9.23	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.23	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.23	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.23	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.23	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.23	   A^2 -> H(U1(k, d), f(e))
28.45/9.23	   A^2 -> H(U1(k, d), f(k))
28.45/9.23	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.23	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.23	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.23	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.23	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.23	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.23	   A^2 -> H(U1(d, k), f(e))
28.45/9.23	   A^2 -> H(U1(d, k), f(k))
28.45/9.23	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.23	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.23	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.23	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.23	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.23	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.23	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.23	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.23	   A^2 -> H(f(d), b)
28.45/9.23	   A^2 -> H(f(d), U1(e, d))
28.45/9.23	   A^2 -> H(f(d), U1(d, e))
28.45/9.23	   A^2 -> H(f(d), c)
28.45/9.23	   A^2 -> H(f(d), U1(e, k))
28.45/9.23	   A^2 -> H(f(d), U1(k, e))
28.45/9.23	   A^2 -> H(f(d), e)
28.45/9.23	   A^2 -> H(f(a), d)
28.45/9.23	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.23	   A^2 -> H(f(c), c)
28.45/9.23	   A^2 -> H(f(c), U1(e, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.23	   A^2 -> H(f(c), U1(k, e))
28.45/9.23	   A^2 -> H(f(c), U1(k, k))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.23	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.23	   A^2 -> H(f(a), k)
28.45/9.23	   A^2 -> H(f(e), U1(e, e))
28.45/9.23	   A^2 -> H(f(c), e)
28.45/9.23	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.23	   A^2 -> H(f(d), U1(k, k))
28.45/9.23	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.23	   A^2 -> H(d, U1(b, b))
28.45/9.23	   A^2 -> H(d, f(c))
28.45/9.23	   A^2 -> H(d, f(d))
28.45/9.23	   A^2 -> H(a, U1(c, b))
28.45/9.23	   A^2 -> H(a, U1(d, b))
28.45/9.23	   A^2 -> H(a, U1(b, c))
28.45/9.23	   A^2 -> H(a, U1(b, d))
28.45/9.23	   A^2 -> H(a, U1(c, c))
28.45/9.23	   A^2 -> H(a, f(e))
28.45/9.23	   A^2 -> H(a, f(k))
28.45/9.23	   A^2 -> H(a, U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.23	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.23	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.23	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.23	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.23	   A^2 -> H(U1(e, d), f(e))
28.45/9.23	   A^2 -> H(U1(e, d), f(k))
28.45/9.23	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.23	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.23	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.23	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.23	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.23	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.23	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.23	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.23	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.23	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.23	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.23	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.23	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.23	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.23	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.23	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.23	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.23	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.24	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.24	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.24	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.24	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.24	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.24	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, a), b)
28.45/9.24	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.24	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.24	   A^2 -> H(U1(c, a), c)
28.45/9.24	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.24	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.24	   A^2 -> H(U1(c, a), e)
28.45/9.24	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.24	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.24	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.24	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.24	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.24	   A^2 -> H(U1(d, e), f(e))
28.45/9.24	   A^2 -> H(U1(d, e), f(k))
28.45/9.24	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.24	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.24	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.24	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.24	   A^2 -> H(U1(d, a), b)
28.45/9.24	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.24	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.24	   A^2 -> H(U1(d, a), c)
28.45/9.24	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.24	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.24	   A^2 -> H(U1(d, a), e)
28.45/9.24	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.24	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.24	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.24	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.24	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.24	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.24	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.24	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.24	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.24	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.24	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.24	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.24	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.24	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.24	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.24	   A^2 -> H(U1(a, c), b)
28.45/9.24	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.24	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.24	   A^2 -> H(U1(a, c), c)
28.45/9.24	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.24	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.24	   A^2 -> H(U1(a, c), e)
28.45/9.24	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, d), b)
28.45/9.24	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.24	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.24	   A^2 -> H(U1(a, d), c)
28.45/9.24	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.24	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.24	   A^2 -> H(U1(a, d), e)
28.45/9.24	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, a), d)
28.45/9.24	   A^2 -> H(U1(a, a), k)
28.45/9.24	   A^2 -> H(k, U1(b, b))
28.45/9.24	   A^2 -> H(k, f(c))
28.45/9.24	   A^2 -> H(k, f(d))
28.45/9.24	   A^2 -> H(c, U1(c, b))
28.45/9.24	   A^2 -> H(c, U1(d, b))
28.45/9.24	   A^2 -> H(c, U1(b, c))
28.45/9.24	   A^2 -> H(c, U1(b, d))
28.45/9.24	   A^2 -> H(c, U1(c, c))
28.45/9.24	   A^2 -> H(c, f(e))
28.45/9.24	   A^2 -> H(c, f(k))
28.45/9.24	   A^2 -> H(c, U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.24	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(e, k), f(e))
28.45/9.24	   A^2 -> H(U1(e, k), f(k))
28.45/9.24	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.24	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.24	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.24	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.24	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.24	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.24	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.24	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.24	   A^2 -> H(U1(k, e), f(e))
28.45/9.24	   A^2 -> H(U1(k, e), f(k))
28.45/9.24	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.24	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.24	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.24	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.24	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.24	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.24	
28.45/9.24	The TRS R consists of the following rules:
28.45/9.24	
28.45/9.24	   f(x) -> U1(x, x)
28.45/9.24	   U1(e, x) -> x
28.45/9.24	   a -> c
28.45/9.24	   a -> d
28.45/9.24	   b -> c
28.45/9.24	   b -> d
28.45/9.24	   d -> k
28.45/9.24	   c -> e
28.45/9.24	   c -> k
28.45/9.24	
28.45/9.24	Q is empty.
28.45/9.24	We have to consider all minimal (P,Q,R)-chains.
28.45/9.24	----------------------------------------
28.45/9.24	
28.45/9.24	(849) TransformationProof (EQUIVALENT)
28.45/9.24	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), f(k)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.24	
28.45/9.24	   (A^2 -> H(U1(e, e), f(k)),A^2 -> H(U1(e, e), f(k)))
28.45/9.24	   (A^2 -> H(U1(k, e), f(k)),A^2 -> H(U1(k, e), f(k)))
28.45/9.24	   (A^2 -> H(U1(c, e), U1(k, k)),A^2 -> H(U1(c, e), U1(k, k)))
28.45/9.24	
28.45/9.24	
28.45/9.24	----------------------------------------
28.45/9.24	
28.45/9.24	(850)
28.45/9.24	Obligation:
28.45/9.24	Q DP problem:
28.45/9.24	The TRS P consists of the following rules:
28.45/9.24	
28.45/9.24	   H(x, x) -> G(x, x, f(k))
28.45/9.24	   G(d, x, x) -> A^2
28.45/9.24	   A^2 -> H(f(c), f(c))
28.45/9.24	   A^2 -> H(f(d), f(d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.24	   A^2 -> H(f(e), f(e))
28.45/9.24	   A^2 -> H(f(k), f(k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.24	   A^2 -> H(U1(c, e), U1(d, d))
28.45/9.24	   A^2 -> H(U1(c, k), U1(c, b))
28.45/9.24	   A^2 -> H(U1(c, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(c, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(c, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(c, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(c, k), f(e))
28.45/9.24	   A^2 -> H(U1(c, k), f(k))
28.45/9.24	   A^2 -> H(U1(c, k), U1(d, d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.24	   A^2 -> H(e, U1(b, b))
28.45/9.24	   A^2 -> H(e, f(c))
28.45/9.24	   A^2 -> H(e, f(d))
28.45/9.24	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.24	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.24	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.24	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.24	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.24	   A^2 -> H(U1(e, e), f(e))
28.45/9.24	   A^2 -> H(U1(e, e), f(k))
28.45/9.24	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.24	   A^2 -> H(f(e), U1(e, b))
28.45/9.24	   A^2 -> H(f(e), U1(k, b))
28.45/9.24	   A^2 -> H(f(e), U1(c, d))
28.45/9.24	   A^2 -> H(f(e), U1(d, c))
28.45/9.24	   A^2 -> H(f(e), U1(b, e))
28.45/9.24	   A^2 -> H(f(e), U1(b, k))
28.45/9.24	   A^2 -> H(f(e), U1(e, c))
28.45/9.24	   A^2 -> H(f(e), U1(k, c))
28.45/9.24	   A^2 -> H(f(e), U1(c, e))
28.45/9.24	   A^2 -> H(f(e), U1(c, k))
28.45/9.24	   A^2 -> H(f(e), U1(k, k))
28.45/9.24	   A^2 -> H(f(e), U1(k, d))
28.45/9.24	   A^2 -> H(f(e), U1(d, k))
28.45/9.24	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.24	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(k, k), f(e))
28.45/9.24	   A^2 -> H(U1(k, k), f(k))
28.45/9.24	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.24	   A^2 -> H(f(k), U1(e, b))
28.45/9.24	   A^2 -> H(f(k), U1(k, b))
28.45/9.24	   A^2 -> H(f(k), U1(c, d))
28.45/9.24	   A^2 -> H(f(k), U1(d, c))
28.45/9.24	   A^2 -> H(f(k), U1(b, e))
28.45/9.24	   A^2 -> H(f(k), U1(b, k))
28.45/9.24	   A^2 -> H(f(k), U1(e, c))
28.45/9.24	   A^2 -> H(f(k), U1(k, c))
28.45/9.24	   A^2 -> H(f(k), U1(c, e))
28.45/9.24	   A^2 -> H(f(k), U1(c, k))
28.45/9.24	   A^2 -> H(f(k), U1(e, e))
28.45/9.24	   A^2 -> H(f(k), U1(k, d))
28.45/9.24	   A^2 -> H(f(k), U1(d, k))
28.45/9.24	   A^2 -> H(f(c), b)
28.45/9.24	   A^2 -> H(f(c), U1(e, d))
28.45/9.24	   A^2 -> H(f(c), U1(d, e))
28.45/9.24	   A^2 -> H(f(k), U1(k, k))
28.45/9.24	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.24	   A^2 -> H(U1(k, k), f(c))
28.45/9.24	   A^2 -> H(U1(k, k), f(d))
28.45/9.24	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.24	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.24	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.24	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.24	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.24	   A^2 -> H(U1(k, d), f(e))
28.45/9.24	   A^2 -> H(U1(k, d), f(k))
28.45/9.24	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.24	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.24	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(d, k), f(e))
28.45/9.24	   A^2 -> H(U1(d, k), f(k))
28.45/9.24	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.24	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.24	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.24	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.24	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.24	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.24	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.24	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.24	   A^2 -> H(f(d), b)
28.45/9.24	   A^2 -> H(f(d), U1(e, d))
28.45/9.24	   A^2 -> H(f(d), U1(d, e))
28.45/9.24	   A^2 -> H(f(d), c)
28.45/9.24	   A^2 -> H(f(d), U1(e, k))
28.45/9.24	   A^2 -> H(f(d), U1(k, e))
28.45/9.24	   A^2 -> H(f(d), e)
28.45/9.24	   A^2 -> H(f(a), d)
28.45/9.24	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.24	   A^2 -> H(f(c), c)
28.45/9.24	   A^2 -> H(f(c), U1(e, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.24	   A^2 -> H(f(c), U1(k, e))
28.45/9.24	   A^2 -> H(f(c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.24	   A^2 -> H(f(a), k)
28.45/9.24	   A^2 -> H(f(e), U1(e, e))
28.45/9.24	   A^2 -> H(f(c), e)
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.24	   A^2 -> H(f(d), U1(k, k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.24	   A^2 -> H(d, U1(b, b))
28.45/9.24	   A^2 -> H(d, f(c))
28.45/9.24	   A^2 -> H(d, f(d))
28.45/9.24	   A^2 -> H(a, U1(c, b))
28.45/9.24	   A^2 -> H(a, U1(d, b))
28.45/9.24	   A^2 -> H(a, U1(b, c))
28.45/9.24	   A^2 -> H(a, U1(b, d))
28.45/9.24	   A^2 -> H(a, U1(c, c))
28.45/9.24	   A^2 -> H(a, f(e))
28.45/9.24	   A^2 -> H(a, f(k))
28.45/9.24	   A^2 -> H(a, U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.24	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.24	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.24	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.24	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.24	   A^2 -> H(U1(e, d), f(e))
28.45/9.24	   A^2 -> H(U1(e, d), f(k))
28.45/9.24	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.24	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.24	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.24	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.24	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.24	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.24	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.24	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.24	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.24	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.24	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.24	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.24	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.24	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.24	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.24	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.24	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.24	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.24	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.24	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, a), b)
28.45/9.24	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.24	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.24	   A^2 -> H(U1(c, a), c)
28.45/9.24	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.24	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.24	   A^2 -> H(U1(c, a), e)
28.45/9.24	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.24	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.24	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.24	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.24	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.24	   A^2 -> H(U1(d, e), f(e))
28.45/9.24	   A^2 -> H(U1(d, e), f(k))
28.45/9.24	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.24	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.24	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.24	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.24	   A^2 -> H(U1(d, a), b)
28.45/9.24	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.24	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.24	   A^2 -> H(U1(d, a), c)
28.45/9.24	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.24	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.24	   A^2 -> H(U1(d, a), e)
28.45/9.24	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.24	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.24	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.24	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.24	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.24	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.24	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.24	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.24	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.24	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.24	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.24	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.24	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.24	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.24	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.24	   A^2 -> H(U1(a, c), b)
28.45/9.24	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.24	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.24	   A^2 -> H(U1(a, c), c)
28.45/9.24	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.24	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.24	   A^2 -> H(U1(a, c), e)
28.45/9.24	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, d), b)
28.45/9.24	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.24	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.24	   A^2 -> H(U1(a, d), c)
28.45/9.24	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.24	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.24	   A^2 -> H(U1(a, d), e)
28.45/9.24	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, a), d)
28.45/9.24	   A^2 -> H(U1(a, a), k)
28.45/9.24	   A^2 -> H(k, U1(b, b))
28.45/9.24	   A^2 -> H(k, f(c))
28.45/9.24	   A^2 -> H(k, f(d))
28.45/9.24	   A^2 -> H(c, U1(c, b))
28.45/9.24	   A^2 -> H(c, U1(d, b))
28.45/9.24	   A^2 -> H(c, U1(b, c))
28.45/9.24	   A^2 -> H(c, U1(b, d))
28.45/9.24	   A^2 -> H(c, U1(c, c))
28.45/9.24	   A^2 -> H(c, f(e))
28.45/9.24	   A^2 -> H(c, f(k))
28.45/9.24	   A^2 -> H(c, U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.24	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(e, k), f(e))
28.45/9.24	   A^2 -> H(U1(e, k), f(k))
28.45/9.24	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.24	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.24	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.24	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.24	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.24	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.24	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.24	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.24	   A^2 -> H(U1(k, e), f(e))
28.45/9.24	   A^2 -> H(U1(k, e), f(k))
28.45/9.24	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.24	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.24	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.24	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.24	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.24	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.24	
28.45/9.24	The TRS R consists of the following rules:
28.45/9.24	
28.45/9.24	   f(x) -> U1(x, x)
28.45/9.24	   U1(e, x) -> x
28.45/9.24	   a -> c
28.45/9.24	   a -> d
28.45/9.24	   b -> c
28.45/9.24	   b -> d
28.45/9.24	   d -> k
28.45/9.24	   c -> e
28.45/9.24	   c -> k
28.45/9.24	
28.45/9.24	Q is empty.
28.45/9.24	We have to consider all minimal (P,Q,R)-chains.
28.45/9.24	----------------------------------------
28.45/9.24	
28.45/9.24	(851) TransformationProof (EQUIVALENT)
28.45/9.24	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.24	
28.45/9.24	   (A^2 -> H(U1(e, e), U1(d, d)),A^2 -> H(U1(e, e), U1(d, d)))
28.45/9.24	   (A^2 -> H(U1(k, e), U1(d, d)),A^2 -> H(U1(k, e), U1(d, d)))
28.45/9.24	   (A^2 -> H(U1(c, e), U1(k, d)),A^2 -> H(U1(c, e), U1(k, d)))
28.45/9.24	   (A^2 -> H(U1(c, e), U1(d, k)),A^2 -> H(U1(c, e), U1(d, k)))
28.45/9.24	
28.45/9.24	
28.45/9.24	----------------------------------------
28.45/9.24	
28.45/9.24	(852)
28.45/9.24	Obligation:
28.45/9.24	Q DP problem:
28.45/9.24	The TRS P consists of the following rules:
28.45/9.24	
28.45/9.24	   H(x, x) -> G(x, x, f(k))
28.45/9.24	   G(d, x, x) -> A^2
28.45/9.24	   A^2 -> H(f(c), f(c))
28.45/9.24	   A^2 -> H(f(d), f(d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.24	   A^2 -> H(f(e), f(e))
28.45/9.24	   A^2 -> H(f(k), f(k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.24	   A^2 -> H(U1(c, k), U1(c, b))
28.45/9.24	   A^2 -> H(U1(c, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(c, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(c, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(c, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(c, k), f(e))
28.45/9.24	   A^2 -> H(U1(c, k), f(k))
28.45/9.24	   A^2 -> H(U1(c, k), U1(d, d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.24	   A^2 -> H(e, U1(b, b))
28.45/9.24	   A^2 -> H(e, f(c))
28.45/9.24	   A^2 -> H(e, f(d))
28.45/9.24	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.24	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.24	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.24	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.24	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.24	   A^2 -> H(U1(e, e), f(e))
28.45/9.24	   A^2 -> H(U1(e, e), f(k))
28.45/9.24	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.24	   A^2 -> H(f(e), U1(e, b))
28.45/9.24	   A^2 -> H(f(e), U1(k, b))
28.45/9.24	   A^2 -> H(f(e), U1(c, d))
28.45/9.24	   A^2 -> H(f(e), U1(d, c))
28.45/9.24	   A^2 -> H(f(e), U1(b, e))
28.45/9.24	   A^2 -> H(f(e), U1(b, k))
28.45/9.24	   A^2 -> H(f(e), U1(e, c))
28.45/9.24	   A^2 -> H(f(e), U1(k, c))
28.45/9.24	   A^2 -> H(f(e), U1(c, e))
28.45/9.24	   A^2 -> H(f(e), U1(c, k))
28.45/9.24	   A^2 -> H(f(e), U1(k, k))
28.45/9.24	   A^2 -> H(f(e), U1(k, d))
28.45/9.24	   A^2 -> H(f(e), U1(d, k))
28.45/9.24	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.24	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(k, k), f(e))
28.45/9.24	   A^2 -> H(U1(k, k), f(k))
28.45/9.24	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.24	   A^2 -> H(f(k), U1(e, b))
28.45/9.24	   A^2 -> H(f(k), U1(k, b))
28.45/9.24	   A^2 -> H(f(k), U1(c, d))
28.45/9.24	   A^2 -> H(f(k), U1(d, c))
28.45/9.24	   A^2 -> H(f(k), U1(b, e))
28.45/9.24	   A^2 -> H(f(k), U1(b, k))
28.45/9.24	   A^2 -> H(f(k), U1(e, c))
28.45/9.24	   A^2 -> H(f(k), U1(k, c))
28.45/9.24	   A^2 -> H(f(k), U1(c, e))
28.45/9.24	   A^2 -> H(f(k), U1(c, k))
28.45/9.24	   A^2 -> H(f(k), U1(e, e))
28.45/9.24	   A^2 -> H(f(k), U1(k, d))
28.45/9.24	   A^2 -> H(f(k), U1(d, k))
28.45/9.24	   A^2 -> H(f(c), b)
28.45/9.24	   A^2 -> H(f(c), U1(e, d))
28.45/9.24	   A^2 -> H(f(c), U1(d, e))
28.45/9.24	   A^2 -> H(f(k), U1(k, k))
28.45/9.24	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.24	   A^2 -> H(U1(k, k), f(c))
28.45/9.24	   A^2 -> H(U1(k, k), f(d))
28.45/9.24	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.24	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.24	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.24	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.24	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.24	   A^2 -> H(U1(k, d), f(e))
28.45/9.24	   A^2 -> H(U1(k, d), f(k))
28.45/9.24	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.24	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.24	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(d, k), f(e))
28.45/9.24	   A^2 -> H(U1(d, k), f(k))
28.45/9.24	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.24	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.24	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.24	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.24	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.24	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.24	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.24	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.24	   A^2 -> H(f(d), b)
28.45/9.24	   A^2 -> H(f(d), U1(e, d))
28.45/9.24	   A^2 -> H(f(d), U1(d, e))
28.45/9.24	   A^2 -> H(f(d), c)
28.45/9.24	   A^2 -> H(f(d), U1(e, k))
28.45/9.24	   A^2 -> H(f(d), U1(k, e))
28.45/9.24	   A^2 -> H(f(d), e)
28.45/9.24	   A^2 -> H(f(a), d)
28.45/9.24	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.24	   A^2 -> H(f(c), c)
28.45/9.24	   A^2 -> H(f(c), U1(e, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.24	   A^2 -> H(f(c), U1(k, e))
28.45/9.24	   A^2 -> H(f(c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.24	   A^2 -> H(f(a), k)
28.45/9.24	   A^2 -> H(f(e), U1(e, e))
28.45/9.24	   A^2 -> H(f(c), e)
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.24	   A^2 -> H(f(d), U1(k, k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.24	   A^2 -> H(d, U1(b, b))
28.45/9.24	   A^2 -> H(d, f(c))
28.45/9.24	   A^2 -> H(d, f(d))
28.45/9.24	   A^2 -> H(a, U1(c, b))
28.45/9.24	   A^2 -> H(a, U1(d, b))
28.45/9.24	   A^2 -> H(a, U1(b, c))
28.45/9.24	   A^2 -> H(a, U1(b, d))
28.45/9.24	   A^2 -> H(a, U1(c, c))
28.45/9.24	   A^2 -> H(a, f(e))
28.45/9.24	   A^2 -> H(a, f(k))
28.45/9.24	   A^2 -> H(a, U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.24	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.24	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.24	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.24	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.24	   A^2 -> H(U1(e, d), f(e))
28.45/9.24	   A^2 -> H(U1(e, d), f(k))
28.45/9.24	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.24	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.24	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.24	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.24	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.24	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.24	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.24	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.24	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.24	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.24	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.24	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.24	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.24	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.24	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.24	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.24	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.24	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.24	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.24	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, a), b)
28.45/9.24	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.24	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.24	   A^2 -> H(U1(c, a), c)
28.45/9.24	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.24	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.24	   A^2 -> H(U1(c, a), e)
28.45/9.24	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.24	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.24	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.24	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.24	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.24	   A^2 -> H(U1(d, e), f(e))
28.45/9.24	   A^2 -> H(U1(d, e), f(k))
28.45/9.24	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.24	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.24	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.24	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.24	   A^2 -> H(U1(d, a), b)
28.45/9.24	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.24	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.24	   A^2 -> H(U1(d, a), c)
28.45/9.24	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.24	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.24	   A^2 -> H(U1(d, a), e)
28.45/9.24	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.24	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.24	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.24	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.24	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.24	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.24	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.24	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.24	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.24	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.24	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.24	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.24	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.24	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.24	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.24	   A^2 -> H(U1(a, c), b)
28.45/9.24	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.24	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.24	   A^2 -> H(U1(a, c), c)
28.45/9.24	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.24	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.24	   A^2 -> H(U1(a, c), e)
28.45/9.24	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, d), b)
28.45/9.24	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.24	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.24	   A^2 -> H(U1(a, d), c)
28.45/9.24	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.24	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.24	   A^2 -> H(U1(a, d), e)
28.45/9.24	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, a), d)
28.45/9.24	   A^2 -> H(U1(a, a), k)
28.45/9.24	   A^2 -> H(k, U1(b, b))
28.45/9.24	   A^2 -> H(k, f(c))
28.45/9.24	   A^2 -> H(k, f(d))
28.45/9.24	   A^2 -> H(c, U1(c, b))
28.45/9.24	   A^2 -> H(c, U1(d, b))
28.45/9.24	   A^2 -> H(c, U1(b, c))
28.45/9.24	   A^2 -> H(c, U1(b, d))
28.45/9.24	   A^2 -> H(c, U1(c, c))
28.45/9.24	   A^2 -> H(c, f(e))
28.45/9.24	   A^2 -> H(c, f(k))
28.45/9.24	   A^2 -> H(c, U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.24	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(e, k), f(e))
28.45/9.24	   A^2 -> H(U1(e, k), f(k))
28.45/9.24	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.24	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.24	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.24	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.24	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.24	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.24	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.24	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.24	   A^2 -> H(U1(k, e), f(e))
28.45/9.24	   A^2 -> H(U1(k, e), f(k))
28.45/9.24	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.24	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.24	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.24	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.24	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.24	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.24	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.24	
28.45/9.24	The TRS R consists of the following rules:
28.45/9.24	
28.45/9.24	   f(x) -> U1(x, x)
28.45/9.24	   U1(e, x) -> x
28.45/9.24	   a -> c
28.45/9.24	   a -> d
28.45/9.24	   b -> c
28.45/9.24	   b -> d
28.45/9.24	   d -> k
28.45/9.24	   c -> e
28.45/9.24	   c -> k
28.45/9.24	
28.45/9.24	Q is empty.
28.45/9.24	We have to consider all minimal (P,Q,R)-chains.
28.45/9.24	----------------------------------------
28.45/9.24	
28.45/9.24	(853) TransformationProof (EQUIVALENT)
28.45/9.24	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.24	
28.45/9.24	   (A^2 -> H(U1(e, k), U1(c, b)),A^2 -> H(U1(e, k), U1(c, b)))
28.45/9.24	   (A^2 -> H(U1(k, k), U1(c, b)),A^2 -> H(U1(k, k), U1(c, b)))
28.45/9.24	   (A^2 -> H(U1(c, k), U1(e, b)),A^2 -> H(U1(c, k), U1(e, b)))
28.45/9.24	   (A^2 -> H(U1(c, k), U1(k, b)),A^2 -> H(U1(c, k), U1(k, b)))
28.45/9.24	   (A^2 -> H(U1(c, k), U1(c, c)),A^2 -> H(U1(c, k), U1(c, c)))
28.45/9.24	   (A^2 -> H(U1(c, k), U1(c, d)),A^2 -> H(U1(c, k), U1(c, d)))
28.45/9.24	
28.45/9.24	
28.45/9.24	----------------------------------------
28.45/9.24	
28.45/9.24	(854)
28.45/9.24	Obligation:
28.45/9.24	Q DP problem:
28.45/9.24	The TRS P consists of the following rules:
28.45/9.24	
28.45/9.24	   H(x, x) -> G(x, x, f(k))
28.45/9.24	   G(d, x, x) -> A^2
28.45/9.24	   A^2 -> H(f(c), f(c))
28.45/9.24	   A^2 -> H(f(d), f(d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.24	   A^2 -> H(f(e), f(e))
28.45/9.24	   A^2 -> H(f(k), f(k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.24	   A^2 -> H(U1(c, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(c, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(c, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(c, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(c, k), f(e))
28.45/9.24	   A^2 -> H(U1(c, k), f(k))
28.45/9.24	   A^2 -> H(U1(c, k), U1(d, d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.24	   A^2 -> H(e, U1(b, b))
28.45/9.24	   A^2 -> H(e, f(c))
28.45/9.24	   A^2 -> H(e, f(d))
28.45/9.24	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.24	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.24	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.24	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.24	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.24	   A^2 -> H(U1(e, e), f(e))
28.45/9.24	   A^2 -> H(U1(e, e), f(k))
28.45/9.24	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.24	   A^2 -> H(f(e), U1(e, b))
28.45/9.24	   A^2 -> H(f(e), U1(k, b))
28.45/9.24	   A^2 -> H(f(e), U1(c, d))
28.45/9.24	   A^2 -> H(f(e), U1(d, c))
28.45/9.24	   A^2 -> H(f(e), U1(b, e))
28.45/9.24	   A^2 -> H(f(e), U1(b, k))
28.45/9.24	   A^2 -> H(f(e), U1(e, c))
28.45/9.24	   A^2 -> H(f(e), U1(k, c))
28.45/9.24	   A^2 -> H(f(e), U1(c, e))
28.45/9.24	   A^2 -> H(f(e), U1(c, k))
28.45/9.24	   A^2 -> H(f(e), U1(k, k))
28.45/9.24	   A^2 -> H(f(e), U1(k, d))
28.45/9.24	   A^2 -> H(f(e), U1(d, k))
28.45/9.24	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.24	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(k, k), f(e))
28.45/9.24	   A^2 -> H(U1(k, k), f(k))
28.45/9.24	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.24	   A^2 -> H(f(k), U1(e, b))
28.45/9.24	   A^2 -> H(f(k), U1(k, b))
28.45/9.24	   A^2 -> H(f(k), U1(c, d))
28.45/9.24	   A^2 -> H(f(k), U1(d, c))
28.45/9.24	   A^2 -> H(f(k), U1(b, e))
28.45/9.24	   A^2 -> H(f(k), U1(b, k))
28.45/9.24	   A^2 -> H(f(k), U1(e, c))
28.45/9.24	   A^2 -> H(f(k), U1(k, c))
28.45/9.24	   A^2 -> H(f(k), U1(c, e))
28.45/9.24	   A^2 -> H(f(k), U1(c, k))
28.45/9.24	   A^2 -> H(f(k), U1(e, e))
28.45/9.24	   A^2 -> H(f(k), U1(k, d))
28.45/9.24	   A^2 -> H(f(k), U1(d, k))
28.45/9.24	   A^2 -> H(f(c), b)
28.45/9.24	   A^2 -> H(f(c), U1(e, d))
28.45/9.24	   A^2 -> H(f(c), U1(d, e))
28.45/9.24	   A^2 -> H(f(k), U1(k, k))
28.45/9.24	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.24	   A^2 -> H(U1(k, k), f(c))
28.45/9.24	   A^2 -> H(U1(k, k), f(d))
28.45/9.24	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.24	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.24	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.24	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.24	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.24	   A^2 -> H(U1(k, d), f(e))
28.45/9.24	   A^2 -> H(U1(k, d), f(k))
28.45/9.24	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.24	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.24	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(d, k), f(e))
28.45/9.24	   A^2 -> H(U1(d, k), f(k))
28.45/9.24	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.24	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.24	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.24	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.24	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.24	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.24	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.24	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.24	   A^2 -> H(f(d), b)
28.45/9.24	   A^2 -> H(f(d), U1(e, d))
28.45/9.24	   A^2 -> H(f(d), U1(d, e))
28.45/9.24	   A^2 -> H(f(d), c)
28.45/9.24	   A^2 -> H(f(d), U1(e, k))
28.45/9.24	   A^2 -> H(f(d), U1(k, e))
28.45/9.24	   A^2 -> H(f(d), e)
28.45/9.24	   A^2 -> H(f(a), d)
28.45/9.24	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.24	   A^2 -> H(f(c), c)
28.45/9.24	   A^2 -> H(f(c), U1(e, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.24	   A^2 -> H(f(c), U1(k, e))
28.45/9.24	   A^2 -> H(f(c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.24	   A^2 -> H(f(a), k)
28.45/9.24	   A^2 -> H(f(e), U1(e, e))
28.45/9.24	   A^2 -> H(f(c), e)
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.24	   A^2 -> H(f(d), U1(k, k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.24	   A^2 -> H(d, U1(b, b))
28.45/9.24	   A^2 -> H(d, f(c))
28.45/9.24	   A^2 -> H(d, f(d))
28.45/9.24	   A^2 -> H(a, U1(c, b))
28.45/9.24	   A^2 -> H(a, U1(d, b))
28.45/9.24	   A^2 -> H(a, U1(b, c))
28.45/9.24	   A^2 -> H(a, U1(b, d))
28.45/9.24	   A^2 -> H(a, U1(c, c))
28.45/9.24	   A^2 -> H(a, f(e))
28.45/9.24	   A^2 -> H(a, f(k))
28.45/9.24	   A^2 -> H(a, U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.24	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.24	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.24	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.24	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.24	   A^2 -> H(U1(e, d), f(e))
28.45/9.24	   A^2 -> H(U1(e, d), f(k))
28.45/9.24	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.24	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.24	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.24	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.24	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.24	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.24	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.24	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.24	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.24	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.24	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.24	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.24	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.24	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.24	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.24	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.24	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.24	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.24	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.24	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, a), b)
28.45/9.24	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.24	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.24	   A^2 -> H(U1(c, a), c)
28.45/9.24	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.24	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.24	   A^2 -> H(U1(c, a), e)
28.45/9.24	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.24	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.24	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.24	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.24	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.24	   A^2 -> H(U1(d, e), f(e))
28.45/9.24	   A^2 -> H(U1(d, e), f(k))
28.45/9.24	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.24	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.24	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.24	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.24	   A^2 -> H(U1(d, a), b)
28.45/9.24	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.24	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.24	   A^2 -> H(U1(d, a), c)
28.45/9.24	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.24	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.24	   A^2 -> H(U1(d, a), e)
28.45/9.24	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.24	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.24	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.24	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.24	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.24	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.24	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.24	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.24	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.24	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.24	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.24	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.24	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.24	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.24	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.24	   A^2 -> H(U1(a, c), b)
28.45/9.24	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.24	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.24	   A^2 -> H(U1(a, c), c)
28.45/9.24	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.24	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.24	   A^2 -> H(U1(a, c), e)
28.45/9.24	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, d), b)
28.45/9.24	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.24	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.24	   A^2 -> H(U1(a, d), c)
28.45/9.24	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.24	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.24	   A^2 -> H(U1(a, d), e)
28.45/9.24	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, a), d)
28.45/9.24	   A^2 -> H(U1(a, a), k)
28.45/9.24	   A^2 -> H(k, U1(b, b))
28.45/9.24	   A^2 -> H(k, f(c))
28.45/9.24	   A^2 -> H(k, f(d))
28.45/9.24	   A^2 -> H(c, U1(c, b))
28.45/9.24	   A^2 -> H(c, U1(d, b))
28.45/9.24	   A^2 -> H(c, U1(b, c))
28.45/9.24	   A^2 -> H(c, U1(b, d))
28.45/9.24	   A^2 -> H(c, U1(c, c))
28.45/9.24	   A^2 -> H(c, f(e))
28.45/9.24	   A^2 -> H(c, f(k))
28.45/9.24	   A^2 -> H(c, U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.24	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(e, k), f(e))
28.45/9.24	   A^2 -> H(U1(e, k), f(k))
28.45/9.24	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.24	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.24	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.24	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.24	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.24	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.24	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.24	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.24	   A^2 -> H(U1(k, e), f(e))
28.45/9.24	   A^2 -> H(U1(k, e), f(k))
28.45/9.24	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.24	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.24	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.24	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.24	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.24	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.24	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.24	
28.45/9.24	The TRS R consists of the following rules:
28.45/9.24	
28.45/9.24	   f(x) -> U1(x, x)
28.45/9.24	   U1(e, x) -> x
28.45/9.24	   a -> c
28.45/9.24	   a -> d
28.45/9.24	   b -> c
28.45/9.24	   b -> d
28.45/9.24	   d -> k
28.45/9.24	   c -> e
28.45/9.24	   c -> k
28.45/9.24	
28.45/9.24	Q is empty.
28.45/9.24	We have to consider all minimal (P,Q,R)-chains.
28.45/9.24	----------------------------------------
28.45/9.24	
28.45/9.24	(855) TransformationProof (EQUIVALENT)
28.45/9.24	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.24	
28.45/9.24	   (A^2 -> H(U1(e, k), U1(d, b)),A^2 -> H(U1(e, k), U1(d, b)))
28.45/9.24	   (A^2 -> H(U1(k, k), U1(d, b)),A^2 -> H(U1(k, k), U1(d, b)))
28.45/9.24	   (A^2 -> H(U1(c, k), U1(k, b)),A^2 -> H(U1(c, k), U1(k, b)))
28.45/9.24	   (A^2 -> H(U1(c, k), U1(d, c)),A^2 -> H(U1(c, k), U1(d, c)))
28.45/9.24	   (A^2 -> H(U1(c, k), U1(d, d)),A^2 -> H(U1(c, k), U1(d, d)))
28.45/9.24	
28.45/9.24	
28.45/9.24	----------------------------------------
28.45/9.24	
28.45/9.24	(856)
28.45/9.24	Obligation:
28.45/9.24	Q DP problem:
28.45/9.24	The TRS P consists of the following rules:
28.45/9.24	
28.45/9.24	   H(x, x) -> G(x, x, f(k))
28.45/9.24	   G(d, x, x) -> A^2
28.45/9.24	   A^2 -> H(f(c), f(c))
28.45/9.24	   A^2 -> H(f(d), f(d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.24	   A^2 -> H(f(e), f(e))
28.45/9.24	   A^2 -> H(f(k), f(k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.24	   A^2 -> H(U1(c, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(c, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(c, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(c, k), f(e))
28.45/9.24	   A^2 -> H(U1(c, k), f(k))
28.45/9.24	   A^2 -> H(U1(c, k), U1(d, d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.24	   A^2 -> H(e, U1(b, b))
28.45/9.24	   A^2 -> H(e, f(c))
28.45/9.24	   A^2 -> H(e, f(d))
28.45/9.24	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.24	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.24	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.24	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.24	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.24	   A^2 -> H(U1(e, e), f(e))
28.45/9.24	   A^2 -> H(U1(e, e), f(k))
28.45/9.24	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.24	   A^2 -> H(f(e), U1(e, b))
28.45/9.24	   A^2 -> H(f(e), U1(k, b))
28.45/9.24	   A^2 -> H(f(e), U1(c, d))
28.45/9.24	   A^2 -> H(f(e), U1(d, c))
28.45/9.24	   A^2 -> H(f(e), U1(b, e))
28.45/9.24	   A^2 -> H(f(e), U1(b, k))
28.45/9.24	   A^2 -> H(f(e), U1(e, c))
28.45/9.24	   A^2 -> H(f(e), U1(k, c))
28.45/9.24	   A^2 -> H(f(e), U1(c, e))
28.45/9.24	   A^2 -> H(f(e), U1(c, k))
28.45/9.24	   A^2 -> H(f(e), U1(k, k))
28.45/9.24	   A^2 -> H(f(e), U1(k, d))
28.45/9.24	   A^2 -> H(f(e), U1(d, k))
28.45/9.24	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.24	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(k, k), f(e))
28.45/9.24	   A^2 -> H(U1(k, k), f(k))
28.45/9.24	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.24	   A^2 -> H(f(k), U1(e, b))
28.45/9.24	   A^2 -> H(f(k), U1(k, b))
28.45/9.24	   A^2 -> H(f(k), U1(c, d))
28.45/9.24	   A^2 -> H(f(k), U1(d, c))
28.45/9.24	   A^2 -> H(f(k), U1(b, e))
28.45/9.24	   A^2 -> H(f(k), U1(b, k))
28.45/9.24	   A^2 -> H(f(k), U1(e, c))
28.45/9.24	   A^2 -> H(f(k), U1(k, c))
28.45/9.24	   A^2 -> H(f(k), U1(c, e))
28.45/9.24	   A^2 -> H(f(k), U1(c, k))
28.45/9.24	   A^2 -> H(f(k), U1(e, e))
28.45/9.24	   A^2 -> H(f(k), U1(k, d))
28.45/9.24	   A^2 -> H(f(k), U1(d, k))
28.45/9.24	   A^2 -> H(f(c), b)
28.45/9.24	   A^2 -> H(f(c), U1(e, d))
28.45/9.24	   A^2 -> H(f(c), U1(d, e))
28.45/9.24	   A^2 -> H(f(k), U1(k, k))
28.45/9.24	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.24	   A^2 -> H(U1(k, k), f(c))
28.45/9.24	   A^2 -> H(U1(k, k), f(d))
28.45/9.24	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.24	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.24	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.24	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.24	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.24	   A^2 -> H(U1(k, d), f(e))
28.45/9.24	   A^2 -> H(U1(k, d), f(k))
28.45/9.24	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.24	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.24	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(d, k), f(e))
28.45/9.24	   A^2 -> H(U1(d, k), f(k))
28.45/9.24	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.24	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.24	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.24	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.24	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.24	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.24	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.24	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.24	   A^2 -> H(f(d), b)
28.45/9.24	   A^2 -> H(f(d), U1(e, d))
28.45/9.24	   A^2 -> H(f(d), U1(d, e))
28.45/9.24	   A^2 -> H(f(d), c)
28.45/9.24	   A^2 -> H(f(d), U1(e, k))
28.45/9.24	   A^2 -> H(f(d), U1(k, e))
28.45/9.24	   A^2 -> H(f(d), e)
28.45/9.24	   A^2 -> H(f(a), d)
28.45/9.24	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.24	   A^2 -> H(f(c), c)
28.45/9.24	   A^2 -> H(f(c), U1(e, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.24	   A^2 -> H(f(c), U1(k, e))
28.45/9.24	   A^2 -> H(f(c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.24	   A^2 -> H(f(a), k)
28.45/9.24	   A^2 -> H(f(e), U1(e, e))
28.45/9.24	   A^2 -> H(f(c), e)
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.24	   A^2 -> H(f(d), U1(k, k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.24	   A^2 -> H(d, U1(b, b))
28.45/9.24	   A^2 -> H(d, f(c))
28.45/9.24	   A^2 -> H(d, f(d))
28.45/9.24	   A^2 -> H(a, U1(c, b))
28.45/9.24	   A^2 -> H(a, U1(d, b))
28.45/9.24	   A^2 -> H(a, U1(b, c))
28.45/9.24	   A^2 -> H(a, U1(b, d))
28.45/9.24	   A^2 -> H(a, U1(c, c))
28.45/9.24	   A^2 -> H(a, f(e))
28.45/9.24	   A^2 -> H(a, f(k))
28.45/9.24	   A^2 -> H(a, U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.24	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.24	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.24	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.24	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.24	   A^2 -> H(U1(e, d), f(e))
28.45/9.24	   A^2 -> H(U1(e, d), f(k))
28.45/9.24	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.24	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.24	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.24	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.24	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.24	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.24	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.24	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.24	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.24	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.24	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.24	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.24	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.24	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.24	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.24	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.24	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.24	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.24	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.24	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, a), b)
28.45/9.24	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.24	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.24	   A^2 -> H(U1(c, a), c)
28.45/9.24	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.24	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.24	   A^2 -> H(U1(c, a), e)
28.45/9.24	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.24	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.24	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.24	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.24	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.24	   A^2 -> H(U1(d, e), f(e))
28.45/9.24	   A^2 -> H(U1(d, e), f(k))
28.45/9.24	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.24	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.24	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.24	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.24	   A^2 -> H(U1(d, a), b)
28.45/9.24	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.24	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.24	   A^2 -> H(U1(d, a), c)
28.45/9.24	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.24	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.24	   A^2 -> H(U1(d, a), e)
28.45/9.24	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.24	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.24	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.24	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.24	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.24	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.24	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.24	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.24	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.24	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.24	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.24	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.24	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.24	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.24	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.24	   A^2 -> H(U1(a, c), b)
28.45/9.24	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.24	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.24	   A^2 -> H(U1(a, c), c)
28.45/9.24	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.24	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.24	   A^2 -> H(U1(a, c), e)
28.45/9.24	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, d), b)
28.45/9.24	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.24	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.24	   A^2 -> H(U1(a, d), c)
28.45/9.24	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.24	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.24	   A^2 -> H(U1(a, d), e)
28.45/9.24	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, a), d)
28.45/9.24	   A^2 -> H(U1(a, a), k)
28.45/9.24	   A^2 -> H(k, U1(b, b))
28.45/9.24	   A^2 -> H(k, f(c))
28.45/9.24	   A^2 -> H(k, f(d))
28.45/9.24	   A^2 -> H(c, U1(c, b))
28.45/9.24	   A^2 -> H(c, U1(d, b))
28.45/9.24	   A^2 -> H(c, U1(b, c))
28.45/9.24	   A^2 -> H(c, U1(b, d))
28.45/9.24	   A^2 -> H(c, U1(c, c))
28.45/9.24	   A^2 -> H(c, f(e))
28.45/9.24	   A^2 -> H(c, f(k))
28.45/9.24	   A^2 -> H(c, U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.24	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(e, k), f(e))
28.45/9.24	   A^2 -> H(U1(e, k), f(k))
28.45/9.24	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.24	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.24	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.24	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.24	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.24	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.24	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.24	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.24	   A^2 -> H(U1(k, e), f(e))
28.45/9.24	   A^2 -> H(U1(k, e), f(k))
28.45/9.24	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.24	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.24	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.24	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.24	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.24	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.24	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.24	
28.45/9.24	The TRS R consists of the following rules:
28.45/9.24	
28.45/9.24	   f(x) -> U1(x, x)
28.45/9.24	   U1(e, x) -> x
28.45/9.24	   a -> c
28.45/9.24	   a -> d
28.45/9.24	   b -> c
28.45/9.24	   b -> d
28.45/9.24	   d -> k
28.45/9.24	   c -> e
28.45/9.24	   c -> k
28.45/9.24	
28.45/9.24	Q is empty.
28.45/9.24	We have to consider all minimal (P,Q,R)-chains.
28.45/9.24	----------------------------------------
28.45/9.24	
28.45/9.24	(857) TransformationProof (EQUIVALENT)
28.45/9.24	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.24	
28.45/9.24	   (A^2 -> H(U1(e, k), U1(b, c)),A^2 -> H(U1(e, k), U1(b, c)))
28.45/9.24	   (A^2 -> H(U1(k, k), U1(b, c)),A^2 -> H(U1(k, k), U1(b, c)))
28.45/9.24	   (A^2 -> H(U1(c, k), U1(c, c)),A^2 -> H(U1(c, k), U1(c, c)))
28.45/9.24	   (A^2 -> H(U1(c, k), U1(d, c)),A^2 -> H(U1(c, k), U1(d, c)))
28.45/9.24	   (A^2 -> H(U1(c, k), U1(b, e)),A^2 -> H(U1(c, k), U1(b, e)))
28.45/9.24	   (A^2 -> H(U1(c, k), U1(b, k)),A^2 -> H(U1(c, k), U1(b, k)))
28.45/9.24	
28.45/9.24	
28.45/9.24	----------------------------------------
28.45/9.24	
28.45/9.24	(858)
28.45/9.24	Obligation:
28.45/9.24	Q DP problem:
28.45/9.24	The TRS P consists of the following rules:
28.45/9.24	
28.45/9.24	   H(x, x) -> G(x, x, f(k))
28.45/9.24	   G(d, x, x) -> A^2
28.45/9.24	   A^2 -> H(f(c), f(c))
28.45/9.24	   A^2 -> H(f(d), f(d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.24	   A^2 -> H(f(e), f(e))
28.45/9.24	   A^2 -> H(f(k), f(k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.24	   A^2 -> H(U1(c, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(c, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(c, k), f(e))
28.45/9.24	   A^2 -> H(U1(c, k), f(k))
28.45/9.24	   A^2 -> H(U1(c, k), U1(d, d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.24	   A^2 -> H(e, U1(b, b))
28.45/9.24	   A^2 -> H(e, f(c))
28.45/9.24	   A^2 -> H(e, f(d))
28.45/9.24	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.24	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.24	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.24	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.24	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.24	   A^2 -> H(U1(e, e), f(e))
28.45/9.24	   A^2 -> H(U1(e, e), f(k))
28.45/9.24	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.24	   A^2 -> H(f(e), U1(e, b))
28.45/9.24	   A^2 -> H(f(e), U1(k, b))
28.45/9.24	   A^2 -> H(f(e), U1(c, d))
28.45/9.24	   A^2 -> H(f(e), U1(d, c))
28.45/9.24	   A^2 -> H(f(e), U1(b, e))
28.45/9.24	   A^2 -> H(f(e), U1(b, k))
28.45/9.24	   A^2 -> H(f(e), U1(e, c))
28.45/9.24	   A^2 -> H(f(e), U1(k, c))
28.45/9.24	   A^2 -> H(f(e), U1(c, e))
28.45/9.24	   A^2 -> H(f(e), U1(c, k))
28.45/9.24	   A^2 -> H(f(e), U1(k, k))
28.45/9.24	   A^2 -> H(f(e), U1(k, d))
28.45/9.24	   A^2 -> H(f(e), U1(d, k))
28.45/9.24	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.24	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(k, k), f(e))
28.45/9.24	   A^2 -> H(U1(k, k), f(k))
28.45/9.24	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.24	   A^2 -> H(f(k), U1(e, b))
28.45/9.24	   A^2 -> H(f(k), U1(k, b))
28.45/9.24	   A^2 -> H(f(k), U1(c, d))
28.45/9.24	   A^2 -> H(f(k), U1(d, c))
28.45/9.24	   A^2 -> H(f(k), U1(b, e))
28.45/9.24	   A^2 -> H(f(k), U1(b, k))
28.45/9.24	   A^2 -> H(f(k), U1(e, c))
28.45/9.24	   A^2 -> H(f(k), U1(k, c))
28.45/9.24	   A^2 -> H(f(k), U1(c, e))
28.45/9.24	   A^2 -> H(f(k), U1(c, k))
28.45/9.24	   A^2 -> H(f(k), U1(e, e))
28.45/9.24	   A^2 -> H(f(k), U1(k, d))
28.45/9.24	   A^2 -> H(f(k), U1(d, k))
28.45/9.24	   A^2 -> H(f(c), b)
28.45/9.24	   A^2 -> H(f(c), U1(e, d))
28.45/9.24	   A^2 -> H(f(c), U1(d, e))
28.45/9.24	   A^2 -> H(f(k), U1(k, k))
28.45/9.24	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.24	   A^2 -> H(U1(k, k), f(c))
28.45/9.24	   A^2 -> H(U1(k, k), f(d))
28.45/9.24	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.24	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.24	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.24	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.24	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.24	   A^2 -> H(U1(k, d), f(e))
28.45/9.24	   A^2 -> H(U1(k, d), f(k))
28.45/9.24	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.24	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.24	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(d, k), f(e))
28.45/9.24	   A^2 -> H(U1(d, k), f(k))
28.45/9.24	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.24	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.24	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.24	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.24	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.24	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.24	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.24	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.24	   A^2 -> H(f(d), b)
28.45/9.24	   A^2 -> H(f(d), U1(e, d))
28.45/9.24	   A^2 -> H(f(d), U1(d, e))
28.45/9.24	   A^2 -> H(f(d), c)
28.45/9.24	   A^2 -> H(f(d), U1(e, k))
28.45/9.24	   A^2 -> H(f(d), U1(k, e))
28.45/9.24	   A^2 -> H(f(d), e)
28.45/9.24	   A^2 -> H(f(a), d)
28.45/9.24	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.24	   A^2 -> H(f(c), c)
28.45/9.24	   A^2 -> H(f(c), U1(e, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.24	   A^2 -> H(f(c), U1(k, e))
28.45/9.24	   A^2 -> H(f(c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.24	   A^2 -> H(f(a), k)
28.45/9.24	   A^2 -> H(f(e), U1(e, e))
28.45/9.24	   A^2 -> H(f(c), e)
28.45/9.24	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.24	   A^2 -> H(f(d), U1(k, k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.24	   A^2 -> H(d, U1(b, b))
28.45/9.24	   A^2 -> H(d, f(c))
28.45/9.24	   A^2 -> H(d, f(d))
28.45/9.24	   A^2 -> H(a, U1(c, b))
28.45/9.24	   A^2 -> H(a, U1(d, b))
28.45/9.24	   A^2 -> H(a, U1(b, c))
28.45/9.24	   A^2 -> H(a, U1(b, d))
28.45/9.24	   A^2 -> H(a, U1(c, c))
28.45/9.24	   A^2 -> H(a, f(e))
28.45/9.24	   A^2 -> H(a, f(k))
28.45/9.24	   A^2 -> H(a, U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.24	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.24	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.24	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.24	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.24	   A^2 -> H(U1(e, d), f(e))
28.45/9.24	   A^2 -> H(U1(e, d), f(k))
28.45/9.24	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.24	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.24	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.24	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.24	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.24	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.24	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.24	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.24	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.24	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.24	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.24	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.24	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.24	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.24	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.24	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.24	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.24	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.24	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.24	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, a), b)
28.45/9.24	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.24	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.24	   A^2 -> H(U1(c, a), c)
28.45/9.24	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.24	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.24	   A^2 -> H(U1(c, a), e)
28.45/9.24	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.24	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.24	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.24	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.24	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.24	   A^2 -> H(U1(d, e), f(e))
28.45/9.24	   A^2 -> H(U1(d, e), f(k))
28.45/9.24	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.24	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.24	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.24	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.24	   A^2 -> H(U1(d, a), b)
28.45/9.24	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.24	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.24	   A^2 -> H(U1(d, a), c)
28.45/9.24	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.24	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.24	   A^2 -> H(U1(d, a), e)
28.45/9.24	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.24	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.24	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.24	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.24	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.24	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.24	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.24	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.24	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.24	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.24	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.24	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.24	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.24	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.24	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.24	   A^2 -> H(U1(a, c), b)
28.45/9.24	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.24	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.24	   A^2 -> H(U1(a, c), c)
28.45/9.24	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.24	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.24	   A^2 -> H(U1(a, c), e)
28.45/9.24	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, d), b)
28.45/9.24	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.24	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.24	   A^2 -> H(U1(a, d), c)
28.45/9.24	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.24	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.24	   A^2 -> H(U1(a, d), e)
28.45/9.24	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.24	   A^2 -> H(U1(a, a), d)
28.45/9.24	   A^2 -> H(U1(a, a), k)
28.45/9.24	   A^2 -> H(k, U1(b, b))
28.45/9.24	   A^2 -> H(k, f(c))
28.45/9.24	   A^2 -> H(k, f(d))
28.45/9.24	   A^2 -> H(c, U1(c, b))
28.45/9.24	   A^2 -> H(c, U1(d, b))
28.45/9.24	   A^2 -> H(c, U1(b, c))
28.45/9.24	   A^2 -> H(c, U1(b, d))
28.45/9.24	   A^2 -> H(c, U1(c, c))
28.45/9.24	   A^2 -> H(c, f(e))
28.45/9.24	   A^2 -> H(c, f(k))
28.45/9.24	   A^2 -> H(c, U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.24	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.24	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.24	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.24	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(e, k), f(e))
28.45/9.24	   A^2 -> H(U1(e, k), f(k))
28.45/9.24	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.24	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.24	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.24	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.24	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.24	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.24	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.24	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.24	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.24	   A^2 -> H(U1(k, e), f(e))
28.45/9.24	   A^2 -> H(U1(k, e), f(k))
28.45/9.24	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.24	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.24	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.24	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.24	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.24	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.24	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.24	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.24	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.24	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.24	
28.45/9.24	The TRS R consists of the following rules:
28.45/9.24	
28.45/9.24	   f(x) -> U1(x, x)
28.45/9.24	   U1(e, x) -> x
28.45/9.24	   a -> c
28.45/9.24	   a -> d
28.45/9.24	   b -> c
28.45/9.24	   b -> d
28.45/9.24	   d -> k
28.45/9.24	   c -> e
28.45/9.24	   c -> k
28.45/9.24	
28.45/9.24	Q is empty.
28.45/9.24	We have to consider all minimal (P,Q,R)-chains.
28.45/9.24	----------------------------------------
28.45/9.24	
28.45/9.24	(859) TransformationProof (EQUIVALENT)
28.45/9.24	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.24	
28.45/9.24	   (A^2 -> H(U1(e, k), U1(b, d)),A^2 -> H(U1(e, k), U1(b, d)))
28.45/9.24	   (A^2 -> H(U1(k, k), U1(b, d)),A^2 -> H(U1(k, k), U1(b, d)))
28.45/9.24	   (A^2 -> H(U1(c, k), U1(c, d)),A^2 -> H(U1(c, k), U1(c, d)))
28.45/9.24	   (A^2 -> H(U1(c, k), U1(d, d)),A^2 -> H(U1(c, k), U1(d, d)))
28.45/9.24	   (A^2 -> H(U1(c, k), U1(b, k)),A^2 -> H(U1(c, k), U1(b, k)))
28.45/9.24	
28.45/9.24	
28.45/9.24	----------------------------------------
28.45/9.24	
28.45/9.24	(860)
28.45/9.24	Obligation:
28.45/9.24	Q DP problem:
28.45/9.24	The TRS P consists of the following rules:
28.45/9.24	
28.45/9.24	   H(x, x) -> G(x, x, f(k))
28.45/9.24	   G(d, x, x) -> A^2
28.45/9.24	   A^2 -> H(f(c), f(c))
28.45/9.24	   A^2 -> H(f(d), f(d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.24	   A^2 -> H(f(e), f(e))
28.45/9.24	   A^2 -> H(f(k), f(k))
28.45/9.24	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.24	   A^2 -> H(U1(c, k), U1(c, c))
28.45/9.24	   A^2 -> H(U1(c, k), f(e))
28.45/9.24	   A^2 -> H(U1(c, k), f(k))
28.45/9.24	   A^2 -> H(U1(c, k), U1(d, d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(e, b))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.24	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.24	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.24	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.24	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.24	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.25	   A^2 -> H(e, U1(b, b))
28.45/9.25	   A^2 -> H(e, f(c))
28.45/9.25	   A^2 -> H(e, f(d))
28.45/9.25	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.25	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.25	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.25	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.25	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.25	   A^2 -> H(U1(e, e), f(e))
28.45/9.25	   A^2 -> H(U1(e, e), f(k))
28.45/9.25	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.25	   A^2 -> H(f(e), U1(e, b))
28.45/9.25	   A^2 -> H(f(e), U1(k, b))
28.45/9.25	   A^2 -> H(f(e), U1(c, d))
28.45/9.25	   A^2 -> H(f(e), U1(d, c))
28.45/9.25	   A^2 -> H(f(e), U1(b, e))
28.45/9.25	   A^2 -> H(f(e), U1(b, k))
28.45/9.25	   A^2 -> H(f(e), U1(e, c))
28.45/9.25	   A^2 -> H(f(e), U1(k, c))
28.45/9.25	   A^2 -> H(f(e), U1(c, e))
28.45/9.25	   A^2 -> H(f(e), U1(c, k))
28.45/9.25	   A^2 -> H(f(e), U1(k, k))
28.45/9.25	   A^2 -> H(f(e), U1(k, d))
28.45/9.25	   A^2 -> H(f(e), U1(d, k))
28.45/9.25	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.25	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.25	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.25	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.25	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.25	   A^2 -> H(U1(k, k), f(e))
28.45/9.25	   A^2 -> H(U1(k, k), f(k))
28.45/9.25	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.25	   A^2 -> H(f(k), U1(e, b))
28.45/9.25	   A^2 -> H(f(k), U1(k, b))
28.45/9.25	   A^2 -> H(f(k), U1(c, d))
28.45/9.25	   A^2 -> H(f(k), U1(d, c))
28.45/9.25	   A^2 -> H(f(k), U1(b, e))
28.45/9.25	   A^2 -> H(f(k), U1(b, k))
28.45/9.25	   A^2 -> H(f(k), U1(e, c))
28.45/9.25	   A^2 -> H(f(k), U1(k, c))
28.45/9.25	   A^2 -> H(f(k), U1(c, e))
28.45/9.25	   A^2 -> H(f(k), U1(c, k))
28.45/9.25	   A^2 -> H(f(k), U1(e, e))
28.45/9.25	   A^2 -> H(f(k), U1(k, d))
28.45/9.25	   A^2 -> H(f(k), U1(d, k))
28.45/9.25	   A^2 -> H(f(c), b)
28.45/9.25	   A^2 -> H(f(c), U1(e, d))
28.45/9.25	   A^2 -> H(f(c), U1(d, e))
28.45/9.25	   A^2 -> H(f(k), U1(k, k))
28.45/9.25	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.25	   A^2 -> H(U1(k, k), f(c))
28.45/9.25	   A^2 -> H(U1(k, k), f(d))
28.45/9.25	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.25	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.25	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.25	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.25	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.25	   A^2 -> H(U1(k, d), f(e))
28.45/9.25	   A^2 -> H(U1(k, d), f(k))
28.45/9.25	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.25	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.25	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.25	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.25	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.25	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.25	   A^2 -> H(U1(d, k), f(e))
28.45/9.25	   A^2 -> H(U1(d, k), f(k))
28.45/9.25	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.25	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.25	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.25	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.25	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.25	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.25	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.25	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.25	   A^2 -> H(f(d), b)
28.45/9.25	   A^2 -> H(f(d), U1(e, d))
28.45/9.25	   A^2 -> H(f(d), U1(d, e))
28.45/9.25	   A^2 -> H(f(d), c)
28.45/9.25	   A^2 -> H(f(d), U1(e, k))
28.45/9.25	   A^2 -> H(f(d), U1(k, e))
28.45/9.25	   A^2 -> H(f(d), e)
28.45/9.25	   A^2 -> H(f(a), d)
28.45/9.25	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.25	   A^2 -> H(f(c), c)
28.45/9.25	   A^2 -> H(f(c), U1(e, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.25	   A^2 -> H(f(c), U1(k, e))
28.45/9.25	   A^2 -> H(f(c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.25	   A^2 -> H(f(a), k)
28.45/9.25	   A^2 -> H(f(e), U1(e, e))
28.45/9.25	   A^2 -> H(f(c), e)
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.25	   A^2 -> H(f(d), U1(k, k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.25	   A^2 -> H(d, U1(b, b))
28.45/9.25	   A^2 -> H(d, f(c))
28.45/9.25	   A^2 -> H(d, f(d))
28.45/9.25	   A^2 -> H(a, U1(c, b))
28.45/9.25	   A^2 -> H(a, U1(d, b))
28.45/9.25	   A^2 -> H(a, U1(b, c))
28.45/9.25	   A^2 -> H(a, U1(b, d))
28.45/9.25	   A^2 -> H(a, U1(c, c))
28.45/9.25	   A^2 -> H(a, f(e))
28.45/9.25	   A^2 -> H(a, f(k))
28.45/9.25	   A^2 -> H(a, U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.25	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.25	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.25	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.25	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.25	   A^2 -> H(U1(e, d), f(e))
28.45/9.25	   A^2 -> H(U1(e, d), f(k))
28.45/9.25	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.25	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.25	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.25	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.25	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.25	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.25	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.25	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.25	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.25	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.25	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.25	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.25	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.25	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.25	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.25	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.25	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.25	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.25	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, a), b)
28.45/9.25	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.25	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.25	   A^2 -> H(U1(c, a), c)
28.45/9.25	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.25	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.25	   A^2 -> H(U1(c, a), e)
28.45/9.25	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.25	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.25	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.25	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.25	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.25	   A^2 -> H(U1(d, e), f(e))
28.45/9.25	   A^2 -> H(U1(d, e), f(k))
28.45/9.25	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.25	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.25	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.25	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.25	   A^2 -> H(U1(d, a), b)
28.45/9.25	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.25	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.25	   A^2 -> H(U1(d, a), c)
28.45/9.25	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.25	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.25	   A^2 -> H(U1(d, a), e)
28.45/9.25	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.25	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.25	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.25	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.25	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.25	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.25	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.25	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.25	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.25	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.25	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.25	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.25	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.25	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.25	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.25	   A^2 -> H(U1(a, c), b)
28.45/9.25	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.25	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.25	   A^2 -> H(U1(a, c), c)
28.45/9.25	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.25	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.25	   A^2 -> H(U1(a, c), e)
28.45/9.25	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, d), b)
28.45/9.25	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.25	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.25	   A^2 -> H(U1(a, d), c)
28.45/9.25	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.25	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.25	   A^2 -> H(U1(a, d), e)
28.45/9.25	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, a), d)
28.45/9.25	   A^2 -> H(U1(a, a), k)
28.45/9.25	   A^2 -> H(k, U1(b, b))
28.45/9.25	   A^2 -> H(k, f(c))
28.45/9.25	   A^2 -> H(k, f(d))
28.45/9.25	   A^2 -> H(c, U1(c, b))
28.45/9.25	   A^2 -> H(c, U1(d, b))
28.45/9.25	   A^2 -> H(c, U1(b, c))
28.45/9.25	   A^2 -> H(c, U1(b, d))
28.45/9.25	   A^2 -> H(c, U1(c, c))
28.45/9.25	   A^2 -> H(c, f(e))
28.45/9.25	   A^2 -> H(c, f(k))
28.45/9.25	   A^2 -> H(c, U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.25	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.25	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.25	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.25	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.25	   A^2 -> H(U1(e, k), f(e))
28.45/9.25	   A^2 -> H(U1(e, k), f(k))
28.45/9.25	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.25	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.25	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.25	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.25	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.25	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.25	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.25	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.25	   A^2 -> H(U1(k, e), f(e))
28.45/9.25	   A^2 -> H(U1(k, e), f(k))
28.45/9.25	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.25	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.25	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.25	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.25	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.25	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.25	
28.45/9.25	The TRS R consists of the following rules:
28.45/9.25	
28.45/9.25	   f(x) -> U1(x, x)
28.45/9.25	   U1(e, x) -> x
28.45/9.25	   a -> c
28.45/9.25	   a -> d
28.45/9.25	   b -> c
28.45/9.25	   b -> d
28.45/9.25	   d -> k
28.45/9.25	   c -> e
28.45/9.25	   c -> k
28.45/9.25	
28.45/9.25	Q is empty.
28.45/9.25	We have to consider all minimal (P,Q,R)-chains.
28.45/9.25	----------------------------------------
28.45/9.25	
28.45/9.25	(861) TransformationProof (EQUIVALENT)
28.45/9.25	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.25	
28.45/9.25	   (A^2 -> H(U1(e, k), U1(c, c)),A^2 -> H(U1(e, k), U1(c, c)))
28.45/9.25	   (A^2 -> H(U1(k, k), U1(c, c)),A^2 -> H(U1(k, k), U1(c, c)))
28.45/9.25	   (A^2 -> H(U1(c, k), U1(e, c)),A^2 -> H(U1(c, k), U1(e, c)))
28.45/9.25	   (A^2 -> H(U1(c, k), U1(k, c)),A^2 -> H(U1(c, k), U1(k, c)))
28.45/9.25	   (A^2 -> H(U1(c, k), U1(c, e)),A^2 -> H(U1(c, k), U1(c, e)))
28.45/9.25	   (A^2 -> H(U1(c, k), U1(c, k)),A^2 -> H(U1(c, k), U1(c, k)))
28.45/9.25	
28.45/9.25	
28.45/9.25	----------------------------------------
28.45/9.25	
28.45/9.25	(862)
28.45/9.25	Obligation:
28.45/9.25	Q DP problem:
28.45/9.25	The TRS P consists of the following rules:
28.45/9.25	
28.45/9.25	   H(x, x) -> G(x, x, f(k))
28.45/9.25	   G(d, x, x) -> A^2
28.45/9.25	   A^2 -> H(f(c), f(c))
28.45/9.25	   A^2 -> H(f(d), f(d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.25	   A^2 -> H(f(e), f(e))
28.45/9.25	   A^2 -> H(f(k), f(k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.25	   A^2 -> H(U1(c, k), f(e))
28.45/9.25	   A^2 -> H(U1(c, k), f(k))
28.45/9.25	   A^2 -> H(U1(c, k), U1(d, d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.25	   A^2 -> H(e, U1(b, b))
28.45/9.25	   A^2 -> H(e, f(c))
28.45/9.25	   A^2 -> H(e, f(d))
28.45/9.25	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.25	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.25	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.25	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.25	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.25	   A^2 -> H(U1(e, e), f(e))
28.45/9.25	   A^2 -> H(U1(e, e), f(k))
28.45/9.25	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.25	   A^2 -> H(f(e), U1(e, b))
28.45/9.25	   A^2 -> H(f(e), U1(k, b))
28.45/9.25	   A^2 -> H(f(e), U1(c, d))
28.45/9.25	   A^2 -> H(f(e), U1(d, c))
28.45/9.25	   A^2 -> H(f(e), U1(b, e))
28.45/9.25	   A^2 -> H(f(e), U1(b, k))
28.45/9.25	   A^2 -> H(f(e), U1(e, c))
28.45/9.25	   A^2 -> H(f(e), U1(k, c))
28.45/9.25	   A^2 -> H(f(e), U1(c, e))
28.45/9.25	   A^2 -> H(f(e), U1(c, k))
28.45/9.25	   A^2 -> H(f(e), U1(k, k))
28.45/9.25	   A^2 -> H(f(e), U1(k, d))
28.45/9.25	   A^2 -> H(f(e), U1(d, k))
28.45/9.25	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.25	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.25	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.25	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.25	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.25	   A^2 -> H(U1(k, k), f(e))
28.45/9.25	   A^2 -> H(U1(k, k), f(k))
28.45/9.25	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.25	   A^2 -> H(f(k), U1(e, b))
28.45/9.25	   A^2 -> H(f(k), U1(k, b))
28.45/9.25	   A^2 -> H(f(k), U1(c, d))
28.45/9.25	   A^2 -> H(f(k), U1(d, c))
28.45/9.25	   A^2 -> H(f(k), U1(b, e))
28.45/9.25	   A^2 -> H(f(k), U1(b, k))
28.45/9.25	   A^2 -> H(f(k), U1(e, c))
28.45/9.25	   A^2 -> H(f(k), U1(k, c))
28.45/9.25	   A^2 -> H(f(k), U1(c, e))
28.45/9.25	   A^2 -> H(f(k), U1(c, k))
28.45/9.25	   A^2 -> H(f(k), U1(e, e))
28.45/9.25	   A^2 -> H(f(k), U1(k, d))
28.45/9.25	   A^2 -> H(f(k), U1(d, k))
28.45/9.25	   A^2 -> H(f(c), b)
28.45/9.25	   A^2 -> H(f(c), U1(e, d))
28.45/9.25	   A^2 -> H(f(c), U1(d, e))
28.45/9.25	   A^2 -> H(f(k), U1(k, k))
28.45/9.25	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.25	   A^2 -> H(U1(k, k), f(c))
28.45/9.25	   A^2 -> H(U1(k, k), f(d))
28.45/9.25	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.25	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.25	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.25	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.25	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.25	   A^2 -> H(U1(k, d), f(e))
28.45/9.25	   A^2 -> H(U1(k, d), f(k))
28.45/9.25	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.25	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.25	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.25	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.25	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.25	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.25	   A^2 -> H(U1(d, k), f(e))
28.45/9.25	   A^2 -> H(U1(d, k), f(k))
28.45/9.25	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.25	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.25	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.25	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.25	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.25	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.25	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.25	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.25	   A^2 -> H(f(d), b)
28.45/9.25	   A^2 -> H(f(d), U1(e, d))
28.45/9.25	   A^2 -> H(f(d), U1(d, e))
28.45/9.25	   A^2 -> H(f(d), c)
28.45/9.25	   A^2 -> H(f(d), U1(e, k))
28.45/9.25	   A^2 -> H(f(d), U1(k, e))
28.45/9.25	   A^2 -> H(f(d), e)
28.45/9.25	   A^2 -> H(f(a), d)
28.45/9.25	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.25	   A^2 -> H(f(c), c)
28.45/9.25	   A^2 -> H(f(c), U1(e, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.25	   A^2 -> H(f(c), U1(k, e))
28.45/9.25	   A^2 -> H(f(c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.25	   A^2 -> H(f(a), k)
28.45/9.25	   A^2 -> H(f(e), U1(e, e))
28.45/9.25	   A^2 -> H(f(c), e)
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.25	   A^2 -> H(f(d), U1(k, k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.25	   A^2 -> H(d, U1(b, b))
28.45/9.25	   A^2 -> H(d, f(c))
28.45/9.25	   A^2 -> H(d, f(d))
28.45/9.25	   A^2 -> H(a, U1(c, b))
28.45/9.25	   A^2 -> H(a, U1(d, b))
28.45/9.25	   A^2 -> H(a, U1(b, c))
28.45/9.25	   A^2 -> H(a, U1(b, d))
28.45/9.25	   A^2 -> H(a, U1(c, c))
28.45/9.25	   A^2 -> H(a, f(e))
28.45/9.25	   A^2 -> H(a, f(k))
28.45/9.25	   A^2 -> H(a, U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.25	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.25	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.25	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.25	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.25	   A^2 -> H(U1(e, d), f(e))
28.45/9.25	   A^2 -> H(U1(e, d), f(k))
28.45/9.25	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.25	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.25	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.25	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.25	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.25	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.25	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.25	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.25	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.25	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.25	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.25	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.25	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.25	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.25	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.25	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.25	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.25	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.25	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, a), b)
28.45/9.25	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.25	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.25	   A^2 -> H(U1(c, a), c)
28.45/9.25	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.25	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.25	   A^2 -> H(U1(c, a), e)
28.45/9.25	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.25	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.25	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.25	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.25	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.25	   A^2 -> H(U1(d, e), f(e))
28.45/9.25	   A^2 -> H(U1(d, e), f(k))
28.45/9.25	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.25	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.25	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.25	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.25	   A^2 -> H(U1(d, a), b)
28.45/9.25	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.25	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.25	   A^2 -> H(U1(d, a), c)
28.45/9.25	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.25	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.25	   A^2 -> H(U1(d, a), e)
28.45/9.25	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.25	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.25	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.25	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.25	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.25	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.25	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.25	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.25	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.25	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.25	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.25	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.25	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.25	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.25	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.25	   A^2 -> H(U1(a, c), b)
28.45/9.25	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.25	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.25	   A^2 -> H(U1(a, c), c)
28.45/9.25	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.25	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.25	   A^2 -> H(U1(a, c), e)
28.45/9.25	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, d), b)
28.45/9.25	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.25	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.25	   A^2 -> H(U1(a, d), c)
28.45/9.25	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.25	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.25	   A^2 -> H(U1(a, d), e)
28.45/9.25	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, a), d)
28.45/9.25	   A^2 -> H(U1(a, a), k)
28.45/9.25	   A^2 -> H(k, U1(b, b))
28.45/9.25	   A^2 -> H(k, f(c))
28.45/9.25	   A^2 -> H(k, f(d))
28.45/9.25	   A^2 -> H(c, U1(c, b))
28.45/9.25	   A^2 -> H(c, U1(d, b))
28.45/9.25	   A^2 -> H(c, U1(b, c))
28.45/9.25	   A^2 -> H(c, U1(b, d))
28.45/9.25	   A^2 -> H(c, U1(c, c))
28.45/9.25	   A^2 -> H(c, f(e))
28.45/9.25	   A^2 -> H(c, f(k))
28.45/9.25	   A^2 -> H(c, U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.25	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.25	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.25	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.25	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.25	   A^2 -> H(U1(e, k), f(e))
28.45/9.25	   A^2 -> H(U1(e, k), f(k))
28.45/9.25	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.25	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.25	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.25	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.25	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.25	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.25	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.25	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.25	   A^2 -> H(U1(k, e), f(e))
28.45/9.25	   A^2 -> H(U1(k, e), f(k))
28.45/9.25	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.25	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.25	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.25	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.25	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.25	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.25	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.25	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.25	
28.45/9.25	The TRS R consists of the following rules:
28.45/9.25	
28.45/9.25	   f(x) -> U1(x, x)
28.45/9.25	   U1(e, x) -> x
28.45/9.25	   a -> c
28.45/9.25	   a -> d
28.45/9.25	   b -> c
28.45/9.25	   b -> d
28.45/9.25	   d -> k
28.45/9.25	   c -> e
28.45/9.25	   c -> k
28.45/9.25	
28.45/9.25	Q is empty.
28.45/9.25	We have to consider all minimal (P,Q,R)-chains.
28.45/9.25	----------------------------------------
28.45/9.25	
28.45/9.25	(863) TransformationProof (EQUIVALENT)
28.45/9.25	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), f(e)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.25	
28.45/9.25	   (A^2 -> H(U1(e, k), f(e)),A^2 -> H(U1(e, k), f(e)))
28.45/9.25	   (A^2 -> H(U1(k, k), f(e)),A^2 -> H(U1(k, k), f(e)))
28.45/9.25	   (A^2 -> H(U1(c, k), U1(e, e)),A^2 -> H(U1(c, k), U1(e, e)))
28.45/9.25	
28.45/9.25	
28.45/9.25	----------------------------------------
28.45/9.25	
28.45/9.25	(864)
28.45/9.25	Obligation:
28.45/9.25	Q DP problem:
28.45/9.25	The TRS P consists of the following rules:
28.45/9.25	
28.45/9.25	   H(x, x) -> G(x, x, f(k))
28.45/9.25	   G(d, x, x) -> A^2
28.45/9.25	   A^2 -> H(f(c), f(c))
28.45/9.25	   A^2 -> H(f(d), f(d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.25	   A^2 -> H(f(e), f(e))
28.45/9.25	   A^2 -> H(f(k), f(k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.25	   A^2 -> H(U1(c, k), f(k))
28.45/9.25	   A^2 -> H(U1(c, k), U1(d, d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.25	   A^2 -> H(e, U1(b, b))
28.45/9.25	   A^2 -> H(e, f(c))
28.45/9.25	   A^2 -> H(e, f(d))
28.45/9.25	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.25	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.25	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.25	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.25	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.25	   A^2 -> H(U1(e, e), f(e))
28.45/9.25	   A^2 -> H(U1(e, e), f(k))
28.45/9.25	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.25	   A^2 -> H(f(e), U1(e, b))
28.45/9.25	   A^2 -> H(f(e), U1(k, b))
28.45/9.25	   A^2 -> H(f(e), U1(c, d))
28.45/9.25	   A^2 -> H(f(e), U1(d, c))
28.45/9.25	   A^2 -> H(f(e), U1(b, e))
28.45/9.25	   A^2 -> H(f(e), U1(b, k))
28.45/9.25	   A^2 -> H(f(e), U1(e, c))
28.45/9.25	   A^2 -> H(f(e), U1(k, c))
28.45/9.25	   A^2 -> H(f(e), U1(c, e))
28.45/9.25	   A^2 -> H(f(e), U1(c, k))
28.45/9.25	   A^2 -> H(f(e), U1(k, k))
28.45/9.25	   A^2 -> H(f(e), U1(k, d))
28.45/9.25	   A^2 -> H(f(e), U1(d, k))
28.45/9.25	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.25	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.25	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.25	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.25	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.25	   A^2 -> H(U1(k, k), f(e))
28.45/9.25	   A^2 -> H(U1(k, k), f(k))
28.45/9.25	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.25	   A^2 -> H(f(k), U1(e, b))
28.45/9.25	   A^2 -> H(f(k), U1(k, b))
28.45/9.25	   A^2 -> H(f(k), U1(c, d))
28.45/9.25	   A^2 -> H(f(k), U1(d, c))
28.45/9.25	   A^2 -> H(f(k), U1(b, e))
28.45/9.25	   A^2 -> H(f(k), U1(b, k))
28.45/9.25	   A^2 -> H(f(k), U1(e, c))
28.45/9.25	   A^2 -> H(f(k), U1(k, c))
28.45/9.25	   A^2 -> H(f(k), U1(c, e))
28.45/9.25	   A^2 -> H(f(k), U1(c, k))
28.45/9.25	   A^2 -> H(f(k), U1(e, e))
28.45/9.25	   A^2 -> H(f(k), U1(k, d))
28.45/9.25	   A^2 -> H(f(k), U1(d, k))
28.45/9.25	   A^2 -> H(f(c), b)
28.45/9.25	   A^2 -> H(f(c), U1(e, d))
28.45/9.25	   A^2 -> H(f(c), U1(d, e))
28.45/9.25	   A^2 -> H(f(k), U1(k, k))
28.45/9.25	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.25	   A^2 -> H(U1(k, k), f(c))
28.45/9.25	   A^2 -> H(U1(k, k), f(d))
28.45/9.25	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.25	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.25	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.25	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.25	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.25	   A^2 -> H(U1(k, d), f(e))
28.45/9.25	   A^2 -> H(U1(k, d), f(k))
28.45/9.25	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.25	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.25	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.25	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.25	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.25	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.25	   A^2 -> H(U1(d, k), f(e))
28.45/9.25	   A^2 -> H(U1(d, k), f(k))
28.45/9.25	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.25	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.25	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.25	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.25	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.25	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.25	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.25	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.25	   A^2 -> H(f(d), b)
28.45/9.25	   A^2 -> H(f(d), U1(e, d))
28.45/9.25	   A^2 -> H(f(d), U1(d, e))
28.45/9.25	   A^2 -> H(f(d), c)
28.45/9.25	   A^2 -> H(f(d), U1(e, k))
28.45/9.25	   A^2 -> H(f(d), U1(k, e))
28.45/9.25	   A^2 -> H(f(d), e)
28.45/9.25	   A^2 -> H(f(a), d)
28.45/9.25	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.25	   A^2 -> H(f(c), c)
28.45/9.25	   A^2 -> H(f(c), U1(e, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.25	   A^2 -> H(f(c), U1(k, e))
28.45/9.25	   A^2 -> H(f(c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.25	   A^2 -> H(f(a), k)
28.45/9.25	   A^2 -> H(f(e), U1(e, e))
28.45/9.25	   A^2 -> H(f(c), e)
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.25	   A^2 -> H(f(d), U1(k, k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.25	   A^2 -> H(d, U1(b, b))
28.45/9.25	   A^2 -> H(d, f(c))
28.45/9.25	   A^2 -> H(d, f(d))
28.45/9.25	   A^2 -> H(a, U1(c, b))
28.45/9.25	   A^2 -> H(a, U1(d, b))
28.45/9.25	   A^2 -> H(a, U1(b, c))
28.45/9.25	   A^2 -> H(a, U1(b, d))
28.45/9.25	   A^2 -> H(a, U1(c, c))
28.45/9.25	   A^2 -> H(a, f(e))
28.45/9.25	   A^2 -> H(a, f(k))
28.45/9.25	   A^2 -> H(a, U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.25	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.25	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.25	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.25	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.25	   A^2 -> H(U1(e, d), f(e))
28.45/9.25	   A^2 -> H(U1(e, d), f(k))
28.45/9.25	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.25	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.25	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.25	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.25	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.25	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.25	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.25	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.25	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.25	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.25	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.25	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.25	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.25	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.25	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.25	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.25	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.25	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.25	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, a), b)
28.45/9.25	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.25	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.25	   A^2 -> H(U1(c, a), c)
28.45/9.25	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.25	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.25	   A^2 -> H(U1(c, a), e)
28.45/9.25	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.25	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.25	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.25	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.25	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.25	   A^2 -> H(U1(d, e), f(e))
28.45/9.25	   A^2 -> H(U1(d, e), f(k))
28.45/9.25	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.25	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.25	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.25	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.25	   A^2 -> H(U1(d, a), b)
28.45/9.25	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.25	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.25	   A^2 -> H(U1(d, a), c)
28.45/9.25	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.25	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.25	   A^2 -> H(U1(d, a), e)
28.45/9.25	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.25	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.25	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.25	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.25	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.25	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.25	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.25	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.25	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.25	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.25	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.25	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.25	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.25	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.25	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.25	   A^2 -> H(U1(a, c), b)
28.45/9.25	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.25	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.25	   A^2 -> H(U1(a, c), c)
28.45/9.25	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.25	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.25	   A^2 -> H(U1(a, c), e)
28.45/9.25	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, d), b)
28.45/9.25	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.25	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.25	   A^2 -> H(U1(a, d), c)
28.45/9.25	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.25	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.25	   A^2 -> H(U1(a, d), e)
28.45/9.25	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, a), d)
28.45/9.25	   A^2 -> H(U1(a, a), k)
28.45/9.25	   A^2 -> H(k, U1(b, b))
28.45/9.25	   A^2 -> H(k, f(c))
28.45/9.25	   A^2 -> H(k, f(d))
28.45/9.25	   A^2 -> H(c, U1(c, b))
28.45/9.25	   A^2 -> H(c, U1(d, b))
28.45/9.25	   A^2 -> H(c, U1(b, c))
28.45/9.25	   A^2 -> H(c, U1(b, d))
28.45/9.25	   A^2 -> H(c, U1(c, c))
28.45/9.25	   A^2 -> H(c, f(e))
28.45/9.25	   A^2 -> H(c, f(k))
28.45/9.25	   A^2 -> H(c, U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.25	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.25	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.25	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.25	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.25	   A^2 -> H(U1(e, k), f(e))
28.45/9.25	   A^2 -> H(U1(e, k), f(k))
28.45/9.25	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.25	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.25	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.25	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.25	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.25	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.25	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.25	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.25	   A^2 -> H(U1(k, e), f(e))
28.45/9.25	   A^2 -> H(U1(k, e), f(k))
28.45/9.25	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.25	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.25	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.25	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.25	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.25	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.25	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.25	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.25	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.25	
28.45/9.25	The TRS R consists of the following rules:
28.45/9.25	
28.45/9.25	   f(x) -> U1(x, x)
28.45/9.25	   U1(e, x) -> x
28.45/9.25	   a -> c
28.45/9.25	   a -> d
28.45/9.25	   b -> c
28.45/9.25	   b -> d
28.45/9.25	   d -> k
28.45/9.25	   c -> e
28.45/9.25	   c -> k
28.45/9.25	
28.45/9.25	Q is empty.
28.45/9.25	We have to consider all minimal (P,Q,R)-chains.
28.45/9.25	----------------------------------------
28.45/9.25	
28.45/9.25	(865) TransformationProof (EQUIVALENT)
28.45/9.25	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), f(k)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.25	
28.45/9.25	   (A^2 -> H(U1(e, k), f(k)),A^2 -> H(U1(e, k), f(k)))
28.45/9.25	   (A^2 -> H(U1(k, k), f(k)),A^2 -> H(U1(k, k), f(k)))
28.45/9.25	   (A^2 -> H(U1(c, k), U1(k, k)),A^2 -> H(U1(c, k), U1(k, k)))
28.45/9.25	
28.45/9.25	
28.45/9.25	----------------------------------------
28.45/9.25	
28.45/9.25	(866)
28.45/9.25	Obligation:
28.45/9.25	Q DP problem:
28.45/9.25	The TRS P consists of the following rules:
28.45/9.25	
28.45/9.25	   H(x, x) -> G(x, x, f(k))
28.45/9.25	   G(d, x, x) -> A^2
28.45/9.25	   A^2 -> H(f(c), f(c))
28.45/9.25	   A^2 -> H(f(d), f(d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.25	   A^2 -> H(f(e), f(e))
28.45/9.25	   A^2 -> H(f(k), f(k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.25	   A^2 -> H(U1(c, k), U1(d, d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.25	   A^2 -> H(e, U1(b, b))
28.45/9.25	   A^2 -> H(e, f(c))
28.45/9.25	   A^2 -> H(e, f(d))
28.45/9.25	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.25	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.25	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.25	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.25	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.25	   A^2 -> H(U1(e, e), f(e))
28.45/9.25	   A^2 -> H(U1(e, e), f(k))
28.45/9.25	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.25	   A^2 -> H(f(e), U1(e, b))
28.45/9.25	   A^2 -> H(f(e), U1(k, b))
28.45/9.25	   A^2 -> H(f(e), U1(c, d))
28.45/9.25	   A^2 -> H(f(e), U1(d, c))
28.45/9.25	   A^2 -> H(f(e), U1(b, e))
28.45/9.25	   A^2 -> H(f(e), U1(b, k))
28.45/9.25	   A^2 -> H(f(e), U1(e, c))
28.45/9.25	   A^2 -> H(f(e), U1(k, c))
28.45/9.25	   A^2 -> H(f(e), U1(c, e))
28.45/9.25	   A^2 -> H(f(e), U1(c, k))
28.45/9.25	   A^2 -> H(f(e), U1(k, k))
28.45/9.25	   A^2 -> H(f(e), U1(k, d))
28.45/9.25	   A^2 -> H(f(e), U1(d, k))
28.45/9.25	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.25	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.25	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.25	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.25	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.25	   A^2 -> H(U1(k, k), f(e))
28.45/9.25	   A^2 -> H(U1(k, k), f(k))
28.45/9.25	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.25	   A^2 -> H(f(k), U1(e, b))
28.45/9.25	   A^2 -> H(f(k), U1(k, b))
28.45/9.25	   A^2 -> H(f(k), U1(c, d))
28.45/9.25	   A^2 -> H(f(k), U1(d, c))
28.45/9.25	   A^2 -> H(f(k), U1(b, e))
28.45/9.25	   A^2 -> H(f(k), U1(b, k))
28.45/9.25	   A^2 -> H(f(k), U1(e, c))
28.45/9.25	   A^2 -> H(f(k), U1(k, c))
28.45/9.25	   A^2 -> H(f(k), U1(c, e))
28.45/9.25	   A^2 -> H(f(k), U1(c, k))
28.45/9.25	   A^2 -> H(f(k), U1(e, e))
28.45/9.25	   A^2 -> H(f(k), U1(k, d))
28.45/9.25	   A^2 -> H(f(k), U1(d, k))
28.45/9.25	   A^2 -> H(f(c), b)
28.45/9.25	   A^2 -> H(f(c), U1(e, d))
28.45/9.25	   A^2 -> H(f(c), U1(d, e))
28.45/9.25	   A^2 -> H(f(k), U1(k, k))
28.45/9.25	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.25	   A^2 -> H(U1(k, k), f(c))
28.45/9.25	   A^2 -> H(U1(k, k), f(d))
28.45/9.25	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.25	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.25	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.25	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.25	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.25	   A^2 -> H(U1(k, d), f(e))
28.45/9.25	   A^2 -> H(U1(k, d), f(k))
28.45/9.25	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.25	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.25	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.25	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.25	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.25	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.25	   A^2 -> H(U1(d, k), f(e))
28.45/9.25	   A^2 -> H(U1(d, k), f(k))
28.45/9.25	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.25	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.25	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.25	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.25	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.25	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.25	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.25	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.25	   A^2 -> H(f(d), b)
28.45/9.25	   A^2 -> H(f(d), U1(e, d))
28.45/9.25	   A^2 -> H(f(d), U1(d, e))
28.45/9.25	   A^2 -> H(f(d), c)
28.45/9.25	   A^2 -> H(f(d), U1(e, k))
28.45/9.25	   A^2 -> H(f(d), U1(k, e))
28.45/9.25	   A^2 -> H(f(d), e)
28.45/9.25	   A^2 -> H(f(a), d)
28.45/9.25	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.25	   A^2 -> H(f(c), c)
28.45/9.25	   A^2 -> H(f(c), U1(e, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.25	   A^2 -> H(f(c), U1(k, e))
28.45/9.25	   A^2 -> H(f(c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.25	   A^2 -> H(f(a), k)
28.45/9.25	   A^2 -> H(f(e), U1(e, e))
28.45/9.25	   A^2 -> H(f(c), e)
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.25	   A^2 -> H(f(d), U1(k, k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.25	   A^2 -> H(d, U1(b, b))
28.45/9.25	   A^2 -> H(d, f(c))
28.45/9.25	   A^2 -> H(d, f(d))
28.45/9.25	   A^2 -> H(a, U1(c, b))
28.45/9.25	   A^2 -> H(a, U1(d, b))
28.45/9.25	   A^2 -> H(a, U1(b, c))
28.45/9.25	   A^2 -> H(a, U1(b, d))
28.45/9.25	   A^2 -> H(a, U1(c, c))
28.45/9.25	   A^2 -> H(a, f(e))
28.45/9.25	   A^2 -> H(a, f(k))
28.45/9.25	   A^2 -> H(a, U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.25	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.25	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.25	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.25	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.25	   A^2 -> H(U1(e, d), f(e))
28.45/9.25	   A^2 -> H(U1(e, d), f(k))
28.45/9.25	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.25	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.25	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.25	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.25	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.25	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.25	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.25	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.25	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.25	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.25	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.25	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.25	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.25	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.25	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.25	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.25	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.25	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.25	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, a), b)
28.45/9.25	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.25	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.25	   A^2 -> H(U1(c, a), c)
28.45/9.25	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.25	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.25	   A^2 -> H(U1(c, a), e)
28.45/9.25	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.25	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.25	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.25	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.25	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.25	   A^2 -> H(U1(d, e), f(e))
28.45/9.25	   A^2 -> H(U1(d, e), f(k))
28.45/9.25	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.25	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.25	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.25	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.25	   A^2 -> H(U1(d, a), b)
28.45/9.25	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.25	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.25	   A^2 -> H(U1(d, a), c)
28.45/9.25	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.25	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.25	   A^2 -> H(U1(d, a), e)
28.45/9.25	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.25	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.25	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.25	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.25	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.25	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.25	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.25	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.25	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.25	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.25	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.25	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.25	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.25	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.25	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.25	   A^2 -> H(U1(a, c), b)
28.45/9.25	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.25	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.25	   A^2 -> H(U1(a, c), c)
28.45/9.25	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.25	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.25	   A^2 -> H(U1(a, c), e)
28.45/9.25	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, d), b)
28.45/9.25	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.25	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.25	   A^2 -> H(U1(a, d), c)
28.45/9.25	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.25	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.25	   A^2 -> H(U1(a, d), e)
28.45/9.25	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, a), d)
28.45/9.25	   A^2 -> H(U1(a, a), k)
28.45/9.25	   A^2 -> H(k, U1(b, b))
28.45/9.25	   A^2 -> H(k, f(c))
28.45/9.25	   A^2 -> H(k, f(d))
28.45/9.25	   A^2 -> H(c, U1(c, b))
28.45/9.25	   A^2 -> H(c, U1(d, b))
28.45/9.25	   A^2 -> H(c, U1(b, c))
28.45/9.25	   A^2 -> H(c, U1(b, d))
28.45/9.25	   A^2 -> H(c, U1(c, c))
28.45/9.25	   A^2 -> H(c, f(e))
28.45/9.25	   A^2 -> H(c, f(k))
28.45/9.25	   A^2 -> H(c, U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.25	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.25	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.25	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.25	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.25	   A^2 -> H(U1(e, k), f(e))
28.45/9.25	   A^2 -> H(U1(e, k), f(k))
28.45/9.25	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.25	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.25	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.25	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.25	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.25	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.25	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.25	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.25	   A^2 -> H(U1(k, e), f(e))
28.45/9.25	   A^2 -> H(U1(k, e), f(k))
28.45/9.25	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.25	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.25	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.25	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.25	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.25	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.25	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.25	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.25	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.25	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.25	
28.45/9.25	The TRS R consists of the following rules:
28.45/9.25	
28.45/9.25	   f(x) -> U1(x, x)
28.45/9.25	   U1(e, x) -> x
28.45/9.25	   a -> c
28.45/9.25	   a -> d
28.45/9.25	   b -> c
28.45/9.25	   b -> d
28.45/9.25	   d -> k
28.45/9.25	   c -> e
28.45/9.25	   c -> k
28.45/9.25	
28.45/9.25	Q is empty.
28.45/9.25	We have to consider all minimal (P,Q,R)-chains.
28.45/9.25	----------------------------------------
28.45/9.25	
28.45/9.25	(867) TransformationProof (EQUIVALENT)
28.45/9.25	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.25	
28.45/9.25	   (A^2 -> H(U1(e, k), U1(d, d)),A^2 -> H(U1(e, k), U1(d, d)))
28.45/9.25	   (A^2 -> H(U1(k, k), U1(d, d)),A^2 -> H(U1(k, k), U1(d, d)))
28.45/9.25	   (A^2 -> H(U1(c, k), U1(k, d)),A^2 -> H(U1(c, k), U1(k, d)))
28.45/9.25	   (A^2 -> H(U1(c, k), U1(d, k)),A^2 -> H(U1(c, k), U1(d, k)))
28.45/9.25	
28.45/9.25	
28.45/9.25	----------------------------------------
28.45/9.25	
28.45/9.25	(868)
28.45/9.25	Obligation:
28.45/9.25	Q DP problem:
28.45/9.25	The TRS P consists of the following rules:
28.45/9.25	
28.45/9.25	   H(x, x) -> G(x, x, f(k))
28.45/9.25	   G(d, x, x) -> A^2
28.45/9.25	   A^2 -> H(f(c), f(c))
28.45/9.25	   A^2 -> H(f(d), f(d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.25	   A^2 -> H(f(e), f(e))
28.45/9.25	   A^2 -> H(f(k), f(k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.25	   A^2 -> H(e, U1(b, b))
28.45/9.25	   A^2 -> H(e, f(c))
28.45/9.25	   A^2 -> H(e, f(d))
28.45/9.25	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.25	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.25	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.25	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.25	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.25	   A^2 -> H(U1(e, e), f(e))
28.45/9.25	   A^2 -> H(U1(e, e), f(k))
28.45/9.25	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.25	   A^2 -> H(f(e), U1(e, b))
28.45/9.25	   A^2 -> H(f(e), U1(k, b))
28.45/9.25	   A^2 -> H(f(e), U1(c, d))
28.45/9.25	   A^2 -> H(f(e), U1(d, c))
28.45/9.25	   A^2 -> H(f(e), U1(b, e))
28.45/9.25	   A^2 -> H(f(e), U1(b, k))
28.45/9.25	   A^2 -> H(f(e), U1(e, c))
28.45/9.25	   A^2 -> H(f(e), U1(k, c))
28.45/9.25	   A^2 -> H(f(e), U1(c, e))
28.45/9.25	   A^2 -> H(f(e), U1(c, k))
28.45/9.25	   A^2 -> H(f(e), U1(k, k))
28.45/9.25	   A^2 -> H(f(e), U1(k, d))
28.45/9.25	   A^2 -> H(f(e), U1(d, k))
28.45/9.25	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.25	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.25	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.25	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.25	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.25	   A^2 -> H(U1(k, k), f(e))
28.45/9.25	   A^2 -> H(U1(k, k), f(k))
28.45/9.25	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.25	   A^2 -> H(f(k), U1(e, b))
28.45/9.25	   A^2 -> H(f(k), U1(k, b))
28.45/9.25	   A^2 -> H(f(k), U1(c, d))
28.45/9.25	   A^2 -> H(f(k), U1(d, c))
28.45/9.25	   A^2 -> H(f(k), U1(b, e))
28.45/9.25	   A^2 -> H(f(k), U1(b, k))
28.45/9.25	   A^2 -> H(f(k), U1(e, c))
28.45/9.25	   A^2 -> H(f(k), U1(k, c))
28.45/9.25	   A^2 -> H(f(k), U1(c, e))
28.45/9.25	   A^2 -> H(f(k), U1(c, k))
28.45/9.25	   A^2 -> H(f(k), U1(e, e))
28.45/9.25	   A^2 -> H(f(k), U1(k, d))
28.45/9.25	   A^2 -> H(f(k), U1(d, k))
28.45/9.25	   A^2 -> H(f(c), b)
28.45/9.25	   A^2 -> H(f(c), U1(e, d))
28.45/9.25	   A^2 -> H(f(c), U1(d, e))
28.45/9.25	   A^2 -> H(f(k), U1(k, k))
28.45/9.25	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.25	   A^2 -> H(U1(k, k), f(c))
28.45/9.25	   A^2 -> H(U1(k, k), f(d))
28.45/9.25	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.25	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.25	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.25	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.25	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.25	   A^2 -> H(U1(k, d), f(e))
28.45/9.25	   A^2 -> H(U1(k, d), f(k))
28.45/9.25	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.25	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.25	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.25	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.25	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.25	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.25	   A^2 -> H(U1(d, k), f(e))
28.45/9.25	   A^2 -> H(U1(d, k), f(k))
28.45/9.25	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.25	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.25	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.25	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.25	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.25	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.25	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.25	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.25	   A^2 -> H(f(d), b)
28.45/9.25	   A^2 -> H(f(d), U1(e, d))
28.45/9.25	   A^2 -> H(f(d), U1(d, e))
28.45/9.25	   A^2 -> H(f(d), c)
28.45/9.25	   A^2 -> H(f(d), U1(e, k))
28.45/9.25	   A^2 -> H(f(d), U1(k, e))
28.45/9.25	   A^2 -> H(f(d), e)
28.45/9.25	   A^2 -> H(f(a), d)
28.45/9.25	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.25	   A^2 -> H(f(c), c)
28.45/9.25	   A^2 -> H(f(c), U1(e, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.25	   A^2 -> H(f(c), U1(k, e))
28.45/9.25	   A^2 -> H(f(c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.25	   A^2 -> H(f(a), k)
28.45/9.25	   A^2 -> H(f(e), U1(e, e))
28.45/9.25	   A^2 -> H(f(c), e)
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.25	   A^2 -> H(f(d), U1(k, k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.25	   A^2 -> H(d, U1(b, b))
28.45/9.25	   A^2 -> H(d, f(c))
28.45/9.25	   A^2 -> H(d, f(d))
28.45/9.25	   A^2 -> H(a, U1(c, b))
28.45/9.25	   A^2 -> H(a, U1(d, b))
28.45/9.25	   A^2 -> H(a, U1(b, c))
28.45/9.25	   A^2 -> H(a, U1(b, d))
28.45/9.25	   A^2 -> H(a, U1(c, c))
28.45/9.25	   A^2 -> H(a, f(e))
28.45/9.25	   A^2 -> H(a, f(k))
28.45/9.25	   A^2 -> H(a, U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.25	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.25	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.25	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.25	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.25	   A^2 -> H(U1(e, d), f(e))
28.45/9.25	   A^2 -> H(U1(e, d), f(k))
28.45/9.25	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.25	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.25	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.25	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.25	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.25	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.25	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.25	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.25	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.25	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.25	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.25	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.25	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.25	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.25	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.25	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.25	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.25	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.25	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, a), b)
28.45/9.25	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.25	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.25	   A^2 -> H(U1(c, a), c)
28.45/9.25	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.25	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.25	   A^2 -> H(U1(c, a), e)
28.45/9.25	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.25	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.25	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.25	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.25	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.25	   A^2 -> H(U1(d, e), f(e))
28.45/9.25	   A^2 -> H(U1(d, e), f(k))
28.45/9.25	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.25	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.25	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.25	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.25	   A^2 -> H(U1(d, a), b)
28.45/9.25	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.25	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.25	   A^2 -> H(U1(d, a), c)
28.45/9.25	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.25	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.25	   A^2 -> H(U1(d, a), e)
28.45/9.25	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.25	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.25	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.25	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.25	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.25	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.25	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.25	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.25	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.25	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.25	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.25	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.25	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.25	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.25	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.25	   A^2 -> H(U1(a, c), b)
28.45/9.25	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.25	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.25	   A^2 -> H(U1(a, c), c)
28.45/9.25	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.25	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.25	   A^2 -> H(U1(a, c), e)
28.45/9.25	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, d), b)
28.45/9.25	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.25	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.25	   A^2 -> H(U1(a, d), c)
28.45/9.25	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.25	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.25	   A^2 -> H(U1(a, d), e)
28.45/9.25	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.25	   A^2 -> H(U1(a, a), d)
28.45/9.25	   A^2 -> H(U1(a, a), k)
28.45/9.25	   A^2 -> H(k, U1(b, b))
28.45/9.25	   A^2 -> H(k, f(c))
28.45/9.25	   A^2 -> H(k, f(d))
28.45/9.25	   A^2 -> H(c, U1(c, b))
28.45/9.25	   A^2 -> H(c, U1(d, b))
28.45/9.25	   A^2 -> H(c, U1(b, c))
28.45/9.25	   A^2 -> H(c, U1(b, d))
28.45/9.25	   A^2 -> H(c, U1(c, c))
28.45/9.25	   A^2 -> H(c, f(e))
28.45/9.25	   A^2 -> H(c, f(k))
28.45/9.25	   A^2 -> H(c, U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.25	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.25	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.25	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.25	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.25	   A^2 -> H(U1(e, k), f(e))
28.45/9.25	   A^2 -> H(U1(e, k), f(k))
28.45/9.25	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.25	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.25	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.25	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.25	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.25	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.25	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.25	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.25	   A^2 -> H(U1(k, e), f(e))
28.45/9.25	   A^2 -> H(U1(k, e), f(k))
28.45/9.25	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.25	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.25	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.25	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.25	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.25	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.25	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.25	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.25	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.25	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.25	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.25	
28.45/9.25	The TRS R consists of the following rules:
28.45/9.25	
28.45/9.25	   f(x) -> U1(x, x)
28.45/9.25	   U1(e, x) -> x
28.45/9.25	   a -> c
28.45/9.25	   a -> d
28.45/9.25	   b -> c
28.45/9.25	   b -> d
28.45/9.25	   d -> k
28.45/9.25	   c -> e
28.45/9.25	   c -> k
28.45/9.25	
28.45/9.25	Q is empty.
28.45/9.25	We have to consider all minimal (P,Q,R)-chains.
28.45/9.25	----------------------------------------
28.45/9.25	
28.45/9.25	(869) TransformationProof (EQUIVALENT)
28.45/9.25	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.25	
28.45/9.25	   (A^2 -> H(U1(e, c), U1(e, b)),A^2 -> H(U1(e, c), U1(e, b)))
28.45/9.25	   (A^2 -> H(U1(k, c), U1(e, b)),A^2 -> H(U1(k, c), U1(e, b)))
28.45/9.25	   (A^2 -> H(U1(c, e), U1(e, b)),A^2 -> H(U1(c, e), U1(e, b)))
28.45/9.25	   (A^2 -> H(U1(c, k), U1(e, b)),A^2 -> H(U1(c, k), U1(e, b)))
28.45/9.25	   (A^2 -> H(U1(c, c), b),A^2 -> H(U1(c, c), b))
28.45/9.25	   (A^2 -> H(U1(c, c), U1(e, c)),A^2 -> H(U1(c, c), U1(e, c)))
28.45/9.25	   (A^2 -> H(U1(c, c), U1(e, d)),A^2 -> H(U1(c, c), U1(e, d)))
28.45/9.25	
28.45/9.25	
28.45/9.25	----------------------------------------
28.45/9.25	
28.45/9.25	(870)
28.45/9.25	Obligation:
28.45/9.25	Q DP problem:
28.45/9.25	The TRS P consists of the following rules:
28.45/9.25	
28.45/9.25	   H(x, x) -> G(x, x, f(k))
28.45/9.25	   G(d, x, x) -> A^2
28.45/9.25	   A^2 -> H(f(c), f(c))
28.45/9.25	   A^2 -> H(f(d), f(d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.25	   A^2 -> H(f(e), f(e))
28.45/9.25	   A^2 -> H(f(k), f(k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.25	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.25	   A^2 -> H(e, U1(b, b))
28.45/9.25	   A^2 -> H(e, f(c))
28.45/9.25	   A^2 -> H(e, f(d))
28.45/9.25	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.25	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.25	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.25	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.25	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.25	   A^2 -> H(U1(e, e), f(e))
28.45/9.25	   A^2 -> H(U1(e, e), f(k))
28.45/9.25	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.25	   A^2 -> H(f(e), U1(e, b))
28.45/9.25	   A^2 -> H(f(e), U1(k, b))
28.45/9.25	   A^2 -> H(f(e), U1(c, d))
28.45/9.25	   A^2 -> H(f(e), U1(d, c))
28.45/9.25	   A^2 -> H(f(e), U1(b, e))
28.45/9.25	   A^2 -> H(f(e), U1(b, k))
28.45/9.25	   A^2 -> H(f(e), U1(e, c))
28.45/9.25	   A^2 -> H(f(e), U1(k, c))
28.45/9.25	   A^2 -> H(f(e), U1(c, e))
28.45/9.25	   A^2 -> H(f(e), U1(c, k))
28.45/9.25	   A^2 -> H(f(e), U1(k, k))
28.45/9.25	   A^2 -> H(f(e), U1(k, d))
28.45/9.25	   A^2 -> H(f(e), U1(d, k))
28.45/9.25	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.25	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.25	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.25	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.25	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.25	   A^2 -> H(U1(k, k), f(e))
28.45/9.25	   A^2 -> H(U1(k, k), f(k))
28.45/9.25	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.25	   A^2 -> H(f(k), U1(e, b))
28.45/9.25	   A^2 -> H(f(k), U1(k, b))
28.45/9.25	   A^2 -> H(f(k), U1(c, d))
28.45/9.25	   A^2 -> H(f(k), U1(d, c))
28.45/9.25	   A^2 -> H(f(k), U1(b, e))
28.45/9.25	   A^2 -> H(f(k), U1(b, k))
28.45/9.25	   A^2 -> H(f(k), U1(e, c))
28.45/9.25	   A^2 -> H(f(k), U1(k, c))
28.45/9.25	   A^2 -> H(f(k), U1(c, e))
28.45/9.25	   A^2 -> H(f(k), U1(c, k))
28.45/9.25	   A^2 -> H(f(k), U1(e, e))
28.45/9.25	   A^2 -> H(f(k), U1(k, d))
28.45/9.25	   A^2 -> H(f(k), U1(d, k))
28.45/9.25	   A^2 -> H(f(c), b)
28.45/9.25	   A^2 -> H(f(c), U1(e, d))
28.45/9.25	   A^2 -> H(f(c), U1(d, e))
28.45/9.25	   A^2 -> H(f(k), U1(k, k))
28.45/9.25	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.25	   A^2 -> H(U1(k, k), f(c))
28.45/9.25	   A^2 -> H(U1(k, k), f(d))
28.45/9.25	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.25	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.25	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.25	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.25	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.25	   A^2 -> H(U1(k, d), f(e))
28.45/9.25	   A^2 -> H(U1(k, d), f(k))
28.45/9.25	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.25	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.25	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.25	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.25	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.25	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.25	   A^2 -> H(U1(d, k), f(e))
28.45/9.25	   A^2 -> H(U1(d, k), f(k))
28.45/9.25	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.25	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.25	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.25	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.25	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.25	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.25	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.25	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.25	   A^2 -> H(f(d), b)
28.45/9.25	   A^2 -> H(f(d), U1(e, d))
28.45/9.25	   A^2 -> H(f(d), U1(d, e))
28.45/9.25	   A^2 -> H(f(d), c)
28.45/9.25	   A^2 -> H(f(d), U1(e, k))
28.45/9.25	   A^2 -> H(f(d), U1(k, e))
28.45/9.25	   A^2 -> H(f(d), e)
28.45/9.25	   A^2 -> H(f(a), d)
28.45/9.25	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.25	   A^2 -> H(f(c), c)
28.45/9.25	   A^2 -> H(f(c), U1(e, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.25	   A^2 -> H(f(c), U1(k, e))
28.45/9.25	   A^2 -> H(f(c), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.25	   A^2 -> H(f(a), k)
28.45/9.25	   A^2 -> H(f(e), U1(e, e))
28.45/9.25	   A^2 -> H(f(c), e)
28.45/9.25	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.25	   A^2 -> H(f(d), U1(k, k))
28.45/9.25	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.25	   A^2 -> H(d, U1(b, b))
28.45/9.25	   A^2 -> H(d, f(c))
28.45/9.25	   A^2 -> H(d, f(d))
28.45/9.25	   A^2 -> H(a, U1(c, b))
28.45/9.25	   A^2 -> H(a, U1(d, b))
28.45/9.25	   A^2 -> H(a, U1(b, c))
28.45/9.25	   A^2 -> H(a, U1(b, d))
28.45/9.25	   A^2 -> H(a, U1(c, c))
28.45/9.25	   A^2 -> H(a, f(e))
28.45/9.25	   A^2 -> H(a, f(k))
28.45/9.25	   A^2 -> H(a, U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.25	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.25	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.25	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.25	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.25	   A^2 -> H(U1(e, d), f(e))
28.45/9.25	   A^2 -> H(U1(e, d), f(k))
28.45/9.25	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.25	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.25	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.25	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.25	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.25	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.25	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.25	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.25	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.25	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.25	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.25	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.25	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.25	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.25	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.25	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.25	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.25	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.25	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.25	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.25	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.25	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.25	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.25	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.25	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.25	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.25	   A^2 -> H(U1(c, a), b)
28.45/9.25	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.25	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.25	   A^2 -> H(U1(c, a), c)
28.45/9.25	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.25	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.25	   A^2 -> H(U1(c, a), e)
28.45/9.25	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.25	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.25	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.25	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.25	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.25	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.25	   A^2 -> H(U1(d, e), f(e))
28.45/9.25	   A^2 -> H(U1(d, e), f(k))
28.45/9.25	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.25	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.25	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.25	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.25	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.26	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.26	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.26	   A^2 -> H(U1(d, a), b)
28.45/9.26	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.26	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.26	   A^2 -> H(U1(d, a), c)
28.45/9.26	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.26	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.26	   A^2 -> H(U1(d, a), e)
28.45/9.26	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.26	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.26	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.26	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.26	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.26	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.26	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.26	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.26	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.26	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.26	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.26	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.26	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.26	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.26	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.26	   A^2 -> H(U1(a, c), b)
28.45/9.26	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.26	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.26	   A^2 -> H(U1(a, c), c)
28.45/9.26	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.26	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.26	   A^2 -> H(U1(a, c), e)
28.45/9.26	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, d), b)
28.45/9.26	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.26	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.26	   A^2 -> H(U1(a, d), c)
28.45/9.26	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.26	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.26	   A^2 -> H(U1(a, d), e)
28.45/9.26	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, a), d)
28.45/9.26	   A^2 -> H(U1(a, a), k)
28.45/9.26	   A^2 -> H(k, U1(b, b))
28.45/9.26	   A^2 -> H(k, f(c))
28.45/9.26	   A^2 -> H(k, f(d))
28.45/9.26	   A^2 -> H(c, U1(c, b))
28.45/9.26	   A^2 -> H(c, U1(d, b))
28.45/9.26	   A^2 -> H(c, U1(b, c))
28.45/9.26	   A^2 -> H(c, U1(b, d))
28.45/9.26	   A^2 -> H(c, U1(c, c))
28.45/9.26	   A^2 -> H(c, f(e))
28.45/9.26	   A^2 -> H(c, f(k))
28.45/9.26	   A^2 -> H(c, U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.26	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.26	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.26	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.26	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.26	   A^2 -> H(U1(e, k), f(e))
28.45/9.26	   A^2 -> H(U1(e, k), f(k))
28.45/9.26	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.26	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.26	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.26	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.26	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.26	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.26	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.26	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.26	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.26	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.26	   A^2 -> H(U1(k, e), f(e))
28.45/9.26	   A^2 -> H(U1(k, e), f(k))
28.45/9.26	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.26	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.26	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.26	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.26	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.26	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.26	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.26	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.26	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.26	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.26	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.26	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, c), b)
28.45/9.26	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.26	
28.45/9.26	The TRS R consists of the following rules:
28.45/9.26	
28.45/9.26	   f(x) -> U1(x, x)
28.45/9.26	   U1(e, x) -> x
28.45/9.26	   a -> c
28.45/9.26	   a -> d
28.45/9.26	   b -> c
28.45/9.26	   b -> d
28.45/9.26	   d -> k
28.45/9.26	   c -> e
28.45/9.26	   c -> k
28.45/9.26	
28.45/9.26	Q is empty.
28.45/9.26	We have to consider all minimal (P,Q,R)-chains.
28.45/9.26	----------------------------------------
28.45/9.26	
28.45/9.26	(871) TransformationProof (EQUIVALENT)
28.45/9.26	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.26	
28.45/9.26	   (A^2 -> H(U1(e, c), U1(k, b)),A^2 -> H(U1(e, c), U1(k, b)))
28.45/9.26	   (A^2 -> H(U1(k, c), U1(k, b)),A^2 -> H(U1(k, c), U1(k, b)))
28.45/9.26	   (A^2 -> H(U1(c, e), U1(k, b)),A^2 -> H(U1(c, e), U1(k, b)))
28.45/9.26	   (A^2 -> H(U1(c, k), U1(k, b)),A^2 -> H(U1(c, k), U1(k, b)))
28.45/9.26	   (A^2 -> H(U1(c, c), U1(k, c)),A^2 -> H(U1(c, c), U1(k, c)))
28.45/9.26	   (A^2 -> H(U1(c, c), U1(k, d)),A^2 -> H(U1(c, c), U1(k, d)))
28.45/9.26	
28.45/9.26	
28.45/9.26	----------------------------------------
28.45/9.26	
28.45/9.26	(872)
28.45/9.26	Obligation:
28.45/9.26	Q DP problem:
28.45/9.26	The TRS P consists of the following rules:
28.45/9.26	
28.45/9.26	   H(x, x) -> G(x, x, f(k))
28.45/9.26	   G(d, x, x) -> A^2
28.45/9.26	   A^2 -> H(f(c), f(c))
28.45/9.26	   A^2 -> H(f(d), f(d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.26	   A^2 -> H(f(e), f(e))
28.45/9.26	   A^2 -> H(f(k), f(k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(c, d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.26	   A^2 -> H(e, U1(b, b))
28.45/9.26	   A^2 -> H(e, f(c))
28.45/9.26	   A^2 -> H(e, f(d))
28.45/9.26	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.26	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.26	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.26	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.26	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.26	   A^2 -> H(U1(e, e), f(e))
28.45/9.26	   A^2 -> H(U1(e, e), f(k))
28.45/9.26	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.26	   A^2 -> H(f(e), U1(e, b))
28.45/9.26	   A^2 -> H(f(e), U1(k, b))
28.45/9.26	   A^2 -> H(f(e), U1(c, d))
28.45/9.26	   A^2 -> H(f(e), U1(d, c))
28.45/9.26	   A^2 -> H(f(e), U1(b, e))
28.45/9.26	   A^2 -> H(f(e), U1(b, k))
28.45/9.26	   A^2 -> H(f(e), U1(e, c))
28.45/9.26	   A^2 -> H(f(e), U1(k, c))
28.45/9.26	   A^2 -> H(f(e), U1(c, e))
28.45/9.26	   A^2 -> H(f(e), U1(c, k))
28.45/9.26	   A^2 -> H(f(e), U1(k, k))
28.45/9.26	   A^2 -> H(f(e), U1(k, d))
28.45/9.26	   A^2 -> H(f(e), U1(d, k))
28.45/9.26	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.26	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.26	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.26	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.26	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.26	   A^2 -> H(U1(k, k), f(e))
28.45/9.26	   A^2 -> H(U1(k, k), f(k))
28.45/9.26	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.26	   A^2 -> H(f(k), U1(e, b))
28.45/9.26	   A^2 -> H(f(k), U1(k, b))
28.45/9.26	   A^2 -> H(f(k), U1(c, d))
28.45/9.26	   A^2 -> H(f(k), U1(d, c))
28.45/9.26	   A^2 -> H(f(k), U1(b, e))
28.45/9.26	   A^2 -> H(f(k), U1(b, k))
28.45/9.26	   A^2 -> H(f(k), U1(e, c))
28.45/9.26	   A^2 -> H(f(k), U1(k, c))
28.45/9.26	   A^2 -> H(f(k), U1(c, e))
28.45/9.26	   A^2 -> H(f(k), U1(c, k))
28.45/9.26	   A^2 -> H(f(k), U1(e, e))
28.45/9.26	   A^2 -> H(f(k), U1(k, d))
28.45/9.26	   A^2 -> H(f(k), U1(d, k))
28.45/9.26	   A^2 -> H(f(c), b)
28.45/9.26	   A^2 -> H(f(c), U1(e, d))
28.45/9.26	   A^2 -> H(f(c), U1(d, e))
28.45/9.26	   A^2 -> H(f(k), U1(k, k))
28.45/9.26	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.26	   A^2 -> H(U1(k, k), f(c))
28.45/9.26	   A^2 -> H(U1(k, k), f(d))
28.45/9.26	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.26	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.26	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.26	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.26	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.26	   A^2 -> H(U1(k, d), f(e))
28.45/9.26	   A^2 -> H(U1(k, d), f(k))
28.45/9.26	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.26	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.26	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.26	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.26	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.26	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.26	   A^2 -> H(U1(d, k), f(e))
28.45/9.26	   A^2 -> H(U1(d, k), f(k))
28.45/9.26	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.26	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.26	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.26	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.26	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.26	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.26	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.26	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.26	   A^2 -> H(f(d), b)
28.45/9.26	   A^2 -> H(f(d), U1(e, d))
28.45/9.26	   A^2 -> H(f(d), U1(d, e))
28.45/9.26	   A^2 -> H(f(d), c)
28.45/9.26	   A^2 -> H(f(d), U1(e, k))
28.45/9.26	   A^2 -> H(f(d), U1(k, e))
28.45/9.26	   A^2 -> H(f(d), e)
28.45/9.26	   A^2 -> H(f(a), d)
28.45/9.26	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.26	   A^2 -> H(f(c), c)
28.45/9.26	   A^2 -> H(f(c), U1(e, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.26	   A^2 -> H(f(c), U1(k, e))
28.45/9.26	   A^2 -> H(f(c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.26	   A^2 -> H(f(a), k)
28.45/9.26	   A^2 -> H(f(e), U1(e, e))
28.45/9.26	   A^2 -> H(f(c), e)
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.26	   A^2 -> H(f(d), U1(k, k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.26	   A^2 -> H(d, U1(b, b))
28.45/9.26	   A^2 -> H(d, f(c))
28.45/9.26	   A^2 -> H(d, f(d))
28.45/9.26	   A^2 -> H(a, U1(c, b))
28.45/9.26	   A^2 -> H(a, U1(d, b))
28.45/9.26	   A^2 -> H(a, U1(b, c))
28.45/9.26	   A^2 -> H(a, U1(b, d))
28.45/9.26	   A^2 -> H(a, U1(c, c))
28.45/9.26	   A^2 -> H(a, f(e))
28.45/9.26	   A^2 -> H(a, f(k))
28.45/9.26	   A^2 -> H(a, U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.26	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.26	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.26	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.26	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.26	   A^2 -> H(U1(e, d), f(e))
28.45/9.26	   A^2 -> H(U1(e, d), f(k))
28.45/9.26	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.26	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.26	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.26	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.26	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.26	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.26	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.26	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.26	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.26	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.26	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.26	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.26	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.26	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.26	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.26	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.26	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.26	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.26	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.26	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, a), b)
28.45/9.26	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.26	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.26	   A^2 -> H(U1(c, a), c)
28.45/9.26	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.26	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.26	   A^2 -> H(U1(c, a), e)
28.45/9.26	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.26	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.26	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.26	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.26	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.26	   A^2 -> H(U1(d, e), f(e))
28.45/9.26	   A^2 -> H(U1(d, e), f(k))
28.45/9.26	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.26	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.26	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.26	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.26	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.26	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.26	   A^2 -> H(U1(d, a), b)
28.45/9.26	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.26	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.26	   A^2 -> H(U1(d, a), c)
28.45/9.26	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.26	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.26	   A^2 -> H(U1(d, a), e)
28.45/9.26	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.26	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.26	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.26	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.26	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.26	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.26	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.26	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.26	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.26	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.26	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.26	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.26	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.26	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.26	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.26	   A^2 -> H(U1(a, c), b)
28.45/9.26	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.26	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.26	   A^2 -> H(U1(a, c), c)
28.45/9.26	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.26	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.26	   A^2 -> H(U1(a, c), e)
28.45/9.26	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, d), b)
28.45/9.26	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.26	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.26	   A^2 -> H(U1(a, d), c)
28.45/9.26	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.26	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.26	   A^2 -> H(U1(a, d), e)
28.45/9.26	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, a), d)
28.45/9.26	   A^2 -> H(U1(a, a), k)
28.45/9.26	   A^2 -> H(k, U1(b, b))
28.45/9.26	   A^2 -> H(k, f(c))
28.45/9.26	   A^2 -> H(k, f(d))
28.45/9.26	   A^2 -> H(c, U1(c, b))
28.45/9.26	   A^2 -> H(c, U1(d, b))
28.45/9.26	   A^2 -> H(c, U1(b, c))
28.45/9.26	   A^2 -> H(c, U1(b, d))
28.45/9.26	   A^2 -> H(c, U1(c, c))
28.45/9.26	   A^2 -> H(c, f(e))
28.45/9.26	   A^2 -> H(c, f(k))
28.45/9.26	   A^2 -> H(c, U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.26	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.26	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.26	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.26	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.26	   A^2 -> H(U1(e, k), f(e))
28.45/9.26	   A^2 -> H(U1(e, k), f(k))
28.45/9.26	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.26	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.26	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.26	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.26	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.26	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.26	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.26	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.26	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.26	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.26	   A^2 -> H(U1(k, e), f(e))
28.45/9.26	   A^2 -> H(U1(k, e), f(k))
28.45/9.26	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.26	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.26	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.26	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.26	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.26	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.26	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.26	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.26	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.26	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.26	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.26	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, c), b)
28.45/9.26	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.26	
28.45/9.26	The TRS R consists of the following rules:
28.45/9.26	
28.45/9.26	   f(x) -> U1(x, x)
28.45/9.26	   U1(e, x) -> x
28.45/9.26	   a -> c
28.45/9.26	   a -> d
28.45/9.26	   b -> c
28.45/9.26	   b -> d
28.45/9.26	   d -> k
28.45/9.26	   c -> e
28.45/9.26	   c -> k
28.45/9.26	
28.45/9.26	Q is empty.
28.45/9.26	We have to consider all minimal (P,Q,R)-chains.
28.45/9.26	----------------------------------------
28.45/9.26	
28.45/9.26	(873) TransformationProof (EQUIVALENT)
28.45/9.26	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.26	
28.45/9.26	   (A^2 -> H(U1(e, c), U1(c, d)),A^2 -> H(U1(e, c), U1(c, d)))
28.45/9.26	   (A^2 -> H(U1(k, c), U1(c, d)),A^2 -> H(U1(k, c), U1(c, d)))
28.45/9.26	   (A^2 -> H(U1(c, e), U1(c, d)),A^2 -> H(U1(c, e), U1(c, d)))
28.45/9.26	   (A^2 -> H(U1(c, k), U1(c, d)),A^2 -> H(U1(c, k), U1(c, d)))
28.45/9.26	   (A^2 -> H(U1(c, c), U1(e, d)),A^2 -> H(U1(c, c), U1(e, d)))
28.45/9.26	   (A^2 -> H(U1(c, c), U1(k, d)),A^2 -> H(U1(c, c), U1(k, d)))
28.45/9.26	   (A^2 -> H(U1(c, c), U1(c, k)),A^2 -> H(U1(c, c), U1(c, k)))
28.45/9.26	
28.45/9.26	
28.45/9.26	----------------------------------------
28.45/9.26	
28.45/9.26	(874)
28.45/9.26	Obligation:
28.45/9.26	Q DP problem:
28.45/9.26	The TRS P consists of the following rules:
28.45/9.26	
28.45/9.26	   H(x, x) -> G(x, x, f(k))
28.45/9.26	   G(d, x, x) -> A^2
28.45/9.26	   A^2 -> H(f(c), f(c))
28.45/9.26	   A^2 -> H(f(d), f(d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.26	   A^2 -> H(f(e), f(e))
28.45/9.26	   A^2 -> H(f(k), f(k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.26	   A^2 -> H(e, U1(b, b))
28.45/9.26	   A^2 -> H(e, f(c))
28.45/9.26	   A^2 -> H(e, f(d))
28.45/9.26	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.26	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.26	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.26	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.26	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.26	   A^2 -> H(U1(e, e), f(e))
28.45/9.26	   A^2 -> H(U1(e, e), f(k))
28.45/9.26	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.26	   A^2 -> H(f(e), U1(e, b))
28.45/9.26	   A^2 -> H(f(e), U1(k, b))
28.45/9.26	   A^2 -> H(f(e), U1(c, d))
28.45/9.26	   A^2 -> H(f(e), U1(d, c))
28.45/9.26	   A^2 -> H(f(e), U1(b, e))
28.45/9.26	   A^2 -> H(f(e), U1(b, k))
28.45/9.26	   A^2 -> H(f(e), U1(e, c))
28.45/9.26	   A^2 -> H(f(e), U1(k, c))
28.45/9.26	   A^2 -> H(f(e), U1(c, e))
28.45/9.26	   A^2 -> H(f(e), U1(c, k))
28.45/9.26	   A^2 -> H(f(e), U1(k, k))
28.45/9.26	   A^2 -> H(f(e), U1(k, d))
28.45/9.26	   A^2 -> H(f(e), U1(d, k))
28.45/9.26	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.26	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.26	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.26	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.26	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.26	   A^2 -> H(U1(k, k), f(e))
28.45/9.26	   A^2 -> H(U1(k, k), f(k))
28.45/9.26	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.26	   A^2 -> H(f(k), U1(e, b))
28.45/9.26	   A^2 -> H(f(k), U1(k, b))
28.45/9.26	   A^2 -> H(f(k), U1(c, d))
28.45/9.26	   A^2 -> H(f(k), U1(d, c))
28.45/9.26	   A^2 -> H(f(k), U1(b, e))
28.45/9.26	   A^2 -> H(f(k), U1(b, k))
28.45/9.26	   A^2 -> H(f(k), U1(e, c))
28.45/9.26	   A^2 -> H(f(k), U1(k, c))
28.45/9.26	   A^2 -> H(f(k), U1(c, e))
28.45/9.26	   A^2 -> H(f(k), U1(c, k))
28.45/9.26	   A^2 -> H(f(k), U1(e, e))
28.45/9.26	   A^2 -> H(f(k), U1(k, d))
28.45/9.26	   A^2 -> H(f(k), U1(d, k))
28.45/9.26	   A^2 -> H(f(c), b)
28.45/9.26	   A^2 -> H(f(c), U1(e, d))
28.45/9.26	   A^2 -> H(f(c), U1(d, e))
28.45/9.26	   A^2 -> H(f(k), U1(k, k))
28.45/9.26	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.26	   A^2 -> H(U1(k, k), f(c))
28.45/9.26	   A^2 -> H(U1(k, k), f(d))
28.45/9.26	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.26	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.26	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.26	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.26	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.26	   A^2 -> H(U1(k, d), f(e))
28.45/9.26	   A^2 -> H(U1(k, d), f(k))
28.45/9.26	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.26	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.26	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.26	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.26	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.26	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.26	   A^2 -> H(U1(d, k), f(e))
28.45/9.26	   A^2 -> H(U1(d, k), f(k))
28.45/9.26	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.26	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.26	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.26	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.26	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.26	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.26	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.26	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.26	   A^2 -> H(f(d), b)
28.45/9.26	   A^2 -> H(f(d), U1(e, d))
28.45/9.26	   A^2 -> H(f(d), U1(d, e))
28.45/9.26	   A^2 -> H(f(d), c)
28.45/9.26	   A^2 -> H(f(d), U1(e, k))
28.45/9.26	   A^2 -> H(f(d), U1(k, e))
28.45/9.26	   A^2 -> H(f(d), e)
28.45/9.26	   A^2 -> H(f(a), d)
28.45/9.26	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.26	   A^2 -> H(f(c), c)
28.45/9.26	   A^2 -> H(f(c), U1(e, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.26	   A^2 -> H(f(c), U1(k, e))
28.45/9.26	   A^2 -> H(f(c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.26	   A^2 -> H(f(a), k)
28.45/9.26	   A^2 -> H(f(e), U1(e, e))
28.45/9.26	   A^2 -> H(f(c), e)
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.26	   A^2 -> H(f(d), U1(k, k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.26	   A^2 -> H(d, U1(b, b))
28.45/9.26	   A^2 -> H(d, f(c))
28.45/9.26	   A^2 -> H(d, f(d))
28.45/9.26	   A^2 -> H(a, U1(c, b))
28.45/9.26	   A^2 -> H(a, U1(d, b))
28.45/9.26	   A^2 -> H(a, U1(b, c))
28.45/9.26	   A^2 -> H(a, U1(b, d))
28.45/9.26	   A^2 -> H(a, U1(c, c))
28.45/9.26	   A^2 -> H(a, f(e))
28.45/9.26	   A^2 -> H(a, f(k))
28.45/9.26	   A^2 -> H(a, U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.26	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.26	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.26	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.26	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.26	   A^2 -> H(U1(e, d), f(e))
28.45/9.26	   A^2 -> H(U1(e, d), f(k))
28.45/9.26	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.26	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.26	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.26	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.26	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.26	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.26	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.26	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.26	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.26	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.26	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.26	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.26	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.26	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.26	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.26	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.26	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.26	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.26	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.26	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, a), b)
28.45/9.26	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.26	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.26	   A^2 -> H(U1(c, a), c)
28.45/9.26	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.26	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.26	   A^2 -> H(U1(c, a), e)
28.45/9.26	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.26	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.26	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.26	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.26	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.26	   A^2 -> H(U1(d, e), f(e))
28.45/9.26	   A^2 -> H(U1(d, e), f(k))
28.45/9.26	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.26	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.26	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.26	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.26	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.26	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.26	   A^2 -> H(U1(d, a), b)
28.45/9.26	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.26	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.26	   A^2 -> H(U1(d, a), c)
28.45/9.26	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.26	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.26	   A^2 -> H(U1(d, a), e)
28.45/9.26	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.26	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.26	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.26	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.26	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.26	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.26	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.26	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.26	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.26	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.26	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.26	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.26	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.26	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.26	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.26	   A^2 -> H(U1(a, c), b)
28.45/9.26	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.26	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.26	   A^2 -> H(U1(a, c), c)
28.45/9.26	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.26	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.26	   A^2 -> H(U1(a, c), e)
28.45/9.26	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, d), b)
28.45/9.26	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.26	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.26	   A^2 -> H(U1(a, d), c)
28.45/9.26	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.26	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.26	   A^2 -> H(U1(a, d), e)
28.45/9.26	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, a), d)
28.45/9.26	   A^2 -> H(U1(a, a), k)
28.45/9.26	   A^2 -> H(k, U1(b, b))
28.45/9.26	   A^2 -> H(k, f(c))
28.45/9.26	   A^2 -> H(k, f(d))
28.45/9.26	   A^2 -> H(c, U1(c, b))
28.45/9.26	   A^2 -> H(c, U1(d, b))
28.45/9.26	   A^2 -> H(c, U1(b, c))
28.45/9.26	   A^2 -> H(c, U1(b, d))
28.45/9.26	   A^2 -> H(c, U1(c, c))
28.45/9.26	   A^2 -> H(c, f(e))
28.45/9.26	   A^2 -> H(c, f(k))
28.45/9.26	   A^2 -> H(c, U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.26	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.26	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.26	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.26	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.26	   A^2 -> H(U1(e, k), f(e))
28.45/9.26	   A^2 -> H(U1(e, k), f(k))
28.45/9.26	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.26	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.26	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.26	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.26	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.26	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.26	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.26	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.26	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.26	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.26	   A^2 -> H(U1(k, e), f(e))
28.45/9.26	   A^2 -> H(U1(k, e), f(k))
28.45/9.26	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.26	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.26	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.26	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.26	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.26	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.26	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.26	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.26	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.26	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.26	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.26	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, c), b)
28.45/9.26	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.26	
28.45/9.26	The TRS R consists of the following rules:
28.45/9.26	
28.45/9.26	   f(x) -> U1(x, x)
28.45/9.26	   U1(e, x) -> x
28.45/9.26	   a -> c
28.45/9.26	   a -> d
28.45/9.26	   b -> c
28.45/9.26	   b -> d
28.45/9.26	   d -> k
28.45/9.26	   c -> e
28.45/9.26	   c -> k
28.45/9.26	
28.45/9.26	Q is empty.
28.45/9.26	We have to consider all minimal (P,Q,R)-chains.
28.45/9.26	----------------------------------------
28.45/9.26	
28.45/9.26	(875) TransformationProof (EQUIVALENT)
28.45/9.26	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.26	
28.45/9.26	   (A^2 -> H(U1(e, c), U1(d, c)),A^2 -> H(U1(e, c), U1(d, c)))
28.45/9.26	   (A^2 -> H(U1(k, c), U1(d, c)),A^2 -> H(U1(k, c), U1(d, c)))
28.45/9.26	   (A^2 -> H(U1(c, e), U1(d, c)),A^2 -> H(U1(c, e), U1(d, c)))
28.45/9.26	   (A^2 -> H(U1(c, k), U1(d, c)),A^2 -> H(U1(c, k), U1(d, c)))
28.45/9.26	   (A^2 -> H(U1(c, c), U1(k, c)),A^2 -> H(U1(c, c), U1(k, c)))
28.45/9.26	   (A^2 -> H(U1(c, c), U1(d, e)),A^2 -> H(U1(c, c), U1(d, e)))
28.45/9.26	   (A^2 -> H(U1(c, c), U1(d, k)),A^2 -> H(U1(c, c), U1(d, k)))
28.45/9.26	
28.45/9.26	
28.45/9.26	----------------------------------------
28.45/9.26	
28.45/9.26	(876)
28.45/9.26	Obligation:
28.45/9.26	Q DP problem:
28.45/9.26	The TRS P consists of the following rules:
28.45/9.26	
28.45/9.26	   H(x, x) -> G(x, x, f(k))
28.45/9.26	   G(d, x, x) -> A^2
28.45/9.26	   A^2 -> H(f(c), f(c))
28.45/9.26	   A^2 -> H(f(d), f(d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.26	   A^2 -> H(f(e), f(e))
28.45/9.26	   A^2 -> H(f(k), f(k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.26	   A^2 -> H(e, U1(b, b))
28.45/9.26	   A^2 -> H(e, f(c))
28.45/9.26	   A^2 -> H(e, f(d))
28.45/9.26	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.26	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.26	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.26	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.26	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.26	   A^2 -> H(U1(e, e), f(e))
28.45/9.26	   A^2 -> H(U1(e, e), f(k))
28.45/9.26	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.26	   A^2 -> H(f(e), U1(e, b))
28.45/9.26	   A^2 -> H(f(e), U1(k, b))
28.45/9.26	   A^2 -> H(f(e), U1(c, d))
28.45/9.26	   A^2 -> H(f(e), U1(d, c))
28.45/9.26	   A^2 -> H(f(e), U1(b, e))
28.45/9.26	   A^2 -> H(f(e), U1(b, k))
28.45/9.26	   A^2 -> H(f(e), U1(e, c))
28.45/9.26	   A^2 -> H(f(e), U1(k, c))
28.45/9.26	   A^2 -> H(f(e), U1(c, e))
28.45/9.26	   A^2 -> H(f(e), U1(c, k))
28.45/9.26	   A^2 -> H(f(e), U1(k, k))
28.45/9.26	   A^2 -> H(f(e), U1(k, d))
28.45/9.26	   A^2 -> H(f(e), U1(d, k))
28.45/9.26	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.26	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.26	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.26	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.26	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.26	   A^2 -> H(U1(k, k), f(e))
28.45/9.26	   A^2 -> H(U1(k, k), f(k))
28.45/9.26	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.26	   A^2 -> H(f(k), U1(e, b))
28.45/9.26	   A^2 -> H(f(k), U1(k, b))
28.45/9.26	   A^2 -> H(f(k), U1(c, d))
28.45/9.26	   A^2 -> H(f(k), U1(d, c))
28.45/9.26	   A^2 -> H(f(k), U1(b, e))
28.45/9.26	   A^2 -> H(f(k), U1(b, k))
28.45/9.26	   A^2 -> H(f(k), U1(e, c))
28.45/9.26	   A^2 -> H(f(k), U1(k, c))
28.45/9.26	   A^2 -> H(f(k), U1(c, e))
28.45/9.26	   A^2 -> H(f(k), U1(c, k))
28.45/9.26	   A^2 -> H(f(k), U1(e, e))
28.45/9.26	   A^2 -> H(f(k), U1(k, d))
28.45/9.26	   A^2 -> H(f(k), U1(d, k))
28.45/9.26	   A^2 -> H(f(c), b)
28.45/9.26	   A^2 -> H(f(c), U1(e, d))
28.45/9.26	   A^2 -> H(f(c), U1(d, e))
28.45/9.26	   A^2 -> H(f(k), U1(k, k))
28.45/9.26	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.26	   A^2 -> H(U1(k, k), f(c))
28.45/9.26	   A^2 -> H(U1(k, k), f(d))
28.45/9.26	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.26	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.26	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.26	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.26	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.26	   A^2 -> H(U1(k, d), f(e))
28.45/9.26	   A^2 -> H(U1(k, d), f(k))
28.45/9.26	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.26	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.26	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.26	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.26	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.26	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.26	   A^2 -> H(U1(d, k), f(e))
28.45/9.26	   A^2 -> H(U1(d, k), f(k))
28.45/9.26	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.26	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.26	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.26	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.26	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.26	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.26	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.26	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.26	   A^2 -> H(f(d), b)
28.45/9.26	   A^2 -> H(f(d), U1(e, d))
28.45/9.26	   A^2 -> H(f(d), U1(d, e))
28.45/9.26	   A^2 -> H(f(d), c)
28.45/9.26	   A^2 -> H(f(d), U1(e, k))
28.45/9.26	   A^2 -> H(f(d), U1(k, e))
28.45/9.26	   A^2 -> H(f(d), e)
28.45/9.26	   A^2 -> H(f(a), d)
28.45/9.26	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.26	   A^2 -> H(f(c), c)
28.45/9.26	   A^2 -> H(f(c), U1(e, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.26	   A^2 -> H(f(c), U1(k, e))
28.45/9.26	   A^2 -> H(f(c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.26	   A^2 -> H(f(a), k)
28.45/9.26	   A^2 -> H(f(e), U1(e, e))
28.45/9.26	   A^2 -> H(f(c), e)
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.26	   A^2 -> H(f(d), U1(k, k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.26	   A^2 -> H(d, U1(b, b))
28.45/9.26	   A^2 -> H(d, f(c))
28.45/9.26	   A^2 -> H(d, f(d))
28.45/9.26	   A^2 -> H(a, U1(c, b))
28.45/9.26	   A^2 -> H(a, U1(d, b))
28.45/9.26	   A^2 -> H(a, U1(b, c))
28.45/9.26	   A^2 -> H(a, U1(b, d))
28.45/9.26	   A^2 -> H(a, U1(c, c))
28.45/9.26	   A^2 -> H(a, f(e))
28.45/9.26	   A^2 -> H(a, f(k))
28.45/9.26	   A^2 -> H(a, U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.26	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.26	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.26	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.26	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.26	   A^2 -> H(U1(e, d), f(e))
28.45/9.26	   A^2 -> H(U1(e, d), f(k))
28.45/9.26	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.26	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.26	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.26	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.26	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.26	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.26	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.26	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.26	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.26	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.26	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.26	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.26	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.26	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.26	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.26	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.26	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.26	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.26	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.26	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, a), b)
28.45/9.26	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.26	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.26	   A^2 -> H(U1(c, a), c)
28.45/9.26	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.26	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.26	   A^2 -> H(U1(c, a), e)
28.45/9.26	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.26	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.26	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.26	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.26	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.26	   A^2 -> H(U1(d, e), f(e))
28.45/9.26	   A^2 -> H(U1(d, e), f(k))
28.45/9.26	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.26	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.26	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.26	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.26	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.26	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.26	   A^2 -> H(U1(d, a), b)
28.45/9.26	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.26	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.26	   A^2 -> H(U1(d, a), c)
28.45/9.26	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.26	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.26	   A^2 -> H(U1(d, a), e)
28.45/9.26	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.26	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.26	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.26	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.26	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.26	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.26	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.26	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.26	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.26	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.26	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.26	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.26	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.26	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.26	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.26	   A^2 -> H(U1(a, c), b)
28.45/9.26	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.26	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.26	   A^2 -> H(U1(a, c), c)
28.45/9.26	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.26	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.26	   A^2 -> H(U1(a, c), e)
28.45/9.26	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, d), b)
28.45/9.26	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.26	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.26	   A^2 -> H(U1(a, d), c)
28.45/9.26	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.26	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.26	   A^2 -> H(U1(a, d), e)
28.45/9.26	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, a), d)
28.45/9.26	   A^2 -> H(U1(a, a), k)
28.45/9.26	   A^2 -> H(k, U1(b, b))
28.45/9.26	   A^2 -> H(k, f(c))
28.45/9.26	   A^2 -> H(k, f(d))
28.45/9.26	   A^2 -> H(c, U1(c, b))
28.45/9.26	   A^2 -> H(c, U1(d, b))
28.45/9.26	   A^2 -> H(c, U1(b, c))
28.45/9.26	   A^2 -> H(c, U1(b, d))
28.45/9.26	   A^2 -> H(c, U1(c, c))
28.45/9.26	   A^2 -> H(c, f(e))
28.45/9.26	   A^2 -> H(c, f(k))
28.45/9.26	   A^2 -> H(c, U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.26	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.26	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.26	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.26	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.26	   A^2 -> H(U1(e, k), f(e))
28.45/9.26	   A^2 -> H(U1(e, k), f(k))
28.45/9.26	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.26	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.26	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.26	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.26	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.26	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.26	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.26	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.26	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.26	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.26	   A^2 -> H(U1(k, e), f(e))
28.45/9.26	   A^2 -> H(U1(k, e), f(k))
28.45/9.26	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.26	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.26	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.26	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.26	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.26	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.26	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.26	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.26	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.26	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.26	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.26	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, c), b)
28.45/9.26	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.26	
28.45/9.26	The TRS R consists of the following rules:
28.45/9.26	
28.45/9.26	   f(x) -> U1(x, x)
28.45/9.26	   U1(e, x) -> x
28.45/9.26	   a -> c
28.45/9.26	   a -> d
28.45/9.26	   b -> c
28.45/9.26	   b -> d
28.45/9.26	   d -> k
28.45/9.26	   c -> e
28.45/9.26	   c -> k
28.45/9.26	
28.45/9.26	Q is empty.
28.45/9.26	We have to consider all minimal (P,Q,R)-chains.
28.45/9.26	----------------------------------------
28.45/9.26	
28.45/9.26	(877) TransformationProof (EQUIVALENT)
28.45/9.26	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.26	
28.45/9.26	   (A^2 -> H(U1(e, c), U1(b, e)),A^2 -> H(U1(e, c), U1(b, e)))
28.45/9.26	   (A^2 -> H(U1(k, c), U1(b, e)),A^2 -> H(U1(k, c), U1(b, e)))
28.45/9.26	   (A^2 -> H(U1(c, e), U1(b, e)),A^2 -> H(U1(c, e), U1(b, e)))
28.45/9.26	   (A^2 -> H(U1(c, k), U1(b, e)),A^2 -> H(U1(c, k), U1(b, e)))
28.45/9.26	   (A^2 -> H(U1(c, c), U1(c, e)),A^2 -> H(U1(c, c), U1(c, e)))
28.45/9.26	   (A^2 -> H(U1(c, c), U1(d, e)),A^2 -> H(U1(c, c), U1(d, e)))
28.45/9.26	
28.45/9.26	
28.45/9.26	----------------------------------------
28.45/9.26	
28.45/9.26	(878)
28.45/9.26	Obligation:
28.45/9.26	Q DP problem:
28.45/9.26	The TRS P consists of the following rules:
28.45/9.26	
28.45/9.26	   H(x, x) -> G(x, x, f(k))
28.45/9.26	   G(d, x, x) -> A^2
28.45/9.26	   A^2 -> H(f(c), f(c))
28.45/9.26	   A^2 -> H(f(d), f(d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.26	   A^2 -> H(f(e), f(e))
28.45/9.26	   A^2 -> H(f(k), f(k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.26	   A^2 -> H(e, U1(b, b))
28.45/9.26	   A^2 -> H(e, f(c))
28.45/9.26	   A^2 -> H(e, f(d))
28.45/9.26	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.26	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.26	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.26	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.26	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.26	   A^2 -> H(U1(e, e), f(e))
28.45/9.26	   A^2 -> H(U1(e, e), f(k))
28.45/9.26	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.26	   A^2 -> H(f(e), U1(e, b))
28.45/9.26	   A^2 -> H(f(e), U1(k, b))
28.45/9.26	   A^2 -> H(f(e), U1(c, d))
28.45/9.26	   A^2 -> H(f(e), U1(d, c))
28.45/9.26	   A^2 -> H(f(e), U1(b, e))
28.45/9.26	   A^2 -> H(f(e), U1(b, k))
28.45/9.26	   A^2 -> H(f(e), U1(e, c))
28.45/9.26	   A^2 -> H(f(e), U1(k, c))
28.45/9.26	   A^2 -> H(f(e), U1(c, e))
28.45/9.26	   A^2 -> H(f(e), U1(c, k))
28.45/9.26	   A^2 -> H(f(e), U1(k, k))
28.45/9.26	   A^2 -> H(f(e), U1(k, d))
28.45/9.26	   A^2 -> H(f(e), U1(d, k))
28.45/9.26	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.26	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.26	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.26	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.26	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.26	   A^2 -> H(U1(k, k), f(e))
28.45/9.26	   A^2 -> H(U1(k, k), f(k))
28.45/9.26	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.26	   A^2 -> H(f(k), U1(e, b))
28.45/9.26	   A^2 -> H(f(k), U1(k, b))
28.45/9.26	   A^2 -> H(f(k), U1(c, d))
28.45/9.26	   A^2 -> H(f(k), U1(d, c))
28.45/9.26	   A^2 -> H(f(k), U1(b, e))
28.45/9.26	   A^2 -> H(f(k), U1(b, k))
28.45/9.26	   A^2 -> H(f(k), U1(e, c))
28.45/9.26	   A^2 -> H(f(k), U1(k, c))
28.45/9.26	   A^2 -> H(f(k), U1(c, e))
28.45/9.26	   A^2 -> H(f(k), U1(c, k))
28.45/9.26	   A^2 -> H(f(k), U1(e, e))
28.45/9.26	   A^2 -> H(f(k), U1(k, d))
28.45/9.26	   A^2 -> H(f(k), U1(d, k))
28.45/9.26	   A^2 -> H(f(c), b)
28.45/9.26	   A^2 -> H(f(c), U1(e, d))
28.45/9.26	   A^2 -> H(f(c), U1(d, e))
28.45/9.26	   A^2 -> H(f(k), U1(k, k))
28.45/9.26	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.26	   A^2 -> H(U1(k, k), f(c))
28.45/9.26	   A^2 -> H(U1(k, k), f(d))
28.45/9.26	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.26	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.26	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.26	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.26	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.26	   A^2 -> H(U1(k, d), f(e))
28.45/9.26	   A^2 -> H(U1(k, d), f(k))
28.45/9.26	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.26	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.26	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.26	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.26	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.26	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.26	   A^2 -> H(U1(d, k), f(e))
28.45/9.26	   A^2 -> H(U1(d, k), f(k))
28.45/9.26	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.26	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.26	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.26	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.26	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.26	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.26	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.26	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.26	   A^2 -> H(f(d), b)
28.45/9.26	   A^2 -> H(f(d), U1(e, d))
28.45/9.26	   A^2 -> H(f(d), U1(d, e))
28.45/9.26	   A^2 -> H(f(d), c)
28.45/9.26	   A^2 -> H(f(d), U1(e, k))
28.45/9.26	   A^2 -> H(f(d), U1(k, e))
28.45/9.26	   A^2 -> H(f(d), e)
28.45/9.26	   A^2 -> H(f(a), d)
28.45/9.26	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.26	   A^2 -> H(f(c), c)
28.45/9.26	   A^2 -> H(f(c), U1(e, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.26	   A^2 -> H(f(c), U1(k, e))
28.45/9.26	   A^2 -> H(f(c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.26	   A^2 -> H(f(a), k)
28.45/9.26	   A^2 -> H(f(e), U1(e, e))
28.45/9.26	   A^2 -> H(f(c), e)
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.26	   A^2 -> H(f(d), U1(k, k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.26	   A^2 -> H(d, U1(b, b))
28.45/9.26	   A^2 -> H(d, f(c))
28.45/9.26	   A^2 -> H(d, f(d))
28.45/9.26	   A^2 -> H(a, U1(c, b))
28.45/9.26	   A^2 -> H(a, U1(d, b))
28.45/9.26	   A^2 -> H(a, U1(b, c))
28.45/9.26	   A^2 -> H(a, U1(b, d))
28.45/9.26	   A^2 -> H(a, U1(c, c))
28.45/9.26	   A^2 -> H(a, f(e))
28.45/9.26	   A^2 -> H(a, f(k))
28.45/9.26	   A^2 -> H(a, U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.26	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.26	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.26	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.26	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.26	   A^2 -> H(U1(e, d), f(e))
28.45/9.26	   A^2 -> H(U1(e, d), f(k))
28.45/9.26	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.26	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.26	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.26	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.26	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.26	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.26	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.26	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.26	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.26	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.26	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.26	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.26	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.26	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.26	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.26	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.26	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.26	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.26	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.26	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, a), b)
28.45/9.26	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.26	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.26	   A^2 -> H(U1(c, a), c)
28.45/9.26	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.26	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.26	   A^2 -> H(U1(c, a), e)
28.45/9.26	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.26	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.26	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.26	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.26	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.26	   A^2 -> H(U1(d, e), f(e))
28.45/9.26	   A^2 -> H(U1(d, e), f(k))
28.45/9.26	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.26	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.26	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.26	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.26	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.26	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.26	   A^2 -> H(U1(d, a), b)
28.45/9.26	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.26	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.26	   A^2 -> H(U1(d, a), c)
28.45/9.26	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.26	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.26	   A^2 -> H(U1(d, a), e)
28.45/9.26	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.26	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.26	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.26	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.26	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.26	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.26	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.26	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.26	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.26	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.26	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.26	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.26	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.26	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.26	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.26	   A^2 -> H(U1(a, c), b)
28.45/9.26	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.26	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.26	   A^2 -> H(U1(a, c), c)
28.45/9.26	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.26	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.26	   A^2 -> H(U1(a, c), e)
28.45/9.26	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, d), b)
28.45/9.26	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.26	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.26	   A^2 -> H(U1(a, d), c)
28.45/9.26	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.26	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.26	   A^2 -> H(U1(a, d), e)
28.45/9.26	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, a), d)
28.45/9.26	   A^2 -> H(U1(a, a), k)
28.45/9.26	   A^2 -> H(k, U1(b, b))
28.45/9.26	   A^2 -> H(k, f(c))
28.45/9.26	   A^2 -> H(k, f(d))
28.45/9.26	   A^2 -> H(c, U1(c, b))
28.45/9.26	   A^2 -> H(c, U1(d, b))
28.45/9.26	   A^2 -> H(c, U1(b, c))
28.45/9.26	   A^2 -> H(c, U1(b, d))
28.45/9.26	   A^2 -> H(c, U1(c, c))
28.45/9.26	   A^2 -> H(c, f(e))
28.45/9.26	   A^2 -> H(c, f(k))
28.45/9.26	   A^2 -> H(c, U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.26	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.26	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.26	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.26	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.26	   A^2 -> H(U1(e, k), f(e))
28.45/9.26	   A^2 -> H(U1(e, k), f(k))
28.45/9.26	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.26	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.26	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.26	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.26	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.26	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.26	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.26	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.26	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.26	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.26	   A^2 -> H(U1(k, e), f(e))
28.45/9.26	   A^2 -> H(U1(k, e), f(k))
28.45/9.26	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.26	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.26	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.26	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.26	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.26	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.26	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.26	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.26	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.26	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.26	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.26	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, c), b)
28.45/9.26	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.26	
28.45/9.26	The TRS R consists of the following rules:
28.45/9.26	
28.45/9.26	   f(x) -> U1(x, x)
28.45/9.26	   U1(e, x) -> x
28.45/9.26	   a -> c
28.45/9.26	   a -> d
28.45/9.26	   b -> c
28.45/9.26	   b -> d
28.45/9.26	   d -> k
28.45/9.26	   c -> e
28.45/9.26	   c -> k
28.45/9.26	
28.45/9.26	Q is empty.
28.45/9.26	We have to consider all minimal (P,Q,R)-chains.
28.45/9.26	----------------------------------------
28.45/9.26	
28.45/9.26	(879) TransformationProof (EQUIVALENT)
28.45/9.26	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.26	
28.45/9.26	   (A^2 -> H(U1(e, c), U1(b, k)),A^2 -> H(U1(e, c), U1(b, k)))
28.45/9.26	   (A^2 -> H(U1(k, c), U1(b, k)),A^2 -> H(U1(k, c), U1(b, k)))
28.45/9.26	   (A^2 -> H(U1(c, e), U1(b, k)),A^2 -> H(U1(c, e), U1(b, k)))
28.45/9.26	   (A^2 -> H(U1(c, k), U1(b, k)),A^2 -> H(U1(c, k), U1(b, k)))
28.45/9.26	   (A^2 -> H(U1(c, c), U1(c, k)),A^2 -> H(U1(c, c), U1(c, k)))
28.45/9.26	   (A^2 -> H(U1(c, c), U1(d, k)),A^2 -> H(U1(c, c), U1(d, k)))
28.45/9.26	
28.45/9.26	
28.45/9.26	----------------------------------------
28.45/9.26	
28.45/9.26	(880)
28.45/9.26	Obligation:
28.45/9.26	Q DP problem:
28.45/9.26	The TRS P consists of the following rules:
28.45/9.26	
28.45/9.26	   H(x, x) -> G(x, x, f(k))
28.45/9.26	   G(d, x, x) -> A^2
28.45/9.26	   A^2 -> H(f(c), f(c))
28.45/9.26	   A^2 -> H(f(d), f(d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.26	   A^2 -> H(f(e), f(e))
28.45/9.26	   A^2 -> H(f(k), f(k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.26	   A^2 -> H(e, U1(b, b))
28.45/9.26	   A^2 -> H(e, f(c))
28.45/9.26	   A^2 -> H(e, f(d))
28.45/9.26	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.26	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.26	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.26	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.26	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.26	   A^2 -> H(U1(e, e), f(e))
28.45/9.26	   A^2 -> H(U1(e, e), f(k))
28.45/9.26	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.26	   A^2 -> H(f(e), U1(e, b))
28.45/9.26	   A^2 -> H(f(e), U1(k, b))
28.45/9.26	   A^2 -> H(f(e), U1(c, d))
28.45/9.26	   A^2 -> H(f(e), U1(d, c))
28.45/9.26	   A^2 -> H(f(e), U1(b, e))
28.45/9.26	   A^2 -> H(f(e), U1(b, k))
28.45/9.26	   A^2 -> H(f(e), U1(e, c))
28.45/9.26	   A^2 -> H(f(e), U1(k, c))
28.45/9.26	   A^2 -> H(f(e), U1(c, e))
28.45/9.26	   A^2 -> H(f(e), U1(c, k))
28.45/9.26	   A^2 -> H(f(e), U1(k, k))
28.45/9.26	   A^2 -> H(f(e), U1(k, d))
28.45/9.26	   A^2 -> H(f(e), U1(d, k))
28.45/9.26	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.26	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.26	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.26	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.26	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.26	   A^2 -> H(U1(k, k), f(e))
28.45/9.26	   A^2 -> H(U1(k, k), f(k))
28.45/9.26	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.26	   A^2 -> H(f(k), U1(e, b))
28.45/9.26	   A^2 -> H(f(k), U1(k, b))
28.45/9.26	   A^2 -> H(f(k), U1(c, d))
28.45/9.26	   A^2 -> H(f(k), U1(d, c))
28.45/9.26	   A^2 -> H(f(k), U1(b, e))
28.45/9.26	   A^2 -> H(f(k), U1(b, k))
28.45/9.26	   A^2 -> H(f(k), U1(e, c))
28.45/9.26	   A^2 -> H(f(k), U1(k, c))
28.45/9.26	   A^2 -> H(f(k), U1(c, e))
28.45/9.26	   A^2 -> H(f(k), U1(c, k))
28.45/9.26	   A^2 -> H(f(k), U1(e, e))
28.45/9.26	   A^2 -> H(f(k), U1(k, d))
28.45/9.26	   A^2 -> H(f(k), U1(d, k))
28.45/9.26	   A^2 -> H(f(c), b)
28.45/9.26	   A^2 -> H(f(c), U1(e, d))
28.45/9.26	   A^2 -> H(f(c), U1(d, e))
28.45/9.26	   A^2 -> H(f(k), U1(k, k))
28.45/9.26	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.26	   A^2 -> H(U1(k, k), f(c))
28.45/9.26	   A^2 -> H(U1(k, k), f(d))
28.45/9.26	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.26	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.26	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.26	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.26	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.26	   A^2 -> H(U1(k, d), f(e))
28.45/9.26	   A^2 -> H(U1(k, d), f(k))
28.45/9.26	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.26	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.26	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.26	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.26	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.26	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.26	   A^2 -> H(U1(d, k), f(e))
28.45/9.26	   A^2 -> H(U1(d, k), f(k))
28.45/9.26	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.26	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.26	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.26	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.26	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.26	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.26	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.26	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.26	   A^2 -> H(f(d), b)
28.45/9.26	   A^2 -> H(f(d), U1(e, d))
28.45/9.26	   A^2 -> H(f(d), U1(d, e))
28.45/9.26	   A^2 -> H(f(d), c)
28.45/9.26	   A^2 -> H(f(d), U1(e, k))
28.45/9.26	   A^2 -> H(f(d), U1(k, e))
28.45/9.26	   A^2 -> H(f(d), e)
28.45/9.26	   A^2 -> H(f(a), d)
28.45/9.26	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.26	   A^2 -> H(f(c), c)
28.45/9.26	   A^2 -> H(f(c), U1(e, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.26	   A^2 -> H(f(c), U1(k, e))
28.45/9.26	   A^2 -> H(f(c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.26	   A^2 -> H(f(a), k)
28.45/9.26	   A^2 -> H(f(e), U1(e, e))
28.45/9.26	   A^2 -> H(f(c), e)
28.45/9.26	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.26	   A^2 -> H(f(d), U1(k, k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.26	   A^2 -> H(d, U1(b, b))
28.45/9.26	   A^2 -> H(d, f(c))
28.45/9.26	   A^2 -> H(d, f(d))
28.45/9.26	   A^2 -> H(a, U1(c, b))
28.45/9.26	   A^2 -> H(a, U1(d, b))
28.45/9.26	   A^2 -> H(a, U1(b, c))
28.45/9.26	   A^2 -> H(a, U1(b, d))
28.45/9.26	   A^2 -> H(a, U1(c, c))
28.45/9.26	   A^2 -> H(a, f(e))
28.45/9.26	   A^2 -> H(a, f(k))
28.45/9.26	   A^2 -> H(a, U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.26	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.26	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.26	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.26	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.26	   A^2 -> H(U1(e, d), f(e))
28.45/9.26	   A^2 -> H(U1(e, d), f(k))
28.45/9.26	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.26	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.26	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.26	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.26	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.26	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.26	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.26	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.26	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.26	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.26	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.26	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.26	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.26	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.26	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.26	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.26	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.26	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.26	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.26	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, a), b)
28.45/9.26	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.26	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.26	   A^2 -> H(U1(c, a), c)
28.45/9.26	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.26	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.26	   A^2 -> H(U1(c, a), e)
28.45/9.26	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.26	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.26	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.26	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.26	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.26	   A^2 -> H(U1(d, e), f(e))
28.45/9.26	   A^2 -> H(U1(d, e), f(k))
28.45/9.26	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.26	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.26	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.26	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.26	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.26	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.26	   A^2 -> H(U1(d, a), b)
28.45/9.26	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.26	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.26	   A^2 -> H(U1(d, a), c)
28.45/9.26	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.26	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.26	   A^2 -> H(U1(d, a), e)
28.45/9.26	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.26	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.26	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.26	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.26	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.26	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.26	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.26	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.26	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.26	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.26	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.26	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.26	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.26	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.26	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.26	   A^2 -> H(U1(a, c), b)
28.45/9.26	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.26	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.26	   A^2 -> H(U1(a, c), c)
28.45/9.26	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.26	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.26	   A^2 -> H(U1(a, c), e)
28.45/9.26	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, d), b)
28.45/9.26	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.26	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.26	   A^2 -> H(U1(a, d), c)
28.45/9.26	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.26	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.26	   A^2 -> H(U1(a, d), e)
28.45/9.26	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.26	   A^2 -> H(U1(a, a), d)
28.45/9.26	   A^2 -> H(U1(a, a), k)
28.45/9.26	   A^2 -> H(k, U1(b, b))
28.45/9.26	   A^2 -> H(k, f(c))
28.45/9.26	   A^2 -> H(k, f(d))
28.45/9.26	   A^2 -> H(c, U1(c, b))
28.45/9.26	   A^2 -> H(c, U1(d, b))
28.45/9.26	   A^2 -> H(c, U1(b, c))
28.45/9.26	   A^2 -> H(c, U1(b, d))
28.45/9.26	   A^2 -> H(c, U1(c, c))
28.45/9.26	   A^2 -> H(c, f(e))
28.45/9.26	   A^2 -> H(c, f(k))
28.45/9.26	   A^2 -> H(c, U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.26	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.26	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.26	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.26	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.26	   A^2 -> H(U1(e, k), f(e))
28.45/9.26	   A^2 -> H(U1(e, k), f(k))
28.45/9.26	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.26	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.26	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.26	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.26	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.26	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.26	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.26	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.26	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.26	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.26	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.26	   A^2 -> H(U1(k, e), f(e))
28.45/9.26	   A^2 -> H(U1(k, e), f(k))
28.45/9.26	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.26	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.26	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.26	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.26	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.26	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.26	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.26	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.26	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.26	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.26	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.26	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.26	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.26	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.26	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.26	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.26	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.26	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.26	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.26	   A^2 -> H(U1(c, c), b)
28.45/9.26	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.26	
28.45/9.26	The TRS R consists of the following rules:
28.45/9.26	
28.45/9.26	   f(x) -> U1(x, x)
28.45/9.26	   U1(e, x) -> x
28.45/9.26	   a -> c
28.45/9.26	   a -> d
28.45/9.26	   b -> c
28.45/9.26	   b -> d
28.45/9.26	   d -> k
28.45/9.26	   c -> e
28.45/9.26	   c -> k
28.45/9.26	
28.45/9.26	Q is empty.
28.45/9.26	We have to consider all minimal (P,Q,R)-chains.
28.45/9.26	----------------------------------------
28.45/9.26	
28.45/9.26	(881) TransformationProof (EQUIVALENT)
28.45/9.26	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.26	
28.45/9.26	   (A^2 -> H(U1(e, c), U1(e, e)),A^2 -> H(U1(e, c), U1(e, e)))
28.45/9.26	   (A^2 -> H(U1(k, c), U1(e, e)),A^2 -> H(U1(k, c), U1(e, e)))
28.45/9.26	   (A^2 -> H(U1(c, e), U1(e, e)),A^2 -> H(U1(c, e), U1(e, e)))
28.45/9.26	   (A^2 -> H(U1(c, k), U1(e, e)),A^2 -> H(U1(c, k), U1(e, e)))
28.45/9.26	   (A^2 -> H(U1(c, c), e),A^2 -> H(U1(c, c), e))
28.45/9.26	
28.45/9.26	
28.45/9.26	----------------------------------------
28.45/9.26	
28.45/9.26	(882)
28.45/9.26	Obligation:
28.45/9.26	Q DP problem:
28.45/9.26	The TRS P consists of the following rules:
28.45/9.26	
28.45/9.26	   H(x, x) -> G(x, x, f(k))
28.45/9.26	   G(d, x, x) -> A^2
28.45/9.26	   A^2 -> H(f(c), f(c))
28.45/9.26	   A^2 -> H(f(d), f(d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.26	   A^2 -> H(f(e), f(e))
28.45/9.26	   A^2 -> H(f(k), f(k))
28.45/9.26	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.26	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.26	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.27	   A^2 -> H(e, U1(b, b))
28.45/9.27	   A^2 -> H(e, f(c))
28.45/9.27	   A^2 -> H(e, f(d))
28.45/9.27	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.27	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.27	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.27	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.27	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.27	   A^2 -> H(U1(e, e), f(e))
28.45/9.27	   A^2 -> H(U1(e, e), f(k))
28.45/9.27	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.27	   A^2 -> H(f(e), U1(e, b))
28.45/9.27	   A^2 -> H(f(e), U1(k, b))
28.45/9.27	   A^2 -> H(f(e), U1(c, d))
28.45/9.27	   A^2 -> H(f(e), U1(d, c))
28.45/9.27	   A^2 -> H(f(e), U1(b, e))
28.45/9.27	   A^2 -> H(f(e), U1(b, k))
28.45/9.27	   A^2 -> H(f(e), U1(e, c))
28.45/9.27	   A^2 -> H(f(e), U1(k, c))
28.45/9.27	   A^2 -> H(f(e), U1(c, e))
28.45/9.27	   A^2 -> H(f(e), U1(c, k))
28.45/9.27	   A^2 -> H(f(e), U1(k, k))
28.45/9.27	   A^2 -> H(f(e), U1(k, d))
28.45/9.27	   A^2 -> H(f(e), U1(d, k))
28.45/9.27	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.27	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.27	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.27	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.27	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.27	   A^2 -> H(U1(k, k), f(e))
28.45/9.27	   A^2 -> H(U1(k, k), f(k))
28.45/9.27	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.27	   A^2 -> H(f(k), U1(e, b))
28.45/9.27	   A^2 -> H(f(k), U1(k, b))
28.45/9.27	   A^2 -> H(f(k), U1(c, d))
28.45/9.27	   A^2 -> H(f(k), U1(d, c))
28.45/9.27	   A^2 -> H(f(k), U1(b, e))
28.45/9.27	   A^2 -> H(f(k), U1(b, k))
28.45/9.27	   A^2 -> H(f(k), U1(e, c))
28.45/9.27	   A^2 -> H(f(k), U1(k, c))
28.45/9.27	   A^2 -> H(f(k), U1(c, e))
28.45/9.27	   A^2 -> H(f(k), U1(c, k))
28.45/9.27	   A^2 -> H(f(k), U1(e, e))
28.45/9.27	   A^2 -> H(f(k), U1(k, d))
28.45/9.27	   A^2 -> H(f(k), U1(d, k))
28.45/9.27	   A^2 -> H(f(c), b)
28.45/9.27	   A^2 -> H(f(c), U1(e, d))
28.45/9.27	   A^2 -> H(f(c), U1(d, e))
28.45/9.27	   A^2 -> H(f(k), U1(k, k))
28.45/9.27	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.27	   A^2 -> H(U1(k, k), f(c))
28.45/9.27	   A^2 -> H(U1(k, k), f(d))
28.45/9.27	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.27	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.27	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.27	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.27	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.27	   A^2 -> H(U1(k, d), f(e))
28.45/9.27	   A^2 -> H(U1(k, d), f(k))
28.45/9.27	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.27	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.27	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.27	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.27	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.27	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.27	   A^2 -> H(U1(d, k), f(e))
28.45/9.27	   A^2 -> H(U1(d, k), f(k))
28.45/9.27	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.27	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.27	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.27	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.27	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.27	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.27	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.27	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.27	   A^2 -> H(f(d), b)
28.45/9.27	   A^2 -> H(f(d), U1(e, d))
28.45/9.27	   A^2 -> H(f(d), U1(d, e))
28.45/9.27	   A^2 -> H(f(d), c)
28.45/9.27	   A^2 -> H(f(d), U1(e, k))
28.45/9.27	   A^2 -> H(f(d), U1(k, e))
28.45/9.27	   A^2 -> H(f(d), e)
28.45/9.27	   A^2 -> H(f(a), d)
28.45/9.27	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.27	   A^2 -> H(f(c), c)
28.45/9.27	   A^2 -> H(f(c), U1(e, k))
28.45/9.27	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.27	   A^2 -> H(f(c), U1(k, e))
28.45/9.27	   A^2 -> H(f(c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.27	   A^2 -> H(f(a), k)
28.45/9.27	   A^2 -> H(f(e), U1(e, e))
28.45/9.27	   A^2 -> H(f(c), e)
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.27	   A^2 -> H(f(d), U1(k, k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.27	   A^2 -> H(d, U1(b, b))
28.45/9.27	   A^2 -> H(d, f(c))
28.45/9.27	   A^2 -> H(d, f(d))
28.45/9.27	   A^2 -> H(a, U1(c, b))
28.45/9.27	   A^2 -> H(a, U1(d, b))
28.45/9.27	   A^2 -> H(a, U1(b, c))
28.45/9.27	   A^2 -> H(a, U1(b, d))
28.45/9.27	   A^2 -> H(a, U1(c, c))
28.45/9.27	   A^2 -> H(a, f(e))
28.45/9.27	   A^2 -> H(a, f(k))
28.45/9.27	   A^2 -> H(a, U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.27	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.27	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.27	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.27	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.27	   A^2 -> H(U1(e, d), f(e))
28.45/9.27	   A^2 -> H(U1(e, d), f(k))
28.45/9.27	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.27	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.27	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.27	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.27	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.27	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.27	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.27	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.27	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.27	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.27	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.27	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.27	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.27	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.27	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.27	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.27	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.27	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.27	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.27	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.27	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.27	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.27	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, a), b)
28.45/9.27	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.27	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.27	   A^2 -> H(U1(c, a), c)
28.45/9.27	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.27	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.27	   A^2 -> H(U1(c, a), e)
28.45/9.27	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.27	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.27	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.27	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.27	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.27	   A^2 -> H(U1(d, e), f(e))
28.45/9.27	   A^2 -> H(U1(d, e), f(k))
28.45/9.27	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.27	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.27	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.27	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.27	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.27	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.27	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.27	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.27	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.27	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.27	   A^2 -> H(U1(d, a), b)
28.45/9.27	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.27	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.27	   A^2 -> H(U1(d, a), c)
28.45/9.27	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.27	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.27	   A^2 -> H(U1(d, a), e)
28.45/9.27	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.27	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.27	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.27	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.27	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.27	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.27	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.27	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.27	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.27	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.27	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.27	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.27	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.27	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.27	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.27	   A^2 -> H(U1(a, c), b)
28.45/9.27	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.27	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.27	   A^2 -> H(U1(a, c), c)
28.45/9.27	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.27	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.27	   A^2 -> H(U1(a, c), e)
28.45/9.27	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, d), b)
28.45/9.27	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.27	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.27	   A^2 -> H(U1(a, d), c)
28.45/9.27	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.27	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.27	   A^2 -> H(U1(a, d), e)
28.45/9.27	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, a), d)
28.45/9.27	   A^2 -> H(U1(a, a), k)
28.45/9.27	   A^2 -> H(k, U1(b, b))
28.45/9.27	   A^2 -> H(k, f(c))
28.45/9.27	   A^2 -> H(k, f(d))
28.45/9.27	   A^2 -> H(c, U1(c, b))
28.45/9.27	   A^2 -> H(c, U1(d, b))
28.45/9.27	   A^2 -> H(c, U1(b, c))
28.45/9.27	   A^2 -> H(c, U1(b, d))
28.45/9.27	   A^2 -> H(c, U1(c, c))
28.45/9.27	   A^2 -> H(c, f(e))
28.45/9.27	   A^2 -> H(c, f(k))
28.45/9.27	   A^2 -> H(c, U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.27	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.27	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.27	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.27	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.27	   A^2 -> H(U1(e, k), f(e))
28.45/9.27	   A^2 -> H(U1(e, k), f(k))
28.45/9.27	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.27	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.27	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.27	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.27	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.27	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.27	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.27	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.27	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.27	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.27	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.27	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.27	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.27	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.27	   A^2 -> H(U1(k, e), f(e))
28.45/9.27	   A^2 -> H(U1(k, e), f(k))
28.45/9.27	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.27	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.27	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.27	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.27	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.27	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.27	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.27	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.27	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.27	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.27	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.27	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.27	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.27	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.27	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.27	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.27	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.27	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.27	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.27	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.27	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.27	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, c), b)
28.45/9.27	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.27	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.27	   A^2 -> H(U1(c, c), e)
28.45/9.27	
28.45/9.27	The TRS R consists of the following rules:
28.45/9.27	
28.45/9.27	   f(x) -> U1(x, x)
28.45/9.27	   U1(e, x) -> x
28.45/9.27	   a -> c
28.45/9.27	   a -> d
28.45/9.27	   b -> c
28.45/9.27	   b -> d
28.45/9.27	   d -> k
28.45/9.27	   c -> e
28.45/9.27	   c -> k
28.45/9.27	
28.45/9.27	Q is empty.
28.45/9.27	We have to consider all minimal (P,Q,R)-chains.
28.45/9.27	----------------------------------------
28.45/9.27	
28.45/9.27	(883) TransformationProof (EQUIVALENT)
28.45/9.27	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.27	
28.45/9.27	   (A^2 -> H(U1(e, c), U1(k, k)),A^2 -> H(U1(e, c), U1(k, k)))
28.45/9.27	   (A^2 -> H(U1(k, c), U1(k, k)),A^2 -> H(U1(k, c), U1(k, k)))
28.45/9.27	   (A^2 -> H(U1(c, e), U1(k, k)),A^2 -> H(U1(c, e), U1(k, k)))
28.45/9.27	   (A^2 -> H(U1(c, k), U1(k, k)),A^2 -> H(U1(c, k), U1(k, k)))
28.45/9.27	
28.45/9.27	
28.45/9.27	----------------------------------------
28.45/9.27	
28.45/9.27	(884)
28.45/9.27	Obligation:
28.45/9.27	Q DP problem:
28.45/9.27	The TRS P consists of the following rules:
28.45/9.27	
28.45/9.27	   H(x, x) -> G(x, x, f(k))
28.45/9.27	   G(d, x, x) -> A^2
28.45/9.27	   A^2 -> H(f(c), f(c))
28.45/9.27	   A^2 -> H(f(d), f(d))
28.45/9.27	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.27	   A^2 -> H(f(e), f(e))
28.45/9.27	   A^2 -> H(f(k), f(k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.27	   A^2 -> H(U1(c, c), U1(k, d))
28.45/9.27	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.27	   A^2 -> H(e, U1(b, b))
28.45/9.27	   A^2 -> H(e, f(c))
28.45/9.27	   A^2 -> H(e, f(d))
28.45/9.27	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.27	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.27	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.27	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.27	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.27	   A^2 -> H(U1(e, e), f(e))
28.45/9.27	   A^2 -> H(U1(e, e), f(k))
28.45/9.27	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.27	   A^2 -> H(f(e), U1(e, b))
28.45/9.27	   A^2 -> H(f(e), U1(k, b))
28.45/9.27	   A^2 -> H(f(e), U1(c, d))
28.45/9.27	   A^2 -> H(f(e), U1(d, c))
28.45/9.27	   A^2 -> H(f(e), U1(b, e))
28.45/9.27	   A^2 -> H(f(e), U1(b, k))
28.45/9.27	   A^2 -> H(f(e), U1(e, c))
28.45/9.27	   A^2 -> H(f(e), U1(k, c))
28.45/9.27	   A^2 -> H(f(e), U1(c, e))
28.45/9.27	   A^2 -> H(f(e), U1(c, k))
28.45/9.27	   A^2 -> H(f(e), U1(k, k))
28.45/9.27	   A^2 -> H(f(e), U1(k, d))
28.45/9.27	   A^2 -> H(f(e), U1(d, k))
28.45/9.27	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.27	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.27	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.27	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.27	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.27	   A^2 -> H(U1(k, k), f(e))
28.45/9.27	   A^2 -> H(U1(k, k), f(k))
28.45/9.27	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.27	   A^2 -> H(f(k), U1(e, b))
28.45/9.27	   A^2 -> H(f(k), U1(k, b))
28.45/9.27	   A^2 -> H(f(k), U1(c, d))
28.45/9.27	   A^2 -> H(f(k), U1(d, c))
28.45/9.27	   A^2 -> H(f(k), U1(b, e))
28.45/9.27	   A^2 -> H(f(k), U1(b, k))
28.45/9.27	   A^2 -> H(f(k), U1(e, c))
28.45/9.27	   A^2 -> H(f(k), U1(k, c))
28.45/9.27	   A^2 -> H(f(k), U1(c, e))
28.45/9.27	   A^2 -> H(f(k), U1(c, k))
28.45/9.27	   A^2 -> H(f(k), U1(e, e))
28.45/9.27	   A^2 -> H(f(k), U1(k, d))
28.45/9.27	   A^2 -> H(f(k), U1(d, k))
28.45/9.27	   A^2 -> H(f(c), b)
28.45/9.27	   A^2 -> H(f(c), U1(e, d))
28.45/9.27	   A^2 -> H(f(c), U1(d, e))
28.45/9.27	   A^2 -> H(f(k), U1(k, k))
28.45/9.27	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.27	   A^2 -> H(U1(k, k), f(c))
28.45/9.27	   A^2 -> H(U1(k, k), f(d))
28.45/9.27	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.27	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.27	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.27	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.27	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.27	   A^2 -> H(U1(k, d), f(e))
28.45/9.27	   A^2 -> H(U1(k, d), f(k))
28.45/9.27	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.27	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.27	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.27	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.27	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.27	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.27	   A^2 -> H(U1(d, k), f(e))
28.45/9.27	   A^2 -> H(U1(d, k), f(k))
28.45/9.27	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.27	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.27	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.27	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.27	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.27	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.27	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.27	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.27	   A^2 -> H(f(d), b)
28.45/9.27	   A^2 -> H(f(d), U1(e, d))
28.45/9.27	   A^2 -> H(f(d), U1(d, e))
28.45/9.27	   A^2 -> H(f(d), c)
28.45/9.27	   A^2 -> H(f(d), U1(e, k))
28.45/9.27	   A^2 -> H(f(d), U1(k, e))
28.45/9.27	   A^2 -> H(f(d), e)
28.45/9.27	   A^2 -> H(f(a), d)
28.45/9.27	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.27	   A^2 -> H(f(c), c)
28.45/9.27	   A^2 -> H(f(c), U1(e, k))
28.45/9.27	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.27	   A^2 -> H(f(c), U1(k, e))
28.45/9.27	   A^2 -> H(f(c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.27	   A^2 -> H(f(a), k)
28.45/9.27	   A^2 -> H(f(e), U1(e, e))
28.45/9.27	   A^2 -> H(f(c), e)
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.27	   A^2 -> H(f(d), U1(k, k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.27	   A^2 -> H(d, U1(b, b))
28.45/9.27	   A^2 -> H(d, f(c))
28.45/9.27	   A^2 -> H(d, f(d))
28.45/9.27	   A^2 -> H(a, U1(c, b))
28.45/9.27	   A^2 -> H(a, U1(d, b))
28.45/9.27	   A^2 -> H(a, U1(b, c))
28.45/9.27	   A^2 -> H(a, U1(b, d))
28.45/9.27	   A^2 -> H(a, U1(c, c))
28.45/9.27	   A^2 -> H(a, f(e))
28.45/9.27	   A^2 -> H(a, f(k))
28.45/9.27	   A^2 -> H(a, U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.27	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.27	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.27	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.27	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.27	   A^2 -> H(U1(e, d), f(e))
28.45/9.27	   A^2 -> H(U1(e, d), f(k))
28.45/9.27	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.27	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.27	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.27	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.27	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.27	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.27	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.27	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.27	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.27	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.27	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.27	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.27	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.27	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.27	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.27	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.27	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.27	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.27	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.27	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.27	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.27	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.27	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, a), b)
28.45/9.27	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.27	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.27	   A^2 -> H(U1(c, a), c)
28.45/9.27	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.27	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.27	   A^2 -> H(U1(c, a), e)
28.45/9.27	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.27	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.27	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.27	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.27	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.27	   A^2 -> H(U1(d, e), f(e))
28.45/9.27	   A^2 -> H(U1(d, e), f(k))
28.45/9.27	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.27	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.27	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.27	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.27	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.27	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.27	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.27	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.27	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.27	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.27	   A^2 -> H(U1(d, a), b)
28.45/9.27	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.27	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.27	   A^2 -> H(U1(d, a), c)
28.45/9.27	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.27	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.27	   A^2 -> H(U1(d, a), e)
28.45/9.27	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.27	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.27	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.27	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.27	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.27	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.27	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.27	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.27	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.27	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.27	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.27	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.27	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.27	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.27	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.27	   A^2 -> H(U1(a, c), b)
28.45/9.27	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.27	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.27	   A^2 -> H(U1(a, c), c)
28.45/9.27	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.27	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.27	   A^2 -> H(U1(a, c), e)
28.45/9.27	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, d), b)
28.45/9.27	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.27	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.27	   A^2 -> H(U1(a, d), c)
28.45/9.27	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.27	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.27	   A^2 -> H(U1(a, d), e)
28.45/9.27	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, a), d)
28.45/9.27	   A^2 -> H(U1(a, a), k)
28.45/9.27	   A^2 -> H(k, U1(b, b))
28.45/9.27	   A^2 -> H(k, f(c))
28.45/9.27	   A^2 -> H(k, f(d))
28.45/9.27	   A^2 -> H(c, U1(c, b))
28.45/9.27	   A^2 -> H(c, U1(d, b))
28.45/9.27	   A^2 -> H(c, U1(b, c))
28.45/9.27	   A^2 -> H(c, U1(b, d))
28.45/9.27	   A^2 -> H(c, U1(c, c))
28.45/9.27	   A^2 -> H(c, f(e))
28.45/9.27	   A^2 -> H(c, f(k))
28.45/9.27	   A^2 -> H(c, U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.27	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.27	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.27	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.27	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.27	   A^2 -> H(U1(e, k), f(e))
28.45/9.27	   A^2 -> H(U1(e, k), f(k))
28.45/9.27	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.27	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.27	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.27	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.27	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.27	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.27	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.27	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.27	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.27	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.27	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.27	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.27	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.27	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.27	   A^2 -> H(U1(k, e), f(e))
28.45/9.27	   A^2 -> H(U1(k, e), f(k))
28.45/9.27	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.27	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.27	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.27	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.27	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.27	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.27	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.27	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.27	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.27	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.27	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.27	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.27	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.27	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.27	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.27	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.27	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.27	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.27	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.27	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.27	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.27	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, c), b)
28.45/9.27	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.27	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.27	   A^2 -> H(U1(c, c), e)
28.45/9.27	
28.45/9.27	The TRS R consists of the following rules:
28.45/9.27	
28.45/9.27	   f(x) -> U1(x, x)
28.45/9.27	   U1(e, x) -> x
28.45/9.27	   a -> c
28.45/9.27	   a -> d
28.45/9.27	   b -> c
28.45/9.27	   b -> d
28.45/9.27	   d -> k
28.45/9.27	   c -> e
28.45/9.27	   c -> k
28.45/9.27	
28.45/9.27	Q is empty.
28.45/9.27	We have to consider all minimal (P,Q,R)-chains.
28.45/9.27	----------------------------------------
28.45/9.27	
28.45/9.27	(885) TransformationProof (EQUIVALENT)
28.45/9.27	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.27	
28.45/9.27	   (A^2 -> H(U1(e, c), U1(k, d)),A^2 -> H(U1(e, c), U1(k, d)))
28.45/9.27	   (A^2 -> H(U1(k, c), U1(k, d)),A^2 -> H(U1(k, c), U1(k, d)))
28.45/9.27	   (A^2 -> H(U1(c, e), U1(k, d)),A^2 -> H(U1(c, e), U1(k, d)))
28.45/9.27	   (A^2 -> H(U1(c, k), U1(k, d)),A^2 -> H(U1(c, k), U1(k, d)))
28.45/9.27	   (A^2 -> H(U1(c, c), U1(k, k)),A^2 -> H(U1(c, c), U1(k, k)))
28.45/9.27	
28.45/9.27	
28.45/9.27	----------------------------------------
28.45/9.27	
28.45/9.27	(886)
28.45/9.27	Obligation:
28.45/9.27	Q DP problem:
28.45/9.27	The TRS P consists of the following rules:
28.45/9.27	
28.45/9.27	   H(x, x) -> G(x, x, f(k))
28.45/9.27	   G(d, x, x) -> A^2
28.45/9.27	   A^2 -> H(f(c), f(c))
28.45/9.27	   A^2 -> H(f(d), f(d))
28.45/9.27	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.27	   A^2 -> H(f(e), f(e))
28.45/9.27	   A^2 -> H(f(k), f(k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.27	   A^2 -> H(U1(c, c), U1(d, k))
28.45/9.27	   A^2 -> H(e, U1(b, b))
28.45/9.27	   A^2 -> H(e, f(c))
28.45/9.27	   A^2 -> H(e, f(d))
28.45/9.27	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.27	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.27	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.27	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.27	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.27	   A^2 -> H(U1(e, e), f(e))
28.45/9.27	   A^2 -> H(U1(e, e), f(k))
28.45/9.27	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.27	   A^2 -> H(f(e), U1(e, b))
28.45/9.27	   A^2 -> H(f(e), U1(k, b))
28.45/9.27	   A^2 -> H(f(e), U1(c, d))
28.45/9.27	   A^2 -> H(f(e), U1(d, c))
28.45/9.27	   A^2 -> H(f(e), U1(b, e))
28.45/9.27	   A^2 -> H(f(e), U1(b, k))
28.45/9.27	   A^2 -> H(f(e), U1(e, c))
28.45/9.27	   A^2 -> H(f(e), U1(k, c))
28.45/9.27	   A^2 -> H(f(e), U1(c, e))
28.45/9.27	   A^2 -> H(f(e), U1(c, k))
28.45/9.27	   A^2 -> H(f(e), U1(k, k))
28.45/9.27	   A^2 -> H(f(e), U1(k, d))
28.45/9.27	   A^2 -> H(f(e), U1(d, k))
28.45/9.27	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.27	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.27	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.27	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.27	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.27	   A^2 -> H(U1(k, k), f(e))
28.45/9.27	   A^2 -> H(U1(k, k), f(k))
28.45/9.27	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.27	   A^2 -> H(f(k), U1(e, b))
28.45/9.27	   A^2 -> H(f(k), U1(k, b))
28.45/9.27	   A^2 -> H(f(k), U1(c, d))
28.45/9.27	   A^2 -> H(f(k), U1(d, c))
28.45/9.27	   A^2 -> H(f(k), U1(b, e))
28.45/9.27	   A^2 -> H(f(k), U1(b, k))
28.45/9.27	   A^2 -> H(f(k), U1(e, c))
28.45/9.27	   A^2 -> H(f(k), U1(k, c))
28.45/9.27	   A^2 -> H(f(k), U1(c, e))
28.45/9.27	   A^2 -> H(f(k), U1(c, k))
28.45/9.27	   A^2 -> H(f(k), U1(e, e))
28.45/9.27	   A^2 -> H(f(k), U1(k, d))
28.45/9.27	   A^2 -> H(f(k), U1(d, k))
28.45/9.27	   A^2 -> H(f(c), b)
28.45/9.27	   A^2 -> H(f(c), U1(e, d))
28.45/9.27	   A^2 -> H(f(c), U1(d, e))
28.45/9.27	   A^2 -> H(f(k), U1(k, k))
28.45/9.27	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.27	   A^2 -> H(U1(k, k), f(c))
28.45/9.27	   A^2 -> H(U1(k, k), f(d))
28.45/9.27	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.27	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.27	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.27	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.27	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.27	   A^2 -> H(U1(k, d), f(e))
28.45/9.27	   A^2 -> H(U1(k, d), f(k))
28.45/9.27	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.27	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.27	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.27	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.27	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.27	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.27	   A^2 -> H(U1(d, k), f(e))
28.45/9.27	   A^2 -> H(U1(d, k), f(k))
28.45/9.27	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.27	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.27	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.27	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.27	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.27	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.27	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.27	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.27	   A^2 -> H(f(d), b)
28.45/9.27	   A^2 -> H(f(d), U1(e, d))
28.45/9.27	   A^2 -> H(f(d), U1(d, e))
28.45/9.27	   A^2 -> H(f(d), c)
28.45/9.27	   A^2 -> H(f(d), U1(e, k))
28.45/9.27	   A^2 -> H(f(d), U1(k, e))
28.45/9.27	   A^2 -> H(f(d), e)
28.45/9.27	   A^2 -> H(f(a), d)
28.45/9.27	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.27	   A^2 -> H(f(c), c)
28.45/9.27	   A^2 -> H(f(c), U1(e, k))
28.45/9.27	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.27	   A^2 -> H(f(c), U1(k, e))
28.45/9.27	   A^2 -> H(f(c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.27	   A^2 -> H(f(a), k)
28.45/9.27	   A^2 -> H(f(e), U1(e, e))
28.45/9.27	   A^2 -> H(f(c), e)
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.27	   A^2 -> H(f(d), U1(k, k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.27	   A^2 -> H(d, U1(b, b))
28.45/9.27	   A^2 -> H(d, f(c))
28.45/9.27	   A^2 -> H(d, f(d))
28.45/9.27	   A^2 -> H(a, U1(c, b))
28.45/9.27	   A^2 -> H(a, U1(d, b))
28.45/9.27	   A^2 -> H(a, U1(b, c))
28.45/9.27	   A^2 -> H(a, U1(b, d))
28.45/9.27	   A^2 -> H(a, U1(c, c))
28.45/9.27	   A^2 -> H(a, f(e))
28.45/9.27	   A^2 -> H(a, f(k))
28.45/9.27	   A^2 -> H(a, U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.27	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.27	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.27	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.27	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.27	   A^2 -> H(U1(e, d), f(e))
28.45/9.27	   A^2 -> H(U1(e, d), f(k))
28.45/9.27	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.27	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.27	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.27	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.27	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.27	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.27	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.27	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.27	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.27	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.27	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.27	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.27	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.27	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.27	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.27	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.27	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.27	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.27	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.27	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.27	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.27	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.27	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, a), b)
28.45/9.27	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.27	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.27	   A^2 -> H(U1(c, a), c)
28.45/9.27	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.27	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.27	   A^2 -> H(U1(c, a), e)
28.45/9.27	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.27	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.27	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.27	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.27	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.27	   A^2 -> H(U1(d, e), f(e))
28.45/9.27	   A^2 -> H(U1(d, e), f(k))
28.45/9.27	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.27	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.27	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.27	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.27	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.27	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.27	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.27	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.27	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.27	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.27	   A^2 -> H(U1(d, a), b)
28.45/9.27	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.27	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.27	   A^2 -> H(U1(d, a), c)
28.45/9.27	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.27	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.27	   A^2 -> H(U1(d, a), e)
28.45/9.27	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.27	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.27	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.27	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.27	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.27	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.27	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.27	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.27	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.27	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.27	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.27	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.27	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.27	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.27	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.27	   A^2 -> H(U1(a, c), b)
28.45/9.27	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.27	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.27	   A^2 -> H(U1(a, c), c)
28.45/9.27	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.27	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.27	   A^2 -> H(U1(a, c), e)
28.45/9.27	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, d), b)
28.45/9.27	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.27	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.27	   A^2 -> H(U1(a, d), c)
28.45/9.27	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.27	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.27	   A^2 -> H(U1(a, d), e)
28.45/9.27	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, a), d)
28.45/9.27	   A^2 -> H(U1(a, a), k)
28.45/9.27	   A^2 -> H(k, U1(b, b))
28.45/9.27	   A^2 -> H(k, f(c))
28.45/9.27	   A^2 -> H(k, f(d))
28.45/9.27	   A^2 -> H(c, U1(c, b))
28.45/9.27	   A^2 -> H(c, U1(d, b))
28.45/9.27	   A^2 -> H(c, U1(b, c))
28.45/9.27	   A^2 -> H(c, U1(b, d))
28.45/9.27	   A^2 -> H(c, U1(c, c))
28.45/9.27	   A^2 -> H(c, f(e))
28.45/9.27	   A^2 -> H(c, f(k))
28.45/9.27	   A^2 -> H(c, U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.27	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.27	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.27	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.27	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.27	   A^2 -> H(U1(e, k), f(e))
28.45/9.27	   A^2 -> H(U1(e, k), f(k))
28.45/9.27	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.27	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.27	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.27	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.27	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.27	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.27	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.27	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.27	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.27	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.27	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.27	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.27	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.27	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.27	   A^2 -> H(U1(k, e), f(e))
28.45/9.27	   A^2 -> H(U1(k, e), f(k))
28.45/9.27	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.27	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.27	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.27	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.27	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.27	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.27	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.27	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.27	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.27	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.27	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.27	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.27	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.27	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.27	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.27	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.27	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.27	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.27	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.27	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.27	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.27	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, c), b)
28.45/9.27	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.27	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.27	   A^2 -> H(U1(c, c), e)
28.45/9.27	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.27	
28.45/9.27	The TRS R consists of the following rules:
28.45/9.27	
28.45/9.27	   f(x) -> U1(x, x)
28.45/9.27	   U1(e, x) -> x
28.45/9.27	   a -> c
28.45/9.27	   a -> d
28.45/9.27	   b -> c
28.45/9.27	   b -> d
28.45/9.27	   d -> k
28.45/9.27	   c -> e
28.45/9.27	   c -> k
28.45/9.27	
28.45/9.27	Q is empty.
28.45/9.27	We have to consider all minimal (P,Q,R)-chains.
28.45/9.27	----------------------------------------
28.45/9.27	
28.45/9.27	(887) TransformationProof (EQUIVALENT)
28.45/9.27	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.27	
28.45/9.27	   (A^2 -> H(U1(e, c), U1(d, k)),A^2 -> H(U1(e, c), U1(d, k)))
28.45/9.27	   (A^2 -> H(U1(k, c), U1(d, k)),A^2 -> H(U1(k, c), U1(d, k)))
28.45/9.27	   (A^2 -> H(U1(c, e), U1(d, k)),A^2 -> H(U1(c, e), U1(d, k)))
28.45/9.27	   (A^2 -> H(U1(c, k), U1(d, k)),A^2 -> H(U1(c, k), U1(d, k)))
28.45/9.27	   (A^2 -> H(U1(c, c), U1(k, k)),A^2 -> H(U1(c, c), U1(k, k)))
28.45/9.27	
28.45/9.27	
28.45/9.27	----------------------------------------
28.45/9.27	
28.45/9.27	(888)
28.45/9.27	Obligation:
28.45/9.27	Q DP problem:
28.45/9.27	The TRS P consists of the following rules:
28.45/9.27	
28.45/9.27	   H(x, x) -> G(x, x, f(k))
28.45/9.27	   G(d, x, x) -> A^2
28.45/9.27	   A^2 -> H(f(c), f(c))
28.45/9.27	   A^2 -> H(f(d), f(d))
28.45/9.27	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.27	   A^2 -> H(f(e), f(e))
28.45/9.27	   A^2 -> H(f(k), f(k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.27	   A^2 -> H(e, U1(b, b))
28.45/9.27	   A^2 -> H(e, f(c))
28.45/9.27	   A^2 -> H(e, f(d))
28.45/9.27	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.27	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.27	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.27	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.27	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.27	   A^2 -> H(U1(e, e), f(e))
28.45/9.27	   A^2 -> H(U1(e, e), f(k))
28.45/9.27	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.27	   A^2 -> H(f(e), U1(e, b))
28.45/9.27	   A^2 -> H(f(e), U1(k, b))
28.45/9.27	   A^2 -> H(f(e), U1(c, d))
28.45/9.27	   A^2 -> H(f(e), U1(d, c))
28.45/9.27	   A^2 -> H(f(e), U1(b, e))
28.45/9.27	   A^2 -> H(f(e), U1(b, k))
28.45/9.27	   A^2 -> H(f(e), U1(e, c))
28.45/9.27	   A^2 -> H(f(e), U1(k, c))
28.45/9.27	   A^2 -> H(f(e), U1(c, e))
28.45/9.27	   A^2 -> H(f(e), U1(c, k))
28.45/9.27	   A^2 -> H(f(e), U1(k, k))
28.45/9.27	   A^2 -> H(f(e), U1(k, d))
28.45/9.27	   A^2 -> H(f(e), U1(d, k))
28.45/9.27	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.27	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.27	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.27	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.27	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.27	   A^2 -> H(U1(k, k), f(e))
28.45/9.27	   A^2 -> H(U1(k, k), f(k))
28.45/9.27	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.27	   A^2 -> H(f(k), U1(e, b))
28.45/9.27	   A^2 -> H(f(k), U1(k, b))
28.45/9.27	   A^2 -> H(f(k), U1(c, d))
28.45/9.27	   A^2 -> H(f(k), U1(d, c))
28.45/9.27	   A^2 -> H(f(k), U1(b, e))
28.45/9.27	   A^2 -> H(f(k), U1(b, k))
28.45/9.27	   A^2 -> H(f(k), U1(e, c))
28.45/9.27	   A^2 -> H(f(k), U1(k, c))
28.45/9.27	   A^2 -> H(f(k), U1(c, e))
28.45/9.27	   A^2 -> H(f(k), U1(c, k))
28.45/9.27	   A^2 -> H(f(k), U1(e, e))
28.45/9.27	   A^2 -> H(f(k), U1(k, d))
28.45/9.27	   A^2 -> H(f(k), U1(d, k))
28.45/9.27	   A^2 -> H(f(c), b)
28.45/9.27	   A^2 -> H(f(c), U1(e, d))
28.45/9.27	   A^2 -> H(f(c), U1(d, e))
28.45/9.27	   A^2 -> H(f(k), U1(k, k))
28.45/9.27	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.27	   A^2 -> H(U1(k, k), f(c))
28.45/9.27	   A^2 -> H(U1(k, k), f(d))
28.45/9.27	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.27	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.27	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.27	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.27	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.27	   A^2 -> H(U1(k, d), f(e))
28.45/9.27	   A^2 -> H(U1(k, d), f(k))
28.45/9.27	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.27	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.27	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.27	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.27	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.27	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.27	   A^2 -> H(U1(d, k), f(e))
28.45/9.27	   A^2 -> H(U1(d, k), f(k))
28.45/9.27	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.27	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.27	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.27	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.27	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.27	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.27	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.27	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.27	   A^2 -> H(f(d), b)
28.45/9.27	   A^2 -> H(f(d), U1(e, d))
28.45/9.27	   A^2 -> H(f(d), U1(d, e))
28.45/9.27	   A^2 -> H(f(d), c)
28.45/9.27	   A^2 -> H(f(d), U1(e, k))
28.45/9.27	   A^2 -> H(f(d), U1(k, e))
28.45/9.27	   A^2 -> H(f(d), e)
28.45/9.27	   A^2 -> H(f(a), d)
28.45/9.27	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.27	   A^2 -> H(f(c), c)
28.45/9.27	   A^2 -> H(f(c), U1(e, k))
28.45/9.27	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.27	   A^2 -> H(f(c), U1(k, e))
28.45/9.27	   A^2 -> H(f(c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.27	   A^2 -> H(f(a), k)
28.45/9.27	   A^2 -> H(f(e), U1(e, e))
28.45/9.27	   A^2 -> H(f(c), e)
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.27	   A^2 -> H(f(d), U1(k, k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.27	   A^2 -> H(d, U1(b, b))
28.45/9.27	   A^2 -> H(d, f(c))
28.45/9.27	   A^2 -> H(d, f(d))
28.45/9.27	   A^2 -> H(a, U1(c, b))
28.45/9.27	   A^2 -> H(a, U1(d, b))
28.45/9.27	   A^2 -> H(a, U1(b, c))
28.45/9.27	   A^2 -> H(a, U1(b, d))
28.45/9.27	   A^2 -> H(a, U1(c, c))
28.45/9.27	   A^2 -> H(a, f(e))
28.45/9.27	   A^2 -> H(a, f(k))
28.45/9.27	   A^2 -> H(a, U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.27	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.27	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.27	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.27	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.27	   A^2 -> H(U1(e, d), f(e))
28.45/9.27	   A^2 -> H(U1(e, d), f(k))
28.45/9.27	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.27	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.27	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.27	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.27	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.27	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.27	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.27	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.27	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.27	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.27	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.27	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.27	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.27	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.27	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.27	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.27	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.27	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.27	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.27	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.27	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.27	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.27	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, a), b)
28.45/9.27	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.27	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.27	   A^2 -> H(U1(c, a), c)
28.45/9.27	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.27	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.27	   A^2 -> H(U1(c, a), e)
28.45/9.27	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.27	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.27	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.27	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.27	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.27	   A^2 -> H(U1(d, e), f(e))
28.45/9.27	   A^2 -> H(U1(d, e), f(k))
28.45/9.27	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.27	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.27	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.27	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.27	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.27	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.27	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.27	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.27	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.27	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.27	   A^2 -> H(U1(d, a), b)
28.45/9.27	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.27	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.27	   A^2 -> H(U1(d, a), c)
28.45/9.27	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.27	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.27	   A^2 -> H(U1(d, a), e)
28.45/9.27	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.27	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.27	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.27	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.27	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.27	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.27	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.27	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.27	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.27	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.27	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.27	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.27	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.27	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.27	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.27	   A^2 -> H(U1(a, c), b)
28.45/9.27	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.27	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.27	   A^2 -> H(U1(a, c), c)
28.45/9.27	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.27	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.27	   A^2 -> H(U1(a, c), e)
28.45/9.27	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, d), b)
28.45/9.27	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.27	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.27	   A^2 -> H(U1(a, d), c)
28.45/9.27	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.27	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.27	   A^2 -> H(U1(a, d), e)
28.45/9.27	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, a), d)
28.45/9.27	   A^2 -> H(U1(a, a), k)
28.45/9.27	   A^2 -> H(k, U1(b, b))
28.45/9.27	   A^2 -> H(k, f(c))
28.45/9.27	   A^2 -> H(k, f(d))
28.45/9.27	   A^2 -> H(c, U1(c, b))
28.45/9.27	   A^2 -> H(c, U1(d, b))
28.45/9.27	   A^2 -> H(c, U1(b, c))
28.45/9.27	   A^2 -> H(c, U1(b, d))
28.45/9.27	   A^2 -> H(c, U1(c, c))
28.45/9.27	   A^2 -> H(c, f(e))
28.45/9.27	   A^2 -> H(c, f(k))
28.45/9.27	   A^2 -> H(c, U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.27	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.27	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.27	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.27	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.27	   A^2 -> H(U1(e, k), f(e))
28.45/9.27	   A^2 -> H(U1(e, k), f(k))
28.45/9.27	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.27	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.27	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.27	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.27	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.27	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.27	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.27	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.27	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.27	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.27	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.27	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.27	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.27	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.27	   A^2 -> H(U1(k, e), f(e))
28.45/9.27	   A^2 -> H(U1(k, e), f(k))
28.45/9.27	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.27	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.27	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.27	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.27	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.27	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.27	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.27	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.27	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.27	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.27	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.27	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.27	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.27	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.27	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.27	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.27	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.27	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.27	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.27	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.27	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.27	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, c), b)
28.45/9.27	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.27	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.27	   A^2 -> H(U1(c, c), e)
28.45/9.27	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.27	
28.45/9.27	The TRS R consists of the following rules:
28.45/9.27	
28.45/9.27	   f(x) -> U1(x, x)
28.45/9.27	   U1(e, x) -> x
28.45/9.27	   a -> c
28.45/9.27	   a -> d
28.45/9.27	   b -> c
28.45/9.27	   b -> d
28.45/9.27	   d -> k
28.45/9.27	   c -> e
28.45/9.27	   c -> k
28.45/9.27	
28.45/9.27	Q is empty.
28.45/9.27	We have to consider all minimal (P,Q,R)-chains.
28.45/9.27	----------------------------------------
28.45/9.27	
28.45/9.27	(889) TransformationProof (EQUIVALENT)
28.45/9.27	By narrowing [LPAR04] the rule A^2 -> H(e, U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.27	
28.45/9.27	   (A^2 -> H(e, U1(c, b)),A^2 -> H(e, U1(c, b)))
28.45/9.27	   (A^2 -> H(e, U1(d, b)),A^2 -> H(e, U1(d, b)))
28.45/9.27	   (A^2 -> H(e, U1(b, c)),A^2 -> H(e, U1(b, c)))
28.45/9.27	   (A^2 -> H(e, U1(b, d)),A^2 -> H(e, U1(b, d)))
28.45/9.27	
28.45/9.27	
28.45/9.27	----------------------------------------
28.45/9.27	
28.45/9.27	(890)
28.45/9.27	Obligation:
28.45/9.27	Q DP problem:
28.45/9.27	The TRS P consists of the following rules:
28.45/9.27	
28.45/9.27	   H(x, x) -> G(x, x, f(k))
28.45/9.27	   G(d, x, x) -> A^2
28.45/9.27	   A^2 -> H(f(c), f(c))
28.45/9.27	   A^2 -> H(f(d), f(d))
28.45/9.27	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.27	   A^2 -> H(f(e), f(e))
28.45/9.27	   A^2 -> H(f(k), f(k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.27	   A^2 -> H(e, f(c))
28.45/9.27	   A^2 -> H(e, f(d))
28.45/9.27	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.27	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.27	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.27	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.27	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.27	   A^2 -> H(U1(e, e), f(e))
28.45/9.27	   A^2 -> H(U1(e, e), f(k))
28.45/9.27	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.27	   A^2 -> H(f(e), U1(e, b))
28.45/9.27	   A^2 -> H(f(e), U1(k, b))
28.45/9.27	   A^2 -> H(f(e), U1(c, d))
28.45/9.27	   A^2 -> H(f(e), U1(d, c))
28.45/9.27	   A^2 -> H(f(e), U1(b, e))
28.45/9.27	   A^2 -> H(f(e), U1(b, k))
28.45/9.27	   A^2 -> H(f(e), U1(e, c))
28.45/9.27	   A^2 -> H(f(e), U1(k, c))
28.45/9.27	   A^2 -> H(f(e), U1(c, e))
28.45/9.27	   A^2 -> H(f(e), U1(c, k))
28.45/9.27	   A^2 -> H(f(e), U1(k, k))
28.45/9.27	   A^2 -> H(f(e), U1(k, d))
28.45/9.27	   A^2 -> H(f(e), U1(d, k))
28.45/9.27	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.27	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.27	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.27	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.27	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.27	   A^2 -> H(U1(k, k), f(e))
28.45/9.27	   A^2 -> H(U1(k, k), f(k))
28.45/9.27	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.27	   A^2 -> H(f(k), U1(e, b))
28.45/9.27	   A^2 -> H(f(k), U1(k, b))
28.45/9.27	   A^2 -> H(f(k), U1(c, d))
28.45/9.27	   A^2 -> H(f(k), U1(d, c))
28.45/9.27	   A^2 -> H(f(k), U1(b, e))
28.45/9.27	   A^2 -> H(f(k), U1(b, k))
28.45/9.27	   A^2 -> H(f(k), U1(e, c))
28.45/9.27	   A^2 -> H(f(k), U1(k, c))
28.45/9.27	   A^2 -> H(f(k), U1(c, e))
28.45/9.27	   A^2 -> H(f(k), U1(c, k))
28.45/9.27	   A^2 -> H(f(k), U1(e, e))
28.45/9.27	   A^2 -> H(f(k), U1(k, d))
28.45/9.27	   A^2 -> H(f(k), U1(d, k))
28.45/9.27	   A^2 -> H(f(c), b)
28.45/9.27	   A^2 -> H(f(c), U1(e, d))
28.45/9.27	   A^2 -> H(f(c), U1(d, e))
28.45/9.27	   A^2 -> H(f(k), U1(k, k))
28.45/9.27	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.27	   A^2 -> H(U1(k, k), f(c))
28.45/9.27	   A^2 -> H(U1(k, k), f(d))
28.45/9.27	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.27	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.27	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.27	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.27	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.27	   A^2 -> H(U1(k, d), f(e))
28.45/9.27	   A^2 -> H(U1(k, d), f(k))
28.45/9.27	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.27	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.27	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.27	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.27	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.27	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.27	   A^2 -> H(U1(d, k), f(e))
28.45/9.27	   A^2 -> H(U1(d, k), f(k))
28.45/9.27	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.27	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.27	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.27	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.27	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.27	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.27	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.27	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.27	   A^2 -> H(f(d), b)
28.45/9.27	   A^2 -> H(f(d), U1(e, d))
28.45/9.27	   A^2 -> H(f(d), U1(d, e))
28.45/9.27	   A^2 -> H(f(d), c)
28.45/9.27	   A^2 -> H(f(d), U1(e, k))
28.45/9.27	   A^2 -> H(f(d), U1(k, e))
28.45/9.27	   A^2 -> H(f(d), e)
28.45/9.27	   A^2 -> H(f(a), d)
28.45/9.27	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.27	   A^2 -> H(f(c), c)
28.45/9.27	   A^2 -> H(f(c), U1(e, k))
28.45/9.27	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.27	   A^2 -> H(f(c), U1(k, e))
28.45/9.27	   A^2 -> H(f(c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.27	   A^2 -> H(f(a), k)
28.45/9.27	   A^2 -> H(f(e), U1(e, e))
28.45/9.27	   A^2 -> H(f(c), e)
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.27	   A^2 -> H(f(d), U1(k, k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.27	   A^2 -> H(d, U1(b, b))
28.45/9.27	   A^2 -> H(d, f(c))
28.45/9.27	   A^2 -> H(d, f(d))
28.45/9.27	   A^2 -> H(a, U1(c, b))
28.45/9.27	   A^2 -> H(a, U1(d, b))
28.45/9.27	   A^2 -> H(a, U1(b, c))
28.45/9.27	   A^2 -> H(a, U1(b, d))
28.45/9.27	   A^2 -> H(a, U1(c, c))
28.45/9.27	   A^2 -> H(a, f(e))
28.45/9.27	   A^2 -> H(a, f(k))
28.45/9.27	   A^2 -> H(a, U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.27	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.27	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.27	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.27	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.27	   A^2 -> H(U1(e, d), f(e))
28.45/9.27	   A^2 -> H(U1(e, d), f(k))
28.45/9.27	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.27	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.27	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.27	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.27	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.27	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.27	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.27	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.27	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.27	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.27	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.27	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.27	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.27	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.27	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.27	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.27	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.27	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.27	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.27	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.27	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.27	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.27	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, a), b)
28.45/9.27	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.27	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.27	   A^2 -> H(U1(c, a), c)
28.45/9.27	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.27	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.27	   A^2 -> H(U1(c, a), e)
28.45/9.27	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.27	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.27	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.27	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.27	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.27	   A^2 -> H(U1(d, e), f(e))
28.45/9.27	   A^2 -> H(U1(d, e), f(k))
28.45/9.27	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.27	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.27	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.27	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.27	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.27	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.27	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.27	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.27	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.27	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.27	   A^2 -> H(U1(d, a), b)
28.45/9.27	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.27	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.27	   A^2 -> H(U1(d, a), c)
28.45/9.27	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.27	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.27	   A^2 -> H(U1(d, a), e)
28.45/9.27	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.27	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.27	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.27	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.27	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.27	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.27	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.27	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.27	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.27	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.27	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.27	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.27	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.27	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.27	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.27	   A^2 -> H(U1(a, c), b)
28.45/9.27	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.27	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.27	   A^2 -> H(U1(a, c), c)
28.45/9.27	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.27	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.27	   A^2 -> H(U1(a, c), e)
28.45/9.27	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, d), b)
28.45/9.27	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.27	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.27	   A^2 -> H(U1(a, d), c)
28.45/9.27	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.27	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.27	   A^2 -> H(U1(a, d), e)
28.45/9.27	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, a), d)
28.45/9.27	   A^2 -> H(U1(a, a), k)
28.45/9.27	   A^2 -> H(k, U1(b, b))
28.45/9.27	   A^2 -> H(k, f(c))
28.45/9.27	   A^2 -> H(k, f(d))
28.45/9.27	   A^2 -> H(c, U1(c, b))
28.45/9.27	   A^2 -> H(c, U1(d, b))
28.45/9.27	   A^2 -> H(c, U1(b, c))
28.45/9.27	   A^2 -> H(c, U1(b, d))
28.45/9.27	   A^2 -> H(c, U1(c, c))
28.45/9.27	   A^2 -> H(c, f(e))
28.45/9.27	   A^2 -> H(c, f(k))
28.45/9.27	   A^2 -> H(c, U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.27	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.27	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.27	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.27	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.27	   A^2 -> H(U1(e, k), f(e))
28.45/9.27	   A^2 -> H(U1(e, k), f(k))
28.45/9.27	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.27	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.27	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.27	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.27	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.27	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.27	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.27	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.27	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.27	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.27	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.27	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.27	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.27	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.27	   A^2 -> H(U1(k, e), f(e))
28.45/9.27	   A^2 -> H(U1(k, e), f(k))
28.45/9.27	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.27	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.27	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.27	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.27	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.27	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.27	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.27	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.27	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.27	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.27	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.27	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.27	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.27	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.27	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.27	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.27	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.27	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.27	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.27	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.27	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.27	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, c), b)
28.45/9.27	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.27	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.27	   A^2 -> H(U1(c, c), e)
28.45/9.27	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.27	   A^2 -> H(e, U1(c, b))
28.45/9.27	   A^2 -> H(e, U1(d, b))
28.45/9.27	   A^2 -> H(e, U1(b, c))
28.45/9.27	   A^2 -> H(e, U1(b, d))
28.45/9.27	
28.45/9.27	The TRS R consists of the following rules:
28.45/9.27	
28.45/9.27	   f(x) -> U1(x, x)
28.45/9.27	   U1(e, x) -> x
28.45/9.27	   a -> c
28.45/9.27	   a -> d
28.45/9.27	   b -> c
28.45/9.27	   b -> d
28.45/9.27	   d -> k
28.45/9.27	   c -> e
28.45/9.27	   c -> k
28.45/9.27	
28.45/9.27	Q is empty.
28.45/9.27	We have to consider all minimal (P,Q,R)-chains.
28.45/9.27	----------------------------------------
28.45/9.27	
28.45/9.27	(891) TransformationProof (EQUIVALENT)
28.45/9.27	By narrowing [LPAR04] the rule A^2 -> H(e, f(c)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.27	
28.45/9.27	   (A^2 -> H(e, U1(c, c)),A^2 -> H(e, U1(c, c)))
28.45/9.27	   (A^2 -> H(e, f(e)),A^2 -> H(e, f(e)))
28.45/9.27	   (A^2 -> H(e, f(k)),A^2 -> H(e, f(k)))
28.45/9.27	
28.45/9.27	
28.45/9.27	----------------------------------------
28.45/9.27	
28.45/9.27	(892)
28.45/9.27	Obligation:
28.45/9.27	Q DP problem:
28.45/9.27	The TRS P consists of the following rules:
28.45/9.27	
28.45/9.27	   H(x, x) -> G(x, x, f(k))
28.45/9.27	   G(d, x, x) -> A^2
28.45/9.27	   A^2 -> H(f(c), f(c))
28.45/9.27	   A^2 -> H(f(d), f(d))
28.45/9.27	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.27	   A^2 -> H(f(e), f(e))
28.45/9.27	   A^2 -> H(f(k), f(k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.27	   A^2 -> H(e, f(d))
28.45/9.27	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.27	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.27	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.27	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.27	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.27	   A^2 -> H(U1(e, e), f(e))
28.45/9.27	   A^2 -> H(U1(e, e), f(k))
28.45/9.27	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.27	   A^2 -> H(f(e), U1(e, b))
28.45/9.27	   A^2 -> H(f(e), U1(k, b))
28.45/9.27	   A^2 -> H(f(e), U1(c, d))
28.45/9.27	   A^2 -> H(f(e), U1(d, c))
28.45/9.27	   A^2 -> H(f(e), U1(b, e))
28.45/9.27	   A^2 -> H(f(e), U1(b, k))
28.45/9.27	   A^2 -> H(f(e), U1(e, c))
28.45/9.27	   A^2 -> H(f(e), U1(k, c))
28.45/9.27	   A^2 -> H(f(e), U1(c, e))
28.45/9.27	   A^2 -> H(f(e), U1(c, k))
28.45/9.27	   A^2 -> H(f(e), U1(k, k))
28.45/9.27	   A^2 -> H(f(e), U1(k, d))
28.45/9.27	   A^2 -> H(f(e), U1(d, k))
28.45/9.27	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.27	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.27	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.27	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.27	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.27	   A^2 -> H(U1(k, k), f(e))
28.45/9.27	   A^2 -> H(U1(k, k), f(k))
28.45/9.27	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.27	   A^2 -> H(f(k), U1(e, b))
28.45/9.27	   A^2 -> H(f(k), U1(k, b))
28.45/9.27	   A^2 -> H(f(k), U1(c, d))
28.45/9.27	   A^2 -> H(f(k), U1(d, c))
28.45/9.27	   A^2 -> H(f(k), U1(b, e))
28.45/9.27	   A^2 -> H(f(k), U1(b, k))
28.45/9.27	   A^2 -> H(f(k), U1(e, c))
28.45/9.27	   A^2 -> H(f(k), U1(k, c))
28.45/9.27	   A^2 -> H(f(k), U1(c, e))
28.45/9.27	   A^2 -> H(f(k), U1(c, k))
28.45/9.27	   A^2 -> H(f(k), U1(e, e))
28.45/9.27	   A^2 -> H(f(k), U1(k, d))
28.45/9.27	   A^2 -> H(f(k), U1(d, k))
28.45/9.27	   A^2 -> H(f(c), b)
28.45/9.27	   A^2 -> H(f(c), U1(e, d))
28.45/9.27	   A^2 -> H(f(c), U1(d, e))
28.45/9.27	   A^2 -> H(f(k), U1(k, k))
28.45/9.27	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.27	   A^2 -> H(U1(k, k), f(c))
28.45/9.27	   A^2 -> H(U1(k, k), f(d))
28.45/9.27	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.27	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.27	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.27	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.27	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.27	   A^2 -> H(U1(k, d), f(e))
28.45/9.27	   A^2 -> H(U1(k, d), f(k))
28.45/9.27	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.27	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.27	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.27	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.27	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.27	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.27	   A^2 -> H(U1(d, k), f(e))
28.45/9.27	   A^2 -> H(U1(d, k), f(k))
28.45/9.27	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.27	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.27	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.27	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.27	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.27	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.27	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.27	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.27	   A^2 -> H(f(d), b)
28.45/9.27	   A^2 -> H(f(d), U1(e, d))
28.45/9.27	   A^2 -> H(f(d), U1(d, e))
28.45/9.27	   A^2 -> H(f(d), c)
28.45/9.27	   A^2 -> H(f(d), U1(e, k))
28.45/9.27	   A^2 -> H(f(d), U1(k, e))
28.45/9.27	   A^2 -> H(f(d), e)
28.45/9.27	   A^2 -> H(f(a), d)
28.45/9.27	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.27	   A^2 -> H(f(c), c)
28.45/9.27	   A^2 -> H(f(c), U1(e, k))
28.45/9.27	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.27	   A^2 -> H(f(c), U1(k, e))
28.45/9.27	   A^2 -> H(f(c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.27	   A^2 -> H(f(a), k)
28.45/9.27	   A^2 -> H(f(e), U1(e, e))
28.45/9.27	   A^2 -> H(f(c), e)
28.45/9.27	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.27	   A^2 -> H(f(d), U1(k, k))
28.45/9.27	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.27	   A^2 -> H(d, U1(b, b))
28.45/9.27	   A^2 -> H(d, f(c))
28.45/9.27	   A^2 -> H(d, f(d))
28.45/9.27	   A^2 -> H(a, U1(c, b))
28.45/9.27	   A^2 -> H(a, U1(d, b))
28.45/9.27	   A^2 -> H(a, U1(b, c))
28.45/9.27	   A^2 -> H(a, U1(b, d))
28.45/9.27	   A^2 -> H(a, U1(c, c))
28.45/9.27	   A^2 -> H(a, f(e))
28.45/9.27	   A^2 -> H(a, f(k))
28.45/9.27	   A^2 -> H(a, U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.27	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.27	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.27	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.27	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.27	   A^2 -> H(U1(e, d), f(e))
28.45/9.27	   A^2 -> H(U1(e, d), f(k))
28.45/9.27	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.27	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.27	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.27	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.27	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.27	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.27	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.27	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.27	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.27	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.27	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.27	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.27	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.27	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.27	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.27	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.27	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.27	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.27	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.27	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.27	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.27	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.27	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.27	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.27	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.27	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.27	   A^2 -> H(U1(c, a), b)
28.45/9.27	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.27	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.27	   A^2 -> H(U1(c, a), c)
28.45/9.27	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.27	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.27	   A^2 -> H(U1(c, a), e)
28.45/9.27	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.27	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.27	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.27	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.27	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.27	   A^2 -> H(U1(d, e), f(e))
28.45/9.27	   A^2 -> H(U1(d, e), f(k))
28.45/9.27	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.27	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.27	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.27	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.27	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.27	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.27	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.27	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.27	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.27	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.27	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.27	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.27	   A^2 -> H(U1(d, a), b)
28.45/9.27	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.27	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.27	   A^2 -> H(U1(d, a), c)
28.45/9.27	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.27	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.27	   A^2 -> H(U1(d, a), e)
28.45/9.27	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.27	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.27	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.27	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.27	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.27	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.27	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.27	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.27	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.27	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.27	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.27	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.27	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.27	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.27	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.27	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.27	   A^2 -> H(U1(a, c), b)
28.45/9.27	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.27	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.27	   A^2 -> H(U1(a, c), c)
28.45/9.27	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.27	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.27	   A^2 -> H(U1(a, c), e)
28.45/9.28	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, d), b)
28.45/9.28	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.28	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.28	   A^2 -> H(U1(a, d), c)
28.45/9.28	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.28	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.28	   A^2 -> H(U1(a, d), e)
28.45/9.28	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, a), d)
28.45/9.28	   A^2 -> H(U1(a, a), k)
28.45/9.28	   A^2 -> H(k, U1(b, b))
28.45/9.28	   A^2 -> H(k, f(c))
28.45/9.28	   A^2 -> H(k, f(d))
28.45/9.28	   A^2 -> H(c, U1(c, b))
28.45/9.28	   A^2 -> H(c, U1(d, b))
28.45/9.28	   A^2 -> H(c, U1(b, c))
28.45/9.28	   A^2 -> H(c, U1(b, d))
28.45/9.28	   A^2 -> H(c, U1(c, c))
28.45/9.28	   A^2 -> H(c, f(e))
28.45/9.28	   A^2 -> H(c, f(k))
28.45/9.28	   A^2 -> H(c, U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.28	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.28	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.28	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.28	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.28	   A^2 -> H(U1(e, k), f(e))
28.45/9.28	   A^2 -> H(U1(e, k), f(k))
28.45/9.28	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.28	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.28	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.28	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.28	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.28	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.28	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.28	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.28	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.28	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.28	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.28	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.28	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.28	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.28	   A^2 -> H(U1(k, e), f(e))
28.45/9.28	   A^2 -> H(U1(k, e), f(k))
28.45/9.28	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.28	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.28	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.28	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.28	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.28	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.28	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.28	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.28	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.28	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.28	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.28	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.28	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.28	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.28	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.28	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.28	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.28	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.28	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.28	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.28	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.28	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, c), b)
28.45/9.28	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.28	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.28	   A^2 -> H(U1(c, c), e)
28.45/9.28	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.28	   A^2 -> H(e, U1(c, b))
28.45/9.28	   A^2 -> H(e, U1(d, b))
28.45/9.28	   A^2 -> H(e, U1(b, c))
28.45/9.28	   A^2 -> H(e, U1(b, d))
28.45/9.28	   A^2 -> H(e, U1(c, c))
28.45/9.28	   A^2 -> H(e, f(e))
28.45/9.28	   A^2 -> H(e, f(k))
28.45/9.28	
28.45/9.28	The TRS R consists of the following rules:
28.45/9.28	
28.45/9.28	   f(x) -> U1(x, x)
28.45/9.28	   U1(e, x) -> x
28.45/9.28	   a -> c
28.45/9.28	   a -> d
28.45/9.28	   b -> c
28.45/9.28	   b -> d
28.45/9.28	   d -> k
28.45/9.28	   c -> e
28.45/9.28	   c -> k
28.45/9.28	
28.45/9.28	Q is empty.
28.45/9.28	We have to consider all minimal (P,Q,R)-chains.
28.45/9.28	----------------------------------------
28.45/9.28	
28.45/9.28	(893) TransformationProof (EQUIVALENT)
28.45/9.28	By narrowing [LPAR04] the rule A^2 -> H(e, f(d)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.28	
28.45/9.28	   (A^2 -> H(e, U1(d, d)),A^2 -> H(e, U1(d, d)))
28.45/9.28	   (A^2 -> H(e, f(k)),A^2 -> H(e, f(k)))
28.45/9.28	
28.45/9.28	
28.45/9.28	----------------------------------------
28.45/9.28	
28.45/9.28	(894)
28.45/9.28	Obligation:
28.45/9.28	Q DP problem:
28.45/9.28	The TRS P consists of the following rules:
28.45/9.28	
28.45/9.28	   H(x, x) -> G(x, x, f(k))
28.45/9.28	   G(d, x, x) -> A^2
28.45/9.28	   A^2 -> H(f(c), f(c))
28.45/9.28	   A^2 -> H(f(d), f(d))
28.45/9.28	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.28	   A^2 -> H(f(e), f(e))
28.45/9.28	   A^2 -> H(f(k), f(k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, e), U1(c, b))
28.45/9.28	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.28	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.28	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.28	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.28	   A^2 -> H(U1(e, e), f(e))
28.45/9.28	   A^2 -> H(U1(e, e), f(k))
28.45/9.28	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.28	   A^2 -> H(f(e), U1(e, b))
28.45/9.28	   A^2 -> H(f(e), U1(k, b))
28.45/9.28	   A^2 -> H(f(e), U1(c, d))
28.45/9.28	   A^2 -> H(f(e), U1(d, c))
28.45/9.28	   A^2 -> H(f(e), U1(b, e))
28.45/9.28	   A^2 -> H(f(e), U1(b, k))
28.45/9.28	   A^2 -> H(f(e), U1(e, c))
28.45/9.28	   A^2 -> H(f(e), U1(k, c))
28.45/9.28	   A^2 -> H(f(e), U1(c, e))
28.45/9.28	   A^2 -> H(f(e), U1(c, k))
28.45/9.28	   A^2 -> H(f(e), U1(k, k))
28.45/9.28	   A^2 -> H(f(e), U1(k, d))
28.45/9.28	   A^2 -> H(f(e), U1(d, k))
28.45/9.28	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.28	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.28	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.28	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.28	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.28	   A^2 -> H(U1(k, k), f(e))
28.45/9.28	   A^2 -> H(U1(k, k), f(k))
28.45/9.28	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.28	   A^2 -> H(f(k), U1(e, b))
28.45/9.28	   A^2 -> H(f(k), U1(k, b))
28.45/9.28	   A^2 -> H(f(k), U1(c, d))
28.45/9.28	   A^2 -> H(f(k), U1(d, c))
28.45/9.28	   A^2 -> H(f(k), U1(b, e))
28.45/9.28	   A^2 -> H(f(k), U1(b, k))
28.45/9.28	   A^2 -> H(f(k), U1(e, c))
28.45/9.28	   A^2 -> H(f(k), U1(k, c))
28.45/9.28	   A^2 -> H(f(k), U1(c, e))
28.45/9.28	   A^2 -> H(f(k), U1(c, k))
28.45/9.28	   A^2 -> H(f(k), U1(e, e))
28.45/9.28	   A^2 -> H(f(k), U1(k, d))
28.45/9.28	   A^2 -> H(f(k), U1(d, k))
28.45/9.28	   A^2 -> H(f(c), b)
28.45/9.28	   A^2 -> H(f(c), U1(e, d))
28.45/9.28	   A^2 -> H(f(c), U1(d, e))
28.45/9.28	   A^2 -> H(f(k), U1(k, k))
28.45/9.28	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.28	   A^2 -> H(U1(k, k), f(c))
28.45/9.28	   A^2 -> H(U1(k, k), f(d))
28.45/9.28	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.28	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.28	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.28	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.28	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.28	   A^2 -> H(U1(k, d), f(e))
28.45/9.28	   A^2 -> H(U1(k, d), f(k))
28.45/9.28	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.28	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.28	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.28	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.28	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.28	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.28	   A^2 -> H(U1(d, k), f(e))
28.45/9.28	   A^2 -> H(U1(d, k), f(k))
28.45/9.28	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.28	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.28	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.28	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.28	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.28	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.28	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.28	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.28	   A^2 -> H(f(d), b)
28.45/9.28	   A^2 -> H(f(d), U1(e, d))
28.45/9.28	   A^2 -> H(f(d), U1(d, e))
28.45/9.28	   A^2 -> H(f(d), c)
28.45/9.28	   A^2 -> H(f(d), U1(e, k))
28.45/9.28	   A^2 -> H(f(d), U1(k, e))
28.45/9.28	   A^2 -> H(f(d), e)
28.45/9.28	   A^2 -> H(f(a), d)
28.45/9.28	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.28	   A^2 -> H(f(c), c)
28.45/9.28	   A^2 -> H(f(c), U1(e, k))
28.45/9.28	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.28	   A^2 -> H(f(c), U1(k, e))
28.45/9.28	   A^2 -> H(f(c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.28	   A^2 -> H(f(a), k)
28.45/9.28	   A^2 -> H(f(e), U1(e, e))
28.45/9.28	   A^2 -> H(f(c), e)
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.28	   A^2 -> H(f(d), U1(k, k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.28	   A^2 -> H(d, U1(b, b))
28.45/9.28	   A^2 -> H(d, f(c))
28.45/9.28	   A^2 -> H(d, f(d))
28.45/9.28	   A^2 -> H(a, U1(c, b))
28.45/9.28	   A^2 -> H(a, U1(d, b))
28.45/9.28	   A^2 -> H(a, U1(b, c))
28.45/9.28	   A^2 -> H(a, U1(b, d))
28.45/9.28	   A^2 -> H(a, U1(c, c))
28.45/9.28	   A^2 -> H(a, f(e))
28.45/9.28	   A^2 -> H(a, f(k))
28.45/9.28	   A^2 -> H(a, U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.28	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.28	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.28	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.28	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.28	   A^2 -> H(U1(e, d), f(e))
28.45/9.28	   A^2 -> H(U1(e, d), f(k))
28.45/9.28	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.28	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.28	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.28	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.28	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.28	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.28	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.28	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.28	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.28	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.28	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.28	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.28	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.28	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.28	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.28	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.28	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.28	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.28	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.28	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.28	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.28	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.28	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, a), b)
28.45/9.28	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.28	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.28	   A^2 -> H(U1(c, a), c)
28.45/9.28	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.28	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.28	   A^2 -> H(U1(c, a), e)
28.45/9.28	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.28	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.28	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.28	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.28	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.28	   A^2 -> H(U1(d, e), f(e))
28.45/9.28	   A^2 -> H(U1(d, e), f(k))
28.45/9.28	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.28	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.28	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.28	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.28	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.28	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.28	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.28	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.28	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.28	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.28	   A^2 -> H(U1(d, a), b)
28.45/9.28	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.28	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.28	   A^2 -> H(U1(d, a), c)
28.45/9.28	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.28	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.28	   A^2 -> H(U1(d, a), e)
28.45/9.28	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.28	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.28	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.28	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.28	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.28	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.28	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.28	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.28	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.28	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.28	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.28	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.28	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.28	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.28	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.28	   A^2 -> H(U1(a, c), b)
28.45/9.28	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.28	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.28	   A^2 -> H(U1(a, c), c)
28.45/9.28	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.28	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.28	   A^2 -> H(U1(a, c), e)
28.45/9.28	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, d), b)
28.45/9.28	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.28	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.28	   A^2 -> H(U1(a, d), c)
28.45/9.28	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.28	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.28	   A^2 -> H(U1(a, d), e)
28.45/9.28	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, a), d)
28.45/9.28	   A^2 -> H(U1(a, a), k)
28.45/9.28	   A^2 -> H(k, U1(b, b))
28.45/9.28	   A^2 -> H(k, f(c))
28.45/9.28	   A^2 -> H(k, f(d))
28.45/9.28	   A^2 -> H(c, U1(c, b))
28.45/9.28	   A^2 -> H(c, U1(d, b))
28.45/9.28	   A^2 -> H(c, U1(b, c))
28.45/9.28	   A^2 -> H(c, U1(b, d))
28.45/9.28	   A^2 -> H(c, U1(c, c))
28.45/9.28	   A^2 -> H(c, f(e))
28.45/9.28	   A^2 -> H(c, f(k))
28.45/9.28	   A^2 -> H(c, U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.28	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.28	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.28	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.28	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.28	   A^2 -> H(U1(e, k), f(e))
28.45/9.28	   A^2 -> H(U1(e, k), f(k))
28.45/9.28	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.28	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.28	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.28	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.28	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.28	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.28	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.28	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.28	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.28	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.28	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.28	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.28	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.28	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.28	   A^2 -> H(U1(k, e), f(e))
28.45/9.28	   A^2 -> H(U1(k, e), f(k))
28.45/9.28	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.28	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.28	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.28	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.28	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.28	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.28	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.28	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.28	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.28	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.28	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.28	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.28	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.28	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.28	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.28	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.28	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.28	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.28	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.28	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.28	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.28	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, c), b)
28.45/9.28	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.28	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.28	   A^2 -> H(U1(c, c), e)
28.45/9.28	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.28	   A^2 -> H(e, U1(c, b))
28.45/9.28	   A^2 -> H(e, U1(d, b))
28.45/9.28	   A^2 -> H(e, U1(b, c))
28.45/9.28	   A^2 -> H(e, U1(b, d))
28.45/9.28	   A^2 -> H(e, U1(c, c))
28.45/9.28	   A^2 -> H(e, f(e))
28.45/9.28	   A^2 -> H(e, f(k))
28.45/9.28	   A^2 -> H(e, U1(d, d))
28.45/9.28	
28.45/9.28	The TRS R consists of the following rules:
28.45/9.28	
28.45/9.28	   f(x) -> U1(x, x)
28.45/9.28	   U1(e, x) -> x
28.45/9.28	   a -> c
28.45/9.28	   a -> d
28.45/9.28	   b -> c
28.45/9.28	   b -> d
28.45/9.28	   d -> k
28.45/9.28	   c -> e
28.45/9.28	   c -> k
28.45/9.28	
28.45/9.28	Q is empty.
28.45/9.28	We have to consider all minimal (P,Q,R)-chains.
28.45/9.28	----------------------------------------
28.45/9.28	
28.45/9.28	(895) TransformationProof (EQUIVALENT)
28.45/9.28	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.28	
28.45/9.28	   (A^2 -> H(e, U1(c, b)),A^2 -> H(e, U1(c, b)))
28.45/9.28	   (A^2 -> H(U1(e, e), U1(e, b)),A^2 -> H(U1(e, e), U1(e, b)))
28.45/9.28	   (A^2 -> H(U1(e, e), U1(k, b)),A^2 -> H(U1(e, e), U1(k, b)))
28.45/9.28	   (A^2 -> H(U1(e, e), U1(c, c)),A^2 -> H(U1(e, e), U1(c, c)))
28.45/9.28	   (A^2 -> H(U1(e, e), U1(c, d)),A^2 -> H(U1(e, e), U1(c, d)))
28.45/9.28	
28.45/9.28	
28.45/9.28	----------------------------------------
28.45/9.28	
28.45/9.28	(896)
28.45/9.28	Obligation:
28.45/9.28	Q DP problem:
28.45/9.28	The TRS P consists of the following rules:
28.45/9.28	
28.45/9.28	   H(x, x) -> G(x, x, f(k))
28.45/9.28	   G(d, x, x) -> A^2
28.45/9.28	   A^2 -> H(f(c), f(c))
28.45/9.28	   A^2 -> H(f(d), f(d))
28.45/9.28	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.28	   A^2 -> H(f(e), f(e))
28.45/9.28	   A^2 -> H(f(k), f(k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, e), U1(d, b))
28.45/9.28	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.28	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.28	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.28	   A^2 -> H(U1(e, e), f(e))
28.45/9.28	   A^2 -> H(U1(e, e), f(k))
28.45/9.28	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.28	   A^2 -> H(f(e), U1(e, b))
28.45/9.28	   A^2 -> H(f(e), U1(k, b))
28.45/9.28	   A^2 -> H(f(e), U1(c, d))
28.45/9.28	   A^2 -> H(f(e), U1(d, c))
28.45/9.28	   A^2 -> H(f(e), U1(b, e))
28.45/9.28	   A^2 -> H(f(e), U1(b, k))
28.45/9.28	   A^2 -> H(f(e), U1(e, c))
28.45/9.28	   A^2 -> H(f(e), U1(k, c))
28.45/9.28	   A^2 -> H(f(e), U1(c, e))
28.45/9.28	   A^2 -> H(f(e), U1(c, k))
28.45/9.28	   A^2 -> H(f(e), U1(k, k))
28.45/9.28	   A^2 -> H(f(e), U1(k, d))
28.45/9.28	   A^2 -> H(f(e), U1(d, k))
28.45/9.28	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.28	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.28	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.28	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.28	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.28	   A^2 -> H(U1(k, k), f(e))
28.45/9.28	   A^2 -> H(U1(k, k), f(k))
28.45/9.28	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.28	   A^2 -> H(f(k), U1(e, b))
28.45/9.28	   A^2 -> H(f(k), U1(k, b))
28.45/9.28	   A^2 -> H(f(k), U1(c, d))
28.45/9.28	   A^2 -> H(f(k), U1(d, c))
28.45/9.28	   A^2 -> H(f(k), U1(b, e))
28.45/9.28	   A^2 -> H(f(k), U1(b, k))
28.45/9.28	   A^2 -> H(f(k), U1(e, c))
28.45/9.28	   A^2 -> H(f(k), U1(k, c))
28.45/9.28	   A^2 -> H(f(k), U1(c, e))
28.45/9.28	   A^2 -> H(f(k), U1(c, k))
28.45/9.28	   A^2 -> H(f(k), U1(e, e))
28.45/9.28	   A^2 -> H(f(k), U1(k, d))
28.45/9.28	   A^2 -> H(f(k), U1(d, k))
28.45/9.28	   A^2 -> H(f(c), b)
28.45/9.28	   A^2 -> H(f(c), U1(e, d))
28.45/9.28	   A^2 -> H(f(c), U1(d, e))
28.45/9.28	   A^2 -> H(f(k), U1(k, k))
28.45/9.28	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.28	   A^2 -> H(U1(k, k), f(c))
28.45/9.28	   A^2 -> H(U1(k, k), f(d))
28.45/9.28	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.28	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.28	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.28	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.28	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.28	   A^2 -> H(U1(k, d), f(e))
28.45/9.28	   A^2 -> H(U1(k, d), f(k))
28.45/9.28	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.28	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.28	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.28	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.28	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.28	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.28	   A^2 -> H(U1(d, k), f(e))
28.45/9.28	   A^2 -> H(U1(d, k), f(k))
28.45/9.28	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.28	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.28	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.28	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.28	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.28	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.28	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.28	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.28	   A^2 -> H(f(d), b)
28.45/9.28	   A^2 -> H(f(d), U1(e, d))
28.45/9.28	   A^2 -> H(f(d), U1(d, e))
28.45/9.28	   A^2 -> H(f(d), c)
28.45/9.28	   A^2 -> H(f(d), U1(e, k))
28.45/9.28	   A^2 -> H(f(d), U1(k, e))
28.45/9.28	   A^2 -> H(f(d), e)
28.45/9.28	   A^2 -> H(f(a), d)
28.45/9.28	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.28	   A^2 -> H(f(c), c)
28.45/9.28	   A^2 -> H(f(c), U1(e, k))
28.45/9.28	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.28	   A^2 -> H(f(c), U1(k, e))
28.45/9.28	   A^2 -> H(f(c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.28	   A^2 -> H(f(a), k)
28.45/9.28	   A^2 -> H(f(e), U1(e, e))
28.45/9.28	   A^2 -> H(f(c), e)
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.28	   A^2 -> H(f(d), U1(k, k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.28	   A^2 -> H(d, U1(b, b))
28.45/9.28	   A^2 -> H(d, f(c))
28.45/9.28	   A^2 -> H(d, f(d))
28.45/9.28	   A^2 -> H(a, U1(c, b))
28.45/9.28	   A^2 -> H(a, U1(d, b))
28.45/9.28	   A^2 -> H(a, U1(b, c))
28.45/9.28	   A^2 -> H(a, U1(b, d))
28.45/9.28	   A^2 -> H(a, U1(c, c))
28.45/9.28	   A^2 -> H(a, f(e))
28.45/9.28	   A^2 -> H(a, f(k))
28.45/9.28	   A^2 -> H(a, U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.28	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.28	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.28	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.28	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.28	   A^2 -> H(U1(e, d), f(e))
28.45/9.28	   A^2 -> H(U1(e, d), f(k))
28.45/9.28	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.28	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.28	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.28	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.28	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.28	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.28	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.28	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.28	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.28	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.28	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.28	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.28	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.28	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.28	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.28	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.28	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.28	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.28	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.28	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.28	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.28	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.28	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, a), b)
28.45/9.28	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.28	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.28	   A^2 -> H(U1(c, a), c)
28.45/9.28	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.28	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.28	   A^2 -> H(U1(c, a), e)
28.45/9.28	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.28	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.28	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.28	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.28	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.28	   A^2 -> H(U1(d, e), f(e))
28.45/9.28	   A^2 -> H(U1(d, e), f(k))
28.45/9.28	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.28	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.28	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.28	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.28	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.28	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.28	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.28	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.28	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.28	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.28	   A^2 -> H(U1(d, a), b)
28.45/9.28	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.28	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.28	   A^2 -> H(U1(d, a), c)
28.45/9.28	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.28	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.28	   A^2 -> H(U1(d, a), e)
28.45/9.28	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.28	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.28	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.28	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.28	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.28	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.28	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.28	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.28	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.28	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.28	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.28	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.28	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.28	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.28	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.28	   A^2 -> H(U1(a, c), b)
28.45/9.28	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.28	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.28	   A^2 -> H(U1(a, c), c)
28.45/9.28	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.28	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.28	   A^2 -> H(U1(a, c), e)
28.45/9.28	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, d), b)
28.45/9.28	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.28	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.28	   A^2 -> H(U1(a, d), c)
28.45/9.28	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.28	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.28	   A^2 -> H(U1(a, d), e)
28.45/9.28	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, a), d)
28.45/9.28	   A^2 -> H(U1(a, a), k)
28.45/9.28	   A^2 -> H(k, U1(b, b))
28.45/9.28	   A^2 -> H(k, f(c))
28.45/9.28	   A^2 -> H(k, f(d))
28.45/9.28	   A^2 -> H(c, U1(c, b))
28.45/9.28	   A^2 -> H(c, U1(d, b))
28.45/9.28	   A^2 -> H(c, U1(b, c))
28.45/9.28	   A^2 -> H(c, U1(b, d))
28.45/9.28	   A^2 -> H(c, U1(c, c))
28.45/9.28	   A^2 -> H(c, f(e))
28.45/9.28	   A^2 -> H(c, f(k))
28.45/9.28	   A^2 -> H(c, U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.28	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.28	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.28	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.28	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.28	   A^2 -> H(U1(e, k), f(e))
28.45/9.28	   A^2 -> H(U1(e, k), f(k))
28.45/9.28	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.28	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.28	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.28	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.28	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.28	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.28	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.28	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.28	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.28	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.28	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.28	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.28	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.28	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.28	   A^2 -> H(U1(k, e), f(e))
28.45/9.28	   A^2 -> H(U1(k, e), f(k))
28.45/9.28	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.28	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.28	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.28	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.28	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.28	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.28	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.28	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.28	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.28	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.28	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.28	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.28	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.28	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.28	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.28	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.28	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.28	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.28	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.28	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.28	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.28	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, c), b)
28.45/9.28	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.28	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.28	   A^2 -> H(U1(c, c), e)
28.45/9.28	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.28	   A^2 -> H(e, U1(c, b))
28.45/9.28	   A^2 -> H(e, U1(d, b))
28.45/9.28	   A^2 -> H(e, U1(b, c))
28.45/9.28	   A^2 -> H(e, U1(b, d))
28.45/9.28	   A^2 -> H(e, U1(c, c))
28.45/9.28	   A^2 -> H(e, f(e))
28.45/9.28	   A^2 -> H(e, f(k))
28.45/9.28	   A^2 -> H(e, U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, e), U1(e, b))
28.45/9.28	   A^2 -> H(U1(e, e), U1(k, b))
28.45/9.28	   A^2 -> H(U1(e, e), U1(c, d))
28.45/9.28	
28.45/9.28	The TRS R consists of the following rules:
28.45/9.28	
28.45/9.28	   f(x) -> U1(x, x)
28.45/9.28	   U1(e, x) -> x
28.45/9.28	   a -> c
28.45/9.28	   a -> d
28.45/9.28	   b -> c
28.45/9.28	   b -> d
28.45/9.28	   d -> k
28.45/9.28	   c -> e
28.45/9.28	   c -> k
28.45/9.28	
28.45/9.28	Q is empty.
28.45/9.28	We have to consider all minimal (P,Q,R)-chains.
28.45/9.28	----------------------------------------
28.45/9.28	
28.45/9.28	(897) TransformationProof (EQUIVALENT)
28.45/9.28	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.28	
28.45/9.28	   (A^2 -> H(e, U1(d, b)),A^2 -> H(e, U1(d, b)))
28.45/9.28	   (A^2 -> H(U1(e, e), U1(k, b)),A^2 -> H(U1(e, e), U1(k, b)))
28.45/9.28	   (A^2 -> H(U1(e, e), U1(d, c)),A^2 -> H(U1(e, e), U1(d, c)))
28.45/9.28	   (A^2 -> H(U1(e, e), U1(d, d)),A^2 -> H(U1(e, e), U1(d, d)))
28.45/9.28	
28.45/9.28	
28.45/9.28	----------------------------------------
28.45/9.28	
28.45/9.28	(898)
28.45/9.28	Obligation:
28.45/9.28	Q DP problem:
28.45/9.28	The TRS P consists of the following rules:
28.45/9.28	
28.45/9.28	   H(x, x) -> G(x, x, f(k))
28.45/9.28	   G(d, x, x) -> A^2
28.45/9.28	   A^2 -> H(f(c), f(c))
28.45/9.28	   A^2 -> H(f(d), f(d))
28.45/9.28	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.28	   A^2 -> H(f(e), f(e))
28.45/9.28	   A^2 -> H(f(k), f(k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, e), U1(b, c))
28.45/9.28	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.28	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.28	   A^2 -> H(U1(e, e), f(e))
28.45/9.28	   A^2 -> H(U1(e, e), f(k))
28.45/9.28	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.28	   A^2 -> H(f(e), U1(e, b))
28.45/9.28	   A^2 -> H(f(e), U1(k, b))
28.45/9.28	   A^2 -> H(f(e), U1(c, d))
28.45/9.28	   A^2 -> H(f(e), U1(d, c))
28.45/9.28	   A^2 -> H(f(e), U1(b, e))
28.45/9.28	   A^2 -> H(f(e), U1(b, k))
28.45/9.28	   A^2 -> H(f(e), U1(e, c))
28.45/9.28	   A^2 -> H(f(e), U1(k, c))
28.45/9.28	   A^2 -> H(f(e), U1(c, e))
28.45/9.28	   A^2 -> H(f(e), U1(c, k))
28.45/9.28	   A^2 -> H(f(e), U1(k, k))
28.45/9.28	   A^2 -> H(f(e), U1(k, d))
28.45/9.28	   A^2 -> H(f(e), U1(d, k))
28.45/9.28	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.28	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.28	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.28	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.28	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.28	   A^2 -> H(U1(k, k), f(e))
28.45/9.28	   A^2 -> H(U1(k, k), f(k))
28.45/9.28	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.28	   A^2 -> H(f(k), U1(e, b))
28.45/9.28	   A^2 -> H(f(k), U1(k, b))
28.45/9.28	   A^2 -> H(f(k), U1(c, d))
28.45/9.28	   A^2 -> H(f(k), U1(d, c))
28.45/9.28	   A^2 -> H(f(k), U1(b, e))
28.45/9.28	   A^2 -> H(f(k), U1(b, k))
28.45/9.28	   A^2 -> H(f(k), U1(e, c))
28.45/9.28	   A^2 -> H(f(k), U1(k, c))
28.45/9.28	   A^2 -> H(f(k), U1(c, e))
28.45/9.28	   A^2 -> H(f(k), U1(c, k))
28.45/9.28	   A^2 -> H(f(k), U1(e, e))
28.45/9.28	   A^2 -> H(f(k), U1(k, d))
28.45/9.28	   A^2 -> H(f(k), U1(d, k))
28.45/9.28	   A^2 -> H(f(c), b)
28.45/9.28	   A^2 -> H(f(c), U1(e, d))
28.45/9.28	   A^2 -> H(f(c), U1(d, e))
28.45/9.28	   A^2 -> H(f(k), U1(k, k))
28.45/9.28	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.28	   A^2 -> H(U1(k, k), f(c))
28.45/9.28	   A^2 -> H(U1(k, k), f(d))
28.45/9.28	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.28	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.28	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.28	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.28	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.28	   A^2 -> H(U1(k, d), f(e))
28.45/9.28	   A^2 -> H(U1(k, d), f(k))
28.45/9.28	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.28	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.28	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.28	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.28	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.28	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.28	   A^2 -> H(U1(d, k), f(e))
28.45/9.28	   A^2 -> H(U1(d, k), f(k))
28.45/9.28	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.28	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.28	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.28	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.28	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.28	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.28	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.28	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.28	   A^2 -> H(f(d), b)
28.45/9.28	   A^2 -> H(f(d), U1(e, d))
28.45/9.28	   A^2 -> H(f(d), U1(d, e))
28.45/9.28	   A^2 -> H(f(d), c)
28.45/9.28	   A^2 -> H(f(d), U1(e, k))
28.45/9.28	   A^2 -> H(f(d), U1(k, e))
28.45/9.28	   A^2 -> H(f(d), e)
28.45/9.28	   A^2 -> H(f(a), d)
28.45/9.28	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.28	   A^2 -> H(f(c), c)
28.45/9.28	   A^2 -> H(f(c), U1(e, k))
28.45/9.28	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.28	   A^2 -> H(f(c), U1(k, e))
28.45/9.28	   A^2 -> H(f(c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.28	   A^2 -> H(f(a), k)
28.45/9.28	   A^2 -> H(f(e), U1(e, e))
28.45/9.28	   A^2 -> H(f(c), e)
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.28	   A^2 -> H(f(d), U1(k, k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.28	   A^2 -> H(d, U1(b, b))
28.45/9.28	   A^2 -> H(d, f(c))
28.45/9.28	   A^2 -> H(d, f(d))
28.45/9.28	   A^2 -> H(a, U1(c, b))
28.45/9.28	   A^2 -> H(a, U1(d, b))
28.45/9.28	   A^2 -> H(a, U1(b, c))
28.45/9.28	   A^2 -> H(a, U1(b, d))
28.45/9.28	   A^2 -> H(a, U1(c, c))
28.45/9.28	   A^2 -> H(a, f(e))
28.45/9.28	   A^2 -> H(a, f(k))
28.45/9.28	   A^2 -> H(a, U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.28	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.28	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.28	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.28	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.28	   A^2 -> H(U1(e, d), f(e))
28.45/9.28	   A^2 -> H(U1(e, d), f(k))
28.45/9.28	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.28	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.28	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.28	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.28	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.28	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.28	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.28	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.28	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.28	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.28	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.28	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.28	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.28	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.28	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.28	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.28	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.28	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.28	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.28	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.28	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.28	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.28	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, a), b)
28.45/9.28	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.28	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.28	   A^2 -> H(U1(c, a), c)
28.45/9.28	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.28	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.28	   A^2 -> H(U1(c, a), e)
28.45/9.28	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.28	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.28	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.28	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.28	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.28	   A^2 -> H(U1(d, e), f(e))
28.45/9.28	   A^2 -> H(U1(d, e), f(k))
28.45/9.28	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.28	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.28	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.28	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.28	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.28	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.28	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.28	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.28	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.28	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.28	   A^2 -> H(U1(d, a), b)
28.45/9.28	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.28	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.28	   A^2 -> H(U1(d, a), c)
28.45/9.28	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.28	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.28	   A^2 -> H(U1(d, a), e)
28.45/9.28	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.28	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.28	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.28	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.28	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.28	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.28	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.28	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.28	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.28	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.28	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.28	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.28	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.28	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.28	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.28	   A^2 -> H(U1(a, c), b)
28.45/9.28	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.28	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.28	   A^2 -> H(U1(a, c), c)
28.45/9.28	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.28	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.28	   A^2 -> H(U1(a, c), e)
28.45/9.28	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, d), b)
28.45/9.28	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.28	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.28	   A^2 -> H(U1(a, d), c)
28.45/9.28	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.28	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.28	   A^2 -> H(U1(a, d), e)
28.45/9.28	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, a), d)
28.45/9.28	   A^2 -> H(U1(a, a), k)
28.45/9.28	   A^2 -> H(k, U1(b, b))
28.45/9.28	   A^2 -> H(k, f(c))
28.45/9.28	   A^2 -> H(k, f(d))
28.45/9.28	   A^2 -> H(c, U1(c, b))
28.45/9.28	   A^2 -> H(c, U1(d, b))
28.45/9.28	   A^2 -> H(c, U1(b, c))
28.45/9.28	   A^2 -> H(c, U1(b, d))
28.45/9.28	   A^2 -> H(c, U1(c, c))
28.45/9.28	   A^2 -> H(c, f(e))
28.45/9.28	   A^2 -> H(c, f(k))
28.45/9.28	   A^2 -> H(c, U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.28	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.28	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.28	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.28	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.28	   A^2 -> H(U1(e, k), f(e))
28.45/9.28	   A^2 -> H(U1(e, k), f(k))
28.45/9.28	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.28	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.28	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.28	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.28	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.28	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.28	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.28	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.28	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.28	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.28	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.28	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.28	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.28	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.28	   A^2 -> H(U1(k, e), f(e))
28.45/9.28	   A^2 -> H(U1(k, e), f(k))
28.45/9.28	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.28	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.28	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.28	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.28	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.28	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.28	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.28	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.28	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.28	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.28	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.28	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.28	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.28	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.28	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.28	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.28	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.28	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.28	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.28	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.28	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.28	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, c), b)
28.45/9.28	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.28	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.28	   A^2 -> H(U1(c, c), e)
28.45/9.28	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.28	   A^2 -> H(e, U1(c, b))
28.45/9.28	   A^2 -> H(e, U1(d, b))
28.45/9.28	   A^2 -> H(e, U1(b, c))
28.45/9.28	   A^2 -> H(e, U1(b, d))
28.45/9.28	   A^2 -> H(e, U1(c, c))
28.45/9.28	   A^2 -> H(e, f(e))
28.45/9.28	   A^2 -> H(e, f(k))
28.45/9.28	   A^2 -> H(e, U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, e), U1(e, b))
28.45/9.28	   A^2 -> H(U1(e, e), U1(k, b))
28.45/9.28	   A^2 -> H(U1(e, e), U1(c, d))
28.45/9.28	   A^2 -> H(U1(e, e), U1(d, c))
28.45/9.28	
28.45/9.28	The TRS R consists of the following rules:
28.45/9.28	
28.45/9.28	   f(x) -> U1(x, x)
28.45/9.28	   U1(e, x) -> x
28.45/9.28	   a -> c
28.45/9.28	   a -> d
28.45/9.28	   b -> c
28.45/9.28	   b -> d
28.45/9.28	   d -> k
28.45/9.28	   c -> e
28.45/9.28	   c -> k
28.45/9.28	
28.45/9.28	Q is empty.
28.45/9.28	We have to consider all minimal (P,Q,R)-chains.
28.45/9.28	----------------------------------------
28.45/9.28	
28.45/9.28	(899) TransformationProof (EQUIVALENT)
28.45/9.28	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.28	
28.45/9.28	   (A^2 -> H(e, U1(b, c)),A^2 -> H(e, U1(b, c)))
28.45/9.28	   (A^2 -> H(U1(e, e), U1(c, c)),A^2 -> H(U1(e, e), U1(c, c)))
28.45/9.28	   (A^2 -> H(U1(e, e), U1(d, c)),A^2 -> H(U1(e, e), U1(d, c)))
28.45/9.28	   (A^2 -> H(U1(e, e), U1(b, e)),A^2 -> H(U1(e, e), U1(b, e)))
28.45/9.28	   (A^2 -> H(U1(e, e), U1(b, k)),A^2 -> H(U1(e, e), U1(b, k)))
28.45/9.28	
28.45/9.28	
28.45/9.28	----------------------------------------
28.45/9.28	
28.45/9.28	(900)
28.45/9.28	Obligation:
28.45/9.28	Q DP problem:
28.45/9.28	The TRS P consists of the following rules:
28.45/9.28	
28.45/9.28	   H(x, x) -> G(x, x, f(k))
28.45/9.28	   G(d, x, x) -> A^2
28.45/9.28	   A^2 -> H(f(c), f(c))
28.45/9.28	   A^2 -> H(f(d), f(d))
28.45/9.28	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.28	   A^2 -> H(f(e), f(e))
28.45/9.28	   A^2 -> H(f(k), f(k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, e), U1(b, d))
28.45/9.28	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.28	   A^2 -> H(U1(e, e), f(e))
28.45/9.28	   A^2 -> H(U1(e, e), f(k))
28.45/9.28	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.28	   A^2 -> H(f(e), U1(e, b))
28.45/9.28	   A^2 -> H(f(e), U1(k, b))
28.45/9.28	   A^2 -> H(f(e), U1(c, d))
28.45/9.28	   A^2 -> H(f(e), U1(d, c))
28.45/9.28	   A^2 -> H(f(e), U1(b, e))
28.45/9.28	   A^2 -> H(f(e), U1(b, k))
28.45/9.28	   A^2 -> H(f(e), U1(e, c))
28.45/9.28	   A^2 -> H(f(e), U1(k, c))
28.45/9.28	   A^2 -> H(f(e), U1(c, e))
28.45/9.28	   A^2 -> H(f(e), U1(c, k))
28.45/9.28	   A^2 -> H(f(e), U1(k, k))
28.45/9.28	   A^2 -> H(f(e), U1(k, d))
28.45/9.28	   A^2 -> H(f(e), U1(d, k))
28.45/9.28	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.28	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.28	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.28	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.28	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.28	   A^2 -> H(U1(k, k), f(e))
28.45/9.28	   A^2 -> H(U1(k, k), f(k))
28.45/9.28	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.28	   A^2 -> H(f(k), U1(e, b))
28.45/9.28	   A^2 -> H(f(k), U1(k, b))
28.45/9.28	   A^2 -> H(f(k), U1(c, d))
28.45/9.28	   A^2 -> H(f(k), U1(d, c))
28.45/9.28	   A^2 -> H(f(k), U1(b, e))
28.45/9.28	   A^2 -> H(f(k), U1(b, k))
28.45/9.28	   A^2 -> H(f(k), U1(e, c))
28.45/9.28	   A^2 -> H(f(k), U1(k, c))
28.45/9.28	   A^2 -> H(f(k), U1(c, e))
28.45/9.28	   A^2 -> H(f(k), U1(c, k))
28.45/9.28	   A^2 -> H(f(k), U1(e, e))
28.45/9.28	   A^2 -> H(f(k), U1(k, d))
28.45/9.28	   A^2 -> H(f(k), U1(d, k))
28.45/9.28	   A^2 -> H(f(c), b)
28.45/9.28	   A^2 -> H(f(c), U1(e, d))
28.45/9.28	   A^2 -> H(f(c), U1(d, e))
28.45/9.28	   A^2 -> H(f(k), U1(k, k))
28.45/9.28	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.28	   A^2 -> H(U1(k, k), f(c))
28.45/9.28	   A^2 -> H(U1(k, k), f(d))
28.45/9.28	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.28	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.28	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.28	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.28	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.28	   A^2 -> H(U1(k, d), f(e))
28.45/9.28	   A^2 -> H(U1(k, d), f(k))
28.45/9.28	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.28	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.28	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.28	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.28	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.28	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.28	   A^2 -> H(U1(d, k), f(e))
28.45/9.28	   A^2 -> H(U1(d, k), f(k))
28.45/9.28	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.28	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.28	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.28	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.28	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.28	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.28	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.28	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.28	   A^2 -> H(f(d), b)
28.45/9.28	   A^2 -> H(f(d), U1(e, d))
28.45/9.28	   A^2 -> H(f(d), U1(d, e))
28.45/9.28	   A^2 -> H(f(d), c)
28.45/9.28	   A^2 -> H(f(d), U1(e, k))
28.45/9.28	   A^2 -> H(f(d), U1(k, e))
28.45/9.28	   A^2 -> H(f(d), e)
28.45/9.28	   A^2 -> H(f(a), d)
28.45/9.28	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.28	   A^2 -> H(f(c), c)
28.45/9.28	   A^2 -> H(f(c), U1(e, k))
28.45/9.28	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.28	   A^2 -> H(f(c), U1(k, e))
28.45/9.28	   A^2 -> H(f(c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.28	   A^2 -> H(f(a), k)
28.45/9.28	   A^2 -> H(f(e), U1(e, e))
28.45/9.28	   A^2 -> H(f(c), e)
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.28	   A^2 -> H(f(d), U1(k, k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.28	   A^2 -> H(d, U1(b, b))
28.45/9.28	   A^2 -> H(d, f(c))
28.45/9.28	   A^2 -> H(d, f(d))
28.45/9.28	   A^2 -> H(a, U1(c, b))
28.45/9.28	   A^2 -> H(a, U1(d, b))
28.45/9.28	   A^2 -> H(a, U1(b, c))
28.45/9.28	   A^2 -> H(a, U1(b, d))
28.45/9.28	   A^2 -> H(a, U1(c, c))
28.45/9.28	   A^2 -> H(a, f(e))
28.45/9.28	   A^2 -> H(a, f(k))
28.45/9.28	   A^2 -> H(a, U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.28	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.28	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.28	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.28	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.28	   A^2 -> H(U1(e, d), f(e))
28.45/9.28	   A^2 -> H(U1(e, d), f(k))
28.45/9.28	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.28	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.28	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.28	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.28	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.28	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.28	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.28	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.28	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.28	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.28	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.28	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.28	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.28	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.28	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.28	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.28	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.28	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.28	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.28	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.28	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.28	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.28	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, a), b)
28.45/9.28	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.28	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.28	   A^2 -> H(U1(c, a), c)
28.45/9.28	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.28	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.28	   A^2 -> H(U1(c, a), e)
28.45/9.28	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.28	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.28	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.28	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.28	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.28	   A^2 -> H(U1(d, e), f(e))
28.45/9.28	   A^2 -> H(U1(d, e), f(k))
28.45/9.28	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.28	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.28	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.28	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.28	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.28	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.28	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.28	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.28	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.28	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.28	   A^2 -> H(U1(d, a), b)
28.45/9.28	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.28	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.28	   A^2 -> H(U1(d, a), c)
28.45/9.28	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.28	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.28	   A^2 -> H(U1(d, a), e)
28.45/9.28	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.28	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.28	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.28	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.28	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.28	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.28	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.28	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.28	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.28	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.28	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.28	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.28	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.28	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.28	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.28	   A^2 -> H(U1(a, c), b)
28.45/9.28	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.28	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.28	   A^2 -> H(U1(a, c), c)
28.45/9.28	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.28	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.28	   A^2 -> H(U1(a, c), e)
28.45/9.28	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, d), b)
28.45/9.28	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.28	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.28	   A^2 -> H(U1(a, d), c)
28.45/9.28	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.28	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.28	   A^2 -> H(U1(a, d), e)
28.45/9.28	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, a), d)
28.45/9.28	   A^2 -> H(U1(a, a), k)
28.45/9.28	   A^2 -> H(k, U1(b, b))
28.45/9.28	   A^2 -> H(k, f(c))
28.45/9.28	   A^2 -> H(k, f(d))
28.45/9.28	   A^2 -> H(c, U1(c, b))
28.45/9.28	   A^2 -> H(c, U1(d, b))
28.45/9.28	   A^2 -> H(c, U1(b, c))
28.45/9.28	   A^2 -> H(c, U1(b, d))
28.45/9.28	   A^2 -> H(c, U1(c, c))
28.45/9.28	   A^2 -> H(c, f(e))
28.45/9.28	   A^2 -> H(c, f(k))
28.45/9.28	   A^2 -> H(c, U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.28	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.28	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.28	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.28	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.28	   A^2 -> H(U1(e, k), f(e))
28.45/9.28	   A^2 -> H(U1(e, k), f(k))
28.45/9.28	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.28	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.28	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.28	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.28	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.28	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.28	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.28	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.28	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.28	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.28	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.28	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.28	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.28	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.28	   A^2 -> H(U1(k, e), f(e))
28.45/9.28	   A^2 -> H(U1(k, e), f(k))
28.45/9.28	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.28	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.28	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.28	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.28	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.28	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.28	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.28	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.28	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.28	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.28	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.28	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.28	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.28	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.28	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.28	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.28	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.28	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.28	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.28	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.28	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.28	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, c), b)
28.45/9.28	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.28	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.28	   A^2 -> H(U1(c, c), e)
28.45/9.28	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.28	   A^2 -> H(e, U1(c, b))
28.45/9.28	   A^2 -> H(e, U1(d, b))
28.45/9.28	   A^2 -> H(e, U1(b, c))
28.45/9.28	   A^2 -> H(e, U1(b, d))
28.45/9.28	   A^2 -> H(e, U1(c, c))
28.45/9.28	   A^2 -> H(e, f(e))
28.45/9.28	   A^2 -> H(e, f(k))
28.45/9.28	   A^2 -> H(e, U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, e), U1(e, b))
28.45/9.28	   A^2 -> H(U1(e, e), U1(k, b))
28.45/9.28	   A^2 -> H(U1(e, e), U1(c, d))
28.45/9.28	   A^2 -> H(U1(e, e), U1(d, c))
28.45/9.28	   A^2 -> H(U1(e, e), U1(b, e))
28.45/9.28	   A^2 -> H(U1(e, e), U1(b, k))
28.45/9.28	
28.45/9.28	The TRS R consists of the following rules:
28.45/9.28	
28.45/9.28	   f(x) -> U1(x, x)
28.45/9.28	   U1(e, x) -> x
28.45/9.28	   a -> c
28.45/9.28	   a -> d
28.45/9.28	   b -> c
28.45/9.28	   b -> d
28.45/9.28	   d -> k
28.45/9.28	   c -> e
28.45/9.28	   c -> k
28.45/9.28	
28.45/9.28	Q is empty.
28.45/9.28	We have to consider all minimal (P,Q,R)-chains.
28.45/9.28	----------------------------------------
28.45/9.28	
28.45/9.28	(901) TransformationProof (EQUIVALENT)
28.45/9.28	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.28	
28.45/9.28	   (A^2 -> H(e, U1(b, d)),A^2 -> H(e, U1(b, d)))
28.45/9.28	   (A^2 -> H(U1(e, e), U1(c, d)),A^2 -> H(U1(e, e), U1(c, d)))
28.45/9.28	   (A^2 -> H(U1(e, e), U1(d, d)),A^2 -> H(U1(e, e), U1(d, d)))
28.45/9.28	   (A^2 -> H(U1(e, e), U1(b, k)),A^2 -> H(U1(e, e), U1(b, k)))
28.45/9.28	
28.45/9.28	
28.45/9.28	----------------------------------------
28.45/9.28	
28.45/9.28	(902)
28.45/9.28	Obligation:
28.45/9.28	Q DP problem:
28.45/9.28	The TRS P consists of the following rules:
28.45/9.28	
28.45/9.28	   H(x, x) -> G(x, x, f(k))
28.45/9.28	   G(d, x, x) -> A^2
28.45/9.28	   A^2 -> H(f(c), f(c))
28.45/9.28	   A^2 -> H(f(d), f(d))
28.45/9.28	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.28	   A^2 -> H(f(e), f(e))
28.45/9.28	   A^2 -> H(f(k), f(k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, e), U1(c, c))
28.45/9.28	   A^2 -> H(U1(e, e), f(e))
28.45/9.28	   A^2 -> H(U1(e, e), f(k))
28.45/9.28	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.28	   A^2 -> H(f(e), U1(e, b))
28.45/9.28	   A^2 -> H(f(e), U1(k, b))
28.45/9.28	   A^2 -> H(f(e), U1(c, d))
28.45/9.28	   A^2 -> H(f(e), U1(d, c))
28.45/9.28	   A^2 -> H(f(e), U1(b, e))
28.45/9.28	   A^2 -> H(f(e), U1(b, k))
28.45/9.28	   A^2 -> H(f(e), U1(e, c))
28.45/9.28	   A^2 -> H(f(e), U1(k, c))
28.45/9.28	   A^2 -> H(f(e), U1(c, e))
28.45/9.28	   A^2 -> H(f(e), U1(c, k))
28.45/9.28	   A^2 -> H(f(e), U1(k, k))
28.45/9.28	   A^2 -> H(f(e), U1(k, d))
28.45/9.28	   A^2 -> H(f(e), U1(d, k))
28.45/9.28	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.28	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.28	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.28	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.28	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.28	   A^2 -> H(U1(k, k), f(e))
28.45/9.28	   A^2 -> H(U1(k, k), f(k))
28.45/9.28	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.28	   A^2 -> H(f(k), U1(e, b))
28.45/9.28	   A^2 -> H(f(k), U1(k, b))
28.45/9.28	   A^2 -> H(f(k), U1(c, d))
28.45/9.28	   A^2 -> H(f(k), U1(d, c))
28.45/9.28	   A^2 -> H(f(k), U1(b, e))
28.45/9.28	   A^2 -> H(f(k), U1(b, k))
28.45/9.28	   A^2 -> H(f(k), U1(e, c))
28.45/9.28	   A^2 -> H(f(k), U1(k, c))
28.45/9.28	   A^2 -> H(f(k), U1(c, e))
28.45/9.28	   A^2 -> H(f(k), U1(c, k))
28.45/9.28	   A^2 -> H(f(k), U1(e, e))
28.45/9.28	   A^2 -> H(f(k), U1(k, d))
28.45/9.28	   A^2 -> H(f(k), U1(d, k))
28.45/9.28	   A^2 -> H(f(c), b)
28.45/9.28	   A^2 -> H(f(c), U1(e, d))
28.45/9.28	   A^2 -> H(f(c), U1(d, e))
28.45/9.28	   A^2 -> H(f(k), U1(k, k))
28.45/9.28	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.28	   A^2 -> H(U1(k, k), f(c))
28.45/9.28	   A^2 -> H(U1(k, k), f(d))
28.45/9.28	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.28	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.28	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.28	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.28	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.28	   A^2 -> H(U1(k, d), f(e))
28.45/9.28	   A^2 -> H(U1(k, d), f(k))
28.45/9.28	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.28	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.28	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.28	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.28	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.28	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.28	   A^2 -> H(U1(d, k), f(e))
28.45/9.28	   A^2 -> H(U1(d, k), f(k))
28.45/9.28	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.28	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.28	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.28	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.28	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.28	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.28	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.28	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.28	   A^2 -> H(f(d), b)
28.45/9.28	   A^2 -> H(f(d), U1(e, d))
28.45/9.28	   A^2 -> H(f(d), U1(d, e))
28.45/9.28	   A^2 -> H(f(d), c)
28.45/9.28	   A^2 -> H(f(d), U1(e, k))
28.45/9.28	   A^2 -> H(f(d), U1(k, e))
28.45/9.28	   A^2 -> H(f(d), e)
28.45/9.28	   A^2 -> H(f(a), d)
28.45/9.28	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.28	   A^2 -> H(f(c), c)
28.45/9.28	   A^2 -> H(f(c), U1(e, k))
28.45/9.28	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.28	   A^2 -> H(f(c), U1(k, e))
28.45/9.28	   A^2 -> H(f(c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.28	   A^2 -> H(f(a), k)
28.45/9.28	   A^2 -> H(f(e), U1(e, e))
28.45/9.28	   A^2 -> H(f(c), e)
28.45/9.28	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.28	   A^2 -> H(f(d), U1(k, k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.28	   A^2 -> H(d, U1(b, b))
28.45/9.28	   A^2 -> H(d, f(c))
28.45/9.28	   A^2 -> H(d, f(d))
28.45/9.28	   A^2 -> H(a, U1(c, b))
28.45/9.28	   A^2 -> H(a, U1(d, b))
28.45/9.28	   A^2 -> H(a, U1(b, c))
28.45/9.28	   A^2 -> H(a, U1(b, d))
28.45/9.28	   A^2 -> H(a, U1(c, c))
28.45/9.28	   A^2 -> H(a, f(e))
28.45/9.28	   A^2 -> H(a, f(k))
28.45/9.28	   A^2 -> H(a, U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.28	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.28	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.28	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.28	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.28	   A^2 -> H(U1(e, d), f(e))
28.45/9.28	   A^2 -> H(U1(e, d), f(k))
28.45/9.28	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.28	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.28	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.28	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.28	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.28	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.28	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.28	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.28	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.28	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.28	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.28	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.28	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.28	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.28	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.28	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.28	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.28	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.28	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.28	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.28	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.28	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.28	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, a), b)
28.45/9.28	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.28	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.28	   A^2 -> H(U1(c, a), c)
28.45/9.28	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.28	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.28	   A^2 -> H(U1(c, a), e)
28.45/9.28	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.28	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.28	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.28	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.28	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.28	   A^2 -> H(U1(d, e), f(e))
28.45/9.28	   A^2 -> H(U1(d, e), f(k))
28.45/9.28	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.28	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.28	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.28	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.28	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.28	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.28	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.28	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.28	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.28	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.28	   A^2 -> H(U1(d, a), b)
28.45/9.28	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.28	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.28	   A^2 -> H(U1(d, a), c)
28.45/9.28	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.28	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.28	   A^2 -> H(U1(d, a), e)
28.45/9.28	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.28	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.28	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.28	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.28	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.28	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.28	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.28	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.28	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.28	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.28	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.28	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.28	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.28	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.28	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.28	   A^2 -> H(U1(a, c), b)
28.45/9.28	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.28	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.28	   A^2 -> H(U1(a, c), c)
28.45/9.28	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.28	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.28	   A^2 -> H(U1(a, c), e)
28.45/9.28	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, d), b)
28.45/9.28	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.28	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.28	   A^2 -> H(U1(a, d), c)
28.45/9.28	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.28	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.28	   A^2 -> H(U1(a, d), e)
28.45/9.28	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.28	   A^2 -> H(U1(a, a), d)
28.45/9.28	   A^2 -> H(U1(a, a), k)
28.45/9.28	   A^2 -> H(k, U1(b, b))
28.45/9.28	   A^2 -> H(k, f(c))
28.45/9.28	   A^2 -> H(k, f(d))
28.45/9.28	   A^2 -> H(c, U1(c, b))
28.45/9.28	   A^2 -> H(c, U1(d, b))
28.45/9.28	   A^2 -> H(c, U1(b, c))
28.45/9.28	   A^2 -> H(c, U1(b, d))
28.45/9.28	   A^2 -> H(c, U1(c, c))
28.45/9.28	   A^2 -> H(c, f(e))
28.45/9.28	   A^2 -> H(c, f(k))
28.45/9.28	   A^2 -> H(c, U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.28	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.28	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.28	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.28	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.28	   A^2 -> H(U1(e, k), f(e))
28.45/9.28	   A^2 -> H(U1(e, k), f(k))
28.45/9.28	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.28	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.28	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.28	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.28	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.28	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.28	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.28	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.28	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.28	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.28	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.28	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.28	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.28	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.28	   A^2 -> H(U1(k, e), f(e))
28.45/9.28	   A^2 -> H(U1(k, e), f(k))
28.45/9.28	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.28	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.28	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.28	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.28	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.28	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.28	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.28	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.28	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.28	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.28	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.28	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.28	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.28	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.28	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.28	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.28	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.28	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.28	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.28	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.28	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.28	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.28	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.28	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.28	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.28	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.28	   A^2 -> H(U1(c, c), b)
28.45/9.28	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.28	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.28	   A^2 -> H(U1(c, c), e)
28.45/9.28	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.28	   A^2 -> H(e, U1(c, b))
28.45/9.28	   A^2 -> H(e, U1(d, b))
28.45/9.28	   A^2 -> H(e, U1(b, c))
28.45/9.28	   A^2 -> H(e, U1(b, d))
28.45/9.28	   A^2 -> H(e, U1(c, c))
28.45/9.28	   A^2 -> H(e, f(e))
28.45/9.28	   A^2 -> H(e, f(k))
28.45/9.28	   A^2 -> H(e, U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, e), U1(e, b))
28.45/9.28	   A^2 -> H(U1(e, e), U1(k, b))
28.45/9.28	   A^2 -> H(U1(e, e), U1(c, d))
28.45/9.28	   A^2 -> H(U1(e, e), U1(d, c))
28.45/9.28	   A^2 -> H(U1(e, e), U1(b, e))
28.45/9.28	   A^2 -> H(U1(e, e), U1(b, k))
28.45/9.28	
28.45/9.28	The TRS R consists of the following rules:
28.45/9.28	
28.45/9.28	   f(x) -> U1(x, x)
28.45/9.28	   U1(e, x) -> x
28.45/9.28	   a -> c
28.45/9.28	   a -> d
28.45/9.28	   b -> c
28.45/9.28	   b -> d
28.45/9.28	   d -> k
28.45/9.28	   c -> e
28.45/9.28	   c -> k
28.45/9.28	
28.45/9.28	Q is empty.
28.45/9.28	We have to consider all minimal (P,Q,R)-chains.
28.45/9.28	----------------------------------------
28.45/9.28	
28.45/9.28	(903) TransformationProof (EQUIVALENT)
28.45/9.28	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.28	
28.45/9.28	   (A^2 -> H(e, U1(c, c)),A^2 -> H(e, U1(c, c)))
28.45/9.28	   (A^2 -> H(U1(e, e), U1(e, c)),A^2 -> H(U1(e, e), U1(e, c)))
28.45/9.28	   (A^2 -> H(U1(e, e), U1(k, c)),A^2 -> H(U1(e, e), U1(k, c)))
28.45/9.28	   (A^2 -> H(U1(e, e), U1(c, e)),A^2 -> H(U1(e, e), U1(c, e)))
28.45/9.28	   (A^2 -> H(U1(e, e), U1(c, k)),A^2 -> H(U1(e, e), U1(c, k)))
28.45/9.28	
28.45/9.28	
28.45/9.28	----------------------------------------
28.45/9.28	
28.45/9.28	(904)
28.45/9.28	Obligation:
28.45/9.28	Q DP problem:
28.45/9.28	The TRS P consists of the following rules:
28.45/9.28	
28.45/9.28	   H(x, x) -> G(x, x, f(k))
28.45/9.28	   G(d, x, x) -> A^2
28.45/9.28	   A^2 -> H(f(c), f(c))
28.45/9.28	   A^2 -> H(f(d), f(d))
28.45/9.28	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.28	   A^2 -> H(f(e), f(e))
28.45/9.28	   A^2 -> H(f(k), f(k))
28.45/9.28	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.28	   A^2 -> H(U1(e, e), f(e))
28.45/9.28	   A^2 -> H(U1(e, e), f(k))
28.45/9.28	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.28	   A^2 -> H(f(e), U1(e, b))
28.45/9.28	   A^2 -> H(f(e), U1(k, b))
28.45/9.28	   A^2 -> H(f(e), U1(c, d))
28.45/9.28	   A^2 -> H(f(e), U1(d, c))
28.45/9.28	   A^2 -> H(f(e), U1(b, e))
28.45/9.28	   A^2 -> H(f(e), U1(b, k))
28.45/9.28	   A^2 -> H(f(e), U1(e, c))
28.45/9.28	   A^2 -> H(f(e), U1(k, c))
28.45/9.28	   A^2 -> H(f(e), U1(c, e))
28.45/9.28	   A^2 -> H(f(e), U1(c, k))
28.45/9.28	   A^2 -> H(f(e), U1(k, k))
28.45/9.28	   A^2 -> H(f(e), U1(k, d))
28.45/9.28	   A^2 -> H(f(e), U1(d, k))
28.45/9.28	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.28	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.28	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.28	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.28	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.28	   A^2 -> H(U1(k, k), f(e))
28.45/9.28	   A^2 -> H(U1(k, k), f(k))
28.45/9.28	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.28	   A^2 -> H(f(k), U1(e, b))
28.45/9.28	   A^2 -> H(f(k), U1(k, b))
28.45/9.28	   A^2 -> H(f(k), U1(c, d))
28.45/9.28	   A^2 -> H(f(k), U1(d, c))
28.45/9.28	   A^2 -> H(f(k), U1(b, e))
28.45/9.28	   A^2 -> H(f(k), U1(b, k))
28.45/9.28	   A^2 -> H(f(k), U1(e, c))
28.45/9.28	   A^2 -> H(f(k), U1(k, c))
28.45/9.28	   A^2 -> H(f(k), U1(c, e))
28.45/9.28	   A^2 -> H(f(k), U1(c, k))
28.45/9.28	   A^2 -> H(f(k), U1(e, e))
28.45/9.29	   A^2 -> H(f(k), U1(k, d))
28.45/9.29	   A^2 -> H(f(k), U1(d, k))
28.45/9.29	   A^2 -> H(f(c), b)
28.45/9.29	   A^2 -> H(f(c), U1(e, d))
28.45/9.29	   A^2 -> H(f(c), U1(d, e))
28.45/9.29	   A^2 -> H(f(k), U1(k, k))
28.45/9.29	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.29	   A^2 -> H(U1(k, k), f(c))
28.45/9.29	   A^2 -> H(U1(k, k), f(d))
28.45/9.29	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.29	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.29	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.29	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.29	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.29	   A^2 -> H(U1(k, d), f(e))
28.45/9.29	   A^2 -> H(U1(k, d), f(k))
28.45/9.29	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.29	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.29	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.29	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.29	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.29	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.29	   A^2 -> H(U1(d, k), f(e))
28.45/9.29	   A^2 -> H(U1(d, k), f(k))
28.45/9.29	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.29	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.29	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.29	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.29	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.29	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.29	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.29	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.29	   A^2 -> H(f(d), b)
28.45/9.29	   A^2 -> H(f(d), U1(e, d))
28.45/9.29	   A^2 -> H(f(d), U1(d, e))
28.45/9.29	   A^2 -> H(f(d), c)
28.45/9.29	   A^2 -> H(f(d), U1(e, k))
28.45/9.29	   A^2 -> H(f(d), U1(k, e))
28.45/9.29	   A^2 -> H(f(d), e)
28.45/9.29	   A^2 -> H(f(a), d)
28.45/9.29	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.29	   A^2 -> H(f(c), c)
28.45/9.29	   A^2 -> H(f(c), U1(e, k))
28.45/9.29	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.29	   A^2 -> H(f(c), U1(k, e))
28.45/9.29	   A^2 -> H(f(c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.29	   A^2 -> H(f(a), k)
28.45/9.29	   A^2 -> H(f(e), U1(e, e))
28.45/9.29	   A^2 -> H(f(c), e)
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.29	   A^2 -> H(f(d), U1(k, k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.29	   A^2 -> H(d, U1(b, b))
28.45/9.29	   A^2 -> H(d, f(c))
28.45/9.29	   A^2 -> H(d, f(d))
28.45/9.29	   A^2 -> H(a, U1(c, b))
28.45/9.29	   A^2 -> H(a, U1(d, b))
28.45/9.29	   A^2 -> H(a, U1(b, c))
28.45/9.29	   A^2 -> H(a, U1(b, d))
28.45/9.29	   A^2 -> H(a, U1(c, c))
28.45/9.29	   A^2 -> H(a, f(e))
28.45/9.29	   A^2 -> H(a, f(k))
28.45/9.29	   A^2 -> H(a, U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.29	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.29	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.29	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.29	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.29	   A^2 -> H(U1(e, d), f(e))
28.45/9.29	   A^2 -> H(U1(e, d), f(k))
28.45/9.29	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.29	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.29	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.29	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.29	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.29	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.29	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.29	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.29	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.29	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.29	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.29	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.29	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.29	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.29	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.29	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.29	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.29	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.29	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.29	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.29	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.29	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.29	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, a), b)
28.45/9.29	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.29	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.29	   A^2 -> H(U1(c, a), c)
28.45/9.29	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.29	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.29	   A^2 -> H(U1(c, a), e)
28.45/9.29	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.29	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.29	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.29	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.29	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.29	   A^2 -> H(U1(d, e), f(e))
28.45/9.29	   A^2 -> H(U1(d, e), f(k))
28.45/9.29	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.29	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.29	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.29	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.29	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.29	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.29	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.29	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.29	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.29	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.29	   A^2 -> H(U1(d, a), b)
28.45/9.29	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.29	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.29	   A^2 -> H(U1(d, a), c)
28.45/9.29	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.29	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.29	   A^2 -> H(U1(d, a), e)
28.45/9.29	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.29	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.29	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.29	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.29	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.29	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.29	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.29	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.29	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.29	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.29	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.29	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.29	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.29	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.29	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.29	   A^2 -> H(U1(a, c), b)
28.45/9.29	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.29	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.29	   A^2 -> H(U1(a, c), c)
28.45/9.29	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.29	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.29	   A^2 -> H(U1(a, c), e)
28.45/9.29	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, d), b)
28.45/9.29	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.29	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.29	   A^2 -> H(U1(a, d), c)
28.45/9.29	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.29	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.29	   A^2 -> H(U1(a, d), e)
28.45/9.29	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, a), d)
28.45/9.29	   A^2 -> H(U1(a, a), k)
28.45/9.29	   A^2 -> H(k, U1(b, b))
28.45/9.29	   A^2 -> H(k, f(c))
28.45/9.29	   A^2 -> H(k, f(d))
28.45/9.29	   A^2 -> H(c, U1(c, b))
28.45/9.29	   A^2 -> H(c, U1(d, b))
28.45/9.29	   A^2 -> H(c, U1(b, c))
28.45/9.29	   A^2 -> H(c, U1(b, d))
28.45/9.29	   A^2 -> H(c, U1(c, c))
28.45/9.29	   A^2 -> H(c, f(e))
28.45/9.29	   A^2 -> H(c, f(k))
28.45/9.29	   A^2 -> H(c, U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.29	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.29	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.29	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.29	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.29	   A^2 -> H(U1(e, k), f(e))
28.45/9.29	   A^2 -> H(U1(e, k), f(k))
28.45/9.29	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.29	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.29	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.29	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.29	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.29	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.29	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.29	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.29	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.29	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.29	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.29	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.29	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.29	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.29	   A^2 -> H(U1(k, e), f(e))
28.45/9.29	   A^2 -> H(U1(k, e), f(k))
28.45/9.29	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.29	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.29	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.29	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.29	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.29	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.29	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.29	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.29	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.29	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.29	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.29	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.29	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.29	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.29	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.29	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.29	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.29	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.29	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.29	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.29	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.29	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, c), b)
28.45/9.29	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.29	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.29	   A^2 -> H(U1(c, c), e)
28.45/9.29	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.29	   A^2 -> H(e, U1(c, b))
28.45/9.29	   A^2 -> H(e, U1(d, b))
28.45/9.29	   A^2 -> H(e, U1(b, c))
28.45/9.29	   A^2 -> H(e, U1(b, d))
28.45/9.29	   A^2 -> H(e, U1(c, c))
28.45/9.29	   A^2 -> H(e, f(e))
28.45/9.29	   A^2 -> H(e, f(k))
28.45/9.29	   A^2 -> H(e, U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, e), U1(e, b))
28.45/9.29	   A^2 -> H(U1(e, e), U1(k, b))
28.45/9.29	   A^2 -> H(U1(e, e), U1(c, d))
28.45/9.29	   A^2 -> H(U1(e, e), U1(d, c))
28.45/9.29	   A^2 -> H(U1(e, e), U1(b, e))
28.45/9.29	   A^2 -> H(U1(e, e), U1(b, k))
28.45/9.29	   A^2 -> H(U1(e, e), U1(e, c))
28.45/9.29	   A^2 -> H(U1(e, e), U1(k, c))
28.45/9.29	   A^2 -> H(U1(e, e), U1(c, e))
28.45/9.29	   A^2 -> H(U1(e, e), U1(c, k))
28.45/9.29	
28.45/9.29	The TRS R consists of the following rules:
28.45/9.29	
28.45/9.29	   f(x) -> U1(x, x)
28.45/9.29	   U1(e, x) -> x
28.45/9.29	   a -> c
28.45/9.29	   a -> d
28.45/9.29	   b -> c
28.45/9.29	   b -> d
28.45/9.29	   d -> k
28.45/9.29	   c -> e
28.45/9.29	   c -> k
28.45/9.29	
28.45/9.29	Q is empty.
28.45/9.29	We have to consider all minimal (P,Q,R)-chains.
28.45/9.29	----------------------------------------
28.45/9.29	
28.45/9.29	(905) TransformationProof (EQUIVALENT)
28.45/9.29	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), f(e)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.29	
28.45/9.29	   (A^2 -> H(e, f(e)),A^2 -> H(e, f(e)))
28.45/9.29	   (A^2 -> H(U1(e, e), U1(e, e)),A^2 -> H(U1(e, e), U1(e, e)))
28.45/9.29	
28.45/9.29	
28.45/9.29	----------------------------------------
28.45/9.29	
28.45/9.29	(906)
28.45/9.29	Obligation:
28.45/9.29	Q DP problem:
28.45/9.29	The TRS P consists of the following rules:
28.45/9.29	
28.45/9.29	   H(x, x) -> G(x, x, f(k))
28.45/9.29	   G(d, x, x) -> A^2
28.45/9.29	   A^2 -> H(f(c), f(c))
28.45/9.29	   A^2 -> H(f(d), f(d))
28.45/9.29	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.29	   A^2 -> H(f(e), f(e))
28.45/9.29	   A^2 -> H(f(k), f(k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, e), f(k))
28.45/9.29	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.29	   A^2 -> H(f(e), U1(e, b))
28.45/9.29	   A^2 -> H(f(e), U1(k, b))
28.45/9.29	   A^2 -> H(f(e), U1(c, d))
28.45/9.29	   A^2 -> H(f(e), U1(d, c))
28.45/9.29	   A^2 -> H(f(e), U1(b, e))
28.45/9.29	   A^2 -> H(f(e), U1(b, k))
28.45/9.29	   A^2 -> H(f(e), U1(e, c))
28.45/9.29	   A^2 -> H(f(e), U1(k, c))
28.45/9.29	   A^2 -> H(f(e), U1(c, e))
28.45/9.29	   A^2 -> H(f(e), U1(c, k))
28.45/9.29	   A^2 -> H(f(e), U1(k, k))
28.45/9.29	   A^2 -> H(f(e), U1(k, d))
28.45/9.29	   A^2 -> H(f(e), U1(d, k))
28.45/9.29	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.29	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.29	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.29	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.29	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.29	   A^2 -> H(U1(k, k), f(e))
28.45/9.29	   A^2 -> H(U1(k, k), f(k))
28.45/9.29	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.29	   A^2 -> H(f(k), U1(e, b))
28.45/9.29	   A^2 -> H(f(k), U1(k, b))
28.45/9.29	   A^2 -> H(f(k), U1(c, d))
28.45/9.29	   A^2 -> H(f(k), U1(d, c))
28.45/9.29	   A^2 -> H(f(k), U1(b, e))
28.45/9.29	   A^2 -> H(f(k), U1(b, k))
28.45/9.29	   A^2 -> H(f(k), U1(e, c))
28.45/9.29	   A^2 -> H(f(k), U1(k, c))
28.45/9.29	   A^2 -> H(f(k), U1(c, e))
28.45/9.29	   A^2 -> H(f(k), U1(c, k))
28.45/9.29	   A^2 -> H(f(k), U1(e, e))
28.45/9.29	   A^2 -> H(f(k), U1(k, d))
28.45/9.29	   A^2 -> H(f(k), U1(d, k))
28.45/9.29	   A^2 -> H(f(c), b)
28.45/9.29	   A^2 -> H(f(c), U1(e, d))
28.45/9.29	   A^2 -> H(f(c), U1(d, e))
28.45/9.29	   A^2 -> H(f(k), U1(k, k))
28.45/9.29	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.29	   A^2 -> H(U1(k, k), f(c))
28.45/9.29	   A^2 -> H(U1(k, k), f(d))
28.45/9.29	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.29	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.29	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.29	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.29	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.29	   A^2 -> H(U1(k, d), f(e))
28.45/9.29	   A^2 -> H(U1(k, d), f(k))
28.45/9.29	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.29	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.29	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.29	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.29	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.29	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.29	   A^2 -> H(U1(d, k), f(e))
28.45/9.29	   A^2 -> H(U1(d, k), f(k))
28.45/9.29	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.29	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.29	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.29	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.29	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.29	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.29	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.29	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.29	   A^2 -> H(f(d), b)
28.45/9.29	   A^2 -> H(f(d), U1(e, d))
28.45/9.29	   A^2 -> H(f(d), U1(d, e))
28.45/9.29	   A^2 -> H(f(d), c)
28.45/9.29	   A^2 -> H(f(d), U1(e, k))
28.45/9.29	   A^2 -> H(f(d), U1(k, e))
28.45/9.29	   A^2 -> H(f(d), e)
28.45/9.29	   A^2 -> H(f(a), d)
28.45/9.29	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.29	   A^2 -> H(f(c), c)
28.45/9.29	   A^2 -> H(f(c), U1(e, k))
28.45/9.29	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.29	   A^2 -> H(f(c), U1(k, e))
28.45/9.29	   A^2 -> H(f(c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.29	   A^2 -> H(f(a), k)
28.45/9.29	   A^2 -> H(f(e), U1(e, e))
28.45/9.29	   A^2 -> H(f(c), e)
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.29	   A^2 -> H(f(d), U1(k, k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.29	   A^2 -> H(d, U1(b, b))
28.45/9.29	   A^2 -> H(d, f(c))
28.45/9.29	   A^2 -> H(d, f(d))
28.45/9.29	   A^2 -> H(a, U1(c, b))
28.45/9.29	   A^2 -> H(a, U1(d, b))
28.45/9.29	   A^2 -> H(a, U1(b, c))
28.45/9.29	   A^2 -> H(a, U1(b, d))
28.45/9.29	   A^2 -> H(a, U1(c, c))
28.45/9.29	   A^2 -> H(a, f(e))
28.45/9.29	   A^2 -> H(a, f(k))
28.45/9.29	   A^2 -> H(a, U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.29	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.29	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.29	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.29	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.29	   A^2 -> H(U1(e, d), f(e))
28.45/9.29	   A^2 -> H(U1(e, d), f(k))
28.45/9.29	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.29	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.29	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.29	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.29	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.29	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.29	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.29	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.29	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.29	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.29	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.29	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.29	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.29	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.29	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.29	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.29	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.29	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.29	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.29	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.29	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.29	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.29	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, a), b)
28.45/9.29	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.29	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.29	   A^2 -> H(U1(c, a), c)
28.45/9.29	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.29	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.29	   A^2 -> H(U1(c, a), e)
28.45/9.29	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.29	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.29	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.29	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.29	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.29	   A^2 -> H(U1(d, e), f(e))
28.45/9.29	   A^2 -> H(U1(d, e), f(k))
28.45/9.29	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.29	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.29	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.29	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.29	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.29	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.29	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.29	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.29	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.29	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.29	   A^2 -> H(U1(d, a), b)
28.45/9.29	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.29	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.29	   A^2 -> H(U1(d, a), c)
28.45/9.29	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.29	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.29	   A^2 -> H(U1(d, a), e)
28.45/9.29	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.29	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.29	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.29	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.29	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.29	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.29	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.29	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.29	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.29	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.29	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.29	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.29	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.29	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.29	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.29	   A^2 -> H(U1(a, c), b)
28.45/9.29	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.29	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.29	   A^2 -> H(U1(a, c), c)
28.45/9.29	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.29	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.29	   A^2 -> H(U1(a, c), e)
28.45/9.29	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, d), b)
28.45/9.29	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.29	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.29	   A^2 -> H(U1(a, d), c)
28.45/9.29	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.29	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.29	   A^2 -> H(U1(a, d), e)
28.45/9.29	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, a), d)
28.45/9.29	   A^2 -> H(U1(a, a), k)
28.45/9.29	   A^2 -> H(k, U1(b, b))
28.45/9.29	   A^2 -> H(k, f(c))
28.45/9.29	   A^2 -> H(k, f(d))
28.45/9.29	   A^2 -> H(c, U1(c, b))
28.45/9.29	   A^2 -> H(c, U1(d, b))
28.45/9.29	   A^2 -> H(c, U1(b, c))
28.45/9.29	   A^2 -> H(c, U1(b, d))
28.45/9.29	   A^2 -> H(c, U1(c, c))
28.45/9.29	   A^2 -> H(c, f(e))
28.45/9.29	   A^2 -> H(c, f(k))
28.45/9.29	   A^2 -> H(c, U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.29	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.29	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.29	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.29	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.29	   A^2 -> H(U1(e, k), f(e))
28.45/9.29	   A^2 -> H(U1(e, k), f(k))
28.45/9.29	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.29	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.29	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.29	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.29	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.29	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.29	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.29	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.29	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.29	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.29	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.29	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.29	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.29	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.29	   A^2 -> H(U1(k, e), f(e))
28.45/9.29	   A^2 -> H(U1(k, e), f(k))
28.45/9.29	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.29	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.29	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.29	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.29	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.29	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.29	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.29	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.29	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.29	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.29	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.29	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.29	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.29	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.29	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.29	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.29	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.29	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.29	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.29	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.29	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.29	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, c), b)
28.45/9.29	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.29	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.29	   A^2 -> H(U1(c, c), e)
28.45/9.29	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.29	   A^2 -> H(e, U1(c, b))
28.45/9.29	   A^2 -> H(e, U1(d, b))
28.45/9.29	   A^2 -> H(e, U1(b, c))
28.45/9.29	   A^2 -> H(e, U1(b, d))
28.45/9.29	   A^2 -> H(e, U1(c, c))
28.45/9.29	   A^2 -> H(e, f(e))
28.45/9.29	   A^2 -> H(e, f(k))
28.45/9.29	   A^2 -> H(e, U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, e), U1(e, b))
28.45/9.29	   A^2 -> H(U1(e, e), U1(k, b))
28.45/9.29	   A^2 -> H(U1(e, e), U1(c, d))
28.45/9.29	   A^2 -> H(U1(e, e), U1(d, c))
28.45/9.29	   A^2 -> H(U1(e, e), U1(b, e))
28.45/9.29	   A^2 -> H(U1(e, e), U1(b, k))
28.45/9.29	   A^2 -> H(U1(e, e), U1(e, c))
28.45/9.29	   A^2 -> H(U1(e, e), U1(k, c))
28.45/9.29	   A^2 -> H(U1(e, e), U1(c, e))
28.45/9.29	   A^2 -> H(U1(e, e), U1(c, k))
28.45/9.29	   A^2 -> H(U1(e, e), U1(e, e))
28.45/9.29	
28.45/9.29	The TRS R consists of the following rules:
28.45/9.29	
28.45/9.29	   f(x) -> U1(x, x)
28.45/9.29	   U1(e, x) -> x
28.45/9.29	   a -> c
28.45/9.29	   a -> d
28.45/9.29	   b -> c
28.45/9.29	   b -> d
28.45/9.29	   d -> k
28.45/9.29	   c -> e
28.45/9.29	   c -> k
28.45/9.29	
28.45/9.29	Q is empty.
28.45/9.29	We have to consider all minimal (P,Q,R)-chains.
28.45/9.29	----------------------------------------
28.45/9.29	
28.45/9.29	(907) TransformationProof (EQUIVALENT)
28.45/9.29	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), f(k)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.29	
28.45/9.29	   (A^2 -> H(e, f(k)),A^2 -> H(e, f(k)))
28.45/9.29	   (A^2 -> H(U1(e, e), U1(k, k)),A^2 -> H(U1(e, e), U1(k, k)))
28.45/9.29	
28.45/9.29	
28.45/9.29	----------------------------------------
28.45/9.29	
28.45/9.29	(908)
28.45/9.29	Obligation:
28.45/9.29	Q DP problem:
28.45/9.29	The TRS P consists of the following rules:
28.45/9.29	
28.45/9.29	   H(x, x) -> G(x, x, f(k))
28.45/9.29	   G(d, x, x) -> A^2
28.45/9.29	   A^2 -> H(f(c), f(c))
28.45/9.29	   A^2 -> H(f(d), f(d))
28.45/9.29	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.29	   A^2 -> H(f(e), f(e))
28.45/9.29	   A^2 -> H(f(k), f(k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, e), U1(d, d))
28.45/9.29	   A^2 -> H(f(e), U1(e, b))
28.45/9.29	   A^2 -> H(f(e), U1(k, b))
28.45/9.29	   A^2 -> H(f(e), U1(c, d))
28.45/9.29	   A^2 -> H(f(e), U1(d, c))
28.45/9.29	   A^2 -> H(f(e), U1(b, e))
28.45/9.29	   A^2 -> H(f(e), U1(b, k))
28.45/9.29	   A^2 -> H(f(e), U1(e, c))
28.45/9.29	   A^2 -> H(f(e), U1(k, c))
28.45/9.29	   A^2 -> H(f(e), U1(c, e))
28.45/9.29	   A^2 -> H(f(e), U1(c, k))
28.45/9.29	   A^2 -> H(f(e), U1(k, k))
28.45/9.29	   A^2 -> H(f(e), U1(k, d))
28.45/9.29	   A^2 -> H(f(e), U1(d, k))
28.45/9.29	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.29	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.29	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.29	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.29	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.29	   A^2 -> H(U1(k, k), f(e))
28.45/9.29	   A^2 -> H(U1(k, k), f(k))
28.45/9.29	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.29	   A^2 -> H(f(k), U1(e, b))
28.45/9.29	   A^2 -> H(f(k), U1(k, b))
28.45/9.29	   A^2 -> H(f(k), U1(c, d))
28.45/9.29	   A^2 -> H(f(k), U1(d, c))
28.45/9.29	   A^2 -> H(f(k), U1(b, e))
28.45/9.29	   A^2 -> H(f(k), U1(b, k))
28.45/9.29	   A^2 -> H(f(k), U1(e, c))
28.45/9.29	   A^2 -> H(f(k), U1(k, c))
28.45/9.29	   A^2 -> H(f(k), U1(c, e))
28.45/9.29	   A^2 -> H(f(k), U1(c, k))
28.45/9.29	   A^2 -> H(f(k), U1(e, e))
28.45/9.29	   A^2 -> H(f(k), U1(k, d))
28.45/9.29	   A^2 -> H(f(k), U1(d, k))
28.45/9.29	   A^2 -> H(f(c), b)
28.45/9.29	   A^2 -> H(f(c), U1(e, d))
28.45/9.29	   A^2 -> H(f(c), U1(d, e))
28.45/9.29	   A^2 -> H(f(k), U1(k, k))
28.45/9.29	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.29	   A^2 -> H(U1(k, k), f(c))
28.45/9.29	   A^2 -> H(U1(k, k), f(d))
28.45/9.29	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.29	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.29	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.29	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.29	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.29	   A^2 -> H(U1(k, d), f(e))
28.45/9.29	   A^2 -> H(U1(k, d), f(k))
28.45/9.29	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.29	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.29	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.29	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.29	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.29	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.29	   A^2 -> H(U1(d, k), f(e))
28.45/9.29	   A^2 -> H(U1(d, k), f(k))
28.45/9.29	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.29	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.29	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.29	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.29	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.29	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.29	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.29	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.29	   A^2 -> H(f(d), b)
28.45/9.29	   A^2 -> H(f(d), U1(e, d))
28.45/9.29	   A^2 -> H(f(d), U1(d, e))
28.45/9.29	   A^2 -> H(f(d), c)
28.45/9.29	   A^2 -> H(f(d), U1(e, k))
28.45/9.29	   A^2 -> H(f(d), U1(k, e))
28.45/9.29	   A^2 -> H(f(d), e)
28.45/9.29	   A^2 -> H(f(a), d)
28.45/9.29	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.29	   A^2 -> H(f(c), c)
28.45/9.29	   A^2 -> H(f(c), U1(e, k))
28.45/9.29	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.29	   A^2 -> H(f(c), U1(k, e))
28.45/9.29	   A^2 -> H(f(c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.29	   A^2 -> H(f(a), k)
28.45/9.29	   A^2 -> H(f(e), U1(e, e))
28.45/9.29	   A^2 -> H(f(c), e)
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.29	   A^2 -> H(f(d), U1(k, k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.29	   A^2 -> H(d, U1(b, b))
28.45/9.29	   A^2 -> H(d, f(c))
28.45/9.29	   A^2 -> H(d, f(d))
28.45/9.29	   A^2 -> H(a, U1(c, b))
28.45/9.29	   A^2 -> H(a, U1(d, b))
28.45/9.29	   A^2 -> H(a, U1(b, c))
28.45/9.29	   A^2 -> H(a, U1(b, d))
28.45/9.29	   A^2 -> H(a, U1(c, c))
28.45/9.29	   A^2 -> H(a, f(e))
28.45/9.29	   A^2 -> H(a, f(k))
28.45/9.29	   A^2 -> H(a, U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.29	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.29	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.29	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.29	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.29	   A^2 -> H(U1(e, d), f(e))
28.45/9.29	   A^2 -> H(U1(e, d), f(k))
28.45/9.29	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.29	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.29	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.29	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.29	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.29	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.29	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.29	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.29	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.29	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.29	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.29	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.29	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.29	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.29	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.29	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.29	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.29	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.29	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.29	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.29	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.29	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.29	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, a), b)
28.45/9.29	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.29	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.29	   A^2 -> H(U1(c, a), c)
28.45/9.29	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.29	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.29	   A^2 -> H(U1(c, a), e)
28.45/9.29	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.29	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.29	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.29	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.29	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.29	   A^2 -> H(U1(d, e), f(e))
28.45/9.29	   A^2 -> H(U1(d, e), f(k))
28.45/9.29	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.29	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.29	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.29	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.29	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.29	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.29	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.29	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.29	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.29	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.29	   A^2 -> H(U1(d, a), b)
28.45/9.29	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.29	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.29	   A^2 -> H(U1(d, a), c)
28.45/9.29	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.29	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.29	   A^2 -> H(U1(d, a), e)
28.45/9.29	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.29	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.29	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.29	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.29	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.29	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.29	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.29	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.29	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.29	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.29	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.29	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.29	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.29	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.29	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.29	   A^2 -> H(U1(a, c), b)
28.45/9.29	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.29	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.29	   A^2 -> H(U1(a, c), c)
28.45/9.29	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.29	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.29	   A^2 -> H(U1(a, c), e)
28.45/9.29	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, d), b)
28.45/9.29	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.29	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.29	   A^2 -> H(U1(a, d), c)
28.45/9.29	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.29	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.29	   A^2 -> H(U1(a, d), e)
28.45/9.29	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, a), d)
28.45/9.29	   A^2 -> H(U1(a, a), k)
28.45/9.29	   A^2 -> H(k, U1(b, b))
28.45/9.29	   A^2 -> H(k, f(c))
28.45/9.29	   A^2 -> H(k, f(d))
28.45/9.29	   A^2 -> H(c, U1(c, b))
28.45/9.29	   A^2 -> H(c, U1(d, b))
28.45/9.29	   A^2 -> H(c, U1(b, c))
28.45/9.29	   A^2 -> H(c, U1(b, d))
28.45/9.29	   A^2 -> H(c, U1(c, c))
28.45/9.29	   A^2 -> H(c, f(e))
28.45/9.29	   A^2 -> H(c, f(k))
28.45/9.29	   A^2 -> H(c, U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.29	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.29	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.29	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.29	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.29	   A^2 -> H(U1(e, k), f(e))
28.45/9.29	   A^2 -> H(U1(e, k), f(k))
28.45/9.29	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.29	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.29	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.29	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.29	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.29	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.29	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.29	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.29	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.29	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.29	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.29	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.29	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.29	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.29	   A^2 -> H(U1(k, e), f(e))
28.45/9.29	   A^2 -> H(U1(k, e), f(k))
28.45/9.29	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.29	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.29	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.29	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.29	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.29	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.29	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.29	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.29	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.29	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.29	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.29	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.29	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.29	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.29	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.29	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.29	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.29	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.29	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.29	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.29	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.29	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, c), b)
28.45/9.29	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.29	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.29	   A^2 -> H(U1(c, c), e)
28.45/9.29	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.29	   A^2 -> H(e, U1(c, b))
28.45/9.29	   A^2 -> H(e, U1(d, b))
28.45/9.29	   A^2 -> H(e, U1(b, c))
28.45/9.29	   A^2 -> H(e, U1(b, d))
28.45/9.29	   A^2 -> H(e, U1(c, c))
28.45/9.29	   A^2 -> H(e, f(e))
28.45/9.29	   A^2 -> H(e, f(k))
28.45/9.29	   A^2 -> H(e, U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, e), U1(e, b))
28.45/9.29	   A^2 -> H(U1(e, e), U1(k, b))
28.45/9.29	   A^2 -> H(U1(e, e), U1(c, d))
28.45/9.29	   A^2 -> H(U1(e, e), U1(d, c))
28.45/9.29	   A^2 -> H(U1(e, e), U1(b, e))
28.45/9.29	   A^2 -> H(U1(e, e), U1(b, k))
28.45/9.29	   A^2 -> H(U1(e, e), U1(e, c))
28.45/9.29	   A^2 -> H(U1(e, e), U1(k, c))
28.45/9.29	   A^2 -> H(U1(e, e), U1(c, e))
28.45/9.29	   A^2 -> H(U1(e, e), U1(c, k))
28.45/9.29	   A^2 -> H(U1(e, e), U1(e, e))
28.45/9.29	   A^2 -> H(U1(e, e), U1(k, k))
28.45/9.29	
28.45/9.29	The TRS R consists of the following rules:
28.45/9.29	
28.45/9.29	   f(x) -> U1(x, x)
28.45/9.29	   U1(e, x) -> x
28.45/9.29	   a -> c
28.45/9.29	   a -> d
28.45/9.29	   b -> c
28.45/9.29	   b -> d
28.45/9.29	   d -> k
28.45/9.29	   c -> e
28.45/9.29	   c -> k
28.45/9.29	
28.45/9.29	Q is empty.
28.45/9.29	We have to consider all minimal (P,Q,R)-chains.
28.45/9.29	----------------------------------------
28.45/9.29	
28.45/9.29	(909) TransformationProof (EQUIVALENT)
28.45/9.29	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.29	
28.45/9.29	   (A^2 -> H(e, U1(d, d)),A^2 -> H(e, U1(d, d)))
28.45/9.29	   (A^2 -> H(U1(e, e), U1(k, d)),A^2 -> H(U1(e, e), U1(k, d)))
28.45/9.29	   (A^2 -> H(U1(e, e), U1(d, k)),A^2 -> H(U1(e, e), U1(d, k)))
28.45/9.29	
28.45/9.29	
28.45/9.29	----------------------------------------
28.45/9.29	
28.45/9.29	(910)
28.45/9.29	Obligation:
28.45/9.29	Q DP problem:
28.45/9.29	The TRS P consists of the following rules:
28.45/9.29	
28.45/9.29	   H(x, x) -> G(x, x, f(k))
28.45/9.29	   G(d, x, x) -> A^2
28.45/9.29	   A^2 -> H(f(c), f(c))
28.45/9.29	   A^2 -> H(f(d), f(d))
28.45/9.29	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.29	   A^2 -> H(f(e), f(e))
28.45/9.29	   A^2 -> H(f(k), f(k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.29	   A^2 -> H(f(e), U1(e, b))
28.45/9.29	   A^2 -> H(f(e), U1(k, b))
28.45/9.29	   A^2 -> H(f(e), U1(c, d))
28.45/9.29	   A^2 -> H(f(e), U1(d, c))
28.45/9.29	   A^2 -> H(f(e), U1(b, e))
28.45/9.29	   A^2 -> H(f(e), U1(b, k))
28.45/9.29	   A^2 -> H(f(e), U1(e, c))
28.45/9.29	   A^2 -> H(f(e), U1(k, c))
28.45/9.29	   A^2 -> H(f(e), U1(c, e))
28.45/9.29	   A^2 -> H(f(e), U1(c, k))
28.45/9.29	   A^2 -> H(f(e), U1(k, k))
28.45/9.29	   A^2 -> H(f(e), U1(k, d))
28.45/9.29	   A^2 -> H(f(e), U1(d, k))
28.45/9.29	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.29	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.29	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.29	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.29	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.29	   A^2 -> H(U1(k, k), f(e))
28.45/9.29	   A^2 -> H(U1(k, k), f(k))
28.45/9.29	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.29	   A^2 -> H(f(k), U1(e, b))
28.45/9.29	   A^2 -> H(f(k), U1(k, b))
28.45/9.29	   A^2 -> H(f(k), U1(c, d))
28.45/9.29	   A^2 -> H(f(k), U1(d, c))
28.45/9.29	   A^2 -> H(f(k), U1(b, e))
28.45/9.29	   A^2 -> H(f(k), U1(b, k))
28.45/9.29	   A^2 -> H(f(k), U1(e, c))
28.45/9.29	   A^2 -> H(f(k), U1(k, c))
28.45/9.29	   A^2 -> H(f(k), U1(c, e))
28.45/9.29	   A^2 -> H(f(k), U1(c, k))
28.45/9.29	   A^2 -> H(f(k), U1(e, e))
28.45/9.29	   A^2 -> H(f(k), U1(k, d))
28.45/9.29	   A^2 -> H(f(k), U1(d, k))
28.45/9.29	   A^2 -> H(f(c), b)
28.45/9.29	   A^2 -> H(f(c), U1(e, d))
28.45/9.29	   A^2 -> H(f(c), U1(d, e))
28.45/9.29	   A^2 -> H(f(k), U1(k, k))
28.45/9.29	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.29	   A^2 -> H(U1(k, k), f(c))
28.45/9.29	   A^2 -> H(U1(k, k), f(d))
28.45/9.29	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.29	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.29	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.29	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.29	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.29	   A^2 -> H(U1(k, d), f(e))
28.45/9.29	   A^2 -> H(U1(k, d), f(k))
28.45/9.29	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.29	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.29	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.29	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.29	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.29	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.29	   A^2 -> H(U1(d, k), f(e))
28.45/9.29	   A^2 -> H(U1(d, k), f(k))
28.45/9.29	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.29	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.29	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.29	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.29	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.29	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.29	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.29	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.29	   A^2 -> H(f(d), b)
28.45/9.29	   A^2 -> H(f(d), U1(e, d))
28.45/9.29	   A^2 -> H(f(d), U1(d, e))
28.45/9.29	   A^2 -> H(f(d), c)
28.45/9.29	   A^2 -> H(f(d), U1(e, k))
28.45/9.29	   A^2 -> H(f(d), U1(k, e))
28.45/9.29	   A^2 -> H(f(d), e)
28.45/9.29	   A^2 -> H(f(a), d)
28.45/9.29	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.29	   A^2 -> H(f(c), c)
28.45/9.29	   A^2 -> H(f(c), U1(e, k))
28.45/9.29	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.29	   A^2 -> H(f(c), U1(k, e))
28.45/9.29	   A^2 -> H(f(c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.29	   A^2 -> H(f(a), k)
28.45/9.29	   A^2 -> H(f(e), U1(e, e))
28.45/9.29	   A^2 -> H(f(c), e)
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.29	   A^2 -> H(f(d), U1(k, k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.29	   A^2 -> H(d, U1(b, b))
28.45/9.29	   A^2 -> H(d, f(c))
28.45/9.29	   A^2 -> H(d, f(d))
28.45/9.29	   A^2 -> H(a, U1(c, b))
28.45/9.29	   A^2 -> H(a, U1(d, b))
28.45/9.29	   A^2 -> H(a, U1(b, c))
28.45/9.29	   A^2 -> H(a, U1(b, d))
28.45/9.29	   A^2 -> H(a, U1(c, c))
28.45/9.29	   A^2 -> H(a, f(e))
28.45/9.29	   A^2 -> H(a, f(k))
28.45/9.29	   A^2 -> H(a, U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.29	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.29	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.29	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.29	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.29	   A^2 -> H(U1(e, d), f(e))
28.45/9.29	   A^2 -> H(U1(e, d), f(k))
28.45/9.29	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.29	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.29	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.29	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.29	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.29	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.29	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.29	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.29	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.29	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.29	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.29	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.29	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.29	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.29	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.29	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.29	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.29	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.29	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.29	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.29	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.29	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.29	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, a), b)
28.45/9.29	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.29	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.29	   A^2 -> H(U1(c, a), c)
28.45/9.29	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.29	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.29	   A^2 -> H(U1(c, a), e)
28.45/9.29	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.29	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.29	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.29	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.29	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.29	   A^2 -> H(U1(d, e), f(e))
28.45/9.29	   A^2 -> H(U1(d, e), f(k))
28.45/9.29	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.29	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.29	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.29	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.29	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.29	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.29	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.29	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.29	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.29	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.29	   A^2 -> H(U1(d, a), b)
28.45/9.29	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.29	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.29	   A^2 -> H(U1(d, a), c)
28.45/9.29	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.29	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.29	   A^2 -> H(U1(d, a), e)
28.45/9.29	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.29	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.29	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.29	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.29	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.29	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.29	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.29	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.29	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.29	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.29	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.29	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.29	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.29	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.29	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.29	   A^2 -> H(U1(a, c), b)
28.45/9.29	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.29	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.29	   A^2 -> H(U1(a, c), c)
28.45/9.29	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.29	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.29	   A^2 -> H(U1(a, c), e)
28.45/9.29	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, d), b)
28.45/9.29	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.29	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.29	   A^2 -> H(U1(a, d), c)
28.45/9.29	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.29	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.29	   A^2 -> H(U1(a, d), e)
28.45/9.29	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, a), d)
28.45/9.29	   A^2 -> H(U1(a, a), k)
28.45/9.29	   A^2 -> H(k, U1(b, b))
28.45/9.29	   A^2 -> H(k, f(c))
28.45/9.29	   A^2 -> H(k, f(d))
28.45/9.29	   A^2 -> H(c, U1(c, b))
28.45/9.29	   A^2 -> H(c, U1(d, b))
28.45/9.29	   A^2 -> H(c, U1(b, c))
28.45/9.29	   A^2 -> H(c, U1(b, d))
28.45/9.29	   A^2 -> H(c, U1(c, c))
28.45/9.29	   A^2 -> H(c, f(e))
28.45/9.29	   A^2 -> H(c, f(k))
28.45/9.29	   A^2 -> H(c, U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.29	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.29	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.29	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.29	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.29	   A^2 -> H(U1(e, k), f(e))
28.45/9.29	   A^2 -> H(U1(e, k), f(k))
28.45/9.29	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.29	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.29	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.29	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.29	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.29	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.29	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.29	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.29	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.29	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.29	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.29	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.29	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.29	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.29	   A^2 -> H(U1(k, e), f(e))
28.45/9.29	   A^2 -> H(U1(k, e), f(k))
28.45/9.29	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.29	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.29	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.29	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.29	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.29	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.29	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.29	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.29	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.29	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.29	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.29	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.29	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.29	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.29	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.29	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.29	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.29	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.29	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.29	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.29	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.29	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, c), b)
28.45/9.29	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.29	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.29	   A^2 -> H(U1(c, c), e)
28.45/9.29	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.29	   A^2 -> H(e, U1(c, b))
28.45/9.29	   A^2 -> H(e, U1(d, b))
28.45/9.29	   A^2 -> H(e, U1(b, c))
28.45/9.29	   A^2 -> H(e, U1(b, d))
28.45/9.29	   A^2 -> H(e, U1(c, c))
28.45/9.29	   A^2 -> H(e, f(e))
28.45/9.29	   A^2 -> H(e, f(k))
28.45/9.29	   A^2 -> H(e, U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, e), U1(e, b))
28.45/9.29	   A^2 -> H(U1(e, e), U1(k, b))
28.45/9.29	   A^2 -> H(U1(e, e), U1(c, d))
28.45/9.29	   A^2 -> H(U1(e, e), U1(d, c))
28.45/9.29	   A^2 -> H(U1(e, e), U1(b, e))
28.45/9.29	   A^2 -> H(U1(e, e), U1(b, k))
28.45/9.29	   A^2 -> H(U1(e, e), U1(e, c))
28.45/9.29	   A^2 -> H(U1(e, e), U1(k, c))
28.45/9.29	   A^2 -> H(U1(e, e), U1(c, e))
28.45/9.29	   A^2 -> H(U1(e, e), U1(c, k))
28.45/9.29	   A^2 -> H(U1(e, e), U1(e, e))
28.45/9.29	   A^2 -> H(U1(e, e), U1(k, k))
28.45/9.29	   A^2 -> H(U1(e, e), U1(k, d))
28.45/9.29	   A^2 -> H(U1(e, e), U1(d, k))
28.45/9.29	
28.45/9.29	The TRS R consists of the following rules:
28.45/9.29	
28.45/9.29	   f(x) -> U1(x, x)
28.45/9.29	   U1(e, x) -> x
28.45/9.29	   a -> c
28.45/9.29	   a -> d
28.45/9.29	   b -> c
28.45/9.29	   b -> d
28.45/9.29	   d -> k
28.45/9.29	   c -> e
28.45/9.29	   c -> k
28.45/9.29	
28.45/9.29	Q is empty.
28.45/9.29	We have to consider all minimal (P,Q,R)-chains.
28.45/9.29	----------------------------------------
28.45/9.29	
28.45/9.29	(911) TransformationProof (EQUIVALENT)
28.45/9.29	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.29	
28.45/9.29	   (A^2 -> H(U1(e, e), U1(e, b)),A^2 -> H(U1(e, e), U1(e, b)))
28.45/9.29	   (A^2 -> H(f(e), b),A^2 -> H(f(e), b))
28.45/9.29	   (A^2 -> H(f(e), U1(e, c)),A^2 -> H(f(e), U1(e, c)))
28.45/9.29	   (A^2 -> H(f(e), U1(e, d)),A^2 -> H(f(e), U1(e, d)))
28.45/9.29	
28.45/9.29	
28.45/9.29	----------------------------------------
28.45/9.29	
28.45/9.29	(912)
28.45/9.29	Obligation:
28.45/9.29	Q DP problem:
28.45/9.29	The TRS P consists of the following rules:
28.45/9.29	
28.45/9.29	   H(x, x) -> G(x, x, f(k))
28.45/9.29	   G(d, x, x) -> A^2
28.45/9.29	   A^2 -> H(f(c), f(c))
28.45/9.29	   A^2 -> H(f(d), f(d))
28.45/9.29	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.29	   A^2 -> H(f(e), f(e))
28.45/9.29	   A^2 -> H(f(k), f(k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.29	   A^2 -> H(f(e), U1(k, b))
28.45/9.29	   A^2 -> H(f(e), U1(c, d))
28.45/9.29	   A^2 -> H(f(e), U1(d, c))
28.45/9.29	   A^2 -> H(f(e), U1(b, e))
28.45/9.29	   A^2 -> H(f(e), U1(b, k))
28.45/9.29	   A^2 -> H(f(e), U1(e, c))
28.45/9.29	   A^2 -> H(f(e), U1(k, c))
28.45/9.29	   A^2 -> H(f(e), U1(c, e))
28.45/9.29	   A^2 -> H(f(e), U1(c, k))
28.45/9.29	   A^2 -> H(f(e), U1(k, k))
28.45/9.29	   A^2 -> H(f(e), U1(k, d))
28.45/9.29	   A^2 -> H(f(e), U1(d, k))
28.45/9.29	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.29	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.29	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.29	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.29	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.29	   A^2 -> H(U1(k, k), f(e))
28.45/9.29	   A^2 -> H(U1(k, k), f(k))
28.45/9.29	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.29	   A^2 -> H(f(k), U1(e, b))
28.45/9.29	   A^2 -> H(f(k), U1(k, b))
28.45/9.29	   A^2 -> H(f(k), U1(c, d))
28.45/9.29	   A^2 -> H(f(k), U1(d, c))
28.45/9.29	   A^2 -> H(f(k), U1(b, e))
28.45/9.29	   A^2 -> H(f(k), U1(b, k))
28.45/9.29	   A^2 -> H(f(k), U1(e, c))
28.45/9.29	   A^2 -> H(f(k), U1(k, c))
28.45/9.29	   A^2 -> H(f(k), U1(c, e))
28.45/9.29	   A^2 -> H(f(k), U1(c, k))
28.45/9.29	   A^2 -> H(f(k), U1(e, e))
28.45/9.29	   A^2 -> H(f(k), U1(k, d))
28.45/9.29	   A^2 -> H(f(k), U1(d, k))
28.45/9.29	   A^2 -> H(f(c), b)
28.45/9.29	   A^2 -> H(f(c), U1(e, d))
28.45/9.29	   A^2 -> H(f(c), U1(d, e))
28.45/9.29	   A^2 -> H(f(k), U1(k, k))
28.45/9.29	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.29	   A^2 -> H(U1(k, k), f(c))
28.45/9.29	   A^2 -> H(U1(k, k), f(d))
28.45/9.29	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.29	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.29	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.29	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.29	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.29	   A^2 -> H(U1(k, d), f(e))
28.45/9.29	   A^2 -> H(U1(k, d), f(k))
28.45/9.29	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.29	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.29	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.29	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.29	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.29	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.29	   A^2 -> H(U1(d, k), f(e))
28.45/9.29	   A^2 -> H(U1(d, k), f(k))
28.45/9.29	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.29	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.29	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.29	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.29	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.29	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.29	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.29	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.29	   A^2 -> H(f(d), b)
28.45/9.29	   A^2 -> H(f(d), U1(e, d))
28.45/9.29	   A^2 -> H(f(d), U1(d, e))
28.45/9.29	   A^2 -> H(f(d), c)
28.45/9.29	   A^2 -> H(f(d), U1(e, k))
28.45/9.29	   A^2 -> H(f(d), U1(k, e))
28.45/9.29	   A^2 -> H(f(d), e)
28.45/9.29	   A^2 -> H(f(a), d)
28.45/9.29	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.29	   A^2 -> H(f(c), c)
28.45/9.29	   A^2 -> H(f(c), U1(e, k))
28.45/9.29	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.29	   A^2 -> H(f(c), U1(k, e))
28.45/9.29	   A^2 -> H(f(c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.29	   A^2 -> H(f(a), k)
28.45/9.29	   A^2 -> H(f(e), U1(e, e))
28.45/9.29	   A^2 -> H(f(c), e)
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.29	   A^2 -> H(f(d), U1(k, k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.29	   A^2 -> H(d, U1(b, b))
28.45/9.29	   A^2 -> H(d, f(c))
28.45/9.29	   A^2 -> H(d, f(d))
28.45/9.29	   A^2 -> H(a, U1(c, b))
28.45/9.29	   A^2 -> H(a, U1(d, b))
28.45/9.29	   A^2 -> H(a, U1(b, c))
28.45/9.29	   A^2 -> H(a, U1(b, d))
28.45/9.29	   A^2 -> H(a, U1(c, c))
28.45/9.29	   A^2 -> H(a, f(e))
28.45/9.29	   A^2 -> H(a, f(k))
28.45/9.29	   A^2 -> H(a, U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.29	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.29	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.29	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.29	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.29	   A^2 -> H(U1(e, d), f(e))
28.45/9.29	   A^2 -> H(U1(e, d), f(k))
28.45/9.29	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.29	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.29	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.29	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.29	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.29	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.29	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.29	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.29	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.29	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.29	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.29	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.29	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.29	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.29	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.29	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.29	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.29	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.29	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.29	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.29	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.29	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.29	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, a), b)
28.45/9.29	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.29	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.29	   A^2 -> H(U1(c, a), c)
28.45/9.29	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.29	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.29	   A^2 -> H(U1(c, a), e)
28.45/9.29	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.29	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.29	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.29	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.29	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.29	   A^2 -> H(U1(d, e), f(e))
28.45/9.29	   A^2 -> H(U1(d, e), f(k))
28.45/9.29	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.29	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.29	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.29	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.29	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.29	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.29	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.29	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.29	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.29	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.29	   A^2 -> H(U1(d, a), b)
28.45/9.29	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.29	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.29	   A^2 -> H(U1(d, a), c)
28.45/9.29	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.29	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.29	   A^2 -> H(U1(d, a), e)
28.45/9.29	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.29	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.29	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.29	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.29	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.29	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.29	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.29	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.29	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.29	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.29	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.29	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.29	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.29	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.29	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.29	   A^2 -> H(U1(a, c), b)
28.45/9.29	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.29	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.29	   A^2 -> H(U1(a, c), c)
28.45/9.29	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.29	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.29	   A^2 -> H(U1(a, c), e)
28.45/9.29	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, d), b)
28.45/9.29	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.29	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.29	   A^2 -> H(U1(a, d), c)
28.45/9.29	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.29	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.29	   A^2 -> H(U1(a, d), e)
28.45/9.29	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, a), d)
28.45/9.29	   A^2 -> H(U1(a, a), k)
28.45/9.29	   A^2 -> H(k, U1(b, b))
28.45/9.29	   A^2 -> H(k, f(c))
28.45/9.29	   A^2 -> H(k, f(d))
28.45/9.29	   A^2 -> H(c, U1(c, b))
28.45/9.29	   A^2 -> H(c, U1(d, b))
28.45/9.29	   A^2 -> H(c, U1(b, c))
28.45/9.29	   A^2 -> H(c, U1(b, d))
28.45/9.29	   A^2 -> H(c, U1(c, c))
28.45/9.29	   A^2 -> H(c, f(e))
28.45/9.29	   A^2 -> H(c, f(k))
28.45/9.29	   A^2 -> H(c, U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.29	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.29	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.29	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.29	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.29	   A^2 -> H(U1(e, k), f(e))
28.45/9.29	   A^2 -> H(U1(e, k), f(k))
28.45/9.29	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.29	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.29	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.29	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.29	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.29	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.29	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.29	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.29	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.29	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.29	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.29	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.29	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.29	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.29	   A^2 -> H(U1(k, e), f(e))
28.45/9.29	   A^2 -> H(U1(k, e), f(k))
28.45/9.29	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.29	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.29	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.29	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.29	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.29	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.29	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.29	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.29	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.29	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.29	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.29	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.29	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.29	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.29	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.29	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.29	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.29	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.29	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.29	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.29	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.29	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, c), b)
28.45/9.29	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.29	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.29	   A^2 -> H(U1(c, c), e)
28.45/9.29	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.29	   A^2 -> H(e, U1(c, b))
28.45/9.29	   A^2 -> H(e, U1(d, b))
28.45/9.29	   A^2 -> H(e, U1(b, c))
28.45/9.29	   A^2 -> H(e, U1(b, d))
28.45/9.29	   A^2 -> H(e, U1(c, c))
28.45/9.29	   A^2 -> H(e, f(e))
28.45/9.29	   A^2 -> H(e, f(k))
28.45/9.29	   A^2 -> H(e, U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, e), U1(e, b))
28.45/9.29	   A^2 -> H(U1(e, e), U1(k, b))
28.45/9.29	   A^2 -> H(U1(e, e), U1(c, d))
28.45/9.29	   A^2 -> H(U1(e, e), U1(d, c))
28.45/9.29	   A^2 -> H(U1(e, e), U1(b, e))
28.45/9.29	   A^2 -> H(U1(e, e), U1(b, k))
28.45/9.29	   A^2 -> H(U1(e, e), U1(e, c))
28.45/9.29	   A^2 -> H(U1(e, e), U1(k, c))
28.45/9.29	   A^2 -> H(U1(e, e), U1(c, e))
28.45/9.29	   A^2 -> H(U1(e, e), U1(c, k))
28.45/9.29	   A^2 -> H(U1(e, e), U1(e, e))
28.45/9.29	   A^2 -> H(U1(e, e), U1(k, k))
28.45/9.29	   A^2 -> H(U1(e, e), U1(k, d))
28.45/9.29	   A^2 -> H(U1(e, e), U1(d, k))
28.45/9.29	   A^2 -> H(f(e), b)
28.45/9.29	   A^2 -> H(f(e), U1(e, d))
28.45/9.29	
28.45/9.29	The TRS R consists of the following rules:
28.45/9.29	
28.45/9.29	   f(x) -> U1(x, x)
28.45/9.29	   U1(e, x) -> x
28.45/9.29	   a -> c
28.45/9.29	   a -> d
28.45/9.29	   b -> c
28.45/9.29	   b -> d
28.45/9.29	   d -> k
28.45/9.29	   c -> e
28.45/9.29	   c -> k
28.45/9.29	
28.45/9.29	Q is empty.
28.45/9.29	We have to consider all minimal (P,Q,R)-chains.
28.45/9.29	----------------------------------------
28.45/9.29	
28.45/9.29	(913) TransformationProof (EQUIVALENT)
28.45/9.29	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.29	
28.45/9.29	   (A^2 -> H(U1(e, e), U1(k, b)),A^2 -> H(U1(e, e), U1(k, b)))
28.45/9.29	   (A^2 -> H(f(e), U1(k, c)),A^2 -> H(f(e), U1(k, c)))
28.45/9.29	   (A^2 -> H(f(e), U1(k, d)),A^2 -> H(f(e), U1(k, d)))
28.45/9.29	
28.45/9.29	
28.45/9.29	----------------------------------------
28.45/9.29	
28.45/9.29	(914)
28.45/9.29	Obligation:
28.45/9.29	Q DP problem:
28.45/9.29	The TRS P consists of the following rules:
28.45/9.29	
28.45/9.29	   H(x, x) -> G(x, x, f(k))
28.45/9.29	   G(d, x, x) -> A^2
28.45/9.29	   A^2 -> H(f(c), f(c))
28.45/9.29	   A^2 -> H(f(d), f(d))
28.45/9.29	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.29	   A^2 -> H(f(e), f(e))
28.45/9.29	   A^2 -> H(f(k), f(k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.29	   A^2 -> H(f(e), U1(c, d))
28.45/9.29	   A^2 -> H(f(e), U1(d, c))
28.45/9.29	   A^2 -> H(f(e), U1(b, e))
28.45/9.29	   A^2 -> H(f(e), U1(b, k))
28.45/9.29	   A^2 -> H(f(e), U1(e, c))
28.45/9.29	   A^2 -> H(f(e), U1(k, c))
28.45/9.29	   A^2 -> H(f(e), U1(c, e))
28.45/9.29	   A^2 -> H(f(e), U1(c, k))
28.45/9.29	   A^2 -> H(f(e), U1(k, k))
28.45/9.29	   A^2 -> H(f(e), U1(k, d))
28.45/9.29	   A^2 -> H(f(e), U1(d, k))
28.45/9.29	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.29	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.29	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.29	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.29	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.29	   A^2 -> H(U1(k, k), f(e))
28.45/9.29	   A^2 -> H(U1(k, k), f(k))
28.45/9.29	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.29	   A^2 -> H(f(k), U1(e, b))
28.45/9.29	   A^2 -> H(f(k), U1(k, b))
28.45/9.29	   A^2 -> H(f(k), U1(c, d))
28.45/9.29	   A^2 -> H(f(k), U1(d, c))
28.45/9.29	   A^2 -> H(f(k), U1(b, e))
28.45/9.29	   A^2 -> H(f(k), U1(b, k))
28.45/9.29	   A^2 -> H(f(k), U1(e, c))
28.45/9.29	   A^2 -> H(f(k), U1(k, c))
28.45/9.29	   A^2 -> H(f(k), U1(c, e))
28.45/9.29	   A^2 -> H(f(k), U1(c, k))
28.45/9.29	   A^2 -> H(f(k), U1(e, e))
28.45/9.29	   A^2 -> H(f(k), U1(k, d))
28.45/9.29	   A^2 -> H(f(k), U1(d, k))
28.45/9.29	   A^2 -> H(f(c), b)
28.45/9.29	   A^2 -> H(f(c), U1(e, d))
28.45/9.29	   A^2 -> H(f(c), U1(d, e))
28.45/9.29	   A^2 -> H(f(k), U1(k, k))
28.45/9.29	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.29	   A^2 -> H(U1(k, k), f(c))
28.45/9.29	   A^2 -> H(U1(k, k), f(d))
28.45/9.29	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.29	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.29	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.29	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.29	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.29	   A^2 -> H(U1(k, d), f(e))
28.45/9.29	   A^2 -> H(U1(k, d), f(k))
28.45/9.29	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.29	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.29	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.29	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.29	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.29	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.29	   A^2 -> H(U1(d, k), f(e))
28.45/9.29	   A^2 -> H(U1(d, k), f(k))
28.45/9.29	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.29	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.29	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.29	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.29	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.29	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.29	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.29	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.29	   A^2 -> H(f(d), b)
28.45/9.29	   A^2 -> H(f(d), U1(e, d))
28.45/9.29	   A^2 -> H(f(d), U1(d, e))
28.45/9.29	   A^2 -> H(f(d), c)
28.45/9.29	   A^2 -> H(f(d), U1(e, k))
28.45/9.29	   A^2 -> H(f(d), U1(k, e))
28.45/9.29	   A^2 -> H(f(d), e)
28.45/9.29	   A^2 -> H(f(a), d)
28.45/9.29	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.29	   A^2 -> H(f(c), c)
28.45/9.29	   A^2 -> H(f(c), U1(e, k))
28.45/9.29	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.29	   A^2 -> H(f(c), U1(k, e))
28.45/9.29	   A^2 -> H(f(c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.29	   A^2 -> H(f(a), k)
28.45/9.29	   A^2 -> H(f(e), U1(e, e))
28.45/9.29	   A^2 -> H(f(c), e)
28.45/9.29	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.29	   A^2 -> H(f(d), U1(k, k))
28.45/9.29	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.29	   A^2 -> H(d, U1(b, b))
28.45/9.29	   A^2 -> H(d, f(c))
28.45/9.29	   A^2 -> H(d, f(d))
28.45/9.29	   A^2 -> H(a, U1(c, b))
28.45/9.29	   A^2 -> H(a, U1(d, b))
28.45/9.29	   A^2 -> H(a, U1(b, c))
28.45/9.29	   A^2 -> H(a, U1(b, d))
28.45/9.29	   A^2 -> H(a, U1(c, c))
28.45/9.29	   A^2 -> H(a, f(e))
28.45/9.29	   A^2 -> H(a, f(k))
28.45/9.29	   A^2 -> H(a, U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.29	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.29	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.29	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.29	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.29	   A^2 -> H(U1(e, d), f(e))
28.45/9.29	   A^2 -> H(U1(e, d), f(k))
28.45/9.29	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.29	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.29	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.29	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.29	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.29	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.29	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.29	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.29	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.29	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.29	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.29	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.29	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.29	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.29	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.29	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.29	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.29	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.29	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.29	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.29	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.29	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.29	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.29	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.29	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.29	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.29	   A^2 -> H(U1(c, a), b)
28.45/9.29	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.29	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.29	   A^2 -> H(U1(c, a), c)
28.45/9.29	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.29	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.29	   A^2 -> H(U1(c, a), e)
28.45/9.29	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.29	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.29	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.29	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.29	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.29	   A^2 -> H(U1(d, e), f(e))
28.45/9.29	   A^2 -> H(U1(d, e), f(k))
28.45/9.29	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.29	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.29	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.29	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.29	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.29	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.29	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.29	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.29	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.29	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.29	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.29	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.29	   A^2 -> H(U1(d, a), b)
28.45/9.29	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.29	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.29	   A^2 -> H(U1(d, a), c)
28.45/9.29	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.29	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.29	   A^2 -> H(U1(d, a), e)
28.45/9.29	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.29	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.29	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.29	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.29	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.29	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.29	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.29	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.29	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.30	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.30	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.30	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.30	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.30	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.30	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.30	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.30	   A^2 -> H(U1(a, c), b)
28.45/9.30	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.30	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.30	   A^2 -> H(U1(a, c), c)
28.45/9.30	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.30	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.30	   A^2 -> H(U1(a, c), e)
28.45/9.30	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, d), b)
28.45/9.30	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.30	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.30	   A^2 -> H(U1(a, d), c)
28.45/9.30	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.30	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.30	   A^2 -> H(U1(a, d), e)
28.45/9.30	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, a), d)
28.45/9.30	   A^2 -> H(U1(a, a), k)
28.45/9.30	   A^2 -> H(k, U1(b, b))
28.45/9.30	   A^2 -> H(k, f(c))
28.45/9.30	   A^2 -> H(k, f(d))
28.45/9.30	   A^2 -> H(c, U1(c, b))
28.45/9.30	   A^2 -> H(c, U1(d, b))
28.45/9.30	   A^2 -> H(c, U1(b, c))
28.45/9.30	   A^2 -> H(c, U1(b, d))
28.45/9.30	   A^2 -> H(c, U1(c, c))
28.45/9.30	   A^2 -> H(c, f(e))
28.45/9.30	   A^2 -> H(c, f(k))
28.45/9.30	   A^2 -> H(c, U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.30	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.30	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.30	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.30	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.30	   A^2 -> H(U1(e, k), f(e))
28.45/9.30	   A^2 -> H(U1(e, k), f(k))
28.45/9.30	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.30	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.30	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.30	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.30	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.30	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.30	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.30	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.30	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.30	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.30	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.30	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.30	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.30	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.30	   A^2 -> H(U1(k, e), f(e))
28.45/9.30	   A^2 -> H(U1(k, e), f(k))
28.45/9.30	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.30	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.30	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.30	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.30	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.30	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.30	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.30	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.30	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.30	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.30	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.30	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.30	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.30	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.30	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.30	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.30	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.30	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.30	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.30	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.30	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.30	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, c), b)
28.45/9.30	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.30	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.30	   A^2 -> H(U1(c, c), e)
28.45/9.30	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.30	   A^2 -> H(e, U1(c, b))
28.45/9.30	   A^2 -> H(e, U1(d, b))
28.45/9.30	   A^2 -> H(e, U1(b, c))
28.45/9.30	   A^2 -> H(e, U1(b, d))
28.45/9.30	   A^2 -> H(e, U1(c, c))
28.45/9.30	   A^2 -> H(e, f(e))
28.45/9.30	   A^2 -> H(e, f(k))
28.45/9.30	   A^2 -> H(e, U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, e), U1(e, b))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, b))
28.45/9.30	   A^2 -> H(U1(e, e), U1(c, d))
28.45/9.30	   A^2 -> H(U1(e, e), U1(d, c))
28.45/9.30	   A^2 -> H(U1(e, e), U1(b, e))
28.45/9.30	   A^2 -> H(U1(e, e), U1(b, k))
28.45/9.30	   A^2 -> H(U1(e, e), U1(e, c))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, c))
28.45/9.30	   A^2 -> H(U1(e, e), U1(c, e))
28.45/9.30	   A^2 -> H(U1(e, e), U1(c, k))
28.45/9.30	   A^2 -> H(U1(e, e), U1(e, e))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, k))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, d))
28.45/9.30	   A^2 -> H(U1(e, e), U1(d, k))
28.45/9.30	   A^2 -> H(f(e), b)
28.45/9.30	   A^2 -> H(f(e), U1(e, d))
28.45/9.30	
28.45/9.30	The TRS R consists of the following rules:
28.45/9.30	
28.45/9.30	   f(x) -> U1(x, x)
28.45/9.30	   U1(e, x) -> x
28.45/9.30	   a -> c
28.45/9.30	   a -> d
28.45/9.30	   b -> c
28.45/9.30	   b -> d
28.45/9.30	   d -> k
28.45/9.30	   c -> e
28.45/9.30	   c -> k
28.45/9.30	
28.45/9.30	Q is empty.
28.45/9.30	We have to consider all minimal (P,Q,R)-chains.
28.45/9.30	----------------------------------------
28.45/9.30	
28.45/9.30	(915) TransformationProof (EQUIVALENT)
28.45/9.30	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.30	
28.45/9.30	   (A^2 -> H(U1(e, e), U1(c, d)),A^2 -> H(U1(e, e), U1(c, d)))
28.45/9.30	   (A^2 -> H(f(e), U1(e, d)),A^2 -> H(f(e), U1(e, d)))
28.45/9.30	   (A^2 -> H(f(e), U1(k, d)),A^2 -> H(f(e), U1(k, d)))
28.45/9.30	   (A^2 -> H(f(e), U1(c, k)),A^2 -> H(f(e), U1(c, k)))
28.45/9.30	
28.45/9.30	
28.45/9.30	----------------------------------------
28.45/9.30	
28.45/9.30	(916)
28.45/9.30	Obligation:
28.45/9.30	Q DP problem:
28.45/9.30	The TRS P consists of the following rules:
28.45/9.30	
28.45/9.30	   H(x, x) -> G(x, x, f(k))
28.45/9.30	   G(d, x, x) -> A^2
28.45/9.30	   A^2 -> H(f(c), f(c))
28.45/9.30	   A^2 -> H(f(d), f(d))
28.45/9.30	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.30	   A^2 -> H(f(e), f(e))
28.45/9.30	   A^2 -> H(f(k), f(k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.30	   A^2 -> H(f(e), U1(d, c))
28.45/9.30	   A^2 -> H(f(e), U1(b, e))
28.45/9.30	   A^2 -> H(f(e), U1(b, k))
28.45/9.30	   A^2 -> H(f(e), U1(e, c))
28.45/9.30	   A^2 -> H(f(e), U1(k, c))
28.45/9.30	   A^2 -> H(f(e), U1(c, e))
28.45/9.30	   A^2 -> H(f(e), U1(c, k))
28.45/9.30	   A^2 -> H(f(e), U1(k, k))
28.45/9.30	   A^2 -> H(f(e), U1(k, d))
28.45/9.30	   A^2 -> H(f(e), U1(d, k))
28.45/9.30	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.30	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.30	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.30	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.30	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.30	   A^2 -> H(U1(k, k), f(e))
28.45/9.30	   A^2 -> H(U1(k, k), f(k))
28.45/9.30	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.30	   A^2 -> H(f(k), U1(e, b))
28.45/9.30	   A^2 -> H(f(k), U1(k, b))
28.45/9.30	   A^2 -> H(f(k), U1(c, d))
28.45/9.30	   A^2 -> H(f(k), U1(d, c))
28.45/9.30	   A^2 -> H(f(k), U1(b, e))
28.45/9.30	   A^2 -> H(f(k), U1(b, k))
28.45/9.30	   A^2 -> H(f(k), U1(e, c))
28.45/9.30	   A^2 -> H(f(k), U1(k, c))
28.45/9.30	   A^2 -> H(f(k), U1(c, e))
28.45/9.30	   A^2 -> H(f(k), U1(c, k))
28.45/9.30	   A^2 -> H(f(k), U1(e, e))
28.45/9.30	   A^2 -> H(f(k), U1(k, d))
28.45/9.30	   A^2 -> H(f(k), U1(d, k))
28.45/9.30	   A^2 -> H(f(c), b)
28.45/9.30	   A^2 -> H(f(c), U1(e, d))
28.45/9.30	   A^2 -> H(f(c), U1(d, e))
28.45/9.30	   A^2 -> H(f(k), U1(k, k))
28.45/9.30	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.30	   A^2 -> H(U1(k, k), f(c))
28.45/9.30	   A^2 -> H(U1(k, k), f(d))
28.45/9.30	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.30	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.30	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.30	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.30	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.30	   A^2 -> H(U1(k, d), f(e))
28.45/9.30	   A^2 -> H(U1(k, d), f(k))
28.45/9.30	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.30	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.30	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.30	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.30	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.30	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.30	   A^2 -> H(U1(d, k), f(e))
28.45/9.30	   A^2 -> H(U1(d, k), f(k))
28.45/9.30	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.30	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.30	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.30	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.30	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.30	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.30	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.30	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.30	   A^2 -> H(f(d), b)
28.45/9.30	   A^2 -> H(f(d), U1(e, d))
28.45/9.30	   A^2 -> H(f(d), U1(d, e))
28.45/9.30	   A^2 -> H(f(d), c)
28.45/9.30	   A^2 -> H(f(d), U1(e, k))
28.45/9.30	   A^2 -> H(f(d), U1(k, e))
28.45/9.30	   A^2 -> H(f(d), e)
28.45/9.30	   A^2 -> H(f(a), d)
28.45/9.30	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.30	   A^2 -> H(f(c), c)
28.45/9.30	   A^2 -> H(f(c), U1(e, k))
28.45/9.30	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.30	   A^2 -> H(f(c), U1(k, e))
28.45/9.30	   A^2 -> H(f(c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.30	   A^2 -> H(f(a), k)
28.45/9.30	   A^2 -> H(f(e), U1(e, e))
28.45/9.30	   A^2 -> H(f(c), e)
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.30	   A^2 -> H(f(d), U1(k, k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.30	   A^2 -> H(d, U1(b, b))
28.45/9.30	   A^2 -> H(d, f(c))
28.45/9.30	   A^2 -> H(d, f(d))
28.45/9.30	   A^2 -> H(a, U1(c, b))
28.45/9.30	   A^2 -> H(a, U1(d, b))
28.45/9.30	   A^2 -> H(a, U1(b, c))
28.45/9.30	   A^2 -> H(a, U1(b, d))
28.45/9.30	   A^2 -> H(a, U1(c, c))
28.45/9.30	   A^2 -> H(a, f(e))
28.45/9.30	   A^2 -> H(a, f(k))
28.45/9.30	   A^2 -> H(a, U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.30	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.30	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.30	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.30	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.30	   A^2 -> H(U1(e, d), f(e))
28.45/9.30	   A^2 -> H(U1(e, d), f(k))
28.45/9.30	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.30	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.30	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.30	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.30	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.30	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.30	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.30	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.30	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.30	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.30	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.30	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.30	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.30	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.30	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.30	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.30	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.30	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.30	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.30	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.30	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.30	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.30	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, a), b)
28.45/9.30	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.30	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.30	   A^2 -> H(U1(c, a), c)
28.45/9.30	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.30	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.30	   A^2 -> H(U1(c, a), e)
28.45/9.30	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.30	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.30	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.30	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.30	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.30	   A^2 -> H(U1(d, e), f(e))
28.45/9.30	   A^2 -> H(U1(d, e), f(k))
28.45/9.30	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.30	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.30	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.30	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.30	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.30	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.30	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.30	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.30	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.30	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.30	   A^2 -> H(U1(d, a), b)
28.45/9.30	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.30	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.30	   A^2 -> H(U1(d, a), c)
28.45/9.30	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.30	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.30	   A^2 -> H(U1(d, a), e)
28.45/9.30	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.30	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.30	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.30	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.30	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.30	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.30	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.30	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.30	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.30	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.30	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.30	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.30	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.30	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.30	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.30	   A^2 -> H(U1(a, c), b)
28.45/9.30	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.30	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.30	   A^2 -> H(U1(a, c), c)
28.45/9.30	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.30	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.30	   A^2 -> H(U1(a, c), e)
28.45/9.30	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, d), b)
28.45/9.30	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.30	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.30	   A^2 -> H(U1(a, d), c)
28.45/9.30	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.30	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.30	   A^2 -> H(U1(a, d), e)
28.45/9.30	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, a), d)
28.45/9.30	   A^2 -> H(U1(a, a), k)
28.45/9.30	   A^2 -> H(k, U1(b, b))
28.45/9.30	   A^2 -> H(k, f(c))
28.45/9.30	   A^2 -> H(k, f(d))
28.45/9.30	   A^2 -> H(c, U1(c, b))
28.45/9.30	   A^2 -> H(c, U1(d, b))
28.45/9.30	   A^2 -> H(c, U1(b, c))
28.45/9.30	   A^2 -> H(c, U1(b, d))
28.45/9.30	   A^2 -> H(c, U1(c, c))
28.45/9.30	   A^2 -> H(c, f(e))
28.45/9.30	   A^2 -> H(c, f(k))
28.45/9.30	   A^2 -> H(c, U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.30	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.30	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.30	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.30	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.30	   A^2 -> H(U1(e, k), f(e))
28.45/9.30	   A^2 -> H(U1(e, k), f(k))
28.45/9.30	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.30	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.30	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.30	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.30	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.30	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.30	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.30	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.30	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.30	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.30	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.30	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.30	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.30	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.30	   A^2 -> H(U1(k, e), f(e))
28.45/9.30	   A^2 -> H(U1(k, e), f(k))
28.45/9.30	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.30	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.30	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.30	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.30	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.30	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.30	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.30	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.30	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.30	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.30	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.30	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.30	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.30	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.30	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.30	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.30	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.30	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.30	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.30	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.30	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.30	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, c), b)
28.45/9.30	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.30	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.30	   A^2 -> H(U1(c, c), e)
28.45/9.30	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.30	   A^2 -> H(e, U1(c, b))
28.45/9.30	   A^2 -> H(e, U1(d, b))
28.45/9.30	   A^2 -> H(e, U1(b, c))
28.45/9.30	   A^2 -> H(e, U1(b, d))
28.45/9.30	   A^2 -> H(e, U1(c, c))
28.45/9.30	   A^2 -> H(e, f(e))
28.45/9.30	   A^2 -> H(e, f(k))
28.45/9.30	   A^2 -> H(e, U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, e), U1(e, b))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, b))
28.45/9.30	   A^2 -> H(U1(e, e), U1(c, d))
28.45/9.30	   A^2 -> H(U1(e, e), U1(d, c))
28.45/9.30	   A^2 -> H(U1(e, e), U1(b, e))
28.45/9.30	   A^2 -> H(U1(e, e), U1(b, k))
28.45/9.30	   A^2 -> H(U1(e, e), U1(e, c))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, c))
28.45/9.30	   A^2 -> H(U1(e, e), U1(c, e))
28.45/9.30	   A^2 -> H(U1(e, e), U1(c, k))
28.45/9.30	   A^2 -> H(U1(e, e), U1(e, e))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, k))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, d))
28.45/9.30	   A^2 -> H(U1(e, e), U1(d, k))
28.45/9.30	   A^2 -> H(f(e), b)
28.45/9.30	   A^2 -> H(f(e), U1(e, d))
28.45/9.30	
28.45/9.30	The TRS R consists of the following rules:
28.45/9.30	
28.45/9.30	   f(x) -> U1(x, x)
28.45/9.30	   U1(e, x) -> x
28.45/9.30	   a -> c
28.45/9.30	   a -> d
28.45/9.30	   b -> c
28.45/9.30	   b -> d
28.45/9.30	   d -> k
28.45/9.30	   c -> e
28.45/9.30	   c -> k
28.45/9.30	
28.45/9.30	Q is empty.
28.45/9.30	We have to consider all minimal (P,Q,R)-chains.
28.45/9.30	----------------------------------------
28.45/9.30	
28.45/9.30	(917) TransformationProof (EQUIVALENT)
28.45/9.30	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.30	
28.45/9.30	   (A^2 -> H(U1(e, e), U1(d, c)),A^2 -> H(U1(e, e), U1(d, c)))
28.45/9.30	   (A^2 -> H(f(e), U1(k, c)),A^2 -> H(f(e), U1(k, c)))
28.45/9.30	   (A^2 -> H(f(e), U1(d, e)),A^2 -> H(f(e), U1(d, e)))
28.45/9.30	   (A^2 -> H(f(e), U1(d, k)),A^2 -> H(f(e), U1(d, k)))
28.45/9.30	
28.45/9.30	
28.45/9.30	----------------------------------------
28.45/9.30	
28.45/9.30	(918)
28.45/9.30	Obligation:
28.45/9.30	Q DP problem:
28.45/9.30	The TRS P consists of the following rules:
28.45/9.30	
28.45/9.30	   H(x, x) -> G(x, x, f(k))
28.45/9.30	   G(d, x, x) -> A^2
28.45/9.30	   A^2 -> H(f(c), f(c))
28.45/9.30	   A^2 -> H(f(d), f(d))
28.45/9.30	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.30	   A^2 -> H(f(e), f(e))
28.45/9.30	   A^2 -> H(f(k), f(k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.30	   A^2 -> H(f(e), U1(b, e))
28.45/9.30	   A^2 -> H(f(e), U1(b, k))
28.45/9.30	   A^2 -> H(f(e), U1(e, c))
28.45/9.30	   A^2 -> H(f(e), U1(k, c))
28.45/9.30	   A^2 -> H(f(e), U1(c, e))
28.45/9.30	   A^2 -> H(f(e), U1(c, k))
28.45/9.30	   A^2 -> H(f(e), U1(k, k))
28.45/9.30	   A^2 -> H(f(e), U1(k, d))
28.45/9.30	   A^2 -> H(f(e), U1(d, k))
28.45/9.30	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.30	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.30	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.30	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.30	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.30	   A^2 -> H(U1(k, k), f(e))
28.45/9.30	   A^2 -> H(U1(k, k), f(k))
28.45/9.30	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.30	   A^2 -> H(f(k), U1(e, b))
28.45/9.30	   A^2 -> H(f(k), U1(k, b))
28.45/9.30	   A^2 -> H(f(k), U1(c, d))
28.45/9.30	   A^2 -> H(f(k), U1(d, c))
28.45/9.30	   A^2 -> H(f(k), U1(b, e))
28.45/9.30	   A^2 -> H(f(k), U1(b, k))
28.45/9.30	   A^2 -> H(f(k), U1(e, c))
28.45/9.30	   A^2 -> H(f(k), U1(k, c))
28.45/9.30	   A^2 -> H(f(k), U1(c, e))
28.45/9.30	   A^2 -> H(f(k), U1(c, k))
28.45/9.30	   A^2 -> H(f(k), U1(e, e))
28.45/9.30	   A^2 -> H(f(k), U1(k, d))
28.45/9.30	   A^2 -> H(f(k), U1(d, k))
28.45/9.30	   A^2 -> H(f(c), b)
28.45/9.30	   A^2 -> H(f(c), U1(e, d))
28.45/9.30	   A^2 -> H(f(c), U1(d, e))
28.45/9.30	   A^2 -> H(f(k), U1(k, k))
28.45/9.30	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.30	   A^2 -> H(U1(k, k), f(c))
28.45/9.30	   A^2 -> H(U1(k, k), f(d))
28.45/9.30	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.30	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.30	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.30	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.30	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.30	   A^2 -> H(U1(k, d), f(e))
28.45/9.30	   A^2 -> H(U1(k, d), f(k))
28.45/9.30	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.30	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.30	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.30	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.30	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.30	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.30	   A^2 -> H(U1(d, k), f(e))
28.45/9.30	   A^2 -> H(U1(d, k), f(k))
28.45/9.30	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.30	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.30	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.30	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.30	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.30	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.30	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.30	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.30	   A^2 -> H(f(d), b)
28.45/9.30	   A^2 -> H(f(d), U1(e, d))
28.45/9.30	   A^2 -> H(f(d), U1(d, e))
28.45/9.30	   A^2 -> H(f(d), c)
28.45/9.30	   A^2 -> H(f(d), U1(e, k))
28.45/9.30	   A^2 -> H(f(d), U1(k, e))
28.45/9.30	   A^2 -> H(f(d), e)
28.45/9.30	   A^2 -> H(f(a), d)
28.45/9.30	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.30	   A^2 -> H(f(c), c)
28.45/9.30	   A^2 -> H(f(c), U1(e, k))
28.45/9.30	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.30	   A^2 -> H(f(c), U1(k, e))
28.45/9.30	   A^2 -> H(f(c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.30	   A^2 -> H(f(a), k)
28.45/9.30	   A^2 -> H(f(e), U1(e, e))
28.45/9.30	   A^2 -> H(f(c), e)
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.30	   A^2 -> H(f(d), U1(k, k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.30	   A^2 -> H(d, U1(b, b))
28.45/9.30	   A^2 -> H(d, f(c))
28.45/9.30	   A^2 -> H(d, f(d))
28.45/9.30	   A^2 -> H(a, U1(c, b))
28.45/9.30	   A^2 -> H(a, U1(d, b))
28.45/9.30	   A^2 -> H(a, U1(b, c))
28.45/9.30	   A^2 -> H(a, U1(b, d))
28.45/9.30	   A^2 -> H(a, U1(c, c))
28.45/9.30	   A^2 -> H(a, f(e))
28.45/9.30	   A^2 -> H(a, f(k))
28.45/9.30	   A^2 -> H(a, U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.30	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.30	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.30	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.30	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.30	   A^2 -> H(U1(e, d), f(e))
28.45/9.30	   A^2 -> H(U1(e, d), f(k))
28.45/9.30	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.30	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.30	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.30	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.30	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.30	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.30	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.30	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.30	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.30	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.30	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.30	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.30	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.30	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.30	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.30	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.30	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.30	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.30	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.30	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.30	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.30	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.30	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, a), b)
28.45/9.30	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.30	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.30	   A^2 -> H(U1(c, a), c)
28.45/9.30	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.30	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.30	   A^2 -> H(U1(c, a), e)
28.45/9.30	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.30	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.30	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.30	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.30	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.30	   A^2 -> H(U1(d, e), f(e))
28.45/9.30	   A^2 -> H(U1(d, e), f(k))
28.45/9.30	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.30	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.30	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.30	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.30	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.30	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.30	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.30	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.30	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.30	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.30	   A^2 -> H(U1(d, a), b)
28.45/9.30	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.30	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.30	   A^2 -> H(U1(d, a), c)
28.45/9.30	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.30	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.30	   A^2 -> H(U1(d, a), e)
28.45/9.30	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.30	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.30	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.30	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.30	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.30	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.30	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.30	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.30	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.30	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.30	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.30	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.30	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.30	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.30	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.30	   A^2 -> H(U1(a, c), b)
28.45/9.30	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.30	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.30	   A^2 -> H(U1(a, c), c)
28.45/9.30	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.30	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.30	   A^2 -> H(U1(a, c), e)
28.45/9.30	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, d), b)
28.45/9.30	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.30	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.30	   A^2 -> H(U1(a, d), c)
28.45/9.30	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.30	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.30	   A^2 -> H(U1(a, d), e)
28.45/9.30	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, a), d)
28.45/9.30	   A^2 -> H(U1(a, a), k)
28.45/9.30	   A^2 -> H(k, U1(b, b))
28.45/9.30	   A^2 -> H(k, f(c))
28.45/9.30	   A^2 -> H(k, f(d))
28.45/9.30	   A^2 -> H(c, U1(c, b))
28.45/9.30	   A^2 -> H(c, U1(d, b))
28.45/9.30	   A^2 -> H(c, U1(b, c))
28.45/9.30	   A^2 -> H(c, U1(b, d))
28.45/9.30	   A^2 -> H(c, U1(c, c))
28.45/9.30	   A^2 -> H(c, f(e))
28.45/9.30	   A^2 -> H(c, f(k))
28.45/9.30	   A^2 -> H(c, U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.30	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.30	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.30	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.30	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.30	   A^2 -> H(U1(e, k), f(e))
28.45/9.30	   A^2 -> H(U1(e, k), f(k))
28.45/9.30	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.30	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.30	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.30	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.30	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.30	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.30	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.30	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.30	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.30	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.30	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.30	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.30	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.30	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.30	   A^2 -> H(U1(k, e), f(e))
28.45/9.30	   A^2 -> H(U1(k, e), f(k))
28.45/9.30	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.30	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.30	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.30	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.30	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.30	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.30	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.30	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.30	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.30	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.30	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.30	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.30	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.30	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.30	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.30	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.30	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.30	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.30	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.30	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.30	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.30	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, c), b)
28.45/9.30	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.30	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.30	   A^2 -> H(U1(c, c), e)
28.45/9.30	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.30	   A^2 -> H(e, U1(c, b))
28.45/9.30	   A^2 -> H(e, U1(d, b))
28.45/9.30	   A^2 -> H(e, U1(b, c))
28.45/9.30	   A^2 -> H(e, U1(b, d))
28.45/9.30	   A^2 -> H(e, U1(c, c))
28.45/9.30	   A^2 -> H(e, f(e))
28.45/9.30	   A^2 -> H(e, f(k))
28.45/9.30	   A^2 -> H(e, U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, e), U1(e, b))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, b))
28.45/9.30	   A^2 -> H(U1(e, e), U1(c, d))
28.45/9.30	   A^2 -> H(U1(e, e), U1(d, c))
28.45/9.30	   A^2 -> H(U1(e, e), U1(b, e))
28.45/9.30	   A^2 -> H(U1(e, e), U1(b, k))
28.45/9.30	   A^2 -> H(U1(e, e), U1(e, c))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, c))
28.45/9.30	   A^2 -> H(U1(e, e), U1(c, e))
28.45/9.30	   A^2 -> H(U1(e, e), U1(c, k))
28.45/9.30	   A^2 -> H(U1(e, e), U1(e, e))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, k))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, d))
28.45/9.30	   A^2 -> H(U1(e, e), U1(d, k))
28.45/9.30	   A^2 -> H(f(e), b)
28.45/9.30	   A^2 -> H(f(e), U1(e, d))
28.45/9.30	   A^2 -> H(f(e), U1(d, e))
28.45/9.30	
28.45/9.30	The TRS R consists of the following rules:
28.45/9.30	
28.45/9.30	   f(x) -> U1(x, x)
28.45/9.30	   U1(e, x) -> x
28.45/9.30	   a -> c
28.45/9.30	   a -> d
28.45/9.30	   b -> c
28.45/9.30	   b -> d
28.45/9.30	   d -> k
28.45/9.30	   c -> e
28.45/9.30	   c -> k
28.45/9.30	
28.45/9.30	Q is empty.
28.45/9.30	We have to consider all minimal (P,Q,R)-chains.
28.45/9.30	----------------------------------------
28.45/9.30	
28.45/9.30	(919) TransformationProof (EQUIVALENT)
28.45/9.30	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.30	
28.45/9.30	   (A^2 -> H(U1(e, e), U1(b, e)),A^2 -> H(U1(e, e), U1(b, e)))
28.45/9.30	   (A^2 -> H(f(e), U1(c, e)),A^2 -> H(f(e), U1(c, e)))
28.45/9.30	   (A^2 -> H(f(e), U1(d, e)),A^2 -> H(f(e), U1(d, e)))
28.45/9.30	
28.45/9.30	
28.45/9.30	----------------------------------------
28.45/9.30	
28.45/9.30	(920)
28.45/9.30	Obligation:
28.45/9.30	Q DP problem:
28.45/9.30	The TRS P consists of the following rules:
28.45/9.30	
28.45/9.30	   H(x, x) -> G(x, x, f(k))
28.45/9.30	   G(d, x, x) -> A^2
28.45/9.30	   A^2 -> H(f(c), f(c))
28.45/9.30	   A^2 -> H(f(d), f(d))
28.45/9.30	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.30	   A^2 -> H(f(e), f(e))
28.45/9.30	   A^2 -> H(f(k), f(k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.30	   A^2 -> H(f(e), U1(b, k))
28.45/9.30	   A^2 -> H(f(e), U1(e, c))
28.45/9.30	   A^2 -> H(f(e), U1(k, c))
28.45/9.30	   A^2 -> H(f(e), U1(c, e))
28.45/9.30	   A^2 -> H(f(e), U1(c, k))
28.45/9.30	   A^2 -> H(f(e), U1(k, k))
28.45/9.30	   A^2 -> H(f(e), U1(k, d))
28.45/9.30	   A^2 -> H(f(e), U1(d, k))
28.45/9.30	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.30	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.30	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.30	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.30	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.30	   A^2 -> H(U1(k, k), f(e))
28.45/9.30	   A^2 -> H(U1(k, k), f(k))
28.45/9.30	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.30	   A^2 -> H(f(k), U1(e, b))
28.45/9.30	   A^2 -> H(f(k), U1(k, b))
28.45/9.30	   A^2 -> H(f(k), U1(c, d))
28.45/9.30	   A^2 -> H(f(k), U1(d, c))
28.45/9.30	   A^2 -> H(f(k), U1(b, e))
28.45/9.30	   A^2 -> H(f(k), U1(b, k))
28.45/9.30	   A^2 -> H(f(k), U1(e, c))
28.45/9.30	   A^2 -> H(f(k), U1(k, c))
28.45/9.30	   A^2 -> H(f(k), U1(c, e))
28.45/9.30	   A^2 -> H(f(k), U1(c, k))
28.45/9.30	   A^2 -> H(f(k), U1(e, e))
28.45/9.30	   A^2 -> H(f(k), U1(k, d))
28.45/9.30	   A^2 -> H(f(k), U1(d, k))
28.45/9.30	   A^2 -> H(f(c), b)
28.45/9.30	   A^2 -> H(f(c), U1(e, d))
28.45/9.30	   A^2 -> H(f(c), U1(d, e))
28.45/9.30	   A^2 -> H(f(k), U1(k, k))
28.45/9.30	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.30	   A^2 -> H(U1(k, k), f(c))
28.45/9.30	   A^2 -> H(U1(k, k), f(d))
28.45/9.30	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.30	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.30	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.30	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.30	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.30	   A^2 -> H(U1(k, d), f(e))
28.45/9.30	   A^2 -> H(U1(k, d), f(k))
28.45/9.30	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.30	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.30	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.30	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.30	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.30	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.30	   A^2 -> H(U1(d, k), f(e))
28.45/9.30	   A^2 -> H(U1(d, k), f(k))
28.45/9.30	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.30	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.30	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.30	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.30	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.30	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.30	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.30	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.30	   A^2 -> H(f(d), b)
28.45/9.30	   A^2 -> H(f(d), U1(e, d))
28.45/9.30	   A^2 -> H(f(d), U1(d, e))
28.45/9.30	   A^2 -> H(f(d), c)
28.45/9.30	   A^2 -> H(f(d), U1(e, k))
28.45/9.30	   A^2 -> H(f(d), U1(k, e))
28.45/9.30	   A^2 -> H(f(d), e)
28.45/9.30	   A^2 -> H(f(a), d)
28.45/9.30	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.30	   A^2 -> H(f(c), c)
28.45/9.30	   A^2 -> H(f(c), U1(e, k))
28.45/9.30	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.30	   A^2 -> H(f(c), U1(k, e))
28.45/9.30	   A^2 -> H(f(c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.30	   A^2 -> H(f(a), k)
28.45/9.30	   A^2 -> H(f(e), U1(e, e))
28.45/9.30	   A^2 -> H(f(c), e)
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.30	   A^2 -> H(f(d), U1(k, k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.30	   A^2 -> H(d, U1(b, b))
28.45/9.30	   A^2 -> H(d, f(c))
28.45/9.30	   A^2 -> H(d, f(d))
28.45/9.30	   A^2 -> H(a, U1(c, b))
28.45/9.30	   A^2 -> H(a, U1(d, b))
28.45/9.30	   A^2 -> H(a, U1(b, c))
28.45/9.30	   A^2 -> H(a, U1(b, d))
28.45/9.30	   A^2 -> H(a, U1(c, c))
28.45/9.30	   A^2 -> H(a, f(e))
28.45/9.30	   A^2 -> H(a, f(k))
28.45/9.30	   A^2 -> H(a, U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.30	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.30	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.30	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.30	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.30	   A^2 -> H(U1(e, d), f(e))
28.45/9.30	   A^2 -> H(U1(e, d), f(k))
28.45/9.30	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.30	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.30	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.30	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.30	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.30	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.30	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.30	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.30	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.30	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.30	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.30	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.30	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.30	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.30	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.30	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.30	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.30	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.30	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.30	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.30	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.30	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.30	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, a), b)
28.45/9.30	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.30	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.30	   A^2 -> H(U1(c, a), c)
28.45/9.30	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.30	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.30	   A^2 -> H(U1(c, a), e)
28.45/9.30	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.30	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.30	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.30	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.30	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.30	   A^2 -> H(U1(d, e), f(e))
28.45/9.30	   A^2 -> H(U1(d, e), f(k))
28.45/9.30	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.30	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.30	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.30	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.30	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.30	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.30	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.30	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.30	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.30	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.30	   A^2 -> H(U1(d, a), b)
28.45/9.30	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.30	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.30	   A^2 -> H(U1(d, a), c)
28.45/9.30	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.30	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.30	   A^2 -> H(U1(d, a), e)
28.45/9.30	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.30	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.30	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.30	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.30	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.30	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.30	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.30	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.30	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.30	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.30	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.30	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.30	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.30	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.30	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.30	   A^2 -> H(U1(a, c), b)
28.45/9.30	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.30	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.30	   A^2 -> H(U1(a, c), c)
28.45/9.30	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.30	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.30	   A^2 -> H(U1(a, c), e)
28.45/9.30	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, d), b)
28.45/9.30	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.30	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.30	   A^2 -> H(U1(a, d), c)
28.45/9.30	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.30	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.30	   A^2 -> H(U1(a, d), e)
28.45/9.30	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, a), d)
28.45/9.30	   A^2 -> H(U1(a, a), k)
28.45/9.30	   A^2 -> H(k, U1(b, b))
28.45/9.30	   A^2 -> H(k, f(c))
28.45/9.30	   A^2 -> H(k, f(d))
28.45/9.30	   A^2 -> H(c, U1(c, b))
28.45/9.30	   A^2 -> H(c, U1(d, b))
28.45/9.30	   A^2 -> H(c, U1(b, c))
28.45/9.30	   A^2 -> H(c, U1(b, d))
28.45/9.30	   A^2 -> H(c, U1(c, c))
28.45/9.30	   A^2 -> H(c, f(e))
28.45/9.30	   A^2 -> H(c, f(k))
28.45/9.30	   A^2 -> H(c, U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.30	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.30	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.30	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.30	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.30	   A^2 -> H(U1(e, k), f(e))
28.45/9.30	   A^2 -> H(U1(e, k), f(k))
28.45/9.30	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.30	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.30	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.30	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.30	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.30	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.30	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.30	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.30	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.30	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.30	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.30	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.30	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.30	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.30	   A^2 -> H(U1(k, e), f(e))
28.45/9.30	   A^2 -> H(U1(k, e), f(k))
28.45/9.30	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.30	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.30	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.30	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.30	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.30	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.30	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.30	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.30	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.30	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.30	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.30	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.30	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.30	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.30	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.30	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.30	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.30	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.30	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.30	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.30	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.30	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, c), b)
28.45/9.30	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.30	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.30	   A^2 -> H(U1(c, c), e)
28.45/9.30	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.30	   A^2 -> H(e, U1(c, b))
28.45/9.30	   A^2 -> H(e, U1(d, b))
28.45/9.30	   A^2 -> H(e, U1(b, c))
28.45/9.30	   A^2 -> H(e, U1(b, d))
28.45/9.30	   A^2 -> H(e, U1(c, c))
28.45/9.30	   A^2 -> H(e, f(e))
28.45/9.30	   A^2 -> H(e, f(k))
28.45/9.30	   A^2 -> H(e, U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, e), U1(e, b))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, b))
28.45/9.30	   A^2 -> H(U1(e, e), U1(c, d))
28.45/9.30	   A^2 -> H(U1(e, e), U1(d, c))
28.45/9.30	   A^2 -> H(U1(e, e), U1(b, e))
28.45/9.30	   A^2 -> H(U1(e, e), U1(b, k))
28.45/9.30	   A^2 -> H(U1(e, e), U1(e, c))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, c))
28.45/9.30	   A^2 -> H(U1(e, e), U1(c, e))
28.45/9.30	   A^2 -> H(U1(e, e), U1(c, k))
28.45/9.30	   A^2 -> H(U1(e, e), U1(e, e))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, k))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, d))
28.45/9.30	   A^2 -> H(U1(e, e), U1(d, k))
28.45/9.30	   A^2 -> H(f(e), b)
28.45/9.30	   A^2 -> H(f(e), U1(e, d))
28.45/9.30	   A^2 -> H(f(e), U1(d, e))
28.45/9.30	
28.45/9.30	The TRS R consists of the following rules:
28.45/9.30	
28.45/9.30	   f(x) -> U1(x, x)
28.45/9.30	   U1(e, x) -> x
28.45/9.30	   a -> c
28.45/9.30	   a -> d
28.45/9.30	   b -> c
28.45/9.30	   b -> d
28.45/9.30	   d -> k
28.45/9.30	   c -> e
28.45/9.30	   c -> k
28.45/9.30	
28.45/9.30	Q is empty.
28.45/9.30	We have to consider all minimal (P,Q,R)-chains.
28.45/9.30	----------------------------------------
28.45/9.30	
28.45/9.30	(921) TransformationProof (EQUIVALENT)
28.45/9.30	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.30	
28.45/9.30	   (A^2 -> H(U1(e, e), U1(b, k)),A^2 -> H(U1(e, e), U1(b, k)))
28.45/9.30	   (A^2 -> H(f(e), U1(c, k)),A^2 -> H(f(e), U1(c, k)))
28.45/9.30	   (A^2 -> H(f(e), U1(d, k)),A^2 -> H(f(e), U1(d, k)))
28.45/9.30	
28.45/9.30	
28.45/9.30	----------------------------------------
28.45/9.30	
28.45/9.30	(922)
28.45/9.30	Obligation:
28.45/9.30	Q DP problem:
28.45/9.30	The TRS P consists of the following rules:
28.45/9.30	
28.45/9.30	   H(x, x) -> G(x, x, f(k))
28.45/9.30	   G(d, x, x) -> A^2
28.45/9.30	   A^2 -> H(f(c), f(c))
28.45/9.30	   A^2 -> H(f(d), f(d))
28.45/9.30	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.30	   A^2 -> H(f(e), f(e))
28.45/9.30	   A^2 -> H(f(k), f(k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.30	   A^2 -> H(f(e), U1(e, c))
28.45/9.30	   A^2 -> H(f(e), U1(k, c))
28.45/9.30	   A^2 -> H(f(e), U1(c, e))
28.45/9.30	   A^2 -> H(f(e), U1(c, k))
28.45/9.30	   A^2 -> H(f(e), U1(k, k))
28.45/9.30	   A^2 -> H(f(e), U1(k, d))
28.45/9.30	   A^2 -> H(f(e), U1(d, k))
28.45/9.30	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.30	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.30	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.30	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.30	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.30	   A^2 -> H(U1(k, k), f(e))
28.45/9.30	   A^2 -> H(U1(k, k), f(k))
28.45/9.30	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.30	   A^2 -> H(f(k), U1(e, b))
28.45/9.30	   A^2 -> H(f(k), U1(k, b))
28.45/9.30	   A^2 -> H(f(k), U1(c, d))
28.45/9.30	   A^2 -> H(f(k), U1(d, c))
28.45/9.30	   A^2 -> H(f(k), U1(b, e))
28.45/9.30	   A^2 -> H(f(k), U1(b, k))
28.45/9.30	   A^2 -> H(f(k), U1(e, c))
28.45/9.30	   A^2 -> H(f(k), U1(k, c))
28.45/9.30	   A^2 -> H(f(k), U1(c, e))
28.45/9.30	   A^2 -> H(f(k), U1(c, k))
28.45/9.30	   A^2 -> H(f(k), U1(e, e))
28.45/9.30	   A^2 -> H(f(k), U1(k, d))
28.45/9.30	   A^2 -> H(f(k), U1(d, k))
28.45/9.30	   A^2 -> H(f(c), b)
28.45/9.30	   A^2 -> H(f(c), U1(e, d))
28.45/9.30	   A^2 -> H(f(c), U1(d, e))
28.45/9.30	   A^2 -> H(f(k), U1(k, k))
28.45/9.30	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.30	   A^2 -> H(U1(k, k), f(c))
28.45/9.30	   A^2 -> H(U1(k, k), f(d))
28.45/9.30	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.30	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.30	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.30	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.30	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.30	   A^2 -> H(U1(k, d), f(e))
28.45/9.30	   A^2 -> H(U1(k, d), f(k))
28.45/9.30	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.30	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.30	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.30	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.30	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.30	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.30	   A^2 -> H(U1(d, k), f(e))
28.45/9.30	   A^2 -> H(U1(d, k), f(k))
28.45/9.30	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.30	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.30	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.30	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.30	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.30	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.30	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.30	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.30	   A^2 -> H(f(d), b)
28.45/9.30	   A^2 -> H(f(d), U1(e, d))
28.45/9.30	   A^2 -> H(f(d), U1(d, e))
28.45/9.30	   A^2 -> H(f(d), c)
28.45/9.30	   A^2 -> H(f(d), U1(e, k))
28.45/9.30	   A^2 -> H(f(d), U1(k, e))
28.45/9.30	   A^2 -> H(f(d), e)
28.45/9.30	   A^2 -> H(f(a), d)
28.45/9.30	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.30	   A^2 -> H(f(c), c)
28.45/9.30	   A^2 -> H(f(c), U1(e, k))
28.45/9.30	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.30	   A^2 -> H(f(c), U1(k, e))
28.45/9.30	   A^2 -> H(f(c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.30	   A^2 -> H(f(a), k)
28.45/9.30	   A^2 -> H(f(e), U1(e, e))
28.45/9.30	   A^2 -> H(f(c), e)
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.30	   A^2 -> H(f(d), U1(k, k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.30	   A^2 -> H(d, U1(b, b))
28.45/9.30	   A^2 -> H(d, f(c))
28.45/9.30	   A^2 -> H(d, f(d))
28.45/9.30	   A^2 -> H(a, U1(c, b))
28.45/9.30	   A^2 -> H(a, U1(d, b))
28.45/9.30	   A^2 -> H(a, U1(b, c))
28.45/9.30	   A^2 -> H(a, U1(b, d))
28.45/9.30	   A^2 -> H(a, U1(c, c))
28.45/9.30	   A^2 -> H(a, f(e))
28.45/9.30	   A^2 -> H(a, f(k))
28.45/9.30	   A^2 -> H(a, U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.30	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.30	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.30	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.30	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.30	   A^2 -> H(U1(e, d), f(e))
28.45/9.30	   A^2 -> H(U1(e, d), f(k))
28.45/9.30	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.30	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.30	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.30	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.30	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.30	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.30	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.30	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.30	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.30	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.30	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.30	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.30	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.30	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.30	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.30	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.30	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.30	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.30	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.30	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.30	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.30	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.30	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, a), b)
28.45/9.30	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.30	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.30	   A^2 -> H(U1(c, a), c)
28.45/9.30	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.30	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.30	   A^2 -> H(U1(c, a), e)
28.45/9.30	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.30	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.30	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.30	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.30	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.30	   A^2 -> H(U1(d, e), f(e))
28.45/9.30	   A^2 -> H(U1(d, e), f(k))
28.45/9.30	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.30	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.30	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.30	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.30	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.30	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.30	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.30	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.30	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.30	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.30	   A^2 -> H(U1(d, a), b)
28.45/9.30	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.30	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.30	   A^2 -> H(U1(d, a), c)
28.45/9.30	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.30	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.30	   A^2 -> H(U1(d, a), e)
28.45/9.30	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.30	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.30	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.30	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.30	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.30	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.30	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.30	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.30	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.30	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.30	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.30	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.30	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.30	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.30	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.30	   A^2 -> H(U1(a, c), b)
28.45/9.30	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.30	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.30	   A^2 -> H(U1(a, c), c)
28.45/9.30	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.30	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.30	   A^2 -> H(U1(a, c), e)
28.45/9.30	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, d), b)
28.45/9.30	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.30	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.30	   A^2 -> H(U1(a, d), c)
28.45/9.30	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.30	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.30	   A^2 -> H(U1(a, d), e)
28.45/9.30	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, a), d)
28.45/9.30	   A^2 -> H(U1(a, a), k)
28.45/9.30	   A^2 -> H(k, U1(b, b))
28.45/9.30	   A^2 -> H(k, f(c))
28.45/9.30	   A^2 -> H(k, f(d))
28.45/9.30	   A^2 -> H(c, U1(c, b))
28.45/9.30	   A^2 -> H(c, U1(d, b))
28.45/9.30	   A^2 -> H(c, U1(b, c))
28.45/9.30	   A^2 -> H(c, U1(b, d))
28.45/9.30	   A^2 -> H(c, U1(c, c))
28.45/9.30	   A^2 -> H(c, f(e))
28.45/9.30	   A^2 -> H(c, f(k))
28.45/9.30	   A^2 -> H(c, U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.30	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.30	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.30	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.30	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.30	   A^2 -> H(U1(e, k), f(e))
28.45/9.30	   A^2 -> H(U1(e, k), f(k))
28.45/9.30	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.30	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.30	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.30	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.30	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.30	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.30	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.30	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.30	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.30	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.30	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.30	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.30	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.30	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.30	   A^2 -> H(U1(k, e), f(e))
28.45/9.30	   A^2 -> H(U1(k, e), f(k))
28.45/9.30	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.30	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.30	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.30	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.30	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.30	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.30	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.30	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.30	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.30	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.30	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.30	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.30	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.30	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.30	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.30	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.30	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.30	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.30	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.30	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.30	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.30	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, c), b)
28.45/9.30	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.30	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.30	   A^2 -> H(U1(c, c), e)
28.45/9.30	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.30	   A^2 -> H(e, U1(c, b))
28.45/9.30	   A^2 -> H(e, U1(d, b))
28.45/9.30	   A^2 -> H(e, U1(b, c))
28.45/9.30	   A^2 -> H(e, U1(b, d))
28.45/9.30	   A^2 -> H(e, U1(c, c))
28.45/9.30	   A^2 -> H(e, f(e))
28.45/9.30	   A^2 -> H(e, f(k))
28.45/9.30	   A^2 -> H(e, U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, e), U1(e, b))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, b))
28.45/9.30	   A^2 -> H(U1(e, e), U1(c, d))
28.45/9.30	   A^2 -> H(U1(e, e), U1(d, c))
28.45/9.30	   A^2 -> H(U1(e, e), U1(b, e))
28.45/9.30	   A^2 -> H(U1(e, e), U1(b, k))
28.45/9.30	   A^2 -> H(U1(e, e), U1(e, c))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, c))
28.45/9.30	   A^2 -> H(U1(e, e), U1(c, e))
28.45/9.30	   A^2 -> H(U1(e, e), U1(c, k))
28.45/9.30	   A^2 -> H(U1(e, e), U1(e, e))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, k))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, d))
28.45/9.30	   A^2 -> H(U1(e, e), U1(d, k))
28.45/9.30	   A^2 -> H(f(e), b)
28.45/9.30	   A^2 -> H(f(e), U1(e, d))
28.45/9.30	   A^2 -> H(f(e), U1(d, e))
28.45/9.30	
28.45/9.30	The TRS R consists of the following rules:
28.45/9.30	
28.45/9.30	   f(x) -> U1(x, x)
28.45/9.30	   U1(e, x) -> x
28.45/9.30	   a -> c
28.45/9.30	   a -> d
28.45/9.30	   b -> c
28.45/9.30	   b -> d
28.45/9.30	   d -> k
28.45/9.30	   c -> e
28.45/9.30	   c -> k
28.45/9.30	
28.45/9.30	Q is empty.
28.45/9.30	We have to consider all minimal (P,Q,R)-chains.
28.45/9.30	----------------------------------------
28.45/9.30	
28.45/9.30	(923) TransformationProof (EQUIVALENT)
28.45/9.30	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.30	
28.45/9.30	   (A^2 -> H(U1(e, e), U1(e, c)),A^2 -> H(U1(e, e), U1(e, c)))
28.45/9.30	   (A^2 -> H(f(e), c),A^2 -> H(f(e), c))
28.45/9.30	   (A^2 -> H(f(e), U1(e, e)),A^2 -> H(f(e), U1(e, e)))
28.45/9.30	   (A^2 -> H(f(e), U1(e, k)),A^2 -> H(f(e), U1(e, k)))
28.45/9.30	
28.45/9.30	
28.45/9.30	----------------------------------------
28.45/9.30	
28.45/9.30	(924)
28.45/9.30	Obligation:
28.45/9.30	Q DP problem:
28.45/9.30	The TRS P consists of the following rules:
28.45/9.30	
28.45/9.30	   H(x, x) -> G(x, x, f(k))
28.45/9.30	   G(d, x, x) -> A^2
28.45/9.30	   A^2 -> H(f(c), f(c))
28.45/9.30	   A^2 -> H(f(d), f(d))
28.45/9.30	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.30	   A^2 -> H(f(e), f(e))
28.45/9.30	   A^2 -> H(f(k), f(k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.30	   A^2 -> H(f(e), U1(k, c))
28.45/9.30	   A^2 -> H(f(e), U1(c, e))
28.45/9.30	   A^2 -> H(f(e), U1(c, k))
28.45/9.30	   A^2 -> H(f(e), U1(k, k))
28.45/9.30	   A^2 -> H(f(e), U1(k, d))
28.45/9.30	   A^2 -> H(f(e), U1(d, k))
28.45/9.30	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.30	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.30	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.30	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.30	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.30	   A^2 -> H(U1(k, k), f(e))
28.45/9.30	   A^2 -> H(U1(k, k), f(k))
28.45/9.30	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.30	   A^2 -> H(f(k), U1(e, b))
28.45/9.30	   A^2 -> H(f(k), U1(k, b))
28.45/9.30	   A^2 -> H(f(k), U1(c, d))
28.45/9.30	   A^2 -> H(f(k), U1(d, c))
28.45/9.30	   A^2 -> H(f(k), U1(b, e))
28.45/9.30	   A^2 -> H(f(k), U1(b, k))
28.45/9.30	   A^2 -> H(f(k), U1(e, c))
28.45/9.30	   A^2 -> H(f(k), U1(k, c))
28.45/9.30	   A^2 -> H(f(k), U1(c, e))
28.45/9.30	   A^2 -> H(f(k), U1(c, k))
28.45/9.30	   A^2 -> H(f(k), U1(e, e))
28.45/9.30	   A^2 -> H(f(k), U1(k, d))
28.45/9.30	   A^2 -> H(f(k), U1(d, k))
28.45/9.30	   A^2 -> H(f(c), b)
28.45/9.30	   A^2 -> H(f(c), U1(e, d))
28.45/9.30	   A^2 -> H(f(c), U1(d, e))
28.45/9.30	   A^2 -> H(f(k), U1(k, k))
28.45/9.30	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.30	   A^2 -> H(U1(k, k), f(c))
28.45/9.30	   A^2 -> H(U1(k, k), f(d))
28.45/9.30	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.30	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.30	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.30	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.30	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.30	   A^2 -> H(U1(k, d), f(e))
28.45/9.30	   A^2 -> H(U1(k, d), f(k))
28.45/9.30	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.30	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.30	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.30	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.30	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.30	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.30	   A^2 -> H(U1(d, k), f(e))
28.45/9.30	   A^2 -> H(U1(d, k), f(k))
28.45/9.30	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.30	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.30	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.30	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.30	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.30	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.30	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.30	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.30	   A^2 -> H(f(d), b)
28.45/9.30	   A^2 -> H(f(d), U1(e, d))
28.45/9.30	   A^2 -> H(f(d), U1(d, e))
28.45/9.30	   A^2 -> H(f(d), c)
28.45/9.30	   A^2 -> H(f(d), U1(e, k))
28.45/9.30	   A^2 -> H(f(d), U1(k, e))
28.45/9.30	   A^2 -> H(f(d), e)
28.45/9.30	   A^2 -> H(f(a), d)
28.45/9.30	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.30	   A^2 -> H(f(c), c)
28.45/9.30	   A^2 -> H(f(c), U1(e, k))
28.45/9.30	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.30	   A^2 -> H(f(c), U1(k, e))
28.45/9.30	   A^2 -> H(f(c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.30	   A^2 -> H(f(a), k)
28.45/9.30	   A^2 -> H(f(e), U1(e, e))
28.45/9.30	   A^2 -> H(f(c), e)
28.45/9.30	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.30	   A^2 -> H(f(d), U1(k, k))
28.45/9.30	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.30	   A^2 -> H(d, U1(b, b))
28.45/9.30	   A^2 -> H(d, f(c))
28.45/9.30	   A^2 -> H(d, f(d))
28.45/9.30	   A^2 -> H(a, U1(c, b))
28.45/9.30	   A^2 -> H(a, U1(d, b))
28.45/9.30	   A^2 -> H(a, U1(b, c))
28.45/9.30	   A^2 -> H(a, U1(b, d))
28.45/9.30	   A^2 -> H(a, U1(c, c))
28.45/9.30	   A^2 -> H(a, f(e))
28.45/9.30	   A^2 -> H(a, f(k))
28.45/9.30	   A^2 -> H(a, U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.30	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.30	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.30	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.30	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.30	   A^2 -> H(U1(e, d), f(e))
28.45/9.30	   A^2 -> H(U1(e, d), f(k))
28.45/9.30	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.30	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.30	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.30	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.30	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.30	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.30	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.30	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.30	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.30	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.30	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.30	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.30	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.30	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.30	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.30	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.30	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.30	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.30	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.30	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.30	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.30	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.30	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, a), b)
28.45/9.30	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.30	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.30	   A^2 -> H(U1(c, a), c)
28.45/9.30	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.30	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.30	   A^2 -> H(U1(c, a), e)
28.45/9.30	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.30	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.30	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.30	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.30	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.30	   A^2 -> H(U1(d, e), f(e))
28.45/9.30	   A^2 -> H(U1(d, e), f(k))
28.45/9.30	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.30	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.30	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.30	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.30	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.30	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.30	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.30	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.30	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.30	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.30	   A^2 -> H(U1(d, a), b)
28.45/9.30	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.30	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.30	   A^2 -> H(U1(d, a), c)
28.45/9.30	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.30	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.30	   A^2 -> H(U1(d, a), e)
28.45/9.30	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.30	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.30	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.30	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.30	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.30	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.30	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.30	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.30	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.30	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.30	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.30	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.30	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.30	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.30	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.30	   A^2 -> H(U1(a, c), b)
28.45/9.30	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.30	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.30	   A^2 -> H(U1(a, c), c)
28.45/9.30	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.30	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.30	   A^2 -> H(U1(a, c), e)
28.45/9.30	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, d), b)
28.45/9.30	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.30	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.30	   A^2 -> H(U1(a, d), c)
28.45/9.30	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.30	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.30	   A^2 -> H(U1(a, d), e)
28.45/9.30	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.30	   A^2 -> H(U1(a, a), d)
28.45/9.30	   A^2 -> H(U1(a, a), k)
28.45/9.30	   A^2 -> H(k, U1(b, b))
28.45/9.30	   A^2 -> H(k, f(c))
28.45/9.30	   A^2 -> H(k, f(d))
28.45/9.30	   A^2 -> H(c, U1(c, b))
28.45/9.30	   A^2 -> H(c, U1(d, b))
28.45/9.30	   A^2 -> H(c, U1(b, c))
28.45/9.30	   A^2 -> H(c, U1(b, d))
28.45/9.30	   A^2 -> H(c, U1(c, c))
28.45/9.30	   A^2 -> H(c, f(e))
28.45/9.30	   A^2 -> H(c, f(k))
28.45/9.30	   A^2 -> H(c, U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.30	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.30	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.30	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.30	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.30	   A^2 -> H(U1(e, k), f(e))
28.45/9.30	   A^2 -> H(U1(e, k), f(k))
28.45/9.30	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.30	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.30	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.30	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.30	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.30	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.30	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.30	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.30	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.30	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.30	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.30	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.30	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.30	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.30	   A^2 -> H(U1(k, e), f(e))
28.45/9.30	   A^2 -> H(U1(k, e), f(k))
28.45/9.30	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.30	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.30	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.30	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.30	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.30	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.30	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.30	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.30	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.30	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.30	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.30	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.30	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.30	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.30	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.30	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.30	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.30	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.30	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.30	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.30	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.30	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.30	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.30	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.30	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.30	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.30	   A^2 -> H(U1(c, c), b)
28.45/9.30	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.30	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.30	   A^2 -> H(U1(c, c), e)
28.45/9.30	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.30	   A^2 -> H(e, U1(c, b))
28.45/9.30	   A^2 -> H(e, U1(d, b))
28.45/9.30	   A^2 -> H(e, U1(b, c))
28.45/9.30	   A^2 -> H(e, U1(b, d))
28.45/9.30	   A^2 -> H(e, U1(c, c))
28.45/9.30	   A^2 -> H(e, f(e))
28.45/9.30	   A^2 -> H(e, f(k))
28.45/9.30	   A^2 -> H(e, U1(d, d))
28.45/9.30	   A^2 -> H(U1(e, e), U1(e, b))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, b))
28.45/9.30	   A^2 -> H(U1(e, e), U1(c, d))
28.45/9.30	   A^2 -> H(U1(e, e), U1(d, c))
28.45/9.30	   A^2 -> H(U1(e, e), U1(b, e))
28.45/9.30	   A^2 -> H(U1(e, e), U1(b, k))
28.45/9.30	   A^2 -> H(U1(e, e), U1(e, c))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, c))
28.45/9.30	   A^2 -> H(U1(e, e), U1(c, e))
28.45/9.30	   A^2 -> H(U1(e, e), U1(c, k))
28.45/9.30	   A^2 -> H(U1(e, e), U1(e, e))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, k))
28.45/9.30	   A^2 -> H(U1(e, e), U1(k, d))
28.45/9.30	   A^2 -> H(U1(e, e), U1(d, k))
28.45/9.30	   A^2 -> H(f(e), b)
28.45/9.30	   A^2 -> H(f(e), U1(e, d))
28.45/9.30	   A^2 -> H(f(e), U1(d, e))
28.45/9.30	   A^2 -> H(f(e), c)
28.45/9.30	   A^2 -> H(f(e), U1(e, k))
28.45/9.30	
28.45/9.30	The TRS R consists of the following rules:
28.45/9.30	
28.45/9.30	   f(x) -> U1(x, x)
28.45/9.30	   U1(e, x) -> x
28.45/9.30	   a -> c
28.45/9.30	   a -> d
28.45/9.30	   b -> c
28.45/9.30	   b -> d
28.45/9.30	   d -> k
28.45/9.30	   c -> e
28.45/9.30	   c -> k
28.45/9.30	
28.45/9.30	Q is empty.
28.45/9.30	We have to consider all minimal (P,Q,R)-chains.
28.45/9.30	----------------------------------------
28.45/9.30	
28.45/9.30	(925) TransformationProof (EQUIVALENT)
28.45/9.30	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.30	
28.45/9.30	   (A^2 -> H(U1(e, e), U1(k, c)),A^2 -> H(U1(e, e), U1(k, c)))
28.45/9.30	   (A^2 -> H(f(e), U1(k, e)),A^2 -> H(f(e), U1(k, e)))
28.45/9.30	   (A^2 -> H(f(e), U1(k, k)),A^2 -> H(f(e), U1(k, k)))
28.45/9.30	
28.45/9.30	
28.45/9.30	----------------------------------------
28.45/9.31	
28.45/9.31	(926)
28.45/9.31	Obligation:
28.45/9.31	Q DP problem:
28.45/9.31	The TRS P consists of the following rules:
28.45/9.31	
28.45/9.31	   H(x, x) -> G(x, x, f(k))
28.45/9.31	   G(d, x, x) -> A^2
28.45/9.31	   A^2 -> H(f(c), f(c))
28.45/9.31	   A^2 -> H(f(d), f(d))
28.45/9.31	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.31	   A^2 -> H(f(e), f(e))
28.45/9.31	   A^2 -> H(f(k), f(k))
28.45/9.31	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.31	   A^2 -> H(f(e), U1(c, e))
28.45/9.31	   A^2 -> H(f(e), U1(c, k))
28.45/9.31	   A^2 -> H(f(e), U1(k, k))
28.45/9.31	   A^2 -> H(f(e), U1(k, d))
28.45/9.31	   A^2 -> H(f(e), U1(d, k))
28.45/9.31	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.31	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.31	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.31	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.31	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.31	   A^2 -> H(U1(k, k), f(e))
28.45/9.31	   A^2 -> H(U1(k, k), f(k))
28.45/9.31	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.31	   A^2 -> H(f(k), U1(e, b))
28.45/9.31	   A^2 -> H(f(k), U1(k, b))
28.45/9.31	   A^2 -> H(f(k), U1(c, d))
28.45/9.31	   A^2 -> H(f(k), U1(d, c))
28.45/9.31	   A^2 -> H(f(k), U1(b, e))
28.45/9.31	   A^2 -> H(f(k), U1(b, k))
28.45/9.31	   A^2 -> H(f(k), U1(e, c))
28.45/9.31	   A^2 -> H(f(k), U1(k, c))
28.45/9.31	   A^2 -> H(f(k), U1(c, e))
28.45/9.31	   A^2 -> H(f(k), U1(c, k))
28.45/9.31	   A^2 -> H(f(k), U1(e, e))
28.45/9.31	   A^2 -> H(f(k), U1(k, d))
28.45/9.31	   A^2 -> H(f(k), U1(d, k))
28.45/9.31	   A^2 -> H(f(c), b)
28.45/9.31	   A^2 -> H(f(c), U1(e, d))
28.45/9.31	   A^2 -> H(f(c), U1(d, e))
28.45/9.31	   A^2 -> H(f(k), U1(k, k))
28.45/9.31	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.31	   A^2 -> H(U1(k, k), f(c))
28.45/9.31	   A^2 -> H(U1(k, k), f(d))
28.45/9.31	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.31	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.31	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.31	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.31	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.31	   A^2 -> H(U1(k, d), f(e))
28.45/9.31	   A^2 -> H(U1(k, d), f(k))
28.45/9.31	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.31	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.31	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.31	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.31	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.31	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.31	   A^2 -> H(U1(d, k), f(e))
28.45/9.31	   A^2 -> H(U1(d, k), f(k))
28.45/9.31	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.31	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.31	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.31	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.31	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.31	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.31	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.31	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.31	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.31	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.31	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.31	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.31	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.31	   A^2 -> H(f(d), b)
28.45/9.31	   A^2 -> H(f(d), U1(e, d))
28.45/9.31	   A^2 -> H(f(d), U1(d, e))
28.45/9.31	   A^2 -> H(f(d), c)
28.45/9.31	   A^2 -> H(f(d), U1(e, k))
28.45/9.31	   A^2 -> H(f(d), U1(k, e))
28.45/9.31	   A^2 -> H(f(d), e)
28.45/9.31	   A^2 -> H(f(a), d)
28.45/9.31	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.31	   A^2 -> H(f(c), c)
28.45/9.31	   A^2 -> H(f(c), U1(e, k))
28.45/9.31	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.31	   A^2 -> H(f(c), U1(k, e))
28.45/9.31	   A^2 -> H(f(c), U1(k, k))
28.45/9.31	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.31	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.31	   A^2 -> H(f(a), k)
28.45/9.31	   A^2 -> H(f(e), U1(e, e))
28.45/9.31	   A^2 -> H(f(c), e)
28.45/9.31	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.31	   A^2 -> H(f(d), U1(k, k))
28.45/9.31	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.31	   A^2 -> H(d, U1(b, b))
28.45/9.31	   A^2 -> H(d, f(c))
28.45/9.31	   A^2 -> H(d, f(d))
28.45/9.31	   A^2 -> H(a, U1(c, b))
28.45/9.31	   A^2 -> H(a, U1(d, b))
28.45/9.31	   A^2 -> H(a, U1(b, c))
28.45/9.31	   A^2 -> H(a, U1(b, d))
28.45/9.31	   A^2 -> H(a, U1(c, c))
28.45/9.31	   A^2 -> H(a, f(e))
28.45/9.31	   A^2 -> H(a, f(k))
28.45/9.31	   A^2 -> H(a, U1(d, d))
28.45/9.31	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.31	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.31	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.31	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.31	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.31	   A^2 -> H(U1(e, d), f(e))
28.45/9.31	   A^2 -> H(U1(e, d), f(k))
28.45/9.31	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.31	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.31	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.31	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.31	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.31	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.31	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.31	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.31	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.31	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.31	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.31	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.31	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.31	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.31	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.31	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.31	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.31	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.31	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.31	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.31	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.31	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.31	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.31	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.31	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.31	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.31	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.31	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.31	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.31	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.31	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.31	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.31	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.31	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.31	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.31	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.31	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.31	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.31	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.31	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.31	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.31	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.31	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.31	   A^2 -> H(U1(c, a), b)
28.45/9.31	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.31	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.31	   A^2 -> H(U1(c, a), c)
28.45/9.31	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.31	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.31	   A^2 -> H(U1(c, a), e)
28.45/9.31	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.31	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.31	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.31	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.31	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.31	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.31	   A^2 -> H(U1(d, e), f(e))
28.45/9.31	   A^2 -> H(U1(d, e), f(k))
28.45/9.31	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.31	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.31	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.31	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.31	   A^2 -> H(U1(d, c), U1(d, c))
28.45/9.31	   A^2 -> H(U1(d, c), U1(b, e))
28.45/9.31	   A^2 -> H(U1(d, c), U1(b, k))
28.45/9.31	   A^2 -> H(U1(d, c), U1(e, c))
28.45/9.31	   A^2 -> H(U1(d, c), U1(k, c))
28.45/9.31	   A^2 -> H(U1(d, c), U1(c, e))
28.45/9.31	   A^2 -> H(U1(d, c), U1(c, k))
28.45/9.31	   A^2 -> H(U1(d, c), U1(e, e))
28.45/9.31	   A^2 -> H(U1(d, c), U1(k, k))
28.45/9.31	   A^2 -> H(U1(d, c), U1(k, d))
28.45/9.31	   A^2 -> H(U1(d, c), U1(d, k))
28.45/9.31	   A^2 -> H(U1(d, a), b)
28.45/9.31	   A^2 -> H(U1(d, a), U1(e, d))
28.45/9.31	   A^2 -> H(U1(d, a), U1(d, e))
28.45/9.31	   A^2 -> H(U1(d, a), c)
28.45/9.31	   A^2 -> H(U1(d, a), U1(e, k))
28.45/9.31	   A^2 -> H(U1(d, a), U1(k, e))
28.45/9.31	   A^2 -> H(U1(d, a), e)
28.45/9.31	   A^2 -> H(U1(d, a), U1(k, k))
28.45/9.31	   A^2 -> H(U1(a, e), U1(e, b))
28.45/9.31	   A^2 -> H(U1(a, e), U1(k, b))
28.45/9.31	   A^2 -> H(U1(a, e), U1(c, d))
28.45/9.31	   A^2 -> H(U1(a, e), U1(d, c))
28.45/9.31	   A^2 -> H(U1(a, e), U1(b, e))
28.45/9.31	   A^2 -> H(U1(a, e), U1(b, k))
28.45/9.31	   A^2 -> H(U1(a, e), U1(e, c))
28.45/9.31	   A^2 -> H(U1(a, e), U1(k, c))
28.45/9.31	   A^2 -> H(U1(a, e), U1(c, e))
28.45/9.31	   A^2 -> H(U1(a, e), U1(c, k))
28.45/9.31	   A^2 -> H(U1(a, e), U1(e, e))
28.45/9.31	   A^2 -> H(U1(a, e), U1(k, k))
28.45/9.31	   A^2 -> H(U1(a, e), U1(k, d))
28.45/9.31	   A^2 -> H(U1(a, e), U1(d, k))
28.45/9.31	   A^2 -> H(U1(a, k), U1(e, b))
28.45/9.31	   A^2 -> H(U1(a, k), U1(k, b))
28.45/9.31	   A^2 -> H(U1(a, k), U1(c, d))
28.45/9.31	   A^2 -> H(U1(a, k), U1(d, c))
28.45/9.31	   A^2 -> H(U1(a, k), U1(b, e))
28.45/9.31	   A^2 -> H(U1(a, k), U1(b, k))
28.45/9.31	   A^2 -> H(U1(a, k), U1(e, c))
28.45/9.31	   A^2 -> H(U1(a, k), U1(k, c))
28.45/9.31	   A^2 -> H(U1(a, k), U1(c, e))
28.45/9.31	   A^2 -> H(U1(a, k), U1(c, k))
28.45/9.31	   A^2 -> H(U1(a, k), U1(e, e))
28.45/9.31	   A^2 -> H(U1(a, k), U1(k, k))
28.45/9.31	   A^2 -> H(U1(a, k), U1(k, d))
28.45/9.31	   A^2 -> H(U1(a, k), U1(d, k))
28.45/9.31	   A^2 -> H(U1(a, c), b)
28.45/9.31	   A^2 -> H(U1(a, c), U1(e, d))
28.45/9.31	   A^2 -> H(U1(a, c), U1(d, e))
28.45/9.31	   A^2 -> H(U1(a, c), c)
28.45/9.31	   A^2 -> H(U1(a, c), U1(e, k))
28.45/9.31	   A^2 -> H(U1(a, c), U1(k, e))
28.45/9.31	   A^2 -> H(U1(a, c), e)
28.45/9.31	   A^2 -> H(U1(a, c), U1(k, k))
28.45/9.31	   A^2 -> H(U1(a, d), b)
28.45/9.31	   A^2 -> H(U1(a, d), U1(e, d))
28.45/9.31	   A^2 -> H(U1(a, d), U1(d, e))
28.45/9.31	   A^2 -> H(U1(a, d), c)
28.45/9.31	   A^2 -> H(U1(a, d), U1(e, k))
28.45/9.31	   A^2 -> H(U1(a, d), U1(k, e))
28.45/9.31	   A^2 -> H(U1(a, d), e)
28.45/9.31	   A^2 -> H(U1(a, d), U1(k, k))
28.45/9.31	   A^2 -> H(U1(a, a), d)
28.45/9.31	   A^2 -> H(U1(a, a), k)
28.45/9.31	   A^2 -> H(k, U1(b, b))
28.45/9.31	   A^2 -> H(k, f(c))
28.45/9.31	   A^2 -> H(k, f(d))
28.45/9.31	   A^2 -> H(c, U1(c, b))
28.45/9.31	   A^2 -> H(c, U1(d, b))
28.45/9.31	   A^2 -> H(c, U1(b, c))
28.45/9.31	   A^2 -> H(c, U1(b, d))
28.45/9.31	   A^2 -> H(c, U1(c, c))
28.45/9.31	   A^2 -> H(c, f(e))
28.45/9.31	   A^2 -> H(c, f(k))
28.45/9.31	   A^2 -> H(c, U1(d, d))
28.45/9.31	   A^2 -> H(U1(e, k), U1(c, b))
28.45/9.31	   A^2 -> H(U1(e, k), U1(d, b))
28.45/9.31	   A^2 -> H(U1(e, k), U1(b, c))
28.45/9.31	   A^2 -> H(U1(e, k), U1(b, d))
28.45/9.31	   A^2 -> H(U1(e, k), U1(c, c))
28.45/9.31	   A^2 -> H(U1(e, k), f(e))
28.45/9.31	   A^2 -> H(U1(e, k), f(k))
28.45/9.31	   A^2 -> H(U1(e, k), U1(d, d))
28.45/9.31	   A^2 -> H(U1(e, c), U1(e, b))
28.45/9.31	   A^2 -> H(U1(e, c), U1(k, b))
28.45/9.31	   A^2 -> H(U1(e, c), U1(c, d))
28.45/9.31	   A^2 -> H(U1(e, c), U1(d, c))
28.45/9.31	   A^2 -> H(U1(e, c), U1(b, e))
28.45/9.31	   A^2 -> H(U1(e, c), U1(b, k))
28.45/9.31	   A^2 -> H(U1(e, c), U1(e, c))
28.45/9.31	   A^2 -> H(U1(e, c), U1(k, c))
28.45/9.31	   A^2 -> H(U1(e, c), U1(c, e))
28.45/9.31	   A^2 -> H(U1(e, c), U1(c, k))
28.45/9.31	   A^2 -> H(U1(e, c), U1(e, e))
28.45/9.31	   A^2 -> H(U1(e, c), U1(k, k))
28.45/9.31	   A^2 -> H(U1(e, c), U1(k, d))
28.45/9.31	   A^2 -> H(U1(e, c), U1(d, k))
28.45/9.31	   A^2 -> H(U1(k, e), U1(c, b))
28.45/9.31	   A^2 -> H(U1(k, e), U1(d, b))
28.45/9.31	   A^2 -> H(U1(k, e), U1(b, c))
28.45/9.31	   A^2 -> H(U1(k, e), U1(b, d))
28.45/9.31	   A^2 -> H(U1(k, e), U1(c, c))
28.45/9.31	   A^2 -> H(U1(k, e), f(e))
28.45/9.31	   A^2 -> H(U1(k, e), f(k))
28.45/9.31	   A^2 -> H(U1(k, e), U1(d, d))
28.45/9.31	   A^2 -> H(U1(k, c), U1(e, b))
28.45/9.31	   A^2 -> H(U1(k, c), U1(k, b))
28.45/9.31	   A^2 -> H(U1(k, c), U1(c, d))
28.45/9.31	   A^2 -> H(U1(k, c), U1(d, c))
28.45/9.31	   A^2 -> H(U1(k, c), U1(b, e))
28.45/9.31	   A^2 -> H(U1(k, c), U1(b, k))
28.45/9.31	   A^2 -> H(U1(k, c), U1(e, c))
28.45/9.31	   A^2 -> H(U1(k, c), U1(k, c))
28.45/9.31	   A^2 -> H(U1(k, c), U1(c, e))
28.45/9.31	   A^2 -> H(U1(k, c), U1(c, k))
28.45/9.31	   A^2 -> H(U1(k, c), U1(e, e))
28.45/9.31	   A^2 -> H(U1(k, c), U1(k, k))
28.45/9.31	   A^2 -> H(U1(k, c), U1(k, d))
28.45/9.31	   A^2 -> H(U1(k, c), U1(d, k))
28.45/9.31	   A^2 -> H(U1(c, e), U1(e, b))
28.45/9.31	   A^2 -> H(U1(c, e), U1(k, b))
28.45/9.31	   A^2 -> H(U1(c, e), U1(c, d))
28.45/9.31	   A^2 -> H(U1(c, e), U1(d, c))
28.45/9.31	   A^2 -> H(U1(c, e), U1(b, e))
28.45/9.31	   A^2 -> H(U1(c, e), U1(b, k))
28.45/9.31	   A^2 -> H(U1(c, e), U1(e, c))
28.45/9.31	   A^2 -> H(U1(c, e), U1(k, c))
28.45/9.31	   A^2 -> H(U1(c, e), U1(c, e))
28.45/9.31	   A^2 -> H(U1(c, e), U1(c, k))
28.45/9.31	   A^2 -> H(U1(c, e), U1(e, e))
28.45/9.31	   A^2 -> H(U1(c, e), U1(k, k))
28.45/9.31	   A^2 -> H(U1(c, e), U1(k, d))
28.45/9.31	   A^2 -> H(U1(c, e), U1(d, k))
28.45/9.31	   A^2 -> H(U1(c, k), U1(e, b))
28.45/9.31	   A^2 -> H(U1(c, k), U1(k, b))
28.45/9.31	   A^2 -> H(U1(c, k), U1(c, d))
28.45/9.31	   A^2 -> H(U1(c, k), U1(d, c))
28.45/9.31	   A^2 -> H(U1(c, k), U1(b, e))
28.45/9.31	   A^2 -> H(U1(c, k), U1(b, k))
28.45/9.31	   A^2 -> H(U1(c, k), U1(e, c))
28.45/9.31	   A^2 -> H(U1(c, k), U1(k, c))
28.45/9.31	   A^2 -> H(U1(c, k), U1(c, e))
28.45/9.31	   A^2 -> H(U1(c, k), U1(c, k))
28.45/9.31	   A^2 -> H(U1(c, k), U1(e, e))
28.45/9.31	   A^2 -> H(U1(c, k), U1(k, k))
28.45/9.31	   A^2 -> H(U1(c, k), U1(k, d))
28.45/9.31	   A^2 -> H(U1(c, k), U1(d, k))
28.45/9.31	   A^2 -> H(U1(c, c), b)
28.45/9.31	   A^2 -> H(U1(c, c), U1(e, d))
28.45/9.31	   A^2 -> H(U1(c, c), U1(d, e))
28.45/9.31	   A^2 -> H(U1(c, c), e)
28.45/9.31	   A^2 -> H(U1(c, c), U1(k, k))
28.45/9.31	   A^2 -> H(e, U1(c, b))
28.45/9.31	   A^2 -> H(e, U1(d, b))
28.45/9.31	   A^2 -> H(e, U1(b, c))
28.45/9.31	   A^2 -> H(e, U1(b, d))
28.45/9.31	   A^2 -> H(e, U1(c, c))
28.45/9.31	   A^2 -> H(e, f(e))
28.45/9.31	   A^2 -> H(e, f(k))
28.45/9.31	   A^2 -> H(e, U1(d, d))
28.45/9.31	   A^2 -> H(U1(e, e), U1(e, b))
28.45/9.31	   A^2 -> H(U1(e, e), U1(k, b))
28.45/9.31	   A^2 -> H(U1(e, e), U1(c, d))
28.45/9.31	   A^2 -> H(U1(e, e), U1(d, c))
28.45/9.31	   A^2 -> H(U1(e, e), U1(b, e))
28.45/9.31	   A^2 -> H(U1(e, e), U1(b, k))
28.45/9.31	   A^2 -> H(U1(e, e), U1(e, c))
28.45/9.31	   A^2 -> H(U1(e, e), U1(k, c))
28.45/9.31	   A^2 -> H(U1(e, e), U1(c, e))
28.45/9.31	   A^2 -> H(U1(e, e), U1(c, k))
28.45/9.31	   A^2 -> H(U1(e, e), U1(e, e))
28.45/9.31	   A^2 -> H(U1(e, e), U1(k, k))
28.45/9.31	   A^2 -> H(U1(e, e), U1(k, d))
28.45/9.31	   A^2 -> H(U1(e, e), U1(d, k))
28.45/9.31	   A^2 -> H(f(e), b)
28.45/9.31	   A^2 -> H(f(e), U1(e, d))
28.45/9.31	   A^2 -> H(f(e), U1(d, e))
28.45/9.31	   A^2 -> H(f(e), c)
28.45/9.31	   A^2 -> H(f(e), U1(e, k))
28.45/9.31	   A^2 -> H(f(e), U1(k, e))
28.45/9.31	
28.45/9.31	The TRS R consists of the following rules:
28.45/9.31	
28.45/9.31	   f(x) -> U1(x, x)
28.45/9.31	   U1(e, x) -> x
28.45/9.31	   a -> c
28.45/9.31	   a -> d
28.45/9.31	   b -> c
28.45/9.31	   b -> d
28.45/9.31	   d -> k
28.45/9.31	   c -> e
28.45/9.31	   c -> k
28.45/9.31	
28.45/9.31	Q is empty.
28.45/9.31	We have to consider all minimal (P,Q,R)-chains.
28.45/9.31	----------------------------------------
28.45/9.31	
28.45/9.31	(927) TransformationProof (EQUIVALENT)
28.45/9.31	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.45/9.31	
28.45/9.31	   (A^2 -> H(U1(e, e), U1(c, e)),A^2 -> H(U1(e, e), U1(c, e)))
28.45/9.31	   (A^2 -> H(f(e), U1(e, e)),A^2 -> H(f(e), U1(e, e)))
28.45/9.31	   (A^2 -> H(f(e), U1(k, e)),A^2 -> H(f(e), U1(k, e)))
28.45/9.31	
28.45/9.31	
28.45/9.31	----------------------------------------
28.45/9.31	
28.45/9.31	(928)
28.45/9.31	Obligation:
28.45/9.31	Q DP problem:
28.45/9.31	The TRS P consists of the following rules:
28.45/9.31	
28.45/9.31	   H(x, x) -> G(x, x, f(k))
28.45/9.31	   G(d, x, x) -> A^2
28.45/9.31	   A^2 -> H(f(c), f(c))
28.45/9.31	   A^2 -> H(f(d), f(d))
28.45/9.31	   A^2 -> H(U1(c, c), U1(c, c))
28.45/9.31	   A^2 -> H(f(e), f(e))
28.45/9.31	   A^2 -> H(f(k), f(k))
28.45/9.31	   A^2 -> H(U1(d, d), U1(d, d))
28.45/9.31	   A^2 -> H(f(e), U1(c, k))
28.45/9.31	   A^2 -> H(f(e), U1(k, k))
28.45/9.31	   A^2 -> H(f(e), U1(k, d))
28.45/9.31	   A^2 -> H(f(e), U1(d, k))
28.45/9.31	   A^2 -> H(U1(k, k), U1(c, b))
28.45/9.31	   A^2 -> H(U1(k, k), U1(d, b))
28.45/9.31	   A^2 -> H(U1(k, k), U1(b, c))
28.45/9.31	   A^2 -> H(U1(k, k), U1(b, d))
28.45/9.31	   A^2 -> H(U1(k, k), U1(c, c))
28.45/9.31	   A^2 -> H(U1(k, k), f(e))
28.45/9.31	   A^2 -> H(U1(k, k), f(k))
28.45/9.31	   A^2 -> H(U1(k, k), U1(d, d))
28.45/9.31	   A^2 -> H(f(k), U1(e, b))
28.45/9.31	   A^2 -> H(f(k), U1(k, b))
28.45/9.31	   A^2 -> H(f(k), U1(c, d))
28.45/9.31	   A^2 -> H(f(k), U1(d, c))
28.45/9.31	   A^2 -> H(f(k), U1(b, e))
28.45/9.31	   A^2 -> H(f(k), U1(b, k))
28.45/9.31	   A^2 -> H(f(k), U1(e, c))
28.45/9.31	   A^2 -> H(f(k), U1(k, c))
28.45/9.31	   A^2 -> H(f(k), U1(c, e))
28.45/9.31	   A^2 -> H(f(k), U1(c, k))
28.45/9.31	   A^2 -> H(f(k), U1(e, e))
28.45/9.31	   A^2 -> H(f(k), U1(k, d))
28.45/9.31	   A^2 -> H(f(k), U1(d, k))
28.45/9.31	   A^2 -> H(f(c), b)
28.45/9.31	   A^2 -> H(f(c), U1(e, d))
28.45/9.31	   A^2 -> H(f(c), U1(d, e))
28.45/9.31	   A^2 -> H(f(k), U1(k, k))
28.45/9.31	   A^2 -> H(U1(k, k), U1(b, b))
28.45/9.31	   A^2 -> H(U1(k, k), f(c))
28.45/9.31	   A^2 -> H(U1(k, k), f(d))
28.45/9.31	   A^2 -> H(U1(k, d), U1(c, b))
28.45/9.31	   A^2 -> H(U1(k, d), U1(d, b))
28.45/9.31	   A^2 -> H(U1(k, d), U1(b, c))
28.45/9.31	   A^2 -> H(U1(k, d), U1(b, d))
28.45/9.31	   A^2 -> H(U1(k, d), U1(c, c))
28.45/9.31	   A^2 -> H(U1(k, d), f(e))
28.45/9.31	   A^2 -> H(U1(k, d), f(k))
28.45/9.31	   A^2 -> H(U1(k, d), U1(d, d))
28.45/9.31	   A^2 -> H(U1(d, k), U1(c, b))
28.45/9.31	   A^2 -> H(U1(d, k), U1(d, b))
28.45/9.31	   A^2 -> H(U1(d, k), U1(b, c))
28.45/9.31	   A^2 -> H(U1(d, k), U1(b, d))
28.45/9.31	   A^2 -> H(U1(d, k), U1(c, c))
28.45/9.31	   A^2 -> H(U1(d, k), f(e))
28.45/9.31	   A^2 -> H(U1(d, k), f(k))
28.45/9.31	   A^2 -> H(U1(d, k), U1(d, d))
28.45/9.31	   A^2 -> H(U1(d, d), U1(e, b))
28.45/9.31	   A^2 -> H(U1(d, d), U1(k, b))
28.45/9.31	   A^2 -> H(U1(d, d), U1(c, d))
28.45/9.31	   A^2 -> H(U1(d, d), U1(d, c))
28.45/9.31	   A^2 -> H(U1(d, d), U1(b, e))
28.45/9.31	   A^2 -> H(U1(d, d), U1(b, k))
28.45/9.31	   A^2 -> H(U1(d, d), U1(e, c))
28.45/9.31	   A^2 -> H(U1(d, d), U1(k, c))
28.45/9.31	   A^2 -> H(U1(d, d), U1(c, e))
28.45/9.31	   A^2 -> H(U1(d, d), U1(c, k))
28.45/9.31	   A^2 -> H(U1(d, d), U1(e, e))
28.45/9.31	   A^2 -> H(U1(d, d), U1(k, k))
28.45/9.31	   A^2 -> H(f(d), b)
28.45/9.31	   A^2 -> H(f(d), U1(e, d))
28.45/9.31	   A^2 -> H(f(d), U1(d, e))
28.45/9.31	   A^2 -> H(f(d), c)
28.45/9.31	   A^2 -> H(f(d), U1(e, k))
28.45/9.31	   A^2 -> H(f(d), U1(k, e))
28.45/9.31	   A^2 -> H(f(d), e)
28.45/9.31	   A^2 -> H(f(a), d)
28.45/9.31	   A^2 -> H(U1(c, c), U1(e, c))
28.45/9.31	   A^2 -> H(f(c), c)
28.45/9.31	   A^2 -> H(f(c), U1(e, k))
28.45/9.31	   A^2 -> H(U1(c, c), U1(k, c))
28.45/9.31	   A^2 -> H(f(c), U1(k, e))
28.45/9.31	   A^2 -> H(f(c), U1(k, k))
28.45/9.31	   A^2 -> H(U1(c, c), U1(c, e))
28.45/9.31	   A^2 -> H(U1(c, c), U1(c, k))
28.45/9.31	   A^2 -> H(f(a), k)
28.45/9.31	   A^2 -> H(f(e), U1(e, e))
28.45/9.31	   A^2 -> H(f(c), e)
28.45/9.31	   A^2 -> H(U1(d, d), U1(k, d))
28.45/9.31	   A^2 -> H(f(d), U1(k, k))
28.45/9.31	   A^2 -> H(U1(d, d), U1(d, k))
28.45/9.31	   A^2 -> H(d, U1(b, b))
28.45/9.31	   A^2 -> H(d, f(c))
28.45/9.31	   A^2 -> H(d, f(d))
28.45/9.31	   A^2 -> H(a, U1(c, b))
28.45/9.31	   A^2 -> H(a, U1(d, b))
28.45/9.31	   A^2 -> H(a, U1(b, c))
28.45/9.31	   A^2 -> H(a, U1(b, d))
28.45/9.31	   A^2 -> H(a, U1(c, c))
28.45/9.31	   A^2 -> H(a, f(e))
28.45/9.31	   A^2 -> H(a, f(k))
28.45/9.31	   A^2 -> H(a, U1(d, d))
28.45/9.31	   A^2 -> H(U1(e, d), U1(c, b))
28.45/9.31	   A^2 -> H(U1(e, d), U1(d, b))
28.45/9.31	   A^2 -> H(U1(e, d), U1(b, c))
28.45/9.31	   A^2 -> H(U1(e, d), U1(b, d))
28.45/9.31	   A^2 -> H(U1(e, d), U1(c, c))
28.45/9.31	   A^2 -> H(U1(e, d), f(e))
28.45/9.31	   A^2 -> H(U1(e, d), f(k))
28.45/9.31	   A^2 -> H(U1(e, d), U1(d, d))
28.45/9.31	   A^2 -> H(U1(e, a), U1(e, b))
28.45/9.31	   A^2 -> H(U1(e, a), U1(k, b))
28.45/9.31	   A^2 -> H(U1(e, a), U1(c, d))
28.45/9.31	   A^2 -> H(U1(e, a), U1(d, c))
28.45/9.31	   A^2 -> H(U1(e, a), U1(b, e))
28.45/9.31	   A^2 -> H(U1(e, a), U1(b, k))
28.45/9.31	   A^2 -> H(U1(e, a), U1(e, c))
28.45/9.31	   A^2 -> H(U1(e, a), U1(k, c))
28.45/9.31	   A^2 -> H(U1(e, a), U1(c, e))
28.45/9.31	   A^2 -> H(U1(e, a), U1(c, k))
28.45/9.31	   A^2 -> H(U1(e, a), U1(e, e))
28.45/9.31	   A^2 -> H(U1(e, a), U1(k, k))
28.45/9.31	   A^2 -> H(U1(e, a), U1(k, d))
28.45/9.31	   A^2 -> H(U1(e, a), U1(d, k))
28.45/9.31	   A^2 -> H(U1(k, a), U1(e, b))
28.45/9.31	   A^2 -> H(U1(k, a), U1(k, b))
28.45/9.31	   A^2 -> H(U1(k, a), U1(c, d))
28.45/9.31	   A^2 -> H(U1(k, a), U1(d, c))
28.45/9.31	   A^2 -> H(U1(k, a), U1(b, e))
28.45/9.31	   A^2 -> H(U1(k, a), U1(b, k))
28.45/9.31	   A^2 -> H(U1(k, a), U1(e, c))
28.45/9.31	   A^2 -> H(U1(k, a), U1(k, c))
28.45/9.31	   A^2 -> H(U1(k, a), U1(c, e))
28.45/9.31	   A^2 -> H(U1(k, a), U1(c, k))
28.45/9.31	   A^2 -> H(U1(k, a), U1(e, e))
28.45/9.31	   A^2 -> H(U1(k, a), U1(k, k))
28.45/9.31	   A^2 -> H(U1(k, a), U1(k, d))
28.45/9.31	   A^2 -> H(U1(k, a), U1(d, k))
28.45/9.31	   A^2 -> H(U1(c, d), U1(e, b))
28.45/9.31	   A^2 -> H(U1(c, d), U1(k, b))
28.45/9.31	   A^2 -> H(U1(c, d), U1(c, d))
28.45/9.31	   A^2 -> H(U1(c, d), U1(d, c))
28.45/9.31	   A^2 -> H(U1(c, d), U1(b, e))
28.45/9.31	   A^2 -> H(U1(c, d), U1(b, k))
28.45/9.31	   A^2 -> H(U1(c, d), U1(e, c))
28.45/9.31	   A^2 -> H(U1(c, d), U1(k, c))
28.45/9.31	   A^2 -> H(U1(c, d), U1(c, e))
28.45/9.31	   A^2 -> H(U1(c, d), U1(c, k))
28.45/9.31	   A^2 -> H(U1(c, d), U1(e, e))
28.45/9.31	   A^2 -> H(U1(c, d), U1(k, k))
28.45/9.31	   A^2 -> H(U1(c, d), U1(k, d))
28.45/9.31	   A^2 -> H(U1(c, d), U1(d, k))
28.45/9.31	   A^2 -> H(U1(c, a), b)
28.45/9.31	   A^2 -> H(U1(c, a), U1(e, d))
28.45/9.31	   A^2 -> H(U1(c, a), U1(d, e))
28.45/9.31	   A^2 -> H(U1(c, a), c)
28.45/9.31	   A^2 -> H(U1(c, a), U1(e, k))
28.45/9.31	   A^2 -> H(U1(c, a), U1(k, e))
28.45/9.31	   A^2 -> H(U1(c, a), e)
28.45/9.31	   A^2 -> H(U1(c, a), U1(k, k))
28.45/9.31	   A^2 -> H(U1(d, e), U1(c, b))
28.45/9.31	   A^2 -> H(U1(d, e), U1(d, b))
28.45/9.31	   A^2 -> H(U1(d, e), U1(b, c))
28.45/9.31	   A^2 -> H(U1(d, e), U1(b, d))
28.45/9.31	   A^2 -> H(U1(d, e), U1(c, c))
28.45/9.31	   A^2 -> H(U1(d, e), f(e))
28.45/9.31	   A^2 -> H(U1(d, e), f(k))
28.45/9.31	   A^2 -> H(U1(d, e), U1(d, d))
28.45/9.31	   A^2 -> H(U1(d, c), U1(e, b))
28.45/9.31	   A^2 -> H(U1(d, c), U1(k, b))
28.45/9.31	   A^2 -> H(U1(d, c), U1(c, d))
28.45/9.31	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.31	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.31	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.31	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.31	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.31	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.31	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.31	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.31	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.31	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.31	   A^2 -> H(U1(d, a), b)
28.54/9.31	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.31	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.31	   A^2 -> H(U1(d, a), c)
28.54/9.31	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.31	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.31	   A^2 -> H(U1(d, a), e)
28.54/9.31	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.31	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.31	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.31	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.31	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.31	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.31	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.31	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.31	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.31	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.31	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.31	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.31	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.31	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.31	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.31	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.31	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.31	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.31	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.31	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.31	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.31	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.31	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.31	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.31	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.31	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.31	   A^2 -> H(U1(a, c), b)
28.54/9.31	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.31	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.31	   A^2 -> H(U1(a, c), c)
28.54/9.31	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.31	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.31	   A^2 -> H(U1(a, c), e)
28.54/9.31	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, d), b)
28.54/9.31	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.31	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.31	   A^2 -> H(U1(a, d), c)
28.54/9.31	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.31	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.31	   A^2 -> H(U1(a, d), e)
28.54/9.31	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, a), d)
28.54/9.31	   A^2 -> H(U1(a, a), k)
28.54/9.31	   A^2 -> H(k, U1(b, b))
28.54/9.31	   A^2 -> H(k, f(c))
28.54/9.31	   A^2 -> H(k, f(d))
28.54/9.31	   A^2 -> H(c, U1(c, b))
28.54/9.31	   A^2 -> H(c, U1(d, b))
28.54/9.31	   A^2 -> H(c, U1(b, c))
28.54/9.31	   A^2 -> H(c, U1(b, d))
28.54/9.31	   A^2 -> H(c, U1(c, c))
28.54/9.31	   A^2 -> H(c, f(e))
28.54/9.31	   A^2 -> H(c, f(k))
28.54/9.31	   A^2 -> H(c, U1(d, d))
28.54/9.31	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.31	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.31	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.31	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.31	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.31	   A^2 -> H(U1(e, k), f(e))
28.54/9.31	   A^2 -> H(U1(e, k), f(k))
28.54/9.31	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.31	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.31	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.31	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.31	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.31	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.31	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.31	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.31	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.31	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.31	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.31	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.31	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.31	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.31	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.31	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.31	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.31	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.31	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.31	   A^2 -> H(U1(k, e), f(e))
28.54/9.31	   A^2 -> H(U1(k, e), f(k))
28.54/9.31	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.31	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.31	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.31	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.31	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.31	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.31	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.31	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.31	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.31	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.31	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.31	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.31	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.31	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.31	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.31	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.31	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.31	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.31	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.31	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.31	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.31	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.31	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.31	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.31	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.31	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.31	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.31	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.31	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.31	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.31	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.31	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.31	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.31	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.31	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.31	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.31	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.31	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.31	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.31	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.31	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.31	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.31	   A^2 -> H(U1(c, c), b)
28.54/9.31	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.31	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.31	   A^2 -> H(U1(c, c), e)
28.54/9.31	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.31	   A^2 -> H(e, U1(c, b))
28.54/9.31	   A^2 -> H(e, U1(d, b))
28.54/9.31	   A^2 -> H(e, U1(b, c))
28.54/9.31	   A^2 -> H(e, U1(b, d))
28.54/9.31	   A^2 -> H(e, U1(c, c))
28.54/9.31	   A^2 -> H(e, f(e))
28.54/9.31	   A^2 -> H(e, f(k))
28.54/9.31	   A^2 -> H(e, U1(d, d))
28.54/9.31	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.31	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.31	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.31	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.31	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.31	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.31	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.31	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.31	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.31	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.31	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.31	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.31	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.31	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.31	   A^2 -> H(f(e), b)
28.54/9.31	   A^2 -> H(f(e), U1(e, d))
28.54/9.31	   A^2 -> H(f(e), U1(d, e))
28.54/9.31	   A^2 -> H(f(e), c)
28.54/9.31	   A^2 -> H(f(e), U1(e, k))
28.54/9.31	   A^2 -> H(f(e), U1(k, e))
28.54/9.31	
28.54/9.31	The TRS R consists of the following rules:
28.54/9.31	
28.54/9.31	   f(x) -> U1(x, x)
28.54/9.31	   U1(e, x) -> x
28.54/9.31	   a -> c
28.54/9.31	   a -> d
28.54/9.31	   b -> c
28.54/9.31	   b -> d
28.54/9.31	   d -> k
28.54/9.31	   c -> e
28.54/9.31	   c -> k
28.54/9.31	
28.54/9.31	Q is empty.
28.54/9.31	We have to consider all minimal (P,Q,R)-chains.
28.54/9.31	----------------------------------------
28.54/9.31	
28.54/9.31	(929) TransformationProof (EQUIVALENT)
28.54/9.31	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.31	
28.54/9.31	   (A^2 -> H(U1(e, e), U1(c, k)),A^2 -> H(U1(e, e), U1(c, k)))
28.54/9.31	   (A^2 -> H(f(e), U1(e, k)),A^2 -> H(f(e), U1(e, k)))
28.54/9.31	   (A^2 -> H(f(e), U1(k, k)),A^2 -> H(f(e), U1(k, k)))
28.54/9.31	
28.54/9.31	
28.54/9.31	----------------------------------------
28.54/9.31	
28.54/9.31	(930)
28.54/9.31	Obligation:
28.54/9.31	Q DP problem:
28.54/9.31	The TRS P consists of the following rules:
28.54/9.31	
28.54/9.31	   H(x, x) -> G(x, x, f(k))
28.54/9.31	   G(d, x, x) -> A^2
28.54/9.31	   A^2 -> H(f(c), f(c))
28.54/9.31	   A^2 -> H(f(d), f(d))
28.54/9.31	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.31	   A^2 -> H(f(e), f(e))
28.54/9.31	   A^2 -> H(f(k), f(k))
28.54/9.31	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.31	   A^2 -> H(f(e), U1(k, k))
28.54/9.31	   A^2 -> H(f(e), U1(k, d))
28.54/9.31	   A^2 -> H(f(e), U1(d, k))
28.54/9.31	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.31	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.31	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.31	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.31	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.31	   A^2 -> H(U1(k, k), f(e))
28.54/9.31	   A^2 -> H(U1(k, k), f(k))
28.54/9.31	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.31	   A^2 -> H(f(k), U1(e, b))
28.54/9.31	   A^2 -> H(f(k), U1(k, b))
28.54/9.31	   A^2 -> H(f(k), U1(c, d))
28.54/9.31	   A^2 -> H(f(k), U1(d, c))
28.54/9.31	   A^2 -> H(f(k), U1(b, e))
28.54/9.31	   A^2 -> H(f(k), U1(b, k))
28.54/9.31	   A^2 -> H(f(k), U1(e, c))
28.54/9.31	   A^2 -> H(f(k), U1(k, c))
28.54/9.31	   A^2 -> H(f(k), U1(c, e))
28.54/9.31	   A^2 -> H(f(k), U1(c, k))
28.54/9.31	   A^2 -> H(f(k), U1(e, e))
28.54/9.31	   A^2 -> H(f(k), U1(k, d))
28.54/9.31	   A^2 -> H(f(k), U1(d, k))
28.54/9.31	   A^2 -> H(f(c), b)
28.54/9.31	   A^2 -> H(f(c), U1(e, d))
28.54/9.31	   A^2 -> H(f(c), U1(d, e))
28.54/9.31	   A^2 -> H(f(k), U1(k, k))
28.54/9.31	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.31	   A^2 -> H(U1(k, k), f(c))
28.54/9.31	   A^2 -> H(U1(k, k), f(d))
28.54/9.31	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.31	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.31	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.31	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.31	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.31	   A^2 -> H(U1(k, d), f(e))
28.54/9.31	   A^2 -> H(U1(k, d), f(k))
28.54/9.31	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.31	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.31	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.31	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.31	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.31	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.31	   A^2 -> H(U1(d, k), f(e))
28.54/9.31	   A^2 -> H(U1(d, k), f(k))
28.54/9.31	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.31	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.31	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.31	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.31	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.31	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.31	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.31	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.31	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.31	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.31	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.31	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.31	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.31	   A^2 -> H(f(d), b)
28.54/9.31	   A^2 -> H(f(d), U1(e, d))
28.54/9.31	   A^2 -> H(f(d), U1(d, e))
28.54/9.31	   A^2 -> H(f(d), c)
28.54/9.31	   A^2 -> H(f(d), U1(e, k))
28.54/9.31	   A^2 -> H(f(d), U1(k, e))
28.54/9.31	   A^2 -> H(f(d), e)
28.54/9.31	   A^2 -> H(f(a), d)
28.54/9.31	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.31	   A^2 -> H(f(c), c)
28.54/9.31	   A^2 -> H(f(c), U1(e, k))
28.54/9.31	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.31	   A^2 -> H(f(c), U1(k, e))
28.54/9.31	   A^2 -> H(f(c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.31	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.31	   A^2 -> H(f(a), k)
28.54/9.31	   A^2 -> H(f(e), U1(e, e))
28.54/9.31	   A^2 -> H(f(c), e)
28.54/9.31	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.31	   A^2 -> H(f(d), U1(k, k))
28.54/9.31	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.31	   A^2 -> H(d, U1(b, b))
28.54/9.31	   A^2 -> H(d, f(c))
28.54/9.31	   A^2 -> H(d, f(d))
28.54/9.31	   A^2 -> H(a, U1(c, b))
28.54/9.31	   A^2 -> H(a, U1(d, b))
28.54/9.31	   A^2 -> H(a, U1(b, c))
28.54/9.31	   A^2 -> H(a, U1(b, d))
28.54/9.31	   A^2 -> H(a, U1(c, c))
28.54/9.31	   A^2 -> H(a, f(e))
28.54/9.31	   A^2 -> H(a, f(k))
28.54/9.31	   A^2 -> H(a, U1(d, d))
28.54/9.31	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.31	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.31	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.31	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.31	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.31	   A^2 -> H(U1(e, d), f(e))
28.54/9.31	   A^2 -> H(U1(e, d), f(k))
28.54/9.31	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.31	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.31	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.31	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.31	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.31	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.31	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.31	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.31	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.31	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.31	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.31	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.31	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.31	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.31	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.31	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.31	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.31	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.31	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.31	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.31	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.31	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.31	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.31	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.31	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.31	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.31	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.31	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.31	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.31	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.31	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.31	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.31	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.31	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.31	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.31	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.31	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.31	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.31	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.31	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.31	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.31	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.31	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.31	   A^2 -> H(U1(c, a), b)
28.54/9.31	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.31	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.31	   A^2 -> H(U1(c, a), c)
28.54/9.31	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.31	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.31	   A^2 -> H(U1(c, a), e)
28.54/9.31	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.31	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.31	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.31	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.31	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.31	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.31	   A^2 -> H(U1(d, e), f(e))
28.54/9.31	   A^2 -> H(U1(d, e), f(k))
28.54/9.31	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.31	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.31	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.31	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.31	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.31	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.31	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.31	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.31	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.31	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.31	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.31	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.31	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.31	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.31	   A^2 -> H(U1(d, a), b)
28.54/9.31	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.31	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.31	   A^2 -> H(U1(d, a), c)
28.54/9.31	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.31	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.31	   A^2 -> H(U1(d, a), e)
28.54/9.31	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.31	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.31	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.31	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.31	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.31	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.31	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.31	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.31	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.31	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.31	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.31	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.31	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.31	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.31	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.31	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.31	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.31	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.31	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.31	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.31	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.31	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.31	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.31	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.31	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.31	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.31	   A^2 -> H(U1(a, c), b)
28.54/9.31	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.31	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.31	   A^2 -> H(U1(a, c), c)
28.54/9.31	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.31	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.31	   A^2 -> H(U1(a, c), e)
28.54/9.31	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, d), b)
28.54/9.31	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.31	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.31	   A^2 -> H(U1(a, d), c)
28.54/9.31	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.31	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.31	   A^2 -> H(U1(a, d), e)
28.54/9.31	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, a), d)
28.54/9.31	   A^2 -> H(U1(a, a), k)
28.54/9.31	   A^2 -> H(k, U1(b, b))
28.54/9.31	   A^2 -> H(k, f(c))
28.54/9.31	   A^2 -> H(k, f(d))
28.54/9.31	   A^2 -> H(c, U1(c, b))
28.54/9.31	   A^2 -> H(c, U1(d, b))
28.54/9.31	   A^2 -> H(c, U1(b, c))
28.54/9.31	   A^2 -> H(c, U1(b, d))
28.54/9.31	   A^2 -> H(c, U1(c, c))
28.54/9.31	   A^2 -> H(c, f(e))
28.54/9.31	   A^2 -> H(c, f(k))
28.54/9.31	   A^2 -> H(c, U1(d, d))
28.54/9.31	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.31	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.31	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.31	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.31	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.31	   A^2 -> H(U1(e, k), f(e))
28.54/9.31	   A^2 -> H(U1(e, k), f(k))
28.54/9.31	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.31	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.31	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.31	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.31	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.31	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.31	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.31	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.31	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.31	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.31	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.31	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.31	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.31	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.31	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.31	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.31	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.31	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.31	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.31	   A^2 -> H(U1(k, e), f(e))
28.54/9.31	   A^2 -> H(U1(k, e), f(k))
28.54/9.31	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.31	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.31	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.31	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.31	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.31	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.31	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.31	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.31	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.31	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.31	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.31	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.31	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.31	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.31	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.31	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.31	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.31	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.31	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.31	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.31	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.31	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.31	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.31	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.31	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.31	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.31	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.31	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.31	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.31	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.31	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.31	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.31	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.31	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.31	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.31	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.31	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.31	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.31	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.31	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.31	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.31	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.31	   A^2 -> H(U1(c, c), b)
28.54/9.31	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.31	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.31	   A^2 -> H(U1(c, c), e)
28.54/9.31	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.31	   A^2 -> H(e, U1(c, b))
28.54/9.31	   A^2 -> H(e, U1(d, b))
28.54/9.31	   A^2 -> H(e, U1(b, c))
28.54/9.31	   A^2 -> H(e, U1(b, d))
28.54/9.31	   A^2 -> H(e, U1(c, c))
28.54/9.31	   A^2 -> H(e, f(e))
28.54/9.31	   A^2 -> H(e, f(k))
28.54/9.31	   A^2 -> H(e, U1(d, d))
28.54/9.31	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.31	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.31	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.31	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.31	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.31	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.31	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.31	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.31	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.31	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.31	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.31	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.31	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.31	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.31	   A^2 -> H(f(e), b)
28.54/9.31	   A^2 -> H(f(e), U1(e, d))
28.54/9.31	   A^2 -> H(f(e), U1(d, e))
28.54/9.31	   A^2 -> H(f(e), c)
28.54/9.31	   A^2 -> H(f(e), U1(e, k))
28.54/9.31	   A^2 -> H(f(e), U1(k, e))
28.54/9.31	
28.54/9.31	The TRS R consists of the following rules:
28.54/9.31	
28.54/9.31	   f(x) -> U1(x, x)
28.54/9.31	   U1(e, x) -> x
28.54/9.31	   a -> c
28.54/9.31	   a -> d
28.54/9.31	   b -> c
28.54/9.31	   b -> d
28.54/9.31	   d -> k
28.54/9.31	   c -> e
28.54/9.31	   c -> k
28.54/9.31	
28.54/9.31	Q is empty.
28.54/9.31	We have to consider all minimal (P,Q,R)-chains.
28.54/9.31	----------------------------------------
28.54/9.31	
28.54/9.31	(931) TransformationProof (EQUIVALENT)
28.54/9.31	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.31	
28.54/9.31	   (A^2 -> H(U1(e, e), U1(k, k)),A^2 -> H(U1(e, e), U1(k, k)))
28.54/9.31	
28.54/9.31	
28.54/9.31	----------------------------------------
28.54/9.31	
28.54/9.31	(932)
28.54/9.31	Obligation:
28.54/9.31	Q DP problem:
28.54/9.31	The TRS P consists of the following rules:
28.54/9.31	
28.54/9.31	   H(x, x) -> G(x, x, f(k))
28.54/9.31	   G(d, x, x) -> A^2
28.54/9.31	   A^2 -> H(f(c), f(c))
28.54/9.31	   A^2 -> H(f(d), f(d))
28.54/9.31	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.31	   A^2 -> H(f(e), f(e))
28.54/9.31	   A^2 -> H(f(k), f(k))
28.54/9.31	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.31	   A^2 -> H(f(e), U1(k, d))
28.54/9.31	   A^2 -> H(f(e), U1(d, k))
28.54/9.31	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.31	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.31	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.31	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.31	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.31	   A^2 -> H(U1(k, k), f(e))
28.54/9.31	   A^2 -> H(U1(k, k), f(k))
28.54/9.31	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.31	   A^2 -> H(f(k), U1(e, b))
28.54/9.31	   A^2 -> H(f(k), U1(k, b))
28.54/9.31	   A^2 -> H(f(k), U1(c, d))
28.54/9.31	   A^2 -> H(f(k), U1(d, c))
28.54/9.31	   A^2 -> H(f(k), U1(b, e))
28.54/9.31	   A^2 -> H(f(k), U1(b, k))
28.54/9.31	   A^2 -> H(f(k), U1(e, c))
28.54/9.31	   A^2 -> H(f(k), U1(k, c))
28.54/9.31	   A^2 -> H(f(k), U1(c, e))
28.54/9.31	   A^2 -> H(f(k), U1(c, k))
28.54/9.31	   A^2 -> H(f(k), U1(e, e))
28.54/9.31	   A^2 -> H(f(k), U1(k, d))
28.54/9.31	   A^2 -> H(f(k), U1(d, k))
28.54/9.31	   A^2 -> H(f(c), b)
28.54/9.31	   A^2 -> H(f(c), U1(e, d))
28.54/9.31	   A^2 -> H(f(c), U1(d, e))
28.54/9.31	   A^2 -> H(f(k), U1(k, k))
28.54/9.31	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.31	   A^2 -> H(U1(k, k), f(c))
28.54/9.31	   A^2 -> H(U1(k, k), f(d))
28.54/9.31	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.31	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.31	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.31	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.31	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.31	   A^2 -> H(U1(k, d), f(e))
28.54/9.31	   A^2 -> H(U1(k, d), f(k))
28.54/9.31	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.31	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.31	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.31	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.31	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.31	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.31	   A^2 -> H(U1(d, k), f(e))
28.54/9.31	   A^2 -> H(U1(d, k), f(k))
28.54/9.31	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.31	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.31	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.31	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.31	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.31	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.31	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.31	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.31	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.31	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.31	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.31	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.31	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.31	   A^2 -> H(f(d), b)
28.54/9.31	   A^2 -> H(f(d), U1(e, d))
28.54/9.31	   A^2 -> H(f(d), U1(d, e))
28.54/9.31	   A^2 -> H(f(d), c)
28.54/9.31	   A^2 -> H(f(d), U1(e, k))
28.54/9.31	   A^2 -> H(f(d), U1(k, e))
28.54/9.31	   A^2 -> H(f(d), e)
28.54/9.31	   A^2 -> H(f(a), d)
28.54/9.31	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.31	   A^2 -> H(f(c), c)
28.54/9.31	   A^2 -> H(f(c), U1(e, k))
28.54/9.31	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.31	   A^2 -> H(f(c), U1(k, e))
28.54/9.31	   A^2 -> H(f(c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.31	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.31	   A^2 -> H(f(a), k)
28.54/9.31	   A^2 -> H(f(e), U1(e, e))
28.54/9.31	   A^2 -> H(f(c), e)
28.54/9.31	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.31	   A^2 -> H(f(d), U1(k, k))
28.54/9.31	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.31	   A^2 -> H(d, U1(b, b))
28.54/9.31	   A^2 -> H(d, f(c))
28.54/9.31	   A^2 -> H(d, f(d))
28.54/9.31	   A^2 -> H(a, U1(c, b))
28.54/9.31	   A^2 -> H(a, U1(d, b))
28.54/9.31	   A^2 -> H(a, U1(b, c))
28.54/9.31	   A^2 -> H(a, U1(b, d))
28.54/9.31	   A^2 -> H(a, U1(c, c))
28.54/9.31	   A^2 -> H(a, f(e))
28.54/9.31	   A^2 -> H(a, f(k))
28.54/9.31	   A^2 -> H(a, U1(d, d))
28.54/9.31	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.31	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.31	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.31	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.31	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.31	   A^2 -> H(U1(e, d), f(e))
28.54/9.31	   A^2 -> H(U1(e, d), f(k))
28.54/9.31	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.31	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.31	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.31	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.31	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.31	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.31	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.31	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.31	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.31	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.31	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.31	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.31	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.31	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.31	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.31	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.31	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.31	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.31	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.31	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.31	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.31	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.31	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.31	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.31	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.31	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.31	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.31	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.31	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.31	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.31	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.31	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.31	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.31	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.31	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.31	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.31	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.31	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.31	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.31	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.31	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.31	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.31	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.31	   A^2 -> H(U1(c, a), b)
28.54/9.31	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.31	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.31	   A^2 -> H(U1(c, a), c)
28.54/9.31	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.31	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.31	   A^2 -> H(U1(c, a), e)
28.54/9.31	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.31	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.31	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.31	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.31	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.31	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.31	   A^2 -> H(U1(d, e), f(e))
28.54/9.31	   A^2 -> H(U1(d, e), f(k))
28.54/9.31	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.31	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.31	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.31	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.31	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.31	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.31	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.31	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.31	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.31	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.31	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.31	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.31	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.31	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.31	   A^2 -> H(U1(d, a), b)
28.54/9.31	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.31	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.31	   A^2 -> H(U1(d, a), c)
28.54/9.31	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.31	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.31	   A^2 -> H(U1(d, a), e)
28.54/9.31	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.31	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.31	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.31	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.31	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.31	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.31	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.31	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.31	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.31	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.31	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.31	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.31	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.31	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.31	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.31	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.31	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.31	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.31	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.31	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.31	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.31	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.31	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.31	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.31	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.31	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.31	   A^2 -> H(U1(a, c), b)
28.54/9.31	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.31	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.31	   A^2 -> H(U1(a, c), c)
28.54/9.31	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.31	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.31	   A^2 -> H(U1(a, c), e)
28.54/9.31	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, d), b)
28.54/9.31	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.31	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.31	   A^2 -> H(U1(a, d), c)
28.54/9.31	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.31	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.31	   A^2 -> H(U1(a, d), e)
28.54/9.31	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, a), d)
28.54/9.31	   A^2 -> H(U1(a, a), k)
28.54/9.31	   A^2 -> H(k, U1(b, b))
28.54/9.31	   A^2 -> H(k, f(c))
28.54/9.31	   A^2 -> H(k, f(d))
28.54/9.31	   A^2 -> H(c, U1(c, b))
28.54/9.31	   A^2 -> H(c, U1(d, b))
28.54/9.31	   A^2 -> H(c, U1(b, c))
28.54/9.31	   A^2 -> H(c, U1(b, d))
28.54/9.31	   A^2 -> H(c, U1(c, c))
28.54/9.31	   A^2 -> H(c, f(e))
28.54/9.31	   A^2 -> H(c, f(k))
28.54/9.31	   A^2 -> H(c, U1(d, d))
28.54/9.31	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.31	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.31	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.31	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.31	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.31	   A^2 -> H(U1(e, k), f(e))
28.54/9.31	   A^2 -> H(U1(e, k), f(k))
28.54/9.31	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.31	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.31	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.31	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.31	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.31	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.31	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.31	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.31	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.31	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.31	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.31	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.31	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.31	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.31	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.31	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.31	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.31	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.31	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.31	   A^2 -> H(U1(k, e), f(e))
28.54/9.31	   A^2 -> H(U1(k, e), f(k))
28.54/9.31	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.31	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.31	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.31	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.31	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.31	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.31	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.31	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.31	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.31	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.31	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.31	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.31	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.31	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.31	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.31	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.31	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.31	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.31	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.31	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.31	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.31	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.31	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.31	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.31	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.31	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.31	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.31	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.31	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.31	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.31	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.31	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.31	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.31	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.31	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.31	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.31	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.31	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.31	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.31	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.31	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.31	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.31	   A^2 -> H(U1(c, c), b)
28.54/9.31	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.31	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.31	   A^2 -> H(U1(c, c), e)
28.54/9.31	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.31	   A^2 -> H(e, U1(c, b))
28.54/9.31	   A^2 -> H(e, U1(d, b))
28.54/9.31	   A^2 -> H(e, U1(b, c))
28.54/9.31	   A^2 -> H(e, U1(b, d))
28.54/9.31	   A^2 -> H(e, U1(c, c))
28.54/9.31	   A^2 -> H(e, f(e))
28.54/9.31	   A^2 -> H(e, f(k))
28.54/9.31	   A^2 -> H(e, U1(d, d))
28.54/9.31	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.31	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.31	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.31	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.31	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.31	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.31	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.31	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.31	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.31	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.31	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.31	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.31	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.31	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.31	   A^2 -> H(f(e), b)
28.54/9.31	   A^2 -> H(f(e), U1(e, d))
28.54/9.31	   A^2 -> H(f(e), U1(d, e))
28.54/9.31	   A^2 -> H(f(e), c)
28.54/9.31	   A^2 -> H(f(e), U1(e, k))
28.54/9.31	   A^2 -> H(f(e), U1(k, e))
28.54/9.31	
28.54/9.31	The TRS R consists of the following rules:
28.54/9.31	
28.54/9.31	   f(x) -> U1(x, x)
28.54/9.31	   U1(e, x) -> x
28.54/9.31	   a -> c
28.54/9.31	   a -> d
28.54/9.31	   b -> c
28.54/9.31	   b -> d
28.54/9.31	   d -> k
28.54/9.31	   c -> e
28.54/9.31	   c -> k
28.54/9.31	
28.54/9.31	Q is empty.
28.54/9.31	We have to consider all minimal (P,Q,R)-chains.
28.54/9.31	----------------------------------------
28.54/9.31	
28.54/9.31	(933) TransformationProof (EQUIVALENT)
28.54/9.31	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.31	
28.54/9.31	   (A^2 -> H(U1(e, e), U1(k, d)),A^2 -> H(U1(e, e), U1(k, d)))
28.54/9.31	   (A^2 -> H(f(e), U1(k, k)),A^2 -> H(f(e), U1(k, k)))
28.54/9.31	
28.54/9.31	
28.54/9.31	----------------------------------------
28.54/9.31	
28.54/9.31	(934)
28.54/9.31	Obligation:
28.54/9.31	Q DP problem:
28.54/9.31	The TRS P consists of the following rules:
28.54/9.31	
28.54/9.31	   H(x, x) -> G(x, x, f(k))
28.54/9.31	   G(d, x, x) -> A^2
28.54/9.31	   A^2 -> H(f(c), f(c))
28.54/9.31	   A^2 -> H(f(d), f(d))
28.54/9.31	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.31	   A^2 -> H(f(e), f(e))
28.54/9.31	   A^2 -> H(f(k), f(k))
28.54/9.31	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.31	   A^2 -> H(f(e), U1(d, k))
28.54/9.31	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.31	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.31	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.31	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.31	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.31	   A^2 -> H(U1(k, k), f(e))
28.54/9.31	   A^2 -> H(U1(k, k), f(k))
28.54/9.31	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.31	   A^2 -> H(f(k), U1(e, b))
28.54/9.31	   A^2 -> H(f(k), U1(k, b))
28.54/9.31	   A^2 -> H(f(k), U1(c, d))
28.54/9.31	   A^2 -> H(f(k), U1(d, c))
28.54/9.31	   A^2 -> H(f(k), U1(b, e))
28.54/9.31	   A^2 -> H(f(k), U1(b, k))
28.54/9.31	   A^2 -> H(f(k), U1(e, c))
28.54/9.31	   A^2 -> H(f(k), U1(k, c))
28.54/9.31	   A^2 -> H(f(k), U1(c, e))
28.54/9.31	   A^2 -> H(f(k), U1(c, k))
28.54/9.31	   A^2 -> H(f(k), U1(e, e))
28.54/9.31	   A^2 -> H(f(k), U1(k, d))
28.54/9.31	   A^2 -> H(f(k), U1(d, k))
28.54/9.31	   A^2 -> H(f(c), b)
28.54/9.31	   A^2 -> H(f(c), U1(e, d))
28.54/9.31	   A^2 -> H(f(c), U1(d, e))
28.54/9.31	   A^2 -> H(f(k), U1(k, k))
28.54/9.31	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.31	   A^2 -> H(U1(k, k), f(c))
28.54/9.31	   A^2 -> H(U1(k, k), f(d))
28.54/9.31	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.31	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.31	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.31	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.31	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.31	   A^2 -> H(U1(k, d), f(e))
28.54/9.31	   A^2 -> H(U1(k, d), f(k))
28.54/9.31	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.31	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.31	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.31	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.31	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.31	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.31	   A^2 -> H(U1(d, k), f(e))
28.54/9.31	   A^2 -> H(U1(d, k), f(k))
28.54/9.31	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.31	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.31	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.31	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.31	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.31	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.31	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.31	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.31	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.31	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.31	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.31	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.31	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.31	   A^2 -> H(f(d), b)
28.54/9.31	   A^2 -> H(f(d), U1(e, d))
28.54/9.31	   A^2 -> H(f(d), U1(d, e))
28.54/9.31	   A^2 -> H(f(d), c)
28.54/9.31	   A^2 -> H(f(d), U1(e, k))
28.54/9.31	   A^2 -> H(f(d), U1(k, e))
28.54/9.31	   A^2 -> H(f(d), e)
28.54/9.31	   A^2 -> H(f(a), d)
28.54/9.31	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.31	   A^2 -> H(f(c), c)
28.54/9.31	   A^2 -> H(f(c), U1(e, k))
28.54/9.31	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.31	   A^2 -> H(f(c), U1(k, e))
28.54/9.31	   A^2 -> H(f(c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.31	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.31	   A^2 -> H(f(a), k)
28.54/9.31	   A^2 -> H(f(e), U1(e, e))
28.54/9.31	   A^2 -> H(f(c), e)
28.54/9.31	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.31	   A^2 -> H(f(d), U1(k, k))
28.54/9.31	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.31	   A^2 -> H(d, U1(b, b))
28.54/9.31	   A^2 -> H(d, f(c))
28.54/9.31	   A^2 -> H(d, f(d))
28.54/9.31	   A^2 -> H(a, U1(c, b))
28.54/9.31	   A^2 -> H(a, U1(d, b))
28.54/9.31	   A^2 -> H(a, U1(b, c))
28.54/9.31	   A^2 -> H(a, U1(b, d))
28.54/9.31	   A^2 -> H(a, U1(c, c))
28.54/9.31	   A^2 -> H(a, f(e))
28.54/9.31	   A^2 -> H(a, f(k))
28.54/9.31	   A^2 -> H(a, U1(d, d))
28.54/9.31	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.31	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.31	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.31	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.31	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.31	   A^2 -> H(U1(e, d), f(e))
28.54/9.31	   A^2 -> H(U1(e, d), f(k))
28.54/9.31	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.31	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.31	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.31	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.31	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.31	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.31	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.31	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.31	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.31	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.31	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.31	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.31	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.31	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.31	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.31	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.31	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.31	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.31	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.31	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.31	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.31	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.31	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.31	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.31	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.31	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.31	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.31	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.31	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.31	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.31	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.31	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.31	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.31	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.31	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.31	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.31	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.31	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.31	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.31	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.31	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.31	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.31	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.31	   A^2 -> H(U1(c, a), b)
28.54/9.31	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.31	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.31	   A^2 -> H(U1(c, a), c)
28.54/9.31	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.31	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.31	   A^2 -> H(U1(c, a), e)
28.54/9.31	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.31	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.31	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.31	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.31	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.31	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.31	   A^2 -> H(U1(d, e), f(e))
28.54/9.31	   A^2 -> H(U1(d, e), f(k))
28.54/9.31	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.31	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.31	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.31	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.31	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.31	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.31	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.31	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.31	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.31	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.31	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.31	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.31	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.31	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.31	   A^2 -> H(U1(d, a), b)
28.54/9.31	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.31	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.31	   A^2 -> H(U1(d, a), c)
28.54/9.31	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.31	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.31	   A^2 -> H(U1(d, a), e)
28.54/9.31	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.31	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.31	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.31	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.31	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.31	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.31	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.31	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.31	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.31	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.31	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.31	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.31	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.31	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.31	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.31	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.31	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.31	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.31	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.31	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.31	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.31	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.31	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.31	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.31	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.31	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.31	   A^2 -> H(U1(a, c), b)
28.54/9.31	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.31	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.31	   A^2 -> H(U1(a, c), c)
28.54/9.31	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.31	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.31	   A^2 -> H(U1(a, c), e)
28.54/9.31	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, d), b)
28.54/9.31	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.31	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.31	   A^2 -> H(U1(a, d), c)
28.54/9.31	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.31	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.31	   A^2 -> H(U1(a, d), e)
28.54/9.31	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.31	   A^2 -> H(U1(a, a), d)
28.54/9.31	   A^2 -> H(U1(a, a), k)
28.54/9.31	   A^2 -> H(k, U1(b, b))
28.54/9.31	   A^2 -> H(k, f(c))
28.54/9.31	   A^2 -> H(k, f(d))
28.54/9.31	   A^2 -> H(c, U1(c, b))
28.54/9.31	   A^2 -> H(c, U1(d, b))
28.54/9.31	   A^2 -> H(c, U1(b, c))
28.54/9.31	   A^2 -> H(c, U1(b, d))
28.54/9.31	   A^2 -> H(c, U1(c, c))
28.54/9.31	   A^2 -> H(c, f(e))
28.54/9.31	   A^2 -> H(c, f(k))
28.54/9.31	   A^2 -> H(c, U1(d, d))
28.54/9.31	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.31	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.31	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.31	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.31	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.31	   A^2 -> H(U1(e, k), f(e))
28.54/9.31	   A^2 -> H(U1(e, k), f(k))
28.54/9.31	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.31	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.31	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.31	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.31	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.31	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.31	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.31	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.31	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.31	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.31	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.31	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.31	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.31	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.31	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.31	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.31	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.31	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.31	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.31	   A^2 -> H(U1(k, e), f(e))
28.54/9.31	   A^2 -> H(U1(k, e), f(k))
28.54/9.31	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.31	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.31	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.31	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.31	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.31	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.31	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.31	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.31	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.31	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.31	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.31	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.31	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.31	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.31	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.31	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.31	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.31	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.31	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.31	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.31	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.31	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.31	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.31	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.31	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.31	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.31	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.31	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.31	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.31	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.31	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.31	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.31	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.31	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.31	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.31	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.31	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.31	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.31	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.31	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.31	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.31	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.31	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.31	   A^2 -> H(U1(c, c), b)
28.54/9.31	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.31	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.31	   A^2 -> H(U1(c, c), e)
28.54/9.31	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.31	   A^2 -> H(e, U1(c, b))
28.54/9.31	   A^2 -> H(e, U1(d, b))
28.54/9.31	   A^2 -> H(e, U1(b, c))
28.54/9.31	   A^2 -> H(e, U1(b, d))
28.54/9.31	   A^2 -> H(e, U1(c, c))
28.54/9.31	   A^2 -> H(e, f(e))
28.54/9.31	   A^2 -> H(e, f(k))
28.54/9.31	   A^2 -> H(e, U1(d, d))
28.54/9.31	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.31	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.31	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.31	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.31	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.31	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.31	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.31	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.31	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.31	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.31	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.31	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.31	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.31	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.31	   A^2 -> H(f(e), b)
28.54/9.31	   A^2 -> H(f(e), U1(e, d))
28.54/9.31	   A^2 -> H(f(e), U1(d, e))
28.54/9.31	   A^2 -> H(f(e), c)
28.54/9.31	   A^2 -> H(f(e), U1(e, k))
28.54/9.31	   A^2 -> H(f(e), U1(k, e))
28.54/9.31	   A^2 -> H(f(e), U1(k, k))
28.54/9.31	
28.54/9.31	The TRS R consists of the following rules:
28.54/9.31	
28.54/9.31	   f(x) -> U1(x, x)
28.54/9.31	   U1(e, x) -> x
28.54/9.31	   a -> c
28.54/9.31	   a -> d
28.54/9.31	   b -> c
28.54/9.31	   b -> d
28.54/9.31	   d -> k
28.54/9.31	   c -> e
28.54/9.31	   c -> k
28.54/9.31	
28.54/9.31	Q is empty.
28.54/9.31	We have to consider all minimal (P,Q,R)-chains.
28.54/9.31	----------------------------------------
28.54/9.31	
28.54/9.31	(935) TransformationProof (EQUIVALENT)
28.54/9.31	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.31	
28.54/9.31	   (A^2 -> H(U1(e, e), U1(d, k)),A^2 -> H(U1(e, e), U1(d, k)))
28.54/9.31	   (A^2 -> H(f(e), U1(k, k)),A^2 -> H(f(e), U1(k, k)))
28.54/9.31	
28.54/9.31	
28.54/9.31	----------------------------------------
28.54/9.31	
28.54/9.31	(936)
28.54/9.31	Obligation:
28.54/9.31	Q DP problem:
28.54/9.31	The TRS P consists of the following rules:
28.54/9.31	
28.54/9.31	   H(x, x) -> G(x, x, f(k))
28.54/9.31	   G(d, x, x) -> A^2
28.54/9.31	   A^2 -> H(f(c), f(c))
28.54/9.31	   A^2 -> H(f(d), f(d))
28.54/9.31	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.31	   A^2 -> H(f(e), f(e))
28.54/9.31	   A^2 -> H(f(k), f(k))
28.54/9.31	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.31	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.31	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.31	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.31	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.31	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.31	   A^2 -> H(U1(k, k), f(e))
28.54/9.31	   A^2 -> H(U1(k, k), f(k))
28.54/9.31	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.32	   A^2 -> H(f(k), U1(e, b))
28.54/9.32	   A^2 -> H(f(k), U1(k, b))
28.54/9.32	   A^2 -> H(f(k), U1(c, d))
28.54/9.32	   A^2 -> H(f(k), U1(d, c))
28.54/9.32	   A^2 -> H(f(k), U1(b, e))
28.54/9.32	   A^2 -> H(f(k), U1(b, k))
28.54/9.32	   A^2 -> H(f(k), U1(e, c))
28.54/9.32	   A^2 -> H(f(k), U1(k, c))
28.54/9.32	   A^2 -> H(f(k), U1(c, e))
28.54/9.32	   A^2 -> H(f(k), U1(c, k))
28.54/9.32	   A^2 -> H(f(k), U1(e, e))
28.54/9.32	   A^2 -> H(f(k), U1(k, d))
28.54/9.32	   A^2 -> H(f(k), U1(d, k))
28.54/9.32	   A^2 -> H(f(c), b)
28.54/9.32	   A^2 -> H(f(c), U1(e, d))
28.54/9.32	   A^2 -> H(f(c), U1(d, e))
28.54/9.32	   A^2 -> H(f(k), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.32	   A^2 -> H(U1(k, k), f(c))
28.54/9.32	   A^2 -> H(U1(k, k), f(d))
28.54/9.32	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.32	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.32	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.32	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.32	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.32	   A^2 -> H(U1(k, d), f(e))
28.54/9.32	   A^2 -> H(U1(k, d), f(k))
28.54/9.32	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.32	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.32	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.32	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.32	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.32	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.32	   A^2 -> H(U1(d, k), f(e))
28.54/9.32	   A^2 -> H(U1(d, k), f(k))
28.54/9.32	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.32	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.32	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.32	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.32	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.32	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.32	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.32	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.32	   A^2 -> H(f(d), b)
28.54/9.32	   A^2 -> H(f(d), U1(e, d))
28.54/9.32	   A^2 -> H(f(d), U1(d, e))
28.54/9.32	   A^2 -> H(f(d), c)
28.54/9.32	   A^2 -> H(f(d), U1(e, k))
28.54/9.32	   A^2 -> H(f(d), U1(k, e))
28.54/9.32	   A^2 -> H(f(d), e)
28.54/9.32	   A^2 -> H(f(a), d)
28.54/9.32	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.32	   A^2 -> H(f(c), c)
28.54/9.32	   A^2 -> H(f(c), U1(e, k))
28.54/9.32	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.32	   A^2 -> H(f(c), U1(k, e))
28.54/9.32	   A^2 -> H(f(c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.32	   A^2 -> H(f(a), k)
28.54/9.32	   A^2 -> H(f(e), U1(e, e))
28.54/9.32	   A^2 -> H(f(c), e)
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.32	   A^2 -> H(f(d), U1(k, k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.32	   A^2 -> H(d, U1(b, b))
28.54/9.32	   A^2 -> H(d, f(c))
28.54/9.32	   A^2 -> H(d, f(d))
28.54/9.32	   A^2 -> H(a, U1(c, b))
28.54/9.32	   A^2 -> H(a, U1(d, b))
28.54/9.32	   A^2 -> H(a, U1(b, c))
28.54/9.32	   A^2 -> H(a, U1(b, d))
28.54/9.32	   A^2 -> H(a, U1(c, c))
28.54/9.32	   A^2 -> H(a, f(e))
28.54/9.32	   A^2 -> H(a, f(k))
28.54/9.32	   A^2 -> H(a, U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.32	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.32	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.32	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.32	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.32	   A^2 -> H(U1(e, d), f(e))
28.54/9.32	   A^2 -> H(U1(e, d), f(k))
28.54/9.32	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.32	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.32	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.32	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.32	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.32	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.32	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.32	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.32	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.32	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.32	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.32	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.32	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.32	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.32	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.32	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.32	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.32	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.32	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.32	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.32	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.32	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.32	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, a), b)
28.54/9.32	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.32	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.32	   A^2 -> H(U1(c, a), c)
28.54/9.32	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.32	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.32	   A^2 -> H(U1(c, a), e)
28.54/9.32	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.32	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.32	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.32	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.32	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.32	   A^2 -> H(U1(d, e), f(e))
28.54/9.32	   A^2 -> H(U1(d, e), f(k))
28.54/9.32	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.32	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.32	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.32	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.32	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.32	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.32	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.32	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.32	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.32	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.32	   A^2 -> H(U1(d, a), b)
28.54/9.32	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.32	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.32	   A^2 -> H(U1(d, a), c)
28.54/9.32	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.32	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.32	   A^2 -> H(U1(d, a), e)
28.54/9.32	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.32	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.32	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.32	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.32	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.32	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.32	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.32	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.32	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.32	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.32	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.32	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.32	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.32	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.32	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.32	   A^2 -> H(U1(a, c), b)
28.54/9.32	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.32	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.32	   A^2 -> H(U1(a, c), c)
28.54/9.32	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.32	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.32	   A^2 -> H(U1(a, c), e)
28.54/9.32	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, d), b)
28.54/9.32	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.32	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.32	   A^2 -> H(U1(a, d), c)
28.54/9.32	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.32	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.32	   A^2 -> H(U1(a, d), e)
28.54/9.32	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, a), d)
28.54/9.32	   A^2 -> H(U1(a, a), k)
28.54/9.32	   A^2 -> H(k, U1(b, b))
28.54/9.32	   A^2 -> H(k, f(c))
28.54/9.32	   A^2 -> H(k, f(d))
28.54/9.32	   A^2 -> H(c, U1(c, b))
28.54/9.32	   A^2 -> H(c, U1(d, b))
28.54/9.32	   A^2 -> H(c, U1(b, c))
28.54/9.32	   A^2 -> H(c, U1(b, d))
28.54/9.32	   A^2 -> H(c, U1(c, c))
28.54/9.32	   A^2 -> H(c, f(e))
28.54/9.32	   A^2 -> H(c, f(k))
28.54/9.32	   A^2 -> H(c, U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.32	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.32	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.32	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.32	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.32	   A^2 -> H(U1(e, k), f(e))
28.54/9.32	   A^2 -> H(U1(e, k), f(k))
28.54/9.32	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.32	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.32	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.32	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.32	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.32	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.32	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.32	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.32	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.32	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.32	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.32	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.32	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.32	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.32	   A^2 -> H(U1(k, e), f(e))
28.54/9.32	   A^2 -> H(U1(k, e), f(k))
28.54/9.32	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.32	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.32	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.32	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.32	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.32	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.32	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.32	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.32	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.32	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.32	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.32	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.32	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.32	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.32	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.32	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.32	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.32	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.32	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.32	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.32	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.32	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, c), b)
28.54/9.32	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.32	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.32	   A^2 -> H(U1(c, c), e)
28.54/9.32	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.32	   A^2 -> H(e, U1(c, b))
28.54/9.32	   A^2 -> H(e, U1(d, b))
28.54/9.32	   A^2 -> H(e, U1(b, c))
28.54/9.32	   A^2 -> H(e, U1(b, d))
28.54/9.32	   A^2 -> H(e, U1(c, c))
28.54/9.32	   A^2 -> H(e, f(e))
28.54/9.32	   A^2 -> H(e, f(k))
28.54/9.32	   A^2 -> H(e, U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.32	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.32	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.32	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.32	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.32	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.32	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.32	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.32	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.32	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.32	   A^2 -> H(f(e), b)
28.54/9.32	   A^2 -> H(f(e), U1(e, d))
28.54/9.32	   A^2 -> H(f(e), U1(d, e))
28.54/9.32	   A^2 -> H(f(e), c)
28.54/9.32	   A^2 -> H(f(e), U1(e, k))
28.54/9.32	   A^2 -> H(f(e), U1(k, e))
28.54/9.32	   A^2 -> H(f(e), U1(k, k))
28.54/9.32	
28.54/9.32	The TRS R consists of the following rules:
28.54/9.32	
28.54/9.32	   f(x) -> U1(x, x)
28.54/9.32	   U1(e, x) -> x
28.54/9.32	   a -> c
28.54/9.32	   a -> d
28.54/9.32	   b -> c
28.54/9.32	   b -> d
28.54/9.32	   d -> k
28.54/9.32	   c -> e
28.54/9.32	   c -> k
28.54/9.32	
28.54/9.32	Q is empty.
28.54/9.32	We have to consider all minimal (P,Q,R)-chains.
28.54/9.32	----------------------------------------
28.54/9.32	
28.54/9.32	(937) TransformationProof (EQUIVALENT)
28.54/9.32	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.32	
28.54/9.32	   (A^2 -> H(U1(k, k), U1(e, b)),A^2 -> H(U1(k, k), U1(e, b)))
28.54/9.32	   (A^2 -> H(U1(k, k), U1(k, b)),A^2 -> H(U1(k, k), U1(k, b)))
28.54/9.32	   (A^2 -> H(U1(k, k), U1(c, c)),A^2 -> H(U1(k, k), U1(c, c)))
28.54/9.32	   (A^2 -> H(U1(k, k), U1(c, d)),A^2 -> H(U1(k, k), U1(c, d)))
28.54/9.32	
28.54/9.32	
28.54/9.32	----------------------------------------
28.54/9.32	
28.54/9.32	(938)
28.54/9.32	Obligation:
28.54/9.32	Q DP problem:
28.54/9.32	The TRS P consists of the following rules:
28.54/9.32	
28.54/9.32	   H(x, x) -> G(x, x, f(k))
28.54/9.32	   G(d, x, x) -> A^2
28.54/9.32	   A^2 -> H(f(c), f(c))
28.54/9.32	   A^2 -> H(f(d), f(d))
28.54/9.32	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.32	   A^2 -> H(f(e), f(e))
28.54/9.32	   A^2 -> H(f(k), f(k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.32	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.32	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.32	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.32	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.32	   A^2 -> H(U1(k, k), f(e))
28.54/9.32	   A^2 -> H(U1(k, k), f(k))
28.54/9.32	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.32	   A^2 -> H(f(k), U1(e, b))
28.54/9.32	   A^2 -> H(f(k), U1(k, b))
28.54/9.32	   A^2 -> H(f(k), U1(c, d))
28.54/9.32	   A^2 -> H(f(k), U1(d, c))
28.54/9.32	   A^2 -> H(f(k), U1(b, e))
28.54/9.32	   A^2 -> H(f(k), U1(b, k))
28.54/9.32	   A^2 -> H(f(k), U1(e, c))
28.54/9.32	   A^2 -> H(f(k), U1(k, c))
28.54/9.32	   A^2 -> H(f(k), U1(c, e))
28.54/9.32	   A^2 -> H(f(k), U1(c, k))
28.54/9.32	   A^2 -> H(f(k), U1(e, e))
28.54/9.32	   A^2 -> H(f(k), U1(k, d))
28.54/9.32	   A^2 -> H(f(k), U1(d, k))
28.54/9.32	   A^2 -> H(f(c), b)
28.54/9.32	   A^2 -> H(f(c), U1(e, d))
28.54/9.32	   A^2 -> H(f(c), U1(d, e))
28.54/9.32	   A^2 -> H(f(k), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.32	   A^2 -> H(U1(k, k), f(c))
28.54/9.32	   A^2 -> H(U1(k, k), f(d))
28.54/9.32	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.32	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.32	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.32	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.32	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.32	   A^2 -> H(U1(k, d), f(e))
28.54/9.32	   A^2 -> H(U1(k, d), f(k))
28.54/9.32	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.32	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.32	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.32	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.32	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.32	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.32	   A^2 -> H(U1(d, k), f(e))
28.54/9.32	   A^2 -> H(U1(d, k), f(k))
28.54/9.32	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.32	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.32	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.32	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.32	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.32	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.32	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.32	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.32	   A^2 -> H(f(d), b)
28.54/9.32	   A^2 -> H(f(d), U1(e, d))
28.54/9.32	   A^2 -> H(f(d), U1(d, e))
28.54/9.32	   A^2 -> H(f(d), c)
28.54/9.32	   A^2 -> H(f(d), U1(e, k))
28.54/9.32	   A^2 -> H(f(d), U1(k, e))
28.54/9.32	   A^2 -> H(f(d), e)
28.54/9.32	   A^2 -> H(f(a), d)
28.54/9.32	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.32	   A^2 -> H(f(c), c)
28.54/9.32	   A^2 -> H(f(c), U1(e, k))
28.54/9.32	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.32	   A^2 -> H(f(c), U1(k, e))
28.54/9.32	   A^2 -> H(f(c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.32	   A^2 -> H(f(a), k)
28.54/9.32	   A^2 -> H(f(e), U1(e, e))
28.54/9.32	   A^2 -> H(f(c), e)
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.32	   A^2 -> H(f(d), U1(k, k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.32	   A^2 -> H(d, U1(b, b))
28.54/9.32	   A^2 -> H(d, f(c))
28.54/9.32	   A^2 -> H(d, f(d))
28.54/9.32	   A^2 -> H(a, U1(c, b))
28.54/9.32	   A^2 -> H(a, U1(d, b))
28.54/9.32	   A^2 -> H(a, U1(b, c))
28.54/9.32	   A^2 -> H(a, U1(b, d))
28.54/9.32	   A^2 -> H(a, U1(c, c))
28.54/9.32	   A^2 -> H(a, f(e))
28.54/9.32	   A^2 -> H(a, f(k))
28.54/9.32	   A^2 -> H(a, U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.32	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.32	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.32	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.32	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.32	   A^2 -> H(U1(e, d), f(e))
28.54/9.32	   A^2 -> H(U1(e, d), f(k))
28.54/9.32	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.32	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.32	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.32	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.32	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.32	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.32	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.32	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.32	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.32	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.32	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.32	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.32	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.32	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.32	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.32	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.32	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.32	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.32	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.32	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.32	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.32	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.32	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, a), b)
28.54/9.32	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.32	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.32	   A^2 -> H(U1(c, a), c)
28.54/9.32	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.32	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.32	   A^2 -> H(U1(c, a), e)
28.54/9.32	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.32	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.32	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.32	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.32	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.32	   A^2 -> H(U1(d, e), f(e))
28.54/9.32	   A^2 -> H(U1(d, e), f(k))
28.54/9.32	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.32	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.32	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.32	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.32	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.32	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.32	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.32	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.32	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.32	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.32	   A^2 -> H(U1(d, a), b)
28.54/9.32	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.32	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.32	   A^2 -> H(U1(d, a), c)
28.54/9.32	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.32	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.32	   A^2 -> H(U1(d, a), e)
28.54/9.32	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.32	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.32	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.32	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.32	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.32	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.32	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.32	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.32	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.32	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.32	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.32	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.32	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.32	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.32	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.32	   A^2 -> H(U1(a, c), b)
28.54/9.32	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.32	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.32	   A^2 -> H(U1(a, c), c)
28.54/9.32	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.32	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.32	   A^2 -> H(U1(a, c), e)
28.54/9.32	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, d), b)
28.54/9.32	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.32	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.32	   A^2 -> H(U1(a, d), c)
28.54/9.32	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.32	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.32	   A^2 -> H(U1(a, d), e)
28.54/9.32	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, a), d)
28.54/9.32	   A^2 -> H(U1(a, a), k)
28.54/9.32	   A^2 -> H(k, U1(b, b))
28.54/9.32	   A^2 -> H(k, f(c))
28.54/9.32	   A^2 -> H(k, f(d))
28.54/9.32	   A^2 -> H(c, U1(c, b))
28.54/9.32	   A^2 -> H(c, U1(d, b))
28.54/9.32	   A^2 -> H(c, U1(b, c))
28.54/9.32	   A^2 -> H(c, U1(b, d))
28.54/9.32	   A^2 -> H(c, U1(c, c))
28.54/9.32	   A^2 -> H(c, f(e))
28.54/9.32	   A^2 -> H(c, f(k))
28.54/9.32	   A^2 -> H(c, U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.32	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.32	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.32	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.32	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.32	   A^2 -> H(U1(e, k), f(e))
28.54/9.32	   A^2 -> H(U1(e, k), f(k))
28.54/9.32	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.32	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.32	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.32	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.32	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.32	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.32	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.32	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.32	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.32	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.32	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.32	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.32	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.32	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.32	   A^2 -> H(U1(k, e), f(e))
28.54/9.32	   A^2 -> H(U1(k, e), f(k))
28.54/9.32	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.32	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.32	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.32	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.32	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.32	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.32	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.32	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.32	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.32	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.32	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.32	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.32	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.32	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.32	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.32	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.32	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.32	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.32	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.32	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.32	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.32	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, c), b)
28.54/9.32	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.32	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.32	   A^2 -> H(U1(c, c), e)
28.54/9.32	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.32	   A^2 -> H(e, U1(c, b))
28.54/9.32	   A^2 -> H(e, U1(d, b))
28.54/9.32	   A^2 -> H(e, U1(b, c))
28.54/9.32	   A^2 -> H(e, U1(b, d))
28.54/9.32	   A^2 -> H(e, U1(c, c))
28.54/9.32	   A^2 -> H(e, f(e))
28.54/9.32	   A^2 -> H(e, f(k))
28.54/9.32	   A^2 -> H(e, U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.32	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.32	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.32	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.32	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.32	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.32	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.32	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.32	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.32	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.32	   A^2 -> H(f(e), b)
28.54/9.32	   A^2 -> H(f(e), U1(e, d))
28.54/9.32	   A^2 -> H(f(e), U1(d, e))
28.54/9.32	   A^2 -> H(f(e), c)
28.54/9.32	   A^2 -> H(f(e), U1(e, k))
28.54/9.32	   A^2 -> H(f(e), U1(k, e))
28.54/9.32	   A^2 -> H(f(e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.32	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.32	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.32	
28.54/9.32	The TRS R consists of the following rules:
28.54/9.32	
28.54/9.32	   f(x) -> U1(x, x)
28.54/9.32	   U1(e, x) -> x
28.54/9.32	   a -> c
28.54/9.32	   a -> d
28.54/9.32	   b -> c
28.54/9.32	   b -> d
28.54/9.32	   d -> k
28.54/9.32	   c -> e
28.54/9.32	   c -> k
28.54/9.32	
28.54/9.32	Q is empty.
28.54/9.32	We have to consider all minimal (P,Q,R)-chains.
28.54/9.32	----------------------------------------
28.54/9.32	
28.54/9.32	(939) TransformationProof (EQUIVALENT)
28.54/9.32	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.32	
28.54/9.32	   (A^2 -> H(U1(k, k), U1(k, b)),A^2 -> H(U1(k, k), U1(k, b)))
28.54/9.32	   (A^2 -> H(U1(k, k), U1(d, c)),A^2 -> H(U1(k, k), U1(d, c)))
28.54/9.32	   (A^2 -> H(U1(k, k), U1(d, d)),A^2 -> H(U1(k, k), U1(d, d)))
28.54/9.32	
28.54/9.32	
28.54/9.32	----------------------------------------
28.54/9.32	
28.54/9.32	(940)
28.54/9.32	Obligation:
28.54/9.32	Q DP problem:
28.54/9.32	The TRS P consists of the following rules:
28.54/9.32	
28.54/9.32	   H(x, x) -> G(x, x, f(k))
28.54/9.32	   G(d, x, x) -> A^2
28.54/9.32	   A^2 -> H(f(c), f(c))
28.54/9.32	   A^2 -> H(f(d), f(d))
28.54/9.32	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.32	   A^2 -> H(f(e), f(e))
28.54/9.32	   A^2 -> H(f(k), f(k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.32	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.32	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.32	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.32	   A^2 -> H(U1(k, k), f(e))
28.54/9.32	   A^2 -> H(U1(k, k), f(k))
28.54/9.32	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.32	   A^2 -> H(f(k), U1(e, b))
28.54/9.32	   A^2 -> H(f(k), U1(k, b))
28.54/9.32	   A^2 -> H(f(k), U1(c, d))
28.54/9.32	   A^2 -> H(f(k), U1(d, c))
28.54/9.32	   A^2 -> H(f(k), U1(b, e))
28.54/9.32	   A^2 -> H(f(k), U1(b, k))
28.54/9.32	   A^2 -> H(f(k), U1(e, c))
28.54/9.32	   A^2 -> H(f(k), U1(k, c))
28.54/9.32	   A^2 -> H(f(k), U1(c, e))
28.54/9.32	   A^2 -> H(f(k), U1(c, k))
28.54/9.32	   A^2 -> H(f(k), U1(e, e))
28.54/9.32	   A^2 -> H(f(k), U1(k, d))
28.54/9.32	   A^2 -> H(f(k), U1(d, k))
28.54/9.32	   A^2 -> H(f(c), b)
28.54/9.32	   A^2 -> H(f(c), U1(e, d))
28.54/9.32	   A^2 -> H(f(c), U1(d, e))
28.54/9.32	   A^2 -> H(f(k), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.32	   A^2 -> H(U1(k, k), f(c))
28.54/9.32	   A^2 -> H(U1(k, k), f(d))
28.54/9.32	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.32	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.32	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.32	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.32	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.32	   A^2 -> H(U1(k, d), f(e))
28.54/9.32	   A^2 -> H(U1(k, d), f(k))
28.54/9.32	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.32	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.32	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.32	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.32	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.32	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.32	   A^2 -> H(U1(d, k), f(e))
28.54/9.32	   A^2 -> H(U1(d, k), f(k))
28.54/9.32	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.32	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.32	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.32	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.32	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.32	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.32	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.32	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.32	   A^2 -> H(f(d), b)
28.54/9.32	   A^2 -> H(f(d), U1(e, d))
28.54/9.32	   A^2 -> H(f(d), U1(d, e))
28.54/9.32	   A^2 -> H(f(d), c)
28.54/9.32	   A^2 -> H(f(d), U1(e, k))
28.54/9.32	   A^2 -> H(f(d), U1(k, e))
28.54/9.32	   A^2 -> H(f(d), e)
28.54/9.32	   A^2 -> H(f(a), d)
28.54/9.32	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.32	   A^2 -> H(f(c), c)
28.54/9.32	   A^2 -> H(f(c), U1(e, k))
28.54/9.32	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.32	   A^2 -> H(f(c), U1(k, e))
28.54/9.32	   A^2 -> H(f(c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.32	   A^2 -> H(f(a), k)
28.54/9.32	   A^2 -> H(f(e), U1(e, e))
28.54/9.32	   A^2 -> H(f(c), e)
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.32	   A^2 -> H(f(d), U1(k, k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.32	   A^2 -> H(d, U1(b, b))
28.54/9.32	   A^2 -> H(d, f(c))
28.54/9.32	   A^2 -> H(d, f(d))
28.54/9.32	   A^2 -> H(a, U1(c, b))
28.54/9.32	   A^2 -> H(a, U1(d, b))
28.54/9.32	   A^2 -> H(a, U1(b, c))
28.54/9.32	   A^2 -> H(a, U1(b, d))
28.54/9.32	   A^2 -> H(a, U1(c, c))
28.54/9.32	   A^2 -> H(a, f(e))
28.54/9.32	   A^2 -> H(a, f(k))
28.54/9.32	   A^2 -> H(a, U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.32	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.32	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.32	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.32	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.32	   A^2 -> H(U1(e, d), f(e))
28.54/9.32	   A^2 -> H(U1(e, d), f(k))
28.54/9.32	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.32	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.32	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.32	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.32	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.32	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.32	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.32	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.32	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.32	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.32	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.32	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.32	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.32	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.32	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.32	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.32	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.32	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.32	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.32	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.32	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.32	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.32	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, a), b)
28.54/9.32	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.32	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.32	   A^2 -> H(U1(c, a), c)
28.54/9.32	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.32	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.32	   A^2 -> H(U1(c, a), e)
28.54/9.32	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.32	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.32	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.32	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.32	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.32	   A^2 -> H(U1(d, e), f(e))
28.54/9.32	   A^2 -> H(U1(d, e), f(k))
28.54/9.32	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.32	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.32	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.32	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.32	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.32	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.32	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.32	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.32	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.32	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.32	   A^2 -> H(U1(d, a), b)
28.54/9.32	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.32	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.32	   A^2 -> H(U1(d, a), c)
28.54/9.32	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.32	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.32	   A^2 -> H(U1(d, a), e)
28.54/9.32	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.32	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.32	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.32	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.32	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.32	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.32	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.32	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.32	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.32	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.32	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.32	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.32	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.32	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.32	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.32	   A^2 -> H(U1(a, c), b)
28.54/9.32	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.32	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.32	   A^2 -> H(U1(a, c), c)
28.54/9.32	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.32	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.32	   A^2 -> H(U1(a, c), e)
28.54/9.32	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, d), b)
28.54/9.32	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.32	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.32	   A^2 -> H(U1(a, d), c)
28.54/9.32	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.32	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.32	   A^2 -> H(U1(a, d), e)
28.54/9.32	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, a), d)
28.54/9.32	   A^2 -> H(U1(a, a), k)
28.54/9.32	   A^2 -> H(k, U1(b, b))
28.54/9.32	   A^2 -> H(k, f(c))
28.54/9.32	   A^2 -> H(k, f(d))
28.54/9.32	   A^2 -> H(c, U1(c, b))
28.54/9.32	   A^2 -> H(c, U1(d, b))
28.54/9.32	   A^2 -> H(c, U1(b, c))
28.54/9.32	   A^2 -> H(c, U1(b, d))
28.54/9.32	   A^2 -> H(c, U1(c, c))
28.54/9.32	   A^2 -> H(c, f(e))
28.54/9.32	   A^2 -> H(c, f(k))
28.54/9.32	   A^2 -> H(c, U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.32	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.32	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.32	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.32	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.32	   A^2 -> H(U1(e, k), f(e))
28.54/9.32	   A^2 -> H(U1(e, k), f(k))
28.54/9.32	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.32	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.32	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.32	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.32	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.32	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.32	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.32	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.32	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.32	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.32	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.32	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.32	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.32	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.32	   A^2 -> H(U1(k, e), f(e))
28.54/9.32	   A^2 -> H(U1(k, e), f(k))
28.54/9.32	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.32	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.32	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.32	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.32	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.32	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.32	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.32	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.32	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.32	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.32	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.32	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.32	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.32	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.32	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.32	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.32	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.32	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.32	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.32	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.32	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.32	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, c), b)
28.54/9.32	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.32	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.32	   A^2 -> H(U1(c, c), e)
28.54/9.32	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.32	   A^2 -> H(e, U1(c, b))
28.54/9.32	   A^2 -> H(e, U1(d, b))
28.54/9.32	   A^2 -> H(e, U1(b, c))
28.54/9.32	   A^2 -> H(e, U1(b, d))
28.54/9.32	   A^2 -> H(e, U1(c, c))
28.54/9.32	   A^2 -> H(e, f(e))
28.54/9.32	   A^2 -> H(e, f(k))
28.54/9.32	   A^2 -> H(e, U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.32	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.32	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.32	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.32	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.32	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.32	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.32	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.32	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.32	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.32	   A^2 -> H(f(e), b)
28.54/9.32	   A^2 -> H(f(e), U1(e, d))
28.54/9.32	   A^2 -> H(f(e), U1(d, e))
28.54/9.32	   A^2 -> H(f(e), c)
28.54/9.32	   A^2 -> H(f(e), U1(e, k))
28.54/9.32	   A^2 -> H(f(e), U1(k, e))
28.54/9.32	   A^2 -> H(f(e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.32	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.32	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.32	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.32	
28.54/9.32	The TRS R consists of the following rules:
28.54/9.32	
28.54/9.32	   f(x) -> U1(x, x)
28.54/9.32	   U1(e, x) -> x
28.54/9.32	   a -> c
28.54/9.32	   a -> d
28.54/9.32	   b -> c
28.54/9.32	   b -> d
28.54/9.32	   d -> k
28.54/9.32	   c -> e
28.54/9.32	   c -> k
28.54/9.32	
28.54/9.32	Q is empty.
28.54/9.32	We have to consider all minimal (P,Q,R)-chains.
28.54/9.32	----------------------------------------
28.54/9.32	
28.54/9.32	(941) TransformationProof (EQUIVALENT)
28.54/9.32	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.32	
28.54/9.32	   (A^2 -> H(U1(k, k), U1(c, c)),A^2 -> H(U1(k, k), U1(c, c)))
28.54/9.32	   (A^2 -> H(U1(k, k), U1(d, c)),A^2 -> H(U1(k, k), U1(d, c)))
28.54/9.32	   (A^2 -> H(U1(k, k), U1(b, e)),A^2 -> H(U1(k, k), U1(b, e)))
28.54/9.32	   (A^2 -> H(U1(k, k), U1(b, k)),A^2 -> H(U1(k, k), U1(b, k)))
28.54/9.32	
28.54/9.32	
28.54/9.32	----------------------------------------
28.54/9.32	
28.54/9.32	(942)
28.54/9.32	Obligation:
28.54/9.32	Q DP problem:
28.54/9.32	The TRS P consists of the following rules:
28.54/9.32	
28.54/9.32	   H(x, x) -> G(x, x, f(k))
28.54/9.32	   G(d, x, x) -> A^2
28.54/9.32	   A^2 -> H(f(c), f(c))
28.54/9.32	   A^2 -> H(f(d), f(d))
28.54/9.32	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.32	   A^2 -> H(f(e), f(e))
28.54/9.32	   A^2 -> H(f(k), f(k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.32	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.32	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.32	   A^2 -> H(U1(k, k), f(e))
28.54/9.32	   A^2 -> H(U1(k, k), f(k))
28.54/9.32	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.32	   A^2 -> H(f(k), U1(e, b))
28.54/9.32	   A^2 -> H(f(k), U1(k, b))
28.54/9.32	   A^2 -> H(f(k), U1(c, d))
28.54/9.32	   A^2 -> H(f(k), U1(d, c))
28.54/9.32	   A^2 -> H(f(k), U1(b, e))
28.54/9.32	   A^2 -> H(f(k), U1(b, k))
28.54/9.32	   A^2 -> H(f(k), U1(e, c))
28.54/9.32	   A^2 -> H(f(k), U1(k, c))
28.54/9.32	   A^2 -> H(f(k), U1(c, e))
28.54/9.32	   A^2 -> H(f(k), U1(c, k))
28.54/9.32	   A^2 -> H(f(k), U1(e, e))
28.54/9.32	   A^2 -> H(f(k), U1(k, d))
28.54/9.32	   A^2 -> H(f(k), U1(d, k))
28.54/9.32	   A^2 -> H(f(c), b)
28.54/9.32	   A^2 -> H(f(c), U1(e, d))
28.54/9.32	   A^2 -> H(f(c), U1(d, e))
28.54/9.32	   A^2 -> H(f(k), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.32	   A^2 -> H(U1(k, k), f(c))
28.54/9.32	   A^2 -> H(U1(k, k), f(d))
28.54/9.32	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.32	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.32	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.32	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.32	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.32	   A^2 -> H(U1(k, d), f(e))
28.54/9.32	   A^2 -> H(U1(k, d), f(k))
28.54/9.32	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.32	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.32	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.32	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.32	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.32	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.32	   A^2 -> H(U1(d, k), f(e))
28.54/9.32	   A^2 -> H(U1(d, k), f(k))
28.54/9.32	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.32	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.32	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.32	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.32	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.32	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.32	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.32	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.32	   A^2 -> H(f(d), b)
28.54/9.32	   A^2 -> H(f(d), U1(e, d))
28.54/9.32	   A^2 -> H(f(d), U1(d, e))
28.54/9.32	   A^2 -> H(f(d), c)
28.54/9.32	   A^2 -> H(f(d), U1(e, k))
28.54/9.32	   A^2 -> H(f(d), U1(k, e))
28.54/9.32	   A^2 -> H(f(d), e)
28.54/9.32	   A^2 -> H(f(a), d)
28.54/9.32	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.32	   A^2 -> H(f(c), c)
28.54/9.32	   A^2 -> H(f(c), U1(e, k))
28.54/9.32	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.32	   A^2 -> H(f(c), U1(k, e))
28.54/9.32	   A^2 -> H(f(c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.32	   A^2 -> H(f(a), k)
28.54/9.32	   A^2 -> H(f(e), U1(e, e))
28.54/9.32	   A^2 -> H(f(c), e)
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.32	   A^2 -> H(f(d), U1(k, k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.32	   A^2 -> H(d, U1(b, b))
28.54/9.32	   A^2 -> H(d, f(c))
28.54/9.32	   A^2 -> H(d, f(d))
28.54/9.32	   A^2 -> H(a, U1(c, b))
28.54/9.32	   A^2 -> H(a, U1(d, b))
28.54/9.32	   A^2 -> H(a, U1(b, c))
28.54/9.32	   A^2 -> H(a, U1(b, d))
28.54/9.32	   A^2 -> H(a, U1(c, c))
28.54/9.32	   A^2 -> H(a, f(e))
28.54/9.32	   A^2 -> H(a, f(k))
28.54/9.32	   A^2 -> H(a, U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.32	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.32	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.32	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.32	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.32	   A^2 -> H(U1(e, d), f(e))
28.54/9.32	   A^2 -> H(U1(e, d), f(k))
28.54/9.32	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.32	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.32	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.32	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.32	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.32	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.32	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.32	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.32	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.32	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.32	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.32	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.32	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.32	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.32	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.32	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.32	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.32	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.32	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.32	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.32	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.32	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.32	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, a), b)
28.54/9.32	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.32	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.32	   A^2 -> H(U1(c, a), c)
28.54/9.32	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.32	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.32	   A^2 -> H(U1(c, a), e)
28.54/9.32	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.32	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.32	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.32	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.32	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.32	   A^2 -> H(U1(d, e), f(e))
28.54/9.32	   A^2 -> H(U1(d, e), f(k))
28.54/9.32	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.32	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.32	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.32	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.32	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.32	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.32	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.32	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.32	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.32	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.32	   A^2 -> H(U1(d, a), b)
28.54/9.32	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.32	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.32	   A^2 -> H(U1(d, a), c)
28.54/9.32	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.32	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.32	   A^2 -> H(U1(d, a), e)
28.54/9.32	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.32	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.32	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.32	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.32	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.32	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.32	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.32	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.32	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.32	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.32	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.32	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.32	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.32	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.32	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.32	   A^2 -> H(U1(a, c), b)
28.54/9.32	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.32	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.32	   A^2 -> H(U1(a, c), c)
28.54/9.32	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.32	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.32	   A^2 -> H(U1(a, c), e)
28.54/9.32	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, d), b)
28.54/9.32	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.32	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.32	   A^2 -> H(U1(a, d), c)
28.54/9.32	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.32	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.32	   A^2 -> H(U1(a, d), e)
28.54/9.32	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, a), d)
28.54/9.32	   A^2 -> H(U1(a, a), k)
28.54/9.32	   A^2 -> H(k, U1(b, b))
28.54/9.32	   A^2 -> H(k, f(c))
28.54/9.32	   A^2 -> H(k, f(d))
28.54/9.32	   A^2 -> H(c, U1(c, b))
28.54/9.32	   A^2 -> H(c, U1(d, b))
28.54/9.32	   A^2 -> H(c, U1(b, c))
28.54/9.32	   A^2 -> H(c, U1(b, d))
28.54/9.32	   A^2 -> H(c, U1(c, c))
28.54/9.32	   A^2 -> H(c, f(e))
28.54/9.32	   A^2 -> H(c, f(k))
28.54/9.32	   A^2 -> H(c, U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.32	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.32	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.32	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.32	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.32	   A^2 -> H(U1(e, k), f(e))
28.54/9.32	   A^2 -> H(U1(e, k), f(k))
28.54/9.32	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.32	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.32	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.32	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.32	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.32	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.32	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.32	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.32	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.32	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.32	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.32	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.32	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.32	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.32	   A^2 -> H(U1(k, e), f(e))
28.54/9.32	   A^2 -> H(U1(k, e), f(k))
28.54/9.32	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.32	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.32	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.32	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.32	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.32	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.32	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.32	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.32	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.32	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.32	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.32	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.32	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.32	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.32	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.32	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.32	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.32	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.32	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.32	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.32	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.32	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, c), b)
28.54/9.32	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.32	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.32	   A^2 -> H(U1(c, c), e)
28.54/9.32	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.32	   A^2 -> H(e, U1(c, b))
28.54/9.32	   A^2 -> H(e, U1(d, b))
28.54/9.32	   A^2 -> H(e, U1(b, c))
28.54/9.32	   A^2 -> H(e, U1(b, d))
28.54/9.32	   A^2 -> H(e, U1(c, c))
28.54/9.32	   A^2 -> H(e, f(e))
28.54/9.32	   A^2 -> H(e, f(k))
28.54/9.32	   A^2 -> H(e, U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.32	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.32	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.32	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.32	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.32	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.32	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.32	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.32	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.32	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.32	   A^2 -> H(f(e), b)
28.54/9.32	   A^2 -> H(f(e), U1(e, d))
28.54/9.32	   A^2 -> H(f(e), U1(d, e))
28.54/9.32	   A^2 -> H(f(e), c)
28.54/9.32	   A^2 -> H(f(e), U1(e, k))
28.54/9.32	   A^2 -> H(f(e), U1(k, e))
28.54/9.32	   A^2 -> H(f(e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.32	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.32	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.32	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.32	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.32	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.32	
28.54/9.32	The TRS R consists of the following rules:
28.54/9.32	
28.54/9.32	   f(x) -> U1(x, x)
28.54/9.32	   U1(e, x) -> x
28.54/9.32	   a -> c
28.54/9.32	   a -> d
28.54/9.32	   b -> c
28.54/9.32	   b -> d
28.54/9.32	   d -> k
28.54/9.32	   c -> e
28.54/9.32	   c -> k
28.54/9.32	
28.54/9.32	Q is empty.
28.54/9.32	We have to consider all minimal (P,Q,R)-chains.
28.54/9.32	----------------------------------------
28.54/9.32	
28.54/9.32	(943) TransformationProof (EQUIVALENT)
28.54/9.32	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.32	
28.54/9.32	   (A^2 -> H(U1(k, k), U1(c, d)),A^2 -> H(U1(k, k), U1(c, d)))
28.54/9.32	   (A^2 -> H(U1(k, k), U1(d, d)),A^2 -> H(U1(k, k), U1(d, d)))
28.54/9.32	   (A^2 -> H(U1(k, k), U1(b, k)),A^2 -> H(U1(k, k), U1(b, k)))
28.54/9.32	
28.54/9.32	
28.54/9.32	----------------------------------------
28.54/9.32	
28.54/9.32	(944)
28.54/9.32	Obligation:
28.54/9.32	Q DP problem:
28.54/9.32	The TRS P consists of the following rules:
28.54/9.32	
28.54/9.32	   H(x, x) -> G(x, x, f(k))
28.54/9.32	   G(d, x, x) -> A^2
28.54/9.32	   A^2 -> H(f(c), f(c))
28.54/9.32	   A^2 -> H(f(d), f(d))
28.54/9.32	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.32	   A^2 -> H(f(e), f(e))
28.54/9.32	   A^2 -> H(f(k), f(k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.32	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.32	   A^2 -> H(U1(k, k), f(e))
28.54/9.32	   A^2 -> H(U1(k, k), f(k))
28.54/9.32	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.32	   A^2 -> H(f(k), U1(e, b))
28.54/9.32	   A^2 -> H(f(k), U1(k, b))
28.54/9.32	   A^2 -> H(f(k), U1(c, d))
28.54/9.32	   A^2 -> H(f(k), U1(d, c))
28.54/9.32	   A^2 -> H(f(k), U1(b, e))
28.54/9.32	   A^2 -> H(f(k), U1(b, k))
28.54/9.32	   A^2 -> H(f(k), U1(e, c))
28.54/9.32	   A^2 -> H(f(k), U1(k, c))
28.54/9.32	   A^2 -> H(f(k), U1(c, e))
28.54/9.32	   A^2 -> H(f(k), U1(c, k))
28.54/9.32	   A^2 -> H(f(k), U1(e, e))
28.54/9.32	   A^2 -> H(f(k), U1(k, d))
28.54/9.32	   A^2 -> H(f(k), U1(d, k))
28.54/9.32	   A^2 -> H(f(c), b)
28.54/9.32	   A^2 -> H(f(c), U1(e, d))
28.54/9.32	   A^2 -> H(f(c), U1(d, e))
28.54/9.32	   A^2 -> H(f(k), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.32	   A^2 -> H(U1(k, k), f(c))
28.54/9.32	   A^2 -> H(U1(k, k), f(d))
28.54/9.32	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.32	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.32	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.32	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.32	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.32	   A^2 -> H(U1(k, d), f(e))
28.54/9.32	   A^2 -> H(U1(k, d), f(k))
28.54/9.32	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.32	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.32	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.32	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.32	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.32	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.32	   A^2 -> H(U1(d, k), f(e))
28.54/9.32	   A^2 -> H(U1(d, k), f(k))
28.54/9.32	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.32	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.32	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.32	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.32	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.32	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.32	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.32	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.32	   A^2 -> H(f(d), b)
28.54/9.32	   A^2 -> H(f(d), U1(e, d))
28.54/9.32	   A^2 -> H(f(d), U1(d, e))
28.54/9.32	   A^2 -> H(f(d), c)
28.54/9.32	   A^2 -> H(f(d), U1(e, k))
28.54/9.32	   A^2 -> H(f(d), U1(k, e))
28.54/9.32	   A^2 -> H(f(d), e)
28.54/9.32	   A^2 -> H(f(a), d)
28.54/9.32	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.32	   A^2 -> H(f(c), c)
28.54/9.32	   A^2 -> H(f(c), U1(e, k))
28.54/9.32	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.32	   A^2 -> H(f(c), U1(k, e))
28.54/9.32	   A^2 -> H(f(c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.32	   A^2 -> H(f(a), k)
28.54/9.32	   A^2 -> H(f(e), U1(e, e))
28.54/9.32	   A^2 -> H(f(c), e)
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.32	   A^2 -> H(f(d), U1(k, k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.32	   A^2 -> H(d, U1(b, b))
28.54/9.32	   A^2 -> H(d, f(c))
28.54/9.32	   A^2 -> H(d, f(d))
28.54/9.32	   A^2 -> H(a, U1(c, b))
28.54/9.32	   A^2 -> H(a, U1(d, b))
28.54/9.32	   A^2 -> H(a, U1(b, c))
28.54/9.32	   A^2 -> H(a, U1(b, d))
28.54/9.32	   A^2 -> H(a, U1(c, c))
28.54/9.32	   A^2 -> H(a, f(e))
28.54/9.32	   A^2 -> H(a, f(k))
28.54/9.32	   A^2 -> H(a, U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.32	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.32	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.32	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.32	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.32	   A^2 -> H(U1(e, d), f(e))
28.54/9.32	   A^2 -> H(U1(e, d), f(k))
28.54/9.32	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.32	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.32	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.32	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.32	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.32	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.32	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.32	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.32	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.32	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.32	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.32	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.32	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.32	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.32	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.32	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.32	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.32	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.32	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.32	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.32	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.32	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.32	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, a), b)
28.54/9.32	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.32	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.32	   A^2 -> H(U1(c, a), c)
28.54/9.32	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.32	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.32	   A^2 -> H(U1(c, a), e)
28.54/9.32	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.32	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.32	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.32	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.32	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.32	   A^2 -> H(U1(d, e), f(e))
28.54/9.32	   A^2 -> H(U1(d, e), f(k))
28.54/9.32	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.32	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.32	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.32	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.32	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.32	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.32	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.32	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.32	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.32	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.32	   A^2 -> H(U1(d, a), b)
28.54/9.32	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.32	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.32	   A^2 -> H(U1(d, a), c)
28.54/9.32	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.32	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.32	   A^2 -> H(U1(d, a), e)
28.54/9.32	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.32	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.32	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.32	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.32	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.32	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.32	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.32	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.32	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.32	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.32	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.32	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.32	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.32	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.32	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.32	   A^2 -> H(U1(a, c), b)
28.54/9.32	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.32	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.32	   A^2 -> H(U1(a, c), c)
28.54/9.32	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.32	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.32	   A^2 -> H(U1(a, c), e)
28.54/9.32	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, d), b)
28.54/9.32	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.32	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.32	   A^2 -> H(U1(a, d), c)
28.54/9.32	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.32	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.32	   A^2 -> H(U1(a, d), e)
28.54/9.32	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, a), d)
28.54/9.32	   A^2 -> H(U1(a, a), k)
28.54/9.32	   A^2 -> H(k, U1(b, b))
28.54/9.32	   A^2 -> H(k, f(c))
28.54/9.32	   A^2 -> H(k, f(d))
28.54/9.32	   A^2 -> H(c, U1(c, b))
28.54/9.32	   A^2 -> H(c, U1(d, b))
28.54/9.32	   A^2 -> H(c, U1(b, c))
28.54/9.32	   A^2 -> H(c, U1(b, d))
28.54/9.32	   A^2 -> H(c, U1(c, c))
28.54/9.32	   A^2 -> H(c, f(e))
28.54/9.32	   A^2 -> H(c, f(k))
28.54/9.32	   A^2 -> H(c, U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.32	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.32	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.32	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.32	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.32	   A^2 -> H(U1(e, k), f(e))
28.54/9.32	   A^2 -> H(U1(e, k), f(k))
28.54/9.32	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.32	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.32	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.32	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.32	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.32	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.32	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.32	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.32	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.32	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.32	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.32	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.32	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.32	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.32	   A^2 -> H(U1(k, e), f(e))
28.54/9.32	   A^2 -> H(U1(k, e), f(k))
28.54/9.32	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.32	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.32	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.32	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.32	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.32	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.32	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.32	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.32	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.32	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.32	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.32	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.32	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.32	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.32	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.32	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.32	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.32	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.32	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.32	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.32	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.32	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, c), b)
28.54/9.32	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.32	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.32	   A^2 -> H(U1(c, c), e)
28.54/9.32	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.32	   A^2 -> H(e, U1(c, b))
28.54/9.32	   A^2 -> H(e, U1(d, b))
28.54/9.32	   A^2 -> H(e, U1(b, c))
28.54/9.32	   A^2 -> H(e, U1(b, d))
28.54/9.32	   A^2 -> H(e, U1(c, c))
28.54/9.32	   A^2 -> H(e, f(e))
28.54/9.32	   A^2 -> H(e, f(k))
28.54/9.32	   A^2 -> H(e, U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.32	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.32	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.32	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.32	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.32	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.32	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.32	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.32	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.32	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.32	   A^2 -> H(f(e), b)
28.54/9.32	   A^2 -> H(f(e), U1(e, d))
28.54/9.32	   A^2 -> H(f(e), U1(d, e))
28.54/9.32	   A^2 -> H(f(e), c)
28.54/9.32	   A^2 -> H(f(e), U1(e, k))
28.54/9.32	   A^2 -> H(f(e), U1(k, e))
28.54/9.32	   A^2 -> H(f(e), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.32	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.32	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.32	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.32	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.32	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.32	
28.54/9.32	The TRS R consists of the following rules:
28.54/9.32	
28.54/9.32	   f(x) -> U1(x, x)
28.54/9.32	   U1(e, x) -> x
28.54/9.32	   a -> c
28.54/9.32	   a -> d
28.54/9.32	   b -> c
28.54/9.32	   b -> d
28.54/9.32	   d -> k
28.54/9.32	   c -> e
28.54/9.32	   c -> k
28.54/9.32	
28.54/9.32	Q is empty.
28.54/9.32	We have to consider all minimal (P,Q,R)-chains.
28.54/9.32	----------------------------------------
28.54/9.32	
28.54/9.32	(945) TransformationProof (EQUIVALENT)
28.54/9.32	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.32	
28.54/9.32	   (A^2 -> H(U1(k, k), U1(e, c)),A^2 -> H(U1(k, k), U1(e, c)))
28.54/9.32	   (A^2 -> H(U1(k, k), U1(k, c)),A^2 -> H(U1(k, k), U1(k, c)))
28.54/9.32	   (A^2 -> H(U1(k, k), U1(c, e)),A^2 -> H(U1(k, k), U1(c, e)))
28.54/9.32	   (A^2 -> H(U1(k, k), U1(c, k)),A^2 -> H(U1(k, k), U1(c, k)))
28.54/9.32	
28.54/9.32	
28.54/9.32	----------------------------------------
28.54/9.32	
28.54/9.32	(946)
28.54/9.32	Obligation:
28.54/9.32	Q DP problem:
28.54/9.32	The TRS P consists of the following rules:
28.54/9.32	
28.54/9.32	   H(x, x) -> G(x, x, f(k))
28.54/9.32	   G(d, x, x) -> A^2
28.54/9.32	   A^2 -> H(f(c), f(c))
28.54/9.32	   A^2 -> H(f(d), f(d))
28.54/9.32	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.32	   A^2 -> H(f(e), f(e))
28.54/9.32	   A^2 -> H(f(k), f(k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.32	   A^2 -> H(U1(k, k), f(e))
28.54/9.32	   A^2 -> H(U1(k, k), f(k))
28.54/9.32	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.32	   A^2 -> H(f(k), U1(e, b))
28.54/9.32	   A^2 -> H(f(k), U1(k, b))
28.54/9.32	   A^2 -> H(f(k), U1(c, d))
28.54/9.32	   A^2 -> H(f(k), U1(d, c))
28.54/9.32	   A^2 -> H(f(k), U1(b, e))
28.54/9.32	   A^2 -> H(f(k), U1(b, k))
28.54/9.32	   A^2 -> H(f(k), U1(e, c))
28.54/9.32	   A^2 -> H(f(k), U1(k, c))
28.54/9.32	   A^2 -> H(f(k), U1(c, e))
28.54/9.32	   A^2 -> H(f(k), U1(c, k))
28.54/9.32	   A^2 -> H(f(k), U1(e, e))
28.54/9.32	   A^2 -> H(f(k), U1(k, d))
28.54/9.32	   A^2 -> H(f(k), U1(d, k))
28.54/9.32	   A^2 -> H(f(c), b)
28.54/9.32	   A^2 -> H(f(c), U1(e, d))
28.54/9.32	   A^2 -> H(f(c), U1(d, e))
28.54/9.32	   A^2 -> H(f(k), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.32	   A^2 -> H(U1(k, k), f(c))
28.54/9.32	   A^2 -> H(U1(k, k), f(d))
28.54/9.32	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.32	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.32	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.32	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.32	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.32	   A^2 -> H(U1(k, d), f(e))
28.54/9.32	   A^2 -> H(U1(k, d), f(k))
28.54/9.32	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.32	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.32	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.32	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.32	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.32	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.32	   A^2 -> H(U1(d, k), f(e))
28.54/9.32	   A^2 -> H(U1(d, k), f(k))
28.54/9.32	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.32	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.32	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.32	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.32	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.32	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.32	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.32	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.32	   A^2 -> H(f(d), b)
28.54/9.32	   A^2 -> H(f(d), U1(e, d))
28.54/9.32	   A^2 -> H(f(d), U1(d, e))
28.54/9.32	   A^2 -> H(f(d), c)
28.54/9.32	   A^2 -> H(f(d), U1(e, k))
28.54/9.32	   A^2 -> H(f(d), U1(k, e))
28.54/9.32	   A^2 -> H(f(d), e)
28.54/9.32	   A^2 -> H(f(a), d)
28.54/9.32	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.32	   A^2 -> H(f(c), c)
28.54/9.32	   A^2 -> H(f(c), U1(e, k))
28.54/9.32	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.32	   A^2 -> H(f(c), U1(k, e))
28.54/9.32	   A^2 -> H(f(c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.32	   A^2 -> H(f(a), k)
28.54/9.32	   A^2 -> H(f(e), U1(e, e))
28.54/9.32	   A^2 -> H(f(c), e)
28.54/9.32	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.32	   A^2 -> H(f(d), U1(k, k))
28.54/9.32	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.32	   A^2 -> H(d, U1(b, b))
28.54/9.32	   A^2 -> H(d, f(c))
28.54/9.32	   A^2 -> H(d, f(d))
28.54/9.32	   A^2 -> H(a, U1(c, b))
28.54/9.32	   A^2 -> H(a, U1(d, b))
28.54/9.32	   A^2 -> H(a, U1(b, c))
28.54/9.32	   A^2 -> H(a, U1(b, d))
28.54/9.32	   A^2 -> H(a, U1(c, c))
28.54/9.32	   A^2 -> H(a, f(e))
28.54/9.32	   A^2 -> H(a, f(k))
28.54/9.32	   A^2 -> H(a, U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.32	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.32	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.32	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.32	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.32	   A^2 -> H(U1(e, d), f(e))
28.54/9.32	   A^2 -> H(U1(e, d), f(k))
28.54/9.32	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.32	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.32	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.32	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.32	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.32	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.32	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.32	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.32	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.32	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.32	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.32	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.32	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.32	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.32	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.32	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.32	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.32	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.32	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.32	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.32	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.32	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.32	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.32	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.32	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.32	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.32	   A^2 -> H(U1(c, a), b)
28.54/9.32	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.32	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.32	   A^2 -> H(U1(c, a), c)
28.54/9.32	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.32	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.32	   A^2 -> H(U1(c, a), e)
28.54/9.32	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.32	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.32	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.32	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.32	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.32	   A^2 -> H(U1(d, e), f(e))
28.54/9.32	   A^2 -> H(U1(d, e), f(k))
28.54/9.32	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.32	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.32	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.32	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.32	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.32	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.32	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.32	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.32	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.32	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.32	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.32	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.32	   A^2 -> H(U1(d, a), b)
28.54/9.32	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.32	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.32	   A^2 -> H(U1(d, a), c)
28.54/9.32	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.32	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.32	   A^2 -> H(U1(d, a), e)
28.54/9.32	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.32	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.32	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.32	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.32	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.32	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.32	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.32	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.33	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.33	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.33	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.33	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.33	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.33	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.33	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.33	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.33	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.33	   A^2 -> H(U1(a, c), b)
28.54/9.33	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.33	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.33	   A^2 -> H(U1(a, c), c)
28.54/9.33	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.33	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.33	   A^2 -> H(U1(a, c), e)
28.54/9.33	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, d), b)
28.54/9.33	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.33	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.33	   A^2 -> H(U1(a, d), c)
28.54/9.33	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.33	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.33	   A^2 -> H(U1(a, d), e)
28.54/9.33	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, a), d)
28.54/9.33	   A^2 -> H(U1(a, a), k)
28.54/9.33	   A^2 -> H(k, U1(b, b))
28.54/9.33	   A^2 -> H(k, f(c))
28.54/9.33	   A^2 -> H(k, f(d))
28.54/9.33	   A^2 -> H(c, U1(c, b))
28.54/9.33	   A^2 -> H(c, U1(d, b))
28.54/9.33	   A^2 -> H(c, U1(b, c))
28.54/9.33	   A^2 -> H(c, U1(b, d))
28.54/9.33	   A^2 -> H(c, U1(c, c))
28.54/9.33	   A^2 -> H(c, f(e))
28.54/9.33	   A^2 -> H(c, f(k))
28.54/9.33	   A^2 -> H(c, U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.33	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.33	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.33	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.33	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.33	   A^2 -> H(U1(e, k), f(e))
28.54/9.33	   A^2 -> H(U1(e, k), f(k))
28.54/9.33	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.33	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.33	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.33	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.33	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.33	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.33	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.33	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.33	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.33	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.33	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.33	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.33	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.33	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.33	   A^2 -> H(U1(k, e), f(e))
28.54/9.33	   A^2 -> H(U1(k, e), f(k))
28.54/9.33	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.33	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.33	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.33	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.33	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.33	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.33	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.33	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.33	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.33	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.33	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.33	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.33	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.33	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.33	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.33	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.33	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.33	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.33	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.33	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.33	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.33	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, c), b)
28.54/9.33	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.33	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.33	   A^2 -> H(U1(c, c), e)
28.54/9.33	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.33	   A^2 -> H(e, U1(c, b))
28.54/9.33	   A^2 -> H(e, U1(d, b))
28.54/9.33	   A^2 -> H(e, U1(b, c))
28.54/9.33	   A^2 -> H(e, U1(b, d))
28.54/9.33	   A^2 -> H(e, U1(c, c))
28.54/9.33	   A^2 -> H(e, f(e))
28.54/9.33	   A^2 -> H(e, f(k))
28.54/9.33	   A^2 -> H(e, U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.33	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.33	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.33	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.33	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.33	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.33	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.33	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.33	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.33	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.33	   A^2 -> H(f(e), b)
28.54/9.33	   A^2 -> H(f(e), U1(e, d))
28.54/9.33	   A^2 -> H(f(e), U1(d, e))
28.54/9.33	   A^2 -> H(f(e), c)
28.54/9.33	   A^2 -> H(f(e), U1(e, k))
28.54/9.33	   A^2 -> H(f(e), U1(k, e))
28.54/9.33	   A^2 -> H(f(e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.33	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.33	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.33	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.33	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.33	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.33	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.33	
28.54/9.33	The TRS R consists of the following rules:
28.54/9.33	
28.54/9.33	   f(x) -> U1(x, x)
28.54/9.33	   U1(e, x) -> x
28.54/9.33	   a -> c
28.54/9.33	   a -> d
28.54/9.33	   b -> c
28.54/9.33	   b -> d
28.54/9.33	   d -> k
28.54/9.33	   c -> e
28.54/9.33	   c -> k
28.54/9.33	
28.54/9.33	Q is empty.
28.54/9.33	We have to consider all minimal (P,Q,R)-chains.
28.54/9.33	----------------------------------------
28.54/9.33	
28.54/9.33	(947) TransformationProof (EQUIVALENT)
28.54/9.33	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), f(e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.33	
28.54/9.33	   (A^2 -> H(U1(k, k), U1(e, e)),A^2 -> H(U1(k, k), U1(e, e)))
28.54/9.33	
28.54/9.33	
28.54/9.33	----------------------------------------
28.54/9.33	
28.54/9.33	(948)
28.54/9.33	Obligation:
28.54/9.33	Q DP problem:
28.54/9.33	The TRS P consists of the following rules:
28.54/9.33	
28.54/9.33	   H(x, x) -> G(x, x, f(k))
28.54/9.33	   G(d, x, x) -> A^2
28.54/9.33	   A^2 -> H(f(c), f(c))
28.54/9.33	   A^2 -> H(f(d), f(d))
28.54/9.33	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.33	   A^2 -> H(f(e), f(e))
28.54/9.33	   A^2 -> H(f(k), f(k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.33	   A^2 -> H(U1(k, k), f(k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.33	   A^2 -> H(f(k), U1(e, b))
28.54/9.33	   A^2 -> H(f(k), U1(k, b))
28.54/9.33	   A^2 -> H(f(k), U1(c, d))
28.54/9.33	   A^2 -> H(f(k), U1(d, c))
28.54/9.33	   A^2 -> H(f(k), U1(b, e))
28.54/9.33	   A^2 -> H(f(k), U1(b, k))
28.54/9.33	   A^2 -> H(f(k), U1(e, c))
28.54/9.33	   A^2 -> H(f(k), U1(k, c))
28.54/9.33	   A^2 -> H(f(k), U1(c, e))
28.54/9.33	   A^2 -> H(f(k), U1(c, k))
28.54/9.33	   A^2 -> H(f(k), U1(e, e))
28.54/9.33	   A^2 -> H(f(k), U1(k, d))
28.54/9.33	   A^2 -> H(f(k), U1(d, k))
28.54/9.33	   A^2 -> H(f(c), b)
28.54/9.33	   A^2 -> H(f(c), U1(e, d))
28.54/9.33	   A^2 -> H(f(c), U1(d, e))
28.54/9.33	   A^2 -> H(f(k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.33	   A^2 -> H(U1(k, k), f(c))
28.54/9.33	   A^2 -> H(U1(k, k), f(d))
28.54/9.33	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.33	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.33	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.33	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.33	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.33	   A^2 -> H(U1(k, d), f(e))
28.54/9.33	   A^2 -> H(U1(k, d), f(k))
28.54/9.33	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.33	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.33	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.33	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.33	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.33	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.33	   A^2 -> H(U1(d, k), f(e))
28.54/9.33	   A^2 -> H(U1(d, k), f(k))
28.54/9.33	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.33	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.33	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.33	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.33	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.33	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.33	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.33	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.33	   A^2 -> H(f(d), b)
28.54/9.33	   A^2 -> H(f(d), U1(e, d))
28.54/9.33	   A^2 -> H(f(d), U1(d, e))
28.54/9.33	   A^2 -> H(f(d), c)
28.54/9.33	   A^2 -> H(f(d), U1(e, k))
28.54/9.33	   A^2 -> H(f(d), U1(k, e))
28.54/9.33	   A^2 -> H(f(d), e)
28.54/9.33	   A^2 -> H(f(a), d)
28.54/9.33	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.33	   A^2 -> H(f(c), c)
28.54/9.33	   A^2 -> H(f(c), U1(e, k))
28.54/9.33	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.33	   A^2 -> H(f(c), U1(k, e))
28.54/9.33	   A^2 -> H(f(c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.33	   A^2 -> H(f(a), k)
28.54/9.33	   A^2 -> H(f(e), U1(e, e))
28.54/9.33	   A^2 -> H(f(c), e)
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.33	   A^2 -> H(f(d), U1(k, k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.33	   A^2 -> H(d, U1(b, b))
28.54/9.33	   A^2 -> H(d, f(c))
28.54/9.33	   A^2 -> H(d, f(d))
28.54/9.33	   A^2 -> H(a, U1(c, b))
28.54/9.33	   A^2 -> H(a, U1(d, b))
28.54/9.33	   A^2 -> H(a, U1(b, c))
28.54/9.33	   A^2 -> H(a, U1(b, d))
28.54/9.33	   A^2 -> H(a, U1(c, c))
28.54/9.33	   A^2 -> H(a, f(e))
28.54/9.33	   A^2 -> H(a, f(k))
28.54/9.33	   A^2 -> H(a, U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.33	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.33	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.33	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.33	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.33	   A^2 -> H(U1(e, d), f(e))
28.54/9.33	   A^2 -> H(U1(e, d), f(k))
28.54/9.33	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.33	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.33	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.33	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.33	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.33	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.33	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.33	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.33	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.33	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.33	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.33	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.33	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.33	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.33	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.33	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.33	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.33	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.33	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.33	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.33	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.33	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.33	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, a), b)
28.54/9.33	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.33	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.33	   A^2 -> H(U1(c, a), c)
28.54/9.33	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.33	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.33	   A^2 -> H(U1(c, a), e)
28.54/9.33	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.33	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.33	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.33	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.33	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.33	   A^2 -> H(U1(d, e), f(e))
28.54/9.33	   A^2 -> H(U1(d, e), f(k))
28.54/9.33	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.33	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.33	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.33	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.33	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.33	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.33	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.33	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.33	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.33	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.33	   A^2 -> H(U1(d, a), b)
28.54/9.33	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.33	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.33	   A^2 -> H(U1(d, a), c)
28.54/9.33	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.33	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.33	   A^2 -> H(U1(d, a), e)
28.54/9.33	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.33	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.33	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.33	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.33	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.33	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.33	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.33	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.33	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.33	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.33	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.33	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.33	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.33	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.33	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.33	   A^2 -> H(U1(a, c), b)
28.54/9.33	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.33	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.33	   A^2 -> H(U1(a, c), c)
28.54/9.33	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.33	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.33	   A^2 -> H(U1(a, c), e)
28.54/9.33	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, d), b)
28.54/9.33	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.33	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.33	   A^2 -> H(U1(a, d), c)
28.54/9.33	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.33	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.33	   A^2 -> H(U1(a, d), e)
28.54/9.33	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, a), d)
28.54/9.33	   A^2 -> H(U1(a, a), k)
28.54/9.33	   A^2 -> H(k, U1(b, b))
28.54/9.33	   A^2 -> H(k, f(c))
28.54/9.33	   A^2 -> H(k, f(d))
28.54/9.33	   A^2 -> H(c, U1(c, b))
28.54/9.33	   A^2 -> H(c, U1(d, b))
28.54/9.33	   A^2 -> H(c, U1(b, c))
28.54/9.33	   A^2 -> H(c, U1(b, d))
28.54/9.33	   A^2 -> H(c, U1(c, c))
28.54/9.33	   A^2 -> H(c, f(e))
28.54/9.33	   A^2 -> H(c, f(k))
28.54/9.33	   A^2 -> H(c, U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.33	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.33	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.33	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.33	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.33	   A^2 -> H(U1(e, k), f(e))
28.54/9.33	   A^2 -> H(U1(e, k), f(k))
28.54/9.33	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.33	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.33	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.33	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.33	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.33	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.33	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.33	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.33	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.33	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.33	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.33	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.33	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.33	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.33	   A^2 -> H(U1(k, e), f(e))
28.54/9.33	   A^2 -> H(U1(k, e), f(k))
28.54/9.33	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.33	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.33	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.33	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.33	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.33	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.33	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.33	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.33	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.33	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.33	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.33	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.33	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.33	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.33	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.33	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.33	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.33	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.33	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.33	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.33	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.33	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, c), b)
28.54/9.33	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.33	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.33	   A^2 -> H(U1(c, c), e)
28.54/9.33	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.33	   A^2 -> H(e, U1(c, b))
28.54/9.33	   A^2 -> H(e, U1(d, b))
28.54/9.33	   A^2 -> H(e, U1(b, c))
28.54/9.33	   A^2 -> H(e, U1(b, d))
28.54/9.33	   A^2 -> H(e, U1(c, c))
28.54/9.33	   A^2 -> H(e, f(e))
28.54/9.33	   A^2 -> H(e, f(k))
28.54/9.33	   A^2 -> H(e, U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.33	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.33	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.33	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.33	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.33	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.33	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.33	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.33	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.33	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.33	   A^2 -> H(f(e), b)
28.54/9.33	   A^2 -> H(f(e), U1(e, d))
28.54/9.33	   A^2 -> H(f(e), U1(d, e))
28.54/9.33	   A^2 -> H(f(e), c)
28.54/9.33	   A^2 -> H(f(e), U1(e, k))
28.54/9.33	   A^2 -> H(f(e), U1(k, e))
28.54/9.33	   A^2 -> H(f(e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.33	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.33	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.33	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.33	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.33	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.33	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.33	
28.54/9.33	The TRS R consists of the following rules:
28.54/9.33	
28.54/9.33	   f(x) -> U1(x, x)
28.54/9.33	   U1(e, x) -> x
28.54/9.33	   a -> c
28.54/9.33	   a -> d
28.54/9.33	   b -> c
28.54/9.33	   b -> d
28.54/9.33	   d -> k
28.54/9.33	   c -> e
28.54/9.33	   c -> k
28.54/9.33	
28.54/9.33	Q is empty.
28.54/9.33	We have to consider all minimal (P,Q,R)-chains.
28.54/9.33	----------------------------------------
28.54/9.33	
28.54/9.33	(949) TransformationProof (EQUIVALENT)
28.54/9.33	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), f(k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.33	
28.54/9.33	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.54/9.33	
28.54/9.33	
28.54/9.33	----------------------------------------
28.54/9.33	
28.54/9.33	(950)
28.54/9.33	Obligation:
28.54/9.33	Q DP problem:
28.54/9.33	The TRS P consists of the following rules:
28.54/9.33	
28.54/9.33	   H(x, x) -> G(x, x, f(k))
28.54/9.33	   G(d, x, x) -> A^2
28.54/9.33	   A^2 -> H(f(c), f(c))
28.54/9.33	   A^2 -> H(f(d), f(d))
28.54/9.33	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.33	   A^2 -> H(f(e), f(e))
28.54/9.33	   A^2 -> H(f(k), f(k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.33	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.33	   A^2 -> H(f(k), U1(e, b))
28.54/9.33	   A^2 -> H(f(k), U1(k, b))
28.54/9.33	   A^2 -> H(f(k), U1(c, d))
28.54/9.33	   A^2 -> H(f(k), U1(d, c))
28.54/9.33	   A^2 -> H(f(k), U1(b, e))
28.54/9.33	   A^2 -> H(f(k), U1(b, k))
28.54/9.33	   A^2 -> H(f(k), U1(e, c))
28.54/9.33	   A^2 -> H(f(k), U1(k, c))
28.54/9.33	   A^2 -> H(f(k), U1(c, e))
28.54/9.33	   A^2 -> H(f(k), U1(c, k))
28.54/9.33	   A^2 -> H(f(k), U1(e, e))
28.54/9.33	   A^2 -> H(f(k), U1(k, d))
28.54/9.33	   A^2 -> H(f(k), U1(d, k))
28.54/9.33	   A^2 -> H(f(c), b)
28.54/9.33	   A^2 -> H(f(c), U1(e, d))
28.54/9.33	   A^2 -> H(f(c), U1(d, e))
28.54/9.33	   A^2 -> H(f(k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.33	   A^2 -> H(U1(k, k), f(c))
28.54/9.33	   A^2 -> H(U1(k, k), f(d))
28.54/9.33	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.33	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.33	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.33	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.33	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.33	   A^2 -> H(U1(k, d), f(e))
28.54/9.33	   A^2 -> H(U1(k, d), f(k))
28.54/9.33	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.33	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.33	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.33	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.33	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.33	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.33	   A^2 -> H(U1(d, k), f(e))
28.54/9.33	   A^2 -> H(U1(d, k), f(k))
28.54/9.33	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.33	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.33	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.33	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.33	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.33	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.33	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.33	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.33	   A^2 -> H(f(d), b)
28.54/9.33	   A^2 -> H(f(d), U1(e, d))
28.54/9.33	   A^2 -> H(f(d), U1(d, e))
28.54/9.33	   A^2 -> H(f(d), c)
28.54/9.33	   A^2 -> H(f(d), U1(e, k))
28.54/9.33	   A^2 -> H(f(d), U1(k, e))
28.54/9.33	   A^2 -> H(f(d), e)
28.54/9.33	   A^2 -> H(f(a), d)
28.54/9.33	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.33	   A^2 -> H(f(c), c)
28.54/9.33	   A^2 -> H(f(c), U1(e, k))
28.54/9.33	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.33	   A^2 -> H(f(c), U1(k, e))
28.54/9.33	   A^2 -> H(f(c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.33	   A^2 -> H(f(a), k)
28.54/9.33	   A^2 -> H(f(e), U1(e, e))
28.54/9.33	   A^2 -> H(f(c), e)
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.33	   A^2 -> H(f(d), U1(k, k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.33	   A^2 -> H(d, U1(b, b))
28.54/9.33	   A^2 -> H(d, f(c))
28.54/9.33	   A^2 -> H(d, f(d))
28.54/9.33	   A^2 -> H(a, U1(c, b))
28.54/9.33	   A^2 -> H(a, U1(d, b))
28.54/9.33	   A^2 -> H(a, U1(b, c))
28.54/9.33	   A^2 -> H(a, U1(b, d))
28.54/9.33	   A^2 -> H(a, U1(c, c))
28.54/9.33	   A^2 -> H(a, f(e))
28.54/9.33	   A^2 -> H(a, f(k))
28.54/9.33	   A^2 -> H(a, U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.33	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.33	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.33	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.33	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.33	   A^2 -> H(U1(e, d), f(e))
28.54/9.33	   A^2 -> H(U1(e, d), f(k))
28.54/9.33	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.33	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.33	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.33	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.33	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.33	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.33	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.33	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.33	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.33	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.33	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.33	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.33	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.33	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.33	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.33	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.33	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.33	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.33	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.33	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.33	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.33	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.33	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, a), b)
28.54/9.33	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.33	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.33	   A^2 -> H(U1(c, a), c)
28.54/9.33	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.33	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.33	   A^2 -> H(U1(c, a), e)
28.54/9.33	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.33	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.33	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.33	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.33	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.33	   A^2 -> H(U1(d, e), f(e))
28.54/9.33	   A^2 -> H(U1(d, e), f(k))
28.54/9.33	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.33	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.33	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.33	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.33	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.33	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.33	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.33	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.33	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.33	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.33	   A^2 -> H(U1(d, a), b)
28.54/9.33	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.33	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.33	   A^2 -> H(U1(d, a), c)
28.54/9.33	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.33	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.33	   A^2 -> H(U1(d, a), e)
28.54/9.33	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.33	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.33	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.33	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.33	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.33	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.33	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.33	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.33	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.33	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.33	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.33	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.33	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.33	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.33	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.33	   A^2 -> H(U1(a, c), b)
28.54/9.33	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.33	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.33	   A^2 -> H(U1(a, c), c)
28.54/9.33	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.33	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.33	   A^2 -> H(U1(a, c), e)
28.54/9.33	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, d), b)
28.54/9.33	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.33	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.33	   A^2 -> H(U1(a, d), c)
28.54/9.33	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.33	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.33	   A^2 -> H(U1(a, d), e)
28.54/9.33	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, a), d)
28.54/9.33	   A^2 -> H(U1(a, a), k)
28.54/9.33	   A^2 -> H(k, U1(b, b))
28.54/9.33	   A^2 -> H(k, f(c))
28.54/9.33	   A^2 -> H(k, f(d))
28.54/9.33	   A^2 -> H(c, U1(c, b))
28.54/9.33	   A^2 -> H(c, U1(d, b))
28.54/9.33	   A^2 -> H(c, U1(b, c))
28.54/9.33	   A^2 -> H(c, U1(b, d))
28.54/9.33	   A^2 -> H(c, U1(c, c))
28.54/9.33	   A^2 -> H(c, f(e))
28.54/9.33	   A^2 -> H(c, f(k))
28.54/9.33	   A^2 -> H(c, U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.33	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.33	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.33	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.33	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.33	   A^2 -> H(U1(e, k), f(e))
28.54/9.33	   A^2 -> H(U1(e, k), f(k))
28.54/9.33	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.33	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.33	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.33	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.33	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.33	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.33	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.33	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.33	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.33	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.33	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.33	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.33	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.33	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.33	   A^2 -> H(U1(k, e), f(e))
28.54/9.33	   A^2 -> H(U1(k, e), f(k))
28.54/9.33	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.33	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.33	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.33	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.33	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.33	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.33	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.33	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.33	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.33	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.33	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.33	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.33	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.33	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.33	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.33	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.33	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.33	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.33	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.33	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.33	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.33	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, c), b)
28.54/9.33	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.33	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.33	   A^2 -> H(U1(c, c), e)
28.54/9.33	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.33	   A^2 -> H(e, U1(c, b))
28.54/9.33	   A^2 -> H(e, U1(d, b))
28.54/9.33	   A^2 -> H(e, U1(b, c))
28.54/9.33	   A^2 -> H(e, U1(b, d))
28.54/9.33	   A^2 -> H(e, U1(c, c))
28.54/9.33	   A^2 -> H(e, f(e))
28.54/9.33	   A^2 -> H(e, f(k))
28.54/9.33	   A^2 -> H(e, U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.33	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.33	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.33	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.33	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.33	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.33	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.33	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.33	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.33	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.33	   A^2 -> H(f(e), b)
28.54/9.33	   A^2 -> H(f(e), U1(e, d))
28.54/9.33	   A^2 -> H(f(e), U1(d, e))
28.54/9.33	   A^2 -> H(f(e), c)
28.54/9.33	   A^2 -> H(f(e), U1(e, k))
28.54/9.33	   A^2 -> H(f(e), U1(k, e))
28.54/9.33	   A^2 -> H(f(e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.33	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.33	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.33	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.33	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.33	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.33	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.33	
28.54/9.33	The TRS R consists of the following rules:
28.54/9.33	
28.54/9.33	   f(x) -> U1(x, x)
28.54/9.33	   U1(e, x) -> x
28.54/9.33	   a -> c
28.54/9.33	   a -> d
28.54/9.33	   b -> c
28.54/9.33	   b -> d
28.54/9.33	   d -> k
28.54/9.33	   c -> e
28.54/9.33	   c -> k
28.54/9.33	
28.54/9.33	Q is empty.
28.54/9.33	We have to consider all minimal (P,Q,R)-chains.
28.54/9.33	----------------------------------------
28.54/9.33	
28.54/9.33	(951) TransformationProof (EQUIVALENT)
28.54/9.33	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.33	
28.54/9.33	   (A^2 -> H(U1(k, k), U1(k, d)),A^2 -> H(U1(k, k), U1(k, d)))
28.54/9.33	   (A^2 -> H(U1(k, k), U1(d, k)),A^2 -> H(U1(k, k), U1(d, k)))
28.54/9.33	
28.54/9.33	
28.54/9.33	----------------------------------------
28.54/9.33	
28.54/9.33	(952)
28.54/9.33	Obligation:
28.54/9.33	Q DP problem:
28.54/9.33	The TRS P consists of the following rules:
28.54/9.33	
28.54/9.33	   H(x, x) -> G(x, x, f(k))
28.54/9.33	   G(d, x, x) -> A^2
28.54/9.33	   A^2 -> H(f(c), f(c))
28.54/9.33	   A^2 -> H(f(d), f(d))
28.54/9.33	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.33	   A^2 -> H(f(e), f(e))
28.54/9.33	   A^2 -> H(f(k), f(k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.33	   A^2 -> H(f(k), U1(e, b))
28.54/9.33	   A^2 -> H(f(k), U1(k, b))
28.54/9.33	   A^2 -> H(f(k), U1(c, d))
28.54/9.33	   A^2 -> H(f(k), U1(d, c))
28.54/9.33	   A^2 -> H(f(k), U1(b, e))
28.54/9.33	   A^2 -> H(f(k), U1(b, k))
28.54/9.33	   A^2 -> H(f(k), U1(e, c))
28.54/9.33	   A^2 -> H(f(k), U1(k, c))
28.54/9.33	   A^2 -> H(f(k), U1(c, e))
28.54/9.33	   A^2 -> H(f(k), U1(c, k))
28.54/9.33	   A^2 -> H(f(k), U1(e, e))
28.54/9.33	   A^2 -> H(f(k), U1(k, d))
28.54/9.33	   A^2 -> H(f(k), U1(d, k))
28.54/9.33	   A^2 -> H(f(c), b)
28.54/9.33	   A^2 -> H(f(c), U1(e, d))
28.54/9.33	   A^2 -> H(f(c), U1(d, e))
28.54/9.33	   A^2 -> H(f(k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.33	   A^2 -> H(U1(k, k), f(c))
28.54/9.33	   A^2 -> H(U1(k, k), f(d))
28.54/9.33	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.33	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.33	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.33	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.33	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.33	   A^2 -> H(U1(k, d), f(e))
28.54/9.33	   A^2 -> H(U1(k, d), f(k))
28.54/9.33	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.33	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.33	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.33	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.33	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.33	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.33	   A^2 -> H(U1(d, k), f(e))
28.54/9.33	   A^2 -> H(U1(d, k), f(k))
28.54/9.33	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.33	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.33	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.33	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.33	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.33	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.33	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.33	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.33	   A^2 -> H(f(d), b)
28.54/9.33	   A^2 -> H(f(d), U1(e, d))
28.54/9.33	   A^2 -> H(f(d), U1(d, e))
28.54/9.33	   A^2 -> H(f(d), c)
28.54/9.33	   A^2 -> H(f(d), U1(e, k))
28.54/9.33	   A^2 -> H(f(d), U1(k, e))
28.54/9.33	   A^2 -> H(f(d), e)
28.54/9.33	   A^2 -> H(f(a), d)
28.54/9.33	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.33	   A^2 -> H(f(c), c)
28.54/9.33	   A^2 -> H(f(c), U1(e, k))
28.54/9.33	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.33	   A^2 -> H(f(c), U1(k, e))
28.54/9.33	   A^2 -> H(f(c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.33	   A^2 -> H(f(a), k)
28.54/9.33	   A^2 -> H(f(e), U1(e, e))
28.54/9.33	   A^2 -> H(f(c), e)
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.33	   A^2 -> H(f(d), U1(k, k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.33	   A^2 -> H(d, U1(b, b))
28.54/9.33	   A^2 -> H(d, f(c))
28.54/9.33	   A^2 -> H(d, f(d))
28.54/9.33	   A^2 -> H(a, U1(c, b))
28.54/9.33	   A^2 -> H(a, U1(d, b))
28.54/9.33	   A^2 -> H(a, U1(b, c))
28.54/9.33	   A^2 -> H(a, U1(b, d))
28.54/9.33	   A^2 -> H(a, U1(c, c))
28.54/9.33	   A^2 -> H(a, f(e))
28.54/9.33	   A^2 -> H(a, f(k))
28.54/9.33	   A^2 -> H(a, U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.33	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.33	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.33	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.33	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.33	   A^2 -> H(U1(e, d), f(e))
28.54/9.33	   A^2 -> H(U1(e, d), f(k))
28.54/9.33	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.33	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.33	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.33	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.33	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.33	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.33	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.33	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.33	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.33	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.33	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.33	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.33	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.33	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.33	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.33	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.33	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.33	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.33	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.33	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.33	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.33	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.33	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, a), b)
28.54/9.33	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.33	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.33	   A^2 -> H(U1(c, a), c)
28.54/9.33	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.33	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.33	   A^2 -> H(U1(c, a), e)
28.54/9.33	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.33	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.33	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.33	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.33	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.33	   A^2 -> H(U1(d, e), f(e))
28.54/9.33	   A^2 -> H(U1(d, e), f(k))
28.54/9.33	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.33	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.33	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.33	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.33	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.33	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.33	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.33	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.33	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.33	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.33	   A^2 -> H(U1(d, a), b)
28.54/9.33	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.33	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.33	   A^2 -> H(U1(d, a), c)
28.54/9.33	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.33	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.33	   A^2 -> H(U1(d, a), e)
28.54/9.33	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.33	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.33	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.33	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.33	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.33	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.33	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.33	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.33	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.33	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.33	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.33	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.33	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.33	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.33	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.33	   A^2 -> H(U1(a, c), b)
28.54/9.33	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.33	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.33	   A^2 -> H(U1(a, c), c)
28.54/9.33	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.33	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.33	   A^2 -> H(U1(a, c), e)
28.54/9.33	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, d), b)
28.54/9.33	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.33	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.33	   A^2 -> H(U1(a, d), c)
28.54/9.33	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.33	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.33	   A^2 -> H(U1(a, d), e)
28.54/9.33	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, a), d)
28.54/9.33	   A^2 -> H(U1(a, a), k)
28.54/9.33	   A^2 -> H(k, U1(b, b))
28.54/9.33	   A^2 -> H(k, f(c))
28.54/9.33	   A^2 -> H(k, f(d))
28.54/9.33	   A^2 -> H(c, U1(c, b))
28.54/9.33	   A^2 -> H(c, U1(d, b))
28.54/9.33	   A^2 -> H(c, U1(b, c))
28.54/9.33	   A^2 -> H(c, U1(b, d))
28.54/9.33	   A^2 -> H(c, U1(c, c))
28.54/9.33	   A^2 -> H(c, f(e))
28.54/9.33	   A^2 -> H(c, f(k))
28.54/9.33	   A^2 -> H(c, U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.33	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.33	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.33	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.33	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.33	   A^2 -> H(U1(e, k), f(e))
28.54/9.33	   A^2 -> H(U1(e, k), f(k))
28.54/9.33	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.33	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.33	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.33	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.33	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.33	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.33	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.33	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.33	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.33	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.33	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.33	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.33	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.33	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.33	   A^2 -> H(U1(k, e), f(e))
28.54/9.33	   A^2 -> H(U1(k, e), f(k))
28.54/9.33	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.33	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.33	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.33	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.33	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.33	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.33	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.33	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.33	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.33	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.33	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.33	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.33	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.33	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.33	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.33	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.33	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.33	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.33	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.33	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.33	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.33	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, c), b)
28.54/9.33	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.33	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.33	   A^2 -> H(U1(c, c), e)
28.54/9.33	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.33	   A^2 -> H(e, U1(c, b))
28.54/9.33	   A^2 -> H(e, U1(d, b))
28.54/9.33	   A^2 -> H(e, U1(b, c))
28.54/9.33	   A^2 -> H(e, U1(b, d))
28.54/9.33	   A^2 -> H(e, U1(c, c))
28.54/9.33	   A^2 -> H(e, f(e))
28.54/9.33	   A^2 -> H(e, f(k))
28.54/9.33	   A^2 -> H(e, U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.33	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.33	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.33	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.33	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.33	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.33	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.33	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.33	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.33	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.33	   A^2 -> H(f(e), b)
28.54/9.33	   A^2 -> H(f(e), U1(e, d))
28.54/9.33	   A^2 -> H(f(e), U1(d, e))
28.54/9.33	   A^2 -> H(f(e), c)
28.54/9.33	   A^2 -> H(f(e), U1(e, k))
28.54/9.33	   A^2 -> H(f(e), U1(k, e))
28.54/9.33	   A^2 -> H(f(e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.33	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.33	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.33	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.33	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.33	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.33	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.33	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.33	
28.54/9.33	The TRS R consists of the following rules:
28.54/9.33	
28.54/9.33	   f(x) -> U1(x, x)
28.54/9.33	   U1(e, x) -> x
28.54/9.33	   a -> c
28.54/9.33	   a -> d
28.54/9.33	   b -> c
28.54/9.33	   b -> d
28.54/9.33	   d -> k
28.54/9.33	   c -> e
28.54/9.33	   c -> k
28.54/9.33	
28.54/9.33	Q is empty.
28.54/9.33	We have to consider all minimal (P,Q,R)-chains.
28.54/9.33	----------------------------------------
28.54/9.33	
28.54/9.33	(953) TransformationProof (EQUIVALENT)
28.54/9.33	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.33	
28.54/9.33	   (A^2 -> H(U1(k, k), U1(e, b)),A^2 -> H(U1(k, k), U1(e, b)))
28.54/9.33	   (A^2 -> H(f(k), b),A^2 -> H(f(k), b))
28.54/9.33	   (A^2 -> H(f(k), U1(e, c)),A^2 -> H(f(k), U1(e, c)))
28.54/9.33	   (A^2 -> H(f(k), U1(e, d)),A^2 -> H(f(k), U1(e, d)))
28.54/9.33	
28.54/9.33	
28.54/9.33	----------------------------------------
28.54/9.33	
28.54/9.33	(954)
28.54/9.33	Obligation:
28.54/9.33	Q DP problem:
28.54/9.33	The TRS P consists of the following rules:
28.54/9.33	
28.54/9.33	   H(x, x) -> G(x, x, f(k))
28.54/9.33	   G(d, x, x) -> A^2
28.54/9.33	   A^2 -> H(f(c), f(c))
28.54/9.33	   A^2 -> H(f(d), f(d))
28.54/9.33	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.33	   A^2 -> H(f(e), f(e))
28.54/9.33	   A^2 -> H(f(k), f(k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.33	   A^2 -> H(f(k), U1(k, b))
28.54/9.33	   A^2 -> H(f(k), U1(c, d))
28.54/9.33	   A^2 -> H(f(k), U1(d, c))
28.54/9.33	   A^2 -> H(f(k), U1(b, e))
28.54/9.33	   A^2 -> H(f(k), U1(b, k))
28.54/9.33	   A^2 -> H(f(k), U1(e, c))
28.54/9.33	   A^2 -> H(f(k), U1(k, c))
28.54/9.33	   A^2 -> H(f(k), U1(c, e))
28.54/9.33	   A^2 -> H(f(k), U1(c, k))
28.54/9.33	   A^2 -> H(f(k), U1(e, e))
28.54/9.33	   A^2 -> H(f(k), U1(k, d))
28.54/9.33	   A^2 -> H(f(k), U1(d, k))
28.54/9.33	   A^2 -> H(f(c), b)
28.54/9.33	   A^2 -> H(f(c), U1(e, d))
28.54/9.33	   A^2 -> H(f(c), U1(d, e))
28.54/9.33	   A^2 -> H(f(k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.33	   A^2 -> H(U1(k, k), f(c))
28.54/9.33	   A^2 -> H(U1(k, k), f(d))
28.54/9.33	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.33	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.33	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.33	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.33	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.33	   A^2 -> H(U1(k, d), f(e))
28.54/9.33	   A^2 -> H(U1(k, d), f(k))
28.54/9.33	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.33	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.33	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.33	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.33	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.33	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.33	   A^2 -> H(U1(d, k), f(e))
28.54/9.33	   A^2 -> H(U1(d, k), f(k))
28.54/9.33	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.33	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.33	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.33	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.33	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.33	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.33	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.33	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.33	   A^2 -> H(f(d), b)
28.54/9.33	   A^2 -> H(f(d), U1(e, d))
28.54/9.33	   A^2 -> H(f(d), U1(d, e))
28.54/9.33	   A^2 -> H(f(d), c)
28.54/9.33	   A^2 -> H(f(d), U1(e, k))
28.54/9.33	   A^2 -> H(f(d), U1(k, e))
28.54/9.33	   A^2 -> H(f(d), e)
28.54/9.33	   A^2 -> H(f(a), d)
28.54/9.33	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.33	   A^2 -> H(f(c), c)
28.54/9.33	   A^2 -> H(f(c), U1(e, k))
28.54/9.33	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.33	   A^2 -> H(f(c), U1(k, e))
28.54/9.33	   A^2 -> H(f(c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.33	   A^2 -> H(f(a), k)
28.54/9.33	   A^2 -> H(f(e), U1(e, e))
28.54/9.33	   A^2 -> H(f(c), e)
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.33	   A^2 -> H(f(d), U1(k, k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.33	   A^2 -> H(d, U1(b, b))
28.54/9.33	   A^2 -> H(d, f(c))
28.54/9.33	   A^2 -> H(d, f(d))
28.54/9.33	   A^2 -> H(a, U1(c, b))
28.54/9.33	   A^2 -> H(a, U1(d, b))
28.54/9.33	   A^2 -> H(a, U1(b, c))
28.54/9.33	   A^2 -> H(a, U1(b, d))
28.54/9.33	   A^2 -> H(a, U1(c, c))
28.54/9.33	   A^2 -> H(a, f(e))
28.54/9.33	   A^2 -> H(a, f(k))
28.54/9.33	   A^2 -> H(a, U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.33	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.33	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.33	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.33	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.33	   A^2 -> H(U1(e, d), f(e))
28.54/9.33	   A^2 -> H(U1(e, d), f(k))
28.54/9.33	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.33	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.33	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.33	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.33	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.33	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.33	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.33	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.33	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.33	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.33	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.33	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.33	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.33	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.33	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.33	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.33	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.33	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.33	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.33	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.33	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.33	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.33	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, a), b)
28.54/9.33	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.33	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.33	   A^2 -> H(U1(c, a), c)
28.54/9.33	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.33	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.33	   A^2 -> H(U1(c, a), e)
28.54/9.33	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.33	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.33	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.33	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.33	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.33	   A^2 -> H(U1(d, e), f(e))
28.54/9.33	   A^2 -> H(U1(d, e), f(k))
28.54/9.33	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.33	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.33	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.33	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.33	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.33	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.33	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.33	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.33	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.33	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.33	   A^2 -> H(U1(d, a), b)
28.54/9.33	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.33	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.33	   A^2 -> H(U1(d, a), c)
28.54/9.33	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.33	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.33	   A^2 -> H(U1(d, a), e)
28.54/9.33	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.33	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.33	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.33	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.33	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.33	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.33	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.33	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.33	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.33	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.33	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.33	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.33	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.33	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.33	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.33	   A^2 -> H(U1(a, c), b)
28.54/9.33	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.33	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.33	   A^2 -> H(U1(a, c), c)
28.54/9.33	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.33	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.33	   A^2 -> H(U1(a, c), e)
28.54/9.33	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, d), b)
28.54/9.33	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.33	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.33	   A^2 -> H(U1(a, d), c)
28.54/9.33	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.33	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.33	   A^2 -> H(U1(a, d), e)
28.54/9.33	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, a), d)
28.54/9.33	   A^2 -> H(U1(a, a), k)
28.54/9.33	   A^2 -> H(k, U1(b, b))
28.54/9.33	   A^2 -> H(k, f(c))
28.54/9.33	   A^2 -> H(k, f(d))
28.54/9.33	   A^2 -> H(c, U1(c, b))
28.54/9.33	   A^2 -> H(c, U1(d, b))
28.54/9.33	   A^2 -> H(c, U1(b, c))
28.54/9.33	   A^2 -> H(c, U1(b, d))
28.54/9.33	   A^2 -> H(c, U1(c, c))
28.54/9.33	   A^2 -> H(c, f(e))
28.54/9.33	   A^2 -> H(c, f(k))
28.54/9.33	   A^2 -> H(c, U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.33	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.33	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.33	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.33	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.33	   A^2 -> H(U1(e, k), f(e))
28.54/9.33	   A^2 -> H(U1(e, k), f(k))
28.54/9.33	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.33	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.33	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.33	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.33	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.33	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.33	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.33	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.33	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.33	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.33	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.33	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.33	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.33	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.33	   A^2 -> H(U1(k, e), f(e))
28.54/9.33	   A^2 -> H(U1(k, e), f(k))
28.54/9.33	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.33	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.33	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.33	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.33	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.33	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.33	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.33	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.33	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.33	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.33	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.33	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.33	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.33	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.33	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.33	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.33	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.33	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.33	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.33	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.33	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.33	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, c), b)
28.54/9.33	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.33	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.33	   A^2 -> H(U1(c, c), e)
28.54/9.33	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.33	   A^2 -> H(e, U1(c, b))
28.54/9.33	   A^2 -> H(e, U1(d, b))
28.54/9.33	   A^2 -> H(e, U1(b, c))
28.54/9.33	   A^2 -> H(e, U1(b, d))
28.54/9.33	   A^2 -> H(e, U1(c, c))
28.54/9.33	   A^2 -> H(e, f(e))
28.54/9.33	   A^2 -> H(e, f(k))
28.54/9.33	   A^2 -> H(e, U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.33	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.33	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.33	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.33	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.33	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.33	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.33	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.33	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.33	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.33	   A^2 -> H(f(e), b)
28.54/9.33	   A^2 -> H(f(e), U1(e, d))
28.54/9.33	   A^2 -> H(f(e), U1(d, e))
28.54/9.33	   A^2 -> H(f(e), c)
28.54/9.33	   A^2 -> H(f(e), U1(e, k))
28.54/9.33	   A^2 -> H(f(e), U1(k, e))
28.54/9.33	   A^2 -> H(f(e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.33	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.33	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.33	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.33	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.33	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.33	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.33	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.33	   A^2 -> H(f(k), b)
28.54/9.33	   A^2 -> H(f(k), U1(e, d))
28.54/9.33	
28.54/9.33	The TRS R consists of the following rules:
28.54/9.33	
28.54/9.33	   f(x) -> U1(x, x)
28.54/9.33	   U1(e, x) -> x
28.54/9.33	   a -> c
28.54/9.33	   a -> d
28.54/9.33	   b -> c
28.54/9.33	   b -> d
28.54/9.33	   d -> k
28.54/9.33	   c -> e
28.54/9.33	   c -> k
28.54/9.33	
28.54/9.33	Q is empty.
28.54/9.33	We have to consider all minimal (P,Q,R)-chains.
28.54/9.33	----------------------------------------
28.54/9.33	
28.54/9.33	(955) TransformationProof (EQUIVALENT)
28.54/9.33	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.33	
28.54/9.33	   (A^2 -> H(U1(k, k), U1(k, b)),A^2 -> H(U1(k, k), U1(k, b)))
28.54/9.33	   (A^2 -> H(f(k), U1(k, c)),A^2 -> H(f(k), U1(k, c)))
28.54/9.33	   (A^2 -> H(f(k), U1(k, d)),A^2 -> H(f(k), U1(k, d)))
28.54/9.33	
28.54/9.33	
28.54/9.33	----------------------------------------
28.54/9.33	
28.54/9.33	(956)
28.54/9.33	Obligation:
28.54/9.33	Q DP problem:
28.54/9.33	The TRS P consists of the following rules:
28.54/9.33	
28.54/9.33	   H(x, x) -> G(x, x, f(k))
28.54/9.33	   G(d, x, x) -> A^2
28.54/9.33	   A^2 -> H(f(c), f(c))
28.54/9.33	   A^2 -> H(f(d), f(d))
28.54/9.33	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.33	   A^2 -> H(f(e), f(e))
28.54/9.33	   A^2 -> H(f(k), f(k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.33	   A^2 -> H(f(k), U1(c, d))
28.54/9.33	   A^2 -> H(f(k), U1(d, c))
28.54/9.33	   A^2 -> H(f(k), U1(b, e))
28.54/9.33	   A^2 -> H(f(k), U1(b, k))
28.54/9.33	   A^2 -> H(f(k), U1(e, c))
28.54/9.33	   A^2 -> H(f(k), U1(k, c))
28.54/9.33	   A^2 -> H(f(k), U1(c, e))
28.54/9.33	   A^2 -> H(f(k), U1(c, k))
28.54/9.33	   A^2 -> H(f(k), U1(e, e))
28.54/9.33	   A^2 -> H(f(k), U1(k, d))
28.54/9.33	   A^2 -> H(f(k), U1(d, k))
28.54/9.33	   A^2 -> H(f(c), b)
28.54/9.33	   A^2 -> H(f(c), U1(e, d))
28.54/9.33	   A^2 -> H(f(c), U1(d, e))
28.54/9.33	   A^2 -> H(f(k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.33	   A^2 -> H(U1(k, k), f(c))
28.54/9.33	   A^2 -> H(U1(k, k), f(d))
28.54/9.33	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.33	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.33	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.33	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.33	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.33	   A^2 -> H(U1(k, d), f(e))
28.54/9.33	   A^2 -> H(U1(k, d), f(k))
28.54/9.33	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.33	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.33	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.33	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.33	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.33	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.33	   A^2 -> H(U1(d, k), f(e))
28.54/9.33	   A^2 -> H(U1(d, k), f(k))
28.54/9.33	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.33	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.33	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.33	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.33	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.33	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.33	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.33	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.33	   A^2 -> H(f(d), b)
28.54/9.33	   A^2 -> H(f(d), U1(e, d))
28.54/9.33	   A^2 -> H(f(d), U1(d, e))
28.54/9.33	   A^2 -> H(f(d), c)
28.54/9.33	   A^2 -> H(f(d), U1(e, k))
28.54/9.33	   A^2 -> H(f(d), U1(k, e))
28.54/9.33	   A^2 -> H(f(d), e)
28.54/9.33	   A^2 -> H(f(a), d)
28.54/9.33	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.33	   A^2 -> H(f(c), c)
28.54/9.33	   A^2 -> H(f(c), U1(e, k))
28.54/9.33	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.33	   A^2 -> H(f(c), U1(k, e))
28.54/9.33	   A^2 -> H(f(c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.33	   A^2 -> H(f(a), k)
28.54/9.33	   A^2 -> H(f(e), U1(e, e))
28.54/9.33	   A^2 -> H(f(c), e)
28.54/9.33	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.33	   A^2 -> H(f(d), U1(k, k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.33	   A^2 -> H(d, U1(b, b))
28.54/9.33	   A^2 -> H(d, f(c))
28.54/9.33	   A^2 -> H(d, f(d))
28.54/9.33	   A^2 -> H(a, U1(c, b))
28.54/9.33	   A^2 -> H(a, U1(d, b))
28.54/9.33	   A^2 -> H(a, U1(b, c))
28.54/9.33	   A^2 -> H(a, U1(b, d))
28.54/9.33	   A^2 -> H(a, U1(c, c))
28.54/9.33	   A^2 -> H(a, f(e))
28.54/9.33	   A^2 -> H(a, f(k))
28.54/9.33	   A^2 -> H(a, U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.33	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.33	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.33	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.33	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.33	   A^2 -> H(U1(e, d), f(e))
28.54/9.33	   A^2 -> H(U1(e, d), f(k))
28.54/9.33	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.33	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.33	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.33	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.33	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.33	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.33	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.33	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.33	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.33	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.33	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.33	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.33	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.33	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.33	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.33	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.33	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.33	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.33	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.33	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.33	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.33	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.33	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, a), b)
28.54/9.33	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.33	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.33	   A^2 -> H(U1(c, a), c)
28.54/9.33	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.33	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.33	   A^2 -> H(U1(c, a), e)
28.54/9.33	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.33	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.33	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.33	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.33	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.33	   A^2 -> H(U1(d, e), f(e))
28.54/9.33	   A^2 -> H(U1(d, e), f(k))
28.54/9.33	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.33	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.33	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.33	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.33	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.33	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.33	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.33	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.33	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.33	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.33	   A^2 -> H(U1(d, a), b)
28.54/9.33	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.33	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.33	   A^2 -> H(U1(d, a), c)
28.54/9.33	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.33	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.33	   A^2 -> H(U1(d, a), e)
28.54/9.33	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.33	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.33	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.33	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.33	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.33	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.33	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.33	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.33	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.33	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.33	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.33	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.33	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.33	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.33	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.33	   A^2 -> H(U1(a, c), b)
28.54/9.33	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.33	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.33	   A^2 -> H(U1(a, c), c)
28.54/9.33	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.33	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.33	   A^2 -> H(U1(a, c), e)
28.54/9.33	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, d), b)
28.54/9.33	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.33	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.33	   A^2 -> H(U1(a, d), c)
28.54/9.33	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.33	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.33	   A^2 -> H(U1(a, d), e)
28.54/9.33	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.33	   A^2 -> H(U1(a, a), d)
28.54/9.33	   A^2 -> H(U1(a, a), k)
28.54/9.33	   A^2 -> H(k, U1(b, b))
28.54/9.33	   A^2 -> H(k, f(c))
28.54/9.33	   A^2 -> H(k, f(d))
28.54/9.33	   A^2 -> H(c, U1(c, b))
28.54/9.33	   A^2 -> H(c, U1(d, b))
28.54/9.33	   A^2 -> H(c, U1(b, c))
28.54/9.33	   A^2 -> H(c, U1(b, d))
28.54/9.33	   A^2 -> H(c, U1(c, c))
28.54/9.33	   A^2 -> H(c, f(e))
28.54/9.33	   A^2 -> H(c, f(k))
28.54/9.33	   A^2 -> H(c, U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.33	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.33	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.33	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.33	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.33	   A^2 -> H(U1(e, k), f(e))
28.54/9.33	   A^2 -> H(U1(e, k), f(k))
28.54/9.33	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.33	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.33	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.33	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.33	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.33	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.33	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.33	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.33	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.33	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.33	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.33	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.33	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.33	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.33	   A^2 -> H(U1(k, e), f(e))
28.54/9.33	   A^2 -> H(U1(k, e), f(k))
28.54/9.33	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.33	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.33	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.33	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.33	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.33	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.33	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.33	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.33	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.33	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.33	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.33	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.33	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.33	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.33	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.33	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.33	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.33	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.33	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.33	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.33	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.33	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.33	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.33	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.33	   A^2 -> H(U1(c, c), b)
28.54/9.33	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.33	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.33	   A^2 -> H(U1(c, c), e)
28.54/9.33	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.33	   A^2 -> H(e, U1(c, b))
28.54/9.33	   A^2 -> H(e, U1(d, b))
28.54/9.33	   A^2 -> H(e, U1(b, c))
28.54/9.33	   A^2 -> H(e, U1(b, d))
28.54/9.33	   A^2 -> H(e, U1(c, c))
28.54/9.33	   A^2 -> H(e, f(e))
28.54/9.33	   A^2 -> H(e, f(k))
28.54/9.33	   A^2 -> H(e, U1(d, d))
28.54/9.33	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.33	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.33	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.33	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.33	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.33	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.33	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.33	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.33	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.33	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.33	   A^2 -> H(f(e), b)
28.54/9.33	   A^2 -> H(f(e), U1(e, d))
28.54/9.33	   A^2 -> H(f(e), U1(d, e))
28.54/9.33	   A^2 -> H(f(e), c)
28.54/9.33	   A^2 -> H(f(e), U1(e, k))
28.54/9.33	   A^2 -> H(f(e), U1(k, e))
28.54/9.33	   A^2 -> H(f(e), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.33	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.33	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.33	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.33	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.33	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.33	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.33	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.33	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.33	   A^2 -> H(f(k), b)
28.54/9.33	   A^2 -> H(f(k), U1(e, d))
28.54/9.33	
28.54/9.33	The TRS R consists of the following rules:
28.54/9.33	
28.54/9.33	   f(x) -> U1(x, x)
28.54/9.33	   U1(e, x) -> x
28.54/9.33	   a -> c
28.54/9.33	   a -> d
28.54/9.33	   b -> c
28.54/9.33	   b -> d
28.54/9.33	   d -> k
28.54/9.33	   c -> e
28.54/9.33	   c -> k
28.54/9.33	
28.54/9.33	Q is empty.
28.54/9.33	We have to consider all minimal (P,Q,R)-chains.
28.54/9.33	----------------------------------------
28.54/9.33	
28.54/9.33	(957) TransformationProof (EQUIVALENT)
28.54/9.33	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.33	
28.54/9.33	   (A^2 -> H(U1(k, k), U1(c, d)),A^2 -> H(U1(k, k), U1(c, d)))
28.54/9.33	   (A^2 -> H(f(k), U1(e, d)),A^2 -> H(f(k), U1(e, d)))
28.54/9.33	   (A^2 -> H(f(k), U1(k, d)),A^2 -> H(f(k), U1(k, d)))
28.54/9.33	   (A^2 -> H(f(k), U1(c, k)),A^2 -> H(f(k), U1(c, k)))
28.54/9.33	
28.54/9.33	
28.54/9.33	----------------------------------------
28.54/9.33	
28.54/9.33	(958)
28.54/9.33	Obligation:
28.54/9.33	Q DP problem:
28.54/9.33	The TRS P consists of the following rules:
28.54/9.33	
28.54/9.33	   H(x, x) -> G(x, x, f(k))
28.54/9.33	   G(d, x, x) -> A^2
28.54/9.33	   A^2 -> H(f(c), f(c))
28.54/9.33	   A^2 -> H(f(d), f(d))
28.54/9.33	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.33	   A^2 -> H(f(e), f(e))
28.54/9.33	   A^2 -> H(f(k), f(k))
28.54/9.33	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.33	   A^2 -> H(f(k), U1(d, c))
28.54/9.33	   A^2 -> H(f(k), U1(b, e))
28.54/9.33	   A^2 -> H(f(k), U1(b, k))
28.54/9.33	   A^2 -> H(f(k), U1(e, c))
28.54/9.34	   A^2 -> H(f(k), U1(k, c))
28.54/9.34	   A^2 -> H(f(k), U1(c, e))
28.54/9.34	   A^2 -> H(f(k), U1(c, k))
28.54/9.34	   A^2 -> H(f(k), U1(e, e))
28.54/9.34	   A^2 -> H(f(k), U1(k, d))
28.54/9.34	   A^2 -> H(f(k), U1(d, k))
28.54/9.34	   A^2 -> H(f(c), b)
28.54/9.34	   A^2 -> H(f(c), U1(e, d))
28.54/9.34	   A^2 -> H(f(c), U1(d, e))
28.54/9.34	   A^2 -> H(f(k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.34	   A^2 -> H(U1(k, k), f(c))
28.54/9.34	   A^2 -> H(U1(k, k), f(d))
28.54/9.34	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.34	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.34	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.34	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.34	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.34	   A^2 -> H(U1(k, d), f(e))
28.54/9.34	   A^2 -> H(U1(k, d), f(k))
28.54/9.34	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.34	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.34	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.34	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.34	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.34	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.34	   A^2 -> H(U1(d, k), f(e))
28.54/9.34	   A^2 -> H(U1(d, k), f(k))
28.54/9.34	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.34	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.34	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.34	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.34	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.34	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.34	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.34	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.34	   A^2 -> H(f(d), b)
28.54/9.34	   A^2 -> H(f(d), U1(e, d))
28.54/9.34	   A^2 -> H(f(d), U1(d, e))
28.54/9.34	   A^2 -> H(f(d), c)
28.54/9.34	   A^2 -> H(f(d), U1(e, k))
28.54/9.34	   A^2 -> H(f(d), U1(k, e))
28.54/9.34	   A^2 -> H(f(d), e)
28.54/9.34	   A^2 -> H(f(a), d)
28.54/9.34	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.34	   A^2 -> H(f(c), c)
28.54/9.34	   A^2 -> H(f(c), U1(e, k))
28.54/9.34	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.34	   A^2 -> H(f(c), U1(k, e))
28.54/9.34	   A^2 -> H(f(c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.34	   A^2 -> H(f(a), k)
28.54/9.34	   A^2 -> H(f(e), U1(e, e))
28.54/9.34	   A^2 -> H(f(c), e)
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.34	   A^2 -> H(f(d), U1(k, k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.34	   A^2 -> H(d, U1(b, b))
28.54/9.34	   A^2 -> H(d, f(c))
28.54/9.34	   A^2 -> H(d, f(d))
28.54/9.34	   A^2 -> H(a, U1(c, b))
28.54/9.34	   A^2 -> H(a, U1(d, b))
28.54/9.34	   A^2 -> H(a, U1(b, c))
28.54/9.34	   A^2 -> H(a, U1(b, d))
28.54/9.34	   A^2 -> H(a, U1(c, c))
28.54/9.34	   A^2 -> H(a, f(e))
28.54/9.34	   A^2 -> H(a, f(k))
28.54/9.34	   A^2 -> H(a, U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.34	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.34	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.34	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.34	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.34	   A^2 -> H(U1(e, d), f(e))
28.54/9.34	   A^2 -> H(U1(e, d), f(k))
28.54/9.34	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.34	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.34	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.34	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.34	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.34	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.34	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.34	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.34	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.34	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.34	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.34	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.34	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.34	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.34	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.34	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.34	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.34	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.34	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.34	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.34	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.34	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.34	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, a), b)
28.54/9.34	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.34	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.34	   A^2 -> H(U1(c, a), c)
28.54/9.34	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.34	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.34	   A^2 -> H(U1(c, a), e)
28.54/9.34	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.34	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.34	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.34	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.34	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.34	   A^2 -> H(U1(d, e), f(e))
28.54/9.34	   A^2 -> H(U1(d, e), f(k))
28.54/9.34	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.34	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.34	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.34	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.34	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.34	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.34	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.34	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.34	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.34	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.34	   A^2 -> H(U1(d, a), b)
28.54/9.34	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.34	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.34	   A^2 -> H(U1(d, a), c)
28.54/9.34	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.34	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.34	   A^2 -> H(U1(d, a), e)
28.54/9.34	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.34	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.34	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.34	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.34	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.34	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.34	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.34	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.34	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.34	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.34	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.34	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.34	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.34	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.34	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.34	   A^2 -> H(U1(a, c), b)
28.54/9.34	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.34	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.34	   A^2 -> H(U1(a, c), c)
28.54/9.34	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.34	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.34	   A^2 -> H(U1(a, c), e)
28.54/9.34	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, d), b)
28.54/9.34	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.34	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.34	   A^2 -> H(U1(a, d), c)
28.54/9.34	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.34	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.34	   A^2 -> H(U1(a, d), e)
28.54/9.34	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, a), d)
28.54/9.34	   A^2 -> H(U1(a, a), k)
28.54/9.34	   A^2 -> H(k, U1(b, b))
28.54/9.34	   A^2 -> H(k, f(c))
28.54/9.34	   A^2 -> H(k, f(d))
28.54/9.34	   A^2 -> H(c, U1(c, b))
28.54/9.34	   A^2 -> H(c, U1(d, b))
28.54/9.34	   A^2 -> H(c, U1(b, c))
28.54/9.34	   A^2 -> H(c, U1(b, d))
28.54/9.34	   A^2 -> H(c, U1(c, c))
28.54/9.34	   A^2 -> H(c, f(e))
28.54/9.34	   A^2 -> H(c, f(k))
28.54/9.34	   A^2 -> H(c, U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.34	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.34	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.34	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.34	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.34	   A^2 -> H(U1(e, k), f(e))
28.54/9.34	   A^2 -> H(U1(e, k), f(k))
28.54/9.34	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.34	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.34	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.34	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.34	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.34	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.34	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.34	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.34	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.34	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.34	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.34	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.34	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.34	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.34	   A^2 -> H(U1(k, e), f(e))
28.54/9.34	   A^2 -> H(U1(k, e), f(k))
28.54/9.34	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.34	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.34	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.34	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.34	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.34	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.34	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.34	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.34	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.34	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.34	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.34	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.34	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.34	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.34	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.34	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.34	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.34	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.34	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.34	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.34	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.34	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, c), b)
28.54/9.34	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.34	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.34	   A^2 -> H(U1(c, c), e)
28.54/9.34	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.34	   A^2 -> H(e, U1(c, b))
28.54/9.34	   A^2 -> H(e, U1(d, b))
28.54/9.34	   A^2 -> H(e, U1(b, c))
28.54/9.34	   A^2 -> H(e, U1(b, d))
28.54/9.34	   A^2 -> H(e, U1(c, c))
28.54/9.34	   A^2 -> H(e, f(e))
28.54/9.34	   A^2 -> H(e, f(k))
28.54/9.34	   A^2 -> H(e, U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.34	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.34	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.34	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.34	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.34	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.34	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.34	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.34	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.34	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.34	   A^2 -> H(f(e), b)
28.54/9.34	   A^2 -> H(f(e), U1(e, d))
28.54/9.34	   A^2 -> H(f(e), U1(d, e))
28.54/9.34	   A^2 -> H(f(e), c)
28.54/9.34	   A^2 -> H(f(e), U1(e, k))
28.54/9.34	   A^2 -> H(f(e), U1(k, e))
28.54/9.34	   A^2 -> H(f(e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.34	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.34	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.34	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.34	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.34	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.34	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.34	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.34	   A^2 -> H(f(k), b)
28.54/9.34	   A^2 -> H(f(k), U1(e, d))
28.54/9.34	
28.54/9.34	The TRS R consists of the following rules:
28.54/9.34	
28.54/9.34	   f(x) -> U1(x, x)
28.54/9.34	   U1(e, x) -> x
28.54/9.34	   a -> c
28.54/9.34	   a -> d
28.54/9.34	   b -> c
28.54/9.34	   b -> d
28.54/9.34	   d -> k
28.54/9.34	   c -> e
28.54/9.34	   c -> k
28.54/9.34	
28.54/9.34	Q is empty.
28.54/9.34	We have to consider all minimal (P,Q,R)-chains.
28.54/9.34	----------------------------------------
28.54/9.34	
28.54/9.34	(959) TransformationProof (EQUIVALENT)
28.54/9.34	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.34	
28.54/9.34	   (A^2 -> H(U1(k, k), U1(d, c)),A^2 -> H(U1(k, k), U1(d, c)))
28.54/9.34	   (A^2 -> H(f(k), U1(k, c)),A^2 -> H(f(k), U1(k, c)))
28.54/9.34	   (A^2 -> H(f(k), U1(d, e)),A^2 -> H(f(k), U1(d, e)))
28.54/9.34	   (A^2 -> H(f(k), U1(d, k)),A^2 -> H(f(k), U1(d, k)))
28.54/9.34	
28.54/9.34	
28.54/9.34	----------------------------------------
28.54/9.34	
28.54/9.34	(960)
28.54/9.34	Obligation:
28.54/9.34	Q DP problem:
28.54/9.34	The TRS P consists of the following rules:
28.54/9.34	
28.54/9.34	   H(x, x) -> G(x, x, f(k))
28.54/9.34	   G(d, x, x) -> A^2
28.54/9.34	   A^2 -> H(f(c), f(c))
28.54/9.34	   A^2 -> H(f(d), f(d))
28.54/9.34	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.34	   A^2 -> H(f(e), f(e))
28.54/9.34	   A^2 -> H(f(k), f(k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.34	   A^2 -> H(f(k), U1(b, e))
28.54/9.34	   A^2 -> H(f(k), U1(b, k))
28.54/9.34	   A^2 -> H(f(k), U1(e, c))
28.54/9.34	   A^2 -> H(f(k), U1(k, c))
28.54/9.34	   A^2 -> H(f(k), U1(c, e))
28.54/9.34	   A^2 -> H(f(k), U1(c, k))
28.54/9.34	   A^2 -> H(f(k), U1(e, e))
28.54/9.34	   A^2 -> H(f(k), U1(k, d))
28.54/9.34	   A^2 -> H(f(k), U1(d, k))
28.54/9.34	   A^2 -> H(f(c), b)
28.54/9.34	   A^2 -> H(f(c), U1(e, d))
28.54/9.34	   A^2 -> H(f(c), U1(d, e))
28.54/9.34	   A^2 -> H(f(k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.34	   A^2 -> H(U1(k, k), f(c))
28.54/9.34	   A^2 -> H(U1(k, k), f(d))
28.54/9.34	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.34	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.34	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.34	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.34	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.34	   A^2 -> H(U1(k, d), f(e))
28.54/9.34	   A^2 -> H(U1(k, d), f(k))
28.54/9.34	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.34	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.34	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.34	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.34	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.34	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.34	   A^2 -> H(U1(d, k), f(e))
28.54/9.34	   A^2 -> H(U1(d, k), f(k))
28.54/9.34	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.34	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.34	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.34	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.34	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.34	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.34	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.34	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.34	   A^2 -> H(f(d), b)
28.54/9.34	   A^2 -> H(f(d), U1(e, d))
28.54/9.34	   A^2 -> H(f(d), U1(d, e))
28.54/9.34	   A^2 -> H(f(d), c)
28.54/9.34	   A^2 -> H(f(d), U1(e, k))
28.54/9.34	   A^2 -> H(f(d), U1(k, e))
28.54/9.34	   A^2 -> H(f(d), e)
28.54/9.34	   A^2 -> H(f(a), d)
28.54/9.34	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.34	   A^2 -> H(f(c), c)
28.54/9.34	   A^2 -> H(f(c), U1(e, k))
28.54/9.34	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.34	   A^2 -> H(f(c), U1(k, e))
28.54/9.34	   A^2 -> H(f(c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.34	   A^2 -> H(f(a), k)
28.54/9.34	   A^2 -> H(f(e), U1(e, e))
28.54/9.34	   A^2 -> H(f(c), e)
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.34	   A^2 -> H(f(d), U1(k, k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.34	   A^2 -> H(d, U1(b, b))
28.54/9.34	   A^2 -> H(d, f(c))
28.54/9.34	   A^2 -> H(d, f(d))
28.54/9.34	   A^2 -> H(a, U1(c, b))
28.54/9.34	   A^2 -> H(a, U1(d, b))
28.54/9.34	   A^2 -> H(a, U1(b, c))
28.54/9.34	   A^2 -> H(a, U1(b, d))
28.54/9.34	   A^2 -> H(a, U1(c, c))
28.54/9.34	   A^2 -> H(a, f(e))
28.54/9.34	   A^2 -> H(a, f(k))
28.54/9.34	   A^2 -> H(a, U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.34	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.34	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.34	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.34	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.34	   A^2 -> H(U1(e, d), f(e))
28.54/9.34	   A^2 -> H(U1(e, d), f(k))
28.54/9.34	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.34	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.34	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.34	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.34	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.34	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.34	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.34	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.34	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.34	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.34	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.34	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.34	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.34	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.34	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.34	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.34	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.34	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.34	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.34	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.34	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.34	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.34	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, a), b)
28.54/9.34	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.34	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.34	   A^2 -> H(U1(c, a), c)
28.54/9.34	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.34	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.34	   A^2 -> H(U1(c, a), e)
28.54/9.34	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.34	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.34	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.34	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.34	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.34	   A^2 -> H(U1(d, e), f(e))
28.54/9.34	   A^2 -> H(U1(d, e), f(k))
28.54/9.34	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.34	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.34	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.34	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.34	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.34	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.34	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.34	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.34	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.34	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.34	   A^2 -> H(U1(d, a), b)
28.54/9.34	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.34	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.34	   A^2 -> H(U1(d, a), c)
28.54/9.34	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.34	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.34	   A^2 -> H(U1(d, a), e)
28.54/9.34	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.34	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.34	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.34	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.34	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.34	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.34	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.34	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.34	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.34	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.34	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.34	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.34	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.34	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.34	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.34	   A^2 -> H(U1(a, c), b)
28.54/9.34	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.34	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.34	   A^2 -> H(U1(a, c), c)
28.54/9.34	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.34	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.34	   A^2 -> H(U1(a, c), e)
28.54/9.34	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, d), b)
28.54/9.34	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.34	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.34	   A^2 -> H(U1(a, d), c)
28.54/9.34	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.34	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.34	   A^2 -> H(U1(a, d), e)
28.54/9.34	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, a), d)
28.54/9.34	   A^2 -> H(U1(a, a), k)
28.54/9.34	   A^2 -> H(k, U1(b, b))
28.54/9.34	   A^2 -> H(k, f(c))
28.54/9.34	   A^2 -> H(k, f(d))
28.54/9.34	   A^2 -> H(c, U1(c, b))
28.54/9.34	   A^2 -> H(c, U1(d, b))
28.54/9.34	   A^2 -> H(c, U1(b, c))
28.54/9.34	   A^2 -> H(c, U1(b, d))
28.54/9.34	   A^2 -> H(c, U1(c, c))
28.54/9.34	   A^2 -> H(c, f(e))
28.54/9.34	   A^2 -> H(c, f(k))
28.54/9.34	   A^2 -> H(c, U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.34	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.34	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.34	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.34	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.34	   A^2 -> H(U1(e, k), f(e))
28.54/9.34	   A^2 -> H(U1(e, k), f(k))
28.54/9.34	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.34	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.34	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.34	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.34	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.34	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.34	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.34	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.34	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.34	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.34	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.34	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.34	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.34	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.34	   A^2 -> H(U1(k, e), f(e))
28.54/9.34	   A^2 -> H(U1(k, e), f(k))
28.54/9.34	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.34	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.34	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.34	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.34	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.34	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.34	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.34	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.34	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.34	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.34	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.34	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.34	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.34	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.34	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.34	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.34	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.34	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.34	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.34	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.34	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.34	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, c), b)
28.54/9.34	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.34	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.34	   A^2 -> H(U1(c, c), e)
28.54/9.34	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.34	   A^2 -> H(e, U1(c, b))
28.54/9.34	   A^2 -> H(e, U1(d, b))
28.54/9.34	   A^2 -> H(e, U1(b, c))
28.54/9.34	   A^2 -> H(e, U1(b, d))
28.54/9.34	   A^2 -> H(e, U1(c, c))
28.54/9.34	   A^2 -> H(e, f(e))
28.54/9.34	   A^2 -> H(e, f(k))
28.54/9.34	   A^2 -> H(e, U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.34	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.34	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.34	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.34	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.34	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.34	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.34	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.34	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.34	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.34	   A^2 -> H(f(e), b)
28.54/9.34	   A^2 -> H(f(e), U1(e, d))
28.54/9.34	   A^2 -> H(f(e), U1(d, e))
28.54/9.34	   A^2 -> H(f(e), c)
28.54/9.34	   A^2 -> H(f(e), U1(e, k))
28.54/9.34	   A^2 -> H(f(e), U1(k, e))
28.54/9.34	   A^2 -> H(f(e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.34	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.34	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.34	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.34	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.34	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.34	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.34	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.34	   A^2 -> H(f(k), b)
28.54/9.34	   A^2 -> H(f(k), U1(e, d))
28.54/9.34	   A^2 -> H(f(k), U1(d, e))
28.54/9.34	
28.54/9.34	The TRS R consists of the following rules:
28.54/9.34	
28.54/9.34	   f(x) -> U1(x, x)
28.54/9.34	   U1(e, x) -> x
28.54/9.34	   a -> c
28.54/9.34	   a -> d
28.54/9.34	   b -> c
28.54/9.34	   b -> d
28.54/9.34	   d -> k
28.54/9.34	   c -> e
28.54/9.34	   c -> k
28.54/9.34	
28.54/9.34	Q is empty.
28.54/9.34	We have to consider all minimal (P,Q,R)-chains.
28.54/9.34	----------------------------------------
28.54/9.34	
28.54/9.34	(961) TransformationProof (EQUIVALENT)
28.54/9.34	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.34	
28.54/9.34	   (A^2 -> H(U1(k, k), U1(b, e)),A^2 -> H(U1(k, k), U1(b, e)))
28.54/9.34	   (A^2 -> H(f(k), U1(c, e)),A^2 -> H(f(k), U1(c, e)))
28.54/9.34	   (A^2 -> H(f(k), U1(d, e)),A^2 -> H(f(k), U1(d, e)))
28.54/9.34	
28.54/9.34	
28.54/9.34	----------------------------------------
28.54/9.34	
28.54/9.34	(962)
28.54/9.34	Obligation:
28.54/9.34	Q DP problem:
28.54/9.34	The TRS P consists of the following rules:
28.54/9.34	
28.54/9.34	   H(x, x) -> G(x, x, f(k))
28.54/9.34	   G(d, x, x) -> A^2
28.54/9.34	   A^2 -> H(f(c), f(c))
28.54/9.34	   A^2 -> H(f(d), f(d))
28.54/9.34	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.34	   A^2 -> H(f(e), f(e))
28.54/9.34	   A^2 -> H(f(k), f(k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.34	   A^2 -> H(f(k), U1(b, k))
28.54/9.34	   A^2 -> H(f(k), U1(e, c))
28.54/9.34	   A^2 -> H(f(k), U1(k, c))
28.54/9.34	   A^2 -> H(f(k), U1(c, e))
28.54/9.34	   A^2 -> H(f(k), U1(c, k))
28.54/9.34	   A^2 -> H(f(k), U1(e, e))
28.54/9.34	   A^2 -> H(f(k), U1(k, d))
28.54/9.34	   A^2 -> H(f(k), U1(d, k))
28.54/9.34	   A^2 -> H(f(c), b)
28.54/9.34	   A^2 -> H(f(c), U1(e, d))
28.54/9.34	   A^2 -> H(f(c), U1(d, e))
28.54/9.34	   A^2 -> H(f(k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.34	   A^2 -> H(U1(k, k), f(c))
28.54/9.34	   A^2 -> H(U1(k, k), f(d))
28.54/9.34	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.34	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.34	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.34	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.34	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.34	   A^2 -> H(U1(k, d), f(e))
28.54/9.34	   A^2 -> H(U1(k, d), f(k))
28.54/9.34	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.34	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.34	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.34	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.34	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.34	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.34	   A^2 -> H(U1(d, k), f(e))
28.54/9.34	   A^2 -> H(U1(d, k), f(k))
28.54/9.34	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.34	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.34	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.34	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.34	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.34	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.34	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.34	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.34	   A^2 -> H(f(d), b)
28.54/9.34	   A^2 -> H(f(d), U1(e, d))
28.54/9.34	   A^2 -> H(f(d), U1(d, e))
28.54/9.34	   A^2 -> H(f(d), c)
28.54/9.34	   A^2 -> H(f(d), U1(e, k))
28.54/9.34	   A^2 -> H(f(d), U1(k, e))
28.54/9.34	   A^2 -> H(f(d), e)
28.54/9.34	   A^2 -> H(f(a), d)
28.54/9.34	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.34	   A^2 -> H(f(c), c)
28.54/9.34	   A^2 -> H(f(c), U1(e, k))
28.54/9.34	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.34	   A^2 -> H(f(c), U1(k, e))
28.54/9.34	   A^2 -> H(f(c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.34	   A^2 -> H(f(a), k)
28.54/9.34	   A^2 -> H(f(e), U1(e, e))
28.54/9.34	   A^2 -> H(f(c), e)
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.34	   A^2 -> H(f(d), U1(k, k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.34	   A^2 -> H(d, U1(b, b))
28.54/9.34	   A^2 -> H(d, f(c))
28.54/9.34	   A^2 -> H(d, f(d))
28.54/9.34	   A^2 -> H(a, U1(c, b))
28.54/9.34	   A^2 -> H(a, U1(d, b))
28.54/9.34	   A^2 -> H(a, U1(b, c))
28.54/9.34	   A^2 -> H(a, U1(b, d))
28.54/9.34	   A^2 -> H(a, U1(c, c))
28.54/9.34	   A^2 -> H(a, f(e))
28.54/9.34	   A^2 -> H(a, f(k))
28.54/9.34	   A^2 -> H(a, U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.34	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.34	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.34	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.34	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.34	   A^2 -> H(U1(e, d), f(e))
28.54/9.34	   A^2 -> H(U1(e, d), f(k))
28.54/9.34	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.34	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.34	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.34	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.34	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.34	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.34	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.34	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.34	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.34	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.34	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.34	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.34	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.34	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.34	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.34	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.34	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.34	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.34	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.34	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.34	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.34	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.34	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, a), b)
28.54/9.34	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.34	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.34	   A^2 -> H(U1(c, a), c)
28.54/9.34	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.34	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.34	   A^2 -> H(U1(c, a), e)
28.54/9.34	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.34	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.34	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.34	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.34	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.34	   A^2 -> H(U1(d, e), f(e))
28.54/9.34	   A^2 -> H(U1(d, e), f(k))
28.54/9.34	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.34	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.34	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.34	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.34	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.34	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.34	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.34	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.34	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.34	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.34	   A^2 -> H(U1(d, a), b)
28.54/9.34	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.34	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.34	   A^2 -> H(U1(d, a), c)
28.54/9.34	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.34	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.34	   A^2 -> H(U1(d, a), e)
28.54/9.34	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.34	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.34	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.34	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.34	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.34	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.34	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.34	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.34	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.34	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.34	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.34	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.34	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.34	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.34	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.34	   A^2 -> H(U1(a, c), b)
28.54/9.34	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.34	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.34	   A^2 -> H(U1(a, c), c)
28.54/9.34	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.34	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.34	   A^2 -> H(U1(a, c), e)
28.54/9.34	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, d), b)
28.54/9.34	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.34	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.34	   A^2 -> H(U1(a, d), c)
28.54/9.34	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.34	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.34	   A^2 -> H(U1(a, d), e)
28.54/9.34	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, a), d)
28.54/9.34	   A^2 -> H(U1(a, a), k)
28.54/9.34	   A^2 -> H(k, U1(b, b))
28.54/9.34	   A^2 -> H(k, f(c))
28.54/9.34	   A^2 -> H(k, f(d))
28.54/9.34	   A^2 -> H(c, U1(c, b))
28.54/9.34	   A^2 -> H(c, U1(d, b))
28.54/9.34	   A^2 -> H(c, U1(b, c))
28.54/9.34	   A^2 -> H(c, U1(b, d))
28.54/9.34	   A^2 -> H(c, U1(c, c))
28.54/9.34	   A^2 -> H(c, f(e))
28.54/9.34	   A^2 -> H(c, f(k))
28.54/9.34	   A^2 -> H(c, U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.34	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.34	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.34	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.34	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.34	   A^2 -> H(U1(e, k), f(e))
28.54/9.34	   A^2 -> H(U1(e, k), f(k))
28.54/9.34	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.34	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.34	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.34	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.34	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.34	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.34	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.34	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.34	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.34	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.34	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.34	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.34	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.34	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.34	   A^2 -> H(U1(k, e), f(e))
28.54/9.34	   A^2 -> H(U1(k, e), f(k))
28.54/9.34	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.34	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.34	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.34	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.34	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.34	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.34	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.34	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.34	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.34	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.34	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.34	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.34	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.34	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.34	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.34	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.34	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.34	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.34	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.34	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.34	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.34	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, c), b)
28.54/9.34	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.34	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.34	   A^2 -> H(U1(c, c), e)
28.54/9.34	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.34	   A^2 -> H(e, U1(c, b))
28.54/9.34	   A^2 -> H(e, U1(d, b))
28.54/9.34	   A^2 -> H(e, U1(b, c))
28.54/9.34	   A^2 -> H(e, U1(b, d))
28.54/9.34	   A^2 -> H(e, U1(c, c))
28.54/9.34	   A^2 -> H(e, f(e))
28.54/9.34	   A^2 -> H(e, f(k))
28.54/9.34	   A^2 -> H(e, U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.34	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.34	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.34	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.34	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.34	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.34	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.34	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.34	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.34	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.34	   A^2 -> H(f(e), b)
28.54/9.34	   A^2 -> H(f(e), U1(e, d))
28.54/9.34	   A^2 -> H(f(e), U1(d, e))
28.54/9.34	   A^2 -> H(f(e), c)
28.54/9.34	   A^2 -> H(f(e), U1(e, k))
28.54/9.34	   A^2 -> H(f(e), U1(k, e))
28.54/9.34	   A^2 -> H(f(e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.34	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.34	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.34	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.34	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.34	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.34	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.34	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.34	   A^2 -> H(f(k), b)
28.54/9.34	   A^2 -> H(f(k), U1(e, d))
28.54/9.34	   A^2 -> H(f(k), U1(d, e))
28.54/9.34	
28.54/9.34	The TRS R consists of the following rules:
28.54/9.34	
28.54/9.34	   f(x) -> U1(x, x)
28.54/9.34	   U1(e, x) -> x
28.54/9.34	   a -> c
28.54/9.34	   a -> d
28.54/9.34	   b -> c
28.54/9.34	   b -> d
28.54/9.34	   d -> k
28.54/9.34	   c -> e
28.54/9.34	   c -> k
28.54/9.34	
28.54/9.34	Q is empty.
28.54/9.34	We have to consider all minimal (P,Q,R)-chains.
28.54/9.34	----------------------------------------
28.54/9.34	
28.54/9.34	(963) TransformationProof (EQUIVALENT)
28.54/9.34	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.34	
28.54/9.34	   (A^2 -> H(U1(k, k), U1(b, k)),A^2 -> H(U1(k, k), U1(b, k)))
28.54/9.34	   (A^2 -> H(f(k), U1(c, k)),A^2 -> H(f(k), U1(c, k)))
28.54/9.34	   (A^2 -> H(f(k), U1(d, k)),A^2 -> H(f(k), U1(d, k)))
28.54/9.34	
28.54/9.34	
28.54/9.34	----------------------------------------
28.54/9.34	
28.54/9.34	(964)
28.54/9.34	Obligation:
28.54/9.34	Q DP problem:
28.54/9.34	The TRS P consists of the following rules:
28.54/9.34	
28.54/9.34	   H(x, x) -> G(x, x, f(k))
28.54/9.34	   G(d, x, x) -> A^2
28.54/9.34	   A^2 -> H(f(c), f(c))
28.54/9.34	   A^2 -> H(f(d), f(d))
28.54/9.34	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.34	   A^2 -> H(f(e), f(e))
28.54/9.34	   A^2 -> H(f(k), f(k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.34	   A^2 -> H(f(k), U1(e, c))
28.54/9.34	   A^2 -> H(f(k), U1(k, c))
28.54/9.34	   A^2 -> H(f(k), U1(c, e))
28.54/9.34	   A^2 -> H(f(k), U1(c, k))
28.54/9.34	   A^2 -> H(f(k), U1(e, e))
28.54/9.34	   A^2 -> H(f(k), U1(k, d))
28.54/9.34	   A^2 -> H(f(k), U1(d, k))
28.54/9.34	   A^2 -> H(f(c), b)
28.54/9.34	   A^2 -> H(f(c), U1(e, d))
28.54/9.34	   A^2 -> H(f(c), U1(d, e))
28.54/9.34	   A^2 -> H(f(k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.34	   A^2 -> H(U1(k, k), f(c))
28.54/9.34	   A^2 -> H(U1(k, k), f(d))
28.54/9.34	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.34	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.34	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.34	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.34	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.34	   A^2 -> H(U1(k, d), f(e))
28.54/9.34	   A^2 -> H(U1(k, d), f(k))
28.54/9.34	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.34	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.34	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.34	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.34	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.34	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.34	   A^2 -> H(U1(d, k), f(e))
28.54/9.34	   A^2 -> H(U1(d, k), f(k))
28.54/9.34	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.34	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.34	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.34	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.34	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.34	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.34	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.34	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.34	   A^2 -> H(f(d), b)
28.54/9.34	   A^2 -> H(f(d), U1(e, d))
28.54/9.34	   A^2 -> H(f(d), U1(d, e))
28.54/9.34	   A^2 -> H(f(d), c)
28.54/9.34	   A^2 -> H(f(d), U1(e, k))
28.54/9.34	   A^2 -> H(f(d), U1(k, e))
28.54/9.34	   A^2 -> H(f(d), e)
28.54/9.34	   A^2 -> H(f(a), d)
28.54/9.34	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.34	   A^2 -> H(f(c), c)
28.54/9.34	   A^2 -> H(f(c), U1(e, k))
28.54/9.34	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.34	   A^2 -> H(f(c), U1(k, e))
28.54/9.34	   A^2 -> H(f(c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.34	   A^2 -> H(f(a), k)
28.54/9.34	   A^2 -> H(f(e), U1(e, e))
28.54/9.34	   A^2 -> H(f(c), e)
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.34	   A^2 -> H(f(d), U1(k, k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.34	   A^2 -> H(d, U1(b, b))
28.54/9.34	   A^2 -> H(d, f(c))
28.54/9.34	   A^2 -> H(d, f(d))
28.54/9.34	   A^2 -> H(a, U1(c, b))
28.54/9.34	   A^2 -> H(a, U1(d, b))
28.54/9.34	   A^2 -> H(a, U1(b, c))
28.54/9.34	   A^2 -> H(a, U1(b, d))
28.54/9.34	   A^2 -> H(a, U1(c, c))
28.54/9.34	   A^2 -> H(a, f(e))
28.54/9.34	   A^2 -> H(a, f(k))
28.54/9.34	   A^2 -> H(a, U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.34	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.34	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.34	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.34	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.34	   A^2 -> H(U1(e, d), f(e))
28.54/9.34	   A^2 -> H(U1(e, d), f(k))
28.54/9.34	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.34	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.34	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.34	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.34	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.34	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.34	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.34	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.34	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.34	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.34	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.34	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.34	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.34	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.34	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.34	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.34	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.34	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.34	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.34	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.34	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.34	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.34	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, a), b)
28.54/9.34	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.34	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.34	   A^2 -> H(U1(c, a), c)
28.54/9.34	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.34	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.34	   A^2 -> H(U1(c, a), e)
28.54/9.34	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.34	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.34	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.34	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.34	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.34	   A^2 -> H(U1(d, e), f(e))
28.54/9.34	   A^2 -> H(U1(d, e), f(k))
28.54/9.34	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.34	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.34	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.34	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.34	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.34	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.34	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.34	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.34	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.34	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.34	   A^2 -> H(U1(d, a), b)
28.54/9.34	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.34	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.34	   A^2 -> H(U1(d, a), c)
28.54/9.34	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.34	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.34	   A^2 -> H(U1(d, a), e)
28.54/9.34	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.34	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.34	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.34	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.34	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.34	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.34	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.34	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.34	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.34	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.34	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.34	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.34	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.34	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.34	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.34	   A^2 -> H(U1(a, c), b)
28.54/9.34	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.34	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.34	   A^2 -> H(U1(a, c), c)
28.54/9.34	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.34	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.34	   A^2 -> H(U1(a, c), e)
28.54/9.34	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, d), b)
28.54/9.34	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.34	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.34	   A^2 -> H(U1(a, d), c)
28.54/9.34	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.34	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.34	   A^2 -> H(U1(a, d), e)
28.54/9.34	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, a), d)
28.54/9.34	   A^2 -> H(U1(a, a), k)
28.54/9.34	   A^2 -> H(k, U1(b, b))
28.54/9.34	   A^2 -> H(k, f(c))
28.54/9.34	   A^2 -> H(k, f(d))
28.54/9.34	   A^2 -> H(c, U1(c, b))
28.54/9.34	   A^2 -> H(c, U1(d, b))
28.54/9.34	   A^2 -> H(c, U1(b, c))
28.54/9.34	   A^2 -> H(c, U1(b, d))
28.54/9.34	   A^2 -> H(c, U1(c, c))
28.54/9.34	   A^2 -> H(c, f(e))
28.54/9.34	   A^2 -> H(c, f(k))
28.54/9.34	   A^2 -> H(c, U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.34	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.34	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.34	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.34	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.34	   A^2 -> H(U1(e, k), f(e))
28.54/9.34	   A^2 -> H(U1(e, k), f(k))
28.54/9.34	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.34	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.34	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.34	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.34	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.34	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.34	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.34	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.34	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.34	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.34	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.34	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.34	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.34	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.34	   A^2 -> H(U1(k, e), f(e))
28.54/9.34	   A^2 -> H(U1(k, e), f(k))
28.54/9.34	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.34	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.34	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.34	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.34	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.34	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.34	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.34	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.34	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.34	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.34	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.34	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.34	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.34	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.34	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.34	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.34	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.34	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.34	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.34	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.34	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.34	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, c), b)
28.54/9.34	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.34	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.34	   A^2 -> H(U1(c, c), e)
28.54/9.34	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.34	   A^2 -> H(e, U1(c, b))
28.54/9.34	   A^2 -> H(e, U1(d, b))
28.54/9.34	   A^2 -> H(e, U1(b, c))
28.54/9.34	   A^2 -> H(e, U1(b, d))
28.54/9.34	   A^2 -> H(e, U1(c, c))
28.54/9.34	   A^2 -> H(e, f(e))
28.54/9.34	   A^2 -> H(e, f(k))
28.54/9.34	   A^2 -> H(e, U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.34	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.34	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.34	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.34	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.34	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.34	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.34	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.34	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.34	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.34	   A^2 -> H(f(e), b)
28.54/9.34	   A^2 -> H(f(e), U1(e, d))
28.54/9.34	   A^2 -> H(f(e), U1(d, e))
28.54/9.34	   A^2 -> H(f(e), c)
28.54/9.34	   A^2 -> H(f(e), U1(e, k))
28.54/9.34	   A^2 -> H(f(e), U1(k, e))
28.54/9.34	   A^2 -> H(f(e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.34	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.34	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.34	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.34	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.34	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.34	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.34	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.34	   A^2 -> H(f(k), b)
28.54/9.34	   A^2 -> H(f(k), U1(e, d))
28.54/9.34	   A^2 -> H(f(k), U1(d, e))
28.54/9.34	
28.54/9.34	The TRS R consists of the following rules:
28.54/9.34	
28.54/9.34	   f(x) -> U1(x, x)
28.54/9.34	   U1(e, x) -> x
28.54/9.34	   a -> c
28.54/9.34	   a -> d
28.54/9.34	   b -> c
28.54/9.34	   b -> d
28.54/9.34	   d -> k
28.54/9.34	   c -> e
28.54/9.34	   c -> k
28.54/9.34	
28.54/9.34	Q is empty.
28.54/9.34	We have to consider all minimal (P,Q,R)-chains.
28.54/9.34	----------------------------------------
28.54/9.34	
28.54/9.34	(965) TransformationProof (EQUIVALENT)
28.54/9.34	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.34	
28.54/9.34	   (A^2 -> H(U1(k, k), U1(e, c)),A^2 -> H(U1(k, k), U1(e, c)))
28.54/9.34	   (A^2 -> H(f(k), c),A^2 -> H(f(k), c))
28.54/9.34	   (A^2 -> H(f(k), U1(e, e)),A^2 -> H(f(k), U1(e, e)))
28.54/9.34	   (A^2 -> H(f(k), U1(e, k)),A^2 -> H(f(k), U1(e, k)))
28.54/9.34	
28.54/9.34	
28.54/9.34	----------------------------------------
28.54/9.34	
28.54/9.34	(966)
28.54/9.34	Obligation:
28.54/9.34	Q DP problem:
28.54/9.34	The TRS P consists of the following rules:
28.54/9.34	
28.54/9.34	   H(x, x) -> G(x, x, f(k))
28.54/9.34	   G(d, x, x) -> A^2
28.54/9.34	   A^2 -> H(f(c), f(c))
28.54/9.34	   A^2 -> H(f(d), f(d))
28.54/9.34	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.34	   A^2 -> H(f(e), f(e))
28.54/9.34	   A^2 -> H(f(k), f(k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.34	   A^2 -> H(f(k), U1(k, c))
28.54/9.34	   A^2 -> H(f(k), U1(c, e))
28.54/9.34	   A^2 -> H(f(k), U1(c, k))
28.54/9.34	   A^2 -> H(f(k), U1(e, e))
28.54/9.34	   A^2 -> H(f(k), U1(k, d))
28.54/9.34	   A^2 -> H(f(k), U1(d, k))
28.54/9.34	   A^2 -> H(f(c), b)
28.54/9.34	   A^2 -> H(f(c), U1(e, d))
28.54/9.34	   A^2 -> H(f(c), U1(d, e))
28.54/9.34	   A^2 -> H(f(k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.34	   A^2 -> H(U1(k, k), f(c))
28.54/9.34	   A^2 -> H(U1(k, k), f(d))
28.54/9.34	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.34	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.34	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.34	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.34	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.34	   A^2 -> H(U1(k, d), f(e))
28.54/9.34	   A^2 -> H(U1(k, d), f(k))
28.54/9.34	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.34	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.34	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.34	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.34	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.34	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.34	   A^2 -> H(U1(d, k), f(e))
28.54/9.34	   A^2 -> H(U1(d, k), f(k))
28.54/9.34	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.34	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.34	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.34	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.34	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.34	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.34	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.34	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.34	   A^2 -> H(f(d), b)
28.54/9.34	   A^2 -> H(f(d), U1(e, d))
28.54/9.34	   A^2 -> H(f(d), U1(d, e))
28.54/9.34	   A^2 -> H(f(d), c)
28.54/9.34	   A^2 -> H(f(d), U1(e, k))
28.54/9.34	   A^2 -> H(f(d), U1(k, e))
28.54/9.34	   A^2 -> H(f(d), e)
28.54/9.34	   A^2 -> H(f(a), d)
28.54/9.34	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.34	   A^2 -> H(f(c), c)
28.54/9.34	   A^2 -> H(f(c), U1(e, k))
28.54/9.34	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.34	   A^2 -> H(f(c), U1(k, e))
28.54/9.34	   A^2 -> H(f(c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.34	   A^2 -> H(f(a), k)
28.54/9.34	   A^2 -> H(f(e), U1(e, e))
28.54/9.34	   A^2 -> H(f(c), e)
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.34	   A^2 -> H(f(d), U1(k, k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.34	   A^2 -> H(d, U1(b, b))
28.54/9.34	   A^2 -> H(d, f(c))
28.54/9.34	   A^2 -> H(d, f(d))
28.54/9.34	   A^2 -> H(a, U1(c, b))
28.54/9.34	   A^2 -> H(a, U1(d, b))
28.54/9.34	   A^2 -> H(a, U1(b, c))
28.54/9.34	   A^2 -> H(a, U1(b, d))
28.54/9.34	   A^2 -> H(a, U1(c, c))
28.54/9.34	   A^2 -> H(a, f(e))
28.54/9.34	   A^2 -> H(a, f(k))
28.54/9.34	   A^2 -> H(a, U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.34	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.34	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.34	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.34	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.34	   A^2 -> H(U1(e, d), f(e))
28.54/9.34	   A^2 -> H(U1(e, d), f(k))
28.54/9.34	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.34	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.34	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.34	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.34	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.34	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.34	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.34	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.34	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.34	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.34	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.34	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.34	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.34	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.34	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.34	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.34	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.34	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.34	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.34	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.34	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.34	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.34	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, a), b)
28.54/9.34	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.34	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.34	   A^2 -> H(U1(c, a), c)
28.54/9.34	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.34	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.34	   A^2 -> H(U1(c, a), e)
28.54/9.34	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.34	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.34	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.34	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.34	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.34	   A^2 -> H(U1(d, e), f(e))
28.54/9.34	   A^2 -> H(U1(d, e), f(k))
28.54/9.34	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.34	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.34	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.34	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.34	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.34	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.34	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.34	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.34	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.34	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.34	   A^2 -> H(U1(d, a), b)
28.54/9.34	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.34	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.34	   A^2 -> H(U1(d, a), c)
28.54/9.34	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.34	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.34	   A^2 -> H(U1(d, a), e)
28.54/9.34	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.34	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.34	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.34	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.34	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.34	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.34	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.34	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.34	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.34	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.34	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.34	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.34	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.34	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.34	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.34	   A^2 -> H(U1(a, c), b)
28.54/9.34	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.34	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.34	   A^2 -> H(U1(a, c), c)
28.54/9.34	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.34	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.34	   A^2 -> H(U1(a, c), e)
28.54/9.34	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, d), b)
28.54/9.34	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.34	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.34	   A^2 -> H(U1(a, d), c)
28.54/9.34	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.34	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.34	   A^2 -> H(U1(a, d), e)
28.54/9.34	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, a), d)
28.54/9.34	   A^2 -> H(U1(a, a), k)
28.54/9.34	   A^2 -> H(k, U1(b, b))
28.54/9.34	   A^2 -> H(k, f(c))
28.54/9.34	   A^2 -> H(k, f(d))
28.54/9.34	   A^2 -> H(c, U1(c, b))
28.54/9.34	   A^2 -> H(c, U1(d, b))
28.54/9.34	   A^2 -> H(c, U1(b, c))
28.54/9.34	   A^2 -> H(c, U1(b, d))
28.54/9.34	   A^2 -> H(c, U1(c, c))
28.54/9.34	   A^2 -> H(c, f(e))
28.54/9.34	   A^2 -> H(c, f(k))
28.54/9.34	   A^2 -> H(c, U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.34	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.34	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.34	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.34	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.34	   A^2 -> H(U1(e, k), f(e))
28.54/9.34	   A^2 -> H(U1(e, k), f(k))
28.54/9.34	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.34	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.34	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.34	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.34	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.34	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.34	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.34	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.34	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.34	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.34	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.34	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.34	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.34	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.34	   A^2 -> H(U1(k, e), f(e))
28.54/9.34	   A^2 -> H(U1(k, e), f(k))
28.54/9.34	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.34	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.34	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.34	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.34	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.34	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.34	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.34	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.34	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.34	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.34	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.34	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.34	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.34	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.34	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.34	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.34	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.34	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.34	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.34	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.34	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.34	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, c), b)
28.54/9.34	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.34	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.34	   A^2 -> H(U1(c, c), e)
28.54/9.34	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.34	   A^2 -> H(e, U1(c, b))
28.54/9.34	   A^2 -> H(e, U1(d, b))
28.54/9.34	   A^2 -> H(e, U1(b, c))
28.54/9.34	   A^2 -> H(e, U1(b, d))
28.54/9.34	   A^2 -> H(e, U1(c, c))
28.54/9.34	   A^2 -> H(e, f(e))
28.54/9.34	   A^2 -> H(e, f(k))
28.54/9.34	   A^2 -> H(e, U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.34	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.34	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.34	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.34	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.34	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.34	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.34	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.34	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.34	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.34	   A^2 -> H(f(e), b)
28.54/9.34	   A^2 -> H(f(e), U1(e, d))
28.54/9.34	   A^2 -> H(f(e), U1(d, e))
28.54/9.34	   A^2 -> H(f(e), c)
28.54/9.34	   A^2 -> H(f(e), U1(e, k))
28.54/9.34	   A^2 -> H(f(e), U1(k, e))
28.54/9.34	   A^2 -> H(f(e), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.34	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.34	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.34	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.34	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.34	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.34	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.34	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.34	   A^2 -> H(f(k), b)
28.54/9.34	   A^2 -> H(f(k), U1(e, d))
28.54/9.34	   A^2 -> H(f(k), U1(d, e))
28.54/9.34	   A^2 -> H(f(k), c)
28.54/9.34	   A^2 -> H(f(k), U1(e, k))
28.54/9.34	
28.54/9.34	The TRS R consists of the following rules:
28.54/9.34	
28.54/9.34	   f(x) -> U1(x, x)
28.54/9.34	   U1(e, x) -> x
28.54/9.34	   a -> c
28.54/9.34	   a -> d
28.54/9.34	   b -> c
28.54/9.34	   b -> d
28.54/9.34	   d -> k
28.54/9.34	   c -> e
28.54/9.34	   c -> k
28.54/9.34	
28.54/9.34	Q is empty.
28.54/9.34	We have to consider all minimal (P,Q,R)-chains.
28.54/9.34	----------------------------------------
28.54/9.34	
28.54/9.34	(967) TransformationProof (EQUIVALENT)
28.54/9.34	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.34	
28.54/9.34	   (A^2 -> H(U1(k, k), U1(k, c)),A^2 -> H(U1(k, k), U1(k, c)))
28.54/9.34	   (A^2 -> H(f(k), U1(k, e)),A^2 -> H(f(k), U1(k, e)))
28.54/9.34	   (A^2 -> H(f(k), U1(k, k)),A^2 -> H(f(k), U1(k, k)))
28.54/9.34	
28.54/9.34	
28.54/9.34	----------------------------------------
28.54/9.34	
28.54/9.34	(968)
28.54/9.34	Obligation:
28.54/9.34	Q DP problem:
28.54/9.34	The TRS P consists of the following rules:
28.54/9.34	
28.54/9.34	   H(x, x) -> G(x, x, f(k))
28.54/9.34	   G(d, x, x) -> A^2
28.54/9.34	   A^2 -> H(f(c), f(c))
28.54/9.34	   A^2 -> H(f(d), f(d))
28.54/9.34	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.34	   A^2 -> H(f(e), f(e))
28.54/9.34	   A^2 -> H(f(k), f(k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.34	   A^2 -> H(f(k), U1(c, e))
28.54/9.34	   A^2 -> H(f(k), U1(c, k))
28.54/9.34	   A^2 -> H(f(k), U1(e, e))
28.54/9.34	   A^2 -> H(f(k), U1(k, d))
28.54/9.34	   A^2 -> H(f(k), U1(d, k))
28.54/9.34	   A^2 -> H(f(c), b)
28.54/9.34	   A^2 -> H(f(c), U1(e, d))
28.54/9.34	   A^2 -> H(f(c), U1(d, e))
28.54/9.34	   A^2 -> H(f(k), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.34	   A^2 -> H(U1(k, k), f(c))
28.54/9.34	   A^2 -> H(U1(k, k), f(d))
28.54/9.34	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.34	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.34	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.34	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.34	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.34	   A^2 -> H(U1(k, d), f(e))
28.54/9.34	   A^2 -> H(U1(k, d), f(k))
28.54/9.34	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.34	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.34	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.34	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.34	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.34	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.34	   A^2 -> H(U1(d, k), f(e))
28.54/9.34	   A^2 -> H(U1(d, k), f(k))
28.54/9.34	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.34	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.34	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.34	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.34	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.34	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.34	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.34	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.34	   A^2 -> H(f(d), b)
28.54/9.34	   A^2 -> H(f(d), U1(e, d))
28.54/9.34	   A^2 -> H(f(d), U1(d, e))
28.54/9.34	   A^2 -> H(f(d), c)
28.54/9.34	   A^2 -> H(f(d), U1(e, k))
28.54/9.34	   A^2 -> H(f(d), U1(k, e))
28.54/9.34	   A^2 -> H(f(d), e)
28.54/9.34	   A^2 -> H(f(a), d)
28.54/9.34	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.34	   A^2 -> H(f(c), c)
28.54/9.34	   A^2 -> H(f(c), U1(e, k))
28.54/9.34	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.34	   A^2 -> H(f(c), U1(k, e))
28.54/9.34	   A^2 -> H(f(c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.34	   A^2 -> H(f(a), k)
28.54/9.34	   A^2 -> H(f(e), U1(e, e))
28.54/9.34	   A^2 -> H(f(c), e)
28.54/9.34	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.34	   A^2 -> H(f(d), U1(k, k))
28.54/9.34	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.34	   A^2 -> H(d, U1(b, b))
28.54/9.34	   A^2 -> H(d, f(c))
28.54/9.34	   A^2 -> H(d, f(d))
28.54/9.34	   A^2 -> H(a, U1(c, b))
28.54/9.34	   A^2 -> H(a, U1(d, b))
28.54/9.34	   A^2 -> H(a, U1(b, c))
28.54/9.34	   A^2 -> H(a, U1(b, d))
28.54/9.34	   A^2 -> H(a, U1(c, c))
28.54/9.34	   A^2 -> H(a, f(e))
28.54/9.34	   A^2 -> H(a, f(k))
28.54/9.34	   A^2 -> H(a, U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.34	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.34	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.34	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.34	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.34	   A^2 -> H(U1(e, d), f(e))
28.54/9.34	   A^2 -> H(U1(e, d), f(k))
28.54/9.34	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.34	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.34	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.34	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.34	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.34	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.34	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.34	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.34	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.34	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.34	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.34	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.34	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.34	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.34	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.34	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.34	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.34	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.34	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.34	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.34	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.34	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.34	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.34	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.34	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.34	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.34	   A^2 -> H(U1(c, a), b)
28.54/9.34	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.34	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.34	   A^2 -> H(U1(c, a), c)
28.54/9.34	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.34	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.34	   A^2 -> H(U1(c, a), e)
28.54/9.34	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.34	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.34	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.34	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.34	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.34	   A^2 -> H(U1(d, e), f(e))
28.54/9.34	   A^2 -> H(U1(d, e), f(k))
28.54/9.34	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.34	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.34	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.34	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.34	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.34	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.34	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.34	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.34	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.34	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.34	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.34	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.34	   A^2 -> H(U1(d, a), b)
28.54/9.34	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.34	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.34	   A^2 -> H(U1(d, a), c)
28.54/9.34	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.34	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.34	   A^2 -> H(U1(d, a), e)
28.54/9.34	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.34	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.34	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.34	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.34	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.34	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.34	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.35	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.35	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.35	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.35	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.35	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.35	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.35	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.35	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.35	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.35	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.35	   A^2 -> H(U1(a, c), b)
28.54/9.35	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.35	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.35	   A^2 -> H(U1(a, c), c)
28.54/9.35	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.35	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.35	   A^2 -> H(U1(a, c), e)
28.54/9.35	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, d), b)
28.54/9.35	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.35	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.35	   A^2 -> H(U1(a, d), c)
28.54/9.35	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.35	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.35	   A^2 -> H(U1(a, d), e)
28.54/9.35	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, a), d)
28.54/9.35	   A^2 -> H(U1(a, a), k)
28.54/9.35	   A^2 -> H(k, U1(b, b))
28.54/9.35	   A^2 -> H(k, f(c))
28.54/9.35	   A^2 -> H(k, f(d))
28.54/9.35	   A^2 -> H(c, U1(c, b))
28.54/9.35	   A^2 -> H(c, U1(d, b))
28.54/9.35	   A^2 -> H(c, U1(b, c))
28.54/9.35	   A^2 -> H(c, U1(b, d))
28.54/9.35	   A^2 -> H(c, U1(c, c))
28.54/9.35	   A^2 -> H(c, f(e))
28.54/9.35	   A^2 -> H(c, f(k))
28.54/9.35	   A^2 -> H(c, U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.35	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.35	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.35	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.35	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.35	   A^2 -> H(U1(e, k), f(e))
28.54/9.35	   A^2 -> H(U1(e, k), f(k))
28.54/9.35	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.35	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.35	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.35	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.35	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.35	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.35	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.35	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.35	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.35	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.35	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.35	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.35	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.35	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.35	   A^2 -> H(U1(k, e), f(e))
28.54/9.35	   A^2 -> H(U1(k, e), f(k))
28.54/9.35	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.35	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.35	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.35	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.35	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.35	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.35	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.35	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.35	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.35	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.35	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.35	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.35	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.35	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.35	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.35	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.35	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.35	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.35	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.35	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.35	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.35	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, c), b)
28.54/9.35	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.35	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.35	   A^2 -> H(U1(c, c), e)
28.54/9.35	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.35	   A^2 -> H(e, U1(c, b))
28.54/9.35	   A^2 -> H(e, U1(d, b))
28.54/9.35	   A^2 -> H(e, U1(b, c))
28.54/9.35	   A^2 -> H(e, U1(b, d))
28.54/9.35	   A^2 -> H(e, U1(c, c))
28.54/9.35	   A^2 -> H(e, f(e))
28.54/9.35	   A^2 -> H(e, f(k))
28.54/9.35	   A^2 -> H(e, U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.35	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.35	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.35	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.35	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.35	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.35	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.35	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.35	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.35	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.35	   A^2 -> H(f(e), b)
28.54/9.35	   A^2 -> H(f(e), U1(e, d))
28.54/9.35	   A^2 -> H(f(e), U1(d, e))
28.54/9.35	   A^2 -> H(f(e), c)
28.54/9.35	   A^2 -> H(f(e), U1(e, k))
28.54/9.35	   A^2 -> H(f(e), U1(k, e))
28.54/9.35	   A^2 -> H(f(e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.35	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.35	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.35	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.35	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.35	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.35	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.35	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.35	   A^2 -> H(f(k), b)
28.54/9.35	   A^2 -> H(f(k), U1(e, d))
28.54/9.35	   A^2 -> H(f(k), U1(d, e))
28.54/9.35	   A^2 -> H(f(k), c)
28.54/9.35	   A^2 -> H(f(k), U1(e, k))
28.54/9.35	   A^2 -> H(f(k), U1(k, e))
28.54/9.35	
28.54/9.35	The TRS R consists of the following rules:
28.54/9.35	
28.54/9.35	   f(x) -> U1(x, x)
28.54/9.35	   U1(e, x) -> x
28.54/9.35	   a -> c
28.54/9.35	   a -> d
28.54/9.35	   b -> c
28.54/9.35	   b -> d
28.54/9.35	   d -> k
28.54/9.35	   c -> e
28.54/9.35	   c -> k
28.54/9.35	
28.54/9.35	Q is empty.
28.54/9.35	We have to consider all minimal (P,Q,R)-chains.
28.54/9.35	----------------------------------------
28.54/9.35	
28.54/9.35	(969) TransformationProof (EQUIVALENT)
28.54/9.35	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.35	
28.54/9.35	   (A^2 -> H(U1(k, k), U1(c, e)),A^2 -> H(U1(k, k), U1(c, e)))
28.54/9.35	   (A^2 -> H(f(k), U1(e, e)),A^2 -> H(f(k), U1(e, e)))
28.54/9.35	   (A^2 -> H(f(k), U1(k, e)),A^2 -> H(f(k), U1(k, e)))
28.54/9.35	
28.54/9.35	
28.54/9.35	----------------------------------------
28.54/9.35	
28.54/9.35	(970)
28.54/9.35	Obligation:
28.54/9.35	Q DP problem:
28.54/9.35	The TRS P consists of the following rules:
28.54/9.35	
28.54/9.35	   H(x, x) -> G(x, x, f(k))
28.54/9.35	   G(d, x, x) -> A^2
28.54/9.35	   A^2 -> H(f(c), f(c))
28.54/9.35	   A^2 -> H(f(d), f(d))
28.54/9.35	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.35	   A^2 -> H(f(e), f(e))
28.54/9.35	   A^2 -> H(f(k), f(k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.35	   A^2 -> H(f(k), U1(c, k))
28.54/9.35	   A^2 -> H(f(k), U1(e, e))
28.54/9.35	   A^2 -> H(f(k), U1(k, d))
28.54/9.35	   A^2 -> H(f(k), U1(d, k))
28.54/9.35	   A^2 -> H(f(c), b)
28.54/9.35	   A^2 -> H(f(c), U1(e, d))
28.54/9.35	   A^2 -> H(f(c), U1(d, e))
28.54/9.35	   A^2 -> H(f(k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.35	   A^2 -> H(U1(k, k), f(c))
28.54/9.35	   A^2 -> H(U1(k, k), f(d))
28.54/9.35	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.35	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.35	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.35	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.35	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.35	   A^2 -> H(U1(k, d), f(e))
28.54/9.35	   A^2 -> H(U1(k, d), f(k))
28.54/9.35	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.35	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.35	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.35	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.35	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.35	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.35	   A^2 -> H(U1(d, k), f(e))
28.54/9.35	   A^2 -> H(U1(d, k), f(k))
28.54/9.35	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.35	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.35	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.35	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.35	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.35	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.35	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.35	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.35	   A^2 -> H(f(d), b)
28.54/9.35	   A^2 -> H(f(d), U1(e, d))
28.54/9.35	   A^2 -> H(f(d), U1(d, e))
28.54/9.35	   A^2 -> H(f(d), c)
28.54/9.35	   A^2 -> H(f(d), U1(e, k))
28.54/9.35	   A^2 -> H(f(d), U1(k, e))
28.54/9.35	   A^2 -> H(f(d), e)
28.54/9.35	   A^2 -> H(f(a), d)
28.54/9.35	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.35	   A^2 -> H(f(c), c)
28.54/9.35	   A^2 -> H(f(c), U1(e, k))
28.54/9.35	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.35	   A^2 -> H(f(c), U1(k, e))
28.54/9.35	   A^2 -> H(f(c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.35	   A^2 -> H(f(a), k)
28.54/9.35	   A^2 -> H(f(e), U1(e, e))
28.54/9.35	   A^2 -> H(f(c), e)
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.35	   A^2 -> H(f(d), U1(k, k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.35	   A^2 -> H(d, U1(b, b))
28.54/9.35	   A^2 -> H(d, f(c))
28.54/9.35	   A^2 -> H(d, f(d))
28.54/9.35	   A^2 -> H(a, U1(c, b))
28.54/9.35	   A^2 -> H(a, U1(d, b))
28.54/9.35	   A^2 -> H(a, U1(b, c))
28.54/9.35	   A^2 -> H(a, U1(b, d))
28.54/9.35	   A^2 -> H(a, U1(c, c))
28.54/9.35	   A^2 -> H(a, f(e))
28.54/9.35	   A^2 -> H(a, f(k))
28.54/9.35	   A^2 -> H(a, U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.35	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.35	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.35	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.35	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.35	   A^2 -> H(U1(e, d), f(e))
28.54/9.35	   A^2 -> H(U1(e, d), f(k))
28.54/9.35	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.35	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.35	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.35	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.35	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.35	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.35	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.35	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.35	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.35	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.35	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.35	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.35	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.35	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.35	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.35	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.35	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.35	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.35	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.35	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.35	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.35	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.35	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, a), b)
28.54/9.35	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.35	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.35	   A^2 -> H(U1(c, a), c)
28.54/9.35	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.35	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.35	   A^2 -> H(U1(c, a), e)
28.54/9.35	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.35	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.35	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.35	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.35	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.35	   A^2 -> H(U1(d, e), f(e))
28.54/9.35	   A^2 -> H(U1(d, e), f(k))
28.54/9.35	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.35	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.35	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.35	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.35	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.35	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.35	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.35	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.35	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.35	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.35	   A^2 -> H(U1(d, a), b)
28.54/9.35	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.35	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.35	   A^2 -> H(U1(d, a), c)
28.54/9.35	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.35	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.35	   A^2 -> H(U1(d, a), e)
28.54/9.35	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.35	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.35	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.35	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.35	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.35	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.35	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.35	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.35	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.35	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.35	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.35	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.35	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.35	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.35	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.35	   A^2 -> H(U1(a, c), b)
28.54/9.35	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.35	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.35	   A^2 -> H(U1(a, c), c)
28.54/9.35	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.35	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.35	   A^2 -> H(U1(a, c), e)
28.54/9.35	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, d), b)
28.54/9.35	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.35	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.35	   A^2 -> H(U1(a, d), c)
28.54/9.35	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.35	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.35	   A^2 -> H(U1(a, d), e)
28.54/9.35	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, a), d)
28.54/9.35	   A^2 -> H(U1(a, a), k)
28.54/9.35	   A^2 -> H(k, U1(b, b))
28.54/9.35	   A^2 -> H(k, f(c))
28.54/9.35	   A^2 -> H(k, f(d))
28.54/9.35	   A^2 -> H(c, U1(c, b))
28.54/9.35	   A^2 -> H(c, U1(d, b))
28.54/9.35	   A^2 -> H(c, U1(b, c))
28.54/9.35	   A^2 -> H(c, U1(b, d))
28.54/9.35	   A^2 -> H(c, U1(c, c))
28.54/9.35	   A^2 -> H(c, f(e))
28.54/9.35	   A^2 -> H(c, f(k))
28.54/9.35	   A^2 -> H(c, U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.35	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.35	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.35	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.35	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.35	   A^2 -> H(U1(e, k), f(e))
28.54/9.35	   A^2 -> H(U1(e, k), f(k))
28.54/9.35	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.35	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.35	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.35	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.35	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.35	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.35	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.35	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.35	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.35	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.35	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.35	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.35	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.35	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.35	   A^2 -> H(U1(k, e), f(e))
28.54/9.35	   A^2 -> H(U1(k, e), f(k))
28.54/9.35	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.35	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.35	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.35	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.35	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.35	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.35	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.35	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.35	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.35	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.35	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.35	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.35	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.35	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.35	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.35	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.35	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.35	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.35	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.35	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.35	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.35	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, c), b)
28.54/9.35	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.35	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.35	   A^2 -> H(U1(c, c), e)
28.54/9.35	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.35	   A^2 -> H(e, U1(c, b))
28.54/9.35	   A^2 -> H(e, U1(d, b))
28.54/9.35	   A^2 -> H(e, U1(b, c))
28.54/9.35	   A^2 -> H(e, U1(b, d))
28.54/9.35	   A^2 -> H(e, U1(c, c))
28.54/9.35	   A^2 -> H(e, f(e))
28.54/9.35	   A^2 -> H(e, f(k))
28.54/9.35	   A^2 -> H(e, U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.35	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.35	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.35	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.35	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.35	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.35	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.35	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.35	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.35	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.35	   A^2 -> H(f(e), b)
28.54/9.35	   A^2 -> H(f(e), U1(e, d))
28.54/9.35	   A^2 -> H(f(e), U1(d, e))
28.54/9.35	   A^2 -> H(f(e), c)
28.54/9.35	   A^2 -> H(f(e), U1(e, k))
28.54/9.35	   A^2 -> H(f(e), U1(k, e))
28.54/9.35	   A^2 -> H(f(e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.35	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.35	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.35	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.35	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.35	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.35	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.35	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.35	   A^2 -> H(f(k), b)
28.54/9.35	   A^2 -> H(f(k), U1(e, d))
28.54/9.35	   A^2 -> H(f(k), U1(d, e))
28.54/9.35	   A^2 -> H(f(k), c)
28.54/9.35	   A^2 -> H(f(k), U1(e, k))
28.54/9.35	   A^2 -> H(f(k), U1(k, e))
28.54/9.35	
28.54/9.35	The TRS R consists of the following rules:
28.54/9.35	
28.54/9.35	   f(x) -> U1(x, x)
28.54/9.35	   U1(e, x) -> x
28.54/9.35	   a -> c
28.54/9.35	   a -> d
28.54/9.35	   b -> c
28.54/9.35	   b -> d
28.54/9.35	   d -> k
28.54/9.35	   c -> e
28.54/9.35	   c -> k
28.54/9.35	
28.54/9.35	Q is empty.
28.54/9.35	We have to consider all minimal (P,Q,R)-chains.
28.54/9.35	----------------------------------------
28.54/9.35	
28.54/9.35	(971) TransformationProof (EQUIVALENT)
28.54/9.35	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.35	
28.54/9.35	   (A^2 -> H(U1(k, k), U1(c, k)),A^2 -> H(U1(k, k), U1(c, k)))
28.54/9.35	   (A^2 -> H(f(k), U1(e, k)),A^2 -> H(f(k), U1(e, k)))
28.54/9.35	   (A^2 -> H(f(k), U1(k, k)),A^2 -> H(f(k), U1(k, k)))
28.54/9.35	
28.54/9.35	
28.54/9.35	----------------------------------------
28.54/9.35	
28.54/9.35	(972)
28.54/9.35	Obligation:
28.54/9.35	Q DP problem:
28.54/9.35	The TRS P consists of the following rules:
28.54/9.35	
28.54/9.35	   H(x, x) -> G(x, x, f(k))
28.54/9.35	   G(d, x, x) -> A^2
28.54/9.35	   A^2 -> H(f(c), f(c))
28.54/9.35	   A^2 -> H(f(d), f(d))
28.54/9.35	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.35	   A^2 -> H(f(e), f(e))
28.54/9.35	   A^2 -> H(f(k), f(k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.35	   A^2 -> H(f(k), U1(e, e))
28.54/9.35	   A^2 -> H(f(k), U1(k, d))
28.54/9.35	   A^2 -> H(f(k), U1(d, k))
28.54/9.35	   A^2 -> H(f(c), b)
28.54/9.35	   A^2 -> H(f(c), U1(e, d))
28.54/9.35	   A^2 -> H(f(c), U1(d, e))
28.54/9.35	   A^2 -> H(f(k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.35	   A^2 -> H(U1(k, k), f(c))
28.54/9.35	   A^2 -> H(U1(k, k), f(d))
28.54/9.35	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.35	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.35	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.35	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.35	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.35	   A^2 -> H(U1(k, d), f(e))
28.54/9.35	   A^2 -> H(U1(k, d), f(k))
28.54/9.35	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.35	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.35	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.35	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.35	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.35	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.35	   A^2 -> H(U1(d, k), f(e))
28.54/9.35	   A^2 -> H(U1(d, k), f(k))
28.54/9.35	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.35	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.35	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.35	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.35	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.35	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.35	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.35	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.35	   A^2 -> H(f(d), b)
28.54/9.35	   A^2 -> H(f(d), U1(e, d))
28.54/9.35	   A^2 -> H(f(d), U1(d, e))
28.54/9.35	   A^2 -> H(f(d), c)
28.54/9.35	   A^2 -> H(f(d), U1(e, k))
28.54/9.35	   A^2 -> H(f(d), U1(k, e))
28.54/9.35	   A^2 -> H(f(d), e)
28.54/9.35	   A^2 -> H(f(a), d)
28.54/9.35	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.35	   A^2 -> H(f(c), c)
28.54/9.35	   A^2 -> H(f(c), U1(e, k))
28.54/9.35	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.35	   A^2 -> H(f(c), U1(k, e))
28.54/9.35	   A^2 -> H(f(c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.35	   A^2 -> H(f(a), k)
28.54/9.35	   A^2 -> H(f(e), U1(e, e))
28.54/9.35	   A^2 -> H(f(c), e)
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.35	   A^2 -> H(f(d), U1(k, k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.35	   A^2 -> H(d, U1(b, b))
28.54/9.35	   A^2 -> H(d, f(c))
28.54/9.35	   A^2 -> H(d, f(d))
28.54/9.35	   A^2 -> H(a, U1(c, b))
28.54/9.35	   A^2 -> H(a, U1(d, b))
28.54/9.35	   A^2 -> H(a, U1(b, c))
28.54/9.35	   A^2 -> H(a, U1(b, d))
28.54/9.35	   A^2 -> H(a, U1(c, c))
28.54/9.35	   A^2 -> H(a, f(e))
28.54/9.35	   A^2 -> H(a, f(k))
28.54/9.35	   A^2 -> H(a, U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.35	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.35	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.35	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.35	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.35	   A^2 -> H(U1(e, d), f(e))
28.54/9.35	   A^2 -> H(U1(e, d), f(k))
28.54/9.35	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.35	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.35	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.35	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.35	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.35	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.35	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.35	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.35	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.35	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.35	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.35	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.35	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.35	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.35	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.35	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.35	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.35	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.35	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.35	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.35	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.35	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.35	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, a), b)
28.54/9.35	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.35	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.35	   A^2 -> H(U1(c, a), c)
28.54/9.35	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.35	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.35	   A^2 -> H(U1(c, a), e)
28.54/9.35	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.35	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.35	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.35	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.35	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.35	   A^2 -> H(U1(d, e), f(e))
28.54/9.35	   A^2 -> H(U1(d, e), f(k))
28.54/9.35	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.35	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.35	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.35	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.35	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.35	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.35	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.35	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.35	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.35	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.35	   A^2 -> H(U1(d, a), b)
28.54/9.35	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.35	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.35	   A^2 -> H(U1(d, a), c)
28.54/9.35	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.35	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.35	   A^2 -> H(U1(d, a), e)
28.54/9.35	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.35	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.35	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.35	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.35	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.35	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.35	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.35	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.35	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.35	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.35	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.35	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.35	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.35	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.35	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.35	   A^2 -> H(U1(a, c), b)
28.54/9.35	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.35	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.35	   A^2 -> H(U1(a, c), c)
28.54/9.35	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.35	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.35	   A^2 -> H(U1(a, c), e)
28.54/9.35	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, d), b)
28.54/9.35	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.35	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.35	   A^2 -> H(U1(a, d), c)
28.54/9.35	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.35	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.35	   A^2 -> H(U1(a, d), e)
28.54/9.35	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, a), d)
28.54/9.35	   A^2 -> H(U1(a, a), k)
28.54/9.35	   A^2 -> H(k, U1(b, b))
28.54/9.35	   A^2 -> H(k, f(c))
28.54/9.35	   A^2 -> H(k, f(d))
28.54/9.35	   A^2 -> H(c, U1(c, b))
28.54/9.35	   A^2 -> H(c, U1(d, b))
28.54/9.35	   A^2 -> H(c, U1(b, c))
28.54/9.35	   A^2 -> H(c, U1(b, d))
28.54/9.35	   A^2 -> H(c, U1(c, c))
28.54/9.35	   A^2 -> H(c, f(e))
28.54/9.35	   A^2 -> H(c, f(k))
28.54/9.35	   A^2 -> H(c, U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.35	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.35	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.35	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.35	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.35	   A^2 -> H(U1(e, k), f(e))
28.54/9.35	   A^2 -> H(U1(e, k), f(k))
28.54/9.35	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.35	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.35	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.35	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.35	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.35	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.35	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.35	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.35	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.35	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.35	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.35	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.35	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.35	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.35	   A^2 -> H(U1(k, e), f(e))
28.54/9.35	   A^2 -> H(U1(k, e), f(k))
28.54/9.35	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.35	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.35	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.35	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.35	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.35	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.35	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.35	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.35	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.35	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.35	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.35	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.35	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.35	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.35	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.35	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.35	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.35	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.35	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.35	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.35	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.35	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, c), b)
28.54/9.35	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.35	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.35	   A^2 -> H(U1(c, c), e)
28.54/9.35	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.35	   A^2 -> H(e, U1(c, b))
28.54/9.35	   A^2 -> H(e, U1(d, b))
28.54/9.35	   A^2 -> H(e, U1(b, c))
28.54/9.35	   A^2 -> H(e, U1(b, d))
28.54/9.35	   A^2 -> H(e, U1(c, c))
28.54/9.35	   A^2 -> H(e, f(e))
28.54/9.35	   A^2 -> H(e, f(k))
28.54/9.35	   A^2 -> H(e, U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.35	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.35	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.35	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.35	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.35	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.35	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.35	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.35	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.35	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.35	   A^2 -> H(f(e), b)
28.54/9.35	   A^2 -> H(f(e), U1(e, d))
28.54/9.35	   A^2 -> H(f(e), U1(d, e))
28.54/9.35	   A^2 -> H(f(e), c)
28.54/9.35	   A^2 -> H(f(e), U1(e, k))
28.54/9.35	   A^2 -> H(f(e), U1(k, e))
28.54/9.35	   A^2 -> H(f(e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.35	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.35	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.35	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.35	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.35	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.35	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.35	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.35	   A^2 -> H(f(k), b)
28.54/9.35	   A^2 -> H(f(k), U1(e, d))
28.54/9.35	   A^2 -> H(f(k), U1(d, e))
28.54/9.35	   A^2 -> H(f(k), c)
28.54/9.35	   A^2 -> H(f(k), U1(e, k))
28.54/9.35	   A^2 -> H(f(k), U1(k, e))
28.54/9.35	
28.54/9.35	The TRS R consists of the following rules:
28.54/9.35	
28.54/9.35	   f(x) -> U1(x, x)
28.54/9.35	   U1(e, x) -> x
28.54/9.35	   a -> c
28.54/9.35	   a -> d
28.54/9.35	   b -> c
28.54/9.35	   b -> d
28.54/9.35	   d -> k
28.54/9.35	   c -> e
28.54/9.35	   c -> k
28.54/9.35	
28.54/9.35	Q is empty.
28.54/9.35	We have to consider all minimal (P,Q,R)-chains.
28.54/9.35	----------------------------------------
28.54/9.35	
28.54/9.35	(973) TransformationProof (EQUIVALENT)
28.54/9.35	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.35	
28.54/9.35	   (A^2 -> H(U1(k, k), U1(e, e)),A^2 -> H(U1(k, k), U1(e, e)))
28.54/9.35	   (A^2 -> H(f(k), e),A^2 -> H(f(k), e))
28.54/9.35	
28.54/9.35	
28.54/9.35	----------------------------------------
28.54/9.35	
28.54/9.35	(974)
28.54/9.35	Obligation:
28.54/9.35	Q DP problem:
28.54/9.35	The TRS P consists of the following rules:
28.54/9.35	
28.54/9.35	   H(x, x) -> G(x, x, f(k))
28.54/9.35	   G(d, x, x) -> A^2
28.54/9.35	   A^2 -> H(f(c), f(c))
28.54/9.35	   A^2 -> H(f(d), f(d))
28.54/9.35	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.35	   A^2 -> H(f(e), f(e))
28.54/9.35	   A^2 -> H(f(k), f(k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.35	   A^2 -> H(f(k), U1(k, d))
28.54/9.35	   A^2 -> H(f(k), U1(d, k))
28.54/9.35	   A^2 -> H(f(c), b)
28.54/9.35	   A^2 -> H(f(c), U1(e, d))
28.54/9.35	   A^2 -> H(f(c), U1(d, e))
28.54/9.35	   A^2 -> H(f(k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.35	   A^2 -> H(U1(k, k), f(c))
28.54/9.35	   A^2 -> H(U1(k, k), f(d))
28.54/9.35	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.35	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.35	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.35	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.35	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.35	   A^2 -> H(U1(k, d), f(e))
28.54/9.35	   A^2 -> H(U1(k, d), f(k))
28.54/9.35	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.35	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.35	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.35	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.35	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.35	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.35	   A^2 -> H(U1(d, k), f(e))
28.54/9.35	   A^2 -> H(U1(d, k), f(k))
28.54/9.35	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.35	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.35	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.35	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.35	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.35	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.35	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.35	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.35	   A^2 -> H(f(d), b)
28.54/9.35	   A^2 -> H(f(d), U1(e, d))
28.54/9.35	   A^2 -> H(f(d), U1(d, e))
28.54/9.35	   A^2 -> H(f(d), c)
28.54/9.35	   A^2 -> H(f(d), U1(e, k))
28.54/9.35	   A^2 -> H(f(d), U1(k, e))
28.54/9.35	   A^2 -> H(f(d), e)
28.54/9.35	   A^2 -> H(f(a), d)
28.54/9.35	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.35	   A^2 -> H(f(c), c)
28.54/9.35	   A^2 -> H(f(c), U1(e, k))
28.54/9.35	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.35	   A^2 -> H(f(c), U1(k, e))
28.54/9.35	   A^2 -> H(f(c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.35	   A^2 -> H(f(a), k)
28.54/9.35	   A^2 -> H(f(e), U1(e, e))
28.54/9.35	   A^2 -> H(f(c), e)
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.35	   A^2 -> H(f(d), U1(k, k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.35	   A^2 -> H(d, U1(b, b))
28.54/9.35	   A^2 -> H(d, f(c))
28.54/9.35	   A^2 -> H(d, f(d))
28.54/9.35	   A^2 -> H(a, U1(c, b))
28.54/9.35	   A^2 -> H(a, U1(d, b))
28.54/9.35	   A^2 -> H(a, U1(b, c))
28.54/9.35	   A^2 -> H(a, U1(b, d))
28.54/9.35	   A^2 -> H(a, U1(c, c))
28.54/9.35	   A^2 -> H(a, f(e))
28.54/9.35	   A^2 -> H(a, f(k))
28.54/9.35	   A^2 -> H(a, U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.35	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.35	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.35	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.35	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.35	   A^2 -> H(U1(e, d), f(e))
28.54/9.35	   A^2 -> H(U1(e, d), f(k))
28.54/9.35	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.35	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.35	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.35	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.35	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.35	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.35	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.35	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.35	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.35	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.35	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.35	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.35	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.35	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.35	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.35	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.35	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.35	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.35	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.35	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.35	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.35	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.35	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, a), b)
28.54/9.35	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.35	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.35	   A^2 -> H(U1(c, a), c)
28.54/9.35	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.35	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.35	   A^2 -> H(U1(c, a), e)
28.54/9.35	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.35	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.35	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.35	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.35	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.35	   A^2 -> H(U1(d, e), f(e))
28.54/9.35	   A^2 -> H(U1(d, e), f(k))
28.54/9.35	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.35	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.35	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.35	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.35	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.35	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.35	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.35	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.35	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.35	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.35	   A^2 -> H(U1(d, a), b)
28.54/9.35	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.35	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.35	   A^2 -> H(U1(d, a), c)
28.54/9.35	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.35	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.35	   A^2 -> H(U1(d, a), e)
28.54/9.35	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.35	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.35	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.35	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.35	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.35	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.35	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.35	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.35	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.35	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.35	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.35	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.35	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.35	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.35	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.35	   A^2 -> H(U1(a, c), b)
28.54/9.35	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.35	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.35	   A^2 -> H(U1(a, c), c)
28.54/9.35	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.35	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.35	   A^2 -> H(U1(a, c), e)
28.54/9.35	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, d), b)
28.54/9.35	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.35	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.35	   A^2 -> H(U1(a, d), c)
28.54/9.35	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.35	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.35	   A^2 -> H(U1(a, d), e)
28.54/9.35	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, a), d)
28.54/9.35	   A^2 -> H(U1(a, a), k)
28.54/9.35	   A^2 -> H(k, U1(b, b))
28.54/9.35	   A^2 -> H(k, f(c))
28.54/9.35	   A^2 -> H(k, f(d))
28.54/9.35	   A^2 -> H(c, U1(c, b))
28.54/9.35	   A^2 -> H(c, U1(d, b))
28.54/9.35	   A^2 -> H(c, U1(b, c))
28.54/9.35	   A^2 -> H(c, U1(b, d))
28.54/9.35	   A^2 -> H(c, U1(c, c))
28.54/9.35	   A^2 -> H(c, f(e))
28.54/9.35	   A^2 -> H(c, f(k))
28.54/9.35	   A^2 -> H(c, U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.35	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.35	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.35	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.35	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.35	   A^2 -> H(U1(e, k), f(e))
28.54/9.35	   A^2 -> H(U1(e, k), f(k))
28.54/9.35	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.35	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.35	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.35	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.35	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.35	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.35	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.35	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.35	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.35	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.35	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.35	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.35	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.35	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.35	   A^2 -> H(U1(k, e), f(e))
28.54/9.35	   A^2 -> H(U1(k, e), f(k))
28.54/9.35	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.35	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.35	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.35	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.35	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.35	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.35	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.35	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.35	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.35	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.35	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.35	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.35	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.35	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.35	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.35	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.35	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.35	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.35	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.35	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.35	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.35	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, c), b)
28.54/9.35	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.35	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.35	   A^2 -> H(U1(c, c), e)
28.54/9.35	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.35	   A^2 -> H(e, U1(c, b))
28.54/9.35	   A^2 -> H(e, U1(d, b))
28.54/9.35	   A^2 -> H(e, U1(b, c))
28.54/9.35	   A^2 -> H(e, U1(b, d))
28.54/9.35	   A^2 -> H(e, U1(c, c))
28.54/9.35	   A^2 -> H(e, f(e))
28.54/9.35	   A^2 -> H(e, f(k))
28.54/9.35	   A^2 -> H(e, U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.35	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.35	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.35	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.35	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.35	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.35	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.35	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.35	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.35	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.35	   A^2 -> H(f(e), b)
28.54/9.35	   A^2 -> H(f(e), U1(e, d))
28.54/9.35	   A^2 -> H(f(e), U1(d, e))
28.54/9.35	   A^2 -> H(f(e), c)
28.54/9.35	   A^2 -> H(f(e), U1(e, k))
28.54/9.35	   A^2 -> H(f(e), U1(k, e))
28.54/9.35	   A^2 -> H(f(e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.35	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.35	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.35	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.35	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.35	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.35	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.35	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.35	   A^2 -> H(f(k), b)
28.54/9.35	   A^2 -> H(f(k), U1(e, d))
28.54/9.35	   A^2 -> H(f(k), U1(d, e))
28.54/9.35	   A^2 -> H(f(k), c)
28.54/9.35	   A^2 -> H(f(k), U1(e, k))
28.54/9.35	   A^2 -> H(f(k), U1(k, e))
28.54/9.35	   A^2 -> H(f(k), e)
28.54/9.35	
28.54/9.35	The TRS R consists of the following rules:
28.54/9.35	
28.54/9.35	   f(x) -> U1(x, x)
28.54/9.35	   U1(e, x) -> x
28.54/9.35	   a -> c
28.54/9.35	   a -> d
28.54/9.35	   b -> c
28.54/9.35	   b -> d
28.54/9.35	   d -> k
28.54/9.35	   c -> e
28.54/9.35	   c -> k
28.54/9.35	
28.54/9.35	Q is empty.
28.54/9.35	We have to consider all minimal (P,Q,R)-chains.
28.54/9.35	----------------------------------------
28.54/9.35	
28.54/9.35	(975) TransformationProof (EQUIVALENT)
28.54/9.35	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.35	
28.54/9.35	   (A^2 -> H(U1(k, k), U1(k, d)),A^2 -> H(U1(k, k), U1(k, d)))
28.54/9.35	   (A^2 -> H(f(k), U1(k, k)),A^2 -> H(f(k), U1(k, k)))
28.54/9.35	
28.54/9.35	
28.54/9.35	----------------------------------------
28.54/9.35	
28.54/9.35	(976)
28.54/9.35	Obligation:
28.54/9.35	Q DP problem:
28.54/9.35	The TRS P consists of the following rules:
28.54/9.35	
28.54/9.35	   H(x, x) -> G(x, x, f(k))
28.54/9.35	   G(d, x, x) -> A^2
28.54/9.35	   A^2 -> H(f(c), f(c))
28.54/9.35	   A^2 -> H(f(d), f(d))
28.54/9.35	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.35	   A^2 -> H(f(e), f(e))
28.54/9.35	   A^2 -> H(f(k), f(k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.35	   A^2 -> H(f(k), U1(d, k))
28.54/9.35	   A^2 -> H(f(c), b)
28.54/9.35	   A^2 -> H(f(c), U1(e, d))
28.54/9.35	   A^2 -> H(f(c), U1(d, e))
28.54/9.35	   A^2 -> H(f(k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.35	   A^2 -> H(U1(k, k), f(c))
28.54/9.35	   A^2 -> H(U1(k, k), f(d))
28.54/9.35	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.35	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.35	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.35	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.35	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.35	   A^2 -> H(U1(k, d), f(e))
28.54/9.35	   A^2 -> H(U1(k, d), f(k))
28.54/9.35	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.35	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.35	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.35	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.35	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.35	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.35	   A^2 -> H(U1(d, k), f(e))
28.54/9.35	   A^2 -> H(U1(d, k), f(k))
28.54/9.35	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.35	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.35	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.35	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.35	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.35	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.35	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.35	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.35	   A^2 -> H(f(d), b)
28.54/9.35	   A^2 -> H(f(d), U1(e, d))
28.54/9.35	   A^2 -> H(f(d), U1(d, e))
28.54/9.35	   A^2 -> H(f(d), c)
28.54/9.35	   A^2 -> H(f(d), U1(e, k))
28.54/9.35	   A^2 -> H(f(d), U1(k, e))
28.54/9.35	   A^2 -> H(f(d), e)
28.54/9.35	   A^2 -> H(f(a), d)
28.54/9.35	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.35	   A^2 -> H(f(c), c)
28.54/9.35	   A^2 -> H(f(c), U1(e, k))
28.54/9.35	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.35	   A^2 -> H(f(c), U1(k, e))
28.54/9.35	   A^2 -> H(f(c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.35	   A^2 -> H(f(a), k)
28.54/9.35	   A^2 -> H(f(e), U1(e, e))
28.54/9.35	   A^2 -> H(f(c), e)
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.35	   A^2 -> H(f(d), U1(k, k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.35	   A^2 -> H(d, U1(b, b))
28.54/9.35	   A^2 -> H(d, f(c))
28.54/9.35	   A^2 -> H(d, f(d))
28.54/9.35	   A^2 -> H(a, U1(c, b))
28.54/9.35	   A^2 -> H(a, U1(d, b))
28.54/9.35	   A^2 -> H(a, U1(b, c))
28.54/9.35	   A^2 -> H(a, U1(b, d))
28.54/9.35	   A^2 -> H(a, U1(c, c))
28.54/9.35	   A^2 -> H(a, f(e))
28.54/9.35	   A^2 -> H(a, f(k))
28.54/9.35	   A^2 -> H(a, U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.35	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.35	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.35	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.35	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.35	   A^2 -> H(U1(e, d), f(e))
28.54/9.35	   A^2 -> H(U1(e, d), f(k))
28.54/9.35	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.35	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.35	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.35	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.35	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.35	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.35	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.35	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.35	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.35	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.35	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.35	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.35	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.35	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.35	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.35	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.35	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.35	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.35	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.35	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.35	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.35	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.35	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, a), b)
28.54/9.35	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.35	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.35	   A^2 -> H(U1(c, a), c)
28.54/9.35	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.35	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.35	   A^2 -> H(U1(c, a), e)
28.54/9.35	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.35	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.35	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.35	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.35	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.35	   A^2 -> H(U1(d, e), f(e))
28.54/9.35	   A^2 -> H(U1(d, e), f(k))
28.54/9.35	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.35	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.35	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.35	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.35	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.35	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.35	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.35	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.35	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.35	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.35	   A^2 -> H(U1(d, a), b)
28.54/9.35	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.35	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.35	   A^2 -> H(U1(d, a), c)
28.54/9.35	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.35	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.35	   A^2 -> H(U1(d, a), e)
28.54/9.35	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.35	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.35	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.35	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.35	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.35	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.35	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.35	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.35	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.35	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.35	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.35	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.35	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.35	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.35	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.35	   A^2 -> H(U1(a, c), b)
28.54/9.35	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.35	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.35	   A^2 -> H(U1(a, c), c)
28.54/9.35	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.35	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.35	   A^2 -> H(U1(a, c), e)
28.54/9.35	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, d), b)
28.54/9.35	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.35	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.35	   A^2 -> H(U1(a, d), c)
28.54/9.35	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.35	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.35	   A^2 -> H(U1(a, d), e)
28.54/9.35	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, a), d)
28.54/9.35	   A^2 -> H(U1(a, a), k)
28.54/9.35	   A^2 -> H(k, U1(b, b))
28.54/9.35	   A^2 -> H(k, f(c))
28.54/9.35	   A^2 -> H(k, f(d))
28.54/9.35	   A^2 -> H(c, U1(c, b))
28.54/9.35	   A^2 -> H(c, U1(d, b))
28.54/9.35	   A^2 -> H(c, U1(b, c))
28.54/9.35	   A^2 -> H(c, U1(b, d))
28.54/9.35	   A^2 -> H(c, U1(c, c))
28.54/9.35	   A^2 -> H(c, f(e))
28.54/9.35	   A^2 -> H(c, f(k))
28.54/9.35	   A^2 -> H(c, U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.35	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.35	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.35	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.35	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.35	   A^2 -> H(U1(e, k), f(e))
28.54/9.35	   A^2 -> H(U1(e, k), f(k))
28.54/9.35	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.35	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.35	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.35	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.35	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.35	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.35	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.35	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.35	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.35	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.35	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.35	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.35	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.35	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.35	   A^2 -> H(U1(k, e), f(e))
28.54/9.35	   A^2 -> H(U1(k, e), f(k))
28.54/9.35	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.35	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.35	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.35	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.35	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.35	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.35	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.35	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.35	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.35	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.35	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.35	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.35	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.35	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.35	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.35	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.35	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.35	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.35	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.35	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.35	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.35	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, c), b)
28.54/9.35	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.35	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.35	   A^2 -> H(U1(c, c), e)
28.54/9.35	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.35	   A^2 -> H(e, U1(c, b))
28.54/9.35	   A^2 -> H(e, U1(d, b))
28.54/9.35	   A^2 -> H(e, U1(b, c))
28.54/9.35	   A^2 -> H(e, U1(b, d))
28.54/9.35	   A^2 -> H(e, U1(c, c))
28.54/9.35	   A^2 -> H(e, f(e))
28.54/9.35	   A^2 -> H(e, f(k))
28.54/9.35	   A^2 -> H(e, U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.35	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.35	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.35	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.35	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.35	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.35	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.35	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.35	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.35	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.35	   A^2 -> H(f(e), b)
28.54/9.35	   A^2 -> H(f(e), U1(e, d))
28.54/9.35	   A^2 -> H(f(e), U1(d, e))
28.54/9.35	   A^2 -> H(f(e), c)
28.54/9.35	   A^2 -> H(f(e), U1(e, k))
28.54/9.35	   A^2 -> H(f(e), U1(k, e))
28.54/9.35	   A^2 -> H(f(e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.35	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.35	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.35	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.35	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.35	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.35	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.35	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.35	   A^2 -> H(f(k), b)
28.54/9.35	   A^2 -> H(f(k), U1(e, d))
28.54/9.35	   A^2 -> H(f(k), U1(d, e))
28.54/9.35	   A^2 -> H(f(k), c)
28.54/9.35	   A^2 -> H(f(k), U1(e, k))
28.54/9.35	   A^2 -> H(f(k), U1(k, e))
28.54/9.35	   A^2 -> H(f(k), e)
28.54/9.35	
28.54/9.35	The TRS R consists of the following rules:
28.54/9.35	
28.54/9.35	   f(x) -> U1(x, x)
28.54/9.35	   U1(e, x) -> x
28.54/9.35	   a -> c
28.54/9.35	   a -> d
28.54/9.35	   b -> c
28.54/9.35	   b -> d
28.54/9.35	   d -> k
28.54/9.35	   c -> e
28.54/9.35	   c -> k
28.54/9.35	
28.54/9.35	Q is empty.
28.54/9.35	We have to consider all minimal (P,Q,R)-chains.
28.54/9.35	----------------------------------------
28.54/9.35	
28.54/9.35	(977) TransformationProof (EQUIVALENT)
28.54/9.35	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.35	
28.54/9.35	   (A^2 -> H(U1(k, k), U1(d, k)),A^2 -> H(U1(k, k), U1(d, k)))
28.54/9.35	   (A^2 -> H(f(k), U1(k, k)),A^2 -> H(f(k), U1(k, k)))
28.54/9.35	
28.54/9.35	
28.54/9.35	----------------------------------------
28.54/9.35	
28.54/9.35	(978)
28.54/9.35	Obligation:
28.54/9.35	Q DP problem:
28.54/9.35	The TRS P consists of the following rules:
28.54/9.35	
28.54/9.35	   H(x, x) -> G(x, x, f(k))
28.54/9.35	   G(d, x, x) -> A^2
28.54/9.35	   A^2 -> H(f(c), f(c))
28.54/9.35	   A^2 -> H(f(d), f(d))
28.54/9.35	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.35	   A^2 -> H(f(e), f(e))
28.54/9.35	   A^2 -> H(f(k), f(k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.35	   A^2 -> H(f(c), b)
28.54/9.35	   A^2 -> H(f(c), U1(e, d))
28.54/9.35	   A^2 -> H(f(c), U1(d, e))
28.54/9.35	   A^2 -> H(f(k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.35	   A^2 -> H(U1(k, k), f(c))
28.54/9.35	   A^2 -> H(U1(k, k), f(d))
28.54/9.35	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.35	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.35	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.35	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.35	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.35	   A^2 -> H(U1(k, d), f(e))
28.54/9.35	   A^2 -> H(U1(k, d), f(k))
28.54/9.35	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.35	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.35	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.35	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.35	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.35	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.35	   A^2 -> H(U1(d, k), f(e))
28.54/9.35	   A^2 -> H(U1(d, k), f(k))
28.54/9.35	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.35	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.35	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.35	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.35	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.35	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.35	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.35	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.35	   A^2 -> H(f(d), b)
28.54/9.35	   A^2 -> H(f(d), U1(e, d))
28.54/9.35	   A^2 -> H(f(d), U1(d, e))
28.54/9.35	   A^2 -> H(f(d), c)
28.54/9.35	   A^2 -> H(f(d), U1(e, k))
28.54/9.35	   A^2 -> H(f(d), U1(k, e))
28.54/9.35	   A^2 -> H(f(d), e)
28.54/9.35	   A^2 -> H(f(a), d)
28.54/9.35	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.35	   A^2 -> H(f(c), c)
28.54/9.35	   A^2 -> H(f(c), U1(e, k))
28.54/9.35	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.35	   A^2 -> H(f(c), U1(k, e))
28.54/9.35	   A^2 -> H(f(c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.35	   A^2 -> H(f(a), k)
28.54/9.35	   A^2 -> H(f(e), U1(e, e))
28.54/9.35	   A^2 -> H(f(c), e)
28.54/9.35	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.35	   A^2 -> H(f(d), U1(k, k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.35	   A^2 -> H(d, U1(b, b))
28.54/9.35	   A^2 -> H(d, f(c))
28.54/9.35	   A^2 -> H(d, f(d))
28.54/9.35	   A^2 -> H(a, U1(c, b))
28.54/9.35	   A^2 -> H(a, U1(d, b))
28.54/9.35	   A^2 -> H(a, U1(b, c))
28.54/9.35	   A^2 -> H(a, U1(b, d))
28.54/9.35	   A^2 -> H(a, U1(c, c))
28.54/9.35	   A^2 -> H(a, f(e))
28.54/9.35	   A^2 -> H(a, f(k))
28.54/9.35	   A^2 -> H(a, U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.35	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.35	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.35	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.35	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.35	   A^2 -> H(U1(e, d), f(e))
28.54/9.35	   A^2 -> H(U1(e, d), f(k))
28.54/9.35	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.35	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.35	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.35	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.35	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.35	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.35	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.35	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.35	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.35	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.35	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.35	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.35	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.35	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.35	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.35	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.35	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.35	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.35	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.35	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.35	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.35	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.35	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, a), b)
28.54/9.35	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.35	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.35	   A^2 -> H(U1(c, a), c)
28.54/9.35	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.35	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.35	   A^2 -> H(U1(c, a), e)
28.54/9.35	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.35	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.35	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.35	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.35	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.35	   A^2 -> H(U1(d, e), f(e))
28.54/9.35	   A^2 -> H(U1(d, e), f(k))
28.54/9.35	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.35	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.35	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.35	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.35	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.35	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.35	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.35	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.35	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.35	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.35	   A^2 -> H(U1(d, a), b)
28.54/9.35	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.35	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.35	   A^2 -> H(U1(d, a), c)
28.54/9.35	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.35	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.35	   A^2 -> H(U1(d, a), e)
28.54/9.35	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.35	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.35	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.35	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.35	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.35	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.35	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.35	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.35	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.35	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.35	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.35	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.35	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.35	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.35	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.35	   A^2 -> H(U1(a, c), b)
28.54/9.35	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.35	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.35	   A^2 -> H(U1(a, c), c)
28.54/9.35	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.35	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.35	   A^2 -> H(U1(a, c), e)
28.54/9.35	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, d), b)
28.54/9.35	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.35	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.35	   A^2 -> H(U1(a, d), c)
28.54/9.35	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.35	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.35	   A^2 -> H(U1(a, d), e)
28.54/9.35	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.35	   A^2 -> H(U1(a, a), d)
28.54/9.35	   A^2 -> H(U1(a, a), k)
28.54/9.35	   A^2 -> H(k, U1(b, b))
28.54/9.35	   A^2 -> H(k, f(c))
28.54/9.35	   A^2 -> H(k, f(d))
28.54/9.35	   A^2 -> H(c, U1(c, b))
28.54/9.35	   A^2 -> H(c, U1(d, b))
28.54/9.35	   A^2 -> H(c, U1(b, c))
28.54/9.35	   A^2 -> H(c, U1(b, d))
28.54/9.35	   A^2 -> H(c, U1(c, c))
28.54/9.35	   A^2 -> H(c, f(e))
28.54/9.35	   A^2 -> H(c, f(k))
28.54/9.35	   A^2 -> H(c, U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.35	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.35	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.35	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.35	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.35	   A^2 -> H(U1(e, k), f(e))
28.54/9.35	   A^2 -> H(U1(e, k), f(k))
28.54/9.35	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.35	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.35	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.35	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.35	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.35	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.35	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.35	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.35	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.35	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.35	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.35	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.35	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.35	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.35	   A^2 -> H(U1(k, e), f(e))
28.54/9.35	   A^2 -> H(U1(k, e), f(k))
28.54/9.35	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.35	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.35	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.35	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.35	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.35	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.35	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.35	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.35	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.35	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.35	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.35	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.35	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.35	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.35	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.35	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.35	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.35	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.35	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.35	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.35	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.35	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.35	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.35	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.35	   A^2 -> H(U1(c, c), b)
28.54/9.35	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.35	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.35	   A^2 -> H(U1(c, c), e)
28.54/9.35	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.35	   A^2 -> H(e, U1(c, b))
28.54/9.35	   A^2 -> H(e, U1(d, b))
28.54/9.35	   A^2 -> H(e, U1(b, c))
28.54/9.35	   A^2 -> H(e, U1(b, d))
28.54/9.35	   A^2 -> H(e, U1(c, c))
28.54/9.35	   A^2 -> H(e, f(e))
28.54/9.35	   A^2 -> H(e, f(k))
28.54/9.35	   A^2 -> H(e, U1(d, d))
28.54/9.35	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.35	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.35	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.35	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.35	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.35	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.35	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.35	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.35	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.35	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.35	   A^2 -> H(f(e), b)
28.54/9.35	   A^2 -> H(f(e), U1(e, d))
28.54/9.35	   A^2 -> H(f(e), U1(d, e))
28.54/9.35	   A^2 -> H(f(e), c)
28.54/9.35	   A^2 -> H(f(e), U1(e, k))
28.54/9.35	   A^2 -> H(f(e), U1(k, e))
28.54/9.35	   A^2 -> H(f(e), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.35	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.35	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.35	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.35	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.35	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.35	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.35	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.35	   A^2 -> H(f(k), b)
28.54/9.35	   A^2 -> H(f(k), U1(e, d))
28.54/9.35	   A^2 -> H(f(k), U1(d, e))
28.54/9.35	   A^2 -> H(f(k), c)
28.54/9.35	   A^2 -> H(f(k), U1(e, k))
28.54/9.35	   A^2 -> H(f(k), U1(k, e))
28.54/9.35	   A^2 -> H(f(k), e)
28.54/9.35	
28.54/9.35	The TRS R consists of the following rules:
28.54/9.35	
28.54/9.35	   f(x) -> U1(x, x)
28.54/9.35	   U1(e, x) -> x
28.54/9.35	   a -> c
28.54/9.35	   a -> d
28.54/9.35	   b -> c
28.54/9.35	   b -> d
28.54/9.35	   d -> k
28.54/9.35	   c -> e
28.54/9.35	   c -> k
28.54/9.35	
28.54/9.35	Q is empty.
28.54/9.35	We have to consider all minimal (P,Q,R)-chains.
28.54/9.35	----------------------------------------
28.54/9.35	
28.54/9.35	(979) TransformationProof (EQUIVALENT)
28.54/9.35	By narrowing [LPAR04] the rule A^2 -> H(f(c), b) at position [] we obtained the following new rules [LPAR04]:
28.54/9.35	
28.54/9.35	   (A^2 -> H(U1(c, c), b),A^2 -> H(U1(c, c), b))
28.54/9.35	   (A^2 -> H(f(e), b),A^2 -> H(f(e), b))
28.54/9.35	   (A^2 -> H(f(k), b),A^2 -> H(f(k), b))
28.54/9.35	   (A^2 -> H(f(c), c),A^2 -> H(f(c), c))
28.54/9.35	   (A^2 -> H(f(c), d),A^2 -> H(f(c), d))
28.54/9.35	
28.54/9.35	
28.54/9.35	----------------------------------------
28.54/9.35	
28.54/9.35	(980)
28.54/9.35	Obligation:
28.54/9.35	Q DP problem:
28.54/9.35	The TRS P consists of the following rules:
28.54/9.35	
28.54/9.35	   H(x, x) -> G(x, x, f(k))
28.54/9.35	   G(d, x, x) -> A^2
28.54/9.35	   A^2 -> H(f(c), f(c))
28.54/9.35	   A^2 -> H(f(d), f(d))
28.54/9.35	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.35	   A^2 -> H(f(e), f(e))
28.54/9.35	   A^2 -> H(f(k), f(k))
28.54/9.35	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.35	   A^2 -> H(f(c), U1(e, d))
28.54/9.35	   A^2 -> H(f(c), U1(d, e))
28.54/9.35	   A^2 -> H(f(k), U1(k, k))
28.54/9.35	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.35	   A^2 -> H(U1(k, k), f(c))
28.54/9.35	   A^2 -> H(U1(k, k), f(d))
28.54/9.35	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.35	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.35	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.35	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.35	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.35	   A^2 -> H(U1(k, d), f(e))
28.54/9.35	   A^2 -> H(U1(k, d), f(k))
28.54/9.35	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.36	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.36	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.36	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.36	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.36	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.36	   A^2 -> H(U1(d, k), f(e))
28.54/9.36	   A^2 -> H(U1(d, k), f(k))
28.54/9.36	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.36	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.36	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.36	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.36	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.36	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.36	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.36	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.36	   A^2 -> H(f(d), b)
28.54/9.36	   A^2 -> H(f(d), U1(e, d))
28.54/9.36	   A^2 -> H(f(d), U1(d, e))
28.54/9.36	   A^2 -> H(f(d), c)
28.54/9.36	   A^2 -> H(f(d), U1(e, k))
28.54/9.36	   A^2 -> H(f(d), U1(k, e))
28.54/9.36	   A^2 -> H(f(d), e)
28.54/9.36	   A^2 -> H(f(a), d)
28.54/9.36	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.36	   A^2 -> H(f(c), c)
28.54/9.36	   A^2 -> H(f(c), U1(e, k))
28.54/9.36	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.36	   A^2 -> H(f(c), U1(k, e))
28.54/9.36	   A^2 -> H(f(c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.36	   A^2 -> H(f(a), k)
28.54/9.36	   A^2 -> H(f(e), U1(e, e))
28.54/9.36	   A^2 -> H(f(c), e)
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.36	   A^2 -> H(f(d), U1(k, k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.36	   A^2 -> H(d, U1(b, b))
28.54/9.36	   A^2 -> H(d, f(c))
28.54/9.36	   A^2 -> H(d, f(d))
28.54/9.36	   A^2 -> H(a, U1(c, b))
28.54/9.36	   A^2 -> H(a, U1(d, b))
28.54/9.36	   A^2 -> H(a, U1(b, c))
28.54/9.36	   A^2 -> H(a, U1(b, d))
28.54/9.36	   A^2 -> H(a, U1(c, c))
28.54/9.36	   A^2 -> H(a, f(e))
28.54/9.36	   A^2 -> H(a, f(k))
28.54/9.36	   A^2 -> H(a, U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.36	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.36	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.36	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.36	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.36	   A^2 -> H(U1(e, d), f(e))
28.54/9.36	   A^2 -> H(U1(e, d), f(k))
28.54/9.36	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.36	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.36	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.36	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.36	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.36	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.36	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.36	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.36	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.36	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.36	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.36	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.36	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.36	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.36	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.36	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.36	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.36	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.36	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.36	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.36	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.36	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.36	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, a), b)
28.54/9.36	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.36	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.36	   A^2 -> H(U1(c, a), c)
28.54/9.36	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.36	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.36	   A^2 -> H(U1(c, a), e)
28.54/9.36	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.36	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.36	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.36	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.36	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.36	   A^2 -> H(U1(d, e), f(e))
28.54/9.36	   A^2 -> H(U1(d, e), f(k))
28.54/9.36	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.36	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.36	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.36	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.36	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.36	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.36	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.36	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.36	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.36	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.36	   A^2 -> H(U1(d, a), b)
28.54/9.36	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.36	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.36	   A^2 -> H(U1(d, a), c)
28.54/9.36	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.36	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.36	   A^2 -> H(U1(d, a), e)
28.54/9.36	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.36	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.36	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.36	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.36	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.36	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.36	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.36	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.36	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.36	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.36	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.36	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.36	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.36	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.36	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.36	   A^2 -> H(U1(a, c), b)
28.54/9.36	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.36	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.36	   A^2 -> H(U1(a, c), c)
28.54/9.36	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.36	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.36	   A^2 -> H(U1(a, c), e)
28.54/9.36	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, d), b)
28.54/9.36	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.36	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.36	   A^2 -> H(U1(a, d), c)
28.54/9.36	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.36	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.36	   A^2 -> H(U1(a, d), e)
28.54/9.36	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, a), d)
28.54/9.36	   A^2 -> H(U1(a, a), k)
28.54/9.36	   A^2 -> H(k, U1(b, b))
28.54/9.36	   A^2 -> H(k, f(c))
28.54/9.36	   A^2 -> H(k, f(d))
28.54/9.36	   A^2 -> H(c, U1(c, b))
28.54/9.36	   A^2 -> H(c, U1(d, b))
28.54/9.36	   A^2 -> H(c, U1(b, c))
28.54/9.36	   A^2 -> H(c, U1(b, d))
28.54/9.36	   A^2 -> H(c, U1(c, c))
28.54/9.36	   A^2 -> H(c, f(e))
28.54/9.36	   A^2 -> H(c, f(k))
28.54/9.36	   A^2 -> H(c, U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.36	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.36	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.36	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.36	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.36	   A^2 -> H(U1(e, k), f(e))
28.54/9.36	   A^2 -> H(U1(e, k), f(k))
28.54/9.36	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.36	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.36	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.36	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.36	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.36	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.36	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.36	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.36	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.36	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.36	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.36	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.36	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.36	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.36	   A^2 -> H(U1(k, e), f(e))
28.54/9.36	   A^2 -> H(U1(k, e), f(k))
28.54/9.36	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.36	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.36	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.36	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.36	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.36	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.36	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.36	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.36	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.36	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.36	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.36	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.36	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.36	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.36	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.36	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.36	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.36	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.36	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.36	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.36	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.36	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, c), b)
28.54/9.36	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.36	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.36	   A^2 -> H(U1(c, c), e)
28.54/9.36	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.36	   A^2 -> H(e, U1(c, b))
28.54/9.36	   A^2 -> H(e, U1(d, b))
28.54/9.36	   A^2 -> H(e, U1(b, c))
28.54/9.36	   A^2 -> H(e, U1(b, d))
28.54/9.36	   A^2 -> H(e, U1(c, c))
28.54/9.36	   A^2 -> H(e, f(e))
28.54/9.36	   A^2 -> H(e, f(k))
28.54/9.36	   A^2 -> H(e, U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.36	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.36	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.36	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.36	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.36	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.36	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.36	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.36	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.36	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.36	   A^2 -> H(f(e), b)
28.54/9.36	   A^2 -> H(f(e), U1(e, d))
28.54/9.36	   A^2 -> H(f(e), U1(d, e))
28.54/9.36	   A^2 -> H(f(e), c)
28.54/9.36	   A^2 -> H(f(e), U1(e, k))
28.54/9.36	   A^2 -> H(f(e), U1(k, e))
28.54/9.36	   A^2 -> H(f(e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.36	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.36	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.36	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.36	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.36	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.36	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.36	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.36	   A^2 -> H(f(k), b)
28.54/9.36	   A^2 -> H(f(k), U1(e, d))
28.54/9.36	   A^2 -> H(f(k), U1(d, e))
28.54/9.36	   A^2 -> H(f(k), c)
28.54/9.36	   A^2 -> H(f(k), U1(e, k))
28.54/9.36	   A^2 -> H(f(k), U1(k, e))
28.54/9.36	   A^2 -> H(f(k), e)
28.54/9.36	   A^2 -> H(f(c), d)
28.54/9.36	
28.54/9.36	The TRS R consists of the following rules:
28.54/9.36	
28.54/9.36	   f(x) -> U1(x, x)
28.54/9.36	   U1(e, x) -> x
28.54/9.36	   a -> c
28.54/9.36	   a -> d
28.54/9.36	   b -> c
28.54/9.36	   b -> d
28.54/9.36	   d -> k
28.54/9.36	   c -> e
28.54/9.36	   c -> k
28.54/9.36	
28.54/9.36	Q is empty.
28.54/9.36	We have to consider all minimal (P,Q,R)-chains.
28.54/9.36	----------------------------------------
28.54/9.36	
28.54/9.36	(981) TransformationProof (EQUIVALENT)
28.54/9.36	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.36	
28.54/9.36	   (A^2 -> H(U1(c, c), U1(e, d)),A^2 -> H(U1(c, c), U1(e, d)))
28.54/9.36	   (A^2 -> H(f(e), U1(e, d)),A^2 -> H(f(e), U1(e, d)))
28.54/9.36	   (A^2 -> H(f(k), U1(e, d)),A^2 -> H(f(k), U1(e, d)))
28.54/9.36	   (A^2 -> H(f(c), d),A^2 -> H(f(c), d))
28.54/9.36	   (A^2 -> H(f(c), U1(e, k)),A^2 -> H(f(c), U1(e, k)))
28.54/9.36	
28.54/9.36	
28.54/9.36	----------------------------------------
28.54/9.36	
28.54/9.36	(982)
28.54/9.36	Obligation:
28.54/9.36	Q DP problem:
28.54/9.36	The TRS P consists of the following rules:
28.54/9.36	
28.54/9.36	   H(x, x) -> G(x, x, f(k))
28.54/9.36	   G(d, x, x) -> A^2
28.54/9.36	   A^2 -> H(f(c), f(c))
28.54/9.36	   A^2 -> H(f(d), f(d))
28.54/9.36	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.36	   A^2 -> H(f(e), f(e))
28.54/9.36	   A^2 -> H(f(k), f(k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.36	   A^2 -> H(f(c), U1(d, e))
28.54/9.36	   A^2 -> H(f(k), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.36	   A^2 -> H(U1(k, k), f(c))
28.54/9.36	   A^2 -> H(U1(k, k), f(d))
28.54/9.36	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.36	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.36	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.36	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.36	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.36	   A^2 -> H(U1(k, d), f(e))
28.54/9.36	   A^2 -> H(U1(k, d), f(k))
28.54/9.36	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.36	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.36	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.36	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.36	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.36	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.36	   A^2 -> H(U1(d, k), f(e))
28.54/9.36	   A^2 -> H(U1(d, k), f(k))
28.54/9.36	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.36	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.36	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.36	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.36	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.36	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.36	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.36	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.36	   A^2 -> H(f(d), b)
28.54/9.36	   A^2 -> H(f(d), U1(e, d))
28.54/9.36	   A^2 -> H(f(d), U1(d, e))
28.54/9.36	   A^2 -> H(f(d), c)
28.54/9.36	   A^2 -> H(f(d), U1(e, k))
28.54/9.36	   A^2 -> H(f(d), U1(k, e))
28.54/9.36	   A^2 -> H(f(d), e)
28.54/9.36	   A^2 -> H(f(a), d)
28.54/9.36	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.36	   A^2 -> H(f(c), c)
28.54/9.36	   A^2 -> H(f(c), U1(e, k))
28.54/9.36	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.36	   A^2 -> H(f(c), U1(k, e))
28.54/9.36	   A^2 -> H(f(c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.36	   A^2 -> H(f(a), k)
28.54/9.36	   A^2 -> H(f(e), U1(e, e))
28.54/9.36	   A^2 -> H(f(c), e)
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.36	   A^2 -> H(f(d), U1(k, k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.36	   A^2 -> H(d, U1(b, b))
28.54/9.36	   A^2 -> H(d, f(c))
28.54/9.36	   A^2 -> H(d, f(d))
28.54/9.36	   A^2 -> H(a, U1(c, b))
28.54/9.36	   A^2 -> H(a, U1(d, b))
28.54/9.36	   A^2 -> H(a, U1(b, c))
28.54/9.36	   A^2 -> H(a, U1(b, d))
28.54/9.36	   A^2 -> H(a, U1(c, c))
28.54/9.36	   A^2 -> H(a, f(e))
28.54/9.36	   A^2 -> H(a, f(k))
28.54/9.36	   A^2 -> H(a, U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.36	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.36	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.36	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.36	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.36	   A^2 -> H(U1(e, d), f(e))
28.54/9.36	   A^2 -> H(U1(e, d), f(k))
28.54/9.36	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.36	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.36	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.36	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.36	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.36	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.36	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.36	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.36	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.36	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.36	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.36	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.36	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.36	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.36	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.36	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.36	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.36	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.36	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.36	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.36	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.36	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.36	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, a), b)
28.54/9.36	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.36	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.36	   A^2 -> H(U1(c, a), c)
28.54/9.36	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.36	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.36	   A^2 -> H(U1(c, a), e)
28.54/9.36	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.36	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.36	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.36	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.36	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.36	   A^2 -> H(U1(d, e), f(e))
28.54/9.36	   A^2 -> H(U1(d, e), f(k))
28.54/9.36	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.36	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.36	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.36	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.36	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.36	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.36	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.36	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.36	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.36	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.36	   A^2 -> H(U1(d, a), b)
28.54/9.36	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.36	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.36	   A^2 -> H(U1(d, a), c)
28.54/9.36	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.36	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.36	   A^2 -> H(U1(d, a), e)
28.54/9.36	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.36	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.36	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.36	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.36	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.36	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.36	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.36	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.36	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.36	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.36	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.36	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.36	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.36	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.36	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.36	   A^2 -> H(U1(a, c), b)
28.54/9.36	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.36	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.36	   A^2 -> H(U1(a, c), c)
28.54/9.36	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.36	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.36	   A^2 -> H(U1(a, c), e)
28.54/9.36	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, d), b)
28.54/9.36	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.36	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.36	   A^2 -> H(U1(a, d), c)
28.54/9.36	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.36	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.36	   A^2 -> H(U1(a, d), e)
28.54/9.36	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, a), d)
28.54/9.36	   A^2 -> H(U1(a, a), k)
28.54/9.36	   A^2 -> H(k, U1(b, b))
28.54/9.36	   A^2 -> H(k, f(c))
28.54/9.36	   A^2 -> H(k, f(d))
28.54/9.36	   A^2 -> H(c, U1(c, b))
28.54/9.36	   A^2 -> H(c, U1(d, b))
28.54/9.36	   A^2 -> H(c, U1(b, c))
28.54/9.36	   A^2 -> H(c, U1(b, d))
28.54/9.36	   A^2 -> H(c, U1(c, c))
28.54/9.36	   A^2 -> H(c, f(e))
28.54/9.36	   A^2 -> H(c, f(k))
28.54/9.36	   A^2 -> H(c, U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.36	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.36	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.36	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.36	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.36	   A^2 -> H(U1(e, k), f(e))
28.54/9.36	   A^2 -> H(U1(e, k), f(k))
28.54/9.36	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.36	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.36	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.36	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.36	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.36	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.36	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.36	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.36	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.36	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.36	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.36	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.36	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.36	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.36	   A^2 -> H(U1(k, e), f(e))
28.54/9.36	   A^2 -> H(U1(k, e), f(k))
28.54/9.36	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.36	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.36	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.36	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.36	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.36	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.36	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.36	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.36	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.36	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.36	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.36	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.36	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.36	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.36	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.36	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.36	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.36	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.36	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.36	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.36	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.36	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, c), b)
28.54/9.36	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.36	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.36	   A^2 -> H(U1(c, c), e)
28.54/9.36	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.36	   A^2 -> H(e, U1(c, b))
28.54/9.36	   A^2 -> H(e, U1(d, b))
28.54/9.36	   A^2 -> H(e, U1(b, c))
28.54/9.36	   A^2 -> H(e, U1(b, d))
28.54/9.36	   A^2 -> H(e, U1(c, c))
28.54/9.36	   A^2 -> H(e, f(e))
28.54/9.36	   A^2 -> H(e, f(k))
28.54/9.36	   A^2 -> H(e, U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.36	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.36	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.36	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.36	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.36	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.36	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.36	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.36	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.36	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.36	   A^2 -> H(f(e), b)
28.54/9.36	   A^2 -> H(f(e), U1(e, d))
28.54/9.36	   A^2 -> H(f(e), U1(d, e))
28.54/9.36	   A^2 -> H(f(e), c)
28.54/9.36	   A^2 -> H(f(e), U1(e, k))
28.54/9.36	   A^2 -> H(f(e), U1(k, e))
28.54/9.36	   A^2 -> H(f(e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.36	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.36	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.36	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.36	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.36	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.36	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.36	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.36	   A^2 -> H(f(k), b)
28.54/9.36	   A^2 -> H(f(k), U1(e, d))
28.54/9.36	   A^2 -> H(f(k), U1(d, e))
28.54/9.36	   A^2 -> H(f(k), c)
28.54/9.36	   A^2 -> H(f(k), U1(e, k))
28.54/9.36	   A^2 -> H(f(k), U1(k, e))
28.54/9.36	   A^2 -> H(f(k), e)
28.54/9.36	   A^2 -> H(f(c), d)
28.54/9.36	
28.54/9.36	The TRS R consists of the following rules:
28.54/9.36	
28.54/9.36	   f(x) -> U1(x, x)
28.54/9.36	   U1(e, x) -> x
28.54/9.36	   a -> c
28.54/9.36	   a -> d
28.54/9.36	   b -> c
28.54/9.36	   b -> d
28.54/9.36	   d -> k
28.54/9.36	   c -> e
28.54/9.36	   c -> k
28.54/9.36	
28.54/9.36	Q is empty.
28.54/9.36	We have to consider all minimal (P,Q,R)-chains.
28.54/9.36	----------------------------------------
28.54/9.36	
28.54/9.36	(983) TransformationProof (EQUIVALENT)
28.54/9.36	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.36	
28.54/9.36	   (A^2 -> H(U1(c, c), U1(d, e)),A^2 -> H(U1(c, c), U1(d, e)))
28.54/9.36	   (A^2 -> H(f(e), U1(d, e)),A^2 -> H(f(e), U1(d, e)))
28.54/9.36	   (A^2 -> H(f(k), U1(d, e)),A^2 -> H(f(k), U1(d, e)))
28.54/9.36	   (A^2 -> H(f(c), U1(k, e)),A^2 -> H(f(c), U1(k, e)))
28.54/9.36	
28.54/9.36	
28.54/9.36	----------------------------------------
28.54/9.36	
28.54/9.36	(984)
28.54/9.36	Obligation:
28.54/9.36	Q DP problem:
28.54/9.36	The TRS P consists of the following rules:
28.54/9.36	
28.54/9.36	   H(x, x) -> G(x, x, f(k))
28.54/9.36	   G(d, x, x) -> A^2
28.54/9.36	   A^2 -> H(f(c), f(c))
28.54/9.36	   A^2 -> H(f(d), f(d))
28.54/9.36	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.36	   A^2 -> H(f(e), f(e))
28.54/9.36	   A^2 -> H(f(k), f(k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.36	   A^2 -> H(f(k), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.36	   A^2 -> H(U1(k, k), f(c))
28.54/9.36	   A^2 -> H(U1(k, k), f(d))
28.54/9.36	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.36	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.36	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.36	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.36	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.36	   A^2 -> H(U1(k, d), f(e))
28.54/9.36	   A^2 -> H(U1(k, d), f(k))
28.54/9.36	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.36	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.36	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.36	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.36	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.36	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.36	   A^2 -> H(U1(d, k), f(e))
28.54/9.36	   A^2 -> H(U1(d, k), f(k))
28.54/9.36	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.36	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.36	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.36	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.36	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.36	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.36	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.36	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.36	   A^2 -> H(f(d), b)
28.54/9.36	   A^2 -> H(f(d), U1(e, d))
28.54/9.36	   A^2 -> H(f(d), U1(d, e))
28.54/9.36	   A^2 -> H(f(d), c)
28.54/9.36	   A^2 -> H(f(d), U1(e, k))
28.54/9.36	   A^2 -> H(f(d), U1(k, e))
28.54/9.36	   A^2 -> H(f(d), e)
28.54/9.36	   A^2 -> H(f(a), d)
28.54/9.36	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.36	   A^2 -> H(f(c), c)
28.54/9.36	   A^2 -> H(f(c), U1(e, k))
28.54/9.36	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.36	   A^2 -> H(f(c), U1(k, e))
28.54/9.36	   A^2 -> H(f(c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.36	   A^2 -> H(f(a), k)
28.54/9.36	   A^2 -> H(f(e), U1(e, e))
28.54/9.36	   A^2 -> H(f(c), e)
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.36	   A^2 -> H(f(d), U1(k, k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.36	   A^2 -> H(d, U1(b, b))
28.54/9.36	   A^2 -> H(d, f(c))
28.54/9.36	   A^2 -> H(d, f(d))
28.54/9.36	   A^2 -> H(a, U1(c, b))
28.54/9.36	   A^2 -> H(a, U1(d, b))
28.54/9.36	   A^2 -> H(a, U1(b, c))
28.54/9.36	   A^2 -> H(a, U1(b, d))
28.54/9.36	   A^2 -> H(a, U1(c, c))
28.54/9.36	   A^2 -> H(a, f(e))
28.54/9.36	   A^2 -> H(a, f(k))
28.54/9.36	   A^2 -> H(a, U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.36	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.36	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.36	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.36	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.36	   A^2 -> H(U1(e, d), f(e))
28.54/9.36	   A^2 -> H(U1(e, d), f(k))
28.54/9.36	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.36	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.36	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.36	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.36	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.36	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.36	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.36	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.36	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.36	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.36	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.36	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.36	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.36	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.36	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.36	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.36	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.36	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.36	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.36	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.36	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.36	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.36	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, a), b)
28.54/9.36	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.36	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.36	   A^2 -> H(U1(c, a), c)
28.54/9.36	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.36	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.36	   A^2 -> H(U1(c, a), e)
28.54/9.36	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.36	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.36	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.36	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.36	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.36	   A^2 -> H(U1(d, e), f(e))
28.54/9.36	   A^2 -> H(U1(d, e), f(k))
28.54/9.36	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.36	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.36	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.36	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.36	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.36	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.36	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.36	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.36	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.36	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.36	   A^2 -> H(U1(d, a), b)
28.54/9.36	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.36	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.36	   A^2 -> H(U1(d, a), c)
28.54/9.36	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.36	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.36	   A^2 -> H(U1(d, a), e)
28.54/9.36	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.36	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.36	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.36	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.36	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.36	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.36	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.36	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.36	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.36	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.36	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.36	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.36	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.36	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.36	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.36	   A^2 -> H(U1(a, c), b)
28.54/9.36	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.36	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.36	   A^2 -> H(U1(a, c), c)
28.54/9.36	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.36	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.36	   A^2 -> H(U1(a, c), e)
28.54/9.36	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, d), b)
28.54/9.36	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.36	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.36	   A^2 -> H(U1(a, d), c)
28.54/9.36	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.36	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.36	   A^2 -> H(U1(a, d), e)
28.54/9.36	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, a), d)
28.54/9.36	   A^2 -> H(U1(a, a), k)
28.54/9.36	   A^2 -> H(k, U1(b, b))
28.54/9.36	   A^2 -> H(k, f(c))
28.54/9.36	   A^2 -> H(k, f(d))
28.54/9.36	   A^2 -> H(c, U1(c, b))
28.54/9.36	   A^2 -> H(c, U1(d, b))
28.54/9.36	   A^2 -> H(c, U1(b, c))
28.54/9.36	   A^2 -> H(c, U1(b, d))
28.54/9.36	   A^2 -> H(c, U1(c, c))
28.54/9.36	   A^2 -> H(c, f(e))
28.54/9.36	   A^2 -> H(c, f(k))
28.54/9.36	   A^2 -> H(c, U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.36	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.36	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.36	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.36	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.36	   A^2 -> H(U1(e, k), f(e))
28.54/9.36	   A^2 -> H(U1(e, k), f(k))
28.54/9.36	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.36	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.36	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.36	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.36	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.36	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.36	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.36	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.36	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.36	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.36	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.36	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.36	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.36	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.36	   A^2 -> H(U1(k, e), f(e))
28.54/9.36	   A^2 -> H(U1(k, e), f(k))
28.54/9.36	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.36	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.36	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.36	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.36	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.36	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.36	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.36	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.36	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.36	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.36	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.36	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.36	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.36	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.36	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.36	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.36	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.36	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.36	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.36	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.36	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.36	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, c), b)
28.54/9.36	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.36	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.36	   A^2 -> H(U1(c, c), e)
28.54/9.36	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.36	   A^2 -> H(e, U1(c, b))
28.54/9.36	   A^2 -> H(e, U1(d, b))
28.54/9.36	   A^2 -> H(e, U1(b, c))
28.54/9.36	   A^2 -> H(e, U1(b, d))
28.54/9.36	   A^2 -> H(e, U1(c, c))
28.54/9.36	   A^2 -> H(e, f(e))
28.54/9.36	   A^2 -> H(e, f(k))
28.54/9.36	   A^2 -> H(e, U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.36	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.36	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.36	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.36	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.36	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.36	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.36	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.36	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.36	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.36	   A^2 -> H(f(e), b)
28.54/9.36	   A^2 -> H(f(e), U1(e, d))
28.54/9.36	   A^2 -> H(f(e), U1(d, e))
28.54/9.36	   A^2 -> H(f(e), c)
28.54/9.36	   A^2 -> H(f(e), U1(e, k))
28.54/9.36	   A^2 -> H(f(e), U1(k, e))
28.54/9.36	   A^2 -> H(f(e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.36	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.36	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.36	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.36	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.36	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.36	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.36	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.36	   A^2 -> H(f(k), b)
28.54/9.36	   A^2 -> H(f(k), U1(e, d))
28.54/9.36	   A^2 -> H(f(k), U1(d, e))
28.54/9.36	   A^2 -> H(f(k), c)
28.54/9.36	   A^2 -> H(f(k), U1(e, k))
28.54/9.36	   A^2 -> H(f(k), U1(k, e))
28.54/9.36	   A^2 -> H(f(k), e)
28.54/9.36	   A^2 -> H(f(c), d)
28.54/9.36	
28.54/9.36	The TRS R consists of the following rules:
28.54/9.36	
28.54/9.36	   f(x) -> U1(x, x)
28.54/9.36	   U1(e, x) -> x
28.54/9.36	   a -> c
28.54/9.36	   a -> d
28.54/9.36	   b -> c
28.54/9.36	   b -> d
28.54/9.36	   d -> k
28.54/9.36	   c -> e
28.54/9.36	   c -> k
28.54/9.36	
28.54/9.36	Q is empty.
28.54/9.36	We have to consider all minimal (P,Q,R)-chains.
28.54/9.36	----------------------------------------
28.54/9.36	
28.54/9.36	(985) TransformationProof (EQUIVALENT)
28.54/9.36	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.36	
28.54/9.36	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.54/9.36	
28.54/9.36	
28.54/9.36	----------------------------------------
28.54/9.36	
28.54/9.36	(986)
28.54/9.36	Obligation:
28.54/9.36	Q DP problem:
28.54/9.36	The TRS P consists of the following rules:
28.54/9.36	
28.54/9.36	   H(x, x) -> G(x, x, f(k))
28.54/9.36	   G(d, x, x) -> A^2
28.54/9.36	   A^2 -> H(f(c), f(c))
28.54/9.36	   A^2 -> H(f(d), f(d))
28.54/9.36	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.36	   A^2 -> H(f(e), f(e))
28.54/9.36	   A^2 -> H(f(k), f(k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.36	   A^2 -> H(U1(k, k), U1(b, b))
28.54/9.36	   A^2 -> H(U1(k, k), f(c))
28.54/9.36	   A^2 -> H(U1(k, k), f(d))
28.54/9.36	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.36	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.36	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.36	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.36	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.36	   A^2 -> H(U1(k, d), f(e))
28.54/9.36	   A^2 -> H(U1(k, d), f(k))
28.54/9.36	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.36	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.36	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.36	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.36	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.36	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.36	   A^2 -> H(U1(d, k), f(e))
28.54/9.36	   A^2 -> H(U1(d, k), f(k))
28.54/9.36	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.36	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.36	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.36	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.36	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.36	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.36	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.36	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.36	   A^2 -> H(f(d), b)
28.54/9.36	   A^2 -> H(f(d), U1(e, d))
28.54/9.36	   A^2 -> H(f(d), U1(d, e))
28.54/9.36	   A^2 -> H(f(d), c)
28.54/9.36	   A^2 -> H(f(d), U1(e, k))
28.54/9.36	   A^2 -> H(f(d), U1(k, e))
28.54/9.36	   A^2 -> H(f(d), e)
28.54/9.36	   A^2 -> H(f(a), d)
28.54/9.36	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.36	   A^2 -> H(f(c), c)
28.54/9.36	   A^2 -> H(f(c), U1(e, k))
28.54/9.36	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.36	   A^2 -> H(f(c), U1(k, e))
28.54/9.36	   A^2 -> H(f(c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.36	   A^2 -> H(f(a), k)
28.54/9.36	   A^2 -> H(f(e), U1(e, e))
28.54/9.36	   A^2 -> H(f(c), e)
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.36	   A^2 -> H(f(d), U1(k, k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.36	   A^2 -> H(d, U1(b, b))
28.54/9.36	   A^2 -> H(d, f(c))
28.54/9.36	   A^2 -> H(d, f(d))
28.54/9.36	   A^2 -> H(a, U1(c, b))
28.54/9.36	   A^2 -> H(a, U1(d, b))
28.54/9.36	   A^2 -> H(a, U1(b, c))
28.54/9.36	   A^2 -> H(a, U1(b, d))
28.54/9.36	   A^2 -> H(a, U1(c, c))
28.54/9.36	   A^2 -> H(a, f(e))
28.54/9.36	   A^2 -> H(a, f(k))
28.54/9.36	   A^2 -> H(a, U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.36	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.36	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.36	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.36	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.36	   A^2 -> H(U1(e, d), f(e))
28.54/9.36	   A^2 -> H(U1(e, d), f(k))
28.54/9.36	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.36	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.36	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.36	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.36	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.36	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.36	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.36	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.36	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.36	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.36	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.36	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.36	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.36	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.36	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.36	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.36	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.36	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.36	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.36	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.36	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.36	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.36	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, a), b)
28.54/9.36	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.36	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.36	   A^2 -> H(U1(c, a), c)
28.54/9.36	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.36	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.36	   A^2 -> H(U1(c, a), e)
28.54/9.36	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.36	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.36	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.36	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.36	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.36	   A^2 -> H(U1(d, e), f(e))
28.54/9.36	   A^2 -> H(U1(d, e), f(k))
28.54/9.36	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.36	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.36	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.36	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.36	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.36	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.36	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.36	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.36	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.36	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.36	   A^2 -> H(U1(d, a), b)
28.54/9.36	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.36	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.36	   A^2 -> H(U1(d, a), c)
28.54/9.36	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.36	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.36	   A^2 -> H(U1(d, a), e)
28.54/9.36	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.36	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.36	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.36	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.36	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.36	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.36	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.36	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.36	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.36	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.36	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.36	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.36	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.36	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.36	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.36	   A^2 -> H(U1(a, c), b)
28.54/9.36	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.36	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.36	   A^2 -> H(U1(a, c), c)
28.54/9.36	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.36	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.36	   A^2 -> H(U1(a, c), e)
28.54/9.36	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, d), b)
28.54/9.36	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.36	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.36	   A^2 -> H(U1(a, d), c)
28.54/9.36	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.36	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.36	   A^2 -> H(U1(a, d), e)
28.54/9.36	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, a), d)
28.54/9.36	   A^2 -> H(U1(a, a), k)
28.54/9.36	   A^2 -> H(k, U1(b, b))
28.54/9.36	   A^2 -> H(k, f(c))
28.54/9.36	   A^2 -> H(k, f(d))
28.54/9.36	   A^2 -> H(c, U1(c, b))
28.54/9.36	   A^2 -> H(c, U1(d, b))
28.54/9.36	   A^2 -> H(c, U1(b, c))
28.54/9.36	   A^2 -> H(c, U1(b, d))
28.54/9.36	   A^2 -> H(c, U1(c, c))
28.54/9.36	   A^2 -> H(c, f(e))
28.54/9.36	   A^2 -> H(c, f(k))
28.54/9.36	   A^2 -> H(c, U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.36	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.36	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.36	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.36	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.36	   A^2 -> H(U1(e, k), f(e))
28.54/9.36	   A^2 -> H(U1(e, k), f(k))
28.54/9.36	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.36	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.36	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.36	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.36	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.36	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.36	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.36	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.36	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.36	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.36	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.36	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.36	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.36	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.36	   A^2 -> H(U1(k, e), f(e))
28.54/9.36	   A^2 -> H(U1(k, e), f(k))
28.54/9.36	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.36	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.36	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.36	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.36	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.36	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.36	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.36	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.36	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.36	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.36	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.36	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.36	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.36	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.36	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.36	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.36	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.36	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.36	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.36	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.36	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.36	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, c), b)
28.54/9.36	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.36	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.36	   A^2 -> H(U1(c, c), e)
28.54/9.36	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.36	   A^2 -> H(e, U1(c, b))
28.54/9.36	   A^2 -> H(e, U1(d, b))
28.54/9.36	   A^2 -> H(e, U1(b, c))
28.54/9.36	   A^2 -> H(e, U1(b, d))
28.54/9.36	   A^2 -> H(e, U1(c, c))
28.54/9.36	   A^2 -> H(e, f(e))
28.54/9.36	   A^2 -> H(e, f(k))
28.54/9.36	   A^2 -> H(e, U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.36	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.36	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.36	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.36	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.36	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.36	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.36	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.36	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.36	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.36	   A^2 -> H(f(e), b)
28.54/9.36	   A^2 -> H(f(e), U1(e, d))
28.54/9.36	   A^2 -> H(f(e), U1(d, e))
28.54/9.36	   A^2 -> H(f(e), c)
28.54/9.36	   A^2 -> H(f(e), U1(e, k))
28.54/9.36	   A^2 -> H(f(e), U1(k, e))
28.54/9.36	   A^2 -> H(f(e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.36	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.36	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.36	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.36	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.36	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.36	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.36	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.36	   A^2 -> H(f(k), b)
28.54/9.36	   A^2 -> H(f(k), U1(e, d))
28.54/9.36	   A^2 -> H(f(k), U1(d, e))
28.54/9.36	   A^2 -> H(f(k), c)
28.54/9.36	   A^2 -> H(f(k), U1(e, k))
28.54/9.36	   A^2 -> H(f(k), U1(k, e))
28.54/9.36	   A^2 -> H(f(k), e)
28.54/9.36	   A^2 -> H(f(c), d)
28.54/9.36	
28.54/9.36	The TRS R consists of the following rules:
28.54/9.36	
28.54/9.36	   f(x) -> U1(x, x)
28.54/9.36	   U1(e, x) -> x
28.54/9.36	   a -> c
28.54/9.36	   a -> d
28.54/9.36	   b -> c
28.54/9.36	   b -> d
28.54/9.36	   d -> k
28.54/9.36	   c -> e
28.54/9.36	   c -> k
28.54/9.36	
28.54/9.36	Q is empty.
28.54/9.36	We have to consider all minimal (P,Q,R)-chains.
28.54/9.36	----------------------------------------
28.54/9.36	
28.54/9.36	(987) TransformationProof (EQUIVALENT)
28.54/9.36	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.36	
28.54/9.36	   (A^2 -> H(U1(k, k), U1(c, b)),A^2 -> H(U1(k, k), U1(c, b)))
28.54/9.36	   (A^2 -> H(U1(k, k), U1(d, b)),A^2 -> H(U1(k, k), U1(d, b)))
28.54/9.36	   (A^2 -> H(U1(k, k), U1(b, c)),A^2 -> H(U1(k, k), U1(b, c)))
28.54/9.36	   (A^2 -> H(U1(k, k), U1(b, d)),A^2 -> H(U1(k, k), U1(b, d)))
28.54/9.36	
28.54/9.36	
28.54/9.36	----------------------------------------
28.54/9.36	
28.54/9.36	(988)
28.54/9.36	Obligation:
28.54/9.36	Q DP problem:
28.54/9.36	The TRS P consists of the following rules:
28.54/9.36	
28.54/9.36	   H(x, x) -> G(x, x, f(k))
28.54/9.36	   G(d, x, x) -> A^2
28.54/9.36	   A^2 -> H(f(c), f(c))
28.54/9.36	   A^2 -> H(f(d), f(d))
28.54/9.36	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.36	   A^2 -> H(f(e), f(e))
28.54/9.36	   A^2 -> H(f(k), f(k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.36	   A^2 -> H(U1(k, k), f(c))
28.54/9.36	   A^2 -> H(U1(k, k), f(d))
28.54/9.36	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.36	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.36	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.36	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.36	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.36	   A^2 -> H(U1(k, d), f(e))
28.54/9.36	   A^2 -> H(U1(k, d), f(k))
28.54/9.36	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.36	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.36	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.36	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.36	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.36	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.36	   A^2 -> H(U1(d, k), f(e))
28.54/9.36	   A^2 -> H(U1(d, k), f(k))
28.54/9.36	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.36	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.36	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.36	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.36	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.36	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.36	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.36	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.36	   A^2 -> H(f(d), b)
28.54/9.36	   A^2 -> H(f(d), U1(e, d))
28.54/9.36	   A^2 -> H(f(d), U1(d, e))
28.54/9.36	   A^2 -> H(f(d), c)
28.54/9.36	   A^2 -> H(f(d), U1(e, k))
28.54/9.36	   A^2 -> H(f(d), U1(k, e))
28.54/9.36	   A^2 -> H(f(d), e)
28.54/9.36	   A^2 -> H(f(a), d)
28.54/9.36	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.36	   A^2 -> H(f(c), c)
28.54/9.36	   A^2 -> H(f(c), U1(e, k))
28.54/9.36	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.36	   A^2 -> H(f(c), U1(k, e))
28.54/9.36	   A^2 -> H(f(c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.36	   A^2 -> H(f(a), k)
28.54/9.36	   A^2 -> H(f(e), U1(e, e))
28.54/9.36	   A^2 -> H(f(c), e)
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.36	   A^2 -> H(f(d), U1(k, k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.36	   A^2 -> H(d, U1(b, b))
28.54/9.36	   A^2 -> H(d, f(c))
28.54/9.36	   A^2 -> H(d, f(d))
28.54/9.36	   A^2 -> H(a, U1(c, b))
28.54/9.36	   A^2 -> H(a, U1(d, b))
28.54/9.36	   A^2 -> H(a, U1(b, c))
28.54/9.36	   A^2 -> H(a, U1(b, d))
28.54/9.36	   A^2 -> H(a, U1(c, c))
28.54/9.36	   A^2 -> H(a, f(e))
28.54/9.36	   A^2 -> H(a, f(k))
28.54/9.36	   A^2 -> H(a, U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.36	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.36	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.36	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.36	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.36	   A^2 -> H(U1(e, d), f(e))
28.54/9.36	   A^2 -> H(U1(e, d), f(k))
28.54/9.36	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.36	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.36	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.36	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.36	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.36	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.36	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.36	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.36	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.36	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.36	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.36	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.36	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.36	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.36	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.36	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.36	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.36	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.36	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.36	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.36	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.36	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.36	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, a), b)
28.54/9.36	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.36	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.36	   A^2 -> H(U1(c, a), c)
28.54/9.36	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.36	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.36	   A^2 -> H(U1(c, a), e)
28.54/9.36	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.36	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.36	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.36	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.36	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.36	   A^2 -> H(U1(d, e), f(e))
28.54/9.36	   A^2 -> H(U1(d, e), f(k))
28.54/9.36	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.36	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.36	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.36	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.36	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.36	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.36	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.36	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.36	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.36	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.36	   A^2 -> H(U1(d, a), b)
28.54/9.36	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.36	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.36	   A^2 -> H(U1(d, a), c)
28.54/9.36	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.36	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.36	   A^2 -> H(U1(d, a), e)
28.54/9.36	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.36	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.36	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.36	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.36	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.36	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.36	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.36	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.36	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.36	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.36	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.36	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.36	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.36	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.36	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.36	   A^2 -> H(U1(a, c), b)
28.54/9.36	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.36	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.36	   A^2 -> H(U1(a, c), c)
28.54/9.36	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.36	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.36	   A^2 -> H(U1(a, c), e)
28.54/9.36	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, d), b)
28.54/9.36	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.36	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.36	   A^2 -> H(U1(a, d), c)
28.54/9.36	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.36	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.36	   A^2 -> H(U1(a, d), e)
28.54/9.36	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, a), d)
28.54/9.36	   A^2 -> H(U1(a, a), k)
28.54/9.36	   A^2 -> H(k, U1(b, b))
28.54/9.36	   A^2 -> H(k, f(c))
28.54/9.36	   A^2 -> H(k, f(d))
28.54/9.36	   A^2 -> H(c, U1(c, b))
28.54/9.36	   A^2 -> H(c, U1(d, b))
28.54/9.36	   A^2 -> H(c, U1(b, c))
28.54/9.36	   A^2 -> H(c, U1(b, d))
28.54/9.36	   A^2 -> H(c, U1(c, c))
28.54/9.36	   A^2 -> H(c, f(e))
28.54/9.36	   A^2 -> H(c, f(k))
28.54/9.36	   A^2 -> H(c, U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.36	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.36	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.36	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.36	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.36	   A^2 -> H(U1(e, k), f(e))
28.54/9.36	   A^2 -> H(U1(e, k), f(k))
28.54/9.36	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.36	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.36	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.36	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.36	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.36	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.36	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.36	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.36	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.36	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.36	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.36	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.36	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.36	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.36	   A^2 -> H(U1(k, e), f(e))
28.54/9.36	   A^2 -> H(U1(k, e), f(k))
28.54/9.36	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.36	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.36	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.36	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.36	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.36	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.36	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.36	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.36	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.36	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.36	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.36	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.36	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.36	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.36	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.36	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.36	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.36	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.36	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.36	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.36	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.36	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, c), b)
28.54/9.36	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.36	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.36	   A^2 -> H(U1(c, c), e)
28.54/9.36	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.36	   A^2 -> H(e, U1(c, b))
28.54/9.36	   A^2 -> H(e, U1(d, b))
28.54/9.36	   A^2 -> H(e, U1(b, c))
28.54/9.36	   A^2 -> H(e, U1(b, d))
28.54/9.36	   A^2 -> H(e, U1(c, c))
28.54/9.36	   A^2 -> H(e, f(e))
28.54/9.36	   A^2 -> H(e, f(k))
28.54/9.36	   A^2 -> H(e, U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.36	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.36	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.36	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.36	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.36	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.36	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.36	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.36	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.36	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.36	   A^2 -> H(f(e), b)
28.54/9.36	   A^2 -> H(f(e), U1(e, d))
28.54/9.36	   A^2 -> H(f(e), U1(d, e))
28.54/9.36	   A^2 -> H(f(e), c)
28.54/9.36	   A^2 -> H(f(e), U1(e, k))
28.54/9.36	   A^2 -> H(f(e), U1(k, e))
28.54/9.36	   A^2 -> H(f(e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.36	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.36	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.36	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.36	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.36	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.36	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.36	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.36	   A^2 -> H(f(k), b)
28.54/9.36	   A^2 -> H(f(k), U1(e, d))
28.54/9.36	   A^2 -> H(f(k), U1(d, e))
28.54/9.36	   A^2 -> H(f(k), c)
28.54/9.36	   A^2 -> H(f(k), U1(e, k))
28.54/9.36	   A^2 -> H(f(k), U1(k, e))
28.54/9.36	   A^2 -> H(f(k), e)
28.54/9.36	   A^2 -> H(f(c), d)
28.54/9.36	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.36	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.36	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.36	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.36	
28.54/9.36	The TRS R consists of the following rules:
28.54/9.36	
28.54/9.36	   f(x) -> U1(x, x)
28.54/9.36	   U1(e, x) -> x
28.54/9.36	   a -> c
28.54/9.36	   a -> d
28.54/9.36	   b -> c
28.54/9.36	   b -> d
28.54/9.36	   d -> k
28.54/9.36	   c -> e
28.54/9.36	   c -> k
28.54/9.36	
28.54/9.36	Q is empty.
28.54/9.36	We have to consider all minimal (P,Q,R)-chains.
28.54/9.36	----------------------------------------
28.54/9.36	
28.54/9.36	(989) TransformationProof (EQUIVALENT)
28.54/9.36	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), f(c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.36	
28.54/9.36	   (A^2 -> H(U1(k, k), U1(c, c)),A^2 -> H(U1(k, k), U1(c, c)))
28.54/9.36	   (A^2 -> H(U1(k, k), f(e)),A^2 -> H(U1(k, k), f(e)))
28.54/9.36	   (A^2 -> H(U1(k, k), f(k)),A^2 -> H(U1(k, k), f(k)))
28.54/9.36	
28.54/9.36	
28.54/9.36	----------------------------------------
28.54/9.36	
28.54/9.36	(990)
28.54/9.36	Obligation:
28.54/9.36	Q DP problem:
28.54/9.36	The TRS P consists of the following rules:
28.54/9.36	
28.54/9.36	   H(x, x) -> G(x, x, f(k))
28.54/9.36	   G(d, x, x) -> A^2
28.54/9.36	   A^2 -> H(f(c), f(c))
28.54/9.36	   A^2 -> H(f(d), f(d))
28.54/9.36	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.36	   A^2 -> H(f(e), f(e))
28.54/9.36	   A^2 -> H(f(k), f(k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.36	   A^2 -> H(U1(k, k), f(d))
28.54/9.36	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.36	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.36	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.36	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.36	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.36	   A^2 -> H(U1(k, d), f(e))
28.54/9.36	   A^2 -> H(U1(k, d), f(k))
28.54/9.36	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.36	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.36	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.36	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.36	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.36	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.36	   A^2 -> H(U1(d, k), f(e))
28.54/9.36	   A^2 -> H(U1(d, k), f(k))
28.54/9.36	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.36	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.36	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.36	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.36	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.36	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.36	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.36	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.36	   A^2 -> H(f(d), b)
28.54/9.36	   A^2 -> H(f(d), U1(e, d))
28.54/9.36	   A^2 -> H(f(d), U1(d, e))
28.54/9.36	   A^2 -> H(f(d), c)
28.54/9.36	   A^2 -> H(f(d), U1(e, k))
28.54/9.36	   A^2 -> H(f(d), U1(k, e))
28.54/9.36	   A^2 -> H(f(d), e)
28.54/9.36	   A^2 -> H(f(a), d)
28.54/9.36	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.36	   A^2 -> H(f(c), c)
28.54/9.36	   A^2 -> H(f(c), U1(e, k))
28.54/9.36	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.36	   A^2 -> H(f(c), U1(k, e))
28.54/9.36	   A^2 -> H(f(c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.36	   A^2 -> H(f(a), k)
28.54/9.36	   A^2 -> H(f(e), U1(e, e))
28.54/9.36	   A^2 -> H(f(c), e)
28.54/9.36	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.36	   A^2 -> H(f(d), U1(k, k))
28.54/9.36	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.36	   A^2 -> H(d, U1(b, b))
28.54/9.36	   A^2 -> H(d, f(c))
28.54/9.36	   A^2 -> H(d, f(d))
28.54/9.36	   A^2 -> H(a, U1(c, b))
28.54/9.36	   A^2 -> H(a, U1(d, b))
28.54/9.36	   A^2 -> H(a, U1(b, c))
28.54/9.36	   A^2 -> H(a, U1(b, d))
28.54/9.36	   A^2 -> H(a, U1(c, c))
28.54/9.36	   A^2 -> H(a, f(e))
28.54/9.36	   A^2 -> H(a, f(k))
28.54/9.36	   A^2 -> H(a, U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.36	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.36	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.36	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.36	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.36	   A^2 -> H(U1(e, d), f(e))
28.54/9.36	   A^2 -> H(U1(e, d), f(k))
28.54/9.36	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.36	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.36	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.36	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.36	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.36	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.36	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.36	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.36	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.36	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.36	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.36	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.36	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.36	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.36	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.36	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.36	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.36	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.36	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.36	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.36	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.36	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.36	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.36	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.36	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.36	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.36	   A^2 -> H(U1(c, a), b)
28.54/9.36	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.36	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.36	   A^2 -> H(U1(c, a), c)
28.54/9.36	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.36	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.36	   A^2 -> H(U1(c, a), e)
28.54/9.36	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.36	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.36	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.36	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.36	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.36	   A^2 -> H(U1(d, e), f(e))
28.54/9.36	   A^2 -> H(U1(d, e), f(k))
28.54/9.36	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.36	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.36	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.36	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.36	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.36	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.36	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.36	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.36	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.36	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.36	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.36	   A^2 -> H(U1(d, a), b)
28.54/9.36	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.36	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.36	   A^2 -> H(U1(d, a), c)
28.54/9.36	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.36	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.36	   A^2 -> H(U1(d, a), e)
28.54/9.36	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.36	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.36	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.36	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.36	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.36	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.36	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.36	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.36	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.36	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.36	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.36	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.36	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.36	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.36	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.36	   A^2 -> H(U1(a, c), b)
28.54/9.36	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.36	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.36	   A^2 -> H(U1(a, c), c)
28.54/9.36	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.36	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.36	   A^2 -> H(U1(a, c), e)
28.54/9.36	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, d), b)
28.54/9.36	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.36	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.36	   A^2 -> H(U1(a, d), c)
28.54/9.36	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.36	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.36	   A^2 -> H(U1(a, d), e)
28.54/9.36	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.36	   A^2 -> H(U1(a, a), d)
28.54/9.36	   A^2 -> H(U1(a, a), k)
28.54/9.36	   A^2 -> H(k, U1(b, b))
28.54/9.36	   A^2 -> H(k, f(c))
28.54/9.36	   A^2 -> H(k, f(d))
28.54/9.36	   A^2 -> H(c, U1(c, b))
28.54/9.36	   A^2 -> H(c, U1(d, b))
28.54/9.36	   A^2 -> H(c, U1(b, c))
28.54/9.36	   A^2 -> H(c, U1(b, d))
28.54/9.36	   A^2 -> H(c, U1(c, c))
28.54/9.36	   A^2 -> H(c, f(e))
28.54/9.37	   A^2 -> H(c, f(k))
28.54/9.37	   A^2 -> H(c, U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.37	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.37	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.37	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.37	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.37	   A^2 -> H(U1(e, k), f(e))
28.54/9.37	   A^2 -> H(U1(e, k), f(k))
28.54/9.37	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.37	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.37	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.37	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.37	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.37	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.37	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.37	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.37	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.37	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.37	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.37	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.37	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.37	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.37	   A^2 -> H(U1(k, e), f(e))
28.54/9.37	   A^2 -> H(U1(k, e), f(k))
28.54/9.37	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.37	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.37	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.37	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.37	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.37	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.37	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.37	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.37	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.37	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.37	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.37	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.37	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.37	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.37	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.37	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.37	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.37	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, c), b)
28.54/9.37	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.37	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.37	   A^2 -> H(U1(c, c), e)
28.54/9.37	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.37	   A^2 -> H(e, U1(c, b))
28.54/9.37	   A^2 -> H(e, U1(d, b))
28.54/9.37	   A^2 -> H(e, U1(b, c))
28.54/9.37	   A^2 -> H(e, U1(b, d))
28.54/9.37	   A^2 -> H(e, U1(c, c))
28.54/9.37	   A^2 -> H(e, f(e))
28.54/9.37	   A^2 -> H(e, f(k))
28.54/9.37	   A^2 -> H(e, U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.37	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.37	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.37	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.37	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.37	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.37	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.37	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.37	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.37	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.37	   A^2 -> H(f(e), b)
28.54/9.37	   A^2 -> H(f(e), U1(e, d))
28.54/9.37	   A^2 -> H(f(e), U1(d, e))
28.54/9.37	   A^2 -> H(f(e), c)
28.54/9.37	   A^2 -> H(f(e), U1(e, k))
28.54/9.37	   A^2 -> H(f(e), U1(k, e))
28.54/9.37	   A^2 -> H(f(e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.37	   A^2 -> H(f(k), b)
28.54/9.37	   A^2 -> H(f(k), U1(e, d))
28.54/9.37	   A^2 -> H(f(k), U1(d, e))
28.54/9.37	   A^2 -> H(f(k), c)
28.54/9.37	   A^2 -> H(f(k), U1(e, k))
28.54/9.37	   A^2 -> H(f(k), U1(k, e))
28.54/9.37	   A^2 -> H(f(k), e)
28.54/9.37	   A^2 -> H(f(c), d)
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.37	   A^2 -> H(U1(k, k), f(e))
28.54/9.37	   A^2 -> H(U1(k, k), f(k))
28.54/9.37	
28.54/9.37	The TRS R consists of the following rules:
28.54/9.37	
28.54/9.37	   f(x) -> U1(x, x)
28.54/9.37	   U1(e, x) -> x
28.54/9.37	   a -> c
28.54/9.37	   a -> d
28.54/9.37	   b -> c
28.54/9.37	   b -> d
28.54/9.37	   d -> k
28.54/9.37	   c -> e
28.54/9.37	   c -> k
28.54/9.37	
28.54/9.37	Q is empty.
28.54/9.37	We have to consider all minimal (P,Q,R)-chains.
28.54/9.37	----------------------------------------
28.54/9.37	
28.54/9.37	(991) TransformationProof (EQUIVALENT)
28.54/9.37	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), f(d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.37	
28.54/9.37	   (A^2 -> H(U1(k, k), U1(d, d)),A^2 -> H(U1(k, k), U1(d, d)))
28.54/9.37	   (A^2 -> H(U1(k, k), f(k)),A^2 -> H(U1(k, k), f(k)))
28.54/9.37	
28.54/9.37	
28.54/9.37	----------------------------------------
28.54/9.37	
28.54/9.37	(992)
28.54/9.37	Obligation:
28.54/9.37	Q DP problem:
28.54/9.37	The TRS P consists of the following rules:
28.54/9.37	
28.54/9.37	   H(x, x) -> G(x, x, f(k))
28.54/9.37	   G(d, x, x) -> A^2
28.54/9.37	   A^2 -> H(f(c), f(c))
28.54/9.37	   A^2 -> H(f(d), f(d))
28.54/9.37	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.37	   A^2 -> H(f(e), f(e))
28.54/9.37	   A^2 -> H(f(k), f(k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.37	   A^2 -> H(U1(k, d), U1(c, b))
28.54/9.37	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.37	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.37	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.37	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.37	   A^2 -> H(U1(k, d), f(e))
28.54/9.37	   A^2 -> H(U1(k, d), f(k))
28.54/9.37	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.37	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.37	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.37	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.37	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.37	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.37	   A^2 -> H(U1(d, k), f(e))
28.54/9.37	   A^2 -> H(U1(d, k), f(k))
28.54/9.37	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.37	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.37	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.37	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.37	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.37	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.37	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.37	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.37	   A^2 -> H(f(d), b)
28.54/9.37	   A^2 -> H(f(d), U1(e, d))
28.54/9.37	   A^2 -> H(f(d), U1(d, e))
28.54/9.37	   A^2 -> H(f(d), c)
28.54/9.37	   A^2 -> H(f(d), U1(e, k))
28.54/9.37	   A^2 -> H(f(d), U1(k, e))
28.54/9.37	   A^2 -> H(f(d), e)
28.54/9.37	   A^2 -> H(f(a), d)
28.54/9.37	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.37	   A^2 -> H(f(c), c)
28.54/9.37	   A^2 -> H(f(c), U1(e, k))
28.54/9.37	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.37	   A^2 -> H(f(c), U1(k, e))
28.54/9.37	   A^2 -> H(f(c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.37	   A^2 -> H(f(a), k)
28.54/9.37	   A^2 -> H(f(e), U1(e, e))
28.54/9.37	   A^2 -> H(f(c), e)
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.37	   A^2 -> H(f(d), U1(k, k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.37	   A^2 -> H(d, U1(b, b))
28.54/9.37	   A^2 -> H(d, f(c))
28.54/9.37	   A^2 -> H(d, f(d))
28.54/9.37	   A^2 -> H(a, U1(c, b))
28.54/9.37	   A^2 -> H(a, U1(d, b))
28.54/9.37	   A^2 -> H(a, U1(b, c))
28.54/9.37	   A^2 -> H(a, U1(b, d))
28.54/9.37	   A^2 -> H(a, U1(c, c))
28.54/9.37	   A^2 -> H(a, f(e))
28.54/9.37	   A^2 -> H(a, f(k))
28.54/9.37	   A^2 -> H(a, U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.37	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.37	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.37	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.37	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.37	   A^2 -> H(U1(e, d), f(e))
28.54/9.37	   A^2 -> H(U1(e, d), f(k))
28.54/9.37	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.37	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.37	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.37	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.37	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.37	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.37	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.37	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.37	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.37	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.37	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.37	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.37	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.37	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.37	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.37	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.37	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.37	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.37	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, a), b)
28.54/9.37	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.37	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.37	   A^2 -> H(U1(c, a), c)
28.54/9.37	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.37	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.37	   A^2 -> H(U1(c, a), e)
28.54/9.37	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.37	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.37	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.37	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.37	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.37	   A^2 -> H(U1(d, e), f(e))
28.54/9.37	   A^2 -> H(U1(d, e), f(k))
28.54/9.37	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.37	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.37	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.37	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.37	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.37	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.37	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.37	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.37	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.37	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.37	   A^2 -> H(U1(d, a), b)
28.54/9.37	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.37	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.37	   A^2 -> H(U1(d, a), c)
28.54/9.37	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.37	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.37	   A^2 -> H(U1(d, a), e)
28.54/9.37	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.37	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.37	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.37	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.37	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.37	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.37	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.37	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.37	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.37	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.37	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.37	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.37	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.37	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.37	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.37	   A^2 -> H(U1(a, c), b)
28.54/9.37	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.37	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.37	   A^2 -> H(U1(a, c), c)
28.54/9.37	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.37	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.37	   A^2 -> H(U1(a, c), e)
28.54/9.37	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, d), b)
28.54/9.37	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.37	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.37	   A^2 -> H(U1(a, d), c)
28.54/9.37	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.37	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.37	   A^2 -> H(U1(a, d), e)
28.54/9.37	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, a), d)
28.54/9.37	   A^2 -> H(U1(a, a), k)
28.54/9.37	   A^2 -> H(k, U1(b, b))
28.54/9.37	   A^2 -> H(k, f(c))
28.54/9.37	   A^2 -> H(k, f(d))
28.54/9.37	   A^2 -> H(c, U1(c, b))
28.54/9.37	   A^2 -> H(c, U1(d, b))
28.54/9.37	   A^2 -> H(c, U1(b, c))
28.54/9.37	   A^2 -> H(c, U1(b, d))
28.54/9.37	   A^2 -> H(c, U1(c, c))
28.54/9.37	   A^2 -> H(c, f(e))
28.54/9.37	   A^2 -> H(c, f(k))
28.54/9.37	   A^2 -> H(c, U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.37	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.37	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.37	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.37	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.37	   A^2 -> H(U1(e, k), f(e))
28.54/9.37	   A^2 -> H(U1(e, k), f(k))
28.54/9.37	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.37	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.37	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.37	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.37	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.37	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.37	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.37	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.37	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.37	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.37	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.37	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.37	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.37	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.37	   A^2 -> H(U1(k, e), f(e))
28.54/9.37	   A^2 -> H(U1(k, e), f(k))
28.54/9.37	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.37	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.37	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.37	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.37	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.37	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.37	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.37	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.37	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.37	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.37	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.37	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.37	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.37	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.37	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.37	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.37	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.37	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, c), b)
28.54/9.37	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.37	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.37	   A^2 -> H(U1(c, c), e)
28.54/9.37	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.37	   A^2 -> H(e, U1(c, b))
28.54/9.37	   A^2 -> H(e, U1(d, b))
28.54/9.37	   A^2 -> H(e, U1(b, c))
28.54/9.37	   A^2 -> H(e, U1(b, d))
28.54/9.37	   A^2 -> H(e, U1(c, c))
28.54/9.37	   A^2 -> H(e, f(e))
28.54/9.37	   A^2 -> H(e, f(k))
28.54/9.37	   A^2 -> H(e, U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.37	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.37	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.37	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.37	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.37	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.37	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.37	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.37	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.37	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.37	   A^2 -> H(f(e), b)
28.54/9.37	   A^2 -> H(f(e), U1(e, d))
28.54/9.37	   A^2 -> H(f(e), U1(d, e))
28.54/9.37	   A^2 -> H(f(e), c)
28.54/9.37	   A^2 -> H(f(e), U1(e, k))
28.54/9.37	   A^2 -> H(f(e), U1(k, e))
28.54/9.37	   A^2 -> H(f(e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.37	   A^2 -> H(f(k), b)
28.54/9.37	   A^2 -> H(f(k), U1(e, d))
28.54/9.37	   A^2 -> H(f(k), U1(d, e))
28.54/9.37	   A^2 -> H(f(k), c)
28.54/9.37	   A^2 -> H(f(k), U1(e, k))
28.54/9.37	   A^2 -> H(f(k), U1(k, e))
28.54/9.37	   A^2 -> H(f(k), e)
28.54/9.37	   A^2 -> H(f(c), d)
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.37	   A^2 -> H(U1(k, k), f(e))
28.54/9.37	   A^2 -> H(U1(k, k), f(k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.37	
28.54/9.37	The TRS R consists of the following rules:
28.54/9.37	
28.54/9.37	   f(x) -> U1(x, x)
28.54/9.37	   U1(e, x) -> x
28.54/9.37	   a -> c
28.54/9.37	   a -> d
28.54/9.37	   b -> c
28.54/9.37	   b -> d
28.54/9.37	   d -> k
28.54/9.37	   c -> e
28.54/9.37	   c -> k
28.54/9.37	
28.54/9.37	Q is empty.
28.54/9.37	We have to consider all minimal (P,Q,R)-chains.
28.54/9.37	----------------------------------------
28.54/9.37	
28.54/9.37	(993) TransformationProof (EQUIVALENT)
28.54/9.37	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.37	
28.54/9.37	   (A^2 -> H(U1(k, k), U1(c, b)),A^2 -> H(U1(k, k), U1(c, b)))
28.54/9.37	   (A^2 -> H(U1(k, d), U1(e, b)),A^2 -> H(U1(k, d), U1(e, b)))
28.54/9.37	   (A^2 -> H(U1(k, d), U1(k, b)),A^2 -> H(U1(k, d), U1(k, b)))
28.54/9.37	   (A^2 -> H(U1(k, d), U1(c, c)),A^2 -> H(U1(k, d), U1(c, c)))
28.54/9.37	   (A^2 -> H(U1(k, d), U1(c, d)),A^2 -> H(U1(k, d), U1(c, d)))
28.54/9.37	
28.54/9.37	
28.54/9.37	----------------------------------------
28.54/9.37	
28.54/9.37	(994)
28.54/9.37	Obligation:
28.54/9.37	Q DP problem:
28.54/9.37	The TRS P consists of the following rules:
28.54/9.37	
28.54/9.37	   H(x, x) -> G(x, x, f(k))
28.54/9.37	   G(d, x, x) -> A^2
28.54/9.37	   A^2 -> H(f(c), f(c))
28.54/9.37	   A^2 -> H(f(d), f(d))
28.54/9.37	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.37	   A^2 -> H(f(e), f(e))
28.54/9.37	   A^2 -> H(f(k), f(k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.37	   A^2 -> H(U1(k, d), U1(d, b))
28.54/9.37	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.37	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.37	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.37	   A^2 -> H(U1(k, d), f(e))
28.54/9.37	   A^2 -> H(U1(k, d), f(k))
28.54/9.37	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.37	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.37	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.37	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.37	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.37	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.37	   A^2 -> H(U1(d, k), f(e))
28.54/9.37	   A^2 -> H(U1(d, k), f(k))
28.54/9.37	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.37	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.37	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.37	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.37	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.37	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.37	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.37	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.37	   A^2 -> H(f(d), b)
28.54/9.37	   A^2 -> H(f(d), U1(e, d))
28.54/9.37	   A^2 -> H(f(d), U1(d, e))
28.54/9.37	   A^2 -> H(f(d), c)
28.54/9.37	   A^2 -> H(f(d), U1(e, k))
28.54/9.37	   A^2 -> H(f(d), U1(k, e))
28.54/9.37	   A^2 -> H(f(d), e)
28.54/9.37	   A^2 -> H(f(a), d)
28.54/9.37	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.37	   A^2 -> H(f(c), c)
28.54/9.37	   A^2 -> H(f(c), U1(e, k))
28.54/9.37	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.37	   A^2 -> H(f(c), U1(k, e))
28.54/9.37	   A^2 -> H(f(c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.37	   A^2 -> H(f(a), k)
28.54/9.37	   A^2 -> H(f(e), U1(e, e))
28.54/9.37	   A^2 -> H(f(c), e)
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.37	   A^2 -> H(f(d), U1(k, k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.37	   A^2 -> H(d, U1(b, b))
28.54/9.37	   A^2 -> H(d, f(c))
28.54/9.37	   A^2 -> H(d, f(d))
28.54/9.37	   A^2 -> H(a, U1(c, b))
28.54/9.37	   A^2 -> H(a, U1(d, b))
28.54/9.37	   A^2 -> H(a, U1(b, c))
28.54/9.37	   A^2 -> H(a, U1(b, d))
28.54/9.37	   A^2 -> H(a, U1(c, c))
28.54/9.37	   A^2 -> H(a, f(e))
28.54/9.37	   A^2 -> H(a, f(k))
28.54/9.37	   A^2 -> H(a, U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.37	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.37	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.37	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.37	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.37	   A^2 -> H(U1(e, d), f(e))
28.54/9.37	   A^2 -> H(U1(e, d), f(k))
28.54/9.37	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.37	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.37	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.37	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.37	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.37	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.37	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.37	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.37	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.37	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.37	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.37	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.37	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.37	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.37	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.37	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.37	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.37	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.37	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, a), b)
28.54/9.37	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.37	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.37	   A^2 -> H(U1(c, a), c)
28.54/9.37	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.37	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.37	   A^2 -> H(U1(c, a), e)
28.54/9.37	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.37	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.37	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.37	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.37	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.37	   A^2 -> H(U1(d, e), f(e))
28.54/9.37	   A^2 -> H(U1(d, e), f(k))
28.54/9.37	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.37	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.37	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.37	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.37	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.37	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.37	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.37	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.37	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.37	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.37	   A^2 -> H(U1(d, a), b)
28.54/9.37	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.37	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.37	   A^2 -> H(U1(d, a), c)
28.54/9.37	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.37	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.37	   A^2 -> H(U1(d, a), e)
28.54/9.37	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.37	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.37	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.37	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.37	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.37	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.37	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.37	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.37	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.37	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.37	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.37	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.37	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.37	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.37	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.37	   A^2 -> H(U1(a, c), b)
28.54/9.37	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.37	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.37	   A^2 -> H(U1(a, c), c)
28.54/9.37	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.37	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.37	   A^2 -> H(U1(a, c), e)
28.54/9.37	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, d), b)
28.54/9.37	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.37	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.37	   A^2 -> H(U1(a, d), c)
28.54/9.37	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.37	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.37	   A^2 -> H(U1(a, d), e)
28.54/9.37	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, a), d)
28.54/9.37	   A^2 -> H(U1(a, a), k)
28.54/9.37	   A^2 -> H(k, U1(b, b))
28.54/9.37	   A^2 -> H(k, f(c))
28.54/9.37	   A^2 -> H(k, f(d))
28.54/9.37	   A^2 -> H(c, U1(c, b))
28.54/9.37	   A^2 -> H(c, U1(d, b))
28.54/9.37	   A^2 -> H(c, U1(b, c))
28.54/9.37	   A^2 -> H(c, U1(b, d))
28.54/9.37	   A^2 -> H(c, U1(c, c))
28.54/9.37	   A^2 -> H(c, f(e))
28.54/9.37	   A^2 -> H(c, f(k))
28.54/9.37	   A^2 -> H(c, U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.37	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.37	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.37	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.37	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.37	   A^2 -> H(U1(e, k), f(e))
28.54/9.37	   A^2 -> H(U1(e, k), f(k))
28.54/9.37	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.37	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.37	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.37	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.37	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.37	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.37	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.37	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.37	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.37	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.37	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.37	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.37	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.37	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.37	   A^2 -> H(U1(k, e), f(e))
28.54/9.37	   A^2 -> H(U1(k, e), f(k))
28.54/9.37	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.37	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.37	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.37	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.37	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.37	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.37	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.37	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.37	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.37	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.37	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.37	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.37	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.37	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.37	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.37	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.37	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.37	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, c), b)
28.54/9.37	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.37	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.37	   A^2 -> H(U1(c, c), e)
28.54/9.37	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.37	   A^2 -> H(e, U1(c, b))
28.54/9.37	   A^2 -> H(e, U1(d, b))
28.54/9.37	   A^2 -> H(e, U1(b, c))
28.54/9.37	   A^2 -> H(e, U1(b, d))
28.54/9.37	   A^2 -> H(e, U1(c, c))
28.54/9.37	   A^2 -> H(e, f(e))
28.54/9.37	   A^2 -> H(e, f(k))
28.54/9.37	   A^2 -> H(e, U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.37	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.37	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.37	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.37	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.37	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.37	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.37	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.37	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.37	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.37	   A^2 -> H(f(e), b)
28.54/9.37	   A^2 -> H(f(e), U1(e, d))
28.54/9.37	   A^2 -> H(f(e), U1(d, e))
28.54/9.37	   A^2 -> H(f(e), c)
28.54/9.37	   A^2 -> H(f(e), U1(e, k))
28.54/9.37	   A^2 -> H(f(e), U1(k, e))
28.54/9.37	   A^2 -> H(f(e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.37	   A^2 -> H(f(k), b)
28.54/9.37	   A^2 -> H(f(k), U1(e, d))
28.54/9.37	   A^2 -> H(f(k), U1(d, e))
28.54/9.37	   A^2 -> H(f(k), c)
28.54/9.37	   A^2 -> H(f(k), U1(e, k))
28.54/9.37	   A^2 -> H(f(k), U1(k, e))
28.54/9.37	   A^2 -> H(f(k), e)
28.54/9.37	   A^2 -> H(f(c), d)
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.37	   A^2 -> H(U1(k, k), f(e))
28.54/9.37	   A^2 -> H(U1(k, k), f(k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.37	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.37	
28.54/9.37	The TRS R consists of the following rules:
28.54/9.37	
28.54/9.37	   f(x) -> U1(x, x)
28.54/9.37	   U1(e, x) -> x
28.54/9.37	   a -> c
28.54/9.37	   a -> d
28.54/9.37	   b -> c
28.54/9.37	   b -> d
28.54/9.37	   d -> k
28.54/9.37	   c -> e
28.54/9.37	   c -> k
28.54/9.37	
28.54/9.37	Q is empty.
28.54/9.37	We have to consider all minimal (P,Q,R)-chains.
28.54/9.37	----------------------------------------
28.54/9.37	
28.54/9.37	(995) TransformationProof (EQUIVALENT)
28.54/9.37	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.37	
28.54/9.37	   (A^2 -> H(U1(k, k), U1(d, b)),A^2 -> H(U1(k, k), U1(d, b)))
28.54/9.37	   (A^2 -> H(U1(k, d), U1(k, b)),A^2 -> H(U1(k, d), U1(k, b)))
28.54/9.37	   (A^2 -> H(U1(k, d), U1(d, c)),A^2 -> H(U1(k, d), U1(d, c)))
28.54/9.37	   (A^2 -> H(U1(k, d), U1(d, d)),A^2 -> H(U1(k, d), U1(d, d)))
28.54/9.37	
28.54/9.37	
28.54/9.37	----------------------------------------
28.54/9.37	
28.54/9.37	(996)
28.54/9.37	Obligation:
28.54/9.37	Q DP problem:
28.54/9.37	The TRS P consists of the following rules:
28.54/9.37	
28.54/9.37	   H(x, x) -> G(x, x, f(k))
28.54/9.37	   G(d, x, x) -> A^2
28.54/9.37	   A^2 -> H(f(c), f(c))
28.54/9.37	   A^2 -> H(f(d), f(d))
28.54/9.37	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.37	   A^2 -> H(f(e), f(e))
28.54/9.37	   A^2 -> H(f(k), f(k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.37	   A^2 -> H(U1(k, d), U1(b, c))
28.54/9.37	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.37	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.37	   A^2 -> H(U1(k, d), f(e))
28.54/9.37	   A^2 -> H(U1(k, d), f(k))
28.54/9.37	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.37	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.37	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.37	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.37	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.37	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.37	   A^2 -> H(U1(d, k), f(e))
28.54/9.37	   A^2 -> H(U1(d, k), f(k))
28.54/9.37	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.37	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.37	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.37	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.37	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.37	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.37	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.37	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.37	   A^2 -> H(f(d), b)
28.54/9.37	   A^2 -> H(f(d), U1(e, d))
28.54/9.37	   A^2 -> H(f(d), U1(d, e))
28.54/9.37	   A^2 -> H(f(d), c)
28.54/9.37	   A^2 -> H(f(d), U1(e, k))
28.54/9.37	   A^2 -> H(f(d), U1(k, e))
28.54/9.37	   A^2 -> H(f(d), e)
28.54/9.37	   A^2 -> H(f(a), d)
28.54/9.37	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.37	   A^2 -> H(f(c), c)
28.54/9.37	   A^2 -> H(f(c), U1(e, k))
28.54/9.37	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.37	   A^2 -> H(f(c), U1(k, e))
28.54/9.37	   A^2 -> H(f(c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.37	   A^2 -> H(f(a), k)
28.54/9.37	   A^2 -> H(f(e), U1(e, e))
28.54/9.37	   A^2 -> H(f(c), e)
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.37	   A^2 -> H(f(d), U1(k, k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.37	   A^2 -> H(d, U1(b, b))
28.54/9.37	   A^2 -> H(d, f(c))
28.54/9.37	   A^2 -> H(d, f(d))
28.54/9.37	   A^2 -> H(a, U1(c, b))
28.54/9.37	   A^2 -> H(a, U1(d, b))
28.54/9.37	   A^2 -> H(a, U1(b, c))
28.54/9.37	   A^2 -> H(a, U1(b, d))
28.54/9.37	   A^2 -> H(a, U1(c, c))
28.54/9.37	   A^2 -> H(a, f(e))
28.54/9.37	   A^2 -> H(a, f(k))
28.54/9.37	   A^2 -> H(a, U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.37	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.37	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.37	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.37	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.37	   A^2 -> H(U1(e, d), f(e))
28.54/9.37	   A^2 -> H(U1(e, d), f(k))
28.54/9.37	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.37	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.37	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.37	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.37	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.37	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.37	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.37	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.37	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.37	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.37	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.37	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.37	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.37	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.37	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.37	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.37	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.37	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.37	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, a), b)
28.54/9.37	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.37	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.37	   A^2 -> H(U1(c, a), c)
28.54/9.37	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.37	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.37	   A^2 -> H(U1(c, a), e)
28.54/9.37	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.37	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.37	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.37	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.37	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.37	   A^2 -> H(U1(d, e), f(e))
28.54/9.37	   A^2 -> H(U1(d, e), f(k))
28.54/9.37	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.37	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.37	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.37	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.37	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.37	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.37	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.37	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.37	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.37	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.37	   A^2 -> H(U1(d, a), b)
28.54/9.37	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.37	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.37	   A^2 -> H(U1(d, a), c)
28.54/9.37	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.37	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.37	   A^2 -> H(U1(d, a), e)
28.54/9.37	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.37	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.37	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.37	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.37	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.37	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.37	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.37	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.37	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.37	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.37	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.37	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.37	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.37	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.37	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.37	   A^2 -> H(U1(a, c), b)
28.54/9.37	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.37	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.37	   A^2 -> H(U1(a, c), c)
28.54/9.37	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.37	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.37	   A^2 -> H(U1(a, c), e)
28.54/9.37	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, d), b)
28.54/9.37	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.37	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.37	   A^2 -> H(U1(a, d), c)
28.54/9.37	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.37	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.37	   A^2 -> H(U1(a, d), e)
28.54/9.37	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, a), d)
28.54/9.37	   A^2 -> H(U1(a, a), k)
28.54/9.37	   A^2 -> H(k, U1(b, b))
28.54/9.37	   A^2 -> H(k, f(c))
28.54/9.37	   A^2 -> H(k, f(d))
28.54/9.37	   A^2 -> H(c, U1(c, b))
28.54/9.37	   A^2 -> H(c, U1(d, b))
28.54/9.37	   A^2 -> H(c, U1(b, c))
28.54/9.37	   A^2 -> H(c, U1(b, d))
28.54/9.37	   A^2 -> H(c, U1(c, c))
28.54/9.37	   A^2 -> H(c, f(e))
28.54/9.37	   A^2 -> H(c, f(k))
28.54/9.37	   A^2 -> H(c, U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.37	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.37	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.37	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.37	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.37	   A^2 -> H(U1(e, k), f(e))
28.54/9.37	   A^2 -> H(U1(e, k), f(k))
28.54/9.37	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.37	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.37	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.37	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.37	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.37	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.37	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.37	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.37	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.37	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.37	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.37	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.37	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.37	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.37	   A^2 -> H(U1(k, e), f(e))
28.54/9.37	   A^2 -> H(U1(k, e), f(k))
28.54/9.37	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.37	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.37	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.37	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.37	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.37	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.37	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.37	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.37	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.37	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.37	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.37	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.37	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.37	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.37	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.37	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.37	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.37	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, c), b)
28.54/9.37	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.37	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.37	   A^2 -> H(U1(c, c), e)
28.54/9.37	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.37	   A^2 -> H(e, U1(c, b))
28.54/9.37	   A^2 -> H(e, U1(d, b))
28.54/9.37	   A^2 -> H(e, U1(b, c))
28.54/9.37	   A^2 -> H(e, U1(b, d))
28.54/9.37	   A^2 -> H(e, U1(c, c))
28.54/9.37	   A^2 -> H(e, f(e))
28.54/9.37	   A^2 -> H(e, f(k))
28.54/9.37	   A^2 -> H(e, U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.37	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.37	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.37	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.37	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.37	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.37	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.37	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.37	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.37	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.37	   A^2 -> H(f(e), b)
28.54/9.37	   A^2 -> H(f(e), U1(e, d))
28.54/9.37	   A^2 -> H(f(e), U1(d, e))
28.54/9.37	   A^2 -> H(f(e), c)
28.54/9.37	   A^2 -> H(f(e), U1(e, k))
28.54/9.37	   A^2 -> H(f(e), U1(k, e))
28.54/9.37	   A^2 -> H(f(e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.37	   A^2 -> H(f(k), b)
28.54/9.37	   A^2 -> H(f(k), U1(e, d))
28.54/9.37	   A^2 -> H(f(k), U1(d, e))
28.54/9.37	   A^2 -> H(f(k), c)
28.54/9.37	   A^2 -> H(f(k), U1(e, k))
28.54/9.37	   A^2 -> H(f(k), U1(k, e))
28.54/9.37	   A^2 -> H(f(k), e)
28.54/9.37	   A^2 -> H(f(c), d)
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.37	   A^2 -> H(U1(k, k), f(e))
28.54/9.37	   A^2 -> H(U1(k, k), f(k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.37	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.37	
28.54/9.37	The TRS R consists of the following rules:
28.54/9.37	
28.54/9.37	   f(x) -> U1(x, x)
28.54/9.37	   U1(e, x) -> x
28.54/9.37	   a -> c
28.54/9.37	   a -> d
28.54/9.37	   b -> c
28.54/9.37	   b -> d
28.54/9.37	   d -> k
28.54/9.37	   c -> e
28.54/9.37	   c -> k
28.54/9.37	
28.54/9.37	Q is empty.
28.54/9.37	We have to consider all minimal (P,Q,R)-chains.
28.54/9.37	----------------------------------------
28.54/9.37	
28.54/9.37	(997) TransformationProof (EQUIVALENT)
28.54/9.37	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.37	
28.54/9.37	   (A^2 -> H(U1(k, k), U1(b, c)),A^2 -> H(U1(k, k), U1(b, c)))
28.54/9.37	   (A^2 -> H(U1(k, d), U1(c, c)),A^2 -> H(U1(k, d), U1(c, c)))
28.54/9.37	   (A^2 -> H(U1(k, d), U1(d, c)),A^2 -> H(U1(k, d), U1(d, c)))
28.54/9.37	   (A^2 -> H(U1(k, d), U1(b, e)),A^2 -> H(U1(k, d), U1(b, e)))
28.54/9.37	   (A^2 -> H(U1(k, d), U1(b, k)),A^2 -> H(U1(k, d), U1(b, k)))
28.54/9.37	
28.54/9.37	
28.54/9.37	----------------------------------------
28.54/9.37	
28.54/9.37	(998)
28.54/9.37	Obligation:
28.54/9.37	Q DP problem:
28.54/9.37	The TRS P consists of the following rules:
28.54/9.37	
28.54/9.37	   H(x, x) -> G(x, x, f(k))
28.54/9.37	   G(d, x, x) -> A^2
28.54/9.37	   A^2 -> H(f(c), f(c))
28.54/9.37	   A^2 -> H(f(d), f(d))
28.54/9.37	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.37	   A^2 -> H(f(e), f(e))
28.54/9.37	   A^2 -> H(f(k), f(k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.37	   A^2 -> H(U1(k, d), U1(b, d))
28.54/9.37	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.37	   A^2 -> H(U1(k, d), f(e))
28.54/9.37	   A^2 -> H(U1(k, d), f(k))
28.54/9.37	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.37	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.37	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.37	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.37	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.37	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.37	   A^2 -> H(U1(d, k), f(e))
28.54/9.37	   A^2 -> H(U1(d, k), f(k))
28.54/9.37	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.37	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.37	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.37	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.37	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.37	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.37	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.37	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.37	   A^2 -> H(f(d), b)
28.54/9.37	   A^2 -> H(f(d), U1(e, d))
28.54/9.37	   A^2 -> H(f(d), U1(d, e))
28.54/9.37	   A^2 -> H(f(d), c)
28.54/9.37	   A^2 -> H(f(d), U1(e, k))
28.54/9.37	   A^2 -> H(f(d), U1(k, e))
28.54/9.37	   A^2 -> H(f(d), e)
28.54/9.37	   A^2 -> H(f(a), d)
28.54/9.37	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.37	   A^2 -> H(f(c), c)
28.54/9.37	   A^2 -> H(f(c), U1(e, k))
28.54/9.37	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.37	   A^2 -> H(f(c), U1(k, e))
28.54/9.37	   A^2 -> H(f(c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.37	   A^2 -> H(f(a), k)
28.54/9.37	   A^2 -> H(f(e), U1(e, e))
28.54/9.37	   A^2 -> H(f(c), e)
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.37	   A^2 -> H(f(d), U1(k, k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.37	   A^2 -> H(d, U1(b, b))
28.54/9.37	   A^2 -> H(d, f(c))
28.54/9.37	   A^2 -> H(d, f(d))
28.54/9.37	   A^2 -> H(a, U1(c, b))
28.54/9.37	   A^2 -> H(a, U1(d, b))
28.54/9.37	   A^2 -> H(a, U1(b, c))
28.54/9.37	   A^2 -> H(a, U1(b, d))
28.54/9.37	   A^2 -> H(a, U1(c, c))
28.54/9.37	   A^2 -> H(a, f(e))
28.54/9.37	   A^2 -> H(a, f(k))
28.54/9.37	   A^2 -> H(a, U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.37	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.37	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.37	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.37	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.37	   A^2 -> H(U1(e, d), f(e))
28.54/9.37	   A^2 -> H(U1(e, d), f(k))
28.54/9.37	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.37	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.37	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.37	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.37	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.37	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.37	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.37	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.37	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.37	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.37	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.37	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.37	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.37	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.37	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.37	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.37	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.37	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.37	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, a), b)
28.54/9.37	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.37	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.37	   A^2 -> H(U1(c, a), c)
28.54/9.37	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.37	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.37	   A^2 -> H(U1(c, a), e)
28.54/9.37	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.37	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.37	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.37	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.37	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.37	   A^2 -> H(U1(d, e), f(e))
28.54/9.37	   A^2 -> H(U1(d, e), f(k))
28.54/9.37	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.37	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.37	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.37	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.37	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.37	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.37	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.37	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.37	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.37	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.37	   A^2 -> H(U1(d, a), b)
28.54/9.37	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.37	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.37	   A^2 -> H(U1(d, a), c)
28.54/9.37	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.37	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.37	   A^2 -> H(U1(d, a), e)
28.54/9.37	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.37	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.37	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.37	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.37	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.37	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.37	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.37	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.37	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.37	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.37	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.37	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.37	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.37	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.37	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.37	   A^2 -> H(U1(a, c), b)
28.54/9.37	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.37	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.37	   A^2 -> H(U1(a, c), c)
28.54/9.37	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.37	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.37	   A^2 -> H(U1(a, c), e)
28.54/9.37	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, d), b)
28.54/9.37	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.37	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.37	   A^2 -> H(U1(a, d), c)
28.54/9.37	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.37	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.37	   A^2 -> H(U1(a, d), e)
28.54/9.37	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, a), d)
28.54/9.37	   A^2 -> H(U1(a, a), k)
28.54/9.37	   A^2 -> H(k, U1(b, b))
28.54/9.37	   A^2 -> H(k, f(c))
28.54/9.37	   A^2 -> H(k, f(d))
28.54/9.37	   A^2 -> H(c, U1(c, b))
28.54/9.37	   A^2 -> H(c, U1(d, b))
28.54/9.37	   A^2 -> H(c, U1(b, c))
28.54/9.37	   A^2 -> H(c, U1(b, d))
28.54/9.37	   A^2 -> H(c, U1(c, c))
28.54/9.37	   A^2 -> H(c, f(e))
28.54/9.37	   A^2 -> H(c, f(k))
28.54/9.37	   A^2 -> H(c, U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.37	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.37	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.37	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.37	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.37	   A^2 -> H(U1(e, k), f(e))
28.54/9.37	   A^2 -> H(U1(e, k), f(k))
28.54/9.37	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.37	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.37	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.37	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.37	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.37	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.37	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.37	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.37	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.37	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.37	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.37	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.37	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.37	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.37	   A^2 -> H(U1(k, e), f(e))
28.54/9.37	   A^2 -> H(U1(k, e), f(k))
28.54/9.37	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.37	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.37	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.37	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.37	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.37	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.37	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.37	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.37	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.37	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.37	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.37	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.37	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.37	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.37	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.37	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.37	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.37	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, c), b)
28.54/9.37	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.37	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.37	   A^2 -> H(U1(c, c), e)
28.54/9.37	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.37	   A^2 -> H(e, U1(c, b))
28.54/9.37	   A^2 -> H(e, U1(d, b))
28.54/9.37	   A^2 -> H(e, U1(b, c))
28.54/9.37	   A^2 -> H(e, U1(b, d))
28.54/9.37	   A^2 -> H(e, U1(c, c))
28.54/9.37	   A^2 -> H(e, f(e))
28.54/9.37	   A^2 -> H(e, f(k))
28.54/9.37	   A^2 -> H(e, U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.37	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.37	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.37	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.37	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.37	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.37	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.37	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.37	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.37	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.37	   A^2 -> H(f(e), b)
28.54/9.37	   A^2 -> H(f(e), U1(e, d))
28.54/9.37	   A^2 -> H(f(e), U1(d, e))
28.54/9.37	   A^2 -> H(f(e), c)
28.54/9.37	   A^2 -> H(f(e), U1(e, k))
28.54/9.37	   A^2 -> H(f(e), U1(k, e))
28.54/9.37	   A^2 -> H(f(e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.37	   A^2 -> H(f(k), b)
28.54/9.37	   A^2 -> H(f(k), U1(e, d))
28.54/9.37	   A^2 -> H(f(k), U1(d, e))
28.54/9.37	   A^2 -> H(f(k), c)
28.54/9.37	   A^2 -> H(f(k), U1(e, k))
28.54/9.37	   A^2 -> H(f(k), U1(k, e))
28.54/9.37	   A^2 -> H(f(k), e)
28.54/9.37	   A^2 -> H(f(c), d)
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.37	   A^2 -> H(U1(k, k), f(e))
28.54/9.37	   A^2 -> H(U1(k, k), f(k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.37	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.37	
28.54/9.37	The TRS R consists of the following rules:
28.54/9.37	
28.54/9.37	   f(x) -> U1(x, x)
28.54/9.37	   U1(e, x) -> x
28.54/9.37	   a -> c
28.54/9.37	   a -> d
28.54/9.37	   b -> c
28.54/9.37	   b -> d
28.54/9.37	   d -> k
28.54/9.37	   c -> e
28.54/9.37	   c -> k
28.54/9.37	
28.54/9.37	Q is empty.
28.54/9.37	We have to consider all minimal (P,Q,R)-chains.
28.54/9.37	----------------------------------------
28.54/9.37	
28.54/9.37	(999) TransformationProof (EQUIVALENT)
28.54/9.37	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.37	
28.54/9.37	   (A^2 -> H(U1(k, k), U1(b, d)),A^2 -> H(U1(k, k), U1(b, d)))
28.54/9.37	   (A^2 -> H(U1(k, d), U1(c, d)),A^2 -> H(U1(k, d), U1(c, d)))
28.54/9.37	   (A^2 -> H(U1(k, d), U1(d, d)),A^2 -> H(U1(k, d), U1(d, d)))
28.54/9.37	   (A^2 -> H(U1(k, d), U1(b, k)),A^2 -> H(U1(k, d), U1(b, k)))
28.54/9.37	
28.54/9.37	
28.54/9.37	----------------------------------------
28.54/9.37	
28.54/9.37	(1000)
28.54/9.37	Obligation:
28.54/9.37	Q DP problem:
28.54/9.37	The TRS P consists of the following rules:
28.54/9.37	
28.54/9.37	   H(x, x) -> G(x, x, f(k))
28.54/9.37	   G(d, x, x) -> A^2
28.54/9.37	   A^2 -> H(f(c), f(c))
28.54/9.37	   A^2 -> H(f(d), f(d))
28.54/9.37	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.37	   A^2 -> H(f(e), f(e))
28.54/9.37	   A^2 -> H(f(k), f(k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.37	   A^2 -> H(U1(k, d), U1(c, c))
28.54/9.37	   A^2 -> H(U1(k, d), f(e))
28.54/9.37	   A^2 -> H(U1(k, d), f(k))
28.54/9.37	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.37	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.37	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.37	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.37	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.37	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.37	   A^2 -> H(U1(d, k), f(e))
28.54/9.37	   A^2 -> H(U1(d, k), f(k))
28.54/9.37	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.37	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.37	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.37	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.37	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.37	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.37	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.37	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.37	   A^2 -> H(f(d), b)
28.54/9.37	   A^2 -> H(f(d), U1(e, d))
28.54/9.37	   A^2 -> H(f(d), U1(d, e))
28.54/9.37	   A^2 -> H(f(d), c)
28.54/9.37	   A^2 -> H(f(d), U1(e, k))
28.54/9.37	   A^2 -> H(f(d), U1(k, e))
28.54/9.37	   A^2 -> H(f(d), e)
28.54/9.37	   A^2 -> H(f(a), d)
28.54/9.37	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.37	   A^2 -> H(f(c), c)
28.54/9.37	   A^2 -> H(f(c), U1(e, k))
28.54/9.37	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.37	   A^2 -> H(f(c), U1(k, e))
28.54/9.37	   A^2 -> H(f(c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.37	   A^2 -> H(f(a), k)
28.54/9.37	   A^2 -> H(f(e), U1(e, e))
28.54/9.37	   A^2 -> H(f(c), e)
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.37	   A^2 -> H(f(d), U1(k, k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.37	   A^2 -> H(d, U1(b, b))
28.54/9.37	   A^2 -> H(d, f(c))
28.54/9.37	   A^2 -> H(d, f(d))
28.54/9.37	   A^2 -> H(a, U1(c, b))
28.54/9.37	   A^2 -> H(a, U1(d, b))
28.54/9.37	   A^2 -> H(a, U1(b, c))
28.54/9.37	   A^2 -> H(a, U1(b, d))
28.54/9.37	   A^2 -> H(a, U1(c, c))
28.54/9.37	   A^2 -> H(a, f(e))
28.54/9.37	   A^2 -> H(a, f(k))
28.54/9.37	   A^2 -> H(a, U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.37	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.37	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.37	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.37	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.37	   A^2 -> H(U1(e, d), f(e))
28.54/9.37	   A^2 -> H(U1(e, d), f(k))
28.54/9.37	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.37	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.37	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.37	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.37	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.37	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.37	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.37	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.37	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.37	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.37	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.37	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.37	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.37	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.37	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.37	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.37	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.37	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.37	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, a), b)
28.54/9.37	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.37	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.37	   A^2 -> H(U1(c, a), c)
28.54/9.37	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.37	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.37	   A^2 -> H(U1(c, a), e)
28.54/9.37	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.37	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.37	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.37	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.37	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.37	   A^2 -> H(U1(d, e), f(e))
28.54/9.37	   A^2 -> H(U1(d, e), f(k))
28.54/9.37	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.37	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.37	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.37	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.37	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.37	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.37	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.37	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.37	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.37	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.37	   A^2 -> H(U1(d, a), b)
28.54/9.37	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.37	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.37	   A^2 -> H(U1(d, a), c)
28.54/9.37	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.37	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.37	   A^2 -> H(U1(d, a), e)
28.54/9.37	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.37	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.37	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.37	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.37	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.37	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.37	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.37	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.37	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.37	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.37	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.37	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.37	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.37	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.37	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.37	   A^2 -> H(U1(a, c), b)
28.54/9.37	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.37	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.37	   A^2 -> H(U1(a, c), c)
28.54/9.37	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.37	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.37	   A^2 -> H(U1(a, c), e)
28.54/9.37	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, d), b)
28.54/9.37	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.37	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.37	   A^2 -> H(U1(a, d), c)
28.54/9.37	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.37	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.37	   A^2 -> H(U1(a, d), e)
28.54/9.37	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.37	   A^2 -> H(U1(a, a), d)
28.54/9.37	   A^2 -> H(U1(a, a), k)
28.54/9.37	   A^2 -> H(k, U1(b, b))
28.54/9.37	   A^2 -> H(k, f(c))
28.54/9.37	   A^2 -> H(k, f(d))
28.54/9.37	   A^2 -> H(c, U1(c, b))
28.54/9.37	   A^2 -> H(c, U1(d, b))
28.54/9.37	   A^2 -> H(c, U1(b, c))
28.54/9.37	   A^2 -> H(c, U1(b, d))
28.54/9.37	   A^2 -> H(c, U1(c, c))
28.54/9.37	   A^2 -> H(c, f(e))
28.54/9.37	   A^2 -> H(c, f(k))
28.54/9.37	   A^2 -> H(c, U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.37	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.37	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.37	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.37	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.37	   A^2 -> H(U1(e, k), f(e))
28.54/9.37	   A^2 -> H(U1(e, k), f(k))
28.54/9.37	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.37	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.37	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.37	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.37	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.37	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.37	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.37	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.37	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.37	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.37	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.37	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.37	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.37	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.37	   A^2 -> H(U1(k, e), f(e))
28.54/9.37	   A^2 -> H(U1(k, e), f(k))
28.54/9.37	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.37	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.37	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.37	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.37	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.37	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.37	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.37	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.37	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.37	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.37	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.37	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.37	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.37	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.37	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.37	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.37	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.37	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.37	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.37	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.37	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.37	   A^2 -> H(U1(c, c), b)
28.54/9.37	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.37	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.37	   A^2 -> H(U1(c, c), e)
28.54/9.37	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.37	   A^2 -> H(e, U1(c, b))
28.54/9.37	   A^2 -> H(e, U1(d, b))
28.54/9.37	   A^2 -> H(e, U1(b, c))
28.54/9.37	   A^2 -> H(e, U1(b, d))
28.54/9.37	   A^2 -> H(e, U1(c, c))
28.54/9.37	   A^2 -> H(e, f(e))
28.54/9.37	   A^2 -> H(e, f(k))
28.54/9.37	   A^2 -> H(e, U1(d, d))
28.54/9.37	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.37	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.37	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.37	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.37	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.37	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.37	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.37	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.37	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.37	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.37	   A^2 -> H(f(e), b)
28.54/9.37	   A^2 -> H(f(e), U1(e, d))
28.54/9.37	   A^2 -> H(f(e), U1(d, e))
28.54/9.37	   A^2 -> H(f(e), c)
28.54/9.37	   A^2 -> H(f(e), U1(e, k))
28.54/9.37	   A^2 -> H(f(e), U1(k, e))
28.54/9.37	   A^2 -> H(f(e), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.37	   A^2 -> H(f(k), b)
28.54/9.37	   A^2 -> H(f(k), U1(e, d))
28.54/9.37	   A^2 -> H(f(k), U1(d, e))
28.54/9.37	   A^2 -> H(f(k), c)
28.54/9.37	   A^2 -> H(f(k), U1(e, k))
28.54/9.37	   A^2 -> H(f(k), U1(k, e))
28.54/9.37	   A^2 -> H(f(k), e)
28.54/9.37	   A^2 -> H(f(c), d)
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.37	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.37	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.37	   A^2 -> H(U1(k, k), f(e))
28.54/9.37	   A^2 -> H(U1(k, k), f(k))
28.54/9.37	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.37	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.37	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.37	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.37	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.37	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.37	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.37	
28.54/9.37	The TRS R consists of the following rules:
28.54/9.37	
28.54/9.37	   f(x) -> U1(x, x)
28.54/9.37	   U1(e, x) -> x
28.54/9.37	   a -> c
28.54/9.37	   a -> d
28.54/9.37	   b -> c
28.54/9.37	   b -> d
28.54/9.37	   d -> k
28.54/9.37	   c -> e
28.54/9.37	   c -> k
28.54/9.37	
28.54/9.37	Q is empty.
28.54/9.37	We have to consider all minimal (P,Q,R)-chains.
28.54/9.37	----------------------------------------
28.54/9.37	
28.54/9.37	(1001) TransformationProof (EQUIVALENT)
28.54/9.37	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.37	
28.54/9.37	   (A^2 -> H(U1(k, k), U1(c, c)),A^2 -> H(U1(k, k), U1(c, c)))
28.54/9.37	   (A^2 -> H(U1(k, d), U1(e, c)),A^2 -> H(U1(k, d), U1(e, c)))
28.54/9.37	   (A^2 -> H(U1(k, d), U1(k, c)),A^2 -> H(U1(k, d), U1(k, c)))
28.54/9.37	   (A^2 -> H(U1(k, d), U1(c, e)),A^2 -> H(U1(k, d), U1(c, e)))
28.54/9.37	   (A^2 -> H(U1(k, d), U1(c, k)),A^2 -> H(U1(k, d), U1(c, k)))
28.54/9.37	
28.54/9.37	
28.54/9.37	----------------------------------------
28.54/9.37	
28.54/9.37	(1002)
28.54/9.37	Obligation:
28.54/9.37	Q DP problem:
28.54/9.37	The TRS P consists of the following rules:
28.54/9.37	
28.54/9.37	   H(x, x) -> G(x, x, f(k))
28.54/9.37	   G(d, x, x) -> A^2
28.54/9.37	   A^2 -> H(f(c), f(c))
28.54/9.37	   A^2 -> H(f(d), f(d))
28.54/9.37	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.37	   A^2 -> H(f(e), f(e))
28.54/9.37	   A^2 -> H(f(k), f(k))
28.54/9.37	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.37	   A^2 -> H(U1(k, d), f(e))
28.54/9.37	   A^2 -> H(U1(k, d), f(k))
28.54/9.37	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.37	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.37	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.37	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.37	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.37	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.37	   A^2 -> H(U1(d, k), f(e))
28.54/9.37	   A^2 -> H(U1(d, k), f(k))
28.54/9.37	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.37	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.37	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.37	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.38	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.38	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.38	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.38	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.38	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.38	   A^2 -> H(f(d), b)
28.54/9.38	   A^2 -> H(f(d), U1(e, d))
28.54/9.38	   A^2 -> H(f(d), U1(d, e))
28.54/9.38	   A^2 -> H(f(d), c)
28.54/9.38	   A^2 -> H(f(d), U1(e, k))
28.54/9.38	   A^2 -> H(f(d), U1(k, e))
28.54/9.38	   A^2 -> H(f(d), e)
28.54/9.38	   A^2 -> H(f(a), d)
28.54/9.38	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.38	   A^2 -> H(f(c), c)
28.54/9.38	   A^2 -> H(f(c), U1(e, k))
28.54/9.38	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.38	   A^2 -> H(f(c), U1(k, e))
28.54/9.38	   A^2 -> H(f(c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.38	   A^2 -> H(f(a), k)
28.54/9.38	   A^2 -> H(f(e), U1(e, e))
28.54/9.38	   A^2 -> H(f(c), e)
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.38	   A^2 -> H(f(d), U1(k, k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.38	   A^2 -> H(d, U1(b, b))
28.54/9.38	   A^2 -> H(d, f(c))
28.54/9.38	   A^2 -> H(d, f(d))
28.54/9.38	   A^2 -> H(a, U1(c, b))
28.54/9.38	   A^2 -> H(a, U1(d, b))
28.54/9.38	   A^2 -> H(a, U1(b, c))
28.54/9.38	   A^2 -> H(a, U1(b, d))
28.54/9.38	   A^2 -> H(a, U1(c, c))
28.54/9.38	   A^2 -> H(a, f(e))
28.54/9.38	   A^2 -> H(a, f(k))
28.54/9.38	   A^2 -> H(a, U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.38	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.38	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.38	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.38	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.38	   A^2 -> H(U1(e, d), f(e))
28.54/9.38	   A^2 -> H(U1(e, d), f(k))
28.54/9.38	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.38	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.38	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.38	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.38	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.38	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.38	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.38	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.38	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.38	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.38	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.38	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.38	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.38	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.38	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.38	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.38	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, a), b)
28.54/9.38	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.38	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.38	   A^2 -> H(U1(c, a), c)
28.54/9.38	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.38	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.38	   A^2 -> H(U1(c, a), e)
28.54/9.38	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.38	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.38	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.38	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.38	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.38	   A^2 -> H(U1(d, e), f(e))
28.54/9.38	   A^2 -> H(U1(d, e), f(k))
28.54/9.38	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.38	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.38	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.38	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.38	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.38	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.38	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.38	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.38	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.38	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.38	   A^2 -> H(U1(d, a), b)
28.54/9.38	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.38	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.38	   A^2 -> H(U1(d, a), c)
28.54/9.38	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.38	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.38	   A^2 -> H(U1(d, a), e)
28.54/9.38	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.38	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.38	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.38	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.38	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.38	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.38	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.38	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.38	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.38	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.38	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.38	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.38	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.38	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.38	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.38	   A^2 -> H(U1(a, c), b)
28.54/9.38	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.38	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.38	   A^2 -> H(U1(a, c), c)
28.54/9.38	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.38	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.38	   A^2 -> H(U1(a, c), e)
28.54/9.38	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, d), b)
28.54/9.38	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.38	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.38	   A^2 -> H(U1(a, d), c)
28.54/9.38	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.38	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.38	   A^2 -> H(U1(a, d), e)
28.54/9.38	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, a), d)
28.54/9.38	   A^2 -> H(U1(a, a), k)
28.54/9.38	   A^2 -> H(k, U1(b, b))
28.54/9.38	   A^2 -> H(k, f(c))
28.54/9.38	   A^2 -> H(k, f(d))
28.54/9.38	   A^2 -> H(c, U1(c, b))
28.54/9.38	   A^2 -> H(c, U1(d, b))
28.54/9.38	   A^2 -> H(c, U1(b, c))
28.54/9.38	   A^2 -> H(c, U1(b, d))
28.54/9.38	   A^2 -> H(c, U1(c, c))
28.54/9.38	   A^2 -> H(c, f(e))
28.54/9.38	   A^2 -> H(c, f(k))
28.54/9.38	   A^2 -> H(c, U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.38	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.38	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.38	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.38	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.38	   A^2 -> H(U1(e, k), f(e))
28.54/9.38	   A^2 -> H(U1(e, k), f(k))
28.54/9.38	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.38	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.38	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.38	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.38	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.38	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.38	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.38	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.38	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.38	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.38	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.38	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.38	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.38	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.38	   A^2 -> H(U1(k, e), f(e))
28.54/9.38	   A^2 -> H(U1(k, e), f(k))
28.54/9.38	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.38	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.38	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.38	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.38	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.38	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.38	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.38	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.38	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.38	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.38	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.38	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.38	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.38	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.38	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, c), b)
28.54/9.38	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.38	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.38	   A^2 -> H(U1(c, c), e)
28.54/9.38	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.38	   A^2 -> H(e, U1(c, b))
28.54/9.38	   A^2 -> H(e, U1(d, b))
28.54/9.38	   A^2 -> H(e, U1(b, c))
28.54/9.38	   A^2 -> H(e, U1(b, d))
28.54/9.38	   A^2 -> H(e, U1(c, c))
28.54/9.38	   A^2 -> H(e, f(e))
28.54/9.38	   A^2 -> H(e, f(k))
28.54/9.38	   A^2 -> H(e, U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.38	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.38	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.38	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.38	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.38	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.38	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.38	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.38	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.38	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.38	   A^2 -> H(f(e), b)
28.54/9.38	   A^2 -> H(f(e), U1(e, d))
28.54/9.38	   A^2 -> H(f(e), U1(d, e))
28.54/9.38	   A^2 -> H(f(e), c)
28.54/9.38	   A^2 -> H(f(e), U1(e, k))
28.54/9.38	   A^2 -> H(f(e), U1(k, e))
28.54/9.38	   A^2 -> H(f(e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.38	   A^2 -> H(f(k), b)
28.54/9.38	   A^2 -> H(f(k), U1(e, d))
28.54/9.38	   A^2 -> H(f(k), U1(d, e))
28.54/9.38	   A^2 -> H(f(k), c)
28.54/9.38	   A^2 -> H(f(k), U1(e, k))
28.54/9.38	   A^2 -> H(f(k), U1(k, e))
28.54/9.38	   A^2 -> H(f(k), e)
28.54/9.38	   A^2 -> H(f(c), d)
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.38	   A^2 -> H(U1(k, k), f(e))
28.54/9.38	   A^2 -> H(U1(k, k), f(k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.38	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.38	
28.54/9.38	The TRS R consists of the following rules:
28.54/9.38	
28.54/9.38	   f(x) -> U1(x, x)
28.54/9.38	   U1(e, x) -> x
28.54/9.38	   a -> c
28.54/9.38	   a -> d
28.54/9.38	   b -> c
28.54/9.38	   b -> d
28.54/9.38	   d -> k
28.54/9.38	   c -> e
28.54/9.38	   c -> k
28.54/9.38	
28.54/9.38	Q is empty.
28.54/9.38	We have to consider all minimal (P,Q,R)-chains.
28.54/9.38	----------------------------------------
28.54/9.38	
28.54/9.38	(1003) TransformationProof (EQUIVALENT)
28.54/9.38	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), f(e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.38	
28.54/9.38	   (A^2 -> H(U1(k, k), f(e)),A^2 -> H(U1(k, k), f(e)))
28.54/9.38	   (A^2 -> H(U1(k, d), U1(e, e)),A^2 -> H(U1(k, d), U1(e, e)))
28.54/9.38	
28.54/9.38	
28.54/9.38	----------------------------------------
28.54/9.38	
28.54/9.38	(1004)
28.54/9.38	Obligation:
28.54/9.38	Q DP problem:
28.54/9.38	The TRS P consists of the following rules:
28.54/9.38	
28.54/9.38	   H(x, x) -> G(x, x, f(k))
28.54/9.38	   G(d, x, x) -> A^2
28.54/9.38	   A^2 -> H(f(c), f(c))
28.54/9.38	   A^2 -> H(f(d), f(d))
28.54/9.38	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.38	   A^2 -> H(f(e), f(e))
28.54/9.38	   A^2 -> H(f(k), f(k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.38	   A^2 -> H(U1(k, d), f(k))
28.54/9.38	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.38	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.38	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.38	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.38	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.38	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.38	   A^2 -> H(U1(d, k), f(e))
28.54/9.38	   A^2 -> H(U1(d, k), f(k))
28.54/9.38	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.38	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.38	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.38	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.38	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.38	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.38	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.38	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.38	   A^2 -> H(f(d), b)
28.54/9.38	   A^2 -> H(f(d), U1(e, d))
28.54/9.38	   A^2 -> H(f(d), U1(d, e))
28.54/9.38	   A^2 -> H(f(d), c)
28.54/9.38	   A^2 -> H(f(d), U1(e, k))
28.54/9.38	   A^2 -> H(f(d), U1(k, e))
28.54/9.38	   A^2 -> H(f(d), e)
28.54/9.38	   A^2 -> H(f(a), d)
28.54/9.38	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.38	   A^2 -> H(f(c), c)
28.54/9.38	   A^2 -> H(f(c), U1(e, k))
28.54/9.38	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.38	   A^2 -> H(f(c), U1(k, e))
28.54/9.38	   A^2 -> H(f(c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.38	   A^2 -> H(f(a), k)
28.54/9.38	   A^2 -> H(f(e), U1(e, e))
28.54/9.38	   A^2 -> H(f(c), e)
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.38	   A^2 -> H(f(d), U1(k, k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.38	   A^2 -> H(d, U1(b, b))
28.54/9.38	   A^2 -> H(d, f(c))
28.54/9.38	   A^2 -> H(d, f(d))
28.54/9.38	   A^2 -> H(a, U1(c, b))
28.54/9.38	   A^2 -> H(a, U1(d, b))
28.54/9.38	   A^2 -> H(a, U1(b, c))
28.54/9.38	   A^2 -> H(a, U1(b, d))
28.54/9.38	   A^2 -> H(a, U1(c, c))
28.54/9.38	   A^2 -> H(a, f(e))
28.54/9.38	   A^2 -> H(a, f(k))
28.54/9.38	   A^2 -> H(a, U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.38	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.38	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.38	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.38	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.38	   A^2 -> H(U1(e, d), f(e))
28.54/9.38	   A^2 -> H(U1(e, d), f(k))
28.54/9.38	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.38	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.38	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.38	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.38	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.38	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.38	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.38	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.38	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.38	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.38	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.38	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.38	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.38	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.38	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.38	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.38	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, a), b)
28.54/9.38	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.38	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.38	   A^2 -> H(U1(c, a), c)
28.54/9.38	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.38	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.38	   A^2 -> H(U1(c, a), e)
28.54/9.38	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.38	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.38	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.38	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.38	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.38	   A^2 -> H(U1(d, e), f(e))
28.54/9.38	   A^2 -> H(U1(d, e), f(k))
28.54/9.38	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.38	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.38	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.38	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.38	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.38	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.38	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.38	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.38	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.38	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.38	   A^2 -> H(U1(d, a), b)
28.54/9.38	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.38	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.38	   A^2 -> H(U1(d, a), c)
28.54/9.38	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.38	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.38	   A^2 -> H(U1(d, a), e)
28.54/9.38	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.38	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.38	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.38	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.38	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.38	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.38	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.38	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.38	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.38	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.38	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.38	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.38	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.38	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.38	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.38	   A^2 -> H(U1(a, c), b)
28.54/9.38	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.38	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.38	   A^2 -> H(U1(a, c), c)
28.54/9.38	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.38	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.38	   A^2 -> H(U1(a, c), e)
28.54/9.38	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, d), b)
28.54/9.38	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.38	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.38	   A^2 -> H(U1(a, d), c)
28.54/9.38	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.38	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.38	   A^2 -> H(U1(a, d), e)
28.54/9.38	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, a), d)
28.54/9.38	   A^2 -> H(U1(a, a), k)
28.54/9.38	   A^2 -> H(k, U1(b, b))
28.54/9.38	   A^2 -> H(k, f(c))
28.54/9.38	   A^2 -> H(k, f(d))
28.54/9.38	   A^2 -> H(c, U1(c, b))
28.54/9.38	   A^2 -> H(c, U1(d, b))
28.54/9.38	   A^2 -> H(c, U1(b, c))
28.54/9.38	   A^2 -> H(c, U1(b, d))
28.54/9.38	   A^2 -> H(c, U1(c, c))
28.54/9.38	   A^2 -> H(c, f(e))
28.54/9.38	   A^2 -> H(c, f(k))
28.54/9.38	   A^2 -> H(c, U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.38	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.38	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.38	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.38	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.38	   A^2 -> H(U1(e, k), f(e))
28.54/9.38	   A^2 -> H(U1(e, k), f(k))
28.54/9.38	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.38	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.38	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.38	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.38	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.38	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.38	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.38	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.38	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.38	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.38	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.38	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.38	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.38	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.38	   A^2 -> H(U1(k, e), f(e))
28.54/9.38	   A^2 -> H(U1(k, e), f(k))
28.54/9.38	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.38	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.38	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.38	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.38	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.38	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.38	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.38	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.38	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.38	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.38	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.38	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.38	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.38	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.38	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, c), b)
28.54/9.38	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.38	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.38	   A^2 -> H(U1(c, c), e)
28.54/9.38	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.38	   A^2 -> H(e, U1(c, b))
28.54/9.38	   A^2 -> H(e, U1(d, b))
28.54/9.38	   A^2 -> H(e, U1(b, c))
28.54/9.38	   A^2 -> H(e, U1(b, d))
28.54/9.38	   A^2 -> H(e, U1(c, c))
28.54/9.38	   A^2 -> H(e, f(e))
28.54/9.38	   A^2 -> H(e, f(k))
28.54/9.38	   A^2 -> H(e, U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.38	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.38	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.38	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.38	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.38	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.38	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.38	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.38	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.38	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.38	   A^2 -> H(f(e), b)
28.54/9.38	   A^2 -> H(f(e), U1(e, d))
28.54/9.38	   A^2 -> H(f(e), U1(d, e))
28.54/9.38	   A^2 -> H(f(e), c)
28.54/9.38	   A^2 -> H(f(e), U1(e, k))
28.54/9.38	   A^2 -> H(f(e), U1(k, e))
28.54/9.38	   A^2 -> H(f(e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.38	   A^2 -> H(f(k), b)
28.54/9.38	   A^2 -> H(f(k), U1(e, d))
28.54/9.38	   A^2 -> H(f(k), U1(d, e))
28.54/9.38	   A^2 -> H(f(k), c)
28.54/9.38	   A^2 -> H(f(k), U1(e, k))
28.54/9.38	   A^2 -> H(f(k), U1(k, e))
28.54/9.38	   A^2 -> H(f(k), e)
28.54/9.38	   A^2 -> H(f(c), d)
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.38	   A^2 -> H(U1(k, k), f(e))
28.54/9.38	   A^2 -> H(U1(k, k), f(k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.38	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.38	
28.54/9.38	The TRS R consists of the following rules:
28.54/9.38	
28.54/9.38	   f(x) -> U1(x, x)
28.54/9.38	   U1(e, x) -> x
28.54/9.38	   a -> c
28.54/9.38	   a -> d
28.54/9.38	   b -> c
28.54/9.38	   b -> d
28.54/9.38	   d -> k
28.54/9.38	   c -> e
28.54/9.38	   c -> k
28.54/9.38	
28.54/9.38	Q is empty.
28.54/9.38	We have to consider all minimal (P,Q,R)-chains.
28.54/9.38	----------------------------------------
28.54/9.38	
28.54/9.38	(1005) TransformationProof (EQUIVALENT)
28.54/9.38	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), f(k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.38	
28.54/9.38	   (A^2 -> H(U1(k, k), f(k)),A^2 -> H(U1(k, k), f(k)))
28.54/9.38	   (A^2 -> H(U1(k, d), U1(k, k)),A^2 -> H(U1(k, d), U1(k, k)))
28.54/9.38	
28.54/9.38	
28.54/9.38	----------------------------------------
28.54/9.38	
28.54/9.38	(1006)
28.54/9.38	Obligation:
28.54/9.38	Q DP problem:
28.54/9.38	The TRS P consists of the following rules:
28.54/9.38	
28.54/9.38	   H(x, x) -> G(x, x, f(k))
28.54/9.38	   G(d, x, x) -> A^2
28.54/9.38	   A^2 -> H(f(c), f(c))
28.54/9.38	   A^2 -> H(f(d), f(d))
28.54/9.38	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.38	   A^2 -> H(f(e), f(e))
28.54/9.38	   A^2 -> H(f(k), f(k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.38	   A^2 -> H(U1(k, d), U1(d, d))
28.54/9.38	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.38	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.38	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.38	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.38	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.38	   A^2 -> H(U1(d, k), f(e))
28.54/9.38	   A^2 -> H(U1(d, k), f(k))
28.54/9.38	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.38	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.38	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.38	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.38	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.38	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.38	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.38	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.38	   A^2 -> H(f(d), b)
28.54/9.38	   A^2 -> H(f(d), U1(e, d))
28.54/9.38	   A^2 -> H(f(d), U1(d, e))
28.54/9.38	   A^2 -> H(f(d), c)
28.54/9.38	   A^2 -> H(f(d), U1(e, k))
28.54/9.38	   A^2 -> H(f(d), U1(k, e))
28.54/9.38	   A^2 -> H(f(d), e)
28.54/9.38	   A^2 -> H(f(a), d)
28.54/9.38	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.38	   A^2 -> H(f(c), c)
28.54/9.38	   A^2 -> H(f(c), U1(e, k))
28.54/9.38	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.38	   A^2 -> H(f(c), U1(k, e))
28.54/9.38	   A^2 -> H(f(c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.38	   A^2 -> H(f(a), k)
28.54/9.38	   A^2 -> H(f(e), U1(e, e))
28.54/9.38	   A^2 -> H(f(c), e)
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.38	   A^2 -> H(f(d), U1(k, k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.38	   A^2 -> H(d, U1(b, b))
28.54/9.38	   A^2 -> H(d, f(c))
28.54/9.38	   A^2 -> H(d, f(d))
28.54/9.38	   A^2 -> H(a, U1(c, b))
28.54/9.38	   A^2 -> H(a, U1(d, b))
28.54/9.38	   A^2 -> H(a, U1(b, c))
28.54/9.38	   A^2 -> H(a, U1(b, d))
28.54/9.38	   A^2 -> H(a, U1(c, c))
28.54/9.38	   A^2 -> H(a, f(e))
28.54/9.38	   A^2 -> H(a, f(k))
28.54/9.38	   A^2 -> H(a, U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.38	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.38	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.38	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.38	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.38	   A^2 -> H(U1(e, d), f(e))
28.54/9.38	   A^2 -> H(U1(e, d), f(k))
28.54/9.38	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.38	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.38	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.38	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.38	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.38	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.38	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.38	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.38	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.38	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.38	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.38	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.38	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.38	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.38	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.38	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.38	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, a), b)
28.54/9.38	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.38	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.38	   A^2 -> H(U1(c, a), c)
28.54/9.38	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.38	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.38	   A^2 -> H(U1(c, a), e)
28.54/9.38	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.38	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.38	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.38	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.38	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.38	   A^2 -> H(U1(d, e), f(e))
28.54/9.38	   A^2 -> H(U1(d, e), f(k))
28.54/9.38	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.38	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.38	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.38	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.38	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.38	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.38	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.38	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.38	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.38	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.38	   A^2 -> H(U1(d, a), b)
28.54/9.38	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.38	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.38	   A^2 -> H(U1(d, a), c)
28.54/9.38	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.38	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.38	   A^2 -> H(U1(d, a), e)
28.54/9.38	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.38	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.38	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.38	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.38	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.38	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.38	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.38	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.38	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.38	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.38	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.38	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.38	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.38	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.38	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.38	   A^2 -> H(U1(a, c), b)
28.54/9.38	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.38	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.38	   A^2 -> H(U1(a, c), c)
28.54/9.38	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.38	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.38	   A^2 -> H(U1(a, c), e)
28.54/9.38	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, d), b)
28.54/9.38	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.38	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.38	   A^2 -> H(U1(a, d), c)
28.54/9.38	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.38	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.38	   A^2 -> H(U1(a, d), e)
28.54/9.38	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, a), d)
28.54/9.38	   A^2 -> H(U1(a, a), k)
28.54/9.38	   A^2 -> H(k, U1(b, b))
28.54/9.38	   A^2 -> H(k, f(c))
28.54/9.38	   A^2 -> H(k, f(d))
28.54/9.38	   A^2 -> H(c, U1(c, b))
28.54/9.38	   A^2 -> H(c, U1(d, b))
28.54/9.38	   A^2 -> H(c, U1(b, c))
28.54/9.38	   A^2 -> H(c, U1(b, d))
28.54/9.38	   A^2 -> H(c, U1(c, c))
28.54/9.38	   A^2 -> H(c, f(e))
28.54/9.38	   A^2 -> H(c, f(k))
28.54/9.38	   A^2 -> H(c, U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.38	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.38	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.38	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.38	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.38	   A^2 -> H(U1(e, k), f(e))
28.54/9.38	   A^2 -> H(U1(e, k), f(k))
28.54/9.38	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.38	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.38	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.38	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.38	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.38	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.38	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.38	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.38	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.38	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.38	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.38	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.38	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.38	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.38	   A^2 -> H(U1(k, e), f(e))
28.54/9.38	   A^2 -> H(U1(k, e), f(k))
28.54/9.38	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.38	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.38	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.38	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.38	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.38	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.38	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.38	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.38	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.38	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.38	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.38	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.38	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.38	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.38	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, c), b)
28.54/9.38	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.38	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.38	   A^2 -> H(U1(c, c), e)
28.54/9.38	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.38	   A^2 -> H(e, U1(c, b))
28.54/9.38	   A^2 -> H(e, U1(d, b))
28.54/9.38	   A^2 -> H(e, U1(b, c))
28.54/9.38	   A^2 -> H(e, U1(b, d))
28.54/9.38	   A^2 -> H(e, U1(c, c))
28.54/9.38	   A^2 -> H(e, f(e))
28.54/9.38	   A^2 -> H(e, f(k))
28.54/9.38	   A^2 -> H(e, U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.38	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.38	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.38	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.38	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.38	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.38	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.38	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.38	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.38	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.38	   A^2 -> H(f(e), b)
28.54/9.38	   A^2 -> H(f(e), U1(e, d))
28.54/9.38	   A^2 -> H(f(e), U1(d, e))
28.54/9.38	   A^2 -> H(f(e), c)
28.54/9.38	   A^2 -> H(f(e), U1(e, k))
28.54/9.38	   A^2 -> H(f(e), U1(k, e))
28.54/9.38	   A^2 -> H(f(e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.38	   A^2 -> H(f(k), b)
28.54/9.38	   A^2 -> H(f(k), U1(e, d))
28.54/9.38	   A^2 -> H(f(k), U1(d, e))
28.54/9.38	   A^2 -> H(f(k), c)
28.54/9.38	   A^2 -> H(f(k), U1(e, k))
28.54/9.38	   A^2 -> H(f(k), U1(k, e))
28.54/9.38	   A^2 -> H(f(k), e)
28.54/9.38	   A^2 -> H(f(c), d)
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.38	   A^2 -> H(U1(k, k), f(e))
28.54/9.38	   A^2 -> H(U1(k, k), f(k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.38	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.38	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.38	
28.54/9.38	The TRS R consists of the following rules:
28.54/9.38	
28.54/9.38	   f(x) -> U1(x, x)
28.54/9.38	   U1(e, x) -> x
28.54/9.38	   a -> c
28.54/9.38	   a -> d
28.54/9.38	   b -> c
28.54/9.38	   b -> d
28.54/9.38	   d -> k
28.54/9.38	   c -> e
28.54/9.38	   c -> k
28.54/9.38	
28.54/9.38	Q is empty.
28.54/9.38	We have to consider all minimal (P,Q,R)-chains.
28.54/9.38	----------------------------------------
28.54/9.38	
28.54/9.38	(1007) TransformationProof (EQUIVALENT)
28.54/9.38	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.38	
28.54/9.38	   (A^2 -> H(U1(k, k), U1(d, d)),A^2 -> H(U1(k, k), U1(d, d)))
28.54/9.38	   (A^2 -> H(U1(k, d), U1(k, d)),A^2 -> H(U1(k, d), U1(k, d)))
28.54/9.38	   (A^2 -> H(U1(k, d), U1(d, k)),A^2 -> H(U1(k, d), U1(d, k)))
28.54/9.38	
28.54/9.38	
28.54/9.38	----------------------------------------
28.54/9.38	
28.54/9.38	(1008)
28.54/9.38	Obligation:
28.54/9.38	Q DP problem:
28.54/9.38	The TRS P consists of the following rules:
28.54/9.38	
28.54/9.38	   H(x, x) -> G(x, x, f(k))
28.54/9.38	   G(d, x, x) -> A^2
28.54/9.38	   A^2 -> H(f(c), f(c))
28.54/9.38	   A^2 -> H(f(d), f(d))
28.54/9.38	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.38	   A^2 -> H(f(e), f(e))
28.54/9.38	   A^2 -> H(f(k), f(k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.38	   A^2 -> H(U1(d, k), U1(c, b))
28.54/9.38	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.38	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.38	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.38	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.38	   A^2 -> H(U1(d, k), f(e))
28.54/9.38	   A^2 -> H(U1(d, k), f(k))
28.54/9.38	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.38	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.38	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.38	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.38	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.38	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.38	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.38	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.38	   A^2 -> H(f(d), b)
28.54/9.38	   A^2 -> H(f(d), U1(e, d))
28.54/9.38	   A^2 -> H(f(d), U1(d, e))
28.54/9.38	   A^2 -> H(f(d), c)
28.54/9.38	   A^2 -> H(f(d), U1(e, k))
28.54/9.38	   A^2 -> H(f(d), U1(k, e))
28.54/9.38	   A^2 -> H(f(d), e)
28.54/9.38	   A^2 -> H(f(a), d)
28.54/9.38	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.38	   A^2 -> H(f(c), c)
28.54/9.38	   A^2 -> H(f(c), U1(e, k))
28.54/9.38	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.38	   A^2 -> H(f(c), U1(k, e))
28.54/9.38	   A^2 -> H(f(c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.38	   A^2 -> H(f(a), k)
28.54/9.38	   A^2 -> H(f(e), U1(e, e))
28.54/9.38	   A^2 -> H(f(c), e)
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.38	   A^2 -> H(f(d), U1(k, k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.38	   A^2 -> H(d, U1(b, b))
28.54/9.38	   A^2 -> H(d, f(c))
28.54/9.38	   A^2 -> H(d, f(d))
28.54/9.38	   A^2 -> H(a, U1(c, b))
28.54/9.38	   A^2 -> H(a, U1(d, b))
28.54/9.38	   A^2 -> H(a, U1(b, c))
28.54/9.38	   A^2 -> H(a, U1(b, d))
28.54/9.38	   A^2 -> H(a, U1(c, c))
28.54/9.38	   A^2 -> H(a, f(e))
28.54/9.38	   A^2 -> H(a, f(k))
28.54/9.38	   A^2 -> H(a, U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.38	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.38	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.38	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.38	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.38	   A^2 -> H(U1(e, d), f(e))
28.54/9.38	   A^2 -> H(U1(e, d), f(k))
28.54/9.38	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.38	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.38	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.38	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.38	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.38	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.38	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.38	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.38	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.38	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.38	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.38	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.38	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.38	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.38	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.38	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.38	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, a), b)
28.54/9.38	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.38	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.38	   A^2 -> H(U1(c, a), c)
28.54/9.38	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.38	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.38	   A^2 -> H(U1(c, a), e)
28.54/9.38	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.38	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.38	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.38	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.38	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.38	   A^2 -> H(U1(d, e), f(e))
28.54/9.38	   A^2 -> H(U1(d, e), f(k))
28.54/9.38	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.38	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.38	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.38	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.38	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.38	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.38	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.38	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.38	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.38	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.38	   A^2 -> H(U1(d, a), b)
28.54/9.38	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.38	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.38	   A^2 -> H(U1(d, a), c)
28.54/9.38	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.38	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.38	   A^2 -> H(U1(d, a), e)
28.54/9.38	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.38	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.38	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.38	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.38	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.38	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.38	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.38	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.38	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.38	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.38	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.38	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.38	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.38	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.38	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.38	   A^2 -> H(U1(a, c), b)
28.54/9.38	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.38	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.38	   A^2 -> H(U1(a, c), c)
28.54/9.38	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.38	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.38	   A^2 -> H(U1(a, c), e)
28.54/9.38	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, d), b)
28.54/9.38	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.38	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.38	   A^2 -> H(U1(a, d), c)
28.54/9.38	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.38	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.38	   A^2 -> H(U1(a, d), e)
28.54/9.38	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, a), d)
28.54/9.38	   A^2 -> H(U1(a, a), k)
28.54/9.38	   A^2 -> H(k, U1(b, b))
28.54/9.38	   A^2 -> H(k, f(c))
28.54/9.38	   A^2 -> H(k, f(d))
28.54/9.38	   A^2 -> H(c, U1(c, b))
28.54/9.38	   A^2 -> H(c, U1(d, b))
28.54/9.38	   A^2 -> H(c, U1(b, c))
28.54/9.38	   A^2 -> H(c, U1(b, d))
28.54/9.38	   A^2 -> H(c, U1(c, c))
28.54/9.38	   A^2 -> H(c, f(e))
28.54/9.38	   A^2 -> H(c, f(k))
28.54/9.38	   A^2 -> H(c, U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.38	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.38	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.38	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.38	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.38	   A^2 -> H(U1(e, k), f(e))
28.54/9.38	   A^2 -> H(U1(e, k), f(k))
28.54/9.38	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.38	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.38	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.38	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.38	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.38	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.38	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.38	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.38	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.38	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.38	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.38	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.38	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.38	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.38	   A^2 -> H(U1(k, e), f(e))
28.54/9.38	   A^2 -> H(U1(k, e), f(k))
28.54/9.38	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.38	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.38	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.38	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.38	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.38	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.38	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.38	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.38	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.38	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.38	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.38	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.38	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.38	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.38	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, c), b)
28.54/9.38	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.38	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.38	   A^2 -> H(U1(c, c), e)
28.54/9.38	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.38	   A^2 -> H(e, U1(c, b))
28.54/9.38	   A^2 -> H(e, U1(d, b))
28.54/9.38	   A^2 -> H(e, U1(b, c))
28.54/9.38	   A^2 -> H(e, U1(b, d))
28.54/9.38	   A^2 -> H(e, U1(c, c))
28.54/9.38	   A^2 -> H(e, f(e))
28.54/9.38	   A^2 -> H(e, f(k))
28.54/9.38	   A^2 -> H(e, U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.38	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.38	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.38	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.38	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.38	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.38	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.38	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.38	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.38	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.38	   A^2 -> H(f(e), b)
28.54/9.38	   A^2 -> H(f(e), U1(e, d))
28.54/9.38	   A^2 -> H(f(e), U1(d, e))
28.54/9.38	   A^2 -> H(f(e), c)
28.54/9.38	   A^2 -> H(f(e), U1(e, k))
28.54/9.38	   A^2 -> H(f(e), U1(k, e))
28.54/9.38	   A^2 -> H(f(e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.38	   A^2 -> H(f(k), b)
28.54/9.38	   A^2 -> H(f(k), U1(e, d))
28.54/9.38	   A^2 -> H(f(k), U1(d, e))
28.54/9.38	   A^2 -> H(f(k), c)
28.54/9.38	   A^2 -> H(f(k), U1(e, k))
28.54/9.38	   A^2 -> H(f(k), U1(k, e))
28.54/9.38	   A^2 -> H(f(k), e)
28.54/9.38	   A^2 -> H(f(c), d)
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.38	   A^2 -> H(U1(k, k), f(e))
28.54/9.38	   A^2 -> H(U1(k, k), f(k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.38	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.38	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.38	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.38	
28.54/9.38	The TRS R consists of the following rules:
28.54/9.38	
28.54/9.38	   f(x) -> U1(x, x)
28.54/9.38	   U1(e, x) -> x
28.54/9.38	   a -> c
28.54/9.38	   a -> d
28.54/9.38	   b -> c
28.54/9.38	   b -> d
28.54/9.38	   d -> k
28.54/9.38	   c -> e
28.54/9.38	   c -> k
28.54/9.38	
28.54/9.38	Q is empty.
28.54/9.38	We have to consider all minimal (P,Q,R)-chains.
28.54/9.38	----------------------------------------
28.54/9.38	
28.54/9.38	(1009) TransformationProof (EQUIVALENT)
28.54/9.38	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.38	
28.54/9.38	   (A^2 -> H(U1(k, k), U1(c, b)),A^2 -> H(U1(k, k), U1(c, b)))
28.54/9.38	   (A^2 -> H(U1(d, k), U1(e, b)),A^2 -> H(U1(d, k), U1(e, b)))
28.54/9.38	   (A^2 -> H(U1(d, k), U1(k, b)),A^2 -> H(U1(d, k), U1(k, b)))
28.54/9.38	   (A^2 -> H(U1(d, k), U1(c, c)),A^2 -> H(U1(d, k), U1(c, c)))
28.54/9.38	   (A^2 -> H(U1(d, k), U1(c, d)),A^2 -> H(U1(d, k), U1(c, d)))
28.54/9.38	
28.54/9.38	
28.54/9.38	----------------------------------------
28.54/9.38	
28.54/9.38	(1010)
28.54/9.38	Obligation:
28.54/9.38	Q DP problem:
28.54/9.38	The TRS P consists of the following rules:
28.54/9.38	
28.54/9.38	   H(x, x) -> G(x, x, f(k))
28.54/9.38	   G(d, x, x) -> A^2
28.54/9.38	   A^2 -> H(f(c), f(c))
28.54/9.38	   A^2 -> H(f(d), f(d))
28.54/9.38	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.38	   A^2 -> H(f(e), f(e))
28.54/9.38	   A^2 -> H(f(k), f(k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.38	   A^2 -> H(U1(d, k), U1(d, b))
28.54/9.38	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.38	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.38	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.38	   A^2 -> H(U1(d, k), f(e))
28.54/9.38	   A^2 -> H(U1(d, k), f(k))
28.54/9.38	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.38	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.38	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.38	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.38	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.38	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.38	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.38	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.38	   A^2 -> H(f(d), b)
28.54/9.38	   A^2 -> H(f(d), U1(e, d))
28.54/9.38	   A^2 -> H(f(d), U1(d, e))
28.54/9.38	   A^2 -> H(f(d), c)
28.54/9.38	   A^2 -> H(f(d), U1(e, k))
28.54/9.38	   A^2 -> H(f(d), U1(k, e))
28.54/9.38	   A^2 -> H(f(d), e)
28.54/9.38	   A^2 -> H(f(a), d)
28.54/9.38	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.38	   A^2 -> H(f(c), c)
28.54/9.38	   A^2 -> H(f(c), U1(e, k))
28.54/9.38	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.38	   A^2 -> H(f(c), U1(k, e))
28.54/9.38	   A^2 -> H(f(c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.38	   A^2 -> H(f(a), k)
28.54/9.38	   A^2 -> H(f(e), U1(e, e))
28.54/9.38	   A^2 -> H(f(c), e)
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.38	   A^2 -> H(f(d), U1(k, k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.38	   A^2 -> H(d, U1(b, b))
28.54/9.38	   A^2 -> H(d, f(c))
28.54/9.38	   A^2 -> H(d, f(d))
28.54/9.38	   A^2 -> H(a, U1(c, b))
28.54/9.38	   A^2 -> H(a, U1(d, b))
28.54/9.38	   A^2 -> H(a, U1(b, c))
28.54/9.38	   A^2 -> H(a, U1(b, d))
28.54/9.38	   A^2 -> H(a, U1(c, c))
28.54/9.38	   A^2 -> H(a, f(e))
28.54/9.38	   A^2 -> H(a, f(k))
28.54/9.38	   A^2 -> H(a, U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.38	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.38	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.38	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.38	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.38	   A^2 -> H(U1(e, d), f(e))
28.54/9.38	   A^2 -> H(U1(e, d), f(k))
28.54/9.38	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.38	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.38	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.38	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.38	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.38	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.38	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.38	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.38	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.38	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.38	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.38	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.38	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.38	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.38	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.38	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.38	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, a), b)
28.54/9.38	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.38	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.38	   A^2 -> H(U1(c, a), c)
28.54/9.38	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.38	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.38	   A^2 -> H(U1(c, a), e)
28.54/9.38	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.38	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.38	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.38	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.38	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.38	   A^2 -> H(U1(d, e), f(e))
28.54/9.38	   A^2 -> H(U1(d, e), f(k))
28.54/9.38	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.38	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.38	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.38	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.38	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.38	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.38	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.38	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.38	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.38	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.38	   A^2 -> H(U1(d, a), b)
28.54/9.38	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.38	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.38	   A^2 -> H(U1(d, a), c)
28.54/9.38	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.38	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.38	   A^2 -> H(U1(d, a), e)
28.54/9.38	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.38	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.38	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.38	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.38	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.38	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.38	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.38	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.38	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.38	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.38	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.38	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.38	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.38	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.38	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.38	   A^2 -> H(U1(a, c), b)
28.54/9.38	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.38	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.38	   A^2 -> H(U1(a, c), c)
28.54/9.38	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.38	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.38	   A^2 -> H(U1(a, c), e)
28.54/9.38	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, d), b)
28.54/9.38	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.38	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.38	   A^2 -> H(U1(a, d), c)
28.54/9.38	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.38	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.38	   A^2 -> H(U1(a, d), e)
28.54/9.38	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.38	   A^2 -> H(U1(a, a), d)
28.54/9.38	   A^2 -> H(U1(a, a), k)
28.54/9.38	   A^2 -> H(k, U1(b, b))
28.54/9.38	   A^2 -> H(k, f(c))
28.54/9.38	   A^2 -> H(k, f(d))
28.54/9.38	   A^2 -> H(c, U1(c, b))
28.54/9.38	   A^2 -> H(c, U1(d, b))
28.54/9.38	   A^2 -> H(c, U1(b, c))
28.54/9.38	   A^2 -> H(c, U1(b, d))
28.54/9.38	   A^2 -> H(c, U1(c, c))
28.54/9.38	   A^2 -> H(c, f(e))
28.54/9.38	   A^2 -> H(c, f(k))
28.54/9.38	   A^2 -> H(c, U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.38	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.38	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.38	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.38	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.38	   A^2 -> H(U1(e, k), f(e))
28.54/9.38	   A^2 -> H(U1(e, k), f(k))
28.54/9.38	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.38	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.38	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.38	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.38	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.38	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.38	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.38	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.38	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.38	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.38	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.38	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.38	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.38	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.38	   A^2 -> H(U1(k, e), f(e))
28.54/9.38	   A^2 -> H(U1(k, e), f(k))
28.54/9.38	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.38	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.38	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.38	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.38	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.38	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.38	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.38	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.38	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.38	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.38	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.38	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.38	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.38	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.38	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.38	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.38	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.38	   A^2 -> H(U1(c, c), b)
28.54/9.38	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.38	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.38	   A^2 -> H(U1(c, c), e)
28.54/9.38	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.38	   A^2 -> H(e, U1(c, b))
28.54/9.38	   A^2 -> H(e, U1(d, b))
28.54/9.38	   A^2 -> H(e, U1(b, c))
28.54/9.38	   A^2 -> H(e, U1(b, d))
28.54/9.38	   A^2 -> H(e, U1(c, c))
28.54/9.38	   A^2 -> H(e, f(e))
28.54/9.38	   A^2 -> H(e, f(k))
28.54/9.38	   A^2 -> H(e, U1(d, d))
28.54/9.38	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.38	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.38	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.38	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.38	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.38	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.38	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.38	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.38	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.38	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.38	   A^2 -> H(f(e), b)
28.54/9.38	   A^2 -> H(f(e), U1(e, d))
28.54/9.38	   A^2 -> H(f(e), U1(d, e))
28.54/9.38	   A^2 -> H(f(e), c)
28.54/9.38	   A^2 -> H(f(e), U1(e, k))
28.54/9.38	   A^2 -> H(f(e), U1(k, e))
28.54/9.38	   A^2 -> H(f(e), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.38	   A^2 -> H(f(k), b)
28.54/9.38	   A^2 -> H(f(k), U1(e, d))
28.54/9.38	   A^2 -> H(f(k), U1(d, e))
28.54/9.38	   A^2 -> H(f(k), c)
28.54/9.38	   A^2 -> H(f(k), U1(e, k))
28.54/9.38	   A^2 -> H(f(k), U1(k, e))
28.54/9.38	   A^2 -> H(f(k), e)
28.54/9.38	   A^2 -> H(f(c), d)
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.38	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.38	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.38	   A^2 -> H(U1(k, k), f(e))
28.54/9.38	   A^2 -> H(U1(k, k), f(k))
28.54/9.38	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.38	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.38	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.38	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.38	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.38	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.38	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.38	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.38	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.38	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.38	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.38	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.38	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.38	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.38	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.38	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.38	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.38	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.38	
28.54/9.38	The TRS R consists of the following rules:
28.54/9.38	
28.54/9.38	   f(x) -> U1(x, x)
28.54/9.38	   U1(e, x) -> x
28.54/9.38	   a -> c
28.54/9.38	   a -> d
28.54/9.38	   b -> c
28.54/9.38	   b -> d
28.54/9.38	   d -> k
28.54/9.38	   c -> e
28.54/9.38	   c -> k
28.54/9.38	
28.54/9.38	Q is empty.
28.54/9.38	We have to consider all minimal (P,Q,R)-chains.
28.54/9.38	----------------------------------------
28.54/9.38	
28.54/9.38	(1011) TransformationProof (EQUIVALENT)
28.54/9.38	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.38	
28.54/9.38	   (A^2 -> H(U1(k, k), U1(d, b)),A^2 -> H(U1(k, k), U1(d, b)))
28.54/9.38	   (A^2 -> H(U1(d, k), U1(k, b)),A^2 -> H(U1(d, k), U1(k, b)))
28.54/9.38	   (A^2 -> H(U1(d, k), U1(d, c)),A^2 -> H(U1(d, k), U1(d, c)))
28.54/9.38	   (A^2 -> H(U1(d, k), U1(d, d)),A^2 -> H(U1(d, k), U1(d, d)))
28.54/9.38	
28.54/9.38	
28.54/9.38	----------------------------------------
28.54/9.38	
28.54/9.38	(1012)
28.54/9.38	Obligation:
28.54/9.38	Q DP problem:
28.54/9.38	The TRS P consists of the following rules:
28.54/9.38	
28.54/9.38	   H(x, x) -> G(x, x, f(k))
28.54/9.38	   G(d, x, x) -> A^2
28.54/9.38	   A^2 -> H(f(c), f(c))
28.54/9.38	   A^2 -> H(f(d), f(d))
28.54/9.38	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.38	   A^2 -> H(f(e), f(e))
28.54/9.38	   A^2 -> H(f(k), f(k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.38	   A^2 -> H(U1(d, k), U1(b, c))
28.54/9.38	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.38	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.38	   A^2 -> H(U1(d, k), f(e))
28.54/9.38	   A^2 -> H(U1(d, k), f(k))
28.54/9.38	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.38	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.38	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.38	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.38	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.38	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.38	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.38	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.38	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.38	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.39	   A^2 -> H(f(d), b)
28.54/9.39	   A^2 -> H(f(d), U1(e, d))
28.54/9.39	   A^2 -> H(f(d), U1(d, e))
28.54/9.39	   A^2 -> H(f(d), c)
28.54/9.39	   A^2 -> H(f(d), U1(e, k))
28.54/9.39	   A^2 -> H(f(d), U1(k, e))
28.54/9.39	   A^2 -> H(f(d), e)
28.54/9.39	   A^2 -> H(f(a), d)
28.54/9.39	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.39	   A^2 -> H(f(c), c)
28.54/9.39	   A^2 -> H(f(c), U1(e, k))
28.54/9.39	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.39	   A^2 -> H(f(c), U1(k, e))
28.54/9.39	   A^2 -> H(f(c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.39	   A^2 -> H(f(a), k)
28.54/9.39	   A^2 -> H(f(e), U1(e, e))
28.54/9.39	   A^2 -> H(f(c), e)
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.39	   A^2 -> H(f(d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.39	   A^2 -> H(d, U1(b, b))
28.54/9.39	   A^2 -> H(d, f(c))
28.54/9.39	   A^2 -> H(d, f(d))
28.54/9.39	   A^2 -> H(a, U1(c, b))
28.54/9.39	   A^2 -> H(a, U1(d, b))
28.54/9.39	   A^2 -> H(a, U1(b, c))
28.54/9.39	   A^2 -> H(a, U1(b, d))
28.54/9.39	   A^2 -> H(a, U1(c, c))
28.54/9.39	   A^2 -> H(a, f(e))
28.54/9.39	   A^2 -> H(a, f(k))
28.54/9.39	   A^2 -> H(a, U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.39	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.39	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.39	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.39	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.39	   A^2 -> H(U1(e, d), f(e))
28.54/9.39	   A^2 -> H(U1(e, d), f(k))
28.54/9.39	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.39	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.39	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.39	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.39	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.39	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.39	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.39	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.39	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.39	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.39	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.39	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.39	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.39	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.39	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.39	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, a), b)
28.54/9.39	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.39	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.39	   A^2 -> H(U1(c, a), c)
28.54/9.39	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.39	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.39	   A^2 -> H(U1(c, a), e)
28.54/9.39	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.39	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.39	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.39	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.39	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.39	   A^2 -> H(U1(d, e), f(e))
28.54/9.39	   A^2 -> H(U1(d, e), f(k))
28.54/9.39	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.39	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.39	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.39	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.39	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.39	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.39	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.39	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.39	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.39	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.39	   A^2 -> H(U1(d, a), b)
28.54/9.39	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.39	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.39	   A^2 -> H(U1(d, a), c)
28.54/9.39	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.39	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.39	   A^2 -> H(U1(d, a), e)
28.54/9.39	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.39	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.39	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.39	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.39	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.39	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.39	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.39	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.39	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.39	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.39	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.39	   A^2 -> H(U1(a, c), b)
28.54/9.39	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.39	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.39	   A^2 -> H(U1(a, c), c)
28.54/9.39	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.39	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.39	   A^2 -> H(U1(a, c), e)
28.54/9.39	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, d), b)
28.54/9.39	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.39	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.39	   A^2 -> H(U1(a, d), c)
28.54/9.39	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.39	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.39	   A^2 -> H(U1(a, d), e)
28.54/9.39	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, a), d)
28.54/9.39	   A^2 -> H(U1(a, a), k)
28.54/9.39	   A^2 -> H(k, U1(b, b))
28.54/9.39	   A^2 -> H(k, f(c))
28.54/9.39	   A^2 -> H(k, f(d))
28.54/9.39	   A^2 -> H(c, U1(c, b))
28.54/9.39	   A^2 -> H(c, U1(d, b))
28.54/9.39	   A^2 -> H(c, U1(b, c))
28.54/9.39	   A^2 -> H(c, U1(b, d))
28.54/9.39	   A^2 -> H(c, U1(c, c))
28.54/9.39	   A^2 -> H(c, f(e))
28.54/9.39	   A^2 -> H(c, f(k))
28.54/9.39	   A^2 -> H(c, U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.39	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.39	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.39	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.39	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.39	   A^2 -> H(U1(e, k), f(e))
28.54/9.39	   A^2 -> H(U1(e, k), f(k))
28.54/9.39	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.39	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.39	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.39	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.39	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.39	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.39	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.39	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.39	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.39	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.39	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.39	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.39	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.39	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.39	   A^2 -> H(U1(k, e), f(e))
28.54/9.39	   A^2 -> H(U1(k, e), f(k))
28.54/9.39	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.39	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.39	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.39	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.39	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.39	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.39	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.39	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.39	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.39	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, c), b)
28.54/9.39	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.39	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.39	   A^2 -> H(U1(c, c), e)
28.54/9.39	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.39	   A^2 -> H(e, U1(c, b))
28.54/9.39	   A^2 -> H(e, U1(d, b))
28.54/9.39	   A^2 -> H(e, U1(b, c))
28.54/9.39	   A^2 -> H(e, U1(b, d))
28.54/9.39	   A^2 -> H(e, U1(c, c))
28.54/9.39	   A^2 -> H(e, f(e))
28.54/9.39	   A^2 -> H(e, f(k))
28.54/9.39	   A^2 -> H(e, U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.39	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.39	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.39	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.39	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.39	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.39	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.39	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.39	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.39	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.39	   A^2 -> H(f(e), b)
28.54/9.39	   A^2 -> H(f(e), U1(e, d))
28.54/9.39	   A^2 -> H(f(e), U1(d, e))
28.54/9.39	   A^2 -> H(f(e), c)
28.54/9.39	   A^2 -> H(f(e), U1(e, k))
28.54/9.39	   A^2 -> H(f(e), U1(k, e))
28.54/9.39	   A^2 -> H(f(e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.39	   A^2 -> H(f(k), b)
28.54/9.39	   A^2 -> H(f(k), U1(e, d))
28.54/9.39	   A^2 -> H(f(k), U1(d, e))
28.54/9.39	   A^2 -> H(f(k), c)
28.54/9.39	   A^2 -> H(f(k), U1(e, k))
28.54/9.39	   A^2 -> H(f(k), U1(k, e))
28.54/9.39	   A^2 -> H(f(k), e)
28.54/9.39	   A^2 -> H(f(c), d)
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.39	   A^2 -> H(U1(k, k), f(e))
28.54/9.39	   A^2 -> H(U1(k, k), f(k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.39	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.39	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.39	
28.54/9.39	The TRS R consists of the following rules:
28.54/9.39	
28.54/9.39	   f(x) -> U1(x, x)
28.54/9.39	   U1(e, x) -> x
28.54/9.39	   a -> c
28.54/9.39	   a -> d
28.54/9.39	   b -> c
28.54/9.39	   b -> d
28.54/9.39	   d -> k
28.54/9.39	   c -> e
28.54/9.39	   c -> k
28.54/9.39	
28.54/9.39	Q is empty.
28.54/9.39	We have to consider all minimal (P,Q,R)-chains.
28.54/9.39	----------------------------------------
28.54/9.39	
28.54/9.39	(1013) TransformationProof (EQUIVALENT)
28.54/9.39	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.39	
28.54/9.39	   (A^2 -> H(U1(k, k), U1(b, c)),A^2 -> H(U1(k, k), U1(b, c)))
28.54/9.39	   (A^2 -> H(U1(d, k), U1(c, c)),A^2 -> H(U1(d, k), U1(c, c)))
28.54/9.39	   (A^2 -> H(U1(d, k), U1(d, c)),A^2 -> H(U1(d, k), U1(d, c)))
28.54/9.39	   (A^2 -> H(U1(d, k), U1(b, e)),A^2 -> H(U1(d, k), U1(b, e)))
28.54/9.39	   (A^2 -> H(U1(d, k), U1(b, k)),A^2 -> H(U1(d, k), U1(b, k)))
28.54/9.39	
28.54/9.39	
28.54/9.39	----------------------------------------
28.54/9.39	
28.54/9.39	(1014)
28.54/9.39	Obligation:
28.54/9.39	Q DP problem:
28.54/9.39	The TRS P consists of the following rules:
28.54/9.39	
28.54/9.39	   H(x, x) -> G(x, x, f(k))
28.54/9.39	   G(d, x, x) -> A^2
28.54/9.39	   A^2 -> H(f(c), f(c))
28.54/9.39	   A^2 -> H(f(d), f(d))
28.54/9.39	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.39	   A^2 -> H(f(e), f(e))
28.54/9.39	   A^2 -> H(f(k), f(k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.39	   A^2 -> H(U1(d, k), U1(b, d))
28.54/9.39	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.39	   A^2 -> H(U1(d, k), f(e))
28.54/9.39	   A^2 -> H(U1(d, k), f(k))
28.54/9.39	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.39	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.39	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.39	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.39	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.39	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.39	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.39	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.39	   A^2 -> H(f(d), b)
28.54/9.39	   A^2 -> H(f(d), U1(e, d))
28.54/9.39	   A^2 -> H(f(d), U1(d, e))
28.54/9.39	   A^2 -> H(f(d), c)
28.54/9.39	   A^2 -> H(f(d), U1(e, k))
28.54/9.39	   A^2 -> H(f(d), U1(k, e))
28.54/9.39	   A^2 -> H(f(d), e)
28.54/9.39	   A^2 -> H(f(a), d)
28.54/9.39	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.39	   A^2 -> H(f(c), c)
28.54/9.39	   A^2 -> H(f(c), U1(e, k))
28.54/9.39	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.39	   A^2 -> H(f(c), U1(k, e))
28.54/9.39	   A^2 -> H(f(c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.39	   A^2 -> H(f(a), k)
28.54/9.39	   A^2 -> H(f(e), U1(e, e))
28.54/9.39	   A^2 -> H(f(c), e)
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.39	   A^2 -> H(f(d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.39	   A^2 -> H(d, U1(b, b))
28.54/9.39	   A^2 -> H(d, f(c))
28.54/9.39	   A^2 -> H(d, f(d))
28.54/9.39	   A^2 -> H(a, U1(c, b))
28.54/9.39	   A^2 -> H(a, U1(d, b))
28.54/9.39	   A^2 -> H(a, U1(b, c))
28.54/9.39	   A^2 -> H(a, U1(b, d))
28.54/9.39	   A^2 -> H(a, U1(c, c))
28.54/9.39	   A^2 -> H(a, f(e))
28.54/9.39	   A^2 -> H(a, f(k))
28.54/9.39	   A^2 -> H(a, U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.39	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.39	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.39	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.39	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.39	   A^2 -> H(U1(e, d), f(e))
28.54/9.39	   A^2 -> H(U1(e, d), f(k))
28.54/9.39	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.39	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.39	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.39	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.39	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.39	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.39	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.39	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.39	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.39	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.39	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.39	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.39	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.39	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.39	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.39	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, a), b)
28.54/9.39	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.39	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.39	   A^2 -> H(U1(c, a), c)
28.54/9.39	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.39	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.39	   A^2 -> H(U1(c, a), e)
28.54/9.39	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.39	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.39	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.39	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.39	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.39	   A^2 -> H(U1(d, e), f(e))
28.54/9.39	   A^2 -> H(U1(d, e), f(k))
28.54/9.39	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.39	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.39	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.39	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.39	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.39	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.39	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.39	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.39	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.39	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.39	   A^2 -> H(U1(d, a), b)
28.54/9.39	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.39	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.39	   A^2 -> H(U1(d, a), c)
28.54/9.39	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.39	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.39	   A^2 -> H(U1(d, a), e)
28.54/9.39	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.39	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.39	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.39	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.39	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.39	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.39	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.39	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.39	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.39	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.39	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.39	   A^2 -> H(U1(a, c), b)
28.54/9.39	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.39	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.39	   A^2 -> H(U1(a, c), c)
28.54/9.39	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.39	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.39	   A^2 -> H(U1(a, c), e)
28.54/9.39	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, d), b)
28.54/9.39	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.39	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.39	   A^2 -> H(U1(a, d), c)
28.54/9.39	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.39	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.39	   A^2 -> H(U1(a, d), e)
28.54/9.39	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, a), d)
28.54/9.39	   A^2 -> H(U1(a, a), k)
28.54/9.39	   A^2 -> H(k, U1(b, b))
28.54/9.39	   A^2 -> H(k, f(c))
28.54/9.39	   A^2 -> H(k, f(d))
28.54/9.39	   A^2 -> H(c, U1(c, b))
28.54/9.39	   A^2 -> H(c, U1(d, b))
28.54/9.39	   A^2 -> H(c, U1(b, c))
28.54/9.39	   A^2 -> H(c, U1(b, d))
28.54/9.39	   A^2 -> H(c, U1(c, c))
28.54/9.39	   A^2 -> H(c, f(e))
28.54/9.39	   A^2 -> H(c, f(k))
28.54/9.39	   A^2 -> H(c, U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.39	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.39	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.39	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.39	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.39	   A^2 -> H(U1(e, k), f(e))
28.54/9.39	   A^2 -> H(U1(e, k), f(k))
28.54/9.39	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.39	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.39	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.39	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.39	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.39	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.39	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.39	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.39	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.39	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.39	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.39	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.39	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.39	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.39	   A^2 -> H(U1(k, e), f(e))
28.54/9.39	   A^2 -> H(U1(k, e), f(k))
28.54/9.39	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.39	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.39	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.39	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.39	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.39	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.39	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.39	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.39	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.39	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, c), b)
28.54/9.39	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.39	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.39	   A^2 -> H(U1(c, c), e)
28.54/9.39	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.39	   A^2 -> H(e, U1(c, b))
28.54/9.39	   A^2 -> H(e, U1(d, b))
28.54/9.39	   A^2 -> H(e, U1(b, c))
28.54/9.39	   A^2 -> H(e, U1(b, d))
28.54/9.39	   A^2 -> H(e, U1(c, c))
28.54/9.39	   A^2 -> H(e, f(e))
28.54/9.39	   A^2 -> H(e, f(k))
28.54/9.39	   A^2 -> H(e, U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.39	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.39	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.39	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.39	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.39	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.39	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.39	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.39	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.39	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.39	   A^2 -> H(f(e), b)
28.54/9.39	   A^2 -> H(f(e), U1(e, d))
28.54/9.39	   A^2 -> H(f(e), U1(d, e))
28.54/9.39	   A^2 -> H(f(e), c)
28.54/9.39	   A^2 -> H(f(e), U1(e, k))
28.54/9.39	   A^2 -> H(f(e), U1(k, e))
28.54/9.39	   A^2 -> H(f(e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.39	   A^2 -> H(f(k), b)
28.54/9.39	   A^2 -> H(f(k), U1(e, d))
28.54/9.39	   A^2 -> H(f(k), U1(d, e))
28.54/9.39	   A^2 -> H(f(k), c)
28.54/9.39	   A^2 -> H(f(k), U1(e, k))
28.54/9.39	   A^2 -> H(f(k), U1(k, e))
28.54/9.39	   A^2 -> H(f(k), e)
28.54/9.39	   A^2 -> H(f(c), d)
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.39	   A^2 -> H(U1(k, k), f(e))
28.54/9.39	   A^2 -> H(U1(k, k), f(k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.39	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.39	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.39	
28.54/9.39	The TRS R consists of the following rules:
28.54/9.39	
28.54/9.39	   f(x) -> U1(x, x)
28.54/9.39	   U1(e, x) -> x
28.54/9.39	   a -> c
28.54/9.39	   a -> d
28.54/9.39	   b -> c
28.54/9.39	   b -> d
28.54/9.39	   d -> k
28.54/9.39	   c -> e
28.54/9.39	   c -> k
28.54/9.39	
28.54/9.39	Q is empty.
28.54/9.39	We have to consider all minimal (P,Q,R)-chains.
28.54/9.39	----------------------------------------
28.54/9.39	
28.54/9.39	(1015) TransformationProof (EQUIVALENT)
28.54/9.39	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.39	
28.54/9.39	   (A^2 -> H(U1(k, k), U1(b, d)),A^2 -> H(U1(k, k), U1(b, d)))
28.54/9.39	   (A^2 -> H(U1(d, k), U1(c, d)),A^2 -> H(U1(d, k), U1(c, d)))
28.54/9.39	   (A^2 -> H(U1(d, k), U1(d, d)),A^2 -> H(U1(d, k), U1(d, d)))
28.54/9.39	   (A^2 -> H(U1(d, k), U1(b, k)),A^2 -> H(U1(d, k), U1(b, k)))
28.54/9.39	
28.54/9.39	
28.54/9.39	----------------------------------------
28.54/9.39	
28.54/9.39	(1016)
28.54/9.39	Obligation:
28.54/9.39	Q DP problem:
28.54/9.39	The TRS P consists of the following rules:
28.54/9.39	
28.54/9.39	   H(x, x) -> G(x, x, f(k))
28.54/9.39	   G(d, x, x) -> A^2
28.54/9.39	   A^2 -> H(f(c), f(c))
28.54/9.39	   A^2 -> H(f(d), f(d))
28.54/9.39	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.39	   A^2 -> H(f(e), f(e))
28.54/9.39	   A^2 -> H(f(k), f(k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.39	   A^2 -> H(U1(d, k), U1(c, c))
28.54/9.39	   A^2 -> H(U1(d, k), f(e))
28.54/9.39	   A^2 -> H(U1(d, k), f(k))
28.54/9.39	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.39	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.39	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.39	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.39	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.39	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.39	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.39	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.39	   A^2 -> H(f(d), b)
28.54/9.39	   A^2 -> H(f(d), U1(e, d))
28.54/9.39	   A^2 -> H(f(d), U1(d, e))
28.54/9.39	   A^2 -> H(f(d), c)
28.54/9.39	   A^2 -> H(f(d), U1(e, k))
28.54/9.39	   A^2 -> H(f(d), U1(k, e))
28.54/9.39	   A^2 -> H(f(d), e)
28.54/9.39	   A^2 -> H(f(a), d)
28.54/9.39	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.39	   A^2 -> H(f(c), c)
28.54/9.39	   A^2 -> H(f(c), U1(e, k))
28.54/9.39	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.39	   A^2 -> H(f(c), U1(k, e))
28.54/9.39	   A^2 -> H(f(c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.39	   A^2 -> H(f(a), k)
28.54/9.39	   A^2 -> H(f(e), U1(e, e))
28.54/9.39	   A^2 -> H(f(c), e)
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.39	   A^2 -> H(f(d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.39	   A^2 -> H(d, U1(b, b))
28.54/9.39	   A^2 -> H(d, f(c))
28.54/9.39	   A^2 -> H(d, f(d))
28.54/9.39	   A^2 -> H(a, U1(c, b))
28.54/9.39	   A^2 -> H(a, U1(d, b))
28.54/9.39	   A^2 -> H(a, U1(b, c))
28.54/9.39	   A^2 -> H(a, U1(b, d))
28.54/9.39	   A^2 -> H(a, U1(c, c))
28.54/9.39	   A^2 -> H(a, f(e))
28.54/9.39	   A^2 -> H(a, f(k))
28.54/9.39	   A^2 -> H(a, U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.39	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.39	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.39	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.39	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.39	   A^2 -> H(U1(e, d), f(e))
28.54/9.39	   A^2 -> H(U1(e, d), f(k))
28.54/9.39	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.39	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.39	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.39	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.39	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.39	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.39	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.39	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.39	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.39	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.39	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.39	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.39	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.39	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.39	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.39	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, a), b)
28.54/9.39	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.39	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.39	   A^2 -> H(U1(c, a), c)
28.54/9.39	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.39	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.39	   A^2 -> H(U1(c, a), e)
28.54/9.39	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.39	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.39	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.39	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.39	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.39	   A^2 -> H(U1(d, e), f(e))
28.54/9.39	   A^2 -> H(U1(d, e), f(k))
28.54/9.39	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.39	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.39	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.39	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.39	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.39	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.39	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.39	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.39	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.39	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.39	   A^2 -> H(U1(d, a), b)
28.54/9.39	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.39	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.39	   A^2 -> H(U1(d, a), c)
28.54/9.39	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.39	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.39	   A^2 -> H(U1(d, a), e)
28.54/9.39	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.39	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.39	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.39	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.39	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.39	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.39	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.39	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.39	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.39	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.39	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.39	   A^2 -> H(U1(a, c), b)
28.54/9.39	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.39	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.39	   A^2 -> H(U1(a, c), c)
28.54/9.39	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.39	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.39	   A^2 -> H(U1(a, c), e)
28.54/9.39	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, d), b)
28.54/9.39	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.39	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.39	   A^2 -> H(U1(a, d), c)
28.54/9.39	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.39	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.39	   A^2 -> H(U1(a, d), e)
28.54/9.39	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, a), d)
28.54/9.39	   A^2 -> H(U1(a, a), k)
28.54/9.39	   A^2 -> H(k, U1(b, b))
28.54/9.39	   A^2 -> H(k, f(c))
28.54/9.39	   A^2 -> H(k, f(d))
28.54/9.39	   A^2 -> H(c, U1(c, b))
28.54/9.39	   A^2 -> H(c, U1(d, b))
28.54/9.39	   A^2 -> H(c, U1(b, c))
28.54/9.39	   A^2 -> H(c, U1(b, d))
28.54/9.39	   A^2 -> H(c, U1(c, c))
28.54/9.39	   A^2 -> H(c, f(e))
28.54/9.39	   A^2 -> H(c, f(k))
28.54/9.39	   A^2 -> H(c, U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.39	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.39	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.39	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.39	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.39	   A^2 -> H(U1(e, k), f(e))
28.54/9.39	   A^2 -> H(U1(e, k), f(k))
28.54/9.39	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.39	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.39	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.39	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.39	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.39	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.39	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.39	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.39	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.39	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.39	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.39	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.39	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.39	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.39	   A^2 -> H(U1(k, e), f(e))
28.54/9.39	   A^2 -> H(U1(k, e), f(k))
28.54/9.39	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.39	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.39	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.39	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.39	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.39	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.39	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.39	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.39	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.39	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, c), b)
28.54/9.39	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.39	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.39	   A^2 -> H(U1(c, c), e)
28.54/9.39	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.39	   A^2 -> H(e, U1(c, b))
28.54/9.39	   A^2 -> H(e, U1(d, b))
28.54/9.39	   A^2 -> H(e, U1(b, c))
28.54/9.39	   A^2 -> H(e, U1(b, d))
28.54/9.39	   A^2 -> H(e, U1(c, c))
28.54/9.39	   A^2 -> H(e, f(e))
28.54/9.39	   A^2 -> H(e, f(k))
28.54/9.39	   A^2 -> H(e, U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.39	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.39	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.39	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.39	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.39	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.39	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.39	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.39	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.39	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.39	   A^2 -> H(f(e), b)
28.54/9.39	   A^2 -> H(f(e), U1(e, d))
28.54/9.39	   A^2 -> H(f(e), U1(d, e))
28.54/9.39	   A^2 -> H(f(e), c)
28.54/9.39	   A^2 -> H(f(e), U1(e, k))
28.54/9.39	   A^2 -> H(f(e), U1(k, e))
28.54/9.39	   A^2 -> H(f(e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.39	   A^2 -> H(f(k), b)
28.54/9.39	   A^2 -> H(f(k), U1(e, d))
28.54/9.39	   A^2 -> H(f(k), U1(d, e))
28.54/9.39	   A^2 -> H(f(k), c)
28.54/9.39	   A^2 -> H(f(k), U1(e, k))
28.54/9.39	   A^2 -> H(f(k), U1(k, e))
28.54/9.39	   A^2 -> H(f(k), e)
28.54/9.39	   A^2 -> H(f(c), d)
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.39	   A^2 -> H(U1(k, k), f(e))
28.54/9.39	   A^2 -> H(U1(k, k), f(k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.39	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.39	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.39	
28.54/9.39	The TRS R consists of the following rules:
28.54/9.39	
28.54/9.39	   f(x) -> U1(x, x)
28.54/9.39	   U1(e, x) -> x
28.54/9.39	   a -> c
28.54/9.39	   a -> d
28.54/9.39	   b -> c
28.54/9.39	   b -> d
28.54/9.39	   d -> k
28.54/9.39	   c -> e
28.54/9.39	   c -> k
28.54/9.39	
28.54/9.39	Q is empty.
28.54/9.39	We have to consider all minimal (P,Q,R)-chains.
28.54/9.39	----------------------------------------
28.54/9.39	
28.54/9.39	(1017) TransformationProof (EQUIVALENT)
28.54/9.39	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.39	
28.54/9.39	   (A^2 -> H(U1(k, k), U1(c, c)),A^2 -> H(U1(k, k), U1(c, c)))
28.54/9.39	   (A^2 -> H(U1(d, k), U1(e, c)),A^2 -> H(U1(d, k), U1(e, c)))
28.54/9.39	   (A^2 -> H(U1(d, k), U1(k, c)),A^2 -> H(U1(d, k), U1(k, c)))
28.54/9.39	   (A^2 -> H(U1(d, k), U1(c, e)),A^2 -> H(U1(d, k), U1(c, e)))
28.54/9.39	   (A^2 -> H(U1(d, k), U1(c, k)),A^2 -> H(U1(d, k), U1(c, k)))
28.54/9.39	
28.54/9.39	
28.54/9.39	----------------------------------------
28.54/9.39	
28.54/9.39	(1018)
28.54/9.39	Obligation:
28.54/9.39	Q DP problem:
28.54/9.39	The TRS P consists of the following rules:
28.54/9.39	
28.54/9.39	   H(x, x) -> G(x, x, f(k))
28.54/9.39	   G(d, x, x) -> A^2
28.54/9.39	   A^2 -> H(f(c), f(c))
28.54/9.39	   A^2 -> H(f(d), f(d))
28.54/9.39	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.39	   A^2 -> H(f(e), f(e))
28.54/9.39	   A^2 -> H(f(k), f(k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.39	   A^2 -> H(U1(d, k), f(e))
28.54/9.39	   A^2 -> H(U1(d, k), f(k))
28.54/9.39	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.39	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.39	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.39	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.39	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.39	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.39	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.39	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.39	   A^2 -> H(f(d), b)
28.54/9.39	   A^2 -> H(f(d), U1(e, d))
28.54/9.39	   A^2 -> H(f(d), U1(d, e))
28.54/9.39	   A^2 -> H(f(d), c)
28.54/9.39	   A^2 -> H(f(d), U1(e, k))
28.54/9.39	   A^2 -> H(f(d), U1(k, e))
28.54/9.39	   A^2 -> H(f(d), e)
28.54/9.39	   A^2 -> H(f(a), d)
28.54/9.39	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.39	   A^2 -> H(f(c), c)
28.54/9.39	   A^2 -> H(f(c), U1(e, k))
28.54/9.39	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.39	   A^2 -> H(f(c), U1(k, e))
28.54/9.39	   A^2 -> H(f(c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.39	   A^2 -> H(f(a), k)
28.54/9.39	   A^2 -> H(f(e), U1(e, e))
28.54/9.39	   A^2 -> H(f(c), e)
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.39	   A^2 -> H(f(d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.39	   A^2 -> H(d, U1(b, b))
28.54/9.39	   A^2 -> H(d, f(c))
28.54/9.39	   A^2 -> H(d, f(d))
28.54/9.39	   A^2 -> H(a, U1(c, b))
28.54/9.39	   A^2 -> H(a, U1(d, b))
28.54/9.39	   A^2 -> H(a, U1(b, c))
28.54/9.39	   A^2 -> H(a, U1(b, d))
28.54/9.39	   A^2 -> H(a, U1(c, c))
28.54/9.39	   A^2 -> H(a, f(e))
28.54/9.39	   A^2 -> H(a, f(k))
28.54/9.39	   A^2 -> H(a, U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.39	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.39	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.39	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.39	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.39	   A^2 -> H(U1(e, d), f(e))
28.54/9.39	   A^2 -> H(U1(e, d), f(k))
28.54/9.39	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.39	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.39	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.39	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.39	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.39	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.39	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.39	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.39	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.39	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.39	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.39	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.39	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.39	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.39	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.39	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, a), b)
28.54/9.39	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.39	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.39	   A^2 -> H(U1(c, a), c)
28.54/9.39	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.39	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.39	   A^2 -> H(U1(c, a), e)
28.54/9.39	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.39	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.39	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.39	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.39	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.39	   A^2 -> H(U1(d, e), f(e))
28.54/9.39	   A^2 -> H(U1(d, e), f(k))
28.54/9.39	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.39	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.39	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.39	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.39	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.39	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.39	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.39	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.39	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.39	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.39	   A^2 -> H(U1(d, a), b)
28.54/9.39	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.39	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.39	   A^2 -> H(U1(d, a), c)
28.54/9.39	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.39	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.39	   A^2 -> H(U1(d, a), e)
28.54/9.39	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.39	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.39	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.39	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.39	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.39	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.39	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.39	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.39	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.39	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.39	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.39	   A^2 -> H(U1(a, c), b)
28.54/9.39	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.39	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.39	   A^2 -> H(U1(a, c), c)
28.54/9.39	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.39	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.39	   A^2 -> H(U1(a, c), e)
28.54/9.39	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, d), b)
28.54/9.39	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.39	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.39	   A^2 -> H(U1(a, d), c)
28.54/9.39	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.39	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.39	   A^2 -> H(U1(a, d), e)
28.54/9.39	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, a), d)
28.54/9.39	   A^2 -> H(U1(a, a), k)
28.54/9.39	   A^2 -> H(k, U1(b, b))
28.54/9.39	   A^2 -> H(k, f(c))
28.54/9.39	   A^2 -> H(k, f(d))
28.54/9.39	   A^2 -> H(c, U1(c, b))
28.54/9.39	   A^2 -> H(c, U1(d, b))
28.54/9.39	   A^2 -> H(c, U1(b, c))
28.54/9.39	   A^2 -> H(c, U1(b, d))
28.54/9.39	   A^2 -> H(c, U1(c, c))
28.54/9.39	   A^2 -> H(c, f(e))
28.54/9.39	   A^2 -> H(c, f(k))
28.54/9.39	   A^2 -> H(c, U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.39	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.39	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.39	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.39	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.39	   A^2 -> H(U1(e, k), f(e))
28.54/9.39	   A^2 -> H(U1(e, k), f(k))
28.54/9.39	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.39	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.39	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.39	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.39	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.39	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.39	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.39	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.39	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.39	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.39	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.39	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.39	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.39	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.39	   A^2 -> H(U1(k, e), f(e))
28.54/9.39	   A^2 -> H(U1(k, e), f(k))
28.54/9.39	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.39	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.39	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.39	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.39	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.39	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.39	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.39	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.39	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.39	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, c), b)
28.54/9.39	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.39	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.39	   A^2 -> H(U1(c, c), e)
28.54/9.39	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.39	   A^2 -> H(e, U1(c, b))
28.54/9.39	   A^2 -> H(e, U1(d, b))
28.54/9.39	   A^2 -> H(e, U1(b, c))
28.54/9.39	   A^2 -> H(e, U1(b, d))
28.54/9.39	   A^2 -> H(e, U1(c, c))
28.54/9.39	   A^2 -> H(e, f(e))
28.54/9.39	   A^2 -> H(e, f(k))
28.54/9.39	   A^2 -> H(e, U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.39	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.39	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.39	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.39	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.39	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.39	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.39	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.39	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.39	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.39	   A^2 -> H(f(e), b)
28.54/9.39	   A^2 -> H(f(e), U1(e, d))
28.54/9.39	   A^2 -> H(f(e), U1(d, e))
28.54/9.39	   A^2 -> H(f(e), c)
28.54/9.39	   A^2 -> H(f(e), U1(e, k))
28.54/9.39	   A^2 -> H(f(e), U1(k, e))
28.54/9.39	   A^2 -> H(f(e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.39	   A^2 -> H(f(k), b)
28.54/9.39	   A^2 -> H(f(k), U1(e, d))
28.54/9.39	   A^2 -> H(f(k), U1(d, e))
28.54/9.39	   A^2 -> H(f(k), c)
28.54/9.39	   A^2 -> H(f(k), U1(e, k))
28.54/9.39	   A^2 -> H(f(k), U1(k, e))
28.54/9.39	   A^2 -> H(f(k), e)
28.54/9.39	   A^2 -> H(f(c), d)
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.39	   A^2 -> H(U1(k, k), f(e))
28.54/9.39	   A^2 -> H(U1(k, k), f(k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.39	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.39	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.39	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.39	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.39	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.39	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.39	
28.54/9.39	The TRS R consists of the following rules:
28.54/9.39	
28.54/9.39	   f(x) -> U1(x, x)
28.54/9.39	   U1(e, x) -> x
28.54/9.39	   a -> c
28.54/9.39	   a -> d
28.54/9.39	   b -> c
28.54/9.39	   b -> d
28.54/9.39	   d -> k
28.54/9.39	   c -> e
28.54/9.39	   c -> k
28.54/9.39	
28.54/9.39	Q is empty.
28.54/9.39	We have to consider all minimal (P,Q,R)-chains.
28.54/9.39	----------------------------------------
28.54/9.39	
28.54/9.39	(1019) TransformationProof (EQUIVALENT)
28.54/9.39	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), f(e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.39	
28.54/9.39	   (A^2 -> H(U1(k, k), f(e)),A^2 -> H(U1(k, k), f(e)))
28.54/9.39	   (A^2 -> H(U1(d, k), U1(e, e)),A^2 -> H(U1(d, k), U1(e, e)))
28.54/9.39	
28.54/9.39	
28.54/9.39	----------------------------------------
28.54/9.39	
28.54/9.39	(1020)
28.54/9.39	Obligation:
28.54/9.39	Q DP problem:
28.54/9.39	The TRS P consists of the following rules:
28.54/9.39	
28.54/9.39	   H(x, x) -> G(x, x, f(k))
28.54/9.39	   G(d, x, x) -> A^2
28.54/9.39	   A^2 -> H(f(c), f(c))
28.54/9.39	   A^2 -> H(f(d), f(d))
28.54/9.39	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.39	   A^2 -> H(f(e), f(e))
28.54/9.39	   A^2 -> H(f(k), f(k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.39	   A^2 -> H(U1(d, k), f(k))
28.54/9.39	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.39	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.39	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.39	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.39	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.39	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.39	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.39	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.39	   A^2 -> H(f(d), b)
28.54/9.39	   A^2 -> H(f(d), U1(e, d))
28.54/9.39	   A^2 -> H(f(d), U1(d, e))
28.54/9.39	   A^2 -> H(f(d), c)
28.54/9.39	   A^2 -> H(f(d), U1(e, k))
28.54/9.39	   A^2 -> H(f(d), U1(k, e))
28.54/9.39	   A^2 -> H(f(d), e)
28.54/9.39	   A^2 -> H(f(a), d)
28.54/9.39	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.39	   A^2 -> H(f(c), c)
28.54/9.39	   A^2 -> H(f(c), U1(e, k))
28.54/9.39	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.39	   A^2 -> H(f(c), U1(k, e))
28.54/9.39	   A^2 -> H(f(c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.39	   A^2 -> H(f(a), k)
28.54/9.39	   A^2 -> H(f(e), U1(e, e))
28.54/9.39	   A^2 -> H(f(c), e)
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.39	   A^2 -> H(f(d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.39	   A^2 -> H(d, U1(b, b))
28.54/9.39	   A^2 -> H(d, f(c))
28.54/9.39	   A^2 -> H(d, f(d))
28.54/9.39	   A^2 -> H(a, U1(c, b))
28.54/9.39	   A^2 -> H(a, U1(d, b))
28.54/9.39	   A^2 -> H(a, U1(b, c))
28.54/9.39	   A^2 -> H(a, U1(b, d))
28.54/9.39	   A^2 -> H(a, U1(c, c))
28.54/9.39	   A^2 -> H(a, f(e))
28.54/9.39	   A^2 -> H(a, f(k))
28.54/9.39	   A^2 -> H(a, U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.39	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.39	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.39	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.39	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.39	   A^2 -> H(U1(e, d), f(e))
28.54/9.39	   A^2 -> H(U1(e, d), f(k))
28.54/9.39	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.39	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.39	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.39	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.39	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.39	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.39	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.39	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.39	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.39	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.39	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.39	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.39	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.39	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.39	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.39	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, a), b)
28.54/9.39	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.39	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.39	   A^2 -> H(U1(c, a), c)
28.54/9.39	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.39	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.39	   A^2 -> H(U1(c, a), e)
28.54/9.39	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.39	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.39	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.39	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.39	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.39	   A^2 -> H(U1(d, e), f(e))
28.54/9.39	   A^2 -> H(U1(d, e), f(k))
28.54/9.39	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.39	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.39	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.39	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.39	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.39	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.39	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.39	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.39	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.39	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.39	   A^2 -> H(U1(d, a), b)
28.54/9.39	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.39	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.39	   A^2 -> H(U1(d, a), c)
28.54/9.39	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.39	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.39	   A^2 -> H(U1(d, a), e)
28.54/9.39	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.39	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.39	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.39	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.39	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.39	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.39	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.39	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.39	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.39	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.39	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.39	   A^2 -> H(U1(a, c), b)
28.54/9.39	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.39	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.39	   A^2 -> H(U1(a, c), c)
28.54/9.39	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.39	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.39	   A^2 -> H(U1(a, c), e)
28.54/9.39	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, d), b)
28.54/9.39	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.39	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.39	   A^2 -> H(U1(a, d), c)
28.54/9.39	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.39	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.39	   A^2 -> H(U1(a, d), e)
28.54/9.39	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, a), d)
28.54/9.39	   A^2 -> H(U1(a, a), k)
28.54/9.39	   A^2 -> H(k, U1(b, b))
28.54/9.39	   A^2 -> H(k, f(c))
28.54/9.39	   A^2 -> H(k, f(d))
28.54/9.39	   A^2 -> H(c, U1(c, b))
28.54/9.39	   A^2 -> H(c, U1(d, b))
28.54/9.39	   A^2 -> H(c, U1(b, c))
28.54/9.39	   A^2 -> H(c, U1(b, d))
28.54/9.39	   A^2 -> H(c, U1(c, c))
28.54/9.39	   A^2 -> H(c, f(e))
28.54/9.39	   A^2 -> H(c, f(k))
28.54/9.39	   A^2 -> H(c, U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.39	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.39	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.39	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.39	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.39	   A^2 -> H(U1(e, k), f(e))
28.54/9.39	   A^2 -> H(U1(e, k), f(k))
28.54/9.39	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.39	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.39	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.39	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.39	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.39	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.39	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.39	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.39	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.39	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.39	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.39	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.39	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.39	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.39	   A^2 -> H(U1(k, e), f(e))
28.54/9.39	   A^2 -> H(U1(k, e), f(k))
28.54/9.39	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.39	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.39	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.39	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.39	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.39	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.39	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.39	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.39	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.39	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, c), b)
28.54/9.39	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.39	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.39	   A^2 -> H(U1(c, c), e)
28.54/9.39	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.39	   A^2 -> H(e, U1(c, b))
28.54/9.39	   A^2 -> H(e, U1(d, b))
28.54/9.39	   A^2 -> H(e, U1(b, c))
28.54/9.39	   A^2 -> H(e, U1(b, d))
28.54/9.39	   A^2 -> H(e, U1(c, c))
28.54/9.39	   A^2 -> H(e, f(e))
28.54/9.39	   A^2 -> H(e, f(k))
28.54/9.39	   A^2 -> H(e, U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.39	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.39	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.39	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.39	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.39	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.39	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.39	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.39	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.39	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.39	   A^2 -> H(f(e), b)
28.54/9.39	   A^2 -> H(f(e), U1(e, d))
28.54/9.39	   A^2 -> H(f(e), U1(d, e))
28.54/9.39	   A^2 -> H(f(e), c)
28.54/9.39	   A^2 -> H(f(e), U1(e, k))
28.54/9.39	   A^2 -> H(f(e), U1(k, e))
28.54/9.39	   A^2 -> H(f(e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.39	   A^2 -> H(f(k), b)
28.54/9.39	   A^2 -> H(f(k), U1(e, d))
28.54/9.39	   A^2 -> H(f(k), U1(d, e))
28.54/9.39	   A^2 -> H(f(k), c)
28.54/9.39	   A^2 -> H(f(k), U1(e, k))
28.54/9.39	   A^2 -> H(f(k), U1(k, e))
28.54/9.39	   A^2 -> H(f(k), e)
28.54/9.39	   A^2 -> H(f(c), d)
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.39	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.39	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.39	   A^2 -> H(U1(k, k), f(e))
28.54/9.39	   A^2 -> H(U1(k, k), f(k))
28.54/9.39	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.39	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.39	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.39	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.39	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.39	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.39	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.39	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.39	
28.54/9.39	The TRS R consists of the following rules:
28.54/9.39	
28.54/9.39	   f(x) -> U1(x, x)
28.54/9.39	   U1(e, x) -> x
28.54/9.39	   a -> c
28.54/9.39	   a -> d
28.54/9.39	   b -> c
28.54/9.39	   b -> d
28.54/9.39	   d -> k
28.54/9.39	   c -> e
28.54/9.39	   c -> k
28.54/9.39	
28.54/9.39	Q is empty.
28.54/9.39	We have to consider all minimal (P,Q,R)-chains.
28.54/9.39	----------------------------------------
28.54/9.39	
28.54/9.39	(1021) TransformationProof (EQUIVALENT)
28.54/9.39	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), f(k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.39	
28.54/9.39	   (A^2 -> H(U1(k, k), f(k)),A^2 -> H(U1(k, k), f(k)))
28.54/9.39	   (A^2 -> H(U1(d, k), U1(k, k)),A^2 -> H(U1(d, k), U1(k, k)))
28.54/9.39	
28.54/9.39	
28.54/9.39	----------------------------------------
28.54/9.39	
28.54/9.39	(1022)
28.54/9.39	Obligation:
28.54/9.39	Q DP problem:
28.54/9.39	The TRS P consists of the following rules:
28.54/9.39	
28.54/9.39	   H(x, x) -> G(x, x, f(k))
28.54/9.39	   G(d, x, x) -> A^2
28.54/9.39	   A^2 -> H(f(c), f(c))
28.54/9.39	   A^2 -> H(f(d), f(d))
28.54/9.39	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.39	   A^2 -> H(f(e), f(e))
28.54/9.39	   A^2 -> H(f(k), f(k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.39	   A^2 -> H(U1(d, k), U1(d, d))
28.54/9.39	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.39	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.39	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.39	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.39	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.39	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.39	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.39	   A^2 -> H(f(d), b)
28.54/9.39	   A^2 -> H(f(d), U1(e, d))
28.54/9.39	   A^2 -> H(f(d), U1(d, e))
28.54/9.39	   A^2 -> H(f(d), c)
28.54/9.39	   A^2 -> H(f(d), U1(e, k))
28.54/9.39	   A^2 -> H(f(d), U1(k, e))
28.54/9.39	   A^2 -> H(f(d), e)
28.54/9.39	   A^2 -> H(f(a), d)
28.54/9.39	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.39	   A^2 -> H(f(c), c)
28.54/9.39	   A^2 -> H(f(c), U1(e, k))
28.54/9.39	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.39	   A^2 -> H(f(c), U1(k, e))
28.54/9.39	   A^2 -> H(f(c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.39	   A^2 -> H(f(a), k)
28.54/9.39	   A^2 -> H(f(e), U1(e, e))
28.54/9.39	   A^2 -> H(f(c), e)
28.54/9.39	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.39	   A^2 -> H(f(d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.39	   A^2 -> H(d, U1(b, b))
28.54/9.39	   A^2 -> H(d, f(c))
28.54/9.39	   A^2 -> H(d, f(d))
28.54/9.39	   A^2 -> H(a, U1(c, b))
28.54/9.39	   A^2 -> H(a, U1(d, b))
28.54/9.39	   A^2 -> H(a, U1(b, c))
28.54/9.39	   A^2 -> H(a, U1(b, d))
28.54/9.39	   A^2 -> H(a, U1(c, c))
28.54/9.39	   A^2 -> H(a, f(e))
28.54/9.39	   A^2 -> H(a, f(k))
28.54/9.39	   A^2 -> H(a, U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.39	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.39	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.39	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.39	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.39	   A^2 -> H(U1(e, d), f(e))
28.54/9.39	   A^2 -> H(U1(e, d), f(k))
28.54/9.39	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.39	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.39	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.39	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.39	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.39	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.39	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.39	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.39	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.39	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.39	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.39	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.39	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.39	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.39	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.39	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.39	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.39	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.39	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.39	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.39	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.39	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.39	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.39	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.39	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.39	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.39	   A^2 -> H(U1(c, a), b)
28.54/9.39	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.39	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.39	   A^2 -> H(U1(c, a), c)
28.54/9.39	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.39	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.39	   A^2 -> H(U1(c, a), e)
28.54/9.39	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.39	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.39	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.39	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.39	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.39	   A^2 -> H(U1(d, e), f(e))
28.54/9.39	   A^2 -> H(U1(d, e), f(k))
28.54/9.39	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.39	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.39	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.39	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.39	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.39	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.39	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.39	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.39	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.39	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.39	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.39	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.39	   A^2 -> H(U1(d, a), b)
28.54/9.39	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.39	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.39	   A^2 -> H(U1(d, a), c)
28.54/9.39	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.39	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.39	   A^2 -> H(U1(d, a), e)
28.54/9.39	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.39	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.39	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.39	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.39	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.39	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.39	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.39	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.39	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.39	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.39	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.39	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.39	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.39	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.39	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.39	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.39	   A^2 -> H(U1(a, c), b)
28.54/9.39	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.39	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.39	   A^2 -> H(U1(a, c), c)
28.54/9.39	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.40	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.40	   A^2 -> H(U1(a, c), e)
28.54/9.40	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, d), b)
28.54/9.40	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.40	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.40	   A^2 -> H(U1(a, d), c)
28.54/9.40	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.40	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.40	   A^2 -> H(U1(a, d), e)
28.54/9.40	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, a), d)
28.54/9.40	   A^2 -> H(U1(a, a), k)
28.54/9.40	   A^2 -> H(k, U1(b, b))
28.54/9.40	   A^2 -> H(k, f(c))
28.54/9.40	   A^2 -> H(k, f(d))
28.54/9.40	   A^2 -> H(c, U1(c, b))
28.54/9.40	   A^2 -> H(c, U1(d, b))
28.54/9.40	   A^2 -> H(c, U1(b, c))
28.54/9.40	   A^2 -> H(c, U1(b, d))
28.54/9.40	   A^2 -> H(c, U1(c, c))
28.54/9.40	   A^2 -> H(c, f(e))
28.54/9.40	   A^2 -> H(c, f(k))
28.54/9.40	   A^2 -> H(c, U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.40	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.40	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.40	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.40	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.40	   A^2 -> H(U1(e, k), f(e))
28.54/9.40	   A^2 -> H(U1(e, k), f(k))
28.54/9.40	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.40	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.40	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.40	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.40	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.40	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.40	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.40	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.40	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.40	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.40	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.40	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.40	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.40	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.40	   A^2 -> H(U1(k, e), f(e))
28.54/9.40	   A^2 -> H(U1(k, e), f(k))
28.54/9.40	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.40	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.40	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.40	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.40	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.40	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.40	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.40	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, c), b)
28.54/9.40	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.40	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.40	   A^2 -> H(U1(c, c), e)
28.54/9.40	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.40	   A^2 -> H(e, U1(c, b))
28.54/9.40	   A^2 -> H(e, U1(d, b))
28.54/9.40	   A^2 -> H(e, U1(b, c))
28.54/9.40	   A^2 -> H(e, U1(b, d))
28.54/9.40	   A^2 -> H(e, U1(c, c))
28.54/9.40	   A^2 -> H(e, f(e))
28.54/9.40	   A^2 -> H(e, f(k))
28.54/9.40	   A^2 -> H(e, U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.40	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.40	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.40	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.40	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.40	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.40	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.40	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.40	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.40	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.40	   A^2 -> H(f(e), b)
28.54/9.40	   A^2 -> H(f(e), U1(e, d))
28.54/9.40	   A^2 -> H(f(e), U1(d, e))
28.54/9.40	   A^2 -> H(f(e), c)
28.54/9.40	   A^2 -> H(f(e), U1(e, k))
28.54/9.40	   A^2 -> H(f(e), U1(k, e))
28.54/9.40	   A^2 -> H(f(e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.40	   A^2 -> H(f(k), b)
28.54/9.40	   A^2 -> H(f(k), U1(e, d))
28.54/9.40	   A^2 -> H(f(k), U1(d, e))
28.54/9.40	   A^2 -> H(f(k), c)
28.54/9.40	   A^2 -> H(f(k), U1(e, k))
28.54/9.40	   A^2 -> H(f(k), U1(k, e))
28.54/9.40	   A^2 -> H(f(k), e)
28.54/9.40	   A^2 -> H(f(c), d)
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.40	   A^2 -> H(U1(k, k), f(e))
28.54/9.40	   A^2 -> H(U1(k, k), f(k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.40	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.40	
28.54/9.40	The TRS R consists of the following rules:
28.54/9.40	
28.54/9.40	   f(x) -> U1(x, x)
28.54/9.40	   U1(e, x) -> x
28.54/9.40	   a -> c
28.54/9.40	   a -> d
28.54/9.40	   b -> c
28.54/9.40	   b -> d
28.54/9.40	   d -> k
28.54/9.40	   c -> e
28.54/9.40	   c -> k
28.54/9.40	
28.54/9.40	Q is empty.
28.54/9.40	We have to consider all minimal (P,Q,R)-chains.
28.54/9.40	----------------------------------------
28.54/9.40	
28.54/9.40	(1023) TransformationProof (EQUIVALENT)
28.54/9.40	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.40	
28.54/9.40	   (A^2 -> H(U1(k, k), U1(d, d)),A^2 -> H(U1(k, k), U1(d, d)))
28.54/9.40	   (A^2 -> H(U1(d, k), U1(k, d)),A^2 -> H(U1(d, k), U1(k, d)))
28.54/9.40	   (A^2 -> H(U1(d, k), U1(d, k)),A^2 -> H(U1(d, k), U1(d, k)))
28.54/9.40	
28.54/9.40	
28.54/9.40	----------------------------------------
28.54/9.40	
28.54/9.40	(1024)
28.54/9.40	Obligation:
28.54/9.40	Q DP problem:
28.54/9.40	The TRS P consists of the following rules:
28.54/9.40	
28.54/9.40	   H(x, x) -> G(x, x, f(k))
28.54/9.40	   G(d, x, x) -> A^2
28.54/9.40	   A^2 -> H(f(c), f(c))
28.54/9.40	   A^2 -> H(f(d), f(d))
28.54/9.40	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.40	   A^2 -> H(f(e), f(e))
28.54/9.40	   A^2 -> H(f(k), f(k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.40	   A^2 -> H(U1(d, d), U1(e, b))
28.54/9.40	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.40	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.40	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.40	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.40	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.40	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.40	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.40	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.40	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.40	   A^2 -> H(f(d), b)
28.54/9.40	   A^2 -> H(f(d), U1(e, d))
28.54/9.40	   A^2 -> H(f(d), U1(d, e))
28.54/9.40	   A^2 -> H(f(d), c)
28.54/9.40	   A^2 -> H(f(d), U1(e, k))
28.54/9.40	   A^2 -> H(f(d), U1(k, e))
28.54/9.40	   A^2 -> H(f(d), e)
28.54/9.40	   A^2 -> H(f(a), d)
28.54/9.40	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.40	   A^2 -> H(f(c), c)
28.54/9.40	   A^2 -> H(f(c), U1(e, k))
28.54/9.40	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.40	   A^2 -> H(f(c), U1(k, e))
28.54/9.40	   A^2 -> H(f(c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.40	   A^2 -> H(f(a), k)
28.54/9.40	   A^2 -> H(f(e), U1(e, e))
28.54/9.40	   A^2 -> H(f(c), e)
28.54/9.40	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.40	   A^2 -> H(f(d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.40	   A^2 -> H(d, U1(b, b))
28.54/9.40	   A^2 -> H(d, f(c))
28.54/9.40	   A^2 -> H(d, f(d))
28.54/9.40	   A^2 -> H(a, U1(c, b))
28.54/9.40	   A^2 -> H(a, U1(d, b))
28.54/9.40	   A^2 -> H(a, U1(b, c))
28.54/9.40	   A^2 -> H(a, U1(b, d))
28.54/9.40	   A^2 -> H(a, U1(c, c))
28.54/9.40	   A^2 -> H(a, f(e))
28.54/9.40	   A^2 -> H(a, f(k))
28.54/9.40	   A^2 -> H(a, U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.40	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.40	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.40	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.40	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.40	   A^2 -> H(U1(e, d), f(e))
28.54/9.40	   A^2 -> H(U1(e, d), f(k))
28.54/9.40	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.40	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.40	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.40	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.40	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.40	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.40	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.40	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.40	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.40	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.40	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.40	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.40	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.40	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.40	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.40	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, a), b)
28.54/9.40	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.40	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.40	   A^2 -> H(U1(c, a), c)
28.54/9.40	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.40	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.40	   A^2 -> H(U1(c, a), e)
28.54/9.40	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.40	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.40	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.40	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.40	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.40	   A^2 -> H(U1(d, e), f(e))
28.54/9.40	   A^2 -> H(U1(d, e), f(k))
28.54/9.40	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.40	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.40	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.40	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.40	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.40	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.40	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.40	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.40	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.40	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.40	   A^2 -> H(U1(d, a), b)
28.54/9.40	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.40	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.40	   A^2 -> H(U1(d, a), c)
28.54/9.40	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.40	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.40	   A^2 -> H(U1(d, a), e)
28.54/9.40	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.40	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.40	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.40	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.40	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.40	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.40	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.40	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.40	   A^2 -> H(U1(a, c), b)
28.54/9.40	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.40	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.40	   A^2 -> H(U1(a, c), c)
28.54/9.40	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.40	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.40	   A^2 -> H(U1(a, c), e)
28.54/9.40	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, d), b)
28.54/9.40	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.40	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.40	   A^2 -> H(U1(a, d), c)
28.54/9.40	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.40	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.40	   A^2 -> H(U1(a, d), e)
28.54/9.40	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, a), d)
28.54/9.40	   A^2 -> H(U1(a, a), k)
28.54/9.40	   A^2 -> H(k, U1(b, b))
28.54/9.40	   A^2 -> H(k, f(c))
28.54/9.40	   A^2 -> H(k, f(d))
28.54/9.40	   A^2 -> H(c, U1(c, b))
28.54/9.40	   A^2 -> H(c, U1(d, b))
28.54/9.40	   A^2 -> H(c, U1(b, c))
28.54/9.40	   A^2 -> H(c, U1(b, d))
28.54/9.40	   A^2 -> H(c, U1(c, c))
28.54/9.40	   A^2 -> H(c, f(e))
28.54/9.40	   A^2 -> H(c, f(k))
28.54/9.40	   A^2 -> H(c, U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.40	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.40	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.40	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.40	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.40	   A^2 -> H(U1(e, k), f(e))
28.54/9.40	   A^2 -> H(U1(e, k), f(k))
28.54/9.40	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.40	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.40	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.40	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.40	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.40	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.40	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.40	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.40	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.40	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.40	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.40	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.40	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.40	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.40	   A^2 -> H(U1(k, e), f(e))
28.54/9.40	   A^2 -> H(U1(k, e), f(k))
28.54/9.40	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.40	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.40	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.40	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.40	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.40	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.40	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.40	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, c), b)
28.54/9.40	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.40	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.40	   A^2 -> H(U1(c, c), e)
28.54/9.40	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.40	   A^2 -> H(e, U1(c, b))
28.54/9.40	   A^2 -> H(e, U1(d, b))
28.54/9.40	   A^2 -> H(e, U1(b, c))
28.54/9.40	   A^2 -> H(e, U1(b, d))
28.54/9.40	   A^2 -> H(e, U1(c, c))
28.54/9.40	   A^2 -> H(e, f(e))
28.54/9.40	   A^2 -> H(e, f(k))
28.54/9.40	   A^2 -> H(e, U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.40	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.40	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.40	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.40	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.40	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.40	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.40	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.40	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.40	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.40	   A^2 -> H(f(e), b)
28.54/9.40	   A^2 -> H(f(e), U1(e, d))
28.54/9.40	   A^2 -> H(f(e), U1(d, e))
28.54/9.40	   A^2 -> H(f(e), c)
28.54/9.40	   A^2 -> H(f(e), U1(e, k))
28.54/9.40	   A^2 -> H(f(e), U1(k, e))
28.54/9.40	   A^2 -> H(f(e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.40	   A^2 -> H(f(k), b)
28.54/9.40	   A^2 -> H(f(k), U1(e, d))
28.54/9.40	   A^2 -> H(f(k), U1(d, e))
28.54/9.40	   A^2 -> H(f(k), c)
28.54/9.40	   A^2 -> H(f(k), U1(e, k))
28.54/9.40	   A^2 -> H(f(k), U1(k, e))
28.54/9.40	   A^2 -> H(f(k), e)
28.54/9.40	   A^2 -> H(f(c), d)
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.40	   A^2 -> H(U1(k, k), f(e))
28.54/9.40	   A^2 -> H(U1(k, k), f(k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.40	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.40	
28.54/9.40	The TRS R consists of the following rules:
28.54/9.40	
28.54/9.40	   f(x) -> U1(x, x)
28.54/9.40	   U1(e, x) -> x
28.54/9.40	   a -> c
28.54/9.40	   a -> d
28.54/9.40	   b -> c
28.54/9.40	   b -> d
28.54/9.40	   d -> k
28.54/9.40	   c -> e
28.54/9.40	   c -> k
28.54/9.40	
28.54/9.40	Q is empty.
28.54/9.40	We have to consider all minimal (P,Q,R)-chains.
28.54/9.40	----------------------------------------
28.54/9.40	
28.54/9.40	(1025) TransformationProof (EQUIVALENT)
28.54/9.40	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.40	
28.54/9.40	   (A^2 -> H(U1(k, d), U1(e, b)),A^2 -> H(U1(k, d), U1(e, b)))
28.54/9.40	   (A^2 -> H(U1(d, k), U1(e, b)),A^2 -> H(U1(d, k), U1(e, b)))
28.54/9.40	   (A^2 -> H(U1(d, d), b),A^2 -> H(U1(d, d), b))
28.54/9.40	   (A^2 -> H(U1(d, d), U1(e, c)),A^2 -> H(U1(d, d), U1(e, c)))
28.54/9.40	   (A^2 -> H(U1(d, d), U1(e, d)),A^2 -> H(U1(d, d), U1(e, d)))
28.54/9.40	
28.54/9.40	
28.54/9.40	----------------------------------------
28.54/9.40	
28.54/9.40	(1026)
28.54/9.40	Obligation:
28.54/9.40	Q DP problem:
28.54/9.40	The TRS P consists of the following rules:
28.54/9.40	
28.54/9.40	   H(x, x) -> G(x, x, f(k))
28.54/9.40	   G(d, x, x) -> A^2
28.54/9.40	   A^2 -> H(f(c), f(c))
28.54/9.40	   A^2 -> H(f(d), f(d))
28.54/9.40	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.40	   A^2 -> H(f(e), f(e))
28.54/9.40	   A^2 -> H(f(k), f(k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.40	   A^2 -> H(U1(d, d), U1(k, b))
28.54/9.40	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.40	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.40	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.40	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.40	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.40	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.40	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.40	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.40	   A^2 -> H(f(d), b)
28.54/9.40	   A^2 -> H(f(d), U1(e, d))
28.54/9.40	   A^2 -> H(f(d), U1(d, e))
28.54/9.40	   A^2 -> H(f(d), c)
28.54/9.40	   A^2 -> H(f(d), U1(e, k))
28.54/9.40	   A^2 -> H(f(d), U1(k, e))
28.54/9.40	   A^2 -> H(f(d), e)
28.54/9.40	   A^2 -> H(f(a), d)
28.54/9.40	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.40	   A^2 -> H(f(c), c)
28.54/9.40	   A^2 -> H(f(c), U1(e, k))
28.54/9.40	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.40	   A^2 -> H(f(c), U1(k, e))
28.54/9.40	   A^2 -> H(f(c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.40	   A^2 -> H(f(a), k)
28.54/9.40	   A^2 -> H(f(e), U1(e, e))
28.54/9.40	   A^2 -> H(f(c), e)
28.54/9.40	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.40	   A^2 -> H(f(d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.40	   A^2 -> H(d, U1(b, b))
28.54/9.40	   A^2 -> H(d, f(c))
28.54/9.40	   A^2 -> H(d, f(d))
28.54/9.40	   A^2 -> H(a, U1(c, b))
28.54/9.40	   A^2 -> H(a, U1(d, b))
28.54/9.40	   A^2 -> H(a, U1(b, c))
28.54/9.40	   A^2 -> H(a, U1(b, d))
28.54/9.40	   A^2 -> H(a, U1(c, c))
28.54/9.40	   A^2 -> H(a, f(e))
28.54/9.40	   A^2 -> H(a, f(k))
28.54/9.40	   A^2 -> H(a, U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.40	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.40	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.40	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.40	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.40	   A^2 -> H(U1(e, d), f(e))
28.54/9.40	   A^2 -> H(U1(e, d), f(k))
28.54/9.40	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.40	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.40	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.40	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.40	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.40	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.40	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.40	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.40	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.40	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.40	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.40	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.40	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.40	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.40	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.40	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, a), b)
28.54/9.40	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.40	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.40	   A^2 -> H(U1(c, a), c)
28.54/9.40	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.40	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.40	   A^2 -> H(U1(c, a), e)
28.54/9.40	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.40	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.40	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.40	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.40	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.40	   A^2 -> H(U1(d, e), f(e))
28.54/9.40	   A^2 -> H(U1(d, e), f(k))
28.54/9.40	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.40	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.40	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.40	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.40	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.40	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.40	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.40	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.40	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.40	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.40	   A^2 -> H(U1(d, a), b)
28.54/9.40	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.40	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.40	   A^2 -> H(U1(d, a), c)
28.54/9.40	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.40	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.40	   A^2 -> H(U1(d, a), e)
28.54/9.40	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.40	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.40	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.40	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.40	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.40	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.40	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.40	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.40	   A^2 -> H(U1(a, c), b)
28.54/9.40	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.40	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.40	   A^2 -> H(U1(a, c), c)
28.54/9.40	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.40	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.40	   A^2 -> H(U1(a, c), e)
28.54/9.40	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, d), b)
28.54/9.40	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.40	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.40	   A^2 -> H(U1(a, d), c)
28.54/9.40	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.40	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.40	   A^2 -> H(U1(a, d), e)
28.54/9.40	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, a), d)
28.54/9.40	   A^2 -> H(U1(a, a), k)
28.54/9.40	   A^2 -> H(k, U1(b, b))
28.54/9.40	   A^2 -> H(k, f(c))
28.54/9.40	   A^2 -> H(k, f(d))
28.54/9.40	   A^2 -> H(c, U1(c, b))
28.54/9.40	   A^2 -> H(c, U1(d, b))
28.54/9.40	   A^2 -> H(c, U1(b, c))
28.54/9.40	   A^2 -> H(c, U1(b, d))
28.54/9.40	   A^2 -> H(c, U1(c, c))
28.54/9.40	   A^2 -> H(c, f(e))
28.54/9.40	   A^2 -> H(c, f(k))
28.54/9.40	   A^2 -> H(c, U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.40	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.40	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.40	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.40	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.40	   A^2 -> H(U1(e, k), f(e))
28.54/9.40	   A^2 -> H(U1(e, k), f(k))
28.54/9.40	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.40	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.40	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.40	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.40	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.40	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.40	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.40	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.40	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.40	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.40	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.40	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.40	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.40	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.40	   A^2 -> H(U1(k, e), f(e))
28.54/9.40	   A^2 -> H(U1(k, e), f(k))
28.54/9.40	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.40	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.40	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.40	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.40	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.40	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.40	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.40	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, c), b)
28.54/9.40	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.40	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.40	   A^2 -> H(U1(c, c), e)
28.54/9.40	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.40	   A^2 -> H(e, U1(c, b))
28.54/9.40	   A^2 -> H(e, U1(d, b))
28.54/9.40	   A^2 -> H(e, U1(b, c))
28.54/9.40	   A^2 -> H(e, U1(b, d))
28.54/9.40	   A^2 -> H(e, U1(c, c))
28.54/9.40	   A^2 -> H(e, f(e))
28.54/9.40	   A^2 -> H(e, f(k))
28.54/9.40	   A^2 -> H(e, U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.40	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.40	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.40	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.40	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.40	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.40	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.40	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.40	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.40	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.40	   A^2 -> H(f(e), b)
28.54/9.40	   A^2 -> H(f(e), U1(e, d))
28.54/9.40	   A^2 -> H(f(e), U1(d, e))
28.54/9.40	   A^2 -> H(f(e), c)
28.54/9.40	   A^2 -> H(f(e), U1(e, k))
28.54/9.40	   A^2 -> H(f(e), U1(k, e))
28.54/9.40	   A^2 -> H(f(e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.40	   A^2 -> H(f(k), b)
28.54/9.40	   A^2 -> H(f(k), U1(e, d))
28.54/9.40	   A^2 -> H(f(k), U1(d, e))
28.54/9.40	   A^2 -> H(f(k), c)
28.54/9.40	   A^2 -> H(f(k), U1(e, k))
28.54/9.40	   A^2 -> H(f(k), U1(k, e))
28.54/9.40	   A^2 -> H(f(k), e)
28.54/9.40	   A^2 -> H(f(c), d)
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.40	   A^2 -> H(U1(k, k), f(e))
28.54/9.40	   A^2 -> H(U1(k, k), f(k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.40	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.40	   A^2 -> H(U1(d, d), b)
28.54/9.40	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.40	
28.54/9.40	The TRS R consists of the following rules:
28.54/9.40	
28.54/9.40	   f(x) -> U1(x, x)
28.54/9.40	   U1(e, x) -> x
28.54/9.40	   a -> c
28.54/9.40	   a -> d
28.54/9.40	   b -> c
28.54/9.40	   b -> d
28.54/9.40	   d -> k
28.54/9.40	   c -> e
28.54/9.40	   c -> k
28.54/9.40	
28.54/9.40	Q is empty.
28.54/9.40	We have to consider all minimal (P,Q,R)-chains.
28.54/9.40	----------------------------------------
28.54/9.40	
28.54/9.40	(1027) TransformationProof (EQUIVALENT)
28.54/9.40	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.40	
28.54/9.40	   (A^2 -> H(U1(k, d), U1(k, b)),A^2 -> H(U1(k, d), U1(k, b)))
28.54/9.40	   (A^2 -> H(U1(d, k), U1(k, b)),A^2 -> H(U1(d, k), U1(k, b)))
28.54/9.40	   (A^2 -> H(U1(d, d), U1(k, c)),A^2 -> H(U1(d, d), U1(k, c)))
28.54/9.40	   (A^2 -> H(U1(d, d), U1(k, d)),A^2 -> H(U1(d, d), U1(k, d)))
28.54/9.40	
28.54/9.40	
28.54/9.40	----------------------------------------
28.54/9.40	
28.54/9.40	(1028)
28.54/9.40	Obligation:
28.54/9.40	Q DP problem:
28.54/9.40	The TRS P consists of the following rules:
28.54/9.40	
28.54/9.40	   H(x, x) -> G(x, x, f(k))
28.54/9.40	   G(d, x, x) -> A^2
28.54/9.40	   A^2 -> H(f(c), f(c))
28.54/9.40	   A^2 -> H(f(d), f(d))
28.54/9.40	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.40	   A^2 -> H(f(e), f(e))
28.54/9.40	   A^2 -> H(f(k), f(k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.40	   A^2 -> H(U1(d, d), U1(c, d))
28.54/9.40	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.40	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.40	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.40	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.40	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.40	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.40	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.40	   A^2 -> H(f(d), b)
28.54/9.40	   A^2 -> H(f(d), U1(e, d))
28.54/9.40	   A^2 -> H(f(d), U1(d, e))
28.54/9.40	   A^2 -> H(f(d), c)
28.54/9.40	   A^2 -> H(f(d), U1(e, k))
28.54/9.40	   A^2 -> H(f(d), U1(k, e))
28.54/9.40	   A^2 -> H(f(d), e)
28.54/9.40	   A^2 -> H(f(a), d)
28.54/9.40	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.40	   A^2 -> H(f(c), c)
28.54/9.40	   A^2 -> H(f(c), U1(e, k))
28.54/9.40	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.40	   A^2 -> H(f(c), U1(k, e))
28.54/9.40	   A^2 -> H(f(c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.40	   A^2 -> H(f(a), k)
28.54/9.40	   A^2 -> H(f(e), U1(e, e))
28.54/9.40	   A^2 -> H(f(c), e)
28.54/9.40	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.40	   A^2 -> H(f(d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.40	   A^2 -> H(d, U1(b, b))
28.54/9.40	   A^2 -> H(d, f(c))
28.54/9.40	   A^2 -> H(d, f(d))
28.54/9.40	   A^2 -> H(a, U1(c, b))
28.54/9.40	   A^2 -> H(a, U1(d, b))
28.54/9.40	   A^2 -> H(a, U1(b, c))
28.54/9.40	   A^2 -> H(a, U1(b, d))
28.54/9.40	   A^2 -> H(a, U1(c, c))
28.54/9.40	   A^2 -> H(a, f(e))
28.54/9.40	   A^2 -> H(a, f(k))
28.54/9.40	   A^2 -> H(a, U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.40	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.40	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.40	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.40	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.40	   A^2 -> H(U1(e, d), f(e))
28.54/9.40	   A^2 -> H(U1(e, d), f(k))
28.54/9.40	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.40	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.40	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.40	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.40	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.40	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.40	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.40	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.40	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.40	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.40	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.40	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.40	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.40	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.40	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.40	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, a), b)
28.54/9.40	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.40	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.40	   A^2 -> H(U1(c, a), c)
28.54/9.40	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.40	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.40	   A^2 -> H(U1(c, a), e)
28.54/9.40	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.40	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.40	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.40	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.40	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.40	   A^2 -> H(U1(d, e), f(e))
28.54/9.40	   A^2 -> H(U1(d, e), f(k))
28.54/9.40	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.40	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.40	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.40	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.40	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.40	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.40	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.40	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.40	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.40	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.40	   A^2 -> H(U1(d, a), b)
28.54/9.40	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.40	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.40	   A^2 -> H(U1(d, a), c)
28.54/9.40	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.40	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.40	   A^2 -> H(U1(d, a), e)
28.54/9.40	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.40	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.40	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.40	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.40	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.40	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.40	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.40	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.40	   A^2 -> H(U1(a, c), b)
28.54/9.40	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.40	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.40	   A^2 -> H(U1(a, c), c)
28.54/9.40	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.40	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.40	   A^2 -> H(U1(a, c), e)
28.54/9.40	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, d), b)
28.54/9.40	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.40	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.40	   A^2 -> H(U1(a, d), c)
28.54/9.40	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.40	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.40	   A^2 -> H(U1(a, d), e)
28.54/9.40	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, a), d)
28.54/9.40	   A^2 -> H(U1(a, a), k)
28.54/9.40	   A^2 -> H(k, U1(b, b))
28.54/9.40	   A^2 -> H(k, f(c))
28.54/9.40	   A^2 -> H(k, f(d))
28.54/9.40	   A^2 -> H(c, U1(c, b))
28.54/9.40	   A^2 -> H(c, U1(d, b))
28.54/9.40	   A^2 -> H(c, U1(b, c))
28.54/9.40	   A^2 -> H(c, U1(b, d))
28.54/9.40	   A^2 -> H(c, U1(c, c))
28.54/9.40	   A^2 -> H(c, f(e))
28.54/9.40	   A^2 -> H(c, f(k))
28.54/9.40	   A^2 -> H(c, U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.40	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.40	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.40	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.40	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.40	   A^2 -> H(U1(e, k), f(e))
28.54/9.40	   A^2 -> H(U1(e, k), f(k))
28.54/9.40	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.40	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.40	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.40	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.40	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.40	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.40	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.40	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.40	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.40	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.40	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.40	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.40	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.40	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.40	   A^2 -> H(U1(k, e), f(e))
28.54/9.40	   A^2 -> H(U1(k, e), f(k))
28.54/9.40	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.40	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.40	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.40	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.40	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.40	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.40	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.40	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, c), b)
28.54/9.40	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.40	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.40	   A^2 -> H(U1(c, c), e)
28.54/9.40	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.40	   A^2 -> H(e, U1(c, b))
28.54/9.40	   A^2 -> H(e, U1(d, b))
28.54/9.40	   A^2 -> H(e, U1(b, c))
28.54/9.40	   A^2 -> H(e, U1(b, d))
28.54/9.40	   A^2 -> H(e, U1(c, c))
28.54/9.40	   A^2 -> H(e, f(e))
28.54/9.40	   A^2 -> H(e, f(k))
28.54/9.40	   A^2 -> H(e, U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.40	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.40	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.40	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.40	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.40	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.40	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.40	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.40	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.40	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.40	   A^2 -> H(f(e), b)
28.54/9.40	   A^2 -> H(f(e), U1(e, d))
28.54/9.40	   A^2 -> H(f(e), U1(d, e))
28.54/9.40	   A^2 -> H(f(e), c)
28.54/9.40	   A^2 -> H(f(e), U1(e, k))
28.54/9.40	   A^2 -> H(f(e), U1(k, e))
28.54/9.40	   A^2 -> H(f(e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.40	   A^2 -> H(f(k), b)
28.54/9.40	   A^2 -> H(f(k), U1(e, d))
28.54/9.40	   A^2 -> H(f(k), U1(d, e))
28.54/9.40	   A^2 -> H(f(k), c)
28.54/9.40	   A^2 -> H(f(k), U1(e, k))
28.54/9.40	   A^2 -> H(f(k), U1(k, e))
28.54/9.40	   A^2 -> H(f(k), e)
28.54/9.40	   A^2 -> H(f(c), d)
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.40	   A^2 -> H(U1(k, k), f(e))
28.54/9.40	   A^2 -> H(U1(k, k), f(k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.40	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.40	   A^2 -> H(U1(d, d), b)
28.54/9.40	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.40	
28.54/9.40	The TRS R consists of the following rules:
28.54/9.40	
28.54/9.40	   f(x) -> U1(x, x)
28.54/9.40	   U1(e, x) -> x
28.54/9.40	   a -> c
28.54/9.40	   a -> d
28.54/9.40	   b -> c
28.54/9.40	   b -> d
28.54/9.40	   d -> k
28.54/9.40	   c -> e
28.54/9.40	   c -> k
28.54/9.40	
28.54/9.40	Q is empty.
28.54/9.40	We have to consider all minimal (P,Q,R)-chains.
28.54/9.40	----------------------------------------
28.54/9.40	
28.54/9.40	(1029) TransformationProof (EQUIVALENT)
28.54/9.40	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.40	
28.54/9.40	   (A^2 -> H(U1(k, d), U1(c, d)),A^2 -> H(U1(k, d), U1(c, d)))
28.54/9.40	   (A^2 -> H(U1(d, k), U1(c, d)),A^2 -> H(U1(d, k), U1(c, d)))
28.54/9.40	   (A^2 -> H(U1(d, d), U1(e, d)),A^2 -> H(U1(d, d), U1(e, d)))
28.54/9.40	   (A^2 -> H(U1(d, d), U1(k, d)),A^2 -> H(U1(d, d), U1(k, d)))
28.54/9.40	   (A^2 -> H(U1(d, d), U1(c, k)),A^2 -> H(U1(d, d), U1(c, k)))
28.54/9.40	
28.54/9.40	
28.54/9.40	----------------------------------------
28.54/9.40	
28.54/9.40	(1030)
28.54/9.40	Obligation:
28.54/9.40	Q DP problem:
28.54/9.40	The TRS P consists of the following rules:
28.54/9.40	
28.54/9.40	   H(x, x) -> G(x, x, f(k))
28.54/9.40	   G(d, x, x) -> A^2
28.54/9.40	   A^2 -> H(f(c), f(c))
28.54/9.40	   A^2 -> H(f(d), f(d))
28.54/9.40	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.40	   A^2 -> H(f(e), f(e))
28.54/9.40	   A^2 -> H(f(k), f(k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.40	   A^2 -> H(U1(d, d), U1(d, c))
28.54/9.40	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.40	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.40	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.40	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.40	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.40	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.40	   A^2 -> H(f(d), b)
28.54/9.40	   A^2 -> H(f(d), U1(e, d))
28.54/9.40	   A^2 -> H(f(d), U1(d, e))
28.54/9.40	   A^2 -> H(f(d), c)
28.54/9.40	   A^2 -> H(f(d), U1(e, k))
28.54/9.40	   A^2 -> H(f(d), U1(k, e))
28.54/9.40	   A^2 -> H(f(d), e)
28.54/9.40	   A^2 -> H(f(a), d)
28.54/9.40	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.40	   A^2 -> H(f(c), c)
28.54/9.40	   A^2 -> H(f(c), U1(e, k))
28.54/9.40	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.40	   A^2 -> H(f(c), U1(k, e))
28.54/9.40	   A^2 -> H(f(c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.40	   A^2 -> H(f(a), k)
28.54/9.40	   A^2 -> H(f(e), U1(e, e))
28.54/9.40	   A^2 -> H(f(c), e)
28.54/9.40	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.40	   A^2 -> H(f(d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.40	   A^2 -> H(d, U1(b, b))
28.54/9.40	   A^2 -> H(d, f(c))
28.54/9.40	   A^2 -> H(d, f(d))
28.54/9.40	   A^2 -> H(a, U1(c, b))
28.54/9.40	   A^2 -> H(a, U1(d, b))
28.54/9.40	   A^2 -> H(a, U1(b, c))
28.54/9.40	   A^2 -> H(a, U1(b, d))
28.54/9.40	   A^2 -> H(a, U1(c, c))
28.54/9.40	   A^2 -> H(a, f(e))
28.54/9.40	   A^2 -> H(a, f(k))
28.54/9.40	   A^2 -> H(a, U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.40	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.40	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.40	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.40	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.40	   A^2 -> H(U1(e, d), f(e))
28.54/9.40	   A^2 -> H(U1(e, d), f(k))
28.54/9.40	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.40	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.40	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.40	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.40	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.40	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.40	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.40	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.40	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.40	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.40	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.40	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.40	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.40	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.40	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.40	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, a), b)
28.54/9.40	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.40	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.40	   A^2 -> H(U1(c, a), c)
28.54/9.40	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.40	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.40	   A^2 -> H(U1(c, a), e)
28.54/9.40	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.40	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.40	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.40	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.40	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.40	   A^2 -> H(U1(d, e), f(e))
28.54/9.40	   A^2 -> H(U1(d, e), f(k))
28.54/9.40	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.40	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.40	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.40	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.40	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.40	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.40	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.40	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.40	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.40	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.40	   A^2 -> H(U1(d, a), b)
28.54/9.40	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.40	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.40	   A^2 -> H(U1(d, a), c)
28.54/9.40	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.40	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.40	   A^2 -> H(U1(d, a), e)
28.54/9.40	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.40	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.40	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.40	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.40	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.40	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.40	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.40	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.40	   A^2 -> H(U1(a, c), b)
28.54/9.40	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.40	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.40	   A^2 -> H(U1(a, c), c)
28.54/9.40	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.40	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.40	   A^2 -> H(U1(a, c), e)
28.54/9.40	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, d), b)
28.54/9.40	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.40	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.40	   A^2 -> H(U1(a, d), c)
28.54/9.40	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.40	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.40	   A^2 -> H(U1(a, d), e)
28.54/9.40	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, a), d)
28.54/9.40	   A^2 -> H(U1(a, a), k)
28.54/9.40	   A^2 -> H(k, U1(b, b))
28.54/9.40	   A^2 -> H(k, f(c))
28.54/9.40	   A^2 -> H(k, f(d))
28.54/9.40	   A^2 -> H(c, U1(c, b))
28.54/9.40	   A^2 -> H(c, U1(d, b))
28.54/9.40	   A^2 -> H(c, U1(b, c))
28.54/9.40	   A^2 -> H(c, U1(b, d))
28.54/9.40	   A^2 -> H(c, U1(c, c))
28.54/9.40	   A^2 -> H(c, f(e))
28.54/9.40	   A^2 -> H(c, f(k))
28.54/9.40	   A^2 -> H(c, U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.40	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.40	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.40	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.40	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.40	   A^2 -> H(U1(e, k), f(e))
28.54/9.40	   A^2 -> H(U1(e, k), f(k))
28.54/9.40	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.40	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.40	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.40	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.40	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.40	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.40	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.40	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.40	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.40	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.40	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.40	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.40	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.40	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.40	   A^2 -> H(U1(k, e), f(e))
28.54/9.40	   A^2 -> H(U1(k, e), f(k))
28.54/9.40	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.40	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.40	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.40	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.40	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.40	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.40	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.40	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, c), b)
28.54/9.40	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.40	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.40	   A^2 -> H(U1(c, c), e)
28.54/9.40	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.40	   A^2 -> H(e, U1(c, b))
28.54/9.40	   A^2 -> H(e, U1(d, b))
28.54/9.40	   A^2 -> H(e, U1(b, c))
28.54/9.40	   A^2 -> H(e, U1(b, d))
28.54/9.40	   A^2 -> H(e, U1(c, c))
28.54/9.40	   A^2 -> H(e, f(e))
28.54/9.40	   A^2 -> H(e, f(k))
28.54/9.40	   A^2 -> H(e, U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.40	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.40	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.40	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.40	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.40	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.40	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.40	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.40	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.40	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.40	   A^2 -> H(f(e), b)
28.54/9.40	   A^2 -> H(f(e), U1(e, d))
28.54/9.40	   A^2 -> H(f(e), U1(d, e))
28.54/9.40	   A^2 -> H(f(e), c)
28.54/9.40	   A^2 -> H(f(e), U1(e, k))
28.54/9.40	   A^2 -> H(f(e), U1(k, e))
28.54/9.40	   A^2 -> H(f(e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.40	   A^2 -> H(f(k), b)
28.54/9.40	   A^2 -> H(f(k), U1(e, d))
28.54/9.40	   A^2 -> H(f(k), U1(d, e))
28.54/9.40	   A^2 -> H(f(k), c)
28.54/9.40	   A^2 -> H(f(k), U1(e, k))
28.54/9.40	   A^2 -> H(f(k), U1(k, e))
28.54/9.40	   A^2 -> H(f(k), e)
28.54/9.40	   A^2 -> H(f(c), d)
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.40	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.40	   A^2 -> H(U1(k, k), f(e))
28.54/9.40	   A^2 -> H(U1(k, k), f(k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.40	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.40	   A^2 -> H(U1(d, d), b)
28.54/9.40	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.40	
28.54/9.40	The TRS R consists of the following rules:
28.54/9.40	
28.54/9.40	   f(x) -> U1(x, x)
28.54/9.40	   U1(e, x) -> x
28.54/9.40	   a -> c
28.54/9.40	   a -> d
28.54/9.40	   b -> c
28.54/9.40	   b -> d
28.54/9.40	   d -> k
28.54/9.40	   c -> e
28.54/9.40	   c -> k
28.54/9.40	
28.54/9.40	Q is empty.
28.54/9.40	We have to consider all minimal (P,Q,R)-chains.
28.54/9.40	----------------------------------------
28.54/9.40	
28.54/9.40	(1031) TransformationProof (EQUIVALENT)
28.54/9.40	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.40	
28.54/9.40	   (A^2 -> H(U1(k, d), U1(d, c)),A^2 -> H(U1(k, d), U1(d, c)))
28.54/9.40	   (A^2 -> H(U1(d, k), U1(d, c)),A^2 -> H(U1(d, k), U1(d, c)))
28.54/9.40	   (A^2 -> H(U1(d, d), U1(k, c)),A^2 -> H(U1(d, d), U1(k, c)))
28.54/9.40	   (A^2 -> H(U1(d, d), U1(d, e)),A^2 -> H(U1(d, d), U1(d, e)))
28.54/9.40	   (A^2 -> H(U1(d, d), U1(d, k)),A^2 -> H(U1(d, d), U1(d, k)))
28.54/9.40	
28.54/9.40	
28.54/9.40	----------------------------------------
28.54/9.40	
28.54/9.40	(1032)
28.54/9.40	Obligation:
28.54/9.40	Q DP problem:
28.54/9.40	The TRS P consists of the following rules:
28.54/9.40	
28.54/9.40	   H(x, x) -> G(x, x, f(k))
28.54/9.40	   G(d, x, x) -> A^2
28.54/9.40	   A^2 -> H(f(c), f(c))
28.54/9.40	   A^2 -> H(f(d), f(d))
28.54/9.40	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.40	   A^2 -> H(f(e), f(e))
28.54/9.40	   A^2 -> H(f(k), f(k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.40	   A^2 -> H(U1(d, d), U1(b, e))
28.54/9.40	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.40	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.40	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.40	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.40	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.40	   A^2 -> H(f(d), b)
28.54/9.40	   A^2 -> H(f(d), U1(e, d))
28.54/9.40	   A^2 -> H(f(d), U1(d, e))
28.54/9.40	   A^2 -> H(f(d), c)
28.54/9.40	   A^2 -> H(f(d), U1(e, k))
28.54/9.40	   A^2 -> H(f(d), U1(k, e))
28.54/9.40	   A^2 -> H(f(d), e)
28.54/9.40	   A^2 -> H(f(a), d)
28.54/9.40	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.40	   A^2 -> H(f(c), c)
28.54/9.40	   A^2 -> H(f(c), U1(e, k))
28.54/9.40	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.40	   A^2 -> H(f(c), U1(k, e))
28.54/9.40	   A^2 -> H(f(c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.40	   A^2 -> H(f(a), k)
28.54/9.40	   A^2 -> H(f(e), U1(e, e))
28.54/9.40	   A^2 -> H(f(c), e)
28.54/9.40	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.40	   A^2 -> H(f(d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.40	   A^2 -> H(d, U1(b, b))
28.54/9.40	   A^2 -> H(d, f(c))
28.54/9.40	   A^2 -> H(d, f(d))
28.54/9.40	   A^2 -> H(a, U1(c, b))
28.54/9.40	   A^2 -> H(a, U1(d, b))
28.54/9.40	   A^2 -> H(a, U1(b, c))
28.54/9.40	   A^2 -> H(a, U1(b, d))
28.54/9.40	   A^2 -> H(a, U1(c, c))
28.54/9.40	   A^2 -> H(a, f(e))
28.54/9.40	   A^2 -> H(a, f(k))
28.54/9.40	   A^2 -> H(a, U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.40	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.40	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.40	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.40	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.40	   A^2 -> H(U1(e, d), f(e))
28.54/9.40	   A^2 -> H(U1(e, d), f(k))
28.54/9.40	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.40	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.40	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.40	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.40	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.40	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.40	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.40	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.40	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.40	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.40	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.40	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.40	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.40	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.40	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.40	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, a), b)
28.54/9.40	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.40	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.40	   A^2 -> H(U1(c, a), c)
28.54/9.40	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.40	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.40	   A^2 -> H(U1(c, a), e)
28.54/9.40	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.40	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.40	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.40	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.40	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.40	   A^2 -> H(U1(d, e), f(e))
28.54/9.40	   A^2 -> H(U1(d, e), f(k))
28.54/9.40	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.40	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.40	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.40	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.40	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.40	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.40	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.40	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.40	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.40	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.40	   A^2 -> H(U1(d, a), b)
28.54/9.40	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.40	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.40	   A^2 -> H(U1(d, a), c)
28.54/9.40	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.40	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.40	   A^2 -> H(U1(d, a), e)
28.54/9.40	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.40	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.40	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.40	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.40	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.40	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.40	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.40	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.40	   A^2 -> H(U1(a, c), b)
28.54/9.40	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.40	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.40	   A^2 -> H(U1(a, c), c)
28.54/9.40	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.40	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.40	   A^2 -> H(U1(a, c), e)
28.54/9.40	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, d), b)
28.54/9.40	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.40	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.40	   A^2 -> H(U1(a, d), c)
28.54/9.40	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.40	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.40	   A^2 -> H(U1(a, d), e)
28.54/9.40	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.40	   A^2 -> H(U1(a, a), d)
28.54/9.40	   A^2 -> H(U1(a, a), k)
28.54/9.40	   A^2 -> H(k, U1(b, b))
28.54/9.40	   A^2 -> H(k, f(c))
28.54/9.40	   A^2 -> H(k, f(d))
28.54/9.40	   A^2 -> H(c, U1(c, b))
28.54/9.40	   A^2 -> H(c, U1(d, b))
28.54/9.40	   A^2 -> H(c, U1(b, c))
28.54/9.40	   A^2 -> H(c, U1(b, d))
28.54/9.40	   A^2 -> H(c, U1(c, c))
28.54/9.40	   A^2 -> H(c, f(e))
28.54/9.40	   A^2 -> H(c, f(k))
28.54/9.40	   A^2 -> H(c, U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.40	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.40	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.40	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.40	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.40	   A^2 -> H(U1(e, k), f(e))
28.54/9.40	   A^2 -> H(U1(e, k), f(k))
28.54/9.40	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.40	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.40	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.40	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.40	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.40	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.40	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.40	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.40	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.40	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.40	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.40	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.40	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.40	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.40	   A^2 -> H(U1(k, e), f(e))
28.54/9.40	   A^2 -> H(U1(k, e), f(k))
28.54/9.40	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.40	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.40	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.40	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.40	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.40	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.40	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.40	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.40	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.40	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.40	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.40	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.40	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.40	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.40	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.40	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.40	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.40	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.40	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.40	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.40	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.40	   A^2 -> H(U1(c, c), b)
28.54/9.40	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.40	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.40	   A^2 -> H(U1(c, c), e)
28.54/9.40	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.40	   A^2 -> H(e, U1(c, b))
28.54/9.40	   A^2 -> H(e, U1(d, b))
28.54/9.40	   A^2 -> H(e, U1(b, c))
28.54/9.40	   A^2 -> H(e, U1(b, d))
28.54/9.40	   A^2 -> H(e, U1(c, c))
28.54/9.40	   A^2 -> H(e, f(e))
28.54/9.40	   A^2 -> H(e, f(k))
28.54/9.40	   A^2 -> H(e, U1(d, d))
28.54/9.40	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.40	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.40	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.40	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.40	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.40	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.40	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.40	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.40	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.40	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.40	   A^2 -> H(f(e), b)
28.54/9.40	   A^2 -> H(f(e), U1(e, d))
28.54/9.40	   A^2 -> H(f(e), U1(d, e))
28.54/9.40	   A^2 -> H(f(e), c)
28.54/9.40	   A^2 -> H(f(e), U1(e, k))
28.54/9.40	   A^2 -> H(f(e), U1(k, e))
28.54/9.40	   A^2 -> H(f(e), U1(k, k))
28.54/9.40	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.40	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.40	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.41	   A^2 -> H(f(k), b)
28.54/9.41	   A^2 -> H(f(k), U1(e, d))
28.54/9.41	   A^2 -> H(f(k), U1(d, e))
28.54/9.41	   A^2 -> H(f(k), c)
28.54/9.41	   A^2 -> H(f(k), U1(e, k))
28.54/9.41	   A^2 -> H(f(k), U1(k, e))
28.54/9.41	   A^2 -> H(f(k), e)
28.54/9.41	   A^2 -> H(f(c), d)
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.41	   A^2 -> H(U1(k, k), f(e))
28.54/9.41	   A^2 -> H(U1(k, k), f(k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.41	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.41	   A^2 -> H(U1(d, d), b)
28.54/9.41	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.41	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.41	
28.54/9.41	The TRS R consists of the following rules:
28.54/9.41	
28.54/9.41	   f(x) -> U1(x, x)
28.54/9.41	   U1(e, x) -> x
28.54/9.41	   a -> c
28.54/9.41	   a -> d
28.54/9.41	   b -> c
28.54/9.41	   b -> d
28.54/9.41	   d -> k
28.54/9.41	   c -> e
28.54/9.41	   c -> k
28.54/9.41	
28.54/9.41	Q is empty.
28.54/9.41	We have to consider all minimal (P,Q,R)-chains.
28.54/9.41	----------------------------------------
28.54/9.41	
28.54/9.41	(1033) TransformationProof (EQUIVALENT)
28.54/9.41	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.41	
28.54/9.41	   (A^2 -> H(U1(k, d), U1(b, e)),A^2 -> H(U1(k, d), U1(b, e)))
28.54/9.41	   (A^2 -> H(U1(d, k), U1(b, e)),A^2 -> H(U1(d, k), U1(b, e)))
28.54/9.41	   (A^2 -> H(U1(d, d), U1(c, e)),A^2 -> H(U1(d, d), U1(c, e)))
28.54/9.41	   (A^2 -> H(U1(d, d), U1(d, e)),A^2 -> H(U1(d, d), U1(d, e)))
28.54/9.41	
28.54/9.41	
28.54/9.41	----------------------------------------
28.54/9.41	
28.54/9.41	(1034)
28.54/9.41	Obligation:
28.54/9.41	Q DP problem:
28.54/9.41	The TRS P consists of the following rules:
28.54/9.41	
28.54/9.41	   H(x, x) -> G(x, x, f(k))
28.54/9.41	   G(d, x, x) -> A^2
28.54/9.41	   A^2 -> H(f(c), f(c))
28.54/9.41	   A^2 -> H(f(d), f(d))
28.54/9.41	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.41	   A^2 -> H(f(e), f(e))
28.54/9.41	   A^2 -> H(f(k), f(k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.41	   A^2 -> H(U1(d, d), U1(b, k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.41	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.41	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.41	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.41	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.41	   A^2 -> H(f(d), b)
28.54/9.41	   A^2 -> H(f(d), U1(e, d))
28.54/9.41	   A^2 -> H(f(d), U1(d, e))
28.54/9.41	   A^2 -> H(f(d), c)
28.54/9.41	   A^2 -> H(f(d), U1(e, k))
28.54/9.41	   A^2 -> H(f(d), U1(k, e))
28.54/9.41	   A^2 -> H(f(d), e)
28.54/9.41	   A^2 -> H(f(a), d)
28.54/9.41	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.41	   A^2 -> H(f(c), c)
28.54/9.41	   A^2 -> H(f(c), U1(e, k))
28.54/9.41	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.41	   A^2 -> H(f(c), U1(k, e))
28.54/9.41	   A^2 -> H(f(c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.41	   A^2 -> H(f(a), k)
28.54/9.41	   A^2 -> H(f(e), U1(e, e))
28.54/9.41	   A^2 -> H(f(c), e)
28.54/9.41	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.41	   A^2 -> H(f(d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.41	   A^2 -> H(d, U1(b, b))
28.54/9.41	   A^2 -> H(d, f(c))
28.54/9.41	   A^2 -> H(d, f(d))
28.54/9.41	   A^2 -> H(a, U1(c, b))
28.54/9.41	   A^2 -> H(a, U1(d, b))
28.54/9.41	   A^2 -> H(a, U1(b, c))
28.54/9.41	   A^2 -> H(a, U1(b, d))
28.54/9.41	   A^2 -> H(a, U1(c, c))
28.54/9.41	   A^2 -> H(a, f(e))
28.54/9.41	   A^2 -> H(a, f(k))
28.54/9.41	   A^2 -> H(a, U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.41	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.41	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.41	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.41	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.41	   A^2 -> H(U1(e, d), f(e))
28.54/9.41	   A^2 -> H(U1(e, d), f(k))
28.54/9.41	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.41	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.41	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.41	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.41	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.41	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.41	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.41	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.41	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.41	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.41	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.41	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.41	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.41	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.41	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.41	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, a), b)
28.54/9.41	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.41	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.41	   A^2 -> H(U1(c, a), c)
28.54/9.41	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.41	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.41	   A^2 -> H(U1(c, a), e)
28.54/9.41	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.41	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.41	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.41	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.41	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.41	   A^2 -> H(U1(d, e), f(e))
28.54/9.41	   A^2 -> H(U1(d, e), f(k))
28.54/9.41	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.41	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.41	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.41	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.41	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.41	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.41	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.41	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.41	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.41	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.41	   A^2 -> H(U1(d, a), b)
28.54/9.41	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.41	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.41	   A^2 -> H(U1(d, a), c)
28.54/9.41	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.41	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.41	   A^2 -> H(U1(d, a), e)
28.54/9.41	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.41	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.41	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.41	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.41	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.41	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.41	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.41	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.41	   A^2 -> H(U1(a, c), b)
28.54/9.41	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.41	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.41	   A^2 -> H(U1(a, c), c)
28.54/9.41	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.41	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.41	   A^2 -> H(U1(a, c), e)
28.54/9.41	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, d), b)
28.54/9.41	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.41	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.41	   A^2 -> H(U1(a, d), c)
28.54/9.41	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.41	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.41	   A^2 -> H(U1(a, d), e)
28.54/9.41	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, a), d)
28.54/9.41	   A^2 -> H(U1(a, a), k)
28.54/9.41	   A^2 -> H(k, U1(b, b))
28.54/9.41	   A^2 -> H(k, f(c))
28.54/9.41	   A^2 -> H(k, f(d))
28.54/9.41	   A^2 -> H(c, U1(c, b))
28.54/9.41	   A^2 -> H(c, U1(d, b))
28.54/9.41	   A^2 -> H(c, U1(b, c))
28.54/9.41	   A^2 -> H(c, U1(b, d))
28.54/9.41	   A^2 -> H(c, U1(c, c))
28.54/9.41	   A^2 -> H(c, f(e))
28.54/9.41	   A^2 -> H(c, f(k))
28.54/9.41	   A^2 -> H(c, U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.41	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.41	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.41	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.41	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.41	   A^2 -> H(U1(e, k), f(e))
28.54/9.41	   A^2 -> H(U1(e, k), f(k))
28.54/9.41	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.41	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.41	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.41	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.41	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.41	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.41	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.41	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.41	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.41	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.41	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.41	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.41	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.41	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.41	   A^2 -> H(U1(k, e), f(e))
28.54/9.41	   A^2 -> H(U1(k, e), f(k))
28.54/9.41	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.41	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.41	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.41	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.41	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.41	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.41	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.41	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, c), b)
28.54/9.41	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.41	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.41	   A^2 -> H(U1(c, c), e)
28.54/9.41	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.41	   A^2 -> H(e, U1(c, b))
28.54/9.41	   A^2 -> H(e, U1(d, b))
28.54/9.41	   A^2 -> H(e, U1(b, c))
28.54/9.41	   A^2 -> H(e, U1(b, d))
28.54/9.41	   A^2 -> H(e, U1(c, c))
28.54/9.41	   A^2 -> H(e, f(e))
28.54/9.41	   A^2 -> H(e, f(k))
28.54/9.41	   A^2 -> H(e, U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.41	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.41	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.41	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.41	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.41	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.41	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.41	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.41	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.41	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.41	   A^2 -> H(f(e), b)
28.54/9.41	   A^2 -> H(f(e), U1(e, d))
28.54/9.41	   A^2 -> H(f(e), U1(d, e))
28.54/9.41	   A^2 -> H(f(e), c)
28.54/9.41	   A^2 -> H(f(e), U1(e, k))
28.54/9.41	   A^2 -> H(f(e), U1(k, e))
28.54/9.41	   A^2 -> H(f(e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.41	   A^2 -> H(f(k), b)
28.54/9.41	   A^2 -> H(f(k), U1(e, d))
28.54/9.41	   A^2 -> H(f(k), U1(d, e))
28.54/9.41	   A^2 -> H(f(k), c)
28.54/9.41	   A^2 -> H(f(k), U1(e, k))
28.54/9.41	   A^2 -> H(f(k), U1(k, e))
28.54/9.41	   A^2 -> H(f(k), e)
28.54/9.41	   A^2 -> H(f(c), d)
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.41	   A^2 -> H(U1(k, k), f(e))
28.54/9.41	   A^2 -> H(U1(k, k), f(k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.41	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.41	   A^2 -> H(U1(d, d), b)
28.54/9.41	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.41	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.41	
28.54/9.41	The TRS R consists of the following rules:
28.54/9.41	
28.54/9.41	   f(x) -> U1(x, x)
28.54/9.41	   U1(e, x) -> x
28.54/9.41	   a -> c
28.54/9.41	   a -> d
28.54/9.41	   b -> c
28.54/9.41	   b -> d
28.54/9.41	   d -> k
28.54/9.41	   c -> e
28.54/9.41	   c -> k
28.54/9.41	
28.54/9.41	Q is empty.
28.54/9.41	We have to consider all minimal (P,Q,R)-chains.
28.54/9.41	----------------------------------------
28.54/9.41	
28.54/9.41	(1035) TransformationProof (EQUIVALENT)
28.54/9.41	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.41	
28.54/9.41	   (A^2 -> H(U1(k, d), U1(b, k)),A^2 -> H(U1(k, d), U1(b, k)))
28.54/9.41	   (A^2 -> H(U1(d, k), U1(b, k)),A^2 -> H(U1(d, k), U1(b, k)))
28.54/9.41	   (A^2 -> H(U1(d, d), U1(c, k)),A^2 -> H(U1(d, d), U1(c, k)))
28.54/9.41	   (A^2 -> H(U1(d, d), U1(d, k)),A^2 -> H(U1(d, d), U1(d, k)))
28.54/9.41	
28.54/9.41	
28.54/9.41	----------------------------------------
28.54/9.41	
28.54/9.41	(1036)
28.54/9.41	Obligation:
28.54/9.41	Q DP problem:
28.54/9.41	The TRS P consists of the following rules:
28.54/9.41	
28.54/9.41	   H(x, x) -> G(x, x, f(k))
28.54/9.41	   G(d, x, x) -> A^2
28.54/9.41	   A^2 -> H(f(c), f(c))
28.54/9.41	   A^2 -> H(f(d), f(d))
28.54/9.41	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.41	   A^2 -> H(f(e), f(e))
28.54/9.41	   A^2 -> H(f(k), f(k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.41	   A^2 -> H(U1(d, d), U1(e, c))
28.54/9.41	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.41	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.41	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.41	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.41	   A^2 -> H(f(d), b)
28.54/9.41	   A^2 -> H(f(d), U1(e, d))
28.54/9.41	   A^2 -> H(f(d), U1(d, e))
28.54/9.41	   A^2 -> H(f(d), c)
28.54/9.41	   A^2 -> H(f(d), U1(e, k))
28.54/9.41	   A^2 -> H(f(d), U1(k, e))
28.54/9.41	   A^2 -> H(f(d), e)
28.54/9.41	   A^2 -> H(f(a), d)
28.54/9.41	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.41	   A^2 -> H(f(c), c)
28.54/9.41	   A^2 -> H(f(c), U1(e, k))
28.54/9.41	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.41	   A^2 -> H(f(c), U1(k, e))
28.54/9.41	   A^2 -> H(f(c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.41	   A^2 -> H(f(a), k)
28.54/9.41	   A^2 -> H(f(e), U1(e, e))
28.54/9.41	   A^2 -> H(f(c), e)
28.54/9.41	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.41	   A^2 -> H(f(d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.41	   A^2 -> H(d, U1(b, b))
28.54/9.41	   A^2 -> H(d, f(c))
28.54/9.41	   A^2 -> H(d, f(d))
28.54/9.41	   A^2 -> H(a, U1(c, b))
28.54/9.41	   A^2 -> H(a, U1(d, b))
28.54/9.41	   A^2 -> H(a, U1(b, c))
28.54/9.41	   A^2 -> H(a, U1(b, d))
28.54/9.41	   A^2 -> H(a, U1(c, c))
28.54/9.41	   A^2 -> H(a, f(e))
28.54/9.41	   A^2 -> H(a, f(k))
28.54/9.41	   A^2 -> H(a, U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.41	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.41	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.41	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.41	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.41	   A^2 -> H(U1(e, d), f(e))
28.54/9.41	   A^2 -> H(U1(e, d), f(k))
28.54/9.41	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.41	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.41	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.41	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.41	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.41	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.41	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.41	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.41	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.41	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.41	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.41	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.41	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.41	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.41	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.41	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, a), b)
28.54/9.41	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.41	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.41	   A^2 -> H(U1(c, a), c)
28.54/9.41	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.41	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.41	   A^2 -> H(U1(c, a), e)
28.54/9.41	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.41	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.41	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.41	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.41	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.41	   A^2 -> H(U1(d, e), f(e))
28.54/9.41	   A^2 -> H(U1(d, e), f(k))
28.54/9.41	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.41	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.41	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.41	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.41	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.41	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.41	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.41	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.41	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.41	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.41	   A^2 -> H(U1(d, a), b)
28.54/9.41	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.41	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.41	   A^2 -> H(U1(d, a), c)
28.54/9.41	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.41	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.41	   A^2 -> H(U1(d, a), e)
28.54/9.41	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.41	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.41	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.41	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.41	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.41	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.41	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.41	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.41	   A^2 -> H(U1(a, c), b)
28.54/9.41	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.41	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.41	   A^2 -> H(U1(a, c), c)
28.54/9.41	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.41	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.41	   A^2 -> H(U1(a, c), e)
28.54/9.41	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, d), b)
28.54/9.41	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.41	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.41	   A^2 -> H(U1(a, d), c)
28.54/9.41	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.41	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.41	   A^2 -> H(U1(a, d), e)
28.54/9.41	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, a), d)
28.54/9.41	   A^2 -> H(U1(a, a), k)
28.54/9.41	   A^2 -> H(k, U1(b, b))
28.54/9.41	   A^2 -> H(k, f(c))
28.54/9.41	   A^2 -> H(k, f(d))
28.54/9.41	   A^2 -> H(c, U1(c, b))
28.54/9.41	   A^2 -> H(c, U1(d, b))
28.54/9.41	   A^2 -> H(c, U1(b, c))
28.54/9.41	   A^2 -> H(c, U1(b, d))
28.54/9.41	   A^2 -> H(c, U1(c, c))
28.54/9.41	   A^2 -> H(c, f(e))
28.54/9.41	   A^2 -> H(c, f(k))
28.54/9.41	   A^2 -> H(c, U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.41	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.41	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.41	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.41	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.41	   A^2 -> H(U1(e, k), f(e))
28.54/9.41	   A^2 -> H(U1(e, k), f(k))
28.54/9.41	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.41	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.41	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.41	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.41	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.41	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.41	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.41	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.41	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.41	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.41	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.41	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.41	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.41	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.41	   A^2 -> H(U1(k, e), f(e))
28.54/9.41	   A^2 -> H(U1(k, e), f(k))
28.54/9.41	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.41	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.41	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.41	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.41	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.41	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.41	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.41	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, c), b)
28.54/9.41	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.41	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.41	   A^2 -> H(U1(c, c), e)
28.54/9.41	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.41	   A^2 -> H(e, U1(c, b))
28.54/9.41	   A^2 -> H(e, U1(d, b))
28.54/9.41	   A^2 -> H(e, U1(b, c))
28.54/9.41	   A^2 -> H(e, U1(b, d))
28.54/9.41	   A^2 -> H(e, U1(c, c))
28.54/9.41	   A^2 -> H(e, f(e))
28.54/9.41	   A^2 -> H(e, f(k))
28.54/9.41	   A^2 -> H(e, U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.41	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.41	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.41	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.41	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.41	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.41	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.41	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.41	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.41	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.41	   A^2 -> H(f(e), b)
28.54/9.41	   A^2 -> H(f(e), U1(e, d))
28.54/9.41	   A^2 -> H(f(e), U1(d, e))
28.54/9.41	   A^2 -> H(f(e), c)
28.54/9.41	   A^2 -> H(f(e), U1(e, k))
28.54/9.41	   A^2 -> H(f(e), U1(k, e))
28.54/9.41	   A^2 -> H(f(e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.41	   A^2 -> H(f(k), b)
28.54/9.41	   A^2 -> H(f(k), U1(e, d))
28.54/9.41	   A^2 -> H(f(k), U1(d, e))
28.54/9.41	   A^2 -> H(f(k), c)
28.54/9.41	   A^2 -> H(f(k), U1(e, k))
28.54/9.41	   A^2 -> H(f(k), U1(k, e))
28.54/9.41	   A^2 -> H(f(k), e)
28.54/9.41	   A^2 -> H(f(c), d)
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.41	   A^2 -> H(U1(k, k), f(e))
28.54/9.41	   A^2 -> H(U1(k, k), f(k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.41	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.41	   A^2 -> H(U1(d, d), b)
28.54/9.41	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.41	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.41	
28.54/9.41	The TRS R consists of the following rules:
28.54/9.41	
28.54/9.41	   f(x) -> U1(x, x)
28.54/9.41	   U1(e, x) -> x
28.54/9.41	   a -> c
28.54/9.41	   a -> d
28.54/9.41	   b -> c
28.54/9.41	   b -> d
28.54/9.41	   d -> k
28.54/9.41	   c -> e
28.54/9.41	   c -> k
28.54/9.41	
28.54/9.41	Q is empty.
28.54/9.41	We have to consider all minimal (P,Q,R)-chains.
28.54/9.41	----------------------------------------
28.54/9.41	
28.54/9.41	(1037) TransformationProof (EQUIVALENT)
28.54/9.41	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.41	
28.54/9.41	   (A^2 -> H(U1(k, d), U1(e, c)),A^2 -> H(U1(k, d), U1(e, c)))
28.54/9.41	   (A^2 -> H(U1(d, k), U1(e, c)),A^2 -> H(U1(d, k), U1(e, c)))
28.54/9.41	   (A^2 -> H(U1(d, d), c),A^2 -> H(U1(d, d), c))
28.54/9.41	   (A^2 -> H(U1(d, d), U1(e, e)),A^2 -> H(U1(d, d), U1(e, e)))
28.54/9.41	   (A^2 -> H(U1(d, d), U1(e, k)),A^2 -> H(U1(d, d), U1(e, k)))
28.54/9.41	
28.54/9.41	
28.54/9.41	----------------------------------------
28.54/9.41	
28.54/9.41	(1038)
28.54/9.41	Obligation:
28.54/9.41	Q DP problem:
28.54/9.41	The TRS P consists of the following rules:
28.54/9.41	
28.54/9.41	   H(x, x) -> G(x, x, f(k))
28.54/9.41	   G(d, x, x) -> A^2
28.54/9.41	   A^2 -> H(f(c), f(c))
28.54/9.41	   A^2 -> H(f(d), f(d))
28.54/9.41	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.41	   A^2 -> H(f(e), f(e))
28.54/9.41	   A^2 -> H(f(k), f(k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.41	   A^2 -> H(U1(d, d), U1(k, c))
28.54/9.41	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.41	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.41	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.41	   A^2 -> H(f(d), b)
28.54/9.41	   A^2 -> H(f(d), U1(e, d))
28.54/9.41	   A^2 -> H(f(d), U1(d, e))
28.54/9.41	   A^2 -> H(f(d), c)
28.54/9.41	   A^2 -> H(f(d), U1(e, k))
28.54/9.41	   A^2 -> H(f(d), U1(k, e))
28.54/9.41	   A^2 -> H(f(d), e)
28.54/9.41	   A^2 -> H(f(a), d)
28.54/9.41	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.41	   A^2 -> H(f(c), c)
28.54/9.41	   A^2 -> H(f(c), U1(e, k))
28.54/9.41	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.41	   A^2 -> H(f(c), U1(k, e))
28.54/9.41	   A^2 -> H(f(c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.41	   A^2 -> H(f(a), k)
28.54/9.41	   A^2 -> H(f(e), U1(e, e))
28.54/9.41	   A^2 -> H(f(c), e)
28.54/9.41	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.41	   A^2 -> H(f(d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.41	   A^2 -> H(d, U1(b, b))
28.54/9.41	   A^2 -> H(d, f(c))
28.54/9.41	   A^2 -> H(d, f(d))
28.54/9.41	   A^2 -> H(a, U1(c, b))
28.54/9.41	   A^2 -> H(a, U1(d, b))
28.54/9.41	   A^2 -> H(a, U1(b, c))
28.54/9.41	   A^2 -> H(a, U1(b, d))
28.54/9.41	   A^2 -> H(a, U1(c, c))
28.54/9.41	   A^2 -> H(a, f(e))
28.54/9.41	   A^2 -> H(a, f(k))
28.54/9.41	   A^2 -> H(a, U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.41	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.41	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.41	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.41	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.41	   A^2 -> H(U1(e, d), f(e))
28.54/9.41	   A^2 -> H(U1(e, d), f(k))
28.54/9.41	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.41	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.41	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.41	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.41	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.41	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.41	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.41	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.41	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.41	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.41	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.41	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.41	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.41	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.41	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.41	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, a), b)
28.54/9.41	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.41	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.41	   A^2 -> H(U1(c, a), c)
28.54/9.41	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.41	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.41	   A^2 -> H(U1(c, a), e)
28.54/9.41	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.41	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.41	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.41	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.41	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.41	   A^2 -> H(U1(d, e), f(e))
28.54/9.41	   A^2 -> H(U1(d, e), f(k))
28.54/9.41	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.41	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.41	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.41	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.41	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.41	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.41	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.41	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.41	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.41	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.41	   A^2 -> H(U1(d, a), b)
28.54/9.41	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.41	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.41	   A^2 -> H(U1(d, a), c)
28.54/9.41	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.41	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.41	   A^2 -> H(U1(d, a), e)
28.54/9.41	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.41	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.41	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.41	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.41	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.41	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.41	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.41	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.41	   A^2 -> H(U1(a, c), b)
28.54/9.41	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.41	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.41	   A^2 -> H(U1(a, c), c)
28.54/9.41	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.41	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.41	   A^2 -> H(U1(a, c), e)
28.54/9.41	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, d), b)
28.54/9.41	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.41	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.41	   A^2 -> H(U1(a, d), c)
28.54/9.41	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.41	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.41	   A^2 -> H(U1(a, d), e)
28.54/9.41	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, a), d)
28.54/9.41	   A^2 -> H(U1(a, a), k)
28.54/9.41	   A^2 -> H(k, U1(b, b))
28.54/9.41	   A^2 -> H(k, f(c))
28.54/9.41	   A^2 -> H(k, f(d))
28.54/9.41	   A^2 -> H(c, U1(c, b))
28.54/9.41	   A^2 -> H(c, U1(d, b))
28.54/9.41	   A^2 -> H(c, U1(b, c))
28.54/9.41	   A^2 -> H(c, U1(b, d))
28.54/9.41	   A^2 -> H(c, U1(c, c))
28.54/9.41	   A^2 -> H(c, f(e))
28.54/9.41	   A^2 -> H(c, f(k))
28.54/9.41	   A^2 -> H(c, U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.41	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.41	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.41	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.41	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.41	   A^2 -> H(U1(e, k), f(e))
28.54/9.41	   A^2 -> H(U1(e, k), f(k))
28.54/9.41	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.41	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.41	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.41	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.41	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.41	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.41	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.41	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.41	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.41	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.41	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.41	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.41	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.41	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.41	   A^2 -> H(U1(k, e), f(e))
28.54/9.41	   A^2 -> H(U1(k, e), f(k))
28.54/9.41	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.41	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.41	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.41	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.41	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.41	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.41	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.41	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, c), b)
28.54/9.41	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.41	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.41	   A^2 -> H(U1(c, c), e)
28.54/9.41	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.41	   A^2 -> H(e, U1(c, b))
28.54/9.41	   A^2 -> H(e, U1(d, b))
28.54/9.41	   A^2 -> H(e, U1(b, c))
28.54/9.41	   A^2 -> H(e, U1(b, d))
28.54/9.41	   A^2 -> H(e, U1(c, c))
28.54/9.41	   A^2 -> H(e, f(e))
28.54/9.41	   A^2 -> H(e, f(k))
28.54/9.41	   A^2 -> H(e, U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.41	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.41	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.41	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.41	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.41	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.41	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.41	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.41	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.41	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.41	   A^2 -> H(f(e), b)
28.54/9.41	   A^2 -> H(f(e), U1(e, d))
28.54/9.41	   A^2 -> H(f(e), U1(d, e))
28.54/9.41	   A^2 -> H(f(e), c)
28.54/9.41	   A^2 -> H(f(e), U1(e, k))
28.54/9.41	   A^2 -> H(f(e), U1(k, e))
28.54/9.41	   A^2 -> H(f(e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.41	   A^2 -> H(f(k), b)
28.54/9.41	   A^2 -> H(f(k), U1(e, d))
28.54/9.41	   A^2 -> H(f(k), U1(d, e))
28.54/9.41	   A^2 -> H(f(k), c)
28.54/9.41	   A^2 -> H(f(k), U1(e, k))
28.54/9.41	   A^2 -> H(f(k), U1(k, e))
28.54/9.41	   A^2 -> H(f(k), e)
28.54/9.41	   A^2 -> H(f(c), d)
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.41	   A^2 -> H(U1(k, k), f(e))
28.54/9.41	   A^2 -> H(U1(k, k), f(k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.41	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.41	   A^2 -> H(U1(d, d), b)
28.54/9.41	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.41	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.41	   A^2 -> H(U1(d, d), c)
28.54/9.41	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.41	
28.54/9.41	The TRS R consists of the following rules:
28.54/9.41	
28.54/9.41	   f(x) -> U1(x, x)
28.54/9.41	   U1(e, x) -> x
28.54/9.41	   a -> c
28.54/9.41	   a -> d
28.54/9.41	   b -> c
28.54/9.41	   b -> d
28.54/9.41	   d -> k
28.54/9.41	   c -> e
28.54/9.41	   c -> k
28.54/9.41	
28.54/9.41	Q is empty.
28.54/9.41	We have to consider all minimal (P,Q,R)-chains.
28.54/9.41	----------------------------------------
28.54/9.41	
28.54/9.41	(1039) TransformationProof (EQUIVALENT)
28.54/9.41	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.41	
28.54/9.41	   (A^2 -> H(U1(k, d), U1(k, c)),A^2 -> H(U1(k, d), U1(k, c)))
28.54/9.41	   (A^2 -> H(U1(d, k), U1(k, c)),A^2 -> H(U1(d, k), U1(k, c)))
28.54/9.41	   (A^2 -> H(U1(d, d), U1(k, e)),A^2 -> H(U1(d, d), U1(k, e)))
28.54/9.41	   (A^2 -> H(U1(d, d), U1(k, k)),A^2 -> H(U1(d, d), U1(k, k)))
28.54/9.41	
28.54/9.41	
28.54/9.41	----------------------------------------
28.54/9.41	
28.54/9.41	(1040)
28.54/9.41	Obligation:
28.54/9.41	Q DP problem:
28.54/9.41	The TRS P consists of the following rules:
28.54/9.41	
28.54/9.41	   H(x, x) -> G(x, x, f(k))
28.54/9.41	   G(d, x, x) -> A^2
28.54/9.41	   A^2 -> H(f(c), f(c))
28.54/9.41	   A^2 -> H(f(d), f(d))
28.54/9.41	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.41	   A^2 -> H(f(e), f(e))
28.54/9.41	   A^2 -> H(f(k), f(k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.41	   A^2 -> H(U1(d, d), U1(c, e))
28.54/9.41	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.41	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.41	   A^2 -> H(f(d), b)
28.54/9.41	   A^2 -> H(f(d), U1(e, d))
28.54/9.41	   A^2 -> H(f(d), U1(d, e))
28.54/9.41	   A^2 -> H(f(d), c)
28.54/9.41	   A^2 -> H(f(d), U1(e, k))
28.54/9.41	   A^2 -> H(f(d), U1(k, e))
28.54/9.41	   A^2 -> H(f(d), e)
28.54/9.41	   A^2 -> H(f(a), d)
28.54/9.41	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.41	   A^2 -> H(f(c), c)
28.54/9.41	   A^2 -> H(f(c), U1(e, k))
28.54/9.41	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.41	   A^2 -> H(f(c), U1(k, e))
28.54/9.41	   A^2 -> H(f(c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.41	   A^2 -> H(f(a), k)
28.54/9.41	   A^2 -> H(f(e), U1(e, e))
28.54/9.41	   A^2 -> H(f(c), e)
28.54/9.41	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.41	   A^2 -> H(f(d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.41	   A^2 -> H(d, U1(b, b))
28.54/9.41	   A^2 -> H(d, f(c))
28.54/9.41	   A^2 -> H(d, f(d))
28.54/9.41	   A^2 -> H(a, U1(c, b))
28.54/9.41	   A^2 -> H(a, U1(d, b))
28.54/9.41	   A^2 -> H(a, U1(b, c))
28.54/9.41	   A^2 -> H(a, U1(b, d))
28.54/9.41	   A^2 -> H(a, U1(c, c))
28.54/9.41	   A^2 -> H(a, f(e))
28.54/9.41	   A^2 -> H(a, f(k))
28.54/9.41	   A^2 -> H(a, U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.41	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.41	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.41	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.41	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.41	   A^2 -> H(U1(e, d), f(e))
28.54/9.41	   A^2 -> H(U1(e, d), f(k))
28.54/9.41	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.41	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.41	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.41	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.41	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.41	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.41	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.41	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.41	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.41	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.41	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.41	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.41	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.41	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.41	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.41	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, a), b)
28.54/9.41	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.41	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.41	   A^2 -> H(U1(c, a), c)
28.54/9.41	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.41	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.41	   A^2 -> H(U1(c, a), e)
28.54/9.41	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.41	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.41	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.41	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.41	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.41	   A^2 -> H(U1(d, e), f(e))
28.54/9.41	   A^2 -> H(U1(d, e), f(k))
28.54/9.41	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.41	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.41	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.41	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.41	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.41	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.41	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.41	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.41	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.41	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.41	   A^2 -> H(U1(d, a), b)
28.54/9.41	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.41	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.41	   A^2 -> H(U1(d, a), c)
28.54/9.41	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.41	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.41	   A^2 -> H(U1(d, a), e)
28.54/9.41	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.41	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.41	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.41	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.41	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.41	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.41	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.41	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.41	   A^2 -> H(U1(a, c), b)
28.54/9.41	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.41	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.41	   A^2 -> H(U1(a, c), c)
28.54/9.41	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.41	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.41	   A^2 -> H(U1(a, c), e)
28.54/9.41	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, d), b)
28.54/9.41	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.41	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.41	   A^2 -> H(U1(a, d), c)
28.54/9.41	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.41	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.41	   A^2 -> H(U1(a, d), e)
28.54/9.41	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, a), d)
28.54/9.41	   A^2 -> H(U1(a, a), k)
28.54/9.41	   A^2 -> H(k, U1(b, b))
28.54/9.41	   A^2 -> H(k, f(c))
28.54/9.41	   A^2 -> H(k, f(d))
28.54/9.41	   A^2 -> H(c, U1(c, b))
28.54/9.41	   A^2 -> H(c, U1(d, b))
28.54/9.41	   A^2 -> H(c, U1(b, c))
28.54/9.41	   A^2 -> H(c, U1(b, d))
28.54/9.41	   A^2 -> H(c, U1(c, c))
28.54/9.41	   A^2 -> H(c, f(e))
28.54/9.41	   A^2 -> H(c, f(k))
28.54/9.41	   A^2 -> H(c, U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.41	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.41	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.41	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.41	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.41	   A^2 -> H(U1(e, k), f(e))
28.54/9.41	   A^2 -> H(U1(e, k), f(k))
28.54/9.41	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.41	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.41	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.41	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.41	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.41	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.41	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.41	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.41	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.41	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.41	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.41	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.41	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.41	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.41	   A^2 -> H(U1(k, e), f(e))
28.54/9.41	   A^2 -> H(U1(k, e), f(k))
28.54/9.41	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.41	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.41	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.41	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.41	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.41	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.41	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.41	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, c), b)
28.54/9.41	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.41	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.41	   A^2 -> H(U1(c, c), e)
28.54/9.41	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.41	   A^2 -> H(e, U1(c, b))
28.54/9.41	   A^2 -> H(e, U1(d, b))
28.54/9.41	   A^2 -> H(e, U1(b, c))
28.54/9.41	   A^2 -> H(e, U1(b, d))
28.54/9.41	   A^2 -> H(e, U1(c, c))
28.54/9.41	   A^2 -> H(e, f(e))
28.54/9.41	   A^2 -> H(e, f(k))
28.54/9.41	   A^2 -> H(e, U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.41	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.41	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.41	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.41	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.41	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.41	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.41	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.41	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.41	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.41	   A^2 -> H(f(e), b)
28.54/9.41	   A^2 -> H(f(e), U1(e, d))
28.54/9.41	   A^2 -> H(f(e), U1(d, e))
28.54/9.41	   A^2 -> H(f(e), c)
28.54/9.41	   A^2 -> H(f(e), U1(e, k))
28.54/9.41	   A^2 -> H(f(e), U1(k, e))
28.54/9.41	   A^2 -> H(f(e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.41	   A^2 -> H(f(k), b)
28.54/9.41	   A^2 -> H(f(k), U1(e, d))
28.54/9.41	   A^2 -> H(f(k), U1(d, e))
28.54/9.41	   A^2 -> H(f(k), c)
28.54/9.41	   A^2 -> H(f(k), U1(e, k))
28.54/9.41	   A^2 -> H(f(k), U1(k, e))
28.54/9.41	   A^2 -> H(f(k), e)
28.54/9.41	   A^2 -> H(f(c), d)
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.41	   A^2 -> H(U1(k, k), f(e))
28.54/9.41	   A^2 -> H(U1(k, k), f(k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.41	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.41	   A^2 -> H(U1(d, d), b)
28.54/9.41	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.41	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.41	   A^2 -> H(U1(d, d), c)
28.54/9.41	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.41	
28.54/9.41	The TRS R consists of the following rules:
28.54/9.41	
28.54/9.41	   f(x) -> U1(x, x)
28.54/9.41	   U1(e, x) -> x
28.54/9.41	   a -> c
28.54/9.41	   a -> d
28.54/9.41	   b -> c
28.54/9.41	   b -> d
28.54/9.41	   d -> k
28.54/9.41	   c -> e
28.54/9.41	   c -> k
28.54/9.41	
28.54/9.41	Q is empty.
28.54/9.41	We have to consider all minimal (P,Q,R)-chains.
28.54/9.41	----------------------------------------
28.54/9.41	
28.54/9.41	(1041) TransformationProof (EQUIVALENT)
28.54/9.41	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.41	
28.54/9.41	   (A^2 -> H(U1(k, d), U1(c, e)),A^2 -> H(U1(k, d), U1(c, e)))
28.54/9.41	   (A^2 -> H(U1(d, k), U1(c, e)),A^2 -> H(U1(d, k), U1(c, e)))
28.54/9.41	   (A^2 -> H(U1(d, d), U1(e, e)),A^2 -> H(U1(d, d), U1(e, e)))
28.54/9.41	   (A^2 -> H(U1(d, d), U1(k, e)),A^2 -> H(U1(d, d), U1(k, e)))
28.54/9.41	
28.54/9.41	
28.54/9.41	----------------------------------------
28.54/9.41	
28.54/9.41	(1042)
28.54/9.41	Obligation:
28.54/9.41	Q DP problem:
28.54/9.41	The TRS P consists of the following rules:
28.54/9.41	
28.54/9.41	   H(x, x) -> G(x, x, f(k))
28.54/9.41	   G(d, x, x) -> A^2
28.54/9.41	   A^2 -> H(f(c), f(c))
28.54/9.41	   A^2 -> H(f(d), f(d))
28.54/9.41	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.41	   A^2 -> H(f(e), f(e))
28.54/9.41	   A^2 -> H(f(k), f(k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.41	   A^2 -> H(U1(d, d), U1(c, k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.41	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.41	   A^2 -> H(f(d), b)
28.54/9.41	   A^2 -> H(f(d), U1(e, d))
28.54/9.41	   A^2 -> H(f(d), U1(d, e))
28.54/9.41	   A^2 -> H(f(d), c)
28.54/9.41	   A^2 -> H(f(d), U1(e, k))
28.54/9.41	   A^2 -> H(f(d), U1(k, e))
28.54/9.41	   A^2 -> H(f(d), e)
28.54/9.41	   A^2 -> H(f(a), d)
28.54/9.41	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.41	   A^2 -> H(f(c), c)
28.54/9.41	   A^2 -> H(f(c), U1(e, k))
28.54/9.41	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.41	   A^2 -> H(f(c), U1(k, e))
28.54/9.41	   A^2 -> H(f(c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.41	   A^2 -> H(f(a), k)
28.54/9.41	   A^2 -> H(f(e), U1(e, e))
28.54/9.41	   A^2 -> H(f(c), e)
28.54/9.41	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.41	   A^2 -> H(f(d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.41	   A^2 -> H(d, U1(b, b))
28.54/9.41	   A^2 -> H(d, f(c))
28.54/9.41	   A^2 -> H(d, f(d))
28.54/9.41	   A^2 -> H(a, U1(c, b))
28.54/9.41	   A^2 -> H(a, U1(d, b))
28.54/9.41	   A^2 -> H(a, U1(b, c))
28.54/9.41	   A^2 -> H(a, U1(b, d))
28.54/9.41	   A^2 -> H(a, U1(c, c))
28.54/9.41	   A^2 -> H(a, f(e))
28.54/9.41	   A^2 -> H(a, f(k))
28.54/9.41	   A^2 -> H(a, U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.41	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.41	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.41	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.41	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.41	   A^2 -> H(U1(e, d), f(e))
28.54/9.41	   A^2 -> H(U1(e, d), f(k))
28.54/9.41	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.41	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.41	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.41	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.41	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.41	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.41	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.41	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.41	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.41	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.41	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.41	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.41	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.41	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.41	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.41	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, a), b)
28.54/9.41	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.41	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.41	   A^2 -> H(U1(c, a), c)
28.54/9.41	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.41	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.41	   A^2 -> H(U1(c, a), e)
28.54/9.41	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.41	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.41	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.41	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.41	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.41	   A^2 -> H(U1(d, e), f(e))
28.54/9.41	   A^2 -> H(U1(d, e), f(k))
28.54/9.41	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.41	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.41	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.41	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.41	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.41	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.41	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.41	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.41	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.41	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.41	   A^2 -> H(U1(d, a), b)
28.54/9.41	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.41	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.41	   A^2 -> H(U1(d, a), c)
28.54/9.41	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.41	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.41	   A^2 -> H(U1(d, a), e)
28.54/9.41	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.41	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.41	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.41	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.41	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.41	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.41	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.41	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.41	   A^2 -> H(U1(a, c), b)
28.54/9.41	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.41	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.41	   A^2 -> H(U1(a, c), c)
28.54/9.41	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.41	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.41	   A^2 -> H(U1(a, c), e)
28.54/9.41	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, d), b)
28.54/9.41	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.41	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.41	   A^2 -> H(U1(a, d), c)
28.54/9.41	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.41	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.41	   A^2 -> H(U1(a, d), e)
28.54/9.41	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(a, a), d)
28.54/9.41	   A^2 -> H(U1(a, a), k)
28.54/9.41	   A^2 -> H(k, U1(b, b))
28.54/9.41	   A^2 -> H(k, f(c))
28.54/9.41	   A^2 -> H(k, f(d))
28.54/9.41	   A^2 -> H(c, U1(c, b))
28.54/9.41	   A^2 -> H(c, U1(d, b))
28.54/9.41	   A^2 -> H(c, U1(b, c))
28.54/9.41	   A^2 -> H(c, U1(b, d))
28.54/9.41	   A^2 -> H(c, U1(c, c))
28.54/9.41	   A^2 -> H(c, f(e))
28.54/9.41	   A^2 -> H(c, f(k))
28.54/9.41	   A^2 -> H(c, U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.41	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.41	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.41	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.41	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.41	   A^2 -> H(U1(e, k), f(e))
28.54/9.41	   A^2 -> H(U1(e, k), f(k))
28.54/9.41	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.41	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.41	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.41	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.41	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.41	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.41	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.41	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.41	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.41	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.41	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.41	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.41	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.41	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.41	   A^2 -> H(U1(k, e), f(e))
28.54/9.41	   A^2 -> H(U1(k, e), f(k))
28.54/9.41	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.41	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.41	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.41	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.41	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.41	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.41	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.41	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.41	   A^2 -> H(U1(c, c), b)
28.54/9.41	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.41	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.41	   A^2 -> H(U1(c, c), e)
28.54/9.41	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.41	   A^2 -> H(e, U1(c, b))
28.54/9.41	   A^2 -> H(e, U1(d, b))
28.54/9.41	   A^2 -> H(e, U1(b, c))
28.54/9.41	   A^2 -> H(e, U1(b, d))
28.54/9.41	   A^2 -> H(e, U1(c, c))
28.54/9.41	   A^2 -> H(e, f(e))
28.54/9.41	   A^2 -> H(e, f(k))
28.54/9.41	   A^2 -> H(e, U1(d, d))
28.54/9.41	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.41	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.41	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.41	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.41	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.41	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.41	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.41	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.41	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.41	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.41	   A^2 -> H(f(e), b)
28.54/9.41	   A^2 -> H(f(e), U1(e, d))
28.54/9.41	   A^2 -> H(f(e), U1(d, e))
28.54/9.41	   A^2 -> H(f(e), c)
28.54/9.41	   A^2 -> H(f(e), U1(e, k))
28.54/9.41	   A^2 -> H(f(e), U1(k, e))
28.54/9.41	   A^2 -> H(f(e), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.41	   A^2 -> H(f(k), b)
28.54/9.41	   A^2 -> H(f(k), U1(e, d))
28.54/9.41	   A^2 -> H(f(k), U1(d, e))
28.54/9.41	   A^2 -> H(f(k), c)
28.54/9.41	   A^2 -> H(f(k), U1(e, k))
28.54/9.41	   A^2 -> H(f(k), U1(k, e))
28.54/9.41	   A^2 -> H(f(k), e)
28.54/9.41	   A^2 -> H(f(c), d)
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.41	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.41	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.41	   A^2 -> H(U1(k, k), f(e))
28.54/9.41	   A^2 -> H(U1(k, k), f(k))
28.54/9.41	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.41	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.41	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.41	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.41	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.41	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.41	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.41	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.41	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.41	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.41	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.41	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.41	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.41	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.41	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.41	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.41	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.41	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.41	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.41	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.41	   A^2 -> H(U1(d, d), b)
28.54/9.41	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.41	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.41	   A^2 -> H(U1(d, d), c)
28.54/9.41	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.41	
28.54/9.41	The TRS R consists of the following rules:
28.54/9.41	
28.54/9.41	   f(x) -> U1(x, x)
28.54/9.41	   U1(e, x) -> x
28.54/9.41	   a -> c
28.54/9.41	   a -> d
28.54/9.41	   b -> c
28.54/9.41	   b -> d
28.54/9.41	   d -> k
28.54/9.41	   c -> e
28.54/9.41	   c -> k
28.54/9.41	
28.54/9.41	Q is empty.
28.54/9.41	We have to consider all minimal (P,Q,R)-chains.
28.54/9.41	----------------------------------------
28.54/9.41	
28.54/9.41	(1043) TransformationProof (EQUIVALENT)
28.54/9.41	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.41	
28.54/9.41	   (A^2 -> H(U1(k, d), U1(c, k)),A^2 -> H(U1(k, d), U1(c, k)))
28.54/9.41	   (A^2 -> H(U1(d, k), U1(c, k)),A^2 -> H(U1(d, k), U1(c, k)))
28.54/9.41	   (A^2 -> H(U1(d, d), U1(e, k)),A^2 -> H(U1(d, d), U1(e, k)))
28.54/9.41	   (A^2 -> H(U1(d, d), U1(k, k)),A^2 -> H(U1(d, d), U1(k, k)))
28.54/9.41	
28.54/9.41	
28.54/9.41	----------------------------------------
28.54/9.41	
28.54/9.41	(1044)
28.54/9.41	Obligation:
28.54/9.41	Q DP problem:
28.54/9.41	The TRS P consists of the following rules:
28.54/9.41	
28.54/9.41	   H(x, x) -> G(x, x, f(k))
28.54/9.41	   G(d, x, x) -> A^2
28.54/9.41	   A^2 -> H(f(c), f(c))
28.54/9.41	   A^2 -> H(f(d), f(d))
28.54/9.41	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.41	   A^2 -> H(f(e), f(e))
28.54/9.41	   A^2 -> H(f(k), f(k))
28.54/9.41	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.41	   A^2 -> H(U1(d, d), U1(e, e))
28.54/9.41	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.41	   A^2 -> H(f(d), b)
28.54/9.41	   A^2 -> H(f(d), U1(e, d))
28.54/9.41	   A^2 -> H(f(d), U1(d, e))
28.54/9.41	   A^2 -> H(f(d), c)
28.54/9.41	   A^2 -> H(f(d), U1(e, k))
28.54/9.41	   A^2 -> H(f(d), U1(k, e))
28.54/9.41	   A^2 -> H(f(d), e)
28.54/9.41	   A^2 -> H(f(a), d)
28.54/9.41	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.41	   A^2 -> H(f(c), c)
28.54/9.41	   A^2 -> H(f(c), U1(e, k))
28.54/9.41	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.41	   A^2 -> H(f(c), U1(k, e))
28.54/9.41	   A^2 -> H(f(c), U1(k, k))
28.54/9.41	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.41	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.41	   A^2 -> H(f(a), k)
28.54/9.42	   A^2 -> H(f(e), U1(e, e))
28.54/9.42	   A^2 -> H(f(c), e)
28.54/9.42	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.42	   A^2 -> H(f(d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.42	   A^2 -> H(d, U1(b, b))
28.54/9.42	   A^2 -> H(d, f(c))
28.54/9.42	   A^2 -> H(d, f(d))
28.54/9.42	   A^2 -> H(a, U1(c, b))
28.54/9.42	   A^2 -> H(a, U1(d, b))
28.54/9.42	   A^2 -> H(a, U1(b, c))
28.54/9.42	   A^2 -> H(a, U1(b, d))
28.54/9.42	   A^2 -> H(a, U1(c, c))
28.54/9.42	   A^2 -> H(a, f(e))
28.54/9.42	   A^2 -> H(a, f(k))
28.54/9.42	   A^2 -> H(a, U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.42	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.42	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.42	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.42	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.42	   A^2 -> H(U1(e, d), f(e))
28.54/9.42	   A^2 -> H(U1(e, d), f(k))
28.54/9.42	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.42	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.42	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.42	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.42	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.42	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.42	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.42	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.42	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.42	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.42	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.42	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.42	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.42	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.42	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.42	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, a), b)
28.54/9.42	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.42	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.42	   A^2 -> H(U1(c, a), c)
28.54/9.42	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.42	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.42	   A^2 -> H(U1(c, a), e)
28.54/9.42	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.42	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.42	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.42	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.42	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.42	   A^2 -> H(U1(d, e), f(e))
28.54/9.42	   A^2 -> H(U1(d, e), f(k))
28.54/9.42	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.42	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.42	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.42	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.42	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.42	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.42	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.42	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.42	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.42	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.42	   A^2 -> H(U1(d, a), b)
28.54/9.42	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.42	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.42	   A^2 -> H(U1(d, a), c)
28.54/9.42	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.42	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.42	   A^2 -> H(U1(d, a), e)
28.54/9.42	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.42	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.42	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.42	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.42	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.42	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.42	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.42	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.42	   A^2 -> H(U1(a, c), b)
28.54/9.42	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.42	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.42	   A^2 -> H(U1(a, c), c)
28.54/9.42	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.42	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.42	   A^2 -> H(U1(a, c), e)
28.54/9.42	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, d), b)
28.54/9.42	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.42	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.42	   A^2 -> H(U1(a, d), c)
28.54/9.42	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.42	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.42	   A^2 -> H(U1(a, d), e)
28.54/9.42	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, a), d)
28.54/9.42	   A^2 -> H(U1(a, a), k)
28.54/9.42	   A^2 -> H(k, U1(b, b))
28.54/9.42	   A^2 -> H(k, f(c))
28.54/9.42	   A^2 -> H(k, f(d))
28.54/9.42	   A^2 -> H(c, U1(c, b))
28.54/9.42	   A^2 -> H(c, U1(d, b))
28.54/9.42	   A^2 -> H(c, U1(b, c))
28.54/9.42	   A^2 -> H(c, U1(b, d))
28.54/9.42	   A^2 -> H(c, U1(c, c))
28.54/9.42	   A^2 -> H(c, f(e))
28.54/9.42	   A^2 -> H(c, f(k))
28.54/9.42	   A^2 -> H(c, U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.42	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.42	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.42	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.42	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.42	   A^2 -> H(U1(e, k), f(e))
28.54/9.42	   A^2 -> H(U1(e, k), f(k))
28.54/9.42	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.42	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.42	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.42	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.42	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.42	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.42	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.42	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.42	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.42	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.42	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.42	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.42	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.42	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.42	   A^2 -> H(U1(k, e), f(e))
28.54/9.42	   A^2 -> H(U1(k, e), f(k))
28.54/9.42	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.42	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.42	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.42	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.42	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.42	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.42	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.42	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, c), b)
28.54/9.42	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.42	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.42	   A^2 -> H(U1(c, c), e)
28.54/9.42	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.42	   A^2 -> H(e, U1(c, b))
28.54/9.42	   A^2 -> H(e, U1(d, b))
28.54/9.42	   A^2 -> H(e, U1(b, c))
28.54/9.42	   A^2 -> H(e, U1(b, d))
28.54/9.42	   A^2 -> H(e, U1(c, c))
28.54/9.42	   A^2 -> H(e, f(e))
28.54/9.42	   A^2 -> H(e, f(k))
28.54/9.42	   A^2 -> H(e, U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.42	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.42	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.42	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.42	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.42	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.42	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.42	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.42	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.42	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.42	   A^2 -> H(f(e), b)
28.54/9.42	   A^2 -> H(f(e), U1(e, d))
28.54/9.42	   A^2 -> H(f(e), U1(d, e))
28.54/9.42	   A^2 -> H(f(e), c)
28.54/9.42	   A^2 -> H(f(e), U1(e, k))
28.54/9.42	   A^2 -> H(f(e), U1(k, e))
28.54/9.42	   A^2 -> H(f(e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.42	   A^2 -> H(f(k), b)
28.54/9.42	   A^2 -> H(f(k), U1(e, d))
28.54/9.42	   A^2 -> H(f(k), U1(d, e))
28.54/9.42	   A^2 -> H(f(k), c)
28.54/9.42	   A^2 -> H(f(k), U1(e, k))
28.54/9.42	   A^2 -> H(f(k), U1(k, e))
28.54/9.42	   A^2 -> H(f(k), e)
28.54/9.42	   A^2 -> H(f(c), d)
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.42	   A^2 -> H(U1(k, k), f(e))
28.54/9.42	   A^2 -> H(U1(k, k), f(k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.42	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.42	   A^2 -> H(U1(d, d), b)
28.54/9.42	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.42	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.42	   A^2 -> H(U1(d, d), c)
28.54/9.42	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.42	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.42	
28.54/9.42	The TRS R consists of the following rules:
28.54/9.42	
28.54/9.42	   f(x) -> U1(x, x)
28.54/9.42	   U1(e, x) -> x
28.54/9.42	   a -> c
28.54/9.42	   a -> d
28.54/9.42	   b -> c
28.54/9.42	   b -> d
28.54/9.42	   d -> k
28.54/9.42	   c -> e
28.54/9.42	   c -> k
28.54/9.42	
28.54/9.42	Q is empty.
28.54/9.42	We have to consider all minimal (P,Q,R)-chains.
28.54/9.42	----------------------------------------
28.54/9.42	
28.54/9.42	(1045) TransformationProof (EQUIVALENT)
28.54/9.42	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.42	
28.54/9.42	   (A^2 -> H(U1(k, d), U1(e, e)),A^2 -> H(U1(k, d), U1(e, e)))
28.54/9.42	   (A^2 -> H(U1(d, k), U1(e, e)),A^2 -> H(U1(d, k), U1(e, e)))
28.54/9.42	   (A^2 -> H(U1(d, d), e),A^2 -> H(U1(d, d), e))
28.54/9.42	
28.54/9.42	
28.54/9.42	----------------------------------------
28.54/9.42	
28.54/9.42	(1046)
28.54/9.42	Obligation:
28.54/9.42	Q DP problem:
28.54/9.42	The TRS P consists of the following rules:
28.54/9.42	
28.54/9.42	   H(x, x) -> G(x, x, f(k))
28.54/9.42	   G(d, x, x) -> A^2
28.54/9.42	   A^2 -> H(f(c), f(c))
28.54/9.42	   A^2 -> H(f(d), f(d))
28.54/9.42	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.42	   A^2 -> H(f(e), f(e))
28.54/9.42	   A^2 -> H(f(k), f(k))
28.54/9.42	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.42	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.42	   A^2 -> H(f(d), b)
28.54/9.42	   A^2 -> H(f(d), U1(e, d))
28.54/9.42	   A^2 -> H(f(d), U1(d, e))
28.54/9.42	   A^2 -> H(f(d), c)
28.54/9.42	   A^2 -> H(f(d), U1(e, k))
28.54/9.42	   A^2 -> H(f(d), U1(k, e))
28.54/9.42	   A^2 -> H(f(d), e)
28.54/9.42	   A^2 -> H(f(a), d)
28.54/9.42	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.42	   A^2 -> H(f(c), c)
28.54/9.42	   A^2 -> H(f(c), U1(e, k))
28.54/9.42	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.42	   A^2 -> H(f(c), U1(k, e))
28.54/9.42	   A^2 -> H(f(c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.42	   A^2 -> H(f(a), k)
28.54/9.42	   A^2 -> H(f(e), U1(e, e))
28.54/9.42	   A^2 -> H(f(c), e)
28.54/9.42	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.42	   A^2 -> H(f(d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.42	   A^2 -> H(d, U1(b, b))
28.54/9.42	   A^2 -> H(d, f(c))
28.54/9.42	   A^2 -> H(d, f(d))
28.54/9.42	   A^2 -> H(a, U1(c, b))
28.54/9.42	   A^2 -> H(a, U1(d, b))
28.54/9.42	   A^2 -> H(a, U1(b, c))
28.54/9.42	   A^2 -> H(a, U1(b, d))
28.54/9.42	   A^2 -> H(a, U1(c, c))
28.54/9.42	   A^2 -> H(a, f(e))
28.54/9.42	   A^2 -> H(a, f(k))
28.54/9.42	   A^2 -> H(a, U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.42	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.42	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.42	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.42	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.42	   A^2 -> H(U1(e, d), f(e))
28.54/9.42	   A^2 -> H(U1(e, d), f(k))
28.54/9.42	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.42	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.42	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.42	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.42	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.42	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.42	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.42	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.42	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.42	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.42	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.42	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.42	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.42	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.42	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.42	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, a), b)
28.54/9.42	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.42	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.42	   A^2 -> H(U1(c, a), c)
28.54/9.42	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.42	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.42	   A^2 -> H(U1(c, a), e)
28.54/9.42	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.42	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.42	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.42	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.42	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.42	   A^2 -> H(U1(d, e), f(e))
28.54/9.42	   A^2 -> H(U1(d, e), f(k))
28.54/9.42	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.42	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.42	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.42	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.42	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.42	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.42	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.42	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.42	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.42	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.42	   A^2 -> H(U1(d, a), b)
28.54/9.42	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.42	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.42	   A^2 -> H(U1(d, a), c)
28.54/9.42	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.42	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.42	   A^2 -> H(U1(d, a), e)
28.54/9.42	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.42	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.42	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.42	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.42	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.42	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.42	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.42	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.42	   A^2 -> H(U1(a, c), b)
28.54/9.42	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.42	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.42	   A^2 -> H(U1(a, c), c)
28.54/9.42	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.42	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.42	   A^2 -> H(U1(a, c), e)
28.54/9.42	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, d), b)
28.54/9.42	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.42	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.42	   A^2 -> H(U1(a, d), c)
28.54/9.42	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.42	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.42	   A^2 -> H(U1(a, d), e)
28.54/9.42	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, a), d)
28.54/9.42	   A^2 -> H(U1(a, a), k)
28.54/9.42	   A^2 -> H(k, U1(b, b))
28.54/9.42	   A^2 -> H(k, f(c))
28.54/9.42	   A^2 -> H(k, f(d))
28.54/9.42	   A^2 -> H(c, U1(c, b))
28.54/9.42	   A^2 -> H(c, U1(d, b))
28.54/9.42	   A^2 -> H(c, U1(b, c))
28.54/9.42	   A^2 -> H(c, U1(b, d))
28.54/9.42	   A^2 -> H(c, U1(c, c))
28.54/9.42	   A^2 -> H(c, f(e))
28.54/9.42	   A^2 -> H(c, f(k))
28.54/9.42	   A^2 -> H(c, U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.42	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.42	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.42	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.42	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.42	   A^2 -> H(U1(e, k), f(e))
28.54/9.42	   A^2 -> H(U1(e, k), f(k))
28.54/9.42	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.42	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.42	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.42	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.42	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.42	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.42	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.42	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.42	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.42	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.42	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.42	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.42	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.42	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.42	   A^2 -> H(U1(k, e), f(e))
28.54/9.42	   A^2 -> H(U1(k, e), f(k))
28.54/9.42	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.42	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.42	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.42	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.42	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.42	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.42	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.42	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, c), b)
28.54/9.42	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.42	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.42	   A^2 -> H(U1(c, c), e)
28.54/9.42	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.42	   A^2 -> H(e, U1(c, b))
28.54/9.42	   A^2 -> H(e, U1(d, b))
28.54/9.42	   A^2 -> H(e, U1(b, c))
28.54/9.42	   A^2 -> H(e, U1(b, d))
28.54/9.42	   A^2 -> H(e, U1(c, c))
28.54/9.42	   A^2 -> H(e, f(e))
28.54/9.42	   A^2 -> H(e, f(k))
28.54/9.42	   A^2 -> H(e, U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.42	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.42	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.42	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.42	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.42	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.42	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.42	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.42	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.42	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.42	   A^2 -> H(f(e), b)
28.54/9.42	   A^2 -> H(f(e), U1(e, d))
28.54/9.42	   A^2 -> H(f(e), U1(d, e))
28.54/9.42	   A^2 -> H(f(e), c)
28.54/9.42	   A^2 -> H(f(e), U1(e, k))
28.54/9.42	   A^2 -> H(f(e), U1(k, e))
28.54/9.42	   A^2 -> H(f(e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.42	   A^2 -> H(f(k), b)
28.54/9.42	   A^2 -> H(f(k), U1(e, d))
28.54/9.42	   A^2 -> H(f(k), U1(d, e))
28.54/9.42	   A^2 -> H(f(k), c)
28.54/9.42	   A^2 -> H(f(k), U1(e, k))
28.54/9.42	   A^2 -> H(f(k), U1(k, e))
28.54/9.42	   A^2 -> H(f(k), e)
28.54/9.42	   A^2 -> H(f(c), d)
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.42	   A^2 -> H(U1(k, k), f(e))
28.54/9.42	   A^2 -> H(U1(k, k), f(k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.42	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.42	   A^2 -> H(U1(d, d), b)
28.54/9.42	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.42	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.42	   A^2 -> H(U1(d, d), c)
28.54/9.42	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.42	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.42	   A^2 -> H(U1(d, d), e)
28.54/9.42	
28.54/9.42	The TRS R consists of the following rules:
28.54/9.42	
28.54/9.42	   f(x) -> U1(x, x)
28.54/9.42	   U1(e, x) -> x
28.54/9.42	   a -> c
28.54/9.42	   a -> d
28.54/9.42	   b -> c
28.54/9.42	   b -> d
28.54/9.42	   d -> k
28.54/9.42	   c -> e
28.54/9.42	   c -> k
28.54/9.42	
28.54/9.42	Q is empty.
28.54/9.42	We have to consider all minimal (P,Q,R)-chains.
28.54/9.42	----------------------------------------
28.54/9.42	
28.54/9.42	(1047) TransformationProof (EQUIVALENT)
28.54/9.42	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.42	
28.54/9.42	   (A^2 -> H(U1(k, d), U1(k, k)),A^2 -> H(U1(k, d), U1(k, k)))
28.54/9.42	   (A^2 -> H(U1(d, k), U1(k, k)),A^2 -> H(U1(d, k), U1(k, k)))
28.54/9.42	
28.54/9.42	
28.54/9.42	----------------------------------------
28.54/9.42	
28.54/9.42	(1048)
28.54/9.42	Obligation:
28.54/9.42	Q DP problem:
28.54/9.42	The TRS P consists of the following rules:
28.54/9.42	
28.54/9.42	   H(x, x) -> G(x, x, f(k))
28.54/9.42	   G(d, x, x) -> A^2
28.54/9.42	   A^2 -> H(f(c), f(c))
28.54/9.42	   A^2 -> H(f(d), f(d))
28.54/9.42	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.42	   A^2 -> H(f(e), f(e))
28.54/9.42	   A^2 -> H(f(k), f(k))
28.54/9.42	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.42	   A^2 -> H(f(d), b)
28.54/9.42	   A^2 -> H(f(d), U1(e, d))
28.54/9.42	   A^2 -> H(f(d), U1(d, e))
28.54/9.42	   A^2 -> H(f(d), c)
28.54/9.42	   A^2 -> H(f(d), U1(e, k))
28.54/9.42	   A^2 -> H(f(d), U1(k, e))
28.54/9.42	   A^2 -> H(f(d), e)
28.54/9.42	   A^2 -> H(f(a), d)
28.54/9.42	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.42	   A^2 -> H(f(c), c)
28.54/9.42	   A^2 -> H(f(c), U1(e, k))
28.54/9.42	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.42	   A^2 -> H(f(c), U1(k, e))
28.54/9.42	   A^2 -> H(f(c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.42	   A^2 -> H(f(a), k)
28.54/9.42	   A^2 -> H(f(e), U1(e, e))
28.54/9.42	   A^2 -> H(f(c), e)
28.54/9.42	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.42	   A^2 -> H(f(d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.42	   A^2 -> H(d, U1(b, b))
28.54/9.42	   A^2 -> H(d, f(c))
28.54/9.42	   A^2 -> H(d, f(d))
28.54/9.42	   A^2 -> H(a, U1(c, b))
28.54/9.42	   A^2 -> H(a, U1(d, b))
28.54/9.42	   A^2 -> H(a, U1(b, c))
28.54/9.42	   A^2 -> H(a, U1(b, d))
28.54/9.42	   A^2 -> H(a, U1(c, c))
28.54/9.42	   A^2 -> H(a, f(e))
28.54/9.42	   A^2 -> H(a, f(k))
28.54/9.42	   A^2 -> H(a, U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.42	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.42	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.42	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.42	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.42	   A^2 -> H(U1(e, d), f(e))
28.54/9.42	   A^2 -> H(U1(e, d), f(k))
28.54/9.42	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.42	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.42	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.42	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.42	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.42	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.42	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.42	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.42	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.42	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.42	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.42	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.42	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.42	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.42	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.42	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, a), b)
28.54/9.42	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.42	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.42	   A^2 -> H(U1(c, a), c)
28.54/9.42	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.42	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.42	   A^2 -> H(U1(c, a), e)
28.54/9.42	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.42	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.42	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.42	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.42	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.42	   A^2 -> H(U1(d, e), f(e))
28.54/9.42	   A^2 -> H(U1(d, e), f(k))
28.54/9.42	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.42	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.42	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.42	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.42	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.42	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.42	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.42	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.42	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.42	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.42	   A^2 -> H(U1(d, a), b)
28.54/9.42	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.42	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.42	   A^2 -> H(U1(d, a), c)
28.54/9.42	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.42	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.42	   A^2 -> H(U1(d, a), e)
28.54/9.42	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.42	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.42	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.42	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.42	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.42	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.42	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.42	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.42	   A^2 -> H(U1(a, c), b)
28.54/9.42	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.42	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.42	   A^2 -> H(U1(a, c), c)
28.54/9.42	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.42	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.42	   A^2 -> H(U1(a, c), e)
28.54/9.42	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, d), b)
28.54/9.42	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.42	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.42	   A^2 -> H(U1(a, d), c)
28.54/9.42	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.42	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.42	   A^2 -> H(U1(a, d), e)
28.54/9.42	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, a), d)
28.54/9.42	   A^2 -> H(U1(a, a), k)
28.54/9.42	   A^2 -> H(k, U1(b, b))
28.54/9.42	   A^2 -> H(k, f(c))
28.54/9.42	   A^2 -> H(k, f(d))
28.54/9.42	   A^2 -> H(c, U1(c, b))
28.54/9.42	   A^2 -> H(c, U1(d, b))
28.54/9.42	   A^2 -> H(c, U1(b, c))
28.54/9.42	   A^2 -> H(c, U1(b, d))
28.54/9.42	   A^2 -> H(c, U1(c, c))
28.54/9.42	   A^2 -> H(c, f(e))
28.54/9.42	   A^2 -> H(c, f(k))
28.54/9.42	   A^2 -> H(c, U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.42	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.42	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.42	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.42	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.42	   A^2 -> H(U1(e, k), f(e))
28.54/9.42	   A^2 -> H(U1(e, k), f(k))
28.54/9.42	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.42	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.42	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.42	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.42	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.42	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.42	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.42	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.42	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.42	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.42	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.42	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.42	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.42	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.42	   A^2 -> H(U1(k, e), f(e))
28.54/9.42	   A^2 -> H(U1(k, e), f(k))
28.54/9.42	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.42	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.42	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.42	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.42	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.42	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.42	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.42	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, c), b)
28.54/9.42	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.42	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.42	   A^2 -> H(U1(c, c), e)
28.54/9.42	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.42	   A^2 -> H(e, U1(c, b))
28.54/9.42	   A^2 -> H(e, U1(d, b))
28.54/9.42	   A^2 -> H(e, U1(b, c))
28.54/9.42	   A^2 -> H(e, U1(b, d))
28.54/9.42	   A^2 -> H(e, U1(c, c))
28.54/9.42	   A^2 -> H(e, f(e))
28.54/9.42	   A^2 -> H(e, f(k))
28.54/9.42	   A^2 -> H(e, U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.42	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.42	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.42	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.42	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.42	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.42	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.42	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.42	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.42	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.42	   A^2 -> H(f(e), b)
28.54/9.42	   A^2 -> H(f(e), U1(e, d))
28.54/9.42	   A^2 -> H(f(e), U1(d, e))
28.54/9.42	   A^2 -> H(f(e), c)
28.54/9.42	   A^2 -> H(f(e), U1(e, k))
28.54/9.42	   A^2 -> H(f(e), U1(k, e))
28.54/9.42	   A^2 -> H(f(e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.42	   A^2 -> H(f(k), b)
28.54/9.42	   A^2 -> H(f(k), U1(e, d))
28.54/9.42	   A^2 -> H(f(k), U1(d, e))
28.54/9.42	   A^2 -> H(f(k), c)
28.54/9.42	   A^2 -> H(f(k), U1(e, k))
28.54/9.42	   A^2 -> H(f(k), U1(k, e))
28.54/9.42	   A^2 -> H(f(k), e)
28.54/9.42	   A^2 -> H(f(c), d)
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.42	   A^2 -> H(U1(k, k), f(e))
28.54/9.42	   A^2 -> H(U1(k, k), f(k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.42	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.42	   A^2 -> H(U1(d, d), b)
28.54/9.42	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.42	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.42	   A^2 -> H(U1(d, d), c)
28.54/9.42	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.42	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.42	   A^2 -> H(U1(d, d), e)
28.54/9.42	
28.54/9.42	The TRS R consists of the following rules:
28.54/9.42	
28.54/9.42	   f(x) -> U1(x, x)
28.54/9.42	   U1(e, x) -> x
28.54/9.42	   a -> c
28.54/9.42	   a -> d
28.54/9.42	   b -> c
28.54/9.42	   b -> d
28.54/9.42	   d -> k
28.54/9.42	   c -> e
28.54/9.42	   c -> k
28.54/9.42	
28.54/9.42	Q is empty.
28.54/9.42	We have to consider all minimal (P,Q,R)-chains.
28.54/9.42	----------------------------------------
28.54/9.42	
28.54/9.42	(1049) TransformationProof (EQUIVALENT)
28.54/9.42	By narrowing [LPAR04] the rule A^2 -> H(f(d), b) at position [] we obtained the following new rules [LPAR04]:
28.54/9.42	
28.54/9.42	   (A^2 -> H(U1(d, d), b),A^2 -> H(U1(d, d), b))
28.54/9.42	   (A^2 -> H(f(k), b),A^2 -> H(f(k), b))
28.54/9.42	   (A^2 -> H(f(d), c),A^2 -> H(f(d), c))
28.54/9.42	   (A^2 -> H(f(d), d),A^2 -> H(f(d), d))
28.54/9.42	
28.54/9.42	
28.54/9.42	----------------------------------------
28.54/9.42	
28.54/9.42	(1050)
28.54/9.42	Obligation:
28.54/9.42	Q DP problem:
28.54/9.42	The TRS P consists of the following rules:
28.54/9.42	
28.54/9.42	   H(x, x) -> G(x, x, f(k))
28.54/9.42	   G(d, x, x) -> A^2
28.54/9.42	   A^2 -> H(f(c), f(c))
28.54/9.42	   A^2 -> H(f(d), f(d))
28.54/9.42	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.42	   A^2 -> H(f(e), f(e))
28.54/9.42	   A^2 -> H(f(k), f(k))
28.54/9.42	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.42	   A^2 -> H(f(d), U1(e, d))
28.54/9.42	   A^2 -> H(f(d), U1(d, e))
28.54/9.42	   A^2 -> H(f(d), c)
28.54/9.42	   A^2 -> H(f(d), U1(e, k))
28.54/9.42	   A^2 -> H(f(d), U1(k, e))
28.54/9.42	   A^2 -> H(f(d), e)
28.54/9.42	   A^2 -> H(f(a), d)
28.54/9.42	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.42	   A^2 -> H(f(c), c)
28.54/9.42	   A^2 -> H(f(c), U1(e, k))
28.54/9.42	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.42	   A^2 -> H(f(c), U1(k, e))
28.54/9.42	   A^2 -> H(f(c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.42	   A^2 -> H(f(a), k)
28.54/9.42	   A^2 -> H(f(e), U1(e, e))
28.54/9.42	   A^2 -> H(f(c), e)
28.54/9.42	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.42	   A^2 -> H(f(d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.42	   A^2 -> H(d, U1(b, b))
28.54/9.42	   A^2 -> H(d, f(c))
28.54/9.42	   A^2 -> H(d, f(d))
28.54/9.42	   A^2 -> H(a, U1(c, b))
28.54/9.42	   A^2 -> H(a, U1(d, b))
28.54/9.42	   A^2 -> H(a, U1(b, c))
28.54/9.42	   A^2 -> H(a, U1(b, d))
28.54/9.42	   A^2 -> H(a, U1(c, c))
28.54/9.42	   A^2 -> H(a, f(e))
28.54/9.42	   A^2 -> H(a, f(k))
28.54/9.42	   A^2 -> H(a, U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.42	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.42	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.42	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.42	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.42	   A^2 -> H(U1(e, d), f(e))
28.54/9.42	   A^2 -> H(U1(e, d), f(k))
28.54/9.42	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.42	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.42	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.42	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.42	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.42	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.42	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.42	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.42	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.42	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.42	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.42	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.42	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.42	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.42	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.42	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, a), b)
28.54/9.42	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.42	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.42	   A^2 -> H(U1(c, a), c)
28.54/9.42	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.42	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.42	   A^2 -> H(U1(c, a), e)
28.54/9.42	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.42	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.42	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.42	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.42	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.42	   A^2 -> H(U1(d, e), f(e))
28.54/9.42	   A^2 -> H(U1(d, e), f(k))
28.54/9.42	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.42	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.42	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.42	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.42	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.42	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.42	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.42	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.42	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.42	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.42	   A^2 -> H(U1(d, a), b)
28.54/9.42	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.42	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.42	   A^2 -> H(U1(d, a), c)
28.54/9.42	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.42	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.42	   A^2 -> H(U1(d, a), e)
28.54/9.42	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.42	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.42	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.42	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.42	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.42	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.42	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.42	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.42	   A^2 -> H(U1(a, c), b)
28.54/9.42	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.42	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.42	   A^2 -> H(U1(a, c), c)
28.54/9.42	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.42	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.42	   A^2 -> H(U1(a, c), e)
28.54/9.42	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, d), b)
28.54/9.42	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.42	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.42	   A^2 -> H(U1(a, d), c)
28.54/9.42	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.42	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.42	   A^2 -> H(U1(a, d), e)
28.54/9.42	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, a), d)
28.54/9.42	   A^2 -> H(U1(a, a), k)
28.54/9.42	   A^2 -> H(k, U1(b, b))
28.54/9.42	   A^2 -> H(k, f(c))
28.54/9.42	   A^2 -> H(k, f(d))
28.54/9.42	   A^2 -> H(c, U1(c, b))
28.54/9.42	   A^2 -> H(c, U1(d, b))
28.54/9.42	   A^2 -> H(c, U1(b, c))
28.54/9.42	   A^2 -> H(c, U1(b, d))
28.54/9.42	   A^2 -> H(c, U1(c, c))
28.54/9.42	   A^2 -> H(c, f(e))
28.54/9.42	   A^2 -> H(c, f(k))
28.54/9.42	   A^2 -> H(c, U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.42	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.42	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.42	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.42	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.42	   A^2 -> H(U1(e, k), f(e))
28.54/9.42	   A^2 -> H(U1(e, k), f(k))
28.54/9.42	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.42	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.42	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.42	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.42	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.42	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.42	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.42	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.42	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.42	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.42	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.42	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.42	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.42	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.42	   A^2 -> H(U1(k, e), f(e))
28.54/9.42	   A^2 -> H(U1(k, e), f(k))
28.54/9.42	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.42	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.42	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.42	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.42	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.42	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.42	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.42	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, c), b)
28.54/9.42	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.42	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.42	   A^2 -> H(U1(c, c), e)
28.54/9.42	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.42	   A^2 -> H(e, U1(c, b))
28.54/9.42	   A^2 -> H(e, U1(d, b))
28.54/9.42	   A^2 -> H(e, U1(b, c))
28.54/9.42	   A^2 -> H(e, U1(b, d))
28.54/9.42	   A^2 -> H(e, U1(c, c))
28.54/9.42	   A^2 -> H(e, f(e))
28.54/9.42	   A^2 -> H(e, f(k))
28.54/9.42	   A^2 -> H(e, U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.42	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.42	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.42	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.42	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.42	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.42	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.42	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.42	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.42	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.42	   A^2 -> H(f(e), b)
28.54/9.42	   A^2 -> H(f(e), U1(e, d))
28.54/9.42	   A^2 -> H(f(e), U1(d, e))
28.54/9.42	   A^2 -> H(f(e), c)
28.54/9.42	   A^2 -> H(f(e), U1(e, k))
28.54/9.42	   A^2 -> H(f(e), U1(k, e))
28.54/9.42	   A^2 -> H(f(e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.42	   A^2 -> H(f(k), b)
28.54/9.42	   A^2 -> H(f(k), U1(e, d))
28.54/9.42	   A^2 -> H(f(k), U1(d, e))
28.54/9.42	   A^2 -> H(f(k), c)
28.54/9.42	   A^2 -> H(f(k), U1(e, k))
28.54/9.42	   A^2 -> H(f(k), U1(k, e))
28.54/9.42	   A^2 -> H(f(k), e)
28.54/9.42	   A^2 -> H(f(c), d)
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.42	   A^2 -> H(U1(k, k), f(e))
28.54/9.42	   A^2 -> H(U1(k, k), f(k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.42	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.42	   A^2 -> H(U1(d, d), b)
28.54/9.42	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.42	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.42	   A^2 -> H(U1(d, d), c)
28.54/9.42	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.42	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.42	   A^2 -> H(U1(d, d), e)
28.54/9.42	   A^2 -> H(f(d), d)
28.54/9.42	
28.54/9.42	The TRS R consists of the following rules:
28.54/9.42	
28.54/9.42	   f(x) -> U1(x, x)
28.54/9.42	   U1(e, x) -> x
28.54/9.42	   a -> c
28.54/9.42	   a -> d
28.54/9.42	   b -> c
28.54/9.42	   b -> d
28.54/9.42	   d -> k
28.54/9.42	   c -> e
28.54/9.42	   c -> k
28.54/9.42	
28.54/9.42	Q is empty.
28.54/9.42	We have to consider all minimal (P,Q,R)-chains.
28.54/9.42	----------------------------------------
28.54/9.42	
28.54/9.42	(1051) TransformationProof (EQUIVALENT)
28.54/9.42	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.42	
28.54/9.42	   (A^2 -> H(U1(d, d), U1(e, d)),A^2 -> H(U1(d, d), U1(e, d)))
28.54/9.42	   (A^2 -> H(f(k), U1(e, d)),A^2 -> H(f(k), U1(e, d)))
28.54/9.42	   (A^2 -> H(f(d), d),A^2 -> H(f(d), d))
28.54/9.42	   (A^2 -> H(f(d), U1(e, k)),A^2 -> H(f(d), U1(e, k)))
28.54/9.42	
28.54/9.42	
28.54/9.42	----------------------------------------
28.54/9.42	
28.54/9.42	(1052)
28.54/9.42	Obligation:
28.54/9.42	Q DP problem:
28.54/9.42	The TRS P consists of the following rules:
28.54/9.42	
28.54/9.42	   H(x, x) -> G(x, x, f(k))
28.54/9.42	   G(d, x, x) -> A^2
28.54/9.42	   A^2 -> H(f(c), f(c))
28.54/9.42	   A^2 -> H(f(d), f(d))
28.54/9.42	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.42	   A^2 -> H(f(e), f(e))
28.54/9.42	   A^2 -> H(f(k), f(k))
28.54/9.42	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.42	   A^2 -> H(f(d), U1(d, e))
28.54/9.42	   A^2 -> H(f(d), c)
28.54/9.42	   A^2 -> H(f(d), U1(e, k))
28.54/9.42	   A^2 -> H(f(d), U1(k, e))
28.54/9.42	   A^2 -> H(f(d), e)
28.54/9.42	   A^2 -> H(f(a), d)
28.54/9.42	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.42	   A^2 -> H(f(c), c)
28.54/9.42	   A^2 -> H(f(c), U1(e, k))
28.54/9.42	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.42	   A^2 -> H(f(c), U1(k, e))
28.54/9.42	   A^2 -> H(f(c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.42	   A^2 -> H(f(a), k)
28.54/9.42	   A^2 -> H(f(e), U1(e, e))
28.54/9.42	   A^2 -> H(f(c), e)
28.54/9.42	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.42	   A^2 -> H(f(d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.42	   A^2 -> H(d, U1(b, b))
28.54/9.42	   A^2 -> H(d, f(c))
28.54/9.42	   A^2 -> H(d, f(d))
28.54/9.42	   A^2 -> H(a, U1(c, b))
28.54/9.42	   A^2 -> H(a, U1(d, b))
28.54/9.42	   A^2 -> H(a, U1(b, c))
28.54/9.42	   A^2 -> H(a, U1(b, d))
28.54/9.42	   A^2 -> H(a, U1(c, c))
28.54/9.42	   A^2 -> H(a, f(e))
28.54/9.42	   A^2 -> H(a, f(k))
28.54/9.42	   A^2 -> H(a, U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.42	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.42	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.42	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.42	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.42	   A^2 -> H(U1(e, d), f(e))
28.54/9.42	   A^2 -> H(U1(e, d), f(k))
28.54/9.42	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.42	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.42	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.42	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.42	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.42	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.42	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.42	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.42	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.42	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.42	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.42	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.42	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.42	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.42	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.42	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, a), b)
28.54/9.42	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.42	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.42	   A^2 -> H(U1(c, a), c)
28.54/9.42	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.42	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.42	   A^2 -> H(U1(c, a), e)
28.54/9.42	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.42	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.42	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.42	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.42	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.42	   A^2 -> H(U1(d, e), f(e))
28.54/9.42	   A^2 -> H(U1(d, e), f(k))
28.54/9.42	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.42	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.42	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.42	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.42	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.42	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.42	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.42	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.42	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.42	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.42	   A^2 -> H(U1(d, a), b)
28.54/9.42	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.42	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.42	   A^2 -> H(U1(d, a), c)
28.54/9.42	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.42	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.42	   A^2 -> H(U1(d, a), e)
28.54/9.42	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.42	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.42	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.42	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.42	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.42	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.42	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.42	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.42	   A^2 -> H(U1(a, c), b)
28.54/9.42	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.42	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.42	   A^2 -> H(U1(a, c), c)
28.54/9.42	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.42	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.42	   A^2 -> H(U1(a, c), e)
28.54/9.42	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, d), b)
28.54/9.42	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.42	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.42	   A^2 -> H(U1(a, d), c)
28.54/9.42	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.42	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.42	   A^2 -> H(U1(a, d), e)
28.54/9.42	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, a), d)
28.54/9.42	   A^2 -> H(U1(a, a), k)
28.54/9.42	   A^2 -> H(k, U1(b, b))
28.54/9.42	   A^2 -> H(k, f(c))
28.54/9.42	   A^2 -> H(k, f(d))
28.54/9.42	   A^2 -> H(c, U1(c, b))
28.54/9.42	   A^2 -> H(c, U1(d, b))
28.54/9.42	   A^2 -> H(c, U1(b, c))
28.54/9.42	   A^2 -> H(c, U1(b, d))
28.54/9.42	   A^2 -> H(c, U1(c, c))
28.54/9.42	   A^2 -> H(c, f(e))
28.54/9.42	   A^2 -> H(c, f(k))
28.54/9.42	   A^2 -> H(c, U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.42	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.42	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.42	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.42	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.42	   A^2 -> H(U1(e, k), f(e))
28.54/9.42	   A^2 -> H(U1(e, k), f(k))
28.54/9.42	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.42	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.42	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.42	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.42	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.42	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.42	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.42	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.42	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.42	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.42	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.42	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.42	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.42	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.42	   A^2 -> H(U1(k, e), f(e))
28.54/9.42	   A^2 -> H(U1(k, e), f(k))
28.54/9.42	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.42	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.42	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.42	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.42	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.42	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.42	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.42	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, c), b)
28.54/9.42	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.42	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.42	   A^2 -> H(U1(c, c), e)
28.54/9.42	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.42	   A^2 -> H(e, U1(c, b))
28.54/9.42	   A^2 -> H(e, U1(d, b))
28.54/9.42	   A^2 -> H(e, U1(b, c))
28.54/9.42	   A^2 -> H(e, U1(b, d))
28.54/9.42	   A^2 -> H(e, U1(c, c))
28.54/9.42	   A^2 -> H(e, f(e))
28.54/9.42	   A^2 -> H(e, f(k))
28.54/9.42	   A^2 -> H(e, U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.42	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.42	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.42	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.42	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.42	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.42	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.42	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.42	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.42	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.42	   A^2 -> H(f(e), b)
28.54/9.42	   A^2 -> H(f(e), U1(e, d))
28.54/9.42	   A^2 -> H(f(e), U1(d, e))
28.54/9.42	   A^2 -> H(f(e), c)
28.54/9.42	   A^2 -> H(f(e), U1(e, k))
28.54/9.42	   A^2 -> H(f(e), U1(k, e))
28.54/9.42	   A^2 -> H(f(e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.42	   A^2 -> H(f(k), b)
28.54/9.42	   A^2 -> H(f(k), U1(e, d))
28.54/9.42	   A^2 -> H(f(k), U1(d, e))
28.54/9.42	   A^2 -> H(f(k), c)
28.54/9.42	   A^2 -> H(f(k), U1(e, k))
28.54/9.42	   A^2 -> H(f(k), U1(k, e))
28.54/9.42	   A^2 -> H(f(k), e)
28.54/9.42	   A^2 -> H(f(c), d)
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.42	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.42	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.42	   A^2 -> H(U1(k, k), f(e))
28.54/9.42	   A^2 -> H(U1(k, k), f(k))
28.54/9.42	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.42	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.42	   A^2 -> H(U1(d, d), b)
28.54/9.42	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.42	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.42	   A^2 -> H(U1(d, d), c)
28.54/9.42	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.42	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.42	   A^2 -> H(U1(d, d), e)
28.54/9.42	   A^2 -> H(f(d), d)
28.54/9.42	
28.54/9.42	The TRS R consists of the following rules:
28.54/9.42	
28.54/9.42	   f(x) -> U1(x, x)
28.54/9.42	   U1(e, x) -> x
28.54/9.42	   a -> c
28.54/9.42	   a -> d
28.54/9.42	   b -> c
28.54/9.42	   b -> d
28.54/9.42	   d -> k
28.54/9.42	   c -> e
28.54/9.42	   c -> k
28.54/9.42	
28.54/9.42	Q is empty.
28.54/9.42	We have to consider all minimal (P,Q,R)-chains.
28.54/9.42	----------------------------------------
28.54/9.42	
28.54/9.42	(1053) TransformationProof (EQUIVALENT)
28.54/9.42	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.42	
28.54/9.42	   (A^2 -> H(U1(d, d), U1(d, e)),A^2 -> H(U1(d, d), U1(d, e)))
28.54/9.42	   (A^2 -> H(f(k), U1(d, e)),A^2 -> H(f(k), U1(d, e)))
28.54/9.42	   (A^2 -> H(f(d), U1(k, e)),A^2 -> H(f(d), U1(k, e)))
28.54/9.42	
28.54/9.42	
28.54/9.42	----------------------------------------
28.54/9.42	
28.54/9.42	(1054)
28.54/9.42	Obligation:
28.54/9.42	Q DP problem:
28.54/9.42	The TRS P consists of the following rules:
28.54/9.42	
28.54/9.42	   H(x, x) -> G(x, x, f(k))
28.54/9.42	   G(d, x, x) -> A^2
28.54/9.42	   A^2 -> H(f(c), f(c))
28.54/9.42	   A^2 -> H(f(d), f(d))
28.54/9.42	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.42	   A^2 -> H(f(e), f(e))
28.54/9.42	   A^2 -> H(f(k), f(k))
28.54/9.42	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.42	   A^2 -> H(f(d), c)
28.54/9.42	   A^2 -> H(f(d), U1(e, k))
28.54/9.42	   A^2 -> H(f(d), U1(k, e))
28.54/9.42	   A^2 -> H(f(d), e)
28.54/9.42	   A^2 -> H(f(a), d)
28.54/9.42	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.42	   A^2 -> H(f(c), c)
28.54/9.42	   A^2 -> H(f(c), U1(e, k))
28.54/9.42	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.42	   A^2 -> H(f(c), U1(k, e))
28.54/9.42	   A^2 -> H(f(c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.42	   A^2 -> H(f(a), k)
28.54/9.42	   A^2 -> H(f(e), U1(e, e))
28.54/9.42	   A^2 -> H(f(c), e)
28.54/9.42	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.42	   A^2 -> H(f(d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.42	   A^2 -> H(d, U1(b, b))
28.54/9.42	   A^2 -> H(d, f(c))
28.54/9.42	   A^2 -> H(d, f(d))
28.54/9.42	   A^2 -> H(a, U1(c, b))
28.54/9.42	   A^2 -> H(a, U1(d, b))
28.54/9.42	   A^2 -> H(a, U1(b, c))
28.54/9.42	   A^2 -> H(a, U1(b, d))
28.54/9.42	   A^2 -> H(a, U1(c, c))
28.54/9.42	   A^2 -> H(a, f(e))
28.54/9.42	   A^2 -> H(a, f(k))
28.54/9.42	   A^2 -> H(a, U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.42	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.42	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.42	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.42	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.42	   A^2 -> H(U1(e, d), f(e))
28.54/9.42	   A^2 -> H(U1(e, d), f(k))
28.54/9.42	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.42	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.42	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.42	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.42	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.42	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.42	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.42	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.42	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.42	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.42	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.42	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.42	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.42	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.42	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.42	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.42	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.42	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.42	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.42	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.42	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.42	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.42	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.42	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.42	   A^2 -> H(U1(c, a), b)
28.54/9.42	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.42	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.42	   A^2 -> H(U1(c, a), c)
28.54/9.42	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.42	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.42	   A^2 -> H(U1(c, a), e)
28.54/9.42	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.42	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.42	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.42	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.42	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.42	   A^2 -> H(U1(d, e), f(e))
28.54/9.42	   A^2 -> H(U1(d, e), f(k))
28.54/9.42	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.42	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.42	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.42	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.42	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.42	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.42	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.42	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.42	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.42	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.42	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.42	   A^2 -> H(U1(d, a), b)
28.54/9.42	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.42	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.42	   A^2 -> H(U1(d, a), c)
28.54/9.42	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.42	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.42	   A^2 -> H(U1(d, a), e)
28.54/9.42	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.42	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.42	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.42	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.42	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.42	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.42	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.42	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.42	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.42	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.42	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.42	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.42	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.42	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.42	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.42	   A^2 -> H(U1(a, c), b)
28.54/9.42	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.42	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.42	   A^2 -> H(U1(a, c), c)
28.54/9.42	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.42	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.42	   A^2 -> H(U1(a, c), e)
28.54/9.42	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, d), b)
28.54/9.42	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.42	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.42	   A^2 -> H(U1(a, d), c)
28.54/9.42	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.42	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.42	   A^2 -> H(U1(a, d), e)
28.54/9.42	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.42	   A^2 -> H(U1(a, a), d)
28.54/9.42	   A^2 -> H(U1(a, a), k)
28.54/9.42	   A^2 -> H(k, U1(b, b))
28.54/9.42	   A^2 -> H(k, f(c))
28.54/9.42	   A^2 -> H(k, f(d))
28.54/9.42	   A^2 -> H(c, U1(c, b))
28.54/9.42	   A^2 -> H(c, U1(d, b))
28.54/9.42	   A^2 -> H(c, U1(b, c))
28.54/9.42	   A^2 -> H(c, U1(b, d))
28.54/9.42	   A^2 -> H(c, U1(c, c))
28.54/9.42	   A^2 -> H(c, f(e))
28.54/9.42	   A^2 -> H(c, f(k))
28.54/9.42	   A^2 -> H(c, U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.42	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.42	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.42	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.42	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.42	   A^2 -> H(U1(e, k), f(e))
28.54/9.42	   A^2 -> H(U1(e, k), f(k))
28.54/9.42	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.42	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.42	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.42	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.42	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.42	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.42	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.42	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.43	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.43	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.43	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.43	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.43	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.43	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.43	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.43	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.43	   A^2 -> H(U1(k, e), f(e))
28.54/9.43	   A^2 -> H(U1(k, e), f(k))
28.54/9.43	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.43	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.43	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.43	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.43	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.43	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.43	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.43	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, c), b)
28.54/9.43	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.43	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.43	   A^2 -> H(U1(c, c), e)
28.54/9.43	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.43	   A^2 -> H(e, U1(c, b))
28.54/9.43	   A^2 -> H(e, U1(d, b))
28.54/9.43	   A^2 -> H(e, U1(b, c))
28.54/9.43	   A^2 -> H(e, U1(b, d))
28.54/9.43	   A^2 -> H(e, U1(c, c))
28.54/9.43	   A^2 -> H(e, f(e))
28.54/9.43	   A^2 -> H(e, f(k))
28.54/9.43	   A^2 -> H(e, U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.43	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.43	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.43	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.43	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.43	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.43	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.43	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.43	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.43	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.43	   A^2 -> H(f(e), b)
28.54/9.43	   A^2 -> H(f(e), U1(e, d))
28.54/9.43	   A^2 -> H(f(e), U1(d, e))
28.54/9.43	   A^2 -> H(f(e), c)
28.54/9.43	   A^2 -> H(f(e), U1(e, k))
28.54/9.43	   A^2 -> H(f(e), U1(k, e))
28.54/9.43	   A^2 -> H(f(e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.43	   A^2 -> H(f(k), b)
28.54/9.43	   A^2 -> H(f(k), U1(e, d))
28.54/9.43	   A^2 -> H(f(k), U1(d, e))
28.54/9.43	   A^2 -> H(f(k), c)
28.54/9.43	   A^2 -> H(f(k), U1(e, k))
28.54/9.43	   A^2 -> H(f(k), U1(k, e))
28.54/9.43	   A^2 -> H(f(k), e)
28.54/9.43	   A^2 -> H(f(c), d)
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.43	   A^2 -> H(U1(k, k), f(e))
28.54/9.43	   A^2 -> H(U1(k, k), f(k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.43	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.43	   A^2 -> H(U1(d, d), b)
28.54/9.43	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.43	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.43	   A^2 -> H(U1(d, d), c)
28.54/9.43	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.43	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.43	   A^2 -> H(U1(d, d), e)
28.54/9.43	   A^2 -> H(f(d), d)
28.54/9.43	
28.54/9.43	The TRS R consists of the following rules:
28.54/9.43	
28.54/9.43	   f(x) -> U1(x, x)
28.54/9.43	   U1(e, x) -> x
28.54/9.43	   a -> c
28.54/9.43	   a -> d
28.54/9.43	   b -> c
28.54/9.43	   b -> d
28.54/9.43	   d -> k
28.54/9.43	   c -> e
28.54/9.43	   c -> k
28.54/9.43	
28.54/9.43	Q is empty.
28.54/9.43	We have to consider all minimal (P,Q,R)-chains.
28.54/9.43	----------------------------------------
28.54/9.43	
28.54/9.43	(1055) TransformationProof (EQUIVALENT)
28.54/9.43	By narrowing [LPAR04] the rule A^2 -> H(f(d), c) at position [] we obtained the following new rules [LPAR04]:
28.54/9.43	
28.54/9.43	   (A^2 -> H(U1(d, d), c),A^2 -> H(U1(d, d), c))
28.54/9.43	   (A^2 -> H(f(k), c),A^2 -> H(f(k), c))
28.54/9.43	   (A^2 -> H(f(d), e),A^2 -> H(f(d), e))
28.54/9.43	   (A^2 -> H(f(d), k),A^2 -> H(f(d), k))
28.54/9.43	
28.54/9.43	
28.54/9.43	----------------------------------------
28.54/9.43	
28.54/9.43	(1056)
28.54/9.43	Obligation:
28.54/9.43	Q DP problem:
28.54/9.43	The TRS P consists of the following rules:
28.54/9.43	
28.54/9.43	   H(x, x) -> G(x, x, f(k))
28.54/9.43	   G(d, x, x) -> A^2
28.54/9.43	   A^2 -> H(f(c), f(c))
28.54/9.43	   A^2 -> H(f(d), f(d))
28.54/9.43	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.43	   A^2 -> H(f(e), f(e))
28.54/9.43	   A^2 -> H(f(k), f(k))
28.54/9.43	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.43	   A^2 -> H(f(d), U1(e, k))
28.54/9.43	   A^2 -> H(f(d), U1(k, e))
28.54/9.43	   A^2 -> H(f(d), e)
28.54/9.43	   A^2 -> H(f(a), d)
28.54/9.43	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.43	   A^2 -> H(f(c), c)
28.54/9.43	   A^2 -> H(f(c), U1(e, k))
28.54/9.43	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.43	   A^2 -> H(f(c), U1(k, e))
28.54/9.43	   A^2 -> H(f(c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.43	   A^2 -> H(f(a), k)
28.54/9.43	   A^2 -> H(f(e), U1(e, e))
28.54/9.43	   A^2 -> H(f(c), e)
28.54/9.43	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.43	   A^2 -> H(f(d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.43	   A^2 -> H(d, U1(b, b))
28.54/9.43	   A^2 -> H(d, f(c))
28.54/9.43	   A^2 -> H(d, f(d))
28.54/9.43	   A^2 -> H(a, U1(c, b))
28.54/9.43	   A^2 -> H(a, U1(d, b))
28.54/9.43	   A^2 -> H(a, U1(b, c))
28.54/9.43	   A^2 -> H(a, U1(b, d))
28.54/9.43	   A^2 -> H(a, U1(c, c))
28.54/9.43	   A^2 -> H(a, f(e))
28.54/9.43	   A^2 -> H(a, f(k))
28.54/9.43	   A^2 -> H(a, U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.43	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.43	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.43	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.43	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.43	   A^2 -> H(U1(e, d), f(e))
28.54/9.43	   A^2 -> H(U1(e, d), f(k))
28.54/9.43	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.43	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.43	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.43	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.43	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.43	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.43	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.43	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.43	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.43	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.43	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.43	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.43	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.43	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.43	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.43	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, a), b)
28.54/9.43	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.43	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.43	   A^2 -> H(U1(c, a), c)
28.54/9.43	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.43	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.43	   A^2 -> H(U1(c, a), e)
28.54/9.43	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.43	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.43	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.43	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.43	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.43	   A^2 -> H(U1(d, e), f(e))
28.54/9.43	   A^2 -> H(U1(d, e), f(k))
28.54/9.43	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.43	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.43	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.43	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.43	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.43	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.43	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.43	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.43	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.43	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.43	   A^2 -> H(U1(d, a), b)
28.54/9.43	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.43	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.43	   A^2 -> H(U1(d, a), c)
28.54/9.43	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.43	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.43	   A^2 -> H(U1(d, a), e)
28.54/9.43	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.43	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.43	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.43	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.43	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.43	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.43	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.43	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.43	   A^2 -> H(U1(a, c), b)
28.54/9.43	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.43	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.43	   A^2 -> H(U1(a, c), c)
28.54/9.43	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.43	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.43	   A^2 -> H(U1(a, c), e)
28.54/9.43	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, d), b)
28.54/9.43	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.43	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.43	   A^2 -> H(U1(a, d), c)
28.54/9.43	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.43	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.43	   A^2 -> H(U1(a, d), e)
28.54/9.43	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, a), d)
28.54/9.43	   A^2 -> H(U1(a, a), k)
28.54/9.43	   A^2 -> H(k, U1(b, b))
28.54/9.43	   A^2 -> H(k, f(c))
28.54/9.43	   A^2 -> H(k, f(d))
28.54/9.43	   A^2 -> H(c, U1(c, b))
28.54/9.43	   A^2 -> H(c, U1(d, b))
28.54/9.43	   A^2 -> H(c, U1(b, c))
28.54/9.43	   A^2 -> H(c, U1(b, d))
28.54/9.43	   A^2 -> H(c, U1(c, c))
28.54/9.43	   A^2 -> H(c, f(e))
28.54/9.43	   A^2 -> H(c, f(k))
28.54/9.43	   A^2 -> H(c, U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.43	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.43	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.43	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.43	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.43	   A^2 -> H(U1(e, k), f(e))
28.54/9.43	   A^2 -> H(U1(e, k), f(k))
28.54/9.43	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.43	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.43	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.43	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.43	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.43	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.43	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.43	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.43	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.43	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.43	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.43	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.43	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.43	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.43	   A^2 -> H(U1(k, e), f(e))
28.54/9.43	   A^2 -> H(U1(k, e), f(k))
28.54/9.43	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.43	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.43	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.43	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.43	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.43	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.43	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.43	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, c), b)
28.54/9.43	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.43	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.43	   A^2 -> H(U1(c, c), e)
28.54/9.43	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.43	   A^2 -> H(e, U1(c, b))
28.54/9.43	   A^2 -> H(e, U1(d, b))
28.54/9.43	   A^2 -> H(e, U1(b, c))
28.54/9.43	   A^2 -> H(e, U1(b, d))
28.54/9.43	   A^2 -> H(e, U1(c, c))
28.54/9.43	   A^2 -> H(e, f(e))
28.54/9.43	   A^2 -> H(e, f(k))
28.54/9.43	   A^2 -> H(e, U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.43	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.43	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.43	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.43	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.43	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.43	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.43	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.43	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.43	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.43	   A^2 -> H(f(e), b)
28.54/9.43	   A^2 -> H(f(e), U1(e, d))
28.54/9.43	   A^2 -> H(f(e), U1(d, e))
28.54/9.43	   A^2 -> H(f(e), c)
28.54/9.43	   A^2 -> H(f(e), U1(e, k))
28.54/9.43	   A^2 -> H(f(e), U1(k, e))
28.54/9.43	   A^2 -> H(f(e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.43	   A^2 -> H(f(k), b)
28.54/9.43	   A^2 -> H(f(k), U1(e, d))
28.54/9.43	   A^2 -> H(f(k), U1(d, e))
28.54/9.43	   A^2 -> H(f(k), c)
28.54/9.43	   A^2 -> H(f(k), U1(e, k))
28.54/9.43	   A^2 -> H(f(k), U1(k, e))
28.54/9.43	   A^2 -> H(f(k), e)
28.54/9.43	   A^2 -> H(f(c), d)
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.43	   A^2 -> H(U1(k, k), f(e))
28.54/9.43	   A^2 -> H(U1(k, k), f(k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.43	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.43	   A^2 -> H(U1(d, d), b)
28.54/9.43	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.43	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.43	   A^2 -> H(U1(d, d), c)
28.54/9.43	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.43	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.43	   A^2 -> H(U1(d, d), e)
28.54/9.43	   A^2 -> H(f(d), d)
28.54/9.43	   A^2 -> H(f(d), k)
28.54/9.43	
28.54/9.43	The TRS R consists of the following rules:
28.54/9.43	
28.54/9.43	   f(x) -> U1(x, x)
28.54/9.43	   U1(e, x) -> x
28.54/9.43	   a -> c
28.54/9.43	   a -> d
28.54/9.43	   b -> c
28.54/9.43	   b -> d
28.54/9.43	   d -> k
28.54/9.43	   c -> e
28.54/9.43	   c -> k
28.54/9.43	
28.54/9.43	Q is empty.
28.54/9.43	We have to consider all minimal (P,Q,R)-chains.
28.54/9.43	----------------------------------------
28.54/9.43	
28.54/9.43	(1057) TransformationProof (EQUIVALENT)
28.54/9.43	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.43	
28.54/9.43	   (A^2 -> H(U1(d, d), U1(e, k)),A^2 -> H(U1(d, d), U1(e, k)))
28.54/9.43	   (A^2 -> H(f(k), U1(e, k)),A^2 -> H(f(k), U1(e, k)))
28.54/9.43	   (A^2 -> H(f(d), k),A^2 -> H(f(d), k))
28.54/9.43	
28.54/9.43	
28.54/9.43	----------------------------------------
28.54/9.43	
28.54/9.43	(1058)
28.54/9.43	Obligation:
28.54/9.43	Q DP problem:
28.54/9.43	The TRS P consists of the following rules:
28.54/9.43	
28.54/9.43	   H(x, x) -> G(x, x, f(k))
28.54/9.43	   G(d, x, x) -> A^2
28.54/9.43	   A^2 -> H(f(c), f(c))
28.54/9.43	   A^2 -> H(f(d), f(d))
28.54/9.43	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.43	   A^2 -> H(f(e), f(e))
28.54/9.43	   A^2 -> H(f(k), f(k))
28.54/9.43	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.43	   A^2 -> H(f(d), U1(k, e))
28.54/9.43	   A^2 -> H(f(d), e)
28.54/9.43	   A^2 -> H(f(a), d)
28.54/9.43	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.43	   A^2 -> H(f(c), c)
28.54/9.43	   A^2 -> H(f(c), U1(e, k))
28.54/9.43	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.43	   A^2 -> H(f(c), U1(k, e))
28.54/9.43	   A^2 -> H(f(c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.43	   A^2 -> H(f(a), k)
28.54/9.43	   A^2 -> H(f(e), U1(e, e))
28.54/9.43	   A^2 -> H(f(c), e)
28.54/9.43	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.43	   A^2 -> H(f(d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.43	   A^2 -> H(d, U1(b, b))
28.54/9.43	   A^2 -> H(d, f(c))
28.54/9.43	   A^2 -> H(d, f(d))
28.54/9.43	   A^2 -> H(a, U1(c, b))
28.54/9.43	   A^2 -> H(a, U1(d, b))
28.54/9.43	   A^2 -> H(a, U1(b, c))
28.54/9.43	   A^2 -> H(a, U1(b, d))
28.54/9.43	   A^2 -> H(a, U1(c, c))
28.54/9.43	   A^2 -> H(a, f(e))
28.54/9.43	   A^2 -> H(a, f(k))
28.54/9.43	   A^2 -> H(a, U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.43	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.43	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.43	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.43	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.43	   A^2 -> H(U1(e, d), f(e))
28.54/9.43	   A^2 -> H(U1(e, d), f(k))
28.54/9.43	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.43	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.43	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.43	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.43	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.43	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.43	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.43	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.43	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.43	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.43	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.43	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.43	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.43	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.43	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.43	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, a), b)
28.54/9.43	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.43	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.43	   A^2 -> H(U1(c, a), c)
28.54/9.43	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.43	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.43	   A^2 -> H(U1(c, a), e)
28.54/9.43	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.43	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.43	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.43	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.43	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.43	   A^2 -> H(U1(d, e), f(e))
28.54/9.43	   A^2 -> H(U1(d, e), f(k))
28.54/9.43	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.43	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.43	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.43	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.43	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.43	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.43	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.43	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.43	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.43	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.43	   A^2 -> H(U1(d, a), b)
28.54/9.43	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.43	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.43	   A^2 -> H(U1(d, a), c)
28.54/9.43	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.43	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.43	   A^2 -> H(U1(d, a), e)
28.54/9.43	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.43	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.43	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.43	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.43	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.43	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.43	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.43	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.43	   A^2 -> H(U1(a, c), b)
28.54/9.43	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.43	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.43	   A^2 -> H(U1(a, c), c)
28.54/9.43	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.43	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.43	   A^2 -> H(U1(a, c), e)
28.54/9.43	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, d), b)
28.54/9.43	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.43	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.43	   A^2 -> H(U1(a, d), c)
28.54/9.43	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.43	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.43	   A^2 -> H(U1(a, d), e)
28.54/9.43	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, a), d)
28.54/9.43	   A^2 -> H(U1(a, a), k)
28.54/9.43	   A^2 -> H(k, U1(b, b))
28.54/9.43	   A^2 -> H(k, f(c))
28.54/9.43	   A^2 -> H(k, f(d))
28.54/9.43	   A^2 -> H(c, U1(c, b))
28.54/9.43	   A^2 -> H(c, U1(d, b))
28.54/9.43	   A^2 -> H(c, U1(b, c))
28.54/9.43	   A^2 -> H(c, U1(b, d))
28.54/9.43	   A^2 -> H(c, U1(c, c))
28.54/9.43	   A^2 -> H(c, f(e))
28.54/9.43	   A^2 -> H(c, f(k))
28.54/9.43	   A^2 -> H(c, U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.43	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.43	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.43	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.43	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.43	   A^2 -> H(U1(e, k), f(e))
28.54/9.43	   A^2 -> H(U1(e, k), f(k))
28.54/9.43	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.43	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.43	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.43	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.43	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.43	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.43	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.43	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.43	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.43	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.43	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.43	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.43	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.43	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.43	   A^2 -> H(U1(k, e), f(e))
28.54/9.43	   A^2 -> H(U1(k, e), f(k))
28.54/9.43	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.43	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.43	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.43	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.43	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.43	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.43	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.43	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, c), b)
28.54/9.43	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.43	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.43	   A^2 -> H(U1(c, c), e)
28.54/9.43	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.43	   A^2 -> H(e, U1(c, b))
28.54/9.43	   A^2 -> H(e, U1(d, b))
28.54/9.43	   A^2 -> H(e, U1(b, c))
28.54/9.43	   A^2 -> H(e, U1(b, d))
28.54/9.43	   A^2 -> H(e, U1(c, c))
28.54/9.43	   A^2 -> H(e, f(e))
28.54/9.43	   A^2 -> H(e, f(k))
28.54/9.43	   A^2 -> H(e, U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.43	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.43	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.43	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.43	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.43	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.43	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.43	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.43	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.43	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.43	   A^2 -> H(f(e), b)
28.54/9.43	   A^2 -> H(f(e), U1(e, d))
28.54/9.43	   A^2 -> H(f(e), U1(d, e))
28.54/9.43	   A^2 -> H(f(e), c)
28.54/9.43	   A^2 -> H(f(e), U1(e, k))
28.54/9.43	   A^2 -> H(f(e), U1(k, e))
28.54/9.43	   A^2 -> H(f(e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.43	   A^2 -> H(f(k), b)
28.54/9.43	   A^2 -> H(f(k), U1(e, d))
28.54/9.43	   A^2 -> H(f(k), U1(d, e))
28.54/9.43	   A^2 -> H(f(k), c)
28.54/9.43	   A^2 -> H(f(k), U1(e, k))
28.54/9.43	   A^2 -> H(f(k), U1(k, e))
28.54/9.43	   A^2 -> H(f(k), e)
28.54/9.43	   A^2 -> H(f(c), d)
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.43	   A^2 -> H(U1(k, k), f(e))
28.54/9.43	   A^2 -> H(U1(k, k), f(k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.43	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.43	   A^2 -> H(U1(d, d), b)
28.54/9.43	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.43	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.43	   A^2 -> H(U1(d, d), c)
28.54/9.43	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.43	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.43	   A^2 -> H(U1(d, d), e)
28.54/9.43	   A^2 -> H(f(d), d)
28.54/9.43	   A^2 -> H(f(d), k)
28.54/9.43	
28.54/9.43	The TRS R consists of the following rules:
28.54/9.43	
28.54/9.43	   f(x) -> U1(x, x)
28.54/9.43	   U1(e, x) -> x
28.54/9.43	   a -> c
28.54/9.43	   a -> d
28.54/9.43	   b -> c
28.54/9.43	   b -> d
28.54/9.43	   d -> k
28.54/9.43	   c -> e
28.54/9.43	   c -> k
28.54/9.43	
28.54/9.43	Q is empty.
28.54/9.43	We have to consider all minimal (P,Q,R)-chains.
28.54/9.43	----------------------------------------
28.54/9.43	
28.54/9.43	(1059) TransformationProof (EQUIVALENT)
28.54/9.43	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.43	
28.54/9.43	   (A^2 -> H(U1(d, d), U1(k, e)),A^2 -> H(U1(d, d), U1(k, e)))
28.54/9.43	   (A^2 -> H(f(k), U1(k, e)),A^2 -> H(f(k), U1(k, e)))
28.54/9.43	
28.54/9.43	
28.54/9.43	----------------------------------------
28.54/9.43	
28.54/9.43	(1060)
28.54/9.43	Obligation:
28.54/9.43	Q DP problem:
28.54/9.43	The TRS P consists of the following rules:
28.54/9.43	
28.54/9.43	   H(x, x) -> G(x, x, f(k))
28.54/9.43	   G(d, x, x) -> A^2
28.54/9.43	   A^2 -> H(f(c), f(c))
28.54/9.43	   A^2 -> H(f(d), f(d))
28.54/9.43	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.43	   A^2 -> H(f(e), f(e))
28.54/9.43	   A^2 -> H(f(k), f(k))
28.54/9.43	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.43	   A^2 -> H(f(d), e)
28.54/9.43	   A^2 -> H(f(a), d)
28.54/9.43	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.43	   A^2 -> H(f(c), c)
28.54/9.43	   A^2 -> H(f(c), U1(e, k))
28.54/9.43	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.43	   A^2 -> H(f(c), U1(k, e))
28.54/9.43	   A^2 -> H(f(c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.43	   A^2 -> H(f(a), k)
28.54/9.43	   A^2 -> H(f(e), U1(e, e))
28.54/9.43	   A^2 -> H(f(c), e)
28.54/9.43	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.43	   A^2 -> H(f(d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.43	   A^2 -> H(d, U1(b, b))
28.54/9.43	   A^2 -> H(d, f(c))
28.54/9.43	   A^2 -> H(d, f(d))
28.54/9.43	   A^2 -> H(a, U1(c, b))
28.54/9.43	   A^2 -> H(a, U1(d, b))
28.54/9.43	   A^2 -> H(a, U1(b, c))
28.54/9.43	   A^2 -> H(a, U1(b, d))
28.54/9.43	   A^2 -> H(a, U1(c, c))
28.54/9.43	   A^2 -> H(a, f(e))
28.54/9.43	   A^2 -> H(a, f(k))
28.54/9.43	   A^2 -> H(a, U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.43	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.43	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.43	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.43	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.43	   A^2 -> H(U1(e, d), f(e))
28.54/9.43	   A^2 -> H(U1(e, d), f(k))
28.54/9.43	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.43	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.43	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.43	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.43	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.43	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.43	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.43	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.43	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.43	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.43	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.43	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.43	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.43	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.43	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.43	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, a), b)
28.54/9.43	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.43	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.43	   A^2 -> H(U1(c, a), c)
28.54/9.43	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.43	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.43	   A^2 -> H(U1(c, a), e)
28.54/9.43	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.43	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.43	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.43	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.43	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.43	   A^2 -> H(U1(d, e), f(e))
28.54/9.43	   A^2 -> H(U1(d, e), f(k))
28.54/9.43	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.43	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.43	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.43	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.43	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.43	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.43	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.43	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.43	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.43	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.43	   A^2 -> H(U1(d, a), b)
28.54/9.43	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.43	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.43	   A^2 -> H(U1(d, a), c)
28.54/9.43	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.43	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.43	   A^2 -> H(U1(d, a), e)
28.54/9.43	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.43	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.43	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.43	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.43	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.43	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.43	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.43	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.43	   A^2 -> H(U1(a, c), b)
28.54/9.43	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.43	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.43	   A^2 -> H(U1(a, c), c)
28.54/9.43	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.43	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.43	   A^2 -> H(U1(a, c), e)
28.54/9.43	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, d), b)
28.54/9.43	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.43	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.43	   A^2 -> H(U1(a, d), c)
28.54/9.43	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.43	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.43	   A^2 -> H(U1(a, d), e)
28.54/9.43	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, a), d)
28.54/9.43	   A^2 -> H(U1(a, a), k)
28.54/9.43	   A^2 -> H(k, U1(b, b))
28.54/9.43	   A^2 -> H(k, f(c))
28.54/9.43	   A^2 -> H(k, f(d))
28.54/9.43	   A^2 -> H(c, U1(c, b))
28.54/9.43	   A^2 -> H(c, U1(d, b))
28.54/9.43	   A^2 -> H(c, U1(b, c))
28.54/9.43	   A^2 -> H(c, U1(b, d))
28.54/9.43	   A^2 -> H(c, U1(c, c))
28.54/9.43	   A^2 -> H(c, f(e))
28.54/9.43	   A^2 -> H(c, f(k))
28.54/9.43	   A^2 -> H(c, U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.43	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.43	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.43	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.43	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.43	   A^2 -> H(U1(e, k), f(e))
28.54/9.43	   A^2 -> H(U1(e, k), f(k))
28.54/9.43	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.43	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.43	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.43	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.43	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.43	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.43	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.43	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.43	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.43	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.43	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.43	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.43	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.43	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.43	   A^2 -> H(U1(k, e), f(e))
28.54/9.43	   A^2 -> H(U1(k, e), f(k))
28.54/9.43	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.43	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.43	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.43	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.43	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.43	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.43	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.43	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, c), b)
28.54/9.43	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.43	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.43	   A^2 -> H(U1(c, c), e)
28.54/9.43	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.43	   A^2 -> H(e, U1(c, b))
28.54/9.43	   A^2 -> H(e, U1(d, b))
28.54/9.43	   A^2 -> H(e, U1(b, c))
28.54/9.43	   A^2 -> H(e, U1(b, d))
28.54/9.43	   A^2 -> H(e, U1(c, c))
28.54/9.43	   A^2 -> H(e, f(e))
28.54/9.43	   A^2 -> H(e, f(k))
28.54/9.43	   A^2 -> H(e, U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.43	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.43	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.43	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.43	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.43	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.43	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.43	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.43	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.43	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.43	   A^2 -> H(f(e), b)
28.54/9.43	   A^2 -> H(f(e), U1(e, d))
28.54/9.43	   A^2 -> H(f(e), U1(d, e))
28.54/9.43	   A^2 -> H(f(e), c)
28.54/9.43	   A^2 -> H(f(e), U1(e, k))
28.54/9.43	   A^2 -> H(f(e), U1(k, e))
28.54/9.43	   A^2 -> H(f(e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.43	   A^2 -> H(f(k), b)
28.54/9.43	   A^2 -> H(f(k), U1(e, d))
28.54/9.43	   A^2 -> H(f(k), U1(d, e))
28.54/9.43	   A^2 -> H(f(k), c)
28.54/9.43	   A^2 -> H(f(k), U1(e, k))
28.54/9.43	   A^2 -> H(f(k), U1(k, e))
28.54/9.43	   A^2 -> H(f(k), e)
28.54/9.43	   A^2 -> H(f(c), d)
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.43	   A^2 -> H(U1(k, k), f(e))
28.54/9.43	   A^2 -> H(U1(k, k), f(k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.43	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.43	   A^2 -> H(U1(d, d), b)
28.54/9.43	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.43	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.43	   A^2 -> H(U1(d, d), c)
28.54/9.43	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.43	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.43	   A^2 -> H(U1(d, d), e)
28.54/9.43	   A^2 -> H(f(d), d)
28.54/9.43	   A^2 -> H(f(d), k)
28.54/9.43	
28.54/9.43	The TRS R consists of the following rules:
28.54/9.43	
28.54/9.43	   f(x) -> U1(x, x)
28.54/9.43	   U1(e, x) -> x
28.54/9.43	   a -> c
28.54/9.43	   a -> d
28.54/9.43	   b -> c
28.54/9.43	   b -> d
28.54/9.43	   d -> k
28.54/9.43	   c -> e
28.54/9.43	   c -> k
28.54/9.43	
28.54/9.43	Q is empty.
28.54/9.43	We have to consider all minimal (P,Q,R)-chains.
28.54/9.43	----------------------------------------
28.54/9.43	
28.54/9.43	(1061) TransformationProof (EQUIVALENT)
28.54/9.43	By narrowing [LPAR04] the rule A^2 -> H(f(d), e) at position [] we obtained the following new rules [LPAR04]:
28.54/9.43	
28.54/9.43	   (A^2 -> H(U1(d, d), e),A^2 -> H(U1(d, d), e))
28.54/9.43	   (A^2 -> H(f(k), e),A^2 -> H(f(k), e))
28.54/9.43	
28.54/9.43	
28.54/9.43	----------------------------------------
28.54/9.43	
28.54/9.43	(1062)
28.54/9.43	Obligation:
28.54/9.43	Q DP problem:
28.54/9.43	The TRS P consists of the following rules:
28.54/9.43	
28.54/9.43	   H(x, x) -> G(x, x, f(k))
28.54/9.43	   G(d, x, x) -> A^2
28.54/9.43	   A^2 -> H(f(c), f(c))
28.54/9.43	   A^2 -> H(f(d), f(d))
28.54/9.43	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.43	   A^2 -> H(f(e), f(e))
28.54/9.43	   A^2 -> H(f(k), f(k))
28.54/9.43	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.43	   A^2 -> H(f(a), d)
28.54/9.43	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.43	   A^2 -> H(f(c), c)
28.54/9.43	   A^2 -> H(f(c), U1(e, k))
28.54/9.43	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.43	   A^2 -> H(f(c), U1(k, e))
28.54/9.43	   A^2 -> H(f(c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.43	   A^2 -> H(f(a), k)
28.54/9.43	   A^2 -> H(f(e), U1(e, e))
28.54/9.43	   A^2 -> H(f(c), e)
28.54/9.43	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.43	   A^2 -> H(f(d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.43	   A^2 -> H(d, U1(b, b))
28.54/9.43	   A^2 -> H(d, f(c))
28.54/9.43	   A^2 -> H(d, f(d))
28.54/9.43	   A^2 -> H(a, U1(c, b))
28.54/9.43	   A^2 -> H(a, U1(d, b))
28.54/9.43	   A^2 -> H(a, U1(b, c))
28.54/9.43	   A^2 -> H(a, U1(b, d))
28.54/9.43	   A^2 -> H(a, U1(c, c))
28.54/9.43	   A^2 -> H(a, f(e))
28.54/9.43	   A^2 -> H(a, f(k))
28.54/9.43	   A^2 -> H(a, U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.43	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.43	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.43	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.43	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.43	   A^2 -> H(U1(e, d), f(e))
28.54/9.43	   A^2 -> H(U1(e, d), f(k))
28.54/9.43	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.43	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.43	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.43	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.43	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.43	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.43	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.43	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.43	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.43	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.43	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.43	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.43	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.43	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.43	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.43	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, a), b)
28.54/9.43	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.43	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.43	   A^2 -> H(U1(c, a), c)
28.54/9.43	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.43	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.43	   A^2 -> H(U1(c, a), e)
28.54/9.43	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.43	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.43	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.43	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.43	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.43	   A^2 -> H(U1(d, e), f(e))
28.54/9.43	   A^2 -> H(U1(d, e), f(k))
28.54/9.43	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.43	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.43	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.43	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.43	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.43	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.43	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.43	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.43	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.43	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.43	   A^2 -> H(U1(d, a), b)
28.54/9.43	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.43	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.43	   A^2 -> H(U1(d, a), c)
28.54/9.43	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.43	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.43	   A^2 -> H(U1(d, a), e)
28.54/9.43	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.43	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.43	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.43	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.43	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.43	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.43	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.43	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.43	   A^2 -> H(U1(a, c), b)
28.54/9.43	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.43	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.43	   A^2 -> H(U1(a, c), c)
28.54/9.43	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.43	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.43	   A^2 -> H(U1(a, c), e)
28.54/9.43	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, d), b)
28.54/9.43	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.43	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.43	   A^2 -> H(U1(a, d), c)
28.54/9.43	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.43	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.43	   A^2 -> H(U1(a, d), e)
28.54/9.43	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, a), d)
28.54/9.43	   A^2 -> H(U1(a, a), k)
28.54/9.43	   A^2 -> H(k, U1(b, b))
28.54/9.43	   A^2 -> H(k, f(c))
28.54/9.43	   A^2 -> H(k, f(d))
28.54/9.43	   A^2 -> H(c, U1(c, b))
28.54/9.43	   A^2 -> H(c, U1(d, b))
28.54/9.43	   A^2 -> H(c, U1(b, c))
28.54/9.43	   A^2 -> H(c, U1(b, d))
28.54/9.43	   A^2 -> H(c, U1(c, c))
28.54/9.43	   A^2 -> H(c, f(e))
28.54/9.43	   A^2 -> H(c, f(k))
28.54/9.43	   A^2 -> H(c, U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.43	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.43	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.43	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.43	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.43	   A^2 -> H(U1(e, k), f(e))
28.54/9.43	   A^2 -> H(U1(e, k), f(k))
28.54/9.43	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.43	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.43	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.43	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.43	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.43	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.43	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.43	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.43	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.43	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.43	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.43	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.43	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.43	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.43	   A^2 -> H(U1(k, e), f(e))
28.54/9.43	   A^2 -> H(U1(k, e), f(k))
28.54/9.43	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.43	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.43	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.43	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.43	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.43	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.43	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.43	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, c), b)
28.54/9.43	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.43	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.43	   A^2 -> H(U1(c, c), e)
28.54/9.43	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.43	   A^2 -> H(e, U1(c, b))
28.54/9.43	   A^2 -> H(e, U1(d, b))
28.54/9.43	   A^2 -> H(e, U1(b, c))
28.54/9.43	   A^2 -> H(e, U1(b, d))
28.54/9.43	   A^2 -> H(e, U1(c, c))
28.54/9.43	   A^2 -> H(e, f(e))
28.54/9.43	   A^2 -> H(e, f(k))
28.54/9.43	   A^2 -> H(e, U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.43	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.43	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.43	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.43	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.43	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.43	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.43	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.43	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.43	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.43	   A^2 -> H(f(e), b)
28.54/9.43	   A^2 -> H(f(e), U1(e, d))
28.54/9.43	   A^2 -> H(f(e), U1(d, e))
28.54/9.43	   A^2 -> H(f(e), c)
28.54/9.43	   A^2 -> H(f(e), U1(e, k))
28.54/9.43	   A^2 -> H(f(e), U1(k, e))
28.54/9.43	   A^2 -> H(f(e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.43	   A^2 -> H(f(k), b)
28.54/9.43	   A^2 -> H(f(k), U1(e, d))
28.54/9.43	   A^2 -> H(f(k), U1(d, e))
28.54/9.43	   A^2 -> H(f(k), c)
28.54/9.43	   A^2 -> H(f(k), U1(e, k))
28.54/9.43	   A^2 -> H(f(k), U1(k, e))
28.54/9.43	   A^2 -> H(f(k), e)
28.54/9.43	   A^2 -> H(f(c), d)
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.43	   A^2 -> H(U1(k, k), f(e))
28.54/9.43	   A^2 -> H(U1(k, k), f(k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.43	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.43	   A^2 -> H(U1(d, d), b)
28.54/9.43	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.43	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.43	   A^2 -> H(U1(d, d), c)
28.54/9.43	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.43	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.43	   A^2 -> H(U1(d, d), e)
28.54/9.43	   A^2 -> H(f(d), d)
28.54/9.43	   A^2 -> H(f(d), k)
28.54/9.43	
28.54/9.43	The TRS R consists of the following rules:
28.54/9.43	
28.54/9.43	   f(x) -> U1(x, x)
28.54/9.43	   U1(e, x) -> x
28.54/9.43	   a -> c
28.54/9.43	   a -> d
28.54/9.43	   b -> c
28.54/9.43	   b -> d
28.54/9.43	   d -> k
28.54/9.43	   c -> e
28.54/9.43	   c -> k
28.54/9.43	
28.54/9.43	Q is empty.
28.54/9.43	We have to consider all minimal (P,Q,R)-chains.
28.54/9.43	----------------------------------------
28.54/9.43	
28.54/9.43	(1063) TransformationProof (EQUIVALENT)
28.54/9.43	By narrowing [LPAR04] the rule A^2 -> H(f(a), d) at position [] we obtained the following new rules [LPAR04]:
28.54/9.43	
28.54/9.43	   (A^2 -> H(U1(a, a), d),A^2 -> H(U1(a, a), d))
28.54/9.43	   (A^2 -> H(f(c), d),A^2 -> H(f(c), d))
28.54/9.43	   (A^2 -> H(f(d), d),A^2 -> H(f(d), d))
28.54/9.43	   (A^2 -> H(f(a), k),A^2 -> H(f(a), k))
28.54/9.43	
28.54/9.43	
28.54/9.43	----------------------------------------
28.54/9.43	
28.54/9.43	(1064)
28.54/9.43	Obligation:
28.54/9.43	Q DP problem:
28.54/9.43	The TRS P consists of the following rules:
28.54/9.43	
28.54/9.43	   H(x, x) -> G(x, x, f(k))
28.54/9.43	   G(d, x, x) -> A^2
28.54/9.43	   A^2 -> H(f(c), f(c))
28.54/9.43	   A^2 -> H(f(d), f(d))
28.54/9.43	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.43	   A^2 -> H(f(e), f(e))
28.54/9.43	   A^2 -> H(f(k), f(k))
28.54/9.43	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.43	   A^2 -> H(U1(c, c), U1(e, c))
28.54/9.43	   A^2 -> H(f(c), c)
28.54/9.43	   A^2 -> H(f(c), U1(e, k))
28.54/9.43	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.43	   A^2 -> H(f(c), U1(k, e))
28.54/9.43	   A^2 -> H(f(c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.43	   A^2 -> H(f(a), k)
28.54/9.43	   A^2 -> H(f(e), U1(e, e))
28.54/9.43	   A^2 -> H(f(c), e)
28.54/9.43	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.43	   A^2 -> H(f(d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.43	   A^2 -> H(d, U1(b, b))
28.54/9.43	   A^2 -> H(d, f(c))
28.54/9.43	   A^2 -> H(d, f(d))
28.54/9.43	   A^2 -> H(a, U1(c, b))
28.54/9.43	   A^2 -> H(a, U1(d, b))
28.54/9.43	   A^2 -> H(a, U1(b, c))
28.54/9.43	   A^2 -> H(a, U1(b, d))
28.54/9.43	   A^2 -> H(a, U1(c, c))
28.54/9.43	   A^2 -> H(a, f(e))
28.54/9.43	   A^2 -> H(a, f(k))
28.54/9.43	   A^2 -> H(a, U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.43	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.43	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.43	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.43	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.43	   A^2 -> H(U1(e, d), f(e))
28.54/9.43	   A^2 -> H(U1(e, d), f(k))
28.54/9.43	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.43	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.43	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.43	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.43	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.43	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.43	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.43	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.43	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.43	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.43	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.43	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.43	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.43	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.43	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.43	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, a), b)
28.54/9.43	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.43	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.43	   A^2 -> H(U1(c, a), c)
28.54/9.43	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.43	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.43	   A^2 -> H(U1(c, a), e)
28.54/9.43	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.43	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.43	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.43	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.43	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.43	   A^2 -> H(U1(d, e), f(e))
28.54/9.43	   A^2 -> H(U1(d, e), f(k))
28.54/9.43	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.43	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.43	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.43	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.43	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.43	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.43	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.43	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.43	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.43	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.43	   A^2 -> H(U1(d, a), b)
28.54/9.43	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.43	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.43	   A^2 -> H(U1(d, a), c)
28.54/9.43	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.43	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.43	   A^2 -> H(U1(d, a), e)
28.54/9.43	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.43	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.43	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.43	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.43	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.43	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.43	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.43	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.43	   A^2 -> H(U1(a, c), b)
28.54/9.43	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.43	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.43	   A^2 -> H(U1(a, c), c)
28.54/9.43	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.43	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.43	   A^2 -> H(U1(a, c), e)
28.54/9.43	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, d), b)
28.54/9.43	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.43	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.43	   A^2 -> H(U1(a, d), c)
28.54/9.43	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.43	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.43	   A^2 -> H(U1(a, d), e)
28.54/9.43	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(a, a), d)
28.54/9.43	   A^2 -> H(U1(a, a), k)
28.54/9.43	   A^2 -> H(k, U1(b, b))
28.54/9.43	   A^2 -> H(k, f(c))
28.54/9.43	   A^2 -> H(k, f(d))
28.54/9.43	   A^2 -> H(c, U1(c, b))
28.54/9.43	   A^2 -> H(c, U1(d, b))
28.54/9.43	   A^2 -> H(c, U1(b, c))
28.54/9.43	   A^2 -> H(c, U1(b, d))
28.54/9.43	   A^2 -> H(c, U1(c, c))
28.54/9.43	   A^2 -> H(c, f(e))
28.54/9.43	   A^2 -> H(c, f(k))
28.54/9.43	   A^2 -> H(c, U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.43	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.43	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.43	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.43	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.43	   A^2 -> H(U1(e, k), f(e))
28.54/9.43	   A^2 -> H(U1(e, k), f(k))
28.54/9.43	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.43	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.43	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.43	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.43	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.43	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.43	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.43	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.43	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.43	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.43	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.43	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.43	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.43	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.43	   A^2 -> H(U1(k, e), f(e))
28.54/9.43	   A^2 -> H(U1(k, e), f(k))
28.54/9.43	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.43	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.43	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.43	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.43	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.43	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.43	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.43	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.43	   A^2 -> H(U1(c, c), b)
28.54/9.43	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.43	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.43	   A^2 -> H(U1(c, c), e)
28.54/9.43	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.43	   A^2 -> H(e, U1(c, b))
28.54/9.43	   A^2 -> H(e, U1(d, b))
28.54/9.43	   A^2 -> H(e, U1(b, c))
28.54/9.43	   A^2 -> H(e, U1(b, d))
28.54/9.43	   A^2 -> H(e, U1(c, c))
28.54/9.43	   A^2 -> H(e, f(e))
28.54/9.43	   A^2 -> H(e, f(k))
28.54/9.43	   A^2 -> H(e, U1(d, d))
28.54/9.43	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.43	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.43	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.43	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.43	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.43	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.43	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.43	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.43	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.43	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.43	   A^2 -> H(f(e), b)
28.54/9.43	   A^2 -> H(f(e), U1(e, d))
28.54/9.43	   A^2 -> H(f(e), U1(d, e))
28.54/9.43	   A^2 -> H(f(e), c)
28.54/9.43	   A^2 -> H(f(e), U1(e, k))
28.54/9.43	   A^2 -> H(f(e), U1(k, e))
28.54/9.43	   A^2 -> H(f(e), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.43	   A^2 -> H(f(k), b)
28.54/9.43	   A^2 -> H(f(k), U1(e, d))
28.54/9.43	   A^2 -> H(f(k), U1(d, e))
28.54/9.43	   A^2 -> H(f(k), c)
28.54/9.43	   A^2 -> H(f(k), U1(e, k))
28.54/9.43	   A^2 -> H(f(k), U1(k, e))
28.54/9.43	   A^2 -> H(f(k), e)
28.54/9.43	   A^2 -> H(f(c), d)
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.43	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.43	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.43	   A^2 -> H(U1(k, k), f(e))
28.54/9.43	   A^2 -> H(U1(k, k), f(k))
28.54/9.43	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.43	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.43	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.43	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.43	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.43	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.43	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.43	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.43	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.43	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.43	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.43	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.43	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.43	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.43	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.43	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.43	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.43	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.43	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.43	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.43	   A^2 -> H(U1(d, d), b)
28.54/9.43	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.43	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.43	   A^2 -> H(U1(d, d), c)
28.54/9.43	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.43	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.43	   A^2 -> H(U1(d, d), e)
28.54/9.43	   A^2 -> H(f(d), d)
28.54/9.43	   A^2 -> H(f(d), k)
28.54/9.43	
28.54/9.43	The TRS R consists of the following rules:
28.54/9.43	
28.54/9.43	   f(x) -> U1(x, x)
28.54/9.43	   U1(e, x) -> x
28.54/9.43	   a -> c
28.54/9.43	   a -> d
28.54/9.43	   b -> c
28.54/9.43	   b -> d
28.54/9.43	   d -> k
28.54/9.43	   c -> e
28.54/9.43	   c -> k
28.54/9.43	
28.54/9.43	Q is empty.
28.54/9.44	We have to consider all minimal (P,Q,R)-chains.
28.54/9.44	----------------------------------------
28.54/9.44	
28.54/9.44	(1065) TransformationProof (EQUIVALENT)
28.54/9.44	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.44	
28.54/9.44	   (A^2 -> H(U1(e, c), U1(e, c)),A^2 -> H(U1(e, c), U1(e, c)))
28.54/9.44	   (A^2 -> H(U1(k, c), U1(e, c)),A^2 -> H(U1(k, c), U1(e, c)))
28.54/9.44	   (A^2 -> H(U1(c, e), U1(e, c)),A^2 -> H(U1(c, e), U1(e, c)))
28.54/9.44	   (A^2 -> H(U1(c, k), U1(e, c)),A^2 -> H(U1(c, k), U1(e, c)))
28.54/9.44	   (A^2 -> H(U1(c, c), c),A^2 -> H(U1(c, c), c))
28.54/9.44	   (A^2 -> H(U1(c, c), U1(e, e)),A^2 -> H(U1(c, c), U1(e, e)))
28.54/9.44	   (A^2 -> H(U1(c, c), U1(e, k)),A^2 -> H(U1(c, c), U1(e, k)))
28.54/9.44	
28.54/9.44	
28.54/9.44	----------------------------------------
28.54/9.44	
28.54/9.44	(1066)
28.54/9.44	Obligation:
28.54/9.44	Q DP problem:
28.54/9.44	The TRS P consists of the following rules:
28.54/9.44	
28.54/9.44	   H(x, x) -> G(x, x, f(k))
28.54/9.44	   G(d, x, x) -> A^2
28.54/9.44	   A^2 -> H(f(c), f(c))
28.54/9.44	   A^2 -> H(f(d), f(d))
28.54/9.44	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.44	   A^2 -> H(f(e), f(e))
28.54/9.44	   A^2 -> H(f(k), f(k))
28.54/9.44	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.44	   A^2 -> H(f(c), c)
28.54/9.44	   A^2 -> H(f(c), U1(e, k))
28.54/9.44	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.44	   A^2 -> H(f(c), U1(k, e))
28.54/9.44	   A^2 -> H(f(c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.44	   A^2 -> H(f(a), k)
28.54/9.44	   A^2 -> H(f(e), U1(e, e))
28.54/9.44	   A^2 -> H(f(c), e)
28.54/9.44	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.44	   A^2 -> H(f(d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.44	   A^2 -> H(d, U1(b, b))
28.54/9.44	   A^2 -> H(d, f(c))
28.54/9.44	   A^2 -> H(d, f(d))
28.54/9.44	   A^2 -> H(a, U1(c, b))
28.54/9.44	   A^2 -> H(a, U1(d, b))
28.54/9.44	   A^2 -> H(a, U1(b, c))
28.54/9.44	   A^2 -> H(a, U1(b, d))
28.54/9.44	   A^2 -> H(a, U1(c, c))
28.54/9.44	   A^2 -> H(a, f(e))
28.54/9.44	   A^2 -> H(a, f(k))
28.54/9.44	   A^2 -> H(a, U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.44	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.44	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.44	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.44	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.44	   A^2 -> H(U1(e, d), f(e))
28.54/9.44	   A^2 -> H(U1(e, d), f(k))
28.54/9.44	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.44	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.44	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.44	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.44	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.44	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.44	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.44	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.44	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.44	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.44	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.44	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.44	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.44	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.44	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.44	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, a), b)
28.54/9.44	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.44	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.44	   A^2 -> H(U1(c, a), c)
28.54/9.44	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.44	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.44	   A^2 -> H(U1(c, a), e)
28.54/9.44	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.44	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.44	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.44	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.44	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.44	   A^2 -> H(U1(d, e), f(e))
28.54/9.44	   A^2 -> H(U1(d, e), f(k))
28.54/9.44	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.44	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.44	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.44	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.44	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.44	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.44	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.44	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.44	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.44	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.44	   A^2 -> H(U1(d, a), b)
28.54/9.44	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.44	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.44	   A^2 -> H(U1(d, a), c)
28.54/9.44	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.44	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.44	   A^2 -> H(U1(d, a), e)
28.54/9.44	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.44	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.44	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.44	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.44	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.44	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.44	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.44	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.44	   A^2 -> H(U1(a, c), b)
28.54/9.44	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.44	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.44	   A^2 -> H(U1(a, c), c)
28.54/9.44	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.44	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.44	   A^2 -> H(U1(a, c), e)
28.54/9.44	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, d), b)
28.54/9.44	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.44	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.44	   A^2 -> H(U1(a, d), c)
28.54/9.44	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.44	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.44	   A^2 -> H(U1(a, d), e)
28.54/9.44	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, a), d)
28.54/9.44	   A^2 -> H(U1(a, a), k)
28.54/9.44	   A^2 -> H(k, U1(b, b))
28.54/9.44	   A^2 -> H(k, f(c))
28.54/9.44	   A^2 -> H(k, f(d))
28.54/9.44	   A^2 -> H(c, U1(c, b))
28.54/9.44	   A^2 -> H(c, U1(d, b))
28.54/9.44	   A^2 -> H(c, U1(b, c))
28.54/9.44	   A^2 -> H(c, U1(b, d))
28.54/9.44	   A^2 -> H(c, U1(c, c))
28.54/9.44	   A^2 -> H(c, f(e))
28.54/9.44	   A^2 -> H(c, f(k))
28.54/9.44	   A^2 -> H(c, U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.44	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.44	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.44	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.44	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.44	   A^2 -> H(U1(e, k), f(e))
28.54/9.44	   A^2 -> H(U1(e, k), f(k))
28.54/9.44	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.44	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.44	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.44	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.44	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.44	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.44	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.44	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.44	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.44	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.44	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.44	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.44	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.44	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.44	   A^2 -> H(U1(k, e), f(e))
28.54/9.44	   A^2 -> H(U1(k, e), f(k))
28.54/9.44	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.44	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.44	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.44	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.44	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.44	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.44	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.44	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, c), b)
28.54/9.44	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.44	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.44	   A^2 -> H(U1(c, c), e)
28.54/9.44	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.44	   A^2 -> H(e, U1(c, b))
28.54/9.44	   A^2 -> H(e, U1(d, b))
28.54/9.44	   A^2 -> H(e, U1(b, c))
28.54/9.44	   A^2 -> H(e, U1(b, d))
28.54/9.44	   A^2 -> H(e, U1(c, c))
28.54/9.44	   A^2 -> H(e, f(e))
28.54/9.44	   A^2 -> H(e, f(k))
28.54/9.44	   A^2 -> H(e, U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.44	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.44	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.44	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.44	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.44	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.44	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.44	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.44	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.44	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.44	   A^2 -> H(f(e), b)
28.54/9.44	   A^2 -> H(f(e), U1(e, d))
28.54/9.44	   A^2 -> H(f(e), U1(d, e))
28.54/9.44	   A^2 -> H(f(e), c)
28.54/9.44	   A^2 -> H(f(e), U1(e, k))
28.54/9.44	   A^2 -> H(f(e), U1(k, e))
28.54/9.44	   A^2 -> H(f(e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.44	   A^2 -> H(f(k), b)
28.54/9.44	   A^2 -> H(f(k), U1(e, d))
28.54/9.44	   A^2 -> H(f(k), U1(d, e))
28.54/9.44	   A^2 -> H(f(k), c)
28.54/9.44	   A^2 -> H(f(k), U1(e, k))
28.54/9.44	   A^2 -> H(f(k), U1(k, e))
28.54/9.44	   A^2 -> H(f(k), e)
28.54/9.44	   A^2 -> H(f(c), d)
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.44	   A^2 -> H(U1(k, k), f(e))
28.54/9.44	   A^2 -> H(U1(k, k), f(k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.44	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.44	   A^2 -> H(U1(d, d), b)
28.54/9.44	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.44	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.44	   A^2 -> H(U1(d, d), c)
28.54/9.44	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.44	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.44	   A^2 -> H(U1(d, d), e)
28.54/9.44	   A^2 -> H(f(d), d)
28.54/9.44	   A^2 -> H(f(d), k)
28.54/9.44	   A^2 -> H(U1(c, c), c)
28.54/9.44	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.44	
28.54/9.44	The TRS R consists of the following rules:
28.54/9.44	
28.54/9.44	   f(x) -> U1(x, x)
28.54/9.44	   U1(e, x) -> x
28.54/9.44	   a -> c
28.54/9.44	   a -> d
28.54/9.44	   b -> c
28.54/9.44	   b -> d
28.54/9.44	   d -> k
28.54/9.44	   c -> e
28.54/9.44	   c -> k
28.54/9.44	
28.54/9.44	Q is empty.
28.54/9.44	We have to consider all minimal (P,Q,R)-chains.
28.54/9.44	----------------------------------------
28.54/9.44	
28.54/9.44	(1067) TransformationProof (EQUIVALENT)
28.54/9.44	By narrowing [LPAR04] the rule A^2 -> H(f(c), c) at position [] we obtained the following new rules [LPAR04]:
28.54/9.44	
28.54/9.44	   (A^2 -> H(U1(c, c), c),A^2 -> H(U1(c, c), c))
28.54/9.44	   (A^2 -> H(f(e), c),A^2 -> H(f(e), c))
28.54/9.44	   (A^2 -> H(f(k), c),A^2 -> H(f(k), c))
28.54/9.44	   (A^2 -> H(f(c), e),A^2 -> H(f(c), e))
28.54/9.44	   (A^2 -> H(f(c), k),A^2 -> H(f(c), k))
28.54/9.44	
28.54/9.44	
28.54/9.44	----------------------------------------
28.54/9.44	
28.54/9.44	(1068)
28.54/9.44	Obligation:
28.54/9.44	Q DP problem:
28.54/9.44	The TRS P consists of the following rules:
28.54/9.44	
28.54/9.44	   H(x, x) -> G(x, x, f(k))
28.54/9.44	   G(d, x, x) -> A^2
28.54/9.44	   A^2 -> H(f(c), f(c))
28.54/9.44	   A^2 -> H(f(d), f(d))
28.54/9.44	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.44	   A^2 -> H(f(e), f(e))
28.54/9.44	   A^2 -> H(f(k), f(k))
28.54/9.44	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.44	   A^2 -> H(f(c), U1(e, k))
28.54/9.44	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.44	   A^2 -> H(f(c), U1(k, e))
28.54/9.44	   A^2 -> H(f(c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.44	   A^2 -> H(f(a), k)
28.54/9.44	   A^2 -> H(f(e), U1(e, e))
28.54/9.44	   A^2 -> H(f(c), e)
28.54/9.44	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.44	   A^2 -> H(f(d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.44	   A^2 -> H(d, U1(b, b))
28.54/9.44	   A^2 -> H(d, f(c))
28.54/9.44	   A^2 -> H(d, f(d))
28.54/9.44	   A^2 -> H(a, U1(c, b))
28.54/9.44	   A^2 -> H(a, U1(d, b))
28.54/9.44	   A^2 -> H(a, U1(b, c))
28.54/9.44	   A^2 -> H(a, U1(b, d))
28.54/9.44	   A^2 -> H(a, U1(c, c))
28.54/9.44	   A^2 -> H(a, f(e))
28.54/9.44	   A^2 -> H(a, f(k))
28.54/9.44	   A^2 -> H(a, U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.44	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.44	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.44	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.44	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.44	   A^2 -> H(U1(e, d), f(e))
28.54/9.44	   A^2 -> H(U1(e, d), f(k))
28.54/9.44	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.44	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.44	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.44	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.44	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.44	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.44	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.44	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.44	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.44	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.44	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.44	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.44	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.44	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.44	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.44	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, a), b)
28.54/9.44	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.44	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.44	   A^2 -> H(U1(c, a), c)
28.54/9.44	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.44	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.44	   A^2 -> H(U1(c, a), e)
28.54/9.44	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.44	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.44	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.44	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.44	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.44	   A^2 -> H(U1(d, e), f(e))
28.54/9.44	   A^2 -> H(U1(d, e), f(k))
28.54/9.44	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.44	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.44	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.44	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.44	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.44	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.44	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.44	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.44	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.44	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.44	   A^2 -> H(U1(d, a), b)
28.54/9.44	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.44	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.44	   A^2 -> H(U1(d, a), c)
28.54/9.44	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.44	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.44	   A^2 -> H(U1(d, a), e)
28.54/9.44	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.44	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.44	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.44	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.44	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.44	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.44	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.44	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.44	   A^2 -> H(U1(a, c), b)
28.54/9.44	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.44	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.44	   A^2 -> H(U1(a, c), c)
28.54/9.44	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.44	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.44	   A^2 -> H(U1(a, c), e)
28.54/9.44	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, d), b)
28.54/9.44	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.44	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.44	   A^2 -> H(U1(a, d), c)
28.54/9.44	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.44	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.44	   A^2 -> H(U1(a, d), e)
28.54/9.44	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, a), d)
28.54/9.44	   A^2 -> H(U1(a, a), k)
28.54/9.44	   A^2 -> H(k, U1(b, b))
28.54/9.44	   A^2 -> H(k, f(c))
28.54/9.44	   A^2 -> H(k, f(d))
28.54/9.44	   A^2 -> H(c, U1(c, b))
28.54/9.44	   A^2 -> H(c, U1(d, b))
28.54/9.44	   A^2 -> H(c, U1(b, c))
28.54/9.44	   A^2 -> H(c, U1(b, d))
28.54/9.44	   A^2 -> H(c, U1(c, c))
28.54/9.44	   A^2 -> H(c, f(e))
28.54/9.44	   A^2 -> H(c, f(k))
28.54/9.44	   A^2 -> H(c, U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.44	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.44	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.44	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.44	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.44	   A^2 -> H(U1(e, k), f(e))
28.54/9.44	   A^2 -> H(U1(e, k), f(k))
28.54/9.44	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.44	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.44	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.44	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.44	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.44	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.44	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.44	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.44	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.44	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.44	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.44	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.44	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.44	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.44	   A^2 -> H(U1(k, e), f(e))
28.54/9.44	   A^2 -> H(U1(k, e), f(k))
28.54/9.44	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.44	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.44	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.44	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.44	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.44	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.44	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.44	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, c), b)
28.54/9.44	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.44	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.44	   A^2 -> H(U1(c, c), e)
28.54/9.44	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.44	   A^2 -> H(e, U1(c, b))
28.54/9.44	   A^2 -> H(e, U1(d, b))
28.54/9.44	   A^2 -> H(e, U1(b, c))
28.54/9.44	   A^2 -> H(e, U1(b, d))
28.54/9.44	   A^2 -> H(e, U1(c, c))
28.54/9.44	   A^2 -> H(e, f(e))
28.54/9.44	   A^2 -> H(e, f(k))
28.54/9.44	   A^2 -> H(e, U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.44	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.44	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.44	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.44	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.44	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.44	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.44	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.44	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.44	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.44	   A^2 -> H(f(e), b)
28.54/9.44	   A^2 -> H(f(e), U1(e, d))
28.54/9.44	   A^2 -> H(f(e), U1(d, e))
28.54/9.44	   A^2 -> H(f(e), c)
28.54/9.44	   A^2 -> H(f(e), U1(e, k))
28.54/9.44	   A^2 -> H(f(e), U1(k, e))
28.54/9.44	   A^2 -> H(f(e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.44	   A^2 -> H(f(k), b)
28.54/9.44	   A^2 -> H(f(k), U1(e, d))
28.54/9.44	   A^2 -> H(f(k), U1(d, e))
28.54/9.44	   A^2 -> H(f(k), c)
28.54/9.44	   A^2 -> H(f(k), U1(e, k))
28.54/9.44	   A^2 -> H(f(k), U1(k, e))
28.54/9.44	   A^2 -> H(f(k), e)
28.54/9.44	   A^2 -> H(f(c), d)
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.44	   A^2 -> H(U1(k, k), f(e))
28.54/9.44	   A^2 -> H(U1(k, k), f(k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.44	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.44	   A^2 -> H(U1(d, d), b)
28.54/9.44	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.44	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.44	   A^2 -> H(U1(d, d), c)
28.54/9.44	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.44	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.44	   A^2 -> H(U1(d, d), e)
28.54/9.44	   A^2 -> H(f(d), d)
28.54/9.44	   A^2 -> H(f(d), k)
28.54/9.44	   A^2 -> H(U1(c, c), c)
28.54/9.44	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.44	   A^2 -> H(f(c), k)
28.54/9.44	
28.54/9.44	The TRS R consists of the following rules:
28.54/9.44	
28.54/9.44	   f(x) -> U1(x, x)
28.54/9.44	   U1(e, x) -> x
28.54/9.44	   a -> c
28.54/9.44	   a -> d
28.54/9.44	   b -> c
28.54/9.44	   b -> d
28.54/9.44	   d -> k
28.54/9.44	   c -> e
28.54/9.44	   c -> k
28.54/9.44	
28.54/9.44	Q is empty.
28.54/9.44	We have to consider all minimal (P,Q,R)-chains.
28.54/9.44	----------------------------------------
28.54/9.44	
28.54/9.44	(1069) TransformationProof (EQUIVALENT)
28.54/9.44	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.44	
28.54/9.44	   (A^2 -> H(U1(c, c), U1(e, k)),A^2 -> H(U1(c, c), U1(e, k)))
28.54/9.44	   (A^2 -> H(f(e), U1(e, k)),A^2 -> H(f(e), U1(e, k)))
28.54/9.44	   (A^2 -> H(f(k), U1(e, k)),A^2 -> H(f(k), U1(e, k)))
28.54/9.44	   (A^2 -> H(f(c), k),A^2 -> H(f(c), k))
28.54/9.44	
28.54/9.44	
28.54/9.44	----------------------------------------
28.54/9.44	
28.54/9.44	(1070)
28.54/9.44	Obligation:
28.54/9.44	Q DP problem:
28.54/9.44	The TRS P consists of the following rules:
28.54/9.44	
28.54/9.44	   H(x, x) -> G(x, x, f(k))
28.54/9.44	   G(d, x, x) -> A^2
28.54/9.44	   A^2 -> H(f(c), f(c))
28.54/9.44	   A^2 -> H(f(d), f(d))
28.54/9.44	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.44	   A^2 -> H(f(e), f(e))
28.54/9.44	   A^2 -> H(f(k), f(k))
28.54/9.44	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.44	   A^2 -> H(U1(c, c), U1(k, c))
28.54/9.44	   A^2 -> H(f(c), U1(k, e))
28.54/9.44	   A^2 -> H(f(c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.44	   A^2 -> H(f(a), k)
28.54/9.44	   A^2 -> H(f(e), U1(e, e))
28.54/9.44	   A^2 -> H(f(c), e)
28.54/9.44	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.44	   A^2 -> H(f(d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.44	   A^2 -> H(d, U1(b, b))
28.54/9.44	   A^2 -> H(d, f(c))
28.54/9.44	   A^2 -> H(d, f(d))
28.54/9.44	   A^2 -> H(a, U1(c, b))
28.54/9.44	   A^2 -> H(a, U1(d, b))
28.54/9.44	   A^2 -> H(a, U1(b, c))
28.54/9.44	   A^2 -> H(a, U1(b, d))
28.54/9.44	   A^2 -> H(a, U1(c, c))
28.54/9.44	   A^2 -> H(a, f(e))
28.54/9.44	   A^2 -> H(a, f(k))
28.54/9.44	   A^2 -> H(a, U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.44	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.44	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.44	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.44	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.44	   A^2 -> H(U1(e, d), f(e))
28.54/9.44	   A^2 -> H(U1(e, d), f(k))
28.54/9.44	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.44	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.44	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.44	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.44	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.44	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.44	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.44	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.44	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.44	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.44	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.44	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.44	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.44	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.44	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.44	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, a), b)
28.54/9.44	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.44	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.44	   A^2 -> H(U1(c, a), c)
28.54/9.44	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.44	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.44	   A^2 -> H(U1(c, a), e)
28.54/9.44	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.44	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.44	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.44	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.44	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.44	   A^2 -> H(U1(d, e), f(e))
28.54/9.44	   A^2 -> H(U1(d, e), f(k))
28.54/9.44	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.44	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.44	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.44	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.44	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.44	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.44	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.44	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.44	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.44	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.44	   A^2 -> H(U1(d, a), b)
28.54/9.44	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.44	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.44	   A^2 -> H(U1(d, a), c)
28.54/9.44	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.44	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.44	   A^2 -> H(U1(d, a), e)
28.54/9.44	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.44	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.44	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.44	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.44	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.44	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.44	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.44	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.44	   A^2 -> H(U1(a, c), b)
28.54/9.44	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.44	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.44	   A^2 -> H(U1(a, c), c)
28.54/9.44	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.44	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.44	   A^2 -> H(U1(a, c), e)
28.54/9.44	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, d), b)
28.54/9.44	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.44	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.44	   A^2 -> H(U1(a, d), c)
28.54/9.44	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.44	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.44	   A^2 -> H(U1(a, d), e)
28.54/9.44	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, a), d)
28.54/9.44	   A^2 -> H(U1(a, a), k)
28.54/9.44	   A^2 -> H(k, U1(b, b))
28.54/9.44	   A^2 -> H(k, f(c))
28.54/9.44	   A^2 -> H(k, f(d))
28.54/9.44	   A^2 -> H(c, U1(c, b))
28.54/9.44	   A^2 -> H(c, U1(d, b))
28.54/9.44	   A^2 -> H(c, U1(b, c))
28.54/9.44	   A^2 -> H(c, U1(b, d))
28.54/9.44	   A^2 -> H(c, U1(c, c))
28.54/9.44	   A^2 -> H(c, f(e))
28.54/9.44	   A^2 -> H(c, f(k))
28.54/9.44	   A^2 -> H(c, U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.44	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.44	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.44	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.44	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.44	   A^2 -> H(U1(e, k), f(e))
28.54/9.44	   A^2 -> H(U1(e, k), f(k))
28.54/9.44	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.44	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.44	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.44	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.44	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.44	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.44	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.44	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.44	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.44	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.44	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.44	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.44	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.44	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.44	   A^2 -> H(U1(k, e), f(e))
28.54/9.44	   A^2 -> H(U1(k, e), f(k))
28.54/9.44	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.44	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.44	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.44	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.44	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.44	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.44	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.44	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, c), b)
28.54/9.44	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.44	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.44	   A^2 -> H(U1(c, c), e)
28.54/9.44	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.44	   A^2 -> H(e, U1(c, b))
28.54/9.44	   A^2 -> H(e, U1(d, b))
28.54/9.44	   A^2 -> H(e, U1(b, c))
28.54/9.44	   A^2 -> H(e, U1(b, d))
28.54/9.44	   A^2 -> H(e, U1(c, c))
28.54/9.44	   A^2 -> H(e, f(e))
28.54/9.44	   A^2 -> H(e, f(k))
28.54/9.44	   A^2 -> H(e, U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.44	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.44	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.44	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.44	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.44	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.44	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.44	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.44	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.44	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.44	   A^2 -> H(f(e), b)
28.54/9.44	   A^2 -> H(f(e), U1(e, d))
28.54/9.44	   A^2 -> H(f(e), U1(d, e))
28.54/9.44	   A^2 -> H(f(e), c)
28.54/9.44	   A^2 -> H(f(e), U1(e, k))
28.54/9.44	   A^2 -> H(f(e), U1(k, e))
28.54/9.44	   A^2 -> H(f(e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.44	   A^2 -> H(f(k), b)
28.54/9.44	   A^2 -> H(f(k), U1(e, d))
28.54/9.44	   A^2 -> H(f(k), U1(d, e))
28.54/9.44	   A^2 -> H(f(k), c)
28.54/9.44	   A^2 -> H(f(k), U1(e, k))
28.54/9.44	   A^2 -> H(f(k), U1(k, e))
28.54/9.44	   A^2 -> H(f(k), e)
28.54/9.44	   A^2 -> H(f(c), d)
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.44	   A^2 -> H(U1(k, k), f(e))
28.54/9.44	   A^2 -> H(U1(k, k), f(k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.44	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.44	   A^2 -> H(U1(d, d), b)
28.54/9.44	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.44	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.44	   A^2 -> H(U1(d, d), c)
28.54/9.44	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.44	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.44	   A^2 -> H(U1(d, d), e)
28.54/9.44	   A^2 -> H(f(d), d)
28.54/9.44	   A^2 -> H(f(d), k)
28.54/9.44	   A^2 -> H(U1(c, c), c)
28.54/9.44	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.44	   A^2 -> H(f(c), k)
28.54/9.44	
28.54/9.44	The TRS R consists of the following rules:
28.54/9.44	
28.54/9.44	   f(x) -> U1(x, x)
28.54/9.44	   U1(e, x) -> x
28.54/9.44	   a -> c
28.54/9.44	   a -> d
28.54/9.44	   b -> c
28.54/9.44	   b -> d
28.54/9.44	   d -> k
28.54/9.44	   c -> e
28.54/9.44	   c -> k
28.54/9.44	
28.54/9.44	Q is empty.
28.54/9.44	We have to consider all minimal (P,Q,R)-chains.
28.54/9.44	----------------------------------------
28.54/9.44	
28.54/9.44	(1071) TransformationProof (EQUIVALENT)
28.54/9.44	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.44	
28.54/9.44	   (A^2 -> H(U1(e, c), U1(k, c)),A^2 -> H(U1(e, c), U1(k, c)))
28.54/9.44	   (A^2 -> H(U1(k, c), U1(k, c)),A^2 -> H(U1(k, c), U1(k, c)))
28.54/9.44	   (A^2 -> H(U1(c, e), U1(k, c)),A^2 -> H(U1(c, e), U1(k, c)))
28.54/9.44	   (A^2 -> H(U1(c, k), U1(k, c)),A^2 -> H(U1(c, k), U1(k, c)))
28.54/9.44	   (A^2 -> H(U1(c, c), U1(k, e)),A^2 -> H(U1(c, c), U1(k, e)))
28.54/9.44	   (A^2 -> H(U1(c, c), U1(k, k)),A^2 -> H(U1(c, c), U1(k, k)))
28.54/9.44	
28.54/9.44	
28.54/9.44	----------------------------------------
28.54/9.44	
28.54/9.44	(1072)
28.54/9.44	Obligation:
28.54/9.44	Q DP problem:
28.54/9.44	The TRS P consists of the following rules:
28.54/9.44	
28.54/9.44	   H(x, x) -> G(x, x, f(k))
28.54/9.44	   G(d, x, x) -> A^2
28.54/9.44	   A^2 -> H(f(c), f(c))
28.54/9.44	   A^2 -> H(f(d), f(d))
28.54/9.44	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.44	   A^2 -> H(f(e), f(e))
28.54/9.44	   A^2 -> H(f(k), f(k))
28.54/9.44	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.44	   A^2 -> H(f(c), U1(k, e))
28.54/9.44	   A^2 -> H(f(c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.44	   A^2 -> H(f(a), k)
28.54/9.44	   A^2 -> H(f(e), U1(e, e))
28.54/9.44	   A^2 -> H(f(c), e)
28.54/9.44	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.44	   A^2 -> H(f(d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.44	   A^2 -> H(d, U1(b, b))
28.54/9.44	   A^2 -> H(d, f(c))
28.54/9.44	   A^2 -> H(d, f(d))
28.54/9.44	   A^2 -> H(a, U1(c, b))
28.54/9.44	   A^2 -> H(a, U1(d, b))
28.54/9.44	   A^2 -> H(a, U1(b, c))
28.54/9.44	   A^2 -> H(a, U1(b, d))
28.54/9.44	   A^2 -> H(a, U1(c, c))
28.54/9.44	   A^2 -> H(a, f(e))
28.54/9.44	   A^2 -> H(a, f(k))
28.54/9.44	   A^2 -> H(a, U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.44	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.44	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.44	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.44	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.44	   A^2 -> H(U1(e, d), f(e))
28.54/9.44	   A^2 -> H(U1(e, d), f(k))
28.54/9.44	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.44	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.44	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.44	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.44	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.44	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.44	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.44	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.44	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.44	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.44	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.44	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.44	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.44	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.44	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.44	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, a), b)
28.54/9.44	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.44	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.44	   A^2 -> H(U1(c, a), c)
28.54/9.44	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.44	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.44	   A^2 -> H(U1(c, a), e)
28.54/9.44	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.44	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.44	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.44	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.44	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.44	   A^2 -> H(U1(d, e), f(e))
28.54/9.44	   A^2 -> H(U1(d, e), f(k))
28.54/9.44	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.44	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.44	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.44	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.44	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.44	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.44	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.44	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.44	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.44	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.44	   A^2 -> H(U1(d, a), b)
28.54/9.44	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.44	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.44	   A^2 -> H(U1(d, a), c)
28.54/9.44	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.44	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.44	   A^2 -> H(U1(d, a), e)
28.54/9.44	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.44	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.44	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.44	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.44	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.44	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.44	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.44	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.44	   A^2 -> H(U1(a, c), b)
28.54/9.44	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.44	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.44	   A^2 -> H(U1(a, c), c)
28.54/9.44	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.44	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.44	   A^2 -> H(U1(a, c), e)
28.54/9.44	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, d), b)
28.54/9.44	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.44	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.44	   A^2 -> H(U1(a, d), c)
28.54/9.44	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.44	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.44	   A^2 -> H(U1(a, d), e)
28.54/9.44	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, a), d)
28.54/9.44	   A^2 -> H(U1(a, a), k)
28.54/9.44	   A^2 -> H(k, U1(b, b))
28.54/9.44	   A^2 -> H(k, f(c))
28.54/9.44	   A^2 -> H(k, f(d))
28.54/9.44	   A^2 -> H(c, U1(c, b))
28.54/9.44	   A^2 -> H(c, U1(d, b))
28.54/9.44	   A^2 -> H(c, U1(b, c))
28.54/9.44	   A^2 -> H(c, U1(b, d))
28.54/9.44	   A^2 -> H(c, U1(c, c))
28.54/9.44	   A^2 -> H(c, f(e))
28.54/9.44	   A^2 -> H(c, f(k))
28.54/9.44	   A^2 -> H(c, U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.44	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.44	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.44	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.44	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.44	   A^2 -> H(U1(e, k), f(e))
28.54/9.44	   A^2 -> H(U1(e, k), f(k))
28.54/9.44	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.44	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.44	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.44	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.44	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.44	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.44	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.44	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.44	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.44	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.44	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.44	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.44	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.44	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.44	   A^2 -> H(U1(k, e), f(e))
28.54/9.44	   A^2 -> H(U1(k, e), f(k))
28.54/9.44	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.44	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.44	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.44	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.44	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.44	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.44	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.44	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, c), b)
28.54/9.44	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.44	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.44	   A^2 -> H(U1(c, c), e)
28.54/9.44	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.44	   A^2 -> H(e, U1(c, b))
28.54/9.44	   A^2 -> H(e, U1(d, b))
28.54/9.44	   A^2 -> H(e, U1(b, c))
28.54/9.44	   A^2 -> H(e, U1(b, d))
28.54/9.44	   A^2 -> H(e, U1(c, c))
28.54/9.44	   A^2 -> H(e, f(e))
28.54/9.44	   A^2 -> H(e, f(k))
28.54/9.44	   A^2 -> H(e, U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.44	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.44	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.44	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.44	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.44	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.44	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.44	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.44	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.44	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.44	   A^2 -> H(f(e), b)
28.54/9.44	   A^2 -> H(f(e), U1(e, d))
28.54/9.44	   A^2 -> H(f(e), U1(d, e))
28.54/9.44	   A^2 -> H(f(e), c)
28.54/9.44	   A^2 -> H(f(e), U1(e, k))
28.54/9.44	   A^2 -> H(f(e), U1(k, e))
28.54/9.44	   A^2 -> H(f(e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.44	   A^2 -> H(f(k), b)
28.54/9.44	   A^2 -> H(f(k), U1(e, d))
28.54/9.44	   A^2 -> H(f(k), U1(d, e))
28.54/9.44	   A^2 -> H(f(k), c)
28.54/9.44	   A^2 -> H(f(k), U1(e, k))
28.54/9.44	   A^2 -> H(f(k), U1(k, e))
28.54/9.44	   A^2 -> H(f(k), e)
28.54/9.44	   A^2 -> H(f(c), d)
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.44	   A^2 -> H(U1(k, k), f(e))
28.54/9.44	   A^2 -> H(U1(k, k), f(k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.44	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.44	   A^2 -> H(U1(d, d), b)
28.54/9.44	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.44	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.44	   A^2 -> H(U1(d, d), c)
28.54/9.44	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.44	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.44	   A^2 -> H(U1(d, d), e)
28.54/9.44	   A^2 -> H(f(d), d)
28.54/9.44	   A^2 -> H(f(d), k)
28.54/9.44	   A^2 -> H(U1(c, c), c)
28.54/9.44	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.44	   A^2 -> H(f(c), k)
28.54/9.44	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.44	
28.54/9.44	The TRS R consists of the following rules:
28.54/9.44	
28.54/9.44	   f(x) -> U1(x, x)
28.54/9.44	   U1(e, x) -> x
28.54/9.44	   a -> c
28.54/9.44	   a -> d
28.54/9.44	   b -> c
28.54/9.44	   b -> d
28.54/9.44	   d -> k
28.54/9.44	   c -> e
28.54/9.44	   c -> k
28.54/9.44	
28.54/9.44	Q is empty.
28.54/9.44	We have to consider all minimal (P,Q,R)-chains.
28.54/9.44	----------------------------------------
28.54/9.44	
28.54/9.44	(1073) TransformationProof (EQUIVALENT)
28.54/9.44	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.44	
28.54/9.44	   (A^2 -> H(U1(c, c), U1(k, e)),A^2 -> H(U1(c, c), U1(k, e)))
28.54/9.44	   (A^2 -> H(f(e), U1(k, e)),A^2 -> H(f(e), U1(k, e)))
28.54/9.44	   (A^2 -> H(f(k), U1(k, e)),A^2 -> H(f(k), U1(k, e)))
28.54/9.44	
28.54/9.44	
28.54/9.44	----------------------------------------
28.54/9.44	
28.54/9.44	(1074)
28.54/9.44	Obligation:
28.54/9.44	Q DP problem:
28.54/9.44	The TRS P consists of the following rules:
28.54/9.44	
28.54/9.44	   H(x, x) -> G(x, x, f(k))
28.54/9.44	   G(d, x, x) -> A^2
28.54/9.44	   A^2 -> H(f(c), f(c))
28.54/9.44	   A^2 -> H(f(d), f(d))
28.54/9.44	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.44	   A^2 -> H(f(e), f(e))
28.54/9.44	   A^2 -> H(f(k), f(k))
28.54/9.44	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.44	   A^2 -> H(f(c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.44	   A^2 -> H(f(a), k)
28.54/9.44	   A^2 -> H(f(e), U1(e, e))
28.54/9.44	   A^2 -> H(f(c), e)
28.54/9.44	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.44	   A^2 -> H(f(d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.44	   A^2 -> H(d, U1(b, b))
28.54/9.44	   A^2 -> H(d, f(c))
28.54/9.44	   A^2 -> H(d, f(d))
28.54/9.44	   A^2 -> H(a, U1(c, b))
28.54/9.44	   A^2 -> H(a, U1(d, b))
28.54/9.44	   A^2 -> H(a, U1(b, c))
28.54/9.44	   A^2 -> H(a, U1(b, d))
28.54/9.44	   A^2 -> H(a, U1(c, c))
28.54/9.44	   A^2 -> H(a, f(e))
28.54/9.44	   A^2 -> H(a, f(k))
28.54/9.44	   A^2 -> H(a, U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.44	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.44	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.44	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.44	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.44	   A^2 -> H(U1(e, d), f(e))
28.54/9.44	   A^2 -> H(U1(e, d), f(k))
28.54/9.44	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.44	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.44	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.44	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.44	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.44	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.44	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.44	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.44	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.44	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.44	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.44	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.44	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.44	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.44	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.44	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, a), b)
28.54/9.44	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.44	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.44	   A^2 -> H(U1(c, a), c)
28.54/9.44	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.44	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.44	   A^2 -> H(U1(c, a), e)
28.54/9.44	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.44	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.44	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.44	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.44	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.44	   A^2 -> H(U1(d, e), f(e))
28.54/9.44	   A^2 -> H(U1(d, e), f(k))
28.54/9.44	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.44	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.44	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.44	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.44	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.44	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.44	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.44	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.44	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.44	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.44	   A^2 -> H(U1(d, a), b)
28.54/9.44	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.44	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.44	   A^2 -> H(U1(d, a), c)
28.54/9.44	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.44	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.44	   A^2 -> H(U1(d, a), e)
28.54/9.44	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.44	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.44	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.44	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.44	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.44	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.44	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.44	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.44	   A^2 -> H(U1(a, c), b)
28.54/9.44	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.44	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.44	   A^2 -> H(U1(a, c), c)
28.54/9.44	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.44	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.44	   A^2 -> H(U1(a, c), e)
28.54/9.44	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, d), b)
28.54/9.44	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.44	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.44	   A^2 -> H(U1(a, d), c)
28.54/9.44	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.44	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.44	   A^2 -> H(U1(a, d), e)
28.54/9.44	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, a), d)
28.54/9.44	   A^2 -> H(U1(a, a), k)
28.54/9.44	   A^2 -> H(k, U1(b, b))
28.54/9.44	   A^2 -> H(k, f(c))
28.54/9.44	   A^2 -> H(k, f(d))
28.54/9.44	   A^2 -> H(c, U1(c, b))
28.54/9.44	   A^2 -> H(c, U1(d, b))
28.54/9.44	   A^2 -> H(c, U1(b, c))
28.54/9.44	   A^2 -> H(c, U1(b, d))
28.54/9.44	   A^2 -> H(c, U1(c, c))
28.54/9.44	   A^2 -> H(c, f(e))
28.54/9.44	   A^2 -> H(c, f(k))
28.54/9.44	   A^2 -> H(c, U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.44	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.44	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.44	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.44	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.44	   A^2 -> H(U1(e, k), f(e))
28.54/9.44	   A^2 -> H(U1(e, k), f(k))
28.54/9.44	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.44	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.44	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.44	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.44	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.44	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.44	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.44	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.44	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.44	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.44	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.44	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.44	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.44	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.44	   A^2 -> H(U1(k, e), f(e))
28.54/9.44	   A^2 -> H(U1(k, e), f(k))
28.54/9.44	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.44	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.44	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.44	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.44	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.44	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.44	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.44	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, c), b)
28.54/9.44	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.44	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.44	   A^2 -> H(U1(c, c), e)
28.54/9.44	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.44	   A^2 -> H(e, U1(c, b))
28.54/9.44	   A^2 -> H(e, U1(d, b))
28.54/9.44	   A^2 -> H(e, U1(b, c))
28.54/9.44	   A^2 -> H(e, U1(b, d))
28.54/9.44	   A^2 -> H(e, U1(c, c))
28.54/9.44	   A^2 -> H(e, f(e))
28.54/9.44	   A^2 -> H(e, f(k))
28.54/9.44	   A^2 -> H(e, U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.44	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.44	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.44	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.44	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.44	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.44	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.44	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.44	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.44	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.44	   A^2 -> H(f(e), b)
28.54/9.44	   A^2 -> H(f(e), U1(e, d))
28.54/9.44	   A^2 -> H(f(e), U1(d, e))
28.54/9.44	   A^2 -> H(f(e), c)
28.54/9.44	   A^2 -> H(f(e), U1(e, k))
28.54/9.44	   A^2 -> H(f(e), U1(k, e))
28.54/9.44	   A^2 -> H(f(e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.44	   A^2 -> H(f(k), b)
28.54/9.44	   A^2 -> H(f(k), U1(e, d))
28.54/9.44	   A^2 -> H(f(k), U1(d, e))
28.54/9.44	   A^2 -> H(f(k), c)
28.54/9.44	   A^2 -> H(f(k), U1(e, k))
28.54/9.44	   A^2 -> H(f(k), U1(k, e))
28.54/9.44	   A^2 -> H(f(k), e)
28.54/9.44	   A^2 -> H(f(c), d)
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.44	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.44	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.44	   A^2 -> H(U1(k, k), f(e))
28.54/9.44	   A^2 -> H(U1(k, k), f(k))
28.54/9.44	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.44	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.44	   A^2 -> H(U1(d, d), b)
28.54/9.44	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.44	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.44	   A^2 -> H(U1(d, d), c)
28.54/9.44	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.44	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.44	   A^2 -> H(U1(d, d), e)
28.54/9.44	   A^2 -> H(f(d), d)
28.54/9.44	   A^2 -> H(f(d), k)
28.54/9.44	   A^2 -> H(U1(c, c), c)
28.54/9.44	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.44	   A^2 -> H(f(c), k)
28.54/9.44	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.44	
28.54/9.44	The TRS R consists of the following rules:
28.54/9.44	
28.54/9.44	   f(x) -> U1(x, x)
28.54/9.44	   U1(e, x) -> x
28.54/9.44	   a -> c
28.54/9.44	   a -> d
28.54/9.44	   b -> c
28.54/9.44	   b -> d
28.54/9.44	   d -> k
28.54/9.44	   c -> e
28.54/9.44	   c -> k
28.54/9.44	
28.54/9.44	Q is empty.
28.54/9.44	We have to consider all minimal (P,Q,R)-chains.
28.54/9.44	----------------------------------------
28.54/9.44	
28.54/9.44	(1075) TransformationProof (EQUIVALENT)
28.54/9.44	By narrowing [LPAR04] the rule A^2 -> H(f(c), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.44	
28.54/9.44	   (A^2 -> H(U1(c, c), U1(k, k)),A^2 -> H(U1(c, c), U1(k, k)))
28.54/9.44	   (A^2 -> H(f(e), U1(k, k)),A^2 -> H(f(e), U1(k, k)))
28.54/9.44	   (A^2 -> H(f(k), U1(k, k)),A^2 -> H(f(k), U1(k, k)))
28.54/9.44	
28.54/9.44	
28.54/9.44	----------------------------------------
28.54/9.44	
28.54/9.44	(1076)
28.54/9.44	Obligation:
28.54/9.44	Q DP problem:
28.54/9.44	The TRS P consists of the following rules:
28.54/9.44	
28.54/9.44	   H(x, x) -> G(x, x, f(k))
28.54/9.44	   G(d, x, x) -> A^2
28.54/9.44	   A^2 -> H(f(c), f(c))
28.54/9.44	   A^2 -> H(f(d), f(d))
28.54/9.44	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.44	   A^2 -> H(f(e), f(e))
28.54/9.44	   A^2 -> H(f(k), f(k))
28.54/9.44	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.44	   A^2 -> H(U1(c, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.44	   A^2 -> H(f(a), k)
28.54/9.44	   A^2 -> H(f(e), U1(e, e))
28.54/9.44	   A^2 -> H(f(c), e)
28.54/9.44	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.44	   A^2 -> H(f(d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.44	   A^2 -> H(d, U1(b, b))
28.54/9.44	   A^2 -> H(d, f(c))
28.54/9.44	   A^2 -> H(d, f(d))
28.54/9.44	   A^2 -> H(a, U1(c, b))
28.54/9.44	   A^2 -> H(a, U1(d, b))
28.54/9.44	   A^2 -> H(a, U1(b, c))
28.54/9.44	   A^2 -> H(a, U1(b, d))
28.54/9.44	   A^2 -> H(a, U1(c, c))
28.54/9.44	   A^2 -> H(a, f(e))
28.54/9.44	   A^2 -> H(a, f(k))
28.54/9.44	   A^2 -> H(a, U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.44	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.44	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.44	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.44	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.44	   A^2 -> H(U1(e, d), f(e))
28.54/9.44	   A^2 -> H(U1(e, d), f(k))
28.54/9.44	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.44	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.44	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.44	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.44	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.44	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.44	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.44	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.44	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.44	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.44	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.44	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.44	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.44	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.44	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.44	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.44	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.44	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.44	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.44	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.44	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.44	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.44	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.44	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.44	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.44	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.44	   A^2 -> H(U1(c, a), b)
28.54/9.44	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.44	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.44	   A^2 -> H(U1(c, a), c)
28.54/9.44	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.44	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.44	   A^2 -> H(U1(c, a), e)
28.54/9.44	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.44	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.44	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.44	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.44	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.44	   A^2 -> H(U1(d, e), f(e))
28.54/9.44	   A^2 -> H(U1(d, e), f(k))
28.54/9.44	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.44	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.44	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.44	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.44	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.44	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.44	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.44	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.44	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.44	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.44	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.44	   A^2 -> H(U1(d, a), b)
28.54/9.44	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.44	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.44	   A^2 -> H(U1(d, a), c)
28.54/9.44	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.44	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.44	   A^2 -> H(U1(d, a), e)
28.54/9.44	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.44	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.44	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.44	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.44	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.44	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.44	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.44	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.44	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.44	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.44	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.44	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.44	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.44	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.44	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.44	   A^2 -> H(U1(a, c), b)
28.54/9.44	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.44	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.44	   A^2 -> H(U1(a, c), c)
28.54/9.44	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.44	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.44	   A^2 -> H(U1(a, c), e)
28.54/9.44	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.44	   A^2 -> H(U1(a, d), b)
28.54/9.44	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.44	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.44	   A^2 -> H(U1(a, d), c)
28.54/9.44	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.44	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.45	   A^2 -> H(U1(a, d), e)
28.54/9.45	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, a), d)
28.54/9.45	   A^2 -> H(U1(a, a), k)
28.54/9.45	   A^2 -> H(k, U1(b, b))
28.54/9.45	   A^2 -> H(k, f(c))
28.54/9.45	   A^2 -> H(k, f(d))
28.54/9.45	   A^2 -> H(c, U1(c, b))
28.54/9.45	   A^2 -> H(c, U1(d, b))
28.54/9.45	   A^2 -> H(c, U1(b, c))
28.54/9.45	   A^2 -> H(c, U1(b, d))
28.54/9.45	   A^2 -> H(c, U1(c, c))
28.54/9.45	   A^2 -> H(c, f(e))
28.54/9.45	   A^2 -> H(c, f(k))
28.54/9.45	   A^2 -> H(c, U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.45	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.45	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.45	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.45	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.45	   A^2 -> H(U1(e, k), f(e))
28.54/9.45	   A^2 -> H(U1(e, k), f(k))
28.54/9.45	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.45	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.45	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.45	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.45	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.45	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.45	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.45	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.45	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.45	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.45	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.45	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.45	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.45	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.45	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.45	   A^2 -> H(U1(k, e), f(e))
28.54/9.45	   A^2 -> H(U1(k, e), f(k))
28.54/9.45	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.45	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.45	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.45	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.45	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.45	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.45	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.45	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.45	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, c), b)
28.54/9.45	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.45	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.45	   A^2 -> H(U1(c, c), e)
28.54/9.45	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.45	   A^2 -> H(e, U1(c, b))
28.54/9.45	   A^2 -> H(e, U1(d, b))
28.54/9.45	   A^2 -> H(e, U1(b, c))
28.54/9.45	   A^2 -> H(e, U1(b, d))
28.54/9.45	   A^2 -> H(e, U1(c, c))
28.54/9.45	   A^2 -> H(e, f(e))
28.54/9.45	   A^2 -> H(e, f(k))
28.54/9.45	   A^2 -> H(e, U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.45	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.45	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.45	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.45	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.45	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.45	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.45	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.45	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.45	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.45	   A^2 -> H(f(e), b)
28.54/9.45	   A^2 -> H(f(e), U1(e, d))
28.54/9.45	   A^2 -> H(f(e), U1(d, e))
28.54/9.45	   A^2 -> H(f(e), c)
28.54/9.45	   A^2 -> H(f(e), U1(e, k))
28.54/9.45	   A^2 -> H(f(e), U1(k, e))
28.54/9.45	   A^2 -> H(f(e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.45	   A^2 -> H(f(k), b)
28.54/9.45	   A^2 -> H(f(k), U1(e, d))
28.54/9.45	   A^2 -> H(f(k), U1(d, e))
28.54/9.45	   A^2 -> H(f(k), c)
28.54/9.45	   A^2 -> H(f(k), U1(e, k))
28.54/9.45	   A^2 -> H(f(k), U1(k, e))
28.54/9.45	   A^2 -> H(f(k), e)
28.54/9.45	   A^2 -> H(f(c), d)
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.45	   A^2 -> H(U1(k, k), f(e))
28.54/9.45	   A^2 -> H(U1(k, k), f(k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.45	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.45	   A^2 -> H(U1(d, d), b)
28.54/9.45	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.45	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.45	   A^2 -> H(U1(d, d), c)
28.54/9.45	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.45	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.45	   A^2 -> H(U1(d, d), e)
28.54/9.45	   A^2 -> H(f(d), d)
28.54/9.45	   A^2 -> H(f(d), k)
28.54/9.45	   A^2 -> H(U1(c, c), c)
28.54/9.45	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.45	   A^2 -> H(f(c), k)
28.54/9.45	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.45	   A^2 -> H(f(k), U1(k, k))
28.54/9.45	
28.54/9.45	The TRS R consists of the following rules:
28.54/9.45	
28.54/9.45	   f(x) -> U1(x, x)
28.54/9.45	   U1(e, x) -> x
28.54/9.45	   a -> c
28.54/9.45	   a -> d
28.54/9.45	   b -> c
28.54/9.45	   b -> d
28.54/9.45	   d -> k
28.54/9.45	   c -> e
28.54/9.45	   c -> k
28.54/9.45	
28.54/9.45	Q is empty.
28.54/9.45	We have to consider all minimal (P,Q,R)-chains.
28.54/9.45	----------------------------------------
28.54/9.45	
28.54/9.45	(1077) TransformationProof (EQUIVALENT)
28.54/9.45	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.45	
28.54/9.45	   (A^2 -> H(U1(e, c), U1(c, e)),A^2 -> H(U1(e, c), U1(c, e)))
28.54/9.45	   (A^2 -> H(U1(k, c), U1(c, e)),A^2 -> H(U1(k, c), U1(c, e)))
28.54/9.45	   (A^2 -> H(U1(c, e), U1(c, e)),A^2 -> H(U1(c, e), U1(c, e)))
28.54/9.45	   (A^2 -> H(U1(c, k), U1(c, e)),A^2 -> H(U1(c, k), U1(c, e)))
28.54/9.45	   (A^2 -> H(U1(c, c), U1(e, e)),A^2 -> H(U1(c, c), U1(e, e)))
28.54/9.45	   (A^2 -> H(U1(c, c), U1(k, e)),A^2 -> H(U1(c, c), U1(k, e)))
28.54/9.45	
28.54/9.45	
28.54/9.45	----------------------------------------
28.54/9.45	
28.54/9.45	(1078)
28.54/9.45	Obligation:
28.54/9.45	Q DP problem:
28.54/9.45	The TRS P consists of the following rules:
28.54/9.45	
28.54/9.45	   H(x, x) -> G(x, x, f(k))
28.54/9.45	   G(d, x, x) -> A^2
28.54/9.45	   A^2 -> H(f(c), f(c))
28.54/9.45	   A^2 -> H(f(d), f(d))
28.54/9.45	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.45	   A^2 -> H(f(e), f(e))
28.54/9.45	   A^2 -> H(f(k), f(k))
28.54/9.45	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.45	   A^2 -> H(U1(c, c), U1(c, k))
28.54/9.45	   A^2 -> H(f(a), k)
28.54/9.45	   A^2 -> H(f(e), U1(e, e))
28.54/9.45	   A^2 -> H(f(c), e)
28.54/9.45	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.45	   A^2 -> H(f(d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.45	   A^2 -> H(d, U1(b, b))
28.54/9.45	   A^2 -> H(d, f(c))
28.54/9.45	   A^2 -> H(d, f(d))
28.54/9.45	   A^2 -> H(a, U1(c, b))
28.54/9.45	   A^2 -> H(a, U1(d, b))
28.54/9.45	   A^2 -> H(a, U1(b, c))
28.54/9.45	   A^2 -> H(a, U1(b, d))
28.54/9.45	   A^2 -> H(a, U1(c, c))
28.54/9.45	   A^2 -> H(a, f(e))
28.54/9.45	   A^2 -> H(a, f(k))
28.54/9.45	   A^2 -> H(a, U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.45	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.45	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.45	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.45	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.45	   A^2 -> H(U1(e, d), f(e))
28.54/9.45	   A^2 -> H(U1(e, d), f(k))
28.54/9.45	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.45	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.45	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.45	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.45	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.45	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.45	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.45	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.45	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.45	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.45	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.45	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.45	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.45	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.45	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.45	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.45	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, a), b)
28.54/9.45	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.45	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.45	   A^2 -> H(U1(c, a), c)
28.54/9.45	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.45	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.45	   A^2 -> H(U1(c, a), e)
28.54/9.45	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.45	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.45	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.45	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.45	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.45	   A^2 -> H(U1(d, e), f(e))
28.54/9.45	   A^2 -> H(U1(d, e), f(k))
28.54/9.45	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.45	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.45	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.45	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.45	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.45	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.45	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.45	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.45	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.45	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.45	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.45	   A^2 -> H(U1(d, a), b)
28.54/9.45	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.45	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.45	   A^2 -> H(U1(d, a), c)
28.54/9.45	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.45	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.45	   A^2 -> H(U1(d, a), e)
28.54/9.45	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.45	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.45	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.45	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.45	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.45	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.45	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.45	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.45	   A^2 -> H(U1(a, c), b)
28.54/9.45	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.45	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.45	   A^2 -> H(U1(a, c), c)
28.54/9.45	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.45	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.45	   A^2 -> H(U1(a, c), e)
28.54/9.45	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, d), b)
28.54/9.45	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.45	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.45	   A^2 -> H(U1(a, d), c)
28.54/9.45	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.45	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.45	   A^2 -> H(U1(a, d), e)
28.54/9.45	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, a), d)
28.54/9.45	   A^2 -> H(U1(a, a), k)
28.54/9.45	   A^2 -> H(k, U1(b, b))
28.54/9.45	   A^2 -> H(k, f(c))
28.54/9.45	   A^2 -> H(k, f(d))
28.54/9.45	   A^2 -> H(c, U1(c, b))
28.54/9.45	   A^2 -> H(c, U1(d, b))
28.54/9.45	   A^2 -> H(c, U1(b, c))
28.54/9.45	   A^2 -> H(c, U1(b, d))
28.54/9.45	   A^2 -> H(c, U1(c, c))
28.54/9.45	   A^2 -> H(c, f(e))
28.54/9.45	   A^2 -> H(c, f(k))
28.54/9.45	   A^2 -> H(c, U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.45	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.45	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.45	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.45	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.45	   A^2 -> H(U1(e, k), f(e))
28.54/9.45	   A^2 -> H(U1(e, k), f(k))
28.54/9.45	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.45	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.45	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.45	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.45	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.45	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.45	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.45	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.45	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.45	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.45	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.45	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.45	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.45	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.45	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.45	   A^2 -> H(U1(k, e), f(e))
28.54/9.45	   A^2 -> H(U1(k, e), f(k))
28.54/9.45	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.45	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.45	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.45	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.45	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.45	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.45	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.45	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.45	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, c), b)
28.54/9.45	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.45	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.45	   A^2 -> H(U1(c, c), e)
28.54/9.45	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.45	   A^2 -> H(e, U1(c, b))
28.54/9.45	   A^2 -> H(e, U1(d, b))
28.54/9.45	   A^2 -> H(e, U1(b, c))
28.54/9.45	   A^2 -> H(e, U1(b, d))
28.54/9.45	   A^2 -> H(e, U1(c, c))
28.54/9.45	   A^2 -> H(e, f(e))
28.54/9.45	   A^2 -> H(e, f(k))
28.54/9.45	   A^2 -> H(e, U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.45	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.45	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.45	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.45	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.45	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.45	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.45	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.45	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.45	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.45	   A^2 -> H(f(e), b)
28.54/9.45	   A^2 -> H(f(e), U1(e, d))
28.54/9.45	   A^2 -> H(f(e), U1(d, e))
28.54/9.45	   A^2 -> H(f(e), c)
28.54/9.45	   A^2 -> H(f(e), U1(e, k))
28.54/9.45	   A^2 -> H(f(e), U1(k, e))
28.54/9.45	   A^2 -> H(f(e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.45	   A^2 -> H(f(k), b)
28.54/9.45	   A^2 -> H(f(k), U1(e, d))
28.54/9.45	   A^2 -> H(f(k), U1(d, e))
28.54/9.45	   A^2 -> H(f(k), c)
28.54/9.45	   A^2 -> H(f(k), U1(e, k))
28.54/9.45	   A^2 -> H(f(k), U1(k, e))
28.54/9.45	   A^2 -> H(f(k), e)
28.54/9.45	   A^2 -> H(f(c), d)
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.45	   A^2 -> H(U1(k, k), f(e))
28.54/9.45	   A^2 -> H(U1(k, k), f(k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.45	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.45	   A^2 -> H(U1(d, d), b)
28.54/9.45	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.45	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.45	   A^2 -> H(U1(d, d), c)
28.54/9.45	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.45	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.45	   A^2 -> H(U1(d, d), e)
28.54/9.45	   A^2 -> H(f(d), d)
28.54/9.45	   A^2 -> H(f(d), k)
28.54/9.45	   A^2 -> H(U1(c, c), c)
28.54/9.45	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.45	   A^2 -> H(f(c), k)
28.54/9.45	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.45	   A^2 -> H(f(k), U1(k, k))
28.54/9.45	
28.54/9.45	The TRS R consists of the following rules:
28.54/9.45	
28.54/9.45	   f(x) -> U1(x, x)
28.54/9.45	   U1(e, x) -> x
28.54/9.45	   a -> c
28.54/9.45	   a -> d
28.54/9.45	   b -> c
28.54/9.45	   b -> d
28.54/9.45	   d -> k
28.54/9.45	   c -> e
28.54/9.45	   c -> k
28.54/9.45	
28.54/9.45	Q is empty.
28.54/9.45	We have to consider all minimal (P,Q,R)-chains.
28.54/9.45	----------------------------------------
28.54/9.45	
28.54/9.45	(1079) TransformationProof (EQUIVALENT)
28.54/9.45	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.45	
28.54/9.45	   (A^2 -> H(U1(e, c), U1(c, k)),A^2 -> H(U1(e, c), U1(c, k)))
28.54/9.45	   (A^2 -> H(U1(k, c), U1(c, k)),A^2 -> H(U1(k, c), U1(c, k)))
28.54/9.45	   (A^2 -> H(U1(c, e), U1(c, k)),A^2 -> H(U1(c, e), U1(c, k)))
28.54/9.45	   (A^2 -> H(U1(c, k), U1(c, k)),A^2 -> H(U1(c, k), U1(c, k)))
28.54/9.45	   (A^2 -> H(U1(c, c), U1(e, k)),A^2 -> H(U1(c, c), U1(e, k)))
28.54/9.45	   (A^2 -> H(U1(c, c), U1(k, k)),A^2 -> H(U1(c, c), U1(k, k)))
28.54/9.45	
28.54/9.45	
28.54/9.45	----------------------------------------
28.54/9.45	
28.54/9.45	(1080)
28.54/9.45	Obligation:
28.54/9.45	Q DP problem:
28.54/9.45	The TRS P consists of the following rules:
28.54/9.45	
28.54/9.45	   H(x, x) -> G(x, x, f(k))
28.54/9.45	   G(d, x, x) -> A^2
28.54/9.45	   A^2 -> H(f(c), f(c))
28.54/9.45	   A^2 -> H(f(d), f(d))
28.54/9.45	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.45	   A^2 -> H(f(e), f(e))
28.54/9.45	   A^2 -> H(f(k), f(k))
28.54/9.45	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.45	   A^2 -> H(f(a), k)
28.54/9.45	   A^2 -> H(f(e), U1(e, e))
28.54/9.45	   A^2 -> H(f(c), e)
28.54/9.45	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.45	   A^2 -> H(f(d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.45	   A^2 -> H(d, U1(b, b))
28.54/9.45	   A^2 -> H(d, f(c))
28.54/9.45	   A^2 -> H(d, f(d))
28.54/9.45	   A^2 -> H(a, U1(c, b))
28.54/9.45	   A^2 -> H(a, U1(d, b))
28.54/9.45	   A^2 -> H(a, U1(b, c))
28.54/9.45	   A^2 -> H(a, U1(b, d))
28.54/9.45	   A^2 -> H(a, U1(c, c))
28.54/9.45	   A^2 -> H(a, f(e))
28.54/9.45	   A^2 -> H(a, f(k))
28.54/9.45	   A^2 -> H(a, U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.45	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.45	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.45	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.45	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.45	   A^2 -> H(U1(e, d), f(e))
28.54/9.45	   A^2 -> H(U1(e, d), f(k))
28.54/9.45	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.45	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.45	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.45	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.45	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.45	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.45	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.45	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.45	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.45	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.45	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.45	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.45	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.45	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.45	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.45	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.45	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, a), b)
28.54/9.45	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.45	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.45	   A^2 -> H(U1(c, a), c)
28.54/9.45	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.45	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.45	   A^2 -> H(U1(c, a), e)
28.54/9.45	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.45	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.45	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.45	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.45	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.45	   A^2 -> H(U1(d, e), f(e))
28.54/9.45	   A^2 -> H(U1(d, e), f(k))
28.54/9.45	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.45	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.45	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.45	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.45	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.45	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.45	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.45	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.45	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.45	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.45	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.45	   A^2 -> H(U1(d, a), b)
28.54/9.45	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.45	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.45	   A^2 -> H(U1(d, a), c)
28.54/9.45	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.45	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.45	   A^2 -> H(U1(d, a), e)
28.54/9.45	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.45	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.45	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.45	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.45	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.45	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.45	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.45	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.45	   A^2 -> H(U1(a, c), b)
28.54/9.45	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.45	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.45	   A^2 -> H(U1(a, c), c)
28.54/9.45	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.45	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.45	   A^2 -> H(U1(a, c), e)
28.54/9.45	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, d), b)
28.54/9.45	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.45	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.45	   A^2 -> H(U1(a, d), c)
28.54/9.45	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.45	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.45	   A^2 -> H(U1(a, d), e)
28.54/9.45	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, a), d)
28.54/9.45	   A^2 -> H(U1(a, a), k)
28.54/9.45	   A^2 -> H(k, U1(b, b))
28.54/9.45	   A^2 -> H(k, f(c))
28.54/9.45	   A^2 -> H(k, f(d))
28.54/9.45	   A^2 -> H(c, U1(c, b))
28.54/9.45	   A^2 -> H(c, U1(d, b))
28.54/9.45	   A^2 -> H(c, U1(b, c))
28.54/9.45	   A^2 -> H(c, U1(b, d))
28.54/9.45	   A^2 -> H(c, U1(c, c))
28.54/9.45	   A^2 -> H(c, f(e))
28.54/9.45	   A^2 -> H(c, f(k))
28.54/9.45	   A^2 -> H(c, U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.45	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.45	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.45	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.45	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.45	   A^2 -> H(U1(e, k), f(e))
28.54/9.45	   A^2 -> H(U1(e, k), f(k))
28.54/9.45	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.45	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.45	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.45	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.45	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.45	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.45	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.45	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.45	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.45	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.45	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.45	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.45	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.45	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.45	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.45	   A^2 -> H(U1(k, e), f(e))
28.54/9.45	   A^2 -> H(U1(k, e), f(k))
28.54/9.45	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.45	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.45	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.45	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.45	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.45	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.45	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.45	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.45	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, c), b)
28.54/9.45	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.45	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.45	   A^2 -> H(U1(c, c), e)
28.54/9.45	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.45	   A^2 -> H(e, U1(c, b))
28.54/9.45	   A^2 -> H(e, U1(d, b))
28.54/9.45	   A^2 -> H(e, U1(b, c))
28.54/9.45	   A^2 -> H(e, U1(b, d))
28.54/9.45	   A^2 -> H(e, U1(c, c))
28.54/9.45	   A^2 -> H(e, f(e))
28.54/9.45	   A^2 -> H(e, f(k))
28.54/9.45	   A^2 -> H(e, U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.45	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.45	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.45	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.45	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.45	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.45	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.45	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.45	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.45	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.45	   A^2 -> H(f(e), b)
28.54/9.45	   A^2 -> H(f(e), U1(e, d))
28.54/9.45	   A^2 -> H(f(e), U1(d, e))
28.54/9.45	   A^2 -> H(f(e), c)
28.54/9.45	   A^2 -> H(f(e), U1(e, k))
28.54/9.45	   A^2 -> H(f(e), U1(k, e))
28.54/9.45	   A^2 -> H(f(e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.45	   A^2 -> H(f(k), b)
28.54/9.45	   A^2 -> H(f(k), U1(e, d))
28.54/9.45	   A^2 -> H(f(k), U1(d, e))
28.54/9.45	   A^2 -> H(f(k), c)
28.54/9.45	   A^2 -> H(f(k), U1(e, k))
28.54/9.45	   A^2 -> H(f(k), U1(k, e))
28.54/9.45	   A^2 -> H(f(k), e)
28.54/9.45	   A^2 -> H(f(c), d)
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.45	   A^2 -> H(U1(k, k), f(e))
28.54/9.45	   A^2 -> H(U1(k, k), f(k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.45	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.45	   A^2 -> H(U1(d, d), b)
28.54/9.45	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.45	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.45	   A^2 -> H(U1(d, d), c)
28.54/9.45	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.45	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.45	   A^2 -> H(U1(d, d), e)
28.54/9.45	   A^2 -> H(f(d), d)
28.54/9.45	   A^2 -> H(f(d), k)
28.54/9.45	   A^2 -> H(U1(c, c), c)
28.54/9.45	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.45	   A^2 -> H(f(c), k)
28.54/9.45	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.45	   A^2 -> H(f(k), U1(k, k))
28.54/9.45	
28.54/9.45	The TRS R consists of the following rules:
28.54/9.45	
28.54/9.45	   f(x) -> U1(x, x)
28.54/9.45	   U1(e, x) -> x
28.54/9.45	   a -> c
28.54/9.45	   a -> d
28.54/9.45	   b -> c
28.54/9.45	   b -> d
28.54/9.45	   d -> k
28.54/9.45	   c -> e
28.54/9.45	   c -> k
28.54/9.45	
28.54/9.45	Q is empty.
28.54/9.45	We have to consider all minimal (P,Q,R)-chains.
28.54/9.45	----------------------------------------
28.54/9.45	
28.54/9.45	(1081) TransformationProof (EQUIVALENT)
28.54/9.45	By narrowing [LPAR04] the rule A^2 -> H(f(a), k) at position [] we obtained the following new rules [LPAR04]:
28.54/9.45	
28.54/9.45	   (A^2 -> H(U1(a, a), k),A^2 -> H(U1(a, a), k))
28.54/9.45	   (A^2 -> H(f(c), k),A^2 -> H(f(c), k))
28.54/9.45	   (A^2 -> H(f(d), k),A^2 -> H(f(d), k))
28.54/9.45	
28.54/9.45	
28.54/9.45	----------------------------------------
28.54/9.45	
28.54/9.45	(1082)
28.54/9.45	Obligation:
28.54/9.45	Q DP problem:
28.54/9.45	The TRS P consists of the following rules:
28.54/9.45	
28.54/9.45	   H(x, x) -> G(x, x, f(k))
28.54/9.45	   G(d, x, x) -> A^2
28.54/9.45	   A^2 -> H(f(c), f(c))
28.54/9.45	   A^2 -> H(f(d), f(d))
28.54/9.45	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.45	   A^2 -> H(f(e), f(e))
28.54/9.45	   A^2 -> H(f(k), f(k))
28.54/9.45	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.45	   A^2 -> H(f(e), U1(e, e))
28.54/9.45	   A^2 -> H(f(c), e)
28.54/9.45	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.45	   A^2 -> H(f(d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.45	   A^2 -> H(d, U1(b, b))
28.54/9.45	   A^2 -> H(d, f(c))
28.54/9.45	   A^2 -> H(d, f(d))
28.54/9.45	   A^2 -> H(a, U1(c, b))
28.54/9.45	   A^2 -> H(a, U1(d, b))
28.54/9.45	   A^2 -> H(a, U1(b, c))
28.54/9.45	   A^2 -> H(a, U1(b, d))
28.54/9.45	   A^2 -> H(a, U1(c, c))
28.54/9.45	   A^2 -> H(a, f(e))
28.54/9.45	   A^2 -> H(a, f(k))
28.54/9.45	   A^2 -> H(a, U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.45	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.45	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.45	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.45	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.45	   A^2 -> H(U1(e, d), f(e))
28.54/9.45	   A^2 -> H(U1(e, d), f(k))
28.54/9.45	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.45	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.45	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.45	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.45	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.45	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.45	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.45	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.45	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.45	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.45	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.45	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.45	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.45	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.45	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.45	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.45	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, a), b)
28.54/9.45	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.45	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.45	   A^2 -> H(U1(c, a), c)
28.54/9.45	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.45	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.45	   A^2 -> H(U1(c, a), e)
28.54/9.45	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.45	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.45	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.45	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.45	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.45	   A^2 -> H(U1(d, e), f(e))
28.54/9.45	   A^2 -> H(U1(d, e), f(k))
28.54/9.45	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.45	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.45	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.45	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.45	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.45	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.45	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.45	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.45	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.45	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.45	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.45	   A^2 -> H(U1(d, a), b)
28.54/9.45	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.45	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.45	   A^2 -> H(U1(d, a), c)
28.54/9.45	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.45	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.45	   A^2 -> H(U1(d, a), e)
28.54/9.45	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.45	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.45	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.45	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.45	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.45	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.45	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.45	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.45	   A^2 -> H(U1(a, c), b)
28.54/9.45	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.45	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.45	   A^2 -> H(U1(a, c), c)
28.54/9.45	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.45	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.45	   A^2 -> H(U1(a, c), e)
28.54/9.45	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, d), b)
28.54/9.45	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.45	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.45	   A^2 -> H(U1(a, d), c)
28.54/9.45	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.45	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.45	   A^2 -> H(U1(a, d), e)
28.54/9.45	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, a), d)
28.54/9.45	   A^2 -> H(U1(a, a), k)
28.54/9.45	   A^2 -> H(k, U1(b, b))
28.54/9.45	   A^2 -> H(k, f(c))
28.54/9.45	   A^2 -> H(k, f(d))
28.54/9.45	   A^2 -> H(c, U1(c, b))
28.54/9.45	   A^2 -> H(c, U1(d, b))
28.54/9.45	   A^2 -> H(c, U1(b, c))
28.54/9.45	   A^2 -> H(c, U1(b, d))
28.54/9.45	   A^2 -> H(c, U1(c, c))
28.54/9.45	   A^2 -> H(c, f(e))
28.54/9.45	   A^2 -> H(c, f(k))
28.54/9.45	   A^2 -> H(c, U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.45	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.45	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.45	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.45	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.45	   A^2 -> H(U1(e, k), f(e))
28.54/9.45	   A^2 -> H(U1(e, k), f(k))
28.54/9.45	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.45	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.45	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.45	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.45	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.45	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.45	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.45	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.45	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.45	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.45	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.45	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.45	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.45	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.45	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.45	   A^2 -> H(U1(k, e), f(e))
28.54/9.45	   A^2 -> H(U1(k, e), f(k))
28.54/9.45	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.45	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.45	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.45	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.45	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.45	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.45	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.45	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.45	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, c), b)
28.54/9.45	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.45	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.45	   A^2 -> H(U1(c, c), e)
28.54/9.45	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.45	   A^2 -> H(e, U1(c, b))
28.54/9.45	   A^2 -> H(e, U1(d, b))
28.54/9.45	   A^2 -> H(e, U1(b, c))
28.54/9.45	   A^2 -> H(e, U1(b, d))
28.54/9.45	   A^2 -> H(e, U1(c, c))
28.54/9.45	   A^2 -> H(e, f(e))
28.54/9.45	   A^2 -> H(e, f(k))
28.54/9.45	   A^2 -> H(e, U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.45	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.45	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.45	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.45	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.45	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.45	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.45	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.45	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.45	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.45	   A^2 -> H(f(e), b)
28.54/9.45	   A^2 -> H(f(e), U1(e, d))
28.54/9.45	   A^2 -> H(f(e), U1(d, e))
28.54/9.45	   A^2 -> H(f(e), c)
28.54/9.45	   A^2 -> H(f(e), U1(e, k))
28.54/9.45	   A^2 -> H(f(e), U1(k, e))
28.54/9.45	   A^2 -> H(f(e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.45	   A^2 -> H(f(k), b)
28.54/9.45	   A^2 -> H(f(k), U1(e, d))
28.54/9.45	   A^2 -> H(f(k), U1(d, e))
28.54/9.45	   A^2 -> H(f(k), c)
28.54/9.45	   A^2 -> H(f(k), U1(e, k))
28.54/9.45	   A^2 -> H(f(k), U1(k, e))
28.54/9.45	   A^2 -> H(f(k), e)
28.54/9.45	   A^2 -> H(f(c), d)
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.45	   A^2 -> H(U1(k, k), f(e))
28.54/9.45	   A^2 -> H(U1(k, k), f(k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.45	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.45	   A^2 -> H(U1(d, d), b)
28.54/9.45	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.45	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.45	   A^2 -> H(U1(d, d), c)
28.54/9.45	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.45	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.45	   A^2 -> H(U1(d, d), e)
28.54/9.45	   A^2 -> H(f(d), d)
28.54/9.45	   A^2 -> H(f(d), k)
28.54/9.45	   A^2 -> H(U1(c, c), c)
28.54/9.45	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.45	   A^2 -> H(f(c), k)
28.54/9.45	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.45	   A^2 -> H(f(k), U1(k, k))
28.54/9.45	
28.54/9.45	The TRS R consists of the following rules:
28.54/9.45	
28.54/9.45	   f(x) -> U1(x, x)
28.54/9.45	   U1(e, x) -> x
28.54/9.45	   a -> c
28.54/9.45	   a -> d
28.54/9.45	   b -> c
28.54/9.45	   b -> d
28.54/9.45	   d -> k
28.54/9.45	   c -> e
28.54/9.45	   c -> k
28.54/9.45	
28.54/9.45	Q is empty.
28.54/9.45	We have to consider all minimal (P,Q,R)-chains.
28.54/9.45	----------------------------------------
28.54/9.45	
28.54/9.45	(1083) TransformationProof (EQUIVALENT)
28.54/9.45	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.45	
28.54/9.45	   (A^2 -> H(U1(e, e), U1(e, e)),A^2 -> H(U1(e, e), U1(e, e)))
28.54/9.45	   (A^2 -> H(f(e), e),A^2 -> H(f(e), e))
28.54/9.45	
28.54/9.45	
28.54/9.45	----------------------------------------
28.54/9.45	
28.54/9.45	(1084)
28.54/9.45	Obligation:
28.54/9.45	Q DP problem:
28.54/9.45	The TRS P consists of the following rules:
28.54/9.45	
28.54/9.45	   H(x, x) -> G(x, x, f(k))
28.54/9.45	   G(d, x, x) -> A^2
28.54/9.45	   A^2 -> H(f(c), f(c))
28.54/9.45	   A^2 -> H(f(d), f(d))
28.54/9.45	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.45	   A^2 -> H(f(e), f(e))
28.54/9.45	   A^2 -> H(f(k), f(k))
28.54/9.45	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.45	   A^2 -> H(f(c), e)
28.54/9.45	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.45	   A^2 -> H(f(d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.45	   A^2 -> H(d, U1(b, b))
28.54/9.45	   A^2 -> H(d, f(c))
28.54/9.45	   A^2 -> H(d, f(d))
28.54/9.45	   A^2 -> H(a, U1(c, b))
28.54/9.45	   A^2 -> H(a, U1(d, b))
28.54/9.45	   A^2 -> H(a, U1(b, c))
28.54/9.45	   A^2 -> H(a, U1(b, d))
28.54/9.45	   A^2 -> H(a, U1(c, c))
28.54/9.45	   A^2 -> H(a, f(e))
28.54/9.45	   A^2 -> H(a, f(k))
28.54/9.45	   A^2 -> H(a, U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.45	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.45	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.45	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.45	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.45	   A^2 -> H(U1(e, d), f(e))
28.54/9.45	   A^2 -> H(U1(e, d), f(k))
28.54/9.45	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.45	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.45	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.45	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.45	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.45	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.45	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.45	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.45	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.45	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.45	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.45	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.45	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.45	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.45	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.45	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.45	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, a), b)
28.54/9.45	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.45	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.45	   A^2 -> H(U1(c, a), c)
28.54/9.45	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.45	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.45	   A^2 -> H(U1(c, a), e)
28.54/9.45	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.45	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.45	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.45	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.45	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.45	   A^2 -> H(U1(d, e), f(e))
28.54/9.45	   A^2 -> H(U1(d, e), f(k))
28.54/9.45	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.45	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.45	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.45	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.45	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.45	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.45	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.45	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.45	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.45	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.45	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.45	   A^2 -> H(U1(d, a), b)
28.54/9.45	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.45	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.45	   A^2 -> H(U1(d, a), c)
28.54/9.45	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.45	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.45	   A^2 -> H(U1(d, a), e)
28.54/9.45	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.45	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.45	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.45	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.45	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.45	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.45	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.45	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.45	   A^2 -> H(U1(a, c), b)
28.54/9.45	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.45	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.45	   A^2 -> H(U1(a, c), c)
28.54/9.45	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.45	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.45	   A^2 -> H(U1(a, c), e)
28.54/9.45	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, d), b)
28.54/9.45	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.45	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.45	   A^2 -> H(U1(a, d), c)
28.54/9.45	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.45	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.45	   A^2 -> H(U1(a, d), e)
28.54/9.45	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, a), d)
28.54/9.45	   A^2 -> H(U1(a, a), k)
28.54/9.45	   A^2 -> H(k, U1(b, b))
28.54/9.45	   A^2 -> H(k, f(c))
28.54/9.45	   A^2 -> H(k, f(d))
28.54/9.45	   A^2 -> H(c, U1(c, b))
28.54/9.45	   A^2 -> H(c, U1(d, b))
28.54/9.45	   A^2 -> H(c, U1(b, c))
28.54/9.45	   A^2 -> H(c, U1(b, d))
28.54/9.45	   A^2 -> H(c, U1(c, c))
28.54/9.45	   A^2 -> H(c, f(e))
28.54/9.45	   A^2 -> H(c, f(k))
28.54/9.45	   A^2 -> H(c, U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.45	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.45	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.45	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.45	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.45	   A^2 -> H(U1(e, k), f(e))
28.54/9.45	   A^2 -> H(U1(e, k), f(k))
28.54/9.45	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.45	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.45	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.45	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.45	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.45	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.45	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.45	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.45	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.45	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.45	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.45	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.45	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.45	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.45	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.45	   A^2 -> H(U1(k, e), f(e))
28.54/9.45	   A^2 -> H(U1(k, e), f(k))
28.54/9.45	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.45	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.45	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.45	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.45	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.45	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.45	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.45	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.45	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, c), b)
28.54/9.45	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.45	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.45	   A^2 -> H(U1(c, c), e)
28.54/9.45	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.45	   A^2 -> H(e, U1(c, b))
28.54/9.45	   A^2 -> H(e, U1(d, b))
28.54/9.45	   A^2 -> H(e, U1(b, c))
28.54/9.45	   A^2 -> H(e, U1(b, d))
28.54/9.45	   A^2 -> H(e, U1(c, c))
28.54/9.45	   A^2 -> H(e, f(e))
28.54/9.45	   A^2 -> H(e, f(k))
28.54/9.45	   A^2 -> H(e, U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.45	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.45	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.45	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.45	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.45	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.45	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.45	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.45	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.45	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.45	   A^2 -> H(f(e), b)
28.54/9.45	   A^2 -> H(f(e), U1(e, d))
28.54/9.45	   A^2 -> H(f(e), U1(d, e))
28.54/9.45	   A^2 -> H(f(e), c)
28.54/9.45	   A^2 -> H(f(e), U1(e, k))
28.54/9.45	   A^2 -> H(f(e), U1(k, e))
28.54/9.45	   A^2 -> H(f(e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.45	   A^2 -> H(f(k), b)
28.54/9.45	   A^2 -> H(f(k), U1(e, d))
28.54/9.45	   A^2 -> H(f(k), U1(d, e))
28.54/9.45	   A^2 -> H(f(k), c)
28.54/9.45	   A^2 -> H(f(k), U1(e, k))
28.54/9.45	   A^2 -> H(f(k), U1(k, e))
28.54/9.45	   A^2 -> H(f(k), e)
28.54/9.45	   A^2 -> H(f(c), d)
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.45	   A^2 -> H(U1(k, k), f(e))
28.54/9.45	   A^2 -> H(U1(k, k), f(k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.45	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.45	   A^2 -> H(U1(d, d), b)
28.54/9.45	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.45	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.45	   A^2 -> H(U1(d, d), c)
28.54/9.45	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.45	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.45	   A^2 -> H(U1(d, d), e)
28.54/9.45	   A^2 -> H(f(d), d)
28.54/9.45	   A^2 -> H(f(d), k)
28.54/9.45	   A^2 -> H(U1(c, c), c)
28.54/9.45	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.45	   A^2 -> H(f(c), k)
28.54/9.45	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.45	   A^2 -> H(f(k), U1(k, k))
28.54/9.45	   A^2 -> H(f(e), e)
28.54/9.45	
28.54/9.45	The TRS R consists of the following rules:
28.54/9.45	
28.54/9.45	   f(x) -> U1(x, x)
28.54/9.45	   U1(e, x) -> x
28.54/9.45	   a -> c
28.54/9.45	   a -> d
28.54/9.45	   b -> c
28.54/9.45	   b -> d
28.54/9.45	   d -> k
28.54/9.45	   c -> e
28.54/9.45	   c -> k
28.54/9.45	
28.54/9.45	Q is empty.
28.54/9.45	We have to consider all minimal (P,Q,R)-chains.
28.54/9.45	----------------------------------------
28.54/9.45	
28.54/9.45	(1085) TransformationProof (EQUIVALENT)
28.54/9.45	By narrowing [LPAR04] the rule A^2 -> H(f(c), e) at position [] we obtained the following new rules [LPAR04]:
28.54/9.45	
28.54/9.45	   (A^2 -> H(U1(c, c), e),A^2 -> H(U1(c, c), e))
28.54/9.45	   (A^2 -> H(f(e), e),A^2 -> H(f(e), e))
28.54/9.45	   (A^2 -> H(f(k), e),A^2 -> H(f(k), e))
28.54/9.45	
28.54/9.45	
28.54/9.45	----------------------------------------
28.54/9.45	
28.54/9.45	(1086)
28.54/9.45	Obligation:
28.54/9.45	Q DP problem:
28.54/9.45	The TRS P consists of the following rules:
28.54/9.45	
28.54/9.45	   H(x, x) -> G(x, x, f(k))
28.54/9.45	   G(d, x, x) -> A^2
28.54/9.45	   A^2 -> H(f(c), f(c))
28.54/9.45	   A^2 -> H(f(d), f(d))
28.54/9.45	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.45	   A^2 -> H(f(e), f(e))
28.54/9.45	   A^2 -> H(f(k), f(k))
28.54/9.45	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.45	   A^2 -> H(U1(d, d), U1(k, d))
28.54/9.45	   A^2 -> H(f(d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.45	   A^2 -> H(d, U1(b, b))
28.54/9.45	   A^2 -> H(d, f(c))
28.54/9.45	   A^2 -> H(d, f(d))
28.54/9.45	   A^2 -> H(a, U1(c, b))
28.54/9.45	   A^2 -> H(a, U1(d, b))
28.54/9.45	   A^2 -> H(a, U1(b, c))
28.54/9.45	   A^2 -> H(a, U1(b, d))
28.54/9.45	   A^2 -> H(a, U1(c, c))
28.54/9.45	   A^2 -> H(a, f(e))
28.54/9.45	   A^2 -> H(a, f(k))
28.54/9.45	   A^2 -> H(a, U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.45	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.45	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.45	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.45	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.45	   A^2 -> H(U1(e, d), f(e))
28.54/9.45	   A^2 -> H(U1(e, d), f(k))
28.54/9.45	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.45	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.45	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.45	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.45	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.45	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.45	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.45	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.45	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.45	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.45	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.45	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.45	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.45	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.45	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.45	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.45	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, a), b)
28.54/9.45	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.45	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.45	   A^2 -> H(U1(c, a), c)
28.54/9.45	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.45	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.45	   A^2 -> H(U1(c, a), e)
28.54/9.45	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.45	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.45	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.45	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.45	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.45	   A^2 -> H(U1(d, e), f(e))
28.54/9.45	   A^2 -> H(U1(d, e), f(k))
28.54/9.45	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.45	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.45	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.45	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.45	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.45	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.45	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.45	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.45	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.45	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.45	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.45	   A^2 -> H(U1(d, a), b)
28.54/9.45	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.45	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.45	   A^2 -> H(U1(d, a), c)
28.54/9.45	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.45	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.45	   A^2 -> H(U1(d, a), e)
28.54/9.45	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.45	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.45	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.45	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.45	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.45	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.45	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.45	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.45	   A^2 -> H(U1(a, c), b)
28.54/9.45	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.45	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.45	   A^2 -> H(U1(a, c), c)
28.54/9.45	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.45	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.45	   A^2 -> H(U1(a, c), e)
28.54/9.45	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, d), b)
28.54/9.45	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.45	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.45	   A^2 -> H(U1(a, d), c)
28.54/9.45	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.45	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.45	   A^2 -> H(U1(a, d), e)
28.54/9.45	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(a, a), d)
28.54/9.45	   A^2 -> H(U1(a, a), k)
28.54/9.45	   A^2 -> H(k, U1(b, b))
28.54/9.45	   A^2 -> H(k, f(c))
28.54/9.45	   A^2 -> H(k, f(d))
28.54/9.45	   A^2 -> H(c, U1(c, b))
28.54/9.45	   A^2 -> H(c, U1(d, b))
28.54/9.45	   A^2 -> H(c, U1(b, c))
28.54/9.45	   A^2 -> H(c, U1(b, d))
28.54/9.45	   A^2 -> H(c, U1(c, c))
28.54/9.45	   A^2 -> H(c, f(e))
28.54/9.45	   A^2 -> H(c, f(k))
28.54/9.45	   A^2 -> H(c, U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.45	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.45	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.45	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.45	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.45	   A^2 -> H(U1(e, k), f(e))
28.54/9.45	   A^2 -> H(U1(e, k), f(k))
28.54/9.45	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.45	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.45	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.45	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.45	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.45	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.45	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.45	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.45	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.45	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.45	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.45	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.45	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.45	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.45	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.45	   A^2 -> H(U1(k, e), f(e))
28.54/9.45	   A^2 -> H(U1(k, e), f(k))
28.54/9.45	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.45	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.45	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.45	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.45	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.45	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.45	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.45	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.45	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.45	   A^2 -> H(U1(c, c), b)
28.54/9.45	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.45	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.45	   A^2 -> H(U1(c, c), e)
28.54/9.45	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.45	   A^2 -> H(e, U1(c, b))
28.54/9.45	   A^2 -> H(e, U1(d, b))
28.54/9.45	   A^2 -> H(e, U1(b, c))
28.54/9.45	   A^2 -> H(e, U1(b, d))
28.54/9.45	   A^2 -> H(e, U1(c, c))
28.54/9.45	   A^2 -> H(e, f(e))
28.54/9.45	   A^2 -> H(e, f(k))
28.54/9.45	   A^2 -> H(e, U1(d, d))
28.54/9.45	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.45	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.45	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.45	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.45	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.45	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.45	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.45	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.45	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.45	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.45	   A^2 -> H(f(e), b)
28.54/9.45	   A^2 -> H(f(e), U1(e, d))
28.54/9.45	   A^2 -> H(f(e), U1(d, e))
28.54/9.45	   A^2 -> H(f(e), c)
28.54/9.45	   A^2 -> H(f(e), U1(e, k))
28.54/9.45	   A^2 -> H(f(e), U1(k, e))
28.54/9.45	   A^2 -> H(f(e), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.45	   A^2 -> H(f(k), b)
28.54/9.45	   A^2 -> H(f(k), U1(e, d))
28.54/9.45	   A^2 -> H(f(k), U1(d, e))
28.54/9.45	   A^2 -> H(f(k), c)
28.54/9.45	   A^2 -> H(f(k), U1(e, k))
28.54/9.45	   A^2 -> H(f(k), U1(k, e))
28.54/9.45	   A^2 -> H(f(k), e)
28.54/9.45	   A^2 -> H(f(c), d)
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.45	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.45	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.45	   A^2 -> H(U1(k, k), f(e))
28.54/9.45	   A^2 -> H(U1(k, k), f(k))
28.54/9.45	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.45	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.45	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.45	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.45	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.45	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.45	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.45	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.45	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.45	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.45	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.45	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.45	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.45	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.45	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.45	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.45	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.45	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.45	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.45	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.45	   A^2 -> H(U1(d, d), b)
28.54/9.45	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.45	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.45	   A^2 -> H(U1(d, d), c)
28.54/9.45	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.45	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.45	   A^2 -> H(U1(d, d), e)
28.54/9.45	   A^2 -> H(f(d), d)
28.54/9.45	   A^2 -> H(f(d), k)
28.54/9.45	   A^2 -> H(U1(c, c), c)
28.54/9.45	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.45	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.45	   A^2 -> H(f(c), k)
28.54/9.45	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.45	   A^2 -> H(f(k), U1(k, k))
28.54/9.45	   A^2 -> H(f(e), e)
28.54/9.45	
28.54/9.45	The TRS R consists of the following rules:
28.54/9.45	
28.54/9.45	   f(x) -> U1(x, x)
28.54/9.45	   U1(e, x) -> x
28.54/9.45	   a -> c
28.54/9.45	   a -> d
28.54/9.45	   b -> c
28.54/9.45	   b -> d
28.54/9.45	   d -> k
28.54/9.45	   c -> e
28.54/9.45	   c -> k
28.54/9.45	
28.54/9.45	Q is empty.
28.54/9.45	We have to consider all minimal (P,Q,R)-chains.
28.54/9.45	----------------------------------------
28.54/9.45	
28.54/9.45	(1087) TransformationProof (EQUIVALENT)
28.54/9.46	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.46	
28.54/9.46	   (A^2 -> H(U1(k, d), U1(k, d)),A^2 -> H(U1(k, d), U1(k, d)))
28.54/9.46	   (A^2 -> H(U1(d, k), U1(k, d)),A^2 -> H(U1(d, k), U1(k, d)))
28.54/9.46	   (A^2 -> H(U1(d, d), U1(k, k)),A^2 -> H(U1(d, d), U1(k, k)))
28.54/9.46	
28.54/9.46	
28.54/9.46	----------------------------------------
28.54/9.46	
28.54/9.46	(1088)
28.54/9.46	Obligation:
28.54/9.46	Q DP problem:
28.54/9.46	The TRS P consists of the following rules:
28.54/9.46	
28.54/9.46	   H(x, x) -> G(x, x, f(k))
28.54/9.46	   G(d, x, x) -> A^2
28.54/9.46	   A^2 -> H(f(c), f(c))
28.54/9.46	   A^2 -> H(f(d), f(d))
28.54/9.46	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.46	   A^2 -> H(f(e), f(e))
28.54/9.46	   A^2 -> H(f(k), f(k))
28.54/9.46	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.46	   A^2 -> H(f(d), U1(k, k))
28.54/9.46	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.46	   A^2 -> H(d, U1(b, b))
28.54/9.46	   A^2 -> H(d, f(c))
28.54/9.46	   A^2 -> H(d, f(d))
28.54/9.46	   A^2 -> H(a, U1(c, b))
28.54/9.46	   A^2 -> H(a, U1(d, b))
28.54/9.46	   A^2 -> H(a, U1(b, c))
28.54/9.46	   A^2 -> H(a, U1(b, d))
28.54/9.46	   A^2 -> H(a, U1(c, c))
28.54/9.46	   A^2 -> H(a, f(e))
28.54/9.46	   A^2 -> H(a, f(k))
28.54/9.46	   A^2 -> H(a, U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.46	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.46	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.46	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.46	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.46	   A^2 -> H(U1(e, d), f(e))
28.54/9.46	   A^2 -> H(U1(e, d), f(k))
28.54/9.46	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.46	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.46	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.46	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.46	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.46	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.46	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.46	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.46	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.46	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.46	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.46	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.46	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.46	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.46	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.46	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.46	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, a), b)
28.54/9.46	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.46	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.46	   A^2 -> H(U1(c, a), c)
28.54/9.46	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.46	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.46	   A^2 -> H(U1(c, a), e)
28.54/9.46	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.46	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.46	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.46	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.46	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.46	   A^2 -> H(U1(d, e), f(e))
28.54/9.46	   A^2 -> H(U1(d, e), f(k))
28.54/9.46	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.46	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.46	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.46	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.46	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.46	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.46	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.46	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.46	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.46	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.46	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.46	   A^2 -> H(U1(d, a), b)
28.54/9.46	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.46	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.46	   A^2 -> H(U1(d, a), c)
28.54/9.46	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.46	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.46	   A^2 -> H(U1(d, a), e)
28.54/9.46	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.46	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.46	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.46	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.46	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.46	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.46	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.46	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.46	   A^2 -> H(U1(a, c), b)
28.54/9.46	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.46	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.46	   A^2 -> H(U1(a, c), c)
28.54/9.46	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.46	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.46	   A^2 -> H(U1(a, c), e)
28.54/9.46	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, d), b)
28.54/9.46	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.46	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.46	   A^2 -> H(U1(a, d), c)
28.54/9.46	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.46	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.46	   A^2 -> H(U1(a, d), e)
28.54/9.46	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, a), d)
28.54/9.46	   A^2 -> H(U1(a, a), k)
28.54/9.46	   A^2 -> H(k, U1(b, b))
28.54/9.46	   A^2 -> H(k, f(c))
28.54/9.46	   A^2 -> H(k, f(d))
28.54/9.46	   A^2 -> H(c, U1(c, b))
28.54/9.46	   A^2 -> H(c, U1(d, b))
28.54/9.46	   A^2 -> H(c, U1(b, c))
28.54/9.46	   A^2 -> H(c, U1(b, d))
28.54/9.46	   A^2 -> H(c, U1(c, c))
28.54/9.46	   A^2 -> H(c, f(e))
28.54/9.46	   A^2 -> H(c, f(k))
28.54/9.46	   A^2 -> H(c, U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.46	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.46	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.46	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.46	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.46	   A^2 -> H(U1(e, k), f(e))
28.54/9.46	   A^2 -> H(U1(e, k), f(k))
28.54/9.46	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.46	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.46	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.46	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.46	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.46	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.46	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.46	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.46	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.46	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.46	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.46	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.46	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.46	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.46	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.46	   A^2 -> H(U1(k, e), f(e))
28.54/9.46	   A^2 -> H(U1(k, e), f(k))
28.54/9.46	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.46	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.46	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.46	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.46	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.46	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.46	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.46	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.46	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, c), b)
28.54/9.46	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.46	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.46	   A^2 -> H(U1(c, c), e)
28.54/9.46	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.46	   A^2 -> H(e, U1(c, b))
28.54/9.46	   A^2 -> H(e, U1(d, b))
28.54/9.46	   A^2 -> H(e, U1(b, c))
28.54/9.46	   A^2 -> H(e, U1(b, d))
28.54/9.46	   A^2 -> H(e, U1(c, c))
28.54/9.46	   A^2 -> H(e, f(e))
28.54/9.46	   A^2 -> H(e, f(k))
28.54/9.46	   A^2 -> H(e, U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.46	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.46	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.46	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.46	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.46	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.46	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.46	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.46	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.46	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.46	   A^2 -> H(f(e), b)
28.54/9.46	   A^2 -> H(f(e), U1(e, d))
28.54/9.46	   A^2 -> H(f(e), U1(d, e))
28.54/9.46	   A^2 -> H(f(e), c)
28.54/9.46	   A^2 -> H(f(e), U1(e, k))
28.54/9.46	   A^2 -> H(f(e), U1(k, e))
28.54/9.46	   A^2 -> H(f(e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.46	   A^2 -> H(f(k), b)
28.54/9.46	   A^2 -> H(f(k), U1(e, d))
28.54/9.46	   A^2 -> H(f(k), U1(d, e))
28.54/9.46	   A^2 -> H(f(k), c)
28.54/9.46	   A^2 -> H(f(k), U1(e, k))
28.54/9.46	   A^2 -> H(f(k), U1(k, e))
28.54/9.46	   A^2 -> H(f(k), e)
28.54/9.46	   A^2 -> H(f(c), d)
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.46	   A^2 -> H(U1(k, k), f(e))
28.54/9.46	   A^2 -> H(U1(k, k), f(k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.46	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.46	   A^2 -> H(U1(d, d), b)
28.54/9.46	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.46	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.46	   A^2 -> H(U1(d, d), c)
28.54/9.46	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.46	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.46	   A^2 -> H(U1(d, d), e)
28.54/9.46	   A^2 -> H(f(d), d)
28.54/9.46	   A^2 -> H(f(d), k)
28.54/9.46	   A^2 -> H(U1(c, c), c)
28.54/9.46	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.46	   A^2 -> H(f(c), k)
28.54/9.46	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.46	   A^2 -> H(f(k), U1(k, k))
28.54/9.46	   A^2 -> H(f(e), e)
28.54/9.46	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.46	
28.54/9.46	The TRS R consists of the following rules:
28.54/9.46	
28.54/9.46	   f(x) -> U1(x, x)
28.54/9.46	   U1(e, x) -> x
28.54/9.46	   a -> c
28.54/9.46	   a -> d
28.54/9.46	   b -> c
28.54/9.46	   b -> d
28.54/9.46	   d -> k
28.54/9.46	   c -> e
28.54/9.46	   c -> k
28.54/9.46	
28.54/9.46	Q is empty.
28.54/9.46	We have to consider all minimal (P,Q,R)-chains.
28.54/9.46	----------------------------------------
28.54/9.46	
28.54/9.46	(1089) TransformationProof (EQUIVALENT)
28.54/9.46	By narrowing [LPAR04] the rule A^2 -> H(f(d), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.46	
28.54/9.46	   (A^2 -> H(U1(d, d), U1(k, k)),A^2 -> H(U1(d, d), U1(k, k)))
28.54/9.46	   (A^2 -> H(f(k), U1(k, k)),A^2 -> H(f(k), U1(k, k)))
28.54/9.46	
28.54/9.46	
28.54/9.46	----------------------------------------
28.54/9.46	
28.54/9.46	(1090)
28.54/9.46	Obligation:
28.54/9.46	Q DP problem:
28.54/9.46	The TRS P consists of the following rules:
28.54/9.46	
28.54/9.46	   H(x, x) -> G(x, x, f(k))
28.54/9.46	   G(d, x, x) -> A^2
28.54/9.46	   A^2 -> H(f(c), f(c))
28.54/9.46	   A^2 -> H(f(d), f(d))
28.54/9.46	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.46	   A^2 -> H(f(e), f(e))
28.54/9.46	   A^2 -> H(f(k), f(k))
28.54/9.46	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.46	   A^2 -> H(U1(d, d), U1(d, k))
28.54/9.46	   A^2 -> H(d, U1(b, b))
28.54/9.46	   A^2 -> H(d, f(c))
28.54/9.46	   A^2 -> H(d, f(d))
28.54/9.46	   A^2 -> H(a, U1(c, b))
28.54/9.46	   A^2 -> H(a, U1(d, b))
28.54/9.46	   A^2 -> H(a, U1(b, c))
28.54/9.46	   A^2 -> H(a, U1(b, d))
28.54/9.46	   A^2 -> H(a, U1(c, c))
28.54/9.46	   A^2 -> H(a, f(e))
28.54/9.46	   A^2 -> H(a, f(k))
28.54/9.46	   A^2 -> H(a, U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.46	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.46	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.46	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.46	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.46	   A^2 -> H(U1(e, d), f(e))
28.54/9.46	   A^2 -> H(U1(e, d), f(k))
28.54/9.46	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.46	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.46	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.46	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.46	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.46	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.46	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.46	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.46	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.46	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.46	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.46	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.46	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.46	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.46	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.46	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.46	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, a), b)
28.54/9.46	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.46	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.46	   A^2 -> H(U1(c, a), c)
28.54/9.46	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.46	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.46	   A^2 -> H(U1(c, a), e)
28.54/9.46	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.46	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.46	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.46	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.46	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.46	   A^2 -> H(U1(d, e), f(e))
28.54/9.46	   A^2 -> H(U1(d, e), f(k))
28.54/9.46	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.46	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.46	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.46	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.46	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.46	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.46	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.46	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.46	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.46	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.46	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.46	   A^2 -> H(U1(d, a), b)
28.54/9.46	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.46	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.46	   A^2 -> H(U1(d, a), c)
28.54/9.46	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.46	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.46	   A^2 -> H(U1(d, a), e)
28.54/9.46	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.46	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.46	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.46	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.46	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.46	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.46	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.46	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.46	   A^2 -> H(U1(a, c), b)
28.54/9.46	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.46	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.46	   A^2 -> H(U1(a, c), c)
28.54/9.46	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.46	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.46	   A^2 -> H(U1(a, c), e)
28.54/9.46	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, d), b)
28.54/9.46	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.46	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.46	   A^2 -> H(U1(a, d), c)
28.54/9.46	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.46	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.46	   A^2 -> H(U1(a, d), e)
28.54/9.46	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, a), d)
28.54/9.46	   A^2 -> H(U1(a, a), k)
28.54/9.46	   A^2 -> H(k, U1(b, b))
28.54/9.46	   A^2 -> H(k, f(c))
28.54/9.46	   A^2 -> H(k, f(d))
28.54/9.46	   A^2 -> H(c, U1(c, b))
28.54/9.46	   A^2 -> H(c, U1(d, b))
28.54/9.46	   A^2 -> H(c, U1(b, c))
28.54/9.46	   A^2 -> H(c, U1(b, d))
28.54/9.46	   A^2 -> H(c, U1(c, c))
28.54/9.46	   A^2 -> H(c, f(e))
28.54/9.46	   A^2 -> H(c, f(k))
28.54/9.46	   A^2 -> H(c, U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.46	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.46	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.46	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.46	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.46	   A^2 -> H(U1(e, k), f(e))
28.54/9.46	   A^2 -> H(U1(e, k), f(k))
28.54/9.46	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.46	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.46	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.46	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.46	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.46	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.46	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.46	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.46	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.46	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.46	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.46	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.46	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.46	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.46	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.46	   A^2 -> H(U1(k, e), f(e))
28.54/9.46	   A^2 -> H(U1(k, e), f(k))
28.54/9.46	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.46	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.46	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.46	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.46	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.46	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.46	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.46	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.46	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, c), b)
28.54/9.46	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.46	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.46	   A^2 -> H(U1(c, c), e)
28.54/9.46	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.46	   A^2 -> H(e, U1(c, b))
28.54/9.46	   A^2 -> H(e, U1(d, b))
28.54/9.46	   A^2 -> H(e, U1(b, c))
28.54/9.46	   A^2 -> H(e, U1(b, d))
28.54/9.46	   A^2 -> H(e, U1(c, c))
28.54/9.46	   A^2 -> H(e, f(e))
28.54/9.46	   A^2 -> H(e, f(k))
28.54/9.46	   A^2 -> H(e, U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.46	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.46	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.46	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.46	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.46	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.46	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.46	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.46	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.46	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.46	   A^2 -> H(f(e), b)
28.54/9.46	   A^2 -> H(f(e), U1(e, d))
28.54/9.46	   A^2 -> H(f(e), U1(d, e))
28.54/9.46	   A^2 -> H(f(e), c)
28.54/9.46	   A^2 -> H(f(e), U1(e, k))
28.54/9.46	   A^2 -> H(f(e), U1(k, e))
28.54/9.46	   A^2 -> H(f(e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.46	   A^2 -> H(f(k), b)
28.54/9.46	   A^2 -> H(f(k), U1(e, d))
28.54/9.46	   A^2 -> H(f(k), U1(d, e))
28.54/9.46	   A^2 -> H(f(k), c)
28.54/9.46	   A^2 -> H(f(k), U1(e, k))
28.54/9.46	   A^2 -> H(f(k), U1(k, e))
28.54/9.46	   A^2 -> H(f(k), e)
28.54/9.46	   A^2 -> H(f(c), d)
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.46	   A^2 -> H(U1(k, k), f(e))
28.54/9.46	   A^2 -> H(U1(k, k), f(k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.46	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.46	   A^2 -> H(U1(d, d), b)
28.54/9.46	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.46	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.46	   A^2 -> H(U1(d, d), c)
28.54/9.46	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.46	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.46	   A^2 -> H(U1(d, d), e)
28.54/9.46	   A^2 -> H(f(d), d)
28.54/9.46	   A^2 -> H(f(d), k)
28.54/9.46	   A^2 -> H(U1(c, c), c)
28.54/9.46	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.46	   A^2 -> H(f(c), k)
28.54/9.46	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.46	   A^2 -> H(f(k), U1(k, k))
28.54/9.46	   A^2 -> H(f(e), e)
28.54/9.46	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.46	
28.54/9.46	The TRS R consists of the following rules:
28.54/9.46	
28.54/9.46	   f(x) -> U1(x, x)
28.54/9.46	   U1(e, x) -> x
28.54/9.46	   a -> c
28.54/9.46	   a -> d
28.54/9.46	   b -> c
28.54/9.46	   b -> d
28.54/9.46	   d -> k
28.54/9.46	   c -> e
28.54/9.46	   c -> k
28.54/9.46	
28.54/9.46	Q is empty.
28.54/9.46	We have to consider all minimal (P,Q,R)-chains.
28.54/9.46	----------------------------------------
28.54/9.46	
28.54/9.46	(1091) TransformationProof (EQUIVALENT)
28.54/9.46	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.46	
28.54/9.46	   (A^2 -> H(U1(k, d), U1(d, k)),A^2 -> H(U1(k, d), U1(d, k)))
28.54/9.46	   (A^2 -> H(U1(d, k), U1(d, k)),A^2 -> H(U1(d, k), U1(d, k)))
28.54/9.46	   (A^2 -> H(U1(d, d), U1(k, k)),A^2 -> H(U1(d, d), U1(k, k)))
28.54/9.46	
28.54/9.46	
28.54/9.46	----------------------------------------
28.54/9.46	
28.54/9.46	(1092)
28.54/9.46	Obligation:
28.54/9.46	Q DP problem:
28.54/9.46	The TRS P consists of the following rules:
28.54/9.46	
28.54/9.46	   H(x, x) -> G(x, x, f(k))
28.54/9.46	   G(d, x, x) -> A^2
28.54/9.46	   A^2 -> H(f(c), f(c))
28.54/9.46	   A^2 -> H(f(d), f(d))
28.54/9.46	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.46	   A^2 -> H(f(e), f(e))
28.54/9.46	   A^2 -> H(f(k), f(k))
28.54/9.46	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.46	   A^2 -> H(d, U1(b, b))
28.54/9.46	   A^2 -> H(d, f(c))
28.54/9.46	   A^2 -> H(d, f(d))
28.54/9.46	   A^2 -> H(a, U1(c, b))
28.54/9.46	   A^2 -> H(a, U1(d, b))
28.54/9.46	   A^2 -> H(a, U1(b, c))
28.54/9.46	   A^2 -> H(a, U1(b, d))
28.54/9.46	   A^2 -> H(a, U1(c, c))
28.54/9.46	   A^2 -> H(a, f(e))
28.54/9.46	   A^2 -> H(a, f(k))
28.54/9.46	   A^2 -> H(a, U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.46	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.46	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.46	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.46	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.46	   A^2 -> H(U1(e, d), f(e))
28.54/9.46	   A^2 -> H(U1(e, d), f(k))
28.54/9.46	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.46	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.46	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.46	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.46	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.46	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.46	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.46	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.46	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.46	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.46	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.46	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.46	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.46	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.46	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.46	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.46	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, a), b)
28.54/9.46	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.46	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.46	   A^2 -> H(U1(c, a), c)
28.54/9.46	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.46	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.46	   A^2 -> H(U1(c, a), e)
28.54/9.46	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.46	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.46	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.46	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.46	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.46	   A^2 -> H(U1(d, e), f(e))
28.54/9.46	   A^2 -> H(U1(d, e), f(k))
28.54/9.46	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.46	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.46	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.46	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.46	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.46	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.46	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.46	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.46	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.46	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.46	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.46	   A^2 -> H(U1(d, a), b)
28.54/9.46	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.46	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.46	   A^2 -> H(U1(d, a), c)
28.54/9.46	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.46	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.46	   A^2 -> H(U1(d, a), e)
28.54/9.46	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.46	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.46	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.46	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.46	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.46	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.46	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.46	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.46	   A^2 -> H(U1(a, c), b)
28.54/9.46	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.46	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.46	   A^2 -> H(U1(a, c), c)
28.54/9.46	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.46	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.46	   A^2 -> H(U1(a, c), e)
28.54/9.46	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, d), b)
28.54/9.46	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.46	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.46	   A^2 -> H(U1(a, d), c)
28.54/9.46	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.46	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.46	   A^2 -> H(U1(a, d), e)
28.54/9.46	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, a), d)
28.54/9.46	   A^2 -> H(U1(a, a), k)
28.54/9.46	   A^2 -> H(k, U1(b, b))
28.54/9.46	   A^2 -> H(k, f(c))
28.54/9.46	   A^2 -> H(k, f(d))
28.54/9.46	   A^2 -> H(c, U1(c, b))
28.54/9.46	   A^2 -> H(c, U1(d, b))
28.54/9.46	   A^2 -> H(c, U1(b, c))
28.54/9.46	   A^2 -> H(c, U1(b, d))
28.54/9.46	   A^2 -> H(c, U1(c, c))
28.54/9.46	   A^2 -> H(c, f(e))
28.54/9.46	   A^2 -> H(c, f(k))
28.54/9.46	   A^2 -> H(c, U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.46	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.46	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.46	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.46	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.46	   A^2 -> H(U1(e, k), f(e))
28.54/9.46	   A^2 -> H(U1(e, k), f(k))
28.54/9.46	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.46	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.46	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.46	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.46	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.46	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.46	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.46	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.46	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.46	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.46	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.46	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.46	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.46	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.46	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.46	   A^2 -> H(U1(k, e), f(e))
28.54/9.46	   A^2 -> H(U1(k, e), f(k))
28.54/9.46	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.46	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.46	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.46	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.46	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.46	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.46	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.46	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.46	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, c), b)
28.54/9.46	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.46	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.46	   A^2 -> H(U1(c, c), e)
28.54/9.46	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.46	   A^2 -> H(e, U1(c, b))
28.54/9.46	   A^2 -> H(e, U1(d, b))
28.54/9.46	   A^2 -> H(e, U1(b, c))
28.54/9.46	   A^2 -> H(e, U1(b, d))
28.54/9.46	   A^2 -> H(e, U1(c, c))
28.54/9.46	   A^2 -> H(e, f(e))
28.54/9.46	   A^2 -> H(e, f(k))
28.54/9.46	   A^2 -> H(e, U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.46	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.46	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.46	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.46	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.46	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.46	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.46	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.46	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.46	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.46	   A^2 -> H(f(e), b)
28.54/9.46	   A^2 -> H(f(e), U1(e, d))
28.54/9.46	   A^2 -> H(f(e), U1(d, e))
28.54/9.46	   A^2 -> H(f(e), c)
28.54/9.46	   A^2 -> H(f(e), U1(e, k))
28.54/9.46	   A^2 -> H(f(e), U1(k, e))
28.54/9.46	   A^2 -> H(f(e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.46	   A^2 -> H(f(k), b)
28.54/9.46	   A^2 -> H(f(k), U1(e, d))
28.54/9.46	   A^2 -> H(f(k), U1(d, e))
28.54/9.46	   A^2 -> H(f(k), c)
28.54/9.46	   A^2 -> H(f(k), U1(e, k))
28.54/9.46	   A^2 -> H(f(k), U1(k, e))
28.54/9.46	   A^2 -> H(f(k), e)
28.54/9.46	   A^2 -> H(f(c), d)
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.46	   A^2 -> H(U1(k, k), f(e))
28.54/9.46	   A^2 -> H(U1(k, k), f(k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.46	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.46	   A^2 -> H(U1(d, d), b)
28.54/9.46	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.46	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.46	   A^2 -> H(U1(d, d), c)
28.54/9.46	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.46	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.46	   A^2 -> H(U1(d, d), e)
28.54/9.46	   A^2 -> H(f(d), d)
28.54/9.46	   A^2 -> H(f(d), k)
28.54/9.46	   A^2 -> H(U1(c, c), c)
28.54/9.46	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.46	   A^2 -> H(f(c), k)
28.54/9.46	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.46	   A^2 -> H(f(k), U1(k, k))
28.54/9.46	   A^2 -> H(f(e), e)
28.54/9.46	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.46	
28.54/9.46	The TRS R consists of the following rules:
28.54/9.46	
28.54/9.46	   f(x) -> U1(x, x)
28.54/9.46	   U1(e, x) -> x
28.54/9.46	   a -> c
28.54/9.46	   a -> d
28.54/9.46	   b -> c
28.54/9.46	   b -> d
28.54/9.46	   d -> k
28.54/9.46	   c -> e
28.54/9.46	   c -> k
28.54/9.46	
28.54/9.46	Q is empty.
28.54/9.46	We have to consider all minimal (P,Q,R)-chains.
28.54/9.46	----------------------------------------
28.54/9.46	
28.54/9.46	(1093) TransformationProof (EQUIVALENT)
28.54/9.46	By narrowing [LPAR04] the rule A^2 -> H(d, U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.46	
28.54/9.46	   (A^2 -> H(k, U1(b, b)),A^2 -> H(k, U1(b, b)))
28.54/9.46	   (A^2 -> H(d, U1(c, b)),A^2 -> H(d, U1(c, b)))
28.54/9.46	   (A^2 -> H(d, U1(d, b)),A^2 -> H(d, U1(d, b)))
28.54/9.46	   (A^2 -> H(d, U1(b, c)),A^2 -> H(d, U1(b, c)))
28.54/9.46	   (A^2 -> H(d, U1(b, d)),A^2 -> H(d, U1(b, d)))
28.54/9.46	
28.54/9.46	
28.54/9.46	----------------------------------------
28.54/9.46	
28.54/9.46	(1094)
28.54/9.46	Obligation:
28.54/9.46	Q DP problem:
28.54/9.46	The TRS P consists of the following rules:
28.54/9.46	
28.54/9.46	   H(x, x) -> G(x, x, f(k))
28.54/9.46	   G(d, x, x) -> A^2
28.54/9.46	   A^2 -> H(f(c), f(c))
28.54/9.46	   A^2 -> H(f(d), f(d))
28.54/9.46	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.46	   A^2 -> H(f(e), f(e))
28.54/9.46	   A^2 -> H(f(k), f(k))
28.54/9.46	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.46	   A^2 -> H(d, f(c))
28.54/9.46	   A^2 -> H(d, f(d))
28.54/9.46	   A^2 -> H(a, U1(c, b))
28.54/9.46	   A^2 -> H(a, U1(d, b))
28.54/9.46	   A^2 -> H(a, U1(b, c))
28.54/9.46	   A^2 -> H(a, U1(b, d))
28.54/9.46	   A^2 -> H(a, U1(c, c))
28.54/9.46	   A^2 -> H(a, f(e))
28.54/9.46	   A^2 -> H(a, f(k))
28.54/9.46	   A^2 -> H(a, U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.46	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.46	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.46	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.46	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.46	   A^2 -> H(U1(e, d), f(e))
28.54/9.46	   A^2 -> H(U1(e, d), f(k))
28.54/9.46	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.46	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.46	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.46	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.46	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.46	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.46	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.46	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.46	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.46	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.46	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.46	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.46	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.46	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.46	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.46	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.46	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, a), b)
28.54/9.46	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.46	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.46	   A^2 -> H(U1(c, a), c)
28.54/9.46	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.46	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.46	   A^2 -> H(U1(c, a), e)
28.54/9.46	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.46	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.46	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.46	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.46	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.46	   A^2 -> H(U1(d, e), f(e))
28.54/9.46	   A^2 -> H(U1(d, e), f(k))
28.54/9.46	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.46	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.46	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.46	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.46	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.46	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.46	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.46	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.46	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.46	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.46	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.46	   A^2 -> H(U1(d, a), b)
28.54/9.46	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.46	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.46	   A^2 -> H(U1(d, a), c)
28.54/9.46	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.46	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.46	   A^2 -> H(U1(d, a), e)
28.54/9.46	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.46	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.46	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.46	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.46	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.46	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.46	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.46	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.46	   A^2 -> H(U1(a, c), b)
28.54/9.46	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.46	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.46	   A^2 -> H(U1(a, c), c)
28.54/9.46	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.46	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.46	   A^2 -> H(U1(a, c), e)
28.54/9.46	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, d), b)
28.54/9.46	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.46	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.46	   A^2 -> H(U1(a, d), c)
28.54/9.46	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.46	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.46	   A^2 -> H(U1(a, d), e)
28.54/9.46	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, a), d)
28.54/9.46	   A^2 -> H(U1(a, a), k)
28.54/9.46	   A^2 -> H(k, U1(b, b))
28.54/9.46	   A^2 -> H(k, f(c))
28.54/9.46	   A^2 -> H(k, f(d))
28.54/9.46	   A^2 -> H(c, U1(c, b))
28.54/9.46	   A^2 -> H(c, U1(d, b))
28.54/9.46	   A^2 -> H(c, U1(b, c))
28.54/9.46	   A^2 -> H(c, U1(b, d))
28.54/9.46	   A^2 -> H(c, U1(c, c))
28.54/9.46	   A^2 -> H(c, f(e))
28.54/9.46	   A^2 -> H(c, f(k))
28.54/9.46	   A^2 -> H(c, U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.46	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.46	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.46	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.46	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.46	   A^2 -> H(U1(e, k), f(e))
28.54/9.46	   A^2 -> H(U1(e, k), f(k))
28.54/9.46	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.46	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.46	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.46	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.46	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.46	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.46	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.46	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.46	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.46	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.46	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.46	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.46	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.46	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.46	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.46	   A^2 -> H(U1(k, e), f(e))
28.54/9.46	   A^2 -> H(U1(k, e), f(k))
28.54/9.46	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.46	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.46	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.46	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.46	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.46	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.46	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.46	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.46	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, c), b)
28.54/9.46	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.46	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.46	   A^2 -> H(U1(c, c), e)
28.54/9.46	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.46	   A^2 -> H(e, U1(c, b))
28.54/9.46	   A^2 -> H(e, U1(d, b))
28.54/9.46	   A^2 -> H(e, U1(b, c))
28.54/9.46	   A^2 -> H(e, U1(b, d))
28.54/9.46	   A^2 -> H(e, U1(c, c))
28.54/9.46	   A^2 -> H(e, f(e))
28.54/9.46	   A^2 -> H(e, f(k))
28.54/9.46	   A^2 -> H(e, U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.46	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.46	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.46	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.46	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.46	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.46	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.46	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.46	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.46	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.46	   A^2 -> H(f(e), b)
28.54/9.46	   A^2 -> H(f(e), U1(e, d))
28.54/9.46	   A^2 -> H(f(e), U1(d, e))
28.54/9.46	   A^2 -> H(f(e), c)
28.54/9.46	   A^2 -> H(f(e), U1(e, k))
28.54/9.46	   A^2 -> H(f(e), U1(k, e))
28.54/9.46	   A^2 -> H(f(e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.46	   A^2 -> H(f(k), b)
28.54/9.46	   A^2 -> H(f(k), U1(e, d))
28.54/9.46	   A^2 -> H(f(k), U1(d, e))
28.54/9.46	   A^2 -> H(f(k), c)
28.54/9.46	   A^2 -> H(f(k), U1(e, k))
28.54/9.46	   A^2 -> H(f(k), U1(k, e))
28.54/9.46	   A^2 -> H(f(k), e)
28.54/9.46	   A^2 -> H(f(c), d)
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.46	   A^2 -> H(U1(k, k), f(e))
28.54/9.46	   A^2 -> H(U1(k, k), f(k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.46	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.46	   A^2 -> H(U1(d, d), b)
28.54/9.46	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.46	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.46	   A^2 -> H(U1(d, d), c)
28.54/9.46	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.46	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.46	   A^2 -> H(U1(d, d), e)
28.54/9.46	   A^2 -> H(f(d), d)
28.54/9.46	   A^2 -> H(f(d), k)
28.54/9.46	   A^2 -> H(U1(c, c), c)
28.54/9.46	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.46	   A^2 -> H(f(c), k)
28.54/9.46	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.46	   A^2 -> H(f(k), U1(k, k))
28.54/9.46	   A^2 -> H(f(e), e)
28.54/9.46	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.46	   A^2 -> H(d, U1(c, b))
28.54/9.46	   A^2 -> H(d, U1(d, b))
28.54/9.46	   A^2 -> H(d, U1(b, c))
28.54/9.46	   A^2 -> H(d, U1(b, d))
28.54/9.46	
28.54/9.46	The TRS R consists of the following rules:
28.54/9.46	
28.54/9.46	   f(x) -> U1(x, x)
28.54/9.46	   U1(e, x) -> x
28.54/9.46	   a -> c
28.54/9.46	   a -> d
28.54/9.46	   b -> c
28.54/9.46	   b -> d
28.54/9.46	   d -> k
28.54/9.46	   c -> e
28.54/9.46	   c -> k
28.54/9.46	
28.54/9.46	Q is empty.
28.54/9.46	We have to consider all minimal (P,Q,R)-chains.
28.54/9.46	----------------------------------------
28.54/9.46	
28.54/9.46	(1095) TransformationProof (EQUIVALENT)
28.54/9.46	By narrowing [LPAR04] the rule A^2 -> H(d, f(c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.46	
28.54/9.46	   (A^2 -> H(k, f(c)),A^2 -> H(k, f(c)))
28.54/9.46	   (A^2 -> H(d, U1(c, c)),A^2 -> H(d, U1(c, c)))
28.54/9.46	   (A^2 -> H(d, f(e)),A^2 -> H(d, f(e)))
28.54/9.46	   (A^2 -> H(d, f(k)),A^2 -> H(d, f(k)))
28.54/9.46	
28.54/9.46	
28.54/9.46	----------------------------------------
28.54/9.46	
28.54/9.46	(1096)
28.54/9.46	Obligation:
28.54/9.46	Q DP problem:
28.54/9.46	The TRS P consists of the following rules:
28.54/9.46	
28.54/9.46	   H(x, x) -> G(x, x, f(k))
28.54/9.46	   G(d, x, x) -> A^2
28.54/9.46	   A^2 -> H(f(c), f(c))
28.54/9.46	   A^2 -> H(f(d), f(d))
28.54/9.46	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.46	   A^2 -> H(f(e), f(e))
28.54/9.46	   A^2 -> H(f(k), f(k))
28.54/9.46	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.46	   A^2 -> H(d, f(d))
28.54/9.46	   A^2 -> H(a, U1(c, b))
28.54/9.46	   A^2 -> H(a, U1(d, b))
28.54/9.46	   A^2 -> H(a, U1(b, c))
28.54/9.46	   A^2 -> H(a, U1(b, d))
28.54/9.46	   A^2 -> H(a, U1(c, c))
28.54/9.46	   A^2 -> H(a, f(e))
28.54/9.46	   A^2 -> H(a, f(k))
28.54/9.46	   A^2 -> H(a, U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.46	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.46	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.46	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.46	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.46	   A^2 -> H(U1(e, d), f(e))
28.54/9.46	   A^2 -> H(U1(e, d), f(k))
28.54/9.46	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.46	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.46	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.46	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.46	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.46	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.46	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.46	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.46	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.46	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.46	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.46	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.46	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.46	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.46	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.46	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.46	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, a), b)
28.54/9.46	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.46	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.46	   A^2 -> H(U1(c, a), c)
28.54/9.46	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.46	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.46	   A^2 -> H(U1(c, a), e)
28.54/9.46	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.46	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.46	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.46	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.46	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.46	   A^2 -> H(U1(d, e), f(e))
28.54/9.46	   A^2 -> H(U1(d, e), f(k))
28.54/9.46	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.46	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.46	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.46	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.46	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.46	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.46	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.46	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.46	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.46	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.46	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.46	   A^2 -> H(U1(d, a), b)
28.54/9.46	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.46	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.46	   A^2 -> H(U1(d, a), c)
28.54/9.46	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.46	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.46	   A^2 -> H(U1(d, a), e)
28.54/9.46	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.46	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.46	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.46	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.46	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.46	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.46	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.46	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.46	   A^2 -> H(U1(a, c), b)
28.54/9.46	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.46	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.46	   A^2 -> H(U1(a, c), c)
28.54/9.46	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.46	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.46	   A^2 -> H(U1(a, c), e)
28.54/9.46	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, d), b)
28.54/9.46	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.46	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.46	   A^2 -> H(U1(a, d), c)
28.54/9.46	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.46	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.46	   A^2 -> H(U1(a, d), e)
28.54/9.46	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, a), d)
28.54/9.46	   A^2 -> H(U1(a, a), k)
28.54/9.46	   A^2 -> H(k, U1(b, b))
28.54/9.46	   A^2 -> H(k, f(c))
28.54/9.46	   A^2 -> H(k, f(d))
28.54/9.46	   A^2 -> H(c, U1(c, b))
28.54/9.46	   A^2 -> H(c, U1(d, b))
28.54/9.46	   A^2 -> H(c, U1(b, c))
28.54/9.46	   A^2 -> H(c, U1(b, d))
28.54/9.46	   A^2 -> H(c, U1(c, c))
28.54/9.46	   A^2 -> H(c, f(e))
28.54/9.46	   A^2 -> H(c, f(k))
28.54/9.46	   A^2 -> H(c, U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.46	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.46	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.46	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.46	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.46	   A^2 -> H(U1(e, k), f(e))
28.54/9.46	   A^2 -> H(U1(e, k), f(k))
28.54/9.46	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.46	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.46	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.46	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.46	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.46	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.46	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.46	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.46	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.46	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.46	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.46	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.46	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.46	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.46	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.46	   A^2 -> H(U1(k, e), f(e))
28.54/9.46	   A^2 -> H(U1(k, e), f(k))
28.54/9.46	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.46	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.46	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.46	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.46	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.46	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.46	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.46	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.46	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, c), b)
28.54/9.46	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.46	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.46	   A^2 -> H(U1(c, c), e)
28.54/9.46	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.46	   A^2 -> H(e, U1(c, b))
28.54/9.46	   A^2 -> H(e, U1(d, b))
28.54/9.46	   A^2 -> H(e, U1(b, c))
28.54/9.46	   A^2 -> H(e, U1(b, d))
28.54/9.46	   A^2 -> H(e, U1(c, c))
28.54/9.46	   A^2 -> H(e, f(e))
28.54/9.46	   A^2 -> H(e, f(k))
28.54/9.46	   A^2 -> H(e, U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.46	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.46	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.46	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.46	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.46	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.46	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.46	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.46	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.46	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.46	   A^2 -> H(f(e), b)
28.54/9.46	   A^2 -> H(f(e), U1(e, d))
28.54/9.46	   A^2 -> H(f(e), U1(d, e))
28.54/9.46	   A^2 -> H(f(e), c)
28.54/9.46	   A^2 -> H(f(e), U1(e, k))
28.54/9.46	   A^2 -> H(f(e), U1(k, e))
28.54/9.46	   A^2 -> H(f(e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.46	   A^2 -> H(f(k), b)
28.54/9.46	   A^2 -> H(f(k), U1(e, d))
28.54/9.46	   A^2 -> H(f(k), U1(d, e))
28.54/9.46	   A^2 -> H(f(k), c)
28.54/9.46	   A^2 -> H(f(k), U1(e, k))
28.54/9.46	   A^2 -> H(f(k), U1(k, e))
28.54/9.46	   A^2 -> H(f(k), e)
28.54/9.46	   A^2 -> H(f(c), d)
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.46	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.46	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.46	   A^2 -> H(U1(k, k), f(e))
28.54/9.46	   A^2 -> H(U1(k, k), f(k))
28.54/9.46	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.46	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.46	   A^2 -> H(U1(d, d), b)
28.54/9.46	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.46	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.46	   A^2 -> H(U1(d, d), c)
28.54/9.46	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.46	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.46	   A^2 -> H(U1(d, d), e)
28.54/9.46	   A^2 -> H(f(d), d)
28.54/9.46	   A^2 -> H(f(d), k)
28.54/9.46	   A^2 -> H(U1(c, c), c)
28.54/9.46	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.46	   A^2 -> H(f(c), k)
28.54/9.46	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.46	   A^2 -> H(f(k), U1(k, k))
28.54/9.46	   A^2 -> H(f(e), e)
28.54/9.46	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.46	   A^2 -> H(d, U1(c, b))
28.54/9.46	   A^2 -> H(d, U1(d, b))
28.54/9.46	   A^2 -> H(d, U1(b, c))
28.54/9.46	   A^2 -> H(d, U1(b, d))
28.54/9.46	   A^2 -> H(d, U1(c, c))
28.54/9.46	   A^2 -> H(d, f(e))
28.54/9.46	   A^2 -> H(d, f(k))
28.54/9.46	
28.54/9.46	The TRS R consists of the following rules:
28.54/9.46	
28.54/9.46	   f(x) -> U1(x, x)
28.54/9.46	   U1(e, x) -> x
28.54/9.46	   a -> c
28.54/9.46	   a -> d
28.54/9.46	   b -> c
28.54/9.46	   b -> d
28.54/9.46	   d -> k
28.54/9.46	   c -> e
28.54/9.46	   c -> k
28.54/9.46	
28.54/9.46	Q is empty.
28.54/9.46	We have to consider all minimal (P,Q,R)-chains.
28.54/9.46	----------------------------------------
28.54/9.46	
28.54/9.46	(1097) TransformationProof (EQUIVALENT)
28.54/9.46	By narrowing [LPAR04] the rule A^2 -> H(d, f(d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.46	
28.54/9.46	   (A^2 -> H(k, f(d)),A^2 -> H(k, f(d)))
28.54/9.46	   (A^2 -> H(d, U1(d, d)),A^2 -> H(d, U1(d, d)))
28.54/9.46	   (A^2 -> H(d, f(k)),A^2 -> H(d, f(k)))
28.54/9.46	
28.54/9.46	
28.54/9.46	----------------------------------------
28.54/9.46	
28.54/9.46	(1098)
28.54/9.46	Obligation:
28.54/9.46	Q DP problem:
28.54/9.46	The TRS P consists of the following rules:
28.54/9.46	
28.54/9.46	   H(x, x) -> G(x, x, f(k))
28.54/9.46	   G(d, x, x) -> A^2
28.54/9.46	   A^2 -> H(f(c), f(c))
28.54/9.46	   A^2 -> H(f(d), f(d))
28.54/9.46	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.46	   A^2 -> H(f(e), f(e))
28.54/9.46	   A^2 -> H(f(k), f(k))
28.54/9.46	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.46	   A^2 -> H(a, U1(c, b))
28.54/9.46	   A^2 -> H(a, U1(d, b))
28.54/9.46	   A^2 -> H(a, U1(b, c))
28.54/9.46	   A^2 -> H(a, U1(b, d))
28.54/9.46	   A^2 -> H(a, U1(c, c))
28.54/9.46	   A^2 -> H(a, f(e))
28.54/9.46	   A^2 -> H(a, f(k))
28.54/9.46	   A^2 -> H(a, U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.46	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.46	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.46	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.46	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.46	   A^2 -> H(U1(e, d), f(e))
28.54/9.46	   A^2 -> H(U1(e, d), f(k))
28.54/9.46	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.46	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.46	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.46	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.46	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.46	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.46	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.46	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.46	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.46	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.46	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.46	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.46	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.46	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.46	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.46	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.46	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.46	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.46	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.46	   A^2 -> H(U1(c, a), b)
28.54/9.46	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.46	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.46	   A^2 -> H(U1(c, a), c)
28.54/9.46	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.46	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.46	   A^2 -> H(U1(c, a), e)
28.54/9.46	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.46	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.46	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.46	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.46	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.46	   A^2 -> H(U1(d, e), f(e))
28.54/9.46	   A^2 -> H(U1(d, e), f(k))
28.54/9.46	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.46	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.46	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.46	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.46	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.46	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.46	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.46	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.46	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.46	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.46	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.46	   A^2 -> H(U1(d, a), b)
28.54/9.46	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.46	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.46	   A^2 -> H(U1(d, a), c)
28.54/9.46	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.46	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.46	   A^2 -> H(U1(d, a), e)
28.54/9.46	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.46	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.46	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.46	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.46	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.46	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.46	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.46	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.46	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.46	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.46	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.46	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.46	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.46	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.46	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.46	   A^2 -> H(U1(a, c), b)
28.54/9.46	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.46	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.46	   A^2 -> H(U1(a, c), c)
28.54/9.46	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.46	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.46	   A^2 -> H(U1(a, c), e)
28.54/9.46	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, d), b)
28.54/9.46	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.46	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.46	   A^2 -> H(U1(a, d), c)
28.54/9.46	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.46	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.46	   A^2 -> H(U1(a, d), e)
28.54/9.46	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.46	   A^2 -> H(U1(a, a), d)
28.54/9.46	   A^2 -> H(U1(a, a), k)
28.54/9.46	   A^2 -> H(k, U1(b, b))
28.54/9.46	   A^2 -> H(k, f(c))
28.54/9.46	   A^2 -> H(k, f(d))
28.54/9.46	   A^2 -> H(c, U1(c, b))
28.54/9.46	   A^2 -> H(c, U1(d, b))
28.54/9.46	   A^2 -> H(c, U1(b, c))
28.54/9.46	   A^2 -> H(c, U1(b, d))
28.54/9.46	   A^2 -> H(c, U1(c, c))
28.54/9.46	   A^2 -> H(c, f(e))
28.54/9.46	   A^2 -> H(c, f(k))
28.54/9.46	   A^2 -> H(c, U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.46	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.46	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.46	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.46	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.46	   A^2 -> H(U1(e, k), f(e))
28.54/9.46	   A^2 -> H(U1(e, k), f(k))
28.54/9.46	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.46	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.46	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.46	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.46	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.46	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.46	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.46	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.46	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.46	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.46	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.46	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.46	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.46	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.46	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.46	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.46	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.46	   A^2 -> H(U1(k, e), f(e))
28.54/9.46	   A^2 -> H(U1(k, e), f(k))
28.54/9.46	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.46	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.46	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.46	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.46	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.46	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.46	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.46	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.46	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.46	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.46	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.47	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.47	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.47	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.47	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.47	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.47	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.47	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, c), b)
28.54/9.47	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.47	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.47	   A^2 -> H(U1(c, c), e)
28.54/9.47	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.47	   A^2 -> H(e, U1(c, b))
28.54/9.47	   A^2 -> H(e, U1(d, b))
28.54/9.47	   A^2 -> H(e, U1(b, c))
28.54/9.47	   A^2 -> H(e, U1(b, d))
28.54/9.47	   A^2 -> H(e, U1(c, c))
28.54/9.47	   A^2 -> H(e, f(e))
28.54/9.47	   A^2 -> H(e, f(k))
28.54/9.47	   A^2 -> H(e, U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.47	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.47	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.47	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.47	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.47	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.47	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.47	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.47	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.47	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.47	   A^2 -> H(f(e), b)
28.54/9.47	   A^2 -> H(f(e), U1(e, d))
28.54/9.47	   A^2 -> H(f(e), U1(d, e))
28.54/9.47	   A^2 -> H(f(e), c)
28.54/9.47	   A^2 -> H(f(e), U1(e, k))
28.54/9.47	   A^2 -> H(f(e), U1(k, e))
28.54/9.47	   A^2 -> H(f(e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.47	   A^2 -> H(f(k), b)
28.54/9.47	   A^2 -> H(f(k), U1(e, d))
28.54/9.47	   A^2 -> H(f(k), U1(d, e))
28.54/9.47	   A^2 -> H(f(k), c)
28.54/9.47	   A^2 -> H(f(k), U1(e, k))
28.54/9.47	   A^2 -> H(f(k), U1(k, e))
28.54/9.47	   A^2 -> H(f(k), e)
28.54/9.47	   A^2 -> H(f(c), d)
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.47	   A^2 -> H(U1(k, k), f(e))
28.54/9.47	   A^2 -> H(U1(k, k), f(k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.47	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.47	   A^2 -> H(U1(d, d), b)
28.54/9.47	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.47	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.47	   A^2 -> H(U1(d, d), c)
28.54/9.47	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.47	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.47	   A^2 -> H(U1(d, d), e)
28.54/9.47	   A^2 -> H(f(d), d)
28.54/9.47	   A^2 -> H(f(d), k)
28.54/9.47	   A^2 -> H(U1(c, c), c)
28.54/9.47	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.47	   A^2 -> H(f(c), k)
28.54/9.47	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.47	   A^2 -> H(f(k), U1(k, k))
28.54/9.47	   A^2 -> H(f(e), e)
28.54/9.47	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.47	   A^2 -> H(d, U1(c, b))
28.54/9.47	   A^2 -> H(d, U1(d, b))
28.54/9.47	   A^2 -> H(d, U1(b, c))
28.54/9.47	   A^2 -> H(d, U1(b, d))
28.54/9.47	   A^2 -> H(d, U1(c, c))
28.54/9.47	   A^2 -> H(d, f(e))
28.54/9.47	   A^2 -> H(d, f(k))
28.54/9.47	   A^2 -> H(d, U1(d, d))
28.54/9.47	
28.54/9.47	The TRS R consists of the following rules:
28.54/9.47	
28.54/9.47	   f(x) -> U1(x, x)
28.54/9.47	   U1(e, x) -> x
28.54/9.47	   a -> c
28.54/9.47	   a -> d
28.54/9.47	   b -> c
28.54/9.47	   b -> d
28.54/9.47	   d -> k
28.54/9.47	   c -> e
28.54/9.47	   c -> k
28.54/9.47	
28.54/9.47	Q is empty.
28.54/9.47	We have to consider all minimal (P,Q,R)-chains.
28.54/9.47	----------------------------------------
28.54/9.47	
28.54/9.47	(1099) TransformationProof (EQUIVALENT)
28.54/9.47	By narrowing [LPAR04] the rule A^2 -> H(a, U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.47	
28.54/9.47	   (A^2 -> H(c, U1(c, b)),A^2 -> H(c, U1(c, b)))
28.54/9.47	   (A^2 -> H(d, U1(c, b)),A^2 -> H(d, U1(c, b)))
28.54/9.47	   (A^2 -> H(a, U1(e, b)),A^2 -> H(a, U1(e, b)))
28.54/9.47	   (A^2 -> H(a, U1(k, b)),A^2 -> H(a, U1(k, b)))
28.54/9.47	   (A^2 -> H(a, U1(c, c)),A^2 -> H(a, U1(c, c)))
28.54/9.47	   (A^2 -> H(a, U1(c, d)),A^2 -> H(a, U1(c, d)))
28.54/9.47	
28.54/9.47	
28.54/9.47	----------------------------------------
28.54/9.47	
28.54/9.47	(1100)
28.54/9.47	Obligation:
28.54/9.47	Q DP problem:
28.54/9.47	The TRS P consists of the following rules:
28.54/9.47	
28.54/9.47	   H(x, x) -> G(x, x, f(k))
28.54/9.47	   G(d, x, x) -> A^2
28.54/9.47	   A^2 -> H(f(c), f(c))
28.54/9.47	   A^2 -> H(f(d), f(d))
28.54/9.47	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.47	   A^2 -> H(f(e), f(e))
28.54/9.47	   A^2 -> H(f(k), f(k))
28.54/9.47	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.47	   A^2 -> H(a, U1(d, b))
28.54/9.47	   A^2 -> H(a, U1(b, c))
28.54/9.47	   A^2 -> H(a, U1(b, d))
28.54/9.47	   A^2 -> H(a, U1(c, c))
28.54/9.47	   A^2 -> H(a, f(e))
28.54/9.47	   A^2 -> H(a, f(k))
28.54/9.47	   A^2 -> H(a, U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.47	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.47	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.47	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.47	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.47	   A^2 -> H(U1(e, d), f(e))
28.54/9.47	   A^2 -> H(U1(e, d), f(k))
28.54/9.47	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.47	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.47	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.47	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.47	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.47	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.47	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.47	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.47	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.47	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.47	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.47	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.47	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.47	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.47	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.47	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.47	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, a), b)
28.54/9.47	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.47	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.47	   A^2 -> H(U1(c, a), c)
28.54/9.47	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.47	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.47	   A^2 -> H(U1(c, a), e)
28.54/9.47	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.47	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.47	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.47	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.47	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.47	   A^2 -> H(U1(d, e), f(e))
28.54/9.47	   A^2 -> H(U1(d, e), f(k))
28.54/9.47	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.47	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.47	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.47	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.47	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.47	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.47	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.47	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.47	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.47	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.47	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.47	   A^2 -> H(U1(d, a), b)
28.54/9.47	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.47	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.47	   A^2 -> H(U1(d, a), c)
28.54/9.47	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.47	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.47	   A^2 -> H(U1(d, a), e)
28.54/9.47	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.47	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.47	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.47	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.47	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.47	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.47	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.47	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.47	   A^2 -> H(U1(a, c), b)
28.54/9.47	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.47	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.47	   A^2 -> H(U1(a, c), c)
28.54/9.47	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.47	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.47	   A^2 -> H(U1(a, c), e)
28.54/9.47	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, d), b)
28.54/9.47	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.47	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.47	   A^2 -> H(U1(a, d), c)
28.54/9.47	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.47	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.47	   A^2 -> H(U1(a, d), e)
28.54/9.47	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, a), d)
28.54/9.47	   A^2 -> H(U1(a, a), k)
28.54/9.47	   A^2 -> H(k, U1(b, b))
28.54/9.47	   A^2 -> H(k, f(c))
28.54/9.47	   A^2 -> H(k, f(d))
28.54/9.47	   A^2 -> H(c, U1(c, b))
28.54/9.47	   A^2 -> H(c, U1(d, b))
28.54/9.47	   A^2 -> H(c, U1(b, c))
28.54/9.47	   A^2 -> H(c, U1(b, d))
28.54/9.47	   A^2 -> H(c, U1(c, c))
28.54/9.47	   A^2 -> H(c, f(e))
28.54/9.47	   A^2 -> H(c, f(k))
28.54/9.47	   A^2 -> H(c, U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.47	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.47	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.47	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.47	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.47	   A^2 -> H(U1(e, k), f(e))
28.54/9.47	   A^2 -> H(U1(e, k), f(k))
28.54/9.47	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.47	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.47	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.47	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.47	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.47	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.47	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.47	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.47	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.47	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.47	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.47	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.47	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.47	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.47	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.47	   A^2 -> H(U1(k, e), f(e))
28.54/9.47	   A^2 -> H(U1(k, e), f(k))
28.54/9.47	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.47	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.47	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.47	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.47	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.47	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.47	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.47	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.47	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, c), b)
28.54/9.47	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.47	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.47	   A^2 -> H(U1(c, c), e)
28.54/9.47	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.47	   A^2 -> H(e, U1(c, b))
28.54/9.47	   A^2 -> H(e, U1(d, b))
28.54/9.47	   A^2 -> H(e, U1(b, c))
28.54/9.47	   A^2 -> H(e, U1(b, d))
28.54/9.47	   A^2 -> H(e, U1(c, c))
28.54/9.47	   A^2 -> H(e, f(e))
28.54/9.47	   A^2 -> H(e, f(k))
28.54/9.47	   A^2 -> H(e, U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.47	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.47	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.47	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.47	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.47	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.47	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.47	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.47	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.47	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.47	   A^2 -> H(f(e), b)
28.54/9.47	   A^2 -> H(f(e), U1(e, d))
28.54/9.47	   A^2 -> H(f(e), U1(d, e))
28.54/9.47	   A^2 -> H(f(e), c)
28.54/9.47	   A^2 -> H(f(e), U1(e, k))
28.54/9.47	   A^2 -> H(f(e), U1(k, e))
28.54/9.47	   A^2 -> H(f(e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.47	   A^2 -> H(f(k), b)
28.54/9.47	   A^2 -> H(f(k), U1(e, d))
28.54/9.47	   A^2 -> H(f(k), U1(d, e))
28.54/9.47	   A^2 -> H(f(k), c)
28.54/9.47	   A^2 -> H(f(k), U1(e, k))
28.54/9.47	   A^2 -> H(f(k), U1(k, e))
28.54/9.47	   A^2 -> H(f(k), e)
28.54/9.47	   A^2 -> H(f(c), d)
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.47	   A^2 -> H(U1(k, k), f(e))
28.54/9.47	   A^2 -> H(U1(k, k), f(k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.47	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.47	   A^2 -> H(U1(d, d), b)
28.54/9.47	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.47	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.47	   A^2 -> H(U1(d, d), c)
28.54/9.47	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.47	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.47	   A^2 -> H(U1(d, d), e)
28.54/9.47	   A^2 -> H(f(d), d)
28.54/9.47	   A^2 -> H(f(d), k)
28.54/9.47	   A^2 -> H(U1(c, c), c)
28.54/9.47	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.47	   A^2 -> H(f(c), k)
28.54/9.47	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.47	   A^2 -> H(f(k), U1(k, k))
28.54/9.47	   A^2 -> H(f(e), e)
28.54/9.47	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.47	   A^2 -> H(d, U1(c, b))
28.54/9.47	   A^2 -> H(d, U1(d, b))
28.54/9.47	   A^2 -> H(d, U1(b, c))
28.54/9.47	   A^2 -> H(d, U1(b, d))
28.54/9.47	   A^2 -> H(d, U1(c, c))
28.54/9.47	   A^2 -> H(d, f(e))
28.54/9.47	   A^2 -> H(d, f(k))
28.54/9.47	   A^2 -> H(d, U1(d, d))
28.54/9.47	   A^2 -> H(a, U1(e, b))
28.54/9.47	   A^2 -> H(a, U1(k, b))
28.54/9.47	   A^2 -> H(a, U1(c, d))
28.54/9.47	
28.54/9.47	The TRS R consists of the following rules:
28.54/9.47	
28.54/9.47	   f(x) -> U1(x, x)
28.54/9.47	   U1(e, x) -> x
28.54/9.47	   a -> c
28.54/9.47	   a -> d
28.54/9.47	   b -> c
28.54/9.47	   b -> d
28.54/9.47	   d -> k
28.54/9.47	   c -> e
28.54/9.47	   c -> k
28.54/9.47	
28.54/9.47	Q is empty.
28.54/9.47	We have to consider all minimal (P,Q,R)-chains.
28.54/9.47	----------------------------------------
28.54/9.47	
28.54/9.47	(1101) TransformationProof (EQUIVALENT)
28.54/9.47	By narrowing [LPAR04] the rule A^2 -> H(a, U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.47	
28.54/9.47	   (A^2 -> H(c, U1(d, b)),A^2 -> H(c, U1(d, b)))
28.54/9.47	   (A^2 -> H(d, U1(d, b)),A^2 -> H(d, U1(d, b)))
28.54/9.47	   (A^2 -> H(a, U1(k, b)),A^2 -> H(a, U1(k, b)))
28.54/9.47	   (A^2 -> H(a, U1(d, c)),A^2 -> H(a, U1(d, c)))
28.54/9.47	   (A^2 -> H(a, U1(d, d)),A^2 -> H(a, U1(d, d)))
28.54/9.47	
28.54/9.47	
28.54/9.47	----------------------------------------
28.54/9.47	
28.54/9.47	(1102)
28.54/9.47	Obligation:
28.54/9.47	Q DP problem:
28.54/9.47	The TRS P consists of the following rules:
28.54/9.47	
28.54/9.47	   H(x, x) -> G(x, x, f(k))
28.54/9.47	   G(d, x, x) -> A^2
28.54/9.47	   A^2 -> H(f(c), f(c))
28.54/9.47	   A^2 -> H(f(d), f(d))
28.54/9.47	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.47	   A^2 -> H(f(e), f(e))
28.54/9.47	   A^2 -> H(f(k), f(k))
28.54/9.47	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.47	   A^2 -> H(a, U1(b, c))
28.54/9.47	   A^2 -> H(a, U1(b, d))
28.54/9.47	   A^2 -> H(a, U1(c, c))
28.54/9.47	   A^2 -> H(a, f(e))
28.54/9.47	   A^2 -> H(a, f(k))
28.54/9.47	   A^2 -> H(a, U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.47	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.47	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.47	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.47	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.47	   A^2 -> H(U1(e, d), f(e))
28.54/9.47	   A^2 -> H(U1(e, d), f(k))
28.54/9.47	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.47	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.47	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.47	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.47	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.47	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.47	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.47	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.47	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.47	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.47	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.47	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.47	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.47	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.47	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.47	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.47	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, a), b)
28.54/9.47	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.47	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.47	   A^2 -> H(U1(c, a), c)
28.54/9.47	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.47	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.47	   A^2 -> H(U1(c, a), e)
28.54/9.47	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.47	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.47	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.47	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.47	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.47	   A^2 -> H(U1(d, e), f(e))
28.54/9.47	   A^2 -> H(U1(d, e), f(k))
28.54/9.47	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.47	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.47	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.47	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.47	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.47	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.47	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.47	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.47	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.47	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.47	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.47	   A^2 -> H(U1(d, a), b)
28.54/9.47	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.47	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.47	   A^2 -> H(U1(d, a), c)
28.54/9.47	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.47	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.47	   A^2 -> H(U1(d, a), e)
28.54/9.47	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.47	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.47	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.47	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.47	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.47	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.47	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.47	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.47	   A^2 -> H(U1(a, c), b)
28.54/9.47	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.47	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.47	   A^2 -> H(U1(a, c), c)
28.54/9.47	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.47	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.47	   A^2 -> H(U1(a, c), e)
28.54/9.47	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, d), b)
28.54/9.47	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.47	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.47	   A^2 -> H(U1(a, d), c)
28.54/9.47	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.47	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.47	   A^2 -> H(U1(a, d), e)
28.54/9.47	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, a), d)
28.54/9.47	   A^2 -> H(U1(a, a), k)
28.54/9.47	   A^2 -> H(k, U1(b, b))
28.54/9.47	   A^2 -> H(k, f(c))
28.54/9.47	   A^2 -> H(k, f(d))
28.54/9.47	   A^2 -> H(c, U1(c, b))
28.54/9.47	   A^2 -> H(c, U1(d, b))
28.54/9.47	   A^2 -> H(c, U1(b, c))
28.54/9.47	   A^2 -> H(c, U1(b, d))
28.54/9.47	   A^2 -> H(c, U1(c, c))
28.54/9.47	   A^2 -> H(c, f(e))
28.54/9.47	   A^2 -> H(c, f(k))
28.54/9.47	   A^2 -> H(c, U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.47	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.47	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.47	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.47	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.47	   A^2 -> H(U1(e, k), f(e))
28.54/9.47	   A^2 -> H(U1(e, k), f(k))
28.54/9.47	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.47	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.47	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.47	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.47	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.47	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.47	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.47	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.47	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.47	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.47	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.47	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.47	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.47	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.47	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.47	   A^2 -> H(U1(k, e), f(e))
28.54/9.47	   A^2 -> H(U1(k, e), f(k))
28.54/9.47	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.47	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.47	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.47	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.47	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.47	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.47	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.47	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.47	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, c), b)
28.54/9.47	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.47	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.47	   A^2 -> H(U1(c, c), e)
28.54/9.47	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.47	   A^2 -> H(e, U1(c, b))
28.54/9.47	   A^2 -> H(e, U1(d, b))
28.54/9.47	   A^2 -> H(e, U1(b, c))
28.54/9.47	   A^2 -> H(e, U1(b, d))
28.54/9.47	   A^2 -> H(e, U1(c, c))
28.54/9.47	   A^2 -> H(e, f(e))
28.54/9.47	   A^2 -> H(e, f(k))
28.54/9.47	   A^2 -> H(e, U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.47	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.47	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.47	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.47	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.47	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.47	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.47	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.47	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.47	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.47	   A^2 -> H(f(e), b)
28.54/9.47	   A^2 -> H(f(e), U1(e, d))
28.54/9.47	   A^2 -> H(f(e), U1(d, e))
28.54/9.47	   A^2 -> H(f(e), c)
28.54/9.47	   A^2 -> H(f(e), U1(e, k))
28.54/9.47	   A^2 -> H(f(e), U1(k, e))
28.54/9.47	   A^2 -> H(f(e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.47	   A^2 -> H(f(k), b)
28.54/9.47	   A^2 -> H(f(k), U1(e, d))
28.54/9.47	   A^2 -> H(f(k), U1(d, e))
28.54/9.47	   A^2 -> H(f(k), c)
28.54/9.47	   A^2 -> H(f(k), U1(e, k))
28.54/9.47	   A^2 -> H(f(k), U1(k, e))
28.54/9.47	   A^2 -> H(f(k), e)
28.54/9.47	   A^2 -> H(f(c), d)
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.47	   A^2 -> H(U1(k, k), f(e))
28.54/9.47	   A^2 -> H(U1(k, k), f(k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.47	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.47	   A^2 -> H(U1(d, d), b)
28.54/9.47	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.47	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.47	   A^2 -> H(U1(d, d), c)
28.54/9.47	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.47	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.47	   A^2 -> H(U1(d, d), e)
28.54/9.47	   A^2 -> H(f(d), d)
28.54/9.47	   A^2 -> H(f(d), k)
28.54/9.47	   A^2 -> H(U1(c, c), c)
28.54/9.47	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.47	   A^2 -> H(f(c), k)
28.54/9.47	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.47	   A^2 -> H(f(k), U1(k, k))
28.54/9.47	   A^2 -> H(f(e), e)
28.54/9.47	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.47	   A^2 -> H(d, U1(c, b))
28.54/9.47	   A^2 -> H(d, U1(d, b))
28.54/9.47	   A^2 -> H(d, U1(b, c))
28.54/9.47	   A^2 -> H(d, U1(b, d))
28.54/9.47	   A^2 -> H(d, U1(c, c))
28.54/9.47	   A^2 -> H(d, f(e))
28.54/9.47	   A^2 -> H(d, f(k))
28.54/9.47	   A^2 -> H(d, U1(d, d))
28.54/9.47	   A^2 -> H(a, U1(e, b))
28.54/9.47	   A^2 -> H(a, U1(k, b))
28.54/9.47	   A^2 -> H(a, U1(c, d))
28.54/9.47	   A^2 -> H(a, U1(d, c))
28.54/9.47	
28.54/9.47	The TRS R consists of the following rules:
28.54/9.47	
28.54/9.47	   f(x) -> U1(x, x)
28.54/9.47	   U1(e, x) -> x
28.54/9.47	   a -> c
28.54/9.47	   a -> d
28.54/9.47	   b -> c
28.54/9.47	   b -> d
28.54/9.47	   d -> k
28.54/9.47	   c -> e
28.54/9.47	   c -> k
28.54/9.47	
28.54/9.47	Q is empty.
28.54/9.47	We have to consider all minimal (P,Q,R)-chains.
28.54/9.47	----------------------------------------
28.54/9.47	
28.54/9.47	(1103) TransformationProof (EQUIVALENT)
28.54/9.47	By narrowing [LPAR04] the rule A^2 -> H(a, U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.47	
28.54/9.47	   (A^2 -> H(c, U1(b, c)),A^2 -> H(c, U1(b, c)))
28.54/9.47	   (A^2 -> H(d, U1(b, c)),A^2 -> H(d, U1(b, c)))
28.54/9.47	   (A^2 -> H(a, U1(c, c)),A^2 -> H(a, U1(c, c)))
28.54/9.47	   (A^2 -> H(a, U1(d, c)),A^2 -> H(a, U1(d, c)))
28.54/9.47	   (A^2 -> H(a, U1(b, e)),A^2 -> H(a, U1(b, e)))
28.54/9.47	   (A^2 -> H(a, U1(b, k)),A^2 -> H(a, U1(b, k)))
28.54/9.47	
28.54/9.47	
28.54/9.47	----------------------------------------
28.54/9.47	
28.54/9.47	(1104)
28.54/9.47	Obligation:
28.54/9.47	Q DP problem:
28.54/9.47	The TRS P consists of the following rules:
28.54/9.47	
28.54/9.47	   H(x, x) -> G(x, x, f(k))
28.54/9.47	   G(d, x, x) -> A^2
28.54/9.47	   A^2 -> H(f(c), f(c))
28.54/9.47	   A^2 -> H(f(d), f(d))
28.54/9.47	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.47	   A^2 -> H(f(e), f(e))
28.54/9.47	   A^2 -> H(f(k), f(k))
28.54/9.47	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.47	   A^2 -> H(a, U1(b, d))
28.54/9.47	   A^2 -> H(a, U1(c, c))
28.54/9.47	   A^2 -> H(a, f(e))
28.54/9.47	   A^2 -> H(a, f(k))
28.54/9.47	   A^2 -> H(a, U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.47	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.47	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.47	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.47	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.47	   A^2 -> H(U1(e, d), f(e))
28.54/9.47	   A^2 -> H(U1(e, d), f(k))
28.54/9.47	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.47	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.47	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.47	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.47	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.47	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.47	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.47	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.47	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.47	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.47	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.47	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.47	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.47	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.47	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.47	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.47	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, a), b)
28.54/9.47	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.47	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.47	   A^2 -> H(U1(c, a), c)
28.54/9.47	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.47	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.47	   A^2 -> H(U1(c, a), e)
28.54/9.47	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.47	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.47	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.47	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.47	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.47	   A^2 -> H(U1(d, e), f(e))
28.54/9.47	   A^2 -> H(U1(d, e), f(k))
28.54/9.47	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.47	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.47	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.47	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.47	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.47	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.47	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.47	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.47	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.47	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.47	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.47	   A^2 -> H(U1(d, a), b)
28.54/9.47	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.47	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.47	   A^2 -> H(U1(d, a), c)
28.54/9.47	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.47	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.47	   A^2 -> H(U1(d, a), e)
28.54/9.47	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.47	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.47	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.47	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.47	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.47	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.47	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.47	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.47	   A^2 -> H(U1(a, c), b)
28.54/9.47	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.47	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.47	   A^2 -> H(U1(a, c), c)
28.54/9.47	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.47	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.47	   A^2 -> H(U1(a, c), e)
28.54/9.47	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, d), b)
28.54/9.47	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.47	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.47	   A^2 -> H(U1(a, d), c)
28.54/9.47	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.47	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.47	   A^2 -> H(U1(a, d), e)
28.54/9.47	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, a), d)
28.54/9.47	   A^2 -> H(U1(a, a), k)
28.54/9.47	   A^2 -> H(k, U1(b, b))
28.54/9.47	   A^2 -> H(k, f(c))
28.54/9.47	   A^2 -> H(k, f(d))
28.54/9.47	   A^2 -> H(c, U1(c, b))
28.54/9.47	   A^2 -> H(c, U1(d, b))
28.54/9.47	   A^2 -> H(c, U1(b, c))
28.54/9.47	   A^2 -> H(c, U1(b, d))
28.54/9.47	   A^2 -> H(c, U1(c, c))
28.54/9.47	   A^2 -> H(c, f(e))
28.54/9.47	   A^2 -> H(c, f(k))
28.54/9.47	   A^2 -> H(c, U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.47	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.47	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.47	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.47	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.47	   A^2 -> H(U1(e, k), f(e))
28.54/9.47	   A^2 -> H(U1(e, k), f(k))
28.54/9.47	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.47	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.47	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.47	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.47	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.47	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.47	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.47	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.47	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.47	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.47	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.47	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.47	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.47	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.47	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.47	   A^2 -> H(U1(k, e), f(e))
28.54/9.47	   A^2 -> H(U1(k, e), f(k))
28.54/9.47	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.47	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.47	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.47	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.47	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.47	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.47	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.47	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.47	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, c), b)
28.54/9.47	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.47	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.47	   A^2 -> H(U1(c, c), e)
28.54/9.47	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.47	   A^2 -> H(e, U1(c, b))
28.54/9.47	   A^2 -> H(e, U1(d, b))
28.54/9.47	   A^2 -> H(e, U1(b, c))
28.54/9.47	   A^2 -> H(e, U1(b, d))
28.54/9.47	   A^2 -> H(e, U1(c, c))
28.54/9.47	   A^2 -> H(e, f(e))
28.54/9.47	   A^2 -> H(e, f(k))
28.54/9.47	   A^2 -> H(e, U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.47	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.47	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.47	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.47	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.47	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.47	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.47	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.47	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.47	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.47	   A^2 -> H(f(e), b)
28.54/9.47	   A^2 -> H(f(e), U1(e, d))
28.54/9.47	   A^2 -> H(f(e), U1(d, e))
28.54/9.47	   A^2 -> H(f(e), c)
28.54/9.47	   A^2 -> H(f(e), U1(e, k))
28.54/9.47	   A^2 -> H(f(e), U1(k, e))
28.54/9.47	   A^2 -> H(f(e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.47	   A^2 -> H(f(k), b)
28.54/9.47	   A^2 -> H(f(k), U1(e, d))
28.54/9.47	   A^2 -> H(f(k), U1(d, e))
28.54/9.47	   A^2 -> H(f(k), c)
28.54/9.47	   A^2 -> H(f(k), U1(e, k))
28.54/9.47	   A^2 -> H(f(k), U1(k, e))
28.54/9.47	   A^2 -> H(f(k), e)
28.54/9.47	   A^2 -> H(f(c), d)
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.47	   A^2 -> H(U1(k, k), f(e))
28.54/9.47	   A^2 -> H(U1(k, k), f(k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.47	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.47	   A^2 -> H(U1(d, d), b)
28.54/9.47	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.47	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.47	   A^2 -> H(U1(d, d), c)
28.54/9.47	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.47	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.47	   A^2 -> H(U1(d, d), e)
28.54/9.47	   A^2 -> H(f(d), d)
28.54/9.47	   A^2 -> H(f(d), k)
28.54/9.47	   A^2 -> H(U1(c, c), c)
28.54/9.47	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.47	   A^2 -> H(f(c), k)
28.54/9.47	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.47	   A^2 -> H(f(k), U1(k, k))
28.54/9.47	   A^2 -> H(f(e), e)
28.54/9.47	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.47	   A^2 -> H(d, U1(c, b))
28.54/9.47	   A^2 -> H(d, U1(d, b))
28.54/9.47	   A^2 -> H(d, U1(b, c))
28.54/9.47	   A^2 -> H(d, U1(b, d))
28.54/9.47	   A^2 -> H(d, U1(c, c))
28.54/9.47	   A^2 -> H(d, f(e))
28.54/9.47	   A^2 -> H(d, f(k))
28.54/9.47	   A^2 -> H(d, U1(d, d))
28.54/9.47	   A^2 -> H(a, U1(e, b))
28.54/9.47	   A^2 -> H(a, U1(k, b))
28.54/9.47	   A^2 -> H(a, U1(c, d))
28.54/9.47	   A^2 -> H(a, U1(d, c))
28.54/9.47	   A^2 -> H(a, U1(b, e))
28.54/9.47	   A^2 -> H(a, U1(b, k))
28.54/9.47	
28.54/9.47	The TRS R consists of the following rules:
28.54/9.47	
28.54/9.47	   f(x) -> U1(x, x)
28.54/9.47	   U1(e, x) -> x
28.54/9.47	   a -> c
28.54/9.47	   a -> d
28.54/9.47	   b -> c
28.54/9.47	   b -> d
28.54/9.47	   d -> k
28.54/9.47	   c -> e
28.54/9.47	   c -> k
28.54/9.47	
28.54/9.47	Q is empty.
28.54/9.47	We have to consider all minimal (P,Q,R)-chains.
28.54/9.47	----------------------------------------
28.54/9.47	
28.54/9.47	(1105) TransformationProof (EQUIVALENT)
28.54/9.47	By narrowing [LPAR04] the rule A^2 -> H(a, U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.47	
28.54/9.47	   (A^2 -> H(c, U1(b, d)),A^2 -> H(c, U1(b, d)))
28.54/9.47	   (A^2 -> H(d, U1(b, d)),A^2 -> H(d, U1(b, d)))
28.54/9.47	   (A^2 -> H(a, U1(c, d)),A^2 -> H(a, U1(c, d)))
28.54/9.47	   (A^2 -> H(a, U1(d, d)),A^2 -> H(a, U1(d, d)))
28.54/9.47	   (A^2 -> H(a, U1(b, k)),A^2 -> H(a, U1(b, k)))
28.54/9.47	
28.54/9.47	
28.54/9.47	----------------------------------------
28.54/9.47	
28.54/9.47	(1106)
28.54/9.47	Obligation:
28.54/9.47	Q DP problem:
28.54/9.47	The TRS P consists of the following rules:
28.54/9.47	
28.54/9.47	   H(x, x) -> G(x, x, f(k))
28.54/9.47	   G(d, x, x) -> A^2
28.54/9.47	   A^2 -> H(f(c), f(c))
28.54/9.47	   A^2 -> H(f(d), f(d))
28.54/9.47	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.47	   A^2 -> H(f(e), f(e))
28.54/9.47	   A^2 -> H(f(k), f(k))
28.54/9.47	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.47	   A^2 -> H(a, U1(c, c))
28.54/9.47	   A^2 -> H(a, f(e))
28.54/9.47	   A^2 -> H(a, f(k))
28.54/9.47	   A^2 -> H(a, U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.47	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.47	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.47	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.47	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.47	   A^2 -> H(U1(e, d), f(e))
28.54/9.47	   A^2 -> H(U1(e, d), f(k))
28.54/9.47	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.47	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.47	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.47	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.47	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.47	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.47	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.47	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.47	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.47	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.47	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.47	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.47	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.47	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.47	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.47	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.47	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, a), b)
28.54/9.47	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.47	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.47	   A^2 -> H(U1(c, a), c)
28.54/9.47	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.47	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.47	   A^2 -> H(U1(c, a), e)
28.54/9.47	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.47	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.47	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.47	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.47	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.47	   A^2 -> H(U1(d, e), f(e))
28.54/9.47	   A^2 -> H(U1(d, e), f(k))
28.54/9.47	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.47	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.47	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.47	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.47	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.47	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.47	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.47	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.47	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.47	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.47	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.47	   A^2 -> H(U1(d, a), b)
28.54/9.47	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.47	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.47	   A^2 -> H(U1(d, a), c)
28.54/9.47	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.47	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.47	   A^2 -> H(U1(d, a), e)
28.54/9.47	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.47	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.47	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.47	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.47	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.47	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.47	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.47	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.47	   A^2 -> H(U1(a, c), b)
28.54/9.47	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.47	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.47	   A^2 -> H(U1(a, c), c)
28.54/9.47	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.47	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.47	   A^2 -> H(U1(a, c), e)
28.54/9.47	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, d), b)
28.54/9.47	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.47	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.47	   A^2 -> H(U1(a, d), c)
28.54/9.47	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.47	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.47	   A^2 -> H(U1(a, d), e)
28.54/9.47	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, a), d)
28.54/9.47	   A^2 -> H(U1(a, a), k)
28.54/9.47	   A^2 -> H(k, U1(b, b))
28.54/9.47	   A^2 -> H(k, f(c))
28.54/9.47	   A^2 -> H(k, f(d))
28.54/9.47	   A^2 -> H(c, U1(c, b))
28.54/9.47	   A^2 -> H(c, U1(d, b))
28.54/9.47	   A^2 -> H(c, U1(b, c))
28.54/9.47	   A^2 -> H(c, U1(b, d))
28.54/9.47	   A^2 -> H(c, U1(c, c))
28.54/9.47	   A^2 -> H(c, f(e))
28.54/9.47	   A^2 -> H(c, f(k))
28.54/9.47	   A^2 -> H(c, U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.47	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.47	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.47	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.47	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.47	   A^2 -> H(U1(e, k), f(e))
28.54/9.47	   A^2 -> H(U1(e, k), f(k))
28.54/9.47	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.47	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.47	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.47	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.47	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.47	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.47	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.47	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.47	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.47	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.47	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.47	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.47	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.47	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.47	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.47	   A^2 -> H(U1(k, e), f(e))
28.54/9.47	   A^2 -> H(U1(k, e), f(k))
28.54/9.47	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.47	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.47	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.47	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.47	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.47	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.47	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.47	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.47	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, c), b)
28.54/9.47	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.47	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.47	   A^2 -> H(U1(c, c), e)
28.54/9.47	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.47	   A^2 -> H(e, U1(c, b))
28.54/9.47	   A^2 -> H(e, U1(d, b))
28.54/9.47	   A^2 -> H(e, U1(b, c))
28.54/9.47	   A^2 -> H(e, U1(b, d))
28.54/9.47	   A^2 -> H(e, U1(c, c))
28.54/9.47	   A^2 -> H(e, f(e))
28.54/9.47	   A^2 -> H(e, f(k))
28.54/9.47	   A^2 -> H(e, U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.47	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.47	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.47	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.47	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.47	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.47	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.47	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.47	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.47	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.47	   A^2 -> H(f(e), b)
28.54/9.47	   A^2 -> H(f(e), U1(e, d))
28.54/9.47	   A^2 -> H(f(e), U1(d, e))
28.54/9.47	   A^2 -> H(f(e), c)
28.54/9.47	   A^2 -> H(f(e), U1(e, k))
28.54/9.47	   A^2 -> H(f(e), U1(k, e))
28.54/9.47	   A^2 -> H(f(e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.47	   A^2 -> H(f(k), b)
28.54/9.47	   A^2 -> H(f(k), U1(e, d))
28.54/9.47	   A^2 -> H(f(k), U1(d, e))
28.54/9.47	   A^2 -> H(f(k), c)
28.54/9.47	   A^2 -> H(f(k), U1(e, k))
28.54/9.47	   A^2 -> H(f(k), U1(k, e))
28.54/9.47	   A^2 -> H(f(k), e)
28.54/9.47	   A^2 -> H(f(c), d)
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.47	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.47	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.47	   A^2 -> H(U1(k, k), f(e))
28.54/9.47	   A^2 -> H(U1(k, k), f(k))
28.54/9.47	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.47	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.47	   A^2 -> H(U1(d, d), b)
28.54/9.47	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.47	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.47	   A^2 -> H(U1(d, d), c)
28.54/9.47	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.47	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.47	   A^2 -> H(U1(d, d), e)
28.54/9.47	   A^2 -> H(f(d), d)
28.54/9.47	   A^2 -> H(f(d), k)
28.54/9.47	   A^2 -> H(U1(c, c), c)
28.54/9.47	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.47	   A^2 -> H(f(c), k)
28.54/9.47	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.47	   A^2 -> H(f(k), U1(k, k))
28.54/9.47	   A^2 -> H(f(e), e)
28.54/9.47	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.47	   A^2 -> H(d, U1(c, b))
28.54/9.47	   A^2 -> H(d, U1(d, b))
28.54/9.47	   A^2 -> H(d, U1(b, c))
28.54/9.47	   A^2 -> H(d, U1(b, d))
28.54/9.47	   A^2 -> H(d, U1(c, c))
28.54/9.47	   A^2 -> H(d, f(e))
28.54/9.47	   A^2 -> H(d, f(k))
28.54/9.47	   A^2 -> H(d, U1(d, d))
28.54/9.47	   A^2 -> H(a, U1(e, b))
28.54/9.47	   A^2 -> H(a, U1(k, b))
28.54/9.47	   A^2 -> H(a, U1(c, d))
28.54/9.47	   A^2 -> H(a, U1(d, c))
28.54/9.47	   A^2 -> H(a, U1(b, e))
28.54/9.47	   A^2 -> H(a, U1(b, k))
28.54/9.47	
28.54/9.47	The TRS R consists of the following rules:
28.54/9.47	
28.54/9.47	   f(x) -> U1(x, x)
28.54/9.47	   U1(e, x) -> x
28.54/9.47	   a -> c
28.54/9.47	   a -> d
28.54/9.47	   b -> c
28.54/9.47	   b -> d
28.54/9.47	   d -> k
28.54/9.47	   c -> e
28.54/9.47	   c -> k
28.54/9.47	
28.54/9.47	Q is empty.
28.54/9.47	We have to consider all minimal (P,Q,R)-chains.
28.54/9.47	----------------------------------------
28.54/9.47	
28.54/9.47	(1107) TransformationProof (EQUIVALENT)
28.54/9.47	By narrowing [LPAR04] the rule A^2 -> H(a, U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.47	
28.54/9.47	   (A^2 -> H(c, U1(c, c)),A^2 -> H(c, U1(c, c)))
28.54/9.47	   (A^2 -> H(d, U1(c, c)),A^2 -> H(d, U1(c, c)))
28.54/9.47	   (A^2 -> H(a, U1(e, c)),A^2 -> H(a, U1(e, c)))
28.54/9.47	   (A^2 -> H(a, U1(k, c)),A^2 -> H(a, U1(k, c)))
28.54/9.47	   (A^2 -> H(a, U1(c, e)),A^2 -> H(a, U1(c, e)))
28.54/9.47	   (A^2 -> H(a, U1(c, k)),A^2 -> H(a, U1(c, k)))
28.54/9.47	
28.54/9.47	
28.54/9.47	----------------------------------------
28.54/9.47	
28.54/9.47	(1108)
28.54/9.47	Obligation:
28.54/9.47	Q DP problem:
28.54/9.47	The TRS P consists of the following rules:
28.54/9.47	
28.54/9.47	   H(x, x) -> G(x, x, f(k))
28.54/9.47	   G(d, x, x) -> A^2
28.54/9.47	   A^2 -> H(f(c), f(c))
28.54/9.47	   A^2 -> H(f(d), f(d))
28.54/9.47	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.47	   A^2 -> H(f(e), f(e))
28.54/9.47	   A^2 -> H(f(k), f(k))
28.54/9.47	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.47	   A^2 -> H(a, f(e))
28.54/9.47	   A^2 -> H(a, f(k))
28.54/9.47	   A^2 -> H(a, U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.47	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.47	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.47	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.47	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.47	   A^2 -> H(U1(e, d), f(e))
28.54/9.47	   A^2 -> H(U1(e, d), f(k))
28.54/9.47	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.47	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.47	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.47	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.47	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.47	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.47	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.47	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.47	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.47	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.47	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.47	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.47	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.47	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.47	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.47	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.47	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.47	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.47	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.47	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.47	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.47	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.47	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.47	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.47	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.47	   A^2 -> H(U1(c, a), b)
28.54/9.47	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.47	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.47	   A^2 -> H(U1(c, a), c)
28.54/9.47	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.47	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.47	   A^2 -> H(U1(c, a), e)
28.54/9.47	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.47	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.47	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.47	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.47	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.47	   A^2 -> H(U1(d, e), f(e))
28.54/9.47	   A^2 -> H(U1(d, e), f(k))
28.54/9.47	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.47	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.47	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.47	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.47	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.47	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.47	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.47	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.47	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.47	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.47	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.47	   A^2 -> H(U1(d, a), b)
28.54/9.47	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.47	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.47	   A^2 -> H(U1(d, a), c)
28.54/9.47	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.47	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.47	   A^2 -> H(U1(d, a), e)
28.54/9.47	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.47	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.47	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.47	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.47	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.47	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.47	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.47	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.47	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.47	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.47	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.47	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.47	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.47	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.47	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.47	   A^2 -> H(U1(a, c), b)
28.54/9.47	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.47	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.47	   A^2 -> H(U1(a, c), c)
28.54/9.47	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.47	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.47	   A^2 -> H(U1(a, c), e)
28.54/9.47	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, d), b)
28.54/9.47	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.47	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.47	   A^2 -> H(U1(a, d), c)
28.54/9.47	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.47	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.47	   A^2 -> H(U1(a, d), e)
28.54/9.47	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.47	   A^2 -> H(U1(a, a), d)
28.54/9.47	   A^2 -> H(U1(a, a), k)
28.54/9.47	   A^2 -> H(k, U1(b, b))
28.54/9.47	   A^2 -> H(k, f(c))
28.54/9.47	   A^2 -> H(k, f(d))
28.54/9.47	   A^2 -> H(c, U1(c, b))
28.54/9.47	   A^2 -> H(c, U1(d, b))
28.54/9.47	   A^2 -> H(c, U1(b, c))
28.54/9.47	   A^2 -> H(c, U1(b, d))
28.54/9.47	   A^2 -> H(c, U1(c, c))
28.54/9.47	   A^2 -> H(c, f(e))
28.54/9.47	   A^2 -> H(c, f(k))
28.54/9.47	   A^2 -> H(c, U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.47	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.47	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.47	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.47	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.47	   A^2 -> H(U1(e, k), f(e))
28.54/9.47	   A^2 -> H(U1(e, k), f(k))
28.54/9.47	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.47	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.47	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.47	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.47	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.47	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.47	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.47	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.47	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.47	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.47	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.47	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.47	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.47	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.47	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.47	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.47	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.48	   A^2 -> H(U1(k, e), f(e))
28.54/9.48	   A^2 -> H(U1(k, e), f(k))
28.54/9.48	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.48	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.48	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.48	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.48	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.48	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.48	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.48	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.48	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, c), b)
28.54/9.48	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.48	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.48	   A^2 -> H(U1(c, c), e)
28.54/9.48	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.48	   A^2 -> H(e, U1(c, b))
28.54/9.48	   A^2 -> H(e, U1(d, b))
28.54/9.48	   A^2 -> H(e, U1(b, c))
28.54/9.48	   A^2 -> H(e, U1(b, d))
28.54/9.48	   A^2 -> H(e, U1(c, c))
28.54/9.48	   A^2 -> H(e, f(e))
28.54/9.48	   A^2 -> H(e, f(k))
28.54/9.48	   A^2 -> H(e, U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.48	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.48	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.48	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.48	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.48	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.48	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.48	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.48	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.48	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.48	   A^2 -> H(f(e), b)
28.54/9.48	   A^2 -> H(f(e), U1(e, d))
28.54/9.48	   A^2 -> H(f(e), U1(d, e))
28.54/9.48	   A^2 -> H(f(e), c)
28.54/9.48	   A^2 -> H(f(e), U1(e, k))
28.54/9.48	   A^2 -> H(f(e), U1(k, e))
28.54/9.48	   A^2 -> H(f(e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.48	   A^2 -> H(f(k), b)
28.54/9.48	   A^2 -> H(f(k), U1(e, d))
28.54/9.48	   A^2 -> H(f(k), U1(d, e))
28.54/9.48	   A^2 -> H(f(k), c)
28.54/9.48	   A^2 -> H(f(k), U1(e, k))
28.54/9.48	   A^2 -> H(f(k), U1(k, e))
28.54/9.48	   A^2 -> H(f(k), e)
28.54/9.48	   A^2 -> H(f(c), d)
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.48	   A^2 -> H(U1(k, k), f(e))
28.54/9.48	   A^2 -> H(U1(k, k), f(k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.48	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.48	   A^2 -> H(U1(d, d), b)
28.54/9.48	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.48	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.48	   A^2 -> H(U1(d, d), c)
28.54/9.48	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.48	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.48	   A^2 -> H(U1(d, d), e)
28.54/9.48	   A^2 -> H(f(d), d)
28.54/9.48	   A^2 -> H(f(d), k)
28.54/9.48	   A^2 -> H(U1(c, c), c)
28.54/9.48	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.48	   A^2 -> H(f(c), k)
28.54/9.48	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.48	   A^2 -> H(f(k), U1(k, k))
28.54/9.48	   A^2 -> H(f(e), e)
28.54/9.48	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.48	   A^2 -> H(d, U1(c, b))
28.54/9.48	   A^2 -> H(d, U1(d, b))
28.54/9.48	   A^2 -> H(d, U1(b, c))
28.54/9.48	   A^2 -> H(d, U1(b, d))
28.54/9.48	   A^2 -> H(d, U1(c, c))
28.54/9.48	   A^2 -> H(d, f(e))
28.54/9.48	   A^2 -> H(d, f(k))
28.54/9.48	   A^2 -> H(d, U1(d, d))
28.54/9.48	   A^2 -> H(a, U1(e, b))
28.54/9.48	   A^2 -> H(a, U1(k, b))
28.54/9.48	   A^2 -> H(a, U1(c, d))
28.54/9.48	   A^2 -> H(a, U1(d, c))
28.54/9.48	   A^2 -> H(a, U1(b, e))
28.54/9.48	   A^2 -> H(a, U1(b, k))
28.54/9.48	   A^2 -> H(a, U1(e, c))
28.54/9.48	   A^2 -> H(a, U1(k, c))
28.54/9.48	   A^2 -> H(a, U1(c, e))
28.54/9.48	   A^2 -> H(a, U1(c, k))
28.54/9.48	
28.54/9.48	The TRS R consists of the following rules:
28.54/9.48	
28.54/9.48	   f(x) -> U1(x, x)
28.54/9.48	   U1(e, x) -> x
28.54/9.48	   a -> c
28.54/9.48	   a -> d
28.54/9.48	   b -> c
28.54/9.48	   b -> d
28.54/9.48	   d -> k
28.54/9.48	   c -> e
28.54/9.48	   c -> k
28.54/9.48	
28.54/9.48	Q is empty.
28.54/9.48	We have to consider all minimal (P,Q,R)-chains.
28.54/9.48	----------------------------------------
28.54/9.48	
28.54/9.48	(1109) TransformationProof (EQUIVALENT)
28.54/9.48	By narrowing [LPAR04] the rule A^2 -> H(a, f(e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.48	
28.54/9.48	   (A^2 -> H(c, f(e)),A^2 -> H(c, f(e)))
28.54/9.48	   (A^2 -> H(d, f(e)),A^2 -> H(d, f(e)))
28.54/9.48	   (A^2 -> H(a, U1(e, e)),A^2 -> H(a, U1(e, e)))
28.54/9.48	
28.54/9.48	
28.54/9.48	----------------------------------------
28.54/9.48	
28.54/9.48	(1110)
28.54/9.48	Obligation:
28.54/9.48	Q DP problem:
28.54/9.48	The TRS P consists of the following rules:
28.54/9.48	
28.54/9.48	   H(x, x) -> G(x, x, f(k))
28.54/9.48	   G(d, x, x) -> A^2
28.54/9.48	   A^2 -> H(f(c), f(c))
28.54/9.48	   A^2 -> H(f(d), f(d))
28.54/9.48	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.48	   A^2 -> H(f(e), f(e))
28.54/9.48	   A^2 -> H(f(k), f(k))
28.54/9.48	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.48	   A^2 -> H(a, f(k))
28.54/9.48	   A^2 -> H(a, U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.48	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.48	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.48	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.48	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.48	   A^2 -> H(U1(e, d), f(e))
28.54/9.48	   A^2 -> H(U1(e, d), f(k))
28.54/9.48	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.48	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.48	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.48	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.48	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.48	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.48	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.48	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.48	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.48	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.48	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.48	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.48	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.48	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.48	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.48	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.48	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, a), b)
28.54/9.48	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.48	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.48	   A^2 -> H(U1(c, a), c)
28.54/9.48	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.48	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.48	   A^2 -> H(U1(c, a), e)
28.54/9.48	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.48	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.48	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.48	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.48	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.48	   A^2 -> H(U1(d, e), f(e))
28.54/9.48	   A^2 -> H(U1(d, e), f(k))
28.54/9.48	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.48	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.48	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.48	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.48	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.48	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.48	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.48	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.48	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.48	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.48	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.48	   A^2 -> H(U1(d, a), b)
28.54/9.48	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.48	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.48	   A^2 -> H(U1(d, a), c)
28.54/9.48	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.48	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.48	   A^2 -> H(U1(d, a), e)
28.54/9.48	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.48	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.48	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.48	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.48	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.48	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.48	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.48	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.48	   A^2 -> H(U1(a, c), b)
28.54/9.48	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.48	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.48	   A^2 -> H(U1(a, c), c)
28.54/9.48	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.48	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.48	   A^2 -> H(U1(a, c), e)
28.54/9.48	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, d), b)
28.54/9.48	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.48	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.48	   A^2 -> H(U1(a, d), c)
28.54/9.48	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.48	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.48	   A^2 -> H(U1(a, d), e)
28.54/9.48	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, a), d)
28.54/9.48	   A^2 -> H(U1(a, a), k)
28.54/9.48	   A^2 -> H(k, U1(b, b))
28.54/9.48	   A^2 -> H(k, f(c))
28.54/9.48	   A^2 -> H(k, f(d))
28.54/9.48	   A^2 -> H(c, U1(c, b))
28.54/9.48	   A^2 -> H(c, U1(d, b))
28.54/9.48	   A^2 -> H(c, U1(b, c))
28.54/9.48	   A^2 -> H(c, U1(b, d))
28.54/9.48	   A^2 -> H(c, U1(c, c))
28.54/9.48	   A^2 -> H(c, f(e))
28.54/9.48	   A^2 -> H(c, f(k))
28.54/9.48	   A^2 -> H(c, U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.48	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.48	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.48	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.48	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.48	   A^2 -> H(U1(e, k), f(e))
28.54/9.48	   A^2 -> H(U1(e, k), f(k))
28.54/9.48	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.48	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.48	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.48	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.48	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.48	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.48	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.48	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.48	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.48	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.48	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.48	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.48	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.48	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.48	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.48	   A^2 -> H(U1(k, e), f(e))
28.54/9.48	   A^2 -> H(U1(k, e), f(k))
28.54/9.48	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.48	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.48	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.48	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.48	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.48	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.48	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.48	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.48	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, c), b)
28.54/9.48	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.48	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.48	   A^2 -> H(U1(c, c), e)
28.54/9.48	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.48	   A^2 -> H(e, U1(c, b))
28.54/9.48	   A^2 -> H(e, U1(d, b))
28.54/9.48	   A^2 -> H(e, U1(b, c))
28.54/9.48	   A^2 -> H(e, U1(b, d))
28.54/9.48	   A^2 -> H(e, U1(c, c))
28.54/9.48	   A^2 -> H(e, f(e))
28.54/9.48	   A^2 -> H(e, f(k))
28.54/9.48	   A^2 -> H(e, U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.48	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.48	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.48	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.48	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.48	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.48	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.48	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.48	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.48	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.48	   A^2 -> H(f(e), b)
28.54/9.48	   A^2 -> H(f(e), U1(e, d))
28.54/9.48	   A^2 -> H(f(e), U1(d, e))
28.54/9.48	   A^2 -> H(f(e), c)
28.54/9.48	   A^2 -> H(f(e), U1(e, k))
28.54/9.48	   A^2 -> H(f(e), U1(k, e))
28.54/9.48	   A^2 -> H(f(e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.48	   A^2 -> H(f(k), b)
28.54/9.48	   A^2 -> H(f(k), U1(e, d))
28.54/9.48	   A^2 -> H(f(k), U1(d, e))
28.54/9.48	   A^2 -> H(f(k), c)
28.54/9.48	   A^2 -> H(f(k), U1(e, k))
28.54/9.48	   A^2 -> H(f(k), U1(k, e))
28.54/9.48	   A^2 -> H(f(k), e)
28.54/9.48	   A^2 -> H(f(c), d)
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.48	   A^2 -> H(U1(k, k), f(e))
28.54/9.48	   A^2 -> H(U1(k, k), f(k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.48	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.48	   A^2 -> H(U1(d, d), b)
28.54/9.48	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.48	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.48	   A^2 -> H(U1(d, d), c)
28.54/9.48	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.48	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.48	   A^2 -> H(U1(d, d), e)
28.54/9.48	   A^2 -> H(f(d), d)
28.54/9.48	   A^2 -> H(f(d), k)
28.54/9.48	   A^2 -> H(U1(c, c), c)
28.54/9.48	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.48	   A^2 -> H(f(c), k)
28.54/9.48	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.48	   A^2 -> H(f(k), U1(k, k))
28.54/9.48	   A^2 -> H(f(e), e)
28.54/9.48	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.48	   A^2 -> H(d, U1(c, b))
28.54/9.48	   A^2 -> H(d, U1(d, b))
28.54/9.48	   A^2 -> H(d, U1(b, c))
28.54/9.48	   A^2 -> H(d, U1(b, d))
28.54/9.48	   A^2 -> H(d, U1(c, c))
28.54/9.48	   A^2 -> H(d, f(e))
28.54/9.48	   A^2 -> H(d, f(k))
28.54/9.48	   A^2 -> H(d, U1(d, d))
28.54/9.48	   A^2 -> H(a, U1(e, b))
28.54/9.48	   A^2 -> H(a, U1(k, b))
28.54/9.48	   A^2 -> H(a, U1(c, d))
28.54/9.48	   A^2 -> H(a, U1(d, c))
28.54/9.48	   A^2 -> H(a, U1(b, e))
28.54/9.48	   A^2 -> H(a, U1(b, k))
28.54/9.48	   A^2 -> H(a, U1(e, c))
28.54/9.48	   A^2 -> H(a, U1(k, c))
28.54/9.48	   A^2 -> H(a, U1(c, e))
28.54/9.48	   A^2 -> H(a, U1(c, k))
28.54/9.48	   A^2 -> H(a, U1(e, e))
28.54/9.48	
28.54/9.48	The TRS R consists of the following rules:
28.54/9.48	
28.54/9.48	   f(x) -> U1(x, x)
28.54/9.48	   U1(e, x) -> x
28.54/9.48	   a -> c
28.54/9.48	   a -> d
28.54/9.48	   b -> c
28.54/9.48	   b -> d
28.54/9.48	   d -> k
28.54/9.48	   c -> e
28.54/9.48	   c -> k
28.54/9.48	
28.54/9.48	Q is empty.
28.54/9.48	We have to consider all minimal (P,Q,R)-chains.
28.54/9.48	----------------------------------------
28.54/9.48	
28.54/9.48	(1111) TransformationProof (EQUIVALENT)
28.54/9.48	By narrowing [LPAR04] the rule A^2 -> H(a, f(k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.48	
28.54/9.48	   (A^2 -> H(c, f(k)),A^2 -> H(c, f(k)))
28.54/9.48	   (A^2 -> H(d, f(k)),A^2 -> H(d, f(k)))
28.54/9.48	   (A^2 -> H(a, U1(k, k)),A^2 -> H(a, U1(k, k)))
28.54/9.48	
28.54/9.48	
28.54/9.48	----------------------------------------
28.54/9.48	
28.54/9.48	(1112)
28.54/9.48	Obligation:
28.54/9.48	Q DP problem:
28.54/9.48	The TRS P consists of the following rules:
28.54/9.48	
28.54/9.48	   H(x, x) -> G(x, x, f(k))
28.54/9.48	   G(d, x, x) -> A^2
28.54/9.48	   A^2 -> H(f(c), f(c))
28.54/9.48	   A^2 -> H(f(d), f(d))
28.54/9.48	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.48	   A^2 -> H(f(e), f(e))
28.54/9.48	   A^2 -> H(f(k), f(k))
28.54/9.48	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.48	   A^2 -> H(a, U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.48	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.48	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.48	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.48	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.48	   A^2 -> H(U1(e, d), f(e))
28.54/9.48	   A^2 -> H(U1(e, d), f(k))
28.54/9.48	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.48	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.48	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.48	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.48	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.48	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.48	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.48	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.48	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.48	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.48	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.48	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.48	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.48	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.48	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.48	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.48	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, a), b)
28.54/9.48	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.48	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.48	   A^2 -> H(U1(c, a), c)
28.54/9.48	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.48	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.48	   A^2 -> H(U1(c, a), e)
28.54/9.48	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.48	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.48	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.48	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.48	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.48	   A^2 -> H(U1(d, e), f(e))
28.54/9.48	   A^2 -> H(U1(d, e), f(k))
28.54/9.48	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.48	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.48	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.48	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.48	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.48	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.48	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.48	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.48	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.48	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.48	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.48	   A^2 -> H(U1(d, a), b)
28.54/9.48	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.48	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.48	   A^2 -> H(U1(d, a), c)
28.54/9.48	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.48	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.48	   A^2 -> H(U1(d, a), e)
28.54/9.48	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.48	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.48	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.48	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.48	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.48	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.48	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.48	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.48	   A^2 -> H(U1(a, c), b)
28.54/9.48	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.48	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.48	   A^2 -> H(U1(a, c), c)
28.54/9.48	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.48	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.48	   A^2 -> H(U1(a, c), e)
28.54/9.48	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, d), b)
28.54/9.48	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.48	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.48	   A^2 -> H(U1(a, d), c)
28.54/9.48	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.48	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.48	   A^2 -> H(U1(a, d), e)
28.54/9.48	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, a), d)
28.54/9.48	   A^2 -> H(U1(a, a), k)
28.54/9.48	   A^2 -> H(k, U1(b, b))
28.54/9.48	   A^2 -> H(k, f(c))
28.54/9.48	   A^2 -> H(k, f(d))
28.54/9.48	   A^2 -> H(c, U1(c, b))
28.54/9.48	   A^2 -> H(c, U1(d, b))
28.54/9.48	   A^2 -> H(c, U1(b, c))
28.54/9.48	   A^2 -> H(c, U1(b, d))
28.54/9.48	   A^2 -> H(c, U1(c, c))
28.54/9.48	   A^2 -> H(c, f(e))
28.54/9.48	   A^2 -> H(c, f(k))
28.54/9.48	   A^2 -> H(c, U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.48	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.48	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.48	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.48	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.48	   A^2 -> H(U1(e, k), f(e))
28.54/9.48	   A^2 -> H(U1(e, k), f(k))
28.54/9.48	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.48	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.48	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.48	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.48	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.48	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.48	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.48	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.48	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.48	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.48	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.48	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.48	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.48	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.48	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.48	   A^2 -> H(U1(k, e), f(e))
28.54/9.48	   A^2 -> H(U1(k, e), f(k))
28.54/9.48	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.48	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.48	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.48	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.48	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.48	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.48	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.48	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.48	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, c), b)
28.54/9.48	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.48	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.48	   A^2 -> H(U1(c, c), e)
28.54/9.48	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.48	   A^2 -> H(e, U1(c, b))
28.54/9.48	   A^2 -> H(e, U1(d, b))
28.54/9.48	   A^2 -> H(e, U1(b, c))
28.54/9.48	   A^2 -> H(e, U1(b, d))
28.54/9.48	   A^2 -> H(e, U1(c, c))
28.54/9.48	   A^2 -> H(e, f(e))
28.54/9.48	   A^2 -> H(e, f(k))
28.54/9.48	   A^2 -> H(e, U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.48	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.48	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.48	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.48	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.48	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.48	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.48	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.48	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.48	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.48	   A^2 -> H(f(e), b)
28.54/9.48	   A^2 -> H(f(e), U1(e, d))
28.54/9.48	   A^2 -> H(f(e), U1(d, e))
28.54/9.48	   A^2 -> H(f(e), c)
28.54/9.48	   A^2 -> H(f(e), U1(e, k))
28.54/9.48	   A^2 -> H(f(e), U1(k, e))
28.54/9.48	   A^2 -> H(f(e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.48	   A^2 -> H(f(k), b)
28.54/9.48	   A^2 -> H(f(k), U1(e, d))
28.54/9.48	   A^2 -> H(f(k), U1(d, e))
28.54/9.48	   A^2 -> H(f(k), c)
28.54/9.48	   A^2 -> H(f(k), U1(e, k))
28.54/9.48	   A^2 -> H(f(k), U1(k, e))
28.54/9.48	   A^2 -> H(f(k), e)
28.54/9.48	   A^2 -> H(f(c), d)
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.48	   A^2 -> H(U1(k, k), f(e))
28.54/9.48	   A^2 -> H(U1(k, k), f(k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.48	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.48	   A^2 -> H(U1(d, d), b)
28.54/9.48	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.48	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.48	   A^2 -> H(U1(d, d), c)
28.54/9.48	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.48	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.48	   A^2 -> H(U1(d, d), e)
28.54/9.48	   A^2 -> H(f(d), d)
28.54/9.48	   A^2 -> H(f(d), k)
28.54/9.48	   A^2 -> H(U1(c, c), c)
28.54/9.48	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.48	   A^2 -> H(f(c), k)
28.54/9.48	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.48	   A^2 -> H(f(k), U1(k, k))
28.54/9.48	   A^2 -> H(f(e), e)
28.54/9.48	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.48	   A^2 -> H(d, U1(c, b))
28.54/9.48	   A^2 -> H(d, U1(d, b))
28.54/9.48	   A^2 -> H(d, U1(b, c))
28.54/9.48	   A^2 -> H(d, U1(b, d))
28.54/9.48	   A^2 -> H(d, U1(c, c))
28.54/9.48	   A^2 -> H(d, f(e))
28.54/9.48	   A^2 -> H(d, f(k))
28.54/9.48	   A^2 -> H(d, U1(d, d))
28.54/9.48	   A^2 -> H(a, U1(e, b))
28.54/9.48	   A^2 -> H(a, U1(k, b))
28.54/9.48	   A^2 -> H(a, U1(c, d))
28.54/9.48	   A^2 -> H(a, U1(d, c))
28.54/9.48	   A^2 -> H(a, U1(b, e))
28.54/9.48	   A^2 -> H(a, U1(b, k))
28.54/9.48	   A^2 -> H(a, U1(e, c))
28.54/9.48	   A^2 -> H(a, U1(k, c))
28.54/9.48	   A^2 -> H(a, U1(c, e))
28.54/9.48	   A^2 -> H(a, U1(c, k))
28.54/9.48	   A^2 -> H(a, U1(e, e))
28.54/9.48	   A^2 -> H(a, U1(k, k))
28.54/9.48	
28.54/9.48	The TRS R consists of the following rules:
28.54/9.48	
28.54/9.48	   f(x) -> U1(x, x)
28.54/9.48	   U1(e, x) -> x
28.54/9.48	   a -> c
28.54/9.48	   a -> d
28.54/9.48	   b -> c
28.54/9.48	   b -> d
28.54/9.48	   d -> k
28.54/9.48	   c -> e
28.54/9.48	   c -> k
28.54/9.48	
28.54/9.48	Q is empty.
28.54/9.48	We have to consider all minimal (P,Q,R)-chains.
28.54/9.48	----------------------------------------
28.54/9.48	
28.54/9.48	(1113) TransformationProof (EQUIVALENT)
28.54/9.48	By narrowing [LPAR04] the rule A^2 -> H(a, U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.48	
28.54/9.48	   (A^2 -> H(c, U1(d, d)),A^2 -> H(c, U1(d, d)))
28.54/9.48	   (A^2 -> H(d, U1(d, d)),A^2 -> H(d, U1(d, d)))
28.54/9.48	   (A^2 -> H(a, U1(k, d)),A^2 -> H(a, U1(k, d)))
28.54/9.48	   (A^2 -> H(a, U1(d, k)),A^2 -> H(a, U1(d, k)))
28.54/9.48	
28.54/9.48	
28.54/9.48	----------------------------------------
28.54/9.48	
28.54/9.48	(1114)
28.54/9.48	Obligation:
28.54/9.48	Q DP problem:
28.54/9.48	The TRS P consists of the following rules:
28.54/9.48	
28.54/9.48	   H(x, x) -> G(x, x, f(k))
28.54/9.48	   G(d, x, x) -> A^2
28.54/9.48	   A^2 -> H(f(c), f(c))
28.54/9.48	   A^2 -> H(f(d), f(d))
28.54/9.48	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.48	   A^2 -> H(f(e), f(e))
28.54/9.48	   A^2 -> H(f(k), f(k))
28.54/9.48	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, d), U1(c, b))
28.54/9.48	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.48	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.48	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.48	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.48	   A^2 -> H(U1(e, d), f(e))
28.54/9.48	   A^2 -> H(U1(e, d), f(k))
28.54/9.48	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.48	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.48	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.48	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.48	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.48	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.48	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.48	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.48	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.48	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.48	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.48	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.48	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.48	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.48	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.48	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.48	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, a), b)
28.54/9.48	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.48	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.48	   A^2 -> H(U1(c, a), c)
28.54/9.48	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.48	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.48	   A^2 -> H(U1(c, a), e)
28.54/9.48	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.48	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.48	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.48	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.48	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.48	   A^2 -> H(U1(d, e), f(e))
28.54/9.48	   A^2 -> H(U1(d, e), f(k))
28.54/9.48	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.48	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.48	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.48	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.48	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.48	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.48	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.48	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.48	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.48	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.48	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.48	   A^2 -> H(U1(d, a), b)
28.54/9.48	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.48	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.48	   A^2 -> H(U1(d, a), c)
28.54/9.48	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.48	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.48	   A^2 -> H(U1(d, a), e)
28.54/9.48	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.48	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.48	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.48	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.48	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.48	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.48	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.48	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.48	   A^2 -> H(U1(a, c), b)
28.54/9.48	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.48	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.48	   A^2 -> H(U1(a, c), c)
28.54/9.48	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.48	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.48	   A^2 -> H(U1(a, c), e)
28.54/9.48	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, d), b)
28.54/9.48	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.48	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.48	   A^2 -> H(U1(a, d), c)
28.54/9.48	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.48	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.48	   A^2 -> H(U1(a, d), e)
28.54/9.48	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, a), d)
28.54/9.48	   A^2 -> H(U1(a, a), k)
28.54/9.48	   A^2 -> H(k, U1(b, b))
28.54/9.48	   A^2 -> H(k, f(c))
28.54/9.48	   A^2 -> H(k, f(d))
28.54/9.48	   A^2 -> H(c, U1(c, b))
28.54/9.48	   A^2 -> H(c, U1(d, b))
28.54/9.48	   A^2 -> H(c, U1(b, c))
28.54/9.48	   A^2 -> H(c, U1(b, d))
28.54/9.48	   A^2 -> H(c, U1(c, c))
28.54/9.48	   A^2 -> H(c, f(e))
28.54/9.48	   A^2 -> H(c, f(k))
28.54/9.48	   A^2 -> H(c, U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.48	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.48	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.48	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.48	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.48	   A^2 -> H(U1(e, k), f(e))
28.54/9.48	   A^2 -> H(U1(e, k), f(k))
28.54/9.48	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.48	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.48	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.48	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.48	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.48	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.48	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.48	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.48	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.48	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.48	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.48	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.48	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.48	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.48	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.48	   A^2 -> H(U1(k, e), f(e))
28.54/9.48	   A^2 -> H(U1(k, e), f(k))
28.54/9.48	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.48	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.48	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.48	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.48	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.48	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.48	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.48	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.48	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, c), b)
28.54/9.48	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.48	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.48	   A^2 -> H(U1(c, c), e)
28.54/9.48	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.48	   A^2 -> H(e, U1(c, b))
28.54/9.48	   A^2 -> H(e, U1(d, b))
28.54/9.48	   A^2 -> H(e, U1(b, c))
28.54/9.48	   A^2 -> H(e, U1(b, d))
28.54/9.48	   A^2 -> H(e, U1(c, c))
28.54/9.48	   A^2 -> H(e, f(e))
28.54/9.48	   A^2 -> H(e, f(k))
28.54/9.48	   A^2 -> H(e, U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.48	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.48	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.48	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.48	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.48	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.48	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.48	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.48	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.48	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.48	   A^2 -> H(f(e), b)
28.54/9.48	   A^2 -> H(f(e), U1(e, d))
28.54/9.48	   A^2 -> H(f(e), U1(d, e))
28.54/9.48	   A^2 -> H(f(e), c)
28.54/9.48	   A^2 -> H(f(e), U1(e, k))
28.54/9.48	   A^2 -> H(f(e), U1(k, e))
28.54/9.48	   A^2 -> H(f(e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.48	   A^2 -> H(f(k), b)
28.54/9.48	   A^2 -> H(f(k), U1(e, d))
28.54/9.48	   A^2 -> H(f(k), U1(d, e))
28.54/9.48	   A^2 -> H(f(k), c)
28.54/9.48	   A^2 -> H(f(k), U1(e, k))
28.54/9.48	   A^2 -> H(f(k), U1(k, e))
28.54/9.48	   A^2 -> H(f(k), e)
28.54/9.48	   A^2 -> H(f(c), d)
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.48	   A^2 -> H(U1(k, k), f(e))
28.54/9.48	   A^2 -> H(U1(k, k), f(k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.48	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.48	   A^2 -> H(U1(d, d), b)
28.54/9.48	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.48	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.48	   A^2 -> H(U1(d, d), c)
28.54/9.48	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.48	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.48	   A^2 -> H(U1(d, d), e)
28.54/9.48	   A^2 -> H(f(d), d)
28.54/9.48	   A^2 -> H(f(d), k)
28.54/9.48	   A^2 -> H(U1(c, c), c)
28.54/9.48	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.48	   A^2 -> H(f(c), k)
28.54/9.48	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.48	   A^2 -> H(f(k), U1(k, k))
28.54/9.48	   A^2 -> H(f(e), e)
28.54/9.48	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.48	   A^2 -> H(d, U1(c, b))
28.54/9.48	   A^2 -> H(d, U1(d, b))
28.54/9.48	   A^2 -> H(d, U1(b, c))
28.54/9.48	   A^2 -> H(d, U1(b, d))
28.54/9.48	   A^2 -> H(d, U1(c, c))
28.54/9.48	   A^2 -> H(d, f(e))
28.54/9.48	   A^2 -> H(d, f(k))
28.54/9.48	   A^2 -> H(d, U1(d, d))
28.54/9.48	   A^2 -> H(a, U1(e, b))
28.54/9.48	   A^2 -> H(a, U1(k, b))
28.54/9.48	   A^2 -> H(a, U1(c, d))
28.54/9.48	   A^2 -> H(a, U1(d, c))
28.54/9.48	   A^2 -> H(a, U1(b, e))
28.54/9.48	   A^2 -> H(a, U1(b, k))
28.54/9.48	   A^2 -> H(a, U1(e, c))
28.54/9.48	   A^2 -> H(a, U1(k, c))
28.54/9.48	   A^2 -> H(a, U1(c, e))
28.54/9.48	   A^2 -> H(a, U1(c, k))
28.54/9.48	   A^2 -> H(a, U1(e, e))
28.54/9.48	   A^2 -> H(a, U1(k, k))
28.54/9.48	   A^2 -> H(a, U1(k, d))
28.54/9.48	   A^2 -> H(a, U1(d, k))
28.54/9.48	
28.54/9.48	The TRS R consists of the following rules:
28.54/9.48	
28.54/9.48	   f(x) -> U1(x, x)
28.54/9.48	   U1(e, x) -> x
28.54/9.48	   a -> c
28.54/9.48	   a -> d
28.54/9.48	   b -> c
28.54/9.48	   b -> d
28.54/9.48	   d -> k
28.54/9.48	   c -> e
28.54/9.48	   c -> k
28.54/9.48	
28.54/9.48	Q is empty.
28.54/9.48	We have to consider all minimal (P,Q,R)-chains.
28.54/9.48	----------------------------------------
28.54/9.48	
28.54/9.48	(1115) TransformationProof (EQUIVALENT)
28.54/9.48	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.48	
28.54/9.48	   (A^2 -> H(d, U1(c, b)),A^2 -> H(d, U1(c, b)))
28.54/9.48	   (A^2 -> H(U1(e, k), U1(c, b)),A^2 -> H(U1(e, k), U1(c, b)))
28.54/9.48	   (A^2 -> H(U1(e, d), U1(e, b)),A^2 -> H(U1(e, d), U1(e, b)))
28.54/9.48	   (A^2 -> H(U1(e, d), U1(k, b)),A^2 -> H(U1(e, d), U1(k, b)))
28.54/9.48	   (A^2 -> H(U1(e, d), U1(c, c)),A^2 -> H(U1(e, d), U1(c, c)))
28.54/9.48	   (A^2 -> H(U1(e, d), U1(c, d)),A^2 -> H(U1(e, d), U1(c, d)))
28.54/9.48	
28.54/9.48	
28.54/9.48	----------------------------------------
28.54/9.48	
28.54/9.48	(1116)
28.54/9.48	Obligation:
28.54/9.48	Q DP problem:
28.54/9.48	The TRS P consists of the following rules:
28.54/9.48	
28.54/9.48	   H(x, x) -> G(x, x, f(k))
28.54/9.48	   G(d, x, x) -> A^2
28.54/9.48	   A^2 -> H(f(c), f(c))
28.54/9.48	   A^2 -> H(f(d), f(d))
28.54/9.48	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.48	   A^2 -> H(f(e), f(e))
28.54/9.48	   A^2 -> H(f(k), f(k))
28.54/9.48	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, d), U1(d, b))
28.54/9.48	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.48	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.48	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.48	   A^2 -> H(U1(e, d), f(e))
28.54/9.48	   A^2 -> H(U1(e, d), f(k))
28.54/9.48	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.48	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.48	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.48	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.48	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.48	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.48	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.48	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.48	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.48	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.48	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.48	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.48	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.48	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.48	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.48	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.48	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, a), b)
28.54/9.48	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.48	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.48	   A^2 -> H(U1(c, a), c)
28.54/9.48	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.48	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.48	   A^2 -> H(U1(c, a), e)
28.54/9.48	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.48	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.48	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.48	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.48	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.48	   A^2 -> H(U1(d, e), f(e))
28.54/9.48	   A^2 -> H(U1(d, e), f(k))
28.54/9.48	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.48	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.48	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.48	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.48	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.48	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.48	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.48	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.48	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.48	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.48	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.48	   A^2 -> H(U1(d, a), b)
28.54/9.48	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.48	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.48	   A^2 -> H(U1(d, a), c)
28.54/9.48	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.48	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.48	   A^2 -> H(U1(d, a), e)
28.54/9.48	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.48	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.48	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.48	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.48	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.48	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.48	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.48	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.48	   A^2 -> H(U1(a, c), b)
28.54/9.48	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.48	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.48	   A^2 -> H(U1(a, c), c)
28.54/9.48	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.48	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.48	   A^2 -> H(U1(a, c), e)
28.54/9.48	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, d), b)
28.54/9.48	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.48	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.48	   A^2 -> H(U1(a, d), c)
28.54/9.48	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.48	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.48	   A^2 -> H(U1(a, d), e)
28.54/9.48	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, a), d)
28.54/9.48	   A^2 -> H(U1(a, a), k)
28.54/9.48	   A^2 -> H(k, U1(b, b))
28.54/9.48	   A^2 -> H(k, f(c))
28.54/9.48	   A^2 -> H(k, f(d))
28.54/9.48	   A^2 -> H(c, U1(c, b))
28.54/9.48	   A^2 -> H(c, U1(d, b))
28.54/9.48	   A^2 -> H(c, U1(b, c))
28.54/9.48	   A^2 -> H(c, U1(b, d))
28.54/9.48	   A^2 -> H(c, U1(c, c))
28.54/9.48	   A^2 -> H(c, f(e))
28.54/9.48	   A^2 -> H(c, f(k))
28.54/9.48	   A^2 -> H(c, U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.48	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.48	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.48	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.48	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.48	   A^2 -> H(U1(e, k), f(e))
28.54/9.48	   A^2 -> H(U1(e, k), f(k))
28.54/9.48	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.48	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.48	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.48	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.48	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.48	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.48	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.48	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.48	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.48	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.48	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.48	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.48	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.48	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.48	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.48	   A^2 -> H(U1(k, e), f(e))
28.54/9.48	   A^2 -> H(U1(k, e), f(k))
28.54/9.48	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.48	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.48	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.48	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.48	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.48	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.48	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.48	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.48	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, c), b)
28.54/9.48	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.48	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.48	   A^2 -> H(U1(c, c), e)
28.54/9.48	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.48	   A^2 -> H(e, U1(c, b))
28.54/9.48	   A^2 -> H(e, U1(d, b))
28.54/9.48	   A^2 -> H(e, U1(b, c))
28.54/9.48	   A^2 -> H(e, U1(b, d))
28.54/9.48	   A^2 -> H(e, U1(c, c))
28.54/9.48	   A^2 -> H(e, f(e))
28.54/9.48	   A^2 -> H(e, f(k))
28.54/9.48	   A^2 -> H(e, U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.48	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.48	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.48	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.48	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.48	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.48	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.48	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.48	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.48	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.48	   A^2 -> H(f(e), b)
28.54/9.48	   A^2 -> H(f(e), U1(e, d))
28.54/9.48	   A^2 -> H(f(e), U1(d, e))
28.54/9.48	   A^2 -> H(f(e), c)
28.54/9.48	   A^2 -> H(f(e), U1(e, k))
28.54/9.48	   A^2 -> H(f(e), U1(k, e))
28.54/9.48	   A^2 -> H(f(e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.48	   A^2 -> H(f(k), b)
28.54/9.48	   A^2 -> H(f(k), U1(e, d))
28.54/9.48	   A^2 -> H(f(k), U1(d, e))
28.54/9.48	   A^2 -> H(f(k), c)
28.54/9.48	   A^2 -> H(f(k), U1(e, k))
28.54/9.48	   A^2 -> H(f(k), U1(k, e))
28.54/9.48	   A^2 -> H(f(k), e)
28.54/9.48	   A^2 -> H(f(c), d)
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.48	   A^2 -> H(U1(k, k), f(e))
28.54/9.48	   A^2 -> H(U1(k, k), f(k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.48	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.48	   A^2 -> H(U1(d, d), b)
28.54/9.48	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.48	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.48	   A^2 -> H(U1(d, d), c)
28.54/9.48	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.48	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.48	   A^2 -> H(U1(d, d), e)
28.54/9.48	   A^2 -> H(f(d), d)
28.54/9.48	   A^2 -> H(f(d), k)
28.54/9.48	   A^2 -> H(U1(c, c), c)
28.54/9.48	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.48	   A^2 -> H(f(c), k)
28.54/9.48	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.48	   A^2 -> H(f(k), U1(k, k))
28.54/9.48	   A^2 -> H(f(e), e)
28.54/9.48	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.48	   A^2 -> H(d, U1(c, b))
28.54/9.48	   A^2 -> H(d, U1(d, b))
28.54/9.48	   A^2 -> H(d, U1(b, c))
28.54/9.48	   A^2 -> H(d, U1(b, d))
28.54/9.48	   A^2 -> H(d, U1(c, c))
28.54/9.48	   A^2 -> H(d, f(e))
28.54/9.48	   A^2 -> H(d, f(k))
28.54/9.48	   A^2 -> H(d, U1(d, d))
28.54/9.48	   A^2 -> H(a, U1(e, b))
28.54/9.48	   A^2 -> H(a, U1(k, b))
28.54/9.48	   A^2 -> H(a, U1(c, d))
28.54/9.48	   A^2 -> H(a, U1(d, c))
28.54/9.48	   A^2 -> H(a, U1(b, e))
28.54/9.48	   A^2 -> H(a, U1(b, k))
28.54/9.48	   A^2 -> H(a, U1(e, c))
28.54/9.48	   A^2 -> H(a, U1(k, c))
28.54/9.48	   A^2 -> H(a, U1(c, e))
28.54/9.48	   A^2 -> H(a, U1(c, k))
28.54/9.48	   A^2 -> H(a, U1(e, e))
28.54/9.48	   A^2 -> H(a, U1(k, k))
28.54/9.48	   A^2 -> H(a, U1(k, d))
28.54/9.48	   A^2 -> H(a, U1(d, k))
28.54/9.48	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.48	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.48	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.48	
28.54/9.48	The TRS R consists of the following rules:
28.54/9.48	
28.54/9.48	   f(x) -> U1(x, x)
28.54/9.48	   U1(e, x) -> x
28.54/9.48	   a -> c
28.54/9.48	   a -> d
28.54/9.48	   b -> c
28.54/9.48	   b -> d
28.54/9.48	   d -> k
28.54/9.48	   c -> e
28.54/9.48	   c -> k
28.54/9.48	
28.54/9.48	Q is empty.
28.54/9.48	We have to consider all minimal (P,Q,R)-chains.
28.54/9.48	----------------------------------------
28.54/9.48	
28.54/9.48	(1117) TransformationProof (EQUIVALENT)
28.54/9.48	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.48	
28.54/9.48	   (A^2 -> H(d, U1(d, b)),A^2 -> H(d, U1(d, b)))
28.54/9.48	   (A^2 -> H(U1(e, k), U1(d, b)),A^2 -> H(U1(e, k), U1(d, b)))
28.54/9.48	   (A^2 -> H(U1(e, d), U1(k, b)),A^2 -> H(U1(e, d), U1(k, b)))
28.54/9.48	   (A^2 -> H(U1(e, d), U1(d, c)),A^2 -> H(U1(e, d), U1(d, c)))
28.54/9.48	   (A^2 -> H(U1(e, d), U1(d, d)),A^2 -> H(U1(e, d), U1(d, d)))
28.54/9.48	
28.54/9.48	
28.54/9.48	----------------------------------------
28.54/9.48	
28.54/9.48	(1118)
28.54/9.48	Obligation:
28.54/9.48	Q DP problem:
28.54/9.48	The TRS P consists of the following rules:
28.54/9.48	
28.54/9.48	   H(x, x) -> G(x, x, f(k))
28.54/9.48	   G(d, x, x) -> A^2
28.54/9.48	   A^2 -> H(f(c), f(c))
28.54/9.48	   A^2 -> H(f(d), f(d))
28.54/9.48	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.48	   A^2 -> H(f(e), f(e))
28.54/9.48	   A^2 -> H(f(k), f(k))
28.54/9.48	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, d), U1(b, c))
28.54/9.48	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.48	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.48	   A^2 -> H(U1(e, d), f(e))
28.54/9.48	   A^2 -> H(U1(e, d), f(k))
28.54/9.48	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.48	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.48	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.48	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.48	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.48	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.48	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.48	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.48	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.48	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.48	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.48	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.48	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.48	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.48	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.48	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.48	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.48	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, a), b)
28.54/9.48	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.48	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.48	   A^2 -> H(U1(c, a), c)
28.54/9.48	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.48	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.48	   A^2 -> H(U1(c, a), e)
28.54/9.48	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.48	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.48	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.48	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.48	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.48	   A^2 -> H(U1(d, e), f(e))
28.54/9.48	   A^2 -> H(U1(d, e), f(k))
28.54/9.48	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.48	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.48	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.48	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.48	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.48	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.48	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.48	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.48	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.48	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.48	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.48	   A^2 -> H(U1(d, a), b)
28.54/9.48	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.48	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.48	   A^2 -> H(U1(d, a), c)
28.54/9.48	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.48	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.48	   A^2 -> H(U1(d, a), e)
28.54/9.48	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.48	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.48	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.48	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.48	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.48	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.48	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.48	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.48	   A^2 -> H(U1(a, c), b)
28.54/9.48	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.48	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.48	   A^2 -> H(U1(a, c), c)
28.54/9.48	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.48	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.48	   A^2 -> H(U1(a, c), e)
28.54/9.48	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, d), b)
28.54/9.48	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.48	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.48	   A^2 -> H(U1(a, d), c)
28.54/9.48	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.48	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.48	   A^2 -> H(U1(a, d), e)
28.54/9.48	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.48	   A^2 -> H(U1(a, a), d)
28.54/9.48	   A^2 -> H(U1(a, a), k)
28.54/9.48	   A^2 -> H(k, U1(b, b))
28.54/9.48	   A^2 -> H(k, f(c))
28.54/9.48	   A^2 -> H(k, f(d))
28.54/9.48	   A^2 -> H(c, U1(c, b))
28.54/9.48	   A^2 -> H(c, U1(d, b))
28.54/9.48	   A^2 -> H(c, U1(b, c))
28.54/9.48	   A^2 -> H(c, U1(b, d))
28.54/9.48	   A^2 -> H(c, U1(c, c))
28.54/9.48	   A^2 -> H(c, f(e))
28.54/9.48	   A^2 -> H(c, f(k))
28.54/9.48	   A^2 -> H(c, U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.48	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.48	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.48	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.48	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.48	   A^2 -> H(U1(e, k), f(e))
28.54/9.48	   A^2 -> H(U1(e, k), f(k))
28.54/9.48	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.48	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.48	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.48	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.48	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.48	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.48	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.48	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.48	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.48	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.48	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.48	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.48	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.48	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.48	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.48	   A^2 -> H(U1(k, e), f(e))
28.54/9.48	   A^2 -> H(U1(k, e), f(k))
28.54/9.48	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.48	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.48	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.48	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.48	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.48	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.48	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.48	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.48	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.48	   A^2 -> H(U1(c, c), b)
28.54/9.48	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.48	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.48	   A^2 -> H(U1(c, c), e)
28.54/9.48	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.48	   A^2 -> H(e, U1(c, b))
28.54/9.48	   A^2 -> H(e, U1(d, b))
28.54/9.48	   A^2 -> H(e, U1(b, c))
28.54/9.48	   A^2 -> H(e, U1(b, d))
28.54/9.48	   A^2 -> H(e, U1(c, c))
28.54/9.48	   A^2 -> H(e, f(e))
28.54/9.48	   A^2 -> H(e, f(k))
28.54/9.48	   A^2 -> H(e, U1(d, d))
28.54/9.48	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.48	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.48	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.48	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.48	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.48	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.48	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.48	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.48	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.48	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.48	   A^2 -> H(f(e), b)
28.54/9.48	   A^2 -> H(f(e), U1(e, d))
28.54/9.48	   A^2 -> H(f(e), U1(d, e))
28.54/9.48	   A^2 -> H(f(e), c)
28.54/9.48	   A^2 -> H(f(e), U1(e, k))
28.54/9.48	   A^2 -> H(f(e), U1(k, e))
28.54/9.48	   A^2 -> H(f(e), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.48	   A^2 -> H(f(k), b)
28.54/9.48	   A^2 -> H(f(k), U1(e, d))
28.54/9.48	   A^2 -> H(f(k), U1(d, e))
28.54/9.48	   A^2 -> H(f(k), c)
28.54/9.48	   A^2 -> H(f(k), U1(e, k))
28.54/9.48	   A^2 -> H(f(k), U1(k, e))
28.54/9.48	   A^2 -> H(f(k), e)
28.54/9.48	   A^2 -> H(f(c), d)
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.48	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.48	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.48	   A^2 -> H(U1(k, k), f(e))
28.54/9.48	   A^2 -> H(U1(k, k), f(k))
28.54/9.48	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.48	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.48	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.48	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.48	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.48	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.48	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.48	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.48	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.48	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.48	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.48	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.48	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.48	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.48	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.48	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.48	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.48	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.48	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.48	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.48	   A^2 -> H(U1(d, d), b)
28.54/9.48	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.48	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.48	   A^2 -> H(U1(d, d), c)
28.54/9.48	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.48	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.48	   A^2 -> H(U1(d, d), e)
28.54/9.48	   A^2 -> H(f(d), d)
28.54/9.48	   A^2 -> H(f(d), k)
28.54/9.48	   A^2 -> H(U1(c, c), c)
28.54/9.48	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.48	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.48	   A^2 -> H(f(c), k)
28.54/9.48	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.48	   A^2 -> H(f(k), U1(k, k))
28.54/9.48	   A^2 -> H(f(e), e)
28.54/9.48	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.48	   A^2 -> H(d, U1(c, b))
28.54/9.48	   A^2 -> H(d, U1(d, b))
28.54/9.48	   A^2 -> H(d, U1(b, c))
28.54/9.48	   A^2 -> H(d, U1(b, d))
28.54/9.48	   A^2 -> H(d, U1(c, c))
28.54/9.48	   A^2 -> H(d, f(e))
28.54/9.48	   A^2 -> H(d, f(k))
28.54/9.48	   A^2 -> H(d, U1(d, d))
28.54/9.48	   A^2 -> H(a, U1(e, b))
28.54/9.48	   A^2 -> H(a, U1(k, b))
28.54/9.48	   A^2 -> H(a, U1(c, d))
28.54/9.48	   A^2 -> H(a, U1(d, c))
28.54/9.48	   A^2 -> H(a, U1(b, e))
28.54/9.48	   A^2 -> H(a, U1(b, k))
28.54/9.48	   A^2 -> H(a, U1(e, c))
28.54/9.48	   A^2 -> H(a, U1(k, c))
28.54/9.48	   A^2 -> H(a, U1(c, e))
28.54/9.48	   A^2 -> H(a, U1(c, k))
28.54/9.48	   A^2 -> H(a, U1(e, e))
28.54/9.48	   A^2 -> H(a, U1(k, k))
28.54/9.48	   A^2 -> H(a, U1(k, d))
28.54/9.48	   A^2 -> H(a, U1(d, k))
28.54/9.48	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.48	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.48	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.48	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.49	
28.54/9.49	The TRS R consists of the following rules:
28.54/9.49	
28.54/9.49	   f(x) -> U1(x, x)
28.54/9.49	   U1(e, x) -> x
28.54/9.49	   a -> c
28.54/9.49	   a -> d
28.54/9.49	   b -> c
28.54/9.49	   b -> d
28.54/9.49	   d -> k
28.54/9.49	   c -> e
28.54/9.49	   c -> k
28.54/9.49	
28.54/9.49	Q is empty.
28.54/9.49	We have to consider all minimal (P,Q,R)-chains.
28.54/9.49	----------------------------------------
28.54/9.49	
28.54/9.49	(1119) TransformationProof (EQUIVALENT)
28.54/9.49	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.49	
28.54/9.49	   (A^2 -> H(d, U1(b, c)),A^2 -> H(d, U1(b, c)))
28.54/9.49	   (A^2 -> H(U1(e, k), U1(b, c)),A^2 -> H(U1(e, k), U1(b, c)))
28.54/9.49	   (A^2 -> H(U1(e, d), U1(c, c)),A^2 -> H(U1(e, d), U1(c, c)))
28.54/9.49	   (A^2 -> H(U1(e, d), U1(d, c)),A^2 -> H(U1(e, d), U1(d, c)))
28.54/9.49	   (A^2 -> H(U1(e, d), U1(b, e)),A^2 -> H(U1(e, d), U1(b, e)))
28.54/9.49	   (A^2 -> H(U1(e, d), U1(b, k)),A^2 -> H(U1(e, d), U1(b, k)))
28.54/9.49	
28.54/9.49	
28.54/9.49	----------------------------------------
28.54/9.49	
28.54/9.49	(1120)
28.54/9.49	Obligation:
28.54/9.49	Q DP problem:
28.54/9.49	The TRS P consists of the following rules:
28.54/9.49	
28.54/9.49	   H(x, x) -> G(x, x, f(k))
28.54/9.49	   G(d, x, x) -> A^2
28.54/9.49	   A^2 -> H(f(c), f(c))
28.54/9.49	   A^2 -> H(f(d), f(d))
28.54/9.49	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.49	   A^2 -> H(f(e), f(e))
28.54/9.49	   A^2 -> H(f(k), f(k))
28.54/9.49	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, d), U1(b, d))
28.54/9.49	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.49	   A^2 -> H(U1(e, d), f(e))
28.54/9.49	   A^2 -> H(U1(e, d), f(k))
28.54/9.49	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.49	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.49	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.49	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.49	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.49	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.49	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.49	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.49	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.49	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.49	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.49	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.49	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, a), b)
28.54/9.49	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.49	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.49	   A^2 -> H(U1(c, a), c)
28.54/9.49	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.49	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.49	   A^2 -> H(U1(c, a), e)
28.54/9.49	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.49	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.49	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.49	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.49	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.49	   A^2 -> H(U1(d, e), f(e))
28.54/9.49	   A^2 -> H(U1(d, e), f(k))
28.54/9.49	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.49	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.49	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.49	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.49	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.49	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.49	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.49	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.49	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.49	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.49	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.49	   A^2 -> H(U1(d, a), b)
28.54/9.49	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.49	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.49	   A^2 -> H(U1(d, a), c)
28.54/9.49	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.49	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.49	   A^2 -> H(U1(d, a), e)
28.54/9.49	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.49	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.49	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.49	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.49	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.49	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.49	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.49	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.49	   A^2 -> H(U1(a, c), b)
28.54/9.49	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.49	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.49	   A^2 -> H(U1(a, c), c)
28.54/9.49	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.49	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.49	   A^2 -> H(U1(a, c), e)
28.54/9.49	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, d), b)
28.54/9.49	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.49	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.49	   A^2 -> H(U1(a, d), c)
28.54/9.49	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.49	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.49	   A^2 -> H(U1(a, d), e)
28.54/9.49	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, a), d)
28.54/9.49	   A^2 -> H(U1(a, a), k)
28.54/9.49	   A^2 -> H(k, U1(b, b))
28.54/9.49	   A^2 -> H(k, f(c))
28.54/9.49	   A^2 -> H(k, f(d))
28.54/9.49	   A^2 -> H(c, U1(c, b))
28.54/9.49	   A^2 -> H(c, U1(d, b))
28.54/9.49	   A^2 -> H(c, U1(b, c))
28.54/9.49	   A^2 -> H(c, U1(b, d))
28.54/9.49	   A^2 -> H(c, U1(c, c))
28.54/9.49	   A^2 -> H(c, f(e))
28.54/9.49	   A^2 -> H(c, f(k))
28.54/9.49	   A^2 -> H(c, U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.49	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.49	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.49	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.49	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.49	   A^2 -> H(U1(e, k), f(e))
28.54/9.49	   A^2 -> H(U1(e, k), f(k))
28.54/9.49	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.49	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.49	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.49	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.49	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.49	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.49	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.49	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.49	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.49	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.49	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.49	   A^2 -> H(U1(k, e), f(e))
28.54/9.49	   A^2 -> H(U1(k, e), f(k))
28.54/9.49	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.49	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.49	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.49	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.49	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.49	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.49	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.49	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.49	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, c), b)
28.54/9.49	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.49	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.49	   A^2 -> H(U1(c, c), e)
28.54/9.49	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.49	   A^2 -> H(e, U1(c, b))
28.54/9.49	   A^2 -> H(e, U1(d, b))
28.54/9.49	   A^2 -> H(e, U1(b, c))
28.54/9.49	   A^2 -> H(e, U1(b, d))
28.54/9.49	   A^2 -> H(e, U1(c, c))
28.54/9.49	   A^2 -> H(e, f(e))
28.54/9.49	   A^2 -> H(e, f(k))
28.54/9.49	   A^2 -> H(e, U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.49	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.49	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.49	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.49	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.49	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.49	   A^2 -> H(f(e), b)
28.54/9.49	   A^2 -> H(f(e), U1(e, d))
28.54/9.49	   A^2 -> H(f(e), U1(d, e))
28.54/9.49	   A^2 -> H(f(e), c)
28.54/9.49	   A^2 -> H(f(e), U1(e, k))
28.54/9.49	   A^2 -> H(f(e), U1(k, e))
28.54/9.49	   A^2 -> H(f(e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.49	   A^2 -> H(f(k), b)
28.54/9.49	   A^2 -> H(f(k), U1(e, d))
28.54/9.49	   A^2 -> H(f(k), U1(d, e))
28.54/9.49	   A^2 -> H(f(k), c)
28.54/9.49	   A^2 -> H(f(k), U1(e, k))
28.54/9.49	   A^2 -> H(f(k), U1(k, e))
28.54/9.49	   A^2 -> H(f(k), e)
28.54/9.49	   A^2 -> H(f(c), d)
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.49	   A^2 -> H(U1(k, k), f(e))
28.54/9.49	   A^2 -> H(U1(k, k), f(k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.49	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.49	   A^2 -> H(U1(d, d), b)
28.54/9.49	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.49	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.49	   A^2 -> H(U1(d, d), c)
28.54/9.49	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.49	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.49	   A^2 -> H(U1(d, d), e)
28.54/9.49	   A^2 -> H(f(d), d)
28.54/9.49	   A^2 -> H(f(d), k)
28.54/9.49	   A^2 -> H(U1(c, c), c)
28.54/9.49	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.49	   A^2 -> H(f(c), k)
28.54/9.49	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.49	   A^2 -> H(f(k), U1(k, k))
28.54/9.49	   A^2 -> H(f(e), e)
28.54/9.49	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.49	   A^2 -> H(d, U1(c, b))
28.54/9.49	   A^2 -> H(d, U1(d, b))
28.54/9.49	   A^2 -> H(d, U1(b, c))
28.54/9.49	   A^2 -> H(d, U1(b, d))
28.54/9.49	   A^2 -> H(d, U1(c, c))
28.54/9.49	   A^2 -> H(d, f(e))
28.54/9.49	   A^2 -> H(d, f(k))
28.54/9.49	   A^2 -> H(d, U1(d, d))
28.54/9.49	   A^2 -> H(a, U1(e, b))
28.54/9.49	   A^2 -> H(a, U1(k, b))
28.54/9.49	   A^2 -> H(a, U1(c, d))
28.54/9.49	   A^2 -> H(a, U1(d, c))
28.54/9.49	   A^2 -> H(a, U1(b, e))
28.54/9.49	   A^2 -> H(a, U1(b, k))
28.54/9.49	   A^2 -> H(a, U1(e, c))
28.54/9.49	   A^2 -> H(a, U1(k, c))
28.54/9.49	   A^2 -> H(a, U1(c, e))
28.54/9.49	   A^2 -> H(a, U1(c, k))
28.54/9.49	   A^2 -> H(a, U1(e, e))
28.54/9.49	   A^2 -> H(a, U1(k, k))
28.54/9.49	   A^2 -> H(a, U1(k, d))
28.54/9.49	   A^2 -> H(a, U1(d, k))
28.54/9.49	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.49	
28.54/9.49	The TRS R consists of the following rules:
28.54/9.49	
28.54/9.49	   f(x) -> U1(x, x)
28.54/9.49	   U1(e, x) -> x
28.54/9.49	   a -> c
28.54/9.49	   a -> d
28.54/9.49	   b -> c
28.54/9.49	   b -> d
28.54/9.49	   d -> k
28.54/9.49	   c -> e
28.54/9.49	   c -> k
28.54/9.49	
28.54/9.49	Q is empty.
28.54/9.49	We have to consider all minimal (P,Q,R)-chains.
28.54/9.49	----------------------------------------
28.54/9.49	
28.54/9.49	(1121) TransformationProof (EQUIVALENT)
28.54/9.49	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.49	
28.54/9.49	   (A^2 -> H(d, U1(b, d)),A^2 -> H(d, U1(b, d)))
28.54/9.49	   (A^2 -> H(U1(e, k), U1(b, d)),A^2 -> H(U1(e, k), U1(b, d)))
28.54/9.49	   (A^2 -> H(U1(e, d), U1(c, d)),A^2 -> H(U1(e, d), U1(c, d)))
28.54/9.49	   (A^2 -> H(U1(e, d), U1(d, d)),A^2 -> H(U1(e, d), U1(d, d)))
28.54/9.49	   (A^2 -> H(U1(e, d), U1(b, k)),A^2 -> H(U1(e, d), U1(b, k)))
28.54/9.49	
28.54/9.49	
28.54/9.49	----------------------------------------
28.54/9.49	
28.54/9.49	(1122)
28.54/9.49	Obligation:
28.54/9.49	Q DP problem:
28.54/9.49	The TRS P consists of the following rules:
28.54/9.49	
28.54/9.49	   H(x, x) -> G(x, x, f(k))
28.54/9.49	   G(d, x, x) -> A^2
28.54/9.49	   A^2 -> H(f(c), f(c))
28.54/9.49	   A^2 -> H(f(d), f(d))
28.54/9.49	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.49	   A^2 -> H(f(e), f(e))
28.54/9.49	   A^2 -> H(f(k), f(k))
28.54/9.49	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, d), U1(c, c))
28.54/9.49	   A^2 -> H(U1(e, d), f(e))
28.54/9.49	   A^2 -> H(U1(e, d), f(k))
28.54/9.49	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.49	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.49	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.49	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.49	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.49	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.49	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.49	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.49	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.49	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.49	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.49	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.49	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, a), b)
28.54/9.49	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.49	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.49	   A^2 -> H(U1(c, a), c)
28.54/9.49	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.49	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.49	   A^2 -> H(U1(c, a), e)
28.54/9.49	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.49	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.49	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.49	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.49	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.49	   A^2 -> H(U1(d, e), f(e))
28.54/9.49	   A^2 -> H(U1(d, e), f(k))
28.54/9.49	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.49	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.49	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.49	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.49	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.49	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.49	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.49	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.49	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.49	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.49	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.49	   A^2 -> H(U1(d, a), b)
28.54/9.49	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.49	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.49	   A^2 -> H(U1(d, a), c)
28.54/9.49	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.49	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.49	   A^2 -> H(U1(d, a), e)
28.54/9.49	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.49	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.49	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.49	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.49	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.49	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.49	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.49	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.49	   A^2 -> H(U1(a, c), b)
28.54/9.49	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.49	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.49	   A^2 -> H(U1(a, c), c)
28.54/9.49	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.49	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.49	   A^2 -> H(U1(a, c), e)
28.54/9.49	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, d), b)
28.54/9.49	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.49	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.49	   A^2 -> H(U1(a, d), c)
28.54/9.49	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.49	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.49	   A^2 -> H(U1(a, d), e)
28.54/9.49	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, a), d)
28.54/9.49	   A^2 -> H(U1(a, a), k)
28.54/9.49	   A^2 -> H(k, U1(b, b))
28.54/9.49	   A^2 -> H(k, f(c))
28.54/9.49	   A^2 -> H(k, f(d))
28.54/9.49	   A^2 -> H(c, U1(c, b))
28.54/9.49	   A^2 -> H(c, U1(d, b))
28.54/9.49	   A^2 -> H(c, U1(b, c))
28.54/9.49	   A^2 -> H(c, U1(b, d))
28.54/9.49	   A^2 -> H(c, U1(c, c))
28.54/9.49	   A^2 -> H(c, f(e))
28.54/9.49	   A^2 -> H(c, f(k))
28.54/9.49	   A^2 -> H(c, U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.49	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.49	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.49	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.49	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.49	   A^2 -> H(U1(e, k), f(e))
28.54/9.49	   A^2 -> H(U1(e, k), f(k))
28.54/9.49	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.49	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.49	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.49	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.49	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.49	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.49	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.49	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.49	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.49	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.49	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.49	   A^2 -> H(U1(k, e), f(e))
28.54/9.49	   A^2 -> H(U1(k, e), f(k))
28.54/9.49	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.49	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.49	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.49	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.49	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.49	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.49	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.49	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.49	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, c), b)
28.54/9.49	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.49	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.49	   A^2 -> H(U1(c, c), e)
28.54/9.49	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.49	   A^2 -> H(e, U1(c, b))
28.54/9.49	   A^2 -> H(e, U1(d, b))
28.54/9.49	   A^2 -> H(e, U1(b, c))
28.54/9.49	   A^2 -> H(e, U1(b, d))
28.54/9.49	   A^2 -> H(e, U1(c, c))
28.54/9.49	   A^2 -> H(e, f(e))
28.54/9.49	   A^2 -> H(e, f(k))
28.54/9.49	   A^2 -> H(e, U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.49	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.49	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.49	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.49	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.49	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.49	   A^2 -> H(f(e), b)
28.54/9.49	   A^2 -> H(f(e), U1(e, d))
28.54/9.49	   A^2 -> H(f(e), U1(d, e))
28.54/9.49	   A^2 -> H(f(e), c)
28.54/9.49	   A^2 -> H(f(e), U1(e, k))
28.54/9.49	   A^2 -> H(f(e), U1(k, e))
28.54/9.49	   A^2 -> H(f(e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.49	   A^2 -> H(f(k), b)
28.54/9.49	   A^2 -> H(f(k), U1(e, d))
28.54/9.49	   A^2 -> H(f(k), U1(d, e))
28.54/9.49	   A^2 -> H(f(k), c)
28.54/9.49	   A^2 -> H(f(k), U1(e, k))
28.54/9.49	   A^2 -> H(f(k), U1(k, e))
28.54/9.49	   A^2 -> H(f(k), e)
28.54/9.49	   A^2 -> H(f(c), d)
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.49	   A^2 -> H(U1(k, k), f(e))
28.54/9.49	   A^2 -> H(U1(k, k), f(k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.49	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.49	   A^2 -> H(U1(d, d), b)
28.54/9.49	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.49	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.49	   A^2 -> H(U1(d, d), c)
28.54/9.49	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.49	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.49	   A^2 -> H(U1(d, d), e)
28.54/9.49	   A^2 -> H(f(d), d)
28.54/9.49	   A^2 -> H(f(d), k)
28.54/9.49	   A^2 -> H(U1(c, c), c)
28.54/9.49	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.49	   A^2 -> H(f(c), k)
28.54/9.49	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.49	   A^2 -> H(f(k), U1(k, k))
28.54/9.49	   A^2 -> H(f(e), e)
28.54/9.49	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.49	   A^2 -> H(d, U1(c, b))
28.54/9.49	   A^2 -> H(d, U1(d, b))
28.54/9.49	   A^2 -> H(d, U1(b, c))
28.54/9.49	   A^2 -> H(d, U1(b, d))
28.54/9.49	   A^2 -> H(d, U1(c, c))
28.54/9.49	   A^2 -> H(d, f(e))
28.54/9.49	   A^2 -> H(d, f(k))
28.54/9.49	   A^2 -> H(d, U1(d, d))
28.54/9.49	   A^2 -> H(a, U1(e, b))
28.54/9.49	   A^2 -> H(a, U1(k, b))
28.54/9.49	   A^2 -> H(a, U1(c, d))
28.54/9.49	   A^2 -> H(a, U1(d, c))
28.54/9.49	   A^2 -> H(a, U1(b, e))
28.54/9.49	   A^2 -> H(a, U1(b, k))
28.54/9.49	   A^2 -> H(a, U1(e, c))
28.54/9.49	   A^2 -> H(a, U1(k, c))
28.54/9.49	   A^2 -> H(a, U1(c, e))
28.54/9.49	   A^2 -> H(a, U1(c, k))
28.54/9.49	   A^2 -> H(a, U1(e, e))
28.54/9.49	   A^2 -> H(a, U1(k, k))
28.54/9.49	   A^2 -> H(a, U1(k, d))
28.54/9.49	   A^2 -> H(a, U1(d, k))
28.54/9.49	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.49	
28.54/9.49	The TRS R consists of the following rules:
28.54/9.49	
28.54/9.49	   f(x) -> U1(x, x)
28.54/9.49	   U1(e, x) -> x
28.54/9.49	   a -> c
28.54/9.49	   a -> d
28.54/9.49	   b -> c
28.54/9.49	   b -> d
28.54/9.49	   d -> k
28.54/9.49	   c -> e
28.54/9.49	   c -> k
28.54/9.49	
28.54/9.49	Q is empty.
28.54/9.49	We have to consider all minimal (P,Q,R)-chains.
28.54/9.49	----------------------------------------
28.54/9.49	
28.54/9.49	(1123) TransformationProof (EQUIVALENT)
28.54/9.49	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.49	
28.54/9.49	   (A^2 -> H(d, U1(c, c)),A^2 -> H(d, U1(c, c)))
28.54/9.49	   (A^2 -> H(U1(e, k), U1(c, c)),A^2 -> H(U1(e, k), U1(c, c)))
28.54/9.49	   (A^2 -> H(U1(e, d), U1(e, c)),A^2 -> H(U1(e, d), U1(e, c)))
28.54/9.49	   (A^2 -> H(U1(e, d), U1(k, c)),A^2 -> H(U1(e, d), U1(k, c)))
28.54/9.49	   (A^2 -> H(U1(e, d), U1(c, e)),A^2 -> H(U1(e, d), U1(c, e)))
28.54/9.49	   (A^2 -> H(U1(e, d), U1(c, k)),A^2 -> H(U1(e, d), U1(c, k)))
28.54/9.49	
28.54/9.49	
28.54/9.49	----------------------------------------
28.54/9.49	
28.54/9.49	(1124)
28.54/9.49	Obligation:
28.54/9.49	Q DP problem:
28.54/9.49	The TRS P consists of the following rules:
28.54/9.49	
28.54/9.49	   H(x, x) -> G(x, x, f(k))
28.54/9.49	   G(d, x, x) -> A^2
28.54/9.49	   A^2 -> H(f(c), f(c))
28.54/9.49	   A^2 -> H(f(d), f(d))
28.54/9.49	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.49	   A^2 -> H(f(e), f(e))
28.54/9.49	   A^2 -> H(f(k), f(k))
28.54/9.49	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, d), f(e))
28.54/9.49	   A^2 -> H(U1(e, d), f(k))
28.54/9.49	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.49	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.49	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.49	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.49	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.49	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.49	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.49	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.49	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.49	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.49	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.49	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.49	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, a), b)
28.54/9.49	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.49	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.49	   A^2 -> H(U1(c, a), c)
28.54/9.49	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.49	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.49	   A^2 -> H(U1(c, a), e)
28.54/9.49	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.49	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.49	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.49	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.49	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.49	   A^2 -> H(U1(d, e), f(e))
28.54/9.49	   A^2 -> H(U1(d, e), f(k))
28.54/9.49	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.49	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.49	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.49	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.49	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.49	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.49	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.49	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.49	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.49	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.49	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.49	   A^2 -> H(U1(d, a), b)
28.54/9.49	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.49	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.49	   A^2 -> H(U1(d, a), c)
28.54/9.49	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.49	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.49	   A^2 -> H(U1(d, a), e)
28.54/9.49	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.49	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.49	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.49	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.49	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.49	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.49	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.49	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.49	   A^2 -> H(U1(a, c), b)
28.54/9.49	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.49	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.49	   A^2 -> H(U1(a, c), c)
28.54/9.49	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.49	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.49	   A^2 -> H(U1(a, c), e)
28.54/9.49	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, d), b)
28.54/9.49	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.49	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.49	   A^2 -> H(U1(a, d), c)
28.54/9.49	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.49	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.49	   A^2 -> H(U1(a, d), e)
28.54/9.49	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, a), d)
28.54/9.49	   A^2 -> H(U1(a, a), k)
28.54/9.49	   A^2 -> H(k, U1(b, b))
28.54/9.49	   A^2 -> H(k, f(c))
28.54/9.49	   A^2 -> H(k, f(d))
28.54/9.49	   A^2 -> H(c, U1(c, b))
28.54/9.49	   A^2 -> H(c, U1(d, b))
28.54/9.49	   A^2 -> H(c, U1(b, c))
28.54/9.49	   A^2 -> H(c, U1(b, d))
28.54/9.49	   A^2 -> H(c, U1(c, c))
28.54/9.49	   A^2 -> H(c, f(e))
28.54/9.49	   A^2 -> H(c, f(k))
28.54/9.49	   A^2 -> H(c, U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.49	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.49	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.49	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.49	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.49	   A^2 -> H(U1(e, k), f(e))
28.54/9.49	   A^2 -> H(U1(e, k), f(k))
28.54/9.49	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.49	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.49	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.49	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.49	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.49	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.49	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.49	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.49	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.49	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.49	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.49	   A^2 -> H(U1(k, e), f(e))
28.54/9.49	   A^2 -> H(U1(k, e), f(k))
28.54/9.49	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.49	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.49	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.49	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.49	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.49	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.49	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.49	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.49	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, c), b)
28.54/9.49	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.49	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.49	   A^2 -> H(U1(c, c), e)
28.54/9.49	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.49	   A^2 -> H(e, U1(c, b))
28.54/9.49	   A^2 -> H(e, U1(d, b))
28.54/9.49	   A^2 -> H(e, U1(b, c))
28.54/9.49	   A^2 -> H(e, U1(b, d))
28.54/9.49	   A^2 -> H(e, U1(c, c))
28.54/9.49	   A^2 -> H(e, f(e))
28.54/9.49	   A^2 -> H(e, f(k))
28.54/9.49	   A^2 -> H(e, U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.49	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.49	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.49	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.49	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.49	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.49	   A^2 -> H(f(e), b)
28.54/9.49	   A^2 -> H(f(e), U1(e, d))
28.54/9.49	   A^2 -> H(f(e), U1(d, e))
28.54/9.49	   A^2 -> H(f(e), c)
28.54/9.49	   A^2 -> H(f(e), U1(e, k))
28.54/9.49	   A^2 -> H(f(e), U1(k, e))
28.54/9.49	   A^2 -> H(f(e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.49	   A^2 -> H(f(k), b)
28.54/9.49	   A^2 -> H(f(k), U1(e, d))
28.54/9.49	   A^2 -> H(f(k), U1(d, e))
28.54/9.49	   A^2 -> H(f(k), c)
28.54/9.49	   A^2 -> H(f(k), U1(e, k))
28.54/9.49	   A^2 -> H(f(k), U1(k, e))
28.54/9.49	   A^2 -> H(f(k), e)
28.54/9.49	   A^2 -> H(f(c), d)
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.49	   A^2 -> H(U1(k, k), f(e))
28.54/9.49	   A^2 -> H(U1(k, k), f(k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.49	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.49	   A^2 -> H(U1(d, d), b)
28.54/9.49	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.49	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.49	   A^2 -> H(U1(d, d), c)
28.54/9.49	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.49	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.49	   A^2 -> H(U1(d, d), e)
28.54/9.49	   A^2 -> H(f(d), d)
28.54/9.49	   A^2 -> H(f(d), k)
28.54/9.49	   A^2 -> H(U1(c, c), c)
28.54/9.49	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.49	   A^2 -> H(f(c), k)
28.54/9.49	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.49	   A^2 -> H(f(k), U1(k, k))
28.54/9.49	   A^2 -> H(f(e), e)
28.54/9.49	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.49	   A^2 -> H(d, U1(c, b))
28.54/9.49	   A^2 -> H(d, U1(d, b))
28.54/9.49	   A^2 -> H(d, U1(b, c))
28.54/9.49	   A^2 -> H(d, U1(b, d))
28.54/9.49	   A^2 -> H(d, U1(c, c))
28.54/9.49	   A^2 -> H(d, f(e))
28.54/9.49	   A^2 -> H(d, f(k))
28.54/9.49	   A^2 -> H(d, U1(d, d))
28.54/9.49	   A^2 -> H(a, U1(e, b))
28.54/9.49	   A^2 -> H(a, U1(k, b))
28.54/9.49	   A^2 -> H(a, U1(c, d))
28.54/9.49	   A^2 -> H(a, U1(d, c))
28.54/9.49	   A^2 -> H(a, U1(b, e))
28.54/9.49	   A^2 -> H(a, U1(b, k))
28.54/9.49	   A^2 -> H(a, U1(e, c))
28.54/9.49	   A^2 -> H(a, U1(k, c))
28.54/9.49	   A^2 -> H(a, U1(c, e))
28.54/9.49	   A^2 -> H(a, U1(c, k))
28.54/9.49	   A^2 -> H(a, U1(e, e))
28.54/9.49	   A^2 -> H(a, U1(k, k))
28.54/9.49	   A^2 -> H(a, U1(k, d))
28.54/9.49	   A^2 -> H(a, U1(d, k))
28.54/9.49	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.49	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.49	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.49	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.49	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.49	
28.54/9.49	The TRS R consists of the following rules:
28.54/9.49	
28.54/9.49	   f(x) -> U1(x, x)
28.54/9.49	   U1(e, x) -> x
28.54/9.49	   a -> c
28.54/9.49	   a -> d
28.54/9.49	   b -> c
28.54/9.49	   b -> d
28.54/9.49	   d -> k
28.54/9.49	   c -> e
28.54/9.49	   c -> k
28.54/9.49	
28.54/9.49	Q is empty.
28.54/9.49	We have to consider all minimal (P,Q,R)-chains.
28.54/9.49	----------------------------------------
28.54/9.49	
28.54/9.49	(1125) TransformationProof (EQUIVALENT)
28.54/9.49	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), f(e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.49	
28.54/9.49	   (A^2 -> H(d, f(e)),A^2 -> H(d, f(e)))
28.54/9.49	   (A^2 -> H(U1(e, k), f(e)),A^2 -> H(U1(e, k), f(e)))
28.54/9.49	   (A^2 -> H(U1(e, d), U1(e, e)),A^2 -> H(U1(e, d), U1(e, e)))
28.54/9.49	
28.54/9.49	
28.54/9.49	----------------------------------------
28.54/9.49	
28.54/9.49	(1126)
28.54/9.49	Obligation:
28.54/9.49	Q DP problem:
28.54/9.49	The TRS P consists of the following rules:
28.54/9.49	
28.54/9.49	   H(x, x) -> G(x, x, f(k))
28.54/9.49	   G(d, x, x) -> A^2
28.54/9.49	   A^2 -> H(f(c), f(c))
28.54/9.49	   A^2 -> H(f(d), f(d))
28.54/9.49	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.49	   A^2 -> H(f(e), f(e))
28.54/9.49	   A^2 -> H(f(k), f(k))
28.54/9.49	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, d), f(k))
28.54/9.49	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.49	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.49	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.49	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.49	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.49	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.49	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.49	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.49	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.49	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.49	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.49	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.49	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, a), b)
28.54/9.49	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.49	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.49	   A^2 -> H(U1(c, a), c)
28.54/9.49	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.49	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.49	   A^2 -> H(U1(c, a), e)
28.54/9.49	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.49	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.49	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.49	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.49	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.49	   A^2 -> H(U1(d, e), f(e))
28.54/9.49	   A^2 -> H(U1(d, e), f(k))
28.54/9.49	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.49	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.49	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.49	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.49	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.49	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.49	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.49	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.49	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.49	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.49	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.49	   A^2 -> H(U1(d, a), b)
28.54/9.49	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.49	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.49	   A^2 -> H(U1(d, a), c)
28.54/9.49	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.49	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.49	   A^2 -> H(U1(d, a), e)
28.54/9.49	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.49	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.49	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.49	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.49	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.49	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.49	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.49	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.49	   A^2 -> H(U1(a, c), b)
28.54/9.49	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.49	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.49	   A^2 -> H(U1(a, c), c)
28.54/9.49	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.49	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.49	   A^2 -> H(U1(a, c), e)
28.54/9.49	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, d), b)
28.54/9.49	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.49	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.49	   A^2 -> H(U1(a, d), c)
28.54/9.49	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.49	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.49	   A^2 -> H(U1(a, d), e)
28.54/9.49	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, a), d)
28.54/9.49	   A^2 -> H(U1(a, a), k)
28.54/9.49	   A^2 -> H(k, U1(b, b))
28.54/9.49	   A^2 -> H(k, f(c))
28.54/9.49	   A^2 -> H(k, f(d))
28.54/9.49	   A^2 -> H(c, U1(c, b))
28.54/9.49	   A^2 -> H(c, U1(d, b))
28.54/9.49	   A^2 -> H(c, U1(b, c))
28.54/9.49	   A^2 -> H(c, U1(b, d))
28.54/9.49	   A^2 -> H(c, U1(c, c))
28.54/9.49	   A^2 -> H(c, f(e))
28.54/9.49	   A^2 -> H(c, f(k))
28.54/9.49	   A^2 -> H(c, U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.49	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.49	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.49	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.49	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.49	   A^2 -> H(U1(e, k), f(e))
28.54/9.49	   A^2 -> H(U1(e, k), f(k))
28.54/9.49	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.49	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.49	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.49	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.49	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.49	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.49	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.49	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.49	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.49	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.49	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.49	   A^2 -> H(U1(k, e), f(e))
28.54/9.49	   A^2 -> H(U1(k, e), f(k))
28.54/9.49	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.49	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.49	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.49	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.49	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.49	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.49	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.49	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.49	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, c), b)
28.54/9.49	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.49	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.49	   A^2 -> H(U1(c, c), e)
28.54/9.49	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.49	   A^2 -> H(e, U1(c, b))
28.54/9.49	   A^2 -> H(e, U1(d, b))
28.54/9.49	   A^2 -> H(e, U1(b, c))
28.54/9.49	   A^2 -> H(e, U1(b, d))
28.54/9.49	   A^2 -> H(e, U1(c, c))
28.54/9.49	   A^2 -> H(e, f(e))
28.54/9.49	   A^2 -> H(e, f(k))
28.54/9.49	   A^2 -> H(e, U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.49	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.49	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.49	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.49	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.49	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.49	   A^2 -> H(f(e), b)
28.54/9.49	   A^2 -> H(f(e), U1(e, d))
28.54/9.49	   A^2 -> H(f(e), U1(d, e))
28.54/9.49	   A^2 -> H(f(e), c)
28.54/9.49	   A^2 -> H(f(e), U1(e, k))
28.54/9.49	   A^2 -> H(f(e), U1(k, e))
28.54/9.49	   A^2 -> H(f(e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.49	   A^2 -> H(f(k), b)
28.54/9.49	   A^2 -> H(f(k), U1(e, d))
28.54/9.49	   A^2 -> H(f(k), U1(d, e))
28.54/9.49	   A^2 -> H(f(k), c)
28.54/9.49	   A^2 -> H(f(k), U1(e, k))
28.54/9.49	   A^2 -> H(f(k), U1(k, e))
28.54/9.49	   A^2 -> H(f(k), e)
28.54/9.49	   A^2 -> H(f(c), d)
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.49	   A^2 -> H(U1(k, k), f(e))
28.54/9.49	   A^2 -> H(U1(k, k), f(k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.49	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.49	   A^2 -> H(U1(d, d), b)
28.54/9.49	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.49	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.49	   A^2 -> H(U1(d, d), c)
28.54/9.49	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.49	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.49	   A^2 -> H(U1(d, d), e)
28.54/9.49	   A^2 -> H(f(d), d)
28.54/9.49	   A^2 -> H(f(d), k)
28.54/9.49	   A^2 -> H(U1(c, c), c)
28.54/9.49	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.49	   A^2 -> H(f(c), k)
28.54/9.49	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.49	   A^2 -> H(f(k), U1(k, k))
28.54/9.49	   A^2 -> H(f(e), e)
28.54/9.49	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.49	   A^2 -> H(d, U1(c, b))
28.54/9.49	   A^2 -> H(d, U1(d, b))
28.54/9.49	   A^2 -> H(d, U1(b, c))
28.54/9.49	   A^2 -> H(d, U1(b, d))
28.54/9.49	   A^2 -> H(d, U1(c, c))
28.54/9.49	   A^2 -> H(d, f(e))
28.54/9.49	   A^2 -> H(d, f(k))
28.54/9.49	   A^2 -> H(d, U1(d, d))
28.54/9.49	   A^2 -> H(a, U1(e, b))
28.54/9.49	   A^2 -> H(a, U1(k, b))
28.54/9.49	   A^2 -> H(a, U1(c, d))
28.54/9.49	   A^2 -> H(a, U1(d, c))
28.54/9.49	   A^2 -> H(a, U1(b, e))
28.54/9.49	   A^2 -> H(a, U1(b, k))
28.54/9.49	   A^2 -> H(a, U1(e, c))
28.54/9.49	   A^2 -> H(a, U1(k, c))
28.54/9.49	   A^2 -> H(a, U1(c, e))
28.54/9.49	   A^2 -> H(a, U1(c, k))
28.54/9.49	   A^2 -> H(a, U1(e, e))
28.54/9.49	   A^2 -> H(a, U1(k, k))
28.54/9.49	   A^2 -> H(a, U1(k, d))
28.54/9.49	   A^2 -> H(a, U1(d, k))
28.54/9.49	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.49	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.49	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.49	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.49	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.49	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.49	
28.54/9.49	The TRS R consists of the following rules:
28.54/9.49	
28.54/9.49	   f(x) -> U1(x, x)
28.54/9.49	   U1(e, x) -> x
28.54/9.49	   a -> c
28.54/9.49	   a -> d
28.54/9.49	   b -> c
28.54/9.49	   b -> d
28.54/9.49	   d -> k
28.54/9.49	   c -> e
28.54/9.49	   c -> k
28.54/9.49	
28.54/9.49	Q is empty.
28.54/9.49	We have to consider all minimal (P,Q,R)-chains.
28.54/9.49	----------------------------------------
28.54/9.49	
28.54/9.49	(1127) TransformationProof (EQUIVALENT)
28.54/9.49	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), f(k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.49	
28.54/9.49	   (A^2 -> H(d, f(k)),A^2 -> H(d, f(k)))
28.54/9.49	   (A^2 -> H(U1(e, k), f(k)),A^2 -> H(U1(e, k), f(k)))
28.54/9.49	   (A^2 -> H(U1(e, d), U1(k, k)),A^2 -> H(U1(e, d), U1(k, k)))
28.54/9.49	
28.54/9.49	
28.54/9.49	----------------------------------------
28.54/9.49	
28.54/9.49	(1128)
28.54/9.49	Obligation:
28.54/9.49	Q DP problem:
28.54/9.49	The TRS P consists of the following rules:
28.54/9.49	
28.54/9.49	   H(x, x) -> G(x, x, f(k))
28.54/9.49	   G(d, x, x) -> A^2
28.54/9.49	   A^2 -> H(f(c), f(c))
28.54/9.49	   A^2 -> H(f(d), f(d))
28.54/9.49	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.49	   A^2 -> H(f(e), f(e))
28.54/9.49	   A^2 -> H(f(k), f(k))
28.54/9.49	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, d), U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.49	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.49	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.49	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.49	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.49	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.49	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.49	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.49	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.49	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.49	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.49	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.49	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.49	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, a), b)
28.54/9.49	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.49	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.49	   A^2 -> H(U1(c, a), c)
28.54/9.49	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.49	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.49	   A^2 -> H(U1(c, a), e)
28.54/9.49	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.49	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.49	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.49	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.49	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.49	   A^2 -> H(U1(d, e), f(e))
28.54/9.49	   A^2 -> H(U1(d, e), f(k))
28.54/9.49	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.49	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.49	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.49	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.49	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.49	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.49	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.49	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.49	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.49	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.49	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.49	   A^2 -> H(U1(d, a), b)
28.54/9.49	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.49	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.49	   A^2 -> H(U1(d, a), c)
28.54/9.49	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.49	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.49	   A^2 -> H(U1(d, a), e)
28.54/9.49	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.49	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.49	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.49	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.49	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.49	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.49	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.49	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.49	   A^2 -> H(U1(a, c), b)
28.54/9.49	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.49	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.49	   A^2 -> H(U1(a, c), c)
28.54/9.49	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.49	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.49	   A^2 -> H(U1(a, c), e)
28.54/9.49	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, d), b)
28.54/9.49	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.49	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.49	   A^2 -> H(U1(a, d), c)
28.54/9.49	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.49	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.49	   A^2 -> H(U1(a, d), e)
28.54/9.49	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.49	   A^2 -> H(U1(a, a), d)
28.54/9.49	   A^2 -> H(U1(a, a), k)
28.54/9.49	   A^2 -> H(k, U1(b, b))
28.54/9.49	   A^2 -> H(k, f(c))
28.54/9.49	   A^2 -> H(k, f(d))
28.54/9.49	   A^2 -> H(c, U1(c, b))
28.54/9.49	   A^2 -> H(c, U1(d, b))
28.54/9.49	   A^2 -> H(c, U1(b, c))
28.54/9.49	   A^2 -> H(c, U1(b, d))
28.54/9.49	   A^2 -> H(c, U1(c, c))
28.54/9.49	   A^2 -> H(c, f(e))
28.54/9.49	   A^2 -> H(c, f(k))
28.54/9.49	   A^2 -> H(c, U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.49	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.49	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.49	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.49	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.49	   A^2 -> H(U1(e, k), f(e))
28.54/9.49	   A^2 -> H(U1(e, k), f(k))
28.54/9.49	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.49	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.49	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.49	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.49	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.49	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.49	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.49	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.49	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.49	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.49	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.49	   A^2 -> H(U1(k, e), f(e))
28.54/9.49	   A^2 -> H(U1(k, e), f(k))
28.54/9.49	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.49	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.49	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.49	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.49	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.49	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.49	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.49	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.49	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.49	   A^2 -> H(U1(c, c), b)
28.54/9.49	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.49	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.49	   A^2 -> H(U1(c, c), e)
28.54/9.49	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.49	   A^2 -> H(e, U1(c, b))
28.54/9.49	   A^2 -> H(e, U1(d, b))
28.54/9.49	   A^2 -> H(e, U1(b, c))
28.54/9.49	   A^2 -> H(e, U1(b, d))
28.54/9.49	   A^2 -> H(e, U1(c, c))
28.54/9.49	   A^2 -> H(e, f(e))
28.54/9.49	   A^2 -> H(e, f(k))
28.54/9.49	   A^2 -> H(e, U1(d, d))
28.54/9.49	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.49	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.49	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.49	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.49	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.49	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.49	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.49	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.49	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.49	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.49	   A^2 -> H(f(e), b)
28.54/9.49	   A^2 -> H(f(e), U1(e, d))
28.54/9.49	   A^2 -> H(f(e), U1(d, e))
28.54/9.49	   A^2 -> H(f(e), c)
28.54/9.49	   A^2 -> H(f(e), U1(e, k))
28.54/9.49	   A^2 -> H(f(e), U1(k, e))
28.54/9.49	   A^2 -> H(f(e), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.49	   A^2 -> H(f(k), b)
28.54/9.49	   A^2 -> H(f(k), U1(e, d))
28.54/9.49	   A^2 -> H(f(k), U1(d, e))
28.54/9.49	   A^2 -> H(f(k), c)
28.54/9.49	   A^2 -> H(f(k), U1(e, k))
28.54/9.49	   A^2 -> H(f(k), U1(k, e))
28.54/9.49	   A^2 -> H(f(k), e)
28.54/9.49	   A^2 -> H(f(c), d)
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.49	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.49	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.49	   A^2 -> H(U1(k, k), f(e))
28.54/9.49	   A^2 -> H(U1(k, k), f(k))
28.54/9.49	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.49	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.49	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.49	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.49	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.49	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.49	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.49	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.49	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.49	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.49	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.49	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.49	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.49	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.49	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.49	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.49	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.49	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.49	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.49	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.49	   A^2 -> H(U1(d, d), b)
28.54/9.49	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.49	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.49	   A^2 -> H(U1(d, d), c)
28.54/9.49	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.49	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.49	   A^2 -> H(U1(d, d), e)
28.54/9.49	   A^2 -> H(f(d), d)
28.54/9.49	   A^2 -> H(f(d), k)
28.54/9.49	   A^2 -> H(U1(c, c), c)
28.54/9.49	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.49	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.49	   A^2 -> H(f(c), k)
28.54/9.49	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.49	   A^2 -> H(f(k), U1(k, k))
28.54/9.49	   A^2 -> H(f(e), e)
28.54/9.49	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.49	   A^2 -> H(d, U1(c, b))
28.54/9.49	   A^2 -> H(d, U1(d, b))
28.54/9.49	   A^2 -> H(d, U1(b, c))
28.54/9.49	   A^2 -> H(d, U1(b, d))
28.54/9.49	   A^2 -> H(d, U1(c, c))
28.54/9.50	   A^2 -> H(d, f(e))
28.54/9.50	   A^2 -> H(d, f(k))
28.54/9.50	   A^2 -> H(d, U1(d, d))
28.54/9.50	   A^2 -> H(a, U1(e, b))
28.54/9.50	   A^2 -> H(a, U1(k, b))
28.54/9.50	   A^2 -> H(a, U1(c, d))
28.54/9.50	   A^2 -> H(a, U1(d, c))
28.54/9.50	   A^2 -> H(a, U1(b, e))
28.54/9.50	   A^2 -> H(a, U1(b, k))
28.54/9.50	   A^2 -> H(a, U1(e, c))
28.54/9.50	   A^2 -> H(a, U1(k, c))
28.54/9.50	   A^2 -> H(a, U1(c, e))
28.54/9.50	   A^2 -> H(a, U1(c, k))
28.54/9.50	   A^2 -> H(a, U1(e, e))
28.54/9.50	   A^2 -> H(a, U1(k, k))
28.54/9.50	   A^2 -> H(a, U1(k, d))
28.54/9.50	   A^2 -> H(a, U1(d, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.50	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.50	
28.54/9.50	The TRS R consists of the following rules:
28.54/9.50	
28.54/9.50	   f(x) -> U1(x, x)
28.54/9.50	   U1(e, x) -> x
28.54/9.50	   a -> c
28.54/9.50	   a -> d
28.54/9.50	   b -> c
28.54/9.50	   b -> d
28.54/9.50	   d -> k
28.54/9.50	   c -> e
28.54/9.50	   c -> k
28.54/9.50	
28.54/9.50	Q is empty.
28.54/9.50	We have to consider all minimal (P,Q,R)-chains.
28.54/9.50	----------------------------------------
28.54/9.50	
28.54/9.50	(1129) TransformationProof (EQUIVALENT)
28.54/9.50	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.50	
28.54/9.50	   (A^2 -> H(d, U1(d, d)),A^2 -> H(d, U1(d, d)))
28.54/9.50	   (A^2 -> H(U1(e, k), U1(d, d)),A^2 -> H(U1(e, k), U1(d, d)))
28.54/9.50	   (A^2 -> H(U1(e, d), U1(k, d)),A^2 -> H(U1(e, d), U1(k, d)))
28.54/9.50	   (A^2 -> H(U1(e, d), U1(d, k)),A^2 -> H(U1(e, d), U1(d, k)))
28.54/9.50	
28.54/9.50	
28.54/9.50	----------------------------------------
28.54/9.50	
28.54/9.50	(1130)
28.54/9.50	Obligation:
28.54/9.50	Q DP problem:
28.54/9.50	The TRS P consists of the following rules:
28.54/9.50	
28.54/9.50	   H(x, x) -> G(x, x, f(k))
28.54/9.50	   G(d, x, x) -> A^2
28.54/9.50	   A^2 -> H(f(c), f(c))
28.54/9.50	   A^2 -> H(f(d), f(d))
28.54/9.50	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.50	   A^2 -> H(f(e), f(e))
28.54/9.50	   A^2 -> H(f(k), f(k))
28.54/9.50	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, a), U1(e, b))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.50	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.50	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.50	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.50	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.50	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.50	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.50	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.50	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, a), b)
28.54/9.50	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.50	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.50	   A^2 -> H(U1(c, a), c)
28.54/9.50	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.50	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.50	   A^2 -> H(U1(c, a), e)
28.54/9.50	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.50	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.50	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.50	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.50	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.50	   A^2 -> H(U1(d, e), f(e))
28.54/9.50	   A^2 -> H(U1(d, e), f(k))
28.54/9.50	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.50	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.50	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.50	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.50	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.50	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.50	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.50	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.50	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.50	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.50	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.50	   A^2 -> H(U1(d, a), b)
28.54/9.50	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.50	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.50	   A^2 -> H(U1(d, a), c)
28.54/9.50	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.50	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.50	   A^2 -> H(U1(d, a), e)
28.54/9.50	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.50	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.50	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.50	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.50	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.50	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.50	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.50	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.50	   A^2 -> H(U1(a, c), b)
28.54/9.50	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.50	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.50	   A^2 -> H(U1(a, c), c)
28.54/9.50	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.50	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.50	   A^2 -> H(U1(a, c), e)
28.54/9.50	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, d), b)
28.54/9.50	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.50	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.50	   A^2 -> H(U1(a, d), c)
28.54/9.50	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.50	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.50	   A^2 -> H(U1(a, d), e)
28.54/9.50	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, a), d)
28.54/9.50	   A^2 -> H(U1(a, a), k)
28.54/9.50	   A^2 -> H(k, U1(b, b))
28.54/9.50	   A^2 -> H(k, f(c))
28.54/9.50	   A^2 -> H(k, f(d))
28.54/9.50	   A^2 -> H(c, U1(c, b))
28.54/9.50	   A^2 -> H(c, U1(d, b))
28.54/9.50	   A^2 -> H(c, U1(b, c))
28.54/9.50	   A^2 -> H(c, U1(b, d))
28.54/9.50	   A^2 -> H(c, U1(c, c))
28.54/9.50	   A^2 -> H(c, f(e))
28.54/9.50	   A^2 -> H(c, f(k))
28.54/9.50	   A^2 -> H(c, U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.50	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.50	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.50	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.50	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.50	   A^2 -> H(U1(e, k), f(e))
28.54/9.50	   A^2 -> H(U1(e, k), f(k))
28.54/9.50	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.50	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.50	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.50	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.50	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.50	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.50	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.50	   A^2 -> H(U1(k, e), f(e))
28.54/9.50	   A^2 -> H(U1(k, e), f(k))
28.54/9.50	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.50	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.50	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.50	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.50	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.50	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.50	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.50	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.50	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, c), b)
28.54/9.50	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.50	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.50	   A^2 -> H(U1(c, c), e)
28.54/9.50	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.50	   A^2 -> H(e, U1(c, b))
28.54/9.50	   A^2 -> H(e, U1(d, b))
28.54/9.50	   A^2 -> H(e, U1(b, c))
28.54/9.50	   A^2 -> H(e, U1(b, d))
28.54/9.50	   A^2 -> H(e, U1(c, c))
28.54/9.50	   A^2 -> H(e, f(e))
28.54/9.50	   A^2 -> H(e, f(k))
28.54/9.50	   A^2 -> H(e, U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.50	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.50	   A^2 -> H(f(e), b)
28.54/9.50	   A^2 -> H(f(e), U1(e, d))
28.54/9.50	   A^2 -> H(f(e), U1(d, e))
28.54/9.50	   A^2 -> H(f(e), c)
28.54/9.50	   A^2 -> H(f(e), U1(e, k))
28.54/9.50	   A^2 -> H(f(e), U1(k, e))
28.54/9.50	   A^2 -> H(f(e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.50	   A^2 -> H(f(k), b)
28.54/9.50	   A^2 -> H(f(k), U1(e, d))
28.54/9.50	   A^2 -> H(f(k), U1(d, e))
28.54/9.50	   A^2 -> H(f(k), c)
28.54/9.50	   A^2 -> H(f(k), U1(e, k))
28.54/9.50	   A^2 -> H(f(k), U1(k, e))
28.54/9.50	   A^2 -> H(f(k), e)
28.54/9.50	   A^2 -> H(f(c), d)
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.50	   A^2 -> H(U1(k, k), f(e))
28.54/9.50	   A^2 -> H(U1(k, k), f(k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.50	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.50	   A^2 -> H(U1(d, d), b)
28.54/9.50	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.50	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.50	   A^2 -> H(U1(d, d), c)
28.54/9.50	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.50	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.50	   A^2 -> H(U1(d, d), e)
28.54/9.50	   A^2 -> H(f(d), d)
28.54/9.50	   A^2 -> H(f(d), k)
28.54/9.50	   A^2 -> H(U1(c, c), c)
28.54/9.50	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.50	   A^2 -> H(f(c), k)
28.54/9.50	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.50	   A^2 -> H(f(k), U1(k, k))
28.54/9.50	   A^2 -> H(f(e), e)
28.54/9.50	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.50	   A^2 -> H(d, U1(c, b))
28.54/9.50	   A^2 -> H(d, U1(d, b))
28.54/9.50	   A^2 -> H(d, U1(b, c))
28.54/9.50	   A^2 -> H(d, U1(b, d))
28.54/9.50	   A^2 -> H(d, U1(c, c))
28.54/9.50	   A^2 -> H(d, f(e))
28.54/9.50	   A^2 -> H(d, f(k))
28.54/9.50	   A^2 -> H(d, U1(d, d))
28.54/9.50	   A^2 -> H(a, U1(e, b))
28.54/9.50	   A^2 -> H(a, U1(k, b))
28.54/9.50	   A^2 -> H(a, U1(c, d))
28.54/9.50	   A^2 -> H(a, U1(d, c))
28.54/9.50	   A^2 -> H(a, U1(b, e))
28.54/9.50	   A^2 -> H(a, U1(b, k))
28.54/9.50	   A^2 -> H(a, U1(e, c))
28.54/9.50	   A^2 -> H(a, U1(k, c))
28.54/9.50	   A^2 -> H(a, U1(c, e))
28.54/9.50	   A^2 -> H(a, U1(c, k))
28.54/9.50	   A^2 -> H(a, U1(e, e))
28.54/9.50	   A^2 -> H(a, U1(k, k))
28.54/9.50	   A^2 -> H(a, U1(k, d))
28.54/9.50	   A^2 -> H(a, U1(d, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.50	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.50	
28.54/9.50	The TRS R consists of the following rules:
28.54/9.50	
28.54/9.50	   f(x) -> U1(x, x)
28.54/9.50	   U1(e, x) -> x
28.54/9.50	   a -> c
28.54/9.50	   a -> d
28.54/9.50	   b -> c
28.54/9.50	   b -> d
28.54/9.50	   d -> k
28.54/9.50	   c -> e
28.54/9.50	   c -> k
28.54/9.50	
28.54/9.50	Q is empty.
28.54/9.50	We have to consider all minimal (P,Q,R)-chains.
28.54/9.50	----------------------------------------
28.54/9.50	
28.54/9.50	(1131) TransformationProof (EQUIVALENT)
28.54/9.50	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.50	
28.54/9.50	   (A^2 -> H(a, U1(e, b)),A^2 -> H(a, U1(e, b)))
28.54/9.50	   (A^2 -> H(U1(e, c), U1(e, b)),A^2 -> H(U1(e, c), U1(e, b)))
28.54/9.50	   (A^2 -> H(U1(e, d), U1(e, b)),A^2 -> H(U1(e, d), U1(e, b)))
28.54/9.50	   (A^2 -> H(U1(e, a), b),A^2 -> H(U1(e, a), b))
28.54/9.50	   (A^2 -> H(U1(e, a), U1(e, c)),A^2 -> H(U1(e, a), U1(e, c)))
28.54/9.50	   (A^2 -> H(U1(e, a), U1(e, d)),A^2 -> H(U1(e, a), U1(e, d)))
28.54/9.50	
28.54/9.50	
28.54/9.50	----------------------------------------
28.54/9.50	
28.54/9.50	(1132)
28.54/9.50	Obligation:
28.54/9.50	Q DP problem:
28.54/9.50	The TRS P consists of the following rules:
28.54/9.50	
28.54/9.50	   H(x, x) -> G(x, x, f(k))
28.54/9.50	   G(d, x, x) -> A^2
28.54/9.50	   A^2 -> H(f(c), f(c))
28.54/9.50	   A^2 -> H(f(d), f(d))
28.54/9.50	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.50	   A^2 -> H(f(e), f(e))
28.54/9.50	   A^2 -> H(f(k), f(k))
28.54/9.50	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, b))
28.54/9.50	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.50	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.50	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.50	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.50	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.50	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.50	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.50	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, a), b)
28.54/9.50	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.50	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.50	   A^2 -> H(U1(c, a), c)
28.54/9.50	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.50	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.50	   A^2 -> H(U1(c, a), e)
28.54/9.50	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.50	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.50	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.50	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.50	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.50	   A^2 -> H(U1(d, e), f(e))
28.54/9.50	   A^2 -> H(U1(d, e), f(k))
28.54/9.50	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.50	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.50	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.50	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.50	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.50	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.50	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.50	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.50	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.50	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.50	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.50	   A^2 -> H(U1(d, a), b)
28.54/9.50	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.50	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.50	   A^2 -> H(U1(d, a), c)
28.54/9.50	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.50	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.50	   A^2 -> H(U1(d, a), e)
28.54/9.50	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.50	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.50	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.50	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.50	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.50	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.50	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.50	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.50	   A^2 -> H(U1(a, c), b)
28.54/9.50	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.50	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.50	   A^2 -> H(U1(a, c), c)
28.54/9.50	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.50	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.50	   A^2 -> H(U1(a, c), e)
28.54/9.50	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, d), b)
28.54/9.50	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.50	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.50	   A^2 -> H(U1(a, d), c)
28.54/9.50	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.50	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.50	   A^2 -> H(U1(a, d), e)
28.54/9.50	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, a), d)
28.54/9.50	   A^2 -> H(U1(a, a), k)
28.54/9.50	   A^2 -> H(k, U1(b, b))
28.54/9.50	   A^2 -> H(k, f(c))
28.54/9.50	   A^2 -> H(k, f(d))
28.54/9.50	   A^2 -> H(c, U1(c, b))
28.54/9.50	   A^2 -> H(c, U1(d, b))
28.54/9.50	   A^2 -> H(c, U1(b, c))
28.54/9.50	   A^2 -> H(c, U1(b, d))
28.54/9.50	   A^2 -> H(c, U1(c, c))
28.54/9.50	   A^2 -> H(c, f(e))
28.54/9.50	   A^2 -> H(c, f(k))
28.54/9.50	   A^2 -> H(c, U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.50	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.50	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.50	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.50	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.50	   A^2 -> H(U1(e, k), f(e))
28.54/9.50	   A^2 -> H(U1(e, k), f(k))
28.54/9.50	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.50	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.50	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.50	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.50	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.50	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.50	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.50	   A^2 -> H(U1(k, e), f(e))
28.54/9.50	   A^2 -> H(U1(k, e), f(k))
28.54/9.50	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.50	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.50	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.50	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.50	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.50	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.50	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.50	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.50	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, c), b)
28.54/9.50	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.50	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.50	   A^2 -> H(U1(c, c), e)
28.54/9.50	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.50	   A^2 -> H(e, U1(c, b))
28.54/9.50	   A^2 -> H(e, U1(d, b))
28.54/9.50	   A^2 -> H(e, U1(b, c))
28.54/9.50	   A^2 -> H(e, U1(b, d))
28.54/9.50	   A^2 -> H(e, U1(c, c))
28.54/9.50	   A^2 -> H(e, f(e))
28.54/9.50	   A^2 -> H(e, f(k))
28.54/9.50	   A^2 -> H(e, U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.50	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.50	   A^2 -> H(f(e), b)
28.54/9.50	   A^2 -> H(f(e), U1(e, d))
28.54/9.50	   A^2 -> H(f(e), U1(d, e))
28.54/9.50	   A^2 -> H(f(e), c)
28.54/9.50	   A^2 -> H(f(e), U1(e, k))
28.54/9.50	   A^2 -> H(f(e), U1(k, e))
28.54/9.50	   A^2 -> H(f(e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.50	   A^2 -> H(f(k), b)
28.54/9.50	   A^2 -> H(f(k), U1(e, d))
28.54/9.50	   A^2 -> H(f(k), U1(d, e))
28.54/9.50	   A^2 -> H(f(k), c)
28.54/9.50	   A^2 -> H(f(k), U1(e, k))
28.54/9.50	   A^2 -> H(f(k), U1(k, e))
28.54/9.50	   A^2 -> H(f(k), e)
28.54/9.50	   A^2 -> H(f(c), d)
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.50	   A^2 -> H(U1(k, k), f(e))
28.54/9.50	   A^2 -> H(U1(k, k), f(k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.50	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.50	   A^2 -> H(U1(d, d), b)
28.54/9.50	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.50	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.50	   A^2 -> H(U1(d, d), c)
28.54/9.50	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.50	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.50	   A^2 -> H(U1(d, d), e)
28.54/9.50	   A^2 -> H(f(d), d)
28.54/9.50	   A^2 -> H(f(d), k)
28.54/9.50	   A^2 -> H(U1(c, c), c)
28.54/9.50	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.50	   A^2 -> H(f(c), k)
28.54/9.50	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.50	   A^2 -> H(f(k), U1(k, k))
28.54/9.50	   A^2 -> H(f(e), e)
28.54/9.50	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.50	   A^2 -> H(d, U1(c, b))
28.54/9.50	   A^2 -> H(d, U1(d, b))
28.54/9.50	   A^2 -> H(d, U1(b, c))
28.54/9.50	   A^2 -> H(d, U1(b, d))
28.54/9.50	   A^2 -> H(d, U1(c, c))
28.54/9.50	   A^2 -> H(d, f(e))
28.54/9.50	   A^2 -> H(d, f(k))
28.54/9.50	   A^2 -> H(d, U1(d, d))
28.54/9.50	   A^2 -> H(a, U1(e, b))
28.54/9.50	   A^2 -> H(a, U1(k, b))
28.54/9.50	   A^2 -> H(a, U1(c, d))
28.54/9.50	   A^2 -> H(a, U1(d, c))
28.54/9.50	   A^2 -> H(a, U1(b, e))
28.54/9.50	   A^2 -> H(a, U1(b, k))
28.54/9.50	   A^2 -> H(a, U1(e, c))
28.54/9.50	   A^2 -> H(a, U1(k, c))
28.54/9.50	   A^2 -> H(a, U1(c, e))
28.54/9.50	   A^2 -> H(a, U1(c, k))
28.54/9.50	   A^2 -> H(a, U1(e, e))
28.54/9.50	   A^2 -> H(a, U1(k, k))
28.54/9.50	   A^2 -> H(a, U1(k, d))
28.54/9.50	   A^2 -> H(a, U1(d, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.50	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.50	   A^2 -> H(U1(e, a), b)
28.54/9.50	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.50	
28.54/9.50	The TRS R consists of the following rules:
28.54/9.50	
28.54/9.50	   f(x) -> U1(x, x)
28.54/9.50	   U1(e, x) -> x
28.54/9.50	   a -> c
28.54/9.50	   a -> d
28.54/9.50	   b -> c
28.54/9.50	   b -> d
28.54/9.50	   d -> k
28.54/9.50	   c -> e
28.54/9.50	   c -> k
28.54/9.50	
28.54/9.50	Q is empty.
28.54/9.50	We have to consider all minimal (P,Q,R)-chains.
28.54/9.50	----------------------------------------
28.54/9.50	
28.54/9.50	(1133) TransformationProof (EQUIVALENT)
28.54/9.50	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.50	
28.54/9.50	   (A^2 -> H(a, U1(k, b)),A^2 -> H(a, U1(k, b)))
28.54/9.50	   (A^2 -> H(U1(e, c), U1(k, b)),A^2 -> H(U1(e, c), U1(k, b)))
28.54/9.50	   (A^2 -> H(U1(e, d), U1(k, b)),A^2 -> H(U1(e, d), U1(k, b)))
28.54/9.50	   (A^2 -> H(U1(e, a), U1(k, c)),A^2 -> H(U1(e, a), U1(k, c)))
28.54/9.50	   (A^2 -> H(U1(e, a), U1(k, d)),A^2 -> H(U1(e, a), U1(k, d)))
28.54/9.50	
28.54/9.50	
28.54/9.50	----------------------------------------
28.54/9.50	
28.54/9.50	(1134)
28.54/9.50	Obligation:
28.54/9.50	Q DP problem:
28.54/9.50	The TRS P consists of the following rules:
28.54/9.50	
28.54/9.50	   H(x, x) -> G(x, x, f(k))
28.54/9.50	   G(d, x, x) -> A^2
28.54/9.50	   A^2 -> H(f(c), f(c))
28.54/9.50	   A^2 -> H(f(d), f(d))
28.54/9.50	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.50	   A^2 -> H(f(e), f(e))
28.54/9.50	   A^2 -> H(f(k), f(k))
28.54/9.50	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, a), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.50	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.50	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.50	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.50	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.50	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.50	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.50	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, a), b)
28.54/9.50	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.50	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.50	   A^2 -> H(U1(c, a), c)
28.54/9.50	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.50	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.50	   A^2 -> H(U1(c, a), e)
28.54/9.50	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.50	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.50	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.50	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.50	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.50	   A^2 -> H(U1(d, e), f(e))
28.54/9.50	   A^2 -> H(U1(d, e), f(k))
28.54/9.50	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.50	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.50	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.50	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.50	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.50	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.50	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.50	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.50	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.50	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.50	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.50	   A^2 -> H(U1(d, a), b)
28.54/9.50	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.50	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.50	   A^2 -> H(U1(d, a), c)
28.54/9.50	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.50	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.50	   A^2 -> H(U1(d, a), e)
28.54/9.50	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.50	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.50	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.50	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.50	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.50	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.50	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.50	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.50	   A^2 -> H(U1(a, c), b)
28.54/9.50	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.50	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.50	   A^2 -> H(U1(a, c), c)
28.54/9.50	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.50	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.50	   A^2 -> H(U1(a, c), e)
28.54/9.50	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, d), b)
28.54/9.50	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.50	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.50	   A^2 -> H(U1(a, d), c)
28.54/9.50	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.50	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.50	   A^2 -> H(U1(a, d), e)
28.54/9.50	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, a), d)
28.54/9.50	   A^2 -> H(U1(a, a), k)
28.54/9.50	   A^2 -> H(k, U1(b, b))
28.54/9.50	   A^2 -> H(k, f(c))
28.54/9.50	   A^2 -> H(k, f(d))
28.54/9.50	   A^2 -> H(c, U1(c, b))
28.54/9.50	   A^2 -> H(c, U1(d, b))
28.54/9.50	   A^2 -> H(c, U1(b, c))
28.54/9.50	   A^2 -> H(c, U1(b, d))
28.54/9.50	   A^2 -> H(c, U1(c, c))
28.54/9.50	   A^2 -> H(c, f(e))
28.54/9.50	   A^2 -> H(c, f(k))
28.54/9.50	   A^2 -> H(c, U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.50	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.50	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.50	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.50	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.50	   A^2 -> H(U1(e, k), f(e))
28.54/9.50	   A^2 -> H(U1(e, k), f(k))
28.54/9.50	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.50	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.50	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.50	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.50	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.50	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.50	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.50	   A^2 -> H(U1(k, e), f(e))
28.54/9.50	   A^2 -> H(U1(k, e), f(k))
28.54/9.50	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.50	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.50	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.50	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.50	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.50	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.50	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.50	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.50	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, c), b)
28.54/9.50	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.50	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.50	   A^2 -> H(U1(c, c), e)
28.54/9.50	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.50	   A^2 -> H(e, U1(c, b))
28.54/9.50	   A^2 -> H(e, U1(d, b))
28.54/9.50	   A^2 -> H(e, U1(b, c))
28.54/9.50	   A^2 -> H(e, U1(b, d))
28.54/9.50	   A^2 -> H(e, U1(c, c))
28.54/9.50	   A^2 -> H(e, f(e))
28.54/9.50	   A^2 -> H(e, f(k))
28.54/9.50	   A^2 -> H(e, U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.50	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.50	   A^2 -> H(f(e), b)
28.54/9.50	   A^2 -> H(f(e), U1(e, d))
28.54/9.50	   A^2 -> H(f(e), U1(d, e))
28.54/9.50	   A^2 -> H(f(e), c)
28.54/9.50	   A^2 -> H(f(e), U1(e, k))
28.54/9.50	   A^2 -> H(f(e), U1(k, e))
28.54/9.50	   A^2 -> H(f(e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.50	   A^2 -> H(f(k), b)
28.54/9.50	   A^2 -> H(f(k), U1(e, d))
28.54/9.50	   A^2 -> H(f(k), U1(d, e))
28.54/9.50	   A^2 -> H(f(k), c)
28.54/9.50	   A^2 -> H(f(k), U1(e, k))
28.54/9.50	   A^2 -> H(f(k), U1(k, e))
28.54/9.50	   A^2 -> H(f(k), e)
28.54/9.50	   A^2 -> H(f(c), d)
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.50	   A^2 -> H(U1(k, k), f(e))
28.54/9.50	   A^2 -> H(U1(k, k), f(k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.50	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.50	   A^2 -> H(U1(d, d), b)
28.54/9.50	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.50	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.50	   A^2 -> H(U1(d, d), c)
28.54/9.50	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.50	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.50	   A^2 -> H(U1(d, d), e)
28.54/9.50	   A^2 -> H(f(d), d)
28.54/9.50	   A^2 -> H(f(d), k)
28.54/9.50	   A^2 -> H(U1(c, c), c)
28.54/9.50	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.50	   A^2 -> H(f(c), k)
28.54/9.50	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.50	   A^2 -> H(f(k), U1(k, k))
28.54/9.50	   A^2 -> H(f(e), e)
28.54/9.50	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.50	   A^2 -> H(d, U1(c, b))
28.54/9.50	   A^2 -> H(d, U1(d, b))
28.54/9.50	   A^2 -> H(d, U1(b, c))
28.54/9.50	   A^2 -> H(d, U1(b, d))
28.54/9.50	   A^2 -> H(d, U1(c, c))
28.54/9.50	   A^2 -> H(d, f(e))
28.54/9.50	   A^2 -> H(d, f(k))
28.54/9.50	   A^2 -> H(d, U1(d, d))
28.54/9.50	   A^2 -> H(a, U1(e, b))
28.54/9.50	   A^2 -> H(a, U1(k, b))
28.54/9.50	   A^2 -> H(a, U1(c, d))
28.54/9.50	   A^2 -> H(a, U1(d, c))
28.54/9.50	   A^2 -> H(a, U1(b, e))
28.54/9.50	   A^2 -> H(a, U1(b, k))
28.54/9.50	   A^2 -> H(a, U1(e, c))
28.54/9.50	   A^2 -> H(a, U1(k, c))
28.54/9.50	   A^2 -> H(a, U1(c, e))
28.54/9.50	   A^2 -> H(a, U1(c, k))
28.54/9.50	   A^2 -> H(a, U1(e, e))
28.54/9.50	   A^2 -> H(a, U1(k, k))
28.54/9.50	   A^2 -> H(a, U1(k, d))
28.54/9.50	   A^2 -> H(a, U1(d, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.50	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.50	   A^2 -> H(U1(e, a), b)
28.54/9.50	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.50	
28.54/9.50	The TRS R consists of the following rules:
28.54/9.50	
28.54/9.50	   f(x) -> U1(x, x)
28.54/9.50	   U1(e, x) -> x
28.54/9.50	   a -> c
28.54/9.50	   a -> d
28.54/9.50	   b -> c
28.54/9.50	   b -> d
28.54/9.50	   d -> k
28.54/9.50	   c -> e
28.54/9.50	   c -> k
28.54/9.50	
28.54/9.50	Q is empty.
28.54/9.50	We have to consider all minimal (P,Q,R)-chains.
28.54/9.50	----------------------------------------
28.54/9.50	
28.54/9.50	(1135) TransformationProof (EQUIVALENT)
28.54/9.50	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.50	
28.54/9.50	   (A^2 -> H(a, U1(c, d)),A^2 -> H(a, U1(c, d)))
28.54/9.50	   (A^2 -> H(U1(e, c), U1(c, d)),A^2 -> H(U1(e, c), U1(c, d)))
28.54/9.50	   (A^2 -> H(U1(e, d), U1(c, d)),A^2 -> H(U1(e, d), U1(c, d)))
28.54/9.50	   (A^2 -> H(U1(e, a), U1(e, d)),A^2 -> H(U1(e, a), U1(e, d)))
28.54/9.50	   (A^2 -> H(U1(e, a), U1(k, d)),A^2 -> H(U1(e, a), U1(k, d)))
28.54/9.50	   (A^2 -> H(U1(e, a), U1(c, k)),A^2 -> H(U1(e, a), U1(c, k)))
28.54/9.50	
28.54/9.50	
28.54/9.50	----------------------------------------
28.54/9.50	
28.54/9.50	(1136)
28.54/9.50	Obligation:
28.54/9.50	Q DP problem:
28.54/9.50	The TRS P consists of the following rules:
28.54/9.50	
28.54/9.50	   H(x, x) -> G(x, x, f(k))
28.54/9.50	   G(d, x, x) -> A^2
28.54/9.50	   A^2 -> H(f(c), f(c))
28.54/9.50	   A^2 -> H(f(d), f(d))
28.54/9.50	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.50	   A^2 -> H(f(e), f(e))
28.54/9.50	   A^2 -> H(f(k), f(k))
28.54/9.50	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, a), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.50	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.50	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.50	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.50	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.50	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.50	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.50	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, a), b)
28.54/9.50	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.50	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.50	   A^2 -> H(U1(c, a), c)
28.54/9.50	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.50	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.50	   A^2 -> H(U1(c, a), e)
28.54/9.50	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.50	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.50	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.50	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.50	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.50	   A^2 -> H(U1(d, e), f(e))
28.54/9.50	   A^2 -> H(U1(d, e), f(k))
28.54/9.50	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.50	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.50	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.50	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.50	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.50	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.50	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.50	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.50	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.50	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.50	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.50	   A^2 -> H(U1(d, a), b)
28.54/9.50	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.50	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.50	   A^2 -> H(U1(d, a), c)
28.54/9.50	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.50	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.50	   A^2 -> H(U1(d, a), e)
28.54/9.50	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.50	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.50	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.50	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.50	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.50	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.50	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.50	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.50	   A^2 -> H(U1(a, c), b)
28.54/9.50	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.50	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.50	   A^2 -> H(U1(a, c), c)
28.54/9.50	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.50	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.50	   A^2 -> H(U1(a, c), e)
28.54/9.50	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, d), b)
28.54/9.50	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.50	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.50	   A^2 -> H(U1(a, d), c)
28.54/9.50	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.50	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.50	   A^2 -> H(U1(a, d), e)
28.54/9.50	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, a), d)
28.54/9.50	   A^2 -> H(U1(a, a), k)
28.54/9.50	   A^2 -> H(k, U1(b, b))
28.54/9.50	   A^2 -> H(k, f(c))
28.54/9.50	   A^2 -> H(k, f(d))
28.54/9.50	   A^2 -> H(c, U1(c, b))
28.54/9.50	   A^2 -> H(c, U1(d, b))
28.54/9.50	   A^2 -> H(c, U1(b, c))
28.54/9.50	   A^2 -> H(c, U1(b, d))
28.54/9.50	   A^2 -> H(c, U1(c, c))
28.54/9.50	   A^2 -> H(c, f(e))
28.54/9.50	   A^2 -> H(c, f(k))
28.54/9.50	   A^2 -> H(c, U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.50	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.50	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.50	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.50	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.50	   A^2 -> H(U1(e, k), f(e))
28.54/9.50	   A^2 -> H(U1(e, k), f(k))
28.54/9.50	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.50	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.50	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.50	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.50	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.50	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.50	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.50	   A^2 -> H(U1(k, e), f(e))
28.54/9.50	   A^2 -> H(U1(k, e), f(k))
28.54/9.50	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.50	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.50	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.50	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.50	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.50	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.50	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.50	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.50	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, c), b)
28.54/9.50	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.50	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.50	   A^2 -> H(U1(c, c), e)
28.54/9.50	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.50	   A^2 -> H(e, U1(c, b))
28.54/9.50	   A^2 -> H(e, U1(d, b))
28.54/9.50	   A^2 -> H(e, U1(b, c))
28.54/9.50	   A^2 -> H(e, U1(b, d))
28.54/9.50	   A^2 -> H(e, U1(c, c))
28.54/9.50	   A^2 -> H(e, f(e))
28.54/9.50	   A^2 -> H(e, f(k))
28.54/9.50	   A^2 -> H(e, U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.50	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.50	   A^2 -> H(f(e), b)
28.54/9.50	   A^2 -> H(f(e), U1(e, d))
28.54/9.50	   A^2 -> H(f(e), U1(d, e))
28.54/9.50	   A^2 -> H(f(e), c)
28.54/9.50	   A^2 -> H(f(e), U1(e, k))
28.54/9.50	   A^2 -> H(f(e), U1(k, e))
28.54/9.50	   A^2 -> H(f(e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.50	   A^2 -> H(f(k), b)
28.54/9.50	   A^2 -> H(f(k), U1(e, d))
28.54/9.50	   A^2 -> H(f(k), U1(d, e))
28.54/9.50	   A^2 -> H(f(k), c)
28.54/9.50	   A^2 -> H(f(k), U1(e, k))
28.54/9.50	   A^2 -> H(f(k), U1(k, e))
28.54/9.50	   A^2 -> H(f(k), e)
28.54/9.50	   A^2 -> H(f(c), d)
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.50	   A^2 -> H(U1(k, k), f(e))
28.54/9.50	   A^2 -> H(U1(k, k), f(k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.50	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.50	   A^2 -> H(U1(d, d), b)
28.54/9.50	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.50	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.50	   A^2 -> H(U1(d, d), c)
28.54/9.50	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.50	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.50	   A^2 -> H(U1(d, d), e)
28.54/9.50	   A^2 -> H(f(d), d)
28.54/9.50	   A^2 -> H(f(d), k)
28.54/9.50	   A^2 -> H(U1(c, c), c)
28.54/9.50	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.50	   A^2 -> H(f(c), k)
28.54/9.50	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.50	   A^2 -> H(f(k), U1(k, k))
28.54/9.50	   A^2 -> H(f(e), e)
28.54/9.50	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.50	   A^2 -> H(d, U1(c, b))
28.54/9.50	   A^2 -> H(d, U1(d, b))
28.54/9.50	   A^2 -> H(d, U1(b, c))
28.54/9.50	   A^2 -> H(d, U1(b, d))
28.54/9.50	   A^2 -> H(d, U1(c, c))
28.54/9.50	   A^2 -> H(d, f(e))
28.54/9.50	   A^2 -> H(d, f(k))
28.54/9.50	   A^2 -> H(d, U1(d, d))
28.54/9.50	   A^2 -> H(a, U1(e, b))
28.54/9.50	   A^2 -> H(a, U1(k, b))
28.54/9.50	   A^2 -> H(a, U1(c, d))
28.54/9.50	   A^2 -> H(a, U1(d, c))
28.54/9.50	   A^2 -> H(a, U1(b, e))
28.54/9.50	   A^2 -> H(a, U1(b, k))
28.54/9.50	   A^2 -> H(a, U1(e, c))
28.54/9.50	   A^2 -> H(a, U1(k, c))
28.54/9.50	   A^2 -> H(a, U1(c, e))
28.54/9.50	   A^2 -> H(a, U1(c, k))
28.54/9.50	   A^2 -> H(a, U1(e, e))
28.54/9.50	   A^2 -> H(a, U1(k, k))
28.54/9.50	   A^2 -> H(a, U1(k, d))
28.54/9.50	   A^2 -> H(a, U1(d, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.50	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.50	   A^2 -> H(U1(e, a), b)
28.54/9.50	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.50	
28.54/9.50	The TRS R consists of the following rules:
28.54/9.50	
28.54/9.50	   f(x) -> U1(x, x)
28.54/9.50	   U1(e, x) -> x
28.54/9.50	   a -> c
28.54/9.50	   a -> d
28.54/9.50	   b -> c
28.54/9.50	   b -> d
28.54/9.50	   d -> k
28.54/9.50	   c -> e
28.54/9.50	   c -> k
28.54/9.50	
28.54/9.50	Q is empty.
28.54/9.50	We have to consider all minimal (P,Q,R)-chains.
28.54/9.50	----------------------------------------
28.54/9.50	
28.54/9.50	(1137) TransformationProof (EQUIVALENT)
28.54/9.50	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.50	
28.54/9.50	   (A^2 -> H(a, U1(d, c)),A^2 -> H(a, U1(d, c)))
28.54/9.50	   (A^2 -> H(U1(e, c), U1(d, c)),A^2 -> H(U1(e, c), U1(d, c)))
28.54/9.50	   (A^2 -> H(U1(e, d), U1(d, c)),A^2 -> H(U1(e, d), U1(d, c)))
28.54/9.50	   (A^2 -> H(U1(e, a), U1(k, c)),A^2 -> H(U1(e, a), U1(k, c)))
28.54/9.50	   (A^2 -> H(U1(e, a), U1(d, e)),A^2 -> H(U1(e, a), U1(d, e)))
28.54/9.50	   (A^2 -> H(U1(e, a), U1(d, k)),A^2 -> H(U1(e, a), U1(d, k)))
28.54/9.50	
28.54/9.50	
28.54/9.50	----------------------------------------
28.54/9.50	
28.54/9.50	(1138)
28.54/9.50	Obligation:
28.54/9.50	Q DP problem:
28.54/9.50	The TRS P consists of the following rules:
28.54/9.50	
28.54/9.50	   H(x, x) -> G(x, x, f(k))
28.54/9.50	   G(d, x, x) -> A^2
28.54/9.50	   A^2 -> H(f(c), f(c))
28.54/9.50	   A^2 -> H(f(d), f(d))
28.54/9.50	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.50	   A^2 -> H(f(e), f(e))
28.54/9.50	   A^2 -> H(f(k), f(k))
28.54/9.50	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, a), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.50	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.50	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.50	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.50	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.50	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.50	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.50	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, a), b)
28.54/9.50	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.50	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.50	   A^2 -> H(U1(c, a), c)
28.54/9.50	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.50	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.50	   A^2 -> H(U1(c, a), e)
28.54/9.50	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.50	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.50	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.50	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.50	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.50	   A^2 -> H(U1(d, e), f(e))
28.54/9.50	   A^2 -> H(U1(d, e), f(k))
28.54/9.50	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.50	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.50	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.50	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.50	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.50	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.50	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.50	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.50	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.50	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.50	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.50	   A^2 -> H(U1(d, a), b)
28.54/9.50	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.50	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.50	   A^2 -> H(U1(d, a), c)
28.54/9.50	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.50	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.50	   A^2 -> H(U1(d, a), e)
28.54/9.50	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.50	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.50	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.50	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.50	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.50	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.50	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.50	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.50	   A^2 -> H(U1(a, c), b)
28.54/9.50	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.50	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.50	   A^2 -> H(U1(a, c), c)
28.54/9.50	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.50	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.50	   A^2 -> H(U1(a, c), e)
28.54/9.50	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, d), b)
28.54/9.50	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.50	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.50	   A^2 -> H(U1(a, d), c)
28.54/9.50	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.50	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.50	   A^2 -> H(U1(a, d), e)
28.54/9.50	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(a, a), d)
28.54/9.50	   A^2 -> H(U1(a, a), k)
28.54/9.50	   A^2 -> H(k, U1(b, b))
28.54/9.50	   A^2 -> H(k, f(c))
28.54/9.50	   A^2 -> H(k, f(d))
28.54/9.50	   A^2 -> H(c, U1(c, b))
28.54/9.50	   A^2 -> H(c, U1(d, b))
28.54/9.50	   A^2 -> H(c, U1(b, c))
28.54/9.50	   A^2 -> H(c, U1(b, d))
28.54/9.50	   A^2 -> H(c, U1(c, c))
28.54/9.50	   A^2 -> H(c, f(e))
28.54/9.50	   A^2 -> H(c, f(k))
28.54/9.50	   A^2 -> H(c, U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.50	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.50	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.50	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.50	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.50	   A^2 -> H(U1(e, k), f(e))
28.54/9.50	   A^2 -> H(U1(e, k), f(k))
28.54/9.50	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.50	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.50	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.50	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.50	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.50	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.50	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.50	   A^2 -> H(U1(k, e), f(e))
28.54/9.50	   A^2 -> H(U1(k, e), f(k))
28.54/9.50	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.50	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.50	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.50	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.50	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.50	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.50	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.50	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.50	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, c), b)
28.54/9.50	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.50	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.50	   A^2 -> H(U1(c, c), e)
28.54/9.50	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.50	   A^2 -> H(e, U1(c, b))
28.54/9.50	   A^2 -> H(e, U1(d, b))
28.54/9.50	   A^2 -> H(e, U1(b, c))
28.54/9.50	   A^2 -> H(e, U1(b, d))
28.54/9.50	   A^2 -> H(e, U1(c, c))
28.54/9.50	   A^2 -> H(e, f(e))
28.54/9.50	   A^2 -> H(e, f(k))
28.54/9.50	   A^2 -> H(e, U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.50	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.50	   A^2 -> H(f(e), b)
28.54/9.50	   A^2 -> H(f(e), U1(e, d))
28.54/9.50	   A^2 -> H(f(e), U1(d, e))
28.54/9.50	   A^2 -> H(f(e), c)
28.54/9.50	   A^2 -> H(f(e), U1(e, k))
28.54/9.50	   A^2 -> H(f(e), U1(k, e))
28.54/9.50	   A^2 -> H(f(e), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.50	   A^2 -> H(f(k), b)
28.54/9.50	   A^2 -> H(f(k), U1(e, d))
28.54/9.50	   A^2 -> H(f(k), U1(d, e))
28.54/9.50	   A^2 -> H(f(k), c)
28.54/9.50	   A^2 -> H(f(k), U1(e, k))
28.54/9.50	   A^2 -> H(f(k), U1(k, e))
28.54/9.50	   A^2 -> H(f(k), e)
28.54/9.50	   A^2 -> H(f(c), d)
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.50	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.50	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.50	   A^2 -> H(U1(k, k), f(e))
28.54/9.50	   A^2 -> H(U1(k, k), f(k))
28.54/9.50	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.50	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.50	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.50	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.50	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.50	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.50	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.50	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.50	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.50	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.50	   A^2 -> H(U1(d, d), b)
28.54/9.50	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.50	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.50	   A^2 -> H(U1(d, d), c)
28.54/9.50	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.50	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.50	   A^2 -> H(U1(d, d), e)
28.54/9.50	   A^2 -> H(f(d), d)
28.54/9.50	   A^2 -> H(f(d), k)
28.54/9.50	   A^2 -> H(U1(c, c), c)
28.54/9.50	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.50	   A^2 -> H(f(c), k)
28.54/9.50	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.50	   A^2 -> H(f(k), U1(k, k))
28.54/9.50	   A^2 -> H(f(e), e)
28.54/9.50	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.50	   A^2 -> H(d, U1(c, b))
28.54/9.50	   A^2 -> H(d, U1(d, b))
28.54/9.50	   A^2 -> H(d, U1(b, c))
28.54/9.50	   A^2 -> H(d, U1(b, d))
28.54/9.50	   A^2 -> H(d, U1(c, c))
28.54/9.50	   A^2 -> H(d, f(e))
28.54/9.50	   A^2 -> H(d, f(k))
28.54/9.50	   A^2 -> H(d, U1(d, d))
28.54/9.50	   A^2 -> H(a, U1(e, b))
28.54/9.50	   A^2 -> H(a, U1(k, b))
28.54/9.50	   A^2 -> H(a, U1(c, d))
28.54/9.50	   A^2 -> H(a, U1(d, c))
28.54/9.50	   A^2 -> H(a, U1(b, e))
28.54/9.50	   A^2 -> H(a, U1(b, k))
28.54/9.50	   A^2 -> H(a, U1(e, c))
28.54/9.50	   A^2 -> H(a, U1(k, c))
28.54/9.50	   A^2 -> H(a, U1(c, e))
28.54/9.50	   A^2 -> H(a, U1(c, k))
28.54/9.50	   A^2 -> H(a, U1(e, e))
28.54/9.50	   A^2 -> H(a, U1(k, k))
28.54/9.50	   A^2 -> H(a, U1(k, d))
28.54/9.50	   A^2 -> H(a, U1(d, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.50	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.50	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.50	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.50	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.50	   A^2 -> H(U1(e, a), b)
28.54/9.50	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.50	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.50	
28.54/9.50	The TRS R consists of the following rules:
28.54/9.50	
28.54/9.50	   f(x) -> U1(x, x)
28.54/9.50	   U1(e, x) -> x
28.54/9.50	   a -> c
28.54/9.50	   a -> d
28.54/9.50	   b -> c
28.54/9.50	   b -> d
28.54/9.50	   d -> k
28.54/9.50	   c -> e
28.54/9.50	   c -> k
28.54/9.50	
28.54/9.50	Q is empty.
28.54/9.50	We have to consider all minimal (P,Q,R)-chains.
28.54/9.50	----------------------------------------
28.54/9.50	
28.54/9.50	(1139) TransformationProof (EQUIVALENT)
28.54/9.50	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.50	
28.54/9.50	   (A^2 -> H(a, U1(b, e)),A^2 -> H(a, U1(b, e)))
28.54/9.50	   (A^2 -> H(U1(e, c), U1(b, e)),A^2 -> H(U1(e, c), U1(b, e)))
28.54/9.50	   (A^2 -> H(U1(e, d), U1(b, e)),A^2 -> H(U1(e, d), U1(b, e)))
28.54/9.50	   (A^2 -> H(U1(e, a), U1(c, e)),A^2 -> H(U1(e, a), U1(c, e)))
28.54/9.50	   (A^2 -> H(U1(e, a), U1(d, e)),A^2 -> H(U1(e, a), U1(d, e)))
28.54/9.50	
28.54/9.50	
28.54/9.50	----------------------------------------
28.54/9.50	
28.54/9.50	(1140)
28.54/9.50	Obligation:
28.54/9.50	Q DP problem:
28.54/9.50	The TRS P consists of the following rules:
28.54/9.50	
28.54/9.50	   H(x, x) -> G(x, x, f(k))
28.54/9.50	   G(d, x, x) -> A^2
28.54/9.50	   A^2 -> H(f(c), f(c))
28.54/9.50	   A^2 -> H(f(d), f(d))
28.54/9.50	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.50	   A^2 -> H(f(e), f(e))
28.54/9.50	   A^2 -> H(f(k), f(k))
28.54/9.50	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.50	   A^2 -> H(U1(e, a), U1(b, k))
28.54/9.50	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.50	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.50	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.50	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.50	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.50	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.50	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.50	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.50	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.50	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.50	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.50	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.50	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.50	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.50	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.50	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.50	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.50	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.50	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.50	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.50	   A^2 -> H(U1(c, a), b)
28.54/9.50	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.50	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.50	   A^2 -> H(U1(c, a), c)
28.54/9.50	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.50	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.50	   A^2 -> H(U1(c, a), e)
28.54/9.50	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.50	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.50	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.50	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.50	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.50	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.50	   A^2 -> H(U1(d, e), f(e))
28.54/9.50	   A^2 -> H(U1(d, e), f(k))
28.54/9.50	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.50	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.50	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.50	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.50	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.50	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.50	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.50	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.51	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.51	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.51	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.51	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.51	   A^2 -> H(U1(d, a), b)
28.54/9.51	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.51	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.51	   A^2 -> H(U1(d, a), c)
28.54/9.51	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.51	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.51	   A^2 -> H(U1(d, a), e)
28.54/9.51	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.51	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.51	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.51	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.51	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.51	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.51	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.51	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.51	   A^2 -> H(U1(a, c), b)
28.54/9.51	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.51	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.51	   A^2 -> H(U1(a, c), c)
28.54/9.51	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.51	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.51	   A^2 -> H(U1(a, c), e)
28.54/9.51	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, d), b)
28.54/9.51	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.51	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.51	   A^2 -> H(U1(a, d), c)
28.54/9.51	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.51	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.51	   A^2 -> H(U1(a, d), e)
28.54/9.51	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, a), d)
28.54/9.51	   A^2 -> H(U1(a, a), k)
28.54/9.51	   A^2 -> H(k, U1(b, b))
28.54/9.51	   A^2 -> H(k, f(c))
28.54/9.51	   A^2 -> H(k, f(d))
28.54/9.51	   A^2 -> H(c, U1(c, b))
28.54/9.51	   A^2 -> H(c, U1(d, b))
28.54/9.51	   A^2 -> H(c, U1(b, c))
28.54/9.51	   A^2 -> H(c, U1(b, d))
28.54/9.51	   A^2 -> H(c, U1(c, c))
28.54/9.51	   A^2 -> H(c, f(e))
28.54/9.51	   A^2 -> H(c, f(k))
28.54/9.51	   A^2 -> H(c, U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.51	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.51	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.51	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.51	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.51	   A^2 -> H(U1(e, k), f(e))
28.54/9.51	   A^2 -> H(U1(e, k), f(k))
28.54/9.51	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.51	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.51	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.51	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.51	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.51	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.51	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.51	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.51	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.51	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.51	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.51	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.51	   A^2 -> H(U1(k, e), f(e))
28.54/9.51	   A^2 -> H(U1(k, e), f(k))
28.54/9.51	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.51	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.51	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.51	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.51	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.51	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.51	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.51	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.51	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, c), b)
28.54/9.51	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.51	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.51	   A^2 -> H(U1(c, c), e)
28.54/9.51	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.51	   A^2 -> H(e, U1(c, b))
28.54/9.51	   A^2 -> H(e, U1(d, b))
28.54/9.51	   A^2 -> H(e, U1(b, c))
28.54/9.51	   A^2 -> H(e, U1(b, d))
28.54/9.51	   A^2 -> H(e, U1(c, c))
28.54/9.51	   A^2 -> H(e, f(e))
28.54/9.51	   A^2 -> H(e, f(k))
28.54/9.51	   A^2 -> H(e, U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.51	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.51	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.51	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.51	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.51	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.51	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.51	   A^2 -> H(f(e), b)
28.54/9.51	   A^2 -> H(f(e), U1(e, d))
28.54/9.51	   A^2 -> H(f(e), U1(d, e))
28.54/9.51	   A^2 -> H(f(e), c)
28.54/9.51	   A^2 -> H(f(e), U1(e, k))
28.54/9.51	   A^2 -> H(f(e), U1(k, e))
28.54/9.51	   A^2 -> H(f(e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.51	   A^2 -> H(f(k), b)
28.54/9.51	   A^2 -> H(f(k), U1(e, d))
28.54/9.51	   A^2 -> H(f(k), U1(d, e))
28.54/9.51	   A^2 -> H(f(k), c)
28.54/9.51	   A^2 -> H(f(k), U1(e, k))
28.54/9.51	   A^2 -> H(f(k), U1(k, e))
28.54/9.51	   A^2 -> H(f(k), e)
28.54/9.51	   A^2 -> H(f(c), d)
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.51	   A^2 -> H(U1(k, k), f(e))
28.54/9.51	   A^2 -> H(U1(k, k), f(k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.51	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.51	   A^2 -> H(U1(d, d), b)
28.54/9.51	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.51	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.51	   A^2 -> H(U1(d, d), c)
28.54/9.51	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.51	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.51	   A^2 -> H(U1(d, d), e)
28.54/9.51	   A^2 -> H(f(d), d)
28.54/9.51	   A^2 -> H(f(d), k)
28.54/9.51	   A^2 -> H(U1(c, c), c)
28.54/9.51	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.51	   A^2 -> H(f(c), k)
28.54/9.51	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.51	   A^2 -> H(f(k), U1(k, k))
28.54/9.51	   A^2 -> H(f(e), e)
28.54/9.51	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.51	   A^2 -> H(d, U1(c, b))
28.54/9.51	   A^2 -> H(d, U1(d, b))
28.54/9.51	   A^2 -> H(d, U1(b, c))
28.54/9.51	   A^2 -> H(d, U1(b, d))
28.54/9.51	   A^2 -> H(d, U1(c, c))
28.54/9.51	   A^2 -> H(d, f(e))
28.54/9.51	   A^2 -> H(d, f(k))
28.54/9.51	   A^2 -> H(d, U1(d, d))
28.54/9.51	   A^2 -> H(a, U1(e, b))
28.54/9.51	   A^2 -> H(a, U1(k, b))
28.54/9.51	   A^2 -> H(a, U1(c, d))
28.54/9.51	   A^2 -> H(a, U1(d, c))
28.54/9.51	   A^2 -> H(a, U1(b, e))
28.54/9.51	   A^2 -> H(a, U1(b, k))
28.54/9.51	   A^2 -> H(a, U1(e, c))
28.54/9.51	   A^2 -> H(a, U1(k, c))
28.54/9.51	   A^2 -> H(a, U1(c, e))
28.54/9.51	   A^2 -> H(a, U1(c, k))
28.54/9.51	   A^2 -> H(a, U1(e, e))
28.54/9.51	   A^2 -> H(a, U1(k, k))
28.54/9.51	   A^2 -> H(a, U1(k, d))
28.54/9.51	   A^2 -> H(a, U1(d, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.51	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.51	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.51	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.51	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.51	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.51	   A^2 -> H(U1(e, a), b)
28.54/9.51	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.51	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.51	
28.54/9.51	The TRS R consists of the following rules:
28.54/9.51	
28.54/9.51	   f(x) -> U1(x, x)
28.54/9.51	   U1(e, x) -> x
28.54/9.51	   a -> c
28.54/9.51	   a -> d
28.54/9.51	   b -> c
28.54/9.51	   b -> d
28.54/9.51	   d -> k
28.54/9.51	   c -> e
28.54/9.51	   c -> k
28.54/9.51	
28.54/9.51	Q is empty.
28.54/9.51	We have to consider all minimal (P,Q,R)-chains.
28.54/9.51	----------------------------------------
28.54/9.51	
28.54/9.51	(1141) TransformationProof (EQUIVALENT)
28.54/9.51	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.51	
28.54/9.51	   (A^2 -> H(a, U1(b, k)),A^2 -> H(a, U1(b, k)))
28.54/9.51	   (A^2 -> H(U1(e, c), U1(b, k)),A^2 -> H(U1(e, c), U1(b, k)))
28.54/9.51	   (A^2 -> H(U1(e, d), U1(b, k)),A^2 -> H(U1(e, d), U1(b, k)))
28.54/9.51	   (A^2 -> H(U1(e, a), U1(c, k)),A^2 -> H(U1(e, a), U1(c, k)))
28.54/9.51	   (A^2 -> H(U1(e, a), U1(d, k)),A^2 -> H(U1(e, a), U1(d, k)))
28.54/9.51	
28.54/9.51	
28.54/9.51	----------------------------------------
28.54/9.51	
28.54/9.51	(1142)
28.54/9.51	Obligation:
28.54/9.51	Q DP problem:
28.54/9.51	The TRS P consists of the following rules:
28.54/9.51	
28.54/9.51	   H(x, x) -> G(x, x, f(k))
28.54/9.51	   G(d, x, x) -> A^2
28.54/9.51	   A^2 -> H(f(c), f(c))
28.54/9.51	   A^2 -> H(f(d), f(d))
28.54/9.51	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.51	   A^2 -> H(f(e), f(e))
28.54/9.51	   A^2 -> H(f(k), f(k))
28.54/9.51	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, a), U1(e, c))
28.54/9.51	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.51	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.51	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.51	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.51	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.51	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.51	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.51	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.51	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, a), b)
28.54/9.51	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.51	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.51	   A^2 -> H(U1(c, a), c)
28.54/9.51	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.51	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.51	   A^2 -> H(U1(c, a), e)
28.54/9.51	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.51	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.51	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.51	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.51	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.51	   A^2 -> H(U1(d, e), f(e))
28.54/9.51	   A^2 -> H(U1(d, e), f(k))
28.54/9.51	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.51	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.51	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.51	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.51	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.51	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.51	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.51	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.51	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.51	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.51	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.51	   A^2 -> H(U1(d, a), b)
28.54/9.51	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.51	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.51	   A^2 -> H(U1(d, a), c)
28.54/9.51	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.51	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.51	   A^2 -> H(U1(d, a), e)
28.54/9.51	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.51	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.51	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.51	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.51	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.51	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.51	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.51	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.51	   A^2 -> H(U1(a, c), b)
28.54/9.51	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.51	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.51	   A^2 -> H(U1(a, c), c)
28.54/9.51	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.51	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.51	   A^2 -> H(U1(a, c), e)
28.54/9.51	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, d), b)
28.54/9.51	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.51	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.51	   A^2 -> H(U1(a, d), c)
28.54/9.51	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.51	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.51	   A^2 -> H(U1(a, d), e)
28.54/9.51	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, a), d)
28.54/9.51	   A^2 -> H(U1(a, a), k)
28.54/9.51	   A^2 -> H(k, U1(b, b))
28.54/9.51	   A^2 -> H(k, f(c))
28.54/9.51	   A^2 -> H(k, f(d))
28.54/9.51	   A^2 -> H(c, U1(c, b))
28.54/9.51	   A^2 -> H(c, U1(d, b))
28.54/9.51	   A^2 -> H(c, U1(b, c))
28.54/9.51	   A^2 -> H(c, U1(b, d))
28.54/9.51	   A^2 -> H(c, U1(c, c))
28.54/9.51	   A^2 -> H(c, f(e))
28.54/9.51	   A^2 -> H(c, f(k))
28.54/9.51	   A^2 -> H(c, U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.51	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.51	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.51	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.51	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.51	   A^2 -> H(U1(e, k), f(e))
28.54/9.51	   A^2 -> H(U1(e, k), f(k))
28.54/9.51	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.51	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.51	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.51	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.51	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.51	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.51	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.51	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.51	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.51	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.51	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.51	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.51	   A^2 -> H(U1(k, e), f(e))
28.54/9.51	   A^2 -> H(U1(k, e), f(k))
28.54/9.51	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.51	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.51	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.51	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.51	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.51	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.51	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.51	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.51	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, c), b)
28.54/9.51	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.51	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.51	   A^2 -> H(U1(c, c), e)
28.54/9.51	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.51	   A^2 -> H(e, U1(c, b))
28.54/9.51	   A^2 -> H(e, U1(d, b))
28.54/9.51	   A^2 -> H(e, U1(b, c))
28.54/9.51	   A^2 -> H(e, U1(b, d))
28.54/9.51	   A^2 -> H(e, U1(c, c))
28.54/9.51	   A^2 -> H(e, f(e))
28.54/9.51	   A^2 -> H(e, f(k))
28.54/9.51	   A^2 -> H(e, U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.51	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.51	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.51	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.51	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.51	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.51	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.51	   A^2 -> H(f(e), b)
28.54/9.51	   A^2 -> H(f(e), U1(e, d))
28.54/9.51	   A^2 -> H(f(e), U1(d, e))
28.54/9.51	   A^2 -> H(f(e), c)
28.54/9.51	   A^2 -> H(f(e), U1(e, k))
28.54/9.51	   A^2 -> H(f(e), U1(k, e))
28.54/9.51	   A^2 -> H(f(e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.51	   A^2 -> H(f(k), b)
28.54/9.51	   A^2 -> H(f(k), U1(e, d))
28.54/9.51	   A^2 -> H(f(k), U1(d, e))
28.54/9.51	   A^2 -> H(f(k), c)
28.54/9.51	   A^2 -> H(f(k), U1(e, k))
28.54/9.51	   A^2 -> H(f(k), U1(k, e))
28.54/9.51	   A^2 -> H(f(k), e)
28.54/9.51	   A^2 -> H(f(c), d)
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.51	   A^2 -> H(U1(k, k), f(e))
28.54/9.51	   A^2 -> H(U1(k, k), f(k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.51	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.51	   A^2 -> H(U1(d, d), b)
28.54/9.51	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.51	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.51	   A^2 -> H(U1(d, d), c)
28.54/9.51	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.51	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.51	   A^2 -> H(U1(d, d), e)
28.54/9.51	   A^2 -> H(f(d), d)
28.54/9.51	   A^2 -> H(f(d), k)
28.54/9.51	   A^2 -> H(U1(c, c), c)
28.54/9.51	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.51	   A^2 -> H(f(c), k)
28.54/9.51	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.51	   A^2 -> H(f(k), U1(k, k))
28.54/9.51	   A^2 -> H(f(e), e)
28.54/9.51	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.51	   A^2 -> H(d, U1(c, b))
28.54/9.51	   A^2 -> H(d, U1(d, b))
28.54/9.51	   A^2 -> H(d, U1(b, c))
28.54/9.51	   A^2 -> H(d, U1(b, d))
28.54/9.51	   A^2 -> H(d, U1(c, c))
28.54/9.51	   A^2 -> H(d, f(e))
28.54/9.51	   A^2 -> H(d, f(k))
28.54/9.51	   A^2 -> H(d, U1(d, d))
28.54/9.51	   A^2 -> H(a, U1(e, b))
28.54/9.51	   A^2 -> H(a, U1(k, b))
28.54/9.51	   A^2 -> H(a, U1(c, d))
28.54/9.51	   A^2 -> H(a, U1(d, c))
28.54/9.51	   A^2 -> H(a, U1(b, e))
28.54/9.51	   A^2 -> H(a, U1(b, k))
28.54/9.51	   A^2 -> H(a, U1(e, c))
28.54/9.51	   A^2 -> H(a, U1(k, c))
28.54/9.51	   A^2 -> H(a, U1(c, e))
28.54/9.51	   A^2 -> H(a, U1(c, k))
28.54/9.51	   A^2 -> H(a, U1(e, e))
28.54/9.51	   A^2 -> H(a, U1(k, k))
28.54/9.51	   A^2 -> H(a, U1(k, d))
28.54/9.51	   A^2 -> H(a, U1(d, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.51	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.51	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.51	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.51	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.51	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.51	   A^2 -> H(U1(e, a), b)
28.54/9.51	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.51	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.51	
28.54/9.51	The TRS R consists of the following rules:
28.54/9.51	
28.54/9.51	   f(x) -> U1(x, x)
28.54/9.51	   U1(e, x) -> x
28.54/9.51	   a -> c
28.54/9.51	   a -> d
28.54/9.51	   b -> c
28.54/9.51	   b -> d
28.54/9.51	   d -> k
28.54/9.51	   c -> e
28.54/9.51	   c -> k
28.54/9.51	
28.54/9.51	Q is empty.
28.54/9.51	We have to consider all minimal (P,Q,R)-chains.
28.54/9.51	----------------------------------------
28.54/9.51	
28.54/9.51	(1143) TransformationProof (EQUIVALENT)
28.54/9.51	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.51	
28.54/9.51	   (A^2 -> H(a, U1(e, c)),A^2 -> H(a, U1(e, c)))
28.54/9.51	   (A^2 -> H(U1(e, c), U1(e, c)),A^2 -> H(U1(e, c), U1(e, c)))
28.54/9.51	   (A^2 -> H(U1(e, d), U1(e, c)),A^2 -> H(U1(e, d), U1(e, c)))
28.54/9.51	   (A^2 -> H(U1(e, a), c),A^2 -> H(U1(e, a), c))
28.54/9.51	   (A^2 -> H(U1(e, a), U1(e, e)),A^2 -> H(U1(e, a), U1(e, e)))
28.54/9.51	   (A^2 -> H(U1(e, a), U1(e, k)),A^2 -> H(U1(e, a), U1(e, k)))
28.54/9.51	
28.54/9.51	
28.54/9.51	----------------------------------------
28.54/9.51	
28.54/9.51	(1144)
28.54/9.51	Obligation:
28.54/9.51	Q DP problem:
28.54/9.51	The TRS P consists of the following rules:
28.54/9.51	
28.54/9.51	   H(x, x) -> G(x, x, f(k))
28.54/9.51	   G(d, x, x) -> A^2
28.54/9.51	   A^2 -> H(f(c), f(c))
28.54/9.51	   A^2 -> H(f(d), f(d))
28.54/9.51	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.51	   A^2 -> H(f(e), f(e))
28.54/9.51	   A^2 -> H(f(k), f(k))
28.54/9.51	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, a), U1(k, c))
28.54/9.51	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.51	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.51	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.51	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.51	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.51	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.51	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.51	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, a), b)
28.54/9.51	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.51	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.51	   A^2 -> H(U1(c, a), c)
28.54/9.51	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.51	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.51	   A^2 -> H(U1(c, a), e)
28.54/9.51	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.51	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.51	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.51	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.51	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.51	   A^2 -> H(U1(d, e), f(e))
28.54/9.51	   A^2 -> H(U1(d, e), f(k))
28.54/9.51	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.51	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.51	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.51	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.51	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.51	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.51	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.51	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.51	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.51	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.51	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.51	   A^2 -> H(U1(d, a), b)
28.54/9.51	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.51	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.51	   A^2 -> H(U1(d, a), c)
28.54/9.51	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.51	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.51	   A^2 -> H(U1(d, a), e)
28.54/9.51	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.51	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.51	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.51	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.51	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.51	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.51	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.51	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.51	   A^2 -> H(U1(a, c), b)
28.54/9.51	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.51	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.51	   A^2 -> H(U1(a, c), c)
28.54/9.51	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.51	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.51	   A^2 -> H(U1(a, c), e)
28.54/9.51	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, d), b)
28.54/9.51	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.51	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.51	   A^2 -> H(U1(a, d), c)
28.54/9.51	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.51	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.51	   A^2 -> H(U1(a, d), e)
28.54/9.51	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, a), d)
28.54/9.51	   A^2 -> H(U1(a, a), k)
28.54/9.51	   A^2 -> H(k, U1(b, b))
28.54/9.51	   A^2 -> H(k, f(c))
28.54/9.51	   A^2 -> H(k, f(d))
28.54/9.51	   A^2 -> H(c, U1(c, b))
28.54/9.51	   A^2 -> H(c, U1(d, b))
28.54/9.51	   A^2 -> H(c, U1(b, c))
28.54/9.51	   A^2 -> H(c, U1(b, d))
28.54/9.51	   A^2 -> H(c, U1(c, c))
28.54/9.51	   A^2 -> H(c, f(e))
28.54/9.51	   A^2 -> H(c, f(k))
28.54/9.51	   A^2 -> H(c, U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.51	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.51	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.51	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.51	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.51	   A^2 -> H(U1(e, k), f(e))
28.54/9.51	   A^2 -> H(U1(e, k), f(k))
28.54/9.51	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.51	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.51	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.51	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.51	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.51	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.51	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.51	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.51	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.51	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.51	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.51	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.51	   A^2 -> H(U1(k, e), f(e))
28.54/9.51	   A^2 -> H(U1(k, e), f(k))
28.54/9.51	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.51	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.51	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.51	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.51	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.51	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.51	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.51	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.51	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, c), b)
28.54/9.51	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.51	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.51	   A^2 -> H(U1(c, c), e)
28.54/9.51	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.51	   A^2 -> H(e, U1(c, b))
28.54/9.51	   A^2 -> H(e, U1(d, b))
28.54/9.51	   A^2 -> H(e, U1(b, c))
28.54/9.51	   A^2 -> H(e, U1(b, d))
28.54/9.51	   A^2 -> H(e, U1(c, c))
28.54/9.51	   A^2 -> H(e, f(e))
28.54/9.51	   A^2 -> H(e, f(k))
28.54/9.51	   A^2 -> H(e, U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.51	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.51	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.51	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.51	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.51	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.51	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.51	   A^2 -> H(f(e), b)
28.54/9.51	   A^2 -> H(f(e), U1(e, d))
28.54/9.51	   A^2 -> H(f(e), U1(d, e))
28.54/9.51	   A^2 -> H(f(e), c)
28.54/9.51	   A^2 -> H(f(e), U1(e, k))
28.54/9.51	   A^2 -> H(f(e), U1(k, e))
28.54/9.51	   A^2 -> H(f(e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.51	   A^2 -> H(f(k), b)
28.54/9.51	   A^2 -> H(f(k), U1(e, d))
28.54/9.51	   A^2 -> H(f(k), U1(d, e))
28.54/9.51	   A^2 -> H(f(k), c)
28.54/9.51	   A^2 -> H(f(k), U1(e, k))
28.54/9.51	   A^2 -> H(f(k), U1(k, e))
28.54/9.51	   A^2 -> H(f(k), e)
28.54/9.51	   A^2 -> H(f(c), d)
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.51	   A^2 -> H(U1(k, k), f(e))
28.54/9.51	   A^2 -> H(U1(k, k), f(k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.51	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.51	   A^2 -> H(U1(d, d), b)
28.54/9.51	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.51	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.51	   A^2 -> H(U1(d, d), c)
28.54/9.51	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.51	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.51	   A^2 -> H(U1(d, d), e)
28.54/9.51	   A^2 -> H(f(d), d)
28.54/9.51	   A^2 -> H(f(d), k)
28.54/9.51	   A^2 -> H(U1(c, c), c)
28.54/9.51	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.51	   A^2 -> H(f(c), k)
28.54/9.51	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.51	   A^2 -> H(f(k), U1(k, k))
28.54/9.51	   A^2 -> H(f(e), e)
28.54/9.51	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.51	   A^2 -> H(d, U1(c, b))
28.54/9.51	   A^2 -> H(d, U1(d, b))
28.54/9.51	   A^2 -> H(d, U1(b, c))
28.54/9.51	   A^2 -> H(d, U1(b, d))
28.54/9.51	   A^2 -> H(d, U1(c, c))
28.54/9.51	   A^2 -> H(d, f(e))
28.54/9.51	   A^2 -> H(d, f(k))
28.54/9.51	   A^2 -> H(d, U1(d, d))
28.54/9.51	   A^2 -> H(a, U1(e, b))
28.54/9.51	   A^2 -> H(a, U1(k, b))
28.54/9.51	   A^2 -> H(a, U1(c, d))
28.54/9.51	   A^2 -> H(a, U1(d, c))
28.54/9.51	   A^2 -> H(a, U1(b, e))
28.54/9.51	   A^2 -> H(a, U1(b, k))
28.54/9.51	   A^2 -> H(a, U1(e, c))
28.54/9.51	   A^2 -> H(a, U1(k, c))
28.54/9.51	   A^2 -> H(a, U1(c, e))
28.54/9.51	   A^2 -> H(a, U1(c, k))
28.54/9.51	   A^2 -> H(a, U1(e, e))
28.54/9.51	   A^2 -> H(a, U1(k, k))
28.54/9.51	   A^2 -> H(a, U1(k, d))
28.54/9.51	   A^2 -> H(a, U1(d, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.51	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.51	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.51	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.51	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.51	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.51	   A^2 -> H(U1(e, a), b)
28.54/9.51	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.51	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.51	   A^2 -> H(U1(e, a), c)
28.54/9.51	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.51	
28.54/9.51	The TRS R consists of the following rules:
28.54/9.51	
28.54/9.51	   f(x) -> U1(x, x)
28.54/9.51	   U1(e, x) -> x
28.54/9.51	   a -> c
28.54/9.51	   a -> d
28.54/9.51	   b -> c
28.54/9.51	   b -> d
28.54/9.51	   d -> k
28.54/9.51	   c -> e
28.54/9.51	   c -> k
28.54/9.51	
28.54/9.51	Q is empty.
28.54/9.51	We have to consider all minimal (P,Q,R)-chains.
28.54/9.51	----------------------------------------
28.54/9.51	
28.54/9.51	(1145) TransformationProof (EQUIVALENT)
28.54/9.51	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.51	
28.54/9.51	   (A^2 -> H(a, U1(k, c)),A^2 -> H(a, U1(k, c)))
28.54/9.51	   (A^2 -> H(U1(e, c), U1(k, c)),A^2 -> H(U1(e, c), U1(k, c)))
28.54/9.51	   (A^2 -> H(U1(e, d), U1(k, c)),A^2 -> H(U1(e, d), U1(k, c)))
28.54/9.51	   (A^2 -> H(U1(e, a), U1(k, e)),A^2 -> H(U1(e, a), U1(k, e)))
28.54/9.51	   (A^2 -> H(U1(e, a), U1(k, k)),A^2 -> H(U1(e, a), U1(k, k)))
28.54/9.51	
28.54/9.51	
28.54/9.51	----------------------------------------
28.54/9.51	
28.54/9.51	(1146)
28.54/9.51	Obligation:
28.54/9.51	Q DP problem:
28.54/9.51	The TRS P consists of the following rules:
28.54/9.51	
28.54/9.51	   H(x, x) -> G(x, x, f(k))
28.54/9.51	   G(d, x, x) -> A^2
28.54/9.51	   A^2 -> H(f(c), f(c))
28.54/9.51	   A^2 -> H(f(d), f(d))
28.54/9.51	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.51	   A^2 -> H(f(e), f(e))
28.54/9.51	   A^2 -> H(f(k), f(k))
28.54/9.51	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, a), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.51	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.51	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.51	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.51	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.51	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.51	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.51	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, a), b)
28.54/9.51	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.51	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.51	   A^2 -> H(U1(c, a), c)
28.54/9.51	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.51	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.51	   A^2 -> H(U1(c, a), e)
28.54/9.51	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.51	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.51	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.51	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.51	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.51	   A^2 -> H(U1(d, e), f(e))
28.54/9.51	   A^2 -> H(U1(d, e), f(k))
28.54/9.51	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.51	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.51	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.51	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.51	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.51	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.51	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.51	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.51	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.51	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.51	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.51	   A^2 -> H(U1(d, a), b)
28.54/9.51	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.51	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.51	   A^2 -> H(U1(d, a), c)
28.54/9.51	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.51	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.51	   A^2 -> H(U1(d, a), e)
28.54/9.51	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.51	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.51	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.51	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.51	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.51	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.51	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.51	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.51	   A^2 -> H(U1(a, c), b)
28.54/9.51	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.51	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.51	   A^2 -> H(U1(a, c), c)
28.54/9.51	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.51	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.51	   A^2 -> H(U1(a, c), e)
28.54/9.51	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, d), b)
28.54/9.51	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.51	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.51	   A^2 -> H(U1(a, d), c)
28.54/9.51	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.51	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.51	   A^2 -> H(U1(a, d), e)
28.54/9.51	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, a), d)
28.54/9.51	   A^2 -> H(U1(a, a), k)
28.54/9.51	   A^2 -> H(k, U1(b, b))
28.54/9.51	   A^2 -> H(k, f(c))
28.54/9.51	   A^2 -> H(k, f(d))
28.54/9.51	   A^2 -> H(c, U1(c, b))
28.54/9.51	   A^2 -> H(c, U1(d, b))
28.54/9.51	   A^2 -> H(c, U1(b, c))
28.54/9.51	   A^2 -> H(c, U1(b, d))
28.54/9.51	   A^2 -> H(c, U1(c, c))
28.54/9.51	   A^2 -> H(c, f(e))
28.54/9.51	   A^2 -> H(c, f(k))
28.54/9.51	   A^2 -> H(c, U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.51	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.51	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.51	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.51	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.51	   A^2 -> H(U1(e, k), f(e))
28.54/9.51	   A^2 -> H(U1(e, k), f(k))
28.54/9.51	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.51	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.51	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.51	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.51	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.51	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.51	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.51	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.51	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.51	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.51	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.51	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.51	   A^2 -> H(U1(k, e), f(e))
28.54/9.51	   A^2 -> H(U1(k, e), f(k))
28.54/9.51	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.51	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.51	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.51	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.51	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.51	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.51	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.51	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.51	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, c), b)
28.54/9.51	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.51	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.51	   A^2 -> H(U1(c, c), e)
28.54/9.51	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.51	   A^2 -> H(e, U1(c, b))
28.54/9.51	   A^2 -> H(e, U1(d, b))
28.54/9.51	   A^2 -> H(e, U1(b, c))
28.54/9.51	   A^2 -> H(e, U1(b, d))
28.54/9.51	   A^2 -> H(e, U1(c, c))
28.54/9.51	   A^2 -> H(e, f(e))
28.54/9.51	   A^2 -> H(e, f(k))
28.54/9.51	   A^2 -> H(e, U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.51	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.51	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.51	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.51	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.51	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.51	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.51	   A^2 -> H(f(e), b)
28.54/9.51	   A^2 -> H(f(e), U1(e, d))
28.54/9.51	   A^2 -> H(f(e), U1(d, e))
28.54/9.51	   A^2 -> H(f(e), c)
28.54/9.51	   A^2 -> H(f(e), U1(e, k))
28.54/9.51	   A^2 -> H(f(e), U1(k, e))
28.54/9.51	   A^2 -> H(f(e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.51	   A^2 -> H(f(k), b)
28.54/9.51	   A^2 -> H(f(k), U1(e, d))
28.54/9.51	   A^2 -> H(f(k), U1(d, e))
28.54/9.51	   A^2 -> H(f(k), c)
28.54/9.51	   A^2 -> H(f(k), U1(e, k))
28.54/9.51	   A^2 -> H(f(k), U1(k, e))
28.54/9.51	   A^2 -> H(f(k), e)
28.54/9.51	   A^2 -> H(f(c), d)
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.51	   A^2 -> H(U1(k, k), f(e))
28.54/9.51	   A^2 -> H(U1(k, k), f(k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.51	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.51	   A^2 -> H(U1(d, d), b)
28.54/9.51	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.51	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.51	   A^2 -> H(U1(d, d), c)
28.54/9.51	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.51	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.51	   A^2 -> H(U1(d, d), e)
28.54/9.51	   A^2 -> H(f(d), d)
28.54/9.51	   A^2 -> H(f(d), k)
28.54/9.51	   A^2 -> H(U1(c, c), c)
28.54/9.51	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.51	   A^2 -> H(f(c), k)
28.54/9.51	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.51	   A^2 -> H(f(k), U1(k, k))
28.54/9.51	   A^2 -> H(f(e), e)
28.54/9.51	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.51	   A^2 -> H(d, U1(c, b))
28.54/9.51	   A^2 -> H(d, U1(d, b))
28.54/9.51	   A^2 -> H(d, U1(b, c))
28.54/9.51	   A^2 -> H(d, U1(b, d))
28.54/9.51	   A^2 -> H(d, U1(c, c))
28.54/9.51	   A^2 -> H(d, f(e))
28.54/9.51	   A^2 -> H(d, f(k))
28.54/9.51	   A^2 -> H(d, U1(d, d))
28.54/9.51	   A^2 -> H(a, U1(e, b))
28.54/9.51	   A^2 -> H(a, U1(k, b))
28.54/9.51	   A^2 -> H(a, U1(c, d))
28.54/9.51	   A^2 -> H(a, U1(d, c))
28.54/9.51	   A^2 -> H(a, U1(b, e))
28.54/9.51	   A^2 -> H(a, U1(b, k))
28.54/9.51	   A^2 -> H(a, U1(e, c))
28.54/9.51	   A^2 -> H(a, U1(k, c))
28.54/9.51	   A^2 -> H(a, U1(c, e))
28.54/9.51	   A^2 -> H(a, U1(c, k))
28.54/9.51	   A^2 -> H(a, U1(e, e))
28.54/9.51	   A^2 -> H(a, U1(k, k))
28.54/9.51	   A^2 -> H(a, U1(k, d))
28.54/9.51	   A^2 -> H(a, U1(d, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.51	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.51	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.51	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.51	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.51	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.51	   A^2 -> H(U1(e, a), b)
28.54/9.51	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.51	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.51	   A^2 -> H(U1(e, a), c)
28.54/9.51	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.51	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.51	
28.54/9.51	The TRS R consists of the following rules:
28.54/9.51	
28.54/9.51	   f(x) -> U1(x, x)
28.54/9.51	   U1(e, x) -> x
28.54/9.51	   a -> c
28.54/9.51	   a -> d
28.54/9.51	   b -> c
28.54/9.51	   b -> d
28.54/9.51	   d -> k
28.54/9.51	   c -> e
28.54/9.51	   c -> k
28.54/9.51	
28.54/9.51	Q is empty.
28.54/9.51	We have to consider all minimal (P,Q,R)-chains.
28.54/9.51	----------------------------------------
28.54/9.51	
28.54/9.51	(1147) TransformationProof (EQUIVALENT)
28.54/9.51	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.51	
28.54/9.51	   (A^2 -> H(a, U1(c, e)),A^2 -> H(a, U1(c, e)))
28.54/9.51	   (A^2 -> H(U1(e, c), U1(c, e)),A^2 -> H(U1(e, c), U1(c, e)))
28.54/9.51	   (A^2 -> H(U1(e, d), U1(c, e)),A^2 -> H(U1(e, d), U1(c, e)))
28.54/9.51	   (A^2 -> H(U1(e, a), U1(e, e)),A^2 -> H(U1(e, a), U1(e, e)))
28.54/9.51	   (A^2 -> H(U1(e, a), U1(k, e)),A^2 -> H(U1(e, a), U1(k, e)))
28.54/9.51	
28.54/9.51	
28.54/9.51	----------------------------------------
28.54/9.51	
28.54/9.51	(1148)
28.54/9.51	Obligation:
28.54/9.51	Q DP problem:
28.54/9.51	The TRS P consists of the following rules:
28.54/9.51	
28.54/9.51	   H(x, x) -> G(x, x, f(k))
28.54/9.51	   G(d, x, x) -> A^2
28.54/9.51	   A^2 -> H(f(c), f(c))
28.54/9.51	   A^2 -> H(f(d), f(d))
28.54/9.51	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.51	   A^2 -> H(f(e), f(e))
28.54/9.51	   A^2 -> H(f(k), f(k))
28.54/9.51	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, a), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.51	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.51	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.51	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.51	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.51	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.51	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.51	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, a), b)
28.54/9.51	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.51	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.51	   A^2 -> H(U1(c, a), c)
28.54/9.51	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.51	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.51	   A^2 -> H(U1(c, a), e)
28.54/9.51	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.51	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.51	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.51	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.51	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.51	   A^2 -> H(U1(d, e), f(e))
28.54/9.51	   A^2 -> H(U1(d, e), f(k))
28.54/9.51	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.51	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.51	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.51	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.51	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.51	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.51	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.51	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.51	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.51	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.51	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.51	   A^2 -> H(U1(d, a), b)
28.54/9.51	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.51	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.51	   A^2 -> H(U1(d, a), c)
28.54/9.51	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.51	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.51	   A^2 -> H(U1(d, a), e)
28.54/9.51	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.51	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.51	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.51	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.51	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.51	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.51	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.51	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.51	   A^2 -> H(U1(a, c), b)
28.54/9.51	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.51	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.51	   A^2 -> H(U1(a, c), c)
28.54/9.51	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.51	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.51	   A^2 -> H(U1(a, c), e)
28.54/9.51	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, d), b)
28.54/9.51	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.51	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.51	   A^2 -> H(U1(a, d), c)
28.54/9.51	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.51	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.51	   A^2 -> H(U1(a, d), e)
28.54/9.51	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, a), d)
28.54/9.51	   A^2 -> H(U1(a, a), k)
28.54/9.51	   A^2 -> H(k, U1(b, b))
28.54/9.51	   A^2 -> H(k, f(c))
28.54/9.51	   A^2 -> H(k, f(d))
28.54/9.51	   A^2 -> H(c, U1(c, b))
28.54/9.51	   A^2 -> H(c, U1(d, b))
28.54/9.51	   A^2 -> H(c, U1(b, c))
28.54/9.51	   A^2 -> H(c, U1(b, d))
28.54/9.51	   A^2 -> H(c, U1(c, c))
28.54/9.51	   A^2 -> H(c, f(e))
28.54/9.51	   A^2 -> H(c, f(k))
28.54/9.51	   A^2 -> H(c, U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.51	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.51	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.51	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.51	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.51	   A^2 -> H(U1(e, k), f(e))
28.54/9.51	   A^2 -> H(U1(e, k), f(k))
28.54/9.51	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.51	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.51	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.51	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.51	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.51	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.51	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.51	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.51	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.51	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.51	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.51	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.51	   A^2 -> H(U1(k, e), f(e))
28.54/9.51	   A^2 -> H(U1(k, e), f(k))
28.54/9.51	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.51	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.51	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.51	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.51	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.51	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.51	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.51	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.51	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, c), b)
28.54/9.51	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.51	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.51	   A^2 -> H(U1(c, c), e)
28.54/9.51	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.51	   A^2 -> H(e, U1(c, b))
28.54/9.51	   A^2 -> H(e, U1(d, b))
28.54/9.51	   A^2 -> H(e, U1(b, c))
28.54/9.51	   A^2 -> H(e, U1(b, d))
28.54/9.51	   A^2 -> H(e, U1(c, c))
28.54/9.51	   A^2 -> H(e, f(e))
28.54/9.51	   A^2 -> H(e, f(k))
28.54/9.51	   A^2 -> H(e, U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.51	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.51	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.51	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.51	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.51	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.51	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.51	   A^2 -> H(f(e), b)
28.54/9.51	   A^2 -> H(f(e), U1(e, d))
28.54/9.51	   A^2 -> H(f(e), U1(d, e))
28.54/9.51	   A^2 -> H(f(e), c)
28.54/9.51	   A^2 -> H(f(e), U1(e, k))
28.54/9.51	   A^2 -> H(f(e), U1(k, e))
28.54/9.51	   A^2 -> H(f(e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.51	   A^2 -> H(f(k), b)
28.54/9.51	   A^2 -> H(f(k), U1(e, d))
28.54/9.51	   A^2 -> H(f(k), U1(d, e))
28.54/9.51	   A^2 -> H(f(k), c)
28.54/9.51	   A^2 -> H(f(k), U1(e, k))
28.54/9.51	   A^2 -> H(f(k), U1(k, e))
28.54/9.51	   A^2 -> H(f(k), e)
28.54/9.51	   A^2 -> H(f(c), d)
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.51	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.51	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.51	   A^2 -> H(U1(k, k), f(e))
28.54/9.51	   A^2 -> H(U1(k, k), f(k))
28.54/9.51	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.51	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.51	   A^2 -> H(U1(d, d), b)
28.54/9.51	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.51	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.51	   A^2 -> H(U1(d, d), c)
28.54/9.51	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.51	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.51	   A^2 -> H(U1(d, d), e)
28.54/9.51	   A^2 -> H(f(d), d)
28.54/9.51	   A^2 -> H(f(d), k)
28.54/9.51	   A^2 -> H(U1(c, c), c)
28.54/9.51	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.51	   A^2 -> H(f(c), k)
28.54/9.51	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.51	   A^2 -> H(f(k), U1(k, k))
28.54/9.51	   A^2 -> H(f(e), e)
28.54/9.51	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.51	   A^2 -> H(d, U1(c, b))
28.54/9.51	   A^2 -> H(d, U1(d, b))
28.54/9.51	   A^2 -> H(d, U1(b, c))
28.54/9.51	   A^2 -> H(d, U1(b, d))
28.54/9.51	   A^2 -> H(d, U1(c, c))
28.54/9.51	   A^2 -> H(d, f(e))
28.54/9.51	   A^2 -> H(d, f(k))
28.54/9.51	   A^2 -> H(d, U1(d, d))
28.54/9.51	   A^2 -> H(a, U1(e, b))
28.54/9.51	   A^2 -> H(a, U1(k, b))
28.54/9.51	   A^2 -> H(a, U1(c, d))
28.54/9.51	   A^2 -> H(a, U1(d, c))
28.54/9.51	   A^2 -> H(a, U1(b, e))
28.54/9.51	   A^2 -> H(a, U1(b, k))
28.54/9.51	   A^2 -> H(a, U1(e, c))
28.54/9.51	   A^2 -> H(a, U1(k, c))
28.54/9.51	   A^2 -> H(a, U1(c, e))
28.54/9.51	   A^2 -> H(a, U1(c, k))
28.54/9.51	   A^2 -> H(a, U1(e, e))
28.54/9.51	   A^2 -> H(a, U1(k, k))
28.54/9.51	   A^2 -> H(a, U1(k, d))
28.54/9.51	   A^2 -> H(a, U1(d, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.51	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.51	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.51	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.51	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.51	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.51	   A^2 -> H(U1(e, a), b)
28.54/9.51	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.51	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.51	   A^2 -> H(U1(e, a), c)
28.54/9.51	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.51	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.51	
28.54/9.51	The TRS R consists of the following rules:
28.54/9.51	
28.54/9.51	   f(x) -> U1(x, x)
28.54/9.51	   U1(e, x) -> x
28.54/9.51	   a -> c
28.54/9.51	   a -> d
28.54/9.51	   b -> c
28.54/9.51	   b -> d
28.54/9.51	   d -> k
28.54/9.51	   c -> e
28.54/9.51	   c -> k
28.54/9.51	
28.54/9.51	Q is empty.
28.54/9.51	We have to consider all minimal (P,Q,R)-chains.
28.54/9.51	----------------------------------------
28.54/9.51	
28.54/9.51	(1149) TransformationProof (EQUIVALENT)
28.54/9.51	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.51	
28.54/9.51	   (A^2 -> H(a, U1(c, k)),A^2 -> H(a, U1(c, k)))
28.54/9.51	   (A^2 -> H(U1(e, c), U1(c, k)),A^2 -> H(U1(e, c), U1(c, k)))
28.54/9.51	   (A^2 -> H(U1(e, d), U1(c, k)),A^2 -> H(U1(e, d), U1(c, k)))
28.54/9.51	   (A^2 -> H(U1(e, a), U1(e, k)),A^2 -> H(U1(e, a), U1(e, k)))
28.54/9.51	   (A^2 -> H(U1(e, a), U1(k, k)),A^2 -> H(U1(e, a), U1(k, k)))
28.54/9.51	
28.54/9.51	
28.54/9.51	----------------------------------------
28.54/9.51	
28.54/9.51	(1150)
28.54/9.51	Obligation:
28.54/9.51	Q DP problem:
28.54/9.51	The TRS P consists of the following rules:
28.54/9.51	
28.54/9.51	   H(x, x) -> G(x, x, f(k))
28.54/9.51	   G(d, x, x) -> A^2
28.54/9.51	   A^2 -> H(f(c), f(c))
28.54/9.51	   A^2 -> H(f(d), f(d))
28.54/9.51	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.51	   A^2 -> H(f(e), f(e))
28.54/9.51	   A^2 -> H(f(k), f(k))
28.54/9.51	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, a), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.51	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.51	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.51	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.51	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.51	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.51	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.51	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.51	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.51	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.51	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.51	   A^2 -> H(U1(c, a), b)
28.54/9.51	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.51	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.51	   A^2 -> H(U1(c, a), c)
28.54/9.51	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.51	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.51	   A^2 -> H(U1(c, a), e)
28.54/9.51	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.51	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.51	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.51	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.51	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.51	   A^2 -> H(U1(d, e), f(e))
28.54/9.51	   A^2 -> H(U1(d, e), f(k))
28.54/9.51	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.51	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.51	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.51	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.51	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.51	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.51	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.51	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.51	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.51	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.51	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.51	   A^2 -> H(U1(d, a), b)
28.54/9.51	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.51	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.51	   A^2 -> H(U1(d, a), c)
28.54/9.51	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.51	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.51	   A^2 -> H(U1(d, a), e)
28.54/9.51	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.51	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.51	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.51	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.51	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.51	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.51	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.51	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.51	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.51	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.51	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.51	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.51	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.51	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.51	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.51	   A^2 -> H(U1(a, c), b)
28.54/9.51	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.51	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.51	   A^2 -> H(U1(a, c), c)
28.54/9.51	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.51	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.51	   A^2 -> H(U1(a, c), e)
28.54/9.51	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, d), b)
28.54/9.51	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.51	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.51	   A^2 -> H(U1(a, d), c)
28.54/9.51	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.51	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.51	   A^2 -> H(U1(a, d), e)
28.54/9.51	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.51	   A^2 -> H(U1(a, a), d)
28.54/9.51	   A^2 -> H(U1(a, a), k)
28.54/9.51	   A^2 -> H(k, U1(b, b))
28.54/9.51	   A^2 -> H(k, f(c))
28.54/9.51	   A^2 -> H(k, f(d))
28.54/9.51	   A^2 -> H(c, U1(c, b))
28.54/9.51	   A^2 -> H(c, U1(d, b))
28.54/9.51	   A^2 -> H(c, U1(b, c))
28.54/9.51	   A^2 -> H(c, U1(b, d))
28.54/9.51	   A^2 -> H(c, U1(c, c))
28.54/9.51	   A^2 -> H(c, f(e))
28.54/9.51	   A^2 -> H(c, f(k))
28.54/9.51	   A^2 -> H(c, U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.51	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.51	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.51	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.51	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.51	   A^2 -> H(U1(e, k), f(e))
28.54/9.51	   A^2 -> H(U1(e, k), f(k))
28.54/9.51	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.51	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.51	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.51	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.51	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.51	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.51	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.51	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.51	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.51	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.51	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.51	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.51	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.51	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.51	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.51	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.51	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.51	   A^2 -> H(U1(k, e), f(e))
28.54/9.51	   A^2 -> H(U1(k, e), f(k))
28.54/9.51	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.51	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.51	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.51	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.51	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.51	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.51	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.51	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.52	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.52	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.52	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.52	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.52	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.52	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.52	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, c), b)
28.54/9.52	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.52	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.52	   A^2 -> H(U1(c, c), e)
28.54/9.52	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.52	   A^2 -> H(e, U1(c, b))
28.54/9.52	   A^2 -> H(e, U1(d, b))
28.54/9.52	   A^2 -> H(e, U1(b, c))
28.54/9.52	   A^2 -> H(e, U1(b, d))
28.54/9.52	   A^2 -> H(e, U1(c, c))
28.54/9.52	   A^2 -> H(e, f(e))
28.54/9.52	   A^2 -> H(e, f(k))
28.54/9.52	   A^2 -> H(e, U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.52	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.52	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.52	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.52	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.52	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.52	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.52	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.52	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.52	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.52	   A^2 -> H(f(e), b)
28.54/9.52	   A^2 -> H(f(e), U1(e, d))
28.54/9.52	   A^2 -> H(f(e), U1(d, e))
28.54/9.52	   A^2 -> H(f(e), c)
28.54/9.52	   A^2 -> H(f(e), U1(e, k))
28.54/9.52	   A^2 -> H(f(e), U1(k, e))
28.54/9.52	   A^2 -> H(f(e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.52	   A^2 -> H(f(k), b)
28.54/9.52	   A^2 -> H(f(k), U1(e, d))
28.54/9.52	   A^2 -> H(f(k), U1(d, e))
28.54/9.52	   A^2 -> H(f(k), c)
28.54/9.52	   A^2 -> H(f(k), U1(e, k))
28.54/9.52	   A^2 -> H(f(k), U1(k, e))
28.54/9.52	   A^2 -> H(f(k), e)
28.54/9.52	   A^2 -> H(f(c), d)
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.52	   A^2 -> H(U1(k, k), f(e))
28.54/9.52	   A^2 -> H(U1(k, k), f(k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.52	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.52	   A^2 -> H(U1(d, d), b)
28.54/9.52	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.52	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.52	   A^2 -> H(U1(d, d), c)
28.54/9.52	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.52	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.52	   A^2 -> H(U1(d, d), e)
28.54/9.52	   A^2 -> H(f(d), d)
28.54/9.52	   A^2 -> H(f(d), k)
28.54/9.52	   A^2 -> H(U1(c, c), c)
28.54/9.52	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.52	   A^2 -> H(f(c), k)
28.54/9.52	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.52	   A^2 -> H(f(k), U1(k, k))
28.54/9.52	   A^2 -> H(f(e), e)
28.54/9.52	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.52	   A^2 -> H(d, U1(c, b))
28.54/9.52	   A^2 -> H(d, U1(d, b))
28.54/9.52	   A^2 -> H(d, U1(b, c))
28.54/9.52	   A^2 -> H(d, U1(b, d))
28.54/9.52	   A^2 -> H(d, U1(c, c))
28.54/9.52	   A^2 -> H(d, f(e))
28.54/9.52	   A^2 -> H(d, f(k))
28.54/9.52	   A^2 -> H(d, U1(d, d))
28.54/9.52	   A^2 -> H(a, U1(e, b))
28.54/9.52	   A^2 -> H(a, U1(k, b))
28.54/9.52	   A^2 -> H(a, U1(c, d))
28.54/9.52	   A^2 -> H(a, U1(d, c))
28.54/9.52	   A^2 -> H(a, U1(b, e))
28.54/9.52	   A^2 -> H(a, U1(b, k))
28.54/9.52	   A^2 -> H(a, U1(e, c))
28.54/9.52	   A^2 -> H(a, U1(k, c))
28.54/9.52	   A^2 -> H(a, U1(c, e))
28.54/9.52	   A^2 -> H(a, U1(c, k))
28.54/9.52	   A^2 -> H(a, U1(e, e))
28.54/9.52	   A^2 -> H(a, U1(k, k))
28.54/9.52	   A^2 -> H(a, U1(k, d))
28.54/9.52	   A^2 -> H(a, U1(d, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.52	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.52	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.52	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.52	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.52	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.52	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.52	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.52	   A^2 -> H(U1(e, a), b)
28.54/9.52	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.52	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.52	   A^2 -> H(U1(e, a), c)
28.54/9.52	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.52	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.52	
28.54/9.52	The TRS R consists of the following rules:
28.54/9.52	
28.54/9.52	   f(x) -> U1(x, x)
28.54/9.52	   U1(e, x) -> x
28.54/9.52	   a -> c
28.54/9.52	   a -> d
28.54/9.52	   b -> c
28.54/9.52	   b -> d
28.54/9.52	   d -> k
28.54/9.52	   c -> e
28.54/9.52	   c -> k
28.54/9.52	
28.54/9.52	Q is empty.
28.54/9.52	We have to consider all minimal (P,Q,R)-chains.
28.54/9.52	----------------------------------------
28.54/9.52	
28.54/9.52	(1151) TransformationProof (EQUIVALENT)
28.54/9.52	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.52	
28.54/9.52	   (A^2 -> H(a, U1(e, e)),A^2 -> H(a, U1(e, e)))
28.54/9.52	   (A^2 -> H(U1(e, c), U1(e, e)),A^2 -> H(U1(e, c), U1(e, e)))
28.54/9.52	   (A^2 -> H(U1(e, d), U1(e, e)),A^2 -> H(U1(e, d), U1(e, e)))
28.54/9.52	   (A^2 -> H(U1(e, a), e),A^2 -> H(U1(e, a), e))
28.54/9.52	
28.54/9.52	
28.54/9.52	----------------------------------------
28.54/9.52	
28.54/9.52	(1152)
28.54/9.52	Obligation:
28.54/9.52	Q DP problem:
28.54/9.52	The TRS P consists of the following rules:
28.54/9.52	
28.54/9.52	   H(x, x) -> G(x, x, f(k))
28.54/9.52	   G(d, x, x) -> A^2
28.54/9.52	   A^2 -> H(f(c), f(c))
28.54/9.52	   A^2 -> H(f(d), f(d))
28.54/9.52	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.52	   A^2 -> H(f(e), f(e))
28.54/9.52	   A^2 -> H(f(k), f(k))
28.54/9.52	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.52	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.52	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.52	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.52	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.52	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.52	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.52	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.52	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.52	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.52	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, a), b)
28.54/9.52	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.52	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.52	   A^2 -> H(U1(c, a), c)
28.54/9.52	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.52	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.52	   A^2 -> H(U1(c, a), e)
28.54/9.52	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.52	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.52	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.52	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.52	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.52	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.52	   A^2 -> H(U1(d, e), f(e))
28.54/9.52	   A^2 -> H(U1(d, e), f(k))
28.54/9.52	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.52	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.52	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.52	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.52	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.52	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.52	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.52	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.52	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.52	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.52	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.52	   A^2 -> H(U1(d, a), b)
28.54/9.52	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.52	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.52	   A^2 -> H(U1(d, a), c)
28.54/9.52	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.52	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.52	   A^2 -> H(U1(d, a), e)
28.54/9.52	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.52	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.52	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.52	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.52	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.52	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.52	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.52	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.52	   A^2 -> H(U1(a, c), b)
28.54/9.52	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.52	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.52	   A^2 -> H(U1(a, c), c)
28.54/9.52	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.52	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.52	   A^2 -> H(U1(a, c), e)
28.54/9.52	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, d), b)
28.54/9.52	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.52	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.52	   A^2 -> H(U1(a, d), c)
28.54/9.52	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.52	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.52	   A^2 -> H(U1(a, d), e)
28.54/9.52	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, a), d)
28.54/9.52	   A^2 -> H(U1(a, a), k)
28.54/9.52	   A^2 -> H(k, U1(b, b))
28.54/9.52	   A^2 -> H(k, f(c))
28.54/9.52	   A^2 -> H(k, f(d))
28.54/9.52	   A^2 -> H(c, U1(c, b))
28.54/9.52	   A^2 -> H(c, U1(d, b))
28.54/9.52	   A^2 -> H(c, U1(b, c))
28.54/9.52	   A^2 -> H(c, U1(b, d))
28.54/9.52	   A^2 -> H(c, U1(c, c))
28.54/9.52	   A^2 -> H(c, f(e))
28.54/9.52	   A^2 -> H(c, f(k))
28.54/9.52	   A^2 -> H(c, U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.52	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.52	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.52	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.52	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.52	   A^2 -> H(U1(e, k), f(e))
28.54/9.52	   A^2 -> H(U1(e, k), f(k))
28.54/9.52	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.52	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.52	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.52	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.52	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.52	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.52	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.52	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.52	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.52	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.52	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.52	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.52	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.52	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.52	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.52	   A^2 -> H(U1(k, e), f(e))
28.54/9.52	   A^2 -> H(U1(k, e), f(k))
28.54/9.52	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.52	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.52	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.52	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.52	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.52	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.52	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.52	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.52	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, c), b)
28.54/9.52	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.52	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.52	   A^2 -> H(U1(c, c), e)
28.54/9.52	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.52	   A^2 -> H(e, U1(c, b))
28.54/9.52	   A^2 -> H(e, U1(d, b))
28.54/9.52	   A^2 -> H(e, U1(b, c))
28.54/9.52	   A^2 -> H(e, U1(b, d))
28.54/9.52	   A^2 -> H(e, U1(c, c))
28.54/9.52	   A^2 -> H(e, f(e))
28.54/9.52	   A^2 -> H(e, f(k))
28.54/9.52	   A^2 -> H(e, U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.52	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.52	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.52	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.52	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.52	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.52	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.52	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.52	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.52	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.52	   A^2 -> H(f(e), b)
28.54/9.52	   A^2 -> H(f(e), U1(e, d))
28.54/9.52	   A^2 -> H(f(e), U1(d, e))
28.54/9.52	   A^2 -> H(f(e), c)
28.54/9.52	   A^2 -> H(f(e), U1(e, k))
28.54/9.52	   A^2 -> H(f(e), U1(k, e))
28.54/9.52	   A^2 -> H(f(e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.52	   A^2 -> H(f(k), b)
28.54/9.52	   A^2 -> H(f(k), U1(e, d))
28.54/9.52	   A^2 -> H(f(k), U1(d, e))
28.54/9.52	   A^2 -> H(f(k), c)
28.54/9.52	   A^2 -> H(f(k), U1(e, k))
28.54/9.52	   A^2 -> H(f(k), U1(k, e))
28.54/9.52	   A^2 -> H(f(k), e)
28.54/9.52	   A^2 -> H(f(c), d)
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.52	   A^2 -> H(U1(k, k), f(e))
28.54/9.52	   A^2 -> H(U1(k, k), f(k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.52	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.52	   A^2 -> H(U1(d, d), b)
28.54/9.52	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.52	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.52	   A^2 -> H(U1(d, d), c)
28.54/9.52	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.52	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.52	   A^2 -> H(U1(d, d), e)
28.54/9.52	   A^2 -> H(f(d), d)
28.54/9.52	   A^2 -> H(f(d), k)
28.54/9.52	   A^2 -> H(U1(c, c), c)
28.54/9.52	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.52	   A^2 -> H(f(c), k)
28.54/9.52	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.52	   A^2 -> H(f(k), U1(k, k))
28.54/9.52	   A^2 -> H(f(e), e)
28.54/9.52	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.52	   A^2 -> H(d, U1(c, b))
28.54/9.52	   A^2 -> H(d, U1(d, b))
28.54/9.52	   A^2 -> H(d, U1(b, c))
28.54/9.52	   A^2 -> H(d, U1(b, d))
28.54/9.52	   A^2 -> H(d, U1(c, c))
28.54/9.52	   A^2 -> H(d, f(e))
28.54/9.52	   A^2 -> H(d, f(k))
28.54/9.52	   A^2 -> H(d, U1(d, d))
28.54/9.52	   A^2 -> H(a, U1(e, b))
28.54/9.52	   A^2 -> H(a, U1(k, b))
28.54/9.52	   A^2 -> H(a, U1(c, d))
28.54/9.52	   A^2 -> H(a, U1(d, c))
28.54/9.52	   A^2 -> H(a, U1(b, e))
28.54/9.52	   A^2 -> H(a, U1(b, k))
28.54/9.52	   A^2 -> H(a, U1(e, c))
28.54/9.52	   A^2 -> H(a, U1(k, c))
28.54/9.52	   A^2 -> H(a, U1(c, e))
28.54/9.52	   A^2 -> H(a, U1(c, k))
28.54/9.52	   A^2 -> H(a, U1(e, e))
28.54/9.52	   A^2 -> H(a, U1(k, k))
28.54/9.52	   A^2 -> H(a, U1(k, d))
28.54/9.52	   A^2 -> H(a, U1(d, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.52	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.52	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.52	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.52	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.52	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.52	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.52	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.52	   A^2 -> H(U1(e, a), b)
28.54/9.52	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.52	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.52	   A^2 -> H(U1(e, a), c)
28.54/9.52	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.52	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.52	   A^2 -> H(U1(e, a), e)
28.54/9.52	
28.54/9.52	The TRS R consists of the following rules:
28.54/9.52	
28.54/9.52	   f(x) -> U1(x, x)
28.54/9.52	   U1(e, x) -> x
28.54/9.52	   a -> c
28.54/9.52	   a -> d
28.54/9.52	   b -> c
28.54/9.52	   b -> d
28.54/9.52	   d -> k
28.54/9.52	   c -> e
28.54/9.52	   c -> k
28.54/9.52	
28.54/9.52	Q is empty.
28.54/9.52	We have to consider all minimal (P,Q,R)-chains.
28.54/9.52	----------------------------------------
28.54/9.52	
28.54/9.52	(1153) TransformationProof (EQUIVALENT)
28.54/9.52	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.52	
28.54/9.52	   (A^2 -> H(a, U1(k, k)),A^2 -> H(a, U1(k, k)))
28.54/9.52	   (A^2 -> H(U1(e, c), U1(k, k)),A^2 -> H(U1(e, c), U1(k, k)))
28.54/9.52	   (A^2 -> H(U1(e, d), U1(k, k)),A^2 -> H(U1(e, d), U1(k, k)))
28.54/9.52	
28.54/9.52	
28.54/9.52	----------------------------------------
28.54/9.52	
28.54/9.52	(1154)
28.54/9.52	Obligation:
28.54/9.52	Q DP problem:
28.54/9.52	The TRS P consists of the following rules:
28.54/9.52	
28.54/9.52	   H(x, x) -> G(x, x, f(k))
28.54/9.52	   G(d, x, x) -> A^2
28.54/9.52	   A^2 -> H(f(c), f(c))
28.54/9.52	   A^2 -> H(f(d), f(d))
28.54/9.52	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.52	   A^2 -> H(f(e), f(e))
28.54/9.52	   A^2 -> H(f(k), f(k))
28.54/9.52	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, a), U1(k, d))
28.54/9.52	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.52	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.52	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.52	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.52	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.52	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.52	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.52	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.52	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, a), b)
28.54/9.52	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.52	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.52	   A^2 -> H(U1(c, a), c)
28.54/9.52	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.52	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.52	   A^2 -> H(U1(c, a), e)
28.54/9.52	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.52	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.52	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.52	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.52	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.52	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.52	   A^2 -> H(U1(d, e), f(e))
28.54/9.52	   A^2 -> H(U1(d, e), f(k))
28.54/9.52	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.52	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.52	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.52	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.52	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.52	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.52	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.52	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.52	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.52	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.52	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.52	   A^2 -> H(U1(d, a), b)
28.54/9.52	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.52	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.52	   A^2 -> H(U1(d, a), c)
28.54/9.52	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.52	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.52	   A^2 -> H(U1(d, a), e)
28.54/9.52	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.52	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.52	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.52	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.52	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.52	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.52	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.52	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.52	   A^2 -> H(U1(a, c), b)
28.54/9.52	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.52	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.52	   A^2 -> H(U1(a, c), c)
28.54/9.52	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.52	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.52	   A^2 -> H(U1(a, c), e)
28.54/9.52	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, d), b)
28.54/9.52	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.52	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.52	   A^2 -> H(U1(a, d), c)
28.54/9.52	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.52	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.52	   A^2 -> H(U1(a, d), e)
28.54/9.52	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, a), d)
28.54/9.52	   A^2 -> H(U1(a, a), k)
28.54/9.52	   A^2 -> H(k, U1(b, b))
28.54/9.52	   A^2 -> H(k, f(c))
28.54/9.52	   A^2 -> H(k, f(d))
28.54/9.52	   A^2 -> H(c, U1(c, b))
28.54/9.52	   A^2 -> H(c, U1(d, b))
28.54/9.52	   A^2 -> H(c, U1(b, c))
28.54/9.52	   A^2 -> H(c, U1(b, d))
28.54/9.52	   A^2 -> H(c, U1(c, c))
28.54/9.52	   A^2 -> H(c, f(e))
28.54/9.52	   A^2 -> H(c, f(k))
28.54/9.52	   A^2 -> H(c, U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.52	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.52	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.52	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.52	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.52	   A^2 -> H(U1(e, k), f(e))
28.54/9.52	   A^2 -> H(U1(e, k), f(k))
28.54/9.52	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.52	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.52	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.52	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.52	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.52	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.52	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.52	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.52	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.52	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.52	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.52	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.52	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.52	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.52	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.52	   A^2 -> H(U1(k, e), f(e))
28.54/9.52	   A^2 -> H(U1(k, e), f(k))
28.54/9.52	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.52	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.52	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.52	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.52	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.52	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.52	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.52	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.52	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, c), b)
28.54/9.52	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.52	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.52	   A^2 -> H(U1(c, c), e)
28.54/9.52	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.52	   A^2 -> H(e, U1(c, b))
28.54/9.52	   A^2 -> H(e, U1(d, b))
28.54/9.52	   A^2 -> H(e, U1(b, c))
28.54/9.52	   A^2 -> H(e, U1(b, d))
28.54/9.52	   A^2 -> H(e, U1(c, c))
28.54/9.52	   A^2 -> H(e, f(e))
28.54/9.52	   A^2 -> H(e, f(k))
28.54/9.52	   A^2 -> H(e, U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.52	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.52	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.52	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.52	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.52	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.52	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.52	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.52	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.52	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.52	   A^2 -> H(f(e), b)
28.54/9.52	   A^2 -> H(f(e), U1(e, d))
28.54/9.52	   A^2 -> H(f(e), U1(d, e))
28.54/9.52	   A^2 -> H(f(e), c)
28.54/9.52	   A^2 -> H(f(e), U1(e, k))
28.54/9.52	   A^2 -> H(f(e), U1(k, e))
28.54/9.52	   A^2 -> H(f(e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.52	   A^2 -> H(f(k), b)
28.54/9.52	   A^2 -> H(f(k), U1(e, d))
28.54/9.52	   A^2 -> H(f(k), U1(d, e))
28.54/9.52	   A^2 -> H(f(k), c)
28.54/9.52	   A^2 -> H(f(k), U1(e, k))
28.54/9.52	   A^2 -> H(f(k), U1(k, e))
28.54/9.52	   A^2 -> H(f(k), e)
28.54/9.52	   A^2 -> H(f(c), d)
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.52	   A^2 -> H(U1(k, k), f(e))
28.54/9.52	   A^2 -> H(U1(k, k), f(k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.52	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.52	   A^2 -> H(U1(d, d), b)
28.54/9.52	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.52	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.52	   A^2 -> H(U1(d, d), c)
28.54/9.52	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.52	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.52	   A^2 -> H(U1(d, d), e)
28.54/9.52	   A^2 -> H(f(d), d)
28.54/9.52	   A^2 -> H(f(d), k)
28.54/9.52	   A^2 -> H(U1(c, c), c)
28.54/9.52	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.52	   A^2 -> H(f(c), k)
28.54/9.52	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.52	   A^2 -> H(f(k), U1(k, k))
28.54/9.52	   A^2 -> H(f(e), e)
28.54/9.52	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.52	   A^2 -> H(d, U1(c, b))
28.54/9.52	   A^2 -> H(d, U1(d, b))
28.54/9.52	   A^2 -> H(d, U1(b, c))
28.54/9.52	   A^2 -> H(d, U1(b, d))
28.54/9.52	   A^2 -> H(d, U1(c, c))
28.54/9.52	   A^2 -> H(d, f(e))
28.54/9.52	   A^2 -> H(d, f(k))
28.54/9.52	   A^2 -> H(d, U1(d, d))
28.54/9.52	   A^2 -> H(a, U1(e, b))
28.54/9.52	   A^2 -> H(a, U1(k, b))
28.54/9.52	   A^2 -> H(a, U1(c, d))
28.54/9.52	   A^2 -> H(a, U1(d, c))
28.54/9.52	   A^2 -> H(a, U1(b, e))
28.54/9.52	   A^2 -> H(a, U1(b, k))
28.54/9.52	   A^2 -> H(a, U1(e, c))
28.54/9.52	   A^2 -> H(a, U1(k, c))
28.54/9.52	   A^2 -> H(a, U1(c, e))
28.54/9.52	   A^2 -> H(a, U1(c, k))
28.54/9.52	   A^2 -> H(a, U1(e, e))
28.54/9.52	   A^2 -> H(a, U1(k, k))
28.54/9.52	   A^2 -> H(a, U1(k, d))
28.54/9.52	   A^2 -> H(a, U1(d, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.52	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.52	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.52	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.52	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.52	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.52	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.52	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.52	   A^2 -> H(U1(e, a), b)
28.54/9.52	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.52	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.52	   A^2 -> H(U1(e, a), c)
28.54/9.52	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.52	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.52	   A^2 -> H(U1(e, a), e)
28.54/9.52	
28.54/9.52	The TRS R consists of the following rules:
28.54/9.52	
28.54/9.52	   f(x) -> U1(x, x)
28.54/9.52	   U1(e, x) -> x
28.54/9.52	   a -> c
28.54/9.52	   a -> d
28.54/9.52	   b -> c
28.54/9.52	   b -> d
28.54/9.52	   d -> k
28.54/9.52	   c -> e
28.54/9.52	   c -> k
28.54/9.52	
28.54/9.52	Q is empty.
28.54/9.52	We have to consider all minimal (P,Q,R)-chains.
28.54/9.52	----------------------------------------
28.54/9.52	
28.54/9.52	(1155) TransformationProof (EQUIVALENT)
28.54/9.52	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.52	
28.54/9.52	   (A^2 -> H(a, U1(k, d)),A^2 -> H(a, U1(k, d)))
28.54/9.52	   (A^2 -> H(U1(e, c), U1(k, d)),A^2 -> H(U1(e, c), U1(k, d)))
28.54/9.52	   (A^2 -> H(U1(e, d), U1(k, d)),A^2 -> H(U1(e, d), U1(k, d)))
28.54/9.52	   (A^2 -> H(U1(e, a), U1(k, k)),A^2 -> H(U1(e, a), U1(k, k)))
28.54/9.52	
28.54/9.52	
28.54/9.52	----------------------------------------
28.54/9.52	
28.54/9.52	(1156)
28.54/9.52	Obligation:
28.54/9.52	Q DP problem:
28.54/9.52	The TRS P consists of the following rules:
28.54/9.52	
28.54/9.52	   H(x, x) -> G(x, x, f(k))
28.54/9.52	   G(d, x, x) -> A^2
28.54/9.52	   A^2 -> H(f(c), f(c))
28.54/9.52	   A^2 -> H(f(d), f(d))
28.54/9.52	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.52	   A^2 -> H(f(e), f(e))
28.54/9.52	   A^2 -> H(f(k), f(k))
28.54/9.52	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, a), U1(d, k))
28.54/9.52	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.52	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.52	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.52	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.52	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.52	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.52	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.52	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, a), b)
28.54/9.52	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.52	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.52	   A^2 -> H(U1(c, a), c)
28.54/9.52	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.52	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.52	   A^2 -> H(U1(c, a), e)
28.54/9.52	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.52	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.52	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.52	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.52	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.52	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.52	   A^2 -> H(U1(d, e), f(e))
28.54/9.52	   A^2 -> H(U1(d, e), f(k))
28.54/9.52	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.52	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.52	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.52	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.52	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.52	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.52	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.52	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.52	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.52	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.52	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.52	   A^2 -> H(U1(d, a), b)
28.54/9.52	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.52	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.52	   A^2 -> H(U1(d, a), c)
28.54/9.52	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.52	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.52	   A^2 -> H(U1(d, a), e)
28.54/9.52	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.52	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.52	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.52	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.52	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.52	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.52	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.52	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.52	   A^2 -> H(U1(a, c), b)
28.54/9.52	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.52	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.52	   A^2 -> H(U1(a, c), c)
28.54/9.52	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.52	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.52	   A^2 -> H(U1(a, c), e)
28.54/9.52	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, d), b)
28.54/9.52	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.52	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.52	   A^2 -> H(U1(a, d), c)
28.54/9.52	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.52	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.52	   A^2 -> H(U1(a, d), e)
28.54/9.52	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, a), d)
28.54/9.52	   A^2 -> H(U1(a, a), k)
28.54/9.52	   A^2 -> H(k, U1(b, b))
28.54/9.52	   A^2 -> H(k, f(c))
28.54/9.52	   A^2 -> H(k, f(d))
28.54/9.52	   A^2 -> H(c, U1(c, b))
28.54/9.52	   A^2 -> H(c, U1(d, b))
28.54/9.52	   A^2 -> H(c, U1(b, c))
28.54/9.52	   A^2 -> H(c, U1(b, d))
28.54/9.52	   A^2 -> H(c, U1(c, c))
28.54/9.52	   A^2 -> H(c, f(e))
28.54/9.52	   A^2 -> H(c, f(k))
28.54/9.52	   A^2 -> H(c, U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.52	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.52	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.52	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.52	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.52	   A^2 -> H(U1(e, k), f(e))
28.54/9.52	   A^2 -> H(U1(e, k), f(k))
28.54/9.52	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.52	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.52	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.52	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.52	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.52	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.52	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.52	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.52	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.52	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.52	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.52	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.52	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.52	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.52	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.52	   A^2 -> H(U1(k, e), f(e))
28.54/9.52	   A^2 -> H(U1(k, e), f(k))
28.54/9.52	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.52	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.52	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.52	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.52	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.52	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.52	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.52	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.52	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, c), b)
28.54/9.52	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.52	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.52	   A^2 -> H(U1(c, c), e)
28.54/9.52	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.52	   A^2 -> H(e, U1(c, b))
28.54/9.52	   A^2 -> H(e, U1(d, b))
28.54/9.52	   A^2 -> H(e, U1(b, c))
28.54/9.52	   A^2 -> H(e, U1(b, d))
28.54/9.52	   A^2 -> H(e, U1(c, c))
28.54/9.52	   A^2 -> H(e, f(e))
28.54/9.52	   A^2 -> H(e, f(k))
28.54/9.52	   A^2 -> H(e, U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.52	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.52	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.52	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.52	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.52	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.52	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.52	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.52	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.52	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.52	   A^2 -> H(f(e), b)
28.54/9.52	   A^2 -> H(f(e), U1(e, d))
28.54/9.52	   A^2 -> H(f(e), U1(d, e))
28.54/9.52	   A^2 -> H(f(e), c)
28.54/9.52	   A^2 -> H(f(e), U1(e, k))
28.54/9.52	   A^2 -> H(f(e), U1(k, e))
28.54/9.52	   A^2 -> H(f(e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.52	   A^2 -> H(f(k), b)
28.54/9.52	   A^2 -> H(f(k), U1(e, d))
28.54/9.52	   A^2 -> H(f(k), U1(d, e))
28.54/9.52	   A^2 -> H(f(k), c)
28.54/9.52	   A^2 -> H(f(k), U1(e, k))
28.54/9.52	   A^2 -> H(f(k), U1(k, e))
28.54/9.52	   A^2 -> H(f(k), e)
28.54/9.52	   A^2 -> H(f(c), d)
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.52	   A^2 -> H(U1(k, k), f(e))
28.54/9.52	   A^2 -> H(U1(k, k), f(k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.52	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.52	   A^2 -> H(U1(d, d), b)
28.54/9.52	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.52	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.52	   A^2 -> H(U1(d, d), c)
28.54/9.52	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.52	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.52	   A^2 -> H(U1(d, d), e)
28.54/9.52	   A^2 -> H(f(d), d)
28.54/9.52	   A^2 -> H(f(d), k)
28.54/9.52	   A^2 -> H(U1(c, c), c)
28.54/9.52	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.52	   A^2 -> H(f(c), k)
28.54/9.52	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.52	   A^2 -> H(f(k), U1(k, k))
28.54/9.52	   A^2 -> H(f(e), e)
28.54/9.52	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.52	   A^2 -> H(d, U1(c, b))
28.54/9.52	   A^2 -> H(d, U1(d, b))
28.54/9.52	   A^2 -> H(d, U1(b, c))
28.54/9.52	   A^2 -> H(d, U1(b, d))
28.54/9.52	   A^2 -> H(d, U1(c, c))
28.54/9.52	   A^2 -> H(d, f(e))
28.54/9.52	   A^2 -> H(d, f(k))
28.54/9.52	   A^2 -> H(d, U1(d, d))
28.54/9.52	   A^2 -> H(a, U1(e, b))
28.54/9.52	   A^2 -> H(a, U1(k, b))
28.54/9.52	   A^2 -> H(a, U1(c, d))
28.54/9.52	   A^2 -> H(a, U1(d, c))
28.54/9.52	   A^2 -> H(a, U1(b, e))
28.54/9.52	   A^2 -> H(a, U1(b, k))
28.54/9.52	   A^2 -> H(a, U1(e, c))
28.54/9.52	   A^2 -> H(a, U1(k, c))
28.54/9.52	   A^2 -> H(a, U1(c, e))
28.54/9.52	   A^2 -> H(a, U1(c, k))
28.54/9.52	   A^2 -> H(a, U1(e, e))
28.54/9.52	   A^2 -> H(a, U1(k, k))
28.54/9.52	   A^2 -> H(a, U1(k, d))
28.54/9.52	   A^2 -> H(a, U1(d, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.52	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.52	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.52	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.52	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.52	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.52	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.52	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.52	   A^2 -> H(U1(e, a), b)
28.54/9.52	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.52	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.52	   A^2 -> H(U1(e, a), c)
28.54/9.52	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.52	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.52	   A^2 -> H(U1(e, a), e)
28.54/9.52	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.52	
28.54/9.52	The TRS R consists of the following rules:
28.54/9.52	
28.54/9.52	   f(x) -> U1(x, x)
28.54/9.52	   U1(e, x) -> x
28.54/9.52	   a -> c
28.54/9.52	   a -> d
28.54/9.52	   b -> c
28.54/9.52	   b -> d
28.54/9.52	   d -> k
28.54/9.52	   c -> e
28.54/9.52	   c -> k
28.54/9.52	
28.54/9.52	Q is empty.
28.54/9.52	We have to consider all minimal (P,Q,R)-chains.
28.54/9.52	----------------------------------------
28.54/9.52	
28.54/9.52	(1157) TransformationProof (EQUIVALENT)
28.54/9.52	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.52	
28.54/9.52	   (A^2 -> H(a, U1(d, k)),A^2 -> H(a, U1(d, k)))
28.54/9.52	   (A^2 -> H(U1(e, c), U1(d, k)),A^2 -> H(U1(e, c), U1(d, k)))
28.54/9.52	   (A^2 -> H(U1(e, d), U1(d, k)),A^2 -> H(U1(e, d), U1(d, k)))
28.54/9.52	   (A^2 -> H(U1(e, a), U1(k, k)),A^2 -> H(U1(e, a), U1(k, k)))
28.54/9.52	
28.54/9.52	
28.54/9.52	----------------------------------------
28.54/9.52	
28.54/9.52	(1158)
28.54/9.52	Obligation:
28.54/9.52	Q DP problem:
28.54/9.52	The TRS P consists of the following rules:
28.54/9.52	
28.54/9.52	   H(x, x) -> G(x, x, f(k))
28.54/9.52	   G(d, x, x) -> A^2
28.54/9.52	   A^2 -> H(f(c), f(c))
28.54/9.52	   A^2 -> H(f(d), f(d))
28.54/9.52	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.52	   A^2 -> H(f(e), f(e))
28.54/9.52	   A^2 -> H(f(k), f(k))
28.54/9.52	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.52	   A^2 -> H(U1(k, a), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.52	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.52	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.52	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.52	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.52	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.52	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.52	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, a), b)
28.54/9.52	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.52	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.52	   A^2 -> H(U1(c, a), c)
28.54/9.52	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.52	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.52	   A^2 -> H(U1(c, a), e)
28.54/9.52	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.52	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.52	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.52	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.52	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.52	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.52	   A^2 -> H(U1(d, e), f(e))
28.54/9.52	   A^2 -> H(U1(d, e), f(k))
28.54/9.52	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.52	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.52	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.52	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.52	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.52	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.52	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.52	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.52	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.52	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.52	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.52	   A^2 -> H(U1(d, a), b)
28.54/9.52	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.52	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.52	   A^2 -> H(U1(d, a), c)
28.54/9.52	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.52	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.52	   A^2 -> H(U1(d, a), e)
28.54/9.52	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.52	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.52	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.52	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.52	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.52	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.52	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.52	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.52	   A^2 -> H(U1(a, c), b)
28.54/9.52	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.52	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.52	   A^2 -> H(U1(a, c), c)
28.54/9.52	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.52	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.52	   A^2 -> H(U1(a, c), e)
28.54/9.52	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, d), b)
28.54/9.52	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.52	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.52	   A^2 -> H(U1(a, d), c)
28.54/9.52	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.52	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.52	   A^2 -> H(U1(a, d), e)
28.54/9.52	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, a), d)
28.54/9.52	   A^2 -> H(U1(a, a), k)
28.54/9.52	   A^2 -> H(k, U1(b, b))
28.54/9.52	   A^2 -> H(k, f(c))
28.54/9.52	   A^2 -> H(k, f(d))
28.54/9.52	   A^2 -> H(c, U1(c, b))
28.54/9.52	   A^2 -> H(c, U1(d, b))
28.54/9.52	   A^2 -> H(c, U1(b, c))
28.54/9.52	   A^2 -> H(c, U1(b, d))
28.54/9.52	   A^2 -> H(c, U1(c, c))
28.54/9.52	   A^2 -> H(c, f(e))
28.54/9.52	   A^2 -> H(c, f(k))
28.54/9.52	   A^2 -> H(c, U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.52	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.52	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.52	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.52	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.52	   A^2 -> H(U1(e, k), f(e))
28.54/9.52	   A^2 -> H(U1(e, k), f(k))
28.54/9.52	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.52	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.52	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.52	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.52	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.52	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.52	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.52	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.52	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.52	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.52	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.52	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.52	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.52	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.52	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.52	   A^2 -> H(U1(k, e), f(e))
28.54/9.52	   A^2 -> H(U1(k, e), f(k))
28.54/9.52	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.52	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.52	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.52	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.52	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.52	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.52	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.52	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.52	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, c), b)
28.54/9.52	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.52	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.52	   A^2 -> H(U1(c, c), e)
28.54/9.52	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.52	   A^2 -> H(e, U1(c, b))
28.54/9.52	   A^2 -> H(e, U1(d, b))
28.54/9.52	   A^2 -> H(e, U1(b, c))
28.54/9.52	   A^2 -> H(e, U1(b, d))
28.54/9.52	   A^2 -> H(e, U1(c, c))
28.54/9.52	   A^2 -> H(e, f(e))
28.54/9.52	   A^2 -> H(e, f(k))
28.54/9.52	   A^2 -> H(e, U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.52	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.52	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.52	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.52	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.52	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.52	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.52	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.52	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.52	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.52	   A^2 -> H(f(e), b)
28.54/9.52	   A^2 -> H(f(e), U1(e, d))
28.54/9.52	   A^2 -> H(f(e), U1(d, e))
28.54/9.52	   A^2 -> H(f(e), c)
28.54/9.52	   A^2 -> H(f(e), U1(e, k))
28.54/9.52	   A^2 -> H(f(e), U1(k, e))
28.54/9.52	   A^2 -> H(f(e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.52	   A^2 -> H(f(k), b)
28.54/9.52	   A^2 -> H(f(k), U1(e, d))
28.54/9.52	   A^2 -> H(f(k), U1(d, e))
28.54/9.52	   A^2 -> H(f(k), c)
28.54/9.52	   A^2 -> H(f(k), U1(e, k))
28.54/9.52	   A^2 -> H(f(k), U1(k, e))
28.54/9.52	   A^2 -> H(f(k), e)
28.54/9.52	   A^2 -> H(f(c), d)
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.52	   A^2 -> H(U1(k, k), f(e))
28.54/9.52	   A^2 -> H(U1(k, k), f(k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.52	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.52	   A^2 -> H(U1(d, d), b)
28.54/9.52	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.52	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.52	   A^2 -> H(U1(d, d), c)
28.54/9.52	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.52	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.52	   A^2 -> H(U1(d, d), e)
28.54/9.52	   A^2 -> H(f(d), d)
28.54/9.52	   A^2 -> H(f(d), k)
28.54/9.52	   A^2 -> H(U1(c, c), c)
28.54/9.52	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.52	   A^2 -> H(f(c), k)
28.54/9.52	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.52	   A^2 -> H(f(k), U1(k, k))
28.54/9.52	   A^2 -> H(f(e), e)
28.54/9.52	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.52	   A^2 -> H(d, U1(c, b))
28.54/9.52	   A^2 -> H(d, U1(d, b))
28.54/9.52	   A^2 -> H(d, U1(b, c))
28.54/9.52	   A^2 -> H(d, U1(b, d))
28.54/9.52	   A^2 -> H(d, U1(c, c))
28.54/9.52	   A^2 -> H(d, f(e))
28.54/9.52	   A^2 -> H(d, f(k))
28.54/9.52	   A^2 -> H(d, U1(d, d))
28.54/9.52	   A^2 -> H(a, U1(e, b))
28.54/9.52	   A^2 -> H(a, U1(k, b))
28.54/9.52	   A^2 -> H(a, U1(c, d))
28.54/9.52	   A^2 -> H(a, U1(d, c))
28.54/9.52	   A^2 -> H(a, U1(b, e))
28.54/9.52	   A^2 -> H(a, U1(b, k))
28.54/9.52	   A^2 -> H(a, U1(e, c))
28.54/9.52	   A^2 -> H(a, U1(k, c))
28.54/9.52	   A^2 -> H(a, U1(c, e))
28.54/9.52	   A^2 -> H(a, U1(c, k))
28.54/9.52	   A^2 -> H(a, U1(e, e))
28.54/9.52	   A^2 -> H(a, U1(k, k))
28.54/9.52	   A^2 -> H(a, U1(k, d))
28.54/9.52	   A^2 -> H(a, U1(d, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.52	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.52	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.52	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.52	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.52	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.52	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.52	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.52	   A^2 -> H(U1(e, a), b)
28.54/9.52	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.52	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.52	   A^2 -> H(U1(e, a), c)
28.54/9.52	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.52	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.52	   A^2 -> H(U1(e, a), e)
28.54/9.52	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.52	
28.54/9.52	The TRS R consists of the following rules:
28.54/9.52	
28.54/9.52	   f(x) -> U1(x, x)
28.54/9.52	   U1(e, x) -> x
28.54/9.52	   a -> c
28.54/9.52	   a -> d
28.54/9.52	   b -> c
28.54/9.52	   b -> d
28.54/9.52	   d -> k
28.54/9.52	   c -> e
28.54/9.52	   c -> k
28.54/9.52	
28.54/9.52	Q is empty.
28.54/9.52	We have to consider all minimal (P,Q,R)-chains.
28.54/9.52	----------------------------------------
28.54/9.52	
28.54/9.52	(1159) TransformationProof (EQUIVALENT)
28.54/9.52	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.52	
28.54/9.52	   (A^2 -> H(U1(k, c), U1(e, b)),A^2 -> H(U1(k, c), U1(e, b)))
28.54/9.52	   (A^2 -> H(U1(k, d), U1(e, b)),A^2 -> H(U1(k, d), U1(e, b)))
28.54/9.52	   (A^2 -> H(U1(k, a), b),A^2 -> H(U1(k, a), b))
28.54/9.52	   (A^2 -> H(U1(k, a), U1(e, c)),A^2 -> H(U1(k, a), U1(e, c)))
28.54/9.52	   (A^2 -> H(U1(k, a), U1(e, d)),A^2 -> H(U1(k, a), U1(e, d)))
28.54/9.52	
28.54/9.52	
28.54/9.52	----------------------------------------
28.54/9.52	
28.54/9.52	(1160)
28.54/9.52	Obligation:
28.54/9.52	Q DP problem:
28.54/9.52	The TRS P consists of the following rules:
28.54/9.52	
28.54/9.52	   H(x, x) -> G(x, x, f(k))
28.54/9.52	   G(d, x, x) -> A^2
28.54/9.52	   A^2 -> H(f(c), f(c))
28.54/9.52	   A^2 -> H(f(d), f(d))
28.54/9.52	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.52	   A^2 -> H(f(e), f(e))
28.54/9.52	   A^2 -> H(f(k), f(k))
28.54/9.52	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.52	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.52	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.52	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.52	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.52	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.52	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.52	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, a), b)
28.54/9.52	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.52	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.52	   A^2 -> H(U1(c, a), c)
28.54/9.52	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.52	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.52	   A^2 -> H(U1(c, a), e)
28.54/9.52	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.52	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.52	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.52	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.52	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.52	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.52	   A^2 -> H(U1(d, e), f(e))
28.54/9.52	   A^2 -> H(U1(d, e), f(k))
28.54/9.52	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.52	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.52	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.52	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.52	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.52	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.52	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.52	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.52	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.52	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.52	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.52	   A^2 -> H(U1(d, a), b)
28.54/9.52	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.52	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.52	   A^2 -> H(U1(d, a), c)
28.54/9.52	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.52	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.52	   A^2 -> H(U1(d, a), e)
28.54/9.52	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.52	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.52	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.52	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.52	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.52	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.52	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.52	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.52	   A^2 -> H(U1(a, c), b)
28.54/9.52	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.52	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.52	   A^2 -> H(U1(a, c), c)
28.54/9.52	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.52	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.52	   A^2 -> H(U1(a, c), e)
28.54/9.52	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, d), b)
28.54/9.52	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.52	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.52	   A^2 -> H(U1(a, d), c)
28.54/9.52	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.52	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.52	   A^2 -> H(U1(a, d), e)
28.54/9.52	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(a, a), d)
28.54/9.52	   A^2 -> H(U1(a, a), k)
28.54/9.52	   A^2 -> H(k, U1(b, b))
28.54/9.52	   A^2 -> H(k, f(c))
28.54/9.52	   A^2 -> H(k, f(d))
28.54/9.52	   A^2 -> H(c, U1(c, b))
28.54/9.52	   A^2 -> H(c, U1(d, b))
28.54/9.52	   A^2 -> H(c, U1(b, c))
28.54/9.52	   A^2 -> H(c, U1(b, d))
28.54/9.52	   A^2 -> H(c, U1(c, c))
28.54/9.52	   A^2 -> H(c, f(e))
28.54/9.52	   A^2 -> H(c, f(k))
28.54/9.52	   A^2 -> H(c, U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.52	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.52	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.52	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.52	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.52	   A^2 -> H(U1(e, k), f(e))
28.54/9.52	   A^2 -> H(U1(e, k), f(k))
28.54/9.52	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.52	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.52	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.52	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.52	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.52	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.52	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.52	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.52	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.52	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.52	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.52	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.52	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.52	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.52	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.52	   A^2 -> H(U1(k, e), f(e))
28.54/9.52	   A^2 -> H(U1(k, e), f(k))
28.54/9.52	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.52	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.52	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.52	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.52	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.52	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.52	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.52	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.52	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.52	   A^2 -> H(U1(c, c), b)
28.54/9.52	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.52	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.52	   A^2 -> H(U1(c, c), e)
28.54/9.52	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.52	   A^2 -> H(e, U1(c, b))
28.54/9.52	   A^2 -> H(e, U1(d, b))
28.54/9.52	   A^2 -> H(e, U1(b, c))
28.54/9.52	   A^2 -> H(e, U1(b, d))
28.54/9.52	   A^2 -> H(e, U1(c, c))
28.54/9.52	   A^2 -> H(e, f(e))
28.54/9.52	   A^2 -> H(e, f(k))
28.54/9.52	   A^2 -> H(e, U1(d, d))
28.54/9.52	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.52	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.52	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.52	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.52	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.52	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.52	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.52	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.52	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.52	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.52	   A^2 -> H(f(e), b)
28.54/9.52	   A^2 -> H(f(e), U1(e, d))
28.54/9.52	   A^2 -> H(f(e), U1(d, e))
28.54/9.52	   A^2 -> H(f(e), c)
28.54/9.52	   A^2 -> H(f(e), U1(e, k))
28.54/9.52	   A^2 -> H(f(e), U1(k, e))
28.54/9.52	   A^2 -> H(f(e), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.52	   A^2 -> H(f(k), b)
28.54/9.52	   A^2 -> H(f(k), U1(e, d))
28.54/9.52	   A^2 -> H(f(k), U1(d, e))
28.54/9.52	   A^2 -> H(f(k), c)
28.54/9.52	   A^2 -> H(f(k), U1(e, k))
28.54/9.52	   A^2 -> H(f(k), U1(k, e))
28.54/9.52	   A^2 -> H(f(k), e)
28.54/9.52	   A^2 -> H(f(c), d)
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.52	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.52	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.52	   A^2 -> H(U1(k, k), f(e))
28.54/9.52	   A^2 -> H(U1(k, k), f(k))
28.54/9.52	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.52	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.52	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.52	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.52	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.52	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.52	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.52	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.52	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.52	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.52	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.52	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.52	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.52	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.52	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.52	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.52	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.52	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.52	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.52	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.52	   A^2 -> H(U1(d, d), b)
28.54/9.52	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.52	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.52	   A^2 -> H(U1(d, d), c)
28.54/9.52	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.52	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.52	   A^2 -> H(U1(d, d), e)
28.54/9.52	   A^2 -> H(f(d), d)
28.54/9.52	   A^2 -> H(f(d), k)
28.54/9.53	   A^2 -> H(U1(c, c), c)
28.54/9.53	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.53	   A^2 -> H(f(c), k)
28.54/9.53	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.53	   A^2 -> H(f(k), U1(k, k))
28.54/9.53	   A^2 -> H(f(e), e)
28.54/9.53	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.53	   A^2 -> H(d, U1(c, b))
28.54/9.53	   A^2 -> H(d, U1(d, b))
28.54/9.53	   A^2 -> H(d, U1(b, c))
28.54/9.53	   A^2 -> H(d, U1(b, d))
28.54/9.53	   A^2 -> H(d, U1(c, c))
28.54/9.53	   A^2 -> H(d, f(e))
28.54/9.53	   A^2 -> H(d, f(k))
28.54/9.53	   A^2 -> H(d, U1(d, d))
28.54/9.53	   A^2 -> H(a, U1(e, b))
28.54/9.53	   A^2 -> H(a, U1(k, b))
28.54/9.53	   A^2 -> H(a, U1(c, d))
28.54/9.53	   A^2 -> H(a, U1(d, c))
28.54/9.53	   A^2 -> H(a, U1(b, e))
28.54/9.53	   A^2 -> H(a, U1(b, k))
28.54/9.53	   A^2 -> H(a, U1(e, c))
28.54/9.53	   A^2 -> H(a, U1(k, c))
28.54/9.53	   A^2 -> H(a, U1(c, e))
28.54/9.53	   A^2 -> H(a, U1(c, k))
28.54/9.53	   A^2 -> H(a, U1(e, e))
28.54/9.53	   A^2 -> H(a, U1(k, k))
28.54/9.53	   A^2 -> H(a, U1(k, d))
28.54/9.53	   A^2 -> H(a, U1(d, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.53	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.53	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.53	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.53	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.53	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.53	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.53	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.53	   A^2 -> H(U1(e, a), b)
28.54/9.53	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.53	   A^2 -> H(U1(e, a), c)
28.54/9.53	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.53	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.53	   A^2 -> H(U1(e, a), e)
28.54/9.53	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, a), b)
28.54/9.53	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.53	
28.54/9.53	The TRS R consists of the following rules:
28.54/9.53	
28.54/9.53	   f(x) -> U1(x, x)
28.54/9.53	   U1(e, x) -> x
28.54/9.53	   a -> c
28.54/9.53	   a -> d
28.54/9.53	   b -> c
28.54/9.53	   b -> d
28.54/9.53	   d -> k
28.54/9.53	   c -> e
28.54/9.53	   c -> k
28.54/9.53	
28.54/9.53	Q is empty.
28.54/9.53	We have to consider all minimal (P,Q,R)-chains.
28.54/9.53	----------------------------------------
28.54/9.53	
28.54/9.53	(1161) TransformationProof (EQUIVALENT)
28.54/9.53	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.53	
28.54/9.53	   (A^2 -> H(U1(k, c), U1(k, b)),A^2 -> H(U1(k, c), U1(k, b)))
28.54/9.53	   (A^2 -> H(U1(k, d), U1(k, b)),A^2 -> H(U1(k, d), U1(k, b)))
28.54/9.53	   (A^2 -> H(U1(k, a), U1(k, c)),A^2 -> H(U1(k, a), U1(k, c)))
28.54/9.53	   (A^2 -> H(U1(k, a), U1(k, d)),A^2 -> H(U1(k, a), U1(k, d)))
28.54/9.53	
28.54/9.53	
28.54/9.53	----------------------------------------
28.54/9.53	
28.54/9.53	(1162)
28.54/9.53	Obligation:
28.54/9.53	Q DP problem:
28.54/9.53	The TRS P consists of the following rules:
28.54/9.53	
28.54/9.53	   H(x, x) -> G(x, x, f(k))
28.54/9.53	   G(d, x, x) -> A^2
28.54/9.53	   A^2 -> H(f(c), f(c))
28.54/9.53	   A^2 -> H(f(d), f(d))
28.54/9.53	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.53	   A^2 -> H(f(e), f(e))
28.54/9.53	   A^2 -> H(f(k), f(k))
28.54/9.53	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.53	   A^2 -> H(U1(k, a), U1(c, d))
28.54/9.53	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.53	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.53	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.53	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.53	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.53	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.53	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.53	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.53	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.53	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, a), b)
28.54/9.53	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.53	   A^2 -> H(U1(c, a), c)
28.54/9.53	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.53	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.53	   A^2 -> H(U1(c, a), e)
28.54/9.53	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.53	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.53	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.53	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.53	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.53	   A^2 -> H(U1(d, e), f(e))
28.54/9.53	   A^2 -> H(U1(d, e), f(k))
28.54/9.53	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.53	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.53	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.53	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.53	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.53	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.53	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.53	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.53	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.53	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.53	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.53	   A^2 -> H(U1(d, a), b)
28.54/9.53	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.53	   A^2 -> H(U1(d, a), c)
28.54/9.53	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.53	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.53	   A^2 -> H(U1(d, a), e)
28.54/9.53	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.53	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.53	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.53	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.53	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.53	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.53	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.53	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.53	   A^2 -> H(U1(a, c), b)
28.54/9.53	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.53	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.53	   A^2 -> H(U1(a, c), c)
28.54/9.53	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.53	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.53	   A^2 -> H(U1(a, c), e)
28.54/9.53	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, d), b)
28.54/9.53	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.53	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.53	   A^2 -> H(U1(a, d), c)
28.54/9.53	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.53	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.53	   A^2 -> H(U1(a, d), e)
28.54/9.53	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, a), d)
28.54/9.53	   A^2 -> H(U1(a, a), k)
28.54/9.53	   A^2 -> H(k, U1(b, b))
28.54/9.53	   A^2 -> H(k, f(c))
28.54/9.53	   A^2 -> H(k, f(d))
28.54/9.53	   A^2 -> H(c, U1(c, b))
28.54/9.53	   A^2 -> H(c, U1(d, b))
28.54/9.53	   A^2 -> H(c, U1(b, c))
28.54/9.53	   A^2 -> H(c, U1(b, d))
28.54/9.53	   A^2 -> H(c, U1(c, c))
28.54/9.53	   A^2 -> H(c, f(e))
28.54/9.53	   A^2 -> H(c, f(k))
28.54/9.53	   A^2 -> H(c, U1(d, d))
28.54/9.53	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.53	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.53	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.53	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.53	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.53	   A^2 -> H(U1(e, k), f(e))
28.54/9.53	   A^2 -> H(U1(e, k), f(k))
28.54/9.53	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.53	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.53	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.53	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.53	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.53	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.53	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.53	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.53	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.53	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.53	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.53	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.53	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.53	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.53	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.53	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.53	   A^2 -> H(U1(k, e), f(e))
28.54/9.53	   A^2 -> H(U1(k, e), f(k))
28.54/9.53	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.53	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.53	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.53	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.53	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.53	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.53	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.53	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.53	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.53	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.53	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.53	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.53	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, c), b)
28.54/9.53	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.53	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.53	   A^2 -> H(U1(c, c), e)
28.54/9.53	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.53	   A^2 -> H(e, U1(c, b))
28.54/9.53	   A^2 -> H(e, U1(d, b))
28.54/9.53	   A^2 -> H(e, U1(b, c))
28.54/9.53	   A^2 -> H(e, U1(b, d))
28.54/9.53	   A^2 -> H(e, U1(c, c))
28.54/9.53	   A^2 -> H(e, f(e))
28.54/9.53	   A^2 -> H(e, f(k))
28.54/9.53	   A^2 -> H(e, U1(d, d))
28.54/9.53	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.53	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.53	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.53	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.53	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.53	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.53	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.53	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.53	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.53	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.53	   A^2 -> H(f(e), b)
28.54/9.53	   A^2 -> H(f(e), U1(e, d))
28.54/9.53	   A^2 -> H(f(e), U1(d, e))
28.54/9.53	   A^2 -> H(f(e), c)
28.54/9.53	   A^2 -> H(f(e), U1(e, k))
28.54/9.53	   A^2 -> H(f(e), U1(k, e))
28.54/9.53	   A^2 -> H(f(e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.53	   A^2 -> H(f(k), b)
28.54/9.53	   A^2 -> H(f(k), U1(e, d))
28.54/9.53	   A^2 -> H(f(k), U1(d, e))
28.54/9.53	   A^2 -> H(f(k), c)
28.54/9.53	   A^2 -> H(f(k), U1(e, k))
28.54/9.53	   A^2 -> H(f(k), U1(k, e))
28.54/9.53	   A^2 -> H(f(k), e)
28.54/9.53	   A^2 -> H(f(c), d)
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.53	   A^2 -> H(U1(k, k), f(e))
28.54/9.53	   A^2 -> H(U1(k, k), f(k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.53	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.53	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.53	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.53	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.53	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.53	   A^2 -> H(U1(d, d), b)
28.54/9.53	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.53	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.53	   A^2 -> H(U1(d, d), c)
28.54/9.53	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.53	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.53	   A^2 -> H(U1(d, d), e)
28.54/9.53	   A^2 -> H(f(d), d)
28.54/9.53	   A^2 -> H(f(d), k)
28.54/9.53	   A^2 -> H(U1(c, c), c)
28.54/9.53	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.53	   A^2 -> H(f(c), k)
28.54/9.53	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.53	   A^2 -> H(f(k), U1(k, k))
28.54/9.53	   A^2 -> H(f(e), e)
28.54/9.53	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.53	   A^2 -> H(d, U1(c, b))
28.54/9.53	   A^2 -> H(d, U1(d, b))
28.54/9.53	   A^2 -> H(d, U1(b, c))
28.54/9.53	   A^2 -> H(d, U1(b, d))
28.54/9.53	   A^2 -> H(d, U1(c, c))
28.54/9.53	   A^2 -> H(d, f(e))
28.54/9.53	   A^2 -> H(d, f(k))
28.54/9.53	   A^2 -> H(d, U1(d, d))
28.54/9.53	   A^2 -> H(a, U1(e, b))
28.54/9.53	   A^2 -> H(a, U1(k, b))
28.54/9.53	   A^2 -> H(a, U1(c, d))
28.54/9.53	   A^2 -> H(a, U1(d, c))
28.54/9.53	   A^2 -> H(a, U1(b, e))
28.54/9.53	   A^2 -> H(a, U1(b, k))
28.54/9.53	   A^2 -> H(a, U1(e, c))
28.54/9.53	   A^2 -> H(a, U1(k, c))
28.54/9.53	   A^2 -> H(a, U1(c, e))
28.54/9.53	   A^2 -> H(a, U1(c, k))
28.54/9.53	   A^2 -> H(a, U1(e, e))
28.54/9.53	   A^2 -> H(a, U1(k, k))
28.54/9.53	   A^2 -> H(a, U1(k, d))
28.54/9.53	   A^2 -> H(a, U1(d, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.53	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.53	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.53	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.53	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.53	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.53	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.53	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.53	   A^2 -> H(U1(e, a), b)
28.54/9.53	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.53	   A^2 -> H(U1(e, a), c)
28.54/9.53	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.53	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.53	   A^2 -> H(U1(e, a), e)
28.54/9.53	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, a), b)
28.54/9.53	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.53	
28.54/9.53	The TRS R consists of the following rules:
28.54/9.53	
28.54/9.53	   f(x) -> U1(x, x)
28.54/9.53	   U1(e, x) -> x
28.54/9.53	   a -> c
28.54/9.53	   a -> d
28.54/9.53	   b -> c
28.54/9.53	   b -> d
28.54/9.53	   d -> k
28.54/9.53	   c -> e
28.54/9.53	   c -> k
28.54/9.53	
28.54/9.53	Q is empty.
28.54/9.53	We have to consider all minimal (P,Q,R)-chains.
28.54/9.53	----------------------------------------
28.54/9.53	
28.54/9.53	(1163) TransformationProof (EQUIVALENT)
28.54/9.53	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.53	
28.54/9.53	   (A^2 -> H(U1(k, c), U1(c, d)),A^2 -> H(U1(k, c), U1(c, d)))
28.54/9.53	   (A^2 -> H(U1(k, d), U1(c, d)),A^2 -> H(U1(k, d), U1(c, d)))
28.54/9.53	   (A^2 -> H(U1(k, a), U1(e, d)),A^2 -> H(U1(k, a), U1(e, d)))
28.54/9.53	   (A^2 -> H(U1(k, a), U1(k, d)),A^2 -> H(U1(k, a), U1(k, d)))
28.54/9.53	   (A^2 -> H(U1(k, a), U1(c, k)),A^2 -> H(U1(k, a), U1(c, k)))
28.54/9.53	
28.54/9.53	
28.54/9.53	----------------------------------------
28.54/9.53	
28.54/9.53	(1164)
28.54/9.53	Obligation:
28.54/9.53	Q DP problem:
28.54/9.53	The TRS P consists of the following rules:
28.54/9.53	
28.54/9.53	   H(x, x) -> G(x, x, f(k))
28.54/9.53	   G(d, x, x) -> A^2
28.54/9.53	   A^2 -> H(f(c), f(c))
28.54/9.53	   A^2 -> H(f(d), f(d))
28.54/9.53	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.53	   A^2 -> H(f(e), f(e))
28.54/9.53	   A^2 -> H(f(k), f(k))
28.54/9.53	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.53	   A^2 -> H(U1(k, a), U1(d, c))
28.54/9.53	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.53	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.53	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.53	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.53	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.53	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.53	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.53	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.53	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, a), b)
28.54/9.53	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.53	   A^2 -> H(U1(c, a), c)
28.54/9.53	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.53	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.53	   A^2 -> H(U1(c, a), e)
28.54/9.53	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.53	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.53	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.53	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.53	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.53	   A^2 -> H(U1(d, e), f(e))
28.54/9.53	   A^2 -> H(U1(d, e), f(k))
28.54/9.53	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.53	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.53	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.53	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.53	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.53	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.53	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.53	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.53	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.53	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.53	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.53	   A^2 -> H(U1(d, a), b)
28.54/9.53	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.53	   A^2 -> H(U1(d, a), c)
28.54/9.53	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.53	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.53	   A^2 -> H(U1(d, a), e)
28.54/9.53	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.53	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.53	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.53	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.53	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.53	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.53	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.53	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.53	   A^2 -> H(U1(a, c), b)
28.54/9.53	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.53	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.53	   A^2 -> H(U1(a, c), c)
28.54/9.53	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.53	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.53	   A^2 -> H(U1(a, c), e)
28.54/9.53	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, d), b)
28.54/9.53	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.53	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.53	   A^2 -> H(U1(a, d), c)
28.54/9.53	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.53	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.53	   A^2 -> H(U1(a, d), e)
28.54/9.53	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, a), d)
28.54/9.53	   A^2 -> H(U1(a, a), k)
28.54/9.53	   A^2 -> H(k, U1(b, b))
28.54/9.53	   A^2 -> H(k, f(c))
28.54/9.53	   A^2 -> H(k, f(d))
28.54/9.53	   A^2 -> H(c, U1(c, b))
28.54/9.53	   A^2 -> H(c, U1(d, b))
28.54/9.53	   A^2 -> H(c, U1(b, c))
28.54/9.53	   A^2 -> H(c, U1(b, d))
28.54/9.53	   A^2 -> H(c, U1(c, c))
28.54/9.53	   A^2 -> H(c, f(e))
28.54/9.53	   A^2 -> H(c, f(k))
28.54/9.53	   A^2 -> H(c, U1(d, d))
28.54/9.53	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.53	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.53	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.53	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.53	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.53	   A^2 -> H(U1(e, k), f(e))
28.54/9.53	   A^2 -> H(U1(e, k), f(k))
28.54/9.53	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.53	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.53	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.53	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.53	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.53	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.53	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.53	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.53	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.53	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.53	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.53	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.53	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.53	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.53	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.53	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.53	   A^2 -> H(U1(k, e), f(e))
28.54/9.53	   A^2 -> H(U1(k, e), f(k))
28.54/9.53	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.53	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.53	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.53	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.53	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.53	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.53	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.53	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.53	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.53	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.53	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.53	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.53	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, c), b)
28.54/9.53	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.53	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.53	   A^2 -> H(U1(c, c), e)
28.54/9.53	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.53	   A^2 -> H(e, U1(c, b))
28.54/9.53	   A^2 -> H(e, U1(d, b))
28.54/9.53	   A^2 -> H(e, U1(b, c))
28.54/9.53	   A^2 -> H(e, U1(b, d))
28.54/9.53	   A^2 -> H(e, U1(c, c))
28.54/9.53	   A^2 -> H(e, f(e))
28.54/9.53	   A^2 -> H(e, f(k))
28.54/9.53	   A^2 -> H(e, U1(d, d))
28.54/9.53	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.53	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.53	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.53	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.53	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.53	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.53	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.53	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.53	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.53	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.53	   A^2 -> H(f(e), b)
28.54/9.53	   A^2 -> H(f(e), U1(e, d))
28.54/9.53	   A^2 -> H(f(e), U1(d, e))
28.54/9.53	   A^2 -> H(f(e), c)
28.54/9.53	   A^2 -> H(f(e), U1(e, k))
28.54/9.53	   A^2 -> H(f(e), U1(k, e))
28.54/9.53	   A^2 -> H(f(e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.53	   A^2 -> H(f(k), b)
28.54/9.53	   A^2 -> H(f(k), U1(e, d))
28.54/9.53	   A^2 -> H(f(k), U1(d, e))
28.54/9.53	   A^2 -> H(f(k), c)
28.54/9.53	   A^2 -> H(f(k), U1(e, k))
28.54/9.53	   A^2 -> H(f(k), U1(k, e))
28.54/9.53	   A^2 -> H(f(k), e)
28.54/9.53	   A^2 -> H(f(c), d)
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.53	   A^2 -> H(U1(k, k), f(e))
28.54/9.53	   A^2 -> H(U1(k, k), f(k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.53	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.53	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.53	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.53	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.53	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.53	   A^2 -> H(U1(d, d), b)
28.54/9.53	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.53	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.53	   A^2 -> H(U1(d, d), c)
28.54/9.53	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.53	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.53	   A^2 -> H(U1(d, d), e)
28.54/9.53	   A^2 -> H(f(d), d)
28.54/9.53	   A^2 -> H(f(d), k)
28.54/9.53	   A^2 -> H(U1(c, c), c)
28.54/9.53	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.53	   A^2 -> H(f(c), k)
28.54/9.53	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.53	   A^2 -> H(f(k), U1(k, k))
28.54/9.53	   A^2 -> H(f(e), e)
28.54/9.53	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.53	   A^2 -> H(d, U1(c, b))
28.54/9.53	   A^2 -> H(d, U1(d, b))
28.54/9.53	   A^2 -> H(d, U1(b, c))
28.54/9.53	   A^2 -> H(d, U1(b, d))
28.54/9.53	   A^2 -> H(d, U1(c, c))
28.54/9.53	   A^2 -> H(d, f(e))
28.54/9.53	   A^2 -> H(d, f(k))
28.54/9.53	   A^2 -> H(d, U1(d, d))
28.54/9.53	   A^2 -> H(a, U1(e, b))
28.54/9.53	   A^2 -> H(a, U1(k, b))
28.54/9.53	   A^2 -> H(a, U1(c, d))
28.54/9.53	   A^2 -> H(a, U1(d, c))
28.54/9.53	   A^2 -> H(a, U1(b, e))
28.54/9.53	   A^2 -> H(a, U1(b, k))
28.54/9.53	   A^2 -> H(a, U1(e, c))
28.54/9.53	   A^2 -> H(a, U1(k, c))
28.54/9.53	   A^2 -> H(a, U1(c, e))
28.54/9.53	   A^2 -> H(a, U1(c, k))
28.54/9.53	   A^2 -> H(a, U1(e, e))
28.54/9.53	   A^2 -> H(a, U1(k, k))
28.54/9.53	   A^2 -> H(a, U1(k, d))
28.54/9.53	   A^2 -> H(a, U1(d, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.53	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.53	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.53	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.53	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.53	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.53	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.53	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.53	   A^2 -> H(U1(e, a), b)
28.54/9.53	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.53	   A^2 -> H(U1(e, a), c)
28.54/9.53	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.53	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.53	   A^2 -> H(U1(e, a), e)
28.54/9.53	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, a), b)
28.54/9.53	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.53	
28.54/9.53	The TRS R consists of the following rules:
28.54/9.53	
28.54/9.53	   f(x) -> U1(x, x)
28.54/9.53	   U1(e, x) -> x
28.54/9.53	   a -> c
28.54/9.53	   a -> d
28.54/9.53	   b -> c
28.54/9.53	   b -> d
28.54/9.53	   d -> k
28.54/9.53	   c -> e
28.54/9.53	   c -> k
28.54/9.53	
28.54/9.53	Q is empty.
28.54/9.53	We have to consider all minimal (P,Q,R)-chains.
28.54/9.53	----------------------------------------
28.54/9.53	
28.54/9.53	(1165) TransformationProof (EQUIVALENT)
28.54/9.53	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.53	
28.54/9.53	   (A^2 -> H(U1(k, c), U1(d, c)),A^2 -> H(U1(k, c), U1(d, c)))
28.54/9.53	   (A^2 -> H(U1(k, d), U1(d, c)),A^2 -> H(U1(k, d), U1(d, c)))
28.54/9.53	   (A^2 -> H(U1(k, a), U1(k, c)),A^2 -> H(U1(k, a), U1(k, c)))
28.54/9.53	   (A^2 -> H(U1(k, a), U1(d, e)),A^2 -> H(U1(k, a), U1(d, e)))
28.54/9.53	   (A^2 -> H(U1(k, a), U1(d, k)),A^2 -> H(U1(k, a), U1(d, k)))
28.54/9.53	
28.54/9.53	
28.54/9.53	----------------------------------------
28.54/9.53	
28.54/9.53	(1166)
28.54/9.53	Obligation:
28.54/9.53	Q DP problem:
28.54/9.53	The TRS P consists of the following rules:
28.54/9.53	
28.54/9.53	   H(x, x) -> G(x, x, f(k))
28.54/9.53	   G(d, x, x) -> A^2
28.54/9.53	   A^2 -> H(f(c), f(c))
28.54/9.53	   A^2 -> H(f(d), f(d))
28.54/9.53	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.53	   A^2 -> H(f(e), f(e))
28.54/9.53	   A^2 -> H(f(k), f(k))
28.54/9.53	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.53	   A^2 -> H(U1(k, a), U1(b, e))
28.54/9.53	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.53	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.53	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.53	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.53	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.53	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.53	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.53	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, a), b)
28.54/9.53	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.53	   A^2 -> H(U1(c, a), c)
28.54/9.53	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.53	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.53	   A^2 -> H(U1(c, a), e)
28.54/9.53	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.53	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.53	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.53	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.53	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.53	   A^2 -> H(U1(d, e), f(e))
28.54/9.53	   A^2 -> H(U1(d, e), f(k))
28.54/9.53	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.53	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.53	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.53	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.53	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.53	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.53	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.53	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.53	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.53	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.53	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.53	   A^2 -> H(U1(d, a), b)
28.54/9.53	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.53	   A^2 -> H(U1(d, a), c)
28.54/9.53	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.53	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.53	   A^2 -> H(U1(d, a), e)
28.54/9.53	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.53	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.53	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.53	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.53	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.53	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.53	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.53	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.53	   A^2 -> H(U1(a, c), b)
28.54/9.53	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.53	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.53	   A^2 -> H(U1(a, c), c)
28.54/9.53	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.53	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.53	   A^2 -> H(U1(a, c), e)
28.54/9.53	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, d), b)
28.54/9.53	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.53	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.53	   A^2 -> H(U1(a, d), c)
28.54/9.53	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.53	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.53	   A^2 -> H(U1(a, d), e)
28.54/9.53	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, a), d)
28.54/9.53	   A^2 -> H(U1(a, a), k)
28.54/9.53	   A^2 -> H(k, U1(b, b))
28.54/9.53	   A^2 -> H(k, f(c))
28.54/9.53	   A^2 -> H(k, f(d))
28.54/9.53	   A^2 -> H(c, U1(c, b))
28.54/9.53	   A^2 -> H(c, U1(d, b))
28.54/9.53	   A^2 -> H(c, U1(b, c))
28.54/9.53	   A^2 -> H(c, U1(b, d))
28.54/9.53	   A^2 -> H(c, U1(c, c))
28.54/9.53	   A^2 -> H(c, f(e))
28.54/9.53	   A^2 -> H(c, f(k))
28.54/9.53	   A^2 -> H(c, U1(d, d))
28.54/9.53	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.53	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.53	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.53	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.53	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.53	   A^2 -> H(U1(e, k), f(e))
28.54/9.53	   A^2 -> H(U1(e, k), f(k))
28.54/9.53	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.53	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.53	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.53	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.53	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.53	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.53	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.53	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.53	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.53	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.53	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.53	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.53	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.53	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.53	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.53	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.53	   A^2 -> H(U1(k, e), f(e))
28.54/9.53	   A^2 -> H(U1(k, e), f(k))
28.54/9.53	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.53	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.53	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.53	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.53	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.53	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.53	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.53	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.53	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.53	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.53	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.53	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.53	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, c), b)
28.54/9.53	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.53	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.53	   A^2 -> H(U1(c, c), e)
28.54/9.53	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.53	   A^2 -> H(e, U1(c, b))
28.54/9.53	   A^2 -> H(e, U1(d, b))
28.54/9.53	   A^2 -> H(e, U1(b, c))
28.54/9.53	   A^2 -> H(e, U1(b, d))
28.54/9.53	   A^2 -> H(e, U1(c, c))
28.54/9.53	   A^2 -> H(e, f(e))
28.54/9.53	   A^2 -> H(e, f(k))
28.54/9.53	   A^2 -> H(e, U1(d, d))
28.54/9.53	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.53	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.53	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.53	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.53	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.53	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.53	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.53	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.53	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.53	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.53	   A^2 -> H(f(e), b)
28.54/9.53	   A^2 -> H(f(e), U1(e, d))
28.54/9.53	   A^2 -> H(f(e), U1(d, e))
28.54/9.53	   A^2 -> H(f(e), c)
28.54/9.53	   A^2 -> H(f(e), U1(e, k))
28.54/9.53	   A^2 -> H(f(e), U1(k, e))
28.54/9.53	   A^2 -> H(f(e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.53	   A^2 -> H(f(k), b)
28.54/9.53	   A^2 -> H(f(k), U1(e, d))
28.54/9.53	   A^2 -> H(f(k), U1(d, e))
28.54/9.53	   A^2 -> H(f(k), c)
28.54/9.53	   A^2 -> H(f(k), U1(e, k))
28.54/9.53	   A^2 -> H(f(k), U1(k, e))
28.54/9.53	   A^2 -> H(f(k), e)
28.54/9.53	   A^2 -> H(f(c), d)
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.53	   A^2 -> H(U1(k, k), f(e))
28.54/9.53	   A^2 -> H(U1(k, k), f(k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.53	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.53	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.53	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.53	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.53	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.53	   A^2 -> H(U1(d, d), b)
28.54/9.53	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.53	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.53	   A^2 -> H(U1(d, d), c)
28.54/9.53	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.53	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.53	   A^2 -> H(U1(d, d), e)
28.54/9.53	   A^2 -> H(f(d), d)
28.54/9.53	   A^2 -> H(f(d), k)
28.54/9.53	   A^2 -> H(U1(c, c), c)
28.54/9.53	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.53	   A^2 -> H(f(c), k)
28.54/9.53	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.53	   A^2 -> H(f(k), U1(k, k))
28.54/9.53	   A^2 -> H(f(e), e)
28.54/9.53	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.53	   A^2 -> H(d, U1(c, b))
28.54/9.53	   A^2 -> H(d, U1(d, b))
28.54/9.53	   A^2 -> H(d, U1(b, c))
28.54/9.53	   A^2 -> H(d, U1(b, d))
28.54/9.53	   A^2 -> H(d, U1(c, c))
28.54/9.53	   A^2 -> H(d, f(e))
28.54/9.53	   A^2 -> H(d, f(k))
28.54/9.53	   A^2 -> H(d, U1(d, d))
28.54/9.53	   A^2 -> H(a, U1(e, b))
28.54/9.53	   A^2 -> H(a, U1(k, b))
28.54/9.53	   A^2 -> H(a, U1(c, d))
28.54/9.53	   A^2 -> H(a, U1(d, c))
28.54/9.53	   A^2 -> H(a, U1(b, e))
28.54/9.53	   A^2 -> H(a, U1(b, k))
28.54/9.53	   A^2 -> H(a, U1(e, c))
28.54/9.53	   A^2 -> H(a, U1(k, c))
28.54/9.53	   A^2 -> H(a, U1(c, e))
28.54/9.53	   A^2 -> H(a, U1(c, k))
28.54/9.53	   A^2 -> H(a, U1(e, e))
28.54/9.53	   A^2 -> H(a, U1(k, k))
28.54/9.53	   A^2 -> H(a, U1(k, d))
28.54/9.53	   A^2 -> H(a, U1(d, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.53	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.53	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.53	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.53	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.53	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.53	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.53	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.53	   A^2 -> H(U1(e, a), b)
28.54/9.53	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.53	   A^2 -> H(U1(e, a), c)
28.54/9.53	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.53	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.53	   A^2 -> H(U1(e, a), e)
28.54/9.53	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, a), b)
28.54/9.53	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.53	
28.54/9.53	The TRS R consists of the following rules:
28.54/9.53	
28.54/9.53	   f(x) -> U1(x, x)
28.54/9.53	   U1(e, x) -> x
28.54/9.53	   a -> c
28.54/9.53	   a -> d
28.54/9.53	   b -> c
28.54/9.53	   b -> d
28.54/9.53	   d -> k
28.54/9.53	   c -> e
28.54/9.53	   c -> k
28.54/9.53	
28.54/9.53	Q is empty.
28.54/9.53	We have to consider all minimal (P,Q,R)-chains.
28.54/9.53	----------------------------------------
28.54/9.53	
28.54/9.53	(1167) TransformationProof (EQUIVALENT)
28.54/9.53	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.53	
28.54/9.53	   (A^2 -> H(U1(k, c), U1(b, e)),A^2 -> H(U1(k, c), U1(b, e)))
28.54/9.53	   (A^2 -> H(U1(k, d), U1(b, e)),A^2 -> H(U1(k, d), U1(b, e)))
28.54/9.53	   (A^2 -> H(U1(k, a), U1(c, e)),A^2 -> H(U1(k, a), U1(c, e)))
28.54/9.53	   (A^2 -> H(U1(k, a), U1(d, e)),A^2 -> H(U1(k, a), U1(d, e)))
28.54/9.53	
28.54/9.53	
28.54/9.53	----------------------------------------
28.54/9.53	
28.54/9.53	(1168)
28.54/9.53	Obligation:
28.54/9.53	Q DP problem:
28.54/9.53	The TRS P consists of the following rules:
28.54/9.53	
28.54/9.53	   H(x, x) -> G(x, x, f(k))
28.54/9.53	   G(d, x, x) -> A^2
28.54/9.53	   A^2 -> H(f(c), f(c))
28.54/9.53	   A^2 -> H(f(d), f(d))
28.54/9.53	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.53	   A^2 -> H(f(e), f(e))
28.54/9.53	   A^2 -> H(f(k), f(k))
28.54/9.53	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.53	   A^2 -> H(U1(k, a), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.53	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.53	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.53	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.53	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.53	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.53	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.53	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, a), b)
28.54/9.53	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.53	   A^2 -> H(U1(c, a), c)
28.54/9.53	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.53	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.53	   A^2 -> H(U1(c, a), e)
28.54/9.53	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.53	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.53	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.53	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.53	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.53	   A^2 -> H(U1(d, e), f(e))
28.54/9.53	   A^2 -> H(U1(d, e), f(k))
28.54/9.53	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.53	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.53	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.53	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.53	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.53	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.53	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.53	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.53	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.53	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.53	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.53	   A^2 -> H(U1(d, a), b)
28.54/9.53	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.53	   A^2 -> H(U1(d, a), c)
28.54/9.53	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.53	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.53	   A^2 -> H(U1(d, a), e)
28.54/9.53	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.53	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.53	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.53	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.53	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.53	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.53	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.53	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.53	   A^2 -> H(U1(a, c), b)
28.54/9.53	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.53	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.53	   A^2 -> H(U1(a, c), c)
28.54/9.53	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.53	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.53	   A^2 -> H(U1(a, c), e)
28.54/9.53	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, d), b)
28.54/9.53	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.53	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.53	   A^2 -> H(U1(a, d), c)
28.54/9.53	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.53	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.53	   A^2 -> H(U1(a, d), e)
28.54/9.53	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, a), d)
28.54/9.53	   A^2 -> H(U1(a, a), k)
28.54/9.53	   A^2 -> H(k, U1(b, b))
28.54/9.53	   A^2 -> H(k, f(c))
28.54/9.53	   A^2 -> H(k, f(d))
28.54/9.53	   A^2 -> H(c, U1(c, b))
28.54/9.53	   A^2 -> H(c, U1(d, b))
28.54/9.53	   A^2 -> H(c, U1(b, c))
28.54/9.53	   A^2 -> H(c, U1(b, d))
28.54/9.53	   A^2 -> H(c, U1(c, c))
28.54/9.53	   A^2 -> H(c, f(e))
28.54/9.53	   A^2 -> H(c, f(k))
28.54/9.53	   A^2 -> H(c, U1(d, d))
28.54/9.53	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.53	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.53	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.53	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.53	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.53	   A^2 -> H(U1(e, k), f(e))
28.54/9.53	   A^2 -> H(U1(e, k), f(k))
28.54/9.53	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.53	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.53	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.53	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.53	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.53	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.53	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.53	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.53	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.53	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.53	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.53	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.53	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.53	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.53	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.53	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.53	   A^2 -> H(U1(k, e), f(e))
28.54/9.53	   A^2 -> H(U1(k, e), f(k))
28.54/9.53	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.53	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.53	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.53	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.53	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.53	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.53	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.53	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.53	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.53	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.53	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.53	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.53	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, c), b)
28.54/9.53	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.53	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.53	   A^2 -> H(U1(c, c), e)
28.54/9.53	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.53	   A^2 -> H(e, U1(c, b))
28.54/9.53	   A^2 -> H(e, U1(d, b))
28.54/9.53	   A^2 -> H(e, U1(b, c))
28.54/9.53	   A^2 -> H(e, U1(b, d))
28.54/9.53	   A^2 -> H(e, U1(c, c))
28.54/9.53	   A^2 -> H(e, f(e))
28.54/9.53	   A^2 -> H(e, f(k))
28.54/9.53	   A^2 -> H(e, U1(d, d))
28.54/9.53	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.53	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.53	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.53	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.53	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.53	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.53	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.53	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.53	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.53	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.53	   A^2 -> H(f(e), b)
28.54/9.53	   A^2 -> H(f(e), U1(e, d))
28.54/9.53	   A^2 -> H(f(e), U1(d, e))
28.54/9.53	   A^2 -> H(f(e), c)
28.54/9.53	   A^2 -> H(f(e), U1(e, k))
28.54/9.53	   A^2 -> H(f(e), U1(k, e))
28.54/9.53	   A^2 -> H(f(e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.53	   A^2 -> H(f(k), b)
28.54/9.53	   A^2 -> H(f(k), U1(e, d))
28.54/9.53	   A^2 -> H(f(k), U1(d, e))
28.54/9.53	   A^2 -> H(f(k), c)
28.54/9.53	   A^2 -> H(f(k), U1(e, k))
28.54/9.53	   A^2 -> H(f(k), U1(k, e))
28.54/9.53	   A^2 -> H(f(k), e)
28.54/9.53	   A^2 -> H(f(c), d)
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.53	   A^2 -> H(U1(k, k), f(e))
28.54/9.53	   A^2 -> H(U1(k, k), f(k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.53	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.53	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.53	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.53	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.53	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.53	   A^2 -> H(U1(d, d), b)
28.54/9.53	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.53	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.53	   A^2 -> H(U1(d, d), c)
28.54/9.53	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.53	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.53	   A^2 -> H(U1(d, d), e)
28.54/9.53	   A^2 -> H(f(d), d)
28.54/9.53	   A^2 -> H(f(d), k)
28.54/9.53	   A^2 -> H(U1(c, c), c)
28.54/9.53	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.53	   A^2 -> H(f(c), k)
28.54/9.53	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.53	   A^2 -> H(f(k), U1(k, k))
28.54/9.53	   A^2 -> H(f(e), e)
28.54/9.53	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.53	   A^2 -> H(d, U1(c, b))
28.54/9.53	   A^2 -> H(d, U1(d, b))
28.54/9.53	   A^2 -> H(d, U1(b, c))
28.54/9.53	   A^2 -> H(d, U1(b, d))
28.54/9.53	   A^2 -> H(d, U1(c, c))
28.54/9.53	   A^2 -> H(d, f(e))
28.54/9.53	   A^2 -> H(d, f(k))
28.54/9.53	   A^2 -> H(d, U1(d, d))
28.54/9.53	   A^2 -> H(a, U1(e, b))
28.54/9.53	   A^2 -> H(a, U1(k, b))
28.54/9.53	   A^2 -> H(a, U1(c, d))
28.54/9.53	   A^2 -> H(a, U1(d, c))
28.54/9.53	   A^2 -> H(a, U1(b, e))
28.54/9.53	   A^2 -> H(a, U1(b, k))
28.54/9.53	   A^2 -> H(a, U1(e, c))
28.54/9.53	   A^2 -> H(a, U1(k, c))
28.54/9.53	   A^2 -> H(a, U1(c, e))
28.54/9.53	   A^2 -> H(a, U1(c, k))
28.54/9.53	   A^2 -> H(a, U1(e, e))
28.54/9.53	   A^2 -> H(a, U1(k, k))
28.54/9.53	   A^2 -> H(a, U1(k, d))
28.54/9.53	   A^2 -> H(a, U1(d, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.53	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.53	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.53	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.53	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.53	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.53	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.53	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.53	   A^2 -> H(U1(e, a), b)
28.54/9.53	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.53	   A^2 -> H(U1(e, a), c)
28.54/9.53	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.53	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.53	   A^2 -> H(U1(e, a), e)
28.54/9.53	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, a), b)
28.54/9.53	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.53	
28.54/9.53	The TRS R consists of the following rules:
28.54/9.53	
28.54/9.53	   f(x) -> U1(x, x)
28.54/9.53	   U1(e, x) -> x
28.54/9.53	   a -> c
28.54/9.53	   a -> d
28.54/9.53	   b -> c
28.54/9.53	   b -> d
28.54/9.53	   d -> k
28.54/9.53	   c -> e
28.54/9.53	   c -> k
28.54/9.53	
28.54/9.53	Q is empty.
28.54/9.53	We have to consider all minimal (P,Q,R)-chains.
28.54/9.53	----------------------------------------
28.54/9.53	
28.54/9.53	(1169) TransformationProof (EQUIVALENT)
28.54/9.53	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.53	
28.54/9.53	   (A^2 -> H(U1(k, c), U1(b, k)),A^2 -> H(U1(k, c), U1(b, k)))
28.54/9.53	   (A^2 -> H(U1(k, d), U1(b, k)),A^2 -> H(U1(k, d), U1(b, k)))
28.54/9.53	   (A^2 -> H(U1(k, a), U1(c, k)),A^2 -> H(U1(k, a), U1(c, k)))
28.54/9.53	   (A^2 -> H(U1(k, a), U1(d, k)),A^2 -> H(U1(k, a), U1(d, k)))
28.54/9.53	
28.54/9.53	
28.54/9.53	----------------------------------------
28.54/9.53	
28.54/9.53	(1170)
28.54/9.53	Obligation:
28.54/9.53	Q DP problem:
28.54/9.53	The TRS P consists of the following rules:
28.54/9.53	
28.54/9.53	   H(x, x) -> G(x, x, f(k))
28.54/9.53	   G(d, x, x) -> A^2
28.54/9.53	   A^2 -> H(f(c), f(c))
28.54/9.53	   A^2 -> H(f(d), f(d))
28.54/9.53	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.53	   A^2 -> H(f(e), f(e))
28.54/9.53	   A^2 -> H(f(k), f(k))
28.54/9.53	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.53	   A^2 -> H(U1(k, a), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.53	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.53	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.53	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.53	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.53	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.53	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.53	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, a), b)
28.54/9.53	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.53	   A^2 -> H(U1(c, a), c)
28.54/9.53	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.53	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.53	   A^2 -> H(U1(c, a), e)
28.54/9.53	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.53	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.53	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.53	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.53	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.53	   A^2 -> H(U1(d, e), f(e))
28.54/9.53	   A^2 -> H(U1(d, e), f(k))
28.54/9.53	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.53	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.53	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.53	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.53	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.53	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.53	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.53	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.53	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.53	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.53	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.53	   A^2 -> H(U1(d, a), b)
28.54/9.53	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.53	   A^2 -> H(U1(d, a), c)
28.54/9.53	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.53	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.53	   A^2 -> H(U1(d, a), e)
28.54/9.53	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.53	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.53	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.53	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.53	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.53	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.53	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.53	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.53	   A^2 -> H(U1(a, c), b)
28.54/9.53	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.53	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.53	   A^2 -> H(U1(a, c), c)
28.54/9.53	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.53	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.53	   A^2 -> H(U1(a, c), e)
28.54/9.53	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, d), b)
28.54/9.53	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.53	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.53	   A^2 -> H(U1(a, d), c)
28.54/9.53	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.53	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.53	   A^2 -> H(U1(a, d), e)
28.54/9.53	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, a), d)
28.54/9.53	   A^2 -> H(U1(a, a), k)
28.54/9.53	   A^2 -> H(k, U1(b, b))
28.54/9.53	   A^2 -> H(k, f(c))
28.54/9.53	   A^2 -> H(k, f(d))
28.54/9.53	   A^2 -> H(c, U1(c, b))
28.54/9.53	   A^2 -> H(c, U1(d, b))
28.54/9.53	   A^2 -> H(c, U1(b, c))
28.54/9.53	   A^2 -> H(c, U1(b, d))
28.54/9.53	   A^2 -> H(c, U1(c, c))
28.54/9.53	   A^2 -> H(c, f(e))
28.54/9.53	   A^2 -> H(c, f(k))
28.54/9.53	   A^2 -> H(c, U1(d, d))
28.54/9.53	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.53	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.53	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.53	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.53	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.53	   A^2 -> H(U1(e, k), f(e))
28.54/9.53	   A^2 -> H(U1(e, k), f(k))
28.54/9.53	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.53	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.53	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.53	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.53	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.53	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.53	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.53	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.53	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.53	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.53	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.53	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.53	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.53	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.53	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.53	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.53	   A^2 -> H(U1(k, e), f(e))
28.54/9.53	   A^2 -> H(U1(k, e), f(k))
28.54/9.53	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.53	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.53	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.53	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.53	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.53	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.53	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.53	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.53	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.53	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.53	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.53	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.53	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, c), b)
28.54/9.53	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.53	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.53	   A^2 -> H(U1(c, c), e)
28.54/9.53	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.53	   A^2 -> H(e, U1(c, b))
28.54/9.53	   A^2 -> H(e, U1(d, b))
28.54/9.53	   A^2 -> H(e, U1(b, c))
28.54/9.53	   A^2 -> H(e, U1(b, d))
28.54/9.53	   A^2 -> H(e, U1(c, c))
28.54/9.53	   A^2 -> H(e, f(e))
28.54/9.53	   A^2 -> H(e, f(k))
28.54/9.53	   A^2 -> H(e, U1(d, d))
28.54/9.53	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.53	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.53	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.53	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.53	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.53	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.53	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.53	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.53	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.53	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.53	   A^2 -> H(f(e), b)
28.54/9.53	   A^2 -> H(f(e), U1(e, d))
28.54/9.53	   A^2 -> H(f(e), U1(d, e))
28.54/9.53	   A^2 -> H(f(e), c)
28.54/9.53	   A^2 -> H(f(e), U1(e, k))
28.54/9.53	   A^2 -> H(f(e), U1(k, e))
28.54/9.53	   A^2 -> H(f(e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.53	   A^2 -> H(f(k), b)
28.54/9.53	   A^2 -> H(f(k), U1(e, d))
28.54/9.53	   A^2 -> H(f(k), U1(d, e))
28.54/9.53	   A^2 -> H(f(k), c)
28.54/9.53	   A^2 -> H(f(k), U1(e, k))
28.54/9.53	   A^2 -> H(f(k), U1(k, e))
28.54/9.53	   A^2 -> H(f(k), e)
28.54/9.53	   A^2 -> H(f(c), d)
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.53	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.53	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.53	   A^2 -> H(U1(k, k), f(e))
28.54/9.53	   A^2 -> H(U1(k, k), f(k))
28.54/9.53	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.53	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.53	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.53	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.53	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.53	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.53	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.53	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.53	   A^2 -> H(U1(d, d), b)
28.54/9.53	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.53	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.53	   A^2 -> H(U1(d, d), c)
28.54/9.53	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.53	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.53	   A^2 -> H(U1(d, d), e)
28.54/9.53	   A^2 -> H(f(d), d)
28.54/9.53	   A^2 -> H(f(d), k)
28.54/9.53	   A^2 -> H(U1(c, c), c)
28.54/9.53	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.53	   A^2 -> H(f(c), k)
28.54/9.53	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.53	   A^2 -> H(f(k), U1(k, k))
28.54/9.53	   A^2 -> H(f(e), e)
28.54/9.53	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.53	   A^2 -> H(d, U1(c, b))
28.54/9.53	   A^2 -> H(d, U1(d, b))
28.54/9.53	   A^2 -> H(d, U1(b, c))
28.54/9.53	   A^2 -> H(d, U1(b, d))
28.54/9.53	   A^2 -> H(d, U1(c, c))
28.54/9.53	   A^2 -> H(d, f(e))
28.54/9.53	   A^2 -> H(d, f(k))
28.54/9.53	   A^2 -> H(d, U1(d, d))
28.54/9.53	   A^2 -> H(a, U1(e, b))
28.54/9.53	   A^2 -> H(a, U1(k, b))
28.54/9.53	   A^2 -> H(a, U1(c, d))
28.54/9.53	   A^2 -> H(a, U1(d, c))
28.54/9.53	   A^2 -> H(a, U1(b, e))
28.54/9.53	   A^2 -> H(a, U1(b, k))
28.54/9.53	   A^2 -> H(a, U1(e, c))
28.54/9.53	   A^2 -> H(a, U1(k, c))
28.54/9.53	   A^2 -> H(a, U1(c, e))
28.54/9.53	   A^2 -> H(a, U1(c, k))
28.54/9.53	   A^2 -> H(a, U1(e, e))
28.54/9.53	   A^2 -> H(a, U1(k, k))
28.54/9.53	   A^2 -> H(a, U1(k, d))
28.54/9.53	   A^2 -> H(a, U1(d, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.53	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.53	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.53	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.53	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.53	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.53	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.53	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.53	   A^2 -> H(U1(e, a), b)
28.54/9.53	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.53	   A^2 -> H(U1(e, a), c)
28.54/9.53	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.53	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.53	   A^2 -> H(U1(e, a), e)
28.54/9.53	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, a), b)
28.54/9.53	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.53	
28.54/9.53	The TRS R consists of the following rules:
28.54/9.53	
28.54/9.53	   f(x) -> U1(x, x)
28.54/9.53	   U1(e, x) -> x
28.54/9.53	   a -> c
28.54/9.53	   a -> d
28.54/9.53	   b -> c
28.54/9.53	   b -> d
28.54/9.53	   d -> k
28.54/9.53	   c -> e
28.54/9.53	   c -> k
28.54/9.53	
28.54/9.53	Q is empty.
28.54/9.53	We have to consider all minimal (P,Q,R)-chains.
28.54/9.53	----------------------------------------
28.54/9.53	
28.54/9.53	(1171) TransformationProof (EQUIVALENT)
28.54/9.53	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.53	
28.54/9.53	   (A^2 -> H(U1(k, c), U1(e, c)),A^2 -> H(U1(k, c), U1(e, c)))
28.54/9.53	   (A^2 -> H(U1(k, d), U1(e, c)),A^2 -> H(U1(k, d), U1(e, c)))
28.54/9.53	   (A^2 -> H(U1(k, a), c),A^2 -> H(U1(k, a), c))
28.54/9.53	   (A^2 -> H(U1(k, a), U1(e, e)),A^2 -> H(U1(k, a), U1(e, e)))
28.54/9.53	   (A^2 -> H(U1(k, a), U1(e, k)),A^2 -> H(U1(k, a), U1(e, k)))
28.54/9.53	
28.54/9.53	
28.54/9.53	----------------------------------------
28.54/9.53	
28.54/9.53	(1172)
28.54/9.53	Obligation:
28.54/9.53	Q DP problem:
28.54/9.53	The TRS P consists of the following rules:
28.54/9.53	
28.54/9.53	   H(x, x) -> G(x, x, f(k))
28.54/9.53	   G(d, x, x) -> A^2
28.54/9.53	   A^2 -> H(f(c), f(c))
28.54/9.53	   A^2 -> H(f(d), f(d))
28.54/9.53	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.53	   A^2 -> H(f(e), f(e))
28.54/9.53	   A^2 -> H(f(k), f(k))
28.54/9.53	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.53	   A^2 -> H(U1(k, a), U1(k, c))
28.54/9.53	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.53	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.53	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.53	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.53	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.53	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.53	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.53	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.53	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.53	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.53	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.53	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.53	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.53	   A^2 -> H(U1(c, a), b)
28.54/9.53	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.53	   A^2 -> H(U1(c, a), c)
28.54/9.53	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.53	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.53	   A^2 -> H(U1(c, a), e)
28.54/9.53	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.53	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.53	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.53	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.53	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.53	   A^2 -> H(U1(d, e), f(e))
28.54/9.53	   A^2 -> H(U1(d, e), f(k))
28.54/9.53	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.53	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.53	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.53	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.53	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.53	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.53	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.53	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.53	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.53	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.53	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.53	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.53	   A^2 -> H(U1(d, a), b)
28.54/9.53	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.53	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.53	   A^2 -> H(U1(d, a), c)
28.54/9.53	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.53	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.53	   A^2 -> H(U1(d, a), e)
28.54/9.53	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.53	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.53	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.53	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.53	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.53	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.53	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.53	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.53	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.53	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.53	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.53	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.53	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.53	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.53	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.54	   A^2 -> H(U1(a, c), b)
28.54/9.54	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.54	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.54	   A^2 -> H(U1(a, c), c)
28.54/9.54	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.54	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.54	   A^2 -> H(U1(a, c), e)
28.54/9.54	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, d), b)
28.54/9.54	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.54	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.54	   A^2 -> H(U1(a, d), c)
28.54/9.54	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.54	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.54	   A^2 -> H(U1(a, d), e)
28.54/9.54	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, a), d)
28.54/9.54	   A^2 -> H(U1(a, a), k)
28.54/9.54	   A^2 -> H(k, U1(b, b))
28.54/9.54	   A^2 -> H(k, f(c))
28.54/9.54	   A^2 -> H(k, f(d))
28.54/9.54	   A^2 -> H(c, U1(c, b))
28.54/9.54	   A^2 -> H(c, U1(d, b))
28.54/9.54	   A^2 -> H(c, U1(b, c))
28.54/9.54	   A^2 -> H(c, U1(b, d))
28.54/9.54	   A^2 -> H(c, U1(c, c))
28.54/9.54	   A^2 -> H(c, f(e))
28.54/9.54	   A^2 -> H(c, f(k))
28.54/9.54	   A^2 -> H(c, U1(d, d))
28.54/9.54	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.54	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.54	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.54	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.54	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.54	   A^2 -> H(U1(e, k), f(e))
28.54/9.54	   A^2 -> H(U1(e, k), f(k))
28.54/9.54	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.54	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.54	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.54	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.54	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.54	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.54	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.54	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.54	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.54	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.54	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.54	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.54	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.54	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.54	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.54	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.54	   A^2 -> H(U1(k, e), f(e))
28.54/9.54	   A^2 -> H(U1(k, e), f(k))
28.54/9.54	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.54	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.54	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.54	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.54	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.54	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.54	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.54	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.54	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.54	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.54	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.54	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.54	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.54	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.54	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.54	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, c), b)
28.54/9.54	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.54	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.54	   A^2 -> H(U1(c, c), e)
28.54/9.54	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.54	   A^2 -> H(e, U1(c, b))
28.54/9.54	   A^2 -> H(e, U1(d, b))
28.54/9.54	   A^2 -> H(e, U1(b, c))
28.54/9.54	   A^2 -> H(e, U1(b, d))
28.54/9.54	   A^2 -> H(e, U1(c, c))
28.54/9.54	   A^2 -> H(e, f(e))
28.54/9.54	   A^2 -> H(e, f(k))
28.54/9.54	   A^2 -> H(e, U1(d, d))
28.54/9.54	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.54	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.54	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.54	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.54	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.54	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.54	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.54	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.54	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.54	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.54	   A^2 -> H(f(e), b)
28.54/9.54	   A^2 -> H(f(e), U1(e, d))
28.54/9.54	   A^2 -> H(f(e), U1(d, e))
28.54/9.54	   A^2 -> H(f(e), c)
28.54/9.54	   A^2 -> H(f(e), U1(e, k))
28.54/9.54	   A^2 -> H(f(e), U1(k, e))
28.54/9.54	   A^2 -> H(f(e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.54	   A^2 -> H(f(k), b)
28.54/9.54	   A^2 -> H(f(k), U1(e, d))
28.54/9.54	   A^2 -> H(f(k), U1(d, e))
28.54/9.54	   A^2 -> H(f(k), c)
28.54/9.54	   A^2 -> H(f(k), U1(e, k))
28.54/9.54	   A^2 -> H(f(k), U1(k, e))
28.54/9.54	   A^2 -> H(f(k), e)
28.54/9.54	   A^2 -> H(f(c), d)
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.54	   A^2 -> H(U1(k, k), f(e))
28.54/9.54	   A^2 -> H(U1(k, k), f(k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.54	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.54	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.54	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.54	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.54	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.54	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.54	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.54	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.54	   A^2 -> H(U1(d, d), b)
28.54/9.54	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.54	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.54	   A^2 -> H(U1(d, d), c)
28.54/9.54	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.54	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.54	   A^2 -> H(U1(d, d), e)
28.54/9.54	   A^2 -> H(f(d), d)
28.54/9.54	   A^2 -> H(f(d), k)
28.54/9.54	   A^2 -> H(U1(c, c), c)
28.54/9.54	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.54	   A^2 -> H(f(c), k)
28.54/9.54	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.54	   A^2 -> H(f(k), U1(k, k))
28.54/9.54	   A^2 -> H(f(e), e)
28.54/9.54	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.54	   A^2 -> H(d, U1(c, b))
28.54/9.54	   A^2 -> H(d, U1(d, b))
28.54/9.54	   A^2 -> H(d, U1(b, c))
28.54/9.54	   A^2 -> H(d, U1(b, d))
28.54/9.54	   A^2 -> H(d, U1(c, c))
28.54/9.54	   A^2 -> H(d, f(e))
28.54/9.54	   A^2 -> H(d, f(k))
28.54/9.54	   A^2 -> H(d, U1(d, d))
28.54/9.54	   A^2 -> H(a, U1(e, b))
28.54/9.54	   A^2 -> H(a, U1(k, b))
28.54/9.54	   A^2 -> H(a, U1(c, d))
28.54/9.54	   A^2 -> H(a, U1(d, c))
28.54/9.54	   A^2 -> H(a, U1(b, e))
28.54/9.54	   A^2 -> H(a, U1(b, k))
28.54/9.54	   A^2 -> H(a, U1(e, c))
28.54/9.54	   A^2 -> H(a, U1(k, c))
28.54/9.54	   A^2 -> H(a, U1(c, e))
28.54/9.54	   A^2 -> H(a, U1(c, k))
28.54/9.54	   A^2 -> H(a, U1(e, e))
28.54/9.54	   A^2 -> H(a, U1(k, k))
28.54/9.54	   A^2 -> H(a, U1(k, d))
28.54/9.54	   A^2 -> H(a, U1(d, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.54	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.54	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.54	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.54	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.54	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.54	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.54	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.54	   A^2 -> H(U1(e, a), b)
28.54/9.54	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(e, a), c)
28.54/9.54	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.54	   A^2 -> H(U1(e, a), e)
28.54/9.54	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, a), b)
28.54/9.54	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(k, a), c)
28.54/9.54	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.54	
28.54/9.54	The TRS R consists of the following rules:
28.54/9.54	
28.54/9.54	   f(x) -> U1(x, x)
28.54/9.54	   U1(e, x) -> x
28.54/9.54	   a -> c
28.54/9.54	   a -> d
28.54/9.54	   b -> c
28.54/9.54	   b -> d
28.54/9.54	   d -> k
28.54/9.54	   c -> e
28.54/9.54	   c -> k
28.54/9.54	
28.54/9.54	Q is empty.
28.54/9.54	We have to consider all minimal (P,Q,R)-chains.
28.54/9.54	----------------------------------------
28.54/9.54	
28.54/9.54	(1173) TransformationProof (EQUIVALENT)
28.54/9.54	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.54	
28.54/9.54	   (A^2 -> H(U1(k, c), U1(k, c)),A^2 -> H(U1(k, c), U1(k, c)))
28.54/9.54	   (A^2 -> H(U1(k, d), U1(k, c)),A^2 -> H(U1(k, d), U1(k, c)))
28.54/9.54	   (A^2 -> H(U1(k, a), U1(k, e)),A^2 -> H(U1(k, a), U1(k, e)))
28.54/9.54	   (A^2 -> H(U1(k, a), U1(k, k)),A^2 -> H(U1(k, a), U1(k, k)))
28.54/9.54	
28.54/9.54	
28.54/9.54	----------------------------------------
28.54/9.54	
28.54/9.54	(1174)
28.54/9.54	Obligation:
28.54/9.54	Q DP problem:
28.54/9.54	The TRS P consists of the following rules:
28.54/9.54	
28.54/9.54	   H(x, x) -> G(x, x, f(k))
28.54/9.54	   G(d, x, x) -> A^2
28.54/9.54	   A^2 -> H(f(c), f(c))
28.54/9.54	   A^2 -> H(f(d), f(d))
28.54/9.54	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.54	   A^2 -> H(f(e), f(e))
28.54/9.54	   A^2 -> H(f(k), f(k))
28.54/9.54	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.54	   A^2 -> H(U1(k, a), U1(c, e))
28.54/9.54	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.54	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.54	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.54	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.54	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.54	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.54	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.54	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, a), b)
28.54/9.54	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(c, a), c)
28.54/9.54	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.54	   A^2 -> H(U1(c, a), e)
28.54/9.54	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.54	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.54	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.54	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.54	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.54	   A^2 -> H(U1(d, e), f(e))
28.54/9.54	   A^2 -> H(U1(d, e), f(k))
28.54/9.54	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.54	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.54	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.54	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.54	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.54	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.54	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.54	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.54	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.54	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.54	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.54	   A^2 -> H(U1(d, a), b)
28.54/9.54	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(d, a), c)
28.54/9.54	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.54	   A^2 -> H(U1(d, a), e)
28.54/9.54	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.54	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.54	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.54	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.54	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.54	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.54	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.54	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.54	   A^2 -> H(U1(a, c), b)
28.54/9.54	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.54	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.54	   A^2 -> H(U1(a, c), c)
28.54/9.54	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.54	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.54	   A^2 -> H(U1(a, c), e)
28.54/9.54	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, d), b)
28.54/9.54	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.54	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.54	   A^2 -> H(U1(a, d), c)
28.54/9.54	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.54	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.54	   A^2 -> H(U1(a, d), e)
28.54/9.54	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, a), d)
28.54/9.54	   A^2 -> H(U1(a, a), k)
28.54/9.54	   A^2 -> H(k, U1(b, b))
28.54/9.54	   A^2 -> H(k, f(c))
28.54/9.54	   A^2 -> H(k, f(d))
28.54/9.54	   A^2 -> H(c, U1(c, b))
28.54/9.54	   A^2 -> H(c, U1(d, b))
28.54/9.54	   A^2 -> H(c, U1(b, c))
28.54/9.54	   A^2 -> H(c, U1(b, d))
28.54/9.54	   A^2 -> H(c, U1(c, c))
28.54/9.54	   A^2 -> H(c, f(e))
28.54/9.54	   A^2 -> H(c, f(k))
28.54/9.54	   A^2 -> H(c, U1(d, d))
28.54/9.54	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.54	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.54	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.54	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.54	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.54	   A^2 -> H(U1(e, k), f(e))
28.54/9.54	   A^2 -> H(U1(e, k), f(k))
28.54/9.54	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.54	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.54	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.54	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.54	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.54	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.54	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.54	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.54	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.54	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.54	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.54	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.54	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.54	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.54	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.54	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.54	   A^2 -> H(U1(k, e), f(e))
28.54/9.54	   A^2 -> H(U1(k, e), f(k))
28.54/9.54	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.54	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.54	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.54	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.54	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.54	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.54	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.54	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.54	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.54	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.54	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.54	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.54	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.54	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.54	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.54	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, c), b)
28.54/9.54	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.54	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.54	   A^2 -> H(U1(c, c), e)
28.54/9.54	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.54	   A^2 -> H(e, U1(c, b))
28.54/9.54	   A^2 -> H(e, U1(d, b))
28.54/9.54	   A^2 -> H(e, U1(b, c))
28.54/9.54	   A^2 -> H(e, U1(b, d))
28.54/9.54	   A^2 -> H(e, U1(c, c))
28.54/9.54	   A^2 -> H(e, f(e))
28.54/9.54	   A^2 -> H(e, f(k))
28.54/9.54	   A^2 -> H(e, U1(d, d))
28.54/9.54	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.54	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.54	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.54	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.54	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.54	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.54	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.54	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.54	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.54	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.54	   A^2 -> H(f(e), b)
28.54/9.54	   A^2 -> H(f(e), U1(e, d))
28.54/9.54	   A^2 -> H(f(e), U1(d, e))
28.54/9.54	   A^2 -> H(f(e), c)
28.54/9.54	   A^2 -> H(f(e), U1(e, k))
28.54/9.54	   A^2 -> H(f(e), U1(k, e))
28.54/9.54	   A^2 -> H(f(e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.54	   A^2 -> H(f(k), b)
28.54/9.54	   A^2 -> H(f(k), U1(e, d))
28.54/9.54	   A^2 -> H(f(k), U1(d, e))
28.54/9.54	   A^2 -> H(f(k), c)
28.54/9.54	   A^2 -> H(f(k), U1(e, k))
28.54/9.54	   A^2 -> H(f(k), U1(k, e))
28.54/9.54	   A^2 -> H(f(k), e)
28.54/9.54	   A^2 -> H(f(c), d)
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.54	   A^2 -> H(U1(k, k), f(e))
28.54/9.54	   A^2 -> H(U1(k, k), f(k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.54	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.54	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.54	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.54	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.54	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.54	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.54	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.54	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.54	   A^2 -> H(U1(d, d), b)
28.54/9.54	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.54	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.54	   A^2 -> H(U1(d, d), c)
28.54/9.54	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.54	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.54	   A^2 -> H(U1(d, d), e)
28.54/9.54	   A^2 -> H(f(d), d)
28.54/9.54	   A^2 -> H(f(d), k)
28.54/9.54	   A^2 -> H(U1(c, c), c)
28.54/9.54	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.54	   A^2 -> H(f(c), k)
28.54/9.54	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.54	   A^2 -> H(f(k), U1(k, k))
28.54/9.54	   A^2 -> H(f(e), e)
28.54/9.54	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.54	   A^2 -> H(d, U1(c, b))
28.54/9.54	   A^2 -> H(d, U1(d, b))
28.54/9.54	   A^2 -> H(d, U1(b, c))
28.54/9.54	   A^2 -> H(d, U1(b, d))
28.54/9.54	   A^2 -> H(d, U1(c, c))
28.54/9.54	   A^2 -> H(d, f(e))
28.54/9.54	   A^2 -> H(d, f(k))
28.54/9.54	   A^2 -> H(d, U1(d, d))
28.54/9.54	   A^2 -> H(a, U1(e, b))
28.54/9.54	   A^2 -> H(a, U1(k, b))
28.54/9.54	   A^2 -> H(a, U1(c, d))
28.54/9.54	   A^2 -> H(a, U1(d, c))
28.54/9.54	   A^2 -> H(a, U1(b, e))
28.54/9.54	   A^2 -> H(a, U1(b, k))
28.54/9.54	   A^2 -> H(a, U1(e, c))
28.54/9.54	   A^2 -> H(a, U1(k, c))
28.54/9.54	   A^2 -> H(a, U1(c, e))
28.54/9.54	   A^2 -> H(a, U1(c, k))
28.54/9.54	   A^2 -> H(a, U1(e, e))
28.54/9.54	   A^2 -> H(a, U1(k, k))
28.54/9.54	   A^2 -> H(a, U1(k, d))
28.54/9.54	   A^2 -> H(a, U1(d, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.54	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.54	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.54	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.54	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.54	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.54	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.54	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.54	   A^2 -> H(U1(e, a), b)
28.54/9.54	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(e, a), c)
28.54/9.54	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.54	   A^2 -> H(U1(e, a), e)
28.54/9.54	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, a), b)
28.54/9.54	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(k, a), c)
28.54/9.54	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.54	
28.54/9.54	The TRS R consists of the following rules:
28.54/9.54	
28.54/9.54	   f(x) -> U1(x, x)
28.54/9.54	   U1(e, x) -> x
28.54/9.54	   a -> c
28.54/9.54	   a -> d
28.54/9.54	   b -> c
28.54/9.54	   b -> d
28.54/9.54	   d -> k
28.54/9.54	   c -> e
28.54/9.54	   c -> k
28.54/9.54	
28.54/9.54	Q is empty.
28.54/9.54	We have to consider all minimal (P,Q,R)-chains.
28.54/9.54	----------------------------------------
28.54/9.54	
28.54/9.54	(1175) TransformationProof (EQUIVALENT)
28.54/9.54	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.54	
28.54/9.54	   (A^2 -> H(U1(k, c), U1(c, e)),A^2 -> H(U1(k, c), U1(c, e)))
28.54/9.54	   (A^2 -> H(U1(k, d), U1(c, e)),A^2 -> H(U1(k, d), U1(c, e)))
28.54/9.54	   (A^2 -> H(U1(k, a), U1(e, e)),A^2 -> H(U1(k, a), U1(e, e)))
28.54/9.54	   (A^2 -> H(U1(k, a), U1(k, e)),A^2 -> H(U1(k, a), U1(k, e)))
28.54/9.54	
28.54/9.54	
28.54/9.54	----------------------------------------
28.54/9.54	
28.54/9.54	(1176)
28.54/9.54	Obligation:
28.54/9.54	Q DP problem:
28.54/9.54	The TRS P consists of the following rules:
28.54/9.54	
28.54/9.54	   H(x, x) -> G(x, x, f(k))
28.54/9.54	   G(d, x, x) -> A^2
28.54/9.54	   A^2 -> H(f(c), f(c))
28.54/9.54	   A^2 -> H(f(d), f(d))
28.54/9.54	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.54	   A^2 -> H(f(e), f(e))
28.54/9.54	   A^2 -> H(f(k), f(k))
28.54/9.54	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.54	   A^2 -> H(U1(k, a), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.54	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.54	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.54	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.54	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.54	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.54	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.54	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, a), b)
28.54/9.54	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(c, a), c)
28.54/9.54	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.54	   A^2 -> H(U1(c, a), e)
28.54/9.54	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.54	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.54	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.54	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.54	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.54	   A^2 -> H(U1(d, e), f(e))
28.54/9.54	   A^2 -> H(U1(d, e), f(k))
28.54/9.54	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.54	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.54	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.54	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.54	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.54	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.54	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.54	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.54	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.54	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.54	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.54	   A^2 -> H(U1(d, a), b)
28.54/9.54	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(d, a), c)
28.54/9.54	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.54	   A^2 -> H(U1(d, a), e)
28.54/9.54	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.54	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.54	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.54	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.54	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.54	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.54	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.54	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.54	   A^2 -> H(U1(a, c), b)
28.54/9.54	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.54	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.54	   A^2 -> H(U1(a, c), c)
28.54/9.54	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.54	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.54	   A^2 -> H(U1(a, c), e)
28.54/9.54	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, d), b)
28.54/9.54	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.54	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.54	   A^2 -> H(U1(a, d), c)
28.54/9.54	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.54	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.54	   A^2 -> H(U1(a, d), e)
28.54/9.54	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, a), d)
28.54/9.54	   A^2 -> H(U1(a, a), k)
28.54/9.54	   A^2 -> H(k, U1(b, b))
28.54/9.54	   A^2 -> H(k, f(c))
28.54/9.54	   A^2 -> H(k, f(d))
28.54/9.54	   A^2 -> H(c, U1(c, b))
28.54/9.54	   A^2 -> H(c, U1(d, b))
28.54/9.54	   A^2 -> H(c, U1(b, c))
28.54/9.54	   A^2 -> H(c, U1(b, d))
28.54/9.54	   A^2 -> H(c, U1(c, c))
28.54/9.54	   A^2 -> H(c, f(e))
28.54/9.54	   A^2 -> H(c, f(k))
28.54/9.54	   A^2 -> H(c, U1(d, d))
28.54/9.54	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.54	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.54	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.54	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.54	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.54	   A^2 -> H(U1(e, k), f(e))
28.54/9.54	   A^2 -> H(U1(e, k), f(k))
28.54/9.54	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.54	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.54	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.54	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.54	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.54	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.54	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.54	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.54	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.54	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.54	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.54	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.54	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.54	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.54	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.54	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.54	   A^2 -> H(U1(k, e), f(e))
28.54/9.54	   A^2 -> H(U1(k, e), f(k))
28.54/9.54	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.54	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.54	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.54	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.54	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.54	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.54	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.54	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.54	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.54	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.54	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.54	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.54	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.54	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.54	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.54	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, c), b)
28.54/9.54	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.54	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.54	   A^2 -> H(U1(c, c), e)
28.54/9.54	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.54	   A^2 -> H(e, U1(c, b))
28.54/9.54	   A^2 -> H(e, U1(d, b))
28.54/9.54	   A^2 -> H(e, U1(b, c))
28.54/9.54	   A^2 -> H(e, U1(b, d))
28.54/9.54	   A^2 -> H(e, U1(c, c))
28.54/9.54	   A^2 -> H(e, f(e))
28.54/9.54	   A^2 -> H(e, f(k))
28.54/9.54	   A^2 -> H(e, U1(d, d))
28.54/9.54	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.54	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.54	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.54	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.54	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.54	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.54	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.54	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.54	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.54	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.54	   A^2 -> H(f(e), b)
28.54/9.54	   A^2 -> H(f(e), U1(e, d))
28.54/9.54	   A^2 -> H(f(e), U1(d, e))
28.54/9.54	   A^2 -> H(f(e), c)
28.54/9.54	   A^2 -> H(f(e), U1(e, k))
28.54/9.54	   A^2 -> H(f(e), U1(k, e))
28.54/9.54	   A^2 -> H(f(e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.54	   A^2 -> H(f(k), b)
28.54/9.54	   A^2 -> H(f(k), U1(e, d))
28.54/9.54	   A^2 -> H(f(k), U1(d, e))
28.54/9.54	   A^2 -> H(f(k), c)
28.54/9.54	   A^2 -> H(f(k), U1(e, k))
28.54/9.54	   A^2 -> H(f(k), U1(k, e))
28.54/9.54	   A^2 -> H(f(k), e)
28.54/9.54	   A^2 -> H(f(c), d)
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.54	   A^2 -> H(U1(k, k), f(e))
28.54/9.54	   A^2 -> H(U1(k, k), f(k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.54	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.54	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.54	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.54	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.54	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.54	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.54	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.54	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.54	   A^2 -> H(U1(d, d), b)
28.54/9.54	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.54	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.54	   A^2 -> H(U1(d, d), c)
28.54/9.54	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.54	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.54	   A^2 -> H(U1(d, d), e)
28.54/9.54	   A^2 -> H(f(d), d)
28.54/9.54	   A^2 -> H(f(d), k)
28.54/9.54	   A^2 -> H(U1(c, c), c)
28.54/9.54	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.54	   A^2 -> H(f(c), k)
28.54/9.54	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.54	   A^2 -> H(f(k), U1(k, k))
28.54/9.54	   A^2 -> H(f(e), e)
28.54/9.54	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.54	   A^2 -> H(d, U1(c, b))
28.54/9.54	   A^2 -> H(d, U1(d, b))
28.54/9.54	   A^2 -> H(d, U1(b, c))
28.54/9.54	   A^2 -> H(d, U1(b, d))
28.54/9.54	   A^2 -> H(d, U1(c, c))
28.54/9.54	   A^2 -> H(d, f(e))
28.54/9.54	   A^2 -> H(d, f(k))
28.54/9.54	   A^2 -> H(d, U1(d, d))
28.54/9.54	   A^2 -> H(a, U1(e, b))
28.54/9.54	   A^2 -> H(a, U1(k, b))
28.54/9.54	   A^2 -> H(a, U1(c, d))
28.54/9.54	   A^2 -> H(a, U1(d, c))
28.54/9.54	   A^2 -> H(a, U1(b, e))
28.54/9.54	   A^2 -> H(a, U1(b, k))
28.54/9.54	   A^2 -> H(a, U1(e, c))
28.54/9.54	   A^2 -> H(a, U1(k, c))
28.54/9.54	   A^2 -> H(a, U1(c, e))
28.54/9.54	   A^2 -> H(a, U1(c, k))
28.54/9.54	   A^2 -> H(a, U1(e, e))
28.54/9.54	   A^2 -> H(a, U1(k, k))
28.54/9.54	   A^2 -> H(a, U1(k, d))
28.54/9.54	   A^2 -> H(a, U1(d, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.54	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.54	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.54	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.54	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.54	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.54	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.54	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.54	   A^2 -> H(U1(e, a), b)
28.54/9.54	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(e, a), c)
28.54/9.54	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.54	   A^2 -> H(U1(e, a), e)
28.54/9.54	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, a), b)
28.54/9.54	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(k, a), c)
28.54/9.54	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.54	
28.54/9.54	The TRS R consists of the following rules:
28.54/9.54	
28.54/9.54	   f(x) -> U1(x, x)
28.54/9.54	   U1(e, x) -> x
28.54/9.54	   a -> c
28.54/9.54	   a -> d
28.54/9.54	   b -> c
28.54/9.54	   b -> d
28.54/9.54	   d -> k
28.54/9.54	   c -> e
28.54/9.54	   c -> k
28.54/9.54	
28.54/9.54	Q is empty.
28.54/9.54	We have to consider all minimal (P,Q,R)-chains.
28.54/9.54	----------------------------------------
28.54/9.54	
28.54/9.54	(1177) TransformationProof (EQUIVALENT)
28.54/9.54	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.54	
28.54/9.54	   (A^2 -> H(U1(k, c), U1(c, k)),A^2 -> H(U1(k, c), U1(c, k)))
28.54/9.54	   (A^2 -> H(U1(k, d), U1(c, k)),A^2 -> H(U1(k, d), U1(c, k)))
28.54/9.54	   (A^2 -> H(U1(k, a), U1(e, k)),A^2 -> H(U1(k, a), U1(e, k)))
28.54/9.54	   (A^2 -> H(U1(k, a), U1(k, k)),A^2 -> H(U1(k, a), U1(k, k)))
28.54/9.54	
28.54/9.54	
28.54/9.54	----------------------------------------
28.54/9.54	
28.54/9.54	(1178)
28.54/9.54	Obligation:
28.54/9.54	Q DP problem:
28.54/9.54	The TRS P consists of the following rules:
28.54/9.54	
28.54/9.54	   H(x, x) -> G(x, x, f(k))
28.54/9.54	   G(d, x, x) -> A^2
28.54/9.54	   A^2 -> H(f(c), f(c))
28.54/9.54	   A^2 -> H(f(d), f(d))
28.54/9.54	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.54	   A^2 -> H(f(e), f(e))
28.54/9.54	   A^2 -> H(f(k), f(k))
28.54/9.54	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.54	   A^2 -> H(U1(k, a), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.54	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.54	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.54	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.54	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.54	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.54	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.54	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, a), b)
28.54/9.54	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(c, a), c)
28.54/9.54	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.54	   A^2 -> H(U1(c, a), e)
28.54/9.54	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.54	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.54	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.54	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.54	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.54	   A^2 -> H(U1(d, e), f(e))
28.54/9.54	   A^2 -> H(U1(d, e), f(k))
28.54/9.54	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.54	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.54	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.54	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.54	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.54	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.54	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.54	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.54	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.54	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.54	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.54	   A^2 -> H(U1(d, a), b)
28.54/9.54	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(d, a), c)
28.54/9.54	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.54	   A^2 -> H(U1(d, a), e)
28.54/9.54	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.54	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.54	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.54	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.54	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.54	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.54	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.54	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.54	   A^2 -> H(U1(a, c), b)
28.54/9.54	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.54	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.54	   A^2 -> H(U1(a, c), c)
28.54/9.54	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.54	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.54	   A^2 -> H(U1(a, c), e)
28.54/9.54	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, d), b)
28.54/9.54	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.54	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.54	   A^2 -> H(U1(a, d), c)
28.54/9.54	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.54	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.54	   A^2 -> H(U1(a, d), e)
28.54/9.54	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, a), d)
28.54/9.54	   A^2 -> H(U1(a, a), k)
28.54/9.54	   A^2 -> H(k, U1(b, b))
28.54/9.54	   A^2 -> H(k, f(c))
28.54/9.54	   A^2 -> H(k, f(d))
28.54/9.54	   A^2 -> H(c, U1(c, b))
28.54/9.54	   A^2 -> H(c, U1(d, b))
28.54/9.54	   A^2 -> H(c, U1(b, c))
28.54/9.54	   A^2 -> H(c, U1(b, d))
28.54/9.54	   A^2 -> H(c, U1(c, c))
28.54/9.54	   A^2 -> H(c, f(e))
28.54/9.54	   A^2 -> H(c, f(k))
28.54/9.54	   A^2 -> H(c, U1(d, d))
28.54/9.54	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.54	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.54	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.54	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.54	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.54	   A^2 -> H(U1(e, k), f(e))
28.54/9.54	   A^2 -> H(U1(e, k), f(k))
28.54/9.54	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.54	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.54	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.54	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.54	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.54	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.54	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.54	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.54	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.54	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.54	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.54	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.54	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.54	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.54	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.54	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.54	   A^2 -> H(U1(k, e), f(e))
28.54/9.54	   A^2 -> H(U1(k, e), f(k))
28.54/9.54	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.54	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.54	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.54	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.54	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.54	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.54	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.54	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.54	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.54	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.54	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.54	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.54	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.54	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.54	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.54	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, c), b)
28.54/9.54	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.54	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.54	   A^2 -> H(U1(c, c), e)
28.54/9.54	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.54	   A^2 -> H(e, U1(c, b))
28.54/9.54	   A^2 -> H(e, U1(d, b))
28.54/9.54	   A^2 -> H(e, U1(b, c))
28.54/9.54	   A^2 -> H(e, U1(b, d))
28.54/9.54	   A^2 -> H(e, U1(c, c))
28.54/9.54	   A^2 -> H(e, f(e))
28.54/9.54	   A^2 -> H(e, f(k))
28.54/9.54	   A^2 -> H(e, U1(d, d))
28.54/9.54	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.54	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.54	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.54	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.54	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.54	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.54	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.54	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.54	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.54	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.54	   A^2 -> H(f(e), b)
28.54/9.54	   A^2 -> H(f(e), U1(e, d))
28.54/9.54	   A^2 -> H(f(e), U1(d, e))
28.54/9.54	   A^2 -> H(f(e), c)
28.54/9.54	   A^2 -> H(f(e), U1(e, k))
28.54/9.54	   A^2 -> H(f(e), U1(k, e))
28.54/9.54	   A^2 -> H(f(e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.54	   A^2 -> H(f(k), b)
28.54/9.54	   A^2 -> H(f(k), U1(e, d))
28.54/9.54	   A^2 -> H(f(k), U1(d, e))
28.54/9.54	   A^2 -> H(f(k), c)
28.54/9.54	   A^2 -> H(f(k), U1(e, k))
28.54/9.54	   A^2 -> H(f(k), U1(k, e))
28.54/9.54	   A^2 -> H(f(k), e)
28.54/9.54	   A^2 -> H(f(c), d)
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.54	   A^2 -> H(U1(k, k), f(e))
28.54/9.54	   A^2 -> H(U1(k, k), f(k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.54	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.54	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.54	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.54	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.54	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.54	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.54	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.54	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.54	   A^2 -> H(U1(d, d), b)
28.54/9.54	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.54	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.54	   A^2 -> H(U1(d, d), c)
28.54/9.54	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.54	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.54	   A^2 -> H(U1(d, d), e)
28.54/9.54	   A^2 -> H(f(d), d)
28.54/9.54	   A^2 -> H(f(d), k)
28.54/9.54	   A^2 -> H(U1(c, c), c)
28.54/9.54	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.54	   A^2 -> H(f(c), k)
28.54/9.54	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.54	   A^2 -> H(f(k), U1(k, k))
28.54/9.54	   A^2 -> H(f(e), e)
28.54/9.54	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.54	   A^2 -> H(d, U1(c, b))
28.54/9.54	   A^2 -> H(d, U1(d, b))
28.54/9.54	   A^2 -> H(d, U1(b, c))
28.54/9.54	   A^2 -> H(d, U1(b, d))
28.54/9.54	   A^2 -> H(d, U1(c, c))
28.54/9.54	   A^2 -> H(d, f(e))
28.54/9.54	   A^2 -> H(d, f(k))
28.54/9.54	   A^2 -> H(d, U1(d, d))
28.54/9.54	   A^2 -> H(a, U1(e, b))
28.54/9.54	   A^2 -> H(a, U1(k, b))
28.54/9.54	   A^2 -> H(a, U1(c, d))
28.54/9.54	   A^2 -> H(a, U1(d, c))
28.54/9.54	   A^2 -> H(a, U1(b, e))
28.54/9.54	   A^2 -> H(a, U1(b, k))
28.54/9.54	   A^2 -> H(a, U1(e, c))
28.54/9.54	   A^2 -> H(a, U1(k, c))
28.54/9.54	   A^2 -> H(a, U1(c, e))
28.54/9.54	   A^2 -> H(a, U1(c, k))
28.54/9.54	   A^2 -> H(a, U1(e, e))
28.54/9.54	   A^2 -> H(a, U1(k, k))
28.54/9.54	   A^2 -> H(a, U1(k, d))
28.54/9.54	   A^2 -> H(a, U1(d, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.54	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.54	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.54	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.54	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.54	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.54	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.54	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.54	   A^2 -> H(U1(e, a), b)
28.54/9.54	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(e, a), c)
28.54/9.54	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.54	   A^2 -> H(U1(e, a), e)
28.54/9.54	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, a), b)
28.54/9.54	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(k, a), c)
28.54/9.54	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.54	
28.54/9.54	The TRS R consists of the following rules:
28.54/9.54	
28.54/9.54	   f(x) -> U1(x, x)
28.54/9.54	   U1(e, x) -> x
28.54/9.54	   a -> c
28.54/9.54	   a -> d
28.54/9.54	   b -> c
28.54/9.54	   b -> d
28.54/9.54	   d -> k
28.54/9.54	   c -> e
28.54/9.54	   c -> k
28.54/9.54	
28.54/9.54	Q is empty.
28.54/9.54	We have to consider all minimal (P,Q,R)-chains.
28.54/9.54	----------------------------------------
28.54/9.54	
28.54/9.54	(1179) TransformationProof (EQUIVALENT)
28.54/9.54	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.54	
28.54/9.54	   (A^2 -> H(U1(k, c), U1(e, e)),A^2 -> H(U1(k, c), U1(e, e)))
28.54/9.54	   (A^2 -> H(U1(k, d), U1(e, e)),A^2 -> H(U1(k, d), U1(e, e)))
28.54/9.54	   (A^2 -> H(U1(k, a), e),A^2 -> H(U1(k, a), e))
28.54/9.54	
28.54/9.54	
28.54/9.54	----------------------------------------
28.54/9.54	
28.54/9.54	(1180)
28.54/9.54	Obligation:
28.54/9.54	Q DP problem:
28.54/9.54	The TRS P consists of the following rules:
28.54/9.54	
28.54/9.54	   H(x, x) -> G(x, x, f(k))
28.54/9.54	   G(d, x, x) -> A^2
28.54/9.54	   A^2 -> H(f(c), f(c))
28.54/9.54	   A^2 -> H(f(d), f(d))
28.54/9.54	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.54	   A^2 -> H(f(e), f(e))
28.54/9.54	   A^2 -> H(f(k), f(k))
28.54/9.54	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.54	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.54	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.54	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.54	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.54	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.54	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.54	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.54	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, a), b)
28.54/9.54	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(c, a), c)
28.54/9.54	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.54	   A^2 -> H(U1(c, a), e)
28.54/9.54	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.54	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.54	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.54	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.54	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.54	   A^2 -> H(U1(d, e), f(e))
28.54/9.54	   A^2 -> H(U1(d, e), f(k))
28.54/9.54	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.54	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.54	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.54	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.54	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.54	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.54	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.54	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.54	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.54	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.54	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.54	   A^2 -> H(U1(d, a), b)
28.54/9.54	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(d, a), c)
28.54/9.54	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.54	   A^2 -> H(U1(d, a), e)
28.54/9.54	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.54	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.54	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.54	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.54	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.54	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.54	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.54	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.54	   A^2 -> H(U1(a, c), b)
28.54/9.54	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.54	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.54	   A^2 -> H(U1(a, c), c)
28.54/9.54	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.54	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.54	   A^2 -> H(U1(a, c), e)
28.54/9.54	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, d), b)
28.54/9.54	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.54	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.54	   A^2 -> H(U1(a, d), c)
28.54/9.54	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.54	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.54	   A^2 -> H(U1(a, d), e)
28.54/9.54	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, a), d)
28.54/9.54	   A^2 -> H(U1(a, a), k)
28.54/9.54	   A^2 -> H(k, U1(b, b))
28.54/9.54	   A^2 -> H(k, f(c))
28.54/9.54	   A^2 -> H(k, f(d))
28.54/9.54	   A^2 -> H(c, U1(c, b))
28.54/9.54	   A^2 -> H(c, U1(d, b))
28.54/9.54	   A^2 -> H(c, U1(b, c))
28.54/9.54	   A^2 -> H(c, U1(b, d))
28.54/9.54	   A^2 -> H(c, U1(c, c))
28.54/9.54	   A^2 -> H(c, f(e))
28.54/9.54	   A^2 -> H(c, f(k))
28.54/9.54	   A^2 -> H(c, U1(d, d))
28.54/9.54	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.54	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.54	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.54	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.54	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.54	   A^2 -> H(U1(e, k), f(e))
28.54/9.54	   A^2 -> H(U1(e, k), f(k))
28.54/9.54	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.54	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.54	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.54	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.54	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.54	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.54	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.54	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.54	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.54	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.54	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.54	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.54	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.54	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.54	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.54	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.54	   A^2 -> H(U1(k, e), f(e))
28.54/9.54	   A^2 -> H(U1(k, e), f(k))
28.54/9.54	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.54	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.54	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.54	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.54	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.54	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.54	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.54	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.54	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.54	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.54	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.54	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.54	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.54	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.54	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.54	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, c), b)
28.54/9.54	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.54	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.54	   A^2 -> H(U1(c, c), e)
28.54/9.54	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.54	   A^2 -> H(e, U1(c, b))
28.54/9.54	   A^2 -> H(e, U1(d, b))
28.54/9.54	   A^2 -> H(e, U1(b, c))
28.54/9.54	   A^2 -> H(e, U1(b, d))
28.54/9.54	   A^2 -> H(e, U1(c, c))
28.54/9.54	   A^2 -> H(e, f(e))
28.54/9.54	   A^2 -> H(e, f(k))
28.54/9.54	   A^2 -> H(e, U1(d, d))
28.54/9.54	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.54	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.54	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.54	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.54	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.54	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.54	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.54	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.54	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.54	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.54	   A^2 -> H(f(e), b)
28.54/9.54	   A^2 -> H(f(e), U1(e, d))
28.54/9.54	   A^2 -> H(f(e), U1(d, e))
28.54/9.54	   A^2 -> H(f(e), c)
28.54/9.54	   A^2 -> H(f(e), U1(e, k))
28.54/9.54	   A^2 -> H(f(e), U1(k, e))
28.54/9.54	   A^2 -> H(f(e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.54	   A^2 -> H(f(k), b)
28.54/9.54	   A^2 -> H(f(k), U1(e, d))
28.54/9.54	   A^2 -> H(f(k), U1(d, e))
28.54/9.54	   A^2 -> H(f(k), c)
28.54/9.54	   A^2 -> H(f(k), U1(e, k))
28.54/9.54	   A^2 -> H(f(k), U1(k, e))
28.54/9.54	   A^2 -> H(f(k), e)
28.54/9.54	   A^2 -> H(f(c), d)
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.54	   A^2 -> H(U1(k, k), f(e))
28.54/9.54	   A^2 -> H(U1(k, k), f(k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.54	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.54	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.54	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.54	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.54	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.54	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.54	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.54	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.54	   A^2 -> H(U1(d, d), b)
28.54/9.54	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.54	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.54	   A^2 -> H(U1(d, d), c)
28.54/9.54	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.54	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.54	   A^2 -> H(U1(d, d), e)
28.54/9.54	   A^2 -> H(f(d), d)
28.54/9.54	   A^2 -> H(f(d), k)
28.54/9.54	   A^2 -> H(U1(c, c), c)
28.54/9.54	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.54	   A^2 -> H(f(c), k)
28.54/9.54	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.54	   A^2 -> H(f(k), U1(k, k))
28.54/9.54	   A^2 -> H(f(e), e)
28.54/9.54	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.54	   A^2 -> H(d, U1(c, b))
28.54/9.54	   A^2 -> H(d, U1(d, b))
28.54/9.54	   A^2 -> H(d, U1(b, c))
28.54/9.54	   A^2 -> H(d, U1(b, d))
28.54/9.54	   A^2 -> H(d, U1(c, c))
28.54/9.54	   A^2 -> H(d, f(e))
28.54/9.54	   A^2 -> H(d, f(k))
28.54/9.54	   A^2 -> H(d, U1(d, d))
28.54/9.54	   A^2 -> H(a, U1(e, b))
28.54/9.54	   A^2 -> H(a, U1(k, b))
28.54/9.54	   A^2 -> H(a, U1(c, d))
28.54/9.54	   A^2 -> H(a, U1(d, c))
28.54/9.54	   A^2 -> H(a, U1(b, e))
28.54/9.54	   A^2 -> H(a, U1(b, k))
28.54/9.54	   A^2 -> H(a, U1(e, c))
28.54/9.54	   A^2 -> H(a, U1(k, c))
28.54/9.54	   A^2 -> H(a, U1(c, e))
28.54/9.54	   A^2 -> H(a, U1(c, k))
28.54/9.54	   A^2 -> H(a, U1(e, e))
28.54/9.54	   A^2 -> H(a, U1(k, k))
28.54/9.54	   A^2 -> H(a, U1(k, d))
28.54/9.54	   A^2 -> H(a, U1(d, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.54	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.54	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.54	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.54	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.54	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.54	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.54	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.54	   A^2 -> H(U1(e, a), b)
28.54/9.54	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(e, a), c)
28.54/9.54	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.54	   A^2 -> H(U1(e, a), e)
28.54/9.54	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, a), b)
28.54/9.54	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(k, a), c)
28.54/9.54	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.54	   A^2 -> H(U1(k, a), e)
28.54/9.54	
28.54/9.54	The TRS R consists of the following rules:
28.54/9.54	
28.54/9.54	   f(x) -> U1(x, x)
28.54/9.54	   U1(e, x) -> x
28.54/9.54	   a -> c
28.54/9.54	   a -> d
28.54/9.54	   b -> c
28.54/9.54	   b -> d
28.54/9.54	   d -> k
28.54/9.54	   c -> e
28.54/9.54	   c -> k
28.54/9.54	
28.54/9.54	Q is empty.
28.54/9.54	We have to consider all minimal (P,Q,R)-chains.
28.54/9.54	----------------------------------------
28.54/9.54	
28.54/9.54	(1181) DependencyGraphProof (EQUIVALENT)
28.54/9.54	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.54/9.54	----------------------------------------
28.54/9.54	
28.54/9.54	(1182)
28.54/9.54	Obligation:
28.54/9.54	Q DP problem:
28.54/9.54	The TRS P consists of the following rules:
28.54/9.54	
28.54/9.54	   G(d, x, x) -> A^2
28.54/9.54	   A^2 -> H(f(c), f(c))
28.54/9.54	   H(x, x) -> G(x, x, f(k))
28.54/9.54	   A^2 -> H(f(d), f(d))
28.54/9.54	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.54	   A^2 -> H(f(e), f(e))
28.54/9.54	   A^2 -> H(f(k), f(k))
28.54/9.54	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.54	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.54	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.54	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.54	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.54	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.54	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.54	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.54	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, a), b)
28.54/9.54	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(c, a), c)
28.54/9.54	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.54	   A^2 -> H(U1(c, a), e)
28.54/9.54	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.54	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.54	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.54	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.54	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.54	   A^2 -> H(U1(d, e), f(e))
28.54/9.54	   A^2 -> H(U1(d, e), f(k))
28.54/9.54	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.54	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.54	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.54	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.54	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.54	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.54	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.54	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.54	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.54	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.54	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.54	   A^2 -> H(U1(d, a), b)
28.54/9.54	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.54	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.54	   A^2 -> H(U1(d, a), c)
28.54/9.54	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.54	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.54	   A^2 -> H(U1(d, a), e)
28.54/9.54	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.54	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.54	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.54	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.54	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.54	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.54	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.54	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.54	   A^2 -> H(U1(a, c), b)
28.54/9.54	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.54	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.54	   A^2 -> H(U1(a, c), c)
28.54/9.54	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.54	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.54	   A^2 -> H(U1(a, c), e)
28.54/9.54	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, d), b)
28.54/9.54	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.54	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.54	   A^2 -> H(U1(a, d), c)
28.54/9.54	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.54	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.54	   A^2 -> H(U1(a, d), e)
28.54/9.54	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.54	   A^2 -> H(U1(a, a), d)
28.54/9.54	   A^2 -> H(U1(a, a), k)
28.54/9.54	   A^2 -> H(k, U1(b, b))
28.54/9.54	   A^2 -> H(k, f(c))
28.54/9.54	   A^2 -> H(k, f(d))
28.54/9.54	   A^2 -> H(c, U1(c, b))
28.54/9.54	   A^2 -> H(c, U1(d, b))
28.54/9.54	   A^2 -> H(c, U1(b, c))
28.54/9.54	   A^2 -> H(c, U1(b, d))
28.54/9.54	   A^2 -> H(c, U1(c, c))
28.54/9.54	   A^2 -> H(c, f(e))
28.54/9.54	   A^2 -> H(c, f(k))
28.54/9.54	   A^2 -> H(c, U1(d, d))
28.54/9.54	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.54	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.54	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.54	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.54	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.54	   A^2 -> H(U1(e, k), f(e))
28.54/9.54	   A^2 -> H(U1(e, k), f(k))
28.54/9.54	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.54	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.54	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.54	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.54	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.54	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.54	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.54	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.54	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.54	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.54	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.54	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.54	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.54	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.54	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.54	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.54	   A^2 -> H(U1(k, e), f(e))
28.54/9.54	   A^2 -> H(U1(k, e), f(k))
28.54/9.54	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.54	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.54	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.54	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.54	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.54	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.54	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.54	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.54	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.54	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.54	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.54	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.54	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.54	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.54	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.54	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.54	   A^2 -> H(U1(c, c), b)
28.54/9.54	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.54	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.54	   A^2 -> H(U1(c, c), e)
28.54/9.54	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.54	   A^2 -> H(e, U1(c, b))
28.54/9.54	   A^2 -> H(e, U1(d, b))
28.54/9.54	   A^2 -> H(e, U1(b, c))
28.54/9.54	   A^2 -> H(e, U1(b, d))
28.54/9.54	   A^2 -> H(e, U1(c, c))
28.54/9.54	   A^2 -> H(e, f(e))
28.54/9.54	   A^2 -> H(e, f(k))
28.54/9.54	   A^2 -> H(e, U1(d, d))
28.54/9.54	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.54	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.54	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.54	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.54	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.54	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.54	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.54	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.54	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.54	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.54	   A^2 -> H(f(e), b)
28.54/9.54	   A^2 -> H(f(e), U1(e, d))
28.54/9.54	   A^2 -> H(f(e), U1(d, e))
28.54/9.54	   A^2 -> H(f(e), c)
28.54/9.54	   A^2 -> H(f(e), U1(e, k))
28.54/9.54	   A^2 -> H(f(e), U1(k, e))
28.54/9.54	   A^2 -> H(f(e), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.54	   A^2 -> H(f(k), b)
28.54/9.54	   A^2 -> H(f(k), U1(e, d))
28.54/9.54	   A^2 -> H(f(k), U1(d, e))
28.54/9.54	   A^2 -> H(f(k), c)
28.54/9.54	   A^2 -> H(f(k), U1(e, k))
28.54/9.54	   A^2 -> H(f(k), U1(k, e))
28.54/9.54	   A^2 -> H(f(k), e)
28.54/9.54	   A^2 -> H(f(c), d)
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.54	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.54	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.54	   A^2 -> H(U1(k, k), f(e))
28.54/9.54	   A^2 -> H(U1(k, k), f(k))
28.54/9.54	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.54	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.54	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.54	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.54	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.55	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.55	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.55	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.55	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.55	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.55	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.55	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.55	   A^2 -> H(U1(d, d), b)
28.54/9.55	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.55	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.55	   A^2 -> H(U1(d, d), c)
28.54/9.55	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.55	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.55	   A^2 -> H(U1(d, d), e)
28.54/9.55	   A^2 -> H(f(d), d)
28.54/9.55	   A^2 -> H(f(d), k)
28.54/9.55	   A^2 -> H(U1(c, c), c)
28.54/9.55	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.55	   A^2 -> H(f(c), k)
28.54/9.55	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.55	   A^2 -> H(f(k), U1(k, k))
28.54/9.55	   A^2 -> H(f(e), e)
28.54/9.55	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.55	   A^2 -> H(d, U1(c, b))
28.54/9.55	   A^2 -> H(d, U1(d, b))
28.54/9.55	   A^2 -> H(d, U1(b, c))
28.54/9.55	   A^2 -> H(d, U1(b, d))
28.54/9.55	   A^2 -> H(d, U1(c, c))
28.54/9.55	   A^2 -> H(d, f(e))
28.54/9.55	   A^2 -> H(d, f(k))
28.54/9.55	   A^2 -> H(d, U1(d, d))
28.54/9.55	   A^2 -> H(a, U1(e, b))
28.54/9.55	   A^2 -> H(a, U1(k, b))
28.54/9.55	   A^2 -> H(a, U1(c, d))
28.54/9.55	   A^2 -> H(a, U1(d, c))
28.54/9.55	   A^2 -> H(a, U1(b, e))
28.54/9.55	   A^2 -> H(a, U1(b, k))
28.54/9.55	   A^2 -> H(a, U1(e, c))
28.54/9.55	   A^2 -> H(a, U1(k, c))
28.54/9.55	   A^2 -> H(a, U1(c, e))
28.54/9.55	   A^2 -> H(a, U1(c, k))
28.54/9.55	   A^2 -> H(a, U1(e, e))
28.54/9.55	   A^2 -> H(a, U1(k, k))
28.54/9.55	   A^2 -> H(a, U1(k, d))
28.54/9.55	   A^2 -> H(a, U1(d, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.55	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.55	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.55	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.55	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.55	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.55	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.55	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.55	   A^2 -> H(U1(e, a), b)
28.54/9.55	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(e, a), c)
28.54/9.55	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(e, a), e)
28.54/9.55	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, a), b)
28.54/9.55	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(k, a), c)
28.54/9.55	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.55	
28.54/9.55	The TRS R consists of the following rules:
28.54/9.55	
28.54/9.55	   f(x) -> U1(x, x)
28.54/9.55	   U1(e, x) -> x
28.54/9.55	   a -> c
28.54/9.55	   a -> d
28.54/9.55	   b -> c
28.54/9.55	   b -> d
28.54/9.55	   d -> k
28.54/9.55	   c -> e
28.54/9.55	   c -> k
28.54/9.55	
28.54/9.55	Q is empty.
28.54/9.55	We have to consider all minimal (P,Q,R)-chains.
28.54/9.55	----------------------------------------
28.54/9.55	
28.54/9.55	(1183) TransformationProof (EQUIVALENT)
28.54/9.55	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.55	
28.54/9.55	   (A^2 -> H(U1(k, c), U1(k, k)),A^2 -> H(U1(k, c), U1(k, k)))
28.54/9.55	   (A^2 -> H(U1(k, d), U1(k, k)),A^2 -> H(U1(k, d), U1(k, k)))
28.54/9.55	
28.54/9.55	
28.54/9.55	----------------------------------------
28.54/9.55	
28.54/9.55	(1184)
28.54/9.55	Obligation:
28.54/9.55	Q DP problem:
28.54/9.55	The TRS P consists of the following rules:
28.54/9.55	
28.54/9.55	   G(d, x, x) -> A^2
28.54/9.55	   A^2 -> H(f(c), f(c))
28.54/9.55	   H(x, x) -> G(x, x, f(k))
28.54/9.55	   A^2 -> H(f(d), f(d))
28.54/9.55	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.55	   A^2 -> H(f(e), f(e))
28.54/9.55	   A^2 -> H(f(k), f(k))
28.54/9.55	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.55	   A^2 -> H(U1(k, a), U1(k, d))
28.54/9.55	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.55	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.55	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.55	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.55	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.55	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.55	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.55	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, a), b)
28.54/9.55	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(c, a), c)
28.54/9.55	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(c, a), e)
28.54/9.55	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.55	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.55	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.55	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.55	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.55	   A^2 -> H(U1(d, e), f(e))
28.54/9.55	   A^2 -> H(U1(d, e), f(k))
28.54/9.55	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.55	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.55	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.55	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.55	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.55	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.55	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.55	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.55	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.55	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.55	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.55	   A^2 -> H(U1(d, a), b)
28.54/9.55	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(d, a), c)
28.54/9.55	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(d, a), e)
28.54/9.55	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.55	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.55	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.55	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.55	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.55	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.55	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.55	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.55	   A^2 -> H(U1(a, c), b)
28.54/9.55	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.55	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.55	   A^2 -> H(U1(a, c), c)
28.54/9.55	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.55	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.55	   A^2 -> H(U1(a, c), e)
28.54/9.55	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, d), b)
28.54/9.55	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.55	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.55	   A^2 -> H(U1(a, d), c)
28.54/9.55	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.55	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.55	   A^2 -> H(U1(a, d), e)
28.54/9.55	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, a), d)
28.54/9.55	   A^2 -> H(U1(a, a), k)
28.54/9.55	   A^2 -> H(k, U1(b, b))
28.54/9.55	   A^2 -> H(k, f(c))
28.54/9.55	   A^2 -> H(k, f(d))
28.54/9.55	   A^2 -> H(c, U1(c, b))
28.54/9.55	   A^2 -> H(c, U1(d, b))
28.54/9.55	   A^2 -> H(c, U1(b, c))
28.54/9.55	   A^2 -> H(c, U1(b, d))
28.54/9.55	   A^2 -> H(c, U1(c, c))
28.54/9.55	   A^2 -> H(c, f(e))
28.54/9.55	   A^2 -> H(c, f(k))
28.54/9.55	   A^2 -> H(c, U1(d, d))
28.54/9.55	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.55	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.55	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.55	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.55	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.55	   A^2 -> H(U1(e, k), f(e))
28.54/9.55	   A^2 -> H(U1(e, k), f(k))
28.54/9.55	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.55	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.55	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.55	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.55	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.55	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.55	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.55	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.55	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.55	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.55	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.55	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.55	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.55	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.55	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.55	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.55	   A^2 -> H(U1(k, e), f(e))
28.54/9.55	   A^2 -> H(U1(k, e), f(k))
28.54/9.55	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.55	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.55	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.55	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.55	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.55	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.55	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.55	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.55	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.55	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.55	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.55	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.55	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.55	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.55	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.55	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.55	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.55	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, c), b)
28.54/9.55	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.55	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.55	   A^2 -> H(U1(c, c), e)
28.54/9.55	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.55	   A^2 -> H(e, U1(c, b))
28.54/9.55	   A^2 -> H(e, U1(d, b))
28.54/9.55	   A^2 -> H(e, U1(b, c))
28.54/9.55	   A^2 -> H(e, U1(b, d))
28.54/9.55	   A^2 -> H(e, U1(c, c))
28.54/9.55	   A^2 -> H(e, f(e))
28.54/9.55	   A^2 -> H(e, f(k))
28.54/9.55	   A^2 -> H(e, U1(d, d))
28.54/9.55	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.55	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.55	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.55	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.55	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.55	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.55	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.55	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.55	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.55	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.55	   A^2 -> H(f(e), b)
28.54/9.55	   A^2 -> H(f(e), U1(e, d))
28.54/9.55	   A^2 -> H(f(e), U1(d, e))
28.54/9.55	   A^2 -> H(f(e), c)
28.54/9.55	   A^2 -> H(f(e), U1(e, k))
28.54/9.55	   A^2 -> H(f(e), U1(k, e))
28.54/9.55	   A^2 -> H(f(e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.55	   A^2 -> H(f(k), b)
28.54/9.55	   A^2 -> H(f(k), U1(e, d))
28.54/9.55	   A^2 -> H(f(k), U1(d, e))
28.54/9.55	   A^2 -> H(f(k), c)
28.54/9.55	   A^2 -> H(f(k), U1(e, k))
28.54/9.55	   A^2 -> H(f(k), U1(k, e))
28.54/9.55	   A^2 -> H(f(k), e)
28.54/9.55	   A^2 -> H(f(c), d)
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.55	   A^2 -> H(U1(k, k), f(e))
28.54/9.55	   A^2 -> H(U1(k, k), f(k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.55	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.55	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.55	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.55	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.55	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.55	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.55	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.55	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.55	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.55	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.55	   A^2 -> H(U1(d, d), b)
28.54/9.55	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.55	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.55	   A^2 -> H(U1(d, d), c)
28.54/9.55	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.55	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.55	   A^2 -> H(U1(d, d), e)
28.54/9.55	   A^2 -> H(f(d), d)
28.54/9.55	   A^2 -> H(f(d), k)
28.54/9.55	   A^2 -> H(U1(c, c), c)
28.54/9.55	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.55	   A^2 -> H(f(c), k)
28.54/9.55	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.55	   A^2 -> H(f(k), U1(k, k))
28.54/9.55	   A^2 -> H(f(e), e)
28.54/9.55	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.55	   A^2 -> H(d, U1(c, b))
28.54/9.55	   A^2 -> H(d, U1(d, b))
28.54/9.55	   A^2 -> H(d, U1(b, c))
28.54/9.55	   A^2 -> H(d, U1(b, d))
28.54/9.55	   A^2 -> H(d, U1(c, c))
28.54/9.55	   A^2 -> H(d, f(e))
28.54/9.55	   A^2 -> H(d, f(k))
28.54/9.55	   A^2 -> H(d, U1(d, d))
28.54/9.55	   A^2 -> H(a, U1(e, b))
28.54/9.55	   A^2 -> H(a, U1(k, b))
28.54/9.55	   A^2 -> H(a, U1(c, d))
28.54/9.55	   A^2 -> H(a, U1(d, c))
28.54/9.55	   A^2 -> H(a, U1(b, e))
28.54/9.55	   A^2 -> H(a, U1(b, k))
28.54/9.55	   A^2 -> H(a, U1(e, c))
28.54/9.55	   A^2 -> H(a, U1(k, c))
28.54/9.55	   A^2 -> H(a, U1(c, e))
28.54/9.55	   A^2 -> H(a, U1(c, k))
28.54/9.55	   A^2 -> H(a, U1(e, e))
28.54/9.55	   A^2 -> H(a, U1(k, k))
28.54/9.55	   A^2 -> H(a, U1(k, d))
28.54/9.55	   A^2 -> H(a, U1(d, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.55	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.55	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.55	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.55	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.55	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.55	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.55	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.55	   A^2 -> H(U1(e, a), b)
28.54/9.55	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(e, a), c)
28.54/9.55	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(e, a), e)
28.54/9.55	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, a), b)
28.54/9.55	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(k, a), c)
28.54/9.55	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.55	
28.54/9.55	The TRS R consists of the following rules:
28.54/9.55	
28.54/9.55	   f(x) -> U1(x, x)
28.54/9.55	   U1(e, x) -> x
28.54/9.55	   a -> c
28.54/9.55	   a -> d
28.54/9.55	   b -> c
28.54/9.55	   b -> d
28.54/9.55	   d -> k
28.54/9.55	   c -> e
28.54/9.55	   c -> k
28.54/9.55	
28.54/9.55	Q is empty.
28.54/9.55	We have to consider all minimal (P,Q,R)-chains.
28.54/9.55	----------------------------------------
28.54/9.55	
28.54/9.55	(1185) TransformationProof (EQUIVALENT)
28.54/9.55	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.55	
28.54/9.55	   (A^2 -> H(U1(k, c), U1(k, d)),A^2 -> H(U1(k, c), U1(k, d)))
28.54/9.55	   (A^2 -> H(U1(k, d), U1(k, d)),A^2 -> H(U1(k, d), U1(k, d)))
28.54/9.55	   (A^2 -> H(U1(k, a), U1(k, k)),A^2 -> H(U1(k, a), U1(k, k)))
28.54/9.55	
28.54/9.55	
28.54/9.55	----------------------------------------
28.54/9.55	
28.54/9.55	(1186)
28.54/9.55	Obligation:
28.54/9.55	Q DP problem:
28.54/9.55	The TRS P consists of the following rules:
28.54/9.55	
28.54/9.55	   G(d, x, x) -> A^2
28.54/9.55	   A^2 -> H(f(c), f(c))
28.54/9.55	   H(x, x) -> G(x, x, f(k))
28.54/9.55	   A^2 -> H(f(d), f(d))
28.54/9.55	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.55	   A^2 -> H(f(e), f(e))
28.54/9.55	   A^2 -> H(f(k), f(k))
28.54/9.55	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.55	   A^2 -> H(U1(k, a), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.55	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.55	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.55	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.55	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.55	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.55	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.55	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, a), b)
28.54/9.55	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(c, a), c)
28.54/9.55	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(c, a), e)
28.54/9.55	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.55	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.55	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.55	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.55	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.55	   A^2 -> H(U1(d, e), f(e))
28.54/9.55	   A^2 -> H(U1(d, e), f(k))
28.54/9.55	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.55	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.55	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.55	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.55	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.55	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.55	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.55	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.55	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.55	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.55	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.55	   A^2 -> H(U1(d, a), b)
28.54/9.55	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(d, a), c)
28.54/9.55	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(d, a), e)
28.54/9.55	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.55	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.55	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.55	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.55	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.55	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.55	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.55	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.55	   A^2 -> H(U1(a, c), b)
28.54/9.55	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.55	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.55	   A^2 -> H(U1(a, c), c)
28.54/9.55	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.55	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.55	   A^2 -> H(U1(a, c), e)
28.54/9.55	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, d), b)
28.54/9.55	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.55	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.55	   A^2 -> H(U1(a, d), c)
28.54/9.55	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.55	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.55	   A^2 -> H(U1(a, d), e)
28.54/9.55	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, a), d)
28.54/9.55	   A^2 -> H(U1(a, a), k)
28.54/9.55	   A^2 -> H(k, U1(b, b))
28.54/9.55	   A^2 -> H(k, f(c))
28.54/9.55	   A^2 -> H(k, f(d))
28.54/9.55	   A^2 -> H(c, U1(c, b))
28.54/9.55	   A^2 -> H(c, U1(d, b))
28.54/9.55	   A^2 -> H(c, U1(b, c))
28.54/9.55	   A^2 -> H(c, U1(b, d))
28.54/9.55	   A^2 -> H(c, U1(c, c))
28.54/9.55	   A^2 -> H(c, f(e))
28.54/9.55	   A^2 -> H(c, f(k))
28.54/9.55	   A^2 -> H(c, U1(d, d))
28.54/9.55	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.55	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.55	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.55	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.55	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.55	   A^2 -> H(U1(e, k), f(e))
28.54/9.55	   A^2 -> H(U1(e, k), f(k))
28.54/9.55	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.55	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.55	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.55	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.55	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.55	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.55	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.55	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.55	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.55	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.55	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.55	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.55	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.55	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.55	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.55	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.55	   A^2 -> H(U1(k, e), f(e))
28.54/9.55	   A^2 -> H(U1(k, e), f(k))
28.54/9.55	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.55	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.55	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.55	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.55	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.55	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.55	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.55	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.55	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.55	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.55	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.55	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.55	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.55	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.55	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.55	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.55	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.55	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, c), b)
28.54/9.55	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.55	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.55	   A^2 -> H(U1(c, c), e)
28.54/9.55	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.55	   A^2 -> H(e, U1(c, b))
28.54/9.55	   A^2 -> H(e, U1(d, b))
28.54/9.55	   A^2 -> H(e, U1(b, c))
28.54/9.55	   A^2 -> H(e, U1(b, d))
28.54/9.55	   A^2 -> H(e, U1(c, c))
28.54/9.55	   A^2 -> H(e, f(e))
28.54/9.55	   A^2 -> H(e, f(k))
28.54/9.55	   A^2 -> H(e, U1(d, d))
28.54/9.55	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.55	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.55	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.55	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.55	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.55	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.55	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.55	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.55	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.55	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.55	   A^2 -> H(f(e), b)
28.54/9.55	   A^2 -> H(f(e), U1(e, d))
28.54/9.55	   A^2 -> H(f(e), U1(d, e))
28.54/9.55	   A^2 -> H(f(e), c)
28.54/9.55	   A^2 -> H(f(e), U1(e, k))
28.54/9.55	   A^2 -> H(f(e), U1(k, e))
28.54/9.55	   A^2 -> H(f(e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.55	   A^2 -> H(f(k), b)
28.54/9.55	   A^2 -> H(f(k), U1(e, d))
28.54/9.55	   A^2 -> H(f(k), U1(d, e))
28.54/9.55	   A^2 -> H(f(k), c)
28.54/9.55	   A^2 -> H(f(k), U1(e, k))
28.54/9.55	   A^2 -> H(f(k), U1(k, e))
28.54/9.55	   A^2 -> H(f(k), e)
28.54/9.55	   A^2 -> H(f(c), d)
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.55	   A^2 -> H(U1(k, k), f(e))
28.54/9.55	   A^2 -> H(U1(k, k), f(k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.55	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.55	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.55	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.55	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.55	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.55	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.55	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.55	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.55	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.55	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.55	   A^2 -> H(U1(d, d), b)
28.54/9.55	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.55	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.55	   A^2 -> H(U1(d, d), c)
28.54/9.55	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.55	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.55	   A^2 -> H(U1(d, d), e)
28.54/9.55	   A^2 -> H(f(d), d)
28.54/9.55	   A^2 -> H(f(d), k)
28.54/9.55	   A^2 -> H(U1(c, c), c)
28.54/9.55	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.55	   A^2 -> H(f(c), k)
28.54/9.55	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.55	   A^2 -> H(f(k), U1(k, k))
28.54/9.55	   A^2 -> H(f(e), e)
28.54/9.55	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.55	   A^2 -> H(d, U1(c, b))
28.54/9.55	   A^2 -> H(d, U1(d, b))
28.54/9.55	   A^2 -> H(d, U1(b, c))
28.54/9.55	   A^2 -> H(d, U1(b, d))
28.54/9.55	   A^2 -> H(d, U1(c, c))
28.54/9.55	   A^2 -> H(d, f(e))
28.54/9.55	   A^2 -> H(d, f(k))
28.54/9.55	   A^2 -> H(d, U1(d, d))
28.54/9.55	   A^2 -> H(a, U1(e, b))
28.54/9.55	   A^2 -> H(a, U1(k, b))
28.54/9.55	   A^2 -> H(a, U1(c, d))
28.54/9.55	   A^2 -> H(a, U1(d, c))
28.54/9.55	   A^2 -> H(a, U1(b, e))
28.54/9.55	   A^2 -> H(a, U1(b, k))
28.54/9.55	   A^2 -> H(a, U1(e, c))
28.54/9.55	   A^2 -> H(a, U1(k, c))
28.54/9.55	   A^2 -> H(a, U1(c, e))
28.54/9.55	   A^2 -> H(a, U1(c, k))
28.54/9.55	   A^2 -> H(a, U1(e, e))
28.54/9.55	   A^2 -> H(a, U1(k, k))
28.54/9.55	   A^2 -> H(a, U1(k, d))
28.54/9.55	   A^2 -> H(a, U1(d, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.55	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.55	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.55	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.55	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.55	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.55	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.55	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.55	   A^2 -> H(U1(e, a), b)
28.54/9.55	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(e, a), c)
28.54/9.55	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(e, a), e)
28.54/9.55	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, a), b)
28.54/9.55	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(k, a), c)
28.54/9.55	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.55	
28.54/9.55	The TRS R consists of the following rules:
28.54/9.55	
28.54/9.55	   f(x) -> U1(x, x)
28.54/9.55	   U1(e, x) -> x
28.54/9.55	   a -> c
28.54/9.55	   a -> d
28.54/9.55	   b -> c
28.54/9.55	   b -> d
28.54/9.55	   d -> k
28.54/9.55	   c -> e
28.54/9.55	   c -> k
28.54/9.55	
28.54/9.55	Q is empty.
28.54/9.55	We have to consider all minimal (P,Q,R)-chains.
28.54/9.55	----------------------------------------
28.54/9.55	
28.54/9.55	(1187) TransformationProof (EQUIVALENT)
28.54/9.55	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.55	
28.54/9.55	   (A^2 -> H(U1(k, c), U1(d, k)),A^2 -> H(U1(k, c), U1(d, k)))
28.54/9.55	   (A^2 -> H(U1(k, d), U1(d, k)),A^2 -> H(U1(k, d), U1(d, k)))
28.54/9.55	   (A^2 -> H(U1(k, a), U1(k, k)),A^2 -> H(U1(k, a), U1(k, k)))
28.54/9.55	
28.54/9.55	
28.54/9.55	----------------------------------------
28.54/9.55	
28.54/9.55	(1188)
28.54/9.55	Obligation:
28.54/9.55	Q DP problem:
28.54/9.55	The TRS P consists of the following rules:
28.54/9.55	
28.54/9.55	   G(d, x, x) -> A^2
28.54/9.55	   A^2 -> H(f(c), f(c))
28.54/9.55	   H(x, x) -> G(x, x, f(k))
28.54/9.55	   A^2 -> H(f(d), f(d))
28.54/9.55	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.55	   A^2 -> H(f(e), f(e))
28.54/9.55	   A^2 -> H(f(k), f(k))
28.54/9.55	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.55	   A^2 -> H(U1(c, d), U1(e, b))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.55	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.55	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.55	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.55	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.55	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.55	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.55	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, a), b)
28.54/9.55	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(c, a), c)
28.54/9.55	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(c, a), e)
28.54/9.55	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.55	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.55	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.55	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.55	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.55	   A^2 -> H(U1(d, e), f(e))
28.54/9.55	   A^2 -> H(U1(d, e), f(k))
28.54/9.55	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.55	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.55	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.55	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.55	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.55	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.55	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.55	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.55	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.55	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.55	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.55	   A^2 -> H(U1(d, a), b)
28.54/9.55	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(d, a), c)
28.54/9.55	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(d, a), e)
28.54/9.55	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.55	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.55	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.55	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.55	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.55	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.55	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.55	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.55	   A^2 -> H(U1(a, c), b)
28.54/9.55	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.55	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.55	   A^2 -> H(U1(a, c), c)
28.54/9.55	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.55	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.55	   A^2 -> H(U1(a, c), e)
28.54/9.55	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, d), b)
28.54/9.55	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.55	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.55	   A^2 -> H(U1(a, d), c)
28.54/9.55	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.55	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.55	   A^2 -> H(U1(a, d), e)
28.54/9.55	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, a), d)
28.54/9.55	   A^2 -> H(U1(a, a), k)
28.54/9.55	   A^2 -> H(k, U1(b, b))
28.54/9.55	   A^2 -> H(k, f(c))
28.54/9.55	   A^2 -> H(k, f(d))
28.54/9.55	   A^2 -> H(c, U1(c, b))
28.54/9.55	   A^2 -> H(c, U1(d, b))
28.54/9.55	   A^2 -> H(c, U1(b, c))
28.54/9.55	   A^2 -> H(c, U1(b, d))
28.54/9.55	   A^2 -> H(c, U1(c, c))
28.54/9.55	   A^2 -> H(c, f(e))
28.54/9.55	   A^2 -> H(c, f(k))
28.54/9.55	   A^2 -> H(c, U1(d, d))
28.54/9.55	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.55	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.55	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.55	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.55	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.55	   A^2 -> H(U1(e, k), f(e))
28.54/9.55	   A^2 -> H(U1(e, k), f(k))
28.54/9.55	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.55	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.55	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.55	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.55	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.55	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.55	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.55	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.55	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.55	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.55	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.55	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.55	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.55	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.55	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.55	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.55	   A^2 -> H(U1(k, e), f(e))
28.54/9.55	   A^2 -> H(U1(k, e), f(k))
28.54/9.55	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.55	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.55	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.55	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.55	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.55	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.55	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.55	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.55	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.55	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.55	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.55	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.55	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.55	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.55	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.55	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.55	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.55	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, c), b)
28.54/9.55	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.55	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.55	   A^2 -> H(U1(c, c), e)
28.54/9.55	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.55	   A^2 -> H(e, U1(c, b))
28.54/9.55	   A^2 -> H(e, U1(d, b))
28.54/9.55	   A^2 -> H(e, U1(b, c))
28.54/9.55	   A^2 -> H(e, U1(b, d))
28.54/9.55	   A^2 -> H(e, U1(c, c))
28.54/9.55	   A^2 -> H(e, f(e))
28.54/9.55	   A^2 -> H(e, f(k))
28.54/9.55	   A^2 -> H(e, U1(d, d))
28.54/9.55	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.55	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.55	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.55	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.55	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.55	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.55	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.55	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.55	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.55	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.55	   A^2 -> H(f(e), b)
28.54/9.55	   A^2 -> H(f(e), U1(e, d))
28.54/9.55	   A^2 -> H(f(e), U1(d, e))
28.54/9.55	   A^2 -> H(f(e), c)
28.54/9.55	   A^2 -> H(f(e), U1(e, k))
28.54/9.55	   A^2 -> H(f(e), U1(k, e))
28.54/9.55	   A^2 -> H(f(e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.55	   A^2 -> H(f(k), b)
28.54/9.55	   A^2 -> H(f(k), U1(e, d))
28.54/9.55	   A^2 -> H(f(k), U1(d, e))
28.54/9.55	   A^2 -> H(f(k), c)
28.54/9.55	   A^2 -> H(f(k), U1(e, k))
28.54/9.55	   A^2 -> H(f(k), U1(k, e))
28.54/9.55	   A^2 -> H(f(k), e)
28.54/9.55	   A^2 -> H(f(c), d)
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.55	   A^2 -> H(U1(k, k), f(e))
28.54/9.55	   A^2 -> H(U1(k, k), f(k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.55	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.55	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.55	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.55	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.55	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.55	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.55	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.55	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.55	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.55	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.55	   A^2 -> H(U1(d, d), b)
28.54/9.55	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.55	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.55	   A^2 -> H(U1(d, d), c)
28.54/9.55	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.55	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.55	   A^2 -> H(U1(d, d), e)
28.54/9.55	   A^2 -> H(f(d), d)
28.54/9.55	   A^2 -> H(f(d), k)
28.54/9.55	   A^2 -> H(U1(c, c), c)
28.54/9.55	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.55	   A^2 -> H(f(c), k)
28.54/9.55	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.55	   A^2 -> H(f(k), U1(k, k))
28.54/9.55	   A^2 -> H(f(e), e)
28.54/9.55	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.55	   A^2 -> H(d, U1(c, b))
28.54/9.55	   A^2 -> H(d, U1(d, b))
28.54/9.55	   A^2 -> H(d, U1(b, c))
28.54/9.55	   A^2 -> H(d, U1(b, d))
28.54/9.55	   A^2 -> H(d, U1(c, c))
28.54/9.55	   A^2 -> H(d, f(e))
28.54/9.55	   A^2 -> H(d, f(k))
28.54/9.55	   A^2 -> H(d, U1(d, d))
28.54/9.55	   A^2 -> H(a, U1(e, b))
28.54/9.55	   A^2 -> H(a, U1(k, b))
28.54/9.55	   A^2 -> H(a, U1(c, d))
28.54/9.55	   A^2 -> H(a, U1(d, c))
28.54/9.55	   A^2 -> H(a, U1(b, e))
28.54/9.55	   A^2 -> H(a, U1(b, k))
28.54/9.55	   A^2 -> H(a, U1(e, c))
28.54/9.55	   A^2 -> H(a, U1(k, c))
28.54/9.55	   A^2 -> H(a, U1(c, e))
28.54/9.55	   A^2 -> H(a, U1(c, k))
28.54/9.55	   A^2 -> H(a, U1(e, e))
28.54/9.55	   A^2 -> H(a, U1(k, k))
28.54/9.55	   A^2 -> H(a, U1(k, d))
28.54/9.55	   A^2 -> H(a, U1(d, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.55	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.55	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.55	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.55	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.55	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.55	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.55	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.55	   A^2 -> H(U1(e, a), b)
28.54/9.55	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(e, a), c)
28.54/9.55	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(e, a), e)
28.54/9.55	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, a), b)
28.54/9.55	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(k, a), c)
28.54/9.55	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.55	
28.54/9.55	The TRS R consists of the following rules:
28.54/9.55	
28.54/9.55	   f(x) -> U1(x, x)
28.54/9.55	   U1(e, x) -> x
28.54/9.55	   a -> c
28.54/9.55	   a -> d
28.54/9.55	   b -> c
28.54/9.55	   b -> d
28.54/9.55	   d -> k
28.54/9.55	   c -> e
28.54/9.55	   c -> k
28.54/9.55	
28.54/9.55	Q is empty.
28.54/9.55	We have to consider all minimal (P,Q,R)-chains.
28.54/9.55	----------------------------------------
28.54/9.55	
28.54/9.55	(1189) TransformationProof (EQUIVALENT)
28.54/9.55	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.55	
28.54/9.55	   (A^2 -> H(U1(e, d), U1(e, b)),A^2 -> H(U1(e, d), U1(e, b)))
28.54/9.55	   (A^2 -> H(U1(k, d), U1(e, b)),A^2 -> H(U1(k, d), U1(e, b)))
28.54/9.55	   (A^2 -> H(U1(c, k), U1(e, b)),A^2 -> H(U1(c, k), U1(e, b)))
28.54/9.55	   (A^2 -> H(U1(c, d), b),A^2 -> H(U1(c, d), b))
28.54/9.55	   (A^2 -> H(U1(c, d), U1(e, c)),A^2 -> H(U1(c, d), U1(e, c)))
28.54/9.55	   (A^2 -> H(U1(c, d), U1(e, d)),A^2 -> H(U1(c, d), U1(e, d)))
28.54/9.55	
28.54/9.55	
28.54/9.55	----------------------------------------
28.54/9.55	
28.54/9.55	(1190)
28.54/9.55	Obligation:
28.54/9.55	Q DP problem:
28.54/9.55	The TRS P consists of the following rules:
28.54/9.55	
28.54/9.55	   G(d, x, x) -> A^2
28.54/9.55	   A^2 -> H(f(c), f(c))
28.54/9.55	   H(x, x) -> G(x, x, f(k))
28.54/9.55	   A^2 -> H(f(d), f(d))
28.54/9.55	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.55	   A^2 -> H(f(e), f(e))
28.54/9.55	   A^2 -> H(f(k), f(k))
28.54/9.55	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, b))
28.54/9.55	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.55	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.55	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.55	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.55	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.55	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.55	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, a), b)
28.54/9.55	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(c, a), c)
28.54/9.55	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(c, a), e)
28.54/9.55	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.55	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.55	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.55	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.55	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.55	   A^2 -> H(U1(d, e), f(e))
28.54/9.55	   A^2 -> H(U1(d, e), f(k))
28.54/9.55	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.55	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.55	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.55	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.55	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.55	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.55	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.55	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.55	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.55	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.55	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.55	   A^2 -> H(U1(d, a), b)
28.54/9.55	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(d, a), c)
28.54/9.55	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(d, a), e)
28.54/9.55	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.55	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.55	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.55	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.55	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.55	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.55	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.55	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.55	   A^2 -> H(U1(a, c), b)
28.54/9.55	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.55	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.55	   A^2 -> H(U1(a, c), c)
28.54/9.55	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.55	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.55	   A^2 -> H(U1(a, c), e)
28.54/9.55	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, d), b)
28.54/9.55	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.55	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.55	   A^2 -> H(U1(a, d), c)
28.54/9.55	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.55	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.55	   A^2 -> H(U1(a, d), e)
28.54/9.55	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, a), d)
28.54/9.55	   A^2 -> H(U1(a, a), k)
28.54/9.55	   A^2 -> H(k, U1(b, b))
28.54/9.55	   A^2 -> H(k, f(c))
28.54/9.55	   A^2 -> H(k, f(d))
28.54/9.55	   A^2 -> H(c, U1(c, b))
28.54/9.55	   A^2 -> H(c, U1(d, b))
28.54/9.55	   A^2 -> H(c, U1(b, c))
28.54/9.55	   A^2 -> H(c, U1(b, d))
28.54/9.55	   A^2 -> H(c, U1(c, c))
28.54/9.55	   A^2 -> H(c, f(e))
28.54/9.55	   A^2 -> H(c, f(k))
28.54/9.55	   A^2 -> H(c, U1(d, d))
28.54/9.55	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.55	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.55	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.55	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.55	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.55	   A^2 -> H(U1(e, k), f(e))
28.54/9.55	   A^2 -> H(U1(e, k), f(k))
28.54/9.55	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.55	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.55	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.55	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.55	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.55	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.55	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.55	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.55	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.55	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.55	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.55	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.55	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.55	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.55	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.55	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.55	   A^2 -> H(U1(k, e), f(e))
28.54/9.55	   A^2 -> H(U1(k, e), f(k))
28.54/9.55	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.55	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.55	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.55	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.55	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.55	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.55	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.55	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.55	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.55	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.55	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.55	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.55	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.55	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.55	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.55	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.55	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.55	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, c), b)
28.54/9.55	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.55	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.55	   A^2 -> H(U1(c, c), e)
28.54/9.55	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.55	   A^2 -> H(e, U1(c, b))
28.54/9.55	   A^2 -> H(e, U1(d, b))
28.54/9.55	   A^2 -> H(e, U1(b, c))
28.54/9.55	   A^2 -> H(e, U1(b, d))
28.54/9.55	   A^2 -> H(e, U1(c, c))
28.54/9.55	   A^2 -> H(e, f(e))
28.54/9.55	   A^2 -> H(e, f(k))
28.54/9.55	   A^2 -> H(e, U1(d, d))
28.54/9.55	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.55	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.55	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.55	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.55	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.55	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.55	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.55	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.55	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.55	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.55	   A^2 -> H(f(e), b)
28.54/9.55	   A^2 -> H(f(e), U1(e, d))
28.54/9.55	   A^2 -> H(f(e), U1(d, e))
28.54/9.55	   A^2 -> H(f(e), c)
28.54/9.55	   A^2 -> H(f(e), U1(e, k))
28.54/9.55	   A^2 -> H(f(e), U1(k, e))
28.54/9.55	   A^2 -> H(f(e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.55	   A^2 -> H(f(k), b)
28.54/9.55	   A^2 -> H(f(k), U1(e, d))
28.54/9.55	   A^2 -> H(f(k), U1(d, e))
28.54/9.55	   A^2 -> H(f(k), c)
28.54/9.55	   A^2 -> H(f(k), U1(e, k))
28.54/9.55	   A^2 -> H(f(k), U1(k, e))
28.54/9.55	   A^2 -> H(f(k), e)
28.54/9.55	   A^2 -> H(f(c), d)
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.55	   A^2 -> H(U1(k, k), f(e))
28.54/9.55	   A^2 -> H(U1(k, k), f(k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.55	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.55	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.55	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.55	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.55	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.55	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.55	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.55	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.55	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.55	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.55	   A^2 -> H(U1(d, d), b)
28.54/9.55	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.55	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.55	   A^2 -> H(U1(d, d), c)
28.54/9.55	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.55	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.55	   A^2 -> H(U1(d, d), e)
28.54/9.55	   A^2 -> H(f(d), d)
28.54/9.55	   A^2 -> H(f(d), k)
28.54/9.55	   A^2 -> H(U1(c, c), c)
28.54/9.55	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.55	   A^2 -> H(f(c), k)
28.54/9.55	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.55	   A^2 -> H(f(k), U1(k, k))
28.54/9.55	   A^2 -> H(f(e), e)
28.54/9.55	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.55	   A^2 -> H(d, U1(c, b))
28.54/9.55	   A^2 -> H(d, U1(d, b))
28.54/9.55	   A^2 -> H(d, U1(b, c))
28.54/9.55	   A^2 -> H(d, U1(b, d))
28.54/9.55	   A^2 -> H(d, U1(c, c))
28.54/9.55	   A^2 -> H(d, f(e))
28.54/9.55	   A^2 -> H(d, f(k))
28.54/9.55	   A^2 -> H(d, U1(d, d))
28.54/9.55	   A^2 -> H(a, U1(e, b))
28.54/9.55	   A^2 -> H(a, U1(k, b))
28.54/9.55	   A^2 -> H(a, U1(c, d))
28.54/9.55	   A^2 -> H(a, U1(d, c))
28.54/9.55	   A^2 -> H(a, U1(b, e))
28.54/9.55	   A^2 -> H(a, U1(b, k))
28.54/9.55	   A^2 -> H(a, U1(e, c))
28.54/9.55	   A^2 -> H(a, U1(k, c))
28.54/9.55	   A^2 -> H(a, U1(c, e))
28.54/9.55	   A^2 -> H(a, U1(c, k))
28.54/9.55	   A^2 -> H(a, U1(e, e))
28.54/9.55	   A^2 -> H(a, U1(k, k))
28.54/9.55	   A^2 -> H(a, U1(k, d))
28.54/9.55	   A^2 -> H(a, U1(d, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.55	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.55	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.55	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.55	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.55	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.55	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.55	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.55	   A^2 -> H(U1(e, a), b)
28.54/9.55	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(e, a), c)
28.54/9.55	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(e, a), e)
28.54/9.55	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, a), b)
28.54/9.55	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(k, a), c)
28.54/9.55	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(c, d), b)
28.54/9.55	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.55	
28.54/9.55	The TRS R consists of the following rules:
28.54/9.55	
28.54/9.55	   f(x) -> U1(x, x)
28.54/9.55	   U1(e, x) -> x
28.54/9.55	   a -> c
28.54/9.55	   a -> d
28.54/9.55	   b -> c
28.54/9.55	   b -> d
28.54/9.55	   d -> k
28.54/9.55	   c -> e
28.54/9.55	   c -> k
28.54/9.55	
28.54/9.55	Q is empty.
28.54/9.55	We have to consider all minimal (P,Q,R)-chains.
28.54/9.55	----------------------------------------
28.54/9.55	
28.54/9.55	(1191) TransformationProof (EQUIVALENT)
28.54/9.55	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.55	
28.54/9.55	   (A^2 -> H(U1(e, d), U1(k, b)),A^2 -> H(U1(e, d), U1(k, b)))
28.54/9.55	   (A^2 -> H(U1(k, d), U1(k, b)),A^2 -> H(U1(k, d), U1(k, b)))
28.54/9.55	   (A^2 -> H(U1(c, k), U1(k, b)),A^2 -> H(U1(c, k), U1(k, b)))
28.54/9.55	   (A^2 -> H(U1(c, d), U1(k, c)),A^2 -> H(U1(c, d), U1(k, c)))
28.54/9.55	   (A^2 -> H(U1(c, d), U1(k, d)),A^2 -> H(U1(c, d), U1(k, d)))
28.54/9.55	
28.54/9.55	
28.54/9.55	----------------------------------------
28.54/9.55	
28.54/9.55	(1192)
28.54/9.55	Obligation:
28.54/9.55	Q DP problem:
28.54/9.55	The TRS P consists of the following rules:
28.54/9.55	
28.54/9.55	   G(d, x, x) -> A^2
28.54/9.55	   A^2 -> H(f(c), f(c))
28.54/9.55	   H(x, x) -> G(x, x, f(k))
28.54/9.55	   A^2 -> H(f(d), f(d))
28.54/9.55	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.55	   A^2 -> H(f(e), f(e))
28.54/9.55	   A^2 -> H(f(k), f(k))
28.54/9.55	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.55	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.55	   A^2 -> H(U1(c, d), U1(d, c))
28.54/9.55	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.55	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.55	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.55	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.55	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, a), b)
28.54/9.55	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(c, a), c)
28.54/9.55	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(c, a), e)
28.54/9.55	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.55	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.55	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.55	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.55	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.55	   A^2 -> H(U1(d, e), f(e))
28.54/9.55	   A^2 -> H(U1(d, e), f(k))
28.54/9.55	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.55	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.55	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.55	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.55	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.55	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.55	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.55	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.55	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.55	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.55	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.55	   A^2 -> H(U1(d, a), b)
28.54/9.55	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(d, a), c)
28.54/9.55	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(d, a), e)
28.54/9.55	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.55	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.55	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.55	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.55	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.55	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.55	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.55	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.55	   A^2 -> H(U1(a, c), b)
28.54/9.55	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.55	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.55	   A^2 -> H(U1(a, c), c)
28.54/9.55	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.55	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.55	   A^2 -> H(U1(a, c), e)
28.54/9.55	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, d), b)
28.54/9.55	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.55	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.55	   A^2 -> H(U1(a, d), c)
28.54/9.55	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.55	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.55	   A^2 -> H(U1(a, d), e)
28.54/9.55	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(a, a), d)
28.54/9.55	   A^2 -> H(U1(a, a), k)
28.54/9.55	   A^2 -> H(k, U1(b, b))
28.54/9.55	   A^2 -> H(k, f(c))
28.54/9.55	   A^2 -> H(k, f(d))
28.54/9.55	   A^2 -> H(c, U1(c, b))
28.54/9.55	   A^2 -> H(c, U1(d, b))
28.54/9.55	   A^2 -> H(c, U1(b, c))
28.54/9.55	   A^2 -> H(c, U1(b, d))
28.54/9.55	   A^2 -> H(c, U1(c, c))
28.54/9.55	   A^2 -> H(c, f(e))
28.54/9.55	   A^2 -> H(c, f(k))
28.54/9.55	   A^2 -> H(c, U1(d, d))
28.54/9.55	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.55	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.55	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.55	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.55	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.55	   A^2 -> H(U1(e, k), f(e))
28.54/9.55	   A^2 -> H(U1(e, k), f(k))
28.54/9.55	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.55	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.55	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.55	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.55	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.55	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.55	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.55	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.55	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.55	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.55	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.55	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.55	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.55	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.55	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.55	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.55	   A^2 -> H(U1(k, e), f(e))
28.54/9.55	   A^2 -> H(U1(k, e), f(k))
28.54/9.55	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.55	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.55	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.55	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.55	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.55	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.55	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.55	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.55	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.55	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.55	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.55	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.55	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.55	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.55	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.55	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.55	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.55	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, c), b)
28.54/9.55	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.55	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.55	   A^2 -> H(U1(c, c), e)
28.54/9.55	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.55	   A^2 -> H(e, U1(c, b))
28.54/9.55	   A^2 -> H(e, U1(d, b))
28.54/9.55	   A^2 -> H(e, U1(b, c))
28.54/9.55	   A^2 -> H(e, U1(b, d))
28.54/9.55	   A^2 -> H(e, U1(c, c))
28.54/9.55	   A^2 -> H(e, f(e))
28.54/9.55	   A^2 -> H(e, f(k))
28.54/9.55	   A^2 -> H(e, U1(d, d))
28.54/9.55	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.55	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.55	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.55	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.55	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.55	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.55	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.55	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.55	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.55	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.55	   A^2 -> H(f(e), b)
28.54/9.55	   A^2 -> H(f(e), U1(e, d))
28.54/9.55	   A^2 -> H(f(e), U1(d, e))
28.54/9.55	   A^2 -> H(f(e), c)
28.54/9.55	   A^2 -> H(f(e), U1(e, k))
28.54/9.55	   A^2 -> H(f(e), U1(k, e))
28.54/9.55	   A^2 -> H(f(e), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.55	   A^2 -> H(f(k), b)
28.54/9.55	   A^2 -> H(f(k), U1(e, d))
28.54/9.55	   A^2 -> H(f(k), U1(d, e))
28.54/9.55	   A^2 -> H(f(k), c)
28.54/9.55	   A^2 -> H(f(k), U1(e, k))
28.54/9.55	   A^2 -> H(f(k), U1(k, e))
28.54/9.55	   A^2 -> H(f(k), e)
28.54/9.55	   A^2 -> H(f(c), d)
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.55	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.55	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.55	   A^2 -> H(U1(k, k), f(e))
28.54/9.55	   A^2 -> H(U1(k, k), f(k))
28.54/9.55	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.55	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.55	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.55	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.55	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.55	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.55	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.55	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.55	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.55	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.55	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.55	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.55	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.55	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.55	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.55	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.55	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.55	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.55	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.55	   A^2 -> H(U1(d, d), b)
28.54/9.55	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.55	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.55	   A^2 -> H(U1(d, d), c)
28.54/9.55	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.55	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.55	   A^2 -> H(U1(d, d), e)
28.54/9.55	   A^2 -> H(f(d), d)
28.54/9.55	   A^2 -> H(f(d), k)
28.54/9.55	   A^2 -> H(U1(c, c), c)
28.54/9.55	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.55	   A^2 -> H(f(c), k)
28.54/9.55	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.55	   A^2 -> H(f(k), U1(k, k))
28.54/9.55	   A^2 -> H(f(e), e)
28.54/9.55	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.55	   A^2 -> H(d, U1(c, b))
28.54/9.55	   A^2 -> H(d, U1(d, b))
28.54/9.55	   A^2 -> H(d, U1(b, c))
28.54/9.55	   A^2 -> H(d, U1(b, d))
28.54/9.55	   A^2 -> H(d, U1(c, c))
28.54/9.55	   A^2 -> H(d, f(e))
28.54/9.55	   A^2 -> H(d, f(k))
28.54/9.55	   A^2 -> H(d, U1(d, d))
28.54/9.55	   A^2 -> H(a, U1(e, b))
28.54/9.55	   A^2 -> H(a, U1(k, b))
28.54/9.55	   A^2 -> H(a, U1(c, d))
28.54/9.55	   A^2 -> H(a, U1(d, c))
28.54/9.55	   A^2 -> H(a, U1(b, e))
28.54/9.55	   A^2 -> H(a, U1(b, k))
28.54/9.55	   A^2 -> H(a, U1(e, c))
28.54/9.55	   A^2 -> H(a, U1(k, c))
28.54/9.55	   A^2 -> H(a, U1(c, e))
28.54/9.55	   A^2 -> H(a, U1(c, k))
28.54/9.55	   A^2 -> H(a, U1(e, e))
28.54/9.55	   A^2 -> H(a, U1(k, k))
28.54/9.55	   A^2 -> H(a, U1(k, d))
28.54/9.55	   A^2 -> H(a, U1(d, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.55	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.55	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.55	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.55	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.55	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.55	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.55	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.55	   A^2 -> H(U1(e, a), b)
28.54/9.55	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(e, a), c)
28.54/9.55	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(e, a), e)
28.54/9.55	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(k, a), b)
28.54/9.55	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(k, a), c)
28.54/9.55	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(c, d), b)
28.54/9.55	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.55	
28.54/9.55	The TRS R consists of the following rules:
28.54/9.55	
28.54/9.55	   f(x) -> U1(x, x)
28.54/9.55	   U1(e, x) -> x
28.54/9.55	   a -> c
28.54/9.55	   a -> d
28.54/9.55	   b -> c
28.54/9.55	   b -> d
28.54/9.55	   d -> k
28.54/9.55	   c -> e
28.54/9.55	   c -> k
28.54/9.55	
28.54/9.55	Q is empty.
28.54/9.55	We have to consider all minimal (P,Q,R)-chains.
28.54/9.55	----------------------------------------
28.54/9.55	
28.54/9.55	(1193) TransformationProof (EQUIVALENT)
28.54/9.55	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.55	
28.54/9.55	   (A^2 -> H(U1(e, d), U1(d, c)),A^2 -> H(U1(e, d), U1(d, c)))
28.54/9.55	   (A^2 -> H(U1(k, d), U1(d, c)),A^2 -> H(U1(k, d), U1(d, c)))
28.54/9.55	   (A^2 -> H(U1(c, k), U1(d, c)),A^2 -> H(U1(c, k), U1(d, c)))
28.54/9.55	   (A^2 -> H(U1(c, d), U1(k, c)),A^2 -> H(U1(c, d), U1(k, c)))
28.54/9.55	   (A^2 -> H(U1(c, d), U1(d, e)),A^2 -> H(U1(c, d), U1(d, e)))
28.54/9.55	   (A^2 -> H(U1(c, d), U1(d, k)),A^2 -> H(U1(c, d), U1(d, k)))
28.54/9.55	
28.54/9.55	
28.54/9.55	----------------------------------------
28.54/9.55	
28.54/9.55	(1194)
28.54/9.55	Obligation:
28.54/9.55	Q DP problem:
28.54/9.55	The TRS P consists of the following rules:
28.54/9.55	
28.54/9.55	   G(d, x, x) -> A^2
28.54/9.55	   A^2 -> H(f(c), f(c))
28.54/9.55	   H(x, x) -> G(x, x, f(k))
28.54/9.55	   A^2 -> H(f(d), f(d))
28.54/9.55	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.55	   A^2 -> H(f(e), f(e))
28.54/9.55	   A^2 -> H(f(k), f(k))
28.54/9.55	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.55	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.55	   A^2 -> H(U1(c, d), U1(b, e))
28.54/9.55	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.55	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.55	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.55	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.55	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.55	   A^2 -> H(U1(c, a), b)
28.54/9.55	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(c, a), c)
28.54/9.55	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(c, a), e)
28.54/9.55	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.55	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.55	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.55	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.55	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.55	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.55	   A^2 -> H(U1(d, e), f(e))
28.54/9.55	   A^2 -> H(U1(d, e), f(k))
28.54/9.55	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.55	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.55	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.55	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.55	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.55	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.55	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.55	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.55	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.55	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.55	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.55	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.55	   A^2 -> H(U1(d, a), b)
28.54/9.55	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.55	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.55	   A^2 -> H(U1(d, a), c)
28.54/9.55	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.55	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.55	   A^2 -> H(U1(d, a), e)
28.54/9.55	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.56	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.56	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.56	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.56	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.56	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.56	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.56	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.56	   A^2 -> H(U1(a, c), b)
28.54/9.56	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.56	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.56	   A^2 -> H(U1(a, c), c)
28.54/9.56	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.56	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.56	   A^2 -> H(U1(a, c), e)
28.54/9.56	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, d), b)
28.54/9.56	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.56	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.56	   A^2 -> H(U1(a, d), c)
28.54/9.56	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.56	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.56	   A^2 -> H(U1(a, d), e)
28.54/9.56	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, a), d)
28.54/9.56	   A^2 -> H(U1(a, a), k)
28.54/9.56	   A^2 -> H(k, U1(b, b))
28.54/9.56	   A^2 -> H(k, f(c))
28.54/9.56	   A^2 -> H(k, f(d))
28.54/9.56	   A^2 -> H(c, U1(c, b))
28.54/9.56	   A^2 -> H(c, U1(d, b))
28.54/9.56	   A^2 -> H(c, U1(b, c))
28.54/9.56	   A^2 -> H(c, U1(b, d))
28.54/9.56	   A^2 -> H(c, U1(c, c))
28.54/9.56	   A^2 -> H(c, f(e))
28.54/9.56	   A^2 -> H(c, f(k))
28.54/9.56	   A^2 -> H(c, U1(d, d))
28.54/9.56	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.56	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.56	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.56	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.56	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.56	   A^2 -> H(U1(e, k), f(e))
28.54/9.56	   A^2 -> H(U1(e, k), f(k))
28.54/9.56	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.56	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.56	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.56	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.56	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.56	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.56	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.56	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.56	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.56	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.56	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.56	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.56	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.56	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.56	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.56	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.56	   A^2 -> H(U1(k, e), f(e))
28.54/9.56	   A^2 -> H(U1(k, e), f(k))
28.54/9.56	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.56	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.56	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.56	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.56	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.56	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.56	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.56	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.56	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.56	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.56	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.56	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.56	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.56	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.56	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.56	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.56	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.56	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, c), b)
28.54/9.56	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.56	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.56	   A^2 -> H(U1(c, c), e)
28.54/9.56	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.56	   A^2 -> H(e, U1(c, b))
28.54/9.56	   A^2 -> H(e, U1(d, b))
28.54/9.56	   A^2 -> H(e, U1(b, c))
28.54/9.56	   A^2 -> H(e, U1(b, d))
28.54/9.56	   A^2 -> H(e, U1(c, c))
28.54/9.56	   A^2 -> H(e, f(e))
28.54/9.56	   A^2 -> H(e, f(k))
28.54/9.56	   A^2 -> H(e, U1(d, d))
28.54/9.56	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.56	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.56	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.56	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.56	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.56	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.56	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.56	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.56	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.56	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.56	   A^2 -> H(f(e), b)
28.54/9.56	   A^2 -> H(f(e), U1(e, d))
28.54/9.56	   A^2 -> H(f(e), U1(d, e))
28.54/9.56	   A^2 -> H(f(e), c)
28.54/9.56	   A^2 -> H(f(e), U1(e, k))
28.54/9.56	   A^2 -> H(f(e), U1(k, e))
28.54/9.56	   A^2 -> H(f(e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.56	   A^2 -> H(f(k), b)
28.54/9.56	   A^2 -> H(f(k), U1(e, d))
28.54/9.56	   A^2 -> H(f(k), U1(d, e))
28.54/9.56	   A^2 -> H(f(k), c)
28.54/9.56	   A^2 -> H(f(k), U1(e, k))
28.54/9.56	   A^2 -> H(f(k), U1(k, e))
28.54/9.56	   A^2 -> H(f(k), e)
28.54/9.56	   A^2 -> H(f(c), d)
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.56	   A^2 -> H(U1(k, k), f(e))
28.54/9.56	   A^2 -> H(U1(k, k), f(k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.56	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.56	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.56	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.56	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.56	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.56	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.56	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.56	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.56	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.56	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.56	   A^2 -> H(U1(d, d), b)
28.54/9.56	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.56	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.56	   A^2 -> H(U1(d, d), c)
28.54/9.56	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.56	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.56	   A^2 -> H(U1(d, d), e)
28.54/9.56	   A^2 -> H(f(d), d)
28.54/9.56	   A^2 -> H(f(d), k)
28.54/9.56	   A^2 -> H(U1(c, c), c)
28.54/9.56	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.56	   A^2 -> H(f(c), k)
28.54/9.56	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.56	   A^2 -> H(f(k), U1(k, k))
28.54/9.56	   A^2 -> H(f(e), e)
28.54/9.56	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.56	   A^2 -> H(d, U1(c, b))
28.54/9.56	   A^2 -> H(d, U1(d, b))
28.54/9.56	   A^2 -> H(d, U1(b, c))
28.54/9.56	   A^2 -> H(d, U1(b, d))
28.54/9.56	   A^2 -> H(d, U1(c, c))
28.54/9.56	   A^2 -> H(d, f(e))
28.54/9.56	   A^2 -> H(d, f(k))
28.54/9.56	   A^2 -> H(d, U1(d, d))
28.54/9.56	   A^2 -> H(a, U1(e, b))
28.54/9.56	   A^2 -> H(a, U1(k, b))
28.54/9.56	   A^2 -> H(a, U1(c, d))
28.54/9.56	   A^2 -> H(a, U1(d, c))
28.54/9.56	   A^2 -> H(a, U1(b, e))
28.54/9.56	   A^2 -> H(a, U1(b, k))
28.54/9.56	   A^2 -> H(a, U1(e, c))
28.54/9.56	   A^2 -> H(a, U1(k, c))
28.54/9.56	   A^2 -> H(a, U1(c, e))
28.54/9.56	   A^2 -> H(a, U1(c, k))
28.54/9.56	   A^2 -> H(a, U1(e, e))
28.54/9.56	   A^2 -> H(a, U1(k, k))
28.54/9.56	   A^2 -> H(a, U1(k, d))
28.54/9.56	   A^2 -> H(a, U1(d, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.56	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.56	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.56	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.56	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.56	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.56	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.56	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.56	   A^2 -> H(U1(e, a), b)
28.54/9.56	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(e, a), c)
28.54/9.56	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(e, a), e)
28.54/9.56	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, a), b)
28.54/9.56	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(k, a), c)
28.54/9.56	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, d), b)
28.54/9.56	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.56	
28.54/9.56	The TRS R consists of the following rules:
28.54/9.56	
28.54/9.56	   f(x) -> U1(x, x)
28.54/9.56	   U1(e, x) -> x
28.54/9.56	   a -> c
28.54/9.56	   a -> d
28.54/9.56	   b -> c
28.54/9.56	   b -> d
28.54/9.56	   d -> k
28.54/9.56	   c -> e
28.54/9.56	   c -> k
28.54/9.56	
28.54/9.56	Q is empty.
28.54/9.56	We have to consider all minimal (P,Q,R)-chains.
28.54/9.56	----------------------------------------
28.54/9.56	
28.54/9.56	(1195) TransformationProof (EQUIVALENT)
28.54/9.56	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.56	
28.54/9.56	   (A^2 -> H(U1(e, d), U1(b, e)),A^2 -> H(U1(e, d), U1(b, e)))
28.54/9.56	   (A^2 -> H(U1(k, d), U1(b, e)),A^2 -> H(U1(k, d), U1(b, e)))
28.54/9.56	   (A^2 -> H(U1(c, k), U1(b, e)),A^2 -> H(U1(c, k), U1(b, e)))
28.54/9.56	   (A^2 -> H(U1(c, d), U1(c, e)),A^2 -> H(U1(c, d), U1(c, e)))
28.54/9.56	   (A^2 -> H(U1(c, d), U1(d, e)),A^2 -> H(U1(c, d), U1(d, e)))
28.54/9.56	
28.54/9.56	
28.54/9.56	----------------------------------------
28.54/9.56	
28.54/9.56	(1196)
28.54/9.56	Obligation:
28.54/9.56	Q DP problem:
28.54/9.56	The TRS P consists of the following rules:
28.54/9.56	
28.54/9.56	   G(d, x, x) -> A^2
28.54/9.56	   A^2 -> H(f(c), f(c))
28.54/9.56	   H(x, x) -> G(x, x, f(k))
28.54/9.56	   A^2 -> H(f(d), f(d))
28.54/9.56	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.56	   A^2 -> H(f(e), f(e))
28.54/9.56	   A^2 -> H(f(k), f(k))
28.54/9.56	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(b, k))
28.54/9.56	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.56	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.56	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.56	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.56	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, a), b)
28.54/9.56	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(c, a), c)
28.54/9.56	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(c, a), e)
28.54/9.56	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.56	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.56	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.56	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.56	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.56	   A^2 -> H(U1(d, e), f(e))
28.54/9.56	   A^2 -> H(U1(d, e), f(k))
28.54/9.56	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.56	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.56	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.56	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.56	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.56	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.56	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.56	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.56	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.56	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.56	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.56	   A^2 -> H(U1(d, a), b)
28.54/9.56	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(d, a), c)
28.54/9.56	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(d, a), e)
28.54/9.56	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.56	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.56	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.56	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.56	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.56	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.56	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.56	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.56	   A^2 -> H(U1(a, c), b)
28.54/9.56	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.56	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.56	   A^2 -> H(U1(a, c), c)
28.54/9.56	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.56	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.56	   A^2 -> H(U1(a, c), e)
28.54/9.56	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, d), b)
28.54/9.56	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.56	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.56	   A^2 -> H(U1(a, d), c)
28.54/9.56	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.56	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.56	   A^2 -> H(U1(a, d), e)
28.54/9.56	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, a), d)
28.54/9.56	   A^2 -> H(U1(a, a), k)
28.54/9.56	   A^2 -> H(k, U1(b, b))
28.54/9.56	   A^2 -> H(k, f(c))
28.54/9.56	   A^2 -> H(k, f(d))
28.54/9.56	   A^2 -> H(c, U1(c, b))
28.54/9.56	   A^2 -> H(c, U1(d, b))
28.54/9.56	   A^2 -> H(c, U1(b, c))
28.54/9.56	   A^2 -> H(c, U1(b, d))
28.54/9.56	   A^2 -> H(c, U1(c, c))
28.54/9.56	   A^2 -> H(c, f(e))
28.54/9.56	   A^2 -> H(c, f(k))
28.54/9.56	   A^2 -> H(c, U1(d, d))
28.54/9.56	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.56	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.56	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.56	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.56	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.56	   A^2 -> H(U1(e, k), f(e))
28.54/9.56	   A^2 -> H(U1(e, k), f(k))
28.54/9.56	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.56	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.56	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.56	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.56	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.56	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.56	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.56	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.56	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.56	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.56	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.56	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.56	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.56	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.56	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.56	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.56	   A^2 -> H(U1(k, e), f(e))
28.54/9.56	   A^2 -> H(U1(k, e), f(k))
28.54/9.56	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.56	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.56	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.56	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.56	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.56	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.56	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.56	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.56	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.56	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.56	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.56	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.56	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.56	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.56	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.56	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.56	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.56	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, c), b)
28.54/9.56	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.56	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.56	   A^2 -> H(U1(c, c), e)
28.54/9.56	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.56	   A^2 -> H(e, U1(c, b))
28.54/9.56	   A^2 -> H(e, U1(d, b))
28.54/9.56	   A^2 -> H(e, U1(b, c))
28.54/9.56	   A^2 -> H(e, U1(b, d))
28.54/9.56	   A^2 -> H(e, U1(c, c))
28.54/9.56	   A^2 -> H(e, f(e))
28.54/9.56	   A^2 -> H(e, f(k))
28.54/9.56	   A^2 -> H(e, U1(d, d))
28.54/9.56	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.56	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.56	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.56	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.56	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.56	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.56	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.56	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.56	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.56	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.56	   A^2 -> H(f(e), b)
28.54/9.56	   A^2 -> H(f(e), U1(e, d))
28.54/9.56	   A^2 -> H(f(e), U1(d, e))
28.54/9.56	   A^2 -> H(f(e), c)
28.54/9.56	   A^2 -> H(f(e), U1(e, k))
28.54/9.56	   A^2 -> H(f(e), U1(k, e))
28.54/9.56	   A^2 -> H(f(e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.56	   A^2 -> H(f(k), b)
28.54/9.56	   A^2 -> H(f(k), U1(e, d))
28.54/9.56	   A^2 -> H(f(k), U1(d, e))
28.54/9.56	   A^2 -> H(f(k), c)
28.54/9.56	   A^2 -> H(f(k), U1(e, k))
28.54/9.56	   A^2 -> H(f(k), U1(k, e))
28.54/9.56	   A^2 -> H(f(k), e)
28.54/9.56	   A^2 -> H(f(c), d)
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.56	   A^2 -> H(U1(k, k), f(e))
28.54/9.56	   A^2 -> H(U1(k, k), f(k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.56	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.56	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.56	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.56	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.56	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.56	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.56	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.56	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.56	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.56	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.56	   A^2 -> H(U1(d, d), b)
28.54/9.56	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.56	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.56	   A^2 -> H(U1(d, d), c)
28.54/9.56	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.56	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.56	   A^2 -> H(U1(d, d), e)
28.54/9.56	   A^2 -> H(f(d), d)
28.54/9.56	   A^2 -> H(f(d), k)
28.54/9.56	   A^2 -> H(U1(c, c), c)
28.54/9.56	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.56	   A^2 -> H(f(c), k)
28.54/9.56	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.56	   A^2 -> H(f(k), U1(k, k))
28.54/9.56	   A^2 -> H(f(e), e)
28.54/9.56	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.56	   A^2 -> H(d, U1(c, b))
28.54/9.56	   A^2 -> H(d, U1(d, b))
28.54/9.56	   A^2 -> H(d, U1(b, c))
28.54/9.56	   A^2 -> H(d, U1(b, d))
28.54/9.56	   A^2 -> H(d, U1(c, c))
28.54/9.56	   A^2 -> H(d, f(e))
28.54/9.56	   A^2 -> H(d, f(k))
28.54/9.56	   A^2 -> H(d, U1(d, d))
28.54/9.56	   A^2 -> H(a, U1(e, b))
28.54/9.56	   A^2 -> H(a, U1(k, b))
28.54/9.56	   A^2 -> H(a, U1(c, d))
28.54/9.56	   A^2 -> H(a, U1(d, c))
28.54/9.56	   A^2 -> H(a, U1(b, e))
28.54/9.56	   A^2 -> H(a, U1(b, k))
28.54/9.56	   A^2 -> H(a, U1(e, c))
28.54/9.56	   A^2 -> H(a, U1(k, c))
28.54/9.56	   A^2 -> H(a, U1(c, e))
28.54/9.56	   A^2 -> H(a, U1(c, k))
28.54/9.56	   A^2 -> H(a, U1(e, e))
28.54/9.56	   A^2 -> H(a, U1(k, k))
28.54/9.56	   A^2 -> H(a, U1(k, d))
28.54/9.56	   A^2 -> H(a, U1(d, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.56	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.56	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.56	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.56	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.56	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.56	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.56	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.56	   A^2 -> H(U1(e, a), b)
28.54/9.56	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(e, a), c)
28.54/9.56	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(e, a), e)
28.54/9.56	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, a), b)
28.54/9.56	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(k, a), c)
28.54/9.56	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, d), b)
28.54/9.56	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.56	
28.54/9.56	The TRS R consists of the following rules:
28.54/9.56	
28.54/9.56	   f(x) -> U1(x, x)
28.54/9.56	   U1(e, x) -> x
28.54/9.56	   a -> c
28.54/9.56	   a -> d
28.54/9.56	   b -> c
28.54/9.56	   b -> d
28.54/9.56	   d -> k
28.54/9.56	   c -> e
28.54/9.56	   c -> k
28.54/9.56	
28.54/9.56	Q is empty.
28.54/9.56	We have to consider all minimal (P,Q,R)-chains.
28.54/9.56	----------------------------------------
28.54/9.56	
28.54/9.56	(1197) TransformationProof (EQUIVALENT)
28.54/9.56	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.56	
28.54/9.56	   (A^2 -> H(U1(e, d), U1(b, k)),A^2 -> H(U1(e, d), U1(b, k)))
28.54/9.56	   (A^2 -> H(U1(k, d), U1(b, k)),A^2 -> H(U1(k, d), U1(b, k)))
28.54/9.56	   (A^2 -> H(U1(c, k), U1(b, k)),A^2 -> H(U1(c, k), U1(b, k)))
28.54/9.56	   (A^2 -> H(U1(c, d), U1(c, k)),A^2 -> H(U1(c, d), U1(c, k)))
28.54/9.56	   (A^2 -> H(U1(c, d), U1(d, k)),A^2 -> H(U1(c, d), U1(d, k)))
28.54/9.56	
28.54/9.56	
28.54/9.56	----------------------------------------
28.54/9.56	
28.54/9.56	(1198)
28.54/9.56	Obligation:
28.54/9.56	Q DP problem:
28.54/9.56	The TRS P consists of the following rules:
28.54/9.56	
28.54/9.56	   G(d, x, x) -> A^2
28.54/9.56	   A^2 -> H(f(c), f(c))
28.54/9.56	   H(x, x) -> G(x, x, f(k))
28.54/9.56	   A^2 -> H(f(d), f(d))
28.54/9.56	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.56	   A^2 -> H(f(e), f(e))
28.54/9.56	   A^2 -> H(f(k), f(k))
28.54/9.56	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(e, c))
28.54/9.56	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.56	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.56	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.56	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, a), b)
28.54/9.56	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(c, a), c)
28.54/9.56	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(c, a), e)
28.54/9.56	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.56	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.56	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.56	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.56	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.56	   A^2 -> H(U1(d, e), f(e))
28.54/9.56	   A^2 -> H(U1(d, e), f(k))
28.54/9.56	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.56	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.56	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.56	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.56	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.56	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.56	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.56	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.56	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.56	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.56	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.56	   A^2 -> H(U1(d, a), b)
28.54/9.56	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(d, a), c)
28.54/9.56	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(d, a), e)
28.54/9.56	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.56	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.56	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.56	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.56	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.56	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.56	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.56	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.56	   A^2 -> H(U1(a, c), b)
28.54/9.56	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.56	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.56	   A^2 -> H(U1(a, c), c)
28.54/9.56	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.56	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.56	   A^2 -> H(U1(a, c), e)
28.54/9.56	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, d), b)
28.54/9.56	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.56	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.56	   A^2 -> H(U1(a, d), c)
28.54/9.56	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.56	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.56	   A^2 -> H(U1(a, d), e)
28.54/9.56	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, a), d)
28.54/9.56	   A^2 -> H(U1(a, a), k)
28.54/9.56	   A^2 -> H(k, U1(b, b))
28.54/9.56	   A^2 -> H(k, f(c))
28.54/9.56	   A^2 -> H(k, f(d))
28.54/9.56	   A^2 -> H(c, U1(c, b))
28.54/9.56	   A^2 -> H(c, U1(d, b))
28.54/9.56	   A^2 -> H(c, U1(b, c))
28.54/9.56	   A^2 -> H(c, U1(b, d))
28.54/9.56	   A^2 -> H(c, U1(c, c))
28.54/9.56	   A^2 -> H(c, f(e))
28.54/9.56	   A^2 -> H(c, f(k))
28.54/9.56	   A^2 -> H(c, U1(d, d))
28.54/9.56	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.56	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.56	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.56	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.56	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.56	   A^2 -> H(U1(e, k), f(e))
28.54/9.56	   A^2 -> H(U1(e, k), f(k))
28.54/9.56	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.56	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.56	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.56	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.56	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.56	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.56	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.56	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.56	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.56	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.56	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.56	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.56	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.56	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.56	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.56	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.56	   A^2 -> H(U1(k, e), f(e))
28.54/9.56	   A^2 -> H(U1(k, e), f(k))
28.54/9.56	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.56	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.56	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.56	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.56	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.56	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.56	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.56	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.56	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.56	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.56	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.56	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.56	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.56	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.56	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.56	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.56	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.56	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, c), b)
28.54/9.56	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.56	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.56	   A^2 -> H(U1(c, c), e)
28.54/9.56	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.56	   A^2 -> H(e, U1(c, b))
28.54/9.56	   A^2 -> H(e, U1(d, b))
28.54/9.56	   A^2 -> H(e, U1(b, c))
28.54/9.56	   A^2 -> H(e, U1(b, d))
28.54/9.56	   A^2 -> H(e, U1(c, c))
28.54/9.56	   A^2 -> H(e, f(e))
28.54/9.56	   A^2 -> H(e, f(k))
28.54/9.56	   A^2 -> H(e, U1(d, d))
28.54/9.56	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.56	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.56	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.56	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.56	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.56	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.56	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.56	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.56	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.56	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.56	   A^2 -> H(f(e), b)
28.54/9.56	   A^2 -> H(f(e), U1(e, d))
28.54/9.56	   A^2 -> H(f(e), U1(d, e))
28.54/9.56	   A^2 -> H(f(e), c)
28.54/9.56	   A^2 -> H(f(e), U1(e, k))
28.54/9.56	   A^2 -> H(f(e), U1(k, e))
28.54/9.56	   A^2 -> H(f(e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.56	   A^2 -> H(f(k), b)
28.54/9.56	   A^2 -> H(f(k), U1(e, d))
28.54/9.56	   A^2 -> H(f(k), U1(d, e))
28.54/9.56	   A^2 -> H(f(k), c)
28.54/9.56	   A^2 -> H(f(k), U1(e, k))
28.54/9.56	   A^2 -> H(f(k), U1(k, e))
28.54/9.56	   A^2 -> H(f(k), e)
28.54/9.56	   A^2 -> H(f(c), d)
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.56	   A^2 -> H(U1(k, k), f(e))
28.54/9.56	   A^2 -> H(U1(k, k), f(k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.56	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.56	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.56	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.56	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.56	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.56	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.56	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.56	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.56	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.56	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.56	   A^2 -> H(U1(d, d), b)
28.54/9.56	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.56	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.56	   A^2 -> H(U1(d, d), c)
28.54/9.56	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.56	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.56	   A^2 -> H(U1(d, d), e)
28.54/9.56	   A^2 -> H(f(d), d)
28.54/9.56	   A^2 -> H(f(d), k)
28.54/9.56	   A^2 -> H(U1(c, c), c)
28.54/9.56	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.56	   A^2 -> H(f(c), k)
28.54/9.56	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.56	   A^2 -> H(f(k), U1(k, k))
28.54/9.56	   A^2 -> H(f(e), e)
28.54/9.56	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.56	   A^2 -> H(d, U1(c, b))
28.54/9.56	   A^2 -> H(d, U1(d, b))
28.54/9.56	   A^2 -> H(d, U1(b, c))
28.54/9.56	   A^2 -> H(d, U1(b, d))
28.54/9.56	   A^2 -> H(d, U1(c, c))
28.54/9.56	   A^2 -> H(d, f(e))
28.54/9.56	   A^2 -> H(d, f(k))
28.54/9.56	   A^2 -> H(d, U1(d, d))
28.54/9.56	   A^2 -> H(a, U1(e, b))
28.54/9.56	   A^2 -> H(a, U1(k, b))
28.54/9.56	   A^2 -> H(a, U1(c, d))
28.54/9.56	   A^2 -> H(a, U1(d, c))
28.54/9.56	   A^2 -> H(a, U1(b, e))
28.54/9.56	   A^2 -> H(a, U1(b, k))
28.54/9.56	   A^2 -> H(a, U1(e, c))
28.54/9.56	   A^2 -> H(a, U1(k, c))
28.54/9.56	   A^2 -> H(a, U1(c, e))
28.54/9.56	   A^2 -> H(a, U1(c, k))
28.54/9.56	   A^2 -> H(a, U1(e, e))
28.54/9.56	   A^2 -> H(a, U1(k, k))
28.54/9.56	   A^2 -> H(a, U1(k, d))
28.54/9.56	   A^2 -> H(a, U1(d, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.56	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.56	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.56	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.56	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.56	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.56	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.56	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.56	   A^2 -> H(U1(e, a), b)
28.54/9.56	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(e, a), c)
28.54/9.56	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(e, a), e)
28.54/9.56	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, a), b)
28.54/9.56	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(k, a), c)
28.54/9.56	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, d), b)
28.54/9.56	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.56	
28.54/9.56	The TRS R consists of the following rules:
28.54/9.56	
28.54/9.56	   f(x) -> U1(x, x)
28.54/9.56	   U1(e, x) -> x
28.54/9.56	   a -> c
28.54/9.56	   a -> d
28.54/9.56	   b -> c
28.54/9.56	   b -> d
28.54/9.56	   d -> k
28.54/9.56	   c -> e
28.54/9.56	   c -> k
28.54/9.56	
28.54/9.56	Q is empty.
28.54/9.56	We have to consider all minimal (P,Q,R)-chains.
28.54/9.56	----------------------------------------
28.54/9.56	
28.54/9.56	(1199) TransformationProof (EQUIVALENT)
28.54/9.56	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.56	
28.54/9.56	   (A^2 -> H(U1(e, d), U1(e, c)),A^2 -> H(U1(e, d), U1(e, c)))
28.54/9.56	   (A^2 -> H(U1(k, d), U1(e, c)),A^2 -> H(U1(k, d), U1(e, c)))
28.54/9.56	   (A^2 -> H(U1(c, k), U1(e, c)),A^2 -> H(U1(c, k), U1(e, c)))
28.54/9.56	   (A^2 -> H(U1(c, d), c),A^2 -> H(U1(c, d), c))
28.54/9.56	   (A^2 -> H(U1(c, d), U1(e, e)),A^2 -> H(U1(c, d), U1(e, e)))
28.54/9.56	   (A^2 -> H(U1(c, d), U1(e, k)),A^2 -> H(U1(c, d), U1(e, k)))
28.54/9.56	
28.54/9.56	
28.54/9.56	----------------------------------------
28.54/9.56	
28.54/9.56	(1200)
28.54/9.56	Obligation:
28.54/9.56	Q DP problem:
28.54/9.56	The TRS P consists of the following rules:
28.54/9.56	
28.54/9.56	   G(d, x, x) -> A^2
28.54/9.56	   A^2 -> H(f(c), f(c))
28.54/9.56	   H(x, x) -> G(x, x, f(k))
28.54/9.56	   A^2 -> H(f(d), f(d))
28.54/9.56	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.56	   A^2 -> H(f(e), f(e))
28.54/9.56	   A^2 -> H(f(k), f(k))
28.54/9.56	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(k, c))
28.54/9.56	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.56	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.56	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, a), b)
28.54/9.56	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(c, a), c)
28.54/9.56	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(c, a), e)
28.54/9.56	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.56	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.56	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.56	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.56	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.56	   A^2 -> H(U1(d, e), f(e))
28.54/9.56	   A^2 -> H(U1(d, e), f(k))
28.54/9.56	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.56	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.56	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.56	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.56	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.56	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.56	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.56	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.56	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.56	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.56	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.56	   A^2 -> H(U1(d, a), b)
28.54/9.56	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(d, a), c)
28.54/9.56	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(d, a), e)
28.54/9.56	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.56	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.56	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.56	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.56	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.56	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.56	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.56	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.56	   A^2 -> H(U1(a, c), b)
28.54/9.56	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.56	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.56	   A^2 -> H(U1(a, c), c)
28.54/9.56	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.56	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.56	   A^2 -> H(U1(a, c), e)
28.54/9.56	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, d), b)
28.54/9.56	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.56	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.56	   A^2 -> H(U1(a, d), c)
28.54/9.56	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.56	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.56	   A^2 -> H(U1(a, d), e)
28.54/9.56	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, a), d)
28.54/9.56	   A^2 -> H(U1(a, a), k)
28.54/9.56	   A^2 -> H(k, U1(b, b))
28.54/9.56	   A^2 -> H(k, f(c))
28.54/9.56	   A^2 -> H(k, f(d))
28.54/9.56	   A^2 -> H(c, U1(c, b))
28.54/9.56	   A^2 -> H(c, U1(d, b))
28.54/9.56	   A^2 -> H(c, U1(b, c))
28.54/9.56	   A^2 -> H(c, U1(b, d))
28.54/9.56	   A^2 -> H(c, U1(c, c))
28.54/9.56	   A^2 -> H(c, f(e))
28.54/9.56	   A^2 -> H(c, f(k))
28.54/9.56	   A^2 -> H(c, U1(d, d))
28.54/9.56	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.56	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.56	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.56	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.56	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.56	   A^2 -> H(U1(e, k), f(e))
28.54/9.56	   A^2 -> H(U1(e, k), f(k))
28.54/9.56	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.56	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.56	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.56	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.56	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.56	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.56	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.56	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.56	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.56	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.56	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.56	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.56	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.56	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.56	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.56	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.56	   A^2 -> H(U1(k, e), f(e))
28.54/9.56	   A^2 -> H(U1(k, e), f(k))
28.54/9.56	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.56	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.56	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.56	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.56	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.56	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.56	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.56	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.56	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.56	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.56	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.56	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.56	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.56	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.56	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.56	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.56	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.56	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, c), b)
28.54/9.56	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.56	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.56	   A^2 -> H(U1(c, c), e)
28.54/9.56	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.56	   A^2 -> H(e, U1(c, b))
28.54/9.56	   A^2 -> H(e, U1(d, b))
28.54/9.56	   A^2 -> H(e, U1(b, c))
28.54/9.56	   A^2 -> H(e, U1(b, d))
28.54/9.56	   A^2 -> H(e, U1(c, c))
28.54/9.56	   A^2 -> H(e, f(e))
28.54/9.56	   A^2 -> H(e, f(k))
28.54/9.56	   A^2 -> H(e, U1(d, d))
28.54/9.56	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.56	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.56	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.56	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.56	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.56	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.56	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.56	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.56	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.56	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.56	   A^2 -> H(f(e), b)
28.54/9.56	   A^2 -> H(f(e), U1(e, d))
28.54/9.56	   A^2 -> H(f(e), U1(d, e))
28.54/9.56	   A^2 -> H(f(e), c)
28.54/9.56	   A^2 -> H(f(e), U1(e, k))
28.54/9.56	   A^2 -> H(f(e), U1(k, e))
28.54/9.56	   A^2 -> H(f(e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.56	   A^2 -> H(f(k), b)
28.54/9.56	   A^2 -> H(f(k), U1(e, d))
28.54/9.56	   A^2 -> H(f(k), U1(d, e))
28.54/9.56	   A^2 -> H(f(k), c)
28.54/9.56	   A^2 -> H(f(k), U1(e, k))
28.54/9.56	   A^2 -> H(f(k), U1(k, e))
28.54/9.56	   A^2 -> H(f(k), e)
28.54/9.56	   A^2 -> H(f(c), d)
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.56	   A^2 -> H(U1(k, k), f(e))
28.54/9.56	   A^2 -> H(U1(k, k), f(k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.56	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.56	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.56	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.56	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.56	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.56	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.56	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.56	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.56	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.56	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.56	   A^2 -> H(U1(d, d), b)
28.54/9.56	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.56	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.56	   A^2 -> H(U1(d, d), c)
28.54/9.56	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.56	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.56	   A^2 -> H(U1(d, d), e)
28.54/9.56	   A^2 -> H(f(d), d)
28.54/9.56	   A^2 -> H(f(d), k)
28.54/9.56	   A^2 -> H(U1(c, c), c)
28.54/9.56	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.56	   A^2 -> H(f(c), k)
28.54/9.56	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.56	   A^2 -> H(f(k), U1(k, k))
28.54/9.56	   A^2 -> H(f(e), e)
28.54/9.56	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.56	   A^2 -> H(d, U1(c, b))
28.54/9.56	   A^2 -> H(d, U1(d, b))
28.54/9.56	   A^2 -> H(d, U1(b, c))
28.54/9.56	   A^2 -> H(d, U1(b, d))
28.54/9.56	   A^2 -> H(d, U1(c, c))
28.54/9.56	   A^2 -> H(d, f(e))
28.54/9.56	   A^2 -> H(d, f(k))
28.54/9.56	   A^2 -> H(d, U1(d, d))
28.54/9.56	   A^2 -> H(a, U1(e, b))
28.54/9.56	   A^2 -> H(a, U1(k, b))
28.54/9.56	   A^2 -> H(a, U1(c, d))
28.54/9.56	   A^2 -> H(a, U1(d, c))
28.54/9.56	   A^2 -> H(a, U1(b, e))
28.54/9.56	   A^2 -> H(a, U1(b, k))
28.54/9.56	   A^2 -> H(a, U1(e, c))
28.54/9.56	   A^2 -> H(a, U1(k, c))
28.54/9.56	   A^2 -> H(a, U1(c, e))
28.54/9.56	   A^2 -> H(a, U1(c, k))
28.54/9.56	   A^2 -> H(a, U1(e, e))
28.54/9.56	   A^2 -> H(a, U1(k, k))
28.54/9.56	   A^2 -> H(a, U1(k, d))
28.54/9.56	   A^2 -> H(a, U1(d, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.56	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.56	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.56	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.56	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.56	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.56	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.56	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.56	   A^2 -> H(U1(e, a), b)
28.54/9.56	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(e, a), c)
28.54/9.56	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(e, a), e)
28.54/9.56	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, a), b)
28.54/9.56	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(k, a), c)
28.54/9.56	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, d), b)
28.54/9.56	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.56	   A^2 -> H(U1(c, d), c)
28.54/9.56	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.56	
28.54/9.56	The TRS R consists of the following rules:
28.54/9.56	
28.54/9.56	   f(x) -> U1(x, x)
28.54/9.56	   U1(e, x) -> x
28.54/9.56	   a -> c
28.54/9.56	   a -> d
28.54/9.56	   b -> c
28.54/9.56	   b -> d
28.54/9.56	   d -> k
28.54/9.56	   c -> e
28.54/9.56	   c -> k
28.54/9.56	
28.54/9.56	Q is empty.
28.54/9.56	We have to consider all minimal (P,Q,R)-chains.
28.54/9.56	----------------------------------------
28.54/9.56	
28.54/9.56	(1201) TransformationProof (EQUIVALENT)
28.54/9.56	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.56	
28.54/9.56	   (A^2 -> H(U1(e, d), U1(k, c)),A^2 -> H(U1(e, d), U1(k, c)))
28.54/9.56	   (A^2 -> H(U1(k, d), U1(k, c)),A^2 -> H(U1(k, d), U1(k, c)))
28.54/9.56	   (A^2 -> H(U1(c, k), U1(k, c)),A^2 -> H(U1(c, k), U1(k, c)))
28.54/9.56	   (A^2 -> H(U1(c, d), U1(k, e)),A^2 -> H(U1(c, d), U1(k, e)))
28.54/9.56	   (A^2 -> H(U1(c, d), U1(k, k)),A^2 -> H(U1(c, d), U1(k, k)))
28.54/9.56	
28.54/9.56	
28.54/9.56	----------------------------------------
28.54/9.56	
28.54/9.56	(1202)
28.54/9.56	Obligation:
28.54/9.56	Q DP problem:
28.54/9.56	The TRS P consists of the following rules:
28.54/9.56	
28.54/9.56	   G(d, x, x) -> A^2
28.54/9.56	   A^2 -> H(f(c), f(c))
28.54/9.56	   H(x, x) -> G(x, x, f(k))
28.54/9.56	   A^2 -> H(f(d), f(d))
28.54/9.56	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.56	   A^2 -> H(f(e), f(e))
28.54/9.56	   A^2 -> H(f(k), f(k))
28.54/9.56	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(c, e))
28.54/9.56	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.56	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, a), b)
28.54/9.56	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(c, a), c)
28.54/9.56	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(c, a), e)
28.54/9.56	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.56	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.56	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.56	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.56	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.56	   A^2 -> H(U1(d, e), f(e))
28.54/9.56	   A^2 -> H(U1(d, e), f(k))
28.54/9.56	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.56	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.56	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.56	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.56	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.56	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.56	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.56	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.56	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.56	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.56	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.56	   A^2 -> H(U1(d, a), b)
28.54/9.56	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(d, a), c)
28.54/9.56	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(d, a), e)
28.54/9.56	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.56	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.56	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.56	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.56	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.56	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.56	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.56	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.56	   A^2 -> H(U1(a, c), b)
28.54/9.56	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.56	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.56	   A^2 -> H(U1(a, c), c)
28.54/9.56	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.56	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.56	   A^2 -> H(U1(a, c), e)
28.54/9.56	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, d), b)
28.54/9.56	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.56	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.56	   A^2 -> H(U1(a, d), c)
28.54/9.56	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.56	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.56	   A^2 -> H(U1(a, d), e)
28.54/9.56	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, a), d)
28.54/9.56	   A^2 -> H(U1(a, a), k)
28.54/9.56	   A^2 -> H(k, U1(b, b))
28.54/9.56	   A^2 -> H(k, f(c))
28.54/9.56	   A^2 -> H(k, f(d))
28.54/9.56	   A^2 -> H(c, U1(c, b))
28.54/9.56	   A^2 -> H(c, U1(d, b))
28.54/9.56	   A^2 -> H(c, U1(b, c))
28.54/9.56	   A^2 -> H(c, U1(b, d))
28.54/9.56	   A^2 -> H(c, U1(c, c))
28.54/9.56	   A^2 -> H(c, f(e))
28.54/9.56	   A^2 -> H(c, f(k))
28.54/9.56	   A^2 -> H(c, U1(d, d))
28.54/9.56	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.56	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.56	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.56	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.56	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.56	   A^2 -> H(U1(e, k), f(e))
28.54/9.56	   A^2 -> H(U1(e, k), f(k))
28.54/9.56	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.56	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.56	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.56	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.56	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.56	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.56	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.56	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.56	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.56	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.56	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.56	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.56	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.56	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.56	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.56	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.56	   A^2 -> H(U1(k, e), f(e))
28.54/9.56	   A^2 -> H(U1(k, e), f(k))
28.54/9.56	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.56	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.56	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.56	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.56	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.56	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.56	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.56	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.56	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.56	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.56	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.56	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.56	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.56	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.56	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.56	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.56	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.56	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, c), b)
28.54/9.56	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.56	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.56	   A^2 -> H(U1(c, c), e)
28.54/9.56	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.56	   A^2 -> H(e, U1(c, b))
28.54/9.56	   A^2 -> H(e, U1(d, b))
28.54/9.56	   A^2 -> H(e, U1(b, c))
28.54/9.56	   A^2 -> H(e, U1(b, d))
28.54/9.56	   A^2 -> H(e, U1(c, c))
28.54/9.56	   A^2 -> H(e, f(e))
28.54/9.56	   A^2 -> H(e, f(k))
28.54/9.56	   A^2 -> H(e, U1(d, d))
28.54/9.56	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.56	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.56	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.56	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.56	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.56	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.56	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.56	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.56	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.56	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.56	   A^2 -> H(f(e), b)
28.54/9.56	   A^2 -> H(f(e), U1(e, d))
28.54/9.56	   A^2 -> H(f(e), U1(d, e))
28.54/9.56	   A^2 -> H(f(e), c)
28.54/9.56	   A^2 -> H(f(e), U1(e, k))
28.54/9.56	   A^2 -> H(f(e), U1(k, e))
28.54/9.56	   A^2 -> H(f(e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.56	   A^2 -> H(f(k), b)
28.54/9.56	   A^2 -> H(f(k), U1(e, d))
28.54/9.56	   A^2 -> H(f(k), U1(d, e))
28.54/9.56	   A^2 -> H(f(k), c)
28.54/9.56	   A^2 -> H(f(k), U1(e, k))
28.54/9.56	   A^2 -> H(f(k), U1(k, e))
28.54/9.56	   A^2 -> H(f(k), e)
28.54/9.56	   A^2 -> H(f(c), d)
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.56	   A^2 -> H(U1(k, k), f(e))
28.54/9.56	   A^2 -> H(U1(k, k), f(k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.56	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.56	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.56	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.56	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.56	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.56	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.56	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.56	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.56	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.56	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.56	   A^2 -> H(U1(d, d), b)
28.54/9.56	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.56	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.56	   A^2 -> H(U1(d, d), c)
28.54/9.56	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.56	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.56	   A^2 -> H(U1(d, d), e)
28.54/9.56	   A^2 -> H(f(d), d)
28.54/9.56	   A^2 -> H(f(d), k)
28.54/9.56	   A^2 -> H(U1(c, c), c)
28.54/9.56	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.56	   A^2 -> H(f(c), k)
28.54/9.56	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.56	   A^2 -> H(f(k), U1(k, k))
28.54/9.56	   A^2 -> H(f(e), e)
28.54/9.56	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.56	   A^2 -> H(d, U1(c, b))
28.54/9.56	   A^2 -> H(d, U1(d, b))
28.54/9.56	   A^2 -> H(d, U1(b, c))
28.54/9.56	   A^2 -> H(d, U1(b, d))
28.54/9.56	   A^2 -> H(d, U1(c, c))
28.54/9.56	   A^2 -> H(d, f(e))
28.54/9.56	   A^2 -> H(d, f(k))
28.54/9.56	   A^2 -> H(d, U1(d, d))
28.54/9.56	   A^2 -> H(a, U1(e, b))
28.54/9.56	   A^2 -> H(a, U1(k, b))
28.54/9.56	   A^2 -> H(a, U1(c, d))
28.54/9.56	   A^2 -> H(a, U1(d, c))
28.54/9.56	   A^2 -> H(a, U1(b, e))
28.54/9.56	   A^2 -> H(a, U1(b, k))
28.54/9.56	   A^2 -> H(a, U1(e, c))
28.54/9.56	   A^2 -> H(a, U1(k, c))
28.54/9.56	   A^2 -> H(a, U1(c, e))
28.54/9.56	   A^2 -> H(a, U1(c, k))
28.54/9.56	   A^2 -> H(a, U1(e, e))
28.54/9.56	   A^2 -> H(a, U1(k, k))
28.54/9.56	   A^2 -> H(a, U1(k, d))
28.54/9.56	   A^2 -> H(a, U1(d, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.56	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.56	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.56	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.56	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.56	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.56	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.56	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.56	   A^2 -> H(U1(e, a), b)
28.54/9.56	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(e, a), c)
28.54/9.56	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(e, a), e)
28.54/9.56	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, a), b)
28.54/9.56	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(k, a), c)
28.54/9.56	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, d), b)
28.54/9.56	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.56	   A^2 -> H(U1(c, d), c)
28.54/9.56	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.56	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.56	
28.54/9.56	The TRS R consists of the following rules:
28.54/9.56	
28.54/9.56	   f(x) -> U1(x, x)
28.54/9.56	   U1(e, x) -> x
28.54/9.56	   a -> c
28.54/9.56	   a -> d
28.54/9.56	   b -> c
28.54/9.56	   b -> d
28.54/9.56	   d -> k
28.54/9.56	   c -> e
28.54/9.56	   c -> k
28.54/9.56	
28.54/9.56	Q is empty.
28.54/9.56	We have to consider all minimal (P,Q,R)-chains.
28.54/9.56	----------------------------------------
28.54/9.56	
28.54/9.56	(1203) TransformationProof (EQUIVALENT)
28.54/9.56	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.56	
28.54/9.56	   (A^2 -> H(U1(e, d), U1(c, e)),A^2 -> H(U1(e, d), U1(c, e)))
28.54/9.56	   (A^2 -> H(U1(k, d), U1(c, e)),A^2 -> H(U1(k, d), U1(c, e)))
28.54/9.56	   (A^2 -> H(U1(c, k), U1(c, e)),A^2 -> H(U1(c, k), U1(c, e)))
28.54/9.56	   (A^2 -> H(U1(c, d), U1(e, e)),A^2 -> H(U1(c, d), U1(e, e)))
28.54/9.56	   (A^2 -> H(U1(c, d), U1(k, e)),A^2 -> H(U1(c, d), U1(k, e)))
28.54/9.56	
28.54/9.56	
28.54/9.56	----------------------------------------
28.54/9.56	
28.54/9.56	(1204)
28.54/9.56	Obligation:
28.54/9.56	Q DP problem:
28.54/9.56	The TRS P consists of the following rules:
28.54/9.56	
28.54/9.56	   G(d, x, x) -> A^2
28.54/9.56	   A^2 -> H(f(c), f(c))
28.54/9.56	   H(x, x) -> G(x, x, f(k))
28.54/9.56	   A^2 -> H(f(d), f(d))
28.54/9.56	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.56	   A^2 -> H(f(e), f(e))
28.54/9.56	   A^2 -> H(f(k), f(k))
28.54/9.56	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(c, k))
28.54/9.56	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.56	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, a), b)
28.54/9.56	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(c, a), c)
28.54/9.56	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(c, a), e)
28.54/9.56	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.56	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.56	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.56	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.56	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.56	   A^2 -> H(U1(d, e), f(e))
28.54/9.56	   A^2 -> H(U1(d, e), f(k))
28.54/9.56	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.56	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.56	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.56	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.56	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.56	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.56	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.56	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.56	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.56	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.56	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.56	   A^2 -> H(U1(d, a), b)
28.54/9.56	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.56	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.56	   A^2 -> H(U1(d, a), c)
28.54/9.56	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.56	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.56	   A^2 -> H(U1(d, a), e)
28.54/9.56	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.56	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.56	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.56	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.56	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.56	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.56	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.56	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.56	   A^2 -> H(U1(a, c), b)
28.54/9.56	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.56	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.56	   A^2 -> H(U1(a, c), c)
28.54/9.56	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.56	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.56	   A^2 -> H(U1(a, c), e)
28.54/9.56	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, d), b)
28.54/9.56	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.56	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.56	   A^2 -> H(U1(a, d), c)
28.54/9.56	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.56	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.56	   A^2 -> H(U1(a, d), e)
28.54/9.56	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(a, a), d)
28.54/9.56	   A^2 -> H(U1(a, a), k)
28.54/9.56	   A^2 -> H(k, U1(b, b))
28.54/9.56	   A^2 -> H(k, f(c))
28.54/9.56	   A^2 -> H(k, f(d))
28.54/9.56	   A^2 -> H(c, U1(c, b))
28.54/9.56	   A^2 -> H(c, U1(d, b))
28.54/9.56	   A^2 -> H(c, U1(b, c))
28.54/9.56	   A^2 -> H(c, U1(b, d))
28.54/9.56	   A^2 -> H(c, U1(c, c))
28.54/9.56	   A^2 -> H(c, f(e))
28.54/9.56	   A^2 -> H(c, f(k))
28.54/9.56	   A^2 -> H(c, U1(d, d))
28.54/9.56	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.56	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.56	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.56	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.56	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.56	   A^2 -> H(U1(e, k), f(e))
28.54/9.56	   A^2 -> H(U1(e, k), f(k))
28.54/9.56	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.56	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.56	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.56	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.56	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.56	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.56	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.56	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.56	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.56	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.56	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.56	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.56	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.56	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.56	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.56	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.56	   A^2 -> H(U1(k, e), f(e))
28.54/9.56	   A^2 -> H(U1(k, e), f(k))
28.54/9.56	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.56	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.56	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.56	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.56	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.56	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.56	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.56	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.56	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.56	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.56	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.56	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.56	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.56	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.56	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.56	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.56	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.56	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.56	   A^2 -> H(U1(c, c), b)
28.54/9.56	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.56	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.56	   A^2 -> H(U1(c, c), e)
28.54/9.56	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.56	   A^2 -> H(e, U1(c, b))
28.54/9.56	   A^2 -> H(e, U1(d, b))
28.54/9.56	   A^2 -> H(e, U1(b, c))
28.54/9.56	   A^2 -> H(e, U1(b, d))
28.54/9.56	   A^2 -> H(e, U1(c, c))
28.54/9.56	   A^2 -> H(e, f(e))
28.54/9.56	   A^2 -> H(e, f(k))
28.54/9.56	   A^2 -> H(e, U1(d, d))
28.54/9.56	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.56	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.56	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.56	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.56	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.56	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.56	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.56	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.56	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.56	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.56	   A^2 -> H(f(e), b)
28.54/9.56	   A^2 -> H(f(e), U1(e, d))
28.54/9.56	   A^2 -> H(f(e), U1(d, e))
28.54/9.56	   A^2 -> H(f(e), c)
28.54/9.56	   A^2 -> H(f(e), U1(e, k))
28.54/9.56	   A^2 -> H(f(e), U1(k, e))
28.54/9.56	   A^2 -> H(f(e), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.56	   A^2 -> H(f(k), b)
28.54/9.56	   A^2 -> H(f(k), U1(e, d))
28.54/9.56	   A^2 -> H(f(k), U1(d, e))
28.54/9.56	   A^2 -> H(f(k), c)
28.54/9.56	   A^2 -> H(f(k), U1(e, k))
28.54/9.56	   A^2 -> H(f(k), U1(k, e))
28.54/9.56	   A^2 -> H(f(k), e)
28.54/9.56	   A^2 -> H(f(c), d)
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.56	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.56	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.56	   A^2 -> H(U1(k, k), f(e))
28.54/9.56	   A^2 -> H(U1(k, k), f(k))
28.54/9.56	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.56	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.56	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.56	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.56	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.56	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.56	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.56	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.56	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.56	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.56	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.56	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.57	   A^2 -> H(U1(d, d), b)
28.54/9.57	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.57	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.57	   A^2 -> H(U1(d, d), c)
28.54/9.57	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.57	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.57	   A^2 -> H(U1(d, d), e)
28.54/9.57	   A^2 -> H(f(d), d)
28.54/9.57	   A^2 -> H(f(d), k)
28.54/9.57	   A^2 -> H(U1(c, c), c)
28.54/9.57	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.57	   A^2 -> H(f(c), k)
28.54/9.57	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.57	   A^2 -> H(f(k), U1(k, k))
28.54/9.57	   A^2 -> H(f(e), e)
28.54/9.57	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.57	   A^2 -> H(d, U1(c, b))
28.54/9.57	   A^2 -> H(d, U1(d, b))
28.54/9.57	   A^2 -> H(d, U1(b, c))
28.54/9.57	   A^2 -> H(d, U1(b, d))
28.54/9.57	   A^2 -> H(d, U1(c, c))
28.54/9.57	   A^2 -> H(d, f(e))
28.54/9.57	   A^2 -> H(d, f(k))
28.54/9.57	   A^2 -> H(d, U1(d, d))
28.54/9.57	   A^2 -> H(a, U1(e, b))
28.54/9.57	   A^2 -> H(a, U1(k, b))
28.54/9.57	   A^2 -> H(a, U1(c, d))
28.54/9.57	   A^2 -> H(a, U1(d, c))
28.54/9.57	   A^2 -> H(a, U1(b, e))
28.54/9.57	   A^2 -> H(a, U1(b, k))
28.54/9.57	   A^2 -> H(a, U1(e, c))
28.54/9.57	   A^2 -> H(a, U1(k, c))
28.54/9.57	   A^2 -> H(a, U1(c, e))
28.54/9.57	   A^2 -> H(a, U1(c, k))
28.54/9.57	   A^2 -> H(a, U1(e, e))
28.54/9.57	   A^2 -> H(a, U1(k, k))
28.54/9.57	   A^2 -> H(a, U1(k, d))
28.54/9.57	   A^2 -> H(a, U1(d, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.57	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.57	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.57	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.57	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.57	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.57	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.57	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.57	   A^2 -> H(U1(e, a), b)
28.54/9.57	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(e, a), c)
28.54/9.57	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(e, a), e)
28.54/9.57	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, a), b)
28.54/9.57	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(k, a), c)
28.54/9.57	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(c, d), b)
28.54/9.57	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.57	   A^2 -> H(U1(c, d), c)
28.54/9.57	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.57	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.57	
28.54/9.57	The TRS R consists of the following rules:
28.54/9.57	
28.54/9.57	   f(x) -> U1(x, x)
28.54/9.57	   U1(e, x) -> x
28.54/9.57	   a -> c
28.54/9.57	   a -> d
28.54/9.57	   b -> c
28.54/9.57	   b -> d
28.54/9.57	   d -> k
28.54/9.57	   c -> e
28.54/9.57	   c -> k
28.54/9.57	
28.54/9.57	Q is empty.
28.54/9.57	We have to consider all minimal (P,Q,R)-chains.
28.54/9.57	----------------------------------------
28.54/9.57	
28.54/9.57	(1205) TransformationProof (EQUIVALENT)
28.54/9.57	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.57	
28.54/9.57	   (A^2 -> H(U1(e, d), U1(c, k)),A^2 -> H(U1(e, d), U1(c, k)))
28.54/9.57	   (A^2 -> H(U1(k, d), U1(c, k)),A^2 -> H(U1(k, d), U1(c, k)))
28.54/9.57	   (A^2 -> H(U1(c, k), U1(c, k)),A^2 -> H(U1(c, k), U1(c, k)))
28.54/9.57	   (A^2 -> H(U1(c, d), U1(e, k)),A^2 -> H(U1(c, d), U1(e, k)))
28.54/9.57	   (A^2 -> H(U1(c, d), U1(k, k)),A^2 -> H(U1(c, d), U1(k, k)))
28.54/9.57	
28.54/9.57	
28.54/9.57	----------------------------------------
28.54/9.57	
28.54/9.57	(1206)
28.54/9.57	Obligation:
28.54/9.57	Q DP problem:
28.54/9.57	The TRS P consists of the following rules:
28.54/9.57	
28.54/9.57	   G(d, x, x) -> A^2
28.54/9.57	   A^2 -> H(f(c), f(c))
28.54/9.57	   H(x, x) -> G(x, x, f(k))
28.54/9.57	   A^2 -> H(f(d), f(d))
28.54/9.57	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.57	   A^2 -> H(f(e), f(e))
28.54/9.57	   A^2 -> H(f(k), f(k))
28.54/9.57	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(e, e))
28.54/9.57	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.57	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, a), b)
28.54/9.57	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(c, a), c)
28.54/9.57	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(c, a), e)
28.54/9.57	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.57	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.57	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.57	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.57	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.57	   A^2 -> H(U1(d, e), f(e))
28.54/9.57	   A^2 -> H(U1(d, e), f(k))
28.54/9.57	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.57	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.57	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.57	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.57	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.57	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.57	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.57	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.57	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.57	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.57	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.57	   A^2 -> H(U1(d, a), b)
28.54/9.57	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(d, a), c)
28.54/9.57	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(d, a), e)
28.54/9.57	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.57	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.57	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.57	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.57	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.57	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.57	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.57	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.57	   A^2 -> H(U1(a, c), b)
28.54/9.57	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.57	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.57	   A^2 -> H(U1(a, c), c)
28.54/9.57	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.57	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.57	   A^2 -> H(U1(a, c), e)
28.54/9.57	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, d), b)
28.54/9.57	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.57	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.57	   A^2 -> H(U1(a, d), c)
28.54/9.57	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.57	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.57	   A^2 -> H(U1(a, d), e)
28.54/9.57	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, a), d)
28.54/9.57	   A^2 -> H(U1(a, a), k)
28.54/9.57	   A^2 -> H(k, U1(b, b))
28.54/9.57	   A^2 -> H(k, f(c))
28.54/9.57	   A^2 -> H(k, f(d))
28.54/9.57	   A^2 -> H(c, U1(c, b))
28.54/9.57	   A^2 -> H(c, U1(d, b))
28.54/9.57	   A^2 -> H(c, U1(b, c))
28.54/9.57	   A^2 -> H(c, U1(b, d))
28.54/9.57	   A^2 -> H(c, U1(c, c))
28.54/9.57	   A^2 -> H(c, f(e))
28.54/9.57	   A^2 -> H(c, f(k))
28.54/9.57	   A^2 -> H(c, U1(d, d))
28.54/9.57	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.57	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.57	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.57	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.57	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.57	   A^2 -> H(U1(e, k), f(e))
28.54/9.57	   A^2 -> H(U1(e, k), f(k))
28.54/9.57	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.57	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.57	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.57	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.57	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.57	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.57	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.57	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.57	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.57	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.57	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.57	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.57	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.57	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.57	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.57	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.57	   A^2 -> H(U1(k, e), f(e))
28.54/9.57	   A^2 -> H(U1(k, e), f(k))
28.54/9.57	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.57	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.57	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.57	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.57	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.57	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.57	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.57	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.57	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.57	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.57	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.57	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.57	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.57	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.57	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.57	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.57	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.57	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, c), b)
28.54/9.57	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.57	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.57	   A^2 -> H(U1(c, c), e)
28.54/9.57	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.57	   A^2 -> H(e, U1(c, b))
28.54/9.57	   A^2 -> H(e, U1(d, b))
28.54/9.57	   A^2 -> H(e, U1(b, c))
28.54/9.57	   A^2 -> H(e, U1(b, d))
28.54/9.57	   A^2 -> H(e, U1(c, c))
28.54/9.57	   A^2 -> H(e, f(e))
28.54/9.57	   A^2 -> H(e, f(k))
28.54/9.57	   A^2 -> H(e, U1(d, d))
28.54/9.57	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.57	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.57	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.57	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.57	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.57	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.57	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.57	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.57	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.57	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.57	   A^2 -> H(f(e), b)
28.54/9.57	   A^2 -> H(f(e), U1(e, d))
28.54/9.57	   A^2 -> H(f(e), U1(d, e))
28.54/9.57	   A^2 -> H(f(e), c)
28.54/9.57	   A^2 -> H(f(e), U1(e, k))
28.54/9.57	   A^2 -> H(f(e), U1(k, e))
28.54/9.57	   A^2 -> H(f(e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.57	   A^2 -> H(f(k), b)
28.54/9.57	   A^2 -> H(f(k), U1(e, d))
28.54/9.57	   A^2 -> H(f(k), U1(d, e))
28.54/9.57	   A^2 -> H(f(k), c)
28.54/9.57	   A^2 -> H(f(k), U1(e, k))
28.54/9.57	   A^2 -> H(f(k), U1(k, e))
28.54/9.57	   A^2 -> H(f(k), e)
28.54/9.57	   A^2 -> H(f(c), d)
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.57	   A^2 -> H(U1(k, k), f(e))
28.54/9.57	   A^2 -> H(U1(k, k), f(k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.57	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.57	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.57	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.57	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.57	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.57	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.57	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.57	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.57	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.57	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.57	   A^2 -> H(U1(d, d), b)
28.54/9.57	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.57	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.57	   A^2 -> H(U1(d, d), c)
28.54/9.57	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.57	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.57	   A^2 -> H(U1(d, d), e)
28.54/9.57	   A^2 -> H(f(d), d)
28.54/9.57	   A^2 -> H(f(d), k)
28.54/9.57	   A^2 -> H(U1(c, c), c)
28.54/9.57	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.57	   A^2 -> H(f(c), k)
28.54/9.57	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.57	   A^2 -> H(f(k), U1(k, k))
28.54/9.57	   A^2 -> H(f(e), e)
28.54/9.57	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.57	   A^2 -> H(d, U1(c, b))
28.54/9.57	   A^2 -> H(d, U1(d, b))
28.54/9.57	   A^2 -> H(d, U1(b, c))
28.54/9.57	   A^2 -> H(d, U1(b, d))
28.54/9.57	   A^2 -> H(d, U1(c, c))
28.54/9.57	   A^2 -> H(d, f(e))
28.54/9.57	   A^2 -> H(d, f(k))
28.54/9.57	   A^2 -> H(d, U1(d, d))
28.54/9.57	   A^2 -> H(a, U1(e, b))
28.54/9.57	   A^2 -> H(a, U1(k, b))
28.54/9.57	   A^2 -> H(a, U1(c, d))
28.54/9.57	   A^2 -> H(a, U1(d, c))
28.54/9.57	   A^2 -> H(a, U1(b, e))
28.54/9.57	   A^2 -> H(a, U1(b, k))
28.54/9.57	   A^2 -> H(a, U1(e, c))
28.54/9.57	   A^2 -> H(a, U1(k, c))
28.54/9.57	   A^2 -> H(a, U1(c, e))
28.54/9.57	   A^2 -> H(a, U1(c, k))
28.54/9.57	   A^2 -> H(a, U1(e, e))
28.54/9.57	   A^2 -> H(a, U1(k, k))
28.54/9.57	   A^2 -> H(a, U1(k, d))
28.54/9.57	   A^2 -> H(a, U1(d, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.57	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.57	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.57	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.57	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.57	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.57	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.57	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.57	   A^2 -> H(U1(e, a), b)
28.54/9.57	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(e, a), c)
28.54/9.57	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(e, a), e)
28.54/9.57	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, a), b)
28.54/9.57	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(k, a), c)
28.54/9.57	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(c, d), b)
28.54/9.57	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.57	   A^2 -> H(U1(c, d), c)
28.54/9.57	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.57	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.57	
28.54/9.57	The TRS R consists of the following rules:
28.54/9.57	
28.54/9.57	   f(x) -> U1(x, x)
28.54/9.57	   U1(e, x) -> x
28.54/9.57	   a -> c
28.54/9.57	   a -> d
28.54/9.57	   b -> c
28.54/9.57	   b -> d
28.54/9.57	   d -> k
28.54/9.57	   c -> e
28.54/9.57	   c -> k
28.54/9.57	
28.54/9.57	Q is empty.
28.54/9.57	We have to consider all minimal (P,Q,R)-chains.
28.54/9.57	----------------------------------------
28.54/9.57	
28.54/9.57	(1207) TransformationProof (EQUIVALENT)
28.54/9.57	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.57	
28.54/9.57	   (A^2 -> H(U1(e, d), U1(e, e)),A^2 -> H(U1(e, d), U1(e, e)))
28.54/9.57	   (A^2 -> H(U1(k, d), U1(e, e)),A^2 -> H(U1(k, d), U1(e, e)))
28.54/9.57	   (A^2 -> H(U1(c, k), U1(e, e)),A^2 -> H(U1(c, k), U1(e, e)))
28.54/9.57	   (A^2 -> H(U1(c, d), e),A^2 -> H(U1(c, d), e))
28.54/9.57	
28.54/9.57	
28.54/9.57	----------------------------------------
28.54/9.57	
28.54/9.57	(1208)
28.54/9.57	Obligation:
28.54/9.57	Q DP problem:
28.54/9.57	The TRS P consists of the following rules:
28.54/9.57	
28.54/9.57	   G(d, x, x) -> A^2
28.54/9.57	   A^2 -> H(f(c), f(c))
28.54/9.57	   H(x, x) -> G(x, x, f(k))
28.54/9.57	   A^2 -> H(f(d), f(d))
28.54/9.57	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.57	   A^2 -> H(f(e), f(e))
28.54/9.57	   A^2 -> H(f(k), f(k))
28.54/9.57	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.57	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, a), b)
28.54/9.57	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(c, a), c)
28.54/9.57	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(c, a), e)
28.54/9.57	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.57	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.57	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.57	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.57	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.57	   A^2 -> H(U1(d, e), f(e))
28.54/9.57	   A^2 -> H(U1(d, e), f(k))
28.54/9.57	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.57	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.57	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.57	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.57	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.57	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.57	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.57	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.57	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.57	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.57	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.57	   A^2 -> H(U1(d, a), b)
28.54/9.57	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(d, a), c)
28.54/9.57	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(d, a), e)
28.54/9.57	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.57	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.57	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.57	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.57	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.57	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.57	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.57	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.57	   A^2 -> H(U1(a, c), b)
28.54/9.57	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.57	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.57	   A^2 -> H(U1(a, c), c)
28.54/9.57	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.57	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.57	   A^2 -> H(U1(a, c), e)
28.54/9.57	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, d), b)
28.54/9.57	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.57	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.57	   A^2 -> H(U1(a, d), c)
28.54/9.57	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.57	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.57	   A^2 -> H(U1(a, d), e)
28.54/9.57	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, a), d)
28.54/9.57	   A^2 -> H(U1(a, a), k)
28.54/9.57	   A^2 -> H(k, U1(b, b))
28.54/9.57	   A^2 -> H(k, f(c))
28.54/9.57	   A^2 -> H(k, f(d))
28.54/9.57	   A^2 -> H(c, U1(c, b))
28.54/9.57	   A^2 -> H(c, U1(d, b))
28.54/9.57	   A^2 -> H(c, U1(b, c))
28.54/9.57	   A^2 -> H(c, U1(b, d))
28.54/9.57	   A^2 -> H(c, U1(c, c))
28.54/9.57	   A^2 -> H(c, f(e))
28.54/9.57	   A^2 -> H(c, f(k))
28.54/9.57	   A^2 -> H(c, U1(d, d))
28.54/9.57	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.57	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.57	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.57	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.57	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.57	   A^2 -> H(U1(e, k), f(e))
28.54/9.57	   A^2 -> H(U1(e, k), f(k))
28.54/9.57	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.57	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.57	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.57	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.57	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.57	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.57	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.57	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.57	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.57	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.57	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.57	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.57	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.57	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.57	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.57	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.57	   A^2 -> H(U1(k, e), f(e))
28.54/9.57	   A^2 -> H(U1(k, e), f(k))
28.54/9.57	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.57	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.57	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.57	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.57	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.57	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.57	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.57	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.57	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.57	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.57	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.57	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.57	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.57	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.57	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.57	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.57	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.57	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, c), b)
28.54/9.57	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.57	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.57	   A^2 -> H(U1(c, c), e)
28.54/9.57	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.57	   A^2 -> H(e, U1(c, b))
28.54/9.57	   A^2 -> H(e, U1(d, b))
28.54/9.57	   A^2 -> H(e, U1(b, c))
28.54/9.57	   A^2 -> H(e, U1(b, d))
28.54/9.57	   A^2 -> H(e, U1(c, c))
28.54/9.57	   A^2 -> H(e, f(e))
28.54/9.57	   A^2 -> H(e, f(k))
28.54/9.57	   A^2 -> H(e, U1(d, d))
28.54/9.57	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.57	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.57	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.57	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.57	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.57	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.57	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.57	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.57	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.57	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.57	   A^2 -> H(f(e), b)
28.54/9.57	   A^2 -> H(f(e), U1(e, d))
28.54/9.57	   A^2 -> H(f(e), U1(d, e))
28.54/9.57	   A^2 -> H(f(e), c)
28.54/9.57	   A^2 -> H(f(e), U1(e, k))
28.54/9.57	   A^2 -> H(f(e), U1(k, e))
28.54/9.57	   A^2 -> H(f(e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.57	   A^2 -> H(f(k), b)
28.54/9.57	   A^2 -> H(f(k), U1(e, d))
28.54/9.57	   A^2 -> H(f(k), U1(d, e))
28.54/9.57	   A^2 -> H(f(k), c)
28.54/9.57	   A^2 -> H(f(k), U1(e, k))
28.54/9.57	   A^2 -> H(f(k), U1(k, e))
28.54/9.57	   A^2 -> H(f(k), e)
28.54/9.57	   A^2 -> H(f(c), d)
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.57	   A^2 -> H(U1(k, k), f(e))
28.54/9.57	   A^2 -> H(U1(k, k), f(k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.57	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.57	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.57	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.57	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.57	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.57	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.57	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.57	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.57	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.57	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.57	   A^2 -> H(U1(d, d), b)
28.54/9.57	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.57	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.57	   A^2 -> H(U1(d, d), c)
28.54/9.57	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.57	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.57	   A^2 -> H(U1(d, d), e)
28.54/9.57	   A^2 -> H(f(d), d)
28.54/9.57	   A^2 -> H(f(d), k)
28.54/9.57	   A^2 -> H(U1(c, c), c)
28.54/9.57	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.57	   A^2 -> H(f(c), k)
28.54/9.57	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.57	   A^2 -> H(f(k), U1(k, k))
28.54/9.57	   A^2 -> H(f(e), e)
28.54/9.57	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.57	   A^2 -> H(d, U1(c, b))
28.54/9.57	   A^2 -> H(d, U1(d, b))
28.54/9.57	   A^2 -> H(d, U1(b, c))
28.54/9.57	   A^2 -> H(d, U1(b, d))
28.54/9.57	   A^2 -> H(d, U1(c, c))
28.54/9.57	   A^2 -> H(d, f(e))
28.54/9.57	   A^2 -> H(d, f(k))
28.54/9.57	   A^2 -> H(d, U1(d, d))
28.54/9.57	   A^2 -> H(a, U1(e, b))
28.54/9.57	   A^2 -> H(a, U1(k, b))
28.54/9.57	   A^2 -> H(a, U1(c, d))
28.54/9.57	   A^2 -> H(a, U1(d, c))
28.54/9.57	   A^2 -> H(a, U1(b, e))
28.54/9.57	   A^2 -> H(a, U1(b, k))
28.54/9.57	   A^2 -> H(a, U1(e, c))
28.54/9.57	   A^2 -> H(a, U1(k, c))
28.54/9.57	   A^2 -> H(a, U1(c, e))
28.54/9.57	   A^2 -> H(a, U1(c, k))
28.54/9.57	   A^2 -> H(a, U1(e, e))
28.54/9.57	   A^2 -> H(a, U1(k, k))
28.54/9.57	   A^2 -> H(a, U1(k, d))
28.54/9.57	   A^2 -> H(a, U1(d, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.57	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.57	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.57	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.57	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.57	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.57	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.57	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.57	   A^2 -> H(U1(e, a), b)
28.54/9.57	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(e, a), c)
28.54/9.57	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(e, a), e)
28.54/9.57	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, a), b)
28.54/9.57	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(k, a), c)
28.54/9.57	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(c, d), b)
28.54/9.57	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.57	   A^2 -> H(U1(c, d), c)
28.54/9.57	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.57	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.57	   A^2 -> H(U1(c, d), e)
28.54/9.57	
28.54/9.57	The TRS R consists of the following rules:
28.54/9.57	
28.54/9.57	   f(x) -> U1(x, x)
28.54/9.57	   U1(e, x) -> x
28.54/9.57	   a -> c
28.54/9.57	   a -> d
28.54/9.57	   b -> c
28.54/9.57	   b -> d
28.54/9.57	   d -> k
28.54/9.57	   c -> e
28.54/9.57	   c -> k
28.54/9.57	
28.54/9.57	Q is empty.
28.54/9.57	We have to consider all minimal (P,Q,R)-chains.
28.54/9.57	----------------------------------------
28.54/9.57	
28.54/9.57	(1209) TransformationProof (EQUIVALENT)
28.54/9.57	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.57	
28.54/9.57	   (A^2 -> H(U1(e, d), U1(k, k)),A^2 -> H(U1(e, d), U1(k, k)))
28.54/9.57	   (A^2 -> H(U1(k, d), U1(k, k)),A^2 -> H(U1(k, d), U1(k, k)))
28.54/9.57	   (A^2 -> H(U1(c, k), U1(k, k)),A^2 -> H(U1(c, k), U1(k, k)))
28.54/9.57	
28.54/9.57	
28.54/9.57	----------------------------------------
28.54/9.57	
28.54/9.57	(1210)
28.54/9.57	Obligation:
28.54/9.57	Q DP problem:
28.54/9.57	The TRS P consists of the following rules:
28.54/9.57	
28.54/9.57	   G(d, x, x) -> A^2
28.54/9.57	   A^2 -> H(f(c), f(c))
28.54/9.57	   H(x, x) -> G(x, x, f(k))
28.54/9.57	   A^2 -> H(f(d), f(d))
28.54/9.57	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.57	   A^2 -> H(f(e), f(e))
28.54/9.57	   A^2 -> H(f(k), f(k))
28.54/9.57	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(k, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, a), b)
28.54/9.57	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(c, a), c)
28.54/9.57	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(c, a), e)
28.54/9.57	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.57	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.57	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.57	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.57	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.57	   A^2 -> H(U1(d, e), f(e))
28.54/9.57	   A^2 -> H(U1(d, e), f(k))
28.54/9.57	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.57	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.57	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.57	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.57	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.57	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.57	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.57	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.57	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.57	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.57	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.57	   A^2 -> H(U1(d, a), b)
28.54/9.57	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(d, a), c)
28.54/9.57	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(d, a), e)
28.54/9.57	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.57	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.57	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.57	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.57	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.57	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.57	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.57	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.57	   A^2 -> H(U1(a, c), b)
28.54/9.57	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.57	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.57	   A^2 -> H(U1(a, c), c)
28.54/9.57	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.57	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.57	   A^2 -> H(U1(a, c), e)
28.54/9.57	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, d), b)
28.54/9.57	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.57	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.57	   A^2 -> H(U1(a, d), c)
28.54/9.57	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.57	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.57	   A^2 -> H(U1(a, d), e)
28.54/9.57	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, a), d)
28.54/9.57	   A^2 -> H(U1(a, a), k)
28.54/9.57	   A^2 -> H(k, U1(b, b))
28.54/9.57	   A^2 -> H(k, f(c))
28.54/9.57	   A^2 -> H(k, f(d))
28.54/9.57	   A^2 -> H(c, U1(c, b))
28.54/9.57	   A^2 -> H(c, U1(d, b))
28.54/9.57	   A^2 -> H(c, U1(b, c))
28.54/9.57	   A^2 -> H(c, U1(b, d))
28.54/9.57	   A^2 -> H(c, U1(c, c))
28.54/9.57	   A^2 -> H(c, f(e))
28.54/9.57	   A^2 -> H(c, f(k))
28.54/9.57	   A^2 -> H(c, U1(d, d))
28.54/9.57	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.57	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.57	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.57	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.57	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.57	   A^2 -> H(U1(e, k), f(e))
28.54/9.57	   A^2 -> H(U1(e, k), f(k))
28.54/9.57	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.57	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.57	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.57	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.57	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.57	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.57	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.57	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.57	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.57	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.57	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.57	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.57	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.57	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.57	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.57	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.57	   A^2 -> H(U1(k, e), f(e))
28.54/9.57	   A^2 -> H(U1(k, e), f(k))
28.54/9.57	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.57	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.57	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.57	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.57	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.57	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.57	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.57	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.57	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.57	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.57	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.57	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.57	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.57	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.57	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.57	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.57	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.57	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, c), b)
28.54/9.57	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.57	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.57	   A^2 -> H(U1(c, c), e)
28.54/9.57	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.57	   A^2 -> H(e, U1(c, b))
28.54/9.57	   A^2 -> H(e, U1(d, b))
28.54/9.57	   A^2 -> H(e, U1(b, c))
28.54/9.57	   A^2 -> H(e, U1(b, d))
28.54/9.57	   A^2 -> H(e, U1(c, c))
28.54/9.57	   A^2 -> H(e, f(e))
28.54/9.57	   A^2 -> H(e, f(k))
28.54/9.57	   A^2 -> H(e, U1(d, d))
28.54/9.57	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.57	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.57	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.57	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.57	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.57	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.57	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.57	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.57	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.57	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.57	   A^2 -> H(f(e), b)
28.54/9.57	   A^2 -> H(f(e), U1(e, d))
28.54/9.57	   A^2 -> H(f(e), U1(d, e))
28.54/9.57	   A^2 -> H(f(e), c)
28.54/9.57	   A^2 -> H(f(e), U1(e, k))
28.54/9.57	   A^2 -> H(f(e), U1(k, e))
28.54/9.57	   A^2 -> H(f(e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.57	   A^2 -> H(f(k), b)
28.54/9.57	   A^2 -> H(f(k), U1(e, d))
28.54/9.57	   A^2 -> H(f(k), U1(d, e))
28.54/9.57	   A^2 -> H(f(k), c)
28.54/9.57	   A^2 -> H(f(k), U1(e, k))
28.54/9.57	   A^2 -> H(f(k), U1(k, e))
28.54/9.57	   A^2 -> H(f(k), e)
28.54/9.57	   A^2 -> H(f(c), d)
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.57	   A^2 -> H(U1(k, k), f(e))
28.54/9.57	   A^2 -> H(U1(k, k), f(k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.57	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.57	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.57	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.57	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.57	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.57	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.57	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.57	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.57	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.57	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.57	   A^2 -> H(U1(d, d), b)
28.54/9.57	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.57	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.57	   A^2 -> H(U1(d, d), c)
28.54/9.57	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.57	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.57	   A^2 -> H(U1(d, d), e)
28.54/9.57	   A^2 -> H(f(d), d)
28.54/9.57	   A^2 -> H(f(d), k)
28.54/9.57	   A^2 -> H(U1(c, c), c)
28.54/9.57	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.57	   A^2 -> H(f(c), k)
28.54/9.57	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.57	   A^2 -> H(f(k), U1(k, k))
28.54/9.57	   A^2 -> H(f(e), e)
28.54/9.57	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.57	   A^2 -> H(d, U1(c, b))
28.54/9.57	   A^2 -> H(d, U1(d, b))
28.54/9.57	   A^2 -> H(d, U1(b, c))
28.54/9.57	   A^2 -> H(d, U1(b, d))
28.54/9.57	   A^2 -> H(d, U1(c, c))
28.54/9.57	   A^2 -> H(d, f(e))
28.54/9.57	   A^2 -> H(d, f(k))
28.54/9.57	   A^2 -> H(d, U1(d, d))
28.54/9.57	   A^2 -> H(a, U1(e, b))
28.54/9.57	   A^2 -> H(a, U1(k, b))
28.54/9.57	   A^2 -> H(a, U1(c, d))
28.54/9.57	   A^2 -> H(a, U1(d, c))
28.54/9.57	   A^2 -> H(a, U1(b, e))
28.54/9.57	   A^2 -> H(a, U1(b, k))
28.54/9.57	   A^2 -> H(a, U1(e, c))
28.54/9.57	   A^2 -> H(a, U1(k, c))
28.54/9.57	   A^2 -> H(a, U1(c, e))
28.54/9.57	   A^2 -> H(a, U1(c, k))
28.54/9.57	   A^2 -> H(a, U1(e, e))
28.54/9.57	   A^2 -> H(a, U1(k, k))
28.54/9.57	   A^2 -> H(a, U1(k, d))
28.54/9.57	   A^2 -> H(a, U1(d, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.57	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.57	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.57	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.57	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.57	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.57	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.57	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.57	   A^2 -> H(U1(e, a), b)
28.54/9.57	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(e, a), c)
28.54/9.57	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(e, a), e)
28.54/9.57	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, a), b)
28.54/9.57	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(k, a), c)
28.54/9.57	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(c, d), b)
28.54/9.57	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.57	   A^2 -> H(U1(c, d), c)
28.54/9.57	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.57	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.57	   A^2 -> H(U1(c, d), e)
28.54/9.57	
28.54/9.57	The TRS R consists of the following rules:
28.54/9.57	
28.54/9.57	   f(x) -> U1(x, x)
28.54/9.57	   U1(e, x) -> x
28.54/9.57	   a -> c
28.54/9.57	   a -> d
28.54/9.57	   b -> c
28.54/9.57	   b -> d
28.54/9.57	   d -> k
28.54/9.57	   c -> e
28.54/9.57	   c -> k
28.54/9.57	
28.54/9.57	Q is empty.
28.54/9.57	We have to consider all minimal (P,Q,R)-chains.
28.54/9.57	----------------------------------------
28.54/9.57	
28.54/9.57	(1211) TransformationProof (EQUIVALENT)
28.54/9.57	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.57	
28.54/9.57	   (A^2 -> H(U1(e, d), U1(k, d)),A^2 -> H(U1(e, d), U1(k, d)))
28.54/9.57	   (A^2 -> H(U1(k, d), U1(k, d)),A^2 -> H(U1(k, d), U1(k, d)))
28.54/9.57	   (A^2 -> H(U1(c, k), U1(k, d)),A^2 -> H(U1(c, k), U1(k, d)))
28.54/9.57	   (A^2 -> H(U1(c, d), U1(k, k)),A^2 -> H(U1(c, d), U1(k, k)))
28.54/9.57	
28.54/9.57	
28.54/9.57	----------------------------------------
28.54/9.57	
28.54/9.57	(1212)
28.54/9.57	Obligation:
28.54/9.57	Q DP problem:
28.54/9.57	The TRS P consists of the following rules:
28.54/9.57	
28.54/9.57	   G(d, x, x) -> A^2
28.54/9.57	   A^2 -> H(f(c), f(c))
28.54/9.57	   H(x, x) -> G(x, x, f(k))
28.54/9.57	   A^2 -> H(f(d), f(d))
28.54/9.57	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.57	   A^2 -> H(f(e), f(e))
28.54/9.57	   A^2 -> H(f(k), f(k))
28.54/9.57	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, a), b)
28.54/9.57	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(c, a), c)
28.54/9.57	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(c, a), e)
28.54/9.57	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.57	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.57	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.57	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.57	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.57	   A^2 -> H(U1(d, e), f(e))
28.54/9.57	   A^2 -> H(U1(d, e), f(k))
28.54/9.57	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.57	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.57	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.57	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.57	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.57	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.57	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.57	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.57	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.57	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.57	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.57	   A^2 -> H(U1(d, a), b)
28.54/9.57	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(d, a), c)
28.54/9.57	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(d, a), e)
28.54/9.57	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.57	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.57	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.57	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.57	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.57	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.57	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.57	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.57	   A^2 -> H(U1(a, c), b)
28.54/9.57	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.57	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.57	   A^2 -> H(U1(a, c), c)
28.54/9.57	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.57	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.57	   A^2 -> H(U1(a, c), e)
28.54/9.57	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, d), b)
28.54/9.57	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.57	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.57	   A^2 -> H(U1(a, d), c)
28.54/9.57	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.57	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.57	   A^2 -> H(U1(a, d), e)
28.54/9.57	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, a), d)
28.54/9.57	   A^2 -> H(U1(a, a), k)
28.54/9.57	   A^2 -> H(k, U1(b, b))
28.54/9.57	   A^2 -> H(k, f(c))
28.54/9.57	   A^2 -> H(k, f(d))
28.54/9.57	   A^2 -> H(c, U1(c, b))
28.54/9.57	   A^2 -> H(c, U1(d, b))
28.54/9.57	   A^2 -> H(c, U1(b, c))
28.54/9.57	   A^2 -> H(c, U1(b, d))
28.54/9.57	   A^2 -> H(c, U1(c, c))
28.54/9.57	   A^2 -> H(c, f(e))
28.54/9.57	   A^2 -> H(c, f(k))
28.54/9.57	   A^2 -> H(c, U1(d, d))
28.54/9.57	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.57	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.57	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.57	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.57	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.57	   A^2 -> H(U1(e, k), f(e))
28.54/9.57	   A^2 -> H(U1(e, k), f(k))
28.54/9.57	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.57	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.57	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.57	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.57	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.57	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.57	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.57	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.57	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.57	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.57	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.57	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.57	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.57	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.57	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.57	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.57	   A^2 -> H(U1(k, e), f(e))
28.54/9.57	   A^2 -> H(U1(k, e), f(k))
28.54/9.57	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.57	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.57	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.57	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.57	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.57	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.57	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.57	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.57	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.57	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.57	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.57	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.57	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.57	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.57	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.57	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.57	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.57	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, c), b)
28.54/9.57	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.57	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.57	   A^2 -> H(U1(c, c), e)
28.54/9.57	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.57	   A^2 -> H(e, U1(c, b))
28.54/9.57	   A^2 -> H(e, U1(d, b))
28.54/9.57	   A^2 -> H(e, U1(b, c))
28.54/9.57	   A^2 -> H(e, U1(b, d))
28.54/9.57	   A^2 -> H(e, U1(c, c))
28.54/9.57	   A^2 -> H(e, f(e))
28.54/9.57	   A^2 -> H(e, f(k))
28.54/9.57	   A^2 -> H(e, U1(d, d))
28.54/9.57	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.57	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.57	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.57	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.57	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.57	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.57	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.57	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.57	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.57	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.57	   A^2 -> H(f(e), b)
28.54/9.57	   A^2 -> H(f(e), U1(e, d))
28.54/9.57	   A^2 -> H(f(e), U1(d, e))
28.54/9.57	   A^2 -> H(f(e), c)
28.54/9.57	   A^2 -> H(f(e), U1(e, k))
28.54/9.57	   A^2 -> H(f(e), U1(k, e))
28.54/9.57	   A^2 -> H(f(e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.57	   A^2 -> H(f(k), b)
28.54/9.57	   A^2 -> H(f(k), U1(e, d))
28.54/9.57	   A^2 -> H(f(k), U1(d, e))
28.54/9.57	   A^2 -> H(f(k), c)
28.54/9.57	   A^2 -> H(f(k), U1(e, k))
28.54/9.57	   A^2 -> H(f(k), U1(k, e))
28.54/9.57	   A^2 -> H(f(k), e)
28.54/9.57	   A^2 -> H(f(c), d)
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.57	   A^2 -> H(U1(k, k), f(e))
28.54/9.57	   A^2 -> H(U1(k, k), f(k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.57	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.57	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.57	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.57	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.57	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.57	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.57	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.57	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.57	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.57	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.57	   A^2 -> H(U1(d, d), b)
28.54/9.57	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.57	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.57	   A^2 -> H(U1(d, d), c)
28.54/9.57	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.57	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.57	   A^2 -> H(U1(d, d), e)
28.54/9.57	   A^2 -> H(f(d), d)
28.54/9.57	   A^2 -> H(f(d), k)
28.54/9.57	   A^2 -> H(U1(c, c), c)
28.54/9.57	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.57	   A^2 -> H(f(c), k)
28.54/9.57	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.57	   A^2 -> H(f(k), U1(k, k))
28.54/9.57	   A^2 -> H(f(e), e)
28.54/9.57	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.57	   A^2 -> H(d, U1(c, b))
28.54/9.57	   A^2 -> H(d, U1(d, b))
28.54/9.57	   A^2 -> H(d, U1(b, c))
28.54/9.57	   A^2 -> H(d, U1(b, d))
28.54/9.57	   A^2 -> H(d, U1(c, c))
28.54/9.57	   A^2 -> H(d, f(e))
28.54/9.57	   A^2 -> H(d, f(k))
28.54/9.57	   A^2 -> H(d, U1(d, d))
28.54/9.57	   A^2 -> H(a, U1(e, b))
28.54/9.57	   A^2 -> H(a, U1(k, b))
28.54/9.57	   A^2 -> H(a, U1(c, d))
28.54/9.57	   A^2 -> H(a, U1(d, c))
28.54/9.57	   A^2 -> H(a, U1(b, e))
28.54/9.57	   A^2 -> H(a, U1(b, k))
28.54/9.57	   A^2 -> H(a, U1(e, c))
28.54/9.57	   A^2 -> H(a, U1(k, c))
28.54/9.57	   A^2 -> H(a, U1(c, e))
28.54/9.57	   A^2 -> H(a, U1(c, k))
28.54/9.57	   A^2 -> H(a, U1(e, e))
28.54/9.57	   A^2 -> H(a, U1(k, k))
28.54/9.57	   A^2 -> H(a, U1(k, d))
28.54/9.57	   A^2 -> H(a, U1(d, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.57	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.57	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.57	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.57	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.57	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.57	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.57	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.57	   A^2 -> H(U1(e, a), b)
28.54/9.57	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(e, a), c)
28.54/9.57	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(e, a), e)
28.54/9.57	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, a), b)
28.54/9.57	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(k, a), c)
28.54/9.57	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(c, d), b)
28.54/9.57	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.57	   A^2 -> H(U1(c, d), c)
28.54/9.57	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.57	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.57	   A^2 -> H(U1(c, d), e)
28.54/9.57	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.57	
28.54/9.57	The TRS R consists of the following rules:
28.54/9.57	
28.54/9.57	   f(x) -> U1(x, x)
28.54/9.57	   U1(e, x) -> x
28.54/9.57	   a -> c
28.54/9.57	   a -> d
28.54/9.57	   b -> c
28.54/9.57	   b -> d
28.54/9.57	   d -> k
28.54/9.57	   c -> e
28.54/9.57	   c -> k
28.54/9.57	
28.54/9.57	Q is empty.
28.54/9.57	We have to consider all minimal (P,Q,R)-chains.
28.54/9.57	----------------------------------------
28.54/9.57	
28.54/9.57	(1213) TransformationProof (EQUIVALENT)
28.54/9.57	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.57	
28.54/9.57	   (A^2 -> H(U1(e, d), U1(d, k)),A^2 -> H(U1(e, d), U1(d, k)))
28.54/9.57	   (A^2 -> H(U1(k, d), U1(d, k)),A^2 -> H(U1(k, d), U1(d, k)))
28.54/9.57	   (A^2 -> H(U1(c, k), U1(d, k)),A^2 -> H(U1(c, k), U1(d, k)))
28.54/9.57	   (A^2 -> H(U1(c, d), U1(k, k)),A^2 -> H(U1(c, d), U1(k, k)))
28.54/9.57	
28.54/9.57	
28.54/9.57	----------------------------------------
28.54/9.57	
28.54/9.57	(1214)
28.54/9.57	Obligation:
28.54/9.57	Q DP problem:
28.54/9.57	The TRS P consists of the following rules:
28.54/9.57	
28.54/9.57	   G(d, x, x) -> A^2
28.54/9.57	   A^2 -> H(f(c), f(c))
28.54/9.57	   H(x, x) -> G(x, x, f(k))
28.54/9.57	   A^2 -> H(f(d), f(d))
28.54/9.57	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.57	   A^2 -> H(f(e), f(e))
28.54/9.57	   A^2 -> H(f(k), f(k))
28.54/9.57	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.57	   A^2 -> H(U1(c, a), b)
28.54/9.57	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(c, a), c)
28.54/9.57	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(c, a), e)
28.54/9.57	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.57	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.57	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.57	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.57	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.57	   A^2 -> H(U1(d, e), f(e))
28.54/9.57	   A^2 -> H(U1(d, e), f(k))
28.54/9.57	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.57	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.57	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.57	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.57	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.57	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.57	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.57	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.57	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.57	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.57	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.57	   A^2 -> H(U1(d, a), b)
28.54/9.57	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(d, a), c)
28.54/9.57	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(d, a), e)
28.54/9.57	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.57	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.57	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.57	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.57	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.57	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.57	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.57	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.57	   A^2 -> H(U1(a, c), b)
28.54/9.57	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.57	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.57	   A^2 -> H(U1(a, c), c)
28.54/9.57	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.57	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.57	   A^2 -> H(U1(a, c), e)
28.54/9.57	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, d), b)
28.54/9.57	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.57	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.57	   A^2 -> H(U1(a, d), c)
28.54/9.57	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.57	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.57	   A^2 -> H(U1(a, d), e)
28.54/9.57	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, a), d)
28.54/9.57	   A^2 -> H(U1(a, a), k)
28.54/9.57	   A^2 -> H(k, U1(b, b))
28.54/9.57	   A^2 -> H(k, f(c))
28.54/9.57	   A^2 -> H(k, f(d))
28.54/9.57	   A^2 -> H(c, U1(c, b))
28.54/9.57	   A^2 -> H(c, U1(d, b))
28.54/9.57	   A^2 -> H(c, U1(b, c))
28.54/9.57	   A^2 -> H(c, U1(b, d))
28.54/9.57	   A^2 -> H(c, U1(c, c))
28.54/9.57	   A^2 -> H(c, f(e))
28.54/9.57	   A^2 -> H(c, f(k))
28.54/9.57	   A^2 -> H(c, U1(d, d))
28.54/9.57	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.57	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.57	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.57	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.57	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.57	   A^2 -> H(U1(e, k), f(e))
28.54/9.57	   A^2 -> H(U1(e, k), f(k))
28.54/9.57	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.57	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.57	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.57	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.57	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.57	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.57	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.57	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.57	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.57	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.57	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.57	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.57	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.57	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.57	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.57	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.57	   A^2 -> H(U1(k, e), f(e))
28.54/9.57	   A^2 -> H(U1(k, e), f(k))
28.54/9.57	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.57	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.57	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.57	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.57	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.57	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.57	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.57	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.57	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.57	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.57	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.57	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.57	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.57	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.57	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.57	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.57	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.57	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.57	   A^2 -> H(U1(c, c), b)
28.54/9.57	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.57	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.57	   A^2 -> H(U1(c, c), e)
28.54/9.57	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.57	   A^2 -> H(e, U1(c, b))
28.54/9.57	   A^2 -> H(e, U1(d, b))
28.54/9.57	   A^2 -> H(e, U1(b, c))
28.54/9.57	   A^2 -> H(e, U1(b, d))
28.54/9.57	   A^2 -> H(e, U1(c, c))
28.54/9.57	   A^2 -> H(e, f(e))
28.54/9.57	   A^2 -> H(e, f(k))
28.54/9.57	   A^2 -> H(e, U1(d, d))
28.54/9.57	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.57	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.57	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.57	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.57	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.57	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.57	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.57	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.57	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.57	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.57	   A^2 -> H(f(e), b)
28.54/9.57	   A^2 -> H(f(e), U1(e, d))
28.54/9.57	   A^2 -> H(f(e), U1(d, e))
28.54/9.57	   A^2 -> H(f(e), c)
28.54/9.57	   A^2 -> H(f(e), U1(e, k))
28.54/9.57	   A^2 -> H(f(e), U1(k, e))
28.54/9.57	   A^2 -> H(f(e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.57	   A^2 -> H(f(k), b)
28.54/9.57	   A^2 -> H(f(k), U1(e, d))
28.54/9.57	   A^2 -> H(f(k), U1(d, e))
28.54/9.57	   A^2 -> H(f(k), c)
28.54/9.57	   A^2 -> H(f(k), U1(e, k))
28.54/9.57	   A^2 -> H(f(k), U1(k, e))
28.54/9.57	   A^2 -> H(f(k), e)
28.54/9.57	   A^2 -> H(f(c), d)
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.57	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.57	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.57	   A^2 -> H(U1(k, k), f(e))
28.54/9.57	   A^2 -> H(U1(k, k), f(k))
28.54/9.57	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.57	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.57	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.57	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.57	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.57	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.57	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.57	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.57	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.57	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.57	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.57	   A^2 -> H(U1(d, d), b)
28.54/9.57	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.57	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.57	   A^2 -> H(U1(d, d), c)
28.54/9.57	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.57	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.57	   A^2 -> H(U1(d, d), e)
28.54/9.57	   A^2 -> H(f(d), d)
28.54/9.57	   A^2 -> H(f(d), k)
28.54/9.57	   A^2 -> H(U1(c, c), c)
28.54/9.57	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.57	   A^2 -> H(f(c), k)
28.54/9.57	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.57	   A^2 -> H(f(k), U1(k, k))
28.54/9.57	   A^2 -> H(f(e), e)
28.54/9.57	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.57	   A^2 -> H(d, U1(c, b))
28.54/9.57	   A^2 -> H(d, U1(d, b))
28.54/9.57	   A^2 -> H(d, U1(b, c))
28.54/9.57	   A^2 -> H(d, U1(b, d))
28.54/9.57	   A^2 -> H(d, U1(c, c))
28.54/9.57	   A^2 -> H(d, f(e))
28.54/9.57	   A^2 -> H(d, f(k))
28.54/9.57	   A^2 -> H(d, U1(d, d))
28.54/9.57	   A^2 -> H(a, U1(e, b))
28.54/9.57	   A^2 -> H(a, U1(k, b))
28.54/9.57	   A^2 -> H(a, U1(c, d))
28.54/9.57	   A^2 -> H(a, U1(d, c))
28.54/9.57	   A^2 -> H(a, U1(b, e))
28.54/9.57	   A^2 -> H(a, U1(b, k))
28.54/9.57	   A^2 -> H(a, U1(e, c))
28.54/9.57	   A^2 -> H(a, U1(k, c))
28.54/9.57	   A^2 -> H(a, U1(c, e))
28.54/9.57	   A^2 -> H(a, U1(c, k))
28.54/9.57	   A^2 -> H(a, U1(e, e))
28.54/9.57	   A^2 -> H(a, U1(k, k))
28.54/9.57	   A^2 -> H(a, U1(k, d))
28.54/9.57	   A^2 -> H(a, U1(d, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.57	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.57	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.57	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.57	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.57	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.57	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.57	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.57	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.57	   A^2 -> H(U1(e, a), b)
28.54/9.57	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(e, a), c)
28.54/9.57	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(e, a), e)
28.54/9.57	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(k, a), b)
28.54/9.57	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(k, a), c)
28.54/9.57	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(c, d), b)
28.54/9.57	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.57	   A^2 -> H(U1(c, d), c)
28.54/9.57	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.57	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.57	   A^2 -> H(U1(c, d), e)
28.54/9.57	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.57	
28.54/9.57	The TRS R consists of the following rules:
28.54/9.57	
28.54/9.57	   f(x) -> U1(x, x)
28.54/9.57	   U1(e, x) -> x
28.54/9.57	   a -> c
28.54/9.57	   a -> d
28.54/9.57	   b -> c
28.54/9.57	   b -> d
28.54/9.57	   d -> k
28.54/9.57	   c -> e
28.54/9.57	   c -> k
28.54/9.57	
28.54/9.57	Q is empty.
28.54/9.57	We have to consider all minimal (P,Q,R)-chains.
28.54/9.57	----------------------------------------
28.54/9.57	
28.54/9.57	(1215) TransformationProof (EQUIVALENT)
28.54/9.57	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), b) at position [] we obtained the following new rules [LPAR04]:
28.54/9.57	
28.54/9.57	   (A^2 -> H(U1(e, a), b),A^2 -> H(U1(e, a), b))
28.54/9.57	   (A^2 -> H(U1(k, a), b),A^2 -> H(U1(k, a), b))
28.54/9.57	   (A^2 -> H(U1(c, c), b),A^2 -> H(U1(c, c), b))
28.54/9.57	   (A^2 -> H(U1(c, d), b),A^2 -> H(U1(c, d), b))
28.54/9.57	   (A^2 -> H(U1(c, a), c),A^2 -> H(U1(c, a), c))
28.54/9.57	   (A^2 -> H(U1(c, a), d),A^2 -> H(U1(c, a), d))
28.54/9.57	
28.54/9.57	
28.54/9.57	----------------------------------------
28.54/9.57	
28.54/9.57	(1216)
28.54/9.57	Obligation:
28.54/9.57	Q DP problem:
28.54/9.57	The TRS P consists of the following rules:
28.54/9.57	
28.54/9.57	   G(d, x, x) -> A^2
28.54/9.57	   A^2 -> H(f(c), f(c))
28.54/9.57	   H(x, x) -> G(x, x, f(k))
28.54/9.57	   A^2 -> H(f(d), f(d))
28.54/9.57	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.57	   A^2 -> H(f(e), f(e))
28.54/9.57	   A^2 -> H(f(k), f(k))
28.54/9.57	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.57	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.57	   A^2 -> H(U1(c, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(c, a), c)
28.54/9.57	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(c, a), e)
28.54/9.57	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.57	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.57	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.57	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.57	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.57	   A^2 -> H(U1(d, e), f(e))
28.54/9.57	   A^2 -> H(U1(d, e), f(k))
28.54/9.57	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.57	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.57	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.57	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.57	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.57	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.57	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.57	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.57	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.57	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.57	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.57	   A^2 -> H(U1(d, a), b)
28.54/9.57	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.57	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.57	   A^2 -> H(U1(d, a), c)
28.54/9.57	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.57	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.57	   A^2 -> H(U1(d, a), e)
28.54/9.57	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.57	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.57	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.57	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.57	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.57	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.57	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.57	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.57	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.57	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.57	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.57	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.57	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.57	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.57	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.57	   A^2 -> H(U1(a, c), b)
28.54/9.57	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.57	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.57	   A^2 -> H(U1(a, c), c)
28.54/9.57	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.57	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.57	   A^2 -> H(U1(a, c), e)
28.54/9.57	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.57	   A^2 -> H(U1(a, d), b)
28.54/9.57	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.57	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.57	   A^2 -> H(U1(a, d), c)
28.54/9.58	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.58	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.58	   A^2 -> H(U1(a, d), e)
28.54/9.58	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, a), d)
28.54/9.58	   A^2 -> H(U1(a, a), k)
28.54/9.58	   A^2 -> H(k, U1(b, b))
28.54/9.58	   A^2 -> H(k, f(c))
28.54/9.58	   A^2 -> H(k, f(d))
28.54/9.58	   A^2 -> H(c, U1(c, b))
28.54/9.58	   A^2 -> H(c, U1(d, b))
28.54/9.58	   A^2 -> H(c, U1(b, c))
28.54/9.58	   A^2 -> H(c, U1(b, d))
28.54/9.58	   A^2 -> H(c, U1(c, c))
28.54/9.58	   A^2 -> H(c, f(e))
28.54/9.58	   A^2 -> H(c, f(k))
28.54/9.58	   A^2 -> H(c, U1(d, d))
28.54/9.58	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.58	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.58	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.58	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.58	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.58	   A^2 -> H(U1(e, k), f(e))
28.54/9.58	   A^2 -> H(U1(e, k), f(k))
28.54/9.58	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.58	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.58	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.58	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.58	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.58	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.58	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.58	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.58	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.58	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.58	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.58	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.58	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.58	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.58	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.58	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.58	   A^2 -> H(U1(k, e), f(e))
28.54/9.58	   A^2 -> H(U1(k, e), f(k))
28.54/9.58	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.58	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.58	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.58	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.58	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.58	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.58	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.58	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.58	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.58	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.58	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.58	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.58	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.58	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.58	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.58	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.58	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.58	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.58	   A^2 -> H(U1(c, c), b)
28.54/9.58	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.58	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.58	   A^2 -> H(U1(c, c), e)
28.54/9.58	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.58	   A^2 -> H(e, U1(c, b))
28.54/9.58	   A^2 -> H(e, U1(d, b))
28.54/9.58	   A^2 -> H(e, U1(b, c))
28.54/9.58	   A^2 -> H(e, U1(b, d))
28.54/9.58	   A^2 -> H(e, U1(c, c))
28.54/9.58	   A^2 -> H(e, f(e))
28.54/9.58	   A^2 -> H(e, f(k))
28.54/9.58	   A^2 -> H(e, U1(d, d))
28.54/9.58	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.58	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.58	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.58	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.58	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.58	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.58	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.58	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.58	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.58	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.58	   A^2 -> H(f(e), b)
28.54/9.58	   A^2 -> H(f(e), U1(e, d))
28.54/9.58	   A^2 -> H(f(e), U1(d, e))
28.54/9.58	   A^2 -> H(f(e), c)
28.54/9.58	   A^2 -> H(f(e), U1(e, k))
28.54/9.58	   A^2 -> H(f(e), U1(k, e))
28.54/9.58	   A^2 -> H(f(e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.58	   A^2 -> H(f(k), b)
28.54/9.58	   A^2 -> H(f(k), U1(e, d))
28.54/9.58	   A^2 -> H(f(k), U1(d, e))
28.54/9.58	   A^2 -> H(f(k), c)
28.54/9.58	   A^2 -> H(f(k), U1(e, k))
28.54/9.58	   A^2 -> H(f(k), U1(k, e))
28.54/9.58	   A^2 -> H(f(k), e)
28.54/9.58	   A^2 -> H(f(c), d)
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.58	   A^2 -> H(U1(k, k), f(e))
28.54/9.58	   A^2 -> H(U1(k, k), f(k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.58	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.58	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.58	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.58	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.58	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.58	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.58	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.58	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.58	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.58	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.58	   A^2 -> H(U1(d, d), b)
28.54/9.58	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.58	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.58	   A^2 -> H(U1(d, d), c)
28.54/9.58	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.58	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.58	   A^2 -> H(U1(d, d), e)
28.54/9.58	   A^2 -> H(f(d), d)
28.54/9.58	   A^2 -> H(f(d), k)
28.54/9.58	   A^2 -> H(U1(c, c), c)
28.54/9.58	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.58	   A^2 -> H(f(c), k)
28.54/9.58	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.58	   A^2 -> H(f(k), U1(k, k))
28.54/9.58	   A^2 -> H(f(e), e)
28.54/9.58	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.58	   A^2 -> H(d, U1(c, b))
28.54/9.58	   A^2 -> H(d, U1(d, b))
28.54/9.58	   A^2 -> H(d, U1(b, c))
28.54/9.58	   A^2 -> H(d, U1(b, d))
28.54/9.58	   A^2 -> H(d, U1(c, c))
28.54/9.58	   A^2 -> H(d, f(e))
28.54/9.58	   A^2 -> H(d, f(k))
28.54/9.58	   A^2 -> H(d, U1(d, d))
28.54/9.58	   A^2 -> H(a, U1(e, b))
28.54/9.58	   A^2 -> H(a, U1(k, b))
28.54/9.58	   A^2 -> H(a, U1(c, d))
28.54/9.58	   A^2 -> H(a, U1(d, c))
28.54/9.58	   A^2 -> H(a, U1(b, e))
28.54/9.58	   A^2 -> H(a, U1(b, k))
28.54/9.58	   A^2 -> H(a, U1(e, c))
28.54/9.58	   A^2 -> H(a, U1(k, c))
28.54/9.58	   A^2 -> H(a, U1(c, e))
28.54/9.58	   A^2 -> H(a, U1(c, k))
28.54/9.58	   A^2 -> H(a, U1(e, e))
28.54/9.58	   A^2 -> H(a, U1(k, k))
28.54/9.58	   A^2 -> H(a, U1(k, d))
28.54/9.58	   A^2 -> H(a, U1(d, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.58	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.58	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.58	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.58	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.58	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.58	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.58	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.58	   A^2 -> H(U1(e, a), b)
28.54/9.58	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.58	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.58	   A^2 -> H(U1(e, a), c)
28.54/9.58	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.58	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(e, a), e)
28.54/9.58	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, a), b)
28.54/9.58	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.58	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.58	   A^2 -> H(U1(k, a), c)
28.54/9.58	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.58	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, d), b)
28.54/9.58	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.58	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.58	   A^2 -> H(U1(c, d), c)
28.54/9.58	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.58	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.58	   A^2 -> H(U1(c, d), e)
28.54/9.58	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, a), d)
28.54/9.58	
28.54/9.58	The TRS R consists of the following rules:
28.54/9.58	
28.54/9.58	   f(x) -> U1(x, x)
28.54/9.58	   U1(e, x) -> x
28.54/9.58	   a -> c
28.54/9.58	   a -> d
28.54/9.58	   b -> c
28.54/9.58	   b -> d
28.54/9.58	   d -> k
28.54/9.58	   c -> e
28.54/9.58	   c -> k
28.54/9.58	
28.54/9.58	Q is empty.
28.54/9.58	We have to consider all minimal (P,Q,R)-chains.
28.54/9.58	----------------------------------------
28.54/9.58	
28.54/9.58	(1217) TransformationProof (EQUIVALENT)
28.54/9.58	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.58	
28.54/9.58	   (A^2 -> H(U1(e, a), U1(e, d)),A^2 -> H(U1(e, a), U1(e, d)))
28.54/9.58	   (A^2 -> H(U1(k, a), U1(e, d)),A^2 -> H(U1(k, a), U1(e, d)))
28.54/9.58	   (A^2 -> H(U1(c, c), U1(e, d)),A^2 -> H(U1(c, c), U1(e, d)))
28.54/9.58	   (A^2 -> H(U1(c, d), U1(e, d)),A^2 -> H(U1(c, d), U1(e, d)))
28.54/9.58	   (A^2 -> H(U1(c, a), d),A^2 -> H(U1(c, a), d))
28.54/9.58	   (A^2 -> H(U1(c, a), U1(e, k)),A^2 -> H(U1(c, a), U1(e, k)))
28.54/9.58	
28.54/9.58	
28.54/9.58	----------------------------------------
28.54/9.58	
28.54/9.58	(1218)
28.54/9.58	Obligation:
28.54/9.58	Q DP problem:
28.54/9.58	The TRS P consists of the following rules:
28.54/9.58	
28.54/9.58	   G(d, x, x) -> A^2
28.54/9.58	   A^2 -> H(f(c), f(c))
28.54/9.58	   H(x, x) -> G(x, x, f(k))
28.54/9.58	   A^2 -> H(f(d), f(d))
28.54/9.58	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.58	   A^2 -> H(f(e), f(e))
28.54/9.58	   A^2 -> H(f(k), f(k))
28.54/9.58	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.58	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.58	   A^2 -> H(U1(c, a), U1(d, e))
28.54/9.58	   A^2 -> H(U1(c, a), c)
28.54/9.58	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.58	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(c, a), e)
28.54/9.58	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.58	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.58	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.58	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.58	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.58	   A^2 -> H(U1(d, e), f(e))
28.54/9.58	   A^2 -> H(U1(d, e), f(k))
28.54/9.58	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.58	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.58	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.58	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.58	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.58	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.58	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.58	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.58	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.58	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.58	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.58	   A^2 -> H(U1(d, a), b)
28.54/9.58	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.58	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.58	   A^2 -> H(U1(d, a), c)
28.54/9.58	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.58	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(d, a), e)
28.54/9.58	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.58	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.58	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.58	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.58	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.58	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.58	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.58	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.58	   A^2 -> H(U1(a, c), b)
28.54/9.58	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.58	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.58	   A^2 -> H(U1(a, c), c)
28.54/9.58	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.58	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.58	   A^2 -> H(U1(a, c), e)
28.54/9.58	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, d), b)
28.54/9.58	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.58	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.58	   A^2 -> H(U1(a, d), c)
28.54/9.58	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.58	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.58	   A^2 -> H(U1(a, d), e)
28.54/9.58	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, a), d)
28.54/9.58	   A^2 -> H(U1(a, a), k)
28.54/9.58	   A^2 -> H(k, U1(b, b))
28.54/9.58	   A^2 -> H(k, f(c))
28.54/9.58	   A^2 -> H(k, f(d))
28.54/9.58	   A^2 -> H(c, U1(c, b))
28.54/9.58	   A^2 -> H(c, U1(d, b))
28.54/9.58	   A^2 -> H(c, U1(b, c))
28.54/9.58	   A^2 -> H(c, U1(b, d))
28.54/9.58	   A^2 -> H(c, U1(c, c))
28.54/9.58	   A^2 -> H(c, f(e))
28.54/9.58	   A^2 -> H(c, f(k))
28.54/9.58	   A^2 -> H(c, U1(d, d))
28.54/9.58	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.58	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.58	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.58	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.58	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.58	   A^2 -> H(U1(e, k), f(e))
28.54/9.58	   A^2 -> H(U1(e, k), f(k))
28.54/9.58	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.58	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.58	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.58	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.58	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.58	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.58	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.58	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.58	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.58	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.58	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.58	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.58	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.58	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.58	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.58	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.58	   A^2 -> H(U1(k, e), f(e))
28.54/9.58	   A^2 -> H(U1(k, e), f(k))
28.54/9.58	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.58	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.58	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.58	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.58	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.58	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.58	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.58	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.58	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.58	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.58	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.58	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.58	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.58	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.58	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.58	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.58	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.58	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.58	   A^2 -> H(U1(c, c), b)
28.54/9.58	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.58	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.58	   A^2 -> H(U1(c, c), e)
28.54/9.58	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.58	   A^2 -> H(e, U1(c, b))
28.54/9.58	   A^2 -> H(e, U1(d, b))
28.54/9.58	   A^2 -> H(e, U1(b, c))
28.54/9.58	   A^2 -> H(e, U1(b, d))
28.54/9.58	   A^2 -> H(e, U1(c, c))
28.54/9.58	   A^2 -> H(e, f(e))
28.54/9.58	   A^2 -> H(e, f(k))
28.54/9.58	   A^2 -> H(e, U1(d, d))
28.54/9.58	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.58	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.58	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.58	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.58	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.58	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.58	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.58	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.58	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.58	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.58	   A^2 -> H(f(e), b)
28.54/9.58	   A^2 -> H(f(e), U1(e, d))
28.54/9.58	   A^2 -> H(f(e), U1(d, e))
28.54/9.58	   A^2 -> H(f(e), c)
28.54/9.58	   A^2 -> H(f(e), U1(e, k))
28.54/9.58	   A^2 -> H(f(e), U1(k, e))
28.54/9.58	   A^2 -> H(f(e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.58	   A^2 -> H(f(k), b)
28.54/9.58	   A^2 -> H(f(k), U1(e, d))
28.54/9.58	   A^2 -> H(f(k), U1(d, e))
28.54/9.58	   A^2 -> H(f(k), c)
28.54/9.58	   A^2 -> H(f(k), U1(e, k))
28.54/9.58	   A^2 -> H(f(k), U1(k, e))
28.54/9.58	   A^2 -> H(f(k), e)
28.54/9.58	   A^2 -> H(f(c), d)
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.58	   A^2 -> H(U1(k, k), f(e))
28.54/9.58	   A^2 -> H(U1(k, k), f(k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.58	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.58	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.58	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.58	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.58	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.58	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.58	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.58	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.58	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.58	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.58	   A^2 -> H(U1(d, d), b)
28.54/9.58	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.58	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.58	   A^2 -> H(U1(d, d), c)
28.54/9.58	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.58	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.58	   A^2 -> H(U1(d, d), e)
28.54/9.58	   A^2 -> H(f(d), d)
28.54/9.58	   A^2 -> H(f(d), k)
28.54/9.58	   A^2 -> H(U1(c, c), c)
28.54/9.58	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.58	   A^2 -> H(f(c), k)
28.54/9.58	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.58	   A^2 -> H(f(k), U1(k, k))
28.54/9.58	   A^2 -> H(f(e), e)
28.54/9.58	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.58	   A^2 -> H(d, U1(c, b))
28.54/9.58	   A^2 -> H(d, U1(d, b))
28.54/9.58	   A^2 -> H(d, U1(b, c))
28.54/9.58	   A^2 -> H(d, U1(b, d))
28.54/9.58	   A^2 -> H(d, U1(c, c))
28.54/9.58	   A^2 -> H(d, f(e))
28.54/9.58	   A^2 -> H(d, f(k))
28.54/9.58	   A^2 -> H(d, U1(d, d))
28.54/9.58	   A^2 -> H(a, U1(e, b))
28.54/9.58	   A^2 -> H(a, U1(k, b))
28.54/9.58	   A^2 -> H(a, U1(c, d))
28.54/9.58	   A^2 -> H(a, U1(d, c))
28.54/9.58	   A^2 -> H(a, U1(b, e))
28.54/9.58	   A^2 -> H(a, U1(b, k))
28.54/9.58	   A^2 -> H(a, U1(e, c))
28.54/9.58	   A^2 -> H(a, U1(k, c))
28.54/9.58	   A^2 -> H(a, U1(c, e))
28.54/9.58	   A^2 -> H(a, U1(c, k))
28.54/9.58	   A^2 -> H(a, U1(e, e))
28.54/9.58	   A^2 -> H(a, U1(k, k))
28.54/9.58	   A^2 -> H(a, U1(k, d))
28.54/9.58	   A^2 -> H(a, U1(d, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.58	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.58	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.58	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.58	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.58	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.58	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.58	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.58	   A^2 -> H(U1(e, a), b)
28.54/9.58	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.58	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.58	   A^2 -> H(U1(e, a), c)
28.54/9.58	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.58	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(e, a), e)
28.54/9.58	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, a), b)
28.54/9.58	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.58	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.58	   A^2 -> H(U1(k, a), c)
28.54/9.58	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.58	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, d), b)
28.54/9.58	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.58	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.58	   A^2 -> H(U1(c, d), c)
28.54/9.58	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.58	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.58	   A^2 -> H(U1(c, d), e)
28.54/9.58	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, a), d)
28.54/9.58	
28.54/9.58	The TRS R consists of the following rules:
28.54/9.58	
28.54/9.58	   f(x) -> U1(x, x)
28.54/9.58	   U1(e, x) -> x
28.54/9.58	   a -> c
28.54/9.58	   a -> d
28.54/9.58	   b -> c
28.54/9.58	   b -> d
28.54/9.58	   d -> k
28.54/9.58	   c -> e
28.54/9.58	   c -> k
28.54/9.58	
28.54/9.58	Q is empty.
28.54/9.58	We have to consider all minimal (P,Q,R)-chains.
28.54/9.58	----------------------------------------
28.54/9.58	
28.54/9.58	(1219) TransformationProof (EQUIVALENT)
28.54/9.58	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.58	
28.54/9.58	   (A^2 -> H(U1(e, a), U1(d, e)),A^2 -> H(U1(e, a), U1(d, e)))
28.54/9.58	   (A^2 -> H(U1(k, a), U1(d, e)),A^2 -> H(U1(k, a), U1(d, e)))
28.54/9.58	   (A^2 -> H(U1(c, c), U1(d, e)),A^2 -> H(U1(c, c), U1(d, e)))
28.54/9.58	   (A^2 -> H(U1(c, d), U1(d, e)),A^2 -> H(U1(c, d), U1(d, e)))
28.54/9.58	   (A^2 -> H(U1(c, a), U1(k, e)),A^2 -> H(U1(c, a), U1(k, e)))
28.54/9.58	
28.54/9.58	
28.54/9.58	----------------------------------------
28.54/9.58	
28.54/9.58	(1220)
28.54/9.58	Obligation:
28.54/9.58	Q DP problem:
28.54/9.58	The TRS P consists of the following rules:
28.54/9.58	
28.54/9.58	   G(d, x, x) -> A^2
28.54/9.58	   A^2 -> H(f(c), f(c))
28.54/9.58	   H(x, x) -> G(x, x, f(k))
28.54/9.58	   A^2 -> H(f(d), f(d))
28.54/9.58	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.58	   A^2 -> H(f(e), f(e))
28.54/9.58	   A^2 -> H(f(k), f(k))
28.54/9.58	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.58	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.58	   A^2 -> H(U1(c, a), c)
28.54/9.58	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.58	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(c, a), e)
28.54/9.58	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.58	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.58	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.58	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.58	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.58	   A^2 -> H(U1(d, e), f(e))
28.54/9.58	   A^2 -> H(U1(d, e), f(k))
28.54/9.58	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.58	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.58	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.58	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.58	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.58	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.58	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.58	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.58	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.58	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.58	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.58	   A^2 -> H(U1(d, a), b)
28.54/9.58	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.58	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.58	   A^2 -> H(U1(d, a), c)
28.54/9.58	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.58	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(d, a), e)
28.54/9.58	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.58	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.58	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.58	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.58	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.58	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.58	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.58	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.58	   A^2 -> H(U1(a, c), b)
28.54/9.58	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.58	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.58	   A^2 -> H(U1(a, c), c)
28.54/9.58	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.58	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.58	   A^2 -> H(U1(a, c), e)
28.54/9.58	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, d), b)
28.54/9.58	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.58	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.58	   A^2 -> H(U1(a, d), c)
28.54/9.58	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.58	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.58	   A^2 -> H(U1(a, d), e)
28.54/9.58	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, a), d)
28.54/9.58	   A^2 -> H(U1(a, a), k)
28.54/9.58	   A^2 -> H(k, U1(b, b))
28.54/9.58	   A^2 -> H(k, f(c))
28.54/9.58	   A^2 -> H(k, f(d))
28.54/9.58	   A^2 -> H(c, U1(c, b))
28.54/9.58	   A^2 -> H(c, U1(d, b))
28.54/9.58	   A^2 -> H(c, U1(b, c))
28.54/9.58	   A^2 -> H(c, U1(b, d))
28.54/9.58	   A^2 -> H(c, U1(c, c))
28.54/9.58	   A^2 -> H(c, f(e))
28.54/9.58	   A^2 -> H(c, f(k))
28.54/9.58	   A^2 -> H(c, U1(d, d))
28.54/9.58	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.58	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.58	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.58	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.58	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.58	   A^2 -> H(U1(e, k), f(e))
28.54/9.58	   A^2 -> H(U1(e, k), f(k))
28.54/9.58	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.58	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.58	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.58	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.58	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.58	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.58	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.58	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.58	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.58	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.58	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.58	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.58	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.58	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.58	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.58	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.58	   A^2 -> H(U1(k, e), f(e))
28.54/9.58	   A^2 -> H(U1(k, e), f(k))
28.54/9.58	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.58	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.58	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.58	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.58	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.58	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.58	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.58	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.58	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.58	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.58	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.58	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.58	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.58	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.58	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.58	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.58	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.58	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.58	   A^2 -> H(U1(c, c), b)
28.54/9.58	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.58	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.58	   A^2 -> H(U1(c, c), e)
28.54/9.58	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.58	   A^2 -> H(e, U1(c, b))
28.54/9.58	   A^2 -> H(e, U1(d, b))
28.54/9.58	   A^2 -> H(e, U1(b, c))
28.54/9.58	   A^2 -> H(e, U1(b, d))
28.54/9.58	   A^2 -> H(e, U1(c, c))
28.54/9.58	   A^2 -> H(e, f(e))
28.54/9.58	   A^2 -> H(e, f(k))
28.54/9.58	   A^2 -> H(e, U1(d, d))
28.54/9.58	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.58	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.58	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.58	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.58	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.58	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.58	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.58	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.58	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.58	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.58	   A^2 -> H(f(e), b)
28.54/9.58	   A^2 -> H(f(e), U1(e, d))
28.54/9.58	   A^2 -> H(f(e), U1(d, e))
28.54/9.58	   A^2 -> H(f(e), c)
28.54/9.58	   A^2 -> H(f(e), U1(e, k))
28.54/9.58	   A^2 -> H(f(e), U1(k, e))
28.54/9.58	   A^2 -> H(f(e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.58	   A^2 -> H(f(k), b)
28.54/9.58	   A^2 -> H(f(k), U1(e, d))
28.54/9.58	   A^2 -> H(f(k), U1(d, e))
28.54/9.58	   A^2 -> H(f(k), c)
28.54/9.58	   A^2 -> H(f(k), U1(e, k))
28.54/9.58	   A^2 -> H(f(k), U1(k, e))
28.54/9.58	   A^2 -> H(f(k), e)
28.54/9.58	   A^2 -> H(f(c), d)
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.58	   A^2 -> H(U1(k, k), f(e))
28.54/9.58	   A^2 -> H(U1(k, k), f(k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.58	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.58	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.58	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.58	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.58	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.58	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.58	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.58	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.58	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.58	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.58	   A^2 -> H(U1(d, d), b)
28.54/9.58	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.58	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.58	   A^2 -> H(U1(d, d), c)
28.54/9.58	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.58	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.58	   A^2 -> H(U1(d, d), e)
28.54/9.58	   A^2 -> H(f(d), d)
28.54/9.58	   A^2 -> H(f(d), k)
28.54/9.58	   A^2 -> H(U1(c, c), c)
28.54/9.58	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.58	   A^2 -> H(f(c), k)
28.54/9.58	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.58	   A^2 -> H(f(k), U1(k, k))
28.54/9.58	   A^2 -> H(f(e), e)
28.54/9.58	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.58	   A^2 -> H(d, U1(c, b))
28.54/9.58	   A^2 -> H(d, U1(d, b))
28.54/9.58	   A^2 -> H(d, U1(b, c))
28.54/9.58	   A^2 -> H(d, U1(b, d))
28.54/9.58	   A^2 -> H(d, U1(c, c))
28.54/9.58	   A^2 -> H(d, f(e))
28.54/9.58	   A^2 -> H(d, f(k))
28.54/9.58	   A^2 -> H(d, U1(d, d))
28.54/9.58	   A^2 -> H(a, U1(e, b))
28.54/9.58	   A^2 -> H(a, U1(k, b))
28.54/9.58	   A^2 -> H(a, U1(c, d))
28.54/9.58	   A^2 -> H(a, U1(d, c))
28.54/9.58	   A^2 -> H(a, U1(b, e))
28.54/9.58	   A^2 -> H(a, U1(b, k))
28.54/9.58	   A^2 -> H(a, U1(e, c))
28.54/9.58	   A^2 -> H(a, U1(k, c))
28.54/9.58	   A^2 -> H(a, U1(c, e))
28.54/9.58	   A^2 -> H(a, U1(c, k))
28.54/9.58	   A^2 -> H(a, U1(e, e))
28.54/9.58	   A^2 -> H(a, U1(k, k))
28.54/9.58	   A^2 -> H(a, U1(k, d))
28.54/9.58	   A^2 -> H(a, U1(d, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.58	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.58	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.58	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.58	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.58	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.58	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.58	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.58	   A^2 -> H(U1(e, a), b)
28.54/9.58	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.58	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.58	   A^2 -> H(U1(e, a), c)
28.54/9.58	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.58	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(e, a), e)
28.54/9.58	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, a), b)
28.54/9.58	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.58	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.58	   A^2 -> H(U1(k, a), c)
28.54/9.58	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.58	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, d), b)
28.54/9.58	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.58	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.58	   A^2 -> H(U1(c, d), c)
28.54/9.58	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.58	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.58	   A^2 -> H(U1(c, d), e)
28.54/9.58	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, a), d)
28.54/9.58	
28.54/9.58	The TRS R consists of the following rules:
28.54/9.58	
28.54/9.58	   f(x) -> U1(x, x)
28.54/9.58	   U1(e, x) -> x
28.54/9.58	   a -> c
28.54/9.58	   a -> d
28.54/9.58	   b -> c
28.54/9.58	   b -> d
28.54/9.58	   d -> k
28.54/9.58	   c -> e
28.54/9.58	   c -> k
28.54/9.58	
28.54/9.58	Q is empty.
28.54/9.58	We have to consider all minimal (P,Q,R)-chains.
28.54/9.58	----------------------------------------
28.54/9.58	
28.54/9.58	(1221) TransformationProof (EQUIVALENT)
28.54/9.58	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), c) at position [] we obtained the following new rules [LPAR04]:
28.54/9.58	
28.54/9.58	   (A^2 -> H(U1(e, a), c),A^2 -> H(U1(e, a), c))
28.54/9.58	   (A^2 -> H(U1(k, a), c),A^2 -> H(U1(k, a), c))
28.54/9.58	   (A^2 -> H(U1(c, c), c),A^2 -> H(U1(c, c), c))
28.54/9.58	   (A^2 -> H(U1(c, d), c),A^2 -> H(U1(c, d), c))
28.54/9.58	   (A^2 -> H(U1(c, a), e),A^2 -> H(U1(c, a), e))
28.54/9.58	   (A^2 -> H(U1(c, a), k),A^2 -> H(U1(c, a), k))
28.54/9.58	
28.54/9.58	
28.54/9.58	----------------------------------------
28.54/9.58	
28.54/9.58	(1222)
28.54/9.58	Obligation:
28.54/9.58	Q DP problem:
28.54/9.58	The TRS P consists of the following rules:
28.54/9.58	
28.54/9.58	   G(d, x, x) -> A^2
28.54/9.58	   A^2 -> H(f(c), f(c))
28.54/9.58	   H(x, x) -> G(x, x, f(k))
28.54/9.58	   A^2 -> H(f(d), f(d))
28.54/9.58	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.58	   A^2 -> H(f(e), f(e))
28.54/9.58	   A^2 -> H(f(k), f(k))
28.54/9.58	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.58	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.58	   A^2 -> H(U1(c, a), U1(e, k))
28.54/9.58	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(c, a), e)
28.54/9.58	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.58	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.58	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.58	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.58	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.58	   A^2 -> H(U1(d, e), f(e))
28.54/9.58	   A^2 -> H(U1(d, e), f(k))
28.54/9.58	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.58	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.58	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.58	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.58	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.58	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.58	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.58	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.58	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.58	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.58	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.58	   A^2 -> H(U1(d, a), b)
28.54/9.58	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.58	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.58	   A^2 -> H(U1(d, a), c)
28.54/9.58	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.58	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(d, a), e)
28.54/9.58	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.58	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.58	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.58	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.58	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.58	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.58	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.58	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.58	   A^2 -> H(U1(a, c), b)
28.54/9.58	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.58	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.58	   A^2 -> H(U1(a, c), c)
28.54/9.58	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.58	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.58	   A^2 -> H(U1(a, c), e)
28.54/9.58	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, d), b)
28.54/9.58	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.58	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.58	   A^2 -> H(U1(a, d), c)
28.54/9.58	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.58	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.58	   A^2 -> H(U1(a, d), e)
28.54/9.58	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, a), d)
28.54/9.58	   A^2 -> H(U1(a, a), k)
28.54/9.58	   A^2 -> H(k, U1(b, b))
28.54/9.58	   A^2 -> H(k, f(c))
28.54/9.58	   A^2 -> H(k, f(d))
28.54/9.58	   A^2 -> H(c, U1(c, b))
28.54/9.58	   A^2 -> H(c, U1(d, b))
28.54/9.58	   A^2 -> H(c, U1(b, c))
28.54/9.58	   A^2 -> H(c, U1(b, d))
28.54/9.58	   A^2 -> H(c, U1(c, c))
28.54/9.58	   A^2 -> H(c, f(e))
28.54/9.58	   A^2 -> H(c, f(k))
28.54/9.58	   A^2 -> H(c, U1(d, d))
28.54/9.58	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.58	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.58	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.58	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.58	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.58	   A^2 -> H(U1(e, k), f(e))
28.54/9.58	   A^2 -> H(U1(e, k), f(k))
28.54/9.58	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.58	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.58	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.58	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.58	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.58	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.58	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.58	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.58	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.58	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.58	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.58	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.58	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.58	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.58	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.58	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.58	   A^2 -> H(U1(k, e), f(e))
28.54/9.58	   A^2 -> H(U1(k, e), f(k))
28.54/9.58	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.58	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.58	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.58	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.58	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.58	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.58	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.58	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.58	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.58	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.58	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.58	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.58	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.58	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.58	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.58	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.58	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.58	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.58	   A^2 -> H(U1(c, c), b)
28.54/9.58	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.58	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.58	   A^2 -> H(U1(c, c), e)
28.54/9.58	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.58	   A^2 -> H(e, U1(c, b))
28.54/9.58	   A^2 -> H(e, U1(d, b))
28.54/9.58	   A^2 -> H(e, U1(b, c))
28.54/9.58	   A^2 -> H(e, U1(b, d))
28.54/9.58	   A^2 -> H(e, U1(c, c))
28.54/9.58	   A^2 -> H(e, f(e))
28.54/9.58	   A^2 -> H(e, f(k))
28.54/9.58	   A^2 -> H(e, U1(d, d))
28.54/9.58	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.58	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.58	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.58	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.58	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.58	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.58	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.58	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.58	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.58	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.58	   A^2 -> H(f(e), b)
28.54/9.58	   A^2 -> H(f(e), U1(e, d))
28.54/9.58	   A^2 -> H(f(e), U1(d, e))
28.54/9.58	   A^2 -> H(f(e), c)
28.54/9.58	   A^2 -> H(f(e), U1(e, k))
28.54/9.58	   A^2 -> H(f(e), U1(k, e))
28.54/9.58	   A^2 -> H(f(e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.58	   A^2 -> H(f(k), b)
28.54/9.58	   A^2 -> H(f(k), U1(e, d))
28.54/9.58	   A^2 -> H(f(k), U1(d, e))
28.54/9.58	   A^2 -> H(f(k), c)
28.54/9.58	   A^2 -> H(f(k), U1(e, k))
28.54/9.58	   A^2 -> H(f(k), U1(k, e))
28.54/9.58	   A^2 -> H(f(k), e)
28.54/9.58	   A^2 -> H(f(c), d)
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.58	   A^2 -> H(U1(k, k), f(e))
28.54/9.58	   A^2 -> H(U1(k, k), f(k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.58	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.58	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.58	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.58	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.58	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.58	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.58	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.58	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.58	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.58	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.58	   A^2 -> H(U1(d, d), b)
28.54/9.58	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.58	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.58	   A^2 -> H(U1(d, d), c)
28.54/9.58	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.58	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.58	   A^2 -> H(U1(d, d), e)
28.54/9.58	   A^2 -> H(f(d), d)
28.54/9.58	   A^2 -> H(f(d), k)
28.54/9.58	   A^2 -> H(U1(c, c), c)
28.54/9.58	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.58	   A^2 -> H(f(c), k)
28.54/9.58	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.58	   A^2 -> H(f(k), U1(k, k))
28.54/9.58	   A^2 -> H(f(e), e)
28.54/9.58	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.58	   A^2 -> H(d, U1(c, b))
28.54/9.58	   A^2 -> H(d, U1(d, b))
28.54/9.58	   A^2 -> H(d, U1(b, c))
28.54/9.58	   A^2 -> H(d, U1(b, d))
28.54/9.58	   A^2 -> H(d, U1(c, c))
28.54/9.58	   A^2 -> H(d, f(e))
28.54/9.58	   A^2 -> H(d, f(k))
28.54/9.58	   A^2 -> H(d, U1(d, d))
28.54/9.58	   A^2 -> H(a, U1(e, b))
28.54/9.58	   A^2 -> H(a, U1(k, b))
28.54/9.58	   A^2 -> H(a, U1(c, d))
28.54/9.58	   A^2 -> H(a, U1(d, c))
28.54/9.58	   A^2 -> H(a, U1(b, e))
28.54/9.58	   A^2 -> H(a, U1(b, k))
28.54/9.58	   A^2 -> H(a, U1(e, c))
28.54/9.58	   A^2 -> H(a, U1(k, c))
28.54/9.58	   A^2 -> H(a, U1(c, e))
28.54/9.58	   A^2 -> H(a, U1(c, k))
28.54/9.58	   A^2 -> H(a, U1(e, e))
28.54/9.58	   A^2 -> H(a, U1(k, k))
28.54/9.58	   A^2 -> H(a, U1(k, d))
28.54/9.58	   A^2 -> H(a, U1(d, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.58	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.58	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.58	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.58	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.58	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.58	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.58	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.58	   A^2 -> H(U1(e, a), b)
28.54/9.58	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.58	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.58	   A^2 -> H(U1(e, a), c)
28.54/9.58	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.58	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(e, a), e)
28.54/9.58	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, a), b)
28.54/9.58	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.58	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.58	   A^2 -> H(U1(k, a), c)
28.54/9.58	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.58	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, d), b)
28.54/9.58	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.58	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.58	   A^2 -> H(U1(c, d), c)
28.54/9.58	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.58	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.58	   A^2 -> H(U1(c, d), e)
28.54/9.58	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, a), d)
28.54/9.58	   A^2 -> H(U1(c, a), k)
28.54/9.58	
28.54/9.58	The TRS R consists of the following rules:
28.54/9.58	
28.54/9.58	   f(x) -> U1(x, x)
28.54/9.58	   U1(e, x) -> x
28.54/9.58	   a -> c
28.54/9.58	   a -> d
28.54/9.58	   b -> c
28.54/9.58	   b -> d
28.54/9.58	   d -> k
28.54/9.58	   c -> e
28.54/9.58	   c -> k
28.54/9.58	
28.54/9.58	Q is empty.
28.54/9.58	We have to consider all minimal (P,Q,R)-chains.
28.54/9.58	----------------------------------------
28.54/9.58	
28.54/9.58	(1223) TransformationProof (EQUIVALENT)
28.54/9.58	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.58	
28.54/9.58	   (A^2 -> H(U1(e, a), U1(e, k)),A^2 -> H(U1(e, a), U1(e, k)))
28.54/9.58	   (A^2 -> H(U1(k, a), U1(e, k)),A^2 -> H(U1(k, a), U1(e, k)))
28.54/9.58	   (A^2 -> H(U1(c, c), U1(e, k)),A^2 -> H(U1(c, c), U1(e, k)))
28.54/9.58	   (A^2 -> H(U1(c, d), U1(e, k)),A^2 -> H(U1(c, d), U1(e, k)))
28.54/9.58	   (A^2 -> H(U1(c, a), k),A^2 -> H(U1(c, a), k))
28.54/9.58	
28.54/9.58	
28.54/9.58	----------------------------------------
28.54/9.58	
28.54/9.58	(1224)
28.54/9.58	Obligation:
28.54/9.58	Q DP problem:
28.54/9.58	The TRS P consists of the following rules:
28.54/9.58	
28.54/9.58	   G(d, x, x) -> A^2
28.54/9.58	   A^2 -> H(f(c), f(c))
28.54/9.58	   H(x, x) -> G(x, x, f(k))
28.54/9.58	   A^2 -> H(f(d), f(d))
28.54/9.58	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.58	   A^2 -> H(f(e), f(e))
28.54/9.58	   A^2 -> H(f(k), f(k))
28.54/9.58	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.58	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.58	   A^2 -> H(U1(c, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(c, a), e)
28.54/9.58	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.58	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.58	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.58	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.58	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.58	   A^2 -> H(U1(d, e), f(e))
28.54/9.58	   A^2 -> H(U1(d, e), f(k))
28.54/9.58	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.58	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.58	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.58	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.58	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.58	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.58	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.58	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.58	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.58	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.58	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.58	   A^2 -> H(U1(d, a), b)
28.54/9.58	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.58	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.58	   A^2 -> H(U1(d, a), c)
28.54/9.58	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.58	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(d, a), e)
28.54/9.58	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.58	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.58	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.58	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.58	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.58	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.58	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.58	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.58	   A^2 -> H(U1(a, c), b)
28.54/9.58	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.58	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.58	   A^2 -> H(U1(a, c), c)
28.54/9.58	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.58	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.58	   A^2 -> H(U1(a, c), e)
28.54/9.58	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, d), b)
28.54/9.58	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.58	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.58	   A^2 -> H(U1(a, d), c)
28.54/9.58	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.58	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.58	   A^2 -> H(U1(a, d), e)
28.54/9.58	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, a), d)
28.54/9.58	   A^2 -> H(U1(a, a), k)
28.54/9.58	   A^2 -> H(k, U1(b, b))
28.54/9.58	   A^2 -> H(k, f(c))
28.54/9.58	   A^2 -> H(k, f(d))
28.54/9.58	   A^2 -> H(c, U1(c, b))
28.54/9.58	   A^2 -> H(c, U1(d, b))
28.54/9.58	   A^2 -> H(c, U1(b, c))
28.54/9.58	   A^2 -> H(c, U1(b, d))
28.54/9.58	   A^2 -> H(c, U1(c, c))
28.54/9.58	   A^2 -> H(c, f(e))
28.54/9.58	   A^2 -> H(c, f(k))
28.54/9.58	   A^2 -> H(c, U1(d, d))
28.54/9.58	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.58	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.58	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.58	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.58	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.58	   A^2 -> H(U1(e, k), f(e))
28.54/9.58	   A^2 -> H(U1(e, k), f(k))
28.54/9.58	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.58	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.58	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.58	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.58	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.58	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.58	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.58	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.58	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.58	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.58	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.58	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.58	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.58	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.58	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.58	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.58	   A^2 -> H(U1(k, e), f(e))
28.54/9.58	   A^2 -> H(U1(k, e), f(k))
28.54/9.58	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.58	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.58	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.58	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.58	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.58	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.58	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.58	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.58	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.58	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.58	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.58	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.58	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.58	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.58	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.58	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.58	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.58	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.58	   A^2 -> H(U1(c, c), b)
28.54/9.58	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.58	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.58	   A^2 -> H(U1(c, c), e)
28.54/9.58	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.58	   A^2 -> H(e, U1(c, b))
28.54/9.58	   A^2 -> H(e, U1(d, b))
28.54/9.58	   A^2 -> H(e, U1(b, c))
28.54/9.58	   A^2 -> H(e, U1(b, d))
28.54/9.58	   A^2 -> H(e, U1(c, c))
28.54/9.58	   A^2 -> H(e, f(e))
28.54/9.58	   A^2 -> H(e, f(k))
28.54/9.58	   A^2 -> H(e, U1(d, d))
28.54/9.58	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.58	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.58	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.58	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.58	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.58	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.58	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.58	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.58	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.58	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.58	   A^2 -> H(f(e), b)
28.54/9.58	   A^2 -> H(f(e), U1(e, d))
28.54/9.58	   A^2 -> H(f(e), U1(d, e))
28.54/9.58	   A^2 -> H(f(e), c)
28.54/9.58	   A^2 -> H(f(e), U1(e, k))
28.54/9.58	   A^2 -> H(f(e), U1(k, e))
28.54/9.58	   A^2 -> H(f(e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.58	   A^2 -> H(f(k), b)
28.54/9.58	   A^2 -> H(f(k), U1(e, d))
28.54/9.58	   A^2 -> H(f(k), U1(d, e))
28.54/9.58	   A^2 -> H(f(k), c)
28.54/9.58	   A^2 -> H(f(k), U1(e, k))
28.54/9.58	   A^2 -> H(f(k), U1(k, e))
28.54/9.58	   A^2 -> H(f(k), e)
28.54/9.58	   A^2 -> H(f(c), d)
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.58	   A^2 -> H(U1(k, k), f(e))
28.54/9.58	   A^2 -> H(U1(k, k), f(k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.58	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.58	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.58	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.58	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.58	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.58	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.58	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.58	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.58	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.58	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.58	   A^2 -> H(U1(d, d), b)
28.54/9.58	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.58	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.58	   A^2 -> H(U1(d, d), c)
28.54/9.58	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.58	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.58	   A^2 -> H(U1(d, d), e)
28.54/9.58	   A^2 -> H(f(d), d)
28.54/9.58	   A^2 -> H(f(d), k)
28.54/9.58	   A^2 -> H(U1(c, c), c)
28.54/9.58	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.58	   A^2 -> H(f(c), k)
28.54/9.58	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.58	   A^2 -> H(f(k), U1(k, k))
28.54/9.58	   A^2 -> H(f(e), e)
28.54/9.58	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.58	   A^2 -> H(d, U1(c, b))
28.54/9.58	   A^2 -> H(d, U1(d, b))
28.54/9.58	   A^2 -> H(d, U1(b, c))
28.54/9.58	   A^2 -> H(d, U1(b, d))
28.54/9.58	   A^2 -> H(d, U1(c, c))
28.54/9.58	   A^2 -> H(d, f(e))
28.54/9.58	   A^2 -> H(d, f(k))
28.54/9.58	   A^2 -> H(d, U1(d, d))
28.54/9.58	   A^2 -> H(a, U1(e, b))
28.54/9.58	   A^2 -> H(a, U1(k, b))
28.54/9.58	   A^2 -> H(a, U1(c, d))
28.54/9.58	   A^2 -> H(a, U1(d, c))
28.54/9.58	   A^2 -> H(a, U1(b, e))
28.54/9.58	   A^2 -> H(a, U1(b, k))
28.54/9.58	   A^2 -> H(a, U1(e, c))
28.54/9.58	   A^2 -> H(a, U1(k, c))
28.54/9.58	   A^2 -> H(a, U1(c, e))
28.54/9.58	   A^2 -> H(a, U1(c, k))
28.54/9.58	   A^2 -> H(a, U1(e, e))
28.54/9.58	   A^2 -> H(a, U1(k, k))
28.54/9.58	   A^2 -> H(a, U1(k, d))
28.54/9.58	   A^2 -> H(a, U1(d, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.58	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.58	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.58	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.58	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.58	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.58	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.58	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.58	   A^2 -> H(U1(e, a), b)
28.54/9.58	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.58	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.58	   A^2 -> H(U1(e, a), c)
28.54/9.58	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.58	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(e, a), e)
28.54/9.58	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, a), b)
28.54/9.58	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.58	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.58	   A^2 -> H(U1(k, a), c)
28.54/9.58	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.58	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, d), b)
28.54/9.58	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.58	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.58	   A^2 -> H(U1(c, d), c)
28.54/9.58	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.58	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.58	   A^2 -> H(U1(c, d), e)
28.54/9.58	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, a), d)
28.54/9.58	   A^2 -> H(U1(c, a), k)
28.54/9.58	
28.54/9.58	The TRS R consists of the following rules:
28.54/9.58	
28.54/9.58	   f(x) -> U1(x, x)
28.54/9.58	   U1(e, x) -> x
28.54/9.58	   a -> c
28.54/9.58	   a -> d
28.54/9.58	   b -> c
28.54/9.58	   b -> d
28.54/9.58	   d -> k
28.54/9.58	   c -> e
28.54/9.58	   c -> k
28.54/9.58	
28.54/9.58	Q is empty.
28.54/9.58	We have to consider all minimal (P,Q,R)-chains.
28.54/9.58	----------------------------------------
28.54/9.58	
28.54/9.58	(1225) TransformationProof (EQUIVALENT)
28.54/9.58	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.58	
28.54/9.58	   (A^2 -> H(U1(e, a), U1(k, e)),A^2 -> H(U1(e, a), U1(k, e)))
28.54/9.58	   (A^2 -> H(U1(k, a), U1(k, e)),A^2 -> H(U1(k, a), U1(k, e)))
28.54/9.58	   (A^2 -> H(U1(c, c), U1(k, e)),A^2 -> H(U1(c, c), U1(k, e)))
28.54/9.58	   (A^2 -> H(U1(c, d), U1(k, e)),A^2 -> H(U1(c, d), U1(k, e)))
28.54/9.58	
28.54/9.58	
28.54/9.58	----------------------------------------
28.54/9.58	
28.54/9.58	(1226)
28.54/9.58	Obligation:
28.54/9.58	Q DP problem:
28.54/9.58	The TRS P consists of the following rules:
28.54/9.58	
28.54/9.58	   G(d, x, x) -> A^2
28.54/9.58	   A^2 -> H(f(c), f(c))
28.54/9.58	   H(x, x) -> G(x, x, f(k))
28.54/9.58	   A^2 -> H(f(d), f(d))
28.54/9.58	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.58	   A^2 -> H(f(e), f(e))
28.54/9.58	   A^2 -> H(f(k), f(k))
28.54/9.58	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.58	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.58	   A^2 -> H(U1(c, a), e)
28.54/9.58	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.58	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.58	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.58	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.58	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.58	   A^2 -> H(U1(d, e), f(e))
28.54/9.58	   A^2 -> H(U1(d, e), f(k))
28.54/9.58	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.58	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.58	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.58	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.58	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.58	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.58	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.58	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.58	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.58	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.58	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.58	   A^2 -> H(U1(d, a), b)
28.54/9.58	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.58	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.58	   A^2 -> H(U1(d, a), c)
28.54/9.58	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.58	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.58	   A^2 -> H(U1(d, a), e)
28.54/9.58	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.58	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.58	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.58	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.58	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.58	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.58	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.58	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.58	   A^2 -> H(U1(a, c), b)
28.54/9.58	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.58	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.58	   A^2 -> H(U1(a, c), c)
28.54/9.58	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.58	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.58	   A^2 -> H(U1(a, c), e)
28.54/9.58	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, d), b)
28.54/9.58	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.58	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.58	   A^2 -> H(U1(a, d), c)
28.54/9.58	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.58	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.58	   A^2 -> H(U1(a, d), e)
28.54/9.58	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(a, a), d)
28.54/9.58	   A^2 -> H(U1(a, a), k)
28.54/9.58	   A^2 -> H(k, U1(b, b))
28.54/9.58	   A^2 -> H(k, f(c))
28.54/9.58	   A^2 -> H(k, f(d))
28.54/9.58	   A^2 -> H(c, U1(c, b))
28.54/9.58	   A^2 -> H(c, U1(d, b))
28.54/9.58	   A^2 -> H(c, U1(b, c))
28.54/9.58	   A^2 -> H(c, U1(b, d))
28.54/9.58	   A^2 -> H(c, U1(c, c))
28.54/9.58	   A^2 -> H(c, f(e))
28.54/9.58	   A^2 -> H(c, f(k))
28.54/9.58	   A^2 -> H(c, U1(d, d))
28.54/9.58	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.58	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.58	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.58	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.58	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.58	   A^2 -> H(U1(e, k), f(e))
28.54/9.58	   A^2 -> H(U1(e, k), f(k))
28.54/9.58	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.58	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.58	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.58	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.58	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.58	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.58	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.58	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.58	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.58	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.58	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.58	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.58	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.58	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.58	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.58	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.58	   A^2 -> H(U1(k, e), f(e))
28.54/9.58	   A^2 -> H(U1(k, e), f(k))
28.54/9.58	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.58	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.58	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.58	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.58	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.58	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.58	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.58	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.58	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.58	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.58	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.58	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.58	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.58	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.58	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.58	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.58	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.58	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.58	   A^2 -> H(U1(c, c), b)
28.54/9.58	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.58	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.58	   A^2 -> H(U1(c, c), e)
28.54/9.58	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.58	   A^2 -> H(e, U1(c, b))
28.54/9.58	   A^2 -> H(e, U1(d, b))
28.54/9.58	   A^2 -> H(e, U1(b, c))
28.54/9.58	   A^2 -> H(e, U1(b, d))
28.54/9.58	   A^2 -> H(e, U1(c, c))
28.54/9.58	   A^2 -> H(e, f(e))
28.54/9.58	   A^2 -> H(e, f(k))
28.54/9.58	   A^2 -> H(e, U1(d, d))
28.54/9.58	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.58	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.58	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.58	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.58	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.58	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.58	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.58	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.58	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.58	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.58	   A^2 -> H(f(e), b)
28.54/9.58	   A^2 -> H(f(e), U1(e, d))
28.54/9.58	   A^2 -> H(f(e), U1(d, e))
28.54/9.58	   A^2 -> H(f(e), c)
28.54/9.58	   A^2 -> H(f(e), U1(e, k))
28.54/9.58	   A^2 -> H(f(e), U1(k, e))
28.54/9.58	   A^2 -> H(f(e), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.58	   A^2 -> H(f(k), b)
28.54/9.58	   A^2 -> H(f(k), U1(e, d))
28.54/9.58	   A^2 -> H(f(k), U1(d, e))
28.54/9.58	   A^2 -> H(f(k), c)
28.54/9.58	   A^2 -> H(f(k), U1(e, k))
28.54/9.58	   A^2 -> H(f(k), U1(k, e))
28.54/9.58	   A^2 -> H(f(k), e)
28.54/9.58	   A^2 -> H(f(c), d)
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.58	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.58	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.58	   A^2 -> H(U1(k, k), f(e))
28.54/9.58	   A^2 -> H(U1(k, k), f(k))
28.54/9.58	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.58	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.58	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.58	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.58	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.58	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.58	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.58	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.58	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.58	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.58	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.58	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.58	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.58	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.58	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.58	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.58	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.58	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.58	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.58	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.58	   A^2 -> H(U1(d, d), b)
28.54/9.58	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.58	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.58	   A^2 -> H(U1(d, d), c)
28.54/9.58	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.58	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.58	   A^2 -> H(U1(d, d), e)
28.54/9.58	   A^2 -> H(f(d), d)
28.54/9.58	   A^2 -> H(f(d), k)
28.54/9.58	   A^2 -> H(U1(c, c), c)
28.54/9.58	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.58	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.58	   A^2 -> H(f(c), k)
28.54/9.58	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.58	   A^2 -> H(f(k), U1(k, k))
28.54/9.58	   A^2 -> H(f(e), e)
28.54/9.58	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.58	   A^2 -> H(d, U1(c, b))
28.54/9.58	   A^2 -> H(d, U1(d, b))
28.54/9.58	   A^2 -> H(d, U1(b, c))
28.54/9.58	   A^2 -> H(d, U1(b, d))
28.54/9.58	   A^2 -> H(d, U1(c, c))
28.54/9.58	   A^2 -> H(d, f(e))
28.54/9.58	   A^2 -> H(d, f(k))
28.54/9.58	   A^2 -> H(d, U1(d, d))
28.54/9.58	   A^2 -> H(a, U1(e, b))
28.54/9.58	   A^2 -> H(a, U1(k, b))
28.54/9.58	   A^2 -> H(a, U1(c, d))
28.54/9.58	   A^2 -> H(a, U1(d, c))
28.54/9.58	   A^2 -> H(a, U1(b, e))
28.54/9.58	   A^2 -> H(a, U1(b, k))
28.54/9.58	   A^2 -> H(a, U1(e, c))
28.54/9.58	   A^2 -> H(a, U1(k, c))
28.54/9.59	   A^2 -> H(a, U1(c, e))
28.54/9.59	   A^2 -> H(a, U1(c, k))
28.54/9.59	   A^2 -> H(a, U1(e, e))
28.54/9.59	   A^2 -> H(a, U1(k, k))
28.54/9.59	   A^2 -> H(a, U1(k, d))
28.54/9.59	   A^2 -> H(a, U1(d, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.59	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.59	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.59	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.59	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.59	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.59	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.59	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.59	   A^2 -> H(U1(e, a), b)
28.54/9.59	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.59	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.59	   A^2 -> H(U1(e, a), c)
28.54/9.59	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.59	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.59	   A^2 -> H(U1(e, a), e)
28.54/9.59	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, a), b)
28.54/9.59	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.59	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.59	   A^2 -> H(U1(k, a), c)
28.54/9.59	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.59	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.59	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, d), b)
28.54/9.59	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.59	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.59	   A^2 -> H(U1(c, d), c)
28.54/9.59	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.59	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.59	   A^2 -> H(U1(c, d), e)
28.54/9.59	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, a), d)
28.54/9.59	   A^2 -> H(U1(c, a), k)
28.54/9.59	
28.54/9.59	The TRS R consists of the following rules:
28.54/9.59	
28.54/9.59	   f(x) -> U1(x, x)
28.54/9.59	   U1(e, x) -> x
28.54/9.59	   a -> c
28.54/9.59	   a -> d
28.54/9.59	   b -> c
28.54/9.59	   b -> d
28.54/9.59	   d -> k
28.54/9.59	   c -> e
28.54/9.59	   c -> k
28.54/9.59	
28.54/9.59	Q is empty.
28.54/9.59	We have to consider all minimal (P,Q,R)-chains.
28.54/9.59	----------------------------------------
28.54/9.59	
28.54/9.59	(1227) TransformationProof (EQUIVALENT)
28.54/9.59	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), e) at position [] we obtained the following new rules [LPAR04]:
28.54/9.59	
28.54/9.59	   (A^2 -> H(U1(e, a), e),A^2 -> H(U1(e, a), e))
28.54/9.59	   (A^2 -> H(U1(k, a), e),A^2 -> H(U1(k, a), e))
28.54/9.59	   (A^2 -> H(U1(c, c), e),A^2 -> H(U1(c, c), e))
28.54/9.59	   (A^2 -> H(U1(c, d), e),A^2 -> H(U1(c, d), e))
28.54/9.59	
28.54/9.59	
28.54/9.59	----------------------------------------
28.54/9.59	
28.54/9.59	(1228)
28.54/9.59	Obligation:
28.54/9.59	Q DP problem:
28.54/9.59	The TRS P consists of the following rules:
28.54/9.59	
28.54/9.59	   G(d, x, x) -> A^2
28.54/9.59	   A^2 -> H(f(c), f(c))
28.54/9.59	   H(x, x) -> G(x, x, f(k))
28.54/9.59	   A^2 -> H(f(d), f(d))
28.54/9.59	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.59	   A^2 -> H(f(e), f(e))
28.54/9.59	   A^2 -> H(f(k), f(k))
28.54/9.59	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.59	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.59	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.59	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.59	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.59	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.59	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.59	   A^2 -> H(U1(d, e), f(e))
28.54/9.59	   A^2 -> H(U1(d, e), f(k))
28.54/9.59	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.59	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.59	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.59	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.59	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.59	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.59	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.59	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.59	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.59	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.59	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.59	   A^2 -> H(U1(d, a), b)
28.54/9.59	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.59	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.59	   A^2 -> H(U1(d, a), c)
28.54/9.59	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.59	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.59	   A^2 -> H(U1(d, a), e)
28.54/9.59	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.59	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.59	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.59	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.59	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.59	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.59	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.59	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.59	   A^2 -> H(U1(a, c), b)
28.54/9.59	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.59	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.59	   A^2 -> H(U1(a, c), c)
28.54/9.59	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.59	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.59	   A^2 -> H(U1(a, c), e)
28.54/9.59	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, d), b)
28.54/9.59	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.59	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.59	   A^2 -> H(U1(a, d), c)
28.54/9.59	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.59	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.59	   A^2 -> H(U1(a, d), e)
28.54/9.59	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, a), d)
28.54/9.59	   A^2 -> H(U1(a, a), k)
28.54/9.59	   A^2 -> H(k, U1(b, b))
28.54/9.59	   A^2 -> H(k, f(c))
28.54/9.59	   A^2 -> H(k, f(d))
28.54/9.59	   A^2 -> H(c, U1(c, b))
28.54/9.59	   A^2 -> H(c, U1(d, b))
28.54/9.59	   A^2 -> H(c, U1(b, c))
28.54/9.59	   A^2 -> H(c, U1(b, d))
28.54/9.59	   A^2 -> H(c, U1(c, c))
28.54/9.59	   A^2 -> H(c, f(e))
28.54/9.59	   A^2 -> H(c, f(k))
28.54/9.59	   A^2 -> H(c, U1(d, d))
28.54/9.59	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.59	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.59	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.59	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.59	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.59	   A^2 -> H(U1(e, k), f(e))
28.54/9.59	   A^2 -> H(U1(e, k), f(k))
28.54/9.59	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.59	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.59	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.59	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.59	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.59	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.59	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.59	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.59	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.59	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.59	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.59	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.59	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.59	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.59	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.59	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.59	   A^2 -> H(U1(k, e), f(e))
28.54/9.59	   A^2 -> H(U1(k, e), f(k))
28.54/9.59	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.59	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.59	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.59	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.59	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.59	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.59	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.59	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.59	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.59	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.59	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.59	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.59	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.59	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.59	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.59	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.59	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.59	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.59	   A^2 -> H(U1(c, c), b)
28.54/9.59	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.59	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.59	   A^2 -> H(U1(c, c), e)
28.54/9.59	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.59	   A^2 -> H(e, U1(c, b))
28.54/9.59	   A^2 -> H(e, U1(d, b))
28.54/9.59	   A^2 -> H(e, U1(b, c))
28.54/9.59	   A^2 -> H(e, U1(b, d))
28.54/9.59	   A^2 -> H(e, U1(c, c))
28.54/9.59	   A^2 -> H(e, f(e))
28.54/9.59	   A^2 -> H(e, f(k))
28.54/9.59	   A^2 -> H(e, U1(d, d))
28.54/9.59	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.59	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.59	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.59	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.59	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.59	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.59	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.59	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.59	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.59	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.59	   A^2 -> H(f(e), b)
28.54/9.59	   A^2 -> H(f(e), U1(e, d))
28.54/9.59	   A^2 -> H(f(e), U1(d, e))
28.54/9.59	   A^2 -> H(f(e), c)
28.54/9.59	   A^2 -> H(f(e), U1(e, k))
28.54/9.59	   A^2 -> H(f(e), U1(k, e))
28.54/9.59	   A^2 -> H(f(e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.59	   A^2 -> H(f(k), b)
28.54/9.59	   A^2 -> H(f(k), U1(e, d))
28.54/9.59	   A^2 -> H(f(k), U1(d, e))
28.54/9.59	   A^2 -> H(f(k), c)
28.54/9.59	   A^2 -> H(f(k), U1(e, k))
28.54/9.59	   A^2 -> H(f(k), U1(k, e))
28.54/9.59	   A^2 -> H(f(k), e)
28.54/9.59	   A^2 -> H(f(c), d)
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.59	   A^2 -> H(U1(k, k), f(e))
28.54/9.59	   A^2 -> H(U1(k, k), f(k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.59	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.59	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.59	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.59	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.59	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.59	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.59	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.59	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.59	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.59	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.59	   A^2 -> H(U1(d, d), b)
28.54/9.59	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.59	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.59	   A^2 -> H(U1(d, d), c)
28.54/9.59	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.59	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.59	   A^2 -> H(U1(d, d), e)
28.54/9.59	   A^2 -> H(f(d), d)
28.54/9.59	   A^2 -> H(f(d), k)
28.54/9.59	   A^2 -> H(U1(c, c), c)
28.54/9.59	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.59	   A^2 -> H(f(c), k)
28.54/9.59	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.59	   A^2 -> H(f(k), U1(k, k))
28.54/9.59	   A^2 -> H(f(e), e)
28.54/9.59	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.59	   A^2 -> H(d, U1(c, b))
28.54/9.59	   A^2 -> H(d, U1(d, b))
28.54/9.59	   A^2 -> H(d, U1(b, c))
28.54/9.59	   A^2 -> H(d, U1(b, d))
28.54/9.59	   A^2 -> H(d, U1(c, c))
28.54/9.59	   A^2 -> H(d, f(e))
28.54/9.59	   A^2 -> H(d, f(k))
28.54/9.59	   A^2 -> H(d, U1(d, d))
28.54/9.59	   A^2 -> H(a, U1(e, b))
28.54/9.59	   A^2 -> H(a, U1(k, b))
28.54/9.59	   A^2 -> H(a, U1(c, d))
28.54/9.59	   A^2 -> H(a, U1(d, c))
28.54/9.59	   A^2 -> H(a, U1(b, e))
28.54/9.59	   A^2 -> H(a, U1(b, k))
28.54/9.59	   A^2 -> H(a, U1(e, c))
28.54/9.59	   A^2 -> H(a, U1(k, c))
28.54/9.59	   A^2 -> H(a, U1(c, e))
28.54/9.59	   A^2 -> H(a, U1(c, k))
28.54/9.59	   A^2 -> H(a, U1(e, e))
28.54/9.59	   A^2 -> H(a, U1(k, k))
28.54/9.59	   A^2 -> H(a, U1(k, d))
28.54/9.59	   A^2 -> H(a, U1(d, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.59	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.59	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.59	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.59	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.59	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.59	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.59	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.59	   A^2 -> H(U1(e, a), b)
28.54/9.59	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.59	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.59	   A^2 -> H(U1(e, a), c)
28.54/9.59	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.59	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.59	   A^2 -> H(U1(e, a), e)
28.54/9.59	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, a), b)
28.54/9.59	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.59	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.59	   A^2 -> H(U1(k, a), c)
28.54/9.59	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.59	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.59	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, d), b)
28.54/9.59	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.59	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.59	   A^2 -> H(U1(c, d), c)
28.54/9.59	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.59	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.59	   A^2 -> H(U1(c, d), e)
28.54/9.59	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, a), d)
28.54/9.59	   A^2 -> H(U1(c, a), k)
28.54/9.59	   A^2 -> H(U1(k, a), e)
28.54/9.59	
28.54/9.59	The TRS R consists of the following rules:
28.54/9.59	
28.54/9.59	   f(x) -> U1(x, x)
28.54/9.59	   U1(e, x) -> x
28.54/9.59	   a -> c
28.54/9.59	   a -> d
28.54/9.59	   b -> c
28.54/9.59	   b -> d
28.54/9.59	   d -> k
28.54/9.59	   c -> e
28.54/9.59	   c -> k
28.54/9.59	
28.54/9.59	Q is empty.
28.54/9.59	We have to consider all minimal (P,Q,R)-chains.
28.54/9.59	----------------------------------------
28.54/9.59	
28.54/9.59	(1229) DependencyGraphProof (EQUIVALENT)
28.54/9.59	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.54/9.59	----------------------------------------
28.54/9.59	
28.54/9.59	(1230)
28.54/9.59	Obligation:
28.54/9.59	Q DP problem:
28.54/9.59	The TRS P consists of the following rules:
28.54/9.59	
28.54/9.59	   A^2 -> H(f(c), f(c))
28.54/9.59	   H(x, x) -> G(x, x, f(k))
28.54/9.59	   G(d, x, x) -> A^2
28.54/9.59	   A^2 -> H(f(d), f(d))
28.54/9.59	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.59	   A^2 -> H(f(e), f(e))
28.54/9.59	   A^2 -> H(f(k), f(k))
28.54/9.59	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.59	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.59	   A^2 -> H(U1(c, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.59	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.59	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.59	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.59	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.59	   A^2 -> H(U1(d, e), f(e))
28.54/9.59	   A^2 -> H(U1(d, e), f(k))
28.54/9.59	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.59	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.59	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.59	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.59	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.59	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.59	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.59	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.59	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.59	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.59	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.59	   A^2 -> H(U1(d, a), b)
28.54/9.59	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.59	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.59	   A^2 -> H(U1(d, a), c)
28.54/9.59	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.59	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.59	   A^2 -> H(U1(d, a), e)
28.54/9.59	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.59	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.59	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.59	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.59	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.59	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.59	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.59	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.59	   A^2 -> H(U1(a, c), b)
28.54/9.59	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.59	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.59	   A^2 -> H(U1(a, c), c)
28.54/9.59	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.59	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.59	   A^2 -> H(U1(a, c), e)
28.54/9.59	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, d), b)
28.54/9.59	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.59	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.59	   A^2 -> H(U1(a, d), c)
28.54/9.59	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.59	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.59	   A^2 -> H(U1(a, d), e)
28.54/9.59	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, a), d)
28.54/9.59	   A^2 -> H(U1(a, a), k)
28.54/9.59	   A^2 -> H(k, U1(b, b))
28.54/9.59	   A^2 -> H(k, f(c))
28.54/9.59	   A^2 -> H(k, f(d))
28.54/9.59	   A^2 -> H(c, U1(c, b))
28.54/9.59	   A^2 -> H(c, U1(d, b))
28.54/9.59	   A^2 -> H(c, U1(b, c))
28.54/9.59	   A^2 -> H(c, U1(b, d))
28.54/9.59	   A^2 -> H(c, U1(c, c))
28.54/9.59	   A^2 -> H(c, f(e))
28.54/9.59	   A^2 -> H(c, f(k))
28.54/9.59	   A^2 -> H(c, U1(d, d))
28.54/9.59	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.59	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.59	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.59	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.59	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.59	   A^2 -> H(U1(e, k), f(e))
28.54/9.59	   A^2 -> H(U1(e, k), f(k))
28.54/9.59	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.59	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.59	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.59	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.59	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.59	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.59	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.59	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.59	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.59	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.59	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.59	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.59	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.59	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.59	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.59	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.59	   A^2 -> H(U1(k, e), f(e))
28.54/9.59	   A^2 -> H(U1(k, e), f(k))
28.54/9.59	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.59	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.59	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.59	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.59	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.59	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.59	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.59	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.59	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.59	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.59	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.59	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.59	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.59	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.59	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.59	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.59	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.59	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.59	   A^2 -> H(U1(c, c), b)
28.54/9.59	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.59	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.59	   A^2 -> H(U1(c, c), e)
28.54/9.59	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.59	   A^2 -> H(e, U1(c, b))
28.54/9.59	   A^2 -> H(e, U1(d, b))
28.54/9.59	   A^2 -> H(e, U1(b, c))
28.54/9.59	   A^2 -> H(e, U1(b, d))
28.54/9.59	   A^2 -> H(e, U1(c, c))
28.54/9.59	   A^2 -> H(e, f(e))
28.54/9.59	   A^2 -> H(e, f(k))
28.54/9.59	   A^2 -> H(e, U1(d, d))
28.54/9.59	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.59	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.59	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.59	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.59	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.59	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.59	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.59	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.59	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.59	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.59	   A^2 -> H(f(e), b)
28.54/9.59	   A^2 -> H(f(e), U1(e, d))
28.54/9.59	   A^2 -> H(f(e), U1(d, e))
28.54/9.59	   A^2 -> H(f(e), c)
28.54/9.59	   A^2 -> H(f(e), U1(e, k))
28.54/9.59	   A^2 -> H(f(e), U1(k, e))
28.54/9.59	   A^2 -> H(f(e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.59	   A^2 -> H(f(k), b)
28.54/9.59	   A^2 -> H(f(k), U1(e, d))
28.54/9.59	   A^2 -> H(f(k), U1(d, e))
28.54/9.59	   A^2 -> H(f(k), c)
28.54/9.59	   A^2 -> H(f(k), U1(e, k))
28.54/9.59	   A^2 -> H(f(k), U1(k, e))
28.54/9.59	   A^2 -> H(f(k), e)
28.54/9.59	   A^2 -> H(f(c), d)
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.59	   A^2 -> H(U1(k, k), f(e))
28.54/9.59	   A^2 -> H(U1(k, k), f(k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.59	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.59	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.59	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.59	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.59	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.59	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.59	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.59	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.59	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.59	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.59	   A^2 -> H(U1(d, d), b)
28.54/9.59	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.59	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.59	   A^2 -> H(U1(d, d), c)
28.54/9.59	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.59	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.59	   A^2 -> H(U1(d, d), e)
28.54/9.59	   A^2 -> H(f(d), d)
28.54/9.59	   A^2 -> H(f(d), k)
28.54/9.59	   A^2 -> H(U1(c, c), c)
28.54/9.59	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.59	   A^2 -> H(f(c), k)
28.54/9.59	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.59	   A^2 -> H(f(k), U1(k, k))
28.54/9.59	   A^2 -> H(f(e), e)
28.54/9.59	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.59	   A^2 -> H(d, U1(c, b))
28.54/9.59	   A^2 -> H(d, U1(d, b))
28.54/9.59	   A^2 -> H(d, U1(b, c))
28.54/9.59	   A^2 -> H(d, U1(b, d))
28.54/9.59	   A^2 -> H(d, U1(c, c))
28.54/9.59	   A^2 -> H(d, f(e))
28.54/9.59	   A^2 -> H(d, f(k))
28.54/9.59	   A^2 -> H(d, U1(d, d))
28.54/9.59	   A^2 -> H(a, U1(e, b))
28.54/9.59	   A^2 -> H(a, U1(k, b))
28.54/9.59	   A^2 -> H(a, U1(c, d))
28.54/9.59	   A^2 -> H(a, U1(d, c))
28.54/9.59	   A^2 -> H(a, U1(b, e))
28.54/9.59	   A^2 -> H(a, U1(b, k))
28.54/9.59	   A^2 -> H(a, U1(e, c))
28.54/9.59	   A^2 -> H(a, U1(k, c))
28.54/9.59	   A^2 -> H(a, U1(c, e))
28.54/9.59	   A^2 -> H(a, U1(c, k))
28.54/9.59	   A^2 -> H(a, U1(e, e))
28.54/9.59	   A^2 -> H(a, U1(k, k))
28.54/9.59	   A^2 -> H(a, U1(k, d))
28.54/9.59	   A^2 -> H(a, U1(d, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.59	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.59	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.59	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.59	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.59	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.59	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.59	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.59	   A^2 -> H(U1(e, a), b)
28.54/9.59	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.59	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.59	   A^2 -> H(U1(e, a), c)
28.54/9.59	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.59	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.59	   A^2 -> H(U1(e, a), e)
28.54/9.59	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, a), b)
28.54/9.59	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.59	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.59	   A^2 -> H(U1(k, a), c)
28.54/9.59	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.59	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.59	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, d), b)
28.54/9.59	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.59	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.59	   A^2 -> H(U1(c, d), c)
28.54/9.59	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.59	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.59	   A^2 -> H(U1(c, d), e)
28.54/9.59	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, a), d)
28.54/9.59	   A^2 -> H(U1(c, a), k)
28.54/9.59	
28.54/9.59	The TRS R consists of the following rules:
28.54/9.59	
28.54/9.59	   f(x) -> U1(x, x)
28.54/9.59	   U1(e, x) -> x
28.54/9.59	   a -> c
28.54/9.59	   a -> d
28.54/9.59	   b -> c
28.54/9.59	   b -> d
28.54/9.59	   d -> k
28.54/9.59	   c -> e
28.54/9.59	   c -> k
28.54/9.59	
28.54/9.59	Q is empty.
28.54/9.59	We have to consider all minimal (P,Q,R)-chains.
28.54/9.59	----------------------------------------
28.54/9.59	
28.54/9.59	(1231) TransformationProof (EQUIVALENT)
28.54/9.59	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.59	
28.54/9.59	   (A^2 -> H(U1(e, a), U1(k, k)),A^2 -> H(U1(e, a), U1(k, k)))
28.54/9.59	   (A^2 -> H(U1(k, a), U1(k, k)),A^2 -> H(U1(k, a), U1(k, k)))
28.54/9.59	   (A^2 -> H(U1(c, c), U1(k, k)),A^2 -> H(U1(c, c), U1(k, k)))
28.54/9.59	   (A^2 -> H(U1(c, d), U1(k, k)),A^2 -> H(U1(c, d), U1(k, k)))
28.54/9.59	
28.54/9.59	
28.54/9.59	----------------------------------------
28.54/9.59	
28.54/9.59	(1232)
28.54/9.59	Obligation:
28.54/9.59	Q DP problem:
28.54/9.59	The TRS P consists of the following rules:
28.54/9.59	
28.54/9.59	   A^2 -> H(f(c), f(c))
28.54/9.59	   H(x, x) -> G(x, x, f(k))
28.54/9.59	   G(d, x, x) -> A^2
28.54/9.59	   A^2 -> H(f(d), f(d))
28.54/9.59	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.59	   A^2 -> H(f(e), f(e))
28.54/9.59	   A^2 -> H(f(k), f(k))
28.54/9.59	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.59	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.59	   A^2 -> H(U1(d, e), U1(c, b))
28.54/9.59	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.59	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.59	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.59	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.59	   A^2 -> H(U1(d, e), f(e))
28.54/9.59	   A^2 -> H(U1(d, e), f(k))
28.54/9.59	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.59	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.59	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.59	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.59	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.59	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.59	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.59	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.59	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.59	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.59	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.59	   A^2 -> H(U1(d, a), b)
28.54/9.59	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.59	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.59	   A^2 -> H(U1(d, a), c)
28.54/9.59	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.59	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.59	   A^2 -> H(U1(d, a), e)
28.54/9.59	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.59	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.59	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.59	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.59	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.59	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.59	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.59	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.59	   A^2 -> H(U1(a, c), b)
28.54/9.59	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.59	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.59	   A^2 -> H(U1(a, c), c)
28.54/9.59	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.59	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.59	   A^2 -> H(U1(a, c), e)
28.54/9.59	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, d), b)
28.54/9.59	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.59	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.59	   A^2 -> H(U1(a, d), c)
28.54/9.59	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.59	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.59	   A^2 -> H(U1(a, d), e)
28.54/9.59	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, a), d)
28.54/9.59	   A^2 -> H(U1(a, a), k)
28.54/9.59	   A^2 -> H(k, U1(b, b))
28.54/9.59	   A^2 -> H(k, f(c))
28.54/9.59	   A^2 -> H(k, f(d))
28.54/9.59	   A^2 -> H(c, U1(c, b))
28.54/9.59	   A^2 -> H(c, U1(d, b))
28.54/9.59	   A^2 -> H(c, U1(b, c))
28.54/9.59	   A^2 -> H(c, U1(b, d))
28.54/9.59	   A^2 -> H(c, U1(c, c))
28.54/9.59	   A^2 -> H(c, f(e))
28.54/9.59	   A^2 -> H(c, f(k))
28.54/9.59	   A^2 -> H(c, U1(d, d))
28.54/9.59	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.59	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.59	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.59	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.59	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.59	   A^2 -> H(U1(e, k), f(e))
28.54/9.59	   A^2 -> H(U1(e, k), f(k))
28.54/9.59	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.59	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.59	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.59	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.59	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.59	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.59	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.59	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.59	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.59	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.59	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.59	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.59	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.59	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.59	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.59	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.59	   A^2 -> H(U1(k, e), f(e))
28.54/9.59	   A^2 -> H(U1(k, e), f(k))
28.54/9.59	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.59	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.59	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.59	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.59	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.59	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.59	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.59	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.59	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.59	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.59	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.59	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.59	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.59	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.59	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.59	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.59	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.59	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.59	   A^2 -> H(U1(c, c), b)
28.54/9.59	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.59	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.59	   A^2 -> H(U1(c, c), e)
28.54/9.59	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.59	   A^2 -> H(e, U1(c, b))
28.54/9.59	   A^2 -> H(e, U1(d, b))
28.54/9.59	   A^2 -> H(e, U1(b, c))
28.54/9.59	   A^2 -> H(e, U1(b, d))
28.54/9.59	   A^2 -> H(e, U1(c, c))
28.54/9.59	   A^2 -> H(e, f(e))
28.54/9.59	   A^2 -> H(e, f(k))
28.54/9.59	   A^2 -> H(e, U1(d, d))
28.54/9.59	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.59	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.59	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.59	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.59	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.59	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.59	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.59	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.59	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.59	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.59	   A^2 -> H(f(e), b)
28.54/9.59	   A^2 -> H(f(e), U1(e, d))
28.54/9.59	   A^2 -> H(f(e), U1(d, e))
28.54/9.59	   A^2 -> H(f(e), c)
28.54/9.59	   A^2 -> H(f(e), U1(e, k))
28.54/9.59	   A^2 -> H(f(e), U1(k, e))
28.54/9.59	   A^2 -> H(f(e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.59	   A^2 -> H(f(k), b)
28.54/9.59	   A^2 -> H(f(k), U1(e, d))
28.54/9.59	   A^2 -> H(f(k), U1(d, e))
28.54/9.59	   A^2 -> H(f(k), c)
28.54/9.59	   A^2 -> H(f(k), U1(e, k))
28.54/9.59	   A^2 -> H(f(k), U1(k, e))
28.54/9.59	   A^2 -> H(f(k), e)
28.54/9.59	   A^2 -> H(f(c), d)
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.59	   A^2 -> H(U1(k, k), f(e))
28.54/9.59	   A^2 -> H(U1(k, k), f(k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.59	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.59	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.59	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.59	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.59	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.59	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.59	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.59	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.59	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.59	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.59	   A^2 -> H(U1(d, d), b)
28.54/9.59	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.59	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.59	   A^2 -> H(U1(d, d), c)
28.54/9.59	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.59	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.59	   A^2 -> H(U1(d, d), e)
28.54/9.59	   A^2 -> H(f(d), d)
28.54/9.59	   A^2 -> H(f(d), k)
28.54/9.59	   A^2 -> H(U1(c, c), c)
28.54/9.59	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.59	   A^2 -> H(f(c), k)
28.54/9.59	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.59	   A^2 -> H(f(k), U1(k, k))
28.54/9.59	   A^2 -> H(f(e), e)
28.54/9.59	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.59	   A^2 -> H(d, U1(c, b))
28.54/9.59	   A^2 -> H(d, U1(d, b))
28.54/9.59	   A^2 -> H(d, U1(b, c))
28.54/9.59	   A^2 -> H(d, U1(b, d))
28.54/9.59	   A^2 -> H(d, U1(c, c))
28.54/9.59	   A^2 -> H(d, f(e))
28.54/9.59	   A^2 -> H(d, f(k))
28.54/9.59	   A^2 -> H(d, U1(d, d))
28.54/9.59	   A^2 -> H(a, U1(e, b))
28.54/9.59	   A^2 -> H(a, U1(k, b))
28.54/9.59	   A^2 -> H(a, U1(c, d))
28.54/9.59	   A^2 -> H(a, U1(d, c))
28.54/9.59	   A^2 -> H(a, U1(b, e))
28.54/9.59	   A^2 -> H(a, U1(b, k))
28.54/9.59	   A^2 -> H(a, U1(e, c))
28.54/9.59	   A^2 -> H(a, U1(k, c))
28.54/9.59	   A^2 -> H(a, U1(c, e))
28.54/9.59	   A^2 -> H(a, U1(c, k))
28.54/9.59	   A^2 -> H(a, U1(e, e))
28.54/9.59	   A^2 -> H(a, U1(k, k))
28.54/9.59	   A^2 -> H(a, U1(k, d))
28.54/9.59	   A^2 -> H(a, U1(d, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.59	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.59	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.59	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.59	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.59	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.59	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.59	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.59	   A^2 -> H(U1(e, a), b)
28.54/9.59	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.59	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.59	   A^2 -> H(U1(e, a), c)
28.54/9.59	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.59	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.59	   A^2 -> H(U1(e, a), e)
28.54/9.59	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, a), b)
28.54/9.59	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.59	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.59	   A^2 -> H(U1(k, a), c)
28.54/9.59	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.59	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.59	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, d), b)
28.54/9.59	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.59	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.59	   A^2 -> H(U1(c, d), c)
28.54/9.59	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.59	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.59	   A^2 -> H(U1(c, d), e)
28.54/9.59	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, a), d)
28.54/9.59	   A^2 -> H(U1(c, a), k)
28.54/9.59	
28.54/9.59	The TRS R consists of the following rules:
28.54/9.59	
28.54/9.59	   f(x) -> U1(x, x)
28.54/9.59	   U1(e, x) -> x
28.54/9.59	   a -> c
28.54/9.59	   a -> d
28.54/9.59	   b -> c
28.54/9.59	   b -> d
28.54/9.59	   d -> k
28.54/9.59	   c -> e
28.54/9.59	   c -> k
28.54/9.59	
28.54/9.59	Q is empty.
28.54/9.59	We have to consider all minimal (P,Q,R)-chains.
28.54/9.59	----------------------------------------
28.54/9.59	
28.54/9.59	(1233) TransformationProof (EQUIVALENT)
28.54/9.59	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.59	
28.54/9.59	   (A^2 -> H(U1(k, e), U1(c, b)),A^2 -> H(U1(k, e), U1(c, b)))
28.54/9.59	   (A^2 -> H(U1(d, e), U1(e, b)),A^2 -> H(U1(d, e), U1(e, b)))
28.54/9.59	   (A^2 -> H(U1(d, e), U1(k, b)),A^2 -> H(U1(d, e), U1(k, b)))
28.54/9.59	   (A^2 -> H(U1(d, e), U1(c, c)),A^2 -> H(U1(d, e), U1(c, c)))
28.54/9.59	   (A^2 -> H(U1(d, e), U1(c, d)),A^2 -> H(U1(d, e), U1(c, d)))
28.54/9.59	
28.54/9.59	
28.54/9.59	----------------------------------------
28.54/9.59	
28.54/9.59	(1234)
28.54/9.59	Obligation:
28.54/9.59	Q DP problem:
28.54/9.59	The TRS P consists of the following rules:
28.54/9.59	
28.54/9.59	   A^2 -> H(f(c), f(c))
28.54/9.59	   H(x, x) -> G(x, x, f(k))
28.54/9.59	   G(d, x, x) -> A^2
28.54/9.59	   A^2 -> H(f(d), f(d))
28.54/9.59	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.59	   A^2 -> H(f(e), f(e))
28.54/9.59	   A^2 -> H(f(k), f(k))
28.54/9.59	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.59	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.59	   A^2 -> H(U1(d, e), U1(d, b))
28.54/9.59	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.59	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.59	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.59	   A^2 -> H(U1(d, e), f(e))
28.54/9.59	   A^2 -> H(U1(d, e), f(k))
28.54/9.59	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.59	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.59	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.59	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.59	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.59	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.59	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.59	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.59	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.59	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.59	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.59	   A^2 -> H(U1(d, a), b)
28.54/9.59	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.59	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.59	   A^2 -> H(U1(d, a), c)
28.54/9.59	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.59	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.59	   A^2 -> H(U1(d, a), e)
28.54/9.59	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.59	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.59	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.59	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.59	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.59	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.59	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.59	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.59	   A^2 -> H(U1(a, c), b)
28.54/9.59	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.59	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.59	   A^2 -> H(U1(a, c), c)
28.54/9.59	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.59	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.59	   A^2 -> H(U1(a, c), e)
28.54/9.59	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, d), b)
28.54/9.59	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.59	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.59	   A^2 -> H(U1(a, d), c)
28.54/9.59	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.59	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.59	   A^2 -> H(U1(a, d), e)
28.54/9.59	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, a), d)
28.54/9.59	   A^2 -> H(U1(a, a), k)
28.54/9.59	   A^2 -> H(k, U1(b, b))
28.54/9.59	   A^2 -> H(k, f(c))
28.54/9.59	   A^2 -> H(k, f(d))
28.54/9.59	   A^2 -> H(c, U1(c, b))
28.54/9.59	   A^2 -> H(c, U1(d, b))
28.54/9.59	   A^2 -> H(c, U1(b, c))
28.54/9.59	   A^2 -> H(c, U1(b, d))
28.54/9.59	   A^2 -> H(c, U1(c, c))
28.54/9.59	   A^2 -> H(c, f(e))
28.54/9.59	   A^2 -> H(c, f(k))
28.54/9.59	   A^2 -> H(c, U1(d, d))
28.54/9.59	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.59	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.59	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.59	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.59	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.59	   A^2 -> H(U1(e, k), f(e))
28.54/9.59	   A^2 -> H(U1(e, k), f(k))
28.54/9.59	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.59	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.59	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.59	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.59	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.59	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.59	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.59	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.59	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.59	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.59	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.59	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.59	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.59	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.59	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.59	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.59	   A^2 -> H(U1(k, e), f(e))
28.54/9.59	   A^2 -> H(U1(k, e), f(k))
28.54/9.59	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.59	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.59	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.59	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.59	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.59	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.59	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.59	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.59	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.59	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.59	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.59	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.59	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.59	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.59	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.59	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.59	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.59	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.59	   A^2 -> H(U1(c, c), b)
28.54/9.59	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.59	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.59	   A^2 -> H(U1(c, c), e)
28.54/9.59	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.59	   A^2 -> H(e, U1(c, b))
28.54/9.59	   A^2 -> H(e, U1(d, b))
28.54/9.59	   A^2 -> H(e, U1(b, c))
28.54/9.59	   A^2 -> H(e, U1(b, d))
28.54/9.59	   A^2 -> H(e, U1(c, c))
28.54/9.59	   A^2 -> H(e, f(e))
28.54/9.59	   A^2 -> H(e, f(k))
28.54/9.59	   A^2 -> H(e, U1(d, d))
28.54/9.59	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.59	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.59	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.59	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.59	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.59	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.59	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.59	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.59	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.59	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.59	   A^2 -> H(f(e), b)
28.54/9.59	   A^2 -> H(f(e), U1(e, d))
28.54/9.59	   A^2 -> H(f(e), U1(d, e))
28.54/9.59	   A^2 -> H(f(e), c)
28.54/9.59	   A^2 -> H(f(e), U1(e, k))
28.54/9.59	   A^2 -> H(f(e), U1(k, e))
28.54/9.59	   A^2 -> H(f(e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.59	   A^2 -> H(f(k), b)
28.54/9.59	   A^2 -> H(f(k), U1(e, d))
28.54/9.59	   A^2 -> H(f(k), U1(d, e))
28.54/9.59	   A^2 -> H(f(k), c)
28.54/9.59	   A^2 -> H(f(k), U1(e, k))
28.54/9.59	   A^2 -> H(f(k), U1(k, e))
28.54/9.59	   A^2 -> H(f(k), e)
28.54/9.59	   A^2 -> H(f(c), d)
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.59	   A^2 -> H(U1(k, k), f(e))
28.54/9.59	   A^2 -> H(U1(k, k), f(k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.59	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.59	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.59	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.59	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.59	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.59	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.59	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.59	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.59	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.59	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.59	   A^2 -> H(U1(d, d), b)
28.54/9.59	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.59	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.59	   A^2 -> H(U1(d, d), c)
28.54/9.59	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.59	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.59	   A^2 -> H(U1(d, d), e)
28.54/9.59	   A^2 -> H(f(d), d)
28.54/9.59	   A^2 -> H(f(d), k)
28.54/9.59	   A^2 -> H(U1(c, c), c)
28.54/9.59	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.59	   A^2 -> H(f(c), k)
28.54/9.59	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.59	   A^2 -> H(f(k), U1(k, k))
28.54/9.59	   A^2 -> H(f(e), e)
28.54/9.59	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.59	   A^2 -> H(d, U1(c, b))
28.54/9.59	   A^2 -> H(d, U1(d, b))
28.54/9.59	   A^2 -> H(d, U1(b, c))
28.54/9.59	   A^2 -> H(d, U1(b, d))
28.54/9.59	   A^2 -> H(d, U1(c, c))
28.54/9.59	   A^2 -> H(d, f(e))
28.54/9.59	   A^2 -> H(d, f(k))
28.54/9.59	   A^2 -> H(d, U1(d, d))
28.54/9.59	   A^2 -> H(a, U1(e, b))
28.54/9.59	   A^2 -> H(a, U1(k, b))
28.54/9.59	   A^2 -> H(a, U1(c, d))
28.54/9.59	   A^2 -> H(a, U1(d, c))
28.54/9.59	   A^2 -> H(a, U1(b, e))
28.54/9.59	   A^2 -> H(a, U1(b, k))
28.54/9.59	   A^2 -> H(a, U1(e, c))
28.54/9.59	   A^2 -> H(a, U1(k, c))
28.54/9.59	   A^2 -> H(a, U1(c, e))
28.54/9.59	   A^2 -> H(a, U1(c, k))
28.54/9.59	   A^2 -> H(a, U1(e, e))
28.54/9.59	   A^2 -> H(a, U1(k, k))
28.54/9.59	   A^2 -> H(a, U1(k, d))
28.54/9.59	   A^2 -> H(a, U1(d, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.59	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.59	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.59	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.59	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.59	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.59	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.59	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.59	   A^2 -> H(U1(e, a), b)
28.54/9.59	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.59	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.59	   A^2 -> H(U1(e, a), c)
28.54/9.59	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.59	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.59	   A^2 -> H(U1(e, a), e)
28.54/9.59	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, a), b)
28.54/9.59	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.59	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.59	   A^2 -> H(U1(k, a), c)
28.54/9.59	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.59	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.59	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, d), b)
28.54/9.59	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.59	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.59	   A^2 -> H(U1(c, d), c)
28.54/9.59	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.59	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.59	   A^2 -> H(U1(c, d), e)
28.54/9.59	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, a), d)
28.54/9.59	   A^2 -> H(U1(c, a), k)
28.54/9.59	   A^2 -> H(U1(d, e), U1(e, b))
28.54/9.59	   A^2 -> H(U1(d, e), U1(k, b))
28.54/9.59	   A^2 -> H(U1(d, e), U1(c, d))
28.54/9.59	
28.54/9.59	The TRS R consists of the following rules:
28.54/9.59	
28.54/9.59	   f(x) -> U1(x, x)
28.54/9.59	   U1(e, x) -> x
28.54/9.59	   a -> c
28.54/9.59	   a -> d
28.54/9.59	   b -> c
28.54/9.59	   b -> d
28.54/9.59	   d -> k
28.54/9.59	   c -> e
28.54/9.59	   c -> k
28.54/9.59	
28.54/9.59	Q is empty.
28.54/9.59	We have to consider all minimal (P,Q,R)-chains.
28.54/9.59	----------------------------------------
28.54/9.59	
28.54/9.59	(1235) TransformationProof (EQUIVALENT)
28.54/9.59	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.59	
28.54/9.59	   (A^2 -> H(U1(k, e), U1(d, b)),A^2 -> H(U1(k, e), U1(d, b)))
28.54/9.59	   (A^2 -> H(U1(d, e), U1(k, b)),A^2 -> H(U1(d, e), U1(k, b)))
28.54/9.59	   (A^2 -> H(U1(d, e), U1(d, c)),A^2 -> H(U1(d, e), U1(d, c)))
28.54/9.59	   (A^2 -> H(U1(d, e), U1(d, d)),A^2 -> H(U1(d, e), U1(d, d)))
28.54/9.59	
28.54/9.59	
28.54/9.59	----------------------------------------
28.54/9.59	
28.54/9.59	(1236)
28.54/9.59	Obligation:
28.54/9.59	Q DP problem:
28.54/9.59	The TRS P consists of the following rules:
28.54/9.59	
28.54/9.59	   A^2 -> H(f(c), f(c))
28.54/9.59	   H(x, x) -> G(x, x, f(k))
28.54/9.59	   G(d, x, x) -> A^2
28.54/9.59	   A^2 -> H(f(d), f(d))
28.54/9.59	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.59	   A^2 -> H(f(e), f(e))
28.54/9.59	   A^2 -> H(f(k), f(k))
28.54/9.59	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.59	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.59	   A^2 -> H(U1(d, e), U1(b, c))
28.54/9.59	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.59	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.59	   A^2 -> H(U1(d, e), f(e))
28.54/9.59	   A^2 -> H(U1(d, e), f(k))
28.54/9.59	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.59	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.59	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.59	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.59	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.59	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.59	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.59	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.59	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.59	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.59	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.59	   A^2 -> H(U1(d, a), b)
28.54/9.59	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.59	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.59	   A^2 -> H(U1(d, a), c)
28.54/9.59	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.59	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.59	   A^2 -> H(U1(d, a), e)
28.54/9.59	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.59	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.59	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.59	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.59	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.59	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.59	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.59	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.59	   A^2 -> H(U1(a, c), b)
28.54/9.59	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.59	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.59	   A^2 -> H(U1(a, c), c)
28.54/9.59	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.59	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.59	   A^2 -> H(U1(a, c), e)
28.54/9.59	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, d), b)
28.54/9.59	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.59	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.59	   A^2 -> H(U1(a, d), c)
28.54/9.59	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.59	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.59	   A^2 -> H(U1(a, d), e)
28.54/9.59	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, a), d)
28.54/9.59	   A^2 -> H(U1(a, a), k)
28.54/9.59	   A^2 -> H(k, U1(b, b))
28.54/9.59	   A^2 -> H(k, f(c))
28.54/9.59	   A^2 -> H(k, f(d))
28.54/9.59	   A^2 -> H(c, U1(c, b))
28.54/9.59	   A^2 -> H(c, U1(d, b))
28.54/9.59	   A^2 -> H(c, U1(b, c))
28.54/9.59	   A^2 -> H(c, U1(b, d))
28.54/9.59	   A^2 -> H(c, U1(c, c))
28.54/9.59	   A^2 -> H(c, f(e))
28.54/9.59	   A^2 -> H(c, f(k))
28.54/9.59	   A^2 -> H(c, U1(d, d))
28.54/9.59	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.59	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.59	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.59	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.59	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.59	   A^2 -> H(U1(e, k), f(e))
28.54/9.59	   A^2 -> H(U1(e, k), f(k))
28.54/9.59	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.59	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.59	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.59	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.59	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.59	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.59	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.59	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.59	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.59	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.59	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.59	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.59	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.59	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.59	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.59	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.59	   A^2 -> H(U1(k, e), f(e))
28.54/9.59	   A^2 -> H(U1(k, e), f(k))
28.54/9.59	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.59	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.59	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.59	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.59	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.59	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.59	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.59	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.59	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.59	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.59	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.59	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.59	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.59	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.59	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.59	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.59	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.59	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.59	   A^2 -> H(U1(c, c), b)
28.54/9.59	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.59	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.59	   A^2 -> H(U1(c, c), e)
28.54/9.59	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.59	   A^2 -> H(e, U1(c, b))
28.54/9.59	   A^2 -> H(e, U1(d, b))
28.54/9.59	   A^2 -> H(e, U1(b, c))
28.54/9.59	   A^2 -> H(e, U1(b, d))
28.54/9.59	   A^2 -> H(e, U1(c, c))
28.54/9.59	   A^2 -> H(e, f(e))
28.54/9.59	   A^2 -> H(e, f(k))
28.54/9.59	   A^2 -> H(e, U1(d, d))
28.54/9.59	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.59	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.59	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.59	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.59	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.59	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.59	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.59	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.59	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.59	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.59	   A^2 -> H(f(e), b)
28.54/9.59	   A^2 -> H(f(e), U1(e, d))
28.54/9.59	   A^2 -> H(f(e), U1(d, e))
28.54/9.59	   A^2 -> H(f(e), c)
28.54/9.59	   A^2 -> H(f(e), U1(e, k))
28.54/9.59	   A^2 -> H(f(e), U1(k, e))
28.54/9.59	   A^2 -> H(f(e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.59	   A^2 -> H(f(k), b)
28.54/9.59	   A^2 -> H(f(k), U1(e, d))
28.54/9.59	   A^2 -> H(f(k), U1(d, e))
28.54/9.59	   A^2 -> H(f(k), c)
28.54/9.59	   A^2 -> H(f(k), U1(e, k))
28.54/9.59	   A^2 -> H(f(k), U1(k, e))
28.54/9.59	   A^2 -> H(f(k), e)
28.54/9.59	   A^2 -> H(f(c), d)
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.59	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.59	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.59	   A^2 -> H(U1(k, k), f(e))
28.54/9.59	   A^2 -> H(U1(k, k), f(k))
28.54/9.59	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.59	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.59	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.59	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.59	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.59	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.59	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.59	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.59	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.59	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.59	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.59	   A^2 -> H(U1(d, d), b)
28.54/9.59	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.59	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.59	   A^2 -> H(U1(d, d), c)
28.54/9.59	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.59	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.59	   A^2 -> H(U1(d, d), e)
28.54/9.59	   A^2 -> H(f(d), d)
28.54/9.59	   A^2 -> H(f(d), k)
28.54/9.59	   A^2 -> H(U1(c, c), c)
28.54/9.59	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.59	   A^2 -> H(f(c), k)
28.54/9.59	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.59	   A^2 -> H(f(k), U1(k, k))
28.54/9.59	   A^2 -> H(f(e), e)
28.54/9.59	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.59	   A^2 -> H(d, U1(c, b))
28.54/9.59	   A^2 -> H(d, U1(d, b))
28.54/9.59	   A^2 -> H(d, U1(b, c))
28.54/9.59	   A^2 -> H(d, U1(b, d))
28.54/9.59	   A^2 -> H(d, U1(c, c))
28.54/9.59	   A^2 -> H(d, f(e))
28.54/9.59	   A^2 -> H(d, f(k))
28.54/9.59	   A^2 -> H(d, U1(d, d))
28.54/9.59	   A^2 -> H(a, U1(e, b))
28.54/9.59	   A^2 -> H(a, U1(k, b))
28.54/9.59	   A^2 -> H(a, U1(c, d))
28.54/9.59	   A^2 -> H(a, U1(d, c))
28.54/9.59	   A^2 -> H(a, U1(b, e))
28.54/9.59	   A^2 -> H(a, U1(b, k))
28.54/9.59	   A^2 -> H(a, U1(e, c))
28.54/9.59	   A^2 -> H(a, U1(k, c))
28.54/9.59	   A^2 -> H(a, U1(c, e))
28.54/9.59	   A^2 -> H(a, U1(c, k))
28.54/9.59	   A^2 -> H(a, U1(e, e))
28.54/9.59	   A^2 -> H(a, U1(k, k))
28.54/9.59	   A^2 -> H(a, U1(k, d))
28.54/9.59	   A^2 -> H(a, U1(d, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.59	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.59	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.59	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.59	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.59	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.59	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.59	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.59	   A^2 -> H(U1(e, a), b)
28.54/9.59	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.59	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.59	   A^2 -> H(U1(e, a), c)
28.54/9.59	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.59	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.59	   A^2 -> H(U1(e, a), e)
28.54/9.59	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(k, a), b)
28.54/9.59	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.59	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.59	   A^2 -> H(U1(k, a), c)
28.54/9.59	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.59	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.59	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, d), b)
28.54/9.59	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.59	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.59	   A^2 -> H(U1(c, d), c)
28.54/9.59	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.59	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.59	   A^2 -> H(U1(c, d), e)
28.54/9.59	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(c, a), d)
28.54/9.59	   A^2 -> H(U1(c, a), k)
28.54/9.59	   A^2 -> H(U1(d, e), U1(e, b))
28.54/9.59	   A^2 -> H(U1(d, e), U1(k, b))
28.54/9.59	   A^2 -> H(U1(d, e), U1(c, d))
28.54/9.59	   A^2 -> H(U1(d, e), U1(d, c))
28.54/9.59	
28.54/9.59	The TRS R consists of the following rules:
28.54/9.59	
28.54/9.59	   f(x) -> U1(x, x)
28.54/9.59	   U1(e, x) -> x
28.54/9.59	   a -> c
28.54/9.59	   a -> d
28.54/9.59	   b -> c
28.54/9.59	   b -> d
28.54/9.59	   d -> k
28.54/9.59	   c -> e
28.54/9.59	   c -> k
28.54/9.59	
28.54/9.59	Q is empty.
28.54/9.59	We have to consider all minimal (P,Q,R)-chains.
28.54/9.59	----------------------------------------
28.54/9.59	
28.54/9.59	(1237) TransformationProof (EQUIVALENT)
28.54/9.59	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.59	
28.54/9.59	   (A^2 -> H(U1(k, e), U1(b, c)),A^2 -> H(U1(k, e), U1(b, c)))
28.54/9.59	   (A^2 -> H(U1(d, e), U1(c, c)),A^2 -> H(U1(d, e), U1(c, c)))
28.54/9.59	   (A^2 -> H(U1(d, e), U1(d, c)),A^2 -> H(U1(d, e), U1(d, c)))
28.54/9.59	   (A^2 -> H(U1(d, e), U1(b, e)),A^2 -> H(U1(d, e), U1(b, e)))
28.54/9.59	   (A^2 -> H(U1(d, e), U1(b, k)),A^2 -> H(U1(d, e), U1(b, k)))
28.54/9.59	
28.54/9.59	
28.54/9.59	----------------------------------------
28.54/9.59	
28.54/9.59	(1238)
28.54/9.59	Obligation:
28.54/9.59	Q DP problem:
28.54/9.59	The TRS P consists of the following rules:
28.54/9.59	
28.54/9.59	   A^2 -> H(f(c), f(c))
28.54/9.59	   H(x, x) -> G(x, x, f(k))
28.54/9.59	   G(d, x, x) -> A^2
28.54/9.59	   A^2 -> H(f(d), f(d))
28.54/9.59	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.59	   A^2 -> H(f(e), f(e))
28.54/9.59	   A^2 -> H(f(k), f(k))
28.54/9.59	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.59	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.59	   A^2 -> H(U1(d, e), U1(b, d))
28.54/9.59	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.59	   A^2 -> H(U1(d, e), f(e))
28.54/9.59	   A^2 -> H(U1(d, e), f(k))
28.54/9.59	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.59	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.59	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.59	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.59	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.59	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.59	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.59	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.59	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.59	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.59	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.59	   A^2 -> H(U1(d, a), b)
28.54/9.59	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.59	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.59	   A^2 -> H(U1(d, a), c)
28.54/9.59	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.59	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.59	   A^2 -> H(U1(d, a), e)
28.54/9.59	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.59	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.59	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.59	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.59	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.59	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.59	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.59	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.59	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.59	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.59	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.59	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.59	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.59	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.59	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.59	   A^2 -> H(U1(a, c), b)
28.54/9.59	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.59	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.59	   A^2 -> H(U1(a, c), c)
28.54/9.59	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.59	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.59	   A^2 -> H(U1(a, c), e)
28.54/9.59	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, d), b)
28.54/9.59	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.59	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.59	   A^2 -> H(U1(a, d), c)
28.54/9.59	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.59	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.59	   A^2 -> H(U1(a, d), e)
28.54/9.59	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.59	   A^2 -> H(U1(a, a), d)
28.54/9.59	   A^2 -> H(U1(a, a), k)
28.54/9.59	   A^2 -> H(k, U1(b, b))
28.54/9.59	   A^2 -> H(k, f(c))
28.54/9.59	   A^2 -> H(k, f(d))
28.54/9.59	   A^2 -> H(c, U1(c, b))
28.54/9.59	   A^2 -> H(c, U1(d, b))
28.54/9.59	   A^2 -> H(c, U1(b, c))
28.54/9.59	   A^2 -> H(c, U1(b, d))
28.54/9.59	   A^2 -> H(c, U1(c, c))
28.54/9.59	   A^2 -> H(c, f(e))
28.54/9.59	   A^2 -> H(c, f(k))
28.54/9.59	   A^2 -> H(c, U1(d, d))
28.54/9.59	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.59	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.59	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.59	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.59	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.59	   A^2 -> H(U1(e, k), f(e))
28.54/9.59	   A^2 -> H(U1(e, k), f(k))
28.54/9.59	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.59	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.59	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.59	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.59	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.59	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.59	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.59	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.59	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.59	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.59	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.59	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.59	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.59	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.59	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.59	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.59	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.59	   A^2 -> H(U1(k, e), f(e))
28.54/9.59	   A^2 -> H(U1(k, e), f(k))
28.54/9.59	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.59	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.59	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.59	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.59	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.59	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.59	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.59	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.60	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.60	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.60	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.60	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.60	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.60	   A^2 -> H(U1(c, c), b)
28.54/9.60	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.60	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.60	   A^2 -> H(U1(c, c), e)
28.54/9.60	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.60	   A^2 -> H(e, U1(c, b))
28.54/9.60	   A^2 -> H(e, U1(d, b))
28.54/9.60	   A^2 -> H(e, U1(b, c))
28.54/9.60	   A^2 -> H(e, U1(b, d))
28.54/9.60	   A^2 -> H(e, U1(c, c))
28.54/9.60	   A^2 -> H(e, f(e))
28.54/9.60	   A^2 -> H(e, f(k))
28.54/9.60	   A^2 -> H(e, U1(d, d))
28.54/9.60	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.60	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.60	   A^2 -> H(f(e), b)
28.54/9.60	   A^2 -> H(f(e), U1(e, d))
28.54/9.60	   A^2 -> H(f(e), U1(d, e))
28.54/9.60	   A^2 -> H(f(e), c)
28.54/9.60	   A^2 -> H(f(e), U1(e, k))
28.54/9.60	   A^2 -> H(f(e), U1(k, e))
28.54/9.60	   A^2 -> H(f(e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.60	   A^2 -> H(f(k), b)
28.54/9.60	   A^2 -> H(f(k), U1(e, d))
28.54/9.60	   A^2 -> H(f(k), U1(d, e))
28.54/9.60	   A^2 -> H(f(k), c)
28.54/9.60	   A^2 -> H(f(k), U1(e, k))
28.54/9.60	   A^2 -> H(f(k), U1(k, e))
28.54/9.60	   A^2 -> H(f(k), e)
28.54/9.60	   A^2 -> H(f(c), d)
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.60	   A^2 -> H(U1(k, k), f(e))
28.54/9.60	   A^2 -> H(U1(k, k), f(k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.60	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.60	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.60	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.60	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.60	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.60	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.60	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.60	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.60	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.60	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.60	   A^2 -> H(U1(d, d), b)
28.54/9.60	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.60	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.60	   A^2 -> H(U1(d, d), c)
28.54/9.60	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.60	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.60	   A^2 -> H(U1(d, d), e)
28.54/9.60	   A^2 -> H(f(d), d)
28.54/9.60	   A^2 -> H(f(d), k)
28.54/9.60	   A^2 -> H(U1(c, c), c)
28.54/9.60	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.60	   A^2 -> H(f(c), k)
28.54/9.60	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.60	   A^2 -> H(f(k), U1(k, k))
28.54/9.60	   A^2 -> H(f(e), e)
28.54/9.60	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.60	   A^2 -> H(d, U1(c, b))
28.54/9.60	   A^2 -> H(d, U1(d, b))
28.54/9.60	   A^2 -> H(d, U1(b, c))
28.54/9.60	   A^2 -> H(d, U1(b, d))
28.54/9.60	   A^2 -> H(d, U1(c, c))
28.54/9.60	   A^2 -> H(d, f(e))
28.54/9.60	   A^2 -> H(d, f(k))
28.54/9.60	   A^2 -> H(d, U1(d, d))
28.54/9.60	   A^2 -> H(a, U1(e, b))
28.54/9.60	   A^2 -> H(a, U1(k, b))
28.54/9.60	   A^2 -> H(a, U1(c, d))
28.54/9.60	   A^2 -> H(a, U1(d, c))
28.54/9.60	   A^2 -> H(a, U1(b, e))
28.54/9.60	   A^2 -> H(a, U1(b, k))
28.54/9.60	   A^2 -> H(a, U1(e, c))
28.54/9.60	   A^2 -> H(a, U1(k, c))
28.54/9.60	   A^2 -> H(a, U1(c, e))
28.54/9.60	   A^2 -> H(a, U1(c, k))
28.54/9.60	   A^2 -> H(a, U1(e, e))
28.54/9.60	   A^2 -> H(a, U1(k, k))
28.54/9.60	   A^2 -> H(a, U1(k, d))
28.54/9.60	   A^2 -> H(a, U1(d, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.60	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.60	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.60	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.60	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.60	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.60	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.60	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.60	   A^2 -> H(U1(e, a), b)
28.54/9.60	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.60	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.60	   A^2 -> H(U1(e, a), c)
28.54/9.60	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.60	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.60	   A^2 -> H(U1(e, a), e)
28.54/9.60	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, a), b)
28.54/9.60	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.60	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.60	   A^2 -> H(U1(k, a), c)
28.54/9.60	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.60	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.60	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, d), b)
28.54/9.60	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.60	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.60	   A^2 -> H(U1(c, d), c)
28.54/9.60	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.60	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.60	   A^2 -> H(U1(c, d), e)
28.54/9.60	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, a), d)
28.54/9.60	   A^2 -> H(U1(c, a), k)
28.54/9.60	   A^2 -> H(U1(d, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(d, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(d, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(d, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(d, e), U1(b, k))
28.54/9.60	
28.54/9.60	The TRS R consists of the following rules:
28.54/9.60	
28.54/9.60	   f(x) -> U1(x, x)
28.54/9.60	   U1(e, x) -> x
28.54/9.60	   a -> c
28.54/9.60	   a -> d
28.54/9.60	   b -> c
28.54/9.60	   b -> d
28.54/9.60	   d -> k
28.54/9.60	   c -> e
28.54/9.60	   c -> k
28.54/9.60	
28.54/9.60	Q is empty.
28.54/9.60	We have to consider all minimal (P,Q,R)-chains.
28.54/9.60	----------------------------------------
28.54/9.60	
28.54/9.60	(1239) TransformationProof (EQUIVALENT)
28.54/9.60	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.60	
28.54/9.60	   (A^2 -> H(U1(k, e), U1(b, d)),A^2 -> H(U1(k, e), U1(b, d)))
28.54/9.60	   (A^2 -> H(U1(d, e), U1(c, d)),A^2 -> H(U1(d, e), U1(c, d)))
28.54/9.60	   (A^2 -> H(U1(d, e), U1(d, d)),A^2 -> H(U1(d, e), U1(d, d)))
28.54/9.60	   (A^2 -> H(U1(d, e), U1(b, k)),A^2 -> H(U1(d, e), U1(b, k)))
28.54/9.60	
28.54/9.60	
28.54/9.60	----------------------------------------
28.54/9.60	
28.54/9.60	(1240)
28.54/9.60	Obligation:
28.54/9.60	Q DP problem:
28.54/9.60	The TRS P consists of the following rules:
28.54/9.60	
28.54/9.60	   A^2 -> H(f(c), f(c))
28.54/9.60	   H(x, x) -> G(x, x, f(k))
28.54/9.60	   G(d, x, x) -> A^2
28.54/9.60	   A^2 -> H(f(d), f(d))
28.54/9.60	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.60	   A^2 -> H(f(e), f(e))
28.54/9.60	   A^2 -> H(f(k), f(k))
28.54/9.60	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.60	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, e), U1(c, c))
28.54/9.60	   A^2 -> H(U1(d, e), f(e))
28.54/9.60	   A^2 -> H(U1(d, e), f(k))
28.54/9.60	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.60	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.60	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.60	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.60	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.60	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.60	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.60	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.60	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.60	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.60	   A^2 -> H(U1(d, a), b)
28.54/9.60	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.60	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.60	   A^2 -> H(U1(d, a), c)
28.54/9.60	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.60	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.60	   A^2 -> H(U1(d, a), e)
28.54/9.60	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.60	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.60	   A^2 -> H(U1(a, c), b)
28.54/9.60	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.60	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.60	   A^2 -> H(U1(a, c), c)
28.54/9.60	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.60	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.60	   A^2 -> H(U1(a, c), e)
28.54/9.60	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, d), b)
28.54/9.60	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.60	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.60	   A^2 -> H(U1(a, d), c)
28.54/9.60	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.60	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.60	   A^2 -> H(U1(a, d), e)
28.54/9.60	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, a), d)
28.54/9.60	   A^2 -> H(U1(a, a), k)
28.54/9.60	   A^2 -> H(k, U1(b, b))
28.54/9.60	   A^2 -> H(k, f(c))
28.54/9.60	   A^2 -> H(k, f(d))
28.54/9.60	   A^2 -> H(c, U1(c, b))
28.54/9.60	   A^2 -> H(c, U1(d, b))
28.54/9.60	   A^2 -> H(c, U1(b, c))
28.54/9.60	   A^2 -> H(c, U1(b, d))
28.54/9.60	   A^2 -> H(c, U1(c, c))
28.54/9.60	   A^2 -> H(c, f(e))
28.54/9.60	   A^2 -> H(c, f(k))
28.54/9.60	   A^2 -> H(c, U1(d, d))
28.54/9.60	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.60	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.60	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.60	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.60	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.60	   A^2 -> H(U1(e, k), f(e))
28.54/9.60	   A^2 -> H(U1(e, k), f(k))
28.54/9.60	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.60	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.60	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.60	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.60	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.60	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.60	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.60	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.60	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.60	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.60	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.60	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.60	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.60	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.60	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.60	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.60	   A^2 -> H(U1(k, e), f(e))
28.54/9.60	   A^2 -> H(U1(k, e), f(k))
28.54/9.60	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.60	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.60	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.60	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.60	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.60	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.60	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.60	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.60	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.60	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.60	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.60	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.60	   A^2 -> H(U1(c, c), b)
28.54/9.60	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.60	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.60	   A^2 -> H(U1(c, c), e)
28.54/9.60	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.60	   A^2 -> H(e, U1(c, b))
28.54/9.60	   A^2 -> H(e, U1(d, b))
28.54/9.60	   A^2 -> H(e, U1(b, c))
28.54/9.60	   A^2 -> H(e, U1(b, d))
28.54/9.60	   A^2 -> H(e, U1(c, c))
28.54/9.60	   A^2 -> H(e, f(e))
28.54/9.60	   A^2 -> H(e, f(k))
28.54/9.60	   A^2 -> H(e, U1(d, d))
28.54/9.60	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.60	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.60	   A^2 -> H(f(e), b)
28.54/9.60	   A^2 -> H(f(e), U1(e, d))
28.54/9.60	   A^2 -> H(f(e), U1(d, e))
28.54/9.60	   A^2 -> H(f(e), c)
28.54/9.60	   A^2 -> H(f(e), U1(e, k))
28.54/9.60	   A^2 -> H(f(e), U1(k, e))
28.54/9.60	   A^2 -> H(f(e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.60	   A^2 -> H(f(k), b)
28.54/9.60	   A^2 -> H(f(k), U1(e, d))
28.54/9.60	   A^2 -> H(f(k), U1(d, e))
28.54/9.60	   A^2 -> H(f(k), c)
28.54/9.60	   A^2 -> H(f(k), U1(e, k))
28.54/9.60	   A^2 -> H(f(k), U1(k, e))
28.54/9.60	   A^2 -> H(f(k), e)
28.54/9.60	   A^2 -> H(f(c), d)
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.60	   A^2 -> H(U1(k, k), f(e))
28.54/9.60	   A^2 -> H(U1(k, k), f(k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.60	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.60	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.60	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.60	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.60	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.60	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.60	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.60	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.60	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.60	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.60	   A^2 -> H(U1(d, d), b)
28.54/9.60	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.60	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.60	   A^2 -> H(U1(d, d), c)
28.54/9.60	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.60	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.60	   A^2 -> H(U1(d, d), e)
28.54/9.60	   A^2 -> H(f(d), d)
28.54/9.60	   A^2 -> H(f(d), k)
28.54/9.60	   A^2 -> H(U1(c, c), c)
28.54/9.60	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.60	   A^2 -> H(f(c), k)
28.54/9.60	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.60	   A^2 -> H(f(k), U1(k, k))
28.54/9.60	   A^2 -> H(f(e), e)
28.54/9.60	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.60	   A^2 -> H(d, U1(c, b))
28.54/9.60	   A^2 -> H(d, U1(d, b))
28.54/9.60	   A^2 -> H(d, U1(b, c))
28.54/9.60	   A^2 -> H(d, U1(b, d))
28.54/9.60	   A^2 -> H(d, U1(c, c))
28.54/9.60	   A^2 -> H(d, f(e))
28.54/9.60	   A^2 -> H(d, f(k))
28.54/9.60	   A^2 -> H(d, U1(d, d))
28.54/9.60	   A^2 -> H(a, U1(e, b))
28.54/9.60	   A^2 -> H(a, U1(k, b))
28.54/9.60	   A^2 -> H(a, U1(c, d))
28.54/9.60	   A^2 -> H(a, U1(d, c))
28.54/9.60	   A^2 -> H(a, U1(b, e))
28.54/9.60	   A^2 -> H(a, U1(b, k))
28.54/9.60	   A^2 -> H(a, U1(e, c))
28.54/9.60	   A^2 -> H(a, U1(k, c))
28.54/9.60	   A^2 -> H(a, U1(c, e))
28.54/9.60	   A^2 -> H(a, U1(c, k))
28.54/9.60	   A^2 -> H(a, U1(e, e))
28.54/9.60	   A^2 -> H(a, U1(k, k))
28.54/9.60	   A^2 -> H(a, U1(k, d))
28.54/9.60	   A^2 -> H(a, U1(d, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.60	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.60	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.60	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.60	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.60	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.60	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.60	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.60	   A^2 -> H(U1(e, a), b)
28.54/9.60	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.60	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.60	   A^2 -> H(U1(e, a), c)
28.54/9.60	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.60	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.60	   A^2 -> H(U1(e, a), e)
28.54/9.60	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, a), b)
28.54/9.60	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.60	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.60	   A^2 -> H(U1(k, a), c)
28.54/9.60	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.60	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.60	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, d), b)
28.54/9.60	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.60	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.60	   A^2 -> H(U1(c, d), c)
28.54/9.60	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.60	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.60	   A^2 -> H(U1(c, d), e)
28.54/9.60	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, a), d)
28.54/9.60	   A^2 -> H(U1(c, a), k)
28.54/9.60	   A^2 -> H(U1(d, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(d, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(d, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(d, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(d, e), U1(b, k))
28.54/9.60	
28.54/9.60	The TRS R consists of the following rules:
28.54/9.60	
28.54/9.60	   f(x) -> U1(x, x)
28.54/9.60	   U1(e, x) -> x
28.54/9.60	   a -> c
28.54/9.60	   a -> d
28.54/9.60	   b -> c
28.54/9.60	   b -> d
28.54/9.60	   d -> k
28.54/9.60	   c -> e
28.54/9.60	   c -> k
28.54/9.60	
28.54/9.60	Q is empty.
28.54/9.60	We have to consider all minimal (P,Q,R)-chains.
28.54/9.60	----------------------------------------
28.54/9.60	
28.54/9.60	(1241) TransformationProof (EQUIVALENT)
28.54/9.60	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.60	
28.54/9.60	   (A^2 -> H(U1(k, e), U1(c, c)),A^2 -> H(U1(k, e), U1(c, c)))
28.54/9.60	   (A^2 -> H(U1(d, e), U1(e, c)),A^2 -> H(U1(d, e), U1(e, c)))
28.54/9.60	   (A^2 -> H(U1(d, e), U1(k, c)),A^2 -> H(U1(d, e), U1(k, c)))
28.54/9.60	   (A^2 -> H(U1(d, e), U1(c, e)),A^2 -> H(U1(d, e), U1(c, e)))
28.54/9.60	   (A^2 -> H(U1(d, e), U1(c, k)),A^2 -> H(U1(d, e), U1(c, k)))
28.54/9.60	
28.54/9.60	
28.54/9.60	----------------------------------------
28.54/9.60	
28.54/9.60	(1242)
28.54/9.60	Obligation:
28.54/9.60	Q DP problem:
28.54/9.60	The TRS P consists of the following rules:
28.54/9.60	
28.54/9.60	   A^2 -> H(f(c), f(c))
28.54/9.60	   H(x, x) -> G(x, x, f(k))
28.54/9.60	   G(d, x, x) -> A^2
28.54/9.60	   A^2 -> H(f(d), f(d))
28.54/9.60	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.60	   A^2 -> H(f(e), f(e))
28.54/9.60	   A^2 -> H(f(k), f(k))
28.54/9.60	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.60	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, e), f(e))
28.54/9.60	   A^2 -> H(U1(d, e), f(k))
28.54/9.60	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.60	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.60	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.60	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.60	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.60	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.60	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.60	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.60	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.60	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.60	   A^2 -> H(U1(d, a), b)
28.54/9.60	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.60	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.60	   A^2 -> H(U1(d, a), c)
28.54/9.60	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.60	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.60	   A^2 -> H(U1(d, a), e)
28.54/9.60	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.60	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.60	   A^2 -> H(U1(a, c), b)
28.54/9.60	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.60	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.60	   A^2 -> H(U1(a, c), c)
28.54/9.60	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.60	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.60	   A^2 -> H(U1(a, c), e)
28.54/9.60	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, d), b)
28.54/9.60	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.60	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.60	   A^2 -> H(U1(a, d), c)
28.54/9.60	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.60	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.60	   A^2 -> H(U1(a, d), e)
28.54/9.60	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, a), d)
28.54/9.60	   A^2 -> H(U1(a, a), k)
28.54/9.60	   A^2 -> H(k, U1(b, b))
28.54/9.60	   A^2 -> H(k, f(c))
28.54/9.60	   A^2 -> H(k, f(d))
28.54/9.60	   A^2 -> H(c, U1(c, b))
28.54/9.60	   A^2 -> H(c, U1(d, b))
28.54/9.60	   A^2 -> H(c, U1(b, c))
28.54/9.60	   A^2 -> H(c, U1(b, d))
28.54/9.60	   A^2 -> H(c, U1(c, c))
28.54/9.60	   A^2 -> H(c, f(e))
28.54/9.60	   A^2 -> H(c, f(k))
28.54/9.60	   A^2 -> H(c, U1(d, d))
28.54/9.60	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.60	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.60	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.60	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.60	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.60	   A^2 -> H(U1(e, k), f(e))
28.54/9.60	   A^2 -> H(U1(e, k), f(k))
28.54/9.60	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.60	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.60	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.60	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.60	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.60	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.60	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.60	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.60	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.60	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.60	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.60	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.60	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.60	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.60	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.60	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.60	   A^2 -> H(U1(k, e), f(e))
28.54/9.60	   A^2 -> H(U1(k, e), f(k))
28.54/9.60	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.60	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.60	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.60	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.60	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.60	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.60	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.60	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.60	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.60	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.60	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.60	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.60	   A^2 -> H(U1(c, c), b)
28.54/9.60	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.60	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.60	   A^2 -> H(U1(c, c), e)
28.54/9.60	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.60	   A^2 -> H(e, U1(c, b))
28.54/9.60	   A^2 -> H(e, U1(d, b))
28.54/9.60	   A^2 -> H(e, U1(b, c))
28.54/9.60	   A^2 -> H(e, U1(b, d))
28.54/9.60	   A^2 -> H(e, U1(c, c))
28.54/9.60	   A^2 -> H(e, f(e))
28.54/9.60	   A^2 -> H(e, f(k))
28.54/9.60	   A^2 -> H(e, U1(d, d))
28.54/9.60	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.60	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.60	   A^2 -> H(f(e), b)
28.54/9.60	   A^2 -> H(f(e), U1(e, d))
28.54/9.60	   A^2 -> H(f(e), U1(d, e))
28.54/9.60	   A^2 -> H(f(e), c)
28.54/9.60	   A^2 -> H(f(e), U1(e, k))
28.54/9.60	   A^2 -> H(f(e), U1(k, e))
28.54/9.60	   A^2 -> H(f(e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.60	   A^2 -> H(f(k), b)
28.54/9.60	   A^2 -> H(f(k), U1(e, d))
28.54/9.60	   A^2 -> H(f(k), U1(d, e))
28.54/9.60	   A^2 -> H(f(k), c)
28.54/9.60	   A^2 -> H(f(k), U1(e, k))
28.54/9.60	   A^2 -> H(f(k), U1(k, e))
28.54/9.60	   A^2 -> H(f(k), e)
28.54/9.60	   A^2 -> H(f(c), d)
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.60	   A^2 -> H(U1(k, k), f(e))
28.54/9.60	   A^2 -> H(U1(k, k), f(k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.60	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.60	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.60	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.60	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.60	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.60	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.60	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.60	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.60	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.60	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.60	   A^2 -> H(U1(d, d), b)
28.54/9.60	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.60	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.60	   A^2 -> H(U1(d, d), c)
28.54/9.60	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.60	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.60	   A^2 -> H(U1(d, d), e)
28.54/9.60	   A^2 -> H(f(d), d)
28.54/9.60	   A^2 -> H(f(d), k)
28.54/9.60	   A^2 -> H(U1(c, c), c)
28.54/9.60	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.60	   A^2 -> H(f(c), k)
28.54/9.60	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.60	   A^2 -> H(f(k), U1(k, k))
28.54/9.60	   A^2 -> H(f(e), e)
28.54/9.60	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.60	   A^2 -> H(d, U1(c, b))
28.54/9.60	   A^2 -> H(d, U1(d, b))
28.54/9.60	   A^2 -> H(d, U1(b, c))
28.54/9.60	   A^2 -> H(d, U1(b, d))
28.54/9.60	   A^2 -> H(d, U1(c, c))
28.54/9.60	   A^2 -> H(d, f(e))
28.54/9.60	   A^2 -> H(d, f(k))
28.54/9.60	   A^2 -> H(d, U1(d, d))
28.54/9.60	   A^2 -> H(a, U1(e, b))
28.54/9.60	   A^2 -> H(a, U1(k, b))
28.54/9.60	   A^2 -> H(a, U1(c, d))
28.54/9.60	   A^2 -> H(a, U1(d, c))
28.54/9.60	   A^2 -> H(a, U1(b, e))
28.54/9.60	   A^2 -> H(a, U1(b, k))
28.54/9.60	   A^2 -> H(a, U1(e, c))
28.54/9.60	   A^2 -> H(a, U1(k, c))
28.54/9.60	   A^2 -> H(a, U1(c, e))
28.54/9.60	   A^2 -> H(a, U1(c, k))
28.54/9.60	   A^2 -> H(a, U1(e, e))
28.54/9.60	   A^2 -> H(a, U1(k, k))
28.54/9.60	   A^2 -> H(a, U1(k, d))
28.54/9.60	   A^2 -> H(a, U1(d, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.60	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.60	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.60	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.60	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.60	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.60	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.60	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.60	   A^2 -> H(U1(e, a), b)
28.54/9.60	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.60	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.60	   A^2 -> H(U1(e, a), c)
28.54/9.60	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.60	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.60	   A^2 -> H(U1(e, a), e)
28.54/9.60	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, a), b)
28.54/9.60	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.60	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.60	   A^2 -> H(U1(k, a), c)
28.54/9.60	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.60	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.60	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, d), b)
28.54/9.60	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.60	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.60	   A^2 -> H(U1(c, d), c)
28.54/9.60	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.60	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.60	   A^2 -> H(U1(c, d), e)
28.54/9.60	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, a), d)
28.54/9.60	   A^2 -> H(U1(c, a), k)
28.54/9.60	   A^2 -> H(U1(d, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(d, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(d, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(d, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(d, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(d, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(d, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(d, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(d, e), U1(c, k))
28.54/9.60	
28.54/9.60	The TRS R consists of the following rules:
28.54/9.60	
28.54/9.60	   f(x) -> U1(x, x)
28.54/9.60	   U1(e, x) -> x
28.54/9.60	   a -> c
28.54/9.60	   a -> d
28.54/9.60	   b -> c
28.54/9.60	   b -> d
28.54/9.60	   d -> k
28.54/9.60	   c -> e
28.54/9.60	   c -> k
28.54/9.60	
28.54/9.60	Q is empty.
28.54/9.60	We have to consider all minimal (P,Q,R)-chains.
28.54/9.60	----------------------------------------
28.54/9.60	
28.54/9.60	(1243) TransformationProof (EQUIVALENT)
28.54/9.60	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), f(e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.60	
28.54/9.60	   (A^2 -> H(U1(k, e), f(e)),A^2 -> H(U1(k, e), f(e)))
28.54/9.60	   (A^2 -> H(U1(d, e), U1(e, e)),A^2 -> H(U1(d, e), U1(e, e)))
28.54/9.60	
28.54/9.60	
28.54/9.60	----------------------------------------
28.54/9.60	
28.54/9.60	(1244)
28.54/9.60	Obligation:
28.54/9.60	Q DP problem:
28.54/9.60	The TRS P consists of the following rules:
28.54/9.60	
28.54/9.60	   A^2 -> H(f(c), f(c))
28.54/9.60	   H(x, x) -> G(x, x, f(k))
28.54/9.60	   G(d, x, x) -> A^2
28.54/9.60	   A^2 -> H(f(d), f(d))
28.54/9.60	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.60	   A^2 -> H(f(e), f(e))
28.54/9.60	   A^2 -> H(f(k), f(k))
28.54/9.60	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.60	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, e), f(k))
28.54/9.60	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.60	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.60	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.60	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.60	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.60	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.60	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.60	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.60	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.60	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.60	   A^2 -> H(U1(d, a), b)
28.54/9.60	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.60	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.60	   A^2 -> H(U1(d, a), c)
28.54/9.60	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.60	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.60	   A^2 -> H(U1(d, a), e)
28.54/9.60	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.60	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.60	   A^2 -> H(U1(a, c), b)
28.54/9.60	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.60	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.60	   A^2 -> H(U1(a, c), c)
28.54/9.60	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.60	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.60	   A^2 -> H(U1(a, c), e)
28.54/9.60	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, d), b)
28.54/9.60	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.60	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.60	   A^2 -> H(U1(a, d), c)
28.54/9.60	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.60	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.60	   A^2 -> H(U1(a, d), e)
28.54/9.60	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, a), d)
28.54/9.60	   A^2 -> H(U1(a, a), k)
28.54/9.60	   A^2 -> H(k, U1(b, b))
28.54/9.60	   A^2 -> H(k, f(c))
28.54/9.60	   A^2 -> H(k, f(d))
28.54/9.60	   A^2 -> H(c, U1(c, b))
28.54/9.60	   A^2 -> H(c, U1(d, b))
28.54/9.60	   A^2 -> H(c, U1(b, c))
28.54/9.60	   A^2 -> H(c, U1(b, d))
28.54/9.60	   A^2 -> H(c, U1(c, c))
28.54/9.60	   A^2 -> H(c, f(e))
28.54/9.60	   A^2 -> H(c, f(k))
28.54/9.60	   A^2 -> H(c, U1(d, d))
28.54/9.60	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.60	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.60	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.60	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.60	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.60	   A^2 -> H(U1(e, k), f(e))
28.54/9.60	   A^2 -> H(U1(e, k), f(k))
28.54/9.60	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.60	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.60	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.60	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.60	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.60	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.60	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.60	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.60	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.60	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.60	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.60	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.60	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.60	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.60	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.60	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.60	   A^2 -> H(U1(k, e), f(e))
28.54/9.60	   A^2 -> H(U1(k, e), f(k))
28.54/9.60	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.60	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.60	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.60	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.60	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.60	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.60	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.60	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.60	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.60	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.60	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.60	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.60	   A^2 -> H(U1(c, c), b)
28.54/9.60	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.60	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.60	   A^2 -> H(U1(c, c), e)
28.54/9.60	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.60	   A^2 -> H(e, U1(c, b))
28.54/9.60	   A^2 -> H(e, U1(d, b))
28.54/9.60	   A^2 -> H(e, U1(b, c))
28.54/9.60	   A^2 -> H(e, U1(b, d))
28.54/9.60	   A^2 -> H(e, U1(c, c))
28.54/9.60	   A^2 -> H(e, f(e))
28.54/9.60	   A^2 -> H(e, f(k))
28.54/9.60	   A^2 -> H(e, U1(d, d))
28.54/9.60	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.60	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.60	   A^2 -> H(f(e), b)
28.54/9.60	   A^2 -> H(f(e), U1(e, d))
28.54/9.60	   A^2 -> H(f(e), U1(d, e))
28.54/9.60	   A^2 -> H(f(e), c)
28.54/9.60	   A^2 -> H(f(e), U1(e, k))
28.54/9.60	   A^2 -> H(f(e), U1(k, e))
28.54/9.60	   A^2 -> H(f(e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.60	   A^2 -> H(f(k), b)
28.54/9.60	   A^2 -> H(f(k), U1(e, d))
28.54/9.60	   A^2 -> H(f(k), U1(d, e))
28.54/9.60	   A^2 -> H(f(k), c)
28.54/9.60	   A^2 -> H(f(k), U1(e, k))
28.54/9.60	   A^2 -> H(f(k), U1(k, e))
28.54/9.60	   A^2 -> H(f(k), e)
28.54/9.60	   A^2 -> H(f(c), d)
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.60	   A^2 -> H(U1(k, k), f(e))
28.54/9.60	   A^2 -> H(U1(k, k), f(k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.60	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.60	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.60	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.60	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.60	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.60	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.60	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.60	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.60	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.60	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.60	   A^2 -> H(U1(d, d), b)
28.54/9.60	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.60	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.60	   A^2 -> H(U1(d, d), c)
28.54/9.60	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.60	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.60	   A^2 -> H(U1(d, d), e)
28.54/9.60	   A^2 -> H(f(d), d)
28.54/9.60	   A^2 -> H(f(d), k)
28.54/9.60	   A^2 -> H(U1(c, c), c)
28.54/9.60	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.60	   A^2 -> H(f(c), k)
28.54/9.60	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.60	   A^2 -> H(f(k), U1(k, k))
28.54/9.60	   A^2 -> H(f(e), e)
28.54/9.60	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.60	   A^2 -> H(d, U1(c, b))
28.54/9.60	   A^2 -> H(d, U1(d, b))
28.54/9.60	   A^2 -> H(d, U1(b, c))
28.54/9.60	   A^2 -> H(d, U1(b, d))
28.54/9.60	   A^2 -> H(d, U1(c, c))
28.54/9.60	   A^2 -> H(d, f(e))
28.54/9.60	   A^2 -> H(d, f(k))
28.54/9.60	   A^2 -> H(d, U1(d, d))
28.54/9.60	   A^2 -> H(a, U1(e, b))
28.54/9.60	   A^2 -> H(a, U1(k, b))
28.54/9.60	   A^2 -> H(a, U1(c, d))
28.54/9.60	   A^2 -> H(a, U1(d, c))
28.54/9.60	   A^2 -> H(a, U1(b, e))
28.54/9.60	   A^2 -> H(a, U1(b, k))
28.54/9.60	   A^2 -> H(a, U1(e, c))
28.54/9.60	   A^2 -> H(a, U1(k, c))
28.54/9.60	   A^2 -> H(a, U1(c, e))
28.54/9.60	   A^2 -> H(a, U1(c, k))
28.54/9.60	   A^2 -> H(a, U1(e, e))
28.54/9.60	   A^2 -> H(a, U1(k, k))
28.54/9.60	   A^2 -> H(a, U1(k, d))
28.54/9.60	   A^2 -> H(a, U1(d, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.60	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.60	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.60	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.60	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.60	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.60	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.60	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.60	   A^2 -> H(U1(e, a), b)
28.54/9.60	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.60	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.60	   A^2 -> H(U1(e, a), c)
28.54/9.60	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.60	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.60	   A^2 -> H(U1(e, a), e)
28.54/9.60	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, a), b)
28.54/9.60	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.60	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.60	   A^2 -> H(U1(k, a), c)
28.54/9.60	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.60	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.60	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, d), b)
28.54/9.60	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.60	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.60	   A^2 -> H(U1(c, d), c)
28.54/9.60	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.60	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.60	   A^2 -> H(U1(c, d), e)
28.54/9.60	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, a), d)
28.54/9.60	   A^2 -> H(U1(c, a), k)
28.54/9.60	   A^2 -> H(U1(d, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(d, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(d, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(d, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(d, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(d, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(d, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(d, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(d, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(d, e), U1(e, e))
28.54/9.60	
28.54/9.60	The TRS R consists of the following rules:
28.54/9.60	
28.54/9.60	   f(x) -> U1(x, x)
28.54/9.60	   U1(e, x) -> x
28.54/9.60	   a -> c
28.54/9.60	   a -> d
28.54/9.60	   b -> c
28.54/9.60	   b -> d
28.54/9.60	   d -> k
28.54/9.60	   c -> e
28.54/9.60	   c -> k
28.54/9.60	
28.54/9.60	Q is empty.
28.54/9.60	We have to consider all minimal (P,Q,R)-chains.
28.54/9.60	----------------------------------------
28.54/9.60	
28.54/9.60	(1245) TransformationProof (EQUIVALENT)
28.54/9.60	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), f(k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.60	
28.54/9.60	   (A^2 -> H(U1(k, e), f(k)),A^2 -> H(U1(k, e), f(k)))
28.54/9.60	   (A^2 -> H(U1(d, e), U1(k, k)),A^2 -> H(U1(d, e), U1(k, k)))
28.54/9.60	
28.54/9.60	
28.54/9.60	----------------------------------------
28.54/9.60	
28.54/9.60	(1246)
28.54/9.60	Obligation:
28.54/9.60	Q DP problem:
28.54/9.60	The TRS P consists of the following rules:
28.54/9.60	
28.54/9.60	   A^2 -> H(f(c), f(c))
28.54/9.60	   H(x, x) -> G(x, x, f(k))
28.54/9.60	   G(d, x, x) -> A^2
28.54/9.60	   A^2 -> H(f(d), f(d))
28.54/9.60	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.60	   A^2 -> H(f(e), f(e))
28.54/9.60	   A^2 -> H(f(k), f(k))
28.54/9.60	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.60	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, e), U1(d, d))
28.54/9.60	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.60	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.60	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.60	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.60	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.60	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.60	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.60	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.60	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.60	   A^2 -> H(U1(d, a), b)
28.54/9.60	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.60	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.60	   A^2 -> H(U1(d, a), c)
28.54/9.60	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.60	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.60	   A^2 -> H(U1(d, a), e)
28.54/9.60	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.60	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.60	   A^2 -> H(U1(a, c), b)
28.54/9.60	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.60	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.60	   A^2 -> H(U1(a, c), c)
28.54/9.60	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.60	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.60	   A^2 -> H(U1(a, c), e)
28.54/9.60	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, d), b)
28.54/9.60	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.60	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.60	   A^2 -> H(U1(a, d), c)
28.54/9.60	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.60	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.60	   A^2 -> H(U1(a, d), e)
28.54/9.60	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, a), d)
28.54/9.60	   A^2 -> H(U1(a, a), k)
28.54/9.60	   A^2 -> H(k, U1(b, b))
28.54/9.60	   A^2 -> H(k, f(c))
28.54/9.60	   A^2 -> H(k, f(d))
28.54/9.60	   A^2 -> H(c, U1(c, b))
28.54/9.60	   A^2 -> H(c, U1(d, b))
28.54/9.60	   A^2 -> H(c, U1(b, c))
28.54/9.60	   A^2 -> H(c, U1(b, d))
28.54/9.60	   A^2 -> H(c, U1(c, c))
28.54/9.60	   A^2 -> H(c, f(e))
28.54/9.60	   A^2 -> H(c, f(k))
28.54/9.60	   A^2 -> H(c, U1(d, d))
28.54/9.60	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.60	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.60	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.60	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.60	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.60	   A^2 -> H(U1(e, k), f(e))
28.54/9.60	   A^2 -> H(U1(e, k), f(k))
28.54/9.60	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.60	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.60	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.60	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.60	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.60	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.60	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.60	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.60	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.60	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.60	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.60	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.60	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.60	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.60	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.60	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.60	   A^2 -> H(U1(k, e), f(e))
28.54/9.60	   A^2 -> H(U1(k, e), f(k))
28.54/9.60	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.60	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.60	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.60	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.60	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.60	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.60	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.60	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.60	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.60	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.60	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.60	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.60	   A^2 -> H(U1(c, c), b)
28.54/9.60	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.60	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.60	   A^2 -> H(U1(c, c), e)
28.54/9.60	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.60	   A^2 -> H(e, U1(c, b))
28.54/9.60	   A^2 -> H(e, U1(d, b))
28.54/9.60	   A^2 -> H(e, U1(b, c))
28.54/9.60	   A^2 -> H(e, U1(b, d))
28.54/9.60	   A^2 -> H(e, U1(c, c))
28.54/9.60	   A^2 -> H(e, f(e))
28.54/9.60	   A^2 -> H(e, f(k))
28.54/9.60	   A^2 -> H(e, U1(d, d))
28.54/9.60	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.60	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.60	   A^2 -> H(f(e), b)
28.54/9.60	   A^2 -> H(f(e), U1(e, d))
28.54/9.60	   A^2 -> H(f(e), U1(d, e))
28.54/9.60	   A^2 -> H(f(e), c)
28.54/9.60	   A^2 -> H(f(e), U1(e, k))
28.54/9.60	   A^2 -> H(f(e), U1(k, e))
28.54/9.60	   A^2 -> H(f(e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.60	   A^2 -> H(f(k), b)
28.54/9.60	   A^2 -> H(f(k), U1(e, d))
28.54/9.60	   A^2 -> H(f(k), U1(d, e))
28.54/9.60	   A^2 -> H(f(k), c)
28.54/9.60	   A^2 -> H(f(k), U1(e, k))
28.54/9.60	   A^2 -> H(f(k), U1(k, e))
28.54/9.60	   A^2 -> H(f(k), e)
28.54/9.60	   A^2 -> H(f(c), d)
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.60	   A^2 -> H(U1(k, k), f(e))
28.54/9.60	   A^2 -> H(U1(k, k), f(k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.60	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.60	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.60	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.60	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.60	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.60	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.60	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.60	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.60	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.60	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.60	   A^2 -> H(U1(d, d), b)
28.54/9.60	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.60	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.60	   A^2 -> H(U1(d, d), c)
28.54/9.60	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.60	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.60	   A^2 -> H(U1(d, d), e)
28.54/9.60	   A^2 -> H(f(d), d)
28.54/9.60	   A^2 -> H(f(d), k)
28.54/9.60	   A^2 -> H(U1(c, c), c)
28.54/9.60	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.60	   A^2 -> H(f(c), k)
28.54/9.60	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.60	   A^2 -> H(f(k), U1(k, k))
28.54/9.60	   A^2 -> H(f(e), e)
28.54/9.60	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.60	   A^2 -> H(d, U1(c, b))
28.54/9.60	   A^2 -> H(d, U1(d, b))
28.54/9.60	   A^2 -> H(d, U1(b, c))
28.54/9.60	   A^2 -> H(d, U1(b, d))
28.54/9.60	   A^2 -> H(d, U1(c, c))
28.54/9.60	   A^2 -> H(d, f(e))
28.54/9.60	   A^2 -> H(d, f(k))
28.54/9.60	   A^2 -> H(d, U1(d, d))
28.54/9.60	   A^2 -> H(a, U1(e, b))
28.54/9.60	   A^2 -> H(a, U1(k, b))
28.54/9.60	   A^2 -> H(a, U1(c, d))
28.54/9.60	   A^2 -> H(a, U1(d, c))
28.54/9.60	   A^2 -> H(a, U1(b, e))
28.54/9.60	   A^2 -> H(a, U1(b, k))
28.54/9.60	   A^2 -> H(a, U1(e, c))
28.54/9.60	   A^2 -> H(a, U1(k, c))
28.54/9.60	   A^2 -> H(a, U1(c, e))
28.54/9.60	   A^2 -> H(a, U1(c, k))
28.54/9.60	   A^2 -> H(a, U1(e, e))
28.54/9.60	   A^2 -> H(a, U1(k, k))
28.54/9.60	   A^2 -> H(a, U1(k, d))
28.54/9.60	   A^2 -> H(a, U1(d, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.60	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.60	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.60	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.60	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.60	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.60	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.60	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.60	   A^2 -> H(U1(e, a), b)
28.54/9.60	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.60	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.60	   A^2 -> H(U1(e, a), c)
28.54/9.60	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.60	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.60	   A^2 -> H(U1(e, a), e)
28.54/9.60	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, a), b)
28.54/9.60	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.60	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.60	   A^2 -> H(U1(k, a), c)
28.54/9.60	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.60	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.60	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, d), b)
28.54/9.60	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.60	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.60	   A^2 -> H(U1(c, d), c)
28.54/9.60	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.60	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.60	   A^2 -> H(U1(c, d), e)
28.54/9.60	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, a), d)
28.54/9.60	   A^2 -> H(U1(c, a), k)
28.54/9.60	   A^2 -> H(U1(d, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(d, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(d, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(d, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(d, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(d, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(d, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(d, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(d, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(d, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(d, e), U1(k, k))
28.54/9.60	
28.54/9.60	The TRS R consists of the following rules:
28.54/9.60	
28.54/9.60	   f(x) -> U1(x, x)
28.54/9.60	   U1(e, x) -> x
28.54/9.60	   a -> c
28.54/9.60	   a -> d
28.54/9.60	   b -> c
28.54/9.60	   b -> d
28.54/9.60	   d -> k
28.54/9.60	   c -> e
28.54/9.60	   c -> k
28.54/9.60	
28.54/9.60	Q is empty.
28.54/9.60	We have to consider all minimal (P,Q,R)-chains.
28.54/9.60	----------------------------------------
28.54/9.60	
28.54/9.60	(1247) TransformationProof (EQUIVALENT)
28.54/9.60	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.60	
28.54/9.60	   (A^2 -> H(U1(k, e), U1(d, d)),A^2 -> H(U1(k, e), U1(d, d)))
28.54/9.60	   (A^2 -> H(U1(d, e), U1(k, d)),A^2 -> H(U1(d, e), U1(k, d)))
28.54/9.60	   (A^2 -> H(U1(d, e), U1(d, k)),A^2 -> H(U1(d, e), U1(d, k)))
28.54/9.60	
28.54/9.60	
28.54/9.60	----------------------------------------
28.54/9.60	
28.54/9.60	(1248)
28.54/9.60	Obligation:
28.54/9.60	Q DP problem:
28.54/9.60	The TRS P consists of the following rules:
28.54/9.60	
28.54/9.60	   A^2 -> H(f(c), f(c))
28.54/9.60	   H(x, x) -> G(x, x, f(k))
28.54/9.60	   G(d, x, x) -> A^2
28.54/9.60	   A^2 -> H(f(d), f(d))
28.54/9.60	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.60	   A^2 -> H(f(e), f(e))
28.54/9.60	   A^2 -> H(f(k), f(k))
28.54/9.60	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.60	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, c), U1(e, b))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.60	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.60	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.60	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.60	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.60	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.60	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.60	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.60	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.60	   A^2 -> H(U1(d, a), b)
28.54/9.60	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.60	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.60	   A^2 -> H(U1(d, a), c)
28.54/9.60	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.60	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.60	   A^2 -> H(U1(d, a), e)
28.54/9.60	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.60	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.60	   A^2 -> H(U1(a, c), b)
28.54/9.60	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.60	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.60	   A^2 -> H(U1(a, c), c)
28.54/9.60	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.60	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.60	   A^2 -> H(U1(a, c), e)
28.54/9.60	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, d), b)
28.54/9.60	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.60	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.60	   A^2 -> H(U1(a, d), c)
28.54/9.60	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.60	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.60	   A^2 -> H(U1(a, d), e)
28.54/9.60	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(a, a), d)
28.54/9.60	   A^2 -> H(U1(a, a), k)
28.54/9.60	   A^2 -> H(k, U1(b, b))
28.54/9.60	   A^2 -> H(k, f(c))
28.54/9.60	   A^2 -> H(k, f(d))
28.54/9.60	   A^2 -> H(c, U1(c, b))
28.54/9.60	   A^2 -> H(c, U1(d, b))
28.54/9.60	   A^2 -> H(c, U1(b, c))
28.54/9.60	   A^2 -> H(c, U1(b, d))
28.54/9.60	   A^2 -> H(c, U1(c, c))
28.54/9.60	   A^2 -> H(c, f(e))
28.54/9.60	   A^2 -> H(c, f(k))
28.54/9.60	   A^2 -> H(c, U1(d, d))
28.54/9.60	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.60	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.60	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.60	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.60	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.60	   A^2 -> H(U1(e, k), f(e))
28.54/9.60	   A^2 -> H(U1(e, k), f(k))
28.54/9.60	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.60	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.60	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.60	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.60	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.60	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.60	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.60	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.60	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.60	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.60	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.60	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.60	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.60	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.60	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.60	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.60	   A^2 -> H(U1(k, e), f(e))
28.54/9.60	   A^2 -> H(U1(k, e), f(k))
28.54/9.60	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.60	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.60	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.60	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.60	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.60	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.60	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.60	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.60	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.60	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.60	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.60	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.60	   A^2 -> H(U1(c, c), b)
28.54/9.60	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.60	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.60	   A^2 -> H(U1(c, c), e)
28.54/9.60	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.60	   A^2 -> H(e, U1(c, b))
28.54/9.60	   A^2 -> H(e, U1(d, b))
28.54/9.60	   A^2 -> H(e, U1(b, c))
28.54/9.60	   A^2 -> H(e, U1(b, d))
28.54/9.60	   A^2 -> H(e, U1(c, c))
28.54/9.60	   A^2 -> H(e, f(e))
28.54/9.60	   A^2 -> H(e, f(k))
28.54/9.60	   A^2 -> H(e, U1(d, d))
28.54/9.60	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.60	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.60	   A^2 -> H(f(e), b)
28.54/9.60	   A^2 -> H(f(e), U1(e, d))
28.54/9.60	   A^2 -> H(f(e), U1(d, e))
28.54/9.60	   A^2 -> H(f(e), c)
28.54/9.60	   A^2 -> H(f(e), U1(e, k))
28.54/9.60	   A^2 -> H(f(e), U1(k, e))
28.54/9.60	   A^2 -> H(f(e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.60	   A^2 -> H(f(k), b)
28.54/9.60	   A^2 -> H(f(k), U1(e, d))
28.54/9.60	   A^2 -> H(f(k), U1(d, e))
28.54/9.60	   A^2 -> H(f(k), c)
28.54/9.60	   A^2 -> H(f(k), U1(e, k))
28.54/9.60	   A^2 -> H(f(k), U1(k, e))
28.54/9.60	   A^2 -> H(f(k), e)
28.54/9.60	   A^2 -> H(f(c), d)
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.60	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.60	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.60	   A^2 -> H(U1(k, k), f(e))
28.54/9.60	   A^2 -> H(U1(k, k), f(k))
28.54/9.60	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.60	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.60	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.60	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.60	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.60	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.60	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.60	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.60	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.60	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.60	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.60	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.60	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.60	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.60	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.60	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.60	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.60	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.60	   A^2 -> H(U1(d, d), b)
28.54/9.60	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.60	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.60	   A^2 -> H(U1(d, d), c)
28.54/9.60	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.60	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.60	   A^2 -> H(U1(d, d), e)
28.54/9.60	   A^2 -> H(f(d), d)
28.54/9.60	   A^2 -> H(f(d), k)
28.54/9.60	   A^2 -> H(U1(c, c), c)
28.54/9.60	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.60	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.60	   A^2 -> H(f(c), k)
28.54/9.60	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.60	   A^2 -> H(f(k), U1(k, k))
28.54/9.60	   A^2 -> H(f(e), e)
28.54/9.60	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.60	   A^2 -> H(d, U1(c, b))
28.54/9.60	   A^2 -> H(d, U1(d, b))
28.54/9.60	   A^2 -> H(d, U1(b, c))
28.54/9.60	   A^2 -> H(d, U1(b, d))
28.54/9.60	   A^2 -> H(d, U1(c, c))
28.54/9.60	   A^2 -> H(d, f(e))
28.54/9.60	   A^2 -> H(d, f(k))
28.54/9.60	   A^2 -> H(d, U1(d, d))
28.54/9.60	   A^2 -> H(a, U1(e, b))
28.54/9.60	   A^2 -> H(a, U1(k, b))
28.54/9.60	   A^2 -> H(a, U1(c, d))
28.54/9.60	   A^2 -> H(a, U1(d, c))
28.54/9.60	   A^2 -> H(a, U1(b, e))
28.54/9.60	   A^2 -> H(a, U1(b, k))
28.54/9.60	   A^2 -> H(a, U1(e, c))
28.54/9.60	   A^2 -> H(a, U1(k, c))
28.54/9.60	   A^2 -> H(a, U1(c, e))
28.54/9.60	   A^2 -> H(a, U1(c, k))
28.54/9.60	   A^2 -> H(a, U1(e, e))
28.54/9.60	   A^2 -> H(a, U1(k, k))
28.54/9.60	   A^2 -> H(a, U1(k, d))
28.54/9.60	   A^2 -> H(a, U1(d, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.60	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.60	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.60	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.60	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.60	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.60	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.60	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.60	   A^2 -> H(U1(e, a), b)
28.54/9.60	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.60	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.60	   A^2 -> H(U1(e, a), c)
28.54/9.60	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.60	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.60	   A^2 -> H(U1(e, a), e)
28.54/9.60	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.60	   A^2 -> H(U1(k, a), b)
28.54/9.60	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.60	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.60	   A^2 -> H(U1(k, a), c)
28.54/9.60	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.60	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.60	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, d), b)
28.54/9.60	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.60	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.60	   A^2 -> H(U1(c, d), c)
28.54/9.60	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.60	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.60	   A^2 -> H(U1(c, d), e)
28.54/9.60	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.60	   A^2 -> H(U1(c, a), d)
28.54/9.60	   A^2 -> H(U1(c, a), k)
28.54/9.60	   A^2 -> H(U1(d, e), U1(e, b))
28.54/9.60	   A^2 -> H(U1(d, e), U1(k, b))
28.54/9.60	   A^2 -> H(U1(d, e), U1(c, d))
28.54/9.60	   A^2 -> H(U1(d, e), U1(d, c))
28.54/9.60	   A^2 -> H(U1(d, e), U1(b, e))
28.54/9.60	   A^2 -> H(U1(d, e), U1(b, k))
28.54/9.60	   A^2 -> H(U1(d, e), U1(e, c))
28.54/9.60	   A^2 -> H(U1(d, e), U1(k, c))
28.54/9.60	   A^2 -> H(U1(d, e), U1(c, e))
28.54/9.60	   A^2 -> H(U1(d, e), U1(c, k))
28.54/9.60	   A^2 -> H(U1(d, e), U1(e, e))
28.54/9.60	   A^2 -> H(U1(d, e), U1(k, k))
28.54/9.60	   A^2 -> H(U1(d, e), U1(k, d))
28.54/9.60	   A^2 -> H(U1(d, e), U1(d, k))
28.54/9.60	
28.54/9.60	The TRS R consists of the following rules:
28.54/9.60	
28.54/9.60	   f(x) -> U1(x, x)
28.54/9.60	   U1(e, x) -> x
28.54/9.60	   a -> c
28.54/9.60	   a -> d
28.54/9.60	   b -> c
28.54/9.60	   b -> d
28.54/9.60	   d -> k
28.54/9.60	   c -> e
28.54/9.60	   c -> k
28.54/9.60	
28.54/9.60	Q is empty.
28.54/9.60	We have to consider all minimal (P,Q,R)-chains.
28.54/9.60	----------------------------------------
28.54/9.60	
28.54/9.60	(1249) TransformationProof (EQUIVALENT)
28.54/9.60	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.61	
28.54/9.61	   (A^2 -> H(U1(k, c), U1(e, b)),A^2 -> H(U1(k, c), U1(e, b)))
28.54/9.61	   (A^2 -> H(U1(d, e), U1(e, b)),A^2 -> H(U1(d, e), U1(e, b)))
28.54/9.61	   (A^2 -> H(U1(d, k), U1(e, b)),A^2 -> H(U1(d, k), U1(e, b)))
28.54/9.61	   (A^2 -> H(U1(d, c), b),A^2 -> H(U1(d, c), b))
28.54/9.61	   (A^2 -> H(U1(d, c), U1(e, c)),A^2 -> H(U1(d, c), U1(e, c)))
28.54/9.61	   (A^2 -> H(U1(d, c), U1(e, d)),A^2 -> H(U1(d, c), U1(e, d)))
28.54/9.61	
28.54/9.61	
28.54/9.61	----------------------------------------
28.54/9.61	
28.54/9.61	(1250)
28.54/9.61	Obligation:
28.54/9.61	Q DP problem:
28.54/9.61	The TRS P consists of the following rules:
28.54/9.61	
28.54/9.61	   A^2 -> H(f(c), f(c))
28.54/9.61	   H(x, x) -> G(x, x, f(k))
28.54/9.61	   G(d, x, x) -> A^2
28.54/9.61	   A^2 -> H(f(d), f(d))
28.54/9.61	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.61	   A^2 -> H(f(e), f(e))
28.54/9.61	   A^2 -> H(f(k), f(k))
28.54/9.61	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.61	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, b))
28.54/9.61	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.61	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.61	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.61	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.61	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.61	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.61	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.61	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.61	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, a), b)
28.54/9.61	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.61	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.61	   A^2 -> H(U1(d, a), c)
28.54/9.61	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.61	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.61	   A^2 -> H(U1(d, a), e)
28.54/9.61	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.61	   A^2 -> H(U1(a, c), b)
28.54/9.61	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.61	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.61	   A^2 -> H(U1(a, c), c)
28.54/9.61	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.61	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.61	   A^2 -> H(U1(a, c), e)
28.54/9.61	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, d), b)
28.54/9.61	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.61	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.61	   A^2 -> H(U1(a, d), c)
28.54/9.61	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.61	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.61	   A^2 -> H(U1(a, d), e)
28.54/9.61	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, a), d)
28.54/9.61	   A^2 -> H(U1(a, a), k)
28.54/9.61	   A^2 -> H(k, U1(b, b))
28.54/9.61	   A^2 -> H(k, f(c))
28.54/9.61	   A^2 -> H(k, f(d))
28.54/9.61	   A^2 -> H(c, U1(c, b))
28.54/9.61	   A^2 -> H(c, U1(d, b))
28.54/9.61	   A^2 -> H(c, U1(b, c))
28.54/9.61	   A^2 -> H(c, U1(b, d))
28.54/9.61	   A^2 -> H(c, U1(c, c))
28.54/9.61	   A^2 -> H(c, f(e))
28.54/9.61	   A^2 -> H(c, f(k))
28.54/9.61	   A^2 -> H(c, U1(d, d))
28.54/9.61	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.61	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.61	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.61	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.61	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.61	   A^2 -> H(U1(e, k), f(e))
28.54/9.61	   A^2 -> H(U1(e, k), f(k))
28.54/9.61	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.61	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.61	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.61	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.61	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.61	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.61	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.61	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.61	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.61	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.61	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.61	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.61	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.61	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.61	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.61	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.61	   A^2 -> H(U1(k, e), f(e))
28.54/9.61	   A^2 -> H(U1(k, e), f(k))
28.54/9.61	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.61	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.61	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.61	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.61	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.61	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.61	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.61	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.61	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.61	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.61	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.61	   A^2 -> H(U1(c, c), b)
28.54/9.61	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.61	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.61	   A^2 -> H(U1(c, c), e)
28.54/9.61	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.61	   A^2 -> H(e, U1(c, b))
28.54/9.61	   A^2 -> H(e, U1(d, b))
28.54/9.61	   A^2 -> H(e, U1(b, c))
28.54/9.61	   A^2 -> H(e, U1(b, d))
28.54/9.61	   A^2 -> H(e, U1(c, c))
28.54/9.61	   A^2 -> H(e, f(e))
28.54/9.61	   A^2 -> H(e, f(k))
28.54/9.61	   A^2 -> H(e, U1(d, d))
28.54/9.61	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.61	   A^2 -> H(f(e), b)
28.54/9.61	   A^2 -> H(f(e), U1(e, d))
28.54/9.61	   A^2 -> H(f(e), U1(d, e))
28.54/9.61	   A^2 -> H(f(e), c)
28.54/9.61	   A^2 -> H(f(e), U1(e, k))
28.54/9.61	   A^2 -> H(f(e), U1(k, e))
28.54/9.61	   A^2 -> H(f(e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.61	   A^2 -> H(f(k), b)
28.54/9.61	   A^2 -> H(f(k), U1(e, d))
28.54/9.61	   A^2 -> H(f(k), U1(d, e))
28.54/9.61	   A^2 -> H(f(k), c)
28.54/9.61	   A^2 -> H(f(k), U1(e, k))
28.54/9.61	   A^2 -> H(f(k), U1(k, e))
28.54/9.61	   A^2 -> H(f(k), e)
28.54/9.61	   A^2 -> H(f(c), d)
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.61	   A^2 -> H(U1(k, k), f(e))
28.54/9.61	   A^2 -> H(U1(k, k), f(k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.61	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.61	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.61	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.61	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.61	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.61	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.61	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.61	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.61	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.61	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, d), b)
28.54/9.61	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.61	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.61	   A^2 -> H(U1(d, d), c)
28.54/9.61	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.61	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.61	   A^2 -> H(U1(d, d), e)
28.54/9.61	   A^2 -> H(f(d), d)
28.54/9.61	   A^2 -> H(f(d), k)
28.54/9.61	   A^2 -> H(U1(c, c), c)
28.54/9.61	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.61	   A^2 -> H(f(c), k)
28.54/9.61	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.61	   A^2 -> H(f(k), U1(k, k))
28.54/9.61	   A^2 -> H(f(e), e)
28.54/9.61	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.61	   A^2 -> H(d, U1(c, b))
28.54/9.61	   A^2 -> H(d, U1(d, b))
28.54/9.61	   A^2 -> H(d, U1(b, c))
28.54/9.61	   A^2 -> H(d, U1(b, d))
28.54/9.61	   A^2 -> H(d, U1(c, c))
28.54/9.61	   A^2 -> H(d, f(e))
28.54/9.61	   A^2 -> H(d, f(k))
28.54/9.61	   A^2 -> H(d, U1(d, d))
28.54/9.61	   A^2 -> H(a, U1(e, b))
28.54/9.61	   A^2 -> H(a, U1(k, b))
28.54/9.61	   A^2 -> H(a, U1(c, d))
28.54/9.61	   A^2 -> H(a, U1(d, c))
28.54/9.61	   A^2 -> H(a, U1(b, e))
28.54/9.61	   A^2 -> H(a, U1(b, k))
28.54/9.61	   A^2 -> H(a, U1(e, c))
28.54/9.61	   A^2 -> H(a, U1(k, c))
28.54/9.61	   A^2 -> H(a, U1(c, e))
28.54/9.61	   A^2 -> H(a, U1(c, k))
28.54/9.61	   A^2 -> H(a, U1(e, e))
28.54/9.61	   A^2 -> H(a, U1(k, k))
28.54/9.61	   A^2 -> H(a, U1(k, d))
28.54/9.61	   A^2 -> H(a, U1(d, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.61	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.61	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.61	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.61	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.61	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.61	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.61	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.61	   A^2 -> H(U1(e, a), b)
28.54/9.61	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.61	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.61	   A^2 -> H(U1(e, a), c)
28.54/9.61	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.61	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.61	   A^2 -> H(U1(e, a), e)
28.54/9.61	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, a), b)
28.54/9.61	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.61	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.61	   A^2 -> H(U1(k, a), c)
28.54/9.61	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.61	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.61	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, d), b)
28.54/9.61	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.61	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.61	   A^2 -> H(U1(c, d), c)
28.54/9.61	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.61	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.61	   A^2 -> H(U1(c, d), e)
28.54/9.61	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, a), d)
28.54/9.61	   A^2 -> H(U1(c, a), k)
28.54/9.61	   A^2 -> H(U1(d, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(d, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(d, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(d, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(d, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(d, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(d, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(d, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(d, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(d, e), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, c), b)
28.54/9.61	   A^2 -> H(U1(d, c), U1(e, d))
28.54/9.61	
28.54/9.61	The TRS R consists of the following rules:
28.54/9.61	
28.54/9.61	   f(x) -> U1(x, x)
28.54/9.61	   U1(e, x) -> x
28.54/9.61	   a -> c
28.54/9.61	   a -> d
28.54/9.61	   b -> c
28.54/9.61	   b -> d
28.54/9.61	   d -> k
28.54/9.61	   c -> e
28.54/9.61	   c -> k
28.54/9.61	
28.54/9.61	Q is empty.
28.54/9.61	We have to consider all minimal (P,Q,R)-chains.
28.54/9.61	----------------------------------------
28.54/9.61	
28.54/9.61	(1251) TransformationProof (EQUIVALENT)
28.54/9.61	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.61	
28.54/9.61	   (A^2 -> H(U1(k, c), U1(k, b)),A^2 -> H(U1(k, c), U1(k, b)))
28.54/9.61	   (A^2 -> H(U1(d, e), U1(k, b)),A^2 -> H(U1(d, e), U1(k, b)))
28.54/9.61	   (A^2 -> H(U1(d, k), U1(k, b)),A^2 -> H(U1(d, k), U1(k, b)))
28.54/9.61	   (A^2 -> H(U1(d, c), U1(k, c)),A^2 -> H(U1(d, c), U1(k, c)))
28.54/9.61	   (A^2 -> H(U1(d, c), U1(k, d)),A^2 -> H(U1(d, c), U1(k, d)))
28.54/9.61	
28.54/9.61	
28.54/9.61	----------------------------------------
28.54/9.61	
28.54/9.61	(1252)
28.54/9.61	Obligation:
28.54/9.61	Q DP problem:
28.54/9.61	The TRS P consists of the following rules:
28.54/9.61	
28.54/9.61	   A^2 -> H(f(c), f(c))
28.54/9.61	   H(x, x) -> G(x, x, f(k))
28.54/9.61	   G(d, x, x) -> A^2
28.54/9.61	   A^2 -> H(f(d), f(d))
28.54/9.61	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.61	   A^2 -> H(f(e), f(e))
28.54/9.61	   A^2 -> H(f(k), f(k))
28.54/9.61	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.61	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.61	   A^2 -> H(U1(d, c), U1(c, d))
28.54/9.61	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.61	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.61	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.61	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.61	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.61	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.61	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.61	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, a), b)
28.54/9.61	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.61	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.61	   A^2 -> H(U1(d, a), c)
28.54/9.61	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.61	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.61	   A^2 -> H(U1(d, a), e)
28.54/9.61	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.61	   A^2 -> H(U1(a, c), b)
28.54/9.61	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.61	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.61	   A^2 -> H(U1(a, c), c)
28.54/9.61	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.61	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.61	   A^2 -> H(U1(a, c), e)
28.54/9.61	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, d), b)
28.54/9.61	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.61	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.61	   A^2 -> H(U1(a, d), c)
28.54/9.61	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.61	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.61	   A^2 -> H(U1(a, d), e)
28.54/9.61	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, a), d)
28.54/9.61	   A^2 -> H(U1(a, a), k)
28.54/9.61	   A^2 -> H(k, U1(b, b))
28.54/9.61	   A^2 -> H(k, f(c))
28.54/9.61	   A^2 -> H(k, f(d))
28.54/9.61	   A^2 -> H(c, U1(c, b))
28.54/9.61	   A^2 -> H(c, U1(d, b))
28.54/9.61	   A^2 -> H(c, U1(b, c))
28.54/9.61	   A^2 -> H(c, U1(b, d))
28.54/9.61	   A^2 -> H(c, U1(c, c))
28.54/9.61	   A^2 -> H(c, f(e))
28.54/9.61	   A^2 -> H(c, f(k))
28.54/9.61	   A^2 -> H(c, U1(d, d))
28.54/9.61	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.61	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.61	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.61	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.61	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.61	   A^2 -> H(U1(e, k), f(e))
28.54/9.61	   A^2 -> H(U1(e, k), f(k))
28.54/9.61	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.61	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.61	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.61	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.61	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.61	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.61	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.61	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.61	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.61	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.61	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.61	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.61	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.61	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.61	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.61	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.61	   A^2 -> H(U1(k, e), f(e))
28.54/9.61	   A^2 -> H(U1(k, e), f(k))
28.54/9.61	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.61	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.61	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.61	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.61	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.61	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.61	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.61	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.61	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.61	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.61	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.61	   A^2 -> H(U1(c, c), b)
28.54/9.61	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.61	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.61	   A^2 -> H(U1(c, c), e)
28.54/9.61	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.61	   A^2 -> H(e, U1(c, b))
28.54/9.61	   A^2 -> H(e, U1(d, b))
28.54/9.61	   A^2 -> H(e, U1(b, c))
28.54/9.61	   A^2 -> H(e, U1(b, d))
28.54/9.61	   A^2 -> H(e, U1(c, c))
28.54/9.61	   A^2 -> H(e, f(e))
28.54/9.61	   A^2 -> H(e, f(k))
28.54/9.61	   A^2 -> H(e, U1(d, d))
28.54/9.61	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.61	   A^2 -> H(f(e), b)
28.54/9.61	   A^2 -> H(f(e), U1(e, d))
28.54/9.61	   A^2 -> H(f(e), U1(d, e))
28.54/9.61	   A^2 -> H(f(e), c)
28.54/9.61	   A^2 -> H(f(e), U1(e, k))
28.54/9.61	   A^2 -> H(f(e), U1(k, e))
28.54/9.61	   A^2 -> H(f(e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.61	   A^2 -> H(f(k), b)
28.54/9.61	   A^2 -> H(f(k), U1(e, d))
28.54/9.61	   A^2 -> H(f(k), U1(d, e))
28.54/9.61	   A^2 -> H(f(k), c)
28.54/9.61	   A^2 -> H(f(k), U1(e, k))
28.54/9.61	   A^2 -> H(f(k), U1(k, e))
28.54/9.61	   A^2 -> H(f(k), e)
28.54/9.61	   A^2 -> H(f(c), d)
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.61	   A^2 -> H(U1(k, k), f(e))
28.54/9.61	   A^2 -> H(U1(k, k), f(k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.61	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.61	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.61	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.61	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.61	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.61	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.61	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.61	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.61	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.61	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, d), b)
28.54/9.61	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.61	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.61	   A^2 -> H(U1(d, d), c)
28.54/9.61	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.61	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.61	   A^2 -> H(U1(d, d), e)
28.54/9.61	   A^2 -> H(f(d), d)
28.54/9.61	   A^2 -> H(f(d), k)
28.54/9.61	   A^2 -> H(U1(c, c), c)
28.54/9.61	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.61	   A^2 -> H(f(c), k)
28.54/9.61	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.61	   A^2 -> H(f(k), U1(k, k))
28.54/9.61	   A^2 -> H(f(e), e)
28.54/9.61	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.61	   A^2 -> H(d, U1(c, b))
28.54/9.61	   A^2 -> H(d, U1(d, b))
28.54/9.61	   A^2 -> H(d, U1(b, c))
28.54/9.61	   A^2 -> H(d, U1(b, d))
28.54/9.61	   A^2 -> H(d, U1(c, c))
28.54/9.61	   A^2 -> H(d, f(e))
28.54/9.61	   A^2 -> H(d, f(k))
28.54/9.61	   A^2 -> H(d, U1(d, d))
28.54/9.61	   A^2 -> H(a, U1(e, b))
28.54/9.61	   A^2 -> H(a, U1(k, b))
28.54/9.61	   A^2 -> H(a, U1(c, d))
28.54/9.61	   A^2 -> H(a, U1(d, c))
28.54/9.61	   A^2 -> H(a, U1(b, e))
28.54/9.61	   A^2 -> H(a, U1(b, k))
28.54/9.61	   A^2 -> H(a, U1(e, c))
28.54/9.61	   A^2 -> H(a, U1(k, c))
28.54/9.61	   A^2 -> H(a, U1(c, e))
28.54/9.61	   A^2 -> H(a, U1(c, k))
28.54/9.61	   A^2 -> H(a, U1(e, e))
28.54/9.61	   A^2 -> H(a, U1(k, k))
28.54/9.61	   A^2 -> H(a, U1(k, d))
28.54/9.61	   A^2 -> H(a, U1(d, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.61	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.61	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.61	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.61	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.61	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.61	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.61	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.61	   A^2 -> H(U1(e, a), b)
28.54/9.61	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.61	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.61	   A^2 -> H(U1(e, a), c)
28.54/9.61	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.61	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.61	   A^2 -> H(U1(e, a), e)
28.54/9.61	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, a), b)
28.54/9.61	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.61	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.61	   A^2 -> H(U1(k, a), c)
28.54/9.61	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.61	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.61	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, d), b)
28.54/9.61	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.61	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.61	   A^2 -> H(U1(c, d), c)
28.54/9.61	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.61	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.61	   A^2 -> H(U1(c, d), e)
28.54/9.61	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, a), d)
28.54/9.61	   A^2 -> H(U1(c, a), k)
28.54/9.61	   A^2 -> H(U1(d, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(d, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(d, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(d, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(d, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(d, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(d, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(d, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(d, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(d, e), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, c), b)
28.54/9.61	   A^2 -> H(U1(d, c), U1(e, d))
28.54/9.61	
28.54/9.61	The TRS R consists of the following rules:
28.54/9.61	
28.54/9.61	   f(x) -> U1(x, x)
28.54/9.61	   U1(e, x) -> x
28.54/9.61	   a -> c
28.54/9.61	   a -> d
28.54/9.61	   b -> c
28.54/9.61	   b -> d
28.54/9.61	   d -> k
28.54/9.61	   c -> e
28.54/9.61	   c -> k
28.54/9.61	
28.54/9.61	Q is empty.
28.54/9.61	We have to consider all minimal (P,Q,R)-chains.
28.54/9.61	----------------------------------------
28.54/9.61	
28.54/9.61	(1253) TransformationProof (EQUIVALENT)
28.54/9.61	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.61	
28.54/9.61	   (A^2 -> H(U1(k, c), U1(c, d)),A^2 -> H(U1(k, c), U1(c, d)))
28.54/9.61	   (A^2 -> H(U1(d, e), U1(c, d)),A^2 -> H(U1(d, e), U1(c, d)))
28.54/9.61	   (A^2 -> H(U1(d, k), U1(c, d)),A^2 -> H(U1(d, k), U1(c, d)))
28.54/9.61	   (A^2 -> H(U1(d, c), U1(e, d)),A^2 -> H(U1(d, c), U1(e, d)))
28.54/9.61	   (A^2 -> H(U1(d, c), U1(k, d)),A^2 -> H(U1(d, c), U1(k, d)))
28.54/9.61	   (A^2 -> H(U1(d, c), U1(c, k)),A^2 -> H(U1(d, c), U1(c, k)))
28.54/9.61	
28.54/9.61	
28.54/9.61	----------------------------------------
28.54/9.61	
28.54/9.61	(1254)
28.54/9.61	Obligation:
28.54/9.61	Q DP problem:
28.54/9.61	The TRS P consists of the following rules:
28.54/9.61	
28.54/9.61	   A^2 -> H(f(c), f(c))
28.54/9.61	   H(x, x) -> G(x, x, f(k))
28.54/9.61	   G(d, x, x) -> A^2
28.54/9.61	   A^2 -> H(f(d), f(d))
28.54/9.61	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.61	   A^2 -> H(f(e), f(e))
28.54/9.61	   A^2 -> H(f(k), f(k))
28.54/9.61	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.61	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.61	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.61	   A^2 -> H(U1(d, c), U1(b, e))
28.54/9.61	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.61	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.61	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.61	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.61	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.61	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, a), b)
28.54/9.61	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.61	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.61	   A^2 -> H(U1(d, a), c)
28.54/9.61	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.61	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.61	   A^2 -> H(U1(d, a), e)
28.54/9.61	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.61	   A^2 -> H(U1(a, c), b)
28.54/9.61	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.61	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.61	   A^2 -> H(U1(a, c), c)
28.54/9.61	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.61	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.61	   A^2 -> H(U1(a, c), e)
28.54/9.61	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, d), b)
28.54/9.61	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.61	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.61	   A^2 -> H(U1(a, d), c)
28.54/9.61	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.61	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.61	   A^2 -> H(U1(a, d), e)
28.54/9.61	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, a), d)
28.54/9.61	   A^2 -> H(U1(a, a), k)
28.54/9.61	   A^2 -> H(k, U1(b, b))
28.54/9.61	   A^2 -> H(k, f(c))
28.54/9.61	   A^2 -> H(k, f(d))
28.54/9.61	   A^2 -> H(c, U1(c, b))
28.54/9.61	   A^2 -> H(c, U1(d, b))
28.54/9.61	   A^2 -> H(c, U1(b, c))
28.54/9.61	   A^2 -> H(c, U1(b, d))
28.54/9.61	   A^2 -> H(c, U1(c, c))
28.54/9.61	   A^2 -> H(c, f(e))
28.54/9.61	   A^2 -> H(c, f(k))
28.54/9.61	   A^2 -> H(c, U1(d, d))
28.54/9.61	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.61	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.61	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.61	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.61	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.61	   A^2 -> H(U1(e, k), f(e))
28.54/9.61	   A^2 -> H(U1(e, k), f(k))
28.54/9.61	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.61	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.61	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.61	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.61	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.61	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.61	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.61	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.61	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.61	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.61	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.61	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.61	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.61	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.61	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.61	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.61	   A^2 -> H(U1(k, e), f(e))
28.54/9.61	   A^2 -> H(U1(k, e), f(k))
28.54/9.61	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.61	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.61	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.61	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.61	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.61	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.61	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.61	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.61	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.61	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.61	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.61	   A^2 -> H(U1(c, c), b)
28.54/9.61	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.61	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.61	   A^2 -> H(U1(c, c), e)
28.54/9.61	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.61	   A^2 -> H(e, U1(c, b))
28.54/9.61	   A^2 -> H(e, U1(d, b))
28.54/9.61	   A^2 -> H(e, U1(b, c))
28.54/9.61	   A^2 -> H(e, U1(b, d))
28.54/9.61	   A^2 -> H(e, U1(c, c))
28.54/9.61	   A^2 -> H(e, f(e))
28.54/9.61	   A^2 -> H(e, f(k))
28.54/9.61	   A^2 -> H(e, U1(d, d))
28.54/9.61	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.61	   A^2 -> H(f(e), b)
28.54/9.61	   A^2 -> H(f(e), U1(e, d))
28.54/9.61	   A^2 -> H(f(e), U1(d, e))
28.54/9.61	   A^2 -> H(f(e), c)
28.54/9.61	   A^2 -> H(f(e), U1(e, k))
28.54/9.61	   A^2 -> H(f(e), U1(k, e))
28.54/9.61	   A^2 -> H(f(e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.61	   A^2 -> H(f(k), b)
28.54/9.61	   A^2 -> H(f(k), U1(e, d))
28.54/9.61	   A^2 -> H(f(k), U1(d, e))
28.54/9.61	   A^2 -> H(f(k), c)
28.54/9.61	   A^2 -> H(f(k), U1(e, k))
28.54/9.61	   A^2 -> H(f(k), U1(k, e))
28.54/9.61	   A^2 -> H(f(k), e)
28.54/9.61	   A^2 -> H(f(c), d)
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.61	   A^2 -> H(U1(k, k), f(e))
28.54/9.61	   A^2 -> H(U1(k, k), f(k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.61	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.61	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.61	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.61	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.61	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.61	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.61	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.61	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.61	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.61	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, d), b)
28.54/9.61	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.61	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.61	   A^2 -> H(U1(d, d), c)
28.54/9.61	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.61	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.61	   A^2 -> H(U1(d, d), e)
28.54/9.61	   A^2 -> H(f(d), d)
28.54/9.61	   A^2 -> H(f(d), k)
28.54/9.61	   A^2 -> H(U1(c, c), c)
28.54/9.61	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.61	   A^2 -> H(f(c), k)
28.54/9.61	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.61	   A^2 -> H(f(k), U1(k, k))
28.54/9.61	   A^2 -> H(f(e), e)
28.54/9.61	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.61	   A^2 -> H(d, U1(c, b))
28.54/9.61	   A^2 -> H(d, U1(d, b))
28.54/9.61	   A^2 -> H(d, U1(b, c))
28.54/9.61	   A^2 -> H(d, U1(b, d))
28.54/9.61	   A^2 -> H(d, U1(c, c))
28.54/9.61	   A^2 -> H(d, f(e))
28.54/9.61	   A^2 -> H(d, f(k))
28.54/9.61	   A^2 -> H(d, U1(d, d))
28.54/9.61	   A^2 -> H(a, U1(e, b))
28.54/9.61	   A^2 -> H(a, U1(k, b))
28.54/9.61	   A^2 -> H(a, U1(c, d))
28.54/9.61	   A^2 -> H(a, U1(d, c))
28.54/9.61	   A^2 -> H(a, U1(b, e))
28.54/9.61	   A^2 -> H(a, U1(b, k))
28.54/9.61	   A^2 -> H(a, U1(e, c))
28.54/9.61	   A^2 -> H(a, U1(k, c))
28.54/9.61	   A^2 -> H(a, U1(c, e))
28.54/9.61	   A^2 -> H(a, U1(c, k))
28.54/9.61	   A^2 -> H(a, U1(e, e))
28.54/9.61	   A^2 -> H(a, U1(k, k))
28.54/9.61	   A^2 -> H(a, U1(k, d))
28.54/9.61	   A^2 -> H(a, U1(d, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.61	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.61	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.61	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.61	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.61	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.61	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.61	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.61	   A^2 -> H(U1(e, a), b)
28.54/9.61	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.61	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.61	   A^2 -> H(U1(e, a), c)
28.54/9.61	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.61	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.61	   A^2 -> H(U1(e, a), e)
28.54/9.61	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, a), b)
28.54/9.61	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.61	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.61	   A^2 -> H(U1(k, a), c)
28.54/9.61	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.61	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.61	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, d), b)
28.54/9.61	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.61	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.61	   A^2 -> H(U1(c, d), c)
28.54/9.61	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.61	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.61	   A^2 -> H(U1(c, d), e)
28.54/9.61	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, a), d)
28.54/9.61	   A^2 -> H(U1(c, a), k)
28.54/9.61	   A^2 -> H(U1(d, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(d, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(d, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(d, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(d, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(d, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(d, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(d, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(d, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(d, e), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, c), b)
28.54/9.61	   A^2 -> H(U1(d, c), U1(e, d))
28.54/9.61	
28.54/9.61	The TRS R consists of the following rules:
28.54/9.61	
28.54/9.61	   f(x) -> U1(x, x)
28.54/9.61	   U1(e, x) -> x
28.54/9.61	   a -> c
28.54/9.61	   a -> d
28.54/9.61	   b -> c
28.54/9.61	   b -> d
28.54/9.61	   d -> k
28.54/9.61	   c -> e
28.54/9.61	   c -> k
28.54/9.61	
28.54/9.61	Q is empty.
28.54/9.61	We have to consider all minimal (P,Q,R)-chains.
28.54/9.61	----------------------------------------
28.54/9.61	
28.54/9.61	(1255) TransformationProof (EQUIVALENT)
28.54/9.61	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.61	
28.54/9.61	   (A^2 -> H(U1(k, c), U1(b, e)),A^2 -> H(U1(k, c), U1(b, e)))
28.54/9.61	   (A^2 -> H(U1(d, e), U1(b, e)),A^2 -> H(U1(d, e), U1(b, e)))
28.54/9.61	   (A^2 -> H(U1(d, k), U1(b, e)),A^2 -> H(U1(d, k), U1(b, e)))
28.54/9.61	   (A^2 -> H(U1(d, c), U1(c, e)),A^2 -> H(U1(d, c), U1(c, e)))
28.54/9.61	   (A^2 -> H(U1(d, c), U1(d, e)),A^2 -> H(U1(d, c), U1(d, e)))
28.54/9.61	
28.54/9.61	
28.54/9.61	----------------------------------------
28.54/9.61	
28.54/9.61	(1256)
28.54/9.61	Obligation:
28.54/9.61	Q DP problem:
28.54/9.61	The TRS P consists of the following rules:
28.54/9.61	
28.54/9.61	   A^2 -> H(f(c), f(c))
28.54/9.61	   H(x, x) -> G(x, x, f(k))
28.54/9.61	   G(d, x, x) -> A^2
28.54/9.61	   A^2 -> H(f(d), f(d))
28.54/9.61	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.61	   A^2 -> H(f(e), f(e))
28.54/9.61	   A^2 -> H(f(k), f(k))
28.54/9.61	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.61	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.61	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.61	   A^2 -> H(U1(d, c), U1(b, k))
28.54/9.61	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.61	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.61	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.61	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.61	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, a), b)
28.54/9.61	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.61	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.61	   A^2 -> H(U1(d, a), c)
28.54/9.61	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.61	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.61	   A^2 -> H(U1(d, a), e)
28.54/9.61	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.61	   A^2 -> H(U1(a, c), b)
28.54/9.61	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.61	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.61	   A^2 -> H(U1(a, c), c)
28.54/9.61	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.61	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.61	   A^2 -> H(U1(a, c), e)
28.54/9.61	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, d), b)
28.54/9.61	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.61	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.61	   A^2 -> H(U1(a, d), c)
28.54/9.61	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.61	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.61	   A^2 -> H(U1(a, d), e)
28.54/9.61	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, a), d)
28.54/9.61	   A^2 -> H(U1(a, a), k)
28.54/9.61	   A^2 -> H(k, U1(b, b))
28.54/9.61	   A^2 -> H(k, f(c))
28.54/9.61	   A^2 -> H(k, f(d))
28.54/9.61	   A^2 -> H(c, U1(c, b))
28.54/9.61	   A^2 -> H(c, U1(d, b))
28.54/9.61	   A^2 -> H(c, U1(b, c))
28.54/9.61	   A^2 -> H(c, U1(b, d))
28.54/9.61	   A^2 -> H(c, U1(c, c))
28.54/9.61	   A^2 -> H(c, f(e))
28.54/9.61	   A^2 -> H(c, f(k))
28.54/9.61	   A^2 -> H(c, U1(d, d))
28.54/9.61	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.61	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.61	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.61	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.61	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.61	   A^2 -> H(U1(e, k), f(e))
28.54/9.61	   A^2 -> H(U1(e, k), f(k))
28.54/9.61	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.61	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.61	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.61	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.61	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.61	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.61	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.61	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.61	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.61	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.61	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.61	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.61	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.61	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.61	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.61	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.61	   A^2 -> H(U1(k, e), f(e))
28.54/9.61	   A^2 -> H(U1(k, e), f(k))
28.54/9.61	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.61	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.61	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.61	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.61	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.61	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.61	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.61	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.61	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.61	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.61	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.61	   A^2 -> H(U1(c, c), b)
28.54/9.61	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.61	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.61	   A^2 -> H(U1(c, c), e)
28.54/9.61	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.61	   A^2 -> H(e, U1(c, b))
28.54/9.61	   A^2 -> H(e, U1(d, b))
28.54/9.61	   A^2 -> H(e, U1(b, c))
28.54/9.61	   A^2 -> H(e, U1(b, d))
28.54/9.61	   A^2 -> H(e, U1(c, c))
28.54/9.61	   A^2 -> H(e, f(e))
28.54/9.61	   A^2 -> H(e, f(k))
28.54/9.61	   A^2 -> H(e, U1(d, d))
28.54/9.61	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.61	   A^2 -> H(f(e), b)
28.54/9.61	   A^2 -> H(f(e), U1(e, d))
28.54/9.61	   A^2 -> H(f(e), U1(d, e))
28.54/9.61	   A^2 -> H(f(e), c)
28.54/9.61	   A^2 -> H(f(e), U1(e, k))
28.54/9.61	   A^2 -> H(f(e), U1(k, e))
28.54/9.61	   A^2 -> H(f(e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.61	   A^2 -> H(f(k), b)
28.54/9.61	   A^2 -> H(f(k), U1(e, d))
28.54/9.61	   A^2 -> H(f(k), U1(d, e))
28.54/9.61	   A^2 -> H(f(k), c)
28.54/9.61	   A^2 -> H(f(k), U1(e, k))
28.54/9.61	   A^2 -> H(f(k), U1(k, e))
28.54/9.61	   A^2 -> H(f(k), e)
28.54/9.61	   A^2 -> H(f(c), d)
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.61	   A^2 -> H(U1(k, k), f(e))
28.54/9.61	   A^2 -> H(U1(k, k), f(k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.61	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.61	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.61	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.61	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.61	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.61	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.61	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.61	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.61	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.61	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, d), b)
28.54/9.61	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.61	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.61	   A^2 -> H(U1(d, d), c)
28.54/9.61	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.61	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.61	   A^2 -> H(U1(d, d), e)
28.54/9.61	   A^2 -> H(f(d), d)
28.54/9.61	   A^2 -> H(f(d), k)
28.54/9.61	   A^2 -> H(U1(c, c), c)
28.54/9.61	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.61	   A^2 -> H(f(c), k)
28.54/9.61	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.61	   A^2 -> H(f(k), U1(k, k))
28.54/9.61	   A^2 -> H(f(e), e)
28.54/9.61	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.61	   A^2 -> H(d, U1(c, b))
28.54/9.61	   A^2 -> H(d, U1(d, b))
28.54/9.61	   A^2 -> H(d, U1(b, c))
28.54/9.61	   A^2 -> H(d, U1(b, d))
28.54/9.61	   A^2 -> H(d, U1(c, c))
28.54/9.61	   A^2 -> H(d, f(e))
28.54/9.61	   A^2 -> H(d, f(k))
28.54/9.61	   A^2 -> H(d, U1(d, d))
28.54/9.61	   A^2 -> H(a, U1(e, b))
28.54/9.61	   A^2 -> H(a, U1(k, b))
28.54/9.61	   A^2 -> H(a, U1(c, d))
28.54/9.61	   A^2 -> H(a, U1(d, c))
28.54/9.61	   A^2 -> H(a, U1(b, e))
28.54/9.61	   A^2 -> H(a, U1(b, k))
28.54/9.61	   A^2 -> H(a, U1(e, c))
28.54/9.61	   A^2 -> H(a, U1(k, c))
28.54/9.61	   A^2 -> H(a, U1(c, e))
28.54/9.61	   A^2 -> H(a, U1(c, k))
28.54/9.61	   A^2 -> H(a, U1(e, e))
28.54/9.61	   A^2 -> H(a, U1(k, k))
28.54/9.61	   A^2 -> H(a, U1(k, d))
28.54/9.61	   A^2 -> H(a, U1(d, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.61	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.61	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.61	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.61	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.61	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.61	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.61	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.61	   A^2 -> H(U1(e, a), b)
28.54/9.61	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.61	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.61	   A^2 -> H(U1(e, a), c)
28.54/9.61	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.61	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.61	   A^2 -> H(U1(e, a), e)
28.54/9.61	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, a), b)
28.54/9.61	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.61	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.61	   A^2 -> H(U1(k, a), c)
28.54/9.61	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.61	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.61	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, d), b)
28.54/9.61	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.61	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.61	   A^2 -> H(U1(c, d), c)
28.54/9.61	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.61	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.61	   A^2 -> H(U1(c, d), e)
28.54/9.61	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, a), d)
28.54/9.61	   A^2 -> H(U1(c, a), k)
28.54/9.61	   A^2 -> H(U1(d, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(d, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(d, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(d, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(d, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(d, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(d, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(d, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(d, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(d, e), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, c), b)
28.54/9.61	   A^2 -> H(U1(d, c), U1(e, d))
28.54/9.61	   A^2 -> H(U1(d, c), U1(d, e))
28.54/9.61	
28.54/9.61	The TRS R consists of the following rules:
28.54/9.61	
28.54/9.61	   f(x) -> U1(x, x)
28.54/9.61	   U1(e, x) -> x
28.54/9.61	   a -> c
28.54/9.61	   a -> d
28.54/9.61	   b -> c
28.54/9.61	   b -> d
28.54/9.61	   d -> k
28.54/9.61	   c -> e
28.54/9.61	   c -> k
28.54/9.61	
28.54/9.61	Q is empty.
28.54/9.61	We have to consider all minimal (P,Q,R)-chains.
28.54/9.61	----------------------------------------
28.54/9.61	
28.54/9.61	(1257) TransformationProof (EQUIVALENT)
28.54/9.61	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.61	
28.54/9.61	   (A^2 -> H(U1(k, c), U1(b, k)),A^2 -> H(U1(k, c), U1(b, k)))
28.54/9.61	   (A^2 -> H(U1(d, e), U1(b, k)),A^2 -> H(U1(d, e), U1(b, k)))
28.54/9.61	   (A^2 -> H(U1(d, k), U1(b, k)),A^2 -> H(U1(d, k), U1(b, k)))
28.54/9.61	   (A^2 -> H(U1(d, c), U1(c, k)),A^2 -> H(U1(d, c), U1(c, k)))
28.54/9.61	   (A^2 -> H(U1(d, c), U1(d, k)),A^2 -> H(U1(d, c), U1(d, k)))
28.54/9.61	
28.54/9.61	
28.54/9.61	----------------------------------------
28.54/9.61	
28.54/9.61	(1258)
28.54/9.61	Obligation:
28.54/9.61	Q DP problem:
28.54/9.61	The TRS P consists of the following rules:
28.54/9.61	
28.54/9.61	   A^2 -> H(f(c), f(c))
28.54/9.61	   H(x, x) -> G(x, x, f(k))
28.54/9.61	   G(d, x, x) -> A^2
28.54/9.61	   A^2 -> H(f(d), f(d))
28.54/9.61	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.61	   A^2 -> H(f(e), f(e))
28.54/9.61	   A^2 -> H(f(k), f(k))
28.54/9.61	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.61	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.61	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.61	   A^2 -> H(U1(d, c), U1(e, c))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.61	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.61	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.61	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.61	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, a), b)
28.54/9.61	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.61	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.61	   A^2 -> H(U1(d, a), c)
28.54/9.61	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.61	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.61	   A^2 -> H(U1(d, a), e)
28.54/9.61	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.61	   A^2 -> H(U1(a, c), b)
28.54/9.61	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.61	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.61	   A^2 -> H(U1(a, c), c)
28.54/9.61	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.61	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.61	   A^2 -> H(U1(a, c), e)
28.54/9.61	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, d), b)
28.54/9.61	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.61	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.61	   A^2 -> H(U1(a, d), c)
28.54/9.61	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.61	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.61	   A^2 -> H(U1(a, d), e)
28.54/9.61	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, a), d)
28.54/9.61	   A^2 -> H(U1(a, a), k)
28.54/9.61	   A^2 -> H(k, U1(b, b))
28.54/9.61	   A^2 -> H(k, f(c))
28.54/9.61	   A^2 -> H(k, f(d))
28.54/9.61	   A^2 -> H(c, U1(c, b))
28.54/9.61	   A^2 -> H(c, U1(d, b))
28.54/9.61	   A^2 -> H(c, U1(b, c))
28.54/9.61	   A^2 -> H(c, U1(b, d))
28.54/9.61	   A^2 -> H(c, U1(c, c))
28.54/9.61	   A^2 -> H(c, f(e))
28.54/9.61	   A^2 -> H(c, f(k))
28.54/9.61	   A^2 -> H(c, U1(d, d))
28.54/9.61	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.61	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.61	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.61	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.61	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.61	   A^2 -> H(U1(e, k), f(e))
28.54/9.61	   A^2 -> H(U1(e, k), f(k))
28.54/9.61	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.61	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.61	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.61	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.61	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.61	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.61	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.61	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.61	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.61	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.61	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.61	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.61	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.61	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.61	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.61	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.61	   A^2 -> H(U1(k, e), f(e))
28.54/9.61	   A^2 -> H(U1(k, e), f(k))
28.54/9.61	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.61	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.61	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.61	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.61	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.61	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.61	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.61	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.61	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.61	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.61	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.61	   A^2 -> H(U1(c, c), b)
28.54/9.61	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.61	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.61	   A^2 -> H(U1(c, c), e)
28.54/9.61	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.61	   A^2 -> H(e, U1(c, b))
28.54/9.61	   A^2 -> H(e, U1(d, b))
28.54/9.61	   A^2 -> H(e, U1(b, c))
28.54/9.61	   A^2 -> H(e, U1(b, d))
28.54/9.61	   A^2 -> H(e, U1(c, c))
28.54/9.61	   A^2 -> H(e, f(e))
28.54/9.61	   A^2 -> H(e, f(k))
28.54/9.61	   A^2 -> H(e, U1(d, d))
28.54/9.61	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.61	   A^2 -> H(f(e), b)
28.54/9.61	   A^2 -> H(f(e), U1(e, d))
28.54/9.61	   A^2 -> H(f(e), U1(d, e))
28.54/9.61	   A^2 -> H(f(e), c)
28.54/9.61	   A^2 -> H(f(e), U1(e, k))
28.54/9.61	   A^2 -> H(f(e), U1(k, e))
28.54/9.61	   A^2 -> H(f(e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.61	   A^2 -> H(f(k), b)
28.54/9.61	   A^2 -> H(f(k), U1(e, d))
28.54/9.61	   A^2 -> H(f(k), U1(d, e))
28.54/9.61	   A^2 -> H(f(k), c)
28.54/9.61	   A^2 -> H(f(k), U1(e, k))
28.54/9.61	   A^2 -> H(f(k), U1(k, e))
28.54/9.61	   A^2 -> H(f(k), e)
28.54/9.61	   A^2 -> H(f(c), d)
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.61	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.61	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.61	   A^2 -> H(U1(k, k), f(e))
28.54/9.61	   A^2 -> H(U1(k, k), f(k))
28.54/9.61	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.61	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.61	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.61	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.61	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.61	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.61	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.61	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.61	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.61	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.61	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, d), b)
28.54/9.61	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.61	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.61	   A^2 -> H(U1(d, d), c)
28.54/9.61	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.61	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.61	   A^2 -> H(U1(d, d), e)
28.54/9.61	   A^2 -> H(f(d), d)
28.54/9.61	   A^2 -> H(f(d), k)
28.54/9.61	   A^2 -> H(U1(c, c), c)
28.54/9.61	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.61	   A^2 -> H(f(c), k)
28.54/9.61	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.61	   A^2 -> H(f(k), U1(k, k))
28.54/9.61	   A^2 -> H(f(e), e)
28.54/9.61	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.61	   A^2 -> H(d, U1(c, b))
28.54/9.61	   A^2 -> H(d, U1(d, b))
28.54/9.61	   A^2 -> H(d, U1(b, c))
28.54/9.61	   A^2 -> H(d, U1(b, d))
28.54/9.61	   A^2 -> H(d, U1(c, c))
28.54/9.61	   A^2 -> H(d, f(e))
28.54/9.61	   A^2 -> H(d, f(k))
28.54/9.61	   A^2 -> H(d, U1(d, d))
28.54/9.61	   A^2 -> H(a, U1(e, b))
28.54/9.61	   A^2 -> H(a, U1(k, b))
28.54/9.61	   A^2 -> H(a, U1(c, d))
28.54/9.61	   A^2 -> H(a, U1(d, c))
28.54/9.61	   A^2 -> H(a, U1(b, e))
28.54/9.61	   A^2 -> H(a, U1(b, k))
28.54/9.61	   A^2 -> H(a, U1(e, c))
28.54/9.61	   A^2 -> H(a, U1(k, c))
28.54/9.61	   A^2 -> H(a, U1(c, e))
28.54/9.61	   A^2 -> H(a, U1(c, k))
28.54/9.61	   A^2 -> H(a, U1(e, e))
28.54/9.61	   A^2 -> H(a, U1(k, k))
28.54/9.61	   A^2 -> H(a, U1(k, d))
28.54/9.61	   A^2 -> H(a, U1(d, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.61	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.61	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.61	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.61	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.61	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.61	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.61	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.61	   A^2 -> H(U1(e, a), b)
28.54/9.61	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.61	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.61	   A^2 -> H(U1(e, a), c)
28.54/9.61	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.61	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.61	   A^2 -> H(U1(e, a), e)
28.54/9.61	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.61	   A^2 -> H(U1(k, a), b)
28.54/9.61	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.61	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.61	   A^2 -> H(U1(k, a), c)
28.54/9.61	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.61	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.61	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, d), b)
28.54/9.61	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.61	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.61	   A^2 -> H(U1(c, d), c)
28.54/9.61	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.61	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.61	   A^2 -> H(U1(c, d), e)
28.54/9.61	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(c, a), d)
28.54/9.61	   A^2 -> H(U1(c, a), k)
28.54/9.61	   A^2 -> H(U1(d, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(d, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(d, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(d, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(d, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(d, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(d, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(d, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(d, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(d, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(d, e), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, c), b)
28.54/9.61	   A^2 -> H(U1(d, c), U1(e, d))
28.54/9.61	   A^2 -> H(U1(d, c), U1(d, e))
28.54/9.61	
28.54/9.61	The TRS R consists of the following rules:
28.54/9.61	
28.54/9.61	   f(x) -> U1(x, x)
28.54/9.61	   U1(e, x) -> x
28.54/9.61	   a -> c
28.54/9.61	   a -> d
28.54/9.61	   b -> c
28.54/9.61	   b -> d
28.54/9.61	   d -> k
28.54/9.61	   c -> e
28.54/9.61	   c -> k
28.54/9.61	
28.54/9.61	Q is empty.
28.54/9.61	We have to consider all minimal (P,Q,R)-chains.
28.54/9.61	----------------------------------------
28.54/9.61	
28.54/9.61	(1259) TransformationProof (EQUIVALENT)
28.54/9.61	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.61	
28.54/9.61	   (A^2 -> H(U1(k, c), U1(e, c)),A^2 -> H(U1(k, c), U1(e, c)))
28.54/9.61	   (A^2 -> H(U1(d, e), U1(e, c)),A^2 -> H(U1(d, e), U1(e, c)))
28.54/9.61	   (A^2 -> H(U1(d, k), U1(e, c)),A^2 -> H(U1(d, k), U1(e, c)))
28.54/9.61	   (A^2 -> H(U1(d, c), c),A^2 -> H(U1(d, c), c))
28.54/9.61	   (A^2 -> H(U1(d, c), U1(e, e)),A^2 -> H(U1(d, c), U1(e, e)))
28.54/9.61	   (A^2 -> H(U1(d, c), U1(e, k)),A^2 -> H(U1(d, c), U1(e, k)))
28.54/9.61	
28.54/9.61	
28.54/9.61	----------------------------------------
28.54/9.61	
28.54/9.61	(1260)
28.54/9.61	Obligation:
28.54/9.61	Q DP problem:
28.54/9.61	The TRS P consists of the following rules:
28.54/9.61	
28.54/9.61	   A^2 -> H(f(c), f(c))
28.54/9.61	   H(x, x) -> G(x, x, f(k))
28.54/9.61	   G(d, x, x) -> A^2
28.54/9.61	   A^2 -> H(f(d), f(d))
28.54/9.61	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.61	   A^2 -> H(f(e), f(e))
28.54/9.61	   A^2 -> H(f(k), f(k))
28.54/9.61	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.61	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.61	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, c))
28.54/9.61	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.61	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.61	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.61	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.61	   A^2 -> H(U1(d, a), b)
28.54/9.61	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.61	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.61	   A^2 -> H(U1(d, a), c)
28.54/9.61	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.61	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.61	   A^2 -> H(U1(d, a), e)
28.54/9.61	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.61	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.61	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.61	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.61	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.61	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.61	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.61	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.61	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.61	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.61	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.61	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.61	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.61	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.61	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.61	   A^2 -> H(U1(a, c), b)
28.54/9.61	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.61	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.61	   A^2 -> H(U1(a, c), c)
28.54/9.61	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.61	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.61	   A^2 -> H(U1(a, c), e)
28.54/9.61	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, d), b)
28.54/9.61	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.61	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.61	   A^2 -> H(U1(a, d), c)
28.54/9.61	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.61	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.61	   A^2 -> H(U1(a, d), e)
28.54/9.61	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.61	   A^2 -> H(U1(a, a), d)
28.54/9.61	   A^2 -> H(U1(a, a), k)
28.54/9.61	   A^2 -> H(k, U1(b, b))
28.54/9.61	   A^2 -> H(k, f(c))
28.54/9.61	   A^2 -> H(k, f(d))
28.54/9.62	   A^2 -> H(c, U1(c, b))
28.54/9.62	   A^2 -> H(c, U1(d, b))
28.54/9.62	   A^2 -> H(c, U1(b, c))
28.54/9.62	   A^2 -> H(c, U1(b, d))
28.54/9.62	   A^2 -> H(c, U1(c, c))
28.54/9.62	   A^2 -> H(c, f(e))
28.54/9.62	   A^2 -> H(c, f(k))
28.54/9.62	   A^2 -> H(c, U1(d, d))
28.54/9.62	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.62	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.62	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.62	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.62	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.62	   A^2 -> H(U1(e, k), f(e))
28.54/9.62	   A^2 -> H(U1(e, k), f(k))
28.54/9.62	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.62	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.62	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.62	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.62	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.62	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.62	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.62	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.62	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.62	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.62	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.62	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.62	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.62	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.62	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.62	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.62	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.62	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.62	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.62	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.62	   A^2 -> H(U1(k, e), f(e))
28.54/9.62	   A^2 -> H(U1(k, e), f(k))
28.54/9.62	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.62	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.62	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.62	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.62	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.62	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.62	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.62	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.62	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.62	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.62	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.62	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.62	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.62	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.62	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.62	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.62	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.62	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.62	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.62	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.62	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.62	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.62	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.62	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.62	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.62	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.62	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.62	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.62	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.62	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.62	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.62	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.62	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.62	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.62	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.62	   A^2 -> H(U1(c, k), U1(e, c))
28.54/9.62	   A^2 -> H(U1(c, k), U1(k, c))
28.54/9.62	   A^2 -> H(U1(c, k), U1(c, e))
28.54/9.62	   A^2 -> H(U1(c, k), U1(c, k))
28.54/9.62	   A^2 -> H(U1(c, k), U1(e, e))
28.54/9.62	   A^2 -> H(U1(c, k), U1(k, k))
28.54/9.62	   A^2 -> H(U1(c, k), U1(k, d))
28.54/9.62	   A^2 -> H(U1(c, k), U1(d, k))
28.54/9.62	   A^2 -> H(U1(c, c), b)
28.54/9.62	   A^2 -> H(U1(c, c), U1(e, d))
28.54/9.62	   A^2 -> H(U1(c, c), U1(d, e))
28.54/9.62	   A^2 -> H(U1(c, c), e)
28.54/9.62	   A^2 -> H(U1(c, c), U1(k, k))
28.54/9.62	   A^2 -> H(e, U1(c, b))
28.54/9.62	   A^2 -> H(e, U1(d, b))
28.54/9.62	   A^2 -> H(e, U1(b, c))
28.54/9.62	   A^2 -> H(e, U1(b, d))
28.54/9.62	   A^2 -> H(e, U1(c, c))
28.54/9.62	   A^2 -> H(e, f(e))
28.54/9.62	   A^2 -> H(e, f(k))
28.54/9.62	   A^2 -> H(e, U1(d, d))
28.54/9.62	   A^2 -> H(U1(e, e), U1(e, b))
28.54/9.62	   A^2 -> H(U1(e, e), U1(k, b))
28.54/9.62	   A^2 -> H(U1(e, e), U1(c, d))
28.54/9.62	   A^2 -> H(U1(e, e), U1(d, c))
28.54/9.62	   A^2 -> H(U1(e, e), U1(b, e))
28.54/9.62	   A^2 -> H(U1(e, e), U1(b, k))
28.54/9.62	   A^2 -> H(U1(e, e), U1(e, c))
28.54/9.62	   A^2 -> H(U1(e, e), U1(k, c))
28.54/9.62	   A^2 -> H(U1(e, e), U1(c, e))
28.54/9.62	   A^2 -> H(U1(e, e), U1(c, k))
28.54/9.62	   A^2 -> H(U1(e, e), U1(e, e))
28.54/9.62	   A^2 -> H(U1(e, e), U1(k, k))
28.54/9.62	   A^2 -> H(U1(e, e), U1(k, d))
28.54/9.62	   A^2 -> H(U1(e, e), U1(d, k))
28.54/9.62	   A^2 -> H(f(e), b)
28.54/9.62	   A^2 -> H(f(e), U1(e, d))
28.54/9.62	   A^2 -> H(f(e), U1(d, e))
28.54/9.62	   A^2 -> H(f(e), c)
28.54/9.62	   A^2 -> H(f(e), U1(e, k))
28.54/9.62	   A^2 -> H(f(e), U1(k, e))
28.54/9.62	   A^2 -> H(f(e), U1(k, k))
28.54/9.62	   A^2 -> H(U1(k, k), U1(e, b))
28.54/9.62	   A^2 -> H(U1(k, k), U1(k, b))
28.54/9.62	   A^2 -> H(U1(k, k), U1(c, d))
28.54/9.62	   A^2 -> H(U1(k, k), U1(d, c))
28.54/9.62	   A^2 -> H(U1(k, k), U1(b, e))
28.54/9.62	   A^2 -> H(U1(k, k), U1(b, k))
28.54/9.62	   A^2 -> H(U1(k, k), U1(e, c))
28.54/9.62	   A^2 -> H(U1(k, k), U1(k, c))
28.54/9.62	   A^2 -> H(U1(k, k), U1(c, e))
28.54/9.62	   A^2 -> H(U1(k, k), U1(c, k))
28.54/9.62	   A^2 -> H(U1(k, k), U1(e, e))
28.54/9.62	   A^2 -> H(U1(k, k), U1(k, k))
28.54/9.62	   A^2 -> H(U1(k, k), U1(k, d))
28.54/9.62	   A^2 -> H(U1(k, k), U1(d, k))
28.54/9.62	   A^2 -> H(f(k), b)
28.54/9.62	   A^2 -> H(f(k), U1(e, d))
28.54/9.62	   A^2 -> H(f(k), U1(d, e))
28.54/9.62	   A^2 -> H(f(k), c)
28.54/9.62	   A^2 -> H(f(k), U1(e, k))
28.54/9.62	   A^2 -> H(f(k), U1(k, e))
28.54/9.62	   A^2 -> H(f(k), e)
28.54/9.62	   A^2 -> H(f(c), d)
28.54/9.62	   A^2 -> H(U1(k, k), U1(c, b))
28.54/9.62	   A^2 -> H(U1(k, k), U1(d, b))
28.54/9.62	   A^2 -> H(U1(k, k), U1(b, c))
28.54/9.62	   A^2 -> H(U1(k, k), U1(b, d))
28.54/9.62	   A^2 -> H(U1(k, k), U1(c, c))
28.54/9.62	   A^2 -> H(U1(k, k), f(e))
28.54/9.62	   A^2 -> H(U1(k, k), f(k))
28.54/9.62	   A^2 -> H(U1(k, k), U1(d, d))
28.54/9.62	   A^2 -> H(U1(k, d), U1(e, b))
28.54/9.62	   A^2 -> H(U1(k, d), U1(k, b))
28.54/9.62	   A^2 -> H(U1(k, d), U1(c, d))
28.54/9.62	   A^2 -> H(U1(k, d), U1(d, c))
28.54/9.62	   A^2 -> H(U1(k, d), U1(b, e))
28.54/9.62	   A^2 -> H(U1(k, d), U1(b, k))
28.54/9.62	   A^2 -> H(U1(k, d), U1(e, c))
28.54/9.62	   A^2 -> H(U1(k, d), U1(k, c))
28.54/9.62	   A^2 -> H(U1(k, d), U1(c, e))
28.54/9.62	   A^2 -> H(U1(k, d), U1(c, k))
28.54/9.62	   A^2 -> H(U1(k, d), U1(e, e))
28.54/9.62	   A^2 -> H(U1(k, d), U1(k, k))
28.54/9.62	   A^2 -> H(U1(k, d), U1(k, d))
28.54/9.62	   A^2 -> H(U1(k, d), U1(d, k))
28.54/9.62	   A^2 -> H(U1(d, k), U1(e, b))
28.54/9.62	   A^2 -> H(U1(d, k), U1(k, b))
28.54/9.62	   A^2 -> H(U1(d, k), U1(c, d))
28.54/9.62	   A^2 -> H(U1(d, k), U1(d, c))
28.54/9.62	   A^2 -> H(U1(d, k), U1(b, e))
28.54/9.62	   A^2 -> H(U1(d, k), U1(b, k))
28.54/9.62	   A^2 -> H(U1(d, k), U1(e, c))
28.54/9.62	   A^2 -> H(U1(d, k), U1(k, c))
28.54/9.62	   A^2 -> H(U1(d, k), U1(c, e))
28.54/9.62	   A^2 -> H(U1(d, k), U1(c, k))
28.54/9.62	   A^2 -> H(U1(d, k), U1(e, e))
28.54/9.62	   A^2 -> H(U1(d, k), U1(k, k))
28.54/9.62	   A^2 -> H(U1(d, k), U1(k, d))
28.54/9.62	   A^2 -> H(U1(d, k), U1(d, k))
28.54/9.62	   A^2 -> H(U1(d, d), b)
28.54/9.62	   A^2 -> H(U1(d, d), U1(e, d))
28.54/9.62	   A^2 -> H(U1(d, d), U1(d, e))
28.54/9.62	   A^2 -> H(U1(d, d), c)
28.54/9.62	   A^2 -> H(U1(d, d), U1(e, k))
28.54/9.62	   A^2 -> H(U1(d, d), U1(k, e))
28.54/9.62	   A^2 -> H(U1(d, d), e)
28.54/9.62	   A^2 -> H(f(d), d)
28.54/9.62	   A^2 -> H(f(d), k)
28.54/9.62	   A^2 -> H(U1(c, c), c)
28.54/9.62	   A^2 -> H(U1(c, c), U1(e, e))
28.54/9.62	   A^2 -> H(U1(c, c), U1(e, k))
28.54/9.62	   A^2 -> H(f(c), k)
28.54/9.62	   A^2 -> H(U1(c, c), U1(k, e))
28.54/9.62	   A^2 -> H(f(k), U1(k, k))
28.54/9.62	   A^2 -> H(f(e), e)
28.54/9.62	   A^2 -> H(U1(d, d), U1(k, k))
28.54/9.62	   A^2 -> H(d, U1(c, b))
28.54/9.62	   A^2 -> H(d, U1(d, b))
28.54/9.62	   A^2 -> H(d, U1(b, c))
28.54/9.62	   A^2 -> H(d, U1(b, d))
28.54/9.62	   A^2 -> H(d, U1(c, c))
28.54/9.62	   A^2 -> H(d, f(e))
28.54/9.62	   A^2 -> H(d, f(k))
28.54/9.62	   A^2 -> H(d, U1(d, d))
28.54/9.62	   A^2 -> H(a, U1(e, b))
28.54/9.62	   A^2 -> H(a, U1(k, b))
28.54/9.62	   A^2 -> H(a, U1(c, d))
28.54/9.62	   A^2 -> H(a, U1(d, c))
28.54/9.62	   A^2 -> H(a, U1(b, e))
28.54/9.62	   A^2 -> H(a, U1(b, k))
28.54/9.62	   A^2 -> H(a, U1(e, c))
28.54/9.62	   A^2 -> H(a, U1(k, c))
28.54/9.62	   A^2 -> H(a, U1(c, e))
28.54/9.62	   A^2 -> H(a, U1(c, k))
28.54/9.62	   A^2 -> H(a, U1(e, e))
28.54/9.62	   A^2 -> H(a, U1(k, k))
28.54/9.62	   A^2 -> H(a, U1(k, d))
28.54/9.62	   A^2 -> H(a, U1(d, k))
28.54/9.62	   A^2 -> H(U1(e, d), U1(e, b))
28.54/9.62	   A^2 -> H(U1(e, d), U1(k, b))
28.54/9.62	   A^2 -> H(U1(e, d), U1(c, d))
28.54/9.62	   A^2 -> H(U1(e, d), U1(d, c))
28.54/9.62	   A^2 -> H(U1(e, d), U1(b, e))
28.54/9.62	   A^2 -> H(U1(e, d), U1(b, k))
28.54/9.62	   A^2 -> H(U1(e, d), U1(e, c))
28.54/9.62	   A^2 -> H(U1(e, d), U1(k, c))
28.54/9.62	   A^2 -> H(U1(e, d), U1(c, e))
28.54/9.62	   A^2 -> H(U1(e, d), U1(c, k))
28.54/9.62	   A^2 -> H(U1(e, d), U1(e, e))
28.54/9.62	   A^2 -> H(U1(e, d), U1(k, k))
28.54/9.62	   A^2 -> H(U1(e, d), U1(k, d))
28.54/9.62	   A^2 -> H(U1(e, d), U1(d, k))
28.54/9.62	   A^2 -> H(U1(e, a), b)
28.54/9.62	   A^2 -> H(U1(e, a), U1(e, d))
28.54/9.62	   A^2 -> H(U1(e, a), U1(d, e))
28.54/9.62	   A^2 -> H(U1(e, a), c)
28.54/9.62	   A^2 -> H(U1(e, a), U1(e, k))
28.54/9.62	   A^2 -> H(U1(e, a), U1(k, e))
28.54/9.62	   A^2 -> H(U1(e, a), e)
28.54/9.62	   A^2 -> H(U1(e, a), U1(k, k))
28.54/9.62	   A^2 -> H(U1(k, a), b)
28.54/9.62	   A^2 -> H(U1(k, a), U1(e, d))
28.54/9.62	   A^2 -> H(U1(k, a), U1(d, e))
28.54/9.62	   A^2 -> H(U1(k, a), c)
28.54/9.62	   A^2 -> H(U1(k, a), U1(e, k))
28.54/9.62	   A^2 -> H(U1(k, a), U1(k, e))
28.54/9.62	   A^2 -> H(U1(k, a), U1(k, k))
28.54/9.62	   A^2 -> H(U1(c, d), b)
28.54/9.62	   A^2 -> H(U1(c, d), U1(e, d))
28.54/9.62	   A^2 -> H(U1(c, d), U1(d, e))
28.54/9.62	   A^2 -> H(U1(c, d), c)
28.54/9.62	   A^2 -> H(U1(c, d), U1(e, k))
28.54/9.62	   A^2 -> H(U1(c, d), U1(k, e))
28.54/9.62	   A^2 -> H(U1(c, d), e)
28.54/9.62	   A^2 -> H(U1(c, d), U1(k, k))
28.54/9.62	   A^2 -> H(U1(c, a), d)
28.54/9.62	   A^2 -> H(U1(c, a), k)
28.54/9.62	   A^2 -> H(U1(d, e), U1(e, b))
28.54/9.62	   A^2 -> H(U1(d, e), U1(k, b))
28.54/9.62	   A^2 -> H(U1(d, e), U1(c, d))
28.54/9.62	   A^2 -> H(U1(d, e), U1(d, c))
28.54/9.62	   A^2 -> H(U1(d, e), U1(b, e))
28.54/9.62	   A^2 -> H(U1(d, e), U1(b, k))
28.54/9.62	   A^2 -> H(U1(d, e), U1(e, c))
28.54/9.62	   A^2 -> H(U1(d, e), U1(k, c))
28.54/9.62	   A^2 -> H(U1(d, e), U1(c, e))
28.54/9.62	   A^2 -> H(U1(d, e), U1(c, k))
28.54/9.62	   A^2 -> H(U1(d, e), U1(e, e))
28.54/9.62	   A^2 -> H(U1(d, e), U1(k, k))
28.54/9.62	   A^2 -> H(U1(d, e), U1(k, d))
28.54/9.62	   A^2 -> H(U1(d, e), U1(d, k))
28.54/9.62	   A^2 -> H(U1(d, c), b)
28.54/9.62	   A^2 -> H(U1(d, c), U1(e, d))
28.54/9.62	   A^2 -> H(U1(d, c), U1(d, e))
28.54/9.62	   A^2 -> H(U1(d, c), c)
28.54/9.62	   A^2 -> H(U1(d, c), U1(e, k))
28.54/9.62	
28.54/9.62	The TRS R consists of the following rules:
28.54/9.62	
28.54/9.62	   f(x) -> U1(x, x)
28.54/9.62	   U1(e, x) -> x
28.54/9.62	   a -> c
28.54/9.62	   a -> d
28.54/9.62	   b -> c
28.54/9.62	   b -> d
28.54/9.62	   d -> k
28.54/9.62	   c -> e
28.54/9.62	   c -> k
28.54/9.62	
28.54/9.62	Q is empty.
28.54/9.62	We have to consider all minimal (P,Q,R)-chains.
28.54/9.62	----------------------------------------
28.54/9.62	
28.54/9.62	(1261) TransformationProof (EQUIVALENT)
28.54/9.62	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.54/9.62	
28.54/9.62	   (A^2 -> H(U1(k, c), U1(k, c)),A^2 -> H(U1(k, c), U1(k, c)))
28.54/9.62	   (A^2 -> H(U1(d, e), U1(k, c)),A^2 -> H(U1(d, e), U1(k, c)))
28.54/9.62	   (A^2 -> H(U1(d, k), U1(k, c)),A^2 -> H(U1(d, k), U1(k, c)))
28.54/9.62	   (A^2 -> H(U1(d, c), U1(k, e)),A^2 -> H(U1(d, c), U1(k, e)))
28.54/9.62	   (A^2 -> H(U1(d, c), U1(k, k)),A^2 -> H(U1(d, c), U1(k, k)))
28.54/9.62	
28.54/9.62	
28.54/9.62	----------------------------------------
28.54/9.62	
28.54/9.62	(1262)
28.54/9.62	Obligation:
28.54/9.62	Q DP problem:
28.54/9.62	The TRS P consists of the following rules:
28.54/9.62	
28.54/9.62	   A^2 -> H(f(c), f(c))
28.54/9.62	   H(x, x) -> G(x, x, f(k))
28.54/9.62	   G(d, x, x) -> A^2
28.54/9.62	   A^2 -> H(f(d), f(d))
28.54/9.62	   A^2 -> H(U1(c, c), U1(c, c))
28.54/9.62	   A^2 -> H(f(e), f(e))
28.54/9.62	   A^2 -> H(f(k), f(k))
28.54/9.62	   A^2 -> H(U1(d, d), U1(d, d))
28.54/9.62	   A^2 -> H(U1(c, d), U1(c, d))
28.54/9.62	   A^2 -> H(U1(d, c), U1(d, c))
28.54/9.62	   A^2 -> H(U1(d, c), U1(c, e))
28.54/9.62	   A^2 -> H(U1(d, c), U1(c, k))
28.54/9.62	   A^2 -> H(U1(d, c), U1(e, e))
28.54/9.62	   A^2 -> H(U1(d, c), U1(k, k))
28.54/9.62	   A^2 -> H(U1(d, c), U1(k, d))
28.54/9.62	   A^2 -> H(U1(d, c), U1(d, k))
28.54/9.62	   A^2 -> H(U1(d, a), b)
28.54/9.62	   A^2 -> H(U1(d, a), U1(e, d))
28.54/9.62	   A^2 -> H(U1(d, a), U1(d, e))
28.54/9.62	   A^2 -> H(U1(d, a), c)
28.54/9.62	   A^2 -> H(U1(d, a), U1(e, k))
28.54/9.62	   A^2 -> H(U1(d, a), U1(k, e))
28.54/9.62	   A^2 -> H(U1(d, a), e)
28.54/9.62	   A^2 -> H(U1(d, a), U1(k, k))
28.54/9.62	   A^2 -> H(U1(a, e), U1(e, b))
28.54/9.62	   A^2 -> H(U1(a, e), U1(k, b))
28.54/9.62	   A^2 -> H(U1(a, e), U1(c, d))
28.54/9.62	   A^2 -> H(U1(a, e), U1(d, c))
28.54/9.62	   A^2 -> H(U1(a, e), U1(b, e))
28.54/9.62	   A^2 -> H(U1(a, e), U1(b, k))
28.54/9.62	   A^2 -> H(U1(a, e), U1(e, c))
28.54/9.62	   A^2 -> H(U1(a, e), U1(k, c))
28.54/9.62	   A^2 -> H(U1(a, e), U1(c, e))
28.54/9.62	   A^2 -> H(U1(a, e), U1(c, k))
28.54/9.62	   A^2 -> H(U1(a, e), U1(e, e))
28.54/9.62	   A^2 -> H(U1(a, e), U1(k, k))
28.54/9.62	   A^2 -> H(U1(a, e), U1(k, d))
28.54/9.62	   A^2 -> H(U1(a, e), U1(d, k))
28.54/9.62	   A^2 -> H(U1(a, k), U1(e, b))
28.54/9.62	   A^2 -> H(U1(a, k), U1(k, b))
28.54/9.62	   A^2 -> H(U1(a, k), U1(c, d))
28.54/9.62	   A^2 -> H(U1(a, k), U1(d, c))
28.54/9.62	   A^2 -> H(U1(a, k), U1(b, e))
28.54/9.62	   A^2 -> H(U1(a, k), U1(b, k))
28.54/9.62	   A^2 -> H(U1(a, k), U1(e, c))
28.54/9.62	   A^2 -> H(U1(a, k), U1(k, c))
28.54/9.62	   A^2 -> H(U1(a, k), U1(c, e))
28.54/9.62	   A^2 -> H(U1(a, k), U1(c, k))
28.54/9.62	   A^2 -> H(U1(a, k), U1(e, e))
28.54/9.62	   A^2 -> H(U1(a, k), U1(k, k))
28.54/9.62	   A^2 -> H(U1(a, k), U1(k, d))
28.54/9.62	   A^2 -> H(U1(a, k), U1(d, k))
28.54/9.62	   A^2 -> H(U1(a, c), b)
28.54/9.62	   A^2 -> H(U1(a, c), U1(e, d))
28.54/9.62	   A^2 -> H(U1(a, c), U1(d, e))
28.54/9.62	   A^2 -> H(U1(a, c), c)
28.54/9.62	   A^2 -> H(U1(a, c), U1(e, k))
28.54/9.62	   A^2 -> H(U1(a, c), U1(k, e))
28.54/9.62	   A^2 -> H(U1(a, c), e)
28.54/9.62	   A^2 -> H(U1(a, c), U1(k, k))
28.54/9.62	   A^2 -> H(U1(a, d), b)
28.54/9.62	   A^2 -> H(U1(a, d), U1(e, d))
28.54/9.62	   A^2 -> H(U1(a, d), U1(d, e))
28.54/9.62	   A^2 -> H(U1(a, d), c)
28.54/9.62	   A^2 -> H(U1(a, d), U1(e, k))
28.54/9.62	   A^2 -> H(U1(a, d), U1(k, e))
28.54/9.62	   A^2 -> H(U1(a, d), e)
28.54/9.62	   A^2 -> H(U1(a, d), U1(k, k))
28.54/9.62	   A^2 -> H(U1(a, a), d)
28.54/9.62	   A^2 -> H(U1(a, a), k)
28.54/9.62	   A^2 -> H(k, U1(b, b))
28.54/9.62	   A^2 -> H(k, f(c))
28.54/9.62	   A^2 -> H(k, f(d))
28.54/9.62	   A^2 -> H(c, U1(c, b))
28.54/9.62	   A^2 -> H(c, U1(d, b))
28.54/9.62	   A^2 -> H(c, U1(b, c))
28.54/9.62	   A^2 -> H(c, U1(b, d))
28.54/9.62	   A^2 -> H(c, U1(c, c))
28.54/9.62	   A^2 -> H(c, f(e))
28.54/9.62	   A^2 -> H(c, f(k))
28.54/9.62	   A^2 -> H(c, U1(d, d))
28.54/9.62	   A^2 -> H(U1(e, k), U1(c, b))
28.54/9.62	   A^2 -> H(U1(e, k), U1(d, b))
28.54/9.62	   A^2 -> H(U1(e, k), U1(b, c))
28.54/9.62	   A^2 -> H(U1(e, k), U1(b, d))
28.54/9.62	   A^2 -> H(U1(e, k), U1(c, c))
28.54/9.62	   A^2 -> H(U1(e, k), f(e))
28.54/9.62	   A^2 -> H(U1(e, k), f(k))
28.54/9.62	   A^2 -> H(U1(e, k), U1(d, d))
28.54/9.62	   A^2 -> H(U1(e, c), U1(e, b))
28.54/9.62	   A^2 -> H(U1(e, c), U1(k, b))
28.54/9.62	   A^2 -> H(U1(e, c), U1(c, d))
28.54/9.62	   A^2 -> H(U1(e, c), U1(d, c))
28.54/9.62	   A^2 -> H(U1(e, c), U1(b, e))
28.54/9.62	   A^2 -> H(U1(e, c), U1(b, k))
28.54/9.62	   A^2 -> H(U1(e, c), U1(e, c))
28.54/9.62	   A^2 -> H(U1(e, c), U1(k, c))
28.54/9.62	   A^2 -> H(U1(e, c), U1(c, e))
28.54/9.62	   A^2 -> H(U1(e, c), U1(c, k))
28.54/9.62	   A^2 -> H(U1(e, c), U1(e, e))
28.54/9.62	   A^2 -> H(U1(e, c), U1(k, k))
28.54/9.62	   A^2 -> H(U1(e, c), U1(k, d))
28.54/9.62	   A^2 -> H(U1(e, c), U1(d, k))
28.54/9.62	   A^2 -> H(U1(k, e), U1(c, b))
28.54/9.62	   A^2 -> H(U1(k, e), U1(d, b))
28.54/9.62	   A^2 -> H(U1(k, e), U1(b, c))
28.54/9.62	   A^2 -> H(U1(k, e), U1(b, d))
28.54/9.62	   A^2 -> H(U1(k, e), U1(c, c))
28.54/9.62	   A^2 -> H(U1(k, e), f(e))
28.54/9.62	   A^2 -> H(U1(k, e), f(k))
28.54/9.62	   A^2 -> H(U1(k, e), U1(d, d))
28.54/9.62	   A^2 -> H(U1(k, c), U1(e, b))
28.54/9.62	   A^2 -> H(U1(k, c), U1(k, b))
28.54/9.62	   A^2 -> H(U1(k, c), U1(c, d))
28.54/9.62	   A^2 -> H(U1(k, c), U1(d, c))
28.54/9.62	   A^2 -> H(U1(k, c), U1(b, e))
28.54/9.62	   A^2 -> H(U1(k, c), U1(b, k))
28.54/9.62	   A^2 -> H(U1(k, c), U1(e, c))
28.54/9.62	   A^2 -> H(U1(k, c), U1(k, c))
28.54/9.62	   A^2 -> H(U1(k, c), U1(c, e))
28.54/9.62	   A^2 -> H(U1(k, c), U1(c, k))
28.54/9.62	   A^2 -> H(U1(k, c), U1(e, e))
28.54/9.62	   A^2 -> H(U1(k, c), U1(k, k))
28.54/9.62	   A^2 -> H(U1(k, c), U1(k, d))
28.54/9.62	   A^2 -> H(U1(k, c), U1(d, k))
28.54/9.62	   A^2 -> H(U1(c, e), U1(e, b))
28.54/9.62	   A^2 -> H(U1(c, e), U1(k, b))
28.54/9.62	   A^2 -> H(U1(c, e), U1(c, d))
28.54/9.62	   A^2 -> H(U1(c, e), U1(d, c))
28.54/9.62	   A^2 -> H(U1(c, e), U1(b, e))
28.54/9.62	   A^2 -> H(U1(c, e), U1(b, k))
28.54/9.62	   A^2 -> H(U1(c, e), U1(e, c))
28.54/9.62	   A^2 -> H(U1(c, e), U1(k, c))
28.54/9.62	   A^2 -> H(U1(c, e), U1(c, e))
28.54/9.62	   A^2 -> H(U1(c, e), U1(c, k))
28.54/9.62	   A^2 -> H(U1(c, e), U1(e, e))
28.54/9.62	   A^2 -> H(U1(c, e), U1(k, k))
28.54/9.62	   A^2 -> H(U1(c, e), U1(k, d))
28.54/9.62	   A^2 -> H(U1(c, e), U1(d, k))
28.54/9.62	   A^2 -> H(U1(c, k), U1(e, b))
28.54/9.62	   A^2 -> H(U1(c, k), U1(k, b))
28.54/9.62	   A^2 -> H(U1(c, k), U1(c, d))
28.54/9.62	   A^2 -> H(U1(c, k), U1(d, c))
28.54/9.62	   A^2 -> H(U1(c, k), U1(b, e))
28.54/9.62	   A^2 -> H(U1(c, k), U1(b, k))
28.54/9.62	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.62	   A^2 -> H(U1(c, c), b)
28.55/9.62	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.62	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.62	   A^2 -> H(U1(c, c), e)
28.55/9.62	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.62	   A^2 -> H(e, U1(c, b))
28.55/9.62	   A^2 -> H(e, U1(d, b))
28.55/9.62	   A^2 -> H(e, U1(b, c))
28.55/9.62	   A^2 -> H(e, U1(b, d))
28.55/9.62	   A^2 -> H(e, U1(c, c))
28.55/9.62	   A^2 -> H(e, f(e))
28.55/9.62	   A^2 -> H(e, f(k))
28.55/9.62	   A^2 -> H(e, U1(d, d))
28.55/9.62	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.62	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.62	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.62	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.62	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.62	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.62	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.62	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.62	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.62	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.62	   A^2 -> H(f(e), b)
28.55/9.62	   A^2 -> H(f(e), U1(e, d))
28.55/9.62	   A^2 -> H(f(e), U1(d, e))
28.55/9.62	   A^2 -> H(f(e), c)
28.55/9.62	   A^2 -> H(f(e), U1(e, k))
28.55/9.62	   A^2 -> H(f(e), U1(k, e))
28.55/9.62	   A^2 -> H(f(e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.62	   A^2 -> H(f(k), b)
28.55/9.62	   A^2 -> H(f(k), U1(e, d))
28.55/9.62	   A^2 -> H(f(k), U1(d, e))
28.55/9.62	   A^2 -> H(f(k), c)
28.55/9.62	   A^2 -> H(f(k), U1(e, k))
28.55/9.62	   A^2 -> H(f(k), U1(k, e))
28.55/9.62	   A^2 -> H(f(k), e)
28.55/9.62	   A^2 -> H(f(c), d)
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.62	   A^2 -> H(U1(k, k), f(e))
28.55/9.62	   A^2 -> H(U1(k, k), f(k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.62	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.62	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.62	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.62	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.62	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.62	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.62	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.62	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.62	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.62	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.62	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.62	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.62	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.62	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.62	   A^2 -> H(U1(d, d), b)
28.55/9.62	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.62	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.62	   A^2 -> H(U1(d, d), c)
28.55/9.62	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.62	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.62	   A^2 -> H(U1(d, d), e)
28.55/9.62	   A^2 -> H(f(d), d)
28.55/9.62	   A^2 -> H(f(d), k)
28.55/9.62	   A^2 -> H(U1(c, c), c)
28.55/9.62	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.62	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.62	   A^2 -> H(f(c), k)
28.55/9.62	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.62	   A^2 -> H(f(k), U1(k, k))
28.55/9.62	   A^2 -> H(f(e), e)
28.55/9.62	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.62	   A^2 -> H(d, U1(c, b))
28.55/9.62	   A^2 -> H(d, U1(d, b))
28.55/9.62	   A^2 -> H(d, U1(b, c))
28.55/9.62	   A^2 -> H(d, U1(b, d))
28.55/9.62	   A^2 -> H(d, U1(c, c))
28.55/9.62	   A^2 -> H(d, f(e))
28.55/9.62	   A^2 -> H(d, f(k))
28.55/9.62	   A^2 -> H(d, U1(d, d))
28.55/9.62	   A^2 -> H(a, U1(e, b))
28.55/9.62	   A^2 -> H(a, U1(k, b))
28.55/9.62	   A^2 -> H(a, U1(c, d))
28.55/9.62	   A^2 -> H(a, U1(d, c))
28.55/9.62	   A^2 -> H(a, U1(b, e))
28.55/9.62	   A^2 -> H(a, U1(b, k))
28.55/9.62	   A^2 -> H(a, U1(e, c))
28.55/9.62	   A^2 -> H(a, U1(k, c))
28.55/9.62	   A^2 -> H(a, U1(c, e))
28.55/9.62	   A^2 -> H(a, U1(c, k))
28.55/9.62	   A^2 -> H(a, U1(e, e))
28.55/9.62	   A^2 -> H(a, U1(k, k))
28.55/9.62	   A^2 -> H(a, U1(k, d))
28.55/9.62	   A^2 -> H(a, U1(d, k))
28.55/9.62	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.62	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.62	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.62	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.62	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.62	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.62	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.62	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.62	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.62	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.62	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.62	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.62	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.62	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.62	   A^2 -> H(U1(e, a), b)
28.55/9.62	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.62	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.62	   A^2 -> H(U1(e, a), c)
28.55/9.62	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.62	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.62	   A^2 -> H(U1(e, a), e)
28.55/9.62	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, a), b)
28.55/9.62	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.62	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.62	   A^2 -> H(U1(k, a), c)
28.55/9.62	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.62	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.62	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.62	   A^2 -> H(U1(c, d), b)
28.55/9.62	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.62	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.62	   A^2 -> H(U1(c, d), c)
28.55/9.62	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.62	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.62	   A^2 -> H(U1(c, d), e)
28.55/9.62	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.62	   A^2 -> H(U1(c, a), d)
28.55/9.62	   A^2 -> H(U1(c, a), k)
28.55/9.62	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.62	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.62	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.62	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.62	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.62	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.62	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.62	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.62	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.62	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.62	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.62	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.62	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.62	   A^2 -> H(U1(d, c), b)
28.55/9.62	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.62	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.62	   A^2 -> H(U1(d, c), c)
28.55/9.62	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.62	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.62	
28.55/9.62	The TRS R consists of the following rules:
28.55/9.62	
28.55/9.62	   f(x) -> U1(x, x)
28.55/9.62	   U1(e, x) -> x
28.55/9.62	   a -> c
28.55/9.62	   a -> d
28.55/9.62	   b -> c
28.55/9.62	   b -> d
28.55/9.62	   d -> k
28.55/9.62	   c -> e
28.55/9.62	   c -> k
28.55/9.62	
28.55/9.62	Q is empty.
28.55/9.62	We have to consider all minimal (P,Q,R)-chains.
28.55/9.62	----------------------------------------
28.55/9.62	
28.55/9.62	(1263) TransformationProof (EQUIVALENT)
28.55/9.62	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.62	
28.55/9.62	   (A^2 -> H(U1(k, c), U1(c, e)),A^2 -> H(U1(k, c), U1(c, e)))
28.55/9.62	   (A^2 -> H(U1(d, e), U1(c, e)),A^2 -> H(U1(d, e), U1(c, e)))
28.55/9.62	   (A^2 -> H(U1(d, k), U1(c, e)),A^2 -> H(U1(d, k), U1(c, e)))
28.55/9.62	   (A^2 -> H(U1(d, c), U1(e, e)),A^2 -> H(U1(d, c), U1(e, e)))
28.55/9.62	   (A^2 -> H(U1(d, c), U1(k, e)),A^2 -> H(U1(d, c), U1(k, e)))
28.55/9.62	
28.55/9.62	
28.55/9.62	----------------------------------------
28.55/9.62	
28.55/9.62	(1264)
28.55/9.62	Obligation:
28.55/9.62	Q DP problem:
28.55/9.62	The TRS P consists of the following rules:
28.55/9.62	
28.55/9.62	   A^2 -> H(f(c), f(c))
28.55/9.62	   H(x, x) -> G(x, x, f(k))
28.55/9.62	   G(d, x, x) -> A^2
28.55/9.62	   A^2 -> H(f(d), f(d))
28.55/9.62	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.62	   A^2 -> H(f(e), f(e))
28.55/9.62	   A^2 -> H(f(k), f(k))
28.55/9.62	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.62	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.62	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.62	   A^2 -> H(U1(d, c), U1(c, k))
28.55/9.62	   A^2 -> H(U1(d, c), U1(e, e))
28.55/9.62	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.62	   A^2 -> H(U1(d, c), U1(k, d))
28.55/9.62	   A^2 -> H(U1(d, c), U1(d, k))
28.55/9.62	   A^2 -> H(U1(d, a), b)
28.55/9.62	   A^2 -> H(U1(d, a), U1(e, d))
28.55/9.62	   A^2 -> H(U1(d, a), U1(d, e))
28.55/9.62	   A^2 -> H(U1(d, a), c)
28.55/9.62	   A^2 -> H(U1(d, a), U1(e, k))
28.55/9.62	   A^2 -> H(U1(d, a), U1(k, e))
28.55/9.62	   A^2 -> H(U1(d, a), e)
28.55/9.62	   A^2 -> H(U1(d, a), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, e), U1(e, b))
28.55/9.62	   A^2 -> H(U1(a, e), U1(k, b))
28.55/9.62	   A^2 -> H(U1(a, e), U1(c, d))
28.55/9.62	   A^2 -> H(U1(a, e), U1(d, c))
28.55/9.62	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.62	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.62	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.62	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.62	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.62	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.62	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.62	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.62	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.62	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.62	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.62	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.62	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.62	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.62	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.62	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.62	   A^2 -> H(U1(a, c), b)
28.55/9.62	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.62	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.62	   A^2 -> H(U1(a, c), c)
28.55/9.62	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.62	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.62	   A^2 -> H(U1(a, c), e)
28.55/9.62	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, d), b)
28.55/9.62	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.62	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.62	   A^2 -> H(U1(a, d), c)
28.55/9.62	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.62	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.62	   A^2 -> H(U1(a, d), e)
28.55/9.62	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, a), d)
28.55/9.62	   A^2 -> H(U1(a, a), k)
28.55/9.62	   A^2 -> H(k, U1(b, b))
28.55/9.62	   A^2 -> H(k, f(c))
28.55/9.62	   A^2 -> H(k, f(d))
28.55/9.62	   A^2 -> H(c, U1(c, b))
28.55/9.62	   A^2 -> H(c, U1(d, b))
28.55/9.62	   A^2 -> H(c, U1(b, c))
28.55/9.62	   A^2 -> H(c, U1(b, d))
28.55/9.62	   A^2 -> H(c, U1(c, c))
28.55/9.62	   A^2 -> H(c, f(e))
28.55/9.62	   A^2 -> H(c, f(k))
28.55/9.62	   A^2 -> H(c, U1(d, d))
28.55/9.62	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.62	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.62	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.62	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.62	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.62	   A^2 -> H(U1(e, k), f(e))
28.55/9.62	   A^2 -> H(U1(e, k), f(k))
28.55/9.62	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.62	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.62	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.62	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.62	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.62	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.62	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.62	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.62	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.62	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.62	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.62	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.62	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.62	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.62	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.62	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.62	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.62	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.62	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.62	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.62	   A^2 -> H(U1(k, e), f(e))
28.55/9.62	   A^2 -> H(U1(k, e), f(k))
28.55/9.62	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.62	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.62	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.62	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.62	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.62	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.62	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.62	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.62	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.62	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.62	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.62	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.62	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.62	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.62	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.62	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.62	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.62	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.62	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.62	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.62	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.62	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.62	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.62	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.62	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.62	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.62	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.62	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.62	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.62	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.62	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.62	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.62	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.62	   A^2 -> H(U1(c, c), b)
28.55/9.62	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.62	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.62	   A^2 -> H(U1(c, c), e)
28.55/9.62	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.62	   A^2 -> H(e, U1(c, b))
28.55/9.62	   A^2 -> H(e, U1(d, b))
28.55/9.62	   A^2 -> H(e, U1(b, c))
28.55/9.62	   A^2 -> H(e, U1(b, d))
28.55/9.62	   A^2 -> H(e, U1(c, c))
28.55/9.62	   A^2 -> H(e, f(e))
28.55/9.62	   A^2 -> H(e, f(k))
28.55/9.62	   A^2 -> H(e, U1(d, d))
28.55/9.62	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.62	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.62	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.62	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.62	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.62	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.62	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.62	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.62	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.62	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.62	   A^2 -> H(f(e), b)
28.55/9.62	   A^2 -> H(f(e), U1(e, d))
28.55/9.62	   A^2 -> H(f(e), U1(d, e))
28.55/9.62	   A^2 -> H(f(e), c)
28.55/9.62	   A^2 -> H(f(e), U1(e, k))
28.55/9.62	   A^2 -> H(f(e), U1(k, e))
28.55/9.62	   A^2 -> H(f(e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.62	   A^2 -> H(f(k), b)
28.55/9.62	   A^2 -> H(f(k), U1(e, d))
28.55/9.62	   A^2 -> H(f(k), U1(d, e))
28.55/9.62	   A^2 -> H(f(k), c)
28.55/9.62	   A^2 -> H(f(k), U1(e, k))
28.55/9.62	   A^2 -> H(f(k), U1(k, e))
28.55/9.62	   A^2 -> H(f(k), e)
28.55/9.62	   A^2 -> H(f(c), d)
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.62	   A^2 -> H(U1(k, k), f(e))
28.55/9.62	   A^2 -> H(U1(k, k), f(k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.62	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.62	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.62	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.62	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.62	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.62	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.62	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.62	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.62	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.62	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.62	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.62	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.62	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.62	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.62	   A^2 -> H(U1(d, d), b)
28.55/9.62	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.62	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.62	   A^2 -> H(U1(d, d), c)
28.55/9.62	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.62	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.62	   A^2 -> H(U1(d, d), e)
28.55/9.62	   A^2 -> H(f(d), d)
28.55/9.62	   A^2 -> H(f(d), k)
28.55/9.62	   A^2 -> H(U1(c, c), c)
28.55/9.62	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.62	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.62	   A^2 -> H(f(c), k)
28.55/9.62	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.62	   A^2 -> H(f(k), U1(k, k))
28.55/9.62	   A^2 -> H(f(e), e)
28.55/9.62	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.62	   A^2 -> H(d, U1(c, b))
28.55/9.62	   A^2 -> H(d, U1(d, b))
28.55/9.62	   A^2 -> H(d, U1(b, c))
28.55/9.62	   A^2 -> H(d, U1(b, d))
28.55/9.62	   A^2 -> H(d, U1(c, c))
28.55/9.62	   A^2 -> H(d, f(e))
28.55/9.62	   A^2 -> H(d, f(k))
28.55/9.62	   A^2 -> H(d, U1(d, d))
28.55/9.62	   A^2 -> H(a, U1(e, b))
28.55/9.62	   A^2 -> H(a, U1(k, b))
28.55/9.62	   A^2 -> H(a, U1(c, d))
28.55/9.62	   A^2 -> H(a, U1(d, c))
28.55/9.62	   A^2 -> H(a, U1(b, e))
28.55/9.62	   A^2 -> H(a, U1(b, k))
28.55/9.62	   A^2 -> H(a, U1(e, c))
28.55/9.62	   A^2 -> H(a, U1(k, c))
28.55/9.62	   A^2 -> H(a, U1(c, e))
28.55/9.62	   A^2 -> H(a, U1(c, k))
28.55/9.62	   A^2 -> H(a, U1(e, e))
28.55/9.62	   A^2 -> H(a, U1(k, k))
28.55/9.62	   A^2 -> H(a, U1(k, d))
28.55/9.62	   A^2 -> H(a, U1(d, k))
28.55/9.62	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.62	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.62	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.62	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.62	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.62	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.62	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.62	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.62	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.62	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.62	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.62	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.62	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.62	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.62	   A^2 -> H(U1(e, a), b)
28.55/9.62	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.62	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.62	   A^2 -> H(U1(e, a), c)
28.55/9.62	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.62	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.62	   A^2 -> H(U1(e, a), e)
28.55/9.62	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, a), b)
28.55/9.62	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.62	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.62	   A^2 -> H(U1(k, a), c)
28.55/9.62	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.62	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.62	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.62	   A^2 -> H(U1(c, d), b)
28.55/9.62	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.62	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.62	   A^2 -> H(U1(c, d), c)
28.55/9.62	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.62	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.62	   A^2 -> H(U1(c, d), e)
28.55/9.62	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.62	   A^2 -> H(U1(c, a), d)
28.55/9.62	   A^2 -> H(U1(c, a), k)
28.55/9.62	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.62	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.62	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.62	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.62	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.62	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.62	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.62	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.62	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.62	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.62	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.62	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.62	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.62	   A^2 -> H(U1(d, c), b)
28.55/9.62	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.62	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.62	   A^2 -> H(U1(d, c), c)
28.55/9.62	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.62	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.62	
28.55/9.62	The TRS R consists of the following rules:
28.55/9.62	
28.55/9.62	   f(x) -> U1(x, x)
28.55/9.62	   U1(e, x) -> x
28.55/9.62	   a -> c
28.55/9.62	   a -> d
28.55/9.62	   b -> c
28.55/9.62	   b -> d
28.55/9.62	   d -> k
28.55/9.62	   c -> e
28.55/9.62	   c -> k
28.55/9.62	
28.55/9.62	Q is empty.
28.55/9.62	We have to consider all minimal (P,Q,R)-chains.
28.55/9.62	----------------------------------------
28.55/9.62	
28.55/9.62	(1265) TransformationProof (EQUIVALENT)
28.55/9.62	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.62	
28.55/9.62	   (A^2 -> H(U1(k, c), U1(c, k)),A^2 -> H(U1(k, c), U1(c, k)))
28.55/9.62	   (A^2 -> H(U1(d, e), U1(c, k)),A^2 -> H(U1(d, e), U1(c, k)))
28.55/9.62	   (A^2 -> H(U1(d, k), U1(c, k)),A^2 -> H(U1(d, k), U1(c, k)))
28.55/9.62	   (A^2 -> H(U1(d, c), U1(e, k)),A^2 -> H(U1(d, c), U1(e, k)))
28.55/9.62	   (A^2 -> H(U1(d, c), U1(k, k)),A^2 -> H(U1(d, c), U1(k, k)))
28.55/9.62	
28.55/9.62	
28.55/9.62	----------------------------------------
28.55/9.62	
28.55/9.62	(1266)
28.55/9.62	Obligation:
28.55/9.62	Q DP problem:
28.55/9.62	The TRS P consists of the following rules:
28.55/9.62	
28.55/9.62	   A^2 -> H(f(c), f(c))
28.55/9.62	   H(x, x) -> G(x, x, f(k))
28.55/9.62	   G(d, x, x) -> A^2
28.55/9.62	   A^2 -> H(f(d), f(d))
28.55/9.62	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.62	   A^2 -> H(f(e), f(e))
28.55/9.62	   A^2 -> H(f(k), f(k))
28.55/9.62	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.62	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.62	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.62	   A^2 -> H(U1(d, c), U1(e, e))
28.55/9.62	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.62	   A^2 -> H(U1(d, c), U1(k, d))
28.55/9.62	   A^2 -> H(U1(d, c), U1(d, k))
28.55/9.62	   A^2 -> H(U1(d, a), b)
28.55/9.62	   A^2 -> H(U1(d, a), U1(e, d))
28.55/9.62	   A^2 -> H(U1(d, a), U1(d, e))
28.55/9.62	   A^2 -> H(U1(d, a), c)
28.55/9.62	   A^2 -> H(U1(d, a), U1(e, k))
28.55/9.62	   A^2 -> H(U1(d, a), U1(k, e))
28.55/9.62	   A^2 -> H(U1(d, a), e)
28.55/9.62	   A^2 -> H(U1(d, a), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, e), U1(e, b))
28.55/9.62	   A^2 -> H(U1(a, e), U1(k, b))
28.55/9.62	   A^2 -> H(U1(a, e), U1(c, d))
28.55/9.62	   A^2 -> H(U1(a, e), U1(d, c))
28.55/9.62	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.62	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.62	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.62	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.62	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.62	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.62	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.62	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.62	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.62	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.62	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.62	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.62	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.62	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.62	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.62	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.62	   A^2 -> H(U1(a, c), b)
28.55/9.62	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.62	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.62	   A^2 -> H(U1(a, c), c)
28.55/9.62	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.62	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.62	   A^2 -> H(U1(a, c), e)
28.55/9.62	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, d), b)
28.55/9.62	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.62	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.62	   A^2 -> H(U1(a, d), c)
28.55/9.62	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.62	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.62	   A^2 -> H(U1(a, d), e)
28.55/9.62	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, a), d)
28.55/9.62	   A^2 -> H(U1(a, a), k)
28.55/9.62	   A^2 -> H(k, U1(b, b))
28.55/9.62	   A^2 -> H(k, f(c))
28.55/9.62	   A^2 -> H(k, f(d))
28.55/9.62	   A^2 -> H(c, U1(c, b))
28.55/9.62	   A^2 -> H(c, U1(d, b))
28.55/9.62	   A^2 -> H(c, U1(b, c))
28.55/9.62	   A^2 -> H(c, U1(b, d))
28.55/9.62	   A^2 -> H(c, U1(c, c))
28.55/9.62	   A^2 -> H(c, f(e))
28.55/9.62	   A^2 -> H(c, f(k))
28.55/9.62	   A^2 -> H(c, U1(d, d))
28.55/9.62	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.62	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.62	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.62	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.62	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.62	   A^2 -> H(U1(e, k), f(e))
28.55/9.62	   A^2 -> H(U1(e, k), f(k))
28.55/9.62	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.62	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.62	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.62	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.62	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.62	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.62	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.62	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.62	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.62	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.62	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.62	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.62	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.62	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.62	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.62	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.62	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.62	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.62	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.62	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.62	   A^2 -> H(U1(k, e), f(e))
28.55/9.62	   A^2 -> H(U1(k, e), f(k))
28.55/9.62	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.62	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.62	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.62	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.62	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.62	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.62	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.62	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.62	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.62	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.62	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.62	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.62	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.62	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.62	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.62	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.62	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.62	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.62	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.62	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.62	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.62	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.62	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.62	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.62	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.62	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.62	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.62	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.62	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.62	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.62	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.62	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.62	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.62	   A^2 -> H(U1(c, c), b)
28.55/9.62	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.62	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.62	   A^2 -> H(U1(c, c), e)
28.55/9.62	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.62	   A^2 -> H(e, U1(c, b))
28.55/9.62	   A^2 -> H(e, U1(d, b))
28.55/9.62	   A^2 -> H(e, U1(b, c))
28.55/9.62	   A^2 -> H(e, U1(b, d))
28.55/9.62	   A^2 -> H(e, U1(c, c))
28.55/9.62	   A^2 -> H(e, f(e))
28.55/9.62	   A^2 -> H(e, f(k))
28.55/9.62	   A^2 -> H(e, U1(d, d))
28.55/9.62	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.62	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.62	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.62	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.62	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.62	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.62	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.62	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.62	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.62	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.62	   A^2 -> H(f(e), b)
28.55/9.62	   A^2 -> H(f(e), U1(e, d))
28.55/9.62	   A^2 -> H(f(e), U1(d, e))
28.55/9.62	   A^2 -> H(f(e), c)
28.55/9.62	   A^2 -> H(f(e), U1(e, k))
28.55/9.62	   A^2 -> H(f(e), U1(k, e))
28.55/9.62	   A^2 -> H(f(e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.62	   A^2 -> H(f(k), b)
28.55/9.62	   A^2 -> H(f(k), U1(e, d))
28.55/9.62	   A^2 -> H(f(k), U1(d, e))
28.55/9.62	   A^2 -> H(f(k), c)
28.55/9.62	   A^2 -> H(f(k), U1(e, k))
28.55/9.62	   A^2 -> H(f(k), U1(k, e))
28.55/9.62	   A^2 -> H(f(k), e)
28.55/9.62	   A^2 -> H(f(c), d)
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.62	   A^2 -> H(U1(k, k), f(e))
28.55/9.62	   A^2 -> H(U1(k, k), f(k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.62	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.62	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.62	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.62	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.62	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.62	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.62	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.62	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.62	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.62	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.62	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.62	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.62	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.62	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.62	   A^2 -> H(U1(d, d), b)
28.55/9.62	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.62	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.62	   A^2 -> H(U1(d, d), c)
28.55/9.62	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.62	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.62	   A^2 -> H(U1(d, d), e)
28.55/9.62	   A^2 -> H(f(d), d)
28.55/9.62	   A^2 -> H(f(d), k)
28.55/9.62	   A^2 -> H(U1(c, c), c)
28.55/9.62	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.62	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.62	   A^2 -> H(f(c), k)
28.55/9.62	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.62	   A^2 -> H(f(k), U1(k, k))
28.55/9.62	   A^2 -> H(f(e), e)
28.55/9.62	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.62	   A^2 -> H(d, U1(c, b))
28.55/9.62	   A^2 -> H(d, U1(d, b))
28.55/9.62	   A^2 -> H(d, U1(b, c))
28.55/9.62	   A^2 -> H(d, U1(b, d))
28.55/9.62	   A^2 -> H(d, U1(c, c))
28.55/9.62	   A^2 -> H(d, f(e))
28.55/9.62	   A^2 -> H(d, f(k))
28.55/9.62	   A^2 -> H(d, U1(d, d))
28.55/9.62	   A^2 -> H(a, U1(e, b))
28.55/9.62	   A^2 -> H(a, U1(k, b))
28.55/9.62	   A^2 -> H(a, U1(c, d))
28.55/9.62	   A^2 -> H(a, U1(d, c))
28.55/9.62	   A^2 -> H(a, U1(b, e))
28.55/9.62	   A^2 -> H(a, U1(b, k))
28.55/9.62	   A^2 -> H(a, U1(e, c))
28.55/9.62	   A^2 -> H(a, U1(k, c))
28.55/9.62	   A^2 -> H(a, U1(c, e))
28.55/9.62	   A^2 -> H(a, U1(c, k))
28.55/9.62	   A^2 -> H(a, U1(e, e))
28.55/9.62	   A^2 -> H(a, U1(k, k))
28.55/9.62	   A^2 -> H(a, U1(k, d))
28.55/9.62	   A^2 -> H(a, U1(d, k))
28.55/9.62	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.62	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.62	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.62	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.62	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.62	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.62	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.62	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.62	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.62	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.62	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.62	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.62	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.62	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.62	   A^2 -> H(U1(e, a), b)
28.55/9.62	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.62	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.62	   A^2 -> H(U1(e, a), c)
28.55/9.62	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.62	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.62	   A^2 -> H(U1(e, a), e)
28.55/9.62	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, a), b)
28.55/9.62	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.62	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.62	   A^2 -> H(U1(k, a), c)
28.55/9.62	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.62	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.62	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.62	   A^2 -> H(U1(c, d), b)
28.55/9.62	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.62	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.62	   A^2 -> H(U1(c, d), c)
28.55/9.62	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.62	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.62	   A^2 -> H(U1(c, d), e)
28.55/9.62	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.62	   A^2 -> H(U1(c, a), d)
28.55/9.62	   A^2 -> H(U1(c, a), k)
28.55/9.62	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.62	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.62	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.62	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.62	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.62	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.62	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.62	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.62	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.62	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.62	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.62	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.62	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.62	   A^2 -> H(U1(d, c), b)
28.55/9.62	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.62	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.62	   A^2 -> H(U1(d, c), c)
28.55/9.62	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.62	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.62	
28.55/9.62	The TRS R consists of the following rules:
28.55/9.62	
28.55/9.62	   f(x) -> U1(x, x)
28.55/9.62	   U1(e, x) -> x
28.55/9.62	   a -> c
28.55/9.62	   a -> d
28.55/9.62	   b -> c
28.55/9.62	   b -> d
28.55/9.62	   d -> k
28.55/9.62	   c -> e
28.55/9.62	   c -> k
28.55/9.62	
28.55/9.62	Q is empty.
28.55/9.62	We have to consider all minimal (P,Q,R)-chains.
28.55/9.62	----------------------------------------
28.55/9.62	
28.55/9.62	(1267) TransformationProof (EQUIVALENT)
28.55/9.62	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.62	
28.55/9.62	   (A^2 -> H(U1(k, c), U1(e, e)),A^2 -> H(U1(k, c), U1(e, e)))
28.55/9.62	   (A^2 -> H(U1(d, e), U1(e, e)),A^2 -> H(U1(d, e), U1(e, e)))
28.55/9.62	   (A^2 -> H(U1(d, k), U1(e, e)),A^2 -> H(U1(d, k), U1(e, e)))
28.55/9.62	   (A^2 -> H(U1(d, c), e),A^2 -> H(U1(d, c), e))
28.55/9.62	
28.55/9.62	
28.55/9.62	----------------------------------------
28.55/9.62	
28.55/9.62	(1268)
28.55/9.62	Obligation:
28.55/9.62	Q DP problem:
28.55/9.62	The TRS P consists of the following rules:
28.55/9.62	
28.55/9.62	   A^2 -> H(f(c), f(c))
28.55/9.62	   H(x, x) -> G(x, x, f(k))
28.55/9.62	   G(d, x, x) -> A^2
28.55/9.62	   A^2 -> H(f(d), f(d))
28.55/9.62	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.62	   A^2 -> H(f(e), f(e))
28.55/9.62	   A^2 -> H(f(k), f(k))
28.55/9.62	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.62	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.62	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.62	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.62	   A^2 -> H(U1(d, c), U1(k, d))
28.55/9.62	   A^2 -> H(U1(d, c), U1(d, k))
28.55/9.62	   A^2 -> H(U1(d, a), b)
28.55/9.62	   A^2 -> H(U1(d, a), U1(e, d))
28.55/9.62	   A^2 -> H(U1(d, a), U1(d, e))
28.55/9.62	   A^2 -> H(U1(d, a), c)
28.55/9.62	   A^2 -> H(U1(d, a), U1(e, k))
28.55/9.62	   A^2 -> H(U1(d, a), U1(k, e))
28.55/9.62	   A^2 -> H(U1(d, a), e)
28.55/9.62	   A^2 -> H(U1(d, a), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, e), U1(e, b))
28.55/9.62	   A^2 -> H(U1(a, e), U1(k, b))
28.55/9.62	   A^2 -> H(U1(a, e), U1(c, d))
28.55/9.62	   A^2 -> H(U1(a, e), U1(d, c))
28.55/9.62	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.62	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.62	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.62	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.62	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.62	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.62	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.62	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.62	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.62	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.62	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.62	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.62	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.62	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.62	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.62	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.62	   A^2 -> H(U1(a, c), b)
28.55/9.62	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.62	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.62	   A^2 -> H(U1(a, c), c)
28.55/9.62	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.62	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.62	   A^2 -> H(U1(a, c), e)
28.55/9.62	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, d), b)
28.55/9.62	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.62	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.62	   A^2 -> H(U1(a, d), c)
28.55/9.62	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.62	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.62	   A^2 -> H(U1(a, d), e)
28.55/9.62	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, a), d)
28.55/9.62	   A^2 -> H(U1(a, a), k)
28.55/9.62	   A^2 -> H(k, U1(b, b))
28.55/9.62	   A^2 -> H(k, f(c))
28.55/9.62	   A^2 -> H(k, f(d))
28.55/9.62	   A^2 -> H(c, U1(c, b))
28.55/9.62	   A^2 -> H(c, U1(d, b))
28.55/9.62	   A^2 -> H(c, U1(b, c))
28.55/9.62	   A^2 -> H(c, U1(b, d))
28.55/9.62	   A^2 -> H(c, U1(c, c))
28.55/9.62	   A^2 -> H(c, f(e))
28.55/9.62	   A^2 -> H(c, f(k))
28.55/9.62	   A^2 -> H(c, U1(d, d))
28.55/9.62	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.62	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.62	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.62	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.62	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.62	   A^2 -> H(U1(e, k), f(e))
28.55/9.62	   A^2 -> H(U1(e, k), f(k))
28.55/9.62	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.62	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.62	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.62	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.62	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.62	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.62	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.62	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.62	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.62	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.62	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.62	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.62	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.62	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.62	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.62	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.62	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.62	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.62	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.62	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.62	   A^2 -> H(U1(k, e), f(e))
28.55/9.62	   A^2 -> H(U1(k, e), f(k))
28.55/9.62	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.62	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.62	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.62	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.62	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.62	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.62	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.62	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.62	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.62	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.62	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.62	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.62	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.62	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.62	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.62	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.62	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.62	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.62	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.62	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.62	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.62	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.62	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.62	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.62	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.62	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.62	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.62	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.62	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.62	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.62	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.62	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.62	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.62	   A^2 -> H(U1(c, c), b)
28.55/9.62	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.62	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.62	   A^2 -> H(U1(c, c), e)
28.55/9.62	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.62	   A^2 -> H(e, U1(c, b))
28.55/9.62	   A^2 -> H(e, U1(d, b))
28.55/9.62	   A^2 -> H(e, U1(b, c))
28.55/9.62	   A^2 -> H(e, U1(b, d))
28.55/9.62	   A^2 -> H(e, U1(c, c))
28.55/9.62	   A^2 -> H(e, f(e))
28.55/9.62	   A^2 -> H(e, f(k))
28.55/9.62	   A^2 -> H(e, U1(d, d))
28.55/9.62	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.62	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.62	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.62	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.62	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.62	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.62	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.62	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.62	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.62	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.62	   A^2 -> H(f(e), b)
28.55/9.62	   A^2 -> H(f(e), U1(e, d))
28.55/9.62	   A^2 -> H(f(e), U1(d, e))
28.55/9.62	   A^2 -> H(f(e), c)
28.55/9.62	   A^2 -> H(f(e), U1(e, k))
28.55/9.62	   A^2 -> H(f(e), U1(k, e))
28.55/9.62	   A^2 -> H(f(e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.62	   A^2 -> H(f(k), b)
28.55/9.62	   A^2 -> H(f(k), U1(e, d))
28.55/9.62	   A^2 -> H(f(k), U1(d, e))
28.55/9.62	   A^2 -> H(f(k), c)
28.55/9.62	   A^2 -> H(f(k), U1(e, k))
28.55/9.62	   A^2 -> H(f(k), U1(k, e))
28.55/9.62	   A^2 -> H(f(k), e)
28.55/9.62	   A^2 -> H(f(c), d)
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.62	   A^2 -> H(U1(k, k), f(e))
28.55/9.62	   A^2 -> H(U1(k, k), f(k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.62	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.62	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.62	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.62	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.62	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.62	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.62	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.62	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.62	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.62	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.62	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.62	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.62	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.62	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.62	   A^2 -> H(U1(d, d), b)
28.55/9.62	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.62	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.62	   A^2 -> H(U1(d, d), c)
28.55/9.62	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.62	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.62	   A^2 -> H(U1(d, d), e)
28.55/9.62	   A^2 -> H(f(d), d)
28.55/9.62	   A^2 -> H(f(d), k)
28.55/9.62	   A^2 -> H(U1(c, c), c)
28.55/9.62	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.62	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.62	   A^2 -> H(f(c), k)
28.55/9.62	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.62	   A^2 -> H(f(k), U1(k, k))
28.55/9.62	   A^2 -> H(f(e), e)
28.55/9.62	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.62	   A^2 -> H(d, U1(c, b))
28.55/9.62	   A^2 -> H(d, U1(d, b))
28.55/9.62	   A^2 -> H(d, U1(b, c))
28.55/9.62	   A^2 -> H(d, U1(b, d))
28.55/9.62	   A^2 -> H(d, U1(c, c))
28.55/9.62	   A^2 -> H(d, f(e))
28.55/9.62	   A^2 -> H(d, f(k))
28.55/9.62	   A^2 -> H(d, U1(d, d))
28.55/9.62	   A^2 -> H(a, U1(e, b))
28.55/9.62	   A^2 -> H(a, U1(k, b))
28.55/9.62	   A^2 -> H(a, U1(c, d))
28.55/9.62	   A^2 -> H(a, U1(d, c))
28.55/9.62	   A^2 -> H(a, U1(b, e))
28.55/9.62	   A^2 -> H(a, U1(b, k))
28.55/9.62	   A^2 -> H(a, U1(e, c))
28.55/9.62	   A^2 -> H(a, U1(k, c))
28.55/9.62	   A^2 -> H(a, U1(c, e))
28.55/9.62	   A^2 -> H(a, U1(c, k))
28.55/9.62	   A^2 -> H(a, U1(e, e))
28.55/9.62	   A^2 -> H(a, U1(k, k))
28.55/9.62	   A^2 -> H(a, U1(k, d))
28.55/9.62	   A^2 -> H(a, U1(d, k))
28.55/9.62	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.62	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.62	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.62	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.62	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.62	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.62	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.62	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.62	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.62	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.62	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.62	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.62	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.62	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.62	   A^2 -> H(U1(e, a), b)
28.55/9.62	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.62	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.62	   A^2 -> H(U1(e, a), c)
28.55/9.62	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.62	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.62	   A^2 -> H(U1(e, a), e)
28.55/9.62	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, a), b)
28.55/9.62	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.62	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.62	   A^2 -> H(U1(k, a), c)
28.55/9.62	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.62	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.62	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.62	   A^2 -> H(U1(c, d), b)
28.55/9.62	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.62	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.62	   A^2 -> H(U1(c, d), c)
28.55/9.62	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.62	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.62	   A^2 -> H(U1(c, d), e)
28.55/9.62	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.62	   A^2 -> H(U1(c, a), d)
28.55/9.62	   A^2 -> H(U1(c, a), k)
28.55/9.62	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.62	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.62	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.62	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.62	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.62	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.62	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.62	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.62	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.62	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.62	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.62	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.62	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.62	   A^2 -> H(U1(d, c), b)
28.55/9.62	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.62	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.62	   A^2 -> H(U1(d, c), c)
28.55/9.62	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.62	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.62	   A^2 -> H(U1(d, c), e)
28.55/9.62	
28.55/9.62	The TRS R consists of the following rules:
28.55/9.62	
28.55/9.62	   f(x) -> U1(x, x)
28.55/9.62	   U1(e, x) -> x
28.55/9.62	   a -> c
28.55/9.62	   a -> d
28.55/9.62	   b -> c
28.55/9.62	   b -> d
28.55/9.62	   d -> k
28.55/9.62	   c -> e
28.55/9.62	   c -> k
28.55/9.62	
28.55/9.62	Q is empty.
28.55/9.62	We have to consider all minimal (P,Q,R)-chains.
28.55/9.62	----------------------------------------
28.55/9.62	
28.55/9.62	(1269) TransformationProof (EQUIVALENT)
28.55/9.62	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.62	
28.55/9.62	   (A^2 -> H(U1(k, c), U1(k, k)),A^2 -> H(U1(k, c), U1(k, k)))
28.55/9.62	   (A^2 -> H(U1(d, e), U1(k, k)),A^2 -> H(U1(d, e), U1(k, k)))
28.55/9.62	   (A^2 -> H(U1(d, k), U1(k, k)),A^2 -> H(U1(d, k), U1(k, k)))
28.55/9.62	
28.55/9.62	
28.55/9.62	----------------------------------------
28.55/9.62	
28.55/9.62	(1270)
28.55/9.62	Obligation:
28.55/9.62	Q DP problem:
28.55/9.62	The TRS P consists of the following rules:
28.55/9.62	
28.55/9.62	   A^2 -> H(f(c), f(c))
28.55/9.62	   H(x, x) -> G(x, x, f(k))
28.55/9.62	   G(d, x, x) -> A^2
28.55/9.62	   A^2 -> H(f(d), f(d))
28.55/9.62	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.62	   A^2 -> H(f(e), f(e))
28.55/9.62	   A^2 -> H(f(k), f(k))
28.55/9.62	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.62	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.62	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.62	   A^2 -> H(U1(d, c), U1(k, d))
28.55/9.62	   A^2 -> H(U1(d, c), U1(d, k))
28.55/9.62	   A^2 -> H(U1(d, a), b)
28.55/9.62	   A^2 -> H(U1(d, a), U1(e, d))
28.55/9.62	   A^2 -> H(U1(d, a), U1(d, e))
28.55/9.62	   A^2 -> H(U1(d, a), c)
28.55/9.62	   A^2 -> H(U1(d, a), U1(e, k))
28.55/9.62	   A^2 -> H(U1(d, a), U1(k, e))
28.55/9.62	   A^2 -> H(U1(d, a), e)
28.55/9.62	   A^2 -> H(U1(d, a), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, e), U1(e, b))
28.55/9.62	   A^2 -> H(U1(a, e), U1(k, b))
28.55/9.62	   A^2 -> H(U1(a, e), U1(c, d))
28.55/9.62	   A^2 -> H(U1(a, e), U1(d, c))
28.55/9.62	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.62	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.62	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.62	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.62	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.62	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.62	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.62	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.62	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.62	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.62	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.62	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.62	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.62	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.62	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.62	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.62	   A^2 -> H(U1(a, c), b)
28.55/9.62	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.62	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.62	   A^2 -> H(U1(a, c), c)
28.55/9.62	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.62	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.62	   A^2 -> H(U1(a, c), e)
28.55/9.62	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, d), b)
28.55/9.62	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.62	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.62	   A^2 -> H(U1(a, d), c)
28.55/9.62	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.62	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.62	   A^2 -> H(U1(a, d), e)
28.55/9.62	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.62	   A^2 -> H(U1(a, a), d)
28.55/9.62	   A^2 -> H(U1(a, a), k)
28.55/9.62	   A^2 -> H(k, U1(b, b))
28.55/9.62	   A^2 -> H(k, f(c))
28.55/9.62	   A^2 -> H(k, f(d))
28.55/9.62	   A^2 -> H(c, U1(c, b))
28.55/9.62	   A^2 -> H(c, U1(d, b))
28.55/9.62	   A^2 -> H(c, U1(b, c))
28.55/9.62	   A^2 -> H(c, U1(b, d))
28.55/9.62	   A^2 -> H(c, U1(c, c))
28.55/9.62	   A^2 -> H(c, f(e))
28.55/9.62	   A^2 -> H(c, f(k))
28.55/9.62	   A^2 -> H(c, U1(d, d))
28.55/9.62	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.62	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.62	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.62	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.62	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.62	   A^2 -> H(U1(e, k), f(e))
28.55/9.62	   A^2 -> H(U1(e, k), f(k))
28.55/9.62	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.62	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.62	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.62	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.62	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.62	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.62	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.62	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.62	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.62	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.62	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.62	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.62	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.62	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.62	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.62	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.62	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.62	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.62	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.62	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.62	   A^2 -> H(U1(k, e), f(e))
28.55/9.62	   A^2 -> H(U1(k, e), f(k))
28.55/9.62	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.62	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.62	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.62	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.62	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.62	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.62	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.62	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.62	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.62	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.62	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.62	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.62	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.62	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.62	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.62	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.62	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.62	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.62	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.62	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.62	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.62	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.62	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.62	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.62	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.62	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.62	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.62	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.62	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.62	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.62	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.62	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.62	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.62	   A^2 -> H(U1(c, c), b)
28.55/9.62	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.62	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.62	   A^2 -> H(U1(c, c), e)
28.55/9.62	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.62	   A^2 -> H(e, U1(c, b))
28.55/9.62	   A^2 -> H(e, U1(d, b))
28.55/9.62	   A^2 -> H(e, U1(b, c))
28.55/9.62	   A^2 -> H(e, U1(b, d))
28.55/9.62	   A^2 -> H(e, U1(c, c))
28.55/9.62	   A^2 -> H(e, f(e))
28.55/9.62	   A^2 -> H(e, f(k))
28.55/9.62	   A^2 -> H(e, U1(d, d))
28.55/9.62	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.62	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.62	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.62	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.62	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.62	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.62	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.62	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.62	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.62	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.62	   A^2 -> H(f(e), b)
28.55/9.62	   A^2 -> H(f(e), U1(e, d))
28.55/9.62	   A^2 -> H(f(e), U1(d, e))
28.55/9.62	   A^2 -> H(f(e), c)
28.55/9.62	   A^2 -> H(f(e), U1(e, k))
28.55/9.62	   A^2 -> H(f(e), U1(k, e))
28.55/9.62	   A^2 -> H(f(e), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.62	   A^2 -> H(f(k), b)
28.55/9.62	   A^2 -> H(f(k), U1(e, d))
28.55/9.62	   A^2 -> H(f(k), U1(d, e))
28.55/9.62	   A^2 -> H(f(k), c)
28.55/9.62	   A^2 -> H(f(k), U1(e, k))
28.55/9.62	   A^2 -> H(f(k), U1(k, e))
28.55/9.62	   A^2 -> H(f(k), e)
28.55/9.62	   A^2 -> H(f(c), d)
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.62	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.62	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.62	   A^2 -> H(U1(k, k), f(e))
28.55/9.62	   A^2 -> H(U1(k, k), f(k))
28.55/9.62	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.62	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.62	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.62	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.62	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.62	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.62	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.62	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.62	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.62	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.62	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.62	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.62	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.62	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.62	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.62	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.62	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.62	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.62	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.62	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.62	   A^2 -> H(U1(d, d), b)
28.55/9.62	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.62	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.62	   A^2 -> H(U1(d, d), c)
28.55/9.62	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.62	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.62	   A^2 -> H(U1(d, d), e)
28.55/9.62	   A^2 -> H(f(d), d)
28.55/9.62	   A^2 -> H(f(d), k)
28.55/9.62	   A^2 -> H(U1(c, c), c)
28.55/9.62	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.62	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.62	   A^2 -> H(f(c), k)
28.55/9.62	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.62	   A^2 -> H(f(k), U1(k, k))
28.55/9.62	   A^2 -> H(f(e), e)
28.55/9.62	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.62	   A^2 -> H(d, U1(c, b))
28.55/9.62	   A^2 -> H(d, U1(d, b))
28.55/9.62	   A^2 -> H(d, U1(b, c))
28.55/9.62	   A^2 -> H(d, U1(b, d))
28.55/9.62	   A^2 -> H(d, U1(c, c))
28.55/9.62	   A^2 -> H(d, f(e))
28.55/9.62	   A^2 -> H(d, f(k))
28.55/9.62	   A^2 -> H(d, U1(d, d))
28.55/9.62	   A^2 -> H(a, U1(e, b))
28.55/9.62	   A^2 -> H(a, U1(k, b))
28.55/9.62	   A^2 -> H(a, U1(c, d))
28.55/9.62	   A^2 -> H(a, U1(d, c))
28.55/9.62	   A^2 -> H(a, U1(b, e))
28.55/9.62	   A^2 -> H(a, U1(b, k))
28.55/9.62	   A^2 -> H(a, U1(e, c))
28.55/9.62	   A^2 -> H(a, U1(k, c))
28.55/9.62	   A^2 -> H(a, U1(c, e))
28.55/9.62	   A^2 -> H(a, U1(c, k))
28.55/9.62	   A^2 -> H(a, U1(e, e))
28.55/9.62	   A^2 -> H(a, U1(k, k))
28.55/9.62	   A^2 -> H(a, U1(k, d))
28.55/9.62	   A^2 -> H(a, U1(d, k))
28.55/9.62	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.62	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.62	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.62	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.62	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.62	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.62	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.62	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.62	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.63	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.63	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.63	   A^2 -> H(U1(e, a), b)
28.55/9.63	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.63	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.63	   A^2 -> H(U1(e, a), c)
28.55/9.63	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.63	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.63	   A^2 -> H(U1(e, a), e)
28.55/9.63	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, a), b)
28.55/9.63	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.63	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.63	   A^2 -> H(U1(k, a), c)
28.55/9.63	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.63	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.63	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, d), b)
28.55/9.63	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.63	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.63	   A^2 -> H(U1(c, d), c)
28.55/9.63	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.63	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.63	   A^2 -> H(U1(c, d), e)
28.55/9.63	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, a), d)
28.55/9.63	   A^2 -> H(U1(c, a), k)
28.55/9.63	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.63	   A^2 -> H(U1(d, c), b)
28.55/9.63	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.63	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.63	   A^2 -> H(U1(d, c), c)
28.55/9.63	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.63	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.63	   A^2 -> H(U1(d, c), e)
28.55/9.63	
28.55/9.63	The TRS R consists of the following rules:
28.55/9.63	
28.55/9.63	   f(x) -> U1(x, x)
28.55/9.63	   U1(e, x) -> x
28.55/9.63	   a -> c
28.55/9.63	   a -> d
28.55/9.63	   b -> c
28.55/9.63	   b -> d
28.55/9.63	   d -> k
28.55/9.63	   c -> e
28.55/9.63	   c -> k
28.55/9.63	
28.55/9.63	Q is empty.
28.55/9.63	We have to consider all minimal (P,Q,R)-chains.
28.55/9.63	----------------------------------------
28.55/9.63	
28.55/9.63	(1271) TransformationProof (EQUIVALENT)
28.55/9.63	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.63	
28.55/9.63	   (A^2 -> H(U1(k, c), U1(k, d)),A^2 -> H(U1(k, c), U1(k, d)))
28.55/9.63	   (A^2 -> H(U1(d, e), U1(k, d)),A^2 -> H(U1(d, e), U1(k, d)))
28.55/9.63	   (A^2 -> H(U1(d, k), U1(k, d)),A^2 -> H(U1(d, k), U1(k, d)))
28.55/9.63	   (A^2 -> H(U1(d, c), U1(k, k)),A^2 -> H(U1(d, c), U1(k, k)))
28.55/9.63	
28.55/9.63	
28.55/9.63	----------------------------------------
28.55/9.63	
28.55/9.63	(1272)
28.55/9.63	Obligation:
28.55/9.63	Q DP problem:
28.55/9.63	The TRS P consists of the following rules:
28.55/9.63	
28.55/9.63	   A^2 -> H(f(c), f(c))
28.55/9.63	   H(x, x) -> G(x, x, f(k))
28.55/9.63	   G(d, x, x) -> A^2
28.55/9.63	   A^2 -> H(f(d), f(d))
28.55/9.63	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.63	   A^2 -> H(f(e), f(e))
28.55/9.63	   A^2 -> H(f(k), f(k))
28.55/9.63	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.63	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.63	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.63	   A^2 -> H(U1(d, c), U1(d, k))
28.55/9.63	   A^2 -> H(U1(d, a), b)
28.55/9.63	   A^2 -> H(U1(d, a), U1(e, d))
28.55/9.63	   A^2 -> H(U1(d, a), U1(d, e))
28.55/9.63	   A^2 -> H(U1(d, a), c)
28.55/9.63	   A^2 -> H(U1(d, a), U1(e, k))
28.55/9.63	   A^2 -> H(U1(d, a), U1(k, e))
28.55/9.63	   A^2 -> H(U1(d, a), e)
28.55/9.63	   A^2 -> H(U1(d, a), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(a, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(a, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.63	   A^2 -> H(U1(a, c), b)
28.55/9.63	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.63	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.63	   A^2 -> H(U1(a, c), c)
28.55/9.63	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.63	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.63	   A^2 -> H(U1(a, c), e)
28.55/9.63	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, d), b)
28.55/9.63	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.63	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.63	   A^2 -> H(U1(a, d), c)
28.55/9.63	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.63	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.63	   A^2 -> H(U1(a, d), e)
28.55/9.63	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, a), d)
28.55/9.63	   A^2 -> H(U1(a, a), k)
28.55/9.63	   A^2 -> H(k, U1(b, b))
28.55/9.63	   A^2 -> H(k, f(c))
28.55/9.63	   A^2 -> H(k, f(d))
28.55/9.63	   A^2 -> H(c, U1(c, b))
28.55/9.63	   A^2 -> H(c, U1(d, b))
28.55/9.63	   A^2 -> H(c, U1(b, c))
28.55/9.63	   A^2 -> H(c, U1(b, d))
28.55/9.63	   A^2 -> H(c, U1(c, c))
28.55/9.63	   A^2 -> H(c, f(e))
28.55/9.63	   A^2 -> H(c, f(k))
28.55/9.63	   A^2 -> H(c, U1(d, d))
28.55/9.63	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.63	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.63	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.63	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.63	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.63	   A^2 -> H(U1(e, k), f(e))
28.55/9.63	   A^2 -> H(U1(e, k), f(k))
28.55/9.63	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.63	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.63	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.63	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.63	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.63	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.63	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.63	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.63	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.63	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.63	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.63	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.63	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.63	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.63	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.63	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.63	   A^2 -> H(U1(k, e), f(e))
28.55/9.63	   A^2 -> H(U1(k, e), f(k))
28.55/9.63	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.63	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.63	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.63	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.63	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.63	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.63	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.63	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.63	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.63	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.63	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.63	   A^2 -> H(U1(c, c), b)
28.55/9.63	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.63	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.63	   A^2 -> H(U1(c, c), e)
28.55/9.63	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.63	   A^2 -> H(e, U1(c, b))
28.55/9.63	   A^2 -> H(e, U1(d, b))
28.55/9.63	   A^2 -> H(e, U1(b, c))
28.55/9.63	   A^2 -> H(e, U1(b, d))
28.55/9.63	   A^2 -> H(e, U1(c, c))
28.55/9.63	   A^2 -> H(e, f(e))
28.55/9.63	   A^2 -> H(e, f(k))
28.55/9.63	   A^2 -> H(e, U1(d, d))
28.55/9.63	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.63	   A^2 -> H(f(e), b)
28.55/9.63	   A^2 -> H(f(e), U1(e, d))
28.55/9.63	   A^2 -> H(f(e), U1(d, e))
28.55/9.63	   A^2 -> H(f(e), c)
28.55/9.63	   A^2 -> H(f(e), U1(e, k))
28.55/9.63	   A^2 -> H(f(e), U1(k, e))
28.55/9.63	   A^2 -> H(f(e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.63	   A^2 -> H(f(k), b)
28.55/9.63	   A^2 -> H(f(k), U1(e, d))
28.55/9.63	   A^2 -> H(f(k), U1(d, e))
28.55/9.63	   A^2 -> H(f(k), c)
28.55/9.63	   A^2 -> H(f(k), U1(e, k))
28.55/9.63	   A^2 -> H(f(k), U1(k, e))
28.55/9.63	   A^2 -> H(f(k), e)
28.55/9.63	   A^2 -> H(f(c), d)
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.63	   A^2 -> H(U1(k, k), f(e))
28.55/9.63	   A^2 -> H(U1(k, k), f(k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.63	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.63	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.63	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.63	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.63	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.63	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.63	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.63	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.63	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.63	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.63	   A^2 -> H(U1(d, d), b)
28.55/9.63	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.63	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.63	   A^2 -> H(U1(d, d), c)
28.55/9.63	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.63	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.63	   A^2 -> H(U1(d, d), e)
28.55/9.63	   A^2 -> H(f(d), d)
28.55/9.63	   A^2 -> H(f(d), k)
28.55/9.63	   A^2 -> H(U1(c, c), c)
28.55/9.63	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.63	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.63	   A^2 -> H(f(c), k)
28.55/9.63	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.63	   A^2 -> H(f(k), U1(k, k))
28.55/9.63	   A^2 -> H(f(e), e)
28.55/9.63	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.63	   A^2 -> H(d, U1(c, b))
28.55/9.63	   A^2 -> H(d, U1(d, b))
28.55/9.63	   A^2 -> H(d, U1(b, c))
28.55/9.63	   A^2 -> H(d, U1(b, d))
28.55/9.63	   A^2 -> H(d, U1(c, c))
28.55/9.63	   A^2 -> H(d, f(e))
28.55/9.63	   A^2 -> H(d, f(k))
28.55/9.63	   A^2 -> H(d, U1(d, d))
28.55/9.63	   A^2 -> H(a, U1(e, b))
28.55/9.63	   A^2 -> H(a, U1(k, b))
28.55/9.63	   A^2 -> H(a, U1(c, d))
28.55/9.63	   A^2 -> H(a, U1(d, c))
28.55/9.63	   A^2 -> H(a, U1(b, e))
28.55/9.63	   A^2 -> H(a, U1(b, k))
28.55/9.63	   A^2 -> H(a, U1(e, c))
28.55/9.63	   A^2 -> H(a, U1(k, c))
28.55/9.63	   A^2 -> H(a, U1(c, e))
28.55/9.63	   A^2 -> H(a, U1(c, k))
28.55/9.63	   A^2 -> H(a, U1(e, e))
28.55/9.63	   A^2 -> H(a, U1(k, k))
28.55/9.63	   A^2 -> H(a, U1(k, d))
28.55/9.63	   A^2 -> H(a, U1(d, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.63	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.63	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.63	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.63	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.63	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.63	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.63	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.63	   A^2 -> H(U1(e, a), b)
28.55/9.63	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.63	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.63	   A^2 -> H(U1(e, a), c)
28.55/9.63	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.63	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.63	   A^2 -> H(U1(e, a), e)
28.55/9.63	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, a), b)
28.55/9.63	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.63	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.63	   A^2 -> H(U1(k, a), c)
28.55/9.63	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.63	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.63	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, d), b)
28.55/9.63	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.63	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.63	   A^2 -> H(U1(c, d), c)
28.55/9.63	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.63	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.63	   A^2 -> H(U1(c, d), e)
28.55/9.63	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, a), d)
28.55/9.63	   A^2 -> H(U1(c, a), k)
28.55/9.63	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.63	   A^2 -> H(U1(d, c), b)
28.55/9.63	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.63	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.63	   A^2 -> H(U1(d, c), c)
28.55/9.63	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.63	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.63	   A^2 -> H(U1(d, c), e)
28.55/9.63	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.63	
28.55/9.63	The TRS R consists of the following rules:
28.55/9.63	
28.55/9.63	   f(x) -> U1(x, x)
28.55/9.63	   U1(e, x) -> x
28.55/9.63	   a -> c
28.55/9.63	   a -> d
28.55/9.63	   b -> c
28.55/9.63	   b -> d
28.55/9.63	   d -> k
28.55/9.63	   c -> e
28.55/9.63	   c -> k
28.55/9.63	
28.55/9.63	Q is empty.
28.55/9.63	We have to consider all minimal (P,Q,R)-chains.
28.55/9.63	----------------------------------------
28.55/9.63	
28.55/9.63	(1273) TransformationProof (EQUIVALENT)
28.55/9.63	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.63	
28.55/9.63	   (A^2 -> H(U1(k, c), U1(d, k)),A^2 -> H(U1(k, c), U1(d, k)))
28.55/9.63	   (A^2 -> H(U1(d, e), U1(d, k)),A^2 -> H(U1(d, e), U1(d, k)))
28.55/9.63	   (A^2 -> H(U1(d, k), U1(d, k)),A^2 -> H(U1(d, k), U1(d, k)))
28.55/9.63	   (A^2 -> H(U1(d, c), U1(k, k)),A^2 -> H(U1(d, c), U1(k, k)))
28.55/9.63	
28.55/9.63	
28.55/9.63	----------------------------------------
28.55/9.63	
28.55/9.63	(1274)
28.55/9.63	Obligation:
28.55/9.63	Q DP problem:
28.55/9.63	The TRS P consists of the following rules:
28.55/9.63	
28.55/9.63	   A^2 -> H(f(c), f(c))
28.55/9.63	   H(x, x) -> G(x, x, f(k))
28.55/9.63	   G(d, x, x) -> A^2
28.55/9.63	   A^2 -> H(f(d), f(d))
28.55/9.63	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.63	   A^2 -> H(f(e), f(e))
28.55/9.63	   A^2 -> H(f(k), f(k))
28.55/9.63	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.63	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.63	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.63	   A^2 -> H(U1(d, a), b)
28.55/9.63	   A^2 -> H(U1(d, a), U1(e, d))
28.55/9.63	   A^2 -> H(U1(d, a), U1(d, e))
28.55/9.63	   A^2 -> H(U1(d, a), c)
28.55/9.63	   A^2 -> H(U1(d, a), U1(e, k))
28.55/9.63	   A^2 -> H(U1(d, a), U1(k, e))
28.55/9.63	   A^2 -> H(U1(d, a), e)
28.55/9.63	   A^2 -> H(U1(d, a), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(a, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(a, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.63	   A^2 -> H(U1(a, c), b)
28.55/9.63	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.63	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.63	   A^2 -> H(U1(a, c), c)
28.55/9.63	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.63	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.63	   A^2 -> H(U1(a, c), e)
28.55/9.63	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, d), b)
28.55/9.63	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.63	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.63	   A^2 -> H(U1(a, d), c)
28.55/9.63	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.63	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.63	   A^2 -> H(U1(a, d), e)
28.55/9.63	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, a), d)
28.55/9.63	   A^2 -> H(U1(a, a), k)
28.55/9.63	   A^2 -> H(k, U1(b, b))
28.55/9.63	   A^2 -> H(k, f(c))
28.55/9.63	   A^2 -> H(k, f(d))
28.55/9.63	   A^2 -> H(c, U1(c, b))
28.55/9.63	   A^2 -> H(c, U1(d, b))
28.55/9.63	   A^2 -> H(c, U1(b, c))
28.55/9.63	   A^2 -> H(c, U1(b, d))
28.55/9.63	   A^2 -> H(c, U1(c, c))
28.55/9.63	   A^2 -> H(c, f(e))
28.55/9.63	   A^2 -> H(c, f(k))
28.55/9.63	   A^2 -> H(c, U1(d, d))
28.55/9.63	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.63	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.63	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.63	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.63	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.63	   A^2 -> H(U1(e, k), f(e))
28.55/9.63	   A^2 -> H(U1(e, k), f(k))
28.55/9.63	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.63	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.63	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.63	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.63	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.63	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.63	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.63	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.63	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.63	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.63	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.63	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.63	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.63	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.63	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.63	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.63	   A^2 -> H(U1(k, e), f(e))
28.55/9.63	   A^2 -> H(U1(k, e), f(k))
28.55/9.63	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.63	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.63	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.63	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.63	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.63	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.63	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.63	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.63	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.63	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.63	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.63	   A^2 -> H(U1(c, c), b)
28.55/9.63	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.63	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.63	   A^2 -> H(U1(c, c), e)
28.55/9.63	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.63	   A^2 -> H(e, U1(c, b))
28.55/9.63	   A^2 -> H(e, U1(d, b))
28.55/9.63	   A^2 -> H(e, U1(b, c))
28.55/9.63	   A^2 -> H(e, U1(b, d))
28.55/9.63	   A^2 -> H(e, U1(c, c))
28.55/9.63	   A^2 -> H(e, f(e))
28.55/9.63	   A^2 -> H(e, f(k))
28.55/9.63	   A^2 -> H(e, U1(d, d))
28.55/9.63	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.63	   A^2 -> H(f(e), b)
28.55/9.63	   A^2 -> H(f(e), U1(e, d))
28.55/9.63	   A^2 -> H(f(e), U1(d, e))
28.55/9.63	   A^2 -> H(f(e), c)
28.55/9.63	   A^2 -> H(f(e), U1(e, k))
28.55/9.63	   A^2 -> H(f(e), U1(k, e))
28.55/9.63	   A^2 -> H(f(e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.63	   A^2 -> H(f(k), b)
28.55/9.63	   A^2 -> H(f(k), U1(e, d))
28.55/9.63	   A^2 -> H(f(k), U1(d, e))
28.55/9.63	   A^2 -> H(f(k), c)
28.55/9.63	   A^2 -> H(f(k), U1(e, k))
28.55/9.63	   A^2 -> H(f(k), U1(k, e))
28.55/9.63	   A^2 -> H(f(k), e)
28.55/9.63	   A^2 -> H(f(c), d)
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.63	   A^2 -> H(U1(k, k), f(e))
28.55/9.63	   A^2 -> H(U1(k, k), f(k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.63	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.63	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.63	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.63	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.63	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.63	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.63	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.63	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.63	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.63	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.63	   A^2 -> H(U1(d, d), b)
28.55/9.63	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.63	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.63	   A^2 -> H(U1(d, d), c)
28.55/9.63	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.63	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.63	   A^2 -> H(U1(d, d), e)
28.55/9.63	   A^2 -> H(f(d), d)
28.55/9.63	   A^2 -> H(f(d), k)
28.55/9.63	   A^2 -> H(U1(c, c), c)
28.55/9.63	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.63	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.63	   A^2 -> H(f(c), k)
28.55/9.63	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.63	   A^2 -> H(f(k), U1(k, k))
28.55/9.63	   A^2 -> H(f(e), e)
28.55/9.63	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.63	   A^2 -> H(d, U1(c, b))
28.55/9.63	   A^2 -> H(d, U1(d, b))
28.55/9.63	   A^2 -> H(d, U1(b, c))
28.55/9.63	   A^2 -> H(d, U1(b, d))
28.55/9.63	   A^2 -> H(d, U1(c, c))
28.55/9.63	   A^2 -> H(d, f(e))
28.55/9.63	   A^2 -> H(d, f(k))
28.55/9.63	   A^2 -> H(d, U1(d, d))
28.55/9.63	   A^2 -> H(a, U1(e, b))
28.55/9.63	   A^2 -> H(a, U1(k, b))
28.55/9.63	   A^2 -> H(a, U1(c, d))
28.55/9.63	   A^2 -> H(a, U1(d, c))
28.55/9.63	   A^2 -> H(a, U1(b, e))
28.55/9.63	   A^2 -> H(a, U1(b, k))
28.55/9.63	   A^2 -> H(a, U1(e, c))
28.55/9.63	   A^2 -> H(a, U1(k, c))
28.55/9.63	   A^2 -> H(a, U1(c, e))
28.55/9.63	   A^2 -> H(a, U1(c, k))
28.55/9.63	   A^2 -> H(a, U1(e, e))
28.55/9.63	   A^2 -> H(a, U1(k, k))
28.55/9.63	   A^2 -> H(a, U1(k, d))
28.55/9.63	   A^2 -> H(a, U1(d, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.63	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.63	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.63	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.63	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.63	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.63	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.63	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.63	   A^2 -> H(U1(e, a), b)
28.55/9.63	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.63	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.63	   A^2 -> H(U1(e, a), c)
28.55/9.63	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.63	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.63	   A^2 -> H(U1(e, a), e)
28.55/9.63	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, a), b)
28.55/9.63	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.63	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.63	   A^2 -> H(U1(k, a), c)
28.55/9.63	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.63	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.63	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, d), b)
28.55/9.63	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.63	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.63	   A^2 -> H(U1(c, d), c)
28.55/9.63	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.63	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.63	   A^2 -> H(U1(c, d), e)
28.55/9.63	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, a), d)
28.55/9.63	   A^2 -> H(U1(c, a), k)
28.55/9.63	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.63	   A^2 -> H(U1(d, c), b)
28.55/9.63	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.63	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.63	   A^2 -> H(U1(d, c), c)
28.55/9.63	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.63	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.63	   A^2 -> H(U1(d, c), e)
28.55/9.63	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.63	
28.55/9.63	The TRS R consists of the following rules:
28.55/9.63	
28.55/9.63	   f(x) -> U1(x, x)
28.55/9.63	   U1(e, x) -> x
28.55/9.63	   a -> c
28.55/9.63	   a -> d
28.55/9.63	   b -> c
28.55/9.63	   b -> d
28.55/9.63	   d -> k
28.55/9.63	   c -> e
28.55/9.63	   c -> k
28.55/9.63	
28.55/9.63	Q is empty.
28.55/9.63	We have to consider all minimal (P,Q,R)-chains.
28.55/9.63	----------------------------------------
28.55/9.63	
28.55/9.63	(1275) TransformationProof (EQUIVALENT)
28.55/9.63	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), b) at position [] we obtained the following new rules [LPAR04]:
28.55/9.63	
28.55/9.63	   (A^2 -> H(U1(k, a), b),A^2 -> H(U1(k, a), b))
28.55/9.63	   (A^2 -> H(U1(d, c), b),A^2 -> H(U1(d, c), b))
28.55/9.63	   (A^2 -> H(U1(d, d), b),A^2 -> H(U1(d, d), b))
28.55/9.63	   (A^2 -> H(U1(d, a), c),A^2 -> H(U1(d, a), c))
28.55/9.63	   (A^2 -> H(U1(d, a), d),A^2 -> H(U1(d, a), d))
28.55/9.63	
28.55/9.63	
28.55/9.63	----------------------------------------
28.55/9.63	
28.55/9.63	(1276)
28.55/9.63	Obligation:
28.55/9.63	Q DP problem:
28.55/9.63	The TRS P consists of the following rules:
28.55/9.63	
28.55/9.63	   A^2 -> H(f(c), f(c))
28.55/9.63	   H(x, x) -> G(x, x, f(k))
28.55/9.63	   G(d, x, x) -> A^2
28.55/9.63	   A^2 -> H(f(d), f(d))
28.55/9.63	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.63	   A^2 -> H(f(e), f(e))
28.55/9.63	   A^2 -> H(f(k), f(k))
28.55/9.63	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.63	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.63	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.63	   A^2 -> H(U1(d, a), U1(e, d))
28.55/9.63	   A^2 -> H(U1(d, a), U1(d, e))
28.55/9.63	   A^2 -> H(U1(d, a), c)
28.55/9.63	   A^2 -> H(U1(d, a), U1(e, k))
28.55/9.63	   A^2 -> H(U1(d, a), U1(k, e))
28.55/9.63	   A^2 -> H(U1(d, a), e)
28.55/9.63	   A^2 -> H(U1(d, a), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(a, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(a, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.63	   A^2 -> H(U1(a, c), b)
28.55/9.63	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.63	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.63	   A^2 -> H(U1(a, c), c)
28.55/9.63	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.63	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.63	   A^2 -> H(U1(a, c), e)
28.55/9.63	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, d), b)
28.55/9.63	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.63	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.63	   A^2 -> H(U1(a, d), c)
28.55/9.63	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.63	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.63	   A^2 -> H(U1(a, d), e)
28.55/9.63	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, a), d)
28.55/9.63	   A^2 -> H(U1(a, a), k)
28.55/9.63	   A^2 -> H(k, U1(b, b))
28.55/9.63	   A^2 -> H(k, f(c))
28.55/9.63	   A^2 -> H(k, f(d))
28.55/9.63	   A^2 -> H(c, U1(c, b))
28.55/9.63	   A^2 -> H(c, U1(d, b))
28.55/9.63	   A^2 -> H(c, U1(b, c))
28.55/9.63	   A^2 -> H(c, U1(b, d))
28.55/9.63	   A^2 -> H(c, U1(c, c))
28.55/9.63	   A^2 -> H(c, f(e))
28.55/9.63	   A^2 -> H(c, f(k))
28.55/9.63	   A^2 -> H(c, U1(d, d))
28.55/9.63	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.63	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.63	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.63	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.63	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.63	   A^2 -> H(U1(e, k), f(e))
28.55/9.63	   A^2 -> H(U1(e, k), f(k))
28.55/9.63	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.63	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.63	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.63	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.63	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.63	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.63	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.63	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.63	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.63	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.63	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.63	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.63	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.63	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.63	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.63	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.63	   A^2 -> H(U1(k, e), f(e))
28.55/9.63	   A^2 -> H(U1(k, e), f(k))
28.55/9.63	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.63	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.63	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.63	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.63	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.63	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.63	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.63	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.63	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.63	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.63	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.63	   A^2 -> H(U1(c, c), b)
28.55/9.63	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.63	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.63	   A^2 -> H(U1(c, c), e)
28.55/9.63	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.63	   A^2 -> H(e, U1(c, b))
28.55/9.63	   A^2 -> H(e, U1(d, b))
28.55/9.63	   A^2 -> H(e, U1(b, c))
28.55/9.63	   A^2 -> H(e, U1(b, d))
28.55/9.63	   A^2 -> H(e, U1(c, c))
28.55/9.63	   A^2 -> H(e, f(e))
28.55/9.63	   A^2 -> H(e, f(k))
28.55/9.63	   A^2 -> H(e, U1(d, d))
28.55/9.63	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.63	   A^2 -> H(f(e), b)
28.55/9.63	   A^2 -> H(f(e), U1(e, d))
28.55/9.63	   A^2 -> H(f(e), U1(d, e))
28.55/9.63	   A^2 -> H(f(e), c)
28.55/9.63	   A^2 -> H(f(e), U1(e, k))
28.55/9.63	   A^2 -> H(f(e), U1(k, e))
28.55/9.63	   A^2 -> H(f(e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.63	   A^2 -> H(f(k), b)
28.55/9.63	   A^2 -> H(f(k), U1(e, d))
28.55/9.63	   A^2 -> H(f(k), U1(d, e))
28.55/9.63	   A^2 -> H(f(k), c)
28.55/9.63	   A^2 -> H(f(k), U1(e, k))
28.55/9.63	   A^2 -> H(f(k), U1(k, e))
28.55/9.63	   A^2 -> H(f(k), e)
28.55/9.63	   A^2 -> H(f(c), d)
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.63	   A^2 -> H(U1(k, k), f(e))
28.55/9.63	   A^2 -> H(U1(k, k), f(k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.63	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.63	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.63	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.63	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.63	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.63	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.63	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.63	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.63	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.63	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.63	   A^2 -> H(U1(d, d), b)
28.55/9.63	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.63	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.63	   A^2 -> H(U1(d, d), c)
28.55/9.63	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.63	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.63	   A^2 -> H(U1(d, d), e)
28.55/9.63	   A^2 -> H(f(d), d)
28.55/9.63	   A^2 -> H(f(d), k)
28.55/9.63	   A^2 -> H(U1(c, c), c)
28.55/9.63	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.63	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.63	   A^2 -> H(f(c), k)
28.55/9.63	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.63	   A^2 -> H(f(k), U1(k, k))
28.55/9.63	   A^2 -> H(f(e), e)
28.55/9.63	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.63	   A^2 -> H(d, U1(c, b))
28.55/9.63	   A^2 -> H(d, U1(d, b))
28.55/9.63	   A^2 -> H(d, U1(b, c))
28.55/9.63	   A^2 -> H(d, U1(b, d))
28.55/9.63	   A^2 -> H(d, U1(c, c))
28.55/9.63	   A^2 -> H(d, f(e))
28.55/9.63	   A^2 -> H(d, f(k))
28.55/9.63	   A^2 -> H(d, U1(d, d))
28.55/9.63	   A^2 -> H(a, U1(e, b))
28.55/9.63	   A^2 -> H(a, U1(k, b))
28.55/9.63	   A^2 -> H(a, U1(c, d))
28.55/9.63	   A^2 -> H(a, U1(d, c))
28.55/9.63	   A^2 -> H(a, U1(b, e))
28.55/9.63	   A^2 -> H(a, U1(b, k))
28.55/9.63	   A^2 -> H(a, U1(e, c))
28.55/9.63	   A^2 -> H(a, U1(k, c))
28.55/9.63	   A^2 -> H(a, U1(c, e))
28.55/9.63	   A^2 -> H(a, U1(c, k))
28.55/9.63	   A^2 -> H(a, U1(e, e))
28.55/9.63	   A^2 -> H(a, U1(k, k))
28.55/9.63	   A^2 -> H(a, U1(k, d))
28.55/9.63	   A^2 -> H(a, U1(d, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.63	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.63	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.63	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.63	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.63	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.63	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.63	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.63	   A^2 -> H(U1(e, a), b)
28.55/9.63	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.63	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.63	   A^2 -> H(U1(e, a), c)
28.55/9.63	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.63	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.63	   A^2 -> H(U1(e, a), e)
28.55/9.63	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, a), b)
28.55/9.63	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.63	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.63	   A^2 -> H(U1(k, a), c)
28.55/9.63	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.63	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.63	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, d), b)
28.55/9.63	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.63	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.63	   A^2 -> H(U1(c, d), c)
28.55/9.63	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.63	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.63	   A^2 -> H(U1(c, d), e)
28.55/9.63	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, a), d)
28.55/9.63	   A^2 -> H(U1(c, a), k)
28.55/9.63	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.63	   A^2 -> H(U1(d, c), b)
28.55/9.63	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.63	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.63	   A^2 -> H(U1(d, c), c)
28.55/9.63	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.63	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.63	   A^2 -> H(U1(d, c), e)
28.55/9.63	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(d, a), d)
28.55/9.63	
28.55/9.63	The TRS R consists of the following rules:
28.55/9.63	
28.55/9.63	   f(x) -> U1(x, x)
28.55/9.63	   U1(e, x) -> x
28.55/9.63	   a -> c
28.55/9.63	   a -> d
28.55/9.63	   b -> c
28.55/9.63	   b -> d
28.55/9.63	   d -> k
28.55/9.63	   c -> e
28.55/9.63	   c -> k
28.55/9.63	
28.55/9.63	Q is empty.
28.55/9.63	We have to consider all minimal (P,Q,R)-chains.
28.55/9.63	----------------------------------------
28.55/9.63	
28.55/9.63	(1277) TransformationProof (EQUIVALENT)
28.55/9.63	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.63	
28.55/9.63	   (A^2 -> H(U1(k, a), U1(e, d)),A^2 -> H(U1(k, a), U1(e, d)))
28.55/9.63	   (A^2 -> H(U1(d, c), U1(e, d)),A^2 -> H(U1(d, c), U1(e, d)))
28.55/9.63	   (A^2 -> H(U1(d, d), U1(e, d)),A^2 -> H(U1(d, d), U1(e, d)))
28.55/9.63	   (A^2 -> H(U1(d, a), d),A^2 -> H(U1(d, a), d))
28.55/9.63	   (A^2 -> H(U1(d, a), U1(e, k)),A^2 -> H(U1(d, a), U1(e, k)))
28.55/9.63	
28.55/9.63	
28.55/9.63	----------------------------------------
28.55/9.63	
28.55/9.63	(1278)
28.55/9.63	Obligation:
28.55/9.63	Q DP problem:
28.55/9.63	The TRS P consists of the following rules:
28.55/9.63	
28.55/9.63	   A^2 -> H(f(c), f(c))
28.55/9.63	   H(x, x) -> G(x, x, f(k))
28.55/9.63	   G(d, x, x) -> A^2
28.55/9.63	   A^2 -> H(f(d), f(d))
28.55/9.63	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.63	   A^2 -> H(f(e), f(e))
28.55/9.63	   A^2 -> H(f(k), f(k))
28.55/9.63	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.63	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.63	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.63	   A^2 -> H(U1(d, a), U1(d, e))
28.55/9.63	   A^2 -> H(U1(d, a), c)
28.55/9.63	   A^2 -> H(U1(d, a), U1(e, k))
28.55/9.63	   A^2 -> H(U1(d, a), U1(k, e))
28.55/9.63	   A^2 -> H(U1(d, a), e)
28.55/9.63	   A^2 -> H(U1(d, a), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(a, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(a, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.63	   A^2 -> H(U1(a, c), b)
28.55/9.63	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.63	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.63	   A^2 -> H(U1(a, c), c)
28.55/9.63	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.63	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.63	   A^2 -> H(U1(a, c), e)
28.55/9.63	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, d), b)
28.55/9.63	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.63	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.63	   A^2 -> H(U1(a, d), c)
28.55/9.63	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.63	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.63	   A^2 -> H(U1(a, d), e)
28.55/9.63	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, a), d)
28.55/9.63	   A^2 -> H(U1(a, a), k)
28.55/9.63	   A^2 -> H(k, U1(b, b))
28.55/9.63	   A^2 -> H(k, f(c))
28.55/9.63	   A^2 -> H(k, f(d))
28.55/9.63	   A^2 -> H(c, U1(c, b))
28.55/9.63	   A^2 -> H(c, U1(d, b))
28.55/9.63	   A^2 -> H(c, U1(b, c))
28.55/9.63	   A^2 -> H(c, U1(b, d))
28.55/9.63	   A^2 -> H(c, U1(c, c))
28.55/9.63	   A^2 -> H(c, f(e))
28.55/9.63	   A^2 -> H(c, f(k))
28.55/9.63	   A^2 -> H(c, U1(d, d))
28.55/9.63	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.63	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.63	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.63	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.63	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.63	   A^2 -> H(U1(e, k), f(e))
28.55/9.63	   A^2 -> H(U1(e, k), f(k))
28.55/9.63	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.63	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.63	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.63	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.63	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.63	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.63	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.63	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.63	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.63	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.63	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.63	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.63	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.63	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.63	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.63	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.63	   A^2 -> H(U1(k, e), f(e))
28.55/9.63	   A^2 -> H(U1(k, e), f(k))
28.55/9.63	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.63	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.63	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.63	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.63	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.63	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.63	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.63	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.63	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.63	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.63	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.63	   A^2 -> H(U1(c, c), b)
28.55/9.63	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.63	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.63	   A^2 -> H(U1(c, c), e)
28.55/9.63	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.63	   A^2 -> H(e, U1(c, b))
28.55/9.63	   A^2 -> H(e, U1(d, b))
28.55/9.63	   A^2 -> H(e, U1(b, c))
28.55/9.63	   A^2 -> H(e, U1(b, d))
28.55/9.63	   A^2 -> H(e, U1(c, c))
28.55/9.63	   A^2 -> H(e, f(e))
28.55/9.63	   A^2 -> H(e, f(k))
28.55/9.63	   A^2 -> H(e, U1(d, d))
28.55/9.63	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.63	   A^2 -> H(f(e), b)
28.55/9.63	   A^2 -> H(f(e), U1(e, d))
28.55/9.63	   A^2 -> H(f(e), U1(d, e))
28.55/9.63	   A^2 -> H(f(e), c)
28.55/9.63	   A^2 -> H(f(e), U1(e, k))
28.55/9.63	   A^2 -> H(f(e), U1(k, e))
28.55/9.63	   A^2 -> H(f(e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.63	   A^2 -> H(f(k), b)
28.55/9.63	   A^2 -> H(f(k), U1(e, d))
28.55/9.63	   A^2 -> H(f(k), U1(d, e))
28.55/9.63	   A^2 -> H(f(k), c)
28.55/9.63	   A^2 -> H(f(k), U1(e, k))
28.55/9.63	   A^2 -> H(f(k), U1(k, e))
28.55/9.63	   A^2 -> H(f(k), e)
28.55/9.63	   A^2 -> H(f(c), d)
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.63	   A^2 -> H(U1(k, k), f(e))
28.55/9.63	   A^2 -> H(U1(k, k), f(k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.63	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.63	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.63	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.63	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.63	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.63	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.63	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.63	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.63	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.63	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.63	   A^2 -> H(U1(d, d), b)
28.55/9.63	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.63	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.63	   A^2 -> H(U1(d, d), c)
28.55/9.63	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.63	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.63	   A^2 -> H(U1(d, d), e)
28.55/9.63	   A^2 -> H(f(d), d)
28.55/9.63	   A^2 -> H(f(d), k)
28.55/9.63	   A^2 -> H(U1(c, c), c)
28.55/9.63	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.63	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.63	   A^2 -> H(f(c), k)
28.55/9.63	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.63	   A^2 -> H(f(k), U1(k, k))
28.55/9.63	   A^2 -> H(f(e), e)
28.55/9.63	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.63	   A^2 -> H(d, U1(c, b))
28.55/9.63	   A^2 -> H(d, U1(d, b))
28.55/9.63	   A^2 -> H(d, U1(b, c))
28.55/9.63	   A^2 -> H(d, U1(b, d))
28.55/9.63	   A^2 -> H(d, U1(c, c))
28.55/9.63	   A^2 -> H(d, f(e))
28.55/9.63	   A^2 -> H(d, f(k))
28.55/9.63	   A^2 -> H(d, U1(d, d))
28.55/9.63	   A^2 -> H(a, U1(e, b))
28.55/9.63	   A^2 -> H(a, U1(k, b))
28.55/9.63	   A^2 -> H(a, U1(c, d))
28.55/9.63	   A^2 -> H(a, U1(d, c))
28.55/9.63	   A^2 -> H(a, U1(b, e))
28.55/9.63	   A^2 -> H(a, U1(b, k))
28.55/9.63	   A^2 -> H(a, U1(e, c))
28.55/9.63	   A^2 -> H(a, U1(k, c))
28.55/9.63	   A^2 -> H(a, U1(c, e))
28.55/9.63	   A^2 -> H(a, U1(c, k))
28.55/9.63	   A^2 -> H(a, U1(e, e))
28.55/9.63	   A^2 -> H(a, U1(k, k))
28.55/9.63	   A^2 -> H(a, U1(k, d))
28.55/9.63	   A^2 -> H(a, U1(d, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.63	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.63	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.63	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.63	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.63	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.63	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.63	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.63	   A^2 -> H(U1(e, a), b)
28.55/9.63	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.63	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.63	   A^2 -> H(U1(e, a), c)
28.55/9.63	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.63	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.63	   A^2 -> H(U1(e, a), e)
28.55/9.63	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, a), b)
28.55/9.63	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.63	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.63	   A^2 -> H(U1(k, a), c)
28.55/9.63	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.63	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.63	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, d), b)
28.55/9.63	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.63	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.63	   A^2 -> H(U1(c, d), c)
28.55/9.63	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.63	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.63	   A^2 -> H(U1(c, d), e)
28.55/9.63	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, a), d)
28.55/9.63	   A^2 -> H(U1(c, a), k)
28.55/9.63	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.63	   A^2 -> H(U1(d, c), b)
28.55/9.63	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.63	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.63	   A^2 -> H(U1(d, c), c)
28.55/9.63	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.63	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.63	   A^2 -> H(U1(d, c), e)
28.55/9.63	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(d, a), d)
28.55/9.63	
28.55/9.63	The TRS R consists of the following rules:
28.55/9.63	
28.55/9.63	   f(x) -> U1(x, x)
28.55/9.63	   U1(e, x) -> x
28.55/9.63	   a -> c
28.55/9.63	   a -> d
28.55/9.63	   b -> c
28.55/9.63	   b -> d
28.55/9.63	   d -> k
28.55/9.63	   c -> e
28.55/9.63	   c -> k
28.55/9.63	
28.55/9.63	Q is empty.
28.55/9.63	We have to consider all minimal (P,Q,R)-chains.
28.55/9.63	----------------------------------------
28.55/9.63	
28.55/9.63	(1279) TransformationProof (EQUIVALENT)
28.55/9.63	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.63	
28.55/9.63	   (A^2 -> H(U1(k, a), U1(d, e)),A^2 -> H(U1(k, a), U1(d, e)))
28.55/9.63	   (A^2 -> H(U1(d, c), U1(d, e)),A^2 -> H(U1(d, c), U1(d, e)))
28.55/9.63	   (A^2 -> H(U1(d, d), U1(d, e)),A^2 -> H(U1(d, d), U1(d, e)))
28.55/9.63	   (A^2 -> H(U1(d, a), U1(k, e)),A^2 -> H(U1(d, a), U1(k, e)))
28.55/9.63	
28.55/9.63	
28.55/9.63	----------------------------------------
28.55/9.63	
28.55/9.63	(1280)
28.55/9.63	Obligation:
28.55/9.63	Q DP problem:
28.55/9.63	The TRS P consists of the following rules:
28.55/9.63	
28.55/9.63	   A^2 -> H(f(c), f(c))
28.55/9.63	   H(x, x) -> G(x, x, f(k))
28.55/9.63	   G(d, x, x) -> A^2
28.55/9.63	   A^2 -> H(f(d), f(d))
28.55/9.63	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.63	   A^2 -> H(f(e), f(e))
28.55/9.63	   A^2 -> H(f(k), f(k))
28.55/9.63	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.63	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.63	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.63	   A^2 -> H(U1(d, a), c)
28.55/9.63	   A^2 -> H(U1(d, a), U1(e, k))
28.55/9.63	   A^2 -> H(U1(d, a), U1(k, e))
28.55/9.63	   A^2 -> H(U1(d, a), e)
28.55/9.63	   A^2 -> H(U1(d, a), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(a, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(a, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.63	   A^2 -> H(U1(a, c), b)
28.55/9.63	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.63	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.63	   A^2 -> H(U1(a, c), c)
28.55/9.63	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.63	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.63	   A^2 -> H(U1(a, c), e)
28.55/9.63	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, d), b)
28.55/9.63	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.63	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.63	   A^2 -> H(U1(a, d), c)
28.55/9.63	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.63	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.63	   A^2 -> H(U1(a, d), e)
28.55/9.63	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, a), d)
28.55/9.63	   A^2 -> H(U1(a, a), k)
28.55/9.63	   A^2 -> H(k, U1(b, b))
28.55/9.63	   A^2 -> H(k, f(c))
28.55/9.63	   A^2 -> H(k, f(d))
28.55/9.63	   A^2 -> H(c, U1(c, b))
28.55/9.63	   A^2 -> H(c, U1(d, b))
28.55/9.63	   A^2 -> H(c, U1(b, c))
28.55/9.63	   A^2 -> H(c, U1(b, d))
28.55/9.63	   A^2 -> H(c, U1(c, c))
28.55/9.63	   A^2 -> H(c, f(e))
28.55/9.63	   A^2 -> H(c, f(k))
28.55/9.63	   A^2 -> H(c, U1(d, d))
28.55/9.63	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.63	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.63	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.63	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.63	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.63	   A^2 -> H(U1(e, k), f(e))
28.55/9.63	   A^2 -> H(U1(e, k), f(k))
28.55/9.63	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.63	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.63	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.63	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.63	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.63	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.63	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.63	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.63	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.63	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.63	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.63	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.63	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.63	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.63	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.63	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.63	   A^2 -> H(U1(k, e), f(e))
28.55/9.63	   A^2 -> H(U1(k, e), f(k))
28.55/9.63	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.63	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.63	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.63	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.63	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.63	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.63	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.63	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.63	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.63	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.63	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.63	   A^2 -> H(U1(c, c), b)
28.55/9.63	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.63	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.63	   A^2 -> H(U1(c, c), e)
28.55/9.63	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.63	   A^2 -> H(e, U1(c, b))
28.55/9.63	   A^2 -> H(e, U1(d, b))
28.55/9.63	   A^2 -> H(e, U1(b, c))
28.55/9.63	   A^2 -> H(e, U1(b, d))
28.55/9.63	   A^2 -> H(e, U1(c, c))
28.55/9.63	   A^2 -> H(e, f(e))
28.55/9.63	   A^2 -> H(e, f(k))
28.55/9.63	   A^2 -> H(e, U1(d, d))
28.55/9.63	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.63	   A^2 -> H(f(e), b)
28.55/9.63	   A^2 -> H(f(e), U1(e, d))
28.55/9.63	   A^2 -> H(f(e), U1(d, e))
28.55/9.63	   A^2 -> H(f(e), c)
28.55/9.63	   A^2 -> H(f(e), U1(e, k))
28.55/9.63	   A^2 -> H(f(e), U1(k, e))
28.55/9.63	   A^2 -> H(f(e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.63	   A^2 -> H(f(k), b)
28.55/9.63	   A^2 -> H(f(k), U1(e, d))
28.55/9.63	   A^2 -> H(f(k), U1(d, e))
28.55/9.63	   A^2 -> H(f(k), c)
28.55/9.63	   A^2 -> H(f(k), U1(e, k))
28.55/9.63	   A^2 -> H(f(k), U1(k, e))
28.55/9.63	   A^2 -> H(f(k), e)
28.55/9.63	   A^2 -> H(f(c), d)
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.63	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.63	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.63	   A^2 -> H(U1(k, k), f(e))
28.55/9.63	   A^2 -> H(U1(k, k), f(k))
28.55/9.63	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.63	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.63	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.63	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.63	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.63	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.63	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.63	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.63	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.63	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.63	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.63	   A^2 -> H(U1(d, d), b)
28.55/9.63	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.63	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.63	   A^2 -> H(U1(d, d), c)
28.55/9.63	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.63	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.63	   A^2 -> H(U1(d, d), e)
28.55/9.63	   A^2 -> H(f(d), d)
28.55/9.63	   A^2 -> H(f(d), k)
28.55/9.63	   A^2 -> H(U1(c, c), c)
28.55/9.63	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.63	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.63	   A^2 -> H(f(c), k)
28.55/9.63	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.63	   A^2 -> H(f(k), U1(k, k))
28.55/9.63	   A^2 -> H(f(e), e)
28.55/9.63	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.63	   A^2 -> H(d, U1(c, b))
28.55/9.63	   A^2 -> H(d, U1(d, b))
28.55/9.63	   A^2 -> H(d, U1(b, c))
28.55/9.63	   A^2 -> H(d, U1(b, d))
28.55/9.63	   A^2 -> H(d, U1(c, c))
28.55/9.63	   A^2 -> H(d, f(e))
28.55/9.63	   A^2 -> H(d, f(k))
28.55/9.63	   A^2 -> H(d, U1(d, d))
28.55/9.63	   A^2 -> H(a, U1(e, b))
28.55/9.63	   A^2 -> H(a, U1(k, b))
28.55/9.63	   A^2 -> H(a, U1(c, d))
28.55/9.63	   A^2 -> H(a, U1(d, c))
28.55/9.63	   A^2 -> H(a, U1(b, e))
28.55/9.63	   A^2 -> H(a, U1(b, k))
28.55/9.63	   A^2 -> H(a, U1(e, c))
28.55/9.63	   A^2 -> H(a, U1(k, c))
28.55/9.63	   A^2 -> H(a, U1(c, e))
28.55/9.63	   A^2 -> H(a, U1(c, k))
28.55/9.63	   A^2 -> H(a, U1(e, e))
28.55/9.63	   A^2 -> H(a, U1(k, k))
28.55/9.63	   A^2 -> H(a, U1(k, d))
28.55/9.63	   A^2 -> H(a, U1(d, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.63	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.63	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.63	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.63	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.63	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.63	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.63	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.63	   A^2 -> H(U1(e, a), b)
28.55/9.63	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.63	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.63	   A^2 -> H(U1(e, a), c)
28.55/9.63	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.63	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.63	   A^2 -> H(U1(e, a), e)
28.55/9.63	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, a), b)
28.55/9.63	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.63	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.63	   A^2 -> H(U1(k, a), c)
28.55/9.63	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.63	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.63	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, d), b)
28.55/9.63	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.63	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.63	   A^2 -> H(U1(c, d), c)
28.55/9.63	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.63	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.63	   A^2 -> H(U1(c, d), e)
28.55/9.63	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(c, a), d)
28.55/9.63	   A^2 -> H(U1(c, a), k)
28.55/9.63	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.63	   A^2 -> H(U1(d, c), b)
28.55/9.63	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.63	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.63	   A^2 -> H(U1(d, c), c)
28.55/9.63	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.63	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.63	   A^2 -> H(U1(d, c), e)
28.55/9.63	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(d, a), d)
28.55/9.63	
28.55/9.63	The TRS R consists of the following rules:
28.55/9.63	
28.55/9.63	   f(x) -> U1(x, x)
28.55/9.63	   U1(e, x) -> x
28.55/9.63	   a -> c
28.55/9.63	   a -> d
28.55/9.63	   b -> c
28.55/9.63	   b -> d
28.55/9.63	   d -> k
28.55/9.63	   c -> e
28.55/9.63	   c -> k
28.55/9.63	
28.55/9.63	Q is empty.
28.55/9.63	We have to consider all minimal (P,Q,R)-chains.
28.55/9.63	----------------------------------------
28.55/9.63	
28.55/9.63	(1281) TransformationProof (EQUIVALENT)
28.55/9.63	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), c) at position [] we obtained the following new rules [LPAR04]:
28.55/9.63	
28.55/9.63	   (A^2 -> H(U1(k, a), c),A^2 -> H(U1(k, a), c))
28.55/9.63	   (A^2 -> H(U1(d, c), c),A^2 -> H(U1(d, c), c))
28.55/9.63	   (A^2 -> H(U1(d, d), c),A^2 -> H(U1(d, d), c))
28.55/9.63	   (A^2 -> H(U1(d, a), e),A^2 -> H(U1(d, a), e))
28.55/9.63	   (A^2 -> H(U1(d, a), k),A^2 -> H(U1(d, a), k))
28.55/9.63	
28.55/9.63	
28.55/9.63	----------------------------------------
28.55/9.63	
28.55/9.63	(1282)
28.55/9.63	Obligation:
28.55/9.63	Q DP problem:
28.55/9.63	The TRS P consists of the following rules:
28.55/9.63	
28.55/9.63	   A^2 -> H(f(c), f(c))
28.55/9.63	   H(x, x) -> G(x, x, f(k))
28.55/9.63	   G(d, x, x) -> A^2
28.55/9.63	   A^2 -> H(f(d), f(d))
28.55/9.63	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.63	   A^2 -> H(f(e), f(e))
28.55/9.63	   A^2 -> H(f(k), f(k))
28.55/9.63	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.63	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.63	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.63	   A^2 -> H(U1(d, a), U1(e, k))
28.55/9.63	   A^2 -> H(U1(d, a), U1(k, e))
28.55/9.63	   A^2 -> H(U1(d, a), e)
28.55/9.63	   A^2 -> H(U1(d, a), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(a, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(a, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.63	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.63	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.63	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.63	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.63	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.63	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.63	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.63	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.63	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.63	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.63	   A^2 -> H(U1(a, c), b)
28.55/9.63	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.63	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.63	   A^2 -> H(U1(a, c), c)
28.55/9.63	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.63	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.63	   A^2 -> H(U1(a, c), e)
28.55/9.63	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, d), b)
28.55/9.63	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.63	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.63	   A^2 -> H(U1(a, d), c)
28.55/9.63	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.63	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.63	   A^2 -> H(U1(a, d), e)
28.55/9.63	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.63	   A^2 -> H(U1(a, a), d)
28.55/9.63	   A^2 -> H(U1(a, a), k)
28.55/9.63	   A^2 -> H(k, U1(b, b))
28.55/9.63	   A^2 -> H(k, f(c))
28.55/9.63	   A^2 -> H(k, f(d))
28.55/9.63	   A^2 -> H(c, U1(c, b))
28.55/9.63	   A^2 -> H(c, U1(d, b))
28.55/9.63	   A^2 -> H(c, U1(b, c))
28.55/9.63	   A^2 -> H(c, U1(b, d))
28.55/9.63	   A^2 -> H(c, U1(c, c))
28.55/9.63	   A^2 -> H(c, f(e))
28.55/9.63	   A^2 -> H(c, f(k))
28.55/9.63	   A^2 -> H(c, U1(d, d))
28.55/9.63	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.63	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.63	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.63	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.63	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.63	   A^2 -> H(U1(e, k), f(e))
28.55/9.63	   A^2 -> H(U1(e, k), f(k))
28.55/9.63	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.63	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.63	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.63	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.63	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.63	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.63	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.63	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.63	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.63	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.63	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.63	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.63	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.63	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.63	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.63	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.63	   A^2 -> H(U1(k, e), f(e))
28.55/9.63	   A^2 -> H(U1(k, e), f(k))
28.55/9.63	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.63	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.63	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.63	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.63	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.63	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.63	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.63	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.63	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.63	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.63	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.63	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.63	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.63	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.63	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.63	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.63	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.63	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.64	   A^2 -> H(U1(c, c), b)
28.55/9.64	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.64	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.64	   A^2 -> H(U1(c, c), e)
28.55/9.64	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.64	   A^2 -> H(e, U1(c, b))
28.55/9.64	   A^2 -> H(e, U1(d, b))
28.55/9.64	   A^2 -> H(e, U1(b, c))
28.55/9.64	   A^2 -> H(e, U1(b, d))
28.55/9.64	   A^2 -> H(e, U1(c, c))
28.55/9.64	   A^2 -> H(e, f(e))
28.55/9.64	   A^2 -> H(e, f(k))
28.55/9.64	   A^2 -> H(e, U1(d, d))
28.55/9.64	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.64	   A^2 -> H(f(e), b)
28.55/9.64	   A^2 -> H(f(e), U1(e, d))
28.55/9.64	   A^2 -> H(f(e), U1(d, e))
28.55/9.64	   A^2 -> H(f(e), c)
28.55/9.64	   A^2 -> H(f(e), U1(e, k))
28.55/9.64	   A^2 -> H(f(e), U1(k, e))
28.55/9.64	   A^2 -> H(f(e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.64	   A^2 -> H(f(k), b)
28.55/9.64	   A^2 -> H(f(k), U1(e, d))
28.55/9.64	   A^2 -> H(f(k), U1(d, e))
28.55/9.64	   A^2 -> H(f(k), c)
28.55/9.64	   A^2 -> H(f(k), U1(e, k))
28.55/9.64	   A^2 -> H(f(k), U1(k, e))
28.55/9.64	   A^2 -> H(f(k), e)
28.55/9.64	   A^2 -> H(f(c), d)
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.64	   A^2 -> H(U1(k, k), f(e))
28.55/9.64	   A^2 -> H(U1(k, k), f(k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.64	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.64	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.64	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.64	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.64	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.64	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.64	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.64	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.64	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.64	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.64	   A^2 -> H(U1(d, d), b)
28.55/9.64	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.64	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.64	   A^2 -> H(U1(d, d), c)
28.55/9.64	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.64	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.64	   A^2 -> H(U1(d, d), e)
28.55/9.64	   A^2 -> H(f(d), d)
28.55/9.64	   A^2 -> H(f(d), k)
28.55/9.64	   A^2 -> H(U1(c, c), c)
28.55/9.64	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.64	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.64	   A^2 -> H(f(c), k)
28.55/9.64	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.64	   A^2 -> H(f(k), U1(k, k))
28.55/9.64	   A^2 -> H(f(e), e)
28.55/9.64	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.64	   A^2 -> H(d, U1(c, b))
28.55/9.64	   A^2 -> H(d, U1(d, b))
28.55/9.64	   A^2 -> H(d, U1(b, c))
28.55/9.64	   A^2 -> H(d, U1(b, d))
28.55/9.64	   A^2 -> H(d, U1(c, c))
28.55/9.64	   A^2 -> H(d, f(e))
28.55/9.64	   A^2 -> H(d, f(k))
28.55/9.64	   A^2 -> H(d, U1(d, d))
28.55/9.64	   A^2 -> H(a, U1(e, b))
28.55/9.64	   A^2 -> H(a, U1(k, b))
28.55/9.64	   A^2 -> H(a, U1(c, d))
28.55/9.64	   A^2 -> H(a, U1(d, c))
28.55/9.64	   A^2 -> H(a, U1(b, e))
28.55/9.64	   A^2 -> H(a, U1(b, k))
28.55/9.64	   A^2 -> H(a, U1(e, c))
28.55/9.64	   A^2 -> H(a, U1(k, c))
28.55/9.64	   A^2 -> H(a, U1(c, e))
28.55/9.64	   A^2 -> H(a, U1(c, k))
28.55/9.64	   A^2 -> H(a, U1(e, e))
28.55/9.64	   A^2 -> H(a, U1(k, k))
28.55/9.64	   A^2 -> H(a, U1(k, d))
28.55/9.64	   A^2 -> H(a, U1(d, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.64	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.64	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.64	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.64	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.64	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.64	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.64	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.64	   A^2 -> H(U1(e, a), b)
28.55/9.64	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.64	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.64	   A^2 -> H(U1(e, a), c)
28.55/9.64	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.64	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.64	   A^2 -> H(U1(e, a), e)
28.55/9.64	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, a), b)
28.55/9.64	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.64	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.64	   A^2 -> H(U1(k, a), c)
28.55/9.64	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.64	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.64	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, d), b)
28.55/9.64	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.64	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.64	   A^2 -> H(U1(c, d), c)
28.55/9.64	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.64	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.64	   A^2 -> H(U1(c, d), e)
28.55/9.64	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, a), d)
28.55/9.64	   A^2 -> H(U1(c, a), k)
28.55/9.64	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.64	   A^2 -> H(U1(d, c), b)
28.55/9.64	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.64	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.64	   A^2 -> H(U1(d, c), c)
28.55/9.64	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.64	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.64	   A^2 -> H(U1(d, c), e)
28.55/9.64	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(d, a), d)
28.55/9.64	   A^2 -> H(U1(d, a), k)
28.55/9.64	
28.55/9.64	The TRS R consists of the following rules:
28.55/9.64	
28.55/9.64	   f(x) -> U1(x, x)
28.55/9.64	   U1(e, x) -> x
28.55/9.64	   a -> c
28.55/9.64	   a -> d
28.55/9.64	   b -> c
28.55/9.64	   b -> d
28.55/9.64	   d -> k
28.55/9.64	   c -> e
28.55/9.64	   c -> k
28.55/9.64	
28.55/9.64	Q is empty.
28.55/9.64	We have to consider all minimal (P,Q,R)-chains.
28.55/9.64	----------------------------------------
28.55/9.64	
28.55/9.64	(1283) TransformationProof (EQUIVALENT)
28.55/9.64	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.64	
28.55/9.64	   (A^2 -> H(U1(k, a), U1(e, k)),A^2 -> H(U1(k, a), U1(e, k)))
28.55/9.64	   (A^2 -> H(U1(d, c), U1(e, k)),A^2 -> H(U1(d, c), U1(e, k)))
28.55/9.64	   (A^2 -> H(U1(d, d), U1(e, k)),A^2 -> H(U1(d, d), U1(e, k)))
28.55/9.64	   (A^2 -> H(U1(d, a), k),A^2 -> H(U1(d, a), k))
28.55/9.64	
28.55/9.64	
28.55/9.64	----------------------------------------
28.55/9.64	
28.55/9.64	(1284)
28.55/9.64	Obligation:
28.55/9.64	Q DP problem:
28.55/9.64	The TRS P consists of the following rules:
28.55/9.64	
28.55/9.64	   A^2 -> H(f(c), f(c))
28.55/9.64	   H(x, x) -> G(x, x, f(k))
28.55/9.64	   G(d, x, x) -> A^2
28.55/9.64	   A^2 -> H(f(d), f(d))
28.55/9.64	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.64	   A^2 -> H(f(e), f(e))
28.55/9.64	   A^2 -> H(f(k), f(k))
28.55/9.64	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.64	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.64	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.64	   A^2 -> H(U1(d, a), U1(k, e))
28.55/9.64	   A^2 -> H(U1(d, a), e)
28.55/9.64	   A^2 -> H(U1(d, a), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(a, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(a, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.64	   A^2 -> H(U1(a, c), b)
28.55/9.64	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.64	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.64	   A^2 -> H(U1(a, c), c)
28.55/9.64	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.64	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.64	   A^2 -> H(U1(a, c), e)
28.55/9.64	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, d), b)
28.55/9.64	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.64	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.64	   A^2 -> H(U1(a, d), c)
28.55/9.64	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.64	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.64	   A^2 -> H(U1(a, d), e)
28.55/9.64	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, a), d)
28.55/9.64	   A^2 -> H(U1(a, a), k)
28.55/9.64	   A^2 -> H(k, U1(b, b))
28.55/9.64	   A^2 -> H(k, f(c))
28.55/9.64	   A^2 -> H(k, f(d))
28.55/9.64	   A^2 -> H(c, U1(c, b))
28.55/9.64	   A^2 -> H(c, U1(d, b))
28.55/9.64	   A^2 -> H(c, U1(b, c))
28.55/9.64	   A^2 -> H(c, U1(b, d))
28.55/9.64	   A^2 -> H(c, U1(c, c))
28.55/9.64	   A^2 -> H(c, f(e))
28.55/9.64	   A^2 -> H(c, f(k))
28.55/9.64	   A^2 -> H(c, U1(d, d))
28.55/9.64	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.64	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.64	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.64	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.64	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.64	   A^2 -> H(U1(e, k), f(e))
28.55/9.64	   A^2 -> H(U1(e, k), f(k))
28.55/9.64	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.64	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.64	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.64	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.64	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.64	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.64	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.64	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.64	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.64	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.64	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.64	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.64	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.64	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.64	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.64	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.64	   A^2 -> H(U1(k, e), f(e))
28.55/9.64	   A^2 -> H(U1(k, e), f(k))
28.55/9.64	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.64	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.64	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.64	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.64	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.64	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.64	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.64	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.64	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.64	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.64	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.64	   A^2 -> H(U1(c, c), b)
28.55/9.64	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.64	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.64	   A^2 -> H(U1(c, c), e)
28.55/9.64	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.64	   A^2 -> H(e, U1(c, b))
28.55/9.64	   A^2 -> H(e, U1(d, b))
28.55/9.64	   A^2 -> H(e, U1(b, c))
28.55/9.64	   A^2 -> H(e, U1(b, d))
28.55/9.64	   A^2 -> H(e, U1(c, c))
28.55/9.64	   A^2 -> H(e, f(e))
28.55/9.64	   A^2 -> H(e, f(k))
28.55/9.64	   A^2 -> H(e, U1(d, d))
28.55/9.64	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.64	   A^2 -> H(f(e), b)
28.55/9.64	   A^2 -> H(f(e), U1(e, d))
28.55/9.64	   A^2 -> H(f(e), U1(d, e))
28.55/9.64	   A^2 -> H(f(e), c)
28.55/9.64	   A^2 -> H(f(e), U1(e, k))
28.55/9.64	   A^2 -> H(f(e), U1(k, e))
28.55/9.64	   A^2 -> H(f(e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.64	   A^2 -> H(f(k), b)
28.55/9.64	   A^2 -> H(f(k), U1(e, d))
28.55/9.64	   A^2 -> H(f(k), U1(d, e))
28.55/9.64	   A^2 -> H(f(k), c)
28.55/9.64	   A^2 -> H(f(k), U1(e, k))
28.55/9.64	   A^2 -> H(f(k), U1(k, e))
28.55/9.64	   A^2 -> H(f(k), e)
28.55/9.64	   A^2 -> H(f(c), d)
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.64	   A^2 -> H(U1(k, k), f(e))
28.55/9.64	   A^2 -> H(U1(k, k), f(k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.64	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.64	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.64	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.64	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.64	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.64	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.64	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.64	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.64	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.64	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.64	   A^2 -> H(U1(d, d), b)
28.55/9.64	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.64	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.64	   A^2 -> H(U1(d, d), c)
28.55/9.64	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.64	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.64	   A^2 -> H(U1(d, d), e)
28.55/9.64	   A^2 -> H(f(d), d)
28.55/9.64	   A^2 -> H(f(d), k)
28.55/9.64	   A^2 -> H(U1(c, c), c)
28.55/9.64	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.64	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.64	   A^2 -> H(f(c), k)
28.55/9.64	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.64	   A^2 -> H(f(k), U1(k, k))
28.55/9.64	   A^2 -> H(f(e), e)
28.55/9.64	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.64	   A^2 -> H(d, U1(c, b))
28.55/9.64	   A^2 -> H(d, U1(d, b))
28.55/9.64	   A^2 -> H(d, U1(b, c))
28.55/9.64	   A^2 -> H(d, U1(b, d))
28.55/9.64	   A^2 -> H(d, U1(c, c))
28.55/9.64	   A^2 -> H(d, f(e))
28.55/9.64	   A^2 -> H(d, f(k))
28.55/9.64	   A^2 -> H(d, U1(d, d))
28.55/9.64	   A^2 -> H(a, U1(e, b))
28.55/9.64	   A^2 -> H(a, U1(k, b))
28.55/9.64	   A^2 -> H(a, U1(c, d))
28.55/9.64	   A^2 -> H(a, U1(d, c))
28.55/9.64	   A^2 -> H(a, U1(b, e))
28.55/9.64	   A^2 -> H(a, U1(b, k))
28.55/9.64	   A^2 -> H(a, U1(e, c))
28.55/9.64	   A^2 -> H(a, U1(k, c))
28.55/9.64	   A^2 -> H(a, U1(c, e))
28.55/9.64	   A^2 -> H(a, U1(c, k))
28.55/9.64	   A^2 -> H(a, U1(e, e))
28.55/9.64	   A^2 -> H(a, U1(k, k))
28.55/9.64	   A^2 -> H(a, U1(k, d))
28.55/9.64	   A^2 -> H(a, U1(d, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.64	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.64	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.64	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.64	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.64	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.64	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.64	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.64	   A^2 -> H(U1(e, a), b)
28.55/9.64	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.64	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.64	   A^2 -> H(U1(e, a), c)
28.55/9.64	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.64	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.64	   A^2 -> H(U1(e, a), e)
28.55/9.64	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, a), b)
28.55/9.64	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.64	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.64	   A^2 -> H(U1(k, a), c)
28.55/9.64	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.64	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.64	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, d), b)
28.55/9.64	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.64	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.64	   A^2 -> H(U1(c, d), c)
28.55/9.64	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.64	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.64	   A^2 -> H(U1(c, d), e)
28.55/9.64	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, a), d)
28.55/9.64	   A^2 -> H(U1(c, a), k)
28.55/9.64	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.64	   A^2 -> H(U1(d, c), b)
28.55/9.64	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.64	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.64	   A^2 -> H(U1(d, c), c)
28.55/9.64	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.64	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.64	   A^2 -> H(U1(d, c), e)
28.55/9.64	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(d, a), d)
28.55/9.64	   A^2 -> H(U1(d, a), k)
28.55/9.64	
28.55/9.64	The TRS R consists of the following rules:
28.55/9.64	
28.55/9.64	   f(x) -> U1(x, x)
28.55/9.64	   U1(e, x) -> x
28.55/9.64	   a -> c
28.55/9.64	   a -> d
28.55/9.64	   b -> c
28.55/9.64	   b -> d
28.55/9.64	   d -> k
28.55/9.64	   c -> e
28.55/9.64	   c -> k
28.55/9.64	
28.55/9.64	Q is empty.
28.55/9.64	We have to consider all minimal (P,Q,R)-chains.
28.55/9.64	----------------------------------------
28.55/9.64	
28.55/9.64	(1285) TransformationProof (EQUIVALENT)
28.55/9.64	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.64	
28.55/9.64	   (A^2 -> H(U1(k, a), U1(k, e)),A^2 -> H(U1(k, a), U1(k, e)))
28.55/9.64	   (A^2 -> H(U1(d, c), U1(k, e)),A^2 -> H(U1(d, c), U1(k, e)))
28.55/9.64	   (A^2 -> H(U1(d, d), U1(k, e)),A^2 -> H(U1(d, d), U1(k, e)))
28.55/9.64	
28.55/9.64	
28.55/9.64	----------------------------------------
28.55/9.64	
28.55/9.64	(1286)
28.55/9.64	Obligation:
28.55/9.64	Q DP problem:
28.55/9.64	The TRS P consists of the following rules:
28.55/9.64	
28.55/9.64	   A^2 -> H(f(c), f(c))
28.55/9.64	   H(x, x) -> G(x, x, f(k))
28.55/9.64	   G(d, x, x) -> A^2
28.55/9.64	   A^2 -> H(f(d), f(d))
28.55/9.64	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.64	   A^2 -> H(f(e), f(e))
28.55/9.64	   A^2 -> H(f(k), f(k))
28.55/9.64	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.64	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.64	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.64	   A^2 -> H(U1(d, a), e)
28.55/9.64	   A^2 -> H(U1(d, a), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(a, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(a, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.64	   A^2 -> H(U1(a, c), b)
28.55/9.64	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.64	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.64	   A^2 -> H(U1(a, c), c)
28.55/9.64	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.64	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.64	   A^2 -> H(U1(a, c), e)
28.55/9.64	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, d), b)
28.55/9.64	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.64	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.64	   A^2 -> H(U1(a, d), c)
28.55/9.64	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.64	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.64	   A^2 -> H(U1(a, d), e)
28.55/9.64	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, a), d)
28.55/9.64	   A^2 -> H(U1(a, a), k)
28.55/9.64	   A^2 -> H(k, U1(b, b))
28.55/9.64	   A^2 -> H(k, f(c))
28.55/9.64	   A^2 -> H(k, f(d))
28.55/9.64	   A^2 -> H(c, U1(c, b))
28.55/9.64	   A^2 -> H(c, U1(d, b))
28.55/9.64	   A^2 -> H(c, U1(b, c))
28.55/9.64	   A^2 -> H(c, U1(b, d))
28.55/9.64	   A^2 -> H(c, U1(c, c))
28.55/9.64	   A^2 -> H(c, f(e))
28.55/9.64	   A^2 -> H(c, f(k))
28.55/9.64	   A^2 -> H(c, U1(d, d))
28.55/9.64	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.64	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.64	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.64	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.64	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.64	   A^2 -> H(U1(e, k), f(e))
28.55/9.64	   A^2 -> H(U1(e, k), f(k))
28.55/9.64	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.64	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.64	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.64	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.64	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.64	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.64	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.64	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.64	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.64	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.64	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.64	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.64	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.64	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.64	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.64	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.64	   A^2 -> H(U1(k, e), f(e))
28.55/9.64	   A^2 -> H(U1(k, e), f(k))
28.55/9.64	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.64	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.64	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.64	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.64	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.64	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.64	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.64	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.64	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.64	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.64	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.64	   A^2 -> H(U1(c, c), b)
28.55/9.64	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.64	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.64	   A^2 -> H(U1(c, c), e)
28.55/9.64	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.64	   A^2 -> H(e, U1(c, b))
28.55/9.64	   A^2 -> H(e, U1(d, b))
28.55/9.64	   A^2 -> H(e, U1(b, c))
28.55/9.64	   A^2 -> H(e, U1(b, d))
28.55/9.64	   A^2 -> H(e, U1(c, c))
28.55/9.64	   A^2 -> H(e, f(e))
28.55/9.64	   A^2 -> H(e, f(k))
28.55/9.64	   A^2 -> H(e, U1(d, d))
28.55/9.64	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.64	   A^2 -> H(f(e), b)
28.55/9.64	   A^2 -> H(f(e), U1(e, d))
28.55/9.64	   A^2 -> H(f(e), U1(d, e))
28.55/9.64	   A^2 -> H(f(e), c)
28.55/9.64	   A^2 -> H(f(e), U1(e, k))
28.55/9.64	   A^2 -> H(f(e), U1(k, e))
28.55/9.64	   A^2 -> H(f(e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.64	   A^2 -> H(f(k), b)
28.55/9.64	   A^2 -> H(f(k), U1(e, d))
28.55/9.64	   A^2 -> H(f(k), U1(d, e))
28.55/9.64	   A^2 -> H(f(k), c)
28.55/9.64	   A^2 -> H(f(k), U1(e, k))
28.55/9.64	   A^2 -> H(f(k), U1(k, e))
28.55/9.64	   A^2 -> H(f(k), e)
28.55/9.64	   A^2 -> H(f(c), d)
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.64	   A^2 -> H(U1(k, k), f(e))
28.55/9.64	   A^2 -> H(U1(k, k), f(k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.64	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.64	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.64	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.64	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.64	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.64	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.64	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.64	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.64	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.64	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.64	   A^2 -> H(U1(d, d), b)
28.55/9.64	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.64	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.64	   A^2 -> H(U1(d, d), c)
28.55/9.64	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.64	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.64	   A^2 -> H(U1(d, d), e)
28.55/9.64	   A^2 -> H(f(d), d)
28.55/9.64	   A^2 -> H(f(d), k)
28.55/9.64	   A^2 -> H(U1(c, c), c)
28.55/9.64	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.64	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.64	   A^2 -> H(f(c), k)
28.55/9.64	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.64	   A^2 -> H(f(k), U1(k, k))
28.55/9.64	   A^2 -> H(f(e), e)
28.55/9.64	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.64	   A^2 -> H(d, U1(c, b))
28.55/9.64	   A^2 -> H(d, U1(d, b))
28.55/9.64	   A^2 -> H(d, U1(b, c))
28.55/9.64	   A^2 -> H(d, U1(b, d))
28.55/9.64	   A^2 -> H(d, U1(c, c))
28.55/9.64	   A^2 -> H(d, f(e))
28.55/9.64	   A^2 -> H(d, f(k))
28.55/9.64	   A^2 -> H(d, U1(d, d))
28.55/9.64	   A^2 -> H(a, U1(e, b))
28.55/9.64	   A^2 -> H(a, U1(k, b))
28.55/9.64	   A^2 -> H(a, U1(c, d))
28.55/9.64	   A^2 -> H(a, U1(d, c))
28.55/9.64	   A^2 -> H(a, U1(b, e))
28.55/9.64	   A^2 -> H(a, U1(b, k))
28.55/9.64	   A^2 -> H(a, U1(e, c))
28.55/9.64	   A^2 -> H(a, U1(k, c))
28.55/9.64	   A^2 -> H(a, U1(c, e))
28.55/9.64	   A^2 -> H(a, U1(c, k))
28.55/9.64	   A^2 -> H(a, U1(e, e))
28.55/9.64	   A^2 -> H(a, U1(k, k))
28.55/9.64	   A^2 -> H(a, U1(k, d))
28.55/9.64	   A^2 -> H(a, U1(d, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.64	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.64	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.64	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.64	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.64	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.64	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.64	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.64	   A^2 -> H(U1(e, a), b)
28.55/9.64	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.64	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.64	   A^2 -> H(U1(e, a), c)
28.55/9.64	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.64	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.64	   A^2 -> H(U1(e, a), e)
28.55/9.64	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, a), b)
28.55/9.64	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.64	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.64	   A^2 -> H(U1(k, a), c)
28.55/9.64	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.64	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.64	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, d), b)
28.55/9.64	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.64	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.64	   A^2 -> H(U1(c, d), c)
28.55/9.64	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.64	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.64	   A^2 -> H(U1(c, d), e)
28.55/9.64	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, a), d)
28.55/9.64	   A^2 -> H(U1(c, a), k)
28.55/9.64	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.64	   A^2 -> H(U1(d, c), b)
28.55/9.64	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.64	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.64	   A^2 -> H(U1(d, c), c)
28.55/9.64	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.64	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.64	   A^2 -> H(U1(d, c), e)
28.55/9.64	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(d, a), d)
28.55/9.64	   A^2 -> H(U1(d, a), k)
28.55/9.64	
28.55/9.64	The TRS R consists of the following rules:
28.55/9.64	
28.55/9.64	   f(x) -> U1(x, x)
28.55/9.64	   U1(e, x) -> x
28.55/9.64	   a -> c
28.55/9.64	   a -> d
28.55/9.64	   b -> c
28.55/9.64	   b -> d
28.55/9.64	   d -> k
28.55/9.64	   c -> e
28.55/9.64	   c -> k
28.55/9.64	
28.55/9.64	Q is empty.
28.55/9.64	We have to consider all minimal (P,Q,R)-chains.
28.55/9.64	----------------------------------------
28.55/9.64	
28.55/9.64	(1287) TransformationProof (EQUIVALENT)
28.55/9.64	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), e) at position [] we obtained the following new rules [LPAR04]:
28.55/9.64	
28.55/9.64	   (A^2 -> H(U1(k, a), e),A^2 -> H(U1(k, a), e))
28.55/9.64	   (A^2 -> H(U1(d, c), e),A^2 -> H(U1(d, c), e))
28.55/9.64	   (A^2 -> H(U1(d, d), e),A^2 -> H(U1(d, d), e))
28.55/9.64	
28.55/9.64	
28.55/9.64	----------------------------------------
28.55/9.64	
28.55/9.64	(1288)
28.55/9.64	Obligation:
28.55/9.64	Q DP problem:
28.55/9.64	The TRS P consists of the following rules:
28.55/9.64	
28.55/9.64	   A^2 -> H(f(c), f(c))
28.55/9.64	   H(x, x) -> G(x, x, f(k))
28.55/9.64	   G(d, x, x) -> A^2
28.55/9.64	   A^2 -> H(f(d), f(d))
28.55/9.64	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.64	   A^2 -> H(f(e), f(e))
28.55/9.64	   A^2 -> H(f(k), f(k))
28.55/9.64	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.64	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.64	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.64	   A^2 -> H(U1(d, a), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(a, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(a, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.64	   A^2 -> H(U1(a, c), b)
28.55/9.64	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.64	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.64	   A^2 -> H(U1(a, c), c)
28.55/9.64	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.64	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.64	   A^2 -> H(U1(a, c), e)
28.55/9.64	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, d), b)
28.55/9.64	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.64	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.64	   A^2 -> H(U1(a, d), c)
28.55/9.64	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.64	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.64	   A^2 -> H(U1(a, d), e)
28.55/9.64	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, a), d)
28.55/9.64	   A^2 -> H(U1(a, a), k)
28.55/9.64	   A^2 -> H(k, U1(b, b))
28.55/9.64	   A^2 -> H(k, f(c))
28.55/9.64	   A^2 -> H(k, f(d))
28.55/9.64	   A^2 -> H(c, U1(c, b))
28.55/9.64	   A^2 -> H(c, U1(d, b))
28.55/9.64	   A^2 -> H(c, U1(b, c))
28.55/9.64	   A^2 -> H(c, U1(b, d))
28.55/9.64	   A^2 -> H(c, U1(c, c))
28.55/9.64	   A^2 -> H(c, f(e))
28.55/9.64	   A^2 -> H(c, f(k))
28.55/9.64	   A^2 -> H(c, U1(d, d))
28.55/9.64	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.64	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.64	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.64	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.64	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.64	   A^2 -> H(U1(e, k), f(e))
28.55/9.64	   A^2 -> H(U1(e, k), f(k))
28.55/9.64	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.64	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.64	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.64	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.64	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.64	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.64	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.64	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.64	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.64	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.64	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.64	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.64	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.64	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.64	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.64	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.64	   A^2 -> H(U1(k, e), f(e))
28.55/9.64	   A^2 -> H(U1(k, e), f(k))
28.55/9.64	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.64	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.64	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.64	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.64	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.64	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.64	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.64	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.64	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.64	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.64	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.64	   A^2 -> H(U1(c, c), b)
28.55/9.64	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.64	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.64	   A^2 -> H(U1(c, c), e)
28.55/9.64	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.64	   A^2 -> H(e, U1(c, b))
28.55/9.64	   A^2 -> H(e, U1(d, b))
28.55/9.64	   A^2 -> H(e, U1(b, c))
28.55/9.64	   A^2 -> H(e, U1(b, d))
28.55/9.64	   A^2 -> H(e, U1(c, c))
28.55/9.64	   A^2 -> H(e, f(e))
28.55/9.64	   A^2 -> H(e, f(k))
28.55/9.64	   A^2 -> H(e, U1(d, d))
28.55/9.64	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.64	   A^2 -> H(f(e), b)
28.55/9.64	   A^2 -> H(f(e), U1(e, d))
28.55/9.64	   A^2 -> H(f(e), U1(d, e))
28.55/9.64	   A^2 -> H(f(e), c)
28.55/9.64	   A^2 -> H(f(e), U1(e, k))
28.55/9.64	   A^2 -> H(f(e), U1(k, e))
28.55/9.64	   A^2 -> H(f(e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.64	   A^2 -> H(f(k), b)
28.55/9.64	   A^2 -> H(f(k), U1(e, d))
28.55/9.64	   A^2 -> H(f(k), U1(d, e))
28.55/9.64	   A^2 -> H(f(k), c)
28.55/9.64	   A^2 -> H(f(k), U1(e, k))
28.55/9.64	   A^2 -> H(f(k), U1(k, e))
28.55/9.64	   A^2 -> H(f(k), e)
28.55/9.64	   A^2 -> H(f(c), d)
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.64	   A^2 -> H(U1(k, k), f(e))
28.55/9.64	   A^2 -> H(U1(k, k), f(k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.64	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.64	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.64	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.64	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.64	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.64	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.64	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.64	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.64	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.64	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.64	   A^2 -> H(U1(d, d), b)
28.55/9.64	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.64	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.64	   A^2 -> H(U1(d, d), c)
28.55/9.64	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.64	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.64	   A^2 -> H(U1(d, d), e)
28.55/9.64	   A^2 -> H(f(d), d)
28.55/9.64	   A^2 -> H(f(d), k)
28.55/9.64	   A^2 -> H(U1(c, c), c)
28.55/9.64	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.64	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.64	   A^2 -> H(f(c), k)
28.55/9.64	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.64	   A^2 -> H(f(k), U1(k, k))
28.55/9.64	   A^2 -> H(f(e), e)
28.55/9.64	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.64	   A^2 -> H(d, U1(c, b))
28.55/9.64	   A^2 -> H(d, U1(d, b))
28.55/9.64	   A^2 -> H(d, U1(b, c))
28.55/9.64	   A^2 -> H(d, U1(b, d))
28.55/9.64	   A^2 -> H(d, U1(c, c))
28.55/9.64	   A^2 -> H(d, f(e))
28.55/9.64	   A^2 -> H(d, f(k))
28.55/9.64	   A^2 -> H(d, U1(d, d))
28.55/9.64	   A^2 -> H(a, U1(e, b))
28.55/9.64	   A^2 -> H(a, U1(k, b))
28.55/9.64	   A^2 -> H(a, U1(c, d))
28.55/9.64	   A^2 -> H(a, U1(d, c))
28.55/9.64	   A^2 -> H(a, U1(b, e))
28.55/9.64	   A^2 -> H(a, U1(b, k))
28.55/9.64	   A^2 -> H(a, U1(e, c))
28.55/9.64	   A^2 -> H(a, U1(k, c))
28.55/9.64	   A^2 -> H(a, U1(c, e))
28.55/9.64	   A^2 -> H(a, U1(c, k))
28.55/9.64	   A^2 -> H(a, U1(e, e))
28.55/9.64	   A^2 -> H(a, U1(k, k))
28.55/9.64	   A^2 -> H(a, U1(k, d))
28.55/9.64	   A^2 -> H(a, U1(d, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.64	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.64	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.64	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.64	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.64	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.64	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.64	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.64	   A^2 -> H(U1(e, a), b)
28.55/9.64	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.64	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.64	   A^2 -> H(U1(e, a), c)
28.55/9.64	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.64	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.64	   A^2 -> H(U1(e, a), e)
28.55/9.64	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, a), b)
28.55/9.64	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.64	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.64	   A^2 -> H(U1(k, a), c)
28.55/9.64	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.64	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.64	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, d), b)
28.55/9.64	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.64	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.64	   A^2 -> H(U1(c, d), c)
28.55/9.64	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.64	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.64	   A^2 -> H(U1(c, d), e)
28.55/9.64	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, a), d)
28.55/9.64	   A^2 -> H(U1(c, a), k)
28.55/9.64	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.64	   A^2 -> H(U1(d, c), b)
28.55/9.64	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.64	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.64	   A^2 -> H(U1(d, c), c)
28.55/9.64	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.64	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.64	   A^2 -> H(U1(d, c), e)
28.55/9.64	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(d, a), d)
28.55/9.64	   A^2 -> H(U1(d, a), k)
28.55/9.64	   A^2 -> H(U1(k, a), e)
28.55/9.64	
28.55/9.64	The TRS R consists of the following rules:
28.55/9.64	
28.55/9.64	   f(x) -> U1(x, x)
28.55/9.64	   U1(e, x) -> x
28.55/9.64	   a -> c
28.55/9.64	   a -> d
28.55/9.64	   b -> c
28.55/9.64	   b -> d
28.55/9.64	   d -> k
28.55/9.64	   c -> e
28.55/9.64	   c -> k
28.55/9.64	
28.55/9.64	Q is empty.
28.55/9.64	We have to consider all minimal (P,Q,R)-chains.
28.55/9.64	----------------------------------------
28.55/9.64	
28.55/9.64	(1289) DependencyGraphProof (EQUIVALENT)
28.55/9.64	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.55/9.64	----------------------------------------
28.55/9.64	
28.55/9.64	(1290)
28.55/9.64	Obligation:
28.55/9.64	Q DP problem:
28.55/9.64	The TRS P consists of the following rules:
28.55/9.64	
28.55/9.64	   H(x, x) -> G(x, x, f(k))
28.55/9.64	   G(d, x, x) -> A^2
28.55/9.64	   A^2 -> H(f(c), f(c))
28.55/9.64	   A^2 -> H(f(d), f(d))
28.55/9.64	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.64	   A^2 -> H(f(e), f(e))
28.55/9.64	   A^2 -> H(f(k), f(k))
28.55/9.64	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.64	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.64	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.64	   A^2 -> H(U1(d, a), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(a, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(a, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.64	   A^2 -> H(U1(a, c), b)
28.55/9.64	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.64	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.64	   A^2 -> H(U1(a, c), c)
28.55/9.64	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.64	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.64	   A^2 -> H(U1(a, c), e)
28.55/9.64	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, d), b)
28.55/9.64	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.64	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.64	   A^2 -> H(U1(a, d), c)
28.55/9.64	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.64	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.64	   A^2 -> H(U1(a, d), e)
28.55/9.64	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, a), d)
28.55/9.64	   A^2 -> H(U1(a, a), k)
28.55/9.64	   A^2 -> H(k, U1(b, b))
28.55/9.64	   A^2 -> H(k, f(c))
28.55/9.64	   A^2 -> H(k, f(d))
28.55/9.64	   A^2 -> H(c, U1(c, b))
28.55/9.64	   A^2 -> H(c, U1(d, b))
28.55/9.64	   A^2 -> H(c, U1(b, c))
28.55/9.64	   A^2 -> H(c, U1(b, d))
28.55/9.64	   A^2 -> H(c, U1(c, c))
28.55/9.64	   A^2 -> H(c, f(e))
28.55/9.64	   A^2 -> H(c, f(k))
28.55/9.64	   A^2 -> H(c, U1(d, d))
28.55/9.64	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.64	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.64	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.64	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.64	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.64	   A^2 -> H(U1(e, k), f(e))
28.55/9.64	   A^2 -> H(U1(e, k), f(k))
28.55/9.64	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.64	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.64	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.64	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.64	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.64	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.64	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.64	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.64	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.64	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.64	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.64	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.64	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.64	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.64	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.64	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.64	   A^2 -> H(U1(k, e), f(e))
28.55/9.64	   A^2 -> H(U1(k, e), f(k))
28.55/9.64	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.64	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.64	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.64	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.64	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.64	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.64	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.64	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.64	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.64	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.64	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.64	   A^2 -> H(U1(c, c), b)
28.55/9.64	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.64	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.64	   A^2 -> H(U1(c, c), e)
28.55/9.64	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.64	   A^2 -> H(e, U1(c, b))
28.55/9.64	   A^2 -> H(e, U1(d, b))
28.55/9.64	   A^2 -> H(e, U1(b, c))
28.55/9.64	   A^2 -> H(e, U1(b, d))
28.55/9.64	   A^2 -> H(e, U1(c, c))
28.55/9.64	   A^2 -> H(e, f(e))
28.55/9.64	   A^2 -> H(e, f(k))
28.55/9.64	   A^2 -> H(e, U1(d, d))
28.55/9.64	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.64	   A^2 -> H(f(e), b)
28.55/9.64	   A^2 -> H(f(e), U1(e, d))
28.55/9.64	   A^2 -> H(f(e), U1(d, e))
28.55/9.64	   A^2 -> H(f(e), c)
28.55/9.64	   A^2 -> H(f(e), U1(e, k))
28.55/9.64	   A^2 -> H(f(e), U1(k, e))
28.55/9.64	   A^2 -> H(f(e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.64	   A^2 -> H(f(k), b)
28.55/9.64	   A^2 -> H(f(k), U1(e, d))
28.55/9.64	   A^2 -> H(f(k), U1(d, e))
28.55/9.64	   A^2 -> H(f(k), c)
28.55/9.64	   A^2 -> H(f(k), U1(e, k))
28.55/9.64	   A^2 -> H(f(k), U1(k, e))
28.55/9.64	   A^2 -> H(f(k), e)
28.55/9.64	   A^2 -> H(f(c), d)
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.64	   A^2 -> H(U1(k, k), f(e))
28.55/9.64	   A^2 -> H(U1(k, k), f(k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.64	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.64	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.64	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.64	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.64	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.64	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.64	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.64	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.64	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.64	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.64	   A^2 -> H(U1(d, d), b)
28.55/9.64	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.64	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.64	   A^2 -> H(U1(d, d), c)
28.55/9.64	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.64	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.64	   A^2 -> H(U1(d, d), e)
28.55/9.64	   A^2 -> H(f(d), d)
28.55/9.64	   A^2 -> H(f(d), k)
28.55/9.64	   A^2 -> H(U1(c, c), c)
28.55/9.64	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.64	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.64	   A^2 -> H(f(c), k)
28.55/9.64	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.64	   A^2 -> H(f(k), U1(k, k))
28.55/9.64	   A^2 -> H(f(e), e)
28.55/9.64	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.64	   A^2 -> H(d, U1(c, b))
28.55/9.64	   A^2 -> H(d, U1(d, b))
28.55/9.64	   A^2 -> H(d, U1(b, c))
28.55/9.64	   A^2 -> H(d, U1(b, d))
28.55/9.64	   A^2 -> H(d, U1(c, c))
28.55/9.64	   A^2 -> H(d, f(e))
28.55/9.64	   A^2 -> H(d, f(k))
28.55/9.64	   A^2 -> H(d, U1(d, d))
28.55/9.64	   A^2 -> H(a, U1(e, b))
28.55/9.64	   A^2 -> H(a, U1(k, b))
28.55/9.64	   A^2 -> H(a, U1(c, d))
28.55/9.64	   A^2 -> H(a, U1(d, c))
28.55/9.64	   A^2 -> H(a, U1(b, e))
28.55/9.64	   A^2 -> H(a, U1(b, k))
28.55/9.64	   A^2 -> H(a, U1(e, c))
28.55/9.64	   A^2 -> H(a, U1(k, c))
28.55/9.64	   A^2 -> H(a, U1(c, e))
28.55/9.64	   A^2 -> H(a, U1(c, k))
28.55/9.64	   A^2 -> H(a, U1(e, e))
28.55/9.64	   A^2 -> H(a, U1(k, k))
28.55/9.64	   A^2 -> H(a, U1(k, d))
28.55/9.64	   A^2 -> H(a, U1(d, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.64	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.64	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.64	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.64	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.64	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.64	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.64	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.64	   A^2 -> H(U1(e, a), b)
28.55/9.64	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.64	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.64	   A^2 -> H(U1(e, a), c)
28.55/9.64	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.64	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.64	   A^2 -> H(U1(e, a), e)
28.55/9.64	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, a), b)
28.55/9.64	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.64	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.64	   A^2 -> H(U1(k, a), c)
28.55/9.64	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.64	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.64	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, d), b)
28.55/9.64	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.64	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.64	   A^2 -> H(U1(c, d), c)
28.55/9.64	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.64	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.64	   A^2 -> H(U1(c, d), e)
28.55/9.64	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, a), d)
28.55/9.64	   A^2 -> H(U1(c, a), k)
28.55/9.64	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.64	   A^2 -> H(U1(d, c), b)
28.55/9.64	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.64	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.64	   A^2 -> H(U1(d, c), c)
28.55/9.64	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.64	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.64	   A^2 -> H(U1(d, c), e)
28.55/9.64	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(d, a), d)
28.55/9.64	   A^2 -> H(U1(d, a), k)
28.55/9.64	
28.55/9.64	The TRS R consists of the following rules:
28.55/9.64	
28.55/9.64	   f(x) -> U1(x, x)
28.55/9.64	   U1(e, x) -> x
28.55/9.64	   a -> c
28.55/9.64	   a -> d
28.55/9.64	   b -> c
28.55/9.64	   b -> d
28.55/9.64	   d -> k
28.55/9.64	   c -> e
28.55/9.64	   c -> k
28.55/9.64	
28.55/9.64	Q is empty.
28.55/9.64	We have to consider all minimal (P,Q,R)-chains.
28.55/9.64	----------------------------------------
28.55/9.64	
28.55/9.64	(1291) TransformationProof (EQUIVALENT)
28.55/9.64	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.64	
28.55/9.64	   (A^2 -> H(U1(k, a), U1(k, k)),A^2 -> H(U1(k, a), U1(k, k)))
28.55/9.64	   (A^2 -> H(U1(d, c), U1(k, k)),A^2 -> H(U1(d, c), U1(k, k)))
28.55/9.64	   (A^2 -> H(U1(d, d), U1(k, k)),A^2 -> H(U1(d, d), U1(k, k)))
28.55/9.64	
28.55/9.64	
28.55/9.64	----------------------------------------
28.55/9.64	
28.55/9.64	(1292)
28.55/9.64	Obligation:
28.55/9.64	Q DP problem:
28.55/9.64	The TRS P consists of the following rules:
28.55/9.64	
28.55/9.64	   H(x, x) -> G(x, x, f(k))
28.55/9.64	   G(d, x, x) -> A^2
28.55/9.64	   A^2 -> H(f(c), f(c))
28.55/9.64	   A^2 -> H(f(d), f(d))
28.55/9.64	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.64	   A^2 -> H(f(e), f(e))
28.55/9.64	   A^2 -> H(f(k), f(k))
28.55/9.64	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.64	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.64	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(a, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(a, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.64	   A^2 -> H(U1(a, c), b)
28.55/9.64	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.64	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.64	   A^2 -> H(U1(a, c), c)
28.55/9.64	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.64	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.64	   A^2 -> H(U1(a, c), e)
28.55/9.64	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, d), b)
28.55/9.64	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.64	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.64	   A^2 -> H(U1(a, d), c)
28.55/9.64	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.64	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.64	   A^2 -> H(U1(a, d), e)
28.55/9.64	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, a), d)
28.55/9.64	   A^2 -> H(U1(a, a), k)
28.55/9.64	   A^2 -> H(k, U1(b, b))
28.55/9.64	   A^2 -> H(k, f(c))
28.55/9.64	   A^2 -> H(k, f(d))
28.55/9.64	   A^2 -> H(c, U1(c, b))
28.55/9.64	   A^2 -> H(c, U1(d, b))
28.55/9.64	   A^2 -> H(c, U1(b, c))
28.55/9.64	   A^2 -> H(c, U1(b, d))
28.55/9.64	   A^2 -> H(c, U1(c, c))
28.55/9.64	   A^2 -> H(c, f(e))
28.55/9.64	   A^2 -> H(c, f(k))
28.55/9.64	   A^2 -> H(c, U1(d, d))
28.55/9.64	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.64	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.64	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.64	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.64	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.64	   A^2 -> H(U1(e, k), f(e))
28.55/9.64	   A^2 -> H(U1(e, k), f(k))
28.55/9.64	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.64	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.64	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.64	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.64	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.64	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.64	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.64	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.64	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.64	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.64	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.64	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.64	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.64	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.64	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.64	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.64	   A^2 -> H(U1(k, e), f(e))
28.55/9.64	   A^2 -> H(U1(k, e), f(k))
28.55/9.64	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.64	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.64	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.64	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.64	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.64	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.64	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.64	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.64	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.64	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.64	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.64	   A^2 -> H(U1(c, c), b)
28.55/9.64	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.64	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.64	   A^2 -> H(U1(c, c), e)
28.55/9.64	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.64	   A^2 -> H(e, U1(c, b))
28.55/9.64	   A^2 -> H(e, U1(d, b))
28.55/9.64	   A^2 -> H(e, U1(b, c))
28.55/9.64	   A^2 -> H(e, U1(b, d))
28.55/9.64	   A^2 -> H(e, U1(c, c))
28.55/9.64	   A^2 -> H(e, f(e))
28.55/9.64	   A^2 -> H(e, f(k))
28.55/9.64	   A^2 -> H(e, U1(d, d))
28.55/9.64	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.64	   A^2 -> H(f(e), b)
28.55/9.64	   A^2 -> H(f(e), U1(e, d))
28.55/9.64	   A^2 -> H(f(e), U1(d, e))
28.55/9.64	   A^2 -> H(f(e), c)
28.55/9.64	   A^2 -> H(f(e), U1(e, k))
28.55/9.64	   A^2 -> H(f(e), U1(k, e))
28.55/9.64	   A^2 -> H(f(e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.64	   A^2 -> H(f(k), b)
28.55/9.64	   A^2 -> H(f(k), U1(e, d))
28.55/9.64	   A^2 -> H(f(k), U1(d, e))
28.55/9.64	   A^2 -> H(f(k), c)
28.55/9.64	   A^2 -> H(f(k), U1(e, k))
28.55/9.64	   A^2 -> H(f(k), U1(k, e))
28.55/9.64	   A^2 -> H(f(k), e)
28.55/9.64	   A^2 -> H(f(c), d)
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.64	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.64	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.64	   A^2 -> H(U1(k, k), f(e))
28.55/9.64	   A^2 -> H(U1(k, k), f(k))
28.55/9.64	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.64	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.64	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.64	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.64	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.64	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.64	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.64	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.64	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.64	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.64	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.64	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.64	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.64	   A^2 -> H(U1(d, d), b)
28.55/9.64	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.64	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.64	   A^2 -> H(U1(d, d), c)
28.55/9.64	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.64	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.64	   A^2 -> H(U1(d, d), e)
28.55/9.64	   A^2 -> H(f(d), d)
28.55/9.64	   A^2 -> H(f(d), k)
28.55/9.64	   A^2 -> H(U1(c, c), c)
28.55/9.64	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.64	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.64	   A^2 -> H(f(c), k)
28.55/9.64	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.64	   A^2 -> H(f(k), U1(k, k))
28.55/9.64	   A^2 -> H(f(e), e)
28.55/9.64	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.64	   A^2 -> H(d, U1(c, b))
28.55/9.64	   A^2 -> H(d, U1(d, b))
28.55/9.64	   A^2 -> H(d, U1(b, c))
28.55/9.64	   A^2 -> H(d, U1(b, d))
28.55/9.64	   A^2 -> H(d, U1(c, c))
28.55/9.64	   A^2 -> H(d, f(e))
28.55/9.64	   A^2 -> H(d, f(k))
28.55/9.64	   A^2 -> H(d, U1(d, d))
28.55/9.64	   A^2 -> H(a, U1(e, b))
28.55/9.64	   A^2 -> H(a, U1(k, b))
28.55/9.64	   A^2 -> H(a, U1(c, d))
28.55/9.64	   A^2 -> H(a, U1(d, c))
28.55/9.64	   A^2 -> H(a, U1(b, e))
28.55/9.64	   A^2 -> H(a, U1(b, k))
28.55/9.64	   A^2 -> H(a, U1(e, c))
28.55/9.64	   A^2 -> H(a, U1(k, c))
28.55/9.64	   A^2 -> H(a, U1(c, e))
28.55/9.64	   A^2 -> H(a, U1(c, k))
28.55/9.64	   A^2 -> H(a, U1(e, e))
28.55/9.64	   A^2 -> H(a, U1(k, k))
28.55/9.64	   A^2 -> H(a, U1(k, d))
28.55/9.64	   A^2 -> H(a, U1(d, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.64	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.64	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.64	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.64	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.64	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.64	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.64	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.64	   A^2 -> H(U1(e, a), b)
28.55/9.64	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.64	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.64	   A^2 -> H(U1(e, a), c)
28.55/9.64	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.64	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.64	   A^2 -> H(U1(e, a), e)
28.55/9.64	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.64	   A^2 -> H(U1(k, a), b)
28.55/9.64	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.64	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.64	   A^2 -> H(U1(k, a), c)
28.55/9.64	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.64	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.64	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, d), b)
28.55/9.64	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.64	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.64	   A^2 -> H(U1(c, d), c)
28.55/9.64	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.64	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.64	   A^2 -> H(U1(c, d), e)
28.55/9.64	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.64	   A^2 -> H(U1(c, a), d)
28.55/9.64	   A^2 -> H(U1(c, a), k)
28.55/9.64	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.64	   A^2 -> H(U1(d, c), b)
28.55/9.64	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.64	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.64	   A^2 -> H(U1(d, c), c)
28.55/9.64	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.64	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.64	   A^2 -> H(U1(d, c), e)
28.55/9.64	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.64	   A^2 -> H(U1(d, a), d)
28.55/9.64	   A^2 -> H(U1(d, a), k)
28.55/9.64	
28.55/9.64	The TRS R consists of the following rules:
28.55/9.64	
28.55/9.64	   f(x) -> U1(x, x)
28.55/9.64	   U1(e, x) -> x
28.55/9.64	   a -> c
28.55/9.64	   a -> d
28.55/9.64	   b -> c
28.55/9.64	   b -> d
28.55/9.64	   d -> k
28.55/9.64	   c -> e
28.55/9.64	   c -> k
28.55/9.64	
28.55/9.64	Q is empty.
28.55/9.64	We have to consider all minimal (P,Q,R)-chains.
28.55/9.64	----------------------------------------
28.55/9.64	
28.55/9.64	(1293) TransformationProof (EQUIVALENT)
28.55/9.64	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.64	
28.55/9.64	   (A^2 -> H(U1(c, e), U1(e, b)),A^2 -> H(U1(c, e), U1(e, b)))
28.55/9.64	   (A^2 -> H(U1(d, e), U1(e, b)),A^2 -> H(U1(d, e), U1(e, b)))
28.55/9.64	   (A^2 -> H(U1(a, e), b),A^2 -> H(U1(a, e), b))
28.55/9.64	   (A^2 -> H(U1(a, e), U1(e, c)),A^2 -> H(U1(a, e), U1(e, c)))
28.55/9.64	   (A^2 -> H(U1(a, e), U1(e, d)),A^2 -> H(U1(a, e), U1(e, d)))
28.55/9.64	
28.55/9.64	
28.55/9.64	----------------------------------------
28.55/9.64	
28.55/9.64	(1294)
28.55/9.64	Obligation:
28.55/9.64	Q DP problem:
28.55/9.64	The TRS P consists of the following rules:
28.55/9.64	
28.55/9.64	   H(x, x) -> G(x, x, f(k))
28.55/9.64	   G(d, x, x) -> A^2
28.55/9.64	   A^2 -> H(f(c), f(c))
28.55/9.64	   A^2 -> H(f(d), f(d))
28.55/9.64	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.64	   A^2 -> H(f(e), f(e))
28.55/9.64	   A^2 -> H(f(k), f(k))
28.55/9.64	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.64	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.64	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, b))
28.55/9.64	   A^2 -> H(U1(a, e), U1(c, d))
28.55/9.64	   A^2 -> H(U1(a, e), U1(d, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.64	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.64	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.64	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.64	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.64	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.64	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.64	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.64	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.64	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.64	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.64	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.64	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.64	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.65	   A^2 -> H(U1(a, c), b)
28.55/9.65	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.65	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.65	   A^2 -> H(U1(a, c), c)
28.55/9.65	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.65	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.65	   A^2 -> H(U1(a, c), e)
28.55/9.65	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, d), b)
28.55/9.65	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.65	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.65	   A^2 -> H(U1(a, d), c)
28.55/9.65	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.65	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.65	   A^2 -> H(U1(a, d), e)
28.55/9.65	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, a), d)
28.55/9.65	   A^2 -> H(U1(a, a), k)
28.55/9.65	   A^2 -> H(k, U1(b, b))
28.55/9.65	   A^2 -> H(k, f(c))
28.55/9.65	   A^2 -> H(k, f(d))
28.55/9.65	   A^2 -> H(c, U1(c, b))
28.55/9.65	   A^2 -> H(c, U1(d, b))
28.55/9.65	   A^2 -> H(c, U1(b, c))
28.55/9.65	   A^2 -> H(c, U1(b, d))
28.55/9.65	   A^2 -> H(c, U1(c, c))
28.55/9.65	   A^2 -> H(c, f(e))
28.55/9.65	   A^2 -> H(c, f(k))
28.55/9.65	   A^2 -> H(c, U1(d, d))
28.55/9.65	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.65	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.65	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.65	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.65	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.65	   A^2 -> H(U1(e, k), f(e))
28.55/9.65	   A^2 -> H(U1(e, k), f(k))
28.55/9.65	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.65	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.65	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.65	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.65	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.65	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.65	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.65	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.65	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.65	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.65	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.65	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.65	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.65	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.65	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.65	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.65	   A^2 -> H(U1(k, e), f(e))
28.55/9.65	   A^2 -> H(U1(k, e), f(k))
28.55/9.65	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.65	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.65	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.65	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.65	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.65	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.65	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.65	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.65	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.65	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.65	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.65	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.65	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.65	   A^2 -> H(U1(c, c), b)
28.55/9.65	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.65	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.65	   A^2 -> H(U1(c, c), e)
28.55/9.65	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.65	   A^2 -> H(e, U1(c, b))
28.55/9.65	   A^2 -> H(e, U1(d, b))
28.55/9.65	   A^2 -> H(e, U1(b, c))
28.55/9.65	   A^2 -> H(e, U1(b, d))
28.55/9.65	   A^2 -> H(e, U1(c, c))
28.55/9.65	   A^2 -> H(e, f(e))
28.55/9.65	   A^2 -> H(e, f(k))
28.55/9.65	   A^2 -> H(e, U1(d, d))
28.55/9.65	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.65	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.65	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.65	   A^2 -> H(f(e), b)
28.55/9.65	   A^2 -> H(f(e), U1(e, d))
28.55/9.65	   A^2 -> H(f(e), U1(d, e))
28.55/9.65	   A^2 -> H(f(e), c)
28.55/9.65	   A^2 -> H(f(e), U1(e, k))
28.55/9.65	   A^2 -> H(f(e), U1(k, e))
28.55/9.65	   A^2 -> H(f(e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.65	   A^2 -> H(f(k), b)
28.55/9.65	   A^2 -> H(f(k), U1(e, d))
28.55/9.65	   A^2 -> H(f(k), U1(d, e))
28.55/9.65	   A^2 -> H(f(k), c)
28.55/9.65	   A^2 -> H(f(k), U1(e, k))
28.55/9.65	   A^2 -> H(f(k), U1(k, e))
28.55/9.65	   A^2 -> H(f(k), e)
28.55/9.65	   A^2 -> H(f(c), d)
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.65	   A^2 -> H(U1(k, k), f(e))
28.55/9.65	   A^2 -> H(U1(k, k), f(k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.65	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.65	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.65	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.65	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.65	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.65	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.65	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.65	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.65	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.65	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.65	   A^2 -> H(U1(d, d), b)
28.55/9.65	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.65	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.65	   A^2 -> H(U1(d, d), c)
28.55/9.65	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.65	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.65	   A^2 -> H(U1(d, d), e)
28.55/9.65	   A^2 -> H(f(d), d)
28.55/9.65	   A^2 -> H(f(d), k)
28.55/9.65	   A^2 -> H(U1(c, c), c)
28.55/9.65	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.65	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.65	   A^2 -> H(f(c), k)
28.55/9.65	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.65	   A^2 -> H(f(k), U1(k, k))
28.55/9.65	   A^2 -> H(f(e), e)
28.55/9.65	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.65	   A^2 -> H(d, U1(c, b))
28.55/9.65	   A^2 -> H(d, U1(d, b))
28.55/9.65	   A^2 -> H(d, U1(b, c))
28.55/9.65	   A^2 -> H(d, U1(b, d))
28.55/9.65	   A^2 -> H(d, U1(c, c))
28.55/9.65	   A^2 -> H(d, f(e))
28.55/9.65	   A^2 -> H(d, f(k))
28.55/9.65	   A^2 -> H(d, U1(d, d))
28.55/9.65	   A^2 -> H(a, U1(e, b))
28.55/9.65	   A^2 -> H(a, U1(k, b))
28.55/9.65	   A^2 -> H(a, U1(c, d))
28.55/9.65	   A^2 -> H(a, U1(d, c))
28.55/9.65	   A^2 -> H(a, U1(b, e))
28.55/9.65	   A^2 -> H(a, U1(b, k))
28.55/9.65	   A^2 -> H(a, U1(e, c))
28.55/9.65	   A^2 -> H(a, U1(k, c))
28.55/9.65	   A^2 -> H(a, U1(c, e))
28.55/9.65	   A^2 -> H(a, U1(c, k))
28.55/9.65	   A^2 -> H(a, U1(e, e))
28.55/9.65	   A^2 -> H(a, U1(k, k))
28.55/9.65	   A^2 -> H(a, U1(k, d))
28.55/9.65	   A^2 -> H(a, U1(d, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.65	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.65	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.65	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.65	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.65	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.65	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.65	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.65	   A^2 -> H(U1(e, a), b)
28.55/9.65	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.65	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.65	   A^2 -> H(U1(e, a), c)
28.55/9.65	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.65	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.65	   A^2 -> H(U1(e, a), e)
28.55/9.65	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, a), b)
28.55/9.65	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.65	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.65	   A^2 -> H(U1(k, a), c)
28.55/9.65	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.65	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.65	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, d), b)
28.55/9.65	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.65	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.65	   A^2 -> H(U1(c, d), c)
28.55/9.65	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.65	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.65	   A^2 -> H(U1(c, d), e)
28.55/9.65	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, a), d)
28.55/9.65	   A^2 -> H(U1(c, a), k)
28.55/9.65	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.65	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.65	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.65	   A^2 -> H(U1(d, c), b)
28.55/9.65	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.65	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.65	   A^2 -> H(U1(d, c), c)
28.55/9.65	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.65	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.65	   A^2 -> H(U1(d, c), e)
28.55/9.65	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(d, a), d)
28.55/9.65	   A^2 -> H(U1(d, a), k)
28.55/9.65	   A^2 -> H(U1(a, e), b)
28.55/9.65	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.65	
28.55/9.65	The TRS R consists of the following rules:
28.55/9.65	
28.55/9.65	   f(x) -> U1(x, x)
28.55/9.65	   U1(e, x) -> x
28.55/9.65	   a -> c
28.55/9.65	   a -> d
28.55/9.65	   b -> c
28.55/9.65	   b -> d
28.55/9.65	   d -> k
28.55/9.65	   c -> e
28.55/9.65	   c -> k
28.55/9.65	
28.55/9.65	Q is empty.
28.55/9.65	We have to consider all minimal (P,Q,R)-chains.
28.55/9.65	----------------------------------------
28.55/9.65	
28.55/9.65	(1295) TransformationProof (EQUIVALENT)
28.55/9.65	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.65	
28.55/9.65	   (A^2 -> H(U1(c, e), U1(k, b)),A^2 -> H(U1(c, e), U1(k, b)))
28.55/9.65	   (A^2 -> H(U1(d, e), U1(k, b)),A^2 -> H(U1(d, e), U1(k, b)))
28.55/9.65	   (A^2 -> H(U1(a, e), U1(k, c)),A^2 -> H(U1(a, e), U1(k, c)))
28.55/9.65	   (A^2 -> H(U1(a, e), U1(k, d)),A^2 -> H(U1(a, e), U1(k, d)))
28.55/9.65	
28.55/9.65	
28.55/9.65	----------------------------------------
28.55/9.65	
28.55/9.65	(1296)
28.55/9.65	Obligation:
28.55/9.65	Q DP problem:
28.55/9.65	The TRS P consists of the following rules:
28.55/9.65	
28.55/9.65	   H(x, x) -> G(x, x, f(k))
28.55/9.65	   G(d, x, x) -> A^2
28.55/9.65	   A^2 -> H(f(c), f(c))
28.55/9.65	   A^2 -> H(f(d), f(d))
28.55/9.65	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.65	   A^2 -> H(f(e), f(e))
28.55/9.65	   A^2 -> H(f(k), f(k))
28.55/9.65	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.65	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.65	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.65	   A^2 -> H(U1(a, e), U1(c, d))
28.55/9.65	   A^2 -> H(U1(a, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.65	   A^2 -> H(U1(a, c), b)
28.55/9.65	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.65	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.65	   A^2 -> H(U1(a, c), c)
28.55/9.65	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.65	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.65	   A^2 -> H(U1(a, c), e)
28.55/9.65	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, d), b)
28.55/9.65	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.65	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.65	   A^2 -> H(U1(a, d), c)
28.55/9.65	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.65	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.65	   A^2 -> H(U1(a, d), e)
28.55/9.65	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, a), d)
28.55/9.65	   A^2 -> H(U1(a, a), k)
28.55/9.65	   A^2 -> H(k, U1(b, b))
28.55/9.65	   A^2 -> H(k, f(c))
28.55/9.65	   A^2 -> H(k, f(d))
28.55/9.65	   A^2 -> H(c, U1(c, b))
28.55/9.65	   A^2 -> H(c, U1(d, b))
28.55/9.65	   A^2 -> H(c, U1(b, c))
28.55/9.65	   A^2 -> H(c, U1(b, d))
28.55/9.65	   A^2 -> H(c, U1(c, c))
28.55/9.65	   A^2 -> H(c, f(e))
28.55/9.65	   A^2 -> H(c, f(k))
28.55/9.65	   A^2 -> H(c, U1(d, d))
28.55/9.65	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.65	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.65	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.65	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.65	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.65	   A^2 -> H(U1(e, k), f(e))
28.55/9.65	   A^2 -> H(U1(e, k), f(k))
28.55/9.65	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.65	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.65	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.65	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.65	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.65	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.65	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.65	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.65	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.65	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.65	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.65	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.65	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.65	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.65	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.65	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.65	   A^2 -> H(U1(k, e), f(e))
28.55/9.65	   A^2 -> H(U1(k, e), f(k))
28.55/9.65	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.65	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.65	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.65	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.65	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.65	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.65	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.65	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.65	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.65	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.65	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.65	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.65	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.65	   A^2 -> H(U1(c, c), b)
28.55/9.65	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.65	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.65	   A^2 -> H(U1(c, c), e)
28.55/9.65	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.65	   A^2 -> H(e, U1(c, b))
28.55/9.65	   A^2 -> H(e, U1(d, b))
28.55/9.65	   A^2 -> H(e, U1(b, c))
28.55/9.65	   A^2 -> H(e, U1(b, d))
28.55/9.65	   A^2 -> H(e, U1(c, c))
28.55/9.65	   A^2 -> H(e, f(e))
28.55/9.65	   A^2 -> H(e, f(k))
28.55/9.65	   A^2 -> H(e, U1(d, d))
28.55/9.65	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.65	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.65	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.65	   A^2 -> H(f(e), b)
28.55/9.65	   A^2 -> H(f(e), U1(e, d))
28.55/9.65	   A^2 -> H(f(e), U1(d, e))
28.55/9.65	   A^2 -> H(f(e), c)
28.55/9.65	   A^2 -> H(f(e), U1(e, k))
28.55/9.65	   A^2 -> H(f(e), U1(k, e))
28.55/9.65	   A^2 -> H(f(e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.65	   A^2 -> H(f(k), b)
28.55/9.65	   A^2 -> H(f(k), U1(e, d))
28.55/9.65	   A^2 -> H(f(k), U1(d, e))
28.55/9.65	   A^2 -> H(f(k), c)
28.55/9.65	   A^2 -> H(f(k), U1(e, k))
28.55/9.65	   A^2 -> H(f(k), U1(k, e))
28.55/9.65	   A^2 -> H(f(k), e)
28.55/9.65	   A^2 -> H(f(c), d)
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.65	   A^2 -> H(U1(k, k), f(e))
28.55/9.65	   A^2 -> H(U1(k, k), f(k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.65	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.65	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.65	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.65	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.65	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.65	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.65	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.65	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.65	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.65	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.65	   A^2 -> H(U1(d, d), b)
28.55/9.65	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.65	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.65	   A^2 -> H(U1(d, d), c)
28.55/9.65	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.65	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.65	   A^2 -> H(U1(d, d), e)
28.55/9.65	   A^2 -> H(f(d), d)
28.55/9.65	   A^2 -> H(f(d), k)
28.55/9.65	   A^2 -> H(U1(c, c), c)
28.55/9.65	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.65	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.65	   A^2 -> H(f(c), k)
28.55/9.65	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.65	   A^2 -> H(f(k), U1(k, k))
28.55/9.65	   A^2 -> H(f(e), e)
28.55/9.65	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.65	   A^2 -> H(d, U1(c, b))
28.55/9.65	   A^2 -> H(d, U1(d, b))
28.55/9.65	   A^2 -> H(d, U1(b, c))
28.55/9.65	   A^2 -> H(d, U1(b, d))
28.55/9.65	   A^2 -> H(d, U1(c, c))
28.55/9.65	   A^2 -> H(d, f(e))
28.55/9.65	   A^2 -> H(d, f(k))
28.55/9.65	   A^2 -> H(d, U1(d, d))
28.55/9.65	   A^2 -> H(a, U1(e, b))
28.55/9.65	   A^2 -> H(a, U1(k, b))
28.55/9.65	   A^2 -> H(a, U1(c, d))
28.55/9.65	   A^2 -> H(a, U1(d, c))
28.55/9.65	   A^2 -> H(a, U1(b, e))
28.55/9.65	   A^2 -> H(a, U1(b, k))
28.55/9.65	   A^2 -> H(a, U1(e, c))
28.55/9.65	   A^2 -> H(a, U1(k, c))
28.55/9.65	   A^2 -> H(a, U1(c, e))
28.55/9.65	   A^2 -> H(a, U1(c, k))
28.55/9.65	   A^2 -> H(a, U1(e, e))
28.55/9.65	   A^2 -> H(a, U1(k, k))
28.55/9.65	   A^2 -> H(a, U1(k, d))
28.55/9.65	   A^2 -> H(a, U1(d, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.65	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.65	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.65	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.65	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.65	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.65	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.65	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.65	   A^2 -> H(U1(e, a), b)
28.55/9.65	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.65	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.65	   A^2 -> H(U1(e, a), c)
28.55/9.65	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.65	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.65	   A^2 -> H(U1(e, a), e)
28.55/9.65	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, a), b)
28.55/9.65	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.65	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.65	   A^2 -> H(U1(k, a), c)
28.55/9.65	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.65	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.65	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, d), b)
28.55/9.65	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.65	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.65	   A^2 -> H(U1(c, d), c)
28.55/9.65	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.65	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.65	   A^2 -> H(U1(c, d), e)
28.55/9.65	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, a), d)
28.55/9.65	   A^2 -> H(U1(c, a), k)
28.55/9.65	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.65	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.65	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.65	   A^2 -> H(U1(d, c), b)
28.55/9.65	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.65	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.65	   A^2 -> H(U1(d, c), c)
28.55/9.65	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.65	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.65	   A^2 -> H(U1(d, c), e)
28.55/9.65	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(d, a), d)
28.55/9.65	   A^2 -> H(U1(d, a), k)
28.55/9.65	   A^2 -> H(U1(a, e), b)
28.55/9.65	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.65	
28.55/9.65	The TRS R consists of the following rules:
28.55/9.65	
28.55/9.65	   f(x) -> U1(x, x)
28.55/9.65	   U1(e, x) -> x
28.55/9.65	   a -> c
28.55/9.65	   a -> d
28.55/9.65	   b -> c
28.55/9.65	   b -> d
28.55/9.65	   d -> k
28.55/9.65	   c -> e
28.55/9.65	   c -> k
28.55/9.65	
28.55/9.65	Q is empty.
28.55/9.65	We have to consider all minimal (P,Q,R)-chains.
28.55/9.65	----------------------------------------
28.55/9.65	
28.55/9.65	(1297) TransformationProof (EQUIVALENT)
28.55/9.65	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.65	
28.55/9.65	   (A^2 -> H(U1(c, e), U1(c, d)),A^2 -> H(U1(c, e), U1(c, d)))
28.55/9.65	   (A^2 -> H(U1(d, e), U1(c, d)),A^2 -> H(U1(d, e), U1(c, d)))
28.55/9.65	   (A^2 -> H(U1(a, e), U1(e, d)),A^2 -> H(U1(a, e), U1(e, d)))
28.55/9.65	   (A^2 -> H(U1(a, e), U1(k, d)),A^2 -> H(U1(a, e), U1(k, d)))
28.55/9.65	   (A^2 -> H(U1(a, e), U1(c, k)),A^2 -> H(U1(a, e), U1(c, k)))
28.55/9.65	
28.55/9.65	
28.55/9.65	----------------------------------------
28.55/9.65	
28.55/9.65	(1298)
28.55/9.65	Obligation:
28.55/9.65	Q DP problem:
28.55/9.65	The TRS P consists of the following rules:
28.55/9.65	
28.55/9.65	   H(x, x) -> G(x, x, f(k))
28.55/9.65	   G(d, x, x) -> A^2
28.55/9.65	   A^2 -> H(f(c), f(c))
28.55/9.65	   A^2 -> H(f(d), f(d))
28.55/9.65	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.65	   A^2 -> H(f(e), f(e))
28.55/9.65	   A^2 -> H(f(k), f(k))
28.55/9.65	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.65	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.65	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.65	   A^2 -> H(U1(a, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.65	   A^2 -> H(U1(a, c), b)
28.55/9.65	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.65	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.65	   A^2 -> H(U1(a, c), c)
28.55/9.65	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.65	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.65	   A^2 -> H(U1(a, c), e)
28.55/9.65	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, d), b)
28.55/9.65	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.65	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.65	   A^2 -> H(U1(a, d), c)
28.55/9.65	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.65	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.65	   A^2 -> H(U1(a, d), e)
28.55/9.65	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, a), d)
28.55/9.65	   A^2 -> H(U1(a, a), k)
28.55/9.65	   A^2 -> H(k, U1(b, b))
28.55/9.65	   A^2 -> H(k, f(c))
28.55/9.65	   A^2 -> H(k, f(d))
28.55/9.65	   A^2 -> H(c, U1(c, b))
28.55/9.65	   A^2 -> H(c, U1(d, b))
28.55/9.65	   A^2 -> H(c, U1(b, c))
28.55/9.65	   A^2 -> H(c, U1(b, d))
28.55/9.65	   A^2 -> H(c, U1(c, c))
28.55/9.65	   A^2 -> H(c, f(e))
28.55/9.65	   A^2 -> H(c, f(k))
28.55/9.65	   A^2 -> H(c, U1(d, d))
28.55/9.65	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.65	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.65	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.65	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.65	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.65	   A^2 -> H(U1(e, k), f(e))
28.55/9.65	   A^2 -> H(U1(e, k), f(k))
28.55/9.65	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.65	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.65	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.65	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.65	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.65	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.65	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.65	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.65	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.65	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.65	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.65	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.65	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.65	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.65	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.65	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.65	   A^2 -> H(U1(k, e), f(e))
28.55/9.65	   A^2 -> H(U1(k, e), f(k))
28.55/9.65	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.65	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.65	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.65	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.65	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.65	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.65	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.65	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.65	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.65	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.65	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.65	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.65	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.65	   A^2 -> H(U1(c, c), b)
28.55/9.65	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.65	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.65	   A^2 -> H(U1(c, c), e)
28.55/9.65	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.65	   A^2 -> H(e, U1(c, b))
28.55/9.65	   A^2 -> H(e, U1(d, b))
28.55/9.65	   A^2 -> H(e, U1(b, c))
28.55/9.65	   A^2 -> H(e, U1(b, d))
28.55/9.65	   A^2 -> H(e, U1(c, c))
28.55/9.65	   A^2 -> H(e, f(e))
28.55/9.65	   A^2 -> H(e, f(k))
28.55/9.65	   A^2 -> H(e, U1(d, d))
28.55/9.65	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.65	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.65	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.65	   A^2 -> H(f(e), b)
28.55/9.65	   A^2 -> H(f(e), U1(e, d))
28.55/9.65	   A^2 -> H(f(e), U1(d, e))
28.55/9.65	   A^2 -> H(f(e), c)
28.55/9.65	   A^2 -> H(f(e), U1(e, k))
28.55/9.65	   A^2 -> H(f(e), U1(k, e))
28.55/9.65	   A^2 -> H(f(e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.65	   A^2 -> H(f(k), b)
28.55/9.65	   A^2 -> H(f(k), U1(e, d))
28.55/9.65	   A^2 -> H(f(k), U1(d, e))
28.55/9.65	   A^2 -> H(f(k), c)
28.55/9.65	   A^2 -> H(f(k), U1(e, k))
28.55/9.65	   A^2 -> H(f(k), U1(k, e))
28.55/9.65	   A^2 -> H(f(k), e)
28.55/9.65	   A^2 -> H(f(c), d)
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.65	   A^2 -> H(U1(k, k), f(e))
28.55/9.65	   A^2 -> H(U1(k, k), f(k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.65	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.65	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.65	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.65	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.65	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.65	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.65	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.65	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.65	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.65	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.65	   A^2 -> H(U1(d, d), b)
28.55/9.65	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.65	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.65	   A^2 -> H(U1(d, d), c)
28.55/9.65	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.65	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.65	   A^2 -> H(U1(d, d), e)
28.55/9.65	   A^2 -> H(f(d), d)
28.55/9.65	   A^2 -> H(f(d), k)
28.55/9.65	   A^2 -> H(U1(c, c), c)
28.55/9.65	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.65	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.65	   A^2 -> H(f(c), k)
28.55/9.65	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.65	   A^2 -> H(f(k), U1(k, k))
28.55/9.65	   A^2 -> H(f(e), e)
28.55/9.65	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.65	   A^2 -> H(d, U1(c, b))
28.55/9.65	   A^2 -> H(d, U1(d, b))
28.55/9.65	   A^2 -> H(d, U1(b, c))
28.55/9.65	   A^2 -> H(d, U1(b, d))
28.55/9.65	   A^2 -> H(d, U1(c, c))
28.55/9.65	   A^2 -> H(d, f(e))
28.55/9.65	   A^2 -> H(d, f(k))
28.55/9.65	   A^2 -> H(d, U1(d, d))
28.55/9.65	   A^2 -> H(a, U1(e, b))
28.55/9.65	   A^2 -> H(a, U1(k, b))
28.55/9.65	   A^2 -> H(a, U1(c, d))
28.55/9.65	   A^2 -> H(a, U1(d, c))
28.55/9.65	   A^2 -> H(a, U1(b, e))
28.55/9.65	   A^2 -> H(a, U1(b, k))
28.55/9.65	   A^2 -> H(a, U1(e, c))
28.55/9.65	   A^2 -> H(a, U1(k, c))
28.55/9.65	   A^2 -> H(a, U1(c, e))
28.55/9.65	   A^2 -> H(a, U1(c, k))
28.55/9.65	   A^2 -> H(a, U1(e, e))
28.55/9.65	   A^2 -> H(a, U1(k, k))
28.55/9.65	   A^2 -> H(a, U1(k, d))
28.55/9.65	   A^2 -> H(a, U1(d, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.65	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.65	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.65	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.65	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.65	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.65	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.65	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.65	   A^2 -> H(U1(e, a), b)
28.55/9.65	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.65	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.65	   A^2 -> H(U1(e, a), c)
28.55/9.65	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.65	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.65	   A^2 -> H(U1(e, a), e)
28.55/9.65	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, a), b)
28.55/9.65	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.65	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.65	   A^2 -> H(U1(k, a), c)
28.55/9.65	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.65	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.65	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, d), b)
28.55/9.65	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.65	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.65	   A^2 -> H(U1(c, d), c)
28.55/9.65	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.65	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.65	   A^2 -> H(U1(c, d), e)
28.55/9.65	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, a), d)
28.55/9.65	   A^2 -> H(U1(c, a), k)
28.55/9.65	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.65	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.65	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.65	   A^2 -> H(U1(d, c), b)
28.55/9.65	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.65	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.65	   A^2 -> H(U1(d, c), c)
28.55/9.65	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.65	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.65	   A^2 -> H(U1(d, c), e)
28.55/9.65	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(d, a), d)
28.55/9.65	   A^2 -> H(U1(d, a), k)
28.55/9.65	   A^2 -> H(U1(a, e), b)
28.55/9.65	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.65	
28.55/9.65	The TRS R consists of the following rules:
28.55/9.65	
28.55/9.65	   f(x) -> U1(x, x)
28.55/9.65	   U1(e, x) -> x
28.55/9.65	   a -> c
28.55/9.65	   a -> d
28.55/9.65	   b -> c
28.55/9.65	   b -> d
28.55/9.65	   d -> k
28.55/9.65	   c -> e
28.55/9.65	   c -> k
28.55/9.65	
28.55/9.65	Q is empty.
28.55/9.65	We have to consider all minimal (P,Q,R)-chains.
28.55/9.65	----------------------------------------
28.55/9.65	
28.55/9.65	(1299) TransformationProof (EQUIVALENT)
28.55/9.65	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.65	
28.55/9.65	   (A^2 -> H(U1(c, e), U1(d, c)),A^2 -> H(U1(c, e), U1(d, c)))
28.55/9.65	   (A^2 -> H(U1(d, e), U1(d, c)),A^2 -> H(U1(d, e), U1(d, c)))
28.55/9.65	   (A^2 -> H(U1(a, e), U1(k, c)),A^2 -> H(U1(a, e), U1(k, c)))
28.55/9.65	   (A^2 -> H(U1(a, e), U1(d, e)),A^2 -> H(U1(a, e), U1(d, e)))
28.55/9.65	   (A^2 -> H(U1(a, e), U1(d, k)),A^2 -> H(U1(a, e), U1(d, k)))
28.55/9.65	
28.55/9.65	
28.55/9.65	----------------------------------------
28.55/9.65	
28.55/9.65	(1300)
28.55/9.65	Obligation:
28.55/9.65	Q DP problem:
28.55/9.65	The TRS P consists of the following rules:
28.55/9.65	
28.55/9.65	   H(x, x) -> G(x, x, f(k))
28.55/9.65	   G(d, x, x) -> A^2
28.55/9.65	   A^2 -> H(f(c), f(c))
28.55/9.65	   A^2 -> H(f(d), f(d))
28.55/9.65	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.65	   A^2 -> H(f(e), f(e))
28.55/9.65	   A^2 -> H(f(k), f(k))
28.55/9.65	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.65	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.65	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.65	   A^2 -> H(U1(a, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.65	   A^2 -> H(U1(a, c), b)
28.55/9.65	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.65	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.65	   A^2 -> H(U1(a, c), c)
28.55/9.65	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.65	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.65	   A^2 -> H(U1(a, c), e)
28.55/9.65	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, d), b)
28.55/9.65	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.65	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.65	   A^2 -> H(U1(a, d), c)
28.55/9.65	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.65	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.65	   A^2 -> H(U1(a, d), e)
28.55/9.65	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, a), d)
28.55/9.65	   A^2 -> H(U1(a, a), k)
28.55/9.65	   A^2 -> H(k, U1(b, b))
28.55/9.65	   A^2 -> H(k, f(c))
28.55/9.65	   A^2 -> H(k, f(d))
28.55/9.65	   A^2 -> H(c, U1(c, b))
28.55/9.65	   A^2 -> H(c, U1(d, b))
28.55/9.65	   A^2 -> H(c, U1(b, c))
28.55/9.65	   A^2 -> H(c, U1(b, d))
28.55/9.65	   A^2 -> H(c, U1(c, c))
28.55/9.65	   A^2 -> H(c, f(e))
28.55/9.65	   A^2 -> H(c, f(k))
28.55/9.65	   A^2 -> H(c, U1(d, d))
28.55/9.65	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.65	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.65	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.65	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.65	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.65	   A^2 -> H(U1(e, k), f(e))
28.55/9.65	   A^2 -> H(U1(e, k), f(k))
28.55/9.65	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.65	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.65	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.65	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.65	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.65	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.65	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.65	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.65	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.65	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.65	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.65	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.65	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.65	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.65	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.65	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.65	   A^2 -> H(U1(k, e), f(e))
28.55/9.65	   A^2 -> H(U1(k, e), f(k))
28.55/9.65	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.65	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.65	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.65	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.65	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.65	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.65	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.65	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.65	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.65	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.65	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.65	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.65	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.65	   A^2 -> H(U1(c, c), b)
28.55/9.65	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.65	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.65	   A^2 -> H(U1(c, c), e)
28.55/9.65	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.65	   A^2 -> H(e, U1(c, b))
28.55/9.65	   A^2 -> H(e, U1(d, b))
28.55/9.65	   A^2 -> H(e, U1(b, c))
28.55/9.65	   A^2 -> H(e, U1(b, d))
28.55/9.65	   A^2 -> H(e, U1(c, c))
28.55/9.65	   A^2 -> H(e, f(e))
28.55/9.65	   A^2 -> H(e, f(k))
28.55/9.65	   A^2 -> H(e, U1(d, d))
28.55/9.65	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.65	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.65	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.65	   A^2 -> H(f(e), b)
28.55/9.65	   A^2 -> H(f(e), U1(e, d))
28.55/9.65	   A^2 -> H(f(e), U1(d, e))
28.55/9.65	   A^2 -> H(f(e), c)
28.55/9.65	   A^2 -> H(f(e), U1(e, k))
28.55/9.65	   A^2 -> H(f(e), U1(k, e))
28.55/9.65	   A^2 -> H(f(e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.65	   A^2 -> H(f(k), b)
28.55/9.65	   A^2 -> H(f(k), U1(e, d))
28.55/9.65	   A^2 -> H(f(k), U1(d, e))
28.55/9.65	   A^2 -> H(f(k), c)
28.55/9.65	   A^2 -> H(f(k), U1(e, k))
28.55/9.65	   A^2 -> H(f(k), U1(k, e))
28.55/9.65	   A^2 -> H(f(k), e)
28.55/9.65	   A^2 -> H(f(c), d)
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.65	   A^2 -> H(U1(k, k), f(e))
28.55/9.65	   A^2 -> H(U1(k, k), f(k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.65	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.65	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.65	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.65	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.65	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.65	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.65	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.65	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.65	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.65	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.65	   A^2 -> H(U1(d, d), b)
28.55/9.65	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.65	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.65	   A^2 -> H(U1(d, d), c)
28.55/9.65	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.65	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.65	   A^2 -> H(U1(d, d), e)
28.55/9.65	   A^2 -> H(f(d), d)
28.55/9.65	   A^2 -> H(f(d), k)
28.55/9.65	   A^2 -> H(U1(c, c), c)
28.55/9.65	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.65	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.65	   A^2 -> H(f(c), k)
28.55/9.65	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.65	   A^2 -> H(f(k), U1(k, k))
28.55/9.65	   A^2 -> H(f(e), e)
28.55/9.65	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.65	   A^2 -> H(d, U1(c, b))
28.55/9.65	   A^2 -> H(d, U1(d, b))
28.55/9.65	   A^2 -> H(d, U1(b, c))
28.55/9.65	   A^2 -> H(d, U1(b, d))
28.55/9.65	   A^2 -> H(d, U1(c, c))
28.55/9.65	   A^2 -> H(d, f(e))
28.55/9.65	   A^2 -> H(d, f(k))
28.55/9.65	   A^2 -> H(d, U1(d, d))
28.55/9.65	   A^2 -> H(a, U1(e, b))
28.55/9.65	   A^2 -> H(a, U1(k, b))
28.55/9.65	   A^2 -> H(a, U1(c, d))
28.55/9.65	   A^2 -> H(a, U1(d, c))
28.55/9.65	   A^2 -> H(a, U1(b, e))
28.55/9.65	   A^2 -> H(a, U1(b, k))
28.55/9.65	   A^2 -> H(a, U1(e, c))
28.55/9.65	   A^2 -> H(a, U1(k, c))
28.55/9.65	   A^2 -> H(a, U1(c, e))
28.55/9.65	   A^2 -> H(a, U1(c, k))
28.55/9.65	   A^2 -> H(a, U1(e, e))
28.55/9.65	   A^2 -> H(a, U1(k, k))
28.55/9.65	   A^2 -> H(a, U1(k, d))
28.55/9.65	   A^2 -> H(a, U1(d, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.65	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.65	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.65	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.65	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.65	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.65	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.65	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.65	   A^2 -> H(U1(e, a), b)
28.55/9.65	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.65	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.65	   A^2 -> H(U1(e, a), c)
28.55/9.65	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.65	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.65	   A^2 -> H(U1(e, a), e)
28.55/9.65	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, a), b)
28.55/9.65	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.65	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.65	   A^2 -> H(U1(k, a), c)
28.55/9.65	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.65	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.65	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, d), b)
28.55/9.65	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.65	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.65	   A^2 -> H(U1(c, d), c)
28.55/9.65	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.65	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.65	   A^2 -> H(U1(c, d), e)
28.55/9.65	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, a), d)
28.55/9.65	   A^2 -> H(U1(c, a), k)
28.55/9.65	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.65	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.65	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.65	   A^2 -> H(U1(d, c), b)
28.55/9.65	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.65	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.65	   A^2 -> H(U1(d, c), c)
28.55/9.65	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.65	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.65	   A^2 -> H(U1(d, c), e)
28.55/9.65	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(d, a), d)
28.55/9.65	   A^2 -> H(U1(d, a), k)
28.55/9.65	   A^2 -> H(U1(a, e), b)
28.55/9.65	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.65	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.65	
28.55/9.65	The TRS R consists of the following rules:
28.55/9.65	
28.55/9.65	   f(x) -> U1(x, x)
28.55/9.65	   U1(e, x) -> x
28.55/9.65	   a -> c
28.55/9.65	   a -> d
28.55/9.65	   b -> c
28.55/9.65	   b -> d
28.55/9.65	   d -> k
28.55/9.65	   c -> e
28.55/9.65	   c -> k
28.55/9.65	
28.55/9.65	Q is empty.
28.55/9.65	We have to consider all minimal (P,Q,R)-chains.
28.55/9.65	----------------------------------------
28.55/9.65	
28.55/9.65	(1301) TransformationProof (EQUIVALENT)
28.55/9.65	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.65	
28.55/9.65	   (A^2 -> H(U1(c, e), U1(b, e)),A^2 -> H(U1(c, e), U1(b, e)))
28.55/9.65	   (A^2 -> H(U1(d, e), U1(b, e)),A^2 -> H(U1(d, e), U1(b, e)))
28.55/9.65	   (A^2 -> H(U1(a, e), U1(c, e)),A^2 -> H(U1(a, e), U1(c, e)))
28.55/9.65	   (A^2 -> H(U1(a, e), U1(d, e)),A^2 -> H(U1(a, e), U1(d, e)))
28.55/9.65	
28.55/9.65	
28.55/9.65	----------------------------------------
28.55/9.65	
28.55/9.65	(1302)
28.55/9.65	Obligation:
28.55/9.65	Q DP problem:
28.55/9.65	The TRS P consists of the following rules:
28.55/9.65	
28.55/9.65	   H(x, x) -> G(x, x, f(k))
28.55/9.65	   G(d, x, x) -> A^2
28.55/9.65	   A^2 -> H(f(c), f(c))
28.55/9.65	   A^2 -> H(f(d), f(d))
28.55/9.65	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.65	   A^2 -> H(f(e), f(e))
28.55/9.65	   A^2 -> H(f(k), f(k))
28.55/9.65	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.65	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.65	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.65	   A^2 -> H(U1(a, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.65	   A^2 -> H(U1(a, c), b)
28.55/9.65	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.65	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.65	   A^2 -> H(U1(a, c), c)
28.55/9.65	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.65	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.65	   A^2 -> H(U1(a, c), e)
28.55/9.65	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, d), b)
28.55/9.65	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.65	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.65	   A^2 -> H(U1(a, d), c)
28.55/9.65	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.65	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.65	   A^2 -> H(U1(a, d), e)
28.55/9.65	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, a), d)
28.55/9.65	   A^2 -> H(U1(a, a), k)
28.55/9.65	   A^2 -> H(k, U1(b, b))
28.55/9.65	   A^2 -> H(k, f(c))
28.55/9.65	   A^2 -> H(k, f(d))
28.55/9.65	   A^2 -> H(c, U1(c, b))
28.55/9.65	   A^2 -> H(c, U1(d, b))
28.55/9.65	   A^2 -> H(c, U1(b, c))
28.55/9.65	   A^2 -> H(c, U1(b, d))
28.55/9.65	   A^2 -> H(c, U1(c, c))
28.55/9.65	   A^2 -> H(c, f(e))
28.55/9.65	   A^2 -> H(c, f(k))
28.55/9.65	   A^2 -> H(c, U1(d, d))
28.55/9.65	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.65	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.65	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.65	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.65	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.65	   A^2 -> H(U1(e, k), f(e))
28.55/9.65	   A^2 -> H(U1(e, k), f(k))
28.55/9.65	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.65	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.65	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.65	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.65	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.65	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.65	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.65	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.65	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.65	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.65	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.65	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.65	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.65	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.65	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.65	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.65	   A^2 -> H(U1(k, e), f(e))
28.55/9.65	   A^2 -> H(U1(k, e), f(k))
28.55/9.65	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.65	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.65	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.65	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.65	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.65	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.65	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.65	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.65	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.65	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.65	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.65	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.65	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.65	   A^2 -> H(U1(c, c), b)
28.55/9.65	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.65	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.65	   A^2 -> H(U1(c, c), e)
28.55/9.65	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.65	   A^2 -> H(e, U1(c, b))
28.55/9.65	   A^2 -> H(e, U1(d, b))
28.55/9.65	   A^2 -> H(e, U1(b, c))
28.55/9.65	   A^2 -> H(e, U1(b, d))
28.55/9.65	   A^2 -> H(e, U1(c, c))
28.55/9.65	   A^2 -> H(e, f(e))
28.55/9.65	   A^2 -> H(e, f(k))
28.55/9.65	   A^2 -> H(e, U1(d, d))
28.55/9.65	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.65	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.65	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.65	   A^2 -> H(f(e), b)
28.55/9.65	   A^2 -> H(f(e), U1(e, d))
28.55/9.65	   A^2 -> H(f(e), U1(d, e))
28.55/9.65	   A^2 -> H(f(e), c)
28.55/9.65	   A^2 -> H(f(e), U1(e, k))
28.55/9.65	   A^2 -> H(f(e), U1(k, e))
28.55/9.65	   A^2 -> H(f(e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.65	   A^2 -> H(f(k), b)
28.55/9.65	   A^2 -> H(f(k), U1(e, d))
28.55/9.65	   A^2 -> H(f(k), U1(d, e))
28.55/9.65	   A^2 -> H(f(k), c)
28.55/9.65	   A^2 -> H(f(k), U1(e, k))
28.55/9.65	   A^2 -> H(f(k), U1(k, e))
28.55/9.65	   A^2 -> H(f(k), e)
28.55/9.65	   A^2 -> H(f(c), d)
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.65	   A^2 -> H(U1(k, k), f(e))
28.55/9.65	   A^2 -> H(U1(k, k), f(k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.65	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.65	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.65	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.65	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.65	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.65	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.65	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.65	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.65	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.65	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.65	   A^2 -> H(U1(d, d), b)
28.55/9.65	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.65	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.65	   A^2 -> H(U1(d, d), c)
28.55/9.65	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.65	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.65	   A^2 -> H(U1(d, d), e)
28.55/9.65	   A^2 -> H(f(d), d)
28.55/9.65	   A^2 -> H(f(d), k)
28.55/9.65	   A^2 -> H(U1(c, c), c)
28.55/9.65	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.65	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.65	   A^2 -> H(f(c), k)
28.55/9.65	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.65	   A^2 -> H(f(k), U1(k, k))
28.55/9.65	   A^2 -> H(f(e), e)
28.55/9.65	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.65	   A^2 -> H(d, U1(c, b))
28.55/9.65	   A^2 -> H(d, U1(d, b))
28.55/9.65	   A^2 -> H(d, U1(b, c))
28.55/9.65	   A^2 -> H(d, U1(b, d))
28.55/9.65	   A^2 -> H(d, U1(c, c))
28.55/9.65	   A^2 -> H(d, f(e))
28.55/9.65	   A^2 -> H(d, f(k))
28.55/9.65	   A^2 -> H(d, U1(d, d))
28.55/9.65	   A^2 -> H(a, U1(e, b))
28.55/9.65	   A^2 -> H(a, U1(k, b))
28.55/9.65	   A^2 -> H(a, U1(c, d))
28.55/9.65	   A^2 -> H(a, U1(d, c))
28.55/9.65	   A^2 -> H(a, U1(b, e))
28.55/9.65	   A^2 -> H(a, U1(b, k))
28.55/9.65	   A^2 -> H(a, U1(e, c))
28.55/9.65	   A^2 -> H(a, U1(k, c))
28.55/9.65	   A^2 -> H(a, U1(c, e))
28.55/9.65	   A^2 -> H(a, U1(c, k))
28.55/9.65	   A^2 -> H(a, U1(e, e))
28.55/9.65	   A^2 -> H(a, U1(k, k))
28.55/9.65	   A^2 -> H(a, U1(k, d))
28.55/9.65	   A^2 -> H(a, U1(d, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.65	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.65	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.65	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.65	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.65	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.65	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.65	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.65	   A^2 -> H(U1(e, a), b)
28.55/9.65	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.65	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.65	   A^2 -> H(U1(e, a), c)
28.55/9.65	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.65	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.65	   A^2 -> H(U1(e, a), e)
28.55/9.65	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, a), b)
28.55/9.65	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.65	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.65	   A^2 -> H(U1(k, a), c)
28.55/9.65	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.65	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.65	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, d), b)
28.55/9.65	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.65	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.65	   A^2 -> H(U1(c, d), c)
28.55/9.65	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.65	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.65	   A^2 -> H(U1(c, d), e)
28.55/9.65	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, a), d)
28.55/9.65	   A^2 -> H(U1(c, a), k)
28.55/9.65	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.65	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.65	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.65	   A^2 -> H(U1(d, c), b)
28.55/9.65	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.65	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.65	   A^2 -> H(U1(d, c), c)
28.55/9.65	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.65	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.65	   A^2 -> H(U1(d, c), e)
28.55/9.65	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(d, a), d)
28.55/9.65	   A^2 -> H(U1(d, a), k)
28.55/9.65	   A^2 -> H(U1(a, e), b)
28.55/9.65	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.65	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.65	
28.55/9.65	The TRS R consists of the following rules:
28.55/9.65	
28.55/9.65	   f(x) -> U1(x, x)
28.55/9.65	   U1(e, x) -> x
28.55/9.65	   a -> c
28.55/9.65	   a -> d
28.55/9.65	   b -> c
28.55/9.65	   b -> d
28.55/9.65	   d -> k
28.55/9.65	   c -> e
28.55/9.65	   c -> k
28.55/9.65	
28.55/9.65	Q is empty.
28.55/9.65	We have to consider all minimal (P,Q,R)-chains.
28.55/9.65	----------------------------------------
28.55/9.65	
28.55/9.65	(1303) TransformationProof (EQUIVALENT)
28.55/9.65	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.65	
28.55/9.65	   (A^2 -> H(U1(c, e), U1(b, k)),A^2 -> H(U1(c, e), U1(b, k)))
28.55/9.65	   (A^2 -> H(U1(d, e), U1(b, k)),A^2 -> H(U1(d, e), U1(b, k)))
28.55/9.65	   (A^2 -> H(U1(a, e), U1(c, k)),A^2 -> H(U1(a, e), U1(c, k)))
28.55/9.65	   (A^2 -> H(U1(a, e), U1(d, k)),A^2 -> H(U1(a, e), U1(d, k)))
28.55/9.65	
28.55/9.65	
28.55/9.65	----------------------------------------
28.55/9.65	
28.55/9.65	(1304)
28.55/9.65	Obligation:
28.55/9.65	Q DP problem:
28.55/9.65	The TRS P consists of the following rules:
28.55/9.65	
28.55/9.65	   H(x, x) -> G(x, x, f(k))
28.55/9.65	   G(d, x, x) -> A^2
28.55/9.65	   A^2 -> H(f(c), f(c))
28.55/9.65	   A^2 -> H(f(d), f(d))
28.55/9.65	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.65	   A^2 -> H(f(e), f(e))
28.55/9.65	   A^2 -> H(f(k), f(k))
28.55/9.65	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.65	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.65	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.65	   A^2 -> H(U1(a, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.65	   A^2 -> H(U1(a, c), b)
28.55/9.65	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.65	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.65	   A^2 -> H(U1(a, c), c)
28.55/9.65	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.65	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.65	   A^2 -> H(U1(a, c), e)
28.55/9.65	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, d), b)
28.55/9.65	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.65	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.65	   A^2 -> H(U1(a, d), c)
28.55/9.65	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.65	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.65	   A^2 -> H(U1(a, d), e)
28.55/9.65	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(a, a), d)
28.55/9.65	   A^2 -> H(U1(a, a), k)
28.55/9.65	   A^2 -> H(k, U1(b, b))
28.55/9.65	   A^2 -> H(k, f(c))
28.55/9.65	   A^2 -> H(k, f(d))
28.55/9.65	   A^2 -> H(c, U1(c, b))
28.55/9.65	   A^2 -> H(c, U1(d, b))
28.55/9.65	   A^2 -> H(c, U1(b, c))
28.55/9.65	   A^2 -> H(c, U1(b, d))
28.55/9.65	   A^2 -> H(c, U1(c, c))
28.55/9.65	   A^2 -> H(c, f(e))
28.55/9.65	   A^2 -> H(c, f(k))
28.55/9.65	   A^2 -> H(c, U1(d, d))
28.55/9.65	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.65	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.65	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.65	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.65	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.65	   A^2 -> H(U1(e, k), f(e))
28.55/9.65	   A^2 -> H(U1(e, k), f(k))
28.55/9.65	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.65	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.65	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.65	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.65	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.65	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.65	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.65	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.65	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.65	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.65	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.65	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.65	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.65	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.65	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.65	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.65	   A^2 -> H(U1(k, e), f(e))
28.55/9.65	   A^2 -> H(U1(k, e), f(k))
28.55/9.65	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.65	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.65	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.65	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.65	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.65	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.65	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.65	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.65	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.65	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.65	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.65	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.65	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.65	   A^2 -> H(U1(c, c), b)
28.55/9.65	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.65	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.65	   A^2 -> H(U1(c, c), e)
28.55/9.65	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.65	   A^2 -> H(e, U1(c, b))
28.55/9.65	   A^2 -> H(e, U1(d, b))
28.55/9.65	   A^2 -> H(e, U1(b, c))
28.55/9.65	   A^2 -> H(e, U1(b, d))
28.55/9.65	   A^2 -> H(e, U1(c, c))
28.55/9.65	   A^2 -> H(e, f(e))
28.55/9.65	   A^2 -> H(e, f(k))
28.55/9.65	   A^2 -> H(e, U1(d, d))
28.55/9.65	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.65	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.65	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.65	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.65	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.65	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.65	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.65	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.65	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.65	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.65	   A^2 -> H(f(e), b)
28.55/9.65	   A^2 -> H(f(e), U1(e, d))
28.55/9.65	   A^2 -> H(f(e), U1(d, e))
28.55/9.65	   A^2 -> H(f(e), c)
28.55/9.65	   A^2 -> H(f(e), U1(e, k))
28.55/9.65	   A^2 -> H(f(e), U1(k, e))
28.55/9.65	   A^2 -> H(f(e), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.65	   A^2 -> H(f(k), b)
28.55/9.65	   A^2 -> H(f(k), U1(e, d))
28.55/9.65	   A^2 -> H(f(k), U1(d, e))
28.55/9.65	   A^2 -> H(f(k), c)
28.55/9.65	   A^2 -> H(f(k), U1(e, k))
28.55/9.65	   A^2 -> H(f(k), U1(k, e))
28.55/9.65	   A^2 -> H(f(k), e)
28.55/9.65	   A^2 -> H(f(c), d)
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.65	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.65	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.65	   A^2 -> H(U1(k, k), f(e))
28.55/9.65	   A^2 -> H(U1(k, k), f(k))
28.55/9.65	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.65	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.65	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.65	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.65	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.65	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.65	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.65	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.65	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.65	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.65	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.65	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.65	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.65	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.65	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.65	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.65	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.65	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.65	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.65	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.65	   A^2 -> H(U1(d, d), b)
28.55/9.65	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.65	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.65	   A^2 -> H(U1(d, d), c)
28.55/9.65	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.65	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.65	   A^2 -> H(U1(d, d), e)
28.55/9.65	   A^2 -> H(f(d), d)
28.55/9.65	   A^2 -> H(f(d), k)
28.55/9.65	   A^2 -> H(U1(c, c), c)
28.55/9.65	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.65	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.65	   A^2 -> H(f(c), k)
28.55/9.65	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.65	   A^2 -> H(f(k), U1(k, k))
28.55/9.65	   A^2 -> H(f(e), e)
28.55/9.65	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.65	   A^2 -> H(d, U1(c, b))
28.55/9.65	   A^2 -> H(d, U1(d, b))
28.55/9.65	   A^2 -> H(d, U1(b, c))
28.55/9.65	   A^2 -> H(d, U1(b, d))
28.55/9.65	   A^2 -> H(d, U1(c, c))
28.55/9.65	   A^2 -> H(d, f(e))
28.55/9.65	   A^2 -> H(d, f(k))
28.55/9.65	   A^2 -> H(d, U1(d, d))
28.55/9.65	   A^2 -> H(a, U1(e, b))
28.55/9.65	   A^2 -> H(a, U1(k, b))
28.55/9.65	   A^2 -> H(a, U1(c, d))
28.55/9.65	   A^2 -> H(a, U1(d, c))
28.55/9.65	   A^2 -> H(a, U1(b, e))
28.55/9.65	   A^2 -> H(a, U1(b, k))
28.55/9.65	   A^2 -> H(a, U1(e, c))
28.55/9.65	   A^2 -> H(a, U1(k, c))
28.55/9.65	   A^2 -> H(a, U1(c, e))
28.55/9.65	   A^2 -> H(a, U1(c, k))
28.55/9.65	   A^2 -> H(a, U1(e, e))
28.55/9.65	   A^2 -> H(a, U1(k, k))
28.55/9.65	   A^2 -> H(a, U1(k, d))
28.55/9.65	   A^2 -> H(a, U1(d, k))
28.55/9.65	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.65	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.65	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.65	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.66	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.66	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.66	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.66	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.66	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.66	   A^2 -> H(U1(e, a), b)
28.55/9.66	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.66	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.66	   A^2 -> H(U1(e, a), c)
28.55/9.66	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.66	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.66	   A^2 -> H(U1(e, a), e)
28.55/9.66	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, a), b)
28.55/9.66	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.66	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.66	   A^2 -> H(U1(k, a), c)
28.55/9.66	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.66	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.66	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, d), b)
28.55/9.66	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.66	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.66	   A^2 -> H(U1(c, d), c)
28.55/9.66	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.66	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.66	   A^2 -> H(U1(c, d), e)
28.55/9.66	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, a), d)
28.55/9.66	   A^2 -> H(U1(c, a), k)
28.55/9.66	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.66	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.66	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.66	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.66	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.66	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.66	   A^2 -> H(U1(d, c), b)
28.55/9.66	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.66	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.66	   A^2 -> H(U1(d, c), c)
28.55/9.66	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.66	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.66	   A^2 -> H(U1(d, c), e)
28.55/9.66	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(d, a), d)
28.55/9.66	   A^2 -> H(U1(d, a), k)
28.55/9.66	   A^2 -> H(U1(a, e), b)
28.55/9.66	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.66	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.66	
28.55/9.66	The TRS R consists of the following rules:
28.55/9.66	
28.55/9.66	   f(x) -> U1(x, x)
28.55/9.66	   U1(e, x) -> x
28.55/9.66	   a -> c
28.55/9.66	   a -> d
28.55/9.66	   b -> c
28.55/9.66	   b -> d
28.55/9.66	   d -> k
28.55/9.66	   c -> e
28.55/9.66	   c -> k
28.55/9.66	
28.55/9.66	Q is empty.
28.55/9.66	We have to consider all minimal (P,Q,R)-chains.
28.55/9.66	----------------------------------------
28.55/9.66	
28.55/9.66	(1305) TransformationProof (EQUIVALENT)
28.55/9.66	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.66	
28.55/9.66	   (A^2 -> H(U1(c, e), U1(e, c)),A^2 -> H(U1(c, e), U1(e, c)))
28.55/9.66	   (A^2 -> H(U1(d, e), U1(e, c)),A^2 -> H(U1(d, e), U1(e, c)))
28.55/9.66	   (A^2 -> H(U1(a, e), c),A^2 -> H(U1(a, e), c))
28.55/9.66	   (A^2 -> H(U1(a, e), U1(e, e)),A^2 -> H(U1(a, e), U1(e, e)))
28.55/9.66	   (A^2 -> H(U1(a, e), U1(e, k)),A^2 -> H(U1(a, e), U1(e, k)))
28.55/9.66	
28.55/9.66	
28.55/9.66	----------------------------------------
28.55/9.66	
28.55/9.66	(1306)
28.55/9.66	Obligation:
28.55/9.66	Q DP problem:
28.55/9.66	The TRS P consists of the following rules:
28.55/9.66	
28.55/9.66	   H(x, x) -> G(x, x, f(k))
28.55/9.66	   G(d, x, x) -> A^2
28.55/9.66	   A^2 -> H(f(c), f(c))
28.55/9.66	   A^2 -> H(f(d), f(d))
28.55/9.66	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.66	   A^2 -> H(f(e), f(e))
28.55/9.66	   A^2 -> H(f(k), f(k))
28.55/9.66	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.66	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.66	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.66	   A^2 -> H(U1(a, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.66	   A^2 -> H(U1(a, c), b)
28.55/9.66	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.66	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.66	   A^2 -> H(U1(a, c), c)
28.55/9.66	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.66	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.66	   A^2 -> H(U1(a, c), e)
28.55/9.66	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, d), b)
28.55/9.66	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.66	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.66	   A^2 -> H(U1(a, d), c)
28.55/9.66	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.66	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.66	   A^2 -> H(U1(a, d), e)
28.55/9.66	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, a), d)
28.55/9.66	   A^2 -> H(U1(a, a), k)
28.55/9.66	   A^2 -> H(k, U1(b, b))
28.55/9.66	   A^2 -> H(k, f(c))
28.55/9.66	   A^2 -> H(k, f(d))
28.55/9.66	   A^2 -> H(c, U1(c, b))
28.55/9.66	   A^2 -> H(c, U1(d, b))
28.55/9.66	   A^2 -> H(c, U1(b, c))
28.55/9.66	   A^2 -> H(c, U1(b, d))
28.55/9.66	   A^2 -> H(c, U1(c, c))
28.55/9.66	   A^2 -> H(c, f(e))
28.55/9.66	   A^2 -> H(c, f(k))
28.55/9.66	   A^2 -> H(c, U1(d, d))
28.55/9.66	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.66	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.66	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.66	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.66	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.66	   A^2 -> H(U1(e, k), f(e))
28.55/9.66	   A^2 -> H(U1(e, k), f(k))
28.55/9.66	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.66	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.66	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.66	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.66	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.66	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.66	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.66	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.66	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.66	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.66	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.66	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.66	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.66	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.66	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.66	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.66	   A^2 -> H(U1(k, e), f(e))
28.55/9.66	   A^2 -> H(U1(k, e), f(k))
28.55/9.66	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.66	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.66	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.66	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.66	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.66	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.66	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.66	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.66	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.66	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.66	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.66	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.66	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.66	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.66	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.66	   A^2 -> H(U1(c, c), b)
28.55/9.66	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.66	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.66	   A^2 -> H(U1(c, c), e)
28.55/9.66	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.66	   A^2 -> H(e, U1(c, b))
28.55/9.66	   A^2 -> H(e, U1(d, b))
28.55/9.66	   A^2 -> H(e, U1(b, c))
28.55/9.66	   A^2 -> H(e, U1(b, d))
28.55/9.66	   A^2 -> H(e, U1(c, c))
28.55/9.66	   A^2 -> H(e, f(e))
28.55/9.66	   A^2 -> H(e, f(k))
28.55/9.66	   A^2 -> H(e, U1(d, d))
28.55/9.66	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.66	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.66	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.66	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.66	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.66	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.66	   A^2 -> H(f(e), b)
28.55/9.66	   A^2 -> H(f(e), U1(e, d))
28.55/9.66	   A^2 -> H(f(e), U1(d, e))
28.55/9.66	   A^2 -> H(f(e), c)
28.55/9.66	   A^2 -> H(f(e), U1(e, k))
28.55/9.66	   A^2 -> H(f(e), U1(k, e))
28.55/9.66	   A^2 -> H(f(e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.66	   A^2 -> H(f(k), b)
28.55/9.66	   A^2 -> H(f(k), U1(e, d))
28.55/9.66	   A^2 -> H(f(k), U1(d, e))
28.55/9.66	   A^2 -> H(f(k), c)
28.55/9.66	   A^2 -> H(f(k), U1(e, k))
28.55/9.66	   A^2 -> H(f(k), U1(k, e))
28.55/9.66	   A^2 -> H(f(k), e)
28.55/9.66	   A^2 -> H(f(c), d)
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.66	   A^2 -> H(U1(k, k), f(e))
28.55/9.66	   A^2 -> H(U1(k, k), f(k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.66	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.66	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.66	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.66	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.66	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.66	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.66	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.66	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.66	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.66	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.66	   A^2 -> H(U1(d, d), b)
28.55/9.66	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.66	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.66	   A^2 -> H(U1(d, d), c)
28.55/9.66	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.66	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.66	   A^2 -> H(U1(d, d), e)
28.55/9.66	   A^2 -> H(f(d), d)
28.55/9.66	   A^2 -> H(f(d), k)
28.55/9.66	   A^2 -> H(U1(c, c), c)
28.55/9.66	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.66	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.66	   A^2 -> H(f(c), k)
28.55/9.66	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.66	   A^2 -> H(f(k), U1(k, k))
28.55/9.66	   A^2 -> H(f(e), e)
28.55/9.66	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.66	   A^2 -> H(d, U1(c, b))
28.55/9.66	   A^2 -> H(d, U1(d, b))
28.55/9.66	   A^2 -> H(d, U1(b, c))
28.55/9.66	   A^2 -> H(d, U1(b, d))
28.55/9.66	   A^2 -> H(d, U1(c, c))
28.55/9.66	   A^2 -> H(d, f(e))
28.55/9.66	   A^2 -> H(d, f(k))
28.55/9.66	   A^2 -> H(d, U1(d, d))
28.55/9.66	   A^2 -> H(a, U1(e, b))
28.55/9.66	   A^2 -> H(a, U1(k, b))
28.55/9.66	   A^2 -> H(a, U1(c, d))
28.55/9.66	   A^2 -> H(a, U1(d, c))
28.55/9.66	   A^2 -> H(a, U1(b, e))
28.55/9.66	   A^2 -> H(a, U1(b, k))
28.55/9.66	   A^2 -> H(a, U1(e, c))
28.55/9.66	   A^2 -> H(a, U1(k, c))
28.55/9.66	   A^2 -> H(a, U1(c, e))
28.55/9.66	   A^2 -> H(a, U1(c, k))
28.55/9.66	   A^2 -> H(a, U1(e, e))
28.55/9.66	   A^2 -> H(a, U1(k, k))
28.55/9.66	   A^2 -> H(a, U1(k, d))
28.55/9.66	   A^2 -> H(a, U1(d, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.66	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.66	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.66	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.66	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.66	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.66	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.66	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.66	   A^2 -> H(U1(e, a), b)
28.55/9.66	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.66	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.66	   A^2 -> H(U1(e, a), c)
28.55/9.66	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.66	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.66	   A^2 -> H(U1(e, a), e)
28.55/9.66	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, a), b)
28.55/9.66	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.66	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.66	   A^2 -> H(U1(k, a), c)
28.55/9.66	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.66	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.66	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, d), b)
28.55/9.66	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.66	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.66	   A^2 -> H(U1(c, d), c)
28.55/9.66	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.66	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.66	   A^2 -> H(U1(c, d), e)
28.55/9.66	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, a), d)
28.55/9.66	   A^2 -> H(U1(c, a), k)
28.55/9.66	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.66	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.66	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.66	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.66	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.66	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.66	   A^2 -> H(U1(d, c), b)
28.55/9.66	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.66	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.66	   A^2 -> H(U1(d, c), c)
28.55/9.66	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.66	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.66	   A^2 -> H(U1(d, c), e)
28.55/9.66	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(d, a), d)
28.55/9.66	   A^2 -> H(U1(d, a), k)
28.55/9.66	   A^2 -> H(U1(a, e), b)
28.55/9.66	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.66	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.66	   A^2 -> H(U1(a, e), c)
28.55/9.66	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.66	
28.55/9.66	The TRS R consists of the following rules:
28.55/9.66	
28.55/9.66	   f(x) -> U1(x, x)
28.55/9.66	   U1(e, x) -> x
28.55/9.66	   a -> c
28.55/9.66	   a -> d
28.55/9.66	   b -> c
28.55/9.66	   b -> d
28.55/9.66	   d -> k
28.55/9.66	   c -> e
28.55/9.66	   c -> k
28.55/9.66	
28.55/9.66	Q is empty.
28.55/9.66	We have to consider all minimal (P,Q,R)-chains.
28.55/9.66	----------------------------------------
28.55/9.66	
28.55/9.66	(1307) TransformationProof (EQUIVALENT)
28.55/9.66	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.66	
28.55/9.66	   (A^2 -> H(U1(c, e), U1(k, c)),A^2 -> H(U1(c, e), U1(k, c)))
28.55/9.66	   (A^2 -> H(U1(d, e), U1(k, c)),A^2 -> H(U1(d, e), U1(k, c)))
28.55/9.66	   (A^2 -> H(U1(a, e), U1(k, e)),A^2 -> H(U1(a, e), U1(k, e)))
28.55/9.66	   (A^2 -> H(U1(a, e), U1(k, k)),A^2 -> H(U1(a, e), U1(k, k)))
28.55/9.66	
28.55/9.66	
28.55/9.66	----------------------------------------
28.55/9.66	
28.55/9.66	(1308)
28.55/9.66	Obligation:
28.55/9.66	Q DP problem:
28.55/9.66	The TRS P consists of the following rules:
28.55/9.66	
28.55/9.66	   H(x, x) -> G(x, x, f(k))
28.55/9.66	   G(d, x, x) -> A^2
28.55/9.66	   A^2 -> H(f(c), f(c))
28.55/9.66	   A^2 -> H(f(d), f(d))
28.55/9.66	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.66	   A^2 -> H(f(e), f(e))
28.55/9.66	   A^2 -> H(f(k), f(k))
28.55/9.66	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.66	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.66	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.66	   A^2 -> H(U1(a, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.66	   A^2 -> H(U1(a, c), b)
28.55/9.66	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.66	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.66	   A^2 -> H(U1(a, c), c)
28.55/9.66	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.66	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.66	   A^2 -> H(U1(a, c), e)
28.55/9.66	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, d), b)
28.55/9.66	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.66	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.66	   A^2 -> H(U1(a, d), c)
28.55/9.66	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.66	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.66	   A^2 -> H(U1(a, d), e)
28.55/9.66	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, a), d)
28.55/9.66	   A^2 -> H(U1(a, a), k)
28.55/9.66	   A^2 -> H(k, U1(b, b))
28.55/9.66	   A^2 -> H(k, f(c))
28.55/9.66	   A^2 -> H(k, f(d))
28.55/9.66	   A^2 -> H(c, U1(c, b))
28.55/9.66	   A^2 -> H(c, U1(d, b))
28.55/9.66	   A^2 -> H(c, U1(b, c))
28.55/9.66	   A^2 -> H(c, U1(b, d))
28.55/9.66	   A^2 -> H(c, U1(c, c))
28.55/9.66	   A^2 -> H(c, f(e))
28.55/9.66	   A^2 -> H(c, f(k))
28.55/9.66	   A^2 -> H(c, U1(d, d))
28.55/9.66	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.66	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.66	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.66	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.66	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.66	   A^2 -> H(U1(e, k), f(e))
28.55/9.66	   A^2 -> H(U1(e, k), f(k))
28.55/9.66	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.66	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.66	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.66	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.66	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.66	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.66	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.66	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.66	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.66	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.66	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.66	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.66	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.66	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.66	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.66	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.66	   A^2 -> H(U1(k, e), f(e))
28.55/9.66	   A^2 -> H(U1(k, e), f(k))
28.55/9.66	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.66	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.66	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.66	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.66	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.66	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.66	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.66	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.66	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.66	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.66	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.66	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.66	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.66	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.66	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.66	   A^2 -> H(U1(c, c), b)
28.55/9.66	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.66	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.66	   A^2 -> H(U1(c, c), e)
28.55/9.66	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.66	   A^2 -> H(e, U1(c, b))
28.55/9.66	   A^2 -> H(e, U1(d, b))
28.55/9.66	   A^2 -> H(e, U1(b, c))
28.55/9.66	   A^2 -> H(e, U1(b, d))
28.55/9.66	   A^2 -> H(e, U1(c, c))
28.55/9.66	   A^2 -> H(e, f(e))
28.55/9.66	   A^2 -> H(e, f(k))
28.55/9.66	   A^2 -> H(e, U1(d, d))
28.55/9.66	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.66	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.66	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.66	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.66	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.66	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.66	   A^2 -> H(f(e), b)
28.55/9.66	   A^2 -> H(f(e), U1(e, d))
28.55/9.66	   A^2 -> H(f(e), U1(d, e))
28.55/9.66	   A^2 -> H(f(e), c)
28.55/9.66	   A^2 -> H(f(e), U1(e, k))
28.55/9.66	   A^2 -> H(f(e), U1(k, e))
28.55/9.66	   A^2 -> H(f(e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.66	   A^2 -> H(f(k), b)
28.55/9.66	   A^2 -> H(f(k), U1(e, d))
28.55/9.66	   A^2 -> H(f(k), U1(d, e))
28.55/9.66	   A^2 -> H(f(k), c)
28.55/9.66	   A^2 -> H(f(k), U1(e, k))
28.55/9.66	   A^2 -> H(f(k), U1(k, e))
28.55/9.66	   A^2 -> H(f(k), e)
28.55/9.66	   A^2 -> H(f(c), d)
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.66	   A^2 -> H(U1(k, k), f(e))
28.55/9.66	   A^2 -> H(U1(k, k), f(k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.66	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.66	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.66	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.66	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.66	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.66	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.66	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.66	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.66	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.66	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.66	   A^2 -> H(U1(d, d), b)
28.55/9.66	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.66	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.66	   A^2 -> H(U1(d, d), c)
28.55/9.66	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.66	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.66	   A^2 -> H(U1(d, d), e)
28.55/9.66	   A^2 -> H(f(d), d)
28.55/9.66	   A^2 -> H(f(d), k)
28.55/9.66	   A^2 -> H(U1(c, c), c)
28.55/9.66	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.66	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.66	   A^2 -> H(f(c), k)
28.55/9.66	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.66	   A^2 -> H(f(k), U1(k, k))
28.55/9.66	   A^2 -> H(f(e), e)
28.55/9.66	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.66	   A^2 -> H(d, U1(c, b))
28.55/9.66	   A^2 -> H(d, U1(d, b))
28.55/9.66	   A^2 -> H(d, U1(b, c))
28.55/9.66	   A^2 -> H(d, U1(b, d))
28.55/9.66	   A^2 -> H(d, U1(c, c))
28.55/9.66	   A^2 -> H(d, f(e))
28.55/9.66	   A^2 -> H(d, f(k))
28.55/9.66	   A^2 -> H(d, U1(d, d))
28.55/9.66	   A^2 -> H(a, U1(e, b))
28.55/9.66	   A^2 -> H(a, U1(k, b))
28.55/9.66	   A^2 -> H(a, U1(c, d))
28.55/9.66	   A^2 -> H(a, U1(d, c))
28.55/9.66	   A^2 -> H(a, U1(b, e))
28.55/9.66	   A^2 -> H(a, U1(b, k))
28.55/9.66	   A^2 -> H(a, U1(e, c))
28.55/9.66	   A^2 -> H(a, U1(k, c))
28.55/9.66	   A^2 -> H(a, U1(c, e))
28.55/9.66	   A^2 -> H(a, U1(c, k))
28.55/9.66	   A^2 -> H(a, U1(e, e))
28.55/9.66	   A^2 -> H(a, U1(k, k))
28.55/9.66	   A^2 -> H(a, U1(k, d))
28.55/9.66	   A^2 -> H(a, U1(d, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.66	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.66	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.66	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.66	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.66	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.66	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.66	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.66	   A^2 -> H(U1(e, a), b)
28.55/9.66	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.66	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.66	   A^2 -> H(U1(e, a), c)
28.55/9.66	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.66	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.66	   A^2 -> H(U1(e, a), e)
28.55/9.66	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, a), b)
28.55/9.66	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.66	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.66	   A^2 -> H(U1(k, a), c)
28.55/9.66	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.66	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.66	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, d), b)
28.55/9.66	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.66	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.66	   A^2 -> H(U1(c, d), c)
28.55/9.66	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.66	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.66	   A^2 -> H(U1(c, d), e)
28.55/9.66	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, a), d)
28.55/9.66	   A^2 -> H(U1(c, a), k)
28.55/9.66	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.66	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.66	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.66	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.66	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.66	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.66	   A^2 -> H(U1(d, c), b)
28.55/9.66	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.66	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.66	   A^2 -> H(U1(d, c), c)
28.55/9.66	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.66	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.66	   A^2 -> H(U1(d, c), e)
28.55/9.66	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(d, a), d)
28.55/9.66	   A^2 -> H(U1(d, a), k)
28.55/9.66	   A^2 -> H(U1(a, e), b)
28.55/9.66	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.66	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.66	   A^2 -> H(U1(a, e), c)
28.55/9.66	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.66	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.66	
28.55/9.66	The TRS R consists of the following rules:
28.55/9.66	
28.55/9.66	   f(x) -> U1(x, x)
28.55/9.66	   U1(e, x) -> x
28.55/9.66	   a -> c
28.55/9.66	   a -> d
28.55/9.66	   b -> c
28.55/9.66	   b -> d
28.55/9.66	   d -> k
28.55/9.66	   c -> e
28.55/9.66	   c -> k
28.55/9.66	
28.55/9.66	Q is empty.
28.55/9.66	We have to consider all minimal (P,Q,R)-chains.
28.55/9.66	----------------------------------------
28.55/9.66	
28.55/9.66	(1309) TransformationProof (EQUIVALENT)
28.55/9.66	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.66	
28.55/9.66	   (A^2 -> H(U1(c, e), U1(c, e)),A^2 -> H(U1(c, e), U1(c, e)))
28.55/9.66	   (A^2 -> H(U1(d, e), U1(c, e)),A^2 -> H(U1(d, e), U1(c, e)))
28.55/9.66	   (A^2 -> H(U1(a, e), U1(e, e)),A^2 -> H(U1(a, e), U1(e, e)))
28.55/9.66	   (A^2 -> H(U1(a, e), U1(k, e)),A^2 -> H(U1(a, e), U1(k, e)))
28.55/9.66	
28.55/9.66	
28.55/9.66	----------------------------------------
28.55/9.66	
28.55/9.66	(1310)
28.55/9.66	Obligation:
28.55/9.66	Q DP problem:
28.55/9.66	The TRS P consists of the following rules:
28.55/9.66	
28.55/9.66	   H(x, x) -> G(x, x, f(k))
28.55/9.66	   G(d, x, x) -> A^2
28.55/9.66	   A^2 -> H(f(c), f(c))
28.55/9.66	   A^2 -> H(f(d), f(d))
28.55/9.66	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.66	   A^2 -> H(f(e), f(e))
28.55/9.66	   A^2 -> H(f(k), f(k))
28.55/9.66	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.66	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.66	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.66	   A^2 -> H(U1(a, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.66	   A^2 -> H(U1(a, c), b)
28.55/9.66	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.66	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.66	   A^2 -> H(U1(a, c), c)
28.55/9.66	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.66	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.66	   A^2 -> H(U1(a, c), e)
28.55/9.66	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, d), b)
28.55/9.66	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.66	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.66	   A^2 -> H(U1(a, d), c)
28.55/9.66	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.66	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.66	   A^2 -> H(U1(a, d), e)
28.55/9.66	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, a), d)
28.55/9.66	   A^2 -> H(U1(a, a), k)
28.55/9.66	   A^2 -> H(k, U1(b, b))
28.55/9.66	   A^2 -> H(k, f(c))
28.55/9.66	   A^2 -> H(k, f(d))
28.55/9.66	   A^2 -> H(c, U1(c, b))
28.55/9.66	   A^2 -> H(c, U1(d, b))
28.55/9.66	   A^2 -> H(c, U1(b, c))
28.55/9.66	   A^2 -> H(c, U1(b, d))
28.55/9.66	   A^2 -> H(c, U1(c, c))
28.55/9.66	   A^2 -> H(c, f(e))
28.55/9.66	   A^2 -> H(c, f(k))
28.55/9.66	   A^2 -> H(c, U1(d, d))
28.55/9.66	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.66	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.66	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.66	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.66	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.66	   A^2 -> H(U1(e, k), f(e))
28.55/9.66	   A^2 -> H(U1(e, k), f(k))
28.55/9.66	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.66	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.66	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.66	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.66	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.66	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.66	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.66	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.66	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.66	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.66	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.66	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.66	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.66	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.66	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.66	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.66	   A^2 -> H(U1(k, e), f(e))
28.55/9.66	   A^2 -> H(U1(k, e), f(k))
28.55/9.66	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.66	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.66	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.66	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.66	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.66	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.66	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.66	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.66	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.66	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.66	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.66	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.66	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.66	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.66	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.66	   A^2 -> H(U1(c, c), b)
28.55/9.66	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.66	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.66	   A^2 -> H(U1(c, c), e)
28.55/9.66	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.66	   A^2 -> H(e, U1(c, b))
28.55/9.66	   A^2 -> H(e, U1(d, b))
28.55/9.66	   A^2 -> H(e, U1(b, c))
28.55/9.66	   A^2 -> H(e, U1(b, d))
28.55/9.66	   A^2 -> H(e, U1(c, c))
28.55/9.66	   A^2 -> H(e, f(e))
28.55/9.66	   A^2 -> H(e, f(k))
28.55/9.66	   A^2 -> H(e, U1(d, d))
28.55/9.66	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.66	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.66	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.66	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.66	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.66	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.66	   A^2 -> H(f(e), b)
28.55/9.66	   A^2 -> H(f(e), U1(e, d))
28.55/9.66	   A^2 -> H(f(e), U1(d, e))
28.55/9.66	   A^2 -> H(f(e), c)
28.55/9.66	   A^2 -> H(f(e), U1(e, k))
28.55/9.66	   A^2 -> H(f(e), U1(k, e))
28.55/9.66	   A^2 -> H(f(e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.66	   A^2 -> H(f(k), b)
28.55/9.66	   A^2 -> H(f(k), U1(e, d))
28.55/9.66	   A^2 -> H(f(k), U1(d, e))
28.55/9.66	   A^2 -> H(f(k), c)
28.55/9.66	   A^2 -> H(f(k), U1(e, k))
28.55/9.66	   A^2 -> H(f(k), U1(k, e))
28.55/9.66	   A^2 -> H(f(k), e)
28.55/9.66	   A^2 -> H(f(c), d)
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.66	   A^2 -> H(U1(k, k), f(e))
28.55/9.66	   A^2 -> H(U1(k, k), f(k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.66	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.66	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.66	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.66	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.66	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.66	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.66	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.66	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.66	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.66	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.66	   A^2 -> H(U1(d, d), b)
28.55/9.66	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.66	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.66	   A^2 -> H(U1(d, d), c)
28.55/9.66	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.66	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.66	   A^2 -> H(U1(d, d), e)
28.55/9.66	   A^2 -> H(f(d), d)
28.55/9.66	   A^2 -> H(f(d), k)
28.55/9.66	   A^2 -> H(U1(c, c), c)
28.55/9.66	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.66	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.66	   A^2 -> H(f(c), k)
28.55/9.66	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.66	   A^2 -> H(f(k), U1(k, k))
28.55/9.66	   A^2 -> H(f(e), e)
28.55/9.66	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.66	   A^2 -> H(d, U1(c, b))
28.55/9.66	   A^2 -> H(d, U1(d, b))
28.55/9.66	   A^2 -> H(d, U1(b, c))
28.55/9.66	   A^2 -> H(d, U1(b, d))
28.55/9.66	   A^2 -> H(d, U1(c, c))
28.55/9.66	   A^2 -> H(d, f(e))
28.55/9.66	   A^2 -> H(d, f(k))
28.55/9.66	   A^2 -> H(d, U1(d, d))
28.55/9.66	   A^2 -> H(a, U1(e, b))
28.55/9.66	   A^2 -> H(a, U1(k, b))
28.55/9.66	   A^2 -> H(a, U1(c, d))
28.55/9.66	   A^2 -> H(a, U1(d, c))
28.55/9.66	   A^2 -> H(a, U1(b, e))
28.55/9.66	   A^2 -> H(a, U1(b, k))
28.55/9.66	   A^2 -> H(a, U1(e, c))
28.55/9.66	   A^2 -> H(a, U1(k, c))
28.55/9.66	   A^2 -> H(a, U1(c, e))
28.55/9.66	   A^2 -> H(a, U1(c, k))
28.55/9.66	   A^2 -> H(a, U1(e, e))
28.55/9.66	   A^2 -> H(a, U1(k, k))
28.55/9.66	   A^2 -> H(a, U1(k, d))
28.55/9.66	   A^2 -> H(a, U1(d, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.66	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.66	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.66	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.66	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.66	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.66	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.66	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.66	   A^2 -> H(U1(e, a), b)
28.55/9.66	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.66	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.66	   A^2 -> H(U1(e, a), c)
28.55/9.66	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.66	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.66	   A^2 -> H(U1(e, a), e)
28.55/9.66	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, a), b)
28.55/9.66	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.66	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.66	   A^2 -> H(U1(k, a), c)
28.55/9.66	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.66	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.66	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, d), b)
28.55/9.66	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.66	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.66	   A^2 -> H(U1(c, d), c)
28.55/9.66	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.66	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.66	   A^2 -> H(U1(c, d), e)
28.55/9.66	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, a), d)
28.55/9.66	   A^2 -> H(U1(c, a), k)
28.55/9.66	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.66	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.66	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.66	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.66	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.66	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.66	   A^2 -> H(U1(d, c), b)
28.55/9.66	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.66	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.66	   A^2 -> H(U1(d, c), c)
28.55/9.66	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.66	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.66	   A^2 -> H(U1(d, c), e)
28.55/9.66	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(d, a), d)
28.55/9.66	   A^2 -> H(U1(d, a), k)
28.55/9.66	   A^2 -> H(U1(a, e), b)
28.55/9.66	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.66	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.66	   A^2 -> H(U1(a, e), c)
28.55/9.66	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.66	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.66	
28.55/9.66	The TRS R consists of the following rules:
28.55/9.66	
28.55/9.66	   f(x) -> U1(x, x)
28.55/9.66	   U1(e, x) -> x
28.55/9.66	   a -> c
28.55/9.66	   a -> d
28.55/9.66	   b -> c
28.55/9.66	   b -> d
28.55/9.66	   d -> k
28.55/9.66	   c -> e
28.55/9.66	   c -> k
28.55/9.66	
28.55/9.66	Q is empty.
28.55/9.66	We have to consider all minimal (P,Q,R)-chains.
28.55/9.66	----------------------------------------
28.55/9.66	
28.55/9.66	(1311) TransformationProof (EQUIVALENT)
28.55/9.66	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.66	
28.55/9.66	   (A^2 -> H(U1(c, e), U1(c, k)),A^2 -> H(U1(c, e), U1(c, k)))
28.55/9.66	   (A^2 -> H(U1(d, e), U1(c, k)),A^2 -> H(U1(d, e), U1(c, k)))
28.55/9.66	   (A^2 -> H(U1(a, e), U1(e, k)),A^2 -> H(U1(a, e), U1(e, k)))
28.55/9.66	   (A^2 -> H(U1(a, e), U1(k, k)),A^2 -> H(U1(a, e), U1(k, k)))
28.55/9.66	
28.55/9.66	
28.55/9.66	----------------------------------------
28.55/9.66	
28.55/9.66	(1312)
28.55/9.66	Obligation:
28.55/9.66	Q DP problem:
28.55/9.66	The TRS P consists of the following rules:
28.55/9.66	
28.55/9.66	   H(x, x) -> G(x, x, f(k))
28.55/9.66	   G(d, x, x) -> A^2
28.55/9.66	   A^2 -> H(f(c), f(c))
28.55/9.66	   A^2 -> H(f(d), f(d))
28.55/9.66	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.66	   A^2 -> H(f(e), f(e))
28.55/9.66	   A^2 -> H(f(k), f(k))
28.55/9.66	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.66	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.66	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.66	   A^2 -> H(U1(a, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.66	   A^2 -> H(U1(a, c), b)
28.55/9.66	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.66	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.66	   A^2 -> H(U1(a, c), c)
28.55/9.66	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.66	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.66	   A^2 -> H(U1(a, c), e)
28.55/9.66	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, d), b)
28.55/9.66	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.66	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.66	   A^2 -> H(U1(a, d), c)
28.55/9.66	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.66	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.66	   A^2 -> H(U1(a, d), e)
28.55/9.66	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, a), d)
28.55/9.66	   A^2 -> H(U1(a, a), k)
28.55/9.66	   A^2 -> H(k, U1(b, b))
28.55/9.66	   A^2 -> H(k, f(c))
28.55/9.66	   A^2 -> H(k, f(d))
28.55/9.66	   A^2 -> H(c, U1(c, b))
28.55/9.66	   A^2 -> H(c, U1(d, b))
28.55/9.66	   A^2 -> H(c, U1(b, c))
28.55/9.66	   A^2 -> H(c, U1(b, d))
28.55/9.66	   A^2 -> H(c, U1(c, c))
28.55/9.66	   A^2 -> H(c, f(e))
28.55/9.66	   A^2 -> H(c, f(k))
28.55/9.66	   A^2 -> H(c, U1(d, d))
28.55/9.66	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.66	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.66	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.66	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.66	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.66	   A^2 -> H(U1(e, k), f(e))
28.55/9.66	   A^2 -> H(U1(e, k), f(k))
28.55/9.66	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.66	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.66	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.66	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.66	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.66	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.66	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.66	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.66	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.66	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.66	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.66	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.66	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.66	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.66	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.66	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.66	   A^2 -> H(U1(k, e), f(e))
28.55/9.66	   A^2 -> H(U1(k, e), f(k))
28.55/9.66	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.66	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.66	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.66	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.66	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.66	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.66	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.66	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.66	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.66	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.66	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.66	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.66	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.66	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.66	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.66	   A^2 -> H(U1(c, c), b)
28.55/9.66	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.66	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.66	   A^2 -> H(U1(c, c), e)
28.55/9.66	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.66	   A^2 -> H(e, U1(c, b))
28.55/9.66	   A^2 -> H(e, U1(d, b))
28.55/9.66	   A^2 -> H(e, U1(b, c))
28.55/9.66	   A^2 -> H(e, U1(b, d))
28.55/9.66	   A^2 -> H(e, U1(c, c))
28.55/9.66	   A^2 -> H(e, f(e))
28.55/9.66	   A^2 -> H(e, f(k))
28.55/9.66	   A^2 -> H(e, U1(d, d))
28.55/9.66	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.66	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.66	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.66	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.66	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.66	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.66	   A^2 -> H(f(e), b)
28.55/9.66	   A^2 -> H(f(e), U1(e, d))
28.55/9.66	   A^2 -> H(f(e), U1(d, e))
28.55/9.66	   A^2 -> H(f(e), c)
28.55/9.66	   A^2 -> H(f(e), U1(e, k))
28.55/9.66	   A^2 -> H(f(e), U1(k, e))
28.55/9.66	   A^2 -> H(f(e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.66	   A^2 -> H(f(k), b)
28.55/9.66	   A^2 -> H(f(k), U1(e, d))
28.55/9.66	   A^2 -> H(f(k), U1(d, e))
28.55/9.66	   A^2 -> H(f(k), c)
28.55/9.66	   A^2 -> H(f(k), U1(e, k))
28.55/9.66	   A^2 -> H(f(k), U1(k, e))
28.55/9.66	   A^2 -> H(f(k), e)
28.55/9.66	   A^2 -> H(f(c), d)
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.66	   A^2 -> H(U1(k, k), f(e))
28.55/9.66	   A^2 -> H(U1(k, k), f(k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.66	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.66	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.66	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.66	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.66	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.66	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.66	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.66	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.66	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.66	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.66	   A^2 -> H(U1(d, d), b)
28.55/9.66	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.66	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.66	   A^2 -> H(U1(d, d), c)
28.55/9.66	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.66	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.66	   A^2 -> H(U1(d, d), e)
28.55/9.66	   A^2 -> H(f(d), d)
28.55/9.66	   A^2 -> H(f(d), k)
28.55/9.66	   A^2 -> H(U1(c, c), c)
28.55/9.66	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.66	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.66	   A^2 -> H(f(c), k)
28.55/9.66	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.66	   A^2 -> H(f(k), U1(k, k))
28.55/9.66	   A^2 -> H(f(e), e)
28.55/9.66	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.66	   A^2 -> H(d, U1(c, b))
28.55/9.66	   A^2 -> H(d, U1(d, b))
28.55/9.66	   A^2 -> H(d, U1(b, c))
28.55/9.66	   A^2 -> H(d, U1(b, d))
28.55/9.66	   A^2 -> H(d, U1(c, c))
28.55/9.66	   A^2 -> H(d, f(e))
28.55/9.66	   A^2 -> H(d, f(k))
28.55/9.66	   A^2 -> H(d, U1(d, d))
28.55/9.66	   A^2 -> H(a, U1(e, b))
28.55/9.66	   A^2 -> H(a, U1(k, b))
28.55/9.66	   A^2 -> H(a, U1(c, d))
28.55/9.66	   A^2 -> H(a, U1(d, c))
28.55/9.66	   A^2 -> H(a, U1(b, e))
28.55/9.66	   A^2 -> H(a, U1(b, k))
28.55/9.66	   A^2 -> H(a, U1(e, c))
28.55/9.66	   A^2 -> H(a, U1(k, c))
28.55/9.66	   A^2 -> H(a, U1(c, e))
28.55/9.66	   A^2 -> H(a, U1(c, k))
28.55/9.66	   A^2 -> H(a, U1(e, e))
28.55/9.66	   A^2 -> H(a, U1(k, k))
28.55/9.66	   A^2 -> H(a, U1(k, d))
28.55/9.66	   A^2 -> H(a, U1(d, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.66	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.66	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.66	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.66	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.66	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.66	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.66	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.66	   A^2 -> H(U1(e, a), b)
28.55/9.66	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.66	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.66	   A^2 -> H(U1(e, a), c)
28.55/9.66	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.66	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.66	   A^2 -> H(U1(e, a), e)
28.55/9.66	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, a), b)
28.55/9.66	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.66	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.66	   A^2 -> H(U1(k, a), c)
28.55/9.66	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.66	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.66	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, d), b)
28.55/9.66	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.66	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.66	   A^2 -> H(U1(c, d), c)
28.55/9.66	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.66	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.66	   A^2 -> H(U1(c, d), e)
28.55/9.66	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, a), d)
28.55/9.66	   A^2 -> H(U1(c, a), k)
28.55/9.66	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.66	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.66	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.66	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.66	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.66	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.66	   A^2 -> H(U1(d, c), b)
28.55/9.66	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.66	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.66	   A^2 -> H(U1(d, c), c)
28.55/9.66	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.66	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.66	   A^2 -> H(U1(d, c), e)
28.55/9.66	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(d, a), d)
28.55/9.66	   A^2 -> H(U1(d, a), k)
28.55/9.66	   A^2 -> H(U1(a, e), b)
28.55/9.66	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.66	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.66	   A^2 -> H(U1(a, e), c)
28.55/9.66	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.66	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.66	
28.55/9.66	The TRS R consists of the following rules:
28.55/9.66	
28.55/9.66	   f(x) -> U1(x, x)
28.55/9.66	   U1(e, x) -> x
28.55/9.66	   a -> c
28.55/9.66	   a -> d
28.55/9.66	   b -> c
28.55/9.66	   b -> d
28.55/9.66	   d -> k
28.55/9.66	   c -> e
28.55/9.66	   c -> k
28.55/9.66	
28.55/9.66	Q is empty.
28.55/9.66	We have to consider all minimal (P,Q,R)-chains.
28.55/9.66	----------------------------------------
28.55/9.66	
28.55/9.66	(1313) TransformationProof (EQUIVALENT)
28.55/9.66	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.66	
28.55/9.66	   (A^2 -> H(U1(c, e), U1(e, e)),A^2 -> H(U1(c, e), U1(e, e)))
28.55/9.66	   (A^2 -> H(U1(d, e), U1(e, e)),A^2 -> H(U1(d, e), U1(e, e)))
28.55/9.66	   (A^2 -> H(U1(a, e), e),A^2 -> H(U1(a, e), e))
28.55/9.66	
28.55/9.66	
28.55/9.66	----------------------------------------
28.55/9.66	
28.55/9.66	(1314)
28.55/9.66	Obligation:
28.55/9.66	Q DP problem:
28.55/9.66	The TRS P consists of the following rules:
28.55/9.66	
28.55/9.66	   H(x, x) -> G(x, x, f(k))
28.55/9.66	   G(d, x, x) -> A^2
28.55/9.66	   A^2 -> H(f(c), f(c))
28.55/9.66	   A^2 -> H(f(d), f(d))
28.55/9.66	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.66	   A^2 -> H(f(e), f(e))
28.55/9.66	   A^2 -> H(f(k), f(k))
28.55/9.66	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.66	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.66	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.66	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.66	   A^2 -> H(U1(a, c), b)
28.55/9.66	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.66	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.66	   A^2 -> H(U1(a, c), c)
28.55/9.66	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.66	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.66	   A^2 -> H(U1(a, c), e)
28.55/9.66	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, d), b)
28.55/9.66	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.66	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.66	   A^2 -> H(U1(a, d), c)
28.55/9.66	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.66	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.66	   A^2 -> H(U1(a, d), e)
28.55/9.66	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, a), d)
28.55/9.66	   A^2 -> H(U1(a, a), k)
28.55/9.66	   A^2 -> H(k, U1(b, b))
28.55/9.66	   A^2 -> H(k, f(c))
28.55/9.66	   A^2 -> H(k, f(d))
28.55/9.66	   A^2 -> H(c, U1(c, b))
28.55/9.66	   A^2 -> H(c, U1(d, b))
28.55/9.66	   A^2 -> H(c, U1(b, c))
28.55/9.66	   A^2 -> H(c, U1(b, d))
28.55/9.66	   A^2 -> H(c, U1(c, c))
28.55/9.66	   A^2 -> H(c, f(e))
28.55/9.66	   A^2 -> H(c, f(k))
28.55/9.66	   A^2 -> H(c, U1(d, d))
28.55/9.66	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.66	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.66	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.66	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.66	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.66	   A^2 -> H(U1(e, k), f(e))
28.55/9.66	   A^2 -> H(U1(e, k), f(k))
28.55/9.66	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.66	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.66	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.66	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.66	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.66	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.66	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.66	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.66	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.66	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.66	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.66	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.66	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.66	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.66	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.66	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.66	   A^2 -> H(U1(k, e), f(e))
28.55/9.66	   A^2 -> H(U1(k, e), f(k))
28.55/9.66	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.66	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.66	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.66	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.66	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.66	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.66	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.66	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.66	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.66	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.66	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.66	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.66	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.66	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.66	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.66	   A^2 -> H(U1(c, c), b)
28.55/9.66	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.66	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.66	   A^2 -> H(U1(c, c), e)
28.55/9.66	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.66	   A^2 -> H(e, U1(c, b))
28.55/9.66	   A^2 -> H(e, U1(d, b))
28.55/9.66	   A^2 -> H(e, U1(b, c))
28.55/9.66	   A^2 -> H(e, U1(b, d))
28.55/9.66	   A^2 -> H(e, U1(c, c))
28.55/9.66	   A^2 -> H(e, f(e))
28.55/9.66	   A^2 -> H(e, f(k))
28.55/9.66	   A^2 -> H(e, U1(d, d))
28.55/9.66	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.66	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.66	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.66	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.66	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.66	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.66	   A^2 -> H(f(e), b)
28.55/9.66	   A^2 -> H(f(e), U1(e, d))
28.55/9.66	   A^2 -> H(f(e), U1(d, e))
28.55/9.66	   A^2 -> H(f(e), c)
28.55/9.66	   A^2 -> H(f(e), U1(e, k))
28.55/9.66	   A^2 -> H(f(e), U1(k, e))
28.55/9.66	   A^2 -> H(f(e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.66	   A^2 -> H(f(k), b)
28.55/9.66	   A^2 -> H(f(k), U1(e, d))
28.55/9.66	   A^2 -> H(f(k), U1(d, e))
28.55/9.66	   A^2 -> H(f(k), c)
28.55/9.66	   A^2 -> H(f(k), U1(e, k))
28.55/9.66	   A^2 -> H(f(k), U1(k, e))
28.55/9.66	   A^2 -> H(f(k), e)
28.55/9.66	   A^2 -> H(f(c), d)
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.66	   A^2 -> H(U1(k, k), f(e))
28.55/9.66	   A^2 -> H(U1(k, k), f(k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.66	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.66	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.66	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.66	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.66	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.66	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.66	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.66	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.66	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.66	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.66	   A^2 -> H(U1(d, d), b)
28.55/9.66	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.66	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.66	   A^2 -> H(U1(d, d), c)
28.55/9.66	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.66	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.66	   A^2 -> H(U1(d, d), e)
28.55/9.66	   A^2 -> H(f(d), d)
28.55/9.66	   A^2 -> H(f(d), k)
28.55/9.66	   A^2 -> H(U1(c, c), c)
28.55/9.66	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.66	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.66	   A^2 -> H(f(c), k)
28.55/9.66	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.66	   A^2 -> H(f(k), U1(k, k))
28.55/9.66	   A^2 -> H(f(e), e)
28.55/9.66	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.66	   A^2 -> H(d, U1(c, b))
28.55/9.66	   A^2 -> H(d, U1(d, b))
28.55/9.66	   A^2 -> H(d, U1(b, c))
28.55/9.66	   A^2 -> H(d, U1(b, d))
28.55/9.66	   A^2 -> H(d, U1(c, c))
28.55/9.66	   A^2 -> H(d, f(e))
28.55/9.66	   A^2 -> H(d, f(k))
28.55/9.66	   A^2 -> H(d, U1(d, d))
28.55/9.66	   A^2 -> H(a, U1(e, b))
28.55/9.66	   A^2 -> H(a, U1(k, b))
28.55/9.66	   A^2 -> H(a, U1(c, d))
28.55/9.66	   A^2 -> H(a, U1(d, c))
28.55/9.66	   A^2 -> H(a, U1(b, e))
28.55/9.66	   A^2 -> H(a, U1(b, k))
28.55/9.66	   A^2 -> H(a, U1(e, c))
28.55/9.66	   A^2 -> H(a, U1(k, c))
28.55/9.66	   A^2 -> H(a, U1(c, e))
28.55/9.66	   A^2 -> H(a, U1(c, k))
28.55/9.66	   A^2 -> H(a, U1(e, e))
28.55/9.66	   A^2 -> H(a, U1(k, k))
28.55/9.66	   A^2 -> H(a, U1(k, d))
28.55/9.66	   A^2 -> H(a, U1(d, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.66	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.66	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.66	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.66	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.66	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.66	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.66	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.66	   A^2 -> H(U1(e, a), b)
28.55/9.66	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.66	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.66	   A^2 -> H(U1(e, a), c)
28.55/9.66	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.66	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.66	   A^2 -> H(U1(e, a), e)
28.55/9.66	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, a), b)
28.55/9.66	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.66	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.66	   A^2 -> H(U1(k, a), c)
28.55/9.66	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.66	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.66	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, d), b)
28.55/9.66	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.66	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.66	   A^2 -> H(U1(c, d), c)
28.55/9.66	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.66	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.66	   A^2 -> H(U1(c, d), e)
28.55/9.66	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, a), d)
28.55/9.66	   A^2 -> H(U1(c, a), k)
28.55/9.66	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.66	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.66	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.66	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.66	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.66	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.66	   A^2 -> H(U1(d, c), b)
28.55/9.66	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.66	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.66	   A^2 -> H(U1(d, c), c)
28.55/9.66	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.66	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.66	   A^2 -> H(U1(d, c), e)
28.55/9.66	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(d, a), d)
28.55/9.66	   A^2 -> H(U1(d, a), k)
28.55/9.66	   A^2 -> H(U1(a, e), b)
28.55/9.66	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.66	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.66	   A^2 -> H(U1(a, e), c)
28.55/9.66	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.66	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.66	   A^2 -> H(U1(a, e), e)
28.55/9.66	
28.55/9.66	The TRS R consists of the following rules:
28.55/9.66	
28.55/9.66	   f(x) -> U1(x, x)
28.55/9.66	   U1(e, x) -> x
28.55/9.66	   a -> c
28.55/9.66	   a -> d
28.55/9.66	   b -> c
28.55/9.66	   b -> d
28.55/9.66	   d -> k
28.55/9.66	   c -> e
28.55/9.66	   c -> k
28.55/9.66	
28.55/9.66	Q is empty.
28.55/9.66	We have to consider all minimal (P,Q,R)-chains.
28.55/9.66	----------------------------------------
28.55/9.66	
28.55/9.66	(1315) TransformationProof (EQUIVALENT)
28.55/9.66	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.66	
28.55/9.66	   (A^2 -> H(U1(c, e), U1(k, k)),A^2 -> H(U1(c, e), U1(k, k)))
28.55/9.66	   (A^2 -> H(U1(d, e), U1(k, k)),A^2 -> H(U1(d, e), U1(k, k)))
28.55/9.66	
28.55/9.66	
28.55/9.66	----------------------------------------
28.55/9.66	
28.55/9.66	(1316)
28.55/9.66	Obligation:
28.55/9.66	Q DP problem:
28.55/9.66	The TRS P consists of the following rules:
28.55/9.66	
28.55/9.66	   H(x, x) -> G(x, x, f(k))
28.55/9.66	   G(d, x, x) -> A^2
28.55/9.66	   A^2 -> H(f(c), f(c))
28.55/9.66	   A^2 -> H(f(d), f(d))
28.55/9.66	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.66	   A^2 -> H(f(e), f(e))
28.55/9.66	   A^2 -> H(f(k), f(k))
28.55/9.66	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.66	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.66	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.66	   A^2 -> H(U1(a, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.66	   A^2 -> H(U1(a, c), b)
28.55/9.66	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.66	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.66	   A^2 -> H(U1(a, c), c)
28.55/9.66	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.66	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.66	   A^2 -> H(U1(a, c), e)
28.55/9.66	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, d), b)
28.55/9.66	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.66	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.66	   A^2 -> H(U1(a, d), c)
28.55/9.66	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.66	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.66	   A^2 -> H(U1(a, d), e)
28.55/9.66	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.66	   A^2 -> H(U1(a, a), d)
28.55/9.66	   A^2 -> H(U1(a, a), k)
28.55/9.66	   A^2 -> H(k, U1(b, b))
28.55/9.66	   A^2 -> H(k, f(c))
28.55/9.66	   A^2 -> H(k, f(d))
28.55/9.66	   A^2 -> H(c, U1(c, b))
28.55/9.66	   A^2 -> H(c, U1(d, b))
28.55/9.66	   A^2 -> H(c, U1(b, c))
28.55/9.66	   A^2 -> H(c, U1(b, d))
28.55/9.66	   A^2 -> H(c, U1(c, c))
28.55/9.66	   A^2 -> H(c, f(e))
28.55/9.66	   A^2 -> H(c, f(k))
28.55/9.66	   A^2 -> H(c, U1(d, d))
28.55/9.66	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.66	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.66	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.66	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.66	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.66	   A^2 -> H(U1(e, k), f(e))
28.55/9.66	   A^2 -> H(U1(e, k), f(k))
28.55/9.66	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.66	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.66	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.66	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.66	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.66	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.66	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.66	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.66	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.66	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.66	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.66	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.66	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.66	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.66	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.66	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.66	   A^2 -> H(U1(k, e), f(e))
28.55/9.66	   A^2 -> H(U1(k, e), f(k))
28.55/9.66	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.66	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.66	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.66	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.66	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.66	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.66	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.66	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.66	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.66	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.66	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.66	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.66	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.66	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.66	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.66	   A^2 -> H(U1(c, c), b)
28.55/9.66	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.66	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.66	   A^2 -> H(U1(c, c), e)
28.55/9.66	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.66	   A^2 -> H(e, U1(c, b))
28.55/9.66	   A^2 -> H(e, U1(d, b))
28.55/9.66	   A^2 -> H(e, U1(b, c))
28.55/9.66	   A^2 -> H(e, U1(b, d))
28.55/9.66	   A^2 -> H(e, U1(c, c))
28.55/9.66	   A^2 -> H(e, f(e))
28.55/9.66	   A^2 -> H(e, f(k))
28.55/9.66	   A^2 -> H(e, U1(d, d))
28.55/9.66	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.66	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.66	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.66	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.66	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.66	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.66	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.66	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.66	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.66	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.66	   A^2 -> H(f(e), b)
28.55/9.66	   A^2 -> H(f(e), U1(e, d))
28.55/9.66	   A^2 -> H(f(e), U1(d, e))
28.55/9.66	   A^2 -> H(f(e), c)
28.55/9.66	   A^2 -> H(f(e), U1(e, k))
28.55/9.66	   A^2 -> H(f(e), U1(k, e))
28.55/9.66	   A^2 -> H(f(e), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.66	   A^2 -> H(f(k), b)
28.55/9.66	   A^2 -> H(f(k), U1(e, d))
28.55/9.66	   A^2 -> H(f(k), U1(d, e))
28.55/9.66	   A^2 -> H(f(k), c)
28.55/9.66	   A^2 -> H(f(k), U1(e, k))
28.55/9.66	   A^2 -> H(f(k), U1(k, e))
28.55/9.66	   A^2 -> H(f(k), e)
28.55/9.66	   A^2 -> H(f(c), d)
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.66	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.66	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.66	   A^2 -> H(U1(k, k), f(e))
28.55/9.66	   A^2 -> H(U1(k, k), f(k))
28.55/9.66	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.66	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.66	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.66	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.66	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.66	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.66	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.66	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.67	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.67	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.67	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.67	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.67	   A^2 -> H(U1(d, d), b)
28.55/9.67	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.67	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.67	   A^2 -> H(U1(d, d), c)
28.55/9.67	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.67	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.67	   A^2 -> H(U1(d, d), e)
28.55/9.67	   A^2 -> H(f(d), d)
28.55/9.67	   A^2 -> H(f(d), k)
28.55/9.67	   A^2 -> H(U1(c, c), c)
28.55/9.67	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.67	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.67	   A^2 -> H(f(c), k)
28.55/9.67	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.67	   A^2 -> H(f(k), U1(k, k))
28.55/9.67	   A^2 -> H(f(e), e)
28.55/9.67	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.67	   A^2 -> H(d, U1(c, b))
28.55/9.67	   A^2 -> H(d, U1(d, b))
28.55/9.67	   A^2 -> H(d, U1(b, c))
28.55/9.67	   A^2 -> H(d, U1(b, d))
28.55/9.67	   A^2 -> H(d, U1(c, c))
28.55/9.67	   A^2 -> H(d, f(e))
28.55/9.67	   A^2 -> H(d, f(k))
28.55/9.67	   A^2 -> H(d, U1(d, d))
28.55/9.67	   A^2 -> H(a, U1(e, b))
28.55/9.67	   A^2 -> H(a, U1(k, b))
28.55/9.67	   A^2 -> H(a, U1(c, d))
28.55/9.67	   A^2 -> H(a, U1(d, c))
28.55/9.67	   A^2 -> H(a, U1(b, e))
28.55/9.67	   A^2 -> H(a, U1(b, k))
28.55/9.67	   A^2 -> H(a, U1(e, c))
28.55/9.67	   A^2 -> H(a, U1(k, c))
28.55/9.67	   A^2 -> H(a, U1(c, e))
28.55/9.67	   A^2 -> H(a, U1(c, k))
28.55/9.67	   A^2 -> H(a, U1(e, e))
28.55/9.67	   A^2 -> H(a, U1(k, k))
28.55/9.67	   A^2 -> H(a, U1(k, d))
28.55/9.67	   A^2 -> H(a, U1(d, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.67	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.67	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.67	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.67	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.67	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.67	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.67	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.67	   A^2 -> H(U1(e, a), b)
28.55/9.67	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.67	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.67	   A^2 -> H(U1(e, a), c)
28.55/9.67	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.67	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.67	   A^2 -> H(U1(e, a), e)
28.55/9.67	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, a), b)
28.55/9.67	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.67	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.67	   A^2 -> H(U1(k, a), c)
28.55/9.67	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.67	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.67	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, d), b)
28.55/9.67	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.67	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.67	   A^2 -> H(U1(c, d), c)
28.55/9.67	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.67	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.67	   A^2 -> H(U1(c, d), e)
28.55/9.67	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, a), d)
28.55/9.67	   A^2 -> H(U1(c, a), k)
28.55/9.67	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.67	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.67	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.67	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.67	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.67	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.67	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.67	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.67	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.67	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.67	   A^2 -> H(U1(d, c), b)
28.55/9.67	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.67	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.67	   A^2 -> H(U1(d, c), c)
28.55/9.67	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.67	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.67	   A^2 -> H(U1(d, c), e)
28.55/9.67	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(d, a), d)
28.55/9.67	   A^2 -> H(U1(d, a), k)
28.55/9.67	   A^2 -> H(U1(a, e), b)
28.55/9.67	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.67	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.67	   A^2 -> H(U1(a, e), c)
28.55/9.67	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.67	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.67	   A^2 -> H(U1(a, e), e)
28.55/9.67	
28.55/9.67	The TRS R consists of the following rules:
28.55/9.67	
28.55/9.67	   f(x) -> U1(x, x)
28.55/9.67	   U1(e, x) -> x
28.55/9.67	   a -> c
28.55/9.67	   a -> d
28.55/9.67	   b -> c
28.55/9.67	   b -> d
28.55/9.67	   d -> k
28.55/9.67	   c -> e
28.55/9.67	   c -> k
28.55/9.67	
28.55/9.67	Q is empty.
28.55/9.67	We have to consider all minimal (P,Q,R)-chains.
28.55/9.67	----------------------------------------
28.55/9.67	
28.55/9.67	(1317) TransformationProof (EQUIVALENT)
28.55/9.67	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.67	
28.55/9.67	   (A^2 -> H(U1(c, e), U1(k, d)),A^2 -> H(U1(c, e), U1(k, d)))
28.55/9.67	   (A^2 -> H(U1(d, e), U1(k, d)),A^2 -> H(U1(d, e), U1(k, d)))
28.55/9.67	   (A^2 -> H(U1(a, e), U1(k, k)),A^2 -> H(U1(a, e), U1(k, k)))
28.55/9.67	
28.55/9.67	
28.55/9.67	----------------------------------------
28.55/9.67	
28.55/9.67	(1318)
28.55/9.67	Obligation:
28.55/9.67	Q DP problem:
28.55/9.67	The TRS P consists of the following rules:
28.55/9.67	
28.55/9.67	   H(x, x) -> G(x, x, f(k))
28.55/9.67	   G(d, x, x) -> A^2
28.55/9.67	   A^2 -> H(f(c), f(c))
28.55/9.67	   A^2 -> H(f(d), f(d))
28.55/9.67	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.67	   A^2 -> H(f(e), f(e))
28.55/9.67	   A^2 -> H(f(k), f(k))
28.55/9.67	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.67	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.67	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.67	   A^2 -> H(U1(a, e), U1(d, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.67	   A^2 -> H(U1(a, c), b)
28.55/9.67	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.67	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.67	   A^2 -> H(U1(a, c), c)
28.55/9.67	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.67	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.67	   A^2 -> H(U1(a, c), e)
28.55/9.67	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, d), b)
28.55/9.67	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.67	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.67	   A^2 -> H(U1(a, d), c)
28.55/9.67	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.67	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.67	   A^2 -> H(U1(a, d), e)
28.55/9.67	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, a), d)
28.55/9.67	   A^2 -> H(U1(a, a), k)
28.55/9.67	   A^2 -> H(k, U1(b, b))
28.55/9.67	   A^2 -> H(k, f(c))
28.55/9.67	   A^2 -> H(k, f(d))
28.55/9.67	   A^2 -> H(c, U1(c, b))
28.55/9.67	   A^2 -> H(c, U1(d, b))
28.55/9.67	   A^2 -> H(c, U1(b, c))
28.55/9.67	   A^2 -> H(c, U1(b, d))
28.55/9.67	   A^2 -> H(c, U1(c, c))
28.55/9.67	   A^2 -> H(c, f(e))
28.55/9.67	   A^2 -> H(c, f(k))
28.55/9.67	   A^2 -> H(c, U1(d, d))
28.55/9.67	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.67	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.67	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.67	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.67	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.67	   A^2 -> H(U1(e, k), f(e))
28.55/9.67	   A^2 -> H(U1(e, k), f(k))
28.55/9.67	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.67	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.67	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.67	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.67	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.67	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.67	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.67	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.67	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.67	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.67	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.67	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.67	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.67	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.67	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.67	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.67	   A^2 -> H(U1(k, e), f(e))
28.55/9.67	   A^2 -> H(U1(k, e), f(k))
28.55/9.67	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.67	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.67	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.67	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.67	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.67	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.67	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.67	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.67	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.67	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.67	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.67	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.67	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.67	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.67	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.67	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.67	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.67	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.67	   A^2 -> H(U1(c, c), b)
28.55/9.67	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.67	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.67	   A^2 -> H(U1(c, c), e)
28.55/9.67	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.67	   A^2 -> H(e, U1(c, b))
28.55/9.67	   A^2 -> H(e, U1(d, b))
28.55/9.67	   A^2 -> H(e, U1(b, c))
28.55/9.67	   A^2 -> H(e, U1(b, d))
28.55/9.67	   A^2 -> H(e, U1(c, c))
28.55/9.67	   A^2 -> H(e, f(e))
28.55/9.67	   A^2 -> H(e, f(k))
28.55/9.67	   A^2 -> H(e, U1(d, d))
28.55/9.67	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.67	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.67	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.67	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.67	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.67	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.67	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.67	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.67	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.67	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.67	   A^2 -> H(f(e), b)
28.55/9.67	   A^2 -> H(f(e), U1(e, d))
28.55/9.67	   A^2 -> H(f(e), U1(d, e))
28.55/9.67	   A^2 -> H(f(e), c)
28.55/9.67	   A^2 -> H(f(e), U1(e, k))
28.55/9.67	   A^2 -> H(f(e), U1(k, e))
28.55/9.67	   A^2 -> H(f(e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.67	   A^2 -> H(f(k), b)
28.55/9.67	   A^2 -> H(f(k), U1(e, d))
28.55/9.67	   A^2 -> H(f(k), U1(d, e))
28.55/9.67	   A^2 -> H(f(k), c)
28.55/9.67	   A^2 -> H(f(k), U1(e, k))
28.55/9.67	   A^2 -> H(f(k), U1(k, e))
28.55/9.67	   A^2 -> H(f(k), e)
28.55/9.67	   A^2 -> H(f(c), d)
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.67	   A^2 -> H(U1(k, k), f(e))
28.55/9.67	   A^2 -> H(U1(k, k), f(k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.67	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.67	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.67	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.67	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.67	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.67	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.67	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.67	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.67	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.67	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.67	   A^2 -> H(U1(d, d), b)
28.55/9.67	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.67	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.67	   A^2 -> H(U1(d, d), c)
28.55/9.67	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.67	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.67	   A^2 -> H(U1(d, d), e)
28.55/9.67	   A^2 -> H(f(d), d)
28.55/9.67	   A^2 -> H(f(d), k)
28.55/9.67	   A^2 -> H(U1(c, c), c)
28.55/9.67	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.67	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.67	   A^2 -> H(f(c), k)
28.55/9.67	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.67	   A^2 -> H(f(k), U1(k, k))
28.55/9.67	   A^2 -> H(f(e), e)
28.55/9.67	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.67	   A^2 -> H(d, U1(c, b))
28.55/9.67	   A^2 -> H(d, U1(d, b))
28.55/9.67	   A^2 -> H(d, U1(b, c))
28.55/9.67	   A^2 -> H(d, U1(b, d))
28.55/9.67	   A^2 -> H(d, U1(c, c))
28.55/9.67	   A^2 -> H(d, f(e))
28.55/9.67	   A^2 -> H(d, f(k))
28.55/9.67	   A^2 -> H(d, U1(d, d))
28.55/9.67	   A^2 -> H(a, U1(e, b))
28.55/9.67	   A^2 -> H(a, U1(k, b))
28.55/9.67	   A^2 -> H(a, U1(c, d))
28.55/9.67	   A^2 -> H(a, U1(d, c))
28.55/9.67	   A^2 -> H(a, U1(b, e))
28.55/9.67	   A^2 -> H(a, U1(b, k))
28.55/9.67	   A^2 -> H(a, U1(e, c))
28.55/9.67	   A^2 -> H(a, U1(k, c))
28.55/9.67	   A^2 -> H(a, U1(c, e))
28.55/9.67	   A^2 -> H(a, U1(c, k))
28.55/9.67	   A^2 -> H(a, U1(e, e))
28.55/9.67	   A^2 -> H(a, U1(k, k))
28.55/9.67	   A^2 -> H(a, U1(k, d))
28.55/9.67	   A^2 -> H(a, U1(d, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.67	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.67	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.67	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.67	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.67	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.67	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.67	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.67	   A^2 -> H(U1(e, a), b)
28.55/9.67	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.67	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.67	   A^2 -> H(U1(e, a), c)
28.55/9.67	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.67	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.67	   A^2 -> H(U1(e, a), e)
28.55/9.67	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, a), b)
28.55/9.67	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.67	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.67	   A^2 -> H(U1(k, a), c)
28.55/9.67	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.67	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.67	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, d), b)
28.55/9.67	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.67	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.67	   A^2 -> H(U1(c, d), c)
28.55/9.67	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.67	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.67	   A^2 -> H(U1(c, d), e)
28.55/9.67	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, a), d)
28.55/9.67	   A^2 -> H(U1(c, a), k)
28.55/9.67	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.67	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.67	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.67	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.67	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.67	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.67	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.67	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.67	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.67	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.67	   A^2 -> H(U1(d, c), b)
28.55/9.67	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.67	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.67	   A^2 -> H(U1(d, c), c)
28.55/9.67	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.67	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.67	   A^2 -> H(U1(d, c), e)
28.55/9.67	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(d, a), d)
28.55/9.67	   A^2 -> H(U1(d, a), k)
28.55/9.67	   A^2 -> H(U1(a, e), b)
28.55/9.67	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.67	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.67	   A^2 -> H(U1(a, e), c)
28.55/9.67	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.67	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.67	   A^2 -> H(U1(a, e), e)
28.55/9.67	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.67	
28.55/9.67	The TRS R consists of the following rules:
28.55/9.67	
28.55/9.67	   f(x) -> U1(x, x)
28.55/9.67	   U1(e, x) -> x
28.55/9.67	   a -> c
28.55/9.67	   a -> d
28.55/9.67	   b -> c
28.55/9.67	   b -> d
28.55/9.67	   d -> k
28.55/9.67	   c -> e
28.55/9.67	   c -> k
28.55/9.67	
28.55/9.67	Q is empty.
28.55/9.67	We have to consider all minimal (P,Q,R)-chains.
28.55/9.67	----------------------------------------
28.55/9.67	
28.55/9.67	(1319) TransformationProof (EQUIVALENT)
28.55/9.67	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.67	
28.55/9.67	   (A^2 -> H(U1(c, e), U1(d, k)),A^2 -> H(U1(c, e), U1(d, k)))
28.55/9.67	   (A^2 -> H(U1(d, e), U1(d, k)),A^2 -> H(U1(d, e), U1(d, k)))
28.55/9.67	   (A^2 -> H(U1(a, e), U1(k, k)),A^2 -> H(U1(a, e), U1(k, k)))
28.55/9.67	
28.55/9.67	
28.55/9.67	----------------------------------------
28.55/9.67	
28.55/9.67	(1320)
28.55/9.67	Obligation:
28.55/9.67	Q DP problem:
28.55/9.67	The TRS P consists of the following rules:
28.55/9.67	
28.55/9.67	   H(x, x) -> G(x, x, f(k))
28.55/9.67	   G(d, x, x) -> A^2
28.55/9.67	   A^2 -> H(f(c), f(c))
28.55/9.67	   A^2 -> H(f(d), f(d))
28.55/9.67	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.67	   A^2 -> H(f(e), f(e))
28.55/9.67	   A^2 -> H(f(k), f(k))
28.55/9.67	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.67	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.67	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.67	   A^2 -> H(U1(a, c), b)
28.55/9.67	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.67	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.67	   A^2 -> H(U1(a, c), c)
28.55/9.67	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.67	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.67	   A^2 -> H(U1(a, c), e)
28.55/9.67	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, d), b)
28.55/9.67	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.67	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.67	   A^2 -> H(U1(a, d), c)
28.55/9.67	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.67	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.67	   A^2 -> H(U1(a, d), e)
28.55/9.67	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, a), d)
28.55/9.67	   A^2 -> H(U1(a, a), k)
28.55/9.67	   A^2 -> H(k, U1(b, b))
28.55/9.67	   A^2 -> H(k, f(c))
28.55/9.67	   A^2 -> H(k, f(d))
28.55/9.67	   A^2 -> H(c, U1(c, b))
28.55/9.67	   A^2 -> H(c, U1(d, b))
28.55/9.67	   A^2 -> H(c, U1(b, c))
28.55/9.67	   A^2 -> H(c, U1(b, d))
28.55/9.67	   A^2 -> H(c, U1(c, c))
28.55/9.67	   A^2 -> H(c, f(e))
28.55/9.67	   A^2 -> H(c, f(k))
28.55/9.67	   A^2 -> H(c, U1(d, d))
28.55/9.67	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.67	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.67	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.67	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.67	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.67	   A^2 -> H(U1(e, k), f(e))
28.55/9.67	   A^2 -> H(U1(e, k), f(k))
28.55/9.67	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.67	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.67	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.67	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.67	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.67	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.67	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.67	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.67	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.67	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.67	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.67	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.67	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.67	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.67	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.67	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.67	   A^2 -> H(U1(k, e), f(e))
28.55/9.67	   A^2 -> H(U1(k, e), f(k))
28.55/9.67	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.67	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.67	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.67	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.67	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.67	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.67	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.67	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.67	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.67	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.67	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.67	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.67	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.67	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.67	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.67	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.67	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.67	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.67	   A^2 -> H(U1(c, c), b)
28.55/9.67	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.67	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.67	   A^2 -> H(U1(c, c), e)
28.55/9.67	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.67	   A^2 -> H(e, U1(c, b))
28.55/9.67	   A^2 -> H(e, U1(d, b))
28.55/9.67	   A^2 -> H(e, U1(b, c))
28.55/9.67	   A^2 -> H(e, U1(b, d))
28.55/9.67	   A^2 -> H(e, U1(c, c))
28.55/9.67	   A^2 -> H(e, f(e))
28.55/9.67	   A^2 -> H(e, f(k))
28.55/9.67	   A^2 -> H(e, U1(d, d))
28.55/9.67	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.67	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.67	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.67	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.67	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.67	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.67	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.67	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.67	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.67	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.67	   A^2 -> H(f(e), b)
28.55/9.67	   A^2 -> H(f(e), U1(e, d))
28.55/9.67	   A^2 -> H(f(e), U1(d, e))
28.55/9.67	   A^2 -> H(f(e), c)
28.55/9.67	   A^2 -> H(f(e), U1(e, k))
28.55/9.67	   A^2 -> H(f(e), U1(k, e))
28.55/9.67	   A^2 -> H(f(e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.67	   A^2 -> H(f(k), b)
28.55/9.67	   A^2 -> H(f(k), U1(e, d))
28.55/9.67	   A^2 -> H(f(k), U1(d, e))
28.55/9.67	   A^2 -> H(f(k), c)
28.55/9.67	   A^2 -> H(f(k), U1(e, k))
28.55/9.67	   A^2 -> H(f(k), U1(k, e))
28.55/9.67	   A^2 -> H(f(k), e)
28.55/9.67	   A^2 -> H(f(c), d)
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.67	   A^2 -> H(U1(k, k), f(e))
28.55/9.67	   A^2 -> H(U1(k, k), f(k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.67	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.67	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.67	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.67	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.67	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.67	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.67	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.67	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.67	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.67	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.67	   A^2 -> H(U1(d, d), b)
28.55/9.67	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.67	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.67	   A^2 -> H(U1(d, d), c)
28.55/9.67	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.67	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.67	   A^2 -> H(U1(d, d), e)
28.55/9.67	   A^2 -> H(f(d), d)
28.55/9.67	   A^2 -> H(f(d), k)
28.55/9.67	   A^2 -> H(U1(c, c), c)
28.55/9.67	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.67	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.67	   A^2 -> H(f(c), k)
28.55/9.67	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.67	   A^2 -> H(f(k), U1(k, k))
28.55/9.67	   A^2 -> H(f(e), e)
28.55/9.67	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.67	   A^2 -> H(d, U1(c, b))
28.55/9.67	   A^2 -> H(d, U1(d, b))
28.55/9.67	   A^2 -> H(d, U1(b, c))
28.55/9.67	   A^2 -> H(d, U1(b, d))
28.55/9.67	   A^2 -> H(d, U1(c, c))
28.55/9.67	   A^2 -> H(d, f(e))
28.55/9.67	   A^2 -> H(d, f(k))
28.55/9.67	   A^2 -> H(d, U1(d, d))
28.55/9.67	   A^2 -> H(a, U1(e, b))
28.55/9.67	   A^2 -> H(a, U1(k, b))
28.55/9.67	   A^2 -> H(a, U1(c, d))
28.55/9.67	   A^2 -> H(a, U1(d, c))
28.55/9.67	   A^2 -> H(a, U1(b, e))
28.55/9.67	   A^2 -> H(a, U1(b, k))
28.55/9.67	   A^2 -> H(a, U1(e, c))
28.55/9.67	   A^2 -> H(a, U1(k, c))
28.55/9.67	   A^2 -> H(a, U1(c, e))
28.55/9.67	   A^2 -> H(a, U1(c, k))
28.55/9.67	   A^2 -> H(a, U1(e, e))
28.55/9.67	   A^2 -> H(a, U1(k, k))
28.55/9.67	   A^2 -> H(a, U1(k, d))
28.55/9.67	   A^2 -> H(a, U1(d, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.67	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.67	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.67	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.67	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.67	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.67	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.67	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.67	   A^2 -> H(U1(e, a), b)
28.55/9.67	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.67	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.67	   A^2 -> H(U1(e, a), c)
28.55/9.67	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.67	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.67	   A^2 -> H(U1(e, a), e)
28.55/9.67	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, a), b)
28.55/9.67	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.67	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.67	   A^2 -> H(U1(k, a), c)
28.55/9.67	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.67	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.67	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, d), b)
28.55/9.67	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.67	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.67	   A^2 -> H(U1(c, d), c)
28.55/9.67	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.67	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.67	   A^2 -> H(U1(c, d), e)
28.55/9.67	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, a), d)
28.55/9.67	   A^2 -> H(U1(c, a), k)
28.55/9.67	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.67	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.67	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.67	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.67	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.67	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.67	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.67	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.67	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.67	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.67	   A^2 -> H(U1(d, c), b)
28.55/9.67	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.67	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.67	   A^2 -> H(U1(d, c), c)
28.55/9.67	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.67	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.67	   A^2 -> H(U1(d, c), e)
28.55/9.67	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(d, a), d)
28.55/9.67	   A^2 -> H(U1(d, a), k)
28.55/9.67	   A^2 -> H(U1(a, e), b)
28.55/9.67	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.67	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.67	   A^2 -> H(U1(a, e), c)
28.55/9.67	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.67	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.67	   A^2 -> H(U1(a, e), e)
28.55/9.67	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.67	
28.55/9.67	The TRS R consists of the following rules:
28.55/9.67	
28.55/9.67	   f(x) -> U1(x, x)
28.55/9.67	   U1(e, x) -> x
28.55/9.67	   a -> c
28.55/9.67	   a -> d
28.55/9.67	   b -> c
28.55/9.67	   b -> d
28.55/9.67	   d -> k
28.55/9.67	   c -> e
28.55/9.67	   c -> k
28.55/9.67	
28.55/9.67	Q is empty.
28.55/9.67	We have to consider all minimal (P,Q,R)-chains.
28.55/9.67	----------------------------------------
28.55/9.67	
28.55/9.67	(1321) TransformationProof (EQUIVALENT)
28.55/9.67	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.67	
28.55/9.67	   (A^2 -> H(U1(c, k), U1(e, b)),A^2 -> H(U1(c, k), U1(e, b)))
28.55/9.67	   (A^2 -> H(U1(d, k), U1(e, b)),A^2 -> H(U1(d, k), U1(e, b)))
28.55/9.67	   (A^2 -> H(U1(a, k), b),A^2 -> H(U1(a, k), b))
28.55/9.67	   (A^2 -> H(U1(a, k), U1(e, c)),A^2 -> H(U1(a, k), U1(e, c)))
28.55/9.67	   (A^2 -> H(U1(a, k), U1(e, d)),A^2 -> H(U1(a, k), U1(e, d)))
28.55/9.67	
28.55/9.67	
28.55/9.67	----------------------------------------
28.55/9.67	
28.55/9.67	(1322)
28.55/9.67	Obligation:
28.55/9.67	Q DP problem:
28.55/9.67	The TRS P consists of the following rules:
28.55/9.67	
28.55/9.67	   H(x, x) -> G(x, x, f(k))
28.55/9.67	   G(d, x, x) -> A^2
28.55/9.67	   A^2 -> H(f(c), f(c))
28.55/9.67	   A^2 -> H(f(d), f(d))
28.55/9.67	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.67	   A^2 -> H(f(e), f(e))
28.55/9.67	   A^2 -> H(f(k), f(k))
28.55/9.67	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.67	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.67	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.67	   A^2 -> H(U1(a, c), b)
28.55/9.67	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.67	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.67	   A^2 -> H(U1(a, c), c)
28.55/9.67	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.67	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.67	   A^2 -> H(U1(a, c), e)
28.55/9.67	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, d), b)
28.55/9.67	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.67	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.67	   A^2 -> H(U1(a, d), c)
28.55/9.67	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.67	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.67	   A^2 -> H(U1(a, d), e)
28.55/9.67	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, a), d)
28.55/9.67	   A^2 -> H(U1(a, a), k)
28.55/9.67	   A^2 -> H(k, U1(b, b))
28.55/9.67	   A^2 -> H(k, f(c))
28.55/9.67	   A^2 -> H(k, f(d))
28.55/9.67	   A^2 -> H(c, U1(c, b))
28.55/9.67	   A^2 -> H(c, U1(d, b))
28.55/9.67	   A^2 -> H(c, U1(b, c))
28.55/9.67	   A^2 -> H(c, U1(b, d))
28.55/9.67	   A^2 -> H(c, U1(c, c))
28.55/9.67	   A^2 -> H(c, f(e))
28.55/9.67	   A^2 -> H(c, f(k))
28.55/9.67	   A^2 -> H(c, U1(d, d))
28.55/9.67	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.67	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.67	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.67	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.67	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.67	   A^2 -> H(U1(e, k), f(e))
28.55/9.67	   A^2 -> H(U1(e, k), f(k))
28.55/9.67	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.67	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.67	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.67	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.67	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.67	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.67	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.67	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.67	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.67	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.67	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.67	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.67	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.67	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.67	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.67	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.67	   A^2 -> H(U1(k, e), f(e))
28.55/9.67	   A^2 -> H(U1(k, e), f(k))
28.55/9.67	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.67	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.67	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.67	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.67	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.67	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.67	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.67	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.67	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.67	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.67	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.67	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.67	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.67	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.67	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.67	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.67	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.67	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.67	   A^2 -> H(U1(c, c), b)
28.55/9.67	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.67	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.67	   A^2 -> H(U1(c, c), e)
28.55/9.67	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.67	   A^2 -> H(e, U1(c, b))
28.55/9.67	   A^2 -> H(e, U1(d, b))
28.55/9.67	   A^2 -> H(e, U1(b, c))
28.55/9.67	   A^2 -> H(e, U1(b, d))
28.55/9.67	   A^2 -> H(e, U1(c, c))
28.55/9.67	   A^2 -> H(e, f(e))
28.55/9.67	   A^2 -> H(e, f(k))
28.55/9.67	   A^2 -> H(e, U1(d, d))
28.55/9.67	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.67	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.67	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.67	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.67	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.67	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.67	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.67	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.67	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.67	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.67	   A^2 -> H(f(e), b)
28.55/9.67	   A^2 -> H(f(e), U1(e, d))
28.55/9.67	   A^2 -> H(f(e), U1(d, e))
28.55/9.67	   A^2 -> H(f(e), c)
28.55/9.67	   A^2 -> H(f(e), U1(e, k))
28.55/9.67	   A^2 -> H(f(e), U1(k, e))
28.55/9.67	   A^2 -> H(f(e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.67	   A^2 -> H(f(k), b)
28.55/9.67	   A^2 -> H(f(k), U1(e, d))
28.55/9.67	   A^2 -> H(f(k), U1(d, e))
28.55/9.67	   A^2 -> H(f(k), c)
28.55/9.67	   A^2 -> H(f(k), U1(e, k))
28.55/9.67	   A^2 -> H(f(k), U1(k, e))
28.55/9.67	   A^2 -> H(f(k), e)
28.55/9.67	   A^2 -> H(f(c), d)
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.67	   A^2 -> H(U1(k, k), f(e))
28.55/9.67	   A^2 -> H(U1(k, k), f(k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.67	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.67	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.67	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.67	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.67	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.67	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.67	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.67	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.67	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.67	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.67	   A^2 -> H(U1(d, d), b)
28.55/9.67	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.67	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.67	   A^2 -> H(U1(d, d), c)
28.55/9.67	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.67	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.67	   A^2 -> H(U1(d, d), e)
28.55/9.67	   A^2 -> H(f(d), d)
28.55/9.67	   A^2 -> H(f(d), k)
28.55/9.67	   A^2 -> H(U1(c, c), c)
28.55/9.67	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.67	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.67	   A^2 -> H(f(c), k)
28.55/9.67	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.67	   A^2 -> H(f(k), U1(k, k))
28.55/9.67	   A^2 -> H(f(e), e)
28.55/9.67	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.67	   A^2 -> H(d, U1(c, b))
28.55/9.67	   A^2 -> H(d, U1(d, b))
28.55/9.67	   A^2 -> H(d, U1(b, c))
28.55/9.67	   A^2 -> H(d, U1(b, d))
28.55/9.67	   A^2 -> H(d, U1(c, c))
28.55/9.67	   A^2 -> H(d, f(e))
28.55/9.67	   A^2 -> H(d, f(k))
28.55/9.67	   A^2 -> H(d, U1(d, d))
28.55/9.67	   A^2 -> H(a, U1(e, b))
28.55/9.67	   A^2 -> H(a, U1(k, b))
28.55/9.67	   A^2 -> H(a, U1(c, d))
28.55/9.67	   A^2 -> H(a, U1(d, c))
28.55/9.67	   A^2 -> H(a, U1(b, e))
28.55/9.67	   A^2 -> H(a, U1(b, k))
28.55/9.67	   A^2 -> H(a, U1(e, c))
28.55/9.67	   A^2 -> H(a, U1(k, c))
28.55/9.67	   A^2 -> H(a, U1(c, e))
28.55/9.67	   A^2 -> H(a, U1(c, k))
28.55/9.67	   A^2 -> H(a, U1(e, e))
28.55/9.67	   A^2 -> H(a, U1(k, k))
28.55/9.67	   A^2 -> H(a, U1(k, d))
28.55/9.67	   A^2 -> H(a, U1(d, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.67	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.67	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.67	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.67	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.67	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.67	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.67	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.67	   A^2 -> H(U1(e, a), b)
28.55/9.67	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.67	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.67	   A^2 -> H(U1(e, a), c)
28.55/9.67	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.67	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.67	   A^2 -> H(U1(e, a), e)
28.55/9.67	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, a), b)
28.55/9.67	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.67	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.67	   A^2 -> H(U1(k, a), c)
28.55/9.67	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.67	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.67	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, d), b)
28.55/9.67	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.67	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.67	   A^2 -> H(U1(c, d), c)
28.55/9.67	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.67	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.67	   A^2 -> H(U1(c, d), e)
28.55/9.67	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, a), d)
28.55/9.67	   A^2 -> H(U1(c, a), k)
28.55/9.67	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.67	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.67	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.67	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.67	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.67	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.67	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.67	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.67	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.67	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.67	   A^2 -> H(U1(d, c), b)
28.55/9.67	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.67	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.67	   A^2 -> H(U1(d, c), c)
28.55/9.67	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.67	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.67	   A^2 -> H(U1(d, c), e)
28.55/9.67	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(d, a), d)
28.55/9.67	   A^2 -> H(U1(d, a), k)
28.55/9.67	   A^2 -> H(U1(a, e), b)
28.55/9.67	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.67	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.67	   A^2 -> H(U1(a, e), c)
28.55/9.67	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.67	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.67	   A^2 -> H(U1(a, e), e)
28.55/9.67	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, k), b)
28.55/9.67	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.67	
28.55/9.67	The TRS R consists of the following rules:
28.55/9.67	
28.55/9.67	   f(x) -> U1(x, x)
28.55/9.67	   U1(e, x) -> x
28.55/9.67	   a -> c
28.55/9.67	   a -> d
28.55/9.67	   b -> c
28.55/9.67	   b -> d
28.55/9.67	   d -> k
28.55/9.67	   c -> e
28.55/9.67	   c -> k
28.55/9.67	
28.55/9.67	Q is empty.
28.55/9.67	We have to consider all minimal (P,Q,R)-chains.
28.55/9.67	----------------------------------------
28.55/9.67	
28.55/9.67	(1323) TransformationProof (EQUIVALENT)
28.55/9.67	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.67	
28.55/9.67	   (A^2 -> H(U1(c, k), U1(k, b)),A^2 -> H(U1(c, k), U1(k, b)))
28.55/9.67	   (A^2 -> H(U1(d, k), U1(k, b)),A^2 -> H(U1(d, k), U1(k, b)))
28.55/9.67	   (A^2 -> H(U1(a, k), U1(k, c)),A^2 -> H(U1(a, k), U1(k, c)))
28.55/9.67	   (A^2 -> H(U1(a, k), U1(k, d)),A^2 -> H(U1(a, k), U1(k, d)))
28.55/9.67	
28.55/9.67	
28.55/9.67	----------------------------------------
28.55/9.67	
28.55/9.67	(1324)
28.55/9.67	Obligation:
28.55/9.67	Q DP problem:
28.55/9.67	The TRS P consists of the following rules:
28.55/9.67	
28.55/9.67	   H(x, x) -> G(x, x, f(k))
28.55/9.67	   G(d, x, x) -> A^2
28.55/9.67	   A^2 -> H(f(c), f(c))
28.55/9.67	   A^2 -> H(f(d), f(d))
28.55/9.67	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.67	   A^2 -> H(f(e), f(e))
28.55/9.67	   A^2 -> H(f(k), f(k))
28.55/9.67	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.67	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.67	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.67	   A^2 -> H(U1(a, c), b)
28.55/9.67	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.67	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.67	   A^2 -> H(U1(a, c), c)
28.55/9.67	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.67	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.67	   A^2 -> H(U1(a, c), e)
28.55/9.67	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, d), b)
28.55/9.67	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.67	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.67	   A^2 -> H(U1(a, d), c)
28.55/9.67	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.67	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.67	   A^2 -> H(U1(a, d), e)
28.55/9.67	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, a), d)
28.55/9.67	   A^2 -> H(U1(a, a), k)
28.55/9.67	   A^2 -> H(k, U1(b, b))
28.55/9.67	   A^2 -> H(k, f(c))
28.55/9.67	   A^2 -> H(k, f(d))
28.55/9.67	   A^2 -> H(c, U1(c, b))
28.55/9.67	   A^2 -> H(c, U1(d, b))
28.55/9.67	   A^2 -> H(c, U1(b, c))
28.55/9.67	   A^2 -> H(c, U1(b, d))
28.55/9.67	   A^2 -> H(c, U1(c, c))
28.55/9.67	   A^2 -> H(c, f(e))
28.55/9.67	   A^2 -> H(c, f(k))
28.55/9.67	   A^2 -> H(c, U1(d, d))
28.55/9.67	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.67	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.67	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.67	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.67	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.67	   A^2 -> H(U1(e, k), f(e))
28.55/9.67	   A^2 -> H(U1(e, k), f(k))
28.55/9.67	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.67	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.67	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.67	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.67	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.67	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.67	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.67	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.67	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.67	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.67	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.67	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.67	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.67	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.67	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.67	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.67	   A^2 -> H(U1(k, e), f(e))
28.55/9.67	   A^2 -> H(U1(k, e), f(k))
28.55/9.67	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.67	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.67	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.67	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.67	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.67	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.67	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.67	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.67	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.67	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.67	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.67	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.67	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.67	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.67	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.67	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.67	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.67	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.67	   A^2 -> H(U1(c, c), b)
28.55/9.67	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.67	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.67	   A^2 -> H(U1(c, c), e)
28.55/9.67	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.67	   A^2 -> H(e, U1(c, b))
28.55/9.67	   A^2 -> H(e, U1(d, b))
28.55/9.67	   A^2 -> H(e, U1(b, c))
28.55/9.67	   A^2 -> H(e, U1(b, d))
28.55/9.67	   A^2 -> H(e, U1(c, c))
28.55/9.67	   A^2 -> H(e, f(e))
28.55/9.67	   A^2 -> H(e, f(k))
28.55/9.67	   A^2 -> H(e, U1(d, d))
28.55/9.67	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.67	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.67	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.67	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.67	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.67	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.67	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.67	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.67	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.67	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.67	   A^2 -> H(f(e), b)
28.55/9.67	   A^2 -> H(f(e), U1(e, d))
28.55/9.67	   A^2 -> H(f(e), U1(d, e))
28.55/9.67	   A^2 -> H(f(e), c)
28.55/9.67	   A^2 -> H(f(e), U1(e, k))
28.55/9.67	   A^2 -> H(f(e), U1(k, e))
28.55/9.67	   A^2 -> H(f(e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.67	   A^2 -> H(f(k), b)
28.55/9.67	   A^2 -> H(f(k), U1(e, d))
28.55/9.67	   A^2 -> H(f(k), U1(d, e))
28.55/9.67	   A^2 -> H(f(k), c)
28.55/9.67	   A^2 -> H(f(k), U1(e, k))
28.55/9.67	   A^2 -> H(f(k), U1(k, e))
28.55/9.67	   A^2 -> H(f(k), e)
28.55/9.67	   A^2 -> H(f(c), d)
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.67	   A^2 -> H(U1(k, k), f(e))
28.55/9.67	   A^2 -> H(U1(k, k), f(k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.67	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.67	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.67	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.67	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.67	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.67	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.67	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.67	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.67	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.67	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.67	   A^2 -> H(U1(d, d), b)
28.55/9.67	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.67	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.67	   A^2 -> H(U1(d, d), c)
28.55/9.67	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.67	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.67	   A^2 -> H(U1(d, d), e)
28.55/9.67	   A^2 -> H(f(d), d)
28.55/9.67	   A^2 -> H(f(d), k)
28.55/9.67	   A^2 -> H(U1(c, c), c)
28.55/9.67	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.67	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.67	   A^2 -> H(f(c), k)
28.55/9.67	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.67	   A^2 -> H(f(k), U1(k, k))
28.55/9.67	   A^2 -> H(f(e), e)
28.55/9.67	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.67	   A^2 -> H(d, U1(c, b))
28.55/9.67	   A^2 -> H(d, U1(d, b))
28.55/9.67	   A^2 -> H(d, U1(b, c))
28.55/9.67	   A^2 -> H(d, U1(b, d))
28.55/9.67	   A^2 -> H(d, U1(c, c))
28.55/9.67	   A^2 -> H(d, f(e))
28.55/9.67	   A^2 -> H(d, f(k))
28.55/9.67	   A^2 -> H(d, U1(d, d))
28.55/9.67	   A^2 -> H(a, U1(e, b))
28.55/9.67	   A^2 -> H(a, U1(k, b))
28.55/9.67	   A^2 -> H(a, U1(c, d))
28.55/9.67	   A^2 -> H(a, U1(d, c))
28.55/9.67	   A^2 -> H(a, U1(b, e))
28.55/9.67	   A^2 -> H(a, U1(b, k))
28.55/9.67	   A^2 -> H(a, U1(e, c))
28.55/9.67	   A^2 -> H(a, U1(k, c))
28.55/9.67	   A^2 -> H(a, U1(c, e))
28.55/9.67	   A^2 -> H(a, U1(c, k))
28.55/9.67	   A^2 -> H(a, U1(e, e))
28.55/9.67	   A^2 -> H(a, U1(k, k))
28.55/9.67	   A^2 -> H(a, U1(k, d))
28.55/9.67	   A^2 -> H(a, U1(d, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.67	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.67	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.67	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.67	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.67	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.67	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.67	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.67	   A^2 -> H(U1(e, a), b)
28.55/9.67	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.67	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.67	   A^2 -> H(U1(e, a), c)
28.55/9.67	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.67	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.67	   A^2 -> H(U1(e, a), e)
28.55/9.67	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, a), b)
28.55/9.67	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.67	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.67	   A^2 -> H(U1(k, a), c)
28.55/9.67	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.67	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.67	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, d), b)
28.55/9.67	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.67	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.67	   A^2 -> H(U1(c, d), c)
28.55/9.67	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.67	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.67	   A^2 -> H(U1(c, d), e)
28.55/9.67	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, a), d)
28.55/9.67	   A^2 -> H(U1(c, a), k)
28.55/9.67	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.67	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.67	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.67	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.67	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.67	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.67	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.67	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.67	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.67	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.67	   A^2 -> H(U1(d, c), b)
28.55/9.67	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.67	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.67	   A^2 -> H(U1(d, c), c)
28.55/9.67	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.67	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.67	   A^2 -> H(U1(d, c), e)
28.55/9.67	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(d, a), d)
28.55/9.67	   A^2 -> H(U1(d, a), k)
28.55/9.67	   A^2 -> H(U1(a, e), b)
28.55/9.67	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.67	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.67	   A^2 -> H(U1(a, e), c)
28.55/9.67	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.67	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.67	   A^2 -> H(U1(a, e), e)
28.55/9.67	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, k), b)
28.55/9.67	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.67	
28.55/9.67	The TRS R consists of the following rules:
28.55/9.67	
28.55/9.67	   f(x) -> U1(x, x)
28.55/9.67	   U1(e, x) -> x
28.55/9.67	   a -> c
28.55/9.67	   a -> d
28.55/9.67	   b -> c
28.55/9.67	   b -> d
28.55/9.67	   d -> k
28.55/9.67	   c -> e
28.55/9.67	   c -> k
28.55/9.67	
28.55/9.67	Q is empty.
28.55/9.67	We have to consider all minimal (P,Q,R)-chains.
28.55/9.67	----------------------------------------
28.55/9.67	
28.55/9.67	(1325) TransformationProof (EQUIVALENT)
28.55/9.67	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.67	
28.55/9.67	   (A^2 -> H(U1(c, k), U1(c, d)),A^2 -> H(U1(c, k), U1(c, d)))
28.55/9.67	   (A^2 -> H(U1(d, k), U1(c, d)),A^2 -> H(U1(d, k), U1(c, d)))
28.55/9.67	   (A^2 -> H(U1(a, k), U1(e, d)),A^2 -> H(U1(a, k), U1(e, d)))
28.55/9.67	   (A^2 -> H(U1(a, k), U1(k, d)),A^2 -> H(U1(a, k), U1(k, d)))
28.55/9.67	   (A^2 -> H(U1(a, k), U1(c, k)),A^2 -> H(U1(a, k), U1(c, k)))
28.55/9.67	
28.55/9.67	
28.55/9.67	----------------------------------------
28.55/9.67	
28.55/9.67	(1326)
28.55/9.67	Obligation:
28.55/9.67	Q DP problem:
28.55/9.67	The TRS P consists of the following rules:
28.55/9.67	
28.55/9.67	   H(x, x) -> G(x, x, f(k))
28.55/9.67	   G(d, x, x) -> A^2
28.55/9.67	   A^2 -> H(f(c), f(c))
28.55/9.67	   A^2 -> H(f(d), f(d))
28.55/9.67	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.67	   A^2 -> H(f(e), f(e))
28.55/9.67	   A^2 -> H(f(k), f(k))
28.55/9.67	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.67	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.67	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.67	   A^2 -> H(U1(a, c), b)
28.55/9.67	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.67	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.67	   A^2 -> H(U1(a, c), c)
28.55/9.67	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.67	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.67	   A^2 -> H(U1(a, c), e)
28.55/9.67	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, d), b)
28.55/9.67	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.67	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.67	   A^2 -> H(U1(a, d), c)
28.55/9.67	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.67	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.67	   A^2 -> H(U1(a, d), e)
28.55/9.67	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, a), d)
28.55/9.67	   A^2 -> H(U1(a, a), k)
28.55/9.67	   A^2 -> H(k, U1(b, b))
28.55/9.67	   A^2 -> H(k, f(c))
28.55/9.67	   A^2 -> H(k, f(d))
28.55/9.67	   A^2 -> H(c, U1(c, b))
28.55/9.67	   A^2 -> H(c, U1(d, b))
28.55/9.67	   A^2 -> H(c, U1(b, c))
28.55/9.67	   A^2 -> H(c, U1(b, d))
28.55/9.67	   A^2 -> H(c, U1(c, c))
28.55/9.67	   A^2 -> H(c, f(e))
28.55/9.67	   A^2 -> H(c, f(k))
28.55/9.67	   A^2 -> H(c, U1(d, d))
28.55/9.67	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.67	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.67	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.67	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.67	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.67	   A^2 -> H(U1(e, k), f(e))
28.55/9.67	   A^2 -> H(U1(e, k), f(k))
28.55/9.67	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.67	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.67	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.67	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.67	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.67	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.67	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.67	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.67	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.67	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.67	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.67	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.67	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.67	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.67	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.67	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.67	   A^2 -> H(U1(k, e), f(e))
28.55/9.67	   A^2 -> H(U1(k, e), f(k))
28.55/9.67	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.67	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.67	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.67	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.67	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.67	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.67	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.67	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.67	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.67	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.67	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.67	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.67	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.67	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.67	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.67	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.67	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.67	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.67	   A^2 -> H(U1(c, c), b)
28.55/9.67	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.67	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.67	   A^2 -> H(U1(c, c), e)
28.55/9.67	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.67	   A^2 -> H(e, U1(c, b))
28.55/9.67	   A^2 -> H(e, U1(d, b))
28.55/9.67	   A^2 -> H(e, U1(b, c))
28.55/9.67	   A^2 -> H(e, U1(b, d))
28.55/9.67	   A^2 -> H(e, U1(c, c))
28.55/9.67	   A^2 -> H(e, f(e))
28.55/9.67	   A^2 -> H(e, f(k))
28.55/9.67	   A^2 -> H(e, U1(d, d))
28.55/9.67	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.67	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.67	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.67	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.67	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.67	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.67	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.67	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.67	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.67	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.67	   A^2 -> H(f(e), b)
28.55/9.67	   A^2 -> H(f(e), U1(e, d))
28.55/9.67	   A^2 -> H(f(e), U1(d, e))
28.55/9.67	   A^2 -> H(f(e), c)
28.55/9.67	   A^2 -> H(f(e), U1(e, k))
28.55/9.67	   A^2 -> H(f(e), U1(k, e))
28.55/9.67	   A^2 -> H(f(e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.67	   A^2 -> H(f(k), b)
28.55/9.67	   A^2 -> H(f(k), U1(e, d))
28.55/9.67	   A^2 -> H(f(k), U1(d, e))
28.55/9.67	   A^2 -> H(f(k), c)
28.55/9.67	   A^2 -> H(f(k), U1(e, k))
28.55/9.67	   A^2 -> H(f(k), U1(k, e))
28.55/9.67	   A^2 -> H(f(k), e)
28.55/9.67	   A^2 -> H(f(c), d)
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.67	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.67	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.67	   A^2 -> H(U1(k, k), f(e))
28.55/9.67	   A^2 -> H(U1(k, k), f(k))
28.55/9.67	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.67	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.67	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.67	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.67	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.67	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.67	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.67	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.67	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.67	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.67	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.67	   A^2 -> H(U1(d, d), b)
28.55/9.67	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.67	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.67	   A^2 -> H(U1(d, d), c)
28.55/9.67	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.67	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.67	   A^2 -> H(U1(d, d), e)
28.55/9.67	   A^2 -> H(f(d), d)
28.55/9.67	   A^2 -> H(f(d), k)
28.55/9.67	   A^2 -> H(U1(c, c), c)
28.55/9.67	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.67	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.67	   A^2 -> H(f(c), k)
28.55/9.67	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.67	   A^2 -> H(f(k), U1(k, k))
28.55/9.67	   A^2 -> H(f(e), e)
28.55/9.67	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.67	   A^2 -> H(d, U1(c, b))
28.55/9.67	   A^2 -> H(d, U1(d, b))
28.55/9.67	   A^2 -> H(d, U1(b, c))
28.55/9.67	   A^2 -> H(d, U1(b, d))
28.55/9.67	   A^2 -> H(d, U1(c, c))
28.55/9.67	   A^2 -> H(d, f(e))
28.55/9.67	   A^2 -> H(d, f(k))
28.55/9.67	   A^2 -> H(d, U1(d, d))
28.55/9.67	   A^2 -> H(a, U1(e, b))
28.55/9.67	   A^2 -> H(a, U1(k, b))
28.55/9.67	   A^2 -> H(a, U1(c, d))
28.55/9.67	   A^2 -> H(a, U1(d, c))
28.55/9.67	   A^2 -> H(a, U1(b, e))
28.55/9.67	   A^2 -> H(a, U1(b, k))
28.55/9.67	   A^2 -> H(a, U1(e, c))
28.55/9.67	   A^2 -> H(a, U1(k, c))
28.55/9.67	   A^2 -> H(a, U1(c, e))
28.55/9.67	   A^2 -> H(a, U1(c, k))
28.55/9.67	   A^2 -> H(a, U1(e, e))
28.55/9.67	   A^2 -> H(a, U1(k, k))
28.55/9.67	   A^2 -> H(a, U1(k, d))
28.55/9.67	   A^2 -> H(a, U1(d, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.67	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.67	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.67	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.67	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.67	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.67	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.67	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.67	   A^2 -> H(U1(e, a), b)
28.55/9.67	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.67	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.67	   A^2 -> H(U1(e, a), c)
28.55/9.67	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.67	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.67	   A^2 -> H(U1(e, a), e)
28.55/9.67	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, a), b)
28.55/9.67	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.67	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.67	   A^2 -> H(U1(k, a), c)
28.55/9.67	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.67	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.67	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, d), b)
28.55/9.67	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.67	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.67	   A^2 -> H(U1(c, d), c)
28.55/9.67	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.67	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.67	   A^2 -> H(U1(c, d), e)
28.55/9.67	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, a), d)
28.55/9.67	   A^2 -> H(U1(c, a), k)
28.55/9.67	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.67	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.67	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.67	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.67	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.67	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.67	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.67	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.67	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.67	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.67	   A^2 -> H(U1(d, c), b)
28.55/9.67	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.67	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.67	   A^2 -> H(U1(d, c), c)
28.55/9.67	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.67	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.67	   A^2 -> H(U1(d, c), e)
28.55/9.67	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(d, a), d)
28.55/9.67	   A^2 -> H(U1(d, a), k)
28.55/9.67	   A^2 -> H(U1(a, e), b)
28.55/9.67	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.67	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.67	   A^2 -> H(U1(a, e), c)
28.55/9.67	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.67	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.67	   A^2 -> H(U1(a, e), e)
28.55/9.67	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, k), b)
28.55/9.67	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.67	
28.55/9.67	The TRS R consists of the following rules:
28.55/9.67	
28.55/9.67	   f(x) -> U1(x, x)
28.55/9.67	   U1(e, x) -> x
28.55/9.67	   a -> c
28.55/9.67	   a -> d
28.55/9.67	   b -> c
28.55/9.67	   b -> d
28.55/9.67	   d -> k
28.55/9.67	   c -> e
28.55/9.67	   c -> k
28.55/9.67	
28.55/9.67	Q is empty.
28.55/9.67	We have to consider all minimal (P,Q,R)-chains.
28.55/9.67	----------------------------------------
28.55/9.67	
28.55/9.67	(1327) TransformationProof (EQUIVALENT)
28.55/9.67	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.67	
28.55/9.67	   (A^2 -> H(U1(c, k), U1(d, c)),A^2 -> H(U1(c, k), U1(d, c)))
28.55/9.67	   (A^2 -> H(U1(d, k), U1(d, c)),A^2 -> H(U1(d, k), U1(d, c)))
28.55/9.67	   (A^2 -> H(U1(a, k), U1(k, c)),A^2 -> H(U1(a, k), U1(k, c)))
28.55/9.67	   (A^2 -> H(U1(a, k), U1(d, e)),A^2 -> H(U1(a, k), U1(d, e)))
28.55/9.67	   (A^2 -> H(U1(a, k), U1(d, k)),A^2 -> H(U1(a, k), U1(d, k)))
28.55/9.67	
28.55/9.67	
28.55/9.67	----------------------------------------
28.55/9.67	
28.55/9.67	(1328)
28.55/9.67	Obligation:
28.55/9.67	Q DP problem:
28.55/9.67	The TRS P consists of the following rules:
28.55/9.67	
28.55/9.67	   H(x, x) -> G(x, x, f(k))
28.55/9.67	   G(d, x, x) -> A^2
28.55/9.67	   A^2 -> H(f(c), f(c))
28.55/9.67	   A^2 -> H(f(d), f(d))
28.55/9.67	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.67	   A^2 -> H(f(e), f(e))
28.55/9.67	   A^2 -> H(f(k), f(k))
28.55/9.67	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.67	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.67	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(b, e))
28.55/9.67	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.67	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.67	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.67	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.67	   A^2 -> H(U1(a, c), b)
28.55/9.67	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.67	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.67	   A^2 -> H(U1(a, c), c)
28.55/9.67	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.67	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.67	   A^2 -> H(U1(a, c), e)
28.55/9.67	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, d), b)
28.55/9.67	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.67	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.67	   A^2 -> H(U1(a, d), c)
28.55/9.67	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.67	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.67	   A^2 -> H(U1(a, d), e)
28.55/9.67	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.67	   A^2 -> H(U1(a, a), d)
28.55/9.67	   A^2 -> H(U1(a, a), k)
28.55/9.67	   A^2 -> H(k, U1(b, b))
28.55/9.67	   A^2 -> H(k, f(c))
28.55/9.67	   A^2 -> H(k, f(d))
28.55/9.67	   A^2 -> H(c, U1(c, b))
28.55/9.67	   A^2 -> H(c, U1(d, b))
28.55/9.67	   A^2 -> H(c, U1(b, c))
28.55/9.67	   A^2 -> H(c, U1(b, d))
28.55/9.67	   A^2 -> H(c, U1(c, c))
28.55/9.67	   A^2 -> H(c, f(e))
28.55/9.67	   A^2 -> H(c, f(k))
28.55/9.67	   A^2 -> H(c, U1(d, d))
28.55/9.67	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.67	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.67	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.67	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.67	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.67	   A^2 -> H(U1(e, k), f(e))
28.55/9.67	   A^2 -> H(U1(e, k), f(k))
28.55/9.67	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.67	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.67	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.67	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.67	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.67	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.67	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.67	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.67	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.67	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.67	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.67	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.67	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.67	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.67	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.67	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.67	   A^2 -> H(U1(k, e), f(e))
28.55/9.67	   A^2 -> H(U1(k, e), f(k))
28.55/9.67	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.67	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.67	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.67	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.67	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.67	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.67	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.67	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.67	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.67	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.67	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.67	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.67	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.67	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.67	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.67	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.67	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.67	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.67	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.67	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.67	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.67	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.67	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.67	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.67	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.68	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.68	   A^2 -> H(U1(c, c), b)
28.55/9.68	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.68	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.68	   A^2 -> H(U1(c, c), e)
28.55/9.68	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.68	   A^2 -> H(e, U1(c, b))
28.55/9.68	   A^2 -> H(e, U1(d, b))
28.55/9.68	   A^2 -> H(e, U1(b, c))
28.55/9.68	   A^2 -> H(e, U1(b, d))
28.55/9.68	   A^2 -> H(e, U1(c, c))
28.55/9.68	   A^2 -> H(e, f(e))
28.55/9.68	   A^2 -> H(e, f(k))
28.55/9.68	   A^2 -> H(e, U1(d, d))
28.55/9.68	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.68	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.68	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.68	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.68	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.68	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.68	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.68	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.68	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.68	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.68	   A^2 -> H(f(e), b)
28.55/9.68	   A^2 -> H(f(e), U1(e, d))
28.55/9.68	   A^2 -> H(f(e), U1(d, e))
28.55/9.68	   A^2 -> H(f(e), c)
28.55/9.68	   A^2 -> H(f(e), U1(e, k))
28.55/9.68	   A^2 -> H(f(e), U1(k, e))
28.55/9.68	   A^2 -> H(f(e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.68	   A^2 -> H(f(k), b)
28.55/9.68	   A^2 -> H(f(k), U1(e, d))
28.55/9.68	   A^2 -> H(f(k), U1(d, e))
28.55/9.68	   A^2 -> H(f(k), c)
28.55/9.68	   A^2 -> H(f(k), U1(e, k))
28.55/9.68	   A^2 -> H(f(k), U1(k, e))
28.55/9.68	   A^2 -> H(f(k), e)
28.55/9.68	   A^2 -> H(f(c), d)
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.68	   A^2 -> H(U1(k, k), f(e))
28.55/9.68	   A^2 -> H(U1(k, k), f(k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.68	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.68	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.68	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.68	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.68	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.68	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.68	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.68	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.68	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.68	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.68	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.68	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.68	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.68	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.68	   A^2 -> H(U1(d, d), b)
28.55/9.68	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.68	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.68	   A^2 -> H(U1(d, d), c)
28.55/9.68	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.68	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.68	   A^2 -> H(U1(d, d), e)
28.55/9.68	   A^2 -> H(f(d), d)
28.55/9.68	   A^2 -> H(f(d), k)
28.55/9.68	   A^2 -> H(U1(c, c), c)
28.55/9.68	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.68	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.68	   A^2 -> H(f(c), k)
28.55/9.68	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.68	   A^2 -> H(f(k), U1(k, k))
28.55/9.68	   A^2 -> H(f(e), e)
28.55/9.68	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.68	   A^2 -> H(d, U1(c, b))
28.55/9.68	   A^2 -> H(d, U1(d, b))
28.55/9.68	   A^2 -> H(d, U1(b, c))
28.55/9.68	   A^2 -> H(d, U1(b, d))
28.55/9.68	   A^2 -> H(d, U1(c, c))
28.55/9.68	   A^2 -> H(d, f(e))
28.55/9.68	   A^2 -> H(d, f(k))
28.55/9.68	   A^2 -> H(d, U1(d, d))
28.55/9.68	   A^2 -> H(a, U1(e, b))
28.55/9.68	   A^2 -> H(a, U1(k, b))
28.55/9.68	   A^2 -> H(a, U1(c, d))
28.55/9.68	   A^2 -> H(a, U1(d, c))
28.55/9.68	   A^2 -> H(a, U1(b, e))
28.55/9.68	   A^2 -> H(a, U1(b, k))
28.55/9.68	   A^2 -> H(a, U1(e, c))
28.55/9.68	   A^2 -> H(a, U1(k, c))
28.55/9.68	   A^2 -> H(a, U1(c, e))
28.55/9.68	   A^2 -> H(a, U1(c, k))
28.55/9.68	   A^2 -> H(a, U1(e, e))
28.55/9.68	   A^2 -> H(a, U1(k, k))
28.55/9.68	   A^2 -> H(a, U1(k, d))
28.55/9.68	   A^2 -> H(a, U1(d, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.68	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.68	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.68	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.68	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.68	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.68	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.68	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.68	   A^2 -> H(U1(e, a), b)
28.55/9.68	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.68	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.68	   A^2 -> H(U1(e, a), c)
28.55/9.68	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.68	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.68	   A^2 -> H(U1(e, a), e)
28.55/9.68	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, a), b)
28.55/9.68	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.68	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.68	   A^2 -> H(U1(k, a), c)
28.55/9.68	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.68	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.68	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, d), b)
28.55/9.68	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.68	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.68	   A^2 -> H(U1(c, d), c)
28.55/9.68	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.68	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.68	   A^2 -> H(U1(c, d), e)
28.55/9.68	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, a), d)
28.55/9.68	   A^2 -> H(U1(c, a), k)
28.55/9.68	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.68	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.68	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.68	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.68	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.68	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.68	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.68	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.68	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.68	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.68	   A^2 -> H(U1(d, c), b)
28.55/9.68	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.68	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.68	   A^2 -> H(U1(d, c), c)
28.55/9.68	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.68	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.68	   A^2 -> H(U1(d, c), e)
28.55/9.68	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(d, a), d)
28.55/9.68	   A^2 -> H(U1(d, a), k)
28.55/9.68	   A^2 -> H(U1(a, e), b)
28.55/9.68	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, e), c)
28.55/9.68	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.68	   A^2 -> H(U1(a, e), e)
28.55/9.68	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, k), b)
28.55/9.68	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.68	
28.55/9.68	The TRS R consists of the following rules:
28.55/9.68	
28.55/9.68	   f(x) -> U1(x, x)
28.55/9.68	   U1(e, x) -> x
28.55/9.68	   a -> c
28.55/9.68	   a -> d
28.55/9.68	   b -> c
28.55/9.68	   b -> d
28.55/9.68	   d -> k
28.55/9.68	   c -> e
28.55/9.68	   c -> k
28.55/9.68	
28.55/9.68	Q is empty.
28.55/9.68	We have to consider all minimal (P,Q,R)-chains.
28.55/9.68	----------------------------------------
28.55/9.68	
28.55/9.68	(1329) TransformationProof (EQUIVALENT)
28.55/9.68	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.68	
28.55/9.68	   (A^2 -> H(U1(c, k), U1(b, e)),A^2 -> H(U1(c, k), U1(b, e)))
28.55/9.68	   (A^2 -> H(U1(d, k), U1(b, e)),A^2 -> H(U1(d, k), U1(b, e)))
28.55/9.68	   (A^2 -> H(U1(a, k), U1(c, e)),A^2 -> H(U1(a, k), U1(c, e)))
28.55/9.68	   (A^2 -> H(U1(a, k), U1(d, e)),A^2 -> H(U1(a, k), U1(d, e)))
28.55/9.68	
28.55/9.68	
28.55/9.68	----------------------------------------
28.55/9.68	
28.55/9.68	(1330)
28.55/9.68	Obligation:
28.55/9.68	Q DP problem:
28.55/9.68	The TRS P consists of the following rules:
28.55/9.68	
28.55/9.68	   H(x, x) -> G(x, x, f(k))
28.55/9.68	   G(d, x, x) -> A^2
28.55/9.68	   A^2 -> H(f(c), f(c))
28.55/9.68	   A^2 -> H(f(d), f(d))
28.55/9.68	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.68	   A^2 -> H(f(e), f(e))
28.55/9.68	   A^2 -> H(f(k), f(k))
28.55/9.68	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.68	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.68	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.68	   A^2 -> H(U1(a, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.68	   A^2 -> H(U1(a, c), b)
28.55/9.68	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, c), c)
28.55/9.68	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.68	   A^2 -> H(U1(a, c), e)
28.55/9.68	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, d), b)
28.55/9.68	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, d), c)
28.55/9.68	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.68	   A^2 -> H(U1(a, d), e)
28.55/9.68	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, a), d)
28.55/9.68	   A^2 -> H(U1(a, a), k)
28.55/9.68	   A^2 -> H(k, U1(b, b))
28.55/9.68	   A^2 -> H(k, f(c))
28.55/9.68	   A^2 -> H(k, f(d))
28.55/9.68	   A^2 -> H(c, U1(c, b))
28.55/9.68	   A^2 -> H(c, U1(d, b))
28.55/9.68	   A^2 -> H(c, U1(b, c))
28.55/9.68	   A^2 -> H(c, U1(b, d))
28.55/9.68	   A^2 -> H(c, U1(c, c))
28.55/9.68	   A^2 -> H(c, f(e))
28.55/9.68	   A^2 -> H(c, f(k))
28.55/9.68	   A^2 -> H(c, U1(d, d))
28.55/9.68	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.68	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.68	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.68	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.68	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.68	   A^2 -> H(U1(e, k), f(e))
28.55/9.68	   A^2 -> H(U1(e, k), f(k))
28.55/9.68	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.68	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.68	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.68	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.68	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.68	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.68	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.68	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.68	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.68	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.68	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.68	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.68	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.68	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.68	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.68	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.68	   A^2 -> H(U1(k, e), f(e))
28.55/9.68	   A^2 -> H(U1(k, e), f(k))
28.55/9.68	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.68	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.68	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.68	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.68	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.68	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.68	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.68	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.68	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.68	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.68	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.68	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.68	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.68	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.68	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.68	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.68	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.68	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.68	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.68	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.68	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.68	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.68	   A^2 -> H(U1(c, c), b)
28.55/9.68	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.68	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.68	   A^2 -> H(U1(c, c), e)
28.55/9.68	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.68	   A^2 -> H(e, U1(c, b))
28.55/9.68	   A^2 -> H(e, U1(d, b))
28.55/9.68	   A^2 -> H(e, U1(b, c))
28.55/9.68	   A^2 -> H(e, U1(b, d))
28.55/9.68	   A^2 -> H(e, U1(c, c))
28.55/9.68	   A^2 -> H(e, f(e))
28.55/9.68	   A^2 -> H(e, f(k))
28.55/9.68	   A^2 -> H(e, U1(d, d))
28.55/9.68	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.68	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.68	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.68	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.68	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.68	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.68	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.68	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.68	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.68	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.68	   A^2 -> H(f(e), b)
28.55/9.68	   A^2 -> H(f(e), U1(e, d))
28.55/9.68	   A^2 -> H(f(e), U1(d, e))
28.55/9.68	   A^2 -> H(f(e), c)
28.55/9.68	   A^2 -> H(f(e), U1(e, k))
28.55/9.68	   A^2 -> H(f(e), U1(k, e))
28.55/9.68	   A^2 -> H(f(e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.68	   A^2 -> H(f(k), b)
28.55/9.68	   A^2 -> H(f(k), U1(e, d))
28.55/9.68	   A^2 -> H(f(k), U1(d, e))
28.55/9.68	   A^2 -> H(f(k), c)
28.55/9.68	   A^2 -> H(f(k), U1(e, k))
28.55/9.68	   A^2 -> H(f(k), U1(k, e))
28.55/9.68	   A^2 -> H(f(k), e)
28.55/9.68	   A^2 -> H(f(c), d)
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.68	   A^2 -> H(U1(k, k), f(e))
28.55/9.68	   A^2 -> H(U1(k, k), f(k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.68	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.68	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.68	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.68	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.68	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.68	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.68	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.68	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.68	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.68	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.68	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.68	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.68	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.68	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.68	   A^2 -> H(U1(d, d), b)
28.55/9.68	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.68	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.68	   A^2 -> H(U1(d, d), c)
28.55/9.68	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.68	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.68	   A^2 -> H(U1(d, d), e)
28.55/9.68	   A^2 -> H(f(d), d)
28.55/9.68	   A^2 -> H(f(d), k)
28.55/9.68	   A^2 -> H(U1(c, c), c)
28.55/9.68	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.68	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.68	   A^2 -> H(f(c), k)
28.55/9.68	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.68	   A^2 -> H(f(k), U1(k, k))
28.55/9.68	   A^2 -> H(f(e), e)
28.55/9.68	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.68	   A^2 -> H(d, U1(c, b))
28.55/9.68	   A^2 -> H(d, U1(d, b))
28.55/9.68	   A^2 -> H(d, U1(b, c))
28.55/9.68	   A^2 -> H(d, U1(b, d))
28.55/9.68	   A^2 -> H(d, U1(c, c))
28.55/9.68	   A^2 -> H(d, f(e))
28.55/9.68	   A^2 -> H(d, f(k))
28.55/9.68	   A^2 -> H(d, U1(d, d))
28.55/9.68	   A^2 -> H(a, U1(e, b))
28.55/9.68	   A^2 -> H(a, U1(k, b))
28.55/9.68	   A^2 -> H(a, U1(c, d))
28.55/9.68	   A^2 -> H(a, U1(d, c))
28.55/9.68	   A^2 -> H(a, U1(b, e))
28.55/9.68	   A^2 -> H(a, U1(b, k))
28.55/9.68	   A^2 -> H(a, U1(e, c))
28.55/9.68	   A^2 -> H(a, U1(k, c))
28.55/9.68	   A^2 -> H(a, U1(c, e))
28.55/9.68	   A^2 -> H(a, U1(c, k))
28.55/9.68	   A^2 -> H(a, U1(e, e))
28.55/9.68	   A^2 -> H(a, U1(k, k))
28.55/9.68	   A^2 -> H(a, U1(k, d))
28.55/9.68	   A^2 -> H(a, U1(d, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.68	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.68	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.68	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.68	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.68	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.68	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.68	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.68	   A^2 -> H(U1(e, a), b)
28.55/9.68	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.68	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.68	   A^2 -> H(U1(e, a), c)
28.55/9.68	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.68	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.68	   A^2 -> H(U1(e, a), e)
28.55/9.68	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, a), b)
28.55/9.68	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.68	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.68	   A^2 -> H(U1(k, a), c)
28.55/9.68	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.68	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.68	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, d), b)
28.55/9.68	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.68	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.68	   A^2 -> H(U1(c, d), c)
28.55/9.68	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.68	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.68	   A^2 -> H(U1(c, d), e)
28.55/9.68	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, a), d)
28.55/9.68	   A^2 -> H(U1(c, a), k)
28.55/9.68	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.68	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.68	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.68	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.68	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.68	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.68	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.68	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.68	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.68	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.68	   A^2 -> H(U1(d, c), b)
28.55/9.68	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.68	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.68	   A^2 -> H(U1(d, c), c)
28.55/9.68	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.68	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.68	   A^2 -> H(U1(d, c), e)
28.55/9.68	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(d, a), d)
28.55/9.68	   A^2 -> H(U1(d, a), k)
28.55/9.68	   A^2 -> H(U1(a, e), b)
28.55/9.68	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, e), c)
28.55/9.68	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.68	   A^2 -> H(U1(a, e), e)
28.55/9.68	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, k), b)
28.55/9.68	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.68	
28.55/9.68	The TRS R consists of the following rules:
28.55/9.68	
28.55/9.68	   f(x) -> U1(x, x)
28.55/9.68	   U1(e, x) -> x
28.55/9.68	   a -> c
28.55/9.68	   a -> d
28.55/9.68	   b -> c
28.55/9.68	   b -> d
28.55/9.68	   d -> k
28.55/9.68	   c -> e
28.55/9.68	   c -> k
28.55/9.68	
28.55/9.68	Q is empty.
28.55/9.68	We have to consider all minimal (P,Q,R)-chains.
28.55/9.68	----------------------------------------
28.55/9.68	
28.55/9.68	(1331) TransformationProof (EQUIVALENT)
28.55/9.68	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.68	
28.55/9.68	   (A^2 -> H(U1(c, k), U1(b, k)),A^2 -> H(U1(c, k), U1(b, k)))
28.55/9.68	   (A^2 -> H(U1(d, k), U1(b, k)),A^2 -> H(U1(d, k), U1(b, k)))
28.55/9.68	   (A^2 -> H(U1(a, k), U1(c, k)),A^2 -> H(U1(a, k), U1(c, k)))
28.55/9.68	   (A^2 -> H(U1(a, k), U1(d, k)),A^2 -> H(U1(a, k), U1(d, k)))
28.55/9.68	
28.55/9.68	
28.55/9.68	----------------------------------------
28.55/9.68	
28.55/9.68	(1332)
28.55/9.68	Obligation:
28.55/9.68	Q DP problem:
28.55/9.68	The TRS P consists of the following rules:
28.55/9.68	
28.55/9.68	   H(x, x) -> G(x, x, f(k))
28.55/9.68	   G(d, x, x) -> A^2
28.55/9.68	   A^2 -> H(f(c), f(c))
28.55/9.68	   A^2 -> H(f(d), f(d))
28.55/9.68	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.68	   A^2 -> H(f(e), f(e))
28.55/9.68	   A^2 -> H(f(k), f(k))
28.55/9.68	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.68	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.68	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.68	   A^2 -> H(U1(a, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.68	   A^2 -> H(U1(a, c), b)
28.55/9.68	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, c), c)
28.55/9.68	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.68	   A^2 -> H(U1(a, c), e)
28.55/9.68	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, d), b)
28.55/9.68	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, d), c)
28.55/9.68	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.68	   A^2 -> H(U1(a, d), e)
28.55/9.68	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, a), d)
28.55/9.68	   A^2 -> H(U1(a, a), k)
28.55/9.68	   A^2 -> H(k, U1(b, b))
28.55/9.68	   A^2 -> H(k, f(c))
28.55/9.68	   A^2 -> H(k, f(d))
28.55/9.68	   A^2 -> H(c, U1(c, b))
28.55/9.68	   A^2 -> H(c, U1(d, b))
28.55/9.68	   A^2 -> H(c, U1(b, c))
28.55/9.68	   A^2 -> H(c, U1(b, d))
28.55/9.68	   A^2 -> H(c, U1(c, c))
28.55/9.68	   A^2 -> H(c, f(e))
28.55/9.68	   A^2 -> H(c, f(k))
28.55/9.68	   A^2 -> H(c, U1(d, d))
28.55/9.68	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.68	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.68	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.68	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.68	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.68	   A^2 -> H(U1(e, k), f(e))
28.55/9.68	   A^2 -> H(U1(e, k), f(k))
28.55/9.68	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.68	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.68	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.68	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.68	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.68	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.68	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.68	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.68	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.68	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.68	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.68	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.68	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.68	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.68	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.68	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.68	   A^2 -> H(U1(k, e), f(e))
28.55/9.68	   A^2 -> H(U1(k, e), f(k))
28.55/9.68	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.68	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.68	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.68	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.68	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.68	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.68	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.68	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.68	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.68	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.68	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.68	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.68	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.68	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.68	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.68	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.68	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.68	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.68	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.68	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.68	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.68	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.68	   A^2 -> H(U1(c, c), b)
28.55/9.68	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.68	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.68	   A^2 -> H(U1(c, c), e)
28.55/9.68	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.68	   A^2 -> H(e, U1(c, b))
28.55/9.68	   A^2 -> H(e, U1(d, b))
28.55/9.68	   A^2 -> H(e, U1(b, c))
28.55/9.68	   A^2 -> H(e, U1(b, d))
28.55/9.68	   A^2 -> H(e, U1(c, c))
28.55/9.68	   A^2 -> H(e, f(e))
28.55/9.68	   A^2 -> H(e, f(k))
28.55/9.68	   A^2 -> H(e, U1(d, d))
28.55/9.68	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.68	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.68	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.68	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.68	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.68	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.68	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.68	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.68	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.68	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.68	   A^2 -> H(f(e), b)
28.55/9.68	   A^2 -> H(f(e), U1(e, d))
28.55/9.68	   A^2 -> H(f(e), U1(d, e))
28.55/9.68	   A^2 -> H(f(e), c)
28.55/9.68	   A^2 -> H(f(e), U1(e, k))
28.55/9.68	   A^2 -> H(f(e), U1(k, e))
28.55/9.68	   A^2 -> H(f(e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.68	   A^2 -> H(f(k), b)
28.55/9.68	   A^2 -> H(f(k), U1(e, d))
28.55/9.68	   A^2 -> H(f(k), U1(d, e))
28.55/9.68	   A^2 -> H(f(k), c)
28.55/9.68	   A^2 -> H(f(k), U1(e, k))
28.55/9.68	   A^2 -> H(f(k), U1(k, e))
28.55/9.68	   A^2 -> H(f(k), e)
28.55/9.68	   A^2 -> H(f(c), d)
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.68	   A^2 -> H(U1(k, k), f(e))
28.55/9.68	   A^2 -> H(U1(k, k), f(k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.68	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.68	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.68	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.68	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.68	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.68	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.68	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.68	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.68	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.68	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.68	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.68	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.68	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.68	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.68	   A^2 -> H(U1(d, d), b)
28.55/9.68	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.68	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.68	   A^2 -> H(U1(d, d), c)
28.55/9.68	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.68	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.68	   A^2 -> H(U1(d, d), e)
28.55/9.68	   A^2 -> H(f(d), d)
28.55/9.68	   A^2 -> H(f(d), k)
28.55/9.68	   A^2 -> H(U1(c, c), c)
28.55/9.68	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.68	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.68	   A^2 -> H(f(c), k)
28.55/9.68	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.68	   A^2 -> H(f(k), U1(k, k))
28.55/9.68	   A^2 -> H(f(e), e)
28.55/9.68	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.68	   A^2 -> H(d, U1(c, b))
28.55/9.68	   A^2 -> H(d, U1(d, b))
28.55/9.68	   A^2 -> H(d, U1(b, c))
28.55/9.68	   A^2 -> H(d, U1(b, d))
28.55/9.68	   A^2 -> H(d, U1(c, c))
28.55/9.68	   A^2 -> H(d, f(e))
28.55/9.68	   A^2 -> H(d, f(k))
28.55/9.68	   A^2 -> H(d, U1(d, d))
28.55/9.68	   A^2 -> H(a, U1(e, b))
28.55/9.68	   A^2 -> H(a, U1(k, b))
28.55/9.68	   A^2 -> H(a, U1(c, d))
28.55/9.68	   A^2 -> H(a, U1(d, c))
28.55/9.68	   A^2 -> H(a, U1(b, e))
28.55/9.68	   A^2 -> H(a, U1(b, k))
28.55/9.68	   A^2 -> H(a, U1(e, c))
28.55/9.68	   A^2 -> H(a, U1(k, c))
28.55/9.68	   A^2 -> H(a, U1(c, e))
28.55/9.68	   A^2 -> H(a, U1(c, k))
28.55/9.68	   A^2 -> H(a, U1(e, e))
28.55/9.68	   A^2 -> H(a, U1(k, k))
28.55/9.68	   A^2 -> H(a, U1(k, d))
28.55/9.68	   A^2 -> H(a, U1(d, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.68	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.68	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.68	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.68	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.68	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.68	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.68	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.68	   A^2 -> H(U1(e, a), b)
28.55/9.68	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.68	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.68	   A^2 -> H(U1(e, a), c)
28.55/9.68	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.68	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.68	   A^2 -> H(U1(e, a), e)
28.55/9.68	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, a), b)
28.55/9.68	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.68	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.68	   A^2 -> H(U1(k, a), c)
28.55/9.68	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.68	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.68	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, d), b)
28.55/9.68	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.68	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.68	   A^2 -> H(U1(c, d), c)
28.55/9.68	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.68	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.68	   A^2 -> H(U1(c, d), e)
28.55/9.68	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, a), d)
28.55/9.68	   A^2 -> H(U1(c, a), k)
28.55/9.68	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.68	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.68	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.68	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.68	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.68	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.68	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.68	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.68	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.68	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.68	   A^2 -> H(U1(d, c), b)
28.55/9.68	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.68	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.68	   A^2 -> H(U1(d, c), c)
28.55/9.68	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.68	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.68	   A^2 -> H(U1(d, c), e)
28.55/9.68	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(d, a), d)
28.55/9.68	   A^2 -> H(U1(d, a), k)
28.55/9.68	   A^2 -> H(U1(a, e), b)
28.55/9.68	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, e), c)
28.55/9.68	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.68	   A^2 -> H(U1(a, e), e)
28.55/9.68	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, k), b)
28.55/9.68	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.68	
28.55/9.68	The TRS R consists of the following rules:
28.55/9.68	
28.55/9.68	   f(x) -> U1(x, x)
28.55/9.68	   U1(e, x) -> x
28.55/9.68	   a -> c
28.55/9.68	   a -> d
28.55/9.68	   b -> c
28.55/9.68	   b -> d
28.55/9.68	   d -> k
28.55/9.68	   c -> e
28.55/9.68	   c -> k
28.55/9.68	
28.55/9.68	Q is empty.
28.55/9.68	We have to consider all minimal (P,Q,R)-chains.
28.55/9.68	----------------------------------------
28.55/9.68	
28.55/9.68	(1333) TransformationProof (EQUIVALENT)
28.55/9.68	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.68	
28.55/9.68	   (A^2 -> H(U1(c, k), U1(e, c)),A^2 -> H(U1(c, k), U1(e, c)))
28.55/9.68	   (A^2 -> H(U1(d, k), U1(e, c)),A^2 -> H(U1(d, k), U1(e, c)))
28.55/9.68	   (A^2 -> H(U1(a, k), c),A^2 -> H(U1(a, k), c))
28.55/9.68	   (A^2 -> H(U1(a, k), U1(e, e)),A^2 -> H(U1(a, k), U1(e, e)))
28.55/9.68	   (A^2 -> H(U1(a, k), U1(e, k)),A^2 -> H(U1(a, k), U1(e, k)))
28.55/9.68	
28.55/9.68	
28.55/9.68	----------------------------------------
28.55/9.68	
28.55/9.68	(1334)
28.55/9.68	Obligation:
28.55/9.68	Q DP problem:
28.55/9.68	The TRS P consists of the following rules:
28.55/9.68	
28.55/9.68	   H(x, x) -> G(x, x, f(k))
28.55/9.68	   G(d, x, x) -> A^2
28.55/9.68	   A^2 -> H(f(c), f(c))
28.55/9.68	   A^2 -> H(f(d), f(d))
28.55/9.68	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.68	   A^2 -> H(f(e), f(e))
28.55/9.68	   A^2 -> H(f(k), f(k))
28.55/9.68	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.68	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.68	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.68	   A^2 -> H(U1(a, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.68	   A^2 -> H(U1(a, c), b)
28.55/9.68	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, c), c)
28.55/9.68	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.68	   A^2 -> H(U1(a, c), e)
28.55/9.68	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, d), b)
28.55/9.68	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, d), c)
28.55/9.68	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.68	   A^2 -> H(U1(a, d), e)
28.55/9.68	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, a), d)
28.55/9.68	   A^2 -> H(U1(a, a), k)
28.55/9.68	   A^2 -> H(k, U1(b, b))
28.55/9.68	   A^2 -> H(k, f(c))
28.55/9.68	   A^2 -> H(k, f(d))
28.55/9.68	   A^2 -> H(c, U1(c, b))
28.55/9.68	   A^2 -> H(c, U1(d, b))
28.55/9.68	   A^2 -> H(c, U1(b, c))
28.55/9.68	   A^2 -> H(c, U1(b, d))
28.55/9.68	   A^2 -> H(c, U1(c, c))
28.55/9.68	   A^2 -> H(c, f(e))
28.55/9.68	   A^2 -> H(c, f(k))
28.55/9.68	   A^2 -> H(c, U1(d, d))
28.55/9.68	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.68	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.68	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.68	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.68	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.68	   A^2 -> H(U1(e, k), f(e))
28.55/9.68	   A^2 -> H(U1(e, k), f(k))
28.55/9.68	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.68	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.68	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.68	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.68	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.68	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.68	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.68	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.68	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.68	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.68	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.68	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.68	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.68	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.68	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.68	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.68	   A^2 -> H(U1(k, e), f(e))
28.55/9.68	   A^2 -> H(U1(k, e), f(k))
28.55/9.68	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.68	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.68	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.68	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.68	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.68	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.68	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.68	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.68	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.68	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.68	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.68	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.68	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.68	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.68	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.68	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.68	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.68	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.68	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.68	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.68	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.68	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.68	   A^2 -> H(U1(c, c), b)
28.55/9.68	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.68	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.68	   A^2 -> H(U1(c, c), e)
28.55/9.68	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.68	   A^2 -> H(e, U1(c, b))
28.55/9.68	   A^2 -> H(e, U1(d, b))
28.55/9.68	   A^2 -> H(e, U1(b, c))
28.55/9.68	   A^2 -> H(e, U1(b, d))
28.55/9.68	   A^2 -> H(e, U1(c, c))
28.55/9.68	   A^2 -> H(e, f(e))
28.55/9.68	   A^2 -> H(e, f(k))
28.55/9.68	   A^2 -> H(e, U1(d, d))
28.55/9.68	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.68	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.68	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.68	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.68	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.68	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.68	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.68	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.68	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.68	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.68	   A^2 -> H(f(e), b)
28.55/9.68	   A^2 -> H(f(e), U1(e, d))
28.55/9.68	   A^2 -> H(f(e), U1(d, e))
28.55/9.68	   A^2 -> H(f(e), c)
28.55/9.68	   A^2 -> H(f(e), U1(e, k))
28.55/9.68	   A^2 -> H(f(e), U1(k, e))
28.55/9.68	   A^2 -> H(f(e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.68	   A^2 -> H(f(k), b)
28.55/9.68	   A^2 -> H(f(k), U1(e, d))
28.55/9.68	   A^2 -> H(f(k), U1(d, e))
28.55/9.68	   A^2 -> H(f(k), c)
28.55/9.68	   A^2 -> H(f(k), U1(e, k))
28.55/9.68	   A^2 -> H(f(k), U1(k, e))
28.55/9.68	   A^2 -> H(f(k), e)
28.55/9.68	   A^2 -> H(f(c), d)
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.68	   A^2 -> H(U1(k, k), f(e))
28.55/9.68	   A^2 -> H(U1(k, k), f(k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.68	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.68	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.68	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.68	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.68	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.68	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.68	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.68	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.68	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.68	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.68	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.68	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.68	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.68	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.68	   A^2 -> H(U1(d, d), b)
28.55/9.68	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.68	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.68	   A^2 -> H(U1(d, d), c)
28.55/9.68	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.68	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.68	   A^2 -> H(U1(d, d), e)
28.55/9.68	   A^2 -> H(f(d), d)
28.55/9.68	   A^2 -> H(f(d), k)
28.55/9.68	   A^2 -> H(U1(c, c), c)
28.55/9.68	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.68	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.68	   A^2 -> H(f(c), k)
28.55/9.68	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.68	   A^2 -> H(f(k), U1(k, k))
28.55/9.68	   A^2 -> H(f(e), e)
28.55/9.68	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.68	   A^2 -> H(d, U1(c, b))
28.55/9.68	   A^2 -> H(d, U1(d, b))
28.55/9.68	   A^2 -> H(d, U1(b, c))
28.55/9.68	   A^2 -> H(d, U1(b, d))
28.55/9.68	   A^2 -> H(d, U1(c, c))
28.55/9.68	   A^2 -> H(d, f(e))
28.55/9.68	   A^2 -> H(d, f(k))
28.55/9.68	   A^2 -> H(d, U1(d, d))
28.55/9.68	   A^2 -> H(a, U1(e, b))
28.55/9.68	   A^2 -> H(a, U1(k, b))
28.55/9.68	   A^2 -> H(a, U1(c, d))
28.55/9.68	   A^2 -> H(a, U1(d, c))
28.55/9.68	   A^2 -> H(a, U1(b, e))
28.55/9.68	   A^2 -> H(a, U1(b, k))
28.55/9.68	   A^2 -> H(a, U1(e, c))
28.55/9.68	   A^2 -> H(a, U1(k, c))
28.55/9.68	   A^2 -> H(a, U1(c, e))
28.55/9.68	   A^2 -> H(a, U1(c, k))
28.55/9.68	   A^2 -> H(a, U1(e, e))
28.55/9.68	   A^2 -> H(a, U1(k, k))
28.55/9.68	   A^2 -> H(a, U1(k, d))
28.55/9.68	   A^2 -> H(a, U1(d, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.68	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.68	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.68	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.68	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.68	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.68	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.68	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.68	   A^2 -> H(U1(e, a), b)
28.55/9.68	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.68	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.68	   A^2 -> H(U1(e, a), c)
28.55/9.68	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.68	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.68	   A^2 -> H(U1(e, a), e)
28.55/9.68	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, a), b)
28.55/9.68	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.68	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.68	   A^2 -> H(U1(k, a), c)
28.55/9.68	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.68	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.68	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, d), b)
28.55/9.68	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.68	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.68	   A^2 -> H(U1(c, d), c)
28.55/9.68	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.68	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.68	   A^2 -> H(U1(c, d), e)
28.55/9.68	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, a), d)
28.55/9.68	   A^2 -> H(U1(c, a), k)
28.55/9.68	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.68	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.68	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.68	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.68	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.68	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.68	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.68	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.68	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.68	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.68	   A^2 -> H(U1(d, c), b)
28.55/9.68	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.68	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.68	   A^2 -> H(U1(d, c), c)
28.55/9.68	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.68	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.68	   A^2 -> H(U1(d, c), e)
28.55/9.68	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(d, a), d)
28.55/9.68	   A^2 -> H(U1(d, a), k)
28.55/9.68	   A^2 -> H(U1(a, e), b)
28.55/9.68	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, e), c)
28.55/9.68	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.68	   A^2 -> H(U1(a, e), e)
28.55/9.68	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, k), b)
28.55/9.68	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, k), c)
28.55/9.68	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.68	
28.55/9.68	The TRS R consists of the following rules:
28.55/9.68	
28.55/9.68	   f(x) -> U1(x, x)
28.55/9.68	   U1(e, x) -> x
28.55/9.68	   a -> c
28.55/9.68	   a -> d
28.55/9.68	   b -> c
28.55/9.68	   b -> d
28.55/9.68	   d -> k
28.55/9.68	   c -> e
28.55/9.68	   c -> k
28.55/9.68	
28.55/9.68	Q is empty.
28.55/9.68	We have to consider all minimal (P,Q,R)-chains.
28.55/9.68	----------------------------------------
28.55/9.68	
28.55/9.68	(1335) TransformationProof (EQUIVALENT)
28.55/9.68	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.68	
28.55/9.68	   (A^2 -> H(U1(c, k), U1(k, c)),A^2 -> H(U1(c, k), U1(k, c)))
28.55/9.68	   (A^2 -> H(U1(d, k), U1(k, c)),A^2 -> H(U1(d, k), U1(k, c)))
28.55/9.68	   (A^2 -> H(U1(a, k), U1(k, e)),A^2 -> H(U1(a, k), U1(k, e)))
28.55/9.68	   (A^2 -> H(U1(a, k), U1(k, k)),A^2 -> H(U1(a, k), U1(k, k)))
28.55/9.68	
28.55/9.68	
28.55/9.68	----------------------------------------
28.55/9.68	
28.55/9.68	(1336)
28.55/9.68	Obligation:
28.55/9.68	Q DP problem:
28.55/9.68	The TRS P consists of the following rules:
28.55/9.68	
28.55/9.68	   H(x, x) -> G(x, x, f(k))
28.55/9.68	   G(d, x, x) -> A^2
28.55/9.68	   A^2 -> H(f(c), f(c))
28.55/9.68	   A^2 -> H(f(d), f(d))
28.55/9.68	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.68	   A^2 -> H(f(e), f(e))
28.55/9.68	   A^2 -> H(f(k), f(k))
28.55/9.68	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.68	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.68	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.68	   A^2 -> H(U1(a, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.68	   A^2 -> H(U1(a, c), b)
28.55/9.68	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, c), c)
28.55/9.68	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.68	   A^2 -> H(U1(a, c), e)
28.55/9.68	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, d), b)
28.55/9.68	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, d), c)
28.55/9.68	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.68	   A^2 -> H(U1(a, d), e)
28.55/9.68	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, a), d)
28.55/9.68	   A^2 -> H(U1(a, a), k)
28.55/9.68	   A^2 -> H(k, U1(b, b))
28.55/9.68	   A^2 -> H(k, f(c))
28.55/9.68	   A^2 -> H(k, f(d))
28.55/9.68	   A^2 -> H(c, U1(c, b))
28.55/9.68	   A^2 -> H(c, U1(d, b))
28.55/9.68	   A^2 -> H(c, U1(b, c))
28.55/9.68	   A^2 -> H(c, U1(b, d))
28.55/9.68	   A^2 -> H(c, U1(c, c))
28.55/9.68	   A^2 -> H(c, f(e))
28.55/9.68	   A^2 -> H(c, f(k))
28.55/9.68	   A^2 -> H(c, U1(d, d))
28.55/9.68	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.68	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.68	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.68	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.68	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.68	   A^2 -> H(U1(e, k), f(e))
28.55/9.68	   A^2 -> H(U1(e, k), f(k))
28.55/9.68	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.68	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.68	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.68	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.68	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.68	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.68	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.68	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.68	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.68	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.68	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.68	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.68	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.68	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.68	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.68	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.68	   A^2 -> H(U1(k, e), f(e))
28.55/9.68	   A^2 -> H(U1(k, e), f(k))
28.55/9.68	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.68	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.68	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.68	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.68	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.68	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.68	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.68	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.68	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.68	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.68	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.68	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.68	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.68	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.68	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.68	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.68	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.68	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.68	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.68	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.68	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.68	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.68	   A^2 -> H(U1(c, c), b)
28.55/9.68	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.68	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.68	   A^2 -> H(U1(c, c), e)
28.55/9.68	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.68	   A^2 -> H(e, U1(c, b))
28.55/9.68	   A^2 -> H(e, U1(d, b))
28.55/9.68	   A^2 -> H(e, U1(b, c))
28.55/9.68	   A^2 -> H(e, U1(b, d))
28.55/9.68	   A^2 -> H(e, U1(c, c))
28.55/9.68	   A^2 -> H(e, f(e))
28.55/9.68	   A^2 -> H(e, f(k))
28.55/9.68	   A^2 -> H(e, U1(d, d))
28.55/9.68	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.68	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.68	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.68	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.68	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.68	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.68	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.68	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.68	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.68	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.68	   A^2 -> H(f(e), b)
28.55/9.68	   A^2 -> H(f(e), U1(e, d))
28.55/9.68	   A^2 -> H(f(e), U1(d, e))
28.55/9.68	   A^2 -> H(f(e), c)
28.55/9.68	   A^2 -> H(f(e), U1(e, k))
28.55/9.68	   A^2 -> H(f(e), U1(k, e))
28.55/9.68	   A^2 -> H(f(e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.68	   A^2 -> H(f(k), b)
28.55/9.68	   A^2 -> H(f(k), U1(e, d))
28.55/9.68	   A^2 -> H(f(k), U1(d, e))
28.55/9.68	   A^2 -> H(f(k), c)
28.55/9.68	   A^2 -> H(f(k), U1(e, k))
28.55/9.68	   A^2 -> H(f(k), U1(k, e))
28.55/9.68	   A^2 -> H(f(k), e)
28.55/9.68	   A^2 -> H(f(c), d)
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.68	   A^2 -> H(U1(k, k), f(e))
28.55/9.68	   A^2 -> H(U1(k, k), f(k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.68	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.68	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.68	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.68	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.68	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.68	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.68	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.68	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.68	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.68	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.68	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.68	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.68	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.68	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.68	   A^2 -> H(U1(d, d), b)
28.55/9.68	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.68	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.68	   A^2 -> H(U1(d, d), c)
28.55/9.68	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.68	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.68	   A^2 -> H(U1(d, d), e)
28.55/9.68	   A^2 -> H(f(d), d)
28.55/9.68	   A^2 -> H(f(d), k)
28.55/9.68	   A^2 -> H(U1(c, c), c)
28.55/9.68	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.68	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.68	   A^2 -> H(f(c), k)
28.55/9.68	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.68	   A^2 -> H(f(k), U1(k, k))
28.55/9.68	   A^2 -> H(f(e), e)
28.55/9.68	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.68	   A^2 -> H(d, U1(c, b))
28.55/9.68	   A^2 -> H(d, U1(d, b))
28.55/9.68	   A^2 -> H(d, U1(b, c))
28.55/9.68	   A^2 -> H(d, U1(b, d))
28.55/9.68	   A^2 -> H(d, U1(c, c))
28.55/9.68	   A^2 -> H(d, f(e))
28.55/9.68	   A^2 -> H(d, f(k))
28.55/9.68	   A^2 -> H(d, U1(d, d))
28.55/9.68	   A^2 -> H(a, U1(e, b))
28.55/9.68	   A^2 -> H(a, U1(k, b))
28.55/9.68	   A^2 -> H(a, U1(c, d))
28.55/9.68	   A^2 -> H(a, U1(d, c))
28.55/9.68	   A^2 -> H(a, U1(b, e))
28.55/9.68	   A^2 -> H(a, U1(b, k))
28.55/9.68	   A^2 -> H(a, U1(e, c))
28.55/9.68	   A^2 -> H(a, U1(k, c))
28.55/9.68	   A^2 -> H(a, U1(c, e))
28.55/9.68	   A^2 -> H(a, U1(c, k))
28.55/9.68	   A^2 -> H(a, U1(e, e))
28.55/9.68	   A^2 -> H(a, U1(k, k))
28.55/9.68	   A^2 -> H(a, U1(k, d))
28.55/9.68	   A^2 -> H(a, U1(d, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.68	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.68	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.68	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.68	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.68	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.68	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.68	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.68	   A^2 -> H(U1(e, a), b)
28.55/9.68	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.68	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.68	   A^2 -> H(U1(e, a), c)
28.55/9.68	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.68	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.68	   A^2 -> H(U1(e, a), e)
28.55/9.68	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, a), b)
28.55/9.68	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.68	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.68	   A^2 -> H(U1(k, a), c)
28.55/9.68	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.68	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.68	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, d), b)
28.55/9.68	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.68	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.68	   A^2 -> H(U1(c, d), c)
28.55/9.68	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.68	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.68	   A^2 -> H(U1(c, d), e)
28.55/9.68	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, a), d)
28.55/9.68	   A^2 -> H(U1(c, a), k)
28.55/9.68	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.68	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.68	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.68	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.68	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.68	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.68	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.68	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.68	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.68	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.68	   A^2 -> H(U1(d, c), b)
28.55/9.68	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.68	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.68	   A^2 -> H(U1(d, c), c)
28.55/9.68	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.68	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.68	   A^2 -> H(U1(d, c), e)
28.55/9.68	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(d, a), d)
28.55/9.68	   A^2 -> H(U1(d, a), k)
28.55/9.68	   A^2 -> H(U1(a, e), b)
28.55/9.68	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, e), c)
28.55/9.68	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.68	   A^2 -> H(U1(a, e), e)
28.55/9.68	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, k), b)
28.55/9.68	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, k), c)
28.55/9.68	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.68	
28.55/9.68	The TRS R consists of the following rules:
28.55/9.68	
28.55/9.68	   f(x) -> U1(x, x)
28.55/9.68	   U1(e, x) -> x
28.55/9.68	   a -> c
28.55/9.68	   a -> d
28.55/9.68	   b -> c
28.55/9.68	   b -> d
28.55/9.68	   d -> k
28.55/9.68	   c -> e
28.55/9.68	   c -> k
28.55/9.68	
28.55/9.68	Q is empty.
28.55/9.68	We have to consider all minimal (P,Q,R)-chains.
28.55/9.68	----------------------------------------
28.55/9.68	
28.55/9.68	(1337) TransformationProof (EQUIVALENT)
28.55/9.68	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.68	
28.55/9.68	   (A^2 -> H(U1(c, k), U1(c, e)),A^2 -> H(U1(c, k), U1(c, e)))
28.55/9.68	   (A^2 -> H(U1(d, k), U1(c, e)),A^2 -> H(U1(d, k), U1(c, e)))
28.55/9.68	   (A^2 -> H(U1(a, k), U1(e, e)),A^2 -> H(U1(a, k), U1(e, e)))
28.55/9.68	   (A^2 -> H(U1(a, k), U1(k, e)),A^2 -> H(U1(a, k), U1(k, e)))
28.55/9.68	
28.55/9.68	
28.55/9.68	----------------------------------------
28.55/9.68	
28.55/9.68	(1338)
28.55/9.68	Obligation:
28.55/9.68	Q DP problem:
28.55/9.68	The TRS P consists of the following rules:
28.55/9.68	
28.55/9.68	   H(x, x) -> G(x, x, f(k))
28.55/9.68	   G(d, x, x) -> A^2
28.55/9.68	   A^2 -> H(f(c), f(c))
28.55/9.68	   A^2 -> H(f(d), f(d))
28.55/9.68	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.68	   A^2 -> H(f(e), f(e))
28.55/9.68	   A^2 -> H(f(k), f(k))
28.55/9.68	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.68	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.68	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.68	   A^2 -> H(U1(a, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.68	   A^2 -> H(U1(a, c), b)
28.55/9.68	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, c), c)
28.55/9.68	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.68	   A^2 -> H(U1(a, c), e)
28.55/9.68	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, d), b)
28.55/9.68	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, d), c)
28.55/9.68	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.68	   A^2 -> H(U1(a, d), e)
28.55/9.68	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, a), d)
28.55/9.68	   A^2 -> H(U1(a, a), k)
28.55/9.68	   A^2 -> H(k, U1(b, b))
28.55/9.68	   A^2 -> H(k, f(c))
28.55/9.68	   A^2 -> H(k, f(d))
28.55/9.68	   A^2 -> H(c, U1(c, b))
28.55/9.68	   A^2 -> H(c, U1(d, b))
28.55/9.68	   A^2 -> H(c, U1(b, c))
28.55/9.68	   A^2 -> H(c, U1(b, d))
28.55/9.68	   A^2 -> H(c, U1(c, c))
28.55/9.68	   A^2 -> H(c, f(e))
28.55/9.68	   A^2 -> H(c, f(k))
28.55/9.68	   A^2 -> H(c, U1(d, d))
28.55/9.68	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.68	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.68	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.68	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.68	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.68	   A^2 -> H(U1(e, k), f(e))
28.55/9.68	   A^2 -> H(U1(e, k), f(k))
28.55/9.68	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.68	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.68	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.68	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.68	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.68	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.68	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.68	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.68	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.68	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.68	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.68	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.68	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.68	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.68	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.68	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.68	   A^2 -> H(U1(k, e), f(e))
28.55/9.68	   A^2 -> H(U1(k, e), f(k))
28.55/9.68	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.68	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.68	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.68	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.68	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.68	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.68	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.68	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.68	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.68	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.68	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.68	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.68	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.68	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.68	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.68	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.68	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.68	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.68	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.68	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.68	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.68	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.68	   A^2 -> H(U1(c, c), b)
28.55/9.68	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.68	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.68	   A^2 -> H(U1(c, c), e)
28.55/9.68	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.68	   A^2 -> H(e, U1(c, b))
28.55/9.68	   A^2 -> H(e, U1(d, b))
28.55/9.68	   A^2 -> H(e, U1(b, c))
28.55/9.68	   A^2 -> H(e, U1(b, d))
28.55/9.68	   A^2 -> H(e, U1(c, c))
28.55/9.68	   A^2 -> H(e, f(e))
28.55/9.68	   A^2 -> H(e, f(k))
28.55/9.68	   A^2 -> H(e, U1(d, d))
28.55/9.68	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.68	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.68	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.68	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.68	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.68	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.68	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.68	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.68	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.68	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.68	   A^2 -> H(f(e), b)
28.55/9.68	   A^2 -> H(f(e), U1(e, d))
28.55/9.68	   A^2 -> H(f(e), U1(d, e))
28.55/9.68	   A^2 -> H(f(e), c)
28.55/9.68	   A^2 -> H(f(e), U1(e, k))
28.55/9.68	   A^2 -> H(f(e), U1(k, e))
28.55/9.68	   A^2 -> H(f(e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.68	   A^2 -> H(f(k), b)
28.55/9.68	   A^2 -> H(f(k), U1(e, d))
28.55/9.68	   A^2 -> H(f(k), U1(d, e))
28.55/9.68	   A^2 -> H(f(k), c)
28.55/9.68	   A^2 -> H(f(k), U1(e, k))
28.55/9.68	   A^2 -> H(f(k), U1(k, e))
28.55/9.68	   A^2 -> H(f(k), e)
28.55/9.68	   A^2 -> H(f(c), d)
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.68	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.68	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.68	   A^2 -> H(U1(k, k), f(e))
28.55/9.68	   A^2 -> H(U1(k, k), f(k))
28.55/9.68	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.68	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.68	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.68	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.68	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.68	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.68	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.68	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.68	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.68	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.68	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.68	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.68	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.68	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.68	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.68	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.68	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.68	   A^2 -> H(U1(d, d), b)
28.55/9.68	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.68	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.68	   A^2 -> H(U1(d, d), c)
28.55/9.68	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.68	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.68	   A^2 -> H(U1(d, d), e)
28.55/9.68	   A^2 -> H(f(d), d)
28.55/9.68	   A^2 -> H(f(d), k)
28.55/9.68	   A^2 -> H(U1(c, c), c)
28.55/9.68	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.68	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.68	   A^2 -> H(f(c), k)
28.55/9.68	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.68	   A^2 -> H(f(k), U1(k, k))
28.55/9.68	   A^2 -> H(f(e), e)
28.55/9.68	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.68	   A^2 -> H(d, U1(c, b))
28.55/9.68	   A^2 -> H(d, U1(d, b))
28.55/9.68	   A^2 -> H(d, U1(b, c))
28.55/9.68	   A^2 -> H(d, U1(b, d))
28.55/9.68	   A^2 -> H(d, U1(c, c))
28.55/9.68	   A^2 -> H(d, f(e))
28.55/9.68	   A^2 -> H(d, f(k))
28.55/9.68	   A^2 -> H(d, U1(d, d))
28.55/9.68	   A^2 -> H(a, U1(e, b))
28.55/9.68	   A^2 -> H(a, U1(k, b))
28.55/9.68	   A^2 -> H(a, U1(c, d))
28.55/9.68	   A^2 -> H(a, U1(d, c))
28.55/9.68	   A^2 -> H(a, U1(b, e))
28.55/9.68	   A^2 -> H(a, U1(b, k))
28.55/9.68	   A^2 -> H(a, U1(e, c))
28.55/9.68	   A^2 -> H(a, U1(k, c))
28.55/9.68	   A^2 -> H(a, U1(c, e))
28.55/9.68	   A^2 -> H(a, U1(c, k))
28.55/9.68	   A^2 -> H(a, U1(e, e))
28.55/9.68	   A^2 -> H(a, U1(k, k))
28.55/9.68	   A^2 -> H(a, U1(k, d))
28.55/9.68	   A^2 -> H(a, U1(d, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.68	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.68	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.68	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.68	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.68	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.68	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.68	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.68	   A^2 -> H(U1(e, a), b)
28.55/9.68	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.68	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.68	   A^2 -> H(U1(e, a), c)
28.55/9.68	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.68	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.68	   A^2 -> H(U1(e, a), e)
28.55/9.68	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.68	   A^2 -> H(U1(k, a), b)
28.55/9.68	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.68	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.68	   A^2 -> H(U1(k, a), c)
28.55/9.68	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.68	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.68	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, d), b)
28.55/9.68	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.68	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.68	   A^2 -> H(U1(c, d), c)
28.55/9.68	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.68	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.68	   A^2 -> H(U1(c, d), e)
28.55/9.68	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(c, a), d)
28.55/9.68	   A^2 -> H(U1(c, a), k)
28.55/9.68	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.68	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.68	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.68	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.68	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.68	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.68	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.68	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.68	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.68	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.68	   A^2 -> H(U1(d, c), b)
28.55/9.68	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.68	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.68	   A^2 -> H(U1(d, c), c)
28.55/9.68	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.68	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.68	   A^2 -> H(U1(d, c), e)
28.55/9.68	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(d, a), d)
28.55/9.68	   A^2 -> H(U1(d, a), k)
28.55/9.68	   A^2 -> H(U1(a, e), b)
28.55/9.68	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, e), c)
28.55/9.68	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.68	   A^2 -> H(U1(a, e), e)
28.55/9.68	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, k), b)
28.55/9.68	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, k), c)
28.55/9.68	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.68	
28.55/9.68	The TRS R consists of the following rules:
28.55/9.68	
28.55/9.68	   f(x) -> U1(x, x)
28.55/9.68	   U1(e, x) -> x
28.55/9.68	   a -> c
28.55/9.68	   a -> d
28.55/9.68	   b -> c
28.55/9.68	   b -> d
28.55/9.68	   d -> k
28.55/9.68	   c -> e
28.55/9.68	   c -> k
28.55/9.68	
28.55/9.68	Q is empty.
28.55/9.68	We have to consider all minimal (P,Q,R)-chains.
28.55/9.68	----------------------------------------
28.55/9.68	
28.55/9.68	(1339) TransformationProof (EQUIVALENT)
28.55/9.68	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.68	
28.55/9.68	   (A^2 -> H(U1(c, k), U1(c, k)),A^2 -> H(U1(c, k), U1(c, k)))
28.55/9.68	   (A^2 -> H(U1(d, k), U1(c, k)),A^2 -> H(U1(d, k), U1(c, k)))
28.55/9.68	   (A^2 -> H(U1(a, k), U1(e, k)),A^2 -> H(U1(a, k), U1(e, k)))
28.55/9.68	   (A^2 -> H(U1(a, k), U1(k, k)),A^2 -> H(U1(a, k), U1(k, k)))
28.55/9.68	
28.55/9.68	
28.55/9.68	----------------------------------------
28.55/9.68	
28.55/9.68	(1340)
28.55/9.68	Obligation:
28.55/9.68	Q DP problem:
28.55/9.68	The TRS P consists of the following rules:
28.55/9.68	
28.55/9.68	   H(x, x) -> G(x, x, f(k))
28.55/9.68	   G(d, x, x) -> A^2
28.55/9.68	   A^2 -> H(f(c), f(c))
28.55/9.68	   A^2 -> H(f(d), f(d))
28.55/9.68	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.68	   A^2 -> H(f(e), f(e))
28.55/9.68	   A^2 -> H(f(k), f(k))
28.55/9.68	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.68	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.68	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.68	   A^2 -> H(U1(a, k), U1(e, e))
28.55/9.68	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.68	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.68	   A^2 -> H(U1(a, c), b)
28.55/9.68	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, c), c)
28.55/9.68	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.68	   A^2 -> H(U1(a, c), e)
28.55/9.68	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, d), b)
28.55/9.68	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.68	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.68	   A^2 -> H(U1(a, d), c)
28.55/9.68	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.68	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.68	   A^2 -> H(U1(a, d), e)
28.55/9.68	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.68	   A^2 -> H(U1(a, a), d)
28.55/9.68	   A^2 -> H(U1(a, a), k)
28.55/9.68	   A^2 -> H(k, U1(b, b))
28.55/9.68	   A^2 -> H(k, f(c))
28.55/9.68	   A^2 -> H(k, f(d))
28.55/9.68	   A^2 -> H(c, U1(c, b))
28.55/9.68	   A^2 -> H(c, U1(d, b))
28.55/9.68	   A^2 -> H(c, U1(b, c))
28.55/9.68	   A^2 -> H(c, U1(b, d))
28.55/9.68	   A^2 -> H(c, U1(c, c))
28.55/9.68	   A^2 -> H(c, f(e))
28.55/9.68	   A^2 -> H(c, f(k))
28.55/9.68	   A^2 -> H(c, U1(d, d))
28.55/9.68	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.68	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.68	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.69	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.69	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.69	   A^2 -> H(U1(e, k), f(e))
28.55/9.69	   A^2 -> H(U1(e, k), f(k))
28.55/9.69	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.69	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.69	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.69	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.69	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.69	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.69	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.69	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.69	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.69	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.69	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.69	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.69	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.69	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.69	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.69	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.69	   A^2 -> H(U1(k, e), f(e))
28.55/9.69	   A^2 -> H(U1(k, e), f(k))
28.55/9.69	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.69	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.69	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.69	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.69	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.69	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.69	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.69	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.69	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.69	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.69	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.69	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.69	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.69	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.69	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.69	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.69	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.69	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.69	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.69	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.69	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.69	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.69	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.69	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.69	   A^2 -> H(U1(c, c), b)
28.55/9.69	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.69	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.69	   A^2 -> H(U1(c, c), e)
28.55/9.69	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.69	   A^2 -> H(e, U1(c, b))
28.55/9.69	   A^2 -> H(e, U1(d, b))
28.55/9.69	   A^2 -> H(e, U1(b, c))
28.55/9.69	   A^2 -> H(e, U1(b, d))
28.55/9.69	   A^2 -> H(e, U1(c, c))
28.55/9.69	   A^2 -> H(e, f(e))
28.55/9.69	   A^2 -> H(e, f(k))
28.55/9.69	   A^2 -> H(e, U1(d, d))
28.55/9.69	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.69	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.69	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.69	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.69	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.69	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.69	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.69	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.69	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.69	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.69	   A^2 -> H(f(e), b)
28.55/9.69	   A^2 -> H(f(e), U1(e, d))
28.55/9.69	   A^2 -> H(f(e), U1(d, e))
28.55/9.69	   A^2 -> H(f(e), c)
28.55/9.69	   A^2 -> H(f(e), U1(e, k))
28.55/9.69	   A^2 -> H(f(e), U1(k, e))
28.55/9.69	   A^2 -> H(f(e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.69	   A^2 -> H(f(k), b)
28.55/9.69	   A^2 -> H(f(k), U1(e, d))
28.55/9.69	   A^2 -> H(f(k), U1(d, e))
28.55/9.69	   A^2 -> H(f(k), c)
28.55/9.69	   A^2 -> H(f(k), U1(e, k))
28.55/9.69	   A^2 -> H(f(k), U1(k, e))
28.55/9.69	   A^2 -> H(f(k), e)
28.55/9.69	   A^2 -> H(f(c), d)
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.69	   A^2 -> H(U1(k, k), f(e))
28.55/9.69	   A^2 -> H(U1(k, k), f(k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.69	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.69	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.69	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.69	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.69	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.69	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.69	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.69	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.69	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.69	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.69	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.69	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.69	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.69	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.69	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.69	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.69	   A^2 -> H(U1(d, d), b)
28.55/9.69	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.69	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.69	   A^2 -> H(U1(d, d), c)
28.55/9.69	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.69	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.69	   A^2 -> H(U1(d, d), e)
28.55/9.69	   A^2 -> H(f(d), d)
28.55/9.69	   A^2 -> H(f(d), k)
28.55/9.69	   A^2 -> H(U1(c, c), c)
28.55/9.69	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.69	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.69	   A^2 -> H(f(c), k)
28.55/9.69	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.69	   A^2 -> H(f(k), U1(k, k))
28.55/9.69	   A^2 -> H(f(e), e)
28.55/9.69	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.69	   A^2 -> H(d, U1(c, b))
28.55/9.69	   A^2 -> H(d, U1(d, b))
28.55/9.69	   A^2 -> H(d, U1(b, c))
28.55/9.69	   A^2 -> H(d, U1(b, d))
28.55/9.69	   A^2 -> H(d, U1(c, c))
28.55/9.69	   A^2 -> H(d, f(e))
28.55/9.69	   A^2 -> H(d, f(k))
28.55/9.69	   A^2 -> H(d, U1(d, d))
28.55/9.69	   A^2 -> H(a, U1(e, b))
28.55/9.69	   A^2 -> H(a, U1(k, b))
28.55/9.69	   A^2 -> H(a, U1(c, d))
28.55/9.69	   A^2 -> H(a, U1(d, c))
28.55/9.69	   A^2 -> H(a, U1(b, e))
28.55/9.69	   A^2 -> H(a, U1(b, k))
28.55/9.69	   A^2 -> H(a, U1(e, c))
28.55/9.69	   A^2 -> H(a, U1(k, c))
28.55/9.69	   A^2 -> H(a, U1(c, e))
28.55/9.69	   A^2 -> H(a, U1(c, k))
28.55/9.69	   A^2 -> H(a, U1(e, e))
28.55/9.69	   A^2 -> H(a, U1(k, k))
28.55/9.69	   A^2 -> H(a, U1(k, d))
28.55/9.69	   A^2 -> H(a, U1(d, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.69	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.69	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.69	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.69	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.69	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.69	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.69	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.69	   A^2 -> H(U1(e, a), b)
28.55/9.69	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.69	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.69	   A^2 -> H(U1(e, a), c)
28.55/9.69	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.69	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.69	   A^2 -> H(U1(e, a), e)
28.55/9.69	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, a), b)
28.55/9.69	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.69	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.69	   A^2 -> H(U1(k, a), c)
28.55/9.69	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.69	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.69	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, d), b)
28.55/9.69	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.69	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.69	   A^2 -> H(U1(c, d), c)
28.55/9.69	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.69	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.69	   A^2 -> H(U1(c, d), e)
28.55/9.69	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, a), d)
28.55/9.69	   A^2 -> H(U1(c, a), k)
28.55/9.69	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.69	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.69	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.69	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.69	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.69	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.69	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.69	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.69	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.69	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.69	   A^2 -> H(U1(d, c), b)
28.55/9.69	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.69	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.69	   A^2 -> H(U1(d, c), c)
28.55/9.69	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.69	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.69	   A^2 -> H(U1(d, c), e)
28.55/9.69	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(d, a), d)
28.55/9.69	   A^2 -> H(U1(d, a), k)
28.55/9.69	   A^2 -> H(U1(a, e), b)
28.55/9.69	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, e), c)
28.55/9.69	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, e), e)
28.55/9.69	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(a, k), b)
28.55/9.69	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, k), c)
28.55/9.69	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.69	
28.55/9.69	The TRS R consists of the following rules:
28.55/9.69	
28.55/9.69	   f(x) -> U1(x, x)
28.55/9.69	   U1(e, x) -> x
28.55/9.69	   a -> c
28.55/9.69	   a -> d
28.55/9.69	   b -> c
28.55/9.69	   b -> d
28.55/9.69	   d -> k
28.55/9.69	   c -> e
28.55/9.69	   c -> k
28.55/9.69	
28.55/9.69	Q is empty.
28.55/9.69	We have to consider all minimal (P,Q,R)-chains.
28.55/9.69	----------------------------------------
28.55/9.69	
28.55/9.69	(1341) TransformationProof (EQUIVALENT)
28.55/9.69	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.69	
28.55/9.69	   (A^2 -> H(U1(c, k), U1(e, e)),A^2 -> H(U1(c, k), U1(e, e)))
28.55/9.69	   (A^2 -> H(U1(d, k), U1(e, e)),A^2 -> H(U1(d, k), U1(e, e)))
28.55/9.69	   (A^2 -> H(U1(a, k), e),A^2 -> H(U1(a, k), e))
28.55/9.69	
28.55/9.69	
28.55/9.69	----------------------------------------
28.55/9.69	
28.55/9.69	(1342)
28.55/9.69	Obligation:
28.55/9.69	Q DP problem:
28.55/9.69	The TRS P consists of the following rules:
28.55/9.69	
28.55/9.69	   H(x, x) -> G(x, x, f(k))
28.55/9.69	   G(d, x, x) -> A^2
28.55/9.69	   A^2 -> H(f(c), f(c))
28.55/9.69	   A^2 -> H(f(d), f(d))
28.55/9.69	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.69	   A^2 -> H(f(e), f(e))
28.55/9.69	   A^2 -> H(f(k), f(k))
28.55/9.69	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.69	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.69	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.69	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.69	   A^2 -> H(U1(a, c), b)
28.55/9.69	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, c), c)
28.55/9.69	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, c), e)
28.55/9.69	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(a, d), b)
28.55/9.69	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, d), c)
28.55/9.69	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, d), e)
28.55/9.69	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(a, a), d)
28.55/9.69	   A^2 -> H(U1(a, a), k)
28.55/9.69	   A^2 -> H(k, U1(b, b))
28.55/9.69	   A^2 -> H(k, f(c))
28.55/9.69	   A^2 -> H(k, f(d))
28.55/9.69	   A^2 -> H(c, U1(c, b))
28.55/9.69	   A^2 -> H(c, U1(d, b))
28.55/9.69	   A^2 -> H(c, U1(b, c))
28.55/9.69	   A^2 -> H(c, U1(b, d))
28.55/9.69	   A^2 -> H(c, U1(c, c))
28.55/9.69	   A^2 -> H(c, f(e))
28.55/9.69	   A^2 -> H(c, f(k))
28.55/9.69	   A^2 -> H(c, U1(d, d))
28.55/9.69	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.69	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.69	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.69	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.69	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.69	   A^2 -> H(U1(e, k), f(e))
28.55/9.69	   A^2 -> H(U1(e, k), f(k))
28.55/9.69	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.69	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.69	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.69	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.69	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.69	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.69	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.69	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.69	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.69	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.69	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.69	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.69	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.69	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.69	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.69	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.69	   A^2 -> H(U1(k, e), f(e))
28.55/9.69	   A^2 -> H(U1(k, e), f(k))
28.55/9.69	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.69	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.69	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.69	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.69	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.69	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.69	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.69	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.69	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.69	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.69	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.69	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.69	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.69	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.69	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.69	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.69	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.69	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.69	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.69	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.69	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.69	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.69	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.69	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.69	   A^2 -> H(U1(c, c), b)
28.55/9.69	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.69	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.69	   A^2 -> H(U1(c, c), e)
28.55/9.69	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.69	   A^2 -> H(e, U1(c, b))
28.55/9.69	   A^2 -> H(e, U1(d, b))
28.55/9.69	   A^2 -> H(e, U1(b, c))
28.55/9.69	   A^2 -> H(e, U1(b, d))
28.55/9.69	   A^2 -> H(e, U1(c, c))
28.55/9.69	   A^2 -> H(e, f(e))
28.55/9.69	   A^2 -> H(e, f(k))
28.55/9.69	   A^2 -> H(e, U1(d, d))
28.55/9.69	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.69	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.69	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.69	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.69	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.69	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.69	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.69	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.69	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.69	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.69	   A^2 -> H(f(e), b)
28.55/9.69	   A^2 -> H(f(e), U1(e, d))
28.55/9.69	   A^2 -> H(f(e), U1(d, e))
28.55/9.69	   A^2 -> H(f(e), c)
28.55/9.69	   A^2 -> H(f(e), U1(e, k))
28.55/9.69	   A^2 -> H(f(e), U1(k, e))
28.55/9.69	   A^2 -> H(f(e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.69	   A^2 -> H(f(k), b)
28.55/9.69	   A^2 -> H(f(k), U1(e, d))
28.55/9.69	   A^2 -> H(f(k), U1(d, e))
28.55/9.69	   A^2 -> H(f(k), c)
28.55/9.69	   A^2 -> H(f(k), U1(e, k))
28.55/9.69	   A^2 -> H(f(k), U1(k, e))
28.55/9.69	   A^2 -> H(f(k), e)
28.55/9.69	   A^2 -> H(f(c), d)
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.69	   A^2 -> H(U1(k, k), f(e))
28.55/9.69	   A^2 -> H(U1(k, k), f(k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.69	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.69	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.69	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.69	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.69	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.69	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.69	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.69	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.69	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.69	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.69	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.69	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.69	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.69	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.69	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.69	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.69	   A^2 -> H(U1(d, d), b)
28.55/9.69	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.69	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.69	   A^2 -> H(U1(d, d), c)
28.55/9.69	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.69	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.69	   A^2 -> H(U1(d, d), e)
28.55/9.69	   A^2 -> H(f(d), d)
28.55/9.69	   A^2 -> H(f(d), k)
28.55/9.69	   A^2 -> H(U1(c, c), c)
28.55/9.69	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.69	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.69	   A^2 -> H(f(c), k)
28.55/9.69	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.69	   A^2 -> H(f(k), U1(k, k))
28.55/9.69	   A^2 -> H(f(e), e)
28.55/9.69	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.69	   A^2 -> H(d, U1(c, b))
28.55/9.69	   A^2 -> H(d, U1(d, b))
28.55/9.69	   A^2 -> H(d, U1(b, c))
28.55/9.69	   A^2 -> H(d, U1(b, d))
28.55/9.69	   A^2 -> H(d, U1(c, c))
28.55/9.69	   A^2 -> H(d, f(e))
28.55/9.69	   A^2 -> H(d, f(k))
28.55/9.69	   A^2 -> H(d, U1(d, d))
28.55/9.69	   A^2 -> H(a, U1(e, b))
28.55/9.69	   A^2 -> H(a, U1(k, b))
28.55/9.69	   A^2 -> H(a, U1(c, d))
28.55/9.69	   A^2 -> H(a, U1(d, c))
28.55/9.69	   A^2 -> H(a, U1(b, e))
28.55/9.69	   A^2 -> H(a, U1(b, k))
28.55/9.69	   A^2 -> H(a, U1(e, c))
28.55/9.69	   A^2 -> H(a, U1(k, c))
28.55/9.69	   A^2 -> H(a, U1(c, e))
28.55/9.69	   A^2 -> H(a, U1(c, k))
28.55/9.69	   A^2 -> H(a, U1(e, e))
28.55/9.69	   A^2 -> H(a, U1(k, k))
28.55/9.69	   A^2 -> H(a, U1(k, d))
28.55/9.69	   A^2 -> H(a, U1(d, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.69	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.69	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.69	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.69	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.69	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.69	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.69	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.69	   A^2 -> H(U1(e, a), b)
28.55/9.69	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.69	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.69	   A^2 -> H(U1(e, a), c)
28.55/9.69	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.69	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.69	   A^2 -> H(U1(e, a), e)
28.55/9.69	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, a), b)
28.55/9.69	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.69	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.69	   A^2 -> H(U1(k, a), c)
28.55/9.69	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.69	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.69	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, d), b)
28.55/9.69	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.69	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.69	   A^2 -> H(U1(c, d), c)
28.55/9.69	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.69	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.69	   A^2 -> H(U1(c, d), e)
28.55/9.69	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, a), d)
28.55/9.69	   A^2 -> H(U1(c, a), k)
28.55/9.69	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.69	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.69	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.69	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.69	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.69	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.69	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.69	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.69	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.69	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.69	   A^2 -> H(U1(d, c), b)
28.55/9.69	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.69	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.69	   A^2 -> H(U1(d, c), c)
28.55/9.69	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.69	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.69	   A^2 -> H(U1(d, c), e)
28.55/9.69	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(d, a), d)
28.55/9.69	   A^2 -> H(U1(d, a), k)
28.55/9.69	   A^2 -> H(U1(a, e), b)
28.55/9.69	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, e), c)
28.55/9.69	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, e), e)
28.55/9.69	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(a, k), b)
28.55/9.69	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, k), c)
28.55/9.69	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, k), e)
28.55/9.69	
28.55/9.69	The TRS R consists of the following rules:
28.55/9.69	
28.55/9.69	   f(x) -> U1(x, x)
28.55/9.69	   U1(e, x) -> x
28.55/9.69	   a -> c
28.55/9.69	   a -> d
28.55/9.69	   b -> c
28.55/9.69	   b -> d
28.55/9.69	   d -> k
28.55/9.69	   c -> e
28.55/9.69	   c -> k
28.55/9.69	
28.55/9.69	Q is empty.
28.55/9.69	We have to consider all minimal (P,Q,R)-chains.
28.55/9.69	----------------------------------------
28.55/9.69	
28.55/9.69	(1343) TransformationProof (EQUIVALENT)
28.55/9.69	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.69	
28.55/9.69	   (A^2 -> H(U1(c, k), U1(k, k)),A^2 -> H(U1(c, k), U1(k, k)))
28.55/9.69	   (A^2 -> H(U1(d, k), U1(k, k)),A^2 -> H(U1(d, k), U1(k, k)))
28.55/9.69	
28.55/9.69	
28.55/9.69	----------------------------------------
28.55/9.69	
28.55/9.69	(1344)
28.55/9.69	Obligation:
28.55/9.69	Q DP problem:
28.55/9.69	The TRS P consists of the following rules:
28.55/9.69	
28.55/9.69	   H(x, x) -> G(x, x, f(k))
28.55/9.69	   G(d, x, x) -> A^2
28.55/9.69	   A^2 -> H(f(c), f(c))
28.55/9.69	   A^2 -> H(f(d), f(d))
28.55/9.69	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.69	   A^2 -> H(f(e), f(e))
28.55/9.69	   A^2 -> H(f(k), f(k))
28.55/9.69	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.69	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.69	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.69	   A^2 -> H(U1(a, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.69	   A^2 -> H(U1(a, c), b)
28.55/9.69	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, c), c)
28.55/9.69	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, c), e)
28.55/9.69	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(a, d), b)
28.55/9.69	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, d), c)
28.55/9.69	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, d), e)
28.55/9.69	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(a, a), d)
28.55/9.69	   A^2 -> H(U1(a, a), k)
28.55/9.69	   A^2 -> H(k, U1(b, b))
28.55/9.69	   A^2 -> H(k, f(c))
28.55/9.69	   A^2 -> H(k, f(d))
28.55/9.69	   A^2 -> H(c, U1(c, b))
28.55/9.69	   A^2 -> H(c, U1(d, b))
28.55/9.69	   A^2 -> H(c, U1(b, c))
28.55/9.69	   A^2 -> H(c, U1(b, d))
28.55/9.69	   A^2 -> H(c, U1(c, c))
28.55/9.69	   A^2 -> H(c, f(e))
28.55/9.69	   A^2 -> H(c, f(k))
28.55/9.69	   A^2 -> H(c, U1(d, d))
28.55/9.69	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.69	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.69	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.69	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.69	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.69	   A^2 -> H(U1(e, k), f(e))
28.55/9.69	   A^2 -> H(U1(e, k), f(k))
28.55/9.69	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.69	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.69	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.69	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.69	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.69	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.69	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.69	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.69	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.69	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.69	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.69	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.69	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.69	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.69	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.69	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.69	   A^2 -> H(U1(k, e), f(e))
28.55/9.69	   A^2 -> H(U1(k, e), f(k))
28.55/9.69	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.69	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.69	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.69	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.69	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.69	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.69	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.69	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.69	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.69	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.69	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.69	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.69	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.69	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.69	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.69	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.69	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.69	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.69	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.69	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.69	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.69	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.69	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.69	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.69	   A^2 -> H(U1(c, c), b)
28.55/9.69	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.69	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.69	   A^2 -> H(U1(c, c), e)
28.55/9.69	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.69	   A^2 -> H(e, U1(c, b))
28.55/9.69	   A^2 -> H(e, U1(d, b))
28.55/9.69	   A^2 -> H(e, U1(b, c))
28.55/9.69	   A^2 -> H(e, U1(b, d))
28.55/9.69	   A^2 -> H(e, U1(c, c))
28.55/9.69	   A^2 -> H(e, f(e))
28.55/9.69	   A^2 -> H(e, f(k))
28.55/9.69	   A^2 -> H(e, U1(d, d))
28.55/9.69	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.69	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.69	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.69	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.69	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.69	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.69	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.69	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.69	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.69	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.69	   A^2 -> H(f(e), b)
28.55/9.69	   A^2 -> H(f(e), U1(e, d))
28.55/9.69	   A^2 -> H(f(e), U1(d, e))
28.55/9.69	   A^2 -> H(f(e), c)
28.55/9.69	   A^2 -> H(f(e), U1(e, k))
28.55/9.69	   A^2 -> H(f(e), U1(k, e))
28.55/9.69	   A^2 -> H(f(e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.69	   A^2 -> H(f(k), b)
28.55/9.69	   A^2 -> H(f(k), U1(e, d))
28.55/9.69	   A^2 -> H(f(k), U1(d, e))
28.55/9.69	   A^2 -> H(f(k), c)
28.55/9.69	   A^2 -> H(f(k), U1(e, k))
28.55/9.69	   A^2 -> H(f(k), U1(k, e))
28.55/9.69	   A^2 -> H(f(k), e)
28.55/9.69	   A^2 -> H(f(c), d)
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.69	   A^2 -> H(U1(k, k), f(e))
28.55/9.69	   A^2 -> H(U1(k, k), f(k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.69	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.69	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.69	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.69	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.69	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.69	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.69	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.69	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.69	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.69	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.69	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.69	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.69	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.69	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.69	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.69	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.69	   A^2 -> H(U1(d, d), b)
28.55/9.69	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.69	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.69	   A^2 -> H(U1(d, d), c)
28.55/9.69	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.69	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.69	   A^2 -> H(U1(d, d), e)
28.55/9.69	   A^2 -> H(f(d), d)
28.55/9.69	   A^2 -> H(f(d), k)
28.55/9.69	   A^2 -> H(U1(c, c), c)
28.55/9.69	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.69	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.69	   A^2 -> H(f(c), k)
28.55/9.69	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.69	   A^2 -> H(f(k), U1(k, k))
28.55/9.69	   A^2 -> H(f(e), e)
28.55/9.69	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.69	   A^2 -> H(d, U1(c, b))
28.55/9.69	   A^2 -> H(d, U1(d, b))
28.55/9.69	   A^2 -> H(d, U1(b, c))
28.55/9.69	   A^2 -> H(d, U1(b, d))
28.55/9.69	   A^2 -> H(d, U1(c, c))
28.55/9.69	   A^2 -> H(d, f(e))
28.55/9.69	   A^2 -> H(d, f(k))
28.55/9.69	   A^2 -> H(d, U1(d, d))
28.55/9.69	   A^2 -> H(a, U1(e, b))
28.55/9.69	   A^2 -> H(a, U1(k, b))
28.55/9.69	   A^2 -> H(a, U1(c, d))
28.55/9.69	   A^2 -> H(a, U1(d, c))
28.55/9.69	   A^2 -> H(a, U1(b, e))
28.55/9.69	   A^2 -> H(a, U1(b, k))
28.55/9.69	   A^2 -> H(a, U1(e, c))
28.55/9.69	   A^2 -> H(a, U1(k, c))
28.55/9.69	   A^2 -> H(a, U1(c, e))
28.55/9.69	   A^2 -> H(a, U1(c, k))
28.55/9.69	   A^2 -> H(a, U1(e, e))
28.55/9.69	   A^2 -> H(a, U1(k, k))
28.55/9.69	   A^2 -> H(a, U1(k, d))
28.55/9.69	   A^2 -> H(a, U1(d, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.69	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.69	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.69	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.69	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.69	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.69	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.69	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.69	   A^2 -> H(U1(e, a), b)
28.55/9.69	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.69	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.69	   A^2 -> H(U1(e, a), c)
28.55/9.69	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.69	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.69	   A^2 -> H(U1(e, a), e)
28.55/9.69	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, a), b)
28.55/9.69	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.69	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.69	   A^2 -> H(U1(k, a), c)
28.55/9.69	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.69	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.69	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, d), b)
28.55/9.69	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.69	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.69	   A^2 -> H(U1(c, d), c)
28.55/9.69	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.69	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.69	   A^2 -> H(U1(c, d), e)
28.55/9.69	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, a), d)
28.55/9.69	   A^2 -> H(U1(c, a), k)
28.55/9.69	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.69	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.69	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.69	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.69	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.69	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.69	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.69	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.69	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.69	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.69	   A^2 -> H(U1(d, c), b)
28.55/9.69	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.69	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.69	   A^2 -> H(U1(d, c), c)
28.55/9.69	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.69	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.69	   A^2 -> H(U1(d, c), e)
28.55/9.69	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(d, a), d)
28.55/9.69	   A^2 -> H(U1(d, a), k)
28.55/9.69	   A^2 -> H(U1(a, e), b)
28.55/9.69	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, e), c)
28.55/9.69	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, e), e)
28.55/9.69	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(a, k), b)
28.55/9.69	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, k), c)
28.55/9.69	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, k), e)
28.55/9.69	
28.55/9.69	The TRS R consists of the following rules:
28.55/9.69	
28.55/9.69	   f(x) -> U1(x, x)
28.55/9.69	   U1(e, x) -> x
28.55/9.69	   a -> c
28.55/9.69	   a -> d
28.55/9.69	   b -> c
28.55/9.69	   b -> d
28.55/9.69	   d -> k
28.55/9.69	   c -> e
28.55/9.69	   c -> k
28.55/9.69	
28.55/9.69	Q is empty.
28.55/9.69	We have to consider all minimal (P,Q,R)-chains.
28.55/9.69	----------------------------------------
28.55/9.69	
28.55/9.69	(1345) TransformationProof (EQUIVALENT)
28.55/9.69	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.69	
28.55/9.69	   (A^2 -> H(U1(c, k), U1(k, d)),A^2 -> H(U1(c, k), U1(k, d)))
28.55/9.69	   (A^2 -> H(U1(d, k), U1(k, d)),A^2 -> H(U1(d, k), U1(k, d)))
28.55/9.69	   (A^2 -> H(U1(a, k), U1(k, k)),A^2 -> H(U1(a, k), U1(k, k)))
28.55/9.69	
28.55/9.69	
28.55/9.69	----------------------------------------
28.55/9.69	
28.55/9.69	(1346)
28.55/9.69	Obligation:
28.55/9.69	Q DP problem:
28.55/9.69	The TRS P consists of the following rules:
28.55/9.69	
28.55/9.69	   H(x, x) -> G(x, x, f(k))
28.55/9.69	   G(d, x, x) -> A^2
28.55/9.69	   A^2 -> H(f(c), f(c))
28.55/9.69	   A^2 -> H(f(d), f(d))
28.55/9.69	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.69	   A^2 -> H(f(e), f(e))
28.55/9.69	   A^2 -> H(f(k), f(k))
28.55/9.69	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.69	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.69	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.69	   A^2 -> H(U1(a, k), U1(d, k))
28.55/9.69	   A^2 -> H(U1(a, c), b)
28.55/9.69	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, c), c)
28.55/9.69	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, c), e)
28.55/9.69	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(a, d), b)
28.55/9.69	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, d), c)
28.55/9.69	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, d), e)
28.55/9.69	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(a, a), d)
28.55/9.69	   A^2 -> H(U1(a, a), k)
28.55/9.69	   A^2 -> H(k, U1(b, b))
28.55/9.69	   A^2 -> H(k, f(c))
28.55/9.69	   A^2 -> H(k, f(d))
28.55/9.69	   A^2 -> H(c, U1(c, b))
28.55/9.69	   A^2 -> H(c, U1(d, b))
28.55/9.69	   A^2 -> H(c, U1(b, c))
28.55/9.69	   A^2 -> H(c, U1(b, d))
28.55/9.69	   A^2 -> H(c, U1(c, c))
28.55/9.69	   A^2 -> H(c, f(e))
28.55/9.69	   A^2 -> H(c, f(k))
28.55/9.69	   A^2 -> H(c, U1(d, d))
28.55/9.69	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.69	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.69	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.69	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.69	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.69	   A^2 -> H(U1(e, k), f(e))
28.55/9.69	   A^2 -> H(U1(e, k), f(k))
28.55/9.69	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.69	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.69	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.69	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.69	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.69	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.69	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.69	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.69	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.69	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.69	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.69	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.69	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.69	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.69	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.69	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.69	   A^2 -> H(U1(k, e), f(e))
28.55/9.69	   A^2 -> H(U1(k, e), f(k))
28.55/9.69	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.69	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.69	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.69	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.69	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.69	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.69	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.69	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.69	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.69	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.69	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.69	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.69	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.69	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.69	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.69	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.69	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.69	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.69	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.69	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.69	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.69	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.69	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.69	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.69	   A^2 -> H(U1(c, c), b)
28.55/9.69	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.69	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.69	   A^2 -> H(U1(c, c), e)
28.55/9.69	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.69	   A^2 -> H(e, U1(c, b))
28.55/9.69	   A^2 -> H(e, U1(d, b))
28.55/9.69	   A^2 -> H(e, U1(b, c))
28.55/9.69	   A^2 -> H(e, U1(b, d))
28.55/9.69	   A^2 -> H(e, U1(c, c))
28.55/9.69	   A^2 -> H(e, f(e))
28.55/9.69	   A^2 -> H(e, f(k))
28.55/9.69	   A^2 -> H(e, U1(d, d))
28.55/9.69	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.69	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.69	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.69	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.69	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.69	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.69	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.69	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.69	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.69	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.69	   A^2 -> H(f(e), b)
28.55/9.69	   A^2 -> H(f(e), U1(e, d))
28.55/9.69	   A^2 -> H(f(e), U1(d, e))
28.55/9.69	   A^2 -> H(f(e), c)
28.55/9.69	   A^2 -> H(f(e), U1(e, k))
28.55/9.69	   A^2 -> H(f(e), U1(k, e))
28.55/9.69	   A^2 -> H(f(e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.69	   A^2 -> H(f(k), b)
28.55/9.69	   A^2 -> H(f(k), U1(e, d))
28.55/9.69	   A^2 -> H(f(k), U1(d, e))
28.55/9.69	   A^2 -> H(f(k), c)
28.55/9.69	   A^2 -> H(f(k), U1(e, k))
28.55/9.69	   A^2 -> H(f(k), U1(k, e))
28.55/9.69	   A^2 -> H(f(k), e)
28.55/9.69	   A^2 -> H(f(c), d)
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.69	   A^2 -> H(U1(k, k), f(e))
28.55/9.69	   A^2 -> H(U1(k, k), f(k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.69	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.69	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.69	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.69	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.69	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.69	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.69	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.69	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.69	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.69	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.69	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.69	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.69	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.69	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.69	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.69	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.69	   A^2 -> H(U1(d, d), b)
28.55/9.69	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.69	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.69	   A^2 -> H(U1(d, d), c)
28.55/9.69	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.69	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.69	   A^2 -> H(U1(d, d), e)
28.55/9.69	   A^2 -> H(f(d), d)
28.55/9.69	   A^2 -> H(f(d), k)
28.55/9.69	   A^2 -> H(U1(c, c), c)
28.55/9.69	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.69	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.69	   A^2 -> H(f(c), k)
28.55/9.69	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.69	   A^2 -> H(f(k), U1(k, k))
28.55/9.69	   A^2 -> H(f(e), e)
28.55/9.69	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.69	   A^2 -> H(d, U1(c, b))
28.55/9.69	   A^2 -> H(d, U1(d, b))
28.55/9.69	   A^2 -> H(d, U1(b, c))
28.55/9.69	   A^2 -> H(d, U1(b, d))
28.55/9.69	   A^2 -> H(d, U1(c, c))
28.55/9.69	   A^2 -> H(d, f(e))
28.55/9.69	   A^2 -> H(d, f(k))
28.55/9.69	   A^2 -> H(d, U1(d, d))
28.55/9.69	   A^2 -> H(a, U1(e, b))
28.55/9.69	   A^2 -> H(a, U1(k, b))
28.55/9.69	   A^2 -> H(a, U1(c, d))
28.55/9.69	   A^2 -> H(a, U1(d, c))
28.55/9.69	   A^2 -> H(a, U1(b, e))
28.55/9.69	   A^2 -> H(a, U1(b, k))
28.55/9.69	   A^2 -> H(a, U1(e, c))
28.55/9.69	   A^2 -> H(a, U1(k, c))
28.55/9.69	   A^2 -> H(a, U1(c, e))
28.55/9.69	   A^2 -> H(a, U1(c, k))
28.55/9.69	   A^2 -> H(a, U1(e, e))
28.55/9.69	   A^2 -> H(a, U1(k, k))
28.55/9.69	   A^2 -> H(a, U1(k, d))
28.55/9.69	   A^2 -> H(a, U1(d, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.69	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.69	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.69	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.69	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.69	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.69	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.69	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.69	   A^2 -> H(U1(e, a), b)
28.55/9.69	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.69	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.69	   A^2 -> H(U1(e, a), c)
28.55/9.69	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.69	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.69	   A^2 -> H(U1(e, a), e)
28.55/9.69	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, a), b)
28.55/9.69	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.69	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.69	   A^2 -> H(U1(k, a), c)
28.55/9.69	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.69	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.69	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, d), b)
28.55/9.69	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.69	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.69	   A^2 -> H(U1(c, d), c)
28.55/9.69	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.69	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.69	   A^2 -> H(U1(c, d), e)
28.55/9.69	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, a), d)
28.55/9.69	   A^2 -> H(U1(c, a), k)
28.55/9.69	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.69	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.69	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.69	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.69	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.69	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.69	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.69	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.69	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.69	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.69	   A^2 -> H(U1(d, c), b)
28.55/9.69	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.69	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.69	   A^2 -> H(U1(d, c), c)
28.55/9.69	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.69	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.69	   A^2 -> H(U1(d, c), e)
28.55/9.69	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(d, a), d)
28.55/9.69	   A^2 -> H(U1(d, a), k)
28.55/9.69	   A^2 -> H(U1(a, e), b)
28.55/9.69	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, e), c)
28.55/9.69	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, e), e)
28.55/9.69	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(a, k), b)
28.55/9.69	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, k), c)
28.55/9.69	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, k), e)
28.55/9.69	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.69	
28.55/9.69	The TRS R consists of the following rules:
28.55/9.69	
28.55/9.69	   f(x) -> U1(x, x)
28.55/9.69	   U1(e, x) -> x
28.55/9.69	   a -> c
28.55/9.69	   a -> d
28.55/9.69	   b -> c
28.55/9.69	   b -> d
28.55/9.69	   d -> k
28.55/9.69	   c -> e
28.55/9.69	   c -> k
28.55/9.69	
28.55/9.69	Q is empty.
28.55/9.69	We have to consider all minimal (P,Q,R)-chains.
28.55/9.69	----------------------------------------
28.55/9.69	
28.55/9.69	(1347) TransformationProof (EQUIVALENT)
28.55/9.69	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.69	
28.55/9.69	   (A^2 -> H(U1(c, k), U1(d, k)),A^2 -> H(U1(c, k), U1(d, k)))
28.55/9.69	   (A^2 -> H(U1(d, k), U1(d, k)),A^2 -> H(U1(d, k), U1(d, k)))
28.55/9.69	   (A^2 -> H(U1(a, k), U1(k, k)),A^2 -> H(U1(a, k), U1(k, k)))
28.55/9.69	
28.55/9.69	
28.55/9.69	----------------------------------------
28.55/9.69	
28.55/9.69	(1348)
28.55/9.69	Obligation:
28.55/9.69	Q DP problem:
28.55/9.69	The TRS P consists of the following rules:
28.55/9.69	
28.55/9.69	   H(x, x) -> G(x, x, f(k))
28.55/9.69	   G(d, x, x) -> A^2
28.55/9.69	   A^2 -> H(f(c), f(c))
28.55/9.69	   A^2 -> H(f(d), f(d))
28.55/9.69	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.69	   A^2 -> H(f(e), f(e))
28.55/9.69	   A^2 -> H(f(k), f(k))
28.55/9.69	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.69	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.69	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.69	   A^2 -> H(U1(a, c), b)
28.55/9.69	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, c), c)
28.55/9.69	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, c), e)
28.55/9.69	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(a, d), b)
28.55/9.69	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, d), c)
28.55/9.69	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, d), e)
28.55/9.69	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(a, a), d)
28.55/9.69	   A^2 -> H(U1(a, a), k)
28.55/9.69	   A^2 -> H(k, U1(b, b))
28.55/9.69	   A^2 -> H(k, f(c))
28.55/9.69	   A^2 -> H(k, f(d))
28.55/9.69	   A^2 -> H(c, U1(c, b))
28.55/9.69	   A^2 -> H(c, U1(d, b))
28.55/9.69	   A^2 -> H(c, U1(b, c))
28.55/9.69	   A^2 -> H(c, U1(b, d))
28.55/9.69	   A^2 -> H(c, U1(c, c))
28.55/9.69	   A^2 -> H(c, f(e))
28.55/9.69	   A^2 -> H(c, f(k))
28.55/9.69	   A^2 -> H(c, U1(d, d))
28.55/9.69	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.69	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.69	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.69	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.69	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.69	   A^2 -> H(U1(e, k), f(e))
28.55/9.69	   A^2 -> H(U1(e, k), f(k))
28.55/9.69	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.69	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.69	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.69	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.69	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.69	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.69	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.69	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.69	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.69	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.69	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.69	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.69	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.69	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.69	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.69	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.69	   A^2 -> H(U1(k, e), f(e))
28.55/9.69	   A^2 -> H(U1(k, e), f(k))
28.55/9.69	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.69	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.69	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.69	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.69	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.69	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.69	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.69	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.69	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.69	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.69	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.69	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.69	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.69	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.69	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.69	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.69	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.69	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.69	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.69	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.69	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.69	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.69	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.69	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.69	   A^2 -> H(U1(c, c), b)
28.55/9.69	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.69	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.69	   A^2 -> H(U1(c, c), e)
28.55/9.69	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.69	   A^2 -> H(e, U1(c, b))
28.55/9.69	   A^2 -> H(e, U1(d, b))
28.55/9.69	   A^2 -> H(e, U1(b, c))
28.55/9.69	   A^2 -> H(e, U1(b, d))
28.55/9.69	   A^2 -> H(e, U1(c, c))
28.55/9.69	   A^2 -> H(e, f(e))
28.55/9.69	   A^2 -> H(e, f(k))
28.55/9.69	   A^2 -> H(e, U1(d, d))
28.55/9.69	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.69	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.69	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.69	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.69	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.69	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.69	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.69	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.69	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.69	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.69	   A^2 -> H(f(e), b)
28.55/9.69	   A^2 -> H(f(e), U1(e, d))
28.55/9.69	   A^2 -> H(f(e), U1(d, e))
28.55/9.69	   A^2 -> H(f(e), c)
28.55/9.69	   A^2 -> H(f(e), U1(e, k))
28.55/9.69	   A^2 -> H(f(e), U1(k, e))
28.55/9.69	   A^2 -> H(f(e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.69	   A^2 -> H(f(k), b)
28.55/9.69	   A^2 -> H(f(k), U1(e, d))
28.55/9.69	   A^2 -> H(f(k), U1(d, e))
28.55/9.69	   A^2 -> H(f(k), c)
28.55/9.69	   A^2 -> H(f(k), U1(e, k))
28.55/9.69	   A^2 -> H(f(k), U1(k, e))
28.55/9.69	   A^2 -> H(f(k), e)
28.55/9.69	   A^2 -> H(f(c), d)
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.69	   A^2 -> H(U1(k, k), f(e))
28.55/9.69	   A^2 -> H(U1(k, k), f(k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.69	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.69	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.69	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.69	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.69	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.69	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.69	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.69	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.69	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.69	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.69	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.69	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.69	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.69	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.69	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.69	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.69	   A^2 -> H(U1(d, d), b)
28.55/9.69	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.69	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.69	   A^2 -> H(U1(d, d), c)
28.55/9.69	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.69	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.69	   A^2 -> H(U1(d, d), e)
28.55/9.69	   A^2 -> H(f(d), d)
28.55/9.69	   A^2 -> H(f(d), k)
28.55/9.69	   A^2 -> H(U1(c, c), c)
28.55/9.69	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.69	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.69	   A^2 -> H(f(c), k)
28.55/9.69	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.69	   A^2 -> H(f(k), U1(k, k))
28.55/9.69	   A^2 -> H(f(e), e)
28.55/9.69	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.69	   A^2 -> H(d, U1(c, b))
28.55/9.69	   A^2 -> H(d, U1(d, b))
28.55/9.69	   A^2 -> H(d, U1(b, c))
28.55/9.69	   A^2 -> H(d, U1(b, d))
28.55/9.69	   A^2 -> H(d, U1(c, c))
28.55/9.69	   A^2 -> H(d, f(e))
28.55/9.69	   A^2 -> H(d, f(k))
28.55/9.69	   A^2 -> H(d, U1(d, d))
28.55/9.69	   A^2 -> H(a, U1(e, b))
28.55/9.69	   A^2 -> H(a, U1(k, b))
28.55/9.69	   A^2 -> H(a, U1(c, d))
28.55/9.69	   A^2 -> H(a, U1(d, c))
28.55/9.69	   A^2 -> H(a, U1(b, e))
28.55/9.69	   A^2 -> H(a, U1(b, k))
28.55/9.69	   A^2 -> H(a, U1(e, c))
28.55/9.69	   A^2 -> H(a, U1(k, c))
28.55/9.69	   A^2 -> H(a, U1(c, e))
28.55/9.69	   A^2 -> H(a, U1(c, k))
28.55/9.69	   A^2 -> H(a, U1(e, e))
28.55/9.69	   A^2 -> H(a, U1(k, k))
28.55/9.69	   A^2 -> H(a, U1(k, d))
28.55/9.69	   A^2 -> H(a, U1(d, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.69	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.69	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.69	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.69	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.69	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.69	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.69	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.69	   A^2 -> H(U1(e, a), b)
28.55/9.69	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.69	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.69	   A^2 -> H(U1(e, a), c)
28.55/9.69	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.69	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.69	   A^2 -> H(U1(e, a), e)
28.55/9.69	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, a), b)
28.55/9.69	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.69	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.69	   A^2 -> H(U1(k, a), c)
28.55/9.69	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.69	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.69	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, d), b)
28.55/9.69	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.69	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.69	   A^2 -> H(U1(c, d), c)
28.55/9.69	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.69	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.69	   A^2 -> H(U1(c, d), e)
28.55/9.69	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, a), d)
28.55/9.69	   A^2 -> H(U1(c, a), k)
28.55/9.69	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.69	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.69	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.69	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.69	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.69	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.69	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.69	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.69	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.69	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.69	   A^2 -> H(U1(d, c), b)
28.55/9.69	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.69	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.69	   A^2 -> H(U1(d, c), c)
28.55/9.69	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.69	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.69	   A^2 -> H(U1(d, c), e)
28.55/9.69	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(d, a), d)
28.55/9.69	   A^2 -> H(U1(d, a), k)
28.55/9.69	   A^2 -> H(U1(a, e), b)
28.55/9.69	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, e), c)
28.55/9.69	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, e), e)
28.55/9.69	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(a, k), b)
28.55/9.69	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, k), c)
28.55/9.69	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, k), e)
28.55/9.69	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.69	
28.55/9.69	The TRS R consists of the following rules:
28.55/9.69	
28.55/9.69	   f(x) -> U1(x, x)
28.55/9.69	   U1(e, x) -> x
28.55/9.69	   a -> c
28.55/9.69	   a -> d
28.55/9.69	   b -> c
28.55/9.69	   b -> d
28.55/9.69	   d -> k
28.55/9.69	   c -> e
28.55/9.69	   c -> k
28.55/9.69	
28.55/9.69	Q is empty.
28.55/9.69	We have to consider all minimal (P,Q,R)-chains.
28.55/9.69	----------------------------------------
28.55/9.69	
28.55/9.69	(1349) TransformationProof (EQUIVALENT)
28.55/9.69	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), b) at position [] we obtained the following new rules [LPAR04]:
28.55/9.69	
28.55/9.69	   (A^2 -> H(U1(c, c), b),A^2 -> H(U1(c, c), b))
28.55/9.69	   (A^2 -> H(U1(d, c), b),A^2 -> H(U1(d, c), b))
28.55/9.69	   (A^2 -> H(U1(a, e), b),A^2 -> H(U1(a, e), b))
28.55/9.69	   (A^2 -> H(U1(a, k), b),A^2 -> H(U1(a, k), b))
28.55/9.69	   (A^2 -> H(U1(a, c), c),A^2 -> H(U1(a, c), c))
28.55/9.69	   (A^2 -> H(U1(a, c), d),A^2 -> H(U1(a, c), d))
28.55/9.69	
28.55/9.69	
28.55/9.69	----------------------------------------
28.55/9.69	
28.55/9.69	(1350)
28.55/9.69	Obligation:
28.55/9.69	Q DP problem:
28.55/9.69	The TRS P consists of the following rules:
28.55/9.69	
28.55/9.69	   H(x, x) -> G(x, x, f(k))
28.55/9.69	   G(d, x, x) -> A^2
28.55/9.69	   A^2 -> H(f(c), f(c))
28.55/9.69	   A^2 -> H(f(d), f(d))
28.55/9.69	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.69	   A^2 -> H(f(e), f(e))
28.55/9.69	   A^2 -> H(f(k), f(k))
28.55/9.69	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.69	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.69	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.69	   A^2 -> H(U1(a, c), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, c), c)
28.55/9.69	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, c), e)
28.55/9.69	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(a, d), b)
28.55/9.69	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, d), c)
28.55/9.69	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, d), e)
28.55/9.69	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(a, a), d)
28.55/9.69	   A^2 -> H(U1(a, a), k)
28.55/9.69	   A^2 -> H(k, U1(b, b))
28.55/9.69	   A^2 -> H(k, f(c))
28.55/9.69	   A^2 -> H(k, f(d))
28.55/9.69	   A^2 -> H(c, U1(c, b))
28.55/9.69	   A^2 -> H(c, U1(d, b))
28.55/9.69	   A^2 -> H(c, U1(b, c))
28.55/9.69	   A^2 -> H(c, U1(b, d))
28.55/9.69	   A^2 -> H(c, U1(c, c))
28.55/9.69	   A^2 -> H(c, f(e))
28.55/9.69	   A^2 -> H(c, f(k))
28.55/9.69	   A^2 -> H(c, U1(d, d))
28.55/9.69	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.69	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.69	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.69	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.69	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.69	   A^2 -> H(U1(e, k), f(e))
28.55/9.69	   A^2 -> H(U1(e, k), f(k))
28.55/9.69	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.69	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.69	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.69	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.69	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.69	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.69	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.69	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.69	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.69	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.69	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.69	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.69	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.69	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.69	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.69	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.69	   A^2 -> H(U1(k, e), f(e))
28.55/9.69	   A^2 -> H(U1(k, e), f(k))
28.55/9.69	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.69	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.69	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.69	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.69	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.69	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.69	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.69	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.69	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.69	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.69	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.69	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.69	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.69	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.69	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.69	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.69	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.69	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.69	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.69	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.69	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.69	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.69	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.69	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.69	   A^2 -> H(U1(c, c), b)
28.55/9.69	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.69	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.69	   A^2 -> H(U1(c, c), e)
28.55/9.69	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.69	   A^2 -> H(e, U1(c, b))
28.55/9.69	   A^2 -> H(e, U1(d, b))
28.55/9.69	   A^2 -> H(e, U1(b, c))
28.55/9.69	   A^2 -> H(e, U1(b, d))
28.55/9.69	   A^2 -> H(e, U1(c, c))
28.55/9.69	   A^2 -> H(e, f(e))
28.55/9.69	   A^2 -> H(e, f(k))
28.55/9.69	   A^2 -> H(e, U1(d, d))
28.55/9.69	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.69	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.69	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.69	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.69	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.69	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.69	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.69	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.69	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.69	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.69	   A^2 -> H(f(e), b)
28.55/9.69	   A^2 -> H(f(e), U1(e, d))
28.55/9.69	   A^2 -> H(f(e), U1(d, e))
28.55/9.69	   A^2 -> H(f(e), c)
28.55/9.69	   A^2 -> H(f(e), U1(e, k))
28.55/9.69	   A^2 -> H(f(e), U1(k, e))
28.55/9.69	   A^2 -> H(f(e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.69	   A^2 -> H(f(k), b)
28.55/9.69	   A^2 -> H(f(k), U1(e, d))
28.55/9.69	   A^2 -> H(f(k), U1(d, e))
28.55/9.69	   A^2 -> H(f(k), c)
28.55/9.69	   A^2 -> H(f(k), U1(e, k))
28.55/9.69	   A^2 -> H(f(k), U1(k, e))
28.55/9.69	   A^2 -> H(f(k), e)
28.55/9.69	   A^2 -> H(f(c), d)
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.69	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.69	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.69	   A^2 -> H(U1(k, k), f(e))
28.55/9.69	   A^2 -> H(U1(k, k), f(k))
28.55/9.69	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.69	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.69	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.69	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.69	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.69	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.69	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.69	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.69	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.69	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.69	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.69	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.69	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.69	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.69	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.69	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.69	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.69	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.69	   A^2 -> H(U1(d, d), b)
28.55/9.69	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.69	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.69	   A^2 -> H(U1(d, d), c)
28.55/9.69	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.69	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.69	   A^2 -> H(U1(d, d), e)
28.55/9.69	   A^2 -> H(f(d), d)
28.55/9.69	   A^2 -> H(f(d), k)
28.55/9.69	   A^2 -> H(U1(c, c), c)
28.55/9.69	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.69	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.69	   A^2 -> H(f(c), k)
28.55/9.69	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.69	   A^2 -> H(f(k), U1(k, k))
28.55/9.69	   A^2 -> H(f(e), e)
28.55/9.69	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.69	   A^2 -> H(d, U1(c, b))
28.55/9.69	   A^2 -> H(d, U1(d, b))
28.55/9.69	   A^2 -> H(d, U1(b, c))
28.55/9.69	   A^2 -> H(d, U1(b, d))
28.55/9.69	   A^2 -> H(d, U1(c, c))
28.55/9.69	   A^2 -> H(d, f(e))
28.55/9.69	   A^2 -> H(d, f(k))
28.55/9.69	   A^2 -> H(d, U1(d, d))
28.55/9.69	   A^2 -> H(a, U1(e, b))
28.55/9.69	   A^2 -> H(a, U1(k, b))
28.55/9.69	   A^2 -> H(a, U1(c, d))
28.55/9.69	   A^2 -> H(a, U1(d, c))
28.55/9.69	   A^2 -> H(a, U1(b, e))
28.55/9.69	   A^2 -> H(a, U1(b, k))
28.55/9.69	   A^2 -> H(a, U1(e, c))
28.55/9.69	   A^2 -> H(a, U1(k, c))
28.55/9.69	   A^2 -> H(a, U1(c, e))
28.55/9.69	   A^2 -> H(a, U1(c, k))
28.55/9.69	   A^2 -> H(a, U1(e, e))
28.55/9.69	   A^2 -> H(a, U1(k, k))
28.55/9.69	   A^2 -> H(a, U1(k, d))
28.55/9.69	   A^2 -> H(a, U1(d, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.69	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.69	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.69	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.69	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.69	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.69	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.69	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.69	   A^2 -> H(U1(e, a), b)
28.55/9.69	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.69	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.69	   A^2 -> H(U1(e, a), c)
28.55/9.69	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.69	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.69	   A^2 -> H(U1(e, a), e)
28.55/9.69	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.69	   A^2 -> H(U1(k, a), b)
28.55/9.69	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.69	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.69	   A^2 -> H(U1(k, a), c)
28.55/9.69	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.69	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.69	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, d), b)
28.55/9.69	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.69	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.69	   A^2 -> H(U1(c, d), c)
28.55/9.69	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.69	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.69	   A^2 -> H(U1(c, d), e)
28.55/9.69	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.69	   A^2 -> H(U1(c, a), d)
28.55/9.69	   A^2 -> H(U1(c, a), k)
28.55/9.69	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.69	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.69	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.69	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.69	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.69	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.69	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.69	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.69	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.69	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.69	   A^2 -> H(U1(d, c), b)
28.55/9.69	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.69	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.69	   A^2 -> H(U1(d, c), c)
28.55/9.69	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.69	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.69	   A^2 -> H(U1(d, c), e)
28.55/9.69	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.69	   A^2 -> H(U1(d, a), d)
28.55/9.69	   A^2 -> H(U1(d, a), k)
28.55/9.69	   A^2 -> H(U1(a, e), b)
28.55/9.69	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, e), c)
28.55/9.69	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, e), e)
28.55/9.69	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.69	   A^2 -> H(U1(a, k), b)
28.55/9.69	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.69	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.69	   A^2 -> H(U1(a, k), c)
28.55/9.69	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.69	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.69	   A^2 -> H(U1(a, k), e)
28.55/9.69	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.69	   A^2 -> H(U1(a, c), d)
28.55/9.69	
28.55/9.69	The TRS R consists of the following rules:
28.55/9.69	
28.55/9.69	   f(x) -> U1(x, x)
28.55/9.69	   U1(e, x) -> x
28.55/9.69	   a -> c
28.55/9.69	   a -> d
28.55/9.69	   b -> c
28.55/9.69	   b -> d
28.55/9.69	   d -> k
28.55/9.69	   c -> e
28.55/9.69	   c -> k
28.55/9.69	
28.55/9.69	Q is empty.
28.55/9.69	We have to consider all minimal (P,Q,R)-chains.
28.55/9.69	----------------------------------------
28.55/9.69	
28.55/9.69	(1351) TransformationProof (EQUIVALENT)
28.55/9.69	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.69	
28.55/9.69	   (A^2 -> H(U1(c, c), U1(e, d)),A^2 -> H(U1(c, c), U1(e, d)))
28.55/9.69	   (A^2 -> H(U1(d, c), U1(e, d)),A^2 -> H(U1(d, c), U1(e, d)))
28.55/9.69	   (A^2 -> H(U1(a, e), U1(e, d)),A^2 -> H(U1(a, e), U1(e, d)))
28.55/9.69	   (A^2 -> H(U1(a, k), U1(e, d)),A^2 -> H(U1(a, k), U1(e, d)))
28.55/9.69	   (A^2 -> H(U1(a, c), d),A^2 -> H(U1(a, c), d))
28.55/9.69	   (A^2 -> H(U1(a, c), U1(e, k)),A^2 -> H(U1(a, c), U1(e, k)))
28.55/9.69	
28.55/9.69	
28.55/9.69	----------------------------------------
28.55/9.69	
28.55/9.69	(1352)
28.55/9.69	Obligation:
28.55/9.69	Q DP problem:
28.55/9.69	The TRS P consists of the following rules:
28.55/9.70	
28.55/9.70	   H(x, x) -> G(x, x, f(k))
28.55/9.70	   G(d, x, x) -> A^2
28.55/9.70	   A^2 -> H(f(c), f(c))
28.55/9.70	   A^2 -> H(f(d), f(d))
28.55/9.70	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.70	   A^2 -> H(f(e), f(e))
28.55/9.70	   A^2 -> H(f(k), f(k))
28.55/9.70	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.70	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.70	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.70	   A^2 -> H(U1(a, c), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, c), c)
28.55/9.70	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, c), e)
28.55/9.70	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, d), b)
28.55/9.70	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.70	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, d), c)
28.55/9.70	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, d), e)
28.55/9.70	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, a), d)
28.55/9.70	   A^2 -> H(U1(a, a), k)
28.55/9.70	   A^2 -> H(k, U1(b, b))
28.55/9.70	   A^2 -> H(k, f(c))
28.55/9.70	   A^2 -> H(k, f(d))
28.55/9.70	   A^2 -> H(c, U1(c, b))
28.55/9.70	   A^2 -> H(c, U1(d, b))
28.55/9.70	   A^2 -> H(c, U1(b, c))
28.55/9.70	   A^2 -> H(c, U1(b, d))
28.55/9.70	   A^2 -> H(c, U1(c, c))
28.55/9.70	   A^2 -> H(c, f(e))
28.55/9.70	   A^2 -> H(c, f(k))
28.55/9.70	   A^2 -> H(c, U1(d, d))
28.55/9.70	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.70	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.70	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.70	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.70	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.70	   A^2 -> H(U1(e, k), f(e))
28.55/9.70	   A^2 -> H(U1(e, k), f(k))
28.55/9.70	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.70	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.70	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.70	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.70	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.70	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.70	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.70	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.70	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.70	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.70	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.70	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.70	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.70	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.70	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.70	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.70	   A^2 -> H(U1(k, e), f(e))
28.55/9.70	   A^2 -> H(U1(k, e), f(k))
28.55/9.70	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.70	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.70	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.70	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.70	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.70	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.70	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.70	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.70	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.70	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.70	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.70	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.70	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.70	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.70	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.70	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.70	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.70	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.70	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.70	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.70	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.70	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.70	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.70	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.70	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.70	   A^2 -> H(U1(c, c), b)
28.55/9.70	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.70	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.70	   A^2 -> H(U1(c, c), e)
28.55/9.70	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.70	   A^2 -> H(e, U1(c, b))
28.55/9.70	   A^2 -> H(e, U1(d, b))
28.55/9.70	   A^2 -> H(e, U1(b, c))
28.55/9.70	   A^2 -> H(e, U1(b, d))
28.55/9.70	   A^2 -> H(e, U1(c, c))
28.55/9.70	   A^2 -> H(e, f(e))
28.55/9.70	   A^2 -> H(e, f(k))
28.55/9.70	   A^2 -> H(e, U1(d, d))
28.55/9.70	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.70	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.70	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.70	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.70	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.70	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.70	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.70	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.70	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.70	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.70	   A^2 -> H(f(e), b)
28.55/9.70	   A^2 -> H(f(e), U1(e, d))
28.55/9.70	   A^2 -> H(f(e), U1(d, e))
28.55/9.70	   A^2 -> H(f(e), c)
28.55/9.70	   A^2 -> H(f(e), U1(e, k))
28.55/9.70	   A^2 -> H(f(e), U1(k, e))
28.55/9.70	   A^2 -> H(f(e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.70	   A^2 -> H(f(k), b)
28.55/9.70	   A^2 -> H(f(k), U1(e, d))
28.55/9.70	   A^2 -> H(f(k), U1(d, e))
28.55/9.70	   A^2 -> H(f(k), c)
28.55/9.70	   A^2 -> H(f(k), U1(e, k))
28.55/9.70	   A^2 -> H(f(k), U1(k, e))
28.55/9.70	   A^2 -> H(f(k), e)
28.55/9.70	   A^2 -> H(f(c), d)
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.70	   A^2 -> H(U1(k, k), f(e))
28.55/9.70	   A^2 -> H(U1(k, k), f(k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.70	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.70	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.70	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.70	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.70	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.70	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.70	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.70	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.70	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.70	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.70	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.70	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.70	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.70	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.70	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.70	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.70	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.70	   A^2 -> H(U1(d, d), b)
28.55/9.70	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.70	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.70	   A^2 -> H(U1(d, d), c)
28.55/9.70	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.70	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.70	   A^2 -> H(U1(d, d), e)
28.55/9.70	   A^2 -> H(f(d), d)
28.55/9.70	   A^2 -> H(f(d), k)
28.55/9.70	   A^2 -> H(U1(c, c), c)
28.55/9.70	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.70	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.70	   A^2 -> H(f(c), k)
28.55/9.70	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.70	   A^2 -> H(f(k), U1(k, k))
28.55/9.70	   A^2 -> H(f(e), e)
28.55/9.70	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.70	   A^2 -> H(d, U1(c, b))
28.55/9.70	   A^2 -> H(d, U1(d, b))
28.55/9.70	   A^2 -> H(d, U1(b, c))
28.55/9.70	   A^2 -> H(d, U1(b, d))
28.55/9.70	   A^2 -> H(d, U1(c, c))
28.55/9.70	   A^2 -> H(d, f(e))
28.55/9.70	   A^2 -> H(d, f(k))
28.55/9.70	   A^2 -> H(d, U1(d, d))
28.55/9.70	   A^2 -> H(a, U1(e, b))
28.55/9.70	   A^2 -> H(a, U1(k, b))
28.55/9.70	   A^2 -> H(a, U1(c, d))
28.55/9.70	   A^2 -> H(a, U1(d, c))
28.55/9.70	   A^2 -> H(a, U1(b, e))
28.55/9.70	   A^2 -> H(a, U1(b, k))
28.55/9.70	   A^2 -> H(a, U1(e, c))
28.55/9.70	   A^2 -> H(a, U1(k, c))
28.55/9.70	   A^2 -> H(a, U1(c, e))
28.55/9.70	   A^2 -> H(a, U1(c, k))
28.55/9.70	   A^2 -> H(a, U1(e, e))
28.55/9.70	   A^2 -> H(a, U1(k, k))
28.55/9.70	   A^2 -> H(a, U1(k, d))
28.55/9.70	   A^2 -> H(a, U1(d, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.70	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.70	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.70	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.70	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.70	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.70	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.70	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.70	   A^2 -> H(U1(e, a), b)
28.55/9.70	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.70	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.70	   A^2 -> H(U1(e, a), c)
28.55/9.70	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.70	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.70	   A^2 -> H(U1(e, a), e)
28.55/9.70	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, a), b)
28.55/9.70	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.70	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.70	   A^2 -> H(U1(k, a), c)
28.55/9.70	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.70	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.70	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, d), b)
28.55/9.70	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.70	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.70	   A^2 -> H(U1(c, d), c)
28.55/9.70	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.70	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.70	   A^2 -> H(U1(c, d), e)
28.55/9.70	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, a), d)
28.55/9.70	   A^2 -> H(U1(c, a), k)
28.55/9.70	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.70	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.70	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.70	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.70	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.70	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.70	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.70	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.70	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.70	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.70	   A^2 -> H(U1(d, c), b)
28.55/9.70	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.70	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.70	   A^2 -> H(U1(d, c), c)
28.55/9.70	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.70	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.70	   A^2 -> H(U1(d, c), e)
28.55/9.70	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(d, a), d)
28.55/9.70	   A^2 -> H(U1(d, a), k)
28.55/9.70	   A^2 -> H(U1(a, e), b)
28.55/9.70	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.70	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, e), c)
28.55/9.70	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, e), e)
28.55/9.70	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, k), b)
28.55/9.70	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.70	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, k), c)
28.55/9.70	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, k), e)
28.55/9.70	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, c), d)
28.55/9.70	
28.55/9.70	The TRS R consists of the following rules:
28.55/9.70	
28.55/9.70	   f(x) -> U1(x, x)
28.55/9.70	   U1(e, x) -> x
28.55/9.70	   a -> c
28.55/9.70	   a -> d
28.55/9.70	   b -> c
28.55/9.70	   b -> d
28.55/9.70	   d -> k
28.55/9.70	   c -> e
28.55/9.70	   c -> k
28.55/9.70	
28.55/9.70	Q is empty.
28.55/9.70	We have to consider all minimal (P,Q,R)-chains.
28.55/9.70	----------------------------------------
28.55/9.70	
28.55/9.70	(1353) TransformationProof (EQUIVALENT)
28.55/9.70	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.70	
28.55/9.70	   (A^2 -> H(U1(c, c), U1(d, e)),A^2 -> H(U1(c, c), U1(d, e)))
28.55/9.70	   (A^2 -> H(U1(d, c), U1(d, e)),A^2 -> H(U1(d, c), U1(d, e)))
28.55/9.70	   (A^2 -> H(U1(a, e), U1(d, e)),A^2 -> H(U1(a, e), U1(d, e)))
28.55/9.70	   (A^2 -> H(U1(a, k), U1(d, e)),A^2 -> H(U1(a, k), U1(d, e)))
28.55/9.70	   (A^2 -> H(U1(a, c), U1(k, e)),A^2 -> H(U1(a, c), U1(k, e)))
28.55/9.70	
28.55/9.70	
28.55/9.70	----------------------------------------
28.55/9.70	
28.55/9.70	(1354)
28.55/9.70	Obligation:
28.55/9.70	Q DP problem:
28.55/9.70	The TRS P consists of the following rules:
28.55/9.70	
28.55/9.70	   H(x, x) -> G(x, x, f(k))
28.55/9.70	   G(d, x, x) -> A^2
28.55/9.70	   A^2 -> H(f(c), f(c))
28.55/9.70	   A^2 -> H(f(d), f(d))
28.55/9.70	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.70	   A^2 -> H(f(e), f(e))
28.55/9.70	   A^2 -> H(f(k), f(k))
28.55/9.70	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.70	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.70	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.70	   A^2 -> H(U1(a, c), c)
28.55/9.70	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, c), e)
28.55/9.70	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, d), b)
28.55/9.70	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.70	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, d), c)
28.55/9.70	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, d), e)
28.55/9.70	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, a), d)
28.55/9.70	   A^2 -> H(U1(a, a), k)
28.55/9.70	   A^2 -> H(k, U1(b, b))
28.55/9.70	   A^2 -> H(k, f(c))
28.55/9.70	   A^2 -> H(k, f(d))
28.55/9.70	   A^2 -> H(c, U1(c, b))
28.55/9.70	   A^2 -> H(c, U1(d, b))
28.55/9.70	   A^2 -> H(c, U1(b, c))
28.55/9.70	   A^2 -> H(c, U1(b, d))
28.55/9.70	   A^2 -> H(c, U1(c, c))
28.55/9.70	   A^2 -> H(c, f(e))
28.55/9.70	   A^2 -> H(c, f(k))
28.55/9.70	   A^2 -> H(c, U1(d, d))
28.55/9.70	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.70	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.70	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.70	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.70	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.70	   A^2 -> H(U1(e, k), f(e))
28.55/9.70	   A^2 -> H(U1(e, k), f(k))
28.55/9.70	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.70	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.70	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.70	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.70	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.70	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.70	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.70	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.70	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.70	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.70	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.70	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.70	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.70	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.70	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.70	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.70	   A^2 -> H(U1(k, e), f(e))
28.55/9.70	   A^2 -> H(U1(k, e), f(k))
28.55/9.70	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.70	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.70	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.70	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.70	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.70	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.70	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.70	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.70	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.70	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.70	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.70	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.70	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.70	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.70	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.70	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.70	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.70	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.70	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.70	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.70	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.70	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.70	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.70	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.70	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.70	   A^2 -> H(U1(c, c), b)
28.55/9.70	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.70	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.70	   A^2 -> H(U1(c, c), e)
28.55/9.70	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.70	   A^2 -> H(e, U1(c, b))
28.55/9.70	   A^2 -> H(e, U1(d, b))
28.55/9.70	   A^2 -> H(e, U1(b, c))
28.55/9.70	   A^2 -> H(e, U1(b, d))
28.55/9.70	   A^2 -> H(e, U1(c, c))
28.55/9.70	   A^2 -> H(e, f(e))
28.55/9.70	   A^2 -> H(e, f(k))
28.55/9.70	   A^2 -> H(e, U1(d, d))
28.55/9.70	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.70	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.70	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.70	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.70	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.70	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.70	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.70	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.70	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.70	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.70	   A^2 -> H(f(e), b)
28.55/9.70	   A^2 -> H(f(e), U1(e, d))
28.55/9.70	   A^2 -> H(f(e), U1(d, e))
28.55/9.70	   A^2 -> H(f(e), c)
28.55/9.70	   A^2 -> H(f(e), U1(e, k))
28.55/9.70	   A^2 -> H(f(e), U1(k, e))
28.55/9.70	   A^2 -> H(f(e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.70	   A^2 -> H(f(k), b)
28.55/9.70	   A^2 -> H(f(k), U1(e, d))
28.55/9.70	   A^2 -> H(f(k), U1(d, e))
28.55/9.70	   A^2 -> H(f(k), c)
28.55/9.70	   A^2 -> H(f(k), U1(e, k))
28.55/9.70	   A^2 -> H(f(k), U1(k, e))
28.55/9.70	   A^2 -> H(f(k), e)
28.55/9.70	   A^2 -> H(f(c), d)
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.70	   A^2 -> H(U1(k, k), f(e))
28.55/9.70	   A^2 -> H(U1(k, k), f(k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.70	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.70	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.70	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.70	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.70	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.70	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.70	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.70	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.70	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.70	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.70	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.70	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.70	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.70	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.70	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.70	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.70	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.70	   A^2 -> H(U1(d, d), b)
28.55/9.70	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.70	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.70	   A^2 -> H(U1(d, d), c)
28.55/9.70	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.70	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.70	   A^2 -> H(U1(d, d), e)
28.55/9.70	   A^2 -> H(f(d), d)
28.55/9.70	   A^2 -> H(f(d), k)
28.55/9.70	   A^2 -> H(U1(c, c), c)
28.55/9.70	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.70	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.70	   A^2 -> H(f(c), k)
28.55/9.70	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.70	   A^2 -> H(f(k), U1(k, k))
28.55/9.70	   A^2 -> H(f(e), e)
28.55/9.70	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.70	   A^2 -> H(d, U1(c, b))
28.55/9.70	   A^2 -> H(d, U1(d, b))
28.55/9.70	   A^2 -> H(d, U1(b, c))
28.55/9.70	   A^2 -> H(d, U1(b, d))
28.55/9.70	   A^2 -> H(d, U1(c, c))
28.55/9.70	   A^2 -> H(d, f(e))
28.55/9.70	   A^2 -> H(d, f(k))
28.55/9.70	   A^2 -> H(d, U1(d, d))
28.55/9.70	   A^2 -> H(a, U1(e, b))
28.55/9.70	   A^2 -> H(a, U1(k, b))
28.55/9.70	   A^2 -> H(a, U1(c, d))
28.55/9.70	   A^2 -> H(a, U1(d, c))
28.55/9.70	   A^2 -> H(a, U1(b, e))
28.55/9.70	   A^2 -> H(a, U1(b, k))
28.55/9.70	   A^2 -> H(a, U1(e, c))
28.55/9.70	   A^2 -> H(a, U1(k, c))
28.55/9.70	   A^2 -> H(a, U1(c, e))
28.55/9.70	   A^2 -> H(a, U1(c, k))
28.55/9.70	   A^2 -> H(a, U1(e, e))
28.55/9.70	   A^2 -> H(a, U1(k, k))
28.55/9.70	   A^2 -> H(a, U1(k, d))
28.55/9.70	   A^2 -> H(a, U1(d, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.70	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.70	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.70	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.70	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.70	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.70	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.70	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.70	   A^2 -> H(U1(e, a), b)
28.55/9.70	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.70	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.70	   A^2 -> H(U1(e, a), c)
28.55/9.70	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.70	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.70	   A^2 -> H(U1(e, a), e)
28.55/9.70	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, a), b)
28.55/9.70	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.70	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.70	   A^2 -> H(U1(k, a), c)
28.55/9.70	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.70	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.70	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, d), b)
28.55/9.70	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.70	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.70	   A^2 -> H(U1(c, d), c)
28.55/9.70	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.70	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.70	   A^2 -> H(U1(c, d), e)
28.55/9.70	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, a), d)
28.55/9.70	   A^2 -> H(U1(c, a), k)
28.55/9.70	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.70	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.70	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.70	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.70	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.70	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.70	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.70	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.70	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.70	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.70	   A^2 -> H(U1(d, c), b)
28.55/9.70	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.70	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.70	   A^2 -> H(U1(d, c), c)
28.55/9.70	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.70	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.70	   A^2 -> H(U1(d, c), e)
28.55/9.70	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(d, a), d)
28.55/9.70	   A^2 -> H(U1(d, a), k)
28.55/9.70	   A^2 -> H(U1(a, e), b)
28.55/9.70	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.70	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, e), c)
28.55/9.70	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, e), e)
28.55/9.70	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, k), b)
28.55/9.70	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.70	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, k), c)
28.55/9.70	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, k), e)
28.55/9.70	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, c), d)
28.55/9.70	
28.55/9.70	The TRS R consists of the following rules:
28.55/9.70	
28.55/9.70	   f(x) -> U1(x, x)
28.55/9.70	   U1(e, x) -> x
28.55/9.70	   a -> c
28.55/9.70	   a -> d
28.55/9.70	   b -> c
28.55/9.70	   b -> d
28.55/9.70	   d -> k
28.55/9.70	   c -> e
28.55/9.70	   c -> k
28.55/9.70	
28.55/9.70	Q is empty.
28.55/9.70	We have to consider all minimal (P,Q,R)-chains.
28.55/9.70	----------------------------------------
28.55/9.70	
28.55/9.70	(1355) TransformationProof (EQUIVALENT)
28.55/9.70	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), c) at position [] we obtained the following new rules [LPAR04]:
28.55/9.70	
28.55/9.70	   (A^2 -> H(U1(c, c), c),A^2 -> H(U1(c, c), c))
28.55/9.70	   (A^2 -> H(U1(d, c), c),A^2 -> H(U1(d, c), c))
28.55/9.70	   (A^2 -> H(U1(a, e), c),A^2 -> H(U1(a, e), c))
28.55/9.70	   (A^2 -> H(U1(a, k), c),A^2 -> H(U1(a, k), c))
28.55/9.70	   (A^2 -> H(U1(a, c), e),A^2 -> H(U1(a, c), e))
28.55/9.70	   (A^2 -> H(U1(a, c), k),A^2 -> H(U1(a, c), k))
28.55/9.70	
28.55/9.70	
28.55/9.70	----------------------------------------
28.55/9.70	
28.55/9.70	(1356)
28.55/9.70	Obligation:
28.55/9.70	Q DP problem:
28.55/9.70	The TRS P consists of the following rules:
28.55/9.70	
28.55/9.70	   H(x, x) -> G(x, x, f(k))
28.55/9.70	   G(d, x, x) -> A^2
28.55/9.70	   A^2 -> H(f(c), f(c))
28.55/9.70	   A^2 -> H(f(d), f(d))
28.55/9.70	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.70	   A^2 -> H(f(e), f(e))
28.55/9.70	   A^2 -> H(f(k), f(k))
28.55/9.70	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.70	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.70	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.70	   A^2 -> H(U1(a, c), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, c), e)
28.55/9.70	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, d), b)
28.55/9.70	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.70	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, d), c)
28.55/9.70	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, d), e)
28.55/9.70	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, a), d)
28.55/9.70	   A^2 -> H(U1(a, a), k)
28.55/9.70	   A^2 -> H(k, U1(b, b))
28.55/9.70	   A^2 -> H(k, f(c))
28.55/9.70	   A^2 -> H(k, f(d))
28.55/9.70	   A^2 -> H(c, U1(c, b))
28.55/9.70	   A^2 -> H(c, U1(d, b))
28.55/9.70	   A^2 -> H(c, U1(b, c))
28.55/9.70	   A^2 -> H(c, U1(b, d))
28.55/9.70	   A^2 -> H(c, U1(c, c))
28.55/9.70	   A^2 -> H(c, f(e))
28.55/9.70	   A^2 -> H(c, f(k))
28.55/9.70	   A^2 -> H(c, U1(d, d))
28.55/9.70	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.70	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.70	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.70	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.70	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.70	   A^2 -> H(U1(e, k), f(e))
28.55/9.70	   A^2 -> H(U1(e, k), f(k))
28.55/9.70	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.70	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.70	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.70	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.70	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.70	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.70	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.70	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.70	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.70	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.70	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.70	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.70	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.70	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.70	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.70	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.70	   A^2 -> H(U1(k, e), f(e))
28.55/9.70	   A^2 -> H(U1(k, e), f(k))
28.55/9.70	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.70	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.70	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.70	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.70	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.70	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.70	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.70	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.70	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.70	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.70	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.70	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.70	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.70	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.70	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.70	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.70	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.70	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.70	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.70	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.70	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.70	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.70	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.70	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.70	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.70	   A^2 -> H(U1(c, c), b)
28.55/9.70	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.70	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.70	   A^2 -> H(U1(c, c), e)
28.55/9.70	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.70	   A^2 -> H(e, U1(c, b))
28.55/9.70	   A^2 -> H(e, U1(d, b))
28.55/9.70	   A^2 -> H(e, U1(b, c))
28.55/9.70	   A^2 -> H(e, U1(b, d))
28.55/9.70	   A^2 -> H(e, U1(c, c))
28.55/9.70	   A^2 -> H(e, f(e))
28.55/9.70	   A^2 -> H(e, f(k))
28.55/9.70	   A^2 -> H(e, U1(d, d))
28.55/9.70	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.70	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.70	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.70	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.70	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.70	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.70	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.70	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.70	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.70	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.70	   A^2 -> H(f(e), b)
28.55/9.70	   A^2 -> H(f(e), U1(e, d))
28.55/9.70	   A^2 -> H(f(e), U1(d, e))
28.55/9.70	   A^2 -> H(f(e), c)
28.55/9.70	   A^2 -> H(f(e), U1(e, k))
28.55/9.70	   A^2 -> H(f(e), U1(k, e))
28.55/9.70	   A^2 -> H(f(e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.70	   A^2 -> H(f(k), b)
28.55/9.70	   A^2 -> H(f(k), U1(e, d))
28.55/9.70	   A^2 -> H(f(k), U1(d, e))
28.55/9.70	   A^2 -> H(f(k), c)
28.55/9.70	   A^2 -> H(f(k), U1(e, k))
28.55/9.70	   A^2 -> H(f(k), U1(k, e))
28.55/9.70	   A^2 -> H(f(k), e)
28.55/9.70	   A^2 -> H(f(c), d)
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.70	   A^2 -> H(U1(k, k), f(e))
28.55/9.70	   A^2 -> H(U1(k, k), f(k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.70	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.70	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.70	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.70	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.70	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.70	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.70	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.70	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.70	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.70	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.70	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.70	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.70	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.70	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.70	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.70	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.70	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.70	   A^2 -> H(U1(d, d), b)
28.55/9.70	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.70	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.70	   A^2 -> H(U1(d, d), c)
28.55/9.70	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.70	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.70	   A^2 -> H(U1(d, d), e)
28.55/9.70	   A^2 -> H(f(d), d)
28.55/9.70	   A^2 -> H(f(d), k)
28.55/9.70	   A^2 -> H(U1(c, c), c)
28.55/9.70	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.70	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.70	   A^2 -> H(f(c), k)
28.55/9.70	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.70	   A^2 -> H(f(k), U1(k, k))
28.55/9.70	   A^2 -> H(f(e), e)
28.55/9.70	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.70	   A^2 -> H(d, U1(c, b))
28.55/9.70	   A^2 -> H(d, U1(d, b))
28.55/9.70	   A^2 -> H(d, U1(b, c))
28.55/9.70	   A^2 -> H(d, U1(b, d))
28.55/9.70	   A^2 -> H(d, U1(c, c))
28.55/9.70	   A^2 -> H(d, f(e))
28.55/9.70	   A^2 -> H(d, f(k))
28.55/9.70	   A^2 -> H(d, U1(d, d))
28.55/9.70	   A^2 -> H(a, U1(e, b))
28.55/9.70	   A^2 -> H(a, U1(k, b))
28.55/9.70	   A^2 -> H(a, U1(c, d))
28.55/9.70	   A^2 -> H(a, U1(d, c))
28.55/9.70	   A^2 -> H(a, U1(b, e))
28.55/9.70	   A^2 -> H(a, U1(b, k))
28.55/9.70	   A^2 -> H(a, U1(e, c))
28.55/9.70	   A^2 -> H(a, U1(k, c))
28.55/9.70	   A^2 -> H(a, U1(c, e))
28.55/9.70	   A^2 -> H(a, U1(c, k))
28.55/9.70	   A^2 -> H(a, U1(e, e))
28.55/9.70	   A^2 -> H(a, U1(k, k))
28.55/9.70	   A^2 -> H(a, U1(k, d))
28.55/9.70	   A^2 -> H(a, U1(d, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.70	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.70	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.70	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.70	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.70	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.70	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.70	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.70	   A^2 -> H(U1(e, a), b)
28.55/9.70	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.70	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.70	   A^2 -> H(U1(e, a), c)
28.55/9.70	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.70	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.70	   A^2 -> H(U1(e, a), e)
28.55/9.70	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, a), b)
28.55/9.70	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.70	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.70	   A^2 -> H(U1(k, a), c)
28.55/9.70	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.70	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.70	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, d), b)
28.55/9.70	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.70	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.70	   A^2 -> H(U1(c, d), c)
28.55/9.70	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.70	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.70	   A^2 -> H(U1(c, d), e)
28.55/9.70	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, a), d)
28.55/9.70	   A^2 -> H(U1(c, a), k)
28.55/9.70	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.70	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.70	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.70	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.70	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.70	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.70	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.70	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.70	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.70	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.70	   A^2 -> H(U1(d, c), b)
28.55/9.70	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.70	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.70	   A^2 -> H(U1(d, c), c)
28.55/9.70	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.70	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.70	   A^2 -> H(U1(d, c), e)
28.55/9.70	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(d, a), d)
28.55/9.70	   A^2 -> H(U1(d, a), k)
28.55/9.70	   A^2 -> H(U1(a, e), b)
28.55/9.70	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.70	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, e), c)
28.55/9.70	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, e), e)
28.55/9.70	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, k), b)
28.55/9.70	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.70	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, k), c)
28.55/9.70	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, k), e)
28.55/9.70	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, c), d)
28.55/9.70	   A^2 -> H(U1(a, c), k)
28.55/9.70	
28.55/9.70	The TRS R consists of the following rules:
28.55/9.70	
28.55/9.70	   f(x) -> U1(x, x)
28.55/9.70	   U1(e, x) -> x
28.55/9.70	   a -> c
28.55/9.70	   a -> d
28.55/9.70	   b -> c
28.55/9.70	   b -> d
28.55/9.70	   d -> k
28.55/9.70	   c -> e
28.55/9.70	   c -> k
28.55/9.70	
28.55/9.70	Q is empty.
28.55/9.70	We have to consider all minimal (P,Q,R)-chains.
28.55/9.70	----------------------------------------
28.55/9.70	
28.55/9.70	(1357) TransformationProof (EQUIVALENT)
28.55/9.70	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.70	
28.55/9.70	   (A^2 -> H(U1(c, c), U1(e, k)),A^2 -> H(U1(c, c), U1(e, k)))
28.55/9.70	   (A^2 -> H(U1(d, c), U1(e, k)),A^2 -> H(U1(d, c), U1(e, k)))
28.55/9.70	   (A^2 -> H(U1(a, e), U1(e, k)),A^2 -> H(U1(a, e), U1(e, k)))
28.55/9.70	   (A^2 -> H(U1(a, k), U1(e, k)),A^2 -> H(U1(a, k), U1(e, k)))
28.55/9.70	   (A^2 -> H(U1(a, c), k),A^2 -> H(U1(a, c), k))
28.55/9.70	
28.55/9.70	
28.55/9.70	----------------------------------------
28.55/9.70	
28.55/9.70	(1358)
28.55/9.70	Obligation:
28.55/9.70	Q DP problem:
28.55/9.70	The TRS P consists of the following rules:
28.55/9.70	
28.55/9.70	   H(x, x) -> G(x, x, f(k))
28.55/9.70	   G(d, x, x) -> A^2
28.55/9.70	   A^2 -> H(f(c), f(c))
28.55/9.70	   A^2 -> H(f(d), f(d))
28.55/9.70	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.70	   A^2 -> H(f(e), f(e))
28.55/9.70	   A^2 -> H(f(k), f(k))
28.55/9.70	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.70	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.70	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.70	   A^2 -> H(U1(a, c), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, c), e)
28.55/9.70	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, d), b)
28.55/9.70	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.70	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, d), c)
28.55/9.70	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, d), e)
28.55/9.70	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, a), d)
28.55/9.70	   A^2 -> H(U1(a, a), k)
28.55/9.70	   A^2 -> H(k, U1(b, b))
28.55/9.70	   A^2 -> H(k, f(c))
28.55/9.70	   A^2 -> H(k, f(d))
28.55/9.70	   A^2 -> H(c, U1(c, b))
28.55/9.70	   A^2 -> H(c, U1(d, b))
28.55/9.70	   A^2 -> H(c, U1(b, c))
28.55/9.70	   A^2 -> H(c, U1(b, d))
28.55/9.70	   A^2 -> H(c, U1(c, c))
28.55/9.70	   A^2 -> H(c, f(e))
28.55/9.70	   A^2 -> H(c, f(k))
28.55/9.70	   A^2 -> H(c, U1(d, d))
28.55/9.70	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.70	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.70	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.70	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.70	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.70	   A^2 -> H(U1(e, k), f(e))
28.55/9.70	   A^2 -> H(U1(e, k), f(k))
28.55/9.70	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.70	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.70	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.70	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.70	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.70	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.70	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.70	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.70	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.70	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.70	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.70	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.70	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.70	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.70	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.70	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.70	   A^2 -> H(U1(k, e), f(e))
28.55/9.70	   A^2 -> H(U1(k, e), f(k))
28.55/9.70	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.70	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.70	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.70	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.70	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.70	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.70	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.70	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.70	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.70	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.70	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.70	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.70	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.70	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.70	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.70	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.70	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.70	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.70	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.70	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.70	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.70	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.70	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.70	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.70	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.70	   A^2 -> H(U1(c, c), b)
28.55/9.70	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.70	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.70	   A^2 -> H(U1(c, c), e)
28.55/9.70	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.70	   A^2 -> H(e, U1(c, b))
28.55/9.70	   A^2 -> H(e, U1(d, b))
28.55/9.70	   A^2 -> H(e, U1(b, c))
28.55/9.70	   A^2 -> H(e, U1(b, d))
28.55/9.70	   A^2 -> H(e, U1(c, c))
28.55/9.70	   A^2 -> H(e, f(e))
28.55/9.70	   A^2 -> H(e, f(k))
28.55/9.70	   A^2 -> H(e, U1(d, d))
28.55/9.70	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.70	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.70	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.70	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.70	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.70	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.70	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.70	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.70	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.70	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.70	   A^2 -> H(f(e), b)
28.55/9.70	   A^2 -> H(f(e), U1(e, d))
28.55/9.70	   A^2 -> H(f(e), U1(d, e))
28.55/9.70	   A^2 -> H(f(e), c)
28.55/9.70	   A^2 -> H(f(e), U1(e, k))
28.55/9.70	   A^2 -> H(f(e), U1(k, e))
28.55/9.70	   A^2 -> H(f(e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.70	   A^2 -> H(f(k), b)
28.55/9.70	   A^2 -> H(f(k), U1(e, d))
28.55/9.70	   A^2 -> H(f(k), U1(d, e))
28.55/9.70	   A^2 -> H(f(k), c)
28.55/9.70	   A^2 -> H(f(k), U1(e, k))
28.55/9.70	   A^2 -> H(f(k), U1(k, e))
28.55/9.70	   A^2 -> H(f(k), e)
28.55/9.70	   A^2 -> H(f(c), d)
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.70	   A^2 -> H(U1(k, k), f(e))
28.55/9.70	   A^2 -> H(U1(k, k), f(k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.70	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.70	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.70	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.70	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.70	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.70	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.70	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.70	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.70	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.70	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.70	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.70	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.70	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.70	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.70	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.70	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.70	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.70	   A^2 -> H(U1(d, d), b)
28.55/9.70	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.70	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.70	   A^2 -> H(U1(d, d), c)
28.55/9.70	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.70	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.70	   A^2 -> H(U1(d, d), e)
28.55/9.70	   A^2 -> H(f(d), d)
28.55/9.70	   A^2 -> H(f(d), k)
28.55/9.70	   A^2 -> H(U1(c, c), c)
28.55/9.70	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.70	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.70	   A^2 -> H(f(c), k)
28.55/9.70	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.70	   A^2 -> H(f(k), U1(k, k))
28.55/9.70	   A^2 -> H(f(e), e)
28.55/9.70	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.70	   A^2 -> H(d, U1(c, b))
28.55/9.70	   A^2 -> H(d, U1(d, b))
28.55/9.70	   A^2 -> H(d, U1(b, c))
28.55/9.70	   A^2 -> H(d, U1(b, d))
28.55/9.70	   A^2 -> H(d, U1(c, c))
28.55/9.70	   A^2 -> H(d, f(e))
28.55/9.70	   A^2 -> H(d, f(k))
28.55/9.70	   A^2 -> H(d, U1(d, d))
28.55/9.70	   A^2 -> H(a, U1(e, b))
28.55/9.70	   A^2 -> H(a, U1(k, b))
28.55/9.70	   A^2 -> H(a, U1(c, d))
28.55/9.70	   A^2 -> H(a, U1(d, c))
28.55/9.70	   A^2 -> H(a, U1(b, e))
28.55/9.70	   A^2 -> H(a, U1(b, k))
28.55/9.70	   A^2 -> H(a, U1(e, c))
28.55/9.70	   A^2 -> H(a, U1(k, c))
28.55/9.70	   A^2 -> H(a, U1(c, e))
28.55/9.70	   A^2 -> H(a, U1(c, k))
28.55/9.70	   A^2 -> H(a, U1(e, e))
28.55/9.70	   A^2 -> H(a, U1(k, k))
28.55/9.70	   A^2 -> H(a, U1(k, d))
28.55/9.70	   A^2 -> H(a, U1(d, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.70	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.70	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.70	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.70	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.70	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.70	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.70	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.70	   A^2 -> H(U1(e, a), b)
28.55/9.70	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.70	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.70	   A^2 -> H(U1(e, a), c)
28.55/9.70	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.70	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.70	   A^2 -> H(U1(e, a), e)
28.55/9.70	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, a), b)
28.55/9.70	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.70	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.70	   A^2 -> H(U1(k, a), c)
28.55/9.70	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.70	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.70	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, d), b)
28.55/9.70	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.70	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.70	   A^2 -> H(U1(c, d), c)
28.55/9.70	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.70	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.70	   A^2 -> H(U1(c, d), e)
28.55/9.70	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, a), d)
28.55/9.70	   A^2 -> H(U1(c, a), k)
28.55/9.70	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.70	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.70	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.70	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.70	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.70	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.70	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.70	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.70	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.70	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.70	   A^2 -> H(U1(d, c), b)
28.55/9.70	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.70	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.70	   A^2 -> H(U1(d, c), c)
28.55/9.70	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.70	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.70	   A^2 -> H(U1(d, c), e)
28.55/9.70	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(d, a), d)
28.55/9.70	   A^2 -> H(U1(d, a), k)
28.55/9.70	   A^2 -> H(U1(a, e), b)
28.55/9.70	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.70	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, e), c)
28.55/9.70	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, e), e)
28.55/9.70	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, k), b)
28.55/9.70	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.70	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, k), c)
28.55/9.70	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, k), e)
28.55/9.70	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, c), d)
28.55/9.70	   A^2 -> H(U1(a, c), k)
28.55/9.70	
28.55/9.70	The TRS R consists of the following rules:
28.55/9.70	
28.55/9.70	   f(x) -> U1(x, x)
28.55/9.70	   U1(e, x) -> x
28.55/9.70	   a -> c
28.55/9.70	   a -> d
28.55/9.70	   b -> c
28.55/9.70	   b -> d
28.55/9.70	   d -> k
28.55/9.70	   c -> e
28.55/9.70	   c -> k
28.55/9.70	
28.55/9.70	Q is empty.
28.55/9.70	We have to consider all minimal (P,Q,R)-chains.
28.55/9.70	----------------------------------------
28.55/9.70	
28.55/9.70	(1359) TransformationProof (EQUIVALENT)
28.55/9.70	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.70	
28.55/9.70	   (A^2 -> H(U1(c, c), U1(k, e)),A^2 -> H(U1(c, c), U1(k, e)))
28.55/9.70	   (A^2 -> H(U1(d, c), U1(k, e)),A^2 -> H(U1(d, c), U1(k, e)))
28.55/9.70	   (A^2 -> H(U1(a, e), U1(k, e)),A^2 -> H(U1(a, e), U1(k, e)))
28.55/9.70	   (A^2 -> H(U1(a, k), U1(k, e)),A^2 -> H(U1(a, k), U1(k, e)))
28.55/9.70	
28.55/9.70	
28.55/9.70	----------------------------------------
28.55/9.70	
28.55/9.70	(1360)
28.55/9.70	Obligation:
28.55/9.70	Q DP problem:
28.55/9.70	The TRS P consists of the following rules:
28.55/9.70	
28.55/9.70	   H(x, x) -> G(x, x, f(k))
28.55/9.70	   G(d, x, x) -> A^2
28.55/9.70	   A^2 -> H(f(c), f(c))
28.55/9.70	   A^2 -> H(f(d), f(d))
28.55/9.70	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.70	   A^2 -> H(f(e), f(e))
28.55/9.70	   A^2 -> H(f(k), f(k))
28.55/9.70	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.70	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.70	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.70	   A^2 -> H(U1(a, c), e)
28.55/9.70	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, d), b)
28.55/9.70	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.70	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, d), c)
28.55/9.70	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, d), e)
28.55/9.70	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, a), d)
28.55/9.70	   A^2 -> H(U1(a, a), k)
28.55/9.70	   A^2 -> H(k, U1(b, b))
28.55/9.70	   A^2 -> H(k, f(c))
28.55/9.70	   A^2 -> H(k, f(d))
28.55/9.70	   A^2 -> H(c, U1(c, b))
28.55/9.70	   A^2 -> H(c, U1(d, b))
28.55/9.70	   A^2 -> H(c, U1(b, c))
28.55/9.70	   A^2 -> H(c, U1(b, d))
28.55/9.70	   A^2 -> H(c, U1(c, c))
28.55/9.70	   A^2 -> H(c, f(e))
28.55/9.70	   A^2 -> H(c, f(k))
28.55/9.70	   A^2 -> H(c, U1(d, d))
28.55/9.70	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.70	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.70	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.70	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.70	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.70	   A^2 -> H(U1(e, k), f(e))
28.55/9.70	   A^2 -> H(U1(e, k), f(k))
28.55/9.70	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.70	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.70	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.70	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.70	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.70	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.70	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.70	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.70	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.70	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.70	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.70	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.70	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.70	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.70	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.70	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.70	   A^2 -> H(U1(k, e), f(e))
28.55/9.70	   A^2 -> H(U1(k, e), f(k))
28.55/9.70	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.70	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.70	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.70	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.70	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.70	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.70	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.70	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.70	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.70	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.70	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.70	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.70	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.70	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.70	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.70	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.70	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.70	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.70	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.70	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.70	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.70	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.70	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.70	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.70	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.70	   A^2 -> H(U1(c, c), b)
28.55/9.70	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.70	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.70	   A^2 -> H(U1(c, c), e)
28.55/9.70	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.70	   A^2 -> H(e, U1(c, b))
28.55/9.70	   A^2 -> H(e, U1(d, b))
28.55/9.70	   A^2 -> H(e, U1(b, c))
28.55/9.70	   A^2 -> H(e, U1(b, d))
28.55/9.70	   A^2 -> H(e, U1(c, c))
28.55/9.70	   A^2 -> H(e, f(e))
28.55/9.70	   A^2 -> H(e, f(k))
28.55/9.70	   A^2 -> H(e, U1(d, d))
28.55/9.70	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.70	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.70	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.70	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.70	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.70	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.70	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.70	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.70	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.70	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.70	   A^2 -> H(f(e), b)
28.55/9.70	   A^2 -> H(f(e), U1(e, d))
28.55/9.70	   A^2 -> H(f(e), U1(d, e))
28.55/9.70	   A^2 -> H(f(e), c)
28.55/9.70	   A^2 -> H(f(e), U1(e, k))
28.55/9.70	   A^2 -> H(f(e), U1(k, e))
28.55/9.70	   A^2 -> H(f(e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.70	   A^2 -> H(f(k), b)
28.55/9.70	   A^2 -> H(f(k), U1(e, d))
28.55/9.70	   A^2 -> H(f(k), U1(d, e))
28.55/9.70	   A^2 -> H(f(k), c)
28.55/9.70	   A^2 -> H(f(k), U1(e, k))
28.55/9.70	   A^2 -> H(f(k), U1(k, e))
28.55/9.70	   A^2 -> H(f(k), e)
28.55/9.70	   A^2 -> H(f(c), d)
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.70	   A^2 -> H(U1(k, k), f(e))
28.55/9.70	   A^2 -> H(U1(k, k), f(k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.70	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.70	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.70	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.70	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.70	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.70	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.70	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.70	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.70	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.70	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.70	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.70	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.70	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.70	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.70	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.70	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.70	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.70	   A^2 -> H(U1(d, d), b)
28.55/9.70	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.70	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.70	   A^2 -> H(U1(d, d), c)
28.55/9.70	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.70	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.70	   A^2 -> H(U1(d, d), e)
28.55/9.70	   A^2 -> H(f(d), d)
28.55/9.70	   A^2 -> H(f(d), k)
28.55/9.70	   A^2 -> H(U1(c, c), c)
28.55/9.70	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.70	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.70	   A^2 -> H(f(c), k)
28.55/9.70	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.70	   A^2 -> H(f(k), U1(k, k))
28.55/9.70	   A^2 -> H(f(e), e)
28.55/9.70	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.70	   A^2 -> H(d, U1(c, b))
28.55/9.70	   A^2 -> H(d, U1(d, b))
28.55/9.70	   A^2 -> H(d, U1(b, c))
28.55/9.70	   A^2 -> H(d, U1(b, d))
28.55/9.70	   A^2 -> H(d, U1(c, c))
28.55/9.70	   A^2 -> H(d, f(e))
28.55/9.70	   A^2 -> H(d, f(k))
28.55/9.70	   A^2 -> H(d, U1(d, d))
28.55/9.70	   A^2 -> H(a, U1(e, b))
28.55/9.70	   A^2 -> H(a, U1(k, b))
28.55/9.70	   A^2 -> H(a, U1(c, d))
28.55/9.70	   A^2 -> H(a, U1(d, c))
28.55/9.70	   A^2 -> H(a, U1(b, e))
28.55/9.70	   A^2 -> H(a, U1(b, k))
28.55/9.70	   A^2 -> H(a, U1(e, c))
28.55/9.70	   A^2 -> H(a, U1(k, c))
28.55/9.70	   A^2 -> H(a, U1(c, e))
28.55/9.70	   A^2 -> H(a, U1(c, k))
28.55/9.70	   A^2 -> H(a, U1(e, e))
28.55/9.70	   A^2 -> H(a, U1(k, k))
28.55/9.70	   A^2 -> H(a, U1(k, d))
28.55/9.70	   A^2 -> H(a, U1(d, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.70	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.70	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.70	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.70	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.70	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.70	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.70	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.70	   A^2 -> H(U1(e, a), b)
28.55/9.70	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.70	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.70	   A^2 -> H(U1(e, a), c)
28.55/9.70	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.70	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.70	   A^2 -> H(U1(e, a), e)
28.55/9.70	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, a), b)
28.55/9.70	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.70	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.70	   A^2 -> H(U1(k, a), c)
28.55/9.70	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.70	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.70	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, d), b)
28.55/9.70	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.70	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.70	   A^2 -> H(U1(c, d), c)
28.55/9.70	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.70	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.70	   A^2 -> H(U1(c, d), e)
28.55/9.70	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, a), d)
28.55/9.70	   A^2 -> H(U1(c, a), k)
28.55/9.70	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.70	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.70	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.70	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.70	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.70	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.70	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.70	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.70	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.70	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.70	   A^2 -> H(U1(d, c), b)
28.55/9.70	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.70	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.70	   A^2 -> H(U1(d, c), c)
28.55/9.70	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.70	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.70	   A^2 -> H(U1(d, c), e)
28.55/9.70	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(d, a), d)
28.55/9.70	   A^2 -> H(U1(d, a), k)
28.55/9.70	   A^2 -> H(U1(a, e), b)
28.55/9.70	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.70	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, e), c)
28.55/9.70	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, e), e)
28.55/9.70	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, k), b)
28.55/9.70	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.70	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, k), c)
28.55/9.70	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, k), e)
28.55/9.70	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, c), d)
28.55/9.70	   A^2 -> H(U1(a, c), k)
28.55/9.70	
28.55/9.70	The TRS R consists of the following rules:
28.55/9.70	
28.55/9.70	   f(x) -> U1(x, x)
28.55/9.70	   U1(e, x) -> x
28.55/9.70	   a -> c
28.55/9.70	   a -> d
28.55/9.70	   b -> c
28.55/9.70	   b -> d
28.55/9.70	   d -> k
28.55/9.70	   c -> e
28.55/9.70	   c -> k
28.55/9.70	
28.55/9.70	Q is empty.
28.55/9.70	We have to consider all minimal (P,Q,R)-chains.
28.55/9.70	----------------------------------------
28.55/9.70	
28.55/9.70	(1361) TransformationProof (EQUIVALENT)
28.55/9.70	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), e) at position [] we obtained the following new rules [LPAR04]:
28.55/9.70	
28.55/9.70	   (A^2 -> H(U1(c, c), e),A^2 -> H(U1(c, c), e))
28.55/9.70	   (A^2 -> H(U1(d, c), e),A^2 -> H(U1(d, c), e))
28.55/9.70	   (A^2 -> H(U1(a, e), e),A^2 -> H(U1(a, e), e))
28.55/9.70	   (A^2 -> H(U1(a, k), e),A^2 -> H(U1(a, k), e))
28.55/9.70	
28.55/9.70	
28.55/9.70	----------------------------------------
28.55/9.70	
28.55/9.70	(1362)
28.55/9.70	Obligation:
28.55/9.70	Q DP problem:
28.55/9.70	The TRS P consists of the following rules:
28.55/9.70	
28.55/9.70	   H(x, x) -> G(x, x, f(k))
28.55/9.70	   G(d, x, x) -> A^2
28.55/9.70	   A^2 -> H(f(c), f(c))
28.55/9.70	   A^2 -> H(f(d), f(d))
28.55/9.70	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.70	   A^2 -> H(f(e), f(e))
28.55/9.70	   A^2 -> H(f(k), f(k))
28.55/9.70	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.70	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.70	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.70	   A^2 -> H(U1(a, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, d), b)
28.55/9.70	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.70	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, d), c)
28.55/9.70	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, d), e)
28.55/9.70	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, a), d)
28.55/9.70	   A^2 -> H(U1(a, a), k)
28.55/9.70	   A^2 -> H(k, U1(b, b))
28.55/9.70	   A^2 -> H(k, f(c))
28.55/9.70	   A^2 -> H(k, f(d))
28.55/9.70	   A^2 -> H(c, U1(c, b))
28.55/9.70	   A^2 -> H(c, U1(d, b))
28.55/9.70	   A^2 -> H(c, U1(b, c))
28.55/9.70	   A^2 -> H(c, U1(b, d))
28.55/9.70	   A^2 -> H(c, U1(c, c))
28.55/9.70	   A^2 -> H(c, f(e))
28.55/9.70	   A^2 -> H(c, f(k))
28.55/9.70	   A^2 -> H(c, U1(d, d))
28.55/9.70	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.70	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.70	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.70	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.70	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.70	   A^2 -> H(U1(e, k), f(e))
28.55/9.70	   A^2 -> H(U1(e, k), f(k))
28.55/9.70	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.70	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.70	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.70	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.70	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.70	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.70	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.70	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.70	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.70	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.70	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.70	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.70	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.70	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.70	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.70	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.70	   A^2 -> H(U1(k, e), f(e))
28.55/9.70	   A^2 -> H(U1(k, e), f(k))
28.55/9.70	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.70	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.70	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.70	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.70	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.70	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.70	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.70	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.70	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.70	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.70	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.70	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.70	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.70	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.70	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.70	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.70	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.70	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.70	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.70	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.70	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.70	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.70	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.70	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.70	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.70	   A^2 -> H(U1(c, c), b)
28.55/9.70	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.70	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.70	   A^2 -> H(U1(c, c), e)
28.55/9.70	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.70	   A^2 -> H(e, U1(c, b))
28.55/9.70	   A^2 -> H(e, U1(d, b))
28.55/9.70	   A^2 -> H(e, U1(b, c))
28.55/9.70	   A^2 -> H(e, U1(b, d))
28.55/9.70	   A^2 -> H(e, U1(c, c))
28.55/9.70	   A^2 -> H(e, f(e))
28.55/9.70	   A^2 -> H(e, f(k))
28.55/9.70	   A^2 -> H(e, U1(d, d))
28.55/9.70	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.70	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.70	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.70	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.70	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.70	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.70	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.70	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.70	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.70	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.70	   A^2 -> H(f(e), b)
28.55/9.70	   A^2 -> H(f(e), U1(e, d))
28.55/9.70	   A^2 -> H(f(e), U1(d, e))
28.55/9.70	   A^2 -> H(f(e), c)
28.55/9.70	   A^2 -> H(f(e), U1(e, k))
28.55/9.70	   A^2 -> H(f(e), U1(k, e))
28.55/9.70	   A^2 -> H(f(e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.70	   A^2 -> H(f(k), b)
28.55/9.70	   A^2 -> H(f(k), U1(e, d))
28.55/9.70	   A^2 -> H(f(k), U1(d, e))
28.55/9.70	   A^2 -> H(f(k), c)
28.55/9.70	   A^2 -> H(f(k), U1(e, k))
28.55/9.70	   A^2 -> H(f(k), U1(k, e))
28.55/9.70	   A^2 -> H(f(k), e)
28.55/9.70	   A^2 -> H(f(c), d)
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.70	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.70	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.70	   A^2 -> H(U1(k, k), f(e))
28.55/9.70	   A^2 -> H(U1(k, k), f(k))
28.55/9.70	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.70	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.70	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.70	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.70	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.70	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.70	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.70	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.70	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.70	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.70	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.70	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.70	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.70	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.70	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.70	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.70	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.70	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.70	   A^2 -> H(U1(d, d), b)
28.55/9.70	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.70	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.70	   A^2 -> H(U1(d, d), c)
28.55/9.70	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.70	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.70	   A^2 -> H(U1(d, d), e)
28.55/9.70	   A^2 -> H(f(d), d)
28.55/9.70	   A^2 -> H(f(d), k)
28.55/9.70	   A^2 -> H(U1(c, c), c)
28.55/9.70	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.70	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.70	   A^2 -> H(f(c), k)
28.55/9.70	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.70	   A^2 -> H(f(k), U1(k, k))
28.55/9.70	   A^2 -> H(f(e), e)
28.55/9.70	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.70	   A^2 -> H(d, U1(c, b))
28.55/9.70	   A^2 -> H(d, U1(d, b))
28.55/9.70	   A^2 -> H(d, U1(b, c))
28.55/9.70	   A^2 -> H(d, U1(b, d))
28.55/9.70	   A^2 -> H(d, U1(c, c))
28.55/9.70	   A^2 -> H(d, f(e))
28.55/9.70	   A^2 -> H(d, f(k))
28.55/9.70	   A^2 -> H(d, U1(d, d))
28.55/9.70	   A^2 -> H(a, U1(e, b))
28.55/9.70	   A^2 -> H(a, U1(k, b))
28.55/9.70	   A^2 -> H(a, U1(c, d))
28.55/9.70	   A^2 -> H(a, U1(d, c))
28.55/9.70	   A^2 -> H(a, U1(b, e))
28.55/9.70	   A^2 -> H(a, U1(b, k))
28.55/9.70	   A^2 -> H(a, U1(e, c))
28.55/9.70	   A^2 -> H(a, U1(k, c))
28.55/9.70	   A^2 -> H(a, U1(c, e))
28.55/9.70	   A^2 -> H(a, U1(c, k))
28.55/9.70	   A^2 -> H(a, U1(e, e))
28.55/9.70	   A^2 -> H(a, U1(k, k))
28.55/9.70	   A^2 -> H(a, U1(k, d))
28.55/9.70	   A^2 -> H(a, U1(d, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.70	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.70	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.70	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.70	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.70	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.70	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.70	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.70	   A^2 -> H(U1(e, a), b)
28.55/9.70	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.70	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.70	   A^2 -> H(U1(e, a), c)
28.55/9.70	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.70	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.70	   A^2 -> H(U1(e, a), e)
28.55/9.70	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.70	   A^2 -> H(U1(k, a), b)
28.55/9.70	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.70	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.70	   A^2 -> H(U1(k, a), c)
28.55/9.70	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.70	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.70	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, d), b)
28.55/9.70	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.70	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.70	   A^2 -> H(U1(c, d), c)
28.55/9.70	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.70	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.70	   A^2 -> H(U1(c, d), e)
28.55/9.70	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.70	   A^2 -> H(U1(c, a), d)
28.55/9.70	   A^2 -> H(U1(c, a), k)
28.55/9.70	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.70	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.70	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.70	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.70	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.70	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.70	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.70	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.70	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.70	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.70	   A^2 -> H(U1(d, c), b)
28.55/9.70	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.70	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.70	   A^2 -> H(U1(d, c), c)
28.55/9.70	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.70	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.70	   A^2 -> H(U1(d, c), e)
28.55/9.70	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.70	   A^2 -> H(U1(d, a), d)
28.55/9.70	   A^2 -> H(U1(d, a), k)
28.55/9.70	   A^2 -> H(U1(a, e), b)
28.55/9.70	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.70	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, e), c)
28.55/9.70	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, e), e)
28.55/9.70	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, k), b)
28.55/9.70	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.70	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.70	   A^2 -> H(U1(a, k), c)
28.55/9.70	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.70	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.70	   A^2 -> H(U1(a, k), e)
28.55/9.70	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.70	   A^2 -> H(U1(a, c), d)
28.55/9.70	   A^2 -> H(U1(a, c), k)
28.55/9.70	
28.55/9.70	The TRS R consists of the following rules:
28.55/9.70	
28.55/9.70	   f(x) -> U1(x, x)
28.55/9.70	   U1(e, x) -> x
28.55/9.70	   a -> c
28.55/9.70	   a -> d
28.55/9.70	   b -> c
28.55/9.70	   b -> d
28.55/9.70	   d -> k
28.55/9.70	   c -> e
28.55/9.70	   c -> k
28.55/9.70	
28.55/9.70	Q is empty.
28.55/9.70	We have to consider all minimal (P,Q,R)-chains.
28.55/9.70	----------------------------------------
28.55/9.70	
28.55/9.70	(1363) TransformationProof (EQUIVALENT)
28.55/9.70	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.70	
28.55/9.70	   (A^2 -> H(U1(c, c), U1(k, k)),A^2 -> H(U1(c, c), U1(k, k)))
28.55/9.70	   (A^2 -> H(U1(d, c), U1(k, k)),A^2 -> H(U1(d, c), U1(k, k)))
28.55/9.70	   (A^2 -> H(U1(a, e), U1(k, k)),A^2 -> H(U1(a, e), U1(k, k)))
28.55/9.70	   (A^2 -> H(U1(a, k), U1(k, k)),A^2 -> H(U1(a, k), U1(k, k)))
28.55/9.70	
28.55/9.70	
28.55/9.70	----------------------------------------
28.55/9.70	
28.55/9.70	(1364)
28.55/9.70	Obligation:
28.55/9.70	Q DP problem:
28.55/9.70	The TRS P consists of the following rules:
28.55/9.70	
28.55/9.70	   H(x, x) -> G(x, x, f(k))
28.55/9.70	   G(d, x, x) -> A^2
28.55/9.70	   A^2 -> H(f(c), f(c))
28.55/9.70	   A^2 -> H(f(d), f(d))
28.55/9.70	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.70	   A^2 -> H(f(e), f(e))
28.55/9.70	   A^2 -> H(f(k), f(k))
28.55/9.70	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.70	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.71	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.71	   A^2 -> H(U1(a, d), b)
28.55/9.71	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.71	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.71	   A^2 -> H(U1(a, d), c)
28.55/9.71	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.71	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.71	   A^2 -> H(U1(a, d), e)
28.55/9.71	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(a, a), d)
28.55/9.71	   A^2 -> H(U1(a, a), k)
28.55/9.71	   A^2 -> H(k, U1(b, b))
28.55/9.71	   A^2 -> H(k, f(c))
28.55/9.71	   A^2 -> H(k, f(d))
28.55/9.71	   A^2 -> H(c, U1(c, b))
28.55/9.71	   A^2 -> H(c, U1(d, b))
28.55/9.71	   A^2 -> H(c, U1(b, c))
28.55/9.71	   A^2 -> H(c, U1(b, d))
28.55/9.71	   A^2 -> H(c, U1(c, c))
28.55/9.71	   A^2 -> H(c, f(e))
28.55/9.71	   A^2 -> H(c, f(k))
28.55/9.71	   A^2 -> H(c, U1(d, d))
28.55/9.71	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.71	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.71	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.71	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.71	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.71	   A^2 -> H(U1(e, k), f(e))
28.55/9.71	   A^2 -> H(U1(e, k), f(k))
28.55/9.71	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.71	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.71	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.71	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.71	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.71	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.71	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.71	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.71	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.71	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.71	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.71	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.71	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.71	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.71	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.71	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.71	   A^2 -> H(U1(k, e), f(e))
28.55/9.71	   A^2 -> H(U1(k, e), f(k))
28.55/9.71	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.71	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.71	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.71	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.71	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.71	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.71	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.71	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.71	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.71	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.71	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.71	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.71	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.71	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.71	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.71	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.71	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.71	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.71	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.71	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.71	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.71	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.71	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.71	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.71	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.71	   A^2 -> H(U1(c, c), b)
28.55/9.71	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.71	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.71	   A^2 -> H(U1(c, c), e)
28.55/9.71	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.71	   A^2 -> H(e, U1(c, b))
28.55/9.71	   A^2 -> H(e, U1(d, b))
28.55/9.71	   A^2 -> H(e, U1(b, c))
28.55/9.71	   A^2 -> H(e, U1(b, d))
28.55/9.71	   A^2 -> H(e, U1(c, c))
28.55/9.71	   A^2 -> H(e, f(e))
28.55/9.71	   A^2 -> H(e, f(k))
28.55/9.71	   A^2 -> H(e, U1(d, d))
28.55/9.71	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.71	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.71	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.71	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.71	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.71	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.71	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.71	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.71	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.71	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.71	   A^2 -> H(f(e), b)
28.55/9.71	   A^2 -> H(f(e), U1(e, d))
28.55/9.71	   A^2 -> H(f(e), U1(d, e))
28.55/9.71	   A^2 -> H(f(e), c)
28.55/9.71	   A^2 -> H(f(e), U1(e, k))
28.55/9.71	   A^2 -> H(f(e), U1(k, e))
28.55/9.71	   A^2 -> H(f(e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.71	   A^2 -> H(f(k), b)
28.55/9.71	   A^2 -> H(f(k), U1(e, d))
28.55/9.71	   A^2 -> H(f(k), U1(d, e))
28.55/9.71	   A^2 -> H(f(k), c)
28.55/9.71	   A^2 -> H(f(k), U1(e, k))
28.55/9.71	   A^2 -> H(f(k), U1(k, e))
28.55/9.71	   A^2 -> H(f(k), e)
28.55/9.71	   A^2 -> H(f(c), d)
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.71	   A^2 -> H(U1(k, k), f(e))
28.55/9.71	   A^2 -> H(U1(k, k), f(k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.71	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.71	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.71	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.71	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.71	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.71	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.71	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.71	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.71	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.71	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.71	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.71	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.71	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.71	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.71	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.71	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.71	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.71	   A^2 -> H(U1(d, d), b)
28.55/9.71	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.71	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.71	   A^2 -> H(U1(d, d), c)
28.55/9.71	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.71	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.71	   A^2 -> H(U1(d, d), e)
28.55/9.71	   A^2 -> H(f(d), d)
28.55/9.71	   A^2 -> H(f(d), k)
28.55/9.71	   A^2 -> H(U1(c, c), c)
28.55/9.71	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.71	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.71	   A^2 -> H(f(c), k)
28.55/9.71	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.71	   A^2 -> H(f(k), U1(k, k))
28.55/9.71	   A^2 -> H(f(e), e)
28.55/9.71	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.71	   A^2 -> H(d, U1(c, b))
28.55/9.71	   A^2 -> H(d, U1(d, b))
28.55/9.71	   A^2 -> H(d, U1(b, c))
28.55/9.71	   A^2 -> H(d, U1(b, d))
28.55/9.71	   A^2 -> H(d, U1(c, c))
28.55/9.71	   A^2 -> H(d, f(e))
28.55/9.71	   A^2 -> H(d, f(k))
28.55/9.71	   A^2 -> H(d, U1(d, d))
28.55/9.71	   A^2 -> H(a, U1(e, b))
28.55/9.71	   A^2 -> H(a, U1(k, b))
28.55/9.71	   A^2 -> H(a, U1(c, d))
28.55/9.71	   A^2 -> H(a, U1(d, c))
28.55/9.71	   A^2 -> H(a, U1(b, e))
28.55/9.71	   A^2 -> H(a, U1(b, k))
28.55/9.71	   A^2 -> H(a, U1(e, c))
28.55/9.71	   A^2 -> H(a, U1(k, c))
28.55/9.71	   A^2 -> H(a, U1(c, e))
28.55/9.71	   A^2 -> H(a, U1(c, k))
28.55/9.71	   A^2 -> H(a, U1(e, e))
28.55/9.71	   A^2 -> H(a, U1(k, k))
28.55/9.71	   A^2 -> H(a, U1(k, d))
28.55/9.71	   A^2 -> H(a, U1(d, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.71	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.71	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.71	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.71	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.71	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.71	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.71	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.71	   A^2 -> H(U1(e, a), b)
28.55/9.71	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.71	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.71	   A^2 -> H(U1(e, a), c)
28.55/9.71	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.71	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.71	   A^2 -> H(U1(e, a), e)
28.55/9.71	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, a), b)
28.55/9.71	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.71	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.71	   A^2 -> H(U1(k, a), c)
28.55/9.71	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.71	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.71	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, d), b)
28.55/9.71	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.71	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.71	   A^2 -> H(U1(c, d), c)
28.55/9.71	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.71	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.71	   A^2 -> H(U1(c, d), e)
28.55/9.71	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, a), d)
28.55/9.71	   A^2 -> H(U1(c, a), k)
28.55/9.71	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.71	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.71	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.71	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.71	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.71	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.71	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.71	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.71	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.71	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.71	   A^2 -> H(U1(d, c), b)
28.55/9.71	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.71	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.71	   A^2 -> H(U1(d, c), c)
28.55/9.71	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.71	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.71	   A^2 -> H(U1(d, c), e)
28.55/9.71	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.71	   A^2 -> H(U1(d, a), d)
28.55/9.71	   A^2 -> H(U1(d, a), k)
28.55/9.71	   A^2 -> H(U1(a, e), b)
28.55/9.71	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.71	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.71	   A^2 -> H(U1(a, e), c)
28.55/9.71	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.71	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.71	   A^2 -> H(U1(a, e), e)
28.55/9.71	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(a, k), b)
28.55/9.71	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.71	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.71	   A^2 -> H(U1(a, k), c)
28.55/9.71	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.71	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.71	   A^2 -> H(U1(a, k), e)
28.55/9.71	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(a, c), d)
28.55/9.71	   A^2 -> H(U1(a, c), k)
28.55/9.71	
28.55/9.71	The TRS R consists of the following rules:
28.55/9.71	
28.55/9.71	   f(x) -> U1(x, x)
28.55/9.71	   U1(e, x) -> x
28.55/9.71	   a -> c
28.55/9.71	   a -> d
28.55/9.71	   b -> c
28.55/9.71	   b -> d
28.55/9.71	   d -> k
28.55/9.71	   c -> e
28.55/9.71	   c -> k
28.55/9.71	
28.55/9.71	Q is empty.
28.55/9.71	We have to consider all minimal (P,Q,R)-chains.
28.55/9.71	----------------------------------------
28.55/9.71	
28.55/9.71	(1365) TransformationProof (EQUIVALENT)
28.55/9.71	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), b) at position [] we obtained the following new rules [LPAR04]:
28.55/9.71	
28.55/9.71	   (A^2 -> H(U1(c, d), b),A^2 -> H(U1(c, d), b))
28.55/9.71	   (A^2 -> H(U1(d, d), b),A^2 -> H(U1(d, d), b))
28.55/9.71	   (A^2 -> H(U1(a, k), b),A^2 -> H(U1(a, k), b))
28.55/9.71	   (A^2 -> H(U1(a, d), c),A^2 -> H(U1(a, d), c))
28.55/9.71	   (A^2 -> H(U1(a, d), d),A^2 -> H(U1(a, d), d))
28.55/9.71	
28.55/9.71	
28.55/9.71	----------------------------------------
28.55/9.71	
28.55/9.71	(1366)
28.55/9.71	Obligation:
28.55/9.71	Q DP problem:
28.55/9.71	The TRS P consists of the following rules:
28.55/9.71	
28.55/9.71	   H(x, x) -> G(x, x, f(k))
28.55/9.71	   G(d, x, x) -> A^2
28.55/9.71	   A^2 -> H(f(c), f(c))
28.55/9.71	   A^2 -> H(f(d), f(d))
28.55/9.71	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.71	   A^2 -> H(f(e), f(e))
28.55/9.71	   A^2 -> H(f(k), f(k))
28.55/9.71	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.71	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.71	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.71	   A^2 -> H(U1(a, d), U1(e, d))
28.55/9.71	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.71	   A^2 -> H(U1(a, d), c)
28.55/9.71	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.71	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.71	   A^2 -> H(U1(a, d), e)
28.55/9.71	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(a, a), d)
28.55/9.71	   A^2 -> H(U1(a, a), k)
28.55/9.71	   A^2 -> H(k, U1(b, b))
28.55/9.71	   A^2 -> H(k, f(c))
28.55/9.71	   A^2 -> H(k, f(d))
28.55/9.71	   A^2 -> H(c, U1(c, b))
28.55/9.71	   A^2 -> H(c, U1(d, b))
28.55/9.71	   A^2 -> H(c, U1(b, c))
28.55/9.71	   A^2 -> H(c, U1(b, d))
28.55/9.71	   A^2 -> H(c, U1(c, c))
28.55/9.71	   A^2 -> H(c, f(e))
28.55/9.71	   A^2 -> H(c, f(k))
28.55/9.71	   A^2 -> H(c, U1(d, d))
28.55/9.71	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.71	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.71	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.71	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.71	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.71	   A^2 -> H(U1(e, k), f(e))
28.55/9.71	   A^2 -> H(U1(e, k), f(k))
28.55/9.71	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.71	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.71	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.71	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.71	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.71	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.71	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.71	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.71	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.71	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.71	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.71	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.71	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.71	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.71	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.71	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.71	   A^2 -> H(U1(k, e), f(e))
28.55/9.71	   A^2 -> H(U1(k, e), f(k))
28.55/9.71	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.71	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.71	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.71	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.71	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.71	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.71	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.71	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.71	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.71	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.71	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.71	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.71	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.71	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.71	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.71	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.71	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.71	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.71	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.71	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.71	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.71	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.71	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.71	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.71	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.71	   A^2 -> H(U1(c, c), b)
28.55/9.71	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.71	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.71	   A^2 -> H(U1(c, c), e)
28.55/9.71	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.71	   A^2 -> H(e, U1(c, b))
28.55/9.71	   A^2 -> H(e, U1(d, b))
28.55/9.71	   A^2 -> H(e, U1(b, c))
28.55/9.71	   A^2 -> H(e, U1(b, d))
28.55/9.71	   A^2 -> H(e, U1(c, c))
28.55/9.71	   A^2 -> H(e, f(e))
28.55/9.71	   A^2 -> H(e, f(k))
28.55/9.71	   A^2 -> H(e, U1(d, d))
28.55/9.71	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.71	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.71	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.71	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.71	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.71	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.71	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.71	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.71	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.71	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.71	   A^2 -> H(f(e), b)
28.55/9.71	   A^2 -> H(f(e), U1(e, d))
28.55/9.71	   A^2 -> H(f(e), U1(d, e))
28.55/9.71	   A^2 -> H(f(e), c)
28.55/9.71	   A^2 -> H(f(e), U1(e, k))
28.55/9.71	   A^2 -> H(f(e), U1(k, e))
28.55/9.71	   A^2 -> H(f(e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.71	   A^2 -> H(f(k), b)
28.55/9.71	   A^2 -> H(f(k), U1(e, d))
28.55/9.71	   A^2 -> H(f(k), U1(d, e))
28.55/9.71	   A^2 -> H(f(k), c)
28.55/9.71	   A^2 -> H(f(k), U1(e, k))
28.55/9.71	   A^2 -> H(f(k), U1(k, e))
28.55/9.71	   A^2 -> H(f(k), e)
28.55/9.71	   A^2 -> H(f(c), d)
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.71	   A^2 -> H(U1(k, k), f(e))
28.55/9.71	   A^2 -> H(U1(k, k), f(k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.71	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.71	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.71	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.71	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.71	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.71	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.71	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.71	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.71	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.71	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.71	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.71	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.71	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.71	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.71	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.71	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.71	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.71	   A^2 -> H(U1(d, d), b)
28.55/9.71	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.71	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.71	   A^2 -> H(U1(d, d), c)
28.55/9.71	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.71	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.71	   A^2 -> H(U1(d, d), e)
28.55/9.71	   A^2 -> H(f(d), d)
28.55/9.71	   A^2 -> H(f(d), k)
28.55/9.71	   A^2 -> H(U1(c, c), c)
28.55/9.71	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.71	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.71	   A^2 -> H(f(c), k)
28.55/9.71	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.71	   A^2 -> H(f(k), U1(k, k))
28.55/9.71	   A^2 -> H(f(e), e)
28.55/9.71	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.71	   A^2 -> H(d, U1(c, b))
28.55/9.71	   A^2 -> H(d, U1(d, b))
28.55/9.71	   A^2 -> H(d, U1(b, c))
28.55/9.71	   A^2 -> H(d, U1(b, d))
28.55/9.71	   A^2 -> H(d, U1(c, c))
28.55/9.71	   A^2 -> H(d, f(e))
28.55/9.71	   A^2 -> H(d, f(k))
28.55/9.71	   A^2 -> H(d, U1(d, d))
28.55/9.71	   A^2 -> H(a, U1(e, b))
28.55/9.71	   A^2 -> H(a, U1(k, b))
28.55/9.71	   A^2 -> H(a, U1(c, d))
28.55/9.71	   A^2 -> H(a, U1(d, c))
28.55/9.71	   A^2 -> H(a, U1(b, e))
28.55/9.71	   A^2 -> H(a, U1(b, k))
28.55/9.71	   A^2 -> H(a, U1(e, c))
28.55/9.71	   A^2 -> H(a, U1(k, c))
28.55/9.71	   A^2 -> H(a, U1(c, e))
28.55/9.71	   A^2 -> H(a, U1(c, k))
28.55/9.71	   A^2 -> H(a, U1(e, e))
28.55/9.71	   A^2 -> H(a, U1(k, k))
28.55/9.71	   A^2 -> H(a, U1(k, d))
28.55/9.71	   A^2 -> H(a, U1(d, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.71	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.71	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.71	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.71	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.71	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.71	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.71	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.71	   A^2 -> H(U1(e, a), b)
28.55/9.71	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.71	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.71	   A^2 -> H(U1(e, a), c)
28.55/9.71	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.71	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.71	   A^2 -> H(U1(e, a), e)
28.55/9.71	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, a), b)
28.55/9.71	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.71	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.71	   A^2 -> H(U1(k, a), c)
28.55/9.71	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.71	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.71	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, d), b)
28.55/9.71	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.71	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.71	   A^2 -> H(U1(c, d), c)
28.55/9.71	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.71	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.71	   A^2 -> H(U1(c, d), e)
28.55/9.71	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, a), d)
28.55/9.71	   A^2 -> H(U1(c, a), k)
28.55/9.71	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.71	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.71	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.71	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.71	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.71	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.71	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.71	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.71	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.71	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.71	   A^2 -> H(U1(d, c), b)
28.55/9.71	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.71	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.71	   A^2 -> H(U1(d, c), c)
28.55/9.71	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.71	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.71	   A^2 -> H(U1(d, c), e)
28.55/9.71	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.71	   A^2 -> H(U1(d, a), d)
28.55/9.71	   A^2 -> H(U1(d, a), k)
28.55/9.71	   A^2 -> H(U1(a, e), b)
28.55/9.71	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.71	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.71	   A^2 -> H(U1(a, e), c)
28.55/9.71	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.71	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.71	   A^2 -> H(U1(a, e), e)
28.55/9.71	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(a, k), b)
28.55/9.71	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.71	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.71	   A^2 -> H(U1(a, k), c)
28.55/9.71	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.71	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.71	   A^2 -> H(U1(a, k), e)
28.55/9.71	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(a, c), d)
28.55/9.71	   A^2 -> H(U1(a, c), k)
28.55/9.71	   A^2 -> H(U1(a, d), d)
28.55/9.71	
28.55/9.71	The TRS R consists of the following rules:
28.55/9.71	
28.55/9.71	   f(x) -> U1(x, x)
28.55/9.71	   U1(e, x) -> x
28.55/9.71	   a -> c
28.55/9.71	   a -> d
28.55/9.71	   b -> c
28.55/9.71	   b -> d
28.55/9.71	   d -> k
28.55/9.71	   c -> e
28.55/9.71	   c -> k
28.55/9.71	
28.55/9.71	Q is empty.
28.55/9.71	We have to consider all minimal (P,Q,R)-chains.
28.55/9.71	----------------------------------------
28.55/9.71	
28.55/9.71	(1367) TransformationProof (EQUIVALENT)
28.55/9.71	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.71	
28.55/9.71	   (A^2 -> H(U1(c, d), U1(e, d)),A^2 -> H(U1(c, d), U1(e, d)))
28.55/9.71	   (A^2 -> H(U1(d, d), U1(e, d)),A^2 -> H(U1(d, d), U1(e, d)))
28.55/9.71	   (A^2 -> H(U1(a, k), U1(e, d)),A^2 -> H(U1(a, k), U1(e, d)))
28.55/9.71	   (A^2 -> H(U1(a, d), d),A^2 -> H(U1(a, d), d))
28.55/9.71	   (A^2 -> H(U1(a, d), U1(e, k)),A^2 -> H(U1(a, d), U1(e, k)))
28.55/9.71	
28.55/9.71	
28.55/9.71	----------------------------------------
28.55/9.71	
28.55/9.71	(1368)
28.55/9.71	Obligation:
28.55/9.71	Q DP problem:
28.55/9.71	The TRS P consists of the following rules:
28.55/9.71	
28.55/9.71	   H(x, x) -> G(x, x, f(k))
28.55/9.71	   G(d, x, x) -> A^2
28.55/9.71	   A^2 -> H(f(c), f(c))
28.55/9.71	   A^2 -> H(f(d), f(d))
28.55/9.71	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.71	   A^2 -> H(f(e), f(e))
28.55/9.71	   A^2 -> H(f(k), f(k))
28.55/9.71	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.71	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.71	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.71	   A^2 -> H(U1(a, d), U1(d, e))
28.55/9.71	   A^2 -> H(U1(a, d), c)
28.55/9.71	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.71	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.71	   A^2 -> H(U1(a, d), e)
28.55/9.71	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(a, a), d)
28.55/9.71	   A^2 -> H(U1(a, a), k)
28.55/9.71	   A^2 -> H(k, U1(b, b))
28.55/9.71	   A^2 -> H(k, f(c))
28.55/9.71	   A^2 -> H(k, f(d))
28.55/9.71	   A^2 -> H(c, U1(c, b))
28.55/9.71	   A^2 -> H(c, U1(d, b))
28.55/9.71	   A^2 -> H(c, U1(b, c))
28.55/9.71	   A^2 -> H(c, U1(b, d))
28.55/9.71	   A^2 -> H(c, U1(c, c))
28.55/9.71	   A^2 -> H(c, f(e))
28.55/9.71	   A^2 -> H(c, f(k))
28.55/9.71	   A^2 -> H(c, U1(d, d))
28.55/9.71	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.71	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.71	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.71	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.71	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.71	   A^2 -> H(U1(e, k), f(e))
28.55/9.71	   A^2 -> H(U1(e, k), f(k))
28.55/9.71	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.71	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.71	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.71	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.71	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.71	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.71	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.71	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.71	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.71	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.71	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.71	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.71	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.71	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.71	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.71	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.71	   A^2 -> H(U1(k, e), f(e))
28.55/9.71	   A^2 -> H(U1(k, e), f(k))
28.55/9.71	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.71	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.71	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.71	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.71	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.71	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.71	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.71	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.71	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.71	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.71	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.71	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.71	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.71	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.71	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.71	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.71	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.71	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.71	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.71	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.71	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.71	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.71	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.71	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.71	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.71	   A^2 -> H(U1(c, c), b)
28.55/9.71	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.71	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.71	   A^2 -> H(U1(c, c), e)
28.55/9.71	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.71	   A^2 -> H(e, U1(c, b))
28.55/9.71	   A^2 -> H(e, U1(d, b))
28.55/9.71	   A^2 -> H(e, U1(b, c))
28.55/9.71	   A^2 -> H(e, U1(b, d))
28.55/9.71	   A^2 -> H(e, U1(c, c))
28.55/9.71	   A^2 -> H(e, f(e))
28.55/9.71	   A^2 -> H(e, f(k))
28.55/9.71	   A^2 -> H(e, U1(d, d))
28.55/9.71	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.71	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.71	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.71	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.71	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.71	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.71	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.71	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.71	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.71	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.71	   A^2 -> H(f(e), b)
28.55/9.71	   A^2 -> H(f(e), U1(e, d))
28.55/9.71	   A^2 -> H(f(e), U1(d, e))
28.55/9.71	   A^2 -> H(f(e), c)
28.55/9.71	   A^2 -> H(f(e), U1(e, k))
28.55/9.71	   A^2 -> H(f(e), U1(k, e))
28.55/9.71	   A^2 -> H(f(e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.71	   A^2 -> H(f(k), b)
28.55/9.71	   A^2 -> H(f(k), U1(e, d))
28.55/9.71	   A^2 -> H(f(k), U1(d, e))
28.55/9.71	   A^2 -> H(f(k), c)
28.55/9.71	   A^2 -> H(f(k), U1(e, k))
28.55/9.71	   A^2 -> H(f(k), U1(k, e))
28.55/9.71	   A^2 -> H(f(k), e)
28.55/9.71	   A^2 -> H(f(c), d)
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.71	   A^2 -> H(U1(k, k), f(e))
28.55/9.71	   A^2 -> H(U1(k, k), f(k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.71	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.71	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.71	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.71	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.71	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.71	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.71	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.71	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.71	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.71	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.71	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.71	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.71	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.71	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.71	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.71	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.71	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.71	   A^2 -> H(U1(d, d), b)
28.55/9.71	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.71	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.71	   A^2 -> H(U1(d, d), c)
28.55/9.71	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.71	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.71	   A^2 -> H(U1(d, d), e)
28.55/9.71	   A^2 -> H(f(d), d)
28.55/9.71	   A^2 -> H(f(d), k)
28.55/9.71	   A^2 -> H(U1(c, c), c)
28.55/9.71	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.71	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.71	   A^2 -> H(f(c), k)
28.55/9.71	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.71	   A^2 -> H(f(k), U1(k, k))
28.55/9.71	   A^2 -> H(f(e), e)
28.55/9.71	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.71	   A^2 -> H(d, U1(c, b))
28.55/9.71	   A^2 -> H(d, U1(d, b))
28.55/9.71	   A^2 -> H(d, U1(b, c))
28.55/9.71	   A^2 -> H(d, U1(b, d))
28.55/9.71	   A^2 -> H(d, U1(c, c))
28.55/9.71	   A^2 -> H(d, f(e))
28.55/9.71	   A^2 -> H(d, f(k))
28.55/9.71	   A^2 -> H(d, U1(d, d))
28.55/9.71	   A^2 -> H(a, U1(e, b))
28.55/9.71	   A^2 -> H(a, U1(k, b))
28.55/9.71	   A^2 -> H(a, U1(c, d))
28.55/9.71	   A^2 -> H(a, U1(d, c))
28.55/9.71	   A^2 -> H(a, U1(b, e))
28.55/9.71	   A^2 -> H(a, U1(b, k))
28.55/9.71	   A^2 -> H(a, U1(e, c))
28.55/9.71	   A^2 -> H(a, U1(k, c))
28.55/9.71	   A^2 -> H(a, U1(c, e))
28.55/9.71	   A^2 -> H(a, U1(c, k))
28.55/9.71	   A^2 -> H(a, U1(e, e))
28.55/9.71	   A^2 -> H(a, U1(k, k))
28.55/9.71	   A^2 -> H(a, U1(k, d))
28.55/9.71	   A^2 -> H(a, U1(d, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.71	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.71	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.71	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.71	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.71	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.71	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.71	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.71	   A^2 -> H(U1(e, a), b)
28.55/9.71	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.71	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.71	   A^2 -> H(U1(e, a), c)
28.55/9.71	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.71	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.71	   A^2 -> H(U1(e, a), e)
28.55/9.71	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, a), b)
28.55/9.71	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.71	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.71	   A^2 -> H(U1(k, a), c)
28.55/9.71	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.71	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.71	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, d), b)
28.55/9.71	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.71	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.71	   A^2 -> H(U1(c, d), c)
28.55/9.71	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.71	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.71	   A^2 -> H(U1(c, d), e)
28.55/9.71	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, a), d)
28.55/9.71	   A^2 -> H(U1(c, a), k)
28.55/9.71	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.71	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.71	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.71	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.71	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.71	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.71	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.71	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.71	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.71	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.71	   A^2 -> H(U1(d, c), b)
28.55/9.71	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.71	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.71	   A^2 -> H(U1(d, c), c)
28.55/9.71	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.71	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.71	   A^2 -> H(U1(d, c), e)
28.55/9.71	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.71	   A^2 -> H(U1(d, a), d)
28.55/9.71	   A^2 -> H(U1(d, a), k)
28.55/9.71	   A^2 -> H(U1(a, e), b)
28.55/9.71	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.71	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.71	   A^2 -> H(U1(a, e), c)
28.55/9.71	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.71	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.71	   A^2 -> H(U1(a, e), e)
28.55/9.71	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(a, k), b)
28.55/9.71	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.71	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.71	   A^2 -> H(U1(a, k), c)
28.55/9.71	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.71	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.71	   A^2 -> H(U1(a, k), e)
28.55/9.71	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(a, c), d)
28.55/9.71	   A^2 -> H(U1(a, c), k)
28.55/9.71	   A^2 -> H(U1(a, d), d)
28.55/9.71	
28.55/9.71	The TRS R consists of the following rules:
28.55/9.71	
28.55/9.71	   f(x) -> U1(x, x)
28.55/9.71	   U1(e, x) -> x
28.55/9.71	   a -> c
28.55/9.71	   a -> d
28.55/9.71	   b -> c
28.55/9.71	   b -> d
28.55/9.71	   d -> k
28.55/9.71	   c -> e
28.55/9.71	   c -> k
28.55/9.71	
28.55/9.71	Q is empty.
28.55/9.71	We have to consider all minimal (P,Q,R)-chains.
28.55/9.71	----------------------------------------
28.55/9.71	
28.55/9.71	(1369) TransformationProof (EQUIVALENT)
28.55/9.71	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.71	
28.55/9.71	   (A^2 -> H(U1(c, d), U1(d, e)),A^2 -> H(U1(c, d), U1(d, e)))
28.55/9.71	   (A^2 -> H(U1(d, d), U1(d, e)),A^2 -> H(U1(d, d), U1(d, e)))
28.55/9.71	   (A^2 -> H(U1(a, k), U1(d, e)),A^2 -> H(U1(a, k), U1(d, e)))
28.55/9.71	   (A^2 -> H(U1(a, d), U1(k, e)),A^2 -> H(U1(a, d), U1(k, e)))
28.55/9.71	
28.55/9.71	
28.55/9.71	----------------------------------------
28.55/9.71	
28.55/9.71	(1370)
28.55/9.71	Obligation:
28.55/9.71	Q DP problem:
28.55/9.71	The TRS P consists of the following rules:
28.55/9.71	
28.55/9.71	   H(x, x) -> G(x, x, f(k))
28.55/9.71	   G(d, x, x) -> A^2
28.55/9.71	   A^2 -> H(f(c), f(c))
28.55/9.71	   A^2 -> H(f(d), f(d))
28.55/9.71	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.71	   A^2 -> H(f(e), f(e))
28.55/9.71	   A^2 -> H(f(k), f(k))
28.55/9.71	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.71	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.71	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.71	   A^2 -> H(U1(a, d), c)
28.55/9.71	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.71	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.71	   A^2 -> H(U1(a, d), e)
28.55/9.71	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(a, a), d)
28.55/9.71	   A^2 -> H(U1(a, a), k)
28.55/9.71	   A^2 -> H(k, U1(b, b))
28.55/9.71	   A^2 -> H(k, f(c))
28.55/9.71	   A^2 -> H(k, f(d))
28.55/9.71	   A^2 -> H(c, U1(c, b))
28.55/9.71	   A^2 -> H(c, U1(d, b))
28.55/9.71	   A^2 -> H(c, U1(b, c))
28.55/9.71	   A^2 -> H(c, U1(b, d))
28.55/9.71	   A^2 -> H(c, U1(c, c))
28.55/9.71	   A^2 -> H(c, f(e))
28.55/9.71	   A^2 -> H(c, f(k))
28.55/9.71	   A^2 -> H(c, U1(d, d))
28.55/9.71	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.71	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.71	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.71	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.71	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.71	   A^2 -> H(U1(e, k), f(e))
28.55/9.71	   A^2 -> H(U1(e, k), f(k))
28.55/9.71	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.71	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.71	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.71	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.71	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.71	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.71	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.71	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.71	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.71	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.71	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.71	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.71	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.71	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.71	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.71	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.71	   A^2 -> H(U1(k, e), f(e))
28.55/9.71	   A^2 -> H(U1(k, e), f(k))
28.55/9.71	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.71	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.71	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.71	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.71	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.71	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.71	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.71	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.71	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.71	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.71	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.71	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.71	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.71	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.71	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.71	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.71	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.71	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.71	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.71	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.71	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.71	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.71	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.71	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.71	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.71	   A^2 -> H(U1(c, c), b)
28.55/9.71	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.71	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.71	   A^2 -> H(U1(c, c), e)
28.55/9.71	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.71	   A^2 -> H(e, U1(c, b))
28.55/9.71	   A^2 -> H(e, U1(d, b))
28.55/9.71	   A^2 -> H(e, U1(b, c))
28.55/9.71	   A^2 -> H(e, U1(b, d))
28.55/9.71	   A^2 -> H(e, U1(c, c))
28.55/9.71	   A^2 -> H(e, f(e))
28.55/9.71	   A^2 -> H(e, f(k))
28.55/9.71	   A^2 -> H(e, U1(d, d))
28.55/9.71	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.71	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.71	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.71	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.71	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.71	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.71	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.71	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.71	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.71	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.71	   A^2 -> H(f(e), b)
28.55/9.71	   A^2 -> H(f(e), U1(e, d))
28.55/9.71	   A^2 -> H(f(e), U1(d, e))
28.55/9.71	   A^2 -> H(f(e), c)
28.55/9.71	   A^2 -> H(f(e), U1(e, k))
28.55/9.71	   A^2 -> H(f(e), U1(k, e))
28.55/9.71	   A^2 -> H(f(e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.71	   A^2 -> H(f(k), b)
28.55/9.71	   A^2 -> H(f(k), U1(e, d))
28.55/9.71	   A^2 -> H(f(k), U1(d, e))
28.55/9.71	   A^2 -> H(f(k), c)
28.55/9.71	   A^2 -> H(f(k), U1(e, k))
28.55/9.71	   A^2 -> H(f(k), U1(k, e))
28.55/9.71	   A^2 -> H(f(k), e)
28.55/9.71	   A^2 -> H(f(c), d)
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.71	   A^2 -> H(U1(k, k), f(e))
28.55/9.71	   A^2 -> H(U1(k, k), f(k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.71	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.71	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.71	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.71	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.71	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.71	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.71	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.71	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.71	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.71	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.71	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.71	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.71	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.71	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.71	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.71	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.71	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.71	   A^2 -> H(U1(d, d), b)
28.55/9.71	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.71	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.71	   A^2 -> H(U1(d, d), c)
28.55/9.71	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.71	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.71	   A^2 -> H(U1(d, d), e)
28.55/9.71	   A^2 -> H(f(d), d)
28.55/9.71	   A^2 -> H(f(d), k)
28.55/9.71	   A^2 -> H(U1(c, c), c)
28.55/9.71	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.71	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.71	   A^2 -> H(f(c), k)
28.55/9.71	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.71	   A^2 -> H(f(k), U1(k, k))
28.55/9.71	   A^2 -> H(f(e), e)
28.55/9.71	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.71	   A^2 -> H(d, U1(c, b))
28.55/9.71	   A^2 -> H(d, U1(d, b))
28.55/9.71	   A^2 -> H(d, U1(b, c))
28.55/9.71	   A^2 -> H(d, U1(b, d))
28.55/9.71	   A^2 -> H(d, U1(c, c))
28.55/9.71	   A^2 -> H(d, f(e))
28.55/9.71	   A^2 -> H(d, f(k))
28.55/9.71	   A^2 -> H(d, U1(d, d))
28.55/9.71	   A^2 -> H(a, U1(e, b))
28.55/9.71	   A^2 -> H(a, U1(k, b))
28.55/9.71	   A^2 -> H(a, U1(c, d))
28.55/9.71	   A^2 -> H(a, U1(d, c))
28.55/9.71	   A^2 -> H(a, U1(b, e))
28.55/9.71	   A^2 -> H(a, U1(b, k))
28.55/9.71	   A^2 -> H(a, U1(e, c))
28.55/9.71	   A^2 -> H(a, U1(k, c))
28.55/9.71	   A^2 -> H(a, U1(c, e))
28.55/9.71	   A^2 -> H(a, U1(c, k))
28.55/9.71	   A^2 -> H(a, U1(e, e))
28.55/9.71	   A^2 -> H(a, U1(k, k))
28.55/9.71	   A^2 -> H(a, U1(k, d))
28.55/9.71	   A^2 -> H(a, U1(d, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.71	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.71	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.71	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.71	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.71	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.71	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.71	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.71	   A^2 -> H(U1(e, a), b)
28.55/9.71	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.71	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.71	   A^2 -> H(U1(e, a), c)
28.55/9.71	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.71	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.71	   A^2 -> H(U1(e, a), e)
28.55/9.71	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, a), b)
28.55/9.71	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.71	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.71	   A^2 -> H(U1(k, a), c)
28.55/9.71	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.71	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.71	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, d), b)
28.55/9.71	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.71	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.71	   A^2 -> H(U1(c, d), c)
28.55/9.71	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.71	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.71	   A^2 -> H(U1(c, d), e)
28.55/9.71	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, a), d)
28.55/9.71	   A^2 -> H(U1(c, a), k)
28.55/9.71	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.71	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.71	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.71	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.71	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.71	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.71	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.71	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.71	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.71	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.71	   A^2 -> H(U1(d, c), b)
28.55/9.71	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.71	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.71	   A^2 -> H(U1(d, c), c)
28.55/9.71	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.71	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.71	   A^2 -> H(U1(d, c), e)
28.55/9.71	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.71	   A^2 -> H(U1(d, a), d)
28.55/9.71	   A^2 -> H(U1(d, a), k)
28.55/9.71	   A^2 -> H(U1(a, e), b)
28.55/9.71	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.71	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.71	   A^2 -> H(U1(a, e), c)
28.55/9.71	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.71	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.71	   A^2 -> H(U1(a, e), e)
28.55/9.71	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(a, k), b)
28.55/9.71	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.71	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.71	   A^2 -> H(U1(a, k), c)
28.55/9.71	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.71	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.71	   A^2 -> H(U1(a, k), e)
28.55/9.71	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(a, c), d)
28.55/9.71	   A^2 -> H(U1(a, c), k)
28.55/9.71	   A^2 -> H(U1(a, d), d)
28.55/9.71	
28.55/9.71	The TRS R consists of the following rules:
28.55/9.71	
28.55/9.71	   f(x) -> U1(x, x)
28.55/9.71	   U1(e, x) -> x
28.55/9.71	   a -> c
28.55/9.71	   a -> d
28.55/9.71	   b -> c
28.55/9.71	   b -> d
28.55/9.71	   d -> k
28.55/9.71	   c -> e
28.55/9.71	   c -> k
28.55/9.71	
28.55/9.71	Q is empty.
28.55/9.71	We have to consider all minimal (P,Q,R)-chains.
28.55/9.71	----------------------------------------
28.55/9.71	
28.55/9.71	(1371) TransformationProof (EQUIVALENT)
28.55/9.71	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), c) at position [] we obtained the following new rules [LPAR04]:
28.55/9.71	
28.55/9.71	   (A^2 -> H(U1(c, d), c),A^2 -> H(U1(c, d), c))
28.55/9.71	   (A^2 -> H(U1(d, d), c),A^2 -> H(U1(d, d), c))
28.55/9.71	   (A^2 -> H(U1(a, k), c),A^2 -> H(U1(a, k), c))
28.55/9.71	   (A^2 -> H(U1(a, d), e),A^2 -> H(U1(a, d), e))
28.55/9.71	   (A^2 -> H(U1(a, d), k),A^2 -> H(U1(a, d), k))
28.55/9.71	
28.55/9.71	
28.55/9.71	----------------------------------------
28.55/9.71	
28.55/9.71	(1372)
28.55/9.71	Obligation:
28.55/9.71	Q DP problem:
28.55/9.71	The TRS P consists of the following rules:
28.55/9.71	
28.55/9.71	   H(x, x) -> G(x, x, f(k))
28.55/9.71	   G(d, x, x) -> A^2
28.55/9.71	   A^2 -> H(f(c), f(c))
28.55/9.71	   A^2 -> H(f(d), f(d))
28.55/9.71	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.71	   A^2 -> H(f(e), f(e))
28.55/9.71	   A^2 -> H(f(k), f(k))
28.55/9.71	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.71	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.71	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.71	   A^2 -> H(U1(a, d), U1(e, k))
28.55/9.71	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.71	   A^2 -> H(U1(a, d), e)
28.55/9.71	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(a, a), d)
28.55/9.71	   A^2 -> H(U1(a, a), k)
28.55/9.71	   A^2 -> H(k, U1(b, b))
28.55/9.71	   A^2 -> H(k, f(c))
28.55/9.71	   A^2 -> H(k, f(d))
28.55/9.71	   A^2 -> H(c, U1(c, b))
28.55/9.71	   A^2 -> H(c, U1(d, b))
28.55/9.71	   A^2 -> H(c, U1(b, c))
28.55/9.71	   A^2 -> H(c, U1(b, d))
28.55/9.71	   A^2 -> H(c, U1(c, c))
28.55/9.71	   A^2 -> H(c, f(e))
28.55/9.71	   A^2 -> H(c, f(k))
28.55/9.71	   A^2 -> H(c, U1(d, d))
28.55/9.71	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.71	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.71	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.71	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.71	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.71	   A^2 -> H(U1(e, k), f(e))
28.55/9.71	   A^2 -> H(U1(e, k), f(k))
28.55/9.71	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.71	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.71	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.71	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.71	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.71	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.71	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.71	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.71	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.71	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.71	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.71	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.71	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.71	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.71	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.71	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.71	   A^2 -> H(U1(k, e), f(e))
28.55/9.71	   A^2 -> H(U1(k, e), f(k))
28.55/9.71	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.71	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.71	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.71	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.71	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.71	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.71	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.71	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.71	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.71	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.71	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.71	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.71	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.71	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.71	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.71	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.71	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.71	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.71	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.71	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.71	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.71	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.71	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.71	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.71	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.71	   A^2 -> H(U1(c, c), b)
28.55/9.71	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.71	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.71	   A^2 -> H(U1(c, c), e)
28.55/9.71	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.71	   A^2 -> H(e, U1(c, b))
28.55/9.71	   A^2 -> H(e, U1(d, b))
28.55/9.71	   A^2 -> H(e, U1(b, c))
28.55/9.71	   A^2 -> H(e, U1(b, d))
28.55/9.71	   A^2 -> H(e, U1(c, c))
28.55/9.71	   A^2 -> H(e, f(e))
28.55/9.71	   A^2 -> H(e, f(k))
28.55/9.71	   A^2 -> H(e, U1(d, d))
28.55/9.71	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.71	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.71	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.71	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.71	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.71	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.71	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.71	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.71	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.71	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.71	   A^2 -> H(f(e), b)
28.55/9.71	   A^2 -> H(f(e), U1(e, d))
28.55/9.71	   A^2 -> H(f(e), U1(d, e))
28.55/9.71	   A^2 -> H(f(e), c)
28.55/9.71	   A^2 -> H(f(e), U1(e, k))
28.55/9.71	   A^2 -> H(f(e), U1(k, e))
28.55/9.71	   A^2 -> H(f(e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.71	   A^2 -> H(f(k), b)
28.55/9.71	   A^2 -> H(f(k), U1(e, d))
28.55/9.71	   A^2 -> H(f(k), U1(d, e))
28.55/9.71	   A^2 -> H(f(k), c)
28.55/9.71	   A^2 -> H(f(k), U1(e, k))
28.55/9.71	   A^2 -> H(f(k), U1(k, e))
28.55/9.71	   A^2 -> H(f(k), e)
28.55/9.71	   A^2 -> H(f(c), d)
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.71	   A^2 -> H(U1(k, k), f(e))
28.55/9.71	   A^2 -> H(U1(k, k), f(k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.71	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.71	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.71	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.71	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.71	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.71	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.71	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.71	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.71	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.71	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.71	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.71	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.71	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.71	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.71	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.71	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.71	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.71	   A^2 -> H(U1(d, d), b)
28.55/9.71	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.71	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.71	   A^2 -> H(U1(d, d), c)
28.55/9.71	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.71	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.71	   A^2 -> H(U1(d, d), e)
28.55/9.71	   A^2 -> H(f(d), d)
28.55/9.71	   A^2 -> H(f(d), k)
28.55/9.71	   A^2 -> H(U1(c, c), c)
28.55/9.71	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.71	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.71	   A^2 -> H(f(c), k)
28.55/9.71	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.71	   A^2 -> H(f(k), U1(k, k))
28.55/9.71	   A^2 -> H(f(e), e)
28.55/9.71	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.71	   A^2 -> H(d, U1(c, b))
28.55/9.71	   A^2 -> H(d, U1(d, b))
28.55/9.71	   A^2 -> H(d, U1(b, c))
28.55/9.71	   A^2 -> H(d, U1(b, d))
28.55/9.71	   A^2 -> H(d, U1(c, c))
28.55/9.71	   A^2 -> H(d, f(e))
28.55/9.71	   A^2 -> H(d, f(k))
28.55/9.71	   A^2 -> H(d, U1(d, d))
28.55/9.71	   A^2 -> H(a, U1(e, b))
28.55/9.71	   A^2 -> H(a, U1(k, b))
28.55/9.71	   A^2 -> H(a, U1(c, d))
28.55/9.71	   A^2 -> H(a, U1(d, c))
28.55/9.71	   A^2 -> H(a, U1(b, e))
28.55/9.71	   A^2 -> H(a, U1(b, k))
28.55/9.71	   A^2 -> H(a, U1(e, c))
28.55/9.71	   A^2 -> H(a, U1(k, c))
28.55/9.71	   A^2 -> H(a, U1(c, e))
28.55/9.71	   A^2 -> H(a, U1(c, k))
28.55/9.71	   A^2 -> H(a, U1(e, e))
28.55/9.71	   A^2 -> H(a, U1(k, k))
28.55/9.71	   A^2 -> H(a, U1(k, d))
28.55/9.71	   A^2 -> H(a, U1(d, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.71	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.71	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.71	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.71	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.71	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.71	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.71	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.71	   A^2 -> H(U1(e, a), b)
28.55/9.71	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.71	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.71	   A^2 -> H(U1(e, a), c)
28.55/9.71	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.71	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.71	   A^2 -> H(U1(e, a), e)
28.55/9.71	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, a), b)
28.55/9.71	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.71	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.71	   A^2 -> H(U1(k, a), c)
28.55/9.71	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.71	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.71	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, d), b)
28.55/9.71	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.71	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.71	   A^2 -> H(U1(c, d), c)
28.55/9.71	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.71	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.71	   A^2 -> H(U1(c, d), e)
28.55/9.71	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, a), d)
28.55/9.71	   A^2 -> H(U1(c, a), k)
28.55/9.71	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.71	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.71	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.71	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.71	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.71	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.71	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.71	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.71	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.71	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.71	   A^2 -> H(U1(d, c), b)
28.55/9.71	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.71	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.71	   A^2 -> H(U1(d, c), c)
28.55/9.71	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.71	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.71	   A^2 -> H(U1(d, c), e)
28.55/9.71	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.71	   A^2 -> H(U1(d, a), d)
28.55/9.71	   A^2 -> H(U1(d, a), k)
28.55/9.71	   A^2 -> H(U1(a, e), b)
28.55/9.71	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.71	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.71	   A^2 -> H(U1(a, e), c)
28.55/9.71	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.71	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.71	   A^2 -> H(U1(a, e), e)
28.55/9.71	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(a, k), b)
28.55/9.71	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.71	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.71	   A^2 -> H(U1(a, k), c)
28.55/9.71	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.71	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.71	   A^2 -> H(U1(a, k), e)
28.55/9.71	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(a, c), d)
28.55/9.71	   A^2 -> H(U1(a, c), k)
28.55/9.71	   A^2 -> H(U1(a, d), d)
28.55/9.71	   A^2 -> H(U1(a, d), k)
28.55/9.71	
28.55/9.71	The TRS R consists of the following rules:
28.55/9.71	
28.55/9.71	   f(x) -> U1(x, x)
28.55/9.71	   U1(e, x) -> x
28.55/9.71	   a -> c
28.55/9.71	   a -> d
28.55/9.71	   b -> c
28.55/9.71	   b -> d
28.55/9.71	   d -> k
28.55/9.71	   c -> e
28.55/9.71	   c -> k
28.55/9.71	
28.55/9.71	Q is empty.
28.55/9.71	We have to consider all minimal (P,Q,R)-chains.
28.55/9.71	----------------------------------------
28.55/9.71	
28.55/9.71	(1373) TransformationProof (EQUIVALENT)
28.55/9.71	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.71	
28.55/9.71	   (A^2 -> H(U1(c, d), U1(e, k)),A^2 -> H(U1(c, d), U1(e, k)))
28.55/9.71	   (A^2 -> H(U1(d, d), U1(e, k)),A^2 -> H(U1(d, d), U1(e, k)))
28.55/9.71	   (A^2 -> H(U1(a, k), U1(e, k)),A^2 -> H(U1(a, k), U1(e, k)))
28.55/9.71	   (A^2 -> H(U1(a, d), k),A^2 -> H(U1(a, d), k))
28.55/9.71	
28.55/9.71	
28.55/9.71	----------------------------------------
28.55/9.71	
28.55/9.71	(1374)
28.55/9.71	Obligation:
28.55/9.71	Q DP problem:
28.55/9.71	The TRS P consists of the following rules:
28.55/9.71	
28.55/9.71	   H(x, x) -> G(x, x, f(k))
28.55/9.71	   G(d, x, x) -> A^2
28.55/9.71	   A^2 -> H(f(c), f(c))
28.55/9.71	   A^2 -> H(f(d), f(d))
28.55/9.71	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.71	   A^2 -> H(f(e), f(e))
28.55/9.71	   A^2 -> H(f(k), f(k))
28.55/9.71	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.71	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.71	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.71	   A^2 -> H(U1(a, d), U1(k, e))
28.55/9.71	   A^2 -> H(U1(a, d), e)
28.55/9.71	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(a, a), d)
28.55/9.71	   A^2 -> H(U1(a, a), k)
28.55/9.71	   A^2 -> H(k, U1(b, b))
28.55/9.71	   A^2 -> H(k, f(c))
28.55/9.71	   A^2 -> H(k, f(d))
28.55/9.71	   A^2 -> H(c, U1(c, b))
28.55/9.71	   A^2 -> H(c, U1(d, b))
28.55/9.71	   A^2 -> H(c, U1(b, c))
28.55/9.71	   A^2 -> H(c, U1(b, d))
28.55/9.71	   A^2 -> H(c, U1(c, c))
28.55/9.71	   A^2 -> H(c, f(e))
28.55/9.71	   A^2 -> H(c, f(k))
28.55/9.71	   A^2 -> H(c, U1(d, d))
28.55/9.71	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.71	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.71	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.71	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.71	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.71	   A^2 -> H(U1(e, k), f(e))
28.55/9.71	   A^2 -> H(U1(e, k), f(k))
28.55/9.71	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.71	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.71	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.71	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.71	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.71	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.71	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.71	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.71	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.71	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.71	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.71	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.71	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.71	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.71	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.71	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.71	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.71	   A^2 -> H(U1(k, e), f(e))
28.55/9.71	   A^2 -> H(U1(k, e), f(k))
28.55/9.71	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.71	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.71	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.71	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.71	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.71	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.71	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.71	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.71	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.71	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.71	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.71	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.71	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.71	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.71	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.71	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.71	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.71	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.71	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.71	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.71	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.71	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.71	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.71	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.71	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.71	   A^2 -> H(U1(c, c), b)
28.55/9.71	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.71	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.71	   A^2 -> H(U1(c, c), e)
28.55/9.71	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.71	   A^2 -> H(e, U1(c, b))
28.55/9.71	   A^2 -> H(e, U1(d, b))
28.55/9.71	   A^2 -> H(e, U1(b, c))
28.55/9.71	   A^2 -> H(e, U1(b, d))
28.55/9.71	   A^2 -> H(e, U1(c, c))
28.55/9.71	   A^2 -> H(e, f(e))
28.55/9.71	   A^2 -> H(e, f(k))
28.55/9.71	   A^2 -> H(e, U1(d, d))
28.55/9.71	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.71	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.71	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.71	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.71	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.71	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.71	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.71	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.71	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.71	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.71	   A^2 -> H(f(e), b)
28.55/9.71	   A^2 -> H(f(e), U1(e, d))
28.55/9.71	   A^2 -> H(f(e), U1(d, e))
28.55/9.71	   A^2 -> H(f(e), c)
28.55/9.71	   A^2 -> H(f(e), U1(e, k))
28.55/9.71	   A^2 -> H(f(e), U1(k, e))
28.55/9.71	   A^2 -> H(f(e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.71	   A^2 -> H(f(k), b)
28.55/9.71	   A^2 -> H(f(k), U1(e, d))
28.55/9.71	   A^2 -> H(f(k), U1(d, e))
28.55/9.71	   A^2 -> H(f(k), c)
28.55/9.71	   A^2 -> H(f(k), U1(e, k))
28.55/9.71	   A^2 -> H(f(k), U1(k, e))
28.55/9.71	   A^2 -> H(f(k), e)
28.55/9.71	   A^2 -> H(f(c), d)
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.71	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.71	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.71	   A^2 -> H(U1(k, k), f(e))
28.55/9.71	   A^2 -> H(U1(k, k), f(k))
28.55/9.71	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.71	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.71	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.71	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.71	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.71	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.71	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.71	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.71	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.71	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.71	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.71	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.71	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.71	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.71	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.71	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.71	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.71	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.71	   A^2 -> H(U1(d, d), b)
28.55/9.71	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.71	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.71	   A^2 -> H(U1(d, d), c)
28.55/9.71	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.71	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.71	   A^2 -> H(U1(d, d), e)
28.55/9.71	   A^2 -> H(f(d), d)
28.55/9.71	   A^2 -> H(f(d), k)
28.55/9.71	   A^2 -> H(U1(c, c), c)
28.55/9.71	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.71	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.71	   A^2 -> H(f(c), k)
28.55/9.71	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.71	   A^2 -> H(f(k), U1(k, k))
28.55/9.71	   A^2 -> H(f(e), e)
28.55/9.71	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.71	   A^2 -> H(d, U1(c, b))
28.55/9.71	   A^2 -> H(d, U1(d, b))
28.55/9.71	   A^2 -> H(d, U1(b, c))
28.55/9.71	   A^2 -> H(d, U1(b, d))
28.55/9.71	   A^2 -> H(d, U1(c, c))
28.55/9.71	   A^2 -> H(d, f(e))
28.55/9.71	   A^2 -> H(d, f(k))
28.55/9.71	   A^2 -> H(d, U1(d, d))
28.55/9.71	   A^2 -> H(a, U1(e, b))
28.55/9.71	   A^2 -> H(a, U1(k, b))
28.55/9.71	   A^2 -> H(a, U1(c, d))
28.55/9.71	   A^2 -> H(a, U1(d, c))
28.55/9.71	   A^2 -> H(a, U1(b, e))
28.55/9.71	   A^2 -> H(a, U1(b, k))
28.55/9.71	   A^2 -> H(a, U1(e, c))
28.55/9.71	   A^2 -> H(a, U1(k, c))
28.55/9.71	   A^2 -> H(a, U1(c, e))
28.55/9.71	   A^2 -> H(a, U1(c, k))
28.55/9.71	   A^2 -> H(a, U1(e, e))
28.55/9.71	   A^2 -> H(a, U1(k, k))
28.55/9.71	   A^2 -> H(a, U1(k, d))
28.55/9.71	   A^2 -> H(a, U1(d, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.71	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.71	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.71	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.71	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.71	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.71	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.71	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.71	   A^2 -> H(U1(e, a), b)
28.55/9.71	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.71	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.71	   A^2 -> H(U1(e, a), c)
28.55/9.71	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.71	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.71	   A^2 -> H(U1(e, a), e)
28.55/9.71	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.71	   A^2 -> H(U1(k, a), b)
28.55/9.71	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.71	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.71	   A^2 -> H(U1(k, a), c)
28.55/9.71	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.71	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.71	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, d), b)
28.55/9.71	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.71	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.71	   A^2 -> H(U1(c, d), c)
28.55/9.71	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.71	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.71	   A^2 -> H(U1(c, d), e)
28.55/9.71	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.71	   A^2 -> H(U1(c, a), d)
28.55/9.71	   A^2 -> H(U1(c, a), k)
28.55/9.71	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.71	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.71	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.71	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.71	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.71	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.71	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.71	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.71	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.71	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.71	   A^2 -> H(U1(d, c), b)
28.55/9.71	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.71	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.71	   A^2 -> H(U1(d, c), c)
28.55/9.71	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.71	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.71	   A^2 -> H(U1(d, c), e)
28.55/9.71	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.71	   A^2 -> H(U1(d, a), d)
28.55/9.71	   A^2 -> H(U1(d, a), k)
28.55/9.71	   A^2 -> H(U1(a, e), b)
28.55/9.71	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.71	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.71	   A^2 -> H(U1(a, e), c)
28.55/9.71	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.71	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.71	   A^2 -> H(U1(a, e), e)
28.55/9.71	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.71	   A^2 -> H(U1(a, k), b)
28.55/9.71	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.71	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.71	   A^2 -> H(U1(a, k), c)
28.55/9.71	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.71	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.71	   A^2 -> H(U1(a, k), e)
28.55/9.71	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.71	   A^2 -> H(U1(a, c), d)
28.55/9.71	   A^2 -> H(U1(a, c), k)
28.55/9.71	   A^2 -> H(U1(a, d), d)
28.55/9.71	   A^2 -> H(U1(a, d), k)
28.55/9.71	
28.55/9.71	The TRS R consists of the following rules:
28.55/9.71	
28.55/9.71	   f(x) -> U1(x, x)
28.55/9.71	   U1(e, x) -> x
28.55/9.71	   a -> c
28.55/9.71	   a -> d
28.55/9.72	   b -> c
28.55/9.72	   b -> d
28.55/9.72	   d -> k
28.55/9.72	   c -> e
28.55/9.72	   c -> k
28.55/9.72	
28.55/9.72	Q is empty.
28.55/9.72	We have to consider all minimal (P,Q,R)-chains.
28.55/9.72	----------------------------------------
28.55/9.72	
28.55/9.72	(1375) TransformationProof (EQUIVALENT)
28.55/9.72	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.72	
28.55/9.72	   (A^2 -> H(U1(c, d), U1(k, e)),A^2 -> H(U1(c, d), U1(k, e)))
28.55/9.72	   (A^2 -> H(U1(d, d), U1(k, e)),A^2 -> H(U1(d, d), U1(k, e)))
28.55/9.72	   (A^2 -> H(U1(a, k), U1(k, e)),A^2 -> H(U1(a, k), U1(k, e)))
28.55/9.72	
28.55/9.72	
28.55/9.72	----------------------------------------
28.55/9.72	
28.55/9.72	(1376)
28.55/9.72	Obligation:
28.55/9.72	Q DP problem:
28.55/9.72	The TRS P consists of the following rules:
28.55/9.72	
28.55/9.72	   H(x, x) -> G(x, x, f(k))
28.55/9.72	   G(d, x, x) -> A^2
28.55/9.72	   A^2 -> H(f(c), f(c))
28.55/9.72	   A^2 -> H(f(d), f(d))
28.55/9.72	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.72	   A^2 -> H(f(e), f(e))
28.55/9.72	   A^2 -> H(f(k), f(k))
28.55/9.72	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.72	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.72	   A^2 -> H(U1(a, d), e)
28.55/9.72	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(a, a), d)
28.55/9.72	   A^2 -> H(U1(a, a), k)
28.55/9.72	   A^2 -> H(k, U1(b, b))
28.55/9.72	   A^2 -> H(k, f(c))
28.55/9.72	   A^2 -> H(k, f(d))
28.55/9.72	   A^2 -> H(c, U1(c, b))
28.55/9.72	   A^2 -> H(c, U1(d, b))
28.55/9.72	   A^2 -> H(c, U1(b, c))
28.55/9.72	   A^2 -> H(c, U1(b, d))
28.55/9.72	   A^2 -> H(c, U1(c, c))
28.55/9.72	   A^2 -> H(c, f(e))
28.55/9.72	   A^2 -> H(c, f(k))
28.55/9.72	   A^2 -> H(c, U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.72	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.72	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.72	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.72	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.72	   A^2 -> H(U1(e, k), f(e))
28.55/9.72	   A^2 -> H(U1(e, k), f(k))
28.55/9.72	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.72	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.72	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.72	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.72	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.72	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.72	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.72	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.72	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.72	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.72	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.72	   A^2 -> H(U1(k, e), f(e))
28.55/9.72	   A^2 -> H(U1(k, e), f(k))
28.55/9.72	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.72	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.72	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.72	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.72	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.72	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.72	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.72	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.72	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.72	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.72	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.72	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.72	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.72	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.72	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.72	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.72	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.72	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.72	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.72	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.72	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.72	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.72	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.72	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.72	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.72	   A^2 -> H(U1(c, c), b)
28.55/9.72	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.72	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.72	   A^2 -> H(U1(c, c), e)
28.55/9.72	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.72	   A^2 -> H(e, U1(c, b))
28.55/9.72	   A^2 -> H(e, U1(d, b))
28.55/9.72	   A^2 -> H(e, U1(b, c))
28.55/9.72	   A^2 -> H(e, U1(b, d))
28.55/9.72	   A^2 -> H(e, U1(c, c))
28.55/9.72	   A^2 -> H(e, f(e))
28.55/9.72	   A^2 -> H(e, f(k))
28.55/9.72	   A^2 -> H(e, U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.72	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.72	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.72	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.72	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.72	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.72	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.72	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.72	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.72	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.72	   A^2 -> H(f(e), b)
28.55/9.72	   A^2 -> H(f(e), U1(e, d))
28.55/9.72	   A^2 -> H(f(e), U1(d, e))
28.55/9.72	   A^2 -> H(f(e), c)
28.55/9.72	   A^2 -> H(f(e), U1(e, k))
28.55/9.72	   A^2 -> H(f(e), U1(k, e))
28.55/9.72	   A^2 -> H(f(e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.72	   A^2 -> H(f(k), b)
28.55/9.72	   A^2 -> H(f(k), U1(e, d))
28.55/9.72	   A^2 -> H(f(k), U1(d, e))
28.55/9.72	   A^2 -> H(f(k), c)
28.55/9.72	   A^2 -> H(f(k), U1(e, k))
28.55/9.72	   A^2 -> H(f(k), U1(k, e))
28.55/9.72	   A^2 -> H(f(k), e)
28.55/9.72	   A^2 -> H(f(c), d)
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.72	   A^2 -> H(U1(k, k), f(e))
28.55/9.72	   A^2 -> H(U1(k, k), f(k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.72	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.72	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.72	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.72	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.72	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.72	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.72	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.72	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.72	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.72	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.72	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.72	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.72	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.72	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.72	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.72	   A^2 -> H(U1(d, d), b)
28.55/9.72	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.72	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.72	   A^2 -> H(U1(d, d), c)
28.55/9.72	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.72	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.72	   A^2 -> H(U1(d, d), e)
28.55/9.72	   A^2 -> H(f(d), d)
28.55/9.72	   A^2 -> H(f(d), k)
28.55/9.72	   A^2 -> H(U1(c, c), c)
28.55/9.72	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.72	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.72	   A^2 -> H(f(c), k)
28.55/9.72	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.72	   A^2 -> H(f(k), U1(k, k))
28.55/9.72	   A^2 -> H(f(e), e)
28.55/9.72	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.72	   A^2 -> H(d, U1(c, b))
28.55/9.72	   A^2 -> H(d, U1(d, b))
28.55/9.72	   A^2 -> H(d, U1(b, c))
28.55/9.72	   A^2 -> H(d, U1(b, d))
28.55/9.72	   A^2 -> H(d, U1(c, c))
28.55/9.72	   A^2 -> H(d, f(e))
28.55/9.72	   A^2 -> H(d, f(k))
28.55/9.72	   A^2 -> H(d, U1(d, d))
28.55/9.72	   A^2 -> H(a, U1(e, b))
28.55/9.72	   A^2 -> H(a, U1(k, b))
28.55/9.72	   A^2 -> H(a, U1(c, d))
28.55/9.72	   A^2 -> H(a, U1(d, c))
28.55/9.72	   A^2 -> H(a, U1(b, e))
28.55/9.72	   A^2 -> H(a, U1(b, k))
28.55/9.72	   A^2 -> H(a, U1(e, c))
28.55/9.72	   A^2 -> H(a, U1(k, c))
28.55/9.72	   A^2 -> H(a, U1(c, e))
28.55/9.72	   A^2 -> H(a, U1(c, k))
28.55/9.72	   A^2 -> H(a, U1(e, e))
28.55/9.72	   A^2 -> H(a, U1(k, k))
28.55/9.72	   A^2 -> H(a, U1(k, d))
28.55/9.72	   A^2 -> H(a, U1(d, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.72	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.72	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.72	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.72	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.72	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.72	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.72	   A^2 -> H(U1(e, a), b)
28.55/9.72	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.72	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.72	   A^2 -> H(U1(e, a), c)
28.55/9.72	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.72	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.72	   A^2 -> H(U1(e, a), e)
28.55/9.72	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, a), b)
28.55/9.72	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.72	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.72	   A^2 -> H(U1(k, a), c)
28.55/9.72	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.72	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.72	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, d), b)
28.55/9.72	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.72	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.72	   A^2 -> H(U1(c, d), c)
28.55/9.72	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.72	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.72	   A^2 -> H(U1(c, d), e)
28.55/9.72	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, a), d)
28.55/9.72	   A^2 -> H(U1(c, a), k)
28.55/9.72	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.72	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.72	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.72	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.72	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.72	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.72	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.72	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.72	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.72	   A^2 -> H(U1(d, c), b)
28.55/9.72	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.72	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.72	   A^2 -> H(U1(d, c), c)
28.55/9.72	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.72	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.72	   A^2 -> H(U1(d, c), e)
28.55/9.72	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.72	   A^2 -> H(U1(d, a), d)
28.55/9.72	   A^2 -> H(U1(d, a), k)
28.55/9.72	   A^2 -> H(U1(a, e), b)
28.55/9.72	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.72	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.72	   A^2 -> H(U1(a, e), c)
28.55/9.72	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.72	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.72	   A^2 -> H(U1(a, e), e)
28.55/9.72	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(a, k), b)
28.55/9.72	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.72	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.72	   A^2 -> H(U1(a, k), c)
28.55/9.72	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.72	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.72	   A^2 -> H(U1(a, k), e)
28.55/9.72	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(a, c), d)
28.55/9.72	   A^2 -> H(U1(a, c), k)
28.55/9.72	   A^2 -> H(U1(a, d), d)
28.55/9.72	   A^2 -> H(U1(a, d), k)
28.55/9.72	
28.55/9.72	The TRS R consists of the following rules:
28.55/9.72	
28.55/9.72	   f(x) -> U1(x, x)
28.55/9.72	   U1(e, x) -> x
28.55/9.72	   a -> c
28.55/9.72	   a -> d
28.55/9.72	   b -> c
28.55/9.72	   b -> d
28.55/9.72	   d -> k
28.55/9.72	   c -> e
28.55/9.72	   c -> k
28.55/9.72	
28.55/9.72	Q is empty.
28.55/9.72	We have to consider all minimal (P,Q,R)-chains.
28.55/9.72	----------------------------------------
28.55/9.72	
28.55/9.72	(1377) TransformationProof (EQUIVALENT)
28.55/9.72	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), e) at position [] we obtained the following new rules [LPAR04]:
28.55/9.72	
28.55/9.72	   (A^2 -> H(U1(c, d), e),A^2 -> H(U1(c, d), e))
28.55/9.72	   (A^2 -> H(U1(d, d), e),A^2 -> H(U1(d, d), e))
28.55/9.72	   (A^2 -> H(U1(a, k), e),A^2 -> H(U1(a, k), e))
28.55/9.72	
28.55/9.72	
28.55/9.72	----------------------------------------
28.55/9.72	
28.55/9.72	(1378)
28.55/9.72	Obligation:
28.55/9.72	Q DP problem:
28.55/9.72	The TRS P consists of the following rules:
28.55/9.72	
28.55/9.72	   H(x, x) -> G(x, x, f(k))
28.55/9.72	   G(d, x, x) -> A^2
28.55/9.72	   A^2 -> H(f(c), f(c))
28.55/9.72	   A^2 -> H(f(d), f(d))
28.55/9.72	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.72	   A^2 -> H(f(e), f(e))
28.55/9.72	   A^2 -> H(f(k), f(k))
28.55/9.72	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.72	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.72	   A^2 -> H(U1(a, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(a, a), d)
28.55/9.72	   A^2 -> H(U1(a, a), k)
28.55/9.72	   A^2 -> H(k, U1(b, b))
28.55/9.72	   A^2 -> H(k, f(c))
28.55/9.72	   A^2 -> H(k, f(d))
28.55/9.72	   A^2 -> H(c, U1(c, b))
28.55/9.72	   A^2 -> H(c, U1(d, b))
28.55/9.72	   A^2 -> H(c, U1(b, c))
28.55/9.72	   A^2 -> H(c, U1(b, d))
28.55/9.72	   A^2 -> H(c, U1(c, c))
28.55/9.72	   A^2 -> H(c, f(e))
28.55/9.72	   A^2 -> H(c, f(k))
28.55/9.72	   A^2 -> H(c, U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.72	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.72	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.72	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.72	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.72	   A^2 -> H(U1(e, k), f(e))
28.55/9.72	   A^2 -> H(U1(e, k), f(k))
28.55/9.72	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.72	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.72	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.72	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.72	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.72	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.72	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.72	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.72	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.72	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.72	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.72	   A^2 -> H(U1(k, e), f(e))
28.55/9.72	   A^2 -> H(U1(k, e), f(k))
28.55/9.72	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.72	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.72	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.72	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.72	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.72	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.72	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.72	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.72	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.72	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.72	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.72	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.72	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.72	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.72	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.72	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.72	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.72	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.72	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.72	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.72	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.72	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.72	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.72	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.72	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.72	   A^2 -> H(U1(c, c), b)
28.55/9.72	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.72	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.72	   A^2 -> H(U1(c, c), e)
28.55/9.72	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.72	   A^2 -> H(e, U1(c, b))
28.55/9.72	   A^2 -> H(e, U1(d, b))
28.55/9.72	   A^2 -> H(e, U1(b, c))
28.55/9.72	   A^2 -> H(e, U1(b, d))
28.55/9.72	   A^2 -> H(e, U1(c, c))
28.55/9.72	   A^2 -> H(e, f(e))
28.55/9.72	   A^2 -> H(e, f(k))
28.55/9.72	   A^2 -> H(e, U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.72	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.72	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.72	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.72	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.72	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.72	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.72	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.72	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.72	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.72	   A^2 -> H(f(e), b)
28.55/9.72	   A^2 -> H(f(e), U1(e, d))
28.55/9.72	   A^2 -> H(f(e), U1(d, e))
28.55/9.72	   A^2 -> H(f(e), c)
28.55/9.72	   A^2 -> H(f(e), U1(e, k))
28.55/9.72	   A^2 -> H(f(e), U1(k, e))
28.55/9.72	   A^2 -> H(f(e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.72	   A^2 -> H(f(k), b)
28.55/9.72	   A^2 -> H(f(k), U1(e, d))
28.55/9.72	   A^2 -> H(f(k), U1(d, e))
28.55/9.72	   A^2 -> H(f(k), c)
28.55/9.72	   A^2 -> H(f(k), U1(e, k))
28.55/9.72	   A^2 -> H(f(k), U1(k, e))
28.55/9.72	   A^2 -> H(f(k), e)
28.55/9.72	   A^2 -> H(f(c), d)
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.72	   A^2 -> H(U1(k, k), f(e))
28.55/9.72	   A^2 -> H(U1(k, k), f(k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.72	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.72	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.72	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.72	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.72	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.72	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.72	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.72	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.72	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.72	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.72	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.72	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.72	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.72	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.72	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.72	   A^2 -> H(U1(d, d), b)
28.55/9.72	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.72	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.72	   A^2 -> H(U1(d, d), c)
28.55/9.72	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.72	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.72	   A^2 -> H(U1(d, d), e)
28.55/9.72	   A^2 -> H(f(d), d)
28.55/9.72	   A^2 -> H(f(d), k)
28.55/9.72	   A^2 -> H(U1(c, c), c)
28.55/9.72	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.72	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.72	   A^2 -> H(f(c), k)
28.55/9.72	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.72	   A^2 -> H(f(k), U1(k, k))
28.55/9.72	   A^2 -> H(f(e), e)
28.55/9.72	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.72	   A^2 -> H(d, U1(c, b))
28.55/9.72	   A^2 -> H(d, U1(d, b))
28.55/9.72	   A^2 -> H(d, U1(b, c))
28.55/9.72	   A^2 -> H(d, U1(b, d))
28.55/9.72	   A^2 -> H(d, U1(c, c))
28.55/9.72	   A^2 -> H(d, f(e))
28.55/9.72	   A^2 -> H(d, f(k))
28.55/9.72	   A^2 -> H(d, U1(d, d))
28.55/9.72	   A^2 -> H(a, U1(e, b))
28.55/9.72	   A^2 -> H(a, U1(k, b))
28.55/9.72	   A^2 -> H(a, U1(c, d))
28.55/9.72	   A^2 -> H(a, U1(d, c))
28.55/9.72	   A^2 -> H(a, U1(b, e))
28.55/9.72	   A^2 -> H(a, U1(b, k))
28.55/9.72	   A^2 -> H(a, U1(e, c))
28.55/9.72	   A^2 -> H(a, U1(k, c))
28.55/9.72	   A^2 -> H(a, U1(c, e))
28.55/9.72	   A^2 -> H(a, U1(c, k))
28.55/9.72	   A^2 -> H(a, U1(e, e))
28.55/9.72	   A^2 -> H(a, U1(k, k))
28.55/9.72	   A^2 -> H(a, U1(k, d))
28.55/9.72	   A^2 -> H(a, U1(d, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.72	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.72	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.72	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.72	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.72	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.72	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.72	   A^2 -> H(U1(e, a), b)
28.55/9.72	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.72	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.72	   A^2 -> H(U1(e, a), c)
28.55/9.72	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.72	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.72	   A^2 -> H(U1(e, a), e)
28.55/9.72	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, a), b)
28.55/9.72	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.72	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.72	   A^2 -> H(U1(k, a), c)
28.55/9.72	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.72	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.72	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, d), b)
28.55/9.72	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.72	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.72	   A^2 -> H(U1(c, d), c)
28.55/9.72	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.72	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.72	   A^2 -> H(U1(c, d), e)
28.55/9.72	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, a), d)
28.55/9.72	   A^2 -> H(U1(c, a), k)
28.55/9.72	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.72	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.72	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.72	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.72	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.72	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.72	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.72	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.72	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.72	   A^2 -> H(U1(d, c), b)
28.55/9.72	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.72	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.72	   A^2 -> H(U1(d, c), c)
28.55/9.72	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.72	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.72	   A^2 -> H(U1(d, c), e)
28.55/9.72	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.72	   A^2 -> H(U1(d, a), d)
28.55/9.72	   A^2 -> H(U1(d, a), k)
28.55/9.72	   A^2 -> H(U1(a, e), b)
28.55/9.72	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.72	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.72	   A^2 -> H(U1(a, e), c)
28.55/9.72	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.72	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.72	   A^2 -> H(U1(a, e), e)
28.55/9.72	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(a, k), b)
28.55/9.72	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.72	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.72	   A^2 -> H(U1(a, k), c)
28.55/9.72	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.72	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.72	   A^2 -> H(U1(a, k), e)
28.55/9.72	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(a, c), d)
28.55/9.72	   A^2 -> H(U1(a, c), k)
28.55/9.72	   A^2 -> H(U1(a, d), d)
28.55/9.72	   A^2 -> H(U1(a, d), k)
28.55/9.72	
28.55/9.72	The TRS R consists of the following rules:
28.55/9.72	
28.55/9.72	   f(x) -> U1(x, x)
28.55/9.72	   U1(e, x) -> x
28.55/9.72	   a -> c
28.55/9.72	   a -> d
28.55/9.72	   b -> c
28.55/9.72	   b -> d
28.55/9.72	   d -> k
28.55/9.72	   c -> e
28.55/9.72	   c -> k
28.55/9.72	
28.55/9.72	Q is empty.
28.55/9.72	We have to consider all minimal (P,Q,R)-chains.
28.55/9.72	----------------------------------------
28.55/9.72	
28.55/9.72	(1379) TransformationProof (EQUIVALENT)
28.55/9.72	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.72	
28.55/9.72	   (A^2 -> H(U1(c, d), U1(k, k)),A^2 -> H(U1(c, d), U1(k, k)))
28.55/9.72	   (A^2 -> H(U1(d, d), U1(k, k)),A^2 -> H(U1(d, d), U1(k, k)))
28.55/9.72	   (A^2 -> H(U1(a, k), U1(k, k)),A^2 -> H(U1(a, k), U1(k, k)))
28.55/9.72	
28.55/9.72	
28.55/9.72	----------------------------------------
28.55/9.72	
28.55/9.72	(1380)
28.55/9.72	Obligation:
28.55/9.72	Q DP problem:
28.55/9.72	The TRS P consists of the following rules:
28.55/9.72	
28.55/9.72	   H(x, x) -> G(x, x, f(k))
28.55/9.72	   G(d, x, x) -> A^2
28.55/9.72	   A^2 -> H(f(c), f(c))
28.55/9.72	   A^2 -> H(f(d), f(d))
28.55/9.72	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.72	   A^2 -> H(f(e), f(e))
28.55/9.72	   A^2 -> H(f(k), f(k))
28.55/9.72	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.72	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.72	   A^2 -> H(U1(a, a), d)
28.55/9.72	   A^2 -> H(U1(a, a), k)
28.55/9.72	   A^2 -> H(k, U1(b, b))
28.55/9.72	   A^2 -> H(k, f(c))
28.55/9.72	   A^2 -> H(k, f(d))
28.55/9.72	   A^2 -> H(c, U1(c, b))
28.55/9.72	   A^2 -> H(c, U1(d, b))
28.55/9.72	   A^2 -> H(c, U1(b, c))
28.55/9.72	   A^2 -> H(c, U1(b, d))
28.55/9.72	   A^2 -> H(c, U1(c, c))
28.55/9.72	   A^2 -> H(c, f(e))
28.55/9.72	   A^2 -> H(c, f(k))
28.55/9.72	   A^2 -> H(c, U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.72	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.72	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.72	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.72	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.72	   A^2 -> H(U1(e, k), f(e))
28.55/9.72	   A^2 -> H(U1(e, k), f(k))
28.55/9.72	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.72	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.72	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.72	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.72	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.72	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.72	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.72	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.72	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.72	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.72	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.72	   A^2 -> H(U1(k, e), f(e))
28.55/9.72	   A^2 -> H(U1(k, e), f(k))
28.55/9.72	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.72	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.72	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.72	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.72	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.72	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.72	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.72	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.72	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.72	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.72	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.72	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.72	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.72	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.72	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.72	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.72	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.72	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.72	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.72	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.72	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.72	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.72	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.72	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.72	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.72	   A^2 -> H(U1(c, c), b)
28.55/9.72	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.72	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.72	   A^2 -> H(U1(c, c), e)
28.55/9.72	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.72	   A^2 -> H(e, U1(c, b))
28.55/9.72	   A^2 -> H(e, U1(d, b))
28.55/9.72	   A^2 -> H(e, U1(b, c))
28.55/9.72	   A^2 -> H(e, U1(b, d))
28.55/9.72	   A^2 -> H(e, U1(c, c))
28.55/9.72	   A^2 -> H(e, f(e))
28.55/9.72	   A^2 -> H(e, f(k))
28.55/9.72	   A^2 -> H(e, U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.72	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.72	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.72	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.72	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.72	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.72	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.72	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.72	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.72	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.72	   A^2 -> H(f(e), b)
28.55/9.72	   A^2 -> H(f(e), U1(e, d))
28.55/9.72	   A^2 -> H(f(e), U1(d, e))
28.55/9.72	   A^2 -> H(f(e), c)
28.55/9.72	   A^2 -> H(f(e), U1(e, k))
28.55/9.72	   A^2 -> H(f(e), U1(k, e))
28.55/9.72	   A^2 -> H(f(e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.72	   A^2 -> H(f(k), b)
28.55/9.72	   A^2 -> H(f(k), U1(e, d))
28.55/9.72	   A^2 -> H(f(k), U1(d, e))
28.55/9.72	   A^2 -> H(f(k), c)
28.55/9.72	   A^2 -> H(f(k), U1(e, k))
28.55/9.72	   A^2 -> H(f(k), U1(k, e))
28.55/9.72	   A^2 -> H(f(k), e)
28.55/9.72	   A^2 -> H(f(c), d)
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.72	   A^2 -> H(U1(k, k), f(e))
28.55/9.72	   A^2 -> H(U1(k, k), f(k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.72	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.72	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.72	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.72	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.72	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.72	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.72	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.72	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.72	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.72	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.72	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.72	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.72	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.72	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.72	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.72	   A^2 -> H(U1(d, d), b)
28.55/9.72	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.72	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.72	   A^2 -> H(U1(d, d), c)
28.55/9.72	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.72	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.72	   A^2 -> H(U1(d, d), e)
28.55/9.72	   A^2 -> H(f(d), d)
28.55/9.72	   A^2 -> H(f(d), k)
28.55/9.72	   A^2 -> H(U1(c, c), c)
28.55/9.72	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.72	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.72	   A^2 -> H(f(c), k)
28.55/9.72	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.72	   A^2 -> H(f(k), U1(k, k))
28.55/9.72	   A^2 -> H(f(e), e)
28.55/9.72	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.72	   A^2 -> H(d, U1(c, b))
28.55/9.72	   A^2 -> H(d, U1(d, b))
28.55/9.72	   A^2 -> H(d, U1(b, c))
28.55/9.72	   A^2 -> H(d, U1(b, d))
28.55/9.72	   A^2 -> H(d, U1(c, c))
28.55/9.72	   A^2 -> H(d, f(e))
28.55/9.72	   A^2 -> H(d, f(k))
28.55/9.72	   A^2 -> H(d, U1(d, d))
28.55/9.72	   A^2 -> H(a, U1(e, b))
28.55/9.72	   A^2 -> H(a, U1(k, b))
28.55/9.72	   A^2 -> H(a, U1(c, d))
28.55/9.72	   A^2 -> H(a, U1(d, c))
28.55/9.72	   A^2 -> H(a, U1(b, e))
28.55/9.72	   A^2 -> H(a, U1(b, k))
28.55/9.72	   A^2 -> H(a, U1(e, c))
28.55/9.72	   A^2 -> H(a, U1(k, c))
28.55/9.72	   A^2 -> H(a, U1(c, e))
28.55/9.72	   A^2 -> H(a, U1(c, k))
28.55/9.72	   A^2 -> H(a, U1(e, e))
28.55/9.72	   A^2 -> H(a, U1(k, k))
28.55/9.72	   A^2 -> H(a, U1(k, d))
28.55/9.72	   A^2 -> H(a, U1(d, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.72	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.72	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.72	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.72	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.72	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.72	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.72	   A^2 -> H(U1(e, a), b)
28.55/9.72	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.72	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.72	   A^2 -> H(U1(e, a), c)
28.55/9.72	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.72	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.72	   A^2 -> H(U1(e, a), e)
28.55/9.72	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, a), b)
28.55/9.72	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.72	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.72	   A^2 -> H(U1(k, a), c)
28.55/9.72	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.72	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.72	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, d), b)
28.55/9.72	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.72	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.72	   A^2 -> H(U1(c, d), c)
28.55/9.72	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.72	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.72	   A^2 -> H(U1(c, d), e)
28.55/9.72	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, a), d)
28.55/9.72	   A^2 -> H(U1(c, a), k)
28.55/9.72	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.72	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.72	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.72	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.72	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.72	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.72	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.72	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.72	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.72	   A^2 -> H(U1(d, c), b)
28.55/9.72	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.72	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.72	   A^2 -> H(U1(d, c), c)
28.55/9.72	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.72	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.72	   A^2 -> H(U1(d, c), e)
28.55/9.72	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.72	   A^2 -> H(U1(d, a), d)
28.55/9.72	   A^2 -> H(U1(d, a), k)
28.55/9.72	   A^2 -> H(U1(a, e), b)
28.55/9.72	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.72	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.72	   A^2 -> H(U1(a, e), c)
28.55/9.72	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.72	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.72	   A^2 -> H(U1(a, e), e)
28.55/9.72	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(a, k), b)
28.55/9.72	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.72	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.72	   A^2 -> H(U1(a, k), c)
28.55/9.72	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.72	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.72	   A^2 -> H(U1(a, k), e)
28.55/9.72	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(a, c), d)
28.55/9.72	   A^2 -> H(U1(a, c), k)
28.55/9.72	   A^2 -> H(U1(a, d), d)
28.55/9.72	   A^2 -> H(U1(a, d), k)
28.55/9.72	
28.55/9.72	The TRS R consists of the following rules:
28.55/9.72	
28.55/9.72	   f(x) -> U1(x, x)
28.55/9.72	   U1(e, x) -> x
28.55/9.72	   a -> c
28.55/9.72	   a -> d
28.55/9.72	   b -> c
28.55/9.72	   b -> d
28.55/9.72	   d -> k
28.55/9.72	   c -> e
28.55/9.72	   c -> k
28.55/9.72	
28.55/9.72	Q is empty.
28.55/9.72	We have to consider all minimal (P,Q,R)-chains.
28.55/9.72	----------------------------------------
28.55/9.72	
28.55/9.72	(1381) TransformationProof (EQUIVALENT)
28.55/9.72	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), d) at position [] we obtained the following new rules [LPAR04]:
28.55/9.72	
28.55/9.72	   (A^2 -> H(U1(c, a), d),A^2 -> H(U1(c, a), d))
28.55/9.72	   (A^2 -> H(U1(d, a), d),A^2 -> H(U1(d, a), d))
28.55/9.72	   (A^2 -> H(U1(a, c), d),A^2 -> H(U1(a, c), d))
28.55/9.72	   (A^2 -> H(U1(a, d), d),A^2 -> H(U1(a, d), d))
28.55/9.72	   (A^2 -> H(U1(a, a), k),A^2 -> H(U1(a, a), k))
28.55/9.72	
28.55/9.72	
28.55/9.72	----------------------------------------
28.55/9.72	
28.55/9.72	(1382)
28.55/9.72	Obligation:
28.55/9.72	Q DP problem:
28.55/9.72	The TRS P consists of the following rules:
28.55/9.72	
28.55/9.72	   H(x, x) -> G(x, x, f(k))
28.55/9.72	   G(d, x, x) -> A^2
28.55/9.72	   A^2 -> H(f(c), f(c))
28.55/9.72	   A^2 -> H(f(d), f(d))
28.55/9.72	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.72	   A^2 -> H(f(e), f(e))
28.55/9.72	   A^2 -> H(f(k), f(k))
28.55/9.72	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.72	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.72	   A^2 -> H(U1(a, a), k)
28.55/9.72	   A^2 -> H(k, U1(b, b))
28.55/9.72	   A^2 -> H(k, f(c))
28.55/9.72	   A^2 -> H(k, f(d))
28.55/9.72	   A^2 -> H(c, U1(c, b))
28.55/9.72	   A^2 -> H(c, U1(d, b))
28.55/9.72	   A^2 -> H(c, U1(b, c))
28.55/9.72	   A^2 -> H(c, U1(b, d))
28.55/9.72	   A^2 -> H(c, U1(c, c))
28.55/9.72	   A^2 -> H(c, f(e))
28.55/9.72	   A^2 -> H(c, f(k))
28.55/9.72	   A^2 -> H(c, U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.72	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.72	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.72	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.72	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.72	   A^2 -> H(U1(e, k), f(e))
28.55/9.72	   A^2 -> H(U1(e, k), f(k))
28.55/9.72	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.72	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.72	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.72	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.72	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.72	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.72	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.72	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.72	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.72	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.72	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.72	   A^2 -> H(U1(k, e), f(e))
28.55/9.72	   A^2 -> H(U1(k, e), f(k))
28.55/9.72	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.72	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.72	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.72	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.72	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.72	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.72	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.72	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.72	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.72	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.72	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.72	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.72	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.72	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.72	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.72	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.72	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.72	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.72	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.72	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.72	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.72	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.72	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.72	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.72	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.72	   A^2 -> H(U1(c, c), b)
28.55/9.72	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.72	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.72	   A^2 -> H(U1(c, c), e)
28.55/9.72	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.72	   A^2 -> H(e, U1(c, b))
28.55/9.72	   A^2 -> H(e, U1(d, b))
28.55/9.72	   A^2 -> H(e, U1(b, c))
28.55/9.72	   A^2 -> H(e, U1(b, d))
28.55/9.72	   A^2 -> H(e, U1(c, c))
28.55/9.72	   A^2 -> H(e, f(e))
28.55/9.72	   A^2 -> H(e, f(k))
28.55/9.72	   A^2 -> H(e, U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.72	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.72	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.72	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.72	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.72	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.72	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.72	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.72	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.72	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.72	   A^2 -> H(f(e), b)
28.55/9.72	   A^2 -> H(f(e), U1(e, d))
28.55/9.72	   A^2 -> H(f(e), U1(d, e))
28.55/9.72	   A^2 -> H(f(e), c)
28.55/9.72	   A^2 -> H(f(e), U1(e, k))
28.55/9.72	   A^2 -> H(f(e), U1(k, e))
28.55/9.72	   A^2 -> H(f(e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.72	   A^2 -> H(f(k), b)
28.55/9.72	   A^2 -> H(f(k), U1(e, d))
28.55/9.72	   A^2 -> H(f(k), U1(d, e))
28.55/9.72	   A^2 -> H(f(k), c)
28.55/9.72	   A^2 -> H(f(k), U1(e, k))
28.55/9.72	   A^2 -> H(f(k), U1(k, e))
28.55/9.72	   A^2 -> H(f(k), e)
28.55/9.72	   A^2 -> H(f(c), d)
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.72	   A^2 -> H(U1(k, k), f(e))
28.55/9.72	   A^2 -> H(U1(k, k), f(k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.72	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.72	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.72	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.72	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.72	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.72	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.72	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.72	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.72	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.72	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.72	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.72	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.72	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.72	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.72	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.72	   A^2 -> H(U1(d, d), b)
28.55/9.72	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.72	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.72	   A^2 -> H(U1(d, d), c)
28.55/9.72	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.72	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.72	   A^2 -> H(U1(d, d), e)
28.55/9.72	   A^2 -> H(f(d), d)
28.55/9.72	   A^2 -> H(f(d), k)
28.55/9.72	   A^2 -> H(U1(c, c), c)
28.55/9.72	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.72	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.72	   A^2 -> H(f(c), k)
28.55/9.72	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.72	   A^2 -> H(f(k), U1(k, k))
28.55/9.72	   A^2 -> H(f(e), e)
28.55/9.72	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.72	   A^2 -> H(d, U1(c, b))
28.55/9.72	   A^2 -> H(d, U1(d, b))
28.55/9.72	   A^2 -> H(d, U1(b, c))
28.55/9.72	   A^2 -> H(d, U1(b, d))
28.55/9.72	   A^2 -> H(d, U1(c, c))
28.55/9.72	   A^2 -> H(d, f(e))
28.55/9.72	   A^2 -> H(d, f(k))
28.55/9.72	   A^2 -> H(d, U1(d, d))
28.55/9.72	   A^2 -> H(a, U1(e, b))
28.55/9.72	   A^2 -> H(a, U1(k, b))
28.55/9.72	   A^2 -> H(a, U1(c, d))
28.55/9.72	   A^2 -> H(a, U1(d, c))
28.55/9.72	   A^2 -> H(a, U1(b, e))
28.55/9.72	   A^2 -> H(a, U1(b, k))
28.55/9.72	   A^2 -> H(a, U1(e, c))
28.55/9.72	   A^2 -> H(a, U1(k, c))
28.55/9.72	   A^2 -> H(a, U1(c, e))
28.55/9.72	   A^2 -> H(a, U1(c, k))
28.55/9.72	   A^2 -> H(a, U1(e, e))
28.55/9.72	   A^2 -> H(a, U1(k, k))
28.55/9.72	   A^2 -> H(a, U1(k, d))
28.55/9.72	   A^2 -> H(a, U1(d, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.72	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.72	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.72	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.72	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.72	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.72	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.72	   A^2 -> H(U1(e, a), b)
28.55/9.72	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.72	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.72	   A^2 -> H(U1(e, a), c)
28.55/9.72	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.72	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.72	   A^2 -> H(U1(e, a), e)
28.55/9.72	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, a), b)
28.55/9.72	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.72	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.72	   A^2 -> H(U1(k, a), c)
28.55/9.72	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.72	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.72	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, d), b)
28.55/9.72	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.72	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.72	   A^2 -> H(U1(c, d), c)
28.55/9.72	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.72	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.72	   A^2 -> H(U1(c, d), e)
28.55/9.72	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, a), d)
28.55/9.72	   A^2 -> H(U1(c, a), k)
28.55/9.72	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.72	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.72	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.72	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.72	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.72	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.72	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.72	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.72	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.72	   A^2 -> H(U1(d, c), b)
28.55/9.72	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.72	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.72	   A^2 -> H(U1(d, c), c)
28.55/9.72	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.72	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.72	   A^2 -> H(U1(d, c), e)
28.55/9.72	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.72	   A^2 -> H(U1(d, a), d)
28.55/9.72	   A^2 -> H(U1(d, a), k)
28.55/9.72	   A^2 -> H(U1(a, e), b)
28.55/9.72	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.72	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.72	   A^2 -> H(U1(a, e), c)
28.55/9.72	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.72	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.72	   A^2 -> H(U1(a, e), e)
28.55/9.72	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(a, k), b)
28.55/9.72	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.72	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.72	   A^2 -> H(U1(a, k), c)
28.55/9.72	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.72	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.72	   A^2 -> H(U1(a, k), e)
28.55/9.72	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(a, c), d)
28.55/9.72	   A^2 -> H(U1(a, c), k)
28.55/9.72	   A^2 -> H(U1(a, d), d)
28.55/9.72	   A^2 -> H(U1(a, d), k)
28.55/9.72	
28.55/9.72	The TRS R consists of the following rules:
28.55/9.72	
28.55/9.72	   f(x) -> U1(x, x)
28.55/9.72	   U1(e, x) -> x
28.55/9.72	   a -> c
28.55/9.72	   a -> d
28.55/9.72	   b -> c
28.55/9.72	   b -> d
28.55/9.72	   d -> k
28.55/9.72	   c -> e
28.55/9.72	   c -> k
28.55/9.72	
28.55/9.72	Q is empty.
28.55/9.72	We have to consider all minimal (P,Q,R)-chains.
28.55/9.72	----------------------------------------
28.55/9.72	
28.55/9.72	(1383) TransformationProof (EQUIVALENT)
28.55/9.72	By narrowing [LPAR04] the rule A^2 -> H(U1(a, a), k) at position [] we obtained the following new rules [LPAR04]:
28.55/9.72	
28.55/9.72	   (A^2 -> H(U1(c, a), k),A^2 -> H(U1(c, a), k))
28.55/9.72	   (A^2 -> H(U1(d, a), k),A^2 -> H(U1(d, a), k))
28.55/9.72	   (A^2 -> H(U1(a, c), k),A^2 -> H(U1(a, c), k))
28.55/9.72	   (A^2 -> H(U1(a, d), k),A^2 -> H(U1(a, d), k))
28.55/9.72	
28.55/9.72	
28.55/9.72	----------------------------------------
28.55/9.72	
28.55/9.72	(1384)
28.55/9.72	Obligation:
28.55/9.72	Q DP problem:
28.55/9.72	The TRS P consists of the following rules:
28.55/9.72	
28.55/9.72	   H(x, x) -> G(x, x, f(k))
28.55/9.72	   G(d, x, x) -> A^2
28.55/9.72	   A^2 -> H(f(c), f(c))
28.55/9.72	   A^2 -> H(f(d), f(d))
28.55/9.72	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.72	   A^2 -> H(f(e), f(e))
28.55/9.72	   A^2 -> H(f(k), f(k))
28.55/9.72	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.72	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.72	   A^2 -> H(k, U1(b, b))
28.55/9.72	   A^2 -> H(k, f(c))
28.55/9.72	   A^2 -> H(k, f(d))
28.55/9.72	   A^2 -> H(c, U1(c, b))
28.55/9.72	   A^2 -> H(c, U1(d, b))
28.55/9.72	   A^2 -> H(c, U1(b, c))
28.55/9.72	   A^2 -> H(c, U1(b, d))
28.55/9.72	   A^2 -> H(c, U1(c, c))
28.55/9.72	   A^2 -> H(c, f(e))
28.55/9.72	   A^2 -> H(c, f(k))
28.55/9.72	   A^2 -> H(c, U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.72	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.72	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.72	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.72	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.72	   A^2 -> H(U1(e, k), f(e))
28.55/9.72	   A^2 -> H(U1(e, k), f(k))
28.55/9.72	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.72	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.72	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.72	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.72	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.72	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.72	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.72	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.72	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.72	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.72	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.72	   A^2 -> H(U1(k, e), f(e))
28.55/9.72	   A^2 -> H(U1(k, e), f(k))
28.55/9.72	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.72	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.72	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.72	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.72	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.72	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.72	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.72	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.72	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.72	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.72	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.72	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.72	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.72	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.72	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.72	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.72	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.72	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.72	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.72	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.72	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.72	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.72	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.72	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.72	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.72	   A^2 -> H(U1(c, c), b)
28.55/9.72	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.72	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.72	   A^2 -> H(U1(c, c), e)
28.55/9.72	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.72	   A^2 -> H(e, U1(c, b))
28.55/9.72	   A^2 -> H(e, U1(d, b))
28.55/9.72	   A^2 -> H(e, U1(b, c))
28.55/9.72	   A^2 -> H(e, U1(b, d))
28.55/9.72	   A^2 -> H(e, U1(c, c))
28.55/9.72	   A^2 -> H(e, f(e))
28.55/9.72	   A^2 -> H(e, f(k))
28.55/9.72	   A^2 -> H(e, U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.72	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.72	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.72	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.72	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.72	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.72	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.72	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.72	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.72	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.72	   A^2 -> H(f(e), b)
28.55/9.72	   A^2 -> H(f(e), U1(e, d))
28.55/9.72	   A^2 -> H(f(e), U1(d, e))
28.55/9.72	   A^2 -> H(f(e), c)
28.55/9.72	   A^2 -> H(f(e), U1(e, k))
28.55/9.72	   A^2 -> H(f(e), U1(k, e))
28.55/9.72	   A^2 -> H(f(e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.72	   A^2 -> H(f(k), b)
28.55/9.72	   A^2 -> H(f(k), U1(e, d))
28.55/9.72	   A^2 -> H(f(k), U1(d, e))
28.55/9.72	   A^2 -> H(f(k), c)
28.55/9.72	   A^2 -> H(f(k), U1(e, k))
28.55/9.72	   A^2 -> H(f(k), U1(k, e))
28.55/9.72	   A^2 -> H(f(k), e)
28.55/9.72	   A^2 -> H(f(c), d)
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.72	   A^2 -> H(U1(k, k), f(e))
28.55/9.72	   A^2 -> H(U1(k, k), f(k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.72	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.72	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.72	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.72	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.72	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.72	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.72	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.72	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.72	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.72	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.72	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.72	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.72	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.72	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.72	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.72	   A^2 -> H(U1(d, d), b)
28.55/9.72	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.72	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.72	   A^2 -> H(U1(d, d), c)
28.55/9.72	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.72	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.72	   A^2 -> H(U1(d, d), e)
28.55/9.72	   A^2 -> H(f(d), d)
28.55/9.72	   A^2 -> H(f(d), k)
28.55/9.72	   A^2 -> H(U1(c, c), c)
28.55/9.72	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.72	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.72	   A^2 -> H(f(c), k)
28.55/9.72	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.72	   A^2 -> H(f(k), U1(k, k))
28.55/9.72	   A^2 -> H(f(e), e)
28.55/9.72	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.72	   A^2 -> H(d, U1(c, b))
28.55/9.72	   A^2 -> H(d, U1(d, b))
28.55/9.72	   A^2 -> H(d, U1(b, c))
28.55/9.72	   A^2 -> H(d, U1(b, d))
28.55/9.72	   A^2 -> H(d, U1(c, c))
28.55/9.72	   A^2 -> H(d, f(e))
28.55/9.72	   A^2 -> H(d, f(k))
28.55/9.72	   A^2 -> H(d, U1(d, d))
28.55/9.72	   A^2 -> H(a, U1(e, b))
28.55/9.72	   A^2 -> H(a, U1(k, b))
28.55/9.72	   A^2 -> H(a, U1(c, d))
28.55/9.72	   A^2 -> H(a, U1(d, c))
28.55/9.72	   A^2 -> H(a, U1(b, e))
28.55/9.72	   A^2 -> H(a, U1(b, k))
28.55/9.72	   A^2 -> H(a, U1(e, c))
28.55/9.72	   A^2 -> H(a, U1(k, c))
28.55/9.72	   A^2 -> H(a, U1(c, e))
28.55/9.72	   A^2 -> H(a, U1(c, k))
28.55/9.72	   A^2 -> H(a, U1(e, e))
28.55/9.72	   A^2 -> H(a, U1(k, k))
28.55/9.72	   A^2 -> H(a, U1(k, d))
28.55/9.72	   A^2 -> H(a, U1(d, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.72	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.72	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.72	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.72	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.72	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.72	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.72	   A^2 -> H(U1(e, a), b)
28.55/9.72	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.72	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.72	   A^2 -> H(U1(e, a), c)
28.55/9.72	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.72	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.72	   A^2 -> H(U1(e, a), e)
28.55/9.72	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, a), b)
28.55/9.72	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.72	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.72	   A^2 -> H(U1(k, a), c)
28.55/9.72	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.72	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.72	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, d), b)
28.55/9.72	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.72	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.72	   A^2 -> H(U1(c, d), c)
28.55/9.72	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.72	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.72	   A^2 -> H(U1(c, d), e)
28.55/9.72	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, a), d)
28.55/9.72	   A^2 -> H(U1(c, a), k)
28.55/9.72	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.72	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.72	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.72	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.72	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.72	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.72	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.72	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.72	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.72	   A^2 -> H(U1(d, c), b)
28.55/9.72	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.72	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.72	   A^2 -> H(U1(d, c), c)
28.55/9.72	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.72	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.72	   A^2 -> H(U1(d, c), e)
28.55/9.72	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.72	   A^2 -> H(U1(d, a), d)
28.55/9.72	   A^2 -> H(U1(d, a), k)
28.55/9.72	   A^2 -> H(U1(a, e), b)
28.55/9.72	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.72	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.72	   A^2 -> H(U1(a, e), c)
28.55/9.72	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.72	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.72	   A^2 -> H(U1(a, e), e)
28.55/9.72	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(a, k), b)
28.55/9.72	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.72	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.72	   A^2 -> H(U1(a, k), c)
28.55/9.72	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.72	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.72	   A^2 -> H(U1(a, k), e)
28.55/9.72	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(a, c), d)
28.55/9.72	   A^2 -> H(U1(a, c), k)
28.55/9.72	   A^2 -> H(U1(a, d), d)
28.55/9.72	   A^2 -> H(U1(a, d), k)
28.55/9.72	
28.55/9.72	The TRS R consists of the following rules:
28.55/9.72	
28.55/9.72	   f(x) -> U1(x, x)
28.55/9.72	   U1(e, x) -> x
28.55/9.72	   a -> c
28.55/9.72	   a -> d
28.55/9.72	   b -> c
28.55/9.72	   b -> d
28.55/9.72	   d -> k
28.55/9.72	   c -> e
28.55/9.72	   c -> k
28.55/9.72	
28.55/9.72	Q is empty.
28.55/9.72	We have to consider all minimal (P,Q,R)-chains.
28.55/9.72	----------------------------------------
28.55/9.72	
28.55/9.72	(1385) TransformationProof (EQUIVALENT)
28.55/9.72	By narrowing [LPAR04] the rule A^2 -> H(k, U1(b, b)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.72	
28.55/9.72	   (A^2 -> H(k, U1(c, b)),A^2 -> H(k, U1(c, b)))
28.55/9.72	   (A^2 -> H(k, U1(d, b)),A^2 -> H(k, U1(d, b)))
28.55/9.72	   (A^2 -> H(k, U1(b, c)),A^2 -> H(k, U1(b, c)))
28.55/9.72	   (A^2 -> H(k, U1(b, d)),A^2 -> H(k, U1(b, d)))
28.55/9.72	
28.55/9.72	
28.55/9.72	----------------------------------------
28.55/9.72	
28.55/9.72	(1386)
28.55/9.72	Obligation:
28.55/9.72	Q DP problem:
28.55/9.72	The TRS P consists of the following rules:
28.55/9.72	
28.55/9.72	   H(x, x) -> G(x, x, f(k))
28.55/9.72	   G(d, x, x) -> A^2
28.55/9.72	   A^2 -> H(f(c), f(c))
28.55/9.72	   A^2 -> H(f(d), f(d))
28.55/9.72	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.72	   A^2 -> H(f(e), f(e))
28.55/9.72	   A^2 -> H(f(k), f(k))
28.55/9.72	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.72	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.72	   A^2 -> H(k, f(c))
28.55/9.72	   A^2 -> H(k, f(d))
28.55/9.72	   A^2 -> H(c, U1(c, b))
28.55/9.72	   A^2 -> H(c, U1(d, b))
28.55/9.72	   A^2 -> H(c, U1(b, c))
28.55/9.72	   A^2 -> H(c, U1(b, d))
28.55/9.72	   A^2 -> H(c, U1(c, c))
28.55/9.72	   A^2 -> H(c, f(e))
28.55/9.72	   A^2 -> H(c, f(k))
28.55/9.72	   A^2 -> H(c, U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.72	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.72	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.72	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.72	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.72	   A^2 -> H(U1(e, k), f(e))
28.55/9.72	   A^2 -> H(U1(e, k), f(k))
28.55/9.72	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.72	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.72	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.72	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.72	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.72	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.72	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.72	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.72	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.72	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.72	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.72	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.72	   A^2 -> H(U1(k, e), f(e))
28.55/9.72	   A^2 -> H(U1(k, e), f(k))
28.55/9.72	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.72	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.72	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.72	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.72	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.72	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.72	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.72	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.72	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.72	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.72	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.72	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.72	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.72	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.72	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.72	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.72	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.72	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.72	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.72	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.72	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.72	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.72	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.72	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.72	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.72	   A^2 -> H(U1(c, c), b)
28.55/9.72	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.72	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.72	   A^2 -> H(U1(c, c), e)
28.55/9.72	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.72	   A^2 -> H(e, U1(c, b))
28.55/9.72	   A^2 -> H(e, U1(d, b))
28.55/9.72	   A^2 -> H(e, U1(b, c))
28.55/9.72	   A^2 -> H(e, U1(b, d))
28.55/9.72	   A^2 -> H(e, U1(c, c))
28.55/9.72	   A^2 -> H(e, f(e))
28.55/9.72	   A^2 -> H(e, f(k))
28.55/9.72	   A^2 -> H(e, U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.72	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.72	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.72	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.72	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.72	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.72	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.72	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.72	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.72	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.72	   A^2 -> H(f(e), b)
28.55/9.72	   A^2 -> H(f(e), U1(e, d))
28.55/9.72	   A^2 -> H(f(e), U1(d, e))
28.55/9.72	   A^2 -> H(f(e), c)
28.55/9.72	   A^2 -> H(f(e), U1(e, k))
28.55/9.72	   A^2 -> H(f(e), U1(k, e))
28.55/9.72	   A^2 -> H(f(e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.72	   A^2 -> H(f(k), b)
28.55/9.72	   A^2 -> H(f(k), U1(e, d))
28.55/9.72	   A^2 -> H(f(k), U1(d, e))
28.55/9.72	   A^2 -> H(f(k), c)
28.55/9.72	   A^2 -> H(f(k), U1(e, k))
28.55/9.72	   A^2 -> H(f(k), U1(k, e))
28.55/9.72	   A^2 -> H(f(k), e)
28.55/9.72	   A^2 -> H(f(c), d)
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.72	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.72	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.72	   A^2 -> H(U1(k, k), f(e))
28.55/9.72	   A^2 -> H(U1(k, k), f(k))
28.55/9.72	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.72	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.72	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.72	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.72	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.72	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.72	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.72	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.72	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.72	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.72	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.72	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.72	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.72	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.72	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.72	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.72	   A^2 -> H(U1(d, d), b)
28.55/9.72	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.72	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.72	   A^2 -> H(U1(d, d), c)
28.55/9.72	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.72	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.72	   A^2 -> H(U1(d, d), e)
28.55/9.72	   A^2 -> H(f(d), d)
28.55/9.72	   A^2 -> H(f(d), k)
28.55/9.72	   A^2 -> H(U1(c, c), c)
28.55/9.72	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.72	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.72	   A^2 -> H(f(c), k)
28.55/9.72	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.72	   A^2 -> H(f(k), U1(k, k))
28.55/9.72	   A^2 -> H(f(e), e)
28.55/9.72	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.72	   A^2 -> H(d, U1(c, b))
28.55/9.72	   A^2 -> H(d, U1(d, b))
28.55/9.72	   A^2 -> H(d, U1(b, c))
28.55/9.72	   A^2 -> H(d, U1(b, d))
28.55/9.72	   A^2 -> H(d, U1(c, c))
28.55/9.72	   A^2 -> H(d, f(e))
28.55/9.72	   A^2 -> H(d, f(k))
28.55/9.72	   A^2 -> H(d, U1(d, d))
28.55/9.72	   A^2 -> H(a, U1(e, b))
28.55/9.72	   A^2 -> H(a, U1(k, b))
28.55/9.72	   A^2 -> H(a, U1(c, d))
28.55/9.72	   A^2 -> H(a, U1(d, c))
28.55/9.72	   A^2 -> H(a, U1(b, e))
28.55/9.72	   A^2 -> H(a, U1(b, k))
28.55/9.72	   A^2 -> H(a, U1(e, c))
28.55/9.72	   A^2 -> H(a, U1(k, c))
28.55/9.72	   A^2 -> H(a, U1(c, e))
28.55/9.72	   A^2 -> H(a, U1(c, k))
28.55/9.72	   A^2 -> H(a, U1(e, e))
28.55/9.72	   A^2 -> H(a, U1(k, k))
28.55/9.72	   A^2 -> H(a, U1(k, d))
28.55/9.72	   A^2 -> H(a, U1(d, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.72	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.72	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.72	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.72	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.72	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.72	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.72	   A^2 -> H(U1(e, a), b)
28.55/9.72	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.72	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.72	   A^2 -> H(U1(e, a), c)
28.55/9.72	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.72	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.72	   A^2 -> H(U1(e, a), e)
28.55/9.72	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.72	   A^2 -> H(U1(k, a), b)
28.55/9.72	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.72	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.72	   A^2 -> H(U1(k, a), c)
28.55/9.72	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.72	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.72	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, d), b)
28.55/9.72	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.72	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.72	   A^2 -> H(U1(c, d), c)
28.55/9.72	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.72	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.72	   A^2 -> H(U1(c, d), e)
28.55/9.72	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.72	   A^2 -> H(U1(c, a), d)
28.55/9.72	   A^2 -> H(U1(c, a), k)
28.55/9.72	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.72	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.72	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.72	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.72	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.72	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.72	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.72	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.72	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.72	   A^2 -> H(U1(d, c), b)
28.55/9.72	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.72	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.72	   A^2 -> H(U1(d, c), c)
28.55/9.72	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.72	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.72	   A^2 -> H(U1(d, c), e)
28.55/9.72	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.72	   A^2 -> H(U1(d, a), d)
28.55/9.72	   A^2 -> H(U1(d, a), k)
28.55/9.72	   A^2 -> H(U1(a, e), b)
28.55/9.72	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.72	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.72	   A^2 -> H(U1(a, e), c)
28.55/9.72	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.72	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.72	   A^2 -> H(U1(a, e), e)
28.55/9.72	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.72	   A^2 -> H(U1(a, k), b)
28.55/9.72	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.72	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.72	   A^2 -> H(U1(a, k), c)
28.55/9.72	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.72	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.72	   A^2 -> H(U1(a, k), e)
28.55/9.72	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.72	   A^2 -> H(U1(a, c), d)
28.55/9.72	   A^2 -> H(U1(a, c), k)
28.55/9.72	   A^2 -> H(U1(a, d), d)
28.55/9.72	   A^2 -> H(U1(a, d), k)
28.55/9.72	   A^2 -> H(k, U1(c, b))
28.55/9.72	   A^2 -> H(k, U1(d, b))
28.55/9.72	   A^2 -> H(k, U1(b, c))
28.55/9.72	   A^2 -> H(k, U1(b, d))
28.55/9.72	
28.55/9.72	The TRS R consists of the following rules:
28.55/9.72	
28.55/9.72	   f(x) -> U1(x, x)
28.55/9.72	   U1(e, x) -> x
28.55/9.72	   a -> c
28.55/9.72	   a -> d
28.55/9.72	   b -> c
28.55/9.72	   b -> d
28.55/9.72	   d -> k
28.55/9.72	   c -> e
28.55/9.72	   c -> k
28.55/9.72	
28.55/9.72	Q is empty.
28.55/9.72	We have to consider all minimal (P,Q,R)-chains.
28.55/9.72	----------------------------------------
28.55/9.72	
28.55/9.72	(1387) TransformationProof (EQUIVALENT)
28.55/9.72	By narrowing [LPAR04] the rule A^2 -> H(k, f(c)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.72	
28.55/9.72	   (A^2 -> H(k, U1(c, c)),A^2 -> H(k, U1(c, c)))
28.55/9.72	   (A^2 -> H(k, f(e)),A^2 -> H(k, f(e)))
28.55/9.72	   (A^2 -> H(k, f(k)),A^2 -> H(k, f(k)))
28.55/9.72	
28.55/9.72	
28.55/9.72	----------------------------------------
28.55/9.72	
28.55/9.72	(1388)
28.55/9.72	Obligation:
28.55/9.72	Q DP problem:
28.55/9.72	The TRS P consists of the following rules:
28.55/9.72	
28.55/9.72	   H(x, x) -> G(x, x, f(k))
28.55/9.72	   G(d, x, x) -> A^2
28.55/9.72	   A^2 -> H(f(c), f(c))
28.55/9.72	   A^2 -> H(f(d), f(d))
28.55/9.72	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.72	   A^2 -> H(f(e), f(e))
28.55/9.72	   A^2 -> H(f(k), f(k))
28.55/9.72	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.72	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.72	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.72	   A^2 -> H(k, f(d))
28.55/9.72	   A^2 -> H(c, U1(c, b))
28.55/9.72	   A^2 -> H(c, U1(d, b))
28.55/9.72	   A^2 -> H(c, U1(b, c))
28.55/9.72	   A^2 -> H(c, U1(b, d))
28.55/9.72	   A^2 -> H(c, U1(c, c))
28.55/9.72	   A^2 -> H(c, f(e))
28.55/9.72	   A^2 -> H(c, f(k))
28.55/9.72	   A^2 -> H(c, U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.72	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.72	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.72	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.72	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.72	   A^2 -> H(U1(e, k), f(e))
28.55/9.72	   A^2 -> H(U1(e, k), f(k))
28.55/9.72	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.72	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.73	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.73	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.73	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.73	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.73	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.73	   A^2 -> H(U1(k, e), f(e))
28.55/9.73	   A^2 -> H(U1(k, e), f(k))
28.55/9.73	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.73	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.73	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.73	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.73	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.73	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.73	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.73	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.73	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.73	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.73	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.73	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.73	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.73	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.73	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.73	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.73	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.73	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.73	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.73	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.73	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.73	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.73	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.73	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.73	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.73	   A^2 -> H(U1(c, c), b)
28.55/9.73	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.73	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.73	   A^2 -> H(U1(c, c), e)
28.55/9.73	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.73	   A^2 -> H(e, U1(c, b))
28.55/9.73	   A^2 -> H(e, U1(d, b))
28.55/9.73	   A^2 -> H(e, U1(b, c))
28.55/9.73	   A^2 -> H(e, U1(b, d))
28.55/9.73	   A^2 -> H(e, U1(c, c))
28.55/9.73	   A^2 -> H(e, f(e))
28.55/9.73	   A^2 -> H(e, f(k))
28.55/9.73	   A^2 -> H(e, U1(d, d))
28.55/9.73	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.73	   A^2 -> H(f(e), b)
28.55/9.73	   A^2 -> H(f(e), U1(e, d))
28.55/9.73	   A^2 -> H(f(e), U1(d, e))
28.55/9.73	   A^2 -> H(f(e), c)
28.55/9.73	   A^2 -> H(f(e), U1(e, k))
28.55/9.73	   A^2 -> H(f(e), U1(k, e))
28.55/9.73	   A^2 -> H(f(e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.73	   A^2 -> H(f(k), b)
28.55/9.73	   A^2 -> H(f(k), U1(e, d))
28.55/9.73	   A^2 -> H(f(k), U1(d, e))
28.55/9.73	   A^2 -> H(f(k), c)
28.55/9.73	   A^2 -> H(f(k), U1(e, k))
28.55/9.73	   A^2 -> H(f(k), U1(k, e))
28.55/9.73	   A^2 -> H(f(k), e)
28.55/9.73	   A^2 -> H(f(c), d)
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.73	   A^2 -> H(U1(k, k), f(e))
28.55/9.73	   A^2 -> H(U1(k, k), f(k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.73	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.73	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.73	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.73	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.73	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.73	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.73	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.73	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.73	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.73	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.73	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.73	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.73	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.73	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.73	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.73	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.73	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.73	   A^2 -> H(U1(d, d), b)
28.55/9.73	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.73	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.73	   A^2 -> H(U1(d, d), c)
28.55/9.73	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.73	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.73	   A^2 -> H(U1(d, d), e)
28.55/9.73	   A^2 -> H(f(d), d)
28.55/9.73	   A^2 -> H(f(d), k)
28.55/9.73	   A^2 -> H(U1(c, c), c)
28.55/9.73	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.73	   A^2 -> H(f(c), k)
28.55/9.73	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.73	   A^2 -> H(f(k), U1(k, k))
28.55/9.73	   A^2 -> H(f(e), e)
28.55/9.73	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.73	   A^2 -> H(d, U1(c, b))
28.55/9.73	   A^2 -> H(d, U1(d, b))
28.55/9.73	   A^2 -> H(d, U1(b, c))
28.55/9.73	   A^2 -> H(d, U1(b, d))
28.55/9.73	   A^2 -> H(d, U1(c, c))
28.55/9.73	   A^2 -> H(d, f(e))
28.55/9.73	   A^2 -> H(d, f(k))
28.55/9.73	   A^2 -> H(d, U1(d, d))
28.55/9.73	   A^2 -> H(a, U1(e, b))
28.55/9.73	   A^2 -> H(a, U1(k, b))
28.55/9.73	   A^2 -> H(a, U1(c, d))
28.55/9.73	   A^2 -> H(a, U1(d, c))
28.55/9.73	   A^2 -> H(a, U1(b, e))
28.55/9.73	   A^2 -> H(a, U1(b, k))
28.55/9.73	   A^2 -> H(a, U1(e, c))
28.55/9.73	   A^2 -> H(a, U1(k, c))
28.55/9.73	   A^2 -> H(a, U1(c, e))
28.55/9.73	   A^2 -> H(a, U1(c, k))
28.55/9.73	   A^2 -> H(a, U1(e, e))
28.55/9.73	   A^2 -> H(a, U1(k, k))
28.55/9.73	   A^2 -> H(a, U1(k, d))
28.55/9.73	   A^2 -> H(a, U1(d, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.73	   A^2 -> H(U1(e, a), b)
28.55/9.73	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.73	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.73	   A^2 -> H(U1(e, a), c)
28.55/9.73	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.73	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.73	   A^2 -> H(U1(e, a), e)
28.55/9.73	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, a), b)
28.55/9.73	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.73	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.73	   A^2 -> H(U1(k, a), c)
28.55/9.73	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.73	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.73	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, d), b)
28.55/9.73	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.73	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.73	   A^2 -> H(U1(c, d), c)
28.55/9.73	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.73	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.73	   A^2 -> H(U1(c, d), e)
28.55/9.73	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, a), d)
28.55/9.73	   A^2 -> H(U1(c, a), k)
28.55/9.73	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.73	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.73	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.73	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.73	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.73	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.73	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.73	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.73	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.73	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.73	   A^2 -> H(U1(d, c), b)
28.55/9.73	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.73	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.73	   A^2 -> H(U1(d, c), c)
28.55/9.73	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.73	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.73	   A^2 -> H(U1(d, c), e)
28.55/9.73	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(d, a), d)
28.55/9.73	   A^2 -> H(U1(d, a), k)
28.55/9.73	   A^2 -> H(U1(a, e), b)
28.55/9.73	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.73	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.73	   A^2 -> H(U1(a, e), c)
28.55/9.73	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.73	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.73	   A^2 -> H(U1(a, e), e)
28.55/9.73	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(a, k), b)
28.55/9.73	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.73	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.73	   A^2 -> H(U1(a, k), c)
28.55/9.73	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.73	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.73	   A^2 -> H(U1(a, k), e)
28.55/9.73	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(a, c), d)
28.55/9.73	   A^2 -> H(U1(a, c), k)
28.55/9.73	   A^2 -> H(U1(a, d), d)
28.55/9.73	   A^2 -> H(U1(a, d), k)
28.55/9.73	   A^2 -> H(k, U1(c, b))
28.55/9.73	   A^2 -> H(k, U1(d, b))
28.55/9.73	   A^2 -> H(k, U1(b, c))
28.55/9.73	   A^2 -> H(k, U1(b, d))
28.55/9.73	   A^2 -> H(k, U1(c, c))
28.55/9.73	   A^2 -> H(k, f(e))
28.55/9.73	   A^2 -> H(k, f(k))
28.55/9.73	
28.55/9.73	The TRS R consists of the following rules:
28.55/9.73	
28.55/9.73	   f(x) -> U1(x, x)
28.55/9.73	   U1(e, x) -> x
28.55/9.73	   a -> c
28.55/9.73	   a -> d
28.55/9.73	   b -> c
28.55/9.73	   b -> d
28.55/9.73	   d -> k
28.55/9.73	   c -> e
28.55/9.73	   c -> k
28.55/9.73	
28.55/9.73	Q is empty.
28.55/9.73	We have to consider all minimal (P,Q,R)-chains.
28.55/9.73	----------------------------------------
28.55/9.73	
28.55/9.73	(1389) TransformationProof (EQUIVALENT)
28.55/9.73	By narrowing [LPAR04] the rule A^2 -> H(k, f(d)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.73	
28.55/9.73	   (A^2 -> H(k, U1(d, d)),A^2 -> H(k, U1(d, d)))
28.55/9.73	   (A^2 -> H(k, f(k)),A^2 -> H(k, f(k)))
28.55/9.73	
28.55/9.73	
28.55/9.73	----------------------------------------
28.55/9.73	
28.55/9.73	(1390)
28.55/9.73	Obligation:
28.55/9.73	Q DP problem:
28.55/9.73	The TRS P consists of the following rules:
28.55/9.73	
28.55/9.73	   H(x, x) -> G(x, x, f(k))
28.55/9.73	   G(d, x, x) -> A^2
28.55/9.73	   A^2 -> H(f(c), f(c))
28.55/9.73	   A^2 -> H(f(d), f(d))
28.55/9.73	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.73	   A^2 -> H(f(e), f(e))
28.55/9.73	   A^2 -> H(f(k), f(k))
28.55/9.73	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.73	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.73	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.73	   A^2 -> H(c, U1(c, b))
28.55/9.73	   A^2 -> H(c, U1(d, b))
28.55/9.73	   A^2 -> H(c, U1(b, c))
28.55/9.73	   A^2 -> H(c, U1(b, d))
28.55/9.73	   A^2 -> H(c, U1(c, c))
28.55/9.73	   A^2 -> H(c, f(e))
28.55/9.73	   A^2 -> H(c, f(k))
28.55/9.73	   A^2 -> H(c, U1(d, d))
28.55/9.73	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.73	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.73	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.73	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.73	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.73	   A^2 -> H(U1(e, k), f(e))
28.55/9.73	   A^2 -> H(U1(e, k), f(k))
28.55/9.73	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.73	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.73	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.73	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.73	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.73	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.73	   A^2 -> H(U1(k, e), f(e))
28.55/9.73	   A^2 -> H(U1(k, e), f(k))
28.55/9.73	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.73	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.73	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.73	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.73	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.73	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.73	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.73	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.73	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.73	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.73	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.73	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.73	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.73	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.73	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.73	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.73	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.73	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.73	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.73	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.73	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.73	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.73	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.73	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.73	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.73	   A^2 -> H(U1(c, c), b)
28.55/9.73	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.73	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.73	   A^2 -> H(U1(c, c), e)
28.55/9.73	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.73	   A^2 -> H(e, U1(c, b))
28.55/9.73	   A^2 -> H(e, U1(d, b))
28.55/9.73	   A^2 -> H(e, U1(b, c))
28.55/9.73	   A^2 -> H(e, U1(b, d))
28.55/9.73	   A^2 -> H(e, U1(c, c))
28.55/9.73	   A^2 -> H(e, f(e))
28.55/9.73	   A^2 -> H(e, f(k))
28.55/9.73	   A^2 -> H(e, U1(d, d))
28.55/9.73	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.73	   A^2 -> H(f(e), b)
28.55/9.73	   A^2 -> H(f(e), U1(e, d))
28.55/9.73	   A^2 -> H(f(e), U1(d, e))
28.55/9.73	   A^2 -> H(f(e), c)
28.55/9.73	   A^2 -> H(f(e), U1(e, k))
28.55/9.73	   A^2 -> H(f(e), U1(k, e))
28.55/9.73	   A^2 -> H(f(e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.73	   A^2 -> H(f(k), b)
28.55/9.73	   A^2 -> H(f(k), U1(e, d))
28.55/9.73	   A^2 -> H(f(k), U1(d, e))
28.55/9.73	   A^2 -> H(f(k), c)
28.55/9.73	   A^2 -> H(f(k), U1(e, k))
28.55/9.73	   A^2 -> H(f(k), U1(k, e))
28.55/9.73	   A^2 -> H(f(k), e)
28.55/9.73	   A^2 -> H(f(c), d)
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.73	   A^2 -> H(U1(k, k), f(e))
28.55/9.73	   A^2 -> H(U1(k, k), f(k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.73	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.73	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.73	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.73	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.73	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.73	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.73	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.73	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.73	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.73	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.73	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.73	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.73	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.73	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.73	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.73	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.73	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.73	   A^2 -> H(U1(d, d), b)
28.55/9.73	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.73	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.73	   A^2 -> H(U1(d, d), c)
28.55/9.73	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.73	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.73	   A^2 -> H(U1(d, d), e)
28.55/9.73	   A^2 -> H(f(d), d)
28.55/9.73	   A^2 -> H(f(d), k)
28.55/9.73	   A^2 -> H(U1(c, c), c)
28.55/9.73	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.73	   A^2 -> H(f(c), k)
28.55/9.73	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.73	   A^2 -> H(f(k), U1(k, k))
28.55/9.73	   A^2 -> H(f(e), e)
28.55/9.73	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.73	   A^2 -> H(d, U1(c, b))
28.55/9.73	   A^2 -> H(d, U1(d, b))
28.55/9.73	   A^2 -> H(d, U1(b, c))
28.55/9.73	   A^2 -> H(d, U1(b, d))
28.55/9.73	   A^2 -> H(d, U1(c, c))
28.55/9.73	   A^2 -> H(d, f(e))
28.55/9.73	   A^2 -> H(d, f(k))
28.55/9.73	   A^2 -> H(d, U1(d, d))
28.55/9.73	   A^2 -> H(a, U1(e, b))
28.55/9.73	   A^2 -> H(a, U1(k, b))
28.55/9.73	   A^2 -> H(a, U1(c, d))
28.55/9.73	   A^2 -> H(a, U1(d, c))
28.55/9.73	   A^2 -> H(a, U1(b, e))
28.55/9.73	   A^2 -> H(a, U1(b, k))
28.55/9.73	   A^2 -> H(a, U1(e, c))
28.55/9.73	   A^2 -> H(a, U1(k, c))
28.55/9.73	   A^2 -> H(a, U1(c, e))
28.55/9.73	   A^2 -> H(a, U1(c, k))
28.55/9.73	   A^2 -> H(a, U1(e, e))
28.55/9.73	   A^2 -> H(a, U1(k, k))
28.55/9.73	   A^2 -> H(a, U1(k, d))
28.55/9.73	   A^2 -> H(a, U1(d, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.73	   A^2 -> H(U1(e, a), b)
28.55/9.73	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.73	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.73	   A^2 -> H(U1(e, a), c)
28.55/9.73	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.73	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.73	   A^2 -> H(U1(e, a), e)
28.55/9.73	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, a), b)
28.55/9.73	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.73	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.73	   A^2 -> H(U1(k, a), c)
28.55/9.73	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.73	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.73	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, d), b)
28.55/9.73	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.73	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.73	   A^2 -> H(U1(c, d), c)
28.55/9.73	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.73	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.73	   A^2 -> H(U1(c, d), e)
28.55/9.73	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, a), d)
28.55/9.73	   A^2 -> H(U1(c, a), k)
28.55/9.73	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.73	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.73	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.73	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.73	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.73	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.73	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.73	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.73	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.73	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.73	   A^2 -> H(U1(d, c), b)
28.55/9.73	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.73	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.73	   A^2 -> H(U1(d, c), c)
28.55/9.73	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.73	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.73	   A^2 -> H(U1(d, c), e)
28.55/9.73	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(d, a), d)
28.55/9.73	   A^2 -> H(U1(d, a), k)
28.55/9.73	   A^2 -> H(U1(a, e), b)
28.55/9.73	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.73	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.73	   A^2 -> H(U1(a, e), c)
28.55/9.73	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.73	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.73	   A^2 -> H(U1(a, e), e)
28.55/9.73	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(a, k), b)
28.55/9.73	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.73	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.73	   A^2 -> H(U1(a, k), c)
28.55/9.73	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.73	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.73	   A^2 -> H(U1(a, k), e)
28.55/9.73	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(a, c), d)
28.55/9.73	   A^2 -> H(U1(a, c), k)
28.55/9.73	   A^2 -> H(U1(a, d), d)
28.55/9.73	   A^2 -> H(U1(a, d), k)
28.55/9.73	   A^2 -> H(k, U1(c, b))
28.55/9.73	   A^2 -> H(k, U1(d, b))
28.55/9.73	   A^2 -> H(k, U1(b, c))
28.55/9.73	   A^2 -> H(k, U1(b, d))
28.55/9.73	   A^2 -> H(k, U1(c, c))
28.55/9.73	   A^2 -> H(k, f(e))
28.55/9.73	   A^2 -> H(k, f(k))
28.55/9.73	   A^2 -> H(k, U1(d, d))
28.55/9.73	
28.55/9.73	The TRS R consists of the following rules:
28.55/9.73	
28.55/9.73	   f(x) -> U1(x, x)
28.55/9.73	   U1(e, x) -> x
28.55/9.73	   a -> c
28.55/9.73	   a -> d
28.55/9.73	   b -> c
28.55/9.73	   b -> d
28.55/9.73	   d -> k
28.55/9.73	   c -> e
28.55/9.73	   c -> k
28.55/9.73	
28.55/9.73	Q is empty.
28.55/9.73	We have to consider all minimal (P,Q,R)-chains.
28.55/9.73	----------------------------------------
28.55/9.73	
28.55/9.73	(1391) TransformationProof (EQUIVALENT)
28.55/9.73	By narrowing [LPAR04] the rule A^2 -> H(c, U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.73	
28.55/9.73	   (A^2 -> H(e, U1(c, b)),A^2 -> H(e, U1(c, b)))
28.55/9.73	   (A^2 -> H(k, U1(c, b)),A^2 -> H(k, U1(c, b)))
28.55/9.73	   (A^2 -> H(c, U1(e, b)),A^2 -> H(c, U1(e, b)))
28.55/9.73	   (A^2 -> H(c, U1(k, b)),A^2 -> H(c, U1(k, b)))
28.55/9.73	   (A^2 -> H(c, U1(c, c)),A^2 -> H(c, U1(c, c)))
28.55/9.73	   (A^2 -> H(c, U1(c, d)),A^2 -> H(c, U1(c, d)))
28.55/9.73	
28.55/9.73	
28.55/9.73	----------------------------------------
28.55/9.73	
28.55/9.73	(1392)
28.55/9.73	Obligation:
28.55/9.73	Q DP problem:
28.55/9.73	The TRS P consists of the following rules:
28.55/9.73	
28.55/9.73	   H(x, x) -> G(x, x, f(k))
28.55/9.73	   G(d, x, x) -> A^2
28.55/9.73	   A^2 -> H(f(c), f(c))
28.55/9.73	   A^2 -> H(f(d), f(d))
28.55/9.73	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.73	   A^2 -> H(f(e), f(e))
28.55/9.73	   A^2 -> H(f(k), f(k))
28.55/9.73	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.73	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.73	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.73	   A^2 -> H(c, U1(d, b))
28.55/9.73	   A^2 -> H(c, U1(b, c))
28.55/9.73	   A^2 -> H(c, U1(b, d))
28.55/9.73	   A^2 -> H(c, U1(c, c))
28.55/9.73	   A^2 -> H(c, f(e))
28.55/9.73	   A^2 -> H(c, f(k))
28.55/9.73	   A^2 -> H(c, U1(d, d))
28.55/9.73	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.73	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.73	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.73	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.73	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.73	   A^2 -> H(U1(e, k), f(e))
28.55/9.73	   A^2 -> H(U1(e, k), f(k))
28.55/9.73	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.73	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.73	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.73	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.73	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.73	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.73	   A^2 -> H(U1(k, e), f(e))
28.55/9.73	   A^2 -> H(U1(k, e), f(k))
28.55/9.73	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.73	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.73	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.73	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.73	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.73	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.73	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.73	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.73	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.73	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.73	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.73	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.73	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.73	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.73	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.73	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.73	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.73	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.73	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.73	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.73	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.73	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.73	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.73	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.73	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.73	   A^2 -> H(U1(c, c), b)
28.55/9.73	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.73	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.73	   A^2 -> H(U1(c, c), e)
28.55/9.73	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.73	   A^2 -> H(e, U1(c, b))
28.55/9.73	   A^2 -> H(e, U1(d, b))
28.55/9.73	   A^2 -> H(e, U1(b, c))
28.55/9.73	   A^2 -> H(e, U1(b, d))
28.55/9.73	   A^2 -> H(e, U1(c, c))
28.55/9.73	   A^2 -> H(e, f(e))
28.55/9.73	   A^2 -> H(e, f(k))
28.55/9.73	   A^2 -> H(e, U1(d, d))
28.55/9.73	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.73	   A^2 -> H(f(e), b)
28.55/9.73	   A^2 -> H(f(e), U1(e, d))
28.55/9.73	   A^2 -> H(f(e), U1(d, e))
28.55/9.73	   A^2 -> H(f(e), c)
28.55/9.73	   A^2 -> H(f(e), U1(e, k))
28.55/9.73	   A^2 -> H(f(e), U1(k, e))
28.55/9.73	   A^2 -> H(f(e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.73	   A^2 -> H(f(k), b)
28.55/9.73	   A^2 -> H(f(k), U1(e, d))
28.55/9.73	   A^2 -> H(f(k), U1(d, e))
28.55/9.73	   A^2 -> H(f(k), c)
28.55/9.73	   A^2 -> H(f(k), U1(e, k))
28.55/9.73	   A^2 -> H(f(k), U1(k, e))
28.55/9.73	   A^2 -> H(f(k), e)
28.55/9.73	   A^2 -> H(f(c), d)
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.73	   A^2 -> H(U1(k, k), f(e))
28.55/9.73	   A^2 -> H(U1(k, k), f(k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.73	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.73	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.73	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.73	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.73	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.73	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.73	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.73	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.73	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.73	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.73	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.73	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.73	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.73	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.73	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.73	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.73	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.73	   A^2 -> H(U1(d, d), b)
28.55/9.73	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.73	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.73	   A^2 -> H(U1(d, d), c)
28.55/9.73	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.73	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.73	   A^2 -> H(U1(d, d), e)
28.55/9.73	   A^2 -> H(f(d), d)
28.55/9.73	   A^2 -> H(f(d), k)
28.55/9.73	   A^2 -> H(U1(c, c), c)
28.55/9.73	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.73	   A^2 -> H(f(c), k)
28.55/9.73	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.73	   A^2 -> H(f(k), U1(k, k))
28.55/9.73	   A^2 -> H(f(e), e)
28.55/9.73	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.73	   A^2 -> H(d, U1(c, b))
28.55/9.73	   A^2 -> H(d, U1(d, b))
28.55/9.73	   A^2 -> H(d, U1(b, c))
28.55/9.73	   A^2 -> H(d, U1(b, d))
28.55/9.73	   A^2 -> H(d, U1(c, c))
28.55/9.73	   A^2 -> H(d, f(e))
28.55/9.73	   A^2 -> H(d, f(k))
28.55/9.73	   A^2 -> H(d, U1(d, d))
28.55/9.73	   A^2 -> H(a, U1(e, b))
28.55/9.73	   A^2 -> H(a, U1(k, b))
28.55/9.73	   A^2 -> H(a, U1(c, d))
28.55/9.73	   A^2 -> H(a, U1(d, c))
28.55/9.73	   A^2 -> H(a, U1(b, e))
28.55/9.73	   A^2 -> H(a, U1(b, k))
28.55/9.73	   A^2 -> H(a, U1(e, c))
28.55/9.73	   A^2 -> H(a, U1(k, c))
28.55/9.73	   A^2 -> H(a, U1(c, e))
28.55/9.73	   A^2 -> H(a, U1(c, k))
28.55/9.73	   A^2 -> H(a, U1(e, e))
28.55/9.73	   A^2 -> H(a, U1(k, k))
28.55/9.73	   A^2 -> H(a, U1(k, d))
28.55/9.73	   A^2 -> H(a, U1(d, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.73	   A^2 -> H(U1(e, a), b)
28.55/9.73	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.73	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.73	   A^2 -> H(U1(e, a), c)
28.55/9.73	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.73	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.73	   A^2 -> H(U1(e, a), e)
28.55/9.73	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, a), b)
28.55/9.73	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.73	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.73	   A^2 -> H(U1(k, a), c)
28.55/9.73	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.73	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.73	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, d), b)
28.55/9.73	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.73	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.73	   A^2 -> H(U1(c, d), c)
28.55/9.73	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.73	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.73	   A^2 -> H(U1(c, d), e)
28.55/9.73	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, a), d)
28.55/9.73	   A^2 -> H(U1(c, a), k)
28.55/9.73	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.73	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.73	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.73	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.73	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.73	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.73	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.73	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.73	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.73	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.73	   A^2 -> H(U1(d, c), b)
28.55/9.73	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.73	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.73	   A^2 -> H(U1(d, c), c)
28.55/9.73	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.73	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.73	   A^2 -> H(U1(d, c), e)
28.55/9.73	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(d, a), d)
28.55/9.73	   A^2 -> H(U1(d, a), k)
28.55/9.73	   A^2 -> H(U1(a, e), b)
28.55/9.73	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.73	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.73	   A^2 -> H(U1(a, e), c)
28.55/9.73	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.73	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.73	   A^2 -> H(U1(a, e), e)
28.55/9.73	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(a, k), b)
28.55/9.73	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.73	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.73	   A^2 -> H(U1(a, k), c)
28.55/9.73	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.73	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.73	   A^2 -> H(U1(a, k), e)
28.55/9.73	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(a, c), d)
28.55/9.73	   A^2 -> H(U1(a, c), k)
28.55/9.73	   A^2 -> H(U1(a, d), d)
28.55/9.73	   A^2 -> H(U1(a, d), k)
28.55/9.73	   A^2 -> H(k, U1(c, b))
28.55/9.73	   A^2 -> H(k, U1(d, b))
28.55/9.73	   A^2 -> H(k, U1(b, c))
28.55/9.73	   A^2 -> H(k, U1(b, d))
28.55/9.73	   A^2 -> H(k, U1(c, c))
28.55/9.73	   A^2 -> H(k, f(e))
28.55/9.73	   A^2 -> H(k, f(k))
28.55/9.73	   A^2 -> H(k, U1(d, d))
28.55/9.73	   A^2 -> H(c, U1(e, b))
28.55/9.73	   A^2 -> H(c, U1(k, b))
28.55/9.73	   A^2 -> H(c, U1(c, d))
28.55/9.73	
28.55/9.73	The TRS R consists of the following rules:
28.55/9.73	
28.55/9.73	   f(x) -> U1(x, x)
28.55/9.73	   U1(e, x) -> x
28.55/9.73	   a -> c
28.55/9.73	   a -> d
28.55/9.73	   b -> c
28.55/9.73	   b -> d
28.55/9.73	   d -> k
28.55/9.73	   c -> e
28.55/9.73	   c -> k
28.55/9.73	
28.55/9.73	Q is empty.
28.55/9.73	We have to consider all minimal (P,Q,R)-chains.
28.55/9.73	----------------------------------------
28.55/9.73	
28.55/9.73	(1393) TransformationProof (EQUIVALENT)
28.55/9.73	By narrowing [LPAR04] the rule A^2 -> H(c, U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.73	
28.55/9.73	   (A^2 -> H(e, U1(d, b)),A^2 -> H(e, U1(d, b)))
28.55/9.73	   (A^2 -> H(k, U1(d, b)),A^2 -> H(k, U1(d, b)))
28.55/9.73	   (A^2 -> H(c, U1(k, b)),A^2 -> H(c, U1(k, b)))
28.55/9.73	   (A^2 -> H(c, U1(d, c)),A^2 -> H(c, U1(d, c)))
28.55/9.73	   (A^2 -> H(c, U1(d, d)),A^2 -> H(c, U1(d, d)))
28.55/9.73	
28.55/9.73	
28.55/9.73	----------------------------------------
28.55/9.73	
28.55/9.73	(1394)
28.55/9.73	Obligation:
28.55/9.73	Q DP problem:
28.55/9.73	The TRS P consists of the following rules:
28.55/9.73	
28.55/9.73	   H(x, x) -> G(x, x, f(k))
28.55/9.73	   G(d, x, x) -> A^2
28.55/9.73	   A^2 -> H(f(c), f(c))
28.55/9.73	   A^2 -> H(f(d), f(d))
28.55/9.73	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.73	   A^2 -> H(f(e), f(e))
28.55/9.73	   A^2 -> H(f(k), f(k))
28.55/9.73	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.73	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.73	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.73	   A^2 -> H(c, U1(b, c))
28.55/9.73	   A^2 -> H(c, U1(b, d))
28.55/9.73	   A^2 -> H(c, U1(c, c))
28.55/9.73	   A^2 -> H(c, f(e))
28.55/9.73	   A^2 -> H(c, f(k))
28.55/9.73	   A^2 -> H(c, U1(d, d))
28.55/9.73	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.73	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.73	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.73	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.73	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.73	   A^2 -> H(U1(e, k), f(e))
28.55/9.73	   A^2 -> H(U1(e, k), f(k))
28.55/9.73	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.73	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.73	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.73	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.73	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.73	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.73	   A^2 -> H(U1(k, e), f(e))
28.55/9.73	   A^2 -> H(U1(k, e), f(k))
28.55/9.73	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.73	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.73	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.73	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.73	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.73	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.73	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.73	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.73	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.73	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.73	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.73	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.73	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.73	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.73	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.73	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.73	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.73	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.73	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.73	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.73	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.73	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.73	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.73	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.73	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.73	   A^2 -> H(U1(c, c), b)
28.55/9.73	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.73	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.73	   A^2 -> H(U1(c, c), e)
28.55/9.73	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.73	   A^2 -> H(e, U1(c, b))
28.55/9.73	   A^2 -> H(e, U1(d, b))
28.55/9.73	   A^2 -> H(e, U1(b, c))
28.55/9.73	   A^2 -> H(e, U1(b, d))
28.55/9.73	   A^2 -> H(e, U1(c, c))
28.55/9.73	   A^2 -> H(e, f(e))
28.55/9.73	   A^2 -> H(e, f(k))
28.55/9.73	   A^2 -> H(e, U1(d, d))
28.55/9.73	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.73	   A^2 -> H(f(e), b)
28.55/9.73	   A^2 -> H(f(e), U1(e, d))
28.55/9.73	   A^2 -> H(f(e), U1(d, e))
28.55/9.73	   A^2 -> H(f(e), c)
28.55/9.73	   A^2 -> H(f(e), U1(e, k))
28.55/9.73	   A^2 -> H(f(e), U1(k, e))
28.55/9.73	   A^2 -> H(f(e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.73	   A^2 -> H(f(k), b)
28.55/9.73	   A^2 -> H(f(k), U1(e, d))
28.55/9.73	   A^2 -> H(f(k), U1(d, e))
28.55/9.73	   A^2 -> H(f(k), c)
28.55/9.73	   A^2 -> H(f(k), U1(e, k))
28.55/9.73	   A^2 -> H(f(k), U1(k, e))
28.55/9.73	   A^2 -> H(f(k), e)
28.55/9.73	   A^2 -> H(f(c), d)
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.73	   A^2 -> H(U1(k, k), f(e))
28.55/9.73	   A^2 -> H(U1(k, k), f(k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.73	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.73	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.73	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.73	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.73	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.73	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.73	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.73	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.73	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.73	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.73	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.73	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.73	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.73	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.73	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.73	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.73	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.73	   A^2 -> H(U1(d, d), b)
28.55/9.73	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.73	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.73	   A^2 -> H(U1(d, d), c)
28.55/9.73	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.73	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.73	   A^2 -> H(U1(d, d), e)
28.55/9.73	   A^2 -> H(f(d), d)
28.55/9.73	   A^2 -> H(f(d), k)
28.55/9.73	   A^2 -> H(U1(c, c), c)
28.55/9.73	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.73	   A^2 -> H(f(c), k)
28.55/9.73	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.73	   A^2 -> H(f(k), U1(k, k))
28.55/9.73	   A^2 -> H(f(e), e)
28.55/9.73	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.73	   A^2 -> H(d, U1(c, b))
28.55/9.73	   A^2 -> H(d, U1(d, b))
28.55/9.73	   A^2 -> H(d, U1(b, c))
28.55/9.73	   A^2 -> H(d, U1(b, d))
28.55/9.73	   A^2 -> H(d, U1(c, c))
28.55/9.73	   A^2 -> H(d, f(e))
28.55/9.73	   A^2 -> H(d, f(k))
28.55/9.73	   A^2 -> H(d, U1(d, d))
28.55/9.73	   A^2 -> H(a, U1(e, b))
28.55/9.73	   A^2 -> H(a, U1(k, b))
28.55/9.73	   A^2 -> H(a, U1(c, d))
28.55/9.73	   A^2 -> H(a, U1(d, c))
28.55/9.73	   A^2 -> H(a, U1(b, e))
28.55/9.73	   A^2 -> H(a, U1(b, k))
28.55/9.73	   A^2 -> H(a, U1(e, c))
28.55/9.73	   A^2 -> H(a, U1(k, c))
28.55/9.73	   A^2 -> H(a, U1(c, e))
28.55/9.73	   A^2 -> H(a, U1(c, k))
28.55/9.73	   A^2 -> H(a, U1(e, e))
28.55/9.73	   A^2 -> H(a, U1(k, k))
28.55/9.73	   A^2 -> H(a, U1(k, d))
28.55/9.73	   A^2 -> H(a, U1(d, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.73	   A^2 -> H(U1(e, a), b)
28.55/9.73	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.73	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.73	   A^2 -> H(U1(e, a), c)
28.55/9.73	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.73	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.73	   A^2 -> H(U1(e, a), e)
28.55/9.73	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, a), b)
28.55/9.73	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.73	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.73	   A^2 -> H(U1(k, a), c)
28.55/9.73	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.73	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.73	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, d), b)
28.55/9.73	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.73	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.73	   A^2 -> H(U1(c, d), c)
28.55/9.73	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.73	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.73	   A^2 -> H(U1(c, d), e)
28.55/9.73	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, a), d)
28.55/9.73	   A^2 -> H(U1(c, a), k)
28.55/9.73	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.73	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.73	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.73	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.73	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.73	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.73	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.73	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.73	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.73	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.73	   A^2 -> H(U1(d, c), b)
28.55/9.73	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.73	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.73	   A^2 -> H(U1(d, c), c)
28.55/9.73	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.73	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.73	   A^2 -> H(U1(d, c), e)
28.55/9.73	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(d, a), d)
28.55/9.73	   A^2 -> H(U1(d, a), k)
28.55/9.73	   A^2 -> H(U1(a, e), b)
28.55/9.73	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.73	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.73	   A^2 -> H(U1(a, e), c)
28.55/9.73	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.73	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.73	   A^2 -> H(U1(a, e), e)
28.55/9.73	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(a, k), b)
28.55/9.73	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.73	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.73	   A^2 -> H(U1(a, k), c)
28.55/9.73	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.73	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.73	   A^2 -> H(U1(a, k), e)
28.55/9.73	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(a, c), d)
28.55/9.73	   A^2 -> H(U1(a, c), k)
28.55/9.73	   A^2 -> H(U1(a, d), d)
28.55/9.73	   A^2 -> H(U1(a, d), k)
28.55/9.73	   A^2 -> H(k, U1(c, b))
28.55/9.73	   A^2 -> H(k, U1(d, b))
28.55/9.73	   A^2 -> H(k, U1(b, c))
28.55/9.73	   A^2 -> H(k, U1(b, d))
28.55/9.73	   A^2 -> H(k, U1(c, c))
28.55/9.73	   A^2 -> H(k, f(e))
28.55/9.73	   A^2 -> H(k, f(k))
28.55/9.73	   A^2 -> H(k, U1(d, d))
28.55/9.73	   A^2 -> H(c, U1(e, b))
28.55/9.73	   A^2 -> H(c, U1(k, b))
28.55/9.73	   A^2 -> H(c, U1(c, d))
28.55/9.73	   A^2 -> H(c, U1(d, c))
28.55/9.73	
28.55/9.73	The TRS R consists of the following rules:
28.55/9.73	
28.55/9.73	   f(x) -> U1(x, x)
28.55/9.73	   U1(e, x) -> x
28.55/9.73	   a -> c
28.55/9.73	   a -> d
28.55/9.73	   b -> c
28.55/9.73	   b -> d
28.55/9.73	   d -> k
28.55/9.73	   c -> e
28.55/9.73	   c -> k
28.55/9.73	
28.55/9.73	Q is empty.
28.55/9.73	We have to consider all minimal (P,Q,R)-chains.
28.55/9.73	----------------------------------------
28.55/9.73	
28.55/9.73	(1395) TransformationProof (EQUIVALENT)
28.55/9.73	By narrowing [LPAR04] the rule A^2 -> H(c, U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.73	
28.55/9.73	   (A^2 -> H(e, U1(b, c)),A^2 -> H(e, U1(b, c)))
28.55/9.73	   (A^2 -> H(k, U1(b, c)),A^2 -> H(k, U1(b, c)))
28.55/9.73	   (A^2 -> H(c, U1(c, c)),A^2 -> H(c, U1(c, c)))
28.55/9.73	   (A^2 -> H(c, U1(d, c)),A^2 -> H(c, U1(d, c)))
28.55/9.73	   (A^2 -> H(c, U1(b, e)),A^2 -> H(c, U1(b, e)))
28.55/9.73	   (A^2 -> H(c, U1(b, k)),A^2 -> H(c, U1(b, k)))
28.55/9.73	
28.55/9.73	
28.55/9.73	----------------------------------------
28.55/9.73	
28.55/9.73	(1396)
28.55/9.73	Obligation:
28.55/9.73	Q DP problem:
28.55/9.73	The TRS P consists of the following rules:
28.55/9.73	
28.55/9.73	   H(x, x) -> G(x, x, f(k))
28.55/9.73	   G(d, x, x) -> A^2
28.55/9.73	   A^2 -> H(f(c), f(c))
28.55/9.73	   A^2 -> H(f(d), f(d))
28.55/9.73	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.73	   A^2 -> H(f(e), f(e))
28.55/9.73	   A^2 -> H(f(k), f(k))
28.55/9.73	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.73	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.73	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.73	   A^2 -> H(c, U1(b, d))
28.55/9.73	   A^2 -> H(c, U1(c, c))
28.55/9.73	   A^2 -> H(c, f(e))
28.55/9.73	   A^2 -> H(c, f(k))
28.55/9.73	   A^2 -> H(c, U1(d, d))
28.55/9.73	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.73	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.73	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.73	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.73	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.73	   A^2 -> H(U1(e, k), f(e))
28.55/9.73	   A^2 -> H(U1(e, k), f(k))
28.55/9.73	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.73	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.73	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.73	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.73	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.73	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.73	   A^2 -> H(U1(k, e), f(e))
28.55/9.73	   A^2 -> H(U1(k, e), f(k))
28.55/9.73	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.73	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.73	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.73	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.73	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.73	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.73	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.73	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.73	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.73	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.73	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.73	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.73	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.73	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.73	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.73	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.73	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.73	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.73	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.73	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.73	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.73	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.73	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.73	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.73	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.73	   A^2 -> H(U1(c, c), b)
28.55/9.73	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.73	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.73	   A^2 -> H(U1(c, c), e)
28.55/9.73	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.73	   A^2 -> H(e, U1(c, b))
28.55/9.73	   A^2 -> H(e, U1(d, b))
28.55/9.73	   A^2 -> H(e, U1(b, c))
28.55/9.73	   A^2 -> H(e, U1(b, d))
28.55/9.73	   A^2 -> H(e, U1(c, c))
28.55/9.73	   A^2 -> H(e, f(e))
28.55/9.73	   A^2 -> H(e, f(k))
28.55/9.73	   A^2 -> H(e, U1(d, d))
28.55/9.73	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.73	   A^2 -> H(f(e), b)
28.55/9.73	   A^2 -> H(f(e), U1(e, d))
28.55/9.73	   A^2 -> H(f(e), U1(d, e))
28.55/9.73	   A^2 -> H(f(e), c)
28.55/9.73	   A^2 -> H(f(e), U1(e, k))
28.55/9.73	   A^2 -> H(f(e), U1(k, e))
28.55/9.73	   A^2 -> H(f(e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.73	   A^2 -> H(f(k), b)
28.55/9.73	   A^2 -> H(f(k), U1(e, d))
28.55/9.73	   A^2 -> H(f(k), U1(d, e))
28.55/9.73	   A^2 -> H(f(k), c)
28.55/9.73	   A^2 -> H(f(k), U1(e, k))
28.55/9.73	   A^2 -> H(f(k), U1(k, e))
28.55/9.73	   A^2 -> H(f(k), e)
28.55/9.73	   A^2 -> H(f(c), d)
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.73	   A^2 -> H(U1(k, k), f(e))
28.55/9.73	   A^2 -> H(U1(k, k), f(k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.73	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.73	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.73	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.73	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.73	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.73	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.73	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.73	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.73	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.73	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.73	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.73	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.73	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.73	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.73	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.73	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.73	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.73	   A^2 -> H(U1(d, d), b)
28.55/9.73	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.73	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.73	   A^2 -> H(U1(d, d), c)
28.55/9.73	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.73	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.73	   A^2 -> H(U1(d, d), e)
28.55/9.73	   A^2 -> H(f(d), d)
28.55/9.73	   A^2 -> H(f(d), k)
28.55/9.73	   A^2 -> H(U1(c, c), c)
28.55/9.73	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.73	   A^2 -> H(f(c), k)
28.55/9.73	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.73	   A^2 -> H(f(k), U1(k, k))
28.55/9.73	   A^2 -> H(f(e), e)
28.55/9.73	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.73	   A^2 -> H(d, U1(c, b))
28.55/9.73	   A^2 -> H(d, U1(d, b))
28.55/9.73	   A^2 -> H(d, U1(b, c))
28.55/9.73	   A^2 -> H(d, U1(b, d))
28.55/9.73	   A^2 -> H(d, U1(c, c))
28.55/9.73	   A^2 -> H(d, f(e))
28.55/9.73	   A^2 -> H(d, f(k))
28.55/9.73	   A^2 -> H(d, U1(d, d))
28.55/9.73	   A^2 -> H(a, U1(e, b))
28.55/9.73	   A^2 -> H(a, U1(k, b))
28.55/9.73	   A^2 -> H(a, U1(c, d))
28.55/9.73	   A^2 -> H(a, U1(d, c))
28.55/9.73	   A^2 -> H(a, U1(b, e))
28.55/9.73	   A^2 -> H(a, U1(b, k))
28.55/9.73	   A^2 -> H(a, U1(e, c))
28.55/9.73	   A^2 -> H(a, U1(k, c))
28.55/9.73	   A^2 -> H(a, U1(c, e))
28.55/9.73	   A^2 -> H(a, U1(c, k))
28.55/9.73	   A^2 -> H(a, U1(e, e))
28.55/9.73	   A^2 -> H(a, U1(k, k))
28.55/9.73	   A^2 -> H(a, U1(k, d))
28.55/9.73	   A^2 -> H(a, U1(d, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.73	   A^2 -> H(U1(e, a), b)
28.55/9.73	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.73	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.73	   A^2 -> H(U1(e, a), c)
28.55/9.73	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.73	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.73	   A^2 -> H(U1(e, a), e)
28.55/9.73	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, a), b)
28.55/9.73	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.73	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.73	   A^2 -> H(U1(k, a), c)
28.55/9.73	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.73	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.73	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, d), b)
28.55/9.73	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.73	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.73	   A^2 -> H(U1(c, d), c)
28.55/9.73	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.73	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.73	   A^2 -> H(U1(c, d), e)
28.55/9.73	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, a), d)
28.55/9.73	   A^2 -> H(U1(c, a), k)
28.55/9.73	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.73	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.73	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.73	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.73	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.73	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.73	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.73	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.73	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.73	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.73	   A^2 -> H(U1(d, c), b)
28.55/9.73	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.73	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.73	   A^2 -> H(U1(d, c), c)
28.55/9.73	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.73	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.73	   A^2 -> H(U1(d, c), e)
28.55/9.73	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(d, a), d)
28.55/9.73	   A^2 -> H(U1(d, a), k)
28.55/9.73	   A^2 -> H(U1(a, e), b)
28.55/9.73	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.73	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.73	   A^2 -> H(U1(a, e), c)
28.55/9.73	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.73	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.73	   A^2 -> H(U1(a, e), e)
28.55/9.73	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(a, k), b)
28.55/9.73	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.73	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.73	   A^2 -> H(U1(a, k), c)
28.55/9.73	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.73	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.73	   A^2 -> H(U1(a, k), e)
28.55/9.73	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(a, c), d)
28.55/9.73	   A^2 -> H(U1(a, c), k)
28.55/9.73	   A^2 -> H(U1(a, d), d)
28.55/9.73	   A^2 -> H(U1(a, d), k)
28.55/9.73	   A^2 -> H(k, U1(c, b))
28.55/9.73	   A^2 -> H(k, U1(d, b))
28.55/9.73	   A^2 -> H(k, U1(b, c))
28.55/9.73	   A^2 -> H(k, U1(b, d))
28.55/9.73	   A^2 -> H(k, U1(c, c))
28.55/9.73	   A^2 -> H(k, f(e))
28.55/9.73	   A^2 -> H(k, f(k))
28.55/9.73	   A^2 -> H(k, U1(d, d))
28.55/9.73	   A^2 -> H(c, U1(e, b))
28.55/9.73	   A^2 -> H(c, U1(k, b))
28.55/9.73	   A^2 -> H(c, U1(c, d))
28.55/9.73	   A^2 -> H(c, U1(d, c))
28.55/9.73	   A^2 -> H(c, U1(b, e))
28.55/9.73	   A^2 -> H(c, U1(b, k))
28.55/9.73	
28.55/9.73	The TRS R consists of the following rules:
28.55/9.73	
28.55/9.73	   f(x) -> U1(x, x)
28.55/9.73	   U1(e, x) -> x
28.55/9.73	   a -> c
28.55/9.73	   a -> d
28.55/9.73	   b -> c
28.55/9.73	   b -> d
28.55/9.73	   d -> k
28.55/9.73	   c -> e
28.55/9.73	   c -> k
28.55/9.73	
28.55/9.73	Q is empty.
28.55/9.73	We have to consider all minimal (P,Q,R)-chains.
28.55/9.73	----------------------------------------
28.55/9.73	
28.55/9.73	(1397) TransformationProof (EQUIVALENT)
28.55/9.73	By narrowing [LPAR04] the rule A^2 -> H(c, U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.73	
28.55/9.73	   (A^2 -> H(e, U1(b, d)),A^2 -> H(e, U1(b, d)))
28.55/9.73	   (A^2 -> H(k, U1(b, d)),A^2 -> H(k, U1(b, d)))
28.55/9.73	   (A^2 -> H(c, U1(c, d)),A^2 -> H(c, U1(c, d)))
28.55/9.73	   (A^2 -> H(c, U1(d, d)),A^2 -> H(c, U1(d, d)))
28.55/9.73	   (A^2 -> H(c, U1(b, k)),A^2 -> H(c, U1(b, k)))
28.55/9.73	
28.55/9.73	
28.55/9.73	----------------------------------------
28.55/9.73	
28.55/9.73	(1398)
28.55/9.73	Obligation:
28.55/9.73	Q DP problem:
28.55/9.73	The TRS P consists of the following rules:
28.55/9.73	
28.55/9.73	   H(x, x) -> G(x, x, f(k))
28.55/9.73	   G(d, x, x) -> A^2
28.55/9.73	   A^2 -> H(f(c), f(c))
28.55/9.73	   A^2 -> H(f(d), f(d))
28.55/9.73	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.73	   A^2 -> H(f(e), f(e))
28.55/9.73	   A^2 -> H(f(k), f(k))
28.55/9.73	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.73	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.73	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.73	   A^2 -> H(c, U1(c, c))
28.55/9.73	   A^2 -> H(c, f(e))
28.55/9.73	   A^2 -> H(c, f(k))
28.55/9.73	   A^2 -> H(c, U1(d, d))
28.55/9.73	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.73	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.73	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.73	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.73	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.73	   A^2 -> H(U1(e, k), f(e))
28.55/9.73	   A^2 -> H(U1(e, k), f(k))
28.55/9.73	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.73	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.73	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.73	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.73	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.73	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.73	   A^2 -> H(U1(k, e), f(e))
28.55/9.73	   A^2 -> H(U1(k, e), f(k))
28.55/9.73	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.73	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.73	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.73	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.73	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.73	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.73	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.73	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.73	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.73	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.73	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.73	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.73	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.73	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.73	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.73	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.73	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.73	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.73	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.73	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.73	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.73	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.73	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.73	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.73	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.73	   A^2 -> H(U1(c, c), b)
28.55/9.73	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.73	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.73	   A^2 -> H(U1(c, c), e)
28.55/9.73	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.73	   A^2 -> H(e, U1(c, b))
28.55/9.73	   A^2 -> H(e, U1(d, b))
28.55/9.73	   A^2 -> H(e, U1(b, c))
28.55/9.73	   A^2 -> H(e, U1(b, d))
28.55/9.73	   A^2 -> H(e, U1(c, c))
28.55/9.73	   A^2 -> H(e, f(e))
28.55/9.73	   A^2 -> H(e, f(k))
28.55/9.73	   A^2 -> H(e, U1(d, d))
28.55/9.73	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.73	   A^2 -> H(f(e), b)
28.55/9.73	   A^2 -> H(f(e), U1(e, d))
28.55/9.73	   A^2 -> H(f(e), U1(d, e))
28.55/9.73	   A^2 -> H(f(e), c)
28.55/9.73	   A^2 -> H(f(e), U1(e, k))
28.55/9.73	   A^2 -> H(f(e), U1(k, e))
28.55/9.73	   A^2 -> H(f(e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.73	   A^2 -> H(f(k), b)
28.55/9.73	   A^2 -> H(f(k), U1(e, d))
28.55/9.73	   A^2 -> H(f(k), U1(d, e))
28.55/9.73	   A^2 -> H(f(k), c)
28.55/9.73	   A^2 -> H(f(k), U1(e, k))
28.55/9.73	   A^2 -> H(f(k), U1(k, e))
28.55/9.73	   A^2 -> H(f(k), e)
28.55/9.73	   A^2 -> H(f(c), d)
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.73	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.73	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.73	   A^2 -> H(U1(k, k), f(e))
28.55/9.73	   A^2 -> H(U1(k, k), f(k))
28.55/9.73	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.73	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.73	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.73	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.73	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.73	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.73	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.73	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.73	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.73	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.73	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.73	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.73	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.73	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.73	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.73	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.73	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.73	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.73	   A^2 -> H(U1(d, d), b)
28.55/9.73	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.73	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.73	   A^2 -> H(U1(d, d), c)
28.55/9.73	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.73	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.73	   A^2 -> H(U1(d, d), e)
28.55/9.73	   A^2 -> H(f(d), d)
28.55/9.73	   A^2 -> H(f(d), k)
28.55/9.73	   A^2 -> H(U1(c, c), c)
28.55/9.73	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.73	   A^2 -> H(f(c), k)
28.55/9.73	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.73	   A^2 -> H(f(k), U1(k, k))
28.55/9.73	   A^2 -> H(f(e), e)
28.55/9.73	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.73	   A^2 -> H(d, U1(c, b))
28.55/9.73	   A^2 -> H(d, U1(d, b))
28.55/9.73	   A^2 -> H(d, U1(b, c))
28.55/9.73	   A^2 -> H(d, U1(b, d))
28.55/9.73	   A^2 -> H(d, U1(c, c))
28.55/9.73	   A^2 -> H(d, f(e))
28.55/9.73	   A^2 -> H(d, f(k))
28.55/9.73	   A^2 -> H(d, U1(d, d))
28.55/9.73	   A^2 -> H(a, U1(e, b))
28.55/9.73	   A^2 -> H(a, U1(k, b))
28.55/9.73	   A^2 -> H(a, U1(c, d))
28.55/9.73	   A^2 -> H(a, U1(d, c))
28.55/9.73	   A^2 -> H(a, U1(b, e))
28.55/9.73	   A^2 -> H(a, U1(b, k))
28.55/9.73	   A^2 -> H(a, U1(e, c))
28.55/9.73	   A^2 -> H(a, U1(k, c))
28.55/9.73	   A^2 -> H(a, U1(c, e))
28.55/9.73	   A^2 -> H(a, U1(c, k))
28.55/9.73	   A^2 -> H(a, U1(e, e))
28.55/9.73	   A^2 -> H(a, U1(k, k))
28.55/9.73	   A^2 -> H(a, U1(k, d))
28.55/9.73	   A^2 -> H(a, U1(d, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.73	   A^2 -> H(U1(e, a), b)
28.55/9.73	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.73	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.73	   A^2 -> H(U1(e, a), c)
28.55/9.73	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.73	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.73	   A^2 -> H(U1(e, a), e)
28.55/9.73	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.73	   A^2 -> H(U1(k, a), b)
28.55/9.73	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.73	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.73	   A^2 -> H(U1(k, a), c)
28.55/9.73	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.73	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.73	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, d), b)
28.55/9.73	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.73	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.73	   A^2 -> H(U1(c, d), c)
28.55/9.73	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.73	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.73	   A^2 -> H(U1(c, d), e)
28.55/9.73	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.73	   A^2 -> H(U1(c, a), d)
28.55/9.73	   A^2 -> H(U1(c, a), k)
28.55/9.73	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.73	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.73	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.73	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.73	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.73	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.73	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.73	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.73	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.73	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.73	   A^2 -> H(U1(d, c), b)
28.55/9.73	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.73	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.73	   A^2 -> H(U1(d, c), c)
28.55/9.73	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.73	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.73	   A^2 -> H(U1(d, c), e)
28.55/9.73	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(d, a), d)
28.55/9.73	   A^2 -> H(U1(d, a), k)
28.55/9.73	   A^2 -> H(U1(a, e), b)
28.55/9.73	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.73	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.73	   A^2 -> H(U1(a, e), c)
28.55/9.73	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.73	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.73	   A^2 -> H(U1(a, e), e)
28.55/9.73	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.73	   A^2 -> H(U1(a, k), b)
28.55/9.73	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.73	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.73	   A^2 -> H(U1(a, k), c)
28.55/9.73	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.73	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.73	   A^2 -> H(U1(a, k), e)
28.55/9.73	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.73	   A^2 -> H(U1(a, c), d)
28.55/9.73	   A^2 -> H(U1(a, c), k)
28.55/9.73	   A^2 -> H(U1(a, d), d)
28.55/9.73	   A^2 -> H(U1(a, d), k)
28.55/9.73	   A^2 -> H(k, U1(c, b))
28.55/9.73	   A^2 -> H(k, U1(d, b))
28.55/9.73	   A^2 -> H(k, U1(b, c))
28.55/9.73	   A^2 -> H(k, U1(b, d))
28.55/9.73	   A^2 -> H(k, U1(c, c))
28.55/9.73	   A^2 -> H(k, f(e))
28.55/9.73	   A^2 -> H(k, f(k))
28.55/9.73	   A^2 -> H(k, U1(d, d))
28.55/9.73	   A^2 -> H(c, U1(e, b))
28.55/9.73	   A^2 -> H(c, U1(k, b))
28.55/9.73	   A^2 -> H(c, U1(c, d))
28.55/9.73	   A^2 -> H(c, U1(d, c))
28.55/9.73	   A^2 -> H(c, U1(b, e))
28.55/9.73	   A^2 -> H(c, U1(b, k))
28.55/9.73	
28.55/9.73	The TRS R consists of the following rules:
28.55/9.73	
28.55/9.73	   f(x) -> U1(x, x)
28.55/9.73	   U1(e, x) -> x
28.55/9.73	   a -> c
28.55/9.73	   a -> d
28.55/9.73	   b -> c
28.55/9.73	   b -> d
28.55/9.73	   d -> k
28.55/9.73	   c -> e
28.55/9.73	   c -> k
28.55/9.73	
28.55/9.73	Q is empty.
28.55/9.73	We have to consider all minimal (P,Q,R)-chains.
28.55/9.73	----------------------------------------
28.55/9.73	
28.55/9.73	(1399) TransformationProof (EQUIVALENT)
28.55/9.73	By narrowing [LPAR04] the rule A^2 -> H(c, U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.73	
28.55/9.73	   (A^2 -> H(e, U1(c, c)),A^2 -> H(e, U1(c, c)))
28.55/9.73	   (A^2 -> H(k, U1(c, c)),A^2 -> H(k, U1(c, c)))
28.55/9.73	   (A^2 -> H(c, U1(e, c)),A^2 -> H(c, U1(e, c)))
28.55/9.73	   (A^2 -> H(c, U1(k, c)),A^2 -> H(c, U1(k, c)))
28.55/9.73	   (A^2 -> H(c, U1(c, e)),A^2 -> H(c, U1(c, e)))
28.55/9.73	   (A^2 -> H(c, U1(c, k)),A^2 -> H(c, U1(c, k)))
28.55/9.73	
28.55/9.73	
28.55/9.73	----------------------------------------
28.55/9.73	
28.55/9.73	(1400)
28.55/9.73	Obligation:
28.55/9.73	Q DP problem:
28.55/9.73	The TRS P consists of the following rules:
28.55/9.73	
28.55/9.73	   H(x, x) -> G(x, x, f(k))
28.55/9.73	   G(d, x, x) -> A^2
28.55/9.73	   A^2 -> H(f(c), f(c))
28.55/9.73	   A^2 -> H(f(d), f(d))
28.55/9.73	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.73	   A^2 -> H(f(e), f(e))
28.55/9.73	   A^2 -> H(f(k), f(k))
28.55/9.73	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.73	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.73	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.73	   A^2 -> H(c, f(e))
28.55/9.73	   A^2 -> H(c, f(k))
28.55/9.73	   A^2 -> H(c, U1(d, d))
28.55/9.73	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.73	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.73	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.73	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.73	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.73	   A^2 -> H(U1(e, k), f(e))
28.55/9.73	   A^2 -> H(U1(e, k), f(k))
28.55/9.73	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.73	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.73	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.73	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.73	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.73	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.73	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.74	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.74	   A^2 -> H(U1(k, e), f(e))
28.55/9.74	   A^2 -> H(U1(k, e), f(k))
28.55/9.74	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.74	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.74	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.74	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.74	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.74	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.74	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.74	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.74	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.74	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.74	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.74	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.74	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.74	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.74	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.74	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.74	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.74	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.74	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.74	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.74	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.74	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.74	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.74	   A^2 -> H(U1(c, c), b)
28.55/9.74	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.74	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.74	   A^2 -> H(U1(c, c), e)
28.55/9.74	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.74	   A^2 -> H(e, U1(c, b))
28.55/9.74	   A^2 -> H(e, U1(d, b))
28.55/9.74	   A^2 -> H(e, U1(b, c))
28.55/9.74	   A^2 -> H(e, U1(b, d))
28.55/9.74	   A^2 -> H(e, U1(c, c))
28.55/9.74	   A^2 -> H(e, f(e))
28.55/9.74	   A^2 -> H(e, f(k))
28.55/9.74	   A^2 -> H(e, U1(d, d))
28.55/9.74	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.74	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.74	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.74	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.74	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.74	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.74	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.74	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.74	   A^2 -> H(f(e), b)
28.55/9.74	   A^2 -> H(f(e), U1(e, d))
28.55/9.74	   A^2 -> H(f(e), U1(d, e))
28.55/9.74	   A^2 -> H(f(e), c)
28.55/9.74	   A^2 -> H(f(e), U1(e, k))
28.55/9.74	   A^2 -> H(f(e), U1(k, e))
28.55/9.74	   A^2 -> H(f(e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.74	   A^2 -> H(f(k), b)
28.55/9.74	   A^2 -> H(f(k), U1(e, d))
28.55/9.74	   A^2 -> H(f(k), U1(d, e))
28.55/9.74	   A^2 -> H(f(k), c)
28.55/9.74	   A^2 -> H(f(k), U1(e, k))
28.55/9.74	   A^2 -> H(f(k), U1(k, e))
28.55/9.74	   A^2 -> H(f(k), e)
28.55/9.74	   A^2 -> H(f(c), d)
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.74	   A^2 -> H(U1(k, k), f(e))
28.55/9.74	   A^2 -> H(U1(k, k), f(k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.74	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.74	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.74	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.74	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.74	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.74	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.74	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.74	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.74	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.74	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.74	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.74	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.74	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.74	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.74	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.74	   A^2 -> H(U1(d, d), b)
28.55/9.74	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.74	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.74	   A^2 -> H(U1(d, d), c)
28.55/9.74	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.74	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.74	   A^2 -> H(U1(d, d), e)
28.55/9.74	   A^2 -> H(f(d), d)
28.55/9.74	   A^2 -> H(f(d), k)
28.55/9.74	   A^2 -> H(U1(c, c), c)
28.55/9.74	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.74	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.74	   A^2 -> H(f(c), k)
28.55/9.74	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.74	   A^2 -> H(f(k), U1(k, k))
28.55/9.74	   A^2 -> H(f(e), e)
28.55/9.74	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.74	   A^2 -> H(d, U1(c, b))
28.55/9.74	   A^2 -> H(d, U1(d, b))
28.55/9.74	   A^2 -> H(d, U1(b, c))
28.55/9.74	   A^2 -> H(d, U1(b, d))
28.55/9.74	   A^2 -> H(d, U1(c, c))
28.55/9.74	   A^2 -> H(d, f(e))
28.55/9.74	   A^2 -> H(d, f(k))
28.55/9.74	   A^2 -> H(d, U1(d, d))
28.55/9.74	   A^2 -> H(a, U1(e, b))
28.55/9.74	   A^2 -> H(a, U1(k, b))
28.55/9.74	   A^2 -> H(a, U1(c, d))
28.55/9.74	   A^2 -> H(a, U1(d, c))
28.55/9.74	   A^2 -> H(a, U1(b, e))
28.55/9.74	   A^2 -> H(a, U1(b, k))
28.55/9.74	   A^2 -> H(a, U1(e, c))
28.55/9.74	   A^2 -> H(a, U1(k, c))
28.55/9.74	   A^2 -> H(a, U1(c, e))
28.55/9.74	   A^2 -> H(a, U1(c, k))
28.55/9.74	   A^2 -> H(a, U1(e, e))
28.55/9.74	   A^2 -> H(a, U1(k, k))
28.55/9.74	   A^2 -> H(a, U1(k, d))
28.55/9.74	   A^2 -> H(a, U1(d, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.74	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.74	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.74	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.74	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.74	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.74	   A^2 -> H(U1(e, a), b)
28.55/9.74	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.74	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.74	   A^2 -> H(U1(e, a), c)
28.55/9.74	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.74	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.74	   A^2 -> H(U1(e, a), e)
28.55/9.74	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, a), b)
28.55/9.74	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.74	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.74	   A^2 -> H(U1(k, a), c)
28.55/9.74	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.74	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.74	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, d), b)
28.55/9.74	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.74	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.74	   A^2 -> H(U1(c, d), c)
28.55/9.74	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.74	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.74	   A^2 -> H(U1(c, d), e)
28.55/9.74	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, a), d)
28.55/9.74	   A^2 -> H(U1(c, a), k)
28.55/9.74	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.74	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.74	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.74	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.74	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.74	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.74	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.74	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.74	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.74	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.74	   A^2 -> H(U1(d, c), b)
28.55/9.74	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.74	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.74	   A^2 -> H(U1(d, c), c)
28.55/9.74	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.74	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.74	   A^2 -> H(U1(d, c), e)
28.55/9.74	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.74	   A^2 -> H(U1(d, a), d)
28.55/9.74	   A^2 -> H(U1(d, a), k)
28.55/9.74	   A^2 -> H(U1(a, e), b)
28.55/9.74	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.74	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.74	   A^2 -> H(U1(a, e), c)
28.55/9.74	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.74	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.74	   A^2 -> H(U1(a, e), e)
28.55/9.74	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(a, k), b)
28.55/9.74	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.74	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.74	   A^2 -> H(U1(a, k), c)
28.55/9.74	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.74	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.74	   A^2 -> H(U1(a, k), e)
28.55/9.74	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(a, c), d)
28.55/9.74	   A^2 -> H(U1(a, c), k)
28.55/9.74	   A^2 -> H(U1(a, d), d)
28.55/9.74	   A^2 -> H(U1(a, d), k)
28.55/9.74	   A^2 -> H(k, U1(c, b))
28.55/9.74	   A^2 -> H(k, U1(d, b))
28.55/9.74	   A^2 -> H(k, U1(b, c))
28.55/9.74	   A^2 -> H(k, U1(b, d))
28.55/9.74	   A^2 -> H(k, U1(c, c))
28.55/9.74	   A^2 -> H(k, f(e))
28.55/9.74	   A^2 -> H(k, f(k))
28.55/9.74	   A^2 -> H(k, U1(d, d))
28.55/9.74	   A^2 -> H(c, U1(e, b))
28.55/9.74	   A^2 -> H(c, U1(k, b))
28.55/9.74	   A^2 -> H(c, U1(c, d))
28.55/9.74	   A^2 -> H(c, U1(d, c))
28.55/9.74	   A^2 -> H(c, U1(b, e))
28.55/9.74	   A^2 -> H(c, U1(b, k))
28.55/9.74	   A^2 -> H(c, U1(e, c))
28.55/9.74	   A^2 -> H(c, U1(k, c))
28.55/9.74	   A^2 -> H(c, U1(c, e))
28.55/9.74	   A^2 -> H(c, U1(c, k))
28.55/9.74	
28.55/9.74	The TRS R consists of the following rules:
28.55/9.74	
28.55/9.74	   f(x) -> U1(x, x)
28.55/9.74	   U1(e, x) -> x
28.55/9.74	   a -> c
28.55/9.74	   a -> d
28.55/9.74	   b -> c
28.55/9.74	   b -> d
28.55/9.74	   d -> k
28.55/9.74	   c -> e
28.55/9.74	   c -> k
28.55/9.74	
28.55/9.74	Q is empty.
28.55/9.74	We have to consider all minimal (P,Q,R)-chains.
28.55/9.74	----------------------------------------
28.55/9.74	
28.55/9.74	(1401) TransformationProof (EQUIVALENT)
28.55/9.74	By narrowing [LPAR04] the rule A^2 -> H(c, f(e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.74	
28.55/9.74	   (A^2 -> H(e, f(e)),A^2 -> H(e, f(e)))
28.55/9.74	   (A^2 -> H(k, f(e)),A^2 -> H(k, f(e)))
28.55/9.74	   (A^2 -> H(c, U1(e, e)),A^2 -> H(c, U1(e, e)))
28.55/9.74	
28.55/9.74	
28.55/9.74	----------------------------------------
28.55/9.74	
28.55/9.74	(1402)
28.55/9.74	Obligation:
28.55/9.74	Q DP problem:
28.55/9.74	The TRS P consists of the following rules:
28.55/9.74	
28.55/9.74	   H(x, x) -> G(x, x, f(k))
28.55/9.74	   G(d, x, x) -> A^2
28.55/9.74	   A^2 -> H(f(c), f(c))
28.55/9.74	   A^2 -> H(f(d), f(d))
28.55/9.74	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.74	   A^2 -> H(f(e), f(e))
28.55/9.74	   A^2 -> H(f(k), f(k))
28.55/9.74	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.74	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.74	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.74	   A^2 -> H(c, f(k))
28.55/9.74	   A^2 -> H(c, U1(d, d))
28.55/9.74	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.74	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.74	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.74	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.74	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.74	   A^2 -> H(U1(e, k), f(e))
28.55/9.74	   A^2 -> H(U1(e, k), f(k))
28.55/9.74	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.74	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.74	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.74	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.74	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.74	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.74	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.74	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.74	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.74	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.74	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.74	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.74	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.74	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.74	   A^2 -> H(U1(k, e), f(e))
28.55/9.74	   A^2 -> H(U1(k, e), f(k))
28.55/9.74	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.74	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.74	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.74	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.74	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.74	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.74	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.74	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.74	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.74	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.74	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.74	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.74	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.74	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.74	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.74	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.74	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.74	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.74	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.74	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.74	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.74	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.74	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.74	   A^2 -> H(U1(c, c), b)
28.55/9.74	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.74	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.74	   A^2 -> H(U1(c, c), e)
28.55/9.74	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.74	   A^2 -> H(e, U1(c, b))
28.55/9.74	   A^2 -> H(e, U1(d, b))
28.55/9.74	   A^2 -> H(e, U1(b, c))
28.55/9.74	   A^2 -> H(e, U1(b, d))
28.55/9.74	   A^2 -> H(e, U1(c, c))
28.55/9.74	   A^2 -> H(e, f(e))
28.55/9.74	   A^2 -> H(e, f(k))
28.55/9.74	   A^2 -> H(e, U1(d, d))
28.55/9.74	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.74	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.74	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.74	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.74	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.74	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.74	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.74	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.74	   A^2 -> H(f(e), b)
28.55/9.74	   A^2 -> H(f(e), U1(e, d))
28.55/9.74	   A^2 -> H(f(e), U1(d, e))
28.55/9.74	   A^2 -> H(f(e), c)
28.55/9.74	   A^2 -> H(f(e), U1(e, k))
28.55/9.74	   A^2 -> H(f(e), U1(k, e))
28.55/9.74	   A^2 -> H(f(e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.74	   A^2 -> H(f(k), b)
28.55/9.74	   A^2 -> H(f(k), U1(e, d))
28.55/9.74	   A^2 -> H(f(k), U1(d, e))
28.55/9.74	   A^2 -> H(f(k), c)
28.55/9.74	   A^2 -> H(f(k), U1(e, k))
28.55/9.74	   A^2 -> H(f(k), U1(k, e))
28.55/9.74	   A^2 -> H(f(k), e)
28.55/9.74	   A^2 -> H(f(c), d)
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.74	   A^2 -> H(U1(k, k), f(e))
28.55/9.74	   A^2 -> H(U1(k, k), f(k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.74	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.74	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.74	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.74	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.74	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.74	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.74	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.74	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.74	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.74	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.74	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.74	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.74	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.74	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.74	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.74	   A^2 -> H(U1(d, d), b)
28.55/9.74	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.74	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.74	   A^2 -> H(U1(d, d), c)
28.55/9.74	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.74	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.74	   A^2 -> H(U1(d, d), e)
28.55/9.74	   A^2 -> H(f(d), d)
28.55/9.74	   A^2 -> H(f(d), k)
28.55/9.74	   A^2 -> H(U1(c, c), c)
28.55/9.74	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.74	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.74	   A^2 -> H(f(c), k)
28.55/9.74	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.74	   A^2 -> H(f(k), U1(k, k))
28.55/9.74	   A^2 -> H(f(e), e)
28.55/9.74	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.74	   A^2 -> H(d, U1(c, b))
28.55/9.74	   A^2 -> H(d, U1(d, b))
28.55/9.74	   A^2 -> H(d, U1(b, c))
28.55/9.74	   A^2 -> H(d, U1(b, d))
28.55/9.74	   A^2 -> H(d, U1(c, c))
28.55/9.74	   A^2 -> H(d, f(e))
28.55/9.74	   A^2 -> H(d, f(k))
28.55/9.74	   A^2 -> H(d, U1(d, d))
28.55/9.74	   A^2 -> H(a, U1(e, b))
28.55/9.74	   A^2 -> H(a, U1(k, b))
28.55/9.74	   A^2 -> H(a, U1(c, d))
28.55/9.74	   A^2 -> H(a, U1(d, c))
28.55/9.74	   A^2 -> H(a, U1(b, e))
28.55/9.74	   A^2 -> H(a, U1(b, k))
28.55/9.74	   A^2 -> H(a, U1(e, c))
28.55/9.74	   A^2 -> H(a, U1(k, c))
28.55/9.74	   A^2 -> H(a, U1(c, e))
28.55/9.74	   A^2 -> H(a, U1(c, k))
28.55/9.74	   A^2 -> H(a, U1(e, e))
28.55/9.74	   A^2 -> H(a, U1(k, k))
28.55/9.74	   A^2 -> H(a, U1(k, d))
28.55/9.74	   A^2 -> H(a, U1(d, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.74	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.74	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.74	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.74	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.74	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.74	   A^2 -> H(U1(e, a), b)
28.55/9.74	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.74	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.74	   A^2 -> H(U1(e, a), c)
28.55/9.74	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.74	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.74	   A^2 -> H(U1(e, a), e)
28.55/9.74	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, a), b)
28.55/9.74	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.74	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.74	   A^2 -> H(U1(k, a), c)
28.55/9.74	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.74	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.74	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, d), b)
28.55/9.74	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.74	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.74	   A^2 -> H(U1(c, d), c)
28.55/9.74	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.74	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.74	   A^2 -> H(U1(c, d), e)
28.55/9.74	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, a), d)
28.55/9.74	   A^2 -> H(U1(c, a), k)
28.55/9.74	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.74	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.74	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.74	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.74	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.74	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.74	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.74	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.74	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.74	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.74	   A^2 -> H(U1(d, c), b)
28.55/9.74	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.74	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.74	   A^2 -> H(U1(d, c), c)
28.55/9.74	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.74	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.74	   A^2 -> H(U1(d, c), e)
28.55/9.74	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.74	   A^2 -> H(U1(d, a), d)
28.55/9.74	   A^2 -> H(U1(d, a), k)
28.55/9.74	   A^2 -> H(U1(a, e), b)
28.55/9.74	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.74	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.74	   A^2 -> H(U1(a, e), c)
28.55/9.74	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.74	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.74	   A^2 -> H(U1(a, e), e)
28.55/9.74	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(a, k), b)
28.55/9.74	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.74	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.74	   A^2 -> H(U1(a, k), c)
28.55/9.74	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.74	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.74	   A^2 -> H(U1(a, k), e)
28.55/9.74	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(a, c), d)
28.55/9.74	   A^2 -> H(U1(a, c), k)
28.55/9.74	   A^2 -> H(U1(a, d), d)
28.55/9.74	   A^2 -> H(U1(a, d), k)
28.55/9.74	   A^2 -> H(k, U1(c, b))
28.55/9.74	   A^2 -> H(k, U1(d, b))
28.55/9.74	   A^2 -> H(k, U1(b, c))
28.55/9.74	   A^2 -> H(k, U1(b, d))
28.55/9.74	   A^2 -> H(k, U1(c, c))
28.55/9.74	   A^2 -> H(k, f(e))
28.55/9.74	   A^2 -> H(k, f(k))
28.55/9.74	   A^2 -> H(k, U1(d, d))
28.55/9.74	   A^2 -> H(c, U1(e, b))
28.55/9.74	   A^2 -> H(c, U1(k, b))
28.55/9.74	   A^2 -> H(c, U1(c, d))
28.55/9.74	   A^2 -> H(c, U1(d, c))
28.55/9.74	   A^2 -> H(c, U1(b, e))
28.55/9.74	   A^2 -> H(c, U1(b, k))
28.55/9.74	   A^2 -> H(c, U1(e, c))
28.55/9.74	   A^2 -> H(c, U1(k, c))
28.55/9.74	   A^2 -> H(c, U1(c, e))
28.55/9.74	   A^2 -> H(c, U1(c, k))
28.55/9.74	   A^2 -> H(c, U1(e, e))
28.55/9.74	
28.55/9.74	The TRS R consists of the following rules:
28.55/9.74	
28.55/9.74	   f(x) -> U1(x, x)
28.55/9.74	   U1(e, x) -> x
28.55/9.74	   a -> c
28.55/9.74	   a -> d
28.55/9.74	   b -> c
28.55/9.74	   b -> d
28.55/9.74	   d -> k
28.55/9.74	   c -> e
28.55/9.74	   c -> k
28.55/9.74	
28.55/9.74	Q is empty.
28.55/9.74	We have to consider all minimal (P,Q,R)-chains.
28.55/9.74	----------------------------------------
28.55/9.74	
28.55/9.74	(1403) TransformationProof (EQUIVALENT)
28.55/9.74	By narrowing [LPAR04] the rule A^2 -> H(c, f(k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.74	
28.55/9.74	   (A^2 -> H(e, f(k)),A^2 -> H(e, f(k)))
28.55/9.74	   (A^2 -> H(k, f(k)),A^2 -> H(k, f(k)))
28.55/9.74	   (A^2 -> H(c, U1(k, k)),A^2 -> H(c, U1(k, k)))
28.55/9.74	
28.55/9.74	
28.55/9.74	----------------------------------------
28.55/9.74	
28.55/9.74	(1404)
28.55/9.74	Obligation:
28.55/9.74	Q DP problem:
28.55/9.74	The TRS P consists of the following rules:
28.55/9.74	
28.55/9.74	   H(x, x) -> G(x, x, f(k))
28.55/9.74	   G(d, x, x) -> A^2
28.55/9.74	   A^2 -> H(f(c), f(c))
28.55/9.74	   A^2 -> H(f(d), f(d))
28.55/9.74	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.74	   A^2 -> H(f(e), f(e))
28.55/9.74	   A^2 -> H(f(k), f(k))
28.55/9.74	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.74	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.74	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.74	   A^2 -> H(c, U1(d, d))
28.55/9.74	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.74	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.74	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.74	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.74	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.74	   A^2 -> H(U1(e, k), f(e))
28.55/9.74	   A^2 -> H(U1(e, k), f(k))
28.55/9.74	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.74	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.74	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.74	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.74	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.74	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.74	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.74	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.74	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.74	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.74	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.74	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.74	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.74	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.74	   A^2 -> H(U1(k, e), f(e))
28.55/9.74	   A^2 -> H(U1(k, e), f(k))
28.55/9.74	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.74	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.74	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.74	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.74	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.74	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.74	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.74	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.74	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.74	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.74	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.74	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.74	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.74	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.74	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.74	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.74	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.74	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.74	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.74	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.74	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.74	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.74	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.74	   A^2 -> H(U1(c, c), b)
28.55/9.74	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.74	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.74	   A^2 -> H(U1(c, c), e)
28.55/9.74	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.74	   A^2 -> H(e, U1(c, b))
28.55/9.74	   A^2 -> H(e, U1(d, b))
28.55/9.74	   A^2 -> H(e, U1(b, c))
28.55/9.74	   A^2 -> H(e, U1(b, d))
28.55/9.74	   A^2 -> H(e, U1(c, c))
28.55/9.74	   A^2 -> H(e, f(e))
28.55/9.74	   A^2 -> H(e, f(k))
28.55/9.74	   A^2 -> H(e, U1(d, d))
28.55/9.74	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.74	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.74	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.74	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.74	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.74	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.74	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.74	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.74	   A^2 -> H(f(e), b)
28.55/9.74	   A^2 -> H(f(e), U1(e, d))
28.55/9.74	   A^2 -> H(f(e), U1(d, e))
28.55/9.74	   A^2 -> H(f(e), c)
28.55/9.74	   A^2 -> H(f(e), U1(e, k))
28.55/9.74	   A^2 -> H(f(e), U1(k, e))
28.55/9.74	   A^2 -> H(f(e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.74	   A^2 -> H(f(k), b)
28.55/9.74	   A^2 -> H(f(k), U1(e, d))
28.55/9.74	   A^2 -> H(f(k), U1(d, e))
28.55/9.74	   A^2 -> H(f(k), c)
28.55/9.74	   A^2 -> H(f(k), U1(e, k))
28.55/9.74	   A^2 -> H(f(k), U1(k, e))
28.55/9.74	   A^2 -> H(f(k), e)
28.55/9.74	   A^2 -> H(f(c), d)
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.74	   A^2 -> H(U1(k, k), f(e))
28.55/9.74	   A^2 -> H(U1(k, k), f(k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.74	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.74	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.74	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.74	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.74	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.74	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.74	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.74	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.74	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.74	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.74	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.74	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.74	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.74	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.74	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.74	   A^2 -> H(U1(d, d), b)
28.55/9.74	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.74	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.74	   A^2 -> H(U1(d, d), c)
28.55/9.74	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.74	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.74	   A^2 -> H(U1(d, d), e)
28.55/9.74	   A^2 -> H(f(d), d)
28.55/9.74	   A^2 -> H(f(d), k)
28.55/9.74	   A^2 -> H(U1(c, c), c)
28.55/9.74	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.74	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.74	   A^2 -> H(f(c), k)
28.55/9.74	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.74	   A^2 -> H(f(k), U1(k, k))
28.55/9.74	   A^2 -> H(f(e), e)
28.55/9.74	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.74	   A^2 -> H(d, U1(c, b))
28.55/9.74	   A^2 -> H(d, U1(d, b))
28.55/9.74	   A^2 -> H(d, U1(b, c))
28.55/9.74	   A^2 -> H(d, U1(b, d))
28.55/9.74	   A^2 -> H(d, U1(c, c))
28.55/9.74	   A^2 -> H(d, f(e))
28.55/9.74	   A^2 -> H(d, f(k))
28.55/9.74	   A^2 -> H(d, U1(d, d))
28.55/9.74	   A^2 -> H(a, U1(e, b))
28.55/9.74	   A^2 -> H(a, U1(k, b))
28.55/9.74	   A^2 -> H(a, U1(c, d))
28.55/9.74	   A^2 -> H(a, U1(d, c))
28.55/9.74	   A^2 -> H(a, U1(b, e))
28.55/9.74	   A^2 -> H(a, U1(b, k))
28.55/9.74	   A^2 -> H(a, U1(e, c))
28.55/9.74	   A^2 -> H(a, U1(k, c))
28.55/9.74	   A^2 -> H(a, U1(c, e))
28.55/9.74	   A^2 -> H(a, U1(c, k))
28.55/9.74	   A^2 -> H(a, U1(e, e))
28.55/9.74	   A^2 -> H(a, U1(k, k))
28.55/9.74	   A^2 -> H(a, U1(k, d))
28.55/9.74	   A^2 -> H(a, U1(d, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.74	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.74	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.74	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.74	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.74	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.74	   A^2 -> H(U1(e, a), b)
28.55/9.74	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.74	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.74	   A^2 -> H(U1(e, a), c)
28.55/9.74	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.74	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.74	   A^2 -> H(U1(e, a), e)
28.55/9.74	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, a), b)
28.55/9.74	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.74	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.74	   A^2 -> H(U1(k, a), c)
28.55/9.74	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.74	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.74	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, d), b)
28.55/9.74	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.74	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.74	   A^2 -> H(U1(c, d), c)
28.55/9.74	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.74	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.74	   A^2 -> H(U1(c, d), e)
28.55/9.74	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, a), d)
28.55/9.74	   A^2 -> H(U1(c, a), k)
28.55/9.74	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.74	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.74	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.74	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.74	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.74	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.74	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.74	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.74	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.74	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.74	   A^2 -> H(U1(d, c), b)
28.55/9.74	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.74	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.74	   A^2 -> H(U1(d, c), c)
28.55/9.74	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.74	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.74	   A^2 -> H(U1(d, c), e)
28.55/9.74	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.74	   A^2 -> H(U1(d, a), d)
28.55/9.74	   A^2 -> H(U1(d, a), k)
28.55/9.74	   A^2 -> H(U1(a, e), b)
28.55/9.74	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.74	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.74	   A^2 -> H(U1(a, e), c)
28.55/9.74	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.74	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.74	   A^2 -> H(U1(a, e), e)
28.55/9.74	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(a, k), b)
28.55/9.74	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.74	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.74	   A^2 -> H(U1(a, k), c)
28.55/9.74	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.74	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.74	   A^2 -> H(U1(a, k), e)
28.55/9.74	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(a, c), d)
28.55/9.74	   A^2 -> H(U1(a, c), k)
28.55/9.74	   A^2 -> H(U1(a, d), d)
28.55/9.74	   A^2 -> H(U1(a, d), k)
28.55/9.74	   A^2 -> H(k, U1(c, b))
28.55/9.74	   A^2 -> H(k, U1(d, b))
28.55/9.74	   A^2 -> H(k, U1(b, c))
28.55/9.74	   A^2 -> H(k, U1(b, d))
28.55/9.74	   A^2 -> H(k, U1(c, c))
28.55/9.74	   A^2 -> H(k, f(e))
28.55/9.74	   A^2 -> H(k, f(k))
28.55/9.74	   A^2 -> H(k, U1(d, d))
28.55/9.74	   A^2 -> H(c, U1(e, b))
28.55/9.74	   A^2 -> H(c, U1(k, b))
28.55/9.74	   A^2 -> H(c, U1(c, d))
28.55/9.74	   A^2 -> H(c, U1(d, c))
28.55/9.74	   A^2 -> H(c, U1(b, e))
28.55/9.74	   A^2 -> H(c, U1(b, k))
28.55/9.74	   A^2 -> H(c, U1(e, c))
28.55/9.74	   A^2 -> H(c, U1(k, c))
28.55/9.74	   A^2 -> H(c, U1(c, e))
28.55/9.74	   A^2 -> H(c, U1(c, k))
28.55/9.74	   A^2 -> H(c, U1(e, e))
28.55/9.74	   A^2 -> H(c, U1(k, k))
28.55/9.74	
28.55/9.74	The TRS R consists of the following rules:
28.55/9.74	
28.55/9.74	   f(x) -> U1(x, x)
28.55/9.74	   U1(e, x) -> x
28.55/9.74	   a -> c
28.55/9.74	   a -> d
28.55/9.74	   b -> c
28.55/9.74	   b -> d
28.55/9.74	   d -> k
28.55/9.74	   c -> e
28.55/9.74	   c -> k
28.55/9.74	
28.55/9.74	Q is empty.
28.55/9.74	We have to consider all minimal (P,Q,R)-chains.
28.55/9.74	----------------------------------------
28.55/9.74	
28.55/9.74	(1405) TransformationProof (EQUIVALENT)
28.55/9.74	By narrowing [LPAR04] the rule A^2 -> H(c, U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.74	
28.55/9.74	   (A^2 -> H(e, U1(d, d)),A^2 -> H(e, U1(d, d)))
28.55/9.74	   (A^2 -> H(k, U1(d, d)),A^2 -> H(k, U1(d, d)))
28.55/9.74	   (A^2 -> H(c, U1(k, d)),A^2 -> H(c, U1(k, d)))
28.55/9.74	   (A^2 -> H(c, U1(d, k)),A^2 -> H(c, U1(d, k)))
28.55/9.74	
28.55/9.74	
28.55/9.74	----------------------------------------
28.55/9.74	
28.55/9.74	(1406)
28.55/9.74	Obligation:
28.55/9.74	Q DP problem:
28.55/9.74	The TRS P consists of the following rules:
28.55/9.74	
28.55/9.74	   H(x, x) -> G(x, x, f(k))
28.55/9.74	   G(d, x, x) -> A^2
28.55/9.74	   A^2 -> H(f(c), f(c))
28.55/9.74	   A^2 -> H(f(d), f(d))
28.55/9.74	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.74	   A^2 -> H(f(e), f(e))
28.55/9.74	   A^2 -> H(f(k), f(k))
28.55/9.74	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.74	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.74	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, k), U1(c, b))
28.55/9.74	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.74	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.74	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.74	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.74	   A^2 -> H(U1(e, k), f(e))
28.55/9.74	   A^2 -> H(U1(e, k), f(k))
28.55/9.74	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.74	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.74	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.74	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.74	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.74	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.74	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.74	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.74	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.74	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.74	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.74	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.74	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.74	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.74	   A^2 -> H(U1(k, e), f(e))
28.55/9.74	   A^2 -> H(U1(k, e), f(k))
28.55/9.74	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.74	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.74	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.74	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.74	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.74	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.74	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.74	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.74	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.74	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.74	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.74	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.74	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.74	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.74	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.74	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.74	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.74	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.74	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.74	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.74	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.74	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.74	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.74	   A^2 -> H(U1(c, c), b)
28.55/9.74	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.74	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.74	   A^2 -> H(U1(c, c), e)
28.55/9.74	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.74	   A^2 -> H(e, U1(c, b))
28.55/9.74	   A^2 -> H(e, U1(d, b))
28.55/9.74	   A^2 -> H(e, U1(b, c))
28.55/9.74	   A^2 -> H(e, U1(b, d))
28.55/9.74	   A^2 -> H(e, U1(c, c))
28.55/9.74	   A^2 -> H(e, f(e))
28.55/9.74	   A^2 -> H(e, f(k))
28.55/9.74	   A^2 -> H(e, U1(d, d))
28.55/9.74	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.74	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.74	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.74	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.74	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.74	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.74	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.74	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.74	   A^2 -> H(f(e), b)
28.55/9.74	   A^2 -> H(f(e), U1(e, d))
28.55/9.74	   A^2 -> H(f(e), U1(d, e))
28.55/9.74	   A^2 -> H(f(e), c)
28.55/9.74	   A^2 -> H(f(e), U1(e, k))
28.55/9.74	   A^2 -> H(f(e), U1(k, e))
28.55/9.74	   A^2 -> H(f(e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.74	   A^2 -> H(f(k), b)
28.55/9.74	   A^2 -> H(f(k), U1(e, d))
28.55/9.74	   A^2 -> H(f(k), U1(d, e))
28.55/9.74	   A^2 -> H(f(k), c)
28.55/9.74	   A^2 -> H(f(k), U1(e, k))
28.55/9.74	   A^2 -> H(f(k), U1(k, e))
28.55/9.74	   A^2 -> H(f(k), e)
28.55/9.74	   A^2 -> H(f(c), d)
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.74	   A^2 -> H(U1(k, k), f(e))
28.55/9.74	   A^2 -> H(U1(k, k), f(k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.74	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.74	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.74	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.74	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.74	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.74	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.74	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.74	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.74	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.74	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.74	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.74	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.74	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.74	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.74	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.74	   A^2 -> H(U1(d, d), b)
28.55/9.74	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.74	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.74	   A^2 -> H(U1(d, d), c)
28.55/9.74	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.74	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.74	   A^2 -> H(U1(d, d), e)
28.55/9.74	   A^2 -> H(f(d), d)
28.55/9.74	   A^2 -> H(f(d), k)
28.55/9.74	   A^2 -> H(U1(c, c), c)
28.55/9.74	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.74	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.74	   A^2 -> H(f(c), k)
28.55/9.74	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.74	   A^2 -> H(f(k), U1(k, k))
28.55/9.74	   A^2 -> H(f(e), e)
28.55/9.74	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.74	   A^2 -> H(d, U1(c, b))
28.55/9.74	   A^2 -> H(d, U1(d, b))
28.55/9.74	   A^2 -> H(d, U1(b, c))
28.55/9.74	   A^2 -> H(d, U1(b, d))
28.55/9.74	   A^2 -> H(d, U1(c, c))
28.55/9.74	   A^2 -> H(d, f(e))
28.55/9.74	   A^2 -> H(d, f(k))
28.55/9.74	   A^2 -> H(d, U1(d, d))
28.55/9.74	   A^2 -> H(a, U1(e, b))
28.55/9.74	   A^2 -> H(a, U1(k, b))
28.55/9.74	   A^2 -> H(a, U1(c, d))
28.55/9.74	   A^2 -> H(a, U1(d, c))
28.55/9.74	   A^2 -> H(a, U1(b, e))
28.55/9.74	   A^2 -> H(a, U1(b, k))
28.55/9.74	   A^2 -> H(a, U1(e, c))
28.55/9.74	   A^2 -> H(a, U1(k, c))
28.55/9.74	   A^2 -> H(a, U1(c, e))
28.55/9.74	   A^2 -> H(a, U1(c, k))
28.55/9.74	   A^2 -> H(a, U1(e, e))
28.55/9.74	   A^2 -> H(a, U1(k, k))
28.55/9.74	   A^2 -> H(a, U1(k, d))
28.55/9.74	   A^2 -> H(a, U1(d, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.74	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.74	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.74	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.74	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.74	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.74	   A^2 -> H(U1(e, a), b)
28.55/9.74	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.74	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.74	   A^2 -> H(U1(e, a), c)
28.55/9.74	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.74	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.74	   A^2 -> H(U1(e, a), e)
28.55/9.74	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, a), b)
28.55/9.74	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.74	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.74	   A^2 -> H(U1(k, a), c)
28.55/9.74	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.74	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.74	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, d), b)
28.55/9.74	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.74	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.74	   A^2 -> H(U1(c, d), c)
28.55/9.74	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.74	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.74	   A^2 -> H(U1(c, d), e)
28.55/9.74	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, a), d)
28.55/9.74	   A^2 -> H(U1(c, a), k)
28.55/9.74	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.74	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.74	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.74	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.74	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.74	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.74	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.74	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.74	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.74	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.74	   A^2 -> H(U1(d, c), b)
28.55/9.74	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.74	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.74	   A^2 -> H(U1(d, c), c)
28.55/9.74	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.74	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.74	   A^2 -> H(U1(d, c), e)
28.55/9.74	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.74	   A^2 -> H(U1(d, a), d)
28.55/9.74	   A^2 -> H(U1(d, a), k)
28.55/9.74	   A^2 -> H(U1(a, e), b)
28.55/9.74	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.74	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.74	   A^2 -> H(U1(a, e), c)
28.55/9.74	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.74	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.74	   A^2 -> H(U1(a, e), e)
28.55/9.74	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(a, k), b)
28.55/9.74	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.74	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.74	   A^2 -> H(U1(a, k), c)
28.55/9.74	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.74	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.74	   A^2 -> H(U1(a, k), e)
28.55/9.74	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(a, c), d)
28.55/9.74	   A^2 -> H(U1(a, c), k)
28.55/9.74	   A^2 -> H(U1(a, d), d)
28.55/9.74	   A^2 -> H(U1(a, d), k)
28.55/9.74	   A^2 -> H(k, U1(c, b))
28.55/9.74	   A^2 -> H(k, U1(d, b))
28.55/9.74	   A^2 -> H(k, U1(b, c))
28.55/9.74	   A^2 -> H(k, U1(b, d))
28.55/9.74	   A^2 -> H(k, U1(c, c))
28.55/9.74	   A^2 -> H(k, f(e))
28.55/9.74	   A^2 -> H(k, f(k))
28.55/9.74	   A^2 -> H(k, U1(d, d))
28.55/9.74	   A^2 -> H(c, U1(e, b))
28.55/9.74	   A^2 -> H(c, U1(k, b))
28.55/9.74	   A^2 -> H(c, U1(c, d))
28.55/9.74	   A^2 -> H(c, U1(d, c))
28.55/9.74	   A^2 -> H(c, U1(b, e))
28.55/9.74	   A^2 -> H(c, U1(b, k))
28.55/9.74	   A^2 -> H(c, U1(e, c))
28.55/9.74	   A^2 -> H(c, U1(k, c))
28.55/9.74	   A^2 -> H(c, U1(c, e))
28.55/9.74	   A^2 -> H(c, U1(c, k))
28.55/9.74	   A^2 -> H(c, U1(e, e))
28.55/9.74	   A^2 -> H(c, U1(k, k))
28.55/9.74	   A^2 -> H(c, U1(k, d))
28.55/9.74	   A^2 -> H(c, U1(d, k))
28.55/9.74	
28.55/9.74	The TRS R consists of the following rules:
28.55/9.74	
28.55/9.74	   f(x) -> U1(x, x)
28.55/9.74	   U1(e, x) -> x
28.55/9.74	   a -> c
28.55/9.74	   a -> d
28.55/9.74	   b -> c
28.55/9.74	   b -> d
28.55/9.74	   d -> k
28.55/9.74	   c -> e
28.55/9.74	   c -> k
28.55/9.74	
28.55/9.74	Q is empty.
28.55/9.74	We have to consider all minimal (P,Q,R)-chains.
28.55/9.74	----------------------------------------
28.55/9.74	
28.55/9.74	(1407) TransformationProof (EQUIVALENT)
28.55/9.74	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.74	
28.55/9.74	   (A^2 -> H(k, U1(c, b)),A^2 -> H(k, U1(c, b)))
28.55/9.74	   (A^2 -> H(U1(e, k), U1(e, b)),A^2 -> H(U1(e, k), U1(e, b)))
28.55/9.74	   (A^2 -> H(U1(e, k), U1(k, b)),A^2 -> H(U1(e, k), U1(k, b)))
28.55/9.74	   (A^2 -> H(U1(e, k), U1(c, c)),A^2 -> H(U1(e, k), U1(c, c)))
28.55/9.74	   (A^2 -> H(U1(e, k), U1(c, d)),A^2 -> H(U1(e, k), U1(c, d)))
28.55/9.74	
28.55/9.74	
28.55/9.74	----------------------------------------
28.55/9.74	
28.55/9.74	(1408)
28.55/9.74	Obligation:
28.55/9.74	Q DP problem:
28.55/9.74	The TRS P consists of the following rules:
28.55/9.74	
28.55/9.74	   H(x, x) -> G(x, x, f(k))
28.55/9.74	   G(d, x, x) -> A^2
28.55/9.74	   A^2 -> H(f(c), f(c))
28.55/9.74	   A^2 -> H(f(d), f(d))
28.55/9.74	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.74	   A^2 -> H(f(e), f(e))
28.55/9.74	   A^2 -> H(f(k), f(k))
28.55/9.74	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.74	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.74	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, k), U1(d, b))
28.55/9.74	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.74	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.74	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.74	   A^2 -> H(U1(e, k), f(e))
28.55/9.74	   A^2 -> H(U1(e, k), f(k))
28.55/9.74	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.74	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.74	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.74	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.74	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.74	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.74	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.74	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.74	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.74	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.74	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.74	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.74	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.74	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.74	   A^2 -> H(U1(k, e), f(e))
28.55/9.74	   A^2 -> H(U1(k, e), f(k))
28.55/9.74	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.74	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.74	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.74	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.74	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.74	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.74	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.74	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.74	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.74	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.74	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.74	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.74	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.74	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.74	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.74	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.74	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.74	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.74	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.74	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.74	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.74	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.74	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.74	   A^2 -> H(U1(c, c), b)
28.55/9.74	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.74	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.74	   A^2 -> H(U1(c, c), e)
28.55/9.74	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.74	   A^2 -> H(e, U1(c, b))
28.55/9.74	   A^2 -> H(e, U1(d, b))
28.55/9.74	   A^2 -> H(e, U1(b, c))
28.55/9.74	   A^2 -> H(e, U1(b, d))
28.55/9.74	   A^2 -> H(e, U1(c, c))
28.55/9.74	   A^2 -> H(e, f(e))
28.55/9.74	   A^2 -> H(e, f(k))
28.55/9.74	   A^2 -> H(e, U1(d, d))
28.55/9.74	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.74	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.74	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.74	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.74	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.74	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.74	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.74	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.74	   A^2 -> H(f(e), b)
28.55/9.74	   A^2 -> H(f(e), U1(e, d))
28.55/9.74	   A^2 -> H(f(e), U1(d, e))
28.55/9.74	   A^2 -> H(f(e), c)
28.55/9.74	   A^2 -> H(f(e), U1(e, k))
28.55/9.74	   A^2 -> H(f(e), U1(k, e))
28.55/9.74	   A^2 -> H(f(e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.74	   A^2 -> H(f(k), b)
28.55/9.74	   A^2 -> H(f(k), U1(e, d))
28.55/9.74	   A^2 -> H(f(k), U1(d, e))
28.55/9.74	   A^2 -> H(f(k), c)
28.55/9.74	   A^2 -> H(f(k), U1(e, k))
28.55/9.74	   A^2 -> H(f(k), U1(k, e))
28.55/9.74	   A^2 -> H(f(k), e)
28.55/9.74	   A^2 -> H(f(c), d)
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.74	   A^2 -> H(U1(k, k), f(e))
28.55/9.74	   A^2 -> H(U1(k, k), f(k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.74	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.74	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.74	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.74	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.74	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.74	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.74	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.74	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.74	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.74	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.74	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.74	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.74	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.74	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.74	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.74	   A^2 -> H(U1(d, d), b)
28.55/9.74	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.74	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.74	   A^2 -> H(U1(d, d), c)
28.55/9.74	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.74	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.74	   A^2 -> H(U1(d, d), e)
28.55/9.74	   A^2 -> H(f(d), d)
28.55/9.74	   A^2 -> H(f(d), k)
28.55/9.74	   A^2 -> H(U1(c, c), c)
28.55/9.74	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.74	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.74	   A^2 -> H(f(c), k)
28.55/9.74	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.74	   A^2 -> H(f(k), U1(k, k))
28.55/9.74	   A^2 -> H(f(e), e)
28.55/9.74	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.74	   A^2 -> H(d, U1(c, b))
28.55/9.74	   A^2 -> H(d, U1(d, b))
28.55/9.74	   A^2 -> H(d, U1(b, c))
28.55/9.74	   A^2 -> H(d, U1(b, d))
28.55/9.74	   A^2 -> H(d, U1(c, c))
28.55/9.74	   A^2 -> H(d, f(e))
28.55/9.74	   A^2 -> H(d, f(k))
28.55/9.74	   A^2 -> H(d, U1(d, d))
28.55/9.74	   A^2 -> H(a, U1(e, b))
28.55/9.74	   A^2 -> H(a, U1(k, b))
28.55/9.74	   A^2 -> H(a, U1(c, d))
28.55/9.74	   A^2 -> H(a, U1(d, c))
28.55/9.74	   A^2 -> H(a, U1(b, e))
28.55/9.74	   A^2 -> H(a, U1(b, k))
28.55/9.74	   A^2 -> H(a, U1(e, c))
28.55/9.74	   A^2 -> H(a, U1(k, c))
28.55/9.74	   A^2 -> H(a, U1(c, e))
28.55/9.74	   A^2 -> H(a, U1(c, k))
28.55/9.74	   A^2 -> H(a, U1(e, e))
28.55/9.74	   A^2 -> H(a, U1(k, k))
28.55/9.74	   A^2 -> H(a, U1(k, d))
28.55/9.74	   A^2 -> H(a, U1(d, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.74	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.74	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.74	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.74	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.74	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.74	   A^2 -> H(U1(e, a), b)
28.55/9.74	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.74	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.74	   A^2 -> H(U1(e, a), c)
28.55/9.74	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.74	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.74	   A^2 -> H(U1(e, a), e)
28.55/9.74	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, a), b)
28.55/9.74	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.74	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.74	   A^2 -> H(U1(k, a), c)
28.55/9.74	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.74	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.74	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, d), b)
28.55/9.74	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.74	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.74	   A^2 -> H(U1(c, d), c)
28.55/9.74	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.74	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.74	   A^2 -> H(U1(c, d), e)
28.55/9.74	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, a), d)
28.55/9.74	   A^2 -> H(U1(c, a), k)
28.55/9.74	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.74	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.74	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.74	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.74	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.74	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.74	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.74	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.74	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.74	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.74	   A^2 -> H(U1(d, c), b)
28.55/9.74	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.74	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.74	   A^2 -> H(U1(d, c), c)
28.55/9.74	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.74	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.74	   A^2 -> H(U1(d, c), e)
28.55/9.74	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.74	   A^2 -> H(U1(d, a), d)
28.55/9.74	   A^2 -> H(U1(d, a), k)
28.55/9.74	   A^2 -> H(U1(a, e), b)
28.55/9.74	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.74	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.74	   A^2 -> H(U1(a, e), c)
28.55/9.74	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.74	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.74	   A^2 -> H(U1(a, e), e)
28.55/9.74	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(a, k), b)
28.55/9.74	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.74	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.74	   A^2 -> H(U1(a, k), c)
28.55/9.74	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.74	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.74	   A^2 -> H(U1(a, k), e)
28.55/9.74	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(a, c), d)
28.55/9.74	   A^2 -> H(U1(a, c), k)
28.55/9.74	   A^2 -> H(U1(a, d), d)
28.55/9.74	   A^2 -> H(U1(a, d), k)
28.55/9.74	   A^2 -> H(k, U1(c, b))
28.55/9.74	   A^2 -> H(k, U1(d, b))
28.55/9.74	   A^2 -> H(k, U1(b, c))
28.55/9.74	   A^2 -> H(k, U1(b, d))
28.55/9.74	   A^2 -> H(k, U1(c, c))
28.55/9.74	   A^2 -> H(k, f(e))
28.55/9.74	   A^2 -> H(k, f(k))
28.55/9.74	   A^2 -> H(k, U1(d, d))
28.55/9.74	   A^2 -> H(c, U1(e, b))
28.55/9.74	   A^2 -> H(c, U1(k, b))
28.55/9.74	   A^2 -> H(c, U1(c, d))
28.55/9.74	   A^2 -> H(c, U1(d, c))
28.55/9.74	   A^2 -> H(c, U1(b, e))
28.55/9.74	   A^2 -> H(c, U1(b, k))
28.55/9.74	   A^2 -> H(c, U1(e, c))
28.55/9.74	   A^2 -> H(c, U1(k, c))
28.55/9.74	   A^2 -> H(c, U1(c, e))
28.55/9.74	   A^2 -> H(c, U1(c, k))
28.55/9.74	   A^2 -> H(c, U1(e, e))
28.55/9.74	   A^2 -> H(c, U1(k, k))
28.55/9.74	   A^2 -> H(c, U1(k, d))
28.55/9.74	   A^2 -> H(c, U1(d, k))
28.55/9.74	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.74	
28.55/9.74	The TRS R consists of the following rules:
28.55/9.74	
28.55/9.74	   f(x) -> U1(x, x)
28.55/9.74	   U1(e, x) -> x
28.55/9.74	   a -> c
28.55/9.74	   a -> d
28.55/9.74	   b -> c
28.55/9.74	   b -> d
28.55/9.74	   d -> k
28.55/9.74	   c -> e
28.55/9.74	   c -> k
28.55/9.74	
28.55/9.74	Q is empty.
28.55/9.74	We have to consider all minimal (P,Q,R)-chains.
28.55/9.74	----------------------------------------
28.55/9.74	
28.55/9.74	(1409) TransformationProof (EQUIVALENT)
28.55/9.74	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.74	
28.55/9.74	   (A^2 -> H(k, U1(d, b)),A^2 -> H(k, U1(d, b)))
28.55/9.74	   (A^2 -> H(U1(e, k), U1(k, b)),A^2 -> H(U1(e, k), U1(k, b)))
28.55/9.74	   (A^2 -> H(U1(e, k), U1(d, c)),A^2 -> H(U1(e, k), U1(d, c)))
28.55/9.74	   (A^2 -> H(U1(e, k), U1(d, d)),A^2 -> H(U1(e, k), U1(d, d)))
28.55/9.74	
28.55/9.74	
28.55/9.74	----------------------------------------
28.55/9.74	
28.55/9.74	(1410)
28.55/9.74	Obligation:
28.55/9.74	Q DP problem:
28.55/9.74	The TRS P consists of the following rules:
28.55/9.74	
28.55/9.74	   H(x, x) -> G(x, x, f(k))
28.55/9.74	   G(d, x, x) -> A^2
28.55/9.74	   A^2 -> H(f(c), f(c))
28.55/9.74	   A^2 -> H(f(d), f(d))
28.55/9.74	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.74	   A^2 -> H(f(e), f(e))
28.55/9.74	   A^2 -> H(f(k), f(k))
28.55/9.74	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.74	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.74	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, k), U1(b, c))
28.55/9.74	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.74	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.74	   A^2 -> H(U1(e, k), f(e))
28.55/9.74	   A^2 -> H(U1(e, k), f(k))
28.55/9.74	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.74	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.74	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.74	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.74	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.74	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.74	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.74	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.74	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.74	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.74	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.74	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.74	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.74	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.74	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.74	   A^2 -> H(U1(k, e), f(e))
28.55/9.74	   A^2 -> H(U1(k, e), f(k))
28.55/9.74	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.74	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.74	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.74	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.74	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.74	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.74	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.74	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.74	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.74	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.74	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.74	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.74	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.74	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.74	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.74	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.74	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.74	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.74	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.74	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.74	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.74	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.74	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.74	   A^2 -> H(U1(c, c), b)
28.55/9.74	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.74	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.74	   A^2 -> H(U1(c, c), e)
28.55/9.74	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.74	   A^2 -> H(e, U1(c, b))
28.55/9.74	   A^2 -> H(e, U1(d, b))
28.55/9.74	   A^2 -> H(e, U1(b, c))
28.55/9.74	   A^2 -> H(e, U1(b, d))
28.55/9.74	   A^2 -> H(e, U1(c, c))
28.55/9.74	   A^2 -> H(e, f(e))
28.55/9.74	   A^2 -> H(e, f(k))
28.55/9.74	   A^2 -> H(e, U1(d, d))
28.55/9.74	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.74	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.74	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.74	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.74	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.74	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.74	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.74	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.74	   A^2 -> H(f(e), b)
28.55/9.74	   A^2 -> H(f(e), U1(e, d))
28.55/9.74	   A^2 -> H(f(e), U1(d, e))
28.55/9.74	   A^2 -> H(f(e), c)
28.55/9.74	   A^2 -> H(f(e), U1(e, k))
28.55/9.74	   A^2 -> H(f(e), U1(k, e))
28.55/9.74	   A^2 -> H(f(e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.74	   A^2 -> H(f(k), b)
28.55/9.74	   A^2 -> H(f(k), U1(e, d))
28.55/9.74	   A^2 -> H(f(k), U1(d, e))
28.55/9.74	   A^2 -> H(f(k), c)
28.55/9.74	   A^2 -> H(f(k), U1(e, k))
28.55/9.74	   A^2 -> H(f(k), U1(k, e))
28.55/9.74	   A^2 -> H(f(k), e)
28.55/9.74	   A^2 -> H(f(c), d)
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.74	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.74	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.74	   A^2 -> H(U1(k, k), f(e))
28.55/9.74	   A^2 -> H(U1(k, k), f(k))
28.55/9.74	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.74	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.74	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.74	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.74	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.74	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.74	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.74	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.74	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.74	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.74	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.74	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.74	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.74	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.74	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.74	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.74	   A^2 -> H(U1(d, d), b)
28.55/9.74	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.74	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.74	   A^2 -> H(U1(d, d), c)
28.55/9.74	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.74	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.74	   A^2 -> H(U1(d, d), e)
28.55/9.74	   A^2 -> H(f(d), d)
28.55/9.74	   A^2 -> H(f(d), k)
28.55/9.74	   A^2 -> H(U1(c, c), c)
28.55/9.74	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.74	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.74	   A^2 -> H(f(c), k)
28.55/9.74	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.74	   A^2 -> H(f(k), U1(k, k))
28.55/9.74	   A^2 -> H(f(e), e)
28.55/9.74	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.74	   A^2 -> H(d, U1(c, b))
28.55/9.74	   A^2 -> H(d, U1(d, b))
28.55/9.74	   A^2 -> H(d, U1(b, c))
28.55/9.74	   A^2 -> H(d, U1(b, d))
28.55/9.74	   A^2 -> H(d, U1(c, c))
28.55/9.74	   A^2 -> H(d, f(e))
28.55/9.74	   A^2 -> H(d, f(k))
28.55/9.74	   A^2 -> H(d, U1(d, d))
28.55/9.74	   A^2 -> H(a, U1(e, b))
28.55/9.74	   A^2 -> H(a, U1(k, b))
28.55/9.74	   A^2 -> H(a, U1(c, d))
28.55/9.74	   A^2 -> H(a, U1(d, c))
28.55/9.74	   A^2 -> H(a, U1(b, e))
28.55/9.74	   A^2 -> H(a, U1(b, k))
28.55/9.74	   A^2 -> H(a, U1(e, c))
28.55/9.74	   A^2 -> H(a, U1(k, c))
28.55/9.74	   A^2 -> H(a, U1(c, e))
28.55/9.74	   A^2 -> H(a, U1(c, k))
28.55/9.74	   A^2 -> H(a, U1(e, e))
28.55/9.74	   A^2 -> H(a, U1(k, k))
28.55/9.74	   A^2 -> H(a, U1(k, d))
28.55/9.74	   A^2 -> H(a, U1(d, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.74	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.74	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.74	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.74	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.74	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.74	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.74	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.74	   A^2 -> H(U1(e, a), b)
28.55/9.74	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.74	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.74	   A^2 -> H(U1(e, a), c)
28.55/9.74	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.74	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.74	   A^2 -> H(U1(e, a), e)
28.55/9.74	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.74	   A^2 -> H(U1(k, a), b)
28.55/9.74	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.74	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.74	   A^2 -> H(U1(k, a), c)
28.55/9.74	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.74	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.74	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, d), b)
28.55/9.74	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.74	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.74	   A^2 -> H(U1(c, d), c)
28.55/9.74	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.74	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.74	   A^2 -> H(U1(c, d), e)
28.55/9.74	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.74	   A^2 -> H(U1(c, a), d)
28.55/9.74	   A^2 -> H(U1(c, a), k)
28.55/9.74	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.74	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.74	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.74	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.74	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.74	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.74	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.74	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.74	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.74	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.74	   A^2 -> H(U1(d, c), b)
28.55/9.74	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.74	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.74	   A^2 -> H(U1(d, c), c)
28.55/9.74	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.74	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.74	   A^2 -> H(U1(d, c), e)
28.55/9.74	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.74	   A^2 -> H(U1(d, a), d)
28.55/9.74	   A^2 -> H(U1(d, a), k)
28.55/9.74	   A^2 -> H(U1(a, e), b)
28.55/9.74	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.74	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.74	   A^2 -> H(U1(a, e), c)
28.55/9.74	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.74	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.74	   A^2 -> H(U1(a, e), e)
28.55/9.74	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.74	   A^2 -> H(U1(a, k), b)
28.55/9.74	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.74	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.74	   A^2 -> H(U1(a, k), c)
28.55/9.74	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.74	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.74	   A^2 -> H(U1(a, k), e)
28.55/9.74	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.74	   A^2 -> H(U1(a, c), d)
28.55/9.74	   A^2 -> H(U1(a, c), k)
28.55/9.74	   A^2 -> H(U1(a, d), d)
28.55/9.74	   A^2 -> H(U1(a, d), k)
28.55/9.74	   A^2 -> H(k, U1(c, b))
28.55/9.74	   A^2 -> H(k, U1(d, b))
28.55/9.74	   A^2 -> H(k, U1(b, c))
28.55/9.74	   A^2 -> H(k, U1(b, d))
28.55/9.74	   A^2 -> H(k, U1(c, c))
28.55/9.74	   A^2 -> H(k, f(e))
28.55/9.74	   A^2 -> H(k, f(k))
28.55/9.74	   A^2 -> H(k, U1(d, d))
28.55/9.74	   A^2 -> H(c, U1(e, b))
28.55/9.74	   A^2 -> H(c, U1(k, b))
28.55/9.74	   A^2 -> H(c, U1(c, d))
28.55/9.74	   A^2 -> H(c, U1(d, c))
28.55/9.74	   A^2 -> H(c, U1(b, e))
28.55/9.74	   A^2 -> H(c, U1(b, k))
28.55/9.74	   A^2 -> H(c, U1(e, c))
28.55/9.74	   A^2 -> H(c, U1(k, c))
28.55/9.74	   A^2 -> H(c, U1(c, e))
28.55/9.74	   A^2 -> H(c, U1(c, k))
28.55/9.74	   A^2 -> H(c, U1(e, e))
28.55/9.74	   A^2 -> H(c, U1(k, k))
28.55/9.74	   A^2 -> H(c, U1(k, d))
28.55/9.74	   A^2 -> H(c, U1(d, k))
28.55/9.74	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.74	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.74	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.74	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.74	
28.55/9.74	The TRS R consists of the following rules:
28.55/9.74	
28.55/9.74	   f(x) -> U1(x, x)
28.55/9.74	   U1(e, x) -> x
28.55/9.74	   a -> c
28.55/9.74	   a -> d
28.55/9.74	   b -> c
28.55/9.74	   b -> d
28.55/9.74	   d -> k
28.55/9.74	   c -> e
28.55/9.74	   c -> k
28.55/9.74	
28.55/9.74	Q is empty.
28.55/9.74	We have to consider all minimal (P,Q,R)-chains.
28.55/9.74	----------------------------------------
28.55/9.74	
28.55/9.74	(1411) TransformationProof (EQUIVALENT)
28.55/9.74	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.74	
28.55/9.74	   (A^2 -> H(k, U1(b, c)),A^2 -> H(k, U1(b, c)))
28.55/9.74	   (A^2 -> H(U1(e, k), U1(c, c)),A^2 -> H(U1(e, k), U1(c, c)))
28.55/9.74	   (A^2 -> H(U1(e, k), U1(d, c)),A^2 -> H(U1(e, k), U1(d, c)))
28.55/9.74	   (A^2 -> H(U1(e, k), U1(b, e)),A^2 -> H(U1(e, k), U1(b, e)))
28.55/9.74	   (A^2 -> H(U1(e, k), U1(b, k)),A^2 -> H(U1(e, k), U1(b, k)))
28.55/9.74	
28.55/9.74	
28.55/9.74	----------------------------------------
28.55/9.75	
28.55/9.75	(1412)
28.55/9.75	Obligation:
28.55/9.75	Q DP problem:
28.55/9.75	The TRS P consists of the following rules:
28.55/9.75	
28.55/9.75	   H(x, x) -> G(x, x, f(k))
28.55/9.75	   G(d, x, x) -> A^2
28.55/9.75	   A^2 -> H(f(c), f(c))
28.55/9.75	   A^2 -> H(f(d), f(d))
28.55/9.75	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.75	   A^2 -> H(f(e), f(e))
28.55/9.75	   A^2 -> H(f(k), f(k))
28.55/9.75	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.75	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.75	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, k), U1(b, d))
28.55/9.75	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.75	   A^2 -> H(U1(e, k), f(e))
28.55/9.75	   A^2 -> H(U1(e, k), f(k))
28.55/9.75	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.75	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.75	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.75	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.75	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.75	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.75	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.75	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.75	   A^2 -> H(U1(k, e), f(e))
28.55/9.75	   A^2 -> H(U1(k, e), f(k))
28.55/9.75	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.75	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.75	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.75	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.75	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.75	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.75	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.75	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.75	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.75	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.75	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.75	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.75	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.75	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.75	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.75	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.75	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.75	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.75	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.75	   A^2 -> H(U1(c, c), b)
28.55/9.75	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.75	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.75	   A^2 -> H(U1(c, c), e)
28.55/9.75	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.75	   A^2 -> H(e, U1(c, b))
28.55/9.75	   A^2 -> H(e, U1(d, b))
28.55/9.75	   A^2 -> H(e, U1(b, c))
28.55/9.75	   A^2 -> H(e, U1(b, d))
28.55/9.75	   A^2 -> H(e, U1(c, c))
28.55/9.75	   A^2 -> H(e, f(e))
28.55/9.75	   A^2 -> H(e, f(k))
28.55/9.75	   A^2 -> H(e, U1(d, d))
28.55/9.75	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.75	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.75	   A^2 -> H(f(e), b)
28.55/9.75	   A^2 -> H(f(e), U1(e, d))
28.55/9.75	   A^2 -> H(f(e), U1(d, e))
28.55/9.75	   A^2 -> H(f(e), c)
28.55/9.75	   A^2 -> H(f(e), U1(e, k))
28.55/9.75	   A^2 -> H(f(e), U1(k, e))
28.55/9.75	   A^2 -> H(f(e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.75	   A^2 -> H(f(k), b)
28.55/9.75	   A^2 -> H(f(k), U1(e, d))
28.55/9.75	   A^2 -> H(f(k), U1(d, e))
28.55/9.75	   A^2 -> H(f(k), c)
28.55/9.75	   A^2 -> H(f(k), U1(e, k))
28.55/9.75	   A^2 -> H(f(k), U1(k, e))
28.55/9.75	   A^2 -> H(f(k), e)
28.55/9.75	   A^2 -> H(f(c), d)
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.75	   A^2 -> H(U1(k, k), f(e))
28.55/9.75	   A^2 -> H(U1(k, k), f(k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.75	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.75	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.75	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.75	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.75	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.75	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.75	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.75	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.75	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.75	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.75	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.75	   A^2 -> H(U1(d, d), b)
28.55/9.75	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.75	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.75	   A^2 -> H(U1(d, d), c)
28.55/9.75	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.75	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.75	   A^2 -> H(U1(d, d), e)
28.55/9.75	   A^2 -> H(f(d), d)
28.55/9.75	   A^2 -> H(f(d), k)
28.55/9.75	   A^2 -> H(U1(c, c), c)
28.55/9.75	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.75	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.75	   A^2 -> H(f(c), k)
28.55/9.75	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.75	   A^2 -> H(f(k), U1(k, k))
28.55/9.75	   A^2 -> H(f(e), e)
28.55/9.75	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.75	   A^2 -> H(d, U1(c, b))
28.55/9.75	   A^2 -> H(d, U1(d, b))
28.55/9.75	   A^2 -> H(d, U1(b, c))
28.55/9.75	   A^2 -> H(d, U1(b, d))
28.55/9.75	   A^2 -> H(d, U1(c, c))
28.55/9.75	   A^2 -> H(d, f(e))
28.55/9.75	   A^2 -> H(d, f(k))
28.55/9.75	   A^2 -> H(d, U1(d, d))
28.55/9.75	   A^2 -> H(a, U1(e, b))
28.55/9.75	   A^2 -> H(a, U1(k, b))
28.55/9.75	   A^2 -> H(a, U1(c, d))
28.55/9.75	   A^2 -> H(a, U1(d, c))
28.55/9.75	   A^2 -> H(a, U1(b, e))
28.55/9.75	   A^2 -> H(a, U1(b, k))
28.55/9.75	   A^2 -> H(a, U1(e, c))
28.55/9.75	   A^2 -> H(a, U1(k, c))
28.55/9.75	   A^2 -> H(a, U1(c, e))
28.55/9.75	   A^2 -> H(a, U1(c, k))
28.55/9.75	   A^2 -> H(a, U1(e, e))
28.55/9.75	   A^2 -> H(a, U1(k, k))
28.55/9.75	   A^2 -> H(a, U1(k, d))
28.55/9.75	   A^2 -> H(a, U1(d, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.75	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.75	   A^2 -> H(U1(e, a), b)
28.55/9.75	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.75	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.75	   A^2 -> H(U1(e, a), c)
28.55/9.75	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.75	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.75	   A^2 -> H(U1(e, a), e)
28.55/9.75	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, a), b)
28.55/9.75	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.75	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.75	   A^2 -> H(U1(k, a), c)
28.55/9.75	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.75	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.75	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, d), b)
28.55/9.75	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.75	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.75	   A^2 -> H(U1(c, d), c)
28.55/9.75	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.75	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.75	   A^2 -> H(U1(c, d), e)
28.55/9.75	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, a), d)
28.55/9.75	   A^2 -> H(U1(c, a), k)
28.55/9.75	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.75	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.75	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.75	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.75	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.75	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.75	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.75	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.75	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.75	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.75	   A^2 -> H(U1(d, c), b)
28.55/9.75	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.75	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.75	   A^2 -> H(U1(d, c), c)
28.55/9.75	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.75	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.75	   A^2 -> H(U1(d, c), e)
28.55/9.75	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.75	   A^2 -> H(U1(d, a), d)
28.55/9.75	   A^2 -> H(U1(d, a), k)
28.55/9.75	   A^2 -> H(U1(a, e), b)
28.55/9.75	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.75	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.75	   A^2 -> H(U1(a, e), c)
28.55/9.75	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.75	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.75	   A^2 -> H(U1(a, e), e)
28.55/9.75	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(a, k), b)
28.55/9.75	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.75	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.75	   A^2 -> H(U1(a, k), c)
28.55/9.75	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.75	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.75	   A^2 -> H(U1(a, k), e)
28.55/9.75	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(a, c), d)
28.55/9.75	   A^2 -> H(U1(a, c), k)
28.55/9.75	   A^2 -> H(U1(a, d), d)
28.55/9.75	   A^2 -> H(U1(a, d), k)
28.55/9.75	   A^2 -> H(k, U1(c, b))
28.55/9.75	   A^2 -> H(k, U1(d, b))
28.55/9.75	   A^2 -> H(k, U1(b, c))
28.55/9.75	   A^2 -> H(k, U1(b, d))
28.55/9.75	   A^2 -> H(k, U1(c, c))
28.55/9.75	   A^2 -> H(k, f(e))
28.55/9.75	   A^2 -> H(k, f(k))
28.55/9.75	   A^2 -> H(k, U1(d, d))
28.55/9.75	   A^2 -> H(c, U1(e, b))
28.55/9.75	   A^2 -> H(c, U1(k, b))
28.55/9.75	   A^2 -> H(c, U1(c, d))
28.55/9.75	   A^2 -> H(c, U1(d, c))
28.55/9.75	   A^2 -> H(c, U1(b, e))
28.55/9.75	   A^2 -> H(c, U1(b, k))
28.55/9.75	   A^2 -> H(c, U1(e, c))
28.55/9.75	   A^2 -> H(c, U1(k, c))
28.55/9.75	   A^2 -> H(c, U1(c, e))
28.55/9.75	   A^2 -> H(c, U1(c, k))
28.55/9.75	   A^2 -> H(c, U1(e, e))
28.55/9.75	   A^2 -> H(c, U1(k, k))
28.55/9.75	   A^2 -> H(c, U1(k, d))
28.55/9.75	   A^2 -> H(c, U1(d, k))
28.55/9.75	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.75	
28.55/9.75	The TRS R consists of the following rules:
28.55/9.75	
28.55/9.75	   f(x) -> U1(x, x)
28.55/9.75	   U1(e, x) -> x
28.55/9.75	   a -> c
28.55/9.75	   a -> d
28.55/9.75	   b -> c
28.55/9.75	   b -> d
28.55/9.75	   d -> k
28.55/9.75	   c -> e
28.55/9.75	   c -> k
28.55/9.75	
28.55/9.75	Q is empty.
28.55/9.75	We have to consider all minimal (P,Q,R)-chains.
28.55/9.75	----------------------------------------
28.55/9.75	
28.55/9.75	(1413) TransformationProof (EQUIVALENT)
28.55/9.75	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.75	
28.55/9.75	   (A^2 -> H(k, U1(b, d)),A^2 -> H(k, U1(b, d)))
28.55/9.75	   (A^2 -> H(U1(e, k), U1(c, d)),A^2 -> H(U1(e, k), U1(c, d)))
28.55/9.75	   (A^2 -> H(U1(e, k), U1(d, d)),A^2 -> H(U1(e, k), U1(d, d)))
28.55/9.75	   (A^2 -> H(U1(e, k), U1(b, k)),A^2 -> H(U1(e, k), U1(b, k)))
28.55/9.75	
28.55/9.75	
28.55/9.75	----------------------------------------
28.55/9.75	
28.55/9.75	(1414)
28.55/9.75	Obligation:
28.55/9.75	Q DP problem:
28.55/9.75	The TRS P consists of the following rules:
28.55/9.75	
28.55/9.75	   H(x, x) -> G(x, x, f(k))
28.55/9.75	   G(d, x, x) -> A^2
28.55/9.75	   A^2 -> H(f(c), f(c))
28.55/9.75	   A^2 -> H(f(d), f(d))
28.55/9.75	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.75	   A^2 -> H(f(e), f(e))
28.55/9.75	   A^2 -> H(f(k), f(k))
28.55/9.75	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.75	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.75	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, k), U1(c, c))
28.55/9.75	   A^2 -> H(U1(e, k), f(e))
28.55/9.75	   A^2 -> H(U1(e, k), f(k))
28.55/9.75	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.75	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.75	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.75	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.75	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.75	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.75	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.75	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.75	   A^2 -> H(U1(k, e), f(e))
28.55/9.75	   A^2 -> H(U1(k, e), f(k))
28.55/9.75	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.75	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.75	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.75	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.75	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.75	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.75	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.75	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.75	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.75	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.75	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.75	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.75	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.75	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.75	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.75	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.75	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.75	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.75	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.75	   A^2 -> H(U1(c, c), b)
28.55/9.75	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.75	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.75	   A^2 -> H(U1(c, c), e)
28.55/9.75	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.75	   A^2 -> H(e, U1(c, b))
28.55/9.75	   A^2 -> H(e, U1(d, b))
28.55/9.75	   A^2 -> H(e, U1(b, c))
28.55/9.75	   A^2 -> H(e, U1(b, d))
28.55/9.75	   A^2 -> H(e, U1(c, c))
28.55/9.75	   A^2 -> H(e, f(e))
28.55/9.75	   A^2 -> H(e, f(k))
28.55/9.75	   A^2 -> H(e, U1(d, d))
28.55/9.75	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.75	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.75	   A^2 -> H(f(e), b)
28.55/9.75	   A^2 -> H(f(e), U1(e, d))
28.55/9.75	   A^2 -> H(f(e), U1(d, e))
28.55/9.75	   A^2 -> H(f(e), c)
28.55/9.75	   A^2 -> H(f(e), U1(e, k))
28.55/9.75	   A^2 -> H(f(e), U1(k, e))
28.55/9.75	   A^2 -> H(f(e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.75	   A^2 -> H(f(k), b)
28.55/9.75	   A^2 -> H(f(k), U1(e, d))
28.55/9.75	   A^2 -> H(f(k), U1(d, e))
28.55/9.75	   A^2 -> H(f(k), c)
28.55/9.75	   A^2 -> H(f(k), U1(e, k))
28.55/9.75	   A^2 -> H(f(k), U1(k, e))
28.55/9.75	   A^2 -> H(f(k), e)
28.55/9.75	   A^2 -> H(f(c), d)
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.75	   A^2 -> H(U1(k, k), f(e))
28.55/9.75	   A^2 -> H(U1(k, k), f(k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.75	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.75	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.75	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.75	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.75	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.75	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.75	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.75	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.75	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.75	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.75	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.75	   A^2 -> H(U1(d, d), b)
28.55/9.75	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.75	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.75	   A^2 -> H(U1(d, d), c)
28.55/9.75	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.75	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.75	   A^2 -> H(U1(d, d), e)
28.55/9.75	   A^2 -> H(f(d), d)
28.55/9.75	   A^2 -> H(f(d), k)
28.55/9.75	   A^2 -> H(U1(c, c), c)
28.55/9.75	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.75	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.75	   A^2 -> H(f(c), k)
28.55/9.75	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.75	   A^2 -> H(f(k), U1(k, k))
28.55/9.75	   A^2 -> H(f(e), e)
28.55/9.75	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.75	   A^2 -> H(d, U1(c, b))
28.55/9.75	   A^2 -> H(d, U1(d, b))
28.55/9.75	   A^2 -> H(d, U1(b, c))
28.55/9.75	   A^2 -> H(d, U1(b, d))
28.55/9.75	   A^2 -> H(d, U1(c, c))
28.55/9.75	   A^2 -> H(d, f(e))
28.55/9.75	   A^2 -> H(d, f(k))
28.55/9.75	   A^2 -> H(d, U1(d, d))
28.55/9.75	   A^2 -> H(a, U1(e, b))
28.55/9.75	   A^2 -> H(a, U1(k, b))
28.55/9.75	   A^2 -> H(a, U1(c, d))
28.55/9.75	   A^2 -> H(a, U1(d, c))
28.55/9.75	   A^2 -> H(a, U1(b, e))
28.55/9.75	   A^2 -> H(a, U1(b, k))
28.55/9.75	   A^2 -> H(a, U1(e, c))
28.55/9.75	   A^2 -> H(a, U1(k, c))
28.55/9.75	   A^2 -> H(a, U1(c, e))
28.55/9.75	   A^2 -> H(a, U1(c, k))
28.55/9.75	   A^2 -> H(a, U1(e, e))
28.55/9.75	   A^2 -> H(a, U1(k, k))
28.55/9.75	   A^2 -> H(a, U1(k, d))
28.55/9.75	   A^2 -> H(a, U1(d, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.75	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.75	   A^2 -> H(U1(e, a), b)
28.55/9.75	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.75	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.75	   A^2 -> H(U1(e, a), c)
28.55/9.75	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.75	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.75	   A^2 -> H(U1(e, a), e)
28.55/9.75	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, a), b)
28.55/9.75	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.75	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.75	   A^2 -> H(U1(k, a), c)
28.55/9.75	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.75	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.75	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, d), b)
28.55/9.75	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.75	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.75	   A^2 -> H(U1(c, d), c)
28.55/9.75	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.75	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.75	   A^2 -> H(U1(c, d), e)
28.55/9.75	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, a), d)
28.55/9.75	   A^2 -> H(U1(c, a), k)
28.55/9.75	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.75	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.75	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.75	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.75	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.75	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.75	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.75	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.75	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.75	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.75	   A^2 -> H(U1(d, c), b)
28.55/9.75	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.75	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.75	   A^2 -> H(U1(d, c), c)
28.55/9.75	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.75	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.75	   A^2 -> H(U1(d, c), e)
28.55/9.75	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.75	   A^2 -> H(U1(d, a), d)
28.55/9.75	   A^2 -> H(U1(d, a), k)
28.55/9.75	   A^2 -> H(U1(a, e), b)
28.55/9.75	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.75	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.75	   A^2 -> H(U1(a, e), c)
28.55/9.75	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.75	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.75	   A^2 -> H(U1(a, e), e)
28.55/9.75	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(a, k), b)
28.55/9.75	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.75	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.75	   A^2 -> H(U1(a, k), c)
28.55/9.75	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.75	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.75	   A^2 -> H(U1(a, k), e)
28.55/9.75	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(a, c), d)
28.55/9.75	   A^2 -> H(U1(a, c), k)
28.55/9.75	   A^2 -> H(U1(a, d), d)
28.55/9.75	   A^2 -> H(U1(a, d), k)
28.55/9.75	   A^2 -> H(k, U1(c, b))
28.55/9.75	   A^2 -> H(k, U1(d, b))
28.55/9.75	   A^2 -> H(k, U1(b, c))
28.55/9.75	   A^2 -> H(k, U1(b, d))
28.55/9.75	   A^2 -> H(k, U1(c, c))
28.55/9.75	   A^2 -> H(k, f(e))
28.55/9.75	   A^2 -> H(k, f(k))
28.55/9.75	   A^2 -> H(k, U1(d, d))
28.55/9.75	   A^2 -> H(c, U1(e, b))
28.55/9.75	   A^2 -> H(c, U1(k, b))
28.55/9.75	   A^2 -> H(c, U1(c, d))
28.55/9.75	   A^2 -> H(c, U1(d, c))
28.55/9.75	   A^2 -> H(c, U1(b, e))
28.55/9.75	   A^2 -> H(c, U1(b, k))
28.55/9.75	   A^2 -> H(c, U1(e, c))
28.55/9.75	   A^2 -> H(c, U1(k, c))
28.55/9.75	   A^2 -> H(c, U1(c, e))
28.55/9.75	   A^2 -> H(c, U1(c, k))
28.55/9.75	   A^2 -> H(c, U1(e, e))
28.55/9.75	   A^2 -> H(c, U1(k, k))
28.55/9.75	   A^2 -> H(c, U1(k, d))
28.55/9.75	   A^2 -> H(c, U1(d, k))
28.55/9.75	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.75	
28.55/9.75	The TRS R consists of the following rules:
28.55/9.75	
28.55/9.75	   f(x) -> U1(x, x)
28.55/9.75	   U1(e, x) -> x
28.55/9.75	   a -> c
28.55/9.75	   a -> d
28.55/9.75	   b -> c
28.55/9.75	   b -> d
28.55/9.75	   d -> k
28.55/9.75	   c -> e
28.55/9.75	   c -> k
28.55/9.75	
28.55/9.75	Q is empty.
28.55/9.75	We have to consider all minimal (P,Q,R)-chains.
28.55/9.75	----------------------------------------
28.55/9.75	
28.55/9.75	(1415) TransformationProof (EQUIVALENT)
28.55/9.75	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.75	
28.55/9.75	   (A^2 -> H(k, U1(c, c)),A^2 -> H(k, U1(c, c)))
28.55/9.75	   (A^2 -> H(U1(e, k), U1(e, c)),A^2 -> H(U1(e, k), U1(e, c)))
28.55/9.75	   (A^2 -> H(U1(e, k), U1(k, c)),A^2 -> H(U1(e, k), U1(k, c)))
28.55/9.75	   (A^2 -> H(U1(e, k), U1(c, e)),A^2 -> H(U1(e, k), U1(c, e)))
28.55/9.75	   (A^2 -> H(U1(e, k), U1(c, k)),A^2 -> H(U1(e, k), U1(c, k)))
28.55/9.75	
28.55/9.75	
28.55/9.75	----------------------------------------
28.55/9.75	
28.55/9.75	(1416)
28.55/9.75	Obligation:
28.55/9.75	Q DP problem:
28.55/9.75	The TRS P consists of the following rules:
28.55/9.75	
28.55/9.75	   H(x, x) -> G(x, x, f(k))
28.55/9.75	   G(d, x, x) -> A^2
28.55/9.75	   A^2 -> H(f(c), f(c))
28.55/9.75	   A^2 -> H(f(d), f(d))
28.55/9.75	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.75	   A^2 -> H(f(e), f(e))
28.55/9.75	   A^2 -> H(f(k), f(k))
28.55/9.75	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.75	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.75	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, k), f(e))
28.55/9.75	   A^2 -> H(U1(e, k), f(k))
28.55/9.75	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.75	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.75	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.75	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.75	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.75	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.75	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.75	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.75	   A^2 -> H(U1(k, e), f(e))
28.55/9.75	   A^2 -> H(U1(k, e), f(k))
28.55/9.75	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.75	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.75	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.75	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.75	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.75	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.75	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.75	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.75	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.75	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.75	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.75	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.75	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.75	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.75	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.75	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.75	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.75	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.75	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.75	   A^2 -> H(U1(c, c), b)
28.55/9.75	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.75	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.75	   A^2 -> H(U1(c, c), e)
28.55/9.75	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.75	   A^2 -> H(e, U1(c, b))
28.55/9.75	   A^2 -> H(e, U1(d, b))
28.55/9.75	   A^2 -> H(e, U1(b, c))
28.55/9.75	   A^2 -> H(e, U1(b, d))
28.55/9.75	   A^2 -> H(e, U1(c, c))
28.55/9.75	   A^2 -> H(e, f(e))
28.55/9.75	   A^2 -> H(e, f(k))
28.55/9.75	   A^2 -> H(e, U1(d, d))
28.55/9.75	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.75	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.75	   A^2 -> H(f(e), b)
28.55/9.75	   A^2 -> H(f(e), U1(e, d))
28.55/9.75	   A^2 -> H(f(e), U1(d, e))
28.55/9.75	   A^2 -> H(f(e), c)
28.55/9.75	   A^2 -> H(f(e), U1(e, k))
28.55/9.75	   A^2 -> H(f(e), U1(k, e))
28.55/9.75	   A^2 -> H(f(e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.75	   A^2 -> H(f(k), b)
28.55/9.75	   A^2 -> H(f(k), U1(e, d))
28.55/9.75	   A^2 -> H(f(k), U1(d, e))
28.55/9.75	   A^2 -> H(f(k), c)
28.55/9.75	   A^2 -> H(f(k), U1(e, k))
28.55/9.75	   A^2 -> H(f(k), U1(k, e))
28.55/9.75	   A^2 -> H(f(k), e)
28.55/9.75	   A^2 -> H(f(c), d)
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.75	   A^2 -> H(U1(k, k), f(e))
28.55/9.75	   A^2 -> H(U1(k, k), f(k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.75	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.75	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.75	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.75	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.75	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.75	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.75	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.75	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.75	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.75	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.75	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.75	   A^2 -> H(U1(d, d), b)
28.55/9.75	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.75	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.75	   A^2 -> H(U1(d, d), c)
28.55/9.75	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.75	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.75	   A^2 -> H(U1(d, d), e)
28.55/9.75	   A^2 -> H(f(d), d)
28.55/9.75	   A^2 -> H(f(d), k)
28.55/9.75	   A^2 -> H(U1(c, c), c)
28.55/9.75	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.75	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.75	   A^2 -> H(f(c), k)
28.55/9.75	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.75	   A^2 -> H(f(k), U1(k, k))
28.55/9.75	   A^2 -> H(f(e), e)
28.55/9.75	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.75	   A^2 -> H(d, U1(c, b))
28.55/9.75	   A^2 -> H(d, U1(d, b))
28.55/9.75	   A^2 -> H(d, U1(b, c))
28.55/9.75	   A^2 -> H(d, U1(b, d))
28.55/9.75	   A^2 -> H(d, U1(c, c))
28.55/9.75	   A^2 -> H(d, f(e))
28.55/9.75	   A^2 -> H(d, f(k))
28.55/9.75	   A^2 -> H(d, U1(d, d))
28.55/9.75	   A^2 -> H(a, U1(e, b))
28.55/9.75	   A^2 -> H(a, U1(k, b))
28.55/9.75	   A^2 -> H(a, U1(c, d))
28.55/9.75	   A^2 -> H(a, U1(d, c))
28.55/9.75	   A^2 -> H(a, U1(b, e))
28.55/9.75	   A^2 -> H(a, U1(b, k))
28.55/9.75	   A^2 -> H(a, U1(e, c))
28.55/9.75	   A^2 -> H(a, U1(k, c))
28.55/9.75	   A^2 -> H(a, U1(c, e))
28.55/9.75	   A^2 -> H(a, U1(c, k))
28.55/9.75	   A^2 -> H(a, U1(e, e))
28.55/9.75	   A^2 -> H(a, U1(k, k))
28.55/9.75	   A^2 -> H(a, U1(k, d))
28.55/9.75	   A^2 -> H(a, U1(d, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.75	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.75	   A^2 -> H(U1(e, a), b)
28.55/9.75	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.75	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.75	   A^2 -> H(U1(e, a), c)
28.55/9.75	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.75	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.75	   A^2 -> H(U1(e, a), e)
28.55/9.75	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, a), b)
28.55/9.75	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.75	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.75	   A^2 -> H(U1(k, a), c)
28.55/9.75	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.75	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.75	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, d), b)
28.55/9.75	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.75	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.75	   A^2 -> H(U1(c, d), c)
28.55/9.75	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.75	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.75	   A^2 -> H(U1(c, d), e)
28.55/9.75	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, a), d)
28.55/9.75	   A^2 -> H(U1(c, a), k)
28.55/9.75	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.75	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.75	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.75	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.75	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.75	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.75	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.75	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.75	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.75	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.75	   A^2 -> H(U1(d, c), b)
28.55/9.75	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.75	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.75	   A^2 -> H(U1(d, c), c)
28.55/9.75	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.75	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.75	   A^2 -> H(U1(d, c), e)
28.55/9.75	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.75	   A^2 -> H(U1(d, a), d)
28.55/9.75	   A^2 -> H(U1(d, a), k)
28.55/9.75	   A^2 -> H(U1(a, e), b)
28.55/9.75	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.75	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.75	   A^2 -> H(U1(a, e), c)
28.55/9.75	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.75	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.75	   A^2 -> H(U1(a, e), e)
28.55/9.75	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(a, k), b)
28.55/9.75	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.75	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.75	   A^2 -> H(U1(a, k), c)
28.55/9.75	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.75	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.75	   A^2 -> H(U1(a, k), e)
28.55/9.75	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(a, c), d)
28.55/9.75	   A^2 -> H(U1(a, c), k)
28.55/9.75	   A^2 -> H(U1(a, d), d)
28.55/9.75	   A^2 -> H(U1(a, d), k)
28.55/9.75	   A^2 -> H(k, U1(c, b))
28.55/9.75	   A^2 -> H(k, U1(d, b))
28.55/9.75	   A^2 -> H(k, U1(b, c))
28.55/9.75	   A^2 -> H(k, U1(b, d))
28.55/9.75	   A^2 -> H(k, U1(c, c))
28.55/9.75	   A^2 -> H(k, f(e))
28.55/9.75	   A^2 -> H(k, f(k))
28.55/9.75	   A^2 -> H(k, U1(d, d))
28.55/9.75	   A^2 -> H(c, U1(e, b))
28.55/9.75	   A^2 -> H(c, U1(k, b))
28.55/9.75	   A^2 -> H(c, U1(c, d))
28.55/9.75	   A^2 -> H(c, U1(d, c))
28.55/9.75	   A^2 -> H(c, U1(b, e))
28.55/9.75	   A^2 -> H(c, U1(b, k))
28.55/9.75	   A^2 -> H(c, U1(e, c))
28.55/9.75	   A^2 -> H(c, U1(k, c))
28.55/9.75	   A^2 -> H(c, U1(c, e))
28.55/9.75	   A^2 -> H(c, U1(c, k))
28.55/9.75	   A^2 -> H(c, U1(e, e))
28.55/9.75	   A^2 -> H(c, U1(k, k))
28.55/9.75	   A^2 -> H(c, U1(k, d))
28.55/9.75	   A^2 -> H(c, U1(d, k))
28.55/9.75	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.75	
28.55/9.75	The TRS R consists of the following rules:
28.55/9.75	
28.55/9.75	   f(x) -> U1(x, x)
28.55/9.75	   U1(e, x) -> x
28.55/9.75	   a -> c
28.55/9.75	   a -> d
28.55/9.75	   b -> c
28.55/9.75	   b -> d
28.55/9.75	   d -> k
28.55/9.75	   c -> e
28.55/9.75	   c -> k
28.55/9.75	
28.55/9.75	Q is empty.
28.55/9.75	We have to consider all minimal (P,Q,R)-chains.
28.55/9.75	----------------------------------------
28.55/9.75	
28.55/9.75	(1417) TransformationProof (EQUIVALENT)
28.55/9.75	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), f(e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.75	
28.55/9.75	   (A^2 -> H(k, f(e)),A^2 -> H(k, f(e)))
28.55/9.75	   (A^2 -> H(U1(e, k), U1(e, e)),A^2 -> H(U1(e, k), U1(e, e)))
28.55/9.75	
28.55/9.75	
28.55/9.75	----------------------------------------
28.55/9.75	
28.55/9.75	(1418)
28.55/9.75	Obligation:
28.55/9.75	Q DP problem:
28.55/9.75	The TRS P consists of the following rules:
28.55/9.75	
28.55/9.75	   H(x, x) -> G(x, x, f(k))
28.55/9.75	   G(d, x, x) -> A^2
28.55/9.75	   A^2 -> H(f(c), f(c))
28.55/9.75	   A^2 -> H(f(d), f(d))
28.55/9.75	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.75	   A^2 -> H(f(e), f(e))
28.55/9.75	   A^2 -> H(f(k), f(k))
28.55/9.75	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.75	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.75	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, k), f(k))
28.55/9.75	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.75	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.75	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.75	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.75	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.75	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.75	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.75	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.75	   A^2 -> H(U1(k, e), f(e))
28.55/9.75	   A^2 -> H(U1(k, e), f(k))
28.55/9.75	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.75	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.75	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.75	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.75	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.75	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.75	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.75	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.75	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.75	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.75	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.75	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.75	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.75	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.75	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.75	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.75	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.75	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.75	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.75	   A^2 -> H(U1(c, c), b)
28.55/9.75	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.75	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.75	   A^2 -> H(U1(c, c), e)
28.55/9.75	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.75	   A^2 -> H(e, U1(c, b))
28.55/9.75	   A^2 -> H(e, U1(d, b))
28.55/9.75	   A^2 -> H(e, U1(b, c))
28.55/9.75	   A^2 -> H(e, U1(b, d))
28.55/9.75	   A^2 -> H(e, U1(c, c))
28.55/9.75	   A^2 -> H(e, f(e))
28.55/9.75	   A^2 -> H(e, f(k))
28.55/9.75	   A^2 -> H(e, U1(d, d))
28.55/9.75	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.75	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.75	   A^2 -> H(f(e), b)
28.55/9.75	   A^2 -> H(f(e), U1(e, d))
28.55/9.75	   A^2 -> H(f(e), U1(d, e))
28.55/9.75	   A^2 -> H(f(e), c)
28.55/9.75	   A^2 -> H(f(e), U1(e, k))
28.55/9.75	   A^2 -> H(f(e), U1(k, e))
28.55/9.75	   A^2 -> H(f(e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.75	   A^2 -> H(f(k), b)
28.55/9.75	   A^2 -> H(f(k), U1(e, d))
28.55/9.75	   A^2 -> H(f(k), U1(d, e))
28.55/9.75	   A^2 -> H(f(k), c)
28.55/9.75	   A^2 -> H(f(k), U1(e, k))
28.55/9.75	   A^2 -> H(f(k), U1(k, e))
28.55/9.75	   A^2 -> H(f(k), e)
28.55/9.75	   A^2 -> H(f(c), d)
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.75	   A^2 -> H(U1(k, k), f(e))
28.55/9.75	   A^2 -> H(U1(k, k), f(k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.75	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.75	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.75	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.75	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.75	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.75	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.75	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.75	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.75	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.75	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.75	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.75	   A^2 -> H(U1(d, d), b)
28.55/9.75	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.75	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.75	   A^2 -> H(U1(d, d), c)
28.55/9.75	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.75	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.75	   A^2 -> H(U1(d, d), e)
28.55/9.75	   A^2 -> H(f(d), d)
28.55/9.75	   A^2 -> H(f(d), k)
28.55/9.75	   A^2 -> H(U1(c, c), c)
28.55/9.75	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.75	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.75	   A^2 -> H(f(c), k)
28.55/9.75	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.75	   A^2 -> H(f(k), U1(k, k))
28.55/9.75	   A^2 -> H(f(e), e)
28.55/9.75	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.75	   A^2 -> H(d, U1(c, b))
28.55/9.75	   A^2 -> H(d, U1(d, b))
28.55/9.75	   A^2 -> H(d, U1(b, c))
28.55/9.75	   A^2 -> H(d, U1(b, d))
28.55/9.75	   A^2 -> H(d, U1(c, c))
28.55/9.75	   A^2 -> H(d, f(e))
28.55/9.75	   A^2 -> H(d, f(k))
28.55/9.75	   A^2 -> H(d, U1(d, d))
28.55/9.75	   A^2 -> H(a, U1(e, b))
28.55/9.75	   A^2 -> H(a, U1(k, b))
28.55/9.75	   A^2 -> H(a, U1(c, d))
28.55/9.75	   A^2 -> H(a, U1(d, c))
28.55/9.75	   A^2 -> H(a, U1(b, e))
28.55/9.75	   A^2 -> H(a, U1(b, k))
28.55/9.75	   A^2 -> H(a, U1(e, c))
28.55/9.75	   A^2 -> H(a, U1(k, c))
28.55/9.75	   A^2 -> H(a, U1(c, e))
28.55/9.75	   A^2 -> H(a, U1(c, k))
28.55/9.75	   A^2 -> H(a, U1(e, e))
28.55/9.75	   A^2 -> H(a, U1(k, k))
28.55/9.75	   A^2 -> H(a, U1(k, d))
28.55/9.75	   A^2 -> H(a, U1(d, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.75	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.75	   A^2 -> H(U1(e, a), b)
28.55/9.75	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.75	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.75	   A^2 -> H(U1(e, a), c)
28.55/9.75	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.75	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.75	   A^2 -> H(U1(e, a), e)
28.55/9.75	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, a), b)
28.55/9.75	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.75	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.75	   A^2 -> H(U1(k, a), c)
28.55/9.75	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.75	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.75	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, d), b)
28.55/9.75	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.75	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.75	   A^2 -> H(U1(c, d), c)
28.55/9.75	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.75	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.75	   A^2 -> H(U1(c, d), e)
28.55/9.75	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, a), d)
28.55/9.75	   A^2 -> H(U1(c, a), k)
28.55/9.75	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.75	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.75	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.75	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.75	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.75	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.75	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.75	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.75	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.75	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.75	   A^2 -> H(U1(d, c), b)
28.55/9.75	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.75	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.75	   A^2 -> H(U1(d, c), c)
28.55/9.75	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.75	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.75	   A^2 -> H(U1(d, c), e)
28.55/9.75	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.75	   A^2 -> H(U1(d, a), d)
28.55/9.75	   A^2 -> H(U1(d, a), k)
28.55/9.75	   A^2 -> H(U1(a, e), b)
28.55/9.75	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.75	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.75	   A^2 -> H(U1(a, e), c)
28.55/9.75	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.75	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.75	   A^2 -> H(U1(a, e), e)
28.55/9.75	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(a, k), b)
28.55/9.75	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.75	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.75	   A^2 -> H(U1(a, k), c)
28.55/9.75	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.75	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.75	   A^2 -> H(U1(a, k), e)
28.55/9.75	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(a, c), d)
28.55/9.75	   A^2 -> H(U1(a, c), k)
28.55/9.75	   A^2 -> H(U1(a, d), d)
28.55/9.75	   A^2 -> H(U1(a, d), k)
28.55/9.75	   A^2 -> H(k, U1(c, b))
28.55/9.75	   A^2 -> H(k, U1(d, b))
28.55/9.75	   A^2 -> H(k, U1(b, c))
28.55/9.75	   A^2 -> H(k, U1(b, d))
28.55/9.75	   A^2 -> H(k, U1(c, c))
28.55/9.75	   A^2 -> H(k, f(e))
28.55/9.75	   A^2 -> H(k, f(k))
28.55/9.75	   A^2 -> H(k, U1(d, d))
28.55/9.75	   A^2 -> H(c, U1(e, b))
28.55/9.75	   A^2 -> H(c, U1(k, b))
28.55/9.75	   A^2 -> H(c, U1(c, d))
28.55/9.75	   A^2 -> H(c, U1(d, c))
28.55/9.75	   A^2 -> H(c, U1(b, e))
28.55/9.75	   A^2 -> H(c, U1(b, k))
28.55/9.75	   A^2 -> H(c, U1(e, c))
28.55/9.75	   A^2 -> H(c, U1(k, c))
28.55/9.75	   A^2 -> H(c, U1(c, e))
28.55/9.75	   A^2 -> H(c, U1(c, k))
28.55/9.75	   A^2 -> H(c, U1(e, e))
28.55/9.75	   A^2 -> H(c, U1(k, k))
28.55/9.75	   A^2 -> H(c, U1(k, d))
28.55/9.75	   A^2 -> H(c, U1(d, k))
28.55/9.75	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.75	
28.55/9.75	The TRS R consists of the following rules:
28.55/9.75	
28.55/9.75	   f(x) -> U1(x, x)
28.55/9.75	   U1(e, x) -> x
28.55/9.75	   a -> c
28.55/9.75	   a -> d
28.55/9.75	   b -> c
28.55/9.75	   b -> d
28.55/9.75	   d -> k
28.55/9.75	   c -> e
28.55/9.75	   c -> k
28.55/9.75	
28.55/9.75	Q is empty.
28.55/9.75	We have to consider all minimal (P,Q,R)-chains.
28.55/9.75	----------------------------------------
28.55/9.75	
28.55/9.75	(1419) TransformationProof (EQUIVALENT)
28.55/9.75	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), f(k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.75	
28.55/9.75	   (A^2 -> H(k, f(k)),A^2 -> H(k, f(k)))
28.55/9.75	   (A^2 -> H(U1(e, k), U1(k, k)),A^2 -> H(U1(e, k), U1(k, k)))
28.55/9.75	
28.55/9.75	
28.55/9.75	----------------------------------------
28.55/9.75	
28.55/9.75	(1420)
28.55/9.75	Obligation:
28.55/9.75	Q DP problem:
28.55/9.75	The TRS P consists of the following rules:
28.55/9.75	
28.55/9.75	   H(x, x) -> G(x, x, f(k))
28.55/9.75	   G(d, x, x) -> A^2
28.55/9.75	   A^2 -> H(f(c), f(c))
28.55/9.75	   A^2 -> H(f(d), f(d))
28.55/9.75	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.75	   A^2 -> H(f(e), f(e))
28.55/9.75	   A^2 -> H(f(k), f(k))
28.55/9.75	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.75	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.75	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, k), U1(d, d))
28.55/9.75	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.75	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.75	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.75	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.75	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.75	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.75	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.75	   A^2 -> H(U1(k, e), f(e))
28.55/9.75	   A^2 -> H(U1(k, e), f(k))
28.55/9.75	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.75	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.75	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.75	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.75	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.75	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.75	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.75	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.75	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.75	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.75	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.75	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.75	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.75	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.75	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.75	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.75	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.75	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.75	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.75	   A^2 -> H(U1(c, c), b)
28.55/9.75	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.75	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.75	   A^2 -> H(U1(c, c), e)
28.55/9.75	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.75	   A^2 -> H(e, U1(c, b))
28.55/9.75	   A^2 -> H(e, U1(d, b))
28.55/9.75	   A^2 -> H(e, U1(b, c))
28.55/9.75	   A^2 -> H(e, U1(b, d))
28.55/9.75	   A^2 -> H(e, U1(c, c))
28.55/9.75	   A^2 -> H(e, f(e))
28.55/9.75	   A^2 -> H(e, f(k))
28.55/9.75	   A^2 -> H(e, U1(d, d))
28.55/9.75	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.75	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.75	   A^2 -> H(f(e), b)
28.55/9.75	   A^2 -> H(f(e), U1(e, d))
28.55/9.75	   A^2 -> H(f(e), U1(d, e))
28.55/9.75	   A^2 -> H(f(e), c)
28.55/9.75	   A^2 -> H(f(e), U1(e, k))
28.55/9.75	   A^2 -> H(f(e), U1(k, e))
28.55/9.75	   A^2 -> H(f(e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.75	   A^2 -> H(f(k), b)
28.55/9.75	   A^2 -> H(f(k), U1(e, d))
28.55/9.75	   A^2 -> H(f(k), U1(d, e))
28.55/9.75	   A^2 -> H(f(k), c)
28.55/9.75	   A^2 -> H(f(k), U1(e, k))
28.55/9.75	   A^2 -> H(f(k), U1(k, e))
28.55/9.75	   A^2 -> H(f(k), e)
28.55/9.75	   A^2 -> H(f(c), d)
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.75	   A^2 -> H(U1(k, k), f(e))
28.55/9.75	   A^2 -> H(U1(k, k), f(k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.75	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.75	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.75	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.75	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.75	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.75	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.75	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.75	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.75	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.75	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.75	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.75	   A^2 -> H(U1(d, d), b)
28.55/9.75	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.75	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.75	   A^2 -> H(U1(d, d), c)
28.55/9.75	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.75	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.75	   A^2 -> H(U1(d, d), e)
28.55/9.75	   A^2 -> H(f(d), d)
28.55/9.75	   A^2 -> H(f(d), k)
28.55/9.75	   A^2 -> H(U1(c, c), c)
28.55/9.75	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.75	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.75	   A^2 -> H(f(c), k)
28.55/9.75	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.75	   A^2 -> H(f(k), U1(k, k))
28.55/9.75	   A^2 -> H(f(e), e)
28.55/9.75	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.75	   A^2 -> H(d, U1(c, b))
28.55/9.75	   A^2 -> H(d, U1(d, b))
28.55/9.75	   A^2 -> H(d, U1(b, c))
28.55/9.75	   A^2 -> H(d, U1(b, d))
28.55/9.75	   A^2 -> H(d, U1(c, c))
28.55/9.75	   A^2 -> H(d, f(e))
28.55/9.75	   A^2 -> H(d, f(k))
28.55/9.75	   A^2 -> H(d, U1(d, d))
28.55/9.75	   A^2 -> H(a, U1(e, b))
28.55/9.75	   A^2 -> H(a, U1(k, b))
28.55/9.75	   A^2 -> H(a, U1(c, d))
28.55/9.75	   A^2 -> H(a, U1(d, c))
28.55/9.75	   A^2 -> H(a, U1(b, e))
28.55/9.75	   A^2 -> H(a, U1(b, k))
28.55/9.75	   A^2 -> H(a, U1(e, c))
28.55/9.75	   A^2 -> H(a, U1(k, c))
28.55/9.75	   A^2 -> H(a, U1(c, e))
28.55/9.75	   A^2 -> H(a, U1(c, k))
28.55/9.75	   A^2 -> H(a, U1(e, e))
28.55/9.75	   A^2 -> H(a, U1(k, k))
28.55/9.75	   A^2 -> H(a, U1(k, d))
28.55/9.75	   A^2 -> H(a, U1(d, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.75	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.75	   A^2 -> H(U1(e, a), b)
28.55/9.75	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.75	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.75	   A^2 -> H(U1(e, a), c)
28.55/9.75	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.75	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.75	   A^2 -> H(U1(e, a), e)
28.55/9.75	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, a), b)
28.55/9.75	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.75	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.75	   A^2 -> H(U1(k, a), c)
28.55/9.75	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.75	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.75	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, d), b)
28.55/9.75	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.75	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.75	   A^2 -> H(U1(c, d), c)
28.55/9.75	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.75	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.75	   A^2 -> H(U1(c, d), e)
28.55/9.75	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, a), d)
28.55/9.75	   A^2 -> H(U1(c, a), k)
28.55/9.75	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.75	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.75	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.75	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.75	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.75	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.75	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.75	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.75	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.75	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.75	   A^2 -> H(U1(d, c), b)
28.55/9.75	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.75	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.75	   A^2 -> H(U1(d, c), c)
28.55/9.75	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.75	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.75	   A^2 -> H(U1(d, c), e)
28.55/9.75	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.75	   A^2 -> H(U1(d, a), d)
28.55/9.75	   A^2 -> H(U1(d, a), k)
28.55/9.75	   A^2 -> H(U1(a, e), b)
28.55/9.75	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.75	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.75	   A^2 -> H(U1(a, e), c)
28.55/9.75	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.75	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.75	   A^2 -> H(U1(a, e), e)
28.55/9.75	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(a, k), b)
28.55/9.75	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.75	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.75	   A^2 -> H(U1(a, k), c)
28.55/9.75	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.75	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.75	   A^2 -> H(U1(a, k), e)
28.55/9.75	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(a, c), d)
28.55/9.75	   A^2 -> H(U1(a, c), k)
28.55/9.75	   A^2 -> H(U1(a, d), d)
28.55/9.75	   A^2 -> H(U1(a, d), k)
28.55/9.75	   A^2 -> H(k, U1(c, b))
28.55/9.75	   A^2 -> H(k, U1(d, b))
28.55/9.75	   A^2 -> H(k, U1(b, c))
28.55/9.75	   A^2 -> H(k, U1(b, d))
28.55/9.75	   A^2 -> H(k, U1(c, c))
28.55/9.75	   A^2 -> H(k, f(e))
28.55/9.75	   A^2 -> H(k, f(k))
28.55/9.75	   A^2 -> H(k, U1(d, d))
28.55/9.75	   A^2 -> H(c, U1(e, b))
28.55/9.75	   A^2 -> H(c, U1(k, b))
28.55/9.75	   A^2 -> H(c, U1(c, d))
28.55/9.75	   A^2 -> H(c, U1(d, c))
28.55/9.75	   A^2 -> H(c, U1(b, e))
28.55/9.75	   A^2 -> H(c, U1(b, k))
28.55/9.75	   A^2 -> H(c, U1(e, c))
28.55/9.75	   A^2 -> H(c, U1(k, c))
28.55/9.75	   A^2 -> H(c, U1(c, e))
28.55/9.75	   A^2 -> H(c, U1(c, k))
28.55/9.75	   A^2 -> H(c, U1(e, e))
28.55/9.75	   A^2 -> H(c, U1(k, k))
28.55/9.75	   A^2 -> H(c, U1(k, d))
28.55/9.75	   A^2 -> H(c, U1(d, k))
28.55/9.75	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, k), U1(k, k))
28.55/9.75	
28.55/9.75	The TRS R consists of the following rules:
28.55/9.75	
28.55/9.75	   f(x) -> U1(x, x)
28.55/9.75	   U1(e, x) -> x
28.55/9.75	   a -> c
28.55/9.75	   a -> d
28.55/9.75	   b -> c
28.55/9.75	   b -> d
28.55/9.75	   d -> k
28.55/9.75	   c -> e
28.55/9.75	   c -> k
28.55/9.75	
28.55/9.75	Q is empty.
28.55/9.75	We have to consider all minimal (P,Q,R)-chains.
28.55/9.75	----------------------------------------
28.55/9.75	
28.55/9.75	(1421) TransformationProof (EQUIVALENT)
28.55/9.75	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.75	
28.55/9.75	   (A^2 -> H(k, U1(d, d)),A^2 -> H(k, U1(d, d)))
28.55/9.75	   (A^2 -> H(U1(e, k), U1(k, d)),A^2 -> H(U1(e, k), U1(k, d)))
28.55/9.75	   (A^2 -> H(U1(e, k), U1(d, k)),A^2 -> H(U1(e, k), U1(d, k)))
28.55/9.75	
28.55/9.75	
28.55/9.75	----------------------------------------
28.55/9.75	
28.55/9.75	(1422)
28.55/9.75	Obligation:
28.55/9.75	Q DP problem:
28.55/9.75	The TRS P consists of the following rules:
28.55/9.75	
28.55/9.75	   H(x, x) -> G(x, x, f(k))
28.55/9.75	   G(d, x, x) -> A^2
28.55/9.75	   A^2 -> H(f(c), f(c))
28.55/9.75	   A^2 -> H(f(d), f(d))
28.55/9.75	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.75	   A^2 -> H(f(e), f(e))
28.55/9.75	   A^2 -> H(f(k), f(k))
28.55/9.75	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.75	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.75	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.75	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.75	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.75	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.75	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.75	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.75	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.75	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.75	   A^2 -> H(U1(k, e), f(e))
28.55/9.75	   A^2 -> H(U1(k, e), f(k))
28.55/9.75	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.75	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.75	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.75	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.75	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.75	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.75	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.75	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.75	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.75	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.75	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.75	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.75	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.75	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.75	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.75	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.75	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.75	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.75	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.75	   A^2 -> H(U1(c, c), b)
28.55/9.75	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.75	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.75	   A^2 -> H(U1(c, c), e)
28.55/9.75	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.75	   A^2 -> H(e, U1(c, b))
28.55/9.75	   A^2 -> H(e, U1(d, b))
28.55/9.75	   A^2 -> H(e, U1(b, c))
28.55/9.75	   A^2 -> H(e, U1(b, d))
28.55/9.75	   A^2 -> H(e, U1(c, c))
28.55/9.75	   A^2 -> H(e, f(e))
28.55/9.75	   A^2 -> H(e, f(k))
28.55/9.75	   A^2 -> H(e, U1(d, d))
28.55/9.75	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.75	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.75	   A^2 -> H(f(e), b)
28.55/9.75	   A^2 -> H(f(e), U1(e, d))
28.55/9.75	   A^2 -> H(f(e), U1(d, e))
28.55/9.75	   A^2 -> H(f(e), c)
28.55/9.75	   A^2 -> H(f(e), U1(e, k))
28.55/9.75	   A^2 -> H(f(e), U1(k, e))
28.55/9.75	   A^2 -> H(f(e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.75	   A^2 -> H(f(k), b)
28.55/9.75	   A^2 -> H(f(k), U1(e, d))
28.55/9.75	   A^2 -> H(f(k), U1(d, e))
28.55/9.75	   A^2 -> H(f(k), c)
28.55/9.75	   A^2 -> H(f(k), U1(e, k))
28.55/9.75	   A^2 -> H(f(k), U1(k, e))
28.55/9.75	   A^2 -> H(f(k), e)
28.55/9.75	   A^2 -> H(f(c), d)
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.75	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.75	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.75	   A^2 -> H(U1(k, k), f(e))
28.55/9.75	   A^2 -> H(U1(k, k), f(k))
28.55/9.75	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.75	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.75	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.75	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.75	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.75	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.75	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.75	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.75	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.75	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.75	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.75	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.75	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.75	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.75	   A^2 -> H(U1(d, d), b)
28.55/9.75	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.75	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.75	   A^2 -> H(U1(d, d), c)
28.55/9.75	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.75	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.75	   A^2 -> H(U1(d, d), e)
28.55/9.75	   A^2 -> H(f(d), d)
28.55/9.75	   A^2 -> H(f(d), k)
28.55/9.75	   A^2 -> H(U1(c, c), c)
28.55/9.75	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.75	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.75	   A^2 -> H(f(c), k)
28.55/9.75	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.75	   A^2 -> H(f(k), U1(k, k))
28.55/9.75	   A^2 -> H(f(e), e)
28.55/9.75	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.75	   A^2 -> H(d, U1(c, b))
28.55/9.75	   A^2 -> H(d, U1(d, b))
28.55/9.75	   A^2 -> H(d, U1(b, c))
28.55/9.75	   A^2 -> H(d, U1(b, d))
28.55/9.75	   A^2 -> H(d, U1(c, c))
28.55/9.75	   A^2 -> H(d, f(e))
28.55/9.75	   A^2 -> H(d, f(k))
28.55/9.75	   A^2 -> H(d, U1(d, d))
28.55/9.75	   A^2 -> H(a, U1(e, b))
28.55/9.75	   A^2 -> H(a, U1(k, b))
28.55/9.75	   A^2 -> H(a, U1(c, d))
28.55/9.75	   A^2 -> H(a, U1(d, c))
28.55/9.75	   A^2 -> H(a, U1(b, e))
28.55/9.75	   A^2 -> H(a, U1(b, k))
28.55/9.75	   A^2 -> H(a, U1(e, c))
28.55/9.75	   A^2 -> H(a, U1(k, c))
28.55/9.75	   A^2 -> H(a, U1(c, e))
28.55/9.75	   A^2 -> H(a, U1(c, k))
28.55/9.75	   A^2 -> H(a, U1(e, e))
28.55/9.75	   A^2 -> H(a, U1(k, k))
28.55/9.75	   A^2 -> H(a, U1(k, d))
28.55/9.75	   A^2 -> H(a, U1(d, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.75	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.75	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.75	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.75	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.75	   A^2 -> H(U1(e, a), b)
28.55/9.75	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.75	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.75	   A^2 -> H(U1(e, a), c)
28.55/9.75	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.75	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.75	   A^2 -> H(U1(e, a), e)
28.55/9.75	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.75	   A^2 -> H(U1(k, a), b)
28.55/9.75	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.75	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.75	   A^2 -> H(U1(k, a), c)
28.55/9.75	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.75	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.75	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, d), b)
28.55/9.75	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.75	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.75	   A^2 -> H(U1(c, d), c)
28.55/9.75	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.75	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.75	   A^2 -> H(U1(c, d), e)
28.55/9.75	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.75	   A^2 -> H(U1(c, a), d)
28.55/9.75	   A^2 -> H(U1(c, a), k)
28.55/9.75	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.75	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.75	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.75	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.75	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.75	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.75	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.75	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.75	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.75	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.75	   A^2 -> H(U1(d, c), b)
28.55/9.75	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.75	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.75	   A^2 -> H(U1(d, c), c)
28.55/9.75	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.75	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.75	   A^2 -> H(U1(d, c), e)
28.55/9.75	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.75	   A^2 -> H(U1(d, a), d)
28.55/9.75	   A^2 -> H(U1(d, a), k)
28.55/9.75	   A^2 -> H(U1(a, e), b)
28.55/9.75	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.75	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.75	   A^2 -> H(U1(a, e), c)
28.55/9.75	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.75	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.75	   A^2 -> H(U1(a, e), e)
28.55/9.75	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.75	   A^2 -> H(U1(a, k), b)
28.55/9.75	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.75	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.75	   A^2 -> H(U1(a, k), c)
28.55/9.75	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.75	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.75	   A^2 -> H(U1(a, k), e)
28.55/9.75	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.75	   A^2 -> H(U1(a, c), d)
28.55/9.75	   A^2 -> H(U1(a, c), k)
28.55/9.75	   A^2 -> H(U1(a, d), d)
28.55/9.75	   A^2 -> H(U1(a, d), k)
28.55/9.75	   A^2 -> H(k, U1(c, b))
28.55/9.75	   A^2 -> H(k, U1(d, b))
28.55/9.75	   A^2 -> H(k, U1(b, c))
28.55/9.75	   A^2 -> H(k, U1(b, d))
28.55/9.75	   A^2 -> H(k, U1(c, c))
28.55/9.75	   A^2 -> H(k, f(e))
28.55/9.75	   A^2 -> H(k, f(k))
28.55/9.75	   A^2 -> H(k, U1(d, d))
28.55/9.75	   A^2 -> H(c, U1(e, b))
28.55/9.75	   A^2 -> H(c, U1(k, b))
28.55/9.75	   A^2 -> H(c, U1(c, d))
28.55/9.75	   A^2 -> H(c, U1(d, c))
28.55/9.75	   A^2 -> H(c, U1(b, e))
28.55/9.75	   A^2 -> H(c, U1(b, k))
28.55/9.75	   A^2 -> H(c, U1(e, c))
28.55/9.75	   A^2 -> H(c, U1(k, c))
28.55/9.75	   A^2 -> H(c, U1(c, e))
28.55/9.75	   A^2 -> H(c, U1(c, k))
28.55/9.75	   A^2 -> H(c, U1(e, e))
28.55/9.75	   A^2 -> H(c, U1(k, k))
28.55/9.75	   A^2 -> H(c, U1(k, d))
28.55/9.75	   A^2 -> H(c, U1(d, k))
28.55/9.75	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.75	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.75	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.75	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.75	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.75	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.75	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, k), U1(d, k))
28.55/9.76	
28.55/9.76	The TRS R consists of the following rules:
28.55/9.76	
28.55/9.76	   f(x) -> U1(x, x)
28.55/9.76	   U1(e, x) -> x
28.55/9.76	   a -> c
28.55/9.76	   a -> d
28.55/9.76	   b -> c
28.55/9.76	   b -> d
28.55/9.76	   d -> k
28.55/9.76	   c -> e
28.55/9.76	   c -> k
28.55/9.76	
28.55/9.76	Q is empty.
28.55/9.76	We have to consider all minimal (P,Q,R)-chains.
28.55/9.76	----------------------------------------
28.55/9.76	
28.55/9.76	(1423) TransformationProof (EQUIVALENT)
28.55/9.76	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.76	
28.55/9.76	   (A^2 -> H(c, U1(e, b)),A^2 -> H(c, U1(e, b)))
28.55/9.76	   (A^2 -> H(U1(e, e), U1(e, b)),A^2 -> H(U1(e, e), U1(e, b)))
28.55/9.76	   (A^2 -> H(U1(e, k), U1(e, b)),A^2 -> H(U1(e, k), U1(e, b)))
28.55/9.76	   (A^2 -> H(U1(e, c), b),A^2 -> H(U1(e, c), b))
28.55/9.76	   (A^2 -> H(U1(e, c), U1(e, c)),A^2 -> H(U1(e, c), U1(e, c)))
28.55/9.76	   (A^2 -> H(U1(e, c), U1(e, d)),A^2 -> H(U1(e, c), U1(e, d)))
28.55/9.76	
28.55/9.76	
28.55/9.76	----------------------------------------
28.55/9.76	
28.55/9.76	(1424)
28.55/9.76	Obligation:
28.55/9.76	Q DP problem:
28.55/9.76	The TRS P consists of the following rules:
28.55/9.76	
28.55/9.76	   H(x, x) -> G(x, x, f(k))
28.55/9.76	   G(d, x, x) -> A^2
28.55/9.76	   A^2 -> H(f(c), f(c))
28.55/9.76	   A^2 -> H(f(d), f(d))
28.55/9.76	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.76	   A^2 -> H(f(e), f(e))
28.55/9.76	   A^2 -> H(f(k), f(k))
28.55/9.76	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.76	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.76	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, b))
28.55/9.76	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.76	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.76	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.76	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.76	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.76	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.76	   A^2 -> H(U1(k, e), f(e))
28.55/9.76	   A^2 -> H(U1(k, e), f(k))
28.55/9.76	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.76	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.76	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.76	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.76	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.76	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.76	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.76	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.76	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.76	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.76	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.76	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.76	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.76	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.76	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.76	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.76	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.76	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.76	   A^2 -> H(U1(c, c), b)
28.55/9.76	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.76	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.76	   A^2 -> H(U1(c, c), e)
28.55/9.76	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.76	   A^2 -> H(e, U1(c, b))
28.55/9.76	   A^2 -> H(e, U1(d, b))
28.55/9.76	   A^2 -> H(e, U1(b, c))
28.55/9.76	   A^2 -> H(e, U1(b, d))
28.55/9.76	   A^2 -> H(e, U1(c, c))
28.55/9.76	   A^2 -> H(e, f(e))
28.55/9.76	   A^2 -> H(e, f(k))
28.55/9.76	   A^2 -> H(e, U1(d, d))
28.55/9.76	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.76	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.76	   A^2 -> H(f(e), b)
28.55/9.76	   A^2 -> H(f(e), U1(e, d))
28.55/9.76	   A^2 -> H(f(e), U1(d, e))
28.55/9.76	   A^2 -> H(f(e), c)
28.55/9.76	   A^2 -> H(f(e), U1(e, k))
28.55/9.76	   A^2 -> H(f(e), U1(k, e))
28.55/9.76	   A^2 -> H(f(e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.76	   A^2 -> H(f(k), b)
28.55/9.76	   A^2 -> H(f(k), U1(e, d))
28.55/9.76	   A^2 -> H(f(k), U1(d, e))
28.55/9.76	   A^2 -> H(f(k), c)
28.55/9.76	   A^2 -> H(f(k), U1(e, k))
28.55/9.76	   A^2 -> H(f(k), U1(k, e))
28.55/9.76	   A^2 -> H(f(k), e)
28.55/9.76	   A^2 -> H(f(c), d)
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.76	   A^2 -> H(U1(k, k), f(e))
28.55/9.76	   A^2 -> H(U1(k, k), f(k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.76	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.76	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.76	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.76	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.76	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.76	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.76	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.76	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.76	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.76	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.76	   A^2 -> H(U1(d, d), b)
28.55/9.76	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.76	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.76	   A^2 -> H(U1(d, d), c)
28.55/9.76	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.76	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.76	   A^2 -> H(U1(d, d), e)
28.55/9.76	   A^2 -> H(f(d), d)
28.55/9.76	   A^2 -> H(f(d), k)
28.55/9.76	   A^2 -> H(U1(c, c), c)
28.55/9.76	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.76	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.76	   A^2 -> H(f(c), k)
28.55/9.76	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.76	   A^2 -> H(f(k), U1(k, k))
28.55/9.76	   A^2 -> H(f(e), e)
28.55/9.76	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.76	   A^2 -> H(d, U1(c, b))
28.55/9.76	   A^2 -> H(d, U1(d, b))
28.55/9.76	   A^2 -> H(d, U1(b, c))
28.55/9.76	   A^2 -> H(d, U1(b, d))
28.55/9.76	   A^2 -> H(d, U1(c, c))
28.55/9.76	   A^2 -> H(d, f(e))
28.55/9.76	   A^2 -> H(d, f(k))
28.55/9.76	   A^2 -> H(d, U1(d, d))
28.55/9.76	   A^2 -> H(a, U1(e, b))
28.55/9.76	   A^2 -> H(a, U1(k, b))
28.55/9.76	   A^2 -> H(a, U1(c, d))
28.55/9.76	   A^2 -> H(a, U1(d, c))
28.55/9.76	   A^2 -> H(a, U1(b, e))
28.55/9.76	   A^2 -> H(a, U1(b, k))
28.55/9.76	   A^2 -> H(a, U1(e, c))
28.55/9.76	   A^2 -> H(a, U1(k, c))
28.55/9.76	   A^2 -> H(a, U1(c, e))
28.55/9.76	   A^2 -> H(a, U1(c, k))
28.55/9.76	   A^2 -> H(a, U1(e, e))
28.55/9.76	   A^2 -> H(a, U1(k, k))
28.55/9.76	   A^2 -> H(a, U1(k, d))
28.55/9.76	   A^2 -> H(a, U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.76	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, a), b)
28.55/9.76	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.76	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.76	   A^2 -> H(U1(e, a), c)
28.55/9.76	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.76	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.76	   A^2 -> H(U1(e, a), e)
28.55/9.76	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, a), b)
28.55/9.76	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.76	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.76	   A^2 -> H(U1(k, a), c)
28.55/9.76	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.76	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.76	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, d), b)
28.55/9.76	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.76	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.76	   A^2 -> H(U1(c, d), c)
28.55/9.76	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.76	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.76	   A^2 -> H(U1(c, d), e)
28.55/9.76	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, a), d)
28.55/9.76	   A^2 -> H(U1(c, a), k)
28.55/9.76	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.76	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.76	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.76	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.76	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.76	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.76	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.76	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.76	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.76	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.76	   A^2 -> H(U1(d, c), b)
28.55/9.76	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.76	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.76	   A^2 -> H(U1(d, c), c)
28.55/9.76	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.76	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.76	   A^2 -> H(U1(d, c), e)
28.55/9.76	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.76	   A^2 -> H(U1(d, a), d)
28.55/9.76	   A^2 -> H(U1(d, a), k)
28.55/9.76	   A^2 -> H(U1(a, e), b)
28.55/9.76	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.76	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.76	   A^2 -> H(U1(a, e), c)
28.55/9.76	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.76	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.76	   A^2 -> H(U1(a, e), e)
28.55/9.76	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(a, k), b)
28.55/9.76	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.76	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.76	   A^2 -> H(U1(a, k), c)
28.55/9.76	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.76	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.76	   A^2 -> H(U1(a, k), e)
28.55/9.76	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(a, c), d)
28.55/9.76	   A^2 -> H(U1(a, c), k)
28.55/9.76	   A^2 -> H(U1(a, d), d)
28.55/9.76	   A^2 -> H(U1(a, d), k)
28.55/9.76	   A^2 -> H(k, U1(c, b))
28.55/9.76	   A^2 -> H(k, U1(d, b))
28.55/9.76	   A^2 -> H(k, U1(b, c))
28.55/9.76	   A^2 -> H(k, U1(b, d))
28.55/9.76	   A^2 -> H(k, U1(c, c))
28.55/9.76	   A^2 -> H(k, f(e))
28.55/9.76	   A^2 -> H(k, f(k))
28.55/9.76	   A^2 -> H(k, U1(d, d))
28.55/9.76	   A^2 -> H(c, U1(e, b))
28.55/9.76	   A^2 -> H(c, U1(k, b))
28.55/9.76	   A^2 -> H(c, U1(c, d))
28.55/9.76	   A^2 -> H(c, U1(d, c))
28.55/9.76	   A^2 -> H(c, U1(b, e))
28.55/9.76	   A^2 -> H(c, U1(b, k))
28.55/9.76	   A^2 -> H(c, U1(e, c))
28.55/9.76	   A^2 -> H(c, U1(k, c))
28.55/9.76	   A^2 -> H(c, U1(c, e))
28.55/9.76	   A^2 -> H(c, U1(c, k))
28.55/9.76	   A^2 -> H(c, U1(e, e))
28.55/9.76	   A^2 -> H(c, U1(k, k))
28.55/9.76	   A^2 -> H(c, U1(k, d))
28.55/9.76	   A^2 -> H(c, U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, k), U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, c), b)
28.55/9.76	   A^2 -> H(U1(e, c), U1(e, d))
28.55/9.76	
28.55/9.76	The TRS R consists of the following rules:
28.55/9.76	
28.55/9.76	   f(x) -> U1(x, x)
28.55/9.76	   U1(e, x) -> x
28.55/9.76	   a -> c
28.55/9.76	   a -> d
28.55/9.76	   b -> c
28.55/9.76	   b -> d
28.55/9.76	   d -> k
28.55/9.76	   c -> e
28.55/9.76	   c -> k
28.55/9.76	
28.55/9.76	Q is empty.
28.55/9.76	We have to consider all minimal (P,Q,R)-chains.
28.55/9.76	----------------------------------------
28.55/9.76	
28.55/9.76	(1425) TransformationProof (EQUIVALENT)
28.55/9.76	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.76	
28.55/9.76	   (A^2 -> H(c, U1(k, b)),A^2 -> H(c, U1(k, b)))
28.55/9.76	   (A^2 -> H(U1(e, e), U1(k, b)),A^2 -> H(U1(e, e), U1(k, b)))
28.55/9.76	   (A^2 -> H(U1(e, k), U1(k, b)),A^2 -> H(U1(e, k), U1(k, b)))
28.55/9.76	   (A^2 -> H(U1(e, c), U1(k, c)),A^2 -> H(U1(e, c), U1(k, c)))
28.55/9.76	   (A^2 -> H(U1(e, c), U1(k, d)),A^2 -> H(U1(e, c), U1(k, d)))
28.55/9.76	
28.55/9.76	
28.55/9.76	----------------------------------------
28.55/9.76	
28.55/9.76	(1426)
28.55/9.76	Obligation:
28.55/9.76	Q DP problem:
28.55/9.76	The TRS P consists of the following rules:
28.55/9.76	
28.55/9.76	   H(x, x) -> G(x, x, f(k))
28.55/9.76	   G(d, x, x) -> A^2
28.55/9.76	   A^2 -> H(f(c), f(c))
28.55/9.76	   A^2 -> H(f(d), f(d))
28.55/9.76	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.76	   A^2 -> H(f(e), f(e))
28.55/9.76	   A^2 -> H(f(k), f(k))
28.55/9.76	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.76	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.76	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.76	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.76	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.76	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.76	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.76	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.76	   A^2 -> H(U1(k, e), f(e))
28.55/9.76	   A^2 -> H(U1(k, e), f(k))
28.55/9.76	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.76	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.76	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.76	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.76	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.76	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.76	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.76	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.76	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.76	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.76	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.76	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.76	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.76	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.76	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.76	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.76	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.76	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.76	   A^2 -> H(U1(c, c), b)
28.55/9.76	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.76	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.76	   A^2 -> H(U1(c, c), e)
28.55/9.76	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.76	   A^2 -> H(e, U1(c, b))
28.55/9.76	   A^2 -> H(e, U1(d, b))
28.55/9.76	   A^2 -> H(e, U1(b, c))
28.55/9.76	   A^2 -> H(e, U1(b, d))
28.55/9.76	   A^2 -> H(e, U1(c, c))
28.55/9.76	   A^2 -> H(e, f(e))
28.55/9.76	   A^2 -> H(e, f(k))
28.55/9.76	   A^2 -> H(e, U1(d, d))
28.55/9.76	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.76	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.76	   A^2 -> H(f(e), b)
28.55/9.76	   A^2 -> H(f(e), U1(e, d))
28.55/9.76	   A^2 -> H(f(e), U1(d, e))
28.55/9.76	   A^2 -> H(f(e), c)
28.55/9.76	   A^2 -> H(f(e), U1(e, k))
28.55/9.76	   A^2 -> H(f(e), U1(k, e))
28.55/9.76	   A^2 -> H(f(e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.76	   A^2 -> H(f(k), b)
28.55/9.76	   A^2 -> H(f(k), U1(e, d))
28.55/9.76	   A^2 -> H(f(k), U1(d, e))
28.55/9.76	   A^2 -> H(f(k), c)
28.55/9.76	   A^2 -> H(f(k), U1(e, k))
28.55/9.76	   A^2 -> H(f(k), U1(k, e))
28.55/9.76	   A^2 -> H(f(k), e)
28.55/9.76	   A^2 -> H(f(c), d)
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.76	   A^2 -> H(U1(k, k), f(e))
28.55/9.76	   A^2 -> H(U1(k, k), f(k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.76	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.76	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.76	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.76	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.76	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.76	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.76	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.76	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.76	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.76	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.76	   A^2 -> H(U1(d, d), b)
28.55/9.76	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.76	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.76	   A^2 -> H(U1(d, d), c)
28.55/9.76	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.76	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.76	   A^2 -> H(U1(d, d), e)
28.55/9.76	   A^2 -> H(f(d), d)
28.55/9.76	   A^2 -> H(f(d), k)
28.55/9.76	   A^2 -> H(U1(c, c), c)
28.55/9.76	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.76	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.76	   A^2 -> H(f(c), k)
28.55/9.76	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.76	   A^2 -> H(f(k), U1(k, k))
28.55/9.76	   A^2 -> H(f(e), e)
28.55/9.76	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.76	   A^2 -> H(d, U1(c, b))
28.55/9.76	   A^2 -> H(d, U1(d, b))
28.55/9.76	   A^2 -> H(d, U1(b, c))
28.55/9.76	   A^2 -> H(d, U1(b, d))
28.55/9.76	   A^2 -> H(d, U1(c, c))
28.55/9.76	   A^2 -> H(d, f(e))
28.55/9.76	   A^2 -> H(d, f(k))
28.55/9.76	   A^2 -> H(d, U1(d, d))
28.55/9.76	   A^2 -> H(a, U1(e, b))
28.55/9.76	   A^2 -> H(a, U1(k, b))
28.55/9.76	   A^2 -> H(a, U1(c, d))
28.55/9.76	   A^2 -> H(a, U1(d, c))
28.55/9.76	   A^2 -> H(a, U1(b, e))
28.55/9.76	   A^2 -> H(a, U1(b, k))
28.55/9.76	   A^2 -> H(a, U1(e, c))
28.55/9.76	   A^2 -> H(a, U1(k, c))
28.55/9.76	   A^2 -> H(a, U1(c, e))
28.55/9.76	   A^2 -> H(a, U1(c, k))
28.55/9.76	   A^2 -> H(a, U1(e, e))
28.55/9.76	   A^2 -> H(a, U1(k, k))
28.55/9.76	   A^2 -> H(a, U1(k, d))
28.55/9.76	   A^2 -> H(a, U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.76	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, a), b)
28.55/9.76	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.76	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.76	   A^2 -> H(U1(e, a), c)
28.55/9.76	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.76	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.76	   A^2 -> H(U1(e, a), e)
28.55/9.76	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, a), b)
28.55/9.76	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.76	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.76	   A^2 -> H(U1(k, a), c)
28.55/9.76	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.76	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.76	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, d), b)
28.55/9.76	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.76	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.76	   A^2 -> H(U1(c, d), c)
28.55/9.76	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.76	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.76	   A^2 -> H(U1(c, d), e)
28.55/9.76	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, a), d)
28.55/9.76	   A^2 -> H(U1(c, a), k)
28.55/9.76	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.76	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.76	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.76	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.76	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.76	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.76	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.76	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.76	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.76	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.76	   A^2 -> H(U1(d, c), b)
28.55/9.76	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.76	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.76	   A^2 -> H(U1(d, c), c)
28.55/9.76	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.76	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.76	   A^2 -> H(U1(d, c), e)
28.55/9.76	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.76	   A^2 -> H(U1(d, a), d)
28.55/9.76	   A^2 -> H(U1(d, a), k)
28.55/9.76	   A^2 -> H(U1(a, e), b)
28.55/9.76	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.76	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.76	   A^2 -> H(U1(a, e), c)
28.55/9.76	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.76	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.76	   A^2 -> H(U1(a, e), e)
28.55/9.76	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(a, k), b)
28.55/9.76	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.76	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.76	   A^2 -> H(U1(a, k), c)
28.55/9.76	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.76	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.76	   A^2 -> H(U1(a, k), e)
28.55/9.76	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(a, c), d)
28.55/9.76	   A^2 -> H(U1(a, c), k)
28.55/9.76	   A^2 -> H(U1(a, d), d)
28.55/9.76	   A^2 -> H(U1(a, d), k)
28.55/9.76	   A^2 -> H(k, U1(c, b))
28.55/9.76	   A^2 -> H(k, U1(d, b))
28.55/9.76	   A^2 -> H(k, U1(b, c))
28.55/9.76	   A^2 -> H(k, U1(b, d))
28.55/9.76	   A^2 -> H(k, U1(c, c))
28.55/9.76	   A^2 -> H(k, f(e))
28.55/9.76	   A^2 -> H(k, f(k))
28.55/9.76	   A^2 -> H(k, U1(d, d))
28.55/9.76	   A^2 -> H(c, U1(e, b))
28.55/9.76	   A^2 -> H(c, U1(k, b))
28.55/9.76	   A^2 -> H(c, U1(c, d))
28.55/9.76	   A^2 -> H(c, U1(d, c))
28.55/9.76	   A^2 -> H(c, U1(b, e))
28.55/9.76	   A^2 -> H(c, U1(b, k))
28.55/9.76	   A^2 -> H(c, U1(e, c))
28.55/9.76	   A^2 -> H(c, U1(k, c))
28.55/9.76	   A^2 -> H(c, U1(c, e))
28.55/9.76	   A^2 -> H(c, U1(c, k))
28.55/9.76	   A^2 -> H(c, U1(e, e))
28.55/9.76	   A^2 -> H(c, U1(k, k))
28.55/9.76	   A^2 -> H(c, U1(k, d))
28.55/9.76	   A^2 -> H(c, U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, k), U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, c), b)
28.55/9.76	   A^2 -> H(U1(e, c), U1(e, d))
28.55/9.76	
28.55/9.76	The TRS R consists of the following rules:
28.55/9.76	
28.55/9.76	   f(x) -> U1(x, x)
28.55/9.76	   U1(e, x) -> x
28.55/9.76	   a -> c
28.55/9.76	   a -> d
28.55/9.76	   b -> c
28.55/9.76	   b -> d
28.55/9.76	   d -> k
28.55/9.76	   c -> e
28.55/9.76	   c -> k
28.55/9.76	
28.55/9.76	Q is empty.
28.55/9.76	We have to consider all minimal (P,Q,R)-chains.
28.55/9.76	----------------------------------------
28.55/9.76	
28.55/9.76	(1427) TransformationProof (EQUIVALENT)
28.55/9.76	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.76	
28.55/9.76	   (A^2 -> H(c, U1(c, d)),A^2 -> H(c, U1(c, d)))
28.55/9.76	   (A^2 -> H(U1(e, e), U1(c, d)),A^2 -> H(U1(e, e), U1(c, d)))
28.55/9.76	   (A^2 -> H(U1(e, k), U1(c, d)),A^2 -> H(U1(e, k), U1(c, d)))
28.55/9.76	   (A^2 -> H(U1(e, c), U1(e, d)),A^2 -> H(U1(e, c), U1(e, d)))
28.55/9.76	   (A^2 -> H(U1(e, c), U1(k, d)),A^2 -> H(U1(e, c), U1(k, d)))
28.55/9.76	   (A^2 -> H(U1(e, c), U1(c, k)),A^2 -> H(U1(e, c), U1(c, k)))
28.55/9.76	
28.55/9.76	
28.55/9.76	----------------------------------------
28.55/9.76	
28.55/9.76	(1428)
28.55/9.76	Obligation:
28.55/9.76	Q DP problem:
28.55/9.76	The TRS P consists of the following rules:
28.55/9.76	
28.55/9.76	   H(x, x) -> G(x, x, f(k))
28.55/9.76	   G(d, x, x) -> A^2
28.55/9.76	   A^2 -> H(f(c), f(c))
28.55/9.76	   A^2 -> H(f(d), f(d))
28.55/9.76	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.76	   A^2 -> H(f(e), f(e))
28.55/9.76	   A^2 -> H(f(k), f(k))
28.55/9.76	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.76	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.76	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.76	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.76	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.76	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.76	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.76	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.76	   A^2 -> H(U1(k, e), f(e))
28.55/9.76	   A^2 -> H(U1(k, e), f(k))
28.55/9.76	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.76	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.76	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.76	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.76	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.76	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.76	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.76	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.76	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.76	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.76	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.76	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.76	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.76	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.76	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.76	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.76	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.76	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.76	   A^2 -> H(U1(c, c), b)
28.55/9.76	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.76	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.76	   A^2 -> H(U1(c, c), e)
28.55/9.76	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.76	   A^2 -> H(e, U1(c, b))
28.55/9.76	   A^2 -> H(e, U1(d, b))
28.55/9.76	   A^2 -> H(e, U1(b, c))
28.55/9.76	   A^2 -> H(e, U1(b, d))
28.55/9.76	   A^2 -> H(e, U1(c, c))
28.55/9.76	   A^2 -> H(e, f(e))
28.55/9.76	   A^2 -> H(e, f(k))
28.55/9.76	   A^2 -> H(e, U1(d, d))
28.55/9.76	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.76	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.76	   A^2 -> H(f(e), b)
28.55/9.76	   A^2 -> H(f(e), U1(e, d))
28.55/9.76	   A^2 -> H(f(e), U1(d, e))
28.55/9.76	   A^2 -> H(f(e), c)
28.55/9.76	   A^2 -> H(f(e), U1(e, k))
28.55/9.76	   A^2 -> H(f(e), U1(k, e))
28.55/9.76	   A^2 -> H(f(e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.76	   A^2 -> H(f(k), b)
28.55/9.76	   A^2 -> H(f(k), U1(e, d))
28.55/9.76	   A^2 -> H(f(k), U1(d, e))
28.55/9.76	   A^2 -> H(f(k), c)
28.55/9.76	   A^2 -> H(f(k), U1(e, k))
28.55/9.76	   A^2 -> H(f(k), U1(k, e))
28.55/9.76	   A^2 -> H(f(k), e)
28.55/9.76	   A^2 -> H(f(c), d)
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.76	   A^2 -> H(U1(k, k), f(e))
28.55/9.76	   A^2 -> H(U1(k, k), f(k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.76	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.76	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.76	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.76	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.76	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.76	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.76	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.76	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.76	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.76	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.76	   A^2 -> H(U1(d, d), b)
28.55/9.76	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.76	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.76	   A^2 -> H(U1(d, d), c)
28.55/9.76	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.76	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.76	   A^2 -> H(U1(d, d), e)
28.55/9.76	   A^2 -> H(f(d), d)
28.55/9.76	   A^2 -> H(f(d), k)
28.55/9.76	   A^2 -> H(U1(c, c), c)
28.55/9.76	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.76	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.76	   A^2 -> H(f(c), k)
28.55/9.76	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.76	   A^2 -> H(f(k), U1(k, k))
28.55/9.76	   A^2 -> H(f(e), e)
28.55/9.76	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.76	   A^2 -> H(d, U1(c, b))
28.55/9.76	   A^2 -> H(d, U1(d, b))
28.55/9.76	   A^2 -> H(d, U1(b, c))
28.55/9.76	   A^2 -> H(d, U1(b, d))
28.55/9.76	   A^2 -> H(d, U1(c, c))
28.55/9.76	   A^2 -> H(d, f(e))
28.55/9.76	   A^2 -> H(d, f(k))
28.55/9.76	   A^2 -> H(d, U1(d, d))
28.55/9.76	   A^2 -> H(a, U1(e, b))
28.55/9.76	   A^2 -> H(a, U1(k, b))
28.55/9.76	   A^2 -> H(a, U1(c, d))
28.55/9.76	   A^2 -> H(a, U1(d, c))
28.55/9.76	   A^2 -> H(a, U1(b, e))
28.55/9.76	   A^2 -> H(a, U1(b, k))
28.55/9.76	   A^2 -> H(a, U1(e, c))
28.55/9.76	   A^2 -> H(a, U1(k, c))
28.55/9.76	   A^2 -> H(a, U1(c, e))
28.55/9.76	   A^2 -> H(a, U1(c, k))
28.55/9.76	   A^2 -> H(a, U1(e, e))
28.55/9.76	   A^2 -> H(a, U1(k, k))
28.55/9.76	   A^2 -> H(a, U1(k, d))
28.55/9.76	   A^2 -> H(a, U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.76	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, a), b)
28.55/9.76	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.76	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.76	   A^2 -> H(U1(e, a), c)
28.55/9.76	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.76	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.76	   A^2 -> H(U1(e, a), e)
28.55/9.76	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, a), b)
28.55/9.76	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.76	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.76	   A^2 -> H(U1(k, a), c)
28.55/9.76	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.76	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.76	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, d), b)
28.55/9.76	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.76	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.76	   A^2 -> H(U1(c, d), c)
28.55/9.76	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.76	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.76	   A^2 -> H(U1(c, d), e)
28.55/9.76	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, a), d)
28.55/9.76	   A^2 -> H(U1(c, a), k)
28.55/9.76	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.76	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.76	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.76	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.76	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.76	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.76	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.76	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.76	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.76	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.76	   A^2 -> H(U1(d, c), b)
28.55/9.76	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.76	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.76	   A^2 -> H(U1(d, c), c)
28.55/9.76	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.76	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.76	   A^2 -> H(U1(d, c), e)
28.55/9.76	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.76	   A^2 -> H(U1(d, a), d)
28.55/9.76	   A^2 -> H(U1(d, a), k)
28.55/9.76	   A^2 -> H(U1(a, e), b)
28.55/9.76	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.76	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.76	   A^2 -> H(U1(a, e), c)
28.55/9.76	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.76	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.76	   A^2 -> H(U1(a, e), e)
28.55/9.76	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(a, k), b)
28.55/9.76	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.76	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.76	   A^2 -> H(U1(a, k), c)
28.55/9.76	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.76	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.76	   A^2 -> H(U1(a, k), e)
28.55/9.76	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(a, c), d)
28.55/9.76	   A^2 -> H(U1(a, c), k)
28.55/9.76	   A^2 -> H(U1(a, d), d)
28.55/9.76	   A^2 -> H(U1(a, d), k)
28.55/9.76	   A^2 -> H(k, U1(c, b))
28.55/9.76	   A^2 -> H(k, U1(d, b))
28.55/9.76	   A^2 -> H(k, U1(b, c))
28.55/9.76	   A^2 -> H(k, U1(b, d))
28.55/9.76	   A^2 -> H(k, U1(c, c))
28.55/9.76	   A^2 -> H(k, f(e))
28.55/9.76	   A^2 -> H(k, f(k))
28.55/9.76	   A^2 -> H(k, U1(d, d))
28.55/9.76	   A^2 -> H(c, U1(e, b))
28.55/9.76	   A^2 -> H(c, U1(k, b))
28.55/9.76	   A^2 -> H(c, U1(c, d))
28.55/9.76	   A^2 -> H(c, U1(d, c))
28.55/9.76	   A^2 -> H(c, U1(b, e))
28.55/9.76	   A^2 -> H(c, U1(b, k))
28.55/9.76	   A^2 -> H(c, U1(e, c))
28.55/9.76	   A^2 -> H(c, U1(k, c))
28.55/9.76	   A^2 -> H(c, U1(c, e))
28.55/9.76	   A^2 -> H(c, U1(c, k))
28.55/9.76	   A^2 -> H(c, U1(e, e))
28.55/9.76	   A^2 -> H(c, U1(k, k))
28.55/9.76	   A^2 -> H(c, U1(k, d))
28.55/9.76	   A^2 -> H(c, U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, k), U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, c), b)
28.55/9.76	   A^2 -> H(U1(e, c), U1(e, d))
28.55/9.76	
28.55/9.76	The TRS R consists of the following rules:
28.55/9.76	
28.55/9.76	   f(x) -> U1(x, x)
28.55/9.76	   U1(e, x) -> x
28.55/9.76	   a -> c
28.55/9.76	   a -> d
28.55/9.76	   b -> c
28.55/9.76	   b -> d
28.55/9.76	   d -> k
28.55/9.76	   c -> e
28.55/9.76	   c -> k
28.55/9.76	
28.55/9.76	Q is empty.
28.55/9.76	We have to consider all minimal (P,Q,R)-chains.
28.55/9.76	----------------------------------------
28.55/9.76	
28.55/9.76	(1429) TransformationProof (EQUIVALENT)
28.55/9.76	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.76	
28.55/9.76	   (A^2 -> H(c, U1(d, c)),A^2 -> H(c, U1(d, c)))
28.55/9.76	   (A^2 -> H(U1(e, e), U1(d, c)),A^2 -> H(U1(e, e), U1(d, c)))
28.55/9.76	   (A^2 -> H(U1(e, k), U1(d, c)),A^2 -> H(U1(e, k), U1(d, c)))
28.55/9.76	   (A^2 -> H(U1(e, c), U1(k, c)),A^2 -> H(U1(e, c), U1(k, c)))
28.55/9.76	   (A^2 -> H(U1(e, c), U1(d, e)),A^2 -> H(U1(e, c), U1(d, e)))
28.55/9.76	   (A^2 -> H(U1(e, c), U1(d, k)),A^2 -> H(U1(e, c), U1(d, k)))
28.55/9.76	
28.55/9.76	
28.55/9.76	----------------------------------------
28.55/9.76	
28.55/9.76	(1430)
28.55/9.76	Obligation:
28.55/9.76	Q DP problem:
28.55/9.76	The TRS P consists of the following rules:
28.55/9.76	
28.55/9.76	   H(x, x) -> G(x, x, f(k))
28.55/9.76	   G(d, x, x) -> A^2
28.55/9.76	   A^2 -> H(f(c), f(c))
28.55/9.76	   A^2 -> H(f(d), f(d))
28.55/9.76	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.76	   A^2 -> H(f(e), f(e))
28.55/9.76	   A^2 -> H(f(k), f(k))
28.55/9.76	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.76	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.76	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.76	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.76	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.76	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.76	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.76	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.76	   A^2 -> H(U1(k, e), f(e))
28.55/9.76	   A^2 -> H(U1(k, e), f(k))
28.55/9.76	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.76	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.76	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.76	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.76	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.76	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.76	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.76	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.76	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.76	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.76	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.76	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.76	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.76	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.76	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.76	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.76	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.76	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.76	   A^2 -> H(U1(c, c), b)
28.55/9.76	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.76	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.76	   A^2 -> H(U1(c, c), e)
28.55/9.76	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.76	   A^2 -> H(e, U1(c, b))
28.55/9.76	   A^2 -> H(e, U1(d, b))
28.55/9.76	   A^2 -> H(e, U1(b, c))
28.55/9.76	   A^2 -> H(e, U1(b, d))
28.55/9.76	   A^2 -> H(e, U1(c, c))
28.55/9.76	   A^2 -> H(e, f(e))
28.55/9.76	   A^2 -> H(e, f(k))
28.55/9.76	   A^2 -> H(e, U1(d, d))
28.55/9.76	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.76	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.76	   A^2 -> H(f(e), b)
28.55/9.76	   A^2 -> H(f(e), U1(e, d))
28.55/9.76	   A^2 -> H(f(e), U1(d, e))
28.55/9.76	   A^2 -> H(f(e), c)
28.55/9.76	   A^2 -> H(f(e), U1(e, k))
28.55/9.76	   A^2 -> H(f(e), U1(k, e))
28.55/9.76	   A^2 -> H(f(e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.76	   A^2 -> H(f(k), b)
28.55/9.76	   A^2 -> H(f(k), U1(e, d))
28.55/9.76	   A^2 -> H(f(k), U1(d, e))
28.55/9.76	   A^2 -> H(f(k), c)
28.55/9.76	   A^2 -> H(f(k), U1(e, k))
28.55/9.76	   A^2 -> H(f(k), U1(k, e))
28.55/9.76	   A^2 -> H(f(k), e)
28.55/9.76	   A^2 -> H(f(c), d)
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.76	   A^2 -> H(U1(k, k), f(e))
28.55/9.76	   A^2 -> H(U1(k, k), f(k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.76	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.76	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.76	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.76	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.76	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.76	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.76	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.76	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.76	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.76	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.76	   A^2 -> H(U1(d, d), b)
28.55/9.76	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.76	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.76	   A^2 -> H(U1(d, d), c)
28.55/9.76	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.76	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.76	   A^2 -> H(U1(d, d), e)
28.55/9.76	   A^2 -> H(f(d), d)
28.55/9.76	   A^2 -> H(f(d), k)
28.55/9.76	   A^2 -> H(U1(c, c), c)
28.55/9.76	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.76	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.76	   A^2 -> H(f(c), k)
28.55/9.76	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.76	   A^2 -> H(f(k), U1(k, k))
28.55/9.76	   A^2 -> H(f(e), e)
28.55/9.76	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.76	   A^2 -> H(d, U1(c, b))
28.55/9.76	   A^2 -> H(d, U1(d, b))
28.55/9.76	   A^2 -> H(d, U1(b, c))
28.55/9.76	   A^2 -> H(d, U1(b, d))
28.55/9.76	   A^2 -> H(d, U1(c, c))
28.55/9.76	   A^2 -> H(d, f(e))
28.55/9.76	   A^2 -> H(d, f(k))
28.55/9.76	   A^2 -> H(d, U1(d, d))
28.55/9.76	   A^2 -> H(a, U1(e, b))
28.55/9.76	   A^2 -> H(a, U1(k, b))
28.55/9.76	   A^2 -> H(a, U1(c, d))
28.55/9.76	   A^2 -> H(a, U1(d, c))
28.55/9.76	   A^2 -> H(a, U1(b, e))
28.55/9.76	   A^2 -> H(a, U1(b, k))
28.55/9.76	   A^2 -> H(a, U1(e, c))
28.55/9.76	   A^2 -> H(a, U1(k, c))
28.55/9.76	   A^2 -> H(a, U1(c, e))
28.55/9.76	   A^2 -> H(a, U1(c, k))
28.55/9.76	   A^2 -> H(a, U1(e, e))
28.55/9.76	   A^2 -> H(a, U1(k, k))
28.55/9.76	   A^2 -> H(a, U1(k, d))
28.55/9.76	   A^2 -> H(a, U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.76	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, a), b)
28.55/9.76	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.76	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.76	   A^2 -> H(U1(e, a), c)
28.55/9.76	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.76	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.76	   A^2 -> H(U1(e, a), e)
28.55/9.76	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, a), b)
28.55/9.76	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.76	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.76	   A^2 -> H(U1(k, a), c)
28.55/9.76	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.76	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.76	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, d), b)
28.55/9.76	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.76	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.76	   A^2 -> H(U1(c, d), c)
28.55/9.76	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.76	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.76	   A^2 -> H(U1(c, d), e)
28.55/9.76	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, a), d)
28.55/9.76	   A^2 -> H(U1(c, a), k)
28.55/9.76	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.76	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.76	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.76	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.76	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.76	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.76	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.76	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.76	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.76	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.76	   A^2 -> H(U1(d, c), b)
28.55/9.76	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.76	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.76	   A^2 -> H(U1(d, c), c)
28.55/9.76	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.76	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.76	   A^2 -> H(U1(d, c), e)
28.55/9.76	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.76	   A^2 -> H(U1(d, a), d)
28.55/9.76	   A^2 -> H(U1(d, a), k)
28.55/9.76	   A^2 -> H(U1(a, e), b)
28.55/9.76	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.76	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.76	   A^2 -> H(U1(a, e), c)
28.55/9.76	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.76	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.76	   A^2 -> H(U1(a, e), e)
28.55/9.76	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(a, k), b)
28.55/9.76	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.76	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.76	   A^2 -> H(U1(a, k), c)
28.55/9.76	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.76	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.76	   A^2 -> H(U1(a, k), e)
28.55/9.76	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(a, c), d)
28.55/9.76	   A^2 -> H(U1(a, c), k)
28.55/9.76	   A^2 -> H(U1(a, d), d)
28.55/9.76	   A^2 -> H(U1(a, d), k)
28.55/9.76	   A^2 -> H(k, U1(c, b))
28.55/9.76	   A^2 -> H(k, U1(d, b))
28.55/9.76	   A^2 -> H(k, U1(b, c))
28.55/9.76	   A^2 -> H(k, U1(b, d))
28.55/9.76	   A^2 -> H(k, U1(c, c))
28.55/9.76	   A^2 -> H(k, f(e))
28.55/9.76	   A^2 -> H(k, f(k))
28.55/9.76	   A^2 -> H(k, U1(d, d))
28.55/9.76	   A^2 -> H(c, U1(e, b))
28.55/9.76	   A^2 -> H(c, U1(k, b))
28.55/9.76	   A^2 -> H(c, U1(c, d))
28.55/9.76	   A^2 -> H(c, U1(d, c))
28.55/9.76	   A^2 -> H(c, U1(b, e))
28.55/9.76	   A^2 -> H(c, U1(b, k))
28.55/9.76	   A^2 -> H(c, U1(e, c))
28.55/9.76	   A^2 -> H(c, U1(k, c))
28.55/9.76	   A^2 -> H(c, U1(c, e))
28.55/9.76	   A^2 -> H(c, U1(c, k))
28.55/9.76	   A^2 -> H(c, U1(e, e))
28.55/9.76	   A^2 -> H(c, U1(k, k))
28.55/9.76	   A^2 -> H(c, U1(k, d))
28.55/9.76	   A^2 -> H(c, U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, k), U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, c), b)
28.55/9.76	   A^2 -> H(U1(e, c), U1(e, d))
28.55/9.76	   A^2 -> H(U1(e, c), U1(d, e))
28.55/9.76	
28.55/9.76	The TRS R consists of the following rules:
28.55/9.76	
28.55/9.76	   f(x) -> U1(x, x)
28.55/9.76	   U1(e, x) -> x
28.55/9.76	   a -> c
28.55/9.76	   a -> d
28.55/9.76	   b -> c
28.55/9.76	   b -> d
28.55/9.76	   d -> k
28.55/9.76	   c -> e
28.55/9.76	   c -> k
28.55/9.76	
28.55/9.76	Q is empty.
28.55/9.76	We have to consider all minimal (P,Q,R)-chains.
28.55/9.76	----------------------------------------
28.55/9.76	
28.55/9.76	(1431) TransformationProof (EQUIVALENT)
28.55/9.76	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.76	
28.55/9.76	   (A^2 -> H(c, U1(b, e)),A^2 -> H(c, U1(b, e)))
28.55/9.76	   (A^2 -> H(U1(e, e), U1(b, e)),A^2 -> H(U1(e, e), U1(b, e)))
28.55/9.76	   (A^2 -> H(U1(e, k), U1(b, e)),A^2 -> H(U1(e, k), U1(b, e)))
28.55/9.76	   (A^2 -> H(U1(e, c), U1(c, e)),A^2 -> H(U1(e, c), U1(c, e)))
28.55/9.76	   (A^2 -> H(U1(e, c), U1(d, e)),A^2 -> H(U1(e, c), U1(d, e)))
28.55/9.76	
28.55/9.76	
28.55/9.76	----------------------------------------
28.55/9.76	
28.55/9.76	(1432)
28.55/9.76	Obligation:
28.55/9.76	Q DP problem:
28.55/9.76	The TRS P consists of the following rules:
28.55/9.76	
28.55/9.76	   H(x, x) -> G(x, x, f(k))
28.55/9.76	   G(d, x, x) -> A^2
28.55/9.76	   A^2 -> H(f(c), f(c))
28.55/9.76	   A^2 -> H(f(d), f(d))
28.55/9.76	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.76	   A^2 -> H(f(e), f(e))
28.55/9.76	   A^2 -> H(f(k), f(k))
28.55/9.76	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.76	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.76	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.76	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.76	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.76	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.76	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.76	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.76	   A^2 -> H(U1(k, e), f(e))
28.55/9.76	   A^2 -> H(U1(k, e), f(k))
28.55/9.76	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.76	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.76	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.76	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.76	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.76	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.76	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.76	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.76	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.76	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.76	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.76	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.76	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.76	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.76	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.76	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.76	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.76	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.76	   A^2 -> H(U1(c, c), b)
28.55/9.76	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.76	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.76	   A^2 -> H(U1(c, c), e)
28.55/9.76	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.76	   A^2 -> H(e, U1(c, b))
28.55/9.76	   A^2 -> H(e, U1(d, b))
28.55/9.76	   A^2 -> H(e, U1(b, c))
28.55/9.76	   A^2 -> H(e, U1(b, d))
28.55/9.76	   A^2 -> H(e, U1(c, c))
28.55/9.76	   A^2 -> H(e, f(e))
28.55/9.76	   A^2 -> H(e, f(k))
28.55/9.76	   A^2 -> H(e, U1(d, d))
28.55/9.76	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.76	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.76	   A^2 -> H(f(e), b)
28.55/9.76	   A^2 -> H(f(e), U1(e, d))
28.55/9.76	   A^2 -> H(f(e), U1(d, e))
28.55/9.76	   A^2 -> H(f(e), c)
28.55/9.76	   A^2 -> H(f(e), U1(e, k))
28.55/9.76	   A^2 -> H(f(e), U1(k, e))
28.55/9.76	   A^2 -> H(f(e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.76	   A^2 -> H(f(k), b)
28.55/9.76	   A^2 -> H(f(k), U1(e, d))
28.55/9.76	   A^2 -> H(f(k), U1(d, e))
28.55/9.76	   A^2 -> H(f(k), c)
28.55/9.76	   A^2 -> H(f(k), U1(e, k))
28.55/9.76	   A^2 -> H(f(k), U1(k, e))
28.55/9.76	   A^2 -> H(f(k), e)
28.55/9.76	   A^2 -> H(f(c), d)
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.76	   A^2 -> H(U1(k, k), f(e))
28.55/9.76	   A^2 -> H(U1(k, k), f(k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.76	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.76	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.76	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.76	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.76	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.76	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.76	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.76	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.76	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.76	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.76	   A^2 -> H(U1(d, d), b)
28.55/9.76	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.76	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.76	   A^2 -> H(U1(d, d), c)
28.55/9.76	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.76	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.76	   A^2 -> H(U1(d, d), e)
28.55/9.76	   A^2 -> H(f(d), d)
28.55/9.76	   A^2 -> H(f(d), k)
28.55/9.76	   A^2 -> H(U1(c, c), c)
28.55/9.76	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.76	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.76	   A^2 -> H(f(c), k)
28.55/9.76	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.76	   A^2 -> H(f(k), U1(k, k))
28.55/9.76	   A^2 -> H(f(e), e)
28.55/9.76	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.76	   A^2 -> H(d, U1(c, b))
28.55/9.76	   A^2 -> H(d, U1(d, b))
28.55/9.76	   A^2 -> H(d, U1(b, c))
28.55/9.76	   A^2 -> H(d, U1(b, d))
28.55/9.76	   A^2 -> H(d, U1(c, c))
28.55/9.76	   A^2 -> H(d, f(e))
28.55/9.76	   A^2 -> H(d, f(k))
28.55/9.76	   A^2 -> H(d, U1(d, d))
28.55/9.76	   A^2 -> H(a, U1(e, b))
28.55/9.76	   A^2 -> H(a, U1(k, b))
28.55/9.76	   A^2 -> H(a, U1(c, d))
28.55/9.76	   A^2 -> H(a, U1(d, c))
28.55/9.76	   A^2 -> H(a, U1(b, e))
28.55/9.76	   A^2 -> H(a, U1(b, k))
28.55/9.76	   A^2 -> H(a, U1(e, c))
28.55/9.76	   A^2 -> H(a, U1(k, c))
28.55/9.76	   A^2 -> H(a, U1(c, e))
28.55/9.76	   A^2 -> H(a, U1(c, k))
28.55/9.76	   A^2 -> H(a, U1(e, e))
28.55/9.76	   A^2 -> H(a, U1(k, k))
28.55/9.76	   A^2 -> H(a, U1(k, d))
28.55/9.76	   A^2 -> H(a, U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.76	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, a), b)
28.55/9.76	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.76	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.76	   A^2 -> H(U1(e, a), c)
28.55/9.76	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.76	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.76	   A^2 -> H(U1(e, a), e)
28.55/9.76	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, a), b)
28.55/9.76	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.76	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.76	   A^2 -> H(U1(k, a), c)
28.55/9.76	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.76	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.76	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, d), b)
28.55/9.76	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.76	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.76	   A^2 -> H(U1(c, d), c)
28.55/9.76	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.76	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.76	   A^2 -> H(U1(c, d), e)
28.55/9.76	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, a), d)
28.55/9.76	   A^2 -> H(U1(c, a), k)
28.55/9.76	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.76	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.76	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.76	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.76	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.76	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.76	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.76	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.76	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.76	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.76	   A^2 -> H(U1(d, c), b)
28.55/9.76	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.76	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.76	   A^2 -> H(U1(d, c), c)
28.55/9.76	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.76	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.76	   A^2 -> H(U1(d, c), e)
28.55/9.76	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.76	   A^2 -> H(U1(d, a), d)
28.55/9.76	   A^2 -> H(U1(d, a), k)
28.55/9.76	   A^2 -> H(U1(a, e), b)
28.55/9.76	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.76	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.76	   A^2 -> H(U1(a, e), c)
28.55/9.76	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.76	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.76	   A^2 -> H(U1(a, e), e)
28.55/9.76	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(a, k), b)
28.55/9.76	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.76	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.76	   A^2 -> H(U1(a, k), c)
28.55/9.76	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.76	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.76	   A^2 -> H(U1(a, k), e)
28.55/9.76	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(a, c), d)
28.55/9.76	   A^2 -> H(U1(a, c), k)
28.55/9.76	   A^2 -> H(U1(a, d), d)
28.55/9.76	   A^2 -> H(U1(a, d), k)
28.55/9.76	   A^2 -> H(k, U1(c, b))
28.55/9.76	   A^2 -> H(k, U1(d, b))
28.55/9.76	   A^2 -> H(k, U1(b, c))
28.55/9.76	   A^2 -> H(k, U1(b, d))
28.55/9.76	   A^2 -> H(k, U1(c, c))
28.55/9.76	   A^2 -> H(k, f(e))
28.55/9.76	   A^2 -> H(k, f(k))
28.55/9.76	   A^2 -> H(k, U1(d, d))
28.55/9.76	   A^2 -> H(c, U1(e, b))
28.55/9.76	   A^2 -> H(c, U1(k, b))
28.55/9.76	   A^2 -> H(c, U1(c, d))
28.55/9.76	   A^2 -> H(c, U1(d, c))
28.55/9.76	   A^2 -> H(c, U1(b, e))
28.55/9.76	   A^2 -> H(c, U1(b, k))
28.55/9.76	   A^2 -> H(c, U1(e, c))
28.55/9.76	   A^2 -> H(c, U1(k, c))
28.55/9.76	   A^2 -> H(c, U1(c, e))
28.55/9.76	   A^2 -> H(c, U1(c, k))
28.55/9.76	   A^2 -> H(c, U1(e, e))
28.55/9.76	   A^2 -> H(c, U1(k, k))
28.55/9.76	   A^2 -> H(c, U1(k, d))
28.55/9.76	   A^2 -> H(c, U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, k), U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, c), b)
28.55/9.76	   A^2 -> H(U1(e, c), U1(e, d))
28.55/9.76	   A^2 -> H(U1(e, c), U1(d, e))
28.55/9.76	
28.55/9.76	The TRS R consists of the following rules:
28.55/9.76	
28.55/9.76	   f(x) -> U1(x, x)
28.55/9.76	   U1(e, x) -> x
28.55/9.76	   a -> c
28.55/9.76	   a -> d
28.55/9.76	   b -> c
28.55/9.76	   b -> d
28.55/9.76	   d -> k
28.55/9.76	   c -> e
28.55/9.76	   c -> k
28.55/9.76	
28.55/9.76	Q is empty.
28.55/9.76	We have to consider all minimal (P,Q,R)-chains.
28.55/9.76	----------------------------------------
28.55/9.76	
28.55/9.76	(1433) TransformationProof (EQUIVALENT)
28.55/9.76	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.76	
28.55/9.76	   (A^2 -> H(c, U1(b, k)),A^2 -> H(c, U1(b, k)))
28.55/9.76	   (A^2 -> H(U1(e, e), U1(b, k)),A^2 -> H(U1(e, e), U1(b, k)))
28.55/9.76	   (A^2 -> H(U1(e, k), U1(b, k)),A^2 -> H(U1(e, k), U1(b, k)))
28.55/9.76	   (A^2 -> H(U1(e, c), U1(c, k)),A^2 -> H(U1(e, c), U1(c, k)))
28.55/9.76	   (A^2 -> H(U1(e, c), U1(d, k)),A^2 -> H(U1(e, c), U1(d, k)))
28.55/9.76	
28.55/9.76	
28.55/9.76	----------------------------------------
28.55/9.76	
28.55/9.76	(1434)
28.55/9.76	Obligation:
28.55/9.76	Q DP problem:
28.55/9.76	The TRS P consists of the following rules:
28.55/9.76	
28.55/9.76	   H(x, x) -> G(x, x, f(k))
28.55/9.76	   G(d, x, x) -> A^2
28.55/9.76	   A^2 -> H(f(c), f(c))
28.55/9.76	   A^2 -> H(f(d), f(d))
28.55/9.76	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.76	   A^2 -> H(f(e), f(e))
28.55/9.76	   A^2 -> H(f(k), f(k))
28.55/9.76	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.76	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.76	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.76	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.76	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.76	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.76	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.76	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.76	   A^2 -> H(U1(k, e), f(e))
28.55/9.76	   A^2 -> H(U1(k, e), f(k))
28.55/9.76	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.76	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.76	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.76	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.76	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.76	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.76	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.76	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.76	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.76	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.76	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.76	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.76	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.76	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.76	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.76	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.76	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.76	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.76	   A^2 -> H(U1(c, c), b)
28.55/9.76	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.76	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.76	   A^2 -> H(U1(c, c), e)
28.55/9.76	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.76	   A^2 -> H(e, U1(c, b))
28.55/9.76	   A^2 -> H(e, U1(d, b))
28.55/9.76	   A^2 -> H(e, U1(b, c))
28.55/9.76	   A^2 -> H(e, U1(b, d))
28.55/9.76	   A^2 -> H(e, U1(c, c))
28.55/9.76	   A^2 -> H(e, f(e))
28.55/9.76	   A^2 -> H(e, f(k))
28.55/9.76	   A^2 -> H(e, U1(d, d))
28.55/9.76	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.76	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.76	   A^2 -> H(f(e), b)
28.55/9.76	   A^2 -> H(f(e), U1(e, d))
28.55/9.76	   A^2 -> H(f(e), U1(d, e))
28.55/9.76	   A^2 -> H(f(e), c)
28.55/9.76	   A^2 -> H(f(e), U1(e, k))
28.55/9.76	   A^2 -> H(f(e), U1(k, e))
28.55/9.76	   A^2 -> H(f(e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.76	   A^2 -> H(f(k), b)
28.55/9.76	   A^2 -> H(f(k), U1(e, d))
28.55/9.76	   A^2 -> H(f(k), U1(d, e))
28.55/9.76	   A^2 -> H(f(k), c)
28.55/9.76	   A^2 -> H(f(k), U1(e, k))
28.55/9.76	   A^2 -> H(f(k), U1(k, e))
28.55/9.76	   A^2 -> H(f(k), e)
28.55/9.76	   A^2 -> H(f(c), d)
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.76	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.76	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.76	   A^2 -> H(U1(k, k), f(e))
28.55/9.76	   A^2 -> H(U1(k, k), f(k))
28.55/9.76	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.76	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.76	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.76	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.76	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.76	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.76	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.76	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.76	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.76	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.76	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.76	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.76	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.76	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.76	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.76	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.76	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.76	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.76	   A^2 -> H(U1(d, d), b)
28.55/9.76	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.76	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.76	   A^2 -> H(U1(d, d), c)
28.55/9.76	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.76	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.76	   A^2 -> H(U1(d, d), e)
28.55/9.76	   A^2 -> H(f(d), d)
28.55/9.76	   A^2 -> H(f(d), k)
28.55/9.76	   A^2 -> H(U1(c, c), c)
28.55/9.76	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.76	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.76	   A^2 -> H(f(c), k)
28.55/9.76	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.76	   A^2 -> H(f(k), U1(k, k))
28.55/9.76	   A^2 -> H(f(e), e)
28.55/9.76	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.76	   A^2 -> H(d, U1(c, b))
28.55/9.76	   A^2 -> H(d, U1(d, b))
28.55/9.76	   A^2 -> H(d, U1(b, c))
28.55/9.76	   A^2 -> H(d, U1(b, d))
28.55/9.76	   A^2 -> H(d, U1(c, c))
28.55/9.76	   A^2 -> H(d, f(e))
28.55/9.76	   A^2 -> H(d, f(k))
28.55/9.76	   A^2 -> H(d, U1(d, d))
28.55/9.76	   A^2 -> H(a, U1(e, b))
28.55/9.76	   A^2 -> H(a, U1(k, b))
28.55/9.76	   A^2 -> H(a, U1(c, d))
28.55/9.76	   A^2 -> H(a, U1(d, c))
28.55/9.76	   A^2 -> H(a, U1(b, e))
28.55/9.76	   A^2 -> H(a, U1(b, k))
28.55/9.76	   A^2 -> H(a, U1(e, c))
28.55/9.76	   A^2 -> H(a, U1(k, c))
28.55/9.76	   A^2 -> H(a, U1(c, e))
28.55/9.76	   A^2 -> H(a, U1(c, k))
28.55/9.76	   A^2 -> H(a, U1(e, e))
28.55/9.76	   A^2 -> H(a, U1(k, k))
28.55/9.76	   A^2 -> H(a, U1(k, d))
28.55/9.76	   A^2 -> H(a, U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.76	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.76	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.76	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.76	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.76	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.76	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.76	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.76	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.76	   A^2 -> H(U1(e, a), b)
28.55/9.76	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.76	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.76	   A^2 -> H(U1(e, a), c)
28.55/9.76	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.76	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.76	   A^2 -> H(U1(e, a), e)
28.55/9.76	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.76	   A^2 -> H(U1(k, a), b)
28.55/9.76	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.76	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.76	   A^2 -> H(U1(k, a), c)
28.55/9.76	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.76	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.76	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, d), b)
28.55/9.76	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.76	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.76	   A^2 -> H(U1(c, d), c)
28.55/9.76	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.76	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.76	   A^2 -> H(U1(c, d), e)
28.55/9.76	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.76	   A^2 -> H(U1(c, a), d)
28.55/9.76	   A^2 -> H(U1(c, a), k)
28.55/9.76	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.76	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.76	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.76	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.76	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.76	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.76	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.76	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.76	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.76	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.76	   A^2 -> H(U1(d, c), b)
28.55/9.76	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.76	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.76	   A^2 -> H(U1(d, c), c)
28.55/9.76	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.76	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.76	   A^2 -> H(U1(d, c), e)
28.55/9.76	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.76	   A^2 -> H(U1(d, a), d)
28.55/9.76	   A^2 -> H(U1(d, a), k)
28.55/9.76	   A^2 -> H(U1(a, e), b)
28.55/9.76	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.76	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.76	   A^2 -> H(U1(a, e), c)
28.55/9.76	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.76	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.76	   A^2 -> H(U1(a, e), e)
28.55/9.76	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.76	   A^2 -> H(U1(a, k), b)
28.55/9.76	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.76	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.76	   A^2 -> H(U1(a, k), c)
28.55/9.76	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.76	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.76	   A^2 -> H(U1(a, k), e)
28.55/9.76	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.76	   A^2 -> H(U1(a, c), d)
28.55/9.76	   A^2 -> H(U1(a, c), k)
28.55/9.76	   A^2 -> H(U1(a, d), d)
28.55/9.76	   A^2 -> H(U1(a, d), k)
28.55/9.76	   A^2 -> H(k, U1(c, b))
28.55/9.77	   A^2 -> H(k, U1(d, b))
28.55/9.77	   A^2 -> H(k, U1(b, c))
28.55/9.77	   A^2 -> H(k, U1(b, d))
28.55/9.77	   A^2 -> H(k, U1(c, c))
28.55/9.77	   A^2 -> H(k, f(e))
28.55/9.77	   A^2 -> H(k, f(k))
28.55/9.77	   A^2 -> H(k, U1(d, d))
28.55/9.77	   A^2 -> H(c, U1(e, b))
28.55/9.77	   A^2 -> H(c, U1(k, b))
28.55/9.77	   A^2 -> H(c, U1(c, d))
28.55/9.77	   A^2 -> H(c, U1(d, c))
28.55/9.77	   A^2 -> H(c, U1(b, e))
28.55/9.77	   A^2 -> H(c, U1(b, k))
28.55/9.77	   A^2 -> H(c, U1(e, c))
28.55/9.77	   A^2 -> H(c, U1(k, c))
28.55/9.77	   A^2 -> H(c, U1(c, e))
28.55/9.77	   A^2 -> H(c, U1(c, k))
28.55/9.77	   A^2 -> H(c, U1(e, e))
28.55/9.77	   A^2 -> H(c, U1(k, k))
28.55/9.77	   A^2 -> H(c, U1(k, d))
28.55/9.77	   A^2 -> H(c, U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, k), U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, c), b)
28.55/9.77	   A^2 -> H(U1(e, c), U1(e, d))
28.55/9.77	   A^2 -> H(U1(e, c), U1(d, e))
28.55/9.77	
28.55/9.77	The TRS R consists of the following rules:
28.55/9.77	
28.55/9.77	   f(x) -> U1(x, x)
28.55/9.77	   U1(e, x) -> x
28.55/9.77	   a -> c
28.55/9.77	   a -> d
28.55/9.77	   b -> c
28.55/9.77	   b -> d
28.55/9.77	   d -> k
28.55/9.77	   c -> e
28.55/9.77	   c -> k
28.55/9.77	
28.55/9.77	Q is empty.
28.55/9.77	We have to consider all minimal (P,Q,R)-chains.
28.55/9.77	----------------------------------------
28.55/9.77	
28.55/9.77	(1435) TransformationProof (EQUIVALENT)
28.55/9.77	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.77	
28.55/9.77	   (A^2 -> H(c, U1(k, c)),A^2 -> H(c, U1(k, c)))
28.55/9.77	   (A^2 -> H(U1(e, e), U1(k, c)),A^2 -> H(U1(e, e), U1(k, c)))
28.55/9.77	   (A^2 -> H(U1(e, k), U1(k, c)),A^2 -> H(U1(e, k), U1(k, c)))
28.55/9.77	   (A^2 -> H(U1(e, c), U1(k, e)),A^2 -> H(U1(e, c), U1(k, e)))
28.55/9.77	   (A^2 -> H(U1(e, c), U1(k, k)),A^2 -> H(U1(e, c), U1(k, k)))
28.55/9.77	
28.55/9.77	
28.55/9.77	----------------------------------------
28.55/9.77	
28.55/9.77	(1436)
28.55/9.77	Obligation:
28.55/9.77	Q DP problem:
28.55/9.77	The TRS P consists of the following rules:
28.55/9.77	
28.55/9.77	   H(x, x) -> G(x, x, f(k))
28.55/9.77	   G(d, x, x) -> A^2
28.55/9.77	   A^2 -> H(f(c), f(c))
28.55/9.77	   A^2 -> H(f(d), f(d))
28.55/9.77	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.77	   A^2 -> H(f(e), f(e))
28.55/9.77	   A^2 -> H(f(k), f(k))
28.55/9.77	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.77	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.77	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, c), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.77	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.77	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.77	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.77	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.77	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.77	   A^2 -> H(U1(k, e), f(e))
28.55/9.77	   A^2 -> H(U1(k, e), f(k))
28.55/9.77	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.77	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.77	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.77	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.77	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.77	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.77	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.77	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.77	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.77	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.77	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.77	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.77	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.77	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.77	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.77	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.77	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.77	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.77	   A^2 -> H(U1(c, c), b)
28.55/9.77	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.77	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.77	   A^2 -> H(U1(c, c), e)
28.55/9.77	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.77	   A^2 -> H(e, U1(c, b))
28.55/9.77	   A^2 -> H(e, U1(d, b))
28.55/9.77	   A^2 -> H(e, U1(b, c))
28.55/9.77	   A^2 -> H(e, U1(b, d))
28.55/9.77	   A^2 -> H(e, U1(c, c))
28.55/9.77	   A^2 -> H(e, f(e))
28.55/9.77	   A^2 -> H(e, f(k))
28.55/9.77	   A^2 -> H(e, U1(d, d))
28.55/9.77	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.77	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.77	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.77	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.77	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.77	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.77	   A^2 -> H(f(e), b)
28.55/9.77	   A^2 -> H(f(e), U1(e, d))
28.55/9.77	   A^2 -> H(f(e), U1(d, e))
28.55/9.77	   A^2 -> H(f(e), c)
28.55/9.77	   A^2 -> H(f(e), U1(e, k))
28.55/9.77	   A^2 -> H(f(e), U1(k, e))
28.55/9.77	   A^2 -> H(f(e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.77	   A^2 -> H(f(k), b)
28.55/9.77	   A^2 -> H(f(k), U1(e, d))
28.55/9.77	   A^2 -> H(f(k), U1(d, e))
28.55/9.77	   A^2 -> H(f(k), c)
28.55/9.77	   A^2 -> H(f(k), U1(e, k))
28.55/9.77	   A^2 -> H(f(k), U1(k, e))
28.55/9.77	   A^2 -> H(f(k), e)
28.55/9.77	   A^2 -> H(f(c), d)
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.77	   A^2 -> H(U1(k, k), f(e))
28.55/9.77	   A^2 -> H(U1(k, k), f(k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.77	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.77	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.77	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.77	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.77	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.77	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.77	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.77	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.77	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.77	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.77	   A^2 -> H(U1(d, d), b)
28.55/9.77	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.77	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.77	   A^2 -> H(U1(d, d), c)
28.55/9.77	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.77	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.77	   A^2 -> H(U1(d, d), e)
28.55/9.77	   A^2 -> H(f(d), d)
28.55/9.77	   A^2 -> H(f(d), k)
28.55/9.77	   A^2 -> H(U1(c, c), c)
28.55/9.77	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.77	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.77	   A^2 -> H(f(c), k)
28.55/9.77	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.77	   A^2 -> H(f(k), U1(k, k))
28.55/9.77	   A^2 -> H(f(e), e)
28.55/9.77	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.77	   A^2 -> H(d, U1(c, b))
28.55/9.77	   A^2 -> H(d, U1(d, b))
28.55/9.77	   A^2 -> H(d, U1(b, c))
28.55/9.77	   A^2 -> H(d, U1(b, d))
28.55/9.77	   A^2 -> H(d, U1(c, c))
28.55/9.77	   A^2 -> H(d, f(e))
28.55/9.77	   A^2 -> H(d, f(k))
28.55/9.77	   A^2 -> H(d, U1(d, d))
28.55/9.77	   A^2 -> H(a, U1(e, b))
28.55/9.77	   A^2 -> H(a, U1(k, b))
28.55/9.77	   A^2 -> H(a, U1(c, d))
28.55/9.77	   A^2 -> H(a, U1(d, c))
28.55/9.77	   A^2 -> H(a, U1(b, e))
28.55/9.77	   A^2 -> H(a, U1(b, k))
28.55/9.77	   A^2 -> H(a, U1(e, c))
28.55/9.77	   A^2 -> H(a, U1(k, c))
28.55/9.77	   A^2 -> H(a, U1(c, e))
28.55/9.77	   A^2 -> H(a, U1(c, k))
28.55/9.77	   A^2 -> H(a, U1(e, e))
28.55/9.77	   A^2 -> H(a, U1(k, k))
28.55/9.77	   A^2 -> H(a, U1(k, d))
28.55/9.77	   A^2 -> H(a, U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.77	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.77	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.77	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.77	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, a), b)
28.55/9.77	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.77	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.77	   A^2 -> H(U1(e, a), c)
28.55/9.77	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.77	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.77	   A^2 -> H(U1(e, a), e)
28.55/9.77	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, a), b)
28.55/9.77	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.77	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.77	   A^2 -> H(U1(k, a), c)
28.55/9.77	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.77	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.77	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, d), b)
28.55/9.77	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.77	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.77	   A^2 -> H(U1(c, d), c)
28.55/9.77	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.77	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.77	   A^2 -> H(U1(c, d), e)
28.55/9.77	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, a), d)
28.55/9.77	   A^2 -> H(U1(c, a), k)
28.55/9.77	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.77	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.77	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.77	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.77	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.77	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.77	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.77	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.77	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.77	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.77	   A^2 -> H(U1(d, c), b)
28.55/9.77	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.77	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.77	   A^2 -> H(U1(d, c), c)
28.55/9.77	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.77	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.77	   A^2 -> H(U1(d, c), e)
28.55/9.77	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.77	   A^2 -> H(U1(d, a), d)
28.55/9.77	   A^2 -> H(U1(d, a), k)
28.55/9.77	   A^2 -> H(U1(a, e), b)
28.55/9.77	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.77	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.77	   A^2 -> H(U1(a, e), c)
28.55/9.77	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.77	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.77	   A^2 -> H(U1(a, e), e)
28.55/9.77	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(a, k), b)
28.55/9.77	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.77	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.77	   A^2 -> H(U1(a, k), c)
28.55/9.77	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.77	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.77	   A^2 -> H(U1(a, k), e)
28.55/9.77	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(a, c), d)
28.55/9.77	   A^2 -> H(U1(a, c), k)
28.55/9.77	   A^2 -> H(U1(a, d), d)
28.55/9.77	   A^2 -> H(U1(a, d), k)
28.55/9.77	   A^2 -> H(k, U1(c, b))
28.55/9.77	   A^2 -> H(k, U1(d, b))
28.55/9.77	   A^2 -> H(k, U1(b, c))
28.55/9.77	   A^2 -> H(k, U1(b, d))
28.55/9.77	   A^2 -> H(k, U1(c, c))
28.55/9.77	   A^2 -> H(k, f(e))
28.55/9.77	   A^2 -> H(k, f(k))
28.55/9.77	   A^2 -> H(k, U1(d, d))
28.55/9.77	   A^2 -> H(c, U1(e, b))
28.55/9.77	   A^2 -> H(c, U1(k, b))
28.55/9.77	   A^2 -> H(c, U1(c, d))
28.55/9.77	   A^2 -> H(c, U1(d, c))
28.55/9.77	   A^2 -> H(c, U1(b, e))
28.55/9.77	   A^2 -> H(c, U1(b, k))
28.55/9.77	   A^2 -> H(c, U1(e, c))
28.55/9.77	   A^2 -> H(c, U1(k, c))
28.55/9.77	   A^2 -> H(c, U1(c, e))
28.55/9.77	   A^2 -> H(c, U1(c, k))
28.55/9.77	   A^2 -> H(c, U1(e, e))
28.55/9.77	   A^2 -> H(c, U1(k, k))
28.55/9.77	   A^2 -> H(c, U1(k, d))
28.55/9.77	   A^2 -> H(c, U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, k), U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, c), b)
28.55/9.77	   A^2 -> H(U1(e, c), U1(e, d))
28.55/9.77	   A^2 -> H(U1(e, c), U1(d, e))
28.55/9.77	   A^2 -> H(U1(e, c), U1(k, e))
28.55/9.77	
28.55/9.77	The TRS R consists of the following rules:
28.55/9.77	
28.55/9.77	   f(x) -> U1(x, x)
28.55/9.77	   U1(e, x) -> x
28.55/9.77	   a -> c
28.55/9.77	   a -> d
28.55/9.77	   b -> c
28.55/9.77	   b -> d
28.55/9.77	   d -> k
28.55/9.77	   c -> e
28.55/9.77	   c -> k
28.55/9.77	
28.55/9.77	Q is empty.
28.55/9.77	We have to consider all minimal (P,Q,R)-chains.
28.55/9.77	----------------------------------------
28.55/9.77	
28.55/9.77	(1437) TransformationProof (EQUIVALENT)
28.55/9.77	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.77	
28.55/9.77	   (A^2 -> H(c, U1(c, e)),A^2 -> H(c, U1(c, e)))
28.55/9.77	   (A^2 -> H(U1(e, e), U1(c, e)),A^2 -> H(U1(e, e), U1(c, e)))
28.55/9.77	   (A^2 -> H(U1(e, k), U1(c, e)),A^2 -> H(U1(e, k), U1(c, e)))
28.55/9.77	   (A^2 -> H(U1(e, c), U1(e, e)),A^2 -> H(U1(e, c), U1(e, e)))
28.55/9.77	   (A^2 -> H(U1(e, c), U1(k, e)),A^2 -> H(U1(e, c), U1(k, e)))
28.55/9.77	
28.55/9.77	
28.55/9.77	----------------------------------------
28.55/9.77	
28.55/9.77	(1438)
28.55/9.77	Obligation:
28.55/9.77	Q DP problem:
28.55/9.77	The TRS P consists of the following rules:
28.55/9.77	
28.55/9.77	   H(x, x) -> G(x, x, f(k))
28.55/9.77	   G(d, x, x) -> A^2
28.55/9.77	   A^2 -> H(f(c), f(c))
28.55/9.77	   A^2 -> H(f(d), f(d))
28.55/9.77	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.77	   A^2 -> H(f(e), f(e))
28.55/9.77	   A^2 -> H(f(k), f(k))
28.55/9.77	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.77	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.77	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, c), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.77	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.77	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.77	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.77	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.77	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.77	   A^2 -> H(U1(k, e), f(e))
28.55/9.77	   A^2 -> H(U1(k, e), f(k))
28.55/9.77	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.77	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.77	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.77	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.77	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.77	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.77	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.77	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.77	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.77	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.77	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.77	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.77	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.77	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.77	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.77	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.77	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.77	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.77	   A^2 -> H(U1(c, c), b)
28.55/9.77	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.77	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.77	   A^2 -> H(U1(c, c), e)
28.55/9.77	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.77	   A^2 -> H(e, U1(c, b))
28.55/9.77	   A^2 -> H(e, U1(d, b))
28.55/9.77	   A^2 -> H(e, U1(b, c))
28.55/9.77	   A^2 -> H(e, U1(b, d))
28.55/9.77	   A^2 -> H(e, U1(c, c))
28.55/9.77	   A^2 -> H(e, f(e))
28.55/9.77	   A^2 -> H(e, f(k))
28.55/9.77	   A^2 -> H(e, U1(d, d))
28.55/9.77	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.77	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.77	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.77	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.77	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.77	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.77	   A^2 -> H(f(e), b)
28.55/9.77	   A^2 -> H(f(e), U1(e, d))
28.55/9.77	   A^2 -> H(f(e), U1(d, e))
28.55/9.77	   A^2 -> H(f(e), c)
28.55/9.77	   A^2 -> H(f(e), U1(e, k))
28.55/9.77	   A^2 -> H(f(e), U1(k, e))
28.55/9.77	   A^2 -> H(f(e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.77	   A^2 -> H(f(k), b)
28.55/9.77	   A^2 -> H(f(k), U1(e, d))
28.55/9.77	   A^2 -> H(f(k), U1(d, e))
28.55/9.77	   A^2 -> H(f(k), c)
28.55/9.77	   A^2 -> H(f(k), U1(e, k))
28.55/9.77	   A^2 -> H(f(k), U1(k, e))
28.55/9.77	   A^2 -> H(f(k), e)
28.55/9.77	   A^2 -> H(f(c), d)
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.77	   A^2 -> H(U1(k, k), f(e))
28.55/9.77	   A^2 -> H(U1(k, k), f(k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.77	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.77	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.77	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.77	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.77	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.77	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.77	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.77	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.77	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.77	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.77	   A^2 -> H(U1(d, d), b)
28.55/9.77	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.77	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.77	   A^2 -> H(U1(d, d), c)
28.55/9.77	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.77	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.77	   A^2 -> H(U1(d, d), e)
28.55/9.77	   A^2 -> H(f(d), d)
28.55/9.77	   A^2 -> H(f(d), k)
28.55/9.77	   A^2 -> H(U1(c, c), c)
28.55/9.77	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.77	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.77	   A^2 -> H(f(c), k)
28.55/9.77	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.77	   A^2 -> H(f(k), U1(k, k))
28.55/9.77	   A^2 -> H(f(e), e)
28.55/9.77	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.77	   A^2 -> H(d, U1(c, b))
28.55/9.77	   A^2 -> H(d, U1(d, b))
28.55/9.77	   A^2 -> H(d, U1(b, c))
28.55/9.77	   A^2 -> H(d, U1(b, d))
28.55/9.77	   A^2 -> H(d, U1(c, c))
28.55/9.77	   A^2 -> H(d, f(e))
28.55/9.77	   A^2 -> H(d, f(k))
28.55/9.77	   A^2 -> H(d, U1(d, d))
28.55/9.77	   A^2 -> H(a, U1(e, b))
28.55/9.77	   A^2 -> H(a, U1(k, b))
28.55/9.77	   A^2 -> H(a, U1(c, d))
28.55/9.77	   A^2 -> H(a, U1(d, c))
28.55/9.77	   A^2 -> H(a, U1(b, e))
28.55/9.77	   A^2 -> H(a, U1(b, k))
28.55/9.77	   A^2 -> H(a, U1(e, c))
28.55/9.77	   A^2 -> H(a, U1(k, c))
28.55/9.77	   A^2 -> H(a, U1(c, e))
28.55/9.77	   A^2 -> H(a, U1(c, k))
28.55/9.77	   A^2 -> H(a, U1(e, e))
28.55/9.77	   A^2 -> H(a, U1(k, k))
28.55/9.77	   A^2 -> H(a, U1(k, d))
28.55/9.77	   A^2 -> H(a, U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.77	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.77	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.77	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.77	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, a), b)
28.55/9.77	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.77	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.77	   A^2 -> H(U1(e, a), c)
28.55/9.77	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.77	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.77	   A^2 -> H(U1(e, a), e)
28.55/9.77	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, a), b)
28.55/9.77	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.77	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.77	   A^2 -> H(U1(k, a), c)
28.55/9.77	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.77	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.77	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, d), b)
28.55/9.77	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.77	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.77	   A^2 -> H(U1(c, d), c)
28.55/9.77	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.77	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.77	   A^2 -> H(U1(c, d), e)
28.55/9.77	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, a), d)
28.55/9.77	   A^2 -> H(U1(c, a), k)
28.55/9.77	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.77	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.77	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.77	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.77	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.77	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.77	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.77	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.77	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.77	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.77	   A^2 -> H(U1(d, c), b)
28.55/9.77	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.77	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.77	   A^2 -> H(U1(d, c), c)
28.55/9.77	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.77	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.77	   A^2 -> H(U1(d, c), e)
28.55/9.77	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.77	   A^2 -> H(U1(d, a), d)
28.55/9.77	   A^2 -> H(U1(d, a), k)
28.55/9.77	   A^2 -> H(U1(a, e), b)
28.55/9.77	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.77	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.77	   A^2 -> H(U1(a, e), c)
28.55/9.77	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.77	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.77	   A^2 -> H(U1(a, e), e)
28.55/9.77	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(a, k), b)
28.55/9.77	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.77	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.77	   A^2 -> H(U1(a, k), c)
28.55/9.77	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.77	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.77	   A^2 -> H(U1(a, k), e)
28.55/9.77	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(a, c), d)
28.55/9.77	   A^2 -> H(U1(a, c), k)
28.55/9.77	   A^2 -> H(U1(a, d), d)
28.55/9.77	   A^2 -> H(U1(a, d), k)
28.55/9.77	   A^2 -> H(k, U1(c, b))
28.55/9.77	   A^2 -> H(k, U1(d, b))
28.55/9.77	   A^2 -> H(k, U1(b, c))
28.55/9.77	   A^2 -> H(k, U1(b, d))
28.55/9.77	   A^2 -> H(k, U1(c, c))
28.55/9.77	   A^2 -> H(k, f(e))
28.55/9.77	   A^2 -> H(k, f(k))
28.55/9.77	   A^2 -> H(k, U1(d, d))
28.55/9.77	   A^2 -> H(c, U1(e, b))
28.55/9.77	   A^2 -> H(c, U1(k, b))
28.55/9.77	   A^2 -> H(c, U1(c, d))
28.55/9.77	   A^2 -> H(c, U1(d, c))
28.55/9.77	   A^2 -> H(c, U1(b, e))
28.55/9.77	   A^2 -> H(c, U1(b, k))
28.55/9.77	   A^2 -> H(c, U1(e, c))
28.55/9.77	   A^2 -> H(c, U1(k, c))
28.55/9.77	   A^2 -> H(c, U1(c, e))
28.55/9.77	   A^2 -> H(c, U1(c, k))
28.55/9.77	   A^2 -> H(c, U1(e, e))
28.55/9.77	   A^2 -> H(c, U1(k, k))
28.55/9.77	   A^2 -> H(c, U1(k, d))
28.55/9.77	   A^2 -> H(c, U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, k), U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, c), b)
28.55/9.77	   A^2 -> H(U1(e, c), U1(e, d))
28.55/9.77	   A^2 -> H(U1(e, c), U1(d, e))
28.55/9.77	   A^2 -> H(U1(e, c), U1(k, e))
28.55/9.77	
28.55/9.77	The TRS R consists of the following rules:
28.55/9.77	
28.55/9.77	   f(x) -> U1(x, x)
28.55/9.77	   U1(e, x) -> x
28.55/9.77	   a -> c
28.55/9.77	   a -> d
28.55/9.77	   b -> c
28.55/9.77	   b -> d
28.55/9.77	   d -> k
28.55/9.77	   c -> e
28.55/9.77	   c -> k
28.55/9.77	
28.55/9.77	Q is empty.
28.55/9.77	We have to consider all minimal (P,Q,R)-chains.
28.55/9.77	----------------------------------------
28.55/9.77	
28.55/9.77	(1439) TransformationProof (EQUIVALENT)
28.55/9.77	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.77	
28.55/9.77	   (A^2 -> H(c, U1(c, k)),A^2 -> H(c, U1(c, k)))
28.55/9.77	   (A^2 -> H(U1(e, e), U1(c, k)),A^2 -> H(U1(e, e), U1(c, k)))
28.55/9.77	   (A^2 -> H(U1(e, k), U1(c, k)),A^2 -> H(U1(e, k), U1(c, k)))
28.55/9.77	   (A^2 -> H(U1(e, c), U1(e, k)),A^2 -> H(U1(e, c), U1(e, k)))
28.55/9.77	   (A^2 -> H(U1(e, c), U1(k, k)),A^2 -> H(U1(e, c), U1(k, k)))
28.55/9.77	
28.55/9.77	
28.55/9.77	----------------------------------------
28.55/9.77	
28.55/9.77	(1440)
28.55/9.77	Obligation:
28.55/9.77	Q DP problem:
28.55/9.77	The TRS P consists of the following rules:
28.55/9.77	
28.55/9.77	   H(x, x) -> G(x, x, f(k))
28.55/9.77	   G(d, x, x) -> A^2
28.55/9.77	   A^2 -> H(f(c), f(c))
28.55/9.77	   A^2 -> H(f(d), f(d))
28.55/9.77	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.77	   A^2 -> H(f(e), f(e))
28.55/9.77	   A^2 -> H(f(k), f(k))
28.55/9.77	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.77	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.77	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, c), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.77	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.77	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.77	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.77	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.77	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.77	   A^2 -> H(U1(k, e), f(e))
28.55/9.77	   A^2 -> H(U1(k, e), f(k))
28.55/9.77	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.77	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.77	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.77	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.77	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.77	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.77	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.77	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.77	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.77	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.77	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.77	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.77	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.77	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.77	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.77	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.77	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.77	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.77	   A^2 -> H(U1(c, c), b)
28.55/9.77	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.77	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.77	   A^2 -> H(U1(c, c), e)
28.55/9.77	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.77	   A^2 -> H(e, U1(c, b))
28.55/9.77	   A^2 -> H(e, U1(d, b))
28.55/9.77	   A^2 -> H(e, U1(b, c))
28.55/9.77	   A^2 -> H(e, U1(b, d))
28.55/9.77	   A^2 -> H(e, U1(c, c))
28.55/9.77	   A^2 -> H(e, f(e))
28.55/9.77	   A^2 -> H(e, f(k))
28.55/9.77	   A^2 -> H(e, U1(d, d))
28.55/9.77	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.77	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.77	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.77	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.77	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.77	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.77	   A^2 -> H(f(e), b)
28.55/9.77	   A^2 -> H(f(e), U1(e, d))
28.55/9.77	   A^2 -> H(f(e), U1(d, e))
28.55/9.77	   A^2 -> H(f(e), c)
28.55/9.77	   A^2 -> H(f(e), U1(e, k))
28.55/9.77	   A^2 -> H(f(e), U1(k, e))
28.55/9.77	   A^2 -> H(f(e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.77	   A^2 -> H(f(k), b)
28.55/9.77	   A^2 -> H(f(k), U1(e, d))
28.55/9.77	   A^2 -> H(f(k), U1(d, e))
28.55/9.77	   A^2 -> H(f(k), c)
28.55/9.77	   A^2 -> H(f(k), U1(e, k))
28.55/9.77	   A^2 -> H(f(k), U1(k, e))
28.55/9.77	   A^2 -> H(f(k), e)
28.55/9.77	   A^2 -> H(f(c), d)
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.77	   A^2 -> H(U1(k, k), f(e))
28.55/9.77	   A^2 -> H(U1(k, k), f(k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.77	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.77	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.77	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.77	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.77	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.77	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.77	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.77	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.77	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.77	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.77	   A^2 -> H(U1(d, d), b)
28.55/9.77	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.77	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.77	   A^2 -> H(U1(d, d), c)
28.55/9.77	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.77	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.77	   A^2 -> H(U1(d, d), e)
28.55/9.77	   A^2 -> H(f(d), d)
28.55/9.77	   A^2 -> H(f(d), k)
28.55/9.77	   A^2 -> H(U1(c, c), c)
28.55/9.77	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.77	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.77	   A^2 -> H(f(c), k)
28.55/9.77	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.77	   A^2 -> H(f(k), U1(k, k))
28.55/9.77	   A^2 -> H(f(e), e)
28.55/9.77	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.77	   A^2 -> H(d, U1(c, b))
28.55/9.77	   A^2 -> H(d, U1(d, b))
28.55/9.77	   A^2 -> H(d, U1(b, c))
28.55/9.77	   A^2 -> H(d, U1(b, d))
28.55/9.77	   A^2 -> H(d, U1(c, c))
28.55/9.77	   A^2 -> H(d, f(e))
28.55/9.77	   A^2 -> H(d, f(k))
28.55/9.77	   A^2 -> H(d, U1(d, d))
28.55/9.77	   A^2 -> H(a, U1(e, b))
28.55/9.77	   A^2 -> H(a, U1(k, b))
28.55/9.77	   A^2 -> H(a, U1(c, d))
28.55/9.77	   A^2 -> H(a, U1(d, c))
28.55/9.77	   A^2 -> H(a, U1(b, e))
28.55/9.77	   A^2 -> H(a, U1(b, k))
28.55/9.77	   A^2 -> H(a, U1(e, c))
28.55/9.77	   A^2 -> H(a, U1(k, c))
28.55/9.77	   A^2 -> H(a, U1(c, e))
28.55/9.77	   A^2 -> H(a, U1(c, k))
28.55/9.77	   A^2 -> H(a, U1(e, e))
28.55/9.77	   A^2 -> H(a, U1(k, k))
28.55/9.77	   A^2 -> H(a, U1(k, d))
28.55/9.77	   A^2 -> H(a, U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.77	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.77	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.77	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.77	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, a), b)
28.55/9.77	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.77	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.77	   A^2 -> H(U1(e, a), c)
28.55/9.77	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.77	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.77	   A^2 -> H(U1(e, a), e)
28.55/9.77	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, a), b)
28.55/9.77	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.77	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.77	   A^2 -> H(U1(k, a), c)
28.55/9.77	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.77	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.77	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, d), b)
28.55/9.77	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.77	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.77	   A^2 -> H(U1(c, d), c)
28.55/9.77	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.77	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.77	   A^2 -> H(U1(c, d), e)
28.55/9.77	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, a), d)
28.55/9.77	   A^2 -> H(U1(c, a), k)
28.55/9.77	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.77	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.77	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.77	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.77	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.77	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.77	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.77	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.77	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.77	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.77	   A^2 -> H(U1(d, c), b)
28.55/9.77	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.77	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.77	   A^2 -> H(U1(d, c), c)
28.55/9.77	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.77	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.77	   A^2 -> H(U1(d, c), e)
28.55/9.77	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.77	   A^2 -> H(U1(d, a), d)
28.55/9.77	   A^2 -> H(U1(d, a), k)
28.55/9.77	   A^2 -> H(U1(a, e), b)
28.55/9.77	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.77	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.77	   A^2 -> H(U1(a, e), c)
28.55/9.77	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.77	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.77	   A^2 -> H(U1(a, e), e)
28.55/9.77	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(a, k), b)
28.55/9.77	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.77	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.77	   A^2 -> H(U1(a, k), c)
28.55/9.77	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.77	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.77	   A^2 -> H(U1(a, k), e)
28.55/9.77	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(a, c), d)
28.55/9.77	   A^2 -> H(U1(a, c), k)
28.55/9.77	   A^2 -> H(U1(a, d), d)
28.55/9.77	   A^2 -> H(U1(a, d), k)
28.55/9.77	   A^2 -> H(k, U1(c, b))
28.55/9.77	   A^2 -> H(k, U1(d, b))
28.55/9.77	   A^2 -> H(k, U1(b, c))
28.55/9.77	   A^2 -> H(k, U1(b, d))
28.55/9.77	   A^2 -> H(k, U1(c, c))
28.55/9.77	   A^2 -> H(k, f(e))
28.55/9.77	   A^2 -> H(k, f(k))
28.55/9.77	   A^2 -> H(k, U1(d, d))
28.55/9.77	   A^2 -> H(c, U1(e, b))
28.55/9.77	   A^2 -> H(c, U1(k, b))
28.55/9.77	   A^2 -> H(c, U1(c, d))
28.55/9.77	   A^2 -> H(c, U1(d, c))
28.55/9.77	   A^2 -> H(c, U1(b, e))
28.55/9.77	   A^2 -> H(c, U1(b, k))
28.55/9.77	   A^2 -> H(c, U1(e, c))
28.55/9.77	   A^2 -> H(c, U1(k, c))
28.55/9.77	   A^2 -> H(c, U1(c, e))
28.55/9.77	   A^2 -> H(c, U1(c, k))
28.55/9.77	   A^2 -> H(c, U1(e, e))
28.55/9.77	   A^2 -> H(c, U1(k, k))
28.55/9.77	   A^2 -> H(c, U1(k, d))
28.55/9.77	   A^2 -> H(c, U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, k), U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, c), b)
28.55/9.77	   A^2 -> H(U1(e, c), U1(e, d))
28.55/9.77	   A^2 -> H(U1(e, c), U1(d, e))
28.55/9.77	   A^2 -> H(U1(e, c), U1(k, e))
28.55/9.77	   A^2 -> H(U1(e, c), U1(e, k))
28.55/9.77	
28.55/9.77	The TRS R consists of the following rules:
28.55/9.77	
28.55/9.77	   f(x) -> U1(x, x)
28.55/9.77	   U1(e, x) -> x
28.55/9.77	   a -> c
28.55/9.77	   a -> d
28.55/9.77	   b -> c
28.55/9.77	   b -> d
28.55/9.77	   d -> k
28.55/9.77	   c -> e
28.55/9.77	   c -> k
28.55/9.77	
28.55/9.77	Q is empty.
28.55/9.77	We have to consider all minimal (P,Q,R)-chains.
28.55/9.77	----------------------------------------
28.55/9.77	
28.55/9.77	(1441) TransformationProof (EQUIVALENT)
28.55/9.77	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.77	
28.55/9.77	   (A^2 -> H(c, U1(e, e)),A^2 -> H(c, U1(e, e)))
28.55/9.77	   (A^2 -> H(U1(e, e), U1(e, e)),A^2 -> H(U1(e, e), U1(e, e)))
28.55/9.77	   (A^2 -> H(U1(e, k), U1(e, e)),A^2 -> H(U1(e, k), U1(e, e)))
28.55/9.77	   (A^2 -> H(U1(e, c), e),A^2 -> H(U1(e, c), e))
28.55/9.77	
28.55/9.77	
28.55/9.77	----------------------------------------
28.55/9.77	
28.55/9.77	(1442)
28.55/9.77	Obligation:
28.55/9.77	Q DP problem:
28.55/9.77	The TRS P consists of the following rules:
28.55/9.77	
28.55/9.77	   H(x, x) -> G(x, x, f(k))
28.55/9.77	   G(d, x, x) -> A^2
28.55/9.77	   A^2 -> H(f(c), f(c))
28.55/9.77	   A^2 -> H(f(d), f(d))
28.55/9.77	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.77	   A^2 -> H(f(e), f(e))
28.55/9.77	   A^2 -> H(f(k), f(k))
28.55/9.77	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.77	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.77	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.77	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.77	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.77	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.77	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.77	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.77	   A^2 -> H(U1(k, e), f(e))
28.55/9.77	   A^2 -> H(U1(k, e), f(k))
28.55/9.77	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.77	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.77	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.77	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.77	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.77	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.77	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.77	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.77	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.77	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.77	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.77	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.77	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.77	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.77	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.77	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.77	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.77	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.77	   A^2 -> H(U1(c, c), b)
28.55/9.77	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.77	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.77	   A^2 -> H(U1(c, c), e)
28.55/9.77	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.77	   A^2 -> H(e, U1(c, b))
28.55/9.77	   A^2 -> H(e, U1(d, b))
28.55/9.77	   A^2 -> H(e, U1(b, c))
28.55/9.77	   A^2 -> H(e, U1(b, d))
28.55/9.77	   A^2 -> H(e, U1(c, c))
28.55/9.77	   A^2 -> H(e, f(e))
28.55/9.77	   A^2 -> H(e, f(k))
28.55/9.77	   A^2 -> H(e, U1(d, d))
28.55/9.77	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.77	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.77	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.77	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.77	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.77	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.77	   A^2 -> H(f(e), b)
28.55/9.77	   A^2 -> H(f(e), U1(e, d))
28.55/9.77	   A^2 -> H(f(e), U1(d, e))
28.55/9.77	   A^2 -> H(f(e), c)
28.55/9.77	   A^2 -> H(f(e), U1(e, k))
28.55/9.77	   A^2 -> H(f(e), U1(k, e))
28.55/9.77	   A^2 -> H(f(e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.77	   A^2 -> H(f(k), b)
28.55/9.77	   A^2 -> H(f(k), U1(e, d))
28.55/9.77	   A^2 -> H(f(k), U1(d, e))
28.55/9.77	   A^2 -> H(f(k), c)
28.55/9.77	   A^2 -> H(f(k), U1(e, k))
28.55/9.77	   A^2 -> H(f(k), U1(k, e))
28.55/9.77	   A^2 -> H(f(k), e)
28.55/9.77	   A^2 -> H(f(c), d)
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.77	   A^2 -> H(U1(k, k), f(e))
28.55/9.77	   A^2 -> H(U1(k, k), f(k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.77	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.77	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.77	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.77	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.77	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.77	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.77	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.77	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.77	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.77	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.77	   A^2 -> H(U1(d, d), b)
28.55/9.77	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.77	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.77	   A^2 -> H(U1(d, d), c)
28.55/9.77	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.77	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.77	   A^2 -> H(U1(d, d), e)
28.55/9.77	   A^2 -> H(f(d), d)
28.55/9.77	   A^2 -> H(f(d), k)
28.55/9.77	   A^2 -> H(U1(c, c), c)
28.55/9.77	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.77	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.77	   A^2 -> H(f(c), k)
28.55/9.77	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.77	   A^2 -> H(f(k), U1(k, k))
28.55/9.77	   A^2 -> H(f(e), e)
28.55/9.77	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.77	   A^2 -> H(d, U1(c, b))
28.55/9.77	   A^2 -> H(d, U1(d, b))
28.55/9.77	   A^2 -> H(d, U1(b, c))
28.55/9.77	   A^2 -> H(d, U1(b, d))
28.55/9.77	   A^2 -> H(d, U1(c, c))
28.55/9.77	   A^2 -> H(d, f(e))
28.55/9.77	   A^2 -> H(d, f(k))
28.55/9.77	   A^2 -> H(d, U1(d, d))
28.55/9.77	   A^2 -> H(a, U1(e, b))
28.55/9.77	   A^2 -> H(a, U1(k, b))
28.55/9.77	   A^2 -> H(a, U1(c, d))
28.55/9.77	   A^2 -> H(a, U1(d, c))
28.55/9.77	   A^2 -> H(a, U1(b, e))
28.55/9.77	   A^2 -> H(a, U1(b, k))
28.55/9.77	   A^2 -> H(a, U1(e, c))
28.55/9.77	   A^2 -> H(a, U1(k, c))
28.55/9.77	   A^2 -> H(a, U1(c, e))
28.55/9.77	   A^2 -> H(a, U1(c, k))
28.55/9.77	   A^2 -> H(a, U1(e, e))
28.55/9.77	   A^2 -> H(a, U1(k, k))
28.55/9.77	   A^2 -> H(a, U1(k, d))
28.55/9.77	   A^2 -> H(a, U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.77	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.77	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.77	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.77	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, a), b)
28.55/9.77	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.77	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.77	   A^2 -> H(U1(e, a), c)
28.55/9.77	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.77	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.77	   A^2 -> H(U1(e, a), e)
28.55/9.77	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, a), b)
28.55/9.77	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.77	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.77	   A^2 -> H(U1(k, a), c)
28.55/9.77	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.77	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.77	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, d), b)
28.55/9.77	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.77	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.77	   A^2 -> H(U1(c, d), c)
28.55/9.77	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.77	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.77	   A^2 -> H(U1(c, d), e)
28.55/9.77	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, a), d)
28.55/9.77	   A^2 -> H(U1(c, a), k)
28.55/9.77	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.77	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.77	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.77	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.77	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.77	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.77	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.77	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.77	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.77	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.77	   A^2 -> H(U1(d, c), b)
28.55/9.77	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.77	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.77	   A^2 -> H(U1(d, c), c)
28.55/9.77	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.77	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.77	   A^2 -> H(U1(d, c), e)
28.55/9.77	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.77	   A^2 -> H(U1(d, a), d)
28.55/9.77	   A^2 -> H(U1(d, a), k)
28.55/9.77	   A^2 -> H(U1(a, e), b)
28.55/9.77	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.77	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.77	   A^2 -> H(U1(a, e), c)
28.55/9.77	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.77	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.77	   A^2 -> H(U1(a, e), e)
28.55/9.77	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(a, k), b)
28.55/9.77	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.77	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.77	   A^2 -> H(U1(a, k), c)
28.55/9.77	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.77	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.77	   A^2 -> H(U1(a, k), e)
28.55/9.77	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(a, c), d)
28.55/9.77	   A^2 -> H(U1(a, c), k)
28.55/9.77	   A^2 -> H(U1(a, d), d)
28.55/9.77	   A^2 -> H(U1(a, d), k)
28.55/9.77	   A^2 -> H(k, U1(c, b))
28.55/9.77	   A^2 -> H(k, U1(d, b))
28.55/9.77	   A^2 -> H(k, U1(b, c))
28.55/9.77	   A^2 -> H(k, U1(b, d))
28.55/9.77	   A^2 -> H(k, U1(c, c))
28.55/9.77	   A^2 -> H(k, f(e))
28.55/9.77	   A^2 -> H(k, f(k))
28.55/9.77	   A^2 -> H(k, U1(d, d))
28.55/9.77	   A^2 -> H(c, U1(e, b))
28.55/9.77	   A^2 -> H(c, U1(k, b))
28.55/9.77	   A^2 -> H(c, U1(c, d))
28.55/9.77	   A^2 -> H(c, U1(d, c))
28.55/9.77	   A^2 -> H(c, U1(b, e))
28.55/9.77	   A^2 -> H(c, U1(b, k))
28.55/9.77	   A^2 -> H(c, U1(e, c))
28.55/9.77	   A^2 -> H(c, U1(k, c))
28.55/9.77	   A^2 -> H(c, U1(c, e))
28.55/9.77	   A^2 -> H(c, U1(c, k))
28.55/9.77	   A^2 -> H(c, U1(e, e))
28.55/9.77	   A^2 -> H(c, U1(k, k))
28.55/9.77	   A^2 -> H(c, U1(k, d))
28.55/9.77	   A^2 -> H(c, U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, k), U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, c), b)
28.55/9.77	   A^2 -> H(U1(e, c), U1(e, d))
28.55/9.77	   A^2 -> H(U1(e, c), U1(d, e))
28.55/9.77	   A^2 -> H(U1(e, c), U1(k, e))
28.55/9.77	   A^2 -> H(U1(e, c), U1(e, k))
28.55/9.77	   A^2 -> H(U1(e, c), e)
28.55/9.77	
28.55/9.77	The TRS R consists of the following rules:
28.55/9.77	
28.55/9.77	   f(x) -> U1(x, x)
28.55/9.77	   U1(e, x) -> x
28.55/9.77	   a -> c
28.55/9.77	   a -> d
28.55/9.77	   b -> c
28.55/9.77	   b -> d
28.55/9.77	   d -> k
28.55/9.77	   c -> e
28.55/9.77	   c -> k
28.55/9.77	
28.55/9.77	Q is empty.
28.55/9.77	We have to consider all minimal (P,Q,R)-chains.
28.55/9.77	----------------------------------------
28.55/9.77	
28.55/9.77	(1443) TransformationProof (EQUIVALENT)
28.55/9.77	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.77	
28.55/9.77	   (A^2 -> H(c, U1(k, k)),A^2 -> H(c, U1(k, k)))
28.55/9.77	   (A^2 -> H(U1(e, e), U1(k, k)),A^2 -> H(U1(e, e), U1(k, k)))
28.55/9.77	   (A^2 -> H(U1(e, k), U1(k, k)),A^2 -> H(U1(e, k), U1(k, k)))
28.55/9.77	
28.55/9.77	
28.55/9.77	----------------------------------------
28.55/9.77	
28.55/9.77	(1444)
28.55/9.77	Obligation:
28.55/9.77	Q DP problem:
28.55/9.77	The TRS P consists of the following rules:
28.55/9.77	
28.55/9.77	   H(x, x) -> G(x, x, f(k))
28.55/9.77	   G(d, x, x) -> A^2
28.55/9.77	   A^2 -> H(f(c), f(c))
28.55/9.77	   A^2 -> H(f(d), f(d))
28.55/9.77	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.77	   A^2 -> H(f(e), f(e))
28.55/9.77	   A^2 -> H(f(k), f(k))
28.55/9.77	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.77	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.77	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, c), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.77	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.77	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.77	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.77	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.77	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.77	   A^2 -> H(U1(k, e), f(e))
28.55/9.77	   A^2 -> H(U1(k, e), f(k))
28.55/9.77	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.77	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.77	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.77	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.77	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.77	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.77	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.77	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.77	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.77	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.77	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.77	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.77	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.77	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.77	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.77	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.77	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.77	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.77	   A^2 -> H(U1(c, c), b)
28.55/9.77	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.77	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.77	   A^2 -> H(U1(c, c), e)
28.55/9.77	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.77	   A^2 -> H(e, U1(c, b))
28.55/9.77	   A^2 -> H(e, U1(d, b))
28.55/9.77	   A^2 -> H(e, U1(b, c))
28.55/9.77	   A^2 -> H(e, U1(b, d))
28.55/9.77	   A^2 -> H(e, U1(c, c))
28.55/9.77	   A^2 -> H(e, f(e))
28.55/9.77	   A^2 -> H(e, f(k))
28.55/9.77	   A^2 -> H(e, U1(d, d))
28.55/9.77	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.77	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.77	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.77	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.77	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.77	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.77	   A^2 -> H(f(e), b)
28.55/9.77	   A^2 -> H(f(e), U1(e, d))
28.55/9.77	   A^2 -> H(f(e), U1(d, e))
28.55/9.77	   A^2 -> H(f(e), c)
28.55/9.77	   A^2 -> H(f(e), U1(e, k))
28.55/9.77	   A^2 -> H(f(e), U1(k, e))
28.55/9.77	   A^2 -> H(f(e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.77	   A^2 -> H(f(k), b)
28.55/9.77	   A^2 -> H(f(k), U1(e, d))
28.55/9.77	   A^2 -> H(f(k), U1(d, e))
28.55/9.77	   A^2 -> H(f(k), c)
28.55/9.77	   A^2 -> H(f(k), U1(e, k))
28.55/9.77	   A^2 -> H(f(k), U1(k, e))
28.55/9.77	   A^2 -> H(f(k), e)
28.55/9.77	   A^2 -> H(f(c), d)
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.77	   A^2 -> H(U1(k, k), f(e))
28.55/9.77	   A^2 -> H(U1(k, k), f(k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.77	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.77	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.77	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.77	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.77	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.77	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.77	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.77	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.77	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.77	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.77	   A^2 -> H(U1(d, d), b)
28.55/9.77	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.77	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.77	   A^2 -> H(U1(d, d), c)
28.55/9.77	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.77	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.77	   A^2 -> H(U1(d, d), e)
28.55/9.77	   A^2 -> H(f(d), d)
28.55/9.77	   A^2 -> H(f(d), k)
28.55/9.77	   A^2 -> H(U1(c, c), c)
28.55/9.77	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.77	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.77	   A^2 -> H(f(c), k)
28.55/9.77	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.77	   A^2 -> H(f(k), U1(k, k))
28.55/9.77	   A^2 -> H(f(e), e)
28.55/9.77	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.77	   A^2 -> H(d, U1(c, b))
28.55/9.77	   A^2 -> H(d, U1(d, b))
28.55/9.77	   A^2 -> H(d, U1(b, c))
28.55/9.77	   A^2 -> H(d, U1(b, d))
28.55/9.77	   A^2 -> H(d, U1(c, c))
28.55/9.77	   A^2 -> H(d, f(e))
28.55/9.77	   A^2 -> H(d, f(k))
28.55/9.77	   A^2 -> H(d, U1(d, d))
28.55/9.77	   A^2 -> H(a, U1(e, b))
28.55/9.77	   A^2 -> H(a, U1(k, b))
28.55/9.77	   A^2 -> H(a, U1(c, d))
28.55/9.77	   A^2 -> H(a, U1(d, c))
28.55/9.77	   A^2 -> H(a, U1(b, e))
28.55/9.77	   A^2 -> H(a, U1(b, k))
28.55/9.77	   A^2 -> H(a, U1(e, c))
28.55/9.77	   A^2 -> H(a, U1(k, c))
28.55/9.77	   A^2 -> H(a, U1(c, e))
28.55/9.77	   A^2 -> H(a, U1(c, k))
28.55/9.77	   A^2 -> H(a, U1(e, e))
28.55/9.77	   A^2 -> H(a, U1(k, k))
28.55/9.77	   A^2 -> H(a, U1(k, d))
28.55/9.77	   A^2 -> H(a, U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.77	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.77	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.77	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.77	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, a), b)
28.55/9.77	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.77	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.77	   A^2 -> H(U1(e, a), c)
28.55/9.77	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.77	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.77	   A^2 -> H(U1(e, a), e)
28.55/9.77	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, a), b)
28.55/9.77	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.77	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.77	   A^2 -> H(U1(k, a), c)
28.55/9.77	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.77	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.77	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, d), b)
28.55/9.77	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.77	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.77	   A^2 -> H(U1(c, d), c)
28.55/9.77	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.77	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.77	   A^2 -> H(U1(c, d), e)
28.55/9.77	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, a), d)
28.55/9.77	   A^2 -> H(U1(c, a), k)
28.55/9.77	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.77	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.77	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.77	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.77	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.77	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.77	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.77	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.77	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.77	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.77	   A^2 -> H(U1(d, c), b)
28.55/9.77	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.77	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.77	   A^2 -> H(U1(d, c), c)
28.55/9.77	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.77	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.77	   A^2 -> H(U1(d, c), e)
28.55/9.77	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.77	   A^2 -> H(U1(d, a), d)
28.55/9.77	   A^2 -> H(U1(d, a), k)
28.55/9.77	   A^2 -> H(U1(a, e), b)
28.55/9.77	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.77	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.77	   A^2 -> H(U1(a, e), c)
28.55/9.77	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.77	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.77	   A^2 -> H(U1(a, e), e)
28.55/9.77	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(a, k), b)
28.55/9.77	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.77	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.77	   A^2 -> H(U1(a, k), c)
28.55/9.77	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.77	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.77	   A^2 -> H(U1(a, k), e)
28.55/9.77	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(a, c), d)
28.55/9.77	   A^2 -> H(U1(a, c), k)
28.55/9.77	   A^2 -> H(U1(a, d), d)
28.55/9.77	   A^2 -> H(U1(a, d), k)
28.55/9.77	   A^2 -> H(k, U1(c, b))
28.55/9.77	   A^2 -> H(k, U1(d, b))
28.55/9.77	   A^2 -> H(k, U1(b, c))
28.55/9.77	   A^2 -> H(k, U1(b, d))
28.55/9.77	   A^2 -> H(k, U1(c, c))
28.55/9.77	   A^2 -> H(k, f(e))
28.55/9.77	   A^2 -> H(k, f(k))
28.55/9.77	   A^2 -> H(k, U1(d, d))
28.55/9.77	   A^2 -> H(c, U1(e, b))
28.55/9.77	   A^2 -> H(c, U1(k, b))
28.55/9.77	   A^2 -> H(c, U1(c, d))
28.55/9.77	   A^2 -> H(c, U1(d, c))
28.55/9.77	   A^2 -> H(c, U1(b, e))
28.55/9.77	   A^2 -> H(c, U1(b, k))
28.55/9.77	   A^2 -> H(c, U1(e, c))
28.55/9.77	   A^2 -> H(c, U1(k, c))
28.55/9.77	   A^2 -> H(c, U1(c, e))
28.55/9.77	   A^2 -> H(c, U1(c, k))
28.55/9.77	   A^2 -> H(c, U1(e, e))
28.55/9.77	   A^2 -> H(c, U1(k, k))
28.55/9.77	   A^2 -> H(c, U1(k, d))
28.55/9.77	   A^2 -> H(c, U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, k), U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, c), b)
28.55/9.77	   A^2 -> H(U1(e, c), U1(e, d))
28.55/9.77	   A^2 -> H(U1(e, c), U1(d, e))
28.55/9.77	   A^2 -> H(U1(e, c), U1(k, e))
28.55/9.77	   A^2 -> H(U1(e, c), U1(e, k))
28.55/9.77	   A^2 -> H(U1(e, c), e)
28.55/9.77	
28.55/9.77	The TRS R consists of the following rules:
28.55/9.77	
28.55/9.77	   f(x) -> U1(x, x)
28.55/9.77	   U1(e, x) -> x
28.55/9.77	   a -> c
28.55/9.77	   a -> d
28.55/9.77	   b -> c
28.55/9.77	   b -> d
28.55/9.77	   d -> k
28.55/9.77	   c -> e
28.55/9.77	   c -> k
28.55/9.77	
28.55/9.77	Q is empty.
28.55/9.77	We have to consider all minimal (P,Q,R)-chains.
28.55/9.77	----------------------------------------
28.55/9.77	
28.55/9.77	(1445) TransformationProof (EQUIVALENT)
28.55/9.77	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.77	
28.55/9.77	   (A^2 -> H(c, U1(k, d)),A^2 -> H(c, U1(k, d)))
28.55/9.77	   (A^2 -> H(U1(e, e), U1(k, d)),A^2 -> H(U1(e, e), U1(k, d)))
28.55/9.77	   (A^2 -> H(U1(e, k), U1(k, d)),A^2 -> H(U1(e, k), U1(k, d)))
28.55/9.77	   (A^2 -> H(U1(e, c), U1(k, k)),A^2 -> H(U1(e, c), U1(k, k)))
28.55/9.77	
28.55/9.77	
28.55/9.77	----------------------------------------
28.55/9.77	
28.55/9.77	(1446)
28.55/9.77	Obligation:
28.55/9.77	Q DP problem:
28.55/9.77	The TRS P consists of the following rules:
28.55/9.77	
28.55/9.77	   H(x, x) -> G(x, x, f(k))
28.55/9.77	   G(d, x, x) -> A^2
28.55/9.77	   A^2 -> H(f(c), f(c))
28.55/9.77	   A^2 -> H(f(d), f(d))
28.55/9.77	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.77	   A^2 -> H(f(e), f(e))
28.55/9.77	   A^2 -> H(f(k), f(k))
28.55/9.77	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.77	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.77	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, c), U1(d, k))
28.55/9.77	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.77	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.77	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.77	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.77	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.77	   A^2 -> H(U1(k, e), f(e))
28.55/9.77	   A^2 -> H(U1(k, e), f(k))
28.55/9.77	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.77	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.77	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.77	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.77	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.77	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.77	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.77	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.77	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.77	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.77	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.77	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.77	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.77	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.77	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.77	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.77	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.77	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.77	   A^2 -> H(U1(c, c), b)
28.55/9.77	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.77	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.77	   A^2 -> H(U1(c, c), e)
28.55/9.77	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.77	   A^2 -> H(e, U1(c, b))
28.55/9.77	   A^2 -> H(e, U1(d, b))
28.55/9.77	   A^2 -> H(e, U1(b, c))
28.55/9.77	   A^2 -> H(e, U1(b, d))
28.55/9.77	   A^2 -> H(e, U1(c, c))
28.55/9.77	   A^2 -> H(e, f(e))
28.55/9.77	   A^2 -> H(e, f(k))
28.55/9.77	   A^2 -> H(e, U1(d, d))
28.55/9.77	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.77	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.77	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.77	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.77	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.77	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.77	   A^2 -> H(f(e), b)
28.55/9.77	   A^2 -> H(f(e), U1(e, d))
28.55/9.77	   A^2 -> H(f(e), U1(d, e))
28.55/9.77	   A^2 -> H(f(e), c)
28.55/9.77	   A^2 -> H(f(e), U1(e, k))
28.55/9.77	   A^2 -> H(f(e), U1(k, e))
28.55/9.77	   A^2 -> H(f(e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.77	   A^2 -> H(f(k), b)
28.55/9.77	   A^2 -> H(f(k), U1(e, d))
28.55/9.77	   A^2 -> H(f(k), U1(d, e))
28.55/9.77	   A^2 -> H(f(k), c)
28.55/9.77	   A^2 -> H(f(k), U1(e, k))
28.55/9.77	   A^2 -> H(f(k), U1(k, e))
28.55/9.77	   A^2 -> H(f(k), e)
28.55/9.77	   A^2 -> H(f(c), d)
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.77	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.77	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.77	   A^2 -> H(U1(k, k), f(e))
28.55/9.77	   A^2 -> H(U1(k, k), f(k))
28.55/9.77	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.77	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.77	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.77	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.77	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.77	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.77	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.77	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.77	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.77	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.77	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.77	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.77	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.77	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.77	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.77	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.77	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.77	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.77	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.77	   A^2 -> H(U1(d, d), b)
28.55/9.77	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.77	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.77	   A^2 -> H(U1(d, d), c)
28.55/9.77	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.77	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.77	   A^2 -> H(U1(d, d), e)
28.55/9.77	   A^2 -> H(f(d), d)
28.55/9.77	   A^2 -> H(f(d), k)
28.55/9.77	   A^2 -> H(U1(c, c), c)
28.55/9.77	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.77	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.77	   A^2 -> H(f(c), k)
28.55/9.77	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.77	   A^2 -> H(f(k), U1(k, k))
28.55/9.77	   A^2 -> H(f(e), e)
28.55/9.77	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.77	   A^2 -> H(d, U1(c, b))
28.55/9.77	   A^2 -> H(d, U1(d, b))
28.55/9.77	   A^2 -> H(d, U1(b, c))
28.55/9.77	   A^2 -> H(d, U1(b, d))
28.55/9.77	   A^2 -> H(d, U1(c, c))
28.55/9.77	   A^2 -> H(d, f(e))
28.55/9.77	   A^2 -> H(d, f(k))
28.55/9.77	   A^2 -> H(d, U1(d, d))
28.55/9.77	   A^2 -> H(a, U1(e, b))
28.55/9.77	   A^2 -> H(a, U1(k, b))
28.55/9.77	   A^2 -> H(a, U1(c, d))
28.55/9.77	   A^2 -> H(a, U1(d, c))
28.55/9.77	   A^2 -> H(a, U1(b, e))
28.55/9.77	   A^2 -> H(a, U1(b, k))
28.55/9.77	   A^2 -> H(a, U1(e, c))
28.55/9.77	   A^2 -> H(a, U1(k, c))
28.55/9.77	   A^2 -> H(a, U1(c, e))
28.55/9.77	   A^2 -> H(a, U1(c, k))
28.55/9.77	   A^2 -> H(a, U1(e, e))
28.55/9.77	   A^2 -> H(a, U1(k, k))
28.55/9.77	   A^2 -> H(a, U1(k, d))
28.55/9.77	   A^2 -> H(a, U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.77	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.77	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.77	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.77	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.77	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.77	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.77	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.77	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.77	   A^2 -> H(U1(e, a), b)
28.55/9.77	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.77	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.77	   A^2 -> H(U1(e, a), c)
28.55/9.77	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.77	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.77	   A^2 -> H(U1(e, a), e)
28.55/9.77	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.77	   A^2 -> H(U1(k, a), b)
28.55/9.77	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.77	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.77	   A^2 -> H(U1(k, a), c)
28.55/9.77	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.77	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.77	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, d), b)
28.55/9.77	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.77	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.77	   A^2 -> H(U1(c, d), c)
28.55/9.77	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.77	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.77	   A^2 -> H(U1(c, d), e)
28.55/9.77	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.77	   A^2 -> H(U1(c, a), d)
28.55/9.77	   A^2 -> H(U1(c, a), k)
28.55/9.77	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.77	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.77	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.77	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.77	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.77	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.77	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.77	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.77	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.77	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.77	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.77	   A^2 -> H(U1(d, c), b)
28.55/9.77	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.77	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.77	   A^2 -> H(U1(d, c), c)
28.55/9.77	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.77	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.77	   A^2 -> H(U1(d, c), e)
28.55/9.78	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.78	   A^2 -> H(U1(d, a), d)
28.55/9.78	   A^2 -> H(U1(d, a), k)
28.55/9.78	   A^2 -> H(U1(a, e), b)
28.55/9.78	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.78	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.78	   A^2 -> H(U1(a, e), c)
28.55/9.78	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.78	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.78	   A^2 -> H(U1(a, e), e)
28.55/9.78	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(a, k), b)
28.55/9.78	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.78	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.78	   A^2 -> H(U1(a, k), c)
28.55/9.78	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.78	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.78	   A^2 -> H(U1(a, k), e)
28.55/9.78	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(a, c), d)
28.55/9.78	   A^2 -> H(U1(a, c), k)
28.55/9.78	   A^2 -> H(U1(a, d), d)
28.55/9.78	   A^2 -> H(U1(a, d), k)
28.55/9.78	   A^2 -> H(k, U1(c, b))
28.55/9.78	   A^2 -> H(k, U1(d, b))
28.55/9.78	   A^2 -> H(k, U1(b, c))
28.55/9.78	   A^2 -> H(k, U1(b, d))
28.55/9.78	   A^2 -> H(k, U1(c, c))
28.55/9.78	   A^2 -> H(k, f(e))
28.55/9.78	   A^2 -> H(k, f(k))
28.55/9.78	   A^2 -> H(k, U1(d, d))
28.55/9.78	   A^2 -> H(c, U1(e, b))
28.55/9.78	   A^2 -> H(c, U1(k, b))
28.55/9.78	   A^2 -> H(c, U1(c, d))
28.55/9.78	   A^2 -> H(c, U1(d, c))
28.55/9.78	   A^2 -> H(c, U1(b, e))
28.55/9.78	   A^2 -> H(c, U1(b, k))
28.55/9.78	   A^2 -> H(c, U1(e, c))
28.55/9.78	   A^2 -> H(c, U1(k, c))
28.55/9.78	   A^2 -> H(c, U1(c, e))
28.55/9.78	   A^2 -> H(c, U1(c, k))
28.55/9.78	   A^2 -> H(c, U1(e, e))
28.55/9.78	   A^2 -> H(c, U1(k, k))
28.55/9.78	   A^2 -> H(c, U1(k, d))
28.55/9.78	   A^2 -> H(c, U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(e, k), U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, c), b)
28.55/9.78	   A^2 -> H(U1(e, c), U1(e, d))
28.55/9.78	   A^2 -> H(U1(e, c), U1(d, e))
28.55/9.78	   A^2 -> H(U1(e, c), U1(k, e))
28.55/9.78	   A^2 -> H(U1(e, c), U1(e, k))
28.55/9.78	   A^2 -> H(U1(e, c), e)
28.55/9.78	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.78	
28.55/9.78	The TRS R consists of the following rules:
28.55/9.78	
28.55/9.78	   f(x) -> U1(x, x)
28.55/9.78	   U1(e, x) -> x
28.55/9.78	   a -> c
28.55/9.78	   a -> d
28.55/9.78	   b -> c
28.55/9.78	   b -> d
28.55/9.78	   d -> k
28.55/9.78	   c -> e
28.55/9.78	   c -> k
28.55/9.78	
28.55/9.78	Q is empty.
28.55/9.78	We have to consider all minimal (P,Q,R)-chains.
28.55/9.78	----------------------------------------
28.55/9.78	
28.55/9.78	(1447) TransformationProof (EQUIVALENT)
28.55/9.78	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.78	
28.55/9.78	   (A^2 -> H(c, U1(d, k)),A^2 -> H(c, U1(d, k)))
28.55/9.78	   (A^2 -> H(U1(e, e), U1(d, k)),A^2 -> H(U1(e, e), U1(d, k)))
28.55/9.78	   (A^2 -> H(U1(e, k), U1(d, k)),A^2 -> H(U1(e, k), U1(d, k)))
28.55/9.78	   (A^2 -> H(U1(e, c), U1(k, k)),A^2 -> H(U1(e, c), U1(k, k)))
28.55/9.78	
28.55/9.78	
28.55/9.78	----------------------------------------
28.55/9.78	
28.55/9.78	(1448)
28.55/9.78	Obligation:
28.55/9.78	Q DP problem:
28.55/9.78	The TRS P consists of the following rules:
28.55/9.78	
28.55/9.78	   H(x, x) -> G(x, x, f(k))
28.55/9.78	   G(d, x, x) -> A^2
28.55/9.78	   A^2 -> H(f(c), f(c))
28.55/9.78	   A^2 -> H(f(d), f(d))
28.55/9.78	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.78	   A^2 -> H(f(e), f(e))
28.55/9.78	   A^2 -> H(f(k), f(k))
28.55/9.78	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.78	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.78	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, e), U1(c, b))
28.55/9.78	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.78	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.78	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.78	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.78	   A^2 -> H(U1(k, e), f(e))
28.55/9.78	   A^2 -> H(U1(k, e), f(k))
28.55/9.78	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.78	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.78	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.78	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.78	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.78	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.78	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.78	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.78	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.78	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.78	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.78	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.78	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.78	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.78	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.78	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.78	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.78	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.78	   A^2 -> H(U1(c, c), b)
28.55/9.78	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.78	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.78	   A^2 -> H(U1(c, c), e)
28.55/9.78	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.78	   A^2 -> H(e, U1(c, b))
28.55/9.78	   A^2 -> H(e, U1(d, b))
28.55/9.78	   A^2 -> H(e, U1(b, c))
28.55/9.78	   A^2 -> H(e, U1(b, d))
28.55/9.78	   A^2 -> H(e, U1(c, c))
28.55/9.78	   A^2 -> H(e, f(e))
28.55/9.78	   A^2 -> H(e, f(k))
28.55/9.78	   A^2 -> H(e, U1(d, d))
28.55/9.78	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.78	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.78	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.78	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.78	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.78	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.78	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.78	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.78	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.78	   A^2 -> H(f(e), b)
28.55/9.78	   A^2 -> H(f(e), U1(e, d))
28.55/9.78	   A^2 -> H(f(e), U1(d, e))
28.55/9.78	   A^2 -> H(f(e), c)
28.55/9.78	   A^2 -> H(f(e), U1(e, k))
28.55/9.78	   A^2 -> H(f(e), U1(k, e))
28.55/9.78	   A^2 -> H(f(e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.78	   A^2 -> H(f(k), b)
28.55/9.78	   A^2 -> H(f(k), U1(e, d))
28.55/9.78	   A^2 -> H(f(k), U1(d, e))
28.55/9.78	   A^2 -> H(f(k), c)
28.55/9.78	   A^2 -> H(f(k), U1(e, k))
28.55/9.78	   A^2 -> H(f(k), U1(k, e))
28.55/9.78	   A^2 -> H(f(k), e)
28.55/9.78	   A^2 -> H(f(c), d)
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.78	   A^2 -> H(U1(k, k), f(e))
28.55/9.78	   A^2 -> H(U1(k, k), f(k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.78	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.78	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.78	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.78	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.78	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.78	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.78	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.78	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.78	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.78	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.78	   A^2 -> H(U1(d, d), b)
28.55/9.78	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.78	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.78	   A^2 -> H(U1(d, d), c)
28.55/9.78	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.78	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.78	   A^2 -> H(U1(d, d), e)
28.55/9.78	   A^2 -> H(f(d), d)
28.55/9.78	   A^2 -> H(f(d), k)
28.55/9.78	   A^2 -> H(U1(c, c), c)
28.55/9.78	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.78	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.78	   A^2 -> H(f(c), k)
28.55/9.78	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.78	   A^2 -> H(f(k), U1(k, k))
28.55/9.78	   A^2 -> H(f(e), e)
28.55/9.78	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.78	   A^2 -> H(d, U1(c, b))
28.55/9.78	   A^2 -> H(d, U1(d, b))
28.55/9.78	   A^2 -> H(d, U1(b, c))
28.55/9.78	   A^2 -> H(d, U1(b, d))
28.55/9.78	   A^2 -> H(d, U1(c, c))
28.55/9.78	   A^2 -> H(d, f(e))
28.55/9.78	   A^2 -> H(d, f(k))
28.55/9.78	   A^2 -> H(d, U1(d, d))
28.55/9.78	   A^2 -> H(a, U1(e, b))
28.55/9.78	   A^2 -> H(a, U1(k, b))
28.55/9.78	   A^2 -> H(a, U1(c, d))
28.55/9.78	   A^2 -> H(a, U1(d, c))
28.55/9.78	   A^2 -> H(a, U1(b, e))
28.55/9.78	   A^2 -> H(a, U1(b, k))
28.55/9.78	   A^2 -> H(a, U1(e, c))
28.55/9.78	   A^2 -> H(a, U1(k, c))
28.55/9.78	   A^2 -> H(a, U1(c, e))
28.55/9.78	   A^2 -> H(a, U1(c, k))
28.55/9.78	   A^2 -> H(a, U1(e, e))
28.55/9.78	   A^2 -> H(a, U1(k, k))
28.55/9.78	   A^2 -> H(a, U1(k, d))
28.55/9.78	   A^2 -> H(a, U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.78	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.78	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.78	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.78	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.78	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.78	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.78	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.78	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.78	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, a), b)
28.55/9.78	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.78	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.78	   A^2 -> H(U1(e, a), c)
28.55/9.78	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.78	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.78	   A^2 -> H(U1(e, a), e)
28.55/9.78	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, a), b)
28.55/9.78	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.78	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.78	   A^2 -> H(U1(k, a), c)
28.55/9.78	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.78	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.78	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.78	   A^2 -> H(U1(c, d), b)
28.55/9.78	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.78	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.78	   A^2 -> H(U1(c, d), c)
28.55/9.78	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.78	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.78	   A^2 -> H(U1(c, d), e)
28.55/9.78	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.78	   A^2 -> H(U1(c, a), d)
28.55/9.78	   A^2 -> H(U1(c, a), k)
28.55/9.78	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.78	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.78	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.78	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.78	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.78	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.78	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.78	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.78	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.78	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.78	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.78	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.78	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.78	   A^2 -> H(U1(d, c), b)
28.55/9.78	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.78	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.78	   A^2 -> H(U1(d, c), c)
28.55/9.78	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.78	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.78	   A^2 -> H(U1(d, c), e)
28.55/9.78	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.78	   A^2 -> H(U1(d, a), d)
28.55/9.78	   A^2 -> H(U1(d, a), k)
28.55/9.78	   A^2 -> H(U1(a, e), b)
28.55/9.78	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.78	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.78	   A^2 -> H(U1(a, e), c)
28.55/9.78	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.78	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.78	   A^2 -> H(U1(a, e), e)
28.55/9.78	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(a, k), b)
28.55/9.78	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.78	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.78	   A^2 -> H(U1(a, k), c)
28.55/9.78	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.78	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.78	   A^2 -> H(U1(a, k), e)
28.55/9.78	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(a, c), d)
28.55/9.78	   A^2 -> H(U1(a, c), k)
28.55/9.78	   A^2 -> H(U1(a, d), d)
28.55/9.78	   A^2 -> H(U1(a, d), k)
28.55/9.78	   A^2 -> H(k, U1(c, b))
28.55/9.78	   A^2 -> H(k, U1(d, b))
28.55/9.78	   A^2 -> H(k, U1(b, c))
28.55/9.78	   A^2 -> H(k, U1(b, d))
28.55/9.78	   A^2 -> H(k, U1(c, c))
28.55/9.78	   A^2 -> H(k, f(e))
28.55/9.78	   A^2 -> H(k, f(k))
28.55/9.78	   A^2 -> H(k, U1(d, d))
28.55/9.78	   A^2 -> H(c, U1(e, b))
28.55/9.78	   A^2 -> H(c, U1(k, b))
28.55/9.78	   A^2 -> H(c, U1(c, d))
28.55/9.78	   A^2 -> H(c, U1(d, c))
28.55/9.78	   A^2 -> H(c, U1(b, e))
28.55/9.78	   A^2 -> H(c, U1(b, k))
28.55/9.78	   A^2 -> H(c, U1(e, c))
28.55/9.78	   A^2 -> H(c, U1(k, c))
28.55/9.78	   A^2 -> H(c, U1(c, e))
28.55/9.78	   A^2 -> H(c, U1(c, k))
28.55/9.78	   A^2 -> H(c, U1(e, e))
28.55/9.78	   A^2 -> H(c, U1(k, k))
28.55/9.78	   A^2 -> H(c, U1(k, d))
28.55/9.78	   A^2 -> H(c, U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(e, k), U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, c), b)
28.55/9.78	   A^2 -> H(U1(e, c), U1(e, d))
28.55/9.78	   A^2 -> H(U1(e, c), U1(d, e))
28.55/9.78	   A^2 -> H(U1(e, c), U1(k, e))
28.55/9.78	   A^2 -> H(U1(e, c), U1(e, k))
28.55/9.78	   A^2 -> H(U1(e, c), e)
28.55/9.78	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.78	
28.55/9.78	The TRS R consists of the following rules:
28.55/9.78	
28.55/9.78	   f(x) -> U1(x, x)
28.55/9.78	   U1(e, x) -> x
28.55/9.78	   a -> c
28.55/9.78	   a -> d
28.55/9.78	   b -> c
28.55/9.78	   b -> d
28.55/9.78	   d -> k
28.55/9.78	   c -> e
28.55/9.78	   c -> k
28.55/9.78	
28.55/9.78	Q is empty.
28.55/9.78	We have to consider all minimal (P,Q,R)-chains.
28.55/9.78	----------------------------------------
28.55/9.78	
28.55/9.78	(1449) TransformationProof (EQUIVALENT)
28.55/9.78	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.78	
28.55/9.78	   (A^2 -> H(U1(k, e), U1(e, b)),A^2 -> H(U1(k, e), U1(e, b)))
28.55/9.78	   (A^2 -> H(U1(k, e), U1(k, b)),A^2 -> H(U1(k, e), U1(k, b)))
28.55/9.78	   (A^2 -> H(U1(k, e), U1(c, c)),A^2 -> H(U1(k, e), U1(c, c)))
28.55/9.78	   (A^2 -> H(U1(k, e), U1(c, d)),A^2 -> H(U1(k, e), U1(c, d)))
28.55/9.78	
28.55/9.78	
28.55/9.78	----------------------------------------
28.55/9.78	
28.55/9.78	(1450)
28.55/9.78	Obligation:
28.55/9.78	Q DP problem:
28.55/9.78	The TRS P consists of the following rules:
28.55/9.78	
28.55/9.78	   H(x, x) -> G(x, x, f(k))
28.55/9.78	   G(d, x, x) -> A^2
28.55/9.78	   A^2 -> H(f(c), f(c))
28.55/9.78	   A^2 -> H(f(d), f(d))
28.55/9.78	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.78	   A^2 -> H(f(e), f(e))
28.55/9.78	   A^2 -> H(f(k), f(k))
28.55/9.78	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.78	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.78	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, e), U1(d, b))
28.55/9.78	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.78	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.78	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.78	   A^2 -> H(U1(k, e), f(e))
28.55/9.78	   A^2 -> H(U1(k, e), f(k))
28.55/9.78	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.78	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.78	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.78	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.78	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.78	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.78	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.78	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.78	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.78	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.78	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.78	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.78	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.78	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.78	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.78	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.78	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.78	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.78	   A^2 -> H(U1(c, c), b)
28.55/9.78	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.78	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.78	   A^2 -> H(U1(c, c), e)
28.55/9.78	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.78	   A^2 -> H(e, U1(c, b))
28.55/9.78	   A^2 -> H(e, U1(d, b))
28.55/9.78	   A^2 -> H(e, U1(b, c))
28.55/9.78	   A^2 -> H(e, U1(b, d))
28.55/9.78	   A^2 -> H(e, U1(c, c))
28.55/9.78	   A^2 -> H(e, f(e))
28.55/9.78	   A^2 -> H(e, f(k))
28.55/9.78	   A^2 -> H(e, U1(d, d))
28.55/9.78	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.78	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.78	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.78	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.78	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.78	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.78	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.78	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.78	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.78	   A^2 -> H(f(e), b)
28.55/9.78	   A^2 -> H(f(e), U1(e, d))
28.55/9.78	   A^2 -> H(f(e), U1(d, e))
28.55/9.78	   A^2 -> H(f(e), c)
28.55/9.78	   A^2 -> H(f(e), U1(e, k))
28.55/9.78	   A^2 -> H(f(e), U1(k, e))
28.55/9.78	   A^2 -> H(f(e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.78	   A^2 -> H(f(k), b)
28.55/9.78	   A^2 -> H(f(k), U1(e, d))
28.55/9.78	   A^2 -> H(f(k), U1(d, e))
28.55/9.78	   A^2 -> H(f(k), c)
28.55/9.78	   A^2 -> H(f(k), U1(e, k))
28.55/9.78	   A^2 -> H(f(k), U1(k, e))
28.55/9.78	   A^2 -> H(f(k), e)
28.55/9.78	   A^2 -> H(f(c), d)
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.78	   A^2 -> H(U1(k, k), f(e))
28.55/9.78	   A^2 -> H(U1(k, k), f(k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.78	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.78	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.78	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.78	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.78	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.78	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.78	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.78	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.78	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.78	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.78	   A^2 -> H(U1(d, d), b)
28.55/9.78	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.78	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.78	   A^2 -> H(U1(d, d), c)
28.55/9.78	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.78	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.78	   A^2 -> H(U1(d, d), e)
28.55/9.78	   A^2 -> H(f(d), d)
28.55/9.78	   A^2 -> H(f(d), k)
28.55/9.78	   A^2 -> H(U1(c, c), c)
28.55/9.78	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.78	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.78	   A^2 -> H(f(c), k)
28.55/9.78	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.78	   A^2 -> H(f(k), U1(k, k))
28.55/9.78	   A^2 -> H(f(e), e)
28.55/9.78	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.78	   A^2 -> H(d, U1(c, b))
28.55/9.78	   A^2 -> H(d, U1(d, b))
28.55/9.78	   A^2 -> H(d, U1(b, c))
28.55/9.78	   A^2 -> H(d, U1(b, d))
28.55/9.78	   A^2 -> H(d, U1(c, c))
28.55/9.78	   A^2 -> H(d, f(e))
28.55/9.78	   A^2 -> H(d, f(k))
28.55/9.78	   A^2 -> H(d, U1(d, d))
28.55/9.78	   A^2 -> H(a, U1(e, b))
28.55/9.78	   A^2 -> H(a, U1(k, b))
28.55/9.78	   A^2 -> H(a, U1(c, d))
28.55/9.78	   A^2 -> H(a, U1(d, c))
28.55/9.78	   A^2 -> H(a, U1(b, e))
28.55/9.78	   A^2 -> H(a, U1(b, k))
28.55/9.78	   A^2 -> H(a, U1(e, c))
28.55/9.78	   A^2 -> H(a, U1(k, c))
28.55/9.78	   A^2 -> H(a, U1(c, e))
28.55/9.78	   A^2 -> H(a, U1(c, k))
28.55/9.78	   A^2 -> H(a, U1(e, e))
28.55/9.78	   A^2 -> H(a, U1(k, k))
28.55/9.78	   A^2 -> H(a, U1(k, d))
28.55/9.78	   A^2 -> H(a, U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.78	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.78	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.78	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.78	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.78	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.78	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.78	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.78	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.78	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, a), b)
28.55/9.78	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.78	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.78	   A^2 -> H(U1(e, a), c)
28.55/9.78	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.78	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.78	   A^2 -> H(U1(e, a), e)
28.55/9.78	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, a), b)
28.55/9.78	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.78	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.78	   A^2 -> H(U1(k, a), c)
28.55/9.78	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.78	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.78	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.78	   A^2 -> H(U1(c, d), b)
28.55/9.78	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.78	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.78	   A^2 -> H(U1(c, d), c)
28.55/9.78	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.78	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.78	   A^2 -> H(U1(c, d), e)
28.55/9.78	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.78	   A^2 -> H(U1(c, a), d)
28.55/9.78	   A^2 -> H(U1(c, a), k)
28.55/9.78	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.78	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.78	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.78	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.78	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.78	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.78	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.78	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.78	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.78	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.78	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.78	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.78	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.78	   A^2 -> H(U1(d, c), b)
28.55/9.78	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.78	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.78	   A^2 -> H(U1(d, c), c)
28.55/9.78	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.78	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.78	   A^2 -> H(U1(d, c), e)
28.55/9.78	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.78	   A^2 -> H(U1(d, a), d)
28.55/9.78	   A^2 -> H(U1(d, a), k)
28.55/9.78	   A^2 -> H(U1(a, e), b)
28.55/9.78	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.78	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.78	   A^2 -> H(U1(a, e), c)
28.55/9.78	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.78	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.78	   A^2 -> H(U1(a, e), e)
28.55/9.78	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(a, k), b)
28.55/9.78	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.78	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.78	   A^2 -> H(U1(a, k), c)
28.55/9.78	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.78	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.78	   A^2 -> H(U1(a, k), e)
28.55/9.78	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(a, c), d)
28.55/9.78	   A^2 -> H(U1(a, c), k)
28.55/9.78	   A^2 -> H(U1(a, d), d)
28.55/9.78	   A^2 -> H(U1(a, d), k)
28.55/9.78	   A^2 -> H(k, U1(c, b))
28.55/9.78	   A^2 -> H(k, U1(d, b))
28.55/9.78	   A^2 -> H(k, U1(b, c))
28.55/9.78	   A^2 -> H(k, U1(b, d))
28.55/9.78	   A^2 -> H(k, U1(c, c))
28.55/9.78	   A^2 -> H(k, f(e))
28.55/9.78	   A^2 -> H(k, f(k))
28.55/9.78	   A^2 -> H(k, U1(d, d))
28.55/9.78	   A^2 -> H(c, U1(e, b))
28.55/9.78	   A^2 -> H(c, U1(k, b))
28.55/9.78	   A^2 -> H(c, U1(c, d))
28.55/9.78	   A^2 -> H(c, U1(d, c))
28.55/9.78	   A^2 -> H(c, U1(b, e))
28.55/9.78	   A^2 -> H(c, U1(b, k))
28.55/9.78	   A^2 -> H(c, U1(e, c))
28.55/9.78	   A^2 -> H(c, U1(k, c))
28.55/9.78	   A^2 -> H(c, U1(c, e))
28.55/9.78	   A^2 -> H(c, U1(c, k))
28.55/9.78	   A^2 -> H(c, U1(e, e))
28.55/9.78	   A^2 -> H(c, U1(k, k))
28.55/9.78	   A^2 -> H(c, U1(k, d))
28.55/9.78	   A^2 -> H(c, U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(e, k), U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, c), b)
28.55/9.78	   A^2 -> H(U1(e, c), U1(e, d))
28.55/9.78	   A^2 -> H(U1(e, c), U1(d, e))
28.55/9.78	   A^2 -> H(U1(e, c), U1(k, e))
28.55/9.78	   A^2 -> H(U1(e, c), U1(e, k))
28.55/9.78	   A^2 -> H(U1(e, c), e)
28.55/9.78	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, e), U1(e, b))
28.55/9.78	   A^2 -> H(U1(k, e), U1(k, b))
28.55/9.78	   A^2 -> H(U1(k, e), U1(c, d))
28.55/9.78	
28.55/9.78	The TRS R consists of the following rules:
28.55/9.78	
28.55/9.78	   f(x) -> U1(x, x)
28.55/9.78	   U1(e, x) -> x
28.55/9.78	   a -> c
28.55/9.78	   a -> d
28.55/9.78	   b -> c
28.55/9.78	   b -> d
28.55/9.78	   d -> k
28.55/9.78	   c -> e
28.55/9.78	   c -> k
28.55/9.78	
28.55/9.78	Q is empty.
28.55/9.78	We have to consider all minimal (P,Q,R)-chains.
28.55/9.78	----------------------------------------
28.55/9.78	
28.55/9.78	(1451) TransformationProof (EQUIVALENT)
28.55/9.78	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.78	
28.55/9.78	   (A^2 -> H(U1(k, e), U1(k, b)),A^2 -> H(U1(k, e), U1(k, b)))
28.55/9.78	   (A^2 -> H(U1(k, e), U1(d, c)),A^2 -> H(U1(k, e), U1(d, c)))
28.55/9.78	   (A^2 -> H(U1(k, e), U1(d, d)),A^2 -> H(U1(k, e), U1(d, d)))
28.55/9.78	
28.55/9.78	
28.55/9.78	----------------------------------------
28.55/9.78	
28.55/9.78	(1452)
28.55/9.78	Obligation:
28.55/9.78	Q DP problem:
28.55/9.78	The TRS P consists of the following rules:
28.55/9.78	
28.55/9.78	   H(x, x) -> G(x, x, f(k))
28.55/9.78	   G(d, x, x) -> A^2
28.55/9.78	   A^2 -> H(f(c), f(c))
28.55/9.78	   A^2 -> H(f(d), f(d))
28.55/9.78	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.78	   A^2 -> H(f(e), f(e))
28.55/9.78	   A^2 -> H(f(k), f(k))
28.55/9.78	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.78	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.78	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, e), U1(b, c))
28.55/9.78	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.78	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.78	   A^2 -> H(U1(k, e), f(e))
28.55/9.78	   A^2 -> H(U1(k, e), f(k))
28.55/9.78	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.78	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.78	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.78	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.78	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.78	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.78	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.78	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.78	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.78	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.78	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.78	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.78	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.78	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.78	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.78	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.78	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.78	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.78	   A^2 -> H(U1(c, c), b)
28.55/9.78	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.78	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.78	   A^2 -> H(U1(c, c), e)
28.55/9.78	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.78	   A^2 -> H(e, U1(c, b))
28.55/9.78	   A^2 -> H(e, U1(d, b))
28.55/9.78	   A^2 -> H(e, U1(b, c))
28.55/9.78	   A^2 -> H(e, U1(b, d))
28.55/9.78	   A^2 -> H(e, U1(c, c))
28.55/9.78	   A^2 -> H(e, f(e))
28.55/9.78	   A^2 -> H(e, f(k))
28.55/9.78	   A^2 -> H(e, U1(d, d))
28.55/9.78	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.78	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.78	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.78	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.78	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.78	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.78	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.78	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.78	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.78	   A^2 -> H(f(e), b)
28.55/9.78	   A^2 -> H(f(e), U1(e, d))
28.55/9.78	   A^2 -> H(f(e), U1(d, e))
28.55/9.78	   A^2 -> H(f(e), c)
28.55/9.78	   A^2 -> H(f(e), U1(e, k))
28.55/9.78	   A^2 -> H(f(e), U1(k, e))
28.55/9.78	   A^2 -> H(f(e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.78	   A^2 -> H(f(k), b)
28.55/9.78	   A^2 -> H(f(k), U1(e, d))
28.55/9.78	   A^2 -> H(f(k), U1(d, e))
28.55/9.78	   A^2 -> H(f(k), c)
28.55/9.78	   A^2 -> H(f(k), U1(e, k))
28.55/9.78	   A^2 -> H(f(k), U1(k, e))
28.55/9.78	   A^2 -> H(f(k), e)
28.55/9.78	   A^2 -> H(f(c), d)
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.78	   A^2 -> H(U1(k, k), f(e))
28.55/9.78	   A^2 -> H(U1(k, k), f(k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.78	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.78	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.78	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.78	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.78	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.78	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.78	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.78	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.78	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.78	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.78	   A^2 -> H(U1(d, d), b)
28.55/9.78	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.78	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.78	   A^2 -> H(U1(d, d), c)
28.55/9.78	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.78	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.78	   A^2 -> H(U1(d, d), e)
28.55/9.78	   A^2 -> H(f(d), d)
28.55/9.78	   A^2 -> H(f(d), k)
28.55/9.78	   A^2 -> H(U1(c, c), c)
28.55/9.78	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.78	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.78	   A^2 -> H(f(c), k)
28.55/9.78	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.78	   A^2 -> H(f(k), U1(k, k))
28.55/9.78	   A^2 -> H(f(e), e)
28.55/9.78	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.78	   A^2 -> H(d, U1(c, b))
28.55/9.78	   A^2 -> H(d, U1(d, b))
28.55/9.78	   A^2 -> H(d, U1(b, c))
28.55/9.78	   A^2 -> H(d, U1(b, d))
28.55/9.78	   A^2 -> H(d, U1(c, c))
28.55/9.78	   A^2 -> H(d, f(e))
28.55/9.78	   A^2 -> H(d, f(k))
28.55/9.78	   A^2 -> H(d, U1(d, d))
28.55/9.78	   A^2 -> H(a, U1(e, b))
28.55/9.78	   A^2 -> H(a, U1(k, b))
28.55/9.78	   A^2 -> H(a, U1(c, d))
28.55/9.78	   A^2 -> H(a, U1(d, c))
28.55/9.78	   A^2 -> H(a, U1(b, e))
28.55/9.78	   A^2 -> H(a, U1(b, k))
28.55/9.78	   A^2 -> H(a, U1(e, c))
28.55/9.78	   A^2 -> H(a, U1(k, c))
28.55/9.78	   A^2 -> H(a, U1(c, e))
28.55/9.78	   A^2 -> H(a, U1(c, k))
28.55/9.78	   A^2 -> H(a, U1(e, e))
28.55/9.78	   A^2 -> H(a, U1(k, k))
28.55/9.78	   A^2 -> H(a, U1(k, d))
28.55/9.78	   A^2 -> H(a, U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.78	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.78	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.78	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.78	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.78	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.78	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.78	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.78	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.78	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, a), b)
28.55/9.78	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.78	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.78	   A^2 -> H(U1(e, a), c)
28.55/9.78	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.78	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.78	   A^2 -> H(U1(e, a), e)
28.55/9.78	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, a), b)
28.55/9.78	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.78	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.78	   A^2 -> H(U1(k, a), c)
28.55/9.78	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.78	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.78	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.78	   A^2 -> H(U1(c, d), b)
28.55/9.78	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.78	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.78	   A^2 -> H(U1(c, d), c)
28.55/9.78	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.78	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.78	   A^2 -> H(U1(c, d), e)
28.55/9.78	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.78	   A^2 -> H(U1(c, a), d)
28.55/9.78	   A^2 -> H(U1(c, a), k)
28.55/9.78	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.78	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.78	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.78	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.78	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.78	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.78	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.78	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.78	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.78	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.78	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.78	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.78	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.78	   A^2 -> H(U1(d, c), b)
28.55/9.78	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.78	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.78	   A^2 -> H(U1(d, c), c)
28.55/9.78	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.78	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.78	   A^2 -> H(U1(d, c), e)
28.55/9.78	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.78	   A^2 -> H(U1(d, a), d)
28.55/9.78	   A^2 -> H(U1(d, a), k)
28.55/9.78	   A^2 -> H(U1(a, e), b)
28.55/9.78	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.78	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.78	   A^2 -> H(U1(a, e), c)
28.55/9.78	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.78	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.78	   A^2 -> H(U1(a, e), e)
28.55/9.78	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(a, k), b)
28.55/9.78	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.78	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.78	   A^2 -> H(U1(a, k), c)
28.55/9.78	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.78	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.78	   A^2 -> H(U1(a, k), e)
28.55/9.78	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(a, c), d)
28.55/9.78	   A^2 -> H(U1(a, c), k)
28.55/9.78	   A^2 -> H(U1(a, d), d)
28.55/9.78	   A^2 -> H(U1(a, d), k)
28.55/9.78	   A^2 -> H(k, U1(c, b))
28.55/9.78	   A^2 -> H(k, U1(d, b))
28.55/9.78	   A^2 -> H(k, U1(b, c))
28.55/9.78	   A^2 -> H(k, U1(b, d))
28.55/9.78	   A^2 -> H(k, U1(c, c))
28.55/9.78	   A^2 -> H(k, f(e))
28.55/9.78	   A^2 -> H(k, f(k))
28.55/9.78	   A^2 -> H(k, U1(d, d))
28.55/9.78	   A^2 -> H(c, U1(e, b))
28.55/9.78	   A^2 -> H(c, U1(k, b))
28.55/9.78	   A^2 -> H(c, U1(c, d))
28.55/9.78	   A^2 -> H(c, U1(d, c))
28.55/9.78	   A^2 -> H(c, U1(b, e))
28.55/9.78	   A^2 -> H(c, U1(b, k))
28.55/9.78	   A^2 -> H(c, U1(e, c))
28.55/9.78	   A^2 -> H(c, U1(k, c))
28.55/9.78	   A^2 -> H(c, U1(c, e))
28.55/9.78	   A^2 -> H(c, U1(c, k))
28.55/9.78	   A^2 -> H(c, U1(e, e))
28.55/9.78	   A^2 -> H(c, U1(k, k))
28.55/9.78	   A^2 -> H(c, U1(k, d))
28.55/9.78	   A^2 -> H(c, U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(e, k), U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, c), b)
28.55/9.78	   A^2 -> H(U1(e, c), U1(e, d))
28.55/9.78	   A^2 -> H(U1(e, c), U1(d, e))
28.55/9.78	   A^2 -> H(U1(e, c), U1(k, e))
28.55/9.78	   A^2 -> H(U1(e, c), U1(e, k))
28.55/9.78	   A^2 -> H(U1(e, c), e)
28.55/9.78	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, e), U1(e, b))
28.55/9.78	   A^2 -> H(U1(k, e), U1(k, b))
28.55/9.78	   A^2 -> H(U1(k, e), U1(c, d))
28.55/9.78	   A^2 -> H(U1(k, e), U1(d, c))
28.55/9.78	
28.55/9.78	The TRS R consists of the following rules:
28.55/9.78	
28.55/9.78	   f(x) -> U1(x, x)
28.55/9.78	   U1(e, x) -> x
28.55/9.78	   a -> c
28.55/9.78	   a -> d
28.55/9.78	   b -> c
28.55/9.78	   b -> d
28.55/9.78	   d -> k
28.55/9.78	   c -> e
28.55/9.78	   c -> k
28.55/9.78	
28.55/9.78	Q is empty.
28.55/9.78	We have to consider all minimal (P,Q,R)-chains.
28.55/9.78	----------------------------------------
28.55/9.78	
28.55/9.78	(1453) TransformationProof (EQUIVALENT)
28.55/9.78	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.78	
28.55/9.78	   (A^2 -> H(U1(k, e), U1(c, c)),A^2 -> H(U1(k, e), U1(c, c)))
28.55/9.78	   (A^2 -> H(U1(k, e), U1(d, c)),A^2 -> H(U1(k, e), U1(d, c)))
28.55/9.78	   (A^2 -> H(U1(k, e), U1(b, e)),A^2 -> H(U1(k, e), U1(b, e)))
28.55/9.78	   (A^2 -> H(U1(k, e), U1(b, k)),A^2 -> H(U1(k, e), U1(b, k)))
28.55/9.78	
28.55/9.78	
28.55/9.78	----------------------------------------
28.55/9.78	
28.55/9.78	(1454)
28.55/9.78	Obligation:
28.55/9.78	Q DP problem:
28.55/9.78	The TRS P consists of the following rules:
28.55/9.78	
28.55/9.78	   H(x, x) -> G(x, x, f(k))
28.55/9.78	   G(d, x, x) -> A^2
28.55/9.78	   A^2 -> H(f(c), f(c))
28.55/9.78	   A^2 -> H(f(d), f(d))
28.55/9.78	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.78	   A^2 -> H(f(e), f(e))
28.55/9.78	   A^2 -> H(f(k), f(k))
28.55/9.78	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.78	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.78	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, e), U1(b, d))
28.55/9.78	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.78	   A^2 -> H(U1(k, e), f(e))
28.55/9.78	   A^2 -> H(U1(k, e), f(k))
28.55/9.78	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.78	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.78	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.78	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.78	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.78	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.78	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.78	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.78	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.78	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.78	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.78	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.78	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.78	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.78	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.78	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.78	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.78	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.78	   A^2 -> H(U1(c, c), b)
28.55/9.78	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.78	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.78	   A^2 -> H(U1(c, c), e)
28.55/9.78	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.78	   A^2 -> H(e, U1(c, b))
28.55/9.78	   A^2 -> H(e, U1(d, b))
28.55/9.78	   A^2 -> H(e, U1(b, c))
28.55/9.78	   A^2 -> H(e, U1(b, d))
28.55/9.78	   A^2 -> H(e, U1(c, c))
28.55/9.78	   A^2 -> H(e, f(e))
28.55/9.78	   A^2 -> H(e, f(k))
28.55/9.78	   A^2 -> H(e, U1(d, d))
28.55/9.78	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.78	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.78	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.78	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.78	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.78	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.78	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.78	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.78	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.78	   A^2 -> H(f(e), b)
28.55/9.78	   A^2 -> H(f(e), U1(e, d))
28.55/9.78	   A^2 -> H(f(e), U1(d, e))
28.55/9.78	   A^2 -> H(f(e), c)
28.55/9.78	   A^2 -> H(f(e), U1(e, k))
28.55/9.78	   A^2 -> H(f(e), U1(k, e))
28.55/9.78	   A^2 -> H(f(e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.78	   A^2 -> H(f(k), b)
28.55/9.78	   A^2 -> H(f(k), U1(e, d))
28.55/9.78	   A^2 -> H(f(k), U1(d, e))
28.55/9.78	   A^2 -> H(f(k), c)
28.55/9.78	   A^2 -> H(f(k), U1(e, k))
28.55/9.78	   A^2 -> H(f(k), U1(k, e))
28.55/9.78	   A^2 -> H(f(k), e)
28.55/9.78	   A^2 -> H(f(c), d)
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.78	   A^2 -> H(U1(k, k), f(e))
28.55/9.78	   A^2 -> H(U1(k, k), f(k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.78	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.78	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.78	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.78	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.78	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.78	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.78	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.78	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.78	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.78	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.78	   A^2 -> H(U1(d, d), b)
28.55/9.78	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.78	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.78	   A^2 -> H(U1(d, d), c)
28.55/9.78	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.78	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.78	   A^2 -> H(U1(d, d), e)
28.55/9.78	   A^2 -> H(f(d), d)
28.55/9.78	   A^2 -> H(f(d), k)
28.55/9.78	   A^2 -> H(U1(c, c), c)
28.55/9.78	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.78	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.78	   A^2 -> H(f(c), k)
28.55/9.78	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.78	   A^2 -> H(f(k), U1(k, k))
28.55/9.78	   A^2 -> H(f(e), e)
28.55/9.78	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.78	   A^2 -> H(d, U1(c, b))
28.55/9.78	   A^2 -> H(d, U1(d, b))
28.55/9.78	   A^2 -> H(d, U1(b, c))
28.55/9.78	   A^2 -> H(d, U1(b, d))
28.55/9.78	   A^2 -> H(d, U1(c, c))
28.55/9.78	   A^2 -> H(d, f(e))
28.55/9.78	   A^2 -> H(d, f(k))
28.55/9.78	   A^2 -> H(d, U1(d, d))
28.55/9.78	   A^2 -> H(a, U1(e, b))
28.55/9.78	   A^2 -> H(a, U1(k, b))
28.55/9.78	   A^2 -> H(a, U1(c, d))
28.55/9.78	   A^2 -> H(a, U1(d, c))
28.55/9.78	   A^2 -> H(a, U1(b, e))
28.55/9.78	   A^2 -> H(a, U1(b, k))
28.55/9.78	   A^2 -> H(a, U1(e, c))
28.55/9.78	   A^2 -> H(a, U1(k, c))
28.55/9.78	   A^2 -> H(a, U1(c, e))
28.55/9.78	   A^2 -> H(a, U1(c, k))
28.55/9.78	   A^2 -> H(a, U1(e, e))
28.55/9.78	   A^2 -> H(a, U1(k, k))
28.55/9.78	   A^2 -> H(a, U1(k, d))
28.55/9.78	   A^2 -> H(a, U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.78	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.78	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.78	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.78	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.78	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.78	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.78	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(e, e))
28.55/9.78	   A^2 -> H(U1(e, d), U1(k, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(k, d))
28.55/9.78	   A^2 -> H(U1(e, d), U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, a), b)
28.55/9.78	   A^2 -> H(U1(e, a), U1(e, d))
28.55/9.78	   A^2 -> H(U1(e, a), U1(d, e))
28.55/9.78	   A^2 -> H(U1(e, a), c)
28.55/9.78	   A^2 -> H(U1(e, a), U1(e, k))
28.55/9.78	   A^2 -> H(U1(e, a), U1(k, e))
28.55/9.78	   A^2 -> H(U1(e, a), e)
28.55/9.78	   A^2 -> H(U1(e, a), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, a), b)
28.55/9.78	   A^2 -> H(U1(k, a), U1(e, d))
28.55/9.78	   A^2 -> H(U1(k, a), U1(d, e))
28.55/9.78	   A^2 -> H(U1(k, a), c)
28.55/9.78	   A^2 -> H(U1(k, a), U1(e, k))
28.55/9.78	   A^2 -> H(U1(k, a), U1(k, e))
28.55/9.78	   A^2 -> H(U1(k, a), U1(k, k))
28.55/9.78	   A^2 -> H(U1(c, d), b)
28.55/9.78	   A^2 -> H(U1(c, d), U1(e, d))
28.55/9.78	   A^2 -> H(U1(c, d), U1(d, e))
28.55/9.78	   A^2 -> H(U1(c, d), c)
28.55/9.78	   A^2 -> H(U1(c, d), U1(e, k))
28.55/9.78	   A^2 -> H(U1(c, d), U1(k, e))
28.55/9.78	   A^2 -> H(U1(c, d), e)
28.55/9.78	   A^2 -> H(U1(c, d), U1(k, k))
28.55/9.78	   A^2 -> H(U1(c, a), d)
28.55/9.78	   A^2 -> H(U1(c, a), k)
28.55/9.78	   A^2 -> H(U1(d, e), U1(e, b))
28.55/9.78	   A^2 -> H(U1(d, e), U1(k, b))
28.55/9.78	   A^2 -> H(U1(d, e), U1(c, d))
28.55/9.78	   A^2 -> H(U1(d, e), U1(d, c))
28.55/9.78	   A^2 -> H(U1(d, e), U1(b, e))
28.55/9.78	   A^2 -> H(U1(d, e), U1(b, k))
28.55/9.78	   A^2 -> H(U1(d, e), U1(e, c))
28.55/9.78	   A^2 -> H(U1(d, e), U1(k, c))
28.55/9.78	   A^2 -> H(U1(d, e), U1(c, e))
28.55/9.78	   A^2 -> H(U1(d, e), U1(c, k))
28.55/9.78	   A^2 -> H(U1(d, e), U1(e, e))
28.55/9.78	   A^2 -> H(U1(d, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(d, e), U1(k, d))
28.55/9.78	   A^2 -> H(U1(d, e), U1(d, k))
28.55/9.78	   A^2 -> H(U1(d, c), b)
28.55/9.78	   A^2 -> H(U1(d, c), U1(e, d))
28.55/9.78	   A^2 -> H(U1(d, c), U1(d, e))
28.55/9.78	   A^2 -> H(U1(d, c), c)
28.55/9.78	   A^2 -> H(U1(d, c), U1(e, k))
28.55/9.78	   A^2 -> H(U1(d, c), U1(k, e))
28.55/9.78	   A^2 -> H(U1(d, c), e)
28.55/9.78	   A^2 -> H(U1(d, c), U1(k, k))
28.55/9.78	   A^2 -> H(U1(d, a), d)
28.55/9.78	   A^2 -> H(U1(d, a), k)
28.55/9.78	   A^2 -> H(U1(a, e), b)
28.55/9.78	   A^2 -> H(U1(a, e), U1(e, d))
28.55/9.78	   A^2 -> H(U1(a, e), U1(d, e))
28.55/9.78	   A^2 -> H(U1(a, e), c)
28.55/9.78	   A^2 -> H(U1(a, e), U1(e, k))
28.55/9.78	   A^2 -> H(U1(a, e), U1(k, e))
28.55/9.78	   A^2 -> H(U1(a, e), e)
28.55/9.78	   A^2 -> H(U1(a, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(a, k), b)
28.55/9.78	   A^2 -> H(U1(a, k), U1(e, d))
28.55/9.78	   A^2 -> H(U1(a, k), U1(d, e))
28.55/9.78	   A^2 -> H(U1(a, k), c)
28.55/9.78	   A^2 -> H(U1(a, k), U1(e, k))
28.55/9.78	   A^2 -> H(U1(a, k), U1(k, e))
28.55/9.78	   A^2 -> H(U1(a, k), e)
28.55/9.78	   A^2 -> H(U1(a, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(a, c), d)
28.55/9.78	   A^2 -> H(U1(a, c), k)
28.55/9.78	   A^2 -> H(U1(a, d), d)
28.55/9.78	   A^2 -> H(U1(a, d), k)
28.55/9.78	   A^2 -> H(k, U1(c, b))
28.55/9.78	   A^2 -> H(k, U1(d, b))
28.55/9.78	   A^2 -> H(k, U1(b, c))
28.55/9.78	   A^2 -> H(k, U1(b, d))
28.55/9.78	   A^2 -> H(k, U1(c, c))
28.55/9.78	   A^2 -> H(k, f(e))
28.55/9.78	   A^2 -> H(k, f(k))
28.55/9.78	   A^2 -> H(k, U1(d, d))
28.55/9.78	   A^2 -> H(c, U1(e, b))
28.55/9.78	   A^2 -> H(c, U1(k, b))
28.55/9.78	   A^2 -> H(c, U1(c, d))
28.55/9.78	   A^2 -> H(c, U1(d, c))
28.55/9.78	   A^2 -> H(c, U1(b, e))
28.55/9.78	   A^2 -> H(c, U1(b, k))
28.55/9.78	   A^2 -> H(c, U1(e, c))
28.55/9.78	   A^2 -> H(c, U1(k, c))
28.55/9.78	   A^2 -> H(c, U1(c, e))
28.55/9.78	   A^2 -> H(c, U1(c, k))
28.55/9.78	   A^2 -> H(c, U1(e, e))
28.55/9.78	   A^2 -> H(c, U1(k, k))
28.55/9.78	   A^2 -> H(c, U1(k, d))
28.55/9.78	   A^2 -> H(c, U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(e, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(e, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(e, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(e, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(e, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(e, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(e, k), U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, c), b)
28.55/9.78	   A^2 -> H(U1(e, c), U1(e, d))
28.55/9.78	   A^2 -> H(U1(e, c), U1(d, e))
28.55/9.78	   A^2 -> H(U1(e, c), U1(k, e))
28.55/9.78	   A^2 -> H(U1(e, c), U1(e, k))
28.55/9.78	   A^2 -> H(U1(e, c), e)
28.55/9.78	   A^2 -> H(U1(e, c), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, e), U1(e, b))
28.55/9.78	   A^2 -> H(U1(k, e), U1(k, b))
28.55/9.78	   A^2 -> H(U1(k, e), U1(c, d))
28.55/9.78	   A^2 -> H(U1(k, e), U1(d, c))
28.55/9.78	   A^2 -> H(U1(k, e), U1(b, e))
28.55/9.78	   A^2 -> H(U1(k, e), U1(b, k))
28.55/9.78	
28.55/9.78	The TRS R consists of the following rules:
28.55/9.78	
28.55/9.78	   f(x) -> U1(x, x)
28.55/9.78	   U1(e, x) -> x
28.55/9.78	   a -> c
28.55/9.78	   a -> d
28.55/9.78	   b -> c
28.55/9.78	   b -> d
28.55/9.78	   d -> k
28.55/9.78	   c -> e
28.55/9.78	   c -> k
28.55/9.78	
28.55/9.78	Q is empty.
28.55/9.78	We have to consider all minimal (P,Q,R)-chains.
28.55/9.78	----------------------------------------
28.55/9.78	
28.55/9.78	(1455) TransformationProof (EQUIVALENT)
28.55/9.78	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
28.55/9.78	
28.55/9.78	   (A^2 -> H(U1(k, e), U1(c, d)),A^2 -> H(U1(k, e), U1(c, d)))
28.55/9.78	   (A^2 -> H(U1(k, e), U1(d, d)),A^2 -> H(U1(k, e), U1(d, d)))
28.55/9.78	   (A^2 -> H(U1(k, e), U1(b, k)),A^2 -> H(U1(k, e), U1(b, k)))
28.55/9.78	
28.55/9.78	
28.55/9.78	----------------------------------------
28.55/9.78	
28.55/9.78	(1456)
28.55/9.78	Obligation:
28.55/9.78	Q DP problem:
28.55/9.78	The TRS P consists of the following rules:
28.55/9.78	
28.55/9.78	   H(x, x) -> G(x, x, f(k))
28.55/9.78	   G(d, x, x) -> A^2
28.55/9.78	   A^2 -> H(f(c), f(c))
28.55/9.78	   A^2 -> H(f(d), f(d))
28.55/9.78	   A^2 -> H(U1(c, c), U1(c, c))
28.55/9.78	   A^2 -> H(f(e), f(e))
28.55/9.78	   A^2 -> H(f(k), f(k))
28.55/9.78	   A^2 -> H(U1(d, d), U1(d, d))
28.55/9.78	   A^2 -> H(U1(c, d), U1(c, d))
28.55/9.78	   A^2 -> H(U1(d, c), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, c), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, e), U1(c, c))
28.55/9.78	   A^2 -> H(U1(k, e), f(e))
28.55/9.78	   A^2 -> H(U1(k, e), f(k))
28.55/9.78	   A^2 -> H(U1(k, e), U1(d, d))
28.55/9.78	   A^2 -> H(U1(k, c), U1(e, b))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, b))
28.55/9.78	   A^2 -> H(U1(k, c), U1(c, d))
28.55/9.78	   A^2 -> H(U1(k, c), U1(d, c))
28.55/9.78	   A^2 -> H(U1(k, c), U1(b, e))
28.55/9.78	   A^2 -> H(U1(k, c), U1(b, k))
28.55/9.78	   A^2 -> H(U1(k, c), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, c))
28.55/9.78	   A^2 -> H(U1(k, c), U1(c, e))
28.55/9.78	   A^2 -> H(U1(k, c), U1(c, k))
28.55/9.78	   A^2 -> H(U1(k, c), U1(e, e))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, c), U1(k, d))
28.55/9.78	   A^2 -> H(U1(k, c), U1(d, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(e, b))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, b))
28.55/9.78	   A^2 -> H(U1(c, e), U1(c, d))
28.55/9.78	   A^2 -> H(U1(c, e), U1(d, c))
28.55/9.78	   A^2 -> H(U1(c, e), U1(b, e))
28.55/9.78	   A^2 -> H(U1(c, e), U1(b, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(e, c))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, c))
28.55/9.78	   A^2 -> H(U1(c, e), U1(c, e))
28.55/9.78	   A^2 -> H(U1(c, e), U1(c, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(e, e))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(c, e), U1(k, d))
28.55/9.78	   A^2 -> H(U1(c, e), U1(d, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(c, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(c, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(c, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(c, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(c, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(c, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(c, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(c, k), U1(d, k))
28.55/9.78	   A^2 -> H(U1(c, c), b)
28.55/9.78	   A^2 -> H(U1(c, c), U1(e, d))
28.55/9.78	   A^2 -> H(U1(c, c), U1(d, e))
28.55/9.78	   A^2 -> H(U1(c, c), e)
28.55/9.78	   A^2 -> H(U1(c, c), U1(k, k))
28.55/9.78	   A^2 -> H(e, U1(c, b))
28.55/9.78	   A^2 -> H(e, U1(d, b))
28.55/9.78	   A^2 -> H(e, U1(b, c))
28.55/9.78	   A^2 -> H(e, U1(b, d))
28.55/9.78	   A^2 -> H(e, U1(c, c))
28.55/9.78	   A^2 -> H(e, f(e))
28.55/9.78	   A^2 -> H(e, f(k))
28.55/9.78	   A^2 -> H(e, U1(d, d))
28.55/9.78	   A^2 -> H(U1(e, e), U1(e, b))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, b))
28.55/9.78	   A^2 -> H(U1(e, e), U1(c, d))
28.55/9.78	   A^2 -> H(U1(e, e), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, e), U1(b, e))
28.55/9.78	   A^2 -> H(U1(e, e), U1(b, k))
28.55/9.78	   A^2 -> H(U1(e, e), U1(e, c))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, c))
28.55/9.78	   A^2 -> H(U1(e, e), U1(c, e))
28.55/9.78	   A^2 -> H(U1(e, e), U1(c, k))
28.55/9.78	   A^2 -> H(U1(e, e), U1(e, e))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(e, e), U1(k, d))
28.55/9.78	   A^2 -> H(U1(e, e), U1(d, k))
28.55/9.78	   A^2 -> H(f(e), b)
28.55/9.78	   A^2 -> H(f(e), U1(e, d))
28.55/9.78	   A^2 -> H(f(e), U1(d, e))
28.55/9.78	   A^2 -> H(f(e), c)
28.55/9.78	   A^2 -> H(f(e), U1(e, k))
28.55/9.78	   A^2 -> H(f(e), U1(k, e))
28.55/9.78	   A^2 -> H(f(e), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, k))
28.55/9.78	   A^2 -> H(f(k), b)
28.55/9.78	   A^2 -> H(f(k), U1(e, d))
28.55/9.78	   A^2 -> H(f(k), U1(d, e))
28.55/9.78	   A^2 -> H(f(k), c)
28.55/9.78	   A^2 -> H(f(k), U1(e, k))
28.55/9.78	   A^2 -> H(f(k), U1(k, e))
28.55/9.78	   A^2 -> H(f(k), e)
28.55/9.78	   A^2 -> H(f(c), d)
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, b))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, c))
28.55/9.78	   A^2 -> H(U1(k, k), U1(b, d))
28.55/9.78	   A^2 -> H(U1(k, k), U1(c, c))
28.55/9.78	   A^2 -> H(U1(k, k), f(e))
28.55/9.78	   A^2 -> H(U1(k, k), f(k))
28.55/9.78	   A^2 -> H(U1(k, k), U1(d, d))
28.55/9.78	   A^2 -> H(U1(k, d), U1(e, b))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, b))
28.55/9.78	   A^2 -> H(U1(k, d), U1(c, d))
28.55/9.78	   A^2 -> H(U1(k, d), U1(d, c))
28.55/9.78	   A^2 -> H(U1(k, d), U1(b, e))
28.55/9.78	   A^2 -> H(U1(k, d), U1(b, k))
28.55/9.78	   A^2 -> H(U1(k, d), U1(e, c))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, c))
28.55/9.78	   A^2 -> H(U1(k, d), U1(c, e))
28.55/9.78	   A^2 -> H(U1(k, d), U1(c, k))
28.55/9.78	   A^2 -> H(U1(k, d), U1(e, e))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, k))
28.55/9.78	   A^2 -> H(U1(k, d), U1(k, d))
28.55/9.78	   A^2 -> H(U1(k, d), U1(d, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(e, b))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, b))
28.55/9.78	   A^2 -> H(U1(d, k), U1(c, d))
28.55/9.78	   A^2 -> H(U1(d, k), U1(d, c))
28.55/9.78	   A^2 -> H(U1(d, k), U1(b, e))
28.55/9.78	   A^2 -> H(U1(d, k), U1(b, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(e, c))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, c))
28.55/9.78	   A^2 -> H(U1(d, k), U1(c, e))
28.55/9.78	   A^2 -> H(U1(d, k), U1(c, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(e, e))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, k))
28.55/9.78	   A^2 -> H(U1(d, k), U1(k, d))
28.55/9.78	   A^2 -> H(U1(d, k), U1(d, k))
28.55/9.78	   A^2 -> H(U1(d, d), b)
28.55/9.78	   A^2 -> H(U1(d, d), U1(e, d))
28.55/9.78	   A^2 -> H(U1(d, d), U1(d, e))
28.55/9.78	   A^2 -> H(U1(d, d), c)
28.55/9.78	   A^2 -> H(U1(d, d), U1(e, k))
28.55/9.78	   A^2 -> H(U1(d, d), U1(k, e))
28.55/9.78	   A^2 -> H(U1(d, d), e)
28.55/9.78	   A^2 -> H(f(d), d)
28.55/9.78	   A^2 -> H(f(d), k)
28.55/9.78	   A^2 -> H(U1(c, c), c)
28.55/9.78	   A^2 -> H(U1(c, c), U1(e, e))
28.55/9.78	   A^2 -> H(U1(c, c), U1(e, k))
28.55/9.78	   A^2 -> H(f(c), k)
28.55/9.78	   A^2 -> H(U1(c, c), U1(k, e))
28.55/9.78	   A^2 -> H(f(k), U1(k, k))
28.55/9.78	   A^2 -> H(f(e), e)
28.55/9.78	   A^2 -> H(U1(d, d), U1(k, k))
28.55/9.78	   A^2 -> H(d, U1(c, b))
28.55/9.78	   A^2 -> H(d, U1(d, b))
28.55/9.78	   A^2 -> H(d, U1(b, c))
28.55/9.78	   A^2 -> H(d, U1(b, d))
28.55/9.78	   A^2 -> H(d, U1(c, c))
28.55/9.78	   A^2 -> H(d, f(e))
28.55/9.78	   A^2 -> H(d, f(k))
28.55/9.78	   A^2 -> H(d, U1(d, d))
28.55/9.78	   A^2 -> H(a, U1(e, b))
28.55/9.78	   A^2 -> H(a, U1(k, b))
28.55/9.78	   A^2 -> H(a, U1(c, d))
28.55/9.78	   A^2 -> H(a, U1(d, c))
28.55/9.78	   A^2 -> H(a, U1(b, e))
28.55/9.78	   A^2 -> H(a, U1(b, k))
28.55/9.78	   A^2 -> H(a, U1(e, c))
28.55/9.78	   A^2 -> H(a, U1(k, c))
28.55/9.78	   A^2 -> H(a, U1(c, e))
28.55/9.78	   A^2 -> H(a, U1(c, k))
28.55/9.78	   A^2 -> H(a, U1(e, e))
28.55/9.78	   A^2 -> H(a, U1(k, k))
28.55/9.78	   A^2 -> H(a, U1(k, d))
28.55/9.78	   A^2 -> H(a, U1(d, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(e, b))
28.55/9.78	   A^2 -> H(U1(e, d), U1(k, b))
28.55/9.78	   A^2 -> H(U1(e, d), U1(c, d))
28.55/9.78	   A^2 -> H(U1(e, d), U1(d, c))
28.55/9.78	   A^2 -> H(U1(e, d), U1(b, e))
28.55/9.78	   A^2 -> H(U1(e, d), U1(b, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(e, c))
28.55/9.78	   A^2 -> H(U1(e, d), U1(k, c))
28.55/9.78	   A^2 -> H(U1(e, d), U1(c, e))
28.55/9.78	   A^2 -> H(U1(e, d), U1(c, k))
28.55/9.78	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.78	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.78	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.78	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.78	   A^2 -> H(U1(e, a), b)
28.56/9.78	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.78	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.78	   A^2 -> H(U1(e, a), c)
28.56/9.78	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.78	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.78	   A^2 -> H(U1(e, a), e)
28.56/9.78	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.78	   A^2 -> H(U1(k, a), b)
28.56/9.78	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.78	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.78	   A^2 -> H(U1(k, a), c)
28.56/9.78	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.78	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.78	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.78	   A^2 -> H(U1(c, d), b)
28.56/9.78	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.78	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.78	   A^2 -> H(U1(c, d), c)
28.56/9.78	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.78	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.78	   A^2 -> H(U1(c, d), e)
28.56/9.78	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.78	   A^2 -> H(U1(c, a), d)
28.56/9.78	   A^2 -> H(U1(c, a), k)
28.56/9.78	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.78	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.78	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.78	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.78	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.78	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.78	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.78	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.78	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.78	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.78	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.78	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.78	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.78	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.78	   A^2 -> H(U1(d, c), b)
28.56/9.78	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.78	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.78	   A^2 -> H(U1(d, c), c)
28.56/9.78	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.78	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.78	   A^2 -> H(U1(d, c), e)
28.56/9.78	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.78	   A^2 -> H(U1(d, a), d)
28.56/9.78	   A^2 -> H(U1(d, a), k)
28.56/9.78	   A^2 -> H(U1(a, e), b)
28.56/9.78	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.78	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.78	   A^2 -> H(U1(a, e), c)
28.56/9.78	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.78	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.78	   A^2 -> H(U1(a, e), e)
28.56/9.78	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.78	   A^2 -> H(U1(a, k), b)
28.56/9.78	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.78	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.78	   A^2 -> H(U1(a, k), c)
28.56/9.78	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.78	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.78	   A^2 -> H(U1(a, k), e)
28.56/9.78	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.78	   A^2 -> H(U1(a, c), d)
28.56/9.78	   A^2 -> H(U1(a, c), k)
28.56/9.78	   A^2 -> H(U1(a, d), d)
28.56/9.78	   A^2 -> H(U1(a, d), k)
28.56/9.78	   A^2 -> H(k, U1(c, b))
28.56/9.78	   A^2 -> H(k, U1(d, b))
28.56/9.78	   A^2 -> H(k, U1(b, c))
28.56/9.78	   A^2 -> H(k, U1(b, d))
28.56/9.78	   A^2 -> H(k, U1(c, c))
28.56/9.78	   A^2 -> H(k, f(e))
28.56/9.78	   A^2 -> H(k, f(k))
28.56/9.78	   A^2 -> H(k, U1(d, d))
28.56/9.78	   A^2 -> H(c, U1(e, b))
28.56/9.78	   A^2 -> H(c, U1(k, b))
28.56/9.78	   A^2 -> H(c, U1(c, d))
28.56/9.78	   A^2 -> H(c, U1(d, c))
28.56/9.78	   A^2 -> H(c, U1(b, e))
28.56/9.78	   A^2 -> H(c, U1(b, k))
28.56/9.78	   A^2 -> H(c, U1(e, c))
28.56/9.78	   A^2 -> H(c, U1(k, c))
28.56/9.78	   A^2 -> H(c, U1(c, e))
28.56/9.78	   A^2 -> H(c, U1(c, k))
28.56/9.78	   A^2 -> H(c, U1(e, e))
28.56/9.78	   A^2 -> H(c, U1(k, k))
28.56/9.78	   A^2 -> H(c, U1(k, d))
28.56/9.78	   A^2 -> H(c, U1(d, k))
28.56/9.78	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.78	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.78	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.78	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.78	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.78	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.78	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.78	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.78	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.78	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.78	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.78	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.78	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.78	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.78	   A^2 -> H(U1(e, c), b)
28.56/9.78	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.78	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.78	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.78	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.78	   A^2 -> H(U1(e, c), e)
28.56/9.78	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.78	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.78	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.78	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.78	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.78	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.78	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.78	
28.56/9.78	The TRS R consists of the following rules:
28.56/9.78	
28.56/9.78	   f(x) -> U1(x, x)
28.56/9.78	   U1(e, x) -> x
28.56/9.78	   a -> c
28.56/9.78	   a -> d
28.56/9.78	   b -> c
28.56/9.78	   b -> d
28.56/9.78	   d -> k
28.56/9.78	   c -> e
28.56/9.78	   c -> k
28.56/9.78	
28.56/9.78	Q is empty.
28.56/9.78	We have to consider all minimal (P,Q,R)-chains.
28.56/9.78	----------------------------------------
28.56/9.78	
28.56/9.78	(1457) TransformationProof (EQUIVALENT)
28.56/9.78	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.78	
28.56/9.78	   (A^2 -> H(U1(k, e), U1(e, c)),A^2 -> H(U1(k, e), U1(e, c)))
28.56/9.78	   (A^2 -> H(U1(k, e), U1(k, c)),A^2 -> H(U1(k, e), U1(k, c)))
28.56/9.78	   (A^2 -> H(U1(k, e), U1(c, e)),A^2 -> H(U1(k, e), U1(c, e)))
28.56/9.78	   (A^2 -> H(U1(k, e), U1(c, k)),A^2 -> H(U1(k, e), U1(c, k)))
28.56/9.78	
28.56/9.78	
28.56/9.78	----------------------------------------
28.56/9.78	
28.56/9.78	(1458)
28.56/9.78	Obligation:
28.56/9.78	Q DP problem:
28.56/9.78	The TRS P consists of the following rules:
28.56/9.78	
28.56/9.78	   H(x, x) -> G(x, x, f(k))
28.56/9.78	   G(d, x, x) -> A^2
28.56/9.78	   A^2 -> H(f(c), f(c))
28.56/9.78	   A^2 -> H(f(d), f(d))
28.56/9.78	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.78	   A^2 -> H(f(e), f(e))
28.56/9.78	   A^2 -> H(f(k), f(k))
28.56/9.78	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.78	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.78	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.78	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.78	   A^2 -> H(U1(k, e), f(e))
28.56/9.78	   A^2 -> H(U1(k, e), f(k))
28.56/9.78	   A^2 -> H(U1(k, e), U1(d, d))
28.56/9.78	   A^2 -> H(U1(k, c), U1(e, b))
28.56/9.78	   A^2 -> H(U1(k, c), U1(k, b))
28.56/9.78	   A^2 -> H(U1(k, c), U1(c, d))
28.56/9.78	   A^2 -> H(U1(k, c), U1(d, c))
28.56/9.78	   A^2 -> H(U1(k, c), U1(b, e))
28.56/9.78	   A^2 -> H(U1(k, c), U1(b, k))
28.56/9.78	   A^2 -> H(U1(k, c), U1(e, c))
28.56/9.78	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.78	   A^2 -> H(U1(k, c), U1(c, e))
28.56/9.78	   A^2 -> H(U1(k, c), U1(c, k))
28.56/9.78	   A^2 -> H(U1(k, c), U1(e, e))
28.56/9.78	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.78	   A^2 -> H(U1(k, c), U1(k, d))
28.56/9.78	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.78	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.78	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.78	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.78	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.78	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.78	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.78	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.78	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.78	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.78	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.78	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.78	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.78	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.78	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.78	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.78	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.78	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.78	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.78	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.78	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.78	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.78	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.78	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.78	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.78	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.78	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.78	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.78	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.78	   A^2 -> H(U1(c, c), b)
28.56/9.78	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.78	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.78	   A^2 -> H(U1(c, c), e)
28.56/9.78	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.78	   A^2 -> H(e, U1(c, b))
28.56/9.78	   A^2 -> H(e, U1(d, b))
28.56/9.78	   A^2 -> H(e, U1(b, c))
28.56/9.78	   A^2 -> H(e, U1(b, d))
28.56/9.78	   A^2 -> H(e, U1(c, c))
28.56/9.78	   A^2 -> H(e, f(e))
28.56/9.78	   A^2 -> H(e, f(k))
28.56/9.78	   A^2 -> H(e, U1(d, d))
28.56/9.78	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.78	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.78	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.78	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.78	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.78	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.78	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.78	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.78	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.78	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.78	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.78	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.78	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.78	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.78	   A^2 -> H(f(e), b)
28.56/9.78	   A^2 -> H(f(e), U1(e, d))
28.56/9.78	   A^2 -> H(f(e), U1(d, e))
28.56/9.78	   A^2 -> H(f(e), c)
28.56/9.78	   A^2 -> H(f(e), U1(e, k))
28.56/9.78	   A^2 -> H(f(e), U1(k, e))
28.56/9.78	   A^2 -> H(f(e), U1(k, k))
28.56/9.78	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.78	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.78	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.78	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.78	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.78	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.78	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.78	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.78	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.78	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.78	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.78	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.78	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.78	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.78	   A^2 -> H(f(k), b)
28.56/9.78	   A^2 -> H(f(k), U1(e, d))
28.56/9.78	   A^2 -> H(f(k), U1(d, e))
28.56/9.78	   A^2 -> H(f(k), c)
28.56/9.78	   A^2 -> H(f(k), U1(e, k))
28.56/9.78	   A^2 -> H(f(k), U1(k, e))
28.56/9.78	   A^2 -> H(f(k), e)
28.56/9.78	   A^2 -> H(f(c), d)
28.56/9.78	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.78	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.78	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.78	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.78	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.78	   A^2 -> H(U1(k, k), f(e))
28.56/9.78	   A^2 -> H(U1(k, k), f(k))
28.56/9.78	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.78	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.78	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.78	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.78	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.78	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.78	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.78	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.78	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.78	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.78	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.78	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.78	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.78	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.78	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.78	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.78	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.78	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.78	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.78	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.78	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.78	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.78	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.78	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.78	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.78	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.78	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.78	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.78	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.78	   A^2 -> H(U1(d, d), b)
28.56/9.78	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.78	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.78	   A^2 -> H(U1(d, d), c)
28.56/9.78	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.78	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.78	   A^2 -> H(U1(d, d), e)
28.56/9.78	   A^2 -> H(f(d), d)
28.56/9.78	   A^2 -> H(f(d), k)
28.56/9.78	   A^2 -> H(U1(c, c), c)
28.56/9.78	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.78	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.78	   A^2 -> H(f(c), k)
28.56/9.78	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.78	   A^2 -> H(f(k), U1(k, k))
28.56/9.78	   A^2 -> H(f(e), e)
28.56/9.78	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.78	   A^2 -> H(d, U1(c, b))
28.56/9.78	   A^2 -> H(d, U1(d, b))
28.56/9.78	   A^2 -> H(d, U1(b, c))
28.56/9.78	   A^2 -> H(d, U1(b, d))
28.56/9.78	   A^2 -> H(d, U1(c, c))
28.56/9.78	   A^2 -> H(d, f(e))
28.56/9.78	   A^2 -> H(d, f(k))
28.56/9.78	   A^2 -> H(d, U1(d, d))
28.56/9.78	   A^2 -> H(a, U1(e, b))
28.56/9.78	   A^2 -> H(a, U1(k, b))
28.56/9.78	   A^2 -> H(a, U1(c, d))
28.56/9.78	   A^2 -> H(a, U1(d, c))
28.56/9.78	   A^2 -> H(a, U1(b, e))
28.56/9.78	   A^2 -> H(a, U1(b, k))
28.56/9.78	   A^2 -> H(a, U1(e, c))
28.56/9.78	   A^2 -> H(a, U1(k, c))
28.56/9.78	   A^2 -> H(a, U1(c, e))
28.56/9.78	   A^2 -> H(a, U1(c, k))
28.56/9.78	   A^2 -> H(a, U1(e, e))
28.56/9.78	   A^2 -> H(a, U1(k, k))
28.56/9.78	   A^2 -> H(a, U1(k, d))
28.56/9.78	   A^2 -> H(a, U1(d, k))
28.56/9.78	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.78	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.78	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.78	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.78	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.78	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.78	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.78	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.78	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.78	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.78	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.78	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.78	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.78	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, a), b)
28.56/9.79	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.79	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.79	   A^2 -> H(U1(e, a), c)
28.56/9.79	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.79	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.79	   A^2 -> H(U1(e, a), e)
28.56/9.79	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, a), b)
28.56/9.79	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.79	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.79	   A^2 -> H(U1(k, a), c)
28.56/9.79	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.79	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.79	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, d), b)
28.56/9.79	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.79	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.79	   A^2 -> H(U1(c, d), c)
28.56/9.79	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.79	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.79	   A^2 -> H(U1(c, d), e)
28.56/9.79	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, a), d)
28.56/9.79	   A^2 -> H(U1(c, a), k)
28.56/9.79	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.79	   A^2 -> H(U1(d, c), b)
28.56/9.79	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.79	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.79	   A^2 -> H(U1(d, c), c)
28.56/9.79	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.79	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.79	   A^2 -> H(U1(d, c), e)
28.56/9.79	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.79	   A^2 -> H(U1(d, a), d)
28.56/9.79	   A^2 -> H(U1(d, a), k)
28.56/9.79	   A^2 -> H(U1(a, e), b)
28.56/9.79	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.79	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.79	   A^2 -> H(U1(a, e), c)
28.56/9.79	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.79	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.79	   A^2 -> H(U1(a, e), e)
28.56/9.79	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(a, k), b)
28.56/9.79	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.79	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.79	   A^2 -> H(U1(a, k), c)
28.56/9.79	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.79	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.79	   A^2 -> H(U1(a, k), e)
28.56/9.79	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(a, c), d)
28.56/9.79	   A^2 -> H(U1(a, c), k)
28.56/9.79	   A^2 -> H(U1(a, d), d)
28.56/9.79	   A^2 -> H(U1(a, d), k)
28.56/9.79	   A^2 -> H(k, U1(c, b))
28.56/9.79	   A^2 -> H(k, U1(d, b))
28.56/9.79	   A^2 -> H(k, U1(b, c))
28.56/9.79	   A^2 -> H(k, U1(b, d))
28.56/9.79	   A^2 -> H(k, U1(c, c))
28.56/9.79	   A^2 -> H(k, f(e))
28.56/9.79	   A^2 -> H(k, f(k))
28.56/9.79	   A^2 -> H(k, U1(d, d))
28.56/9.79	   A^2 -> H(c, U1(e, b))
28.56/9.79	   A^2 -> H(c, U1(k, b))
28.56/9.79	   A^2 -> H(c, U1(c, d))
28.56/9.79	   A^2 -> H(c, U1(d, c))
28.56/9.79	   A^2 -> H(c, U1(b, e))
28.56/9.79	   A^2 -> H(c, U1(b, k))
28.56/9.79	   A^2 -> H(c, U1(e, c))
28.56/9.79	   A^2 -> H(c, U1(k, c))
28.56/9.79	   A^2 -> H(c, U1(c, e))
28.56/9.79	   A^2 -> H(c, U1(c, k))
28.56/9.79	   A^2 -> H(c, U1(e, e))
28.56/9.79	   A^2 -> H(c, U1(k, k))
28.56/9.79	   A^2 -> H(c, U1(k, d))
28.56/9.79	   A^2 -> H(c, U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, c), b)
28.56/9.79	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.79	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.79	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.79	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.79	   A^2 -> H(U1(e, c), e)
28.56/9.79	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.79	
28.56/9.79	The TRS R consists of the following rules:
28.56/9.79	
28.56/9.79	   f(x) -> U1(x, x)
28.56/9.79	   U1(e, x) -> x
28.56/9.79	   a -> c
28.56/9.79	   a -> d
28.56/9.79	   b -> c
28.56/9.79	   b -> d
28.56/9.79	   d -> k
28.56/9.79	   c -> e
28.56/9.79	   c -> k
28.56/9.79	
28.56/9.79	Q is empty.
28.56/9.79	We have to consider all minimal (P,Q,R)-chains.
28.56/9.79	----------------------------------------
28.56/9.79	
28.56/9.79	(1459) TransformationProof (EQUIVALENT)
28.56/9.79	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), f(e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.79	
28.56/9.79	   (A^2 -> H(U1(k, e), U1(e, e)),A^2 -> H(U1(k, e), U1(e, e)))
28.56/9.79	
28.56/9.79	
28.56/9.79	----------------------------------------
28.56/9.79	
28.56/9.79	(1460)
28.56/9.79	Obligation:
28.56/9.79	Q DP problem:
28.56/9.79	The TRS P consists of the following rules:
28.56/9.79	
28.56/9.79	   H(x, x) -> G(x, x, f(k))
28.56/9.79	   G(d, x, x) -> A^2
28.56/9.79	   A^2 -> H(f(c), f(c))
28.56/9.79	   A^2 -> H(f(d), f(d))
28.56/9.79	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.79	   A^2 -> H(f(e), f(e))
28.56/9.79	   A^2 -> H(f(k), f(k))
28.56/9.79	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.79	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.79	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, e), f(k))
28.56/9.79	   A^2 -> H(U1(k, e), U1(d, d))
28.56/9.79	   A^2 -> H(U1(k, c), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, c), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, c), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, c), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, c), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, c), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, c), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.79	   A^2 -> H(U1(c, c), b)
28.56/9.79	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.79	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.79	   A^2 -> H(U1(c, c), e)
28.56/9.79	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.79	   A^2 -> H(e, U1(c, b))
28.56/9.79	   A^2 -> H(e, U1(d, b))
28.56/9.79	   A^2 -> H(e, U1(b, c))
28.56/9.79	   A^2 -> H(e, U1(b, d))
28.56/9.79	   A^2 -> H(e, U1(c, c))
28.56/9.79	   A^2 -> H(e, f(e))
28.56/9.79	   A^2 -> H(e, f(k))
28.56/9.79	   A^2 -> H(e, U1(d, d))
28.56/9.79	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.79	   A^2 -> H(f(e), b)
28.56/9.79	   A^2 -> H(f(e), U1(e, d))
28.56/9.79	   A^2 -> H(f(e), U1(d, e))
28.56/9.79	   A^2 -> H(f(e), c)
28.56/9.79	   A^2 -> H(f(e), U1(e, k))
28.56/9.79	   A^2 -> H(f(e), U1(k, e))
28.56/9.79	   A^2 -> H(f(e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.79	   A^2 -> H(f(k), b)
28.56/9.79	   A^2 -> H(f(k), U1(e, d))
28.56/9.79	   A^2 -> H(f(k), U1(d, e))
28.56/9.79	   A^2 -> H(f(k), c)
28.56/9.79	   A^2 -> H(f(k), U1(e, k))
28.56/9.79	   A^2 -> H(f(k), U1(k, e))
28.56/9.79	   A^2 -> H(f(k), e)
28.56/9.79	   A^2 -> H(f(c), d)
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.79	   A^2 -> H(U1(k, k), f(e))
28.56/9.79	   A^2 -> H(U1(k, k), f(k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.79	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.79	   A^2 -> H(U1(d, d), b)
28.56/9.79	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.79	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.79	   A^2 -> H(U1(d, d), c)
28.56/9.79	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.79	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.79	   A^2 -> H(U1(d, d), e)
28.56/9.79	   A^2 -> H(f(d), d)
28.56/9.79	   A^2 -> H(f(d), k)
28.56/9.79	   A^2 -> H(U1(c, c), c)
28.56/9.79	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.79	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.79	   A^2 -> H(f(c), k)
28.56/9.79	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.79	   A^2 -> H(f(k), U1(k, k))
28.56/9.79	   A^2 -> H(f(e), e)
28.56/9.79	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.79	   A^2 -> H(d, U1(c, b))
28.56/9.79	   A^2 -> H(d, U1(d, b))
28.56/9.79	   A^2 -> H(d, U1(b, c))
28.56/9.79	   A^2 -> H(d, U1(b, d))
28.56/9.79	   A^2 -> H(d, U1(c, c))
28.56/9.79	   A^2 -> H(d, f(e))
28.56/9.79	   A^2 -> H(d, f(k))
28.56/9.79	   A^2 -> H(d, U1(d, d))
28.56/9.79	   A^2 -> H(a, U1(e, b))
28.56/9.79	   A^2 -> H(a, U1(k, b))
28.56/9.79	   A^2 -> H(a, U1(c, d))
28.56/9.79	   A^2 -> H(a, U1(d, c))
28.56/9.79	   A^2 -> H(a, U1(b, e))
28.56/9.79	   A^2 -> H(a, U1(b, k))
28.56/9.79	   A^2 -> H(a, U1(e, c))
28.56/9.79	   A^2 -> H(a, U1(k, c))
28.56/9.79	   A^2 -> H(a, U1(c, e))
28.56/9.79	   A^2 -> H(a, U1(c, k))
28.56/9.79	   A^2 -> H(a, U1(e, e))
28.56/9.79	   A^2 -> H(a, U1(k, k))
28.56/9.79	   A^2 -> H(a, U1(k, d))
28.56/9.79	   A^2 -> H(a, U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.79	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.79	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.79	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.79	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.79	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.79	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, a), b)
28.56/9.79	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.79	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.79	   A^2 -> H(U1(e, a), c)
28.56/9.79	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.79	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.79	   A^2 -> H(U1(e, a), e)
28.56/9.79	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, a), b)
28.56/9.79	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.79	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.79	   A^2 -> H(U1(k, a), c)
28.56/9.79	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.79	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.79	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, d), b)
28.56/9.79	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.79	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.79	   A^2 -> H(U1(c, d), c)
28.56/9.79	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.79	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.79	   A^2 -> H(U1(c, d), e)
28.56/9.79	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, a), d)
28.56/9.79	   A^2 -> H(U1(c, a), k)
28.56/9.79	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.79	   A^2 -> H(U1(d, c), b)
28.56/9.79	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.79	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.79	   A^2 -> H(U1(d, c), c)
28.56/9.79	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.79	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.79	   A^2 -> H(U1(d, c), e)
28.56/9.79	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.79	   A^2 -> H(U1(d, a), d)
28.56/9.79	   A^2 -> H(U1(d, a), k)
28.56/9.79	   A^2 -> H(U1(a, e), b)
28.56/9.79	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.79	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.79	   A^2 -> H(U1(a, e), c)
28.56/9.79	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.79	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.79	   A^2 -> H(U1(a, e), e)
28.56/9.79	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(a, k), b)
28.56/9.79	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.79	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.79	   A^2 -> H(U1(a, k), c)
28.56/9.79	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.79	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.79	   A^2 -> H(U1(a, k), e)
28.56/9.79	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(a, c), d)
28.56/9.79	   A^2 -> H(U1(a, c), k)
28.56/9.79	   A^2 -> H(U1(a, d), d)
28.56/9.79	   A^2 -> H(U1(a, d), k)
28.56/9.79	   A^2 -> H(k, U1(c, b))
28.56/9.79	   A^2 -> H(k, U1(d, b))
28.56/9.79	   A^2 -> H(k, U1(b, c))
28.56/9.79	   A^2 -> H(k, U1(b, d))
28.56/9.79	   A^2 -> H(k, U1(c, c))
28.56/9.79	   A^2 -> H(k, f(e))
28.56/9.79	   A^2 -> H(k, f(k))
28.56/9.79	   A^2 -> H(k, U1(d, d))
28.56/9.79	   A^2 -> H(c, U1(e, b))
28.56/9.79	   A^2 -> H(c, U1(k, b))
28.56/9.79	   A^2 -> H(c, U1(c, d))
28.56/9.79	   A^2 -> H(c, U1(d, c))
28.56/9.79	   A^2 -> H(c, U1(b, e))
28.56/9.79	   A^2 -> H(c, U1(b, k))
28.56/9.79	   A^2 -> H(c, U1(e, c))
28.56/9.79	   A^2 -> H(c, U1(k, c))
28.56/9.79	   A^2 -> H(c, U1(c, e))
28.56/9.79	   A^2 -> H(c, U1(c, k))
28.56/9.79	   A^2 -> H(c, U1(e, e))
28.56/9.79	   A^2 -> H(c, U1(k, k))
28.56/9.79	   A^2 -> H(c, U1(k, d))
28.56/9.79	   A^2 -> H(c, U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, c), b)
28.56/9.79	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.79	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.79	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.79	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.79	   A^2 -> H(U1(e, c), e)
28.56/9.79	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.79	
28.56/9.79	The TRS R consists of the following rules:
28.56/9.79	
28.56/9.79	   f(x) -> U1(x, x)
28.56/9.79	   U1(e, x) -> x
28.56/9.79	   a -> c
28.56/9.79	   a -> d
28.56/9.79	   b -> c
28.56/9.79	   b -> d
28.56/9.79	   d -> k
28.56/9.79	   c -> e
28.56/9.79	   c -> k
28.56/9.79	
28.56/9.79	Q is empty.
28.56/9.79	We have to consider all minimal (P,Q,R)-chains.
28.56/9.79	----------------------------------------
28.56/9.79	
28.56/9.79	(1461) TransformationProof (EQUIVALENT)
28.56/9.79	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), f(k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.79	
28.56/9.79	   (A^2 -> H(U1(k, e), U1(k, k)),A^2 -> H(U1(k, e), U1(k, k)))
28.56/9.79	
28.56/9.79	
28.56/9.79	----------------------------------------
28.56/9.79	
28.56/9.79	(1462)
28.56/9.79	Obligation:
28.56/9.79	Q DP problem:
28.56/9.79	The TRS P consists of the following rules:
28.56/9.79	
28.56/9.79	   H(x, x) -> G(x, x, f(k))
28.56/9.79	   G(d, x, x) -> A^2
28.56/9.79	   A^2 -> H(f(c), f(c))
28.56/9.79	   A^2 -> H(f(d), f(d))
28.56/9.79	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.79	   A^2 -> H(f(e), f(e))
28.56/9.79	   A^2 -> H(f(k), f(k))
28.56/9.79	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.79	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.79	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(d, d))
28.56/9.79	   A^2 -> H(U1(k, c), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, c), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, c), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, c), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, c), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, c), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, c), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.79	   A^2 -> H(U1(c, c), b)
28.56/9.79	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.79	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.79	   A^2 -> H(U1(c, c), e)
28.56/9.79	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.79	   A^2 -> H(e, U1(c, b))
28.56/9.79	   A^2 -> H(e, U1(d, b))
28.56/9.79	   A^2 -> H(e, U1(b, c))
28.56/9.79	   A^2 -> H(e, U1(b, d))
28.56/9.79	   A^2 -> H(e, U1(c, c))
28.56/9.79	   A^2 -> H(e, f(e))
28.56/9.79	   A^2 -> H(e, f(k))
28.56/9.79	   A^2 -> H(e, U1(d, d))
28.56/9.79	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.79	   A^2 -> H(f(e), b)
28.56/9.79	   A^2 -> H(f(e), U1(e, d))
28.56/9.79	   A^2 -> H(f(e), U1(d, e))
28.56/9.79	   A^2 -> H(f(e), c)
28.56/9.79	   A^2 -> H(f(e), U1(e, k))
28.56/9.79	   A^2 -> H(f(e), U1(k, e))
28.56/9.79	   A^2 -> H(f(e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.79	   A^2 -> H(f(k), b)
28.56/9.79	   A^2 -> H(f(k), U1(e, d))
28.56/9.79	   A^2 -> H(f(k), U1(d, e))
28.56/9.79	   A^2 -> H(f(k), c)
28.56/9.79	   A^2 -> H(f(k), U1(e, k))
28.56/9.79	   A^2 -> H(f(k), U1(k, e))
28.56/9.79	   A^2 -> H(f(k), e)
28.56/9.79	   A^2 -> H(f(c), d)
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.79	   A^2 -> H(U1(k, k), f(e))
28.56/9.79	   A^2 -> H(U1(k, k), f(k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.79	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.79	   A^2 -> H(U1(d, d), b)
28.56/9.79	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.79	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.79	   A^2 -> H(U1(d, d), c)
28.56/9.79	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.79	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.79	   A^2 -> H(U1(d, d), e)
28.56/9.79	   A^2 -> H(f(d), d)
28.56/9.79	   A^2 -> H(f(d), k)
28.56/9.79	   A^2 -> H(U1(c, c), c)
28.56/9.79	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.79	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.79	   A^2 -> H(f(c), k)
28.56/9.79	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.79	   A^2 -> H(f(k), U1(k, k))
28.56/9.79	   A^2 -> H(f(e), e)
28.56/9.79	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.79	   A^2 -> H(d, U1(c, b))
28.56/9.79	   A^2 -> H(d, U1(d, b))
28.56/9.79	   A^2 -> H(d, U1(b, c))
28.56/9.79	   A^2 -> H(d, U1(b, d))
28.56/9.79	   A^2 -> H(d, U1(c, c))
28.56/9.79	   A^2 -> H(d, f(e))
28.56/9.79	   A^2 -> H(d, f(k))
28.56/9.79	   A^2 -> H(d, U1(d, d))
28.56/9.79	   A^2 -> H(a, U1(e, b))
28.56/9.79	   A^2 -> H(a, U1(k, b))
28.56/9.79	   A^2 -> H(a, U1(c, d))
28.56/9.79	   A^2 -> H(a, U1(d, c))
28.56/9.79	   A^2 -> H(a, U1(b, e))
28.56/9.79	   A^2 -> H(a, U1(b, k))
28.56/9.79	   A^2 -> H(a, U1(e, c))
28.56/9.79	   A^2 -> H(a, U1(k, c))
28.56/9.79	   A^2 -> H(a, U1(c, e))
28.56/9.79	   A^2 -> H(a, U1(c, k))
28.56/9.79	   A^2 -> H(a, U1(e, e))
28.56/9.79	   A^2 -> H(a, U1(k, k))
28.56/9.79	   A^2 -> H(a, U1(k, d))
28.56/9.79	   A^2 -> H(a, U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.79	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.79	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.79	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.79	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.79	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.79	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, a), b)
28.56/9.79	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.79	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.79	   A^2 -> H(U1(e, a), c)
28.56/9.79	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.79	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.79	   A^2 -> H(U1(e, a), e)
28.56/9.79	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, a), b)
28.56/9.79	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.79	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.79	   A^2 -> H(U1(k, a), c)
28.56/9.79	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.79	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.79	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, d), b)
28.56/9.79	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.79	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.79	   A^2 -> H(U1(c, d), c)
28.56/9.79	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.79	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.79	   A^2 -> H(U1(c, d), e)
28.56/9.79	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, a), d)
28.56/9.79	   A^2 -> H(U1(c, a), k)
28.56/9.79	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.79	   A^2 -> H(U1(d, c), b)
28.56/9.79	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.79	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.79	   A^2 -> H(U1(d, c), c)
28.56/9.79	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.79	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.79	   A^2 -> H(U1(d, c), e)
28.56/9.79	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.79	   A^2 -> H(U1(d, a), d)
28.56/9.79	   A^2 -> H(U1(d, a), k)
28.56/9.79	   A^2 -> H(U1(a, e), b)
28.56/9.79	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.79	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.79	   A^2 -> H(U1(a, e), c)
28.56/9.79	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.79	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.79	   A^2 -> H(U1(a, e), e)
28.56/9.79	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(a, k), b)
28.56/9.79	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.79	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.79	   A^2 -> H(U1(a, k), c)
28.56/9.79	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.79	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.79	   A^2 -> H(U1(a, k), e)
28.56/9.79	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(a, c), d)
28.56/9.79	   A^2 -> H(U1(a, c), k)
28.56/9.79	   A^2 -> H(U1(a, d), d)
28.56/9.79	   A^2 -> H(U1(a, d), k)
28.56/9.79	   A^2 -> H(k, U1(c, b))
28.56/9.79	   A^2 -> H(k, U1(d, b))
28.56/9.79	   A^2 -> H(k, U1(b, c))
28.56/9.79	   A^2 -> H(k, U1(b, d))
28.56/9.79	   A^2 -> H(k, U1(c, c))
28.56/9.79	   A^2 -> H(k, f(e))
28.56/9.79	   A^2 -> H(k, f(k))
28.56/9.79	   A^2 -> H(k, U1(d, d))
28.56/9.79	   A^2 -> H(c, U1(e, b))
28.56/9.79	   A^2 -> H(c, U1(k, b))
28.56/9.79	   A^2 -> H(c, U1(c, d))
28.56/9.79	   A^2 -> H(c, U1(d, c))
28.56/9.79	   A^2 -> H(c, U1(b, e))
28.56/9.79	   A^2 -> H(c, U1(b, k))
28.56/9.79	   A^2 -> H(c, U1(e, c))
28.56/9.79	   A^2 -> H(c, U1(k, c))
28.56/9.79	   A^2 -> H(c, U1(c, e))
28.56/9.79	   A^2 -> H(c, U1(c, k))
28.56/9.79	   A^2 -> H(c, U1(e, e))
28.56/9.79	   A^2 -> H(c, U1(k, k))
28.56/9.79	   A^2 -> H(c, U1(k, d))
28.56/9.79	   A^2 -> H(c, U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, c), b)
28.56/9.79	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.79	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.79	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.79	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.79	   A^2 -> H(U1(e, c), e)
28.56/9.79	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, e), U1(k, k))
28.56/9.79	
28.56/9.79	The TRS R consists of the following rules:
28.56/9.79	
28.56/9.79	   f(x) -> U1(x, x)
28.56/9.79	   U1(e, x) -> x
28.56/9.79	   a -> c
28.56/9.79	   a -> d
28.56/9.79	   b -> c
28.56/9.79	   b -> d
28.56/9.79	   d -> k
28.56/9.79	   c -> e
28.56/9.79	   c -> k
28.56/9.79	
28.56/9.79	Q is empty.
28.56/9.79	We have to consider all minimal (P,Q,R)-chains.
28.56/9.79	----------------------------------------
28.56/9.79	
28.56/9.79	(1463) DependencyGraphProof (EQUIVALENT)
28.56/9.79	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.79	----------------------------------------
28.56/9.79	
28.56/9.79	(1464)
28.56/9.79	Obligation:
28.56/9.79	Q DP problem:
28.56/9.79	The TRS P consists of the following rules:
28.56/9.79	
28.56/9.79	   G(d, x, x) -> A^2
28.56/9.79	   A^2 -> H(f(c), f(c))
28.56/9.79	   H(x, x) -> G(x, x, f(k))
28.56/9.79	   A^2 -> H(f(d), f(d))
28.56/9.79	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.79	   A^2 -> H(f(e), f(e))
28.56/9.79	   A^2 -> H(f(k), f(k))
28.56/9.79	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.79	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.79	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(d, d))
28.56/9.79	   A^2 -> H(U1(k, c), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, c), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, c), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, c), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, c), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, c), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, c), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.79	   A^2 -> H(U1(c, c), b)
28.56/9.79	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.79	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.79	   A^2 -> H(U1(c, c), e)
28.56/9.79	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.79	   A^2 -> H(e, U1(c, b))
28.56/9.79	   A^2 -> H(e, U1(d, b))
28.56/9.79	   A^2 -> H(e, U1(b, c))
28.56/9.79	   A^2 -> H(e, U1(b, d))
28.56/9.79	   A^2 -> H(e, U1(c, c))
28.56/9.79	   A^2 -> H(e, f(e))
28.56/9.79	   A^2 -> H(e, f(k))
28.56/9.79	   A^2 -> H(e, U1(d, d))
28.56/9.79	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.79	   A^2 -> H(f(e), b)
28.56/9.79	   A^2 -> H(f(e), U1(e, d))
28.56/9.79	   A^2 -> H(f(e), U1(d, e))
28.56/9.79	   A^2 -> H(f(e), c)
28.56/9.79	   A^2 -> H(f(e), U1(e, k))
28.56/9.79	   A^2 -> H(f(e), U1(k, e))
28.56/9.79	   A^2 -> H(f(e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.79	   A^2 -> H(f(k), b)
28.56/9.79	   A^2 -> H(f(k), U1(e, d))
28.56/9.79	   A^2 -> H(f(k), U1(d, e))
28.56/9.79	   A^2 -> H(f(k), c)
28.56/9.79	   A^2 -> H(f(k), U1(e, k))
28.56/9.79	   A^2 -> H(f(k), U1(k, e))
28.56/9.79	   A^2 -> H(f(k), e)
28.56/9.79	   A^2 -> H(f(c), d)
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.79	   A^2 -> H(U1(k, k), f(e))
28.56/9.79	   A^2 -> H(U1(k, k), f(k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.79	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.79	   A^2 -> H(U1(d, d), b)
28.56/9.79	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.79	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.79	   A^2 -> H(U1(d, d), c)
28.56/9.79	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.79	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.79	   A^2 -> H(U1(d, d), e)
28.56/9.79	   A^2 -> H(f(d), d)
28.56/9.79	   A^2 -> H(f(d), k)
28.56/9.79	   A^2 -> H(U1(c, c), c)
28.56/9.79	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.79	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.79	   A^2 -> H(f(c), k)
28.56/9.79	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.79	   A^2 -> H(f(k), U1(k, k))
28.56/9.79	   A^2 -> H(f(e), e)
28.56/9.79	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.79	   A^2 -> H(d, U1(c, b))
28.56/9.79	   A^2 -> H(d, U1(d, b))
28.56/9.79	   A^2 -> H(d, U1(b, c))
28.56/9.79	   A^2 -> H(d, U1(b, d))
28.56/9.79	   A^2 -> H(d, U1(c, c))
28.56/9.79	   A^2 -> H(d, f(e))
28.56/9.79	   A^2 -> H(d, f(k))
28.56/9.79	   A^2 -> H(d, U1(d, d))
28.56/9.79	   A^2 -> H(a, U1(e, b))
28.56/9.79	   A^2 -> H(a, U1(k, b))
28.56/9.79	   A^2 -> H(a, U1(c, d))
28.56/9.79	   A^2 -> H(a, U1(d, c))
28.56/9.79	   A^2 -> H(a, U1(b, e))
28.56/9.79	   A^2 -> H(a, U1(b, k))
28.56/9.79	   A^2 -> H(a, U1(e, c))
28.56/9.79	   A^2 -> H(a, U1(k, c))
28.56/9.79	   A^2 -> H(a, U1(c, e))
28.56/9.79	   A^2 -> H(a, U1(c, k))
28.56/9.79	   A^2 -> H(a, U1(e, e))
28.56/9.79	   A^2 -> H(a, U1(k, k))
28.56/9.79	   A^2 -> H(a, U1(k, d))
28.56/9.79	   A^2 -> H(a, U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.79	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.79	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.79	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.79	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.79	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.79	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, a), b)
28.56/9.79	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.79	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.79	   A^2 -> H(U1(e, a), c)
28.56/9.79	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.79	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.79	   A^2 -> H(U1(e, a), e)
28.56/9.79	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, a), b)
28.56/9.79	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.79	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.79	   A^2 -> H(U1(k, a), c)
28.56/9.79	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.79	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.79	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, d), b)
28.56/9.79	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.79	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.79	   A^2 -> H(U1(c, d), c)
28.56/9.79	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.79	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.79	   A^2 -> H(U1(c, d), e)
28.56/9.79	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, a), d)
28.56/9.79	   A^2 -> H(U1(c, a), k)
28.56/9.79	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.79	   A^2 -> H(U1(d, c), b)
28.56/9.79	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.79	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.79	   A^2 -> H(U1(d, c), c)
28.56/9.79	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.79	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.79	   A^2 -> H(U1(d, c), e)
28.56/9.79	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.79	   A^2 -> H(U1(d, a), d)
28.56/9.79	   A^2 -> H(U1(d, a), k)
28.56/9.79	   A^2 -> H(U1(a, e), b)
28.56/9.79	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.79	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.79	   A^2 -> H(U1(a, e), c)
28.56/9.79	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.79	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.79	   A^2 -> H(U1(a, e), e)
28.56/9.79	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(a, k), b)
28.56/9.79	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.79	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.79	   A^2 -> H(U1(a, k), c)
28.56/9.79	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.79	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.79	   A^2 -> H(U1(a, k), e)
28.56/9.79	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(a, c), d)
28.56/9.79	   A^2 -> H(U1(a, c), k)
28.56/9.79	   A^2 -> H(U1(a, d), d)
28.56/9.79	   A^2 -> H(U1(a, d), k)
28.56/9.79	   A^2 -> H(k, U1(c, b))
28.56/9.79	   A^2 -> H(k, U1(d, b))
28.56/9.79	   A^2 -> H(k, U1(b, c))
28.56/9.79	   A^2 -> H(k, U1(b, d))
28.56/9.79	   A^2 -> H(k, U1(c, c))
28.56/9.79	   A^2 -> H(k, f(e))
28.56/9.79	   A^2 -> H(k, f(k))
28.56/9.79	   A^2 -> H(k, U1(d, d))
28.56/9.79	   A^2 -> H(c, U1(e, b))
28.56/9.79	   A^2 -> H(c, U1(k, b))
28.56/9.79	   A^2 -> H(c, U1(c, d))
28.56/9.79	   A^2 -> H(c, U1(d, c))
28.56/9.79	   A^2 -> H(c, U1(b, e))
28.56/9.79	   A^2 -> H(c, U1(b, k))
28.56/9.79	   A^2 -> H(c, U1(e, c))
28.56/9.79	   A^2 -> H(c, U1(k, c))
28.56/9.79	   A^2 -> H(c, U1(c, e))
28.56/9.79	   A^2 -> H(c, U1(c, k))
28.56/9.79	   A^2 -> H(c, U1(e, e))
28.56/9.79	   A^2 -> H(c, U1(k, k))
28.56/9.79	   A^2 -> H(c, U1(k, d))
28.56/9.79	   A^2 -> H(c, U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, c), b)
28.56/9.79	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.79	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.79	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.79	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.79	   A^2 -> H(U1(e, c), e)
28.56/9.79	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.79	
28.56/9.79	The TRS R consists of the following rules:
28.56/9.79	
28.56/9.79	   f(x) -> U1(x, x)
28.56/9.79	   U1(e, x) -> x
28.56/9.79	   a -> c
28.56/9.79	   a -> d
28.56/9.79	   b -> c
28.56/9.79	   b -> d
28.56/9.79	   d -> k
28.56/9.79	   c -> e
28.56/9.79	   c -> k
28.56/9.79	
28.56/9.79	Q is empty.
28.56/9.79	We have to consider all minimal (P,Q,R)-chains.
28.56/9.79	----------------------------------------
28.56/9.79	
28.56/9.79	(1465) TransformationProof (EQUIVALENT)
28.56/9.79	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.79	
28.56/9.79	   (A^2 -> H(U1(k, e), U1(k, d)),A^2 -> H(U1(k, e), U1(k, d)))
28.56/9.79	   (A^2 -> H(U1(k, e), U1(d, k)),A^2 -> H(U1(k, e), U1(d, k)))
28.56/9.79	
28.56/9.79	
28.56/9.79	----------------------------------------
28.56/9.79	
28.56/9.79	(1466)
28.56/9.79	Obligation:
28.56/9.79	Q DP problem:
28.56/9.79	The TRS P consists of the following rules:
28.56/9.79	
28.56/9.79	   G(d, x, x) -> A^2
28.56/9.79	   A^2 -> H(f(c), f(c))
28.56/9.79	   H(x, x) -> G(x, x, f(k))
28.56/9.79	   A^2 -> H(f(d), f(d))
28.56/9.79	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.79	   A^2 -> H(f(e), f(e))
28.56/9.79	   A^2 -> H(f(k), f(k))
28.56/9.79	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.79	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.79	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, c), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, c), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, c), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, c), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, c), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, c), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.79	   A^2 -> H(U1(c, c), b)
28.56/9.79	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.79	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.79	   A^2 -> H(U1(c, c), e)
28.56/9.79	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.79	   A^2 -> H(e, U1(c, b))
28.56/9.79	   A^2 -> H(e, U1(d, b))
28.56/9.79	   A^2 -> H(e, U1(b, c))
28.56/9.79	   A^2 -> H(e, U1(b, d))
28.56/9.79	   A^2 -> H(e, U1(c, c))
28.56/9.79	   A^2 -> H(e, f(e))
28.56/9.79	   A^2 -> H(e, f(k))
28.56/9.79	   A^2 -> H(e, U1(d, d))
28.56/9.79	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.79	   A^2 -> H(f(e), b)
28.56/9.79	   A^2 -> H(f(e), U1(e, d))
28.56/9.79	   A^2 -> H(f(e), U1(d, e))
28.56/9.79	   A^2 -> H(f(e), c)
28.56/9.79	   A^2 -> H(f(e), U1(e, k))
28.56/9.79	   A^2 -> H(f(e), U1(k, e))
28.56/9.79	   A^2 -> H(f(e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.79	   A^2 -> H(f(k), b)
28.56/9.79	   A^2 -> H(f(k), U1(e, d))
28.56/9.79	   A^2 -> H(f(k), U1(d, e))
28.56/9.79	   A^2 -> H(f(k), c)
28.56/9.79	   A^2 -> H(f(k), U1(e, k))
28.56/9.79	   A^2 -> H(f(k), U1(k, e))
28.56/9.79	   A^2 -> H(f(k), e)
28.56/9.79	   A^2 -> H(f(c), d)
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.79	   A^2 -> H(U1(k, k), f(e))
28.56/9.79	   A^2 -> H(U1(k, k), f(k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.79	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.79	   A^2 -> H(U1(d, d), b)
28.56/9.79	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.79	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.79	   A^2 -> H(U1(d, d), c)
28.56/9.79	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.79	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.79	   A^2 -> H(U1(d, d), e)
28.56/9.79	   A^2 -> H(f(d), d)
28.56/9.79	   A^2 -> H(f(d), k)
28.56/9.79	   A^2 -> H(U1(c, c), c)
28.56/9.79	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.79	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.79	   A^2 -> H(f(c), k)
28.56/9.79	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.79	   A^2 -> H(f(k), U1(k, k))
28.56/9.79	   A^2 -> H(f(e), e)
28.56/9.79	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.79	   A^2 -> H(d, U1(c, b))
28.56/9.79	   A^2 -> H(d, U1(d, b))
28.56/9.79	   A^2 -> H(d, U1(b, c))
28.56/9.79	   A^2 -> H(d, U1(b, d))
28.56/9.79	   A^2 -> H(d, U1(c, c))
28.56/9.79	   A^2 -> H(d, f(e))
28.56/9.79	   A^2 -> H(d, f(k))
28.56/9.79	   A^2 -> H(d, U1(d, d))
28.56/9.79	   A^2 -> H(a, U1(e, b))
28.56/9.79	   A^2 -> H(a, U1(k, b))
28.56/9.79	   A^2 -> H(a, U1(c, d))
28.56/9.79	   A^2 -> H(a, U1(d, c))
28.56/9.79	   A^2 -> H(a, U1(b, e))
28.56/9.79	   A^2 -> H(a, U1(b, k))
28.56/9.79	   A^2 -> H(a, U1(e, c))
28.56/9.79	   A^2 -> H(a, U1(k, c))
28.56/9.79	   A^2 -> H(a, U1(c, e))
28.56/9.79	   A^2 -> H(a, U1(c, k))
28.56/9.79	   A^2 -> H(a, U1(e, e))
28.56/9.79	   A^2 -> H(a, U1(k, k))
28.56/9.79	   A^2 -> H(a, U1(k, d))
28.56/9.79	   A^2 -> H(a, U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.79	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.79	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.79	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.79	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.79	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.79	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, a), b)
28.56/9.79	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.79	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.79	   A^2 -> H(U1(e, a), c)
28.56/9.79	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.79	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.79	   A^2 -> H(U1(e, a), e)
28.56/9.79	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, a), b)
28.56/9.79	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.79	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.79	   A^2 -> H(U1(k, a), c)
28.56/9.79	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.79	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.79	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, d), b)
28.56/9.79	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.79	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.79	   A^2 -> H(U1(c, d), c)
28.56/9.79	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.79	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.79	   A^2 -> H(U1(c, d), e)
28.56/9.79	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, a), d)
28.56/9.79	   A^2 -> H(U1(c, a), k)
28.56/9.79	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.79	   A^2 -> H(U1(d, c), b)
28.56/9.79	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.79	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.79	   A^2 -> H(U1(d, c), c)
28.56/9.79	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.79	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.79	   A^2 -> H(U1(d, c), e)
28.56/9.79	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.79	   A^2 -> H(U1(d, a), d)
28.56/9.79	   A^2 -> H(U1(d, a), k)
28.56/9.79	   A^2 -> H(U1(a, e), b)
28.56/9.79	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.79	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.79	   A^2 -> H(U1(a, e), c)
28.56/9.79	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.79	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.79	   A^2 -> H(U1(a, e), e)
28.56/9.79	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(a, k), b)
28.56/9.79	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.79	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.79	   A^2 -> H(U1(a, k), c)
28.56/9.79	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.79	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.79	   A^2 -> H(U1(a, k), e)
28.56/9.79	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(a, c), d)
28.56/9.79	   A^2 -> H(U1(a, c), k)
28.56/9.79	   A^2 -> H(U1(a, d), d)
28.56/9.79	   A^2 -> H(U1(a, d), k)
28.56/9.79	   A^2 -> H(k, U1(c, b))
28.56/9.79	   A^2 -> H(k, U1(d, b))
28.56/9.79	   A^2 -> H(k, U1(b, c))
28.56/9.79	   A^2 -> H(k, U1(b, d))
28.56/9.79	   A^2 -> H(k, U1(c, c))
28.56/9.79	   A^2 -> H(k, f(e))
28.56/9.79	   A^2 -> H(k, f(k))
28.56/9.79	   A^2 -> H(k, U1(d, d))
28.56/9.79	   A^2 -> H(c, U1(e, b))
28.56/9.79	   A^2 -> H(c, U1(k, b))
28.56/9.79	   A^2 -> H(c, U1(c, d))
28.56/9.79	   A^2 -> H(c, U1(d, c))
28.56/9.79	   A^2 -> H(c, U1(b, e))
28.56/9.79	   A^2 -> H(c, U1(b, k))
28.56/9.79	   A^2 -> H(c, U1(e, c))
28.56/9.79	   A^2 -> H(c, U1(k, c))
28.56/9.79	   A^2 -> H(c, U1(c, e))
28.56/9.79	   A^2 -> H(c, U1(c, k))
28.56/9.79	   A^2 -> H(c, U1(e, e))
28.56/9.79	   A^2 -> H(c, U1(k, k))
28.56/9.79	   A^2 -> H(c, U1(k, d))
28.56/9.79	   A^2 -> H(c, U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, c), b)
28.56/9.79	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.79	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.79	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.79	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.79	   A^2 -> H(U1(e, c), e)
28.56/9.79	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.79	
28.56/9.79	The TRS R consists of the following rules:
28.56/9.79	
28.56/9.79	   f(x) -> U1(x, x)
28.56/9.79	   U1(e, x) -> x
28.56/9.79	   a -> c
28.56/9.79	   a -> d
28.56/9.79	   b -> c
28.56/9.79	   b -> d
28.56/9.79	   d -> k
28.56/9.79	   c -> e
28.56/9.79	   c -> k
28.56/9.79	
28.56/9.79	Q is empty.
28.56/9.79	We have to consider all minimal (P,Q,R)-chains.
28.56/9.79	----------------------------------------
28.56/9.79	
28.56/9.79	(1467) TransformationProof (EQUIVALENT)
28.56/9.79	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.79	
28.56/9.79	   (A^2 -> H(U1(k, e), U1(e, b)),A^2 -> H(U1(k, e), U1(e, b)))
28.56/9.79	   (A^2 -> H(U1(k, k), U1(e, b)),A^2 -> H(U1(k, k), U1(e, b)))
28.56/9.79	   (A^2 -> H(U1(k, c), b),A^2 -> H(U1(k, c), b))
28.56/9.79	   (A^2 -> H(U1(k, c), U1(e, c)),A^2 -> H(U1(k, c), U1(e, c)))
28.56/9.79	   (A^2 -> H(U1(k, c), U1(e, d)),A^2 -> H(U1(k, c), U1(e, d)))
28.56/9.79	
28.56/9.79	
28.56/9.79	----------------------------------------
28.56/9.79	
28.56/9.79	(1468)
28.56/9.79	Obligation:
28.56/9.79	Q DP problem:
28.56/9.79	The TRS P consists of the following rules:
28.56/9.79	
28.56/9.79	   G(d, x, x) -> A^2
28.56/9.79	   A^2 -> H(f(c), f(c))
28.56/9.79	   H(x, x) -> G(x, x, f(k))
28.56/9.79	   A^2 -> H(f(d), f(d))
28.56/9.79	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.79	   A^2 -> H(f(e), f(e))
28.56/9.79	   A^2 -> H(f(k), f(k))
28.56/9.79	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.79	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.79	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, c), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, c), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, c), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, c), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, c), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, c), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.79	   A^2 -> H(U1(c, c), b)
28.56/9.79	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.79	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.79	   A^2 -> H(U1(c, c), e)
28.56/9.79	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.79	   A^2 -> H(e, U1(c, b))
28.56/9.79	   A^2 -> H(e, U1(d, b))
28.56/9.79	   A^2 -> H(e, U1(b, c))
28.56/9.79	   A^2 -> H(e, U1(b, d))
28.56/9.79	   A^2 -> H(e, U1(c, c))
28.56/9.79	   A^2 -> H(e, f(e))
28.56/9.79	   A^2 -> H(e, f(k))
28.56/9.79	   A^2 -> H(e, U1(d, d))
28.56/9.79	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.79	   A^2 -> H(f(e), b)
28.56/9.79	   A^2 -> H(f(e), U1(e, d))
28.56/9.79	   A^2 -> H(f(e), U1(d, e))
28.56/9.79	   A^2 -> H(f(e), c)
28.56/9.79	   A^2 -> H(f(e), U1(e, k))
28.56/9.79	   A^2 -> H(f(e), U1(k, e))
28.56/9.79	   A^2 -> H(f(e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.79	   A^2 -> H(f(k), b)
28.56/9.79	   A^2 -> H(f(k), U1(e, d))
28.56/9.79	   A^2 -> H(f(k), U1(d, e))
28.56/9.79	   A^2 -> H(f(k), c)
28.56/9.79	   A^2 -> H(f(k), U1(e, k))
28.56/9.79	   A^2 -> H(f(k), U1(k, e))
28.56/9.79	   A^2 -> H(f(k), e)
28.56/9.79	   A^2 -> H(f(c), d)
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.79	   A^2 -> H(U1(k, k), f(e))
28.56/9.79	   A^2 -> H(U1(k, k), f(k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.79	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.79	   A^2 -> H(U1(d, d), b)
28.56/9.79	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.79	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.79	   A^2 -> H(U1(d, d), c)
28.56/9.79	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.79	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.79	   A^2 -> H(U1(d, d), e)
28.56/9.79	   A^2 -> H(f(d), d)
28.56/9.79	   A^2 -> H(f(d), k)
28.56/9.79	   A^2 -> H(U1(c, c), c)
28.56/9.79	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.79	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.79	   A^2 -> H(f(c), k)
28.56/9.79	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.79	   A^2 -> H(f(k), U1(k, k))
28.56/9.79	   A^2 -> H(f(e), e)
28.56/9.79	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.79	   A^2 -> H(d, U1(c, b))
28.56/9.79	   A^2 -> H(d, U1(d, b))
28.56/9.79	   A^2 -> H(d, U1(b, c))
28.56/9.79	   A^2 -> H(d, U1(b, d))
28.56/9.79	   A^2 -> H(d, U1(c, c))
28.56/9.79	   A^2 -> H(d, f(e))
28.56/9.79	   A^2 -> H(d, f(k))
28.56/9.79	   A^2 -> H(d, U1(d, d))
28.56/9.79	   A^2 -> H(a, U1(e, b))
28.56/9.79	   A^2 -> H(a, U1(k, b))
28.56/9.79	   A^2 -> H(a, U1(c, d))
28.56/9.79	   A^2 -> H(a, U1(d, c))
28.56/9.79	   A^2 -> H(a, U1(b, e))
28.56/9.79	   A^2 -> H(a, U1(b, k))
28.56/9.79	   A^2 -> H(a, U1(e, c))
28.56/9.79	   A^2 -> H(a, U1(k, c))
28.56/9.79	   A^2 -> H(a, U1(c, e))
28.56/9.79	   A^2 -> H(a, U1(c, k))
28.56/9.79	   A^2 -> H(a, U1(e, e))
28.56/9.79	   A^2 -> H(a, U1(k, k))
28.56/9.79	   A^2 -> H(a, U1(k, d))
28.56/9.79	   A^2 -> H(a, U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.79	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.79	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.79	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.79	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.79	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.79	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.79	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, a), b)
28.56/9.79	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.79	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.79	   A^2 -> H(U1(e, a), c)
28.56/9.79	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.79	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.79	   A^2 -> H(U1(e, a), e)
28.56/9.79	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, a), b)
28.56/9.79	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.79	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.79	   A^2 -> H(U1(k, a), c)
28.56/9.79	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.79	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.79	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, d), b)
28.56/9.79	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.79	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.79	   A^2 -> H(U1(c, d), c)
28.56/9.79	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.79	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.79	   A^2 -> H(U1(c, d), e)
28.56/9.79	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, a), d)
28.56/9.79	   A^2 -> H(U1(c, a), k)
28.56/9.79	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.79	   A^2 -> H(U1(d, c), b)
28.56/9.79	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.79	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.79	   A^2 -> H(U1(d, c), c)
28.56/9.79	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.79	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.79	   A^2 -> H(U1(d, c), e)
28.56/9.79	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.79	   A^2 -> H(U1(d, a), d)
28.56/9.79	   A^2 -> H(U1(d, a), k)
28.56/9.79	   A^2 -> H(U1(a, e), b)
28.56/9.79	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.79	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.79	   A^2 -> H(U1(a, e), c)
28.56/9.79	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.79	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.79	   A^2 -> H(U1(a, e), e)
28.56/9.79	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(a, k), b)
28.56/9.79	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.79	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.79	   A^2 -> H(U1(a, k), c)
28.56/9.79	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.79	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.79	   A^2 -> H(U1(a, k), e)
28.56/9.79	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(a, c), d)
28.56/9.79	   A^2 -> H(U1(a, c), k)
28.56/9.79	   A^2 -> H(U1(a, d), d)
28.56/9.79	   A^2 -> H(U1(a, d), k)
28.56/9.79	   A^2 -> H(k, U1(c, b))
28.56/9.79	   A^2 -> H(k, U1(d, b))
28.56/9.79	   A^2 -> H(k, U1(b, c))
28.56/9.79	   A^2 -> H(k, U1(b, d))
28.56/9.79	   A^2 -> H(k, U1(c, c))
28.56/9.79	   A^2 -> H(k, f(e))
28.56/9.79	   A^2 -> H(k, f(k))
28.56/9.79	   A^2 -> H(k, U1(d, d))
28.56/9.79	   A^2 -> H(c, U1(e, b))
28.56/9.79	   A^2 -> H(c, U1(k, b))
28.56/9.79	   A^2 -> H(c, U1(c, d))
28.56/9.79	   A^2 -> H(c, U1(d, c))
28.56/9.79	   A^2 -> H(c, U1(b, e))
28.56/9.79	   A^2 -> H(c, U1(b, k))
28.56/9.79	   A^2 -> H(c, U1(e, c))
28.56/9.79	   A^2 -> H(c, U1(k, c))
28.56/9.79	   A^2 -> H(c, U1(c, e))
28.56/9.79	   A^2 -> H(c, U1(c, k))
28.56/9.79	   A^2 -> H(c, U1(e, e))
28.56/9.79	   A^2 -> H(c, U1(k, k))
28.56/9.79	   A^2 -> H(c, U1(k, d))
28.56/9.79	   A^2 -> H(c, U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.79	   A^2 -> H(U1(e, c), b)
28.56/9.79	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.79	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.79	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.79	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.79	   A^2 -> H(U1(e, c), e)
28.56/9.79	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.79	   A^2 -> H(U1(k, c), b)
28.56/9.79	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.79	
28.56/9.79	The TRS R consists of the following rules:
28.56/9.79	
28.56/9.79	   f(x) -> U1(x, x)
28.56/9.79	   U1(e, x) -> x
28.56/9.79	   a -> c
28.56/9.79	   a -> d
28.56/9.79	   b -> c
28.56/9.79	   b -> d
28.56/9.79	   d -> k
28.56/9.79	   c -> e
28.56/9.79	   c -> k
28.56/9.79	
28.56/9.79	Q is empty.
28.56/9.79	We have to consider all minimal (P,Q,R)-chains.
28.56/9.79	----------------------------------------
28.56/9.79	
28.56/9.79	(1469) TransformationProof (EQUIVALENT)
28.56/9.79	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.79	
28.56/9.79	   (A^2 -> H(U1(k, e), U1(k, b)),A^2 -> H(U1(k, e), U1(k, b)))
28.56/9.79	   (A^2 -> H(U1(k, k), U1(k, b)),A^2 -> H(U1(k, k), U1(k, b)))
28.56/9.79	   (A^2 -> H(U1(k, c), U1(k, c)),A^2 -> H(U1(k, c), U1(k, c)))
28.56/9.79	   (A^2 -> H(U1(k, c), U1(k, d)),A^2 -> H(U1(k, c), U1(k, d)))
28.56/9.79	
28.56/9.79	
28.56/9.79	----------------------------------------
28.56/9.79	
28.56/9.79	(1470)
28.56/9.79	Obligation:
28.56/9.79	Q DP problem:
28.56/9.79	The TRS P consists of the following rules:
28.56/9.79	
28.56/9.79	   G(d, x, x) -> A^2
28.56/9.79	   A^2 -> H(f(c), f(c))
28.56/9.79	   H(x, x) -> G(x, x, f(k))
28.56/9.79	   A^2 -> H(f(d), f(d))
28.56/9.79	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.79	   A^2 -> H(f(e), f(e))
28.56/9.79	   A^2 -> H(f(k), f(k))
28.56/9.79	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.79	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.79	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, c), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, c), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, c), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, c), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, c), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, c), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, c), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.79	   A^2 -> H(U1(c, c), b)
28.56/9.79	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.79	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.79	   A^2 -> H(U1(c, c), e)
28.56/9.79	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.79	   A^2 -> H(e, U1(c, b))
28.56/9.79	   A^2 -> H(e, U1(d, b))
28.56/9.79	   A^2 -> H(e, U1(b, c))
28.56/9.79	   A^2 -> H(e, U1(b, d))
28.56/9.79	   A^2 -> H(e, U1(c, c))
28.56/9.79	   A^2 -> H(e, f(e))
28.56/9.79	   A^2 -> H(e, f(k))
28.56/9.79	   A^2 -> H(e, U1(d, d))
28.56/9.79	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.79	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.79	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.79	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.79	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.79	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.79	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.79	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.79	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.79	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.79	   A^2 -> H(f(e), b)
28.56/9.79	   A^2 -> H(f(e), U1(e, d))
28.56/9.79	   A^2 -> H(f(e), U1(d, e))
28.56/9.79	   A^2 -> H(f(e), c)
28.56/9.79	   A^2 -> H(f(e), U1(e, k))
28.56/9.79	   A^2 -> H(f(e), U1(k, e))
28.56/9.79	   A^2 -> H(f(e), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.79	   A^2 -> H(f(k), b)
28.56/9.79	   A^2 -> H(f(k), U1(e, d))
28.56/9.79	   A^2 -> H(f(k), U1(d, e))
28.56/9.79	   A^2 -> H(f(k), c)
28.56/9.79	   A^2 -> H(f(k), U1(e, k))
28.56/9.79	   A^2 -> H(f(k), U1(k, e))
28.56/9.79	   A^2 -> H(f(k), e)
28.56/9.79	   A^2 -> H(f(c), d)
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.79	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.79	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.79	   A^2 -> H(U1(k, k), f(e))
28.56/9.79	   A^2 -> H(U1(k, k), f(k))
28.56/9.79	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.79	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.79	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.79	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.79	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.79	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.79	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.79	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.79	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.79	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.79	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.79	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.79	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.79	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.79	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.79	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.79	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.79	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.79	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.79	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.79	   A^2 -> H(U1(d, d), b)
28.56/9.79	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.79	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.79	   A^2 -> H(U1(d, d), c)
28.56/9.79	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.79	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.79	   A^2 -> H(U1(d, d), e)
28.56/9.79	   A^2 -> H(f(d), d)
28.56/9.79	   A^2 -> H(f(d), k)
28.56/9.79	   A^2 -> H(U1(c, c), c)
28.56/9.79	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.79	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.79	   A^2 -> H(f(c), k)
28.56/9.79	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.79	   A^2 -> H(f(k), U1(k, k))
28.56/9.79	   A^2 -> H(f(e), e)
28.56/9.79	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.79	   A^2 -> H(d, U1(c, b))
28.56/9.79	   A^2 -> H(d, U1(d, b))
28.56/9.79	   A^2 -> H(d, U1(b, c))
28.56/9.79	   A^2 -> H(d, U1(b, d))
28.56/9.79	   A^2 -> H(d, U1(c, c))
28.56/9.79	   A^2 -> H(d, f(e))
28.56/9.79	   A^2 -> H(d, f(k))
28.56/9.79	   A^2 -> H(d, U1(d, d))
28.56/9.79	   A^2 -> H(a, U1(e, b))
28.56/9.79	   A^2 -> H(a, U1(k, b))
28.56/9.79	   A^2 -> H(a, U1(c, d))
28.56/9.79	   A^2 -> H(a, U1(d, c))
28.56/9.79	   A^2 -> H(a, U1(b, e))
28.56/9.79	   A^2 -> H(a, U1(b, k))
28.56/9.79	   A^2 -> H(a, U1(e, c))
28.56/9.79	   A^2 -> H(a, U1(k, c))
28.56/9.79	   A^2 -> H(a, U1(c, e))
28.56/9.79	   A^2 -> H(a, U1(c, k))
28.56/9.79	   A^2 -> H(a, U1(e, e))
28.56/9.79	   A^2 -> H(a, U1(k, k))
28.56/9.80	   A^2 -> H(a, U1(k, d))
28.56/9.80	   A^2 -> H(a, U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.80	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.80	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.80	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.80	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.80	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.80	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, a), b)
28.56/9.80	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.80	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.80	   A^2 -> H(U1(e, a), c)
28.56/9.80	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.80	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.80	   A^2 -> H(U1(e, a), e)
28.56/9.80	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, a), b)
28.56/9.80	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.80	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.80	   A^2 -> H(U1(k, a), c)
28.56/9.80	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.80	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.80	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, d), b)
28.56/9.80	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.80	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.80	   A^2 -> H(U1(c, d), c)
28.56/9.80	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.80	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.80	   A^2 -> H(U1(c, d), e)
28.56/9.80	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, a), d)
28.56/9.80	   A^2 -> H(U1(c, a), k)
28.56/9.80	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.80	   A^2 -> H(U1(d, c), b)
28.56/9.80	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(d, c), c)
28.56/9.80	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.80	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.80	   A^2 -> H(U1(d, c), e)
28.56/9.80	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.80	   A^2 -> H(U1(d, a), d)
28.56/9.80	   A^2 -> H(U1(d, a), k)
28.56/9.80	   A^2 -> H(U1(a, e), b)
28.56/9.80	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.80	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.80	   A^2 -> H(U1(a, e), c)
28.56/9.80	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.80	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.80	   A^2 -> H(U1(a, e), e)
28.56/9.80	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(a, k), b)
28.56/9.80	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.80	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.80	   A^2 -> H(U1(a, k), c)
28.56/9.80	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.80	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.80	   A^2 -> H(U1(a, k), e)
28.56/9.80	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(a, c), d)
28.56/9.80	   A^2 -> H(U1(a, c), k)
28.56/9.80	   A^2 -> H(U1(a, d), d)
28.56/9.80	   A^2 -> H(U1(a, d), k)
28.56/9.80	   A^2 -> H(k, U1(c, b))
28.56/9.80	   A^2 -> H(k, U1(d, b))
28.56/9.80	   A^2 -> H(k, U1(b, c))
28.56/9.80	   A^2 -> H(k, U1(b, d))
28.56/9.80	   A^2 -> H(k, U1(c, c))
28.56/9.80	   A^2 -> H(k, f(e))
28.56/9.80	   A^2 -> H(k, f(k))
28.56/9.80	   A^2 -> H(k, U1(d, d))
28.56/9.80	   A^2 -> H(c, U1(e, b))
28.56/9.80	   A^2 -> H(c, U1(k, b))
28.56/9.80	   A^2 -> H(c, U1(c, d))
28.56/9.80	   A^2 -> H(c, U1(d, c))
28.56/9.80	   A^2 -> H(c, U1(b, e))
28.56/9.80	   A^2 -> H(c, U1(b, k))
28.56/9.80	   A^2 -> H(c, U1(e, c))
28.56/9.80	   A^2 -> H(c, U1(k, c))
28.56/9.80	   A^2 -> H(c, U1(c, e))
28.56/9.80	   A^2 -> H(c, U1(c, k))
28.56/9.80	   A^2 -> H(c, U1(e, e))
28.56/9.80	   A^2 -> H(c, U1(k, k))
28.56/9.80	   A^2 -> H(c, U1(k, d))
28.56/9.80	   A^2 -> H(c, U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, c), b)
28.56/9.80	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.80	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.80	   A^2 -> H(U1(e, c), e)
28.56/9.80	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.80	   A^2 -> H(U1(k, c), b)
28.56/9.80	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.80	
28.56/9.80	The TRS R consists of the following rules:
28.56/9.80	
28.56/9.80	   f(x) -> U1(x, x)
28.56/9.80	   U1(e, x) -> x
28.56/9.80	   a -> c
28.56/9.80	   a -> d
28.56/9.80	   b -> c
28.56/9.80	   b -> d
28.56/9.80	   d -> k
28.56/9.80	   c -> e
28.56/9.80	   c -> k
28.56/9.80	
28.56/9.80	Q is empty.
28.56/9.80	We have to consider all minimal (P,Q,R)-chains.
28.56/9.80	----------------------------------------
28.56/9.80	
28.56/9.80	(1471) TransformationProof (EQUIVALENT)
28.56/9.80	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.80	
28.56/9.80	   (A^2 -> H(U1(k, e), U1(c, d)),A^2 -> H(U1(k, e), U1(c, d)))
28.56/9.80	   (A^2 -> H(U1(k, k), U1(c, d)),A^2 -> H(U1(k, k), U1(c, d)))
28.56/9.80	   (A^2 -> H(U1(k, c), U1(e, d)),A^2 -> H(U1(k, c), U1(e, d)))
28.56/9.80	   (A^2 -> H(U1(k, c), U1(k, d)),A^2 -> H(U1(k, c), U1(k, d)))
28.56/9.80	   (A^2 -> H(U1(k, c), U1(c, k)),A^2 -> H(U1(k, c), U1(c, k)))
28.56/9.80	
28.56/9.80	
28.56/9.80	----------------------------------------
28.56/9.80	
28.56/9.80	(1472)
28.56/9.80	Obligation:
28.56/9.80	Q DP problem:
28.56/9.80	The TRS P consists of the following rules:
28.56/9.80	
28.56/9.80	   G(d, x, x) -> A^2
28.56/9.80	   A^2 -> H(f(c), f(c))
28.56/9.80	   H(x, x) -> G(x, x, f(k))
28.56/9.80	   A^2 -> H(f(d), f(d))
28.56/9.80	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.80	   A^2 -> H(f(e), f(e))
28.56/9.80	   A^2 -> H(f(k), f(k))
28.56/9.80	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.80	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.80	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, c), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, c), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, c), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, c), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, c), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, c), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, c), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, c), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.80	   A^2 -> H(U1(c, c), b)
28.56/9.80	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(c, c), e)
28.56/9.80	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.80	   A^2 -> H(e, U1(c, b))
28.56/9.80	   A^2 -> H(e, U1(d, b))
28.56/9.80	   A^2 -> H(e, U1(b, c))
28.56/9.80	   A^2 -> H(e, U1(b, d))
28.56/9.80	   A^2 -> H(e, U1(c, c))
28.56/9.80	   A^2 -> H(e, f(e))
28.56/9.80	   A^2 -> H(e, f(k))
28.56/9.80	   A^2 -> H(e, U1(d, d))
28.56/9.80	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.80	   A^2 -> H(f(e), b)
28.56/9.80	   A^2 -> H(f(e), U1(e, d))
28.56/9.80	   A^2 -> H(f(e), U1(d, e))
28.56/9.80	   A^2 -> H(f(e), c)
28.56/9.80	   A^2 -> H(f(e), U1(e, k))
28.56/9.80	   A^2 -> H(f(e), U1(k, e))
28.56/9.80	   A^2 -> H(f(e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.80	   A^2 -> H(f(k), b)
28.56/9.80	   A^2 -> H(f(k), U1(e, d))
28.56/9.80	   A^2 -> H(f(k), U1(d, e))
28.56/9.80	   A^2 -> H(f(k), c)
28.56/9.80	   A^2 -> H(f(k), U1(e, k))
28.56/9.80	   A^2 -> H(f(k), U1(k, e))
28.56/9.80	   A^2 -> H(f(k), e)
28.56/9.80	   A^2 -> H(f(c), d)
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.80	   A^2 -> H(U1(k, k), f(e))
28.56/9.80	   A^2 -> H(U1(k, k), f(k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.80	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.80	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.80	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.80	   A^2 -> H(U1(d, d), b)
28.56/9.80	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.80	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.80	   A^2 -> H(U1(d, d), c)
28.56/9.80	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.80	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.80	   A^2 -> H(U1(d, d), e)
28.56/9.80	   A^2 -> H(f(d), d)
28.56/9.80	   A^2 -> H(f(d), k)
28.56/9.80	   A^2 -> H(U1(c, c), c)
28.56/9.80	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.80	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.80	   A^2 -> H(f(c), k)
28.56/9.80	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.80	   A^2 -> H(f(k), U1(k, k))
28.56/9.80	   A^2 -> H(f(e), e)
28.56/9.80	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.80	   A^2 -> H(d, U1(c, b))
28.56/9.80	   A^2 -> H(d, U1(d, b))
28.56/9.80	   A^2 -> H(d, U1(b, c))
28.56/9.80	   A^2 -> H(d, U1(b, d))
28.56/9.80	   A^2 -> H(d, U1(c, c))
28.56/9.80	   A^2 -> H(d, f(e))
28.56/9.80	   A^2 -> H(d, f(k))
28.56/9.80	   A^2 -> H(d, U1(d, d))
28.56/9.80	   A^2 -> H(a, U1(e, b))
28.56/9.80	   A^2 -> H(a, U1(k, b))
28.56/9.80	   A^2 -> H(a, U1(c, d))
28.56/9.80	   A^2 -> H(a, U1(d, c))
28.56/9.80	   A^2 -> H(a, U1(b, e))
28.56/9.80	   A^2 -> H(a, U1(b, k))
28.56/9.80	   A^2 -> H(a, U1(e, c))
28.56/9.80	   A^2 -> H(a, U1(k, c))
28.56/9.80	   A^2 -> H(a, U1(c, e))
28.56/9.80	   A^2 -> H(a, U1(c, k))
28.56/9.80	   A^2 -> H(a, U1(e, e))
28.56/9.80	   A^2 -> H(a, U1(k, k))
28.56/9.80	   A^2 -> H(a, U1(k, d))
28.56/9.80	   A^2 -> H(a, U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.80	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.80	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.80	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.80	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.80	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.80	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, a), b)
28.56/9.80	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.80	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.80	   A^2 -> H(U1(e, a), c)
28.56/9.80	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.80	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.80	   A^2 -> H(U1(e, a), e)
28.56/9.80	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, a), b)
28.56/9.80	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.80	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.80	   A^2 -> H(U1(k, a), c)
28.56/9.80	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.80	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.80	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, d), b)
28.56/9.80	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.80	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.80	   A^2 -> H(U1(c, d), c)
28.56/9.80	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.80	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.80	   A^2 -> H(U1(c, d), e)
28.56/9.80	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, a), d)
28.56/9.80	   A^2 -> H(U1(c, a), k)
28.56/9.80	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.80	   A^2 -> H(U1(d, c), b)
28.56/9.80	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(d, c), c)
28.56/9.80	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.80	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.80	   A^2 -> H(U1(d, c), e)
28.56/9.80	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.80	   A^2 -> H(U1(d, a), d)
28.56/9.80	   A^2 -> H(U1(d, a), k)
28.56/9.80	   A^2 -> H(U1(a, e), b)
28.56/9.80	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.80	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.80	   A^2 -> H(U1(a, e), c)
28.56/9.80	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.80	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.80	   A^2 -> H(U1(a, e), e)
28.56/9.80	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(a, k), b)
28.56/9.80	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.80	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.80	   A^2 -> H(U1(a, k), c)
28.56/9.80	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.80	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.80	   A^2 -> H(U1(a, k), e)
28.56/9.80	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(a, c), d)
28.56/9.80	   A^2 -> H(U1(a, c), k)
28.56/9.80	   A^2 -> H(U1(a, d), d)
28.56/9.80	   A^2 -> H(U1(a, d), k)
28.56/9.80	   A^2 -> H(k, U1(c, b))
28.56/9.80	   A^2 -> H(k, U1(d, b))
28.56/9.80	   A^2 -> H(k, U1(b, c))
28.56/9.80	   A^2 -> H(k, U1(b, d))
28.56/9.80	   A^2 -> H(k, U1(c, c))
28.56/9.80	   A^2 -> H(k, f(e))
28.56/9.80	   A^2 -> H(k, f(k))
28.56/9.80	   A^2 -> H(k, U1(d, d))
28.56/9.80	   A^2 -> H(c, U1(e, b))
28.56/9.80	   A^2 -> H(c, U1(k, b))
28.56/9.80	   A^2 -> H(c, U1(c, d))
28.56/9.80	   A^2 -> H(c, U1(d, c))
28.56/9.80	   A^2 -> H(c, U1(b, e))
28.56/9.80	   A^2 -> H(c, U1(b, k))
28.56/9.80	   A^2 -> H(c, U1(e, c))
28.56/9.80	   A^2 -> H(c, U1(k, c))
28.56/9.80	   A^2 -> H(c, U1(c, e))
28.56/9.80	   A^2 -> H(c, U1(c, k))
28.56/9.80	   A^2 -> H(c, U1(e, e))
28.56/9.80	   A^2 -> H(c, U1(k, k))
28.56/9.80	   A^2 -> H(c, U1(k, d))
28.56/9.80	   A^2 -> H(c, U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, c), b)
28.56/9.80	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.80	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.80	   A^2 -> H(U1(e, c), e)
28.56/9.80	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.80	   A^2 -> H(U1(k, c), b)
28.56/9.80	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.80	
28.56/9.80	The TRS R consists of the following rules:
28.56/9.80	
28.56/9.80	   f(x) -> U1(x, x)
28.56/9.80	   U1(e, x) -> x
28.56/9.80	   a -> c
28.56/9.80	   a -> d
28.56/9.80	   b -> c
28.56/9.80	   b -> d
28.56/9.80	   d -> k
28.56/9.80	   c -> e
28.56/9.80	   c -> k
28.56/9.80	
28.56/9.80	Q is empty.
28.56/9.80	We have to consider all minimal (P,Q,R)-chains.
28.56/9.80	----------------------------------------
28.56/9.80	
28.56/9.80	(1473) TransformationProof (EQUIVALENT)
28.56/9.80	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.80	
28.56/9.80	   (A^2 -> H(U1(k, e), U1(d, c)),A^2 -> H(U1(k, e), U1(d, c)))
28.56/9.80	   (A^2 -> H(U1(k, k), U1(d, c)),A^2 -> H(U1(k, k), U1(d, c)))
28.56/9.80	   (A^2 -> H(U1(k, c), U1(k, c)),A^2 -> H(U1(k, c), U1(k, c)))
28.56/9.80	   (A^2 -> H(U1(k, c), U1(d, e)),A^2 -> H(U1(k, c), U1(d, e)))
28.56/9.80	   (A^2 -> H(U1(k, c), U1(d, k)),A^2 -> H(U1(k, c), U1(d, k)))
28.56/9.80	
28.56/9.80	
28.56/9.80	----------------------------------------
28.56/9.80	
28.56/9.80	(1474)
28.56/9.80	Obligation:
28.56/9.80	Q DP problem:
28.56/9.80	The TRS P consists of the following rules:
28.56/9.80	
28.56/9.80	   G(d, x, x) -> A^2
28.56/9.80	   A^2 -> H(f(c), f(c))
28.56/9.80	   H(x, x) -> G(x, x, f(k))
28.56/9.80	   A^2 -> H(f(d), f(d))
28.56/9.80	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.80	   A^2 -> H(f(e), f(e))
28.56/9.80	   A^2 -> H(f(k), f(k))
28.56/9.80	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.80	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.80	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, c), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, c), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, c), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, c), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, c), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, c), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, c), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.80	   A^2 -> H(U1(c, c), b)
28.56/9.80	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(c, c), e)
28.56/9.80	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.80	   A^2 -> H(e, U1(c, b))
28.56/9.80	   A^2 -> H(e, U1(d, b))
28.56/9.80	   A^2 -> H(e, U1(b, c))
28.56/9.80	   A^2 -> H(e, U1(b, d))
28.56/9.80	   A^2 -> H(e, U1(c, c))
28.56/9.80	   A^2 -> H(e, f(e))
28.56/9.80	   A^2 -> H(e, f(k))
28.56/9.80	   A^2 -> H(e, U1(d, d))
28.56/9.80	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.80	   A^2 -> H(f(e), b)
28.56/9.80	   A^2 -> H(f(e), U1(e, d))
28.56/9.80	   A^2 -> H(f(e), U1(d, e))
28.56/9.80	   A^2 -> H(f(e), c)
28.56/9.80	   A^2 -> H(f(e), U1(e, k))
28.56/9.80	   A^2 -> H(f(e), U1(k, e))
28.56/9.80	   A^2 -> H(f(e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.80	   A^2 -> H(f(k), b)
28.56/9.80	   A^2 -> H(f(k), U1(e, d))
28.56/9.80	   A^2 -> H(f(k), U1(d, e))
28.56/9.80	   A^2 -> H(f(k), c)
28.56/9.80	   A^2 -> H(f(k), U1(e, k))
28.56/9.80	   A^2 -> H(f(k), U1(k, e))
28.56/9.80	   A^2 -> H(f(k), e)
28.56/9.80	   A^2 -> H(f(c), d)
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.80	   A^2 -> H(U1(k, k), f(e))
28.56/9.80	   A^2 -> H(U1(k, k), f(k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.80	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.80	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.80	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.80	   A^2 -> H(U1(d, d), b)
28.56/9.80	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.80	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.80	   A^2 -> H(U1(d, d), c)
28.56/9.80	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.80	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.80	   A^2 -> H(U1(d, d), e)
28.56/9.80	   A^2 -> H(f(d), d)
28.56/9.80	   A^2 -> H(f(d), k)
28.56/9.80	   A^2 -> H(U1(c, c), c)
28.56/9.80	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.80	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.80	   A^2 -> H(f(c), k)
28.56/9.80	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.80	   A^2 -> H(f(k), U1(k, k))
28.56/9.80	   A^2 -> H(f(e), e)
28.56/9.80	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.80	   A^2 -> H(d, U1(c, b))
28.56/9.80	   A^2 -> H(d, U1(d, b))
28.56/9.80	   A^2 -> H(d, U1(b, c))
28.56/9.80	   A^2 -> H(d, U1(b, d))
28.56/9.80	   A^2 -> H(d, U1(c, c))
28.56/9.80	   A^2 -> H(d, f(e))
28.56/9.80	   A^2 -> H(d, f(k))
28.56/9.80	   A^2 -> H(d, U1(d, d))
28.56/9.80	   A^2 -> H(a, U1(e, b))
28.56/9.80	   A^2 -> H(a, U1(k, b))
28.56/9.80	   A^2 -> H(a, U1(c, d))
28.56/9.80	   A^2 -> H(a, U1(d, c))
28.56/9.80	   A^2 -> H(a, U1(b, e))
28.56/9.80	   A^2 -> H(a, U1(b, k))
28.56/9.80	   A^2 -> H(a, U1(e, c))
28.56/9.80	   A^2 -> H(a, U1(k, c))
28.56/9.80	   A^2 -> H(a, U1(c, e))
28.56/9.80	   A^2 -> H(a, U1(c, k))
28.56/9.80	   A^2 -> H(a, U1(e, e))
28.56/9.80	   A^2 -> H(a, U1(k, k))
28.56/9.80	   A^2 -> H(a, U1(k, d))
28.56/9.80	   A^2 -> H(a, U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.80	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.80	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.80	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.80	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.80	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.80	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, a), b)
28.56/9.80	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.80	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.80	   A^2 -> H(U1(e, a), c)
28.56/9.80	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.80	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.80	   A^2 -> H(U1(e, a), e)
28.56/9.80	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, a), b)
28.56/9.80	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.80	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.80	   A^2 -> H(U1(k, a), c)
28.56/9.80	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.80	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.80	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, d), b)
28.56/9.80	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.80	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.80	   A^2 -> H(U1(c, d), c)
28.56/9.80	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.80	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.80	   A^2 -> H(U1(c, d), e)
28.56/9.80	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, a), d)
28.56/9.80	   A^2 -> H(U1(c, a), k)
28.56/9.80	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.80	   A^2 -> H(U1(d, c), b)
28.56/9.80	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(d, c), c)
28.56/9.80	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.80	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.80	   A^2 -> H(U1(d, c), e)
28.56/9.80	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.80	   A^2 -> H(U1(d, a), d)
28.56/9.80	   A^2 -> H(U1(d, a), k)
28.56/9.80	   A^2 -> H(U1(a, e), b)
28.56/9.80	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.80	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.80	   A^2 -> H(U1(a, e), c)
28.56/9.80	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.80	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.80	   A^2 -> H(U1(a, e), e)
28.56/9.80	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(a, k), b)
28.56/9.80	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.80	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.80	   A^2 -> H(U1(a, k), c)
28.56/9.80	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.80	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.80	   A^2 -> H(U1(a, k), e)
28.56/9.80	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(a, c), d)
28.56/9.80	   A^2 -> H(U1(a, c), k)
28.56/9.80	   A^2 -> H(U1(a, d), d)
28.56/9.80	   A^2 -> H(U1(a, d), k)
28.56/9.80	   A^2 -> H(k, U1(c, b))
28.56/9.80	   A^2 -> H(k, U1(d, b))
28.56/9.80	   A^2 -> H(k, U1(b, c))
28.56/9.80	   A^2 -> H(k, U1(b, d))
28.56/9.80	   A^2 -> H(k, U1(c, c))
28.56/9.80	   A^2 -> H(k, f(e))
28.56/9.80	   A^2 -> H(k, f(k))
28.56/9.80	   A^2 -> H(k, U1(d, d))
28.56/9.80	   A^2 -> H(c, U1(e, b))
28.56/9.80	   A^2 -> H(c, U1(k, b))
28.56/9.80	   A^2 -> H(c, U1(c, d))
28.56/9.80	   A^2 -> H(c, U1(d, c))
28.56/9.80	   A^2 -> H(c, U1(b, e))
28.56/9.80	   A^2 -> H(c, U1(b, k))
28.56/9.80	   A^2 -> H(c, U1(e, c))
28.56/9.80	   A^2 -> H(c, U1(k, c))
28.56/9.80	   A^2 -> H(c, U1(c, e))
28.56/9.80	   A^2 -> H(c, U1(c, k))
28.56/9.80	   A^2 -> H(c, U1(e, e))
28.56/9.80	   A^2 -> H(c, U1(k, k))
28.56/9.80	   A^2 -> H(c, U1(k, d))
28.56/9.80	   A^2 -> H(c, U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, c), b)
28.56/9.80	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.80	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.80	   A^2 -> H(U1(e, c), e)
28.56/9.80	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.80	   A^2 -> H(U1(k, c), b)
28.56/9.80	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.80	
28.56/9.80	The TRS R consists of the following rules:
28.56/9.80	
28.56/9.80	   f(x) -> U1(x, x)
28.56/9.80	   U1(e, x) -> x
28.56/9.80	   a -> c
28.56/9.80	   a -> d
28.56/9.80	   b -> c
28.56/9.80	   b -> d
28.56/9.80	   d -> k
28.56/9.80	   c -> e
28.56/9.80	   c -> k
28.56/9.80	
28.56/9.80	Q is empty.
28.56/9.80	We have to consider all minimal (P,Q,R)-chains.
28.56/9.80	----------------------------------------
28.56/9.80	
28.56/9.80	(1475) TransformationProof (EQUIVALENT)
28.56/9.80	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.80	
28.56/9.80	   (A^2 -> H(U1(k, e), U1(b, e)),A^2 -> H(U1(k, e), U1(b, e)))
28.56/9.80	   (A^2 -> H(U1(k, k), U1(b, e)),A^2 -> H(U1(k, k), U1(b, e)))
28.56/9.80	   (A^2 -> H(U1(k, c), U1(c, e)),A^2 -> H(U1(k, c), U1(c, e)))
28.56/9.80	   (A^2 -> H(U1(k, c), U1(d, e)),A^2 -> H(U1(k, c), U1(d, e)))
28.56/9.80	
28.56/9.80	
28.56/9.80	----------------------------------------
28.56/9.80	
28.56/9.80	(1476)
28.56/9.80	Obligation:
28.56/9.80	Q DP problem:
28.56/9.80	The TRS P consists of the following rules:
28.56/9.80	
28.56/9.80	   G(d, x, x) -> A^2
28.56/9.80	   A^2 -> H(f(c), f(c))
28.56/9.80	   H(x, x) -> G(x, x, f(k))
28.56/9.80	   A^2 -> H(f(d), f(d))
28.56/9.80	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.80	   A^2 -> H(f(e), f(e))
28.56/9.80	   A^2 -> H(f(k), f(k))
28.56/9.80	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.80	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.80	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, c), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, c), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, c), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, c), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, c), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, c), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.80	   A^2 -> H(U1(c, c), b)
28.56/9.80	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(c, c), e)
28.56/9.80	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.80	   A^2 -> H(e, U1(c, b))
28.56/9.80	   A^2 -> H(e, U1(d, b))
28.56/9.80	   A^2 -> H(e, U1(b, c))
28.56/9.80	   A^2 -> H(e, U1(b, d))
28.56/9.80	   A^2 -> H(e, U1(c, c))
28.56/9.80	   A^2 -> H(e, f(e))
28.56/9.80	   A^2 -> H(e, f(k))
28.56/9.80	   A^2 -> H(e, U1(d, d))
28.56/9.80	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.80	   A^2 -> H(f(e), b)
28.56/9.80	   A^2 -> H(f(e), U1(e, d))
28.56/9.80	   A^2 -> H(f(e), U1(d, e))
28.56/9.80	   A^2 -> H(f(e), c)
28.56/9.80	   A^2 -> H(f(e), U1(e, k))
28.56/9.80	   A^2 -> H(f(e), U1(k, e))
28.56/9.80	   A^2 -> H(f(e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.80	   A^2 -> H(f(k), b)
28.56/9.80	   A^2 -> H(f(k), U1(e, d))
28.56/9.80	   A^2 -> H(f(k), U1(d, e))
28.56/9.80	   A^2 -> H(f(k), c)
28.56/9.80	   A^2 -> H(f(k), U1(e, k))
28.56/9.80	   A^2 -> H(f(k), U1(k, e))
28.56/9.80	   A^2 -> H(f(k), e)
28.56/9.80	   A^2 -> H(f(c), d)
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.80	   A^2 -> H(U1(k, k), f(e))
28.56/9.80	   A^2 -> H(U1(k, k), f(k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.80	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.80	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.80	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.80	   A^2 -> H(U1(d, d), b)
28.56/9.80	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.80	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.80	   A^2 -> H(U1(d, d), c)
28.56/9.80	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.80	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.80	   A^2 -> H(U1(d, d), e)
28.56/9.80	   A^2 -> H(f(d), d)
28.56/9.80	   A^2 -> H(f(d), k)
28.56/9.80	   A^2 -> H(U1(c, c), c)
28.56/9.80	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.80	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.80	   A^2 -> H(f(c), k)
28.56/9.80	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.80	   A^2 -> H(f(k), U1(k, k))
28.56/9.80	   A^2 -> H(f(e), e)
28.56/9.80	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.80	   A^2 -> H(d, U1(c, b))
28.56/9.80	   A^2 -> H(d, U1(d, b))
28.56/9.80	   A^2 -> H(d, U1(b, c))
28.56/9.80	   A^2 -> H(d, U1(b, d))
28.56/9.80	   A^2 -> H(d, U1(c, c))
28.56/9.80	   A^2 -> H(d, f(e))
28.56/9.80	   A^2 -> H(d, f(k))
28.56/9.80	   A^2 -> H(d, U1(d, d))
28.56/9.80	   A^2 -> H(a, U1(e, b))
28.56/9.80	   A^2 -> H(a, U1(k, b))
28.56/9.80	   A^2 -> H(a, U1(c, d))
28.56/9.80	   A^2 -> H(a, U1(d, c))
28.56/9.80	   A^2 -> H(a, U1(b, e))
28.56/9.80	   A^2 -> H(a, U1(b, k))
28.56/9.80	   A^2 -> H(a, U1(e, c))
28.56/9.80	   A^2 -> H(a, U1(k, c))
28.56/9.80	   A^2 -> H(a, U1(c, e))
28.56/9.80	   A^2 -> H(a, U1(c, k))
28.56/9.80	   A^2 -> H(a, U1(e, e))
28.56/9.80	   A^2 -> H(a, U1(k, k))
28.56/9.80	   A^2 -> H(a, U1(k, d))
28.56/9.80	   A^2 -> H(a, U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.80	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.80	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.80	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.80	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.80	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.80	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, a), b)
28.56/9.80	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.80	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.80	   A^2 -> H(U1(e, a), c)
28.56/9.80	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.80	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.80	   A^2 -> H(U1(e, a), e)
28.56/9.80	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, a), b)
28.56/9.80	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.80	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.80	   A^2 -> H(U1(k, a), c)
28.56/9.80	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.80	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.80	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, d), b)
28.56/9.80	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.80	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.80	   A^2 -> H(U1(c, d), c)
28.56/9.80	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.80	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.80	   A^2 -> H(U1(c, d), e)
28.56/9.80	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, a), d)
28.56/9.80	   A^2 -> H(U1(c, a), k)
28.56/9.80	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.80	   A^2 -> H(U1(d, c), b)
28.56/9.80	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(d, c), c)
28.56/9.80	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.80	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.80	   A^2 -> H(U1(d, c), e)
28.56/9.80	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.80	   A^2 -> H(U1(d, a), d)
28.56/9.80	   A^2 -> H(U1(d, a), k)
28.56/9.80	   A^2 -> H(U1(a, e), b)
28.56/9.80	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.80	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.80	   A^2 -> H(U1(a, e), c)
28.56/9.80	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.80	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.80	   A^2 -> H(U1(a, e), e)
28.56/9.80	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(a, k), b)
28.56/9.80	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.80	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.80	   A^2 -> H(U1(a, k), c)
28.56/9.80	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.80	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.80	   A^2 -> H(U1(a, k), e)
28.56/9.80	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(a, c), d)
28.56/9.80	   A^2 -> H(U1(a, c), k)
28.56/9.80	   A^2 -> H(U1(a, d), d)
28.56/9.80	   A^2 -> H(U1(a, d), k)
28.56/9.80	   A^2 -> H(k, U1(c, b))
28.56/9.80	   A^2 -> H(k, U1(d, b))
28.56/9.80	   A^2 -> H(k, U1(b, c))
28.56/9.80	   A^2 -> H(k, U1(b, d))
28.56/9.80	   A^2 -> H(k, U1(c, c))
28.56/9.80	   A^2 -> H(k, f(e))
28.56/9.80	   A^2 -> H(k, f(k))
28.56/9.80	   A^2 -> H(k, U1(d, d))
28.56/9.80	   A^2 -> H(c, U1(e, b))
28.56/9.80	   A^2 -> H(c, U1(k, b))
28.56/9.80	   A^2 -> H(c, U1(c, d))
28.56/9.80	   A^2 -> H(c, U1(d, c))
28.56/9.80	   A^2 -> H(c, U1(b, e))
28.56/9.80	   A^2 -> H(c, U1(b, k))
28.56/9.80	   A^2 -> H(c, U1(e, c))
28.56/9.80	   A^2 -> H(c, U1(k, c))
28.56/9.80	   A^2 -> H(c, U1(c, e))
28.56/9.80	   A^2 -> H(c, U1(c, k))
28.56/9.80	   A^2 -> H(c, U1(e, e))
28.56/9.80	   A^2 -> H(c, U1(k, k))
28.56/9.80	   A^2 -> H(c, U1(k, d))
28.56/9.80	   A^2 -> H(c, U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, c), b)
28.56/9.80	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.80	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.80	   A^2 -> H(U1(e, c), e)
28.56/9.80	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.80	   A^2 -> H(U1(k, c), b)
28.56/9.80	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.80	
28.56/9.80	The TRS R consists of the following rules:
28.56/9.80	
28.56/9.80	   f(x) -> U1(x, x)
28.56/9.80	   U1(e, x) -> x
28.56/9.80	   a -> c
28.56/9.80	   a -> d
28.56/9.80	   b -> c
28.56/9.80	   b -> d
28.56/9.80	   d -> k
28.56/9.80	   c -> e
28.56/9.80	   c -> k
28.56/9.80	
28.56/9.80	Q is empty.
28.56/9.80	We have to consider all minimal (P,Q,R)-chains.
28.56/9.80	----------------------------------------
28.56/9.80	
28.56/9.80	(1477) TransformationProof (EQUIVALENT)
28.56/9.80	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.80	
28.56/9.80	   (A^2 -> H(U1(k, e), U1(b, k)),A^2 -> H(U1(k, e), U1(b, k)))
28.56/9.80	   (A^2 -> H(U1(k, k), U1(b, k)),A^2 -> H(U1(k, k), U1(b, k)))
28.56/9.80	   (A^2 -> H(U1(k, c), U1(c, k)),A^2 -> H(U1(k, c), U1(c, k)))
28.56/9.80	   (A^2 -> H(U1(k, c), U1(d, k)),A^2 -> H(U1(k, c), U1(d, k)))
28.56/9.80	
28.56/9.80	
28.56/9.80	----------------------------------------
28.56/9.80	
28.56/9.80	(1478)
28.56/9.80	Obligation:
28.56/9.80	Q DP problem:
28.56/9.80	The TRS P consists of the following rules:
28.56/9.80	
28.56/9.80	   G(d, x, x) -> A^2
28.56/9.80	   A^2 -> H(f(c), f(c))
28.56/9.80	   H(x, x) -> G(x, x, f(k))
28.56/9.80	   A^2 -> H(f(d), f(d))
28.56/9.80	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.80	   A^2 -> H(f(e), f(e))
28.56/9.80	   A^2 -> H(f(k), f(k))
28.56/9.80	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.80	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.80	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, c), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, c), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, c), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, c), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, c), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.80	   A^2 -> H(U1(c, c), b)
28.56/9.80	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(c, c), e)
28.56/9.80	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.80	   A^2 -> H(e, U1(c, b))
28.56/9.80	   A^2 -> H(e, U1(d, b))
28.56/9.80	   A^2 -> H(e, U1(b, c))
28.56/9.80	   A^2 -> H(e, U1(b, d))
28.56/9.80	   A^2 -> H(e, U1(c, c))
28.56/9.80	   A^2 -> H(e, f(e))
28.56/9.80	   A^2 -> H(e, f(k))
28.56/9.80	   A^2 -> H(e, U1(d, d))
28.56/9.80	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.80	   A^2 -> H(f(e), b)
28.56/9.80	   A^2 -> H(f(e), U1(e, d))
28.56/9.80	   A^2 -> H(f(e), U1(d, e))
28.56/9.80	   A^2 -> H(f(e), c)
28.56/9.80	   A^2 -> H(f(e), U1(e, k))
28.56/9.80	   A^2 -> H(f(e), U1(k, e))
28.56/9.80	   A^2 -> H(f(e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.80	   A^2 -> H(f(k), b)
28.56/9.80	   A^2 -> H(f(k), U1(e, d))
28.56/9.80	   A^2 -> H(f(k), U1(d, e))
28.56/9.80	   A^2 -> H(f(k), c)
28.56/9.80	   A^2 -> H(f(k), U1(e, k))
28.56/9.80	   A^2 -> H(f(k), U1(k, e))
28.56/9.80	   A^2 -> H(f(k), e)
28.56/9.80	   A^2 -> H(f(c), d)
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.80	   A^2 -> H(U1(k, k), f(e))
28.56/9.80	   A^2 -> H(U1(k, k), f(k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.80	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.80	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.80	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.80	   A^2 -> H(U1(d, d), b)
28.56/9.80	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.80	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.80	   A^2 -> H(U1(d, d), c)
28.56/9.80	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.80	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.80	   A^2 -> H(U1(d, d), e)
28.56/9.80	   A^2 -> H(f(d), d)
28.56/9.80	   A^2 -> H(f(d), k)
28.56/9.80	   A^2 -> H(U1(c, c), c)
28.56/9.80	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.80	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.80	   A^2 -> H(f(c), k)
28.56/9.80	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.80	   A^2 -> H(f(k), U1(k, k))
28.56/9.80	   A^2 -> H(f(e), e)
28.56/9.80	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.80	   A^2 -> H(d, U1(c, b))
28.56/9.80	   A^2 -> H(d, U1(d, b))
28.56/9.80	   A^2 -> H(d, U1(b, c))
28.56/9.80	   A^2 -> H(d, U1(b, d))
28.56/9.80	   A^2 -> H(d, U1(c, c))
28.56/9.80	   A^2 -> H(d, f(e))
28.56/9.80	   A^2 -> H(d, f(k))
28.56/9.80	   A^2 -> H(d, U1(d, d))
28.56/9.80	   A^2 -> H(a, U1(e, b))
28.56/9.80	   A^2 -> H(a, U1(k, b))
28.56/9.80	   A^2 -> H(a, U1(c, d))
28.56/9.80	   A^2 -> H(a, U1(d, c))
28.56/9.80	   A^2 -> H(a, U1(b, e))
28.56/9.80	   A^2 -> H(a, U1(b, k))
28.56/9.80	   A^2 -> H(a, U1(e, c))
28.56/9.80	   A^2 -> H(a, U1(k, c))
28.56/9.80	   A^2 -> H(a, U1(c, e))
28.56/9.80	   A^2 -> H(a, U1(c, k))
28.56/9.80	   A^2 -> H(a, U1(e, e))
28.56/9.80	   A^2 -> H(a, U1(k, k))
28.56/9.80	   A^2 -> H(a, U1(k, d))
28.56/9.80	   A^2 -> H(a, U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.80	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.80	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.80	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.80	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.80	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.80	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, a), b)
28.56/9.80	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.80	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.80	   A^2 -> H(U1(e, a), c)
28.56/9.80	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.80	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.80	   A^2 -> H(U1(e, a), e)
28.56/9.80	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, a), b)
28.56/9.80	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.80	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.80	   A^2 -> H(U1(k, a), c)
28.56/9.80	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.80	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.80	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, d), b)
28.56/9.80	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.80	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.80	   A^2 -> H(U1(c, d), c)
28.56/9.80	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.80	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.80	   A^2 -> H(U1(c, d), e)
28.56/9.80	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, a), d)
28.56/9.80	   A^2 -> H(U1(c, a), k)
28.56/9.80	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.80	   A^2 -> H(U1(d, c), b)
28.56/9.80	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(d, c), c)
28.56/9.80	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.80	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.80	   A^2 -> H(U1(d, c), e)
28.56/9.80	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.80	   A^2 -> H(U1(d, a), d)
28.56/9.80	   A^2 -> H(U1(d, a), k)
28.56/9.80	   A^2 -> H(U1(a, e), b)
28.56/9.80	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.80	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.80	   A^2 -> H(U1(a, e), c)
28.56/9.80	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.80	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.80	   A^2 -> H(U1(a, e), e)
28.56/9.80	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(a, k), b)
28.56/9.80	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.80	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.80	   A^2 -> H(U1(a, k), c)
28.56/9.80	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.80	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.80	   A^2 -> H(U1(a, k), e)
28.56/9.80	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(a, c), d)
28.56/9.80	   A^2 -> H(U1(a, c), k)
28.56/9.80	   A^2 -> H(U1(a, d), d)
28.56/9.80	   A^2 -> H(U1(a, d), k)
28.56/9.80	   A^2 -> H(k, U1(c, b))
28.56/9.80	   A^2 -> H(k, U1(d, b))
28.56/9.80	   A^2 -> H(k, U1(b, c))
28.56/9.80	   A^2 -> H(k, U1(b, d))
28.56/9.80	   A^2 -> H(k, U1(c, c))
28.56/9.80	   A^2 -> H(k, f(e))
28.56/9.80	   A^2 -> H(k, f(k))
28.56/9.80	   A^2 -> H(k, U1(d, d))
28.56/9.80	   A^2 -> H(c, U1(e, b))
28.56/9.80	   A^2 -> H(c, U1(k, b))
28.56/9.80	   A^2 -> H(c, U1(c, d))
28.56/9.80	   A^2 -> H(c, U1(d, c))
28.56/9.80	   A^2 -> H(c, U1(b, e))
28.56/9.80	   A^2 -> H(c, U1(b, k))
28.56/9.80	   A^2 -> H(c, U1(e, c))
28.56/9.80	   A^2 -> H(c, U1(k, c))
28.56/9.80	   A^2 -> H(c, U1(c, e))
28.56/9.80	   A^2 -> H(c, U1(c, k))
28.56/9.80	   A^2 -> H(c, U1(e, e))
28.56/9.80	   A^2 -> H(c, U1(k, k))
28.56/9.80	   A^2 -> H(c, U1(k, d))
28.56/9.80	   A^2 -> H(c, U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, c), b)
28.56/9.80	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.80	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.80	   A^2 -> H(U1(e, c), e)
28.56/9.80	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.80	   A^2 -> H(U1(k, c), b)
28.56/9.80	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.80	
28.56/9.80	The TRS R consists of the following rules:
28.56/9.80	
28.56/9.80	   f(x) -> U1(x, x)
28.56/9.80	   U1(e, x) -> x
28.56/9.80	   a -> c
28.56/9.80	   a -> d
28.56/9.80	   b -> c
28.56/9.80	   b -> d
28.56/9.80	   d -> k
28.56/9.80	   c -> e
28.56/9.80	   c -> k
28.56/9.80	
28.56/9.80	Q is empty.
28.56/9.80	We have to consider all minimal (P,Q,R)-chains.
28.56/9.80	----------------------------------------
28.56/9.80	
28.56/9.80	(1479) TransformationProof (EQUIVALENT)
28.56/9.80	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.80	
28.56/9.80	   (A^2 -> H(U1(k, e), U1(e, c)),A^2 -> H(U1(k, e), U1(e, c)))
28.56/9.80	   (A^2 -> H(U1(k, k), U1(e, c)),A^2 -> H(U1(k, k), U1(e, c)))
28.56/9.80	   (A^2 -> H(U1(k, c), c),A^2 -> H(U1(k, c), c))
28.56/9.80	   (A^2 -> H(U1(k, c), U1(e, e)),A^2 -> H(U1(k, c), U1(e, e)))
28.56/9.80	   (A^2 -> H(U1(k, c), U1(e, k)),A^2 -> H(U1(k, c), U1(e, k)))
28.56/9.80	
28.56/9.80	
28.56/9.80	----------------------------------------
28.56/9.80	
28.56/9.80	(1480)
28.56/9.80	Obligation:
28.56/9.80	Q DP problem:
28.56/9.80	The TRS P consists of the following rules:
28.56/9.80	
28.56/9.80	   G(d, x, x) -> A^2
28.56/9.80	   A^2 -> H(f(c), f(c))
28.56/9.80	   H(x, x) -> G(x, x, f(k))
28.56/9.80	   A^2 -> H(f(d), f(d))
28.56/9.80	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.80	   A^2 -> H(f(e), f(e))
28.56/9.80	   A^2 -> H(f(k), f(k))
28.56/9.80	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.80	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.80	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, c), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, c), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, c), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, c), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.80	   A^2 -> H(U1(c, c), b)
28.56/9.80	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(c, c), e)
28.56/9.80	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.80	   A^2 -> H(e, U1(c, b))
28.56/9.80	   A^2 -> H(e, U1(d, b))
28.56/9.80	   A^2 -> H(e, U1(b, c))
28.56/9.80	   A^2 -> H(e, U1(b, d))
28.56/9.80	   A^2 -> H(e, U1(c, c))
28.56/9.80	   A^2 -> H(e, f(e))
28.56/9.80	   A^2 -> H(e, f(k))
28.56/9.80	   A^2 -> H(e, U1(d, d))
28.56/9.80	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.80	   A^2 -> H(f(e), b)
28.56/9.80	   A^2 -> H(f(e), U1(e, d))
28.56/9.80	   A^2 -> H(f(e), U1(d, e))
28.56/9.80	   A^2 -> H(f(e), c)
28.56/9.80	   A^2 -> H(f(e), U1(e, k))
28.56/9.80	   A^2 -> H(f(e), U1(k, e))
28.56/9.80	   A^2 -> H(f(e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.80	   A^2 -> H(f(k), b)
28.56/9.80	   A^2 -> H(f(k), U1(e, d))
28.56/9.80	   A^2 -> H(f(k), U1(d, e))
28.56/9.80	   A^2 -> H(f(k), c)
28.56/9.80	   A^2 -> H(f(k), U1(e, k))
28.56/9.80	   A^2 -> H(f(k), U1(k, e))
28.56/9.80	   A^2 -> H(f(k), e)
28.56/9.80	   A^2 -> H(f(c), d)
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.80	   A^2 -> H(U1(k, k), f(e))
28.56/9.80	   A^2 -> H(U1(k, k), f(k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.80	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.80	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.80	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.80	   A^2 -> H(U1(d, d), b)
28.56/9.80	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.80	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.80	   A^2 -> H(U1(d, d), c)
28.56/9.80	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.80	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.80	   A^2 -> H(U1(d, d), e)
28.56/9.80	   A^2 -> H(f(d), d)
28.56/9.80	   A^2 -> H(f(d), k)
28.56/9.80	   A^2 -> H(U1(c, c), c)
28.56/9.80	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.80	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.80	   A^2 -> H(f(c), k)
28.56/9.80	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.80	   A^2 -> H(f(k), U1(k, k))
28.56/9.80	   A^2 -> H(f(e), e)
28.56/9.80	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.80	   A^2 -> H(d, U1(c, b))
28.56/9.80	   A^2 -> H(d, U1(d, b))
28.56/9.80	   A^2 -> H(d, U1(b, c))
28.56/9.80	   A^2 -> H(d, U1(b, d))
28.56/9.80	   A^2 -> H(d, U1(c, c))
28.56/9.80	   A^2 -> H(d, f(e))
28.56/9.80	   A^2 -> H(d, f(k))
28.56/9.80	   A^2 -> H(d, U1(d, d))
28.56/9.80	   A^2 -> H(a, U1(e, b))
28.56/9.80	   A^2 -> H(a, U1(k, b))
28.56/9.80	   A^2 -> H(a, U1(c, d))
28.56/9.80	   A^2 -> H(a, U1(d, c))
28.56/9.80	   A^2 -> H(a, U1(b, e))
28.56/9.80	   A^2 -> H(a, U1(b, k))
28.56/9.80	   A^2 -> H(a, U1(e, c))
28.56/9.80	   A^2 -> H(a, U1(k, c))
28.56/9.80	   A^2 -> H(a, U1(c, e))
28.56/9.80	   A^2 -> H(a, U1(c, k))
28.56/9.80	   A^2 -> H(a, U1(e, e))
28.56/9.80	   A^2 -> H(a, U1(k, k))
28.56/9.80	   A^2 -> H(a, U1(k, d))
28.56/9.80	   A^2 -> H(a, U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.80	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.80	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.80	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.80	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.80	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.80	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.80	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, a), b)
28.56/9.80	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.80	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.80	   A^2 -> H(U1(e, a), c)
28.56/9.80	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.80	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.80	   A^2 -> H(U1(e, a), e)
28.56/9.80	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, a), b)
28.56/9.80	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.80	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.80	   A^2 -> H(U1(k, a), c)
28.56/9.80	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.80	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.80	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, d), b)
28.56/9.80	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.80	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.80	   A^2 -> H(U1(c, d), c)
28.56/9.80	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.80	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.80	   A^2 -> H(U1(c, d), e)
28.56/9.80	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, a), d)
28.56/9.80	   A^2 -> H(U1(c, a), k)
28.56/9.80	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.80	   A^2 -> H(U1(d, c), b)
28.56/9.80	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(d, c), c)
28.56/9.80	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.80	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.80	   A^2 -> H(U1(d, c), e)
28.56/9.80	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.80	   A^2 -> H(U1(d, a), d)
28.56/9.80	   A^2 -> H(U1(d, a), k)
28.56/9.80	   A^2 -> H(U1(a, e), b)
28.56/9.80	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.80	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.80	   A^2 -> H(U1(a, e), c)
28.56/9.80	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.80	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.80	   A^2 -> H(U1(a, e), e)
28.56/9.80	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(a, k), b)
28.56/9.80	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.80	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.80	   A^2 -> H(U1(a, k), c)
28.56/9.80	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.80	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.80	   A^2 -> H(U1(a, k), e)
28.56/9.80	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(a, c), d)
28.56/9.80	   A^2 -> H(U1(a, c), k)
28.56/9.80	   A^2 -> H(U1(a, d), d)
28.56/9.80	   A^2 -> H(U1(a, d), k)
28.56/9.80	   A^2 -> H(k, U1(c, b))
28.56/9.80	   A^2 -> H(k, U1(d, b))
28.56/9.80	   A^2 -> H(k, U1(b, c))
28.56/9.80	   A^2 -> H(k, U1(b, d))
28.56/9.80	   A^2 -> H(k, U1(c, c))
28.56/9.80	   A^2 -> H(k, f(e))
28.56/9.80	   A^2 -> H(k, f(k))
28.56/9.80	   A^2 -> H(k, U1(d, d))
28.56/9.80	   A^2 -> H(c, U1(e, b))
28.56/9.80	   A^2 -> H(c, U1(k, b))
28.56/9.80	   A^2 -> H(c, U1(c, d))
28.56/9.80	   A^2 -> H(c, U1(d, c))
28.56/9.80	   A^2 -> H(c, U1(b, e))
28.56/9.80	   A^2 -> H(c, U1(b, k))
28.56/9.80	   A^2 -> H(c, U1(e, c))
28.56/9.80	   A^2 -> H(c, U1(k, c))
28.56/9.80	   A^2 -> H(c, U1(c, e))
28.56/9.80	   A^2 -> H(c, U1(c, k))
28.56/9.80	   A^2 -> H(c, U1(e, e))
28.56/9.80	   A^2 -> H(c, U1(k, k))
28.56/9.80	   A^2 -> H(c, U1(k, d))
28.56/9.80	   A^2 -> H(c, U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.80	   A^2 -> H(U1(e, c), b)
28.56/9.80	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.80	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.80	   A^2 -> H(U1(e, c), e)
28.56/9.80	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.80	   A^2 -> H(U1(k, c), b)
28.56/9.80	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(k, c), c)
28.56/9.80	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.80	
28.56/9.80	The TRS R consists of the following rules:
28.56/9.80	
28.56/9.80	   f(x) -> U1(x, x)
28.56/9.80	   U1(e, x) -> x
28.56/9.80	   a -> c
28.56/9.80	   a -> d
28.56/9.80	   b -> c
28.56/9.80	   b -> d
28.56/9.80	   d -> k
28.56/9.80	   c -> e
28.56/9.80	   c -> k
28.56/9.80	
28.56/9.80	Q is empty.
28.56/9.80	We have to consider all minimal (P,Q,R)-chains.
28.56/9.80	----------------------------------------
28.56/9.80	
28.56/9.80	(1481) TransformationProof (EQUIVALENT)
28.56/9.80	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.80	
28.56/9.80	   (A^2 -> H(U1(k, e), U1(c, e)),A^2 -> H(U1(k, e), U1(c, e)))
28.56/9.80	   (A^2 -> H(U1(k, k), U1(c, e)),A^2 -> H(U1(k, k), U1(c, e)))
28.56/9.80	   (A^2 -> H(U1(k, c), U1(e, e)),A^2 -> H(U1(k, c), U1(e, e)))
28.56/9.80	   (A^2 -> H(U1(k, c), U1(k, e)),A^2 -> H(U1(k, c), U1(k, e)))
28.56/9.80	
28.56/9.80	
28.56/9.80	----------------------------------------
28.56/9.80	
28.56/9.80	(1482)
28.56/9.80	Obligation:
28.56/9.80	Q DP problem:
28.56/9.80	The TRS P consists of the following rules:
28.56/9.80	
28.56/9.80	   G(d, x, x) -> A^2
28.56/9.80	   A^2 -> H(f(c), f(c))
28.56/9.80	   H(x, x) -> G(x, x, f(k))
28.56/9.80	   A^2 -> H(f(d), f(d))
28.56/9.80	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.80	   A^2 -> H(f(e), f(e))
28.56/9.80	   A^2 -> H(f(k), f(k))
28.56/9.80	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.80	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.80	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, c), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, c), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, c), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.80	   A^2 -> H(U1(c, c), b)
28.56/9.80	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.80	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.80	   A^2 -> H(U1(c, c), e)
28.56/9.80	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.80	   A^2 -> H(e, U1(c, b))
28.56/9.80	   A^2 -> H(e, U1(d, b))
28.56/9.80	   A^2 -> H(e, U1(b, c))
28.56/9.80	   A^2 -> H(e, U1(b, d))
28.56/9.80	   A^2 -> H(e, U1(c, c))
28.56/9.80	   A^2 -> H(e, f(e))
28.56/9.80	   A^2 -> H(e, f(k))
28.56/9.80	   A^2 -> H(e, U1(d, d))
28.56/9.80	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.80	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.80	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.80	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.80	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.80	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.80	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.80	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.80	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.80	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.80	   A^2 -> H(f(e), b)
28.56/9.80	   A^2 -> H(f(e), U1(e, d))
28.56/9.80	   A^2 -> H(f(e), U1(d, e))
28.56/9.80	   A^2 -> H(f(e), c)
28.56/9.80	   A^2 -> H(f(e), U1(e, k))
28.56/9.80	   A^2 -> H(f(e), U1(k, e))
28.56/9.80	   A^2 -> H(f(e), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.80	   A^2 -> H(f(k), b)
28.56/9.80	   A^2 -> H(f(k), U1(e, d))
28.56/9.80	   A^2 -> H(f(k), U1(d, e))
28.56/9.80	   A^2 -> H(f(k), c)
28.56/9.80	   A^2 -> H(f(k), U1(e, k))
28.56/9.80	   A^2 -> H(f(k), U1(k, e))
28.56/9.80	   A^2 -> H(f(k), e)
28.56/9.80	   A^2 -> H(f(c), d)
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.80	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.80	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.80	   A^2 -> H(U1(k, k), f(e))
28.56/9.80	   A^2 -> H(U1(k, k), f(k))
28.56/9.80	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.80	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.80	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.80	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.80	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.80	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.80	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.80	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.80	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.80	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.80	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.80	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.80	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.80	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.80	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.80	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.80	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.80	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.80	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.80	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.81	   A^2 -> H(U1(d, d), b)
28.56/9.81	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.81	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.81	   A^2 -> H(U1(d, d), c)
28.56/9.81	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.81	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.81	   A^2 -> H(U1(d, d), e)
28.56/9.81	   A^2 -> H(f(d), d)
28.56/9.81	   A^2 -> H(f(d), k)
28.56/9.81	   A^2 -> H(U1(c, c), c)
28.56/9.81	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.81	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.81	   A^2 -> H(f(c), k)
28.56/9.81	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.81	   A^2 -> H(f(k), U1(k, k))
28.56/9.81	   A^2 -> H(f(e), e)
28.56/9.81	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.81	   A^2 -> H(d, U1(c, b))
28.56/9.81	   A^2 -> H(d, U1(d, b))
28.56/9.81	   A^2 -> H(d, U1(b, c))
28.56/9.81	   A^2 -> H(d, U1(b, d))
28.56/9.81	   A^2 -> H(d, U1(c, c))
28.56/9.81	   A^2 -> H(d, f(e))
28.56/9.81	   A^2 -> H(d, f(k))
28.56/9.81	   A^2 -> H(d, U1(d, d))
28.56/9.81	   A^2 -> H(a, U1(e, b))
28.56/9.81	   A^2 -> H(a, U1(k, b))
28.56/9.81	   A^2 -> H(a, U1(c, d))
28.56/9.81	   A^2 -> H(a, U1(d, c))
28.56/9.81	   A^2 -> H(a, U1(b, e))
28.56/9.81	   A^2 -> H(a, U1(b, k))
28.56/9.81	   A^2 -> H(a, U1(e, c))
28.56/9.81	   A^2 -> H(a, U1(k, c))
28.56/9.81	   A^2 -> H(a, U1(c, e))
28.56/9.81	   A^2 -> H(a, U1(c, k))
28.56/9.81	   A^2 -> H(a, U1(e, e))
28.56/9.81	   A^2 -> H(a, U1(k, k))
28.56/9.81	   A^2 -> H(a, U1(k, d))
28.56/9.81	   A^2 -> H(a, U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.81	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.81	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.81	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.81	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.81	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.81	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, a), b)
28.56/9.81	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.81	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.81	   A^2 -> H(U1(e, a), c)
28.56/9.81	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.81	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.81	   A^2 -> H(U1(e, a), e)
28.56/9.81	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, a), b)
28.56/9.81	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.81	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.81	   A^2 -> H(U1(k, a), c)
28.56/9.81	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.81	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.81	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, d), b)
28.56/9.81	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.81	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.81	   A^2 -> H(U1(c, d), c)
28.56/9.81	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.81	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.81	   A^2 -> H(U1(c, d), e)
28.56/9.81	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, a), d)
28.56/9.81	   A^2 -> H(U1(c, a), k)
28.56/9.81	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.81	   A^2 -> H(U1(d, c), b)
28.56/9.81	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(d, c), c)
28.56/9.81	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.81	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.81	   A^2 -> H(U1(d, c), e)
28.56/9.81	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.81	   A^2 -> H(U1(d, a), d)
28.56/9.81	   A^2 -> H(U1(d, a), k)
28.56/9.81	   A^2 -> H(U1(a, e), b)
28.56/9.81	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.81	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.81	   A^2 -> H(U1(a, e), c)
28.56/9.81	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.81	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.81	   A^2 -> H(U1(a, e), e)
28.56/9.81	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(a, k), b)
28.56/9.81	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.81	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.81	   A^2 -> H(U1(a, k), c)
28.56/9.81	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.81	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.81	   A^2 -> H(U1(a, k), e)
28.56/9.81	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(a, c), d)
28.56/9.81	   A^2 -> H(U1(a, c), k)
28.56/9.81	   A^2 -> H(U1(a, d), d)
28.56/9.81	   A^2 -> H(U1(a, d), k)
28.56/9.81	   A^2 -> H(k, U1(c, b))
28.56/9.81	   A^2 -> H(k, U1(d, b))
28.56/9.81	   A^2 -> H(k, U1(b, c))
28.56/9.81	   A^2 -> H(k, U1(b, d))
28.56/9.81	   A^2 -> H(k, U1(c, c))
28.56/9.81	   A^2 -> H(k, f(e))
28.56/9.81	   A^2 -> H(k, f(k))
28.56/9.81	   A^2 -> H(k, U1(d, d))
28.56/9.81	   A^2 -> H(c, U1(e, b))
28.56/9.81	   A^2 -> H(c, U1(k, b))
28.56/9.81	   A^2 -> H(c, U1(c, d))
28.56/9.81	   A^2 -> H(c, U1(d, c))
28.56/9.81	   A^2 -> H(c, U1(b, e))
28.56/9.81	   A^2 -> H(c, U1(b, k))
28.56/9.81	   A^2 -> H(c, U1(e, c))
28.56/9.81	   A^2 -> H(c, U1(k, c))
28.56/9.81	   A^2 -> H(c, U1(c, e))
28.56/9.81	   A^2 -> H(c, U1(c, k))
28.56/9.81	   A^2 -> H(c, U1(e, e))
28.56/9.81	   A^2 -> H(c, U1(k, k))
28.56/9.81	   A^2 -> H(c, U1(k, d))
28.56/9.81	   A^2 -> H(c, U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, c), b)
28.56/9.81	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.81	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.81	   A^2 -> H(U1(e, c), e)
28.56/9.81	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.81	   A^2 -> H(U1(k, c), b)
28.56/9.81	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(k, c), c)
28.56/9.81	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.81	
28.56/9.81	The TRS R consists of the following rules:
28.56/9.81	
28.56/9.81	   f(x) -> U1(x, x)
28.56/9.81	   U1(e, x) -> x
28.56/9.81	   a -> c
28.56/9.81	   a -> d
28.56/9.81	   b -> c
28.56/9.81	   b -> d
28.56/9.81	   d -> k
28.56/9.81	   c -> e
28.56/9.81	   c -> k
28.56/9.81	
28.56/9.81	Q is empty.
28.56/9.81	We have to consider all minimal (P,Q,R)-chains.
28.56/9.81	----------------------------------------
28.56/9.81	
28.56/9.81	(1483) TransformationProof (EQUIVALENT)
28.56/9.81	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.81	
28.56/9.81	   (A^2 -> H(U1(k, e), U1(c, k)),A^2 -> H(U1(k, e), U1(c, k)))
28.56/9.81	   (A^2 -> H(U1(k, k), U1(c, k)),A^2 -> H(U1(k, k), U1(c, k)))
28.56/9.81	   (A^2 -> H(U1(k, c), U1(e, k)),A^2 -> H(U1(k, c), U1(e, k)))
28.56/9.81	   (A^2 -> H(U1(k, c), U1(k, k)),A^2 -> H(U1(k, c), U1(k, k)))
28.56/9.81	
28.56/9.81	
28.56/9.81	----------------------------------------
28.56/9.81	
28.56/9.81	(1484)
28.56/9.81	Obligation:
28.56/9.81	Q DP problem:
28.56/9.81	The TRS P consists of the following rules:
28.56/9.81	
28.56/9.81	   G(d, x, x) -> A^2
28.56/9.81	   A^2 -> H(f(c), f(c))
28.56/9.81	   H(x, x) -> G(x, x, f(k))
28.56/9.81	   A^2 -> H(f(d), f(d))
28.56/9.81	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.81	   A^2 -> H(f(e), f(e))
28.56/9.81	   A^2 -> H(f(k), f(k))
28.56/9.81	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.81	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.81	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, c), U1(e, e))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.81	   A^2 -> H(U1(c, c), b)
28.56/9.81	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(c, c), e)
28.56/9.81	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.81	   A^2 -> H(e, U1(c, b))
28.56/9.81	   A^2 -> H(e, U1(d, b))
28.56/9.81	   A^2 -> H(e, U1(b, c))
28.56/9.81	   A^2 -> H(e, U1(b, d))
28.56/9.81	   A^2 -> H(e, U1(c, c))
28.56/9.81	   A^2 -> H(e, f(e))
28.56/9.81	   A^2 -> H(e, f(k))
28.56/9.81	   A^2 -> H(e, U1(d, d))
28.56/9.81	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.81	   A^2 -> H(f(e), b)
28.56/9.81	   A^2 -> H(f(e), U1(e, d))
28.56/9.81	   A^2 -> H(f(e), U1(d, e))
28.56/9.81	   A^2 -> H(f(e), c)
28.56/9.81	   A^2 -> H(f(e), U1(e, k))
28.56/9.81	   A^2 -> H(f(e), U1(k, e))
28.56/9.81	   A^2 -> H(f(e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.81	   A^2 -> H(f(k), b)
28.56/9.81	   A^2 -> H(f(k), U1(e, d))
28.56/9.81	   A^2 -> H(f(k), U1(d, e))
28.56/9.81	   A^2 -> H(f(k), c)
28.56/9.81	   A^2 -> H(f(k), U1(e, k))
28.56/9.81	   A^2 -> H(f(k), U1(k, e))
28.56/9.81	   A^2 -> H(f(k), e)
28.56/9.81	   A^2 -> H(f(c), d)
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.81	   A^2 -> H(U1(k, k), f(e))
28.56/9.81	   A^2 -> H(U1(k, k), f(k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.81	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.81	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.81	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.81	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.81	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.81	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.81	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.81	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.81	   A^2 -> H(U1(d, d), b)
28.56/9.81	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.81	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.81	   A^2 -> H(U1(d, d), c)
28.56/9.81	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.81	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.81	   A^2 -> H(U1(d, d), e)
28.56/9.81	   A^2 -> H(f(d), d)
28.56/9.81	   A^2 -> H(f(d), k)
28.56/9.81	   A^2 -> H(U1(c, c), c)
28.56/9.81	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.81	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.81	   A^2 -> H(f(c), k)
28.56/9.81	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.81	   A^2 -> H(f(k), U1(k, k))
28.56/9.81	   A^2 -> H(f(e), e)
28.56/9.81	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.81	   A^2 -> H(d, U1(c, b))
28.56/9.81	   A^2 -> H(d, U1(d, b))
28.56/9.81	   A^2 -> H(d, U1(b, c))
28.56/9.81	   A^2 -> H(d, U1(b, d))
28.56/9.81	   A^2 -> H(d, U1(c, c))
28.56/9.81	   A^2 -> H(d, f(e))
28.56/9.81	   A^2 -> H(d, f(k))
28.56/9.81	   A^2 -> H(d, U1(d, d))
28.56/9.81	   A^2 -> H(a, U1(e, b))
28.56/9.81	   A^2 -> H(a, U1(k, b))
28.56/9.81	   A^2 -> H(a, U1(c, d))
28.56/9.81	   A^2 -> H(a, U1(d, c))
28.56/9.81	   A^2 -> H(a, U1(b, e))
28.56/9.81	   A^2 -> H(a, U1(b, k))
28.56/9.81	   A^2 -> H(a, U1(e, c))
28.56/9.81	   A^2 -> H(a, U1(k, c))
28.56/9.81	   A^2 -> H(a, U1(c, e))
28.56/9.81	   A^2 -> H(a, U1(c, k))
28.56/9.81	   A^2 -> H(a, U1(e, e))
28.56/9.81	   A^2 -> H(a, U1(k, k))
28.56/9.81	   A^2 -> H(a, U1(k, d))
28.56/9.81	   A^2 -> H(a, U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.81	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.81	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.81	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.81	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.81	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.81	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, a), b)
28.56/9.81	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.81	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.81	   A^2 -> H(U1(e, a), c)
28.56/9.81	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.81	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.81	   A^2 -> H(U1(e, a), e)
28.56/9.81	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, a), b)
28.56/9.81	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.81	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.81	   A^2 -> H(U1(k, a), c)
28.56/9.81	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.81	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.81	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, d), b)
28.56/9.81	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.81	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.81	   A^2 -> H(U1(c, d), c)
28.56/9.81	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.81	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.81	   A^2 -> H(U1(c, d), e)
28.56/9.81	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, a), d)
28.56/9.81	   A^2 -> H(U1(c, a), k)
28.56/9.81	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.81	   A^2 -> H(U1(d, c), b)
28.56/9.81	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(d, c), c)
28.56/9.81	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.81	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.81	   A^2 -> H(U1(d, c), e)
28.56/9.81	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.81	   A^2 -> H(U1(d, a), d)
28.56/9.81	   A^2 -> H(U1(d, a), k)
28.56/9.81	   A^2 -> H(U1(a, e), b)
28.56/9.81	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.81	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.81	   A^2 -> H(U1(a, e), c)
28.56/9.81	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.81	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.81	   A^2 -> H(U1(a, e), e)
28.56/9.81	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(a, k), b)
28.56/9.81	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.81	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.81	   A^2 -> H(U1(a, k), c)
28.56/9.81	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.81	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.81	   A^2 -> H(U1(a, k), e)
28.56/9.81	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(a, c), d)
28.56/9.81	   A^2 -> H(U1(a, c), k)
28.56/9.81	   A^2 -> H(U1(a, d), d)
28.56/9.81	   A^2 -> H(U1(a, d), k)
28.56/9.81	   A^2 -> H(k, U1(c, b))
28.56/9.81	   A^2 -> H(k, U1(d, b))
28.56/9.81	   A^2 -> H(k, U1(b, c))
28.56/9.81	   A^2 -> H(k, U1(b, d))
28.56/9.81	   A^2 -> H(k, U1(c, c))
28.56/9.81	   A^2 -> H(k, f(e))
28.56/9.81	   A^2 -> H(k, f(k))
28.56/9.81	   A^2 -> H(k, U1(d, d))
28.56/9.81	   A^2 -> H(c, U1(e, b))
28.56/9.81	   A^2 -> H(c, U1(k, b))
28.56/9.81	   A^2 -> H(c, U1(c, d))
28.56/9.81	   A^2 -> H(c, U1(d, c))
28.56/9.81	   A^2 -> H(c, U1(b, e))
28.56/9.81	   A^2 -> H(c, U1(b, k))
28.56/9.81	   A^2 -> H(c, U1(e, c))
28.56/9.81	   A^2 -> H(c, U1(k, c))
28.56/9.81	   A^2 -> H(c, U1(c, e))
28.56/9.81	   A^2 -> H(c, U1(c, k))
28.56/9.81	   A^2 -> H(c, U1(e, e))
28.56/9.81	   A^2 -> H(c, U1(k, k))
28.56/9.81	   A^2 -> H(c, U1(k, d))
28.56/9.81	   A^2 -> H(c, U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, c), b)
28.56/9.81	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.81	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.81	   A^2 -> H(U1(e, c), e)
28.56/9.81	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.81	   A^2 -> H(U1(k, c), b)
28.56/9.81	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(k, c), c)
28.56/9.81	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.81	
28.56/9.81	The TRS R consists of the following rules:
28.56/9.81	
28.56/9.81	   f(x) -> U1(x, x)
28.56/9.81	   U1(e, x) -> x
28.56/9.81	   a -> c
28.56/9.81	   a -> d
28.56/9.81	   b -> c
28.56/9.81	   b -> d
28.56/9.81	   d -> k
28.56/9.81	   c -> e
28.56/9.81	   c -> k
28.56/9.81	
28.56/9.81	Q is empty.
28.56/9.81	We have to consider all minimal (P,Q,R)-chains.
28.56/9.81	----------------------------------------
28.56/9.81	
28.56/9.81	(1485) TransformationProof (EQUIVALENT)
28.56/9.81	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.81	
28.56/9.81	   (A^2 -> H(U1(k, e), U1(e, e)),A^2 -> H(U1(k, e), U1(e, e)))
28.56/9.81	   (A^2 -> H(U1(k, k), U1(e, e)),A^2 -> H(U1(k, k), U1(e, e)))
28.56/9.81	   (A^2 -> H(U1(k, c), e),A^2 -> H(U1(k, c), e))
28.56/9.81	
28.56/9.81	
28.56/9.81	----------------------------------------
28.56/9.81	
28.56/9.81	(1486)
28.56/9.81	Obligation:
28.56/9.81	Q DP problem:
28.56/9.81	The TRS P consists of the following rules:
28.56/9.81	
28.56/9.81	   G(d, x, x) -> A^2
28.56/9.81	   A^2 -> H(f(c), f(c))
28.56/9.81	   H(x, x) -> G(x, x, f(k))
28.56/9.81	   A^2 -> H(f(d), f(d))
28.56/9.81	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.81	   A^2 -> H(f(e), f(e))
28.56/9.81	   A^2 -> H(f(k), f(k))
28.56/9.81	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.81	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.81	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.81	   A^2 -> H(U1(c, c), b)
28.56/9.81	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(c, c), e)
28.56/9.81	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.81	   A^2 -> H(e, U1(c, b))
28.56/9.81	   A^2 -> H(e, U1(d, b))
28.56/9.81	   A^2 -> H(e, U1(b, c))
28.56/9.81	   A^2 -> H(e, U1(b, d))
28.56/9.81	   A^2 -> H(e, U1(c, c))
28.56/9.81	   A^2 -> H(e, f(e))
28.56/9.81	   A^2 -> H(e, f(k))
28.56/9.81	   A^2 -> H(e, U1(d, d))
28.56/9.81	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.81	   A^2 -> H(f(e), b)
28.56/9.81	   A^2 -> H(f(e), U1(e, d))
28.56/9.81	   A^2 -> H(f(e), U1(d, e))
28.56/9.81	   A^2 -> H(f(e), c)
28.56/9.81	   A^2 -> H(f(e), U1(e, k))
28.56/9.81	   A^2 -> H(f(e), U1(k, e))
28.56/9.81	   A^2 -> H(f(e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.81	   A^2 -> H(f(k), b)
28.56/9.81	   A^2 -> H(f(k), U1(e, d))
28.56/9.81	   A^2 -> H(f(k), U1(d, e))
28.56/9.81	   A^2 -> H(f(k), c)
28.56/9.81	   A^2 -> H(f(k), U1(e, k))
28.56/9.81	   A^2 -> H(f(k), U1(k, e))
28.56/9.81	   A^2 -> H(f(k), e)
28.56/9.81	   A^2 -> H(f(c), d)
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.81	   A^2 -> H(U1(k, k), f(e))
28.56/9.81	   A^2 -> H(U1(k, k), f(k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.81	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.81	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.81	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.81	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.81	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.81	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.81	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.81	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.81	   A^2 -> H(U1(d, d), b)
28.56/9.81	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.81	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.81	   A^2 -> H(U1(d, d), c)
28.56/9.81	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.81	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.81	   A^2 -> H(U1(d, d), e)
28.56/9.81	   A^2 -> H(f(d), d)
28.56/9.81	   A^2 -> H(f(d), k)
28.56/9.81	   A^2 -> H(U1(c, c), c)
28.56/9.81	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.81	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.81	   A^2 -> H(f(c), k)
28.56/9.81	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.81	   A^2 -> H(f(k), U1(k, k))
28.56/9.81	   A^2 -> H(f(e), e)
28.56/9.81	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.81	   A^2 -> H(d, U1(c, b))
28.56/9.81	   A^2 -> H(d, U1(d, b))
28.56/9.81	   A^2 -> H(d, U1(b, c))
28.56/9.81	   A^2 -> H(d, U1(b, d))
28.56/9.81	   A^2 -> H(d, U1(c, c))
28.56/9.81	   A^2 -> H(d, f(e))
28.56/9.81	   A^2 -> H(d, f(k))
28.56/9.81	   A^2 -> H(d, U1(d, d))
28.56/9.81	   A^2 -> H(a, U1(e, b))
28.56/9.81	   A^2 -> H(a, U1(k, b))
28.56/9.81	   A^2 -> H(a, U1(c, d))
28.56/9.81	   A^2 -> H(a, U1(d, c))
28.56/9.81	   A^2 -> H(a, U1(b, e))
28.56/9.81	   A^2 -> H(a, U1(b, k))
28.56/9.81	   A^2 -> H(a, U1(e, c))
28.56/9.81	   A^2 -> H(a, U1(k, c))
28.56/9.81	   A^2 -> H(a, U1(c, e))
28.56/9.81	   A^2 -> H(a, U1(c, k))
28.56/9.81	   A^2 -> H(a, U1(e, e))
28.56/9.81	   A^2 -> H(a, U1(k, k))
28.56/9.81	   A^2 -> H(a, U1(k, d))
28.56/9.81	   A^2 -> H(a, U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.81	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.81	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.81	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.81	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.81	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.81	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, a), b)
28.56/9.81	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.81	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.81	   A^2 -> H(U1(e, a), c)
28.56/9.81	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.81	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.81	   A^2 -> H(U1(e, a), e)
28.56/9.81	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, a), b)
28.56/9.81	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.81	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.81	   A^2 -> H(U1(k, a), c)
28.56/9.81	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.81	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.81	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, d), b)
28.56/9.81	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.81	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.81	   A^2 -> H(U1(c, d), c)
28.56/9.81	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.81	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.81	   A^2 -> H(U1(c, d), e)
28.56/9.81	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, a), d)
28.56/9.81	   A^2 -> H(U1(c, a), k)
28.56/9.81	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.81	   A^2 -> H(U1(d, c), b)
28.56/9.81	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(d, c), c)
28.56/9.81	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.81	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.81	   A^2 -> H(U1(d, c), e)
28.56/9.81	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.81	   A^2 -> H(U1(d, a), d)
28.56/9.81	   A^2 -> H(U1(d, a), k)
28.56/9.81	   A^2 -> H(U1(a, e), b)
28.56/9.81	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.81	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.81	   A^2 -> H(U1(a, e), c)
28.56/9.81	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.81	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.81	   A^2 -> H(U1(a, e), e)
28.56/9.81	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(a, k), b)
28.56/9.81	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.81	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.81	   A^2 -> H(U1(a, k), c)
28.56/9.81	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.81	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.81	   A^2 -> H(U1(a, k), e)
28.56/9.81	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(a, c), d)
28.56/9.81	   A^2 -> H(U1(a, c), k)
28.56/9.81	   A^2 -> H(U1(a, d), d)
28.56/9.81	   A^2 -> H(U1(a, d), k)
28.56/9.81	   A^2 -> H(k, U1(c, b))
28.56/9.81	   A^2 -> H(k, U1(d, b))
28.56/9.81	   A^2 -> H(k, U1(b, c))
28.56/9.81	   A^2 -> H(k, U1(b, d))
28.56/9.81	   A^2 -> H(k, U1(c, c))
28.56/9.81	   A^2 -> H(k, f(e))
28.56/9.81	   A^2 -> H(k, f(k))
28.56/9.81	   A^2 -> H(k, U1(d, d))
28.56/9.81	   A^2 -> H(c, U1(e, b))
28.56/9.81	   A^2 -> H(c, U1(k, b))
28.56/9.81	   A^2 -> H(c, U1(c, d))
28.56/9.81	   A^2 -> H(c, U1(d, c))
28.56/9.81	   A^2 -> H(c, U1(b, e))
28.56/9.81	   A^2 -> H(c, U1(b, k))
28.56/9.81	   A^2 -> H(c, U1(e, c))
28.56/9.81	   A^2 -> H(c, U1(k, c))
28.56/9.81	   A^2 -> H(c, U1(c, e))
28.56/9.81	   A^2 -> H(c, U1(c, k))
28.56/9.81	   A^2 -> H(c, U1(e, e))
28.56/9.81	   A^2 -> H(c, U1(k, k))
28.56/9.81	   A^2 -> H(c, U1(k, d))
28.56/9.81	   A^2 -> H(c, U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, c), b)
28.56/9.81	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.81	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.81	   A^2 -> H(U1(e, c), e)
28.56/9.81	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.81	   A^2 -> H(U1(k, c), b)
28.56/9.81	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(k, c), c)
28.56/9.81	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.81	   A^2 -> H(U1(k, c), e)
28.56/9.81	
28.56/9.81	The TRS R consists of the following rules:
28.56/9.81	
28.56/9.81	   f(x) -> U1(x, x)
28.56/9.81	   U1(e, x) -> x
28.56/9.81	   a -> c
28.56/9.81	   a -> d
28.56/9.81	   b -> c
28.56/9.81	   b -> d
28.56/9.81	   d -> k
28.56/9.81	   c -> e
28.56/9.81	   c -> k
28.56/9.81	
28.56/9.81	Q is empty.
28.56/9.81	We have to consider all minimal (P,Q,R)-chains.
28.56/9.81	----------------------------------------
28.56/9.81	
28.56/9.81	(1487) DependencyGraphProof (EQUIVALENT)
28.56/9.81	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.81	----------------------------------------
28.56/9.81	
28.56/9.81	(1488)
28.56/9.81	Obligation:
28.56/9.81	Q DP problem:
28.56/9.81	The TRS P consists of the following rules:
28.56/9.81	
28.56/9.81	   A^2 -> H(f(c), f(c))
28.56/9.81	   H(x, x) -> G(x, x, f(k))
28.56/9.81	   G(d, x, x) -> A^2
28.56/9.81	   A^2 -> H(f(d), f(d))
28.56/9.81	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.81	   A^2 -> H(f(e), f(e))
28.56/9.81	   A^2 -> H(f(k), f(k))
28.56/9.81	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.81	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.81	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.81	   A^2 -> H(U1(c, c), b)
28.56/9.81	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(c, c), e)
28.56/9.81	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.81	   A^2 -> H(e, U1(c, b))
28.56/9.81	   A^2 -> H(e, U1(d, b))
28.56/9.81	   A^2 -> H(e, U1(b, c))
28.56/9.81	   A^2 -> H(e, U1(b, d))
28.56/9.81	   A^2 -> H(e, U1(c, c))
28.56/9.81	   A^2 -> H(e, f(e))
28.56/9.81	   A^2 -> H(e, f(k))
28.56/9.81	   A^2 -> H(e, U1(d, d))
28.56/9.81	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.81	   A^2 -> H(f(e), b)
28.56/9.81	   A^2 -> H(f(e), U1(e, d))
28.56/9.81	   A^2 -> H(f(e), U1(d, e))
28.56/9.81	   A^2 -> H(f(e), c)
28.56/9.81	   A^2 -> H(f(e), U1(e, k))
28.56/9.81	   A^2 -> H(f(e), U1(k, e))
28.56/9.81	   A^2 -> H(f(e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.81	   A^2 -> H(f(k), b)
28.56/9.81	   A^2 -> H(f(k), U1(e, d))
28.56/9.81	   A^2 -> H(f(k), U1(d, e))
28.56/9.81	   A^2 -> H(f(k), c)
28.56/9.81	   A^2 -> H(f(k), U1(e, k))
28.56/9.81	   A^2 -> H(f(k), U1(k, e))
28.56/9.81	   A^2 -> H(f(k), e)
28.56/9.81	   A^2 -> H(f(c), d)
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.81	   A^2 -> H(U1(k, k), f(e))
28.56/9.81	   A^2 -> H(U1(k, k), f(k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.81	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.81	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.81	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.81	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.81	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.81	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.81	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.81	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.81	   A^2 -> H(U1(d, d), b)
28.56/9.81	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.81	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.81	   A^2 -> H(U1(d, d), c)
28.56/9.81	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.81	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.81	   A^2 -> H(U1(d, d), e)
28.56/9.81	   A^2 -> H(f(d), d)
28.56/9.81	   A^2 -> H(f(d), k)
28.56/9.81	   A^2 -> H(U1(c, c), c)
28.56/9.81	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.81	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.81	   A^2 -> H(f(c), k)
28.56/9.81	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.81	   A^2 -> H(f(k), U1(k, k))
28.56/9.81	   A^2 -> H(f(e), e)
28.56/9.81	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.81	   A^2 -> H(d, U1(c, b))
28.56/9.81	   A^2 -> H(d, U1(d, b))
28.56/9.81	   A^2 -> H(d, U1(b, c))
28.56/9.81	   A^2 -> H(d, U1(b, d))
28.56/9.81	   A^2 -> H(d, U1(c, c))
28.56/9.81	   A^2 -> H(d, f(e))
28.56/9.81	   A^2 -> H(d, f(k))
28.56/9.81	   A^2 -> H(d, U1(d, d))
28.56/9.81	   A^2 -> H(a, U1(e, b))
28.56/9.81	   A^2 -> H(a, U1(k, b))
28.56/9.81	   A^2 -> H(a, U1(c, d))
28.56/9.81	   A^2 -> H(a, U1(d, c))
28.56/9.81	   A^2 -> H(a, U1(b, e))
28.56/9.81	   A^2 -> H(a, U1(b, k))
28.56/9.81	   A^2 -> H(a, U1(e, c))
28.56/9.81	   A^2 -> H(a, U1(k, c))
28.56/9.81	   A^2 -> H(a, U1(c, e))
28.56/9.81	   A^2 -> H(a, U1(c, k))
28.56/9.81	   A^2 -> H(a, U1(e, e))
28.56/9.81	   A^2 -> H(a, U1(k, k))
28.56/9.81	   A^2 -> H(a, U1(k, d))
28.56/9.81	   A^2 -> H(a, U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.81	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.81	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.81	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.81	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.81	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.81	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, a), b)
28.56/9.81	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.81	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.81	   A^2 -> H(U1(e, a), c)
28.56/9.81	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.81	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.81	   A^2 -> H(U1(e, a), e)
28.56/9.81	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, a), b)
28.56/9.81	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.81	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.81	   A^2 -> H(U1(k, a), c)
28.56/9.81	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.81	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.81	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, d), b)
28.56/9.81	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.81	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.81	   A^2 -> H(U1(c, d), c)
28.56/9.81	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.81	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.81	   A^2 -> H(U1(c, d), e)
28.56/9.81	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, a), d)
28.56/9.81	   A^2 -> H(U1(c, a), k)
28.56/9.81	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.81	   A^2 -> H(U1(d, c), b)
28.56/9.81	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(d, c), c)
28.56/9.81	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.81	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.81	   A^2 -> H(U1(d, c), e)
28.56/9.81	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.81	   A^2 -> H(U1(d, a), d)
28.56/9.81	   A^2 -> H(U1(d, a), k)
28.56/9.81	   A^2 -> H(U1(a, e), b)
28.56/9.81	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.81	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.81	   A^2 -> H(U1(a, e), c)
28.56/9.81	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.81	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.81	   A^2 -> H(U1(a, e), e)
28.56/9.81	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(a, k), b)
28.56/9.81	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.81	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.81	   A^2 -> H(U1(a, k), c)
28.56/9.81	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.81	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.81	   A^2 -> H(U1(a, k), e)
28.56/9.81	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(a, c), d)
28.56/9.81	   A^2 -> H(U1(a, c), k)
28.56/9.81	   A^2 -> H(U1(a, d), d)
28.56/9.81	   A^2 -> H(U1(a, d), k)
28.56/9.81	   A^2 -> H(k, U1(c, b))
28.56/9.81	   A^2 -> H(k, U1(d, b))
28.56/9.81	   A^2 -> H(k, U1(b, c))
28.56/9.81	   A^2 -> H(k, U1(b, d))
28.56/9.81	   A^2 -> H(k, U1(c, c))
28.56/9.81	   A^2 -> H(k, f(e))
28.56/9.81	   A^2 -> H(k, f(k))
28.56/9.81	   A^2 -> H(k, U1(d, d))
28.56/9.81	   A^2 -> H(c, U1(e, b))
28.56/9.81	   A^2 -> H(c, U1(k, b))
28.56/9.81	   A^2 -> H(c, U1(c, d))
28.56/9.81	   A^2 -> H(c, U1(d, c))
28.56/9.81	   A^2 -> H(c, U1(b, e))
28.56/9.81	   A^2 -> H(c, U1(b, k))
28.56/9.81	   A^2 -> H(c, U1(e, c))
28.56/9.81	   A^2 -> H(c, U1(k, c))
28.56/9.81	   A^2 -> H(c, U1(c, e))
28.56/9.81	   A^2 -> H(c, U1(c, k))
28.56/9.81	   A^2 -> H(c, U1(e, e))
28.56/9.81	   A^2 -> H(c, U1(k, k))
28.56/9.81	   A^2 -> H(c, U1(k, d))
28.56/9.81	   A^2 -> H(c, U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, c), b)
28.56/9.81	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.81	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.81	   A^2 -> H(U1(e, c), e)
28.56/9.81	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.81	   A^2 -> H(U1(k, c), b)
28.56/9.81	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(k, c), c)
28.56/9.81	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.81	
28.56/9.81	The TRS R consists of the following rules:
28.56/9.81	
28.56/9.81	   f(x) -> U1(x, x)
28.56/9.81	   U1(e, x) -> x
28.56/9.81	   a -> c
28.56/9.81	   a -> d
28.56/9.81	   b -> c
28.56/9.81	   b -> d
28.56/9.81	   d -> k
28.56/9.81	   c -> e
28.56/9.81	   c -> k
28.56/9.81	
28.56/9.81	Q is empty.
28.56/9.81	We have to consider all minimal (P,Q,R)-chains.
28.56/9.81	----------------------------------------
28.56/9.81	
28.56/9.81	(1489) TransformationProof (EQUIVALENT)
28.56/9.81	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.81	
28.56/9.81	   (A^2 -> H(U1(k, e), U1(k, k)),A^2 -> H(U1(k, e), U1(k, k)))
28.56/9.81	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.56/9.81	
28.56/9.81	
28.56/9.81	----------------------------------------
28.56/9.81	
28.56/9.81	(1490)
28.56/9.81	Obligation:
28.56/9.81	Q DP problem:
28.56/9.81	The TRS P consists of the following rules:
28.56/9.81	
28.56/9.81	   A^2 -> H(f(c), f(c))
28.56/9.81	   H(x, x) -> G(x, x, f(k))
28.56/9.81	   G(d, x, x) -> A^2
28.56/9.81	   A^2 -> H(f(d), f(d))
28.56/9.81	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.81	   A^2 -> H(f(e), f(e))
28.56/9.81	   A^2 -> H(f(k), f(k))
28.56/9.81	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.81	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.81	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.81	   A^2 -> H(U1(c, c), b)
28.56/9.81	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(c, c), e)
28.56/9.81	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.81	   A^2 -> H(e, U1(c, b))
28.56/9.81	   A^2 -> H(e, U1(d, b))
28.56/9.81	   A^2 -> H(e, U1(b, c))
28.56/9.81	   A^2 -> H(e, U1(b, d))
28.56/9.81	   A^2 -> H(e, U1(c, c))
28.56/9.81	   A^2 -> H(e, f(e))
28.56/9.81	   A^2 -> H(e, f(k))
28.56/9.81	   A^2 -> H(e, U1(d, d))
28.56/9.81	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.81	   A^2 -> H(f(e), b)
28.56/9.81	   A^2 -> H(f(e), U1(e, d))
28.56/9.81	   A^2 -> H(f(e), U1(d, e))
28.56/9.81	   A^2 -> H(f(e), c)
28.56/9.81	   A^2 -> H(f(e), U1(e, k))
28.56/9.81	   A^2 -> H(f(e), U1(k, e))
28.56/9.81	   A^2 -> H(f(e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.81	   A^2 -> H(f(k), b)
28.56/9.81	   A^2 -> H(f(k), U1(e, d))
28.56/9.81	   A^2 -> H(f(k), U1(d, e))
28.56/9.81	   A^2 -> H(f(k), c)
28.56/9.81	   A^2 -> H(f(k), U1(e, k))
28.56/9.81	   A^2 -> H(f(k), U1(k, e))
28.56/9.81	   A^2 -> H(f(k), e)
28.56/9.81	   A^2 -> H(f(c), d)
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.81	   A^2 -> H(U1(k, k), f(e))
28.56/9.81	   A^2 -> H(U1(k, k), f(k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.81	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.81	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.81	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.81	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.81	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.81	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.81	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.81	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.81	   A^2 -> H(U1(d, d), b)
28.56/9.81	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.81	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.81	   A^2 -> H(U1(d, d), c)
28.56/9.81	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.81	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.81	   A^2 -> H(U1(d, d), e)
28.56/9.81	   A^2 -> H(f(d), d)
28.56/9.81	   A^2 -> H(f(d), k)
28.56/9.81	   A^2 -> H(U1(c, c), c)
28.56/9.81	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.81	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.81	   A^2 -> H(f(c), k)
28.56/9.81	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.81	   A^2 -> H(f(k), U1(k, k))
28.56/9.81	   A^2 -> H(f(e), e)
28.56/9.81	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.81	   A^2 -> H(d, U1(c, b))
28.56/9.81	   A^2 -> H(d, U1(d, b))
28.56/9.81	   A^2 -> H(d, U1(b, c))
28.56/9.81	   A^2 -> H(d, U1(b, d))
28.56/9.81	   A^2 -> H(d, U1(c, c))
28.56/9.81	   A^2 -> H(d, f(e))
28.56/9.81	   A^2 -> H(d, f(k))
28.56/9.81	   A^2 -> H(d, U1(d, d))
28.56/9.81	   A^2 -> H(a, U1(e, b))
28.56/9.81	   A^2 -> H(a, U1(k, b))
28.56/9.81	   A^2 -> H(a, U1(c, d))
28.56/9.81	   A^2 -> H(a, U1(d, c))
28.56/9.81	   A^2 -> H(a, U1(b, e))
28.56/9.81	   A^2 -> H(a, U1(b, k))
28.56/9.81	   A^2 -> H(a, U1(e, c))
28.56/9.81	   A^2 -> H(a, U1(k, c))
28.56/9.81	   A^2 -> H(a, U1(c, e))
28.56/9.81	   A^2 -> H(a, U1(c, k))
28.56/9.81	   A^2 -> H(a, U1(e, e))
28.56/9.81	   A^2 -> H(a, U1(k, k))
28.56/9.81	   A^2 -> H(a, U1(k, d))
28.56/9.81	   A^2 -> H(a, U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.81	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.81	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.81	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.81	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.81	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.81	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, a), b)
28.56/9.81	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.81	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.81	   A^2 -> H(U1(e, a), c)
28.56/9.81	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.81	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.81	   A^2 -> H(U1(e, a), e)
28.56/9.81	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, a), b)
28.56/9.81	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.81	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.81	   A^2 -> H(U1(k, a), c)
28.56/9.81	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.81	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.81	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, d), b)
28.56/9.81	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.81	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.81	   A^2 -> H(U1(c, d), c)
28.56/9.81	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.81	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.81	   A^2 -> H(U1(c, d), e)
28.56/9.81	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, a), d)
28.56/9.81	   A^2 -> H(U1(c, a), k)
28.56/9.81	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.81	   A^2 -> H(U1(d, c), b)
28.56/9.81	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(d, c), c)
28.56/9.81	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.81	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.81	   A^2 -> H(U1(d, c), e)
28.56/9.81	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.81	   A^2 -> H(U1(d, a), d)
28.56/9.81	   A^2 -> H(U1(d, a), k)
28.56/9.81	   A^2 -> H(U1(a, e), b)
28.56/9.81	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.81	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.81	   A^2 -> H(U1(a, e), c)
28.56/9.81	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.81	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.81	   A^2 -> H(U1(a, e), e)
28.56/9.81	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(a, k), b)
28.56/9.81	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.81	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.81	   A^2 -> H(U1(a, k), c)
28.56/9.81	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.81	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.81	   A^2 -> H(U1(a, k), e)
28.56/9.81	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(a, c), d)
28.56/9.81	   A^2 -> H(U1(a, c), k)
28.56/9.81	   A^2 -> H(U1(a, d), d)
28.56/9.81	   A^2 -> H(U1(a, d), k)
28.56/9.81	   A^2 -> H(k, U1(c, b))
28.56/9.81	   A^2 -> H(k, U1(d, b))
28.56/9.81	   A^2 -> H(k, U1(b, c))
28.56/9.81	   A^2 -> H(k, U1(b, d))
28.56/9.81	   A^2 -> H(k, U1(c, c))
28.56/9.81	   A^2 -> H(k, f(e))
28.56/9.81	   A^2 -> H(k, f(k))
28.56/9.81	   A^2 -> H(k, U1(d, d))
28.56/9.81	   A^2 -> H(c, U1(e, b))
28.56/9.81	   A^2 -> H(c, U1(k, b))
28.56/9.81	   A^2 -> H(c, U1(c, d))
28.56/9.81	   A^2 -> H(c, U1(d, c))
28.56/9.81	   A^2 -> H(c, U1(b, e))
28.56/9.81	   A^2 -> H(c, U1(b, k))
28.56/9.81	   A^2 -> H(c, U1(e, c))
28.56/9.81	   A^2 -> H(c, U1(k, c))
28.56/9.81	   A^2 -> H(c, U1(c, e))
28.56/9.81	   A^2 -> H(c, U1(c, k))
28.56/9.81	   A^2 -> H(c, U1(e, e))
28.56/9.81	   A^2 -> H(c, U1(k, k))
28.56/9.81	   A^2 -> H(c, U1(k, d))
28.56/9.81	   A^2 -> H(c, U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, c), b)
28.56/9.81	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.81	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.81	   A^2 -> H(U1(e, c), e)
28.56/9.81	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.81	   A^2 -> H(U1(k, c), b)
28.56/9.81	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(k, c), c)
28.56/9.81	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, k))
28.56/9.81	
28.56/9.81	The TRS R consists of the following rules:
28.56/9.81	
28.56/9.81	   f(x) -> U1(x, x)
28.56/9.81	   U1(e, x) -> x
28.56/9.81	   a -> c
28.56/9.81	   a -> d
28.56/9.81	   b -> c
28.56/9.81	   b -> d
28.56/9.81	   d -> k
28.56/9.81	   c -> e
28.56/9.81	   c -> k
28.56/9.81	
28.56/9.81	Q is empty.
28.56/9.81	We have to consider all minimal (P,Q,R)-chains.
28.56/9.81	----------------------------------------
28.56/9.81	
28.56/9.81	(1491) DependencyGraphProof (EQUIVALENT)
28.56/9.81	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.81	----------------------------------------
28.56/9.81	
28.56/9.81	(1492)
28.56/9.81	Obligation:
28.56/9.81	Q DP problem:
28.56/9.81	The TRS P consists of the following rules:
28.56/9.81	
28.56/9.81	   H(x, x) -> G(x, x, f(k))
28.56/9.81	   G(d, x, x) -> A^2
28.56/9.81	   A^2 -> H(f(c), f(c))
28.56/9.81	   A^2 -> H(f(d), f(d))
28.56/9.81	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.81	   A^2 -> H(f(e), f(e))
28.56/9.81	   A^2 -> H(f(k), f(k))
28.56/9.81	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.81	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.81	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.81	   A^2 -> H(U1(c, c), b)
28.56/9.81	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(c, c), e)
28.56/9.81	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.81	   A^2 -> H(e, U1(c, b))
28.56/9.81	   A^2 -> H(e, U1(d, b))
28.56/9.81	   A^2 -> H(e, U1(b, c))
28.56/9.81	   A^2 -> H(e, U1(b, d))
28.56/9.81	   A^2 -> H(e, U1(c, c))
28.56/9.81	   A^2 -> H(e, f(e))
28.56/9.81	   A^2 -> H(e, f(k))
28.56/9.81	   A^2 -> H(e, U1(d, d))
28.56/9.81	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.81	   A^2 -> H(f(e), b)
28.56/9.81	   A^2 -> H(f(e), U1(e, d))
28.56/9.81	   A^2 -> H(f(e), U1(d, e))
28.56/9.81	   A^2 -> H(f(e), c)
28.56/9.81	   A^2 -> H(f(e), U1(e, k))
28.56/9.81	   A^2 -> H(f(e), U1(k, e))
28.56/9.81	   A^2 -> H(f(e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.81	   A^2 -> H(f(k), b)
28.56/9.81	   A^2 -> H(f(k), U1(e, d))
28.56/9.81	   A^2 -> H(f(k), U1(d, e))
28.56/9.81	   A^2 -> H(f(k), c)
28.56/9.81	   A^2 -> H(f(k), U1(e, k))
28.56/9.81	   A^2 -> H(f(k), U1(k, e))
28.56/9.81	   A^2 -> H(f(k), e)
28.56/9.81	   A^2 -> H(f(c), d)
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.81	   A^2 -> H(U1(k, k), f(e))
28.56/9.81	   A^2 -> H(U1(k, k), f(k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.81	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.81	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.81	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.81	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.81	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.81	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.81	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.81	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.81	   A^2 -> H(U1(d, d), b)
28.56/9.81	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.81	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.81	   A^2 -> H(U1(d, d), c)
28.56/9.81	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.81	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.81	   A^2 -> H(U1(d, d), e)
28.56/9.81	   A^2 -> H(f(d), d)
28.56/9.81	   A^2 -> H(f(d), k)
28.56/9.81	   A^2 -> H(U1(c, c), c)
28.56/9.81	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.81	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.81	   A^2 -> H(f(c), k)
28.56/9.81	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.81	   A^2 -> H(f(k), U1(k, k))
28.56/9.81	   A^2 -> H(f(e), e)
28.56/9.81	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.81	   A^2 -> H(d, U1(c, b))
28.56/9.81	   A^2 -> H(d, U1(d, b))
28.56/9.81	   A^2 -> H(d, U1(b, c))
28.56/9.81	   A^2 -> H(d, U1(b, d))
28.56/9.81	   A^2 -> H(d, U1(c, c))
28.56/9.81	   A^2 -> H(d, f(e))
28.56/9.81	   A^2 -> H(d, f(k))
28.56/9.81	   A^2 -> H(d, U1(d, d))
28.56/9.81	   A^2 -> H(a, U1(e, b))
28.56/9.81	   A^2 -> H(a, U1(k, b))
28.56/9.81	   A^2 -> H(a, U1(c, d))
28.56/9.81	   A^2 -> H(a, U1(d, c))
28.56/9.81	   A^2 -> H(a, U1(b, e))
28.56/9.81	   A^2 -> H(a, U1(b, k))
28.56/9.81	   A^2 -> H(a, U1(e, c))
28.56/9.81	   A^2 -> H(a, U1(k, c))
28.56/9.81	   A^2 -> H(a, U1(c, e))
28.56/9.81	   A^2 -> H(a, U1(c, k))
28.56/9.81	   A^2 -> H(a, U1(e, e))
28.56/9.81	   A^2 -> H(a, U1(k, k))
28.56/9.81	   A^2 -> H(a, U1(k, d))
28.56/9.81	   A^2 -> H(a, U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.81	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.81	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.81	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.81	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.81	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.81	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.81	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, a), b)
28.56/9.81	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.81	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.81	   A^2 -> H(U1(e, a), c)
28.56/9.81	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.81	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.81	   A^2 -> H(U1(e, a), e)
28.56/9.81	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, a), b)
28.56/9.81	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.81	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.81	   A^2 -> H(U1(k, a), c)
28.56/9.81	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.81	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.81	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, d), b)
28.56/9.81	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.81	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.81	   A^2 -> H(U1(c, d), c)
28.56/9.81	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.81	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.81	   A^2 -> H(U1(c, d), e)
28.56/9.81	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, a), d)
28.56/9.81	   A^2 -> H(U1(c, a), k)
28.56/9.81	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.81	   A^2 -> H(U1(d, c), b)
28.56/9.81	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(d, c), c)
28.56/9.81	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.81	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.81	   A^2 -> H(U1(d, c), e)
28.56/9.81	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.81	   A^2 -> H(U1(d, a), d)
28.56/9.81	   A^2 -> H(U1(d, a), k)
28.56/9.81	   A^2 -> H(U1(a, e), b)
28.56/9.81	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.81	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.81	   A^2 -> H(U1(a, e), c)
28.56/9.81	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.81	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.81	   A^2 -> H(U1(a, e), e)
28.56/9.81	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(a, k), b)
28.56/9.81	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.81	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.81	   A^2 -> H(U1(a, k), c)
28.56/9.81	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.81	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.81	   A^2 -> H(U1(a, k), e)
28.56/9.81	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(a, c), d)
28.56/9.81	   A^2 -> H(U1(a, c), k)
28.56/9.81	   A^2 -> H(U1(a, d), d)
28.56/9.81	   A^2 -> H(U1(a, d), k)
28.56/9.81	   A^2 -> H(k, U1(c, b))
28.56/9.81	   A^2 -> H(k, U1(d, b))
28.56/9.81	   A^2 -> H(k, U1(b, c))
28.56/9.81	   A^2 -> H(k, U1(b, d))
28.56/9.81	   A^2 -> H(k, U1(c, c))
28.56/9.81	   A^2 -> H(k, f(e))
28.56/9.81	   A^2 -> H(k, f(k))
28.56/9.81	   A^2 -> H(k, U1(d, d))
28.56/9.81	   A^2 -> H(c, U1(e, b))
28.56/9.81	   A^2 -> H(c, U1(k, b))
28.56/9.81	   A^2 -> H(c, U1(c, d))
28.56/9.81	   A^2 -> H(c, U1(d, c))
28.56/9.81	   A^2 -> H(c, U1(b, e))
28.56/9.81	   A^2 -> H(c, U1(b, k))
28.56/9.81	   A^2 -> H(c, U1(e, c))
28.56/9.81	   A^2 -> H(c, U1(k, c))
28.56/9.81	   A^2 -> H(c, U1(c, e))
28.56/9.81	   A^2 -> H(c, U1(c, k))
28.56/9.81	   A^2 -> H(c, U1(e, e))
28.56/9.81	   A^2 -> H(c, U1(k, k))
28.56/9.81	   A^2 -> H(c, U1(k, d))
28.56/9.81	   A^2 -> H(c, U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.81	   A^2 -> H(U1(e, c), b)
28.56/9.81	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.81	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.81	   A^2 -> H(U1(e, c), e)
28.56/9.81	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.81	   A^2 -> H(U1(k, c), b)
28.56/9.81	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(k, c), c)
28.56/9.81	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.81	
28.56/9.81	The TRS R consists of the following rules:
28.56/9.81	
28.56/9.81	   f(x) -> U1(x, x)
28.56/9.81	   U1(e, x) -> x
28.56/9.81	   a -> c
28.56/9.81	   a -> d
28.56/9.81	   b -> c
28.56/9.81	   b -> d
28.56/9.81	   d -> k
28.56/9.81	   c -> e
28.56/9.81	   c -> k
28.56/9.81	
28.56/9.81	Q is empty.
28.56/9.81	We have to consider all minimal (P,Q,R)-chains.
28.56/9.81	----------------------------------------
28.56/9.81	
28.56/9.81	(1493) TransformationProof (EQUIVALENT)
28.56/9.81	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.81	
28.56/9.81	   (A^2 -> H(U1(k, e), U1(k, d)),A^2 -> H(U1(k, e), U1(k, d)))
28.56/9.81	   (A^2 -> H(U1(k, k), U1(k, d)),A^2 -> H(U1(k, k), U1(k, d)))
28.56/9.81	   (A^2 -> H(U1(k, c), U1(k, k)),A^2 -> H(U1(k, c), U1(k, k)))
28.56/9.81	
28.56/9.81	
28.56/9.81	----------------------------------------
28.56/9.81	
28.56/9.81	(1494)
28.56/9.81	Obligation:
28.56/9.81	Q DP problem:
28.56/9.81	The TRS P consists of the following rules:
28.56/9.81	
28.56/9.81	   H(x, x) -> G(x, x, f(k))
28.56/9.81	   G(d, x, x) -> A^2
28.56/9.81	   A^2 -> H(f(c), f(c))
28.56/9.81	   A^2 -> H(f(d), f(d))
28.56/9.81	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.81	   A^2 -> H(f(e), f(e))
28.56/9.81	   A^2 -> H(f(k), f(k))
28.56/9.81	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.81	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.81	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, c), U1(d, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.81	   A^2 -> H(U1(c, c), b)
28.56/9.81	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.81	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.81	   A^2 -> H(U1(c, c), e)
28.56/9.81	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.81	   A^2 -> H(e, U1(c, b))
28.56/9.81	   A^2 -> H(e, U1(d, b))
28.56/9.81	   A^2 -> H(e, U1(b, c))
28.56/9.81	   A^2 -> H(e, U1(b, d))
28.56/9.81	   A^2 -> H(e, U1(c, c))
28.56/9.81	   A^2 -> H(e, f(e))
28.56/9.81	   A^2 -> H(e, f(k))
28.56/9.81	   A^2 -> H(e, U1(d, d))
28.56/9.81	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.81	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.81	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.81	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.81	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.81	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.81	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.81	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.81	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.81	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.81	   A^2 -> H(f(e), b)
28.56/9.81	   A^2 -> H(f(e), U1(e, d))
28.56/9.81	   A^2 -> H(f(e), U1(d, e))
28.56/9.81	   A^2 -> H(f(e), c)
28.56/9.81	   A^2 -> H(f(e), U1(e, k))
28.56/9.81	   A^2 -> H(f(e), U1(k, e))
28.56/9.81	   A^2 -> H(f(e), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.81	   A^2 -> H(f(k), b)
28.56/9.81	   A^2 -> H(f(k), U1(e, d))
28.56/9.81	   A^2 -> H(f(k), U1(d, e))
28.56/9.81	   A^2 -> H(f(k), c)
28.56/9.81	   A^2 -> H(f(k), U1(e, k))
28.56/9.81	   A^2 -> H(f(k), U1(k, e))
28.56/9.81	   A^2 -> H(f(k), e)
28.56/9.81	   A^2 -> H(f(c), d)
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.81	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.81	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.81	   A^2 -> H(U1(k, k), f(e))
28.56/9.81	   A^2 -> H(U1(k, k), f(k))
28.56/9.81	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.81	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.81	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.81	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.82	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.82	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.82	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.82	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.82	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.82	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.82	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.82	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.82	   A^2 -> H(U1(d, d), b)
28.56/9.82	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.82	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.82	   A^2 -> H(U1(d, d), c)
28.56/9.82	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.82	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.82	   A^2 -> H(U1(d, d), e)
28.56/9.82	   A^2 -> H(f(d), d)
28.56/9.82	   A^2 -> H(f(d), k)
28.56/9.82	   A^2 -> H(U1(c, c), c)
28.56/9.82	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.82	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.82	   A^2 -> H(f(c), k)
28.56/9.82	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.82	   A^2 -> H(f(k), U1(k, k))
28.56/9.82	   A^2 -> H(f(e), e)
28.56/9.82	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.82	   A^2 -> H(d, U1(c, b))
28.56/9.82	   A^2 -> H(d, U1(d, b))
28.56/9.82	   A^2 -> H(d, U1(b, c))
28.56/9.82	   A^2 -> H(d, U1(b, d))
28.56/9.82	   A^2 -> H(d, U1(c, c))
28.56/9.82	   A^2 -> H(d, f(e))
28.56/9.82	   A^2 -> H(d, f(k))
28.56/9.82	   A^2 -> H(d, U1(d, d))
28.56/9.82	   A^2 -> H(a, U1(e, b))
28.56/9.82	   A^2 -> H(a, U1(k, b))
28.56/9.82	   A^2 -> H(a, U1(c, d))
28.56/9.82	   A^2 -> H(a, U1(d, c))
28.56/9.82	   A^2 -> H(a, U1(b, e))
28.56/9.82	   A^2 -> H(a, U1(b, k))
28.56/9.82	   A^2 -> H(a, U1(e, c))
28.56/9.82	   A^2 -> H(a, U1(k, c))
28.56/9.82	   A^2 -> H(a, U1(c, e))
28.56/9.82	   A^2 -> H(a, U1(c, k))
28.56/9.82	   A^2 -> H(a, U1(e, e))
28.56/9.82	   A^2 -> H(a, U1(k, k))
28.56/9.82	   A^2 -> H(a, U1(k, d))
28.56/9.82	   A^2 -> H(a, U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.82	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.82	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.82	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.82	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.82	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.82	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, a), b)
28.56/9.82	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.82	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.82	   A^2 -> H(U1(e, a), c)
28.56/9.82	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.82	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.82	   A^2 -> H(U1(e, a), e)
28.56/9.82	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, a), b)
28.56/9.82	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.82	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.82	   A^2 -> H(U1(k, a), c)
28.56/9.82	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.82	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.82	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, d), b)
28.56/9.82	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.82	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.82	   A^2 -> H(U1(c, d), c)
28.56/9.82	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.82	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.82	   A^2 -> H(U1(c, d), e)
28.56/9.82	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, a), d)
28.56/9.82	   A^2 -> H(U1(c, a), k)
28.56/9.82	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.82	   A^2 -> H(U1(d, c), b)
28.56/9.82	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(d, c), c)
28.56/9.82	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.82	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.82	   A^2 -> H(U1(d, c), e)
28.56/9.82	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.82	   A^2 -> H(U1(d, a), d)
28.56/9.82	   A^2 -> H(U1(d, a), k)
28.56/9.82	   A^2 -> H(U1(a, e), b)
28.56/9.82	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.82	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.82	   A^2 -> H(U1(a, e), c)
28.56/9.82	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.82	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.82	   A^2 -> H(U1(a, e), e)
28.56/9.82	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(a, k), b)
28.56/9.82	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.82	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.82	   A^2 -> H(U1(a, k), c)
28.56/9.82	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.82	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.82	   A^2 -> H(U1(a, k), e)
28.56/9.82	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(a, c), d)
28.56/9.82	   A^2 -> H(U1(a, c), k)
28.56/9.82	   A^2 -> H(U1(a, d), d)
28.56/9.82	   A^2 -> H(U1(a, d), k)
28.56/9.82	   A^2 -> H(k, U1(c, b))
28.56/9.82	   A^2 -> H(k, U1(d, b))
28.56/9.82	   A^2 -> H(k, U1(b, c))
28.56/9.82	   A^2 -> H(k, U1(b, d))
28.56/9.82	   A^2 -> H(k, U1(c, c))
28.56/9.82	   A^2 -> H(k, f(e))
28.56/9.82	   A^2 -> H(k, f(k))
28.56/9.82	   A^2 -> H(k, U1(d, d))
28.56/9.82	   A^2 -> H(c, U1(e, b))
28.56/9.82	   A^2 -> H(c, U1(k, b))
28.56/9.82	   A^2 -> H(c, U1(c, d))
28.56/9.82	   A^2 -> H(c, U1(d, c))
28.56/9.82	   A^2 -> H(c, U1(b, e))
28.56/9.82	   A^2 -> H(c, U1(b, k))
28.56/9.82	   A^2 -> H(c, U1(e, c))
28.56/9.82	   A^2 -> H(c, U1(k, c))
28.56/9.82	   A^2 -> H(c, U1(c, e))
28.56/9.82	   A^2 -> H(c, U1(c, k))
28.56/9.82	   A^2 -> H(c, U1(e, e))
28.56/9.82	   A^2 -> H(c, U1(k, k))
28.56/9.82	   A^2 -> H(c, U1(k, d))
28.56/9.82	   A^2 -> H(c, U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, c), b)
28.56/9.82	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.82	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.82	   A^2 -> H(U1(e, c), e)
28.56/9.82	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.82	   A^2 -> H(U1(k, c), b)
28.56/9.82	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(k, c), c)
28.56/9.82	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.82	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.82	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.82	
28.56/9.82	The TRS R consists of the following rules:
28.56/9.82	
28.56/9.82	   f(x) -> U1(x, x)
28.56/9.82	   U1(e, x) -> x
28.56/9.82	   a -> c
28.56/9.82	   a -> d
28.56/9.82	   b -> c
28.56/9.82	   b -> d
28.56/9.82	   d -> k
28.56/9.82	   c -> e
28.56/9.82	   c -> k
28.56/9.82	
28.56/9.82	Q is empty.
28.56/9.82	We have to consider all minimal (P,Q,R)-chains.
28.56/9.82	----------------------------------------
28.56/9.82	
28.56/9.82	(1495) TransformationProof (EQUIVALENT)
28.56/9.82	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.82	
28.56/9.82	   (A^2 -> H(U1(k, e), U1(d, k)),A^2 -> H(U1(k, e), U1(d, k)))
28.56/9.82	   (A^2 -> H(U1(k, k), U1(d, k)),A^2 -> H(U1(k, k), U1(d, k)))
28.56/9.82	   (A^2 -> H(U1(k, c), U1(k, k)),A^2 -> H(U1(k, c), U1(k, k)))
28.56/9.82	
28.56/9.82	
28.56/9.82	----------------------------------------
28.56/9.82	
28.56/9.82	(1496)
28.56/9.82	Obligation:
28.56/9.82	Q DP problem:
28.56/9.82	The TRS P consists of the following rules:
28.56/9.82	
28.56/9.82	   H(x, x) -> G(x, x, f(k))
28.56/9.82	   G(d, x, x) -> A^2
28.56/9.82	   A^2 -> H(f(c), f(c))
28.56/9.82	   A^2 -> H(f(d), f(d))
28.56/9.82	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.82	   A^2 -> H(f(e), f(e))
28.56/9.82	   A^2 -> H(f(k), f(k))
28.56/9.82	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.82	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.82	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.82	   A^2 -> H(U1(c, c), b)
28.56/9.82	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(c, c), e)
28.56/9.82	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.82	   A^2 -> H(e, U1(c, b))
28.56/9.82	   A^2 -> H(e, U1(d, b))
28.56/9.82	   A^2 -> H(e, U1(b, c))
28.56/9.82	   A^2 -> H(e, U1(b, d))
28.56/9.82	   A^2 -> H(e, U1(c, c))
28.56/9.82	   A^2 -> H(e, f(e))
28.56/9.82	   A^2 -> H(e, f(k))
28.56/9.82	   A^2 -> H(e, U1(d, d))
28.56/9.82	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.82	   A^2 -> H(f(e), b)
28.56/9.82	   A^2 -> H(f(e), U1(e, d))
28.56/9.82	   A^2 -> H(f(e), U1(d, e))
28.56/9.82	   A^2 -> H(f(e), c)
28.56/9.82	   A^2 -> H(f(e), U1(e, k))
28.56/9.82	   A^2 -> H(f(e), U1(k, e))
28.56/9.82	   A^2 -> H(f(e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.82	   A^2 -> H(f(k), b)
28.56/9.82	   A^2 -> H(f(k), U1(e, d))
28.56/9.82	   A^2 -> H(f(k), U1(d, e))
28.56/9.82	   A^2 -> H(f(k), c)
28.56/9.82	   A^2 -> H(f(k), U1(e, k))
28.56/9.82	   A^2 -> H(f(k), U1(k, e))
28.56/9.82	   A^2 -> H(f(k), e)
28.56/9.82	   A^2 -> H(f(c), d)
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.82	   A^2 -> H(U1(k, k), f(e))
28.56/9.82	   A^2 -> H(U1(k, k), f(k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.82	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.82	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.82	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.82	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.82	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.82	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.82	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.82	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.82	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.82	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.82	   A^2 -> H(U1(d, d), b)
28.56/9.82	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.82	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.82	   A^2 -> H(U1(d, d), c)
28.56/9.82	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.82	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.82	   A^2 -> H(U1(d, d), e)
28.56/9.82	   A^2 -> H(f(d), d)
28.56/9.82	   A^2 -> H(f(d), k)
28.56/9.82	   A^2 -> H(U1(c, c), c)
28.56/9.82	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.82	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.82	   A^2 -> H(f(c), k)
28.56/9.82	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.82	   A^2 -> H(f(k), U1(k, k))
28.56/9.82	   A^2 -> H(f(e), e)
28.56/9.82	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.82	   A^2 -> H(d, U1(c, b))
28.56/9.82	   A^2 -> H(d, U1(d, b))
28.56/9.82	   A^2 -> H(d, U1(b, c))
28.56/9.82	   A^2 -> H(d, U1(b, d))
28.56/9.82	   A^2 -> H(d, U1(c, c))
28.56/9.82	   A^2 -> H(d, f(e))
28.56/9.82	   A^2 -> H(d, f(k))
28.56/9.82	   A^2 -> H(d, U1(d, d))
28.56/9.82	   A^2 -> H(a, U1(e, b))
28.56/9.82	   A^2 -> H(a, U1(k, b))
28.56/9.82	   A^2 -> H(a, U1(c, d))
28.56/9.82	   A^2 -> H(a, U1(d, c))
28.56/9.82	   A^2 -> H(a, U1(b, e))
28.56/9.82	   A^2 -> H(a, U1(b, k))
28.56/9.82	   A^2 -> H(a, U1(e, c))
28.56/9.82	   A^2 -> H(a, U1(k, c))
28.56/9.82	   A^2 -> H(a, U1(c, e))
28.56/9.82	   A^2 -> H(a, U1(c, k))
28.56/9.82	   A^2 -> H(a, U1(e, e))
28.56/9.82	   A^2 -> H(a, U1(k, k))
28.56/9.82	   A^2 -> H(a, U1(k, d))
28.56/9.82	   A^2 -> H(a, U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.82	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.82	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.82	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.82	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.82	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.82	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, a), b)
28.56/9.82	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.82	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.82	   A^2 -> H(U1(e, a), c)
28.56/9.82	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.82	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.82	   A^2 -> H(U1(e, a), e)
28.56/9.82	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, a), b)
28.56/9.82	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.82	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.82	   A^2 -> H(U1(k, a), c)
28.56/9.82	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.82	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.82	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, d), b)
28.56/9.82	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.82	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.82	   A^2 -> H(U1(c, d), c)
28.56/9.82	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.82	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.82	   A^2 -> H(U1(c, d), e)
28.56/9.82	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, a), d)
28.56/9.82	   A^2 -> H(U1(c, a), k)
28.56/9.82	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.82	   A^2 -> H(U1(d, c), b)
28.56/9.82	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(d, c), c)
28.56/9.82	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.82	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.82	   A^2 -> H(U1(d, c), e)
28.56/9.82	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.82	   A^2 -> H(U1(d, a), d)
28.56/9.82	   A^2 -> H(U1(d, a), k)
28.56/9.82	   A^2 -> H(U1(a, e), b)
28.56/9.82	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.82	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.82	   A^2 -> H(U1(a, e), c)
28.56/9.82	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.82	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.82	   A^2 -> H(U1(a, e), e)
28.56/9.82	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(a, k), b)
28.56/9.82	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.82	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.82	   A^2 -> H(U1(a, k), c)
28.56/9.82	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.82	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.82	   A^2 -> H(U1(a, k), e)
28.56/9.82	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(a, c), d)
28.56/9.82	   A^2 -> H(U1(a, c), k)
28.56/9.82	   A^2 -> H(U1(a, d), d)
28.56/9.82	   A^2 -> H(U1(a, d), k)
28.56/9.82	   A^2 -> H(k, U1(c, b))
28.56/9.82	   A^2 -> H(k, U1(d, b))
28.56/9.82	   A^2 -> H(k, U1(b, c))
28.56/9.82	   A^2 -> H(k, U1(b, d))
28.56/9.82	   A^2 -> H(k, U1(c, c))
28.56/9.82	   A^2 -> H(k, f(e))
28.56/9.82	   A^2 -> H(k, f(k))
28.56/9.82	   A^2 -> H(k, U1(d, d))
28.56/9.82	   A^2 -> H(c, U1(e, b))
28.56/9.82	   A^2 -> H(c, U1(k, b))
28.56/9.82	   A^2 -> H(c, U1(c, d))
28.56/9.82	   A^2 -> H(c, U1(d, c))
28.56/9.82	   A^2 -> H(c, U1(b, e))
28.56/9.82	   A^2 -> H(c, U1(b, k))
28.56/9.82	   A^2 -> H(c, U1(e, c))
28.56/9.82	   A^2 -> H(c, U1(k, c))
28.56/9.82	   A^2 -> H(c, U1(c, e))
28.56/9.82	   A^2 -> H(c, U1(c, k))
28.56/9.82	   A^2 -> H(c, U1(e, e))
28.56/9.82	   A^2 -> H(c, U1(k, k))
28.56/9.82	   A^2 -> H(c, U1(k, d))
28.56/9.82	   A^2 -> H(c, U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, c), b)
28.56/9.82	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.82	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.82	   A^2 -> H(U1(e, c), e)
28.56/9.82	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.82	   A^2 -> H(U1(k, c), b)
28.56/9.82	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(k, c), c)
28.56/9.82	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.82	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.82	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.82	
28.56/9.82	The TRS R consists of the following rules:
28.56/9.82	
28.56/9.82	   f(x) -> U1(x, x)
28.56/9.82	   U1(e, x) -> x
28.56/9.82	   a -> c
28.56/9.82	   a -> d
28.56/9.82	   b -> c
28.56/9.82	   b -> d
28.56/9.82	   d -> k
28.56/9.82	   c -> e
28.56/9.82	   c -> k
28.56/9.82	
28.56/9.82	Q is empty.
28.56/9.82	We have to consider all minimal (P,Q,R)-chains.
28.56/9.82	----------------------------------------
28.56/9.82	
28.56/9.82	(1497) TransformationProof (EQUIVALENT)
28.56/9.82	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.82	
28.56/9.82	   (A^2 -> H(U1(e, e), U1(e, b)),A^2 -> H(U1(e, e), U1(e, b)))
28.56/9.82	   (A^2 -> H(U1(k, e), U1(e, b)),A^2 -> H(U1(k, e), U1(e, b)))
28.56/9.82	   (A^2 -> H(U1(c, e), b),A^2 -> H(U1(c, e), b))
28.56/9.82	   (A^2 -> H(U1(c, e), U1(e, c)),A^2 -> H(U1(c, e), U1(e, c)))
28.56/9.82	   (A^2 -> H(U1(c, e), U1(e, d)),A^2 -> H(U1(c, e), U1(e, d)))
28.56/9.82	
28.56/9.82	
28.56/9.82	----------------------------------------
28.56/9.82	
28.56/9.82	(1498)
28.56/9.82	Obligation:
28.56/9.82	Q DP problem:
28.56/9.82	The TRS P consists of the following rules:
28.56/9.82	
28.56/9.82	   H(x, x) -> G(x, x, f(k))
28.56/9.82	   G(d, x, x) -> A^2
28.56/9.82	   A^2 -> H(f(c), f(c))
28.56/9.82	   A^2 -> H(f(d), f(d))
28.56/9.82	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.82	   A^2 -> H(f(e), f(e))
28.56/9.82	   A^2 -> H(f(k), f(k))
28.56/9.82	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.82	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.82	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.82	   A^2 -> H(U1(c, c), b)
28.56/9.82	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(c, c), e)
28.56/9.82	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.82	   A^2 -> H(e, U1(c, b))
28.56/9.82	   A^2 -> H(e, U1(d, b))
28.56/9.82	   A^2 -> H(e, U1(b, c))
28.56/9.82	   A^2 -> H(e, U1(b, d))
28.56/9.82	   A^2 -> H(e, U1(c, c))
28.56/9.82	   A^2 -> H(e, f(e))
28.56/9.82	   A^2 -> H(e, f(k))
28.56/9.82	   A^2 -> H(e, U1(d, d))
28.56/9.82	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.82	   A^2 -> H(f(e), b)
28.56/9.82	   A^2 -> H(f(e), U1(e, d))
28.56/9.82	   A^2 -> H(f(e), U1(d, e))
28.56/9.82	   A^2 -> H(f(e), c)
28.56/9.82	   A^2 -> H(f(e), U1(e, k))
28.56/9.82	   A^2 -> H(f(e), U1(k, e))
28.56/9.82	   A^2 -> H(f(e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.82	   A^2 -> H(f(k), b)
28.56/9.82	   A^2 -> H(f(k), U1(e, d))
28.56/9.82	   A^2 -> H(f(k), U1(d, e))
28.56/9.82	   A^2 -> H(f(k), c)
28.56/9.82	   A^2 -> H(f(k), U1(e, k))
28.56/9.82	   A^2 -> H(f(k), U1(k, e))
28.56/9.82	   A^2 -> H(f(k), e)
28.56/9.82	   A^2 -> H(f(c), d)
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.82	   A^2 -> H(U1(k, k), f(e))
28.56/9.82	   A^2 -> H(U1(k, k), f(k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.82	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.82	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.82	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.82	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.82	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.82	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.82	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.82	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.82	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.82	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.82	   A^2 -> H(U1(d, d), b)
28.56/9.82	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.82	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.82	   A^2 -> H(U1(d, d), c)
28.56/9.82	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.82	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.82	   A^2 -> H(U1(d, d), e)
28.56/9.82	   A^2 -> H(f(d), d)
28.56/9.82	   A^2 -> H(f(d), k)
28.56/9.82	   A^2 -> H(U1(c, c), c)
28.56/9.82	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.82	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.82	   A^2 -> H(f(c), k)
28.56/9.82	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.82	   A^2 -> H(f(k), U1(k, k))
28.56/9.82	   A^2 -> H(f(e), e)
28.56/9.82	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.82	   A^2 -> H(d, U1(c, b))
28.56/9.82	   A^2 -> H(d, U1(d, b))
28.56/9.82	   A^2 -> H(d, U1(b, c))
28.56/9.82	   A^2 -> H(d, U1(b, d))
28.56/9.82	   A^2 -> H(d, U1(c, c))
28.56/9.82	   A^2 -> H(d, f(e))
28.56/9.82	   A^2 -> H(d, f(k))
28.56/9.82	   A^2 -> H(d, U1(d, d))
28.56/9.82	   A^2 -> H(a, U1(e, b))
28.56/9.82	   A^2 -> H(a, U1(k, b))
28.56/9.82	   A^2 -> H(a, U1(c, d))
28.56/9.82	   A^2 -> H(a, U1(d, c))
28.56/9.82	   A^2 -> H(a, U1(b, e))
28.56/9.82	   A^2 -> H(a, U1(b, k))
28.56/9.82	   A^2 -> H(a, U1(e, c))
28.56/9.82	   A^2 -> H(a, U1(k, c))
28.56/9.82	   A^2 -> H(a, U1(c, e))
28.56/9.82	   A^2 -> H(a, U1(c, k))
28.56/9.82	   A^2 -> H(a, U1(e, e))
28.56/9.82	   A^2 -> H(a, U1(k, k))
28.56/9.82	   A^2 -> H(a, U1(k, d))
28.56/9.82	   A^2 -> H(a, U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.82	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.82	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.82	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.82	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.82	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.82	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, a), b)
28.56/9.82	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.82	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.82	   A^2 -> H(U1(e, a), c)
28.56/9.82	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.82	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.82	   A^2 -> H(U1(e, a), e)
28.56/9.82	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, a), b)
28.56/9.82	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.82	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.82	   A^2 -> H(U1(k, a), c)
28.56/9.82	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.82	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.82	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, d), b)
28.56/9.82	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.82	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.82	   A^2 -> H(U1(c, d), c)
28.56/9.82	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.82	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.82	   A^2 -> H(U1(c, d), e)
28.56/9.82	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, a), d)
28.56/9.82	   A^2 -> H(U1(c, a), k)
28.56/9.82	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.82	   A^2 -> H(U1(d, c), b)
28.56/9.82	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(d, c), c)
28.56/9.82	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.82	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.82	   A^2 -> H(U1(d, c), e)
28.56/9.82	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.82	   A^2 -> H(U1(d, a), d)
28.56/9.82	   A^2 -> H(U1(d, a), k)
28.56/9.82	   A^2 -> H(U1(a, e), b)
28.56/9.82	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.82	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.82	   A^2 -> H(U1(a, e), c)
28.56/9.82	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.82	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.82	   A^2 -> H(U1(a, e), e)
28.56/9.82	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(a, k), b)
28.56/9.82	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.82	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.82	   A^2 -> H(U1(a, k), c)
28.56/9.82	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.82	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.82	   A^2 -> H(U1(a, k), e)
28.56/9.82	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(a, c), d)
28.56/9.82	   A^2 -> H(U1(a, c), k)
28.56/9.82	   A^2 -> H(U1(a, d), d)
28.56/9.82	   A^2 -> H(U1(a, d), k)
28.56/9.82	   A^2 -> H(k, U1(c, b))
28.56/9.82	   A^2 -> H(k, U1(d, b))
28.56/9.82	   A^2 -> H(k, U1(b, c))
28.56/9.82	   A^2 -> H(k, U1(b, d))
28.56/9.82	   A^2 -> H(k, U1(c, c))
28.56/9.82	   A^2 -> H(k, f(e))
28.56/9.82	   A^2 -> H(k, f(k))
28.56/9.82	   A^2 -> H(k, U1(d, d))
28.56/9.82	   A^2 -> H(c, U1(e, b))
28.56/9.82	   A^2 -> H(c, U1(k, b))
28.56/9.82	   A^2 -> H(c, U1(c, d))
28.56/9.82	   A^2 -> H(c, U1(d, c))
28.56/9.82	   A^2 -> H(c, U1(b, e))
28.56/9.82	   A^2 -> H(c, U1(b, k))
28.56/9.82	   A^2 -> H(c, U1(e, c))
28.56/9.82	   A^2 -> H(c, U1(k, c))
28.56/9.82	   A^2 -> H(c, U1(c, e))
28.56/9.82	   A^2 -> H(c, U1(c, k))
28.56/9.82	   A^2 -> H(c, U1(e, e))
28.56/9.82	   A^2 -> H(c, U1(k, k))
28.56/9.82	   A^2 -> H(c, U1(k, d))
28.56/9.82	   A^2 -> H(c, U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, c), b)
28.56/9.82	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.82	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.82	   A^2 -> H(U1(e, c), e)
28.56/9.82	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.82	   A^2 -> H(U1(k, c), b)
28.56/9.82	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(k, c), c)
28.56/9.82	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.82	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.82	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, e), b)
28.56/9.82	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.82	
28.56/9.82	The TRS R consists of the following rules:
28.56/9.82	
28.56/9.82	   f(x) -> U1(x, x)
28.56/9.82	   U1(e, x) -> x
28.56/9.82	   a -> c
28.56/9.82	   a -> d
28.56/9.82	   b -> c
28.56/9.82	   b -> d
28.56/9.82	   d -> k
28.56/9.82	   c -> e
28.56/9.82	   c -> k
28.56/9.82	
28.56/9.82	Q is empty.
28.56/9.82	We have to consider all minimal (P,Q,R)-chains.
28.56/9.82	----------------------------------------
28.56/9.82	
28.56/9.82	(1499) TransformationProof (EQUIVALENT)
28.56/9.82	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.82	
28.56/9.82	   (A^2 -> H(U1(e, e), U1(k, b)),A^2 -> H(U1(e, e), U1(k, b)))
28.56/9.82	   (A^2 -> H(U1(k, e), U1(k, b)),A^2 -> H(U1(k, e), U1(k, b)))
28.56/9.82	   (A^2 -> H(U1(c, e), U1(k, c)),A^2 -> H(U1(c, e), U1(k, c)))
28.56/9.82	   (A^2 -> H(U1(c, e), U1(k, d)),A^2 -> H(U1(c, e), U1(k, d)))
28.56/9.82	
28.56/9.82	
28.56/9.82	----------------------------------------
28.56/9.82	
28.56/9.82	(1500)
28.56/9.82	Obligation:
28.56/9.82	Q DP problem:
28.56/9.82	The TRS P consists of the following rules:
28.56/9.82	
28.56/9.82	   H(x, x) -> G(x, x, f(k))
28.56/9.82	   G(d, x, x) -> A^2
28.56/9.82	   A^2 -> H(f(c), f(c))
28.56/9.82	   A^2 -> H(f(d), f(d))
28.56/9.82	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.82	   A^2 -> H(f(e), f(e))
28.56/9.82	   A^2 -> H(f(k), f(k))
28.56/9.82	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.82	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.82	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.82	   A^2 -> H(U1(c, c), b)
28.56/9.82	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(c, c), e)
28.56/9.82	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.82	   A^2 -> H(e, U1(c, b))
28.56/9.82	   A^2 -> H(e, U1(d, b))
28.56/9.82	   A^2 -> H(e, U1(b, c))
28.56/9.82	   A^2 -> H(e, U1(b, d))
28.56/9.82	   A^2 -> H(e, U1(c, c))
28.56/9.82	   A^2 -> H(e, f(e))
28.56/9.82	   A^2 -> H(e, f(k))
28.56/9.82	   A^2 -> H(e, U1(d, d))
28.56/9.82	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.82	   A^2 -> H(f(e), b)
28.56/9.82	   A^2 -> H(f(e), U1(e, d))
28.56/9.82	   A^2 -> H(f(e), U1(d, e))
28.56/9.82	   A^2 -> H(f(e), c)
28.56/9.82	   A^2 -> H(f(e), U1(e, k))
28.56/9.82	   A^2 -> H(f(e), U1(k, e))
28.56/9.82	   A^2 -> H(f(e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.82	   A^2 -> H(f(k), b)
28.56/9.82	   A^2 -> H(f(k), U1(e, d))
28.56/9.82	   A^2 -> H(f(k), U1(d, e))
28.56/9.82	   A^2 -> H(f(k), c)
28.56/9.82	   A^2 -> H(f(k), U1(e, k))
28.56/9.82	   A^2 -> H(f(k), U1(k, e))
28.56/9.82	   A^2 -> H(f(k), e)
28.56/9.82	   A^2 -> H(f(c), d)
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.82	   A^2 -> H(U1(k, k), f(e))
28.56/9.82	   A^2 -> H(U1(k, k), f(k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.82	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.82	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.82	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.82	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.82	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.82	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.82	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.82	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.82	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.82	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.82	   A^2 -> H(U1(d, d), b)
28.56/9.82	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.82	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.82	   A^2 -> H(U1(d, d), c)
28.56/9.82	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.82	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.82	   A^2 -> H(U1(d, d), e)
28.56/9.82	   A^2 -> H(f(d), d)
28.56/9.82	   A^2 -> H(f(d), k)
28.56/9.82	   A^2 -> H(U1(c, c), c)
28.56/9.82	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.82	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.82	   A^2 -> H(f(c), k)
28.56/9.82	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.82	   A^2 -> H(f(k), U1(k, k))
28.56/9.82	   A^2 -> H(f(e), e)
28.56/9.82	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.82	   A^2 -> H(d, U1(c, b))
28.56/9.82	   A^2 -> H(d, U1(d, b))
28.56/9.82	   A^2 -> H(d, U1(b, c))
28.56/9.82	   A^2 -> H(d, U1(b, d))
28.56/9.82	   A^2 -> H(d, U1(c, c))
28.56/9.82	   A^2 -> H(d, f(e))
28.56/9.82	   A^2 -> H(d, f(k))
28.56/9.82	   A^2 -> H(d, U1(d, d))
28.56/9.82	   A^2 -> H(a, U1(e, b))
28.56/9.82	   A^2 -> H(a, U1(k, b))
28.56/9.82	   A^2 -> H(a, U1(c, d))
28.56/9.82	   A^2 -> H(a, U1(d, c))
28.56/9.82	   A^2 -> H(a, U1(b, e))
28.56/9.82	   A^2 -> H(a, U1(b, k))
28.56/9.82	   A^2 -> H(a, U1(e, c))
28.56/9.82	   A^2 -> H(a, U1(k, c))
28.56/9.82	   A^2 -> H(a, U1(c, e))
28.56/9.82	   A^2 -> H(a, U1(c, k))
28.56/9.82	   A^2 -> H(a, U1(e, e))
28.56/9.82	   A^2 -> H(a, U1(k, k))
28.56/9.82	   A^2 -> H(a, U1(k, d))
28.56/9.82	   A^2 -> H(a, U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.82	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.82	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.82	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.82	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.82	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.82	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, a), b)
28.56/9.82	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.82	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.82	   A^2 -> H(U1(e, a), c)
28.56/9.82	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.82	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.82	   A^2 -> H(U1(e, a), e)
28.56/9.82	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, a), b)
28.56/9.82	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.82	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.82	   A^2 -> H(U1(k, a), c)
28.56/9.82	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.82	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.82	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, d), b)
28.56/9.82	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.82	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.82	   A^2 -> H(U1(c, d), c)
28.56/9.82	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.82	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.82	   A^2 -> H(U1(c, d), e)
28.56/9.82	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, a), d)
28.56/9.82	   A^2 -> H(U1(c, a), k)
28.56/9.82	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.82	   A^2 -> H(U1(d, c), b)
28.56/9.82	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(d, c), c)
28.56/9.82	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.82	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.82	   A^2 -> H(U1(d, c), e)
28.56/9.82	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.82	   A^2 -> H(U1(d, a), d)
28.56/9.82	   A^2 -> H(U1(d, a), k)
28.56/9.82	   A^2 -> H(U1(a, e), b)
28.56/9.82	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.82	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.82	   A^2 -> H(U1(a, e), c)
28.56/9.82	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.82	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.82	   A^2 -> H(U1(a, e), e)
28.56/9.82	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(a, k), b)
28.56/9.82	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.82	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.82	   A^2 -> H(U1(a, k), c)
28.56/9.82	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.82	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.82	   A^2 -> H(U1(a, k), e)
28.56/9.82	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(a, c), d)
28.56/9.82	   A^2 -> H(U1(a, c), k)
28.56/9.82	   A^2 -> H(U1(a, d), d)
28.56/9.82	   A^2 -> H(U1(a, d), k)
28.56/9.82	   A^2 -> H(k, U1(c, b))
28.56/9.82	   A^2 -> H(k, U1(d, b))
28.56/9.82	   A^2 -> H(k, U1(b, c))
28.56/9.82	   A^2 -> H(k, U1(b, d))
28.56/9.82	   A^2 -> H(k, U1(c, c))
28.56/9.82	   A^2 -> H(k, f(e))
28.56/9.82	   A^2 -> H(k, f(k))
28.56/9.82	   A^2 -> H(k, U1(d, d))
28.56/9.82	   A^2 -> H(c, U1(e, b))
28.56/9.82	   A^2 -> H(c, U1(k, b))
28.56/9.82	   A^2 -> H(c, U1(c, d))
28.56/9.82	   A^2 -> H(c, U1(d, c))
28.56/9.82	   A^2 -> H(c, U1(b, e))
28.56/9.82	   A^2 -> H(c, U1(b, k))
28.56/9.82	   A^2 -> H(c, U1(e, c))
28.56/9.82	   A^2 -> H(c, U1(k, c))
28.56/9.82	   A^2 -> H(c, U1(c, e))
28.56/9.82	   A^2 -> H(c, U1(c, k))
28.56/9.82	   A^2 -> H(c, U1(e, e))
28.56/9.82	   A^2 -> H(c, U1(k, k))
28.56/9.82	   A^2 -> H(c, U1(k, d))
28.56/9.82	   A^2 -> H(c, U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, c), b)
28.56/9.82	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.82	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.82	   A^2 -> H(U1(e, c), e)
28.56/9.82	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.82	   A^2 -> H(U1(k, c), b)
28.56/9.82	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(k, c), c)
28.56/9.82	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.82	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.82	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, e), b)
28.56/9.82	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.82	
28.56/9.82	The TRS R consists of the following rules:
28.56/9.82	
28.56/9.82	   f(x) -> U1(x, x)
28.56/9.82	   U1(e, x) -> x
28.56/9.82	   a -> c
28.56/9.82	   a -> d
28.56/9.82	   b -> c
28.56/9.82	   b -> d
28.56/9.82	   d -> k
28.56/9.82	   c -> e
28.56/9.82	   c -> k
28.56/9.82	
28.56/9.82	Q is empty.
28.56/9.82	We have to consider all minimal (P,Q,R)-chains.
28.56/9.82	----------------------------------------
28.56/9.82	
28.56/9.82	(1501) TransformationProof (EQUIVALENT)
28.56/9.82	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.82	
28.56/9.82	   (A^2 -> H(U1(e, e), U1(c, d)),A^2 -> H(U1(e, e), U1(c, d)))
28.56/9.82	   (A^2 -> H(U1(k, e), U1(c, d)),A^2 -> H(U1(k, e), U1(c, d)))
28.56/9.82	   (A^2 -> H(U1(c, e), U1(e, d)),A^2 -> H(U1(c, e), U1(e, d)))
28.56/9.82	   (A^2 -> H(U1(c, e), U1(k, d)),A^2 -> H(U1(c, e), U1(k, d)))
28.56/9.82	   (A^2 -> H(U1(c, e), U1(c, k)),A^2 -> H(U1(c, e), U1(c, k)))
28.56/9.82	
28.56/9.82	
28.56/9.82	----------------------------------------
28.56/9.82	
28.56/9.82	(1502)
28.56/9.82	Obligation:
28.56/9.82	Q DP problem:
28.56/9.82	The TRS P consists of the following rules:
28.56/9.82	
28.56/9.82	   H(x, x) -> G(x, x, f(k))
28.56/9.82	   G(d, x, x) -> A^2
28.56/9.82	   A^2 -> H(f(c), f(c))
28.56/9.82	   A^2 -> H(f(d), f(d))
28.56/9.82	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.82	   A^2 -> H(f(e), f(e))
28.56/9.82	   A^2 -> H(f(k), f(k))
28.56/9.82	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.82	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.82	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.82	   A^2 -> H(U1(c, c), b)
28.56/9.82	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(c, c), e)
28.56/9.82	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.82	   A^2 -> H(e, U1(c, b))
28.56/9.82	   A^2 -> H(e, U1(d, b))
28.56/9.82	   A^2 -> H(e, U1(b, c))
28.56/9.82	   A^2 -> H(e, U1(b, d))
28.56/9.82	   A^2 -> H(e, U1(c, c))
28.56/9.82	   A^2 -> H(e, f(e))
28.56/9.82	   A^2 -> H(e, f(k))
28.56/9.82	   A^2 -> H(e, U1(d, d))
28.56/9.82	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.82	   A^2 -> H(f(e), b)
28.56/9.82	   A^2 -> H(f(e), U1(e, d))
28.56/9.82	   A^2 -> H(f(e), U1(d, e))
28.56/9.82	   A^2 -> H(f(e), c)
28.56/9.82	   A^2 -> H(f(e), U1(e, k))
28.56/9.82	   A^2 -> H(f(e), U1(k, e))
28.56/9.82	   A^2 -> H(f(e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.82	   A^2 -> H(f(k), b)
28.56/9.82	   A^2 -> H(f(k), U1(e, d))
28.56/9.82	   A^2 -> H(f(k), U1(d, e))
28.56/9.82	   A^2 -> H(f(k), c)
28.56/9.82	   A^2 -> H(f(k), U1(e, k))
28.56/9.82	   A^2 -> H(f(k), U1(k, e))
28.56/9.82	   A^2 -> H(f(k), e)
28.56/9.82	   A^2 -> H(f(c), d)
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.82	   A^2 -> H(U1(k, k), f(e))
28.56/9.82	   A^2 -> H(U1(k, k), f(k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.82	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.82	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.82	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.82	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.82	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.82	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.82	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.82	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.82	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.82	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.82	   A^2 -> H(U1(d, d), b)
28.56/9.82	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.82	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.82	   A^2 -> H(U1(d, d), c)
28.56/9.82	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.82	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.82	   A^2 -> H(U1(d, d), e)
28.56/9.82	   A^2 -> H(f(d), d)
28.56/9.82	   A^2 -> H(f(d), k)
28.56/9.82	   A^2 -> H(U1(c, c), c)
28.56/9.82	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.82	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.82	   A^2 -> H(f(c), k)
28.56/9.82	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.82	   A^2 -> H(f(k), U1(k, k))
28.56/9.82	   A^2 -> H(f(e), e)
28.56/9.82	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.82	   A^2 -> H(d, U1(c, b))
28.56/9.82	   A^2 -> H(d, U1(d, b))
28.56/9.82	   A^2 -> H(d, U1(b, c))
28.56/9.82	   A^2 -> H(d, U1(b, d))
28.56/9.82	   A^2 -> H(d, U1(c, c))
28.56/9.82	   A^2 -> H(d, f(e))
28.56/9.82	   A^2 -> H(d, f(k))
28.56/9.82	   A^2 -> H(d, U1(d, d))
28.56/9.82	   A^2 -> H(a, U1(e, b))
28.56/9.82	   A^2 -> H(a, U1(k, b))
28.56/9.82	   A^2 -> H(a, U1(c, d))
28.56/9.82	   A^2 -> H(a, U1(d, c))
28.56/9.82	   A^2 -> H(a, U1(b, e))
28.56/9.82	   A^2 -> H(a, U1(b, k))
28.56/9.82	   A^2 -> H(a, U1(e, c))
28.56/9.82	   A^2 -> H(a, U1(k, c))
28.56/9.82	   A^2 -> H(a, U1(c, e))
28.56/9.82	   A^2 -> H(a, U1(c, k))
28.56/9.82	   A^2 -> H(a, U1(e, e))
28.56/9.82	   A^2 -> H(a, U1(k, k))
28.56/9.82	   A^2 -> H(a, U1(k, d))
28.56/9.82	   A^2 -> H(a, U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.82	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.82	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.82	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.82	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.82	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.82	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, a), b)
28.56/9.82	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.82	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.82	   A^2 -> H(U1(e, a), c)
28.56/9.82	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.82	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.82	   A^2 -> H(U1(e, a), e)
28.56/9.82	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, a), b)
28.56/9.82	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.82	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.82	   A^2 -> H(U1(k, a), c)
28.56/9.82	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.82	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.82	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, d), b)
28.56/9.82	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.82	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.82	   A^2 -> H(U1(c, d), c)
28.56/9.82	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.82	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.82	   A^2 -> H(U1(c, d), e)
28.56/9.82	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, a), d)
28.56/9.82	   A^2 -> H(U1(c, a), k)
28.56/9.82	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.82	   A^2 -> H(U1(d, c), b)
28.56/9.82	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(d, c), c)
28.56/9.82	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.82	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.82	   A^2 -> H(U1(d, c), e)
28.56/9.82	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.82	   A^2 -> H(U1(d, a), d)
28.56/9.82	   A^2 -> H(U1(d, a), k)
28.56/9.82	   A^2 -> H(U1(a, e), b)
28.56/9.82	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.82	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.82	   A^2 -> H(U1(a, e), c)
28.56/9.82	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.82	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.82	   A^2 -> H(U1(a, e), e)
28.56/9.82	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(a, k), b)
28.56/9.82	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.82	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.82	   A^2 -> H(U1(a, k), c)
28.56/9.82	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.82	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.82	   A^2 -> H(U1(a, k), e)
28.56/9.82	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(a, c), d)
28.56/9.82	   A^2 -> H(U1(a, c), k)
28.56/9.82	   A^2 -> H(U1(a, d), d)
28.56/9.82	   A^2 -> H(U1(a, d), k)
28.56/9.82	   A^2 -> H(k, U1(c, b))
28.56/9.82	   A^2 -> H(k, U1(d, b))
28.56/9.82	   A^2 -> H(k, U1(b, c))
28.56/9.82	   A^2 -> H(k, U1(b, d))
28.56/9.82	   A^2 -> H(k, U1(c, c))
28.56/9.82	   A^2 -> H(k, f(e))
28.56/9.82	   A^2 -> H(k, f(k))
28.56/9.82	   A^2 -> H(k, U1(d, d))
28.56/9.82	   A^2 -> H(c, U1(e, b))
28.56/9.82	   A^2 -> H(c, U1(k, b))
28.56/9.82	   A^2 -> H(c, U1(c, d))
28.56/9.82	   A^2 -> H(c, U1(d, c))
28.56/9.82	   A^2 -> H(c, U1(b, e))
28.56/9.82	   A^2 -> H(c, U1(b, k))
28.56/9.82	   A^2 -> H(c, U1(e, c))
28.56/9.82	   A^2 -> H(c, U1(k, c))
28.56/9.82	   A^2 -> H(c, U1(c, e))
28.56/9.82	   A^2 -> H(c, U1(c, k))
28.56/9.82	   A^2 -> H(c, U1(e, e))
28.56/9.82	   A^2 -> H(c, U1(k, k))
28.56/9.82	   A^2 -> H(c, U1(k, d))
28.56/9.82	   A^2 -> H(c, U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, c), b)
28.56/9.82	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.82	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.82	   A^2 -> H(U1(e, c), e)
28.56/9.82	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.82	   A^2 -> H(U1(k, c), b)
28.56/9.82	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(k, c), c)
28.56/9.82	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.82	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.82	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, e), b)
28.56/9.82	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.82	
28.56/9.82	The TRS R consists of the following rules:
28.56/9.82	
28.56/9.82	   f(x) -> U1(x, x)
28.56/9.82	   U1(e, x) -> x
28.56/9.82	   a -> c
28.56/9.82	   a -> d
28.56/9.82	   b -> c
28.56/9.82	   b -> d
28.56/9.82	   d -> k
28.56/9.82	   c -> e
28.56/9.82	   c -> k
28.56/9.82	
28.56/9.82	Q is empty.
28.56/9.82	We have to consider all minimal (P,Q,R)-chains.
28.56/9.82	----------------------------------------
28.56/9.82	
28.56/9.82	(1503) TransformationProof (EQUIVALENT)
28.56/9.82	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.82	
28.56/9.82	   (A^2 -> H(U1(e, e), U1(d, c)),A^2 -> H(U1(e, e), U1(d, c)))
28.56/9.82	   (A^2 -> H(U1(k, e), U1(d, c)),A^2 -> H(U1(k, e), U1(d, c)))
28.56/9.82	   (A^2 -> H(U1(c, e), U1(k, c)),A^2 -> H(U1(c, e), U1(k, c)))
28.56/9.82	   (A^2 -> H(U1(c, e), U1(d, e)),A^2 -> H(U1(c, e), U1(d, e)))
28.56/9.82	   (A^2 -> H(U1(c, e), U1(d, k)),A^2 -> H(U1(c, e), U1(d, k)))
28.56/9.82	
28.56/9.82	
28.56/9.82	----------------------------------------
28.56/9.82	
28.56/9.82	(1504)
28.56/9.82	Obligation:
28.56/9.82	Q DP problem:
28.56/9.82	The TRS P consists of the following rules:
28.56/9.82	
28.56/9.82	   H(x, x) -> G(x, x, f(k))
28.56/9.82	   G(d, x, x) -> A^2
28.56/9.82	   A^2 -> H(f(c), f(c))
28.56/9.82	   A^2 -> H(f(d), f(d))
28.56/9.82	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.82	   A^2 -> H(f(e), f(e))
28.56/9.82	   A^2 -> H(f(k), f(k))
28.56/9.82	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.82	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.82	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.82	   A^2 -> H(U1(c, c), b)
28.56/9.82	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(c, c), e)
28.56/9.82	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.82	   A^2 -> H(e, U1(c, b))
28.56/9.82	   A^2 -> H(e, U1(d, b))
28.56/9.82	   A^2 -> H(e, U1(b, c))
28.56/9.82	   A^2 -> H(e, U1(b, d))
28.56/9.82	   A^2 -> H(e, U1(c, c))
28.56/9.82	   A^2 -> H(e, f(e))
28.56/9.82	   A^2 -> H(e, f(k))
28.56/9.82	   A^2 -> H(e, U1(d, d))
28.56/9.82	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.82	   A^2 -> H(f(e), b)
28.56/9.82	   A^2 -> H(f(e), U1(e, d))
28.56/9.82	   A^2 -> H(f(e), U1(d, e))
28.56/9.82	   A^2 -> H(f(e), c)
28.56/9.82	   A^2 -> H(f(e), U1(e, k))
28.56/9.82	   A^2 -> H(f(e), U1(k, e))
28.56/9.82	   A^2 -> H(f(e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.82	   A^2 -> H(f(k), b)
28.56/9.82	   A^2 -> H(f(k), U1(e, d))
28.56/9.82	   A^2 -> H(f(k), U1(d, e))
28.56/9.82	   A^2 -> H(f(k), c)
28.56/9.82	   A^2 -> H(f(k), U1(e, k))
28.56/9.82	   A^2 -> H(f(k), U1(k, e))
28.56/9.82	   A^2 -> H(f(k), e)
28.56/9.82	   A^2 -> H(f(c), d)
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.82	   A^2 -> H(U1(k, k), f(e))
28.56/9.82	   A^2 -> H(U1(k, k), f(k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.82	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.82	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.82	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.82	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.82	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.82	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.82	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.82	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.82	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.82	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.82	   A^2 -> H(U1(d, d), b)
28.56/9.82	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.82	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.82	   A^2 -> H(U1(d, d), c)
28.56/9.82	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.82	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.82	   A^2 -> H(U1(d, d), e)
28.56/9.82	   A^2 -> H(f(d), d)
28.56/9.82	   A^2 -> H(f(d), k)
28.56/9.82	   A^2 -> H(U1(c, c), c)
28.56/9.82	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.82	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.82	   A^2 -> H(f(c), k)
28.56/9.82	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.82	   A^2 -> H(f(k), U1(k, k))
28.56/9.82	   A^2 -> H(f(e), e)
28.56/9.82	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.82	   A^2 -> H(d, U1(c, b))
28.56/9.82	   A^2 -> H(d, U1(d, b))
28.56/9.82	   A^2 -> H(d, U1(b, c))
28.56/9.82	   A^2 -> H(d, U1(b, d))
28.56/9.82	   A^2 -> H(d, U1(c, c))
28.56/9.82	   A^2 -> H(d, f(e))
28.56/9.82	   A^2 -> H(d, f(k))
28.56/9.82	   A^2 -> H(d, U1(d, d))
28.56/9.82	   A^2 -> H(a, U1(e, b))
28.56/9.82	   A^2 -> H(a, U1(k, b))
28.56/9.82	   A^2 -> H(a, U1(c, d))
28.56/9.82	   A^2 -> H(a, U1(d, c))
28.56/9.82	   A^2 -> H(a, U1(b, e))
28.56/9.82	   A^2 -> H(a, U1(b, k))
28.56/9.82	   A^2 -> H(a, U1(e, c))
28.56/9.82	   A^2 -> H(a, U1(k, c))
28.56/9.82	   A^2 -> H(a, U1(c, e))
28.56/9.82	   A^2 -> H(a, U1(c, k))
28.56/9.82	   A^2 -> H(a, U1(e, e))
28.56/9.82	   A^2 -> H(a, U1(k, k))
28.56/9.82	   A^2 -> H(a, U1(k, d))
28.56/9.82	   A^2 -> H(a, U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.82	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.82	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.82	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.82	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.82	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.82	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.82	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, a), b)
28.56/9.82	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.82	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.82	   A^2 -> H(U1(e, a), c)
28.56/9.82	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.82	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.82	   A^2 -> H(U1(e, a), e)
28.56/9.82	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, a), b)
28.56/9.82	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.82	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.82	   A^2 -> H(U1(k, a), c)
28.56/9.82	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.82	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.82	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, d), b)
28.56/9.82	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.82	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.82	   A^2 -> H(U1(c, d), c)
28.56/9.82	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.82	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.82	   A^2 -> H(U1(c, d), e)
28.56/9.82	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, a), d)
28.56/9.82	   A^2 -> H(U1(c, a), k)
28.56/9.82	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.82	   A^2 -> H(U1(d, c), b)
28.56/9.82	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(d, c), c)
28.56/9.82	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.82	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.82	   A^2 -> H(U1(d, c), e)
28.56/9.82	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.82	   A^2 -> H(U1(d, a), d)
28.56/9.82	   A^2 -> H(U1(d, a), k)
28.56/9.82	   A^2 -> H(U1(a, e), b)
28.56/9.82	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.82	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.82	   A^2 -> H(U1(a, e), c)
28.56/9.82	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.82	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.82	   A^2 -> H(U1(a, e), e)
28.56/9.82	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(a, k), b)
28.56/9.82	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.82	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.82	   A^2 -> H(U1(a, k), c)
28.56/9.82	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.82	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.82	   A^2 -> H(U1(a, k), e)
28.56/9.82	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(a, c), d)
28.56/9.82	   A^2 -> H(U1(a, c), k)
28.56/9.82	   A^2 -> H(U1(a, d), d)
28.56/9.82	   A^2 -> H(U1(a, d), k)
28.56/9.82	   A^2 -> H(k, U1(c, b))
28.56/9.82	   A^2 -> H(k, U1(d, b))
28.56/9.82	   A^2 -> H(k, U1(b, c))
28.56/9.82	   A^2 -> H(k, U1(b, d))
28.56/9.82	   A^2 -> H(k, U1(c, c))
28.56/9.82	   A^2 -> H(k, f(e))
28.56/9.82	   A^2 -> H(k, f(k))
28.56/9.82	   A^2 -> H(k, U1(d, d))
28.56/9.82	   A^2 -> H(c, U1(e, b))
28.56/9.82	   A^2 -> H(c, U1(k, b))
28.56/9.82	   A^2 -> H(c, U1(c, d))
28.56/9.82	   A^2 -> H(c, U1(d, c))
28.56/9.82	   A^2 -> H(c, U1(b, e))
28.56/9.82	   A^2 -> H(c, U1(b, k))
28.56/9.82	   A^2 -> H(c, U1(e, c))
28.56/9.82	   A^2 -> H(c, U1(k, c))
28.56/9.82	   A^2 -> H(c, U1(c, e))
28.56/9.82	   A^2 -> H(c, U1(c, k))
28.56/9.82	   A^2 -> H(c, U1(e, e))
28.56/9.82	   A^2 -> H(c, U1(k, k))
28.56/9.82	   A^2 -> H(c, U1(k, d))
28.56/9.82	   A^2 -> H(c, U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.82	   A^2 -> H(U1(e, c), b)
28.56/9.82	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.82	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.82	   A^2 -> H(U1(e, c), e)
28.56/9.82	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.82	   A^2 -> H(U1(k, c), b)
28.56/9.82	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(k, c), c)
28.56/9.82	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.82	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.82	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, e), b)
28.56/9.82	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.82	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.82	
28.56/9.82	The TRS R consists of the following rules:
28.56/9.82	
28.56/9.82	   f(x) -> U1(x, x)
28.56/9.82	   U1(e, x) -> x
28.56/9.82	   a -> c
28.56/9.82	   a -> d
28.56/9.82	   b -> c
28.56/9.82	   b -> d
28.56/9.82	   d -> k
28.56/9.82	   c -> e
28.56/9.82	   c -> k
28.56/9.82	
28.56/9.82	Q is empty.
28.56/9.82	We have to consider all minimal (P,Q,R)-chains.
28.56/9.82	----------------------------------------
28.56/9.82	
28.56/9.82	(1505) TransformationProof (EQUIVALENT)
28.56/9.82	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.82	
28.56/9.82	   (A^2 -> H(U1(e, e), U1(b, e)),A^2 -> H(U1(e, e), U1(b, e)))
28.56/9.82	   (A^2 -> H(U1(k, e), U1(b, e)),A^2 -> H(U1(k, e), U1(b, e)))
28.56/9.82	   (A^2 -> H(U1(c, e), U1(c, e)),A^2 -> H(U1(c, e), U1(c, e)))
28.56/9.82	   (A^2 -> H(U1(c, e), U1(d, e)),A^2 -> H(U1(c, e), U1(d, e)))
28.56/9.82	
28.56/9.82	
28.56/9.82	----------------------------------------
28.56/9.82	
28.56/9.82	(1506)
28.56/9.82	Obligation:
28.56/9.82	Q DP problem:
28.56/9.82	The TRS P consists of the following rules:
28.56/9.82	
28.56/9.82	   H(x, x) -> G(x, x, f(k))
28.56/9.82	   G(d, x, x) -> A^2
28.56/9.82	   A^2 -> H(f(c), f(c))
28.56/9.82	   A^2 -> H(f(d), f(d))
28.56/9.82	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.82	   A^2 -> H(f(e), f(e))
28.56/9.82	   A^2 -> H(f(k), f(k))
28.56/9.82	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.82	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.82	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.82	   A^2 -> H(U1(c, c), b)
28.56/9.82	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.82	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.82	   A^2 -> H(U1(c, c), e)
28.56/9.82	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.82	   A^2 -> H(e, U1(c, b))
28.56/9.82	   A^2 -> H(e, U1(d, b))
28.56/9.82	   A^2 -> H(e, U1(b, c))
28.56/9.82	   A^2 -> H(e, U1(b, d))
28.56/9.82	   A^2 -> H(e, U1(c, c))
28.56/9.82	   A^2 -> H(e, f(e))
28.56/9.82	   A^2 -> H(e, f(k))
28.56/9.82	   A^2 -> H(e, U1(d, d))
28.56/9.82	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.82	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.82	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.82	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.82	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.82	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.82	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.82	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.82	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.82	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.82	   A^2 -> H(f(e), b)
28.56/9.82	   A^2 -> H(f(e), U1(e, d))
28.56/9.82	   A^2 -> H(f(e), U1(d, e))
28.56/9.82	   A^2 -> H(f(e), c)
28.56/9.82	   A^2 -> H(f(e), U1(e, k))
28.56/9.82	   A^2 -> H(f(e), U1(k, e))
28.56/9.82	   A^2 -> H(f(e), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.82	   A^2 -> H(f(k), b)
28.56/9.82	   A^2 -> H(f(k), U1(e, d))
28.56/9.82	   A^2 -> H(f(k), U1(d, e))
28.56/9.82	   A^2 -> H(f(k), c)
28.56/9.82	   A^2 -> H(f(k), U1(e, k))
28.56/9.82	   A^2 -> H(f(k), U1(k, e))
28.56/9.82	   A^2 -> H(f(k), e)
28.56/9.82	   A^2 -> H(f(c), d)
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.82	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.82	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.82	   A^2 -> H(U1(k, k), f(e))
28.56/9.82	   A^2 -> H(U1(k, k), f(k))
28.56/9.82	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.82	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, d), b)
28.56/9.83	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.83	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.83	   A^2 -> H(U1(d, d), c)
28.56/9.83	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.83	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.83	   A^2 -> H(U1(d, d), e)
28.56/9.83	   A^2 -> H(f(d), d)
28.56/9.83	   A^2 -> H(f(d), k)
28.56/9.83	   A^2 -> H(U1(c, c), c)
28.56/9.83	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.83	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.83	   A^2 -> H(f(c), k)
28.56/9.83	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.83	   A^2 -> H(f(k), U1(k, k))
28.56/9.83	   A^2 -> H(f(e), e)
28.56/9.83	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.83	   A^2 -> H(d, U1(c, b))
28.56/9.83	   A^2 -> H(d, U1(d, b))
28.56/9.83	   A^2 -> H(d, U1(b, c))
28.56/9.83	   A^2 -> H(d, U1(b, d))
28.56/9.83	   A^2 -> H(d, U1(c, c))
28.56/9.83	   A^2 -> H(d, f(e))
28.56/9.83	   A^2 -> H(d, f(k))
28.56/9.83	   A^2 -> H(d, U1(d, d))
28.56/9.83	   A^2 -> H(a, U1(e, b))
28.56/9.83	   A^2 -> H(a, U1(k, b))
28.56/9.83	   A^2 -> H(a, U1(c, d))
28.56/9.83	   A^2 -> H(a, U1(d, c))
28.56/9.83	   A^2 -> H(a, U1(b, e))
28.56/9.83	   A^2 -> H(a, U1(b, k))
28.56/9.83	   A^2 -> H(a, U1(e, c))
28.56/9.83	   A^2 -> H(a, U1(k, c))
28.56/9.83	   A^2 -> H(a, U1(c, e))
28.56/9.83	   A^2 -> H(a, U1(c, k))
28.56/9.83	   A^2 -> H(a, U1(e, e))
28.56/9.83	   A^2 -> H(a, U1(k, k))
28.56/9.83	   A^2 -> H(a, U1(k, d))
28.56/9.83	   A^2 -> H(a, U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.83	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.83	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.83	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.83	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.83	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, a), b)
28.56/9.83	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.83	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.83	   A^2 -> H(U1(e, a), c)
28.56/9.83	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.83	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.83	   A^2 -> H(U1(e, a), e)
28.56/9.83	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, a), b)
28.56/9.83	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.83	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.83	   A^2 -> H(U1(k, a), c)
28.56/9.83	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.83	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.83	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, d), b)
28.56/9.83	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.83	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.83	   A^2 -> H(U1(c, d), c)
28.56/9.83	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.83	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.83	   A^2 -> H(U1(c, d), e)
28.56/9.83	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, a), d)
28.56/9.83	   A^2 -> H(U1(c, a), k)
28.56/9.83	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.83	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.83	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.83	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.83	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, c), b)
28.56/9.83	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(d, c), c)
28.56/9.83	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.83	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.83	   A^2 -> H(U1(d, c), e)
28.56/9.83	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.83	   A^2 -> H(U1(d, a), d)
28.56/9.83	   A^2 -> H(U1(d, a), k)
28.56/9.83	   A^2 -> H(U1(a, e), b)
28.56/9.83	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.83	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.83	   A^2 -> H(U1(a, e), c)
28.56/9.83	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.83	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.83	   A^2 -> H(U1(a, e), e)
28.56/9.83	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(a, k), b)
28.56/9.83	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.83	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.83	   A^2 -> H(U1(a, k), c)
28.56/9.83	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.83	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.83	   A^2 -> H(U1(a, k), e)
28.56/9.83	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(a, c), d)
28.56/9.83	   A^2 -> H(U1(a, c), k)
28.56/9.83	   A^2 -> H(U1(a, d), d)
28.56/9.83	   A^2 -> H(U1(a, d), k)
28.56/9.83	   A^2 -> H(k, U1(c, b))
28.56/9.83	   A^2 -> H(k, U1(d, b))
28.56/9.83	   A^2 -> H(k, U1(b, c))
28.56/9.83	   A^2 -> H(k, U1(b, d))
28.56/9.83	   A^2 -> H(k, U1(c, c))
28.56/9.83	   A^2 -> H(k, f(e))
28.56/9.83	   A^2 -> H(k, f(k))
28.56/9.83	   A^2 -> H(k, U1(d, d))
28.56/9.83	   A^2 -> H(c, U1(e, b))
28.56/9.83	   A^2 -> H(c, U1(k, b))
28.56/9.83	   A^2 -> H(c, U1(c, d))
28.56/9.83	   A^2 -> H(c, U1(d, c))
28.56/9.83	   A^2 -> H(c, U1(b, e))
28.56/9.83	   A^2 -> H(c, U1(b, k))
28.56/9.83	   A^2 -> H(c, U1(e, c))
28.56/9.83	   A^2 -> H(c, U1(k, c))
28.56/9.83	   A^2 -> H(c, U1(c, e))
28.56/9.83	   A^2 -> H(c, U1(c, k))
28.56/9.83	   A^2 -> H(c, U1(e, e))
28.56/9.83	   A^2 -> H(c, U1(k, k))
28.56/9.83	   A^2 -> H(c, U1(k, d))
28.56/9.83	   A^2 -> H(c, U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, c), b)
28.56/9.83	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.83	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.83	   A^2 -> H(U1(e, c), e)
28.56/9.83	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.83	   A^2 -> H(U1(k, c), b)
28.56/9.83	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(k, c), c)
28.56/9.83	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.83	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.83	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, e), b)
28.56/9.83	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.83	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.83	
28.56/9.83	The TRS R consists of the following rules:
28.56/9.83	
28.56/9.83	   f(x) -> U1(x, x)
28.56/9.83	   U1(e, x) -> x
28.56/9.83	   a -> c
28.56/9.83	   a -> d
28.56/9.83	   b -> c
28.56/9.83	   b -> d
28.56/9.83	   d -> k
28.56/9.83	   c -> e
28.56/9.83	   c -> k
28.56/9.83	
28.56/9.83	Q is empty.
28.56/9.83	We have to consider all minimal (P,Q,R)-chains.
28.56/9.83	----------------------------------------
28.56/9.83	
28.56/9.83	(1507) TransformationProof (EQUIVALENT)
28.56/9.83	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.83	
28.56/9.83	   (A^2 -> H(U1(e, e), U1(b, k)),A^2 -> H(U1(e, e), U1(b, k)))
28.56/9.83	   (A^2 -> H(U1(k, e), U1(b, k)),A^2 -> H(U1(k, e), U1(b, k)))
28.56/9.83	   (A^2 -> H(U1(c, e), U1(c, k)),A^2 -> H(U1(c, e), U1(c, k)))
28.56/9.83	   (A^2 -> H(U1(c, e), U1(d, k)),A^2 -> H(U1(c, e), U1(d, k)))
28.56/9.83	
28.56/9.83	
28.56/9.83	----------------------------------------
28.56/9.83	
28.56/9.83	(1508)
28.56/9.83	Obligation:
28.56/9.83	Q DP problem:
28.56/9.83	The TRS P consists of the following rules:
28.56/9.83	
28.56/9.83	   H(x, x) -> G(x, x, f(k))
28.56/9.83	   G(d, x, x) -> A^2
28.56/9.83	   A^2 -> H(f(c), f(c))
28.56/9.83	   A^2 -> H(f(d), f(d))
28.56/9.83	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.83	   A^2 -> H(f(e), f(e))
28.56/9.83	   A^2 -> H(f(k), f(k))
28.56/9.83	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.83	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.83	   A^2 -> H(U1(c, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.83	   A^2 -> H(U1(c, c), b)
28.56/9.83	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(c, c), e)
28.56/9.83	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.83	   A^2 -> H(e, U1(c, b))
28.56/9.83	   A^2 -> H(e, U1(d, b))
28.56/9.83	   A^2 -> H(e, U1(b, c))
28.56/9.83	   A^2 -> H(e, U1(b, d))
28.56/9.83	   A^2 -> H(e, U1(c, c))
28.56/9.83	   A^2 -> H(e, f(e))
28.56/9.83	   A^2 -> H(e, f(k))
28.56/9.83	   A^2 -> H(e, U1(d, d))
28.56/9.83	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.83	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.83	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.83	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.83	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.83	   A^2 -> H(f(e), b)
28.56/9.83	   A^2 -> H(f(e), U1(e, d))
28.56/9.83	   A^2 -> H(f(e), U1(d, e))
28.56/9.83	   A^2 -> H(f(e), c)
28.56/9.83	   A^2 -> H(f(e), U1(e, k))
28.56/9.83	   A^2 -> H(f(e), U1(k, e))
28.56/9.83	   A^2 -> H(f(e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.83	   A^2 -> H(f(k), b)
28.56/9.83	   A^2 -> H(f(k), U1(e, d))
28.56/9.83	   A^2 -> H(f(k), U1(d, e))
28.56/9.83	   A^2 -> H(f(k), c)
28.56/9.83	   A^2 -> H(f(k), U1(e, k))
28.56/9.83	   A^2 -> H(f(k), U1(k, e))
28.56/9.83	   A^2 -> H(f(k), e)
28.56/9.83	   A^2 -> H(f(c), d)
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.83	   A^2 -> H(U1(k, k), f(e))
28.56/9.83	   A^2 -> H(U1(k, k), f(k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, d), b)
28.56/9.83	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.83	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.83	   A^2 -> H(U1(d, d), c)
28.56/9.83	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.83	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.83	   A^2 -> H(U1(d, d), e)
28.56/9.83	   A^2 -> H(f(d), d)
28.56/9.83	   A^2 -> H(f(d), k)
28.56/9.83	   A^2 -> H(U1(c, c), c)
28.56/9.83	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.83	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.83	   A^2 -> H(f(c), k)
28.56/9.83	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.83	   A^2 -> H(f(k), U1(k, k))
28.56/9.83	   A^2 -> H(f(e), e)
28.56/9.83	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.83	   A^2 -> H(d, U1(c, b))
28.56/9.83	   A^2 -> H(d, U1(d, b))
28.56/9.83	   A^2 -> H(d, U1(b, c))
28.56/9.83	   A^2 -> H(d, U1(b, d))
28.56/9.83	   A^2 -> H(d, U1(c, c))
28.56/9.83	   A^2 -> H(d, f(e))
28.56/9.83	   A^2 -> H(d, f(k))
28.56/9.83	   A^2 -> H(d, U1(d, d))
28.56/9.83	   A^2 -> H(a, U1(e, b))
28.56/9.83	   A^2 -> H(a, U1(k, b))
28.56/9.83	   A^2 -> H(a, U1(c, d))
28.56/9.83	   A^2 -> H(a, U1(d, c))
28.56/9.83	   A^2 -> H(a, U1(b, e))
28.56/9.83	   A^2 -> H(a, U1(b, k))
28.56/9.83	   A^2 -> H(a, U1(e, c))
28.56/9.83	   A^2 -> H(a, U1(k, c))
28.56/9.83	   A^2 -> H(a, U1(c, e))
28.56/9.83	   A^2 -> H(a, U1(c, k))
28.56/9.83	   A^2 -> H(a, U1(e, e))
28.56/9.83	   A^2 -> H(a, U1(k, k))
28.56/9.83	   A^2 -> H(a, U1(k, d))
28.56/9.83	   A^2 -> H(a, U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.83	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.83	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.83	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.83	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.83	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, a), b)
28.56/9.83	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.83	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.83	   A^2 -> H(U1(e, a), c)
28.56/9.83	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.83	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.83	   A^2 -> H(U1(e, a), e)
28.56/9.83	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, a), b)
28.56/9.83	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.83	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.83	   A^2 -> H(U1(k, a), c)
28.56/9.83	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.83	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.83	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, d), b)
28.56/9.83	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.83	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.83	   A^2 -> H(U1(c, d), c)
28.56/9.83	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.83	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.83	   A^2 -> H(U1(c, d), e)
28.56/9.83	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, a), d)
28.56/9.83	   A^2 -> H(U1(c, a), k)
28.56/9.83	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.83	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.83	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.83	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.83	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, c), b)
28.56/9.83	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(d, c), c)
28.56/9.83	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.83	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.83	   A^2 -> H(U1(d, c), e)
28.56/9.83	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.83	   A^2 -> H(U1(d, a), d)
28.56/9.83	   A^2 -> H(U1(d, a), k)
28.56/9.83	   A^2 -> H(U1(a, e), b)
28.56/9.83	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.83	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.83	   A^2 -> H(U1(a, e), c)
28.56/9.83	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.83	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.83	   A^2 -> H(U1(a, e), e)
28.56/9.83	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(a, k), b)
28.56/9.83	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.83	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.83	   A^2 -> H(U1(a, k), c)
28.56/9.83	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.83	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.83	   A^2 -> H(U1(a, k), e)
28.56/9.83	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(a, c), d)
28.56/9.83	   A^2 -> H(U1(a, c), k)
28.56/9.83	   A^2 -> H(U1(a, d), d)
28.56/9.83	   A^2 -> H(U1(a, d), k)
28.56/9.83	   A^2 -> H(k, U1(c, b))
28.56/9.83	   A^2 -> H(k, U1(d, b))
28.56/9.83	   A^2 -> H(k, U1(b, c))
28.56/9.83	   A^2 -> H(k, U1(b, d))
28.56/9.83	   A^2 -> H(k, U1(c, c))
28.56/9.83	   A^2 -> H(k, f(e))
28.56/9.83	   A^2 -> H(k, f(k))
28.56/9.83	   A^2 -> H(k, U1(d, d))
28.56/9.83	   A^2 -> H(c, U1(e, b))
28.56/9.83	   A^2 -> H(c, U1(k, b))
28.56/9.83	   A^2 -> H(c, U1(c, d))
28.56/9.83	   A^2 -> H(c, U1(d, c))
28.56/9.83	   A^2 -> H(c, U1(b, e))
28.56/9.83	   A^2 -> H(c, U1(b, k))
28.56/9.83	   A^2 -> H(c, U1(e, c))
28.56/9.83	   A^2 -> H(c, U1(k, c))
28.56/9.83	   A^2 -> H(c, U1(c, e))
28.56/9.83	   A^2 -> H(c, U1(c, k))
28.56/9.83	   A^2 -> H(c, U1(e, e))
28.56/9.83	   A^2 -> H(c, U1(k, k))
28.56/9.83	   A^2 -> H(c, U1(k, d))
28.56/9.83	   A^2 -> H(c, U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, c), b)
28.56/9.83	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.83	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.83	   A^2 -> H(U1(e, c), e)
28.56/9.83	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.83	   A^2 -> H(U1(k, c), b)
28.56/9.83	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(k, c), c)
28.56/9.83	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.83	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.83	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, e), b)
28.56/9.83	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.83	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.83	
28.56/9.83	The TRS R consists of the following rules:
28.56/9.83	
28.56/9.83	   f(x) -> U1(x, x)
28.56/9.83	   U1(e, x) -> x
28.56/9.83	   a -> c
28.56/9.83	   a -> d
28.56/9.83	   b -> c
28.56/9.83	   b -> d
28.56/9.83	   d -> k
28.56/9.83	   c -> e
28.56/9.83	   c -> k
28.56/9.83	
28.56/9.83	Q is empty.
28.56/9.83	We have to consider all minimal (P,Q,R)-chains.
28.56/9.83	----------------------------------------
28.56/9.83	
28.56/9.83	(1509) TransformationProof (EQUIVALENT)
28.56/9.83	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.83	
28.56/9.83	   (A^2 -> H(U1(e, e), U1(e, c)),A^2 -> H(U1(e, e), U1(e, c)))
28.56/9.83	   (A^2 -> H(U1(k, e), U1(e, c)),A^2 -> H(U1(k, e), U1(e, c)))
28.56/9.83	   (A^2 -> H(U1(c, e), c),A^2 -> H(U1(c, e), c))
28.56/9.83	   (A^2 -> H(U1(c, e), U1(e, e)),A^2 -> H(U1(c, e), U1(e, e)))
28.56/9.83	   (A^2 -> H(U1(c, e), U1(e, k)),A^2 -> H(U1(c, e), U1(e, k)))
28.56/9.83	
28.56/9.83	
28.56/9.83	----------------------------------------
28.56/9.83	
28.56/9.83	(1510)
28.56/9.83	Obligation:
28.56/9.83	Q DP problem:
28.56/9.83	The TRS P consists of the following rules:
28.56/9.83	
28.56/9.83	   H(x, x) -> G(x, x, f(k))
28.56/9.83	   G(d, x, x) -> A^2
28.56/9.83	   A^2 -> H(f(c), f(c))
28.56/9.83	   A^2 -> H(f(d), f(d))
28.56/9.83	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.83	   A^2 -> H(f(e), f(e))
28.56/9.83	   A^2 -> H(f(k), f(k))
28.56/9.83	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.83	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.83	   A^2 -> H(U1(c, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.83	   A^2 -> H(U1(c, c), b)
28.56/9.83	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(c, c), e)
28.56/9.83	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.83	   A^2 -> H(e, U1(c, b))
28.56/9.83	   A^2 -> H(e, U1(d, b))
28.56/9.83	   A^2 -> H(e, U1(b, c))
28.56/9.83	   A^2 -> H(e, U1(b, d))
28.56/9.83	   A^2 -> H(e, U1(c, c))
28.56/9.83	   A^2 -> H(e, f(e))
28.56/9.83	   A^2 -> H(e, f(k))
28.56/9.83	   A^2 -> H(e, U1(d, d))
28.56/9.83	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.83	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.83	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.83	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.83	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.83	   A^2 -> H(f(e), b)
28.56/9.83	   A^2 -> H(f(e), U1(e, d))
28.56/9.83	   A^2 -> H(f(e), U1(d, e))
28.56/9.83	   A^2 -> H(f(e), c)
28.56/9.83	   A^2 -> H(f(e), U1(e, k))
28.56/9.83	   A^2 -> H(f(e), U1(k, e))
28.56/9.83	   A^2 -> H(f(e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.83	   A^2 -> H(f(k), b)
28.56/9.83	   A^2 -> H(f(k), U1(e, d))
28.56/9.83	   A^2 -> H(f(k), U1(d, e))
28.56/9.83	   A^2 -> H(f(k), c)
28.56/9.83	   A^2 -> H(f(k), U1(e, k))
28.56/9.83	   A^2 -> H(f(k), U1(k, e))
28.56/9.83	   A^2 -> H(f(k), e)
28.56/9.83	   A^2 -> H(f(c), d)
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.83	   A^2 -> H(U1(k, k), f(e))
28.56/9.83	   A^2 -> H(U1(k, k), f(k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, d), b)
28.56/9.83	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.83	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.83	   A^2 -> H(U1(d, d), c)
28.56/9.83	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.83	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.83	   A^2 -> H(U1(d, d), e)
28.56/9.83	   A^2 -> H(f(d), d)
28.56/9.83	   A^2 -> H(f(d), k)
28.56/9.83	   A^2 -> H(U1(c, c), c)
28.56/9.83	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.83	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.83	   A^2 -> H(f(c), k)
28.56/9.83	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.83	   A^2 -> H(f(k), U1(k, k))
28.56/9.83	   A^2 -> H(f(e), e)
28.56/9.83	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.83	   A^2 -> H(d, U1(c, b))
28.56/9.83	   A^2 -> H(d, U1(d, b))
28.56/9.83	   A^2 -> H(d, U1(b, c))
28.56/9.83	   A^2 -> H(d, U1(b, d))
28.56/9.83	   A^2 -> H(d, U1(c, c))
28.56/9.83	   A^2 -> H(d, f(e))
28.56/9.83	   A^2 -> H(d, f(k))
28.56/9.83	   A^2 -> H(d, U1(d, d))
28.56/9.83	   A^2 -> H(a, U1(e, b))
28.56/9.83	   A^2 -> H(a, U1(k, b))
28.56/9.83	   A^2 -> H(a, U1(c, d))
28.56/9.83	   A^2 -> H(a, U1(d, c))
28.56/9.83	   A^2 -> H(a, U1(b, e))
28.56/9.83	   A^2 -> H(a, U1(b, k))
28.56/9.83	   A^2 -> H(a, U1(e, c))
28.56/9.83	   A^2 -> H(a, U1(k, c))
28.56/9.83	   A^2 -> H(a, U1(c, e))
28.56/9.83	   A^2 -> H(a, U1(c, k))
28.56/9.83	   A^2 -> H(a, U1(e, e))
28.56/9.83	   A^2 -> H(a, U1(k, k))
28.56/9.83	   A^2 -> H(a, U1(k, d))
28.56/9.83	   A^2 -> H(a, U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.83	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.83	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.83	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.83	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.83	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, a), b)
28.56/9.83	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.83	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.83	   A^2 -> H(U1(e, a), c)
28.56/9.83	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.83	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.83	   A^2 -> H(U1(e, a), e)
28.56/9.83	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, a), b)
28.56/9.83	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.83	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.83	   A^2 -> H(U1(k, a), c)
28.56/9.83	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.83	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.83	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, d), b)
28.56/9.83	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.83	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.83	   A^2 -> H(U1(c, d), c)
28.56/9.83	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.83	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.83	   A^2 -> H(U1(c, d), e)
28.56/9.83	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, a), d)
28.56/9.83	   A^2 -> H(U1(c, a), k)
28.56/9.83	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.83	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.83	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.83	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.83	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, c), b)
28.56/9.83	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(d, c), c)
28.56/9.83	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.83	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.83	   A^2 -> H(U1(d, c), e)
28.56/9.83	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.83	   A^2 -> H(U1(d, a), d)
28.56/9.83	   A^2 -> H(U1(d, a), k)
28.56/9.83	   A^2 -> H(U1(a, e), b)
28.56/9.83	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.83	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.83	   A^2 -> H(U1(a, e), c)
28.56/9.83	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.83	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.83	   A^2 -> H(U1(a, e), e)
28.56/9.83	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(a, k), b)
28.56/9.83	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.83	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.83	   A^2 -> H(U1(a, k), c)
28.56/9.83	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.83	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.83	   A^2 -> H(U1(a, k), e)
28.56/9.83	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(a, c), d)
28.56/9.83	   A^2 -> H(U1(a, c), k)
28.56/9.83	   A^2 -> H(U1(a, d), d)
28.56/9.83	   A^2 -> H(U1(a, d), k)
28.56/9.83	   A^2 -> H(k, U1(c, b))
28.56/9.83	   A^2 -> H(k, U1(d, b))
28.56/9.83	   A^2 -> H(k, U1(b, c))
28.56/9.83	   A^2 -> H(k, U1(b, d))
28.56/9.83	   A^2 -> H(k, U1(c, c))
28.56/9.83	   A^2 -> H(k, f(e))
28.56/9.83	   A^2 -> H(k, f(k))
28.56/9.83	   A^2 -> H(k, U1(d, d))
28.56/9.83	   A^2 -> H(c, U1(e, b))
28.56/9.83	   A^2 -> H(c, U1(k, b))
28.56/9.83	   A^2 -> H(c, U1(c, d))
28.56/9.83	   A^2 -> H(c, U1(d, c))
28.56/9.83	   A^2 -> H(c, U1(b, e))
28.56/9.83	   A^2 -> H(c, U1(b, k))
28.56/9.83	   A^2 -> H(c, U1(e, c))
28.56/9.83	   A^2 -> H(c, U1(k, c))
28.56/9.83	   A^2 -> H(c, U1(c, e))
28.56/9.83	   A^2 -> H(c, U1(c, k))
28.56/9.83	   A^2 -> H(c, U1(e, e))
28.56/9.83	   A^2 -> H(c, U1(k, k))
28.56/9.83	   A^2 -> H(c, U1(k, d))
28.56/9.83	   A^2 -> H(c, U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, c), b)
28.56/9.83	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.83	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.83	   A^2 -> H(U1(e, c), e)
28.56/9.83	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.83	   A^2 -> H(U1(k, c), b)
28.56/9.83	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(k, c), c)
28.56/9.83	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.83	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.83	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, e), b)
28.56/9.83	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.83	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.83	   A^2 -> H(U1(c, e), c)
28.56/9.83	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.83	
28.56/9.83	The TRS R consists of the following rules:
28.56/9.83	
28.56/9.83	   f(x) -> U1(x, x)
28.56/9.83	   U1(e, x) -> x
28.56/9.83	   a -> c
28.56/9.83	   a -> d
28.56/9.83	   b -> c
28.56/9.83	   b -> d
28.56/9.83	   d -> k
28.56/9.83	   c -> e
28.56/9.83	   c -> k
28.56/9.83	
28.56/9.83	Q is empty.
28.56/9.83	We have to consider all minimal (P,Q,R)-chains.
28.56/9.83	----------------------------------------
28.56/9.83	
28.56/9.83	(1511) TransformationProof (EQUIVALENT)
28.56/9.83	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.83	
28.56/9.83	   (A^2 -> H(U1(e, e), U1(k, c)),A^2 -> H(U1(e, e), U1(k, c)))
28.56/9.83	   (A^2 -> H(U1(k, e), U1(k, c)),A^2 -> H(U1(k, e), U1(k, c)))
28.56/9.83	   (A^2 -> H(U1(c, e), U1(k, e)),A^2 -> H(U1(c, e), U1(k, e)))
28.56/9.83	   (A^2 -> H(U1(c, e), U1(k, k)),A^2 -> H(U1(c, e), U1(k, k)))
28.56/9.83	
28.56/9.83	
28.56/9.83	----------------------------------------
28.56/9.83	
28.56/9.83	(1512)
28.56/9.83	Obligation:
28.56/9.83	Q DP problem:
28.56/9.83	The TRS P consists of the following rules:
28.56/9.83	
28.56/9.83	   H(x, x) -> G(x, x, f(k))
28.56/9.83	   G(d, x, x) -> A^2
28.56/9.83	   A^2 -> H(f(c), f(c))
28.56/9.83	   A^2 -> H(f(d), f(d))
28.56/9.83	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.83	   A^2 -> H(f(e), f(e))
28.56/9.83	   A^2 -> H(f(k), f(k))
28.56/9.83	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.83	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.83	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(c, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.83	   A^2 -> H(U1(c, c), b)
28.56/9.83	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(c, c), e)
28.56/9.83	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.83	   A^2 -> H(e, U1(c, b))
28.56/9.83	   A^2 -> H(e, U1(d, b))
28.56/9.83	   A^2 -> H(e, U1(b, c))
28.56/9.83	   A^2 -> H(e, U1(b, d))
28.56/9.83	   A^2 -> H(e, U1(c, c))
28.56/9.83	   A^2 -> H(e, f(e))
28.56/9.83	   A^2 -> H(e, f(k))
28.56/9.83	   A^2 -> H(e, U1(d, d))
28.56/9.83	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.83	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.83	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.83	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.83	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.83	   A^2 -> H(f(e), b)
28.56/9.83	   A^2 -> H(f(e), U1(e, d))
28.56/9.83	   A^2 -> H(f(e), U1(d, e))
28.56/9.83	   A^2 -> H(f(e), c)
28.56/9.83	   A^2 -> H(f(e), U1(e, k))
28.56/9.83	   A^2 -> H(f(e), U1(k, e))
28.56/9.83	   A^2 -> H(f(e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.83	   A^2 -> H(f(k), b)
28.56/9.83	   A^2 -> H(f(k), U1(e, d))
28.56/9.83	   A^2 -> H(f(k), U1(d, e))
28.56/9.83	   A^2 -> H(f(k), c)
28.56/9.83	   A^2 -> H(f(k), U1(e, k))
28.56/9.83	   A^2 -> H(f(k), U1(k, e))
28.56/9.83	   A^2 -> H(f(k), e)
28.56/9.83	   A^2 -> H(f(c), d)
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.83	   A^2 -> H(U1(k, k), f(e))
28.56/9.83	   A^2 -> H(U1(k, k), f(k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, d), b)
28.56/9.83	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.83	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.83	   A^2 -> H(U1(d, d), c)
28.56/9.83	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.83	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.83	   A^2 -> H(U1(d, d), e)
28.56/9.83	   A^2 -> H(f(d), d)
28.56/9.83	   A^2 -> H(f(d), k)
28.56/9.83	   A^2 -> H(U1(c, c), c)
28.56/9.83	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.83	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.83	   A^2 -> H(f(c), k)
28.56/9.83	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.83	   A^2 -> H(f(k), U1(k, k))
28.56/9.83	   A^2 -> H(f(e), e)
28.56/9.83	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.83	   A^2 -> H(d, U1(c, b))
28.56/9.83	   A^2 -> H(d, U1(d, b))
28.56/9.83	   A^2 -> H(d, U1(b, c))
28.56/9.83	   A^2 -> H(d, U1(b, d))
28.56/9.83	   A^2 -> H(d, U1(c, c))
28.56/9.83	   A^2 -> H(d, f(e))
28.56/9.83	   A^2 -> H(d, f(k))
28.56/9.83	   A^2 -> H(d, U1(d, d))
28.56/9.83	   A^2 -> H(a, U1(e, b))
28.56/9.83	   A^2 -> H(a, U1(k, b))
28.56/9.83	   A^2 -> H(a, U1(c, d))
28.56/9.83	   A^2 -> H(a, U1(d, c))
28.56/9.83	   A^2 -> H(a, U1(b, e))
28.56/9.83	   A^2 -> H(a, U1(b, k))
28.56/9.83	   A^2 -> H(a, U1(e, c))
28.56/9.83	   A^2 -> H(a, U1(k, c))
28.56/9.83	   A^2 -> H(a, U1(c, e))
28.56/9.83	   A^2 -> H(a, U1(c, k))
28.56/9.83	   A^2 -> H(a, U1(e, e))
28.56/9.83	   A^2 -> H(a, U1(k, k))
28.56/9.83	   A^2 -> H(a, U1(k, d))
28.56/9.83	   A^2 -> H(a, U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.83	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.83	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.83	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.83	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.83	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, a), b)
28.56/9.83	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.83	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.83	   A^2 -> H(U1(e, a), c)
28.56/9.83	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.83	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.83	   A^2 -> H(U1(e, a), e)
28.56/9.83	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, a), b)
28.56/9.83	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.83	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.83	   A^2 -> H(U1(k, a), c)
28.56/9.83	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.83	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.83	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, d), b)
28.56/9.83	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.83	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.83	   A^2 -> H(U1(c, d), c)
28.56/9.83	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.83	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.83	   A^2 -> H(U1(c, d), e)
28.56/9.83	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, a), d)
28.56/9.83	   A^2 -> H(U1(c, a), k)
28.56/9.83	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.83	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.83	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.83	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.83	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, c), b)
28.56/9.83	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(d, c), c)
28.56/9.83	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.83	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.83	   A^2 -> H(U1(d, c), e)
28.56/9.83	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.83	   A^2 -> H(U1(d, a), d)
28.56/9.83	   A^2 -> H(U1(d, a), k)
28.56/9.83	   A^2 -> H(U1(a, e), b)
28.56/9.83	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.83	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.83	   A^2 -> H(U1(a, e), c)
28.56/9.83	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.83	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.83	   A^2 -> H(U1(a, e), e)
28.56/9.83	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(a, k), b)
28.56/9.83	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.83	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.83	   A^2 -> H(U1(a, k), c)
28.56/9.83	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.83	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.83	   A^2 -> H(U1(a, k), e)
28.56/9.83	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(a, c), d)
28.56/9.83	   A^2 -> H(U1(a, c), k)
28.56/9.83	   A^2 -> H(U1(a, d), d)
28.56/9.83	   A^2 -> H(U1(a, d), k)
28.56/9.83	   A^2 -> H(k, U1(c, b))
28.56/9.83	   A^2 -> H(k, U1(d, b))
28.56/9.83	   A^2 -> H(k, U1(b, c))
28.56/9.83	   A^2 -> H(k, U1(b, d))
28.56/9.83	   A^2 -> H(k, U1(c, c))
28.56/9.83	   A^2 -> H(k, f(e))
28.56/9.83	   A^2 -> H(k, f(k))
28.56/9.83	   A^2 -> H(k, U1(d, d))
28.56/9.83	   A^2 -> H(c, U1(e, b))
28.56/9.83	   A^2 -> H(c, U1(k, b))
28.56/9.83	   A^2 -> H(c, U1(c, d))
28.56/9.83	   A^2 -> H(c, U1(d, c))
28.56/9.83	   A^2 -> H(c, U1(b, e))
28.56/9.83	   A^2 -> H(c, U1(b, k))
28.56/9.83	   A^2 -> H(c, U1(e, c))
28.56/9.83	   A^2 -> H(c, U1(k, c))
28.56/9.83	   A^2 -> H(c, U1(c, e))
28.56/9.83	   A^2 -> H(c, U1(c, k))
28.56/9.83	   A^2 -> H(c, U1(e, e))
28.56/9.83	   A^2 -> H(c, U1(k, k))
28.56/9.83	   A^2 -> H(c, U1(k, d))
28.56/9.83	   A^2 -> H(c, U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, c), b)
28.56/9.83	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.83	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.83	   A^2 -> H(U1(e, c), e)
28.56/9.83	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.83	   A^2 -> H(U1(k, c), b)
28.56/9.83	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(k, c), c)
28.56/9.83	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.83	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.83	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, e), b)
28.56/9.83	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.83	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.83	   A^2 -> H(U1(c, e), c)
28.56/9.83	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.83	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.83	
28.56/9.83	The TRS R consists of the following rules:
28.56/9.83	
28.56/9.83	   f(x) -> U1(x, x)
28.56/9.83	   U1(e, x) -> x
28.56/9.83	   a -> c
28.56/9.83	   a -> d
28.56/9.83	   b -> c
28.56/9.83	   b -> d
28.56/9.83	   d -> k
28.56/9.83	   c -> e
28.56/9.83	   c -> k
28.56/9.83	
28.56/9.83	Q is empty.
28.56/9.83	We have to consider all minimal (P,Q,R)-chains.
28.56/9.83	----------------------------------------
28.56/9.83	
28.56/9.83	(1513) TransformationProof (EQUIVALENT)
28.56/9.83	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.83	
28.56/9.83	   (A^2 -> H(U1(e, e), U1(c, k)),A^2 -> H(U1(e, e), U1(c, k)))
28.56/9.83	   (A^2 -> H(U1(k, e), U1(c, k)),A^2 -> H(U1(k, e), U1(c, k)))
28.56/9.83	   (A^2 -> H(U1(c, e), U1(e, k)),A^2 -> H(U1(c, e), U1(e, k)))
28.56/9.83	   (A^2 -> H(U1(c, e), U1(k, k)),A^2 -> H(U1(c, e), U1(k, k)))
28.56/9.83	
28.56/9.83	
28.56/9.83	----------------------------------------
28.56/9.83	
28.56/9.83	(1514)
28.56/9.83	Obligation:
28.56/9.83	Q DP problem:
28.56/9.83	The TRS P consists of the following rules:
28.56/9.83	
28.56/9.83	   H(x, x) -> G(x, x, f(k))
28.56/9.83	   G(d, x, x) -> A^2
28.56/9.83	   A^2 -> H(f(c), f(c))
28.56/9.83	   A^2 -> H(f(d), f(d))
28.56/9.83	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.83	   A^2 -> H(f(e), f(e))
28.56/9.83	   A^2 -> H(f(k), f(k))
28.56/9.83	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.83	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.83	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(c, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.83	   A^2 -> H(U1(c, c), b)
28.56/9.83	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(c, c), e)
28.56/9.83	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.83	   A^2 -> H(e, U1(c, b))
28.56/9.83	   A^2 -> H(e, U1(d, b))
28.56/9.83	   A^2 -> H(e, U1(b, c))
28.56/9.83	   A^2 -> H(e, U1(b, d))
28.56/9.83	   A^2 -> H(e, U1(c, c))
28.56/9.83	   A^2 -> H(e, f(e))
28.56/9.83	   A^2 -> H(e, f(k))
28.56/9.83	   A^2 -> H(e, U1(d, d))
28.56/9.83	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.83	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.83	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.83	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.83	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.83	   A^2 -> H(f(e), b)
28.56/9.83	   A^2 -> H(f(e), U1(e, d))
28.56/9.83	   A^2 -> H(f(e), U1(d, e))
28.56/9.83	   A^2 -> H(f(e), c)
28.56/9.83	   A^2 -> H(f(e), U1(e, k))
28.56/9.83	   A^2 -> H(f(e), U1(k, e))
28.56/9.83	   A^2 -> H(f(e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.83	   A^2 -> H(f(k), b)
28.56/9.83	   A^2 -> H(f(k), U1(e, d))
28.56/9.83	   A^2 -> H(f(k), U1(d, e))
28.56/9.83	   A^2 -> H(f(k), c)
28.56/9.83	   A^2 -> H(f(k), U1(e, k))
28.56/9.83	   A^2 -> H(f(k), U1(k, e))
28.56/9.83	   A^2 -> H(f(k), e)
28.56/9.83	   A^2 -> H(f(c), d)
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.83	   A^2 -> H(U1(k, k), f(e))
28.56/9.83	   A^2 -> H(U1(k, k), f(k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, d), b)
28.56/9.83	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.83	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.83	   A^2 -> H(U1(d, d), c)
28.56/9.83	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.83	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.83	   A^2 -> H(U1(d, d), e)
28.56/9.83	   A^2 -> H(f(d), d)
28.56/9.83	   A^2 -> H(f(d), k)
28.56/9.83	   A^2 -> H(U1(c, c), c)
28.56/9.83	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.83	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.83	   A^2 -> H(f(c), k)
28.56/9.83	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.83	   A^2 -> H(f(k), U1(k, k))
28.56/9.83	   A^2 -> H(f(e), e)
28.56/9.83	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.83	   A^2 -> H(d, U1(c, b))
28.56/9.83	   A^2 -> H(d, U1(d, b))
28.56/9.83	   A^2 -> H(d, U1(b, c))
28.56/9.83	   A^2 -> H(d, U1(b, d))
28.56/9.83	   A^2 -> H(d, U1(c, c))
28.56/9.83	   A^2 -> H(d, f(e))
28.56/9.83	   A^2 -> H(d, f(k))
28.56/9.83	   A^2 -> H(d, U1(d, d))
28.56/9.83	   A^2 -> H(a, U1(e, b))
28.56/9.83	   A^2 -> H(a, U1(k, b))
28.56/9.83	   A^2 -> H(a, U1(c, d))
28.56/9.83	   A^2 -> H(a, U1(d, c))
28.56/9.83	   A^2 -> H(a, U1(b, e))
28.56/9.83	   A^2 -> H(a, U1(b, k))
28.56/9.83	   A^2 -> H(a, U1(e, c))
28.56/9.83	   A^2 -> H(a, U1(k, c))
28.56/9.83	   A^2 -> H(a, U1(c, e))
28.56/9.83	   A^2 -> H(a, U1(c, k))
28.56/9.83	   A^2 -> H(a, U1(e, e))
28.56/9.83	   A^2 -> H(a, U1(k, k))
28.56/9.83	   A^2 -> H(a, U1(k, d))
28.56/9.83	   A^2 -> H(a, U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.83	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.83	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.83	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.83	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.83	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, a), b)
28.56/9.83	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.83	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.83	   A^2 -> H(U1(e, a), c)
28.56/9.83	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.83	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.83	   A^2 -> H(U1(e, a), e)
28.56/9.83	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, a), b)
28.56/9.83	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.83	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.83	   A^2 -> H(U1(k, a), c)
28.56/9.83	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.83	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.83	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, d), b)
28.56/9.83	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.83	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.83	   A^2 -> H(U1(c, d), c)
28.56/9.83	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.83	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.83	   A^2 -> H(U1(c, d), e)
28.56/9.83	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, a), d)
28.56/9.83	   A^2 -> H(U1(c, a), k)
28.56/9.83	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.83	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.83	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.83	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.83	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, c), b)
28.56/9.83	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(d, c), c)
28.56/9.83	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.83	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.83	   A^2 -> H(U1(d, c), e)
28.56/9.83	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.83	   A^2 -> H(U1(d, a), d)
28.56/9.83	   A^2 -> H(U1(d, a), k)
28.56/9.83	   A^2 -> H(U1(a, e), b)
28.56/9.83	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.83	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.83	   A^2 -> H(U1(a, e), c)
28.56/9.83	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.83	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.83	   A^2 -> H(U1(a, e), e)
28.56/9.83	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(a, k), b)
28.56/9.83	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.83	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.83	   A^2 -> H(U1(a, k), c)
28.56/9.83	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.83	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.83	   A^2 -> H(U1(a, k), e)
28.56/9.83	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(a, c), d)
28.56/9.83	   A^2 -> H(U1(a, c), k)
28.56/9.83	   A^2 -> H(U1(a, d), d)
28.56/9.83	   A^2 -> H(U1(a, d), k)
28.56/9.83	   A^2 -> H(k, U1(c, b))
28.56/9.83	   A^2 -> H(k, U1(d, b))
28.56/9.83	   A^2 -> H(k, U1(b, c))
28.56/9.83	   A^2 -> H(k, U1(b, d))
28.56/9.83	   A^2 -> H(k, U1(c, c))
28.56/9.83	   A^2 -> H(k, f(e))
28.56/9.83	   A^2 -> H(k, f(k))
28.56/9.83	   A^2 -> H(k, U1(d, d))
28.56/9.83	   A^2 -> H(c, U1(e, b))
28.56/9.83	   A^2 -> H(c, U1(k, b))
28.56/9.83	   A^2 -> H(c, U1(c, d))
28.56/9.83	   A^2 -> H(c, U1(d, c))
28.56/9.83	   A^2 -> H(c, U1(b, e))
28.56/9.83	   A^2 -> H(c, U1(b, k))
28.56/9.83	   A^2 -> H(c, U1(e, c))
28.56/9.83	   A^2 -> H(c, U1(k, c))
28.56/9.83	   A^2 -> H(c, U1(c, e))
28.56/9.83	   A^2 -> H(c, U1(c, k))
28.56/9.83	   A^2 -> H(c, U1(e, e))
28.56/9.83	   A^2 -> H(c, U1(k, k))
28.56/9.83	   A^2 -> H(c, U1(k, d))
28.56/9.83	   A^2 -> H(c, U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, c), b)
28.56/9.83	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.83	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.83	   A^2 -> H(U1(e, c), e)
28.56/9.83	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.83	   A^2 -> H(U1(k, c), b)
28.56/9.83	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(k, c), c)
28.56/9.83	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.83	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.83	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, e), b)
28.56/9.83	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.83	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.83	   A^2 -> H(U1(c, e), c)
28.56/9.83	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.83	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.83	
28.56/9.83	The TRS R consists of the following rules:
28.56/9.83	
28.56/9.83	   f(x) -> U1(x, x)
28.56/9.83	   U1(e, x) -> x
28.56/9.83	   a -> c
28.56/9.83	   a -> d
28.56/9.83	   b -> c
28.56/9.83	   b -> d
28.56/9.83	   d -> k
28.56/9.83	   c -> e
28.56/9.83	   c -> k
28.56/9.83	
28.56/9.83	Q is empty.
28.56/9.83	We have to consider all minimal (P,Q,R)-chains.
28.56/9.83	----------------------------------------
28.56/9.83	
28.56/9.83	(1515) TransformationProof (EQUIVALENT)
28.56/9.83	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.83	
28.56/9.83	   (A^2 -> H(U1(e, e), U1(e, e)),A^2 -> H(U1(e, e), U1(e, e)))
28.56/9.83	   (A^2 -> H(U1(k, e), U1(e, e)),A^2 -> H(U1(k, e), U1(e, e)))
28.56/9.83	   (A^2 -> H(U1(c, e), e),A^2 -> H(U1(c, e), e))
28.56/9.83	
28.56/9.83	
28.56/9.83	----------------------------------------
28.56/9.83	
28.56/9.83	(1516)
28.56/9.83	Obligation:
28.56/9.83	Q DP problem:
28.56/9.83	The TRS P consists of the following rules:
28.56/9.83	
28.56/9.83	   H(x, x) -> G(x, x, f(k))
28.56/9.83	   G(d, x, x) -> A^2
28.56/9.83	   A^2 -> H(f(c), f(c))
28.56/9.83	   A^2 -> H(f(d), f(d))
28.56/9.83	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.83	   A^2 -> H(f(e), f(e))
28.56/9.83	   A^2 -> H(f(k), f(k))
28.56/9.83	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.83	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.83	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.83	   A^2 -> H(U1(c, c), b)
28.56/9.83	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(c, c), e)
28.56/9.83	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.83	   A^2 -> H(e, U1(c, b))
28.56/9.83	   A^2 -> H(e, U1(d, b))
28.56/9.83	   A^2 -> H(e, U1(b, c))
28.56/9.83	   A^2 -> H(e, U1(b, d))
28.56/9.83	   A^2 -> H(e, U1(c, c))
28.56/9.83	   A^2 -> H(e, f(e))
28.56/9.83	   A^2 -> H(e, f(k))
28.56/9.83	   A^2 -> H(e, U1(d, d))
28.56/9.83	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.83	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.83	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.83	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.83	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.83	   A^2 -> H(f(e), b)
28.56/9.83	   A^2 -> H(f(e), U1(e, d))
28.56/9.83	   A^2 -> H(f(e), U1(d, e))
28.56/9.83	   A^2 -> H(f(e), c)
28.56/9.83	   A^2 -> H(f(e), U1(e, k))
28.56/9.83	   A^2 -> H(f(e), U1(k, e))
28.56/9.83	   A^2 -> H(f(e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.83	   A^2 -> H(f(k), b)
28.56/9.83	   A^2 -> H(f(k), U1(e, d))
28.56/9.83	   A^2 -> H(f(k), U1(d, e))
28.56/9.83	   A^2 -> H(f(k), c)
28.56/9.83	   A^2 -> H(f(k), U1(e, k))
28.56/9.83	   A^2 -> H(f(k), U1(k, e))
28.56/9.83	   A^2 -> H(f(k), e)
28.56/9.83	   A^2 -> H(f(c), d)
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.83	   A^2 -> H(U1(k, k), f(e))
28.56/9.83	   A^2 -> H(U1(k, k), f(k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, d), b)
28.56/9.83	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.83	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.83	   A^2 -> H(U1(d, d), c)
28.56/9.83	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.83	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.83	   A^2 -> H(U1(d, d), e)
28.56/9.83	   A^2 -> H(f(d), d)
28.56/9.83	   A^2 -> H(f(d), k)
28.56/9.83	   A^2 -> H(U1(c, c), c)
28.56/9.83	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.83	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.83	   A^2 -> H(f(c), k)
28.56/9.83	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.83	   A^2 -> H(f(k), U1(k, k))
28.56/9.83	   A^2 -> H(f(e), e)
28.56/9.83	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.83	   A^2 -> H(d, U1(c, b))
28.56/9.83	   A^2 -> H(d, U1(d, b))
28.56/9.83	   A^2 -> H(d, U1(b, c))
28.56/9.83	   A^2 -> H(d, U1(b, d))
28.56/9.83	   A^2 -> H(d, U1(c, c))
28.56/9.83	   A^2 -> H(d, f(e))
28.56/9.83	   A^2 -> H(d, f(k))
28.56/9.83	   A^2 -> H(d, U1(d, d))
28.56/9.83	   A^2 -> H(a, U1(e, b))
28.56/9.83	   A^2 -> H(a, U1(k, b))
28.56/9.83	   A^2 -> H(a, U1(c, d))
28.56/9.83	   A^2 -> H(a, U1(d, c))
28.56/9.83	   A^2 -> H(a, U1(b, e))
28.56/9.83	   A^2 -> H(a, U1(b, k))
28.56/9.83	   A^2 -> H(a, U1(e, c))
28.56/9.83	   A^2 -> H(a, U1(k, c))
28.56/9.83	   A^2 -> H(a, U1(c, e))
28.56/9.83	   A^2 -> H(a, U1(c, k))
28.56/9.83	   A^2 -> H(a, U1(e, e))
28.56/9.83	   A^2 -> H(a, U1(k, k))
28.56/9.83	   A^2 -> H(a, U1(k, d))
28.56/9.83	   A^2 -> H(a, U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.83	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.83	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.83	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.83	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.83	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, a), b)
28.56/9.83	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.83	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.83	   A^2 -> H(U1(e, a), c)
28.56/9.83	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.83	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.83	   A^2 -> H(U1(e, a), e)
28.56/9.83	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, a), b)
28.56/9.83	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.83	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.83	   A^2 -> H(U1(k, a), c)
28.56/9.83	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.83	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.83	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, d), b)
28.56/9.83	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.83	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.83	   A^2 -> H(U1(c, d), c)
28.56/9.83	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.83	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.83	   A^2 -> H(U1(c, d), e)
28.56/9.83	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, a), d)
28.56/9.83	   A^2 -> H(U1(c, a), k)
28.56/9.83	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.83	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.83	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.83	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.83	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, c), b)
28.56/9.83	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(d, c), c)
28.56/9.83	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.83	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.83	   A^2 -> H(U1(d, c), e)
28.56/9.83	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.83	   A^2 -> H(U1(d, a), d)
28.56/9.83	   A^2 -> H(U1(d, a), k)
28.56/9.83	   A^2 -> H(U1(a, e), b)
28.56/9.83	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.83	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.83	   A^2 -> H(U1(a, e), c)
28.56/9.83	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.83	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.83	   A^2 -> H(U1(a, e), e)
28.56/9.83	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(a, k), b)
28.56/9.83	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.83	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.83	   A^2 -> H(U1(a, k), c)
28.56/9.83	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.83	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.83	   A^2 -> H(U1(a, k), e)
28.56/9.83	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(a, c), d)
28.56/9.83	   A^2 -> H(U1(a, c), k)
28.56/9.83	   A^2 -> H(U1(a, d), d)
28.56/9.83	   A^2 -> H(U1(a, d), k)
28.56/9.83	   A^2 -> H(k, U1(c, b))
28.56/9.83	   A^2 -> H(k, U1(d, b))
28.56/9.83	   A^2 -> H(k, U1(b, c))
28.56/9.83	   A^2 -> H(k, U1(b, d))
28.56/9.83	   A^2 -> H(k, U1(c, c))
28.56/9.83	   A^2 -> H(k, f(e))
28.56/9.83	   A^2 -> H(k, f(k))
28.56/9.83	   A^2 -> H(k, U1(d, d))
28.56/9.83	   A^2 -> H(c, U1(e, b))
28.56/9.83	   A^2 -> H(c, U1(k, b))
28.56/9.83	   A^2 -> H(c, U1(c, d))
28.56/9.83	   A^2 -> H(c, U1(d, c))
28.56/9.83	   A^2 -> H(c, U1(b, e))
28.56/9.83	   A^2 -> H(c, U1(b, k))
28.56/9.83	   A^2 -> H(c, U1(e, c))
28.56/9.83	   A^2 -> H(c, U1(k, c))
28.56/9.83	   A^2 -> H(c, U1(c, e))
28.56/9.83	   A^2 -> H(c, U1(c, k))
28.56/9.83	   A^2 -> H(c, U1(e, e))
28.56/9.83	   A^2 -> H(c, U1(k, k))
28.56/9.83	   A^2 -> H(c, U1(k, d))
28.56/9.83	   A^2 -> H(c, U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.83	   A^2 -> H(U1(e, c), b)
28.56/9.83	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.83	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.83	   A^2 -> H(U1(e, c), e)
28.56/9.83	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.83	   A^2 -> H(U1(k, c), b)
28.56/9.83	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(k, c), c)
28.56/9.83	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.83	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.83	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, e), b)
28.56/9.83	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.83	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.83	   A^2 -> H(U1(c, e), c)
28.56/9.83	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.83	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.83	   A^2 -> H(U1(c, e), e)
28.56/9.83	
28.56/9.83	The TRS R consists of the following rules:
28.56/9.83	
28.56/9.83	   f(x) -> U1(x, x)
28.56/9.83	   U1(e, x) -> x
28.56/9.83	   a -> c
28.56/9.83	   a -> d
28.56/9.83	   b -> c
28.56/9.83	   b -> d
28.56/9.83	   d -> k
28.56/9.83	   c -> e
28.56/9.83	   c -> k
28.56/9.83	
28.56/9.83	Q is empty.
28.56/9.83	We have to consider all minimal (P,Q,R)-chains.
28.56/9.83	----------------------------------------
28.56/9.83	
28.56/9.83	(1517) TransformationProof (EQUIVALENT)
28.56/9.83	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.83	
28.56/9.83	   (A^2 -> H(U1(e, e), U1(k, k)),A^2 -> H(U1(e, e), U1(k, k)))
28.56/9.83	   (A^2 -> H(U1(k, e), U1(k, k)),A^2 -> H(U1(k, e), U1(k, k)))
28.56/9.83	
28.56/9.83	
28.56/9.83	----------------------------------------
28.56/9.83	
28.56/9.83	(1518)
28.56/9.83	Obligation:
28.56/9.83	Q DP problem:
28.56/9.83	The TRS P consists of the following rules:
28.56/9.83	
28.56/9.83	   H(x, x) -> G(x, x, f(k))
28.56/9.83	   G(d, x, x) -> A^2
28.56/9.83	   A^2 -> H(f(c), f(c))
28.56/9.83	   A^2 -> H(f(d), f(d))
28.56/9.83	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.83	   A^2 -> H(f(e), f(e))
28.56/9.83	   A^2 -> H(f(k), f(k))
28.56/9.83	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.83	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.83	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.83	   A^2 -> H(U1(c, c), b)
28.56/9.83	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.83	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.83	   A^2 -> H(U1(c, c), e)
28.56/9.83	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.83	   A^2 -> H(e, U1(c, b))
28.56/9.83	   A^2 -> H(e, U1(d, b))
28.56/9.83	   A^2 -> H(e, U1(b, c))
28.56/9.83	   A^2 -> H(e, U1(b, d))
28.56/9.83	   A^2 -> H(e, U1(c, c))
28.56/9.83	   A^2 -> H(e, f(e))
28.56/9.83	   A^2 -> H(e, f(k))
28.56/9.83	   A^2 -> H(e, U1(d, d))
28.56/9.83	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.83	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.83	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.83	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.83	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.83	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.83	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.83	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.83	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.83	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.83	   A^2 -> H(f(e), b)
28.56/9.83	   A^2 -> H(f(e), U1(e, d))
28.56/9.83	   A^2 -> H(f(e), U1(d, e))
28.56/9.83	   A^2 -> H(f(e), c)
28.56/9.83	   A^2 -> H(f(e), U1(e, k))
28.56/9.83	   A^2 -> H(f(e), U1(k, e))
28.56/9.83	   A^2 -> H(f(e), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.83	   A^2 -> H(f(k), b)
28.56/9.83	   A^2 -> H(f(k), U1(e, d))
28.56/9.83	   A^2 -> H(f(k), U1(d, e))
28.56/9.83	   A^2 -> H(f(k), c)
28.56/9.83	   A^2 -> H(f(k), U1(e, k))
28.56/9.83	   A^2 -> H(f(k), U1(k, e))
28.56/9.83	   A^2 -> H(f(k), e)
28.56/9.83	   A^2 -> H(f(c), d)
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.83	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.83	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.83	   A^2 -> H(U1(k, k), f(e))
28.56/9.83	   A^2 -> H(U1(k, k), f(k))
28.56/9.83	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.83	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.83	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.83	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.83	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.83	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, d), b)
28.56/9.84	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.84	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.84	   A^2 -> H(U1(d, d), c)
28.56/9.84	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.84	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.84	   A^2 -> H(U1(d, d), e)
28.56/9.84	   A^2 -> H(f(d), d)
28.56/9.84	   A^2 -> H(f(d), k)
28.56/9.84	   A^2 -> H(U1(c, c), c)
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.84	   A^2 -> H(f(c), k)
28.56/9.84	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.84	   A^2 -> H(f(k), U1(k, k))
28.56/9.84	   A^2 -> H(f(e), e)
28.56/9.84	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.84	   A^2 -> H(d, U1(c, b))
28.56/9.84	   A^2 -> H(d, U1(d, b))
28.56/9.84	   A^2 -> H(d, U1(b, c))
28.56/9.84	   A^2 -> H(d, U1(b, d))
28.56/9.84	   A^2 -> H(d, U1(c, c))
28.56/9.84	   A^2 -> H(d, f(e))
28.56/9.84	   A^2 -> H(d, f(k))
28.56/9.84	   A^2 -> H(d, U1(d, d))
28.56/9.84	   A^2 -> H(a, U1(e, b))
28.56/9.84	   A^2 -> H(a, U1(k, b))
28.56/9.84	   A^2 -> H(a, U1(c, d))
28.56/9.84	   A^2 -> H(a, U1(d, c))
28.56/9.84	   A^2 -> H(a, U1(b, e))
28.56/9.84	   A^2 -> H(a, U1(b, k))
28.56/9.84	   A^2 -> H(a, U1(e, c))
28.56/9.84	   A^2 -> H(a, U1(k, c))
28.56/9.84	   A^2 -> H(a, U1(c, e))
28.56/9.84	   A^2 -> H(a, U1(c, k))
28.56/9.84	   A^2 -> H(a, U1(e, e))
28.56/9.84	   A^2 -> H(a, U1(k, k))
28.56/9.84	   A^2 -> H(a, U1(k, d))
28.56/9.84	   A^2 -> H(a, U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.84	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.84	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.84	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, a), b)
28.56/9.84	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.84	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.84	   A^2 -> H(U1(e, a), c)
28.56/9.84	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.84	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.84	   A^2 -> H(U1(e, a), e)
28.56/9.84	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, a), b)
28.56/9.84	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.84	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.84	   A^2 -> H(U1(k, a), c)
28.56/9.84	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.84	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.84	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, d), b)
28.56/9.84	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.84	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.84	   A^2 -> H(U1(c, d), c)
28.56/9.84	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.84	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.84	   A^2 -> H(U1(c, d), e)
28.56/9.84	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, a), d)
28.56/9.84	   A^2 -> H(U1(c, a), k)
28.56/9.84	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.84	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.84	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.84	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.84	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.84	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.84	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.84	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, c), b)
28.56/9.84	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(d, c), c)
28.56/9.84	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.84	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.84	   A^2 -> H(U1(d, c), e)
28.56/9.84	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, a), d)
28.56/9.84	   A^2 -> H(U1(d, a), k)
28.56/9.84	   A^2 -> H(U1(a, e), b)
28.56/9.84	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.84	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.84	   A^2 -> H(U1(a, e), c)
28.56/9.84	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.84	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.84	   A^2 -> H(U1(a, e), e)
28.56/9.84	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(a, k), b)
28.56/9.84	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.84	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.84	   A^2 -> H(U1(a, k), c)
28.56/9.84	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.84	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.84	   A^2 -> H(U1(a, k), e)
28.56/9.84	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(a, c), d)
28.56/9.84	   A^2 -> H(U1(a, c), k)
28.56/9.84	   A^2 -> H(U1(a, d), d)
28.56/9.84	   A^2 -> H(U1(a, d), k)
28.56/9.84	   A^2 -> H(k, U1(c, b))
28.56/9.84	   A^2 -> H(k, U1(d, b))
28.56/9.84	   A^2 -> H(k, U1(b, c))
28.56/9.84	   A^2 -> H(k, U1(b, d))
28.56/9.84	   A^2 -> H(k, U1(c, c))
28.56/9.84	   A^2 -> H(k, f(e))
28.56/9.84	   A^2 -> H(k, f(k))
28.56/9.84	   A^2 -> H(k, U1(d, d))
28.56/9.84	   A^2 -> H(c, U1(e, b))
28.56/9.84	   A^2 -> H(c, U1(k, b))
28.56/9.84	   A^2 -> H(c, U1(c, d))
28.56/9.84	   A^2 -> H(c, U1(d, c))
28.56/9.84	   A^2 -> H(c, U1(b, e))
28.56/9.84	   A^2 -> H(c, U1(b, k))
28.56/9.84	   A^2 -> H(c, U1(e, c))
28.56/9.84	   A^2 -> H(c, U1(k, c))
28.56/9.84	   A^2 -> H(c, U1(c, e))
28.56/9.84	   A^2 -> H(c, U1(c, k))
28.56/9.84	   A^2 -> H(c, U1(e, e))
28.56/9.84	   A^2 -> H(c, U1(k, k))
28.56/9.84	   A^2 -> H(c, U1(k, d))
28.56/9.84	   A^2 -> H(c, U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, c), b)
28.56/9.84	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.84	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.84	   A^2 -> H(U1(e, c), e)
28.56/9.84	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.84	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.84	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.84	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.84	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.84	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.84	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.84	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.84	   A^2 -> H(U1(k, c), b)
28.56/9.84	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(k, c), c)
28.56/9.84	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.84	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.84	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, e), b)
28.56/9.84	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.84	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.84	   A^2 -> H(U1(c, e), c)
28.56/9.84	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.84	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.84	   A^2 -> H(U1(c, e), e)
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, k))
28.56/9.84	
28.56/9.84	The TRS R consists of the following rules:
28.56/9.84	
28.56/9.84	   f(x) -> U1(x, x)
28.56/9.84	   U1(e, x) -> x
28.56/9.84	   a -> c
28.56/9.84	   a -> d
28.56/9.84	   b -> c
28.56/9.84	   b -> d
28.56/9.84	   d -> k
28.56/9.84	   c -> e
28.56/9.84	   c -> k
28.56/9.84	
28.56/9.84	Q is empty.
28.56/9.84	We have to consider all minimal (P,Q,R)-chains.
28.56/9.84	----------------------------------------
28.56/9.84	
28.56/9.84	(1519) DependencyGraphProof (EQUIVALENT)
28.56/9.84	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.84	----------------------------------------
28.56/9.84	
28.56/9.84	(1520)
28.56/9.84	Obligation:
28.56/9.84	Q DP problem:
28.56/9.84	The TRS P consists of the following rules:
28.56/9.84	
28.56/9.84	   G(d, x, x) -> A^2
28.56/9.84	   A^2 -> H(f(c), f(c))
28.56/9.84	   H(x, x) -> G(x, x, f(k))
28.56/9.84	   A^2 -> H(f(d), f(d))
28.56/9.84	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.84	   A^2 -> H(f(e), f(e))
28.56/9.84	   A^2 -> H(f(k), f(k))
28.56/9.84	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.84	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.84	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.84	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(c, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(c, c), b)
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(c, c), e)
28.56/9.84	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.84	   A^2 -> H(e, U1(c, b))
28.56/9.84	   A^2 -> H(e, U1(d, b))
28.56/9.84	   A^2 -> H(e, U1(b, c))
28.56/9.84	   A^2 -> H(e, U1(b, d))
28.56/9.84	   A^2 -> H(e, U1(c, c))
28.56/9.84	   A^2 -> H(e, f(e))
28.56/9.84	   A^2 -> H(e, f(k))
28.56/9.84	   A^2 -> H(e, U1(d, d))
28.56/9.84	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.84	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.84	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.84	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.84	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.84	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.84	   A^2 -> H(f(e), b)
28.56/9.84	   A^2 -> H(f(e), U1(e, d))
28.56/9.84	   A^2 -> H(f(e), U1(d, e))
28.56/9.84	   A^2 -> H(f(e), c)
28.56/9.84	   A^2 -> H(f(e), U1(e, k))
28.56/9.84	   A^2 -> H(f(e), U1(k, e))
28.56/9.84	   A^2 -> H(f(e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.84	   A^2 -> H(f(k), b)
28.56/9.84	   A^2 -> H(f(k), U1(e, d))
28.56/9.84	   A^2 -> H(f(k), U1(d, e))
28.56/9.84	   A^2 -> H(f(k), c)
28.56/9.84	   A^2 -> H(f(k), U1(e, k))
28.56/9.84	   A^2 -> H(f(k), U1(k, e))
28.56/9.84	   A^2 -> H(f(k), e)
28.56/9.84	   A^2 -> H(f(c), d)
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.84	   A^2 -> H(U1(k, k), f(e))
28.56/9.84	   A^2 -> H(U1(k, k), f(k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.84	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.84	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.84	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.84	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.84	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.84	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.84	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.84	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.84	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.84	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, d), b)
28.56/9.84	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.84	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.84	   A^2 -> H(U1(d, d), c)
28.56/9.84	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.84	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.84	   A^2 -> H(U1(d, d), e)
28.56/9.84	   A^2 -> H(f(d), d)
28.56/9.84	   A^2 -> H(f(d), k)
28.56/9.84	   A^2 -> H(U1(c, c), c)
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.84	   A^2 -> H(f(c), k)
28.56/9.84	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.84	   A^2 -> H(f(k), U1(k, k))
28.56/9.84	   A^2 -> H(f(e), e)
28.56/9.84	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.84	   A^2 -> H(d, U1(c, b))
28.56/9.84	   A^2 -> H(d, U1(d, b))
28.56/9.84	   A^2 -> H(d, U1(b, c))
28.56/9.84	   A^2 -> H(d, U1(b, d))
28.56/9.84	   A^2 -> H(d, U1(c, c))
28.56/9.84	   A^2 -> H(d, f(e))
28.56/9.84	   A^2 -> H(d, f(k))
28.56/9.84	   A^2 -> H(d, U1(d, d))
28.56/9.84	   A^2 -> H(a, U1(e, b))
28.56/9.84	   A^2 -> H(a, U1(k, b))
28.56/9.84	   A^2 -> H(a, U1(c, d))
28.56/9.84	   A^2 -> H(a, U1(d, c))
28.56/9.84	   A^2 -> H(a, U1(b, e))
28.56/9.84	   A^2 -> H(a, U1(b, k))
28.56/9.84	   A^2 -> H(a, U1(e, c))
28.56/9.84	   A^2 -> H(a, U1(k, c))
28.56/9.84	   A^2 -> H(a, U1(c, e))
28.56/9.84	   A^2 -> H(a, U1(c, k))
28.56/9.84	   A^2 -> H(a, U1(e, e))
28.56/9.84	   A^2 -> H(a, U1(k, k))
28.56/9.84	   A^2 -> H(a, U1(k, d))
28.56/9.84	   A^2 -> H(a, U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.84	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.84	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.84	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, a), b)
28.56/9.84	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.84	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.84	   A^2 -> H(U1(e, a), c)
28.56/9.84	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.84	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.84	   A^2 -> H(U1(e, a), e)
28.56/9.84	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, a), b)
28.56/9.84	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.84	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.84	   A^2 -> H(U1(k, a), c)
28.56/9.84	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.84	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.84	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, d), b)
28.56/9.84	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.84	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.84	   A^2 -> H(U1(c, d), c)
28.56/9.84	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.84	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.84	   A^2 -> H(U1(c, d), e)
28.56/9.84	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, a), d)
28.56/9.84	   A^2 -> H(U1(c, a), k)
28.56/9.84	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.84	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.84	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.84	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.84	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.84	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.84	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.84	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, c), b)
28.56/9.84	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(d, c), c)
28.56/9.84	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.84	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.84	   A^2 -> H(U1(d, c), e)
28.56/9.84	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, a), d)
28.56/9.84	   A^2 -> H(U1(d, a), k)
28.56/9.84	   A^2 -> H(U1(a, e), b)
28.56/9.84	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.84	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.84	   A^2 -> H(U1(a, e), c)
28.56/9.84	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.84	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.84	   A^2 -> H(U1(a, e), e)
28.56/9.84	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(a, k), b)
28.56/9.84	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.84	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.84	   A^2 -> H(U1(a, k), c)
28.56/9.84	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.84	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.84	   A^2 -> H(U1(a, k), e)
28.56/9.84	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(a, c), d)
28.56/9.84	   A^2 -> H(U1(a, c), k)
28.56/9.84	   A^2 -> H(U1(a, d), d)
28.56/9.84	   A^2 -> H(U1(a, d), k)
28.56/9.84	   A^2 -> H(k, U1(c, b))
28.56/9.84	   A^2 -> H(k, U1(d, b))
28.56/9.84	   A^2 -> H(k, U1(b, c))
28.56/9.84	   A^2 -> H(k, U1(b, d))
28.56/9.84	   A^2 -> H(k, U1(c, c))
28.56/9.84	   A^2 -> H(k, f(e))
28.56/9.84	   A^2 -> H(k, f(k))
28.56/9.84	   A^2 -> H(k, U1(d, d))
28.56/9.84	   A^2 -> H(c, U1(e, b))
28.56/9.84	   A^2 -> H(c, U1(k, b))
28.56/9.84	   A^2 -> H(c, U1(c, d))
28.56/9.84	   A^2 -> H(c, U1(d, c))
28.56/9.84	   A^2 -> H(c, U1(b, e))
28.56/9.84	   A^2 -> H(c, U1(b, k))
28.56/9.84	   A^2 -> H(c, U1(e, c))
28.56/9.84	   A^2 -> H(c, U1(k, c))
28.56/9.84	   A^2 -> H(c, U1(c, e))
28.56/9.84	   A^2 -> H(c, U1(c, k))
28.56/9.84	   A^2 -> H(c, U1(e, e))
28.56/9.84	   A^2 -> H(c, U1(k, k))
28.56/9.84	   A^2 -> H(c, U1(k, d))
28.56/9.84	   A^2 -> H(c, U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, c), b)
28.56/9.84	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.84	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.84	   A^2 -> H(U1(e, c), e)
28.56/9.84	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.84	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.84	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.84	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.84	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.84	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.84	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.84	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.84	   A^2 -> H(U1(k, c), b)
28.56/9.84	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(k, c), c)
28.56/9.84	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.84	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.84	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, e), b)
28.56/9.84	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.84	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.84	   A^2 -> H(U1(c, e), c)
28.56/9.84	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.84	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.84	   A^2 -> H(U1(c, e), e)
28.56/9.84	
28.56/9.84	The TRS R consists of the following rules:
28.56/9.84	
28.56/9.84	   f(x) -> U1(x, x)
28.56/9.84	   U1(e, x) -> x
28.56/9.84	   a -> c
28.56/9.84	   a -> d
28.56/9.84	   b -> c
28.56/9.84	   b -> d
28.56/9.84	   d -> k
28.56/9.84	   c -> e
28.56/9.84	   c -> k
28.56/9.84	
28.56/9.84	Q is empty.
28.56/9.84	We have to consider all minimal (P,Q,R)-chains.
28.56/9.84	----------------------------------------
28.56/9.84	
28.56/9.84	(1521) TransformationProof (EQUIVALENT)
28.56/9.84	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.84	
28.56/9.84	   (A^2 -> H(U1(e, e), U1(k, d)),A^2 -> H(U1(e, e), U1(k, d)))
28.56/9.84	   (A^2 -> H(U1(k, e), U1(k, d)),A^2 -> H(U1(k, e), U1(k, d)))
28.56/9.84	   (A^2 -> H(U1(c, e), U1(k, k)),A^2 -> H(U1(c, e), U1(k, k)))
28.56/9.84	
28.56/9.84	
28.56/9.84	----------------------------------------
28.56/9.84	
28.56/9.84	(1522)
28.56/9.84	Obligation:
28.56/9.84	Q DP problem:
28.56/9.84	The TRS P consists of the following rules:
28.56/9.84	
28.56/9.84	   G(d, x, x) -> A^2
28.56/9.84	   A^2 -> H(f(c), f(c))
28.56/9.84	   H(x, x) -> G(x, x, f(k))
28.56/9.84	   A^2 -> H(f(d), f(d))
28.56/9.84	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.84	   A^2 -> H(f(e), f(e))
28.56/9.84	   A^2 -> H(f(k), f(k))
28.56/9.84	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.84	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.84	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.84	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(c, e), U1(d, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(c, c), b)
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(c, c), e)
28.56/9.84	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.84	   A^2 -> H(e, U1(c, b))
28.56/9.84	   A^2 -> H(e, U1(d, b))
28.56/9.84	   A^2 -> H(e, U1(b, c))
28.56/9.84	   A^2 -> H(e, U1(b, d))
28.56/9.84	   A^2 -> H(e, U1(c, c))
28.56/9.84	   A^2 -> H(e, f(e))
28.56/9.84	   A^2 -> H(e, f(k))
28.56/9.84	   A^2 -> H(e, U1(d, d))
28.56/9.84	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.84	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.84	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.84	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.84	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.84	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.84	   A^2 -> H(f(e), b)
28.56/9.84	   A^2 -> H(f(e), U1(e, d))
28.56/9.84	   A^2 -> H(f(e), U1(d, e))
28.56/9.84	   A^2 -> H(f(e), c)
28.56/9.84	   A^2 -> H(f(e), U1(e, k))
28.56/9.84	   A^2 -> H(f(e), U1(k, e))
28.56/9.84	   A^2 -> H(f(e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.84	   A^2 -> H(f(k), b)
28.56/9.84	   A^2 -> H(f(k), U1(e, d))
28.56/9.84	   A^2 -> H(f(k), U1(d, e))
28.56/9.84	   A^2 -> H(f(k), c)
28.56/9.84	   A^2 -> H(f(k), U1(e, k))
28.56/9.84	   A^2 -> H(f(k), U1(k, e))
28.56/9.84	   A^2 -> H(f(k), e)
28.56/9.84	   A^2 -> H(f(c), d)
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.84	   A^2 -> H(U1(k, k), f(e))
28.56/9.84	   A^2 -> H(U1(k, k), f(k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.84	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.84	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.84	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.84	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.84	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.84	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.84	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.84	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.84	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.84	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, d), b)
28.56/9.84	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.84	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.84	   A^2 -> H(U1(d, d), c)
28.56/9.84	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.84	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.84	   A^2 -> H(U1(d, d), e)
28.56/9.84	   A^2 -> H(f(d), d)
28.56/9.84	   A^2 -> H(f(d), k)
28.56/9.84	   A^2 -> H(U1(c, c), c)
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.84	   A^2 -> H(f(c), k)
28.56/9.84	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.84	   A^2 -> H(f(k), U1(k, k))
28.56/9.84	   A^2 -> H(f(e), e)
28.56/9.84	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.84	   A^2 -> H(d, U1(c, b))
28.56/9.84	   A^2 -> H(d, U1(d, b))
28.56/9.84	   A^2 -> H(d, U1(b, c))
28.56/9.84	   A^2 -> H(d, U1(b, d))
28.56/9.84	   A^2 -> H(d, U1(c, c))
28.56/9.84	   A^2 -> H(d, f(e))
28.56/9.84	   A^2 -> H(d, f(k))
28.56/9.84	   A^2 -> H(d, U1(d, d))
28.56/9.84	   A^2 -> H(a, U1(e, b))
28.56/9.84	   A^2 -> H(a, U1(k, b))
28.56/9.84	   A^2 -> H(a, U1(c, d))
28.56/9.84	   A^2 -> H(a, U1(d, c))
28.56/9.84	   A^2 -> H(a, U1(b, e))
28.56/9.84	   A^2 -> H(a, U1(b, k))
28.56/9.84	   A^2 -> H(a, U1(e, c))
28.56/9.84	   A^2 -> H(a, U1(k, c))
28.56/9.84	   A^2 -> H(a, U1(c, e))
28.56/9.84	   A^2 -> H(a, U1(c, k))
28.56/9.84	   A^2 -> H(a, U1(e, e))
28.56/9.84	   A^2 -> H(a, U1(k, k))
28.56/9.84	   A^2 -> H(a, U1(k, d))
28.56/9.84	   A^2 -> H(a, U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.84	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.84	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.84	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, a), b)
28.56/9.84	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.84	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.84	   A^2 -> H(U1(e, a), c)
28.56/9.84	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.84	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.84	   A^2 -> H(U1(e, a), e)
28.56/9.84	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, a), b)
28.56/9.84	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.84	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.84	   A^2 -> H(U1(k, a), c)
28.56/9.84	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.84	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.84	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, d), b)
28.56/9.84	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.84	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.84	   A^2 -> H(U1(c, d), c)
28.56/9.84	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.84	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.84	   A^2 -> H(U1(c, d), e)
28.56/9.84	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, a), d)
28.56/9.84	   A^2 -> H(U1(c, a), k)
28.56/9.84	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.84	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.84	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.84	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.84	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.84	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.84	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.84	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, c), b)
28.56/9.84	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(d, c), c)
28.56/9.84	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.84	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.84	   A^2 -> H(U1(d, c), e)
28.56/9.84	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, a), d)
28.56/9.84	   A^2 -> H(U1(d, a), k)
28.56/9.84	   A^2 -> H(U1(a, e), b)
28.56/9.84	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.84	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.84	   A^2 -> H(U1(a, e), c)
28.56/9.84	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.84	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.84	   A^2 -> H(U1(a, e), e)
28.56/9.84	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(a, k), b)
28.56/9.84	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.84	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.84	   A^2 -> H(U1(a, k), c)
28.56/9.84	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.84	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.84	   A^2 -> H(U1(a, k), e)
28.56/9.84	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(a, c), d)
28.56/9.84	   A^2 -> H(U1(a, c), k)
28.56/9.84	   A^2 -> H(U1(a, d), d)
28.56/9.84	   A^2 -> H(U1(a, d), k)
28.56/9.84	   A^2 -> H(k, U1(c, b))
28.56/9.84	   A^2 -> H(k, U1(d, b))
28.56/9.84	   A^2 -> H(k, U1(b, c))
28.56/9.84	   A^2 -> H(k, U1(b, d))
28.56/9.84	   A^2 -> H(k, U1(c, c))
28.56/9.84	   A^2 -> H(k, f(e))
28.56/9.84	   A^2 -> H(k, f(k))
28.56/9.84	   A^2 -> H(k, U1(d, d))
28.56/9.84	   A^2 -> H(c, U1(e, b))
28.56/9.84	   A^2 -> H(c, U1(k, b))
28.56/9.84	   A^2 -> H(c, U1(c, d))
28.56/9.84	   A^2 -> H(c, U1(d, c))
28.56/9.84	   A^2 -> H(c, U1(b, e))
28.56/9.84	   A^2 -> H(c, U1(b, k))
28.56/9.84	   A^2 -> H(c, U1(e, c))
28.56/9.84	   A^2 -> H(c, U1(k, c))
28.56/9.84	   A^2 -> H(c, U1(c, e))
28.56/9.84	   A^2 -> H(c, U1(c, k))
28.56/9.84	   A^2 -> H(c, U1(e, e))
28.56/9.84	   A^2 -> H(c, U1(k, k))
28.56/9.84	   A^2 -> H(c, U1(k, d))
28.56/9.84	   A^2 -> H(c, U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, c), b)
28.56/9.84	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.84	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.84	   A^2 -> H(U1(e, c), e)
28.56/9.84	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.84	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.84	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.84	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.84	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.84	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.84	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.84	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.84	   A^2 -> H(U1(k, c), b)
28.56/9.84	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(k, c), c)
28.56/9.84	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.84	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.84	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, e), b)
28.56/9.84	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.84	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.84	   A^2 -> H(U1(c, e), c)
28.56/9.84	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.84	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.84	   A^2 -> H(U1(c, e), e)
28.56/9.84	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.84	
28.56/9.84	The TRS R consists of the following rules:
28.56/9.84	
28.56/9.84	   f(x) -> U1(x, x)
28.56/9.84	   U1(e, x) -> x
28.56/9.84	   a -> c
28.56/9.84	   a -> d
28.56/9.84	   b -> c
28.56/9.84	   b -> d
28.56/9.84	   d -> k
28.56/9.84	   c -> e
28.56/9.84	   c -> k
28.56/9.84	
28.56/9.84	Q is empty.
28.56/9.84	We have to consider all minimal (P,Q,R)-chains.
28.56/9.84	----------------------------------------
28.56/9.84	
28.56/9.84	(1523) TransformationProof (EQUIVALENT)
28.56/9.84	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.84	
28.56/9.84	   (A^2 -> H(U1(e, e), U1(d, k)),A^2 -> H(U1(e, e), U1(d, k)))
28.56/9.84	   (A^2 -> H(U1(k, e), U1(d, k)),A^2 -> H(U1(k, e), U1(d, k)))
28.56/9.84	   (A^2 -> H(U1(c, e), U1(k, k)),A^2 -> H(U1(c, e), U1(k, k)))
28.56/9.84	
28.56/9.84	
28.56/9.84	----------------------------------------
28.56/9.84	
28.56/9.84	(1524)
28.56/9.84	Obligation:
28.56/9.84	Q DP problem:
28.56/9.84	The TRS P consists of the following rules:
28.56/9.84	
28.56/9.84	   G(d, x, x) -> A^2
28.56/9.84	   A^2 -> H(f(c), f(c))
28.56/9.84	   H(x, x) -> G(x, x, f(k))
28.56/9.84	   A^2 -> H(f(d), f(d))
28.56/9.84	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.84	   A^2 -> H(f(e), f(e))
28.56/9.84	   A^2 -> H(f(k), f(k))
28.56/9.84	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.84	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.84	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.84	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(c, c), b)
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(c, c), e)
28.56/9.84	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.84	   A^2 -> H(e, U1(c, b))
28.56/9.84	   A^2 -> H(e, U1(d, b))
28.56/9.84	   A^2 -> H(e, U1(b, c))
28.56/9.84	   A^2 -> H(e, U1(b, d))
28.56/9.84	   A^2 -> H(e, U1(c, c))
28.56/9.84	   A^2 -> H(e, f(e))
28.56/9.84	   A^2 -> H(e, f(k))
28.56/9.84	   A^2 -> H(e, U1(d, d))
28.56/9.84	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.84	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.84	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.84	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.84	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.84	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.84	   A^2 -> H(f(e), b)
28.56/9.84	   A^2 -> H(f(e), U1(e, d))
28.56/9.84	   A^2 -> H(f(e), U1(d, e))
28.56/9.84	   A^2 -> H(f(e), c)
28.56/9.84	   A^2 -> H(f(e), U1(e, k))
28.56/9.84	   A^2 -> H(f(e), U1(k, e))
28.56/9.84	   A^2 -> H(f(e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.84	   A^2 -> H(f(k), b)
28.56/9.84	   A^2 -> H(f(k), U1(e, d))
28.56/9.84	   A^2 -> H(f(k), U1(d, e))
28.56/9.84	   A^2 -> H(f(k), c)
28.56/9.84	   A^2 -> H(f(k), U1(e, k))
28.56/9.84	   A^2 -> H(f(k), U1(k, e))
28.56/9.84	   A^2 -> H(f(k), e)
28.56/9.84	   A^2 -> H(f(c), d)
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.84	   A^2 -> H(U1(k, k), f(e))
28.56/9.84	   A^2 -> H(U1(k, k), f(k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.84	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.84	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.84	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.84	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.84	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.84	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.84	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.84	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.84	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.84	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, d), b)
28.56/9.84	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.84	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.84	   A^2 -> H(U1(d, d), c)
28.56/9.84	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.84	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.84	   A^2 -> H(U1(d, d), e)
28.56/9.84	   A^2 -> H(f(d), d)
28.56/9.84	   A^2 -> H(f(d), k)
28.56/9.84	   A^2 -> H(U1(c, c), c)
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.84	   A^2 -> H(f(c), k)
28.56/9.84	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.84	   A^2 -> H(f(k), U1(k, k))
28.56/9.84	   A^2 -> H(f(e), e)
28.56/9.84	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.84	   A^2 -> H(d, U1(c, b))
28.56/9.84	   A^2 -> H(d, U1(d, b))
28.56/9.84	   A^2 -> H(d, U1(b, c))
28.56/9.84	   A^2 -> H(d, U1(b, d))
28.56/9.84	   A^2 -> H(d, U1(c, c))
28.56/9.84	   A^2 -> H(d, f(e))
28.56/9.84	   A^2 -> H(d, f(k))
28.56/9.84	   A^2 -> H(d, U1(d, d))
28.56/9.84	   A^2 -> H(a, U1(e, b))
28.56/9.84	   A^2 -> H(a, U1(k, b))
28.56/9.84	   A^2 -> H(a, U1(c, d))
28.56/9.84	   A^2 -> H(a, U1(d, c))
28.56/9.84	   A^2 -> H(a, U1(b, e))
28.56/9.84	   A^2 -> H(a, U1(b, k))
28.56/9.84	   A^2 -> H(a, U1(e, c))
28.56/9.84	   A^2 -> H(a, U1(k, c))
28.56/9.84	   A^2 -> H(a, U1(c, e))
28.56/9.84	   A^2 -> H(a, U1(c, k))
28.56/9.84	   A^2 -> H(a, U1(e, e))
28.56/9.84	   A^2 -> H(a, U1(k, k))
28.56/9.84	   A^2 -> H(a, U1(k, d))
28.56/9.84	   A^2 -> H(a, U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.84	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.84	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.84	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, a), b)
28.56/9.84	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.84	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.84	   A^2 -> H(U1(e, a), c)
28.56/9.84	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.84	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.84	   A^2 -> H(U1(e, a), e)
28.56/9.84	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, a), b)
28.56/9.84	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.84	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.84	   A^2 -> H(U1(k, a), c)
28.56/9.84	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.84	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.84	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, d), b)
28.56/9.84	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.84	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.84	   A^2 -> H(U1(c, d), c)
28.56/9.84	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.84	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.84	   A^2 -> H(U1(c, d), e)
28.56/9.84	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, a), d)
28.56/9.84	   A^2 -> H(U1(c, a), k)
28.56/9.84	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.84	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.84	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.84	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.84	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.84	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.84	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.84	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, c), b)
28.56/9.84	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(d, c), c)
28.56/9.84	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.84	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.84	   A^2 -> H(U1(d, c), e)
28.56/9.84	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, a), d)
28.56/9.84	   A^2 -> H(U1(d, a), k)
28.56/9.84	   A^2 -> H(U1(a, e), b)
28.56/9.84	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.84	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.84	   A^2 -> H(U1(a, e), c)
28.56/9.84	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.84	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.84	   A^2 -> H(U1(a, e), e)
28.56/9.84	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(a, k), b)
28.56/9.84	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.84	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.84	   A^2 -> H(U1(a, k), c)
28.56/9.84	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.84	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.84	   A^2 -> H(U1(a, k), e)
28.56/9.84	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(a, c), d)
28.56/9.84	   A^2 -> H(U1(a, c), k)
28.56/9.84	   A^2 -> H(U1(a, d), d)
28.56/9.84	   A^2 -> H(U1(a, d), k)
28.56/9.84	   A^2 -> H(k, U1(c, b))
28.56/9.84	   A^2 -> H(k, U1(d, b))
28.56/9.84	   A^2 -> H(k, U1(b, c))
28.56/9.84	   A^2 -> H(k, U1(b, d))
28.56/9.84	   A^2 -> H(k, U1(c, c))
28.56/9.84	   A^2 -> H(k, f(e))
28.56/9.84	   A^2 -> H(k, f(k))
28.56/9.84	   A^2 -> H(k, U1(d, d))
28.56/9.84	   A^2 -> H(c, U1(e, b))
28.56/9.84	   A^2 -> H(c, U1(k, b))
28.56/9.84	   A^2 -> H(c, U1(c, d))
28.56/9.84	   A^2 -> H(c, U1(d, c))
28.56/9.84	   A^2 -> H(c, U1(b, e))
28.56/9.84	   A^2 -> H(c, U1(b, k))
28.56/9.84	   A^2 -> H(c, U1(e, c))
28.56/9.84	   A^2 -> H(c, U1(k, c))
28.56/9.84	   A^2 -> H(c, U1(c, e))
28.56/9.84	   A^2 -> H(c, U1(c, k))
28.56/9.84	   A^2 -> H(c, U1(e, e))
28.56/9.84	   A^2 -> H(c, U1(k, k))
28.56/9.84	   A^2 -> H(c, U1(k, d))
28.56/9.84	   A^2 -> H(c, U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, c), b)
28.56/9.84	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.84	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.84	   A^2 -> H(U1(e, c), e)
28.56/9.84	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.84	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.84	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.84	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.84	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.84	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.84	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.84	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.84	   A^2 -> H(U1(k, c), b)
28.56/9.84	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(k, c), c)
28.56/9.84	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.84	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.84	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, e), b)
28.56/9.84	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.84	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.84	   A^2 -> H(U1(c, e), c)
28.56/9.84	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.84	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.84	   A^2 -> H(U1(c, e), e)
28.56/9.84	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.84	
28.56/9.84	The TRS R consists of the following rules:
28.56/9.84	
28.56/9.84	   f(x) -> U1(x, x)
28.56/9.84	   U1(e, x) -> x
28.56/9.84	   a -> c
28.56/9.84	   a -> d
28.56/9.84	   b -> c
28.56/9.84	   b -> d
28.56/9.84	   d -> k
28.56/9.84	   c -> e
28.56/9.84	   c -> k
28.56/9.84	
28.56/9.84	Q is empty.
28.56/9.84	We have to consider all minimal (P,Q,R)-chains.
28.56/9.84	----------------------------------------
28.56/9.84	
28.56/9.84	(1525) TransformationProof (EQUIVALENT)
28.56/9.84	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.84	
28.56/9.84	   (A^2 -> H(U1(e, k), U1(e, b)),A^2 -> H(U1(e, k), U1(e, b)))
28.56/9.84	   (A^2 -> H(U1(k, k), U1(e, b)),A^2 -> H(U1(k, k), U1(e, b)))
28.56/9.84	   (A^2 -> H(U1(c, k), b),A^2 -> H(U1(c, k), b))
28.56/9.84	   (A^2 -> H(U1(c, k), U1(e, c)),A^2 -> H(U1(c, k), U1(e, c)))
28.56/9.84	   (A^2 -> H(U1(c, k), U1(e, d)),A^2 -> H(U1(c, k), U1(e, d)))
28.56/9.84	
28.56/9.84	
28.56/9.84	----------------------------------------
28.56/9.84	
28.56/9.84	(1526)
28.56/9.84	Obligation:
28.56/9.84	Q DP problem:
28.56/9.84	The TRS P consists of the following rules:
28.56/9.84	
28.56/9.84	   G(d, x, x) -> A^2
28.56/9.84	   A^2 -> H(f(c), f(c))
28.56/9.84	   H(x, x) -> G(x, x, f(k))
28.56/9.84	   A^2 -> H(f(d), f(d))
28.56/9.84	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.84	   A^2 -> H(f(e), f(e))
28.56/9.84	   A^2 -> H(f(k), f(k))
28.56/9.84	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.84	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.84	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.84	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(c, c), b)
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(c, c), e)
28.56/9.84	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.84	   A^2 -> H(e, U1(c, b))
28.56/9.84	   A^2 -> H(e, U1(d, b))
28.56/9.84	   A^2 -> H(e, U1(b, c))
28.56/9.84	   A^2 -> H(e, U1(b, d))
28.56/9.84	   A^2 -> H(e, U1(c, c))
28.56/9.84	   A^2 -> H(e, f(e))
28.56/9.84	   A^2 -> H(e, f(k))
28.56/9.84	   A^2 -> H(e, U1(d, d))
28.56/9.84	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.84	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.84	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.84	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.84	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.84	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.84	   A^2 -> H(f(e), b)
28.56/9.84	   A^2 -> H(f(e), U1(e, d))
28.56/9.84	   A^2 -> H(f(e), U1(d, e))
28.56/9.84	   A^2 -> H(f(e), c)
28.56/9.84	   A^2 -> H(f(e), U1(e, k))
28.56/9.84	   A^2 -> H(f(e), U1(k, e))
28.56/9.84	   A^2 -> H(f(e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.84	   A^2 -> H(f(k), b)
28.56/9.84	   A^2 -> H(f(k), U1(e, d))
28.56/9.84	   A^2 -> H(f(k), U1(d, e))
28.56/9.84	   A^2 -> H(f(k), c)
28.56/9.84	   A^2 -> H(f(k), U1(e, k))
28.56/9.84	   A^2 -> H(f(k), U1(k, e))
28.56/9.84	   A^2 -> H(f(k), e)
28.56/9.84	   A^2 -> H(f(c), d)
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.84	   A^2 -> H(U1(k, k), f(e))
28.56/9.84	   A^2 -> H(U1(k, k), f(k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.84	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.84	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.84	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.84	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.84	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.84	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.84	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.84	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.84	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.84	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, d), b)
28.56/9.84	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.84	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.84	   A^2 -> H(U1(d, d), c)
28.56/9.84	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.84	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.84	   A^2 -> H(U1(d, d), e)
28.56/9.84	   A^2 -> H(f(d), d)
28.56/9.84	   A^2 -> H(f(d), k)
28.56/9.84	   A^2 -> H(U1(c, c), c)
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.84	   A^2 -> H(f(c), k)
28.56/9.84	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.84	   A^2 -> H(f(k), U1(k, k))
28.56/9.84	   A^2 -> H(f(e), e)
28.56/9.84	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.84	   A^2 -> H(d, U1(c, b))
28.56/9.84	   A^2 -> H(d, U1(d, b))
28.56/9.84	   A^2 -> H(d, U1(b, c))
28.56/9.84	   A^2 -> H(d, U1(b, d))
28.56/9.84	   A^2 -> H(d, U1(c, c))
28.56/9.84	   A^2 -> H(d, f(e))
28.56/9.84	   A^2 -> H(d, f(k))
28.56/9.84	   A^2 -> H(d, U1(d, d))
28.56/9.84	   A^2 -> H(a, U1(e, b))
28.56/9.84	   A^2 -> H(a, U1(k, b))
28.56/9.84	   A^2 -> H(a, U1(c, d))
28.56/9.84	   A^2 -> H(a, U1(d, c))
28.56/9.84	   A^2 -> H(a, U1(b, e))
28.56/9.84	   A^2 -> H(a, U1(b, k))
28.56/9.84	   A^2 -> H(a, U1(e, c))
28.56/9.84	   A^2 -> H(a, U1(k, c))
28.56/9.84	   A^2 -> H(a, U1(c, e))
28.56/9.84	   A^2 -> H(a, U1(c, k))
28.56/9.84	   A^2 -> H(a, U1(e, e))
28.56/9.84	   A^2 -> H(a, U1(k, k))
28.56/9.84	   A^2 -> H(a, U1(k, d))
28.56/9.84	   A^2 -> H(a, U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.84	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.84	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.84	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, a), b)
28.56/9.84	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.84	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.84	   A^2 -> H(U1(e, a), c)
28.56/9.84	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.84	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.84	   A^2 -> H(U1(e, a), e)
28.56/9.84	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, a), b)
28.56/9.84	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.84	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.84	   A^2 -> H(U1(k, a), c)
28.56/9.84	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.84	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.84	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, d), b)
28.56/9.84	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.84	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.84	   A^2 -> H(U1(c, d), c)
28.56/9.84	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.84	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.84	   A^2 -> H(U1(c, d), e)
28.56/9.84	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, a), d)
28.56/9.84	   A^2 -> H(U1(c, a), k)
28.56/9.84	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.84	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.84	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.84	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.84	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.84	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.84	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.84	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, c), b)
28.56/9.84	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(d, c), c)
28.56/9.84	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.84	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.84	   A^2 -> H(U1(d, c), e)
28.56/9.84	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, a), d)
28.56/9.84	   A^2 -> H(U1(d, a), k)
28.56/9.84	   A^2 -> H(U1(a, e), b)
28.56/9.84	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.84	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.84	   A^2 -> H(U1(a, e), c)
28.56/9.84	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.84	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.84	   A^2 -> H(U1(a, e), e)
28.56/9.84	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(a, k), b)
28.56/9.84	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.84	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.84	   A^2 -> H(U1(a, k), c)
28.56/9.84	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.84	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.84	   A^2 -> H(U1(a, k), e)
28.56/9.84	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(a, c), d)
28.56/9.84	   A^2 -> H(U1(a, c), k)
28.56/9.84	   A^2 -> H(U1(a, d), d)
28.56/9.84	   A^2 -> H(U1(a, d), k)
28.56/9.84	   A^2 -> H(k, U1(c, b))
28.56/9.84	   A^2 -> H(k, U1(d, b))
28.56/9.84	   A^2 -> H(k, U1(b, c))
28.56/9.84	   A^2 -> H(k, U1(b, d))
28.56/9.84	   A^2 -> H(k, U1(c, c))
28.56/9.84	   A^2 -> H(k, f(e))
28.56/9.84	   A^2 -> H(k, f(k))
28.56/9.84	   A^2 -> H(k, U1(d, d))
28.56/9.84	   A^2 -> H(c, U1(e, b))
28.56/9.84	   A^2 -> H(c, U1(k, b))
28.56/9.84	   A^2 -> H(c, U1(c, d))
28.56/9.84	   A^2 -> H(c, U1(d, c))
28.56/9.84	   A^2 -> H(c, U1(b, e))
28.56/9.84	   A^2 -> H(c, U1(b, k))
28.56/9.84	   A^2 -> H(c, U1(e, c))
28.56/9.84	   A^2 -> H(c, U1(k, c))
28.56/9.84	   A^2 -> H(c, U1(c, e))
28.56/9.84	   A^2 -> H(c, U1(c, k))
28.56/9.84	   A^2 -> H(c, U1(e, e))
28.56/9.84	   A^2 -> H(c, U1(k, k))
28.56/9.84	   A^2 -> H(c, U1(k, d))
28.56/9.84	   A^2 -> H(c, U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, c), b)
28.56/9.84	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.84	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.84	   A^2 -> H(U1(e, c), e)
28.56/9.84	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.84	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.84	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.84	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.84	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.84	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.84	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.84	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.84	   A^2 -> H(U1(k, c), b)
28.56/9.84	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(k, c), c)
28.56/9.84	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.84	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.84	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, e), b)
28.56/9.84	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.84	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.84	   A^2 -> H(U1(c, e), c)
28.56/9.84	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.84	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.84	   A^2 -> H(U1(c, e), e)
28.56/9.84	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, k), b)
28.56/9.84	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.84	
28.56/9.84	The TRS R consists of the following rules:
28.56/9.84	
28.56/9.84	   f(x) -> U1(x, x)
28.56/9.84	   U1(e, x) -> x
28.56/9.84	   a -> c
28.56/9.84	   a -> d
28.56/9.84	   b -> c
28.56/9.84	   b -> d
28.56/9.84	   d -> k
28.56/9.84	   c -> e
28.56/9.84	   c -> k
28.56/9.84	
28.56/9.84	Q is empty.
28.56/9.84	We have to consider all minimal (P,Q,R)-chains.
28.56/9.84	----------------------------------------
28.56/9.84	
28.56/9.84	(1527) TransformationProof (EQUIVALENT)
28.56/9.84	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.84	
28.56/9.84	   (A^2 -> H(U1(e, k), U1(k, b)),A^2 -> H(U1(e, k), U1(k, b)))
28.56/9.84	   (A^2 -> H(U1(k, k), U1(k, b)),A^2 -> H(U1(k, k), U1(k, b)))
28.56/9.84	   (A^2 -> H(U1(c, k), U1(k, c)),A^2 -> H(U1(c, k), U1(k, c)))
28.56/9.84	   (A^2 -> H(U1(c, k), U1(k, d)),A^2 -> H(U1(c, k), U1(k, d)))
28.56/9.84	
28.56/9.84	
28.56/9.84	----------------------------------------
28.56/9.84	
28.56/9.84	(1528)
28.56/9.84	Obligation:
28.56/9.84	Q DP problem:
28.56/9.84	The TRS P consists of the following rules:
28.56/9.84	
28.56/9.84	   G(d, x, x) -> A^2
28.56/9.84	   A^2 -> H(f(c), f(c))
28.56/9.84	   H(x, x) -> G(x, x, f(k))
28.56/9.84	   A^2 -> H(f(d), f(d))
28.56/9.84	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.84	   A^2 -> H(f(e), f(e))
28.56/9.84	   A^2 -> H(f(k), f(k))
28.56/9.84	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.84	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.84	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.84	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(c, c), b)
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(c, c), e)
28.56/9.84	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.84	   A^2 -> H(e, U1(c, b))
28.56/9.84	   A^2 -> H(e, U1(d, b))
28.56/9.84	   A^2 -> H(e, U1(b, c))
28.56/9.84	   A^2 -> H(e, U1(b, d))
28.56/9.84	   A^2 -> H(e, U1(c, c))
28.56/9.84	   A^2 -> H(e, f(e))
28.56/9.84	   A^2 -> H(e, f(k))
28.56/9.84	   A^2 -> H(e, U1(d, d))
28.56/9.84	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.84	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.84	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.84	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.84	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.84	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.84	   A^2 -> H(f(e), b)
28.56/9.84	   A^2 -> H(f(e), U1(e, d))
28.56/9.84	   A^2 -> H(f(e), U1(d, e))
28.56/9.84	   A^2 -> H(f(e), c)
28.56/9.84	   A^2 -> H(f(e), U1(e, k))
28.56/9.84	   A^2 -> H(f(e), U1(k, e))
28.56/9.84	   A^2 -> H(f(e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.84	   A^2 -> H(f(k), b)
28.56/9.84	   A^2 -> H(f(k), U1(e, d))
28.56/9.84	   A^2 -> H(f(k), U1(d, e))
28.56/9.84	   A^2 -> H(f(k), c)
28.56/9.84	   A^2 -> H(f(k), U1(e, k))
28.56/9.84	   A^2 -> H(f(k), U1(k, e))
28.56/9.84	   A^2 -> H(f(k), e)
28.56/9.84	   A^2 -> H(f(c), d)
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.84	   A^2 -> H(U1(k, k), f(e))
28.56/9.84	   A^2 -> H(U1(k, k), f(k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.84	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.84	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.84	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.84	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.84	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.84	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.84	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.84	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.84	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.84	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, d), b)
28.56/9.84	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.84	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.84	   A^2 -> H(U1(d, d), c)
28.56/9.84	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.84	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.84	   A^2 -> H(U1(d, d), e)
28.56/9.84	   A^2 -> H(f(d), d)
28.56/9.84	   A^2 -> H(f(d), k)
28.56/9.84	   A^2 -> H(U1(c, c), c)
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.84	   A^2 -> H(f(c), k)
28.56/9.84	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.84	   A^2 -> H(f(k), U1(k, k))
28.56/9.84	   A^2 -> H(f(e), e)
28.56/9.84	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.84	   A^2 -> H(d, U1(c, b))
28.56/9.84	   A^2 -> H(d, U1(d, b))
28.56/9.84	   A^2 -> H(d, U1(b, c))
28.56/9.84	   A^2 -> H(d, U1(b, d))
28.56/9.84	   A^2 -> H(d, U1(c, c))
28.56/9.84	   A^2 -> H(d, f(e))
28.56/9.84	   A^2 -> H(d, f(k))
28.56/9.84	   A^2 -> H(d, U1(d, d))
28.56/9.84	   A^2 -> H(a, U1(e, b))
28.56/9.84	   A^2 -> H(a, U1(k, b))
28.56/9.84	   A^2 -> H(a, U1(c, d))
28.56/9.84	   A^2 -> H(a, U1(d, c))
28.56/9.84	   A^2 -> H(a, U1(b, e))
28.56/9.84	   A^2 -> H(a, U1(b, k))
28.56/9.84	   A^2 -> H(a, U1(e, c))
28.56/9.84	   A^2 -> H(a, U1(k, c))
28.56/9.84	   A^2 -> H(a, U1(c, e))
28.56/9.84	   A^2 -> H(a, U1(c, k))
28.56/9.84	   A^2 -> H(a, U1(e, e))
28.56/9.84	   A^2 -> H(a, U1(k, k))
28.56/9.84	   A^2 -> H(a, U1(k, d))
28.56/9.84	   A^2 -> H(a, U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.84	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.84	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.84	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, a), b)
28.56/9.84	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.84	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.84	   A^2 -> H(U1(e, a), c)
28.56/9.84	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.84	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.84	   A^2 -> H(U1(e, a), e)
28.56/9.84	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, a), b)
28.56/9.84	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.84	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.84	   A^2 -> H(U1(k, a), c)
28.56/9.84	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.84	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.84	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, d), b)
28.56/9.84	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.84	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.84	   A^2 -> H(U1(c, d), c)
28.56/9.84	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.84	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.84	   A^2 -> H(U1(c, d), e)
28.56/9.84	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, a), d)
28.56/9.84	   A^2 -> H(U1(c, a), k)
28.56/9.84	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.84	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.84	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.84	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.84	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.84	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.84	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.84	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, c), b)
28.56/9.84	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(d, c), c)
28.56/9.84	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.84	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.84	   A^2 -> H(U1(d, c), e)
28.56/9.84	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, a), d)
28.56/9.84	   A^2 -> H(U1(d, a), k)
28.56/9.84	   A^2 -> H(U1(a, e), b)
28.56/9.84	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.84	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.84	   A^2 -> H(U1(a, e), c)
28.56/9.84	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.84	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.84	   A^2 -> H(U1(a, e), e)
28.56/9.84	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(a, k), b)
28.56/9.84	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.84	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.84	   A^2 -> H(U1(a, k), c)
28.56/9.84	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.84	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.84	   A^2 -> H(U1(a, k), e)
28.56/9.84	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(a, c), d)
28.56/9.84	   A^2 -> H(U1(a, c), k)
28.56/9.84	   A^2 -> H(U1(a, d), d)
28.56/9.84	   A^2 -> H(U1(a, d), k)
28.56/9.84	   A^2 -> H(k, U1(c, b))
28.56/9.84	   A^2 -> H(k, U1(d, b))
28.56/9.84	   A^2 -> H(k, U1(b, c))
28.56/9.84	   A^2 -> H(k, U1(b, d))
28.56/9.84	   A^2 -> H(k, U1(c, c))
28.56/9.84	   A^2 -> H(k, f(e))
28.56/9.84	   A^2 -> H(k, f(k))
28.56/9.84	   A^2 -> H(k, U1(d, d))
28.56/9.84	   A^2 -> H(c, U1(e, b))
28.56/9.84	   A^2 -> H(c, U1(k, b))
28.56/9.84	   A^2 -> H(c, U1(c, d))
28.56/9.84	   A^2 -> H(c, U1(d, c))
28.56/9.84	   A^2 -> H(c, U1(b, e))
28.56/9.84	   A^2 -> H(c, U1(b, k))
28.56/9.84	   A^2 -> H(c, U1(e, c))
28.56/9.84	   A^2 -> H(c, U1(k, c))
28.56/9.84	   A^2 -> H(c, U1(c, e))
28.56/9.84	   A^2 -> H(c, U1(c, k))
28.56/9.84	   A^2 -> H(c, U1(e, e))
28.56/9.84	   A^2 -> H(c, U1(k, k))
28.56/9.84	   A^2 -> H(c, U1(k, d))
28.56/9.84	   A^2 -> H(c, U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, c), b)
28.56/9.84	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.84	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.84	   A^2 -> H(U1(e, c), e)
28.56/9.84	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.84	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.84	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.84	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.84	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.84	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.84	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.84	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.84	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.84	   A^2 -> H(U1(k, c), b)
28.56/9.84	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(k, c), c)
28.56/9.84	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.84	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.84	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, e), b)
28.56/9.84	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.84	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.84	   A^2 -> H(U1(c, e), c)
28.56/9.84	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.84	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.84	   A^2 -> H(U1(c, e), e)
28.56/9.84	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, k), b)
28.56/9.84	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.84	
28.56/9.84	The TRS R consists of the following rules:
28.56/9.84	
28.56/9.84	   f(x) -> U1(x, x)
28.56/9.84	   U1(e, x) -> x
28.56/9.84	   a -> c
28.56/9.84	   a -> d
28.56/9.84	   b -> c
28.56/9.84	   b -> d
28.56/9.84	   d -> k
28.56/9.84	   c -> e
28.56/9.84	   c -> k
28.56/9.84	
28.56/9.84	Q is empty.
28.56/9.84	We have to consider all minimal (P,Q,R)-chains.
28.56/9.84	----------------------------------------
28.56/9.84	
28.56/9.84	(1529) TransformationProof (EQUIVALENT)
28.56/9.84	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.84	
28.56/9.84	   (A^2 -> H(U1(e, k), U1(c, d)),A^2 -> H(U1(e, k), U1(c, d)))
28.56/9.84	   (A^2 -> H(U1(k, k), U1(c, d)),A^2 -> H(U1(k, k), U1(c, d)))
28.56/9.84	   (A^2 -> H(U1(c, k), U1(e, d)),A^2 -> H(U1(c, k), U1(e, d)))
28.56/9.84	   (A^2 -> H(U1(c, k), U1(k, d)),A^2 -> H(U1(c, k), U1(k, d)))
28.56/9.84	   (A^2 -> H(U1(c, k), U1(c, k)),A^2 -> H(U1(c, k), U1(c, k)))
28.56/9.84	
28.56/9.84	
28.56/9.84	----------------------------------------
28.56/9.84	
28.56/9.84	(1530)
28.56/9.84	Obligation:
28.56/9.84	Q DP problem:
28.56/9.84	The TRS P consists of the following rules:
28.56/9.84	
28.56/9.84	   G(d, x, x) -> A^2
28.56/9.84	   A^2 -> H(f(c), f(c))
28.56/9.84	   H(x, x) -> G(x, x, f(k))
28.56/9.84	   A^2 -> H(f(d), f(d))
28.56/9.84	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.84	   A^2 -> H(f(e), f(e))
28.56/9.84	   A^2 -> H(f(k), f(k))
28.56/9.84	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.84	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.84	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.84	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(c, c), b)
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.84	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.84	   A^2 -> H(U1(c, c), e)
28.56/9.84	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.84	   A^2 -> H(e, U1(c, b))
28.56/9.84	   A^2 -> H(e, U1(d, b))
28.56/9.84	   A^2 -> H(e, U1(b, c))
28.56/9.84	   A^2 -> H(e, U1(b, d))
28.56/9.84	   A^2 -> H(e, U1(c, c))
28.56/9.84	   A^2 -> H(e, f(e))
28.56/9.84	   A^2 -> H(e, f(k))
28.56/9.84	   A^2 -> H(e, U1(d, d))
28.56/9.84	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.84	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.84	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.84	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.84	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.84	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.84	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.84	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.84	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.84	   A^2 -> H(f(e), b)
28.56/9.84	   A^2 -> H(f(e), U1(e, d))
28.56/9.84	   A^2 -> H(f(e), U1(d, e))
28.56/9.84	   A^2 -> H(f(e), c)
28.56/9.84	   A^2 -> H(f(e), U1(e, k))
28.56/9.84	   A^2 -> H(f(e), U1(k, e))
28.56/9.84	   A^2 -> H(f(e), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.84	   A^2 -> H(f(k), b)
28.56/9.84	   A^2 -> H(f(k), U1(e, d))
28.56/9.84	   A^2 -> H(f(k), U1(d, e))
28.56/9.84	   A^2 -> H(f(k), c)
28.56/9.84	   A^2 -> H(f(k), U1(e, k))
28.56/9.84	   A^2 -> H(f(k), U1(k, e))
28.56/9.84	   A^2 -> H(f(k), e)
28.56/9.84	   A^2 -> H(f(c), d)
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.84	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.84	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.84	   A^2 -> H(U1(k, k), f(e))
28.56/9.84	   A^2 -> H(U1(k, k), f(k))
28.56/9.84	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.84	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.84	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.84	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.84	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.84	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.84	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.84	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.84	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.84	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.84	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.84	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.84	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.84	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.84	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.84	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.84	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.84	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.84	   A^2 -> H(U1(d, d), b)
28.56/9.84	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.84	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.84	   A^2 -> H(U1(d, d), c)
28.56/9.84	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.84	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.84	   A^2 -> H(U1(d, d), e)
28.56/9.84	   A^2 -> H(f(d), d)
28.56/9.84	   A^2 -> H(f(d), k)
28.56/9.84	   A^2 -> H(U1(c, c), c)
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.84	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.84	   A^2 -> H(f(c), k)
28.56/9.84	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.84	   A^2 -> H(f(k), U1(k, k))
28.56/9.84	   A^2 -> H(f(e), e)
28.56/9.84	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.84	   A^2 -> H(d, U1(c, b))
28.56/9.84	   A^2 -> H(d, U1(d, b))
28.56/9.84	   A^2 -> H(d, U1(b, c))
28.56/9.84	   A^2 -> H(d, U1(b, d))
28.56/9.84	   A^2 -> H(d, U1(c, c))
28.56/9.84	   A^2 -> H(d, f(e))
28.56/9.84	   A^2 -> H(d, f(k))
28.56/9.84	   A^2 -> H(d, U1(d, d))
28.56/9.84	   A^2 -> H(a, U1(e, b))
28.56/9.84	   A^2 -> H(a, U1(k, b))
28.56/9.84	   A^2 -> H(a, U1(c, d))
28.56/9.84	   A^2 -> H(a, U1(d, c))
28.56/9.84	   A^2 -> H(a, U1(b, e))
28.56/9.84	   A^2 -> H(a, U1(b, k))
28.56/9.84	   A^2 -> H(a, U1(e, c))
28.56/9.84	   A^2 -> H(a, U1(k, c))
28.56/9.84	   A^2 -> H(a, U1(c, e))
28.56/9.84	   A^2 -> H(a, U1(c, k))
28.56/9.84	   A^2 -> H(a, U1(e, e))
28.56/9.84	   A^2 -> H(a, U1(k, k))
28.56/9.84	   A^2 -> H(a, U1(k, d))
28.56/9.84	   A^2 -> H(a, U1(d, k))
28.56/9.84	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.84	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.84	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, a), b)
28.56/9.85	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.85	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.85	   A^2 -> H(U1(e, a), c)
28.56/9.85	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.85	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.85	   A^2 -> H(U1(e, a), e)
28.56/9.85	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, a), b)
28.56/9.85	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.85	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.85	   A^2 -> H(U1(k, a), c)
28.56/9.85	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.85	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.85	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, d), b)
28.56/9.85	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, d), c)
28.56/9.85	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.85	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.85	   A^2 -> H(U1(c, d), e)
28.56/9.85	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, a), d)
28.56/9.85	   A^2 -> H(U1(c, a), k)
28.56/9.85	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.85	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.85	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.85	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.85	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.85	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.85	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.85	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.85	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.85	   A^2 -> H(U1(d, c), b)
28.56/9.85	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(d, c), c)
28.56/9.85	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.85	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.85	   A^2 -> H(U1(d, c), e)
28.56/9.85	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.85	   A^2 -> H(U1(d, a), d)
28.56/9.85	   A^2 -> H(U1(d, a), k)
28.56/9.85	   A^2 -> H(U1(a, e), b)
28.56/9.85	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.85	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.85	   A^2 -> H(U1(a, e), c)
28.56/9.85	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.85	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.85	   A^2 -> H(U1(a, e), e)
28.56/9.85	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(a, k), b)
28.56/9.85	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.85	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.85	   A^2 -> H(U1(a, k), c)
28.56/9.85	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.85	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.85	   A^2 -> H(U1(a, k), e)
28.56/9.85	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(a, c), d)
28.56/9.85	   A^2 -> H(U1(a, c), k)
28.56/9.85	   A^2 -> H(U1(a, d), d)
28.56/9.85	   A^2 -> H(U1(a, d), k)
28.56/9.85	   A^2 -> H(k, U1(c, b))
28.56/9.85	   A^2 -> H(k, U1(d, b))
28.56/9.85	   A^2 -> H(k, U1(b, c))
28.56/9.85	   A^2 -> H(k, U1(b, d))
28.56/9.85	   A^2 -> H(k, U1(c, c))
28.56/9.85	   A^2 -> H(k, f(e))
28.56/9.85	   A^2 -> H(k, f(k))
28.56/9.85	   A^2 -> H(k, U1(d, d))
28.56/9.85	   A^2 -> H(c, U1(e, b))
28.56/9.85	   A^2 -> H(c, U1(k, b))
28.56/9.85	   A^2 -> H(c, U1(c, d))
28.56/9.85	   A^2 -> H(c, U1(d, c))
28.56/9.85	   A^2 -> H(c, U1(b, e))
28.56/9.85	   A^2 -> H(c, U1(b, k))
28.56/9.85	   A^2 -> H(c, U1(e, c))
28.56/9.85	   A^2 -> H(c, U1(k, c))
28.56/9.85	   A^2 -> H(c, U1(c, e))
28.56/9.85	   A^2 -> H(c, U1(c, k))
28.56/9.85	   A^2 -> H(c, U1(e, e))
28.56/9.85	   A^2 -> H(c, U1(k, k))
28.56/9.85	   A^2 -> H(c, U1(k, d))
28.56/9.85	   A^2 -> H(c, U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.85	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, c), b)
28.56/9.85	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.85	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.85	   A^2 -> H(U1(e, c), e)
28.56/9.85	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.85	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.85	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.85	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.85	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.85	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.85	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.85	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.85	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.85	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.85	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.85	   A^2 -> H(U1(k, c), b)
28.56/9.85	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(k, c), c)
28.56/9.85	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.85	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.85	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, e), b)
28.56/9.85	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, e), c)
28.56/9.85	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.85	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.85	   A^2 -> H(U1(c, e), e)
28.56/9.85	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, k), b)
28.56/9.85	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.85	
28.56/9.85	The TRS R consists of the following rules:
28.56/9.85	
28.56/9.85	   f(x) -> U1(x, x)
28.56/9.85	   U1(e, x) -> x
28.56/9.85	   a -> c
28.56/9.85	   a -> d
28.56/9.85	   b -> c
28.56/9.85	   b -> d
28.56/9.85	   d -> k
28.56/9.85	   c -> e
28.56/9.85	   c -> k
28.56/9.85	
28.56/9.85	Q is empty.
28.56/9.85	We have to consider all minimal (P,Q,R)-chains.
28.56/9.85	----------------------------------------
28.56/9.85	
28.56/9.85	(1531) TransformationProof (EQUIVALENT)
28.56/9.85	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.85	
28.56/9.85	   (A^2 -> H(U1(e, k), U1(d, c)),A^2 -> H(U1(e, k), U1(d, c)))
28.56/9.85	   (A^2 -> H(U1(k, k), U1(d, c)),A^2 -> H(U1(k, k), U1(d, c)))
28.56/9.85	   (A^2 -> H(U1(c, k), U1(k, c)),A^2 -> H(U1(c, k), U1(k, c)))
28.56/9.85	   (A^2 -> H(U1(c, k), U1(d, e)),A^2 -> H(U1(c, k), U1(d, e)))
28.56/9.85	   (A^2 -> H(U1(c, k), U1(d, k)),A^2 -> H(U1(c, k), U1(d, k)))
28.56/9.85	
28.56/9.85	
28.56/9.85	----------------------------------------
28.56/9.85	
28.56/9.85	(1532)
28.56/9.85	Obligation:
28.56/9.85	Q DP problem:
28.56/9.85	The TRS P consists of the following rules:
28.56/9.85	
28.56/9.85	   G(d, x, x) -> A^2
28.56/9.85	   A^2 -> H(f(c), f(c))
28.56/9.85	   H(x, x) -> G(x, x, f(k))
28.56/9.85	   A^2 -> H(f(d), f(d))
28.56/9.85	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.85	   A^2 -> H(f(e), f(e))
28.56/9.85	   A^2 -> H(f(k), f(k))
28.56/9.85	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.85	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.85	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(c, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.85	   A^2 -> H(U1(c, c), b)
28.56/9.85	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, c), e)
28.56/9.85	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.85	   A^2 -> H(e, U1(c, b))
28.56/9.85	   A^2 -> H(e, U1(d, b))
28.56/9.85	   A^2 -> H(e, U1(b, c))
28.56/9.85	   A^2 -> H(e, U1(b, d))
28.56/9.85	   A^2 -> H(e, U1(c, c))
28.56/9.85	   A^2 -> H(e, f(e))
28.56/9.85	   A^2 -> H(e, f(k))
28.56/9.85	   A^2 -> H(e, U1(d, d))
28.56/9.85	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.85	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.85	   A^2 -> H(f(e), b)
28.56/9.85	   A^2 -> H(f(e), U1(e, d))
28.56/9.85	   A^2 -> H(f(e), U1(d, e))
28.56/9.85	   A^2 -> H(f(e), c)
28.56/9.85	   A^2 -> H(f(e), U1(e, k))
28.56/9.85	   A^2 -> H(f(e), U1(k, e))
28.56/9.85	   A^2 -> H(f(e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.85	   A^2 -> H(f(k), b)
28.56/9.85	   A^2 -> H(f(k), U1(e, d))
28.56/9.85	   A^2 -> H(f(k), U1(d, e))
28.56/9.85	   A^2 -> H(f(k), c)
28.56/9.85	   A^2 -> H(f(k), U1(e, k))
28.56/9.85	   A^2 -> H(f(k), U1(k, e))
28.56/9.85	   A^2 -> H(f(k), e)
28.56/9.85	   A^2 -> H(f(c), d)
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.85	   A^2 -> H(U1(k, k), f(e))
28.56/9.85	   A^2 -> H(U1(k, k), f(k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.85	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.85	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.85	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.85	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.85	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.85	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.85	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.85	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.85	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.85	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.85	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.85	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.85	   A^2 -> H(U1(d, d), b)
28.56/9.85	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.85	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.85	   A^2 -> H(U1(d, d), c)
28.56/9.85	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.85	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.85	   A^2 -> H(U1(d, d), e)
28.56/9.85	   A^2 -> H(f(d), d)
28.56/9.85	   A^2 -> H(f(d), k)
28.56/9.85	   A^2 -> H(U1(c, c), c)
28.56/9.85	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.85	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.85	   A^2 -> H(f(c), k)
28.56/9.85	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.85	   A^2 -> H(f(k), U1(k, k))
28.56/9.85	   A^2 -> H(f(e), e)
28.56/9.85	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.85	   A^2 -> H(d, U1(c, b))
28.56/9.85	   A^2 -> H(d, U1(d, b))
28.56/9.85	   A^2 -> H(d, U1(b, c))
28.56/9.85	   A^2 -> H(d, U1(b, d))
28.56/9.85	   A^2 -> H(d, U1(c, c))
28.56/9.85	   A^2 -> H(d, f(e))
28.56/9.85	   A^2 -> H(d, f(k))
28.56/9.85	   A^2 -> H(d, U1(d, d))
28.56/9.85	   A^2 -> H(a, U1(e, b))
28.56/9.85	   A^2 -> H(a, U1(k, b))
28.56/9.85	   A^2 -> H(a, U1(c, d))
28.56/9.85	   A^2 -> H(a, U1(d, c))
28.56/9.85	   A^2 -> H(a, U1(b, e))
28.56/9.85	   A^2 -> H(a, U1(b, k))
28.56/9.85	   A^2 -> H(a, U1(e, c))
28.56/9.85	   A^2 -> H(a, U1(k, c))
28.56/9.85	   A^2 -> H(a, U1(c, e))
28.56/9.85	   A^2 -> H(a, U1(c, k))
28.56/9.85	   A^2 -> H(a, U1(e, e))
28.56/9.85	   A^2 -> H(a, U1(k, k))
28.56/9.85	   A^2 -> H(a, U1(k, d))
28.56/9.85	   A^2 -> H(a, U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, a), b)
28.56/9.85	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.85	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.85	   A^2 -> H(U1(e, a), c)
28.56/9.85	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.85	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.85	   A^2 -> H(U1(e, a), e)
28.56/9.85	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, a), b)
28.56/9.85	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.85	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.85	   A^2 -> H(U1(k, a), c)
28.56/9.85	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.85	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.85	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, d), b)
28.56/9.85	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, d), c)
28.56/9.85	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.85	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.85	   A^2 -> H(U1(c, d), e)
28.56/9.85	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, a), d)
28.56/9.85	   A^2 -> H(U1(c, a), k)
28.56/9.85	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.85	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.85	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.85	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.85	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.85	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.85	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.85	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.85	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.85	   A^2 -> H(U1(d, c), b)
28.56/9.85	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(d, c), c)
28.56/9.85	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.85	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.85	   A^2 -> H(U1(d, c), e)
28.56/9.85	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.85	   A^2 -> H(U1(d, a), d)
28.56/9.85	   A^2 -> H(U1(d, a), k)
28.56/9.85	   A^2 -> H(U1(a, e), b)
28.56/9.85	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.85	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.85	   A^2 -> H(U1(a, e), c)
28.56/9.85	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.85	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.85	   A^2 -> H(U1(a, e), e)
28.56/9.85	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(a, k), b)
28.56/9.85	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.85	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.85	   A^2 -> H(U1(a, k), c)
28.56/9.85	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.85	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.85	   A^2 -> H(U1(a, k), e)
28.56/9.85	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(a, c), d)
28.56/9.85	   A^2 -> H(U1(a, c), k)
28.56/9.85	   A^2 -> H(U1(a, d), d)
28.56/9.85	   A^2 -> H(U1(a, d), k)
28.56/9.85	   A^2 -> H(k, U1(c, b))
28.56/9.85	   A^2 -> H(k, U1(d, b))
28.56/9.85	   A^2 -> H(k, U1(b, c))
28.56/9.85	   A^2 -> H(k, U1(b, d))
28.56/9.85	   A^2 -> H(k, U1(c, c))
28.56/9.85	   A^2 -> H(k, f(e))
28.56/9.85	   A^2 -> H(k, f(k))
28.56/9.85	   A^2 -> H(k, U1(d, d))
28.56/9.85	   A^2 -> H(c, U1(e, b))
28.56/9.85	   A^2 -> H(c, U1(k, b))
28.56/9.85	   A^2 -> H(c, U1(c, d))
28.56/9.85	   A^2 -> H(c, U1(d, c))
28.56/9.85	   A^2 -> H(c, U1(b, e))
28.56/9.85	   A^2 -> H(c, U1(b, k))
28.56/9.85	   A^2 -> H(c, U1(e, c))
28.56/9.85	   A^2 -> H(c, U1(k, c))
28.56/9.85	   A^2 -> H(c, U1(c, e))
28.56/9.85	   A^2 -> H(c, U1(c, k))
28.56/9.85	   A^2 -> H(c, U1(e, e))
28.56/9.85	   A^2 -> H(c, U1(k, k))
28.56/9.85	   A^2 -> H(c, U1(k, d))
28.56/9.85	   A^2 -> H(c, U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.85	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, c), b)
28.56/9.85	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.85	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.85	   A^2 -> H(U1(e, c), e)
28.56/9.85	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.85	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.85	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.85	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.85	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.85	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.85	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.85	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.85	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.85	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.85	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.85	   A^2 -> H(U1(k, c), b)
28.56/9.85	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(k, c), c)
28.56/9.85	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.85	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.85	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, e), b)
28.56/9.85	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, e), c)
28.56/9.85	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.85	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.85	   A^2 -> H(U1(c, e), e)
28.56/9.85	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, k), b)
28.56/9.85	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.85	
28.56/9.85	The TRS R consists of the following rules:
28.56/9.85	
28.56/9.85	   f(x) -> U1(x, x)
28.56/9.85	   U1(e, x) -> x
28.56/9.85	   a -> c
28.56/9.85	   a -> d
28.56/9.85	   b -> c
28.56/9.85	   b -> d
28.56/9.85	   d -> k
28.56/9.85	   c -> e
28.56/9.85	   c -> k
28.56/9.85	
28.56/9.85	Q is empty.
28.56/9.85	We have to consider all minimal (P,Q,R)-chains.
28.56/9.85	----------------------------------------
28.56/9.85	
28.56/9.85	(1533) TransformationProof (EQUIVALENT)
28.56/9.85	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.85	
28.56/9.85	   (A^2 -> H(U1(e, k), U1(b, e)),A^2 -> H(U1(e, k), U1(b, e)))
28.56/9.85	   (A^2 -> H(U1(k, k), U1(b, e)),A^2 -> H(U1(k, k), U1(b, e)))
28.56/9.85	   (A^2 -> H(U1(c, k), U1(c, e)),A^2 -> H(U1(c, k), U1(c, e)))
28.56/9.85	   (A^2 -> H(U1(c, k), U1(d, e)),A^2 -> H(U1(c, k), U1(d, e)))
28.56/9.85	
28.56/9.85	
28.56/9.85	----------------------------------------
28.56/9.85	
28.56/9.85	(1534)
28.56/9.85	Obligation:
28.56/9.85	Q DP problem:
28.56/9.85	The TRS P consists of the following rules:
28.56/9.85	
28.56/9.85	   G(d, x, x) -> A^2
28.56/9.85	   A^2 -> H(f(c), f(c))
28.56/9.85	   H(x, x) -> G(x, x, f(k))
28.56/9.85	   A^2 -> H(f(d), f(d))
28.56/9.85	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.85	   A^2 -> H(f(e), f(e))
28.56/9.85	   A^2 -> H(f(k), f(k))
28.56/9.85	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.85	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.85	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(c, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.85	   A^2 -> H(U1(c, c), b)
28.56/9.85	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, c), e)
28.56/9.85	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.85	   A^2 -> H(e, U1(c, b))
28.56/9.85	   A^2 -> H(e, U1(d, b))
28.56/9.85	   A^2 -> H(e, U1(b, c))
28.56/9.85	   A^2 -> H(e, U1(b, d))
28.56/9.85	   A^2 -> H(e, U1(c, c))
28.56/9.85	   A^2 -> H(e, f(e))
28.56/9.85	   A^2 -> H(e, f(k))
28.56/9.85	   A^2 -> H(e, U1(d, d))
28.56/9.85	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.85	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.85	   A^2 -> H(f(e), b)
28.56/9.85	   A^2 -> H(f(e), U1(e, d))
28.56/9.85	   A^2 -> H(f(e), U1(d, e))
28.56/9.85	   A^2 -> H(f(e), c)
28.56/9.85	   A^2 -> H(f(e), U1(e, k))
28.56/9.85	   A^2 -> H(f(e), U1(k, e))
28.56/9.85	   A^2 -> H(f(e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.85	   A^2 -> H(f(k), b)
28.56/9.85	   A^2 -> H(f(k), U1(e, d))
28.56/9.85	   A^2 -> H(f(k), U1(d, e))
28.56/9.85	   A^2 -> H(f(k), c)
28.56/9.85	   A^2 -> H(f(k), U1(e, k))
28.56/9.85	   A^2 -> H(f(k), U1(k, e))
28.56/9.85	   A^2 -> H(f(k), e)
28.56/9.85	   A^2 -> H(f(c), d)
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.85	   A^2 -> H(U1(k, k), f(e))
28.56/9.85	   A^2 -> H(U1(k, k), f(k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.85	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.85	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.85	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.85	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.85	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.85	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.85	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.85	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.85	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.85	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.85	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.85	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.85	   A^2 -> H(U1(d, d), b)
28.56/9.85	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.85	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.85	   A^2 -> H(U1(d, d), c)
28.56/9.85	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.85	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.85	   A^2 -> H(U1(d, d), e)
28.56/9.85	   A^2 -> H(f(d), d)
28.56/9.85	   A^2 -> H(f(d), k)
28.56/9.85	   A^2 -> H(U1(c, c), c)
28.56/9.85	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.85	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.85	   A^2 -> H(f(c), k)
28.56/9.85	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.85	   A^2 -> H(f(k), U1(k, k))
28.56/9.85	   A^2 -> H(f(e), e)
28.56/9.85	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.85	   A^2 -> H(d, U1(c, b))
28.56/9.85	   A^2 -> H(d, U1(d, b))
28.56/9.85	   A^2 -> H(d, U1(b, c))
28.56/9.85	   A^2 -> H(d, U1(b, d))
28.56/9.85	   A^2 -> H(d, U1(c, c))
28.56/9.85	   A^2 -> H(d, f(e))
28.56/9.85	   A^2 -> H(d, f(k))
28.56/9.85	   A^2 -> H(d, U1(d, d))
28.56/9.85	   A^2 -> H(a, U1(e, b))
28.56/9.85	   A^2 -> H(a, U1(k, b))
28.56/9.85	   A^2 -> H(a, U1(c, d))
28.56/9.85	   A^2 -> H(a, U1(d, c))
28.56/9.85	   A^2 -> H(a, U1(b, e))
28.56/9.85	   A^2 -> H(a, U1(b, k))
28.56/9.85	   A^2 -> H(a, U1(e, c))
28.56/9.85	   A^2 -> H(a, U1(k, c))
28.56/9.85	   A^2 -> H(a, U1(c, e))
28.56/9.85	   A^2 -> H(a, U1(c, k))
28.56/9.85	   A^2 -> H(a, U1(e, e))
28.56/9.85	   A^2 -> H(a, U1(k, k))
28.56/9.85	   A^2 -> H(a, U1(k, d))
28.56/9.85	   A^2 -> H(a, U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, a), b)
28.56/9.85	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.85	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.85	   A^2 -> H(U1(e, a), c)
28.56/9.85	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.85	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.85	   A^2 -> H(U1(e, a), e)
28.56/9.85	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, a), b)
28.56/9.85	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.85	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.85	   A^2 -> H(U1(k, a), c)
28.56/9.85	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.85	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.85	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, d), b)
28.56/9.85	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, d), c)
28.56/9.85	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.85	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.85	   A^2 -> H(U1(c, d), e)
28.56/9.85	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, a), d)
28.56/9.85	   A^2 -> H(U1(c, a), k)
28.56/9.85	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.85	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.85	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.85	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.85	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.85	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.85	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.85	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.85	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.85	   A^2 -> H(U1(d, c), b)
28.56/9.85	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(d, c), c)
28.56/9.85	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.85	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.85	   A^2 -> H(U1(d, c), e)
28.56/9.85	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.85	   A^2 -> H(U1(d, a), d)
28.56/9.85	   A^2 -> H(U1(d, a), k)
28.56/9.85	   A^2 -> H(U1(a, e), b)
28.56/9.85	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.85	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.85	   A^2 -> H(U1(a, e), c)
28.56/9.85	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.85	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.85	   A^2 -> H(U1(a, e), e)
28.56/9.85	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(a, k), b)
28.56/9.85	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.85	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.85	   A^2 -> H(U1(a, k), c)
28.56/9.85	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.85	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.85	   A^2 -> H(U1(a, k), e)
28.56/9.85	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(a, c), d)
28.56/9.85	   A^2 -> H(U1(a, c), k)
28.56/9.85	   A^2 -> H(U1(a, d), d)
28.56/9.85	   A^2 -> H(U1(a, d), k)
28.56/9.85	   A^2 -> H(k, U1(c, b))
28.56/9.85	   A^2 -> H(k, U1(d, b))
28.56/9.85	   A^2 -> H(k, U1(b, c))
28.56/9.85	   A^2 -> H(k, U1(b, d))
28.56/9.85	   A^2 -> H(k, U1(c, c))
28.56/9.85	   A^2 -> H(k, f(e))
28.56/9.85	   A^2 -> H(k, f(k))
28.56/9.85	   A^2 -> H(k, U1(d, d))
28.56/9.85	   A^2 -> H(c, U1(e, b))
28.56/9.85	   A^2 -> H(c, U1(k, b))
28.56/9.85	   A^2 -> H(c, U1(c, d))
28.56/9.85	   A^2 -> H(c, U1(d, c))
28.56/9.85	   A^2 -> H(c, U1(b, e))
28.56/9.85	   A^2 -> H(c, U1(b, k))
28.56/9.85	   A^2 -> H(c, U1(e, c))
28.56/9.85	   A^2 -> H(c, U1(k, c))
28.56/9.85	   A^2 -> H(c, U1(c, e))
28.56/9.85	   A^2 -> H(c, U1(c, k))
28.56/9.85	   A^2 -> H(c, U1(e, e))
28.56/9.85	   A^2 -> H(c, U1(k, k))
28.56/9.85	   A^2 -> H(c, U1(k, d))
28.56/9.85	   A^2 -> H(c, U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.85	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, c), b)
28.56/9.85	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.85	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.85	   A^2 -> H(U1(e, c), e)
28.56/9.85	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.85	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.85	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.85	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.85	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.85	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.85	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.85	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.85	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.85	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.85	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.85	   A^2 -> H(U1(k, c), b)
28.56/9.85	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(k, c), c)
28.56/9.85	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.85	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.85	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, e), b)
28.56/9.85	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, e), c)
28.56/9.85	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.85	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.85	   A^2 -> H(U1(c, e), e)
28.56/9.85	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, k), b)
28.56/9.85	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.85	
28.56/9.85	The TRS R consists of the following rules:
28.56/9.85	
28.56/9.85	   f(x) -> U1(x, x)
28.56/9.85	   U1(e, x) -> x
28.56/9.85	   a -> c
28.56/9.85	   a -> d
28.56/9.85	   b -> c
28.56/9.85	   b -> d
28.56/9.85	   d -> k
28.56/9.85	   c -> e
28.56/9.85	   c -> k
28.56/9.85	
28.56/9.85	Q is empty.
28.56/9.85	We have to consider all minimal (P,Q,R)-chains.
28.56/9.85	----------------------------------------
28.56/9.85	
28.56/9.85	(1535) TransformationProof (EQUIVALENT)
28.56/9.85	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.85	
28.56/9.85	   (A^2 -> H(U1(e, k), U1(b, k)),A^2 -> H(U1(e, k), U1(b, k)))
28.56/9.85	   (A^2 -> H(U1(k, k), U1(b, k)),A^2 -> H(U1(k, k), U1(b, k)))
28.56/9.85	   (A^2 -> H(U1(c, k), U1(c, k)),A^2 -> H(U1(c, k), U1(c, k)))
28.56/9.85	   (A^2 -> H(U1(c, k), U1(d, k)),A^2 -> H(U1(c, k), U1(d, k)))
28.56/9.85	
28.56/9.85	
28.56/9.85	----------------------------------------
28.56/9.85	
28.56/9.85	(1536)
28.56/9.85	Obligation:
28.56/9.85	Q DP problem:
28.56/9.85	The TRS P consists of the following rules:
28.56/9.85	
28.56/9.85	   G(d, x, x) -> A^2
28.56/9.85	   A^2 -> H(f(c), f(c))
28.56/9.85	   H(x, x) -> G(x, x, f(k))
28.56/9.85	   A^2 -> H(f(d), f(d))
28.56/9.85	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.85	   A^2 -> H(f(e), f(e))
28.56/9.85	   A^2 -> H(f(k), f(k))
28.56/9.85	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.85	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.85	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(c, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.85	   A^2 -> H(U1(c, c), b)
28.56/9.85	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, c), e)
28.56/9.85	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.85	   A^2 -> H(e, U1(c, b))
28.56/9.85	   A^2 -> H(e, U1(d, b))
28.56/9.85	   A^2 -> H(e, U1(b, c))
28.56/9.85	   A^2 -> H(e, U1(b, d))
28.56/9.85	   A^2 -> H(e, U1(c, c))
28.56/9.85	   A^2 -> H(e, f(e))
28.56/9.85	   A^2 -> H(e, f(k))
28.56/9.85	   A^2 -> H(e, U1(d, d))
28.56/9.85	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.85	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.85	   A^2 -> H(f(e), b)
28.56/9.85	   A^2 -> H(f(e), U1(e, d))
28.56/9.85	   A^2 -> H(f(e), U1(d, e))
28.56/9.85	   A^2 -> H(f(e), c)
28.56/9.85	   A^2 -> H(f(e), U1(e, k))
28.56/9.85	   A^2 -> H(f(e), U1(k, e))
28.56/9.85	   A^2 -> H(f(e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.85	   A^2 -> H(f(k), b)
28.56/9.85	   A^2 -> H(f(k), U1(e, d))
28.56/9.85	   A^2 -> H(f(k), U1(d, e))
28.56/9.85	   A^2 -> H(f(k), c)
28.56/9.85	   A^2 -> H(f(k), U1(e, k))
28.56/9.85	   A^2 -> H(f(k), U1(k, e))
28.56/9.85	   A^2 -> H(f(k), e)
28.56/9.85	   A^2 -> H(f(c), d)
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.85	   A^2 -> H(U1(k, k), f(e))
28.56/9.85	   A^2 -> H(U1(k, k), f(k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.85	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.85	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.85	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.85	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.85	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.85	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.85	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.85	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.85	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.85	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.85	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.85	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.85	   A^2 -> H(U1(d, d), b)
28.56/9.85	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.85	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.85	   A^2 -> H(U1(d, d), c)
28.56/9.85	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.85	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.85	   A^2 -> H(U1(d, d), e)
28.56/9.85	   A^2 -> H(f(d), d)
28.56/9.85	   A^2 -> H(f(d), k)
28.56/9.85	   A^2 -> H(U1(c, c), c)
28.56/9.85	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.85	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.85	   A^2 -> H(f(c), k)
28.56/9.85	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.85	   A^2 -> H(f(k), U1(k, k))
28.56/9.85	   A^2 -> H(f(e), e)
28.56/9.85	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.85	   A^2 -> H(d, U1(c, b))
28.56/9.85	   A^2 -> H(d, U1(d, b))
28.56/9.85	   A^2 -> H(d, U1(b, c))
28.56/9.85	   A^2 -> H(d, U1(b, d))
28.56/9.85	   A^2 -> H(d, U1(c, c))
28.56/9.85	   A^2 -> H(d, f(e))
28.56/9.85	   A^2 -> H(d, f(k))
28.56/9.85	   A^2 -> H(d, U1(d, d))
28.56/9.85	   A^2 -> H(a, U1(e, b))
28.56/9.85	   A^2 -> H(a, U1(k, b))
28.56/9.85	   A^2 -> H(a, U1(c, d))
28.56/9.85	   A^2 -> H(a, U1(d, c))
28.56/9.85	   A^2 -> H(a, U1(b, e))
28.56/9.85	   A^2 -> H(a, U1(b, k))
28.56/9.85	   A^2 -> H(a, U1(e, c))
28.56/9.85	   A^2 -> H(a, U1(k, c))
28.56/9.85	   A^2 -> H(a, U1(c, e))
28.56/9.85	   A^2 -> H(a, U1(c, k))
28.56/9.85	   A^2 -> H(a, U1(e, e))
28.56/9.85	   A^2 -> H(a, U1(k, k))
28.56/9.85	   A^2 -> H(a, U1(k, d))
28.56/9.85	   A^2 -> H(a, U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, a), b)
28.56/9.85	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.85	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.85	   A^2 -> H(U1(e, a), c)
28.56/9.85	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.85	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.85	   A^2 -> H(U1(e, a), e)
28.56/9.85	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, a), b)
28.56/9.85	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.85	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.85	   A^2 -> H(U1(k, a), c)
28.56/9.85	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.85	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.85	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, d), b)
28.56/9.85	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, d), c)
28.56/9.85	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.85	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.85	   A^2 -> H(U1(c, d), e)
28.56/9.85	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, a), d)
28.56/9.85	   A^2 -> H(U1(c, a), k)
28.56/9.85	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.85	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.85	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.85	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.85	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.85	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.85	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.85	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.85	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.85	   A^2 -> H(U1(d, c), b)
28.56/9.85	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(d, c), c)
28.56/9.85	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.85	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.85	   A^2 -> H(U1(d, c), e)
28.56/9.85	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.85	   A^2 -> H(U1(d, a), d)
28.56/9.85	   A^2 -> H(U1(d, a), k)
28.56/9.85	   A^2 -> H(U1(a, e), b)
28.56/9.85	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.85	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.85	   A^2 -> H(U1(a, e), c)
28.56/9.85	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.85	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.85	   A^2 -> H(U1(a, e), e)
28.56/9.85	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(a, k), b)
28.56/9.85	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.85	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.85	   A^2 -> H(U1(a, k), c)
28.56/9.85	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.85	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.85	   A^2 -> H(U1(a, k), e)
28.56/9.85	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(a, c), d)
28.56/9.85	   A^2 -> H(U1(a, c), k)
28.56/9.85	   A^2 -> H(U1(a, d), d)
28.56/9.85	   A^2 -> H(U1(a, d), k)
28.56/9.85	   A^2 -> H(k, U1(c, b))
28.56/9.85	   A^2 -> H(k, U1(d, b))
28.56/9.85	   A^2 -> H(k, U1(b, c))
28.56/9.85	   A^2 -> H(k, U1(b, d))
28.56/9.85	   A^2 -> H(k, U1(c, c))
28.56/9.85	   A^2 -> H(k, f(e))
28.56/9.85	   A^2 -> H(k, f(k))
28.56/9.85	   A^2 -> H(k, U1(d, d))
28.56/9.85	   A^2 -> H(c, U1(e, b))
28.56/9.85	   A^2 -> H(c, U1(k, b))
28.56/9.85	   A^2 -> H(c, U1(c, d))
28.56/9.85	   A^2 -> H(c, U1(d, c))
28.56/9.85	   A^2 -> H(c, U1(b, e))
28.56/9.85	   A^2 -> H(c, U1(b, k))
28.56/9.85	   A^2 -> H(c, U1(e, c))
28.56/9.85	   A^2 -> H(c, U1(k, c))
28.56/9.85	   A^2 -> H(c, U1(c, e))
28.56/9.85	   A^2 -> H(c, U1(c, k))
28.56/9.85	   A^2 -> H(c, U1(e, e))
28.56/9.85	   A^2 -> H(c, U1(k, k))
28.56/9.85	   A^2 -> H(c, U1(k, d))
28.56/9.85	   A^2 -> H(c, U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.85	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, c), b)
28.56/9.85	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.85	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.85	   A^2 -> H(U1(e, c), e)
28.56/9.85	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.85	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.85	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.85	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.85	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.85	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.85	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.85	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.85	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.85	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.85	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.85	   A^2 -> H(U1(k, c), b)
28.56/9.85	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(k, c), c)
28.56/9.85	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.85	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.85	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, e), b)
28.56/9.85	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, e), c)
28.56/9.85	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.85	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.85	   A^2 -> H(U1(c, e), e)
28.56/9.85	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, k), b)
28.56/9.85	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.85	
28.56/9.85	The TRS R consists of the following rules:
28.56/9.85	
28.56/9.85	   f(x) -> U1(x, x)
28.56/9.85	   U1(e, x) -> x
28.56/9.85	   a -> c
28.56/9.85	   a -> d
28.56/9.85	   b -> c
28.56/9.85	   b -> d
28.56/9.85	   d -> k
28.56/9.85	   c -> e
28.56/9.85	   c -> k
28.56/9.85	
28.56/9.85	Q is empty.
28.56/9.85	We have to consider all minimal (P,Q,R)-chains.
28.56/9.85	----------------------------------------
28.56/9.85	
28.56/9.85	(1537) TransformationProof (EQUIVALENT)
28.56/9.85	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.85	
28.56/9.85	   (A^2 -> H(U1(e, k), U1(e, c)),A^2 -> H(U1(e, k), U1(e, c)))
28.56/9.85	   (A^2 -> H(U1(k, k), U1(e, c)),A^2 -> H(U1(k, k), U1(e, c)))
28.56/9.85	   (A^2 -> H(U1(c, k), c),A^2 -> H(U1(c, k), c))
28.56/9.85	   (A^2 -> H(U1(c, k), U1(e, e)),A^2 -> H(U1(c, k), U1(e, e)))
28.56/9.85	   (A^2 -> H(U1(c, k), U1(e, k)),A^2 -> H(U1(c, k), U1(e, k)))
28.56/9.85	
28.56/9.85	
28.56/9.85	----------------------------------------
28.56/9.85	
28.56/9.85	(1538)
28.56/9.85	Obligation:
28.56/9.85	Q DP problem:
28.56/9.85	The TRS P consists of the following rules:
28.56/9.85	
28.56/9.85	   G(d, x, x) -> A^2
28.56/9.85	   A^2 -> H(f(c), f(c))
28.56/9.85	   H(x, x) -> G(x, x, f(k))
28.56/9.85	   A^2 -> H(f(d), f(d))
28.56/9.85	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.85	   A^2 -> H(f(e), f(e))
28.56/9.85	   A^2 -> H(f(k), f(k))
28.56/9.85	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.85	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.85	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(c, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.85	   A^2 -> H(U1(c, c), b)
28.56/9.85	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, c), e)
28.56/9.85	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.85	   A^2 -> H(e, U1(c, b))
28.56/9.85	   A^2 -> H(e, U1(d, b))
28.56/9.85	   A^2 -> H(e, U1(b, c))
28.56/9.85	   A^2 -> H(e, U1(b, d))
28.56/9.85	   A^2 -> H(e, U1(c, c))
28.56/9.85	   A^2 -> H(e, f(e))
28.56/9.85	   A^2 -> H(e, f(k))
28.56/9.85	   A^2 -> H(e, U1(d, d))
28.56/9.85	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.85	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.85	   A^2 -> H(f(e), b)
28.56/9.85	   A^2 -> H(f(e), U1(e, d))
28.56/9.85	   A^2 -> H(f(e), U1(d, e))
28.56/9.85	   A^2 -> H(f(e), c)
28.56/9.85	   A^2 -> H(f(e), U1(e, k))
28.56/9.85	   A^2 -> H(f(e), U1(k, e))
28.56/9.85	   A^2 -> H(f(e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.85	   A^2 -> H(f(k), b)
28.56/9.85	   A^2 -> H(f(k), U1(e, d))
28.56/9.85	   A^2 -> H(f(k), U1(d, e))
28.56/9.85	   A^2 -> H(f(k), c)
28.56/9.85	   A^2 -> H(f(k), U1(e, k))
28.56/9.85	   A^2 -> H(f(k), U1(k, e))
28.56/9.85	   A^2 -> H(f(k), e)
28.56/9.85	   A^2 -> H(f(c), d)
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.85	   A^2 -> H(U1(k, k), f(e))
28.56/9.85	   A^2 -> H(U1(k, k), f(k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.85	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.85	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.85	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.85	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.85	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.85	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.85	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.85	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.85	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.85	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.85	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.85	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.85	   A^2 -> H(U1(d, d), b)
28.56/9.85	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.85	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.85	   A^2 -> H(U1(d, d), c)
28.56/9.85	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.85	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.85	   A^2 -> H(U1(d, d), e)
28.56/9.85	   A^2 -> H(f(d), d)
28.56/9.85	   A^2 -> H(f(d), k)
28.56/9.85	   A^2 -> H(U1(c, c), c)
28.56/9.85	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.85	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.85	   A^2 -> H(f(c), k)
28.56/9.85	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.85	   A^2 -> H(f(k), U1(k, k))
28.56/9.85	   A^2 -> H(f(e), e)
28.56/9.85	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.85	   A^2 -> H(d, U1(c, b))
28.56/9.85	   A^2 -> H(d, U1(d, b))
28.56/9.85	   A^2 -> H(d, U1(b, c))
28.56/9.85	   A^2 -> H(d, U1(b, d))
28.56/9.85	   A^2 -> H(d, U1(c, c))
28.56/9.85	   A^2 -> H(d, f(e))
28.56/9.85	   A^2 -> H(d, f(k))
28.56/9.85	   A^2 -> H(d, U1(d, d))
28.56/9.85	   A^2 -> H(a, U1(e, b))
28.56/9.85	   A^2 -> H(a, U1(k, b))
28.56/9.85	   A^2 -> H(a, U1(c, d))
28.56/9.85	   A^2 -> H(a, U1(d, c))
28.56/9.85	   A^2 -> H(a, U1(b, e))
28.56/9.85	   A^2 -> H(a, U1(b, k))
28.56/9.85	   A^2 -> H(a, U1(e, c))
28.56/9.85	   A^2 -> H(a, U1(k, c))
28.56/9.85	   A^2 -> H(a, U1(c, e))
28.56/9.85	   A^2 -> H(a, U1(c, k))
28.56/9.85	   A^2 -> H(a, U1(e, e))
28.56/9.85	   A^2 -> H(a, U1(k, k))
28.56/9.85	   A^2 -> H(a, U1(k, d))
28.56/9.85	   A^2 -> H(a, U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, a), b)
28.56/9.85	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.85	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.85	   A^2 -> H(U1(e, a), c)
28.56/9.85	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.85	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.85	   A^2 -> H(U1(e, a), e)
28.56/9.85	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, a), b)
28.56/9.85	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.85	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.85	   A^2 -> H(U1(k, a), c)
28.56/9.85	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.85	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.85	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, d), b)
28.56/9.85	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, d), c)
28.56/9.85	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.85	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.85	   A^2 -> H(U1(c, d), e)
28.56/9.85	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, a), d)
28.56/9.85	   A^2 -> H(U1(c, a), k)
28.56/9.85	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.85	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.85	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.85	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.85	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.85	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.85	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.85	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.85	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.85	   A^2 -> H(U1(d, c), b)
28.56/9.85	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(d, c), c)
28.56/9.85	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.85	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.85	   A^2 -> H(U1(d, c), e)
28.56/9.85	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.85	   A^2 -> H(U1(d, a), d)
28.56/9.85	   A^2 -> H(U1(d, a), k)
28.56/9.85	   A^2 -> H(U1(a, e), b)
28.56/9.85	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.85	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.85	   A^2 -> H(U1(a, e), c)
28.56/9.85	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.85	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.85	   A^2 -> H(U1(a, e), e)
28.56/9.85	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(a, k), b)
28.56/9.85	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.85	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.85	   A^2 -> H(U1(a, k), c)
28.56/9.85	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.85	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.85	   A^2 -> H(U1(a, k), e)
28.56/9.85	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(a, c), d)
28.56/9.85	   A^2 -> H(U1(a, c), k)
28.56/9.85	   A^2 -> H(U1(a, d), d)
28.56/9.85	   A^2 -> H(U1(a, d), k)
28.56/9.85	   A^2 -> H(k, U1(c, b))
28.56/9.85	   A^2 -> H(k, U1(d, b))
28.56/9.85	   A^2 -> H(k, U1(b, c))
28.56/9.85	   A^2 -> H(k, U1(b, d))
28.56/9.85	   A^2 -> H(k, U1(c, c))
28.56/9.85	   A^2 -> H(k, f(e))
28.56/9.85	   A^2 -> H(k, f(k))
28.56/9.85	   A^2 -> H(k, U1(d, d))
28.56/9.85	   A^2 -> H(c, U1(e, b))
28.56/9.85	   A^2 -> H(c, U1(k, b))
28.56/9.85	   A^2 -> H(c, U1(c, d))
28.56/9.85	   A^2 -> H(c, U1(d, c))
28.56/9.85	   A^2 -> H(c, U1(b, e))
28.56/9.85	   A^2 -> H(c, U1(b, k))
28.56/9.85	   A^2 -> H(c, U1(e, c))
28.56/9.85	   A^2 -> H(c, U1(k, c))
28.56/9.85	   A^2 -> H(c, U1(c, e))
28.56/9.85	   A^2 -> H(c, U1(c, k))
28.56/9.85	   A^2 -> H(c, U1(e, e))
28.56/9.85	   A^2 -> H(c, U1(k, k))
28.56/9.85	   A^2 -> H(c, U1(k, d))
28.56/9.85	   A^2 -> H(c, U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.85	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, c), b)
28.56/9.85	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.85	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.85	   A^2 -> H(U1(e, c), e)
28.56/9.85	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.85	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.85	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.85	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.85	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.85	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.85	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.85	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.85	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.85	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.85	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.85	   A^2 -> H(U1(k, c), b)
28.56/9.85	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(k, c), c)
28.56/9.85	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.85	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.85	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, e), b)
28.56/9.85	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, e), c)
28.56/9.85	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.85	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.85	   A^2 -> H(U1(c, e), e)
28.56/9.85	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, k), b)
28.56/9.85	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, k), c)
28.56/9.85	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.85	
28.56/9.85	The TRS R consists of the following rules:
28.56/9.85	
28.56/9.85	   f(x) -> U1(x, x)
28.56/9.85	   U1(e, x) -> x
28.56/9.85	   a -> c
28.56/9.85	   a -> d
28.56/9.85	   b -> c
28.56/9.85	   b -> d
28.56/9.85	   d -> k
28.56/9.85	   c -> e
28.56/9.85	   c -> k
28.56/9.85	
28.56/9.85	Q is empty.
28.56/9.85	We have to consider all minimal (P,Q,R)-chains.
28.56/9.85	----------------------------------------
28.56/9.85	
28.56/9.85	(1539) TransformationProof (EQUIVALENT)
28.56/9.85	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.85	
28.56/9.85	   (A^2 -> H(U1(e, k), U1(k, c)),A^2 -> H(U1(e, k), U1(k, c)))
28.56/9.85	   (A^2 -> H(U1(k, k), U1(k, c)),A^2 -> H(U1(k, k), U1(k, c)))
28.56/9.85	   (A^2 -> H(U1(c, k), U1(k, e)),A^2 -> H(U1(c, k), U1(k, e)))
28.56/9.85	   (A^2 -> H(U1(c, k), U1(k, k)),A^2 -> H(U1(c, k), U1(k, k)))
28.56/9.85	
28.56/9.85	
28.56/9.85	----------------------------------------
28.56/9.85	
28.56/9.85	(1540)
28.56/9.85	Obligation:
28.56/9.85	Q DP problem:
28.56/9.85	The TRS P consists of the following rules:
28.56/9.85	
28.56/9.85	   G(d, x, x) -> A^2
28.56/9.85	   A^2 -> H(f(c), f(c))
28.56/9.85	   H(x, x) -> G(x, x, f(k))
28.56/9.85	   A^2 -> H(f(d), f(d))
28.56/9.85	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.85	   A^2 -> H(f(e), f(e))
28.56/9.85	   A^2 -> H(f(k), f(k))
28.56/9.85	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.85	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.85	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(c, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.85	   A^2 -> H(U1(c, c), b)
28.56/9.85	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, c), e)
28.56/9.85	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.85	   A^2 -> H(e, U1(c, b))
28.56/9.85	   A^2 -> H(e, U1(d, b))
28.56/9.85	   A^2 -> H(e, U1(b, c))
28.56/9.85	   A^2 -> H(e, U1(b, d))
28.56/9.85	   A^2 -> H(e, U1(c, c))
28.56/9.85	   A^2 -> H(e, f(e))
28.56/9.85	   A^2 -> H(e, f(k))
28.56/9.85	   A^2 -> H(e, U1(d, d))
28.56/9.85	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.85	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.85	   A^2 -> H(f(e), b)
28.56/9.85	   A^2 -> H(f(e), U1(e, d))
28.56/9.85	   A^2 -> H(f(e), U1(d, e))
28.56/9.85	   A^2 -> H(f(e), c)
28.56/9.85	   A^2 -> H(f(e), U1(e, k))
28.56/9.85	   A^2 -> H(f(e), U1(k, e))
28.56/9.85	   A^2 -> H(f(e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.85	   A^2 -> H(f(k), b)
28.56/9.85	   A^2 -> H(f(k), U1(e, d))
28.56/9.85	   A^2 -> H(f(k), U1(d, e))
28.56/9.85	   A^2 -> H(f(k), c)
28.56/9.85	   A^2 -> H(f(k), U1(e, k))
28.56/9.85	   A^2 -> H(f(k), U1(k, e))
28.56/9.85	   A^2 -> H(f(k), e)
28.56/9.85	   A^2 -> H(f(c), d)
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.85	   A^2 -> H(U1(k, k), f(e))
28.56/9.85	   A^2 -> H(U1(k, k), f(k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.85	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.85	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.85	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.85	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.85	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.85	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.85	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.85	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.85	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.85	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.85	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.85	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.85	   A^2 -> H(U1(d, d), b)
28.56/9.85	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.85	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.85	   A^2 -> H(U1(d, d), c)
28.56/9.85	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.85	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.85	   A^2 -> H(U1(d, d), e)
28.56/9.85	   A^2 -> H(f(d), d)
28.56/9.85	   A^2 -> H(f(d), k)
28.56/9.85	   A^2 -> H(U1(c, c), c)
28.56/9.85	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.85	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.85	   A^2 -> H(f(c), k)
28.56/9.85	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.85	   A^2 -> H(f(k), U1(k, k))
28.56/9.85	   A^2 -> H(f(e), e)
28.56/9.85	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.85	   A^2 -> H(d, U1(c, b))
28.56/9.85	   A^2 -> H(d, U1(d, b))
28.56/9.85	   A^2 -> H(d, U1(b, c))
28.56/9.85	   A^2 -> H(d, U1(b, d))
28.56/9.85	   A^2 -> H(d, U1(c, c))
28.56/9.85	   A^2 -> H(d, f(e))
28.56/9.85	   A^2 -> H(d, f(k))
28.56/9.85	   A^2 -> H(d, U1(d, d))
28.56/9.85	   A^2 -> H(a, U1(e, b))
28.56/9.85	   A^2 -> H(a, U1(k, b))
28.56/9.85	   A^2 -> H(a, U1(c, d))
28.56/9.85	   A^2 -> H(a, U1(d, c))
28.56/9.85	   A^2 -> H(a, U1(b, e))
28.56/9.85	   A^2 -> H(a, U1(b, k))
28.56/9.85	   A^2 -> H(a, U1(e, c))
28.56/9.85	   A^2 -> H(a, U1(k, c))
28.56/9.85	   A^2 -> H(a, U1(c, e))
28.56/9.85	   A^2 -> H(a, U1(c, k))
28.56/9.85	   A^2 -> H(a, U1(e, e))
28.56/9.85	   A^2 -> H(a, U1(k, k))
28.56/9.85	   A^2 -> H(a, U1(k, d))
28.56/9.85	   A^2 -> H(a, U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, a), b)
28.56/9.85	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.85	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.85	   A^2 -> H(U1(e, a), c)
28.56/9.85	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.85	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.85	   A^2 -> H(U1(e, a), e)
28.56/9.85	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, a), b)
28.56/9.85	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.85	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.85	   A^2 -> H(U1(k, a), c)
28.56/9.85	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.85	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.85	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, d), b)
28.56/9.85	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, d), c)
28.56/9.85	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.85	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.85	   A^2 -> H(U1(c, d), e)
28.56/9.85	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, a), d)
28.56/9.85	   A^2 -> H(U1(c, a), k)
28.56/9.85	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.85	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.85	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.85	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.85	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.85	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.85	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.85	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.85	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.85	   A^2 -> H(U1(d, c), b)
28.56/9.85	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(d, c), c)
28.56/9.85	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.85	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.85	   A^2 -> H(U1(d, c), e)
28.56/9.85	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.85	   A^2 -> H(U1(d, a), d)
28.56/9.85	   A^2 -> H(U1(d, a), k)
28.56/9.85	   A^2 -> H(U1(a, e), b)
28.56/9.85	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.85	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.85	   A^2 -> H(U1(a, e), c)
28.56/9.85	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.85	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.85	   A^2 -> H(U1(a, e), e)
28.56/9.85	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(a, k), b)
28.56/9.85	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.85	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.85	   A^2 -> H(U1(a, k), c)
28.56/9.85	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.85	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.85	   A^2 -> H(U1(a, k), e)
28.56/9.85	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(a, c), d)
28.56/9.85	   A^2 -> H(U1(a, c), k)
28.56/9.85	   A^2 -> H(U1(a, d), d)
28.56/9.85	   A^2 -> H(U1(a, d), k)
28.56/9.85	   A^2 -> H(k, U1(c, b))
28.56/9.85	   A^2 -> H(k, U1(d, b))
28.56/9.85	   A^2 -> H(k, U1(b, c))
28.56/9.85	   A^2 -> H(k, U1(b, d))
28.56/9.85	   A^2 -> H(k, U1(c, c))
28.56/9.85	   A^2 -> H(k, f(e))
28.56/9.85	   A^2 -> H(k, f(k))
28.56/9.85	   A^2 -> H(k, U1(d, d))
28.56/9.85	   A^2 -> H(c, U1(e, b))
28.56/9.85	   A^2 -> H(c, U1(k, b))
28.56/9.85	   A^2 -> H(c, U1(c, d))
28.56/9.85	   A^2 -> H(c, U1(d, c))
28.56/9.85	   A^2 -> H(c, U1(b, e))
28.56/9.85	   A^2 -> H(c, U1(b, k))
28.56/9.85	   A^2 -> H(c, U1(e, c))
28.56/9.85	   A^2 -> H(c, U1(k, c))
28.56/9.85	   A^2 -> H(c, U1(c, e))
28.56/9.85	   A^2 -> H(c, U1(c, k))
28.56/9.85	   A^2 -> H(c, U1(e, e))
28.56/9.85	   A^2 -> H(c, U1(k, k))
28.56/9.85	   A^2 -> H(c, U1(k, d))
28.56/9.85	   A^2 -> H(c, U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.85	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, c), b)
28.56/9.85	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.85	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.85	   A^2 -> H(U1(e, c), e)
28.56/9.85	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.85	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.85	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.85	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.85	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.85	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.85	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.85	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.85	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.85	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.85	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.85	   A^2 -> H(U1(k, c), b)
28.56/9.85	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(k, c), c)
28.56/9.85	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.85	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.85	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, e), b)
28.56/9.85	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, e), c)
28.56/9.85	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.85	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.85	   A^2 -> H(U1(c, e), e)
28.56/9.85	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, k), b)
28.56/9.85	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, k), c)
28.56/9.85	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.85	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.85	
28.56/9.85	The TRS R consists of the following rules:
28.56/9.85	
28.56/9.85	   f(x) -> U1(x, x)
28.56/9.85	   U1(e, x) -> x
28.56/9.85	   a -> c
28.56/9.85	   a -> d
28.56/9.85	   b -> c
28.56/9.85	   b -> d
28.56/9.85	   d -> k
28.56/9.85	   c -> e
28.56/9.85	   c -> k
28.56/9.85	
28.56/9.85	Q is empty.
28.56/9.85	We have to consider all minimal (P,Q,R)-chains.
28.56/9.85	----------------------------------------
28.56/9.85	
28.56/9.85	(1541) TransformationProof (EQUIVALENT)
28.56/9.85	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.85	
28.56/9.85	   (A^2 -> H(U1(e, k), U1(c, e)),A^2 -> H(U1(e, k), U1(c, e)))
28.56/9.85	   (A^2 -> H(U1(k, k), U1(c, e)),A^2 -> H(U1(k, k), U1(c, e)))
28.56/9.85	   (A^2 -> H(U1(c, k), U1(e, e)),A^2 -> H(U1(c, k), U1(e, e)))
28.56/9.85	   (A^2 -> H(U1(c, k), U1(k, e)),A^2 -> H(U1(c, k), U1(k, e)))
28.56/9.85	
28.56/9.85	
28.56/9.85	----------------------------------------
28.56/9.85	
28.56/9.85	(1542)
28.56/9.85	Obligation:
28.56/9.85	Q DP problem:
28.56/9.85	The TRS P consists of the following rules:
28.56/9.85	
28.56/9.85	   G(d, x, x) -> A^2
28.56/9.85	   A^2 -> H(f(c), f(c))
28.56/9.85	   H(x, x) -> G(x, x, f(k))
28.56/9.85	   A^2 -> H(f(d), f(d))
28.56/9.85	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.85	   A^2 -> H(f(e), f(e))
28.56/9.85	   A^2 -> H(f(k), f(k))
28.56/9.85	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.85	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.85	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(c, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.85	   A^2 -> H(U1(c, c), b)
28.56/9.85	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.85	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.85	   A^2 -> H(U1(c, c), e)
28.56/9.85	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.85	   A^2 -> H(e, U1(c, b))
28.56/9.85	   A^2 -> H(e, U1(d, b))
28.56/9.85	   A^2 -> H(e, U1(b, c))
28.56/9.85	   A^2 -> H(e, U1(b, d))
28.56/9.85	   A^2 -> H(e, U1(c, c))
28.56/9.85	   A^2 -> H(e, f(e))
28.56/9.85	   A^2 -> H(e, f(k))
28.56/9.85	   A^2 -> H(e, U1(d, d))
28.56/9.85	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.85	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.85	   A^2 -> H(f(e), b)
28.56/9.85	   A^2 -> H(f(e), U1(e, d))
28.56/9.85	   A^2 -> H(f(e), U1(d, e))
28.56/9.85	   A^2 -> H(f(e), c)
28.56/9.85	   A^2 -> H(f(e), U1(e, k))
28.56/9.85	   A^2 -> H(f(e), U1(k, e))
28.56/9.85	   A^2 -> H(f(e), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.85	   A^2 -> H(f(k), b)
28.56/9.85	   A^2 -> H(f(k), U1(e, d))
28.56/9.85	   A^2 -> H(f(k), U1(d, e))
28.56/9.85	   A^2 -> H(f(k), c)
28.56/9.85	   A^2 -> H(f(k), U1(e, k))
28.56/9.85	   A^2 -> H(f(k), U1(k, e))
28.56/9.85	   A^2 -> H(f(k), e)
28.56/9.85	   A^2 -> H(f(c), d)
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.85	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.85	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.85	   A^2 -> H(U1(k, k), f(e))
28.56/9.85	   A^2 -> H(U1(k, k), f(k))
28.56/9.85	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.85	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.85	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.85	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.85	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.85	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.85	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.85	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.85	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.85	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.85	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.85	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.85	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.85	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.85	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.85	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.85	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.85	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.85	   A^2 -> H(U1(d, d), b)
28.56/9.85	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.85	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.85	   A^2 -> H(U1(d, d), c)
28.56/9.85	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.85	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.85	   A^2 -> H(U1(d, d), e)
28.56/9.85	   A^2 -> H(f(d), d)
28.56/9.85	   A^2 -> H(f(d), k)
28.56/9.85	   A^2 -> H(U1(c, c), c)
28.56/9.85	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.85	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.85	   A^2 -> H(f(c), k)
28.56/9.85	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.85	   A^2 -> H(f(k), U1(k, k))
28.56/9.85	   A^2 -> H(f(e), e)
28.56/9.85	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.85	   A^2 -> H(d, U1(c, b))
28.56/9.85	   A^2 -> H(d, U1(d, b))
28.56/9.85	   A^2 -> H(d, U1(b, c))
28.56/9.85	   A^2 -> H(d, U1(b, d))
28.56/9.85	   A^2 -> H(d, U1(c, c))
28.56/9.85	   A^2 -> H(d, f(e))
28.56/9.85	   A^2 -> H(d, f(k))
28.56/9.85	   A^2 -> H(d, U1(d, d))
28.56/9.85	   A^2 -> H(a, U1(e, b))
28.56/9.85	   A^2 -> H(a, U1(k, b))
28.56/9.85	   A^2 -> H(a, U1(c, d))
28.56/9.85	   A^2 -> H(a, U1(d, c))
28.56/9.85	   A^2 -> H(a, U1(b, e))
28.56/9.85	   A^2 -> H(a, U1(b, k))
28.56/9.85	   A^2 -> H(a, U1(e, c))
28.56/9.85	   A^2 -> H(a, U1(k, c))
28.56/9.85	   A^2 -> H(a, U1(c, e))
28.56/9.85	   A^2 -> H(a, U1(c, k))
28.56/9.85	   A^2 -> H(a, U1(e, e))
28.56/9.85	   A^2 -> H(a, U1(k, k))
28.56/9.85	   A^2 -> H(a, U1(k, d))
28.56/9.85	   A^2 -> H(a, U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.85	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.85	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.85	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.85	   A^2 -> H(U1(e, a), b)
28.56/9.85	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.86	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.86	   A^2 -> H(U1(e, a), c)
28.56/9.86	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.86	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.86	   A^2 -> H(U1(e, a), e)
28.56/9.86	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, a), b)
28.56/9.86	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.86	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.86	   A^2 -> H(U1(k, a), c)
28.56/9.86	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.86	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.86	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, d), b)
28.56/9.86	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, d), c)
28.56/9.86	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.86	   A^2 -> H(U1(c, d), e)
28.56/9.86	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, a), d)
28.56/9.86	   A^2 -> H(U1(c, a), k)
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, c), b)
28.56/9.86	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(d, c), c)
28.56/9.86	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(d, c), e)
28.56/9.86	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, a), d)
28.56/9.86	   A^2 -> H(U1(d, a), k)
28.56/9.86	   A^2 -> H(U1(a, e), b)
28.56/9.86	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.86	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.86	   A^2 -> H(U1(a, e), c)
28.56/9.86	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.86	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.86	   A^2 -> H(U1(a, e), e)
28.56/9.86	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(a, k), b)
28.56/9.86	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.86	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.86	   A^2 -> H(U1(a, k), c)
28.56/9.86	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.86	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.86	   A^2 -> H(U1(a, k), e)
28.56/9.86	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(a, c), d)
28.56/9.86	   A^2 -> H(U1(a, c), k)
28.56/9.86	   A^2 -> H(U1(a, d), d)
28.56/9.86	   A^2 -> H(U1(a, d), k)
28.56/9.86	   A^2 -> H(k, U1(c, b))
28.56/9.86	   A^2 -> H(k, U1(d, b))
28.56/9.86	   A^2 -> H(k, U1(b, c))
28.56/9.86	   A^2 -> H(k, U1(b, d))
28.56/9.86	   A^2 -> H(k, U1(c, c))
28.56/9.86	   A^2 -> H(k, f(e))
28.56/9.86	   A^2 -> H(k, f(k))
28.56/9.86	   A^2 -> H(k, U1(d, d))
28.56/9.86	   A^2 -> H(c, U1(e, b))
28.56/9.86	   A^2 -> H(c, U1(k, b))
28.56/9.86	   A^2 -> H(c, U1(c, d))
28.56/9.86	   A^2 -> H(c, U1(d, c))
28.56/9.86	   A^2 -> H(c, U1(b, e))
28.56/9.86	   A^2 -> H(c, U1(b, k))
28.56/9.86	   A^2 -> H(c, U1(e, c))
28.56/9.86	   A^2 -> H(c, U1(k, c))
28.56/9.86	   A^2 -> H(c, U1(c, e))
28.56/9.86	   A^2 -> H(c, U1(c, k))
28.56/9.86	   A^2 -> H(c, U1(e, e))
28.56/9.86	   A^2 -> H(c, U1(k, k))
28.56/9.86	   A^2 -> H(c, U1(k, d))
28.56/9.86	   A^2 -> H(c, U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.86	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.86	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.86	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.86	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.86	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, c), b)
28.56/9.86	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(e, c), e)
28.56/9.86	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.86	   A^2 -> H(U1(k, c), b)
28.56/9.86	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(k, c), c)
28.56/9.86	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, e), b)
28.56/9.86	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, e), c)
28.56/9.86	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.86	   A^2 -> H(U1(c, e), e)
28.56/9.86	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, k), b)
28.56/9.86	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, k), c)
28.56/9.86	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.86	
28.56/9.86	The TRS R consists of the following rules:
28.56/9.86	
28.56/9.86	   f(x) -> U1(x, x)
28.56/9.86	   U1(e, x) -> x
28.56/9.86	   a -> c
28.56/9.86	   a -> d
28.56/9.86	   b -> c
28.56/9.86	   b -> d
28.56/9.86	   d -> k
28.56/9.86	   c -> e
28.56/9.86	   c -> k
28.56/9.86	
28.56/9.86	Q is empty.
28.56/9.86	We have to consider all minimal (P,Q,R)-chains.
28.56/9.86	----------------------------------------
28.56/9.86	
28.56/9.86	(1543) TransformationProof (EQUIVALENT)
28.56/9.86	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.86	
28.56/9.86	   (A^2 -> H(U1(e, k), U1(e, e)),A^2 -> H(U1(e, k), U1(e, e)))
28.56/9.86	   (A^2 -> H(U1(k, k), U1(e, e)),A^2 -> H(U1(k, k), U1(e, e)))
28.56/9.86	   (A^2 -> H(U1(c, k), e),A^2 -> H(U1(c, k), e))
28.56/9.86	
28.56/9.86	
28.56/9.86	----------------------------------------
28.56/9.86	
28.56/9.86	(1544)
28.56/9.86	Obligation:
28.56/9.86	Q DP problem:
28.56/9.86	The TRS P consists of the following rules:
28.56/9.86	
28.56/9.86	   G(d, x, x) -> A^2
28.56/9.86	   A^2 -> H(f(c), f(c))
28.56/9.86	   H(x, x) -> G(x, x, f(k))
28.56/9.86	   A^2 -> H(f(d), f(d))
28.56/9.86	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.86	   A^2 -> H(f(e), f(e))
28.56/9.86	   A^2 -> H(f(k), f(k))
28.56/9.86	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.86	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.86	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.86	   A^2 -> H(U1(c, c), b)
28.56/9.86	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, c), e)
28.56/9.86	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.86	   A^2 -> H(e, U1(c, b))
28.56/9.86	   A^2 -> H(e, U1(d, b))
28.56/9.86	   A^2 -> H(e, U1(b, c))
28.56/9.86	   A^2 -> H(e, U1(b, d))
28.56/9.86	   A^2 -> H(e, U1(c, c))
28.56/9.86	   A^2 -> H(e, f(e))
28.56/9.86	   A^2 -> H(e, f(k))
28.56/9.86	   A^2 -> H(e, U1(d, d))
28.56/9.86	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.86	   A^2 -> H(f(e), b)
28.56/9.86	   A^2 -> H(f(e), U1(e, d))
28.56/9.86	   A^2 -> H(f(e), U1(d, e))
28.56/9.86	   A^2 -> H(f(e), c)
28.56/9.86	   A^2 -> H(f(e), U1(e, k))
28.56/9.86	   A^2 -> H(f(e), U1(k, e))
28.56/9.86	   A^2 -> H(f(e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.86	   A^2 -> H(f(k), b)
28.56/9.86	   A^2 -> H(f(k), U1(e, d))
28.56/9.86	   A^2 -> H(f(k), U1(d, e))
28.56/9.86	   A^2 -> H(f(k), c)
28.56/9.86	   A^2 -> H(f(k), U1(e, k))
28.56/9.86	   A^2 -> H(f(k), U1(k, e))
28.56/9.86	   A^2 -> H(f(k), e)
28.56/9.86	   A^2 -> H(f(c), d)
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.86	   A^2 -> H(U1(k, k), f(e))
28.56/9.86	   A^2 -> H(U1(k, k), f(k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.86	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.86	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.86	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.86	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.86	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.86	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.86	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.86	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.86	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.86	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.86	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.86	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.86	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.86	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.86	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, d), b)
28.56/9.86	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.86	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.86	   A^2 -> H(U1(d, d), c)
28.56/9.86	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.86	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.86	   A^2 -> H(U1(d, d), e)
28.56/9.86	   A^2 -> H(f(d), d)
28.56/9.86	   A^2 -> H(f(d), k)
28.56/9.86	   A^2 -> H(U1(c, c), c)
28.56/9.86	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.86	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.86	   A^2 -> H(f(c), k)
28.56/9.86	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.86	   A^2 -> H(f(k), U1(k, k))
28.56/9.86	   A^2 -> H(f(e), e)
28.56/9.86	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.86	   A^2 -> H(d, U1(c, b))
28.56/9.86	   A^2 -> H(d, U1(d, b))
28.56/9.86	   A^2 -> H(d, U1(b, c))
28.56/9.86	   A^2 -> H(d, U1(b, d))
28.56/9.86	   A^2 -> H(d, U1(c, c))
28.56/9.86	   A^2 -> H(d, f(e))
28.56/9.86	   A^2 -> H(d, f(k))
28.56/9.86	   A^2 -> H(d, U1(d, d))
28.56/9.86	   A^2 -> H(a, U1(e, b))
28.56/9.86	   A^2 -> H(a, U1(k, b))
28.56/9.86	   A^2 -> H(a, U1(c, d))
28.56/9.86	   A^2 -> H(a, U1(d, c))
28.56/9.86	   A^2 -> H(a, U1(b, e))
28.56/9.86	   A^2 -> H(a, U1(b, k))
28.56/9.86	   A^2 -> H(a, U1(e, c))
28.56/9.86	   A^2 -> H(a, U1(k, c))
28.56/9.86	   A^2 -> H(a, U1(c, e))
28.56/9.86	   A^2 -> H(a, U1(c, k))
28.56/9.86	   A^2 -> H(a, U1(e, e))
28.56/9.86	   A^2 -> H(a, U1(k, k))
28.56/9.86	   A^2 -> H(a, U1(k, d))
28.56/9.86	   A^2 -> H(a, U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.86	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.86	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.86	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.86	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.86	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.86	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, a), b)
28.56/9.86	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.86	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.86	   A^2 -> H(U1(e, a), c)
28.56/9.86	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.86	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.86	   A^2 -> H(U1(e, a), e)
28.56/9.86	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, a), b)
28.56/9.86	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.86	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.86	   A^2 -> H(U1(k, a), c)
28.56/9.86	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.86	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.86	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, d), b)
28.56/9.86	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, d), c)
28.56/9.86	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.86	   A^2 -> H(U1(c, d), e)
28.56/9.86	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, a), d)
28.56/9.86	   A^2 -> H(U1(c, a), k)
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, c), b)
28.56/9.86	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(d, c), c)
28.56/9.86	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(d, c), e)
28.56/9.86	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, a), d)
28.56/9.86	   A^2 -> H(U1(d, a), k)
28.56/9.86	   A^2 -> H(U1(a, e), b)
28.56/9.86	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.86	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.86	   A^2 -> H(U1(a, e), c)
28.56/9.86	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.86	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.86	   A^2 -> H(U1(a, e), e)
28.56/9.86	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(a, k), b)
28.56/9.86	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.86	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.86	   A^2 -> H(U1(a, k), c)
28.56/9.86	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.86	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.86	   A^2 -> H(U1(a, k), e)
28.56/9.86	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(a, c), d)
28.56/9.86	   A^2 -> H(U1(a, c), k)
28.56/9.86	   A^2 -> H(U1(a, d), d)
28.56/9.86	   A^2 -> H(U1(a, d), k)
28.56/9.86	   A^2 -> H(k, U1(c, b))
28.56/9.86	   A^2 -> H(k, U1(d, b))
28.56/9.86	   A^2 -> H(k, U1(b, c))
28.56/9.86	   A^2 -> H(k, U1(b, d))
28.56/9.86	   A^2 -> H(k, U1(c, c))
28.56/9.86	   A^2 -> H(k, f(e))
28.56/9.86	   A^2 -> H(k, f(k))
28.56/9.86	   A^2 -> H(k, U1(d, d))
28.56/9.86	   A^2 -> H(c, U1(e, b))
28.56/9.86	   A^2 -> H(c, U1(k, b))
28.56/9.86	   A^2 -> H(c, U1(c, d))
28.56/9.86	   A^2 -> H(c, U1(d, c))
28.56/9.86	   A^2 -> H(c, U1(b, e))
28.56/9.86	   A^2 -> H(c, U1(b, k))
28.56/9.86	   A^2 -> H(c, U1(e, c))
28.56/9.86	   A^2 -> H(c, U1(k, c))
28.56/9.86	   A^2 -> H(c, U1(c, e))
28.56/9.86	   A^2 -> H(c, U1(c, k))
28.56/9.86	   A^2 -> H(c, U1(e, e))
28.56/9.86	   A^2 -> H(c, U1(k, k))
28.56/9.86	   A^2 -> H(c, U1(k, d))
28.56/9.86	   A^2 -> H(c, U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.86	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.86	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.86	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.86	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.86	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, c), b)
28.56/9.86	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(e, c), e)
28.56/9.86	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.86	   A^2 -> H(U1(k, c), b)
28.56/9.86	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(k, c), c)
28.56/9.86	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, e), b)
28.56/9.86	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, e), c)
28.56/9.86	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.86	   A^2 -> H(U1(c, e), e)
28.56/9.86	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, k), b)
28.56/9.86	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, k), c)
28.56/9.86	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.86	   A^2 -> H(U1(c, k), e)
28.56/9.86	
28.56/9.86	The TRS R consists of the following rules:
28.56/9.86	
28.56/9.86	   f(x) -> U1(x, x)
28.56/9.86	   U1(e, x) -> x
28.56/9.86	   a -> c
28.56/9.86	   a -> d
28.56/9.86	   b -> c
28.56/9.86	   b -> d
28.56/9.86	   d -> k
28.56/9.86	   c -> e
28.56/9.86	   c -> k
28.56/9.86	
28.56/9.86	Q is empty.
28.56/9.86	We have to consider all minimal (P,Q,R)-chains.
28.56/9.86	----------------------------------------
28.56/9.86	
28.56/9.86	(1545) TransformationProof (EQUIVALENT)
28.56/9.86	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.86	
28.56/9.86	   (A^2 -> H(U1(e, k), U1(k, k)),A^2 -> H(U1(e, k), U1(k, k)))
28.56/9.86	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.56/9.86	
28.56/9.86	
28.56/9.86	----------------------------------------
28.56/9.86	
28.56/9.86	(1546)
28.56/9.86	Obligation:
28.56/9.86	Q DP problem:
28.56/9.86	The TRS P consists of the following rules:
28.56/9.86	
28.56/9.86	   G(d, x, x) -> A^2
28.56/9.86	   A^2 -> H(f(c), f(c))
28.56/9.86	   H(x, x) -> G(x, x, f(k))
28.56/9.86	   A^2 -> H(f(d), f(d))
28.56/9.86	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.86	   A^2 -> H(f(e), f(e))
28.56/9.86	   A^2 -> H(f(k), f(k))
28.56/9.86	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.86	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.86	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(c, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.86	   A^2 -> H(U1(c, c), b)
28.56/9.86	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, c), e)
28.56/9.86	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.86	   A^2 -> H(e, U1(c, b))
28.56/9.86	   A^2 -> H(e, U1(d, b))
28.56/9.86	   A^2 -> H(e, U1(b, c))
28.56/9.86	   A^2 -> H(e, U1(b, d))
28.56/9.86	   A^2 -> H(e, U1(c, c))
28.56/9.86	   A^2 -> H(e, f(e))
28.56/9.86	   A^2 -> H(e, f(k))
28.56/9.86	   A^2 -> H(e, U1(d, d))
28.56/9.86	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.86	   A^2 -> H(f(e), b)
28.56/9.86	   A^2 -> H(f(e), U1(e, d))
28.56/9.86	   A^2 -> H(f(e), U1(d, e))
28.56/9.86	   A^2 -> H(f(e), c)
28.56/9.86	   A^2 -> H(f(e), U1(e, k))
28.56/9.86	   A^2 -> H(f(e), U1(k, e))
28.56/9.86	   A^2 -> H(f(e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.86	   A^2 -> H(f(k), b)
28.56/9.86	   A^2 -> H(f(k), U1(e, d))
28.56/9.86	   A^2 -> H(f(k), U1(d, e))
28.56/9.86	   A^2 -> H(f(k), c)
28.56/9.86	   A^2 -> H(f(k), U1(e, k))
28.56/9.86	   A^2 -> H(f(k), U1(k, e))
28.56/9.86	   A^2 -> H(f(k), e)
28.56/9.86	   A^2 -> H(f(c), d)
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.86	   A^2 -> H(U1(k, k), f(e))
28.56/9.86	   A^2 -> H(U1(k, k), f(k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.86	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.86	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.86	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.86	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.86	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.86	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.86	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.86	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.86	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.86	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.86	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.86	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.86	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.86	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.86	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, d), b)
28.56/9.86	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.86	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.86	   A^2 -> H(U1(d, d), c)
28.56/9.86	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.86	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.86	   A^2 -> H(U1(d, d), e)
28.56/9.86	   A^2 -> H(f(d), d)
28.56/9.86	   A^2 -> H(f(d), k)
28.56/9.86	   A^2 -> H(U1(c, c), c)
28.56/9.86	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.86	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.86	   A^2 -> H(f(c), k)
28.56/9.86	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.86	   A^2 -> H(f(k), U1(k, k))
28.56/9.86	   A^2 -> H(f(e), e)
28.56/9.86	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.86	   A^2 -> H(d, U1(c, b))
28.56/9.86	   A^2 -> H(d, U1(d, b))
28.56/9.86	   A^2 -> H(d, U1(b, c))
28.56/9.86	   A^2 -> H(d, U1(b, d))
28.56/9.86	   A^2 -> H(d, U1(c, c))
28.56/9.86	   A^2 -> H(d, f(e))
28.56/9.86	   A^2 -> H(d, f(k))
28.56/9.86	   A^2 -> H(d, U1(d, d))
28.56/9.86	   A^2 -> H(a, U1(e, b))
28.56/9.86	   A^2 -> H(a, U1(k, b))
28.56/9.86	   A^2 -> H(a, U1(c, d))
28.56/9.86	   A^2 -> H(a, U1(d, c))
28.56/9.86	   A^2 -> H(a, U1(b, e))
28.56/9.86	   A^2 -> H(a, U1(b, k))
28.56/9.86	   A^2 -> H(a, U1(e, c))
28.56/9.86	   A^2 -> H(a, U1(k, c))
28.56/9.86	   A^2 -> H(a, U1(c, e))
28.56/9.86	   A^2 -> H(a, U1(c, k))
28.56/9.86	   A^2 -> H(a, U1(e, e))
28.56/9.86	   A^2 -> H(a, U1(k, k))
28.56/9.86	   A^2 -> H(a, U1(k, d))
28.56/9.86	   A^2 -> H(a, U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.86	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.86	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.86	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.86	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.86	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.86	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, a), b)
28.56/9.86	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.86	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.86	   A^2 -> H(U1(e, a), c)
28.56/9.86	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.86	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.86	   A^2 -> H(U1(e, a), e)
28.56/9.86	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, a), b)
28.56/9.86	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.86	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.86	   A^2 -> H(U1(k, a), c)
28.56/9.86	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.86	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.86	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, d), b)
28.56/9.86	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, d), c)
28.56/9.86	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.86	   A^2 -> H(U1(c, d), e)
28.56/9.86	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, a), d)
28.56/9.86	   A^2 -> H(U1(c, a), k)
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, c), b)
28.56/9.86	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(d, c), c)
28.56/9.86	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(d, c), e)
28.56/9.86	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, a), d)
28.56/9.86	   A^2 -> H(U1(d, a), k)
28.56/9.86	   A^2 -> H(U1(a, e), b)
28.56/9.86	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.86	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.86	   A^2 -> H(U1(a, e), c)
28.56/9.86	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.86	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.86	   A^2 -> H(U1(a, e), e)
28.56/9.86	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(a, k), b)
28.56/9.86	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.86	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.86	   A^2 -> H(U1(a, k), c)
28.56/9.86	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.86	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.86	   A^2 -> H(U1(a, k), e)
28.56/9.86	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(a, c), d)
28.56/9.86	   A^2 -> H(U1(a, c), k)
28.56/9.86	   A^2 -> H(U1(a, d), d)
28.56/9.86	   A^2 -> H(U1(a, d), k)
28.56/9.86	   A^2 -> H(k, U1(c, b))
28.56/9.86	   A^2 -> H(k, U1(d, b))
28.56/9.86	   A^2 -> H(k, U1(b, c))
28.56/9.86	   A^2 -> H(k, U1(b, d))
28.56/9.86	   A^2 -> H(k, U1(c, c))
28.56/9.86	   A^2 -> H(k, f(e))
28.56/9.86	   A^2 -> H(k, f(k))
28.56/9.86	   A^2 -> H(k, U1(d, d))
28.56/9.86	   A^2 -> H(c, U1(e, b))
28.56/9.86	   A^2 -> H(c, U1(k, b))
28.56/9.86	   A^2 -> H(c, U1(c, d))
28.56/9.86	   A^2 -> H(c, U1(d, c))
28.56/9.86	   A^2 -> H(c, U1(b, e))
28.56/9.86	   A^2 -> H(c, U1(b, k))
28.56/9.86	   A^2 -> H(c, U1(e, c))
28.56/9.86	   A^2 -> H(c, U1(k, c))
28.56/9.86	   A^2 -> H(c, U1(c, e))
28.56/9.86	   A^2 -> H(c, U1(c, k))
28.56/9.86	   A^2 -> H(c, U1(e, e))
28.56/9.86	   A^2 -> H(c, U1(k, k))
28.56/9.86	   A^2 -> H(c, U1(k, d))
28.56/9.86	   A^2 -> H(c, U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.86	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.86	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.86	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.86	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.86	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, c), b)
28.56/9.86	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(e, c), e)
28.56/9.86	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.86	   A^2 -> H(U1(k, c), b)
28.56/9.86	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(k, c), c)
28.56/9.86	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, e), b)
28.56/9.86	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, e), c)
28.56/9.86	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.86	   A^2 -> H(U1(c, e), e)
28.56/9.86	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, k), b)
28.56/9.86	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, k), c)
28.56/9.86	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.86	   A^2 -> H(U1(c, k), e)
28.56/9.86	
28.56/9.86	The TRS R consists of the following rules:
28.56/9.86	
28.56/9.86	   f(x) -> U1(x, x)
28.56/9.86	   U1(e, x) -> x
28.56/9.86	   a -> c
28.56/9.86	   a -> d
28.56/9.86	   b -> c
28.56/9.86	   b -> d
28.56/9.86	   d -> k
28.56/9.86	   c -> e
28.56/9.86	   c -> k
28.56/9.86	
28.56/9.86	Q is empty.
28.56/9.86	We have to consider all minimal (P,Q,R)-chains.
28.56/9.86	----------------------------------------
28.56/9.86	
28.56/9.86	(1547) TransformationProof (EQUIVALENT)
28.56/9.86	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.86	
28.56/9.86	   (A^2 -> H(U1(e, k), U1(k, d)),A^2 -> H(U1(e, k), U1(k, d)))
28.56/9.86	   (A^2 -> H(U1(k, k), U1(k, d)),A^2 -> H(U1(k, k), U1(k, d)))
28.56/9.86	   (A^2 -> H(U1(c, k), U1(k, k)),A^2 -> H(U1(c, k), U1(k, k)))
28.56/9.86	
28.56/9.86	
28.56/9.86	----------------------------------------
28.56/9.86	
28.56/9.86	(1548)
28.56/9.86	Obligation:
28.56/9.86	Q DP problem:
28.56/9.86	The TRS P consists of the following rules:
28.56/9.86	
28.56/9.86	   G(d, x, x) -> A^2
28.56/9.86	   A^2 -> H(f(c), f(c))
28.56/9.86	   H(x, x) -> G(x, x, f(k))
28.56/9.86	   A^2 -> H(f(d), f(d))
28.56/9.86	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.86	   A^2 -> H(f(e), f(e))
28.56/9.86	   A^2 -> H(f(k), f(k))
28.56/9.86	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.86	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.86	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(c, k), U1(d, k))
28.56/9.86	   A^2 -> H(U1(c, c), b)
28.56/9.86	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, c), e)
28.56/9.86	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.86	   A^2 -> H(e, U1(c, b))
28.56/9.86	   A^2 -> H(e, U1(d, b))
28.56/9.86	   A^2 -> H(e, U1(b, c))
28.56/9.86	   A^2 -> H(e, U1(b, d))
28.56/9.86	   A^2 -> H(e, U1(c, c))
28.56/9.86	   A^2 -> H(e, f(e))
28.56/9.86	   A^2 -> H(e, f(k))
28.56/9.86	   A^2 -> H(e, U1(d, d))
28.56/9.86	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.86	   A^2 -> H(f(e), b)
28.56/9.86	   A^2 -> H(f(e), U1(e, d))
28.56/9.86	   A^2 -> H(f(e), U1(d, e))
28.56/9.86	   A^2 -> H(f(e), c)
28.56/9.86	   A^2 -> H(f(e), U1(e, k))
28.56/9.86	   A^2 -> H(f(e), U1(k, e))
28.56/9.86	   A^2 -> H(f(e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.86	   A^2 -> H(f(k), b)
28.56/9.86	   A^2 -> H(f(k), U1(e, d))
28.56/9.86	   A^2 -> H(f(k), U1(d, e))
28.56/9.86	   A^2 -> H(f(k), c)
28.56/9.86	   A^2 -> H(f(k), U1(e, k))
28.56/9.86	   A^2 -> H(f(k), U1(k, e))
28.56/9.86	   A^2 -> H(f(k), e)
28.56/9.86	   A^2 -> H(f(c), d)
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.86	   A^2 -> H(U1(k, k), f(e))
28.56/9.86	   A^2 -> H(U1(k, k), f(k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.86	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.86	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.86	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.86	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.86	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.86	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.86	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.86	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.86	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.86	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.86	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.86	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.86	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.86	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.86	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, d), b)
28.56/9.86	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.86	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.86	   A^2 -> H(U1(d, d), c)
28.56/9.86	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.86	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.86	   A^2 -> H(U1(d, d), e)
28.56/9.86	   A^2 -> H(f(d), d)
28.56/9.86	   A^2 -> H(f(d), k)
28.56/9.86	   A^2 -> H(U1(c, c), c)
28.56/9.86	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.86	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.86	   A^2 -> H(f(c), k)
28.56/9.86	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.86	   A^2 -> H(f(k), U1(k, k))
28.56/9.86	   A^2 -> H(f(e), e)
28.56/9.86	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.86	   A^2 -> H(d, U1(c, b))
28.56/9.86	   A^2 -> H(d, U1(d, b))
28.56/9.86	   A^2 -> H(d, U1(b, c))
28.56/9.86	   A^2 -> H(d, U1(b, d))
28.56/9.86	   A^2 -> H(d, U1(c, c))
28.56/9.86	   A^2 -> H(d, f(e))
28.56/9.86	   A^2 -> H(d, f(k))
28.56/9.86	   A^2 -> H(d, U1(d, d))
28.56/9.86	   A^2 -> H(a, U1(e, b))
28.56/9.86	   A^2 -> H(a, U1(k, b))
28.56/9.86	   A^2 -> H(a, U1(c, d))
28.56/9.86	   A^2 -> H(a, U1(d, c))
28.56/9.86	   A^2 -> H(a, U1(b, e))
28.56/9.86	   A^2 -> H(a, U1(b, k))
28.56/9.86	   A^2 -> H(a, U1(e, c))
28.56/9.86	   A^2 -> H(a, U1(k, c))
28.56/9.86	   A^2 -> H(a, U1(c, e))
28.56/9.86	   A^2 -> H(a, U1(c, k))
28.56/9.86	   A^2 -> H(a, U1(e, e))
28.56/9.86	   A^2 -> H(a, U1(k, k))
28.56/9.86	   A^2 -> H(a, U1(k, d))
28.56/9.86	   A^2 -> H(a, U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.86	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.86	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.86	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.86	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.86	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.86	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, a), b)
28.56/9.86	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.86	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.86	   A^2 -> H(U1(e, a), c)
28.56/9.86	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.86	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.86	   A^2 -> H(U1(e, a), e)
28.56/9.86	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, a), b)
28.56/9.86	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.86	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.86	   A^2 -> H(U1(k, a), c)
28.56/9.86	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.86	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.86	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, d), b)
28.56/9.86	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, d), c)
28.56/9.86	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.86	   A^2 -> H(U1(c, d), e)
28.56/9.86	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, a), d)
28.56/9.86	   A^2 -> H(U1(c, a), k)
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, c), b)
28.56/9.86	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(d, c), c)
28.56/9.86	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(d, c), e)
28.56/9.86	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, a), d)
28.56/9.86	   A^2 -> H(U1(d, a), k)
28.56/9.86	   A^2 -> H(U1(a, e), b)
28.56/9.86	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.86	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.86	   A^2 -> H(U1(a, e), c)
28.56/9.86	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.86	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.86	   A^2 -> H(U1(a, e), e)
28.56/9.86	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(a, k), b)
28.56/9.86	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.86	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.86	   A^2 -> H(U1(a, k), c)
28.56/9.86	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.86	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.86	   A^2 -> H(U1(a, k), e)
28.56/9.86	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(a, c), d)
28.56/9.86	   A^2 -> H(U1(a, c), k)
28.56/9.86	   A^2 -> H(U1(a, d), d)
28.56/9.86	   A^2 -> H(U1(a, d), k)
28.56/9.86	   A^2 -> H(k, U1(c, b))
28.56/9.86	   A^2 -> H(k, U1(d, b))
28.56/9.86	   A^2 -> H(k, U1(b, c))
28.56/9.86	   A^2 -> H(k, U1(b, d))
28.56/9.86	   A^2 -> H(k, U1(c, c))
28.56/9.86	   A^2 -> H(k, f(e))
28.56/9.86	   A^2 -> H(k, f(k))
28.56/9.86	   A^2 -> H(k, U1(d, d))
28.56/9.86	   A^2 -> H(c, U1(e, b))
28.56/9.86	   A^2 -> H(c, U1(k, b))
28.56/9.86	   A^2 -> H(c, U1(c, d))
28.56/9.86	   A^2 -> H(c, U1(d, c))
28.56/9.86	   A^2 -> H(c, U1(b, e))
28.56/9.86	   A^2 -> H(c, U1(b, k))
28.56/9.86	   A^2 -> H(c, U1(e, c))
28.56/9.86	   A^2 -> H(c, U1(k, c))
28.56/9.86	   A^2 -> H(c, U1(c, e))
28.56/9.86	   A^2 -> H(c, U1(c, k))
28.56/9.86	   A^2 -> H(c, U1(e, e))
28.56/9.86	   A^2 -> H(c, U1(k, k))
28.56/9.86	   A^2 -> H(c, U1(k, d))
28.56/9.86	   A^2 -> H(c, U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.86	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.86	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.86	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.86	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.86	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, c), b)
28.56/9.86	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(e, c), e)
28.56/9.86	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.86	   A^2 -> H(U1(k, c), b)
28.56/9.86	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(k, c), c)
28.56/9.86	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, e), b)
28.56/9.86	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, e), c)
28.56/9.86	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.86	   A^2 -> H(U1(c, e), e)
28.56/9.86	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, k), b)
28.56/9.86	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, k), c)
28.56/9.86	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.86	   A^2 -> H(U1(c, k), e)
28.56/9.86	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.86	
28.56/9.86	The TRS R consists of the following rules:
28.56/9.86	
28.56/9.86	   f(x) -> U1(x, x)
28.56/9.86	   U1(e, x) -> x
28.56/9.86	   a -> c
28.56/9.86	   a -> d
28.56/9.86	   b -> c
28.56/9.86	   b -> d
28.56/9.86	   d -> k
28.56/9.86	   c -> e
28.56/9.86	   c -> k
28.56/9.86	
28.56/9.86	Q is empty.
28.56/9.86	We have to consider all minimal (P,Q,R)-chains.
28.56/9.86	----------------------------------------
28.56/9.86	
28.56/9.86	(1549) TransformationProof (EQUIVALENT)
28.56/9.86	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.86	
28.56/9.86	   (A^2 -> H(U1(e, k), U1(d, k)),A^2 -> H(U1(e, k), U1(d, k)))
28.56/9.86	   (A^2 -> H(U1(k, k), U1(d, k)),A^2 -> H(U1(k, k), U1(d, k)))
28.56/9.86	   (A^2 -> H(U1(c, k), U1(k, k)),A^2 -> H(U1(c, k), U1(k, k)))
28.56/9.86	
28.56/9.86	
28.56/9.86	----------------------------------------
28.56/9.86	
28.56/9.86	(1550)
28.56/9.86	Obligation:
28.56/9.86	Q DP problem:
28.56/9.86	The TRS P consists of the following rules:
28.56/9.86	
28.56/9.86	   G(d, x, x) -> A^2
28.56/9.86	   A^2 -> H(f(c), f(c))
28.56/9.86	   H(x, x) -> G(x, x, f(k))
28.56/9.86	   A^2 -> H(f(d), f(d))
28.56/9.86	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.86	   A^2 -> H(f(e), f(e))
28.56/9.86	   A^2 -> H(f(k), f(k))
28.56/9.86	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.86	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.86	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(c, c), b)
28.56/9.86	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, c), e)
28.56/9.86	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.86	   A^2 -> H(e, U1(c, b))
28.56/9.86	   A^2 -> H(e, U1(d, b))
28.56/9.86	   A^2 -> H(e, U1(b, c))
28.56/9.86	   A^2 -> H(e, U1(b, d))
28.56/9.86	   A^2 -> H(e, U1(c, c))
28.56/9.86	   A^2 -> H(e, f(e))
28.56/9.86	   A^2 -> H(e, f(k))
28.56/9.86	   A^2 -> H(e, U1(d, d))
28.56/9.86	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.86	   A^2 -> H(f(e), b)
28.56/9.86	   A^2 -> H(f(e), U1(e, d))
28.56/9.86	   A^2 -> H(f(e), U1(d, e))
28.56/9.86	   A^2 -> H(f(e), c)
28.56/9.86	   A^2 -> H(f(e), U1(e, k))
28.56/9.86	   A^2 -> H(f(e), U1(k, e))
28.56/9.86	   A^2 -> H(f(e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.86	   A^2 -> H(f(k), b)
28.56/9.86	   A^2 -> H(f(k), U1(e, d))
28.56/9.86	   A^2 -> H(f(k), U1(d, e))
28.56/9.86	   A^2 -> H(f(k), c)
28.56/9.86	   A^2 -> H(f(k), U1(e, k))
28.56/9.86	   A^2 -> H(f(k), U1(k, e))
28.56/9.86	   A^2 -> H(f(k), e)
28.56/9.86	   A^2 -> H(f(c), d)
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.86	   A^2 -> H(U1(k, k), f(e))
28.56/9.86	   A^2 -> H(U1(k, k), f(k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.86	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.86	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.86	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.86	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.86	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.86	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.86	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.86	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.86	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.86	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.86	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.86	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.86	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.86	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.86	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, d), b)
28.56/9.86	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.86	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.86	   A^2 -> H(U1(d, d), c)
28.56/9.86	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.86	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.86	   A^2 -> H(U1(d, d), e)
28.56/9.86	   A^2 -> H(f(d), d)
28.56/9.86	   A^2 -> H(f(d), k)
28.56/9.86	   A^2 -> H(U1(c, c), c)
28.56/9.86	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.86	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.86	   A^2 -> H(f(c), k)
28.56/9.86	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.86	   A^2 -> H(f(k), U1(k, k))
28.56/9.86	   A^2 -> H(f(e), e)
28.56/9.86	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.86	   A^2 -> H(d, U1(c, b))
28.56/9.86	   A^2 -> H(d, U1(d, b))
28.56/9.86	   A^2 -> H(d, U1(b, c))
28.56/9.86	   A^2 -> H(d, U1(b, d))
28.56/9.86	   A^2 -> H(d, U1(c, c))
28.56/9.86	   A^2 -> H(d, f(e))
28.56/9.86	   A^2 -> H(d, f(k))
28.56/9.86	   A^2 -> H(d, U1(d, d))
28.56/9.86	   A^2 -> H(a, U1(e, b))
28.56/9.86	   A^2 -> H(a, U1(k, b))
28.56/9.86	   A^2 -> H(a, U1(c, d))
28.56/9.86	   A^2 -> H(a, U1(d, c))
28.56/9.86	   A^2 -> H(a, U1(b, e))
28.56/9.86	   A^2 -> H(a, U1(b, k))
28.56/9.86	   A^2 -> H(a, U1(e, c))
28.56/9.86	   A^2 -> H(a, U1(k, c))
28.56/9.86	   A^2 -> H(a, U1(c, e))
28.56/9.86	   A^2 -> H(a, U1(c, k))
28.56/9.86	   A^2 -> H(a, U1(e, e))
28.56/9.86	   A^2 -> H(a, U1(k, k))
28.56/9.86	   A^2 -> H(a, U1(k, d))
28.56/9.86	   A^2 -> H(a, U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.86	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.86	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.86	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.86	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.86	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.86	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, a), b)
28.56/9.86	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.86	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.86	   A^2 -> H(U1(e, a), c)
28.56/9.86	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.86	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.86	   A^2 -> H(U1(e, a), e)
28.56/9.86	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, a), b)
28.56/9.86	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.86	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.86	   A^2 -> H(U1(k, a), c)
28.56/9.86	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.86	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.86	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, d), b)
28.56/9.86	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, d), c)
28.56/9.86	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.86	   A^2 -> H(U1(c, d), e)
28.56/9.86	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, a), d)
28.56/9.86	   A^2 -> H(U1(c, a), k)
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, c), b)
28.56/9.86	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(d, c), c)
28.56/9.86	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(d, c), e)
28.56/9.86	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, a), d)
28.56/9.86	   A^2 -> H(U1(d, a), k)
28.56/9.86	   A^2 -> H(U1(a, e), b)
28.56/9.86	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.86	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.86	   A^2 -> H(U1(a, e), c)
28.56/9.86	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.86	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.86	   A^2 -> H(U1(a, e), e)
28.56/9.86	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(a, k), b)
28.56/9.86	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.86	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.86	   A^2 -> H(U1(a, k), c)
28.56/9.86	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.86	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.86	   A^2 -> H(U1(a, k), e)
28.56/9.86	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(a, c), d)
28.56/9.86	   A^2 -> H(U1(a, c), k)
28.56/9.86	   A^2 -> H(U1(a, d), d)
28.56/9.86	   A^2 -> H(U1(a, d), k)
28.56/9.86	   A^2 -> H(k, U1(c, b))
28.56/9.86	   A^2 -> H(k, U1(d, b))
28.56/9.86	   A^2 -> H(k, U1(b, c))
28.56/9.86	   A^2 -> H(k, U1(b, d))
28.56/9.86	   A^2 -> H(k, U1(c, c))
28.56/9.86	   A^2 -> H(k, f(e))
28.56/9.86	   A^2 -> H(k, f(k))
28.56/9.86	   A^2 -> H(k, U1(d, d))
28.56/9.86	   A^2 -> H(c, U1(e, b))
28.56/9.86	   A^2 -> H(c, U1(k, b))
28.56/9.86	   A^2 -> H(c, U1(c, d))
28.56/9.86	   A^2 -> H(c, U1(d, c))
28.56/9.86	   A^2 -> H(c, U1(b, e))
28.56/9.86	   A^2 -> H(c, U1(b, k))
28.56/9.86	   A^2 -> H(c, U1(e, c))
28.56/9.86	   A^2 -> H(c, U1(k, c))
28.56/9.86	   A^2 -> H(c, U1(c, e))
28.56/9.86	   A^2 -> H(c, U1(c, k))
28.56/9.86	   A^2 -> H(c, U1(e, e))
28.56/9.86	   A^2 -> H(c, U1(k, k))
28.56/9.86	   A^2 -> H(c, U1(k, d))
28.56/9.86	   A^2 -> H(c, U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.86	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.86	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.86	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.86	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.86	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, c), b)
28.56/9.86	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(e, c), e)
28.56/9.86	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.86	   A^2 -> H(U1(k, c), b)
28.56/9.86	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(k, c), c)
28.56/9.86	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, e), b)
28.56/9.86	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, e), c)
28.56/9.86	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.86	   A^2 -> H(U1(c, e), e)
28.56/9.86	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, k), b)
28.56/9.86	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, k), c)
28.56/9.86	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.86	   A^2 -> H(U1(c, k), e)
28.56/9.86	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.86	
28.56/9.86	The TRS R consists of the following rules:
28.56/9.86	
28.56/9.86	   f(x) -> U1(x, x)
28.56/9.86	   U1(e, x) -> x
28.56/9.86	   a -> c
28.56/9.86	   a -> d
28.56/9.86	   b -> c
28.56/9.86	   b -> d
28.56/9.86	   d -> k
28.56/9.86	   c -> e
28.56/9.86	   c -> k
28.56/9.86	
28.56/9.86	Q is empty.
28.56/9.86	We have to consider all minimal (P,Q,R)-chains.
28.56/9.86	----------------------------------------
28.56/9.86	
28.56/9.86	(1551) TransformationProof (EQUIVALENT)
28.56/9.86	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), b) at position [] we obtained the following new rules [LPAR04]:
28.56/9.86	
28.56/9.86	   (A^2 -> H(U1(e, c), b),A^2 -> H(U1(e, c), b))
28.56/9.86	   (A^2 -> H(U1(k, c), b),A^2 -> H(U1(k, c), b))
28.56/9.86	   (A^2 -> H(U1(c, e), b),A^2 -> H(U1(c, e), b))
28.56/9.86	   (A^2 -> H(U1(c, k), b),A^2 -> H(U1(c, k), b))
28.56/9.86	   (A^2 -> H(U1(c, c), c),A^2 -> H(U1(c, c), c))
28.56/9.86	   (A^2 -> H(U1(c, c), d),A^2 -> H(U1(c, c), d))
28.56/9.86	
28.56/9.86	
28.56/9.86	----------------------------------------
28.56/9.86	
28.56/9.86	(1552)
28.56/9.86	Obligation:
28.56/9.86	Q DP problem:
28.56/9.86	The TRS P consists of the following rules:
28.56/9.86	
28.56/9.86	   G(d, x, x) -> A^2
28.56/9.86	   A^2 -> H(f(c), f(c))
28.56/9.86	   H(x, x) -> G(x, x, f(k))
28.56/9.86	   A^2 -> H(f(d), f(d))
28.56/9.86	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.86	   A^2 -> H(f(e), f(e))
28.56/9.86	   A^2 -> H(f(k), f(k))
28.56/9.86	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.86	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.86	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(c, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, c), e)
28.56/9.86	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.86	   A^2 -> H(e, U1(c, b))
28.56/9.86	   A^2 -> H(e, U1(d, b))
28.56/9.86	   A^2 -> H(e, U1(b, c))
28.56/9.86	   A^2 -> H(e, U1(b, d))
28.56/9.86	   A^2 -> H(e, U1(c, c))
28.56/9.86	   A^2 -> H(e, f(e))
28.56/9.86	   A^2 -> H(e, f(k))
28.56/9.86	   A^2 -> H(e, U1(d, d))
28.56/9.86	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.86	   A^2 -> H(f(e), b)
28.56/9.86	   A^2 -> H(f(e), U1(e, d))
28.56/9.86	   A^2 -> H(f(e), U1(d, e))
28.56/9.86	   A^2 -> H(f(e), c)
28.56/9.86	   A^2 -> H(f(e), U1(e, k))
28.56/9.86	   A^2 -> H(f(e), U1(k, e))
28.56/9.86	   A^2 -> H(f(e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.86	   A^2 -> H(f(k), b)
28.56/9.86	   A^2 -> H(f(k), U1(e, d))
28.56/9.86	   A^2 -> H(f(k), U1(d, e))
28.56/9.86	   A^2 -> H(f(k), c)
28.56/9.86	   A^2 -> H(f(k), U1(e, k))
28.56/9.86	   A^2 -> H(f(k), U1(k, e))
28.56/9.86	   A^2 -> H(f(k), e)
28.56/9.86	   A^2 -> H(f(c), d)
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.86	   A^2 -> H(U1(k, k), f(e))
28.56/9.86	   A^2 -> H(U1(k, k), f(k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.86	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.86	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.86	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.86	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.86	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.86	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.86	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.86	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.86	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.86	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.86	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.86	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.86	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.86	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.86	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, d), b)
28.56/9.86	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.86	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.86	   A^2 -> H(U1(d, d), c)
28.56/9.86	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.86	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.86	   A^2 -> H(U1(d, d), e)
28.56/9.86	   A^2 -> H(f(d), d)
28.56/9.86	   A^2 -> H(f(d), k)
28.56/9.86	   A^2 -> H(U1(c, c), c)
28.56/9.86	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.86	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.86	   A^2 -> H(f(c), k)
28.56/9.86	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.86	   A^2 -> H(f(k), U1(k, k))
28.56/9.86	   A^2 -> H(f(e), e)
28.56/9.86	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.86	   A^2 -> H(d, U1(c, b))
28.56/9.86	   A^2 -> H(d, U1(d, b))
28.56/9.86	   A^2 -> H(d, U1(b, c))
28.56/9.86	   A^2 -> H(d, U1(b, d))
28.56/9.86	   A^2 -> H(d, U1(c, c))
28.56/9.86	   A^2 -> H(d, f(e))
28.56/9.86	   A^2 -> H(d, f(k))
28.56/9.86	   A^2 -> H(d, U1(d, d))
28.56/9.86	   A^2 -> H(a, U1(e, b))
28.56/9.86	   A^2 -> H(a, U1(k, b))
28.56/9.86	   A^2 -> H(a, U1(c, d))
28.56/9.86	   A^2 -> H(a, U1(d, c))
28.56/9.86	   A^2 -> H(a, U1(b, e))
28.56/9.86	   A^2 -> H(a, U1(b, k))
28.56/9.86	   A^2 -> H(a, U1(e, c))
28.56/9.86	   A^2 -> H(a, U1(k, c))
28.56/9.86	   A^2 -> H(a, U1(c, e))
28.56/9.86	   A^2 -> H(a, U1(c, k))
28.56/9.86	   A^2 -> H(a, U1(e, e))
28.56/9.86	   A^2 -> H(a, U1(k, k))
28.56/9.86	   A^2 -> H(a, U1(k, d))
28.56/9.86	   A^2 -> H(a, U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.86	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.86	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.86	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.86	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.86	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.86	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, a), b)
28.56/9.86	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.86	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.86	   A^2 -> H(U1(e, a), c)
28.56/9.86	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.86	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.86	   A^2 -> H(U1(e, a), e)
28.56/9.86	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, a), b)
28.56/9.86	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.86	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.86	   A^2 -> H(U1(k, a), c)
28.56/9.86	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.86	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.86	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, d), b)
28.56/9.86	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, d), c)
28.56/9.86	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.86	   A^2 -> H(U1(c, d), e)
28.56/9.86	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, a), d)
28.56/9.86	   A^2 -> H(U1(c, a), k)
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, c), b)
28.56/9.86	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(d, c), c)
28.56/9.86	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(d, c), e)
28.56/9.86	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, a), d)
28.56/9.86	   A^2 -> H(U1(d, a), k)
28.56/9.86	   A^2 -> H(U1(a, e), b)
28.56/9.86	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.86	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.86	   A^2 -> H(U1(a, e), c)
28.56/9.86	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.86	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.86	   A^2 -> H(U1(a, e), e)
28.56/9.86	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(a, k), b)
28.56/9.86	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.86	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.86	   A^2 -> H(U1(a, k), c)
28.56/9.86	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.86	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.86	   A^2 -> H(U1(a, k), e)
28.56/9.86	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(a, c), d)
28.56/9.86	   A^2 -> H(U1(a, c), k)
28.56/9.86	   A^2 -> H(U1(a, d), d)
28.56/9.86	   A^2 -> H(U1(a, d), k)
28.56/9.86	   A^2 -> H(k, U1(c, b))
28.56/9.86	   A^2 -> H(k, U1(d, b))
28.56/9.86	   A^2 -> H(k, U1(b, c))
28.56/9.86	   A^2 -> H(k, U1(b, d))
28.56/9.86	   A^2 -> H(k, U1(c, c))
28.56/9.86	   A^2 -> H(k, f(e))
28.56/9.86	   A^2 -> H(k, f(k))
28.56/9.86	   A^2 -> H(k, U1(d, d))
28.56/9.86	   A^2 -> H(c, U1(e, b))
28.56/9.86	   A^2 -> H(c, U1(k, b))
28.56/9.86	   A^2 -> H(c, U1(c, d))
28.56/9.86	   A^2 -> H(c, U1(d, c))
28.56/9.86	   A^2 -> H(c, U1(b, e))
28.56/9.86	   A^2 -> H(c, U1(b, k))
28.56/9.86	   A^2 -> H(c, U1(e, c))
28.56/9.86	   A^2 -> H(c, U1(k, c))
28.56/9.86	   A^2 -> H(c, U1(c, e))
28.56/9.86	   A^2 -> H(c, U1(c, k))
28.56/9.86	   A^2 -> H(c, U1(e, e))
28.56/9.86	   A^2 -> H(c, U1(k, k))
28.56/9.86	   A^2 -> H(c, U1(k, d))
28.56/9.86	   A^2 -> H(c, U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.86	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.86	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.86	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.86	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.86	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, c), b)
28.56/9.86	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(e, c), e)
28.56/9.86	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.86	   A^2 -> H(U1(k, c), b)
28.56/9.86	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(k, c), c)
28.56/9.86	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, e), b)
28.56/9.86	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, e), c)
28.56/9.86	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.86	   A^2 -> H(U1(c, e), e)
28.56/9.86	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, k), b)
28.56/9.86	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, k), c)
28.56/9.86	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.86	   A^2 -> H(U1(c, k), e)
28.56/9.86	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, c), d)
28.56/9.86	
28.56/9.86	The TRS R consists of the following rules:
28.56/9.86	
28.56/9.86	   f(x) -> U1(x, x)
28.56/9.86	   U1(e, x) -> x
28.56/9.86	   a -> c
28.56/9.86	   a -> d
28.56/9.86	   b -> c
28.56/9.86	   b -> d
28.56/9.86	   d -> k
28.56/9.86	   c -> e
28.56/9.86	   c -> k
28.56/9.86	
28.56/9.86	Q is empty.
28.56/9.86	We have to consider all minimal (P,Q,R)-chains.
28.56/9.86	----------------------------------------
28.56/9.86	
28.56/9.86	(1553) TransformationProof (EQUIVALENT)
28.56/9.86	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.86	
28.56/9.86	   (A^2 -> H(U1(e, c), U1(e, d)),A^2 -> H(U1(e, c), U1(e, d)))
28.56/9.86	   (A^2 -> H(U1(k, c), U1(e, d)),A^2 -> H(U1(k, c), U1(e, d)))
28.56/9.86	   (A^2 -> H(U1(c, e), U1(e, d)),A^2 -> H(U1(c, e), U1(e, d)))
28.56/9.86	   (A^2 -> H(U1(c, k), U1(e, d)),A^2 -> H(U1(c, k), U1(e, d)))
28.56/9.86	   (A^2 -> H(U1(c, c), d),A^2 -> H(U1(c, c), d))
28.56/9.86	   (A^2 -> H(U1(c, c), U1(e, k)),A^2 -> H(U1(c, c), U1(e, k)))
28.56/9.86	
28.56/9.86	
28.56/9.86	----------------------------------------
28.56/9.86	
28.56/9.86	(1554)
28.56/9.86	Obligation:
28.56/9.86	Q DP problem:
28.56/9.86	The TRS P consists of the following rules:
28.56/9.86	
28.56/9.86	   G(d, x, x) -> A^2
28.56/9.86	   A^2 -> H(f(c), f(c))
28.56/9.86	   H(x, x) -> G(x, x, f(k))
28.56/9.86	   A^2 -> H(f(d), f(d))
28.56/9.86	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.86	   A^2 -> H(f(e), f(e))
28.56/9.86	   A^2 -> H(f(k), f(k))
28.56/9.86	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.86	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.86	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(c, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, c), e)
28.56/9.86	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.86	   A^2 -> H(e, U1(c, b))
28.56/9.86	   A^2 -> H(e, U1(d, b))
28.56/9.86	   A^2 -> H(e, U1(b, c))
28.56/9.86	   A^2 -> H(e, U1(b, d))
28.56/9.86	   A^2 -> H(e, U1(c, c))
28.56/9.86	   A^2 -> H(e, f(e))
28.56/9.86	   A^2 -> H(e, f(k))
28.56/9.86	   A^2 -> H(e, U1(d, d))
28.56/9.86	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.86	   A^2 -> H(f(e), b)
28.56/9.86	   A^2 -> H(f(e), U1(e, d))
28.56/9.86	   A^2 -> H(f(e), U1(d, e))
28.56/9.86	   A^2 -> H(f(e), c)
28.56/9.86	   A^2 -> H(f(e), U1(e, k))
28.56/9.86	   A^2 -> H(f(e), U1(k, e))
28.56/9.86	   A^2 -> H(f(e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.86	   A^2 -> H(f(k), b)
28.56/9.86	   A^2 -> H(f(k), U1(e, d))
28.56/9.86	   A^2 -> H(f(k), U1(d, e))
28.56/9.86	   A^2 -> H(f(k), c)
28.56/9.86	   A^2 -> H(f(k), U1(e, k))
28.56/9.86	   A^2 -> H(f(k), U1(k, e))
28.56/9.86	   A^2 -> H(f(k), e)
28.56/9.86	   A^2 -> H(f(c), d)
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.86	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.86	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.86	   A^2 -> H(U1(k, k), f(e))
28.56/9.86	   A^2 -> H(U1(k, k), f(k))
28.56/9.86	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.86	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.86	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.86	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.86	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.86	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.86	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.86	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.86	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.86	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.86	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.86	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.86	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.86	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.86	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.86	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.86	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, d), b)
28.56/9.86	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.86	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.86	   A^2 -> H(U1(d, d), c)
28.56/9.86	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.86	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.86	   A^2 -> H(U1(d, d), e)
28.56/9.86	   A^2 -> H(f(d), d)
28.56/9.86	   A^2 -> H(f(d), k)
28.56/9.86	   A^2 -> H(U1(c, c), c)
28.56/9.86	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.86	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.86	   A^2 -> H(f(c), k)
28.56/9.86	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.86	   A^2 -> H(f(k), U1(k, k))
28.56/9.86	   A^2 -> H(f(e), e)
28.56/9.86	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.86	   A^2 -> H(d, U1(c, b))
28.56/9.86	   A^2 -> H(d, U1(d, b))
28.56/9.86	   A^2 -> H(d, U1(b, c))
28.56/9.86	   A^2 -> H(d, U1(b, d))
28.56/9.86	   A^2 -> H(d, U1(c, c))
28.56/9.86	   A^2 -> H(d, f(e))
28.56/9.86	   A^2 -> H(d, f(k))
28.56/9.86	   A^2 -> H(d, U1(d, d))
28.56/9.86	   A^2 -> H(a, U1(e, b))
28.56/9.86	   A^2 -> H(a, U1(k, b))
28.56/9.86	   A^2 -> H(a, U1(c, d))
28.56/9.86	   A^2 -> H(a, U1(d, c))
28.56/9.86	   A^2 -> H(a, U1(b, e))
28.56/9.86	   A^2 -> H(a, U1(b, k))
28.56/9.86	   A^2 -> H(a, U1(e, c))
28.56/9.86	   A^2 -> H(a, U1(k, c))
28.56/9.86	   A^2 -> H(a, U1(c, e))
28.56/9.86	   A^2 -> H(a, U1(c, k))
28.56/9.86	   A^2 -> H(a, U1(e, e))
28.56/9.86	   A^2 -> H(a, U1(k, k))
28.56/9.86	   A^2 -> H(a, U1(k, d))
28.56/9.86	   A^2 -> H(a, U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.86	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.86	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.86	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.86	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.86	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.86	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.86	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.86	   A^2 -> H(U1(e, a), b)
28.56/9.86	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.86	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.86	   A^2 -> H(U1(e, a), c)
28.56/9.86	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.86	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.86	   A^2 -> H(U1(e, a), e)
28.56/9.86	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.86	   A^2 -> H(U1(k, a), b)
28.56/9.86	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.86	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.86	   A^2 -> H(U1(k, a), c)
28.56/9.86	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.86	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.86	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, d), b)
28.56/9.86	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.86	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.86	   A^2 -> H(U1(c, d), c)
28.56/9.86	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.86	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.86	   A^2 -> H(U1(c, d), e)
28.56/9.86	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.86	   A^2 -> H(U1(c, a), d)
28.56/9.86	   A^2 -> H(U1(c, a), k)
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.86	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.86	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.86	   A^2 -> H(U1(d, c), b)
28.56/9.86	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.86	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.86	   A^2 -> H(U1(d, c), c)
28.56/9.86	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.86	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.86	   A^2 -> H(U1(d, c), e)
28.56/9.86	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.86	   A^2 -> H(U1(d, a), d)
28.56/9.86	   A^2 -> H(U1(d, a), k)
28.56/9.86	   A^2 -> H(U1(a, e), b)
28.56/9.86	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.86	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.86	   A^2 -> H(U1(a, e), c)
28.56/9.86	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.86	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.86	   A^2 -> H(U1(a, e), e)
28.56/9.86	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.86	   A^2 -> H(U1(a, k), b)
28.56/9.86	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.86	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.86	   A^2 -> H(U1(a, k), c)
28.56/9.86	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.86	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.86	   A^2 -> H(U1(a, k), e)
28.56/9.86	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.86	   A^2 -> H(U1(a, c), d)
28.56/9.86	   A^2 -> H(U1(a, c), k)
28.56/9.86	   A^2 -> H(U1(a, d), d)
28.56/9.86	   A^2 -> H(U1(a, d), k)
28.56/9.86	   A^2 -> H(k, U1(c, b))
28.56/9.86	   A^2 -> H(k, U1(d, b))
28.56/9.86	   A^2 -> H(k, U1(b, c))
28.56/9.86	   A^2 -> H(k, U1(b, d))
28.56/9.86	   A^2 -> H(k, U1(c, c))
28.56/9.86	   A^2 -> H(k, f(e))
28.56/9.86	   A^2 -> H(k, f(k))
28.56/9.86	   A^2 -> H(k, U1(d, d))
28.56/9.87	   A^2 -> H(c, U1(e, b))
28.56/9.87	   A^2 -> H(c, U1(k, b))
28.56/9.87	   A^2 -> H(c, U1(c, d))
28.56/9.87	   A^2 -> H(c, U1(d, c))
28.56/9.87	   A^2 -> H(c, U1(b, e))
28.56/9.87	   A^2 -> H(c, U1(b, k))
28.56/9.87	   A^2 -> H(c, U1(e, c))
28.56/9.87	   A^2 -> H(c, U1(k, c))
28.56/9.87	   A^2 -> H(c, U1(c, e))
28.56/9.87	   A^2 -> H(c, U1(c, k))
28.56/9.87	   A^2 -> H(c, U1(e, e))
28.56/9.87	   A^2 -> H(c, U1(k, k))
28.56/9.87	   A^2 -> H(c, U1(k, d))
28.56/9.87	   A^2 -> H(c, U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, c), b)
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(e, c), e)
28.56/9.87	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.87	   A^2 -> H(U1(k, c), b)
28.56/9.87	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(k, c), c)
28.56/9.87	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, e), b)
28.56/9.87	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, e), c)
28.56/9.87	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, e), e)
28.56/9.87	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, k), b)
28.56/9.87	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, k), c)
28.56/9.87	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, k), e)
28.56/9.87	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, c), d)
28.56/9.87	
28.56/9.87	The TRS R consists of the following rules:
28.56/9.87	
28.56/9.87	   f(x) -> U1(x, x)
28.56/9.87	   U1(e, x) -> x
28.56/9.87	   a -> c
28.56/9.87	   a -> d
28.56/9.87	   b -> c
28.56/9.87	   b -> d
28.56/9.87	   d -> k
28.56/9.87	   c -> e
28.56/9.87	   c -> k
28.56/9.87	
28.56/9.87	Q is empty.
28.56/9.87	We have to consider all minimal (P,Q,R)-chains.
28.56/9.87	----------------------------------------
28.56/9.87	
28.56/9.87	(1555) TransformationProof (EQUIVALENT)
28.56/9.87	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.87	
28.56/9.87	   (A^2 -> H(U1(e, c), U1(d, e)),A^2 -> H(U1(e, c), U1(d, e)))
28.56/9.87	   (A^2 -> H(U1(k, c), U1(d, e)),A^2 -> H(U1(k, c), U1(d, e)))
28.56/9.87	   (A^2 -> H(U1(c, e), U1(d, e)),A^2 -> H(U1(c, e), U1(d, e)))
28.56/9.87	   (A^2 -> H(U1(c, k), U1(d, e)),A^2 -> H(U1(c, k), U1(d, e)))
28.56/9.87	   (A^2 -> H(U1(c, c), U1(k, e)),A^2 -> H(U1(c, c), U1(k, e)))
28.56/9.87	
28.56/9.87	
28.56/9.87	----------------------------------------
28.56/9.87	
28.56/9.87	(1556)
28.56/9.87	Obligation:
28.56/9.87	Q DP problem:
28.56/9.87	The TRS P consists of the following rules:
28.56/9.87	
28.56/9.87	   G(d, x, x) -> A^2
28.56/9.87	   A^2 -> H(f(c), f(c))
28.56/9.87	   H(x, x) -> G(x, x, f(k))
28.56/9.87	   A^2 -> H(f(d), f(d))
28.56/9.87	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.87	   A^2 -> H(f(e), f(e))
28.56/9.87	   A^2 -> H(f(k), f(k))
28.56/9.87	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.87	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.87	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(c, c), e)
28.56/9.87	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.87	   A^2 -> H(e, U1(c, b))
28.56/9.87	   A^2 -> H(e, U1(d, b))
28.56/9.87	   A^2 -> H(e, U1(b, c))
28.56/9.87	   A^2 -> H(e, U1(b, d))
28.56/9.87	   A^2 -> H(e, U1(c, c))
28.56/9.87	   A^2 -> H(e, f(e))
28.56/9.87	   A^2 -> H(e, f(k))
28.56/9.87	   A^2 -> H(e, U1(d, d))
28.56/9.87	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.87	   A^2 -> H(f(e), b)
28.56/9.87	   A^2 -> H(f(e), U1(e, d))
28.56/9.87	   A^2 -> H(f(e), U1(d, e))
28.56/9.87	   A^2 -> H(f(e), c)
28.56/9.87	   A^2 -> H(f(e), U1(e, k))
28.56/9.87	   A^2 -> H(f(e), U1(k, e))
28.56/9.87	   A^2 -> H(f(e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.87	   A^2 -> H(f(k), b)
28.56/9.87	   A^2 -> H(f(k), U1(e, d))
28.56/9.87	   A^2 -> H(f(k), U1(d, e))
28.56/9.87	   A^2 -> H(f(k), c)
28.56/9.87	   A^2 -> H(f(k), U1(e, k))
28.56/9.87	   A^2 -> H(f(k), U1(k, e))
28.56/9.87	   A^2 -> H(f(k), e)
28.56/9.87	   A^2 -> H(f(c), d)
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.87	   A^2 -> H(U1(k, k), f(e))
28.56/9.87	   A^2 -> H(U1(k, k), f(k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.87	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.87	   A^2 -> H(U1(d, d), b)
28.56/9.87	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.87	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.87	   A^2 -> H(U1(d, d), c)
28.56/9.87	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.87	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.87	   A^2 -> H(U1(d, d), e)
28.56/9.87	   A^2 -> H(f(d), d)
28.56/9.87	   A^2 -> H(f(d), k)
28.56/9.87	   A^2 -> H(U1(c, c), c)
28.56/9.87	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.87	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.87	   A^2 -> H(f(c), k)
28.56/9.87	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.87	   A^2 -> H(f(k), U1(k, k))
28.56/9.87	   A^2 -> H(f(e), e)
28.56/9.87	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.87	   A^2 -> H(d, U1(c, b))
28.56/9.87	   A^2 -> H(d, U1(d, b))
28.56/9.87	   A^2 -> H(d, U1(b, c))
28.56/9.87	   A^2 -> H(d, U1(b, d))
28.56/9.87	   A^2 -> H(d, U1(c, c))
28.56/9.87	   A^2 -> H(d, f(e))
28.56/9.87	   A^2 -> H(d, f(k))
28.56/9.87	   A^2 -> H(d, U1(d, d))
28.56/9.87	   A^2 -> H(a, U1(e, b))
28.56/9.87	   A^2 -> H(a, U1(k, b))
28.56/9.87	   A^2 -> H(a, U1(c, d))
28.56/9.87	   A^2 -> H(a, U1(d, c))
28.56/9.87	   A^2 -> H(a, U1(b, e))
28.56/9.87	   A^2 -> H(a, U1(b, k))
28.56/9.87	   A^2 -> H(a, U1(e, c))
28.56/9.87	   A^2 -> H(a, U1(k, c))
28.56/9.87	   A^2 -> H(a, U1(c, e))
28.56/9.87	   A^2 -> H(a, U1(c, k))
28.56/9.87	   A^2 -> H(a, U1(e, e))
28.56/9.87	   A^2 -> H(a, U1(k, k))
28.56/9.87	   A^2 -> H(a, U1(k, d))
28.56/9.87	   A^2 -> H(a, U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, a), b)
28.56/9.87	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.87	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.87	   A^2 -> H(U1(e, a), c)
28.56/9.87	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.87	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.87	   A^2 -> H(U1(e, a), e)
28.56/9.87	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, a), b)
28.56/9.87	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.87	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.87	   A^2 -> H(U1(k, a), c)
28.56/9.87	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.87	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.87	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, d), b)
28.56/9.87	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, d), c)
28.56/9.87	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, d), e)
28.56/9.87	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, a), d)
28.56/9.87	   A^2 -> H(U1(c, a), k)
28.56/9.87	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.87	   A^2 -> H(U1(d, c), b)
28.56/9.87	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(d, c), c)
28.56/9.87	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(d, c), e)
28.56/9.87	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(d, a), d)
28.56/9.87	   A^2 -> H(U1(d, a), k)
28.56/9.87	   A^2 -> H(U1(a, e), b)
28.56/9.87	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.87	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.87	   A^2 -> H(U1(a, e), c)
28.56/9.87	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.87	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.87	   A^2 -> H(U1(a, e), e)
28.56/9.87	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(a, k), b)
28.56/9.87	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.87	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.87	   A^2 -> H(U1(a, k), c)
28.56/9.87	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.87	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.87	   A^2 -> H(U1(a, k), e)
28.56/9.87	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(a, c), d)
28.56/9.87	   A^2 -> H(U1(a, c), k)
28.56/9.87	   A^2 -> H(U1(a, d), d)
28.56/9.87	   A^2 -> H(U1(a, d), k)
28.56/9.87	   A^2 -> H(k, U1(c, b))
28.56/9.87	   A^2 -> H(k, U1(d, b))
28.56/9.87	   A^2 -> H(k, U1(b, c))
28.56/9.87	   A^2 -> H(k, U1(b, d))
28.56/9.87	   A^2 -> H(k, U1(c, c))
28.56/9.87	   A^2 -> H(k, f(e))
28.56/9.87	   A^2 -> H(k, f(k))
28.56/9.87	   A^2 -> H(k, U1(d, d))
28.56/9.87	   A^2 -> H(c, U1(e, b))
28.56/9.87	   A^2 -> H(c, U1(k, b))
28.56/9.87	   A^2 -> H(c, U1(c, d))
28.56/9.87	   A^2 -> H(c, U1(d, c))
28.56/9.87	   A^2 -> H(c, U1(b, e))
28.56/9.87	   A^2 -> H(c, U1(b, k))
28.56/9.87	   A^2 -> H(c, U1(e, c))
28.56/9.87	   A^2 -> H(c, U1(k, c))
28.56/9.87	   A^2 -> H(c, U1(c, e))
28.56/9.87	   A^2 -> H(c, U1(c, k))
28.56/9.87	   A^2 -> H(c, U1(e, e))
28.56/9.87	   A^2 -> H(c, U1(k, k))
28.56/9.87	   A^2 -> H(c, U1(k, d))
28.56/9.87	   A^2 -> H(c, U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, c), b)
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(e, c), e)
28.56/9.87	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.87	   A^2 -> H(U1(k, c), b)
28.56/9.87	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(k, c), c)
28.56/9.87	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, e), b)
28.56/9.87	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, e), c)
28.56/9.87	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, e), e)
28.56/9.87	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, k), b)
28.56/9.87	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, k), c)
28.56/9.87	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, k), e)
28.56/9.87	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, c), d)
28.56/9.87	
28.56/9.87	The TRS R consists of the following rules:
28.56/9.87	
28.56/9.87	   f(x) -> U1(x, x)
28.56/9.87	   U1(e, x) -> x
28.56/9.87	   a -> c
28.56/9.87	   a -> d
28.56/9.87	   b -> c
28.56/9.87	   b -> d
28.56/9.87	   d -> k
28.56/9.87	   c -> e
28.56/9.87	   c -> k
28.56/9.87	
28.56/9.87	Q is empty.
28.56/9.87	We have to consider all minimal (P,Q,R)-chains.
28.56/9.87	----------------------------------------
28.56/9.87	
28.56/9.87	(1557) TransformationProof (EQUIVALENT)
28.56/9.87	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), e) at position [] we obtained the following new rules [LPAR04]:
28.56/9.87	
28.56/9.87	   (A^2 -> H(U1(e, c), e),A^2 -> H(U1(e, c), e))
28.56/9.87	   (A^2 -> H(U1(k, c), e),A^2 -> H(U1(k, c), e))
28.56/9.87	   (A^2 -> H(U1(c, e), e),A^2 -> H(U1(c, e), e))
28.56/9.87	   (A^2 -> H(U1(c, k), e),A^2 -> H(U1(c, k), e))
28.56/9.87	
28.56/9.87	
28.56/9.87	----------------------------------------
28.56/9.87	
28.56/9.87	(1558)
28.56/9.87	Obligation:
28.56/9.87	Q DP problem:
28.56/9.87	The TRS P consists of the following rules:
28.56/9.87	
28.56/9.87	   G(d, x, x) -> A^2
28.56/9.87	   A^2 -> H(f(c), f(c))
28.56/9.87	   H(x, x) -> G(x, x, f(k))
28.56/9.87	   A^2 -> H(f(d), f(d))
28.56/9.87	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.87	   A^2 -> H(f(e), f(e))
28.56/9.87	   A^2 -> H(f(k), f(k))
28.56/9.87	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.87	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.87	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.87	   A^2 -> H(e, U1(c, b))
28.56/9.87	   A^2 -> H(e, U1(d, b))
28.56/9.87	   A^2 -> H(e, U1(b, c))
28.56/9.87	   A^2 -> H(e, U1(b, d))
28.56/9.87	   A^2 -> H(e, U1(c, c))
28.56/9.87	   A^2 -> H(e, f(e))
28.56/9.87	   A^2 -> H(e, f(k))
28.56/9.87	   A^2 -> H(e, U1(d, d))
28.56/9.87	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.87	   A^2 -> H(f(e), b)
28.56/9.87	   A^2 -> H(f(e), U1(e, d))
28.56/9.87	   A^2 -> H(f(e), U1(d, e))
28.56/9.87	   A^2 -> H(f(e), c)
28.56/9.87	   A^2 -> H(f(e), U1(e, k))
28.56/9.87	   A^2 -> H(f(e), U1(k, e))
28.56/9.87	   A^2 -> H(f(e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.87	   A^2 -> H(f(k), b)
28.56/9.87	   A^2 -> H(f(k), U1(e, d))
28.56/9.87	   A^2 -> H(f(k), U1(d, e))
28.56/9.87	   A^2 -> H(f(k), c)
28.56/9.87	   A^2 -> H(f(k), U1(e, k))
28.56/9.87	   A^2 -> H(f(k), U1(k, e))
28.56/9.87	   A^2 -> H(f(k), e)
28.56/9.87	   A^2 -> H(f(c), d)
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.87	   A^2 -> H(U1(k, k), f(e))
28.56/9.87	   A^2 -> H(U1(k, k), f(k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.87	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.87	   A^2 -> H(U1(d, d), b)
28.56/9.87	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.87	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.87	   A^2 -> H(U1(d, d), c)
28.56/9.87	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.87	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.87	   A^2 -> H(U1(d, d), e)
28.56/9.87	   A^2 -> H(f(d), d)
28.56/9.87	   A^2 -> H(f(d), k)
28.56/9.87	   A^2 -> H(U1(c, c), c)
28.56/9.87	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.87	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.87	   A^2 -> H(f(c), k)
28.56/9.87	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.87	   A^2 -> H(f(k), U1(k, k))
28.56/9.87	   A^2 -> H(f(e), e)
28.56/9.87	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.87	   A^2 -> H(d, U1(c, b))
28.56/9.87	   A^2 -> H(d, U1(d, b))
28.56/9.87	   A^2 -> H(d, U1(b, c))
28.56/9.87	   A^2 -> H(d, U1(b, d))
28.56/9.87	   A^2 -> H(d, U1(c, c))
28.56/9.87	   A^2 -> H(d, f(e))
28.56/9.87	   A^2 -> H(d, f(k))
28.56/9.87	   A^2 -> H(d, U1(d, d))
28.56/9.87	   A^2 -> H(a, U1(e, b))
28.56/9.87	   A^2 -> H(a, U1(k, b))
28.56/9.87	   A^2 -> H(a, U1(c, d))
28.56/9.87	   A^2 -> H(a, U1(d, c))
28.56/9.87	   A^2 -> H(a, U1(b, e))
28.56/9.87	   A^2 -> H(a, U1(b, k))
28.56/9.87	   A^2 -> H(a, U1(e, c))
28.56/9.87	   A^2 -> H(a, U1(k, c))
28.56/9.87	   A^2 -> H(a, U1(c, e))
28.56/9.87	   A^2 -> H(a, U1(c, k))
28.56/9.87	   A^2 -> H(a, U1(e, e))
28.56/9.87	   A^2 -> H(a, U1(k, k))
28.56/9.87	   A^2 -> H(a, U1(k, d))
28.56/9.87	   A^2 -> H(a, U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, a), b)
28.56/9.87	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.87	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.87	   A^2 -> H(U1(e, a), c)
28.56/9.87	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.87	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.87	   A^2 -> H(U1(e, a), e)
28.56/9.87	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, a), b)
28.56/9.87	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.87	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.87	   A^2 -> H(U1(k, a), c)
28.56/9.87	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.87	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.87	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, d), b)
28.56/9.87	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, d), c)
28.56/9.87	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, d), e)
28.56/9.87	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, a), d)
28.56/9.87	   A^2 -> H(U1(c, a), k)
28.56/9.87	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.87	   A^2 -> H(U1(d, c), b)
28.56/9.87	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(d, c), c)
28.56/9.87	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(d, c), e)
28.56/9.87	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(d, a), d)
28.56/9.87	   A^2 -> H(U1(d, a), k)
28.56/9.87	   A^2 -> H(U1(a, e), b)
28.56/9.87	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.87	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.87	   A^2 -> H(U1(a, e), c)
28.56/9.87	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.87	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.87	   A^2 -> H(U1(a, e), e)
28.56/9.87	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(a, k), b)
28.56/9.87	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.87	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.87	   A^2 -> H(U1(a, k), c)
28.56/9.87	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.87	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.87	   A^2 -> H(U1(a, k), e)
28.56/9.87	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(a, c), d)
28.56/9.87	   A^2 -> H(U1(a, c), k)
28.56/9.87	   A^2 -> H(U1(a, d), d)
28.56/9.87	   A^2 -> H(U1(a, d), k)
28.56/9.87	   A^2 -> H(k, U1(c, b))
28.56/9.87	   A^2 -> H(k, U1(d, b))
28.56/9.87	   A^2 -> H(k, U1(b, c))
28.56/9.87	   A^2 -> H(k, U1(b, d))
28.56/9.87	   A^2 -> H(k, U1(c, c))
28.56/9.87	   A^2 -> H(k, f(e))
28.56/9.87	   A^2 -> H(k, f(k))
28.56/9.87	   A^2 -> H(k, U1(d, d))
28.56/9.87	   A^2 -> H(c, U1(e, b))
28.56/9.87	   A^2 -> H(c, U1(k, b))
28.56/9.87	   A^2 -> H(c, U1(c, d))
28.56/9.87	   A^2 -> H(c, U1(d, c))
28.56/9.87	   A^2 -> H(c, U1(b, e))
28.56/9.87	   A^2 -> H(c, U1(b, k))
28.56/9.87	   A^2 -> H(c, U1(e, c))
28.56/9.87	   A^2 -> H(c, U1(k, c))
28.56/9.87	   A^2 -> H(c, U1(c, e))
28.56/9.87	   A^2 -> H(c, U1(c, k))
28.56/9.87	   A^2 -> H(c, U1(e, e))
28.56/9.87	   A^2 -> H(c, U1(k, k))
28.56/9.87	   A^2 -> H(c, U1(k, d))
28.56/9.87	   A^2 -> H(c, U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, c), b)
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(e, c), e)
28.56/9.87	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.87	   A^2 -> H(U1(k, c), b)
28.56/9.87	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(k, c), c)
28.56/9.87	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, e), b)
28.56/9.87	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, e), c)
28.56/9.87	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, e), e)
28.56/9.87	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, k), b)
28.56/9.87	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, k), c)
28.56/9.87	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, k), e)
28.56/9.87	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, c), d)
28.56/9.87	   A^2 -> H(U1(k, c), e)
28.56/9.87	
28.56/9.87	The TRS R consists of the following rules:
28.56/9.87	
28.56/9.87	   f(x) -> U1(x, x)
28.56/9.87	   U1(e, x) -> x
28.56/9.87	   a -> c
28.56/9.87	   a -> d
28.56/9.87	   b -> c
28.56/9.87	   b -> d
28.56/9.87	   d -> k
28.56/9.87	   c -> e
28.56/9.87	   c -> k
28.56/9.87	
28.56/9.87	Q is empty.
28.56/9.87	We have to consider all minimal (P,Q,R)-chains.
28.56/9.87	----------------------------------------
28.56/9.87	
28.56/9.87	(1559) DependencyGraphProof (EQUIVALENT)
28.56/9.87	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.87	----------------------------------------
28.56/9.87	
28.56/9.87	(1560)
28.56/9.87	Obligation:
28.56/9.87	Q DP problem:
28.56/9.87	The TRS P consists of the following rules:
28.56/9.87	
28.56/9.87	   A^2 -> H(f(c), f(c))
28.56/9.87	   H(x, x) -> G(x, x, f(k))
28.56/9.87	   G(d, x, x) -> A^2
28.56/9.87	   A^2 -> H(f(d), f(d))
28.56/9.87	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.87	   A^2 -> H(f(e), f(e))
28.56/9.87	   A^2 -> H(f(k), f(k))
28.56/9.87	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.87	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.87	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(c, c), U1(k, k))
28.56/9.87	   A^2 -> H(e, U1(c, b))
28.56/9.87	   A^2 -> H(e, U1(d, b))
28.56/9.87	   A^2 -> H(e, U1(b, c))
28.56/9.87	   A^2 -> H(e, U1(b, d))
28.56/9.87	   A^2 -> H(e, U1(c, c))
28.56/9.87	   A^2 -> H(e, f(e))
28.56/9.87	   A^2 -> H(e, f(k))
28.56/9.87	   A^2 -> H(e, U1(d, d))
28.56/9.87	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.87	   A^2 -> H(f(e), b)
28.56/9.87	   A^2 -> H(f(e), U1(e, d))
28.56/9.87	   A^2 -> H(f(e), U1(d, e))
28.56/9.87	   A^2 -> H(f(e), c)
28.56/9.87	   A^2 -> H(f(e), U1(e, k))
28.56/9.87	   A^2 -> H(f(e), U1(k, e))
28.56/9.87	   A^2 -> H(f(e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.87	   A^2 -> H(f(k), b)
28.56/9.87	   A^2 -> H(f(k), U1(e, d))
28.56/9.87	   A^2 -> H(f(k), U1(d, e))
28.56/9.87	   A^2 -> H(f(k), c)
28.56/9.87	   A^2 -> H(f(k), U1(e, k))
28.56/9.87	   A^2 -> H(f(k), U1(k, e))
28.56/9.87	   A^2 -> H(f(k), e)
28.56/9.87	   A^2 -> H(f(c), d)
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.87	   A^2 -> H(U1(k, k), f(e))
28.56/9.87	   A^2 -> H(U1(k, k), f(k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.87	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.87	   A^2 -> H(U1(d, d), b)
28.56/9.87	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.87	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.87	   A^2 -> H(U1(d, d), c)
28.56/9.87	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.87	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.87	   A^2 -> H(U1(d, d), e)
28.56/9.87	   A^2 -> H(f(d), d)
28.56/9.87	   A^2 -> H(f(d), k)
28.56/9.87	   A^2 -> H(U1(c, c), c)
28.56/9.87	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.87	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.87	   A^2 -> H(f(c), k)
28.56/9.87	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.87	   A^2 -> H(f(k), U1(k, k))
28.56/9.87	   A^2 -> H(f(e), e)
28.56/9.87	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.87	   A^2 -> H(d, U1(c, b))
28.56/9.87	   A^2 -> H(d, U1(d, b))
28.56/9.87	   A^2 -> H(d, U1(b, c))
28.56/9.87	   A^2 -> H(d, U1(b, d))
28.56/9.87	   A^2 -> H(d, U1(c, c))
28.56/9.87	   A^2 -> H(d, f(e))
28.56/9.87	   A^2 -> H(d, f(k))
28.56/9.87	   A^2 -> H(d, U1(d, d))
28.56/9.87	   A^2 -> H(a, U1(e, b))
28.56/9.87	   A^2 -> H(a, U1(k, b))
28.56/9.87	   A^2 -> H(a, U1(c, d))
28.56/9.87	   A^2 -> H(a, U1(d, c))
28.56/9.87	   A^2 -> H(a, U1(b, e))
28.56/9.87	   A^2 -> H(a, U1(b, k))
28.56/9.87	   A^2 -> H(a, U1(e, c))
28.56/9.87	   A^2 -> H(a, U1(k, c))
28.56/9.87	   A^2 -> H(a, U1(c, e))
28.56/9.87	   A^2 -> H(a, U1(c, k))
28.56/9.87	   A^2 -> H(a, U1(e, e))
28.56/9.87	   A^2 -> H(a, U1(k, k))
28.56/9.87	   A^2 -> H(a, U1(k, d))
28.56/9.87	   A^2 -> H(a, U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, a), b)
28.56/9.87	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.87	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.87	   A^2 -> H(U1(e, a), c)
28.56/9.87	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.87	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.87	   A^2 -> H(U1(e, a), e)
28.56/9.87	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, a), b)
28.56/9.87	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.87	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.87	   A^2 -> H(U1(k, a), c)
28.56/9.87	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.87	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.87	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, d), b)
28.56/9.87	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, d), c)
28.56/9.87	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, d), e)
28.56/9.87	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, a), d)
28.56/9.87	   A^2 -> H(U1(c, a), k)
28.56/9.87	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.87	   A^2 -> H(U1(d, c), b)
28.56/9.87	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(d, c), c)
28.56/9.87	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(d, c), e)
28.56/9.87	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(d, a), d)
28.56/9.87	   A^2 -> H(U1(d, a), k)
28.56/9.87	   A^2 -> H(U1(a, e), b)
28.56/9.87	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.87	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.87	   A^2 -> H(U1(a, e), c)
28.56/9.87	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.87	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.87	   A^2 -> H(U1(a, e), e)
28.56/9.87	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(a, k), b)
28.56/9.87	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.87	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.87	   A^2 -> H(U1(a, k), c)
28.56/9.87	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.87	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.87	   A^2 -> H(U1(a, k), e)
28.56/9.87	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(a, c), d)
28.56/9.87	   A^2 -> H(U1(a, c), k)
28.56/9.87	   A^2 -> H(U1(a, d), d)
28.56/9.87	   A^2 -> H(U1(a, d), k)
28.56/9.87	   A^2 -> H(k, U1(c, b))
28.56/9.87	   A^2 -> H(k, U1(d, b))
28.56/9.87	   A^2 -> H(k, U1(b, c))
28.56/9.87	   A^2 -> H(k, U1(b, d))
28.56/9.87	   A^2 -> H(k, U1(c, c))
28.56/9.87	   A^2 -> H(k, f(e))
28.56/9.87	   A^2 -> H(k, f(k))
28.56/9.87	   A^2 -> H(k, U1(d, d))
28.56/9.87	   A^2 -> H(c, U1(e, b))
28.56/9.87	   A^2 -> H(c, U1(k, b))
28.56/9.87	   A^2 -> H(c, U1(c, d))
28.56/9.87	   A^2 -> H(c, U1(d, c))
28.56/9.87	   A^2 -> H(c, U1(b, e))
28.56/9.87	   A^2 -> H(c, U1(b, k))
28.56/9.87	   A^2 -> H(c, U1(e, c))
28.56/9.87	   A^2 -> H(c, U1(k, c))
28.56/9.87	   A^2 -> H(c, U1(c, e))
28.56/9.87	   A^2 -> H(c, U1(c, k))
28.56/9.87	   A^2 -> H(c, U1(e, e))
28.56/9.87	   A^2 -> H(c, U1(k, k))
28.56/9.87	   A^2 -> H(c, U1(k, d))
28.56/9.87	   A^2 -> H(c, U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, c), b)
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(e, c), e)
28.56/9.87	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.87	   A^2 -> H(U1(k, c), b)
28.56/9.87	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(k, c), c)
28.56/9.87	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, e), b)
28.56/9.87	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, e), c)
28.56/9.87	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, e), e)
28.56/9.87	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, k), b)
28.56/9.87	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, k), c)
28.56/9.87	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, k), e)
28.56/9.87	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, c), d)
28.56/9.87	
28.56/9.87	The TRS R consists of the following rules:
28.56/9.87	
28.56/9.87	   f(x) -> U1(x, x)
28.56/9.87	   U1(e, x) -> x
28.56/9.87	   a -> c
28.56/9.87	   a -> d
28.56/9.87	   b -> c
28.56/9.87	   b -> d
28.56/9.87	   d -> k
28.56/9.87	   c -> e
28.56/9.87	   c -> k
28.56/9.87	
28.56/9.87	Q is empty.
28.56/9.87	We have to consider all minimal (P,Q,R)-chains.
28.56/9.87	----------------------------------------
28.56/9.87	
28.56/9.87	(1561) TransformationProof (EQUIVALENT)
28.56/9.87	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.87	
28.56/9.87	   (A^2 -> H(U1(e, c), U1(k, k)),A^2 -> H(U1(e, c), U1(k, k)))
28.56/9.87	   (A^2 -> H(U1(k, c), U1(k, k)),A^2 -> H(U1(k, c), U1(k, k)))
28.56/9.87	   (A^2 -> H(U1(c, e), U1(k, k)),A^2 -> H(U1(c, e), U1(k, k)))
28.56/9.87	   (A^2 -> H(U1(c, k), U1(k, k)),A^2 -> H(U1(c, k), U1(k, k)))
28.56/9.87	
28.56/9.87	
28.56/9.87	----------------------------------------
28.56/9.87	
28.56/9.87	(1562)
28.56/9.87	Obligation:
28.56/9.87	Q DP problem:
28.56/9.87	The TRS P consists of the following rules:
28.56/9.87	
28.56/9.87	   A^2 -> H(f(c), f(c))
28.56/9.87	   H(x, x) -> G(x, x, f(k))
28.56/9.87	   G(d, x, x) -> A^2
28.56/9.87	   A^2 -> H(f(d), f(d))
28.56/9.87	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.87	   A^2 -> H(f(e), f(e))
28.56/9.87	   A^2 -> H(f(k), f(k))
28.56/9.87	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.87	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.87	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.87	   A^2 -> H(e, U1(c, b))
28.56/9.87	   A^2 -> H(e, U1(d, b))
28.56/9.87	   A^2 -> H(e, U1(b, c))
28.56/9.87	   A^2 -> H(e, U1(b, d))
28.56/9.87	   A^2 -> H(e, U1(c, c))
28.56/9.87	   A^2 -> H(e, f(e))
28.56/9.87	   A^2 -> H(e, f(k))
28.56/9.87	   A^2 -> H(e, U1(d, d))
28.56/9.87	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.87	   A^2 -> H(f(e), b)
28.56/9.87	   A^2 -> H(f(e), U1(e, d))
28.56/9.87	   A^2 -> H(f(e), U1(d, e))
28.56/9.87	   A^2 -> H(f(e), c)
28.56/9.87	   A^2 -> H(f(e), U1(e, k))
28.56/9.87	   A^2 -> H(f(e), U1(k, e))
28.56/9.87	   A^2 -> H(f(e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.87	   A^2 -> H(f(k), b)
28.56/9.87	   A^2 -> H(f(k), U1(e, d))
28.56/9.87	   A^2 -> H(f(k), U1(d, e))
28.56/9.87	   A^2 -> H(f(k), c)
28.56/9.87	   A^2 -> H(f(k), U1(e, k))
28.56/9.87	   A^2 -> H(f(k), U1(k, e))
28.56/9.87	   A^2 -> H(f(k), e)
28.56/9.87	   A^2 -> H(f(c), d)
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.87	   A^2 -> H(U1(k, k), f(e))
28.56/9.87	   A^2 -> H(U1(k, k), f(k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.87	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.87	   A^2 -> H(U1(d, d), b)
28.56/9.87	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.87	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.87	   A^2 -> H(U1(d, d), c)
28.56/9.87	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.87	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.87	   A^2 -> H(U1(d, d), e)
28.56/9.87	   A^2 -> H(f(d), d)
28.56/9.87	   A^2 -> H(f(d), k)
28.56/9.87	   A^2 -> H(U1(c, c), c)
28.56/9.87	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.87	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.87	   A^2 -> H(f(c), k)
28.56/9.87	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.87	   A^2 -> H(f(k), U1(k, k))
28.56/9.87	   A^2 -> H(f(e), e)
28.56/9.87	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.87	   A^2 -> H(d, U1(c, b))
28.56/9.87	   A^2 -> H(d, U1(d, b))
28.56/9.87	   A^2 -> H(d, U1(b, c))
28.56/9.87	   A^2 -> H(d, U1(b, d))
28.56/9.87	   A^2 -> H(d, U1(c, c))
28.56/9.87	   A^2 -> H(d, f(e))
28.56/9.87	   A^2 -> H(d, f(k))
28.56/9.87	   A^2 -> H(d, U1(d, d))
28.56/9.87	   A^2 -> H(a, U1(e, b))
28.56/9.87	   A^2 -> H(a, U1(k, b))
28.56/9.87	   A^2 -> H(a, U1(c, d))
28.56/9.87	   A^2 -> H(a, U1(d, c))
28.56/9.87	   A^2 -> H(a, U1(b, e))
28.56/9.87	   A^2 -> H(a, U1(b, k))
28.56/9.87	   A^2 -> H(a, U1(e, c))
28.56/9.87	   A^2 -> H(a, U1(k, c))
28.56/9.87	   A^2 -> H(a, U1(c, e))
28.56/9.87	   A^2 -> H(a, U1(c, k))
28.56/9.87	   A^2 -> H(a, U1(e, e))
28.56/9.87	   A^2 -> H(a, U1(k, k))
28.56/9.87	   A^2 -> H(a, U1(k, d))
28.56/9.87	   A^2 -> H(a, U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, a), b)
28.56/9.87	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.87	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.87	   A^2 -> H(U1(e, a), c)
28.56/9.87	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.87	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.87	   A^2 -> H(U1(e, a), e)
28.56/9.87	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, a), b)
28.56/9.87	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.87	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.87	   A^2 -> H(U1(k, a), c)
28.56/9.87	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.87	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.87	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, d), b)
28.56/9.87	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, d), c)
28.56/9.87	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, d), e)
28.56/9.87	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, a), d)
28.56/9.87	   A^2 -> H(U1(c, a), k)
28.56/9.87	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.87	   A^2 -> H(U1(d, c), b)
28.56/9.87	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(d, c), c)
28.56/9.87	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(d, c), e)
28.56/9.87	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(d, a), d)
28.56/9.87	   A^2 -> H(U1(d, a), k)
28.56/9.87	   A^2 -> H(U1(a, e), b)
28.56/9.87	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.87	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.87	   A^2 -> H(U1(a, e), c)
28.56/9.87	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.87	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.87	   A^2 -> H(U1(a, e), e)
28.56/9.87	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(a, k), b)
28.56/9.87	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.87	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.87	   A^2 -> H(U1(a, k), c)
28.56/9.87	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.87	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.87	   A^2 -> H(U1(a, k), e)
28.56/9.87	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(a, c), d)
28.56/9.87	   A^2 -> H(U1(a, c), k)
28.56/9.87	   A^2 -> H(U1(a, d), d)
28.56/9.87	   A^2 -> H(U1(a, d), k)
28.56/9.87	   A^2 -> H(k, U1(c, b))
28.56/9.87	   A^2 -> H(k, U1(d, b))
28.56/9.87	   A^2 -> H(k, U1(b, c))
28.56/9.87	   A^2 -> H(k, U1(b, d))
28.56/9.87	   A^2 -> H(k, U1(c, c))
28.56/9.87	   A^2 -> H(k, f(e))
28.56/9.87	   A^2 -> H(k, f(k))
28.56/9.87	   A^2 -> H(k, U1(d, d))
28.56/9.87	   A^2 -> H(c, U1(e, b))
28.56/9.87	   A^2 -> H(c, U1(k, b))
28.56/9.87	   A^2 -> H(c, U1(c, d))
28.56/9.87	   A^2 -> H(c, U1(d, c))
28.56/9.87	   A^2 -> H(c, U1(b, e))
28.56/9.87	   A^2 -> H(c, U1(b, k))
28.56/9.87	   A^2 -> H(c, U1(e, c))
28.56/9.87	   A^2 -> H(c, U1(k, c))
28.56/9.87	   A^2 -> H(c, U1(c, e))
28.56/9.87	   A^2 -> H(c, U1(c, k))
28.56/9.87	   A^2 -> H(c, U1(e, e))
28.56/9.87	   A^2 -> H(c, U1(k, k))
28.56/9.87	   A^2 -> H(c, U1(k, d))
28.56/9.87	   A^2 -> H(c, U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, c), b)
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(e, c), e)
28.56/9.87	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.87	   A^2 -> H(U1(k, c), b)
28.56/9.87	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(k, c), c)
28.56/9.87	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, e), b)
28.56/9.87	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, e), c)
28.56/9.87	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, e), e)
28.56/9.87	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, k), b)
28.56/9.87	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, k), c)
28.56/9.87	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, k), e)
28.56/9.87	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, c), d)
28.56/9.87	
28.56/9.87	The TRS R consists of the following rules:
28.56/9.87	
28.56/9.87	   f(x) -> U1(x, x)
28.56/9.87	   U1(e, x) -> x
28.56/9.87	   a -> c
28.56/9.87	   a -> d
28.56/9.87	   b -> c
28.56/9.87	   b -> d
28.56/9.87	   d -> k
28.56/9.87	   c -> e
28.56/9.87	   c -> k
28.56/9.87	
28.56/9.87	Q is empty.
28.56/9.87	We have to consider all minimal (P,Q,R)-chains.
28.56/9.87	----------------------------------------
28.56/9.87	
28.56/9.87	(1563) TransformationProof (EQUIVALENT)
28.56/9.87	By narrowing [LPAR04] the rule A^2 -> H(e, U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.87	
28.56/9.87	   (A^2 -> H(e, U1(e, b)),A^2 -> H(e, U1(e, b)))
28.56/9.87	   (A^2 -> H(e, U1(k, b)),A^2 -> H(e, U1(k, b)))
28.56/9.87	   (A^2 -> H(e, U1(c, c)),A^2 -> H(e, U1(c, c)))
28.56/9.87	   (A^2 -> H(e, U1(c, d)),A^2 -> H(e, U1(c, d)))
28.56/9.87	
28.56/9.87	
28.56/9.87	----------------------------------------
28.56/9.87	
28.56/9.87	(1564)
28.56/9.87	Obligation:
28.56/9.87	Q DP problem:
28.56/9.87	The TRS P consists of the following rules:
28.56/9.87	
28.56/9.87	   A^2 -> H(f(c), f(c))
28.56/9.87	   H(x, x) -> G(x, x, f(k))
28.56/9.87	   G(d, x, x) -> A^2
28.56/9.87	   A^2 -> H(f(d), f(d))
28.56/9.87	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.87	   A^2 -> H(f(e), f(e))
28.56/9.87	   A^2 -> H(f(k), f(k))
28.56/9.87	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.87	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.87	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.87	   A^2 -> H(e, U1(d, b))
28.56/9.87	   A^2 -> H(e, U1(b, c))
28.56/9.87	   A^2 -> H(e, U1(b, d))
28.56/9.87	   A^2 -> H(e, U1(c, c))
28.56/9.87	   A^2 -> H(e, f(e))
28.56/9.87	   A^2 -> H(e, f(k))
28.56/9.87	   A^2 -> H(e, U1(d, d))
28.56/9.87	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.87	   A^2 -> H(f(e), b)
28.56/9.87	   A^2 -> H(f(e), U1(e, d))
28.56/9.87	   A^2 -> H(f(e), U1(d, e))
28.56/9.87	   A^2 -> H(f(e), c)
28.56/9.87	   A^2 -> H(f(e), U1(e, k))
28.56/9.87	   A^2 -> H(f(e), U1(k, e))
28.56/9.87	   A^2 -> H(f(e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.87	   A^2 -> H(f(k), b)
28.56/9.87	   A^2 -> H(f(k), U1(e, d))
28.56/9.87	   A^2 -> H(f(k), U1(d, e))
28.56/9.87	   A^2 -> H(f(k), c)
28.56/9.87	   A^2 -> H(f(k), U1(e, k))
28.56/9.87	   A^2 -> H(f(k), U1(k, e))
28.56/9.87	   A^2 -> H(f(k), e)
28.56/9.87	   A^2 -> H(f(c), d)
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.87	   A^2 -> H(U1(k, k), f(e))
28.56/9.87	   A^2 -> H(U1(k, k), f(k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.87	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.87	   A^2 -> H(U1(d, d), b)
28.56/9.87	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.87	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.87	   A^2 -> H(U1(d, d), c)
28.56/9.87	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.87	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.87	   A^2 -> H(U1(d, d), e)
28.56/9.87	   A^2 -> H(f(d), d)
28.56/9.87	   A^2 -> H(f(d), k)
28.56/9.87	   A^2 -> H(U1(c, c), c)
28.56/9.87	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.87	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.87	   A^2 -> H(f(c), k)
28.56/9.87	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.87	   A^2 -> H(f(k), U1(k, k))
28.56/9.87	   A^2 -> H(f(e), e)
28.56/9.87	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.87	   A^2 -> H(d, U1(c, b))
28.56/9.87	   A^2 -> H(d, U1(d, b))
28.56/9.87	   A^2 -> H(d, U1(b, c))
28.56/9.87	   A^2 -> H(d, U1(b, d))
28.56/9.87	   A^2 -> H(d, U1(c, c))
28.56/9.87	   A^2 -> H(d, f(e))
28.56/9.87	   A^2 -> H(d, f(k))
28.56/9.87	   A^2 -> H(d, U1(d, d))
28.56/9.87	   A^2 -> H(a, U1(e, b))
28.56/9.87	   A^2 -> H(a, U1(k, b))
28.56/9.87	   A^2 -> H(a, U1(c, d))
28.56/9.87	   A^2 -> H(a, U1(d, c))
28.56/9.87	   A^2 -> H(a, U1(b, e))
28.56/9.87	   A^2 -> H(a, U1(b, k))
28.56/9.87	   A^2 -> H(a, U1(e, c))
28.56/9.87	   A^2 -> H(a, U1(k, c))
28.56/9.87	   A^2 -> H(a, U1(c, e))
28.56/9.87	   A^2 -> H(a, U1(c, k))
28.56/9.87	   A^2 -> H(a, U1(e, e))
28.56/9.87	   A^2 -> H(a, U1(k, k))
28.56/9.87	   A^2 -> H(a, U1(k, d))
28.56/9.87	   A^2 -> H(a, U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, a), b)
28.56/9.87	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.87	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.87	   A^2 -> H(U1(e, a), c)
28.56/9.87	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.87	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.87	   A^2 -> H(U1(e, a), e)
28.56/9.87	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, a), b)
28.56/9.87	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.87	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.87	   A^2 -> H(U1(k, a), c)
28.56/9.87	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.87	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.87	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, d), b)
28.56/9.87	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, d), c)
28.56/9.87	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, d), e)
28.56/9.87	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, a), d)
28.56/9.87	   A^2 -> H(U1(c, a), k)
28.56/9.87	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.87	   A^2 -> H(U1(d, c), b)
28.56/9.87	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(d, c), c)
28.56/9.87	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(d, c), e)
28.56/9.87	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(d, a), d)
28.56/9.87	   A^2 -> H(U1(d, a), k)
28.56/9.87	   A^2 -> H(U1(a, e), b)
28.56/9.87	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.87	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.87	   A^2 -> H(U1(a, e), c)
28.56/9.87	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.87	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.87	   A^2 -> H(U1(a, e), e)
28.56/9.87	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(a, k), b)
28.56/9.87	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.87	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.87	   A^2 -> H(U1(a, k), c)
28.56/9.87	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.87	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.87	   A^2 -> H(U1(a, k), e)
28.56/9.87	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(a, c), d)
28.56/9.87	   A^2 -> H(U1(a, c), k)
28.56/9.87	   A^2 -> H(U1(a, d), d)
28.56/9.87	   A^2 -> H(U1(a, d), k)
28.56/9.87	   A^2 -> H(k, U1(c, b))
28.56/9.87	   A^2 -> H(k, U1(d, b))
28.56/9.87	   A^2 -> H(k, U1(b, c))
28.56/9.87	   A^2 -> H(k, U1(b, d))
28.56/9.87	   A^2 -> H(k, U1(c, c))
28.56/9.87	   A^2 -> H(k, f(e))
28.56/9.87	   A^2 -> H(k, f(k))
28.56/9.87	   A^2 -> H(k, U1(d, d))
28.56/9.87	   A^2 -> H(c, U1(e, b))
28.56/9.87	   A^2 -> H(c, U1(k, b))
28.56/9.87	   A^2 -> H(c, U1(c, d))
28.56/9.87	   A^2 -> H(c, U1(d, c))
28.56/9.87	   A^2 -> H(c, U1(b, e))
28.56/9.87	   A^2 -> H(c, U1(b, k))
28.56/9.87	   A^2 -> H(c, U1(e, c))
28.56/9.87	   A^2 -> H(c, U1(k, c))
28.56/9.87	   A^2 -> H(c, U1(c, e))
28.56/9.87	   A^2 -> H(c, U1(c, k))
28.56/9.87	   A^2 -> H(c, U1(e, e))
28.56/9.87	   A^2 -> H(c, U1(k, k))
28.56/9.87	   A^2 -> H(c, U1(k, d))
28.56/9.87	   A^2 -> H(c, U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, c), b)
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(e, c), e)
28.56/9.87	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.87	   A^2 -> H(U1(k, c), b)
28.56/9.87	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(k, c), c)
28.56/9.87	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, e), b)
28.56/9.87	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, e), c)
28.56/9.87	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, e), e)
28.56/9.87	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, k), b)
28.56/9.87	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, k), c)
28.56/9.87	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, k), e)
28.56/9.87	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, c), d)
28.56/9.87	   A^2 -> H(e, U1(e, b))
28.56/9.87	   A^2 -> H(e, U1(k, b))
28.56/9.87	   A^2 -> H(e, U1(c, d))
28.56/9.87	
28.56/9.87	The TRS R consists of the following rules:
28.56/9.87	
28.56/9.87	   f(x) -> U1(x, x)
28.56/9.87	   U1(e, x) -> x
28.56/9.87	   a -> c
28.56/9.87	   a -> d
28.56/9.87	   b -> c
28.56/9.87	   b -> d
28.56/9.87	   d -> k
28.56/9.87	   c -> e
28.56/9.87	   c -> k
28.56/9.87	
28.56/9.87	Q is empty.
28.56/9.87	We have to consider all minimal (P,Q,R)-chains.
28.56/9.87	----------------------------------------
28.56/9.87	
28.56/9.87	(1565) DependencyGraphProof (EQUIVALENT)
28.56/9.87	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.87	----------------------------------------
28.56/9.87	
28.56/9.87	(1566)
28.56/9.87	Obligation:
28.56/9.87	Q DP problem:
28.56/9.87	The TRS P consists of the following rules:
28.56/9.87	
28.56/9.87	   H(x, x) -> G(x, x, f(k))
28.56/9.87	   G(d, x, x) -> A^2
28.56/9.87	   A^2 -> H(f(c), f(c))
28.56/9.87	   A^2 -> H(f(d), f(d))
28.56/9.87	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.87	   A^2 -> H(f(e), f(e))
28.56/9.87	   A^2 -> H(f(k), f(k))
28.56/9.87	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.87	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.87	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.87	   A^2 -> H(e, U1(d, b))
28.56/9.87	   A^2 -> H(e, U1(b, c))
28.56/9.87	   A^2 -> H(e, U1(b, d))
28.56/9.87	   A^2 -> H(e, U1(c, c))
28.56/9.87	   A^2 -> H(e, f(e))
28.56/9.87	   A^2 -> H(e, f(k))
28.56/9.87	   A^2 -> H(e, U1(d, d))
28.56/9.87	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.87	   A^2 -> H(f(e), b)
28.56/9.87	   A^2 -> H(f(e), U1(e, d))
28.56/9.87	   A^2 -> H(f(e), U1(d, e))
28.56/9.87	   A^2 -> H(f(e), c)
28.56/9.87	   A^2 -> H(f(e), U1(e, k))
28.56/9.87	   A^2 -> H(f(e), U1(k, e))
28.56/9.87	   A^2 -> H(f(e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.87	   A^2 -> H(f(k), b)
28.56/9.87	   A^2 -> H(f(k), U1(e, d))
28.56/9.87	   A^2 -> H(f(k), U1(d, e))
28.56/9.87	   A^2 -> H(f(k), c)
28.56/9.87	   A^2 -> H(f(k), U1(e, k))
28.56/9.87	   A^2 -> H(f(k), U1(k, e))
28.56/9.87	   A^2 -> H(f(k), e)
28.56/9.87	   A^2 -> H(f(c), d)
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.87	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.87	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.87	   A^2 -> H(U1(k, k), f(e))
28.56/9.87	   A^2 -> H(U1(k, k), f(k))
28.56/9.87	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.87	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.87	   A^2 -> H(U1(d, d), b)
28.56/9.87	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.87	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.87	   A^2 -> H(U1(d, d), c)
28.56/9.87	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.87	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.87	   A^2 -> H(U1(d, d), e)
28.56/9.87	   A^2 -> H(f(d), d)
28.56/9.87	   A^2 -> H(f(d), k)
28.56/9.87	   A^2 -> H(U1(c, c), c)
28.56/9.87	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.87	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.87	   A^2 -> H(f(c), k)
28.56/9.87	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.87	   A^2 -> H(f(k), U1(k, k))
28.56/9.87	   A^2 -> H(f(e), e)
28.56/9.87	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.87	   A^2 -> H(d, U1(c, b))
28.56/9.87	   A^2 -> H(d, U1(d, b))
28.56/9.87	   A^2 -> H(d, U1(b, c))
28.56/9.87	   A^2 -> H(d, U1(b, d))
28.56/9.87	   A^2 -> H(d, U1(c, c))
28.56/9.87	   A^2 -> H(d, f(e))
28.56/9.87	   A^2 -> H(d, f(k))
28.56/9.87	   A^2 -> H(d, U1(d, d))
28.56/9.87	   A^2 -> H(a, U1(e, b))
28.56/9.87	   A^2 -> H(a, U1(k, b))
28.56/9.87	   A^2 -> H(a, U1(c, d))
28.56/9.87	   A^2 -> H(a, U1(d, c))
28.56/9.87	   A^2 -> H(a, U1(b, e))
28.56/9.87	   A^2 -> H(a, U1(b, k))
28.56/9.87	   A^2 -> H(a, U1(e, c))
28.56/9.87	   A^2 -> H(a, U1(k, c))
28.56/9.87	   A^2 -> H(a, U1(c, e))
28.56/9.87	   A^2 -> H(a, U1(c, k))
28.56/9.87	   A^2 -> H(a, U1(e, e))
28.56/9.87	   A^2 -> H(a, U1(k, k))
28.56/9.87	   A^2 -> H(a, U1(k, d))
28.56/9.87	   A^2 -> H(a, U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, a), b)
28.56/9.87	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.87	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.87	   A^2 -> H(U1(e, a), c)
28.56/9.87	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.87	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.87	   A^2 -> H(U1(e, a), e)
28.56/9.87	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, a), b)
28.56/9.87	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.87	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.87	   A^2 -> H(U1(k, a), c)
28.56/9.87	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.87	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.87	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, d), b)
28.56/9.87	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, d), c)
28.56/9.87	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, d), e)
28.56/9.87	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, a), d)
28.56/9.87	   A^2 -> H(U1(c, a), k)
28.56/9.87	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.87	   A^2 -> H(U1(d, c), b)
28.56/9.87	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(d, c), c)
28.56/9.87	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(d, c), e)
28.56/9.87	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(d, a), d)
28.56/9.87	   A^2 -> H(U1(d, a), k)
28.56/9.87	   A^2 -> H(U1(a, e), b)
28.56/9.87	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.87	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.87	   A^2 -> H(U1(a, e), c)
28.56/9.87	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.87	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.87	   A^2 -> H(U1(a, e), e)
28.56/9.87	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(a, k), b)
28.56/9.87	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.87	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.87	   A^2 -> H(U1(a, k), c)
28.56/9.87	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.87	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.87	   A^2 -> H(U1(a, k), e)
28.56/9.87	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(a, c), d)
28.56/9.87	   A^2 -> H(U1(a, c), k)
28.56/9.87	   A^2 -> H(U1(a, d), d)
28.56/9.87	   A^2 -> H(U1(a, d), k)
28.56/9.87	   A^2 -> H(k, U1(c, b))
28.56/9.87	   A^2 -> H(k, U1(d, b))
28.56/9.87	   A^2 -> H(k, U1(b, c))
28.56/9.87	   A^2 -> H(k, U1(b, d))
28.56/9.87	   A^2 -> H(k, U1(c, c))
28.56/9.87	   A^2 -> H(k, f(e))
28.56/9.87	   A^2 -> H(k, f(k))
28.56/9.87	   A^2 -> H(k, U1(d, d))
28.56/9.87	   A^2 -> H(c, U1(e, b))
28.56/9.87	   A^2 -> H(c, U1(k, b))
28.56/9.87	   A^2 -> H(c, U1(c, d))
28.56/9.87	   A^2 -> H(c, U1(d, c))
28.56/9.87	   A^2 -> H(c, U1(b, e))
28.56/9.87	   A^2 -> H(c, U1(b, k))
28.56/9.87	   A^2 -> H(c, U1(e, c))
28.56/9.87	   A^2 -> H(c, U1(k, c))
28.56/9.87	   A^2 -> H(c, U1(c, e))
28.56/9.87	   A^2 -> H(c, U1(c, k))
28.56/9.87	   A^2 -> H(c, U1(e, e))
28.56/9.87	   A^2 -> H(c, U1(k, k))
28.56/9.87	   A^2 -> H(c, U1(k, d))
28.56/9.87	   A^2 -> H(c, U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.87	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.87	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.87	   A^2 -> H(U1(e, c), b)
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(e, c), e)
28.56/9.87	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.87	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.87	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.87	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.87	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.87	   A^2 -> H(U1(k, c), b)
28.56/9.87	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.87	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.87	   A^2 -> H(U1(k, c), c)
28.56/9.87	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, e), b)
28.56/9.87	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, e), c)
28.56/9.87	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, e), e)
28.56/9.87	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, k), b)
28.56/9.87	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.87	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.87	   A^2 -> H(U1(c, k), c)
28.56/9.87	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.87	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.87	   A^2 -> H(U1(c, k), e)
28.56/9.87	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.87	   A^2 -> H(U1(c, c), d)
28.56/9.87	   A^2 -> H(e, U1(e, b))
28.56/9.87	   A^2 -> H(e, U1(c, d))
28.56/9.87	
28.56/9.87	The TRS R consists of the following rules:
28.56/9.87	
28.56/9.87	   f(x) -> U1(x, x)
28.56/9.87	   U1(e, x) -> x
28.56/9.87	   a -> c
28.56/9.87	   a -> d
28.56/9.87	   b -> c
28.56/9.87	   b -> d
28.56/9.87	   d -> k
28.56/9.87	   c -> e
28.56/9.87	   c -> k
28.56/9.87	
28.56/9.87	Q is empty.
28.56/9.87	We have to consider all minimal (P,Q,R)-chains.
28.56/9.87	----------------------------------------
28.56/9.87	
28.56/9.87	(1567) TransformationProof (EQUIVALENT)
28.56/9.87	By narrowing [LPAR04] the rule A^2 -> H(e, U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.87	
28.56/9.87	   (A^2 -> H(e, U1(k, b)),A^2 -> H(e, U1(k, b)))
28.56/9.87	   (A^2 -> H(e, U1(d, c)),A^2 -> H(e, U1(d, c)))
28.56/9.87	   (A^2 -> H(e, U1(d, d)),A^2 -> H(e, U1(d, d)))
28.56/9.87	
28.56/9.87	
28.56/9.87	----------------------------------------
28.56/9.87	
28.56/9.87	(1568)
28.56/9.87	Obligation:
28.56/9.87	Q DP problem:
28.56/9.87	The TRS P consists of the following rules:
28.56/9.87	
28.56/9.87	   H(x, x) -> G(x, x, f(k))
28.56/9.87	   G(d, x, x) -> A^2
28.56/9.87	   A^2 -> H(f(c), f(c))
28.56/9.87	   A^2 -> H(f(d), f(d))
28.56/9.87	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.87	   A^2 -> H(f(e), f(e))
28.56/9.87	   A^2 -> H(f(k), f(k))
28.56/9.87	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.87	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.87	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.87	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.87	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.88	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.88	   A^2 -> H(e, U1(b, c))
28.56/9.88	   A^2 -> H(e, U1(b, d))
28.56/9.88	   A^2 -> H(e, U1(c, c))
28.56/9.88	   A^2 -> H(e, f(e))
28.56/9.88	   A^2 -> H(e, f(k))
28.56/9.88	   A^2 -> H(e, U1(d, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.88	   A^2 -> H(f(e), b)
28.56/9.88	   A^2 -> H(f(e), U1(e, d))
28.56/9.88	   A^2 -> H(f(e), U1(d, e))
28.56/9.88	   A^2 -> H(f(e), c)
28.56/9.88	   A^2 -> H(f(e), U1(e, k))
28.56/9.88	   A^2 -> H(f(e), U1(k, e))
28.56/9.88	   A^2 -> H(f(e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.88	   A^2 -> H(f(k), b)
28.56/9.88	   A^2 -> H(f(k), U1(e, d))
28.56/9.88	   A^2 -> H(f(k), U1(d, e))
28.56/9.88	   A^2 -> H(f(k), c)
28.56/9.88	   A^2 -> H(f(k), U1(e, k))
28.56/9.88	   A^2 -> H(f(k), U1(k, e))
28.56/9.88	   A^2 -> H(f(k), e)
28.56/9.88	   A^2 -> H(f(c), d)
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.88	   A^2 -> H(U1(k, k), f(e))
28.56/9.88	   A^2 -> H(U1(k, k), f(k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, d), b)
28.56/9.88	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.88	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.88	   A^2 -> H(U1(d, d), c)
28.56/9.88	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.88	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.88	   A^2 -> H(U1(d, d), e)
28.56/9.88	   A^2 -> H(f(d), d)
28.56/9.88	   A^2 -> H(f(d), k)
28.56/9.88	   A^2 -> H(U1(c, c), c)
28.56/9.88	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.88	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.88	   A^2 -> H(f(c), k)
28.56/9.88	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.88	   A^2 -> H(f(k), U1(k, k))
28.56/9.88	   A^2 -> H(f(e), e)
28.56/9.88	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.88	   A^2 -> H(d, U1(c, b))
28.56/9.88	   A^2 -> H(d, U1(d, b))
28.56/9.88	   A^2 -> H(d, U1(b, c))
28.56/9.88	   A^2 -> H(d, U1(b, d))
28.56/9.88	   A^2 -> H(d, U1(c, c))
28.56/9.88	   A^2 -> H(d, f(e))
28.56/9.88	   A^2 -> H(d, f(k))
28.56/9.88	   A^2 -> H(d, U1(d, d))
28.56/9.88	   A^2 -> H(a, U1(e, b))
28.56/9.88	   A^2 -> H(a, U1(k, b))
28.56/9.88	   A^2 -> H(a, U1(c, d))
28.56/9.88	   A^2 -> H(a, U1(d, c))
28.56/9.88	   A^2 -> H(a, U1(b, e))
28.56/9.88	   A^2 -> H(a, U1(b, k))
28.56/9.88	   A^2 -> H(a, U1(e, c))
28.56/9.88	   A^2 -> H(a, U1(k, c))
28.56/9.88	   A^2 -> H(a, U1(c, e))
28.56/9.88	   A^2 -> H(a, U1(c, k))
28.56/9.88	   A^2 -> H(a, U1(e, e))
28.56/9.88	   A^2 -> H(a, U1(k, k))
28.56/9.88	   A^2 -> H(a, U1(k, d))
28.56/9.88	   A^2 -> H(a, U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, a), b)
28.56/9.88	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.88	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.88	   A^2 -> H(U1(e, a), c)
28.56/9.88	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.88	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.88	   A^2 -> H(U1(e, a), e)
28.56/9.88	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, a), b)
28.56/9.88	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.88	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.88	   A^2 -> H(U1(k, a), c)
28.56/9.88	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.88	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.88	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, d), b)
28.56/9.88	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.88	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.88	   A^2 -> H(U1(c, d), c)
28.56/9.88	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.88	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.88	   A^2 -> H(U1(c, d), e)
28.56/9.88	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, a), d)
28.56/9.88	   A^2 -> H(U1(c, a), k)
28.56/9.88	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, c), b)
28.56/9.88	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.88	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.88	   A^2 -> H(U1(d, c), c)
28.56/9.88	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.88	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.88	   A^2 -> H(U1(d, c), e)
28.56/9.88	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.88	   A^2 -> H(U1(d, a), d)
28.56/9.88	   A^2 -> H(U1(d, a), k)
28.56/9.88	   A^2 -> H(U1(a, e), b)
28.56/9.88	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.88	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.88	   A^2 -> H(U1(a, e), c)
28.56/9.88	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.88	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.88	   A^2 -> H(U1(a, e), e)
28.56/9.88	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(a, k), b)
28.56/9.88	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.88	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.88	   A^2 -> H(U1(a, k), c)
28.56/9.88	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.88	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.88	   A^2 -> H(U1(a, k), e)
28.56/9.88	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(a, c), d)
28.56/9.88	   A^2 -> H(U1(a, c), k)
28.56/9.88	   A^2 -> H(U1(a, d), d)
28.56/9.88	   A^2 -> H(U1(a, d), k)
28.56/9.88	   A^2 -> H(k, U1(c, b))
28.56/9.88	   A^2 -> H(k, U1(d, b))
28.56/9.88	   A^2 -> H(k, U1(b, c))
28.56/9.88	   A^2 -> H(k, U1(b, d))
28.56/9.88	   A^2 -> H(k, U1(c, c))
28.56/9.88	   A^2 -> H(k, f(e))
28.56/9.88	   A^2 -> H(k, f(k))
28.56/9.88	   A^2 -> H(k, U1(d, d))
28.56/9.88	   A^2 -> H(c, U1(e, b))
28.56/9.88	   A^2 -> H(c, U1(k, b))
28.56/9.88	   A^2 -> H(c, U1(c, d))
28.56/9.88	   A^2 -> H(c, U1(d, c))
28.56/9.88	   A^2 -> H(c, U1(b, e))
28.56/9.88	   A^2 -> H(c, U1(b, k))
28.56/9.88	   A^2 -> H(c, U1(e, c))
28.56/9.88	   A^2 -> H(c, U1(k, c))
28.56/9.88	   A^2 -> H(c, U1(c, e))
28.56/9.88	   A^2 -> H(c, U1(c, k))
28.56/9.88	   A^2 -> H(c, U1(e, e))
28.56/9.88	   A^2 -> H(c, U1(k, k))
28.56/9.88	   A^2 -> H(c, U1(k, d))
28.56/9.88	   A^2 -> H(c, U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, c), b)
28.56/9.88	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.88	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.88	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.88	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.88	   A^2 -> H(U1(e, c), e)
28.56/9.88	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.88	   A^2 -> H(U1(k, c), b)
28.56/9.88	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.88	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.88	   A^2 -> H(U1(k, c), c)
28.56/9.88	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.88	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.88	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, e), b)
28.56/9.88	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.88	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.88	   A^2 -> H(U1(c, e), c)
28.56/9.88	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.88	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.88	   A^2 -> H(U1(c, e), e)
28.56/9.88	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, k), b)
28.56/9.88	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.88	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.88	   A^2 -> H(U1(c, k), c)
28.56/9.88	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.88	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.88	   A^2 -> H(U1(c, k), e)
28.56/9.88	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, c), d)
28.56/9.88	   A^2 -> H(e, U1(e, b))
28.56/9.88	   A^2 -> H(e, U1(c, d))
28.56/9.88	   A^2 -> H(e, U1(k, b))
28.56/9.88	   A^2 -> H(e, U1(d, c))
28.56/9.88	
28.56/9.88	The TRS R consists of the following rules:
28.56/9.88	
28.56/9.88	   f(x) -> U1(x, x)
28.56/9.88	   U1(e, x) -> x
28.56/9.88	   a -> c
28.56/9.88	   a -> d
28.56/9.88	   b -> c
28.56/9.88	   b -> d
28.56/9.88	   d -> k
28.56/9.88	   c -> e
28.56/9.88	   c -> k
28.56/9.88	
28.56/9.88	Q is empty.
28.56/9.88	We have to consider all minimal (P,Q,R)-chains.
28.56/9.88	----------------------------------------
28.56/9.88	
28.56/9.88	(1569) DependencyGraphProof (EQUIVALENT)
28.56/9.88	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.88	----------------------------------------
28.56/9.88	
28.56/9.88	(1570)
28.56/9.88	Obligation:
28.56/9.88	Q DP problem:
28.56/9.88	The TRS P consists of the following rules:
28.56/9.88	
28.56/9.88	   G(d, x, x) -> A^2
28.56/9.88	   A^2 -> H(f(c), f(c))
28.56/9.88	   H(x, x) -> G(x, x, f(k))
28.56/9.88	   A^2 -> H(f(d), f(d))
28.56/9.88	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.88	   A^2 -> H(f(e), f(e))
28.56/9.88	   A^2 -> H(f(k), f(k))
28.56/9.88	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.88	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.88	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.88	   A^2 -> H(e, U1(b, c))
28.56/9.88	   A^2 -> H(e, U1(b, d))
28.56/9.88	   A^2 -> H(e, U1(c, c))
28.56/9.88	   A^2 -> H(e, f(e))
28.56/9.88	   A^2 -> H(e, f(k))
28.56/9.88	   A^2 -> H(e, U1(d, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.88	   A^2 -> H(f(e), b)
28.56/9.88	   A^2 -> H(f(e), U1(e, d))
28.56/9.88	   A^2 -> H(f(e), U1(d, e))
28.56/9.88	   A^2 -> H(f(e), c)
28.56/9.88	   A^2 -> H(f(e), U1(e, k))
28.56/9.88	   A^2 -> H(f(e), U1(k, e))
28.56/9.88	   A^2 -> H(f(e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.88	   A^2 -> H(f(k), b)
28.56/9.88	   A^2 -> H(f(k), U1(e, d))
28.56/9.88	   A^2 -> H(f(k), U1(d, e))
28.56/9.88	   A^2 -> H(f(k), c)
28.56/9.88	   A^2 -> H(f(k), U1(e, k))
28.56/9.88	   A^2 -> H(f(k), U1(k, e))
28.56/9.88	   A^2 -> H(f(k), e)
28.56/9.88	   A^2 -> H(f(c), d)
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.88	   A^2 -> H(U1(k, k), f(e))
28.56/9.88	   A^2 -> H(U1(k, k), f(k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, d), b)
28.56/9.88	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.88	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.88	   A^2 -> H(U1(d, d), c)
28.56/9.88	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.88	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.88	   A^2 -> H(U1(d, d), e)
28.56/9.88	   A^2 -> H(f(d), d)
28.56/9.88	   A^2 -> H(f(d), k)
28.56/9.88	   A^2 -> H(U1(c, c), c)
28.56/9.88	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.88	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.88	   A^2 -> H(f(c), k)
28.56/9.88	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.88	   A^2 -> H(f(k), U1(k, k))
28.56/9.88	   A^2 -> H(f(e), e)
28.56/9.88	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.88	   A^2 -> H(d, U1(c, b))
28.56/9.88	   A^2 -> H(d, U1(d, b))
28.56/9.88	   A^2 -> H(d, U1(b, c))
28.56/9.88	   A^2 -> H(d, U1(b, d))
28.56/9.88	   A^2 -> H(d, U1(c, c))
28.56/9.88	   A^2 -> H(d, f(e))
28.56/9.88	   A^2 -> H(d, f(k))
28.56/9.88	   A^2 -> H(d, U1(d, d))
28.56/9.88	   A^2 -> H(a, U1(e, b))
28.56/9.88	   A^2 -> H(a, U1(k, b))
28.56/9.88	   A^2 -> H(a, U1(c, d))
28.56/9.88	   A^2 -> H(a, U1(d, c))
28.56/9.88	   A^2 -> H(a, U1(b, e))
28.56/9.88	   A^2 -> H(a, U1(b, k))
28.56/9.88	   A^2 -> H(a, U1(e, c))
28.56/9.88	   A^2 -> H(a, U1(k, c))
28.56/9.88	   A^2 -> H(a, U1(c, e))
28.56/9.88	   A^2 -> H(a, U1(c, k))
28.56/9.88	   A^2 -> H(a, U1(e, e))
28.56/9.88	   A^2 -> H(a, U1(k, k))
28.56/9.88	   A^2 -> H(a, U1(k, d))
28.56/9.88	   A^2 -> H(a, U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, a), b)
28.56/9.88	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.88	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.88	   A^2 -> H(U1(e, a), c)
28.56/9.88	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.88	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.88	   A^2 -> H(U1(e, a), e)
28.56/9.88	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, a), b)
28.56/9.88	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.88	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.88	   A^2 -> H(U1(k, a), c)
28.56/9.88	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.88	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.88	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, d), b)
28.56/9.88	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.88	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.88	   A^2 -> H(U1(c, d), c)
28.56/9.88	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.88	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.88	   A^2 -> H(U1(c, d), e)
28.56/9.88	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, a), d)
28.56/9.88	   A^2 -> H(U1(c, a), k)
28.56/9.88	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, c), b)
28.56/9.88	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.88	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.88	   A^2 -> H(U1(d, c), c)
28.56/9.88	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.88	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.88	   A^2 -> H(U1(d, c), e)
28.56/9.88	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.88	   A^2 -> H(U1(d, a), d)
28.56/9.88	   A^2 -> H(U1(d, a), k)
28.56/9.88	   A^2 -> H(U1(a, e), b)
28.56/9.88	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.88	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.88	   A^2 -> H(U1(a, e), c)
28.56/9.88	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.88	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.88	   A^2 -> H(U1(a, e), e)
28.56/9.88	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(a, k), b)
28.56/9.88	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.88	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.88	   A^2 -> H(U1(a, k), c)
28.56/9.88	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.88	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.88	   A^2 -> H(U1(a, k), e)
28.56/9.88	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(a, c), d)
28.56/9.88	   A^2 -> H(U1(a, c), k)
28.56/9.88	   A^2 -> H(U1(a, d), d)
28.56/9.88	   A^2 -> H(U1(a, d), k)
28.56/9.88	   A^2 -> H(k, U1(c, b))
28.56/9.88	   A^2 -> H(k, U1(d, b))
28.56/9.88	   A^2 -> H(k, U1(b, c))
28.56/9.88	   A^2 -> H(k, U1(b, d))
28.56/9.88	   A^2 -> H(k, U1(c, c))
28.56/9.88	   A^2 -> H(k, f(e))
28.56/9.88	   A^2 -> H(k, f(k))
28.56/9.88	   A^2 -> H(k, U1(d, d))
28.56/9.88	   A^2 -> H(c, U1(e, b))
28.56/9.88	   A^2 -> H(c, U1(k, b))
28.56/9.88	   A^2 -> H(c, U1(c, d))
28.56/9.88	   A^2 -> H(c, U1(d, c))
28.56/9.88	   A^2 -> H(c, U1(b, e))
28.56/9.88	   A^2 -> H(c, U1(b, k))
28.56/9.88	   A^2 -> H(c, U1(e, c))
28.56/9.88	   A^2 -> H(c, U1(k, c))
28.56/9.88	   A^2 -> H(c, U1(c, e))
28.56/9.88	   A^2 -> H(c, U1(c, k))
28.56/9.88	   A^2 -> H(c, U1(e, e))
28.56/9.88	   A^2 -> H(c, U1(k, k))
28.56/9.88	   A^2 -> H(c, U1(k, d))
28.56/9.88	   A^2 -> H(c, U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, c), b)
28.56/9.88	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.88	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.88	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.88	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.88	   A^2 -> H(U1(e, c), e)
28.56/9.88	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.88	   A^2 -> H(U1(k, c), b)
28.56/9.88	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.88	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.88	   A^2 -> H(U1(k, c), c)
28.56/9.88	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.88	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.88	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, e), b)
28.56/9.88	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.88	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.88	   A^2 -> H(U1(c, e), c)
28.56/9.88	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.88	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.88	   A^2 -> H(U1(c, e), e)
28.56/9.88	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, k), b)
28.56/9.88	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.88	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.88	   A^2 -> H(U1(c, k), c)
28.56/9.88	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.88	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.88	   A^2 -> H(U1(c, k), e)
28.56/9.88	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, c), d)
28.56/9.88	   A^2 -> H(e, U1(e, b))
28.56/9.88	   A^2 -> H(e, U1(c, d))
28.56/9.88	   A^2 -> H(e, U1(d, c))
28.56/9.88	
28.56/9.88	The TRS R consists of the following rules:
28.56/9.88	
28.56/9.88	   f(x) -> U1(x, x)
28.56/9.88	   U1(e, x) -> x
28.56/9.88	   a -> c
28.56/9.88	   a -> d
28.56/9.88	   b -> c
28.56/9.88	   b -> d
28.56/9.88	   d -> k
28.56/9.88	   c -> e
28.56/9.88	   c -> k
28.56/9.88	
28.56/9.88	Q is empty.
28.56/9.88	We have to consider all minimal (P,Q,R)-chains.
28.56/9.88	----------------------------------------
28.56/9.88	
28.56/9.88	(1571) TransformationProof (EQUIVALENT)
28.56/9.88	By narrowing [LPAR04] the rule A^2 -> H(e, U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.88	
28.56/9.88	   (A^2 -> H(e, U1(c, c)),A^2 -> H(e, U1(c, c)))
28.56/9.88	   (A^2 -> H(e, U1(d, c)),A^2 -> H(e, U1(d, c)))
28.56/9.88	   (A^2 -> H(e, U1(b, e)),A^2 -> H(e, U1(b, e)))
28.56/9.88	   (A^2 -> H(e, U1(b, k)),A^2 -> H(e, U1(b, k)))
28.56/9.88	
28.56/9.88	
28.56/9.88	----------------------------------------
28.56/9.88	
28.56/9.88	(1572)
28.56/9.88	Obligation:
28.56/9.88	Q DP problem:
28.56/9.88	The TRS P consists of the following rules:
28.56/9.88	
28.56/9.88	   G(d, x, x) -> A^2
28.56/9.88	   A^2 -> H(f(c), f(c))
28.56/9.88	   H(x, x) -> G(x, x, f(k))
28.56/9.88	   A^2 -> H(f(d), f(d))
28.56/9.88	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.88	   A^2 -> H(f(e), f(e))
28.56/9.88	   A^2 -> H(f(k), f(k))
28.56/9.88	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.88	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.88	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.88	   A^2 -> H(e, U1(b, d))
28.56/9.88	   A^2 -> H(e, U1(c, c))
28.56/9.88	   A^2 -> H(e, f(e))
28.56/9.88	   A^2 -> H(e, f(k))
28.56/9.88	   A^2 -> H(e, U1(d, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.88	   A^2 -> H(f(e), b)
28.56/9.88	   A^2 -> H(f(e), U1(e, d))
28.56/9.88	   A^2 -> H(f(e), U1(d, e))
28.56/9.88	   A^2 -> H(f(e), c)
28.56/9.88	   A^2 -> H(f(e), U1(e, k))
28.56/9.88	   A^2 -> H(f(e), U1(k, e))
28.56/9.88	   A^2 -> H(f(e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.88	   A^2 -> H(f(k), b)
28.56/9.88	   A^2 -> H(f(k), U1(e, d))
28.56/9.88	   A^2 -> H(f(k), U1(d, e))
28.56/9.88	   A^2 -> H(f(k), c)
28.56/9.88	   A^2 -> H(f(k), U1(e, k))
28.56/9.88	   A^2 -> H(f(k), U1(k, e))
28.56/9.88	   A^2 -> H(f(k), e)
28.56/9.88	   A^2 -> H(f(c), d)
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.88	   A^2 -> H(U1(k, k), f(e))
28.56/9.88	   A^2 -> H(U1(k, k), f(k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, d), b)
28.56/9.88	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.88	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.88	   A^2 -> H(U1(d, d), c)
28.56/9.88	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.88	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.88	   A^2 -> H(U1(d, d), e)
28.56/9.88	   A^2 -> H(f(d), d)
28.56/9.88	   A^2 -> H(f(d), k)
28.56/9.88	   A^2 -> H(U1(c, c), c)
28.56/9.88	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.88	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.88	   A^2 -> H(f(c), k)
28.56/9.88	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.88	   A^2 -> H(f(k), U1(k, k))
28.56/9.88	   A^2 -> H(f(e), e)
28.56/9.88	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.88	   A^2 -> H(d, U1(c, b))
28.56/9.88	   A^2 -> H(d, U1(d, b))
28.56/9.88	   A^2 -> H(d, U1(b, c))
28.56/9.88	   A^2 -> H(d, U1(b, d))
28.56/9.88	   A^2 -> H(d, U1(c, c))
28.56/9.88	   A^2 -> H(d, f(e))
28.56/9.88	   A^2 -> H(d, f(k))
28.56/9.88	   A^2 -> H(d, U1(d, d))
28.56/9.88	   A^2 -> H(a, U1(e, b))
28.56/9.88	   A^2 -> H(a, U1(k, b))
28.56/9.88	   A^2 -> H(a, U1(c, d))
28.56/9.88	   A^2 -> H(a, U1(d, c))
28.56/9.88	   A^2 -> H(a, U1(b, e))
28.56/9.88	   A^2 -> H(a, U1(b, k))
28.56/9.88	   A^2 -> H(a, U1(e, c))
28.56/9.88	   A^2 -> H(a, U1(k, c))
28.56/9.88	   A^2 -> H(a, U1(c, e))
28.56/9.88	   A^2 -> H(a, U1(c, k))
28.56/9.88	   A^2 -> H(a, U1(e, e))
28.56/9.88	   A^2 -> H(a, U1(k, k))
28.56/9.88	   A^2 -> H(a, U1(k, d))
28.56/9.88	   A^2 -> H(a, U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, a), b)
28.56/9.88	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.88	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.88	   A^2 -> H(U1(e, a), c)
28.56/9.88	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.88	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.88	   A^2 -> H(U1(e, a), e)
28.56/9.88	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, a), b)
28.56/9.88	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.88	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.88	   A^2 -> H(U1(k, a), c)
28.56/9.88	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.88	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.88	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, d), b)
28.56/9.88	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.88	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.88	   A^2 -> H(U1(c, d), c)
28.56/9.88	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.88	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.88	   A^2 -> H(U1(c, d), e)
28.56/9.88	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, a), d)
28.56/9.88	   A^2 -> H(U1(c, a), k)
28.56/9.88	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, c), b)
28.56/9.88	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.88	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.88	   A^2 -> H(U1(d, c), c)
28.56/9.88	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.88	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.88	   A^2 -> H(U1(d, c), e)
28.56/9.88	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.88	   A^2 -> H(U1(d, a), d)
28.56/9.88	   A^2 -> H(U1(d, a), k)
28.56/9.88	   A^2 -> H(U1(a, e), b)
28.56/9.88	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.88	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.88	   A^2 -> H(U1(a, e), c)
28.56/9.88	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.88	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.88	   A^2 -> H(U1(a, e), e)
28.56/9.88	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(a, k), b)
28.56/9.88	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.88	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.88	   A^2 -> H(U1(a, k), c)
28.56/9.88	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.88	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.88	   A^2 -> H(U1(a, k), e)
28.56/9.88	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(a, c), d)
28.56/9.88	   A^2 -> H(U1(a, c), k)
28.56/9.88	   A^2 -> H(U1(a, d), d)
28.56/9.88	   A^2 -> H(U1(a, d), k)
28.56/9.88	   A^2 -> H(k, U1(c, b))
28.56/9.88	   A^2 -> H(k, U1(d, b))
28.56/9.88	   A^2 -> H(k, U1(b, c))
28.56/9.88	   A^2 -> H(k, U1(b, d))
28.56/9.88	   A^2 -> H(k, U1(c, c))
28.56/9.88	   A^2 -> H(k, f(e))
28.56/9.88	   A^2 -> H(k, f(k))
28.56/9.88	   A^2 -> H(k, U1(d, d))
28.56/9.88	   A^2 -> H(c, U1(e, b))
28.56/9.88	   A^2 -> H(c, U1(k, b))
28.56/9.88	   A^2 -> H(c, U1(c, d))
28.56/9.88	   A^2 -> H(c, U1(d, c))
28.56/9.88	   A^2 -> H(c, U1(b, e))
28.56/9.88	   A^2 -> H(c, U1(b, k))
28.56/9.88	   A^2 -> H(c, U1(e, c))
28.56/9.88	   A^2 -> H(c, U1(k, c))
28.56/9.88	   A^2 -> H(c, U1(c, e))
28.56/9.88	   A^2 -> H(c, U1(c, k))
28.56/9.88	   A^2 -> H(c, U1(e, e))
28.56/9.88	   A^2 -> H(c, U1(k, k))
28.56/9.88	   A^2 -> H(c, U1(k, d))
28.56/9.88	   A^2 -> H(c, U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, c), b)
28.56/9.88	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.88	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.88	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.88	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.88	   A^2 -> H(U1(e, c), e)
28.56/9.88	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.88	   A^2 -> H(U1(k, c), b)
28.56/9.88	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.88	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.88	   A^2 -> H(U1(k, c), c)
28.56/9.88	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.88	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.88	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, e), b)
28.56/9.88	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.88	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.88	   A^2 -> H(U1(c, e), c)
28.56/9.88	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.88	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.88	   A^2 -> H(U1(c, e), e)
28.56/9.88	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, k), b)
28.56/9.88	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.88	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.88	   A^2 -> H(U1(c, k), c)
28.56/9.88	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.88	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.88	   A^2 -> H(U1(c, k), e)
28.56/9.88	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, c), d)
28.56/9.88	   A^2 -> H(e, U1(e, b))
28.56/9.88	   A^2 -> H(e, U1(c, d))
28.56/9.88	   A^2 -> H(e, U1(d, c))
28.56/9.88	   A^2 -> H(e, U1(b, e))
28.56/9.88	   A^2 -> H(e, U1(b, k))
28.56/9.88	
28.56/9.88	The TRS R consists of the following rules:
28.56/9.88	
28.56/9.88	   f(x) -> U1(x, x)
28.56/9.88	   U1(e, x) -> x
28.56/9.88	   a -> c
28.56/9.88	   a -> d
28.56/9.88	   b -> c
28.56/9.88	   b -> d
28.56/9.88	   d -> k
28.56/9.88	   c -> e
28.56/9.88	   c -> k
28.56/9.88	
28.56/9.88	Q is empty.
28.56/9.88	We have to consider all minimal (P,Q,R)-chains.
28.56/9.88	----------------------------------------
28.56/9.88	
28.56/9.88	(1573) TransformationProof (EQUIVALENT)
28.56/9.88	By narrowing [LPAR04] the rule A^2 -> H(e, U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.88	
28.56/9.88	   (A^2 -> H(e, U1(c, d)),A^2 -> H(e, U1(c, d)))
28.56/9.88	   (A^2 -> H(e, U1(d, d)),A^2 -> H(e, U1(d, d)))
28.56/9.88	   (A^2 -> H(e, U1(b, k)),A^2 -> H(e, U1(b, k)))
28.56/9.88	
28.56/9.88	
28.56/9.88	----------------------------------------
28.56/9.88	
28.56/9.88	(1574)
28.56/9.88	Obligation:
28.56/9.88	Q DP problem:
28.56/9.88	The TRS P consists of the following rules:
28.56/9.88	
28.56/9.88	   G(d, x, x) -> A^2
28.56/9.88	   A^2 -> H(f(c), f(c))
28.56/9.88	   H(x, x) -> G(x, x, f(k))
28.56/9.88	   A^2 -> H(f(d), f(d))
28.56/9.88	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.88	   A^2 -> H(f(e), f(e))
28.56/9.88	   A^2 -> H(f(k), f(k))
28.56/9.88	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.88	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.88	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.88	   A^2 -> H(e, U1(c, c))
28.56/9.88	   A^2 -> H(e, f(e))
28.56/9.88	   A^2 -> H(e, f(k))
28.56/9.88	   A^2 -> H(e, U1(d, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.88	   A^2 -> H(f(e), b)
28.56/9.88	   A^2 -> H(f(e), U1(e, d))
28.56/9.88	   A^2 -> H(f(e), U1(d, e))
28.56/9.88	   A^2 -> H(f(e), c)
28.56/9.88	   A^2 -> H(f(e), U1(e, k))
28.56/9.88	   A^2 -> H(f(e), U1(k, e))
28.56/9.88	   A^2 -> H(f(e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.88	   A^2 -> H(f(k), b)
28.56/9.88	   A^2 -> H(f(k), U1(e, d))
28.56/9.88	   A^2 -> H(f(k), U1(d, e))
28.56/9.88	   A^2 -> H(f(k), c)
28.56/9.88	   A^2 -> H(f(k), U1(e, k))
28.56/9.88	   A^2 -> H(f(k), U1(k, e))
28.56/9.88	   A^2 -> H(f(k), e)
28.56/9.88	   A^2 -> H(f(c), d)
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.88	   A^2 -> H(U1(k, k), f(e))
28.56/9.88	   A^2 -> H(U1(k, k), f(k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, d), b)
28.56/9.88	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.88	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.88	   A^2 -> H(U1(d, d), c)
28.56/9.88	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.88	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.88	   A^2 -> H(U1(d, d), e)
28.56/9.88	   A^2 -> H(f(d), d)
28.56/9.88	   A^2 -> H(f(d), k)
28.56/9.88	   A^2 -> H(U1(c, c), c)
28.56/9.88	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.88	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.88	   A^2 -> H(f(c), k)
28.56/9.88	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.88	   A^2 -> H(f(k), U1(k, k))
28.56/9.88	   A^2 -> H(f(e), e)
28.56/9.88	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.88	   A^2 -> H(d, U1(c, b))
28.56/9.88	   A^2 -> H(d, U1(d, b))
28.56/9.88	   A^2 -> H(d, U1(b, c))
28.56/9.88	   A^2 -> H(d, U1(b, d))
28.56/9.88	   A^2 -> H(d, U1(c, c))
28.56/9.88	   A^2 -> H(d, f(e))
28.56/9.88	   A^2 -> H(d, f(k))
28.56/9.88	   A^2 -> H(d, U1(d, d))
28.56/9.88	   A^2 -> H(a, U1(e, b))
28.56/9.88	   A^2 -> H(a, U1(k, b))
28.56/9.88	   A^2 -> H(a, U1(c, d))
28.56/9.88	   A^2 -> H(a, U1(d, c))
28.56/9.88	   A^2 -> H(a, U1(b, e))
28.56/9.88	   A^2 -> H(a, U1(b, k))
28.56/9.88	   A^2 -> H(a, U1(e, c))
28.56/9.88	   A^2 -> H(a, U1(k, c))
28.56/9.88	   A^2 -> H(a, U1(c, e))
28.56/9.88	   A^2 -> H(a, U1(c, k))
28.56/9.88	   A^2 -> H(a, U1(e, e))
28.56/9.88	   A^2 -> H(a, U1(k, k))
28.56/9.88	   A^2 -> H(a, U1(k, d))
28.56/9.88	   A^2 -> H(a, U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, a), b)
28.56/9.88	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.88	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.88	   A^2 -> H(U1(e, a), c)
28.56/9.88	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.88	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.88	   A^2 -> H(U1(e, a), e)
28.56/9.88	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, a), b)
28.56/9.88	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.88	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.88	   A^2 -> H(U1(k, a), c)
28.56/9.88	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.88	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.88	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, d), b)
28.56/9.88	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.88	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.88	   A^2 -> H(U1(c, d), c)
28.56/9.88	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.88	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.88	   A^2 -> H(U1(c, d), e)
28.56/9.88	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, a), d)
28.56/9.88	   A^2 -> H(U1(c, a), k)
28.56/9.88	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, c), b)
28.56/9.88	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.88	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.88	   A^2 -> H(U1(d, c), c)
28.56/9.88	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.88	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.88	   A^2 -> H(U1(d, c), e)
28.56/9.88	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.88	   A^2 -> H(U1(d, a), d)
28.56/9.88	   A^2 -> H(U1(d, a), k)
28.56/9.88	   A^2 -> H(U1(a, e), b)
28.56/9.88	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.88	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.88	   A^2 -> H(U1(a, e), c)
28.56/9.88	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.88	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.88	   A^2 -> H(U1(a, e), e)
28.56/9.88	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(a, k), b)
28.56/9.88	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.88	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.88	   A^2 -> H(U1(a, k), c)
28.56/9.88	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.88	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.88	   A^2 -> H(U1(a, k), e)
28.56/9.88	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(a, c), d)
28.56/9.88	   A^2 -> H(U1(a, c), k)
28.56/9.88	   A^2 -> H(U1(a, d), d)
28.56/9.88	   A^2 -> H(U1(a, d), k)
28.56/9.88	   A^2 -> H(k, U1(c, b))
28.56/9.88	   A^2 -> H(k, U1(d, b))
28.56/9.88	   A^2 -> H(k, U1(b, c))
28.56/9.88	   A^2 -> H(k, U1(b, d))
28.56/9.88	   A^2 -> H(k, U1(c, c))
28.56/9.88	   A^2 -> H(k, f(e))
28.56/9.88	   A^2 -> H(k, f(k))
28.56/9.88	   A^2 -> H(k, U1(d, d))
28.56/9.88	   A^2 -> H(c, U1(e, b))
28.56/9.88	   A^2 -> H(c, U1(k, b))
28.56/9.88	   A^2 -> H(c, U1(c, d))
28.56/9.88	   A^2 -> H(c, U1(d, c))
28.56/9.88	   A^2 -> H(c, U1(b, e))
28.56/9.88	   A^2 -> H(c, U1(b, k))
28.56/9.88	   A^2 -> H(c, U1(e, c))
28.56/9.88	   A^2 -> H(c, U1(k, c))
28.56/9.88	   A^2 -> H(c, U1(c, e))
28.56/9.88	   A^2 -> H(c, U1(c, k))
28.56/9.88	   A^2 -> H(c, U1(e, e))
28.56/9.88	   A^2 -> H(c, U1(k, k))
28.56/9.88	   A^2 -> H(c, U1(k, d))
28.56/9.88	   A^2 -> H(c, U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, c), b)
28.56/9.88	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.88	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.88	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.88	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.88	   A^2 -> H(U1(e, c), e)
28.56/9.88	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.88	   A^2 -> H(U1(k, c), b)
28.56/9.88	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.88	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.88	   A^2 -> H(U1(k, c), c)
28.56/9.88	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.88	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.88	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, e), b)
28.56/9.88	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.88	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.88	   A^2 -> H(U1(c, e), c)
28.56/9.88	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.88	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.88	   A^2 -> H(U1(c, e), e)
28.56/9.88	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, k), b)
28.56/9.88	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.88	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.88	   A^2 -> H(U1(c, k), c)
28.56/9.88	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.88	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.88	   A^2 -> H(U1(c, k), e)
28.56/9.88	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, c), d)
28.56/9.88	   A^2 -> H(e, U1(e, b))
28.56/9.88	   A^2 -> H(e, U1(c, d))
28.56/9.88	   A^2 -> H(e, U1(d, c))
28.56/9.88	   A^2 -> H(e, U1(b, e))
28.56/9.88	   A^2 -> H(e, U1(b, k))
28.56/9.88	
28.56/9.88	The TRS R consists of the following rules:
28.56/9.88	
28.56/9.88	   f(x) -> U1(x, x)
28.56/9.88	   U1(e, x) -> x
28.56/9.88	   a -> c
28.56/9.88	   a -> d
28.56/9.88	   b -> c
28.56/9.88	   b -> d
28.56/9.88	   d -> k
28.56/9.88	   c -> e
28.56/9.88	   c -> k
28.56/9.88	
28.56/9.88	Q is empty.
28.56/9.88	We have to consider all minimal (P,Q,R)-chains.
28.56/9.88	----------------------------------------
28.56/9.88	
28.56/9.88	(1575) TransformationProof (EQUIVALENT)
28.56/9.88	By narrowing [LPAR04] the rule A^2 -> H(e, U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.88	
28.56/9.88	   (A^2 -> H(e, U1(e, c)),A^2 -> H(e, U1(e, c)))
28.56/9.88	   (A^2 -> H(e, U1(k, c)),A^2 -> H(e, U1(k, c)))
28.56/9.88	   (A^2 -> H(e, U1(c, e)),A^2 -> H(e, U1(c, e)))
28.56/9.88	   (A^2 -> H(e, U1(c, k)),A^2 -> H(e, U1(c, k)))
28.56/9.88	
28.56/9.88	
28.56/9.88	----------------------------------------
28.56/9.88	
28.56/9.88	(1576)
28.56/9.88	Obligation:
28.56/9.88	Q DP problem:
28.56/9.88	The TRS P consists of the following rules:
28.56/9.88	
28.56/9.88	   G(d, x, x) -> A^2
28.56/9.88	   A^2 -> H(f(c), f(c))
28.56/9.88	   H(x, x) -> G(x, x, f(k))
28.56/9.88	   A^2 -> H(f(d), f(d))
28.56/9.88	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.88	   A^2 -> H(f(e), f(e))
28.56/9.88	   A^2 -> H(f(k), f(k))
28.56/9.88	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.88	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.88	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.88	   A^2 -> H(e, f(e))
28.56/9.88	   A^2 -> H(e, f(k))
28.56/9.88	   A^2 -> H(e, U1(d, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.88	   A^2 -> H(f(e), b)
28.56/9.88	   A^2 -> H(f(e), U1(e, d))
28.56/9.88	   A^2 -> H(f(e), U1(d, e))
28.56/9.88	   A^2 -> H(f(e), c)
28.56/9.88	   A^2 -> H(f(e), U1(e, k))
28.56/9.88	   A^2 -> H(f(e), U1(k, e))
28.56/9.88	   A^2 -> H(f(e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.88	   A^2 -> H(f(k), b)
28.56/9.88	   A^2 -> H(f(k), U1(e, d))
28.56/9.88	   A^2 -> H(f(k), U1(d, e))
28.56/9.88	   A^2 -> H(f(k), c)
28.56/9.88	   A^2 -> H(f(k), U1(e, k))
28.56/9.88	   A^2 -> H(f(k), U1(k, e))
28.56/9.88	   A^2 -> H(f(k), e)
28.56/9.88	   A^2 -> H(f(c), d)
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.88	   A^2 -> H(U1(k, k), f(e))
28.56/9.88	   A^2 -> H(U1(k, k), f(k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, d), b)
28.56/9.88	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.88	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.88	   A^2 -> H(U1(d, d), c)
28.56/9.88	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.88	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.88	   A^2 -> H(U1(d, d), e)
28.56/9.88	   A^2 -> H(f(d), d)
28.56/9.88	   A^2 -> H(f(d), k)
28.56/9.88	   A^2 -> H(U1(c, c), c)
28.56/9.88	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.88	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.88	   A^2 -> H(f(c), k)
28.56/9.88	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.88	   A^2 -> H(f(k), U1(k, k))
28.56/9.88	   A^2 -> H(f(e), e)
28.56/9.88	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.88	   A^2 -> H(d, U1(c, b))
28.56/9.88	   A^2 -> H(d, U1(d, b))
28.56/9.88	   A^2 -> H(d, U1(b, c))
28.56/9.88	   A^2 -> H(d, U1(b, d))
28.56/9.88	   A^2 -> H(d, U1(c, c))
28.56/9.88	   A^2 -> H(d, f(e))
28.56/9.88	   A^2 -> H(d, f(k))
28.56/9.88	   A^2 -> H(d, U1(d, d))
28.56/9.88	   A^2 -> H(a, U1(e, b))
28.56/9.88	   A^2 -> H(a, U1(k, b))
28.56/9.88	   A^2 -> H(a, U1(c, d))
28.56/9.88	   A^2 -> H(a, U1(d, c))
28.56/9.88	   A^2 -> H(a, U1(b, e))
28.56/9.88	   A^2 -> H(a, U1(b, k))
28.56/9.88	   A^2 -> H(a, U1(e, c))
28.56/9.88	   A^2 -> H(a, U1(k, c))
28.56/9.88	   A^2 -> H(a, U1(c, e))
28.56/9.88	   A^2 -> H(a, U1(c, k))
28.56/9.88	   A^2 -> H(a, U1(e, e))
28.56/9.88	   A^2 -> H(a, U1(k, k))
28.56/9.88	   A^2 -> H(a, U1(k, d))
28.56/9.88	   A^2 -> H(a, U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, a), b)
28.56/9.88	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.88	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.88	   A^2 -> H(U1(e, a), c)
28.56/9.88	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.88	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.88	   A^2 -> H(U1(e, a), e)
28.56/9.88	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, a), b)
28.56/9.88	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.88	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.88	   A^2 -> H(U1(k, a), c)
28.56/9.88	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.88	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.88	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, d), b)
28.56/9.88	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.88	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.88	   A^2 -> H(U1(c, d), c)
28.56/9.88	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.88	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.88	   A^2 -> H(U1(c, d), e)
28.56/9.88	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, a), d)
28.56/9.88	   A^2 -> H(U1(c, a), k)
28.56/9.88	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, c), b)
28.56/9.88	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.88	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.88	   A^2 -> H(U1(d, c), c)
28.56/9.88	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.88	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.88	   A^2 -> H(U1(d, c), e)
28.56/9.88	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.88	   A^2 -> H(U1(d, a), d)
28.56/9.88	   A^2 -> H(U1(d, a), k)
28.56/9.88	   A^2 -> H(U1(a, e), b)
28.56/9.88	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.88	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.88	   A^2 -> H(U1(a, e), c)
28.56/9.88	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.88	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.88	   A^2 -> H(U1(a, e), e)
28.56/9.88	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(a, k), b)
28.56/9.88	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.88	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.88	   A^2 -> H(U1(a, k), c)
28.56/9.88	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.88	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.88	   A^2 -> H(U1(a, k), e)
28.56/9.88	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(a, c), d)
28.56/9.88	   A^2 -> H(U1(a, c), k)
28.56/9.88	   A^2 -> H(U1(a, d), d)
28.56/9.88	   A^2 -> H(U1(a, d), k)
28.56/9.88	   A^2 -> H(k, U1(c, b))
28.56/9.88	   A^2 -> H(k, U1(d, b))
28.56/9.88	   A^2 -> H(k, U1(b, c))
28.56/9.88	   A^2 -> H(k, U1(b, d))
28.56/9.88	   A^2 -> H(k, U1(c, c))
28.56/9.88	   A^2 -> H(k, f(e))
28.56/9.88	   A^2 -> H(k, f(k))
28.56/9.88	   A^2 -> H(k, U1(d, d))
28.56/9.88	   A^2 -> H(c, U1(e, b))
28.56/9.88	   A^2 -> H(c, U1(k, b))
28.56/9.88	   A^2 -> H(c, U1(c, d))
28.56/9.88	   A^2 -> H(c, U1(d, c))
28.56/9.88	   A^2 -> H(c, U1(b, e))
28.56/9.88	   A^2 -> H(c, U1(b, k))
28.56/9.88	   A^2 -> H(c, U1(e, c))
28.56/9.88	   A^2 -> H(c, U1(k, c))
28.56/9.88	   A^2 -> H(c, U1(c, e))
28.56/9.88	   A^2 -> H(c, U1(c, k))
28.56/9.88	   A^2 -> H(c, U1(e, e))
28.56/9.88	   A^2 -> H(c, U1(k, k))
28.56/9.88	   A^2 -> H(c, U1(k, d))
28.56/9.88	   A^2 -> H(c, U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, c), b)
28.56/9.88	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.88	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.88	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.88	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.88	   A^2 -> H(U1(e, c), e)
28.56/9.88	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.88	   A^2 -> H(U1(k, c), b)
28.56/9.88	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.88	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.88	   A^2 -> H(U1(k, c), c)
28.56/9.88	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.88	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.88	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, e), b)
28.56/9.88	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.88	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.88	   A^2 -> H(U1(c, e), c)
28.56/9.88	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.88	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.88	   A^2 -> H(U1(c, e), e)
28.56/9.88	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, k), b)
28.56/9.88	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.88	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.88	   A^2 -> H(U1(c, k), c)
28.56/9.88	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.88	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.88	   A^2 -> H(U1(c, k), e)
28.56/9.88	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, c), d)
28.56/9.88	   A^2 -> H(e, U1(e, b))
28.56/9.88	   A^2 -> H(e, U1(c, d))
28.56/9.88	   A^2 -> H(e, U1(d, c))
28.56/9.88	   A^2 -> H(e, U1(b, e))
28.56/9.88	   A^2 -> H(e, U1(b, k))
28.56/9.88	   A^2 -> H(e, U1(e, c))
28.56/9.88	   A^2 -> H(e, U1(k, c))
28.56/9.88	   A^2 -> H(e, U1(c, e))
28.56/9.88	   A^2 -> H(e, U1(c, k))
28.56/9.88	
28.56/9.88	The TRS R consists of the following rules:
28.56/9.88	
28.56/9.88	   f(x) -> U1(x, x)
28.56/9.88	   U1(e, x) -> x
28.56/9.88	   a -> c
28.56/9.88	   a -> d
28.56/9.88	   b -> c
28.56/9.88	   b -> d
28.56/9.88	   d -> k
28.56/9.88	   c -> e
28.56/9.88	   c -> k
28.56/9.88	
28.56/9.88	Q is empty.
28.56/9.88	We have to consider all minimal (P,Q,R)-chains.
28.56/9.88	----------------------------------------
28.56/9.88	
28.56/9.88	(1577) DependencyGraphProof (EQUIVALENT)
28.56/9.88	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.88	----------------------------------------
28.56/9.88	
28.56/9.88	(1578)
28.56/9.88	Obligation:
28.56/9.88	Q DP problem:
28.56/9.88	The TRS P consists of the following rules:
28.56/9.88	
28.56/9.88	   A^2 -> H(f(c), f(c))
28.56/9.88	   H(x, x) -> G(x, x, f(k))
28.56/9.88	   G(d, x, x) -> A^2
28.56/9.88	   A^2 -> H(f(d), f(d))
28.56/9.88	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.88	   A^2 -> H(f(e), f(e))
28.56/9.88	   A^2 -> H(f(k), f(k))
28.56/9.88	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.88	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.88	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.88	   A^2 -> H(e, f(e))
28.56/9.88	   A^2 -> H(e, f(k))
28.56/9.88	   A^2 -> H(e, U1(d, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.88	   A^2 -> H(f(e), b)
28.56/9.88	   A^2 -> H(f(e), U1(e, d))
28.56/9.88	   A^2 -> H(f(e), U1(d, e))
28.56/9.88	   A^2 -> H(f(e), c)
28.56/9.88	   A^2 -> H(f(e), U1(e, k))
28.56/9.88	   A^2 -> H(f(e), U1(k, e))
28.56/9.88	   A^2 -> H(f(e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.88	   A^2 -> H(f(k), b)
28.56/9.88	   A^2 -> H(f(k), U1(e, d))
28.56/9.88	   A^2 -> H(f(k), U1(d, e))
28.56/9.88	   A^2 -> H(f(k), c)
28.56/9.88	   A^2 -> H(f(k), U1(e, k))
28.56/9.88	   A^2 -> H(f(k), U1(k, e))
28.56/9.88	   A^2 -> H(f(k), e)
28.56/9.88	   A^2 -> H(f(c), d)
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.88	   A^2 -> H(U1(k, k), f(e))
28.56/9.88	   A^2 -> H(U1(k, k), f(k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, d), b)
28.56/9.88	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.88	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.88	   A^2 -> H(U1(d, d), c)
28.56/9.88	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.88	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.88	   A^2 -> H(U1(d, d), e)
28.56/9.88	   A^2 -> H(f(d), d)
28.56/9.88	   A^2 -> H(f(d), k)
28.56/9.88	   A^2 -> H(U1(c, c), c)
28.56/9.88	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.88	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.88	   A^2 -> H(f(c), k)
28.56/9.88	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.88	   A^2 -> H(f(k), U1(k, k))
28.56/9.88	   A^2 -> H(f(e), e)
28.56/9.88	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.88	   A^2 -> H(d, U1(c, b))
28.56/9.88	   A^2 -> H(d, U1(d, b))
28.56/9.88	   A^2 -> H(d, U1(b, c))
28.56/9.88	   A^2 -> H(d, U1(b, d))
28.56/9.88	   A^2 -> H(d, U1(c, c))
28.56/9.88	   A^2 -> H(d, f(e))
28.56/9.88	   A^2 -> H(d, f(k))
28.56/9.88	   A^2 -> H(d, U1(d, d))
28.56/9.88	   A^2 -> H(a, U1(e, b))
28.56/9.88	   A^2 -> H(a, U1(k, b))
28.56/9.88	   A^2 -> H(a, U1(c, d))
28.56/9.88	   A^2 -> H(a, U1(d, c))
28.56/9.88	   A^2 -> H(a, U1(b, e))
28.56/9.88	   A^2 -> H(a, U1(b, k))
28.56/9.88	   A^2 -> H(a, U1(e, c))
28.56/9.88	   A^2 -> H(a, U1(k, c))
28.56/9.88	   A^2 -> H(a, U1(c, e))
28.56/9.88	   A^2 -> H(a, U1(c, k))
28.56/9.88	   A^2 -> H(a, U1(e, e))
28.56/9.88	   A^2 -> H(a, U1(k, k))
28.56/9.88	   A^2 -> H(a, U1(k, d))
28.56/9.88	   A^2 -> H(a, U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, a), b)
28.56/9.88	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.88	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.88	   A^2 -> H(U1(e, a), c)
28.56/9.88	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.88	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.88	   A^2 -> H(U1(e, a), e)
28.56/9.88	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, a), b)
28.56/9.88	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.88	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.88	   A^2 -> H(U1(k, a), c)
28.56/9.88	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.88	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.88	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, d), b)
28.56/9.88	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.88	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.88	   A^2 -> H(U1(c, d), c)
28.56/9.88	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.88	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.88	   A^2 -> H(U1(c, d), e)
28.56/9.88	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, a), d)
28.56/9.88	   A^2 -> H(U1(c, a), k)
28.56/9.88	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, c), b)
28.56/9.88	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.88	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.88	   A^2 -> H(U1(d, c), c)
28.56/9.88	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.88	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.88	   A^2 -> H(U1(d, c), e)
28.56/9.88	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.88	   A^2 -> H(U1(d, a), d)
28.56/9.88	   A^2 -> H(U1(d, a), k)
28.56/9.88	   A^2 -> H(U1(a, e), b)
28.56/9.88	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.88	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.88	   A^2 -> H(U1(a, e), c)
28.56/9.88	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.88	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.88	   A^2 -> H(U1(a, e), e)
28.56/9.88	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(a, k), b)
28.56/9.88	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.88	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.88	   A^2 -> H(U1(a, k), c)
28.56/9.88	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.88	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.88	   A^2 -> H(U1(a, k), e)
28.56/9.88	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(a, c), d)
28.56/9.88	   A^2 -> H(U1(a, c), k)
28.56/9.88	   A^2 -> H(U1(a, d), d)
28.56/9.88	   A^2 -> H(U1(a, d), k)
28.56/9.88	   A^2 -> H(k, U1(c, b))
28.56/9.88	   A^2 -> H(k, U1(d, b))
28.56/9.88	   A^2 -> H(k, U1(b, c))
28.56/9.88	   A^2 -> H(k, U1(b, d))
28.56/9.88	   A^2 -> H(k, U1(c, c))
28.56/9.88	   A^2 -> H(k, f(e))
28.56/9.88	   A^2 -> H(k, f(k))
28.56/9.88	   A^2 -> H(k, U1(d, d))
28.56/9.88	   A^2 -> H(c, U1(e, b))
28.56/9.88	   A^2 -> H(c, U1(k, b))
28.56/9.88	   A^2 -> H(c, U1(c, d))
28.56/9.88	   A^2 -> H(c, U1(d, c))
28.56/9.88	   A^2 -> H(c, U1(b, e))
28.56/9.88	   A^2 -> H(c, U1(b, k))
28.56/9.88	   A^2 -> H(c, U1(e, c))
28.56/9.88	   A^2 -> H(c, U1(k, c))
28.56/9.88	   A^2 -> H(c, U1(c, e))
28.56/9.88	   A^2 -> H(c, U1(c, k))
28.56/9.88	   A^2 -> H(c, U1(e, e))
28.56/9.88	   A^2 -> H(c, U1(k, k))
28.56/9.88	   A^2 -> H(c, U1(k, d))
28.56/9.88	   A^2 -> H(c, U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.88	   A^2 -> H(U1(e, c), b)
28.56/9.88	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.88	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.88	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.88	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.88	   A^2 -> H(U1(e, c), e)
28.56/9.88	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.88	   A^2 -> H(U1(k, c), b)
28.56/9.88	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.88	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.88	   A^2 -> H(U1(k, c), c)
28.56/9.88	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.88	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.88	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, e), b)
28.56/9.88	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.88	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.88	   A^2 -> H(U1(c, e), c)
28.56/9.88	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.88	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.88	   A^2 -> H(U1(c, e), e)
28.56/9.88	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, k), b)
28.56/9.88	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.88	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.88	   A^2 -> H(U1(c, k), c)
28.56/9.88	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.88	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.88	   A^2 -> H(U1(c, k), e)
28.56/9.88	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(c, c), d)
28.56/9.88	   A^2 -> H(e, U1(e, b))
28.56/9.88	   A^2 -> H(e, U1(c, d))
28.56/9.88	   A^2 -> H(e, U1(d, c))
28.56/9.88	   A^2 -> H(e, U1(b, e))
28.56/9.88	   A^2 -> H(e, U1(b, k))
28.56/9.88	   A^2 -> H(e, U1(e, c))
28.56/9.88	   A^2 -> H(e, U1(c, e))
28.56/9.88	   A^2 -> H(e, U1(c, k))
28.56/9.88	
28.56/9.88	The TRS R consists of the following rules:
28.56/9.88	
28.56/9.88	   f(x) -> U1(x, x)
28.56/9.88	   U1(e, x) -> x
28.56/9.88	   a -> c
28.56/9.88	   a -> d
28.56/9.88	   b -> c
28.56/9.88	   b -> d
28.56/9.88	   d -> k
28.56/9.88	   c -> e
28.56/9.88	   c -> k
28.56/9.88	
28.56/9.88	Q is empty.
28.56/9.88	We have to consider all minimal (P,Q,R)-chains.
28.56/9.88	----------------------------------------
28.56/9.88	
28.56/9.88	(1579) TransformationProof (EQUIVALENT)
28.56/9.88	By narrowing [LPAR04] the rule A^2 -> H(e, f(e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.88	
28.56/9.88	   (A^2 -> H(e, U1(e, e)),A^2 -> H(e, U1(e, e)))
28.56/9.88	
28.56/9.88	
28.56/9.88	----------------------------------------
28.56/9.88	
28.56/9.88	(1580)
28.56/9.88	Obligation:
28.56/9.88	Q DP problem:
28.56/9.88	The TRS P consists of the following rules:
28.56/9.88	
28.56/9.88	   A^2 -> H(f(c), f(c))
28.56/9.88	   H(x, x) -> G(x, x, f(k))
28.56/9.88	   G(d, x, x) -> A^2
28.56/9.88	   A^2 -> H(f(d), f(d))
28.56/9.88	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.88	   A^2 -> H(f(e), f(e))
28.56/9.88	   A^2 -> H(f(k), f(k))
28.56/9.88	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.88	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.88	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.88	   A^2 -> H(e, f(k))
28.56/9.88	   A^2 -> H(e, U1(d, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.88	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.88	   A^2 -> H(f(e), b)
28.56/9.88	   A^2 -> H(f(e), U1(e, d))
28.56/9.88	   A^2 -> H(f(e), U1(d, e))
28.56/9.88	   A^2 -> H(f(e), c)
28.56/9.88	   A^2 -> H(f(e), U1(e, k))
28.56/9.88	   A^2 -> H(f(e), U1(k, e))
28.56/9.88	   A^2 -> H(f(e), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.88	   A^2 -> H(f(k), b)
28.56/9.88	   A^2 -> H(f(k), U1(e, d))
28.56/9.88	   A^2 -> H(f(k), U1(d, e))
28.56/9.88	   A^2 -> H(f(k), c)
28.56/9.88	   A^2 -> H(f(k), U1(e, k))
28.56/9.88	   A^2 -> H(f(k), U1(k, e))
28.56/9.88	   A^2 -> H(f(k), e)
28.56/9.88	   A^2 -> H(f(c), d)
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.88	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.88	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.88	   A^2 -> H(U1(k, k), f(e))
28.56/9.88	   A^2 -> H(U1(k, k), f(k))
28.56/9.88	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.88	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.88	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.88	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.88	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.88	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.88	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, d), b)
28.56/9.89	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.89	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.89	   A^2 -> H(U1(d, d), c)
28.56/9.89	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.89	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.89	   A^2 -> H(U1(d, d), e)
28.56/9.89	   A^2 -> H(f(d), d)
28.56/9.89	   A^2 -> H(f(d), k)
28.56/9.89	   A^2 -> H(U1(c, c), c)
28.56/9.89	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.89	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.89	   A^2 -> H(f(c), k)
28.56/9.89	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.89	   A^2 -> H(f(k), U1(k, k))
28.56/9.89	   A^2 -> H(f(e), e)
28.56/9.89	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.89	   A^2 -> H(d, U1(c, b))
28.56/9.89	   A^2 -> H(d, U1(d, b))
28.56/9.89	   A^2 -> H(d, U1(b, c))
28.56/9.89	   A^2 -> H(d, U1(b, d))
28.56/9.89	   A^2 -> H(d, U1(c, c))
28.56/9.89	   A^2 -> H(d, f(e))
28.56/9.89	   A^2 -> H(d, f(k))
28.56/9.89	   A^2 -> H(d, U1(d, d))
28.56/9.89	   A^2 -> H(a, U1(e, b))
28.56/9.89	   A^2 -> H(a, U1(k, b))
28.56/9.89	   A^2 -> H(a, U1(c, d))
28.56/9.89	   A^2 -> H(a, U1(d, c))
28.56/9.89	   A^2 -> H(a, U1(b, e))
28.56/9.89	   A^2 -> H(a, U1(b, k))
28.56/9.89	   A^2 -> H(a, U1(e, c))
28.56/9.89	   A^2 -> H(a, U1(k, c))
28.56/9.89	   A^2 -> H(a, U1(c, e))
28.56/9.89	   A^2 -> H(a, U1(c, k))
28.56/9.89	   A^2 -> H(a, U1(e, e))
28.56/9.89	   A^2 -> H(a, U1(k, k))
28.56/9.89	   A^2 -> H(a, U1(k, d))
28.56/9.89	   A^2 -> H(a, U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, a), b)
28.56/9.89	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.89	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.89	   A^2 -> H(U1(e, a), c)
28.56/9.89	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.89	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.89	   A^2 -> H(U1(e, a), e)
28.56/9.89	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, a), b)
28.56/9.89	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.89	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.89	   A^2 -> H(U1(k, a), c)
28.56/9.89	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.89	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.89	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, d), b)
28.56/9.89	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, d), c)
28.56/9.89	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, d), e)
28.56/9.89	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, a), d)
28.56/9.89	   A^2 -> H(U1(c, a), k)
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.89	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.89	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.89	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.89	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.89	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.89	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, c), b)
28.56/9.89	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.89	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.89	   A^2 -> H(U1(d, c), c)
28.56/9.89	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.89	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.89	   A^2 -> H(U1(d, c), e)
28.56/9.89	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, a), d)
28.56/9.89	   A^2 -> H(U1(d, a), k)
28.56/9.89	   A^2 -> H(U1(a, e), b)
28.56/9.89	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.89	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.89	   A^2 -> H(U1(a, e), c)
28.56/9.89	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.89	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.89	   A^2 -> H(U1(a, e), e)
28.56/9.89	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(a, k), b)
28.56/9.89	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.89	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.89	   A^2 -> H(U1(a, k), c)
28.56/9.89	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.89	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.89	   A^2 -> H(U1(a, k), e)
28.56/9.89	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(a, c), d)
28.56/9.89	   A^2 -> H(U1(a, c), k)
28.56/9.89	   A^2 -> H(U1(a, d), d)
28.56/9.89	   A^2 -> H(U1(a, d), k)
28.56/9.89	   A^2 -> H(k, U1(c, b))
28.56/9.89	   A^2 -> H(k, U1(d, b))
28.56/9.89	   A^2 -> H(k, U1(b, c))
28.56/9.89	   A^2 -> H(k, U1(b, d))
28.56/9.89	   A^2 -> H(k, U1(c, c))
28.56/9.89	   A^2 -> H(k, f(e))
28.56/9.89	   A^2 -> H(k, f(k))
28.56/9.89	   A^2 -> H(k, U1(d, d))
28.56/9.89	   A^2 -> H(c, U1(e, b))
28.56/9.89	   A^2 -> H(c, U1(k, b))
28.56/9.89	   A^2 -> H(c, U1(c, d))
28.56/9.89	   A^2 -> H(c, U1(d, c))
28.56/9.89	   A^2 -> H(c, U1(b, e))
28.56/9.89	   A^2 -> H(c, U1(b, k))
28.56/9.89	   A^2 -> H(c, U1(e, c))
28.56/9.89	   A^2 -> H(c, U1(k, c))
28.56/9.89	   A^2 -> H(c, U1(c, e))
28.56/9.89	   A^2 -> H(c, U1(c, k))
28.56/9.89	   A^2 -> H(c, U1(e, e))
28.56/9.89	   A^2 -> H(c, U1(k, k))
28.56/9.89	   A^2 -> H(c, U1(k, d))
28.56/9.89	   A^2 -> H(c, U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.89	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, c), b)
28.56/9.89	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.89	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.89	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.89	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.89	   A^2 -> H(U1(e, c), e)
28.56/9.89	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.89	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.89	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.89	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.89	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.89	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.89	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.89	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.89	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.89	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.89	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.89	   A^2 -> H(U1(k, c), b)
28.56/9.89	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.89	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.89	   A^2 -> H(U1(k, c), c)
28.56/9.89	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.89	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.89	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, e), b)
28.56/9.89	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, e), c)
28.56/9.89	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, e), e)
28.56/9.89	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, k), b)
28.56/9.89	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, k), c)
28.56/9.89	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, k), e)
28.56/9.89	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, c), d)
28.56/9.89	   A^2 -> H(e, U1(e, b))
28.56/9.89	   A^2 -> H(e, U1(c, d))
28.56/9.89	   A^2 -> H(e, U1(d, c))
28.56/9.89	   A^2 -> H(e, U1(b, e))
28.56/9.89	   A^2 -> H(e, U1(b, k))
28.56/9.89	   A^2 -> H(e, U1(e, c))
28.56/9.89	   A^2 -> H(e, U1(c, e))
28.56/9.89	   A^2 -> H(e, U1(c, k))
28.56/9.89	   A^2 -> H(e, U1(e, e))
28.56/9.89	
28.56/9.89	The TRS R consists of the following rules:
28.56/9.89	
28.56/9.89	   f(x) -> U1(x, x)
28.56/9.89	   U1(e, x) -> x
28.56/9.89	   a -> c
28.56/9.89	   a -> d
28.56/9.89	   b -> c
28.56/9.89	   b -> d
28.56/9.89	   d -> k
28.56/9.89	   c -> e
28.56/9.89	   c -> k
28.56/9.89	
28.56/9.89	Q is empty.
28.56/9.89	We have to consider all minimal (P,Q,R)-chains.
28.56/9.89	----------------------------------------
28.56/9.89	
28.56/9.89	(1581) TransformationProof (EQUIVALENT)
28.56/9.89	By narrowing [LPAR04] the rule A^2 -> H(e, f(k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.89	
28.56/9.89	   (A^2 -> H(e, U1(k, k)),A^2 -> H(e, U1(k, k)))
28.56/9.89	
28.56/9.89	
28.56/9.89	----------------------------------------
28.56/9.89	
28.56/9.89	(1582)
28.56/9.89	Obligation:
28.56/9.89	Q DP problem:
28.56/9.89	The TRS P consists of the following rules:
28.56/9.89	
28.56/9.89	   A^2 -> H(f(c), f(c))
28.56/9.89	   H(x, x) -> G(x, x, f(k))
28.56/9.89	   G(d, x, x) -> A^2
28.56/9.89	   A^2 -> H(f(d), f(d))
28.56/9.89	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.89	   A^2 -> H(f(e), f(e))
28.56/9.89	   A^2 -> H(f(k), f(k))
28.56/9.89	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.89	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.89	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.89	   A^2 -> H(e, U1(d, d))
28.56/9.89	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.89	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.89	   A^2 -> H(f(e), b)
28.56/9.89	   A^2 -> H(f(e), U1(e, d))
28.56/9.89	   A^2 -> H(f(e), U1(d, e))
28.56/9.89	   A^2 -> H(f(e), c)
28.56/9.89	   A^2 -> H(f(e), U1(e, k))
28.56/9.89	   A^2 -> H(f(e), U1(k, e))
28.56/9.89	   A^2 -> H(f(e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.89	   A^2 -> H(f(k), b)
28.56/9.89	   A^2 -> H(f(k), U1(e, d))
28.56/9.89	   A^2 -> H(f(k), U1(d, e))
28.56/9.89	   A^2 -> H(f(k), c)
28.56/9.89	   A^2 -> H(f(k), U1(e, k))
28.56/9.89	   A^2 -> H(f(k), U1(k, e))
28.56/9.89	   A^2 -> H(f(k), e)
28.56/9.89	   A^2 -> H(f(c), d)
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.89	   A^2 -> H(U1(k, k), f(e))
28.56/9.89	   A^2 -> H(U1(k, k), f(k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.89	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.89	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.89	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.89	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.89	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.89	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.89	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.89	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.89	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.89	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.89	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, d), b)
28.56/9.89	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.89	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.89	   A^2 -> H(U1(d, d), c)
28.56/9.89	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.89	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.89	   A^2 -> H(U1(d, d), e)
28.56/9.89	   A^2 -> H(f(d), d)
28.56/9.89	   A^2 -> H(f(d), k)
28.56/9.89	   A^2 -> H(U1(c, c), c)
28.56/9.89	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.89	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.89	   A^2 -> H(f(c), k)
28.56/9.89	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.89	   A^2 -> H(f(k), U1(k, k))
28.56/9.89	   A^2 -> H(f(e), e)
28.56/9.89	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.89	   A^2 -> H(d, U1(c, b))
28.56/9.89	   A^2 -> H(d, U1(d, b))
28.56/9.89	   A^2 -> H(d, U1(b, c))
28.56/9.89	   A^2 -> H(d, U1(b, d))
28.56/9.89	   A^2 -> H(d, U1(c, c))
28.56/9.89	   A^2 -> H(d, f(e))
28.56/9.89	   A^2 -> H(d, f(k))
28.56/9.89	   A^2 -> H(d, U1(d, d))
28.56/9.89	   A^2 -> H(a, U1(e, b))
28.56/9.89	   A^2 -> H(a, U1(k, b))
28.56/9.89	   A^2 -> H(a, U1(c, d))
28.56/9.89	   A^2 -> H(a, U1(d, c))
28.56/9.89	   A^2 -> H(a, U1(b, e))
28.56/9.89	   A^2 -> H(a, U1(b, k))
28.56/9.89	   A^2 -> H(a, U1(e, c))
28.56/9.89	   A^2 -> H(a, U1(k, c))
28.56/9.89	   A^2 -> H(a, U1(c, e))
28.56/9.89	   A^2 -> H(a, U1(c, k))
28.56/9.89	   A^2 -> H(a, U1(e, e))
28.56/9.89	   A^2 -> H(a, U1(k, k))
28.56/9.89	   A^2 -> H(a, U1(k, d))
28.56/9.89	   A^2 -> H(a, U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, a), b)
28.56/9.89	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.89	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.89	   A^2 -> H(U1(e, a), c)
28.56/9.89	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.89	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.89	   A^2 -> H(U1(e, a), e)
28.56/9.89	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, a), b)
28.56/9.89	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.89	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.89	   A^2 -> H(U1(k, a), c)
28.56/9.89	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.89	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.89	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, d), b)
28.56/9.89	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, d), c)
28.56/9.89	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, d), e)
28.56/9.89	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, a), d)
28.56/9.89	   A^2 -> H(U1(c, a), k)
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.89	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.89	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.89	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.89	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.89	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.89	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, c), b)
28.56/9.89	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.89	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.89	   A^2 -> H(U1(d, c), c)
28.56/9.89	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.89	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.89	   A^2 -> H(U1(d, c), e)
28.56/9.89	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, a), d)
28.56/9.89	   A^2 -> H(U1(d, a), k)
28.56/9.89	   A^2 -> H(U1(a, e), b)
28.56/9.89	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.89	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.89	   A^2 -> H(U1(a, e), c)
28.56/9.89	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.89	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.89	   A^2 -> H(U1(a, e), e)
28.56/9.89	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(a, k), b)
28.56/9.89	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.89	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.89	   A^2 -> H(U1(a, k), c)
28.56/9.89	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.89	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.89	   A^2 -> H(U1(a, k), e)
28.56/9.89	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(a, c), d)
28.56/9.89	   A^2 -> H(U1(a, c), k)
28.56/9.89	   A^2 -> H(U1(a, d), d)
28.56/9.89	   A^2 -> H(U1(a, d), k)
28.56/9.89	   A^2 -> H(k, U1(c, b))
28.56/9.89	   A^2 -> H(k, U1(d, b))
28.56/9.89	   A^2 -> H(k, U1(b, c))
28.56/9.89	   A^2 -> H(k, U1(b, d))
28.56/9.89	   A^2 -> H(k, U1(c, c))
28.56/9.89	   A^2 -> H(k, f(e))
28.56/9.89	   A^2 -> H(k, f(k))
28.56/9.89	   A^2 -> H(k, U1(d, d))
28.56/9.89	   A^2 -> H(c, U1(e, b))
28.56/9.89	   A^2 -> H(c, U1(k, b))
28.56/9.89	   A^2 -> H(c, U1(c, d))
28.56/9.89	   A^2 -> H(c, U1(d, c))
28.56/9.89	   A^2 -> H(c, U1(b, e))
28.56/9.89	   A^2 -> H(c, U1(b, k))
28.56/9.89	   A^2 -> H(c, U1(e, c))
28.56/9.89	   A^2 -> H(c, U1(k, c))
28.56/9.89	   A^2 -> H(c, U1(c, e))
28.56/9.89	   A^2 -> H(c, U1(c, k))
28.56/9.89	   A^2 -> H(c, U1(e, e))
28.56/9.89	   A^2 -> H(c, U1(k, k))
28.56/9.89	   A^2 -> H(c, U1(k, d))
28.56/9.89	   A^2 -> H(c, U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.89	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, c), b)
28.56/9.89	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.89	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.89	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.89	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.89	   A^2 -> H(U1(e, c), e)
28.56/9.89	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.89	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.89	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.89	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.89	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.89	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.89	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.89	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.89	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.89	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.89	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.89	   A^2 -> H(U1(k, c), b)
28.56/9.89	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.89	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.89	   A^2 -> H(U1(k, c), c)
28.56/9.89	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.89	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.89	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, e), b)
28.56/9.89	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, e), c)
28.56/9.89	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, e), e)
28.56/9.89	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, k), b)
28.56/9.89	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, k), c)
28.56/9.89	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, k), e)
28.56/9.89	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, c), d)
28.56/9.89	   A^2 -> H(e, U1(e, b))
28.56/9.89	   A^2 -> H(e, U1(c, d))
28.56/9.89	   A^2 -> H(e, U1(d, c))
28.56/9.89	   A^2 -> H(e, U1(b, e))
28.56/9.89	   A^2 -> H(e, U1(b, k))
28.56/9.89	   A^2 -> H(e, U1(e, c))
28.56/9.89	   A^2 -> H(e, U1(c, e))
28.56/9.89	   A^2 -> H(e, U1(c, k))
28.56/9.89	   A^2 -> H(e, U1(e, e))
28.56/9.89	   A^2 -> H(e, U1(k, k))
28.56/9.89	
28.56/9.89	The TRS R consists of the following rules:
28.56/9.89	
28.56/9.89	   f(x) -> U1(x, x)
28.56/9.89	   U1(e, x) -> x
28.56/9.89	   a -> c
28.56/9.89	   a -> d
28.56/9.89	   b -> c
28.56/9.89	   b -> d
28.56/9.89	   d -> k
28.56/9.89	   c -> e
28.56/9.89	   c -> k
28.56/9.89	
28.56/9.89	Q is empty.
28.56/9.89	We have to consider all minimal (P,Q,R)-chains.
28.56/9.89	----------------------------------------
28.56/9.89	
28.56/9.89	(1583) DependencyGraphProof (EQUIVALENT)
28.56/9.89	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.89	----------------------------------------
28.56/9.89	
28.56/9.89	(1584)
28.56/9.89	Obligation:
28.56/9.89	Q DP problem:
28.56/9.89	The TRS P consists of the following rules:
28.56/9.89	
28.56/9.89	   H(x, x) -> G(x, x, f(k))
28.56/9.89	   G(d, x, x) -> A^2
28.56/9.89	   A^2 -> H(f(c), f(c))
28.56/9.89	   A^2 -> H(f(d), f(d))
28.56/9.89	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.89	   A^2 -> H(f(e), f(e))
28.56/9.89	   A^2 -> H(f(k), f(k))
28.56/9.89	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.89	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.89	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.89	   A^2 -> H(e, U1(d, d))
28.56/9.89	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.89	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.89	   A^2 -> H(f(e), b)
28.56/9.89	   A^2 -> H(f(e), U1(e, d))
28.56/9.89	   A^2 -> H(f(e), U1(d, e))
28.56/9.89	   A^2 -> H(f(e), c)
28.56/9.89	   A^2 -> H(f(e), U1(e, k))
28.56/9.89	   A^2 -> H(f(e), U1(k, e))
28.56/9.89	   A^2 -> H(f(e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.89	   A^2 -> H(f(k), b)
28.56/9.89	   A^2 -> H(f(k), U1(e, d))
28.56/9.89	   A^2 -> H(f(k), U1(d, e))
28.56/9.89	   A^2 -> H(f(k), c)
28.56/9.89	   A^2 -> H(f(k), U1(e, k))
28.56/9.89	   A^2 -> H(f(k), U1(k, e))
28.56/9.89	   A^2 -> H(f(k), e)
28.56/9.89	   A^2 -> H(f(c), d)
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.89	   A^2 -> H(U1(k, k), f(e))
28.56/9.89	   A^2 -> H(U1(k, k), f(k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.89	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.89	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.89	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.89	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.89	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.89	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.89	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.89	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.89	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.89	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.89	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, d), b)
28.56/9.89	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.89	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.89	   A^2 -> H(U1(d, d), c)
28.56/9.89	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.89	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.89	   A^2 -> H(U1(d, d), e)
28.56/9.89	   A^2 -> H(f(d), d)
28.56/9.89	   A^2 -> H(f(d), k)
28.56/9.89	   A^2 -> H(U1(c, c), c)
28.56/9.89	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.89	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.89	   A^2 -> H(f(c), k)
28.56/9.89	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.89	   A^2 -> H(f(k), U1(k, k))
28.56/9.89	   A^2 -> H(f(e), e)
28.56/9.89	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.89	   A^2 -> H(d, U1(c, b))
28.56/9.89	   A^2 -> H(d, U1(d, b))
28.56/9.89	   A^2 -> H(d, U1(b, c))
28.56/9.89	   A^2 -> H(d, U1(b, d))
28.56/9.89	   A^2 -> H(d, U1(c, c))
28.56/9.89	   A^2 -> H(d, f(e))
28.56/9.89	   A^2 -> H(d, f(k))
28.56/9.89	   A^2 -> H(d, U1(d, d))
28.56/9.89	   A^2 -> H(a, U1(e, b))
28.56/9.89	   A^2 -> H(a, U1(k, b))
28.56/9.89	   A^2 -> H(a, U1(c, d))
28.56/9.89	   A^2 -> H(a, U1(d, c))
28.56/9.89	   A^2 -> H(a, U1(b, e))
28.56/9.89	   A^2 -> H(a, U1(b, k))
28.56/9.89	   A^2 -> H(a, U1(e, c))
28.56/9.89	   A^2 -> H(a, U1(k, c))
28.56/9.89	   A^2 -> H(a, U1(c, e))
28.56/9.89	   A^2 -> H(a, U1(c, k))
28.56/9.89	   A^2 -> H(a, U1(e, e))
28.56/9.89	   A^2 -> H(a, U1(k, k))
28.56/9.89	   A^2 -> H(a, U1(k, d))
28.56/9.89	   A^2 -> H(a, U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, a), b)
28.56/9.89	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.89	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.89	   A^2 -> H(U1(e, a), c)
28.56/9.89	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.89	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.89	   A^2 -> H(U1(e, a), e)
28.56/9.89	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, a), b)
28.56/9.89	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.89	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.89	   A^2 -> H(U1(k, a), c)
28.56/9.89	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.89	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.89	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, d), b)
28.56/9.89	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, d), c)
28.56/9.89	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, d), e)
28.56/9.89	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, a), d)
28.56/9.89	   A^2 -> H(U1(c, a), k)
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.89	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.89	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.89	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.89	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.89	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.89	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, c), b)
28.56/9.89	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.89	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.89	   A^2 -> H(U1(d, c), c)
28.56/9.89	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.89	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.89	   A^2 -> H(U1(d, c), e)
28.56/9.89	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, a), d)
28.56/9.89	   A^2 -> H(U1(d, a), k)
28.56/9.89	   A^2 -> H(U1(a, e), b)
28.56/9.89	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.89	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.89	   A^2 -> H(U1(a, e), c)
28.56/9.89	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.89	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.89	   A^2 -> H(U1(a, e), e)
28.56/9.89	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(a, k), b)
28.56/9.89	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.89	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.89	   A^2 -> H(U1(a, k), c)
28.56/9.89	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.89	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.89	   A^2 -> H(U1(a, k), e)
28.56/9.89	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(a, c), d)
28.56/9.89	   A^2 -> H(U1(a, c), k)
28.56/9.89	   A^2 -> H(U1(a, d), d)
28.56/9.89	   A^2 -> H(U1(a, d), k)
28.56/9.89	   A^2 -> H(k, U1(c, b))
28.56/9.89	   A^2 -> H(k, U1(d, b))
28.56/9.89	   A^2 -> H(k, U1(b, c))
28.56/9.89	   A^2 -> H(k, U1(b, d))
28.56/9.89	   A^2 -> H(k, U1(c, c))
28.56/9.89	   A^2 -> H(k, f(e))
28.56/9.89	   A^2 -> H(k, f(k))
28.56/9.89	   A^2 -> H(k, U1(d, d))
28.56/9.89	   A^2 -> H(c, U1(e, b))
28.56/9.89	   A^2 -> H(c, U1(k, b))
28.56/9.89	   A^2 -> H(c, U1(c, d))
28.56/9.89	   A^2 -> H(c, U1(d, c))
28.56/9.89	   A^2 -> H(c, U1(b, e))
28.56/9.89	   A^2 -> H(c, U1(b, k))
28.56/9.89	   A^2 -> H(c, U1(e, c))
28.56/9.89	   A^2 -> H(c, U1(k, c))
28.56/9.89	   A^2 -> H(c, U1(c, e))
28.56/9.89	   A^2 -> H(c, U1(c, k))
28.56/9.89	   A^2 -> H(c, U1(e, e))
28.56/9.89	   A^2 -> H(c, U1(k, k))
28.56/9.89	   A^2 -> H(c, U1(k, d))
28.56/9.89	   A^2 -> H(c, U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.89	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, c), b)
28.56/9.89	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.89	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.89	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.89	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.89	   A^2 -> H(U1(e, c), e)
28.56/9.89	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.89	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.89	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.89	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.89	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.89	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.89	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.89	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.89	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.89	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.89	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.89	   A^2 -> H(U1(k, c), b)
28.56/9.89	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.89	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.89	   A^2 -> H(U1(k, c), c)
28.56/9.89	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.89	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.89	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, e), b)
28.56/9.89	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, e), c)
28.56/9.89	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, e), e)
28.56/9.89	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, k), b)
28.56/9.89	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, k), c)
28.56/9.89	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, k), e)
28.56/9.89	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, c), d)
28.56/9.89	   A^2 -> H(e, U1(e, b))
28.56/9.89	   A^2 -> H(e, U1(c, d))
28.56/9.89	   A^2 -> H(e, U1(d, c))
28.56/9.89	   A^2 -> H(e, U1(b, e))
28.56/9.89	   A^2 -> H(e, U1(b, k))
28.56/9.89	   A^2 -> H(e, U1(e, c))
28.56/9.89	   A^2 -> H(e, U1(c, e))
28.56/9.89	   A^2 -> H(e, U1(c, k))
28.56/9.89	   A^2 -> H(e, U1(e, e))
28.56/9.89	
28.56/9.89	The TRS R consists of the following rules:
28.56/9.89	
28.56/9.89	   f(x) -> U1(x, x)
28.56/9.89	   U1(e, x) -> x
28.56/9.89	   a -> c
28.56/9.89	   a -> d
28.56/9.89	   b -> c
28.56/9.89	   b -> d
28.56/9.89	   d -> k
28.56/9.89	   c -> e
28.56/9.89	   c -> k
28.56/9.89	
28.56/9.89	Q is empty.
28.56/9.89	We have to consider all minimal (P,Q,R)-chains.
28.56/9.89	----------------------------------------
28.56/9.89	
28.56/9.89	(1585) TransformationProof (EQUIVALENT)
28.56/9.89	By narrowing [LPAR04] the rule A^2 -> H(e, U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.89	
28.56/9.89	   (A^2 -> H(e, U1(k, d)),A^2 -> H(e, U1(k, d)))
28.56/9.89	   (A^2 -> H(e, U1(d, k)),A^2 -> H(e, U1(d, k)))
28.56/9.89	
28.56/9.89	
28.56/9.89	----------------------------------------
28.56/9.89	
28.56/9.89	(1586)
28.56/9.89	Obligation:
28.56/9.89	Q DP problem:
28.56/9.89	The TRS P consists of the following rules:
28.56/9.89	
28.56/9.89	   H(x, x) -> G(x, x, f(k))
28.56/9.89	   G(d, x, x) -> A^2
28.56/9.89	   A^2 -> H(f(c), f(c))
28.56/9.89	   A^2 -> H(f(d), f(d))
28.56/9.89	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.89	   A^2 -> H(f(e), f(e))
28.56/9.89	   A^2 -> H(f(k), f(k))
28.56/9.89	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.89	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.89	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.89	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.89	   A^2 -> H(f(e), b)
28.56/9.89	   A^2 -> H(f(e), U1(e, d))
28.56/9.89	   A^2 -> H(f(e), U1(d, e))
28.56/9.89	   A^2 -> H(f(e), c)
28.56/9.89	   A^2 -> H(f(e), U1(e, k))
28.56/9.89	   A^2 -> H(f(e), U1(k, e))
28.56/9.89	   A^2 -> H(f(e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.89	   A^2 -> H(f(k), b)
28.56/9.89	   A^2 -> H(f(k), U1(e, d))
28.56/9.89	   A^2 -> H(f(k), U1(d, e))
28.56/9.89	   A^2 -> H(f(k), c)
28.56/9.89	   A^2 -> H(f(k), U1(e, k))
28.56/9.89	   A^2 -> H(f(k), U1(k, e))
28.56/9.89	   A^2 -> H(f(k), e)
28.56/9.89	   A^2 -> H(f(c), d)
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.89	   A^2 -> H(U1(k, k), f(e))
28.56/9.89	   A^2 -> H(U1(k, k), f(k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.89	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.89	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.89	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.89	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.89	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.89	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.89	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.89	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.89	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.89	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.89	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, d), b)
28.56/9.89	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.89	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.89	   A^2 -> H(U1(d, d), c)
28.56/9.89	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.89	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.89	   A^2 -> H(U1(d, d), e)
28.56/9.89	   A^2 -> H(f(d), d)
28.56/9.89	   A^2 -> H(f(d), k)
28.56/9.89	   A^2 -> H(U1(c, c), c)
28.56/9.89	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.89	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.89	   A^2 -> H(f(c), k)
28.56/9.89	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.89	   A^2 -> H(f(k), U1(k, k))
28.56/9.89	   A^2 -> H(f(e), e)
28.56/9.89	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.89	   A^2 -> H(d, U1(c, b))
28.56/9.89	   A^2 -> H(d, U1(d, b))
28.56/9.89	   A^2 -> H(d, U1(b, c))
28.56/9.89	   A^2 -> H(d, U1(b, d))
28.56/9.89	   A^2 -> H(d, U1(c, c))
28.56/9.89	   A^2 -> H(d, f(e))
28.56/9.89	   A^2 -> H(d, f(k))
28.56/9.89	   A^2 -> H(d, U1(d, d))
28.56/9.89	   A^2 -> H(a, U1(e, b))
28.56/9.89	   A^2 -> H(a, U1(k, b))
28.56/9.89	   A^2 -> H(a, U1(c, d))
28.56/9.89	   A^2 -> H(a, U1(d, c))
28.56/9.89	   A^2 -> H(a, U1(b, e))
28.56/9.89	   A^2 -> H(a, U1(b, k))
28.56/9.89	   A^2 -> H(a, U1(e, c))
28.56/9.89	   A^2 -> H(a, U1(k, c))
28.56/9.89	   A^2 -> H(a, U1(c, e))
28.56/9.89	   A^2 -> H(a, U1(c, k))
28.56/9.89	   A^2 -> H(a, U1(e, e))
28.56/9.89	   A^2 -> H(a, U1(k, k))
28.56/9.89	   A^2 -> H(a, U1(k, d))
28.56/9.89	   A^2 -> H(a, U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, a), b)
28.56/9.89	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.89	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.89	   A^2 -> H(U1(e, a), c)
28.56/9.89	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.89	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.89	   A^2 -> H(U1(e, a), e)
28.56/9.89	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, a), b)
28.56/9.89	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.89	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.89	   A^2 -> H(U1(k, a), c)
28.56/9.89	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.89	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.89	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, d), b)
28.56/9.89	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, d), c)
28.56/9.89	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, d), e)
28.56/9.89	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, a), d)
28.56/9.89	   A^2 -> H(U1(c, a), k)
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.89	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.89	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.89	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.89	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.89	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.89	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, c), b)
28.56/9.89	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.89	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.89	   A^2 -> H(U1(d, c), c)
28.56/9.89	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.89	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.89	   A^2 -> H(U1(d, c), e)
28.56/9.89	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, a), d)
28.56/9.89	   A^2 -> H(U1(d, a), k)
28.56/9.89	   A^2 -> H(U1(a, e), b)
28.56/9.89	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.89	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.89	   A^2 -> H(U1(a, e), c)
28.56/9.89	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.89	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.89	   A^2 -> H(U1(a, e), e)
28.56/9.89	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(a, k), b)
28.56/9.89	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.89	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.89	   A^2 -> H(U1(a, k), c)
28.56/9.89	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.89	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.89	   A^2 -> H(U1(a, k), e)
28.56/9.89	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(a, c), d)
28.56/9.89	   A^2 -> H(U1(a, c), k)
28.56/9.89	   A^2 -> H(U1(a, d), d)
28.56/9.89	   A^2 -> H(U1(a, d), k)
28.56/9.89	   A^2 -> H(k, U1(c, b))
28.56/9.89	   A^2 -> H(k, U1(d, b))
28.56/9.89	   A^2 -> H(k, U1(b, c))
28.56/9.89	   A^2 -> H(k, U1(b, d))
28.56/9.89	   A^2 -> H(k, U1(c, c))
28.56/9.89	   A^2 -> H(k, f(e))
28.56/9.89	   A^2 -> H(k, f(k))
28.56/9.89	   A^2 -> H(k, U1(d, d))
28.56/9.89	   A^2 -> H(c, U1(e, b))
28.56/9.89	   A^2 -> H(c, U1(k, b))
28.56/9.89	   A^2 -> H(c, U1(c, d))
28.56/9.89	   A^2 -> H(c, U1(d, c))
28.56/9.89	   A^2 -> H(c, U1(b, e))
28.56/9.89	   A^2 -> H(c, U1(b, k))
28.56/9.89	   A^2 -> H(c, U1(e, c))
28.56/9.89	   A^2 -> H(c, U1(k, c))
28.56/9.89	   A^2 -> H(c, U1(c, e))
28.56/9.89	   A^2 -> H(c, U1(c, k))
28.56/9.89	   A^2 -> H(c, U1(e, e))
28.56/9.89	   A^2 -> H(c, U1(k, k))
28.56/9.89	   A^2 -> H(c, U1(k, d))
28.56/9.89	   A^2 -> H(c, U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.89	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, c), b)
28.56/9.89	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.89	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.89	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.89	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.89	   A^2 -> H(U1(e, c), e)
28.56/9.89	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.89	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.89	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.89	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.89	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.89	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.89	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.89	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.89	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.89	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.89	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.89	   A^2 -> H(U1(k, c), b)
28.56/9.89	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.89	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.89	   A^2 -> H(U1(k, c), c)
28.56/9.89	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.89	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.89	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, e), b)
28.56/9.89	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, e), c)
28.56/9.89	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, e), e)
28.56/9.89	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, k), b)
28.56/9.89	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, k), c)
28.56/9.89	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, k), e)
28.56/9.89	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, c), d)
28.56/9.89	   A^2 -> H(e, U1(e, b))
28.56/9.89	   A^2 -> H(e, U1(c, d))
28.56/9.89	   A^2 -> H(e, U1(d, c))
28.56/9.89	   A^2 -> H(e, U1(b, e))
28.56/9.89	   A^2 -> H(e, U1(b, k))
28.56/9.89	   A^2 -> H(e, U1(e, c))
28.56/9.89	   A^2 -> H(e, U1(c, e))
28.56/9.89	   A^2 -> H(e, U1(c, k))
28.56/9.89	   A^2 -> H(e, U1(e, e))
28.56/9.89	   A^2 -> H(e, U1(k, d))
28.56/9.89	   A^2 -> H(e, U1(d, k))
28.56/9.89	
28.56/9.89	The TRS R consists of the following rules:
28.56/9.89	
28.56/9.89	   f(x) -> U1(x, x)
28.56/9.89	   U1(e, x) -> x
28.56/9.89	   a -> c
28.56/9.89	   a -> d
28.56/9.89	   b -> c
28.56/9.89	   b -> d
28.56/9.89	   d -> k
28.56/9.89	   c -> e
28.56/9.89	   c -> k
28.56/9.89	
28.56/9.89	Q is empty.
28.56/9.89	We have to consider all minimal (P,Q,R)-chains.
28.56/9.89	----------------------------------------
28.56/9.89	
28.56/9.89	(1587) DependencyGraphProof (EQUIVALENT)
28.56/9.89	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.89	----------------------------------------
28.56/9.89	
28.56/9.89	(1588)
28.56/9.89	Obligation:
28.56/9.89	Q DP problem:
28.56/9.89	The TRS P consists of the following rules:
28.56/9.89	
28.56/9.89	   G(d, x, x) -> A^2
28.56/9.89	   A^2 -> H(f(c), f(c))
28.56/9.89	   H(x, x) -> G(x, x, f(k))
28.56/9.89	   A^2 -> H(f(d), f(d))
28.56/9.89	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.89	   A^2 -> H(f(e), f(e))
28.56/9.89	   A^2 -> H(f(k), f(k))
28.56/9.89	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.89	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.89	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(e, b))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.89	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.89	   A^2 -> H(f(e), b)
28.56/9.89	   A^2 -> H(f(e), U1(e, d))
28.56/9.89	   A^2 -> H(f(e), U1(d, e))
28.56/9.89	   A^2 -> H(f(e), c)
28.56/9.89	   A^2 -> H(f(e), U1(e, k))
28.56/9.89	   A^2 -> H(f(e), U1(k, e))
28.56/9.89	   A^2 -> H(f(e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.89	   A^2 -> H(f(k), b)
28.56/9.89	   A^2 -> H(f(k), U1(e, d))
28.56/9.89	   A^2 -> H(f(k), U1(d, e))
28.56/9.89	   A^2 -> H(f(k), c)
28.56/9.89	   A^2 -> H(f(k), U1(e, k))
28.56/9.89	   A^2 -> H(f(k), U1(k, e))
28.56/9.89	   A^2 -> H(f(k), e)
28.56/9.89	   A^2 -> H(f(c), d)
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.89	   A^2 -> H(U1(k, k), f(e))
28.56/9.89	   A^2 -> H(U1(k, k), f(k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.89	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.89	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.89	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.89	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.89	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.89	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.89	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.89	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.89	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.89	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.89	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, d), b)
28.56/9.89	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.89	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.89	   A^2 -> H(U1(d, d), c)
28.56/9.89	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.89	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.89	   A^2 -> H(U1(d, d), e)
28.56/9.89	   A^2 -> H(f(d), d)
28.56/9.89	   A^2 -> H(f(d), k)
28.56/9.89	   A^2 -> H(U1(c, c), c)
28.56/9.89	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.89	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.89	   A^2 -> H(f(c), k)
28.56/9.89	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.89	   A^2 -> H(f(k), U1(k, k))
28.56/9.89	   A^2 -> H(f(e), e)
28.56/9.89	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.89	   A^2 -> H(d, U1(c, b))
28.56/9.89	   A^2 -> H(d, U1(d, b))
28.56/9.89	   A^2 -> H(d, U1(b, c))
28.56/9.89	   A^2 -> H(d, U1(b, d))
28.56/9.89	   A^2 -> H(d, U1(c, c))
28.56/9.89	   A^2 -> H(d, f(e))
28.56/9.89	   A^2 -> H(d, f(k))
28.56/9.89	   A^2 -> H(d, U1(d, d))
28.56/9.89	   A^2 -> H(a, U1(e, b))
28.56/9.89	   A^2 -> H(a, U1(k, b))
28.56/9.89	   A^2 -> H(a, U1(c, d))
28.56/9.89	   A^2 -> H(a, U1(d, c))
28.56/9.89	   A^2 -> H(a, U1(b, e))
28.56/9.89	   A^2 -> H(a, U1(b, k))
28.56/9.89	   A^2 -> H(a, U1(e, c))
28.56/9.89	   A^2 -> H(a, U1(k, c))
28.56/9.89	   A^2 -> H(a, U1(c, e))
28.56/9.89	   A^2 -> H(a, U1(c, k))
28.56/9.89	   A^2 -> H(a, U1(e, e))
28.56/9.89	   A^2 -> H(a, U1(k, k))
28.56/9.89	   A^2 -> H(a, U1(k, d))
28.56/9.89	   A^2 -> H(a, U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, a), b)
28.56/9.89	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.89	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.89	   A^2 -> H(U1(e, a), c)
28.56/9.89	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.89	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.89	   A^2 -> H(U1(e, a), e)
28.56/9.89	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, a), b)
28.56/9.89	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.89	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.89	   A^2 -> H(U1(k, a), c)
28.56/9.89	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.89	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.89	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, d), b)
28.56/9.89	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, d), c)
28.56/9.89	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, d), e)
28.56/9.89	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, a), d)
28.56/9.89	   A^2 -> H(U1(c, a), k)
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.89	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.89	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.89	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.89	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.89	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.89	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, c), b)
28.56/9.89	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.89	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.89	   A^2 -> H(U1(d, c), c)
28.56/9.89	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.89	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.89	   A^2 -> H(U1(d, c), e)
28.56/9.89	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, a), d)
28.56/9.89	   A^2 -> H(U1(d, a), k)
28.56/9.89	   A^2 -> H(U1(a, e), b)
28.56/9.89	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.89	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.89	   A^2 -> H(U1(a, e), c)
28.56/9.89	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.89	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.89	   A^2 -> H(U1(a, e), e)
28.56/9.89	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(a, k), b)
28.56/9.89	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.89	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.89	   A^2 -> H(U1(a, k), c)
28.56/9.89	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.89	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.89	   A^2 -> H(U1(a, k), e)
28.56/9.89	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(a, c), d)
28.56/9.89	   A^2 -> H(U1(a, c), k)
28.56/9.89	   A^2 -> H(U1(a, d), d)
28.56/9.89	   A^2 -> H(U1(a, d), k)
28.56/9.89	   A^2 -> H(k, U1(c, b))
28.56/9.89	   A^2 -> H(k, U1(d, b))
28.56/9.89	   A^2 -> H(k, U1(b, c))
28.56/9.89	   A^2 -> H(k, U1(b, d))
28.56/9.89	   A^2 -> H(k, U1(c, c))
28.56/9.89	   A^2 -> H(k, f(e))
28.56/9.89	   A^2 -> H(k, f(k))
28.56/9.89	   A^2 -> H(k, U1(d, d))
28.56/9.89	   A^2 -> H(c, U1(e, b))
28.56/9.89	   A^2 -> H(c, U1(k, b))
28.56/9.89	   A^2 -> H(c, U1(c, d))
28.56/9.89	   A^2 -> H(c, U1(d, c))
28.56/9.89	   A^2 -> H(c, U1(b, e))
28.56/9.89	   A^2 -> H(c, U1(b, k))
28.56/9.89	   A^2 -> H(c, U1(e, c))
28.56/9.89	   A^2 -> H(c, U1(k, c))
28.56/9.89	   A^2 -> H(c, U1(c, e))
28.56/9.89	   A^2 -> H(c, U1(c, k))
28.56/9.89	   A^2 -> H(c, U1(e, e))
28.56/9.89	   A^2 -> H(c, U1(k, k))
28.56/9.89	   A^2 -> H(c, U1(k, d))
28.56/9.89	   A^2 -> H(c, U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.89	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, c), b)
28.56/9.89	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.89	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.89	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.89	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.89	   A^2 -> H(U1(e, c), e)
28.56/9.89	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.89	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.89	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.89	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.89	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.89	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.89	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.89	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.89	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.89	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.89	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.89	   A^2 -> H(U1(k, c), b)
28.56/9.89	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.89	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.89	   A^2 -> H(U1(k, c), c)
28.56/9.89	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.89	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.89	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, e), b)
28.56/9.89	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, e), c)
28.56/9.89	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, e), e)
28.56/9.89	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, k), b)
28.56/9.89	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, k), c)
28.56/9.89	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, k), e)
28.56/9.89	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, c), d)
28.56/9.89	   A^2 -> H(e, U1(e, b))
28.56/9.89	   A^2 -> H(e, U1(c, d))
28.56/9.89	   A^2 -> H(e, U1(d, c))
28.56/9.89	   A^2 -> H(e, U1(b, e))
28.56/9.89	   A^2 -> H(e, U1(b, k))
28.56/9.89	   A^2 -> H(e, U1(e, c))
28.56/9.89	   A^2 -> H(e, U1(c, e))
28.56/9.89	   A^2 -> H(e, U1(c, k))
28.56/9.89	   A^2 -> H(e, U1(e, e))
28.56/9.89	   A^2 -> H(e, U1(d, k))
28.56/9.89	
28.56/9.89	The TRS R consists of the following rules:
28.56/9.89	
28.56/9.89	   f(x) -> U1(x, x)
28.56/9.89	   U1(e, x) -> x
28.56/9.89	   a -> c
28.56/9.89	   a -> d
28.56/9.89	   b -> c
28.56/9.89	   b -> d
28.56/9.89	   d -> k
28.56/9.89	   c -> e
28.56/9.89	   c -> k
28.56/9.89	
28.56/9.89	Q is empty.
28.56/9.89	We have to consider all minimal (P,Q,R)-chains.
28.56/9.89	----------------------------------------
28.56/9.89	
28.56/9.89	(1589) TransformationProof (EQUIVALENT)
28.56/9.89	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.89	
28.56/9.89	   (A^2 -> H(e, U1(e, b)),A^2 -> H(e, U1(e, b)))
28.56/9.89	   (A^2 -> H(U1(e, e), b),A^2 -> H(U1(e, e), b))
28.56/9.89	   (A^2 -> H(U1(e, e), U1(e, c)),A^2 -> H(U1(e, e), U1(e, c)))
28.56/9.89	   (A^2 -> H(U1(e, e), U1(e, d)),A^2 -> H(U1(e, e), U1(e, d)))
28.56/9.89	
28.56/9.89	
28.56/9.89	----------------------------------------
28.56/9.89	
28.56/9.89	(1590)
28.56/9.89	Obligation:
28.56/9.89	Q DP problem:
28.56/9.89	The TRS P consists of the following rules:
28.56/9.89	
28.56/9.89	   G(d, x, x) -> A^2
28.56/9.89	   A^2 -> H(f(c), f(c))
28.56/9.89	   H(x, x) -> G(x, x, f(k))
28.56/9.89	   A^2 -> H(f(d), f(d))
28.56/9.89	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.89	   A^2 -> H(f(e), f(e))
28.56/9.89	   A^2 -> H(f(k), f(k))
28.56/9.89	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.89	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.89	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, b))
28.56/9.89	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.89	   A^2 -> H(f(e), b)
28.56/9.89	   A^2 -> H(f(e), U1(e, d))
28.56/9.89	   A^2 -> H(f(e), U1(d, e))
28.56/9.89	   A^2 -> H(f(e), c)
28.56/9.89	   A^2 -> H(f(e), U1(e, k))
28.56/9.89	   A^2 -> H(f(e), U1(k, e))
28.56/9.89	   A^2 -> H(f(e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.89	   A^2 -> H(f(k), b)
28.56/9.89	   A^2 -> H(f(k), U1(e, d))
28.56/9.89	   A^2 -> H(f(k), U1(d, e))
28.56/9.89	   A^2 -> H(f(k), c)
28.56/9.89	   A^2 -> H(f(k), U1(e, k))
28.56/9.89	   A^2 -> H(f(k), U1(k, e))
28.56/9.89	   A^2 -> H(f(k), e)
28.56/9.89	   A^2 -> H(f(c), d)
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.89	   A^2 -> H(U1(k, k), f(e))
28.56/9.89	   A^2 -> H(U1(k, k), f(k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.89	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.89	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.89	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.89	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.89	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.89	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.89	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.89	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.89	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.89	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.89	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, d), b)
28.56/9.89	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.89	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.89	   A^2 -> H(U1(d, d), c)
28.56/9.89	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.89	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.89	   A^2 -> H(U1(d, d), e)
28.56/9.89	   A^2 -> H(f(d), d)
28.56/9.89	   A^2 -> H(f(d), k)
28.56/9.89	   A^2 -> H(U1(c, c), c)
28.56/9.89	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.89	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.89	   A^2 -> H(f(c), k)
28.56/9.89	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.89	   A^2 -> H(f(k), U1(k, k))
28.56/9.89	   A^2 -> H(f(e), e)
28.56/9.89	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.89	   A^2 -> H(d, U1(c, b))
28.56/9.89	   A^2 -> H(d, U1(d, b))
28.56/9.89	   A^2 -> H(d, U1(b, c))
28.56/9.89	   A^2 -> H(d, U1(b, d))
28.56/9.89	   A^2 -> H(d, U1(c, c))
28.56/9.89	   A^2 -> H(d, f(e))
28.56/9.89	   A^2 -> H(d, f(k))
28.56/9.89	   A^2 -> H(d, U1(d, d))
28.56/9.89	   A^2 -> H(a, U1(e, b))
28.56/9.89	   A^2 -> H(a, U1(k, b))
28.56/9.89	   A^2 -> H(a, U1(c, d))
28.56/9.89	   A^2 -> H(a, U1(d, c))
28.56/9.89	   A^2 -> H(a, U1(b, e))
28.56/9.89	   A^2 -> H(a, U1(b, k))
28.56/9.89	   A^2 -> H(a, U1(e, c))
28.56/9.89	   A^2 -> H(a, U1(k, c))
28.56/9.89	   A^2 -> H(a, U1(c, e))
28.56/9.89	   A^2 -> H(a, U1(c, k))
28.56/9.89	   A^2 -> H(a, U1(e, e))
28.56/9.89	   A^2 -> H(a, U1(k, k))
28.56/9.89	   A^2 -> H(a, U1(k, d))
28.56/9.89	   A^2 -> H(a, U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, a), b)
28.56/9.89	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.89	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.89	   A^2 -> H(U1(e, a), c)
28.56/9.89	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.89	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.89	   A^2 -> H(U1(e, a), e)
28.56/9.89	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, a), b)
28.56/9.89	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.89	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.89	   A^2 -> H(U1(k, a), c)
28.56/9.89	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.89	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.89	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, d), b)
28.56/9.89	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, d), c)
28.56/9.89	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, d), e)
28.56/9.89	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, a), d)
28.56/9.89	   A^2 -> H(U1(c, a), k)
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.89	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.89	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.89	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.89	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.89	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.89	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, c), b)
28.56/9.89	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.89	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.89	   A^2 -> H(U1(d, c), c)
28.56/9.89	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.89	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.89	   A^2 -> H(U1(d, c), e)
28.56/9.89	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, a), d)
28.56/9.89	   A^2 -> H(U1(d, a), k)
28.56/9.89	   A^2 -> H(U1(a, e), b)
28.56/9.89	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.89	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.89	   A^2 -> H(U1(a, e), c)
28.56/9.89	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.89	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.89	   A^2 -> H(U1(a, e), e)
28.56/9.89	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(a, k), b)
28.56/9.89	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.89	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.89	   A^2 -> H(U1(a, k), c)
28.56/9.89	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.89	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.89	   A^2 -> H(U1(a, k), e)
28.56/9.89	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(a, c), d)
28.56/9.89	   A^2 -> H(U1(a, c), k)
28.56/9.89	   A^2 -> H(U1(a, d), d)
28.56/9.89	   A^2 -> H(U1(a, d), k)
28.56/9.89	   A^2 -> H(k, U1(c, b))
28.56/9.89	   A^2 -> H(k, U1(d, b))
28.56/9.89	   A^2 -> H(k, U1(b, c))
28.56/9.89	   A^2 -> H(k, U1(b, d))
28.56/9.89	   A^2 -> H(k, U1(c, c))
28.56/9.89	   A^2 -> H(k, f(e))
28.56/9.89	   A^2 -> H(k, f(k))
28.56/9.89	   A^2 -> H(k, U1(d, d))
28.56/9.89	   A^2 -> H(c, U1(e, b))
28.56/9.89	   A^2 -> H(c, U1(k, b))
28.56/9.89	   A^2 -> H(c, U1(c, d))
28.56/9.89	   A^2 -> H(c, U1(d, c))
28.56/9.89	   A^2 -> H(c, U1(b, e))
28.56/9.89	   A^2 -> H(c, U1(b, k))
28.56/9.89	   A^2 -> H(c, U1(e, c))
28.56/9.89	   A^2 -> H(c, U1(k, c))
28.56/9.89	   A^2 -> H(c, U1(c, e))
28.56/9.89	   A^2 -> H(c, U1(c, k))
28.56/9.89	   A^2 -> H(c, U1(e, e))
28.56/9.89	   A^2 -> H(c, U1(k, k))
28.56/9.89	   A^2 -> H(c, U1(k, d))
28.56/9.89	   A^2 -> H(c, U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.89	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, c), b)
28.56/9.89	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.89	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.89	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.89	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.89	   A^2 -> H(U1(e, c), e)
28.56/9.89	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.89	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.89	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.89	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.89	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.89	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.89	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.89	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.89	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.89	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.89	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.89	   A^2 -> H(U1(k, c), b)
28.56/9.89	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.89	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.89	   A^2 -> H(U1(k, c), c)
28.56/9.89	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.89	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.89	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, e), b)
28.56/9.89	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, e), c)
28.56/9.89	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, e), e)
28.56/9.89	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, k), b)
28.56/9.89	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, k), c)
28.56/9.89	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, k), e)
28.56/9.89	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, c), d)
28.56/9.89	   A^2 -> H(e, U1(e, b))
28.56/9.89	   A^2 -> H(e, U1(c, d))
28.56/9.89	   A^2 -> H(e, U1(d, c))
28.56/9.89	   A^2 -> H(e, U1(b, e))
28.56/9.89	   A^2 -> H(e, U1(b, k))
28.56/9.89	   A^2 -> H(e, U1(e, c))
28.56/9.89	   A^2 -> H(e, U1(c, e))
28.56/9.89	   A^2 -> H(e, U1(c, k))
28.56/9.89	   A^2 -> H(e, U1(e, e))
28.56/9.89	   A^2 -> H(e, U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, e), b)
28.56/9.89	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.89	
28.56/9.89	The TRS R consists of the following rules:
28.56/9.89	
28.56/9.89	   f(x) -> U1(x, x)
28.56/9.89	   U1(e, x) -> x
28.56/9.89	   a -> c
28.56/9.89	   a -> d
28.56/9.89	   b -> c
28.56/9.89	   b -> d
28.56/9.89	   d -> k
28.56/9.89	   c -> e
28.56/9.89	   c -> k
28.56/9.89	
28.56/9.89	Q is empty.
28.56/9.89	We have to consider all minimal (P,Q,R)-chains.
28.56/9.89	----------------------------------------
28.56/9.89	
28.56/9.89	(1591) TransformationProof (EQUIVALENT)
28.56/9.89	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.89	
28.56/9.89	   (A^2 -> H(e, U1(k, b)),A^2 -> H(e, U1(k, b)))
28.56/9.89	   (A^2 -> H(U1(e, e), U1(k, c)),A^2 -> H(U1(e, e), U1(k, c)))
28.56/9.89	   (A^2 -> H(U1(e, e), U1(k, d)),A^2 -> H(U1(e, e), U1(k, d)))
28.56/9.89	
28.56/9.89	
28.56/9.89	----------------------------------------
28.56/9.89	
28.56/9.89	(1592)
28.56/9.89	Obligation:
28.56/9.89	Q DP problem:
28.56/9.89	The TRS P consists of the following rules:
28.56/9.89	
28.56/9.89	   G(d, x, x) -> A^2
28.56/9.89	   A^2 -> H(f(c), f(c))
28.56/9.89	   H(x, x) -> G(x, x, f(k))
28.56/9.89	   A^2 -> H(f(d), f(d))
28.56/9.89	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.89	   A^2 -> H(f(e), f(e))
28.56/9.89	   A^2 -> H(f(k), f(k))
28.56/9.89	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.89	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.89	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.89	   A^2 -> H(f(e), b)
28.56/9.89	   A^2 -> H(f(e), U1(e, d))
28.56/9.89	   A^2 -> H(f(e), U1(d, e))
28.56/9.89	   A^2 -> H(f(e), c)
28.56/9.89	   A^2 -> H(f(e), U1(e, k))
28.56/9.89	   A^2 -> H(f(e), U1(k, e))
28.56/9.89	   A^2 -> H(f(e), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.89	   A^2 -> H(f(k), b)
28.56/9.89	   A^2 -> H(f(k), U1(e, d))
28.56/9.89	   A^2 -> H(f(k), U1(d, e))
28.56/9.89	   A^2 -> H(f(k), c)
28.56/9.89	   A^2 -> H(f(k), U1(e, k))
28.56/9.89	   A^2 -> H(f(k), U1(k, e))
28.56/9.89	   A^2 -> H(f(k), e)
28.56/9.89	   A^2 -> H(f(c), d)
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.89	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.89	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.89	   A^2 -> H(U1(k, k), f(e))
28.56/9.89	   A^2 -> H(U1(k, k), f(k))
28.56/9.89	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.89	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.89	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.89	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.89	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.89	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.89	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.89	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.89	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.89	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.89	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.89	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.89	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.89	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.89	   A^2 -> H(U1(d, d), b)
28.56/9.89	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.89	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.89	   A^2 -> H(U1(d, d), c)
28.56/9.89	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.89	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.89	   A^2 -> H(U1(d, d), e)
28.56/9.89	   A^2 -> H(f(d), d)
28.56/9.89	   A^2 -> H(f(d), k)
28.56/9.89	   A^2 -> H(U1(c, c), c)
28.56/9.89	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.89	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.89	   A^2 -> H(f(c), k)
28.56/9.89	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.89	   A^2 -> H(f(k), U1(k, k))
28.56/9.89	   A^2 -> H(f(e), e)
28.56/9.89	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.89	   A^2 -> H(d, U1(c, b))
28.56/9.89	   A^2 -> H(d, U1(d, b))
28.56/9.89	   A^2 -> H(d, U1(b, c))
28.56/9.89	   A^2 -> H(d, U1(b, d))
28.56/9.89	   A^2 -> H(d, U1(c, c))
28.56/9.89	   A^2 -> H(d, f(e))
28.56/9.89	   A^2 -> H(d, f(k))
28.56/9.89	   A^2 -> H(d, U1(d, d))
28.56/9.89	   A^2 -> H(a, U1(e, b))
28.56/9.89	   A^2 -> H(a, U1(k, b))
28.56/9.89	   A^2 -> H(a, U1(c, d))
28.56/9.89	   A^2 -> H(a, U1(d, c))
28.56/9.89	   A^2 -> H(a, U1(b, e))
28.56/9.89	   A^2 -> H(a, U1(b, k))
28.56/9.89	   A^2 -> H(a, U1(e, c))
28.56/9.89	   A^2 -> H(a, U1(k, c))
28.56/9.89	   A^2 -> H(a, U1(c, e))
28.56/9.89	   A^2 -> H(a, U1(c, k))
28.56/9.89	   A^2 -> H(a, U1(e, e))
28.56/9.89	   A^2 -> H(a, U1(k, k))
28.56/9.89	   A^2 -> H(a, U1(k, d))
28.56/9.89	   A^2 -> H(a, U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.89	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.89	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.89	   A^2 -> H(U1(e, a), b)
28.56/9.89	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.89	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.89	   A^2 -> H(U1(e, a), c)
28.56/9.89	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.89	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.89	   A^2 -> H(U1(e, a), e)
28.56/9.89	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.89	   A^2 -> H(U1(k, a), b)
28.56/9.89	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.89	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.89	   A^2 -> H(U1(k, a), c)
28.56/9.89	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.89	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.89	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, d), b)
28.56/9.89	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.89	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.89	   A^2 -> H(U1(c, d), c)
28.56/9.89	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.89	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.89	   A^2 -> H(U1(c, d), e)
28.56/9.89	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.89	   A^2 -> H(U1(c, a), d)
28.56/9.89	   A^2 -> H(U1(c, a), k)
28.56/9.89	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.89	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, c), b)
28.56/9.90	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(d, c), c)
28.56/9.90	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(d, c), e)
28.56/9.90	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, a), d)
28.56/9.90	   A^2 -> H(U1(d, a), k)
28.56/9.90	   A^2 -> H(U1(a, e), b)
28.56/9.90	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.90	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.90	   A^2 -> H(U1(a, e), c)
28.56/9.90	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.90	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.90	   A^2 -> H(U1(a, e), e)
28.56/9.90	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(a, k), b)
28.56/9.90	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.90	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.90	   A^2 -> H(U1(a, k), c)
28.56/9.90	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.90	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.90	   A^2 -> H(U1(a, k), e)
28.56/9.90	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(a, c), d)
28.56/9.90	   A^2 -> H(U1(a, c), k)
28.56/9.90	   A^2 -> H(U1(a, d), d)
28.56/9.90	   A^2 -> H(U1(a, d), k)
28.56/9.90	   A^2 -> H(k, U1(c, b))
28.56/9.90	   A^2 -> H(k, U1(d, b))
28.56/9.90	   A^2 -> H(k, U1(b, c))
28.56/9.90	   A^2 -> H(k, U1(b, d))
28.56/9.90	   A^2 -> H(k, U1(c, c))
28.56/9.90	   A^2 -> H(k, f(e))
28.56/9.90	   A^2 -> H(k, f(k))
28.56/9.90	   A^2 -> H(k, U1(d, d))
28.56/9.90	   A^2 -> H(c, U1(e, b))
28.56/9.90	   A^2 -> H(c, U1(k, b))
28.56/9.90	   A^2 -> H(c, U1(c, d))
28.56/9.90	   A^2 -> H(c, U1(d, c))
28.56/9.90	   A^2 -> H(c, U1(b, e))
28.56/9.90	   A^2 -> H(c, U1(b, k))
28.56/9.90	   A^2 -> H(c, U1(e, c))
28.56/9.90	   A^2 -> H(c, U1(k, c))
28.56/9.90	   A^2 -> H(c, U1(c, e))
28.56/9.90	   A^2 -> H(c, U1(c, k))
28.56/9.90	   A^2 -> H(c, U1(e, e))
28.56/9.90	   A^2 -> H(c, U1(k, k))
28.56/9.90	   A^2 -> H(c, U1(k, d))
28.56/9.90	   A^2 -> H(c, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, c), b)
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(e, c), e)
28.56/9.90	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.90	   A^2 -> H(U1(k, c), b)
28.56/9.90	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(k, c), c)
28.56/9.90	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, e), b)
28.56/9.90	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, e), c)
28.56/9.90	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, e), e)
28.56/9.90	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, k), b)
28.56/9.90	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, k), c)
28.56/9.90	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, k), e)
28.56/9.90	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, c), d)
28.56/9.90	   A^2 -> H(e, U1(e, b))
28.56/9.90	   A^2 -> H(e, U1(c, d))
28.56/9.90	   A^2 -> H(e, U1(d, c))
28.56/9.90	   A^2 -> H(e, U1(b, e))
28.56/9.90	   A^2 -> H(e, U1(b, k))
28.56/9.90	   A^2 -> H(e, U1(e, c))
28.56/9.90	   A^2 -> H(e, U1(c, e))
28.56/9.90	   A^2 -> H(e, U1(c, k))
28.56/9.90	   A^2 -> H(e, U1(e, e))
28.56/9.90	   A^2 -> H(e, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, e), b)
28.56/9.90	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.90	   A^2 -> H(e, U1(k, b))
28.56/9.90	
28.56/9.90	The TRS R consists of the following rules:
28.56/9.90	
28.56/9.90	   f(x) -> U1(x, x)
28.56/9.90	   U1(e, x) -> x
28.56/9.90	   a -> c
28.56/9.90	   a -> d
28.56/9.90	   b -> c
28.56/9.90	   b -> d
28.56/9.90	   d -> k
28.56/9.90	   c -> e
28.56/9.90	   c -> k
28.56/9.90	
28.56/9.90	Q is empty.
28.56/9.90	We have to consider all minimal (P,Q,R)-chains.
28.56/9.90	----------------------------------------
28.56/9.90	
28.56/9.90	(1593) DependencyGraphProof (EQUIVALENT)
28.56/9.90	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.90	----------------------------------------
28.56/9.90	
28.56/9.90	(1594)
28.56/9.90	Obligation:
28.56/9.90	Q DP problem:
28.56/9.90	The TRS P consists of the following rules:
28.56/9.90	
28.56/9.90	   A^2 -> H(f(c), f(c))
28.56/9.90	   H(x, x) -> G(x, x, f(k))
28.56/9.90	   G(d, x, x) -> A^2
28.56/9.90	   A^2 -> H(f(d), f(d))
28.56/9.90	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.90	   A^2 -> H(f(e), f(e))
28.56/9.90	   A^2 -> H(f(k), f(k))
28.56/9.90	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.90	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.90	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(c, d))
28.56/9.90	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.90	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.90	   A^2 -> H(f(e), b)
28.56/9.90	   A^2 -> H(f(e), U1(e, d))
28.56/9.90	   A^2 -> H(f(e), U1(d, e))
28.56/9.90	   A^2 -> H(f(e), c)
28.56/9.90	   A^2 -> H(f(e), U1(e, k))
28.56/9.90	   A^2 -> H(f(e), U1(k, e))
28.56/9.90	   A^2 -> H(f(e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.90	   A^2 -> H(f(k), b)
28.56/9.90	   A^2 -> H(f(k), U1(e, d))
28.56/9.90	   A^2 -> H(f(k), U1(d, e))
28.56/9.90	   A^2 -> H(f(k), c)
28.56/9.90	   A^2 -> H(f(k), U1(e, k))
28.56/9.90	   A^2 -> H(f(k), U1(k, e))
28.56/9.90	   A^2 -> H(f(k), e)
28.56/9.90	   A^2 -> H(f(c), d)
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.90	   A^2 -> H(U1(k, k), f(e))
28.56/9.90	   A^2 -> H(U1(k, k), f(k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.90	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, d), b)
28.56/9.90	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.90	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.90	   A^2 -> H(U1(d, d), c)
28.56/9.90	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.90	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.90	   A^2 -> H(U1(d, d), e)
28.56/9.90	   A^2 -> H(f(d), d)
28.56/9.90	   A^2 -> H(f(d), k)
28.56/9.90	   A^2 -> H(U1(c, c), c)
28.56/9.90	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.90	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.90	   A^2 -> H(f(c), k)
28.56/9.90	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.90	   A^2 -> H(f(k), U1(k, k))
28.56/9.90	   A^2 -> H(f(e), e)
28.56/9.90	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.90	   A^2 -> H(d, U1(c, b))
28.56/9.90	   A^2 -> H(d, U1(d, b))
28.56/9.90	   A^2 -> H(d, U1(b, c))
28.56/9.90	   A^2 -> H(d, U1(b, d))
28.56/9.90	   A^2 -> H(d, U1(c, c))
28.56/9.90	   A^2 -> H(d, f(e))
28.56/9.90	   A^2 -> H(d, f(k))
28.56/9.90	   A^2 -> H(d, U1(d, d))
28.56/9.90	   A^2 -> H(a, U1(e, b))
28.56/9.90	   A^2 -> H(a, U1(k, b))
28.56/9.90	   A^2 -> H(a, U1(c, d))
28.56/9.90	   A^2 -> H(a, U1(d, c))
28.56/9.90	   A^2 -> H(a, U1(b, e))
28.56/9.90	   A^2 -> H(a, U1(b, k))
28.56/9.90	   A^2 -> H(a, U1(e, c))
28.56/9.90	   A^2 -> H(a, U1(k, c))
28.56/9.90	   A^2 -> H(a, U1(c, e))
28.56/9.90	   A^2 -> H(a, U1(c, k))
28.56/9.90	   A^2 -> H(a, U1(e, e))
28.56/9.90	   A^2 -> H(a, U1(k, k))
28.56/9.90	   A^2 -> H(a, U1(k, d))
28.56/9.90	   A^2 -> H(a, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.90	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.90	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.90	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, a), b)
28.56/9.90	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.90	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.90	   A^2 -> H(U1(e, a), c)
28.56/9.90	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.90	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.90	   A^2 -> H(U1(e, a), e)
28.56/9.90	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, a), b)
28.56/9.90	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.90	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.90	   A^2 -> H(U1(k, a), c)
28.56/9.90	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.90	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.90	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, d), b)
28.56/9.90	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, d), c)
28.56/9.90	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, d), e)
28.56/9.90	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, a), d)
28.56/9.90	   A^2 -> H(U1(c, a), k)
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, c), b)
28.56/9.90	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(d, c), c)
28.56/9.90	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(d, c), e)
28.56/9.90	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, a), d)
28.56/9.90	   A^2 -> H(U1(d, a), k)
28.56/9.90	   A^2 -> H(U1(a, e), b)
28.56/9.90	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.90	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.90	   A^2 -> H(U1(a, e), c)
28.56/9.90	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.90	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.90	   A^2 -> H(U1(a, e), e)
28.56/9.90	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(a, k), b)
28.56/9.90	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.90	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.90	   A^2 -> H(U1(a, k), c)
28.56/9.90	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.90	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.90	   A^2 -> H(U1(a, k), e)
28.56/9.90	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(a, c), d)
28.56/9.90	   A^2 -> H(U1(a, c), k)
28.56/9.90	   A^2 -> H(U1(a, d), d)
28.56/9.90	   A^2 -> H(U1(a, d), k)
28.56/9.90	   A^2 -> H(k, U1(c, b))
28.56/9.90	   A^2 -> H(k, U1(d, b))
28.56/9.90	   A^2 -> H(k, U1(b, c))
28.56/9.90	   A^2 -> H(k, U1(b, d))
28.56/9.90	   A^2 -> H(k, U1(c, c))
28.56/9.90	   A^2 -> H(k, f(e))
28.56/9.90	   A^2 -> H(k, f(k))
28.56/9.90	   A^2 -> H(k, U1(d, d))
28.56/9.90	   A^2 -> H(c, U1(e, b))
28.56/9.90	   A^2 -> H(c, U1(k, b))
28.56/9.90	   A^2 -> H(c, U1(c, d))
28.56/9.90	   A^2 -> H(c, U1(d, c))
28.56/9.90	   A^2 -> H(c, U1(b, e))
28.56/9.90	   A^2 -> H(c, U1(b, k))
28.56/9.90	   A^2 -> H(c, U1(e, c))
28.56/9.90	   A^2 -> H(c, U1(k, c))
28.56/9.90	   A^2 -> H(c, U1(c, e))
28.56/9.90	   A^2 -> H(c, U1(c, k))
28.56/9.90	   A^2 -> H(c, U1(e, e))
28.56/9.90	   A^2 -> H(c, U1(k, k))
28.56/9.90	   A^2 -> H(c, U1(k, d))
28.56/9.90	   A^2 -> H(c, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, c), b)
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(e, c), e)
28.56/9.90	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.90	   A^2 -> H(U1(k, c), b)
28.56/9.90	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(k, c), c)
28.56/9.90	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, e), b)
28.56/9.90	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, e), c)
28.56/9.90	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, e), e)
28.56/9.90	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, k), b)
28.56/9.90	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, k), c)
28.56/9.90	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, k), e)
28.56/9.90	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, c), d)
28.56/9.90	   A^2 -> H(e, U1(e, b))
28.56/9.90	   A^2 -> H(e, U1(c, d))
28.56/9.90	   A^2 -> H(e, U1(d, c))
28.56/9.90	   A^2 -> H(e, U1(b, e))
28.56/9.90	   A^2 -> H(e, U1(b, k))
28.56/9.90	   A^2 -> H(e, U1(e, c))
28.56/9.90	   A^2 -> H(e, U1(c, e))
28.56/9.90	   A^2 -> H(e, U1(c, k))
28.56/9.90	   A^2 -> H(e, U1(e, e))
28.56/9.90	   A^2 -> H(e, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, e), b)
28.56/9.90	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.90	
28.56/9.90	The TRS R consists of the following rules:
28.56/9.90	
28.56/9.90	   f(x) -> U1(x, x)
28.56/9.90	   U1(e, x) -> x
28.56/9.90	   a -> c
28.56/9.90	   a -> d
28.56/9.90	   b -> c
28.56/9.90	   b -> d
28.56/9.90	   d -> k
28.56/9.90	   c -> e
28.56/9.90	   c -> k
28.56/9.90	
28.56/9.90	Q is empty.
28.56/9.90	We have to consider all minimal (P,Q,R)-chains.
28.56/9.90	----------------------------------------
28.56/9.90	
28.56/9.90	(1595) TransformationProof (EQUIVALENT)
28.56/9.90	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.90	
28.56/9.90	   (A^2 -> H(e, U1(c, d)),A^2 -> H(e, U1(c, d)))
28.56/9.90	   (A^2 -> H(U1(e, e), U1(e, d)),A^2 -> H(U1(e, e), U1(e, d)))
28.56/9.90	   (A^2 -> H(U1(e, e), U1(k, d)),A^2 -> H(U1(e, e), U1(k, d)))
28.56/9.90	   (A^2 -> H(U1(e, e), U1(c, k)),A^2 -> H(U1(e, e), U1(c, k)))
28.56/9.90	
28.56/9.90	
28.56/9.90	----------------------------------------
28.56/9.90	
28.56/9.90	(1596)
28.56/9.90	Obligation:
28.56/9.90	Q DP problem:
28.56/9.90	The TRS P consists of the following rules:
28.56/9.90	
28.56/9.90	   A^2 -> H(f(c), f(c))
28.56/9.90	   H(x, x) -> G(x, x, f(k))
28.56/9.90	   G(d, x, x) -> A^2
28.56/9.90	   A^2 -> H(f(d), f(d))
28.56/9.90	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.90	   A^2 -> H(f(e), f(e))
28.56/9.90	   A^2 -> H(f(k), f(k))
28.56/9.90	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.90	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.90	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.90	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.90	   A^2 -> H(f(e), b)
28.56/9.90	   A^2 -> H(f(e), U1(e, d))
28.56/9.90	   A^2 -> H(f(e), U1(d, e))
28.56/9.90	   A^2 -> H(f(e), c)
28.56/9.90	   A^2 -> H(f(e), U1(e, k))
28.56/9.90	   A^2 -> H(f(e), U1(k, e))
28.56/9.90	   A^2 -> H(f(e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.90	   A^2 -> H(f(k), b)
28.56/9.90	   A^2 -> H(f(k), U1(e, d))
28.56/9.90	   A^2 -> H(f(k), U1(d, e))
28.56/9.90	   A^2 -> H(f(k), c)
28.56/9.90	   A^2 -> H(f(k), U1(e, k))
28.56/9.90	   A^2 -> H(f(k), U1(k, e))
28.56/9.90	   A^2 -> H(f(k), e)
28.56/9.90	   A^2 -> H(f(c), d)
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.90	   A^2 -> H(U1(k, k), f(e))
28.56/9.90	   A^2 -> H(U1(k, k), f(k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.90	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, d), b)
28.56/9.90	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.90	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.90	   A^2 -> H(U1(d, d), c)
28.56/9.90	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.90	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.90	   A^2 -> H(U1(d, d), e)
28.56/9.90	   A^2 -> H(f(d), d)
28.56/9.90	   A^2 -> H(f(d), k)
28.56/9.90	   A^2 -> H(U1(c, c), c)
28.56/9.90	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.90	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.90	   A^2 -> H(f(c), k)
28.56/9.90	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.90	   A^2 -> H(f(k), U1(k, k))
28.56/9.90	   A^2 -> H(f(e), e)
28.56/9.90	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.90	   A^2 -> H(d, U1(c, b))
28.56/9.90	   A^2 -> H(d, U1(d, b))
28.56/9.90	   A^2 -> H(d, U1(b, c))
28.56/9.90	   A^2 -> H(d, U1(b, d))
28.56/9.90	   A^2 -> H(d, U1(c, c))
28.56/9.90	   A^2 -> H(d, f(e))
28.56/9.90	   A^2 -> H(d, f(k))
28.56/9.90	   A^2 -> H(d, U1(d, d))
28.56/9.90	   A^2 -> H(a, U1(e, b))
28.56/9.90	   A^2 -> H(a, U1(k, b))
28.56/9.90	   A^2 -> H(a, U1(c, d))
28.56/9.90	   A^2 -> H(a, U1(d, c))
28.56/9.90	   A^2 -> H(a, U1(b, e))
28.56/9.90	   A^2 -> H(a, U1(b, k))
28.56/9.90	   A^2 -> H(a, U1(e, c))
28.56/9.90	   A^2 -> H(a, U1(k, c))
28.56/9.90	   A^2 -> H(a, U1(c, e))
28.56/9.90	   A^2 -> H(a, U1(c, k))
28.56/9.90	   A^2 -> H(a, U1(e, e))
28.56/9.90	   A^2 -> H(a, U1(k, k))
28.56/9.90	   A^2 -> H(a, U1(k, d))
28.56/9.90	   A^2 -> H(a, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.90	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.90	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.90	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, a), b)
28.56/9.90	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.90	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.90	   A^2 -> H(U1(e, a), c)
28.56/9.90	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.90	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.90	   A^2 -> H(U1(e, a), e)
28.56/9.90	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, a), b)
28.56/9.90	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.90	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.90	   A^2 -> H(U1(k, a), c)
28.56/9.90	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.90	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.90	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, d), b)
28.56/9.90	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, d), c)
28.56/9.90	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, d), e)
28.56/9.90	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, a), d)
28.56/9.90	   A^2 -> H(U1(c, a), k)
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, c), b)
28.56/9.90	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(d, c), c)
28.56/9.90	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(d, c), e)
28.56/9.90	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, a), d)
28.56/9.90	   A^2 -> H(U1(d, a), k)
28.56/9.90	   A^2 -> H(U1(a, e), b)
28.56/9.90	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.90	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.90	   A^2 -> H(U1(a, e), c)
28.56/9.90	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.90	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.90	   A^2 -> H(U1(a, e), e)
28.56/9.90	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(a, k), b)
28.56/9.90	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.90	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.90	   A^2 -> H(U1(a, k), c)
28.56/9.90	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.90	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.90	   A^2 -> H(U1(a, k), e)
28.56/9.90	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(a, c), d)
28.56/9.90	   A^2 -> H(U1(a, c), k)
28.56/9.90	   A^2 -> H(U1(a, d), d)
28.56/9.90	   A^2 -> H(U1(a, d), k)
28.56/9.90	   A^2 -> H(k, U1(c, b))
28.56/9.90	   A^2 -> H(k, U1(d, b))
28.56/9.90	   A^2 -> H(k, U1(b, c))
28.56/9.90	   A^2 -> H(k, U1(b, d))
28.56/9.90	   A^2 -> H(k, U1(c, c))
28.56/9.90	   A^2 -> H(k, f(e))
28.56/9.90	   A^2 -> H(k, f(k))
28.56/9.90	   A^2 -> H(k, U1(d, d))
28.56/9.90	   A^2 -> H(c, U1(e, b))
28.56/9.90	   A^2 -> H(c, U1(k, b))
28.56/9.90	   A^2 -> H(c, U1(c, d))
28.56/9.90	   A^2 -> H(c, U1(d, c))
28.56/9.90	   A^2 -> H(c, U1(b, e))
28.56/9.90	   A^2 -> H(c, U1(b, k))
28.56/9.90	   A^2 -> H(c, U1(e, c))
28.56/9.90	   A^2 -> H(c, U1(k, c))
28.56/9.90	   A^2 -> H(c, U1(c, e))
28.56/9.90	   A^2 -> H(c, U1(c, k))
28.56/9.90	   A^2 -> H(c, U1(e, e))
28.56/9.90	   A^2 -> H(c, U1(k, k))
28.56/9.90	   A^2 -> H(c, U1(k, d))
28.56/9.90	   A^2 -> H(c, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, c), b)
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(e, c), e)
28.56/9.90	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.90	   A^2 -> H(U1(k, c), b)
28.56/9.90	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(k, c), c)
28.56/9.90	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, e), b)
28.56/9.90	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, e), c)
28.56/9.90	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, e), e)
28.56/9.90	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, k), b)
28.56/9.90	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, k), c)
28.56/9.90	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, k), e)
28.56/9.90	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, c), d)
28.56/9.90	   A^2 -> H(e, U1(e, b))
28.56/9.90	   A^2 -> H(e, U1(c, d))
28.56/9.90	   A^2 -> H(e, U1(d, c))
28.56/9.90	   A^2 -> H(e, U1(b, e))
28.56/9.90	   A^2 -> H(e, U1(b, k))
28.56/9.90	   A^2 -> H(e, U1(e, c))
28.56/9.90	   A^2 -> H(e, U1(c, e))
28.56/9.90	   A^2 -> H(e, U1(c, k))
28.56/9.90	   A^2 -> H(e, U1(e, e))
28.56/9.90	   A^2 -> H(e, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, e), b)
28.56/9.90	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.90	
28.56/9.90	The TRS R consists of the following rules:
28.56/9.90	
28.56/9.90	   f(x) -> U1(x, x)
28.56/9.90	   U1(e, x) -> x
28.56/9.90	   a -> c
28.56/9.90	   a -> d
28.56/9.90	   b -> c
28.56/9.90	   b -> d
28.56/9.90	   d -> k
28.56/9.90	   c -> e
28.56/9.90	   c -> k
28.56/9.90	
28.56/9.90	Q is empty.
28.56/9.90	We have to consider all minimal (P,Q,R)-chains.
28.56/9.90	----------------------------------------
28.56/9.90	
28.56/9.90	(1597) TransformationProof (EQUIVALENT)
28.56/9.90	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.90	
28.56/9.90	   (A^2 -> H(e, U1(d, c)),A^2 -> H(e, U1(d, c)))
28.56/9.90	   (A^2 -> H(U1(e, e), U1(k, c)),A^2 -> H(U1(e, e), U1(k, c)))
28.56/9.90	   (A^2 -> H(U1(e, e), U1(d, e)),A^2 -> H(U1(e, e), U1(d, e)))
28.56/9.90	   (A^2 -> H(U1(e, e), U1(d, k)),A^2 -> H(U1(e, e), U1(d, k)))
28.56/9.90	
28.56/9.90	
28.56/9.90	----------------------------------------
28.56/9.90	
28.56/9.90	(1598)
28.56/9.90	Obligation:
28.56/9.90	Q DP problem:
28.56/9.90	The TRS P consists of the following rules:
28.56/9.90	
28.56/9.90	   A^2 -> H(f(c), f(c))
28.56/9.90	   H(x, x) -> G(x, x, f(k))
28.56/9.90	   G(d, x, x) -> A^2
28.56/9.90	   A^2 -> H(f(d), f(d))
28.56/9.90	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.90	   A^2 -> H(f(e), f(e))
28.56/9.90	   A^2 -> H(f(k), f(k))
28.56/9.90	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.90	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.90	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(b, e))
28.56/9.90	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.90	   A^2 -> H(f(e), b)
28.56/9.90	   A^2 -> H(f(e), U1(e, d))
28.56/9.90	   A^2 -> H(f(e), U1(d, e))
28.56/9.90	   A^2 -> H(f(e), c)
28.56/9.90	   A^2 -> H(f(e), U1(e, k))
28.56/9.90	   A^2 -> H(f(e), U1(k, e))
28.56/9.90	   A^2 -> H(f(e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.90	   A^2 -> H(f(k), b)
28.56/9.90	   A^2 -> H(f(k), U1(e, d))
28.56/9.90	   A^2 -> H(f(k), U1(d, e))
28.56/9.90	   A^2 -> H(f(k), c)
28.56/9.90	   A^2 -> H(f(k), U1(e, k))
28.56/9.90	   A^2 -> H(f(k), U1(k, e))
28.56/9.90	   A^2 -> H(f(k), e)
28.56/9.90	   A^2 -> H(f(c), d)
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.90	   A^2 -> H(U1(k, k), f(e))
28.56/9.90	   A^2 -> H(U1(k, k), f(k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.90	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, d), b)
28.56/9.90	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.90	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.90	   A^2 -> H(U1(d, d), c)
28.56/9.90	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.90	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.90	   A^2 -> H(U1(d, d), e)
28.56/9.90	   A^2 -> H(f(d), d)
28.56/9.90	   A^2 -> H(f(d), k)
28.56/9.90	   A^2 -> H(U1(c, c), c)
28.56/9.90	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.90	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.90	   A^2 -> H(f(c), k)
28.56/9.90	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.90	   A^2 -> H(f(k), U1(k, k))
28.56/9.90	   A^2 -> H(f(e), e)
28.56/9.90	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.90	   A^2 -> H(d, U1(c, b))
28.56/9.90	   A^2 -> H(d, U1(d, b))
28.56/9.90	   A^2 -> H(d, U1(b, c))
28.56/9.90	   A^2 -> H(d, U1(b, d))
28.56/9.90	   A^2 -> H(d, U1(c, c))
28.56/9.90	   A^2 -> H(d, f(e))
28.56/9.90	   A^2 -> H(d, f(k))
28.56/9.90	   A^2 -> H(d, U1(d, d))
28.56/9.90	   A^2 -> H(a, U1(e, b))
28.56/9.90	   A^2 -> H(a, U1(k, b))
28.56/9.90	   A^2 -> H(a, U1(c, d))
28.56/9.90	   A^2 -> H(a, U1(d, c))
28.56/9.90	   A^2 -> H(a, U1(b, e))
28.56/9.90	   A^2 -> H(a, U1(b, k))
28.56/9.90	   A^2 -> H(a, U1(e, c))
28.56/9.90	   A^2 -> H(a, U1(k, c))
28.56/9.90	   A^2 -> H(a, U1(c, e))
28.56/9.90	   A^2 -> H(a, U1(c, k))
28.56/9.90	   A^2 -> H(a, U1(e, e))
28.56/9.90	   A^2 -> H(a, U1(k, k))
28.56/9.90	   A^2 -> H(a, U1(k, d))
28.56/9.90	   A^2 -> H(a, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.90	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.90	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.90	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, a), b)
28.56/9.90	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.90	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.90	   A^2 -> H(U1(e, a), c)
28.56/9.90	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.90	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.90	   A^2 -> H(U1(e, a), e)
28.56/9.90	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, a), b)
28.56/9.90	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.90	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.90	   A^2 -> H(U1(k, a), c)
28.56/9.90	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.90	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.90	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, d), b)
28.56/9.90	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, d), c)
28.56/9.90	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, d), e)
28.56/9.90	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, a), d)
28.56/9.90	   A^2 -> H(U1(c, a), k)
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, c), b)
28.56/9.90	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(d, c), c)
28.56/9.90	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(d, c), e)
28.56/9.90	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, a), d)
28.56/9.90	   A^2 -> H(U1(d, a), k)
28.56/9.90	   A^2 -> H(U1(a, e), b)
28.56/9.90	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.90	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.90	   A^2 -> H(U1(a, e), c)
28.56/9.90	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.90	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.90	   A^2 -> H(U1(a, e), e)
28.56/9.90	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(a, k), b)
28.56/9.90	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.90	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.90	   A^2 -> H(U1(a, k), c)
28.56/9.90	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.90	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.90	   A^2 -> H(U1(a, k), e)
28.56/9.90	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(a, c), d)
28.56/9.90	   A^2 -> H(U1(a, c), k)
28.56/9.90	   A^2 -> H(U1(a, d), d)
28.56/9.90	   A^2 -> H(U1(a, d), k)
28.56/9.90	   A^2 -> H(k, U1(c, b))
28.56/9.90	   A^2 -> H(k, U1(d, b))
28.56/9.90	   A^2 -> H(k, U1(b, c))
28.56/9.90	   A^2 -> H(k, U1(b, d))
28.56/9.90	   A^2 -> H(k, U1(c, c))
28.56/9.90	   A^2 -> H(k, f(e))
28.56/9.90	   A^2 -> H(k, f(k))
28.56/9.90	   A^2 -> H(k, U1(d, d))
28.56/9.90	   A^2 -> H(c, U1(e, b))
28.56/9.90	   A^2 -> H(c, U1(k, b))
28.56/9.90	   A^2 -> H(c, U1(c, d))
28.56/9.90	   A^2 -> H(c, U1(d, c))
28.56/9.90	   A^2 -> H(c, U1(b, e))
28.56/9.90	   A^2 -> H(c, U1(b, k))
28.56/9.90	   A^2 -> H(c, U1(e, c))
28.56/9.90	   A^2 -> H(c, U1(k, c))
28.56/9.90	   A^2 -> H(c, U1(c, e))
28.56/9.90	   A^2 -> H(c, U1(c, k))
28.56/9.90	   A^2 -> H(c, U1(e, e))
28.56/9.90	   A^2 -> H(c, U1(k, k))
28.56/9.90	   A^2 -> H(c, U1(k, d))
28.56/9.90	   A^2 -> H(c, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, c), b)
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(e, c), e)
28.56/9.90	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.90	   A^2 -> H(U1(k, c), b)
28.56/9.90	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(k, c), c)
28.56/9.90	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, e), b)
28.56/9.90	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, e), c)
28.56/9.90	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, e), e)
28.56/9.90	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, k), b)
28.56/9.90	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, k), c)
28.56/9.90	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, k), e)
28.56/9.90	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, c), d)
28.56/9.90	   A^2 -> H(e, U1(e, b))
28.56/9.90	   A^2 -> H(e, U1(c, d))
28.56/9.90	   A^2 -> H(e, U1(d, c))
28.56/9.90	   A^2 -> H(e, U1(b, e))
28.56/9.90	   A^2 -> H(e, U1(b, k))
28.56/9.90	   A^2 -> H(e, U1(e, c))
28.56/9.90	   A^2 -> H(e, U1(c, e))
28.56/9.90	   A^2 -> H(e, U1(c, k))
28.56/9.90	   A^2 -> H(e, U1(e, e))
28.56/9.90	   A^2 -> H(e, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, e), b)
28.56/9.90	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.90	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.90	
28.56/9.90	The TRS R consists of the following rules:
28.56/9.90	
28.56/9.90	   f(x) -> U1(x, x)
28.56/9.90	   U1(e, x) -> x
28.56/9.90	   a -> c
28.56/9.90	   a -> d
28.56/9.90	   b -> c
28.56/9.90	   b -> d
28.56/9.90	   d -> k
28.56/9.90	   c -> e
28.56/9.90	   c -> k
28.56/9.90	
28.56/9.90	Q is empty.
28.56/9.90	We have to consider all minimal (P,Q,R)-chains.
28.56/9.90	----------------------------------------
28.56/9.90	
28.56/9.90	(1599) TransformationProof (EQUIVALENT)
28.56/9.90	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.90	
28.56/9.90	   (A^2 -> H(e, U1(b, e)),A^2 -> H(e, U1(b, e)))
28.56/9.90	   (A^2 -> H(U1(e, e), U1(c, e)),A^2 -> H(U1(e, e), U1(c, e)))
28.56/9.90	   (A^2 -> H(U1(e, e), U1(d, e)),A^2 -> H(U1(e, e), U1(d, e)))
28.56/9.90	
28.56/9.90	
28.56/9.90	----------------------------------------
28.56/9.90	
28.56/9.90	(1600)
28.56/9.90	Obligation:
28.56/9.90	Q DP problem:
28.56/9.90	The TRS P consists of the following rules:
28.56/9.90	
28.56/9.90	   A^2 -> H(f(c), f(c))
28.56/9.90	   H(x, x) -> G(x, x, f(k))
28.56/9.90	   G(d, x, x) -> A^2
28.56/9.90	   A^2 -> H(f(d), f(d))
28.56/9.90	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.90	   A^2 -> H(f(e), f(e))
28.56/9.90	   A^2 -> H(f(k), f(k))
28.56/9.90	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.90	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.90	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(b, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.90	   A^2 -> H(f(e), b)
28.56/9.90	   A^2 -> H(f(e), U1(e, d))
28.56/9.90	   A^2 -> H(f(e), U1(d, e))
28.56/9.90	   A^2 -> H(f(e), c)
28.56/9.90	   A^2 -> H(f(e), U1(e, k))
28.56/9.90	   A^2 -> H(f(e), U1(k, e))
28.56/9.90	   A^2 -> H(f(e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.90	   A^2 -> H(f(k), b)
28.56/9.90	   A^2 -> H(f(k), U1(e, d))
28.56/9.90	   A^2 -> H(f(k), U1(d, e))
28.56/9.90	   A^2 -> H(f(k), c)
28.56/9.90	   A^2 -> H(f(k), U1(e, k))
28.56/9.90	   A^2 -> H(f(k), U1(k, e))
28.56/9.90	   A^2 -> H(f(k), e)
28.56/9.90	   A^2 -> H(f(c), d)
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.90	   A^2 -> H(U1(k, k), f(e))
28.56/9.90	   A^2 -> H(U1(k, k), f(k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.90	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, d), b)
28.56/9.90	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.90	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.90	   A^2 -> H(U1(d, d), c)
28.56/9.90	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.90	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.90	   A^2 -> H(U1(d, d), e)
28.56/9.90	   A^2 -> H(f(d), d)
28.56/9.90	   A^2 -> H(f(d), k)
28.56/9.90	   A^2 -> H(U1(c, c), c)
28.56/9.90	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.90	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.90	   A^2 -> H(f(c), k)
28.56/9.90	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.90	   A^2 -> H(f(k), U1(k, k))
28.56/9.90	   A^2 -> H(f(e), e)
28.56/9.90	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.90	   A^2 -> H(d, U1(c, b))
28.56/9.90	   A^2 -> H(d, U1(d, b))
28.56/9.90	   A^2 -> H(d, U1(b, c))
28.56/9.90	   A^2 -> H(d, U1(b, d))
28.56/9.90	   A^2 -> H(d, U1(c, c))
28.56/9.90	   A^2 -> H(d, f(e))
28.56/9.90	   A^2 -> H(d, f(k))
28.56/9.90	   A^2 -> H(d, U1(d, d))
28.56/9.90	   A^2 -> H(a, U1(e, b))
28.56/9.90	   A^2 -> H(a, U1(k, b))
28.56/9.90	   A^2 -> H(a, U1(c, d))
28.56/9.90	   A^2 -> H(a, U1(d, c))
28.56/9.90	   A^2 -> H(a, U1(b, e))
28.56/9.90	   A^2 -> H(a, U1(b, k))
28.56/9.90	   A^2 -> H(a, U1(e, c))
28.56/9.90	   A^2 -> H(a, U1(k, c))
28.56/9.90	   A^2 -> H(a, U1(c, e))
28.56/9.90	   A^2 -> H(a, U1(c, k))
28.56/9.90	   A^2 -> H(a, U1(e, e))
28.56/9.90	   A^2 -> H(a, U1(k, k))
28.56/9.90	   A^2 -> H(a, U1(k, d))
28.56/9.90	   A^2 -> H(a, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.90	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.90	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.90	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, a), b)
28.56/9.90	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.90	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.90	   A^2 -> H(U1(e, a), c)
28.56/9.90	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.90	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.90	   A^2 -> H(U1(e, a), e)
28.56/9.90	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, a), b)
28.56/9.90	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.90	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.90	   A^2 -> H(U1(k, a), c)
28.56/9.90	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.90	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.90	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, d), b)
28.56/9.90	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, d), c)
28.56/9.90	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, d), e)
28.56/9.90	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, a), d)
28.56/9.90	   A^2 -> H(U1(c, a), k)
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, c), b)
28.56/9.90	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(d, c), c)
28.56/9.90	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(d, c), e)
28.56/9.90	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, a), d)
28.56/9.90	   A^2 -> H(U1(d, a), k)
28.56/9.90	   A^2 -> H(U1(a, e), b)
28.56/9.90	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.90	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.90	   A^2 -> H(U1(a, e), c)
28.56/9.90	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.90	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.90	   A^2 -> H(U1(a, e), e)
28.56/9.90	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(a, k), b)
28.56/9.90	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.90	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.90	   A^2 -> H(U1(a, k), c)
28.56/9.90	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.90	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.90	   A^2 -> H(U1(a, k), e)
28.56/9.90	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(a, c), d)
28.56/9.90	   A^2 -> H(U1(a, c), k)
28.56/9.90	   A^2 -> H(U1(a, d), d)
28.56/9.90	   A^2 -> H(U1(a, d), k)
28.56/9.90	   A^2 -> H(k, U1(c, b))
28.56/9.90	   A^2 -> H(k, U1(d, b))
28.56/9.90	   A^2 -> H(k, U1(b, c))
28.56/9.90	   A^2 -> H(k, U1(b, d))
28.56/9.90	   A^2 -> H(k, U1(c, c))
28.56/9.90	   A^2 -> H(k, f(e))
28.56/9.90	   A^2 -> H(k, f(k))
28.56/9.90	   A^2 -> H(k, U1(d, d))
28.56/9.90	   A^2 -> H(c, U1(e, b))
28.56/9.90	   A^2 -> H(c, U1(k, b))
28.56/9.90	   A^2 -> H(c, U1(c, d))
28.56/9.90	   A^2 -> H(c, U1(d, c))
28.56/9.90	   A^2 -> H(c, U1(b, e))
28.56/9.90	   A^2 -> H(c, U1(b, k))
28.56/9.90	   A^2 -> H(c, U1(e, c))
28.56/9.90	   A^2 -> H(c, U1(k, c))
28.56/9.90	   A^2 -> H(c, U1(c, e))
28.56/9.90	   A^2 -> H(c, U1(c, k))
28.56/9.90	   A^2 -> H(c, U1(e, e))
28.56/9.90	   A^2 -> H(c, U1(k, k))
28.56/9.90	   A^2 -> H(c, U1(k, d))
28.56/9.90	   A^2 -> H(c, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, c), b)
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(e, c), e)
28.56/9.90	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.90	   A^2 -> H(U1(k, c), b)
28.56/9.90	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(k, c), c)
28.56/9.90	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, e), b)
28.56/9.90	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, e), c)
28.56/9.90	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, e), e)
28.56/9.90	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, k), b)
28.56/9.90	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, k), c)
28.56/9.90	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, k), e)
28.56/9.90	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, c), d)
28.56/9.90	   A^2 -> H(e, U1(e, b))
28.56/9.90	   A^2 -> H(e, U1(c, d))
28.56/9.90	   A^2 -> H(e, U1(d, c))
28.56/9.90	   A^2 -> H(e, U1(b, e))
28.56/9.90	   A^2 -> H(e, U1(b, k))
28.56/9.90	   A^2 -> H(e, U1(e, c))
28.56/9.90	   A^2 -> H(e, U1(c, e))
28.56/9.90	   A^2 -> H(e, U1(c, k))
28.56/9.90	   A^2 -> H(e, U1(e, e))
28.56/9.90	   A^2 -> H(e, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, e), b)
28.56/9.90	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.90	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.90	
28.56/9.90	The TRS R consists of the following rules:
28.56/9.90	
28.56/9.90	   f(x) -> U1(x, x)
28.56/9.90	   U1(e, x) -> x
28.56/9.90	   a -> c
28.56/9.90	   a -> d
28.56/9.90	   b -> c
28.56/9.90	   b -> d
28.56/9.90	   d -> k
28.56/9.90	   c -> e
28.56/9.90	   c -> k
28.56/9.90	
28.56/9.90	Q is empty.
28.56/9.90	We have to consider all minimal (P,Q,R)-chains.
28.56/9.90	----------------------------------------
28.56/9.90	
28.56/9.90	(1601) TransformationProof (EQUIVALENT)
28.56/9.90	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.90	
28.56/9.90	   (A^2 -> H(e, U1(b, k)),A^2 -> H(e, U1(b, k)))
28.56/9.90	   (A^2 -> H(U1(e, e), U1(c, k)),A^2 -> H(U1(e, e), U1(c, k)))
28.56/9.90	   (A^2 -> H(U1(e, e), U1(d, k)),A^2 -> H(U1(e, e), U1(d, k)))
28.56/9.90	
28.56/9.90	
28.56/9.90	----------------------------------------
28.56/9.90	
28.56/9.90	(1602)
28.56/9.90	Obligation:
28.56/9.90	Q DP problem:
28.56/9.90	The TRS P consists of the following rules:
28.56/9.90	
28.56/9.90	   A^2 -> H(f(c), f(c))
28.56/9.90	   H(x, x) -> G(x, x, f(k))
28.56/9.90	   G(d, x, x) -> A^2
28.56/9.90	   A^2 -> H(f(d), f(d))
28.56/9.90	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.90	   A^2 -> H(f(e), f(e))
28.56/9.90	   A^2 -> H(f(k), f(k))
28.56/9.90	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.90	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.90	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.90	   A^2 -> H(f(e), b)
28.56/9.90	   A^2 -> H(f(e), U1(e, d))
28.56/9.90	   A^2 -> H(f(e), U1(d, e))
28.56/9.90	   A^2 -> H(f(e), c)
28.56/9.90	   A^2 -> H(f(e), U1(e, k))
28.56/9.90	   A^2 -> H(f(e), U1(k, e))
28.56/9.90	   A^2 -> H(f(e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.90	   A^2 -> H(f(k), b)
28.56/9.90	   A^2 -> H(f(k), U1(e, d))
28.56/9.90	   A^2 -> H(f(k), U1(d, e))
28.56/9.90	   A^2 -> H(f(k), c)
28.56/9.90	   A^2 -> H(f(k), U1(e, k))
28.56/9.90	   A^2 -> H(f(k), U1(k, e))
28.56/9.90	   A^2 -> H(f(k), e)
28.56/9.90	   A^2 -> H(f(c), d)
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.90	   A^2 -> H(U1(k, k), f(e))
28.56/9.90	   A^2 -> H(U1(k, k), f(k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.90	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, d), b)
28.56/9.90	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.90	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.90	   A^2 -> H(U1(d, d), c)
28.56/9.90	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.90	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.90	   A^2 -> H(U1(d, d), e)
28.56/9.90	   A^2 -> H(f(d), d)
28.56/9.90	   A^2 -> H(f(d), k)
28.56/9.90	   A^2 -> H(U1(c, c), c)
28.56/9.90	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.90	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.90	   A^2 -> H(f(c), k)
28.56/9.90	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.90	   A^2 -> H(f(k), U1(k, k))
28.56/9.90	   A^2 -> H(f(e), e)
28.56/9.90	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.90	   A^2 -> H(d, U1(c, b))
28.56/9.90	   A^2 -> H(d, U1(d, b))
28.56/9.90	   A^2 -> H(d, U1(b, c))
28.56/9.90	   A^2 -> H(d, U1(b, d))
28.56/9.90	   A^2 -> H(d, U1(c, c))
28.56/9.90	   A^2 -> H(d, f(e))
28.56/9.90	   A^2 -> H(d, f(k))
28.56/9.90	   A^2 -> H(d, U1(d, d))
28.56/9.90	   A^2 -> H(a, U1(e, b))
28.56/9.90	   A^2 -> H(a, U1(k, b))
28.56/9.90	   A^2 -> H(a, U1(c, d))
28.56/9.90	   A^2 -> H(a, U1(d, c))
28.56/9.90	   A^2 -> H(a, U1(b, e))
28.56/9.90	   A^2 -> H(a, U1(b, k))
28.56/9.90	   A^2 -> H(a, U1(e, c))
28.56/9.90	   A^2 -> H(a, U1(k, c))
28.56/9.90	   A^2 -> H(a, U1(c, e))
28.56/9.90	   A^2 -> H(a, U1(c, k))
28.56/9.90	   A^2 -> H(a, U1(e, e))
28.56/9.90	   A^2 -> H(a, U1(k, k))
28.56/9.90	   A^2 -> H(a, U1(k, d))
28.56/9.90	   A^2 -> H(a, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.90	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.90	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.90	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, a), b)
28.56/9.90	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.90	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.90	   A^2 -> H(U1(e, a), c)
28.56/9.90	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.90	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.90	   A^2 -> H(U1(e, a), e)
28.56/9.90	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, a), b)
28.56/9.90	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.90	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.90	   A^2 -> H(U1(k, a), c)
28.56/9.90	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.90	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.90	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, d), b)
28.56/9.90	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, d), c)
28.56/9.90	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, d), e)
28.56/9.90	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, a), d)
28.56/9.90	   A^2 -> H(U1(c, a), k)
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, c), b)
28.56/9.90	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(d, c), c)
28.56/9.90	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(d, c), e)
28.56/9.90	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, a), d)
28.56/9.90	   A^2 -> H(U1(d, a), k)
28.56/9.90	   A^2 -> H(U1(a, e), b)
28.56/9.90	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.90	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.90	   A^2 -> H(U1(a, e), c)
28.56/9.90	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.90	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.90	   A^2 -> H(U1(a, e), e)
28.56/9.90	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(a, k), b)
28.56/9.90	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.90	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.90	   A^2 -> H(U1(a, k), c)
28.56/9.90	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.90	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.90	   A^2 -> H(U1(a, k), e)
28.56/9.90	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(a, c), d)
28.56/9.90	   A^2 -> H(U1(a, c), k)
28.56/9.90	   A^2 -> H(U1(a, d), d)
28.56/9.90	   A^2 -> H(U1(a, d), k)
28.56/9.90	   A^2 -> H(k, U1(c, b))
28.56/9.90	   A^2 -> H(k, U1(d, b))
28.56/9.90	   A^2 -> H(k, U1(b, c))
28.56/9.90	   A^2 -> H(k, U1(b, d))
28.56/9.90	   A^2 -> H(k, U1(c, c))
28.56/9.90	   A^2 -> H(k, f(e))
28.56/9.90	   A^2 -> H(k, f(k))
28.56/9.90	   A^2 -> H(k, U1(d, d))
28.56/9.90	   A^2 -> H(c, U1(e, b))
28.56/9.90	   A^2 -> H(c, U1(k, b))
28.56/9.90	   A^2 -> H(c, U1(c, d))
28.56/9.90	   A^2 -> H(c, U1(d, c))
28.56/9.90	   A^2 -> H(c, U1(b, e))
28.56/9.90	   A^2 -> H(c, U1(b, k))
28.56/9.90	   A^2 -> H(c, U1(e, c))
28.56/9.90	   A^2 -> H(c, U1(k, c))
28.56/9.90	   A^2 -> H(c, U1(c, e))
28.56/9.90	   A^2 -> H(c, U1(c, k))
28.56/9.90	   A^2 -> H(c, U1(e, e))
28.56/9.90	   A^2 -> H(c, U1(k, k))
28.56/9.90	   A^2 -> H(c, U1(k, d))
28.56/9.90	   A^2 -> H(c, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, c), b)
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(e, c), e)
28.56/9.90	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.90	   A^2 -> H(U1(k, c), b)
28.56/9.90	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(k, c), c)
28.56/9.90	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, e), b)
28.56/9.90	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, e), c)
28.56/9.90	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, e), e)
28.56/9.90	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, k), b)
28.56/9.90	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, k), c)
28.56/9.90	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, k), e)
28.56/9.90	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, c), d)
28.56/9.90	   A^2 -> H(e, U1(e, b))
28.56/9.90	   A^2 -> H(e, U1(c, d))
28.56/9.90	   A^2 -> H(e, U1(d, c))
28.56/9.90	   A^2 -> H(e, U1(b, e))
28.56/9.90	   A^2 -> H(e, U1(b, k))
28.56/9.90	   A^2 -> H(e, U1(e, c))
28.56/9.90	   A^2 -> H(e, U1(c, e))
28.56/9.90	   A^2 -> H(e, U1(c, k))
28.56/9.90	   A^2 -> H(e, U1(e, e))
28.56/9.90	   A^2 -> H(e, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, e), b)
28.56/9.90	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.90	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.90	
28.56/9.90	The TRS R consists of the following rules:
28.56/9.90	
28.56/9.90	   f(x) -> U1(x, x)
28.56/9.90	   U1(e, x) -> x
28.56/9.90	   a -> c
28.56/9.90	   a -> d
28.56/9.90	   b -> c
28.56/9.90	   b -> d
28.56/9.90	   d -> k
28.56/9.90	   c -> e
28.56/9.90	   c -> k
28.56/9.90	
28.56/9.90	Q is empty.
28.56/9.90	We have to consider all minimal (P,Q,R)-chains.
28.56/9.90	----------------------------------------
28.56/9.90	
28.56/9.90	(1603) TransformationProof (EQUIVALENT)
28.56/9.90	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.90	
28.56/9.90	   (A^2 -> H(e, U1(e, c)),A^2 -> H(e, U1(e, c)))
28.56/9.90	   (A^2 -> H(U1(e, e), c),A^2 -> H(U1(e, e), c))
28.56/9.90	   (A^2 -> H(U1(e, e), U1(e, e)),A^2 -> H(U1(e, e), U1(e, e)))
28.56/9.90	   (A^2 -> H(U1(e, e), U1(e, k)),A^2 -> H(U1(e, e), U1(e, k)))
28.56/9.90	
28.56/9.90	
28.56/9.90	----------------------------------------
28.56/9.90	
28.56/9.90	(1604)
28.56/9.90	Obligation:
28.56/9.90	Q DP problem:
28.56/9.90	The TRS P consists of the following rules:
28.56/9.90	
28.56/9.90	   A^2 -> H(f(c), f(c))
28.56/9.90	   H(x, x) -> G(x, x, f(k))
28.56/9.90	   G(d, x, x) -> A^2
28.56/9.90	   A^2 -> H(f(d), f(d))
28.56/9.90	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.90	   A^2 -> H(f(e), f(e))
28.56/9.90	   A^2 -> H(f(k), f(k))
28.56/9.90	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.90	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.90	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.90	   A^2 -> H(f(e), b)
28.56/9.90	   A^2 -> H(f(e), U1(e, d))
28.56/9.90	   A^2 -> H(f(e), U1(d, e))
28.56/9.90	   A^2 -> H(f(e), c)
28.56/9.90	   A^2 -> H(f(e), U1(e, k))
28.56/9.90	   A^2 -> H(f(e), U1(k, e))
28.56/9.90	   A^2 -> H(f(e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.90	   A^2 -> H(f(k), b)
28.56/9.90	   A^2 -> H(f(k), U1(e, d))
28.56/9.90	   A^2 -> H(f(k), U1(d, e))
28.56/9.90	   A^2 -> H(f(k), c)
28.56/9.90	   A^2 -> H(f(k), U1(e, k))
28.56/9.90	   A^2 -> H(f(k), U1(k, e))
28.56/9.90	   A^2 -> H(f(k), e)
28.56/9.90	   A^2 -> H(f(c), d)
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.90	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.90	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.90	   A^2 -> H(U1(k, k), f(e))
28.56/9.90	   A^2 -> H(U1(k, k), f(k))
28.56/9.90	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.90	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, d), b)
28.56/9.90	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.90	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.90	   A^2 -> H(U1(d, d), c)
28.56/9.90	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.90	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.90	   A^2 -> H(U1(d, d), e)
28.56/9.90	   A^2 -> H(f(d), d)
28.56/9.90	   A^2 -> H(f(d), k)
28.56/9.90	   A^2 -> H(U1(c, c), c)
28.56/9.90	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.90	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.90	   A^2 -> H(f(c), k)
28.56/9.90	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.90	   A^2 -> H(f(k), U1(k, k))
28.56/9.90	   A^2 -> H(f(e), e)
28.56/9.90	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.90	   A^2 -> H(d, U1(c, b))
28.56/9.90	   A^2 -> H(d, U1(d, b))
28.56/9.90	   A^2 -> H(d, U1(b, c))
28.56/9.90	   A^2 -> H(d, U1(b, d))
28.56/9.90	   A^2 -> H(d, U1(c, c))
28.56/9.90	   A^2 -> H(d, f(e))
28.56/9.90	   A^2 -> H(d, f(k))
28.56/9.90	   A^2 -> H(d, U1(d, d))
28.56/9.90	   A^2 -> H(a, U1(e, b))
28.56/9.90	   A^2 -> H(a, U1(k, b))
28.56/9.90	   A^2 -> H(a, U1(c, d))
28.56/9.90	   A^2 -> H(a, U1(d, c))
28.56/9.90	   A^2 -> H(a, U1(b, e))
28.56/9.90	   A^2 -> H(a, U1(b, k))
28.56/9.90	   A^2 -> H(a, U1(e, c))
28.56/9.90	   A^2 -> H(a, U1(k, c))
28.56/9.90	   A^2 -> H(a, U1(c, e))
28.56/9.90	   A^2 -> H(a, U1(c, k))
28.56/9.90	   A^2 -> H(a, U1(e, e))
28.56/9.90	   A^2 -> H(a, U1(k, k))
28.56/9.90	   A^2 -> H(a, U1(k, d))
28.56/9.90	   A^2 -> H(a, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.90	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.90	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.90	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, a), b)
28.56/9.90	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.90	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.90	   A^2 -> H(U1(e, a), c)
28.56/9.90	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.90	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.90	   A^2 -> H(U1(e, a), e)
28.56/9.90	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, a), b)
28.56/9.90	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.90	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.90	   A^2 -> H(U1(k, a), c)
28.56/9.90	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.90	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.90	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, d), b)
28.56/9.90	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, d), c)
28.56/9.90	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, d), e)
28.56/9.90	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, a), d)
28.56/9.90	   A^2 -> H(U1(c, a), k)
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.90	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.90	   A^2 -> H(U1(d, c), b)
28.56/9.90	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(d, c), c)
28.56/9.90	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(d, c), e)
28.56/9.90	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(d, a), d)
28.56/9.90	   A^2 -> H(U1(d, a), k)
28.56/9.90	   A^2 -> H(U1(a, e), b)
28.56/9.90	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.90	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.90	   A^2 -> H(U1(a, e), c)
28.56/9.90	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.90	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.90	   A^2 -> H(U1(a, e), e)
28.56/9.90	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.90	   A^2 -> H(U1(a, k), b)
28.56/9.90	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.90	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.90	   A^2 -> H(U1(a, k), c)
28.56/9.90	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.90	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.90	   A^2 -> H(U1(a, k), e)
28.56/9.90	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(a, c), d)
28.56/9.90	   A^2 -> H(U1(a, c), k)
28.56/9.90	   A^2 -> H(U1(a, d), d)
28.56/9.90	   A^2 -> H(U1(a, d), k)
28.56/9.90	   A^2 -> H(k, U1(c, b))
28.56/9.90	   A^2 -> H(k, U1(d, b))
28.56/9.90	   A^2 -> H(k, U1(b, c))
28.56/9.90	   A^2 -> H(k, U1(b, d))
28.56/9.90	   A^2 -> H(k, U1(c, c))
28.56/9.90	   A^2 -> H(k, f(e))
28.56/9.90	   A^2 -> H(k, f(k))
28.56/9.90	   A^2 -> H(k, U1(d, d))
28.56/9.90	   A^2 -> H(c, U1(e, b))
28.56/9.90	   A^2 -> H(c, U1(k, b))
28.56/9.90	   A^2 -> H(c, U1(c, d))
28.56/9.90	   A^2 -> H(c, U1(d, c))
28.56/9.90	   A^2 -> H(c, U1(b, e))
28.56/9.90	   A^2 -> H(c, U1(b, k))
28.56/9.90	   A^2 -> H(c, U1(e, c))
28.56/9.90	   A^2 -> H(c, U1(k, c))
28.56/9.90	   A^2 -> H(c, U1(c, e))
28.56/9.90	   A^2 -> H(c, U1(c, k))
28.56/9.90	   A^2 -> H(c, U1(e, e))
28.56/9.90	   A^2 -> H(c, U1(k, k))
28.56/9.90	   A^2 -> H(c, U1(k, d))
28.56/9.90	   A^2 -> H(c, U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.90	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.90	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.90	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.90	   A^2 -> H(U1(e, c), b)
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(e, c), e)
28.56/9.90	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.90	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.90	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.90	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.90	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.90	   A^2 -> H(U1(k, c), b)
28.56/9.90	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.90	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.90	   A^2 -> H(U1(k, c), c)
28.56/9.90	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.90	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.90	   A^2 -> H(U1(c, e), b)
28.56/9.90	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.90	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.90	   A^2 -> H(U1(c, e), c)
28.56/9.90	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.90	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.90	   A^2 -> H(U1(c, e), e)
28.56/9.90	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, k), b)
28.56/9.91	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, k), c)
28.56/9.91	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, k), e)
28.56/9.91	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, c), d)
28.56/9.91	   A^2 -> H(e, U1(e, b))
28.56/9.91	   A^2 -> H(e, U1(c, d))
28.56/9.91	   A^2 -> H(e, U1(d, c))
28.56/9.91	   A^2 -> H(e, U1(b, e))
28.56/9.91	   A^2 -> H(e, U1(b, k))
28.56/9.91	   A^2 -> H(e, U1(e, c))
28.56/9.91	   A^2 -> H(e, U1(c, e))
28.56/9.91	   A^2 -> H(e, U1(c, k))
28.56/9.91	   A^2 -> H(e, U1(e, e))
28.56/9.91	   A^2 -> H(e, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, e), b)
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, e), c)
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.91	
28.56/9.91	The TRS R consists of the following rules:
28.56/9.91	
28.56/9.91	   f(x) -> U1(x, x)
28.56/9.91	   U1(e, x) -> x
28.56/9.91	   a -> c
28.56/9.91	   a -> d
28.56/9.91	   b -> c
28.56/9.91	   b -> d
28.56/9.91	   d -> k
28.56/9.91	   c -> e
28.56/9.91	   c -> k
28.56/9.91	
28.56/9.91	Q is empty.
28.56/9.91	We have to consider all minimal (P,Q,R)-chains.
28.56/9.91	----------------------------------------
28.56/9.91	
28.56/9.91	(1605) TransformationProof (EQUIVALENT)
28.56/9.91	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.91	
28.56/9.91	   (A^2 -> H(e, U1(k, c)),A^2 -> H(e, U1(k, c)))
28.56/9.91	   (A^2 -> H(U1(e, e), U1(k, e)),A^2 -> H(U1(e, e), U1(k, e)))
28.56/9.91	   (A^2 -> H(U1(e, e), U1(k, k)),A^2 -> H(U1(e, e), U1(k, k)))
28.56/9.91	
28.56/9.91	
28.56/9.91	----------------------------------------
28.56/9.91	
28.56/9.91	(1606)
28.56/9.91	Obligation:
28.56/9.91	Q DP problem:
28.56/9.91	The TRS P consists of the following rules:
28.56/9.91	
28.56/9.91	   A^2 -> H(f(c), f(c))
28.56/9.91	   H(x, x) -> G(x, x, f(k))
28.56/9.91	   G(d, x, x) -> A^2
28.56/9.91	   A^2 -> H(f(d), f(d))
28.56/9.91	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.91	   A^2 -> H(f(e), f(e))
28.56/9.91	   A^2 -> H(f(k), f(k))
28.56/9.91	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.91	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.91	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.91	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.91	   A^2 -> H(f(e), b)
28.56/9.91	   A^2 -> H(f(e), U1(e, d))
28.56/9.91	   A^2 -> H(f(e), U1(d, e))
28.56/9.91	   A^2 -> H(f(e), c)
28.56/9.91	   A^2 -> H(f(e), U1(e, k))
28.56/9.91	   A^2 -> H(f(e), U1(k, e))
28.56/9.91	   A^2 -> H(f(e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.91	   A^2 -> H(f(k), b)
28.56/9.91	   A^2 -> H(f(k), U1(e, d))
28.56/9.91	   A^2 -> H(f(k), U1(d, e))
28.56/9.91	   A^2 -> H(f(k), c)
28.56/9.91	   A^2 -> H(f(k), U1(e, k))
28.56/9.91	   A^2 -> H(f(k), U1(k, e))
28.56/9.91	   A^2 -> H(f(k), e)
28.56/9.91	   A^2 -> H(f(c), d)
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.91	   A^2 -> H(U1(k, k), f(e))
28.56/9.91	   A^2 -> H(U1(k, k), f(k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.91	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.91	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.91	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.91	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.91	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.91	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.91	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.91	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.91	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.91	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.91	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.91	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.91	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.91	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.91	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.91	   A^2 -> H(U1(d, d), b)
28.56/9.91	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.91	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.91	   A^2 -> H(U1(d, d), c)
28.56/9.91	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.91	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.91	   A^2 -> H(U1(d, d), e)
28.56/9.91	   A^2 -> H(f(d), d)
28.56/9.91	   A^2 -> H(f(d), k)
28.56/9.91	   A^2 -> H(U1(c, c), c)
28.56/9.91	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.91	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.91	   A^2 -> H(f(c), k)
28.56/9.91	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.91	   A^2 -> H(f(k), U1(k, k))
28.56/9.91	   A^2 -> H(f(e), e)
28.56/9.91	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.91	   A^2 -> H(d, U1(c, b))
28.56/9.91	   A^2 -> H(d, U1(d, b))
28.56/9.91	   A^2 -> H(d, U1(b, c))
28.56/9.91	   A^2 -> H(d, U1(b, d))
28.56/9.91	   A^2 -> H(d, U1(c, c))
28.56/9.91	   A^2 -> H(d, f(e))
28.56/9.91	   A^2 -> H(d, f(k))
28.56/9.91	   A^2 -> H(d, U1(d, d))
28.56/9.91	   A^2 -> H(a, U1(e, b))
28.56/9.91	   A^2 -> H(a, U1(k, b))
28.56/9.91	   A^2 -> H(a, U1(c, d))
28.56/9.91	   A^2 -> H(a, U1(d, c))
28.56/9.91	   A^2 -> H(a, U1(b, e))
28.56/9.91	   A^2 -> H(a, U1(b, k))
28.56/9.91	   A^2 -> H(a, U1(e, c))
28.56/9.91	   A^2 -> H(a, U1(k, c))
28.56/9.91	   A^2 -> H(a, U1(c, e))
28.56/9.91	   A^2 -> H(a, U1(c, k))
28.56/9.91	   A^2 -> H(a, U1(e, e))
28.56/9.91	   A^2 -> H(a, U1(k, k))
28.56/9.91	   A^2 -> H(a, U1(k, d))
28.56/9.91	   A^2 -> H(a, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.91	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.91	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.91	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.91	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.91	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, a), b)
28.56/9.91	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, a), c)
28.56/9.91	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.91	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.91	   A^2 -> H(U1(e, a), e)
28.56/9.91	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, a), b)
28.56/9.91	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.91	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.91	   A^2 -> H(U1(k, a), c)
28.56/9.91	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.91	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.91	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, d), b)
28.56/9.91	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, d), c)
28.56/9.91	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, d), e)
28.56/9.91	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, a), d)
28.56/9.91	   A^2 -> H(U1(c, a), k)
28.56/9.91	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.91	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.91	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.91	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.91	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.91	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.91	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.91	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.91	   A^2 -> H(U1(d, c), b)
28.56/9.91	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.91	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.91	   A^2 -> H(U1(d, c), c)
28.56/9.91	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.91	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.91	   A^2 -> H(U1(d, c), e)
28.56/9.91	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.91	   A^2 -> H(U1(d, a), d)
28.56/9.91	   A^2 -> H(U1(d, a), k)
28.56/9.91	   A^2 -> H(U1(a, e), b)
28.56/9.91	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(a, e), c)
28.56/9.91	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.91	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.91	   A^2 -> H(U1(a, e), e)
28.56/9.91	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(a, k), b)
28.56/9.91	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.91	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.91	   A^2 -> H(U1(a, k), c)
28.56/9.91	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.91	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.91	   A^2 -> H(U1(a, k), e)
28.56/9.91	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(a, c), d)
28.56/9.91	   A^2 -> H(U1(a, c), k)
28.56/9.91	   A^2 -> H(U1(a, d), d)
28.56/9.91	   A^2 -> H(U1(a, d), k)
28.56/9.91	   A^2 -> H(k, U1(c, b))
28.56/9.91	   A^2 -> H(k, U1(d, b))
28.56/9.91	   A^2 -> H(k, U1(b, c))
28.56/9.91	   A^2 -> H(k, U1(b, d))
28.56/9.91	   A^2 -> H(k, U1(c, c))
28.56/9.91	   A^2 -> H(k, f(e))
28.56/9.91	   A^2 -> H(k, f(k))
28.56/9.91	   A^2 -> H(k, U1(d, d))
28.56/9.91	   A^2 -> H(c, U1(e, b))
28.56/9.91	   A^2 -> H(c, U1(k, b))
28.56/9.91	   A^2 -> H(c, U1(c, d))
28.56/9.91	   A^2 -> H(c, U1(d, c))
28.56/9.91	   A^2 -> H(c, U1(b, e))
28.56/9.91	   A^2 -> H(c, U1(b, k))
28.56/9.91	   A^2 -> H(c, U1(e, c))
28.56/9.91	   A^2 -> H(c, U1(k, c))
28.56/9.91	   A^2 -> H(c, U1(c, e))
28.56/9.91	   A^2 -> H(c, U1(c, k))
28.56/9.91	   A^2 -> H(c, U1(e, e))
28.56/9.91	   A^2 -> H(c, U1(k, k))
28.56/9.91	   A^2 -> H(c, U1(k, d))
28.56/9.91	   A^2 -> H(c, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.91	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.91	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.91	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.91	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.91	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.91	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, c), b)
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.91	   A^2 -> H(U1(e, c), e)
28.56/9.91	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.91	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.91	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.91	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.91	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.91	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.91	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.91	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.91	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.91	   A^2 -> H(U1(k, c), b)
28.56/9.91	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.91	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.91	   A^2 -> H(U1(k, c), c)
28.56/9.91	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, e), b)
28.56/9.91	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, e), c)
28.56/9.91	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, e), e)
28.56/9.91	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, k), b)
28.56/9.91	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, k), c)
28.56/9.91	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, k), e)
28.56/9.91	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, c), d)
28.56/9.91	   A^2 -> H(e, U1(e, b))
28.56/9.91	   A^2 -> H(e, U1(c, d))
28.56/9.91	   A^2 -> H(e, U1(d, c))
28.56/9.91	   A^2 -> H(e, U1(b, e))
28.56/9.91	   A^2 -> H(e, U1(b, k))
28.56/9.91	   A^2 -> H(e, U1(e, c))
28.56/9.91	   A^2 -> H(e, U1(c, e))
28.56/9.91	   A^2 -> H(e, U1(c, k))
28.56/9.91	   A^2 -> H(e, U1(e, e))
28.56/9.91	   A^2 -> H(e, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, e), b)
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, e), c)
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.91	   A^2 -> H(e, U1(k, c))
28.56/9.91	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.91	
28.56/9.91	The TRS R consists of the following rules:
28.56/9.91	
28.56/9.91	   f(x) -> U1(x, x)
28.56/9.91	   U1(e, x) -> x
28.56/9.91	   a -> c
28.56/9.91	   a -> d
28.56/9.91	   b -> c
28.56/9.91	   b -> d
28.56/9.91	   d -> k
28.56/9.91	   c -> e
28.56/9.91	   c -> k
28.56/9.91	
28.56/9.91	Q is empty.
28.56/9.91	We have to consider all minimal (P,Q,R)-chains.
28.56/9.91	----------------------------------------
28.56/9.91	
28.56/9.91	(1607) DependencyGraphProof (EQUIVALENT)
28.56/9.91	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.91	----------------------------------------
28.56/9.91	
28.56/9.91	(1608)
28.56/9.91	Obligation:
28.56/9.91	Q DP problem:
28.56/9.91	The TRS P consists of the following rules:
28.56/9.91	
28.56/9.91	   H(x, x) -> G(x, x, f(k))
28.56/9.91	   G(d, x, x) -> A^2
28.56/9.91	   A^2 -> H(f(c), f(c))
28.56/9.91	   A^2 -> H(f(d), f(d))
28.56/9.91	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.91	   A^2 -> H(f(e), f(e))
28.56/9.91	   A^2 -> H(f(k), f(k))
28.56/9.91	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.91	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.91	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.91	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.91	   A^2 -> H(f(e), b)
28.56/9.91	   A^2 -> H(f(e), U1(e, d))
28.56/9.91	   A^2 -> H(f(e), U1(d, e))
28.56/9.91	   A^2 -> H(f(e), c)
28.56/9.91	   A^2 -> H(f(e), U1(e, k))
28.56/9.91	   A^2 -> H(f(e), U1(k, e))
28.56/9.91	   A^2 -> H(f(e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.91	   A^2 -> H(f(k), b)
28.56/9.91	   A^2 -> H(f(k), U1(e, d))
28.56/9.91	   A^2 -> H(f(k), U1(d, e))
28.56/9.91	   A^2 -> H(f(k), c)
28.56/9.91	   A^2 -> H(f(k), U1(e, k))
28.56/9.91	   A^2 -> H(f(k), U1(k, e))
28.56/9.91	   A^2 -> H(f(k), e)
28.56/9.91	   A^2 -> H(f(c), d)
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.91	   A^2 -> H(U1(k, k), f(e))
28.56/9.91	   A^2 -> H(U1(k, k), f(k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.91	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.91	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.91	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.91	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.91	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.91	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.91	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.91	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.91	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.91	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.91	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.91	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.91	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.91	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.91	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.91	   A^2 -> H(U1(d, d), b)
28.56/9.91	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.91	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.91	   A^2 -> H(U1(d, d), c)
28.56/9.91	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.91	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.91	   A^2 -> H(U1(d, d), e)
28.56/9.91	   A^2 -> H(f(d), d)
28.56/9.91	   A^2 -> H(f(d), k)
28.56/9.91	   A^2 -> H(U1(c, c), c)
28.56/9.91	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.91	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.91	   A^2 -> H(f(c), k)
28.56/9.91	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.91	   A^2 -> H(f(k), U1(k, k))
28.56/9.91	   A^2 -> H(f(e), e)
28.56/9.91	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.91	   A^2 -> H(d, U1(c, b))
28.56/9.91	   A^2 -> H(d, U1(d, b))
28.56/9.91	   A^2 -> H(d, U1(b, c))
28.56/9.91	   A^2 -> H(d, U1(b, d))
28.56/9.91	   A^2 -> H(d, U1(c, c))
28.56/9.91	   A^2 -> H(d, f(e))
28.56/9.91	   A^2 -> H(d, f(k))
28.56/9.91	   A^2 -> H(d, U1(d, d))
28.56/9.91	   A^2 -> H(a, U1(e, b))
28.56/9.91	   A^2 -> H(a, U1(k, b))
28.56/9.91	   A^2 -> H(a, U1(c, d))
28.56/9.91	   A^2 -> H(a, U1(d, c))
28.56/9.91	   A^2 -> H(a, U1(b, e))
28.56/9.91	   A^2 -> H(a, U1(b, k))
28.56/9.91	   A^2 -> H(a, U1(e, c))
28.56/9.91	   A^2 -> H(a, U1(k, c))
28.56/9.91	   A^2 -> H(a, U1(c, e))
28.56/9.91	   A^2 -> H(a, U1(c, k))
28.56/9.91	   A^2 -> H(a, U1(e, e))
28.56/9.91	   A^2 -> H(a, U1(k, k))
28.56/9.91	   A^2 -> H(a, U1(k, d))
28.56/9.91	   A^2 -> H(a, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.91	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.91	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.91	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.91	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.91	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, a), b)
28.56/9.91	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, a), c)
28.56/9.91	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.91	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.91	   A^2 -> H(U1(e, a), e)
28.56/9.91	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, a), b)
28.56/9.91	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.91	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.91	   A^2 -> H(U1(k, a), c)
28.56/9.91	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.91	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.91	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, d), b)
28.56/9.91	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, d), c)
28.56/9.91	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, d), e)
28.56/9.91	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, a), d)
28.56/9.91	   A^2 -> H(U1(c, a), k)
28.56/9.91	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.91	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.91	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.91	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.91	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.91	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.91	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.91	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.91	   A^2 -> H(U1(d, c), b)
28.56/9.91	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.91	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.91	   A^2 -> H(U1(d, c), c)
28.56/9.91	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.91	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.91	   A^2 -> H(U1(d, c), e)
28.56/9.91	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.91	   A^2 -> H(U1(d, a), d)
28.56/9.91	   A^2 -> H(U1(d, a), k)
28.56/9.91	   A^2 -> H(U1(a, e), b)
28.56/9.91	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(a, e), c)
28.56/9.91	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.91	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.91	   A^2 -> H(U1(a, e), e)
28.56/9.91	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(a, k), b)
28.56/9.91	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.91	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.91	   A^2 -> H(U1(a, k), c)
28.56/9.91	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.91	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.91	   A^2 -> H(U1(a, k), e)
28.56/9.91	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(a, c), d)
28.56/9.91	   A^2 -> H(U1(a, c), k)
28.56/9.91	   A^2 -> H(U1(a, d), d)
28.56/9.91	   A^2 -> H(U1(a, d), k)
28.56/9.91	   A^2 -> H(k, U1(c, b))
28.56/9.91	   A^2 -> H(k, U1(d, b))
28.56/9.91	   A^2 -> H(k, U1(b, c))
28.56/9.91	   A^2 -> H(k, U1(b, d))
28.56/9.91	   A^2 -> H(k, U1(c, c))
28.56/9.91	   A^2 -> H(k, f(e))
28.56/9.91	   A^2 -> H(k, f(k))
28.56/9.91	   A^2 -> H(k, U1(d, d))
28.56/9.91	   A^2 -> H(c, U1(e, b))
28.56/9.91	   A^2 -> H(c, U1(k, b))
28.56/9.91	   A^2 -> H(c, U1(c, d))
28.56/9.91	   A^2 -> H(c, U1(d, c))
28.56/9.91	   A^2 -> H(c, U1(b, e))
28.56/9.91	   A^2 -> H(c, U1(b, k))
28.56/9.91	   A^2 -> H(c, U1(e, c))
28.56/9.91	   A^2 -> H(c, U1(k, c))
28.56/9.91	   A^2 -> H(c, U1(c, e))
28.56/9.91	   A^2 -> H(c, U1(c, k))
28.56/9.91	   A^2 -> H(c, U1(e, e))
28.56/9.91	   A^2 -> H(c, U1(k, k))
28.56/9.91	   A^2 -> H(c, U1(k, d))
28.56/9.91	   A^2 -> H(c, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.91	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.91	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.91	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.91	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.91	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.91	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, c), b)
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.91	   A^2 -> H(U1(e, c), e)
28.56/9.91	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.91	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.91	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.91	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.91	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.91	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.91	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.91	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.91	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.91	   A^2 -> H(U1(k, c), b)
28.56/9.91	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.91	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.91	   A^2 -> H(U1(k, c), c)
28.56/9.91	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, e), b)
28.56/9.91	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, e), c)
28.56/9.91	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, e), e)
28.56/9.91	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, k), b)
28.56/9.91	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, k), c)
28.56/9.91	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, k), e)
28.56/9.91	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, c), d)
28.56/9.91	   A^2 -> H(e, U1(e, b))
28.56/9.91	   A^2 -> H(e, U1(c, d))
28.56/9.91	   A^2 -> H(e, U1(d, c))
28.56/9.91	   A^2 -> H(e, U1(b, e))
28.56/9.91	   A^2 -> H(e, U1(b, k))
28.56/9.91	   A^2 -> H(e, U1(e, c))
28.56/9.91	   A^2 -> H(e, U1(c, e))
28.56/9.91	   A^2 -> H(e, U1(c, k))
28.56/9.91	   A^2 -> H(e, U1(e, e))
28.56/9.91	   A^2 -> H(e, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, e), b)
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, e), c)
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.91	
28.56/9.91	The TRS R consists of the following rules:
28.56/9.91	
28.56/9.91	   f(x) -> U1(x, x)
28.56/9.91	   U1(e, x) -> x
28.56/9.91	   a -> c
28.56/9.91	   a -> d
28.56/9.91	   b -> c
28.56/9.91	   b -> d
28.56/9.91	   d -> k
28.56/9.91	   c -> e
28.56/9.91	   c -> k
28.56/9.91	
28.56/9.91	Q is empty.
28.56/9.91	We have to consider all minimal (P,Q,R)-chains.
28.56/9.91	----------------------------------------
28.56/9.91	
28.56/9.91	(1609) TransformationProof (EQUIVALENT)
28.56/9.91	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.91	
28.56/9.91	   (A^2 -> H(e, U1(c, e)),A^2 -> H(e, U1(c, e)))
28.56/9.91	   (A^2 -> H(U1(e, e), U1(e, e)),A^2 -> H(U1(e, e), U1(e, e)))
28.56/9.91	   (A^2 -> H(U1(e, e), U1(k, e)),A^2 -> H(U1(e, e), U1(k, e)))
28.56/9.91	
28.56/9.91	
28.56/9.91	----------------------------------------
28.56/9.91	
28.56/9.91	(1610)
28.56/9.91	Obligation:
28.56/9.91	Q DP problem:
28.56/9.91	The TRS P consists of the following rules:
28.56/9.91	
28.56/9.91	   H(x, x) -> G(x, x, f(k))
28.56/9.91	   G(d, x, x) -> A^2
28.56/9.91	   A^2 -> H(f(c), f(c))
28.56/9.91	   A^2 -> H(f(d), f(d))
28.56/9.91	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.91	   A^2 -> H(f(e), f(e))
28.56/9.91	   A^2 -> H(f(k), f(k))
28.56/9.91	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.91	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.91	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.91	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.91	   A^2 -> H(f(e), b)
28.56/9.91	   A^2 -> H(f(e), U1(e, d))
28.56/9.91	   A^2 -> H(f(e), U1(d, e))
28.56/9.91	   A^2 -> H(f(e), c)
28.56/9.91	   A^2 -> H(f(e), U1(e, k))
28.56/9.91	   A^2 -> H(f(e), U1(k, e))
28.56/9.91	   A^2 -> H(f(e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.91	   A^2 -> H(f(k), b)
28.56/9.91	   A^2 -> H(f(k), U1(e, d))
28.56/9.91	   A^2 -> H(f(k), U1(d, e))
28.56/9.91	   A^2 -> H(f(k), c)
28.56/9.91	   A^2 -> H(f(k), U1(e, k))
28.56/9.91	   A^2 -> H(f(k), U1(k, e))
28.56/9.91	   A^2 -> H(f(k), e)
28.56/9.91	   A^2 -> H(f(c), d)
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.91	   A^2 -> H(U1(k, k), f(e))
28.56/9.91	   A^2 -> H(U1(k, k), f(k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.91	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.91	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.91	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.91	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.91	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.91	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.91	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.91	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.91	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.91	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.91	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.91	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.91	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.91	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.91	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.91	   A^2 -> H(U1(d, d), b)
28.56/9.91	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.91	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.91	   A^2 -> H(U1(d, d), c)
28.56/9.91	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.91	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.91	   A^2 -> H(U1(d, d), e)
28.56/9.91	   A^2 -> H(f(d), d)
28.56/9.91	   A^2 -> H(f(d), k)
28.56/9.91	   A^2 -> H(U1(c, c), c)
28.56/9.91	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.91	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.91	   A^2 -> H(f(c), k)
28.56/9.91	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.91	   A^2 -> H(f(k), U1(k, k))
28.56/9.91	   A^2 -> H(f(e), e)
28.56/9.91	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.91	   A^2 -> H(d, U1(c, b))
28.56/9.91	   A^2 -> H(d, U1(d, b))
28.56/9.91	   A^2 -> H(d, U1(b, c))
28.56/9.91	   A^2 -> H(d, U1(b, d))
28.56/9.91	   A^2 -> H(d, U1(c, c))
28.56/9.91	   A^2 -> H(d, f(e))
28.56/9.91	   A^2 -> H(d, f(k))
28.56/9.91	   A^2 -> H(d, U1(d, d))
28.56/9.91	   A^2 -> H(a, U1(e, b))
28.56/9.91	   A^2 -> H(a, U1(k, b))
28.56/9.91	   A^2 -> H(a, U1(c, d))
28.56/9.91	   A^2 -> H(a, U1(d, c))
28.56/9.91	   A^2 -> H(a, U1(b, e))
28.56/9.91	   A^2 -> H(a, U1(b, k))
28.56/9.91	   A^2 -> H(a, U1(e, c))
28.56/9.91	   A^2 -> H(a, U1(k, c))
28.56/9.91	   A^2 -> H(a, U1(c, e))
28.56/9.91	   A^2 -> H(a, U1(c, k))
28.56/9.91	   A^2 -> H(a, U1(e, e))
28.56/9.91	   A^2 -> H(a, U1(k, k))
28.56/9.91	   A^2 -> H(a, U1(k, d))
28.56/9.91	   A^2 -> H(a, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.91	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.91	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.91	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.91	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.91	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, a), b)
28.56/9.91	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, a), c)
28.56/9.91	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.91	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.91	   A^2 -> H(U1(e, a), e)
28.56/9.91	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, a), b)
28.56/9.91	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.91	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.91	   A^2 -> H(U1(k, a), c)
28.56/9.91	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.91	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.91	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, d), b)
28.56/9.91	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, d), c)
28.56/9.91	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, d), e)
28.56/9.91	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, a), d)
28.56/9.91	   A^2 -> H(U1(c, a), k)
28.56/9.91	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.91	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.91	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.91	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.91	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.91	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.91	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.91	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.91	   A^2 -> H(U1(d, c), b)
28.56/9.91	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.91	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.91	   A^2 -> H(U1(d, c), c)
28.56/9.91	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.91	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.91	   A^2 -> H(U1(d, c), e)
28.56/9.91	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.91	   A^2 -> H(U1(d, a), d)
28.56/9.91	   A^2 -> H(U1(d, a), k)
28.56/9.91	   A^2 -> H(U1(a, e), b)
28.56/9.91	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(a, e), c)
28.56/9.91	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.91	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.91	   A^2 -> H(U1(a, e), e)
28.56/9.91	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(a, k), b)
28.56/9.91	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.91	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.91	   A^2 -> H(U1(a, k), c)
28.56/9.91	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.91	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.91	   A^2 -> H(U1(a, k), e)
28.56/9.91	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(a, c), d)
28.56/9.91	   A^2 -> H(U1(a, c), k)
28.56/9.91	   A^2 -> H(U1(a, d), d)
28.56/9.91	   A^2 -> H(U1(a, d), k)
28.56/9.91	   A^2 -> H(k, U1(c, b))
28.56/9.91	   A^2 -> H(k, U1(d, b))
28.56/9.91	   A^2 -> H(k, U1(b, c))
28.56/9.91	   A^2 -> H(k, U1(b, d))
28.56/9.91	   A^2 -> H(k, U1(c, c))
28.56/9.91	   A^2 -> H(k, f(e))
28.56/9.91	   A^2 -> H(k, f(k))
28.56/9.91	   A^2 -> H(k, U1(d, d))
28.56/9.91	   A^2 -> H(c, U1(e, b))
28.56/9.91	   A^2 -> H(c, U1(k, b))
28.56/9.91	   A^2 -> H(c, U1(c, d))
28.56/9.91	   A^2 -> H(c, U1(d, c))
28.56/9.91	   A^2 -> H(c, U1(b, e))
28.56/9.91	   A^2 -> H(c, U1(b, k))
28.56/9.91	   A^2 -> H(c, U1(e, c))
28.56/9.91	   A^2 -> H(c, U1(k, c))
28.56/9.91	   A^2 -> H(c, U1(c, e))
28.56/9.91	   A^2 -> H(c, U1(c, k))
28.56/9.91	   A^2 -> H(c, U1(e, e))
28.56/9.91	   A^2 -> H(c, U1(k, k))
28.56/9.91	   A^2 -> H(c, U1(k, d))
28.56/9.91	   A^2 -> H(c, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.91	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.91	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.91	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.91	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.91	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.91	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, c), b)
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.91	   A^2 -> H(U1(e, c), e)
28.56/9.91	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.91	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.91	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.91	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.91	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.91	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.91	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.91	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.91	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.91	   A^2 -> H(U1(k, c), b)
28.56/9.91	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.91	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.91	   A^2 -> H(U1(k, c), c)
28.56/9.91	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, e), b)
28.56/9.91	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, e), c)
28.56/9.91	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, e), e)
28.56/9.91	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, k), b)
28.56/9.91	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, k), c)
28.56/9.91	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, k), e)
28.56/9.91	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, c), d)
28.56/9.91	   A^2 -> H(e, U1(e, b))
28.56/9.91	   A^2 -> H(e, U1(c, d))
28.56/9.91	   A^2 -> H(e, U1(d, c))
28.56/9.91	   A^2 -> H(e, U1(b, e))
28.56/9.91	   A^2 -> H(e, U1(b, k))
28.56/9.91	   A^2 -> H(e, U1(e, c))
28.56/9.91	   A^2 -> H(e, U1(c, e))
28.56/9.91	   A^2 -> H(e, U1(c, k))
28.56/9.91	   A^2 -> H(e, U1(e, e))
28.56/9.91	   A^2 -> H(e, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, e), b)
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, e), c)
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.91	
28.56/9.91	The TRS R consists of the following rules:
28.56/9.91	
28.56/9.91	   f(x) -> U1(x, x)
28.56/9.91	   U1(e, x) -> x
28.56/9.91	   a -> c
28.56/9.91	   a -> d
28.56/9.91	   b -> c
28.56/9.91	   b -> d
28.56/9.91	   d -> k
28.56/9.91	   c -> e
28.56/9.91	   c -> k
28.56/9.91	
28.56/9.91	Q is empty.
28.56/9.91	We have to consider all minimal (P,Q,R)-chains.
28.56/9.91	----------------------------------------
28.56/9.91	
28.56/9.91	(1611) TransformationProof (EQUIVALENT)
28.56/9.91	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.91	
28.56/9.91	   (A^2 -> H(e, U1(c, k)),A^2 -> H(e, U1(c, k)))
28.56/9.91	   (A^2 -> H(U1(e, e), U1(e, k)),A^2 -> H(U1(e, e), U1(e, k)))
28.56/9.91	   (A^2 -> H(U1(e, e), U1(k, k)),A^2 -> H(U1(e, e), U1(k, k)))
28.56/9.91	
28.56/9.91	
28.56/9.91	----------------------------------------
28.56/9.91	
28.56/9.91	(1612)
28.56/9.91	Obligation:
28.56/9.91	Q DP problem:
28.56/9.91	The TRS P consists of the following rules:
28.56/9.91	
28.56/9.91	   H(x, x) -> G(x, x, f(k))
28.56/9.91	   G(d, x, x) -> A^2
28.56/9.91	   A^2 -> H(f(c), f(c))
28.56/9.91	   A^2 -> H(f(d), f(d))
28.56/9.91	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.91	   A^2 -> H(f(e), f(e))
28.56/9.91	   A^2 -> H(f(k), f(k))
28.56/9.91	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.91	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.91	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.91	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.91	   A^2 -> H(f(e), b)
28.56/9.91	   A^2 -> H(f(e), U1(e, d))
28.56/9.91	   A^2 -> H(f(e), U1(d, e))
28.56/9.91	   A^2 -> H(f(e), c)
28.56/9.91	   A^2 -> H(f(e), U1(e, k))
28.56/9.91	   A^2 -> H(f(e), U1(k, e))
28.56/9.91	   A^2 -> H(f(e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.91	   A^2 -> H(f(k), b)
28.56/9.91	   A^2 -> H(f(k), U1(e, d))
28.56/9.91	   A^2 -> H(f(k), U1(d, e))
28.56/9.91	   A^2 -> H(f(k), c)
28.56/9.91	   A^2 -> H(f(k), U1(e, k))
28.56/9.91	   A^2 -> H(f(k), U1(k, e))
28.56/9.91	   A^2 -> H(f(k), e)
28.56/9.91	   A^2 -> H(f(c), d)
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.91	   A^2 -> H(U1(k, k), f(e))
28.56/9.91	   A^2 -> H(U1(k, k), f(k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.91	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.91	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.91	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.91	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.91	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.91	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.91	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.91	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.91	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.91	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.91	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.91	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.91	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.91	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.91	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.91	   A^2 -> H(U1(d, d), b)
28.56/9.91	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.91	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.91	   A^2 -> H(U1(d, d), c)
28.56/9.91	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.91	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.91	   A^2 -> H(U1(d, d), e)
28.56/9.91	   A^2 -> H(f(d), d)
28.56/9.91	   A^2 -> H(f(d), k)
28.56/9.91	   A^2 -> H(U1(c, c), c)
28.56/9.91	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.91	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.91	   A^2 -> H(f(c), k)
28.56/9.91	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.91	   A^2 -> H(f(k), U1(k, k))
28.56/9.91	   A^2 -> H(f(e), e)
28.56/9.91	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.91	   A^2 -> H(d, U1(c, b))
28.56/9.91	   A^2 -> H(d, U1(d, b))
28.56/9.91	   A^2 -> H(d, U1(b, c))
28.56/9.91	   A^2 -> H(d, U1(b, d))
28.56/9.91	   A^2 -> H(d, U1(c, c))
28.56/9.91	   A^2 -> H(d, f(e))
28.56/9.91	   A^2 -> H(d, f(k))
28.56/9.91	   A^2 -> H(d, U1(d, d))
28.56/9.91	   A^2 -> H(a, U1(e, b))
28.56/9.91	   A^2 -> H(a, U1(k, b))
28.56/9.91	   A^2 -> H(a, U1(c, d))
28.56/9.91	   A^2 -> H(a, U1(d, c))
28.56/9.91	   A^2 -> H(a, U1(b, e))
28.56/9.91	   A^2 -> H(a, U1(b, k))
28.56/9.91	   A^2 -> H(a, U1(e, c))
28.56/9.91	   A^2 -> H(a, U1(k, c))
28.56/9.91	   A^2 -> H(a, U1(c, e))
28.56/9.91	   A^2 -> H(a, U1(c, k))
28.56/9.91	   A^2 -> H(a, U1(e, e))
28.56/9.91	   A^2 -> H(a, U1(k, k))
28.56/9.91	   A^2 -> H(a, U1(k, d))
28.56/9.91	   A^2 -> H(a, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.91	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.91	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.91	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.91	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.91	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, a), b)
28.56/9.91	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, a), c)
28.56/9.91	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.91	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.91	   A^2 -> H(U1(e, a), e)
28.56/9.91	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, a), b)
28.56/9.91	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.91	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.91	   A^2 -> H(U1(k, a), c)
28.56/9.91	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.91	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.91	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, d), b)
28.56/9.91	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, d), c)
28.56/9.91	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, d), e)
28.56/9.91	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, a), d)
28.56/9.91	   A^2 -> H(U1(c, a), k)
28.56/9.91	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.91	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.91	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.91	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.91	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.91	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.91	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.91	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.91	   A^2 -> H(U1(d, c), b)
28.56/9.91	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.91	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.91	   A^2 -> H(U1(d, c), c)
28.56/9.91	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.91	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.91	   A^2 -> H(U1(d, c), e)
28.56/9.91	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.91	   A^2 -> H(U1(d, a), d)
28.56/9.91	   A^2 -> H(U1(d, a), k)
28.56/9.91	   A^2 -> H(U1(a, e), b)
28.56/9.91	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(a, e), c)
28.56/9.91	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.91	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.91	   A^2 -> H(U1(a, e), e)
28.56/9.91	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(a, k), b)
28.56/9.91	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.91	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.91	   A^2 -> H(U1(a, k), c)
28.56/9.91	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.91	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.91	   A^2 -> H(U1(a, k), e)
28.56/9.91	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(a, c), d)
28.56/9.91	   A^2 -> H(U1(a, c), k)
28.56/9.91	   A^2 -> H(U1(a, d), d)
28.56/9.91	   A^2 -> H(U1(a, d), k)
28.56/9.91	   A^2 -> H(k, U1(c, b))
28.56/9.91	   A^2 -> H(k, U1(d, b))
28.56/9.91	   A^2 -> H(k, U1(b, c))
28.56/9.91	   A^2 -> H(k, U1(b, d))
28.56/9.91	   A^2 -> H(k, U1(c, c))
28.56/9.91	   A^2 -> H(k, f(e))
28.56/9.91	   A^2 -> H(k, f(k))
28.56/9.91	   A^2 -> H(k, U1(d, d))
28.56/9.91	   A^2 -> H(c, U1(e, b))
28.56/9.91	   A^2 -> H(c, U1(k, b))
28.56/9.91	   A^2 -> H(c, U1(c, d))
28.56/9.91	   A^2 -> H(c, U1(d, c))
28.56/9.91	   A^2 -> H(c, U1(b, e))
28.56/9.91	   A^2 -> H(c, U1(b, k))
28.56/9.91	   A^2 -> H(c, U1(e, c))
28.56/9.91	   A^2 -> H(c, U1(k, c))
28.56/9.91	   A^2 -> H(c, U1(c, e))
28.56/9.91	   A^2 -> H(c, U1(c, k))
28.56/9.91	   A^2 -> H(c, U1(e, e))
28.56/9.91	   A^2 -> H(c, U1(k, k))
28.56/9.91	   A^2 -> H(c, U1(k, d))
28.56/9.91	   A^2 -> H(c, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.91	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.91	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.91	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.91	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.91	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.91	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, c), b)
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.91	   A^2 -> H(U1(e, c), e)
28.56/9.91	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.91	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.91	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.91	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.91	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.91	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.91	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.91	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.91	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.91	   A^2 -> H(U1(k, c), b)
28.56/9.91	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.91	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.91	   A^2 -> H(U1(k, c), c)
28.56/9.91	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, e), b)
28.56/9.91	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, e), c)
28.56/9.91	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, e), e)
28.56/9.91	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, k), b)
28.56/9.91	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, k), c)
28.56/9.91	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, k), e)
28.56/9.91	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, c), d)
28.56/9.91	   A^2 -> H(e, U1(e, b))
28.56/9.91	   A^2 -> H(e, U1(c, d))
28.56/9.91	   A^2 -> H(e, U1(d, c))
28.56/9.91	   A^2 -> H(e, U1(b, e))
28.56/9.91	   A^2 -> H(e, U1(b, k))
28.56/9.91	   A^2 -> H(e, U1(e, c))
28.56/9.91	   A^2 -> H(e, U1(c, e))
28.56/9.91	   A^2 -> H(e, U1(c, k))
28.56/9.91	   A^2 -> H(e, U1(e, e))
28.56/9.91	   A^2 -> H(e, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, e), b)
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, e), c)
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.91	
28.56/9.91	The TRS R consists of the following rules:
28.56/9.91	
28.56/9.91	   f(x) -> U1(x, x)
28.56/9.91	   U1(e, x) -> x
28.56/9.91	   a -> c
28.56/9.91	   a -> d
28.56/9.91	   b -> c
28.56/9.91	   b -> d
28.56/9.91	   d -> k
28.56/9.91	   c -> e
28.56/9.91	   c -> k
28.56/9.91	
28.56/9.91	Q is empty.
28.56/9.91	We have to consider all minimal (P,Q,R)-chains.
28.56/9.91	----------------------------------------
28.56/9.91	
28.56/9.91	(1613) TransformationProof (EQUIVALENT)
28.56/9.91	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.91	
28.56/9.91	   (A^2 -> H(e, U1(k, k)),A^2 -> H(e, U1(k, k)))
28.56/9.91	
28.56/9.91	
28.56/9.91	----------------------------------------
28.56/9.91	
28.56/9.91	(1614)
28.56/9.91	Obligation:
28.56/9.91	Q DP problem:
28.56/9.91	The TRS P consists of the following rules:
28.56/9.91	
28.56/9.91	   H(x, x) -> G(x, x, f(k))
28.56/9.91	   G(d, x, x) -> A^2
28.56/9.91	   A^2 -> H(f(c), f(c))
28.56/9.91	   A^2 -> H(f(d), f(d))
28.56/9.91	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.91	   A^2 -> H(f(e), f(e))
28.56/9.91	   A^2 -> H(f(k), f(k))
28.56/9.91	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.91	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.91	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.91	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.91	   A^2 -> H(f(e), b)
28.56/9.91	   A^2 -> H(f(e), U1(e, d))
28.56/9.91	   A^2 -> H(f(e), U1(d, e))
28.56/9.91	   A^2 -> H(f(e), c)
28.56/9.91	   A^2 -> H(f(e), U1(e, k))
28.56/9.91	   A^2 -> H(f(e), U1(k, e))
28.56/9.91	   A^2 -> H(f(e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.91	   A^2 -> H(f(k), b)
28.56/9.91	   A^2 -> H(f(k), U1(e, d))
28.56/9.91	   A^2 -> H(f(k), U1(d, e))
28.56/9.91	   A^2 -> H(f(k), c)
28.56/9.91	   A^2 -> H(f(k), U1(e, k))
28.56/9.91	   A^2 -> H(f(k), U1(k, e))
28.56/9.91	   A^2 -> H(f(k), e)
28.56/9.91	   A^2 -> H(f(c), d)
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.91	   A^2 -> H(U1(k, k), f(e))
28.56/9.91	   A^2 -> H(U1(k, k), f(k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.91	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.91	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.91	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.91	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.91	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.91	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.91	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.91	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.91	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.91	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.91	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.91	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.91	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.91	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.91	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.91	   A^2 -> H(U1(d, d), b)
28.56/9.91	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.91	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.91	   A^2 -> H(U1(d, d), c)
28.56/9.91	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.91	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.91	   A^2 -> H(U1(d, d), e)
28.56/9.91	   A^2 -> H(f(d), d)
28.56/9.91	   A^2 -> H(f(d), k)
28.56/9.91	   A^2 -> H(U1(c, c), c)
28.56/9.91	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.91	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.91	   A^2 -> H(f(c), k)
28.56/9.91	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.91	   A^2 -> H(f(k), U1(k, k))
28.56/9.91	   A^2 -> H(f(e), e)
28.56/9.91	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.91	   A^2 -> H(d, U1(c, b))
28.56/9.91	   A^2 -> H(d, U1(d, b))
28.56/9.91	   A^2 -> H(d, U1(b, c))
28.56/9.91	   A^2 -> H(d, U1(b, d))
28.56/9.91	   A^2 -> H(d, U1(c, c))
28.56/9.91	   A^2 -> H(d, f(e))
28.56/9.91	   A^2 -> H(d, f(k))
28.56/9.91	   A^2 -> H(d, U1(d, d))
28.56/9.91	   A^2 -> H(a, U1(e, b))
28.56/9.91	   A^2 -> H(a, U1(k, b))
28.56/9.91	   A^2 -> H(a, U1(c, d))
28.56/9.91	   A^2 -> H(a, U1(d, c))
28.56/9.91	   A^2 -> H(a, U1(b, e))
28.56/9.91	   A^2 -> H(a, U1(b, k))
28.56/9.91	   A^2 -> H(a, U1(e, c))
28.56/9.91	   A^2 -> H(a, U1(k, c))
28.56/9.91	   A^2 -> H(a, U1(c, e))
28.56/9.91	   A^2 -> H(a, U1(c, k))
28.56/9.91	   A^2 -> H(a, U1(e, e))
28.56/9.91	   A^2 -> H(a, U1(k, k))
28.56/9.91	   A^2 -> H(a, U1(k, d))
28.56/9.91	   A^2 -> H(a, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.91	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.91	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.91	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.91	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.91	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, a), b)
28.56/9.91	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, a), c)
28.56/9.91	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.91	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.91	   A^2 -> H(U1(e, a), e)
28.56/9.91	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, a), b)
28.56/9.91	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.91	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.91	   A^2 -> H(U1(k, a), c)
28.56/9.91	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.91	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.91	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, d), b)
28.56/9.91	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, d), c)
28.56/9.91	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, d), e)
28.56/9.91	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, a), d)
28.56/9.91	   A^2 -> H(U1(c, a), k)
28.56/9.91	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.91	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.91	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.91	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.91	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.91	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.91	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.91	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.91	   A^2 -> H(U1(d, c), b)
28.56/9.91	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.91	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.91	   A^2 -> H(U1(d, c), c)
28.56/9.91	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.91	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.91	   A^2 -> H(U1(d, c), e)
28.56/9.91	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.91	   A^2 -> H(U1(d, a), d)
28.56/9.91	   A^2 -> H(U1(d, a), k)
28.56/9.91	   A^2 -> H(U1(a, e), b)
28.56/9.91	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(a, e), c)
28.56/9.91	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.91	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.91	   A^2 -> H(U1(a, e), e)
28.56/9.91	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(a, k), b)
28.56/9.91	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.91	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.91	   A^2 -> H(U1(a, k), c)
28.56/9.91	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.91	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.91	   A^2 -> H(U1(a, k), e)
28.56/9.91	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(a, c), d)
28.56/9.91	   A^2 -> H(U1(a, c), k)
28.56/9.91	   A^2 -> H(U1(a, d), d)
28.56/9.91	   A^2 -> H(U1(a, d), k)
28.56/9.91	   A^2 -> H(k, U1(c, b))
28.56/9.91	   A^2 -> H(k, U1(d, b))
28.56/9.91	   A^2 -> H(k, U1(b, c))
28.56/9.91	   A^2 -> H(k, U1(b, d))
28.56/9.91	   A^2 -> H(k, U1(c, c))
28.56/9.91	   A^2 -> H(k, f(e))
28.56/9.91	   A^2 -> H(k, f(k))
28.56/9.91	   A^2 -> H(k, U1(d, d))
28.56/9.91	   A^2 -> H(c, U1(e, b))
28.56/9.91	   A^2 -> H(c, U1(k, b))
28.56/9.91	   A^2 -> H(c, U1(c, d))
28.56/9.91	   A^2 -> H(c, U1(d, c))
28.56/9.91	   A^2 -> H(c, U1(b, e))
28.56/9.91	   A^2 -> H(c, U1(b, k))
28.56/9.91	   A^2 -> H(c, U1(e, c))
28.56/9.91	   A^2 -> H(c, U1(k, c))
28.56/9.91	   A^2 -> H(c, U1(c, e))
28.56/9.91	   A^2 -> H(c, U1(c, k))
28.56/9.91	   A^2 -> H(c, U1(e, e))
28.56/9.91	   A^2 -> H(c, U1(k, k))
28.56/9.91	   A^2 -> H(c, U1(k, d))
28.56/9.91	   A^2 -> H(c, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.91	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.91	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.91	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.91	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.91	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.91	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, c), b)
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.91	   A^2 -> H(U1(e, c), e)
28.56/9.91	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.91	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.91	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.91	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.91	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.91	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.91	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.91	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.91	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.91	   A^2 -> H(U1(k, c), b)
28.56/9.91	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.91	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.91	   A^2 -> H(U1(k, c), c)
28.56/9.91	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, e), b)
28.56/9.91	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, e), c)
28.56/9.91	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, e), e)
28.56/9.91	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, k), b)
28.56/9.91	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, k), c)
28.56/9.91	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, k), e)
28.56/9.91	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, c), d)
28.56/9.91	   A^2 -> H(e, U1(e, b))
28.56/9.91	   A^2 -> H(e, U1(c, d))
28.56/9.91	   A^2 -> H(e, U1(d, c))
28.56/9.91	   A^2 -> H(e, U1(b, e))
28.56/9.91	   A^2 -> H(e, U1(b, k))
28.56/9.91	   A^2 -> H(e, U1(e, c))
28.56/9.91	   A^2 -> H(e, U1(c, e))
28.56/9.91	   A^2 -> H(e, U1(c, k))
28.56/9.91	   A^2 -> H(e, U1(e, e))
28.56/9.91	   A^2 -> H(e, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, e), b)
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, e), c)
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.91	   A^2 -> H(e, U1(k, k))
28.56/9.91	
28.56/9.91	The TRS R consists of the following rules:
28.56/9.91	
28.56/9.91	   f(x) -> U1(x, x)
28.56/9.91	   U1(e, x) -> x
28.56/9.91	   a -> c
28.56/9.91	   a -> d
28.56/9.91	   b -> c
28.56/9.91	   b -> d
28.56/9.91	   d -> k
28.56/9.91	   c -> e
28.56/9.91	   c -> k
28.56/9.91	
28.56/9.91	Q is empty.
28.56/9.91	We have to consider all minimal (P,Q,R)-chains.
28.56/9.91	----------------------------------------
28.56/9.91	
28.56/9.91	(1615) DependencyGraphProof (EQUIVALENT)
28.56/9.91	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.91	----------------------------------------
28.56/9.91	
28.56/9.91	(1616)
28.56/9.91	Obligation:
28.56/9.91	Q DP problem:
28.56/9.91	The TRS P consists of the following rules:
28.56/9.91	
28.56/9.91	   G(d, x, x) -> A^2
28.56/9.91	   A^2 -> H(f(c), f(c))
28.56/9.91	   H(x, x) -> G(x, x, f(k))
28.56/9.91	   A^2 -> H(f(d), f(d))
28.56/9.91	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.91	   A^2 -> H(f(e), f(e))
28.56/9.91	   A^2 -> H(f(k), f(k))
28.56/9.91	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.91	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.91	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, e), U1(k, d))
28.56/9.91	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.91	   A^2 -> H(f(e), b)
28.56/9.91	   A^2 -> H(f(e), U1(e, d))
28.56/9.91	   A^2 -> H(f(e), U1(d, e))
28.56/9.91	   A^2 -> H(f(e), c)
28.56/9.91	   A^2 -> H(f(e), U1(e, k))
28.56/9.91	   A^2 -> H(f(e), U1(k, e))
28.56/9.91	   A^2 -> H(f(e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.91	   A^2 -> H(f(k), b)
28.56/9.91	   A^2 -> H(f(k), U1(e, d))
28.56/9.91	   A^2 -> H(f(k), U1(d, e))
28.56/9.91	   A^2 -> H(f(k), c)
28.56/9.91	   A^2 -> H(f(k), U1(e, k))
28.56/9.91	   A^2 -> H(f(k), U1(k, e))
28.56/9.91	   A^2 -> H(f(k), e)
28.56/9.91	   A^2 -> H(f(c), d)
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.91	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.91	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.91	   A^2 -> H(U1(k, k), f(e))
28.56/9.91	   A^2 -> H(U1(k, k), f(k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.91	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.91	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.91	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.91	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.91	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.91	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.91	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.91	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.91	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.91	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.91	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.91	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.91	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.91	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.91	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.91	   A^2 -> H(U1(d, d), b)
28.56/9.91	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.91	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.91	   A^2 -> H(U1(d, d), c)
28.56/9.91	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.91	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.91	   A^2 -> H(U1(d, d), e)
28.56/9.91	   A^2 -> H(f(d), d)
28.56/9.91	   A^2 -> H(f(d), k)
28.56/9.91	   A^2 -> H(U1(c, c), c)
28.56/9.91	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.91	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.91	   A^2 -> H(f(c), k)
28.56/9.91	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.91	   A^2 -> H(f(k), U1(k, k))
28.56/9.91	   A^2 -> H(f(e), e)
28.56/9.91	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.91	   A^2 -> H(d, U1(c, b))
28.56/9.91	   A^2 -> H(d, U1(d, b))
28.56/9.91	   A^2 -> H(d, U1(b, c))
28.56/9.91	   A^2 -> H(d, U1(b, d))
28.56/9.91	   A^2 -> H(d, U1(c, c))
28.56/9.91	   A^2 -> H(d, f(e))
28.56/9.91	   A^2 -> H(d, f(k))
28.56/9.91	   A^2 -> H(d, U1(d, d))
28.56/9.91	   A^2 -> H(a, U1(e, b))
28.56/9.91	   A^2 -> H(a, U1(k, b))
28.56/9.91	   A^2 -> H(a, U1(c, d))
28.56/9.91	   A^2 -> H(a, U1(d, c))
28.56/9.91	   A^2 -> H(a, U1(b, e))
28.56/9.91	   A^2 -> H(a, U1(b, k))
28.56/9.91	   A^2 -> H(a, U1(e, c))
28.56/9.91	   A^2 -> H(a, U1(k, c))
28.56/9.91	   A^2 -> H(a, U1(c, e))
28.56/9.91	   A^2 -> H(a, U1(c, k))
28.56/9.91	   A^2 -> H(a, U1(e, e))
28.56/9.91	   A^2 -> H(a, U1(k, k))
28.56/9.91	   A^2 -> H(a, U1(k, d))
28.56/9.91	   A^2 -> H(a, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.91	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.91	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.91	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.91	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.91	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.91	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, a), b)
28.56/9.91	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, a), c)
28.56/9.91	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.91	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.91	   A^2 -> H(U1(e, a), e)
28.56/9.91	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, a), b)
28.56/9.91	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.91	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.91	   A^2 -> H(U1(k, a), c)
28.56/9.91	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.91	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.91	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, d), b)
28.56/9.91	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, d), c)
28.56/9.91	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, d), e)
28.56/9.91	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, a), d)
28.56/9.91	   A^2 -> H(U1(c, a), k)
28.56/9.91	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.91	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.91	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.91	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.91	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.91	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.91	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.91	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.91	   A^2 -> H(U1(d, c), b)
28.56/9.91	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.91	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.91	   A^2 -> H(U1(d, c), c)
28.56/9.91	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.91	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.91	   A^2 -> H(U1(d, c), e)
28.56/9.91	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.91	   A^2 -> H(U1(d, a), d)
28.56/9.91	   A^2 -> H(U1(d, a), k)
28.56/9.91	   A^2 -> H(U1(a, e), b)
28.56/9.91	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(a, e), c)
28.56/9.91	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.91	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.91	   A^2 -> H(U1(a, e), e)
28.56/9.91	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(a, k), b)
28.56/9.91	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.91	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.91	   A^2 -> H(U1(a, k), c)
28.56/9.91	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.91	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.91	   A^2 -> H(U1(a, k), e)
28.56/9.91	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(a, c), d)
28.56/9.91	   A^2 -> H(U1(a, c), k)
28.56/9.91	   A^2 -> H(U1(a, d), d)
28.56/9.91	   A^2 -> H(U1(a, d), k)
28.56/9.91	   A^2 -> H(k, U1(c, b))
28.56/9.91	   A^2 -> H(k, U1(d, b))
28.56/9.91	   A^2 -> H(k, U1(b, c))
28.56/9.91	   A^2 -> H(k, U1(b, d))
28.56/9.91	   A^2 -> H(k, U1(c, c))
28.56/9.91	   A^2 -> H(k, f(e))
28.56/9.91	   A^2 -> H(k, f(k))
28.56/9.91	   A^2 -> H(k, U1(d, d))
28.56/9.91	   A^2 -> H(c, U1(e, b))
28.56/9.91	   A^2 -> H(c, U1(k, b))
28.56/9.91	   A^2 -> H(c, U1(c, d))
28.56/9.91	   A^2 -> H(c, U1(d, c))
28.56/9.91	   A^2 -> H(c, U1(b, e))
28.56/9.91	   A^2 -> H(c, U1(b, k))
28.56/9.91	   A^2 -> H(c, U1(e, c))
28.56/9.91	   A^2 -> H(c, U1(k, c))
28.56/9.91	   A^2 -> H(c, U1(c, e))
28.56/9.91	   A^2 -> H(c, U1(c, k))
28.56/9.91	   A^2 -> H(c, U1(e, e))
28.56/9.91	   A^2 -> H(c, U1(k, k))
28.56/9.91	   A^2 -> H(c, U1(k, d))
28.56/9.91	   A^2 -> H(c, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.91	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.91	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.91	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.91	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.91	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.91	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, c), b)
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.91	   A^2 -> H(U1(e, c), e)
28.56/9.91	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.91	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.91	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.91	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.91	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.91	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.91	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.91	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.91	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.91	   A^2 -> H(U1(k, c), b)
28.56/9.91	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.91	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.91	   A^2 -> H(U1(k, c), c)
28.56/9.91	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, e), b)
28.56/9.91	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, e), c)
28.56/9.91	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, e), e)
28.56/9.91	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, k), b)
28.56/9.91	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.91	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.91	   A^2 -> H(U1(c, k), c)
28.56/9.91	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.91	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.91	   A^2 -> H(U1(c, k), e)
28.56/9.91	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.91	   A^2 -> H(U1(c, c), d)
28.56/9.91	   A^2 -> H(e, U1(e, b))
28.56/9.91	   A^2 -> H(e, U1(c, d))
28.56/9.91	   A^2 -> H(e, U1(d, c))
28.56/9.91	   A^2 -> H(e, U1(b, e))
28.56/9.91	   A^2 -> H(e, U1(b, k))
28.56/9.91	   A^2 -> H(e, U1(e, c))
28.56/9.91	   A^2 -> H(e, U1(c, e))
28.56/9.91	   A^2 -> H(e, U1(c, k))
28.56/9.91	   A^2 -> H(e, U1(e, e))
28.56/9.91	   A^2 -> H(e, U1(d, k))
28.56/9.91	   A^2 -> H(U1(e, e), b)
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.91	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.91	   A^2 -> H(U1(e, e), c)
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.91	
28.56/9.91	The TRS R consists of the following rules:
28.56/9.91	
28.56/9.91	   f(x) -> U1(x, x)
28.56/9.91	   U1(e, x) -> x
28.56/9.91	   a -> c
28.56/9.91	   a -> d
28.56/9.91	   b -> c
28.56/9.91	   b -> d
28.56/9.91	   d -> k
28.56/9.91	   c -> e
28.56/9.91	   c -> k
28.56/9.91	
28.56/9.91	Q is empty.
28.56/9.91	We have to consider all minimal (P,Q,R)-chains.
28.56/9.91	----------------------------------------
28.56/9.91	
28.56/9.91	(1617) TransformationProof (EQUIVALENT)
28.56/9.91	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.91	
28.56/9.91	   (A^2 -> H(e, U1(k, d)),A^2 -> H(e, U1(k, d)))
28.56/9.91	   (A^2 -> H(U1(e, e), U1(k, k)),A^2 -> H(U1(e, e), U1(k, k)))
28.56/9.91	
28.56/9.91	
28.56/9.91	----------------------------------------
28.56/9.91	
28.56/9.91	(1618)
28.56/9.91	Obligation:
28.56/9.91	Q DP problem:
28.56/9.91	The TRS P consists of the following rules:
28.56/9.91	
28.56/9.91	   G(d, x, x) -> A^2
28.56/9.91	   A^2 -> H(f(c), f(c))
28.56/9.91	   H(x, x) -> G(x, x, f(k))
28.56/9.91	   A^2 -> H(f(d), f(d))
28.56/9.91	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.91	   A^2 -> H(f(e), f(e))
28.56/9.91	   A^2 -> H(f(k), f(k))
28.56/9.91	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.91	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.91	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.91	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.91	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.91	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.91	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.91	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.91	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.91	   A^2 -> H(f(e), b)
28.56/9.91	   A^2 -> H(f(e), U1(e, d))
28.56/9.91	   A^2 -> H(f(e), U1(d, e))
28.56/9.91	   A^2 -> H(f(e), c)
28.56/9.91	   A^2 -> H(f(e), U1(e, k))
28.56/9.91	   A^2 -> H(f(e), U1(k, e))
28.56/9.91	   A^2 -> H(f(e), U1(k, k))
28.56/9.91	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.91	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.92	   A^2 -> H(f(k), b)
28.56/9.92	   A^2 -> H(f(k), U1(e, d))
28.56/9.92	   A^2 -> H(f(k), U1(d, e))
28.56/9.92	   A^2 -> H(f(k), c)
28.56/9.92	   A^2 -> H(f(k), U1(e, k))
28.56/9.92	   A^2 -> H(f(k), U1(k, e))
28.56/9.92	   A^2 -> H(f(k), e)
28.56/9.92	   A^2 -> H(f(c), d)
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.92	   A^2 -> H(U1(k, k), f(e))
28.56/9.92	   A^2 -> H(U1(k, k), f(k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, d), b)
28.56/9.92	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.92	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.92	   A^2 -> H(U1(d, d), c)
28.56/9.92	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.92	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.92	   A^2 -> H(U1(d, d), e)
28.56/9.92	   A^2 -> H(f(d), d)
28.56/9.92	   A^2 -> H(f(d), k)
28.56/9.92	   A^2 -> H(U1(c, c), c)
28.56/9.92	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.92	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.92	   A^2 -> H(f(c), k)
28.56/9.92	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.92	   A^2 -> H(f(k), U1(k, k))
28.56/9.92	   A^2 -> H(f(e), e)
28.56/9.92	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.92	   A^2 -> H(d, U1(c, b))
28.56/9.92	   A^2 -> H(d, U1(d, b))
28.56/9.92	   A^2 -> H(d, U1(b, c))
28.56/9.92	   A^2 -> H(d, U1(b, d))
28.56/9.92	   A^2 -> H(d, U1(c, c))
28.56/9.92	   A^2 -> H(d, f(e))
28.56/9.92	   A^2 -> H(d, f(k))
28.56/9.92	   A^2 -> H(d, U1(d, d))
28.56/9.92	   A^2 -> H(a, U1(e, b))
28.56/9.92	   A^2 -> H(a, U1(k, b))
28.56/9.92	   A^2 -> H(a, U1(c, d))
28.56/9.92	   A^2 -> H(a, U1(d, c))
28.56/9.92	   A^2 -> H(a, U1(b, e))
28.56/9.92	   A^2 -> H(a, U1(b, k))
28.56/9.92	   A^2 -> H(a, U1(e, c))
28.56/9.92	   A^2 -> H(a, U1(k, c))
28.56/9.92	   A^2 -> H(a, U1(c, e))
28.56/9.92	   A^2 -> H(a, U1(c, k))
28.56/9.92	   A^2 -> H(a, U1(e, e))
28.56/9.92	   A^2 -> H(a, U1(k, k))
28.56/9.92	   A^2 -> H(a, U1(k, d))
28.56/9.92	   A^2 -> H(a, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.92	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, a), b)
28.56/9.92	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, a), c)
28.56/9.92	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.92	   A^2 -> H(U1(e, a), e)
28.56/9.92	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, a), b)
28.56/9.92	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.92	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.92	   A^2 -> H(U1(k, a), c)
28.56/9.92	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.92	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.92	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, d), b)
28.56/9.92	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, d), c)
28.56/9.92	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, d), e)
28.56/9.92	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, a), d)
28.56/9.92	   A^2 -> H(U1(c, a), k)
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.92	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, c), b)
28.56/9.92	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(d, c), c)
28.56/9.92	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(d, c), e)
28.56/9.92	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, a), d)
28.56/9.92	   A^2 -> H(U1(d, a), k)
28.56/9.92	   A^2 -> H(U1(a, e), b)
28.56/9.92	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.92	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.92	   A^2 -> H(U1(a, e), c)
28.56/9.92	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.92	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.92	   A^2 -> H(U1(a, e), e)
28.56/9.92	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(a, k), b)
28.56/9.92	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.92	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.92	   A^2 -> H(U1(a, k), c)
28.56/9.92	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.92	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.92	   A^2 -> H(U1(a, k), e)
28.56/9.92	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(a, c), d)
28.56/9.92	   A^2 -> H(U1(a, c), k)
28.56/9.92	   A^2 -> H(U1(a, d), d)
28.56/9.92	   A^2 -> H(U1(a, d), k)
28.56/9.92	   A^2 -> H(k, U1(c, b))
28.56/9.92	   A^2 -> H(k, U1(d, b))
28.56/9.92	   A^2 -> H(k, U1(b, c))
28.56/9.92	   A^2 -> H(k, U1(b, d))
28.56/9.92	   A^2 -> H(k, U1(c, c))
28.56/9.92	   A^2 -> H(k, f(e))
28.56/9.92	   A^2 -> H(k, f(k))
28.56/9.92	   A^2 -> H(k, U1(d, d))
28.56/9.92	   A^2 -> H(c, U1(e, b))
28.56/9.92	   A^2 -> H(c, U1(k, b))
28.56/9.92	   A^2 -> H(c, U1(c, d))
28.56/9.92	   A^2 -> H(c, U1(d, c))
28.56/9.92	   A^2 -> H(c, U1(b, e))
28.56/9.92	   A^2 -> H(c, U1(b, k))
28.56/9.92	   A^2 -> H(c, U1(e, c))
28.56/9.92	   A^2 -> H(c, U1(k, c))
28.56/9.92	   A^2 -> H(c, U1(c, e))
28.56/9.92	   A^2 -> H(c, U1(c, k))
28.56/9.92	   A^2 -> H(c, U1(e, e))
28.56/9.92	   A^2 -> H(c, U1(k, k))
28.56/9.92	   A^2 -> H(c, U1(k, d))
28.56/9.92	   A^2 -> H(c, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, c), b)
28.56/9.92	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, c), e)
28.56/9.92	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.92	   A^2 -> H(U1(k, c), b)
28.56/9.92	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(k, c), c)
28.56/9.92	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, e), b)
28.56/9.92	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, e), c)
28.56/9.92	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, e), e)
28.56/9.92	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, k), b)
28.56/9.92	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, k), c)
28.56/9.92	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, k), e)
28.56/9.92	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, c), d)
28.56/9.92	   A^2 -> H(e, U1(e, b))
28.56/9.92	   A^2 -> H(e, U1(c, d))
28.56/9.92	   A^2 -> H(e, U1(d, c))
28.56/9.92	   A^2 -> H(e, U1(b, e))
28.56/9.92	   A^2 -> H(e, U1(b, k))
28.56/9.92	   A^2 -> H(e, U1(e, c))
28.56/9.92	   A^2 -> H(e, U1(c, e))
28.56/9.92	   A^2 -> H(e, U1(c, k))
28.56/9.92	   A^2 -> H(e, U1(e, e))
28.56/9.92	   A^2 -> H(e, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, e), b)
28.56/9.92	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, e), c)
28.56/9.92	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.92	   A^2 -> H(e, U1(k, d))
28.56/9.92	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.92	
28.56/9.92	The TRS R consists of the following rules:
28.56/9.92	
28.56/9.92	   f(x) -> U1(x, x)
28.56/9.92	   U1(e, x) -> x
28.56/9.92	   a -> c
28.56/9.92	   a -> d
28.56/9.92	   b -> c
28.56/9.92	   b -> d
28.56/9.92	   d -> k
28.56/9.92	   c -> e
28.56/9.92	   c -> k
28.56/9.92	
28.56/9.92	Q is empty.
28.56/9.92	We have to consider all minimal (P,Q,R)-chains.
28.56/9.92	----------------------------------------
28.56/9.92	
28.56/9.92	(1619) DependencyGraphProof (EQUIVALENT)
28.56/9.92	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.92	----------------------------------------
28.56/9.92	
28.56/9.92	(1620)
28.56/9.92	Obligation:
28.56/9.92	Q DP problem:
28.56/9.92	The TRS P consists of the following rules:
28.56/9.92	
28.56/9.92	   A^2 -> H(f(c), f(c))
28.56/9.92	   H(x, x) -> G(x, x, f(k))
28.56/9.92	   G(d, x, x) -> A^2
28.56/9.92	   A^2 -> H(f(d), f(d))
28.56/9.92	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.92	   A^2 -> H(f(e), f(e))
28.56/9.92	   A^2 -> H(f(k), f(k))
28.56/9.92	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.92	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.92	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.92	   A^2 -> H(U1(e, e), U1(d, k))
28.56/9.92	   A^2 -> H(f(e), b)
28.56/9.92	   A^2 -> H(f(e), U1(e, d))
28.56/9.92	   A^2 -> H(f(e), U1(d, e))
28.56/9.92	   A^2 -> H(f(e), c)
28.56/9.92	   A^2 -> H(f(e), U1(e, k))
28.56/9.92	   A^2 -> H(f(e), U1(k, e))
28.56/9.92	   A^2 -> H(f(e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.92	   A^2 -> H(f(k), b)
28.56/9.92	   A^2 -> H(f(k), U1(e, d))
28.56/9.92	   A^2 -> H(f(k), U1(d, e))
28.56/9.92	   A^2 -> H(f(k), c)
28.56/9.92	   A^2 -> H(f(k), U1(e, k))
28.56/9.92	   A^2 -> H(f(k), U1(k, e))
28.56/9.92	   A^2 -> H(f(k), e)
28.56/9.92	   A^2 -> H(f(c), d)
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.92	   A^2 -> H(U1(k, k), f(e))
28.56/9.92	   A^2 -> H(U1(k, k), f(k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, d), b)
28.56/9.92	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.92	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.92	   A^2 -> H(U1(d, d), c)
28.56/9.92	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.92	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.92	   A^2 -> H(U1(d, d), e)
28.56/9.92	   A^2 -> H(f(d), d)
28.56/9.92	   A^2 -> H(f(d), k)
28.56/9.92	   A^2 -> H(U1(c, c), c)
28.56/9.92	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.92	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.92	   A^2 -> H(f(c), k)
28.56/9.92	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.92	   A^2 -> H(f(k), U1(k, k))
28.56/9.92	   A^2 -> H(f(e), e)
28.56/9.92	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.92	   A^2 -> H(d, U1(c, b))
28.56/9.92	   A^2 -> H(d, U1(d, b))
28.56/9.92	   A^2 -> H(d, U1(b, c))
28.56/9.92	   A^2 -> H(d, U1(b, d))
28.56/9.92	   A^2 -> H(d, U1(c, c))
28.56/9.92	   A^2 -> H(d, f(e))
28.56/9.92	   A^2 -> H(d, f(k))
28.56/9.92	   A^2 -> H(d, U1(d, d))
28.56/9.92	   A^2 -> H(a, U1(e, b))
28.56/9.92	   A^2 -> H(a, U1(k, b))
28.56/9.92	   A^2 -> H(a, U1(c, d))
28.56/9.92	   A^2 -> H(a, U1(d, c))
28.56/9.92	   A^2 -> H(a, U1(b, e))
28.56/9.92	   A^2 -> H(a, U1(b, k))
28.56/9.92	   A^2 -> H(a, U1(e, c))
28.56/9.92	   A^2 -> H(a, U1(k, c))
28.56/9.92	   A^2 -> H(a, U1(c, e))
28.56/9.92	   A^2 -> H(a, U1(c, k))
28.56/9.92	   A^2 -> H(a, U1(e, e))
28.56/9.92	   A^2 -> H(a, U1(k, k))
28.56/9.92	   A^2 -> H(a, U1(k, d))
28.56/9.92	   A^2 -> H(a, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.92	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, a), b)
28.56/9.92	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, a), c)
28.56/9.92	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.92	   A^2 -> H(U1(e, a), e)
28.56/9.92	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, a), b)
28.56/9.92	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.92	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.92	   A^2 -> H(U1(k, a), c)
28.56/9.92	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.92	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.92	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, d), b)
28.56/9.92	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, d), c)
28.56/9.92	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, d), e)
28.56/9.92	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, a), d)
28.56/9.92	   A^2 -> H(U1(c, a), k)
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.92	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, c), b)
28.56/9.92	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(d, c), c)
28.56/9.92	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(d, c), e)
28.56/9.92	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, a), d)
28.56/9.92	   A^2 -> H(U1(d, a), k)
28.56/9.92	   A^2 -> H(U1(a, e), b)
28.56/9.92	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.92	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.92	   A^2 -> H(U1(a, e), c)
28.56/9.92	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.92	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.92	   A^2 -> H(U1(a, e), e)
28.56/9.92	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(a, k), b)
28.56/9.92	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.92	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.92	   A^2 -> H(U1(a, k), c)
28.56/9.92	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.92	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.92	   A^2 -> H(U1(a, k), e)
28.56/9.92	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(a, c), d)
28.56/9.92	   A^2 -> H(U1(a, c), k)
28.56/9.92	   A^2 -> H(U1(a, d), d)
28.56/9.92	   A^2 -> H(U1(a, d), k)
28.56/9.92	   A^2 -> H(k, U1(c, b))
28.56/9.92	   A^2 -> H(k, U1(d, b))
28.56/9.92	   A^2 -> H(k, U1(b, c))
28.56/9.92	   A^2 -> H(k, U1(b, d))
28.56/9.92	   A^2 -> H(k, U1(c, c))
28.56/9.92	   A^2 -> H(k, f(e))
28.56/9.92	   A^2 -> H(k, f(k))
28.56/9.92	   A^2 -> H(k, U1(d, d))
28.56/9.92	   A^2 -> H(c, U1(e, b))
28.56/9.92	   A^2 -> H(c, U1(k, b))
28.56/9.92	   A^2 -> H(c, U1(c, d))
28.56/9.92	   A^2 -> H(c, U1(d, c))
28.56/9.92	   A^2 -> H(c, U1(b, e))
28.56/9.92	   A^2 -> H(c, U1(b, k))
28.56/9.92	   A^2 -> H(c, U1(e, c))
28.56/9.92	   A^2 -> H(c, U1(k, c))
28.56/9.92	   A^2 -> H(c, U1(c, e))
28.56/9.92	   A^2 -> H(c, U1(c, k))
28.56/9.92	   A^2 -> H(c, U1(e, e))
28.56/9.92	   A^2 -> H(c, U1(k, k))
28.56/9.92	   A^2 -> H(c, U1(k, d))
28.56/9.92	   A^2 -> H(c, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, c), b)
28.56/9.92	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, c), e)
28.56/9.92	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.92	   A^2 -> H(U1(k, c), b)
28.56/9.92	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(k, c), c)
28.56/9.92	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, e), b)
28.56/9.92	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, e), c)
28.56/9.92	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, e), e)
28.56/9.92	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, k), b)
28.56/9.92	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, k), c)
28.56/9.92	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, k), e)
28.56/9.92	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, c), d)
28.56/9.92	   A^2 -> H(e, U1(e, b))
28.56/9.92	   A^2 -> H(e, U1(c, d))
28.56/9.92	   A^2 -> H(e, U1(d, c))
28.56/9.92	   A^2 -> H(e, U1(b, e))
28.56/9.92	   A^2 -> H(e, U1(b, k))
28.56/9.92	   A^2 -> H(e, U1(e, c))
28.56/9.92	   A^2 -> H(e, U1(c, e))
28.56/9.92	   A^2 -> H(e, U1(c, k))
28.56/9.92	   A^2 -> H(e, U1(e, e))
28.56/9.92	   A^2 -> H(e, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, e), b)
28.56/9.92	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, e), c)
28.56/9.92	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.92	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.92	
28.56/9.92	The TRS R consists of the following rules:
28.56/9.92	
28.56/9.92	   f(x) -> U1(x, x)
28.56/9.92	   U1(e, x) -> x
28.56/9.92	   a -> c
28.56/9.92	   a -> d
28.56/9.92	   b -> c
28.56/9.92	   b -> d
28.56/9.92	   d -> k
28.56/9.92	   c -> e
28.56/9.92	   c -> k
28.56/9.92	
28.56/9.92	Q is empty.
28.56/9.92	We have to consider all minimal (P,Q,R)-chains.
28.56/9.92	----------------------------------------
28.56/9.92	
28.56/9.92	(1621) TransformationProof (EQUIVALENT)
28.56/9.92	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.92	
28.56/9.92	   (A^2 -> H(e, U1(d, k)),A^2 -> H(e, U1(d, k)))
28.56/9.92	   (A^2 -> H(U1(e, e), U1(k, k)),A^2 -> H(U1(e, e), U1(k, k)))
28.56/9.92	
28.56/9.92	
28.56/9.92	----------------------------------------
28.56/9.92	
28.56/9.92	(1622)
28.56/9.92	Obligation:
28.56/9.92	Q DP problem:
28.56/9.92	The TRS P consists of the following rules:
28.56/9.92	
28.56/9.92	   A^2 -> H(f(c), f(c))
28.56/9.92	   H(x, x) -> G(x, x, f(k))
28.56/9.92	   G(d, x, x) -> A^2
28.56/9.92	   A^2 -> H(f(d), f(d))
28.56/9.92	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.92	   A^2 -> H(f(e), f(e))
28.56/9.92	   A^2 -> H(f(k), f(k))
28.56/9.92	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.92	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.92	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.92	   A^2 -> H(f(e), b)
28.56/9.92	   A^2 -> H(f(e), U1(e, d))
28.56/9.92	   A^2 -> H(f(e), U1(d, e))
28.56/9.92	   A^2 -> H(f(e), c)
28.56/9.92	   A^2 -> H(f(e), U1(e, k))
28.56/9.92	   A^2 -> H(f(e), U1(k, e))
28.56/9.92	   A^2 -> H(f(e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.92	   A^2 -> H(f(k), b)
28.56/9.92	   A^2 -> H(f(k), U1(e, d))
28.56/9.92	   A^2 -> H(f(k), U1(d, e))
28.56/9.92	   A^2 -> H(f(k), c)
28.56/9.92	   A^2 -> H(f(k), U1(e, k))
28.56/9.92	   A^2 -> H(f(k), U1(k, e))
28.56/9.92	   A^2 -> H(f(k), e)
28.56/9.92	   A^2 -> H(f(c), d)
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.92	   A^2 -> H(U1(k, k), f(e))
28.56/9.92	   A^2 -> H(U1(k, k), f(k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, d), b)
28.56/9.92	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.92	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.92	   A^2 -> H(U1(d, d), c)
28.56/9.92	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.92	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.92	   A^2 -> H(U1(d, d), e)
28.56/9.92	   A^2 -> H(f(d), d)
28.56/9.92	   A^2 -> H(f(d), k)
28.56/9.92	   A^2 -> H(U1(c, c), c)
28.56/9.92	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.92	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.92	   A^2 -> H(f(c), k)
28.56/9.92	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.92	   A^2 -> H(f(k), U1(k, k))
28.56/9.92	   A^2 -> H(f(e), e)
28.56/9.92	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.92	   A^2 -> H(d, U1(c, b))
28.56/9.92	   A^2 -> H(d, U1(d, b))
28.56/9.92	   A^2 -> H(d, U1(b, c))
28.56/9.92	   A^2 -> H(d, U1(b, d))
28.56/9.92	   A^2 -> H(d, U1(c, c))
28.56/9.92	   A^2 -> H(d, f(e))
28.56/9.92	   A^2 -> H(d, f(k))
28.56/9.92	   A^2 -> H(d, U1(d, d))
28.56/9.92	   A^2 -> H(a, U1(e, b))
28.56/9.92	   A^2 -> H(a, U1(k, b))
28.56/9.92	   A^2 -> H(a, U1(c, d))
28.56/9.92	   A^2 -> H(a, U1(d, c))
28.56/9.92	   A^2 -> H(a, U1(b, e))
28.56/9.92	   A^2 -> H(a, U1(b, k))
28.56/9.92	   A^2 -> H(a, U1(e, c))
28.56/9.92	   A^2 -> H(a, U1(k, c))
28.56/9.92	   A^2 -> H(a, U1(c, e))
28.56/9.92	   A^2 -> H(a, U1(c, k))
28.56/9.92	   A^2 -> H(a, U1(e, e))
28.56/9.92	   A^2 -> H(a, U1(k, k))
28.56/9.92	   A^2 -> H(a, U1(k, d))
28.56/9.92	   A^2 -> H(a, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.92	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, a), b)
28.56/9.92	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, a), c)
28.56/9.92	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.92	   A^2 -> H(U1(e, a), e)
28.56/9.92	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, a), b)
28.56/9.92	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.92	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.92	   A^2 -> H(U1(k, a), c)
28.56/9.92	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.92	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.92	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, d), b)
28.56/9.92	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, d), c)
28.56/9.92	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, d), e)
28.56/9.92	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, a), d)
28.56/9.92	   A^2 -> H(U1(c, a), k)
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.92	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, c), b)
28.56/9.92	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(d, c), c)
28.56/9.92	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(d, c), e)
28.56/9.92	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, a), d)
28.56/9.92	   A^2 -> H(U1(d, a), k)
28.56/9.92	   A^2 -> H(U1(a, e), b)
28.56/9.92	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.92	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.92	   A^2 -> H(U1(a, e), c)
28.56/9.92	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.92	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.92	   A^2 -> H(U1(a, e), e)
28.56/9.92	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(a, k), b)
28.56/9.92	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.92	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.92	   A^2 -> H(U1(a, k), c)
28.56/9.92	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.92	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.92	   A^2 -> H(U1(a, k), e)
28.56/9.92	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(a, c), d)
28.56/9.92	   A^2 -> H(U1(a, c), k)
28.56/9.92	   A^2 -> H(U1(a, d), d)
28.56/9.92	   A^2 -> H(U1(a, d), k)
28.56/9.92	   A^2 -> H(k, U1(c, b))
28.56/9.92	   A^2 -> H(k, U1(d, b))
28.56/9.92	   A^2 -> H(k, U1(b, c))
28.56/9.92	   A^2 -> H(k, U1(b, d))
28.56/9.92	   A^2 -> H(k, U1(c, c))
28.56/9.92	   A^2 -> H(k, f(e))
28.56/9.92	   A^2 -> H(k, f(k))
28.56/9.92	   A^2 -> H(k, U1(d, d))
28.56/9.92	   A^2 -> H(c, U1(e, b))
28.56/9.92	   A^2 -> H(c, U1(k, b))
28.56/9.92	   A^2 -> H(c, U1(c, d))
28.56/9.92	   A^2 -> H(c, U1(d, c))
28.56/9.92	   A^2 -> H(c, U1(b, e))
28.56/9.92	   A^2 -> H(c, U1(b, k))
28.56/9.92	   A^2 -> H(c, U1(e, c))
28.56/9.92	   A^2 -> H(c, U1(k, c))
28.56/9.92	   A^2 -> H(c, U1(c, e))
28.56/9.92	   A^2 -> H(c, U1(c, k))
28.56/9.92	   A^2 -> H(c, U1(e, e))
28.56/9.92	   A^2 -> H(c, U1(k, k))
28.56/9.92	   A^2 -> H(c, U1(k, d))
28.56/9.92	   A^2 -> H(c, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, c), b)
28.56/9.92	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, c), e)
28.56/9.92	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.92	   A^2 -> H(U1(k, c), b)
28.56/9.92	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(k, c), c)
28.56/9.92	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, e), b)
28.56/9.92	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, e), c)
28.56/9.92	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, e), e)
28.56/9.92	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, k), b)
28.56/9.92	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, k), c)
28.56/9.92	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, k), e)
28.56/9.92	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, c), d)
28.56/9.92	   A^2 -> H(e, U1(e, b))
28.56/9.92	   A^2 -> H(e, U1(c, d))
28.56/9.92	   A^2 -> H(e, U1(d, c))
28.56/9.92	   A^2 -> H(e, U1(b, e))
28.56/9.92	   A^2 -> H(e, U1(b, k))
28.56/9.92	   A^2 -> H(e, U1(e, c))
28.56/9.92	   A^2 -> H(e, U1(c, e))
28.56/9.92	   A^2 -> H(e, U1(c, k))
28.56/9.92	   A^2 -> H(e, U1(e, e))
28.56/9.92	   A^2 -> H(e, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, e), b)
28.56/9.92	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, e), c)
28.56/9.92	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.92	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.92	
28.56/9.92	The TRS R consists of the following rules:
28.56/9.92	
28.56/9.92	   f(x) -> U1(x, x)
28.56/9.92	   U1(e, x) -> x
28.56/9.92	   a -> c
28.56/9.92	   a -> d
28.56/9.92	   b -> c
28.56/9.92	   b -> d
28.56/9.92	   d -> k
28.56/9.92	   c -> e
28.56/9.92	   c -> k
28.56/9.92	
28.56/9.92	Q is empty.
28.56/9.92	We have to consider all minimal (P,Q,R)-chains.
28.56/9.92	----------------------------------------
28.56/9.92	
28.56/9.92	(1623) TransformationProof (EQUIVALENT)
28.56/9.92	By narrowing [LPAR04] the rule A^2 -> H(f(e), b) at position [] we obtained the following new rules [LPAR04]:
28.56/9.92	
28.56/9.92	   (A^2 -> H(U1(e, e), b),A^2 -> H(U1(e, e), b))
28.56/9.92	   (A^2 -> H(f(e), c),A^2 -> H(f(e), c))
28.56/9.92	   (A^2 -> H(f(e), d),A^2 -> H(f(e), d))
28.56/9.92	
28.56/9.92	
28.56/9.92	----------------------------------------
28.56/9.92	
28.56/9.92	(1624)
28.56/9.92	Obligation:
28.56/9.92	Q DP problem:
28.56/9.92	The TRS P consists of the following rules:
28.56/9.92	
28.56/9.92	   A^2 -> H(f(c), f(c))
28.56/9.92	   H(x, x) -> G(x, x, f(k))
28.56/9.92	   G(d, x, x) -> A^2
28.56/9.92	   A^2 -> H(f(d), f(d))
28.56/9.92	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.92	   A^2 -> H(f(e), f(e))
28.56/9.92	   A^2 -> H(f(k), f(k))
28.56/9.92	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.92	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.92	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.92	   A^2 -> H(f(e), U1(e, d))
28.56/9.92	   A^2 -> H(f(e), U1(d, e))
28.56/9.92	   A^2 -> H(f(e), c)
28.56/9.92	   A^2 -> H(f(e), U1(e, k))
28.56/9.92	   A^2 -> H(f(e), U1(k, e))
28.56/9.92	   A^2 -> H(f(e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.92	   A^2 -> H(f(k), b)
28.56/9.92	   A^2 -> H(f(k), U1(e, d))
28.56/9.92	   A^2 -> H(f(k), U1(d, e))
28.56/9.92	   A^2 -> H(f(k), c)
28.56/9.92	   A^2 -> H(f(k), U1(e, k))
28.56/9.92	   A^2 -> H(f(k), U1(k, e))
28.56/9.92	   A^2 -> H(f(k), e)
28.56/9.92	   A^2 -> H(f(c), d)
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.92	   A^2 -> H(U1(k, k), f(e))
28.56/9.92	   A^2 -> H(U1(k, k), f(k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, d), b)
28.56/9.92	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.92	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.92	   A^2 -> H(U1(d, d), c)
28.56/9.92	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.92	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.92	   A^2 -> H(U1(d, d), e)
28.56/9.92	   A^2 -> H(f(d), d)
28.56/9.92	   A^2 -> H(f(d), k)
28.56/9.92	   A^2 -> H(U1(c, c), c)
28.56/9.92	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.92	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.92	   A^2 -> H(f(c), k)
28.56/9.92	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.92	   A^2 -> H(f(k), U1(k, k))
28.56/9.92	   A^2 -> H(f(e), e)
28.56/9.92	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.92	   A^2 -> H(d, U1(c, b))
28.56/9.92	   A^2 -> H(d, U1(d, b))
28.56/9.92	   A^2 -> H(d, U1(b, c))
28.56/9.92	   A^2 -> H(d, U1(b, d))
28.56/9.92	   A^2 -> H(d, U1(c, c))
28.56/9.92	   A^2 -> H(d, f(e))
28.56/9.92	   A^2 -> H(d, f(k))
28.56/9.92	   A^2 -> H(d, U1(d, d))
28.56/9.92	   A^2 -> H(a, U1(e, b))
28.56/9.92	   A^2 -> H(a, U1(k, b))
28.56/9.92	   A^2 -> H(a, U1(c, d))
28.56/9.92	   A^2 -> H(a, U1(d, c))
28.56/9.92	   A^2 -> H(a, U1(b, e))
28.56/9.92	   A^2 -> H(a, U1(b, k))
28.56/9.92	   A^2 -> H(a, U1(e, c))
28.56/9.92	   A^2 -> H(a, U1(k, c))
28.56/9.92	   A^2 -> H(a, U1(c, e))
28.56/9.92	   A^2 -> H(a, U1(c, k))
28.56/9.92	   A^2 -> H(a, U1(e, e))
28.56/9.92	   A^2 -> H(a, U1(k, k))
28.56/9.92	   A^2 -> H(a, U1(k, d))
28.56/9.92	   A^2 -> H(a, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.92	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, a), b)
28.56/9.92	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, a), c)
28.56/9.92	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.92	   A^2 -> H(U1(e, a), e)
28.56/9.92	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, a), b)
28.56/9.92	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.92	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.92	   A^2 -> H(U1(k, a), c)
28.56/9.92	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.92	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.92	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, d), b)
28.56/9.92	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, d), c)
28.56/9.92	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, d), e)
28.56/9.92	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, a), d)
28.56/9.92	   A^2 -> H(U1(c, a), k)
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.92	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, c), b)
28.56/9.92	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(d, c), c)
28.56/9.92	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(d, c), e)
28.56/9.92	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, a), d)
28.56/9.92	   A^2 -> H(U1(d, a), k)
28.56/9.92	   A^2 -> H(U1(a, e), b)
28.56/9.92	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.92	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.92	   A^2 -> H(U1(a, e), c)
28.56/9.92	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.92	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.92	   A^2 -> H(U1(a, e), e)
28.56/9.92	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(a, k), b)
28.56/9.92	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.92	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.92	   A^2 -> H(U1(a, k), c)
28.56/9.92	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.92	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.92	   A^2 -> H(U1(a, k), e)
28.56/9.92	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(a, c), d)
28.56/9.92	   A^2 -> H(U1(a, c), k)
28.56/9.92	   A^2 -> H(U1(a, d), d)
28.56/9.92	   A^2 -> H(U1(a, d), k)
28.56/9.92	   A^2 -> H(k, U1(c, b))
28.56/9.92	   A^2 -> H(k, U1(d, b))
28.56/9.92	   A^2 -> H(k, U1(b, c))
28.56/9.92	   A^2 -> H(k, U1(b, d))
28.56/9.92	   A^2 -> H(k, U1(c, c))
28.56/9.92	   A^2 -> H(k, f(e))
28.56/9.92	   A^2 -> H(k, f(k))
28.56/9.92	   A^2 -> H(k, U1(d, d))
28.56/9.92	   A^2 -> H(c, U1(e, b))
28.56/9.92	   A^2 -> H(c, U1(k, b))
28.56/9.92	   A^2 -> H(c, U1(c, d))
28.56/9.92	   A^2 -> H(c, U1(d, c))
28.56/9.92	   A^2 -> H(c, U1(b, e))
28.56/9.92	   A^2 -> H(c, U1(b, k))
28.56/9.92	   A^2 -> H(c, U1(e, c))
28.56/9.92	   A^2 -> H(c, U1(k, c))
28.56/9.92	   A^2 -> H(c, U1(c, e))
28.56/9.92	   A^2 -> H(c, U1(c, k))
28.56/9.92	   A^2 -> H(c, U1(e, e))
28.56/9.92	   A^2 -> H(c, U1(k, k))
28.56/9.92	   A^2 -> H(c, U1(k, d))
28.56/9.92	   A^2 -> H(c, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, c), b)
28.56/9.92	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, c), e)
28.56/9.92	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.92	   A^2 -> H(U1(k, c), b)
28.56/9.92	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(k, c), c)
28.56/9.92	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, e), b)
28.56/9.92	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, e), c)
28.56/9.92	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, e), e)
28.56/9.92	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, k), b)
28.56/9.92	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, k), c)
28.56/9.92	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, k), e)
28.56/9.92	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, c), d)
28.56/9.92	   A^2 -> H(e, U1(e, b))
28.56/9.92	   A^2 -> H(e, U1(c, d))
28.56/9.92	   A^2 -> H(e, U1(d, c))
28.56/9.92	   A^2 -> H(e, U1(b, e))
28.56/9.92	   A^2 -> H(e, U1(b, k))
28.56/9.92	   A^2 -> H(e, U1(e, c))
28.56/9.92	   A^2 -> H(e, U1(c, e))
28.56/9.92	   A^2 -> H(e, U1(c, k))
28.56/9.92	   A^2 -> H(e, U1(e, e))
28.56/9.92	   A^2 -> H(e, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, e), b)
28.56/9.92	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, e), c)
28.56/9.92	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.92	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.92	   A^2 -> H(f(e), d)
28.56/9.92	
28.56/9.92	The TRS R consists of the following rules:
28.56/9.92	
28.56/9.92	   f(x) -> U1(x, x)
28.56/9.92	   U1(e, x) -> x
28.56/9.92	   a -> c
28.56/9.92	   a -> d
28.56/9.92	   b -> c
28.56/9.92	   b -> d
28.56/9.92	   d -> k
28.56/9.92	   c -> e
28.56/9.92	   c -> k
28.56/9.92	
28.56/9.92	Q is empty.
28.56/9.92	We have to consider all minimal (P,Q,R)-chains.
28.56/9.92	----------------------------------------
28.56/9.92	
28.56/9.92	(1625) TransformationProof (EQUIVALENT)
28.56/9.92	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.92	
28.56/9.92	   (A^2 -> H(U1(e, e), U1(e, d)),A^2 -> H(U1(e, e), U1(e, d)))
28.56/9.92	   (A^2 -> H(f(e), d),A^2 -> H(f(e), d))
28.56/9.92	   (A^2 -> H(f(e), U1(e, k)),A^2 -> H(f(e), U1(e, k)))
28.56/9.92	
28.56/9.92	
28.56/9.92	----------------------------------------
28.56/9.92	
28.56/9.92	(1626)
28.56/9.92	Obligation:
28.56/9.92	Q DP problem:
28.56/9.92	The TRS P consists of the following rules:
28.56/9.92	
28.56/9.92	   A^2 -> H(f(c), f(c))
28.56/9.92	   H(x, x) -> G(x, x, f(k))
28.56/9.92	   G(d, x, x) -> A^2
28.56/9.92	   A^2 -> H(f(d), f(d))
28.56/9.92	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.92	   A^2 -> H(f(e), f(e))
28.56/9.92	   A^2 -> H(f(k), f(k))
28.56/9.92	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.92	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.92	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.92	   A^2 -> H(f(e), U1(d, e))
28.56/9.92	   A^2 -> H(f(e), c)
28.56/9.92	   A^2 -> H(f(e), U1(e, k))
28.56/9.92	   A^2 -> H(f(e), U1(k, e))
28.56/9.92	   A^2 -> H(f(e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.92	   A^2 -> H(f(k), b)
28.56/9.92	   A^2 -> H(f(k), U1(e, d))
28.56/9.92	   A^2 -> H(f(k), U1(d, e))
28.56/9.92	   A^2 -> H(f(k), c)
28.56/9.92	   A^2 -> H(f(k), U1(e, k))
28.56/9.92	   A^2 -> H(f(k), U1(k, e))
28.56/9.92	   A^2 -> H(f(k), e)
28.56/9.92	   A^2 -> H(f(c), d)
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.92	   A^2 -> H(U1(k, k), f(e))
28.56/9.92	   A^2 -> H(U1(k, k), f(k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, d), b)
28.56/9.92	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.92	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.92	   A^2 -> H(U1(d, d), c)
28.56/9.92	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.92	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.92	   A^2 -> H(U1(d, d), e)
28.56/9.92	   A^2 -> H(f(d), d)
28.56/9.92	   A^2 -> H(f(d), k)
28.56/9.92	   A^2 -> H(U1(c, c), c)
28.56/9.92	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.92	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.92	   A^2 -> H(f(c), k)
28.56/9.92	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.92	   A^2 -> H(f(k), U1(k, k))
28.56/9.92	   A^2 -> H(f(e), e)
28.56/9.92	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.92	   A^2 -> H(d, U1(c, b))
28.56/9.92	   A^2 -> H(d, U1(d, b))
28.56/9.92	   A^2 -> H(d, U1(b, c))
28.56/9.92	   A^2 -> H(d, U1(b, d))
28.56/9.92	   A^2 -> H(d, U1(c, c))
28.56/9.92	   A^2 -> H(d, f(e))
28.56/9.92	   A^2 -> H(d, f(k))
28.56/9.92	   A^2 -> H(d, U1(d, d))
28.56/9.92	   A^2 -> H(a, U1(e, b))
28.56/9.92	   A^2 -> H(a, U1(k, b))
28.56/9.92	   A^2 -> H(a, U1(c, d))
28.56/9.92	   A^2 -> H(a, U1(d, c))
28.56/9.92	   A^2 -> H(a, U1(b, e))
28.56/9.92	   A^2 -> H(a, U1(b, k))
28.56/9.92	   A^2 -> H(a, U1(e, c))
28.56/9.92	   A^2 -> H(a, U1(k, c))
28.56/9.92	   A^2 -> H(a, U1(c, e))
28.56/9.92	   A^2 -> H(a, U1(c, k))
28.56/9.92	   A^2 -> H(a, U1(e, e))
28.56/9.92	   A^2 -> H(a, U1(k, k))
28.56/9.92	   A^2 -> H(a, U1(k, d))
28.56/9.92	   A^2 -> H(a, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.92	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, a), b)
28.56/9.92	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, a), c)
28.56/9.92	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.92	   A^2 -> H(U1(e, a), e)
28.56/9.92	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, a), b)
28.56/9.92	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.92	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.92	   A^2 -> H(U1(k, a), c)
28.56/9.92	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.92	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.92	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, d), b)
28.56/9.92	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, d), c)
28.56/9.92	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, d), e)
28.56/9.92	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, a), d)
28.56/9.92	   A^2 -> H(U1(c, a), k)
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.92	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, c), b)
28.56/9.92	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(d, c), c)
28.56/9.92	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(d, c), e)
28.56/9.92	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, a), d)
28.56/9.92	   A^2 -> H(U1(d, a), k)
28.56/9.92	   A^2 -> H(U1(a, e), b)
28.56/9.92	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.92	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.92	   A^2 -> H(U1(a, e), c)
28.56/9.92	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.92	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.92	   A^2 -> H(U1(a, e), e)
28.56/9.92	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(a, k), b)
28.56/9.92	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.92	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.92	   A^2 -> H(U1(a, k), c)
28.56/9.92	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.92	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.92	   A^2 -> H(U1(a, k), e)
28.56/9.92	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(a, c), d)
28.56/9.92	   A^2 -> H(U1(a, c), k)
28.56/9.92	   A^2 -> H(U1(a, d), d)
28.56/9.92	   A^2 -> H(U1(a, d), k)
28.56/9.92	   A^2 -> H(k, U1(c, b))
28.56/9.92	   A^2 -> H(k, U1(d, b))
28.56/9.92	   A^2 -> H(k, U1(b, c))
28.56/9.92	   A^2 -> H(k, U1(b, d))
28.56/9.92	   A^2 -> H(k, U1(c, c))
28.56/9.92	   A^2 -> H(k, f(e))
28.56/9.92	   A^2 -> H(k, f(k))
28.56/9.92	   A^2 -> H(k, U1(d, d))
28.56/9.92	   A^2 -> H(c, U1(e, b))
28.56/9.92	   A^2 -> H(c, U1(k, b))
28.56/9.92	   A^2 -> H(c, U1(c, d))
28.56/9.92	   A^2 -> H(c, U1(d, c))
28.56/9.92	   A^2 -> H(c, U1(b, e))
28.56/9.92	   A^2 -> H(c, U1(b, k))
28.56/9.92	   A^2 -> H(c, U1(e, c))
28.56/9.92	   A^2 -> H(c, U1(k, c))
28.56/9.92	   A^2 -> H(c, U1(c, e))
28.56/9.92	   A^2 -> H(c, U1(c, k))
28.56/9.92	   A^2 -> H(c, U1(e, e))
28.56/9.92	   A^2 -> H(c, U1(k, k))
28.56/9.92	   A^2 -> H(c, U1(k, d))
28.56/9.92	   A^2 -> H(c, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, c), b)
28.56/9.92	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, c), e)
28.56/9.92	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.92	   A^2 -> H(U1(k, c), b)
28.56/9.92	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(k, c), c)
28.56/9.92	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, e), b)
28.56/9.92	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, e), c)
28.56/9.92	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, e), e)
28.56/9.92	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, k), b)
28.56/9.92	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, k), c)
28.56/9.92	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, k), e)
28.56/9.92	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, c), d)
28.56/9.92	   A^2 -> H(e, U1(e, b))
28.56/9.92	   A^2 -> H(e, U1(c, d))
28.56/9.92	   A^2 -> H(e, U1(d, c))
28.56/9.92	   A^2 -> H(e, U1(b, e))
28.56/9.92	   A^2 -> H(e, U1(b, k))
28.56/9.92	   A^2 -> H(e, U1(e, c))
28.56/9.92	   A^2 -> H(e, U1(c, e))
28.56/9.92	   A^2 -> H(e, U1(c, k))
28.56/9.92	   A^2 -> H(e, U1(e, e))
28.56/9.92	   A^2 -> H(e, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, e), b)
28.56/9.92	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, e), c)
28.56/9.92	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.92	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.92	   A^2 -> H(f(e), d)
28.56/9.92	
28.56/9.92	The TRS R consists of the following rules:
28.56/9.92	
28.56/9.92	   f(x) -> U1(x, x)
28.56/9.92	   U1(e, x) -> x
28.56/9.92	   a -> c
28.56/9.92	   a -> d
28.56/9.92	   b -> c
28.56/9.92	   b -> d
28.56/9.92	   d -> k
28.56/9.92	   c -> e
28.56/9.92	   c -> k
28.56/9.92	
28.56/9.92	Q is empty.
28.56/9.92	We have to consider all minimal (P,Q,R)-chains.
28.56/9.92	----------------------------------------
28.56/9.92	
28.56/9.92	(1627) TransformationProof (EQUIVALENT)
28.56/9.92	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.92	
28.56/9.92	   (A^2 -> H(U1(e, e), U1(d, e)),A^2 -> H(U1(e, e), U1(d, e)))
28.56/9.92	   (A^2 -> H(f(e), U1(k, e)),A^2 -> H(f(e), U1(k, e)))
28.56/9.92	
28.56/9.92	
28.56/9.92	----------------------------------------
28.56/9.92	
28.56/9.92	(1628)
28.56/9.92	Obligation:
28.56/9.92	Q DP problem:
28.56/9.92	The TRS P consists of the following rules:
28.56/9.92	
28.56/9.92	   A^2 -> H(f(c), f(c))
28.56/9.92	   H(x, x) -> G(x, x, f(k))
28.56/9.92	   G(d, x, x) -> A^2
28.56/9.92	   A^2 -> H(f(d), f(d))
28.56/9.92	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.92	   A^2 -> H(f(e), f(e))
28.56/9.92	   A^2 -> H(f(k), f(k))
28.56/9.92	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.92	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.92	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.92	   A^2 -> H(f(e), c)
28.56/9.92	   A^2 -> H(f(e), U1(e, k))
28.56/9.92	   A^2 -> H(f(e), U1(k, e))
28.56/9.92	   A^2 -> H(f(e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.92	   A^2 -> H(f(k), b)
28.56/9.92	   A^2 -> H(f(k), U1(e, d))
28.56/9.92	   A^2 -> H(f(k), U1(d, e))
28.56/9.92	   A^2 -> H(f(k), c)
28.56/9.92	   A^2 -> H(f(k), U1(e, k))
28.56/9.92	   A^2 -> H(f(k), U1(k, e))
28.56/9.92	   A^2 -> H(f(k), e)
28.56/9.92	   A^2 -> H(f(c), d)
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.92	   A^2 -> H(U1(k, k), f(e))
28.56/9.92	   A^2 -> H(U1(k, k), f(k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, d), b)
28.56/9.92	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.92	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.92	   A^2 -> H(U1(d, d), c)
28.56/9.92	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.92	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.92	   A^2 -> H(U1(d, d), e)
28.56/9.92	   A^2 -> H(f(d), d)
28.56/9.92	   A^2 -> H(f(d), k)
28.56/9.92	   A^2 -> H(U1(c, c), c)
28.56/9.92	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.92	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.92	   A^2 -> H(f(c), k)
28.56/9.92	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.92	   A^2 -> H(f(k), U1(k, k))
28.56/9.92	   A^2 -> H(f(e), e)
28.56/9.92	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.92	   A^2 -> H(d, U1(c, b))
28.56/9.92	   A^2 -> H(d, U1(d, b))
28.56/9.92	   A^2 -> H(d, U1(b, c))
28.56/9.92	   A^2 -> H(d, U1(b, d))
28.56/9.92	   A^2 -> H(d, U1(c, c))
28.56/9.92	   A^2 -> H(d, f(e))
28.56/9.92	   A^2 -> H(d, f(k))
28.56/9.92	   A^2 -> H(d, U1(d, d))
28.56/9.92	   A^2 -> H(a, U1(e, b))
28.56/9.92	   A^2 -> H(a, U1(k, b))
28.56/9.92	   A^2 -> H(a, U1(c, d))
28.56/9.92	   A^2 -> H(a, U1(d, c))
28.56/9.92	   A^2 -> H(a, U1(b, e))
28.56/9.92	   A^2 -> H(a, U1(b, k))
28.56/9.92	   A^2 -> H(a, U1(e, c))
28.56/9.92	   A^2 -> H(a, U1(k, c))
28.56/9.92	   A^2 -> H(a, U1(c, e))
28.56/9.92	   A^2 -> H(a, U1(c, k))
28.56/9.92	   A^2 -> H(a, U1(e, e))
28.56/9.92	   A^2 -> H(a, U1(k, k))
28.56/9.92	   A^2 -> H(a, U1(k, d))
28.56/9.92	   A^2 -> H(a, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.92	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, a), b)
28.56/9.92	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, a), c)
28.56/9.92	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.92	   A^2 -> H(U1(e, a), e)
28.56/9.92	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, a), b)
28.56/9.92	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.92	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.92	   A^2 -> H(U1(k, a), c)
28.56/9.92	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.92	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.92	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, d), b)
28.56/9.92	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, d), c)
28.56/9.92	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, d), e)
28.56/9.92	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, a), d)
28.56/9.92	   A^2 -> H(U1(c, a), k)
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.92	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, c), b)
28.56/9.92	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(d, c), c)
28.56/9.92	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(d, c), e)
28.56/9.92	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, a), d)
28.56/9.92	   A^2 -> H(U1(d, a), k)
28.56/9.92	   A^2 -> H(U1(a, e), b)
28.56/9.92	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.92	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.92	   A^2 -> H(U1(a, e), c)
28.56/9.92	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.92	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.92	   A^2 -> H(U1(a, e), e)
28.56/9.92	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(a, k), b)
28.56/9.92	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.92	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.92	   A^2 -> H(U1(a, k), c)
28.56/9.92	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.92	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.92	   A^2 -> H(U1(a, k), e)
28.56/9.92	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(a, c), d)
28.56/9.92	   A^2 -> H(U1(a, c), k)
28.56/9.92	   A^2 -> H(U1(a, d), d)
28.56/9.92	   A^2 -> H(U1(a, d), k)
28.56/9.92	   A^2 -> H(k, U1(c, b))
28.56/9.92	   A^2 -> H(k, U1(d, b))
28.56/9.92	   A^2 -> H(k, U1(b, c))
28.56/9.92	   A^2 -> H(k, U1(b, d))
28.56/9.92	   A^2 -> H(k, U1(c, c))
28.56/9.92	   A^2 -> H(k, f(e))
28.56/9.92	   A^2 -> H(k, f(k))
28.56/9.92	   A^2 -> H(k, U1(d, d))
28.56/9.92	   A^2 -> H(c, U1(e, b))
28.56/9.92	   A^2 -> H(c, U1(k, b))
28.56/9.92	   A^2 -> H(c, U1(c, d))
28.56/9.92	   A^2 -> H(c, U1(d, c))
28.56/9.92	   A^2 -> H(c, U1(b, e))
28.56/9.92	   A^2 -> H(c, U1(b, k))
28.56/9.92	   A^2 -> H(c, U1(e, c))
28.56/9.92	   A^2 -> H(c, U1(k, c))
28.56/9.92	   A^2 -> H(c, U1(c, e))
28.56/9.92	   A^2 -> H(c, U1(c, k))
28.56/9.92	   A^2 -> H(c, U1(e, e))
28.56/9.92	   A^2 -> H(c, U1(k, k))
28.56/9.92	   A^2 -> H(c, U1(k, d))
28.56/9.92	   A^2 -> H(c, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, c), b)
28.56/9.92	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, c), e)
28.56/9.92	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.92	   A^2 -> H(U1(k, c), b)
28.56/9.92	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(k, c), c)
28.56/9.92	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, e), b)
28.56/9.92	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, e), c)
28.56/9.92	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, e), e)
28.56/9.92	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, k), b)
28.56/9.92	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, k), c)
28.56/9.92	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, k), e)
28.56/9.92	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, c), d)
28.56/9.92	   A^2 -> H(e, U1(e, b))
28.56/9.92	   A^2 -> H(e, U1(c, d))
28.56/9.92	   A^2 -> H(e, U1(d, c))
28.56/9.92	   A^2 -> H(e, U1(b, e))
28.56/9.92	   A^2 -> H(e, U1(b, k))
28.56/9.92	   A^2 -> H(e, U1(e, c))
28.56/9.92	   A^2 -> H(e, U1(c, e))
28.56/9.92	   A^2 -> H(e, U1(c, k))
28.56/9.92	   A^2 -> H(e, U1(e, e))
28.56/9.92	   A^2 -> H(e, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, e), b)
28.56/9.92	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, e), c)
28.56/9.92	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.92	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.92	   A^2 -> H(f(e), d)
28.56/9.92	
28.56/9.92	The TRS R consists of the following rules:
28.56/9.92	
28.56/9.92	   f(x) -> U1(x, x)
28.56/9.92	   U1(e, x) -> x
28.56/9.92	   a -> c
28.56/9.92	   a -> d
28.56/9.92	   b -> c
28.56/9.92	   b -> d
28.56/9.92	   d -> k
28.56/9.92	   c -> e
28.56/9.92	   c -> k
28.56/9.92	
28.56/9.92	Q is empty.
28.56/9.92	We have to consider all minimal (P,Q,R)-chains.
28.56/9.92	----------------------------------------
28.56/9.92	
28.56/9.92	(1629) TransformationProof (EQUIVALENT)
28.56/9.92	By narrowing [LPAR04] the rule A^2 -> H(f(e), c) at position [] we obtained the following new rules [LPAR04]:
28.56/9.92	
28.56/9.92	   (A^2 -> H(U1(e, e), c),A^2 -> H(U1(e, e), c))
28.56/9.92	   (A^2 -> H(f(e), e),A^2 -> H(f(e), e))
28.56/9.92	   (A^2 -> H(f(e), k),A^2 -> H(f(e), k))
28.56/9.92	
28.56/9.92	
28.56/9.92	----------------------------------------
28.56/9.92	
28.56/9.92	(1630)
28.56/9.92	Obligation:
28.56/9.92	Q DP problem:
28.56/9.92	The TRS P consists of the following rules:
28.56/9.92	
28.56/9.92	   A^2 -> H(f(c), f(c))
28.56/9.92	   H(x, x) -> G(x, x, f(k))
28.56/9.92	   G(d, x, x) -> A^2
28.56/9.92	   A^2 -> H(f(d), f(d))
28.56/9.92	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.92	   A^2 -> H(f(e), f(e))
28.56/9.92	   A^2 -> H(f(k), f(k))
28.56/9.92	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.92	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.92	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.92	   A^2 -> H(f(e), U1(e, k))
28.56/9.92	   A^2 -> H(f(e), U1(k, e))
28.56/9.92	   A^2 -> H(f(e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.92	   A^2 -> H(f(k), b)
28.56/9.92	   A^2 -> H(f(k), U1(e, d))
28.56/9.92	   A^2 -> H(f(k), U1(d, e))
28.56/9.92	   A^2 -> H(f(k), c)
28.56/9.92	   A^2 -> H(f(k), U1(e, k))
28.56/9.92	   A^2 -> H(f(k), U1(k, e))
28.56/9.92	   A^2 -> H(f(k), e)
28.56/9.92	   A^2 -> H(f(c), d)
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.92	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.92	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.92	   A^2 -> H(U1(k, k), f(e))
28.56/9.92	   A^2 -> H(U1(k, k), f(k))
28.56/9.92	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.92	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.92	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, d), b)
28.56/9.92	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.92	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.92	   A^2 -> H(U1(d, d), c)
28.56/9.92	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.92	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.92	   A^2 -> H(U1(d, d), e)
28.56/9.92	   A^2 -> H(f(d), d)
28.56/9.92	   A^2 -> H(f(d), k)
28.56/9.92	   A^2 -> H(U1(c, c), c)
28.56/9.92	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.92	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.92	   A^2 -> H(f(c), k)
28.56/9.92	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.92	   A^2 -> H(f(k), U1(k, k))
28.56/9.92	   A^2 -> H(f(e), e)
28.56/9.92	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.92	   A^2 -> H(d, U1(c, b))
28.56/9.92	   A^2 -> H(d, U1(d, b))
28.56/9.92	   A^2 -> H(d, U1(b, c))
28.56/9.92	   A^2 -> H(d, U1(b, d))
28.56/9.92	   A^2 -> H(d, U1(c, c))
28.56/9.92	   A^2 -> H(d, f(e))
28.56/9.92	   A^2 -> H(d, f(k))
28.56/9.92	   A^2 -> H(d, U1(d, d))
28.56/9.92	   A^2 -> H(a, U1(e, b))
28.56/9.92	   A^2 -> H(a, U1(k, b))
28.56/9.92	   A^2 -> H(a, U1(c, d))
28.56/9.92	   A^2 -> H(a, U1(d, c))
28.56/9.92	   A^2 -> H(a, U1(b, e))
28.56/9.92	   A^2 -> H(a, U1(b, k))
28.56/9.92	   A^2 -> H(a, U1(e, c))
28.56/9.92	   A^2 -> H(a, U1(k, c))
28.56/9.92	   A^2 -> H(a, U1(c, e))
28.56/9.92	   A^2 -> H(a, U1(c, k))
28.56/9.92	   A^2 -> H(a, U1(e, e))
28.56/9.92	   A^2 -> H(a, U1(k, k))
28.56/9.92	   A^2 -> H(a, U1(k, d))
28.56/9.92	   A^2 -> H(a, U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.92	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.92	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.92	   A^2 -> H(U1(e, a), b)
28.56/9.92	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.92	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.92	   A^2 -> H(U1(e, a), c)
28.56/9.92	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.92	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.92	   A^2 -> H(U1(e, a), e)
28.56/9.92	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.92	   A^2 -> H(U1(k, a), b)
28.56/9.92	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.92	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.92	   A^2 -> H(U1(k, a), c)
28.56/9.92	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.92	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.92	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, d), b)
28.56/9.92	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.92	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.92	   A^2 -> H(U1(c, d), c)
28.56/9.92	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.92	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.92	   A^2 -> H(U1(c, d), e)
28.56/9.92	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.92	   A^2 -> H(U1(c, a), d)
28.56/9.92	   A^2 -> H(U1(c, a), k)
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.92	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.92	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.92	   A^2 -> H(U1(d, c), b)
28.56/9.92	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.92	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.92	   A^2 -> H(U1(d, c), c)
28.56/9.92	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.92	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.92	   A^2 -> H(U1(d, c), e)
28.56/9.92	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.92	   A^2 -> H(U1(d, a), d)
28.56/9.92	   A^2 -> H(U1(d, a), k)
28.56/9.92	   A^2 -> H(U1(a, e), b)
28.56/9.93	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(a, e), c)
28.56/9.93	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(a, e), e)
28.56/9.93	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(a, k), b)
28.56/9.93	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.93	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.93	   A^2 -> H(U1(a, k), c)
28.56/9.93	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.93	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.93	   A^2 -> H(U1(a, k), e)
28.56/9.93	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(a, c), d)
28.56/9.93	   A^2 -> H(U1(a, c), k)
28.56/9.93	   A^2 -> H(U1(a, d), d)
28.56/9.93	   A^2 -> H(U1(a, d), k)
28.56/9.93	   A^2 -> H(k, U1(c, b))
28.56/9.93	   A^2 -> H(k, U1(d, b))
28.56/9.93	   A^2 -> H(k, U1(b, c))
28.56/9.93	   A^2 -> H(k, U1(b, d))
28.56/9.93	   A^2 -> H(k, U1(c, c))
28.56/9.93	   A^2 -> H(k, f(e))
28.56/9.93	   A^2 -> H(k, f(k))
28.56/9.93	   A^2 -> H(k, U1(d, d))
28.56/9.93	   A^2 -> H(c, U1(e, b))
28.56/9.93	   A^2 -> H(c, U1(k, b))
28.56/9.93	   A^2 -> H(c, U1(c, d))
28.56/9.93	   A^2 -> H(c, U1(d, c))
28.56/9.93	   A^2 -> H(c, U1(b, e))
28.56/9.93	   A^2 -> H(c, U1(b, k))
28.56/9.93	   A^2 -> H(c, U1(e, c))
28.56/9.93	   A^2 -> H(c, U1(k, c))
28.56/9.93	   A^2 -> H(c, U1(c, e))
28.56/9.93	   A^2 -> H(c, U1(c, k))
28.56/9.93	   A^2 -> H(c, U1(e, e))
28.56/9.93	   A^2 -> H(c, U1(k, k))
28.56/9.93	   A^2 -> H(c, U1(k, d))
28.56/9.93	   A^2 -> H(c, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.93	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, c), b)
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, c), e)
28.56/9.93	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.93	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.93	   A^2 -> H(U1(k, c), b)
28.56/9.93	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(k, c), c)
28.56/9.93	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, e), b)
28.56/9.93	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, e), c)
28.56/9.93	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, e), e)
28.56/9.93	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, k), b)
28.56/9.93	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, k), c)
28.56/9.93	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, k), e)
28.56/9.93	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, c), d)
28.56/9.93	   A^2 -> H(e, U1(e, b))
28.56/9.93	   A^2 -> H(e, U1(c, d))
28.56/9.93	   A^2 -> H(e, U1(d, c))
28.56/9.93	   A^2 -> H(e, U1(b, e))
28.56/9.93	   A^2 -> H(e, U1(b, k))
28.56/9.93	   A^2 -> H(e, U1(e, c))
28.56/9.93	   A^2 -> H(e, U1(c, e))
28.56/9.93	   A^2 -> H(e, U1(c, k))
28.56/9.93	   A^2 -> H(e, U1(e, e))
28.56/9.93	   A^2 -> H(e, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, e), b)
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, e), c)
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.93	   A^2 -> H(f(e), d)
28.56/9.93	   A^2 -> H(f(e), k)
28.56/9.93	
28.56/9.93	The TRS R consists of the following rules:
28.56/9.93	
28.56/9.93	   f(x) -> U1(x, x)
28.56/9.93	   U1(e, x) -> x
28.56/9.93	   a -> c
28.56/9.93	   a -> d
28.56/9.93	   b -> c
28.56/9.93	   b -> d
28.56/9.93	   d -> k
28.56/9.93	   c -> e
28.56/9.93	   c -> k
28.56/9.93	
28.56/9.93	Q is empty.
28.56/9.93	We have to consider all minimal (P,Q,R)-chains.
28.56/9.93	----------------------------------------
28.56/9.93	
28.56/9.93	(1631) TransformationProof (EQUIVALENT)
28.56/9.93	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.93	
28.56/9.93	   (A^2 -> H(U1(e, e), U1(e, k)),A^2 -> H(U1(e, e), U1(e, k)))
28.56/9.93	   (A^2 -> H(f(e), k),A^2 -> H(f(e), k))
28.56/9.93	
28.56/9.93	
28.56/9.93	----------------------------------------
28.56/9.93	
28.56/9.93	(1632)
28.56/9.93	Obligation:
28.56/9.93	Q DP problem:
28.56/9.93	The TRS P consists of the following rules:
28.56/9.93	
28.56/9.93	   A^2 -> H(f(c), f(c))
28.56/9.93	   H(x, x) -> G(x, x, f(k))
28.56/9.93	   G(d, x, x) -> A^2
28.56/9.93	   A^2 -> H(f(d), f(d))
28.56/9.93	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.93	   A^2 -> H(f(e), f(e))
28.56/9.93	   A^2 -> H(f(k), f(k))
28.56/9.93	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.93	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.93	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.93	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.93	   A^2 -> H(f(e), U1(k, e))
28.56/9.93	   A^2 -> H(f(e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.93	   A^2 -> H(f(k), b)
28.56/9.93	   A^2 -> H(f(k), U1(e, d))
28.56/9.93	   A^2 -> H(f(k), U1(d, e))
28.56/9.93	   A^2 -> H(f(k), c)
28.56/9.93	   A^2 -> H(f(k), U1(e, k))
28.56/9.93	   A^2 -> H(f(k), U1(k, e))
28.56/9.93	   A^2 -> H(f(k), e)
28.56/9.93	   A^2 -> H(f(c), d)
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.93	   A^2 -> H(U1(k, k), f(e))
28.56/9.93	   A^2 -> H(U1(k, k), f(k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.93	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.93	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.93	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.93	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.93	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.93	   A^2 -> H(U1(d, d), b)
28.56/9.93	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.93	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.93	   A^2 -> H(U1(d, d), c)
28.56/9.93	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.93	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.93	   A^2 -> H(U1(d, d), e)
28.56/9.93	   A^2 -> H(f(d), d)
28.56/9.93	   A^2 -> H(f(d), k)
28.56/9.93	   A^2 -> H(U1(c, c), c)
28.56/9.93	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.93	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.93	   A^2 -> H(f(c), k)
28.56/9.93	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.93	   A^2 -> H(f(k), U1(k, k))
28.56/9.93	   A^2 -> H(f(e), e)
28.56/9.93	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.93	   A^2 -> H(d, U1(c, b))
28.56/9.93	   A^2 -> H(d, U1(d, b))
28.56/9.93	   A^2 -> H(d, U1(b, c))
28.56/9.93	   A^2 -> H(d, U1(b, d))
28.56/9.93	   A^2 -> H(d, U1(c, c))
28.56/9.93	   A^2 -> H(d, f(e))
28.56/9.93	   A^2 -> H(d, f(k))
28.56/9.93	   A^2 -> H(d, U1(d, d))
28.56/9.93	   A^2 -> H(a, U1(e, b))
28.56/9.93	   A^2 -> H(a, U1(k, b))
28.56/9.93	   A^2 -> H(a, U1(c, d))
28.56/9.93	   A^2 -> H(a, U1(d, c))
28.56/9.93	   A^2 -> H(a, U1(b, e))
28.56/9.93	   A^2 -> H(a, U1(b, k))
28.56/9.93	   A^2 -> H(a, U1(e, c))
28.56/9.93	   A^2 -> H(a, U1(k, c))
28.56/9.93	   A^2 -> H(a, U1(c, e))
28.56/9.93	   A^2 -> H(a, U1(c, k))
28.56/9.93	   A^2 -> H(a, U1(e, e))
28.56/9.93	   A^2 -> H(a, U1(k, k))
28.56/9.93	   A^2 -> H(a, U1(k, d))
28.56/9.93	   A^2 -> H(a, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.93	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.93	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.93	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.93	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.93	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.93	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, a), b)
28.56/9.93	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, a), c)
28.56/9.93	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, a), e)
28.56/9.93	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, a), b)
28.56/9.93	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.93	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.93	   A^2 -> H(U1(k, a), c)
28.56/9.93	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.93	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.93	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, d), b)
28.56/9.93	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, d), c)
28.56/9.93	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, d), e)
28.56/9.93	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, a), d)
28.56/9.93	   A^2 -> H(U1(c, a), k)
28.56/9.93	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.93	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.93	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.93	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.93	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.93	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.93	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.93	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.93	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.93	   A^2 -> H(U1(d, c), b)
28.56/9.93	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(d, c), c)
28.56/9.93	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(d, c), e)
28.56/9.93	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(d, a), d)
28.56/9.93	   A^2 -> H(U1(d, a), k)
28.56/9.93	   A^2 -> H(U1(a, e), b)
28.56/9.93	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(a, e), c)
28.56/9.93	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(a, e), e)
28.56/9.93	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(a, k), b)
28.56/9.93	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.93	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.93	   A^2 -> H(U1(a, k), c)
28.56/9.93	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.93	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.93	   A^2 -> H(U1(a, k), e)
28.56/9.93	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(a, c), d)
28.56/9.93	   A^2 -> H(U1(a, c), k)
28.56/9.93	   A^2 -> H(U1(a, d), d)
28.56/9.93	   A^2 -> H(U1(a, d), k)
28.56/9.93	   A^2 -> H(k, U1(c, b))
28.56/9.93	   A^2 -> H(k, U1(d, b))
28.56/9.93	   A^2 -> H(k, U1(b, c))
28.56/9.93	   A^2 -> H(k, U1(b, d))
28.56/9.93	   A^2 -> H(k, U1(c, c))
28.56/9.93	   A^2 -> H(k, f(e))
28.56/9.93	   A^2 -> H(k, f(k))
28.56/9.93	   A^2 -> H(k, U1(d, d))
28.56/9.93	   A^2 -> H(c, U1(e, b))
28.56/9.93	   A^2 -> H(c, U1(k, b))
28.56/9.93	   A^2 -> H(c, U1(c, d))
28.56/9.93	   A^2 -> H(c, U1(d, c))
28.56/9.93	   A^2 -> H(c, U1(b, e))
28.56/9.93	   A^2 -> H(c, U1(b, k))
28.56/9.93	   A^2 -> H(c, U1(e, c))
28.56/9.93	   A^2 -> H(c, U1(k, c))
28.56/9.93	   A^2 -> H(c, U1(c, e))
28.56/9.93	   A^2 -> H(c, U1(c, k))
28.56/9.93	   A^2 -> H(c, U1(e, e))
28.56/9.93	   A^2 -> H(c, U1(k, k))
28.56/9.93	   A^2 -> H(c, U1(k, d))
28.56/9.93	   A^2 -> H(c, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.93	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, c), b)
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, c), e)
28.56/9.93	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.93	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.93	   A^2 -> H(U1(k, c), b)
28.56/9.93	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(k, c), c)
28.56/9.93	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, e), b)
28.56/9.93	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, e), c)
28.56/9.93	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, e), e)
28.56/9.93	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, k), b)
28.56/9.93	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, k), c)
28.56/9.93	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, k), e)
28.56/9.93	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, c), d)
28.56/9.93	   A^2 -> H(e, U1(e, b))
28.56/9.93	   A^2 -> H(e, U1(c, d))
28.56/9.93	   A^2 -> H(e, U1(d, c))
28.56/9.93	   A^2 -> H(e, U1(b, e))
28.56/9.93	   A^2 -> H(e, U1(b, k))
28.56/9.93	   A^2 -> H(e, U1(e, c))
28.56/9.93	   A^2 -> H(e, U1(c, e))
28.56/9.93	   A^2 -> H(e, U1(c, k))
28.56/9.93	   A^2 -> H(e, U1(e, e))
28.56/9.93	   A^2 -> H(e, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, e), b)
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, e), c)
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.93	   A^2 -> H(f(e), d)
28.56/9.93	   A^2 -> H(f(e), k)
28.56/9.93	
28.56/9.93	The TRS R consists of the following rules:
28.56/9.93	
28.56/9.93	   f(x) -> U1(x, x)
28.56/9.93	   U1(e, x) -> x
28.56/9.93	   a -> c
28.56/9.93	   a -> d
28.56/9.93	   b -> c
28.56/9.93	   b -> d
28.56/9.93	   d -> k
28.56/9.93	   c -> e
28.56/9.93	   c -> k
28.56/9.93	
28.56/9.93	Q is empty.
28.56/9.93	We have to consider all minimal (P,Q,R)-chains.
28.56/9.93	----------------------------------------
28.56/9.93	
28.56/9.93	(1633) TransformationProof (EQUIVALENT)
28.56/9.93	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.93	
28.56/9.93	   (A^2 -> H(U1(e, e), U1(k, e)),A^2 -> H(U1(e, e), U1(k, e)))
28.56/9.93	
28.56/9.93	
28.56/9.93	----------------------------------------
28.56/9.93	
28.56/9.93	(1634)
28.56/9.93	Obligation:
28.56/9.93	Q DP problem:
28.56/9.93	The TRS P consists of the following rules:
28.56/9.93	
28.56/9.93	   A^2 -> H(f(c), f(c))
28.56/9.93	   H(x, x) -> G(x, x, f(k))
28.56/9.93	   G(d, x, x) -> A^2
28.56/9.93	   A^2 -> H(f(d), f(d))
28.56/9.93	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.93	   A^2 -> H(f(e), f(e))
28.56/9.93	   A^2 -> H(f(k), f(k))
28.56/9.93	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.93	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.93	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.93	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.93	   A^2 -> H(f(e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.93	   A^2 -> H(f(k), b)
28.56/9.93	   A^2 -> H(f(k), U1(e, d))
28.56/9.93	   A^2 -> H(f(k), U1(d, e))
28.56/9.93	   A^2 -> H(f(k), c)
28.56/9.93	   A^2 -> H(f(k), U1(e, k))
28.56/9.93	   A^2 -> H(f(k), U1(k, e))
28.56/9.93	   A^2 -> H(f(k), e)
28.56/9.93	   A^2 -> H(f(c), d)
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.93	   A^2 -> H(U1(k, k), f(e))
28.56/9.93	   A^2 -> H(U1(k, k), f(k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.93	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.93	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.93	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.93	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.93	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.93	   A^2 -> H(U1(d, d), b)
28.56/9.93	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.93	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.93	   A^2 -> H(U1(d, d), c)
28.56/9.93	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.93	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.93	   A^2 -> H(U1(d, d), e)
28.56/9.93	   A^2 -> H(f(d), d)
28.56/9.93	   A^2 -> H(f(d), k)
28.56/9.93	   A^2 -> H(U1(c, c), c)
28.56/9.93	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.93	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.93	   A^2 -> H(f(c), k)
28.56/9.93	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.93	   A^2 -> H(f(k), U1(k, k))
28.56/9.93	   A^2 -> H(f(e), e)
28.56/9.93	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.93	   A^2 -> H(d, U1(c, b))
28.56/9.93	   A^2 -> H(d, U1(d, b))
28.56/9.93	   A^2 -> H(d, U1(b, c))
28.56/9.93	   A^2 -> H(d, U1(b, d))
28.56/9.93	   A^2 -> H(d, U1(c, c))
28.56/9.93	   A^2 -> H(d, f(e))
28.56/9.93	   A^2 -> H(d, f(k))
28.56/9.93	   A^2 -> H(d, U1(d, d))
28.56/9.93	   A^2 -> H(a, U1(e, b))
28.56/9.93	   A^2 -> H(a, U1(k, b))
28.56/9.93	   A^2 -> H(a, U1(c, d))
28.56/9.93	   A^2 -> H(a, U1(d, c))
28.56/9.93	   A^2 -> H(a, U1(b, e))
28.56/9.93	   A^2 -> H(a, U1(b, k))
28.56/9.93	   A^2 -> H(a, U1(e, c))
28.56/9.93	   A^2 -> H(a, U1(k, c))
28.56/9.93	   A^2 -> H(a, U1(c, e))
28.56/9.93	   A^2 -> H(a, U1(c, k))
28.56/9.93	   A^2 -> H(a, U1(e, e))
28.56/9.93	   A^2 -> H(a, U1(k, k))
28.56/9.93	   A^2 -> H(a, U1(k, d))
28.56/9.93	   A^2 -> H(a, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.93	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.93	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.93	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.93	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.93	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.93	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, a), b)
28.56/9.93	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, a), c)
28.56/9.93	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, a), e)
28.56/9.93	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, a), b)
28.56/9.93	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.93	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.93	   A^2 -> H(U1(k, a), c)
28.56/9.93	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.93	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.93	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, d), b)
28.56/9.93	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, d), c)
28.56/9.93	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, d), e)
28.56/9.93	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, a), d)
28.56/9.93	   A^2 -> H(U1(c, a), k)
28.56/9.93	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.93	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.93	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.93	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.93	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.93	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.93	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.93	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.93	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.93	   A^2 -> H(U1(d, c), b)
28.56/9.93	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(d, c), c)
28.56/9.93	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(d, c), e)
28.56/9.93	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(d, a), d)
28.56/9.93	   A^2 -> H(U1(d, a), k)
28.56/9.93	   A^2 -> H(U1(a, e), b)
28.56/9.93	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(a, e), c)
28.56/9.93	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(a, e), e)
28.56/9.93	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(a, k), b)
28.56/9.93	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.93	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.93	   A^2 -> H(U1(a, k), c)
28.56/9.93	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.93	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.93	   A^2 -> H(U1(a, k), e)
28.56/9.93	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(a, c), d)
28.56/9.93	   A^2 -> H(U1(a, c), k)
28.56/9.93	   A^2 -> H(U1(a, d), d)
28.56/9.93	   A^2 -> H(U1(a, d), k)
28.56/9.93	   A^2 -> H(k, U1(c, b))
28.56/9.93	   A^2 -> H(k, U1(d, b))
28.56/9.93	   A^2 -> H(k, U1(b, c))
28.56/9.93	   A^2 -> H(k, U1(b, d))
28.56/9.93	   A^2 -> H(k, U1(c, c))
28.56/9.93	   A^2 -> H(k, f(e))
28.56/9.93	   A^2 -> H(k, f(k))
28.56/9.93	   A^2 -> H(k, U1(d, d))
28.56/9.93	   A^2 -> H(c, U1(e, b))
28.56/9.93	   A^2 -> H(c, U1(k, b))
28.56/9.93	   A^2 -> H(c, U1(c, d))
28.56/9.93	   A^2 -> H(c, U1(d, c))
28.56/9.93	   A^2 -> H(c, U1(b, e))
28.56/9.93	   A^2 -> H(c, U1(b, k))
28.56/9.93	   A^2 -> H(c, U1(e, c))
28.56/9.93	   A^2 -> H(c, U1(k, c))
28.56/9.93	   A^2 -> H(c, U1(c, e))
28.56/9.93	   A^2 -> H(c, U1(c, k))
28.56/9.93	   A^2 -> H(c, U1(e, e))
28.56/9.93	   A^2 -> H(c, U1(k, k))
28.56/9.93	   A^2 -> H(c, U1(k, d))
28.56/9.93	   A^2 -> H(c, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.93	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, c), b)
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, c), e)
28.56/9.93	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.93	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.93	   A^2 -> H(U1(k, c), b)
28.56/9.93	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(k, c), c)
28.56/9.93	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, e), b)
28.56/9.93	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, e), c)
28.56/9.93	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, e), e)
28.56/9.93	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, k), b)
28.56/9.93	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, k), c)
28.56/9.93	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, k), e)
28.56/9.93	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, c), d)
28.56/9.93	   A^2 -> H(e, U1(e, b))
28.56/9.93	   A^2 -> H(e, U1(c, d))
28.56/9.93	   A^2 -> H(e, U1(d, c))
28.56/9.93	   A^2 -> H(e, U1(b, e))
28.56/9.93	   A^2 -> H(e, U1(b, k))
28.56/9.93	   A^2 -> H(e, U1(e, c))
28.56/9.93	   A^2 -> H(e, U1(c, e))
28.56/9.93	   A^2 -> H(e, U1(c, k))
28.56/9.93	   A^2 -> H(e, U1(e, e))
28.56/9.93	   A^2 -> H(e, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, e), b)
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, e), c)
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.93	   A^2 -> H(f(e), d)
28.56/9.93	   A^2 -> H(f(e), k)
28.56/9.93	
28.56/9.93	The TRS R consists of the following rules:
28.56/9.93	
28.56/9.93	   f(x) -> U1(x, x)
28.56/9.93	   U1(e, x) -> x
28.56/9.93	   a -> c
28.56/9.93	   a -> d
28.56/9.93	   b -> c
28.56/9.93	   b -> d
28.56/9.93	   d -> k
28.56/9.93	   c -> e
28.56/9.93	   c -> k
28.56/9.93	
28.56/9.93	Q is empty.
28.56/9.93	We have to consider all minimal (P,Q,R)-chains.
28.56/9.93	----------------------------------------
28.56/9.93	
28.56/9.93	(1635) TransformationProof (EQUIVALENT)
28.56/9.93	By narrowing [LPAR04] the rule A^2 -> H(f(e), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.93	
28.56/9.93	   (A^2 -> H(U1(e, e), U1(k, k)),A^2 -> H(U1(e, e), U1(k, k)))
28.56/9.93	
28.56/9.93	
28.56/9.93	----------------------------------------
28.56/9.93	
28.56/9.93	(1636)
28.56/9.93	Obligation:
28.56/9.93	Q DP problem:
28.56/9.93	The TRS P consists of the following rules:
28.56/9.93	
28.56/9.93	   A^2 -> H(f(c), f(c))
28.56/9.93	   H(x, x) -> G(x, x, f(k))
28.56/9.93	   G(d, x, x) -> A^2
28.56/9.93	   A^2 -> H(f(d), f(d))
28.56/9.93	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.93	   A^2 -> H(f(e), f(e))
28.56/9.93	   A^2 -> H(f(k), f(k))
28.56/9.93	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.93	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.93	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.93	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.93	   A^2 -> H(f(k), b)
28.56/9.93	   A^2 -> H(f(k), U1(e, d))
28.56/9.93	   A^2 -> H(f(k), U1(d, e))
28.56/9.93	   A^2 -> H(f(k), c)
28.56/9.93	   A^2 -> H(f(k), U1(e, k))
28.56/9.93	   A^2 -> H(f(k), U1(k, e))
28.56/9.93	   A^2 -> H(f(k), e)
28.56/9.93	   A^2 -> H(f(c), d)
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.93	   A^2 -> H(U1(k, k), f(e))
28.56/9.93	   A^2 -> H(U1(k, k), f(k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.93	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.93	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.93	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.93	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.93	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.93	   A^2 -> H(U1(d, d), b)
28.56/9.93	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.93	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.93	   A^2 -> H(U1(d, d), c)
28.56/9.93	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.93	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.93	   A^2 -> H(U1(d, d), e)
28.56/9.93	   A^2 -> H(f(d), d)
28.56/9.93	   A^2 -> H(f(d), k)
28.56/9.93	   A^2 -> H(U1(c, c), c)
28.56/9.93	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.93	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.93	   A^2 -> H(f(c), k)
28.56/9.93	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.93	   A^2 -> H(f(k), U1(k, k))
28.56/9.93	   A^2 -> H(f(e), e)
28.56/9.93	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.93	   A^2 -> H(d, U1(c, b))
28.56/9.93	   A^2 -> H(d, U1(d, b))
28.56/9.93	   A^2 -> H(d, U1(b, c))
28.56/9.93	   A^2 -> H(d, U1(b, d))
28.56/9.93	   A^2 -> H(d, U1(c, c))
28.56/9.93	   A^2 -> H(d, f(e))
28.56/9.93	   A^2 -> H(d, f(k))
28.56/9.93	   A^2 -> H(d, U1(d, d))
28.56/9.93	   A^2 -> H(a, U1(e, b))
28.56/9.93	   A^2 -> H(a, U1(k, b))
28.56/9.93	   A^2 -> H(a, U1(c, d))
28.56/9.93	   A^2 -> H(a, U1(d, c))
28.56/9.93	   A^2 -> H(a, U1(b, e))
28.56/9.93	   A^2 -> H(a, U1(b, k))
28.56/9.93	   A^2 -> H(a, U1(e, c))
28.56/9.93	   A^2 -> H(a, U1(k, c))
28.56/9.93	   A^2 -> H(a, U1(c, e))
28.56/9.93	   A^2 -> H(a, U1(c, k))
28.56/9.93	   A^2 -> H(a, U1(e, e))
28.56/9.93	   A^2 -> H(a, U1(k, k))
28.56/9.93	   A^2 -> H(a, U1(k, d))
28.56/9.93	   A^2 -> H(a, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.93	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.93	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.93	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.93	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.93	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.93	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, a), b)
28.56/9.93	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, a), c)
28.56/9.93	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, a), e)
28.56/9.93	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, a), b)
28.56/9.93	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.93	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.93	   A^2 -> H(U1(k, a), c)
28.56/9.93	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.93	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.93	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, d), b)
28.56/9.93	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, d), c)
28.56/9.93	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, d), e)
28.56/9.93	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, a), d)
28.56/9.93	   A^2 -> H(U1(c, a), k)
28.56/9.93	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.93	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.93	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.93	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.93	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.93	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.93	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.93	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.93	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.93	   A^2 -> H(U1(d, c), b)
28.56/9.93	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(d, c), c)
28.56/9.93	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(d, c), e)
28.56/9.93	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(d, a), d)
28.56/9.93	   A^2 -> H(U1(d, a), k)
28.56/9.93	   A^2 -> H(U1(a, e), b)
28.56/9.93	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(a, e), c)
28.56/9.93	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(a, e), e)
28.56/9.93	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(a, k), b)
28.56/9.93	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.93	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.93	   A^2 -> H(U1(a, k), c)
28.56/9.93	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.93	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.93	   A^2 -> H(U1(a, k), e)
28.56/9.93	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(a, c), d)
28.56/9.93	   A^2 -> H(U1(a, c), k)
28.56/9.93	   A^2 -> H(U1(a, d), d)
28.56/9.93	   A^2 -> H(U1(a, d), k)
28.56/9.93	   A^2 -> H(k, U1(c, b))
28.56/9.93	   A^2 -> H(k, U1(d, b))
28.56/9.93	   A^2 -> H(k, U1(b, c))
28.56/9.93	   A^2 -> H(k, U1(b, d))
28.56/9.93	   A^2 -> H(k, U1(c, c))
28.56/9.93	   A^2 -> H(k, f(e))
28.56/9.93	   A^2 -> H(k, f(k))
28.56/9.93	   A^2 -> H(k, U1(d, d))
28.56/9.93	   A^2 -> H(c, U1(e, b))
28.56/9.93	   A^2 -> H(c, U1(k, b))
28.56/9.93	   A^2 -> H(c, U1(c, d))
28.56/9.93	   A^2 -> H(c, U1(d, c))
28.56/9.93	   A^2 -> H(c, U1(b, e))
28.56/9.93	   A^2 -> H(c, U1(b, k))
28.56/9.93	   A^2 -> H(c, U1(e, c))
28.56/9.93	   A^2 -> H(c, U1(k, c))
28.56/9.93	   A^2 -> H(c, U1(c, e))
28.56/9.93	   A^2 -> H(c, U1(c, k))
28.56/9.93	   A^2 -> H(c, U1(e, e))
28.56/9.93	   A^2 -> H(c, U1(k, k))
28.56/9.93	   A^2 -> H(c, U1(k, d))
28.56/9.93	   A^2 -> H(c, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.93	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, c), b)
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, c), e)
28.56/9.93	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.93	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.93	   A^2 -> H(U1(k, c), b)
28.56/9.93	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(k, c), c)
28.56/9.93	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, e), b)
28.56/9.93	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, e), c)
28.56/9.93	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, e), e)
28.56/9.93	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, k), b)
28.56/9.93	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, k), c)
28.56/9.93	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, k), e)
28.56/9.93	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, c), d)
28.56/9.93	   A^2 -> H(e, U1(e, b))
28.56/9.93	   A^2 -> H(e, U1(c, d))
28.56/9.93	   A^2 -> H(e, U1(d, c))
28.56/9.93	   A^2 -> H(e, U1(b, e))
28.56/9.93	   A^2 -> H(e, U1(b, k))
28.56/9.93	   A^2 -> H(e, U1(e, c))
28.56/9.93	   A^2 -> H(e, U1(c, e))
28.56/9.93	   A^2 -> H(e, U1(c, k))
28.56/9.93	   A^2 -> H(e, U1(e, e))
28.56/9.93	   A^2 -> H(e, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, e), b)
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, e), c)
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.93	   A^2 -> H(f(e), d)
28.56/9.93	   A^2 -> H(f(e), k)
28.56/9.93	
28.56/9.93	The TRS R consists of the following rules:
28.56/9.93	
28.56/9.93	   f(x) -> U1(x, x)
28.56/9.93	   U1(e, x) -> x
28.56/9.93	   a -> c
28.56/9.93	   a -> d
28.56/9.93	   b -> c
28.56/9.93	   b -> d
28.56/9.93	   d -> k
28.56/9.93	   c -> e
28.56/9.93	   c -> k
28.56/9.93	
28.56/9.93	Q is empty.
28.56/9.93	We have to consider all minimal (P,Q,R)-chains.
28.56/9.93	----------------------------------------
28.56/9.93	
28.56/9.93	(1637) TransformationProof (EQUIVALENT)
28.56/9.93	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.93	
28.56/9.93	   (A^2 -> H(U1(k, k), b),A^2 -> H(U1(k, k), b))
28.56/9.93	   (A^2 -> H(U1(k, k), U1(e, c)),A^2 -> H(U1(k, k), U1(e, c)))
28.56/9.93	   (A^2 -> H(U1(k, k), U1(e, d)),A^2 -> H(U1(k, k), U1(e, d)))
28.56/9.93	
28.56/9.93	
28.56/9.93	----------------------------------------
28.56/9.93	
28.56/9.93	(1638)
28.56/9.93	Obligation:
28.56/9.93	Q DP problem:
28.56/9.93	The TRS P consists of the following rules:
28.56/9.93	
28.56/9.93	   A^2 -> H(f(c), f(c))
28.56/9.93	   H(x, x) -> G(x, x, f(k))
28.56/9.93	   G(d, x, x) -> A^2
28.56/9.93	   A^2 -> H(f(d), f(d))
28.56/9.93	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.93	   A^2 -> H(f(e), f(e))
28.56/9.93	   A^2 -> H(f(k), f(k))
28.56/9.93	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.93	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.93	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.93	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.93	   A^2 -> H(f(k), b)
28.56/9.93	   A^2 -> H(f(k), U1(e, d))
28.56/9.93	   A^2 -> H(f(k), U1(d, e))
28.56/9.93	   A^2 -> H(f(k), c)
28.56/9.93	   A^2 -> H(f(k), U1(e, k))
28.56/9.93	   A^2 -> H(f(k), U1(k, e))
28.56/9.93	   A^2 -> H(f(k), e)
28.56/9.93	   A^2 -> H(f(c), d)
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.93	   A^2 -> H(U1(k, k), f(e))
28.56/9.93	   A^2 -> H(U1(k, k), f(k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.93	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.93	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.93	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.93	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.93	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.93	   A^2 -> H(U1(d, d), b)
28.56/9.93	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.93	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.93	   A^2 -> H(U1(d, d), c)
28.56/9.93	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.93	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.93	   A^2 -> H(U1(d, d), e)
28.56/9.93	   A^2 -> H(f(d), d)
28.56/9.93	   A^2 -> H(f(d), k)
28.56/9.93	   A^2 -> H(U1(c, c), c)
28.56/9.93	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.93	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.93	   A^2 -> H(f(c), k)
28.56/9.93	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.93	   A^2 -> H(f(k), U1(k, k))
28.56/9.93	   A^2 -> H(f(e), e)
28.56/9.93	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.93	   A^2 -> H(d, U1(c, b))
28.56/9.93	   A^2 -> H(d, U1(d, b))
28.56/9.93	   A^2 -> H(d, U1(b, c))
28.56/9.93	   A^2 -> H(d, U1(b, d))
28.56/9.93	   A^2 -> H(d, U1(c, c))
28.56/9.93	   A^2 -> H(d, f(e))
28.56/9.93	   A^2 -> H(d, f(k))
28.56/9.93	   A^2 -> H(d, U1(d, d))
28.56/9.93	   A^2 -> H(a, U1(e, b))
28.56/9.93	   A^2 -> H(a, U1(k, b))
28.56/9.93	   A^2 -> H(a, U1(c, d))
28.56/9.93	   A^2 -> H(a, U1(d, c))
28.56/9.93	   A^2 -> H(a, U1(b, e))
28.56/9.93	   A^2 -> H(a, U1(b, k))
28.56/9.93	   A^2 -> H(a, U1(e, c))
28.56/9.93	   A^2 -> H(a, U1(k, c))
28.56/9.93	   A^2 -> H(a, U1(c, e))
28.56/9.93	   A^2 -> H(a, U1(c, k))
28.56/9.93	   A^2 -> H(a, U1(e, e))
28.56/9.93	   A^2 -> H(a, U1(k, k))
28.56/9.93	   A^2 -> H(a, U1(k, d))
28.56/9.93	   A^2 -> H(a, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.93	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.93	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.93	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.93	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.93	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.93	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, a), b)
28.56/9.93	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, a), c)
28.56/9.93	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, a), e)
28.56/9.93	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, a), b)
28.56/9.93	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.93	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.93	   A^2 -> H(U1(k, a), c)
28.56/9.93	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.93	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.93	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, d), b)
28.56/9.93	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, d), c)
28.56/9.93	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, d), e)
28.56/9.93	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, a), d)
28.56/9.93	   A^2 -> H(U1(c, a), k)
28.56/9.93	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.93	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.93	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.93	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.93	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.93	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.93	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.93	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.93	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.93	   A^2 -> H(U1(d, c), b)
28.56/9.93	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(d, c), c)
28.56/9.93	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(d, c), e)
28.56/9.93	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(d, a), d)
28.56/9.93	   A^2 -> H(U1(d, a), k)
28.56/9.93	   A^2 -> H(U1(a, e), b)
28.56/9.93	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(a, e), c)
28.56/9.93	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(a, e), e)
28.56/9.93	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(a, k), b)
28.56/9.93	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.93	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.93	   A^2 -> H(U1(a, k), c)
28.56/9.93	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.93	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.93	   A^2 -> H(U1(a, k), e)
28.56/9.93	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(a, c), d)
28.56/9.93	   A^2 -> H(U1(a, c), k)
28.56/9.93	   A^2 -> H(U1(a, d), d)
28.56/9.93	   A^2 -> H(U1(a, d), k)
28.56/9.93	   A^2 -> H(k, U1(c, b))
28.56/9.93	   A^2 -> H(k, U1(d, b))
28.56/9.93	   A^2 -> H(k, U1(b, c))
28.56/9.93	   A^2 -> H(k, U1(b, d))
28.56/9.93	   A^2 -> H(k, U1(c, c))
28.56/9.93	   A^2 -> H(k, f(e))
28.56/9.93	   A^2 -> H(k, f(k))
28.56/9.93	   A^2 -> H(k, U1(d, d))
28.56/9.93	   A^2 -> H(c, U1(e, b))
28.56/9.93	   A^2 -> H(c, U1(k, b))
28.56/9.93	   A^2 -> H(c, U1(c, d))
28.56/9.93	   A^2 -> H(c, U1(d, c))
28.56/9.93	   A^2 -> H(c, U1(b, e))
28.56/9.93	   A^2 -> H(c, U1(b, k))
28.56/9.93	   A^2 -> H(c, U1(e, c))
28.56/9.93	   A^2 -> H(c, U1(k, c))
28.56/9.93	   A^2 -> H(c, U1(c, e))
28.56/9.93	   A^2 -> H(c, U1(c, k))
28.56/9.93	   A^2 -> H(c, U1(e, e))
28.56/9.93	   A^2 -> H(c, U1(k, k))
28.56/9.93	   A^2 -> H(c, U1(k, d))
28.56/9.93	   A^2 -> H(c, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.93	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, c), b)
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, c), e)
28.56/9.93	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.93	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.93	   A^2 -> H(U1(k, c), b)
28.56/9.93	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(k, c), c)
28.56/9.93	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, e), b)
28.56/9.93	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, e), c)
28.56/9.93	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, e), e)
28.56/9.93	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, k), b)
28.56/9.93	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, k), c)
28.56/9.93	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, k), e)
28.56/9.93	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, c), d)
28.56/9.93	   A^2 -> H(e, U1(e, b))
28.56/9.93	   A^2 -> H(e, U1(c, d))
28.56/9.93	   A^2 -> H(e, U1(d, c))
28.56/9.93	   A^2 -> H(e, U1(b, e))
28.56/9.93	   A^2 -> H(e, U1(b, k))
28.56/9.93	   A^2 -> H(e, U1(e, c))
28.56/9.93	   A^2 -> H(e, U1(c, e))
28.56/9.93	   A^2 -> H(e, U1(c, k))
28.56/9.93	   A^2 -> H(e, U1(e, e))
28.56/9.93	   A^2 -> H(e, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, e), b)
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, e), c)
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.93	   A^2 -> H(f(e), d)
28.56/9.93	   A^2 -> H(f(e), k)
28.56/9.93	   A^2 -> H(U1(k, k), b)
28.56/9.93	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.93	
28.56/9.93	The TRS R consists of the following rules:
28.56/9.93	
28.56/9.93	   f(x) -> U1(x, x)
28.56/9.93	   U1(e, x) -> x
28.56/9.93	   a -> c
28.56/9.93	   a -> d
28.56/9.93	   b -> c
28.56/9.93	   b -> d
28.56/9.93	   d -> k
28.56/9.93	   c -> e
28.56/9.93	   c -> k
28.56/9.93	
28.56/9.93	Q is empty.
28.56/9.93	We have to consider all minimal (P,Q,R)-chains.
28.56/9.93	----------------------------------------
28.56/9.93	
28.56/9.93	(1639) TransformationProof (EQUIVALENT)
28.56/9.93	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.93	
28.56/9.93	   (A^2 -> H(U1(k, k), U1(k, c)),A^2 -> H(U1(k, k), U1(k, c)))
28.56/9.93	   (A^2 -> H(U1(k, k), U1(k, d)),A^2 -> H(U1(k, k), U1(k, d)))
28.56/9.93	
28.56/9.93	
28.56/9.93	----------------------------------------
28.56/9.93	
28.56/9.93	(1640)
28.56/9.93	Obligation:
28.56/9.93	Q DP problem:
28.56/9.93	The TRS P consists of the following rules:
28.56/9.93	
28.56/9.93	   A^2 -> H(f(c), f(c))
28.56/9.93	   H(x, x) -> G(x, x, f(k))
28.56/9.93	   G(d, x, x) -> A^2
28.56/9.93	   A^2 -> H(f(d), f(d))
28.56/9.93	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.93	   A^2 -> H(f(e), f(e))
28.56/9.93	   A^2 -> H(f(k), f(k))
28.56/9.93	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.93	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.93	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.93	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.93	   A^2 -> H(f(k), b)
28.56/9.93	   A^2 -> H(f(k), U1(e, d))
28.56/9.93	   A^2 -> H(f(k), U1(d, e))
28.56/9.93	   A^2 -> H(f(k), c)
28.56/9.93	   A^2 -> H(f(k), U1(e, k))
28.56/9.93	   A^2 -> H(f(k), U1(k, e))
28.56/9.93	   A^2 -> H(f(k), e)
28.56/9.93	   A^2 -> H(f(c), d)
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.93	   A^2 -> H(U1(k, k), f(e))
28.56/9.93	   A^2 -> H(U1(k, k), f(k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.93	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.93	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.93	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.93	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.93	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.93	   A^2 -> H(U1(d, d), b)
28.56/9.93	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.93	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.93	   A^2 -> H(U1(d, d), c)
28.56/9.93	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.93	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.93	   A^2 -> H(U1(d, d), e)
28.56/9.93	   A^2 -> H(f(d), d)
28.56/9.93	   A^2 -> H(f(d), k)
28.56/9.93	   A^2 -> H(U1(c, c), c)
28.56/9.93	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.93	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.93	   A^2 -> H(f(c), k)
28.56/9.93	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.93	   A^2 -> H(f(k), U1(k, k))
28.56/9.93	   A^2 -> H(f(e), e)
28.56/9.93	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.93	   A^2 -> H(d, U1(c, b))
28.56/9.93	   A^2 -> H(d, U1(d, b))
28.56/9.93	   A^2 -> H(d, U1(b, c))
28.56/9.93	   A^2 -> H(d, U1(b, d))
28.56/9.93	   A^2 -> H(d, U1(c, c))
28.56/9.93	   A^2 -> H(d, f(e))
28.56/9.93	   A^2 -> H(d, f(k))
28.56/9.93	   A^2 -> H(d, U1(d, d))
28.56/9.93	   A^2 -> H(a, U1(e, b))
28.56/9.93	   A^2 -> H(a, U1(k, b))
28.56/9.93	   A^2 -> H(a, U1(c, d))
28.56/9.93	   A^2 -> H(a, U1(d, c))
28.56/9.93	   A^2 -> H(a, U1(b, e))
28.56/9.93	   A^2 -> H(a, U1(b, k))
28.56/9.93	   A^2 -> H(a, U1(e, c))
28.56/9.93	   A^2 -> H(a, U1(k, c))
28.56/9.93	   A^2 -> H(a, U1(c, e))
28.56/9.93	   A^2 -> H(a, U1(c, k))
28.56/9.93	   A^2 -> H(a, U1(e, e))
28.56/9.93	   A^2 -> H(a, U1(k, k))
28.56/9.93	   A^2 -> H(a, U1(k, d))
28.56/9.93	   A^2 -> H(a, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.93	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.93	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.93	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.93	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.93	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.93	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, a), b)
28.56/9.93	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, a), c)
28.56/9.93	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, a), e)
28.56/9.93	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, a), b)
28.56/9.93	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.93	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.93	   A^2 -> H(U1(k, a), c)
28.56/9.93	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.93	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.93	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, d), b)
28.56/9.93	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, d), c)
28.56/9.93	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, d), e)
28.56/9.93	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, a), d)
28.56/9.93	   A^2 -> H(U1(c, a), k)
28.56/9.93	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.93	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.93	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.93	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.93	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.93	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.93	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.93	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.93	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.93	   A^2 -> H(U1(d, c), b)
28.56/9.93	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(d, c), c)
28.56/9.93	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(d, c), e)
28.56/9.93	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(d, a), d)
28.56/9.93	   A^2 -> H(U1(d, a), k)
28.56/9.93	   A^2 -> H(U1(a, e), b)
28.56/9.93	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(a, e), c)
28.56/9.93	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(a, e), e)
28.56/9.93	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(a, k), b)
28.56/9.93	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.93	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.93	   A^2 -> H(U1(a, k), c)
28.56/9.93	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.93	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.93	   A^2 -> H(U1(a, k), e)
28.56/9.93	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(a, c), d)
28.56/9.93	   A^2 -> H(U1(a, c), k)
28.56/9.93	   A^2 -> H(U1(a, d), d)
28.56/9.93	   A^2 -> H(U1(a, d), k)
28.56/9.93	   A^2 -> H(k, U1(c, b))
28.56/9.93	   A^2 -> H(k, U1(d, b))
28.56/9.93	   A^2 -> H(k, U1(b, c))
28.56/9.93	   A^2 -> H(k, U1(b, d))
28.56/9.93	   A^2 -> H(k, U1(c, c))
28.56/9.93	   A^2 -> H(k, f(e))
28.56/9.93	   A^2 -> H(k, f(k))
28.56/9.93	   A^2 -> H(k, U1(d, d))
28.56/9.93	   A^2 -> H(c, U1(e, b))
28.56/9.93	   A^2 -> H(c, U1(k, b))
28.56/9.93	   A^2 -> H(c, U1(c, d))
28.56/9.93	   A^2 -> H(c, U1(d, c))
28.56/9.93	   A^2 -> H(c, U1(b, e))
28.56/9.93	   A^2 -> H(c, U1(b, k))
28.56/9.93	   A^2 -> H(c, U1(e, c))
28.56/9.93	   A^2 -> H(c, U1(k, c))
28.56/9.93	   A^2 -> H(c, U1(c, e))
28.56/9.93	   A^2 -> H(c, U1(c, k))
28.56/9.93	   A^2 -> H(c, U1(e, e))
28.56/9.93	   A^2 -> H(c, U1(k, k))
28.56/9.93	   A^2 -> H(c, U1(k, d))
28.56/9.93	   A^2 -> H(c, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.93	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, c), b)
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, c), e)
28.56/9.93	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.93	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.93	   A^2 -> H(U1(k, c), b)
28.56/9.93	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(k, c), c)
28.56/9.93	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, e), b)
28.56/9.93	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, e), c)
28.56/9.93	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, e), e)
28.56/9.93	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, k), b)
28.56/9.93	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, k), c)
28.56/9.93	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, k), e)
28.56/9.93	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, c), d)
28.56/9.93	   A^2 -> H(e, U1(e, b))
28.56/9.93	   A^2 -> H(e, U1(c, d))
28.56/9.93	   A^2 -> H(e, U1(d, c))
28.56/9.93	   A^2 -> H(e, U1(b, e))
28.56/9.93	   A^2 -> H(e, U1(b, k))
28.56/9.93	   A^2 -> H(e, U1(e, c))
28.56/9.93	   A^2 -> H(e, U1(c, e))
28.56/9.93	   A^2 -> H(e, U1(c, k))
28.56/9.93	   A^2 -> H(e, U1(e, e))
28.56/9.93	   A^2 -> H(e, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, e), b)
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, e), c)
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.93	   A^2 -> H(f(e), d)
28.56/9.93	   A^2 -> H(f(e), k)
28.56/9.93	   A^2 -> H(U1(k, k), b)
28.56/9.93	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.93	
28.56/9.93	The TRS R consists of the following rules:
28.56/9.93	
28.56/9.93	   f(x) -> U1(x, x)
28.56/9.93	   U1(e, x) -> x
28.56/9.93	   a -> c
28.56/9.93	   a -> d
28.56/9.93	   b -> c
28.56/9.93	   b -> d
28.56/9.93	   d -> k
28.56/9.93	   c -> e
28.56/9.93	   c -> k
28.56/9.93	
28.56/9.93	Q is empty.
28.56/9.93	We have to consider all minimal (P,Q,R)-chains.
28.56/9.93	----------------------------------------
28.56/9.93	
28.56/9.93	(1641) TransformationProof (EQUIVALENT)
28.56/9.93	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.93	
28.56/9.93	   (A^2 -> H(U1(k, k), U1(e, d)),A^2 -> H(U1(k, k), U1(e, d)))
28.56/9.93	   (A^2 -> H(U1(k, k), U1(k, d)),A^2 -> H(U1(k, k), U1(k, d)))
28.56/9.93	   (A^2 -> H(U1(k, k), U1(c, k)),A^2 -> H(U1(k, k), U1(c, k)))
28.56/9.93	
28.56/9.93	
28.56/9.93	----------------------------------------
28.56/9.93	
28.56/9.93	(1642)
28.56/9.93	Obligation:
28.56/9.93	Q DP problem:
28.56/9.93	The TRS P consists of the following rules:
28.56/9.93	
28.56/9.93	   A^2 -> H(f(c), f(c))
28.56/9.93	   H(x, x) -> G(x, x, f(k))
28.56/9.93	   G(d, x, x) -> A^2
28.56/9.93	   A^2 -> H(f(d), f(d))
28.56/9.93	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.93	   A^2 -> H(f(e), f(e))
28.56/9.93	   A^2 -> H(f(k), f(k))
28.56/9.93	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.93	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.93	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.93	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.93	   A^2 -> H(f(k), b)
28.56/9.93	   A^2 -> H(f(k), U1(e, d))
28.56/9.93	   A^2 -> H(f(k), U1(d, e))
28.56/9.93	   A^2 -> H(f(k), c)
28.56/9.93	   A^2 -> H(f(k), U1(e, k))
28.56/9.93	   A^2 -> H(f(k), U1(k, e))
28.56/9.93	   A^2 -> H(f(k), e)
28.56/9.93	   A^2 -> H(f(c), d)
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.93	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.93	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.93	   A^2 -> H(U1(k, k), f(e))
28.56/9.93	   A^2 -> H(U1(k, k), f(k))
28.56/9.93	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.93	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.93	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.93	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.93	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.93	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.93	   A^2 -> H(U1(d, d), b)
28.56/9.93	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.93	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.93	   A^2 -> H(U1(d, d), c)
28.56/9.93	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.93	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.93	   A^2 -> H(U1(d, d), e)
28.56/9.93	   A^2 -> H(f(d), d)
28.56/9.93	   A^2 -> H(f(d), k)
28.56/9.93	   A^2 -> H(U1(c, c), c)
28.56/9.93	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.93	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.93	   A^2 -> H(f(c), k)
28.56/9.93	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.93	   A^2 -> H(f(k), U1(k, k))
28.56/9.93	   A^2 -> H(f(e), e)
28.56/9.93	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.93	   A^2 -> H(d, U1(c, b))
28.56/9.93	   A^2 -> H(d, U1(d, b))
28.56/9.93	   A^2 -> H(d, U1(b, c))
28.56/9.93	   A^2 -> H(d, U1(b, d))
28.56/9.93	   A^2 -> H(d, U1(c, c))
28.56/9.93	   A^2 -> H(d, f(e))
28.56/9.93	   A^2 -> H(d, f(k))
28.56/9.93	   A^2 -> H(d, U1(d, d))
28.56/9.93	   A^2 -> H(a, U1(e, b))
28.56/9.93	   A^2 -> H(a, U1(k, b))
28.56/9.93	   A^2 -> H(a, U1(c, d))
28.56/9.93	   A^2 -> H(a, U1(d, c))
28.56/9.93	   A^2 -> H(a, U1(b, e))
28.56/9.93	   A^2 -> H(a, U1(b, k))
28.56/9.93	   A^2 -> H(a, U1(e, c))
28.56/9.93	   A^2 -> H(a, U1(k, c))
28.56/9.93	   A^2 -> H(a, U1(c, e))
28.56/9.93	   A^2 -> H(a, U1(c, k))
28.56/9.93	   A^2 -> H(a, U1(e, e))
28.56/9.93	   A^2 -> H(a, U1(k, k))
28.56/9.93	   A^2 -> H(a, U1(k, d))
28.56/9.93	   A^2 -> H(a, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.93	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.93	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.93	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.93	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.93	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.93	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.93	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, a), b)
28.56/9.93	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, a), c)
28.56/9.93	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, a), e)
28.56/9.93	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, a), b)
28.56/9.93	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.93	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.93	   A^2 -> H(U1(k, a), c)
28.56/9.93	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.93	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.93	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, d), b)
28.56/9.93	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, d), c)
28.56/9.93	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, d), e)
28.56/9.93	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, a), d)
28.56/9.93	   A^2 -> H(U1(c, a), k)
28.56/9.93	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.93	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.93	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.93	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.93	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.93	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.93	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.93	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.93	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.93	   A^2 -> H(U1(d, c), b)
28.56/9.93	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(d, c), c)
28.56/9.93	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(d, c), e)
28.56/9.93	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(d, a), d)
28.56/9.93	   A^2 -> H(U1(d, a), k)
28.56/9.93	   A^2 -> H(U1(a, e), b)
28.56/9.93	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(a, e), c)
28.56/9.93	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(a, e), e)
28.56/9.93	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(a, k), b)
28.56/9.93	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.93	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.93	   A^2 -> H(U1(a, k), c)
28.56/9.93	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.93	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.93	   A^2 -> H(U1(a, k), e)
28.56/9.93	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(a, c), d)
28.56/9.93	   A^2 -> H(U1(a, c), k)
28.56/9.93	   A^2 -> H(U1(a, d), d)
28.56/9.93	   A^2 -> H(U1(a, d), k)
28.56/9.93	   A^2 -> H(k, U1(c, b))
28.56/9.93	   A^2 -> H(k, U1(d, b))
28.56/9.93	   A^2 -> H(k, U1(b, c))
28.56/9.93	   A^2 -> H(k, U1(b, d))
28.56/9.93	   A^2 -> H(k, U1(c, c))
28.56/9.93	   A^2 -> H(k, f(e))
28.56/9.93	   A^2 -> H(k, f(k))
28.56/9.93	   A^2 -> H(k, U1(d, d))
28.56/9.93	   A^2 -> H(c, U1(e, b))
28.56/9.93	   A^2 -> H(c, U1(k, b))
28.56/9.93	   A^2 -> H(c, U1(c, d))
28.56/9.93	   A^2 -> H(c, U1(d, c))
28.56/9.93	   A^2 -> H(c, U1(b, e))
28.56/9.93	   A^2 -> H(c, U1(b, k))
28.56/9.93	   A^2 -> H(c, U1(e, c))
28.56/9.93	   A^2 -> H(c, U1(k, c))
28.56/9.93	   A^2 -> H(c, U1(c, e))
28.56/9.93	   A^2 -> H(c, U1(c, k))
28.56/9.93	   A^2 -> H(c, U1(e, e))
28.56/9.93	   A^2 -> H(c, U1(k, k))
28.56/9.93	   A^2 -> H(c, U1(k, d))
28.56/9.93	   A^2 -> H(c, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.93	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.93	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, c), b)
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, c), e)
28.56/9.93	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.93	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.93	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.93	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.93	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.93	   A^2 -> H(U1(k, c), b)
28.56/9.93	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.93	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.93	   A^2 -> H(U1(k, c), c)
28.56/9.93	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.93	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, e), b)
28.56/9.93	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, e), c)
28.56/9.93	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, e), e)
28.56/9.93	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, k), b)
28.56/9.93	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.93	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.93	   A^2 -> H(U1(c, k), c)
28.56/9.93	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.93	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.93	   A^2 -> H(U1(c, k), e)
28.56/9.93	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.93	   A^2 -> H(U1(c, c), d)
28.56/9.93	   A^2 -> H(e, U1(e, b))
28.56/9.93	   A^2 -> H(e, U1(c, d))
28.56/9.93	   A^2 -> H(e, U1(d, c))
28.56/9.93	   A^2 -> H(e, U1(b, e))
28.56/9.93	   A^2 -> H(e, U1(b, k))
28.56/9.93	   A^2 -> H(e, U1(e, c))
28.56/9.93	   A^2 -> H(e, U1(c, e))
28.56/9.93	   A^2 -> H(e, U1(c, k))
28.56/9.93	   A^2 -> H(e, U1(e, e))
28.56/9.93	   A^2 -> H(e, U1(d, k))
28.56/9.93	   A^2 -> H(U1(e, e), b)
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.93	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.93	   A^2 -> H(U1(e, e), c)
28.56/9.93	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.93	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.93	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.93	   A^2 -> H(f(e), d)
28.56/9.93	   A^2 -> H(f(e), k)
28.56/9.93	   A^2 -> H(U1(k, k), b)
28.56/9.93	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.93	
28.56/9.93	The TRS R consists of the following rules:
28.56/9.93	
28.56/9.93	   f(x) -> U1(x, x)
28.56/9.93	   U1(e, x) -> x
28.56/9.93	   a -> c
28.56/9.93	   a -> d
28.56/9.93	   b -> c
28.56/9.93	   b -> d
28.56/9.93	   d -> k
28.56/9.93	   c -> e
28.56/9.93	   c -> k
28.56/9.93	
28.56/9.93	Q is empty.
28.56/9.93	We have to consider all minimal (P,Q,R)-chains.
28.56/9.93	----------------------------------------
28.56/9.93	
28.56/9.93	(1643) TransformationProof (EQUIVALENT)
28.56/9.93	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.93	
28.56/9.93	   (A^2 -> H(U1(k, k), U1(k, c)),A^2 -> H(U1(k, k), U1(k, c)))
28.56/9.93	   (A^2 -> H(U1(k, k), U1(d, e)),A^2 -> H(U1(k, k), U1(d, e)))
28.56/9.93	   (A^2 -> H(U1(k, k), U1(d, k)),A^2 -> H(U1(k, k), U1(d, k)))
28.56/9.93	
28.56/9.93	
28.56/9.93	----------------------------------------
28.56/9.93	
28.56/9.93	(1644)
28.56/9.93	Obligation:
28.56/9.93	Q DP problem:
28.56/9.93	The TRS P consists of the following rules:
28.56/9.93	
28.56/9.93	   A^2 -> H(f(c), f(c))
28.56/9.93	   H(x, x) -> G(x, x, f(k))
28.56/9.93	   G(d, x, x) -> A^2
28.56/9.94	   A^2 -> H(f(d), f(d))
28.56/9.94	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.94	   A^2 -> H(f(e), f(e))
28.56/9.94	   A^2 -> H(f(k), f(k))
28.56/9.94	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.94	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.94	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.94	   A^2 -> H(f(k), b)
28.56/9.94	   A^2 -> H(f(k), U1(e, d))
28.56/9.94	   A^2 -> H(f(k), U1(d, e))
28.56/9.94	   A^2 -> H(f(k), c)
28.56/9.94	   A^2 -> H(f(k), U1(e, k))
28.56/9.94	   A^2 -> H(f(k), U1(k, e))
28.56/9.94	   A^2 -> H(f(k), e)
28.56/9.94	   A^2 -> H(f(c), d)
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.94	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.94	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.94	   A^2 -> H(U1(k, k), f(e))
28.56/9.94	   A^2 -> H(U1(k, k), f(k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, d), b)
28.56/9.94	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.94	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.94	   A^2 -> H(U1(d, d), c)
28.56/9.94	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.94	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.94	   A^2 -> H(U1(d, d), e)
28.56/9.94	   A^2 -> H(f(d), d)
28.56/9.94	   A^2 -> H(f(d), k)
28.56/9.94	   A^2 -> H(U1(c, c), c)
28.56/9.94	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.94	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.94	   A^2 -> H(f(c), k)
28.56/9.94	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.94	   A^2 -> H(f(k), U1(k, k))
28.56/9.94	   A^2 -> H(f(e), e)
28.56/9.94	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.94	   A^2 -> H(d, U1(c, b))
28.56/9.94	   A^2 -> H(d, U1(d, b))
28.56/9.94	   A^2 -> H(d, U1(b, c))
28.56/9.94	   A^2 -> H(d, U1(b, d))
28.56/9.94	   A^2 -> H(d, U1(c, c))
28.56/9.94	   A^2 -> H(d, f(e))
28.56/9.94	   A^2 -> H(d, f(k))
28.56/9.94	   A^2 -> H(d, U1(d, d))
28.56/9.94	   A^2 -> H(a, U1(e, b))
28.56/9.94	   A^2 -> H(a, U1(k, b))
28.56/9.94	   A^2 -> H(a, U1(c, d))
28.56/9.94	   A^2 -> H(a, U1(d, c))
28.56/9.94	   A^2 -> H(a, U1(b, e))
28.56/9.94	   A^2 -> H(a, U1(b, k))
28.56/9.94	   A^2 -> H(a, U1(e, c))
28.56/9.94	   A^2 -> H(a, U1(k, c))
28.56/9.94	   A^2 -> H(a, U1(c, e))
28.56/9.94	   A^2 -> H(a, U1(c, k))
28.56/9.94	   A^2 -> H(a, U1(e, e))
28.56/9.94	   A^2 -> H(a, U1(k, k))
28.56/9.94	   A^2 -> H(a, U1(k, d))
28.56/9.94	   A^2 -> H(a, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.94	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, a), b)
28.56/9.94	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, a), c)
28.56/9.94	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, a), e)
28.56/9.94	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, a), b)
28.56/9.94	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.94	   A^2 -> H(U1(k, a), c)
28.56/9.94	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.94	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.94	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, d), b)
28.56/9.94	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.94	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.94	   A^2 -> H(U1(c, d), c)
28.56/9.94	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.94	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.94	   A^2 -> H(U1(c, d), e)
28.56/9.94	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, a), d)
28.56/9.94	   A^2 -> H(U1(c, a), k)
28.56/9.94	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.94	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.94	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.94	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.94	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.94	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.94	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.94	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, c), b)
28.56/9.94	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.94	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.94	   A^2 -> H(U1(d, c), c)
28.56/9.94	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.94	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.94	   A^2 -> H(U1(d, c), e)
28.56/9.94	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, a), d)
28.56/9.94	   A^2 -> H(U1(d, a), k)
28.56/9.94	   A^2 -> H(U1(a, e), b)
28.56/9.94	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.94	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.94	   A^2 -> H(U1(a, e), c)
28.56/9.94	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.94	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.94	   A^2 -> H(U1(a, e), e)
28.56/9.94	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.94	   A^2 -> H(U1(a, k), b)
28.56/9.94	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.94	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.94	   A^2 -> H(U1(a, k), c)
28.56/9.94	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.94	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.94	   A^2 -> H(U1(a, k), e)
28.56/9.94	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(a, c), d)
28.56/9.94	   A^2 -> H(U1(a, c), k)
28.56/9.94	   A^2 -> H(U1(a, d), d)
28.56/9.94	   A^2 -> H(U1(a, d), k)
28.56/9.94	   A^2 -> H(k, U1(c, b))
28.56/9.94	   A^2 -> H(k, U1(d, b))
28.56/9.94	   A^2 -> H(k, U1(b, c))
28.56/9.94	   A^2 -> H(k, U1(b, d))
28.56/9.94	   A^2 -> H(k, U1(c, c))
28.56/9.94	   A^2 -> H(k, f(e))
28.56/9.94	   A^2 -> H(k, f(k))
28.56/9.94	   A^2 -> H(k, U1(d, d))
28.56/9.94	   A^2 -> H(c, U1(e, b))
28.56/9.94	   A^2 -> H(c, U1(k, b))
28.56/9.94	   A^2 -> H(c, U1(c, d))
28.56/9.94	   A^2 -> H(c, U1(d, c))
28.56/9.94	   A^2 -> H(c, U1(b, e))
28.56/9.94	   A^2 -> H(c, U1(b, k))
28.56/9.94	   A^2 -> H(c, U1(e, c))
28.56/9.94	   A^2 -> H(c, U1(k, c))
28.56/9.94	   A^2 -> H(c, U1(c, e))
28.56/9.94	   A^2 -> H(c, U1(c, k))
28.56/9.94	   A^2 -> H(c, U1(e, e))
28.56/9.94	   A^2 -> H(c, U1(k, k))
28.56/9.94	   A^2 -> H(c, U1(k, d))
28.56/9.94	   A^2 -> H(c, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.94	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.94	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.94	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.94	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, c), b)
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, c), e)
28.56/9.94	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.94	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.94	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.94	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.94	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.94	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.94	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.94	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.94	   A^2 -> H(U1(k, c), b)
28.56/9.94	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.94	   A^2 -> H(U1(k, c), c)
28.56/9.94	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, e), b)
28.56/9.94	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.94	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.94	   A^2 -> H(U1(c, e), c)
28.56/9.94	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.94	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.94	   A^2 -> H(U1(c, e), e)
28.56/9.94	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, k), b)
28.56/9.94	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.94	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.94	   A^2 -> H(U1(c, k), c)
28.56/9.94	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.94	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.94	   A^2 -> H(U1(c, k), e)
28.56/9.94	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, c), d)
28.56/9.94	   A^2 -> H(e, U1(e, b))
28.56/9.94	   A^2 -> H(e, U1(c, d))
28.56/9.94	   A^2 -> H(e, U1(d, c))
28.56/9.94	   A^2 -> H(e, U1(b, e))
28.56/9.94	   A^2 -> H(e, U1(b, k))
28.56/9.94	   A^2 -> H(e, U1(e, c))
28.56/9.94	   A^2 -> H(e, U1(c, e))
28.56/9.94	   A^2 -> H(e, U1(c, k))
28.56/9.94	   A^2 -> H(e, U1(e, e))
28.56/9.94	   A^2 -> H(e, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, e), b)
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, e), c)
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.94	   A^2 -> H(f(e), d)
28.56/9.94	   A^2 -> H(f(e), k)
28.56/9.94	   A^2 -> H(U1(k, k), b)
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.94	
28.56/9.94	The TRS R consists of the following rules:
28.56/9.94	
28.56/9.94	   f(x) -> U1(x, x)
28.56/9.94	   U1(e, x) -> x
28.56/9.94	   a -> c
28.56/9.94	   a -> d
28.56/9.94	   b -> c
28.56/9.94	   b -> d
28.56/9.94	   d -> k
28.56/9.94	   c -> e
28.56/9.94	   c -> k
28.56/9.94	
28.56/9.94	Q is empty.
28.56/9.94	We have to consider all minimal (P,Q,R)-chains.
28.56/9.94	----------------------------------------
28.56/9.94	
28.56/9.94	(1645) TransformationProof (EQUIVALENT)
28.56/9.94	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.94	
28.56/9.94	   (A^2 -> H(U1(k, k), U1(c, e)),A^2 -> H(U1(k, k), U1(c, e)))
28.56/9.94	   (A^2 -> H(U1(k, k), U1(d, e)),A^2 -> H(U1(k, k), U1(d, e)))
28.56/9.94	
28.56/9.94	
28.56/9.94	----------------------------------------
28.56/9.94	
28.56/9.94	(1646)
28.56/9.94	Obligation:
28.56/9.94	Q DP problem:
28.56/9.94	The TRS P consists of the following rules:
28.56/9.94	
28.56/9.94	   A^2 -> H(f(c), f(c))
28.56/9.94	   H(x, x) -> G(x, x, f(k))
28.56/9.94	   G(d, x, x) -> A^2
28.56/9.94	   A^2 -> H(f(d), f(d))
28.56/9.94	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.94	   A^2 -> H(f(e), f(e))
28.56/9.94	   A^2 -> H(f(k), f(k))
28.56/9.94	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.94	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.94	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.94	   A^2 -> H(f(k), b)
28.56/9.94	   A^2 -> H(f(k), U1(e, d))
28.56/9.94	   A^2 -> H(f(k), U1(d, e))
28.56/9.94	   A^2 -> H(f(k), c)
28.56/9.94	   A^2 -> H(f(k), U1(e, k))
28.56/9.94	   A^2 -> H(f(k), U1(k, e))
28.56/9.94	   A^2 -> H(f(k), e)
28.56/9.94	   A^2 -> H(f(c), d)
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.94	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.94	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.94	   A^2 -> H(U1(k, k), f(e))
28.56/9.94	   A^2 -> H(U1(k, k), f(k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, d), b)
28.56/9.94	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.94	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.94	   A^2 -> H(U1(d, d), c)
28.56/9.94	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.94	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.94	   A^2 -> H(U1(d, d), e)
28.56/9.94	   A^2 -> H(f(d), d)
28.56/9.94	   A^2 -> H(f(d), k)
28.56/9.94	   A^2 -> H(U1(c, c), c)
28.56/9.94	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.94	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.94	   A^2 -> H(f(c), k)
28.56/9.94	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.94	   A^2 -> H(f(k), U1(k, k))
28.56/9.94	   A^2 -> H(f(e), e)
28.56/9.94	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.94	   A^2 -> H(d, U1(c, b))
28.56/9.94	   A^2 -> H(d, U1(d, b))
28.56/9.94	   A^2 -> H(d, U1(b, c))
28.56/9.94	   A^2 -> H(d, U1(b, d))
28.56/9.94	   A^2 -> H(d, U1(c, c))
28.56/9.94	   A^2 -> H(d, f(e))
28.56/9.94	   A^2 -> H(d, f(k))
28.56/9.94	   A^2 -> H(d, U1(d, d))
28.56/9.94	   A^2 -> H(a, U1(e, b))
28.56/9.94	   A^2 -> H(a, U1(k, b))
28.56/9.94	   A^2 -> H(a, U1(c, d))
28.56/9.94	   A^2 -> H(a, U1(d, c))
28.56/9.94	   A^2 -> H(a, U1(b, e))
28.56/9.94	   A^2 -> H(a, U1(b, k))
28.56/9.94	   A^2 -> H(a, U1(e, c))
28.56/9.94	   A^2 -> H(a, U1(k, c))
28.56/9.94	   A^2 -> H(a, U1(c, e))
28.56/9.94	   A^2 -> H(a, U1(c, k))
28.56/9.94	   A^2 -> H(a, U1(e, e))
28.56/9.94	   A^2 -> H(a, U1(k, k))
28.56/9.94	   A^2 -> H(a, U1(k, d))
28.56/9.94	   A^2 -> H(a, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.94	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, a), b)
28.56/9.94	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, a), c)
28.56/9.94	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, a), e)
28.56/9.94	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, a), b)
28.56/9.94	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.94	   A^2 -> H(U1(k, a), c)
28.56/9.94	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.94	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.94	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, d), b)
28.56/9.94	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.94	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.94	   A^2 -> H(U1(c, d), c)
28.56/9.94	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.94	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.94	   A^2 -> H(U1(c, d), e)
28.56/9.94	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, a), d)
28.56/9.94	   A^2 -> H(U1(c, a), k)
28.56/9.94	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.94	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.94	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.94	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.94	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.94	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.94	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.94	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, c), b)
28.56/9.94	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.94	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.94	   A^2 -> H(U1(d, c), c)
28.56/9.94	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.94	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.94	   A^2 -> H(U1(d, c), e)
28.56/9.94	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, a), d)
28.56/9.94	   A^2 -> H(U1(d, a), k)
28.56/9.94	   A^2 -> H(U1(a, e), b)
28.56/9.94	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.94	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.94	   A^2 -> H(U1(a, e), c)
28.56/9.94	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.94	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.94	   A^2 -> H(U1(a, e), e)
28.56/9.94	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.94	   A^2 -> H(U1(a, k), b)
28.56/9.94	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.94	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.94	   A^2 -> H(U1(a, k), c)
28.56/9.94	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.94	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.94	   A^2 -> H(U1(a, k), e)
28.56/9.94	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(a, c), d)
28.56/9.94	   A^2 -> H(U1(a, c), k)
28.56/9.94	   A^2 -> H(U1(a, d), d)
28.56/9.94	   A^2 -> H(U1(a, d), k)
28.56/9.94	   A^2 -> H(k, U1(c, b))
28.56/9.94	   A^2 -> H(k, U1(d, b))
28.56/9.94	   A^2 -> H(k, U1(b, c))
28.56/9.94	   A^2 -> H(k, U1(b, d))
28.56/9.94	   A^2 -> H(k, U1(c, c))
28.56/9.94	   A^2 -> H(k, f(e))
28.56/9.94	   A^2 -> H(k, f(k))
28.56/9.94	   A^2 -> H(k, U1(d, d))
28.56/9.94	   A^2 -> H(c, U1(e, b))
28.56/9.94	   A^2 -> H(c, U1(k, b))
28.56/9.94	   A^2 -> H(c, U1(c, d))
28.56/9.94	   A^2 -> H(c, U1(d, c))
28.56/9.94	   A^2 -> H(c, U1(b, e))
28.56/9.94	   A^2 -> H(c, U1(b, k))
28.56/9.94	   A^2 -> H(c, U1(e, c))
28.56/9.94	   A^2 -> H(c, U1(k, c))
28.56/9.94	   A^2 -> H(c, U1(c, e))
28.56/9.94	   A^2 -> H(c, U1(c, k))
28.56/9.94	   A^2 -> H(c, U1(e, e))
28.56/9.94	   A^2 -> H(c, U1(k, k))
28.56/9.94	   A^2 -> H(c, U1(k, d))
28.56/9.94	   A^2 -> H(c, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.94	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.94	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.94	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.94	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, c), b)
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, c), e)
28.56/9.94	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.94	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.94	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.94	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.94	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.94	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.94	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.94	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.94	   A^2 -> H(U1(k, c), b)
28.56/9.94	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.94	   A^2 -> H(U1(k, c), c)
28.56/9.94	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, e), b)
28.56/9.94	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.94	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.94	   A^2 -> H(U1(c, e), c)
28.56/9.94	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.94	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.94	   A^2 -> H(U1(c, e), e)
28.56/9.94	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, k), b)
28.56/9.94	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.94	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.94	   A^2 -> H(U1(c, k), c)
28.56/9.94	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.94	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.94	   A^2 -> H(U1(c, k), e)
28.56/9.94	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, c), d)
28.56/9.94	   A^2 -> H(e, U1(e, b))
28.56/9.94	   A^2 -> H(e, U1(c, d))
28.56/9.94	   A^2 -> H(e, U1(d, c))
28.56/9.94	   A^2 -> H(e, U1(b, e))
28.56/9.94	   A^2 -> H(e, U1(b, k))
28.56/9.94	   A^2 -> H(e, U1(e, c))
28.56/9.94	   A^2 -> H(e, U1(c, e))
28.56/9.94	   A^2 -> H(e, U1(c, k))
28.56/9.94	   A^2 -> H(e, U1(e, e))
28.56/9.94	   A^2 -> H(e, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, e), b)
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, e), c)
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.94	   A^2 -> H(f(e), d)
28.56/9.94	   A^2 -> H(f(e), k)
28.56/9.94	   A^2 -> H(U1(k, k), b)
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.94	
28.56/9.94	The TRS R consists of the following rules:
28.56/9.94	
28.56/9.94	   f(x) -> U1(x, x)
28.56/9.94	   U1(e, x) -> x
28.56/9.94	   a -> c
28.56/9.94	   a -> d
28.56/9.94	   b -> c
28.56/9.94	   b -> d
28.56/9.94	   d -> k
28.56/9.94	   c -> e
28.56/9.94	   c -> k
28.56/9.94	
28.56/9.94	Q is empty.
28.56/9.94	We have to consider all minimal (P,Q,R)-chains.
28.56/9.94	----------------------------------------
28.56/9.94	
28.56/9.94	(1647) TransformationProof (EQUIVALENT)
28.56/9.94	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.94	
28.56/9.94	   (A^2 -> H(U1(k, k), U1(c, k)),A^2 -> H(U1(k, k), U1(c, k)))
28.56/9.94	   (A^2 -> H(U1(k, k), U1(d, k)),A^2 -> H(U1(k, k), U1(d, k)))
28.56/9.94	
28.56/9.94	
28.56/9.94	----------------------------------------
28.56/9.94	
28.56/9.94	(1648)
28.56/9.94	Obligation:
28.56/9.94	Q DP problem:
28.56/9.94	The TRS P consists of the following rules:
28.56/9.94	
28.56/9.94	   A^2 -> H(f(c), f(c))
28.56/9.94	   H(x, x) -> G(x, x, f(k))
28.56/9.94	   G(d, x, x) -> A^2
28.56/9.94	   A^2 -> H(f(d), f(d))
28.56/9.94	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.94	   A^2 -> H(f(e), f(e))
28.56/9.94	   A^2 -> H(f(k), f(k))
28.56/9.94	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.94	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.94	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.94	   A^2 -> H(f(k), b)
28.56/9.94	   A^2 -> H(f(k), U1(e, d))
28.56/9.94	   A^2 -> H(f(k), U1(d, e))
28.56/9.94	   A^2 -> H(f(k), c)
28.56/9.94	   A^2 -> H(f(k), U1(e, k))
28.56/9.94	   A^2 -> H(f(k), U1(k, e))
28.56/9.94	   A^2 -> H(f(k), e)
28.56/9.94	   A^2 -> H(f(c), d)
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.94	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.94	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.94	   A^2 -> H(U1(k, k), f(e))
28.56/9.94	   A^2 -> H(U1(k, k), f(k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, d), b)
28.56/9.94	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.94	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.94	   A^2 -> H(U1(d, d), c)
28.56/9.94	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.94	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.94	   A^2 -> H(U1(d, d), e)
28.56/9.94	   A^2 -> H(f(d), d)
28.56/9.94	   A^2 -> H(f(d), k)
28.56/9.94	   A^2 -> H(U1(c, c), c)
28.56/9.94	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.94	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.94	   A^2 -> H(f(c), k)
28.56/9.94	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.94	   A^2 -> H(f(k), U1(k, k))
28.56/9.94	   A^2 -> H(f(e), e)
28.56/9.94	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.94	   A^2 -> H(d, U1(c, b))
28.56/9.94	   A^2 -> H(d, U1(d, b))
28.56/9.94	   A^2 -> H(d, U1(b, c))
28.56/9.94	   A^2 -> H(d, U1(b, d))
28.56/9.94	   A^2 -> H(d, U1(c, c))
28.56/9.94	   A^2 -> H(d, f(e))
28.56/9.94	   A^2 -> H(d, f(k))
28.56/9.94	   A^2 -> H(d, U1(d, d))
28.56/9.94	   A^2 -> H(a, U1(e, b))
28.56/9.94	   A^2 -> H(a, U1(k, b))
28.56/9.94	   A^2 -> H(a, U1(c, d))
28.56/9.94	   A^2 -> H(a, U1(d, c))
28.56/9.94	   A^2 -> H(a, U1(b, e))
28.56/9.94	   A^2 -> H(a, U1(b, k))
28.56/9.94	   A^2 -> H(a, U1(e, c))
28.56/9.94	   A^2 -> H(a, U1(k, c))
28.56/9.94	   A^2 -> H(a, U1(c, e))
28.56/9.94	   A^2 -> H(a, U1(c, k))
28.56/9.94	   A^2 -> H(a, U1(e, e))
28.56/9.94	   A^2 -> H(a, U1(k, k))
28.56/9.94	   A^2 -> H(a, U1(k, d))
28.56/9.94	   A^2 -> H(a, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.94	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, a), b)
28.56/9.94	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, a), c)
28.56/9.94	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, a), e)
28.56/9.94	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, a), b)
28.56/9.94	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.94	   A^2 -> H(U1(k, a), c)
28.56/9.94	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.94	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.94	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, d), b)
28.56/9.94	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.94	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.94	   A^2 -> H(U1(c, d), c)
28.56/9.94	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.94	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.94	   A^2 -> H(U1(c, d), e)
28.56/9.94	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, a), d)
28.56/9.94	   A^2 -> H(U1(c, a), k)
28.56/9.94	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.94	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.94	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.94	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.94	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.94	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.94	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.94	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, c), b)
28.56/9.94	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.94	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.94	   A^2 -> H(U1(d, c), c)
28.56/9.94	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.94	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.94	   A^2 -> H(U1(d, c), e)
28.56/9.94	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, a), d)
28.56/9.94	   A^2 -> H(U1(d, a), k)
28.56/9.94	   A^2 -> H(U1(a, e), b)
28.56/9.94	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.94	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.94	   A^2 -> H(U1(a, e), c)
28.56/9.94	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.94	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.94	   A^2 -> H(U1(a, e), e)
28.56/9.94	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.94	   A^2 -> H(U1(a, k), b)
28.56/9.94	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.94	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.94	   A^2 -> H(U1(a, k), c)
28.56/9.94	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.94	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.94	   A^2 -> H(U1(a, k), e)
28.56/9.94	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(a, c), d)
28.56/9.94	   A^2 -> H(U1(a, c), k)
28.56/9.94	   A^2 -> H(U1(a, d), d)
28.56/9.94	   A^2 -> H(U1(a, d), k)
28.56/9.94	   A^2 -> H(k, U1(c, b))
28.56/9.94	   A^2 -> H(k, U1(d, b))
28.56/9.94	   A^2 -> H(k, U1(b, c))
28.56/9.94	   A^2 -> H(k, U1(b, d))
28.56/9.94	   A^2 -> H(k, U1(c, c))
28.56/9.94	   A^2 -> H(k, f(e))
28.56/9.94	   A^2 -> H(k, f(k))
28.56/9.94	   A^2 -> H(k, U1(d, d))
28.56/9.94	   A^2 -> H(c, U1(e, b))
28.56/9.94	   A^2 -> H(c, U1(k, b))
28.56/9.94	   A^2 -> H(c, U1(c, d))
28.56/9.94	   A^2 -> H(c, U1(d, c))
28.56/9.94	   A^2 -> H(c, U1(b, e))
28.56/9.94	   A^2 -> H(c, U1(b, k))
28.56/9.94	   A^2 -> H(c, U1(e, c))
28.56/9.94	   A^2 -> H(c, U1(k, c))
28.56/9.94	   A^2 -> H(c, U1(c, e))
28.56/9.94	   A^2 -> H(c, U1(c, k))
28.56/9.94	   A^2 -> H(c, U1(e, e))
28.56/9.94	   A^2 -> H(c, U1(k, k))
28.56/9.94	   A^2 -> H(c, U1(k, d))
28.56/9.94	   A^2 -> H(c, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.94	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.94	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.94	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.94	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, c), b)
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, c), e)
28.56/9.94	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.94	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.94	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.94	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.94	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.94	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.94	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.94	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.94	   A^2 -> H(U1(k, c), b)
28.56/9.94	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.94	   A^2 -> H(U1(k, c), c)
28.56/9.94	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, e), b)
28.56/9.94	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.94	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.94	   A^2 -> H(U1(c, e), c)
28.56/9.94	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.94	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.94	   A^2 -> H(U1(c, e), e)
28.56/9.94	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, k), b)
28.56/9.94	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.94	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.94	   A^2 -> H(U1(c, k), c)
28.56/9.94	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.94	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.94	   A^2 -> H(U1(c, k), e)
28.56/9.94	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, c), d)
28.56/9.94	   A^2 -> H(e, U1(e, b))
28.56/9.94	   A^2 -> H(e, U1(c, d))
28.56/9.94	   A^2 -> H(e, U1(d, c))
28.56/9.94	   A^2 -> H(e, U1(b, e))
28.56/9.94	   A^2 -> H(e, U1(b, k))
28.56/9.94	   A^2 -> H(e, U1(e, c))
28.56/9.94	   A^2 -> H(e, U1(c, e))
28.56/9.94	   A^2 -> H(e, U1(c, k))
28.56/9.94	   A^2 -> H(e, U1(e, e))
28.56/9.94	   A^2 -> H(e, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, e), b)
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, e), c)
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.94	   A^2 -> H(f(e), d)
28.56/9.94	   A^2 -> H(f(e), k)
28.56/9.94	   A^2 -> H(U1(k, k), b)
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.94	
28.56/9.94	The TRS R consists of the following rules:
28.56/9.94	
28.56/9.94	   f(x) -> U1(x, x)
28.56/9.94	   U1(e, x) -> x
28.56/9.94	   a -> c
28.56/9.94	   a -> d
28.56/9.94	   b -> c
28.56/9.94	   b -> d
28.56/9.94	   d -> k
28.56/9.94	   c -> e
28.56/9.94	   c -> k
28.56/9.94	
28.56/9.94	Q is empty.
28.56/9.94	We have to consider all minimal (P,Q,R)-chains.
28.56/9.94	----------------------------------------
28.56/9.94	
28.56/9.94	(1649) TransformationProof (EQUIVALENT)
28.56/9.94	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.94	
28.56/9.94	   (A^2 -> H(U1(k, k), c),A^2 -> H(U1(k, k), c))
28.56/9.94	   (A^2 -> H(U1(k, k), U1(e, e)),A^2 -> H(U1(k, k), U1(e, e)))
28.56/9.94	   (A^2 -> H(U1(k, k), U1(e, k)),A^2 -> H(U1(k, k), U1(e, k)))
28.56/9.94	
28.56/9.94	
28.56/9.94	----------------------------------------
28.56/9.94	
28.56/9.94	(1650)
28.56/9.94	Obligation:
28.56/9.94	Q DP problem:
28.56/9.94	The TRS P consists of the following rules:
28.56/9.94	
28.56/9.94	   A^2 -> H(f(c), f(c))
28.56/9.94	   H(x, x) -> G(x, x, f(k))
28.56/9.94	   G(d, x, x) -> A^2
28.56/9.94	   A^2 -> H(f(d), f(d))
28.56/9.94	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.94	   A^2 -> H(f(e), f(e))
28.56/9.94	   A^2 -> H(f(k), f(k))
28.56/9.94	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.94	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.94	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.94	   A^2 -> H(f(k), b)
28.56/9.94	   A^2 -> H(f(k), U1(e, d))
28.56/9.94	   A^2 -> H(f(k), U1(d, e))
28.56/9.94	   A^2 -> H(f(k), c)
28.56/9.94	   A^2 -> H(f(k), U1(e, k))
28.56/9.94	   A^2 -> H(f(k), U1(k, e))
28.56/9.94	   A^2 -> H(f(k), e)
28.56/9.94	   A^2 -> H(f(c), d)
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.94	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.94	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.94	   A^2 -> H(U1(k, k), f(e))
28.56/9.94	   A^2 -> H(U1(k, k), f(k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, d), b)
28.56/9.94	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.94	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.94	   A^2 -> H(U1(d, d), c)
28.56/9.94	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.94	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.94	   A^2 -> H(U1(d, d), e)
28.56/9.94	   A^2 -> H(f(d), d)
28.56/9.94	   A^2 -> H(f(d), k)
28.56/9.94	   A^2 -> H(U1(c, c), c)
28.56/9.94	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.94	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.94	   A^2 -> H(f(c), k)
28.56/9.94	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.94	   A^2 -> H(f(k), U1(k, k))
28.56/9.94	   A^2 -> H(f(e), e)
28.56/9.94	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.94	   A^2 -> H(d, U1(c, b))
28.56/9.94	   A^2 -> H(d, U1(d, b))
28.56/9.94	   A^2 -> H(d, U1(b, c))
28.56/9.94	   A^2 -> H(d, U1(b, d))
28.56/9.94	   A^2 -> H(d, U1(c, c))
28.56/9.94	   A^2 -> H(d, f(e))
28.56/9.94	   A^2 -> H(d, f(k))
28.56/9.94	   A^2 -> H(d, U1(d, d))
28.56/9.94	   A^2 -> H(a, U1(e, b))
28.56/9.94	   A^2 -> H(a, U1(k, b))
28.56/9.94	   A^2 -> H(a, U1(c, d))
28.56/9.94	   A^2 -> H(a, U1(d, c))
28.56/9.94	   A^2 -> H(a, U1(b, e))
28.56/9.94	   A^2 -> H(a, U1(b, k))
28.56/9.94	   A^2 -> H(a, U1(e, c))
28.56/9.94	   A^2 -> H(a, U1(k, c))
28.56/9.94	   A^2 -> H(a, U1(c, e))
28.56/9.94	   A^2 -> H(a, U1(c, k))
28.56/9.94	   A^2 -> H(a, U1(e, e))
28.56/9.94	   A^2 -> H(a, U1(k, k))
28.56/9.94	   A^2 -> H(a, U1(k, d))
28.56/9.94	   A^2 -> H(a, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.94	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, a), b)
28.56/9.94	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, a), c)
28.56/9.94	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, a), e)
28.56/9.94	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, a), b)
28.56/9.94	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.94	   A^2 -> H(U1(k, a), c)
28.56/9.94	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.94	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.94	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, d), b)
28.56/9.94	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.94	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.94	   A^2 -> H(U1(c, d), c)
28.56/9.94	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.94	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.94	   A^2 -> H(U1(c, d), e)
28.56/9.94	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, a), d)
28.56/9.94	   A^2 -> H(U1(c, a), k)
28.56/9.94	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.94	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.94	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.94	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.94	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.94	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.94	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.94	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, c), b)
28.56/9.94	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.94	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.94	   A^2 -> H(U1(d, c), c)
28.56/9.94	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.94	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.94	   A^2 -> H(U1(d, c), e)
28.56/9.94	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, a), d)
28.56/9.94	   A^2 -> H(U1(d, a), k)
28.56/9.94	   A^2 -> H(U1(a, e), b)
28.56/9.94	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.94	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.94	   A^2 -> H(U1(a, e), c)
28.56/9.94	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.94	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.94	   A^2 -> H(U1(a, e), e)
28.56/9.94	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.94	   A^2 -> H(U1(a, k), b)
28.56/9.94	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.94	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.94	   A^2 -> H(U1(a, k), c)
28.56/9.94	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.94	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.94	   A^2 -> H(U1(a, k), e)
28.56/9.94	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(a, c), d)
28.56/9.94	   A^2 -> H(U1(a, c), k)
28.56/9.94	   A^2 -> H(U1(a, d), d)
28.56/9.94	   A^2 -> H(U1(a, d), k)
28.56/9.94	   A^2 -> H(k, U1(c, b))
28.56/9.94	   A^2 -> H(k, U1(d, b))
28.56/9.94	   A^2 -> H(k, U1(b, c))
28.56/9.94	   A^2 -> H(k, U1(b, d))
28.56/9.94	   A^2 -> H(k, U1(c, c))
28.56/9.94	   A^2 -> H(k, f(e))
28.56/9.94	   A^2 -> H(k, f(k))
28.56/9.94	   A^2 -> H(k, U1(d, d))
28.56/9.94	   A^2 -> H(c, U1(e, b))
28.56/9.94	   A^2 -> H(c, U1(k, b))
28.56/9.94	   A^2 -> H(c, U1(c, d))
28.56/9.94	   A^2 -> H(c, U1(d, c))
28.56/9.94	   A^2 -> H(c, U1(b, e))
28.56/9.94	   A^2 -> H(c, U1(b, k))
28.56/9.94	   A^2 -> H(c, U1(e, c))
28.56/9.94	   A^2 -> H(c, U1(k, c))
28.56/9.94	   A^2 -> H(c, U1(c, e))
28.56/9.94	   A^2 -> H(c, U1(c, k))
28.56/9.94	   A^2 -> H(c, U1(e, e))
28.56/9.94	   A^2 -> H(c, U1(k, k))
28.56/9.94	   A^2 -> H(c, U1(k, d))
28.56/9.94	   A^2 -> H(c, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.94	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.94	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.94	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.94	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, c), b)
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, c), e)
28.56/9.94	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.94	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.94	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.94	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.94	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.94	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.94	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.94	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.94	   A^2 -> H(U1(k, c), b)
28.56/9.94	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.94	   A^2 -> H(U1(k, c), c)
28.56/9.94	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, e), b)
28.56/9.94	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.94	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.94	   A^2 -> H(U1(c, e), c)
28.56/9.94	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.94	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.94	   A^2 -> H(U1(c, e), e)
28.56/9.94	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, k), b)
28.56/9.94	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.94	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.94	   A^2 -> H(U1(c, k), c)
28.56/9.94	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.94	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.94	   A^2 -> H(U1(c, k), e)
28.56/9.94	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, c), d)
28.56/9.94	   A^2 -> H(e, U1(e, b))
28.56/9.94	   A^2 -> H(e, U1(c, d))
28.56/9.94	   A^2 -> H(e, U1(d, c))
28.56/9.94	   A^2 -> H(e, U1(b, e))
28.56/9.94	   A^2 -> H(e, U1(b, k))
28.56/9.94	   A^2 -> H(e, U1(e, c))
28.56/9.94	   A^2 -> H(e, U1(c, e))
28.56/9.94	   A^2 -> H(e, U1(c, k))
28.56/9.94	   A^2 -> H(e, U1(e, e))
28.56/9.94	   A^2 -> H(e, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, e), b)
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, e), c)
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.94	   A^2 -> H(f(e), d)
28.56/9.94	   A^2 -> H(f(e), k)
28.56/9.94	   A^2 -> H(U1(k, k), b)
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.94	   A^2 -> H(U1(k, k), c)
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.94	
28.56/9.94	The TRS R consists of the following rules:
28.56/9.94	
28.56/9.94	   f(x) -> U1(x, x)
28.56/9.94	   U1(e, x) -> x
28.56/9.94	   a -> c
28.56/9.94	   a -> d
28.56/9.94	   b -> c
28.56/9.94	   b -> d
28.56/9.94	   d -> k
28.56/9.94	   c -> e
28.56/9.94	   c -> k
28.56/9.94	
28.56/9.94	Q is empty.
28.56/9.94	We have to consider all minimal (P,Q,R)-chains.
28.56/9.94	----------------------------------------
28.56/9.94	
28.56/9.94	(1651) TransformationProof (EQUIVALENT)
28.56/9.94	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.94	
28.56/9.94	   (A^2 -> H(U1(k, k), U1(k, e)),A^2 -> H(U1(k, k), U1(k, e)))
28.56/9.94	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.56/9.94	
28.56/9.94	
28.56/9.94	----------------------------------------
28.56/9.94	
28.56/9.94	(1652)
28.56/9.94	Obligation:
28.56/9.94	Q DP problem:
28.56/9.94	The TRS P consists of the following rules:
28.56/9.94	
28.56/9.94	   A^2 -> H(f(c), f(c))
28.56/9.94	   H(x, x) -> G(x, x, f(k))
28.56/9.94	   G(d, x, x) -> A^2
28.56/9.94	   A^2 -> H(f(d), f(d))
28.56/9.94	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.94	   A^2 -> H(f(e), f(e))
28.56/9.94	   A^2 -> H(f(k), f(k))
28.56/9.94	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.94	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.94	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.94	   A^2 -> H(f(k), b)
28.56/9.94	   A^2 -> H(f(k), U1(e, d))
28.56/9.94	   A^2 -> H(f(k), U1(d, e))
28.56/9.94	   A^2 -> H(f(k), c)
28.56/9.94	   A^2 -> H(f(k), U1(e, k))
28.56/9.94	   A^2 -> H(f(k), U1(k, e))
28.56/9.94	   A^2 -> H(f(k), e)
28.56/9.94	   A^2 -> H(f(c), d)
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.94	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.94	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.94	   A^2 -> H(U1(k, k), f(e))
28.56/9.94	   A^2 -> H(U1(k, k), f(k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, d), b)
28.56/9.94	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.94	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.94	   A^2 -> H(U1(d, d), c)
28.56/9.94	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.94	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.94	   A^2 -> H(U1(d, d), e)
28.56/9.94	   A^2 -> H(f(d), d)
28.56/9.94	   A^2 -> H(f(d), k)
28.56/9.94	   A^2 -> H(U1(c, c), c)
28.56/9.94	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.94	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.94	   A^2 -> H(f(c), k)
28.56/9.94	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.94	   A^2 -> H(f(k), U1(k, k))
28.56/9.94	   A^2 -> H(f(e), e)
28.56/9.94	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.94	   A^2 -> H(d, U1(c, b))
28.56/9.94	   A^2 -> H(d, U1(d, b))
28.56/9.94	   A^2 -> H(d, U1(b, c))
28.56/9.94	   A^2 -> H(d, U1(b, d))
28.56/9.94	   A^2 -> H(d, U1(c, c))
28.56/9.94	   A^2 -> H(d, f(e))
28.56/9.94	   A^2 -> H(d, f(k))
28.56/9.94	   A^2 -> H(d, U1(d, d))
28.56/9.94	   A^2 -> H(a, U1(e, b))
28.56/9.94	   A^2 -> H(a, U1(k, b))
28.56/9.94	   A^2 -> H(a, U1(c, d))
28.56/9.94	   A^2 -> H(a, U1(d, c))
28.56/9.94	   A^2 -> H(a, U1(b, e))
28.56/9.94	   A^2 -> H(a, U1(b, k))
28.56/9.94	   A^2 -> H(a, U1(e, c))
28.56/9.94	   A^2 -> H(a, U1(k, c))
28.56/9.94	   A^2 -> H(a, U1(c, e))
28.56/9.94	   A^2 -> H(a, U1(c, k))
28.56/9.94	   A^2 -> H(a, U1(e, e))
28.56/9.94	   A^2 -> H(a, U1(k, k))
28.56/9.94	   A^2 -> H(a, U1(k, d))
28.56/9.94	   A^2 -> H(a, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.94	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, a), b)
28.56/9.94	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, a), c)
28.56/9.94	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, a), e)
28.56/9.94	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, a), b)
28.56/9.94	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.94	   A^2 -> H(U1(k, a), c)
28.56/9.94	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.94	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.94	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, d), b)
28.56/9.94	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.94	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.94	   A^2 -> H(U1(c, d), c)
28.56/9.94	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.94	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.94	   A^2 -> H(U1(c, d), e)
28.56/9.94	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, a), d)
28.56/9.94	   A^2 -> H(U1(c, a), k)
28.56/9.94	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.94	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.94	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.94	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.94	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.94	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.94	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.94	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, c), b)
28.56/9.94	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.94	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.94	   A^2 -> H(U1(d, c), c)
28.56/9.94	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.94	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.94	   A^2 -> H(U1(d, c), e)
28.56/9.94	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, a), d)
28.56/9.94	   A^2 -> H(U1(d, a), k)
28.56/9.94	   A^2 -> H(U1(a, e), b)
28.56/9.94	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.94	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.94	   A^2 -> H(U1(a, e), c)
28.56/9.94	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.94	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.94	   A^2 -> H(U1(a, e), e)
28.56/9.94	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.94	   A^2 -> H(U1(a, k), b)
28.56/9.94	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.94	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.94	   A^2 -> H(U1(a, k), c)
28.56/9.94	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.94	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.94	   A^2 -> H(U1(a, k), e)
28.56/9.94	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(a, c), d)
28.56/9.94	   A^2 -> H(U1(a, c), k)
28.56/9.94	   A^2 -> H(U1(a, d), d)
28.56/9.94	   A^2 -> H(U1(a, d), k)
28.56/9.94	   A^2 -> H(k, U1(c, b))
28.56/9.94	   A^2 -> H(k, U1(d, b))
28.56/9.94	   A^2 -> H(k, U1(b, c))
28.56/9.94	   A^2 -> H(k, U1(b, d))
28.56/9.94	   A^2 -> H(k, U1(c, c))
28.56/9.94	   A^2 -> H(k, f(e))
28.56/9.94	   A^2 -> H(k, f(k))
28.56/9.94	   A^2 -> H(k, U1(d, d))
28.56/9.94	   A^2 -> H(c, U1(e, b))
28.56/9.94	   A^2 -> H(c, U1(k, b))
28.56/9.94	   A^2 -> H(c, U1(c, d))
28.56/9.94	   A^2 -> H(c, U1(d, c))
28.56/9.94	   A^2 -> H(c, U1(b, e))
28.56/9.94	   A^2 -> H(c, U1(b, k))
28.56/9.94	   A^2 -> H(c, U1(e, c))
28.56/9.94	   A^2 -> H(c, U1(k, c))
28.56/9.94	   A^2 -> H(c, U1(c, e))
28.56/9.94	   A^2 -> H(c, U1(c, k))
28.56/9.94	   A^2 -> H(c, U1(e, e))
28.56/9.94	   A^2 -> H(c, U1(k, k))
28.56/9.94	   A^2 -> H(c, U1(k, d))
28.56/9.94	   A^2 -> H(c, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.94	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.94	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.94	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.94	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, c), b)
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, c), e)
28.56/9.94	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.94	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.94	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.94	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.94	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.94	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.94	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.94	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.94	   A^2 -> H(U1(k, c), b)
28.56/9.94	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.94	   A^2 -> H(U1(k, c), c)
28.56/9.94	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, e), b)
28.56/9.94	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.94	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.94	   A^2 -> H(U1(c, e), c)
28.56/9.94	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.94	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.94	   A^2 -> H(U1(c, e), e)
28.56/9.94	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, k), b)
28.56/9.94	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.94	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.94	   A^2 -> H(U1(c, k), c)
28.56/9.94	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.94	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.94	   A^2 -> H(U1(c, k), e)
28.56/9.94	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, c), d)
28.56/9.94	   A^2 -> H(e, U1(e, b))
28.56/9.94	   A^2 -> H(e, U1(c, d))
28.56/9.94	   A^2 -> H(e, U1(d, c))
28.56/9.94	   A^2 -> H(e, U1(b, e))
28.56/9.94	   A^2 -> H(e, U1(b, k))
28.56/9.94	   A^2 -> H(e, U1(e, c))
28.56/9.94	   A^2 -> H(e, U1(c, e))
28.56/9.94	   A^2 -> H(e, U1(c, k))
28.56/9.94	   A^2 -> H(e, U1(e, e))
28.56/9.94	   A^2 -> H(e, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, e), b)
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, e), c)
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.94	   A^2 -> H(f(e), d)
28.56/9.94	   A^2 -> H(f(e), k)
28.56/9.94	   A^2 -> H(U1(k, k), b)
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.94	   A^2 -> H(U1(k, k), c)
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, e))
28.56/9.94	
28.56/9.94	The TRS R consists of the following rules:
28.56/9.94	
28.56/9.94	   f(x) -> U1(x, x)
28.56/9.94	   U1(e, x) -> x
28.56/9.94	   a -> c
28.56/9.94	   a -> d
28.56/9.94	   b -> c
28.56/9.94	   b -> d
28.56/9.94	   d -> k
28.56/9.94	   c -> e
28.56/9.94	   c -> k
28.56/9.94	
28.56/9.94	Q is empty.
28.56/9.94	We have to consider all minimal (P,Q,R)-chains.
28.56/9.94	----------------------------------------
28.56/9.94	
28.56/9.94	(1653) DependencyGraphProof (EQUIVALENT)
28.56/9.94	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.94	----------------------------------------
28.56/9.94	
28.56/9.94	(1654)
28.56/9.94	Obligation:
28.56/9.94	Q DP problem:
28.56/9.94	The TRS P consists of the following rules:
28.56/9.94	
28.56/9.94	   H(x, x) -> G(x, x, f(k))
28.56/9.94	   G(d, x, x) -> A^2
28.56/9.94	   A^2 -> H(f(c), f(c))
28.56/9.94	   A^2 -> H(f(d), f(d))
28.56/9.94	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.94	   A^2 -> H(f(e), f(e))
28.56/9.94	   A^2 -> H(f(k), f(k))
28.56/9.94	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.94	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.94	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.94	   A^2 -> H(f(k), b)
28.56/9.94	   A^2 -> H(f(k), U1(e, d))
28.56/9.94	   A^2 -> H(f(k), U1(d, e))
28.56/9.94	   A^2 -> H(f(k), c)
28.56/9.94	   A^2 -> H(f(k), U1(e, k))
28.56/9.94	   A^2 -> H(f(k), U1(k, e))
28.56/9.94	   A^2 -> H(f(k), e)
28.56/9.94	   A^2 -> H(f(c), d)
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.94	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.94	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.94	   A^2 -> H(U1(k, k), f(e))
28.56/9.94	   A^2 -> H(U1(k, k), f(k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, d), b)
28.56/9.94	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.94	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.94	   A^2 -> H(U1(d, d), c)
28.56/9.94	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.94	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.94	   A^2 -> H(U1(d, d), e)
28.56/9.94	   A^2 -> H(f(d), d)
28.56/9.94	   A^2 -> H(f(d), k)
28.56/9.94	   A^2 -> H(U1(c, c), c)
28.56/9.94	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.94	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.94	   A^2 -> H(f(c), k)
28.56/9.94	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.94	   A^2 -> H(f(k), U1(k, k))
28.56/9.94	   A^2 -> H(f(e), e)
28.56/9.94	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.94	   A^2 -> H(d, U1(c, b))
28.56/9.94	   A^2 -> H(d, U1(d, b))
28.56/9.94	   A^2 -> H(d, U1(b, c))
28.56/9.94	   A^2 -> H(d, U1(b, d))
28.56/9.94	   A^2 -> H(d, U1(c, c))
28.56/9.94	   A^2 -> H(d, f(e))
28.56/9.94	   A^2 -> H(d, f(k))
28.56/9.94	   A^2 -> H(d, U1(d, d))
28.56/9.94	   A^2 -> H(a, U1(e, b))
28.56/9.94	   A^2 -> H(a, U1(k, b))
28.56/9.94	   A^2 -> H(a, U1(c, d))
28.56/9.94	   A^2 -> H(a, U1(d, c))
28.56/9.94	   A^2 -> H(a, U1(b, e))
28.56/9.94	   A^2 -> H(a, U1(b, k))
28.56/9.94	   A^2 -> H(a, U1(e, c))
28.56/9.94	   A^2 -> H(a, U1(k, c))
28.56/9.94	   A^2 -> H(a, U1(c, e))
28.56/9.94	   A^2 -> H(a, U1(c, k))
28.56/9.94	   A^2 -> H(a, U1(e, e))
28.56/9.94	   A^2 -> H(a, U1(k, k))
28.56/9.94	   A^2 -> H(a, U1(k, d))
28.56/9.94	   A^2 -> H(a, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.94	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, a), b)
28.56/9.94	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, a), c)
28.56/9.94	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, a), e)
28.56/9.94	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, a), b)
28.56/9.94	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.94	   A^2 -> H(U1(k, a), c)
28.56/9.94	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.94	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.94	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, d), b)
28.56/9.94	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.94	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.94	   A^2 -> H(U1(c, d), c)
28.56/9.94	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.94	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.94	   A^2 -> H(U1(c, d), e)
28.56/9.94	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, a), d)
28.56/9.94	   A^2 -> H(U1(c, a), k)
28.56/9.94	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.94	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.94	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.94	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.94	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.94	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.94	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.94	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, c), b)
28.56/9.94	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.94	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.94	   A^2 -> H(U1(d, c), c)
28.56/9.94	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.94	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.94	   A^2 -> H(U1(d, c), e)
28.56/9.94	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, a), d)
28.56/9.94	   A^2 -> H(U1(d, a), k)
28.56/9.94	   A^2 -> H(U1(a, e), b)
28.56/9.94	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.94	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.94	   A^2 -> H(U1(a, e), c)
28.56/9.94	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.94	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.94	   A^2 -> H(U1(a, e), e)
28.56/9.94	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.94	   A^2 -> H(U1(a, k), b)
28.56/9.94	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.94	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.94	   A^2 -> H(U1(a, k), c)
28.56/9.94	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.94	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.94	   A^2 -> H(U1(a, k), e)
28.56/9.94	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(a, c), d)
28.56/9.94	   A^2 -> H(U1(a, c), k)
28.56/9.94	   A^2 -> H(U1(a, d), d)
28.56/9.94	   A^2 -> H(U1(a, d), k)
28.56/9.94	   A^2 -> H(k, U1(c, b))
28.56/9.94	   A^2 -> H(k, U1(d, b))
28.56/9.94	   A^2 -> H(k, U1(b, c))
28.56/9.94	   A^2 -> H(k, U1(b, d))
28.56/9.94	   A^2 -> H(k, U1(c, c))
28.56/9.94	   A^2 -> H(k, f(e))
28.56/9.94	   A^2 -> H(k, f(k))
28.56/9.94	   A^2 -> H(k, U1(d, d))
28.56/9.94	   A^2 -> H(c, U1(e, b))
28.56/9.94	   A^2 -> H(c, U1(k, b))
28.56/9.94	   A^2 -> H(c, U1(c, d))
28.56/9.94	   A^2 -> H(c, U1(d, c))
28.56/9.94	   A^2 -> H(c, U1(b, e))
28.56/9.94	   A^2 -> H(c, U1(b, k))
28.56/9.94	   A^2 -> H(c, U1(e, c))
28.56/9.94	   A^2 -> H(c, U1(k, c))
28.56/9.94	   A^2 -> H(c, U1(c, e))
28.56/9.94	   A^2 -> H(c, U1(c, k))
28.56/9.94	   A^2 -> H(c, U1(e, e))
28.56/9.94	   A^2 -> H(c, U1(k, k))
28.56/9.94	   A^2 -> H(c, U1(k, d))
28.56/9.94	   A^2 -> H(c, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.94	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.94	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.94	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.94	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, c), b)
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, c), e)
28.56/9.94	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.94	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.94	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.94	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.94	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.94	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.94	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.94	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.94	   A^2 -> H(U1(k, c), b)
28.56/9.94	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.94	   A^2 -> H(U1(k, c), c)
28.56/9.94	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, e), b)
28.56/9.94	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.94	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.94	   A^2 -> H(U1(c, e), c)
28.56/9.94	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.94	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.94	   A^2 -> H(U1(c, e), e)
28.56/9.94	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, k), b)
28.56/9.94	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.94	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.94	   A^2 -> H(U1(c, k), c)
28.56/9.94	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.94	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.94	   A^2 -> H(U1(c, k), e)
28.56/9.94	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(c, c), d)
28.56/9.94	   A^2 -> H(e, U1(e, b))
28.56/9.94	   A^2 -> H(e, U1(c, d))
28.56/9.94	   A^2 -> H(e, U1(d, c))
28.56/9.94	   A^2 -> H(e, U1(b, e))
28.56/9.94	   A^2 -> H(e, U1(b, k))
28.56/9.94	   A^2 -> H(e, U1(e, c))
28.56/9.94	   A^2 -> H(e, U1(c, e))
28.56/9.94	   A^2 -> H(e, U1(c, k))
28.56/9.94	   A^2 -> H(e, U1(e, e))
28.56/9.94	   A^2 -> H(e, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, e), b)
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, e), c)
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.94	   A^2 -> H(f(e), d)
28.56/9.94	   A^2 -> H(f(e), k)
28.56/9.94	   A^2 -> H(U1(k, k), b)
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.94	   A^2 -> H(U1(k, k), c)
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.94	
28.56/9.94	The TRS R consists of the following rules:
28.56/9.94	
28.56/9.94	   f(x) -> U1(x, x)
28.56/9.94	   U1(e, x) -> x
28.56/9.94	   a -> c
28.56/9.94	   a -> d
28.56/9.94	   b -> c
28.56/9.94	   b -> d
28.56/9.94	   d -> k
28.56/9.94	   c -> e
28.56/9.94	   c -> k
28.56/9.94	
28.56/9.94	Q is empty.
28.56/9.94	We have to consider all minimal (P,Q,R)-chains.
28.56/9.94	----------------------------------------
28.56/9.94	
28.56/9.94	(1655) TransformationProof (EQUIVALENT)
28.56/9.94	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.94	
28.56/9.94	   (A^2 -> H(U1(k, k), U1(e, e)),A^2 -> H(U1(k, k), U1(e, e)))
28.56/9.94	   (A^2 -> H(U1(k, k), U1(k, e)),A^2 -> H(U1(k, k), U1(k, e)))
28.56/9.94	
28.56/9.94	
28.56/9.94	----------------------------------------
28.56/9.94	
28.56/9.94	(1656)
28.56/9.94	Obligation:
28.56/9.94	Q DP problem:
28.56/9.94	The TRS P consists of the following rules:
28.56/9.94	
28.56/9.94	   H(x, x) -> G(x, x, f(k))
28.56/9.94	   G(d, x, x) -> A^2
28.56/9.94	   A^2 -> H(f(c), f(c))
28.56/9.94	   A^2 -> H(f(d), f(d))
28.56/9.94	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.94	   A^2 -> H(f(e), f(e))
28.56/9.94	   A^2 -> H(f(k), f(k))
28.56/9.94	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.94	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.94	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.94	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.94	   A^2 -> H(f(k), b)
28.56/9.94	   A^2 -> H(f(k), U1(e, d))
28.56/9.94	   A^2 -> H(f(k), U1(d, e))
28.56/9.94	   A^2 -> H(f(k), c)
28.56/9.94	   A^2 -> H(f(k), U1(e, k))
28.56/9.94	   A^2 -> H(f(k), U1(k, e))
28.56/9.94	   A^2 -> H(f(k), e)
28.56/9.94	   A^2 -> H(f(c), d)
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.94	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.94	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.94	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.94	   A^2 -> H(U1(k, k), f(e))
28.56/9.94	   A^2 -> H(U1(k, k), f(k))
28.56/9.94	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.94	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.94	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.94	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.94	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.94	   A^2 -> H(U1(d, d), b)
28.56/9.94	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.94	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.94	   A^2 -> H(U1(d, d), c)
28.56/9.94	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.94	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.94	   A^2 -> H(U1(d, d), e)
28.56/9.94	   A^2 -> H(f(d), d)
28.56/9.94	   A^2 -> H(f(d), k)
28.56/9.94	   A^2 -> H(U1(c, c), c)
28.56/9.94	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.94	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.94	   A^2 -> H(f(c), k)
28.56/9.94	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.94	   A^2 -> H(f(k), U1(k, k))
28.56/9.94	   A^2 -> H(f(e), e)
28.56/9.94	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.94	   A^2 -> H(d, U1(c, b))
28.56/9.94	   A^2 -> H(d, U1(d, b))
28.56/9.94	   A^2 -> H(d, U1(b, c))
28.56/9.94	   A^2 -> H(d, U1(b, d))
28.56/9.94	   A^2 -> H(d, U1(c, c))
28.56/9.94	   A^2 -> H(d, f(e))
28.56/9.94	   A^2 -> H(d, f(k))
28.56/9.94	   A^2 -> H(d, U1(d, d))
28.56/9.94	   A^2 -> H(a, U1(e, b))
28.56/9.94	   A^2 -> H(a, U1(k, b))
28.56/9.94	   A^2 -> H(a, U1(c, d))
28.56/9.94	   A^2 -> H(a, U1(d, c))
28.56/9.94	   A^2 -> H(a, U1(b, e))
28.56/9.94	   A^2 -> H(a, U1(b, k))
28.56/9.94	   A^2 -> H(a, U1(e, c))
28.56/9.94	   A^2 -> H(a, U1(k, c))
28.56/9.94	   A^2 -> H(a, U1(c, e))
28.56/9.94	   A^2 -> H(a, U1(c, k))
28.56/9.94	   A^2 -> H(a, U1(e, e))
28.56/9.94	   A^2 -> H(a, U1(k, k))
28.56/9.94	   A^2 -> H(a, U1(k, d))
28.56/9.94	   A^2 -> H(a, U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.94	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.94	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.94	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.94	   A^2 -> H(U1(e, a), b)
28.56/9.94	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.94	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.94	   A^2 -> H(U1(e, a), c)
28.56/9.94	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.94	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.94	   A^2 -> H(U1(e, a), e)
28.56/9.94	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.94	   A^2 -> H(U1(k, a), b)
28.56/9.94	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.94	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.94	   A^2 -> H(U1(k, a), c)
28.56/9.94	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.94	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.94	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, d), b)
28.56/9.95	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, d), c)
28.56/9.95	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, d), e)
28.56/9.95	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, a), d)
28.56/9.95	   A^2 -> H(U1(c, a), k)
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.95	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, c), b)
28.56/9.95	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(d, c), c)
28.56/9.95	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(d, c), e)
28.56/9.95	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, a), d)
28.56/9.95	   A^2 -> H(U1(d, a), k)
28.56/9.95	   A^2 -> H(U1(a, e), b)
28.56/9.95	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(a, e), c)
28.56/9.95	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(a, e), e)
28.56/9.95	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(a, k), b)
28.56/9.95	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(a, k), c)
28.56/9.95	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.95	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.95	   A^2 -> H(U1(a, k), e)
28.56/9.95	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(a, c), d)
28.56/9.95	   A^2 -> H(U1(a, c), k)
28.56/9.95	   A^2 -> H(U1(a, d), d)
28.56/9.95	   A^2 -> H(U1(a, d), k)
28.56/9.95	   A^2 -> H(k, U1(c, b))
28.56/9.95	   A^2 -> H(k, U1(d, b))
28.56/9.95	   A^2 -> H(k, U1(b, c))
28.56/9.95	   A^2 -> H(k, U1(b, d))
28.56/9.95	   A^2 -> H(k, U1(c, c))
28.56/9.95	   A^2 -> H(k, f(e))
28.56/9.95	   A^2 -> H(k, f(k))
28.56/9.95	   A^2 -> H(k, U1(d, d))
28.56/9.95	   A^2 -> H(c, U1(e, b))
28.56/9.95	   A^2 -> H(c, U1(k, b))
28.56/9.95	   A^2 -> H(c, U1(c, d))
28.56/9.95	   A^2 -> H(c, U1(d, c))
28.56/9.95	   A^2 -> H(c, U1(b, e))
28.56/9.95	   A^2 -> H(c, U1(b, k))
28.56/9.95	   A^2 -> H(c, U1(e, c))
28.56/9.95	   A^2 -> H(c, U1(k, c))
28.56/9.95	   A^2 -> H(c, U1(c, e))
28.56/9.95	   A^2 -> H(c, U1(c, k))
28.56/9.95	   A^2 -> H(c, U1(e, e))
28.56/9.95	   A^2 -> H(c, U1(k, k))
28.56/9.95	   A^2 -> H(c, U1(k, d))
28.56/9.95	   A^2 -> H(c, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.95	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.95	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, c), b)
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, c), e)
28.56/9.95	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.95	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.95	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.95	   A^2 -> H(U1(k, c), b)
28.56/9.95	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, c), c)
28.56/9.95	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, e), b)
28.56/9.95	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, e), c)
28.56/9.95	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, e), e)
28.56/9.95	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, k), b)
28.56/9.95	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, k), c)
28.56/9.95	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, k), e)
28.56/9.95	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, c), d)
28.56/9.95	   A^2 -> H(e, U1(e, b))
28.56/9.95	   A^2 -> H(e, U1(c, d))
28.56/9.95	   A^2 -> H(e, U1(d, c))
28.56/9.95	   A^2 -> H(e, U1(b, e))
28.56/9.95	   A^2 -> H(e, U1(b, k))
28.56/9.95	   A^2 -> H(e, U1(e, c))
28.56/9.95	   A^2 -> H(e, U1(c, e))
28.56/9.95	   A^2 -> H(e, U1(c, k))
28.56/9.95	   A^2 -> H(e, U1(e, e))
28.56/9.95	   A^2 -> H(e, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, e), b)
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, e), c)
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.95	   A^2 -> H(f(e), d)
28.56/9.95	   A^2 -> H(f(e), k)
28.56/9.95	   A^2 -> H(U1(k, k), b)
28.56/9.95	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, k), c)
28.56/9.95	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.95	   A^2 -> H(U1(k, k), U1(k, e))
28.56/9.95	
28.56/9.95	The TRS R consists of the following rules:
28.56/9.95	
28.56/9.95	   f(x) -> U1(x, x)
28.56/9.95	   U1(e, x) -> x
28.56/9.95	   a -> c
28.56/9.95	   a -> d
28.56/9.95	   b -> c
28.56/9.95	   b -> d
28.56/9.95	   d -> k
28.56/9.95	   c -> e
28.56/9.95	   c -> k
28.56/9.95	
28.56/9.95	Q is empty.
28.56/9.95	We have to consider all minimal (P,Q,R)-chains.
28.56/9.95	----------------------------------------
28.56/9.95	
28.56/9.95	(1657) DependencyGraphProof (EQUIVALENT)
28.56/9.95	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.95	----------------------------------------
28.56/9.95	
28.56/9.95	(1658)
28.56/9.95	Obligation:
28.56/9.95	Q DP problem:
28.56/9.95	The TRS P consists of the following rules:
28.56/9.95	
28.56/9.95	   G(d, x, x) -> A^2
28.56/9.95	   A^2 -> H(f(c), f(c))
28.56/9.95	   H(x, x) -> G(x, x, f(k))
28.56/9.95	   A^2 -> H(f(d), f(d))
28.56/9.95	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.95	   A^2 -> H(f(e), f(e))
28.56/9.95	   A^2 -> H(f(k), f(k))
28.56/9.95	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.95	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.95	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.95	   A^2 -> H(f(k), b)
28.56/9.95	   A^2 -> H(f(k), U1(e, d))
28.56/9.95	   A^2 -> H(f(k), U1(d, e))
28.56/9.95	   A^2 -> H(f(k), c)
28.56/9.95	   A^2 -> H(f(k), U1(e, k))
28.56/9.95	   A^2 -> H(f(k), U1(k, e))
28.56/9.95	   A^2 -> H(f(k), e)
28.56/9.95	   A^2 -> H(f(c), d)
28.56/9.95	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.95	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.95	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.95	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.95	   A^2 -> H(U1(k, k), f(e))
28.56/9.95	   A^2 -> H(U1(k, k), f(k))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.95	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.95	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.95	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.95	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.95	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.95	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.95	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.95	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.95	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.95	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.95	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.95	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.95	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.95	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.95	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, d), b)
28.56/9.95	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.95	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.95	   A^2 -> H(U1(d, d), c)
28.56/9.95	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.95	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.95	   A^2 -> H(U1(d, d), e)
28.56/9.95	   A^2 -> H(f(d), d)
28.56/9.95	   A^2 -> H(f(d), k)
28.56/9.95	   A^2 -> H(U1(c, c), c)
28.56/9.95	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.95	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.95	   A^2 -> H(f(c), k)
28.56/9.95	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.95	   A^2 -> H(f(k), U1(k, k))
28.56/9.95	   A^2 -> H(f(e), e)
28.56/9.95	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.95	   A^2 -> H(d, U1(c, b))
28.56/9.95	   A^2 -> H(d, U1(d, b))
28.56/9.95	   A^2 -> H(d, U1(b, c))
28.56/9.95	   A^2 -> H(d, U1(b, d))
28.56/9.95	   A^2 -> H(d, U1(c, c))
28.56/9.95	   A^2 -> H(d, f(e))
28.56/9.95	   A^2 -> H(d, f(k))
28.56/9.95	   A^2 -> H(d, U1(d, d))
28.56/9.95	   A^2 -> H(a, U1(e, b))
28.56/9.95	   A^2 -> H(a, U1(k, b))
28.56/9.95	   A^2 -> H(a, U1(c, d))
28.56/9.95	   A^2 -> H(a, U1(d, c))
28.56/9.95	   A^2 -> H(a, U1(b, e))
28.56/9.95	   A^2 -> H(a, U1(b, k))
28.56/9.95	   A^2 -> H(a, U1(e, c))
28.56/9.95	   A^2 -> H(a, U1(k, c))
28.56/9.95	   A^2 -> H(a, U1(c, e))
28.56/9.95	   A^2 -> H(a, U1(c, k))
28.56/9.95	   A^2 -> H(a, U1(e, e))
28.56/9.95	   A^2 -> H(a, U1(k, k))
28.56/9.95	   A^2 -> H(a, U1(k, d))
28.56/9.95	   A^2 -> H(a, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.95	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.95	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.95	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.95	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.95	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, a), b)
28.56/9.95	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, a), c)
28.56/9.95	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, a), e)
28.56/9.95	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, a), b)
28.56/9.95	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, a), c)
28.56/9.95	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.95	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.95	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, d), b)
28.56/9.95	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, d), c)
28.56/9.95	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, d), e)
28.56/9.95	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, a), d)
28.56/9.95	   A^2 -> H(U1(c, a), k)
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.95	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, c), b)
28.56/9.95	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(d, c), c)
28.56/9.95	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(d, c), e)
28.56/9.95	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, a), d)
28.56/9.95	   A^2 -> H(U1(d, a), k)
28.56/9.95	   A^2 -> H(U1(a, e), b)
28.56/9.95	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(a, e), c)
28.56/9.95	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(a, e), e)
28.56/9.95	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(a, k), b)
28.56/9.95	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(a, k), c)
28.56/9.95	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.95	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.95	   A^2 -> H(U1(a, k), e)
28.56/9.95	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(a, c), d)
28.56/9.95	   A^2 -> H(U1(a, c), k)
28.56/9.95	   A^2 -> H(U1(a, d), d)
28.56/9.95	   A^2 -> H(U1(a, d), k)
28.56/9.95	   A^2 -> H(k, U1(c, b))
28.56/9.95	   A^2 -> H(k, U1(d, b))
28.56/9.95	   A^2 -> H(k, U1(b, c))
28.56/9.95	   A^2 -> H(k, U1(b, d))
28.56/9.95	   A^2 -> H(k, U1(c, c))
28.56/9.95	   A^2 -> H(k, f(e))
28.56/9.95	   A^2 -> H(k, f(k))
28.56/9.95	   A^2 -> H(k, U1(d, d))
28.56/9.95	   A^2 -> H(c, U1(e, b))
28.56/9.95	   A^2 -> H(c, U1(k, b))
28.56/9.95	   A^2 -> H(c, U1(c, d))
28.56/9.95	   A^2 -> H(c, U1(d, c))
28.56/9.95	   A^2 -> H(c, U1(b, e))
28.56/9.95	   A^2 -> H(c, U1(b, k))
28.56/9.95	   A^2 -> H(c, U1(e, c))
28.56/9.95	   A^2 -> H(c, U1(k, c))
28.56/9.95	   A^2 -> H(c, U1(c, e))
28.56/9.95	   A^2 -> H(c, U1(c, k))
28.56/9.95	   A^2 -> H(c, U1(e, e))
28.56/9.95	   A^2 -> H(c, U1(k, k))
28.56/9.95	   A^2 -> H(c, U1(k, d))
28.56/9.95	   A^2 -> H(c, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.95	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.95	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, c), b)
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, c), e)
28.56/9.95	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.95	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.95	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.95	   A^2 -> H(U1(k, c), b)
28.56/9.95	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, c), c)
28.56/9.95	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, e), b)
28.56/9.95	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, e), c)
28.56/9.95	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, e), e)
28.56/9.95	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, k), b)
28.56/9.95	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, k), c)
28.56/9.95	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, k), e)
28.56/9.95	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, c), d)
28.56/9.95	   A^2 -> H(e, U1(e, b))
28.56/9.95	   A^2 -> H(e, U1(c, d))
28.56/9.95	   A^2 -> H(e, U1(d, c))
28.56/9.95	   A^2 -> H(e, U1(b, e))
28.56/9.95	   A^2 -> H(e, U1(b, k))
28.56/9.95	   A^2 -> H(e, U1(e, c))
28.56/9.95	   A^2 -> H(e, U1(c, e))
28.56/9.95	   A^2 -> H(e, U1(c, k))
28.56/9.95	   A^2 -> H(e, U1(e, e))
28.56/9.95	   A^2 -> H(e, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, e), b)
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, e), c)
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.95	   A^2 -> H(f(e), d)
28.56/9.95	   A^2 -> H(f(e), k)
28.56/9.95	   A^2 -> H(U1(k, k), b)
28.56/9.95	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, k), c)
28.56/9.95	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.95	
28.56/9.95	The TRS R consists of the following rules:
28.56/9.95	
28.56/9.95	   f(x) -> U1(x, x)
28.56/9.95	   U1(e, x) -> x
28.56/9.95	   a -> c
28.56/9.95	   a -> d
28.56/9.95	   b -> c
28.56/9.95	   b -> d
28.56/9.95	   d -> k
28.56/9.95	   c -> e
28.56/9.95	   c -> k
28.56/9.95	
28.56/9.95	Q is empty.
28.56/9.95	We have to consider all minimal (P,Q,R)-chains.
28.56/9.95	----------------------------------------
28.56/9.95	
28.56/9.95	(1659) TransformationProof (EQUIVALENT)
28.56/9.95	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.95	
28.56/9.95	   (A^2 -> H(U1(k, k), U1(e, k)),A^2 -> H(U1(k, k), U1(e, k)))
28.56/9.95	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.56/9.95	
28.56/9.95	
28.56/9.95	----------------------------------------
28.56/9.95	
28.56/9.95	(1660)
28.56/9.95	Obligation:
28.56/9.95	Q DP problem:
28.56/9.95	The TRS P consists of the following rules:
28.56/9.95	
28.56/9.95	   G(d, x, x) -> A^2
28.56/9.95	   A^2 -> H(f(c), f(c))
28.56/9.95	   H(x, x) -> G(x, x, f(k))
28.56/9.95	   A^2 -> H(f(d), f(d))
28.56/9.95	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.95	   A^2 -> H(f(e), f(e))
28.56/9.95	   A^2 -> H(f(k), f(k))
28.56/9.95	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.95	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.95	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.95	   A^2 -> H(f(k), b)
28.56/9.95	   A^2 -> H(f(k), U1(e, d))
28.56/9.95	   A^2 -> H(f(k), U1(d, e))
28.56/9.95	   A^2 -> H(f(k), c)
28.56/9.95	   A^2 -> H(f(k), U1(e, k))
28.56/9.95	   A^2 -> H(f(k), U1(k, e))
28.56/9.95	   A^2 -> H(f(k), e)
28.56/9.95	   A^2 -> H(f(c), d)
28.56/9.95	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.95	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.95	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.95	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.95	   A^2 -> H(U1(k, k), f(e))
28.56/9.95	   A^2 -> H(U1(k, k), f(k))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.95	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.95	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.95	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.95	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.95	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.95	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.95	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.95	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.95	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.95	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.95	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.95	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.95	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.95	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.95	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, d), b)
28.56/9.95	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.95	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.95	   A^2 -> H(U1(d, d), c)
28.56/9.95	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.95	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.95	   A^2 -> H(U1(d, d), e)
28.56/9.95	   A^2 -> H(f(d), d)
28.56/9.95	   A^2 -> H(f(d), k)
28.56/9.95	   A^2 -> H(U1(c, c), c)
28.56/9.95	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.95	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.95	   A^2 -> H(f(c), k)
28.56/9.95	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.95	   A^2 -> H(f(k), U1(k, k))
28.56/9.95	   A^2 -> H(f(e), e)
28.56/9.95	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.95	   A^2 -> H(d, U1(c, b))
28.56/9.95	   A^2 -> H(d, U1(d, b))
28.56/9.95	   A^2 -> H(d, U1(b, c))
28.56/9.95	   A^2 -> H(d, U1(b, d))
28.56/9.95	   A^2 -> H(d, U1(c, c))
28.56/9.95	   A^2 -> H(d, f(e))
28.56/9.95	   A^2 -> H(d, f(k))
28.56/9.95	   A^2 -> H(d, U1(d, d))
28.56/9.95	   A^2 -> H(a, U1(e, b))
28.56/9.95	   A^2 -> H(a, U1(k, b))
28.56/9.95	   A^2 -> H(a, U1(c, d))
28.56/9.95	   A^2 -> H(a, U1(d, c))
28.56/9.95	   A^2 -> H(a, U1(b, e))
28.56/9.95	   A^2 -> H(a, U1(b, k))
28.56/9.95	   A^2 -> H(a, U1(e, c))
28.56/9.95	   A^2 -> H(a, U1(k, c))
28.56/9.95	   A^2 -> H(a, U1(c, e))
28.56/9.95	   A^2 -> H(a, U1(c, k))
28.56/9.95	   A^2 -> H(a, U1(e, e))
28.56/9.95	   A^2 -> H(a, U1(k, k))
28.56/9.95	   A^2 -> H(a, U1(k, d))
28.56/9.95	   A^2 -> H(a, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.95	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.95	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.95	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.95	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.95	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, a), b)
28.56/9.95	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, a), c)
28.56/9.95	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, a), e)
28.56/9.95	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, a), b)
28.56/9.95	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, a), c)
28.56/9.95	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.95	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.95	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, d), b)
28.56/9.95	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, d), c)
28.56/9.95	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, d), e)
28.56/9.95	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, a), d)
28.56/9.95	   A^2 -> H(U1(c, a), k)
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.95	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, c), b)
28.56/9.95	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(d, c), c)
28.56/9.95	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(d, c), e)
28.56/9.95	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, a), d)
28.56/9.95	   A^2 -> H(U1(d, a), k)
28.56/9.95	   A^2 -> H(U1(a, e), b)
28.56/9.95	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(a, e), c)
28.56/9.95	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(a, e), e)
28.56/9.95	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(a, k), b)
28.56/9.95	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(a, k), c)
28.56/9.95	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.95	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.95	   A^2 -> H(U1(a, k), e)
28.56/9.95	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(a, c), d)
28.56/9.95	   A^2 -> H(U1(a, c), k)
28.56/9.95	   A^2 -> H(U1(a, d), d)
28.56/9.95	   A^2 -> H(U1(a, d), k)
28.56/9.95	   A^2 -> H(k, U1(c, b))
28.56/9.95	   A^2 -> H(k, U1(d, b))
28.56/9.95	   A^2 -> H(k, U1(b, c))
28.56/9.95	   A^2 -> H(k, U1(b, d))
28.56/9.95	   A^2 -> H(k, U1(c, c))
28.56/9.95	   A^2 -> H(k, f(e))
28.56/9.95	   A^2 -> H(k, f(k))
28.56/9.95	   A^2 -> H(k, U1(d, d))
28.56/9.95	   A^2 -> H(c, U1(e, b))
28.56/9.95	   A^2 -> H(c, U1(k, b))
28.56/9.95	   A^2 -> H(c, U1(c, d))
28.56/9.95	   A^2 -> H(c, U1(d, c))
28.56/9.95	   A^2 -> H(c, U1(b, e))
28.56/9.95	   A^2 -> H(c, U1(b, k))
28.56/9.95	   A^2 -> H(c, U1(e, c))
28.56/9.95	   A^2 -> H(c, U1(k, c))
28.56/9.95	   A^2 -> H(c, U1(c, e))
28.56/9.95	   A^2 -> H(c, U1(c, k))
28.56/9.95	   A^2 -> H(c, U1(e, e))
28.56/9.95	   A^2 -> H(c, U1(k, k))
28.56/9.95	   A^2 -> H(c, U1(k, d))
28.56/9.95	   A^2 -> H(c, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.95	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.95	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, c), b)
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, c), e)
28.56/9.95	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.95	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.95	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.95	   A^2 -> H(U1(k, c), b)
28.56/9.95	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, c), c)
28.56/9.95	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, e), b)
28.56/9.95	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, e), c)
28.56/9.95	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, e), e)
28.56/9.95	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, k), b)
28.56/9.95	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, k), c)
28.56/9.95	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, k), e)
28.56/9.95	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, c), d)
28.56/9.95	   A^2 -> H(e, U1(e, b))
28.56/9.95	   A^2 -> H(e, U1(c, d))
28.56/9.95	   A^2 -> H(e, U1(d, c))
28.56/9.95	   A^2 -> H(e, U1(b, e))
28.56/9.95	   A^2 -> H(e, U1(b, k))
28.56/9.95	   A^2 -> H(e, U1(e, c))
28.56/9.95	   A^2 -> H(e, U1(c, e))
28.56/9.95	   A^2 -> H(e, U1(c, k))
28.56/9.95	   A^2 -> H(e, U1(e, e))
28.56/9.95	   A^2 -> H(e, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, e), b)
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, e), c)
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.95	   A^2 -> H(f(e), d)
28.56/9.95	   A^2 -> H(f(e), k)
28.56/9.95	   A^2 -> H(U1(k, k), b)
28.56/9.95	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, k), c)
28.56/9.95	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.95	
28.56/9.95	The TRS R consists of the following rules:
28.56/9.95	
28.56/9.95	   f(x) -> U1(x, x)
28.56/9.95	   U1(e, x) -> x
28.56/9.95	   a -> c
28.56/9.95	   a -> d
28.56/9.95	   b -> c
28.56/9.95	   b -> d
28.56/9.95	   d -> k
28.56/9.95	   c -> e
28.56/9.95	   c -> k
28.56/9.95	
28.56/9.95	Q is empty.
28.56/9.95	We have to consider all minimal (P,Q,R)-chains.
28.56/9.95	----------------------------------------
28.56/9.95	
28.56/9.95	(1661) TransformationProof (EQUIVALENT)
28.56/9.95	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.95	
28.56/9.95	   (A^2 -> H(U1(k, k), e),A^2 -> H(U1(k, k), e))
28.56/9.95	
28.56/9.95	
28.56/9.95	----------------------------------------
28.56/9.95	
28.56/9.95	(1662)
28.56/9.95	Obligation:
28.56/9.95	Q DP problem:
28.56/9.95	The TRS P consists of the following rules:
28.56/9.95	
28.56/9.95	   G(d, x, x) -> A^2
28.56/9.95	   A^2 -> H(f(c), f(c))
28.56/9.95	   H(x, x) -> G(x, x, f(k))
28.56/9.95	   A^2 -> H(f(d), f(d))
28.56/9.95	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.95	   A^2 -> H(f(e), f(e))
28.56/9.95	   A^2 -> H(f(k), f(k))
28.56/9.95	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.95	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.95	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.95	   A^2 -> H(f(k), b)
28.56/9.95	   A^2 -> H(f(k), U1(e, d))
28.56/9.95	   A^2 -> H(f(k), U1(d, e))
28.56/9.95	   A^2 -> H(f(k), c)
28.56/9.95	   A^2 -> H(f(k), U1(e, k))
28.56/9.95	   A^2 -> H(f(k), U1(k, e))
28.56/9.95	   A^2 -> H(f(k), e)
28.56/9.95	   A^2 -> H(f(c), d)
28.56/9.95	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.95	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.95	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.95	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.95	   A^2 -> H(U1(k, k), f(e))
28.56/9.95	   A^2 -> H(U1(k, k), f(k))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.95	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.95	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.95	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.95	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.95	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.95	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.95	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.95	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.95	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.95	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.95	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.95	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.95	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.95	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.95	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, d), b)
28.56/9.95	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.95	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.95	   A^2 -> H(U1(d, d), c)
28.56/9.95	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.95	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.95	   A^2 -> H(U1(d, d), e)
28.56/9.95	   A^2 -> H(f(d), d)
28.56/9.95	   A^2 -> H(f(d), k)
28.56/9.95	   A^2 -> H(U1(c, c), c)
28.56/9.95	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.95	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.95	   A^2 -> H(f(c), k)
28.56/9.95	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.95	   A^2 -> H(f(k), U1(k, k))
28.56/9.95	   A^2 -> H(f(e), e)
28.56/9.95	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.95	   A^2 -> H(d, U1(c, b))
28.56/9.95	   A^2 -> H(d, U1(d, b))
28.56/9.95	   A^2 -> H(d, U1(b, c))
28.56/9.95	   A^2 -> H(d, U1(b, d))
28.56/9.95	   A^2 -> H(d, U1(c, c))
28.56/9.95	   A^2 -> H(d, f(e))
28.56/9.95	   A^2 -> H(d, f(k))
28.56/9.95	   A^2 -> H(d, U1(d, d))
28.56/9.95	   A^2 -> H(a, U1(e, b))
28.56/9.95	   A^2 -> H(a, U1(k, b))
28.56/9.95	   A^2 -> H(a, U1(c, d))
28.56/9.95	   A^2 -> H(a, U1(d, c))
28.56/9.95	   A^2 -> H(a, U1(b, e))
28.56/9.95	   A^2 -> H(a, U1(b, k))
28.56/9.95	   A^2 -> H(a, U1(e, c))
28.56/9.95	   A^2 -> H(a, U1(k, c))
28.56/9.95	   A^2 -> H(a, U1(c, e))
28.56/9.95	   A^2 -> H(a, U1(c, k))
28.56/9.95	   A^2 -> H(a, U1(e, e))
28.56/9.95	   A^2 -> H(a, U1(k, k))
28.56/9.95	   A^2 -> H(a, U1(k, d))
28.56/9.95	   A^2 -> H(a, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.95	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.95	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.95	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.95	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.95	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, a), b)
28.56/9.95	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, a), c)
28.56/9.95	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, a), e)
28.56/9.95	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, a), b)
28.56/9.95	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, a), c)
28.56/9.95	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.95	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.95	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, d), b)
28.56/9.95	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, d), c)
28.56/9.95	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, d), e)
28.56/9.95	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, a), d)
28.56/9.95	   A^2 -> H(U1(c, a), k)
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.95	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, c), b)
28.56/9.95	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(d, c), c)
28.56/9.95	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(d, c), e)
28.56/9.95	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, a), d)
28.56/9.95	   A^2 -> H(U1(d, a), k)
28.56/9.95	   A^2 -> H(U1(a, e), b)
28.56/9.95	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(a, e), c)
28.56/9.95	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(a, e), e)
28.56/9.95	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(a, k), b)
28.56/9.95	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(a, k), c)
28.56/9.95	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.95	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.95	   A^2 -> H(U1(a, k), e)
28.56/9.95	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(a, c), d)
28.56/9.95	   A^2 -> H(U1(a, c), k)
28.56/9.95	   A^2 -> H(U1(a, d), d)
28.56/9.95	   A^2 -> H(U1(a, d), k)
28.56/9.95	   A^2 -> H(k, U1(c, b))
28.56/9.95	   A^2 -> H(k, U1(d, b))
28.56/9.95	   A^2 -> H(k, U1(b, c))
28.56/9.95	   A^2 -> H(k, U1(b, d))
28.56/9.95	   A^2 -> H(k, U1(c, c))
28.56/9.95	   A^2 -> H(k, f(e))
28.56/9.95	   A^2 -> H(k, f(k))
28.56/9.95	   A^2 -> H(k, U1(d, d))
28.56/9.95	   A^2 -> H(c, U1(e, b))
28.56/9.95	   A^2 -> H(c, U1(k, b))
28.56/9.95	   A^2 -> H(c, U1(c, d))
28.56/9.95	   A^2 -> H(c, U1(d, c))
28.56/9.95	   A^2 -> H(c, U1(b, e))
28.56/9.95	   A^2 -> H(c, U1(b, k))
28.56/9.95	   A^2 -> H(c, U1(e, c))
28.56/9.95	   A^2 -> H(c, U1(k, c))
28.56/9.95	   A^2 -> H(c, U1(c, e))
28.56/9.95	   A^2 -> H(c, U1(c, k))
28.56/9.95	   A^2 -> H(c, U1(e, e))
28.56/9.95	   A^2 -> H(c, U1(k, k))
28.56/9.95	   A^2 -> H(c, U1(k, d))
28.56/9.95	   A^2 -> H(c, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.95	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.95	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, c), b)
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, c), e)
28.56/9.95	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.95	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.95	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.95	   A^2 -> H(U1(k, c), b)
28.56/9.95	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, c), c)
28.56/9.95	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, e), b)
28.56/9.95	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, e), c)
28.56/9.95	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, e), e)
28.56/9.95	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, k), b)
28.56/9.95	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, k), c)
28.56/9.95	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, k), e)
28.56/9.95	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, c), d)
28.56/9.95	   A^2 -> H(e, U1(e, b))
28.56/9.95	   A^2 -> H(e, U1(c, d))
28.56/9.95	   A^2 -> H(e, U1(d, c))
28.56/9.95	   A^2 -> H(e, U1(b, e))
28.56/9.95	   A^2 -> H(e, U1(b, k))
28.56/9.95	   A^2 -> H(e, U1(e, c))
28.56/9.95	   A^2 -> H(e, U1(c, e))
28.56/9.95	   A^2 -> H(e, U1(c, k))
28.56/9.95	   A^2 -> H(e, U1(e, e))
28.56/9.95	   A^2 -> H(e, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, e), b)
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, e), c)
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.95	   A^2 -> H(f(e), d)
28.56/9.95	   A^2 -> H(f(e), k)
28.56/9.95	   A^2 -> H(U1(k, k), b)
28.56/9.95	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, k), c)
28.56/9.95	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.95	   A^2 -> H(U1(k, k), e)
28.56/9.95	
28.56/9.95	The TRS R consists of the following rules:
28.56/9.95	
28.56/9.95	   f(x) -> U1(x, x)
28.56/9.95	   U1(e, x) -> x
28.56/9.95	   a -> c
28.56/9.95	   a -> d
28.56/9.95	   b -> c
28.56/9.95	   b -> d
28.56/9.95	   d -> k
28.56/9.95	   c -> e
28.56/9.95	   c -> k
28.56/9.95	
28.56/9.95	Q is empty.
28.56/9.95	We have to consider all minimal (P,Q,R)-chains.
28.56/9.95	----------------------------------------
28.56/9.95	
28.56/9.95	(1663) DependencyGraphProof (EQUIVALENT)
28.56/9.95	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.95	----------------------------------------
28.56/9.95	
28.56/9.95	(1664)
28.56/9.95	Obligation:
28.56/9.95	Q DP problem:
28.56/9.95	The TRS P consists of the following rules:
28.56/9.95	
28.56/9.95	   A^2 -> H(f(c), f(c))
28.56/9.95	   H(x, x) -> G(x, x, f(k))
28.56/9.95	   G(d, x, x) -> A^2
28.56/9.95	   A^2 -> H(f(d), f(d))
28.56/9.95	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.95	   A^2 -> H(f(e), f(e))
28.56/9.95	   A^2 -> H(f(k), f(k))
28.56/9.95	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.95	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.95	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.95	   A^2 -> H(f(k), b)
28.56/9.95	   A^2 -> H(f(k), U1(e, d))
28.56/9.95	   A^2 -> H(f(k), U1(d, e))
28.56/9.95	   A^2 -> H(f(k), c)
28.56/9.95	   A^2 -> H(f(k), U1(e, k))
28.56/9.95	   A^2 -> H(f(k), U1(k, e))
28.56/9.95	   A^2 -> H(f(k), e)
28.56/9.95	   A^2 -> H(f(c), d)
28.56/9.95	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.95	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.95	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.95	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.95	   A^2 -> H(U1(k, k), f(e))
28.56/9.95	   A^2 -> H(U1(k, k), f(k))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.95	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.95	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.95	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.95	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.95	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.95	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.95	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.95	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.95	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.95	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.95	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.95	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.95	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.95	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.95	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, d), b)
28.56/9.95	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.95	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.95	   A^2 -> H(U1(d, d), c)
28.56/9.95	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.95	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.95	   A^2 -> H(U1(d, d), e)
28.56/9.95	   A^2 -> H(f(d), d)
28.56/9.95	   A^2 -> H(f(d), k)
28.56/9.95	   A^2 -> H(U1(c, c), c)
28.56/9.95	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.95	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.95	   A^2 -> H(f(c), k)
28.56/9.95	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.95	   A^2 -> H(f(k), U1(k, k))
28.56/9.95	   A^2 -> H(f(e), e)
28.56/9.95	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.95	   A^2 -> H(d, U1(c, b))
28.56/9.95	   A^2 -> H(d, U1(d, b))
28.56/9.95	   A^2 -> H(d, U1(b, c))
28.56/9.95	   A^2 -> H(d, U1(b, d))
28.56/9.95	   A^2 -> H(d, U1(c, c))
28.56/9.95	   A^2 -> H(d, f(e))
28.56/9.95	   A^2 -> H(d, f(k))
28.56/9.95	   A^2 -> H(d, U1(d, d))
28.56/9.95	   A^2 -> H(a, U1(e, b))
28.56/9.95	   A^2 -> H(a, U1(k, b))
28.56/9.95	   A^2 -> H(a, U1(c, d))
28.56/9.95	   A^2 -> H(a, U1(d, c))
28.56/9.95	   A^2 -> H(a, U1(b, e))
28.56/9.95	   A^2 -> H(a, U1(b, k))
28.56/9.95	   A^2 -> H(a, U1(e, c))
28.56/9.95	   A^2 -> H(a, U1(k, c))
28.56/9.95	   A^2 -> H(a, U1(c, e))
28.56/9.95	   A^2 -> H(a, U1(c, k))
28.56/9.95	   A^2 -> H(a, U1(e, e))
28.56/9.95	   A^2 -> H(a, U1(k, k))
28.56/9.95	   A^2 -> H(a, U1(k, d))
28.56/9.95	   A^2 -> H(a, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.95	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.95	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.95	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.95	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.95	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, a), b)
28.56/9.95	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, a), c)
28.56/9.95	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, a), e)
28.56/9.95	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, a), b)
28.56/9.95	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, a), c)
28.56/9.95	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.95	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.95	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, d), b)
28.56/9.95	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, d), c)
28.56/9.95	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, d), e)
28.56/9.95	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, a), d)
28.56/9.95	   A^2 -> H(U1(c, a), k)
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.95	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, c), b)
28.56/9.95	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(d, c), c)
28.56/9.95	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(d, c), e)
28.56/9.95	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, a), d)
28.56/9.95	   A^2 -> H(U1(d, a), k)
28.56/9.95	   A^2 -> H(U1(a, e), b)
28.56/9.95	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(a, e), c)
28.56/9.95	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(a, e), e)
28.56/9.95	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(a, k), b)
28.56/9.95	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(a, k), c)
28.56/9.95	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.95	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.95	   A^2 -> H(U1(a, k), e)
28.56/9.95	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(a, c), d)
28.56/9.95	   A^2 -> H(U1(a, c), k)
28.56/9.95	   A^2 -> H(U1(a, d), d)
28.56/9.95	   A^2 -> H(U1(a, d), k)
28.56/9.95	   A^2 -> H(k, U1(c, b))
28.56/9.95	   A^2 -> H(k, U1(d, b))
28.56/9.95	   A^2 -> H(k, U1(b, c))
28.56/9.95	   A^2 -> H(k, U1(b, d))
28.56/9.95	   A^2 -> H(k, U1(c, c))
28.56/9.95	   A^2 -> H(k, f(e))
28.56/9.95	   A^2 -> H(k, f(k))
28.56/9.95	   A^2 -> H(k, U1(d, d))
28.56/9.95	   A^2 -> H(c, U1(e, b))
28.56/9.95	   A^2 -> H(c, U1(k, b))
28.56/9.95	   A^2 -> H(c, U1(c, d))
28.56/9.95	   A^2 -> H(c, U1(d, c))
28.56/9.95	   A^2 -> H(c, U1(b, e))
28.56/9.95	   A^2 -> H(c, U1(b, k))
28.56/9.95	   A^2 -> H(c, U1(e, c))
28.56/9.95	   A^2 -> H(c, U1(k, c))
28.56/9.95	   A^2 -> H(c, U1(c, e))
28.56/9.95	   A^2 -> H(c, U1(c, k))
28.56/9.95	   A^2 -> H(c, U1(e, e))
28.56/9.95	   A^2 -> H(c, U1(k, k))
28.56/9.95	   A^2 -> H(c, U1(k, d))
28.56/9.95	   A^2 -> H(c, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.95	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.95	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, c), b)
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, c), e)
28.56/9.95	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.95	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.95	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.95	   A^2 -> H(U1(k, c), b)
28.56/9.95	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, c), c)
28.56/9.95	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, e), b)
28.56/9.95	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, e), c)
28.56/9.95	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, e), e)
28.56/9.95	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, k), b)
28.56/9.95	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, k), c)
28.56/9.95	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, k), e)
28.56/9.95	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, c), d)
28.56/9.95	   A^2 -> H(e, U1(e, b))
28.56/9.95	   A^2 -> H(e, U1(c, d))
28.56/9.95	   A^2 -> H(e, U1(d, c))
28.56/9.95	   A^2 -> H(e, U1(b, e))
28.56/9.95	   A^2 -> H(e, U1(b, k))
28.56/9.95	   A^2 -> H(e, U1(e, c))
28.56/9.95	   A^2 -> H(e, U1(c, e))
28.56/9.95	   A^2 -> H(e, U1(c, k))
28.56/9.95	   A^2 -> H(e, U1(e, e))
28.56/9.95	   A^2 -> H(e, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, e), b)
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, e), c)
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.95	   A^2 -> H(f(e), d)
28.56/9.95	   A^2 -> H(f(e), k)
28.56/9.95	   A^2 -> H(U1(k, k), b)
28.56/9.95	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, k), c)
28.56/9.95	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.95	
28.56/9.95	The TRS R consists of the following rules:
28.56/9.95	
28.56/9.95	   f(x) -> U1(x, x)
28.56/9.95	   U1(e, x) -> x
28.56/9.95	   a -> c
28.56/9.95	   a -> d
28.56/9.95	   b -> c
28.56/9.95	   b -> d
28.56/9.95	   d -> k
28.56/9.95	   c -> e
28.56/9.95	   c -> k
28.56/9.95	
28.56/9.95	Q is empty.
28.56/9.95	We have to consider all minimal (P,Q,R)-chains.
28.56/9.95	----------------------------------------
28.56/9.95	
28.56/9.95	(1665) TransformationProof (EQUIVALENT)
28.56/9.95	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.95	
28.56/9.95	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.56/9.95	
28.56/9.95	
28.56/9.95	----------------------------------------
28.56/9.95	
28.56/9.95	(1666)
28.56/9.95	Obligation:
28.56/9.95	Q DP problem:
28.56/9.95	The TRS P consists of the following rules:
28.56/9.95	
28.56/9.95	   A^2 -> H(f(c), f(c))
28.56/9.95	   H(x, x) -> G(x, x, f(k))
28.56/9.95	   G(d, x, x) -> A^2
28.56/9.95	   A^2 -> H(f(d), f(d))
28.56/9.95	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.95	   A^2 -> H(f(e), f(e))
28.56/9.95	   A^2 -> H(f(k), f(k))
28.56/9.95	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.95	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.95	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.95	   A^2 -> H(f(k), b)
28.56/9.95	   A^2 -> H(f(k), U1(e, d))
28.56/9.95	   A^2 -> H(f(k), U1(d, e))
28.56/9.95	   A^2 -> H(f(k), c)
28.56/9.95	   A^2 -> H(f(k), U1(e, k))
28.56/9.95	   A^2 -> H(f(k), U1(k, e))
28.56/9.95	   A^2 -> H(f(k), e)
28.56/9.95	   A^2 -> H(f(c), d)
28.56/9.95	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.95	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.95	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.95	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.95	   A^2 -> H(U1(k, k), f(e))
28.56/9.95	   A^2 -> H(U1(k, k), f(k))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.95	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.95	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.95	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.95	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.95	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.95	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.95	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.95	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.95	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.95	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.95	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.95	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.95	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.95	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.95	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, d), b)
28.56/9.95	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.95	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.95	   A^2 -> H(U1(d, d), c)
28.56/9.95	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.95	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.95	   A^2 -> H(U1(d, d), e)
28.56/9.95	   A^2 -> H(f(d), d)
28.56/9.95	   A^2 -> H(f(d), k)
28.56/9.95	   A^2 -> H(U1(c, c), c)
28.56/9.95	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.95	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.95	   A^2 -> H(f(c), k)
28.56/9.95	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.95	   A^2 -> H(f(k), U1(k, k))
28.56/9.95	   A^2 -> H(f(e), e)
28.56/9.95	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.95	   A^2 -> H(d, U1(c, b))
28.56/9.95	   A^2 -> H(d, U1(d, b))
28.56/9.95	   A^2 -> H(d, U1(b, c))
28.56/9.95	   A^2 -> H(d, U1(b, d))
28.56/9.95	   A^2 -> H(d, U1(c, c))
28.56/9.95	   A^2 -> H(d, f(e))
28.56/9.95	   A^2 -> H(d, f(k))
28.56/9.95	   A^2 -> H(d, U1(d, d))
28.56/9.95	   A^2 -> H(a, U1(e, b))
28.56/9.95	   A^2 -> H(a, U1(k, b))
28.56/9.95	   A^2 -> H(a, U1(c, d))
28.56/9.95	   A^2 -> H(a, U1(d, c))
28.56/9.95	   A^2 -> H(a, U1(b, e))
28.56/9.95	   A^2 -> H(a, U1(b, k))
28.56/9.95	   A^2 -> H(a, U1(e, c))
28.56/9.95	   A^2 -> H(a, U1(k, c))
28.56/9.95	   A^2 -> H(a, U1(c, e))
28.56/9.95	   A^2 -> H(a, U1(c, k))
28.56/9.95	   A^2 -> H(a, U1(e, e))
28.56/9.95	   A^2 -> H(a, U1(k, k))
28.56/9.95	   A^2 -> H(a, U1(k, d))
28.56/9.95	   A^2 -> H(a, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.95	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.95	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.95	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.95	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.95	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, a), b)
28.56/9.95	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, a), c)
28.56/9.95	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, a), e)
28.56/9.95	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, a), b)
28.56/9.95	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, a), c)
28.56/9.95	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.95	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.95	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, d), b)
28.56/9.95	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, d), c)
28.56/9.95	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, d), e)
28.56/9.95	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, a), d)
28.56/9.95	   A^2 -> H(U1(c, a), k)
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.95	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, c), b)
28.56/9.95	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(d, c), c)
28.56/9.95	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(d, c), e)
28.56/9.95	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, a), d)
28.56/9.95	   A^2 -> H(U1(d, a), k)
28.56/9.95	   A^2 -> H(U1(a, e), b)
28.56/9.95	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(a, e), c)
28.56/9.95	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(a, e), e)
28.56/9.95	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(a, k), b)
28.56/9.95	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(a, k), c)
28.56/9.95	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.95	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.95	   A^2 -> H(U1(a, k), e)
28.56/9.95	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(a, c), d)
28.56/9.95	   A^2 -> H(U1(a, c), k)
28.56/9.95	   A^2 -> H(U1(a, d), d)
28.56/9.95	   A^2 -> H(U1(a, d), k)
28.56/9.95	   A^2 -> H(k, U1(c, b))
28.56/9.95	   A^2 -> H(k, U1(d, b))
28.56/9.95	   A^2 -> H(k, U1(b, c))
28.56/9.95	   A^2 -> H(k, U1(b, d))
28.56/9.95	   A^2 -> H(k, U1(c, c))
28.56/9.95	   A^2 -> H(k, f(e))
28.56/9.95	   A^2 -> H(k, f(k))
28.56/9.95	   A^2 -> H(k, U1(d, d))
28.56/9.95	   A^2 -> H(c, U1(e, b))
28.56/9.95	   A^2 -> H(c, U1(k, b))
28.56/9.95	   A^2 -> H(c, U1(c, d))
28.56/9.95	   A^2 -> H(c, U1(d, c))
28.56/9.95	   A^2 -> H(c, U1(b, e))
28.56/9.95	   A^2 -> H(c, U1(b, k))
28.56/9.95	   A^2 -> H(c, U1(e, c))
28.56/9.95	   A^2 -> H(c, U1(k, c))
28.56/9.95	   A^2 -> H(c, U1(c, e))
28.56/9.95	   A^2 -> H(c, U1(c, k))
28.56/9.95	   A^2 -> H(c, U1(e, e))
28.56/9.95	   A^2 -> H(c, U1(k, k))
28.56/9.95	   A^2 -> H(c, U1(k, d))
28.56/9.95	   A^2 -> H(c, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.95	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.95	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, c), b)
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, c), e)
28.56/9.95	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.95	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.95	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.95	   A^2 -> H(U1(k, c), b)
28.56/9.95	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, c), c)
28.56/9.95	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, e), b)
28.56/9.95	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, e), c)
28.56/9.95	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, e), e)
28.56/9.95	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, k), b)
28.56/9.95	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, k), c)
28.56/9.95	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, k), e)
28.56/9.95	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, c), d)
28.56/9.95	   A^2 -> H(e, U1(e, b))
28.56/9.95	   A^2 -> H(e, U1(c, d))
28.56/9.95	   A^2 -> H(e, U1(d, c))
28.56/9.95	   A^2 -> H(e, U1(b, e))
28.56/9.95	   A^2 -> H(e, U1(b, k))
28.56/9.95	   A^2 -> H(e, U1(e, c))
28.56/9.95	   A^2 -> H(e, U1(c, e))
28.56/9.95	   A^2 -> H(e, U1(c, k))
28.56/9.95	   A^2 -> H(e, U1(e, e))
28.56/9.95	   A^2 -> H(e, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, e), b)
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, e), c)
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.95	   A^2 -> H(f(e), d)
28.56/9.95	   A^2 -> H(f(e), k)
28.56/9.95	   A^2 -> H(U1(k, k), b)
28.56/9.95	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, k), c)
28.56/9.95	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.95	
28.56/9.95	The TRS R consists of the following rules:
28.56/9.95	
28.56/9.95	   f(x) -> U1(x, x)
28.56/9.95	   U1(e, x) -> x
28.56/9.95	   a -> c
28.56/9.95	   a -> d
28.56/9.95	   b -> c
28.56/9.95	   b -> d
28.56/9.95	   d -> k
28.56/9.95	   c -> e
28.56/9.95	   c -> k
28.56/9.95	
28.56/9.95	Q is empty.
28.56/9.95	We have to consider all minimal (P,Q,R)-chains.
28.56/9.95	----------------------------------------
28.56/9.95	
28.56/9.95	(1667) TransformationProof (EQUIVALENT)
28.56/9.95	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.95	
28.56/9.95	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.56/9.95	
28.56/9.95	
28.56/9.95	----------------------------------------
28.56/9.95	
28.56/9.95	(1668)
28.56/9.95	Obligation:
28.56/9.95	Q DP problem:
28.56/9.95	The TRS P consists of the following rules:
28.56/9.95	
28.56/9.95	   A^2 -> H(f(c), f(c))
28.56/9.95	   H(x, x) -> G(x, x, f(k))
28.56/9.95	   G(d, x, x) -> A^2
28.56/9.95	   A^2 -> H(f(d), f(d))
28.56/9.95	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.95	   A^2 -> H(f(e), f(e))
28.56/9.95	   A^2 -> H(f(k), f(k))
28.56/9.95	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.95	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.95	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.95	   A^2 -> H(f(k), b)
28.56/9.95	   A^2 -> H(f(k), U1(e, d))
28.56/9.95	   A^2 -> H(f(k), U1(d, e))
28.56/9.95	   A^2 -> H(f(k), c)
28.56/9.95	   A^2 -> H(f(k), U1(e, k))
28.56/9.95	   A^2 -> H(f(k), U1(k, e))
28.56/9.95	   A^2 -> H(f(k), e)
28.56/9.95	   A^2 -> H(f(c), d)
28.56/9.95	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.95	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.95	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.95	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.95	   A^2 -> H(U1(k, k), f(e))
28.56/9.95	   A^2 -> H(U1(k, k), f(k))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.95	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.95	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.95	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.95	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.95	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.95	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.95	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.95	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.95	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.95	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.95	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.95	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.95	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.95	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.95	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, d), b)
28.56/9.95	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.95	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.95	   A^2 -> H(U1(d, d), c)
28.56/9.95	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.95	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.95	   A^2 -> H(U1(d, d), e)
28.56/9.95	   A^2 -> H(f(d), d)
28.56/9.95	   A^2 -> H(f(d), k)
28.56/9.95	   A^2 -> H(U1(c, c), c)
28.56/9.95	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.95	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.95	   A^2 -> H(f(c), k)
28.56/9.95	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.95	   A^2 -> H(f(k), U1(k, k))
28.56/9.95	   A^2 -> H(f(e), e)
28.56/9.95	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.95	   A^2 -> H(d, U1(c, b))
28.56/9.95	   A^2 -> H(d, U1(d, b))
28.56/9.95	   A^2 -> H(d, U1(b, c))
28.56/9.95	   A^2 -> H(d, U1(b, d))
28.56/9.95	   A^2 -> H(d, U1(c, c))
28.56/9.95	   A^2 -> H(d, f(e))
28.56/9.95	   A^2 -> H(d, f(k))
28.56/9.95	   A^2 -> H(d, U1(d, d))
28.56/9.95	   A^2 -> H(a, U1(e, b))
28.56/9.95	   A^2 -> H(a, U1(k, b))
28.56/9.95	   A^2 -> H(a, U1(c, d))
28.56/9.95	   A^2 -> H(a, U1(d, c))
28.56/9.95	   A^2 -> H(a, U1(b, e))
28.56/9.95	   A^2 -> H(a, U1(b, k))
28.56/9.95	   A^2 -> H(a, U1(e, c))
28.56/9.95	   A^2 -> H(a, U1(k, c))
28.56/9.95	   A^2 -> H(a, U1(c, e))
28.56/9.95	   A^2 -> H(a, U1(c, k))
28.56/9.95	   A^2 -> H(a, U1(e, e))
28.56/9.95	   A^2 -> H(a, U1(k, k))
28.56/9.95	   A^2 -> H(a, U1(k, d))
28.56/9.95	   A^2 -> H(a, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.95	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.95	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.95	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.95	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.95	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, a), b)
28.56/9.95	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, a), c)
28.56/9.95	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, a), e)
28.56/9.95	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, a), b)
28.56/9.95	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, a), c)
28.56/9.95	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.95	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.95	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, d), b)
28.56/9.95	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, d), c)
28.56/9.95	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, d), e)
28.56/9.95	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, a), d)
28.56/9.95	   A^2 -> H(U1(c, a), k)
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.95	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.95	   A^2 -> H(U1(d, c), b)
28.56/9.95	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(d, c), c)
28.56/9.95	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(d, c), e)
28.56/9.95	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(d, a), d)
28.56/9.95	   A^2 -> H(U1(d, a), k)
28.56/9.95	   A^2 -> H(U1(a, e), b)
28.56/9.95	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(a, e), c)
28.56/9.95	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(a, e), e)
28.56/9.95	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(a, k), b)
28.56/9.95	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(a, k), c)
28.56/9.95	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.95	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.95	   A^2 -> H(U1(a, k), e)
28.56/9.95	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(a, c), d)
28.56/9.95	   A^2 -> H(U1(a, c), k)
28.56/9.95	   A^2 -> H(U1(a, d), d)
28.56/9.95	   A^2 -> H(U1(a, d), k)
28.56/9.95	   A^2 -> H(k, U1(c, b))
28.56/9.95	   A^2 -> H(k, U1(d, b))
28.56/9.95	   A^2 -> H(k, U1(b, c))
28.56/9.95	   A^2 -> H(k, U1(b, d))
28.56/9.95	   A^2 -> H(k, U1(c, c))
28.56/9.95	   A^2 -> H(k, f(e))
28.56/9.95	   A^2 -> H(k, f(k))
28.56/9.95	   A^2 -> H(k, U1(d, d))
28.56/9.95	   A^2 -> H(c, U1(e, b))
28.56/9.95	   A^2 -> H(c, U1(k, b))
28.56/9.95	   A^2 -> H(c, U1(c, d))
28.56/9.95	   A^2 -> H(c, U1(d, c))
28.56/9.95	   A^2 -> H(c, U1(b, e))
28.56/9.95	   A^2 -> H(c, U1(b, k))
28.56/9.95	   A^2 -> H(c, U1(e, c))
28.56/9.95	   A^2 -> H(c, U1(k, c))
28.56/9.95	   A^2 -> H(c, U1(c, e))
28.56/9.95	   A^2 -> H(c, U1(c, k))
28.56/9.95	   A^2 -> H(c, U1(e, e))
28.56/9.95	   A^2 -> H(c, U1(k, k))
28.56/9.95	   A^2 -> H(c, U1(k, d))
28.56/9.95	   A^2 -> H(c, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.95	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.95	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, c), b)
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, c), e)
28.56/9.95	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.95	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.95	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.95	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.95	   A^2 -> H(U1(k, c), b)
28.56/9.95	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, c), c)
28.56/9.95	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, e), b)
28.56/9.95	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, e), c)
28.56/9.95	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, e), e)
28.56/9.95	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, k), b)
28.56/9.95	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(c, k), c)
28.56/9.95	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.95	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.95	   A^2 -> H(U1(c, k), e)
28.56/9.95	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.95	   A^2 -> H(U1(c, c), d)
28.56/9.95	   A^2 -> H(e, U1(e, b))
28.56/9.95	   A^2 -> H(e, U1(c, d))
28.56/9.95	   A^2 -> H(e, U1(d, c))
28.56/9.95	   A^2 -> H(e, U1(b, e))
28.56/9.95	   A^2 -> H(e, U1(b, k))
28.56/9.95	   A^2 -> H(e, U1(e, c))
28.56/9.95	   A^2 -> H(e, U1(c, e))
28.56/9.95	   A^2 -> H(e, U1(c, k))
28.56/9.95	   A^2 -> H(e, U1(e, e))
28.56/9.95	   A^2 -> H(e, U1(d, k))
28.56/9.95	   A^2 -> H(U1(e, e), b)
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.95	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.95	   A^2 -> H(U1(e, e), c)
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.95	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.95	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.95	   A^2 -> H(f(e), d)
28.56/9.95	   A^2 -> H(f(e), k)
28.56/9.95	   A^2 -> H(U1(k, k), b)
28.56/9.95	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.95	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.95	   A^2 -> H(U1(k, k), c)
28.56/9.95	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.95	
28.56/9.95	The TRS R consists of the following rules:
28.56/9.95	
28.56/9.95	   f(x) -> U1(x, x)
28.56/9.95	   U1(e, x) -> x
28.56/9.95	   a -> c
28.56/9.95	   a -> d
28.56/9.95	   b -> c
28.56/9.95	   b -> d
28.56/9.95	   d -> k
28.56/9.95	   c -> e
28.56/9.95	   c -> k
28.56/9.95	
28.56/9.95	Q is empty.
28.56/9.95	We have to consider all minimal (P,Q,R)-chains.
28.56/9.95	----------------------------------------
28.56/9.95	
28.56/9.95	(1669) TransformationProof (EQUIVALENT)
28.56/9.95	By narrowing [LPAR04] the rule A^2 -> H(f(k), b) at position [] we obtained the following new rules [LPAR04]:
28.56/9.95	
28.56/9.95	   (A^2 -> H(U1(k, k), b),A^2 -> H(U1(k, k), b))
28.56/9.95	   (A^2 -> H(f(k), c),A^2 -> H(f(k), c))
28.56/9.95	   (A^2 -> H(f(k), d),A^2 -> H(f(k), d))
28.56/9.95	
28.56/9.95	
28.56/9.95	----------------------------------------
28.56/9.95	
28.56/9.95	(1670)
28.56/9.95	Obligation:
28.56/9.95	Q DP problem:
28.56/9.95	The TRS P consists of the following rules:
28.56/9.95	
28.56/9.95	   A^2 -> H(f(c), f(c))
28.56/9.95	   H(x, x) -> G(x, x, f(k))
28.56/9.95	   G(d, x, x) -> A^2
28.56/9.95	   A^2 -> H(f(d), f(d))
28.56/9.95	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.95	   A^2 -> H(f(e), f(e))
28.56/9.95	   A^2 -> H(f(k), f(k))
28.56/9.95	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.95	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.95	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.95	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.95	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.95	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.95	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.95	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.95	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.95	   A^2 -> H(f(k), U1(e, d))
28.56/9.95	   A^2 -> H(f(k), U1(d, e))
28.56/9.95	   A^2 -> H(f(k), c)
28.56/9.95	   A^2 -> H(f(k), U1(e, k))
28.56/9.95	   A^2 -> H(f(k), U1(k, e))
28.56/9.95	   A^2 -> H(f(k), e)
28.56/9.95	   A^2 -> H(f(c), d)
28.56/9.95	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.96	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.96	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.96	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.96	   A^2 -> H(U1(k, k), f(e))
28.56/9.96	   A^2 -> H(U1(k, k), f(k))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.96	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, d), b)
28.56/9.96	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.96	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.96	   A^2 -> H(U1(d, d), c)
28.56/9.96	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.96	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.96	   A^2 -> H(U1(d, d), e)
28.56/9.96	   A^2 -> H(f(d), d)
28.56/9.96	   A^2 -> H(f(d), k)
28.56/9.96	   A^2 -> H(U1(c, c), c)
28.56/9.96	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.96	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.96	   A^2 -> H(f(c), k)
28.56/9.96	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.96	   A^2 -> H(f(k), U1(k, k))
28.56/9.96	   A^2 -> H(f(e), e)
28.56/9.96	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.96	   A^2 -> H(d, U1(c, b))
28.56/9.96	   A^2 -> H(d, U1(d, b))
28.56/9.96	   A^2 -> H(d, U1(b, c))
28.56/9.96	   A^2 -> H(d, U1(b, d))
28.56/9.96	   A^2 -> H(d, U1(c, c))
28.56/9.96	   A^2 -> H(d, f(e))
28.56/9.96	   A^2 -> H(d, f(k))
28.56/9.96	   A^2 -> H(d, U1(d, d))
28.56/9.96	   A^2 -> H(a, U1(e, b))
28.56/9.96	   A^2 -> H(a, U1(k, b))
28.56/9.96	   A^2 -> H(a, U1(c, d))
28.56/9.96	   A^2 -> H(a, U1(d, c))
28.56/9.96	   A^2 -> H(a, U1(b, e))
28.56/9.96	   A^2 -> H(a, U1(b, k))
28.56/9.96	   A^2 -> H(a, U1(e, c))
28.56/9.96	   A^2 -> H(a, U1(k, c))
28.56/9.96	   A^2 -> H(a, U1(c, e))
28.56/9.96	   A^2 -> H(a, U1(c, k))
28.56/9.96	   A^2 -> H(a, U1(e, e))
28.56/9.96	   A^2 -> H(a, U1(k, k))
28.56/9.96	   A^2 -> H(a, U1(k, d))
28.56/9.96	   A^2 -> H(a, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.96	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, a), b)
28.56/9.96	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, a), c)
28.56/9.96	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, a), e)
28.56/9.96	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, a), b)
28.56/9.96	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, a), c)
28.56/9.96	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.96	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.96	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, d), b)
28.56/9.96	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, d), c)
28.56/9.96	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, d), e)
28.56/9.96	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, a), d)
28.56/9.96	   A^2 -> H(U1(c, a), k)
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.96	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, c), b)
28.56/9.96	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(d, c), c)
28.56/9.96	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(d, c), e)
28.56/9.96	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, a), d)
28.56/9.96	   A^2 -> H(U1(d, a), k)
28.56/9.96	   A^2 -> H(U1(a, e), b)
28.56/9.96	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(a, e), c)
28.56/9.96	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(a, e), e)
28.56/9.96	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(a, k), b)
28.56/9.96	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(a, k), c)
28.56/9.96	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.96	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.96	   A^2 -> H(U1(a, k), e)
28.56/9.96	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(a, c), d)
28.56/9.96	   A^2 -> H(U1(a, c), k)
28.56/9.96	   A^2 -> H(U1(a, d), d)
28.56/9.96	   A^2 -> H(U1(a, d), k)
28.56/9.96	   A^2 -> H(k, U1(c, b))
28.56/9.96	   A^2 -> H(k, U1(d, b))
28.56/9.96	   A^2 -> H(k, U1(b, c))
28.56/9.96	   A^2 -> H(k, U1(b, d))
28.56/9.96	   A^2 -> H(k, U1(c, c))
28.56/9.96	   A^2 -> H(k, f(e))
28.56/9.96	   A^2 -> H(k, f(k))
28.56/9.96	   A^2 -> H(k, U1(d, d))
28.56/9.96	   A^2 -> H(c, U1(e, b))
28.56/9.96	   A^2 -> H(c, U1(k, b))
28.56/9.96	   A^2 -> H(c, U1(c, d))
28.56/9.96	   A^2 -> H(c, U1(d, c))
28.56/9.96	   A^2 -> H(c, U1(b, e))
28.56/9.96	   A^2 -> H(c, U1(b, k))
28.56/9.96	   A^2 -> H(c, U1(e, c))
28.56/9.96	   A^2 -> H(c, U1(k, c))
28.56/9.96	   A^2 -> H(c, U1(c, e))
28.56/9.96	   A^2 -> H(c, U1(c, k))
28.56/9.96	   A^2 -> H(c, U1(e, e))
28.56/9.96	   A^2 -> H(c, U1(k, k))
28.56/9.96	   A^2 -> H(c, U1(k, d))
28.56/9.96	   A^2 -> H(c, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.96	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.96	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, c), b)
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, c), e)
28.56/9.96	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.96	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.96	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.96	   A^2 -> H(U1(k, c), b)
28.56/9.96	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, c), c)
28.56/9.96	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, e), b)
28.56/9.96	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, e), c)
28.56/9.96	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, e), e)
28.56/9.96	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, k), b)
28.56/9.96	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, k), c)
28.56/9.96	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, k), e)
28.56/9.96	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, c), d)
28.56/9.96	   A^2 -> H(e, U1(e, b))
28.56/9.96	   A^2 -> H(e, U1(c, d))
28.56/9.96	   A^2 -> H(e, U1(d, c))
28.56/9.96	   A^2 -> H(e, U1(b, e))
28.56/9.96	   A^2 -> H(e, U1(b, k))
28.56/9.96	   A^2 -> H(e, U1(e, c))
28.56/9.96	   A^2 -> H(e, U1(c, e))
28.56/9.96	   A^2 -> H(e, U1(c, k))
28.56/9.96	   A^2 -> H(e, U1(e, e))
28.56/9.96	   A^2 -> H(e, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, e), b)
28.56/9.96	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, e), c)
28.56/9.96	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.96	   A^2 -> H(f(e), d)
28.56/9.96	   A^2 -> H(f(e), k)
28.56/9.96	   A^2 -> H(U1(k, k), b)
28.56/9.96	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, k), c)
28.56/9.96	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.96	   A^2 -> H(f(k), d)
28.56/9.96	
28.56/9.96	The TRS R consists of the following rules:
28.56/9.96	
28.56/9.96	   f(x) -> U1(x, x)
28.56/9.96	   U1(e, x) -> x
28.56/9.96	   a -> c
28.56/9.96	   a -> d
28.56/9.96	   b -> c
28.56/9.96	   b -> d
28.56/9.96	   d -> k
28.56/9.96	   c -> e
28.56/9.96	   c -> k
28.56/9.96	
28.56/9.96	Q is empty.
28.56/9.96	We have to consider all minimal (P,Q,R)-chains.
28.56/9.96	----------------------------------------
28.56/9.96	
28.56/9.96	(1671) TransformationProof (EQUIVALENT)
28.56/9.96	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.96	
28.56/9.96	   (A^2 -> H(U1(k, k), U1(e, d)),A^2 -> H(U1(k, k), U1(e, d)))
28.56/9.96	   (A^2 -> H(f(k), d),A^2 -> H(f(k), d))
28.56/9.96	   (A^2 -> H(f(k), U1(e, k)),A^2 -> H(f(k), U1(e, k)))
28.56/9.96	
28.56/9.96	
28.56/9.96	----------------------------------------
28.56/9.96	
28.56/9.96	(1672)
28.56/9.96	Obligation:
28.56/9.96	Q DP problem:
28.56/9.96	The TRS P consists of the following rules:
28.56/9.96	
28.56/9.96	   A^2 -> H(f(c), f(c))
28.56/9.96	   H(x, x) -> G(x, x, f(k))
28.56/9.96	   G(d, x, x) -> A^2
28.56/9.96	   A^2 -> H(f(d), f(d))
28.56/9.96	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.96	   A^2 -> H(f(e), f(e))
28.56/9.96	   A^2 -> H(f(k), f(k))
28.56/9.96	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.96	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.96	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.96	   A^2 -> H(f(k), U1(d, e))
28.56/9.96	   A^2 -> H(f(k), c)
28.56/9.96	   A^2 -> H(f(k), U1(e, k))
28.56/9.96	   A^2 -> H(f(k), U1(k, e))
28.56/9.96	   A^2 -> H(f(k), e)
28.56/9.96	   A^2 -> H(f(c), d)
28.56/9.96	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.96	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.96	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.96	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.96	   A^2 -> H(U1(k, k), f(e))
28.56/9.96	   A^2 -> H(U1(k, k), f(k))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.96	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, d), b)
28.56/9.96	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.96	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.96	   A^2 -> H(U1(d, d), c)
28.56/9.96	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.96	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.96	   A^2 -> H(U1(d, d), e)
28.56/9.96	   A^2 -> H(f(d), d)
28.56/9.96	   A^2 -> H(f(d), k)
28.56/9.96	   A^2 -> H(U1(c, c), c)
28.56/9.96	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.96	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.96	   A^2 -> H(f(c), k)
28.56/9.96	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.96	   A^2 -> H(f(k), U1(k, k))
28.56/9.96	   A^2 -> H(f(e), e)
28.56/9.96	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.96	   A^2 -> H(d, U1(c, b))
28.56/9.96	   A^2 -> H(d, U1(d, b))
28.56/9.96	   A^2 -> H(d, U1(b, c))
28.56/9.96	   A^2 -> H(d, U1(b, d))
28.56/9.96	   A^2 -> H(d, U1(c, c))
28.56/9.96	   A^2 -> H(d, f(e))
28.56/9.96	   A^2 -> H(d, f(k))
28.56/9.96	   A^2 -> H(d, U1(d, d))
28.56/9.96	   A^2 -> H(a, U1(e, b))
28.56/9.96	   A^2 -> H(a, U1(k, b))
28.56/9.96	   A^2 -> H(a, U1(c, d))
28.56/9.96	   A^2 -> H(a, U1(d, c))
28.56/9.96	   A^2 -> H(a, U1(b, e))
28.56/9.96	   A^2 -> H(a, U1(b, k))
28.56/9.96	   A^2 -> H(a, U1(e, c))
28.56/9.96	   A^2 -> H(a, U1(k, c))
28.56/9.96	   A^2 -> H(a, U1(c, e))
28.56/9.96	   A^2 -> H(a, U1(c, k))
28.56/9.96	   A^2 -> H(a, U1(e, e))
28.56/9.96	   A^2 -> H(a, U1(k, k))
28.56/9.96	   A^2 -> H(a, U1(k, d))
28.56/9.96	   A^2 -> H(a, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.96	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, a), b)
28.56/9.96	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, a), c)
28.56/9.96	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, a), e)
28.56/9.96	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, a), b)
28.56/9.96	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, a), c)
28.56/9.96	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.96	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.96	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, d), b)
28.56/9.96	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, d), c)
28.56/9.96	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, d), e)
28.56/9.96	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, a), d)
28.56/9.96	   A^2 -> H(U1(c, a), k)
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.96	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, c), b)
28.56/9.96	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(d, c), c)
28.56/9.96	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(d, c), e)
28.56/9.96	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, a), d)
28.56/9.96	   A^2 -> H(U1(d, a), k)
28.56/9.96	   A^2 -> H(U1(a, e), b)
28.56/9.96	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(a, e), c)
28.56/9.96	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(a, e), e)
28.56/9.96	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(a, k), b)
28.56/9.96	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(a, k), c)
28.56/9.96	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.96	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.96	   A^2 -> H(U1(a, k), e)
28.56/9.96	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(a, c), d)
28.56/9.96	   A^2 -> H(U1(a, c), k)
28.56/9.96	   A^2 -> H(U1(a, d), d)
28.56/9.96	   A^2 -> H(U1(a, d), k)
28.56/9.96	   A^2 -> H(k, U1(c, b))
28.56/9.96	   A^2 -> H(k, U1(d, b))
28.56/9.96	   A^2 -> H(k, U1(b, c))
28.56/9.96	   A^2 -> H(k, U1(b, d))
28.56/9.96	   A^2 -> H(k, U1(c, c))
28.56/9.96	   A^2 -> H(k, f(e))
28.56/9.96	   A^2 -> H(k, f(k))
28.56/9.96	   A^2 -> H(k, U1(d, d))
28.56/9.96	   A^2 -> H(c, U1(e, b))
28.56/9.96	   A^2 -> H(c, U1(k, b))
28.56/9.96	   A^2 -> H(c, U1(c, d))
28.56/9.96	   A^2 -> H(c, U1(d, c))
28.56/9.96	   A^2 -> H(c, U1(b, e))
28.56/9.96	   A^2 -> H(c, U1(b, k))
28.56/9.96	   A^2 -> H(c, U1(e, c))
28.56/9.96	   A^2 -> H(c, U1(k, c))
28.56/9.96	   A^2 -> H(c, U1(c, e))
28.56/9.96	   A^2 -> H(c, U1(c, k))
28.56/9.96	   A^2 -> H(c, U1(e, e))
28.56/9.96	   A^2 -> H(c, U1(k, k))
28.56/9.96	   A^2 -> H(c, U1(k, d))
28.56/9.96	   A^2 -> H(c, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.96	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.96	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, c), b)
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, c), e)
28.56/9.96	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.96	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.96	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.96	   A^2 -> H(U1(k, c), b)
28.56/9.96	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, c), c)
28.56/9.96	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, e), b)
28.56/9.96	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, e), c)
28.56/9.96	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, e), e)
28.56/9.96	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, k), b)
28.56/9.96	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, k), c)
28.56/9.96	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, k), e)
28.56/9.96	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, c), d)
28.56/9.96	   A^2 -> H(e, U1(e, b))
28.56/9.96	   A^2 -> H(e, U1(c, d))
28.56/9.96	   A^2 -> H(e, U1(d, c))
28.56/9.96	   A^2 -> H(e, U1(b, e))
28.56/9.96	   A^2 -> H(e, U1(b, k))
28.56/9.96	   A^2 -> H(e, U1(e, c))
28.56/9.96	   A^2 -> H(e, U1(c, e))
28.56/9.96	   A^2 -> H(e, U1(c, k))
28.56/9.96	   A^2 -> H(e, U1(e, e))
28.56/9.96	   A^2 -> H(e, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, e), b)
28.56/9.96	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, e), c)
28.56/9.96	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.96	   A^2 -> H(f(e), d)
28.56/9.96	   A^2 -> H(f(e), k)
28.56/9.96	   A^2 -> H(U1(k, k), b)
28.56/9.96	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, k), c)
28.56/9.96	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.96	   A^2 -> H(f(k), d)
28.56/9.96	
28.56/9.96	The TRS R consists of the following rules:
28.56/9.96	
28.56/9.96	   f(x) -> U1(x, x)
28.56/9.96	   U1(e, x) -> x
28.56/9.96	   a -> c
28.56/9.96	   a -> d
28.56/9.96	   b -> c
28.56/9.96	   b -> d
28.56/9.96	   d -> k
28.56/9.96	   c -> e
28.56/9.96	   c -> k
28.56/9.96	
28.56/9.96	Q is empty.
28.56/9.96	We have to consider all minimal (P,Q,R)-chains.
28.56/9.96	----------------------------------------
28.56/9.96	
28.56/9.96	(1673) TransformationProof (EQUIVALENT)
28.56/9.96	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.96	
28.56/9.96	   (A^2 -> H(U1(k, k), U1(d, e)),A^2 -> H(U1(k, k), U1(d, e)))
28.56/9.96	   (A^2 -> H(f(k), U1(k, e)),A^2 -> H(f(k), U1(k, e)))
28.56/9.96	
28.56/9.96	
28.56/9.96	----------------------------------------
28.56/9.96	
28.56/9.96	(1674)
28.56/9.96	Obligation:
28.56/9.96	Q DP problem:
28.56/9.96	The TRS P consists of the following rules:
28.56/9.96	
28.56/9.96	   A^2 -> H(f(c), f(c))
28.56/9.96	   H(x, x) -> G(x, x, f(k))
28.56/9.96	   G(d, x, x) -> A^2
28.56/9.96	   A^2 -> H(f(d), f(d))
28.56/9.96	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.96	   A^2 -> H(f(e), f(e))
28.56/9.96	   A^2 -> H(f(k), f(k))
28.56/9.96	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.96	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.96	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.96	   A^2 -> H(f(k), c)
28.56/9.96	   A^2 -> H(f(k), U1(e, k))
28.56/9.96	   A^2 -> H(f(k), U1(k, e))
28.56/9.96	   A^2 -> H(f(k), e)
28.56/9.96	   A^2 -> H(f(c), d)
28.56/9.96	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.96	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.96	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.96	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.96	   A^2 -> H(U1(k, k), f(e))
28.56/9.96	   A^2 -> H(U1(k, k), f(k))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.96	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, d), b)
28.56/9.96	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.96	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.96	   A^2 -> H(U1(d, d), c)
28.56/9.96	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.96	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.96	   A^2 -> H(U1(d, d), e)
28.56/9.96	   A^2 -> H(f(d), d)
28.56/9.96	   A^2 -> H(f(d), k)
28.56/9.96	   A^2 -> H(U1(c, c), c)
28.56/9.96	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.96	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.96	   A^2 -> H(f(c), k)
28.56/9.96	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.96	   A^2 -> H(f(k), U1(k, k))
28.56/9.96	   A^2 -> H(f(e), e)
28.56/9.96	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.96	   A^2 -> H(d, U1(c, b))
28.56/9.96	   A^2 -> H(d, U1(d, b))
28.56/9.96	   A^2 -> H(d, U1(b, c))
28.56/9.96	   A^2 -> H(d, U1(b, d))
28.56/9.96	   A^2 -> H(d, U1(c, c))
28.56/9.96	   A^2 -> H(d, f(e))
28.56/9.96	   A^2 -> H(d, f(k))
28.56/9.96	   A^2 -> H(d, U1(d, d))
28.56/9.96	   A^2 -> H(a, U1(e, b))
28.56/9.96	   A^2 -> H(a, U1(k, b))
28.56/9.96	   A^2 -> H(a, U1(c, d))
28.56/9.96	   A^2 -> H(a, U1(d, c))
28.56/9.96	   A^2 -> H(a, U1(b, e))
28.56/9.96	   A^2 -> H(a, U1(b, k))
28.56/9.96	   A^2 -> H(a, U1(e, c))
28.56/9.96	   A^2 -> H(a, U1(k, c))
28.56/9.96	   A^2 -> H(a, U1(c, e))
28.56/9.96	   A^2 -> H(a, U1(c, k))
28.56/9.96	   A^2 -> H(a, U1(e, e))
28.56/9.96	   A^2 -> H(a, U1(k, k))
28.56/9.96	   A^2 -> H(a, U1(k, d))
28.56/9.96	   A^2 -> H(a, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.96	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, a), b)
28.56/9.96	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, a), c)
28.56/9.96	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, a), e)
28.56/9.96	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, a), b)
28.56/9.96	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, a), c)
28.56/9.96	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.96	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.96	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, d), b)
28.56/9.96	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, d), c)
28.56/9.96	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, d), e)
28.56/9.96	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, a), d)
28.56/9.96	   A^2 -> H(U1(c, a), k)
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.96	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, c), b)
28.56/9.96	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(d, c), c)
28.56/9.96	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(d, c), e)
28.56/9.96	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, a), d)
28.56/9.96	   A^2 -> H(U1(d, a), k)
28.56/9.96	   A^2 -> H(U1(a, e), b)
28.56/9.96	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(a, e), c)
28.56/9.96	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(a, e), e)
28.56/9.96	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(a, k), b)
28.56/9.96	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(a, k), c)
28.56/9.96	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.96	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.96	   A^2 -> H(U1(a, k), e)
28.56/9.96	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(a, c), d)
28.56/9.96	   A^2 -> H(U1(a, c), k)
28.56/9.96	   A^2 -> H(U1(a, d), d)
28.56/9.96	   A^2 -> H(U1(a, d), k)
28.56/9.96	   A^2 -> H(k, U1(c, b))
28.56/9.96	   A^2 -> H(k, U1(d, b))
28.56/9.96	   A^2 -> H(k, U1(b, c))
28.56/9.96	   A^2 -> H(k, U1(b, d))
28.56/9.96	   A^2 -> H(k, U1(c, c))
28.56/9.96	   A^2 -> H(k, f(e))
28.56/9.96	   A^2 -> H(k, f(k))
28.56/9.96	   A^2 -> H(k, U1(d, d))
28.56/9.96	   A^2 -> H(c, U1(e, b))
28.56/9.96	   A^2 -> H(c, U1(k, b))
28.56/9.96	   A^2 -> H(c, U1(c, d))
28.56/9.96	   A^2 -> H(c, U1(d, c))
28.56/9.96	   A^2 -> H(c, U1(b, e))
28.56/9.96	   A^2 -> H(c, U1(b, k))
28.56/9.96	   A^2 -> H(c, U1(e, c))
28.56/9.96	   A^2 -> H(c, U1(k, c))
28.56/9.96	   A^2 -> H(c, U1(c, e))
28.56/9.96	   A^2 -> H(c, U1(c, k))
28.56/9.96	   A^2 -> H(c, U1(e, e))
28.56/9.96	   A^2 -> H(c, U1(k, k))
28.56/9.96	   A^2 -> H(c, U1(k, d))
28.56/9.96	   A^2 -> H(c, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.96	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.96	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, c), b)
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, c), e)
28.56/9.96	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.96	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.96	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.96	   A^2 -> H(U1(k, c), b)
28.56/9.96	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, c), c)
28.56/9.96	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, e), b)
28.56/9.96	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, e), c)
28.56/9.96	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, e), e)
28.56/9.96	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, k), b)
28.56/9.96	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, k), c)
28.56/9.96	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, k), e)
28.56/9.96	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, c), d)
28.56/9.96	   A^2 -> H(e, U1(e, b))
28.56/9.96	   A^2 -> H(e, U1(c, d))
28.56/9.96	   A^2 -> H(e, U1(d, c))
28.56/9.96	   A^2 -> H(e, U1(b, e))
28.56/9.96	   A^2 -> H(e, U1(b, k))
28.56/9.96	   A^2 -> H(e, U1(e, c))
28.56/9.96	   A^2 -> H(e, U1(c, e))
28.56/9.96	   A^2 -> H(e, U1(c, k))
28.56/9.96	   A^2 -> H(e, U1(e, e))
28.56/9.96	   A^2 -> H(e, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, e), b)
28.56/9.96	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, e), c)
28.56/9.96	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.96	   A^2 -> H(f(e), d)
28.56/9.96	   A^2 -> H(f(e), k)
28.56/9.96	   A^2 -> H(U1(k, k), b)
28.56/9.96	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, k), c)
28.56/9.96	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.96	   A^2 -> H(f(k), d)
28.56/9.96	
28.56/9.96	The TRS R consists of the following rules:
28.56/9.96	
28.56/9.96	   f(x) -> U1(x, x)
28.56/9.96	   U1(e, x) -> x
28.56/9.96	   a -> c
28.56/9.96	   a -> d
28.56/9.96	   b -> c
28.56/9.96	   b -> d
28.56/9.96	   d -> k
28.56/9.96	   c -> e
28.56/9.96	   c -> k
28.56/9.96	
28.56/9.96	Q is empty.
28.56/9.96	We have to consider all minimal (P,Q,R)-chains.
28.56/9.96	----------------------------------------
28.56/9.96	
28.56/9.96	(1675) TransformationProof (EQUIVALENT)
28.56/9.96	By narrowing [LPAR04] the rule A^2 -> H(f(k), c) at position [] we obtained the following new rules [LPAR04]:
28.56/9.96	
28.56/9.96	   (A^2 -> H(U1(k, k), c),A^2 -> H(U1(k, k), c))
28.56/9.96	   (A^2 -> H(f(k), e),A^2 -> H(f(k), e))
28.56/9.96	   (A^2 -> H(f(k), k),A^2 -> H(f(k), k))
28.56/9.96	
28.56/9.96	
28.56/9.96	----------------------------------------
28.56/9.96	
28.56/9.96	(1676)
28.56/9.96	Obligation:
28.56/9.96	Q DP problem:
28.56/9.96	The TRS P consists of the following rules:
28.56/9.96	
28.56/9.96	   A^2 -> H(f(c), f(c))
28.56/9.96	   H(x, x) -> G(x, x, f(k))
28.56/9.96	   G(d, x, x) -> A^2
28.56/9.96	   A^2 -> H(f(d), f(d))
28.56/9.96	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.96	   A^2 -> H(f(e), f(e))
28.56/9.96	   A^2 -> H(f(k), f(k))
28.56/9.96	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.96	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.96	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.96	   A^2 -> H(f(k), U1(e, k))
28.56/9.96	   A^2 -> H(f(k), U1(k, e))
28.56/9.96	   A^2 -> H(f(k), e)
28.56/9.96	   A^2 -> H(f(c), d)
28.56/9.96	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.96	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.96	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.96	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.96	   A^2 -> H(U1(k, k), f(e))
28.56/9.96	   A^2 -> H(U1(k, k), f(k))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.96	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, d), b)
28.56/9.96	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.96	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.96	   A^2 -> H(U1(d, d), c)
28.56/9.96	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.96	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.96	   A^2 -> H(U1(d, d), e)
28.56/9.96	   A^2 -> H(f(d), d)
28.56/9.96	   A^2 -> H(f(d), k)
28.56/9.96	   A^2 -> H(U1(c, c), c)
28.56/9.96	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.96	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.96	   A^2 -> H(f(c), k)
28.56/9.96	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.96	   A^2 -> H(f(k), U1(k, k))
28.56/9.96	   A^2 -> H(f(e), e)
28.56/9.96	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.96	   A^2 -> H(d, U1(c, b))
28.56/9.96	   A^2 -> H(d, U1(d, b))
28.56/9.96	   A^2 -> H(d, U1(b, c))
28.56/9.96	   A^2 -> H(d, U1(b, d))
28.56/9.96	   A^2 -> H(d, U1(c, c))
28.56/9.96	   A^2 -> H(d, f(e))
28.56/9.96	   A^2 -> H(d, f(k))
28.56/9.96	   A^2 -> H(d, U1(d, d))
28.56/9.96	   A^2 -> H(a, U1(e, b))
28.56/9.96	   A^2 -> H(a, U1(k, b))
28.56/9.96	   A^2 -> H(a, U1(c, d))
28.56/9.96	   A^2 -> H(a, U1(d, c))
28.56/9.96	   A^2 -> H(a, U1(b, e))
28.56/9.96	   A^2 -> H(a, U1(b, k))
28.56/9.96	   A^2 -> H(a, U1(e, c))
28.56/9.96	   A^2 -> H(a, U1(k, c))
28.56/9.96	   A^2 -> H(a, U1(c, e))
28.56/9.96	   A^2 -> H(a, U1(c, k))
28.56/9.96	   A^2 -> H(a, U1(e, e))
28.56/9.96	   A^2 -> H(a, U1(k, k))
28.56/9.96	   A^2 -> H(a, U1(k, d))
28.56/9.96	   A^2 -> H(a, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.96	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, a), b)
28.56/9.96	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, a), c)
28.56/9.96	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, a), e)
28.56/9.96	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, a), b)
28.56/9.96	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, a), c)
28.56/9.96	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.96	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.96	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, d), b)
28.56/9.96	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, d), c)
28.56/9.96	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, d), e)
28.56/9.96	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, a), d)
28.56/9.96	   A^2 -> H(U1(c, a), k)
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.96	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, c), b)
28.56/9.96	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(d, c), c)
28.56/9.96	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(d, c), e)
28.56/9.96	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, a), d)
28.56/9.96	   A^2 -> H(U1(d, a), k)
28.56/9.96	   A^2 -> H(U1(a, e), b)
28.56/9.96	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(a, e), c)
28.56/9.96	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(a, e), e)
28.56/9.96	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(a, k), b)
28.56/9.96	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(a, k), c)
28.56/9.96	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.96	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.96	   A^2 -> H(U1(a, k), e)
28.56/9.96	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(a, c), d)
28.56/9.96	   A^2 -> H(U1(a, c), k)
28.56/9.96	   A^2 -> H(U1(a, d), d)
28.56/9.96	   A^2 -> H(U1(a, d), k)
28.56/9.96	   A^2 -> H(k, U1(c, b))
28.56/9.96	   A^2 -> H(k, U1(d, b))
28.56/9.96	   A^2 -> H(k, U1(b, c))
28.56/9.96	   A^2 -> H(k, U1(b, d))
28.56/9.96	   A^2 -> H(k, U1(c, c))
28.56/9.96	   A^2 -> H(k, f(e))
28.56/9.96	   A^2 -> H(k, f(k))
28.56/9.96	   A^2 -> H(k, U1(d, d))
28.56/9.96	   A^2 -> H(c, U1(e, b))
28.56/9.96	   A^2 -> H(c, U1(k, b))
28.56/9.96	   A^2 -> H(c, U1(c, d))
28.56/9.96	   A^2 -> H(c, U1(d, c))
28.56/9.96	   A^2 -> H(c, U1(b, e))
28.56/9.96	   A^2 -> H(c, U1(b, k))
28.56/9.96	   A^2 -> H(c, U1(e, c))
28.56/9.96	   A^2 -> H(c, U1(k, c))
28.56/9.96	   A^2 -> H(c, U1(c, e))
28.56/9.96	   A^2 -> H(c, U1(c, k))
28.56/9.96	   A^2 -> H(c, U1(e, e))
28.56/9.96	   A^2 -> H(c, U1(k, k))
28.56/9.96	   A^2 -> H(c, U1(k, d))
28.56/9.96	   A^2 -> H(c, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.96	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.96	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, c), b)
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, c), e)
28.56/9.96	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.96	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.96	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.96	   A^2 -> H(U1(k, c), b)
28.56/9.96	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, c), c)
28.56/9.96	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, e), b)
28.56/9.96	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, e), c)
28.56/9.96	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, e), e)
28.56/9.96	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, k), b)
28.56/9.96	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, k), c)
28.56/9.96	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, k), e)
28.56/9.96	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, c), d)
28.56/9.96	   A^2 -> H(e, U1(e, b))
28.56/9.96	   A^2 -> H(e, U1(c, d))
28.56/9.96	   A^2 -> H(e, U1(d, c))
28.56/9.96	   A^2 -> H(e, U1(b, e))
28.56/9.96	   A^2 -> H(e, U1(b, k))
28.56/9.96	   A^2 -> H(e, U1(e, c))
28.56/9.96	   A^2 -> H(e, U1(c, e))
28.56/9.96	   A^2 -> H(e, U1(c, k))
28.56/9.96	   A^2 -> H(e, U1(e, e))
28.56/9.96	   A^2 -> H(e, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, e), b)
28.56/9.96	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, e), c)
28.56/9.96	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.96	   A^2 -> H(f(e), d)
28.56/9.96	   A^2 -> H(f(e), k)
28.56/9.96	   A^2 -> H(U1(k, k), b)
28.56/9.96	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, k), c)
28.56/9.96	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.96	   A^2 -> H(f(k), d)
28.56/9.96	   A^2 -> H(f(k), k)
28.56/9.96	
28.56/9.96	The TRS R consists of the following rules:
28.56/9.96	
28.56/9.96	   f(x) -> U1(x, x)
28.56/9.96	   U1(e, x) -> x
28.56/9.96	   a -> c
28.56/9.96	   a -> d
28.56/9.96	   b -> c
28.56/9.96	   b -> d
28.56/9.96	   d -> k
28.56/9.96	   c -> e
28.56/9.96	   c -> k
28.56/9.96	
28.56/9.96	Q is empty.
28.56/9.96	We have to consider all minimal (P,Q,R)-chains.
28.56/9.96	----------------------------------------
28.56/9.96	
28.56/9.96	(1677) TransformationProof (EQUIVALENT)
28.56/9.96	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.96	
28.56/9.96	   (A^2 -> H(U1(k, k), U1(e, k)),A^2 -> H(U1(k, k), U1(e, k)))
28.56/9.96	   (A^2 -> H(f(k), k),A^2 -> H(f(k), k))
28.56/9.96	
28.56/9.96	
28.56/9.96	----------------------------------------
28.56/9.96	
28.56/9.96	(1678)
28.56/9.96	Obligation:
28.56/9.96	Q DP problem:
28.56/9.96	The TRS P consists of the following rules:
28.56/9.96	
28.56/9.96	   A^2 -> H(f(c), f(c))
28.56/9.96	   H(x, x) -> G(x, x, f(k))
28.56/9.96	   G(d, x, x) -> A^2
28.56/9.96	   A^2 -> H(f(d), f(d))
28.56/9.96	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.96	   A^2 -> H(f(e), f(e))
28.56/9.96	   A^2 -> H(f(k), f(k))
28.56/9.96	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.96	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.96	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.96	   A^2 -> H(f(k), U1(k, e))
28.56/9.96	   A^2 -> H(f(k), e)
28.56/9.96	   A^2 -> H(f(c), d)
28.56/9.96	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.96	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.96	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.96	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.96	   A^2 -> H(U1(k, k), f(e))
28.56/9.96	   A^2 -> H(U1(k, k), f(k))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.96	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, d), b)
28.56/9.96	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.96	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.96	   A^2 -> H(U1(d, d), c)
28.56/9.96	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.96	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.96	   A^2 -> H(U1(d, d), e)
28.56/9.96	   A^2 -> H(f(d), d)
28.56/9.96	   A^2 -> H(f(d), k)
28.56/9.96	   A^2 -> H(U1(c, c), c)
28.56/9.96	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.96	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.96	   A^2 -> H(f(c), k)
28.56/9.96	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.96	   A^2 -> H(f(k), U1(k, k))
28.56/9.96	   A^2 -> H(f(e), e)
28.56/9.96	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.96	   A^2 -> H(d, U1(c, b))
28.56/9.96	   A^2 -> H(d, U1(d, b))
28.56/9.96	   A^2 -> H(d, U1(b, c))
28.56/9.96	   A^2 -> H(d, U1(b, d))
28.56/9.96	   A^2 -> H(d, U1(c, c))
28.56/9.96	   A^2 -> H(d, f(e))
28.56/9.96	   A^2 -> H(d, f(k))
28.56/9.96	   A^2 -> H(d, U1(d, d))
28.56/9.96	   A^2 -> H(a, U1(e, b))
28.56/9.96	   A^2 -> H(a, U1(k, b))
28.56/9.96	   A^2 -> H(a, U1(c, d))
28.56/9.96	   A^2 -> H(a, U1(d, c))
28.56/9.96	   A^2 -> H(a, U1(b, e))
28.56/9.96	   A^2 -> H(a, U1(b, k))
28.56/9.96	   A^2 -> H(a, U1(e, c))
28.56/9.96	   A^2 -> H(a, U1(k, c))
28.56/9.96	   A^2 -> H(a, U1(c, e))
28.56/9.96	   A^2 -> H(a, U1(c, k))
28.56/9.96	   A^2 -> H(a, U1(e, e))
28.56/9.96	   A^2 -> H(a, U1(k, k))
28.56/9.96	   A^2 -> H(a, U1(k, d))
28.56/9.96	   A^2 -> H(a, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.96	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, a), b)
28.56/9.96	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, a), c)
28.56/9.96	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, a), e)
28.56/9.96	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, a), b)
28.56/9.96	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, a), c)
28.56/9.96	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.96	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.96	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, d), b)
28.56/9.96	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, d), c)
28.56/9.96	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, d), e)
28.56/9.96	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, a), d)
28.56/9.96	   A^2 -> H(U1(c, a), k)
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.96	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, c), b)
28.56/9.96	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(d, c), c)
28.56/9.96	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(d, c), e)
28.56/9.96	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, a), d)
28.56/9.96	   A^2 -> H(U1(d, a), k)
28.56/9.96	   A^2 -> H(U1(a, e), b)
28.56/9.96	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(a, e), c)
28.56/9.96	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(a, e), e)
28.56/9.96	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(a, k), b)
28.56/9.96	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(a, k), c)
28.56/9.96	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.96	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.96	   A^2 -> H(U1(a, k), e)
28.56/9.96	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(a, c), d)
28.56/9.96	   A^2 -> H(U1(a, c), k)
28.56/9.96	   A^2 -> H(U1(a, d), d)
28.56/9.96	   A^2 -> H(U1(a, d), k)
28.56/9.96	   A^2 -> H(k, U1(c, b))
28.56/9.96	   A^2 -> H(k, U1(d, b))
28.56/9.96	   A^2 -> H(k, U1(b, c))
28.56/9.96	   A^2 -> H(k, U1(b, d))
28.56/9.96	   A^2 -> H(k, U1(c, c))
28.56/9.96	   A^2 -> H(k, f(e))
28.56/9.96	   A^2 -> H(k, f(k))
28.56/9.96	   A^2 -> H(k, U1(d, d))
28.56/9.96	   A^2 -> H(c, U1(e, b))
28.56/9.96	   A^2 -> H(c, U1(k, b))
28.56/9.96	   A^2 -> H(c, U1(c, d))
28.56/9.96	   A^2 -> H(c, U1(d, c))
28.56/9.96	   A^2 -> H(c, U1(b, e))
28.56/9.96	   A^2 -> H(c, U1(b, k))
28.56/9.96	   A^2 -> H(c, U1(e, c))
28.56/9.96	   A^2 -> H(c, U1(k, c))
28.56/9.96	   A^2 -> H(c, U1(c, e))
28.56/9.96	   A^2 -> H(c, U1(c, k))
28.56/9.96	   A^2 -> H(c, U1(e, e))
28.56/9.96	   A^2 -> H(c, U1(k, k))
28.56/9.96	   A^2 -> H(c, U1(k, d))
28.56/9.96	   A^2 -> H(c, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.96	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.96	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, c), b)
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, c), e)
28.56/9.96	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.96	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.96	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.96	   A^2 -> H(U1(k, c), b)
28.56/9.96	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, c), c)
28.56/9.96	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, e), b)
28.56/9.96	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, e), c)
28.56/9.96	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, e), e)
28.56/9.96	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, k), b)
28.56/9.96	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, k), c)
28.56/9.96	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, k), e)
28.56/9.96	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, c), d)
28.56/9.96	   A^2 -> H(e, U1(e, b))
28.56/9.96	   A^2 -> H(e, U1(c, d))
28.56/9.96	   A^2 -> H(e, U1(d, c))
28.56/9.96	   A^2 -> H(e, U1(b, e))
28.56/9.96	   A^2 -> H(e, U1(b, k))
28.56/9.96	   A^2 -> H(e, U1(e, c))
28.56/9.96	   A^2 -> H(e, U1(c, e))
28.56/9.96	   A^2 -> H(e, U1(c, k))
28.56/9.96	   A^2 -> H(e, U1(e, e))
28.56/9.96	   A^2 -> H(e, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, e), b)
28.56/9.96	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, e), c)
28.56/9.96	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.96	   A^2 -> H(f(e), d)
28.56/9.96	   A^2 -> H(f(e), k)
28.56/9.96	   A^2 -> H(U1(k, k), b)
28.56/9.96	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, k), c)
28.56/9.96	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.96	   A^2 -> H(f(k), d)
28.56/9.96	   A^2 -> H(f(k), k)
28.56/9.96	
28.56/9.96	The TRS R consists of the following rules:
28.56/9.96	
28.56/9.96	   f(x) -> U1(x, x)
28.56/9.96	   U1(e, x) -> x
28.56/9.96	   a -> c
28.56/9.96	   a -> d
28.56/9.96	   b -> c
28.56/9.96	   b -> d
28.56/9.96	   d -> k
28.56/9.96	   c -> e
28.56/9.96	   c -> k
28.56/9.96	
28.56/9.96	Q is empty.
28.56/9.96	We have to consider all minimal (P,Q,R)-chains.
28.56/9.96	----------------------------------------
28.56/9.96	
28.56/9.96	(1679) TransformationProof (EQUIVALENT)
28.56/9.96	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.96	
28.56/9.96	   (A^2 -> H(U1(k, k), U1(k, e)),A^2 -> H(U1(k, k), U1(k, e)))
28.56/9.96	
28.56/9.96	
28.56/9.96	----------------------------------------
28.56/9.96	
28.56/9.96	(1680)
28.56/9.96	Obligation:
28.56/9.96	Q DP problem:
28.56/9.96	The TRS P consists of the following rules:
28.56/9.96	
28.56/9.96	   A^2 -> H(f(c), f(c))
28.56/9.96	   H(x, x) -> G(x, x, f(k))
28.56/9.96	   G(d, x, x) -> A^2
28.56/9.96	   A^2 -> H(f(d), f(d))
28.56/9.96	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.96	   A^2 -> H(f(e), f(e))
28.56/9.96	   A^2 -> H(f(k), f(k))
28.56/9.96	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.96	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.96	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.96	   A^2 -> H(f(k), e)
28.56/9.96	   A^2 -> H(f(c), d)
28.56/9.96	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.96	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.96	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.96	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.96	   A^2 -> H(U1(k, k), f(e))
28.56/9.96	   A^2 -> H(U1(k, k), f(k))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.96	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, d), b)
28.56/9.96	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.96	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.96	   A^2 -> H(U1(d, d), c)
28.56/9.96	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.96	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.96	   A^2 -> H(U1(d, d), e)
28.56/9.96	   A^2 -> H(f(d), d)
28.56/9.96	   A^2 -> H(f(d), k)
28.56/9.96	   A^2 -> H(U1(c, c), c)
28.56/9.96	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.96	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.96	   A^2 -> H(f(c), k)
28.56/9.96	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.96	   A^2 -> H(f(k), U1(k, k))
28.56/9.96	   A^2 -> H(f(e), e)
28.56/9.96	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.96	   A^2 -> H(d, U1(c, b))
28.56/9.96	   A^2 -> H(d, U1(d, b))
28.56/9.96	   A^2 -> H(d, U1(b, c))
28.56/9.96	   A^2 -> H(d, U1(b, d))
28.56/9.96	   A^2 -> H(d, U1(c, c))
28.56/9.96	   A^2 -> H(d, f(e))
28.56/9.96	   A^2 -> H(d, f(k))
28.56/9.96	   A^2 -> H(d, U1(d, d))
28.56/9.96	   A^2 -> H(a, U1(e, b))
28.56/9.96	   A^2 -> H(a, U1(k, b))
28.56/9.96	   A^2 -> H(a, U1(c, d))
28.56/9.96	   A^2 -> H(a, U1(d, c))
28.56/9.96	   A^2 -> H(a, U1(b, e))
28.56/9.96	   A^2 -> H(a, U1(b, k))
28.56/9.96	   A^2 -> H(a, U1(e, c))
28.56/9.96	   A^2 -> H(a, U1(k, c))
28.56/9.96	   A^2 -> H(a, U1(c, e))
28.56/9.96	   A^2 -> H(a, U1(c, k))
28.56/9.96	   A^2 -> H(a, U1(e, e))
28.56/9.96	   A^2 -> H(a, U1(k, k))
28.56/9.96	   A^2 -> H(a, U1(k, d))
28.56/9.96	   A^2 -> H(a, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.96	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, a), b)
28.56/9.96	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, a), c)
28.56/9.96	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, a), e)
28.56/9.96	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, a), b)
28.56/9.96	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, a), c)
28.56/9.96	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.96	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.96	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, d), b)
28.56/9.96	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, d), c)
28.56/9.96	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, d), e)
28.56/9.96	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, a), d)
28.56/9.96	   A^2 -> H(U1(c, a), k)
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.96	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, c), b)
28.56/9.96	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(d, c), c)
28.56/9.96	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(d, c), e)
28.56/9.96	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, a), d)
28.56/9.96	   A^2 -> H(U1(d, a), k)
28.56/9.96	   A^2 -> H(U1(a, e), b)
28.56/9.96	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(a, e), c)
28.56/9.96	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(a, e), e)
28.56/9.96	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(a, k), b)
28.56/9.96	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(a, k), c)
28.56/9.96	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.96	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.96	   A^2 -> H(U1(a, k), e)
28.56/9.96	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(a, c), d)
28.56/9.96	   A^2 -> H(U1(a, c), k)
28.56/9.96	   A^2 -> H(U1(a, d), d)
28.56/9.96	   A^2 -> H(U1(a, d), k)
28.56/9.96	   A^2 -> H(k, U1(c, b))
28.56/9.96	   A^2 -> H(k, U1(d, b))
28.56/9.96	   A^2 -> H(k, U1(b, c))
28.56/9.96	   A^2 -> H(k, U1(b, d))
28.56/9.96	   A^2 -> H(k, U1(c, c))
28.56/9.96	   A^2 -> H(k, f(e))
28.56/9.96	   A^2 -> H(k, f(k))
28.56/9.96	   A^2 -> H(k, U1(d, d))
28.56/9.96	   A^2 -> H(c, U1(e, b))
28.56/9.96	   A^2 -> H(c, U1(k, b))
28.56/9.96	   A^2 -> H(c, U1(c, d))
28.56/9.96	   A^2 -> H(c, U1(d, c))
28.56/9.96	   A^2 -> H(c, U1(b, e))
28.56/9.96	   A^2 -> H(c, U1(b, k))
28.56/9.96	   A^2 -> H(c, U1(e, c))
28.56/9.96	   A^2 -> H(c, U1(k, c))
28.56/9.96	   A^2 -> H(c, U1(c, e))
28.56/9.96	   A^2 -> H(c, U1(c, k))
28.56/9.96	   A^2 -> H(c, U1(e, e))
28.56/9.96	   A^2 -> H(c, U1(k, k))
28.56/9.96	   A^2 -> H(c, U1(k, d))
28.56/9.96	   A^2 -> H(c, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.96	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.96	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, c), b)
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, c), e)
28.56/9.96	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.96	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.96	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.96	   A^2 -> H(U1(k, c), b)
28.56/9.96	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, c), c)
28.56/9.96	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, e), b)
28.56/9.96	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, e), c)
28.56/9.96	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, e), e)
28.56/9.96	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, k), b)
28.56/9.96	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, k), c)
28.56/9.96	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, k), e)
28.56/9.96	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, c), d)
28.56/9.96	   A^2 -> H(e, U1(e, b))
28.56/9.96	   A^2 -> H(e, U1(c, d))
28.56/9.96	   A^2 -> H(e, U1(d, c))
28.56/9.96	   A^2 -> H(e, U1(b, e))
28.56/9.96	   A^2 -> H(e, U1(b, k))
28.56/9.96	   A^2 -> H(e, U1(e, c))
28.56/9.96	   A^2 -> H(e, U1(c, e))
28.56/9.96	   A^2 -> H(e, U1(c, k))
28.56/9.96	   A^2 -> H(e, U1(e, e))
28.56/9.96	   A^2 -> H(e, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, e), b)
28.56/9.96	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, e), c)
28.56/9.96	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.96	   A^2 -> H(f(e), d)
28.56/9.96	   A^2 -> H(f(e), k)
28.56/9.96	   A^2 -> H(U1(k, k), b)
28.56/9.96	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, k), c)
28.56/9.96	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.96	   A^2 -> H(f(k), d)
28.56/9.96	   A^2 -> H(f(k), k)
28.56/9.96	   A^2 -> H(U1(k, k), U1(k, e))
28.56/9.96	
28.56/9.96	The TRS R consists of the following rules:
28.56/9.96	
28.56/9.96	   f(x) -> U1(x, x)
28.56/9.96	   U1(e, x) -> x
28.56/9.96	   a -> c
28.56/9.96	   a -> d
28.56/9.96	   b -> c
28.56/9.96	   b -> d
28.56/9.96	   d -> k
28.56/9.96	   c -> e
28.56/9.96	   c -> k
28.56/9.96	
28.56/9.96	Q is empty.
28.56/9.96	We have to consider all minimal (P,Q,R)-chains.
28.56/9.96	----------------------------------------
28.56/9.96	
28.56/9.96	(1681) DependencyGraphProof (EQUIVALENT)
28.56/9.96	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.96	----------------------------------------
28.56/9.96	
28.56/9.96	(1682)
28.56/9.96	Obligation:
28.56/9.96	Q DP problem:
28.56/9.96	The TRS P consists of the following rules:
28.56/9.96	
28.56/9.96	   H(x, x) -> G(x, x, f(k))
28.56/9.96	   G(d, x, x) -> A^2
28.56/9.96	   A^2 -> H(f(c), f(c))
28.56/9.96	   A^2 -> H(f(d), f(d))
28.56/9.96	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.96	   A^2 -> H(f(e), f(e))
28.56/9.96	   A^2 -> H(f(k), f(k))
28.56/9.96	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.96	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.96	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.96	   A^2 -> H(f(k), e)
28.56/9.96	   A^2 -> H(f(c), d)
28.56/9.96	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.96	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.96	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.96	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.96	   A^2 -> H(U1(k, k), f(e))
28.56/9.96	   A^2 -> H(U1(k, k), f(k))
28.56/9.96	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.96	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.96	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, d), b)
28.56/9.96	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.96	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.96	   A^2 -> H(U1(d, d), c)
28.56/9.96	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.96	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.96	   A^2 -> H(U1(d, d), e)
28.56/9.96	   A^2 -> H(f(d), d)
28.56/9.96	   A^2 -> H(f(d), k)
28.56/9.96	   A^2 -> H(U1(c, c), c)
28.56/9.96	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.96	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.96	   A^2 -> H(f(c), k)
28.56/9.96	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.96	   A^2 -> H(f(k), U1(k, k))
28.56/9.96	   A^2 -> H(f(e), e)
28.56/9.96	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.96	   A^2 -> H(d, U1(c, b))
28.56/9.96	   A^2 -> H(d, U1(d, b))
28.56/9.96	   A^2 -> H(d, U1(b, c))
28.56/9.96	   A^2 -> H(d, U1(b, d))
28.56/9.96	   A^2 -> H(d, U1(c, c))
28.56/9.96	   A^2 -> H(d, f(e))
28.56/9.96	   A^2 -> H(d, f(k))
28.56/9.96	   A^2 -> H(d, U1(d, d))
28.56/9.96	   A^2 -> H(a, U1(e, b))
28.56/9.96	   A^2 -> H(a, U1(k, b))
28.56/9.96	   A^2 -> H(a, U1(c, d))
28.56/9.96	   A^2 -> H(a, U1(d, c))
28.56/9.96	   A^2 -> H(a, U1(b, e))
28.56/9.96	   A^2 -> H(a, U1(b, k))
28.56/9.96	   A^2 -> H(a, U1(e, c))
28.56/9.96	   A^2 -> H(a, U1(k, c))
28.56/9.96	   A^2 -> H(a, U1(c, e))
28.56/9.96	   A^2 -> H(a, U1(c, k))
28.56/9.96	   A^2 -> H(a, U1(e, e))
28.56/9.96	   A^2 -> H(a, U1(k, k))
28.56/9.96	   A^2 -> H(a, U1(k, d))
28.56/9.96	   A^2 -> H(a, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.96	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.96	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, a), b)
28.56/9.96	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, a), c)
28.56/9.96	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, a), e)
28.56/9.96	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, a), b)
28.56/9.96	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, a), c)
28.56/9.96	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.96	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.96	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, d), b)
28.56/9.96	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.96	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.96	   A^2 -> H(U1(c, d), c)
28.56/9.96	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.96	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.96	   A^2 -> H(U1(c, d), e)
28.56/9.96	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, a), d)
28.56/9.96	   A^2 -> H(U1(c, a), k)
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.96	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.96	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.96	   A^2 -> H(U1(d, c), b)
28.56/9.96	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(d, c), c)
28.56/9.96	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(d, c), e)
28.56/9.96	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(d, a), d)
28.56/9.96	   A^2 -> H(U1(d, a), k)
28.56/9.96	   A^2 -> H(U1(a, e), b)
28.56/9.96	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.96	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.96	   A^2 -> H(U1(a, e), c)
28.56/9.96	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.96	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.96	   A^2 -> H(U1(a, e), e)
28.56/9.96	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.96	   A^2 -> H(U1(a, k), b)
28.56/9.96	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.96	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.96	   A^2 -> H(U1(a, k), c)
28.56/9.96	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.96	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.96	   A^2 -> H(U1(a, k), e)
28.56/9.96	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(a, c), d)
28.56/9.96	   A^2 -> H(U1(a, c), k)
28.56/9.96	   A^2 -> H(U1(a, d), d)
28.56/9.96	   A^2 -> H(U1(a, d), k)
28.56/9.96	   A^2 -> H(k, U1(c, b))
28.56/9.96	   A^2 -> H(k, U1(d, b))
28.56/9.96	   A^2 -> H(k, U1(b, c))
28.56/9.96	   A^2 -> H(k, U1(b, d))
28.56/9.96	   A^2 -> H(k, U1(c, c))
28.56/9.96	   A^2 -> H(k, f(e))
28.56/9.96	   A^2 -> H(k, f(k))
28.56/9.96	   A^2 -> H(k, U1(d, d))
28.56/9.96	   A^2 -> H(c, U1(e, b))
28.56/9.96	   A^2 -> H(c, U1(k, b))
28.56/9.96	   A^2 -> H(c, U1(c, d))
28.56/9.96	   A^2 -> H(c, U1(d, c))
28.56/9.96	   A^2 -> H(c, U1(b, e))
28.56/9.96	   A^2 -> H(c, U1(b, k))
28.56/9.96	   A^2 -> H(c, U1(e, c))
28.56/9.96	   A^2 -> H(c, U1(k, c))
28.56/9.96	   A^2 -> H(c, U1(c, e))
28.56/9.96	   A^2 -> H(c, U1(c, k))
28.56/9.96	   A^2 -> H(c, U1(e, e))
28.56/9.96	   A^2 -> H(c, U1(k, k))
28.56/9.96	   A^2 -> H(c, U1(k, d))
28.56/9.96	   A^2 -> H(c, U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.96	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.96	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.96	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.96	   A^2 -> H(U1(e, c), b)
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(e, c), e)
28.56/9.96	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.96	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.96	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.96	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.96	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.96	   A^2 -> H(U1(k, c), b)
28.56/9.96	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.96	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.96	   A^2 -> H(U1(k, c), c)
28.56/9.96	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.96	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.96	   A^2 -> H(U1(c, e), b)
28.56/9.97	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, e), c)
28.56/9.97	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, e), e)
28.56/9.97	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, k), b)
28.56/9.97	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, k), c)
28.56/9.97	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, k), e)
28.56/9.97	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, c), d)
28.56/9.97	   A^2 -> H(e, U1(e, b))
28.56/9.97	   A^2 -> H(e, U1(c, d))
28.56/9.97	   A^2 -> H(e, U1(d, c))
28.56/9.97	   A^2 -> H(e, U1(b, e))
28.56/9.97	   A^2 -> H(e, U1(b, k))
28.56/9.97	   A^2 -> H(e, U1(e, c))
28.56/9.97	   A^2 -> H(e, U1(c, e))
28.56/9.97	   A^2 -> H(e, U1(c, k))
28.56/9.97	   A^2 -> H(e, U1(e, e))
28.56/9.97	   A^2 -> H(e, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, e), b)
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, e), c)
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.97	   A^2 -> H(f(e), d)
28.56/9.97	   A^2 -> H(f(e), k)
28.56/9.97	   A^2 -> H(U1(k, k), b)
28.56/9.97	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, k), c)
28.56/9.97	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.97	   A^2 -> H(f(k), d)
28.56/9.97	   A^2 -> H(f(k), k)
28.56/9.97	
28.56/9.97	The TRS R consists of the following rules:
28.56/9.97	
28.56/9.97	   f(x) -> U1(x, x)
28.56/9.97	   U1(e, x) -> x
28.56/9.97	   a -> c
28.56/9.97	   a -> d
28.56/9.97	   b -> c
28.56/9.97	   b -> d
28.56/9.97	   d -> k
28.56/9.97	   c -> e
28.56/9.97	   c -> k
28.56/9.97	
28.56/9.97	Q is empty.
28.56/9.97	We have to consider all minimal (P,Q,R)-chains.
28.56/9.97	----------------------------------------
28.56/9.97	
28.56/9.97	(1683) TransformationProof (EQUIVALENT)
28.56/9.97	By narrowing [LPAR04] the rule A^2 -> H(f(k), e) at position [] we obtained the following new rules [LPAR04]:
28.56/9.97	
28.56/9.97	   (A^2 -> H(U1(k, k), e),A^2 -> H(U1(k, k), e))
28.56/9.97	
28.56/9.97	
28.56/9.97	----------------------------------------
28.56/9.97	
28.56/9.97	(1684)
28.56/9.97	Obligation:
28.56/9.97	Q DP problem:
28.56/9.97	The TRS P consists of the following rules:
28.56/9.97	
28.56/9.97	   H(x, x) -> G(x, x, f(k))
28.56/9.97	   G(d, x, x) -> A^2
28.56/9.97	   A^2 -> H(f(c), f(c))
28.56/9.97	   A^2 -> H(f(d), f(d))
28.56/9.97	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.97	   A^2 -> H(f(e), f(e))
28.56/9.97	   A^2 -> H(f(k), f(k))
28.56/9.97	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.97	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.97	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.97	   A^2 -> H(f(c), d)
28.56/9.97	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.97	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.97	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.97	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.97	   A^2 -> H(U1(k, k), f(e))
28.56/9.97	   A^2 -> H(U1(k, k), f(k))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.97	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, d), b)
28.56/9.97	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.97	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.97	   A^2 -> H(U1(d, d), c)
28.56/9.97	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.97	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.97	   A^2 -> H(U1(d, d), e)
28.56/9.97	   A^2 -> H(f(d), d)
28.56/9.97	   A^2 -> H(f(d), k)
28.56/9.97	   A^2 -> H(U1(c, c), c)
28.56/9.97	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.97	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.97	   A^2 -> H(f(c), k)
28.56/9.97	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.97	   A^2 -> H(f(k), U1(k, k))
28.56/9.97	   A^2 -> H(f(e), e)
28.56/9.97	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.97	   A^2 -> H(d, U1(c, b))
28.56/9.97	   A^2 -> H(d, U1(d, b))
28.56/9.97	   A^2 -> H(d, U1(b, c))
28.56/9.97	   A^2 -> H(d, U1(b, d))
28.56/9.97	   A^2 -> H(d, U1(c, c))
28.56/9.97	   A^2 -> H(d, f(e))
28.56/9.97	   A^2 -> H(d, f(k))
28.56/9.97	   A^2 -> H(d, U1(d, d))
28.56/9.97	   A^2 -> H(a, U1(e, b))
28.56/9.97	   A^2 -> H(a, U1(k, b))
28.56/9.97	   A^2 -> H(a, U1(c, d))
28.56/9.97	   A^2 -> H(a, U1(d, c))
28.56/9.97	   A^2 -> H(a, U1(b, e))
28.56/9.97	   A^2 -> H(a, U1(b, k))
28.56/9.97	   A^2 -> H(a, U1(e, c))
28.56/9.97	   A^2 -> H(a, U1(k, c))
28.56/9.97	   A^2 -> H(a, U1(c, e))
28.56/9.97	   A^2 -> H(a, U1(c, k))
28.56/9.97	   A^2 -> H(a, U1(e, e))
28.56/9.97	   A^2 -> H(a, U1(k, k))
28.56/9.97	   A^2 -> H(a, U1(k, d))
28.56/9.97	   A^2 -> H(a, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.97	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, a), b)
28.56/9.97	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, a), c)
28.56/9.97	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, a), e)
28.56/9.97	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, a), b)
28.56/9.97	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, a), c)
28.56/9.97	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.97	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.97	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, d), b)
28.56/9.97	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, d), c)
28.56/9.97	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, d), e)
28.56/9.97	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, a), d)
28.56/9.97	   A^2 -> H(U1(c, a), k)
28.56/9.97	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.97	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.97	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.97	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.97	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.97	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.97	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.97	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, c), b)
28.56/9.97	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.97	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.97	   A^2 -> H(U1(d, c), c)
28.56/9.97	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.97	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.97	   A^2 -> H(U1(d, c), e)
28.56/9.97	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, a), d)
28.56/9.97	   A^2 -> H(U1(d, a), k)
28.56/9.97	   A^2 -> H(U1(a, e), b)
28.56/9.97	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(a, e), c)
28.56/9.97	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(a, e), e)
28.56/9.97	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(a, k), b)
28.56/9.97	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(a, k), c)
28.56/9.97	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.97	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.97	   A^2 -> H(U1(a, k), e)
28.56/9.97	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(a, c), d)
28.56/9.97	   A^2 -> H(U1(a, c), k)
28.56/9.97	   A^2 -> H(U1(a, d), d)
28.56/9.97	   A^2 -> H(U1(a, d), k)
28.56/9.97	   A^2 -> H(k, U1(c, b))
28.56/9.97	   A^2 -> H(k, U1(d, b))
28.56/9.97	   A^2 -> H(k, U1(b, c))
28.56/9.97	   A^2 -> H(k, U1(b, d))
28.56/9.97	   A^2 -> H(k, U1(c, c))
28.56/9.97	   A^2 -> H(k, f(e))
28.56/9.97	   A^2 -> H(k, f(k))
28.56/9.97	   A^2 -> H(k, U1(d, d))
28.56/9.97	   A^2 -> H(c, U1(e, b))
28.56/9.97	   A^2 -> H(c, U1(k, b))
28.56/9.97	   A^2 -> H(c, U1(c, d))
28.56/9.97	   A^2 -> H(c, U1(d, c))
28.56/9.97	   A^2 -> H(c, U1(b, e))
28.56/9.97	   A^2 -> H(c, U1(b, k))
28.56/9.97	   A^2 -> H(c, U1(e, c))
28.56/9.97	   A^2 -> H(c, U1(k, c))
28.56/9.97	   A^2 -> H(c, U1(c, e))
28.56/9.97	   A^2 -> H(c, U1(c, k))
28.56/9.97	   A^2 -> H(c, U1(e, e))
28.56/9.97	   A^2 -> H(c, U1(k, k))
28.56/9.97	   A^2 -> H(c, U1(k, d))
28.56/9.97	   A^2 -> H(c, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.97	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.97	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.97	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.97	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.97	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.97	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, c), b)
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, c), e)
28.56/9.97	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.97	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.97	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.97	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.97	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.97	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.97	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.97	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.97	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.97	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.97	   A^2 -> H(U1(k, c), b)
28.56/9.97	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, c), c)
28.56/9.97	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, e), b)
28.56/9.97	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, e), c)
28.56/9.97	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, e), e)
28.56/9.97	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, k), b)
28.56/9.97	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, k), c)
28.56/9.97	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, k), e)
28.56/9.97	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, c), d)
28.56/9.97	   A^2 -> H(e, U1(e, b))
28.56/9.97	   A^2 -> H(e, U1(c, d))
28.56/9.97	   A^2 -> H(e, U1(d, c))
28.56/9.97	   A^2 -> H(e, U1(b, e))
28.56/9.97	   A^2 -> H(e, U1(b, k))
28.56/9.97	   A^2 -> H(e, U1(e, c))
28.56/9.97	   A^2 -> H(e, U1(c, e))
28.56/9.97	   A^2 -> H(e, U1(c, k))
28.56/9.97	   A^2 -> H(e, U1(e, e))
28.56/9.97	   A^2 -> H(e, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, e), b)
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, e), c)
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.97	   A^2 -> H(f(e), d)
28.56/9.97	   A^2 -> H(f(e), k)
28.56/9.97	   A^2 -> H(U1(k, k), b)
28.56/9.97	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, k), c)
28.56/9.97	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.97	   A^2 -> H(f(k), d)
28.56/9.97	   A^2 -> H(f(k), k)
28.56/9.97	   A^2 -> H(U1(k, k), e)
28.56/9.97	
28.56/9.97	The TRS R consists of the following rules:
28.56/9.97	
28.56/9.97	   f(x) -> U1(x, x)
28.56/9.97	   U1(e, x) -> x
28.56/9.97	   a -> c
28.56/9.97	   a -> d
28.56/9.97	   b -> c
28.56/9.97	   b -> d
28.56/9.97	   d -> k
28.56/9.97	   c -> e
28.56/9.97	   c -> k
28.56/9.97	
28.56/9.97	Q is empty.
28.56/9.97	We have to consider all minimal (P,Q,R)-chains.
28.56/9.97	----------------------------------------
28.56/9.97	
28.56/9.97	(1685) DependencyGraphProof (EQUIVALENT)
28.56/9.97	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/9.97	----------------------------------------
28.56/9.97	
28.56/9.97	(1686)
28.56/9.97	Obligation:
28.56/9.97	Q DP problem:
28.56/9.97	The TRS P consists of the following rules:
28.56/9.97	
28.56/9.97	   G(d, x, x) -> A^2
28.56/9.97	   A^2 -> H(f(c), f(c))
28.56/9.97	   H(x, x) -> G(x, x, f(k))
28.56/9.97	   A^2 -> H(f(d), f(d))
28.56/9.97	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.97	   A^2 -> H(f(e), f(e))
28.56/9.97	   A^2 -> H(f(k), f(k))
28.56/9.97	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.97	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.97	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.97	   A^2 -> H(f(c), d)
28.56/9.97	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.97	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.97	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.97	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.97	   A^2 -> H(U1(k, k), f(e))
28.56/9.97	   A^2 -> H(U1(k, k), f(k))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.97	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, d), b)
28.56/9.97	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.97	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.97	   A^2 -> H(U1(d, d), c)
28.56/9.97	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.97	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.97	   A^2 -> H(U1(d, d), e)
28.56/9.97	   A^2 -> H(f(d), d)
28.56/9.97	   A^2 -> H(f(d), k)
28.56/9.97	   A^2 -> H(U1(c, c), c)
28.56/9.97	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.97	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.97	   A^2 -> H(f(c), k)
28.56/9.97	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.97	   A^2 -> H(f(k), U1(k, k))
28.56/9.97	   A^2 -> H(f(e), e)
28.56/9.97	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.97	   A^2 -> H(d, U1(c, b))
28.56/9.97	   A^2 -> H(d, U1(d, b))
28.56/9.97	   A^2 -> H(d, U1(b, c))
28.56/9.97	   A^2 -> H(d, U1(b, d))
28.56/9.97	   A^2 -> H(d, U1(c, c))
28.56/9.97	   A^2 -> H(d, f(e))
28.56/9.97	   A^2 -> H(d, f(k))
28.56/9.97	   A^2 -> H(d, U1(d, d))
28.56/9.97	   A^2 -> H(a, U1(e, b))
28.56/9.97	   A^2 -> H(a, U1(k, b))
28.56/9.97	   A^2 -> H(a, U1(c, d))
28.56/9.97	   A^2 -> H(a, U1(d, c))
28.56/9.97	   A^2 -> H(a, U1(b, e))
28.56/9.97	   A^2 -> H(a, U1(b, k))
28.56/9.97	   A^2 -> H(a, U1(e, c))
28.56/9.97	   A^2 -> H(a, U1(k, c))
28.56/9.97	   A^2 -> H(a, U1(c, e))
28.56/9.97	   A^2 -> H(a, U1(c, k))
28.56/9.97	   A^2 -> H(a, U1(e, e))
28.56/9.97	   A^2 -> H(a, U1(k, k))
28.56/9.97	   A^2 -> H(a, U1(k, d))
28.56/9.97	   A^2 -> H(a, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.97	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, a), b)
28.56/9.97	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, a), c)
28.56/9.97	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, a), e)
28.56/9.97	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, a), b)
28.56/9.97	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, a), c)
28.56/9.97	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.97	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.97	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, d), b)
28.56/9.97	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, d), c)
28.56/9.97	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, d), e)
28.56/9.97	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, a), d)
28.56/9.97	   A^2 -> H(U1(c, a), k)
28.56/9.97	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.97	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.97	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.97	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.97	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.97	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.97	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.97	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, c), b)
28.56/9.97	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.97	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.97	   A^2 -> H(U1(d, c), c)
28.56/9.97	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.97	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.97	   A^2 -> H(U1(d, c), e)
28.56/9.97	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, a), d)
28.56/9.97	   A^2 -> H(U1(d, a), k)
28.56/9.97	   A^2 -> H(U1(a, e), b)
28.56/9.97	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(a, e), c)
28.56/9.97	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(a, e), e)
28.56/9.97	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(a, k), b)
28.56/9.97	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(a, k), c)
28.56/9.97	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.97	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.97	   A^2 -> H(U1(a, k), e)
28.56/9.97	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(a, c), d)
28.56/9.97	   A^2 -> H(U1(a, c), k)
28.56/9.97	   A^2 -> H(U1(a, d), d)
28.56/9.97	   A^2 -> H(U1(a, d), k)
28.56/9.97	   A^2 -> H(k, U1(c, b))
28.56/9.97	   A^2 -> H(k, U1(d, b))
28.56/9.97	   A^2 -> H(k, U1(b, c))
28.56/9.97	   A^2 -> H(k, U1(b, d))
28.56/9.97	   A^2 -> H(k, U1(c, c))
28.56/9.97	   A^2 -> H(k, f(e))
28.56/9.97	   A^2 -> H(k, f(k))
28.56/9.97	   A^2 -> H(k, U1(d, d))
28.56/9.97	   A^2 -> H(c, U1(e, b))
28.56/9.97	   A^2 -> H(c, U1(k, b))
28.56/9.97	   A^2 -> H(c, U1(c, d))
28.56/9.97	   A^2 -> H(c, U1(d, c))
28.56/9.97	   A^2 -> H(c, U1(b, e))
28.56/9.97	   A^2 -> H(c, U1(b, k))
28.56/9.97	   A^2 -> H(c, U1(e, c))
28.56/9.97	   A^2 -> H(c, U1(k, c))
28.56/9.97	   A^2 -> H(c, U1(c, e))
28.56/9.97	   A^2 -> H(c, U1(c, k))
28.56/9.97	   A^2 -> H(c, U1(e, e))
28.56/9.97	   A^2 -> H(c, U1(k, k))
28.56/9.97	   A^2 -> H(c, U1(k, d))
28.56/9.97	   A^2 -> H(c, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.97	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.97	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.97	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.97	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.97	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.97	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, c), b)
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, c), e)
28.56/9.97	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.97	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.97	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.97	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.97	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.97	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.97	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.97	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.97	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.97	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.97	   A^2 -> H(U1(k, c), b)
28.56/9.97	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, c), c)
28.56/9.97	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, e), b)
28.56/9.97	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, e), c)
28.56/9.97	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, e), e)
28.56/9.97	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, k), b)
28.56/9.97	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, k), c)
28.56/9.97	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, k), e)
28.56/9.97	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, c), d)
28.56/9.97	   A^2 -> H(e, U1(e, b))
28.56/9.97	   A^2 -> H(e, U1(c, d))
28.56/9.97	   A^2 -> H(e, U1(d, c))
28.56/9.97	   A^2 -> H(e, U1(b, e))
28.56/9.97	   A^2 -> H(e, U1(b, k))
28.56/9.97	   A^2 -> H(e, U1(e, c))
28.56/9.97	   A^2 -> H(e, U1(c, e))
28.56/9.97	   A^2 -> H(e, U1(c, k))
28.56/9.97	   A^2 -> H(e, U1(e, e))
28.56/9.97	   A^2 -> H(e, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, e), b)
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, e), c)
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.97	   A^2 -> H(f(e), d)
28.56/9.97	   A^2 -> H(f(e), k)
28.56/9.97	   A^2 -> H(U1(k, k), b)
28.56/9.97	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, k), c)
28.56/9.97	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.97	   A^2 -> H(f(k), d)
28.56/9.97	   A^2 -> H(f(k), k)
28.56/9.97	
28.56/9.97	The TRS R consists of the following rules:
28.56/9.97	
28.56/9.97	   f(x) -> U1(x, x)
28.56/9.97	   U1(e, x) -> x
28.56/9.97	   a -> c
28.56/9.97	   a -> d
28.56/9.97	   b -> c
28.56/9.97	   b -> d
28.56/9.97	   d -> k
28.56/9.97	   c -> e
28.56/9.97	   c -> k
28.56/9.97	
28.56/9.97	Q is empty.
28.56/9.97	We have to consider all minimal (P,Q,R)-chains.
28.56/9.97	----------------------------------------
28.56/9.97	
28.56/9.97	(1687) TransformationProof (EQUIVALENT)
28.56/9.97	By narrowing [LPAR04] the rule A^2 -> H(f(c), d) at position [] we obtained the following new rules [LPAR04]:
28.56/9.97	
28.56/9.97	   (A^2 -> H(U1(c, c), d),A^2 -> H(U1(c, c), d))
28.56/9.97	   (A^2 -> H(f(e), d),A^2 -> H(f(e), d))
28.56/9.97	   (A^2 -> H(f(k), d),A^2 -> H(f(k), d))
28.56/9.97	   (A^2 -> H(f(c), k),A^2 -> H(f(c), k))
28.56/9.97	
28.56/9.97	
28.56/9.97	----------------------------------------
28.56/9.97	
28.56/9.97	(1688)
28.56/9.97	Obligation:
28.56/9.97	Q DP problem:
28.56/9.97	The TRS P consists of the following rules:
28.56/9.97	
28.56/9.97	   G(d, x, x) -> A^2
28.56/9.97	   A^2 -> H(f(c), f(c))
28.56/9.97	   H(x, x) -> G(x, x, f(k))
28.56/9.97	   A^2 -> H(f(d), f(d))
28.56/9.97	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.97	   A^2 -> H(f(e), f(e))
28.56/9.97	   A^2 -> H(f(k), f(k))
28.56/9.97	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.97	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.97	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, k), U1(c, b))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.97	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.97	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.97	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.97	   A^2 -> H(U1(k, k), f(e))
28.56/9.97	   A^2 -> H(U1(k, k), f(k))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.97	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, d), b)
28.56/9.97	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.97	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.97	   A^2 -> H(U1(d, d), c)
28.56/9.97	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.97	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.97	   A^2 -> H(U1(d, d), e)
28.56/9.97	   A^2 -> H(f(d), d)
28.56/9.97	   A^2 -> H(f(d), k)
28.56/9.97	   A^2 -> H(U1(c, c), c)
28.56/9.97	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.97	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.97	   A^2 -> H(f(c), k)
28.56/9.97	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.97	   A^2 -> H(f(k), U1(k, k))
28.56/9.97	   A^2 -> H(f(e), e)
28.56/9.97	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.97	   A^2 -> H(d, U1(c, b))
28.56/9.97	   A^2 -> H(d, U1(d, b))
28.56/9.97	   A^2 -> H(d, U1(b, c))
28.56/9.97	   A^2 -> H(d, U1(b, d))
28.56/9.97	   A^2 -> H(d, U1(c, c))
28.56/9.97	   A^2 -> H(d, f(e))
28.56/9.97	   A^2 -> H(d, f(k))
28.56/9.97	   A^2 -> H(d, U1(d, d))
28.56/9.97	   A^2 -> H(a, U1(e, b))
28.56/9.97	   A^2 -> H(a, U1(k, b))
28.56/9.97	   A^2 -> H(a, U1(c, d))
28.56/9.97	   A^2 -> H(a, U1(d, c))
28.56/9.97	   A^2 -> H(a, U1(b, e))
28.56/9.97	   A^2 -> H(a, U1(b, k))
28.56/9.97	   A^2 -> H(a, U1(e, c))
28.56/9.97	   A^2 -> H(a, U1(k, c))
28.56/9.97	   A^2 -> H(a, U1(c, e))
28.56/9.97	   A^2 -> H(a, U1(c, k))
28.56/9.97	   A^2 -> H(a, U1(e, e))
28.56/9.97	   A^2 -> H(a, U1(k, k))
28.56/9.97	   A^2 -> H(a, U1(k, d))
28.56/9.97	   A^2 -> H(a, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.97	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, a), b)
28.56/9.97	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, a), c)
28.56/9.97	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, a), e)
28.56/9.97	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, a), b)
28.56/9.97	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, a), c)
28.56/9.97	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.97	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.97	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, d), b)
28.56/9.97	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, d), c)
28.56/9.97	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, d), e)
28.56/9.97	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, a), d)
28.56/9.97	   A^2 -> H(U1(c, a), k)
28.56/9.97	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.97	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.97	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.97	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.97	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.97	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.97	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.97	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, c), b)
28.56/9.97	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.97	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.97	   A^2 -> H(U1(d, c), c)
28.56/9.97	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.97	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.97	   A^2 -> H(U1(d, c), e)
28.56/9.97	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, a), d)
28.56/9.97	   A^2 -> H(U1(d, a), k)
28.56/9.97	   A^2 -> H(U1(a, e), b)
28.56/9.97	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(a, e), c)
28.56/9.97	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(a, e), e)
28.56/9.97	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(a, k), b)
28.56/9.97	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(a, k), c)
28.56/9.97	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.97	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.97	   A^2 -> H(U1(a, k), e)
28.56/9.97	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(a, c), d)
28.56/9.97	   A^2 -> H(U1(a, c), k)
28.56/9.97	   A^2 -> H(U1(a, d), d)
28.56/9.97	   A^2 -> H(U1(a, d), k)
28.56/9.97	   A^2 -> H(k, U1(c, b))
28.56/9.97	   A^2 -> H(k, U1(d, b))
28.56/9.97	   A^2 -> H(k, U1(b, c))
28.56/9.97	   A^2 -> H(k, U1(b, d))
28.56/9.97	   A^2 -> H(k, U1(c, c))
28.56/9.97	   A^2 -> H(k, f(e))
28.56/9.97	   A^2 -> H(k, f(k))
28.56/9.97	   A^2 -> H(k, U1(d, d))
28.56/9.97	   A^2 -> H(c, U1(e, b))
28.56/9.97	   A^2 -> H(c, U1(k, b))
28.56/9.97	   A^2 -> H(c, U1(c, d))
28.56/9.97	   A^2 -> H(c, U1(d, c))
28.56/9.97	   A^2 -> H(c, U1(b, e))
28.56/9.97	   A^2 -> H(c, U1(b, k))
28.56/9.97	   A^2 -> H(c, U1(e, c))
28.56/9.97	   A^2 -> H(c, U1(k, c))
28.56/9.97	   A^2 -> H(c, U1(c, e))
28.56/9.97	   A^2 -> H(c, U1(c, k))
28.56/9.97	   A^2 -> H(c, U1(e, e))
28.56/9.97	   A^2 -> H(c, U1(k, k))
28.56/9.97	   A^2 -> H(c, U1(k, d))
28.56/9.97	   A^2 -> H(c, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.97	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.97	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.97	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.97	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.97	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.97	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, c), b)
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, c), e)
28.56/9.97	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.97	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.97	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.97	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.97	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.97	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.97	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.97	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.97	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.97	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.97	   A^2 -> H(U1(k, c), b)
28.56/9.97	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, c), c)
28.56/9.97	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, e), b)
28.56/9.97	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, e), c)
28.56/9.97	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, e), e)
28.56/9.97	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, k), b)
28.56/9.97	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, k), c)
28.56/9.97	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, k), e)
28.56/9.97	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, c), d)
28.56/9.97	   A^2 -> H(e, U1(e, b))
28.56/9.97	   A^2 -> H(e, U1(c, d))
28.56/9.97	   A^2 -> H(e, U1(d, c))
28.56/9.97	   A^2 -> H(e, U1(b, e))
28.56/9.97	   A^2 -> H(e, U1(b, k))
28.56/9.97	   A^2 -> H(e, U1(e, c))
28.56/9.97	   A^2 -> H(e, U1(c, e))
28.56/9.97	   A^2 -> H(e, U1(c, k))
28.56/9.97	   A^2 -> H(e, U1(e, e))
28.56/9.97	   A^2 -> H(e, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, e), b)
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, e), c)
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.97	   A^2 -> H(f(e), d)
28.56/9.97	   A^2 -> H(f(e), k)
28.56/9.97	   A^2 -> H(U1(k, k), b)
28.56/9.97	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, k), c)
28.56/9.97	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.97	   A^2 -> H(f(k), d)
28.56/9.97	   A^2 -> H(f(k), k)
28.56/9.97	
28.56/9.97	The TRS R consists of the following rules:
28.56/9.97	
28.56/9.97	   f(x) -> U1(x, x)
28.56/9.97	   U1(e, x) -> x
28.56/9.97	   a -> c
28.56/9.97	   a -> d
28.56/9.97	   b -> c
28.56/9.97	   b -> d
28.56/9.97	   d -> k
28.56/9.97	   c -> e
28.56/9.97	   c -> k
28.56/9.97	
28.56/9.97	Q is empty.
28.56/9.97	We have to consider all minimal (P,Q,R)-chains.
28.56/9.97	----------------------------------------
28.56/9.97	
28.56/9.97	(1689) TransformationProof (EQUIVALENT)
28.56/9.97	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.97	
28.56/9.97	   (A^2 -> H(U1(k, k), U1(e, b)),A^2 -> H(U1(k, k), U1(e, b)))
28.56/9.97	   (A^2 -> H(U1(k, k), U1(k, b)),A^2 -> H(U1(k, k), U1(k, b)))
28.56/9.97	   (A^2 -> H(U1(k, k), U1(c, c)),A^2 -> H(U1(k, k), U1(c, c)))
28.56/9.97	   (A^2 -> H(U1(k, k), U1(c, d)),A^2 -> H(U1(k, k), U1(c, d)))
28.56/9.97	
28.56/9.97	
28.56/9.97	----------------------------------------
28.56/9.97	
28.56/9.97	(1690)
28.56/9.97	Obligation:
28.56/9.97	Q DP problem:
28.56/9.97	The TRS P consists of the following rules:
28.56/9.97	
28.56/9.97	   G(d, x, x) -> A^2
28.56/9.97	   A^2 -> H(f(c), f(c))
28.56/9.97	   H(x, x) -> G(x, x, f(k))
28.56/9.97	   A^2 -> H(f(d), f(d))
28.56/9.97	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.97	   A^2 -> H(f(e), f(e))
28.56/9.97	   A^2 -> H(f(k), f(k))
28.56/9.97	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.97	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.97	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, b))
28.56/9.97	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.97	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.97	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.97	   A^2 -> H(U1(k, k), f(e))
28.56/9.97	   A^2 -> H(U1(k, k), f(k))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.97	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, d), b)
28.56/9.97	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.97	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.97	   A^2 -> H(U1(d, d), c)
28.56/9.97	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.97	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.97	   A^2 -> H(U1(d, d), e)
28.56/9.97	   A^2 -> H(f(d), d)
28.56/9.97	   A^2 -> H(f(d), k)
28.56/9.97	   A^2 -> H(U1(c, c), c)
28.56/9.97	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.97	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.97	   A^2 -> H(f(c), k)
28.56/9.97	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.97	   A^2 -> H(f(k), U1(k, k))
28.56/9.97	   A^2 -> H(f(e), e)
28.56/9.97	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.97	   A^2 -> H(d, U1(c, b))
28.56/9.97	   A^2 -> H(d, U1(d, b))
28.56/9.97	   A^2 -> H(d, U1(b, c))
28.56/9.97	   A^2 -> H(d, U1(b, d))
28.56/9.97	   A^2 -> H(d, U1(c, c))
28.56/9.97	   A^2 -> H(d, f(e))
28.56/9.97	   A^2 -> H(d, f(k))
28.56/9.97	   A^2 -> H(d, U1(d, d))
28.56/9.97	   A^2 -> H(a, U1(e, b))
28.56/9.97	   A^2 -> H(a, U1(k, b))
28.56/9.97	   A^2 -> H(a, U1(c, d))
28.56/9.97	   A^2 -> H(a, U1(d, c))
28.56/9.97	   A^2 -> H(a, U1(b, e))
28.56/9.97	   A^2 -> H(a, U1(b, k))
28.56/9.97	   A^2 -> H(a, U1(e, c))
28.56/9.97	   A^2 -> H(a, U1(k, c))
28.56/9.97	   A^2 -> H(a, U1(c, e))
28.56/9.97	   A^2 -> H(a, U1(c, k))
28.56/9.97	   A^2 -> H(a, U1(e, e))
28.56/9.97	   A^2 -> H(a, U1(k, k))
28.56/9.97	   A^2 -> H(a, U1(k, d))
28.56/9.97	   A^2 -> H(a, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.97	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, a), b)
28.56/9.97	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, a), c)
28.56/9.97	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, a), e)
28.56/9.97	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, a), b)
28.56/9.97	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, a), c)
28.56/9.97	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.97	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.97	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, d), b)
28.56/9.97	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, d), c)
28.56/9.97	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, d), e)
28.56/9.97	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, a), d)
28.56/9.97	   A^2 -> H(U1(c, a), k)
28.56/9.97	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.97	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.97	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.97	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.97	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.97	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.97	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.97	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, c), b)
28.56/9.97	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.97	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.97	   A^2 -> H(U1(d, c), c)
28.56/9.97	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.97	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.97	   A^2 -> H(U1(d, c), e)
28.56/9.97	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, a), d)
28.56/9.97	   A^2 -> H(U1(d, a), k)
28.56/9.97	   A^2 -> H(U1(a, e), b)
28.56/9.97	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(a, e), c)
28.56/9.97	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(a, e), e)
28.56/9.97	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(a, k), b)
28.56/9.97	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(a, k), c)
28.56/9.97	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.97	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.97	   A^2 -> H(U1(a, k), e)
28.56/9.97	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(a, c), d)
28.56/9.97	   A^2 -> H(U1(a, c), k)
28.56/9.97	   A^2 -> H(U1(a, d), d)
28.56/9.97	   A^2 -> H(U1(a, d), k)
28.56/9.97	   A^2 -> H(k, U1(c, b))
28.56/9.97	   A^2 -> H(k, U1(d, b))
28.56/9.97	   A^2 -> H(k, U1(b, c))
28.56/9.97	   A^2 -> H(k, U1(b, d))
28.56/9.97	   A^2 -> H(k, U1(c, c))
28.56/9.97	   A^2 -> H(k, f(e))
28.56/9.97	   A^2 -> H(k, f(k))
28.56/9.97	   A^2 -> H(k, U1(d, d))
28.56/9.97	   A^2 -> H(c, U1(e, b))
28.56/9.97	   A^2 -> H(c, U1(k, b))
28.56/9.97	   A^2 -> H(c, U1(c, d))
28.56/9.97	   A^2 -> H(c, U1(d, c))
28.56/9.97	   A^2 -> H(c, U1(b, e))
28.56/9.97	   A^2 -> H(c, U1(b, k))
28.56/9.97	   A^2 -> H(c, U1(e, c))
28.56/9.97	   A^2 -> H(c, U1(k, c))
28.56/9.97	   A^2 -> H(c, U1(c, e))
28.56/9.97	   A^2 -> H(c, U1(c, k))
28.56/9.97	   A^2 -> H(c, U1(e, e))
28.56/9.97	   A^2 -> H(c, U1(k, k))
28.56/9.97	   A^2 -> H(c, U1(k, d))
28.56/9.97	   A^2 -> H(c, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.97	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.97	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.97	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.97	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.97	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.97	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, c), b)
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, c), e)
28.56/9.97	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.97	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.97	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.97	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.97	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.97	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.97	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.97	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.97	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.97	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.97	   A^2 -> H(U1(k, c), b)
28.56/9.97	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, c), c)
28.56/9.97	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, e), b)
28.56/9.97	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, e), c)
28.56/9.97	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, e), e)
28.56/9.97	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, k), b)
28.56/9.97	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, k), c)
28.56/9.97	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, k), e)
28.56/9.97	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, c), d)
28.56/9.97	   A^2 -> H(e, U1(e, b))
28.56/9.97	   A^2 -> H(e, U1(c, d))
28.56/9.97	   A^2 -> H(e, U1(d, c))
28.56/9.97	   A^2 -> H(e, U1(b, e))
28.56/9.97	   A^2 -> H(e, U1(b, k))
28.56/9.97	   A^2 -> H(e, U1(e, c))
28.56/9.97	   A^2 -> H(e, U1(c, e))
28.56/9.97	   A^2 -> H(e, U1(c, k))
28.56/9.97	   A^2 -> H(e, U1(e, e))
28.56/9.97	   A^2 -> H(e, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, e), b)
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, e), c)
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.97	   A^2 -> H(f(e), d)
28.56/9.97	   A^2 -> H(f(e), k)
28.56/9.97	   A^2 -> H(U1(k, k), b)
28.56/9.97	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, k), c)
28.56/9.97	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.97	   A^2 -> H(f(k), d)
28.56/9.97	   A^2 -> H(f(k), k)
28.56/9.97	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.97	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.97	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.97	
28.56/9.97	The TRS R consists of the following rules:
28.56/9.97	
28.56/9.97	   f(x) -> U1(x, x)
28.56/9.97	   U1(e, x) -> x
28.56/9.97	   a -> c
28.56/9.97	   a -> d
28.56/9.97	   b -> c
28.56/9.97	   b -> d
28.56/9.97	   d -> k
28.56/9.97	   c -> e
28.56/9.97	   c -> k
28.56/9.97	
28.56/9.97	Q is empty.
28.56/9.97	We have to consider all minimal (P,Q,R)-chains.
28.56/9.97	----------------------------------------
28.56/9.97	
28.56/9.97	(1691) TransformationProof (EQUIVALENT)
28.56/9.97	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.97	
28.56/9.97	   (A^2 -> H(U1(k, k), U1(k, b)),A^2 -> H(U1(k, k), U1(k, b)))
28.56/9.97	   (A^2 -> H(U1(k, k), U1(d, c)),A^2 -> H(U1(k, k), U1(d, c)))
28.56/9.97	   (A^2 -> H(U1(k, k), U1(d, d)),A^2 -> H(U1(k, k), U1(d, d)))
28.56/9.97	
28.56/9.97	
28.56/9.97	----------------------------------------
28.56/9.97	
28.56/9.97	(1692)
28.56/9.97	Obligation:
28.56/9.97	Q DP problem:
28.56/9.97	The TRS P consists of the following rules:
28.56/9.97	
28.56/9.97	   G(d, x, x) -> A^2
28.56/9.97	   A^2 -> H(f(c), f(c))
28.56/9.97	   H(x, x) -> G(x, x, f(k))
28.56/9.97	   A^2 -> H(f(d), f(d))
28.56/9.97	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.97	   A^2 -> H(f(e), f(e))
28.56/9.97	   A^2 -> H(f(k), f(k))
28.56/9.97	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.97	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.97	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, k), U1(b, c))
28.56/9.97	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.97	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.97	   A^2 -> H(U1(k, k), f(e))
28.56/9.97	   A^2 -> H(U1(k, k), f(k))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.97	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, d), b)
28.56/9.97	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.97	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.97	   A^2 -> H(U1(d, d), c)
28.56/9.97	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.97	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.97	   A^2 -> H(U1(d, d), e)
28.56/9.97	   A^2 -> H(f(d), d)
28.56/9.97	   A^2 -> H(f(d), k)
28.56/9.97	   A^2 -> H(U1(c, c), c)
28.56/9.97	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.97	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.97	   A^2 -> H(f(c), k)
28.56/9.97	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.97	   A^2 -> H(f(k), U1(k, k))
28.56/9.97	   A^2 -> H(f(e), e)
28.56/9.97	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.97	   A^2 -> H(d, U1(c, b))
28.56/9.97	   A^2 -> H(d, U1(d, b))
28.56/9.97	   A^2 -> H(d, U1(b, c))
28.56/9.97	   A^2 -> H(d, U1(b, d))
28.56/9.97	   A^2 -> H(d, U1(c, c))
28.56/9.97	   A^2 -> H(d, f(e))
28.56/9.97	   A^2 -> H(d, f(k))
28.56/9.97	   A^2 -> H(d, U1(d, d))
28.56/9.97	   A^2 -> H(a, U1(e, b))
28.56/9.97	   A^2 -> H(a, U1(k, b))
28.56/9.97	   A^2 -> H(a, U1(c, d))
28.56/9.97	   A^2 -> H(a, U1(d, c))
28.56/9.97	   A^2 -> H(a, U1(b, e))
28.56/9.97	   A^2 -> H(a, U1(b, k))
28.56/9.97	   A^2 -> H(a, U1(e, c))
28.56/9.97	   A^2 -> H(a, U1(k, c))
28.56/9.97	   A^2 -> H(a, U1(c, e))
28.56/9.97	   A^2 -> H(a, U1(c, k))
28.56/9.97	   A^2 -> H(a, U1(e, e))
28.56/9.97	   A^2 -> H(a, U1(k, k))
28.56/9.97	   A^2 -> H(a, U1(k, d))
28.56/9.97	   A^2 -> H(a, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.97	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, a), b)
28.56/9.97	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, a), c)
28.56/9.97	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, a), e)
28.56/9.97	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, a), b)
28.56/9.97	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, a), c)
28.56/9.97	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.97	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.97	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, d), b)
28.56/9.97	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, d), c)
28.56/9.97	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, d), e)
28.56/9.97	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, a), d)
28.56/9.97	   A^2 -> H(U1(c, a), k)
28.56/9.97	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.97	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.97	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.97	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.97	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.97	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.97	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.97	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, c), b)
28.56/9.97	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.97	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.97	   A^2 -> H(U1(d, c), c)
28.56/9.97	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.97	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.97	   A^2 -> H(U1(d, c), e)
28.56/9.97	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, a), d)
28.56/9.97	   A^2 -> H(U1(d, a), k)
28.56/9.97	   A^2 -> H(U1(a, e), b)
28.56/9.97	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(a, e), c)
28.56/9.97	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(a, e), e)
28.56/9.97	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(a, k), b)
28.56/9.97	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(a, k), c)
28.56/9.97	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.97	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.97	   A^2 -> H(U1(a, k), e)
28.56/9.97	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(a, c), d)
28.56/9.97	   A^2 -> H(U1(a, c), k)
28.56/9.97	   A^2 -> H(U1(a, d), d)
28.56/9.97	   A^2 -> H(U1(a, d), k)
28.56/9.97	   A^2 -> H(k, U1(c, b))
28.56/9.97	   A^2 -> H(k, U1(d, b))
28.56/9.97	   A^2 -> H(k, U1(b, c))
28.56/9.97	   A^2 -> H(k, U1(b, d))
28.56/9.97	   A^2 -> H(k, U1(c, c))
28.56/9.97	   A^2 -> H(k, f(e))
28.56/9.97	   A^2 -> H(k, f(k))
28.56/9.97	   A^2 -> H(k, U1(d, d))
28.56/9.97	   A^2 -> H(c, U1(e, b))
28.56/9.97	   A^2 -> H(c, U1(k, b))
28.56/9.97	   A^2 -> H(c, U1(c, d))
28.56/9.97	   A^2 -> H(c, U1(d, c))
28.56/9.97	   A^2 -> H(c, U1(b, e))
28.56/9.97	   A^2 -> H(c, U1(b, k))
28.56/9.97	   A^2 -> H(c, U1(e, c))
28.56/9.97	   A^2 -> H(c, U1(k, c))
28.56/9.97	   A^2 -> H(c, U1(c, e))
28.56/9.97	   A^2 -> H(c, U1(c, k))
28.56/9.97	   A^2 -> H(c, U1(e, e))
28.56/9.97	   A^2 -> H(c, U1(k, k))
28.56/9.97	   A^2 -> H(c, U1(k, d))
28.56/9.97	   A^2 -> H(c, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.97	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.97	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.97	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.97	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.97	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.97	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, c), b)
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, c), e)
28.56/9.97	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.97	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.97	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.97	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.97	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.97	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.97	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.97	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.97	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.97	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.97	   A^2 -> H(U1(k, c), b)
28.56/9.97	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, c), c)
28.56/9.97	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, e), b)
28.56/9.97	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, e), c)
28.56/9.97	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, e), e)
28.56/9.97	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, k), b)
28.56/9.97	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, k), c)
28.56/9.97	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, k), e)
28.56/9.97	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, c), d)
28.56/9.97	   A^2 -> H(e, U1(e, b))
28.56/9.97	   A^2 -> H(e, U1(c, d))
28.56/9.97	   A^2 -> H(e, U1(d, c))
28.56/9.97	   A^2 -> H(e, U1(b, e))
28.56/9.97	   A^2 -> H(e, U1(b, k))
28.56/9.97	   A^2 -> H(e, U1(e, c))
28.56/9.97	   A^2 -> H(e, U1(c, e))
28.56/9.97	   A^2 -> H(e, U1(c, k))
28.56/9.97	   A^2 -> H(e, U1(e, e))
28.56/9.97	   A^2 -> H(e, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, e), b)
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, e), c)
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.97	   A^2 -> H(f(e), d)
28.56/9.97	   A^2 -> H(f(e), k)
28.56/9.97	   A^2 -> H(U1(k, k), b)
28.56/9.97	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, k), c)
28.56/9.97	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.97	   A^2 -> H(f(k), d)
28.56/9.97	   A^2 -> H(f(k), k)
28.56/9.97	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.97	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.97	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.97	
28.56/9.97	The TRS R consists of the following rules:
28.56/9.97	
28.56/9.97	   f(x) -> U1(x, x)
28.56/9.97	   U1(e, x) -> x
28.56/9.97	   a -> c
28.56/9.97	   a -> d
28.56/9.97	   b -> c
28.56/9.97	   b -> d
28.56/9.97	   d -> k
28.56/9.97	   c -> e
28.56/9.97	   c -> k
28.56/9.97	
28.56/9.97	Q is empty.
28.56/9.97	We have to consider all minimal (P,Q,R)-chains.
28.56/9.97	----------------------------------------
28.56/9.97	
28.56/9.97	(1693) TransformationProof (EQUIVALENT)
28.56/9.97	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.97	
28.56/9.97	   (A^2 -> H(U1(k, k), U1(c, c)),A^2 -> H(U1(k, k), U1(c, c)))
28.56/9.97	   (A^2 -> H(U1(k, k), U1(d, c)),A^2 -> H(U1(k, k), U1(d, c)))
28.56/9.97	   (A^2 -> H(U1(k, k), U1(b, e)),A^2 -> H(U1(k, k), U1(b, e)))
28.56/9.97	   (A^2 -> H(U1(k, k), U1(b, k)),A^2 -> H(U1(k, k), U1(b, k)))
28.56/9.97	
28.56/9.97	
28.56/9.97	----------------------------------------
28.56/9.97	
28.56/9.97	(1694)
28.56/9.97	Obligation:
28.56/9.97	Q DP problem:
28.56/9.97	The TRS P consists of the following rules:
28.56/9.97	
28.56/9.97	   G(d, x, x) -> A^2
28.56/9.97	   A^2 -> H(f(c), f(c))
28.56/9.97	   H(x, x) -> G(x, x, f(k))
28.56/9.97	   A^2 -> H(f(d), f(d))
28.56/9.97	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.97	   A^2 -> H(f(e), f(e))
28.56/9.97	   A^2 -> H(f(k), f(k))
28.56/9.97	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.97	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.97	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, k), U1(b, d))
28.56/9.97	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.97	   A^2 -> H(U1(k, k), f(e))
28.56/9.97	   A^2 -> H(U1(k, k), f(k))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.97	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, d), b)
28.56/9.97	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.97	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.97	   A^2 -> H(U1(d, d), c)
28.56/9.97	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.97	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.97	   A^2 -> H(U1(d, d), e)
28.56/9.97	   A^2 -> H(f(d), d)
28.56/9.97	   A^2 -> H(f(d), k)
28.56/9.97	   A^2 -> H(U1(c, c), c)
28.56/9.97	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.97	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.97	   A^2 -> H(f(c), k)
28.56/9.97	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.97	   A^2 -> H(f(k), U1(k, k))
28.56/9.97	   A^2 -> H(f(e), e)
28.56/9.97	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.97	   A^2 -> H(d, U1(c, b))
28.56/9.97	   A^2 -> H(d, U1(d, b))
28.56/9.97	   A^2 -> H(d, U1(b, c))
28.56/9.97	   A^2 -> H(d, U1(b, d))
28.56/9.97	   A^2 -> H(d, U1(c, c))
28.56/9.97	   A^2 -> H(d, f(e))
28.56/9.97	   A^2 -> H(d, f(k))
28.56/9.97	   A^2 -> H(d, U1(d, d))
28.56/9.97	   A^2 -> H(a, U1(e, b))
28.56/9.97	   A^2 -> H(a, U1(k, b))
28.56/9.97	   A^2 -> H(a, U1(c, d))
28.56/9.97	   A^2 -> H(a, U1(d, c))
28.56/9.97	   A^2 -> H(a, U1(b, e))
28.56/9.97	   A^2 -> H(a, U1(b, k))
28.56/9.97	   A^2 -> H(a, U1(e, c))
28.56/9.97	   A^2 -> H(a, U1(k, c))
28.56/9.97	   A^2 -> H(a, U1(c, e))
28.56/9.97	   A^2 -> H(a, U1(c, k))
28.56/9.97	   A^2 -> H(a, U1(e, e))
28.56/9.97	   A^2 -> H(a, U1(k, k))
28.56/9.97	   A^2 -> H(a, U1(k, d))
28.56/9.97	   A^2 -> H(a, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.97	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, a), b)
28.56/9.97	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, a), c)
28.56/9.97	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, a), e)
28.56/9.97	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, a), b)
28.56/9.97	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, a), c)
28.56/9.97	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.97	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.97	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, d), b)
28.56/9.97	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, d), c)
28.56/9.97	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, d), e)
28.56/9.97	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, a), d)
28.56/9.97	   A^2 -> H(U1(c, a), k)
28.56/9.97	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.97	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.97	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.97	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.97	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.97	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.97	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.97	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, c), b)
28.56/9.97	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.97	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.97	   A^2 -> H(U1(d, c), c)
28.56/9.97	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.97	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.97	   A^2 -> H(U1(d, c), e)
28.56/9.97	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, a), d)
28.56/9.97	   A^2 -> H(U1(d, a), k)
28.56/9.97	   A^2 -> H(U1(a, e), b)
28.56/9.97	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(a, e), c)
28.56/9.97	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(a, e), e)
28.56/9.97	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(a, k), b)
28.56/9.97	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(a, k), c)
28.56/9.97	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.97	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.97	   A^2 -> H(U1(a, k), e)
28.56/9.97	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(a, c), d)
28.56/9.97	   A^2 -> H(U1(a, c), k)
28.56/9.97	   A^2 -> H(U1(a, d), d)
28.56/9.97	   A^2 -> H(U1(a, d), k)
28.56/9.97	   A^2 -> H(k, U1(c, b))
28.56/9.97	   A^2 -> H(k, U1(d, b))
28.56/9.97	   A^2 -> H(k, U1(b, c))
28.56/9.97	   A^2 -> H(k, U1(b, d))
28.56/9.97	   A^2 -> H(k, U1(c, c))
28.56/9.97	   A^2 -> H(k, f(e))
28.56/9.97	   A^2 -> H(k, f(k))
28.56/9.97	   A^2 -> H(k, U1(d, d))
28.56/9.97	   A^2 -> H(c, U1(e, b))
28.56/9.97	   A^2 -> H(c, U1(k, b))
28.56/9.97	   A^2 -> H(c, U1(c, d))
28.56/9.97	   A^2 -> H(c, U1(d, c))
28.56/9.97	   A^2 -> H(c, U1(b, e))
28.56/9.97	   A^2 -> H(c, U1(b, k))
28.56/9.97	   A^2 -> H(c, U1(e, c))
28.56/9.97	   A^2 -> H(c, U1(k, c))
28.56/9.97	   A^2 -> H(c, U1(c, e))
28.56/9.97	   A^2 -> H(c, U1(c, k))
28.56/9.97	   A^2 -> H(c, U1(e, e))
28.56/9.97	   A^2 -> H(c, U1(k, k))
28.56/9.97	   A^2 -> H(c, U1(k, d))
28.56/9.97	   A^2 -> H(c, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.97	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.97	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.97	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.97	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.97	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.97	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, c), b)
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, c), e)
28.56/9.97	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.97	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.97	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.97	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.97	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.97	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.97	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.97	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.97	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.97	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.97	   A^2 -> H(U1(k, c), b)
28.56/9.97	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, c), c)
28.56/9.97	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, e), b)
28.56/9.97	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, e), c)
28.56/9.97	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, e), e)
28.56/9.97	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, k), b)
28.56/9.97	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(c, k), c)
28.56/9.97	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.97	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.97	   A^2 -> H(U1(c, k), e)
28.56/9.97	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, c), d)
28.56/9.97	   A^2 -> H(e, U1(e, b))
28.56/9.97	   A^2 -> H(e, U1(c, d))
28.56/9.97	   A^2 -> H(e, U1(d, c))
28.56/9.97	   A^2 -> H(e, U1(b, e))
28.56/9.97	   A^2 -> H(e, U1(b, k))
28.56/9.97	   A^2 -> H(e, U1(e, c))
28.56/9.97	   A^2 -> H(e, U1(c, e))
28.56/9.97	   A^2 -> H(e, U1(c, k))
28.56/9.97	   A^2 -> H(e, U1(e, e))
28.56/9.97	   A^2 -> H(e, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, e), b)
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, e), c)
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.97	   A^2 -> H(f(e), d)
28.56/9.97	   A^2 -> H(f(e), k)
28.56/9.97	   A^2 -> H(U1(k, k), b)
28.56/9.97	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, k), c)
28.56/9.97	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.97	   A^2 -> H(f(k), d)
28.56/9.97	   A^2 -> H(f(k), k)
28.56/9.97	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.97	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.97	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.97	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.97	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.97	
28.56/9.97	The TRS R consists of the following rules:
28.56/9.97	
28.56/9.97	   f(x) -> U1(x, x)
28.56/9.97	   U1(e, x) -> x
28.56/9.97	   a -> c
28.56/9.97	   a -> d
28.56/9.97	   b -> c
28.56/9.97	   b -> d
28.56/9.97	   d -> k
28.56/9.97	   c -> e
28.56/9.97	   c -> k
28.56/9.97	
28.56/9.97	Q is empty.
28.56/9.97	We have to consider all minimal (P,Q,R)-chains.
28.56/9.97	----------------------------------------
28.56/9.97	
28.56/9.97	(1695) TransformationProof (EQUIVALENT)
28.56/9.97	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.97	
28.56/9.97	   (A^2 -> H(U1(k, k), U1(c, d)),A^2 -> H(U1(k, k), U1(c, d)))
28.56/9.97	   (A^2 -> H(U1(k, k), U1(d, d)),A^2 -> H(U1(k, k), U1(d, d)))
28.56/9.97	   (A^2 -> H(U1(k, k), U1(b, k)),A^2 -> H(U1(k, k), U1(b, k)))
28.56/9.97	
28.56/9.97	
28.56/9.97	----------------------------------------
28.56/9.97	
28.56/9.97	(1696)
28.56/9.97	Obligation:
28.56/9.97	Q DP problem:
28.56/9.97	The TRS P consists of the following rules:
28.56/9.97	
28.56/9.97	   G(d, x, x) -> A^2
28.56/9.97	   A^2 -> H(f(c), f(c))
28.56/9.97	   H(x, x) -> G(x, x, f(k))
28.56/9.97	   A^2 -> H(f(d), f(d))
28.56/9.97	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.97	   A^2 -> H(f(e), f(e))
28.56/9.97	   A^2 -> H(f(k), f(k))
28.56/9.97	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.97	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.97	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.97	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, k), U1(c, c))
28.56/9.97	   A^2 -> H(U1(k, k), f(e))
28.56/9.97	   A^2 -> H(U1(k, k), f(k))
28.56/9.97	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.97	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.97	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.97	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.97	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.97	   A^2 -> H(U1(d, d), b)
28.56/9.97	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.97	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.97	   A^2 -> H(U1(d, d), c)
28.56/9.97	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.97	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.97	   A^2 -> H(U1(d, d), e)
28.56/9.97	   A^2 -> H(f(d), d)
28.56/9.97	   A^2 -> H(f(d), k)
28.56/9.97	   A^2 -> H(U1(c, c), c)
28.56/9.97	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.97	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.97	   A^2 -> H(f(c), k)
28.56/9.97	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.97	   A^2 -> H(f(k), U1(k, k))
28.56/9.97	   A^2 -> H(f(e), e)
28.56/9.97	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.97	   A^2 -> H(d, U1(c, b))
28.56/9.97	   A^2 -> H(d, U1(d, b))
28.56/9.97	   A^2 -> H(d, U1(b, c))
28.56/9.97	   A^2 -> H(d, U1(b, d))
28.56/9.97	   A^2 -> H(d, U1(c, c))
28.56/9.97	   A^2 -> H(d, f(e))
28.56/9.97	   A^2 -> H(d, f(k))
28.56/9.97	   A^2 -> H(d, U1(d, d))
28.56/9.97	   A^2 -> H(a, U1(e, b))
28.56/9.97	   A^2 -> H(a, U1(k, b))
28.56/9.97	   A^2 -> H(a, U1(c, d))
28.56/9.97	   A^2 -> H(a, U1(d, c))
28.56/9.97	   A^2 -> H(a, U1(b, e))
28.56/9.97	   A^2 -> H(a, U1(b, k))
28.56/9.97	   A^2 -> H(a, U1(e, c))
28.56/9.97	   A^2 -> H(a, U1(k, c))
28.56/9.97	   A^2 -> H(a, U1(c, e))
28.56/9.97	   A^2 -> H(a, U1(c, k))
28.56/9.97	   A^2 -> H(a, U1(e, e))
28.56/9.97	   A^2 -> H(a, U1(k, k))
28.56/9.97	   A^2 -> H(a, U1(k, d))
28.56/9.97	   A^2 -> H(a, U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.97	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.97	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.97	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.97	   A^2 -> H(U1(e, a), b)
28.56/9.97	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.97	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.97	   A^2 -> H(U1(e, a), c)
28.56/9.97	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.97	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.97	   A^2 -> H(U1(e, a), e)
28.56/9.97	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.97	   A^2 -> H(U1(k, a), b)
28.56/9.97	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.97	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.97	   A^2 -> H(U1(k, a), c)
28.56/9.97	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.97	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.97	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.97	   A^2 -> H(U1(c, d), b)
28.56/9.97	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, d), c)
28.56/9.98	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, d), e)
28.56/9.98	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, a), d)
28.56/9.98	   A^2 -> H(U1(c, a), k)
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.98	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, c), b)
28.56/9.98	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(d, c), c)
28.56/9.98	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(d, c), e)
28.56/9.98	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, a), d)
28.56/9.98	   A^2 -> H(U1(d, a), k)
28.56/9.98	   A^2 -> H(U1(a, e), b)
28.56/9.98	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(a, e), c)
28.56/9.98	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(a, e), e)
28.56/9.98	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(a, k), b)
28.56/9.98	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(a, k), c)
28.56/9.98	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.98	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.98	   A^2 -> H(U1(a, k), e)
28.56/9.98	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(a, c), d)
28.56/9.98	   A^2 -> H(U1(a, c), k)
28.56/9.98	   A^2 -> H(U1(a, d), d)
28.56/9.98	   A^2 -> H(U1(a, d), k)
28.56/9.98	   A^2 -> H(k, U1(c, b))
28.56/9.98	   A^2 -> H(k, U1(d, b))
28.56/9.98	   A^2 -> H(k, U1(b, c))
28.56/9.98	   A^2 -> H(k, U1(b, d))
28.56/9.98	   A^2 -> H(k, U1(c, c))
28.56/9.98	   A^2 -> H(k, f(e))
28.56/9.98	   A^2 -> H(k, f(k))
28.56/9.98	   A^2 -> H(k, U1(d, d))
28.56/9.98	   A^2 -> H(c, U1(e, b))
28.56/9.98	   A^2 -> H(c, U1(k, b))
28.56/9.98	   A^2 -> H(c, U1(c, d))
28.56/9.98	   A^2 -> H(c, U1(d, c))
28.56/9.98	   A^2 -> H(c, U1(b, e))
28.56/9.98	   A^2 -> H(c, U1(b, k))
28.56/9.98	   A^2 -> H(c, U1(e, c))
28.56/9.98	   A^2 -> H(c, U1(k, c))
28.56/9.98	   A^2 -> H(c, U1(c, e))
28.56/9.98	   A^2 -> H(c, U1(c, k))
28.56/9.98	   A^2 -> H(c, U1(e, e))
28.56/9.98	   A^2 -> H(c, U1(k, k))
28.56/9.98	   A^2 -> H(c, U1(k, d))
28.56/9.98	   A^2 -> H(c, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.98	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, c), b)
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, c), e)
28.56/9.98	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.98	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.98	   A^2 -> H(U1(k, c), b)
28.56/9.98	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, c), c)
28.56/9.98	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, e), b)
28.56/9.98	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, e), c)
28.56/9.98	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, e), e)
28.56/9.98	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, k), b)
28.56/9.98	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, k), c)
28.56/9.98	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, k), e)
28.56/9.98	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, c), d)
28.56/9.98	   A^2 -> H(e, U1(e, b))
28.56/9.98	   A^2 -> H(e, U1(c, d))
28.56/9.98	   A^2 -> H(e, U1(d, c))
28.56/9.98	   A^2 -> H(e, U1(b, e))
28.56/9.98	   A^2 -> H(e, U1(b, k))
28.56/9.98	   A^2 -> H(e, U1(e, c))
28.56/9.98	   A^2 -> H(e, U1(c, e))
28.56/9.98	   A^2 -> H(e, U1(c, k))
28.56/9.98	   A^2 -> H(e, U1(e, e))
28.56/9.98	   A^2 -> H(e, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, e), b)
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, e), c)
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.98	   A^2 -> H(f(e), d)
28.56/9.98	   A^2 -> H(f(e), k)
28.56/9.98	   A^2 -> H(U1(k, k), b)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, k), c)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.98	   A^2 -> H(f(k), d)
28.56/9.98	   A^2 -> H(f(k), k)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.98	
28.56/9.98	The TRS R consists of the following rules:
28.56/9.98	
28.56/9.98	   f(x) -> U1(x, x)
28.56/9.98	   U1(e, x) -> x
28.56/9.98	   a -> c
28.56/9.98	   a -> d
28.56/9.98	   b -> c
28.56/9.98	   b -> d
28.56/9.98	   d -> k
28.56/9.98	   c -> e
28.56/9.98	   c -> k
28.56/9.98	
28.56/9.98	Q is empty.
28.56/9.98	We have to consider all minimal (P,Q,R)-chains.
28.56/9.98	----------------------------------------
28.56/9.98	
28.56/9.98	(1697) TransformationProof (EQUIVALENT)
28.56/9.98	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.98	
28.56/9.98	   (A^2 -> H(U1(k, k), U1(e, c)),A^2 -> H(U1(k, k), U1(e, c)))
28.56/9.98	   (A^2 -> H(U1(k, k), U1(k, c)),A^2 -> H(U1(k, k), U1(k, c)))
28.56/9.98	   (A^2 -> H(U1(k, k), U1(c, e)),A^2 -> H(U1(k, k), U1(c, e)))
28.56/9.98	   (A^2 -> H(U1(k, k), U1(c, k)),A^2 -> H(U1(k, k), U1(c, k)))
28.56/9.98	
28.56/9.98	
28.56/9.98	----------------------------------------
28.56/9.98	
28.56/9.98	(1698)
28.56/9.98	Obligation:
28.56/9.98	Q DP problem:
28.56/9.98	The TRS P consists of the following rules:
28.56/9.98	
28.56/9.98	   G(d, x, x) -> A^2
28.56/9.98	   A^2 -> H(f(c), f(c))
28.56/9.98	   H(x, x) -> G(x, x, f(k))
28.56/9.98	   A^2 -> H(f(d), f(d))
28.56/9.98	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.98	   A^2 -> H(f(e), f(e))
28.56/9.98	   A^2 -> H(f(k), f(k))
28.56/9.98	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.98	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.98	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, k), f(e))
28.56/9.98	   A^2 -> H(U1(k, k), f(k))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.98	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.98	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.98	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, d), b)
28.56/9.98	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.98	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.98	   A^2 -> H(U1(d, d), c)
28.56/9.98	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.98	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.98	   A^2 -> H(U1(d, d), e)
28.56/9.98	   A^2 -> H(f(d), d)
28.56/9.98	   A^2 -> H(f(d), k)
28.56/9.98	   A^2 -> H(U1(c, c), c)
28.56/9.98	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.98	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.98	   A^2 -> H(f(c), k)
28.56/9.98	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.98	   A^2 -> H(f(k), U1(k, k))
28.56/9.98	   A^2 -> H(f(e), e)
28.56/9.98	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.98	   A^2 -> H(d, U1(c, b))
28.56/9.98	   A^2 -> H(d, U1(d, b))
28.56/9.98	   A^2 -> H(d, U1(b, c))
28.56/9.98	   A^2 -> H(d, U1(b, d))
28.56/9.98	   A^2 -> H(d, U1(c, c))
28.56/9.98	   A^2 -> H(d, f(e))
28.56/9.98	   A^2 -> H(d, f(k))
28.56/9.98	   A^2 -> H(d, U1(d, d))
28.56/9.98	   A^2 -> H(a, U1(e, b))
28.56/9.98	   A^2 -> H(a, U1(k, b))
28.56/9.98	   A^2 -> H(a, U1(c, d))
28.56/9.98	   A^2 -> H(a, U1(d, c))
28.56/9.98	   A^2 -> H(a, U1(b, e))
28.56/9.98	   A^2 -> H(a, U1(b, k))
28.56/9.98	   A^2 -> H(a, U1(e, c))
28.56/9.98	   A^2 -> H(a, U1(k, c))
28.56/9.98	   A^2 -> H(a, U1(c, e))
28.56/9.98	   A^2 -> H(a, U1(c, k))
28.56/9.98	   A^2 -> H(a, U1(e, e))
28.56/9.98	   A^2 -> H(a, U1(k, k))
28.56/9.98	   A^2 -> H(a, U1(k, d))
28.56/9.98	   A^2 -> H(a, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.98	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.98	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.98	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.98	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.98	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.98	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, a), b)
28.56/9.98	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, a), c)
28.56/9.98	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, a), e)
28.56/9.98	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, a), b)
28.56/9.98	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, a), c)
28.56/9.98	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.98	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.98	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, d), b)
28.56/9.98	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, d), c)
28.56/9.98	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, d), e)
28.56/9.98	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, a), d)
28.56/9.98	   A^2 -> H(U1(c, a), k)
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.98	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, c), b)
28.56/9.98	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(d, c), c)
28.56/9.98	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(d, c), e)
28.56/9.98	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, a), d)
28.56/9.98	   A^2 -> H(U1(d, a), k)
28.56/9.98	   A^2 -> H(U1(a, e), b)
28.56/9.98	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(a, e), c)
28.56/9.98	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(a, e), e)
28.56/9.98	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(a, k), b)
28.56/9.98	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(a, k), c)
28.56/9.98	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.98	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.98	   A^2 -> H(U1(a, k), e)
28.56/9.98	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(a, c), d)
28.56/9.98	   A^2 -> H(U1(a, c), k)
28.56/9.98	   A^2 -> H(U1(a, d), d)
28.56/9.98	   A^2 -> H(U1(a, d), k)
28.56/9.98	   A^2 -> H(k, U1(c, b))
28.56/9.98	   A^2 -> H(k, U1(d, b))
28.56/9.98	   A^2 -> H(k, U1(b, c))
28.56/9.98	   A^2 -> H(k, U1(b, d))
28.56/9.98	   A^2 -> H(k, U1(c, c))
28.56/9.98	   A^2 -> H(k, f(e))
28.56/9.98	   A^2 -> H(k, f(k))
28.56/9.98	   A^2 -> H(k, U1(d, d))
28.56/9.98	   A^2 -> H(c, U1(e, b))
28.56/9.98	   A^2 -> H(c, U1(k, b))
28.56/9.98	   A^2 -> H(c, U1(c, d))
28.56/9.98	   A^2 -> H(c, U1(d, c))
28.56/9.98	   A^2 -> H(c, U1(b, e))
28.56/9.98	   A^2 -> H(c, U1(b, k))
28.56/9.98	   A^2 -> H(c, U1(e, c))
28.56/9.98	   A^2 -> H(c, U1(k, c))
28.56/9.98	   A^2 -> H(c, U1(c, e))
28.56/9.98	   A^2 -> H(c, U1(c, k))
28.56/9.98	   A^2 -> H(c, U1(e, e))
28.56/9.98	   A^2 -> H(c, U1(k, k))
28.56/9.98	   A^2 -> H(c, U1(k, d))
28.56/9.98	   A^2 -> H(c, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.98	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, c), b)
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, c), e)
28.56/9.98	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.98	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.98	   A^2 -> H(U1(k, c), b)
28.56/9.98	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, c), c)
28.56/9.98	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, e), b)
28.56/9.98	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, e), c)
28.56/9.98	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, e), e)
28.56/9.98	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, k), b)
28.56/9.98	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, k), c)
28.56/9.98	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, k), e)
28.56/9.98	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, c), d)
28.56/9.98	   A^2 -> H(e, U1(e, b))
28.56/9.98	   A^2 -> H(e, U1(c, d))
28.56/9.98	   A^2 -> H(e, U1(d, c))
28.56/9.98	   A^2 -> H(e, U1(b, e))
28.56/9.98	   A^2 -> H(e, U1(b, k))
28.56/9.98	   A^2 -> H(e, U1(e, c))
28.56/9.98	   A^2 -> H(e, U1(c, e))
28.56/9.98	   A^2 -> H(e, U1(c, k))
28.56/9.98	   A^2 -> H(e, U1(e, e))
28.56/9.98	   A^2 -> H(e, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, e), b)
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, e), c)
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.98	   A^2 -> H(f(e), d)
28.56/9.98	   A^2 -> H(f(e), k)
28.56/9.98	   A^2 -> H(U1(k, k), b)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, k), c)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.98	   A^2 -> H(f(k), d)
28.56/9.98	   A^2 -> H(f(k), k)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.98	
28.56/9.98	The TRS R consists of the following rules:
28.56/9.98	
28.56/9.98	   f(x) -> U1(x, x)
28.56/9.98	   U1(e, x) -> x
28.56/9.98	   a -> c
28.56/9.98	   a -> d
28.56/9.98	   b -> c
28.56/9.98	   b -> d
28.56/9.98	   d -> k
28.56/9.98	   c -> e
28.56/9.98	   c -> k
28.56/9.98	
28.56/9.98	Q is empty.
28.56/9.98	We have to consider all minimal (P,Q,R)-chains.
28.56/9.98	----------------------------------------
28.56/9.98	
28.56/9.98	(1699) TransformationProof (EQUIVALENT)
28.56/9.98	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), f(e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.98	
28.56/9.98	   (A^2 -> H(U1(k, k), U1(e, e)),A^2 -> H(U1(k, k), U1(e, e)))
28.56/9.98	
28.56/9.98	
28.56/9.98	----------------------------------------
28.56/9.98	
28.56/9.98	(1700)
28.56/9.98	Obligation:
28.56/9.98	Q DP problem:
28.56/9.98	The TRS P consists of the following rules:
28.56/9.98	
28.56/9.98	   G(d, x, x) -> A^2
28.56/9.98	   A^2 -> H(f(c), f(c))
28.56/9.98	   H(x, x) -> G(x, x, f(k))
28.56/9.98	   A^2 -> H(f(d), f(d))
28.56/9.98	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.98	   A^2 -> H(f(e), f(e))
28.56/9.98	   A^2 -> H(f(k), f(k))
28.56/9.98	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.98	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.98	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, k), f(k))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.98	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.98	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.98	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, d), b)
28.56/9.98	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.98	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.98	   A^2 -> H(U1(d, d), c)
28.56/9.98	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.98	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.98	   A^2 -> H(U1(d, d), e)
28.56/9.98	   A^2 -> H(f(d), d)
28.56/9.98	   A^2 -> H(f(d), k)
28.56/9.98	   A^2 -> H(U1(c, c), c)
28.56/9.98	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.98	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.98	   A^2 -> H(f(c), k)
28.56/9.98	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.98	   A^2 -> H(f(k), U1(k, k))
28.56/9.98	   A^2 -> H(f(e), e)
28.56/9.98	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.98	   A^2 -> H(d, U1(c, b))
28.56/9.98	   A^2 -> H(d, U1(d, b))
28.56/9.98	   A^2 -> H(d, U1(b, c))
28.56/9.98	   A^2 -> H(d, U1(b, d))
28.56/9.98	   A^2 -> H(d, U1(c, c))
28.56/9.98	   A^2 -> H(d, f(e))
28.56/9.98	   A^2 -> H(d, f(k))
28.56/9.98	   A^2 -> H(d, U1(d, d))
28.56/9.98	   A^2 -> H(a, U1(e, b))
28.56/9.98	   A^2 -> H(a, U1(k, b))
28.56/9.98	   A^2 -> H(a, U1(c, d))
28.56/9.98	   A^2 -> H(a, U1(d, c))
28.56/9.98	   A^2 -> H(a, U1(b, e))
28.56/9.98	   A^2 -> H(a, U1(b, k))
28.56/9.98	   A^2 -> H(a, U1(e, c))
28.56/9.98	   A^2 -> H(a, U1(k, c))
28.56/9.98	   A^2 -> H(a, U1(c, e))
28.56/9.98	   A^2 -> H(a, U1(c, k))
28.56/9.98	   A^2 -> H(a, U1(e, e))
28.56/9.98	   A^2 -> H(a, U1(k, k))
28.56/9.98	   A^2 -> H(a, U1(k, d))
28.56/9.98	   A^2 -> H(a, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.98	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.98	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.98	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.98	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.98	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.98	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, a), b)
28.56/9.98	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, a), c)
28.56/9.98	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, a), e)
28.56/9.98	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, a), b)
28.56/9.98	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, a), c)
28.56/9.98	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.98	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.98	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, d), b)
28.56/9.98	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, d), c)
28.56/9.98	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, d), e)
28.56/9.98	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, a), d)
28.56/9.98	   A^2 -> H(U1(c, a), k)
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.98	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, c), b)
28.56/9.98	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(d, c), c)
28.56/9.98	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(d, c), e)
28.56/9.98	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, a), d)
28.56/9.98	   A^2 -> H(U1(d, a), k)
28.56/9.98	   A^2 -> H(U1(a, e), b)
28.56/9.98	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(a, e), c)
28.56/9.98	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(a, e), e)
28.56/9.98	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(a, k), b)
28.56/9.98	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(a, k), c)
28.56/9.98	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.98	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.98	   A^2 -> H(U1(a, k), e)
28.56/9.98	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(a, c), d)
28.56/9.98	   A^2 -> H(U1(a, c), k)
28.56/9.98	   A^2 -> H(U1(a, d), d)
28.56/9.98	   A^2 -> H(U1(a, d), k)
28.56/9.98	   A^2 -> H(k, U1(c, b))
28.56/9.98	   A^2 -> H(k, U1(d, b))
28.56/9.98	   A^2 -> H(k, U1(b, c))
28.56/9.98	   A^2 -> H(k, U1(b, d))
28.56/9.98	   A^2 -> H(k, U1(c, c))
28.56/9.98	   A^2 -> H(k, f(e))
28.56/9.98	   A^2 -> H(k, f(k))
28.56/9.98	   A^2 -> H(k, U1(d, d))
28.56/9.98	   A^2 -> H(c, U1(e, b))
28.56/9.98	   A^2 -> H(c, U1(k, b))
28.56/9.98	   A^2 -> H(c, U1(c, d))
28.56/9.98	   A^2 -> H(c, U1(d, c))
28.56/9.98	   A^2 -> H(c, U1(b, e))
28.56/9.98	   A^2 -> H(c, U1(b, k))
28.56/9.98	   A^2 -> H(c, U1(e, c))
28.56/9.98	   A^2 -> H(c, U1(k, c))
28.56/9.98	   A^2 -> H(c, U1(c, e))
28.56/9.98	   A^2 -> H(c, U1(c, k))
28.56/9.98	   A^2 -> H(c, U1(e, e))
28.56/9.98	   A^2 -> H(c, U1(k, k))
28.56/9.98	   A^2 -> H(c, U1(k, d))
28.56/9.98	   A^2 -> H(c, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.98	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, c), b)
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, c), e)
28.56/9.98	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.98	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.98	   A^2 -> H(U1(k, c), b)
28.56/9.98	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, c), c)
28.56/9.98	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, e), b)
28.56/9.98	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, e), c)
28.56/9.98	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, e), e)
28.56/9.98	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, k), b)
28.56/9.98	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, k), c)
28.56/9.98	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, k), e)
28.56/9.98	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, c), d)
28.56/9.98	   A^2 -> H(e, U1(e, b))
28.56/9.98	   A^2 -> H(e, U1(c, d))
28.56/9.98	   A^2 -> H(e, U1(d, c))
28.56/9.98	   A^2 -> H(e, U1(b, e))
28.56/9.98	   A^2 -> H(e, U1(b, k))
28.56/9.98	   A^2 -> H(e, U1(e, c))
28.56/9.98	   A^2 -> H(e, U1(c, e))
28.56/9.98	   A^2 -> H(e, U1(c, k))
28.56/9.98	   A^2 -> H(e, U1(e, e))
28.56/9.98	   A^2 -> H(e, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, e), b)
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, e), c)
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.98	   A^2 -> H(f(e), d)
28.56/9.98	   A^2 -> H(f(e), k)
28.56/9.98	   A^2 -> H(U1(k, k), b)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, k), c)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.98	   A^2 -> H(f(k), d)
28.56/9.98	   A^2 -> H(f(k), k)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.98	
28.56/9.98	The TRS R consists of the following rules:
28.56/9.98	
28.56/9.98	   f(x) -> U1(x, x)
28.56/9.98	   U1(e, x) -> x
28.56/9.98	   a -> c
28.56/9.98	   a -> d
28.56/9.98	   b -> c
28.56/9.98	   b -> d
28.56/9.98	   d -> k
28.56/9.98	   c -> e
28.56/9.98	   c -> k
28.56/9.98	
28.56/9.98	Q is empty.
28.56/9.98	We have to consider all minimal (P,Q,R)-chains.
28.56/9.98	----------------------------------------
28.56/9.98	
28.56/9.98	(1701) TransformationProof (EQUIVALENT)
28.56/9.98	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), f(k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.98	
28.56/9.98	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.56/9.98	
28.56/9.98	
28.56/9.98	----------------------------------------
28.56/9.98	
28.56/9.98	(1702)
28.56/9.98	Obligation:
28.56/9.98	Q DP problem:
28.56/9.98	The TRS P consists of the following rules:
28.56/9.98	
28.56/9.98	   G(d, x, x) -> A^2
28.56/9.98	   A^2 -> H(f(c), f(c))
28.56/9.98	   H(x, x) -> G(x, x, f(k))
28.56/9.98	   A^2 -> H(f(d), f(d))
28.56/9.98	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.98	   A^2 -> H(f(e), f(e))
28.56/9.98	   A^2 -> H(f(k), f(k))
28.56/9.98	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.98	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.98	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, d))
28.56/9.98	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.98	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.98	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, d), b)
28.56/9.98	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.98	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.98	   A^2 -> H(U1(d, d), c)
28.56/9.98	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.98	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.98	   A^2 -> H(U1(d, d), e)
28.56/9.98	   A^2 -> H(f(d), d)
28.56/9.98	   A^2 -> H(f(d), k)
28.56/9.98	   A^2 -> H(U1(c, c), c)
28.56/9.98	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.98	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.98	   A^2 -> H(f(c), k)
28.56/9.98	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.98	   A^2 -> H(f(k), U1(k, k))
28.56/9.98	   A^2 -> H(f(e), e)
28.56/9.98	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.98	   A^2 -> H(d, U1(c, b))
28.56/9.98	   A^2 -> H(d, U1(d, b))
28.56/9.98	   A^2 -> H(d, U1(b, c))
28.56/9.98	   A^2 -> H(d, U1(b, d))
28.56/9.98	   A^2 -> H(d, U1(c, c))
28.56/9.98	   A^2 -> H(d, f(e))
28.56/9.98	   A^2 -> H(d, f(k))
28.56/9.98	   A^2 -> H(d, U1(d, d))
28.56/9.98	   A^2 -> H(a, U1(e, b))
28.56/9.98	   A^2 -> H(a, U1(k, b))
28.56/9.98	   A^2 -> H(a, U1(c, d))
28.56/9.98	   A^2 -> H(a, U1(d, c))
28.56/9.98	   A^2 -> H(a, U1(b, e))
28.56/9.98	   A^2 -> H(a, U1(b, k))
28.56/9.98	   A^2 -> H(a, U1(e, c))
28.56/9.98	   A^2 -> H(a, U1(k, c))
28.56/9.98	   A^2 -> H(a, U1(c, e))
28.56/9.98	   A^2 -> H(a, U1(c, k))
28.56/9.98	   A^2 -> H(a, U1(e, e))
28.56/9.98	   A^2 -> H(a, U1(k, k))
28.56/9.98	   A^2 -> H(a, U1(k, d))
28.56/9.98	   A^2 -> H(a, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.98	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.98	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.98	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.98	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.98	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.98	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, a), b)
28.56/9.98	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, a), c)
28.56/9.98	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, a), e)
28.56/9.98	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, a), b)
28.56/9.98	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, a), c)
28.56/9.98	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.98	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.98	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, d), b)
28.56/9.98	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, d), c)
28.56/9.98	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, d), e)
28.56/9.98	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, a), d)
28.56/9.98	   A^2 -> H(U1(c, a), k)
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.98	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, c), b)
28.56/9.98	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(d, c), c)
28.56/9.98	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(d, c), e)
28.56/9.98	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, a), d)
28.56/9.98	   A^2 -> H(U1(d, a), k)
28.56/9.98	   A^2 -> H(U1(a, e), b)
28.56/9.98	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(a, e), c)
28.56/9.98	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(a, e), e)
28.56/9.98	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(a, k), b)
28.56/9.98	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(a, k), c)
28.56/9.98	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.98	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.98	   A^2 -> H(U1(a, k), e)
28.56/9.98	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(a, c), d)
28.56/9.98	   A^2 -> H(U1(a, c), k)
28.56/9.98	   A^2 -> H(U1(a, d), d)
28.56/9.98	   A^2 -> H(U1(a, d), k)
28.56/9.98	   A^2 -> H(k, U1(c, b))
28.56/9.98	   A^2 -> H(k, U1(d, b))
28.56/9.98	   A^2 -> H(k, U1(b, c))
28.56/9.98	   A^2 -> H(k, U1(b, d))
28.56/9.98	   A^2 -> H(k, U1(c, c))
28.56/9.98	   A^2 -> H(k, f(e))
28.56/9.98	   A^2 -> H(k, f(k))
28.56/9.98	   A^2 -> H(k, U1(d, d))
28.56/9.98	   A^2 -> H(c, U1(e, b))
28.56/9.98	   A^2 -> H(c, U1(k, b))
28.56/9.98	   A^2 -> H(c, U1(c, d))
28.56/9.98	   A^2 -> H(c, U1(d, c))
28.56/9.98	   A^2 -> H(c, U1(b, e))
28.56/9.98	   A^2 -> H(c, U1(b, k))
28.56/9.98	   A^2 -> H(c, U1(e, c))
28.56/9.98	   A^2 -> H(c, U1(k, c))
28.56/9.98	   A^2 -> H(c, U1(c, e))
28.56/9.98	   A^2 -> H(c, U1(c, k))
28.56/9.98	   A^2 -> H(c, U1(e, e))
28.56/9.98	   A^2 -> H(c, U1(k, k))
28.56/9.98	   A^2 -> H(c, U1(k, d))
28.56/9.98	   A^2 -> H(c, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.98	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, c), b)
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, c), e)
28.56/9.98	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.98	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.98	   A^2 -> H(U1(k, c), b)
28.56/9.98	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, c), c)
28.56/9.98	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, e), b)
28.56/9.98	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, e), c)
28.56/9.98	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, e), e)
28.56/9.98	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, k), b)
28.56/9.98	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, k), c)
28.56/9.98	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, k), e)
28.56/9.98	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, c), d)
28.56/9.98	   A^2 -> H(e, U1(e, b))
28.56/9.98	   A^2 -> H(e, U1(c, d))
28.56/9.98	   A^2 -> H(e, U1(d, c))
28.56/9.98	   A^2 -> H(e, U1(b, e))
28.56/9.98	   A^2 -> H(e, U1(b, k))
28.56/9.98	   A^2 -> H(e, U1(e, c))
28.56/9.98	   A^2 -> H(e, U1(c, e))
28.56/9.98	   A^2 -> H(e, U1(c, k))
28.56/9.98	   A^2 -> H(e, U1(e, e))
28.56/9.98	   A^2 -> H(e, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, e), b)
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, e), c)
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.98	   A^2 -> H(f(e), d)
28.56/9.98	   A^2 -> H(f(e), k)
28.56/9.98	   A^2 -> H(U1(k, k), b)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, k), c)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.98	   A^2 -> H(f(k), d)
28.56/9.98	   A^2 -> H(f(k), k)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.98	
28.56/9.98	The TRS R consists of the following rules:
28.56/9.98	
28.56/9.98	   f(x) -> U1(x, x)
28.56/9.98	   U1(e, x) -> x
28.56/9.98	   a -> c
28.56/9.98	   a -> d
28.56/9.98	   b -> c
28.56/9.98	   b -> d
28.56/9.98	   d -> k
28.56/9.98	   c -> e
28.56/9.98	   c -> k
28.56/9.98	
28.56/9.98	Q is empty.
28.56/9.98	We have to consider all minimal (P,Q,R)-chains.
28.56/9.98	----------------------------------------
28.56/9.98	
28.56/9.98	(1703) TransformationProof (EQUIVALENT)
28.56/9.98	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.98	
28.56/9.98	   (A^2 -> H(U1(k, k), U1(k, d)),A^2 -> H(U1(k, k), U1(k, d)))
28.56/9.98	   (A^2 -> H(U1(k, k), U1(d, k)),A^2 -> H(U1(k, k), U1(d, k)))
28.56/9.98	
28.56/9.98	
28.56/9.98	----------------------------------------
28.56/9.98	
28.56/9.98	(1704)
28.56/9.98	Obligation:
28.56/9.98	Q DP problem:
28.56/9.98	The TRS P consists of the following rules:
28.56/9.98	
28.56/9.98	   G(d, x, x) -> A^2
28.56/9.98	   A^2 -> H(f(c), f(c))
28.56/9.98	   H(x, x) -> G(x, x, f(k))
28.56/9.98	   A^2 -> H(f(d), f(d))
28.56/9.98	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.98	   A^2 -> H(f(e), f(e))
28.56/9.98	   A^2 -> H(f(k), f(k))
28.56/9.98	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.98	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.98	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(e, b))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.98	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.98	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, d), b)
28.56/9.98	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.98	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.98	   A^2 -> H(U1(d, d), c)
28.56/9.98	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.98	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.98	   A^2 -> H(U1(d, d), e)
28.56/9.98	   A^2 -> H(f(d), d)
28.56/9.98	   A^2 -> H(f(d), k)
28.56/9.98	   A^2 -> H(U1(c, c), c)
28.56/9.98	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.98	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.98	   A^2 -> H(f(c), k)
28.56/9.98	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.98	   A^2 -> H(f(k), U1(k, k))
28.56/9.98	   A^2 -> H(f(e), e)
28.56/9.98	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.98	   A^2 -> H(d, U1(c, b))
28.56/9.98	   A^2 -> H(d, U1(d, b))
28.56/9.98	   A^2 -> H(d, U1(b, c))
28.56/9.98	   A^2 -> H(d, U1(b, d))
28.56/9.98	   A^2 -> H(d, U1(c, c))
28.56/9.98	   A^2 -> H(d, f(e))
28.56/9.98	   A^2 -> H(d, f(k))
28.56/9.98	   A^2 -> H(d, U1(d, d))
28.56/9.98	   A^2 -> H(a, U1(e, b))
28.56/9.98	   A^2 -> H(a, U1(k, b))
28.56/9.98	   A^2 -> H(a, U1(c, d))
28.56/9.98	   A^2 -> H(a, U1(d, c))
28.56/9.98	   A^2 -> H(a, U1(b, e))
28.56/9.98	   A^2 -> H(a, U1(b, k))
28.56/9.98	   A^2 -> H(a, U1(e, c))
28.56/9.98	   A^2 -> H(a, U1(k, c))
28.56/9.98	   A^2 -> H(a, U1(c, e))
28.56/9.98	   A^2 -> H(a, U1(c, k))
28.56/9.98	   A^2 -> H(a, U1(e, e))
28.56/9.98	   A^2 -> H(a, U1(k, k))
28.56/9.98	   A^2 -> H(a, U1(k, d))
28.56/9.98	   A^2 -> H(a, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.98	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.98	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.98	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.98	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.98	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.98	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, a), b)
28.56/9.98	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, a), c)
28.56/9.98	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, a), e)
28.56/9.98	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, a), b)
28.56/9.98	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, a), c)
28.56/9.98	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.98	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.98	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, d), b)
28.56/9.98	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, d), c)
28.56/9.98	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, d), e)
28.56/9.98	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, a), d)
28.56/9.98	   A^2 -> H(U1(c, a), k)
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.98	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, c), b)
28.56/9.98	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(d, c), c)
28.56/9.98	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(d, c), e)
28.56/9.98	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, a), d)
28.56/9.98	   A^2 -> H(U1(d, a), k)
28.56/9.98	   A^2 -> H(U1(a, e), b)
28.56/9.98	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(a, e), c)
28.56/9.98	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(a, e), e)
28.56/9.98	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(a, k), b)
28.56/9.98	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(a, k), c)
28.56/9.98	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.98	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.98	   A^2 -> H(U1(a, k), e)
28.56/9.98	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(a, c), d)
28.56/9.98	   A^2 -> H(U1(a, c), k)
28.56/9.98	   A^2 -> H(U1(a, d), d)
28.56/9.98	   A^2 -> H(U1(a, d), k)
28.56/9.98	   A^2 -> H(k, U1(c, b))
28.56/9.98	   A^2 -> H(k, U1(d, b))
28.56/9.98	   A^2 -> H(k, U1(b, c))
28.56/9.98	   A^2 -> H(k, U1(b, d))
28.56/9.98	   A^2 -> H(k, U1(c, c))
28.56/9.98	   A^2 -> H(k, f(e))
28.56/9.98	   A^2 -> H(k, f(k))
28.56/9.98	   A^2 -> H(k, U1(d, d))
28.56/9.98	   A^2 -> H(c, U1(e, b))
28.56/9.98	   A^2 -> H(c, U1(k, b))
28.56/9.98	   A^2 -> H(c, U1(c, d))
28.56/9.98	   A^2 -> H(c, U1(d, c))
28.56/9.98	   A^2 -> H(c, U1(b, e))
28.56/9.98	   A^2 -> H(c, U1(b, k))
28.56/9.98	   A^2 -> H(c, U1(e, c))
28.56/9.98	   A^2 -> H(c, U1(k, c))
28.56/9.98	   A^2 -> H(c, U1(c, e))
28.56/9.98	   A^2 -> H(c, U1(c, k))
28.56/9.98	   A^2 -> H(c, U1(e, e))
28.56/9.98	   A^2 -> H(c, U1(k, k))
28.56/9.98	   A^2 -> H(c, U1(k, d))
28.56/9.98	   A^2 -> H(c, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.98	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, c), b)
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, c), e)
28.56/9.98	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.98	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.98	   A^2 -> H(U1(k, c), b)
28.56/9.98	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, c), c)
28.56/9.98	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, e), b)
28.56/9.98	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, e), c)
28.56/9.98	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, e), e)
28.56/9.98	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, k), b)
28.56/9.98	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, k), c)
28.56/9.98	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, k), e)
28.56/9.98	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, c), d)
28.56/9.98	   A^2 -> H(e, U1(e, b))
28.56/9.98	   A^2 -> H(e, U1(c, d))
28.56/9.98	   A^2 -> H(e, U1(d, c))
28.56/9.98	   A^2 -> H(e, U1(b, e))
28.56/9.98	   A^2 -> H(e, U1(b, k))
28.56/9.98	   A^2 -> H(e, U1(e, c))
28.56/9.98	   A^2 -> H(e, U1(c, e))
28.56/9.98	   A^2 -> H(e, U1(c, k))
28.56/9.98	   A^2 -> H(e, U1(e, e))
28.56/9.98	   A^2 -> H(e, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, e), b)
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, e), c)
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.98	   A^2 -> H(f(e), d)
28.56/9.98	   A^2 -> H(f(e), k)
28.56/9.98	   A^2 -> H(U1(k, k), b)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, k), c)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.98	   A^2 -> H(f(k), d)
28.56/9.98	   A^2 -> H(f(k), k)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.98	
28.56/9.98	The TRS R consists of the following rules:
28.56/9.98	
28.56/9.98	   f(x) -> U1(x, x)
28.56/9.98	   U1(e, x) -> x
28.56/9.98	   a -> c
28.56/9.98	   a -> d
28.56/9.98	   b -> c
28.56/9.98	   b -> d
28.56/9.98	   d -> k
28.56/9.98	   c -> e
28.56/9.98	   c -> k
28.56/9.98	
28.56/9.98	Q is empty.
28.56/9.98	We have to consider all minimal (P,Q,R)-chains.
28.56/9.98	----------------------------------------
28.56/9.98	
28.56/9.98	(1705) TransformationProof (EQUIVALENT)
28.56/9.98	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.98	
28.56/9.98	   (A^2 -> H(U1(k, k), U1(e, b)),A^2 -> H(U1(k, k), U1(e, b)))
28.56/9.98	   (A^2 -> H(U1(k, d), b),A^2 -> H(U1(k, d), b))
28.56/9.98	   (A^2 -> H(U1(k, d), U1(e, c)),A^2 -> H(U1(k, d), U1(e, c)))
28.56/9.98	   (A^2 -> H(U1(k, d), U1(e, d)),A^2 -> H(U1(k, d), U1(e, d)))
28.56/9.98	
28.56/9.98	
28.56/9.98	----------------------------------------
28.56/9.98	
28.56/9.98	(1706)
28.56/9.98	Obligation:
28.56/9.98	Q DP problem:
28.56/9.98	The TRS P consists of the following rules:
28.56/9.98	
28.56/9.98	   G(d, x, x) -> A^2
28.56/9.98	   A^2 -> H(f(c), f(c))
28.56/9.98	   H(x, x) -> G(x, x, f(k))
28.56/9.98	   A^2 -> H(f(d), f(d))
28.56/9.98	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.98	   A^2 -> H(f(e), f(e))
28.56/9.98	   A^2 -> H(f(k), f(k))
28.56/9.98	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.98	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.98	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.98	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.98	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, d), b)
28.56/9.98	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.98	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.98	   A^2 -> H(U1(d, d), c)
28.56/9.98	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.98	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.98	   A^2 -> H(U1(d, d), e)
28.56/9.98	   A^2 -> H(f(d), d)
28.56/9.98	   A^2 -> H(f(d), k)
28.56/9.98	   A^2 -> H(U1(c, c), c)
28.56/9.98	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.98	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.98	   A^2 -> H(f(c), k)
28.56/9.98	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.98	   A^2 -> H(f(k), U1(k, k))
28.56/9.98	   A^2 -> H(f(e), e)
28.56/9.98	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.98	   A^2 -> H(d, U1(c, b))
28.56/9.98	   A^2 -> H(d, U1(d, b))
28.56/9.98	   A^2 -> H(d, U1(b, c))
28.56/9.98	   A^2 -> H(d, U1(b, d))
28.56/9.98	   A^2 -> H(d, U1(c, c))
28.56/9.98	   A^2 -> H(d, f(e))
28.56/9.98	   A^2 -> H(d, f(k))
28.56/9.98	   A^2 -> H(d, U1(d, d))
28.56/9.98	   A^2 -> H(a, U1(e, b))
28.56/9.98	   A^2 -> H(a, U1(k, b))
28.56/9.98	   A^2 -> H(a, U1(c, d))
28.56/9.98	   A^2 -> H(a, U1(d, c))
28.56/9.98	   A^2 -> H(a, U1(b, e))
28.56/9.98	   A^2 -> H(a, U1(b, k))
28.56/9.98	   A^2 -> H(a, U1(e, c))
28.56/9.98	   A^2 -> H(a, U1(k, c))
28.56/9.98	   A^2 -> H(a, U1(c, e))
28.56/9.98	   A^2 -> H(a, U1(c, k))
28.56/9.98	   A^2 -> H(a, U1(e, e))
28.56/9.98	   A^2 -> H(a, U1(k, k))
28.56/9.98	   A^2 -> H(a, U1(k, d))
28.56/9.98	   A^2 -> H(a, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.98	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.98	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.98	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.98	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.98	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.98	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, a), b)
28.56/9.98	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, a), c)
28.56/9.98	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, a), e)
28.56/9.98	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, a), b)
28.56/9.98	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, a), c)
28.56/9.98	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.98	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.98	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, d), b)
28.56/9.98	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, d), c)
28.56/9.98	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, d), e)
28.56/9.98	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, a), d)
28.56/9.98	   A^2 -> H(U1(c, a), k)
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.98	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, c), b)
28.56/9.98	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(d, c), c)
28.56/9.98	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(d, c), e)
28.56/9.98	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, a), d)
28.56/9.98	   A^2 -> H(U1(d, a), k)
28.56/9.98	   A^2 -> H(U1(a, e), b)
28.56/9.98	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(a, e), c)
28.56/9.98	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(a, e), e)
28.56/9.98	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(a, k), b)
28.56/9.98	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(a, k), c)
28.56/9.98	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.98	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.98	   A^2 -> H(U1(a, k), e)
28.56/9.98	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(a, c), d)
28.56/9.98	   A^2 -> H(U1(a, c), k)
28.56/9.98	   A^2 -> H(U1(a, d), d)
28.56/9.98	   A^2 -> H(U1(a, d), k)
28.56/9.98	   A^2 -> H(k, U1(c, b))
28.56/9.98	   A^2 -> H(k, U1(d, b))
28.56/9.98	   A^2 -> H(k, U1(b, c))
28.56/9.98	   A^2 -> H(k, U1(b, d))
28.56/9.98	   A^2 -> H(k, U1(c, c))
28.56/9.98	   A^2 -> H(k, f(e))
28.56/9.98	   A^2 -> H(k, f(k))
28.56/9.98	   A^2 -> H(k, U1(d, d))
28.56/9.98	   A^2 -> H(c, U1(e, b))
28.56/9.98	   A^2 -> H(c, U1(k, b))
28.56/9.98	   A^2 -> H(c, U1(c, d))
28.56/9.98	   A^2 -> H(c, U1(d, c))
28.56/9.98	   A^2 -> H(c, U1(b, e))
28.56/9.98	   A^2 -> H(c, U1(b, k))
28.56/9.98	   A^2 -> H(c, U1(e, c))
28.56/9.98	   A^2 -> H(c, U1(k, c))
28.56/9.98	   A^2 -> H(c, U1(c, e))
28.56/9.98	   A^2 -> H(c, U1(c, k))
28.56/9.98	   A^2 -> H(c, U1(e, e))
28.56/9.98	   A^2 -> H(c, U1(k, k))
28.56/9.98	   A^2 -> H(c, U1(k, d))
28.56/9.98	   A^2 -> H(c, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.98	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, c), b)
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, c), e)
28.56/9.98	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.98	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.98	   A^2 -> H(U1(k, c), b)
28.56/9.98	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, c), c)
28.56/9.98	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, e), b)
28.56/9.98	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, e), c)
28.56/9.98	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, e), e)
28.56/9.98	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, k), b)
28.56/9.98	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, k), c)
28.56/9.98	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, k), e)
28.56/9.98	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, c), d)
28.56/9.98	   A^2 -> H(e, U1(e, b))
28.56/9.98	   A^2 -> H(e, U1(c, d))
28.56/9.98	   A^2 -> H(e, U1(d, c))
28.56/9.98	   A^2 -> H(e, U1(b, e))
28.56/9.98	   A^2 -> H(e, U1(b, k))
28.56/9.98	   A^2 -> H(e, U1(e, c))
28.56/9.98	   A^2 -> H(e, U1(c, e))
28.56/9.98	   A^2 -> H(e, U1(c, k))
28.56/9.98	   A^2 -> H(e, U1(e, e))
28.56/9.98	   A^2 -> H(e, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, e), b)
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, e), c)
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.98	   A^2 -> H(f(e), d)
28.56/9.98	   A^2 -> H(f(e), k)
28.56/9.98	   A^2 -> H(U1(k, k), b)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, k), c)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.98	   A^2 -> H(f(k), d)
28.56/9.98	   A^2 -> H(f(k), k)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.98	   A^2 -> H(U1(k, d), b)
28.56/9.98	   A^2 -> H(U1(k, d), U1(e, d))
28.56/9.98	
28.56/9.98	The TRS R consists of the following rules:
28.56/9.98	
28.56/9.98	   f(x) -> U1(x, x)
28.56/9.98	   U1(e, x) -> x
28.56/9.98	   a -> c
28.56/9.98	   a -> d
28.56/9.98	   b -> c
28.56/9.98	   b -> d
28.56/9.98	   d -> k
28.56/9.98	   c -> e
28.56/9.98	   c -> k
28.56/9.98	
28.56/9.98	Q is empty.
28.56/9.98	We have to consider all minimal (P,Q,R)-chains.
28.56/9.98	----------------------------------------
28.56/9.98	
28.56/9.98	(1707) TransformationProof (EQUIVALENT)
28.56/9.98	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.98	
28.56/9.98	   (A^2 -> H(U1(k, k), U1(k, b)),A^2 -> H(U1(k, k), U1(k, b)))
28.56/9.98	   (A^2 -> H(U1(k, d), U1(k, c)),A^2 -> H(U1(k, d), U1(k, c)))
28.56/9.98	   (A^2 -> H(U1(k, d), U1(k, d)),A^2 -> H(U1(k, d), U1(k, d)))
28.56/9.98	
28.56/9.98	
28.56/9.98	----------------------------------------
28.56/9.98	
28.56/9.98	(1708)
28.56/9.98	Obligation:
28.56/9.98	Q DP problem:
28.56/9.98	The TRS P consists of the following rules:
28.56/9.98	
28.56/9.98	   G(d, x, x) -> A^2
28.56/9.98	   A^2 -> H(f(c), f(c))
28.56/9.98	   H(x, x) -> G(x, x, f(k))
28.56/9.98	   A^2 -> H(f(d), f(d))
28.56/9.98	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.98	   A^2 -> H(f(e), f(e))
28.56/9.98	   A^2 -> H(f(k), f(k))
28.56/9.98	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.98	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.98	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.98	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.98	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, d), b)
28.56/9.98	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.98	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.98	   A^2 -> H(U1(d, d), c)
28.56/9.98	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.98	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.98	   A^2 -> H(U1(d, d), e)
28.56/9.98	   A^2 -> H(f(d), d)
28.56/9.98	   A^2 -> H(f(d), k)
28.56/9.98	   A^2 -> H(U1(c, c), c)
28.56/9.98	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.98	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.98	   A^2 -> H(f(c), k)
28.56/9.98	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.98	   A^2 -> H(f(k), U1(k, k))
28.56/9.98	   A^2 -> H(f(e), e)
28.56/9.98	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.98	   A^2 -> H(d, U1(c, b))
28.56/9.98	   A^2 -> H(d, U1(d, b))
28.56/9.98	   A^2 -> H(d, U1(b, c))
28.56/9.98	   A^2 -> H(d, U1(b, d))
28.56/9.98	   A^2 -> H(d, U1(c, c))
28.56/9.98	   A^2 -> H(d, f(e))
28.56/9.98	   A^2 -> H(d, f(k))
28.56/9.98	   A^2 -> H(d, U1(d, d))
28.56/9.98	   A^2 -> H(a, U1(e, b))
28.56/9.98	   A^2 -> H(a, U1(k, b))
28.56/9.98	   A^2 -> H(a, U1(c, d))
28.56/9.98	   A^2 -> H(a, U1(d, c))
28.56/9.98	   A^2 -> H(a, U1(b, e))
28.56/9.98	   A^2 -> H(a, U1(b, k))
28.56/9.98	   A^2 -> H(a, U1(e, c))
28.56/9.98	   A^2 -> H(a, U1(k, c))
28.56/9.98	   A^2 -> H(a, U1(c, e))
28.56/9.98	   A^2 -> H(a, U1(c, k))
28.56/9.98	   A^2 -> H(a, U1(e, e))
28.56/9.98	   A^2 -> H(a, U1(k, k))
28.56/9.98	   A^2 -> H(a, U1(k, d))
28.56/9.98	   A^2 -> H(a, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.98	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.98	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.98	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.98	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.98	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.98	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, a), b)
28.56/9.98	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, a), c)
28.56/9.98	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, a), e)
28.56/9.98	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, a), b)
28.56/9.98	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, a), c)
28.56/9.98	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.98	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.98	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, d), b)
28.56/9.98	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, d), c)
28.56/9.98	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, d), e)
28.56/9.98	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, a), d)
28.56/9.98	   A^2 -> H(U1(c, a), k)
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.98	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.98	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.98	   A^2 -> H(U1(d, c), b)
28.56/9.98	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(d, c), c)
28.56/9.98	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(d, c), e)
28.56/9.98	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(d, a), d)
28.56/9.98	   A^2 -> H(U1(d, a), k)
28.56/9.98	   A^2 -> H(U1(a, e), b)
28.56/9.98	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(a, e), c)
28.56/9.98	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(a, e), e)
28.56/9.98	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(a, k), b)
28.56/9.98	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(a, k), c)
28.56/9.98	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.98	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.98	   A^2 -> H(U1(a, k), e)
28.56/9.98	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(a, c), d)
28.56/9.98	   A^2 -> H(U1(a, c), k)
28.56/9.98	   A^2 -> H(U1(a, d), d)
28.56/9.98	   A^2 -> H(U1(a, d), k)
28.56/9.98	   A^2 -> H(k, U1(c, b))
28.56/9.98	   A^2 -> H(k, U1(d, b))
28.56/9.98	   A^2 -> H(k, U1(b, c))
28.56/9.98	   A^2 -> H(k, U1(b, d))
28.56/9.98	   A^2 -> H(k, U1(c, c))
28.56/9.98	   A^2 -> H(k, f(e))
28.56/9.98	   A^2 -> H(k, f(k))
28.56/9.98	   A^2 -> H(k, U1(d, d))
28.56/9.98	   A^2 -> H(c, U1(e, b))
28.56/9.98	   A^2 -> H(c, U1(k, b))
28.56/9.98	   A^2 -> H(c, U1(c, d))
28.56/9.98	   A^2 -> H(c, U1(d, c))
28.56/9.98	   A^2 -> H(c, U1(b, e))
28.56/9.98	   A^2 -> H(c, U1(b, k))
28.56/9.98	   A^2 -> H(c, U1(e, c))
28.56/9.98	   A^2 -> H(c, U1(k, c))
28.56/9.98	   A^2 -> H(c, U1(c, e))
28.56/9.98	   A^2 -> H(c, U1(c, k))
28.56/9.98	   A^2 -> H(c, U1(e, e))
28.56/9.98	   A^2 -> H(c, U1(k, k))
28.56/9.98	   A^2 -> H(c, U1(k, d))
28.56/9.98	   A^2 -> H(c, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.98	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, c), b)
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, c), e)
28.56/9.98	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.98	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.98	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.98	   A^2 -> H(U1(k, c), b)
28.56/9.98	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, c), c)
28.56/9.98	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.98	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, e), b)
28.56/9.98	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, e), c)
28.56/9.98	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, e), e)
28.56/9.98	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, k), b)
28.56/9.98	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(c, k), c)
28.56/9.98	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.98	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.98	   A^2 -> H(U1(c, k), e)
28.56/9.98	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.98	   A^2 -> H(U1(c, c), d)
28.56/9.98	   A^2 -> H(e, U1(e, b))
28.56/9.98	   A^2 -> H(e, U1(c, d))
28.56/9.98	   A^2 -> H(e, U1(d, c))
28.56/9.98	   A^2 -> H(e, U1(b, e))
28.56/9.98	   A^2 -> H(e, U1(b, k))
28.56/9.98	   A^2 -> H(e, U1(e, c))
28.56/9.98	   A^2 -> H(e, U1(c, e))
28.56/9.98	   A^2 -> H(e, U1(c, k))
28.56/9.98	   A^2 -> H(e, U1(e, e))
28.56/9.98	   A^2 -> H(e, U1(d, k))
28.56/9.98	   A^2 -> H(U1(e, e), b)
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.98	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.98	   A^2 -> H(U1(e, e), c)
28.56/9.98	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.98	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.98	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.98	   A^2 -> H(f(e), d)
28.56/9.98	   A^2 -> H(f(e), k)
28.56/9.98	   A^2 -> H(U1(k, k), b)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.98	   A^2 -> H(U1(k, k), c)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.98	   A^2 -> H(f(k), d)
28.56/9.98	   A^2 -> H(f(k), k)
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.98	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.98	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.98	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.98	   A^2 -> H(U1(k, d), b)
28.56/9.98	   A^2 -> H(U1(k, d), U1(e, d))
28.56/9.98	
28.56/9.98	The TRS R consists of the following rules:
28.56/9.98	
28.56/9.98	   f(x) -> U1(x, x)
28.56/9.98	   U1(e, x) -> x
28.56/9.98	   a -> c
28.56/9.98	   a -> d
28.56/9.98	   b -> c
28.56/9.98	   b -> d
28.56/9.98	   d -> k
28.56/9.98	   c -> e
28.56/9.98	   c -> k
28.56/9.98	
28.56/9.98	Q is empty.
28.56/9.98	We have to consider all minimal (P,Q,R)-chains.
28.56/9.98	----------------------------------------
28.56/9.98	
28.56/9.98	(1709) TransformationProof (EQUIVALENT)
28.56/9.98	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.98	
28.56/9.98	   (A^2 -> H(U1(k, k), U1(c, d)),A^2 -> H(U1(k, k), U1(c, d)))
28.56/9.98	   (A^2 -> H(U1(k, d), U1(e, d)),A^2 -> H(U1(k, d), U1(e, d)))
28.56/9.98	   (A^2 -> H(U1(k, d), U1(k, d)),A^2 -> H(U1(k, d), U1(k, d)))
28.56/9.98	   (A^2 -> H(U1(k, d), U1(c, k)),A^2 -> H(U1(k, d), U1(c, k)))
28.56/9.98	
28.56/9.98	
28.56/9.98	----------------------------------------
28.56/9.98	
28.56/9.98	(1710)
28.56/9.98	Obligation:
28.56/9.98	Q DP problem:
28.56/9.98	The TRS P consists of the following rules:
28.56/9.98	
28.56/9.98	   G(d, x, x) -> A^2
28.56/9.98	   A^2 -> H(f(c), f(c))
28.56/9.98	   H(x, x) -> G(x, x, f(k))
28.56/9.99	   A^2 -> H(f(d), f(d))
28.56/9.99	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.99	   A^2 -> H(f(e), f(e))
28.56/9.99	   A^2 -> H(f(k), f(k))
28.56/9.99	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.99	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.99	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(d, c))
28.56/9.99	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.99	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.99	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.99	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, d), b)
28.56/9.99	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.99	   A^2 -> H(U1(d, d), c)
28.56/9.99	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.99	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.99	   A^2 -> H(U1(d, d), e)
28.56/9.99	   A^2 -> H(f(d), d)
28.56/9.99	   A^2 -> H(f(d), k)
28.56/9.99	   A^2 -> H(U1(c, c), c)
28.56/9.99	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.99	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.99	   A^2 -> H(f(c), k)
28.56/9.99	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.99	   A^2 -> H(f(k), U1(k, k))
28.56/9.99	   A^2 -> H(f(e), e)
28.56/9.99	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.99	   A^2 -> H(d, U1(c, b))
28.56/9.99	   A^2 -> H(d, U1(d, b))
28.56/9.99	   A^2 -> H(d, U1(b, c))
28.56/9.99	   A^2 -> H(d, U1(b, d))
28.56/9.99	   A^2 -> H(d, U1(c, c))
28.56/9.99	   A^2 -> H(d, f(e))
28.56/9.99	   A^2 -> H(d, f(k))
28.56/9.99	   A^2 -> H(d, U1(d, d))
28.56/9.99	   A^2 -> H(a, U1(e, b))
28.56/9.99	   A^2 -> H(a, U1(k, b))
28.56/9.99	   A^2 -> H(a, U1(c, d))
28.56/9.99	   A^2 -> H(a, U1(d, c))
28.56/9.99	   A^2 -> H(a, U1(b, e))
28.56/9.99	   A^2 -> H(a, U1(b, k))
28.56/9.99	   A^2 -> H(a, U1(e, c))
28.56/9.99	   A^2 -> H(a, U1(k, c))
28.56/9.99	   A^2 -> H(a, U1(c, e))
28.56/9.99	   A^2 -> H(a, U1(c, k))
28.56/9.99	   A^2 -> H(a, U1(e, e))
28.56/9.99	   A^2 -> H(a, U1(k, k))
28.56/9.99	   A^2 -> H(a, U1(k, d))
28.56/9.99	   A^2 -> H(a, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.99	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.99	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, a), b)
28.56/9.99	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, a), c)
28.56/9.99	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, a), e)
28.56/9.99	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, a), b)
28.56/9.99	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, a), c)
28.56/9.99	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.99	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.99	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, d), b)
28.56/9.99	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, d), c)
28.56/9.99	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, d), e)
28.56/9.99	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, a), d)
28.56/9.99	   A^2 -> H(U1(c, a), k)
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.99	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, c), b)
28.56/9.99	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(d, c), c)
28.56/9.99	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(d, c), e)
28.56/9.99	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, a), d)
28.56/9.99	   A^2 -> H(U1(d, a), k)
28.56/9.99	   A^2 -> H(U1(a, e), b)
28.56/9.99	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(a, e), c)
28.56/9.99	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(a, e), e)
28.56/9.99	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(a, k), b)
28.56/9.99	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(a, k), c)
28.56/9.99	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.99	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.99	   A^2 -> H(U1(a, k), e)
28.56/9.99	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(a, c), d)
28.56/9.99	   A^2 -> H(U1(a, c), k)
28.56/9.99	   A^2 -> H(U1(a, d), d)
28.56/9.99	   A^2 -> H(U1(a, d), k)
28.56/9.99	   A^2 -> H(k, U1(c, b))
28.56/9.99	   A^2 -> H(k, U1(d, b))
28.56/9.99	   A^2 -> H(k, U1(b, c))
28.56/9.99	   A^2 -> H(k, U1(b, d))
28.56/9.99	   A^2 -> H(k, U1(c, c))
28.56/9.99	   A^2 -> H(k, f(e))
28.56/9.99	   A^2 -> H(k, f(k))
28.56/9.99	   A^2 -> H(k, U1(d, d))
28.56/9.99	   A^2 -> H(c, U1(e, b))
28.56/9.99	   A^2 -> H(c, U1(k, b))
28.56/9.99	   A^2 -> H(c, U1(c, d))
28.56/9.99	   A^2 -> H(c, U1(d, c))
28.56/9.99	   A^2 -> H(c, U1(b, e))
28.56/9.99	   A^2 -> H(c, U1(b, k))
28.56/9.99	   A^2 -> H(c, U1(e, c))
28.56/9.99	   A^2 -> H(c, U1(k, c))
28.56/9.99	   A^2 -> H(c, U1(c, e))
28.56/9.99	   A^2 -> H(c, U1(c, k))
28.56/9.99	   A^2 -> H(c, U1(e, e))
28.56/9.99	   A^2 -> H(c, U1(k, k))
28.56/9.99	   A^2 -> H(c, U1(k, d))
28.56/9.99	   A^2 -> H(c, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, c), b)
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, c), e)
28.56/9.99	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.99	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.99	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.99	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.99	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.99	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.99	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.99	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.99	   A^2 -> H(U1(k, c), b)
28.56/9.99	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, c), c)
28.56/9.99	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, e), b)
28.56/9.99	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, e), c)
28.56/9.99	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, e), e)
28.56/9.99	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, k), b)
28.56/9.99	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, k), c)
28.56/9.99	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, k), e)
28.56/9.99	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, c), d)
28.56/9.99	   A^2 -> H(e, U1(e, b))
28.56/9.99	   A^2 -> H(e, U1(c, d))
28.56/9.99	   A^2 -> H(e, U1(d, c))
28.56/9.99	   A^2 -> H(e, U1(b, e))
28.56/9.99	   A^2 -> H(e, U1(b, k))
28.56/9.99	   A^2 -> H(e, U1(e, c))
28.56/9.99	   A^2 -> H(e, U1(c, e))
28.56/9.99	   A^2 -> H(e, U1(c, k))
28.56/9.99	   A^2 -> H(e, U1(e, e))
28.56/9.99	   A^2 -> H(e, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, e), b)
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, e), c)
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.99	   A^2 -> H(f(e), d)
28.56/9.99	   A^2 -> H(f(e), k)
28.56/9.99	   A^2 -> H(U1(k, k), b)
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, k), c)
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.99	   A^2 -> H(f(k), d)
28.56/9.99	   A^2 -> H(f(k), k)
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(k, d), b)
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, d))
28.56/9.99	
28.56/9.99	The TRS R consists of the following rules:
28.56/9.99	
28.56/9.99	   f(x) -> U1(x, x)
28.56/9.99	   U1(e, x) -> x
28.56/9.99	   a -> c
28.56/9.99	   a -> d
28.56/9.99	   b -> c
28.56/9.99	   b -> d
28.56/9.99	   d -> k
28.56/9.99	   c -> e
28.56/9.99	   c -> k
28.56/9.99	
28.56/9.99	Q is empty.
28.56/9.99	We have to consider all minimal (P,Q,R)-chains.
28.56/9.99	----------------------------------------
28.56/9.99	
28.56/9.99	(1711) TransformationProof (EQUIVALENT)
28.56/9.99	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.99	
28.56/9.99	   (A^2 -> H(U1(k, k), U1(d, c)),A^2 -> H(U1(k, k), U1(d, c)))
28.56/9.99	   (A^2 -> H(U1(k, d), U1(k, c)),A^2 -> H(U1(k, d), U1(k, c)))
28.56/9.99	   (A^2 -> H(U1(k, d), U1(d, e)),A^2 -> H(U1(k, d), U1(d, e)))
28.56/9.99	   (A^2 -> H(U1(k, d), U1(d, k)),A^2 -> H(U1(k, d), U1(d, k)))
28.56/9.99	
28.56/9.99	
28.56/9.99	----------------------------------------
28.56/9.99	
28.56/9.99	(1712)
28.56/9.99	Obligation:
28.56/9.99	Q DP problem:
28.56/9.99	The TRS P consists of the following rules:
28.56/9.99	
28.56/9.99	   G(d, x, x) -> A^2
28.56/9.99	   A^2 -> H(f(c), f(c))
28.56/9.99	   H(x, x) -> G(x, x, f(k))
28.56/9.99	   A^2 -> H(f(d), f(d))
28.56/9.99	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.99	   A^2 -> H(f(e), f(e))
28.56/9.99	   A^2 -> H(f(k), f(k))
28.56/9.99	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.99	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.99	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(b, e))
28.56/9.99	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.99	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.99	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, d), b)
28.56/9.99	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.99	   A^2 -> H(U1(d, d), c)
28.56/9.99	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.99	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.99	   A^2 -> H(U1(d, d), e)
28.56/9.99	   A^2 -> H(f(d), d)
28.56/9.99	   A^2 -> H(f(d), k)
28.56/9.99	   A^2 -> H(U1(c, c), c)
28.56/9.99	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.99	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.99	   A^2 -> H(f(c), k)
28.56/9.99	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.99	   A^2 -> H(f(k), U1(k, k))
28.56/9.99	   A^2 -> H(f(e), e)
28.56/9.99	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.99	   A^2 -> H(d, U1(c, b))
28.56/9.99	   A^2 -> H(d, U1(d, b))
28.56/9.99	   A^2 -> H(d, U1(b, c))
28.56/9.99	   A^2 -> H(d, U1(b, d))
28.56/9.99	   A^2 -> H(d, U1(c, c))
28.56/9.99	   A^2 -> H(d, f(e))
28.56/9.99	   A^2 -> H(d, f(k))
28.56/9.99	   A^2 -> H(d, U1(d, d))
28.56/9.99	   A^2 -> H(a, U1(e, b))
28.56/9.99	   A^2 -> H(a, U1(k, b))
28.56/9.99	   A^2 -> H(a, U1(c, d))
28.56/9.99	   A^2 -> H(a, U1(d, c))
28.56/9.99	   A^2 -> H(a, U1(b, e))
28.56/9.99	   A^2 -> H(a, U1(b, k))
28.56/9.99	   A^2 -> H(a, U1(e, c))
28.56/9.99	   A^2 -> H(a, U1(k, c))
28.56/9.99	   A^2 -> H(a, U1(c, e))
28.56/9.99	   A^2 -> H(a, U1(c, k))
28.56/9.99	   A^2 -> H(a, U1(e, e))
28.56/9.99	   A^2 -> H(a, U1(k, k))
28.56/9.99	   A^2 -> H(a, U1(k, d))
28.56/9.99	   A^2 -> H(a, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.99	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.99	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, a), b)
28.56/9.99	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, a), c)
28.56/9.99	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, a), e)
28.56/9.99	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, a), b)
28.56/9.99	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, a), c)
28.56/9.99	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.99	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.99	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, d), b)
28.56/9.99	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, d), c)
28.56/9.99	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, d), e)
28.56/9.99	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, a), d)
28.56/9.99	   A^2 -> H(U1(c, a), k)
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.99	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, c), b)
28.56/9.99	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(d, c), c)
28.56/9.99	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(d, c), e)
28.56/9.99	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, a), d)
28.56/9.99	   A^2 -> H(U1(d, a), k)
28.56/9.99	   A^2 -> H(U1(a, e), b)
28.56/9.99	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(a, e), c)
28.56/9.99	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(a, e), e)
28.56/9.99	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(a, k), b)
28.56/9.99	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(a, k), c)
28.56/9.99	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.99	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.99	   A^2 -> H(U1(a, k), e)
28.56/9.99	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(a, c), d)
28.56/9.99	   A^2 -> H(U1(a, c), k)
28.56/9.99	   A^2 -> H(U1(a, d), d)
28.56/9.99	   A^2 -> H(U1(a, d), k)
28.56/9.99	   A^2 -> H(k, U1(c, b))
28.56/9.99	   A^2 -> H(k, U1(d, b))
28.56/9.99	   A^2 -> H(k, U1(b, c))
28.56/9.99	   A^2 -> H(k, U1(b, d))
28.56/9.99	   A^2 -> H(k, U1(c, c))
28.56/9.99	   A^2 -> H(k, f(e))
28.56/9.99	   A^2 -> H(k, f(k))
28.56/9.99	   A^2 -> H(k, U1(d, d))
28.56/9.99	   A^2 -> H(c, U1(e, b))
28.56/9.99	   A^2 -> H(c, U1(k, b))
28.56/9.99	   A^2 -> H(c, U1(c, d))
28.56/9.99	   A^2 -> H(c, U1(d, c))
28.56/9.99	   A^2 -> H(c, U1(b, e))
28.56/9.99	   A^2 -> H(c, U1(b, k))
28.56/9.99	   A^2 -> H(c, U1(e, c))
28.56/9.99	   A^2 -> H(c, U1(k, c))
28.56/9.99	   A^2 -> H(c, U1(c, e))
28.56/9.99	   A^2 -> H(c, U1(c, k))
28.56/9.99	   A^2 -> H(c, U1(e, e))
28.56/9.99	   A^2 -> H(c, U1(k, k))
28.56/9.99	   A^2 -> H(c, U1(k, d))
28.56/9.99	   A^2 -> H(c, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, c), b)
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, c), e)
28.56/9.99	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.99	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.99	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.99	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.99	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.99	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.99	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.99	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.99	   A^2 -> H(U1(k, c), b)
28.56/9.99	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, c), c)
28.56/9.99	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, e), b)
28.56/9.99	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, e), c)
28.56/9.99	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, e), e)
28.56/9.99	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, k), b)
28.56/9.99	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, k), c)
28.56/9.99	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, k), e)
28.56/9.99	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, c), d)
28.56/9.99	   A^2 -> H(e, U1(e, b))
28.56/9.99	   A^2 -> H(e, U1(c, d))
28.56/9.99	   A^2 -> H(e, U1(d, c))
28.56/9.99	   A^2 -> H(e, U1(b, e))
28.56/9.99	   A^2 -> H(e, U1(b, k))
28.56/9.99	   A^2 -> H(e, U1(e, c))
28.56/9.99	   A^2 -> H(e, U1(c, e))
28.56/9.99	   A^2 -> H(e, U1(c, k))
28.56/9.99	   A^2 -> H(e, U1(e, e))
28.56/9.99	   A^2 -> H(e, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, e), b)
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, e), c)
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.99	   A^2 -> H(f(e), d)
28.56/9.99	   A^2 -> H(f(e), k)
28.56/9.99	   A^2 -> H(U1(k, k), b)
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, k), c)
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.99	   A^2 -> H(f(k), d)
28.56/9.99	   A^2 -> H(f(k), k)
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(k, d), b)
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, d), U1(d, e))
28.56/9.99	
28.56/9.99	The TRS R consists of the following rules:
28.56/9.99	
28.56/9.99	   f(x) -> U1(x, x)
28.56/9.99	   U1(e, x) -> x
28.56/9.99	   a -> c
28.56/9.99	   a -> d
28.56/9.99	   b -> c
28.56/9.99	   b -> d
28.56/9.99	   d -> k
28.56/9.99	   c -> e
28.56/9.99	   c -> k
28.56/9.99	
28.56/9.99	Q is empty.
28.56/9.99	We have to consider all minimal (P,Q,R)-chains.
28.56/9.99	----------------------------------------
28.56/9.99	
28.56/9.99	(1713) TransformationProof (EQUIVALENT)
28.56/9.99	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.99	
28.56/9.99	   (A^2 -> H(U1(k, k), U1(b, e)),A^2 -> H(U1(k, k), U1(b, e)))
28.56/9.99	   (A^2 -> H(U1(k, d), U1(c, e)),A^2 -> H(U1(k, d), U1(c, e)))
28.56/9.99	   (A^2 -> H(U1(k, d), U1(d, e)),A^2 -> H(U1(k, d), U1(d, e)))
28.56/9.99	
28.56/9.99	
28.56/9.99	----------------------------------------
28.56/9.99	
28.56/9.99	(1714)
28.56/9.99	Obligation:
28.56/9.99	Q DP problem:
28.56/9.99	The TRS P consists of the following rules:
28.56/9.99	
28.56/9.99	   G(d, x, x) -> A^2
28.56/9.99	   A^2 -> H(f(c), f(c))
28.56/9.99	   H(x, x) -> G(x, x, f(k))
28.56/9.99	   A^2 -> H(f(d), f(d))
28.56/9.99	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.99	   A^2 -> H(f(e), f(e))
28.56/9.99	   A^2 -> H(f(k), f(k))
28.56/9.99	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.99	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.99	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(b, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.99	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.99	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, d), b)
28.56/9.99	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.99	   A^2 -> H(U1(d, d), c)
28.56/9.99	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.99	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.99	   A^2 -> H(U1(d, d), e)
28.56/9.99	   A^2 -> H(f(d), d)
28.56/9.99	   A^2 -> H(f(d), k)
28.56/9.99	   A^2 -> H(U1(c, c), c)
28.56/9.99	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.99	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.99	   A^2 -> H(f(c), k)
28.56/9.99	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.99	   A^2 -> H(f(k), U1(k, k))
28.56/9.99	   A^2 -> H(f(e), e)
28.56/9.99	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.99	   A^2 -> H(d, U1(c, b))
28.56/9.99	   A^2 -> H(d, U1(d, b))
28.56/9.99	   A^2 -> H(d, U1(b, c))
28.56/9.99	   A^2 -> H(d, U1(b, d))
28.56/9.99	   A^2 -> H(d, U1(c, c))
28.56/9.99	   A^2 -> H(d, f(e))
28.56/9.99	   A^2 -> H(d, f(k))
28.56/9.99	   A^2 -> H(d, U1(d, d))
28.56/9.99	   A^2 -> H(a, U1(e, b))
28.56/9.99	   A^2 -> H(a, U1(k, b))
28.56/9.99	   A^2 -> H(a, U1(c, d))
28.56/9.99	   A^2 -> H(a, U1(d, c))
28.56/9.99	   A^2 -> H(a, U1(b, e))
28.56/9.99	   A^2 -> H(a, U1(b, k))
28.56/9.99	   A^2 -> H(a, U1(e, c))
28.56/9.99	   A^2 -> H(a, U1(k, c))
28.56/9.99	   A^2 -> H(a, U1(c, e))
28.56/9.99	   A^2 -> H(a, U1(c, k))
28.56/9.99	   A^2 -> H(a, U1(e, e))
28.56/9.99	   A^2 -> H(a, U1(k, k))
28.56/9.99	   A^2 -> H(a, U1(k, d))
28.56/9.99	   A^2 -> H(a, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.99	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.99	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, a), b)
28.56/9.99	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, a), c)
28.56/9.99	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, a), e)
28.56/9.99	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, a), b)
28.56/9.99	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, a), c)
28.56/9.99	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.99	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.99	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, d), b)
28.56/9.99	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, d), c)
28.56/9.99	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, d), e)
28.56/9.99	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, a), d)
28.56/9.99	   A^2 -> H(U1(c, a), k)
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.99	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, c), b)
28.56/9.99	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(d, c), c)
28.56/9.99	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(d, c), e)
28.56/9.99	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, a), d)
28.56/9.99	   A^2 -> H(U1(d, a), k)
28.56/9.99	   A^2 -> H(U1(a, e), b)
28.56/9.99	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(a, e), c)
28.56/9.99	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(a, e), e)
28.56/9.99	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(a, k), b)
28.56/9.99	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(a, k), c)
28.56/9.99	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.99	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.99	   A^2 -> H(U1(a, k), e)
28.56/9.99	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(a, c), d)
28.56/9.99	   A^2 -> H(U1(a, c), k)
28.56/9.99	   A^2 -> H(U1(a, d), d)
28.56/9.99	   A^2 -> H(U1(a, d), k)
28.56/9.99	   A^2 -> H(k, U1(c, b))
28.56/9.99	   A^2 -> H(k, U1(d, b))
28.56/9.99	   A^2 -> H(k, U1(b, c))
28.56/9.99	   A^2 -> H(k, U1(b, d))
28.56/9.99	   A^2 -> H(k, U1(c, c))
28.56/9.99	   A^2 -> H(k, f(e))
28.56/9.99	   A^2 -> H(k, f(k))
28.56/9.99	   A^2 -> H(k, U1(d, d))
28.56/9.99	   A^2 -> H(c, U1(e, b))
28.56/9.99	   A^2 -> H(c, U1(k, b))
28.56/9.99	   A^2 -> H(c, U1(c, d))
28.56/9.99	   A^2 -> H(c, U1(d, c))
28.56/9.99	   A^2 -> H(c, U1(b, e))
28.56/9.99	   A^2 -> H(c, U1(b, k))
28.56/9.99	   A^2 -> H(c, U1(e, c))
28.56/9.99	   A^2 -> H(c, U1(k, c))
28.56/9.99	   A^2 -> H(c, U1(c, e))
28.56/9.99	   A^2 -> H(c, U1(c, k))
28.56/9.99	   A^2 -> H(c, U1(e, e))
28.56/9.99	   A^2 -> H(c, U1(k, k))
28.56/9.99	   A^2 -> H(c, U1(k, d))
28.56/9.99	   A^2 -> H(c, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, c), b)
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, c), e)
28.56/9.99	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.99	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.99	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.99	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.99	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.99	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.99	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.99	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.99	   A^2 -> H(U1(k, c), b)
28.56/9.99	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, c), c)
28.56/9.99	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, e), b)
28.56/9.99	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, e), c)
28.56/9.99	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, e), e)
28.56/9.99	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, k), b)
28.56/9.99	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, k), c)
28.56/9.99	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, k), e)
28.56/9.99	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, c), d)
28.56/9.99	   A^2 -> H(e, U1(e, b))
28.56/9.99	   A^2 -> H(e, U1(c, d))
28.56/9.99	   A^2 -> H(e, U1(d, c))
28.56/9.99	   A^2 -> H(e, U1(b, e))
28.56/9.99	   A^2 -> H(e, U1(b, k))
28.56/9.99	   A^2 -> H(e, U1(e, c))
28.56/9.99	   A^2 -> H(e, U1(c, e))
28.56/9.99	   A^2 -> H(e, U1(c, k))
28.56/9.99	   A^2 -> H(e, U1(e, e))
28.56/9.99	   A^2 -> H(e, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, e), b)
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, e), c)
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.99	   A^2 -> H(f(e), d)
28.56/9.99	   A^2 -> H(f(e), k)
28.56/9.99	   A^2 -> H(U1(k, k), b)
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, k), c)
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.99	   A^2 -> H(f(k), d)
28.56/9.99	   A^2 -> H(f(k), k)
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(k, d), b)
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, d), U1(d, e))
28.56/9.99	
28.56/9.99	The TRS R consists of the following rules:
28.56/9.99	
28.56/9.99	   f(x) -> U1(x, x)
28.56/9.99	   U1(e, x) -> x
28.56/9.99	   a -> c
28.56/9.99	   a -> d
28.56/9.99	   b -> c
28.56/9.99	   b -> d
28.56/9.99	   d -> k
28.56/9.99	   c -> e
28.56/9.99	   c -> k
28.56/9.99	
28.56/9.99	Q is empty.
28.56/9.99	We have to consider all minimal (P,Q,R)-chains.
28.56/9.99	----------------------------------------
28.56/9.99	
28.56/9.99	(1715) TransformationProof (EQUIVALENT)
28.56/9.99	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.99	
28.56/9.99	   (A^2 -> H(U1(k, k), U1(b, k)),A^2 -> H(U1(k, k), U1(b, k)))
28.56/9.99	   (A^2 -> H(U1(k, d), U1(c, k)),A^2 -> H(U1(k, d), U1(c, k)))
28.56/9.99	   (A^2 -> H(U1(k, d), U1(d, k)),A^2 -> H(U1(k, d), U1(d, k)))
28.56/9.99	
28.56/9.99	
28.56/9.99	----------------------------------------
28.56/9.99	
28.56/9.99	(1716)
28.56/9.99	Obligation:
28.56/9.99	Q DP problem:
28.56/9.99	The TRS P consists of the following rules:
28.56/9.99	
28.56/9.99	   G(d, x, x) -> A^2
28.56/9.99	   A^2 -> H(f(c), f(c))
28.56/9.99	   H(x, x) -> G(x, x, f(k))
28.56/9.99	   A^2 -> H(f(d), f(d))
28.56/9.99	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.99	   A^2 -> H(f(e), f(e))
28.56/9.99	   A^2 -> H(f(k), f(k))
28.56/9.99	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.99	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.99	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.99	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.99	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, d), b)
28.56/9.99	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.99	   A^2 -> H(U1(d, d), c)
28.56/9.99	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.99	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.99	   A^2 -> H(U1(d, d), e)
28.56/9.99	   A^2 -> H(f(d), d)
28.56/9.99	   A^2 -> H(f(d), k)
28.56/9.99	   A^2 -> H(U1(c, c), c)
28.56/9.99	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.99	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.99	   A^2 -> H(f(c), k)
28.56/9.99	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.99	   A^2 -> H(f(k), U1(k, k))
28.56/9.99	   A^2 -> H(f(e), e)
28.56/9.99	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.99	   A^2 -> H(d, U1(c, b))
28.56/9.99	   A^2 -> H(d, U1(d, b))
28.56/9.99	   A^2 -> H(d, U1(b, c))
28.56/9.99	   A^2 -> H(d, U1(b, d))
28.56/9.99	   A^2 -> H(d, U1(c, c))
28.56/9.99	   A^2 -> H(d, f(e))
28.56/9.99	   A^2 -> H(d, f(k))
28.56/9.99	   A^2 -> H(d, U1(d, d))
28.56/9.99	   A^2 -> H(a, U1(e, b))
28.56/9.99	   A^2 -> H(a, U1(k, b))
28.56/9.99	   A^2 -> H(a, U1(c, d))
28.56/9.99	   A^2 -> H(a, U1(d, c))
28.56/9.99	   A^2 -> H(a, U1(b, e))
28.56/9.99	   A^2 -> H(a, U1(b, k))
28.56/9.99	   A^2 -> H(a, U1(e, c))
28.56/9.99	   A^2 -> H(a, U1(k, c))
28.56/9.99	   A^2 -> H(a, U1(c, e))
28.56/9.99	   A^2 -> H(a, U1(c, k))
28.56/9.99	   A^2 -> H(a, U1(e, e))
28.56/9.99	   A^2 -> H(a, U1(k, k))
28.56/9.99	   A^2 -> H(a, U1(k, d))
28.56/9.99	   A^2 -> H(a, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.99	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.99	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, a), b)
28.56/9.99	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, a), c)
28.56/9.99	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, a), e)
28.56/9.99	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, a), b)
28.56/9.99	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, a), c)
28.56/9.99	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.99	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.99	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, d), b)
28.56/9.99	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, d), c)
28.56/9.99	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, d), e)
28.56/9.99	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, a), d)
28.56/9.99	   A^2 -> H(U1(c, a), k)
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.99	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, c), b)
28.56/9.99	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(d, c), c)
28.56/9.99	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(d, c), e)
28.56/9.99	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, a), d)
28.56/9.99	   A^2 -> H(U1(d, a), k)
28.56/9.99	   A^2 -> H(U1(a, e), b)
28.56/9.99	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(a, e), c)
28.56/9.99	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(a, e), e)
28.56/9.99	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(a, k), b)
28.56/9.99	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(a, k), c)
28.56/9.99	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.99	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.99	   A^2 -> H(U1(a, k), e)
28.56/9.99	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(a, c), d)
28.56/9.99	   A^2 -> H(U1(a, c), k)
28.56/9.99	   A^2 -> H(U1(a, d), d)
28.56/9.99	   A^2 -> H(U1(a, d), k)
28.56/9.99	   A^2 -> H(k, U1(c, b))
28.56/9.99	   A^2 -> H(k, U1(d, b))
28.56/9.99	   A^2 -> H(k, U1(b, c))
28.56/9.99	   A^2 -> H(k, U1(b, d))
28.56/9.99	   A^2 -> H(k, U1(c, c))
28.56/9.99	   A^2 -> H(k, f(e))
28.56/9.99	   A^2 -> H(k, f(k))
28.56/9.99	   A^2 -> H(k, U1(d, d))
28.56/9.99	   A^2 -> H(c, U1(e, b))
28.56/9.99	   A^2 -> H(c, U1(k, b))
28.56/9.99	   A^2 -> H(c, U1(c, d))
28.56/9.99	   A^2 -> H(c, U1(d, c))
28.56/9.99	   A^2 -> H(c, U1(b, e))
28.56/9.99	   A^2 -> H(c, U1(b, k))
28.56/9.99	   A^2 -> H(c, U1(e, c))
28.56/9.99	   A^2 -> H(c, U1(k, c))
28.56/9.99	   A^2 -> H(c, U1(c, e))
28.56/9.99	   A^2 -> H(c, U1(c, k))
28.56/9.99	   A^2 -> H(c, U1(e, e))
28.56/9.99	   A^2 -> H(c, U1(k, k))
28.56/9.99	   A^2 -> H(c, U1(k, d))
28.56/9.99	   A^2 -> H(c, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, c), b)
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, c), e)
28.56/9.99	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.99	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.99	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.99	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.99	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.99	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.99	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.99	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.99	   A^2 -> H(U1(k, c), b)
28.56/9.99	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, c), c)
28.56/9.99	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, e), b)
28.56/9.99	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, e), c)
28.56/9.99	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, e), e)
28.56/9.99	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, k), b)
28.56/9.99	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, k), c)
28.56/9.99	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, k), e)
28.56/9.99	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, c), d)
28.56/9.99	   A^2 -> H(e, U1(e, b))
28.56/9.99	   A^2 -> H(e, U1(c, d))
28.56/9.99	   A^2 -> H(e, U1(d, c))
28.56/9.99	   A^2 -> H(e, U1(b, e))
28.56/9.99	   A^2 -> H(e, U1(b, k))
28.56/9.99	   A^2 -> H(e, U1(e, c))
28.56/9.99	   A^2 -> H(e, U1(c, e))
28.56/9.99	   A^2 -> H(e, U1(c, k))
28.56/9.99	   A^2 -> H(e, U1(e, e))
28.56/9.99	   A^2 -> H(e, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, e), b)
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, e), c)
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.99	   A^2 -> H(f(e), d)
28.56/9.99	   A^2 -> H(f(e), k)
28.56/9.99	   A^2 -> H(U1(k, k), b)
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, k), c)
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.99	   A^2 -> H(f(k), d)
28.56/9.99	   A^2 -> H(f(k), k)
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(k, d), b)
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, d), U1(d, e))
28.56/9.99	
28.56/9.99	The TRS R consists of the following rules:
28.56/9.99	
28.56/9.99	   f(x) -> U1(x, x)
28.56/9.99	   U1(e, x) -> x
28.56/9.99	   a -> c
28.56/9.99	   a -> d
28.56/9.99	   b -> c
28.56/9.99	   b -> d
28.56/9.99	   d -> k
28.56/9.99	   c -> e
28.56/9.99	   c -> k
28.56/9.99	
28.56/9.99	Q is empty.
28.56/9.99	We have to consider all minimal (P,Q,R)-chains.
28.56/9.99	----------------------------------------
28.56/9.99	
28.56/9.99	(1717) TransformationProof (EQUIVALENT)
28.56/9.99	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.99	
28.56/9.99	   (A^2 -> H(U1(k, k), U1(e, c)),A^2 -> H(U1(k, k), U1(e, c)))
28.56/9.99	   (A^2 -> H(U1(k, d), c),A^2 -> H(U1(k, d), c))
28.56/9.99	   (A^2 -> H(U1(k, d), U1(e, e)),A^2 -> H(U1(k, d), U1(e, e)))
28.56/9.99	   (A^2 -> H(U1(k, d), U1(e, k)),A^2 -> H(U1(k, d), U1(e, k)))
28.56/9.99	
28.56/9.99	
28.56/9.99	----------------------------------------
28.56/9.99	
28.56/9.99	(1718)
28.56/9.99	Obligation:
28.56/9.99	Q DP problem:
28.56/9.99	The TRS P consists of the following rules:
28.56/9.99	
28.56/9.99	   G(d, x, x) -> A^2
28.56/9.99	   A^2 -> H(f(c), f(c))
28.56/9.99	   H(x, x) -> G(x, x, f(k))
28.56/9.99	   A^2 -> H(f(d), f(d))
28.56/9.99	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.99	   A^2 -> H(f(e), f(e))
28.56/9.99	   A^2 -> H(f(k), f(k))
28.56/9.99	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.99	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.99	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, c))
28.56/9.99	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.99	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, d), b)
28.56/9.99	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.99	   A^2 -> H(U1(d, d), c)
28.56/9.99	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.99	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.99	   A^2 -> H(U1(d, d), e)
28.56/9.99	   A^2 -> H(f(d), d)
28.56/9.99	   A^2 -> H(f(d), k)
28.56/9.99	   A^2 -> H(U1(c, c), c)
28.56/9.99	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.99	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.99	   A^2 -> H(f(c), k)
28.56/9.99	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.99	   A^2 -> H(f(k), U1(k, k))
28.56/9.99	   A^2 -> H(f(e), e)
28.56/9.99	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.99	   A^2 -> H(d, U1(c, b))
28.56/9.99	   A^2 -> H(d, U1(d, b))
28.56/9.99	   A^2 -> H(d, U1(b, c))
28.56/9.99	   A^2 -> H(d, U1(b, d))
28.56/9.99	   A^2 -> H(d, U1(c, c))
28.56/9.99	   A^2 -> H(d, f(e))
28.56/9.99	   A^2 -> H(d, f(k))
28.56/9.99	   A^2 -> H(d, U1(d, d))
28.56/9.99	   A^2 -> H(a, U1(e, b))
28.56/9.99	   A^2 -> H(a, U1(k, b))
28.56/9.99	   A^2 -> H(a, U1(c, d))
28.56/9.99	   A^2 -> H(a, U1(d, c))
28.56/9.99	   A^2 -> H(a, U1(b, e))
28.56/9.99	   A^2 -> H(a, U1(b, k))
28.56/9.99	   A^2 -> H(a, U1(e, c))
28.56/9.99	   A^2 -> H(a, U1(k, c))
28.56/9.99	   A^2 -> H(a, U1(c, e))
28.56/9.99	   A^2 -> H(a, U1(c, k))
28.56/9.99	   A^2 -> H(a, U1(e, e))
28.56/9.99	   A^2 -> H(a, U1(k, k))
28.56/9.99	   A^2 -> H(a, U1(k, d))
28.56/9.99	   A^2 -> H(a, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.99	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.99	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, a), b)
28.56/9.99	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, a), c)
28.56/9.99	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, a), e)
28.56/9.99	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, a), b)
28.56/9.99	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, a), c)
28.56/9.99	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.99	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.99	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, d), b)
28.56/9.99	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, d), c)
28.56/9.99	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, d), e)
28.56/9.99	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, a), d)
28.56/9.99	   A^2 -> H(U1(c, a), k)
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.99	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, c), b)
28.56/9.99	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(d, c), c)
28.56/9.99	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(d, c), e)
28.56/9.99	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, a), d)
28.56/9.99	   A^2 -> H(U1(d, a), k)
28.56/9.99	   A^2 -> H(U1(a, e), b)
28.56/9.99	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(a, e), c)
28.56/9.99	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(a, e), e)
28.56/9.99	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(a, k), b)
28.56/9.99	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(a, k), c)
28.56/9.99	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.99	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.99	   A^2 -> H(U1(a, k), e)
28.56/9.99	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(a, c), d)
28.56/9.99	   A^2 -> H(U1(a, c), k)
28.56/9.99	   A^2 -> H(U1(a, d), d)
28.56/9.99	   A^2 -> H(U1(a, d), k)
28.56/9.99	   A^2 -> H(k, U1(c, b))
28.56/9.99	   A^2 -> H(k, U1(d, b))
28.56/9.99	   A^2 -> H(k, U1(b, c))
28.56/9.99	   A^2 -> H(k, U1(b, d))
28.56/9.99	   A^2 -> H(k, U1(c, c))
28.56/9.99	   A^2 -> H(k, f(e))
28.56/9.99	   A^2 -> H(k, f(k))
28.56/9.99	   A^2 -> H(k, U1(d, d))
28.56/9.99	   A^2 -> H(c, U1(e, b))
28.56/9.99	   A^2 -> H(c, U1(k, b))
28.56/9.99	   A^2 -> H(c, U1(c, d))
28.56/9.99	   A^2 -> H(c, U1(d, c))
28.56/9.99	   A^2 -> H(c, U1(b, e))
28.56/9.99	   A^2 -> H(c, U1(b, k))
28.56/9.99	   A^2 -> H(c, U1(e, c))
28.56/9.99	   A^2 -> H(c, U1(k, c))
28.56/9.99	   A^2 -> H(c, U1(c, e))
28.56/9.99	   A^2 -> H(c, U1(c, k))
28.56/9.99	   A^2 -> H(c, U1(e, e))
28.56/9.99	   A^2 -> H(c, U1(k, k))
28.56/9.99	   A^2 -> H(c, U1(k, d))
28.56/9.99	   A^2 -> H(c, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, c), b)
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, c), e)
28.56/9.99	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.99	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.99	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.99	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.99	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.99	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.99	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.99	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.99	   A^2 -> H(U1(k, c), b)
28.56/9.99	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, c), c)
28.56/9.99	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, e), b)
28.56/9.99	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, e), c)
28.56/9.99	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, e), e)
28.56/9.99	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, k), b)
28.56/9.99	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, k), c)
28.56/9.99	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, k), e)
28.56/9.99	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, c), d)
28.56/9.99	   A^2 -> H(e, U1(e, b))
28.56/9.99	   A^2 -> H(e, U1(c, d))
28.56/9.99	   A^2 -> H(e, U1(d, c))
28.56/9.99	   A^2 -> H(e, U1(b, e))
28.56/9.99	   A^2 -> H(e, U1(b, k))
28.56/9.99	   A^2 -> H(e, U1(e, c))
28.56/9.99	   A^2 -> H(e, U1(c, e))
28.56/9.99	   A^2 -> H(e, U1(c, k))
28.56/9.99	   A^2 -> H(e, U1(e, e))
28.56/9.99	   A^2 -> H(e, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, e), b)
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, e), c)
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.99	   A^2 -> H(f(e), d)
28.56/9.99	   A^2 -> H(f(e), k)
28.56/9.99	   A^2 -> H(U1(k, k), b)
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, k), c)
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.99	   A^2 -> H(f(k), d)
28.56/9.99	   A^2 -> H(f(k), k)
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(k, d), b)
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, d), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, d), c)
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, k))
28.56/9.99	
28.56/9.99	The TRS R consists of the following rules:
28.56/9.99	
28.56/9.99	   f(x) -> U1(x, x)
28.56/9.99	   U1(e, x) -> x
28.56/9.99	   a -> c
28.56/9.99	   a -> d
28.56/9.99	   b -> c
28.56/9.99	   b -> d
28.56/9.99	   d -> k
28.56/9.99	   c -> e
28.56/9.99	   c -> k
28.56/9.99	
28.56/9.99	Q is empty.
28.56/9.99	We have to consider all minimal (P,Q,R)-chains.
28.56/9.99	----------------------------------------
28.56/9.99	
28.56/9.99	(1719) TransformationProof (EQUIVALENT)
28.56/9.99	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.99	
28.56/9.99	   (A^2 -> H(U1(k, k), U1(k, c)),A^2 -> H(U1(k, k), U1(k, c)))
28.56/9.99	   (A^2 -> H(U1(k, d), U1(k, e)),A^2 -> H(U1(k, d), U1(k, e)))
28.56/9.99	   (A^2 -> H(U1(k, d), U1(k, k)),A^2 -> H(U1(k, d), U1(k, k)))
28.56/9.99	
28.56/9.99	
28.56/9.99	----------------------------------------
28.56/9.99	
28.56/9.99	(1720)
28.56/9.99	Obligation:
28.56/9.99	Q DP problem:
28.56/9.99	The TRS P consists of the following rules:
28.56/9.99	
28.56/9.99	   G(d, x, x) -> A^2
28.56/9.99	   A^2 -> H(f(c), f(c))
28.56/9.99	   H(x, x) -> G(x, x, f(k))
28.56/9.99	   A^2 -> H(f(d), f(d))
28.56/9.99	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.99	   A^2 -> H(f(e), f(e))
28.56/9.99	   A^2 -> H(f(k), f(k))
28.56/9.99	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.99	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.99	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(c, e))
28.56/9.99	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, d), b)
28.56/9.99	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.99	   A^2 -> H(U1(d, d), c)
28.56/9.99	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.99	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.99	   A^2 -> H(U1(d, d), e)
28.56/9.99	   A^2 -> H(f(d), d)
28.56/9.99	   A^2 -> H(f(d), k)
28.56/9.99	   A^2 -> H(U1(c, c), c)
28.56/9.99	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.99	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.99	   A^2 -> H(f(c), k)
28.56/9.99	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.99	   A^2 -> H(f(k), U1(k, k))
28.56/9.99	   A^2 -> H(f(e), e)
28.56/9.99	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.99	   A^2 -> H(d, U1(c, b))
28.56/9.99	   A^2 -> H(d, U1(d, b))
28.56/9.99	   A^2 -> H(d, U1(b, c))
28.56/9.99	   A^2 -> H(d, U1(b, d))
28.56/9.99	   A^2 -> H(d, U1(c, c))
28.56/9.99	   A^2 -> H(d, f(e))
28.56/9.99	   A^2 -> H(d, f(k))
28.56/9.99	   A^2 -> H(d, U1(d, d))
28.56/9.99	   A^2 -> H(a, U1(e, b))
28.56/9.99	   A^2 -> H(a, U1(k, b))
28.56/9.99	   A^2 -> H(a, U1(c, d))
28.56/9.99	   A^2 -> H(a, U1(d, c))
28.56/9.99	   A^2 -> H(a, U1(b, e))
28.56/9.99	   A^2 -> H(a, U1(b, k))
28.56/9.99	   A^2 -> H(a, U1(e, c))
28.56/9.99	   A^2 -> H(a, U1(k, c))
28.56/9.99	   A^2 -> H(a, U1(c, e))
28.56/9.99	   A^2 -> H(a, U1(c, k))
28.56/9.99	   A^2 -> H(a, U1(e, e))
28.56/9.99	   A^2 -> H(a, U1(k, k))
28.56/9.99	   A^2 -> H(a, U1(k, d))
28.56/9.99	   A^2 -> H(a, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.99	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.99	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, a), b)
28.56/9.99	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, a), c)
28.56/9.99	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, a), e)
28.56/9.99	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, a), b)
28.56/9.99	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, a), c)
28.56/9.99	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.99	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.99	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, d), b)
28.56/9.99	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, d), c)
28.56/9.99	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, d), e)
28.56/9.99	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, a), d)
28.56/9.99	   A^2 -> H(U1(c, a), k)
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.99	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, c), b)
28.56/9.99	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(d, c), c)
28.56/9.99	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(d, c), e)
28.56/9.99	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, a), d)
28.56/9.99	   A^2 -> H(U1(d, a), k)
28.56/9.99	   A^2 -> H(U1(a, e), b)
28.56/9.99	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(a, e), c)
28.56/9.99	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(a, e), e)
28.56/9.99	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(a, k), b)
28.56/9.99	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(a, k), c)
28.56/9.99	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.99	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.99	   A^2 -> H(U1(a, k), e)
28.56/9.99	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(a, c), d)
28.56/9.99	   A^2 -> H(U1(a, c), k)
28.56/9.99	   A^2 -> H(U1(a, d), d)
28.56/9.99	   A^2 -> H(U1(a, d), k)
28.56/9.99	   A^2 -> H(k, U1(c, b))
28.56/9.99	   A^2 -> H(k, U1(d, b))
28.56/9.99	   A^2 -> H(k, U1(b, c))
28.56/9.99	   A^2 -> H(k, U1(b, d))
28.56/9.99	   A^2 -> H(k, U1(c, c))
28.56/9.99	   A^2 -> H(k, f(e))
28.56/9.99	   A^2 -> H(k, f(k))
28.56/9.99	   A^2 -> H(k, U1(d, d))
28.56/9.99	   A^2 -> H(c, U1(e, b))
28.56/9.99	   A^2 -> H(c, U1(k, b))
28.56/9.99	   A^2 -> H(c, U1(c, d))
28.56/9.99	   A^2 -> H(c, U1(d, c))
28.56/9.99	   A^2 -> H(c, U1(b, e))
28.56/9.99	   A^2 -> H(c, U1(b, k))
28.56/9.99	   A^2 -> H(c, U1(e, c))
28.56/9.99	   A^2 -> H(c, U1(k, c))
28.56/9.99	   A^2 -> H(c, U1(c, e))
28.56/9.99	   A^2 -> H(c, U1(c, k))
28.56/9.99	   A^2 -> H(c, U1(e, e))
28.56/9.99	   A^2 -> H(c, U1(k, k))
28.56/9.99	   A^2 -> H(c, U1(k, d))
28.56/9.99	   A^2 -> H(c, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, c), b)
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, c), e)
28.56/9.99	   A^2 -> H(U1(e, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, e), U1(e, b))
28.56/9.99	   A^2 -> H(U1(k, e), U1(k, b))
28.56/9.99	   A^2 -> H(U1(k, e), U1(c, d))
28.56/9.99	   A^2 -> H(U1(k, e), U1(d, c))
28.56/9.99	   A^2 -> H(U1(k, e), U1(b, e))
28.56/9.99	   A^2 -> H(U1(k, e), U1(b, k))
28.56/9.99	   A^2 -> H(U1(k, e), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, e), U1(k, c))
28.56/9.99	   A^2 -> H(U1(k, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(k, e), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, e), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, e), U1(d, k))
28.56/9.99	   A^2 -> H(U1(k, c), b)
28.56/9.99	   A^2 -> H(U1(k, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, c), c)
28.56/9.99	   A^2 -> H(U1(k, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, e), b)
28.56/9.99	   A^2 -> H(U1(c, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, e), c)
28.56/9.99	   A^2 -> H(U1(c, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, e), e)
28.56/9.99	   A^2 -> H(U1(c, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, k), b)
28.56/9.99	   A^2 -> H(U1(c, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, k), c)
28.56/9.99	   A^2 -> H(U1(c, k), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, k), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, k), e)
28.56/9.99	   A^2 -> H(U1(c, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, c), d)
28.56/9.99	   A^2 -> H(e, U1(e, b))
28.56/9.99	   A^2 -> H(e, U1(c, d))
28.56/9.99	   A^2 -> H(e, U1(d, c))
28.56/9.99	   A^2 -> H(e, U1(b, e))
28.56/9.99	   A^2 -> H(e, U1(b, k))
28.56/9.99	   A^2 -> H(e, U1(e, c))
28.56/9.99	   A^2 -> H(e, U1(c, e))
28.56/9.99	   A^2 -> H(e, U1(c, k))
28.56/9.99	   A^2 -> H(e, U1(e, e))
28.56/9.99	   A^2 -> H(e, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, e), b)
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, e), c)
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, e), U1(k, k))
28.56/9.99	   A^2 -> H(f(e), d)
28.56/9.99	   A^2 -> H(f(e), k)
28.56/9.99	   A^2 -> H(U1(k, k), b)
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, k), c)
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, k))
28.56/9.99	   A^2 -> H(f(k), d)
28.56/9.99	   A^2 -> H(f(k), k)
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(k, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(k, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(k, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(k, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(k, d), b)
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, d), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, d), c)
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, e))
28.56/9.99	
28.56/9.99	The TRS R consists of the following rules:
28.56/9.99	
28.56/9.99	   f(x) -> U1(x, x)
28.56/9.99	   U1(e, x) -> x
28.56/9.99	   a -> c
28.56/9.99	   a -> d
28.56/9.99	   b -> c
28.56/9.99	   b -> d
28.56/9.99	   d -> k
28.56/9.99	   c -> e
28.56/9.99	   c -> k
28.56/9.99	
28.56/9.99	Q is empty.
28.56/9.99	We have to consider all minimal (P,Q,R)-chains.
28.56/9.99	----------------------------------------
28.56/9.99	
28.56/9.99	(1721) TransformationProof (EQUIVALENT)
28.56/9.99	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/9.99	
28.56/9.99	   (A^2 -> H(U1(k, k), U1(c, e)),A^2 -> H(U1(k, k), U1(c, e)))
28.56/9.99	   (A^2 -> H(U1(k, d), U1(e, e)),A^2 -> H(U1(k, d), U1(e, e)))
28.56/9.99	   (A^2 -> H(U1(k, d), U1(k, e)),A^2 -> H(U1(k, d), U1(k, e)))
28.56/9.99	
28.56/9.99	
28.56/9.99	----------------------------------------
28.56/9.99	
28.56/9.99	(1722)
28.56/9.99	Obligation:
28.56/9.99	Q DP problem:
28.56/9.99	The TRS P consists of the following rules:
28.56/9.99	
28.56/9.99	   G(d, x, x) -> A^2
28.56/9.99	   A^2 -> H(f(c), f(c))
28.56/9.99	   H(x, x) -> G(x, x, f(k))
28.56/9.99	   A^2 -> H(f(d), f(d))
28.56/9.99	   A^2 -> H(U1(c, c), U1(c, c))
28.56/9.99	   A^2 -> H(f(e), f(e))
28.56/9.99	   A^2 -> H(f(k), f(k))
28.56/9.99	   A^2 -> H(U1(d, d), U1(d, d))
28.56/9.99	   A^2 -> H(U1(c, d), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, c), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, c))
28.56/9.99	   A^2 -> H(U1(k, c), U1(k, c))
28.56/9.99	   A^2 -> H(U1(c, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(c, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(c, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(e, e))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, d), U1(k, d))
28.56/9.99	   A^2 -> H(U1(k, d), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(d, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, d), b)
28.56/9.99	   A^2 -> H(U1(d, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(d, d), U1(d, e))
28.56/9.99	   A^2 -> H(U1(d, d), c)
28.56/9.99	   A^2 -> H(U1(d, d), U1(e, k))
28.56/9.99	   A^2 -> H(U1(d, d), U1(k, e))
28.56/9.99	   A^2 -> H(U1(d, d), e)
28.56/9.99	   A^2 -> H(f(d), d)
28.56/9.99	   A^2 -> H(f(d), k)
28.56/9.99	   A^2 -> H(U1(c, c), c)
28.56/9.99	   A^2 -> H(U1(c, c), U1(e, e))
28.56/9.99	   A^2 -> H(U1(c, c), U1(e, k))
28.56/9.99	   A^2 -> H(f(c), k)
28.56/9.99	   A^2 -> H(U1(c, c), U1(k, e))
28.56/9.99	   A^2 -> H(f(k), U1(k, k))
28.56/9.99	   A^2 -> H(f(e), e)
28.56/9.99	   A^2 -> H(U1(d, d), U1(k, k))
28.56/9.99	   A^2 -> H(d, U1(c, b))
28.56/9.99	   A^2 -> H(d, U1(d, b))
28.56/9.99	   A^2 -> H(d, U1(b, c))
28.56/9.99	   A^2 -> H(d, U1(b, d))
28.56/9.99	   A^2 -> H(d, U1(c, c))
28.56/9.99	   A^2 -> H(d, f(e))
28.56/9.99	   A^2 -> H(d, f(k))
28.56/9.99	   A^2 -> H(d, U1(d, d))
28.56/9.99	   A^2 -> H(a, U1(e, b))
28.56/9.99	   A^2 -> H(a, U1(k, b))
28.56/9.99	   A^2 -> H(a, U1(c, d))
28.56/9.99	   A^2 -> H(a, U1(d, c))
28.56/9.99	   A^2 -> H(a, U1(b, e))
28.56/9.99	   A^2 -> H(a, U1(b, k))
28.56/9.99	   A^2 -> H(a, U1(e, c))
28.56/9.99	   A^2 -> H(a, U1(k, c))
28.56/9.99	   A^2 -> H(a, U1(c, e))
28.56/9.99	   A^2 -> H(a, U1(c, k))
28.56/9.99	   A^2 -> H(a, U1(e, e))
28.56/9.99	   A^2 -> H(a, U1(k, k))
28.56/9.99	   A^2 -> H(a, U1(k, d))
28.56/9.99	   A^2 -> H(a, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, b))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, b))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, d))
28.56/9.99	   A^2 -> H(U1(e, d), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(b, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(b, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, c))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(e, e))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(e, d), U1(k, d))
28.56/9.99	   A^2 -> H(U1(e, d), U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, a), b)
28.56/9.99	   A^2 -> H(U1(e, a), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, a), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, a), c)
28.56/9.99	   A^2 -> H(U1(e, a), U1(e, k))
28.56/9.99	   A^2 -> H(U1(e, a), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, a), e)
28.56/9.99	   A^2 -> H(U1(e, a), U1(k, k))
28.56/9.99	   A^2 -> H(U1(k, a), b)
28.56/9.99	   A^2 -> H(U1(k, a), U1(e, d))
28.56/9.99	   A^2 -> H(U1(k, a), U1(d, e))
28.56/9.99	   A^2 -> H(U1(k, a), c)
28.56/9.99	   A^2 -> H(U1(k, a), U1(e, k))
28.56/9.99	   A^2 -> H(U1(k, a), U1(k, e))
28.56/9.99	   A^2 -> H(U1(k, a), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, d), b)
28.56/9.99	   A^2 -> H(U1(c, d), U1(e, d))
28.56/9.99	   A^2 -> H(U1(c, d), U1(d, e))
28.56/9.99	   A^2 -> H(U1(c, d), c)
28.56/9.99	   A^2 -> H(U1(c, d), U1(e, k))
28.56/9.99	   A^2 -> H(U1(c, d), U1(k, e))
28.56/9.99	   A^2 -> H(U1(c, d), e)
28.56/9.99	   A^2 -> H(U1(c, d), U1(k, k))
28.56/9.99	   A^2 -> H(U1(c, a), d)
28.56/9.99	   A^2 -> H(U1(c, a), k)
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, b))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, b))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, d))
28.56/9.99	   A^2 -> H(U1(d, e), U1(d, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(b, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(b, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, c))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(c, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(e, e))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, e), U1(k, d))
28.56/9.99	   A^2 -> H(U1(d, e), U1(d, k))
28.56/9.99	   A^2 -> H(U1(d, c), b)
28.56/9.99	   A^2 -> H(U1(d, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(d, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(d, c), c)
28.56/9.99	   A^2 -> H(U1(d, c), U1(e, k))
28.56/9.99	   A^2 -> H(U1(d, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(d, c), e)
28.56/9.99	   A^2 -> H(U1(d, c), U1(k, k))
28.56/9.99	   A^2 -> H(U1(d, a), d)
28.56/9.99	   A^2 -> H(U1(d, a), k)
28.56/9.99	   A^2 -> H(U1(a, e), b)
28.56/9.99	   A^2 -> H(U1(a, e), U1(e, d))
28.56/9.99	   A^2 -> H(U1(a, e), U1(d, e))
28.56/9.99	   A^2 -> H(U1(a, e), c)
28.56/9.99	   A^2 -> H(U1(a, e), U1(e, k))
28.56/9.99	   A^2 -> H(U1(a, e), U1(k, e))
28.56/9.99	   A^2 -> H(U1(a, e), e)
28.56/9.99	   A^2 -> H(U1(a, e), U1(k, k))
28.56/9.99	   A^2 -> H(U1(a, k), b)
28.56/9.99	   A^2 -> H(U1(a, k), U1(e, d))
28.56/9.99	   A^2 -> H(U1(a, k), U1(d, e))
28.56/9.99	   A^2 -> H(U1(a, k), c)
28.56/9.99	   A^2 -> H(U1(a, k), U1(e, k))
28.56/9.99	   A^2 -> H(U1(a, k), U1(k, e))
28.56/9.99	   A^2 -> H(U1(a, k), e)
28.56/9.99	   A^2 -> H(U1(a, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(a, c), d)
28.56/9.99	   A^2 -> H(U1(a, c), k)
28.56/9.99	   A^2 -> H(U1(a, d), d)
28.56/9.99	   A^2 -> H(U1(a, d), k)
28.56/9.99	   A^2 -> H(k, U1(c, b))
28.56/9.99	   A^2 -> H(k, U1(d, b))
28.56/9.99	   A^2 -> H(k, U1(b, c))
28.56/9.99	   A^2 -> H(k, U1(b, d))
28.56/9.99	   A^2 -> H(k, U1(c, c))
28.56/9.99	   A^2 -> H(k, f(e))
28.56/9.99	   A^2 -> H(k, f(k))
28.56/9.99	   A^2 -> H(k, U1(d, d))
28.56/9.99	   A^2 -> H(c, U1(e, b))
28.56/9.99	   A^2 -> H(c, U1(k, b))
28.56/9.99	   A^2 -> H(c, U1(c, d))
28.56/9.99	   A^2 -> H(c, U1(d, c))
28.56/9.99	   A^2 -> H(c, U1(b, e))
28.56/9.99	   A^2 -> H(c, U1(b, k))
28.56/9.99	   A^2 -> H(c, U1(e, c))
28.56/9.99	   A^2 -> H(c, U1(k, c))
28.56/9.99	   A^2 -> H(c, U1(c, e))
28.56/9.99	   A^2 -> H(c, U1(c, k))
28.56/9.99	   A^2 -> H(c, U1(e, e))
28.56/9.99	   A^2 -> H(c, U1(k, k))
28.56/9.99	   A^2 -> H(c, U1(k, d))
28.56/9.99	   A^2 -> H(c, U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, b))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, b))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, d))
28.56/9.99	   A^2 -> H(U1(e, k), U1(d, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(b, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(b, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, c))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(c, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(e, e))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, k))
28.56/9.99	   A^2 -> H(U1(e, k), U1(k, d))
28.56/9.99	   A^2 -> H(U1(e, k), U1(d, k))
28.56/9.99	   A^2 -> H(U1(e, c), b)
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, d))
28.56/9.99	   A^2 -> H(U1(e, c), U1(d, e))
28.56/9.99	   A^2 -> H(U1(e, c), U1(k, e))
28.56/9.99	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, c), e)
28.56/10.00	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.00	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.00	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.00	   A^2 -> H(U1(k, c), b)
28.56/10.00	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, c), c)
28.56/10.00	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, e), b)
28.56/10.00	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, e), c)
28.56/10.00	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, e), e)
28.56/10.00	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, k), b)
28.56/10.00	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, k), c)
28.56/10.00	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, k), e)
28.56/10.00	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, c), d)
28.56/10.00	   A^2 -> H(e, U1(e, b))
28.56/10.00	   A^2 -> H(e, U1(c, d))
28.56/10.00	   A^2 -> H(e, U1(d, c))
28.56/10.00	   A^2 -> H(e, U1(b, e))
28.56/10.00	   A^2 -> H(e, U1(b, k))
28.56/10.00	   A^2 -> H(e, U1(e, c))
28.56/10.00	   A^2 -> H(e, U1(c, e))
28.56/10.00	   A^2 -> H(e, U1(c, k))
28.56/10.00	   A^2 -> H(e, U1(e, e))
28.56/10.00	   A^2 -> H(e, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, e), b)
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, e), c)
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.00	   A^2 -> H(f(e), d)
28.56/10.00	   A^2 -> H(f(e), k)
28.56/10.00	   A^2 -> H(U1(k, k), b)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, k), c)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.00	   A^2 -> H(f(k), d)
28.56/10.00	   A^2 -> H(f(k), k)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(k, d), b)
28.56/10.00	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, d), c)
28.56/10.00	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.00	
28.56/10.00	The TRS R consists of the following rules:
28.56/10.00	
28.56/10.00	   f(x) -> U1(x, x)
28.56/10.00	   U1(e, x) -> x
28.56/10.00	   a -> c
28.56/10.00	   a -> d
28.56/10.00	   b -> c
28.56/10.00	   b -> d
28.56/10.00	   d -> k
28.56/10.00	   c -> e
28.56/10.00	   c -> k
28.56/10.00	
28.56/10.00	Q is empty.
28.56/10.00	We have to consider all minimal (P,Q,R)-chains.
28.56/10.00	----------------------------------------
28.56/10.00	
28.56/10.00	(1723) TransformationProof (EQUIVALENT)
28.56/10.00	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.00	
28.56/10.00	   (A^2 -> H(U1(k, k), U1(c, k)),A^2 -> H(U1(k, k), U1(c, k)))
28.56/10.00	   (A^2 -> H(U1(k, d), U1(e, k)),A^2 -> H(U1(k, d), U1(e, k)))
28.56/10.00	   (A^2 -> H(U1(k, d), U1(k, k)),A^2 -> H(U1(k, d), U1(k, k)))
28.56/10.00	
28.56/10.00	
28.56/10.00	----------------------------------------
28.56/10.00	
28.56/10.00	(1724)
28.56/10.00	Obligation:
28.56/10.00	Q DP problem:
28.56/10.00	The TRS P consists of the following rules:
28.56/10.00	
28.56/10.00	   G(d, x, x) -> A^2
28.56/10.00	   A^2 -> H(f(c), f(c))
28.56/10.00	   H(x, x) -> G(x, x, f(k))
28.56/10.00	   A^2 -> H(f(d), f(d))
28.56/10.00	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.00	   A^2 -> H(f(e), f(e))
28.56/10.00	   A^2 -> H(f(k), f(k))
28.56/10.00	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.00	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.00	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, d), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.00	   A^2 -> H(U1(k, d), U1(d, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, b))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(d, d), b)
28.56/10.00	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(d, d), c)
28.56/10.00	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.00	   A^2 -> H(U1(d, d), e)
28.56/10.00	   A^2 -> H(f(d), d)
28.56/10.00	   A^2 -> H(f(d), k)
28.56/10.00	   A^2 -> H(U1(c, c), c)
28.56/10.00	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.00	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.00	   A^2 -> H(f(c), k)
28.56/10.00	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.00	   A^2 -> H(f(k), U1(k, k))
28.56/10.00	   A^2 -> H(f(e), e)
28.56/10.00	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.00	   A^2 -> H(d, U1(c, b))
28.56/10.00	   A^2 -> H(d, U1(d, b))
28.56/10.00	   A^2 -> H(d, U1(b, c))
28.56/10.00	   A^2 -> H(d, U1(b, d))
28.56/10.00	   A^2 -> H(d, U1(c, c))
28.56/10.00	   A^2 -> H(d, f(e))
28.56/10.00	   A^2 -> H(d, f(k))
28.56/10.00	   A^2 -> H(d, U1(d, d))
28.56/10.00	   A^2 -> H(a, U1(e, b))
28.56/10.00	   A^2 -> H(a, U1(k, b))
28.56/10.00	   A^2 -> H(a, U1(c, d))
28.56/10.00	   A^2 -> H(a, U1(d, c))
28.56/10.00	   A^2 -> H(a, U1(b, e))
28.56/10.00	   A^2 -> H(a, U1(b, k))
28.56/10.00	   A^2 -> H(a, U1(e, c))
28.56/10.00	   A^2 -> H(a, U1(k, c))
28.56/10.00	   A^2 -> H(a, U1(c, e))
28.56/10.00	   A^2 -> H(a, U1(c, k))
28.56/10.00	   A^2 -> H(a, U1(e, e))
28.56/10.00	   A^2 -> H(a, U1(k, k))
28.56/10.00	   A^2 -> H(a, U1(k, d))
28.56/10.00	   A^2 -> H(a, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.00	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.00	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, a), b)
28.56/10.00	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, a), c)
28.56/10.00	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, a), e)
28.56/10.00	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, a), b)
28.56/10.00	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, a), c)
28.56/10.00	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.00	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, d), b)
28.56/10.00	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, d), c)
28.56/10.00	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, d), e)
28.56/10.00	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, a), d)
28.56/10.00	   A^2 -> H(U1(c, a), k)
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.00	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.00	   A^2 -> H(U1(d, c), b)
28.56/10.00	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(d, c), c)
28.56/10.00	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(d, c), e)
28.56/10.00	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, a), d)
28.56/10.00	   A^2 -> H(U1(d, a), k)
28.56/10.00	   A^2 -> H(U1(a, e), b)
28.56/10.00	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(a, e), c)
28.56/10.00	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(a, e), e)
28.56/10.00	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(a, k), b)
28.56/10.00	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(a, k), c)
28.56/10.00	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.00	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.00	   A^2 -> H(U1(a, k), e)
28.56/10.00	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(a, c), d)
28.56/10.00	   A^2 -> H(U1(a, c), k)
28.56/10.00	   A^2 -> H(U1(a, d), d)
28.56/10.00	   A^2 -> H(U1(a, d), k)
28.56/10.00	   A^2 -> H(k, U1(c, b))
28.56/10.00	   A^2 -> H(k, U1(d, b))
28.56/10.00	   A^2 -> H(k, U1(b, c))
28.56/10.00	   A^2 -> H(k, U1(b, d))
28.56/10.00	   A^2 -> H(k, U1(c, c))
28.56/10.00	   A^2 -> H(k, f(e))
28.56/10.00	   A^2 -> H(k, f(k))
28.56/10.00	   A^2 -> H(k, U1(d, d))
28.56/10.00	   A^2 -> H(c, U1(e, b))
28.56/10.00	   A^2 -> H(c, U1(k, b))
28.56/10.00	   A^2 -> H(c, U1(c, d))
28.56/10.00	   A^2 -> H(c, U1(d, c))
28.56/10.00	   A^2 -> H(c, U1(b, e))
28.56/10.00	   A^2 -> H(c, U1(b, k))
28.56/10.00	   A^2 -> H(c, U1(e, c))
28.56/10.00	   A^2 -> H(c, U1(k, c))
28.56/10.00	   A^2 -> H(c, U1(c, e))
28.56/10.00	   A^2 -> H(c, U1(c, k))
28.56/10.00	   A^2 -> H(c, U1(e, e))
28.56/10.00	   A^2 -> H(c, U1(k, k))
28.56/10.00	   A^2 -> H(c, U1(k, d))
28.56/10.00	   A^2 -> H(c, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, c), b)
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, c), e)
28.56/10.00	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.00	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.00	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.00	   A^2 -> H(U1(k, c), b)
28.56/10.00	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, c), c)
28.56/10.00	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, e), b)
28.56/10.00	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, e), c)
28.56/10.00	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, e), e)
28.56/10.00	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, k), b)
28.56/10.00	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, k), c)
28.56/10.00	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, k), e)
28.56/10.00	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, c), d)
28.56/10.00	   A^2 -> H(e, U1(e, b))
28.56/10.00	   A^2 -> H(e, U1(c, d))
28.56/10.00	   A^2 -> H(e, U1(d, c))
28.56/10.00	   A^2 -> H(e, U1(b, e))
28.56/10.00	   A^2 -> H(e, U1(b, k))
28.56/10.00	   A^2 -> H(e, U1(e, c))
28.56/10.00	   A^2 -> H(e, U1(c, e))
28.56/10.00	   A^2 -> H(e, U1(c, k))
28.56/10.00	   A^2 -> H(e, U1(e, e))
28.56/10.00	   A^2 -> H(e, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, e), b)
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, e), c)
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.00	   A^2 -> H(f(e), d)
28.56/10.00	   A^2 -> H(f(e), k)
28.56/10.00	   A^2 -> H(U1(k, k), b)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, k), c)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.00	   A^2 -> H(f(k), d)
28.56/10.00	   A^2 -> H(f(k), k)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(k, d), b)
28.56/10.00	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, d), c)
28.56/10.00	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.00	
28.56/10.00	The TRS R consists of the following rules:
28.56/10.00	
28.56/10.00	   f(x) -> U1(x, x)
28.56/10.00	   U1(e, x) -> x
28.56/10.00	   a -> c
28.56/10.00	   a -> d
28.56/10.00	   b -> c
28.56/10.00	   b -> d
28.56/10.00	   d -> k
28.56/10.00	   c -> e
28.56/10.00	   c -> k
28.56/10.00	
28.56/10.00	Q is empty.
28.56/10.00	We have to consider all minimal (P,Q,R)-chains.
28.56/10.00	----------------------------------------
28.56/10.00	
28.56/10.00	(1725) TransformationProof (EQUIVALENT)
28.56/10.00	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.00	
28.56/10.00	   (A^2 -> H(U1(k, k), U1(e, e)),A^2 -> H(U1(k, k), U1(e, e)))
28.56/10.00	   (A^2 -> H(U1(k, d), e),A^2 -> H(U1(k, d), e))
28.56/10.00	
28.56/10.00	
28.56/10.00	----------------------------------------
28.56/10.00	
28.56/10.00	(1726)
28.56/10.00	Obligation:
28.56/10.00	Q DP problem:
28.56/10.00	The TRS P consists of the following rules:
28.56/10.00	
28.56/10.00	   G(d, x, x) -> A^2
28.56/10.00	   A^2 -> H(f(c), f(c))
28.56/10.00	   H(x, x) -> G(x, x, f(k))
28.56/10.00	   A^2 -> H(f(d), f(d))
28.56/10.00	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.00	   A^2 -> H(f(e), f(e))
28.56/10.00	   A^2 -> H(f(k), f(k))
28.56/10.00	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.00	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.00	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.00	   A^2 -> H(U1(k, d), U1(d, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, b))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(d, d), b)
28.56/10.00	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(d, d), c)
28.56/10.00	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.00	   A^2 -> H(U1(d, d), e)
28.56/10.00	   A^2 -> H(f(d), d)
28.56/10.00	   A^2 -> H(f(d), k)
28.56/10.00	   A^2 -> H(U1(c, c), c)
28.56/10.00	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.00	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.00	   A^2 -> H(f(c), k)
28.56/10.00	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.00	   A^2 -> H(f(k), U1(k, k))
28.56/10.00	   A^2 -> H(f(e), e)
28.56/10.00	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.00	   A^2 -> H(d, U1(c, b))
28.56/10.00	   A^2 -> H(d, U1(d, b))
28.56/10.00	   A^2 -> H(d, U1(b, c))
28.56/10.00	   A^2 -> H(d, U1(b, d))
28.56/10.00	   A^2 -> H(d, U1(c, c))
28.56/10.00	   A^2 -> H(d, f(e))
28.56/10.00	   A^2 -> H(d, f(k))
28.56/10.00	   A^2 -> H(d, U1(d, d))
28.56/10.00	   A^2 -> H(a, U1(e, b))
28.56/10.00	   A^2 -> H(a, U1(k, b))
28.56/10.00	   A^2 -> H(a, U1(c, d))
28.56/10.00	   A^2 -> H(a, U1(d, c))
28.56/10.00	   A^2 -> H(a, U1(b, e))
28.56/10.00	   A^2 -> H(a, U1(b, k))
28.56/10.00	   A^2 -> H(a, U1(e, c))
28.56/10.00	   A^2 -> H(a, U1(k, c))
28.56/10.00	   A^2 -> H(a, U1(c, e))
28.56/10.00	   A^2 -> H(a, U1(c, k))
28.56/10.00	   A^2 -> H(a, U1(e, e))
28.56/10.00	   A^2 -> H(a, U1(k, k))
28.56/10.00	   A^2 -> H(a, U1(k, d))
28.56/10.00	   A^2 -> H(a, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.00	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.00	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, a), b)
28.56/10.00	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, a), c)
28.56/10.00	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, a), e)
28.56/10.00	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, a), b)
28.56/10.00	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, a), c)
28.56/10.00	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.00	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, d), b)
28.56/10.00	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, d), c)
28.56/10.00	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, d), e)
28.56/10.00	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, a), d)
28.56/10.00	   A^2 -> H(U1(c, a), k)
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.00	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.00	   A^2 -> H(U1(d, c), b)
28.56/10.00	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(d, c), c)
28.56/10.00	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(d, c), e)
28.56/10.00	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, a), d)
28.56/10.00	   A^2 -> H(U1(d, a), k)
28.56/10.00	   A^2 -> H(U1(a, e), b)
28.56/10.00	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(a, e), c)
28.56/10.00	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(a, e), e)
28.56/10.00	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(a, k), b)
28.56/10.00	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(a, k), c)
28.56/10.00	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.00	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.00	   A^2 -> H(U1(a, k), e)
28.56/10.00	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(a, c), d)
28.56/10.00	   A^2 -> H(U1(a, c), k)
28.56/10.00	   A^2 -> H(U1(a, d), d)
28.56/10.00	   A^2 -> H(U1(a, d), k)
28.56/10.00	   A^2 -> H(k, U1(c, b))
28.56/10.00	   A^2 -> H(k, U1(d, b))
28.56/10.00	   A^2 -> H(k, U1(b, c))
28.56/10.00	   A^2 -> H(k, U1(b, d))
28.56/10.00	   A^2 -> H(k, U1(c, c))
28.56/10.00	   A^2 -> H(k, f(e))
28.56/10.00	   A^2 -> H(k, f(k))
28.56/10.00	   A^2 -> H(k, U1(d, d))
28.56/10.00	   A^2 -> H(c, U1(e, b))
28.56/10.00	   A^2 -> H(c, U1(k, b))
28.56/10.00	   A^2 -> H(c, U1(c, d))
28.56/10.00	   A^2 -> H(c, U1(d, c))
28.56/10.00	   A^2 -> H(c, U1(b, e))
28.56/10.00	   A^2 -> H(c, U1(b, k))
28.56/10.00	   A^2 -> H(c, U1(e, c))
28.56/10.00	   A^2 -> H(c, U1(k, c))
28.56/10.00	   A^2 -> H(c, U1(c, e))
28.56/10.00	   A^2 -> H(c, U1(c, k))
28.56/10.00	   A^2 -> H(c, U1(e, e))
28.56/10.00	   A^2 -> H(c, U1(k, k))
28.56/10.00	   A^2 -> H(c, U1(k, d))
28.56/10.00	   A^2 -> H(c, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, c), b)
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, c), e)
28.56/10.00	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.00	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.00	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.00	   A^2 -> H(U1(k, c), b)
28.56/10.00	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, c), c)
28.56/10.00	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, e), b)
28.56/10.00	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, e), c)
28.56/10.00	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, e), e)
28.56/10.00	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, k), b)
28.56/10.00	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, k), c)
28.56/10.00	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, k), e)
28.56/10.00	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, c), d)
28.56/10.00	   A^2 -> H(e, U1(e, b))
28.56/10.00	   A^2 -> H(e, U1(c, d))
28.56/10.00	   A^2 -> H(e, U1(d, c))
28.56/10.00	   A^2 -> H(e, U1(b, e))
28.56/10.00	   A^2 -> H(e, U1(b, k))
28.56/10.00	   A^2 -> H(e, U1(e, c))
28.56/10.00	   A^2 -> H(e, U1(c, e))
28.56/10.00	   A^2 -> H(e, U1(c, k))
28.56/10.00	   A^2 -> H(e, U1(e, e))
28.56/10.00	   A^2 -> H(e, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, e), b)
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, e), c)
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.00	   A^2 -> H(f(e), d)
28.56/10.00	   A^2 -> H(f(e), k)
28.56/10.00	   A^2 -> H(U1(k, k), b)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, k), c)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.00	   A^2 -> H(f(k), d)
28.56/10.00	   A^2 -> H(f(k), k)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(k, d), b)
28.56/10.00	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, d), c)
28.56/10.00	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.00	   A^2 -> H(U1(k, d), e)
28.56/10.00	
28.56/10.00	The TRS R consists of the following rules:
28.56/10.00	
28.56/10.00	   f(x) -> U1(x, x)
28.56/10.00	   U1(e, x) -> x
28.56/10.00	   a -> c
28.56/10.00	   a -> d
28.56/10.00	   b -> c
28.56/10.00	   b -> d
28.56/10.00	   d -> k
28.56/10.00	   c -> e
28.56/10.00	   c -> k
28.56/10.00	
28.56/10.00	Q is empty.
28.56/10.00	We have to consider all minimal (P,Q,R)-chains.
28.56/10.00	----------------------------------------
28.56/10.00	
28.56/10.00	(1727) DependencyGraphProof (EQUIVALENT)
28.56/10.00	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/10.00	----------------------------------------
28.56/10.00	
28.56/10.00	(1728)
28.56/10.00	Obligation:
28.56/10.00	Q DP problem:
28.56/10.00	The TRS P consists of the following rules:
28.56/10.00	
28.56/10.00	   A^2 -> H(f(c), f(c))
28.56/10.00	   H(x, x) -> G(x, x, f(k))
28.56/10.00	   G(d, x, x) -> A^2
28.56/10.00	   A^2 -> H(f(d), f(d))
28.56/10.00	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.00	   A^2 -> H(f(e), f(e))
28.56/10.00	   A^2 -> H(f(k), f(k))
28.56/10.00	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.00	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.00	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.00	   A^2 -> H(U1(k, d), U1(d, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, b))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(d, d), b)
28.56/10.00	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(d, d), c)
28.56/10.00	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.00	   A^2 -> H(U1(d, d), e)
28.56/10.00	   A^2 -> H(f(d), d)
28.56/10.00	   A^2 -> H(f(d), k)
28.56/10.00	   A^2 -> H(U1(c, c), c)
28.56/10.00	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.00	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.00	   A^2 -> H(f(c), k)
28.56/10.00	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.00	   A^2 -> H(f(k), U1(k, k))
28.56/10.00	   A^2 -> H(f(e), e)
28.56/10.00	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.00	   A^2 -> H(d, U1(c, b))
28.56/10.00	   A^2 -> H(d, U1(d, b))
28.56/10.00	   A^2 -> H(d, U1(b, c))
28.56/10.00	   A^2 -> H(d, U1(b, d))
28.56/10.00	   A^2 -> H(d, U1(c, c))
28.56/10.00	   A^2 -> H(d, f(e))
28.56/10.00	   A^2 -> H(d, f(k))
28.56/10.00	   A^2 -> H(d, U1(d, d))
28.56/10.00	   A^2 -> H(a, U1(e, b))
28.56/10.00	   A^2 -> H(a, U1(k, b))
28.56/10.00	   A^2 -> H(a, U1(c, d))
28.56/10.00	   A^2 -> H(a, U1(d, c))
28.56/10.00	   A^2 -> H(a, U1(b, e))
28.56/10.00	   A^2 -> H(a, U1(b, k))
28.56/10.00	   A^2 -> H(a, U1(e, c))
28.56/10.00	   A^2 -> H(a, U1(k, c))
28.56/10.00	   A^2 -> H(a, U1(c, e))
28.56/10.00	   A^2 -> H(a, U1(c, k))
28.56/10.00	   A^2 -> H(a, U1(e, e))
28.56/10.00	   A^2 -> H(a, U1(k, k))
28.56/10.00	   A^2 -> H(a, U1(k, d))
28.56/10.00	   A^2 -> H(a, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.00	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.00	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, a), b)
28.56/10.00	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, a), c)
28.56/10.00	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, a), e)
28.56/10.00	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, a), b)
28.56/10.00	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, a), c)
28.56/10.00	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.00	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, d), b)
28.56/10.00	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, d), c)
28.56/10.00	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, d), e)
28.56/10.00	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, a), d)
28.56/10.00	   A^2 -> H(U1(c, a), k)
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.00	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.00	   A^2 -> H(U1(d, c), b)
28.56/10.00	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(d, c), c)
28.56/10.00	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(d, c), e)
28.56/10.00	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, a), d)
28.56/10.00	   A^2 -> H(U1(d, a), k)
28.56/10.00	   A^2 -> H(U1(a, e), b)
28.56/10.00	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(a, e), c)
28.56/10.00	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(a, e), e)
28.56/10.00	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(a, k), b)
28.56/10.00	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(a, k), c)
28.56/10.00	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.00	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.00	   A^2 -> H(U1(a, k), e)
28.56/10.00	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(a, c), d)
28.56/10.00	   A^2 -> H(U1(a, c), k)
28.56/10.00	   A^2 -> H(U1(a, d), d)
28.56/10.00	   A^2 -> H(U1(a, d), k)
28.56/10.00	   A^2 -> H(k, U1(c, b))
28.56/10.00	   A^2 -> H(k, U1(d, b))
28.56/10.00	   A^2 -> H(k, U1(b, c))
28.56/10.00	   A^2 -> H(k, U1(b, d))
28.56/10.00	   A^2 -> H(k, U1(c, c))
28.56/10.00	   A^2 -> H(k, f(e))
28.56/10.00	   A^2 -> H(k, f(k))
28.56/10.00	   A^2 -> H(k, U1(d, d))
28.56/10.00	   A^2 -> H(c, U1(e, b))
28.56/10.00	   A^2 -> H(c, U1(k, b))
28.56/10.00	   A^2 -> H(c, U1(c, d))
28.56/10.00	   A^2 -> H(c, U1(d, c))
28.56/10.00	   A^2 -> H(c, U1(b, e))
28.56/10.00	   A^2 -> H(c, U1(b, k))
28.56/10.00	   A^2 -> H(c, U1(e, c))
28.56/10.00	   A^2 -> H(c, U1(k, c))
28.56/10.00	   A^2 -> H(c, U1(c, e))
28.56/10.00	   A^2 -> H(c, U1(c, k))
28.56/10.00	   A^2 -> H(c, U1(e, e))
28.56/10.00	   A^2 -> H(c, U1(k, k))
28.56/10.00	   A^2 -> H(c, U1(k, d))
28.56/10.00	   A^2 -> H(c, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, c), b)
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, c), e)
28.56/10.00	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.00	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.00	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.00	   A^2 -> H(U1(k, c), b)
28.56/10.00	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, c), c)
28.56/10.00	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, e), b)
28.56/10.00	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, e), c)
28.56/10.00	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, e), e)
28.56/10.00	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, k), b)
28.56/10.00	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, k), c)
28.56/10.00	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, k), e)
28.56/10.00	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, c), d)
28.56/10.00	   A^2 -> H(e, U1(e, b))
28.56/10.00	   A^2 -> H(e, U1(c, d))
28.56/10.00	   A^2 -> H(e, U1(d, c))
28.56/10.00	   A^2 -> H(e, U1(b, e))
28.56/10.00	   A^2 -> H(e, U1(b, k))
28.56/10.00	   A^2 -> H(e, U1(e, c))
28.56/10.00	   A^2 -> H(e, U1(c, e))
28.56/10.00	   A^2 -> H(e, U1(c, k))
28.56/10.00	   A^2 -> H(e, U1(e, e))
28.56/10.00	   A^2 -> H(e, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, e), b)
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, e), c)
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.00	   A^2 -> H(f(e), d)
28.56/10.00	   A^2 -> H(f(e), k)
28.56/10.00	   A^2 -> H(U1(k, k), b)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, k), c)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.00	   A^2 -> H(f(k), d)
28.56/10.00	   A^2 -> H(f(k), k)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(k, d), b)
28.56/10.00	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, d), c)
28.56/10.00	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.00	
28.56/10.00	The TRS R consists of the following rules:
28.56/10.00	
28.56/10.00	   f(x) -> U1(x, x)
28.56/10.00	   U1(e, x) -> x
28.56/10.00	   a -> c
28.56/10.00	   a -> d
28.56/10.00	   b -> c
28.56/10.00	   b -> d
28.56/10.00	   d -> k
28.56/10.00	   c -> e
28.56/10.00	   c -> k
28.56/10.00	
28.56/10.00	Q is empty.
28.56/10.00	We have to consider all minimal (P,Q,R)-chains.
28.56/10.00	----------------------------------------
28.56/10.00	
28.56/10.00	(1729) TransformationProof (EQUIVALENT)
28.56/10.00	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.00	
28.56/10.00	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.56/10.00	
28.56/10.00	
28.56/10.00	----------------------------------------
28.56/10.00	
28.56/10.00	(1730)
28.56/10.00	Obligation:
28.56/10.00	Q DP problem:
28.56/10.00	The TRS P consists of the following rules:
28.56/10.00	
28.56/10.00	   A^2 -> H(f(c), f(c))
28.56/10.00	   H(x, x) -> G(x, x, f(k))
28.56/10.00	   G(d, x, x) -> A^2
28.56/10.00	   A^2 -> H(f(d), f(d))
28.56/10.00	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.00	   A^2 -> H(f(e), f(e))
28.56/10.00	   A^2 -> H(f(k), f(k))
28.56/10.00	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.00	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.00	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.00	   A^2 -> H(U1(k, d), U1(d, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, b))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(d, d), b)
28.56/10.00	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(d, d), c)
28.56/10.00	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.00	   A^2 -> H(U1(d, d), e)
28.56/10.00	   A^2 -> H(f(d), d)
28.56/10.00	   A^2 -> H(f(d), k)
28.56/10.00	   A^2 -> H(U1(c, c), c)
28.56/10.00	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.00	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.00	   A^2 -> H(f(c), k)
28.56/10.00	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.00	   A^2 -> H(f(k), U1(k, k))
28.56/10.00	   A^2 -> H(f(e), e)
28.56/10.00	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.00	   A^2 -> H(d, U1(c, b))
28.56/10.00	   A^2 -> H(d, U1(d, b))
28.56/10.00	   A^2 -> H(d, U1(b, c))
28.56/10.00	   A^2 -> H(d, U1(b, d))
28.56/10.00	   A^2 -> H(d, U1(c, c))
28.56/10.00	   A^2 -> H(d, f(e))
28.56/10.00	   A^2 -> H(d, f(k))
28.56/10.00	   A^2 -> H(d, U1(d, d))
28.56/10.00	   A^2 -> H(a, U1(e, b))
28.56/10.00	   A^2 -> H(a, U1(k, b))
28.56/10.00	   A^2 -> H(a, U1(c, d))
28.56/10.00	   A^2 -> H(a, U1(d, c))
28.56/10.00	   A^2 -> H(a, U1(b, e))
28.56/10.00	   A^2 -> H(a, U1(b, k))
28.56/10.00	   A^2 -> H(a, U1(e, c))
28.56/10.00	   A^2 -> H(a, U1(k, c))
28.56/10.00	   A^2 -> H(a, U1(c, e))
28.56/10.00	   A^2 -> H(a, U1(c, k))
28.56/10.00	   A^2 -> H(a, U1(e, e))
28.56/10.00	   A^2 -> H(a, U1(k, k))
28.56/10.00	   A^2 -> H(a, U1(k, d))
28.56/10.00	   A^2 -> H(a, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.00	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.00	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, a), b)
28.56/10.00	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, a), c)
28.56/10.00	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, a), e)
28.56/10.00	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, a), b)
28.56/10.00	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, a), c)
28.56/10.00	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.00	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, d), b)
28.56/10.00	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, d), c)
28.56/10.00	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, d), e)
28.56/10.00	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, a), d)
28.56/10.00	   A^2 -> H(U1(c, a), k)
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.00	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.00	   A^2 -> H(U1(d, c), b)
28.56/10.00	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(d, c), c)
28.56/10.00	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(d, c), e)
28.56/10.00	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, a), d)
28.56/10.00	   A^2 -> H(U1(d, a), k)
28.56/10.00	   A^2 -> H(U1(a, e), b)
28.56/10.00	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(a, e), c)
28.56/10.00	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(a, e), e)
28.56/10.00	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(a, k), b)
28.56/10.00	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(a, k), c)
28.56/10.00	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.00	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.00	   A^2 -> H(U1(a, k), e)
28.56/10.00	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(a, c), d)
28.56/10.00	   A^2 -> H(U1(a, c), k)
28.56/10.00	   A^2 -> H(U1(a, d), d)
28.56/10.00	   A^2 -> H(U1(a, d), k)
28.56/10.00	   A^2 -> H(k, U1(c, b))
28.56/10.00	   A^2 -> H(k, U1(d, b))
28.56/10.00	   A^2 -> H(k, U1(b, c))
28.56/10.00	   A^2 -> H(k, U1(b, d))
28.56/10.00	   A^2 -> H(k, U1(c, c))
28.56/10.00	   A^2 -> H(k, f(e))
28.56/10.00	   A^2 -> H(k, f(k))
28.56/10.00	   A^2 -> H(k, U1(d, d))
28.56/10.00	   A^2 -> H(c, U1(e, b))
28.56/10.00	   A^2 -> H(c, U1(k, b))
28.56/10.00	   A^2 -> H(c, U1(c, d))
28.56/10.00	   A^2 -> H(c, U1(d, c))
28.56/10.00	   A^2 -> H(c, U1(b, e))
28.56/10.00	   A^2 -> H(c, U1(b, k))
28.56/10.00	   A^2 -> H(c, U1(e, c))
28.56/10.00	   A^2 -> H(c, U1(k, c))
28.56/10.00	   A^2 -> H(c, U1(c, e))
28.56/10.00	   A^2 -> H(c, U1(c, k))
28.56/10.00	   A^2 -> H(c, U1(e, e))
28.56/10.00	   A^2 -> H(c, U1(k, k))
28.56/10.00	   A^2 -> H(c, U1(k, d))
28.56/10.00	   A^2 -> H(c, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, c), b)
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, c), e)
28.56/10.00	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.00	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.00	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.00	   A^2 -> H(U1(k, c), b)
28.56/10.00	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, c), c)
28.56/10.00	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, e), b)
28.56/10.00	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, e), c)
28.56/10.00	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, e), e)
28.56/10.00	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, k), b)
28.56/10.00	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, k), c)
28.56/10.00	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, k), e)
28.56/10.00	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, c), d)
28.56/10.00	   A^2 -> H(e, U1(e, b))
28.56/10.00	   A^2 -> H(e, U1(c, d))
28.56/10.00	   A^2 -> H(e, U1(d, c))
28.56/10.00	   A^2 -> H(e, U1(b, e))
28.56/10.00	   A^2 -> H(e, U1(b, k))
28.56/10.00	   A^2 -> H(e, U1(e, c))
28.56/10.00	   A^2 -> H(e, U1(c, e))
28.56/10.00	   A^2 -> H(e, U1(c, k))
28.56/10.00	   A^2 -> H(e, U1(e, e))
28.56/10.00	   A^2 -> H(e, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, e), b)
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, e), c)
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.00	   A^2 -> H(f(e), d)
28.56/10.00	   A^2 -> H(f(e), k)
28.56/10.00	   A^2 -> H(U1(k, k), b)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, k), c)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.00	   A^2 -> H(f(k), d)
28.56/10.00	   A^2 -> H(f(k), k)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(k, d), b)
28.56/10.00	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, d), c)
28.56/10.00	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.00	
28.56/10.00	The TRS R consists of the following rules:
28.56/10.00	
28.56/10.00	   f(x) -> U1(x, x)
28.56/10.00	   U1(e, x) -> x
28.56/10.00	   a -> c
28.56/10.00	   a -> d
28.56/10.00	   b -> c
28.56/10.00	   b -> d
28.56/10.00	   d -> k
28.56/10.00	   c -> e
28.56/10.00	   c -> k
28.56/10.00	
28.56/10.00	Q is empty.
28.56/10.00	We have to consider all minimal (P,Q,R)-chains.
28.56/10.00	----------------------------------------
28.56/10.00	
28.56/10.00	(1731) TransformationProof (EQUIVALENT)
28.56/10.00	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.00	
28.56/10.00	   (A^2 -> H(U1(k, k), U1(d, k)),A^2 -> H(U1(k, k), U1(d, k)))
28.56/10.00	   (A^2 -> H(U1(k, d), U1(k, k)),A^2 -> H(U1(k, d), U1(k, k)))
28.56/10.00	
28.56/10.00	
28.56/10.00	----------------------------------------
28.56/10.00	
28.56/10.00	(1732)
28.56/10.00	Obligation:
28.56/10.00	Q DP problem:
28.56/10.00	The TRS P consists of the following rules:
28.56/10.00	
28.56/10.00	   A^2 -> H(f(c), f(c))
28.56/10.00	   H(x, x) -> G(x, x, f(k))
28.56/10.00	   G(d, x, x) -> A^2
28.56/10.00	   A^2 -> H(f(d), f(d))
28.56/10.00	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.00	   A^2 -> H(f(e), f(e))
28.56/10.00	   A^2 -> H(f(k), f(k))
28.56/10.00	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.00	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.00	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, b))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(d, d), b)
28.56/10.00	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(d, d), c)
28.56/10.00	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.00	   A^2 -> H(U1(d, d), e)
28.56/10.00	   A^2 -> H(f(d), d)
28.56/10.00	   A^2 -> H(f(d), k)
28.56/10.00	   A^2 -> H(U1(c, c), c)
28.56/10.00	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.00	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.00	   A^2 -> H(f(c), k)
28.56/10.00	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.00	   A^2 -> H(f(k), U1(k, k))
28.56/10.00	   A^2 -> H(f(e), e)
28.56/10.00	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.00	   A^2 -> H(d, U1(c, b))
28.56/10.00	   A^2 -> H(d, U1(d, b))
28.56/10.00	   A^2 -> H(d, U1(b, c))
28.56/10.00	   A^2 -> H(d, U1(b, d))
28.56/10.00	   A^2 -> H(d, U1(c, c))
28.56/10.00	   A^2 -> H(d, f(e))
28.56/10.00	   A^2 -> H(d, f(k))
28.56/10.00	   A^2 -> H(d, U1(d, d))
28.56/10.00	   A^2 -> H(a, U1(e, b))
28.56/10.00	   A^2 -> H(a, U1(k, b))
28.56/10.00	   A^2 -> H(a, U1(c, d))
28.56/10.00	   A^2 -> H(a, U1(d, c))
28.56/10.00	   A^2 -> H(a, U1(b, e))
28.56/10.00	   A^2 -> H(a, U1(b, k))
28.56/10.00	   A^2 -> H(a, U1(e, c))
28.56/10.00	   A^2 -> H(a, U1(k, c))
28.56/10.00	   A^2 -> H(a, U1(c, e))
28.56/10.00	   A^2 -> H(a, U1(c, k))
28.56/10.00	   A^2 -> H(a, U1(e, e))
28.56/10.00	   A^2 -> H(a, U1(k, k))
28.56/10.00	   A^2 -> H(a, U1(k, d))
28.56/10.00	   A^2 -> H(a, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.00	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.00	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, a), b)
28.56/10.00	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, a), c)
28.56/10.00	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, a), e)
28.56/10.00	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, a), b)
28.56/10.00	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, a), c)
28.56/10.00	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.00	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, d), b)
28.56/10.00	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, d), c)
28.56/10.00	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, d), e)
28.56/10.00	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, a), d)
28.56/10.00	   A^2 -> H(U1(c, a), k)
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.00	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.00	   A^2 -> H(U1(d, c), b)
28.56/10.00	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(d, c), c)
28.56/10.00	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(d, c), e)
28.56/10.00	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, a), d)
28.56/10.00	   A^2 -> H(U1(d, a), k)
28.56/10.00	   A^2 -> H(U1(a, e), b)
28.56/10.00	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(a, e), c)
28.56/10.00	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(a, e), e)
28.56/10.00	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(a, k), b)
28.56/10.00	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(a, k), c)
28.56/10.00	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.00	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.00	   A^2 -> H(U1(a, k), e)
28.56/10.00	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(a, c), d)
28.56/10.00	   A^2 -> H(U1(a, c), k)
28.56/10.00	   A^2 -> H(U1(a, d), d)
28.56/10.00	   A^2 -> H(U1(a, d), k)
28.56/10.00	   A^2 -> H(k, U1(c, b))
28.56/10.00	   A^2 -> H(k, U1(d, b))
28.56/10.00	   A^2 -> H(k, U1(b, c))
28.56/10.00	   A^2 -> H(k, U1(b, d))
28.56/10.00	   A^2 -> H(k, U1(c, c))
28.56/10.00	   A^2 -> H(k, f(e))
28.56/10.00	   A^2 -> H(k, f(k))
28.56/10.00	   A^2 -> H(k, U1(d, d))
28.56/10.00	   A^2 -> H(c, U1(e, b))
28.56/10.00	   A^2 -> H(c, U1(k, b))
28.56/10.00	   A^2 -> H(c, U1(c, d))
28.56/10.00	   A^2 -> H(c, U1(d, c))
28.56/10.00	   A^2 -> H(c, U1(b, e))
28.56/10.00	   A^2 -> H(c, U1(b, k))
28.56/10.00	   A^2 -> H(c, U1(e, c))
28.56/10.00	   A^2 -> H(c, U1(k, c))
28.56/10.00	   A^2 -> H(c, U1(c, e))
28.56/10.00	   A^2 -> H(c, U1(c, k))
28.56/10.00	   A^2 -> H(c, U1(e, e))
28.56/10.00	   A^2 -> H(c, U1(k, k))
28.56/10.00	   A^2 -> H(c, U1(k, d))
28.56/10.00	   A^2 -> H(c, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, c), b)
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, c), e)
28.56/10.00	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.00	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.00	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.00	   A^2 -> H(U1(k, c), b)
28.56/10.00	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, c), c)
28.56/10.00	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, e), b)
28.56/10.00	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, e), c)
28.56/10.00	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, e), e)
28.56/10.00	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, k), b)
28.56/10.00	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, k), c)
28.56/10.00	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, k), e)
28.56/10.00	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, c), d)
28.56/10.00	   A^2 -> H(e, U1(e, b))
28.56/10.00	   A^2 -> H(e, U1(c, d))
28.56/10.00	   A^2 -> H(e, U1(d, c))
28.56/10.00	   A^2 -> H(e, U1(b, e))
28.56/10.00	   A^2 -> H(e, U1(b, k))
28.56/10.00	   A^2 -> H(e, U1(e, c))
28.56/10.00	   A^2 -> H(e, U1(c, e))
28.56/10.00	   A^2 -> H(e, U1(c, k))
28.56/10.00	   A^2 -> H(e, U1(e, e))
28.56/10.00	   A^2 -> H(e, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, e), b)
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, e), c)
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.00	   A^2 -> H(f(e), d)
28.56/10.00	   A^2 -> H(f(e), k)
28.56/10.00	   A^2 -> H(U1(k, k), b)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, k), c)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.00	   A^2 -> H(f(k), d)
28.56/10.00	   A^2 -> H(f(k), k)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(k, d), b)
28.56/10.00	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, d), c)
28.56/10.00	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.00	
28.56/10.00	The TRS R consists of the following rules:
28.56/10.00	
28.56/10.00	   f(x) -> U1(x, x)
28.56/10.00	   U1(e, x) -> x
28.56/10.00	   a -> c
28.56/10.00	   a -> d
28.56/10.00	   b -> c
28.56/10.00	   b -> d
28.56/10.00	   d -> k
28.56/10.00	   c -> e
28.56/10.00	   c -> k
28.56/10.00	
28.56/10.00	Q is empty.
28.56/10.00	We have to consider all minimal (P,Q,R)-chains.
28.56/10.00	----------------------------------------
28.56/10.00	
28.56/10.00	(1733) TransformationProof (EQUIVALENT)
28.56/10.00	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.00	
28.56/10.00	   (A^2 -> H(U1(k, k), U1(e, b)),A^2 -> H(U1(k, k), U1(e, b)))
28.56/10.00	   (A^2 -> H(U1(d, k), b),A^2 -> H(U1(d, k), b))
28.56/10.00	   (A^2 -> H(U1(d, k), U1(e, c)),A^2 -> H(U1(d, k), U1(e, c)))
28.56/10.00	   (A^2 -> H(U1(d, k), U1(e, d)),A^2 -> H(U1(d, k), U1(e, d)))
28.56/10.00	
28.56/10.00	
28.56/10.00	----------------------------------------
28.56/10.00	
28.56/10.00	(1734)
28.56/10.00	Obligation:
28.56/10.00	Q DP problem:
28.56/10.00	The TRS P consists of the following rules:
28.56/10.00	
28.56/10.00	   A^2 -> H(f(c), f(c))
28.56/10.00	   H(x, x) -> G(x, x, f(k))
28.56/10.00	   G(d, x, x) -> A^2
28.56/10.00	   A^2 -> H(f(d), f(d))
28.56/10.00	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.00	   A^2 -> H(f(e), f(e))
28.56/10.00	   A^2 -> H(f(k), f(k))
28.56/10.00	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.00	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.00	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(d, d), b)
28.56/10.00	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(d, d), c)
28.56/10.00	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.00	   A^2 -> H(U1(d, d), e)
28.56/10.00	   A^2 -> H(f(d), d)
28.56/10.00	   A^2 -> H(f(d), k)
28.56/10.00	   A^2 -> H(U1(c, c), c)
28.56/10.00	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.00	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.00	   A^2 -> H(f(c), k)
28.56/10.00	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.00	   A^2 -> H(f(k), U1(k, k))
28.56/10.00	   A^2 -> H(f(e), e)
28.56/10.00	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.00	   A^2 -> H(d, U1(c, b))
28.56/10.00	   A^2 -> H(d, U1(d, b))
28.56/10.00	   A^2 -> H(d, U1(b, c))
28.56/10.00	   A^2 -> H(d, U1(b, d))
28.56/10.00	   A^2 -> H(d, U1(c, c))
28.56/10.00	   A^2 -> H(d, f(e))
28.56/10.00	   A^2 -> H(d, f(k))
28.56/10.00	   A^2 -> H(d, U1(d, d))
28.56/10.00	   A^2 -> H(a, U1(e, b))
28.56/10.00	   A^2 -> H(a, U1(k, b))
28.56/10.00	   A^2 -> H(a, U1(c, d))
28.56/10.00	   A^2 -> H(a, U1(d, c))
28.56/10.00	   A^2 -> H(a, U1(b, e))
28.56/10.00	   A^2 -> H(a, U1(b, k))
28.56/10.00	   A^2 -> H(a, U1(e, c))
28.56/10.00	   A^2 -> H(a, U1(k, c))
28.56/10.00	   A^2 -> H(a, U1(c, e))
28.56/10.00	   A^2 -> H(a, U1(c, k))
28.56/10.00	   A^2 -> H(a, U1(e, e))
28.56/10.00	   A^2 -> H(a, U1(k, k))
28.56/10.00	   A^2 -> H(a, U1(k, d))
28.56/10.00	   A^2 -> H(a, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.00	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.00	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, a), b)
28.56/10.00	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, a), c)
28.56/10.00	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, a), e)
28.56/10.00	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, a), b)
28.56/10.00	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, a), c)
28.56/10.00	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.00	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, d), b)
28.56/10.00	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, d), c)
28.56/10.00	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, d), e)
28.56/10.00	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, a), d)
28.56/10.00	   A^2 -> H(U1(c, a), k)
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.00	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.00	   A^2 -> H(U1(d, c), b)
28.56/10.00	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(d, c), c)
28.56/10.00	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(d, c), e)
28.56/10.00	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, a), d)
28.56/10.00	   A^2 -> H(U1(d, a), k)
28.56/10.00	   A^2 -> H(U1(a, e), b)
28.56/10.00	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(a, e), c)
28.56/10.00	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(a, e), e)
28.56/10.00	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(a, k), b)
28.56/10.00	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(a, k), c)
28.56/10.00	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.00	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.00	   A^2 -> H(U1(a, k), e)
28.56/10.00	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(a, c), d)
28.56/10.00	   A^2 -> H(U1(a, c), k)
28.56/10.00	   A^2 -> H(U1(a, d), d)
28.56/10.00	   A^2 -> H(U1(a, d), k)
28.56/10.00	   A^2 -> H(k, U1(c, b))
28.56/10.00	   A^2 -> H(k, U1(d, b))
28.56/10.00	   A^2 -> H(k, U1(b, c))
28.56/10.00	   A^2 -> H(k, U1(b, d))
28.56/10.00	   A^2 -> H(k, U1(c, c))
28.56/10.00	   A^2 -> H(k, f(e))
28.56/10.00	   A^2 -> H(k, f(k))
28.56/10.00	   A^2 -> H(k, U1(d, d))
28.56/10.00	   A^2 -> H(c, U1(e, b))
28.56/10.00	   A^2 -> H(c, U1(k, b))
28.56/10.00	   A^2 -> H(c, U1(c, d))
28.56/10.00	   A^2 -> H(c, U1(d, c))
28.56/10.00	   A^2 -> H(c, U1(b, e))
28.56/10.00	   A^2 -> H(c, U1(b, k))
28.56/10.00	   A^2 -> H(c, U1(e, c))
28.56/10.00	   A^2 -> H(c, U1(k, c))
28.56/10.00	   A^2 -> H(c, U1(c, e))
28.56/10.00	   A^2 -> H(c, U1(c, k))
28.56/10.00	   A^2 -> H(c, U1(e, e))
28.56/10.00	   A^2 -> H(c, U1(k, k))
28.56/10.00	   A^2 -> H(c, U1(k, d))
28.56/10.00	   A^2 -> H(c, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, c), b)
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, c), e)
28.56/10.00	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.00	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.00	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.00	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.00	   A^2 -> H(U1(k, c), b)
28.56/10.00	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, c), c)
28.56/10.00	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, e), b)
28.56/10.00	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, e), c)
28.56/10.00	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, e), e)
28.56/10.00	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, k), b)
28.56/10.00	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, k), c)
28.56/10.00	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, k), e)
28.56/10.00	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, c), d)
28.56/10.00	   A^2 -> H(e, U1(e, b))
28.56/10.00	   A^2 -> H(e, U1(c, d))
28.56/10.00	   A^2 -> H(e, U1(d, c))
28.56/10.00	   A^2 -> H(e, U1(b, e))
28.56/10.00	   A^2 -> H(e, U1(b, k))
28.56/10.00	   A^2 -> H(e, U1(e, c))
28.56/10.00	   A^2 -> H(e, U1(c, e))
28.56/10.00	   A^2 -> H(e, U1(c, k))
28.56/10.00	   A^2 -> H(e, U1(e, e))
28.56/10.00	   A^2 -> H(e, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, e), b)
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, e), c)
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.00	   A^2 -> H(f(e), d)
28.56/10.00	   A^2 -> H(f(e), k)
28.56/10.00	   A^2 -> H(U1(k, k), b)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, k), c)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.00	   A^2 -> H(f(k), d)
28.56/10.00	   A^2 -> H(f(k), k)
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(k, d), b)
28.56/10.00	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, d), c)
28.56/10.00	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, k), b)
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.00	
28.56/10.00	The TRS R consists of the following rules:
28.56/10.00	
28.56/10.00	   f(x) -> U1(x, x)
28.56/10.00	   U1(e, x) -> x
28.56/10.00	   a -> c
28.56/10.00	   a -> d
28.56/10.00	   b -> c
28.56/10.00	   b -> d
28.56/10.00	   d -> k
28.56/10.00	   c -> e
28.56/10.00	   c -> k
28.56/10.00	
28.56/10.00	Q is empty.
28.56/10.00	We have to consider all minimal (P,Q,R)-chains.
28.56/10.00	----------------------------------------
28.56/10.00	
28.56/10.00	(1735) TransformationProof (EQUIVALENT)
28.56/10.00	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.00	
28.56/10.00	   (A^2 -> H(U1(k, k), U1(k, b)),A^2 -> H(U1(k, k), U1(k, b)))
28.56/10.00	   (A^2 -> H(U1(d, k), U1(k, c)),A^2 -> H(U1(d, k), U1(k, c)))
28.56/10.00	   (A^2 -> H(U1(d, k), U1(k, d)),A^2 -> H(U1(d, k), U1(k, d)))
28.56/10.00	
28.56/10.00	
28.56/10.00	----------------------------------------
28.56/10.00	
28.56/10.00	(1736)
28.56/10.00	Obligation:
28.56/10.00	Q DP problem:
28.56/10.00	The TRS P consists of the following rules:
28.56/10.00	
28.56/10.00	   A^2 -> H(f(c), f(c))
28.56/10.00	   H(x, x) -> G(x, x, f(k))
28.56/10.00	   G(d, x, x) -> A^2
28.56/10.00	   A^2 -> H(f(d), f(d))
28.56/10.00	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.00	   A^2 -> H(f(e), f(e))
28.56/10.00	   A^2 -> H(f(k), f(k))
28.56/10.00	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.00	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.00	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.00	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, k), U1(d, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(b, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(b, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, c))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(c, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(e, e))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, k), U1(k, d))
28.56/10.00	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.00	   A^2 -> H(U1(d, d), b)
28.56/10.00	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(d, d), c)
28.56/10.00	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.00	   A^2 -> H(U1(d, d), e)
28.56/10.00	   A^2 -> H(f(d), d)
28.56/10.00	   A^2 -> H(f(d), k)
28.56/10.00	   A^2 -> H(U1(c, c), c)
28.56/10.00	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.00	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.00	   A^2 -> H(f(c), k)
28.56/10.00	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.00	   A^2 -> H(f(k), U1(k, k))
28.56/10.00	   A^2 -> H(f(e), e)
28.56/10.00	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.00	   A^2 -> H(d, U1(c, b))
28.56/10.00	   A^2 -> H(d, U1(d, b))
28.56/10.00	   A^2 -> H(d, U1(b, c))
28.56/10.00	   A^2 -> H(d, U1(b, d))
28.56/10.00	   A^2 -> H(d, U1(c, c))
28.56/10.00	   A^2 -> H(d, f(e))
28.56/10.00	   A^2 -> H(d, f(k))
28.56/10.00	   A^2 -> H(d, U1(d, d))
28.56/10.00	   A^2 -> H(a, U1(e, b))
28.56/10.00	   A^2 -> H(a, U1(k, b))
28.56/10.00	   A^2 -> H(a, U1(c, d))
28.56/10.00	   A^2 -> H(a, U1(d, c))
28.56/10.00	   A^2 -> H(a, U1(b, e))
28.56/10.00	   A^2 -> H(a, U1(b, k))
28.56/10.00	   A^2 -> H(a, U1(e, c))
28.56/10.00	   A^2 -> H(a, U1(k, c))
28.56/10.00	   A^2 -> H(a, U1(c, e))
28.56/10.00	   A^2 -> H(a, U1(c, k))
28.56/10.00	   A^2 -> H(a, U1(e, e))
28.56/10.00	   A^2 -> H(a, U1(k, k))
28.56/10.00	   A^2 -> H(a, U1(k, d))
28.56/10.00	   A^2 -> H(a, U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.00	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.00	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.00	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.00	   A^2 -> H(U1(e, a), b)
28.56/10.00	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.00	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.00	   A^2 -> H(U1(e, a), c)
28.56/10.00	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.00	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.00	   A^2 -> H(U1(e, a), e)
28.56/10.00	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.00	   A^2 -> H(U1(k, a), b)
28.56/10.00	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.00	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.00	   A^2 -> H(U1(k, a), c)
28.56/10.00	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.00	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.00	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, d), b)
28.56/10.00	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.00	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.00	   A^2 -> H(U1(c, d), c)
28.56/10.00	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.00	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.00	   A^2 -> H(U1(c, d), e)
28.56/10.00	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.00	   A^2 -> H(U1(c, a), d)
28.56/10.00	   A^2 -> H(U1(c, a), k)
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.00	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.00	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.00	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.00	   A^2 -> H(U1(d, c), b)
28.56/10.00	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.00	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.00	   A^2 -> H(U1(d, c), c)
28.56/10.00	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(d, c), e)
28.56/10.01	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, a), d)
28.56/10.01	   A^2 -> H(U1(d, a), k)
28.56/10.01	   A^2 -> H(U1(a, e), b)
28.56/10.01	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(a, e), c)
28.56/10.01	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(a, e), e)
28.56/10.01	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(a, k), b)
28.56/10.01	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(a, k), c)
28.56/10.01	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.01	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.01	   A^2 -> H(U1(a, k), e)
28.56/10.01	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(a, c), d)
28.56/10.01	   A^2 -> H(U1(a, c), k)
28.56/10.01	   A^2 -> H(U1(a, d), d)
28.56/10.01	   A^2 -> H(U1(a, d), k)
28.56/10.01	   A^2 -> H(k, U1(c, b))
28.56/10.01	   A^2 -> H(k, U1(d, b))
28.56/10.01	   A^2 -> H(k, U1(b, c))
28.56/10.01	   A^2 -> H(k, U1(b, d))
28.56/10.01	   A^2 -> H(k, U1(c, c))
28.56/10.01	   A^2 -> H(k, f(e))
28.56/10.01	   A^2 -> H(k, f(k))
28.56/10.01	   A^2 -> H(k, U1(d, d))
28.56/10.01	   A^2 -> H(c, U1(e, b))
28.56/10.01	   A^2 -> H(c, U1(k, b))
28.56/10.01	   A^2 -> H(c, U1(c, d))
28.56/10.01	   A^2 -> H(c, U1(d, c))
28.56/10.01	   A^2 -> H(c, U1(b, e))
28.56/10.01	   A^2 -> H(c, U1(b, k))
28.56/10.01	   A^2 -> H(c, U1(e, c))
28.56/10.01	   A^2 -> H(c, U1(k, c))
28.56/10.01	   A^2 -> H(c, U1(c, e))
28.56/10.01	   A^2 -> H(c, U1(c, k))
28.56/10.01	   A^2 -> H(c, U1(e, e))
28.56/10.01	   A^2 -> H(c, U1(k, k))
28.56/10.01	   A^2 -> H(c, U1(k, d))
28.56/10.01	   A^2 -> H(c, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.01	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, c), b)
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, c), e)
28.56/10.01	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.01	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.01	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.01	   A^2 -> H(U1(k, c), b)
28.56/10.01	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, c), c)
28.56/10.01	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, e), b)
28.56/10.01	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, e), c)
28.56/10.01	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, e), e)
28.56/10.01	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, k), b)
28.56/10.01	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, k), c)
28.56/10.01	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, k), e)
28.56/10.01	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, c), d)
28.56/10.01	   A^2 -> H(e, U1(e, b))
28.56/10.01	   A^2 -> H(e, U1(c, d))
28.56/10.01	   A^2 -> H(e, U1(d, c))
28.56/10.01	   A^2 -> H(e, U1(b, e))
28.56/10.01	   A^2 -> H(e, U1(b, k))
28.56/10.01	   A^2 -> H(e, U1(e, c))
28.56/10.01	   A^2 -> H(e, U1(c, e))
28.56/10.01	   A^2 -> H(e, U1(c, k))
28.56/10.01	   A^2 -> H(e, U1(e, e))
28.56/10.01	   A^2 -> H(e, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, e), b)
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, e), c)
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.01	   A^2 -> H(f(e), d)
28.56/10.01	   A^2 -> H(f(e), k)
28.56/10.01	   A^2 -> H(U1(k, k), b)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, k), c)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.01	   A^2 -> H(f(k), d)
28.56/10.01	   A^2 -> H(f(k), k)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(k, d), b)
28.56/10.01	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, d), c)
28.56/10.01	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, k), b)
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.01	
28.56/10.01	The TRS R consists of the following rules:
28.56/10.01	
28.56/10.01	   f(x) -> U1(x, x)
28.56/10.01	   U1(e, x) -> x
28.56/10.01	   a -> c
28.56/10.01	   a -> d
28.56/10.01	   b -> c
28.56/10.01	   b -> d
28.56/10.01	   d -> k
28.56/10.01	   c -> e
28.56/10.01	   c -> k
28.56/10.01	
28.56/10.01	Q is empty.
28.56/10.01	We have to consider all minimal (P,Q,R)-chains.
28.56/10.01	----------------------------------------
28.56/10.01	
28.56/10.01	(1737) TransformationProof (EQUIVALENT)
28.56/10.01	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.01	
28.56/10.01	   (A^2 -> H(U1(k, k), U1(c, d)),A^2 -> H(U1(k, k), U1(c, d)))
28.56/10.01	   (A^2 -> H(U1(d, k), U1(e, d)),A^2 -> H(U1(d, k), U1(e, d)))
28.56/10.01	   (A^2 -> H(U1(d, k), U1(k, d)),A^2 -> H(U1(d, k), U1(k, d)))
28.56/10.01	   (A^2 -> H(U1(d, k), U1(c, k)),A^2 -> H(U1(d, k), U1(c, k)))
28.56/10.01	
28.56/10.01	
28.56/10.01	----------------------------------------
28.56/10.01	
28.56/10.01	(1738)
28.56/10.01	Obligation:
28.56/10.01	Q DP problem:
28.56/10.01	The TRS P consists of the following rules:
28.56/10.01	
28.56/10.01	   A^2 -> H(f(c), f(c))
28.56/10.01	   H(x, x) -> G(x, x, f(k))
28.56/10.01	   G(d, x, x) -> A^2
28.56/10.01	   A^2 -> H(f(d), f(d))
28.56/10.01	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.01	   A^2 -> H(f(e), f(e))
28.56/10.01	   A^2 -> H(f(k), f(k))
28.56/10.01	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.01	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.01	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.01	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(d, c))
28.56/10.01	   A^2 -> H(U1(d, k), U1(b, e))
28.56/10.01	   A^2 -> H(U1(d, k), U1(b, k))
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, c))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(d, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(d, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(d, d), b)
28.56/10.01	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(d, d), c)
28.56/10.01	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(d, d), e)
28.56/10.01	   A^2 -> H(f(d), d)
28.56/10.01	   A^2 -> H(f(d), k)
28.56/10.01	   A^2 -> H(U1(c, c), c)
28.56/10.01	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.01	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.01	   A^2 -> H(f(c), k)
28.56/10.01	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.01	   A^2 -> H(f(k), U1(k, k))
28.56/10.01	   A^2 -> H(f(e), e)
28.56/10.01	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.01	   A^2 -> H(d, U1(c, b))
28.56/10.01	   A^2 -> H(d, U1(d, b))
28.56/10.01	   A^2 -> H(d, U1(b, c))
28.56/10.01	   A^2 -> H(d, U1(b, d))
28.56/10.01	   A^2 -> H(d, U1(c, c))
28.56/10.01	   A^2 -> H(d, f(e))
28.56/10.01	   A^2 -> H(d, f(k))
28.56/10.01	   A^2 -> H(d, U1(d, d))
28.56/10.01	   A^2 -> H(a, U1(e, b))
28.56/10.01	   A^2 -> H(a, U1(k, b))
28.56/10.01	   A^2 -> H(a, U1(c, d))
28.56/10.01	   A^2 -> H(a, U1(d, c))
28.56/10.01	   A^2 -> H(a, U1(b, e))
28.56/10.01	   A^2 -> H(a, U1(b, k))
28.56/10.01	   A^2 -> H(a, U1(e, c))
28.56/10.01	   A^2 -> H(a, U1(k, c))
28.56/10.01	   A^2 -> H(a, U1(c, e))
28.56/10.01	   A^2 -> H(a, U1(c, k))
28.56/10.01	   A^2 -> H(a, U1(e, e))
28.56/10.01	   A^2 -> H(a, U1(k, k))
28.56/10.01	   A^2 -> H(a, U1(k, d))
28.56/10.01	   A^2 -> H(a, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.01	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.01	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.01	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.01	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.01	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.01	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, a), b)
28.56/10.01	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, a), c)
28.56/10.01	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, a), e)
28.56/10.01	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, a), b)
28.56/10.01	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, a), c)
28.56/10.01	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, d), b)
28.56/10.01	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, d), c)
28.56/10.01	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, d), e)
28.56/10.01	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, a), d)
28.56/10.01	   A^2 -> H(U1(c, a), k)
28.56/10.01	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.01	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.01	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.01	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.01	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.01	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.01	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.01	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.01	   A^2 -> H(U1(d, c), b)
28.56/10.01	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(d, c), c)
28.56/10.01	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(d, c), e)
28.56/10.01	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, a), d)
28.56/10.01	   A^2 -> H(U1(d, a), k)
28.56/10.01	   A^2 -> H(U1(a, e), b)
28.56/10.01	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(a, e), c)
28.56/10.01	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(a, e), e)
28.56/10.01	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(a, k), b)
28.56/10.01	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(a, k), c)
28.56/10.01	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.01	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.01	   A^2 -> H(U1(a, k), e)
28.56/10.01	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(a, c), d)
28.56/10.01	   A^2 -> H(U1(a, c), k)
28.56/10.01	   A^2 -> H(U1(a, d), d)
28.56/10.01	   A^2 -> H(U1(a, d), k)
28.56/10.01	   A^2 -> H(k, U1(c, b))
28.56/10.01	   A^2 -> H(k, U1(d, b))
28.56/10.01	   A^2 -> H(k, U1(b, c))
28.56/10.01	   A^2 -> H(k, U1(b, d))
28.56/10.01	   A^2 -> H(k, U1(c, c))
28.56/10.01	   A^2 -> H(k, f(e))
28.56/10.01	   A^2 -> H(k, f(k))
28.56/10.01	   A^2 -> H(k, U1(d, d))
28.56/10.01	   A^2 -> H(c, U1(e, b))
28.56/10.01	   A^2 -> H(c, U1(k, b))
28.56/10.01	   A^2 -> H(c, U1(c, d))
28.56/10.01	   A^2 -> H(c, U1(d, c))
28.56/10.01	   A^2 -> H(c, U1(b, e))
28.56/10.01	   A^2 -> H(c, U1(b, k))
28.56/10.01	   A^2 -> H(c, U1(e, c))
28.56/10.01	   A^2 -> H(c, U1(k, c))
28.56/10.01	   A^2 -> H(c, U1(c, e))
28.56/10.01	   A^2 -> H(c, U1(c, k))
28.56/10.01	   A^2 -> H(c, U1(e, e))
28.56/10.01	   A^2 -> H(c, U1(k, k))
28.56/10.01	   A^2 -> H(c, U1(k, d))
28.56/10.01	   A^2 -> H(c, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.01	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, c), b)
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, c), e)
28.56/10.01	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.01	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.01	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.01	   A^2 -> H(U1(k, c), b)
28.56/10.01	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, c), c)
28.56/10.01	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, e), b)
28.56/10.01	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, e), c)
28.56/10.01	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, e), e)
28.56/10.01	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, k), b)
28.56/10.01	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, k), c)
28.56/10.01	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, k), e)
28.56/10.01	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, c), d)
28.56/10.01	   A^2 -> H(e, U1(e, b))
28.56/10.01	   A^2 -> H(e, U1(c, d))
28.56/10.01	   A^2 -> H(e, U1(d, c))
28.56/10.01	   A^2 -> H(e, U1(b, e))
28.56/10.01	   A^2 -> H(e, U1(b, k))
28.56/10.01	   A^2 -> H(e, U1(e, c))
28.56/10.01	   A^2 -> H(e, U1(c, e))
28.56/10.01	   A^2 -> H(e, U1(c, k))
28.56/10.01	   A^2 -> H(e, U1(e, e))
28.56/10.01	   A^2 -> H(e, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, e), b)
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, e), c)
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.01	   A^2 -> H(f(e), d)
28.56/10.01	   A^2 -> H(f(e), k)
28.56/10.01	   A^2 -> H(U1(k, k), b)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, k), c)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.01	   A^2 -> H(f(k), d)
28.56/10.01	   A^2 -> H(f(k), k)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(k, d), b)
28.56/10.01	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, d), c)
28.56/10.01	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, k), b)
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.01	
28.56/10.01	The TRS R consists of the following rules:
28.56/10.01	
28.56/10.01	   f(x) -> U1(x, x)
28.56/10.01	   U1(e, x) -> x
28.56/10.01	   a -> c
28.56/10.01	   a -> d
28.56/10.01	   b -> c
28.56/10.01	   b -> d
28.56/10.01	   d -> k
28.56/10.01	   c -> e
28.56/10.01	   c -> k
28.56/10.01	
28.56/10.01	Q is empty.
28.56/10.01	We have to consider all minimal (P,Q,R)-chains.
28.56/10.01	----------------------------------------
28.56/10.01	
28.56/10.01	(1739) TransformationProof (EQUIVALENT)
28.56/10.01	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.01	
28.56/10.01	   (A^2 -> H(U1(k, k), U1(d, c)),A^2 -> H(U1(k, k), U1(d, c)))
28.56/10.01	   (A^2 -> H(U1(d, k), U1(k, c)),A^2 -> H(U1(d, k), U1(k, c)))
28.56/10.01	   (A^2 -> H(U1(d, k), U1(d, e)),A^2 -> H(U1(d, k), U1(d, e)))
28.56/10.01	   (A^2 -> H(U1(d, k), U1(d, k)),A^2 -> H(U1(d, k), U1(d, k)))
28.56/10.01	
28.56/10.01	
28.56/10.01	----------------------------------------
28.56/10.01	
28.56/10.01	(1740)
28.56/10.01	Obligation:
28.56/10.01	Q DP problem:
28.56/10.01	The TRS P consists of the following rules:
28.56/10.01	
28.56/10.01	   A^2 -> H(f(c), f(c))
28.56/10.01	   H(x, x) -> G(x, x, f(k))
28.56/10.01	   G(d, x, x) -> A^2
28.56/10.01	   A^2 -> H(f(d), f(d))
28.56/10.01	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.01	   A^2 -> H(f(e), f(e))
28.56/10.01	   A^2 -> H(f(k), f(k))
28.56/10.01	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.01	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.01	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.01	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(b, e))
28.56/10.01	   A^2 -> H(U1(d, k), U1(b, k))
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, c))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(d, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(d, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(d, d), b)
28.56/10.01	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(d, d), c)
28.56/10.01	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(d, d), e)
28.56/10.01	   A^2 -> H(f(d), d)
28.56/10.01	   A^2 -> H(f(d), k)
28.56/10.01	   A^2 -> H(U1(c, c), c)
28.56/10.01	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.01	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.01	   A^2 -> H(f(c), k)
28.56/10.01	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.01	   A^2 -> H(f(k), U1(k, k))
28.56/10.01	   A^2 -> H(f(e), e)
28.56/10.01	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.01	   A^2 -> H(d, U1(c, b))
28.56/10.01	   A^2 -> H(d, U1(d, b))
28.56/10.01	   A^2 -> H(d, U1(b, c))
28.56/10.01	   A^2 -> H(d, U1(b, d))
28.56/10.01	   A^2 -> H(d, U1(c, c))
28.56/10.01	   A^2 -> H(d, f(e))
28.56/10.01	   A^2 -> H(d, f(k))
28.56/10.01	   A^2 -> H(d, U1(d, d))
28.56/10.01	   A^2 -> H(a, U1(e, b))
28.56/10.01	   A^2 -> H(a, U1(k, b))
28.56/10.01	   A^2 -> H(a, U1(c, d))
28.56/10.01	   A^2 -> H(a, U1(d, c))
28.56/10.01	   A^2 -> H(a, U1(b, e))
28.56/10.01	   A^2 -> H(a, U1(b, k))
28.56/10.01	   A^2 -> H(a, U1(e, c))
28.56/10.01	   A^2 -> H(a, U1(k, c))
28.56/10.01	   A^2 -> H(a, U1(c, e))
28.56/10.01	   A^2 -> H(a, U1(c, k))
28.56/10.01	   A^2 -> H(a, U1(e, e))
28.56/10.01	   A^2 -> H(a, U1(k, k))
28.56/10.01	   A^2 -> H(a, U1(k, d))
28.56/10.01	   A^2 -> H(a, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.01	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.01	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.01	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.01	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.01	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.01	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, a), b)
28.56/10.01	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, a), c)
28.56/10.01	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, a), e)
28.56/10.01	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, a), b)
28.56/10.01	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, a), c)
28.56/10.01	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, d), b)
28.56/10.01	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, d), c)
28.56/10.01	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, d), e)
28.56/10.01	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, a), d)
28.56/10.01	   A^2 -> H(U1(c, a), k)
28.56/10.01	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.01	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.01	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.01	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.01	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.01	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.01	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.01	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.01	   A^2 -> H(U1(d, c), b)
28.56/10.01	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(d, c), c)
28.56/10.01	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(d, c), e)
28.56/10.01	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, a), d)
28.56/10.01	   A^2 -> H(U1(d, a), k)
28.56/10.01	   A^2 -> H(U1(a, e), b)
28.56/10.01	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(a, e), c)
28.56/10.01	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(a, e), e)
28.56/10.01	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(a, k), b)
28.56/10.01	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(a, k), c)
28.56/10.01	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.01	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.01	   A^2 -> H(U1(a, k), e)
28.56/10.01	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(a, c), d)
28.56/10.01	   A^2 -> H(U1(a, c), k)
28.56/10.01	   A^2 -> H(U1(a, d), d)
28.56/10.01	   A^2 -> H(U1(a, d), k)
28.56/10.01	   A^2 -> H(k, U1(c, b))
28.56/10.01	   A^2 -> H(k, U1(d, b))
28.56/10.01	   A^2 -> H(k, U1(b, c))
28.56/10.01	   A^2 -> H(k, U1(b, d))
28.56/10.01	   A^2 -> H(k, U1(c, c))
28.56/10.01	   A^2 -> H(k, f(e))
28.56/10.01	   A^2 -> H(k, f(k))
28.56/10.01	   A^2 -> H(k, U1(d, d))
28.56/10.01	   A^2 -> H(c, U1(e, b))
28.56/10.01	   A^2 -> H(c, U1(k, b))
28.56/10.01	   A^2 -> H(c, U1(c, d))
28.56/10.01	   A^2 -> H(c, U1(d, c))
28.56/10.01	   A^2 -> H(c, U1(b, e))
28.56/10.01	   A^2 -> H(c, U1(b, k))
28.56/10.01	   A^2 -> H(c, U1(e, c))
28.56/10.01	   A^2 -> H(c, U1(k, c))
28.56/10.01	   A^2 -> H(c, U1(c, e))
28.56/10.01	   A^2 -> H(c, U1(c, k))
28.56/10.01	   A^2 -> H(c, U1(e, e))
28.56/10.01	   A^2 -> H(c, U1(k, k))
28.56/10.01	   A^2 -> H(c, U1(k, d))
28.56/10.01	   A^2 -> H(c, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.01	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, c), b)
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, c), e)
28.56/10.01	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.01	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.01	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.01	   A^2 -> H(U1(k, c), b)
28.56/10.01	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, c), c)
28.56/10.01	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, e), b)
28.56/10.01	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, e), c)
28.56/10.01	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, e), e)
28.56/10.01	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, k), b)
28.56/10.01	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, k), c)
28.56/10.01	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, k), e)
28.56/10.01	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, c), d)
28.56/10.01	   A^2 -> H(e, U1(e, b))
28.56/10.01	   A^2 -> H(e, U1(c, d))
28.56/10.01	   A^2 -> H(e, U1(d, c))
28.56/10.01	   A^2 -> H(e, U1(b, e))
28.56/10.01	   A^2 -> H(e, U1(b, k))
28.56/10.01	   A^2 -> H(e, U1(e, c))
28.56/10.01	   A^2 -> H(e, U1(c, e))
28.56/10.01	   A^2 -> H(e, U1(c, k))
28.56/10.01	   A^2 -> H(e, U1(e, e))
28.56/10.01	   A^2 -> H(e, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, e), b)
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, e), c)
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.01	   A^2 -> H(f(e), d)
28.56/10.01	   A^2 -> H(f(e), k)
28.56/10.01	   A^2 -> H(U1(k, k), b)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, k), c)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.01	   A^2 -> H(f(k), d)
28.56/10.01	   A^2 -> H(f(k), k)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(k, d), b)
28.56/10.01	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, d), c)
28.56/10.01	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, k), b)
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.01	
28.56/10.01	The TRS R consists of the following rules:
28.56/10.01	
28.56/10.01	   f(x) -> U1(x, x)
28.56/10.01	   U1(e, x) -> x
28.56/10.01	   a -> c
28.56/10.01	   a -> d
28.56/10.01	   b -> c
28.56/10.01	   b -> d
28.56/10.01	   d -> k
28.56/10.01	   c -> e
28.56/10.01	   c -> k
28.56/10.01	
28.56/10.01	Q is empty.
28.56/10.01	We have to consider all minimal (P,Q,R)-chains.
28.56/10.01	----------------------------------------
28.56/10.01	
28.56/10.01	(1741) TransformationProof (EQUIVALENT)
28.56/10.01	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.01	
28.56/10.01	   (A^2 -> H(U1(k, k), U1(b, e)),A^2 -> H(U1(k, k), U1(b, e)))
28.56/10.01	   (A^2 -> H(U1(d, k), U1(c, e)),A^2 -> H(U1(d, k), U1(c, e)))
28.56/10.01	   (A^2 -> H(U1(d, k), U1(d, e)),A^2 -> H(U1(d, k), U1(d, e)))
28.56/10.01	
28.56/10.01	
28.56/10.01	----------------------------------------
28.56/10.01	
28.56/10.01	(1742)
28.56/10.01	Obligation:
28.56/10.01	Q DP problem:
28.56/10.01	The TRS P consists of the following rules:
28.56/10.01	
28.56/10.01	   A^2 -> H(f(c), f(c))
28.56/10.01	   H(x, x) -> G(x, x, f(k))
28.56/10.01	   G(d, x, x) -> A^2
28.56/10.01	   A^2 -> H(f(d), f(d))
28.56/10.01	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.01	   A^2 -> H(f(e), f(e))
28.56/10.01	   A^2 -> H(f(k), f(k))
28.56/10.01	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.01	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.01	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.01	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(b, k))
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, c))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(d, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(d, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(d, d), b)
28.56/10.01	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(d, d), c)
28.56/10.01	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(d, d), e)
28.56/10.01	   A^2 -> H(f(d), d)
28.56/10.01	   A^2 -> H(f(d), k)
28.56/10.01	   A^2 -> H(U1(c, c), c)
28.56/10.01	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.01	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.01	   A^2 -> H(f(c), k)
28.56/10.01	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.01	   A^2 -> H(f(k), U1(k, k))
28.56/10.01	   A^2 -> H(f(e), e)
28.56/10.01	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.01	   A^2 -> H(d, U1(c, b))
28.56/10.01	   A^2 -> H(d, U1(d, b))
28.56/10.01	   A^2 -> H(d, U1(b, c))
28.56/10.01	   A^2 -> H(d, U1(b, d))
28.56/10.01	   A^2 -> H(d, U1(c, c))
28.56/10.01	   A^2 -> H(d, f(e))
28.56/10.01	   A^2 -> H(d, f(k))
28.56/10.01	   A^2 -> H(d, U1(d, d))
28.56/10.01	   A^2 -> H(a, U1(e, b))
28.56/10.01	   A^2 -> H(a, U1(k, b))
28.56/10.01	   A^2 -> H(a, U1(c, d))
28.56/10.01	   A^2 -> H(a, U1(d, c))
28.56/10.01	   A^2 -> H(a, U1(b, e))
28.56/10.01	   A^2 -> H(a, U1(b, k))
28.56/10.01	   A^2 -> H(a, U1(e, c))
28.56/10.01	   A^2 -> H(a, U1(k, c))
28.56/10.01	   A^2 -> H(a, U1(c, e))
28.56/10.01	   A^2 -> H(a, U1(c, k))
28.56/10.01	   A^2 -> H(a, U1(e, e))
28.56/10.01	   A^2 -> H(a, U1(k, k))
28.56/10.01	   A^2 -> H(a, U1(k, d))
28.56/10.01	   A^2 -> H(a, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.01	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.01	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.01	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.01	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.01	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.01	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, a), b)
28.56/10.01	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, a), c)
28.56/10.01	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, a), e)
28.56/10.01	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, a), b)
28.56/10.01	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, a), c)
28.56/10.01	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, d), b)
28.56/10.01	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, d), c)
28.56/10.01	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, d), e)
28.56/10.01	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, a), d)
28.56/10.01	   A^2 -> H(U1(c, a), k)
28.56/10.01	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.01	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.01	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.01	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.01	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.01	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.01	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.01	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.01	   A^2 -> H(U1(d, c), b)
28.56/10.01	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(d, c), c)
28.56/10.01	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(d, c), e)
28.56/10.01	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, a), d)
28.56/10.01	   A^2 -> H(U1(d, a), k)
28.56/10.01	   A^2 -> H(U1(a, e), b)
28.56/10.01	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(a, e), c)
28.56/10.01	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(a, e), e)
28.56/10.01	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(a, k), b)
28.56/10.01	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(a, k), c)
28.56/10.01	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.01	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.01	   A^2 -> H(U1(a, k), e)
28.56/10.01	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(a, c), d)
28.56/10.01	   A^2 -> H(U1(a, c), k)
28.56/10.01	   A^2 -> H(U1(a, d), d)
28.56/10.01	   A^2 -> H(U1(a, d), k)
28.56/10.01	   A^2 -> H(k, U1(c, b))
28.56/10.01	   A^2 -> H(k, U1(d, b))
28.56/10.01	   A^2 -> H(k, U1(b, c))
28.56/10.01	   A^2 -> H(k, U1(b, d))
28.56/10.01	   A^2 -> H(k, U1(c, c))
28.56/10.01	   A^2 -> H(k, f(e))
28.56/10.01	   A^2 -> H(k, f(k))
28.56/10.01	   A^2 -> H(k, U1(d, d))
28.56/10.01	   A^2 -> H(c, U1(e, b))
28.56/10.01	   A^2 -> H(c, U1(k, b))
28.56/10.01	   A^2 -> H(c, U1(c, d))
28.56/10.01	   A^2 -> H(c, U1(d, c))
28.56/10.01	   A^2 -> H(c, U1(b, e))
28.56/10.01	   A^2 -> H(c, U1(b, k))
28.56/10.01	   A^2 -> H(c, U1(e, c))
28.56/10.01	   A^2 -> H(c, U1(k, c))
28.56/10.01	   A^2 -> H(c, U1(c, e))
28.56/10.01	   A^2 -> H(c, U1(c, k))
28.56/10.01	   A^2 -> H(c, U1(e, e))
28.56/10.01	   A^2 -> H(c, U1(k, k))
28.56/10.01	   A^2 -> H(c, U1(k, d))
28.56/10.01	   A^2 -> H(c, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.01	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, c), b)
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, c), e)
28.56/10.01	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.01	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.01	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.01	   A^2 -> H(U1(k, c), b)
28.56/10.01	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, c), c)
28.56/10.01	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, e), b)
28.56/10.01	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, e), c)
28.56/10.01	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, e), e)
28.56/10.01	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, k), b)
28.56/10.01	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, k), c)
28.56/10.01	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, k), e)
28.56/10.01	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, c), d)
28.56/10.01	   A^2 -> H(e, U1(e, b))
28.56/10.01	   A^2 -> H(e, U1(c, d))
28.56/10.01	   A^2 -> H(e, U1(d, c))
28.56/10.01	   A^2 -> H(e, U1(b, e))
28.56/10.01	   A^2 -> H(e, U1(b, k))
28.56/10.01	   A^2 -> H(e, U1(e, c))
28.56/10.01	   A^2 -> H(e, U1(c, e))
28.56/10.01	   A^2 -> H(e, U1(c, k))
28.56/10.01	   A^2 -> H(e, U1(e, e))
28.56/10.01	   A^2 -> H(e, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, e), b)
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, e), c)
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.01	   A^2 -> H(f(e), d)
28.56/10.01	   A^2 -> H(f(e), k)
28.56/10.01	   A^2 -> H(U1(k, k), b)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, k), c)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.01	   A^2 -> H(f(k), d)
28.56/10.01	   A^2 -> H(f(k), k)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(k, d), b)
28.56/10.01	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, d), c)
28.56/10.01	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, k), b)
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.01	
28.56/10.01	The TRS R consists of the following rules:
28.56/10.01	
28.56/10.01	   f(x) -> U1(x, x)
28.56/10.01	   U1(e, x) -> x
28.56/10.01	   a -> c
28.56/10.01	   a -> d
28.56/10.01	   b -> c
28.56/10.01	   b -> d
28.56/10.01	   d -> k
28.56/10.01	   c -> e
28.56/10.01	   c -> k
28.56/10.01	
28.56/10.01	Q is empty.
28.56/10.01	We have to consider all minimal (P,Q,R)-chains.
28.56/10.01	----------------------------------------
28.56/10.01	
28.56/10.01	(1743) TransformationProof (EQUIVALENT)
28.56/10.01	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.01	
28.56/10.01	   (A^2 -> H(U1(k, k), U1(b, k)),A^2 -> H(U1(k, k), U1(b, k)))
28.56/10.01	   (A^2 -> H(U1(d, k), U1(c, k)),A^2 -> H(U1(d, k), U1(c, k)))
28.56/10.01	   (A^2 -> H(U1(d, k), U1(d, k)),A^2 -> H(U1(d, k), U1(d, k)))
28.56/10.01	
28.56/10.01	
28.56/10.01	----------------------------------------
28.56/10.01	
28.56/10.01	(1744)
28.56/10.01	Obligation:
28.56/10.01	Q DP problem:
28.56/10.01	The TRS P consists of the following rules:
28.56/10.01	
28.56/10.01	   A^2 -> H(f(c), f(c))
28.56/10.01	   H(x, x) -> G(x, x, f(k))
28.56/10.01	   G(d, x, x) -> A^2
28.56/10.01	   A^2 -> H(f(d), f(d))
28.56/10.01	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.01	   A^2 -> H(f(e), f(e))
28.56/10.01	   A^2 -> H(f(k), f(k))
28.56/10.01	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.01	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.01	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.01	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, c))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(d, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(d, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(d, d), b)
28.56/10.01	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(d, d), c)
28.56/10.01	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(d, d), e)
28.56/10.01	   A^2 -> H(f(d), d)
28.56/10.01	   A^2 -> H(f(d), k)
28.56/10.01	   A^2 -> H(U1(c, c), c)
28.56/10.01	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.01	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.01	   A^2 -> H(f(c), k)
28.56/10.01	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.01	   A^2 -> H(f(k), U1(k, k))
28.56/10.01	   A^2 -> H(f(e), e)
28.56/10.01	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.01	   A^2 -> H(d, U1(c, b))
28.56/10.01	   A^2 -> H(d, U1(d, b))
28.56/10.01	   A^2 -> H(d, U1(b, c))
28.56/10.01	   A^2 -> H(d, U1(b, d))
28.56/10.01	   A^2 -> H(d, U1(c, c))
28.56/10.01	   A^2 -> H(d, f(e))
28.56/10.01	   A^2 -> H(d, f(k))
28.56/10.01	   A^2 -> H(d, U1(d, d))
28.56/10.01	   A^2 -> H(a, U1(e, b))
28.56/10.01	   A^2 -> H(a, U1(k, b))
28.56/10.01	   A^2 -> H(a, U1(c, d))
28.56/10.01	   A^2 -> H(a, U1(d, c))
28.56/10.01	   A^2 -> H(a, U1(b, e))
28.56/10.01	   A^2 -> H(a, U1(b, k))
28.56/10.01	   A^2 -> H(a, U1(e, c))
28.56/10.01	   A^2 -> H(a, U1(k, c))
28.56/10.01	   A^2 -> H(a, U1(c, e))
28.56/10.01	   A^2 -> H(a, U1(c, k))
28.56/10.01	   A^2 -> H(a, U1(e, e))
28.56/10.01	   A^2 -> H(a, U1(k, k))
28.56/10.01	   A^2 -> H(a, U1(k, d))
28.56/10.01	   A^2 -> H(a, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.01	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.01	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.01	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.01	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.01	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.01	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, a), b)
28.56/10.01	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, a), c)
28.56/10.01	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, a), e)
28.56/10.01	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, a), b)
28.56/10.01	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, a), c)
28.56/10.01	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, d), b)
28.56/10.01	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, d), c)
28.56/10.01	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, d), e)
28.56/10.01	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, a), d)
28.56/10.01	   A^2 -> H(U1(c, a), k)
28.56/10.01	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.01	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.01	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.01	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.01	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.01	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.01	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.01	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.01	   A^2 -> H(U1(d, c), b)
28.56/10.01	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(d, c), c)
28.56/10.01	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(d, c), e)
28.56/10.01	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, a), d)
28.56/10.01	   A^2 -> H(U1(d, a), k)
28.56/10.01	   A^2 -> H(U1(a, e), b)
28.56/10.01	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(a, e), c)
28.56/10.01	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(a, e), e)
28.56/10.01	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(a, k), b)
28.56/10.01	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(a, k), c)
28.56/10.01	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.01	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.01	   A^2 -> H(U1(a, k), e)
28.56/10.01	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(a, c), d)
28.56/10.01	   A^2 -> H(U1(a, c), k)
28.56/10.01	   A^2 -> H(U1(a, d), d)
28.56/10.01	   A^2 -> H(U1(a, d), k)
28.56/10.01	   A^2 -> H(k, U1(c, b))
28.56/10.01	   A^2 -> H(k, U1(d, b))
28.56/10.01	   A^2 -> H(k, U1(b, c))
28.56/10.01	   A^2 -> H(k, U1(b, d))
28.56/10.01	   A^2 -> H(k, U1(c, c))
28.56/10.01	   A^2 -> H(k, f(e))
28.56/10.01	   A^2 -> H(k, f(k))
28.56/10.01	   A^2 -> H(k, U1(d, d))
28.56/10.01	   A^2 -> H(c, U1(e, b))
28.56/10.01	   A^2 -> H(c, U1(k, b))
28.56/10.01	   A^2 -> H(c, U1(c, d))
28.56/10.01	   A^2 -> H(c, U1(d, c))
28.56/10.01	   A^2 -> H(c, U1(b, e))
28.56/10.01	   A^2 -> H(c, U1(b, k))
28.56/10.01	   A^2 -> H(c, U1(e, c))
28.56/10.01	   A^2 -> H(c, U1(k, c))
28.56/10.01	   A^2 -> H(c, U1(c, e))
28.56/10.01	   A^2 -> H(c, U1(c, k))
28.56/10.01	   A^2 -> H(c, U1(e, e))
28.56/10.01	   A^2 -> H(c, U1(k, k))
28.56/10.01	   A^2 -> H(c, U1(k, d))
28.56/10.01	   A^2 -> H(c, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.01	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, c), b)
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, c), e)
28.56/10.01	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.01	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.01	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.01	   A^2 -> H(U1(k, c), b)
28.56/10.01	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, c), c)
28.56/10.01	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, e), b)
28.56/10.01	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, e), c)
28.56/10.01	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, e), e)
28.56/10.01	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, k), b)
28.56/10.01	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, k), c)
28.56/10.01	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, k), e)
28.56/10.01	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, c), d)
28.56/10.01	   A^2 -> H(e, U1(e, b))
28.56/10.01	   A^2 -> H(e, U1(c, d))
28.56/10.01	   A^2 -> H(e, U1(d, c))
28.56/10.01	   A^2 -> H(e, U1(b, e))
28.56/10.01	   A^2 -> H(e, U1(b, k))
28.56/10.01	   A^2 -> H(e, U1(e, c))
28.56/10.01	   A^2 -> H(e, U1(c, e))
28.56/10.01	   A^2 -> H(e, U1(c, k))
28.56/10.01	   A^2 -> H(e, U1(e, e))
28.56/10.01	   A^2 -> H(e, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, e), b)
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, e), c)
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.01	   A^2 -> H(f(e), d)
28.56/10.01	   A^2 -> H(f(e), k)
28.56/10.01	   A^2 -> H(U1(k, k), b)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, k), c)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.01	   A^2 -> H(f(k), d)
28.56/10.01	   A^2 -> H(f(k), k)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(k, d), b)
28.56/10.01	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, d), c)
28.56/10.01	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, k), b)
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.01	
28.56/10.01	The TRS R consists of the following rules:
28.56/10.01	
28.56/10.01	   f(x) -> U1(x, x)
28.56/10.01	   U1(e, x) -> x
28.56/10.01	   a -> c
28.56/10.01	   a -> d
28.56/10.01	   b -> c
28.56/10.01	   b -> d
28.56/10.01	   d -> k
28.56/10.01	   c -> e
28.56/10.01	   c -> k
28.56/10.01	
28.56/10.01	Q is empty.
28.56/10.01	We have to consider all minimal (P,Q,R)-chains.
28.56/10.01	----------------------------------------
28.56/10.01	
28.56/10.01	(1745) TransformationProof (EQUIVALENT)
28.56/10.01	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.01	
28.56/10.01	   (A^2 -> H(U1(k, k), U1(e, c)),A^2 -> H(U1(k, k), U1(e, c)))
28.56/10.01	   (A^2 -> H(U1(d, k), c),A^2 -> H(U1(d, k), c))
28.56/10.01	   (A^2 -> H(U1(d, k), U1(e, e)),A^2 -> H(U1(d, k), U1(e, e)))
28.56/10.01	   (A^2 -> H(U1(d, k), U1(e, k)),A^2 -> H(U1(d, k), U1(e, k)))
28.56/10.01	
28.56/10.01	
28.56/10.01	----------------------------------------
28.56/10.01	
28.56/10.01	(1746)
28.56/10.01	Obligation:
28.56/10.01	Q DP problem:
28.56/10.01	The TRS P consists of the following rules:
28.56/10.01	
28.56/10.01	   A^2 -> H(f(c), f(c))
28.56/10.01	   H(x, x) -> G(x, x, f(k))
28.56/10.01	   G(d, x, x) -> A^2
28.56/10.01	   A^2 -> H(f(d), f(d))
28.56/10.01	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.01	   A^2 -> H(f(e), f(e))
28.56/10.01	   A^2 -> H(f(k), f(k))
28.56/10.01	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.01	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.01	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.01	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(d, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(d, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(d, d), b)
28.56/10.01	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(d, d), c)
28.56/10.01	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(d, d), e)
28.56/10.01	   A^2 -> H(f(d), d)
28.56/10.01	   A^2 -> H(f(d), k)
28.56/10.01	   A^2 -> H(U1(c, c), c)
28.56/10.01	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.01	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.01	   A^2 -> H(f(c), k)
28.56/10.01	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.01	   A^2 -> H(f(k), U1(k, k))
28.56/10.01	   A^2 -> H(f(e), e)
28.56/10.01	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.01	   A^2 -> H(d, U1(c, b))
28.56/10.01	   A^2 -> H(d, U1(d, b))
28.56/10.01	   A^2 -> H(d, U1(b, c))
28.56/10.01	   A^2 -> H(d, U1(b, d))
28.56/10.01	   A^2 -> H(d, U1(c, c))
28.56/10.01	   A^2 -> H(d, f(e))
28.56/10.01	   A^2 -> H(d, f(k))
28.56/10.01	   A^2 -> H(d, U1(d, d))
28.56/10.01	   A^2 -> H(a, U1(e, b))
28.56/10.01	   A^2 -> H(a, U1(k, b))
28.56/10.01	   A^2 -> H(a, U1(c, d))
28.56/10.01	   A^2 -> H(a, U1(d, c))
28.56/10.01	   A^2 -> H(a, U1(b, e))
28.56/10.01	   A^2 -> H(a, U1(b, k))
28.56/10.01	   A^2 -> H(a, U1(e, c))
28.56/10.01	   A^2 -> H(a, U1(k, c))
28.56/10.01	   A^2 -> H(a, U1(c, e))
28.56/10.01	   A^2 -> H(a, U1(c, k))
28.56/10.01	   A^2 -> H(a, U1(e, e))
28.56/10.01	   A^2 -> H(a, U1(k, k))
28.56/10.01	   A^2 -> H(a, U1(k, d))
28.56/10.01	   A^2 -> H(a, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.01	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.01	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.01	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.01	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.01	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.01	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, a), b)
28.56/10.01	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, a), c)
28.56/10.01	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, a), e)
28.56/10.01	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, a), b)
28.56/10.01	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, a), c)
28.56/10.01	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, d), b)
28.56/10.01	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, d), c)
28.56/10.01	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, d), e)
28.56/10.01	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, a), d)
28.56/10.01	   A^2 -> H(U1(c, a), k)
28.56/10.01	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.01	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.01	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.01	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.01	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.01	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.01	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.01	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.01	   A^2 -> H(U1(d, c), b)
28.56/10.01	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(d, c), c)
28.56/10.01	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(d, c), e)
28.56/10.01	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, a), d)
28.56/10.01	   A^2 -> H(U1(d, a), k)
28.56/10.01	   A^2 -> H(U1(a, e), b)
28.56/10.01	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(a, e), c)
28.56/10.01	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(a, e), e)
28.56/10.01	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(a, k), b)
28.56/10.01	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(a, k), c)
28.56/10.01	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.01	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.01	   A^2 -> H(U1(a, k), e)
28.56/10.01	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(a, c), d)
28.56/10.01	   A^2 -> H(U1(a, c), k)
28.56/10.01	   A^2 -> H(U1(a, d), d)
28.56/10.01	   A^2 -> H(U1(a, d), k)
28.56/10.01	   A^2 -> H(k, U1(c, b))
28.56/10.01	   A^2 -> H(k, U1(d, b))
28.56/10.01	   A^2 -> H(k, U1(b, c))
28.56/10.01	   A^2 -> H(k, U1(b, d))
28.56/10.01	   A^2 -> H(k, U1(c, c))
28.56/10.01	   A^2 -> H(k, f(e))
28.56/10.01	   A^2 -> H(k, f(k))
28.56/10.01	   A^2 -> H(k, U1(d, d))
28.56/10.01	   A^2 -> H(c, U1(e, b))
28.56/10.01	   A^2 -> H(c, U1(k, b))
28.56/10.01	   A^2 -> H(c, U1(c, d))
28.56/10.01	   A^2 -> H(c, U1(d, c))
28.56/10.01	   A^2 -> H(c, U1(b, e))
28.56/10.01	   A^2 -> H(c, U1(b, k))
28.56/10.01	   A^2 -> H(c, U1(e, c))
28.56/10.01	   A^2 -> H(c, U1(k, c))
28.56/10.01	   A^2 -> H(c, U1(c, e))
28.56/10.01	   A^2 -> H(c, U1(c, k))
28.56/10.01	   A^2 -> H(c, U1(e, e))
28.56/10.01	   A^2 -> H(c, U1(k, k))
28.56/10.01	   A^2 -> H(c, U1(k, d))
28.56/10.01	   A^2 -> H(c, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.01	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, c), b)
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, c), e)
28.56/10.01	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.01	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.01	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.01	   A^2 -> H(U1(k, c), b)
28.56/10.01	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, c), c)
28.56/10.01	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, e), b)
28.56/10.01	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, e), c)
28.56/10.01	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, e), e)
28.56/10.01	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, k), b)
28.56/10.01	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, k), c)
28.56/10.01	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, k), e)
28.56/10.01	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, c), d)
28.56/10.01	   A^2 -> H(e, U1(e, b))
28.56/10.01	   A^2 -> H(e, U1(c, d))
28.56/10.01	   A^2 -> H(e, U1(d, c))
28.56/10.01	   A^2 -> H(e, U1(b, e))
28.56/10.01	   A^2 -> H(e, U1(b, k))
28.56/10.01	   A^2 -> H(e, U1(e, c))
28.56/10.01	   A^2 -> H(e, U1(c, e))
28.56/10.01	   A^2 -> H(e, U1(c, k))
28.56/10.01	   A^2 -> H(e, U1(e, e))
28.56/10.01	   A^2 -> H(e, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, e), b)
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, e), c)
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.01	   A^2 -> H(f(e), d)
28.56/10.01	   A^2 -> H(f(e), k)
28.56/10.01	   A^2 -> H(U1(k, k), b)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, k), c)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.01	   A^2 -> H(f(k), d)
28.56/10.01	   A^2 -> H(f(k), k)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(k, d), b)
28.56/10.01	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, d), c)
28.56/10.01	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, k), b)
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(d, k), c)
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.01	
28.56/10.01	The TRS R consists of the following rules:
28.56/10.01	
28.56/10.01	   f(x) -> U1(x, x)
28.56/10.01	   U1(e, x) -> x
28.56/10.01	   a -> c
28.56/10.01	   a -> d
28.56/10.01	   b -> c
28.56/10.01	   b -> d
28.56/10.01	   d -> k
28.56/10.01	   c -> e
28.56/10.01	   c -> k
28.56/10.01	
28.56/10.01	Q is empty.
28.56/10.01	We have to consider all minimal (P,Q,R)-chains.
28.56/10.01	----------------------------------------
28.56/10.01	
28.56/10.01	(1747) TransformationProof (EQUIVALENT)
28.56/10.01	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.01	
28.56/10.01	   (A^2 -> H(U1(k, k), U1(k, c)),A^2 -> H(U1(k, k), U1(k, c)))
28.56/10.01	   (A^2 -> H(U1(d, k), U1(k, e)),A^2 -> H(U1(d, k), U1(k, e)))
28.56/10.01	   (A^2 -> H(U1(d, k), U1(k, k)),A^2 -> H(U1(d, k), U1(k, k)))
28.56/10.01	
28.56/10.01	
28.56/10.01	----------------------------------------
28.56/10.01	
28.56/10.01	(1748)
28.56/10.01	Obligation:
28.56/10.01	Q DP problem:
28.56/10.01	The TRS P consists of the following rules:
28.56/10.01	
28.56/10.01	   A^2 -> H(f(c), f(c))
28.56/10.01	   H(x, x) -> G(x, x, f(k))
28.56/10.01	   G(d, x, x) -> A^2
28.56/10.01	   A^2 -> H(f(d), f(d))
28.56/10.01	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.01	   A^2 -> H(f(e), f(e))
28.56/10.01	   A^2 -> H(f(k), f(k))
28.56/10.01	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.01	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.01	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.01	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(d, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(d, d), b)
28.56/10.01	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(d, d), c)
28.56/10.01	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(d, d), e)
28.56/10.01	   A^2 -> H(f(d), d)
28.56/10.01	   A^2 -> H(f(d), k)
28.56/10.01	   A^2 -> H(U1(c, c), c)
28.56/10.01	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.01	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.01	   A^2 -> H(f(c), k)
28.56/10.01	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.01	   A^2 -> H(f(k), U1(k, k))
28.56/10.01	   A^2 -> H(f(e), e)
28.56/10.01	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.01	   A^2 -> H(d, U1(c, b))
28.56/10.01	   A^2 -> H(d, U1(d, b))
28.56/10.01	   A^2 -> H(d, U1(b, c))
28.56/10.01	   A^2 -> H(d, U1(b, d))
28.56/10.01	   A^2 -> H(d, U1(c, c))
28.56/10.01	   A^2 -> H(d, f(e))
28.56/10.01	   A^2 -> H(d, f(k))
28.56/10.01	   A^2 -> H(d, U1(d, d))
28.56/10.01	   A^2 -> H(a, U1(e, b))
28.56/10.01	   A^2 -> H(a, U1(k, b))
28.56/10.01	   A^2 -> H(a, U1(c, d))
28.56/10.01	   A^2 -> H(a, U1(d, c))
28.56/10.01	   A^2 -> H(a, U1(b, e))
28.56/10.01	   A^2 -> H(a, U1(b, k))
28.56/10.01	   A^2 -> H(a, U1(e, c))
28.56/10.01	   A^2 -> H(a, U1(k, c))
28.56/10.01	   A^2 -> H(a, U1(c, e))
28.56/10.01	   A^2 -> H(a, U1(c, k))
28.56/10.01	   A^2 -> H(a, U1(e, e))
28.56/10.01	   A^2 -> H(a, U1(k, k))
28.56/10.01	   A^2 -> H(a, U1(k, d))
28.56/10.01	   A^2 -> H(a, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.01	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.01	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.01	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.01	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.01	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.01	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, a), b)
28.56/10.01	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, a), c)
28.56/10.01	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, a), e)
28.56/10.01	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, a), b)
28.56/10.01	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, a), c)
28.56/10.01	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, d), b)
28.56/10.01	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, d), c)
28.56/10.01	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, d), e)
28.56/10.01	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, a), d)
28.56/10.01	   A^2 -> H(U1(c, a), k)
28.56/10.01	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.01	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.01	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.01	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.01	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.01	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.01	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.01	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.01	   A^2 -> H(U1(d, c), b)
28.56/10.01	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(d, c), c)
28.56/10.01	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(d, c), e)
28.56/10.01	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, a), d)
28.56/10.01	   A^2 -> H(U1(d, a), k)
28.56/10.01	   A^2 -> H(U1(a, e), b)
28.56/10.01	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(a, e), c)
28.56/10.01	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(a, e), e)
28.56/10.01	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(a, k), b)
28.56/10.01	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(a, k), c)
28.56/10.01	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.01	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.01	   A^2 -> H(U1(a, k), e)
28.56/10.01	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(a, c), d)
28.56/10.01	   A^2 -> H(U1(a, c), k)
28.56/10.01	   A^2 -> H(U1(a, d), d)
28.56/10.01	   A^2 -> H(U1(a, d), k)
28.56/10.01	   A^2 -> H(k, U1(c, b))
28.56/10.01	   A^2 -> H(k, U1(d, b))
28.56/10.01	   A^2 -> H(k, U1(b, c))
28.56/10.01	   A^2 -> H(k, U1(b, d))
28.56/10.01	   A^2 -> H(k, U1(c, c))
28.56/10.01	   A^2 -> H(k, f(e))
28.56/10.01	   A^2 -> H(k, f(k))
28.56/10.01	   A^2 -> H(k, U1(d, d))
28.56/10.01	   A^2 -> H(c, U1(e, b))
28.56/10.01	   A^2 -> H(c, U1(k, b))
28.56/10.01	   A^2 -> H(c, U1(c, d))
28.56/10.01	   A^2 -> H(c, U1(d, c))
28.56/10.01	   A^2 -> H(c, U1(b, e))
28.56/10.01	   A^2 -> H(c, U1(b, k))
28.56/10.01	   A^2 -> H(c, U1(e, c))
28.56/10.01	   A^2 -> H(c, U1(k, c))
28.56/10.01	   A^2 -> H(c, U1(c, e))
28.56/10.01	   A^2 -> H(c, U1(c, k))
28.56/10.01	   A^2 -> H(c, U1(e, e))
28.56/10.01	   A^2 -> H(c, U1(k, k))
28.56/10.01	   A^2 -> H(c, U1(k, d))
28.56/10.01	   A^2 -> H(c, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.01	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, c), b)
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, c), e)
28.56/10.01	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.01	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.01	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.01	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.01	   A^2 -> H(U1(k, c), b)
28.56/10.01	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, c), c)
28.56/10.01	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, e), b)
28.56/10.01	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, e), c)
28.56/10.01	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, e), e)
28.56/10.01	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, k), b)
28.56/10.01	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(c, k), c)
28.56/10.01	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.01	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.01	   A^2 -> H(U1(c, k), e)
28.56/10.01	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(c, c), d)
28.56/10.01	   A^2 -> H(e, U1(e, b))
28.56/10.01	   A^2 -> H(e, U1(c, d))
28.56/10.01	   A^2 -> H(e, U1(d, c))
28.56/10.01	   A^2 -> H(e, U1(b, e))
28.56/10.01	   A^2 -> H(e, U1(b, k))
28.56/10.01	   A^2 -> H(e, U1(e, c))
28.56/10.01	   A^2 -> H(e, U1(c, e))
28.56/10.01	   A^2 -> H(e, U1(c, k))
28.56/10.01	   A^2 -> H(e, U1(e, e))
28.56/10.01	   A^2 -> H(e, U1(d, k))
28.56/10.01	   A^2 -> H(U1(e, e), b)
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.01	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.01	   A^2 -> H(U1(e, e), c)
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.01	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.01	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.01	   A^2 -> H(f(e), d)
28.56/10.01	   A^2 -> H(f(e), k)
28.56/10.01	   A^2 -> H(U1(k, k), b)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, k), c)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.01	   A^2 -> H(f(k), d)
28.56/10.01	   A^2 -> H(f(k), k)
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(k, d), b)
28.56/10.01	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.01	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.01	   A^2 -> H(U1(k, d), c)
28.56/10.01	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, k), b)
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.01	   A^2 -> H(U1(d, k), c)
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.01	
28.56/10.01	The TRS R consists of the following rules:
28.56/10.01	
28.56/10.01	   f(x) -> U1(x, x)
28.56/10.01	   U1(e, x) -> x
28.56/10.01	   a -> c
28.56/10.01	   a -> d
28.56/10.01	   b -> c
28.56/10.01	   b -> d
28.56/10.01	   d -> k
28.56/10.01	   c -> e
28.56/10.01	   c -> k
28.56/10.01	
28.56/10.01	Q is empty.
28.56/10.01	We have to consider all minimal (P,Q,R)-chains.
28.56/10.01	----------------------------------------
28.56/10.01	
28.56/10.01	(1749) TransformationProof (EQUIVALENT)
28.56/10.01	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.01	
28.56/10.01	   (A^2 -> H(U1(k, k), U1(c, e)),A^2 -> H(U1(k, k), U1(c, e)))
28.56/10.01	   (A^2 -> H(U1(d, k), U1(e, e)),A^2 -> H(U1(d, k), U1(e, e)))
28.56/10.01	   (A^2 -> H(U1(d, k), U1(k, e)),A^2 -> H(U1(d, k), U1(k, e)))
28.56/10.01	
28.56/10.01	
28.56/10.01	----------------------------------------
28.56/10.01	
28.56/10.01	(1750)
28.56/10.01	Obligation:
28.56/10.01	Q DP problem:
28.56/10.01	The TRS P consists of the following rules:
28.56/10.01	
28.56/10.01	   A^2 -> H(f(c), f(c))
28.56/10.01	   H(x, x) -> G(x, x, f(k))
28.56/10.01	   G(d, x, x) -> A^2
28.56/10.01	   A^2 -> H(f(d), f(d))
28.56/10.01	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.01	   A^2 -> H(f(e), f(e))
28.56/10.01	   A^2 -> H(f(k), f(k))
28.56/10.01	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.01	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.01	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.01	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.01	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.01	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.01	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.01	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(c, k))
28.56/10.01	   A^2 -> H(U1(d, k), U1(e, e))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.01	   A^2 -> H(U1(d, k), U1(k, d))
28.56/10.01	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.01	   A^2 -> H(U1(d, d), b)
28.56/10.02	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, d), c)
28.56/10.02	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, d), e)
28.56/10.02	   A^2 -> H(f(d), d)
28.56/10.02	   A^2 -> H(f(d), k)
28.56/10.02	   A^2 -> H(U1(c, c), c)
28.56/10.02	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.02	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.02	   A^2 -> H(f(c), k)
28.56/10.02	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.02	   A^2 -> H(f(k), U1(k, k))
28.56/10.02	   A^2 -> H(f(e), e)
28.56/10.02	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.02	   A^2 -> H(d, U1(c, b))
28.56/10.02	   A^2 -> H(d, U1(d, b))
28.56/10.02	   A^2 -> H(d, U1(b, c))
28.56/10.02	   A^2 -> H(d, U1(b, d))
28.56/10.02	   A^2 -> H(d, U1(c, c))
28.56/10.02	   A^2 -> H(d, f(e))
28.56/10.02	   A^2 -> H(d, f(k))
28.56/10.02	   A^2 -> H(d, U1(d, d))
28.56/10.02	   A^2 -> H(a, U1(e, b))
28.56/10.02	   A^2 -> H(a, U1(k, b))
28.56/10.02	   A^2 -> H(a, U1(c, d))
28.56/10.02	   A^2 -> H(a, U1(d, c))
28.56/10.02	   A^2 -> H(a, U1(b, e))
28.56/10.02	   A^2 -> H(a, U1(b, k))
28.56/10.02	   A^2 -> H(a, U1(e, c))
28.56/10.02	   A^2 -> H(a, U1(k, c))
28.56/10.02	   A^2 -> H(a, U1(c, e))
28.56/10.02	   A^2 -> H(a, U1(c, k))
28.56/10.02	   A^2 -> H(a, U1(e, e))
28.56/10.02	   A^2 -> H(a, U1(k, k))
28.56/10.02	   A^2 -> H(a, U1(k, d))
28.56/10.02	   A^2 -> H(a, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.02	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.02	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, a), b)
28.56/10.02	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, a), c)
28.56/10.02	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, a), e)
28.56/10.02	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, a), b)
28.56/10.02	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, a), c)
28.56/10.02	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, d), b)
28.56/10.02	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, d), c)
28.56/10.02	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, d), e)
28.56/10.02	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, a), d)
28.56/10.02	   A^2 -> H(U1(c, a), k)
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.02	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.02	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.02	   A^2 -> H(U1(d, c), b)
28.56/10.02	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, c), c)
28.56/10.02	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, c), e)
28.56/10.02	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, a), d)
28.56/10.02	   A^2 -> H(U1(d, a), k)
28.56/10.02	   A^2 -> H(U1(a, e), b)
28.56/10.02	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(a, e), c)
28.56/10.02	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(a, e), e)
28.56/10.02	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(a, k), b)
28.56/10.02	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(a, k), c)
28.56/10.02	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(a, k), e)
28.56/10.02	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(a, c), d)
28.56/10.02	   A^2 -> H(U1(a, c), k)
28.56/10.02	   A^2 -> H(U1(a, d), d)
28.56/10.02	   A^2 -> H(U1(a, d), k)
28.56/10.02	   A^2 -> H(k, U1(c, b))
28.56/10.02	   A^2 -> H(k, U1(d, b))
28.56/10.02	   A^2 -> H(k, U1(b, c))
28.56/10.02	   A^2 -> H(k, U1(b, d))
28.56/10.02	   A^2 -> H(k, U1(c, c))
28.56/10.02	   A^2 -> H(k, f(e))
28.56/10.02	   A^2 -> H(k, f(k))
28.56/10.02	   A^2 -> H(k, U1(d, d))
28.56/10.02	   A^2 -> H(c, U1(e, b))
28.56/10.02	   A^2 -> H(c, U1(k, b))
28.56/10.02	   A^2 -> H(c, U1(c, d))
28.56/10.02	   A^2 -> H(c, U1(d, c))
28.56/10.02	   A^2 -> H(c, U1(b, e))
28.56/10.02	   A^2 -> H(c, U1(b, k))
28.56/10.02	   A^2 -> H(c, U1(e, c))
28.56/10.02	   A^2 -> H(c, U1(k, c))
28.56/10.02	   A^2 -> H(c, U1(c, e))
28.56/10.02	   A^2 -> H(c, U1(c, k))
28.56/10.02	   A^2 -> H(c, U1(e, e))
28.56/10.02	   A^2 -> H(c, U1(k, k))
28.56/10.02	   A^2 -> H(c, U1(k, d))
28.56/10.02	   A^2 -> H(c, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.02	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.02	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, c), b)
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, c), e)
28.56/10.02	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.02	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.02	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.02	   A^2 -> H(U1(k, c), b)
28.56/10.02	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, c), c)
28.56/10.02	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, e), b)
28.56/10.02	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, e), c)
28.56/10.02	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, e), e)
28.56/10.02	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, k), b)
28.56/10.02	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, k), c)
28.56/10.02	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, k), e)
28.56/10.02	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, c), d)
28.56/10.02	   A^2 -> H(e, U1(e, b))
28.56/10.02	   A^2 -> H(e, U1(c, d))
28.56/10.02	   A^2 -> H(e, U1(d, c))
28.56/10.02	   A^2 -> H(e, U1(b, e))
28.56/10.02	   A^2 -> H(e, U1(b, k))
28.56/10.02	   A^2 -> H(e, U1(e, c))
28.56/10.02	   A^2 -> H(e, U1(c, e))
28.56/10.02	   A^2 -> H(e, U1(c, k))
28.56/10.02	   A^2 -> H(e, U1(e, e))
28.56/10.02	   A^2 -> H(e, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, e), b)
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, e), c)
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.02	   A^2 -> H(f(e), d)
28.56/10.02	   A^2 -> H(f(e), k)
28.56/10.02	   A^2 -> H(U1(k, k), b)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, k), c)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.02	   A^2 -> H(f(k), d)
28.56/10.02	   A^2 -> H(f(k), k)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(k, d), b)
28.56/10.02	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, d), c)
28.56/10.02	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, k), b)
28.56/10.02	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, k), c)
28.56/10.02	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.02	
28.56/10.02	The TRS R consists of the following rules:
28.56/10.02	
28.56/10.02	   f(x) -> U1(x, x)
28.56/10.02	   U1(e, x) -> x
28.56/10.02	   a -> c
28.56/10.02	   a -> d
28.56/10.02	   b -> c
28.56/10.02	   b -> d
28.56/10.02	   d -> k
28.56/10.02	   c -> e
28.56/10.02	   c -> k
28.56/10.02	
28.56/10.02	Q is empty.
28.56/10.02	We have to consider all minimal (P,Q,R)-chains.
28.56/10.02	----------------------------------------
28.56/10.02	
28.56/10.02	(1751) TransformationProof (EQUIVALENT)
28.56/10.02	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.02	
28.56/10.02	   (A^2 -> H(U1(k, k), U1(c, k)),A^2 -> H(U1(k, k), U1(c, k)))
28.56/10.02	   (A^2 -> H(U1(d, k), U1(e, k)),A^2 -> H(U1(d, k), U1(e, k)))
28.56/10.02	   (A^2 -> H(U1(d, k), U1(k, k)),A^2 -> H(U1(d, k), U1(k, k)))
28.56/10.02	
28.56/10.02	
28.56/10.02	----------------------------------------
28.56/10.02	
28.56/10.02	(1752)
28.56/10.02	Obligation:
28.56/10.02	Q DP problem:
28.56/10.02	The TRS P consists of the following rules:
28.56/10.02	
28.56/10.02	   A^2 -> H(f(c), f(c))
28.56/10.02	   H(x, x) -> G(x, x, f(k))
28.56/10.02	   G(d, x, x) -> A^2
28.56/10.02	   A^2 -> H(f(d), f(d))
28.56/10.02	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.02	   A^2 -> H(f(e), f(e))
28.56/10.02	   A^2 -> H(f(k), f(k))
28.56/10.02	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.02	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.02	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.02	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.02	   A^2 -> H(U1(d, k), U1(e, e))
28.56/10.02	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, k), U1(k, d))
28.56/10.02	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(d, d), b)
28.56/10.02	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, d), c)
28.56/10.02	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, d), e)
28.56/10.02	   A^2 -> H(f(d), d)
28.56/10.02	   A^2 -> H(f(d), k)
28.56/10.02	   A^2 -> H(U1(c, c), c)
28.56/10.02	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.02	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.02	   A^2 -> H(f(c), k)
28.56/10.02	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.02	   A^2 -> H(f(k), U1(k, k))
28.56/10.02	   A^2 -> H(f(e), e)
28.56/10.02	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.02	   A^2 -> H(d, U1(c, b))
28.56/10.02	   A^2 -> H(d, U1(d, b))
28.56/10.02	   A^2 -> H(d, U1(b, c))
28.56/10.02	   A^2 -> H(d, U1(b, d))
28.56/10.02	   A^2 -> H(d, U1(c, c))
28.56/10.02	   A^2 -> H(d, f(e))
28.56/10.02	   A^2 -> H(d, f(k))
28.56/10.02	   A^2 -> H(d, U1(d, d))
28.56/10.02	   A^2 -> H(a, U1(e, b))
28.56/10.02	   A^2 -> H(a, U1(k, b))
28.56/10.02	   A^2 -> H(a, U1(c, d))
28.56/10.02	   A^2 -> H(a, U1(d, c))
28.56/10.02	   A^2 -> H(a, U1(b, e))
28.56/10.02	   A^2 -> H(a, U1(b, k))
28.56/10.02	   A^2 -> H(a, U1(e, c))
28.56/10.02	   A^2 -> H(a, U1(k, c))
28.56/10.02	   A^2 -> H(a, U1(c, e))
28.56/10.02	   A^2 -> H(a, U1(c, k))
28.56/10.02	   A^2 -> H(a, U1(e, e))
28.56/10.02	   A^2 -> H(a, U1(k, k))
28.56/10.02	   A^2 -> H(a, U1(k, d))
28.56/10.02	   A^2 -> H(a, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.02	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.02	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, a), b)
28.56/10.02	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, a), c)
28.56/10.02	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, a), e)
28.56/10.02	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, a), b)
28.56/10.02	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, a), c)
28.56/10.02	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, d), b)
28.56/10.02	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, d), c)
28.56/10.02	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, d), e)
28.56/10.02	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, a), d)
28.56/10.02	   A^2 -> H(U1(c, a), k)
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.02	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.02	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.02	   A^2 -> H(U1(d, c), b)
28.56/10.02	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, c), c)
28.56/10.02	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, c), e)
28.56/10.02	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, a), d)
28.56/10.02	   A^2 -> H(U1(d, a), k)
28.56/10.02	   A^2 -> H(U1(a, e), b)
28.56/10.02	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(a, e), c)
28.56/10.02	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(a, e), e)
28.56/10.02	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(a, k), b)
28.56/10.02	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(a, k), c)
28.56/10.02	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(a, k), e)
28.56/10.02	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(a, c), d)
28.56/10.02	   A^2 -> H(U1(a, c), k)
28.56/10.02	   A^2 -> H(U1(a, d), d)
28.56/10.02	   A^2 -> H(U1(a, d), k)
28.56/10.02	   A^2 -> H(k, U1(c, b))
28.56/10.02	   A^2 -> H(k, U1(d, b))
28.56/10.02	   A^2 -> H(k, U1(b, c))
28.56/10.02	   A^2 -> H(k, U1(b, d))
28.56/10.02	   A^2 -> H(k, U1(c, c))
28.56/10.02	   A^2 -> H(k, f(e))
28.56/10.02	   A^2 -> H(k, f(k))
28.56/10.02	   A^2 -> H(k, U1(d, d))
28.56/10.02	   A^2 -> H(c, U1(e, b))
28.56/10.02	   A^2 -> H(c, U1(k, b))
28.56/10.02	   A^2 -> H(c, U1(c, d))
28.56/10.02	   A^2 -> H(c, U1(d, c))
28.56/10.02	   A^2 -> H(c, U1(b, e))
28.56/10.02	   A^2 -> H(c, U1(b, k))
28.56/10.02	   A^2 -> H(c, U1(e, c))
28.56/10.02	   A^2 -> H(c, U1(k, c))
28.56/10.02	   A^2 -> H(c, U1(c, e))
28.56/10.02	   A^2 -> H(c, U1(c, k))
28.56/10.02	   A^2 -> H(c, U1(e, e))
28.56/10.02	   A^2 -> H(c, U1(k, k))
28.56/10.02	   A^2 -> H(c, U1(k, d))
28.56/10.02	   A^2 -> H(c, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.02	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.02	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, c), b)
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, c), e)
28.56/10.02	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.02	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.02	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.02	   A^2 -> H(U1(k, c), b)
28.56/10.02	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, c), c)
28.56/10.02	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, e), b)
28.56/10.02	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, e), c)
28.56/10.02	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, e), e)
28.56/10.02	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, k), b)
28.56/10.02	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, k), c)
28.56/10.02	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, k), e)
28.56/10.02	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, c), d)
28.56/10.02	   A^2 -> H(e, U1(e, b))
28.56/10.02	   A^2 -> H(e, U1(c, d))
28.56/10.02	   A^2 -> H(e, U1(d, c))
28.56/10.02	   A^2 -> H(e, U1(b, e))
28.56/10.02	   A^2 -> H(e, U1(b, k))
28.56/10.02	   A^2 -> H(e, U1(e, c))
28.56/10.02	   A^2 -> H(e, U1(c, e))
28.56/10.02	   A^2 -> H(e, U1(c, k))
28.56/10.02	   A^2 -> H(e, U1(e, e))
28.56/10.02	   A^2 -> H(e, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, e), b)
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, e), c)
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.02	   A^2 -> H(f(e), d)
28.56/10.02	   A^2 -> H(f(e), k)
28.56/10.02	   A^2 -> H(U1(k, k), b)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, k), c)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.02	   A^2 -> H(f(k), d)
28.56/10.02	   A^2 -> H(f(k), k)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(k, d), b)
28.56/10.02	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, d), c)
28.56/10.02	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, k), b)
28.56/10.02	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, k), c)
28.56/10.02	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.02	
28.56/10.02	The TRS R consists of the following rules:
28.56/10.02	
28.56/10.02	   f(x) -> U1(x, x)
28.56/10.02	   U1(e, x) -> x
28.56/10.02	   a -> c
28.56/10.02	   a -> d
28.56/10.02	   b -> c
28.56/10.02	   b -> d
28.56/10.02	   d -> k
28.56/10.02	   c -> e
28.56/10.02	   c -> k
28.56/10.02	
28.56/10.02	Q is empty.
28.56/10.02	We have to consider all minimal (P,Q,R)-chains.
28.56/10.02	----------------------------------------
28.56/10.02	
28.56/10.02	(1753) TransformationProof (EQUIVALENT)
28.56/10.02	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.02	
28.56/10.02	   (A^2 -> H(U1(k, k), U1(e, e)),A^2 -> H(U1(k, k), U1(e, e)))
28.56/10.02	   (A^2 -> H(U1(d, k), e),A^2 -> H(U1(d, k), e))
28.56/10.02	
28.56/10.02	
28.56/10.02	----------------------------------------
28.56/10.02	
28.56/10.02	(1754)
28.56/10.02	Obligation:
28.56/10.02	Q DP problem:
28.56/10.02	The TRS P consists of the following rules:
28.56/10.02	
28.56/10.02	   A^2 -> H(f(c), f(c))
28.56/10.02	   H(x, x) -> G(x, x, f(k))
28.56/10.02	   G(d, x, x) -> A^2
28.56/10.02	   A^2 -> H(f(d), f(d))
28.56/10.02	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.02	   A^2 -> H(f(e), f(e))
28.56/10.02	   A^2 -> H(f(k), f(k))
28.56/10.02	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.02	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.02	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.02	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.02	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, k), U1(k, d))
28.56/10.02	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(d, d), b)
28.56/10.02	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, d), c)
28.56/10.02	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, d), e)
28.56/10.02	   A^2 -> H(f(d), d)
28.56/10.02	   A^2 -> H(f(d), k)
28.56/10.02	   A^2 -> H(U1(c, c), c)
28.56/10.02	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.02	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.02	   A^2 -> H(f(c), k)
28.56/10.02	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.02	   A^2 -> H(f(k), U1(k, k))
28.56/10.02	   A^2 -> H(f(e), e)
28.56/10.02	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.02	   A^2 -> H(d, U1(c, b))
28.56/10.02	   A^2 -> H(d, U1(d, b))
28.56/10.02	   A^2 -> H(d, U1(b, c))
28.56/10.02	   A^2 -> H(d, U1(b, d))
28.56/10.02	   A^2 -> H(d, U1(c, c))
28.56/10.02	   A^2 -> H(d, f(e))
28.56/10.02	   A^2 -> H(d, f(k))
28.56/10.02	   A^2 -> H(d, U1(d, d))
28.56/10.02	   A^2 -> H(a, U1(e, b))
28.56/10.02	   A^2 -> H(a, U1(k, b))
28.56/10.02	   A^2 -> H(a, U1(c, d))
28.56/10.02	   A^2 -> H(a, U1(d, c))
28.56/10.02	   A^2 -> H(a, U1(b, e))
28.56/10.02	   A^2 -> H(a, U1(b, k))
28.56/10.02	   A^2 -> H(a, U1(e, c))
28.56/10.02	   A^2 -> H(a, U1(k, c))
28.56/10.02	   A^2 -> H(a, U1(c, e))
28.56/10.02	   A^2 -> H(a, U1(c, k))
28.56/10.02	   A^2 -> H(a, U1(e, e))
28.56/10.02	   A^2 -> H(a, U1(k, k))
28.56/10.02	   A^2 -> H(a, U1(k, d))
28.56/10.02	   A^2 -> H(a, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.02	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.02	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, a), b)
28.56/10.02	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, a), c)
28.56/10.02	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, a), e)
28.56/10.02	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, a), b)
28.56/10.02	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, a), c)
28.56/10.02	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, d), b)
28.56/10.02	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, d), c)
28.56/10.02	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, d), e)
28.56/10.02	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, a), d)
28.56/10.02	   A^2 -> H(U1(c, a), k)
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.02	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.02	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.02	   A^2 -> H(U1(d, c), b)
28.56/10.02	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, c), c)
28.56/10.02	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, c), e)
28.56/10.02	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, a), d)
28.56/10.02	   A^2 -> H(U1(d, a), k)
28.56/10.02	   A^2 -> H(U1(a, e), b)
28.56/10.02	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(a, e), c)
28.56/10.02	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(a, e), e)
28.56/10.02	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(a, k), b)
28.56/10.02	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(a, k), c)
28.56/10.02	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(a, k), e)
28.56/10.02	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(a, c), d)
28.56/10.02	   A^2 -> H(U1(a, c), k)
28.56/10.02	   A^2 -> H(U1(a, d), d)
28.56/10.02	   A^2 -> H(U1(a, d), k)
28.56/10.02	   A^2 -> H(k, U1(c, b))
28.56/10.02	   A^2 -> H(k, U1(d, b))
28.56/10.02	   A^2 -> H(k, U1(b, c))
28.56/10.02	   A^2 -> H(k, U1(b, d))
28.56/10.02	   A^2 -> H(k, U1(c, c))
28.56/10.02	   A^2 -> H(k, f(e))
28.56/10.02	   A^2 -> H(k, f(k))
28.56/10.02	   A^2 -> H(k, U1(d, d))
28.56/10.02	   A^2 -> H(c, U1(e, b))
28.56/10.02	   A^2 -> H(c, U1(k, b))
28.56/10.02	   A^2 -> H(c, U1(c, d))
28.56/10.02	   A^2 -> H(c, U1(d, c))
28.56/10.02	   A^2 -> H(c, U1(b, e))
28.56/10.02	   A^2 -> H(c, U1(b, k))
28.56/10.02	   A^2 -> H(c, U1(e, c))
28.56/10.02	   A^2 -> H(c, U1(k, c))
28.56/10.02	   A^2 -> H(c, U1(c, e))
28.56/10.02	   A^2 -> H(c, U1(c, k))
28.56/10.02	   A^2 -> H(c, U1(e, e))
28.56/10.02	   A^2 -> H(c, U1(k, k))
28.56/10.02	   A^2 -> H(c, U1(k, d))
28.56/10.02	   A^2 -> H(c, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.02	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.02	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, c), b)
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, c), e)
28.56/10.02	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.02	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.02	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.02	   A^2 -> H(U1(k, c), b)
28.56/10.02	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, c), c)
28.56/10.02	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, e), b)
28.56/10.02	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, e), c)
28.56/10.02	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, e), e)
28.56/10.02	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, k), b)
28.56/10.02	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, k), c)
28.56/10.02	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, k), e)
28.56/10.02	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, c), d)
28.56/10.02	   A^2 -> H(e, U1(e, b))
28.56/10.02	   A^2 -> H(e, U1(c, d))
28.56/10.02	   A^2 -> H(e, U1(d, c))
28.56/10.02	   A^2 -> H(e, U1(b, e))
28.56/10.02	   A^2 -> H(e, U1(b, k))
28.56/10.02	   A^2 -> H(e, U1(e, c))
28.56/10.02	   A^2 -> H(e, U1(c, e))
28.56/10.02	   A^2 -> H(e, U1(c, k))
28.56/10.02	   A^2 -> H(e, U1(e, e))
28.56/10.02	   A^2 -> H(e, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, e), b)
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, e), c)
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.02	   A^2 -> H(f(e), d)
28.56/10.02	   A^2 -> H(f(e), k)
28.56/10.02	   A^2 -> H(U1(k, k), b)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, k), c)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.02	   A^2 -> H(f(k), d)
28.56/10.02	   A^2 -> H(f(k), k)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(k, d), b)
28.56/10.02	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, d), c)
28.56/10.02	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, k), b)
28.56/10.02	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, k), c)
28.56/10.02	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, k), e)
28.56/10.02	
28.56/10.02	The TRS R consists of the following rules:
28.56/10.02	
28.56/10.02	   f(x) -> U1(x, x)
28.56/10.02	   U1(e, x) -> x
28.56/10.02	   a -> c
28.56/10.02	   a -> d
28.56/10.02	   b -> c
28.56/10.02	   b -> d
28.56/10.02	   d -> k
28.56/10.02	   c -> e
28.56/10.02	   c -> k
28.56/10.02	
28.56/10.02	Q is empty.
28.56/10.02	We have to consider all minimal (P,Q,R)-chains.
28.56/10.02	----------------------------------------
28.56/10.02	
28.56/10.02	(1755) TransformationProof (EQUIVALENT)
28.56/10.02	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.02	
28.56/10.02	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.56/10.02	
28.56/10.02	
28.56/10.02	----------------------------------------
28.56/10.02	
28.56/10.02	(1756)
28.56/10.02	Obligation:
28.56/10.02	Q DP problem:
28.56/10.02	The TRS P consists of the following rules:
28.56/10.02	
28.56/10.02	   A^2 -> H(f(c), f(c))
28.56/10.02	   H(x, x) -> G(x, x, f(k))
28.56/10.02	   G(d, x, x) -> A^2
28.56/10.02	   A^2 -> H(f(d), f(d))
28.56/10.02	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.02	   A^2 -> H(f(e), f(e))
28.56/10.02	   A^2 -> H(f(k), f(k))
28.56/10.02	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.02	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.02	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.02	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.02	   A^2 -> H(U1(d, k), U1(k, d))
28.56/10.02	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(d, d), b)
28.56/10.02	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, d), c)
28.56/10.02	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, d), e)
28.56/10.02	   A^2 -> H(f(d), d)
28.56/10.02	   A^2 -> H(f(d), k)
28.56/10.02	   A^2 -> H(U1(c, c), c)
28.56/10.02	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.02	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.02	   A^2 -> H(f(c), k)
28.56/10.02	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.02	   A^2 -> H(f(k), U1(k, k))
28.56/10.02	   A^2 -> H(f(e), e)
28.56/10.02	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.02	   A^2 -> H(d, U1(c, b))
28.56/10.02	   A^2 -> H(d, U1(d, b))
28.56/10.02	   A^2 -> H(d, U1(b, c))
28.56/10.02	   A^2 -> H(d, U1(b, d))
28.56/10.02	   A^2 -> H(d, U1(c, c))
28.56/10.02	   A^2 -> H(d, f(e))
28.56/10.02	   A^2 -> H(d, f(k))
28.56/10.02	   A^2 -> H(d, U1(d, d))
28.56/10.02	   A^2 -> H(a, U1(e, b))
28.56/10.02	   A^2 -> H(a, U1(k, b))
28.56/10.02	   A^2 -> H(a, U1(c, d))
28.56/10.02	   A^2 -> H(a, U1(d, c))
28.56/10.02	   A^2 -> H(a, U1(b, e))
28.56/10.02	   A^2 -> H(a, U1(b, k))
28.56/10.02	   A^2 -> H(a, U1(e, c))
28.56/10.02	   A^2 -> H(a, U1(k, c))
28.56/10.02	   A^2 -> H(a, U1(c, e))
28.56/10.02	   A^2 -> H(a, U1(c, k))
28.56/10.02	   A^2 -> H(a, U1(e, e))
28.56/10.02	   A^2 -> H(a, U1(k, k))
28.56/10.02	   A^2 -> H(a, U1(k, d))
28.56/10.02	   A^2 -> H(a, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.02	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.02	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, a), b)
28.56/10.02	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, a), c)
28.56/10.02	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, a), e)
28.56/10.02	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, a), b)
28.56/10.02	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, a), c)
28.56/10.02	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, d), b)
28.56/10.02	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, d), c)
28.56/10.02	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, d), e)
28.56/10.02	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, a), d)
28.56/10.02	   A^2 -> H(U1(c, a), k)
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.02	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.02	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.02	   A^2 -> H(U1(d, c), b)
28.56/10.02	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, c), c)
28.56/10.02	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, c), e)
28.56/10.02	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, a), d)
28.56/10.02	   A^2 -> H(U1(d, a), k)
28.56/10.02	   A^2 -> H(U1(a, e), b)
28.56/10.02	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(a, e), c)
28.56/10.02	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(a, e), e)
28.56/10.02	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(a, k), b)
28.56/10.02	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(a, k), c)
28.56/10.02	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(a, k), e)
28.56/10.02	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(a, c), d)
28.56/10.02	   A^2 -> H(U1(a, c), k)
28.56/10.02	   A^2 -> H(U1(a, d), d)
28.56/10.02	   A^2 -> H(U1(a, d), k)
28.56/10.02	   A^2 -> H(k, U1(c, b))
28.56/10.02	   A^2 -> H(k, U1(d, b))
28.56/10.02	   A^2 -> H(k, U1(b, c))
28.56/10.02	   A^2 -> H(k, U1(b, d))
28.56/10.02	   A^2 -> H(k, U1(c, c))
28.56/10.02	   A^2 -> H(k, f(e))
28.56/10.02	   A^2 -> H(k, f(k))
28.56/10.02	   A^2 -> H(k, U1(d, d))
28.56/10.02	   A^2 -> H(c, U1(e, b))
28.56/10.02	   A^2 -> H(c, U1(k, b))
28.56/10.02	   A^2 -> H(c, U1(c, d))
28.56/10.02	   A^2 -> H(c, U1(d, c))
28.56/10.02	   A^2 -> H(c, U1(b, e))
28.56/10.02	   A^2 -> H(c, U1(b, k))
28.56/10.02	   A^2 -> H(c, U1(e, c))
28.56/10.02	   A^2 -> H(c, U1(k, c))
28.56/10.02	   A^2 -> H(c, U1(c, e))
28.56/10.02	   A^2 -> H(c, U1(c, k))
28.56/10.02	   A^2 -> H(c, U1(e, e))
28.56/10.02	   A^2 -> H(c, U1(k, k))
28.56/10.02	   A^2 -> H(c, U1(k, d))
28.56/10.02	   A^2 -> H(c, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.02	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.02	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, c), b)
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, c), e)
28.56/10.02	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.02	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.02	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.02	   A^2 -> H(U1(k, c), b)
28.56/10.02	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, c), c)
28.56/10.02	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, e), b)
28.56/10.02	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, e), c)
28.56/10.02	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, e), e)
28.56/10.02	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, k), b)
28.56/10.02	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, k), c)
28.56/10.02	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, k), e)
28.56/10.02	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, c), d)
28.56/10.02	   A^2 -> H(e, U1(e, b))
28.56/10.02	   A^2 -> H(e, U1(c, d))
28.56/10.02	   A^2 -> H(e, U1(d, c))
28.56/10.02	   A^2 -> H(e, U1(b, e))
28.56/10.02	   A^2 -> H(e, U1(b, k))
28.56/10.02	   A^2 -> H(e, U1(e, c))
28.56/10.02	   A^2 -> H(e, U1(c, e))
28.56/10.02	   A^2 -> H(e, U1(c, k))
28.56/10.02	   A^2 -> H(e, U1(e, e))
28.56/10.02	   A^2 -> H(e, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, e), b)
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, e), c)
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.02	   A^2 -> H(f(e), d)
28.56/10.02	   A^2 -> H(f(e), k)
28.56/10.02	   A^2 -> H(U1(k, k), b)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, k), c)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.02	   A^2 -> H(f(k), d)
28.56/10.02	   A^2 -> H(f(k), k)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(k, d), b)
28.56/10.02	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, d), c)
28.56/10.02	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, k), b)
28.56/10.02	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, k), c)
28.56/10.02	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, k), e)
28.56/10.02	
28.56/10.02	The TRS R consists of the following rules:
28.56/10.02	
28.56/10.02	   f(x) -> U1(x, x)
28.56/10.02	   U1(e, x) -> x
28.56/10.02	   a -> c
28.56/10.02	   a -> d
28.56/10.02	   b -> c
28.56/10.02	   b -> d
28.56/10.02	   d -> k
28.56/10.02	   c -> e
28.56/10.02	   c -> k
28.56/10.02	
28.56/10.02	Q is empty.
28.56/10.02	We have to consider all minimal (P,Q,R)-chains.
28.56/10.02	----------------------------------------
28.56/10.02	
28.56/10.02	(1757) TransformationProof (EQUIVALENT)
28.56/10.02	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.02	
28.56/10.02	   (A^2 -> H(U1(k, k), U1(k, d)),A^2 -> H(U1(k, k), U1(k, d)))
28.56/10.02	   (A^2 -> H(U1(d, k), U1(k, k)),A^2 -> H(U1(d, k), U1(k, k)))
28.56/10.02	
28.56/10.02	
28.56/10.02	----------------------------------------
28.56/10.02	
28.56/10.02	(1758)
28.56/10.02	Obligation:
28.56/10.02	Q DP problem:
28.56/10.02	The TRS P consists of the following rules:
28.56/10.02	
28.56/10.02	   A^2 -> H(f(c), f(c))
28.56/10.02	   H(x, x) -> G(x, x, f(k))
28.56/10.02	   G(d, x, x) -> A^2
28.56/10.02	   A^2 -> H(f(d), f(d))
28.56/10.02	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.02	   A^2 -> H(f(e), f(e))
28.56/10.02	   A^2 -> H(f(k), f(k))
28.56/10.02	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.02	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.02	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.02	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.02	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(d, d), b)
28.56/10.02	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, d), c)
28.56/10.02	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, d), e)
28.56/10.02	   A^2 -> H(f(d), d)
28.56/10.02	   A^2 -> H(f(d), k)
28.56/10.02	   A^2 -> H(U1(c, c), c)
28.56/10.02	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.02	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.02	   A^2 -> H(f(c), k)
28.56/10.02	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.02	   A^2 -> H(f(k), U1(k, k))
28.56/10.02	   A^2 -> H(f(e), e)
28.56/10.02	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.02	   A^2 -> H(d, U1(c, b))
28.56/10.02	   A^2 -> H(d, U1(d, b))
28.56/10.02	   A^2 -> H(d, U1(b, c))
28.56/10.02	   A^2 -> H(d, U1(b, d))
28.56/10.02	   A^2 -> H(d, U1(c, c))
28.56/10.02	   A^2 -> H(d, f(e))
28.56/10.02	   A^2 -> H(d, f(k))
28.56/10.02	   A^2 -> H(d, U1(d, d))
28.56/10.02	   A^2 -> H(a, U1(e, b))
28.56/10.02	   A^2 -> H(a, U1(k, b))
28.56/10.02	   A^2 -> H(a, U1(c, d))
28.56/10.02	   A^2 -> H(a, U1(d, c))
28.56/10.02	   A^2 -> H(a, U1(b, e))
28.56/10.02	   A^2 -> H(a, U1(b, k))
28.56/10.02	   A^2 -> H(a, U1(e, c))
28.56/10.02	   A^2 -> H(a, U1(k, c))
28.56/10.02	   A^2 -> H(a, U1(c, e))
28.56/10.02	   A^2 -> H(a, U1(c, k))
28.56/10.02	   A^2 -> H(a, U1(e, e))
28.56/10.02	   A^2 -> H(a, U1(k, k))
28.56/10.02	   A^2 -> H(a, U1(k, d))
28.56/10.02	   A^2 -> H(a, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.02	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.02	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, a), b)
28.56/10.02	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, a), c)
28.56/10.02	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, a), e)
28.56/10.02	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, a), b)
28.56/10.02	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, a), c)
28.56/10.02	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, d), b)
28.56/10.02	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, d), c)
28.56/10.02	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, d), e)
28.56/10.02	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, a), d)
28.56/10.02	   A^2 -> H(U1(c, a), k)
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.02	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.02	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.02	   A^2 -> H(U1(d, c), b)
28.56/10.02	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, c), c)
28.56/10.02	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, c), e)
28.56/10.02	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, a), d)
28.56/10.02	   A^2 -> H(U1(d, a), k)
28.56/10.02	   A^2 -> H(U1(a, e), b)
28.56/10.02	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(a, e), c)
28.56/10.02	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(a, e), e)
28.56/10.02	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(a, k), b)
28.56/10.02	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(a, k), c)
28.56/10.02	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(a, k), e)
28.56/10.02	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(a, c), d)
28.56/10.02	   A^2 -> H(U1(a, c), k)
28.56/10.02	   A^2 -> H(U1(a, d), d)
28.56/10.02	   A^2 -> H(U1(a, d), k)
28.56/10.02	   A^2 -> H(k, U1(c, b))
28.56/10.02	   A^2 -> H(k, U1(d, b))
28.56/10.02	   A^2 -> H(k, U1(b, c))
28.56/10.02	   A^2 -> H(k, U1(b, d))
28.56/10.02	   A^2 -> H(k, U1(c, c))
28.56/10.02	   A^2 -> H(k, f(e))
28.56/10.02	   A^2 -> H(k, f(k))
28.56/10.02	   A^2 -> H(k, U1(d, d))
28.56/10.02	   A^2 -> H(c, U1(e, b))
28.56/10.02	   A^2 -> H(c, U1(k, b))
28.56/10.02	   A^2 -> H(c, U1(c, d))
28.56/10.02	   A^2 -> H(c, U1(d, c))
28.56/10.02	   A^2 -> H(c, U1(b, e))
28.56/10.02	   A^2 -> H(c, U1(b, k))
28.56/10.02	   A^2 -> H(c, U1(e, c))
28.56/10.02	   A^2 -> H(c, U1(k, c))
28.56/10.02	   A^2 -> H(c, U1(c, e))
28.56/10.02	   A^2 -> H(c, U1(c, k))
28.56/10.02	   A^2 -> H(c, U1(e, e))
28.56/10.02	   A^2 -> H(c, U1(k, k))
28.56/10.02	   A^2 -> H(c, U1(k, d))
28.56/10.02	   A^2 -> H(c, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.02	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.02	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, c), b)
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, c), e)
28.56/10.02	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.02	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.02	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.02	   A^2 -> H(U1(k, c), b)
28.56/10.02	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, c), c)
28.56/10.02	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, e), b)
28.56/10.02	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, e), c)
28.56/10.02	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, e), e)
28.56/10.02	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, k), b)
28.56/10.02	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, k), c)
28.56/10.02	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, k), e)
28.56/10.02	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, c), d)
28.56/10.02	   A^2 -> H(e, U1(e, b))
28.56/10.02	   A^2 -> H(e, U1(c, d))
28.56/10.02	   A^2 -> H(e, U1(d, c))
28.56/10.02	   A^2 -> H(e, U1(b, e))
28.56/10.02	   A^2 -> H(e, U1(b, k))
28.56/10.02	   A^2 -> H(e, U1(e, c))
28.56/10.02	   A^2 -> H(e, U1(c, e))
28.56/10.02	   A^2 -> H(e, U1(c, k))
28.56/10.02	   A^2 -> H(e, U1(e, e))
28.56/10.02	   A^2 -> H(e, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, e), b)
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, e), c)
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.02	   A^2 -> H(f(e), d)
28.56/10.02	   A^2 -> H(f(e), k)
28.56/10.02	   A^2 -> H(U1(k, k), b)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, k), c)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.02	   A^2 -> H(f(k), d)
28.56/10.02	   A^2 -> H(f(k), k)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(k, d), b)
28.56/10.02	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, d), c)
28.56/10.02	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, k), b)
28.56/10.02	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, k), c)
28.56/10.02	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, k), e)
28.56/10.02	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.02	
28.56/10.02	The TRS R consists of the following rules:
28.56/10.02	
28.56/10.02	   f(x) -> U1(x, x)
28.56/10.02	   U1(e, x) -> x
28.56/10.02	   a -> c
28.56/10.02	   a -> d
28.56/10.02	   b -> c
28.56/10.02	   b -> d
28.56/10.02	   d -> k
28.56/10.02	   c -> e
28.56/10.02	   c -> k
28.56/10.02	
28.56/10.02	Q is empty.
28.56/10.02	We have to consider all minimal (P,Q,R)-chains.
28.56/10.02	----------------------------------------
28.56/10.02	
28.56/10.02	(1759) TransformationProof (EQUIVALENT)
28.56/10.02	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), b) at position [] we obtained the following new rules [LPAR04]:
28.56/10.02	
28.56/10.02	   (A^2 -> H(U1(k, d), b),A^2 -> H(U1(k, d), b))
28.56/10.02	   (A^2 -> H(U1(d, k), b),A^2 -> H(U1(d, k), b))
28.56/10.02	   (A^2 -> H(U1(d, d), c),A^2 -> H(U1(d, d), c))
28.56/10.02	   (A^2 -> H(U1(d, d), d),A^2 -> H(U1(d, d), d))
28.56/10.02	
28.56/10.02	
28.56/10.02	----------------------------------------
28.56/10.02	
28.56/10.02	(1760)
28.56/10.02	Obligation:
28.56/10.02	Q DP problem:
28.56/10.02	The TRS P consists of the following rules:
28.56/10.02	
28.56/10.02	   A^2 -> H(f(c), f(c))
28.56/10.02	   H(x, x) -> G(x, x, f(k))
28.56/10.02	   G(d, x, x) -> A^2
28.56/10.02	   A^2 -> H(f(d), f(d))
28.56/10.02	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.02	   A^2 -> H(f(e), f(e))
28.56/10.02	   A^2 -> H(f(k), f(k))
28.56/10.02	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.02	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.02	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.02	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.02	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(d, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, d), c)
28.56/10.02	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, d), e)
28.56/10.02	   A^2 -> H(f(d), d)
28.56/10.02	   A^2 -> H(f(d), k)
28.56/10.02	   A^2 -> H(U1(c, c), c)
28.56/10.02	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.02	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.02	   A^2 -> H(f(c), k)
28.56/10.02	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.02	   A^2 -> H(f(k), U1(k, k))
28.56/10.02	   A^2 -> H(f(e), e)
28.56/10.02	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.02	   A^2 -> H(d, U1(c, b))
28.56/10.02	   A^2 -> H(d, U1(d, b))
28.56/10.02	   A^2 -> H(d, U1(b, c))
28.56/10.02	   A^2 -> H(d, U1(b, d))
28.56/10.02	   A^2 -> H(d, U1(c, c))
28.56/10.02	   A^2 -> H(d, f(e))
28.56/10.02	   A^2 -> H(d, f(k))
28.56/10.02	   A^2 -> H(d, U1(d, d))
28.56/10.02	   A^2 -> H(a, U1(e, b))
28.56/10.02	   A^2 -> H(a, U1(k, b))
28.56/10.02	   A^2 -> H(a, U1(c, d))
28.56/10.02	   A^2 -> H(a, U1(d, c))
28.56/10.02	   A^2 -> H(a, U1(b, e))
28.56/10.02	   A^2 -> H(a, U1(b, k))
28.56/10.02	   A^2 -> H(a, U1(e, c))
28.56/10.02	   A^2 -> H(a, U1(k, c))
28.56/10.02	   A^2 -> H(a, U1(c, e))
28.56/10.02	   A^2 -> H(a, U1(c, k))
28.56/10.02	   A^2 -> H(a, U1(e, e))
28.56/10.02	   A^2 -> H(a, U1(k, k))
28.56/10.02	   A^2 -> H(a, U1(k, d))
28.56/10.02	   A^2 -> H(a, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.02	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.02	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, a), b)
28.56/10.02	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, a), c)
28.56/10.02	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, a), e)
28.56/10.02	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, a), b)
28.56/10.02	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, a), c)
28.56/10.02	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, d), b)
28.56/10.02	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, d), c)
28.56/10.02	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, d), e)
28.56/10.02	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, a), d)
28.56/10.02	   A^2 -> H(U1(c, a), k)
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.02	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.02	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.02	   A^2 -> H(U1(d, c), b)
28.56/10.02	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, c), c)
28.56/10.02	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, c), e)
28.56/10.02	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, a), d)
28.56/10.02	   A^2 -> H(U1(d, a), k)
28.56/10.02	   A^2 -> H(U1(a, e), b)
28.56/10.02	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(a, e), c)
28.56/10.02	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(a, e), e)
28.56/10.02	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(a, k), b)
28.56/10.02	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(a, k), c)
28.56/10.02	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(a, k), e)
28.56/10.02	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(a, c), d)
28.56/10.02	   A^2 -> H(U1(a, c), k)
28.56/10.02	   A^2 -> H(U1(a, d), d)
28.56/10.02	   A^2 -> H(U1(a, d), k)
28.56/10.02	   A^2 -> H(k, U1(c, b))
28.56/10.02	   A^2 -> H(k, U1(d, b))
28.56/10.02	   A^2 -> H(k, U1(b, c))
28.56/10.02	   A^2 -> H(k, U1(b, d))
28.56/10.02	   A^2 -> H(k, U1(c, c))
28.56/10.02	   A^2 -> H(k, f(e))
28.56/10.02	   A^2 -> H(k, f(k))
28.56/10.02	   A^2 -> H(k, U1(d, d))
28.56/10.02	   A^2 -> H(c, U1(e, b))
28.56/10.02	   A^2 -> H(c, U1(k, b))
28.56/10.02	   A^2 -> H(c, U1(c, d))
28.56/10.02	   A^2 -> H(c, U1(d, c))
28.56/10.02	   A^2 -> H(c, U1(b, e))
28.56/10.02	   A^2 -> H(c, U1(b, k))
28.56/10.02	   A^2 -> H(c, U1(e, c))
28.56/10.02	   A^2 -> H(c, U1(k, c))
28.56/10.02	   A^2 -> H(c, U1(c, e))
28.56/10.02	   A^2 -> H(c, U1(c, k))
28.56/10.02	   A^2 -> H(c, U1(e, e))
28.56/10.02	   A^2 -> H(c, U1(k, k))
28.56/10.02	   A^2 -> H(c, U1(k, d))
28.56/10.02	   A^2 -> H(c, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.02	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.02	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, c), b)
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, c), e)
28.56/10.02	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.02	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.02	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.02	   A^2 -> H(U1(k, c), b)
28.56/10.02	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, c), c)
28.56/10.02	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, e), b)
28.56/10.02	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, e), c)
28.56/10.02	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, e), e)
28.56/10.02	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, k), b)
28.56/10.02	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, k), c)
28.56/10.02	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, k), e)
28.56/10.02	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, c), d)
28.56/10.02	   A^2 -> H(e, U1(e, b))
28.56/10.02	   A^2 -> H(e, U1(c, d))
28.56/10.02	   A^2 -> H(e, U1(d, c))
28.56/10.02	   A^2 -> H(e, U1(b, e))
28.56/10.02	   A^2 -> H(e, U1(b, k))
28.56/10.02	   A^2 -> H(e, U1(e, c))
28.56/10.02	   A^2 -> H(e, U1(c, e))
28.56/10.02	   A^2 -> H(e, U1(c, k))
28.56/10.02	   A^2 -> H(e, U1(e, e))
28.56/10.02	   A^2 -> H(e, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, e), b)
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, e), c)
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.02	   A^2 -> H(f(e), d)
28.56/10.02	   A^2 -> H(f(e), k)
28.56/10.02	   A^2 -> H(U1(k, k), b)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, k), c)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.02	   A^2 -> H(f(k), d)
28.56/10.02	   A^2 -> H(f(k), k)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(k, d), b)
28.56/10.02	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, d), c)
28.56/10.02	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, k), b)
28.56/10.02	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, k), c)
28.56/10.02	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, k), e)
28.56/10.02	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, d), d)
28.56/10.02	
28.56/10.02	The TRS R consists of the following rules:
28.56/10.02	
28.56/10.02	   f(x) -> U1(x, x)
28.56/10.02	   U1(e, x) -> x
28.56/10.02	   a -> c
28.56/10.02	   a -> d
28.56/10.02	   b -> c
28.56/10.02	   b -> d
28.56/10.02	   d -> k
28.56/10.02	   c -> e
28.56/10.02	   c -> k
28.56/10.02	
28.56/10.02	Q is empty.
28.56/10.02	We have to consider all minimal (P,Q,R)-chains.
28.56/10.02	----------------------------------------
28.56/10.02	
28.56/10.02	(1761) TransformationProof (EQUIVALENT)
28.56/10.02	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.02	
28.56/10.02	   (A^2 -> H(U1(k, d), U1(e, d)),A^2 -> H(U1(k, d), U1(e, d)))
28.56/10.02	   (A^2 -> H(U1(d, k), U1(e, d)),A^2 -> H(U1(d, k), U1(e, d)))
28.56/10.02	   (A^2 -> H(U1(d, d), d),A^2 -> H(U1(d, d), d))
28.56/10.02	   (A^2 -> H(U1(d, d), U1(e, k)),A^2 -> H(U1(d, d), U1(e, k)))
28.56/10.02	
28.56/10.02	
28.56/10.02	----------------------------------------
28.56/10.02	
28.56/10.02	(1762)
28.56/10.02	Obligation:
28.56/10.02	Q DP problem:
28.56/10.02	The TRS P consists of the following rules:
28.56/10.02	
28.56/10.02	   A^2 -> H(f(c), f(c))
28.56/10.02	   H(x, x) -> G(x, x, f(k))
28.56/10.02	   G(d, x, x) -> A^2
28.56/10.02	   A^2 -> H(f(d), f(d))
28.56/10.02	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.02	   A^2 -> H(f(e), f(e))
28.56/10.02	   A^2 -> H(f(k), f(k))
28.56/10.02	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.02	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.02	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.02	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.02	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(d, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, d), c)
28.56/10.02	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, d), e)
28.56/10.02	   A^2 -> H(f(d), d)
28.56/10.02	   A^2 -> H(f(d), k)
28.56/10.02	   A^2 -> H(U1(c, c), c)
28.56/10.02	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.02	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.02	   A^2 -> H(f(c), k)
28.56/10.02	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.02	   A^2 -> H(f(k), U1(k, k))
28.56/10.02	   A^2 -> H(f(e), e)
28.56/10.02	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.02	   A^2 -> H(d, U1(c, b))
28.56/10.02	   A^2 -> H(d, U1(d, b))
28.56/10.02	   A^2 -> H(d, U1(b, c))
28.56/10.02	   A^2 -> H(d, U1(b, d))
28.56/10.02	   A^2 -> H(d, U1(c, c))
28.56/10.02	   A^2 -> H(d, f(e))
28.56/10.02	   A^2 -> H(d, f(k))
28.56/10.02	   A^2 -> H(d, U1(d, d))
28.56/10.02	   A^2 -> H(a, U1(e, b))
28.56/10.02	   A^2 -> H(a, U1(k, b))
28.56/10.02	   A^2 -> H(a, U1(c, d))
28.56/10.02	   A^2 -> H(a, U1(d, c))
28.56/10.02	   A^2 -> H(a, U1(b, e))
28.56/10.02	   A^2 -> H(a, U1(b, k))
28.56/10.02	   A^2 -> H(a, U1(e, c))
28.56/10.02	   A^2 -> H(a, U1(k, c))
28.56/10.02	   A^2 -> H(a, U1(c, e))
28.56/10.02	   A^2 -> H(a, U1(c, k))
28.56/10.02	   A^2 -> H(a, U1(e, e))
28.56/10.02	   A^2 -> H(a, U1(k, k))
28.56/10.02	   A^2 -> H(a, U1(k, d))
28.56/10.02	   A^2 -> H(a, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.02	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.02	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, a), b)
28.56/10.02	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, a), c)
28.56/10.02	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, a), e)
28.56/10.02	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, a), b)
28.56/10.02	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, a), c)
28.56/10.02	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, d), b)
28.56/10.02	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, d), c)
28.56/10.02	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, d), e)
28.56/10.02	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, a), d)
28.56/10.02	   A^2 -> H(U1(c, a), k)
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.02	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.02	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.02	   A^2 -> H(U1(d, c), b)
28.56/10.02	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, c), c)
28.56/10.02	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, c), e)
28.56/10.02	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, a), d)
28.56/10.02	   A^2 -> H(U1(d, a), k)
28.56/10.02	   A^2 -> H(U1(a, e), b)
28.56/10.02	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(a, e), c)
28.56/10.02	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(a, e), e)
28.56/10.02	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(a, k), b)
28.56/10.02	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(a, k), c)
28.56/10.02	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(a, k), e)
28.56/10.02	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(a, c), d)
28.56/10.02	   A^2 -> H(U1(a, c), k)
28.56/10.02	   A^2 -> H(U1(a, d), d)
28.56/10.02	   A^2 -> H(U1(a, d), k)
28.56/10.02	   A^2 -> H(k, U1(c, b))
28.56/10.02	   A^2 -> H(k, U1(d, b))
28.56/10.02	   A^2 -> H(k, U1(b, c))
28.56/10.02	   A^2 -> H(k, U1(b, d))
28.56/10.02	   A^2 -> H(k, U1(c, c))
28.56/10.02	   A^2 -> H(k, f(e))
28.56/10.02	   A^2 -> H(k, f(k))
28.56/10.02	   A^2 -> H(k, U1(d, d))
28.56/10.02	   A^2 -> H(c, U1(e, b))
28.56/10.02	   A^2 -> H(c, U1(k, b))
28.56/10.02	   A^2 -> H(c, U1(c, d))
28.56/10.02	   A^2 -> H(c, U1(d, c))
28.56/10.02	   A^2 -> H(c, U1(b, e))
28.56/10.02	   A^2 -> H(c, U1(b, k))
28.56/10.02	   A^2 -> H(c, U1(e, c))
28.56/10.02	   A^2 -> H(c, U1(k, c))
28.56/10.02	   A^2 -> H(c, U1(c, e))
28.56/10.02	   A^2 -> H(c, U1(c, k))
28.56/10.02	   A^2 -> H(c, U1(e, e))
28.56/10.02	   A^2 -> H(c, U1(k, k))
28.56/10.02	   A^2 -> H(c, U1(k, d))
28.56/10.02	   A^2 -> H(c, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.02	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.02	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, c), b)
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, c), e)
28.56/10.02	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.02	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.02	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.02	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.02	   A^2 -> H(U1(k, c), b)
28.56/10.02	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, c), c)
28.56/10.02	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, e), b)
28.56/10.02	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, e), c)
28.56/10.02	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, e), e)
28.56/10.02	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, k), b)
28.56/10.02	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(c, k), c)
28.56/10.02	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(c, k), e)
28.56/10.02	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(c, c), d)
28.56/10.02	   A^2 -> H(e, U1(e, b))
28.56/10.02	   A^2 -> H(e, U1(c, d))
28.56/10.02	   A^2 -> H(e, U1(d, c))
28.56/10.02	   A^2 -> H(e, U1(b, e))
28.56/10.02	   A^2 -> H(e, U1(b, k))
28.56/10.02	   A^2 -> H(e, U1(e, c))
28.56/10.02	   A^2 -> H(e, U1(c, e))
28.56/10.02	   A^2 -> H(e, U1(c, k))
28.56/10.02	   A^2 -> H(e, U1(e, e))
28.56/10.02	   A^2 -> H(e, U1(d, k))
28.56/10.02	   A^2 -> H(U1(e, e), b)
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.02	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.02	   A^2 -> H(U1(e, e), c)
28.56/10.02	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.02	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.02	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.02	   A^2 -> H(f(e), d)
28.56/10.02	   A^2 -> H(f(e), k)
28.56/10.02	   A^2 -> H(U1(k, k), b)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, k), c)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.02	   A^2 -> H(f(k), d)
28.56/10.02	   A^2 -> H(f(k), k)
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.02	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.02	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.02	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.02	   A^2 -> H(U1(k, d), b)
28.56/10.02	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.02	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.02	   A^2 -> H(U1(k, d), c)
28.56/10.02	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.02	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, k), b)
28.56/10.02	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.02	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.02	   A^2 -> H(U1(d, k), c)
28.56/10.02	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.02	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.02	   A^2 -> H(U1(d, k), e)
28.56/10.02	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.02	   A^2 -> H(U1(d, d), d)
28.56/10.02	
28.56/10.02	The TRS R consists of the following rules:
28.56/10.02	
28.56/10.02	   f(x) -> U1(x, x)
28.56/10.02	   U1(e, x) -> x
28.56/10.02	   a -> c
28.56/10.02	   a -> d
28.56/10.02	   b -> c
28.56/10.02	   b -> d
28.56/10.02	   d -> k
28.56/10.02	   c -> e
28.56/10.02	   c -> k
28.56/10.02	
28.56/10.02	Q is empty.
28.56/10.02	We have to consider all minimal (P,Q,R)-chains.
28.56/10.02	----------------------------------------
28.56/10.02	
28.56/10.02	(1763) TransformationProof (EQUIVALENT)
28.56/10.02	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.02	
28.56/10.02	   (A^2 -> H(U1(k, d), U1(d, e)),A^2 -> H(U1(k, d), U1(d, e)))
28.56/10.02	   (A^2 -> H(U1(d, k), U1(d, e)),A^2 -> H(U1(d, k), U1(d, e)))
28.56/10.02	   (A^2 -> H(U1(d, d), U1(k, e)),A^2 -> H(U1(d, d), U1(k, e)))
28.56/10.03	
28.56/10.03	
28.56/10.03	----------------------------------------
28.56/10.03	
28.56/10.03	(1764)
28.56/10.03	Obligation:
28.56/10.03	Q DP problem:
28.56/10.03	The TRS P consists of the following rules:
28.56/10.03	
28.56/10.03	   A^2 -> H(f(c), f(c))
28.56/10.03	   H(x, x) -> G(x, x, f(k))
28.56/10.03	   G(d, x, x) -> A^2
28.56/10.03	   A^2 -> H(f(d), f(d))
28.56/10.03	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.03	   A^2 -> H(f(e), f(e))
28.56/10.03	   A^2 -> H(f(k), f(k))
28.56/10.03	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.03	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.03	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.03	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.03	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.03	   A^2 -> H(U1(d, d), c)
28.56/10.03	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.03	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.03	   A^2 -> H(U1(d, d), e)
28.56/10.03	   A^2 -> H(f(d), d)
28.56/10.03	   A^2 -> H(f(d), k)
28.56/10.03	   A^2 -> H(U1(c, c), c)
28.56/10.03	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.03	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.03	   A^2 -> H(f(c), k)
28.56/10.03	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.03	   A^2 -> H(f(k), U1(k, k))
28.56/10.03	   A^2 -> H(f(e), e)
28.56/10.03	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.03	   A^2 -> H(d, U1(c, b))
28.56/10.03	   A^2 -> H(d, U1(d, b))
28.56/10.03	   A^2 -> H(d, U1(b, c))
28.56/10.03	   A^2 -> H(d, U1(b, d))
28.56/10.03	   A^2 -> H(d, U1(c, c))
28.56/10.03	   A^2 -> H(d, f(e))
28.56/10.03	   A^2 -> H(d, f(k))
28.56/10.03	   A^2 -> H(d, U1(d, d))
28.56/10.03	   A^2 -> H(a, U1(e, b))
28.56/10.03	   A^2 -> H(a, U1(k, b))
28.56/10.03	   A^2 -> H(a, U1(c, d))
28.56/10.03	   A^2 -> H(a, U1(d, c))
28.56/10.03	   A^2 -> H(a, U1(b, e))
28.56/10.03	   A^2 -> H(a, U1(b, k))
28.56/10.03	   A^2 -> H(a, U1(e, c))
28.56/10.03	   A^2 -> H(a, U1(k, c))
28.56/10.03	   A^2 -> H(a, U1(c, e))
28.56/10.03	   A^2 -> H(a, U1(c, k))
28.56/10.03	   A^2 -> H(a, U1(e, e))
28.56/10.03	   A^2 -> H(a, U1(k, k))
28.56/10.03	   A^2 -> H(a, U1(k, d))
28.56/10.03	   A^2 -> H(a, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.03	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.03	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, a), b)
28.56/10.03	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, a), c)
28.56/10.03	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, a), e)
28.56/10.03	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, a), b)
28.56/10.03	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, a), c)
28.56/10.03	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, d), b)
28.56/10.03	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, d), c)
28.56/10.03	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, d), e)
28.56/10.03	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, a), d)
28.56/10.03	   A^2 -> H(U1(c, a), k)
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.03	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.03	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.03	   A^2 -> H(U1(d, c), b)
28.56/10.03	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(d, c), c)
28.56/10.03	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(d, c), e)
28.56/10.03	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, a), d)
28.56/10.03	   A^2 -> H(U1(d, a), k)
28.56/10.03	   A^2 -> H(U1(a, e), b)
28.56/10.03	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(a, e), c)
28.56/10.03	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(a, e), e)
28.56/10.03	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(a, k), b)
28.56/10.03	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(a, k), c)
28.56/10.03	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(a, k), e)
28.56/10.03	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(a, c), d)
28.56/10.03	   A^2 -> H(U1(a, c), k)
28.56/10.03	   A^2 -> H(U1(a, d), d)
28.56/10.03	   A^2 -> H(U1(a, d), k)
28.56/10.03	   A^2 -> H(k, U1(c, b))
28.56/10.03	   A^2 -> H(k, U1(d, b))
28.56/10.03	   A^2 -> H(k, U1(b, c))
28.56/10.03	   A^2 -> H(k, U1(b, d))
28.56/10.03	   A^2 -> H(k, U1(c, c))
28.56/10.03	   A^2 -> H(k, f(e))
28.56/10.03	   A^2 -> H(k, f(k))
28.56/10.03	   A^2 -> H(k, U1(d, d))
28.56/10.03	   A^2 -> H(c, U1(e, b))
28.56/10.03	   A^2 -> H(c, U1(k, b))
28.56/10.03	   A^2 -> H(c, U1(c, d))
28.56/10.03	   A^2 -> H(c, U1(d, c))
28.56/10.03	   A^2 -> H(c, U1(b, e))
28.56/10.03	   A^2 -> H(c, U1(b, k))
28.56/10.03	   A^2 -> H(c, U1(e, c))
28.56/10.03	   A^2 -> H(c, U1(k, c))
28.56/10.03	   A^2 -> H(c, U1(c, e))
28.56/10.03	   A^2 -> H(c, U1(c, k))
28.56/10.03	   A^2 -> H(c, U1(e, e))
28.56/10.03	   A^2 -> H(c, U1(k, k))
28.56/10.03	   A^2 -> H(c, U1(k, d))
28.56/10.03	   A^2 -> H(c, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.03	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.03	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, c), b)
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, c), e)
28.56/10.03	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.03	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.03	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.03	   A^2 -> H(U1(k, c), b)
28.56/10.03	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, c), c)
28.56/10.03	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, e), b)
28.56/10.03	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, e), c)
28.56/10.03	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, e), e)
28.56/10.03	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, k), b)
28.56/10.03	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, k), c)
28.56/10.03	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, k), e)
28.56/10.03	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, c), d)
28.56/10.03	   A^2 -> H(e, U1(e, b))
28.56/10.03	   A^2 -> H(e, U1(c, d))
28.56/10.03	   A^2 -> H(e, U1(d, c))
28.56/10.03	   A^2 -> H(e, U1(b, e))
28.56/10.03	   A^2 -> H(e, U1(b, k))
28.56/10.03	   A^2 -> H(e, U1(e, c))
28.56/10.03	   A^2 -> H(e, U1(c, e))
28.56/10.03	   A^2 -> H(e, U1(c, k))
28.56/10.03	   A^2 -> H(e, U1(e, e))
28.56/10.03	   A^2 -> H(e, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, e), b)
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, e), c)
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.03	   A^2 -> H(f(e), d)
28.56/10.03	   A^2 -> H(f(e), k)
28.56/10.03	   A^2 -> H(U1(k, k), b)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, k), c)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.03	   A^2 -> H(f(k), d)
28.56/10.03	   A^2 -> H(f(k), k)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.03	   A^2 -> H(U1(k, d), b)
28.56/10.03	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, d), c)
28.56/10.03	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, k), b)
28.56/10.03	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(d, k), c)
28.56/10.03	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(d, k), e)
28.56/10.03	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, d), d)
28.56/10.03	
28.56/10.03	The TRS R consists of the following rules:
28.56/10.03	
28.56/10.03	   f(x) -> U1(x, x)
28.56/10.03	   U1(e, x) -> x
28.56/10.03	   a -> c
28.56/10.03	   a -> d
28.56/10.03	   b -> c
28.56/10.03	   b -> d
28.56/10.03	   d -> k
28.56/10.03	   c -> e
28.56/10.03	   c -> k
28.56/10.03	
28.56/10.03	Q is empty.
28.56/10.03	We have to consider all minimal (P,Q,R)-chains.
28.56/10.03	----------------------------------------
28.56/10.03	
28.56/10.03	(1765) TransformationProof (EQUIVALENT)
28.56/10.03	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), c) at position [] we obtained the following new rules [LPAR04]:
28.56/10.03	
28.56/10.03	   (A^2 -> H(U1(k, d), c),A^2 -> H(U1(k, d), c))
28.56/10.03	   (A^2 -> H(U1(d, k), c),A^2 -> H(U1(d, k), c))
28.56/10.03	   (A^2 -> H(U1(d, d), e),A^2 -> H(U1(d, d), e))
28.56/10.03	   (A^2 -> H(U1(d, d), k),A^2 -> H(U1(d, d), k))
28.56/10.03	
28.56/10.03	
28.56/10.03	----------------------------------------
28.56/10.03	
28.56/10.03	(1766)
28.56/10.03	Obligation:
28.56/10.03	Q DP problem:
28.56/10.03	The TRS P consists of the following rules:
28.56/10.03	
28.56/10.03	   A^2 -> H(f(c), f(c))
28.56/10.03	   H(x, x) -> G(x, x, f(k))
28.56/10.03	   G(d, x, x) -> A^2
28.56/10.03	   A^2 -> H(f(d), f(d))
28.56/10.03	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.03	   A^2 -> H(f(e), f(e))
28.56/10.03	   A^2 -> H(f(k), f(k))
28.56/10.03	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.03	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.03	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.03	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.03	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.03	   A^2 -> H(U1(d, d), U1(e, k))
28.56/10.03	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.03	   A^2 -> H(U1(d, d), e)
28.56/10.03	   A^2 -> H(f(d), d)
28.56/10.03	   A^2 -> H(f(d), k)
28.56/10.03	   A^2 -> H(U1(c, c), c)
28.56/10.03	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.03	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.03	   A^2 -> H(f(c), k)
28.56/10.03	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.03	   A^2 -> H(f(k), U1(k, k))
28.56/10.03	   A^2 -> H(f(e), e)
28.56/10.03	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.03	   A^2 -> H(d, U1(c, b))
28.56/10.03	   A^2 -> H(d, U1(d, b))
28.56/10.03	   A^2 -> H(d, U1(b, c))
28.56/10.03	   A^2 -> H(d, U1(b, d))
28.56/10.03	   A^2 -> H(d, U1(c, c))
28.56/10.03	   A^2 -> H(d, f(e))
28.56/10.03	   A^2 -> H(d, f(k))
28.56/10.03	   A^2 -> H(d, U1(d, d))
28.56/10.03	   A^2 -> H(a, U1(e, b))
28.56/10.03	   A^2 -> H(a, U1(k, b))
28.56/10.03	   A^2 -> H(a, U1(c, d))
28.56/10.03	   A^2 -> H(a, U1(d, c))
28.56/10.03	   A^2 -> H(a, U1(b, e))
28.56/10.03	   A^2 -> H(a, U1(b, k))
28.56/10.03	   A^2 -> H(a, U1(e, c))
28.56/10.03	   A^2 -> H(a, U1(k, c))
28.56/10.03	   A^2 -> H(a, U1(c, e))
28.56/10.03	   A^2 -> H(a, U1(c, k))
28.56/10.03	   A^2 -> H(a, U1(e, e))
28.56/10.03	   A^2 -> H(a, U1(k, k))
28.56/10.03	   A^2 -> H(a, U1(k, d))
28.56/10.03	   A^2 -> H(a, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.03	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.03	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, a), b)
28.56/10.03	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, a), c)
28.56/10.03	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, a), e)
28.56/10.03	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, a), b)
28.56/10.03	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, a), c)
28.56/10.03	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, d), b)
28.56/10.03	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, d), c)
28.56/10.03	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, d), e)
28.56/10.03	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, a), d)
28.56/10.03	   A^2 -> H(U1(c, a), k)
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.03	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.03	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.03	   A^2 -> H(U1(d, c), b)
28.56/10.03	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(d, c), c)
28.56/10.03	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(d, c), e)
28.56/10.03	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, a), d)
28.56/10.03	   A^2 -> H(U1(d, a), k)
28.56/10.03	   A^2 -> H(U1(a, e), b)
28.56/10.03	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(a, e), c)
28.56/10.03	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(a, e), e)
28.56/10.03	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(a, k), b)
28.56/10.03	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(a, k), c)
28.56/10.03	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(a, k), e)
28.56/10.03	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(a, c), d)
28.56/10.03	   A^2 -> H(U1(a, c), k)
28.56/10.03	   A^2 -> H(U1(a, d), d)
28.56/10.03	   A^2 -> H(U1(a, d), k)
28.56/10.03	   A^2 -> H(k, U1(c, b))
28.56/10.03	   A^2 -> H(k, U1(d, b))
28.56/10.03	   A^2 -> H(k, U1(b, c))
28.56/10.03	   A^2 -> H(k, U1(b, d))
28.56/10.03	   A^2 -> H(k, U1(c, c))
28.56/10.03	   A^2 -> H(k, f(e))
28.56/10.03	   A^2 -> H(k, f(k))
28.56/10.03	   A^2 -> H(k, U1(d, d))
28.56/10.03	   A^2 -> H(c, U1(e, b))
28.56/10.03	   A^2 -> H(c, U1(k, b))
28.56/10.03	   A^2 -> H(c, U1(c, d))
28.56/10.03	   A^2 -> H(c, U1(d, c))
28.56/10.03	   A^2 -> H(c, U1(b, e))
28.56/10.03	   A^2 -> H(c, U1(b, k))
28.56/10.03	   A^2 -> H(c, U1(e, c))
28.56/10.03	   A^2 -> H(c, U1(k, c))
28.56/10.03	   A^2 -> H(c, U1(c, e))
28.56/10.03	   A^2 -> H(c, U1(c, k))
28.56/10.03	   A^2 -> H(c, U1(e, e))
28.56/10.03	   A^2 -> H(c, U1(k, k))
28.56/10.03	   A^2 -> H(c, U1(k, d))
28.56/10.03	   A^2 -> H(c, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.03	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.03	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, c), b)
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, c), e)
28.56/10.03	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.03	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.03	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.03	   A^2 -> H(U1(k, c), b)
28.56/10.03	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, c), c)
28.56/10.03	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, e), b)
28.56/10.03	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, e), c)
28.56/10.03	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, e), e)
28.56/10.03	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, k), b)
28.56/10.03	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, k), c)
28.56/10.03	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, k), e)
28.56/10.03	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, c), d)
28.56/10.03	   A^2 -> H(e, U1(e, b))
28.56/10.03	   A^2 -> H(e, U1(c, d))
28.56/10.03	   A^2 -> H(e, U1(d, c))
28.56/10.03	   A^2 -> H(e, U1(b, e))
28.56/10.03	   A^2 -> H(e, U1(b, k))
28.56/10.03	   A^2 -> H(e, U1(e, c))
28.56/10.03	   A^2 -> H(e, U1(c, e))
28.56/10.03	   A^2 -> H(e, U1(c, k))
28.56/10.03	   A^2 -> H(e, U1(e, e))
28.56/10.03	   A^2 -> H(e, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, e), b)
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, e), c)
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.03	   A^2 -> H(f(e), d)
28.56/10.03	   A^2 -> H(f(e), k)
28.56/10.03	   A^2 -> H(U1(k, k), b)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, k), c)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.03	   A^2 -> H(f(k), d)
28.56/10.03	   A^2 -> H(f(k), k)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.03	   A^2 -> H(U1(k, d), b)
28.56/10.03	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, d), c)
28.56/10.03	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, k), b)
28.56/10.03	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(d, k), c)
28.56/10.03	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(d, k), e)
28.56/10.03	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, d), d)
28.56/10.03	   A^2 -> H(U1(d, d), k)
28.56/10.03	
28.56/10.03	The TRS R consists of the following rules:
28.56/10.03	
28.56/10.03	   f(x) -> U1(x, x)
28.56/10.03	   U1(e, x) -> x
28.56/10.03	   a -> c
28.56/10.03	   a -> d
28.56/10.03	   b -> c
28.56/10.03	   b -> d
28.56/10.03	   d -> k
28.56/10.03	   c -> e
28.56/10.03	   c -> k
28.56/10.03	
28.56/10.03	Q is empty.
28.56/10.03	We have to consider all minimal (P,Q,R)-chains.
28.56/10.03	----------------------------------------
28.56/10.03	
28.56/10.03	(1767) TransformationProof (EQUIVALENT)
28.56/10.03	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.03	
28.56/10.03	   (A^2 -> H(U1(k, d), U1(e, k)),A^2 -> H(U1(k, d), U1(e, k)))
28.56/10.03	   (A^2 -> H(U1(d, k), U1(e, k)),A^2 -> H(U1(d, k), U1(e, k)))
28.56/10.03	   (A^2 -> H(U1(d, d), k),A^2 -> H(U1(d, d), k))
28.56/10.03	
28.56/10.03	
28.56/10.03	----------------------------------------
28.56/10.03	
28.56/10.03	(1768)
28.56/10.03	Obligation:
28.56/10.03	Q DP problem:
28.56/10.03	The TRS P consists of the following rules:
28.56/10.03	
28.56/10.03	   A^2 -> H(f(c), f(c))
28.56/10.03	   H(x, x) -> G(x, x, f(k))
28.56/10.03	   G(d, x, x) -> A^2
28.56/10.03	   A^2 -> H(f(d), f(d))
28.56/10.03	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.03	   A^2 -> H(f(e), f(e))
28.56/10.03	   A^2 -> H(f(k), f(k))
28.56/10.03	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.03	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.03	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.03	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.03	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.03	   A^2 -> H(U1(d, d), U1(k, e))
28.56/10.03	   A^2 -> H(U1(d, d), e)
28.56/10.03	   A^2 -> H(f(d), d)
28.56/10.03	   A^2 -> H(f(d), k)
28.56/10.03	   A^2 -> H(U1(c, c), c)
28.56/10.03	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.03	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.03	   A^2 -> H(f(c), k)
28.56/10.03	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.03	   A^2 -> H(f(k), U1(k, k))
28.56/10.03	   A^2 -> H(f(e), e)
28.56/10.03	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.03	   A^2 -> H(d, U1(c, b))
28.56/10.03	   A^2 -> H(d, U1(d, b))
28.56/10.03	   A^2 -> H(d, U1(b, c))
28.56/10.03	   A^2 -> H(d, U1(b, d))
28.56/10.03	   A^2 -> H(d, U1(c, c))
28.56/10.03	   A^2 -> H(d, f(e))
28.56/10.03	   A^2 -> H(d, f(k))
28.56/10.03	   A^2 -> H(d, U1(d, d))
28.56/10.03	   A^2 -> H(a, U1(e, b))
28.56/10.03	   A^2 -> H(a, U1(k, b))
28.56/10.03	   A^2 -> H(a, U1(c, d))
28.56/10.03	   A^2 -> H(a, U1(d, c))
28.56/10.03	   A^2 -> H(a, U1(b, e))
28.56/10.03	   A^2 -> H(a, U1(b, k))
28.56/10.03	   A^2 -> H(a, U1(e, c))
28.56/10.03	   A^2 -> H(a, U1(k, c))
28.56/10.03	   A^2 -> H(a, U1(c, e))
28.56/10.03	   A^2 -> H(a, U1(c, k))
28.56/10.03	   A^2 -> H(a, U1(e, e))
28.56/10.03	   A^2 -> H(a, U1(k, k))
28.56/10.03	   A^2 -> H(a, U1(k, d))
28.56/10.03	   A^2 -> H(a, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.03	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.03	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, a), b)
28.56/10.03	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, a), c)
28.56/10.03	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, a), e)
28.56/10.03	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, a), b)
28.56/10.03	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, a), c)
28.56/10.03	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, d), b)
28.56/10.03	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, d), c)
28.56/10.03	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, d), e)
28.56/10.03	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, a), d)
28.56/10.03	   A^2 -> H(U1(c, a), k)
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.03	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.03	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.03	   A^2 -> H(U1(d, c), b)
28.56/10.03	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(d, c), c)
28.56/10.03	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(d, c), e)
28.56/10.03	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, a), d)
28.56/10.03	   A^2 -> H(U1(d, a), k)
28.56/10.03	   A^2 -> H(U1(a, e), b)
28.56/10.03	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(a, e), c)
28.56/10.03	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(a, e), e)
28.56/10.03	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(a, k), b)
28.56/10.03	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(a, k), c)
28.56/10.03	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(a, k), e)
28.56/10.03	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(a, c), d)
28.56/10.03	   A^2 -> H(U1(a, c), k)
28.56/10.03	   A^2 -> H(U1(a, d), d)
28.56/10.03	   A^2 -> H(U1(a, d), k)
28.56/10.03	   A^2 -> H(k, U1(c, b))
28.56/10.03	   A^2 -> H(k, U1(d, b))
28.56/10.03	   A^2 -> H(k, U1(b, c))
28.56/10.03	   A^2 -> H(k, U1(b, d))
28.56/10.03	   A^2 -> H(k, U1(c, c))
28.56/10.03	   A^2 -> H(k, f(e))
28.56/10.03	   A^2 -> H(k, f(k))
28.56/10.03	   A^2 -> H(k, U1(d, d))
28.56/10.03	   A^2 -> H(c, U1(e, b))
28.56/10.03	   A^2 -> H(c, U1(k, b))
28.56/10.03	   A^2 -> H(c, U1(c, d))
28.56/10.03	   A^2 -> H(c, U1(d, c))
28.56/10.03	   A^2 -> H(c, U1(b, e))
28.56/10.03	   A^2 -> H(c, U1(b, k))
28.56/10.03	   A^2 -> H(c, U1(e, c))
28.56/10.03	   A^2 -> H(c, U1(k, c))
28.56/10.03	   A^2 -> H(c, U1(c, e))
28.56/10.03	   A^2 -> H(c, U1(c, k))
28.56/10.03	   A^2 -> H(c, U1(e, e))
28.56/10.03	   A^2 -> H(c, U1(k, k))
28.56/10.03	   A^2 -> H(c, U1(k, d))
28.56/10.03	   A^2 -> H(c, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.03	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.03	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, c), b)
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, c), e)
28.56/10.03	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.03	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.03	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.03	   A^2 -> H(U1(k, c), b)
28.56/10.03	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, c), c)
28.56/10.03	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, e), b)
28.56/10.03	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, e), c)
28.56/10.03	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, e), e)
28.56/10.03	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, k), b)
28.56/10.03	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, k), c)
28.56/10.03	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, k), e)
28.56/10.03	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, c), d)
28.56/10.03	   A^2 -> H(e, U1(e, b))
28.56/10.03	   A^2 -> H(e, U1(c, d))
28.56/10.03	   A^2 -> H(e, U1(d, c))
28.56/10.03	   A^2 -> H(e, U1(b, e))
28.56/10.03	   A^2 -> H(e, U1(b, k))
28.56/10.03	   A^2 -> H(e, U1(e, c))
28.56/10.03	   A^2 -> H(e, U1(c, e))
28.56/10.03	   A^2 -> H(e, U1(c, k))
28.56/10.03	   A^2 -> H(e, U1(e, e))
28.56/10.03	   A^2 -> H(e, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, e), b)
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, e), c)
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.03	   A^2 -> H(f(e), d)
28.56/10.03	   A^2 -> H(f(e), k)
28.56/10.03	   A^2 -> H(U1(k, k), b)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, k), c)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.03	   A^2 -> H(f(k), d)
28.56/10.03	   A^2 -> H(f(k), k)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.03	   A^2 -> H(U1(k, d), b)
28.56/10.03	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, d), c)
28.56/10.03	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, k), b)
28.56/10.03	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(d, k), c)
28.56/10.03	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(d, k), e)
28.56/10.03	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, d), d)
28.56/10.03	   A^2 -> H(U1(d, d), k)
28.56/10.03	
28.56/10.03	The TRS R consists of the following rules:
28.56/10.03	
28.56/10.03	   f(x) -> U1(x, x)
28.56/10.03	   U1(e, x) -> x
28.56/10.03	   a -> c
28.56/10.03	   a -> d
28.56/10.03	   b -> c
28.56/10.03	   b -> d
28.56/10.03	   d -> k
28.56/10.03	   c -> e
28.56/10.03	   c -> k
28.56/10.03	
28.56/10.03	Q is empty.
28.56/10.03	We have to consider all minimal (P,Q,R)-chains.
28.56/10.03	----------------------------------------
28.56/10.03	
28.56/10.03	(1769) TransformationProof (EQUIVALENT)
28.56/10.03	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.03	
28.56/10.03	   (A^2 -> H(U1(k, d), U1(k, e)),A^2 -> H(U1(k, d), U1(k, e)))
28.56/10.03	   (A^2 -> H(U1(d, k), U1(k, e)),A^2 -> H(U1(d, k), U1(k, e)))
28.56/10.03	
28.56/10.03	
28.56/10.03	----------------------------------------
28.56/10.03	
28.56/10.03	(1770)
28.56/10.03	Obligation:
28.56/10.03	Q DP problem:
28.56/10.03	The TRS P consists of the following rules:
28.56/10.03	
28.56/10.03	   A^2 -> H(f(c), f(c))
28.56/10.03	   H(x, x) -> G(x, x, f(k))
28.56/10.03	   G(d, x, x) -> A^2
28.56/10.03	   A^2 -> H(f(d), f(d))
28.56/10.03	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.03	   A^2 -> H(f(e), f(e))
28.56/10.03	   A^2 -> H(f(k), f(k))
28.56/10.03	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.03	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.03	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.03	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.03	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.03	   A^2 -> H(U1(d, d), e)
28.56/10.03	   A^2 -> H(f(d), d)
28.56/10.03	   A^2 -> H(f(d), k)
28.56/10.03	   A^2 -> H(U1(c, c), c)
28.56/10.03	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.03	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.03	   A^2 -> H(f(c), k)
28.56/10.03	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.03	   A^2 -> H(f(k), U1(k, k))
28.56/10.03	   A^2 -> H(f(e), e)
28.56/10.03	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.03	   A^2 -> H(d, U1(c, b))
28.56/10.03	   A^2 -> H(d, U1(d, b))
28.56/10.03	   A^2 -> H(d, U1(b, c))
28.56/10.03	   A^2 -> H(d, U1(b, d))
28.56/10.03	   A^2 -> H(d, U1(c, c))
28.56/10.03	   A^2 -> H(d, f(e))
28.56/10.03	   A^2 -> H(d, f(k))
28.56/10.03	   A^2 -> H(d, U1(d, d))
28.56/10.03	   A^2 -> H(a, U1(e, b))
28.56/10.03	   A^2 -> H(a, U1(k, b))
28.56/10.03	   A^2 -> H(a, U1(c, d))
28.56/10.03	   A^2 -> H(a, U1(d, c))
28.56/10.03	   A^2 -> H(a, U1(b, e))
28.56/10.03	   A^2 -> H(a, U1(b, k))
28.56/10.03	   A^2 -> H(a, U1(e, c))
28.56/10.03	   A^2 -> H(a, U1(k, c))
28.56/10.03	   A^2 -> H(a, U1(c, e))
28.56/10.03	   A^2 -> H(a, U1(c, k))
28.56/10.03	   A^2 -> H(a, U1(e, e))
28.56/10.03	   A^2 -> H(a, U1(k, k))
28.56/10.03	   A^2 -> H(a, U1(k, d))
28.56/10.03	   A^2 -> H(a, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.03	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.03	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, a), b)
28.56/10.03	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, a), c)
28.56/10.03	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, a), e)
28.56/10.03	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, a), b)
28.56/10.03	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, a), c)
28.56/10.03	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, d), b)
28.56/10.03	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, d), c)
28.56/10.03	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, d), e)
28.56/10.03	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, a), d)
28.56/10.03	   A^2 -> H(U1(c, a), k)
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.03	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.03	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.03	   A^2 -> H(U1(d, c), b)
28.56/10.03	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(d, c), c)
28.56/10.03	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(d, c), e)
28.56/10.03	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, a), d)
28.56/10.03	   A^2 -> H(U1(d, a), k)
28.56/10.03	   A^2 -> H(U1(a, e), b)
28.56/10.03	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(a, e), c)
28.56/10.03	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(a, e), e)
28.56/10.03	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(a, k), b)
28.56/10.03	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(a, k), c)
28.56/10.03	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(a, k), e)
28.56/10.03	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(a, c), d)
28.56/10.03	   A^2 -> H(U1(a, c), k)
28.56/10.03	   A^2 -> H(U1(a, d), d)
28.56/10.03	   A^2 -> H(U1(a, d), k)
28.56/10.03	   A^2 -> H(k, U1(c, b))
28.56/10.03	   A^2 -> H(k, U1(d, b))
28.56/10.03	   A^2 -> H(k, U1(b, c))
28.56/10.03	   A^2 -> H(k, U1(b, d))
28.56/10.03	   A^2 -> H(k, U1(c, c))
28.56/10.03	   A^2 -> H(k, f(e))
28.56/10.03	   A^2 -> H(k, f(k))
28.56/10.03	   A^2 -> H(k, U1(d, d))
28.56/10.03	   A^2 -> H(c, U1(e, b))
28.56/10.03	   A^2 -> H(c, U1(k, b))
28.56/10.03	   A^2 -> H(c, U1(c, d))
28.56/10.03	   A^2 -> H(c, U1(d, c))
28.56/10.03	   A^2 -> H(c, U1(b, e))
28.56/10.03	   A^2 -> H(c, U1(b, k))
28.56/10.03	   A^2 -> H(c, U1(e, c))
28.56/10.03	   A^2 -> H(c, U1(k, c))
28.56/10.03	   A^2 -> H(c, U1(c, e))
28.56/10.03	   A^2 -> H(c, U1(c, k))
28.56/10.03	   A^2 -> H(c, U1(e, e))
28.56/10.03	   A^2 -> H(c, U1(k, k))
28.56/10.03	   A^2 -> H(c, U1(k, d))
28.56/10.03	   A^2 -> H(c, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.03	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.03	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, c), b)
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, c), e)
28.56/10.03	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.03	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.03	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.03	   A^2 -> H(U1(k, c), b)
28.56/10.03	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, c), c)
28.56/10.03	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, e), b)
28.56/10.03	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, e), c)
28.56/10.03	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, e), e)
28.56/10.03	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, k), b)
28.56/10.03	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, k), c)
28.56/10.03	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, k), e)
28.56/10.03	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, c), d)
28.56/10.03	   A^2 -> H(e, U1(e, b))
28.56/10.03	   A^2 -> H(e, U1(c, d))
28.56/10.03	   A^2 -> H(e, U1(d, c))
28.56/10.03	   A^2 -> H(e, U1(b, e))
28.56/10.03	   A^2 -> H(e, U1(b, k))
28.56/10.03	   A^2 -> H(e, U1(e, c))
28.56/10.03	   A^2 -> H(e, U1(c, e))
28.56/10.03	   A^2 -> H(e, U1(c, k))
28.56/10.03	   A^2 -> H(e, U1(e, e))
28.56/10.03	   A^2 -> H(e, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, e), b)
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, e), c)
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.03	   A^2 -> H(f(e), d)
28.56/10.03	   A^2 -> H(f(e), k)
28.56/10.03	   A^2 -> H(U1(k, k), b)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, k), c)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.03	   A^2 -> H(f(k), d)
28.56/10.03	   A^2 -> H(f(k), k)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.03	   A^2 -> H(U1(k, d), b)
28.56/10.03	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, d), c)
28.56/10.03	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, k), b)
28.56/10.03	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(d, k), c)
28.56/10.03	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(d, k), e)
28.56/10.03	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, d), d)
28.56/10.03	   A^2 -> H(U1(d, d), k)
28.56/10.03	
28.56/10.03	The TRS R consists of the following rules:
28.56/10.03	
28.56/10.03	   f(x) -> U1(x, x)
28.56/10.03	   U1(e, x) -> x
28.56/10.03	   a -> c
28.56/10.03	   a -> d
28.56/10.03	   b -> c
28.56/10.03	   b -> d
28.56/10.03	   d -> k
28.56/10.03	   c -> e
28.56/10.03	   c -> k
28.56/10.03	
28.56/10.03	Q is empty.
28.56/10.03	We have to consider all minimal (P,Q,R)-chains.
28.56/10.03	----------------------------------------
28.56/10.03	
28.56/10.03	(1771) TransformationProof (EQUIVALENT)
28.56/10.03	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), e) at position [] we obtained the following new rules [LPAR04]:
28.56/10.03	
28.56/10.03	   (A^2 -> H(U1(k, d), e),A^2 -> H(U1(k, d), e))
28.56/10.03	   (A^2 -> H(U1(d, k), e),A^2 -> H(U1(d, k), e))
28.56/10.03	
28.56/10.03	
28.56/10.03	----------------------------------------
28.56/10.03	
28.56/10.03	(1772)
28.56/10.03	Obligation:
28.56/10.03	Q DP problem:
28.56/10.03	The TRS P consists of the following rules:
28.56/10.03	
28.56/10.03	   A^2 -> H(f(c), f(c))
28.56/10.03	   H(x, x) -> G(x, x, f(k))
28.56/10.03	   G(d, x, x) -> A^2
28.56/10.03	   A^2 -> H(f(d), f(d))
28.56/10.03	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.03	   A^2 -> H(f(e), f(e))
28.56/10.03	   A^2 -> H(f(k), f(k))
28.56/10.03	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.03	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.03	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.03	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.03	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.03	   A^2 -> H(f(d), d)
28.56/10.03	   A^2 -> H(f(d), k)
28.56/10.03	   A^2 -> H(U1(c, c), c)
28.56/10.03	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.03	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.03	   A^2 -> H(f(c), k)
28.56/10.03	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.03	   A^2 -> H(f(k), U1(k, k))
28.56/10.03	   A^2 -> H(f(e), e)
28.56/10.03	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.03	   A^2 -> H(d, U1(c, b))
28.56/10.03	   A^2 -> H(d, U1(d, b))
28.56/10.03	   A^2 -> H(d, U1(b, c))
28.56/10.03	   A^2 -> H(d, U1(b, d))
28.56/10.03	   A^2 -> H(d, U1(c, c))
28.56/10.03	   A^2 -> H(d, f(e))
28.56/10.03	   A^2 -> H(d, f(k))
28.56/10.03	   A^2 -> H(d, U1(d, d))
28.56/10.03	   A^2 -> H(a, U1(e, b))
28.56/10.03	   A^2 -> H(a, U1(k, b))
28.56/10.03	   A^2 -> H(a, U1(c, d))
28.56/10.03	   A^2 -> H(a, U1(d, c))
28.56/10.03	   A^2 -> H(a, U1(b, e))
28.56/10.03	   A^2 -> H(a, U1(b, k))
28.56/10.03	   A^2 -> H(a, U1(e, c))
28.56/10.03	   A^2 -> H(a, U1(k, c))
28.56/10.03	   A^2 -> H(a, U1(c, e))
28.56/10.03	   A^2 -> H(a, U1(c, k))
28.56/10.03	   A^2 -> H(a, U1(e, e))
28.56/10.03	   A^2 -> H(a, U1(k, k))
28.56/10.03	   A^2 -> H(a, U1(k, d))
28.56/10.03	   A^2 -> H(a, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.03	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.03	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, a), b)
28.56/10.03	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, a), c)
28.56/10.03	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, a), e)
28.56/10.03	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, a), b)
28.56/10.03	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, a), c)
28.56/10.03	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, d), b)
28.56/10.03	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, d), c)
28.56/10.03	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, d), e)
28.56/10.03	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, a), d)
28.56/10.03	   A^2 -> H(U1(c, a), k)
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.03	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.03	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.03	   A^2 -> H(U1(d, c), b)
28.56/10.03	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(d, c), c)
28.56/10.03	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(d, c), e)
28.56/10.03	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, a), d)
28.56/10.03	   A^2 -> H(U1(d, a), k)
28.56/10.03	   A^2 -> H(U1(a, e), b)
28.56/10.03	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(a, e), c)
28.56/10.03	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(a, e), e)
28.56/10.03	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(a, k), b)
28.56/10.03	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(a, k), c)
28.56/10.03	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(a, k), e)
28.56/10.03	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(a, c), d)
28.56/10.03	   A^2 -> H(U1(a, c), k)
28.56/10.03	   A^2 -> H(U1(a, d), d)
28.56/10.03	   A^2 -> H(U1(a, d), k)
28.56/10.03	   A^2 -> H(k, U1(c, b))
28.56/10.03	   A^2 -> H(k, U1(d, b))
28.56/10.03	   A^2 -> H(k, U1(b, c))
28.56/10.03	   A^2 -> H(k, U1(b, d))
28.56/10.03	   A^2 -> H(k, U1(c, c))
28.56/10.03	   A^2 -> H(k, f(e))
28.56/10.03	   A^2 -> H(k, f(k))
28.56/10.03	   A^2 -> H(k, U1(d, d))
28.56/10.03	   A^2 -> H(c, U1(e, b))
28.56/10.03	   A^2 -> H(c, U1(k, b))
28.56/10.03	   A^2 -> H(c, U1(c, d))
28.56/10.03	   A^2 -> H(c, U1(d, c))
28.56/10.03	   A^2 -> H(c, U1(b, e))
28.56/10.03	   A^2 -> H(c, U1(b, k))
28.56/10.03	   A^2 -> H(c, U1(e, c))
28.56/10.03	   A^2 -> H(c, U1(k, c))
28.56/10.03	   A^2 -> H(c, U1(c, e))
28.56/10.03	   A^2 -> H(c, U1(c, k))
28.56/10.03	   A^2 -> H(c, U1(e, e))
28.56/10.03	   A^2 -> H(c, U1(k, k))
28.56/10.03	   A^2 -> H(c, U1(k, d))
28.56/10.03	   A^2 -> H(c, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.03	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.03	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, c), b)
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, c), e)
28.56/10.03	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.03	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.03	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.03	   A^2 -> H(U1(k, c), b)
28.56/10.03	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, c), c)
28.56/10.03	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, e), b)
28.56/10.03	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, e), c)
28.56/10.03	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, e), e)
28.56/10.03	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, k), b)
28.56/10.03	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, k), c)
28.56/10.03	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, k), e)
28.56/10.03	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, c), d)
28.56/10.03	   A^2 -> H(e, U1(e, b))
28.56/10.03	   A^2 -> H(e, U1(c, d))
28.56/10.03	   A^2 -> H(e, U1(d, c))
28.56/10.03	   A^2 -> H(e, U1(b, e))
28.56/10.03	   A^2 -> H(e, U1(b, k))
28.56/10.03	   A^2 -> H(e, U1(e, c))
28.56/10.03	   A^2 -> H(e, U1(c, e))
28.56/10.03	   A^2 -> H(e, U1(c, k))
28.56/10.03	   A^2 -> H(e, U1(e, e))
28.56/10.03	   A^2 -> H(e, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, e), b)
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, e), c)
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.03	   A^2 -> H(f(e), d)
28.56/10.03	   A^2 -> H(f(e), k)
28.56/10.03	   A^2 -> H(U1(k, k), b)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, k), c)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.03	   A^2 -> H(f(k), d)
28.56/10.03	   A^2 -> H(f(k), k)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.03	   A^2 -> H(U1(k, d), b)
28.56/10.03	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, d), c)
28.56/10.03	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, k), b)
28.56/10.03	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(d, k), c)
28.56/10.03	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(d, k), e)
28.56/10.03	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, d), d)
28.56/10.03	   A^2 -> H(U1(d, d), k)
28.56/10.03	   A^2 -> H(U1(k, d), e)
28.56/10.03	
28.56/10.03	The TRS R consists of the following rules:
28.56/10.03	
28.56/10.03	   f(x) -> U1(x, x)
28.56/10.03	   U1(e, x) -> x
28.56/10.03	   a -> c
28.56/10.03	   a -> d
28.56/10.03	   b -> c
28.56/10.03	   b -> d
28.56/10.03	   d -> k
28.56/10.03	   c -> e
28.56/10.03	   c -> k
28.56/10.03	
28.56/10.03	Q is empty.
28.56/10.03	We have to consider all minimal (P,Q,R)-chains.
28.56/10.03	----------------------------------------
28.56/10.03	
28.56/10.03	(1773) DependencyGraphProof (EQUIVALENT)
28.56/10.03	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.56/10.03	----------------------------------------
28.56/10.03	
28.56/10.03	(1774)
28.56/10.03	Obligation:
28.56/10.03	Q DP problem:
28.56/10.03	The TRS P consists of the following rules:
28.56/10.03	
28.56/10.03	   H(x, x) -> G(x, x, f(k))
28.56/10.03	   G(d, x, x) -> A^2
28.56/10.03	   A^2 -> H(f(c), f(c))
28.56/10.03	   A^2 -> H(f(d), f(d))
28.56/10.03	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.03	   A^2 -> H(f(e), f(e))
28.56/10.03	   A^2 -> H(f(k), f(k))
28.56/10.03	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.03	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.03	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.03	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.03	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.03	   A^2 -> H(f(d), d)
28.56/10.03	   A^2 -> H(f(d), k)
28.56/10.03	   A^2 -> H(U1(c, c), c)
28.56/10.03	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.03	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.03	   A^2 -> H(f(c), k)
28.56/10.03	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.03	   A^2 -> H(f(k), U1(k, k))
28.56/10.03	   A^2 -> H(f(e), e)
28.56/10.03	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.03	   A^2 -> H(d, U1(c, b))
28.56/10.03	   A^2 -> H(d, U1(d, b))
28.56/10.03	   A^2 -> H(d, U1(b, c))
28.56/10.03	   A^2 -> H(d, U1(b, d))
28.56/10.03	   A^2 -> H(d, U1(c, c))
28.56/10.03	   A^2 -> H(d, f(e))
28.56/10.03	   A^2 -> H(d, f(k))
28.56/10.03	   A^2 -> H(d, U1(d, d))
28.56/10.03	   A^2 -> H(a, U1(e, b))
28.56/10.03	   A^2 -> H(a, U1(k, b))
28.56/10.03	   A^2 -> H(a, U1(c, d))
28.56/10.03	   A^2 -> H(a, U1(d, c))
28.56/10.03	   A^2 -> H(a, U1(b, e))
28.56/10.03	   A^2 -> H(a, U1(b, k))
28.56/10.03	   A^2 -> H(a, U1(e, c))
28.56/10.03	   A^2 -> H(a, U1(k, c))
28.56/10.03	   A^2 -> H(a, U1(c, e))
28.56/10.03	   A^2 -> H(a, U1(c, k))
28.56/10.03	   A^2 -> H(a, U1(e, e))
28.56/10.03	   A^2 -> H(a, U1(k, k))
28.56/10.03	   A^2 -> H(a, U1(k, d))
28.56/10.03	   A^2 -> H(a, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.03	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.03	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, a), b)
28.56/10.03	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, a), c)
28.56/10.03	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, a), e)
28.56/10.03	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, a), b)
28.56/10.03	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, a), c)
28.56/10.03	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, d), b)
28.56/10.03	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, d), c)
28.56/10.03	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, d), e)
28.56/10.03	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, a), d)
28.56/10.03	   A^2 -> H(U1(c, a), k)
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.03	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.03	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.03	   A^2 -> H(U1(d, c), b)
28.56/10.03	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(d, c), c)
28.56/10.03	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(d, c), e)
28.56/10.03	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, a), d)
28.56/10.03	   A^2 -> H(U1(d, a), k)
28.56/10.03	   A^2 -> H(U1(a, e), b)
28.56/10.03	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(a, e), c)
28.56/10.03	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(a, e), e)
28.56/10.03	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(a, k), b)
28.56/10.03	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(a, k), c)
28.56/10.03	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(a, k), e)
28.56/10.03	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(a, c), d)
28.56/10.03	   A^2 -> H(U1(a, c), k)
28.56/10.03	   A^2 -> H(U1(a, d), d)
28.56/10.03	   A^2 -> H(U1(a, d), k)
28.56/10.03	   A^2 -> H(k, U1(c, b))
28.56/10.03	   A^2 -> H(k, U1(d, b))
28.56/10.03	   A^2 -> H(k, U1(b, c))
28.56/10.03	   A^2 -> H(k, U1(b, d))
28.56/10.03	   A^2 -> H(k, U1(c, c))
28.56/10.03	   A^2 -> H(k, f(e))
28.56/10.03	   A^2 -> H(k, f(k))
28.56/10.03	   A^2 -> H(k, U1(d, d))
28.56/10.03	   A^2 -> H(c, U1(e, b))
28.56/10.03	   A^2 -> H(c, U1(k, b))
28.56/10.03	   A^2 -> H(c, U1(c, d))
28.56/10.03	   A^2 -> H(c, U1(d, c))
28.56/10.03	   A^2 -> H(c, U1(b, e))
28.56/10.03	   A^2 -> H(c, U1(b, k))
28.56/10.03	   A^2 -> H(c, U1(e, c))
28.56/10.03	   A^2 -> H(c, U1(k, c))
28.56/10.03	   A^2 -> H(c, U1(c, e))
28.56/10.03	   A^2 -> H(c, U1(c, k))
28.56/10.03	   A^2 -> H(c, U1(e, e))
28.56/10.03	   A^2 -> H(c, U1(k, k))
28.56/10.03	   A^2 -> H(c, U1(k, d))
28.56/10.03	   A^2 -> H(c, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.03	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.03	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, c), b)
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, c), e)
28.56/10.03	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.03	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.03	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.03	   A^2 -> H(U1(k, c), b)
28.56/10.03	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, c), c)
28.56/10.03	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, e), b)
28.56/10.03	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, e), c)
28.56/10.03	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, e), e)
28.56/10.03	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, k), b)
28.56/10.03	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, k), c)
28.56/10.03	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, k), e)
28.56/10.03	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, c), d)
28.56/10.03	   A^2 -> H(e, U1(e, b))
28.56/10.03	   A^2 -> H(e, U1(c, d))
28.56/10.03	   A^2 -> H(e, U1(d, c))
28.56/10.03	   A^2 -> H(e, U1(b, e))
28.56/10.03	   A^2 -> H(e, U1(b, k))
28.56/10.03	   A^2 -> H(e, U1(e, c))
28.56/10.03	   A^2 -> H(e, U1(c, e))
28.56/10.03	   A^2 -> H(e, U1(c, k))
28.56/10.03	   A^2 -> H(e, U1(e, e))
28.56/10.03	   A^2 -> H(e, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, e), b)
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, e), c)
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.03	   A^2 -> H(f(e), d)
28.56/10.03	   A^2 -> H(f(e), k)
28.56/10.03	   A^2 -> H(U1(k, k), b)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, k), c)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.03	   A^2 -> H(f(k), d)
28.56/10.03	   A^2 -> H(f(k), k)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.03	   A^2 -> H(U1(k, d), b)
28.56/10.03	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, d), c)
28.56/10.03	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, k), b)
28.56/10.03	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(d, k), c)
28.56/10.03	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(d, k), e)
28.56/10.03	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, d), d)
28.56/10.03	   A^2 -> H(U1(d, d), k)
28.56/10.03	
28.56/10.03	The TRS R consists of the following rules:
28.56/10.03	
28.56/10.03	   f(x) -> U1(x, x)
28.56/10.03	   U1(e, x) -> x
28.56/10.03	   a -> c
28.56/10.03	   a -> d
28.56/10.03	   b -> c
28.56/10.03	   b -> d
28.56/10.03	   d -> k
28.56/10.03	   c -> e
28.56/10.03	   c -> k
28.56/10.03	
28.56/10.03	Q is empty.
28.56/10.03	We have to consider all minimal (P,Q,R)-chains.
28.56/10.03	----------------------------------------
28.56/10.03	
28.56/10.03	(1775) TransformationProof (EQUIVALENT)
28.56/10.03	By narrowing [LPAR04] the rule A^2 -> H(f(d), d) at position [] we obtained the following new rules [LPAR04]:
28.56/10.03	
28.56/10.03	   (A^2 -> H(U1(d, d), d),A^2 -> H(U1(d, d), d))
28.56/10.03	   (A^2 -> H(f(k), d),A^2 -> H(f(k), d))
28.56/10.03	   (A^2 -> H(f(d), k),A^2 -> H(f(d), k))
28.56/10.03	
28.56/10.03	
28.56/10.03	----------------------------------------
28.56/10.03	
28.56/10.03	(1776)
28.56/10.03	Obligation:
28.56/10.03	Q DP problem:
28.56/10.03	The TRS P consists of the following rules:
28.56/10.03	
28.56/10.03	   H(x, x) -> G(x, x, f(k))
28.56/10.03	   G(d, x, x) -> A^2
28.56/10.03	   A^2 -> H(f(c), f(c))
28.56/10.03	   A^2 -> H(f(d), f(d))
28.56/10.03	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.03	   A^2 -> H(f(e), f(e))
28.56/10.03	   A^2 -> H(f(k), f(k))
28.56/10.03	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.03	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.03	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.03	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.03	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.03	   A^2 -> H(f(d), k)
28.56/10.03	   A^2 -> H(U1(c, c), c)
28.56/10.03	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.03	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.03	   A^2 -> H(f(c), k)
28.56/10.03	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.03	   A^2 -> H(f(k), U1(k, k))
28.56/10.03	   A^2 -> H(f(e), e)
28.56/10.03	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.03	   A^2 -> H(d, U1(c, b))
28.56/10.03	   A^2 -> H(d, U1(d, b))
28.56/10.03	   A^2 -> H(d, U1(b, c))
28.56/10.03	   A^2 -> H(d, U1(b, d))
28.56/10.03	   A^2 -> H(d, U1(c, c))
28.56/10.03	   A^2 -> H(d, f(e))
28.56/10.03	   A^2 -> H(d, f(k))
28.56/10.03	   A^2 -> H(d, U1(d, d))
28.56/10.03	   A^2 -> H(a, U1(e, b))
28.56/10.03	   A^2 -> H(a, U1(k, b))
28.56/10.03	   A^2 -> H(a, U1(c, d))
28.56/10.03	   A^2 -> H(a, U1(d, c))
28.56/10.03	   A^2 -> H(a, U1(b, e))
28.56/10.03	   A^2 -> H(a, U1(b, k))
28.56/10.03	   A^2 -> H(a, U1(e, c))
28.56/10.03	   A^2 -> H(a, U1(k, c))
28.56/10.03	   A^2 -> H(a, U1(c, e))
28.56/10.03	   A^2 -> H(a, U1(c, k))
28.56/10.03	   A^2 -> H(a, U1(e, e))
28.56/10.03	   A^2 -> H(a, U1(k, k))
28.56/10.03	   A^2 -> H(a, U1(k, d))
28.56/10.03	   A^2 -> H(a, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.03	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.03	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, a), b)
28.56/10.03	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, a), c)
28.56/10.03	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, a), e)
28.56/10.03	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, a), b)
28.56/10.03	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, a), c)
28.56/10.03	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, d), b)
28.56/10.03	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, d), c)
28.56/10.03	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, d), e)
28.56/10.03	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, a), d)
28.56/10.03	   A^2 -> H(U1(c, a), k)
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.03	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.03	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.03	   A^2 -> H(U1(d, c), b)
28.56/10.03	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(d, c), c)
28.56/10.03	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(d, c), e)
28.56/10.03	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, a), d)
28.56/10.03	   A^2 -> H(U1(d, a), k)
28.56/10.03	   A^2 -> H(U1(a, e), b)
28.56/10.03	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(a, e), c)
28.56/10.03	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(a, e), e)
28.56/10.03	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(a, k), b)
28.56/10.03	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(a, k), c)
28.56/10.03	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(a, k), e)
28.56/10.03	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(a, c), d)
28.56/10.03	   A^2 -> H(U1(a, c), k)
28.56/10.03	   A^2 -> H(U1(a, d), d)
28.56/10.03	   A^2 -> H(U1(a, d), k)
28.56/10.03	   A^2 -> H(k, U1(c, b))
28.56/10.03	   A^2 -> H(k, U1(d, b))
28.56/10.03	   A^2 -> H(k, U1(b, c))
28.56/10.03	   A^2 -> H(k, U1(b, d))
28.56/10.03	   A^2 -> H(k, U1(c, c))
28.56/10.03	   A^2 -> H(k, f(e))
28.56/10.03	   A^2 -> H(k, f(k))
28.56/10.03	   A^2 -> H(k, U1(d, d))
28.56/10.03	   A^2 -> H(c, U1(e, b))
28.56/10.03	   A^2 -> H(c, U1(k, b))
28.56/10.03	   A^2 -> H(c, U1(c, d))
28.56/10.03	   A^2 -> H(c, U1(d, c))
28.56/10.03	   A^2 -> H(c, U1(b, e))
28.56/10.03	   A^2 -> H(c, U1(b, k))
28.56/10.03	   A^2 -> H(c, U1(e, c))
28.56/10.03	   A^2 -> H(c, U1(k, c))
28.56/10.03	   A^2 -> H(c, U1(c, e))
28.56/10.03	   A^2 -> H(c, U1(c, k))
28.56/10.03	   A^2 -> H(c, U1(e, e))
28.56/10.03	   A^2 -> H(c, U1(k, k))
28.56/10.03	   A^2 -> H(c, U1(k, d))
28.56/10.03	   A^2 -> H(c, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.03	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.03	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, c), b)
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, c), e)
28.56/10.03	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.03	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.03	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.03	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.03	   A^2 -> H(U1(k, c), b)
28.56/10.03	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, c), c)
28.56/10.03	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, e), b)
28.56/10.03	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, e), c)
28.56/10.03	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, e), e)
28.56/10.03	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, k), b)
28.56/10.03	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(c, k), c)
28.56/10.03	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.03	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.03	   A^2 -> H(U1(c, k), e)
28.56/10.03	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.03	   A^2 -> H(U1(c, c), d)
28.56/10.03	   A^2 -> H(e, U1(e, b))
28.56/10.03	   A^2 -> H(e, U1(c, d))
28.56/10.03	   A^2 -> H(e, U1(d, c))
28.56/10.03	   A^2 -> H(e, U1(b, e))
28.56/10.03	   A^2 -> H(e, U1(b, k))
28.56/10.03	   A^2 -> H(e, U1(e, c))
28.56/10.03	   A^2 -> H(e, U1(c, e))
28.56/10.03	   A^2 -> H(e, U1(c, k))
28.56/10.03	   A^2 -> H(e, U1(e, e))
28.56/10.03	   A^2 -> H(e, U1(d, k))
28.56/10.03	   A^2 -> H(U1(e, e), b)
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.03	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.03	   A^2 -> H(U1(e, e), c)
28.56/10.03	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.03	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.03	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.03	   A^2 -> H(f(e), d)
28.56/10.03	   A^2 -> H(f(e), k)
28.56/10.03	   A^2 -> H(U1(k, k), b)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, k), c)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.03	   A^2 -> H(f(k), d)
28.56/10.03	   A^2 -> H(f(k), k)
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.03	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.03	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.03	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.03	   A^2 -> H(U1(k, d), b)
28.56/10.03	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.03	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.03	   A^2 -> H(U1(k, d), c)
28.56/10.03	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.03	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.03	   A^2 -> H(U1(d, k), b)
28.56/10.03	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.03	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.03	   A^2 -> H(U1(d, k), c)
28.56/10.03	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(d, k), e)
28.56/10.04	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, d), d)
28.56/10.04	   A^2 -> H(U1(d, d), k)
28.56/10.04	
28.56/10.04	The TRS R consists of the following rules:
28.56/10.04	
28.56/10.04	   f(x) -> U1(x, x)
28.56/10.04	   U1(e, x) -> x
28.56/10.04	   a -> c
28.56/10.04	   a -> d
28.56/10.04	   b -> c
28.56/10.04	   b -> d
28.56/10.04	   d -> k
28.56/10.04	   c -> e
28.56/10.04	   c -> k
28.56/10.04	
28.56/10.04	Q is empty.
28.56/10.04	We have to consider all minimal (P,Q,R)-chains.
28.56/10.04	----------------------------------------
28.56/10.04	
28.56/10.04	(1777) TransformationProof (EQUIVALENT)
28.56/10.04	By narrowing [LPAR04] the rule A^2 -> H(f(d), k) at position [] we obtained the following new rules [LPAR04]:
28.56/10.04	
28.56/10.04	   (A^2 -> H(U1(d, d), k),A^2 -> H(U1(d, d), k))
28.56/10.04	   (A^2 -> H(f(k), k),A^2 -> H(f(k), k))
28.56/10.04	
28.56/10.04	
28.56/10.04	----------------------------------------
28.56/10.04	
28.56/10.04	(1778)
28.56/10.04	Obligation:
28.56/10.04	Q DP problem:
28.56/10.04	The TRS P consists of the following rules:
28.56/10.04	
28.56/10.04	   H(x, x) -> G(x, x, f(k))
28.56/10.04	   G(d, x, x) -> A^2
28.56/10.04	   A^2 -> H(f(c), f(c))
28.56/10.04	   A^2 -> H(f(d), f(d))
28.56/10.04	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.04	   A^2 -> H(f(e), f(e))
28.56/10.04	   A^2 -> H(f(k), f(k))
28.56/10.04	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.04	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.04	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.04	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.04	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.04	   A^2 -> H(U1(c, c), c)
28.56/10.04	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.04	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.04	   A^2 -> H(f(c), k)
28.56/10.04	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.04	   A^2 -> H(f(k), U1(k, k))
28.56/10.04	   A^2 -> H(f(e), e)
28.56/10.04	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.04	   A^2 -> H(d, U1(c, b))
28.56/10.04	   A^2 -> H(d, U1(d, b))
28.56/10.04	   A^2 -> H(d, U1(b, c))
28.56/10.04	   A^2 -> H(d, U1(b, d))
28.56/10.04	   A^2 -> H(d, U1(c, c))
28.56/10.04	   A^2 -> H(d, f(e))
28.56/10.04	   A^2 -> H(d, f(k))
28.56/10.04	   A^2 -> H(d, U1(d, d))
28.56/10.04	   A^2 -> H(a, U1(e, b))
28.56/10.04	   A^2 -> H(a, U1(k, b))
28.56/10.04	   A^2 -> H(a, U1(c, d))
28.56/10.04	   A^2 -> H(a, U1(d, c))
28.56/10.04	   A^2 -> H(a, U1(b, e))
28.56/10.04	   A^2 -> H(a, U1(b, k))
28.56/10.04	   A^2 -> H(a, U1(e, c))
28.56/10.04	   A^2 -> H(a, U1(k, c))
28.56/10.04	   A^2 -> H(a, U1(c, e))
28.56/10.04	   A^2 -> H(a, U1(c, k))
28.56/10.04	   A^2 -> H(a, U1(e, e))
28.56/10.04	   A^2 -> H(a, U1(k, k))
28.56/10.04	   A^2 -> H(a, U1(k, d))
28.56/10.04	   A^2 -> H(a, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.04	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.04	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, a), b)
28.56/10.04	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, a), c)
28.56/10.04	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, a), e)
28.56/10.04	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, a), b)
28.56/10.04	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, a), c)
28.56/10.04	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, d), b)
28.56/10.04	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, d), c)
28.56/10.04	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, d), e)
28.56/10.04	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, a), d)
28.56/10.04	   A^2 -> H(U1(c, a), k)
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.04	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.04	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.04	   A^2 -> H(U1(d, c), b)
28.56/10.04	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(d, c), c)
28.56/10.04	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(d, c), e)
28.56/10.04	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, a), d)
28.56/10.04	   A^2 -> H(U1(d, a), k)
28.56/10.04	   A^2 -> H(U1(a, e), b)
28.56/10.04	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(a, e), c)
28.56/10.04	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(a, e), e)
28.56/10.04	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(a, k), b)
28.56/10.04	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(a, k), c)
28.56/10.04	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(a, k), e)
28.56/10.04	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(a, c), d)
28.56/10.04	   A^2 -> H(U1(a, c), k)
28.56/10.04	   A^2 -> H(U1(a, d), d)
28.56/10.04	   A^2 -> H(U1(a, d), k)
28.56/10.04	   A^2 -> H(k, U1(c, b))
28.56/10.04	   A^2 -> H(k, U1(d, b))
28.56/10.04	   A^2 -> H(k, U1(b, c))
28.56/10.04	   A^2 -> H(k, U1(b, d))
28.56/10.04	   A^2 -> H(k, U1(c, c))
28.56/10.04	   A^2 -> H(k, f(e))
28.56/10.04	   A^2 -> H(k, f(k))
28.56/10.04	   A^2 -> H(k, U1(d, d))
28.56/10.04	   A^2 -> H(c, U1(e, b))
28.56/10.04	   A^2 -> H(c, U1(k, b))
28.56/10.04	   A^2 -> H(c, U1(c, d))
28.56/10.04	   A^2 -> H(c, U1(d, c))
28.56/10.04	   A^2 -> H(c, U1(b, e))
28.56/10.04	   A^2 -> H(c, U1(b, k))
28.56/10.04	   A^2 -> H(c, U1(e, c))
28.56/10.04	   A^2 -> H(c, U1(k, c))
28.56/10.04	   A^2 -> H(c, U1(c, e))
28.56/10.04	   A^2 -> H(c, U1(c, k))
28.56/10.04	   A^2 -> H(c, U1(e, e))
28.56/10.04	   A^2 -> H(c, U1(k, k))
28.56/10.04	   A^2 -> H(c, U1(k, d))
28.56/10.04	   A^2 -> H(c, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.04	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.04	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, c), b)
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, c), e)
28.56/10.04	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.04	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.04	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.04	   A^2 -> H(U1(k, c), b)
28.56/10.04	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, c), c)
28.56/10.04	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, e), b)
28.56/10.04	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, e), c)
28.56/10.04	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, e), e)
28.56/10.04	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, k), b)
28.56/10.04	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, k), c)
28.56/10.04	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, k), e)
28.56/10.04	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, c), d)
28.56/10.04	   A^2 -> H(e, U1(e, b))
28.56/10.04	   A^2 -> H(e, U1(c, d))
28.56/10.04	   A^2 -> H(e, U1(d, c))
28.56/10.04	   A^2 -> H(e, U1(b, e))
28.56/10.04	   A^2 -> H(e, U1(b, k))
28.56/10.04	   A^2 -> H(e, U1(e, c))
28.56/10.04	   A^2 -> H(e, U1(c, e))
28.56/10.04	   A^2 -> H(e, U1(c, k))
28.56/10.04	   A^2 -> H(e, U1(e, e))
28.56/10.04	   A^2 -> H(e, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, e), b)
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, e), c)
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.04	   A^2 -> H(f(e), d)
28.56/10.04	   A^2 -> H(f(e), k)
28.56/10.04	   A^2 -> H(U1(k, k), b)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, k), c)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.04	   A^2 -> H(f(k), d)
28.56/10.04	   A^2 -> H(f(k), k)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.04	   A^2 -> H(U1(k, d), b)
28.56/10.04	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, d), c)
28.56/10.04	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, k), b)
28.56/10.04	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(d, k), c)
28.56/10.04	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(d, k), e)
28.56/10.04	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, d), d)
28.56/10.04	   A^2 -> H(U1(d, d), k)
28.56/10.04	
28.56/10.04	The TRS R consists of the following rules:
28.56/10.04	
28.56/10.04	   f(x) -> U1(x, x)
28.56/10.04	   U1(e, x) -> x
28.56/10.04	   a -> c
28.56/10.04	   a -> d
28.56/10.04	   b -> c
28.56/10.04	   b -> d
28.56/10.04	   d -> k
28.56/10.04	   c -> e
28.56/10.04	   c -> k
28.56/10.04	
28.56/10.04	Q is empty.
28.56/10.04	We have to consider all minimal (P,Q,R)-chains.
28.56/10.04	----------------------------------------
28.56/10.04	
28.56/10.04	(1779) TransformationProof (EQUIVALENT)
28.56/10.04	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), c) at position [] we obtained the following new rules [LPAR04]:
28.56/10.04	
28.56/10.04	   (A^2 -> H(U1(e, c), c),A^2 -> H(U1(e, c), c))
28.56/10.04	   (A^2 -> H(U1(k, c), c),A^2 -> H(U1(k, c), c))
28.56/10.04	   (A^2 -> H(U1(c, e), c),A^2 -> H(U1(c, e), c))
28.56/10.04	   (A^2 -> H(U1(c, k), c),A^2 -> H(U1(c, k), c))
28.56/10.04	   (A^2 -> H(U1(c, c), e),A^2 -> H(U1(c, c), e))
28.56/10.04	   (A^2 -> H(U1(c, c), k),A^2 -> H(U1(c, c), k))
28.56/10.04	
28.56/10.04	
28.56/10.04	----------------------------------------
28.56/10.04	
28.56/10.04	(1780)
28.56/10.04	Obligation:
28.56/10.04	Q DP problem:
28.56/10.04	The TRS P consists of the following rules:
28.56/10.04	
28.56/10.04	   H(x, x) -> G(x, x, f(k))
28.56/10.04	   G(d, x, x) -> A^2
28.56/10.04	   A^2 -> H(f(c), f(c))
28.56/10.04	   A^2 -> H(f(d), f(d))
28.56/10.04	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.04	   A^2 -> H(f(e), f(e))
28.56/10.04	   A^2 -> H(f(k), f(k))
28.56/10.04	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.04	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.04	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.04	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.04	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.04	   A^2 -> H(U1(c, c), U1(e, e))
28.56/10.04	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.04	   A^2 -> H(f(c), k)
28.56/10.04	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.04	   A^2 -> H(f(k), U1(k, k))
28.56/10.04	   A^2 -> H(f(e), e)
28.56/10.04	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.04	   A^2 -> H(d, U1(c, b))
28.56/10.04	   A^2 -> H(d, U1(d, b))
28.56/10.04	   A^2 -> H(d, U1(b, c))
28.56/10.04	   A^2 -> H(d, U1(b, d))
28.56/10.04	   A^2 -> H(d, U1(c, c))
28.56/10.04	   A^2 -> H(d, f(e))
28.56/10.04	   A^2 -> H(d, f(k))
28.56/10.04	   A^2 -> H(d, U1(d, d))
28.56/10.04	   A^2 -> H(a, U1(e, b))
28.56/10.04	   A^2 -> H(a, U1(k, b))
28.56/10.04	   A^2 -> H(a, U1(c, d))
28.56/10.04	   A^2 -> H(a, U1(d, c))
28.56/10.04	   A^2 -> H(a, U1(b, e))
28.56/10.04	   A^2 -> H(a, U1(b, k))
28.56/10.04	   A^2 -> H(a, U1(e, c))
28.56/10.04	   A^2 -> H(a, U1(k, c))
28.56/10.04	   A^2 -> H(a, U1(c, e))
28.56/10.04	   A^2 -> H(a, U1(c, k))
28.56/10.04	   A^2 -> H(a, U1(e, e))
28.56/10.04	   A^2 -> H(a, U1(k, k))
28.56/10.04	   A^2 -> H(a, U1(k, d))
28.56/10.04	   A^2 -> H(a, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.04	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.04	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, a), b)
28.56/10.04	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, a), c)
28.56/10.04	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, a), e)
28.56/10.04	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, a), b)
28.56/10.04	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, a), c)
28.56/10.04	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, d), b)
28.56/10.04	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, d), c)
28.56/10.04	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, d), e)
28.56/10.04	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, a), d)
28.56/10.04	   A^2 -> H(U1(c, a), k)
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.04	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.04	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.04	   A^2 -> H(U1(d, c), b)
28.56/10.04	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(d, c), c)
28.56/10.04	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(d, c), e)
28.56/10.04	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, a), d)
28.56/10.04	   A^2 -> H(U1(d, a), k)
28.56/10.04	   A^2 -> H(U1(a, e), b)
28.56/10.04	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(a, e), c)
28.56/10.04	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(a, e), e)
28.56/10.04	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(a, k), b)
28.56/10.04	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(a, k), c)
28.56/10.04	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(a, k), e)
28.56/10.04	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(a, c), d)
28.56/10.04	   A^2 -> H(U1(a, c), k)
28.56/10.04	   A^2 -> H(U1(a, d), d)
28.56/10.04	   A^2 -> H(U1(a, d), k)
28.56/10.04	   A^2 -> H(k, U1(c, b))
28.56/10.04	   A^2 -> H(k, U1(d, b))
28.56/10.04	   A^2 -> H(k, U1(b, c))
28.56/10.04	   A^2 -> H(k, U1(b, d))
28.56/10.04	   A^2 -> H(k, U1(c, c))
28.56/10.04	   A^2 -> H(k, f(e))
28.56/10.04	   A^2 -> H(k, f(k))
28.56/10.04	   A^2 -> H(k, U1(d, d))
28.56/10.04	   A^2 -> H(c, U1(e, b))
28.56/10.04	   A^2 -> H(c, U1(k, b))
28.56/10.04	   A^2 -> H(c, U1(c, d))
28.56/10.04	   A^2 -> H(c, U1(d, c))
28.56/10.04	   A^2 -> H(c, U1(b, e))
28.56/10.04	   A^2 -> H(c, U1(b, k))
28.56/10.04	   A^2 -> H(c, U1(e, c))
28.56/10.04	   A^2 -> H(c, U1(k, c))
28.56/10.04	   A^2 -> H(c, U1(c, e))
28.56/10.04	   A^2 -> H(c, U1(c, k))
28.56/10.04	   A^2 -> H(c, U1(e, e))
28.56/10.04	   A^2 -> H(c, U1(k, k))
28.56/10.04	   A^2 -> H(c, U1(k, d))
28.56/10.04	   A^2 -> H(c, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.04	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.04	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, c), b)
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, c), e)
28.56/10.04	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.04	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.04	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.04	   A^2 -> H(U1(k, c), b)
28.56/10.04	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, c), c)
28.56/10.04	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, e), b)
28.56/10.04	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, e), c)
28.56/10.04	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, e), e)
28.56/10.04	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, k), b)
28.56/10.04	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, k), c)
28.56/10.04	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, k), e)
28.56/10.04	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, c), d)
28.56/10.04	   A^2 -> H(e, U1(e, b))
28.56/10.04	   A^2 -> H(e, U1(c, d))
28.56/10.04	   A^2 -> H(e, U1(d, c))
28.56/10.04	   A^2 -> H(e, U1(b, e))
28.56/10.04	   A^2 -> H(e, U1(b, k))
28.56/10.04	   A^2 -> H(e, U1(e, c))
28.56/10.04	   A^2 -> H(e, U1(c, e))
28.56/10.04	   A^2 -> H(e, U1(c, k))
28.56/10.04	   A^2 -> H(e, U1(e, e))
28.56/10.04	   A^2 -> H(e, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, e), b)
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, e), c)
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.04	   A^2 -> H(f(e), d)
28.56/10.04	   A^2 -> H(f(e), k)
28.56/10.04	   A^2 -> H(U1(k, k), b)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, k), c)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.04	   A^2 -> H(f(k), d)
28.56/10.04	   A^2 -> H(f(k), k)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.04	   A^2 -> H(U1(k, d), b)
28.56/10.04	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, d), c)
28.56/10.04	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, k), b)
28.56/10.04	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(d, k), c)
28.56/10.04	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(d, k), e)
28.56/10.04	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, d), d)
28.56/10.04	   A^2 -> H(U1(d, d), k)
28.56/10.04	   A^2 -> H(U1(e, c), c)
28.56/10.04	   A^2 -> H(U1(c, c), e)
28.56/10.04	   A^2 -> H(U1(c, c), k)
28.56/10.04	
28.56/10.04	The TRS R consists of the following rules:
28.56/10.04	
28.56/10.04	   f(x) -> U1(x, x)
28.56/10.04	   U1(e, x) -> x
28.56/10.04	   a -> c
28.56/10.04	   a -> d
28.56/10.04	   b -> c
28.56/10.04	   b -> d
28.56/10.04	   d -> k
28.56/10.04	   c -> e
28.56/10.04	   c -> k
28.56/10.04	
28.56/10.04	Q is empty.
28.56/10.04	We have to consider all minimal (P,Q,R)-chains.
28.56/10.04	----------------------------------------
28.56/10.04	
28.56/10.04	(1781) TransformationProof (EQUIVALENT)
28.56/10.04	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.04	
28.56/10.04	   (A^2 -> H(U1(e, c), U1(e, e)),A^2 -> H(U1(e, c), U1(e, e)))
28.56/10.04	   (A^2 -> H(U1(k, c), U1(e, e)),A^2 -> H(U1(k, c), U1(e, e)))
28.56/10.04	   (A^2 -> H(U1(c, e), U1(e, e)),A^2 -> H(U1(c, e), U1(e, e)))
28.56/10.04	   (A^2 -> H(U1(c, k), U1(e, e)),A^2 -> H(U1(c, k), U1(e, e)))
28.56/10.04	   (A^2 -> H(U1(c, c), e),A^2 -> H(U1(c, c), e))
28.56/10.04	
28.56/10.04	
28.56/10.04	----------------------------------------
28.56/10.04	
28.56/10.04	(1782)
28.56/10.04	Obligation:
28.56/10.04	Q DP problem:
28.56/10.04	The TRS P consists of the following rules:
28.56/10.04	
28.56/10.04	   H(x, x) -> G(x, x, f(k))
28.56/10.04	   G(d, x, x) -> A^2
28.56/10.04	   A^2 -> H(f(c), f(c))
28.56/10.04	   A^2 -> H(f(d), f(d))
28.56/10.04	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.04	   A^2 -> H(f(e), f(e))
28.56/10.04	   A^2 -> H(f(k), f(k))
28.56/10.04	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.04	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.04	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.04	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.04	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.04	   A^2 -> H(U1(c, c), U1(e, k))
28.56/10.04	   A^2 -> H(f(c), k)
28.56/10.04	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.04	   A^2 -> H(f(k), U1(k, k))
28.56/10.04	   A^2 -> H(f(e), e)
28.56/10.04	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.04	   A^2 -> H(d, U1(c, b))
28.56/10.04	   A^2 -> H(d, U1(d, b))
28.56/10.04	   A^2 -> H(d, U1(b, c))
28.56/10.04	   A^2 -> H(d, U1(b, d))
28.56/10.04	   A^2 -> H(d, U1(c, c))
28.56/10.04	   A^2 -> H(d, f(e))
28.56/10.04	   A^2 -> H(d, f(k))
28.56/10.04	   A^2 -> H(d, U1(d, d))
28.56/10.04	   A^2 -> H(a, U1(e, b))
28.56/10.04	   A^2 -> H(a, U1(k, b))
28.56/10.04	   A^2 -> H(a, U1(c, d))
28.56/10.04	   A^2 -> H(a, U1(d, c))
28.56/10.04	   A^2 -> H(a, U1(b, e))
28.56/10.04	   A^2 -> H(a, U1(b, k))
28.56/10.04	   A^2 -> H(a, U1(e, c))
28.56/10.04	   A^2 -> H(a, U1(k, c))
28.56/10.04	   A^2 -> H(a, U1(c, e))
28.56/10.04	   A^2 -> H(a, U1(c, k))
28.56/10.04	   A^2 -> H(a, U1(e, e))
28.56/10.04	   A^2 -> H(a, U1(k, k))
28.56/10.04	   A^2 -> H(a, U1(k, d))
28.56/10.04	   A^2 -> H(a, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.04	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.04	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, a), b)
28.56/10.04	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, a), c)
28.56/10.04	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, a), e)
28.56/10.04	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, a), b)
28.56/10.04	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, a), c)
28.56/10.04	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, d), b)
28.56/10.04	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, d), c)
28.56/10.04	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, d), e)
28.56/10.04	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, a), d)
28.56/10.04	   A^2 -> H(U1(c, a), k)
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.04	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.04	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.04	   A^2 -> H(U1(d, c), b)
28.56/10.04	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(d, c), c)
28.56/10.04	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(d, c), e)
28.56/10.04	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, a), d)
28.56/10.04	   A^2 -> H(U1(d, a), k)
28.56/10.04	   A^2 -> H(U1(a, e), b)
28.56/10.04	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(a, e), c)
28.56/10.04	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(a, e), e)
28.56/10.04	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(a, k), b)
28.56/10.04	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(a, k), c)
28.56/10.04	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(a, k), e)
28.56/10.04	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(a, c), d)
28.56/10.04	   A^2 -> H(U1(a, c), k)
28.56/10.04	   A^2 -> H(U1(a, d), d)
28.56/10.04	   A^2 -> H(U1(a, d), k)
28.56/10.04	   A^2 -> H(k, U1(c, b))
28.56/10.04	   A^2 -> H(k, U1(d, b))
28.56/10.04	   A^2 -> H(k, U1(b, c))
28.56/10.04	   A^2 -> H(k, U1(b, d))
28.56/10.04	   A^2 -> H(k, U1(c, c))
28.56/10.04	   A^2 -> H(k, f(e))
28.56/10.04	   A^2 -> H(k, f(k))
28.56/10.04	   A^2 -> H(k, U1(d, d))
28.56/10.04	   A^2 -> H(c, U1(e, b))
28.56/10.04	   A^2 -> H(c, U1(k, b))
28.56/10.04	   A^2 -> H(c, U1(c, d))
28.56/10.04	   A^2 -> H(c, U1(d, c))
28.56/10.04	   A^2 -> H(c, U1(b, e))
28.56/10.04	   A^2 -> H(c, U1(b, k))
28.56/10.04	   A^2 -> H(c, U1(e, c))
28.56/10.04	   A^2 -> H(c, U1(k, c))
28.56/10.04	   A^2 -> H(c, U1(c, e))
28.56/10.04	   A^2 -> H(c, U1(c, k))
28.56/10.04	   A^2 -> H(c, U1(e, e))
28.56/10.04	   A^2 -> H(c, U1(k, k))
28.56/10.04	   A^2 -> H(c, U1(k, d))
28.56/10.04	   A^2 -> H(c, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.04	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.04	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, c), b)
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, c), e)
28.56/10.04	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.04	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.04	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.04	   A^2 -> H(U1(k, c), b)
28.56/10.04	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, c), c)
28.56/10.04	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, e), b)
28.56/10.04	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, e), c)
28.56/10.04	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, e), e)
28.56/10.04	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, k), b)
28.56/10.04	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, k), c)
28.56/10.04	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, k), e)
28.56/10.04	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, c), d)
28.56/10.04	   A^2 -> H(e, U1(e, b))
28.56/10.04	   A^2 -> H(e, U1(c, d))
28.56/10.04	   A^2 -> H(e, U1(d, c))
28.56/10.04	   A^2 -> H(e, U1(b, e))
28.56/10.04	   A^2 -> H(e, U1(b, k))
28.56/10.04	   A^2 -> H(e, U1(e, c))
28.56/10.04	   A^2 -> H(e, U1(c, e))
28.56/10.04	   A^2 -> H(e, U1(c, k))
28.56/10.04	   A^2 -> H(e, U1(e, e))
28.56/10.04	   A^2 -> H(e, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, e), b)
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, e), c)
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.04	   A^2 -> H(f(e), d)
28.56/10.04	   A^2 -> H(f(e), k)
28.56/10.04	   A^2 -> H(U1(k, k), b)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, k), c)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.04	   A^2 -> H(f(k), d)
28.56/10.04	   A^2 -> H(f(k), k)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.04	   A^2 -> H(U1(k, d), b)
28.56/10.04	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, d), c)
28.56/10.04	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, k), b)
28.56/10.04	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(d, k), c)
28.56/10.04	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(d, k), e)
28.56/10.04	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, d), d)
28.56/10.04	   A^2 -> H(U1(d, d), k)
28.56/10.04	   A^2 -> H(U1(e, c), c)
28.56/10.04	   A^2 -> H(U1(c, c), e)
28.56/10.04	   A^2 -> H(U1(c, c), k)
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.04	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.04	
28.56/10.04	The TRS R consists of the following rules:
28.56/10.04	
28.56/10.04	   f(x) -> U1(x, x)
28.56/10.04	   U1(e, x) -> x
28.56/10.04	   a -> c
28.56/10.04	   a -> d
28.56/10.04	   b -> c
28.56/10.04	   b -> d
28.56/10.04	   d -> k
28.56/10.04	   c -> e
28.56/10.04	   c -> k
28.56/10.04	
28.56/10.04	Q is empty.
28.56/10.04	We have to consider all minimal (P,Q,R)-chains.
28.56/10.04	----------------------------------------
28.56/10.04	
28.56/10.04	(1783) TransformationProof (EQUIVALENT)
28.56/10.04	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.04	
28.56/10.04	   (A^2 -> H(U1(e, c), U1(e, k)),A^2 -> H(U1(e, c), U1(e, k)))
28.56/10.04	   (A^2 -> H(U1(k, c), U1(e, k)),A^2 -> H(U1(k, c), U1(e, k)))
28.56/10.04	   (A^2 -> H(U1(c, e), U1(e, k)),A^2 -> H(U1(c, e), U1(e, k)))
28.56/10.04	   (A^2 -> H(U1(c, k), U1(e, k)),A^2 -> H(U1(c, k), U1(e, k)))
28.56/10.04	   (A^2 -> H(U1(c, c), k),A^2 -> H(U1(c, c), k))
28.56/10.04	
28.56/10.04	
28.56/10.04	----------------------------------------
28.56/10.04	
28.56/10.04	(1784)
28.56/10.04	Obligation:
28.56/10.04	Q DP problem:
28.56/10.04	The TRS P consists of the following rules:
28.56/10.04	
28.56/10.04	   H(x, x) -> G(x, x, f(k))
28.56/10.04	   G(d, x, x) -> A^2
28.56/10.04	   A^2 -> H(f(c), f(c))
28.56/10.04	   A^2 -> H(f(d), f(d))
28.56/10.04	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.04	   A^2 -> H(f(e), f(e))
28.56/10.04	   A^2 -> H(f(k), f(k))
28.56/10.04	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.04	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.04	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.04	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.04	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.04	   A^2 -> H(f(c), k)
28.56/10.04	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.04	   A^2 -> H(f(k), U1(k, k))
28.56/10.04	   A^2 -> H(f(e), e)
28.56/10.04	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.04	   A^2 -> H(d, U1(c, b))
28.56/10.04	   A^2 -> H(d, U1(d, b))
28.56/10.04	   A^2 -> H(d, U1(b, c))
28.56/10.04	   A^2 -> H(d, U1(b, d))
28.56/10.04	   A^2 -> H(d, U1(c, c))
28.56/10.04	   A^2 -> H(d, f(e))
28.56/10.04	   A^2 -> H(d, f(k))
28.56/10.04	   A^2 -> H(d, U1(d, d))
28.56/10.04	   A^2 -> H(a, U1(e, b))
28.56/10.04	   A^2 -> H(a, U1(k, b))
28.56/10.04	   A^2 -> H(a, U1(c, d))
28.56/10.04	   A^2 -> H(a, U1(d, c))
28.56/10.04	   A^2 -> H(a, U1(b, e))
28.56/10.04	   A^2 -> H(a, U1(b, k))
28.56/10.04	   A^2 -> H(a, U1(e, c))
28.56/10.04	   A^2 -> H(a, U1(k, c))
28.56/10.04	   A^2 -> H(a, U1(c, e))
28.56/10.04	   A^2 -> H(a, U1(c, k))
28.56/10.04	   A^2 -> H(a, U1(e, e))
28.56/10.04	   A^2 -> H(a, U1(k, k))
28.56/10.04	   A^2 -> H(a, U1(k, d))
28.56/10.04	   A^2 -> H(a, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.04	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.04	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, a), b)
28.56/10.04	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, a), c)
28.56/10.04	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, a), e)
28.56/10.04	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, a), b)
28.56/10.04	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, a), c)
28.56/10.04	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, d), b)
28.56/10.04	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, d), c)
28.56/10.04	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, d), e)
28.56/10.04	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, a), d)
28.56/10.04	   A^2 -> H(U1(c, a), k)
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.04	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.04	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.04	   A^2 -> H(U1(d, c), b)
28.56/10.04	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(d, c), c)
28.56/10.04	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(d, c), e)
28.56/10.04	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, a), d)
28.56/10.04	   A^2 -> H(U1(d, a), k)
28.56/10.04	   A^2 -> H(U1(a, e), b)
28.56/10.04	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(a, e), c)
28.56/10.04	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(a, e), e)
28.56/10.04	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(a, k), b)
28.56/10.04	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(a, k), c)
28.56/10.04	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(a, k), e)
28.56/10.04	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(a, c), d)
28.56/10.04	   A^2 -> H(U1(a, c), k)
28.56/10.04	   A^2 -> H(U1(a, d), d)
28.56/10.04	   A^2 -> H(U1(a, d), k)
28.56/10.04	   A^2 -> H(k, U1(c, b))
28.56/10.04	   A^2 -> H(k, U1(d, b))
28.56/10.04	   A^2 -> H(k, U1(b, c))
28.56/10.04	   A^2 -> H(k, U1(b, d))
28.56/10.04	   A^2 -> H(k, U1(c, c))
28.56/10.04	   A^2 -> H(k, f(e))
28.56/10.04	   A^2 -> H(k, f(k))
28.56/10.04	   A^2 -> H(k, U1(d, d))
28.56/10.04	   A^2 -> H(c, U1(e, b))
28.56/10.04	   A^2 -> H(c, U1(k, b))
28.56/10.04	   A^2 -> H(c, U1(c, d))
28.56/10.04	   A^2 -> H(c, U1(d, c))
28.56/10.04	   A^2 -> H(c, U1(b, e))
28.56/10.04	   A^2 -> H(c, U1(b, k))
28.56/10.04	   A^2 -> H(c, U1(e, c))
28.56/10.04	   A^2 -> H(c, U1(k, c))
28.56/10.04	   A^2 -> H(c, U1(c, e))
28.56/10.04	   A^2 -> H(c, U1(c, k))
28.56/10.04	   A^2 -> H(c, U1(e, e))
28.56/10.04	   A^2 -> H(c, U1(k, k))
28.56/10.04	   A^2 -> H(c, U1(k, d))
28.56/10.04	   A^2 -> H(c, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.04	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.04	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, c), b)
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, c), e)
28.56/10.04	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.04	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.04	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.04	   A^2 -> H(U1(k, c), b)
28.56/10.04	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, c), c)
28.56/10.04	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, e), b)
28.56/10.04	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, e), c)
28.56/10.04	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, e), e)
28.56/10.04	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, k), b)
28.56/10.04	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, k), c)
28.56/10.04	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, k), e)
28.56/10.04	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, c), d)
28.56/10.04	   A^2 -> H(e, U1(e, b))
28.56/10.04	   A^2 -> H(e, U1(c, d))
28.56/10.04	   A^2 -> H(e, U1(d, c))
28.56/10.04	   A^2 -> H(e, U1(b, e))
28.56/10.04	   A^2 -> H(e, U1(b, k))
28.56/10.04	   A^2 -> H(e, U1(e, c))
28.56/10.04	   A^2 -> H(e, U1(c, e))
28.56/10.04	   A^2 -> H(e, U1(c, k))
28.56/10.04	   A^2 -> H(e, U1(e, e))
28.56/10.04	   A^2 -> H(e, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, e), b)
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, e), c)
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.04	   A^2 -> H(f(e), d)
28.56/10.04	   A^2 -> H(f(e), k)
28.56/10.04	   A^2 -> H(U1(k, k), b)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, k), c)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.04	   A^2 -> H(f(k), d)
28.56/10.04	   A^2 -> H(f(k), k)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.04	   A^2 -> H(U1(k, d), b)
28.56/10.04	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, d), c)
28.56/10.04	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, k), b)
28.56/10.04	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(d, k), c)
28.56/10.04	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(d, k), e)
28.56/10.04	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, d), d)
28.56/10.04	   A^2 -> H(U1(d, d), k)
28.56/10.04	   A^2 -> H(U1(e, c), c)
28.56/10.04	   A^2 -> H(U1(c, c), e)
28.56/10.04	   A^2 -> H(U1(c, c), k)
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.04	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.04	
28.56/10.04	The TRS R consists of the following rules:
28.56/10.04	
28.56/10.04	   f(x) -> U1(x, x)
28.56/10.04	   U1(e, x) -> x
28.56/10.04	   a -> c
28.56/10.04	   a -> d
28.56/10.04	   b -> c
28.56/10.04	   b -> d
28.56/10.04	   d -> k
28.56/10.04	   c -> e
28.56/10.04	   c -> k
28.56/10.04	
28.56/10.04	Q is empty.
28.56/10.04	We have to consider all minimal (P,Q,R)-chains.
28.56/10.04	----------------------------------------
28.56/10.04	
28.56/10.04	(1785) TransformationProof (EQUIVALENT)
28.56/10.04	By narrowing [LPAR04] the rule A^2 -> H(f(c), k) at position [] we obtained the following new rules [LPAR04]:
28.56/10.04	
28.56/10.04	   (A^2 -> H(U1(c, c), k),A^2 -> H(U1(c, c), k))
28.56/10.04	   (A^2 -> H(f(e), k),A^2 -> H(f(e), k))
28.56/10.04	   (A^2 -> H(f(k), k),A^2 -> H(f(k), k))
28.56/10.04	
28.56/10.04	
28.56/10.04	----------------------------------------
28.56/10.04	
28.56/10.04	(1786)
28.56/10.04	Obligation:
28.56/10.04	Q DP problem:
28.56/10.04	The TRS P consists of the following rules:
28.56/10.04	
28.56/10.04	   H(x, x) -> G(x, x, f(k))
28.56/10.04	   G(d, x, x) -> A^2
28.56/10.04	   A^2 -> H(f(c), f(c))
28.56/10.04	   A^2 -> H(f(d), f(d))
28.56/10.04	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.04	   A^2 -> H(f(e), f(e))
28.56/10.04	   A^2 -> H(f(k), f(k))
28.56/10.04	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.04	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.04	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.04	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.04	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.04	   A^2 -> H(U1(c, c), U1(k, e))
28.56/10.04	   A^2 -> H(f(k), U1(k, k))
28.56/10.04	   A^2 -> H(f(e), e)
28.56/10.04	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.04	   A^2 -> H(d, U1(c, b))
28.56/10.04	   A^2 -> H(d, U1(d, b))
28.56/10.04	   A^2 -> H(d, U1(b, c))
28.56/10.04	   A^2 -> H(d, U1(b, d))
28.56/10.04	   A^2 -> H(d, U1(c, c))
28.56/10.04	   A^2 -> H(d, f(e))
28.56/10.04	   A^2 -> H(d, f(k))
28.56/10.04	   A^2 -> H(d, U1(d, d))
28.56/10.04	   A^2 -> H(a, U1(e, b))
28.56/10.04	   A^2 -> H(a, U1(k, b))
28.56/10.04	   A^2 -> H(a, U1(c, d))
28.56/10.04	   A^2 -> H(a, U1(d, c))
28.56/10.04	   A^2 -> H(a, U1(b, e))
28.56/10.04	   A^2 -> H(a, U1(b, k))
28.56/10.04	   A^2 -> H(a, U1(e, c))
28.56/10.04	   A^2 -> H(a, U1(k, c))
28.56/10.04	   A^2 -> H(a, U1(c, e))
28.56/10.04	   A^2 -> H(a, U1(c, k))
28.56/10.04	   A^2 -> H(a, U1(e, e))
28.56/10.04	   A^2 -> H(a, U1(k, k))
28.56/10.04	   A^2 -> H(a, U1(k, d))
28.56/10.04	   A^2 -> H(a, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.04	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.04	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, a), b)
28.56/10.04	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, a), c)
28.56/10.04	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, a), e)
28.56/10.04	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, a), b)
28.56/10.04	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, a), c)
28.56/10.04	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, d), b)
28.56/10.04	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, d), c)
28.56/10.04	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, d), e)
28.56/10.04	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, a), d)
28.56/10.04	   A^2 -> H(U1(c, a), k)
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.04	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.04	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.04	   A^2 -> H(U1(d, c), b)
28.56/10.04	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(d, c), c)
28.56/10.04	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(d, c), e)
28.56/10.04	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, a), d)
28.56/10.04	   A^2 -> H(U1(d, a), k)
28.56/10.04	   A^2 -> H(U1(a, e), b)
28.56/10.04	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(a, e), c)
28.56/10.04	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(a, e), e)
28.56/10.04	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(a, k), b)
28.56/10.04	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(a, k), c)
28.56/10.04	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(a, k), e)
28.56/10.04	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(a, c), d)
28.56/10.04	   A^2 -> H(U1(a, c), k)
28.56/10.04	   A^2 -> H(U1(a, d), d)
28.56/10.04	   A^2 -> H(U1(a, d), k)
28.56/10.04	   A^2 -> H(k, U1(c, b))
28.56/10.04	   A^2 -> H(k, U1(d, b))
28.56/10.04	   A^2 -> H(k, U1(b, c))
28.56/10.04	   A^2 -> H(k, U1(b, d))
28.56/10.04	   A^2 -> H(k, U1(c, c))
28.56/10.04	   A^2 -> H(k, f(e))
28.56/10.04	   A^2 -> H(k, f(k))
28.56/10.04	   A^2 -> H(k, U1(d, d))
28.56/10.04	   A^2 -> H(c, U1(e, b))
28.56/10.04	   A^2 -> H(c, U1(k, b))
28.56/10.04	   A^2 -> H(c, U1(c, d))
28.56/10.04	   A^2 -> H(c, U1(d, c))
28.56/10.04	   A^2 -> H(c, U1(b, e))
28.56/10.04	   A^2 -> H(c, U1(b, k))
28.56/10.04	   A^2 -> H(c, U1(e, c))
28.56/10.04	   A^2 -> H(c, U1(k, c))
28.56/10.04	   A^2 -> H(c, U1(c, e))
28.56/10.04	   A^2 -> H(c, U1(c, k))
28.56/10.04	   A^2 -> H(c, U1(e, e))
28.56/10.04	   A^2 -> H(c, U1(k, k))
28.56/10.04	   A^2 -> H(c, U1(k, d))
28.56/10.04	   A^2 -> H(c, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.04	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.04	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, c), b)
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, c), e)
28.56/10.04	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.04	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.04	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.04	   A^2 -> H(U1(k, c), b)
28.56/10.04	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, c), c)
28.56/10.04	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, e), b)
28.56/10.04	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, e), c)
28.56/10.04	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, e), e)
28.56/10.04	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, k), b)
28.56/10.04	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, k), c)
28.56/10.04	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, k), e)
28.56/10.04	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, c), d)
28.56/10.04	   A^2 -> H(e, U1(e, b))
28.56/10.04	   A^2 -> H(e, U1(c, d))
28.56/10.04	   A^2 -> H(e, U1(d, c))
28.56/10.04	   A^2 -> H(e, U1(b, e))
28.56/10.04	   A^2 -> H(e, U1(b, k))
28.56/10.04	   A^2 -> H(e, U1(e, c))
28.56/10.04	   A^2 -> H(e, U1(c, e))
28.56/10.04	   A^2 -> H(e, U1(c, k))
28.56/10.04	   A^2 -> H(e, U1(e, e))
28.56/10.04	   A^2 -> H(e, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, e), b)
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, e), c)
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.04	   A^2 -> H(f(e), d)
28.56/10.04	   A^2 -> H(f(e), k)
28.56/10.04	   A^2 -> H(U1(k, k), b)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, k), c)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.04	   A^2 -> H(f(k), d)
28.56/10.04	   A^2 -> H(f(k), k)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.04	   A^2 -> H(U1(k, d), b)
28.56/10.04	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, d), c)
28.56/10.04	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, k), b)
28.56/10.04	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(d, k), c)
28.56/10.04	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(d, k), e)
28.56/10.04	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, d), d)
28.56/10.04	   A^2 -> H(U1(d, d), k)
28.56/10.04	   A^2 -> H(U1(e, c), c)
28.56/10.04	   A^2 -> H(U1(c, c), e)
28.56/10.04	   A^2 -> H(U1(c, c), k)
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.04	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.04	
28.56/10.04	The TRS R consists of the following rules:
28.56/10.04	
28.56/10.04	   f(x) -> U1(x, x)
28.56/10.04	   U1(e, x) -> x
28.56/10.04	   a -> c
28.56/10.04	   a -> d
28.56/10.04	   b -> c
28.56/10.04	   b -> d
28.56/10.04	   d -> k
28.56/10.04	   c -> e
28.56/10.04	   c -> k
28.56/10.04	
28.56/10.04	Q is empty.
28.56/10.04	We have to consider all minimal (P,Q,R)-chains.
28.56/10.04	----------------------------------------
28.56/10.04	
28.56/10.04	(1787) TransformationProof (EQUIVALENT)
28.56/10.04	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.04	
28.56/10.04	   (A^2 -> H(U1(e, c), U1(k, e)),A^2 -> H(U1(e, c), U1(k, e)))
28.56/10.04	   (A^2 -> H(U1(k, c), U1(k, e)),A^2 -> H(U1(k, c), U1(k, e)))
28.56/10.04	   (A^2 -> H(U1(c, e), U1(k, e)),A^2 -> H(U1(c, e), U1(k, e)))
28.56/10.04	   (A^2 -> H(U1(c, k), U1(k, e)),A^2 -> H(U1(c, k), U1(k, e)))
28.56/10.04	
28.56/10.04	
28.56/10.04	----------------------------------------
28.56/10.04	
28.56/10.04	(1788)
28.56/10.04	Obligation:
28.56/10.04	Q DP problem:
28.56/10.04	The TRS P consists of the following rules:
28.56/10.04	
28.56/10.04	   H(x, x) -> G(x, x, f(k))
28.56/10.04	   G(d, x, x) -> A^2
28.56/10.04	   A^2 -> H(f(c), f(c))
28.56/10.04	   A^2 -> H(f(d), f(d))
28.56/10.04	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.04	   A^2 -> H(f(e), f(e))
28.56/10.04	   A^2 -> H(f(k), f(k))
28.56/10.04	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.04	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.04	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.04	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.04	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.04	   A^2 -> H(f(k), U1(k, k))
28.56/10.04	   A^2 -> H(f(e), e)
28.56/10.04	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.04	   A^2 -> H(d, U1(c, b))
28.56/10.04	   A^2 -> H(d, U1(d, b))
28.56/10.04	   A^2 -> H(d, U1(b, c))
28.56/10.04	   A^2 -> H(d, U1(b, d))
28.56/10.04	   A^2 -> H(d, U1(c, c))
28.56/10.04	   A^2 -> H(d, f(e))
28.56/10.04	   A^2 -> H(d, f(k))
28.56/10.04	   A^2 -> H(d, U1(d, d))
28.56/10.04	   A^2 -> H(a, U1(e, b))
28.56/10.04	   A^2 -> H(a, U1(k, b))
28.56/10.04	   A^2 -> H(a, U1(c, d))
28.56/10.04	   A^2 -> H(a, U1(d, c))
28.56/10.04	   A^2 -> H(a, U1(b, e))
28.56/10.04	   A^2 -> H(a, U1(b, k))
28.56/10.04	   A^2 -> H(a, U1(e, c))
28.56/10.04	   A^2 -> H(a, U1(k, c))
28.56/10.04	   A^2 -> H(a, U1(c, e))
28.56/10.04	   A^2 -> H(a, U1(c, k))
28.56/10.04	   A^2 -> H(a, U1(e, e))
28.56/10.04	   A^2 -> H(a, U1(k, k))
28.56/10.04	   A^2 -> H(a, U1(k, d))
28.56/10.04	   A^2 -> H(a, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.04	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.04	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, a), b)
28.56/10.04	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, a), c)
28.56/10.04	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, a), e)
28.56/10.04	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, a), b)
28.56/10.04	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, a), c)
28.56/10.04	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, d), b)
28.56/10.04	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, d), c)
28.56/10.04	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, d), e)
28.56/10.04	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, a), d)
28.56/10.04	   A^2 -> H(U1(c, a), k)
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.04	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.04	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.04	   A^2 -> H(U1(d, c), b)
28.56/10.04	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(d, c), c)
28.56/10.04	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(d, c), e)
28.56/10.04	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, a), d)
28.56/10.04	   A^2 -> H(U1(d, a), k)
28.56/10.04	   A^2 -> H(U1(a, e), b)
28.56/10.04	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(a, e), c)
28.56/10.04	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(a, e), e)
28.56/10.04	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(a, k), b)
28.56/10.04	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(a, k), c)
28.56/10.04	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(a, k), e)
28.56/10.04	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(a, c), d)
28.56/10.04	   A^2 -> H(U1(a, c), k)
28.56/10.04	   A^2 -> H(U1(a, d), d)
28.56/10.04	   A^2 -> H(U1(a, d), k)
28.56/10.04	   A^2 -> H(k, U1(c, b))
28.56/10.04	   A^2 -> H(k, U1(d, b))
28.56/10.04	   A^2 -> H(k, U1(b, c))
28.56/10.04	   A^2 -> H(k, U1(b, d))
28.56/10.04	   A^2 -> H(k, U1(c, c))
28.56/10.04	   A^2 -> H(k, f(e))
28.56/10.04	   A^2 -> H(k, f(k))
28.56/10.04	   A^2 -> H(k, U1(d, d))
28.56/10.04	   A^2 -> H(c, U1(e, b))
28.56/10.04	   A^2 -> H(c, U1(k, b))
28.56/10.04	   A^2 -> H(c, U1(c, d))
28.56/10.04	   A^2 -> H(c, U1(d, c))
28.56/10.04	   A^2 -> H(c, U1(b, e))
28.56/10.04	   A^2 -> H(c, U1(b, k))
28.56/10.04	   A^2 -> H(c, U1(e, c))
28.56/10.04	   A^2 -> H(c, U1(k, c))
28.56/10.04	   A^2 -> H(c, U1(c, e))
28.56/10.04	   A^2 -> H(c, U1(c, k))
28.56/10.04	   A^2 -> H(c, U1(e, e))
28.56/10.04	   A^2 -> H(c, U1(k, k))
28.56/10.04	   A^2 -> H(c, U1(k, d))
28.56/10.04	   A^2 -> H(c, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.04	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.04	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, c), b)
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, c), e)
28.56/10.04	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.04	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.04	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.04	   A^2 -> H(U1(k, c), b)
28.56/10.04	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, c), c)
28.56/10.04	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, e), b)
28.56/10.04	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, e), c)
28.56/10.04	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, e), e)
28.56/10.04	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, k), b)
28.56/10.04	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, k), c)
28.56/10.04	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, k), e)
28.56/10.04	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, c), d)
28.56/10.04	   A^2 -> H(e, U1(e, b))
28.56/10.04	   A^2 -> H(e, U1(c, d))
28.56/10.04	   A^2 -> H(e, U1(d, c))
28.56/10.04	   A^2 -> H(e, U1(b, e))
28.56/10.04	   A^2 -> H(e, U1(b, k))
28.56/10.04	   A^2 -> H(e, U1(e, c))
28.56/10.04	   A^2 -> H(e, U1(c, e))
28.56/10.04	   A^2 -> H(e, U1(c, k))
28.56/10.04	   A^2 -> H(e, U1(e, e))
28.56/10.04	   A^2 -> H(e, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, e), b)
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, e), c)
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.04	   A^2 -> H(f(e), d)
28.56/10.04	   A^2 -> H(f(e), k)
28.56/10.04	   A^2 -> H(U1(k, k), b)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, k), c)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.04	   A^2 -> H(f(k), d)
28.56/10.04	   A^2 -> H(f(k), k)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.04	   A^2 -> H(U1(k, d), b)
28.56/10.04	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, d), c)
28.56/10.04	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, k), b)
28.56/10.04	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(d, k), c)
28.56/10.04	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(d, k), e)
28.56/10.04	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, d), d)
28.56/10.04	   A^2 -> H(U1(d, d), k)
28.56/10.04	   A^2 -> H(U1(e, c), c)
28.56/10.04	   A^2 -> H(U1(c, c), e)
28.56/10.04	   A^2 -> H(U1(c, c), k)
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.04	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.04	
28.56/10.04	The TRS R consists of the following rules:
28.56/10.04	
28.56/10.04	   f(x) -> U1(x, x)
28.56/10.04	   U1(e, x) -> x
28.56/10.04	   a -> c
28.56/10.04	   a -> d
28.56/10.04	   b -> c
28.56/10.04	   b -> d
28.56/10.04	   d -> k
28.56/10.04	   c -> e
28.56/10.04	   c -> k
28.56/10.04	
28.56/10.04	Q is empty.
28.56/10.04	We have to consider all minimal (P,Q,R)-chains.
28.56/10.04	----------------------------------------
28.56/10.04	
28.56/10.04	(1789) TransformationProof (EQUIVALENT)
28.56/10.04	By narrowing [LPAR04] the rule A^2 -> H(f(k), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.04	
28.56/10.04	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.56/10.04	
28.56/10.04	
28.56/10.04	----------------------------------------
28.56/10.04	
28.56/10.04	(1790)
28.56/10.04	Obligation:
28.56/10.04	Q DP problem:
28.56/10.04	The TRS P consists of the following rules:
28.56/10.04	
28.56/10.04	   H(x, x) -> G(x, x, f(k))
28.56/10.04	   G(d, x, x) -> A^2
28.56/10.04	   A^2 -> H(f(c), f(c))
28.56/10.04	   A^2 -> H(f(d), f(d))
28.56/10.04	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.04	   A^2 -> H(f(e), f(e))
28.56/10.04	   A^2 -> H(f(k), f(k))
28.56/10.04	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.04	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.04	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.04	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.04	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.04	   A^2 -> H(f(e), e)
28.56/10.04	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.04	   A^2 -> H(d, U1(c, b))
28.56/10.04	   A^2 -> H(d, U1(d, b))
28.56/10.04	   A^2 -> H(d, U1(b, c))
28.56/10.04	   A^2 -> H(d, U1(b, d))
28.56/10.04	   A^2 -> H(d, U1(c, c))
28.56/10.04	   A^2 -> H(d, f(e))
28.56/10.04	   A^2 -> H(d, f(k))
28.56/10.04	   A^2 -> H(d, U1(d, d))
28.56/10.04	   A^2 -> H(a, U1(e, b))
28.56/10.04	   A^2 -> H(a, U1(k, b))
28.56/10.04	   A^2 -> H(a, U1(c, d))
28.56/10.04	   A^2 -> H(a, U1(d, c))
28.56/10.04	   A^2 -> H(a, U1(b, e))
28.56/10.04	   A^2 -> H(a, U1(b, k))
28.56/10.04	   A^2 -> H(a, U1(e, c))
28.56/10.04	   A^2 -> H(a, U1(k, c))
28.56/10.04	   A^2 -> H(a, U1(c, e))
28.56/10.04	   A^2 -> H(a, U1(c, k))
28.56/10.04	   A^2 -> H(a, U1(e, e))
28.56/10.04	   A^2 -> H(a, U1(k, k))
28.56/10.04	   A^2 -> H(a, U1(k, d))
28.56/10.04	   A^2 -> H(a, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.04	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.04	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, a), b)
28.56/10.04	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, a), c)
28.56/10.04	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, a), e)
28.56/10.04	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, a), b)
28.56/10.04	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, a), c)
28.56/10.04	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, d), b)
28.56/10.04	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, d), c)
28.56/10.04	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, d), e)
28.56/10.04	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, a), d)
28.56/10.04	   A^2 -> H(U1(c, a), k)
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.04	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.04	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.04	   A^2 -> H(U1(d, c), b)
28.56/10.04	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(d, c), c)
28.56/10.04	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(d, c), e)
28.56/10.04	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, a), d)
28.56/10.04	   A^2 -> H(U1(d, a), k)
28.56/10.04	   A^2 -> H(U1(a, e), b)
28.56/10.04	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(a, e), c)
28.56/10.04	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(a, e), e)
28.56/10.04	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(a, k), b)
28.56/10.04	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(a, k), c)
28.56/10.04	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(a, k), e)
28.56/10.04	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(a, c), d)
28.56/10.04	   A^2 -> H(U1(a, c), k)
28.56/10.04	   A^2 -> H(U1(a, d), d)
28.56/10.04	   A^2 -> H(U1(a, d), k)
28.56/10.04	   A^2 -> H(k, U1(c, b))
28.56/10.04	   A^2 -> H(k, U1(d, b))
28.56/10.04	   A^2 -> H(k, U1(b, c))
28.56/10.04	   A^2 -> H(k, U1(b, d))
28.56/10.04	   A^2 -> H(k, U1(c, c))
28.56/10.04	   A^2 -> H(k, f(e))
28.56/10.04	   A^2 -> H(k, f(k))
28.56/10.04	   A^2 -> H(k, U1(d, d))
28.56/10.04	   A^2 -> H(c, U1(e, b))
28.56/10.04	   A^2 -> H(c, U1(k, b))
28.56/10.04	   A^2 -> H(c, U1(c, d))
28.56/10.04	   A^2 -> H(c, U1(d, c))
28.56/10.04	   A^2 -> H(c, U1(b, e))
28.56/10.04	   A^2 -> H(c, U1(b, k))
28.56/10.04	   A^2 -> H(c, U1(e, c))
28.56/10.04	   A^2 -> H(c, U1(k, c))
28.56/10.04	   A^2 -> H(c, U1(c, e))
28.56/10.04	   A^2 -> H(c, U1(c, k))
28.56/10.04	   A^2 -> H(c, U1(e, e))
28.56/10.04	   A^2 -> H(c, U1(k, k))
28.56/10.04	   A^2 -> H(c, U1(k, d))
28.56/10.04	   A^2 -> H(c, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.04	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.04	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, c), b)
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, c), e)
28.56/10.04	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.04	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.04	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.04	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.04	   A^2 -> H(U1(k, c), b)
28.56/10.04	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, c), c)
28.56/10.04	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, e), b)
28.56/10.04	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, e), c)
28.56/10.04	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, e), e)
28.56/10.04	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, k), b)
28.56/10.04	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(c, k), c)
28.56/10.04	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(c, k), e)
28.56/10.04	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.04	   A^2 -> H(U1(c, c), d)
28.56/10.04	   A^2 -> H(e, U1(e, b))
28.56/10.04	   A^2 -> H(e, U1(c, d))
28.56/10.04	   A^2 -> H(e, U1(d, c))
28.56/10.04	   A^2 -> H(e, U1(b, e))
28.56/10.04	   A^2 -> H(e, U1(b, k))
28.56/10.04	   A^2 -> H(e, U1(e, c))
28.56/10.04	   A^2 -> H(e, U1(c, e))
28.56/10.04	   A^2 -> H(e, U1(c, k))
28.56/10.04	   A^2 -> H(e, U1(e, e))
28.56/10.04	   A^2 -> H(e, U1(d, k))
28.56/10.04	   A^2 -> H(U1(e, e), b)
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.04	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.04	   A^2 -> H(U1(e, e), c)
28.56/10.04	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.04	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.04	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.04	   A^2 -> H(f(e), d)
28.56/10.04	   A^2 -> H(f(e), k)
28.56/10.04	   A^2 -> H(U1(k, k), b)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, k), c)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.04	   A^2 -> H(f(k), d)
28.56/10.04	   A^2 -> H(f(k), k)
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.04	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.04	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.04	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.04	   A^2 -> H(U1(k, d), b)
28.56/10.04	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.04	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.04	   A^2 -> H(U1(k, d), c)
28.56/10.04	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.04	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.04	   A^2 -> H(U1(d, k), b)
28.56/10.04	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.04	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.04	   A^2 -> H(U1(d, k), c)
28.56/10.04	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.04	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.04	   A^2 -> H(U1(d, k), e)
28.56/10.05	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, d), d)
28.56/10.05	   A^2 -> H(U1(d, d), k)
28.56/10.05	   A^2 -> H(U1(e, c), c)
28.56/10.05	   A^2 -> H(U1(c, c), e)
28.56/10.05	   A^2 -> H(U1(c, c), k)
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.05	
28.56/10.05	The TRS R consists of the following rules:
28.56/10.05	
28.56/10.05	   f(x) -> U1(x, x)
28.56/10.05	   U1(e, x) -> x
28.56/10.05	   a -> c
28.56/10.05	   a -> d
28.56/10.05	   b -> c
28.56/10.05	   b -> d
28.56/10.05	   d -> k
28.56/10.05	   c -> e
28.56/10.05	   c -> k
28.56/10.05	
28.56/10.05	Q is empty.
28.56/10.05	We have to consider all minimal (P,Q,R)-chains.
28.56/10.05	----------------------------------------
28.56/10.05	
28.56/10.05	(1791) TransformationProof (EQUIVALENT)
28.56/10.05	By narrowing [LPAR04] the rule A^2 -> H(f(e), e) at position [] we obtained the following new rules [LPAR04]:
28.56/10.05	
28.56/10.05	   (A^2 -> H(U1(e, e), e),A^2 -> H(U1(e, e), e))
28.56/10.05	
28.56/10.05	
28.56/10.05	----------------------------------------
28.56/10.05	
28.56/10.05	(1792)
28.56/10.05	Obligation:
28.56/10.05	Q DP problem:
28.56/10.05	The TRS P consists of the following rules:
28.56/10.05	
28.56/10.05	   H(x, x) -> G(x, x, f(k))
28.56/10.05	   G(d, x, x) -> A^2
28.56/10.05	   A^2 -> H(f(c), f(c))
28.56/10.05	   A^2 -> H(f(d), f(d))
28.56/10.05	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.05	   A^2 -> H(f(e), f(e))
28.56/10.05	   A^2 -> H(f(k), f(k))
28.56/10.05	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.05	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.05	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.05	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.05	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.05	   A^2 -> H(U1(d, d), U1(k, k))
28.56/10.05	   A^2 -> H(d, U1(c, b))
28.56/10.05	   A^2 -> H(d, U1(d, b))
28.56/10.05	   A^2 -> H(d, U1(b, c))
28.56/10.05	   A^2 -> H(d, U1(b, d))
28.56/10.05	   A^2 -> H(d, U1(c, c))
28.56/10.05	   A^2 -> H(d, f(e))
28.56/10.05	   A^2 -> H(d, f(k))
28.56/10.05	   A^2 -> H(d, U1(d, d))
28.56/10.05	   A^2 -> H(a, U1(e, b))
28.56/10.05	   A^2 -> H(a, U1(k, b))
28.56/10.05	   A^2 -> H(a, U1(c, d))
28.56/10.05	   A^2 -> H(a, U1(d, c))
28.56/10.05	   A^2 -> H(a, U1(b, e))
28.56/10.05	   A^2 -> H(a, U1(b, k))
28.56/10.05	   A^2 -> H(a, U1(e, c))
28.56/10.05	   A^2 -> H(a, U1(k, c))
28.56/10.05	   A^2 -> H(a, U1(c, e))
28.56/10.05	   A^2 -> H(a, U1(c, k))
28.56/10.05	   A^2 -> H(a, U1(e, e))
28.56/10.05	   A^2 -> H(a, U1(k, k))
28.56/10.05	   A^2 -> H(a, U1(k, d))
28.56/10.05	   A^2 -> H(a, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.05	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.05	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, a), b)
28.56/10.05	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, a), c)
28.56/10.05	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, a), e)
28.56/10.05	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, a), b)
28.56/10.05	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, a), c)
28.56/10.05	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, d), b)
28.56/10.05	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, d), c)
28.56/10.05	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, d), e)
28.56/10.05	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, a), d)
28.56/10.05	   A^2 -> H(U1(c, a), k)
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.05	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.05	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.05	   A^2 -> H(U1(d, c), b)
28.56/10.05	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(d, c), c)
28.56/10.05	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(d, c), e)
28.56/10.05	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, a), d)
28.56/10.05	   A^2 -> H(U1(d, a), k)
28.56/10.05	   A^2 -> H(U1(a, e), b)
28.56/10.05	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(a, e), c)
28.56/10.05	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(a, e), e)
28.56/10.05	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(a, k), b)
28.56/10.05	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(a, k), c)
28.56/10.05	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(a, k), e)
28.56/10.05	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(a, c), d)
28.56/10.05	   A^2 -> H(U1(a, c), k)
28.56/10.05	   A^2 -> H(U1(a, d), d)
28.56/10.05	   A^2 -> H(U1(a, d), k)
28.56/10.05	   A^2 -> H(k, U1(c, b))
28.56/10.05	   A^2 -> H(k, U1(d, b))
28.56/10.05	   A^2 -> H(k, U1(b, c))
28.56/10.05	   A^2 -> H(k, U1(b, d))
28.56/10.05	   A^2 -> H(k, U1(c, c))
28.56/10.05	   A^2 -> H(k, f(e))
28.56/10.05	   A^2 -> H(k, f(k))
28.56/10.05	   A^2 -> H(k, U1(d, d))
28.56/10.05	   A^2 -> H(c, U1(e, b))
28.56/10.05	   A^2 -> H(c, U1(k, b))
28.56/10.05	   A^2 -> H(c, U1(c, d))
28.56/10.05	   A^2 -> H(c, U1(d, c))
28.56/10.05	   A^2 -> H(c, U1(b, e))
28.56/10.05	   A^2 -> H(c, U1(b, k))
28.56/10.05	   A^2 -> H(c, U1(e, c))
28.56/10.05	   A^2 -> H(c, U1(k, c))
28.56/10.05	   A^2 -> H(c, U1(c, e))
28.56/10.05	   A^2 -> H(c, U1(c, k))
28.56/10.05	   A^2 -> H(c, U1(e, e))
28.56/10.05	   A^2 -> H(c, U1(k, k))
28.56/10.05	   A^2 -> H(c, U1(k, d))
28.56/10.05	   A^2 -> H(c, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.05	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.05	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, c), b)
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, c), e)
28.56/10.05	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.05	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.05	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.05	   A^2 -> H(U1(k, c), b)
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, c), c)
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, e), b)
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, e), c)
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, e), e)
28.56/10.05	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, k), b)
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, k), c)
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, k), e)
28.56/10.05	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, c), d)
28.56/10.05	   A^2 -> H(e, U1(e, b))
28.56/10.05	   A^2 -> H(e, U1(c, d))
28.56/10.05	   A^2 -> H(e, U1(d, c))
28.56/10.05	   A^2 -> H(e, U1(b, e))
28.56/10.05	   A^2 -> H(e, U1(b, k))
28.56/10.05	   A^2 -> H(e, U1(e, c))
28.56/10.05	   A^2 -> H(e, U1(c, e))
28.56/10.05	   A^2 -> H(e, U1(c, k))
28.56/10.05	   A^2 -> H(e, U1(e, e))
28.56/10.05	   A^2 -> H(e, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, e), b)
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, e), c)
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.05	   A^2 -> H(f(e), d)
28.56/10.05	   A^2 -> H(f(e), k)
28.56/10.05	   A^2 -> H(U1(k, k), b)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, k), c)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.05	   A^2 -> H(f(k), d)
28.56/10.05	   A^2 -> H(f(k), k)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.05	   A^2 -> H(U1(k, d), b)
28.56/10.05	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, d), c)
28.56/10.05	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, k), b)
28.56/10.05	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(d, k), c)
28.56/10.05	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(d, k), e)
28.56/10.05	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, d), d)
28.56/10.05	   A^2 -> H(U1(d, d), k)
28.56/10.05	   A^2 -> H(U1(e, c), c)
28.56/10.05	   A^2 -> H(U1(c, c), e)
28.56/10.05	   A^2 -> H(U1(c, c), k)
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, e), e)
28.56/10.05	
28.56/10.05	The TRS R consists of the following rules:
28.56/10.05	
28.56/10.05	   f(x) -> U1(x, x)
28.56/10.05	   U1(e, x) -> x
28.56/10.05	   a -> c
28.56/10.05	   a -> d
28.56/10.05	   b -> c
28.56/10.05	   b -> d
28.56/10.05	   d -> k
28.56/10.05	   c -> e
28.56/10.05	   c -> k
28.56/10.05	
28.56/10.05	Q is empty.
28.56/10.05	We have to consider all minimal (P,Q,R)-chains.
28.56/10.05	----------------------------------------
28.56/10.05	
28.56/10.05	(1793) TransformationProof (EQUIVALENT)
28.56/10.05	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.05	
28.56/10.05	   (A^2 -> H(U1(k, d), U1(k, k)),A^2 -> H(U1(k, d), U1(k, k)))
28.56/10.05	   (A^2 -> H(U1(d, k), U1(k, k)),A^2 -> H(U1(d, k), U1(k, k)))
28.56/10.05	
28.56/10.05	
28.56/10.05	----------------------------------------
28.56/10.05	
28.56/10.05	(1794)
28.56/10.05	Obligation:
28.56/10.05	Q DP problem:
28.56/10.05	The TRS P consists of the following rules:
28.56/10.05	
28.56/10.05	   H(x, x) -> G(x, x, f(k))
28.56/10.05	   G(d, x, x) -> A^2
28.56/10.05	   A^2 -> H(f(c), f(c))
28.56/10.05	   A^2 -> H(f(d), f(d))
28.56/10.05	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.05	   A^2 -> H(f(e), f(e))
28.56/10.05	   A^2 -> H(f(k), f(k))
28.56/10.05	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.05	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.05	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.05	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.05	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.05	   A^2 -> H(d, U1(c, b))
28.56/10.05	   A^2 -> H(d, U1(d, b))
28.56/10.05	   A^2 -> H(d, U1(b, c))
28.56/10.05	   A^2 -> H(d, U1(b, d))
28.56/10.05	   A^2 -> H(d, U1(c, c))
28.56/10.05	   A^2 -> H(d, f(e))
28.56/10.05	   A^2 -> H(d, f(k))
28.56/10.05	   A^2 -> H(d, U1(d, d))
28.56/10.05	   A^2 -> H(a, U1(e, b))
28.56/10.05	   A^2 -> H(a, U1(k, b))
28.56/10.05	   A^2 -> H(a, U1(c, d))
28.56/10.05	   A^2 -> H(a, U1(d, c))
28.56/10.05	   A^2 -> H(a, U1(b, e))
28.56/10.05	   A^2 -> H(a, U1(b, k))
28.56/10.05	   A^2 -> H(a, U1(e, c))
28.56/10.05	   A^2 -> H(a, U1(k, c))
28.56/10.05	   A^2 -> H(a, U1(c, e))
28.56/10.05	   A^2 -> H(a, U1(c, k))
28.56/10.05	   A^2 -> H(a, U1(e, e))
28.56/10.05	   A^2 -> H(a, U1(k, k))
28.56/10.05	   A^2 -> H(a, U1(k, d))
28.56/10.05	   A^2 -> H(a, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.05	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.05	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, a), b)
28.56/10.05	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, a), c)
28.56/10.05	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, a), e)
28.56/10.05	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, a), b)
28.56/10.05	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, a), c)
28.56/10.05	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, d), b)
28.56/10.05	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, d), c)
28.56/10.05	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, d), e)
28.56/10.05	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, a), d)
28.56/10.05	   A^2 -> H(U1(c, a), k)
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.05	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.05	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.05	   A^2 -> H(U1(d, c), b)
28.56/10.05	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(d, c), c)
28.56/10.05	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(d, c), e)
28.56/10.05	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, a), d)
28.56/10.05	   A^2 -> H(U1(d, a), k)
28.56/10.05	   A^2 -> H(U1(a, e), b)
28.56/10.05	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(a, e), c)
28.56/10.05	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(a, e), e)
28.56/10.05	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(a, k), b)
28.56/10.05	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(a, k), c)
28.56/10.05	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(a, k), e)
28.56/10.05	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(a, c), d)
28.56/10.05	   A^2 -> H(U1(a, c), k)
28.56/10.05	   A^2 -> H(U1(a, d), d)
28.56/10.05	   A^2 -> H(U1(a, d), k)
28.56/10.05	   A^2 -> H(k, U1(c, b))
28.56/10.05	   A^2 -> H(k, U1(d, b))
28.56/10.05	   A^2 -> H(k, U1(b, c))
28.56/10.05	   A^2 -> H(k, U1(b, d))
28.56/10.05	   A^2 -> H(k, U1(c, c))
28.56/10.05	   A^2 -> H(k, f(e))
28.56/10.05	   A^2 -> H(k, f(k))
28.56/10.05	   A^2 -> H(k, U1(d, d))
28.56/10.05	   A^2 -> H(c, U1(e, b))
28.56/10.05	   A^2 -> H(c, U1(k, b))
28.56/10.05	   A^2 -> H(c, U1(c, d))
28.56/10.05	   A^2 -> H(c, U1(d, c))
28.56/10.05	   A^2 -> H(c, U1(b, e))
28.56/10.05	   A^2 -> H(c, U1(b, k))
28.56/10.05	   A^2 -> H(c, U1(e, c))
28.56/10.05	   A^2 -> H(c, U1(k, c))
28.56/10.05	   A^2 -> H(c, U1(c, e))
28.56/10.05	   A^2 -> H(c, U1(c, k))
28.56/10.05	   A^2 -> H(c, U1(e, e))
28.56/10.05	   A^2 -> H(c, U1(k, k))
28.56/10.05	   A^2 -> H(c, U1(k, d))
28.56/10.05	   A^2 -> H(c, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.05	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.05	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, c), b)
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, c), e)
28.56/10.05	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.05	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.05	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.05	   A^2 -> H(U1(k, c), b)
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, c), c)
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, e), b)
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, e), c)
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, e), e)
28.56/10.05	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, k), b)
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, k), c)
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, k), e)
28.56/10.05	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, c), d)
28.56/10.05	   A^2 -> H(e, U1(e, b))
28.56/10.05	   A^2 -> H(e, U1(c, d))
28.56/10.05	   A^2 -> H(e, U1(d, c))
28.56/10.05	   A^2 -> H(e, U1(b, e))
28.56/10.05	   A^2 -> H(e, U1(b, k))
28.56/10.05	   A^2 -> H(e, U1(e, c))
28.56/10.05	   A^2 -> H(e, U1(c, e))
28.56/10.05	   A^2 -> H(e, U1(c, k))
28.56/10.05	   A^2 -> H(e, U1(e, e))
28.56/10.05	   A^2 -> H(e, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, e), b)
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, e), c)
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.05	   A^2 -> H(f(e), d)
28.56/10.05	   A^2 -> H(f(e), k)
28.56/10.05	   A^2 -> H(U1(k, k), b)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, k), c)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.05	   A^2 -> H(f(k), d)
28.56/10.05	   A^2 -> H(f(k), k)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.05	   A^2 -> H(U1(k, d), b)
28.56/10.05	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, d), c)
28.56/10.05	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, k), b)
28.56/10.05	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(d, k), c)
28.56/10.05	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(d, k), e)
28.56/10.05	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, d), d)
28.56/10.05	   A^2 -> H(U1(d, d), k)
28.56/10.05	   A^2 -> H(U1(e, c), c)
28.56/10.05	   A^2 -> H(U1(c, c), e)
28.56/10.05	   A^2 -> H(U1(c, c), k)
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, e), e)
28.56/10.05	
28.56/10.05	The TRS R consists of the following rules:
28.56/10.05	
28.56/10.05	   f(x) -> U1(x, x)
28.56/10.05	   U1(e, x) -> x
28.56/10.05	   a -> c
28.56/10.05	   a -> d
28.56/10.05	   b -> c
28.56/10.05	   b -> d
28.56/10.05	   d -> k
28.56/10.05	   c -> e
28.56/10.05	   c -> k
28.56/10.05	
28.56/10.05	Q is empty.
28.56/10.05	We have to consider all minimal (P,Q,R)-chains.
28.56/10.05	----------------------------------------
28.56/10.05	
28.56/10.05	(1795) TransformationProof (EQUIVALENT)
28.56/10.05	By narrowing [LPAR04] the rule A^2 -> H(d, U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.05	
28.56/10.05	   (A^2 -> H(k, U1(c, b)),A^2 -> H(k, U1(c, b)))
28.56/10.05	   (A^2 -> H(d, U1(e, b)),A^2 -> H(d, U1(e, b)))
28.56/10.05	   (A^2 -> H(d, U1(k, b)),A^2 -> H(d, U1(k, b)))
28.56/10.05	   (A^2 -> H(d, U1(c, c)),A^2 -> H(d, U1(c, c)))
28.56/10.05	   (A^2 -> H(d, U1(c, d)),A^2 -> H(d, U1(c, d)))
28.56/10.05	
28.56/10.05	
28.56/10.05	----------------------------------------
28.56/10.05	
28.56/10.05	(1796)
28.56/10.05	Obligation:
28.56/10.05	Q DP problem:
28.56/10.05	The TRS P consists of the following rules:
28.56/10.05	
28.56/10.05	   H(x, x) -> G(x, x, f(k))
28.56/10.05	   G(d, x, x) -> A^2
28.56/10.05	   A^2 -> H(f(c), f(c))
28.56/10.05	   A^2 -> H(f(d), f(d))
28.56/10.05	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.05	   A^2 -> H(f(e), f(e))
28.56/10.05	   A^2 -> H(f(k), f(k))
28.56/10.05	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.05	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.05	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.05	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.05	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.05	   A^2 -> H(d, U1(d, b))
28.56/10.05	   A^2 -> H(d, U1(b, c))
28.56/10.05	   A^2 -> H(d, U1(b, d))
28.56/10.05	   A^2 -> H(d, U1(c, c))
28.56/10.05	   A^2 -> H(d, f(e))
28.56/10.05	   A^2 -> H(d, f(k))
28.56/10.05	   A^2 -> H(d, U1(d, d))
28.56/10.05	   A^2 -> H(a, U1(e, b))
28.56/10.05	   A^2 -> H(a, U1(k, b))
28.56/10.05	   A^2 -> H(a, U1(c, d))
28.56/10.05	   A^2 -> H(a, U1(d, c))
28.56/10.05	   A^2 -> H(a, U1(b, e))
28.56/10.05	   A^2 -> H(a, U1(b, k))
28.56/10.05	   A^2 -> H(a, U1(e, c))
28.56/10.05	   A^2 -> H(a, U1(k, c))
28.56/10.05	   A^2 -> H(a, U1(c, e))
28.56/10.05	   A^2 -> H(a, U1(c, k))
28.56/10.05	   A^2 -> H(a, U1(e, e))
28.56/10.05	   A^2 -> H(a, U1(k, k))
28.56/10.05	   A^2 -> H(a, U1(k, d))
28.56/10.05	   A^2 -> H(a, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.05	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.05	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, a), b)
28.56/10.05	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, a), c)
28.56/10.05	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, a), e)
28.56/10.05	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, a), b)
28.56/10.05	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, a), c)
28.56/10.05	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, d), b)
28.56/10.05	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, d), c)
28.56/10.05	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, d), e)
28.56/10.05	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, a), d)
28.56/10.05	   A^2 -> H(U1(c, a), k)
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.05	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.05	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.05	   A^2 -> H(U1(d, c), b)
28.56/10.05	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(d, c), c)
28.56/10.05	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(d, c), e)
28.56/10.05	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, a), d)
28.56/10.05	   A^2 -> H(U1(d, a), k)
28.56/10.05	   A^2 -> H(U1(a, e), b)
28.56/10.05	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(a, e), c)
28.56/10.05	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(a, e), e)
28.56/10.05	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(a, k), b)
28.56/10.05	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(a, k), c)
28.56/10.05	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(a, k), e)
28.56/10.05	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(a, c), d)
28.56/10.05	   A^2 -> H(U1(a, c), k)
28.56/10.05	   A^2 -> H(U1(a, d), d)
28.56/10.05	   A^2 -> H(U1(a, d), k)
28.56/10.05	   A^2 -> H(k, U1(c, b))
28.56/10.05	   A^2 -> H(k, U1(d, b))
28.56/10.05	   A^2 -> H(k, U1(b, c))
28.56/10.05	   A^2 -> H(k, U1(b, d))
28.56/10.05	   A^2 -> H(k, U1(c, c))
28.56/10.05	   A^2 -> H(k, f(e))
28.56/10.05	   A^2 -> H(k, f(k))
28.56/10.05	   A^2 -> H(k, U1(d, d))
28.56/10.05	   A^2 -> H(c, U1(e, b))
28.56/10.05	   A^2 -> H(c, U1(k, b))
28.56/10.05	   A^2 -> H(c, U1(c, d))
28.56/10.05	   A^2 -> H(c, U1(d, c))
28.56/10.05	   A^2 -> H(c, U1(b, e))
28.56/10.05	   A^2 -> H(c, U1(b, k))
28.56/10.05	   A^2 -> H(c, U1(e, c))
28.56/10.05	   A^2 -> H(c, U1(k, c))
28.56/10.05	   A^2 -> H(c, U1(c, e))
28.56/10.05	   A^2 -> H(c, U1(c, k))
28.56/10.05	   A^2 -> H(c, U1(e, e))
28.56/10.05	   A^2 -> H(c, U1(k, k))
28.56/10.05	   A^2 -> H(c, U1(k, d))
28.56/10.05	   A^2 -> H(c, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.05	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.05	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, c), b)
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, c), e)
28.56/10.05	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.05	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.05	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.05	   A^2 -> H(U1(k, c), b)
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, c), c)
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, e), b)
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, e), c)
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, e), e)
28.56/10.05	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, k), b)
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, k), c)
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, k), e)
28.56/10.05	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, c), d)
28.56/10.05	   A^2 -> H(e, U1(e, b))
28.56/10.05	   A^2 -> H(e, U1(c, d))
28.56/10.05	   A^2 -> H(e, U1(d, c))
28.56/10.05	   A^2 -> H(e, U1(b, e))
28.56/10.05	   A^2 -> H(e, U1(b, k))
28.56/10.05	   A^2 -> H(e, U1(e, c))
28.56/10.05	   A^2 -> H(e, U1(c, e))
28.56/10.05	   A^2 -> H(e, U1(c, k))
28.56/10.05	   A^2 -> H(e, U1(e, e))
28.56/10.05	   A^2 -> H(e, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, e), b)
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, e), c)
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.05	   A^2 -> H(f(e), d)
28.56/10.05	   A^2 -> H(f(e), k)
28.56/10.05	   A^2 -> H(U1(k, k), b)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, k), c)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.05	   A^2 -> H(f(k), d)
28.56/10.05	   A^2 -> H(f(k), k)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.05	   A^2 -> H(U1(k, d), b)
28.56/10.05	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, d), c)
28.56/10.05	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, k), b)
28.56/10.05	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(d, k), c)
28.56/10.05	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(d, k), e)
28.56/10.05	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, d), d)
28.56/10.05	   A^2 -> H(U1(d, d), k)
28.56/10.05	   A^2 -> H(U1(e, c), c)
28.56/10.05	   A^2 -> H(U1(c, c), e)
28.56/10.05	   A^2 -> H(U1(c, c), k)
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, e), e)
28.56/10.05	   A^2 -> H(d, U1(e, b))
28.56/10.05	   A^2 -> H(d, U1(k, b))
28.56/10.05	   A^2 -> H(d, U1(c, d))
28.56/10.05	
28.56/10.05	The TRS R consists of the following rules:
28.56/10.05	
28.56/10.05	   f(x) -> U1(x, x)
28.56/10.05	   U1(e, x) -> x
28.56/10.05	   a -> c
28.56/10.05	   a -> d
28.56/10.05	   b -> c
28.56/10.05	   b -> d
28.56/10.05	   d -> k
28.56/10.05	   c -> e
28.56/10.05	   c -> k
28.56/10.05	
28.56/10.05	Q is empty.
28.56/10.05	We have to consider all minimal (P,Q,R)-chains.
28.56/10.05	----------------------------------------
28.56/10.05	
28.56/10.05	(1797) TransformationProof (EQUIVALENT)
28.56/10.05	By narrowing [LPAR04] the rule A^2 -> H(d, U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.05	
28.56/10.05	   (A^2 -> H(k, U1(d, b)),A^2 -> H(k, U1(d, b)))
28.56/10.05	   (A^2 -> H(d, U1(k, b)),A^2 -> H(d, U1(k, b)))
28.56/10.05	   (A^2 -> H(d, U1(d, c)),A^2 -> H(d, U1(d, c)))
28.56/10.05	   (A^2 -> H(d, U1(d, d)),A^2 -> H(d, U1(d, d)))
28.56/10.05	
28.56/10.05	
28.56/10.05	----------------------------------------
28.56/10.05	
28.56/10.05	(1798)
28.56/10.05	Obligation:
28.56/10.05	Q DP problem:
28.56/10.05	The TRS P consists of the following rules:
28.56/10.05	
28.56/10.05	   H(x, x) -> G(x, x, f(k))
28.56/10.05	   G(d, x, x) -> A^2
28.56/10.05	   A^2 -> H(f(c), f(c))
28.56/10.05	   A^2 -> H(f(d), f(d))
28.56/10.05	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.05	   A^2 -> H(f(e), f(e))
28.56/10.05	   A^2 -> H(f(k), f(k))
28.56/10.05	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.05	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.05	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.05	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.05	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.05	   A^2 -> H(d, U1(b, c))
28.56/10.05	   A^2 -> H(d, U1(b, d))
28.56/10.05	   A^2 -> H(d, U1(c, c))
28.56/10.05	   A^2 -> H(d, f(e))
28.56/10.05	   A^2 -> H(d, f(k))
28.56/10.05	   A^2 -> H(d, U1(d, d))
28.56/10.05	   A^2 -> H(a, U1(e, b))
28.56/10.05	   A^2 -> H(a, U1(k, b))
28.56/10.05	   A^2 -> H(a, U1(c, d))
28.56/10.05	   A^2 -> H(a, U1(d, c))
28.56/10.05	   A^2 -> H(a, U1(b, e))
28.56/10.05	   A^2 -> H(a, U1(b, k))
28.56/10.05	   A^2 -> H(a, U1(e, c))
28.56/10.05	   A^2 -> H(a, U1(k, c))
28.56/10.05	   A^2 -> H(a, U1(c, e))
28.56/10.05	   A^2 -> H(a, U1(c, k))
28.56/10.05	   A^2 -> H(a, U1(e, e))
28.56/10.05	   A^2 -> H(a, U1(k, k))
28.56/10.05	   A^2 -> H(a, U1(k, d))
28.56/10.05	   A^2 -> H(a, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.05	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.05	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, a), b)
28.56/10.05	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, a), c)
28.56/10.05	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, a), e)
28.56/10.05	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, a), b)
28.56/10.05	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, a), c)
28.56/10.05	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, d), b)
28.56/10.05	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, d), c)
28.56/10.05	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, d), e)
28.56/10.05	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, a), d)
28.56/10.05	   A^2 -> H(U1(c, a), k)
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.05	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.05	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.05	   A^2 -> H(U1(d, c), b)
28.56/10.05	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(d, c), c)
28.56/10.05	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(d, c), e)
28.56/10.05	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, a), d)
28.56/10.05	   A^2 -> H(U1(d, a), k)
28.56/10.05	   A^2 -> H(U1(a, e), b)
28.56/10.05	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(a, e), c)
28.56/10.05	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(a, e), e)
28.56/10.05	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(a, k), b)
28.56/10.05	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(a, k), c)
28.56/10.05	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(a, k), e)
28.56/10.05	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(a, c), d)
28.56/10.05	   A^2 -> H(U1(a, c), k)
28.56/10.05	   A^2 -> H(U1(a, d), d)
28.56/10.05	   A^2 -> H(U1(a, d), k)
28.56/10.05	   A^2 -> H(k, U1(c, b))
28.56/10.05	   A^2 -> H(k, U1(d, b))
28.56/10.05	   A^2 -> H(k, U1(b, c))
28.56/10.05	   A^2 -> H(k, U1(b, d))
28.56/10.05	   A^2 -> H(k, U1(c, c))
28.56/10.05	   A^2 -> H(k, f(e))
28.56/10.05	   A^2 -> H(k, f(k))
28.56/10.05	   A^2 -> H(k, U1(d, d))
28.56/10.05	   A^2 -> H(c, U1(e, b))
28.56/10.05	   A^2 -> H(c, U1(k, b))
28.56/10.05	   A^2 -> H(c, U1(c, d))
28.56/10.05	   A^2 -> H(c, U1(d, c))
28.56/10.05	   A^2 -> H(c, U1(b, e))
28.56/10.05	   A^2 -> H(c, U1(b, k))
28.56/10.05	   A^2 -> H(c, U1(e, c))
28.56/10.05	   A^2 -> H(c, U1(k, c))
28.56/10.05	   A^2 -> H(c, U1(c, e))
28.56/10.05	   A^2 -> H(c, U1(c, k))
28.56/10.05	   A^2 -> H(c, U1(e, e))
28.56/10.05	   A^2 -> H(c, U1(k, k))
28.56/10.05	   A^2 -> H(c, U1(k, d))
28.56/10.05	   A^2 -> H(c, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.05	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.05	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, c), b)
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, c), e)
28.56/10.05	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.05	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.05	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.05	   A^2 -> H(U1(k, c), b)
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, c), c)
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, e), b)
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, e), c)
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, e), e)
28.56/10.05	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, k), b)
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, k), c)
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, k), e)
28.56/10.05	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, c), d)
28.56/10.05	   A^2 -> H(e, U1(e, b))
28.56/10.05	   A^2 -> H(e, U1(c, d))
28.56/10.05	   A^2 -> H(e, U1(d, c))
28.56/10.05	   A^2 -> H(e, U1(b, e))
28.56/10.05	   A^2 -> H(e, U1(b, k))
28.56/10.05	   A^2 -> H(e, U1(e, c))
28.56/10.05	   A^2 -> H(e, U1(c, e))
28.56/10.05	   A^2 -> H(e, U1(c, k))
28.56/10.05	   A^2 -> H(e, U1(e, e))
28.56/10.05	   A^2 -> H(e, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, e), b)
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, e), c)
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.05	   A^2 -> H(f(e), d)
28.56/10.05	   A^2 -> H(f(e), k)
28.56/10.05	   A^2 -> H(U1(k, k), b)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, k), c)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.05	   A^2 -> H(f(k), d)
28.56/10.05	   A^2 -> H(f(k), k)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.05	   A^2 -> H(U1(k, d), b)
28.56/10.05	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, d), c)
28.56/10.05	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, k), b)
28.56/10.05	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(d, k), c)
28.56/10.05	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(d, k), e)
28.56/10.05	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, d), d)
28.56/10.05	   A^2 -> H(U1(d, d), k)
28.56/10.05	   A^2 -> H(U1(e, c), c)
28.56/10.05	   A^2 -> H(U1(c, c), e)
28.56/10.05	   A^2 -> H(U1(c, c), k)
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, e), e)
28.56/10.05	   A^2 -> H(d, U1(e, b))
28.56/10.05	   A^2 -> H(d, U1(k, b))
28.56/10.05	   A^2 -> H(d, U1(c, d))
28.56/10.05	   A^2 -> H(d, U1(d, c))
28.56/10.05	
28.56/10.05	The TRS R consists of the following rules:
28.56/10.05	
28.56/10.05	   f(x) -> U1(x, x)
28.56/10.05	   U1(e, x) -> x
28.56/10.05	   a -> c
28.56/10.05	   a -> d
28.56/10.05	   b -> c
28.56/10.05	   b -> d
28.56/10.05	   d -> k
28.56/10.05	   c -> e
28.56/10.05	   c -> k
28.56/10.05	
28.56/10.05	Q is empty.
28.56/10.05	We have to consider all minimal (P,Q,R)-chains.
28.56/10.05	----------------------------------------
28.56/10.05	
28.56/10.05	(1799) TransformationProof (EQUIVALENT)
28.56/10.05	By narrowing [LPAR04] the rule A^2 -> H(d, U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.05	
28.56/10.05	   (A^2 -> H(k, U1(b, c)),A^2 -> H(k, U1(b, c)))
28.56/10.05	   (A^2 -> H(d, U1(c, c)),A^2 -> H(d, U1(c, c)))
28.56/10.05	   (A^2 -> H(d, U1(d, c)),A^2 -> H(d, U1(d, c)))
28.56/10.05	   (A^2 -> H(d, U1(b, e)),A^2 -> H(d, U1(b, e)))
28.56/10.05	   (A^2 -> H(d, U1(b, k)),A^2 -> H(d, U1(b, k)))
28.56/10.05	
28.56/10.05	
28.56/10.05	----------------------------------------
28.56/10.05	
28.56/10.05	(1800)
28.56/10.05	Obligation:
28.56/10.05	Q DP problem:
28.56/10.05	The TRS P consists of the following rules:
28.56/10.05	
28.56/10.05	   H(x, x) -> G(x, x, f(k))
28.56/10.05	   G(d, x, x) -> A^2
28.56/10.05	   A^2 -> H(f(c), f(c))
28.56/10.05	   A^2 -> H(f(d), f(d))
28.56/10.05	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.05	   A^2 -> H(f(e), f(e))
28.56/10.05	   A^2 -> H(f(k), f(k))
28.56/10.05	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.05	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.05	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.05	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.05	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.05	   A^2 -> H(d, U1(b, d))
28.56/10.05	   A^2 -> H(d, U1(c, c))
28.56/10.05	   A^2 -> H(d, f(e))
28.56/10.05	   A^2 -> H(d, f(k))
28.56/10.05	   A^2 -> H(d, U1(d, d))
28.56/10.05	   A^2 -> H(a, U1(e, b))
28.56/10.05	   A^2 -> H(a, U1(k, b))
28.56/10.05	   A^2 -> H(a, U1(c, d))
28.56/10.05	   A^2 -> H(a, U1(d, c))
28.56/10.05	   A^2 -> H(a, U1(b, e))
28.56/10.05	   A^2 -> H(a, U1(b, k))
28.56/10.05	   A^2 -> H(a, U1(e, c))
28.56/10.05	   A^2 -> H(a, U1(k, c))
28.56/10.05	   A^2 -> H(a, U1(c, e))
28.56/10.05	   A^2 -> H(a, U1(c, k))
28.56/10.05	   A^2 -> H(a, U1(e, e))
28.56/10.05	   A^2 -> H(a, U1(k, k))
28.56/10.05	   A^2 -> H(a, U1(k, d))
28.56/10.05	   A^2 -> H(a, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.05	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.05	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, a), b)
28.56/10.05	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, a), c)
28.56/10.05	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, a), e)
28.56/10.05	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, a), b)
28.56/10.05	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, a), c)
28.56/10.05	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, d), b)
28.56/10.05	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, d), c)
28.56/10.05	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, d), e)
28.56/10.05	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, a), d)
28.56/10.05	   A^2 -> H(U1(c, a), k)
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.05	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.05	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.05	   A^2 -> H(U1(d, c), b)
28.56/10.05	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(d, c), c)
28.56/10.05	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(d, c), e)
28.56/10.05	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, a), d)
28.56/10.05	   A^2 -> H(U1(d, a), k)
28.56/10.05	   A^2 -> H(U1(a, e), b)
28.56/10.05	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(a, e), c)
28.56/10.05	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(a, e), e)
28.56/10.05	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(a, k), b)
28.56/10.05	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(a, k), c)
28.56/10.05	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(a, k), e)
28.56/10.05	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(a, c), d)
28.56/10.05	   A^2 -> H(U1(a, c), k)
28.56/10.05	   A^2 -> H(U1(a, d), d)
28.56/10.05	   A^2 -> H(U1(a, d), k)
28.56/10.05	   A^2 -> H(k, U1(c, b))
28.56/10.05	   A^2 -> H(k, U1(d, b))
28.56/10.05	   A^2 -> H(k, U1(b, c))
28.56/10.05	   A^2 -> H(k, U1(b, d))
28.56/10.05	   A^2 -> H(k, U1(c, c))
28.56/10.05	   A^2 -> H(k, f(e))
28.56/10.05	   A^2 -> H(k, f(k))
28.56/10.05	   A^2 -> H(k, U1(d, d))
28.56/10.05	   A^2 -> H(c, U1(e, b))
28.56/10.05	   A^2 -> H(c, U1(k, b))
28.56/10.05	   A^2 -> H(c, U1(c, d))
28.56/10.05	   A^2 -> H(c, U1(d, c))
28.56/10.05	   A^2 -> H(c, U1(b, e))
28.56/10.05	   A^2 -> H(c, U1(b, k))
28.56/10.05	   A^2 -> H(c, U1(e, c))
28.56/10.05	   A^2 -> H(c, U1(k, c))
28.56/10.05	   A^2 -> H(c, U1(c, e))
28.56/10.05	   A^2 -> H(c, U1(c, k))
28.56/10.05	   A^2 -> H(c, U1(e, e))
28.56/10.05	   A^2 -> H(c, U1(k, k))
28.56/10.05	   A^2 -> H(c, U1(k, d))
28.56/10.05	   A^2 -> H(c, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.05	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.05	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, c), b)
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, c), e)
28.56/10.05	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.05	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.05	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.05	   A^2 -> H(U1(k, c), b)
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, c), c)
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, e), b)
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, e), c)
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, e), e)
28.56/10.05	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, k), b)
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, k), c)
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, k), e)
28.56/10.05	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, c), d)
28.56/10.05	   A^2 -> H(e, U1(e, b))
28.56/10.05	   A^2 -> H(e, U1(c, d))
28.56/10.05	   A^2 -> H(e, U1(d, c))
28.56/10.05	   A^2 -> H(e, U1(b, e))
28.56/10.05	   A^2 -> H(e, U1(b, k))
28.56/10.05	   A^2 -> H(e, U1(e, c))
28.56/10.05	   A^2 -> H(e, U1(c, e))
28.56/10.05	   A^2 -> H(e, U1(c, k))
28.56/10.05	   A^2 -> H(e, U1(e, e))
28.56/10.05	   A^2 -> H(e, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, e), b)
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, e), c)
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.05	   A^2 -> H(f(e), d)
28.56/10.05	   A^2 -> H(f(e), k)
28.56/10.05	   A^2 -> H(U1(k, k), b)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, k), c)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.05	   A^2 -> H(f(k), d)
28.56/10.05	   A^2 -> H(f(k), k)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.05	   A^2 -> H(U1(k, d), b)
28.56/10.05	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, d), c)
28.56/10.05	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, k), b)
28.56/10.05	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(d, k), c)
28.56/10.05	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(d, k), e)
28.56/10.05	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, d), d)
28.56/10.05	   A^2 -> H(U1(d, d), k)
28.56/10.05	   A^2 -> H(U1(e, c), c)
28.56/10.05	   A^2 -> H(U1(c, c), e)
28.56/10.05	   A^2 -> H(U1(c, c), k)
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, e), e)
28.56/10.05	   A^2 -> H(d, U1(e, b))
28.56/10.05	   A^2 -> H(d, U1(k, b))
28.56/10.05	   A^2 -> H(d, U1(c, d))
28.56/10.05	   A^2 -> H(d, U1(d, c))
28.56/10.05	   A^2 -> H(d, U1(b, e))
28.56/10.05	   A^2 -> H(d, U1(b, k))
28.56/10.05	
28.56/10.05	The TRS R consists of the following rules:
28.56/10.05	
28.56/10.05	   f(x) -> U1(x, x)
28.56/10.05	   U1(e, x) -> x
28.56/10.05	   a -> c
28.56/10.05	   a -> d
28.56/10.05	   b -> c
28.56/10.05	   b -> d
28.56/10.05	   d -> k
28.56/10.05	   c -> e
28.56/10.05	   c -> k
28.56/10.05	
28.56/10.05	Q is empty.
28.56/10.05	We have to consider all minimal (P,Q,R)-chains.
28.56/10.05	----------------------------------------
28.56/10.05	
28.56/10.05	(1801) TransformationProof (EQUIVALENT)
28.56/10.05	By narrowing [LPAR04] the rule A^2 -> H(d, U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.05	
28.56/10.05	   (A^2 -> H(k, U1(b, d)),A^2 -> H(k, U1(b, d)))
28.56/10.05	   (A^2 -> H(d, U1(c, d)),A^2 -> H(d, U1(c, d)))
28.56/10.05	   (A^2 -> H(d, U1(d, d)),A^2 -> H(d, U1(d, d)))
28.56/10.05	   (A^2 -> H(d, U1(b, k)),A^2 -> H(d, U1(b, k)))
28.56/10.05	
28.56/10.05	
28.56/10.05	----------------------------------------
28.56/10.05	
28.56/10.05	(1802)
28.56/10.05	Obligation:
28.56/10.05	Q DP problem:
28.56/10.05	The TRS P consists of the following rules:
28.56/10.05	
28.56/10.05	   H(x, x) -> G(x, x, f(k))
28.56/10.05	   G(d, x, x) -> A^2
28.56/10.05	   A^2 -> H(f(c), f(c))
28.56/10.05	   A^2 -> H(f(d), f(d))
28.56/10.05	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.05	   A^2 -> H(f(e), f(e))
28.56/10.05	   A^2 -> H(f(k), f(k))
28.56/10.05	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.05	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.05	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.05	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.05	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.05	   A^2 -> H(d, U1(c, c))
28.56/10.05	   A^2 -> H(d, f(e))
28.56/10.05	   A^2 -> H(d, f(k))
28.56/10.05	   A^2 -> H(d, U1(d, d))
28.56/10.05	   A^2 -> H(a, U1(e, b))
28.56/10.05	   A^2 -> H(a, U1(k, b))
28.56/10.05	   A^2 -> H(a, U1(c, d))
28.56/10.05	   A^2 -> H(a, U1(d, c))
28.56/10.05	   A^2 -> H(a, U1(b, e))
28.56/10.05	   A^2 -> H(a, U1(b, k))
28.56/10.05	   A^2 -> H(a, U1(e, c))
28.56/10.05	   A^2 -> H(a, U1(k, c))
28.56/10.05	   A^2 -> H(a, U1(c, e))
28.56/10.05	   A^2 -> H(a, U1(c, k))
28.56/10.05	   A^2 -> H(a, U1(e, e))
28.56/10.05	   A^2 -> H(a, U1(k, k))
28.56/10.05	   A^2 -> H(a, U1(k, d))
28.56/10.05	   A^2 -> H(a, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.05	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.05	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, a), b)
28.56/10.05	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, a), c)
28.56/10.05	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, a), e)
28.56/10.05	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, a), b)
28.56/10.05	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, a), c)
28.56/10.05	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, d), b)
28.56/10.05	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, d), c)
28.56/10.05	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, d), e)
28.56/10.05	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, a), d)
28.56/10.05	   A^2 -> H(U1(c, a), k)
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.05	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.05	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.05	   A^2 -> H(U1(d, c), b)
28.56/10.05	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(d, c), c)
28.56/10.05	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(d, c), e)
28.56/10.05	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, a), d)
28.56/10.05	   A^2 -> H(U1(d, a), k)
28.56/10.05	   A^2 -> H(U1(a, e), b)
28.56/10.05	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(a, e), c)
28.56/10.05	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(a, e), e)
28.56/10.05	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(a, k), b)
28.56/10.05	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(a, k), c)
28.56/10.05	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(a, k), e)
28.56/10.05	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(a, c), d)
28.56/10.05	   A^2 -> H(U1(a, c), k)
28.56/10.05	   A^2 -> H(U1(a, d), d)
28.56/10.05	   A^2 -> H(U1(a, d), k)
28.56/10.05	   A^2 -> H(k, U1(c, b))
28.56/10.05	   A^2 -> H(k, U1(d, b))
28.56/10.05	   A^2 -> H(k, U1(b, c))
28.56/10.05	   A^2 -> H(k, U1(b, d))
28.56/10.05	   A^2 -> H(k, U1(c, c))
28.56/10.05	   A^2 -> H(k, f(e))
28.56/10.05	   A^2 -> H(k, f(k))
28.56/10.05	   A^2 -> H(k, U1(d, d))
28.56/10.05	   A^2 -> H(c, U1(e, b))
28.56/10.05	   A^2 -> H(c, U1(k, b))
28.56/10.05	   A^2 -> H(c, U1(c, d))
28.56/10.05	   A^2 -> H(c, U1(d, c))
28.56/10.05	   A^2 -> H(c, U1(b, e))
28.56/10.05	   A^2 -> H(c, U1(b, k))
28.56/10.05	   A^2 -> H(c, U1(e, c))
28.56/10.05	   A^2 -> H(c, U1(k, c))
28.56/10.05	   A^2 -> H(c, U1(c, e))
28.56/10.05	   A^2 -> H(c, U1(c, k))
28.56/10.05	   A^2 -> H(c, U1(e, e))
28.56/10.05	   A^2 -> H(c, U1(k, k))
28.56/10.05	   A^2 -> H(c, U1(k, d))
28.56/10.05	   A^2 -> H(c, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.05	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.05	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, c), b)
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, c), e)
28.56/10.05	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.05	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.05	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.05	   A^2 -> H(U1(k, c), b)
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, c), c)
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, e), b)
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, e), c)
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, e), e)
28.56/10.05	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, k), b)
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, k), c)
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, k), e)
28.56/10.05	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, c), d)
28.56/10.05	   A^2 -> H(e, U1(e, b))
28.56/10.05	   A^2 -> H(e, U1(c, d))
28.56/10.05	   A^2 -> H(e, U1(d, c))
28.56/10.05	   A^2 -> H(e, U1(b, e))
28.56/10.05	   A^2 -> H(e, U1(b, k))
28.56/10.05	   A^2 -> H(e, U1(e, c))
28.56/10.05	   A^2 -> H(e, U1(c, e))
28.56/10.05	   A^2 -> H(e, U1(c, k))
28.56/10.05	   A^2 -> H(e, U1(e, e))
28.56/10.05	   A^2 -> H(e, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, e), b)
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, e), c)
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.05	   A^2 -> H(f(e), d)
28.56/10.05	   A^2 -> H(f(e), k)
28.56/10.05	   A^2 -> H(U1(k, k), b)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, k), c)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.05	   A^2 -> H(f(k), d)
28.56/10.05	   A^2 -> H(f(k), k)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.05	   A^2 -> H(U1(k, d), b)
28.56/10.05	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, d), c)
28.56/10.05	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, k), b)
28.56/10.05	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(d, k), c)
28.56/10.05	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(d, k), e)
28.56/10.05	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, d), d)
28.56/10.05	   A^2 -> H(U1(d, d), k)
28.56/10.05	   A^2 -> H(U1(e, c), c)
28.56/10.05	   A^2 -> H(U1(c, c), e)
28.56/10.05	   A^2 -> H(U1(c, c), k)
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, e), e)
28.56/10.05	   A^2 -> H(d, U1(e, b))
28.56/10.05	   A^2 -> H(d, U1(k, b))
28.56/10.05	   A^2 -> H(d, U1(c, d))
28.56/10.05	   A^2 -> H(d, U1(d, c))
28.56/10.05	   A^2 -> H(d, U1(b, e))
28.56/10.05	   A^2 -> H(d, U1(b, k))
28.56/10.05	
28.56/10.05	The TRS R consists of the following rules:
28.56/10.05	
28.56/10.05	   f(x) -> U1(x, x)
28.56/10.05	   U1(e, x) -> x
28.56/10.05	   a -> c
28.56/10.05	   a -> d
28.56/10.05	   b -> c
28.56/10.05	   b -> d
28.56/10.05	   d -> k
28.56/10.05	   c -> e
28.56/10.05	   c -> k
28.56/10.05	
28.56/10.05	Q is empty.
28.56/10.05	We have to consider all minimal (P,Q,R)-chains.
28.56/10.05	----------------------------------------
28.56/10.05	
28.56/10.05	(1803) TransformationProof (EQUIVALENT)
28.56/10.05	By narrowing [LPAR04] the rule A^2 -> H(d, U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.05	
28.56/10.05	   (A^2 -> H(k, U1(c, c)),A^2 -> H(k, U1(c, c)))
28.56/10.05	   (A^2 -> H(d, U1(e, c)),A^2 -> H(d, U1(e, c)))
28.56/10.05	   (A^2 -> H(d, U1(k, c)),A^2 -> H(d, U1(k, c)))
28.56/10.05	   (A^2 -> H(d, U1(c, e)),A^2 -> H(d, U1(c, e)))
28.56/10.05	   (A^2 -> H(d, U1(c, k)),A^2 -> H(d, U1(c, k)))
28.56/10.05	
28.56/10.05	
28.56/10.05	----------------------------------------
28.56/10.05	
28.56/10.05	(1804)
28.56/10.05	Obligation:
28.56/10.05	Q DP problem:
28.56/10.05	The TRS P consists of the following rules:
28.56/10.05	
28.56/10.05	   H(x, x) -> G(x, x, f(k))
28.56/10.05	   G(d, x, x) -> A^2
28.56/10.05	   A^2 -> H(f(c), f(c))
28.56/10.05	   A^2 -> H(f(d), f(d))
28.56/10.05	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.05	   A^2 -> H(f(e), f(e))
28.56/10.05	   A^2 -> H(f(k), f(k))
28.56/10.05	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.05	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.05	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.05	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.05	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.05	   A^2 -> H(d, f(e))
28.56/10.05	   A^2 -> H(d, f(k))
28.56/10.05	   A^2 -> H(d, U1(d, d))
28.56/10.05	   A^2 -> H(a, U1(e, b))
28.56/10.05	   A^2 -> H(a, U1(k, b))
28.56/10.05	   A^2 -> H(a, U1(c, d))
28.56/10.05	   A^2 -> H(a, U1(d, c))
28.56/10.05	   A^2 -> H(a, U1(b, e))
28.56/10.05	   A^2 -> H(a, U1(b, k))
28.56/10.05	   A^2 -> H(a, U1(e, c))
28.56/10.05	   A^2 -> H(a, U1(k, c))
28.56/10.05	   A^2 -> H(a, U1(c, e))
28.56/10.05	   A^2 -> H(a, U1(c, k))
28.56/10.05	   A^2 -> H(a, U1(e, e))
28.56/10.05	   A^2 -> H(a, U1(k, k))
28.56/10.05	   A^2 -> H(a, U1(k, d))
28.56/10.05	   A^2 -> H(a, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.05	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.05	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, a), b)
28.56/10.05	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, a), c)
28.56/10.05	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, a), e)
28.56/10.05	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, a), b)
28.56/10.05	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, a), c)
28.56/10.05	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, d), b)
28.56/10.05	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, d), c)
28.56/10.05	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, d), e)
28.56/10.05	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, a), d)
28.56/10.05	   A^2 -> H(U1(c, a), k)
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.05	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.05	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.05	   A^2 -> H(U1(d, c), b)
28.56/10.05	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(d, c), c)
28.56/10.05	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(d, c), e)
28.56/10.05	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(d, a), d)
28.56/10.05	   A^2 -> H(U1(d, a), k)
28.56/10.05	   A^2 -> H(U1(a, e), b)
28.56/10.05	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(a, e), c)
28.56/10.05	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(a, e), e)
28.56/10.05	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(a, k), b)
28.56/10.05	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(a, k), c)
28.56/10.05	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(a, k), e)
28.56/10.05	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(a, c), d)
28.56/10.05	   A^2 -> H(U1(a, c), k)
28.56/10.05	   A^2 -> H(U1(a, d), d)
28.56/10.05	   A^2 -> H(U1(a, d), k)
28.56/10.05	   A^2 -> H(k, U1(c, b))
28.56/10.05	   A^2 -> H(k, U1(d, b))
28.56/10.05	   A^2 -> H(k, U1(b, c))
28.56/10.05	   A^2 -> H(k, U1(b, d))
28.56/10.05	   A^2 -> H(k, U1(c, c))
28.56/10.05	   A^2 -> H(k, f(e))
28.56/10.05	   A^2 -> H(k, f(k))
28.56/10.05	   A^2 -> H(k, U1(d, d))
28.56/10.05	   A^2 -> H(c, U1(e, b))
28.56/10.05	   A^2 -> H(c, U1(k, b))
28.56/10.05	   A^2 -> H(c, U1(c, d))
28.56/10.05	   A^2 -> H(c, U1(d, c))
28.56/10.05	   A^2 -> H(c, U1(b, e))
28.56/10.05	   A^2 -> H(c, U1(b, k))
28.56/10.05	   A^2 -> H(c, U1(e, c))
28.56/10.05	   A^2 -> H(c, U1(k, c))
28.56/10.05	   A^2 -> H(c, U1(c, e))
28.56/10.05	   A^2 -> H(c, U1(c, k))
28.56/10.05	   A^2 -> H(c, U1(e, e))
28.56/10.05	   A^2 -> H(c, U1(k, k))
28.56/10.05	   A^2 -> H(c, U1(k, d))
28.56/10.05	   A^2 -> H(c, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.05	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.05	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, c), b)
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, c), e)
28.56/10.05	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.05	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.05	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.05	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.05	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.05	   A^2 -> H(U1(k, c), b)
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, c), c)
28.56/10.05	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.05	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, e), b)
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, e), c)
28.56/10.05	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, e), e)
28.56/10.05	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, k), b)
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(c, k), c)
28.56/10.05	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.05	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.05	   A^2 -> H(U1(c, k), e)
28.56/10.05	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.05	   A^2 -> H(U1(c, c), d)
28.56/10.05	   A^2 -> H(e, U1(e, b))
28.56/10.05	   A^2 -> H(e, U1(c, d))
28.56/10.05	   A^2 -> H(e, U1(d, c))
28.56/10.05	   A^2 -> H(e, U1(b, e))
28.56/10.05	   A^2 -> H(e, U1(b, k))
28.56/10.05	   A^2 -> H(e, U1(e, c))
28.56/10.05	   A^2 -> H(e, U1(c, e))
28.56/10.05	   A^2 -> H(e, U1(c, k))
28.56/10.05	   A^2 -> H(e, U1(e, e))
28.56/10.05	   A^2 -> H(e, U1(d, k))
28.56/10.05	   A^2 -> H(U1(e, e), b)
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.05	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.05	   A^2 -> H(U1(e, e), c)
28.56/10.05	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.05	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.05	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.05	   A^2 -> H(f(e), d)
28.56/10.05	   A^2 -> H(f(e), k)
28.56/10.05	   A^2 -> H(U1(k, k), b)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.05	   A^2 -> H(U1(k, k), c)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.05	   A^2 -> H(f(k), d)
28.56/10.05	   A^2 -> H(f(k), k)
28.56/10.05	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.05	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.05	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.05	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.05	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.06	   A^2 -> H(U1(k, d), b)
28.56/10.06	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, d), c)
28.56/10.06	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, k), b)
28.56/10.06	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(d, k), c)
28.56/10.06	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(d, k), e)
28.56/10.06	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, d), d)
28.56/10.06	   A^2 -> H(U1(d, d), k)
28.56/10.06	   A^2 -> H(U1(e, c), c)
28.56/10.06	   A^2 -> H(U1(c, c), e)
28.56/10.06	   A^2 -> H(U1(c, c), k)
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, e), e)
28.56/10.06	   A^2 -> H(d, U1(e, b))
28.56/10.06	   A^2 -> H(d, U1(k, b))
28.56/10.06	   A^2 -> H(d, U1(c, d))
28.56/10.06	   A^2 -> H(d, U1(d, c))
28.56/10.06	   A^2 -> H(d, U1(b, e))
28.56/10.06	   A^2 -> H(d, U1(b, k))
28.56/10.06	   A^2 -> H(d, U1(e, c))
28.56/10.06	   A^2 -> H(d, U1(k, c))
28.56/10.06	   A^2 -> H(d, U1(c, e))
28.56/10.06	   A^2 -> H(d, U1(c, k))
28.56/10.06	
28.56/10.06	The TRS R consists of the following rules:
28.56/10.06	
28.56/10.06	   f(x) -> U1(x, x)
28.56/10.06	   U1(e, x) -> x
28.56/10.06	   a -> c
28.56/10.06	   a -> d
28.56/10.06	   b -> c
28.56/10.06	   b -> d
28.56/10.06	   d -> k
28.56/10.06	   c -> e
28.56/10.06	   c -> k
28.56/10.06	
28.56/10.06	Q is empty.
28.56/10.06	We have to consider all minimal (P,Q,R)-chains.
28.56/10.06	----------------------------------------
28.56/10.06	
28.56/10.06	(1805) TransformationProof (EQUIVALENT)
28.56/10.06	By narrowing [LPAR04] the rule A^2 -> H(d, f(e)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.06	
28.56/10.06	   (A^2 -> H(k, f(e)),A^2 -> H(k, f(e)))
28.56/10.06	   (A^2 -> H(d, U1(e, e)),A^2 -> H(d, U1(e, e)))
28.56/10.06	
28.56/10.06	
28.56/10.06	----------------------------------------
28.56/10.06	
28.56/10.06	(1806)
28.56/10.06	Obligation:
28.56/10.06	Q DP problem:
28.56/10.06	The TRS P consists of the following rules:
28.56/10.06	
28.56/10.06	   H(x, x) -> G(x, x, f(k))
28.56/10.06	   G(d, x, x) -> A^2
28.56/10.06	   A^2 -> H(f(c), f(c))
28.56/10.06	   A^2 -> H(f(d), f(d))
28.56/10.06	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.06	   A^2 -> H(f(e), f(e))
28.56/10.06	   A^2 -> H(f(k), f(k))
28.56/10.06	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.06	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.06	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.06	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.06	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.06	   A^2 -> H(d, f(k))
28.56/10.06	   A^2 -> H(d, U1(d, d))
28.56/10.06	   A^2 -> H(a, U1(e, b))
28.56/10.06	   A^2 -> H(a, U1(k, b))
28.56/10.06	   A^2 -> H(a, U1(c, d))
28.56/10.06	   A^2 -> H(a, U1(d, c))
28.56/10.06	   A^2 -> H(a, U1(b, e))
28.56/10.06	   A^2 -> H(a, U1(b, k))
28.56/10.06	   A^2 -> H(a, U1(e, c))
28.56/10.06	   A^2 -> H(a, U1(k, c))
28.56/10.06	   A^2 -> H(a, U1(c, e))
28.56/10.06	   A^2 -> H(a, U1(c, k))
28.56/10.06	   A^2 -> H(a, U1(e, e))
28.56/10.06	   A^2 -> H(a, U1(k, k))
28.56/10.06	   A^2 -> H(a, U1(k, d))
28.56/10.06	   A^2 -> H(a, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.06	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.06	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, a), b)
28.56/10.06	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, a), c)
28.56/10.06	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, a), e)
28.56/10.06	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, a), b)
28.56/10.06	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, a), c)
28.56/10.06	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, d), b)
28.56/10.06	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, d), c)
28.56/10.06	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, d), e)
28.56/10.06	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, a), d)
28.56/10.06	   A^2 -> H(U1(c, a), k)
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.06	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.06	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.06	   A^2 -> H(U1(d, c), b)
28.56/10.06	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(d, c), c)
28.56/10.06	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(d, c), e)
28.56/10.06	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, a), d)
28.56/10.06	   A^2 -> H(U1(d, a), k)
28.56/10.06	   A^2 -> H(U1(a, e), b)
28.56/10.06	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(a, e), c)
28.56/10.06	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(a, e), e)
28.56/10.06	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(a, k), b)
28.56/10.06	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(a, k), c)
28.56/10.06	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(a, k), e)
28.56/10.06	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(a, c), d)
28.56/10.06	   A^2 -> H(U1(a, c), k)
28.56/10.06	   A^2 -> H(U1(a, d), d)
28.56/10.06	   A^2 -> H(U1(a, d), k)
28.56/10.06	   A^2 -> H(k, U1(c, b))
28.56/10.06	   A^2 -> H(k, U1(d, b))
28.56/10.06	   A^2 -> H(k, U1(b, c))
28.56/10.06	   A^2 -> H(k, U1(b, d))
28.56/10.06	   A^2 -> H(k, U1(c, c))
28.56/10.06	   A^2 -> H(k, f(e))
28.56/10.06	   A^2 -> H(k, f(k))
28.56/10.06	   A^2 -> H(k, U1(d, d))
28.56/10.06	   A^2 -> H(c, U1(e, b))
28.56/10.06	   A^2 -> H(c, U1(k, b))
28.56/10.06	   A^2 -> H(c, U1(c, d))
28.56/10.06	   A^2 -> H(c, U1(d, c))
28.56/10.06	   A^2 -> H(c, U1(b, e))
28.56/10.06	   A^2 -> H(c, U1(b, k))
28.56/10.06	   A^2 -> H(c, U1(e, c))
28.56/10.06	   A^2 -> H(c, U1(k, c))
28.56/10.06	   A^2 -> H(c, U1(c, e))
28.56/10.06	   A^2 -> H(c, U1(c, k))
28.56/10.06	   A^2 -> H(c, U1(e, e))
28.56/10.06	   A^2 -> H(c, U1(k, k))
28.56/10.06	   A^2 -> H(c, U1(k, d))
28.56/10.06	   A^2 -> H(c, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.06	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.06	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, c), b)
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, c), e)
28.56/10.06	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.06	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.06	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.06	   A^2 -> H(U1(k, c), b)
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, c), c)
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, e), b)
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, e), c)
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, e), e)
28.56/10.06	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, k), b)
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, k), c)
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, k), e)
28.56/10.06	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, c), d)
28.56/10.06	   A^2 -> H(e, U1(e, b))
28.56/10.06	   A^2 -> H(e, U1(c, d))
28.56/10.06	   A^2 -> H(e, U1(d, c))
28.56/10.06	   A^2 -> H(e, U1(b, e))
28.56/10.06	   A^2 -> H(e, U1(b, k))
28.56/10.06	   A^2 -> H(e, U1(e, c))
28.56/10.06	   A^2 -> H(e, U1(c, e))
28.56/10.06	   A^2 -> H(e, U1(c, k))
28.56/10.06	   A^2 -> H(e, U1(e, e))
28.56/10.06	   A^2 -> H(e, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, e), b)
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, e), c)
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.06	   A^2 -> H(f(e), d)
28.56/10.06	   A^2 -> H(f(e), k)
28.56/10.06	   A^2 -> H(U1(k, k), b)
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, k), c)
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.06	   A^2 -> H(f(k), d)
28.56/10.06	   A^2 -> H(f(k), k)
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.06	   A^2 -> H(U1(k, d), b)
28.56/10.06	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, d), c)
28.56/10.06	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, k), b)
28.56/10.06	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(d, k), c)
28.56/10.06	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(d, k), e)
28.56/10.06	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, d), d)
28.56/10.06	   A^2 -> H(U1(d, d), k)
28.56/10.06	   A^2 -> H(U1(e, c), c)
28.56/10.06	   A^2 -> H(U1(c, c), e)
28.56/10.06	   A^2 -> H(U1(c, c), k)
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, e), e)
28.56/10.06	   A^2 -> H(d, U1(e, b))
28.56/10.06	   A^2 -> H(d, U1(k, b))
28.56/10.06	   A^2 -> H(d, U1(c, d))
28.56/10.06	   A^2 -> H(d, U1(d, c))
28.56/10.06	   A^2 -> H(d, U1(b, e))
28.56/10.06	   A^2 -> H(d, U1(b, k))
28.56/10.06	   A^2 -> H(d, U1(e, c))
28.56/10.06	   A^2 -> H(d, U1(k, c))
28.56/10.06	   A^2 -> H(d, U1(c, e))
28.56/10.06	   A^2 -> H(d, U1(c, k))
28.56/10.06	   A^2 -> H(d, U1(e, e))
28.56/10.06	
28.56/10.06	The TRS R consists of the following rules:
28.56/10.06	
28.56/10.06	   f(x) -> U1(x, x)
28.56/10.06	   U1(e, x) -> x
28.56/10.06	   a -> c
28.56/10.06	   a -> d
28.56/10.06	   b -> c
28.56/10.06	   b -> d
28.56/10.06	   d -> k
28.56/10.06	   c -> e
28.56/10.06	   c -> k
28.56/10.06	
28.56/10.06	Q is empty.
28.56/10.06	We have to consider all minimal (P,Q,R)-chains.
28.56/10.06	----------------------------------------
28.56/10.06	
28.56/10.06	(1807) TransformationProof (EQUIVALENT)
28.56/10.06	By narrowing [LPAR04] the rule A^2 -> H(d, f(k)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.06	
28.56/10.06	   (A^2 -> H(k, f(k)),A^2 -> H(k, f(k)))
28.56/10.06	   (A^2 -> H(d, U1(k, k)),A^2 -> H(d, U1(k, k)))
28.56/10.06	
28.56/10.06	
28.56/10.06	----------------------------------------
28.56/10.06	
28.56/10.06	(1808)
28.56/10.06	Obligation:
28.56/10.06	Q DP problem:
28.56/10.06	The TRS P consists of the following rules:
28.56/10.06	
28.56/10.06	   H(x, x) -> G(x, x, f(k))
28.56/10.06	   G(d, x, x) -> A^2
28.56/10.06	   A^2 -> H(f(c), f(c))
28.56/10.06	   A^2 -> H(f(d), f(d))
28.56/10.06	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.06	   A^2 -> H(f(e), f(e))
28.56/10.06	   A^2 -> H(f(k), f(k))
28.56/10.06	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.06	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.06	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.06	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.06	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.06	   A^2 -> H(d, U1(d, d))
28.56/10.06	   A^2 -> H(a, U1(e, b))
28.56/10.06	   A^2 -> H(a, U1(k, b))
28.56/10.06	   A^2 -> H(a, U1(c, d))
28.56/10.06	   A^2 -> H(a, U1(d, c))
28.56/10.06	   A^2 -> H(a, U1(b, e))
28.56/10.06	   A^2 -> H(a, U1(b, k))
28.56/10.06	   A^2 -> H(a, U1(e, c))
28.56/10.06	   A^2 -> H(a, U1(k, c))
28.56/10.06	   A^2 -> H(a, U1(c, e))
28.56/10.06	   A^2 -> H(a, U1(c, k))
28.56/10.06	   A^2 -> H(a, U1(e, e))
28.56/10.06	   A^2 -> H(a, U1(k, k))
28.56/10.06	   A^2 -> H(a, U1(k, d))
28.56/10.06	   A^2 -> H(a, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.06	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.06	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, a), b)
28.56/10.06	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, a), c)
28.56/10.06	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, a), e)
28.56/10.06	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, a), b)
28.56/10.06	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, a), c)
28.56/10.06	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, d), b)
28.56/10.06	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, d), c)
28.56/10.06	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, d), e)
28.56/10.06	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, a), d)
28.56/10.06	   A^2 -> H(U1(c, a), k)
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.06	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.06	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.06	   A^2 -> H(U1(d, c), b)
28.56/10.06	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(d, c), c)
28.56/10.06	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(d, c), e)
28.56/10.06	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, a), d)
28.56/10.06	   A^2 -> H(U1(d, a), k)
28.56/10.06	   A^2 -> H(U1(a, e), b)
28.56/10.06	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(a, e), c)
28.56/10.06	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(a, e), e)
28.56/10.06	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(a, k), b)
28.56/10.06	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(a, k), c)
28.56/10.06	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(a, k), e)
28.56/10.06	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(a, c), d)
28.56/10.06	   A^2 -> H(U1(a, c), k)
28.56/10.06	   A^2 -> H(U1(a, d), d)
28.56/10.06	   A^2 -> H(U1(a, d), k)
28.56/10.06	   A^2 -> H(k, U1(c, b))
28.56/10.06	   A^2 -> H(k, U1(d, b))
28.56/10.06	   A^2 -> H(k, U1(b, c))
28.56/10.06	   A^2 -> H(k, U1(b, d))
28.56/10.06	   A^2 -> H(k, U1(c, c))
28.56/10.06	   A^2 -> H(k, f(e))
28.56/10.06	   A^2 -> H(k, f(k))
28.56/10.06	   A^2 -> H(k, U1(d, d))
28.56/10.06	   A^2 -> H(c, U1(e, b))
28.56/10.06	   A^2 -> H(c, U1(k, b))
28.56/10.06	   A^2 -> H(c, U1(c, d))
28.56/10.06	   A^2 -> H(c, U1(d, c))
28.56/10.06	   A^2 -> H(c, U1(b, e))
28.56/10.06	   A^2 -> H(c, U1(b, k))
28.56/10.06	   A^2 -> H(c, U1(e, c))
28.56/10.06	   A^2 -> H(c, U1(k, c))
28.56/10.06	   A^2 -> H(c, U1(c, e))
28.56/10.06	   A^2 -> H(c, U1(c, k))
28.56/10.06	   A^2 -> H(c, U1(e, e))
28.56/10.06	   A^2 -> H(c, U1(k, k))
28.56/10.06	   A^2 -> H(c, U1(k, d))
28.56/10.06	   A^2 -> H(c, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.06	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.06	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, c), b)
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, c), e)
28.56/10.06	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.06	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.06	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.06	   A^2 -> H(U1(k, c), b)
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, c), c)
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, e), b)
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, e), c)
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, e), e)
28.56/10.06	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, k), b)
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, k), c)
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, k), e)
28.56/10.06	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, c), d)
28.56/10.06	   A^2 -> H(e, U1(e, b))
28.56/10.06	   A^2 -> H(e, U1(c, d))
28.56/10.06	   A^2 -> H(e, U1(d, c))
28.56/10.06	   A^2 -> H(e, U1(b, e))
28.56/10.06	   A^2 -> H(e, U1(b, k))
28.56/10.06	   A^2 -> H(e, U1(e, c))
28.56/10.06	   A^2 -> H(e, U1(c, e))
28.56/10.06	   A^2 -> H(e, U1(c, k))
28.56/10.06	   A^2 -> H(e, U1(e, e))
28.56/10.06	   A^2 -> H(e, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, e), b)
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, e), c)
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.06	   A^2 -> H(f(e), d)
28.56/10.06	   A^2 -> H(f(e), k)
28.56/10.06	   A^2 -> H(U1(k, k), b)
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, k), c)
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.06	   A^2 -> H(f(k), d)
28.56/10.06	   A^2 -> H(f(k), k)
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.06	   A^2 -> H(U1(k, d), b)
28.56/10.06	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, d), c)
28.56/10.06	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, k), b)
28.56/10.06	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(d, k), c)
28.56/10.06	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(d, k), e)
28.56/10.06	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, d), d)
28.56/10.06	   A^2 -> H(U1(d, d), k)
28.56/10.06	   A^2 -> H(U1(e, c), c)
28.56/10.06	   A^2 -> H(U1(c, c), e)
28.56/10.06	   A^2 -> H(U1(c, c), k)
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, e), e)
28.56/10.06	   A^2 -> H(d, U1(e, b))
28.56/10.06	   A^2 -> H(d, U1(k, b))
28.56/10.06	   A^2 -> H(d, U1(c, d))
28.56/10.06	   A^2 -> H(d, U1(d, c))
28.56/10.06	   A^2 -> H(d, U1(b, e))
28.56/10.06	   A^2 -> H(d, U1(b, k))
28.56/10.06	   A^2 -> H(d, U1(e, c))
28.56/10.06	   A^2 -> H(d, U1(k, c))
28.56/10.06	   A^2 -> H(d, U1(c, e))
28.56/10.06	   A^2 -> H(d, U1(c, k))
28.56/10.06	   A^2 -> H(d, U1(e, e))
28.56/10.06	   A^2 -> H(d, U1(k, k))
28.56/10.06	
28.56/10.06	The TRS R consists of the following rules:
28.56/10.06	
28.56/10.06	   f(x) -> U1(x, x)
28.56/10.06	   U1(e, x) -> x
28.56/10.06	   a -> c
28.56/10.06	   a -> d
28.56/10.06	   b -> c
28.56/10.06	   b -> d
28.56/10.06	   d -> k
28.56/10.06	   c -> e
28.56/10.06	   c -> k
28.56/10.06	
28.56/10.06	Q is empty.
28.56/10.06	We have to consider all minimal (P,Q,R)-chains.
28.56/10.06	----------------------------------------
28.56/10.06	
28.56/10.06	(1809) TransformationProof (EQUIVALENT)
28.56/10.06	By narrowing [LPAR04] the rule A^2 -> H(d, U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.06	
28.56/10.06	   (A^2 -> H(k, U1(d, d)),A^2 -> H(k, U1(d, d)))
28.56/10.06	   (A^2 -> H(d, U1(k, d)),A^2 -> H(d, U1(k, d)))
28.56/10.06	   (A^2 -> H(d, U1(d, k)),A^2 -> H(d, U1(d, k)))
28.56/10.06	
28.56/10.06	
28.56/10.06	----------------------------------------
28.56/10.06	
28.56/10.06	(1810)
28.56/10.06	Obligation:
28.56/10.06	Q DP problem:
28.56/10.06	The TRS P consists of the following rules:
28.56/10.06	
28.56/10.06	   H(x, x) -> G(x, x, f(k))
28.56/10.06	   G(d, x, x) -> A^2
28.56/10.06	   A^2 -> H(f(c), f(c))
28.56/10.06	   A^2 -> H(f(d), f(d))
28.56/10.06	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.06	   A^2 -> H(f(e), f(e))
28.56/10.06	   A^2 -> H(f(k), f(k))
28.56/10.06	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.06	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.06	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.06	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.06	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.06	   A^2 -> H(a, U1(e, b))
28.56/10.06	   A^2 -> H(a, U1(k, b))
28.56/10.06	   A^2 -> H(a, U1(c, d))
28.56/10.06	   A^2 -> H(a, U1(d, c))
28.56/10.06	   A^2 -> H(a, U1(b, e))
28.56/10.06	   A^2 -> H(a, U1(b, k))
28.56/10.06	   A^2 -> H(a, U1(e, c))
28.56/10.06	   A^2 -> H(a, U1(k, c))
28.56/10.06	   A^2 -> H(a, U1(c, e))
28.56/10.06	   A^2 -> H(a, U1(c, k))
28.56/10.06	   A^2 -> H(a, U1(e, e))
28.56/10.06	   A^2 -> H(a, U1(k, k))
28.56/10.06	   A^2 -> H(a, U1(k, d))
28.56/10.06	   A^2 -> H(a, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.06	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.06	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, a), b)
28.56/10.06	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, a), c)
28.56/10.06	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, a), e)
28.56/10.06	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, a), b)
28.56/10.06	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, a), c)
28.56/10.06	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, d), b)
28.56/10.06	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, d), c)
28.56/10.06	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, d), e)
28.56/10.06	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, a), d)
28.56/10.06	   A^2 -> H(U1(c, a), k)
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.06	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.06	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.06	   A^2 -> H(U1(d, c), b)
28.56/10.06	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(d, c), c)
28.56/10.06	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(d, c), e)
28.56/10.06	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, a), d)
28.56/10.06	   A^2 -> H(U1(d, a), k)
28.56/10.06	   A^2 -> H(U1(a, e), b)
28.56/10.06	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(a, e), c)
28.56/10.06	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(a, e), e)
28.56/10.06	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(a, k), b)
28.56/10.06	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(a, k), c)
28.56/10.06	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(a, k), e)
28.56/10.06	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(a, c), d)
28.56/10.06	   A^2 -> H(U1(a, c), k)
28.56/10.06	   A^2 -> H(U1(a, d), d)
28.56/10.06	   A^2 -> H(U1(a, d), k)
28.56/10.06	   A^2 -> H(k, U1(c, b))
28.56/10.06	   A^2 -> H(k, U1(d, b))
28.56/10.06	   A^2 -> H(k, U1(b, c))
28.56/10.06	   A^2 -> H(k, U1(b, d))
28.56/10.06	   A^2 -> H(k, U1(c, c))
28.56/10.06	   A^2 -> H(k, f(e))
28.56/10.06	   A^2 -> H(k, f(k))
28.56/10.06	   A^2 -> H(k, U1(d, d))
28.56/10.06	   A^2 -> H(c, U1(e, b))
28.56/10.06	   A^2 -> H(c, U1(k, b))
28.56/10.06	   A^2 -> H(c, U1(c, d))
28.56/10.06	   A^2 -> H(c, U1(d, c))
28.56/10.06	   A^2 -> H(c, U1(b, e))
28.56/10.06	   A^2 -> H(c, U1(b, k))
28.56/10.06	   A^2 -> H(c, U1(e, c))
28.56/10.06	   A^2 -> H(c, U1(k, c))
28.56/10.06	   A^2 -> H(c, U1(c, e))
28.56/10.06	   A^2 -> H(c, U1(c, k))
28.56/10.06	   A^2 -> H(c, U1(e, e))
28.56/10.06	   A^2 -> H(c, U1(k, k))
28.56/10.06	   A^2 -> H(c, U1(k, d))
28.56/10.06	   A^2 -> H(c, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.06	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.06	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, c), b)
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, c), e)
28.56/10.06	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.06	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.06	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.06	   A^2 -> H(U1(k, c), b)
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, c), c)
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, e), b)
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, e), c)
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, e), e)
28.56/10.06	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, k), b)
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, k), c)
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, k), e)
28.56/10.06	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, c), d)
28.56/10.06	   A^2 -> H(e, U1(e, b))
28.56/10.06	   A^2 -> H(e, U1(c, d))
28.56/10.06	   A^2 -> H(e, U1(d, c))
28.56/10.06	   A^2 -> H(e, U1(b, e))
28.56/10.06	   A^2 -> H(e, U1(b, k))
28.56/10.06	   A^2 -> H(e, U1(e, c))
28.56/10.06	   A^2 -> H(e, U1(c, e))
28.56/10.06	   A^2 -> H(e, U1(c, k))
28.56/10.06	   A^2 -> H(e, U1(e, e))
28.56/10.06	   A^2 -> H(e, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, e), b)
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, e), c)
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.06	   A^2 -> H(f(e), d)
28.56/10.06	   A^2 -> H(f(e), k)
28.56/10.06	   A^2 -> H(U1(k, k), b)
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, k), c)
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.06	   A^2 -> H(f(k), d)
28.56/10.06	   A^2 -> H(f(k), k)
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.06	   A^2 -> H(U1(k, d), b)
28.56/10.06	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, d), c)
28.56/10.06	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, k), b)
28.56/10.06	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(d, k), c)
28.56/10.06	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(d, k), e)
28.56/10.06	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, d), d)
28.56/10.06	   A^2 -> H(U1(d, d), k)
28.56/10.06	   A^2 -> H(U1(e, c), c)
28.56/10.06	   A^2 -> H(U1(c, c), e)
28.56/10.06	   A^2 -> H(U1(c, c), k)
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, e), e)
28.56/10.06	   A^2 -> H(d, U1(e, b))
28.56/10.06	   A^2 -> H(d, U1(k, b))
28.56/10.06	   A^2 -> H(d, U1(c, d))
28.56/10.06	   A^2 -> H(d, U1(d, c))
28.56/10.06	   A^2 -> H(d, U1(b, e))
28.56/10.06	   A^2 -> H(d, U1(b, k))
28.56/10.06	   A^2 -> H(d, U1(e, c))
28.56/10.06	   A^2 -> H(d, U1(k, c))
28.56/10.06	   A^2 -> H(d, U1(c, e))
28.56/10.06	   A^2 -> H(d, U1(c, k))
28.56/10.06	   A^2 -> H(d, U1(e, e))
28.56/10.06	   A^2 -> H(d, U1(k, k))
28.56/10.06	   A^2 -> H(d, U1(k, d))
28.56/10.06	   A^2 -> H(d, U1(d, k))
28.56/10.06	
28.56/10.06	The TRS R consists of the following rules:
28.56/10.06	
28.56/10.06	   f(x) -> U1(x, x)
28.56/10.06	   U1(e, x) -> x
28.56/10.06	   a -> c
28.56/10.06	   a -> d
28.56/10.06	   b -> c
28.56/10.06	   b -> d
28.56/10.06	   d -> k
28.56/10.06	   c -> e
28.56/10.06	   c -> k
28.56/10.06	
28.56/10.06	Q is empty.
28.56/10.06	We have to consider all minimal (P,Q,R)-chains.
28.56/10.06	----------------------------------------
28.56/10.06	
28.56/10.06	(1811) TransformationProof (EQUIVALENT)
28.56/10.06	By narrowing [LPAR04] the rule A^2 -> H(a, U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.06	
28.56/10.06	   (A^2 -> H(c, U1(e, b)),A^2 -> H(c, U1(e, b)))
28.56/10.06	   (A^2 -> H(d, U1(e, b)),A^2 -> H(d, U1(e, b)))
28.56/10.06	   (A^2 -> H(a, b),A^2 -> H(a, b))
28.56/10.06	   (A^2 -> H(a, U1(e, c)),A^2 -> H(a, U1(e, c)))
28.56/10.06	   (A^2 -> H(a, U1(e, d)),A^2 -> H(a, U1(e, d)))
28.56/10.06	
28.56/10.06	
28.56/10.06	----------------------------------------
28.56/10.06	
28.56/10.06	(1812)
28.56/10.06	Obligation:
28.56/10.06	Q DP problem:
28.56/10.06	The TRS P consists of the following rules:
28.56/10.06	
28.56/10.06	   H(x, x) -> G(x, x, f(k))
28.56/10.06	   G(d, x, x) -> A^2
28.56/10.06	   A^2 -> H(f(c), f(c))
28.56/10.06	   A^2 -> H(f(d), f(d))
28.56/10.06	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.06	   A^2 -> H(f(e), f(e))
28.56/10.06	   A^2 -> H(f(k), f(k))
28.56/10.06	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.06	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.06	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.06	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.06	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.06	   A^2 -> H(a, U1(k, b))
28.56/10.06	   A^2 -> H(a, U1(c, d))
28.56/10.06	   A^2 -> H(a, U1(d, c))
28.56/10.06	   A^2 -> H(a, U1(b, e))
28.56/10.06	   A^2 -> H(a, U1(b, k))
28.56/10.06	   A^2 -> H(a, U1(e, c))
28.56/10.06	   A^2 -> H(a, U1(k, c))
28.56/10.06	   A^2 -> H(a, U1(c, e))
28.56/10.06	   A^2 -> H(a, U1(c, k))
28.56/10.06	   A^2 -> H(a, U1(e, e))
28.56/10.06	   A^2 -> H(a, U1(k, k))
28.56/10.06	   A^2 -> H(a, U1(k, d))
28.56/10.06	   A^2 -> H(a, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.06	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.06	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, a), b)
28.56/10.06	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, a), c)
28.56/10.06	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, a), e)
28.56/10.06	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, a), b)
28.56/10.06	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, a), c)
28.56/10.06	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, d), b)
28.56/10.06	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, d), c)
28.56/10.06	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, d), e)
28.56/10.06	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, a), d)
28.56/10.06	   A^2 -> H(U1(c, a), k)
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.06	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.06	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.06	   A^2 -> H(U1(d, c), b)
28.56/10.06	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(d, c), c)
28.56/10.06	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(d, c), e)
28.56/10.06	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, a), d)
28.56/10.06	   A^2 -> H(U1(d, a), k)
28.56/10.06	   A^2 -> H(U1(a, e), b)
28.56/10.06	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(a, e), c)
28.56/10.06	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(a, e), e)
28.56/10.06	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(a, k), b)
28.56/10.06	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(a, k), c)
28.56/10.06	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(a, k), e)
28.56/10.06	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(a, c), d)
28.56/10.06	   A^2 -> H(U1(a, c), k)
28.56/10.06	   A^2 -> H(U1(a, d), d)
28.56/10.06	   A^2 -> H(U1(a, d), k)
28.56/10.06	   A^2 -> H(k, U1(c, b))
28.56/10.06	   A^2 -> H(k, U1(d, b))
28.56/10.06	   A^2 -> H(k, U1(b, c))
28.56/10.06	   A^2 -> H(k, U1(b, d))
28.56/10.06	   A^2 -> H(k, U1(c, c))
28.56/10.06	   A^2 -> H(k, f(e))
28.56/10.06	   A^2 -> H(k, f(k))
28.56/10.06	   A^2 -> H(k, U1(d, d))
28.56/10.06	   A^2 -> H(c, U1(e, b))
28.56/10.06	   A^2 -> H(c, U1(k, b))
28.56/10.06	   A^2 -> H(c, U1(c, d))
28.56/10.06	   A^2 -> H(c, U1(d, c))
28.56/10.06	   A^2 -> H(c, U1(b, e))
28.56/10.06	   A^2 -> H(c, U1(b, k))
28.56/10.06	   A^2 -> H(c, U1(e, c))
28.56/10.06	   A^2 -> H(c, U1(k, c))
28.56/10.06	   A^2 -> H(c, U1(c, e))
28.56/10.06	   A^2 -> H(c, U1(c, k))
28.56/10.06	   A^2 -> H(c, U1(e, e))
28.56/10.06	   A^2 -> H(c, U1(k, k))
28.56/10.06	   A^2 -> H(c, U1(k, d))
28.56/10.06	   A^2 -> H(c, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.06	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.06	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, c), b)
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, c), e)
28.56/10.06	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.06	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.06	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.06	   A^2 -> H(U1(k, c), b)
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, c), c)
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, e), b)
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, e), c)
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, e), e)
28.56/10.06	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, k), b)
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, k), c)
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, k), e)
28.56/10.06	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, c), d)
28.56/10.06	   A^2 -> H(e, U1(e, b))
28.56/10.06	   A^2 -> H(e, U1(c, d))
28.56/10.06	   A^2 -> H(e, U1(d, c))
28.56/10.06	   A^2 -> H(e, U1(b, e))
28.56/10.06	   A^2 -> H(e, U1(b, k))
28.56/10.06	   A^2 -> H(e, U1(e, c))
28.56/10.06	   A^2 -> H(e, U1(c, e))
28.56/10.06	   A^2 -> H(e, U1(c, k))
28.56/10.06	   A^2 -> H(e, U1(e, e))
28.56/10.06	   A^2 -> H(e, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, e), b)
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, e), c)
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.06	   A^2 -> H(f(e), d)
28.56/10.06	   A^2 -> H(f(e), k)
28.56/10.06	   A^2 -> H(U1(k, k), b)
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, k), c)
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.06	   A^2 -> H(f(k), d)
28.56/10.06	   A^2 -> H(f(k), k)
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.06	   A^2 -> H(U1(k, d), b)
28.56/10.06	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, d), c)
28.56/10.06	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, k), b)
28.56/10.06	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(d, k), c)
28.56/10.06	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(d, k), e)
28.56/10.06	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, d), d)
28.56/10.06	   A^2 -> H(U1(d, d), k)
28.56/10.06	   A^2 -> H(U1(e, c), c)
28.56/10.06	   A^2 -> H(U1(c, c), e)
28.56/10.06	   A^2 -> H(U1(c, c), k)
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, e), e)
28.56/10.06	   A^2 -> H(d, U1(e, b))
28.56/10.06	   A^2 -> H(d, U1(k, b))
28.56/10.06	   A^2 -> H(d, U1(c, d))
28.56/10.06	   A^2 -> H(d, U1(d, c))
28.56/10.06	   A^2 -> H(d, U1(b, e))
28.56/10.06	   A^2 -> H(d, U1(b, k))
28.56/10.06	   A^2 -> H(d, U1(e, c))
28.56/10.06	   A^2 -> H(d, U1(k, c))
28.56/10.06	   A^2 -> H(d, U1(c, e))
28.56/10.06	   A^2 -> H(d, U1(c, k))
28.56/10.06	   A^2 -> H(d, U1(e, e))
28.56/10.06	   A^2 -> H(d, U1(k, k))
28.56/10.06	   A^2 -> H(d, U1(k, d))
28.56/10.06	   A^2 -> H(d, U1(d, k))
28.56/10.06	   A^2 -> H(a, b)
28.56/10.06	   A^2 -> H(a, U1(e, d))
28.56/10.06	
28.56/10.06	The TRS R consists of the following rules:
28.56/10.06	
28.56/10.06	   f(x) -> U1(x, x)
28.56/10.06	   U1(e, x) -> x
28.56/10.06	   a -> c
28.56/10.06	   a -> d
28.56/10.06	   b -> c
28.56/10.06	   b -> d
28.56/10.06	   d -> k
28.56/10.06	   c -> e
28.56/10.06	   c -> k
28.56/10.06	
28.56/10.06	Q is empty.
28.56/10.06	We have to consider all minimal (P,Q,R)-chains.
28.56/10.06	----------------------------------------
28.56/10.06	
28.56/10.06	(1813) TransformationProof (EQUIVALENT)
28.56/10.06	By narrowing [LPAR04] the rule A^2 -> H(a, U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.06	
28.56/10.06	   (A^2 -> H(c, U1(k, b)),A^2 -> H(c, U1(k, b)))
28.56/10.06	   (A^2 -> H(d, U1(k, b)),A^2 -> H(d, U1(k, b)))
28.56/10.06	   (A^2 -> H(a, U1(k, c)),A^2 -> H(a, U1(k, c)))
28.56/10.06	   (A^2 -> H(a, U1(k, d)),A^2 -> H(a, U1(k, d)))
28.56/10.06	
28.56/10.06	
28.56/10.06	----------------------------------------
28.56/10.06	
28.56/10.06	(1814)
28.56/10.06	Obligation:
28.56/10.06	Q DP problem:
28.56/10.06	The TRS P consists of the following rules:
28.56/10.06	
28.56/10.06	   H(x, x) -> G(x, x, f(k))
28.56/10.06	   G(d, x, x) -> A^2
28.56/10.06	   A^2 -> H(f(c), f(c))
28.56/10.06	   A^2 -> H(f(d), f(d))
28.56/10.06	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.06	   A^2 -> H(f(e), f(e))
28.56/10.06	   A^2 -> H(f(k), f(k))
28.56/10.06	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.06	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.06	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.06	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.06	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.06	   A^2 -> H(a, U1(c, d))
28.56/10.06	   A^2 -> H(a, U1(d, c))
28.56/10.06	   A^2 -> H(a, U1(b, e))
28.56/10.06	   A^2 -> H(a, U1(b, k))
28.56/10.06	   A^2 -> H(a, U1(e, c))
28.56/10.06	   A^2 -> H(a, U1(k, c))
28.56/10.06	   A^2 -> H(a, U1(c, e))
28.56/10.06	   A^2 -> H(a, U1(c, k))
28.56/10.06	   A^2 -> H(a, U1(e, e))
28.56/10.06	   A^2 -> H(a, U1(k, k))
28.56/10.06	   A^2 -> H(a, U1(k, d))
28.56/10.06	   A^2 -> H(a, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.06	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.06	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, a), b)
28.56/10.06	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, a), c)
28.56/10.06	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, a), e)
28.56/10.06	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, a), b)
28.56/10.06	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, a), c)
28.56/10.06	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, d), b)
28.56/10.06	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, d), c)
28.56/10.06	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, d), e)
28.56/10.06	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, a), d)
28.56/10.06	   A^2 -> H(U1(c, a), k)
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.06	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.06	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.06	   A^2 -> H(U1(d, c), b)
28.56/10.06	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(d, c), c)
28.56/10.06	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(d, c), e)
28.56/10.06	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, a), d)
28.56/10.06	   A^2 -> H(U1(d, a), k)
28.56/10.06	   A^2 -> H(U1(a, e), b)
28.56/10.06	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(a, e), c)
28.56/10.06	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(a, e), e)
28.56/10.06	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(a, k), b)
28.56/10.06	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(a, k), c)
28.56/10.06	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(a, k), e)
28.56/10.06	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(a, c), d)
28.56/10.06	   A^2 -> H(U1(a, c), k)
28.56/10.06	   A^2 -> H(U1(a, d), d)
28.56/10.06	   A^2 -> H(U1(a, d), k)
28.56/10.06	   A^2 -> H(k, U1(c, b))
28.56/10.06	   A^2 -> H(k, U1(d, b))
28.56/10.06	   A^2 -> H(k, U1(b, c))
28.56/10.06	   A^2 -> H(k, U1(b, d))
28.56/10.06	   A^2 -> H(k, U1(c, c))
28.56/10.06	   A^2 -> H(k, f(e))
28.56/10.06	   A^2 -> H(k, f(k))
28.56/10.06	   A^2 -> H(k, U1(d, d))
28.56/10.06	   A^2 -> H(c, U1(e, b))
28.56/10.06	   A^2 -> H(c, U1(k, b))
28.56/10.06	   A^2 -> H(c, U1(c, d))
28.56/10.06	   A^2 -> H(c, U1(d, c))
28.56/10.06	   A^2 -> H(c, U1(b, e))
28.56/10.06	   A^2 -> H(c, U1(b, k))
28.56/10.06	   A^2 -> H(c, U1(e, c))
28.56/10.06	   A^2 -> H(c, U1(k, c))
28.56/10.06	   A^2 -> H(c, U1(c, e))
28.56/10.06	   A^2 -> H(c, U1(c, k))
28.56/10.06	   A^2 -> H(c, U1(e, e))
28.56/10.06	   A^2 -> H(c, U1(k, k))
28.56/10.06	   A^2 -> H(c, U1(k, d))
28.56/10.06	   A^2 -> H(c, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.06	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.06	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, c), b)
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, c), e)
28.56/10.06	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.06	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.06	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.06	   A^2 -> H(U1(k, c), b)
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, c), c)
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, e), b)
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, e), c)
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, e), e)
28.56/10.06	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, k), b)
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, k), c)
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, k), e)
28.56/10.06	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, c), d)
28.56/10.06	   A^2 -> H(e, U1(e, b))
28.56/10.06	   A^2 -> H(e, U1(c, d))
28.56/10.06	   A^2 -> H(e, U1(d, c))
28.56/10.06	   A^2 -> H(e, U1(b, e))
28.56/10.06	   A^2 -> H(e, U1(b, k))
28.56/10.06	   A^2 -> H(e, U1(e, c))
28.56/10.06	   A^2 -> H(e, U1(c, e))
28.56/10.06	   A^2 -> H(e, U1(c, k))
28.56/10.06	   A^2 -> H(e, U1(e, e))
28.56/10.06	   A^2 -> H(e, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, e), b)
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, e), c)
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.06	   A^2 -> H(f(e), d)
28.56/10.06	   A^2 -> H(f(e), k)
28.56/10.06	   A^2 -> H(U1(k, k), b)
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, k), c)
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.06	   A^2 -> H(f(k), d)
28.56/10.06	   A^2 -> H(f(k), k)
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.06	   A^2 -> H(U1(k, d), b)
28.56/10.06	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, d), c)
28.56/10.06	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, k), b)
28.56/10.06	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(d, k), c)
28.56/10.06	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(d, k), e)
28.56/10.06	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, d), d)
28.56/10.06	   A^2 -> H(U1(d, d), k)
28.56/10.06	   A^2 -> H(U1(e, c), c)
28.56/10.06	   A^2 -> H(U1(c, c), e)
28.56/10.06	   A^2 -> H(U1(c, c), k)
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, e), e)
28.56/10.06	   A^2 -> H(d, U1(e, b))
28.56/10.06	   A^2 -> H(d, U1(k, b))
28.56/10.06	   A^2 -> H(d, U1(c, d))
28.56/10.06	   A^2 -> H(d, U1(d, c))
28.56/10.06	   A^2 -> H(d, U1(b, e))
28.56/10.06	   A^2 -> H(d, U1(b, k))
28.56/10.06	   A^2 -> H(d, U1(e, c))
28.56/10.06	   A^2 -> H(d, U1(k, c))
28.56/10.06	   A^2 -> H(d, U1(c, e))
28.56/10.06	   A^2 -> H(d, U1(c, k))
28.56/10.06	   A^2 -> H(d, U1(e, e))
28.56/10.06	   A^2 -> H(d, U1(k, k))
28.56/10.06	   A^2 -> H(d, U1(k, d))
28.56/10.06	   A^2 -> H(d, U1(d, k))
28.56/10.06	   A^2 -> H(a, b)
28.56/10.06	   A^2 -> H(a, U1(e, d))
28.56/10.06	
28.56/10.06	The TRS R consists of the following rules:
28.56/10.06	
28.56/10.06	   f(x) -> U1(x, x)
28.56/10.06	   U1(e, x) -> x
28.56/10.06	   a -> c
28.56/10.06	   a -> d
28.56/10.06	   b -> c
28.56/10.06	   b -> d
28.56/10.06	   d -> k
28.56/10.06	   c -> e
28.56/10.06	   c -> k
28.56/10.06	
28.56/10.06	Q is empty.
28.56/10.06	We have to consider all minimal (P,Q,R)-chains.
28.56/10.06	----------------------------------------
28.56/10.06	
28.56/10.06	(1815) TransformationProof (EQUIVALENT)
28.56/10.06	By narrowing [LPAR04] the rule A^2 -> H(a, U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.06	
28.56/10.06	   (A^2 -> H(c, U1(c, d)),A^2 -> H(c, U1(c, d)))
28.56/10.06	   (A^2 -> H(d, U1(c, d)),A^2 -> H(d, U1(c, d)))
28.56/10.06	   (A^2 -> H(a, U1(e, d)),A^2 -> H(a, U1(e, d)))
28.56/10.06	   (A^2 -> H(a, U1(k, d)),A^2 -> H(a, U1(k, d)))
28.56/10.06	   (A^2 -> H(a, U1(c, k)),A^2 -> H(a, U1(c, k)))
28.56/10.06	
28.56/10.06	
28.56/10.06	----------------------------------------
28.56/10.06	
28.56/10.06	(1816)
28.56/10.06	Obligation:
28.56/10.06	Q DP problem:
28.56/10.06	The TRS P consists of the following rules:
28.56/10.06	
28.56/10.06	   H(x, x) -> G(x, x, f(k))
28.56/10.06	   G(d, x, x) -> A^2
28.56/10.06	   A^2 -> H(f(c), f(c))
28.56/10.06	   A^2 -> H(f(d), f(d))
28.56/10.06	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.06	   A^2 -> H(f(e), f(e))
28.56/10.06	   A^2 -> H(f(k), f(k))
28.56/10.06	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.06	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.06	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.06	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.06	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.06	   A^2 -> H(a, U1(d, c))
28.56/10.06	   A^2 -> H(a, U1(b, e))
28.56/10.06	   A^2 -> H(a, U1(b, k))
28.56/10.06	   A^2 -> H(a, U1(e, c))
28.56/10.06	   A^2 -> H(a, U1(k, c))
28.56/10.06	   A^2 -> H(a, U1(c, e))
28.56/10.06	   A^2 -> H(a, U1(c, k))
28.56/10.06	   A^2 -> H(a, U1(e, e))
28.56/10.06	   A^2 -> H(a, U1(k, k))
28.56/10.06	   A^2 -> H(a, U1(k, d))
28.56/10.06	   A^2 -> H(a, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.06	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.06	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, a), b)
28.56/10.06	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, a), c)
28.56/10.06	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, a), e)
28.56/10.06	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, a), b)
28.56/10.06	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, a), c)
28.56/10.06	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, d), b)
28.56/10.06	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, d), c)
28.56/10.06	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, d), e)
28.56/10.06	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, a), d)
28.56/10.06	   A^2 -> H(U1(c, a), k)
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.06	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.06	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.06	   A^2 -> H(U1(d, c), b)
28.56/10.06	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(d, c), c)
28.56/10.06	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(d, c), e)
28.56/10.06	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, a), d)
28.56/10.06	   A^2 -> H(U1(d, a), k)
28.56/10.06	   A^2 -> H(U1(a, e), b)
28.56/10.06	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(a, e), c)
28.56/10.06	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(a, e), e)
28.56/10.06	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(a, k), b)
28.56/10.06	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(a, k), c)
28.56/10.06	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(a, k), e)
28.56/10.06	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(a, c), d)
28.56/10.06	   A^2 -> H(U1(a, c), k)
28.56/10.06	   A^2 -> H(U1(a, d), d)
28.56/10.06	   A^2 -> H(U1(a, d), k)
28.56/10.06	   A^2 -> H(k, U1(c, b))
28.56/10.06	   A^2 -> H(k, U1(d, b))
28.56/10.06	   A^2 -> H(k, U1(b, c))
28.56/10.06	   A^2 -> H(k, U1(b, d))
28.56/10.06	   A^2 -> H(k, U1(c, c))
28.56/10.06	   A^2 -> H(k, f(e))
28.56/10.06	   A^2 -> H(k, f(k))
28.56/10.06	   A^2 -> H(k, U1(d, d))
28.56/10.06	   A^2 -> H(c, U1(e, b))
28.56/10.06	   A^2 -> H(c, U1(k, b))
28.56/10.06	   A^2 -> H(c, U1(c, d))
28.56/10.06	   A^2 -> H(c, U1(d, c))
28.56/10.06	   A^2 -> H(c, U1(b, e))
28.56/10.06	   A^2 -> H(c, U1(b, k))
28.56/10.06	   A^2 -> H(c, U1(e, c))
28.56/10.06	   A^2 -> H(c, U1(k, c))
28.56/10.06	   A^2 -> H(c, U1(c, e))
28.56/10.06	   A^2 -> H(c, U1(c, k))
28.56/10.06	   A^2 -> H(c, U1(e, e))
28.56/10.06	   A^2 -> H(c, U1(k, k))
28.56/10.06	   A^2 -> H(c, U1(k, d))
28.56/10.06	   A^2 -> H(c, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.06	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.06	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, c), b)
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, c), e)
28.56/10.06	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.06	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.06	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.06	   A^2 -> H(U1(k, c), b)
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, c), c)
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, e), b)
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, e), c)
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, e), e)
28.56/10.06	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, k), b)
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, k), c)
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, k), e)
28.56/10.06	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, c), d)
28.56/10.06	   A^2 -> H(e, U1(e, b))
28.56/10.06	   A^2 -> H(e, U1(c, d))
28.56/10.06	   A^2 -> H(e, U1(d, c))
28.56/10.06	   A^2 -> H(e, U1(b, e))
28.56/10.06	   A^2 -> H(e, U1(b, k))
28.56/10.06	   A^2 -> H(e, U1(e, c))
28.56/10.06	   A^2 -> H(e, U1(c, e))
28.56/10.06	   A^2 -> H(e, U1(c, k))
28.56/10.06	   A^2 -> H(e, U1(e, e))
28.56/10.06	   A^2 -> H(e, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, e), b)
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, e), c)
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.06	   A^2 -> H(f(e), d)
28.56/10.06	   A^2 -> H(f(e), k)
28.56/10.06	   A^2 -> H(U1(k, k), b)
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, k), c)
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.06	   A^2 -> H(f(k), d)
28.56/10.06	   A^2 -> H(f(k), k)
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.06	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.06	   A^2 -> H(U1(k, d), b)
28.56/10.06	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, d), c)
28.56/10.06	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, k), b)
28.56/10.06	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(d, k), c)
28.56/10.06	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(d, k), e)
28.56/10.06	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, d), d)
28.56/10.06	   A^2 -> H(U1(d, d), k)
28.56/10.06	   A^2 -> H(U1(e, c), c)
28.56/10.06	   A^2 -> H(U1(c, c), e)
28.56/10.06	   A^2 -> H(U1(c, c), k)
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, e), e)
28.56/10.06	   A^2 -> H(d, U1(e, b))
28.56/10.06	   A^2 -> H(d, U1(k, b))
28.56/10.06	   A^2 -> H(d, U1(c, d))
28.56/10.06	   A^2 -> H(d, U1(d, c))
28.56/10.06	   A^2 -> H(d, U1(b, e))
28.56/10.06	   A^2 -> H(d, U1(b, k))
28.56/10.06	   A^2 -> H(d, U1(e, c))
28.56/10.06	   A^2 -> H(d, U1(k, c))
28.56/10.06	   A^2 -> H(d, U1(c, e))
28.56/10.06	   A^2 -> H(d, U1(c, k))
28.56/10.06	   A^2 -> H(d, U1(e, e))
28.56/10.06	   A^2 -> H(d, U1(k, k))
28.56/10.06	   A^2 -> H(d, U1(k, d))
28.56/10.06	   A^2 -> H(d, U1(d, k))
28.56/10.06	   A^2 -> H(a, b)
28.56/10.06	   A^2 -> H(a, U1(e, d))
28.56/10.06	
28.56/10.06	The TRS R consists of the following rules:
28.56/10.06	
28.56/10.06	   f(x) -> U1(x, x)
28.56/10.06	   U1(e, x) -> x
28.56/10.06	   a -> c
28.56/10.06	   a -> d
28.56/10.06	   b -> c
28.56/10.06	   b -> d
28.56/10.06	   d -> k
28.56/10.06	   c -> e
28.56/10.06	   c -> k
28.56/10.06	
28.56/10.06	Q is empty.
28.56/10.06	We have to consider all minimal (P,Q,R)-chains.
28.56/10.06	----------------------------------------
28.56/10.06	
28.56/10.06	(1817) TransformationProof (EQUIVALENT)
28.56/10.06	By narrowing [LPAR04] the rule A^2 -> H(a, U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.06	
28.56/10.06	   (A^2 -> H(c, U1(d, c)),A^2 -> H(c, U1(d, c)))
28.56/10.06	   (A^2 -> H(d, U1(d, c)),A^2 -> H(d, U1(d, c)))
28.56/10.06	   (A^2 -> H(a, U1(k, c)),A^2 -> H(a, U1(k, c)))
28.56/10.06	   (A^2 -> H(a, U1(d, e)),A^2 -> H(a, U1(d, e)))
28.56/10.06	   (A^2 -> H(a, U1(d, k)),A^2 -> H(a, U1(d, k)))
28.56/10.06	
28.56/10.06	
28.56/10.06	----------------------------------------
28.56/10.06	
28.56/10.06	(1818)
28.56/10.06	Obligation:
28.56/10.06	Q DP problem:
28.56/10.06	The TRS P consists of the following rules:
28.56/10.06	
28.56/10.06	   H(x, x) -> G(x, x, f(k))
28.56/10.06	   G(d, x, x) -> A^2
28.56/10.06	   A^2 -> H(f(c), f(c))
28.56/10.06	   A^2 -> H(f(d), f(d))
28.56/10.06	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.06	   A^2 -> H(f(e), f(e))
28.56/10.06	   A^2 -> H(f(k), f(k))
28.56/10.06	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.06	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.06	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.06	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.06	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.06	   A^2 -> H(a, U1(b, e))
28.56/10.06	   A^2 -> H(a, U1(b, k))
28.56/10.06	   A^2 -> H(a, U1(e, c))
28.56/10.06	   A^2 -> H(a, U1(k, c))
28.56/10.06	   A^2 -> H(a, U1(c, e))
28.56/10.06	   A^2 -> H(a, U1(c, k))
28.56/10.06	   A^2 -> H(a, U1(e, e))
28.56/10.06	   A^2 -> H(a, U1(k, k))
28.56/10.06	   A^2 -> H(a, U1(k, d))
28.56/10.06	   A^2 -> H(a, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.06	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.06	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, a), b)
28.56/10.06	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, a), c)
28.56/10.06	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, a), e)
28.56/10.06	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, a), b)
28.56/10.06	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, a), c)
28.56/10.06	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, d), b)
28.56/10.06	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, d), c)
28.56/10.06	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, d), e)
28.56/10.06	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, a), d)
28.56/10.06	   A^2 -> H(U1(c, a), k)
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.06	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.06	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.06	   A^2 -> H(U1(d, c), b)
28.56/10.06	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(d, c), c)
28.56/10.06	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(d, c), e)
28.56/10.06	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(d, a), d)
28.56/10.06	   A^2 -> H(U1(d, a), k)
28.56/10.06	   A^2 -> H(U1(a, e), b)
28.56/10.06	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(a, e), c)
28.56/10.06	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(a, e), e)
28.56/10.06	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(a, k), b)
28.56/10.06	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(a, k), c)
28.56/10.06	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(a, k), e)
28.56/10.06	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(a, c), d)
28.56/10.06	   A^2 -> H(U1(a, c), k)
28.56/10.06	   A^2 -> H(U1(a, d), d)
28.56/10.06	   A^2 -> H(U1(a, d), k)
28.56/10.06	   A^2 -> H(k, U1(c, b))
28.56/10.06	   A^2 -> H(k, U1(d, b))
28.56/10.06	   A^2 -> H(k, U1(b, c))
28.56/10.06	   A^2 -> H(k, U1(b, d))
28.56/10.06	   A^2 -> H(k, U1(c, c))
28.56/10.06	   A^2 -> H(k, f(e))
28.56/10.06	   A^2 -> H(k, f(k))
28.56/10.06	   A^2 -> H(k, U1(d, d))
28.56/10.06	   A^2 -> H(c, U1(e, b))
28.56/10.06	   A^2 -> H(c, U1(k, b))
28.56/10.06	   A^2 -> H(c, U1(c, d))
28.56/10.06	   A^2 -> H(c, U1(d, c))
28.56/10.06	   A^2 -> H(c, U1(b, e))
28.56/10.06	   A^2 -> H(c, U1(b, k))
28.56/10.06	   A^2 -> H(c, U1(e, c))
28.56/10.06	   A^2 -> H(c, U1(k, c))
28.56/10.06	   A^2 -> H(c, U1(c, e))
28.56/10.06	   A^2 -> H(c, U1(c, k))
28.56/10.06	   A^2 -> H(c, U1(e, e))
28.56/10.06	   A^2 -> H(c, U1(k, k))
28.56/10.06	   A^2 -> H(c, U1(k, d))
28.56/10.06	   A^2 -> H(c, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.06	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.06	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, c), b)
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, c), e)
28.56/10.06	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.06	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.06	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.06	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.06	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.06	   A^2 -> H(U1(k, c), b)
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.06	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.06	   A^2 -> H(U1(k, c), c)
28.56/10.06	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.06	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, e), b)
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, e), c)
28.56/10.06	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, e), e)
28.56/10.06	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, k), b)
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.06	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.06	   A^2 -> H(U1(c, k), c)
28.56/10.06	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.06	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.06	   A^2 -> H(U1(c, k), e)
28.56/10.06	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.06	   A^2 -> H(U1(c, c), d)
28.56/10.06	   A^2 -> H(e, U1(e, b))
28.56/10.06	   A^2 -> H(e, U1(c, d))
28.56/10.06	   A^2 -> H(e, U1(d, c))
28.56/10.06	   A^2 -> H(e, U1(b, e))
28.56/10.06	   A^2 -> H(e, U1(b, k))
28.56/10.06	   A^2 -> H(e, U1(e, c))
28.56/10.06	   A^2 -> H(e, U1(c, e))
28.56/10.06	   A^2 -> H(e, U1(c, k))
28.56/10.06	   A^2 -> H(e, U1(e, e))
28.56/10.06	   A^2 -> H(e, U1(d, k))
28.56/10.06	   A^2 -> H(U1(e, e), b)
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.06	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.06	   A^2 -> H(U1(e, e), c)
28.56/10.06	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.06	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.06	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.06	   A^2 -> H(f(e), d)
28.56/10.06	   A^2 -> H(f(e), k)
28.56/10.06	   A^2 -> H(U1(k, k), b)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, k), c)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.07	   A^2 -> H(f(k), d)
28.56/10.07	   A^2 -> H(f(k), k)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.07	   A^2 -> H(U1(k, d), b)
28.56/10.07	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, d), c)
28.56/10.07	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, k), b)
28.56/10.07	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(d, k), c)
28.56/10.07	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(d, k), e)
28.56/10.07	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, d), d)
28.56/10.07	   A^2 -> H(U1(d, d), k)
28.56/10.07	   A^2 -> H(U1(e, c), c)
28.56/10.07	   A^2 -> H(U1(c, c), e)
28.56/10.07	   A^2 -> H(U1(c, c), k)
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, e), e)
28.56/10.07	   A^2 -> H(d, U1(e, b))
28.56/10.07	   A^2 -> H(d, U1(k, b))
28.56/10.07	   A^2 -> H(d, U1(c, d))
28.56/10.07	   A^2 -> H(d, U1(d, c))
28.56/10.07	   A^2 -> H(d, U1(b, e))
28.56/10.07	   A^2 -> H(d, U1(b, k))
28.56/10.07	   A^2 -> H(d, U1(e, c))
28.56/10.07	   A^2 -> H(d, U1(k, c))
28.56/10.07	   A^2 -> H(d, U1(c, e))
28.56/10.07	   A^2 -> H(d, U1(c, k))
28.56/10.07	   A^2 -> H(d, U1(e, e))
28.56/10.07	   A^2 -> H(d, U1(k, k))
28.56/10.07	   A^2 -> H(d, U1(k, d))
28.56/10.07	   A^2 -> H(d, U1(d, k))
28.56/10.07	   A^2 -> H(a, b)
28.56/10.07	   A^2 -> H(a, U1(e, d))
28.56/10.07	   A^2 -> H(a, U1(d, e))
28.56/10.07	
28.56/10.07	The TRS R consists of the following rules:
28.56/10.07	
28.56/10.07	   f(x) -> U1(x, x)
28.56/10.07	   U1(e, x) -> x
28.56/10.07	   a -> c
28.56/10.07	   a -> d
28.56/10.07	   b -> c
28.56/10.07	   b -> d
28.56/10.07	   d -> k
28.56/10.07	   c -> e
28.56/10.07	   c -> k
28.56/10.07	
28.56/10.07	Q is empty.
28.56/10.07	We have to consider all minimal (P,Q,R)-chains.
28.56/10.07	----------------------------------------
28.56/10.07	
28.56/10.07	(1819) TransformationProof (EQUIVALENT)
28.56/10.07	By narrowing [LPAR04] the rule A^2 -> H(a, U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.07	
28.56/10.07	   (A^2 -> H(c, U1(b, e)),A^2 -> H(c, U1(b, e)))
28.56/10.07	   (A^2 -> H(d, U1(b, e)),A^2 -> H(d, U1(b, e)))
28.56/10.07	   (A^2 -> H(a, U1(c, e)),A^2 -> H(a, U1(c, e)))
28.56/10.07	   (A^2 -> H(a, U1(d, e)),A^2 -> H(a, U1(d, e)))
28.56/10.07	
28.56/10.07	
28.56/10.07	----------------------------------------
28.56/10.07	
28.56/10.07	(1820)
28.56/10.07	Obligation:
28.56/10.07	Q DP problem:
28.56/10.07	The TRS P consists of the following rules:
28.56/10.07	
28.56/10.07	   H(x, x) -> G(x, x, f(k))
28.56/10.07	   G(d, x, x) -> A^2
28.56/10.07	   A^2 -> H(f(c), f(c))
28.56/10.07	   A^2 -> H(f(d), f(d))
28.56/10.07	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.07	   A^2 -> H(f(e), f(e))
28.56/10.07	   A^2 -> H(f(k), f(k))
28.56/10.07	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.07	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.07	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.07	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.07	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.07	   A^2 -> H(a, U1(b, k))
28.56/10.07	   A^2 -> H(a, U1(e, c))
28.56/10.07	   A^2 -> H(a, U1(k, c))
28.56/10.07	   A^2 -> H(a, U1(c, e))
28.56/10.07	   A^2 -> H(a, U1(c, k))
28.56/10.07	   A^2 -> H(a, U1(e, e))
28.56/10.07	   A^2 -> H(a, U1(k, k))
28.56/10.07	   A^2 -> H(a, U1(k, d))
28.56/10.07	   A^2 -> H(a, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.07	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.07	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, a), b)
28.56/10.07	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, a), c)
28.56/10.07	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, a), e)
28.56/10.07	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, a), b)
28.56/10.07	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, a), c)
28.56/10.07	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, d), b)
28.56/10.07	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, d), c)
28.56/10.07	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, d), e)
28.56/10.07	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, a), d)
28.56/10.07	   A^2 -> H(U1(c, a), k)
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.07	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.07	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.07	   A^2 -> H(U1(d, c), b)
28.56/10.07	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(d, c), c)
28.56/10.07	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(d, c), e)
28.56/10.07	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, a), d)
28.56/10.07	   A^2 -> H(U1(d, a), k)
28.56/10.07	   A^2 -> H(U1(a, e), b)
28.56/10.07	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(a, e), c)
28.56/10.07	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(a, e), e)
28.56/10.07	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(a, k), b)
28.56/10.07	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(a, k), c)
28.56/10.07	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(a, k), e)
28.56/10.07	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(a, c), d)
28.56/10.07	   A^2 -> H(U1(a, c), k)
28.56/10.07	   A^2 -> H(U1(a, d), d)
28.56/10.07	   A^2 -> H(U1(a, d), k)
28.56/10.07	   A^2 -> H(k, U1(c, b))
28.56/10.07	   A^2 -> H(k, U1(d, b))
28.56/10.07	   A^2 -> H(k, U1(b, c))
28.56/10.07	   A^2 -> H(k, U1(b, d))
28.56/10.07	   A^2 -> H(k, U1(c, c))
28.56/10.07	   A^2 -> H(k, f(e))
28.56/10.07	   A^2 -> H(k, f(k))
28.56/10.07	   A^2 -> H(k, U1(d, d))
28.56/10.07	   A^2 -> H(c, U1(e, b))
28.56/10.07	   A^2 -> H(c, U1(k, b))
28.56/10.07	   A^2 -> H(c, U1(c, d))
28.56/10.07	   A^2 -> H(c, U1(d, c))
28.56/10.07	   A^2 -> H(c, U1(b, e))
28.56/10.07	   A^2 -> H(c, U1(b, k))
28.56/10.07	   A^2 -> H(c, U1(e, c))
28.56/10.07	   A^2 -> H(c, U1(k, c))
28.56/10.07	   A^2 -> H(c, U1(c, e))
28.56/10.07	   A^2 -> H(c, U1(c, k))
28.56/10.07	   A^2 -> H(c, U1(e, e))
28.56/10.07	   A^2 -> H(c, U1(k, k))
28.56/10.07	   A^2 -> H(c, U1(k, d))
28.56/10.07	   A^2 -> H(c, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.07	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.07	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, c), b)
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, c), e)
28.56/10.07	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.07	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.07	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.07	   A^2 -> H(U1(k, c), b)
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, c), c)
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, e), b)
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, e), c)
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, e), e)
28.56/10.07	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, k), b)
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, k), c)
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, k), e)
28.56/10.07	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, c), d)
28.56/10.07	   A^2 -> H(e, U1(e, b))
28.56/10.07	   A^2 -> H(e, U1(c, d))
28.56/10.07	   A^2 -> H(e, U1(d, c))
28.56/10.07	   A^2 -> H(e, U1(b, e))
28.56/10.07	   A^2 -> H(e, U1(b, k))
28.56/10.07	   A^2 -> H(e, U1(e, c))
28.56/10.07	   A^2 -> H(e, U1(c, e))
28.56/10.07	   A^2 -> H(e, U1(c, k))
28.56/10.07	   A^2 -> H(e, U1(e, e))
28.56/10.07	   A^2 -> H(e, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, e), b)
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, e), c)
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.07	   A^2 -> H(f(e), d)
28.56/10.07	   A^2 -> H(f(e), k)
28.56/10.07	   A^2 -> H(U1(k, k), b)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, k), c)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.07	   A^2 -> H(f(k), d)
28.56/10.07	   A^2 -> H(f(k), k)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.07	   A^2 -> H(U1(k, d), b)
28.56/10.07	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, d), c)
28.56/10.07	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, k), b)
28.56/10.07	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(d, k), c)
28.56/10.07	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(d, k), e)
28.56/10.07	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, d), d)
28.56/10.07	   A^2 -> H(U1(d, d), k)
28.56/10.07	   A^2 -> H(U1(e, c), c)
28.56/10.07	   A^2 -> H(U1(c, c), e)
28.56/10.07	   A^2 -> H(U1(c, c), k)
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, e), e)
28.56/10.07	   A^2 -> H(d, U1(e, b))
28.56/10.07	   A^2 -> H(d, U1(k, b))
28.56/10.07	   A^2 -> H(d, U1(c, d))
28.56/10.07	   A^2 -> H(d, U1(d, c))
28.56/10.07	   A^2 -> H(d, U1(b, e))
28.56/10.07	   A^2 -> H(d, U1(b, k))
28.56/10.07	   A^2 -> H(d, U1(e, c))
28.56/10.07	   A^2 -> H(d, U1(k, c))
28.56/10.07	   A^2 -> H(d, U1(c, e))
28.56/10.07	   A^2 -> H(d, U1(c, k))
28.56/10.07	   A^2 -> H(d, U1(e, e))
28.56/10.07	   A^2 -> H(d, U1(k, k))
28.56/10.07	   A^2 -> H(d, U1(k, d))
28.56/10.07	   A^2 -> H(d, U1(d, k))
28.56/10.07	   A^2 -> H(a, b)
28.56/10.07	   A^2 -> H(a, U1(e, d))
28.56/10.07	   A^2 -> H(a, U1(d, e))
28.56/10.07	
28.56/10.07	The TRS R consists of the following rules:
28.56/10.07	
28.56/10.07	   f(x) -> U1(x, x)
28.56/10.07	   U1(e, x) -> x
28.56/10.07	   a -> c
28.56/10.07	   a -> d
28.56/10.07	   b -> c
28.56/10.07	   b -> d
28.56/10.07	   d -> k
28.56/10.07	   c -> e
28.56/10.07	   c -> k
28.56/10.07	
28.56/10.07	Q is empty.
28.56/10.07	We have to consider all minimal (P,Q,R)-chains.
28.56/10.07	----------------------------------------
28.56/10.07	
28.56/10.07	(1821) TransformationProof (EQUIVALENT)
28.56/10.07	By narrowing [LPAR04] the rule A^2 -> H(a, U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.07	
28.56/10.07	   (A^2 -> H(c, U1(b, k)),A^2 -> H(c, U1(b, k)))
28.56/10.07	   (A^2 -> H(d, U1(b, k)),A^2 -> H(d, U1(b, k)))
28.56/10.07	   (A^2 -> H(a, U1(c, k)),A^2 -> H(a, U1(c, k)))
28.56/10.07	   (A^2 -> H(a, U1(d, k)),A^2 -> H(a, U1(d, k)))
28.56/10.07	
28.56/10.07	
28.56/10.07	----------------------------------------
28.56/10.07	
28.56/10.07	(1822)
28.56/10.07	Obligation:
28.56/10.07	Q DP problem:
28.56/10.07	The TRS P consists of the following rules:
28.56/10.07	
28.56/10.07	   H(x, x) -> G(x, x, f(k))
28.56/10.07	   G(d, x, x) -> A^2
28.56/10.07	   A^2 -> H(f(c), f(c))
28.56/10.07	   A^2 -> H(f(d), f(d))
28.56/10.07	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.07	   A^2 -> H(f(e), f(e))
28.56/10.07	   A^2 -> H(f(k), f(k))
28.56/10.07	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.07	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.07	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.07	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.07	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.07	   A^2 -> H(a, U1(e, c))
28.56/10.07	   A^2 -> H(a, U1(k, c))
28.56/10.07	   A^2 -> H(a, U1(c, e))
28.56/10.07	   A^2 -> H(a, U1(c, k))
28.56/10.07	   A^2 -> H(a, U1(e, e))
28.56/10.07	   A^2 -> H(a, U1(k, k))
28.56/10.07	   A^2 -> H(a, U1(k, d))
28.56/10.07	   A^2 -> H(a, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.07	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.07	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, a), b)
28.56/10.07	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, a), c)
28.56/10.07	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, a), e)
28.56/10.07	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, a), b)
28.56/10.07	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, a), c)
28.56/10.07	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, d), b)
28.56/10.07	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, d), c)
28.56/10.07	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, d), e)
28.56/10.07	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, a), d)
28.56/10.07	   A^2 -> H(U1(c, a), k)
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.07	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.07	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.07	   A^2 -> H(U1(d, c), b)
28.56/10.07	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(d, c), c)
28.56/10.07	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(d, c), e)
28.56/10.07	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, a), d)
28.56/10.07	   A^2 -> H(U1(d, a), k)
28.56/10.07	   A^2 -> H(U1(a, e), b)
28.56/10.07	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(a, e), c)
28.56/10.07	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(a, e), e)
28.56/10.07	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(a, k), b)
28.56/10.07	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(a, k), c)
28.56/10.07	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(a, k), e)
28.56/10.07	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(a, c), d)
28.56/10.07	   A^2 -> H(U1(a, c), k)
28.56/10.07	   A^2 -> H(U1(a, d), d)
28.56/10.07	   A^2 -> H(U1(a, d), k)
28.56/10.07	   A^2 -> H(k, U1(c, b))
28.56/10.07	   A^2 -> H(k, U1(d, b))
28.56/10.07	   A^2 -> H(k, U1(b, c))
28.56/10.07	   A^2 -> H(k, U1(b, d))
28.56/10.07	   A^2 -> H(k, U1(c, c))
28.56/10.07	   A^2 -> H(k, f(e))
28.56/10.07	   A^2 -> H(k, f(k))
28.56/10.07	   A^2 -> H(k, U1(d, d))
28.56/10.07	   A^2 -> H(c, U1(e, b))
28.56/10.07	   A^2 -> H(c, U1(k, b))
28.56/10.07	   A^2 -> H(c, U1(c, d))
28.56/10.07	   A^2 -> H(c, U1(d, c))
28.56/10.07	   A^2 -> H(c, U1(b, e))
28.56/10.07	   A^2 -> H(c, U1(b, k))
28.56/10.07	   A^2 -> H(c, U1(e, c))
28.56/10.07	   A^2 -> H(c, U1(k, c))
28.56/10.07	   A^2 -> H(c, U1(c, e))
28.56/10.07	   A^2 -> H(c, U1(c, k))
28.56/10.07	   A^2 -> H(c, U1(e, e))
28.56/10.07	   A^2 -> H(c, U1(k, k))
28.56/10.07	   A^2 -> H(c, U1(k, d))
28.56/10.07	   A^2 -> H(c, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.07	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.07	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, c), b)
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, c), e)
28.56/10.07	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.07	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.07	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.07	   A^2 -> H(U1(k, c), b)
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, c), c)
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, e), b)
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, e), c)
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, e), e)
28.56/10.07	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, k), b)
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, k), c)
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, k), e)
28.56/10.07	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, c), d)
28.56/10.07	   A^2 -> H(e, U1(e, b))
28.56/10.07	   A^2 -> H(e, U1(c, d))
28.56/10.07	   A^2 -> H(e, U1(d, c))
28.56/10.07	   A^2 -> H(e, U1(b, e))
28.56/10.07	   A^2 -> H(e, U1(b, k))
28.56/10.07	   A^2 -> H(e, U1(e, c))
28.56/10.07	   A^2 -> H(e, U1(c, e))
28.56/10.07	   A^2 -> H(e, U1(c, k))
28.56/10.07	   A^2 -> H(e, U1(e, e))
28.56/10.07	   A^2 -> H(e, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, e), b)
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, e), c)
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.07	   A^2 -> H(f(e), d)
28.56/10.07	   A^2 -> H(f(e), k)
28.56/10.07	   A^2 -> H(U1(k, k), b)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, k), c)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.07	   A^2 -> H(f(k), d)
28.56/10.07	   A^2 -> H(f(k), k)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.07	   A^2 -> H(U1(k, d), b)
28.56/10.07	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, d), c)
28.56/10.07	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, k), b)
28.56/10.07	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(d, k), c)
28.56/10.07	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(d, k), e)
28.56/10.07	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, d), d)
28.56/10.07	   A^2 -> H(U1(d, d), k)
28.56/10.07	   A^2 -> H(U1(e, c), c)
28.56/10.07	   A^2 -> H(U1(c, c), e)
28.56/10.07	   A^2 -> H(U1(c, c), k)
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, e), e)
28.56/10.07	   A^2 -> H(d, U1(e, b))
28.56/10.07	   A^2 -> H(d, U1(k, b))
28.56/10.07	   A^2 -> H(d, U1(c, d))
28.56/10.07	   A^2 -> H(d, U1(d, c))
28.56/10.07	   A^2 -> H(d, U1(b, e))
28.56/10.07	   A^2 -> H(d, U1(b, k))
28.56/10.07	   A^2 -> H(d, U1(e, c))
28.56/10.07	   A^2 -> H(d, U1(k, c))
28.56/10.07	   A^2 -> H(d, U1(c, e))
28.56/10.07	   A^2 -> H(d, U1(c, k))
28.56/10.07	   A^2 -> H(d, U1(e, e))
28.56/10.07	   A^2 -> H(d, U1(k, k))
28.56/10.07	   A^2 -> H(d, U1(k, d))
28.56/10.07	   A^2 -> H(d, U1(d, k))
28.56/10.07	   A^2 -> H(a, b)
28.56/10.07	   A^2 -> H(a, U1(e, d))
28.56/10.07	   A^2 -> H(a, U1(d, e))
28.56/10.07	
28.56/10.07	The TRS R consists of the following rules:
28.56/10.07	
28.56/10.07	   f(x) -> U1(x, x)
28.56/10.07	   U1(e, x) -> x
28.56/10.07	   a -> c
28.56/10.07	   a -> d
28.56/10.07	   b -> c
28.56/10.07	   b -> d
28.56/10.07	   d -> k
28.56/10.07	   c -> e
28.56/10.07	   c -> k
28.56/10.07	
28.56/10.07	Q is empty.
28.56/10.07	We have to consider all minimal (P,Q,R)-chains.
28.56/10.07	----------------------------------------
28.56/10.07	
28.56/10.07	(1823) TransformationProof (EQUIVALENT)
28.56/10.07	By narrowing [LPAR04] the rule A^2 -> H(a, U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.07	
28.56/10.07	   (A^2 -> H(c, U1(e, c)),A^2 -> H(c, U1(e, c)))
28.56/10.07	   (A^2 -> H(d, U1(e, c)),A^2 -> H(d, U1(e, c)))
28.56/10.07	   (A^2 -> H(a, c),A^2 -> H(a, c))
28.56/10.07	   (A^2 -> H(a, U1(e, e)),A^2 -> H(a, U1(e, e)))
28.56/10.07	   (A^2 -> H(a, U1(e, k)),A^2 -> H(a, U1(e, k)))
28.56/10.07	
28.56/10.07	
28.56/10.07	----------------------------------------
28.56/10.07	
28.56/10.07	(1824)
28.56/10.07	Obligation:
28.56/10.07	Q DP problem:
28.56/10.07	The TRS P consists of the following rules:
28.56/10.07	
28.56/10.07	   H(x, x) -> G(x, x, f(k))
28.56/10.07	   G(d, x, x) -> A^2
28.56/10.07	   A^2 -> H(f(c), f(c))
28.56/10.07	   A^2 -> H(f(d), f(d))
28.56/10.07	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.07	   A^2 -> H(f(e), f(e))
28.56/10.07	   A^2 -> H(f(k), f(k))
28.56/10.07	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.07	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.07	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.07	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.07	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.07	   A^2 -> H(a, U1(k, c))
28.56/10.07	   A^2 -> H(a, U1(c, e))
28.56/10.07	   A^2 -> H(a, U1(c, k))
28.56/10.07	   A^2 -> H(a, U1(e, e))
28.56/10.07	   A^2 -> H(a, U1(k, k))
28.56/10.07	   A^2 -> H(a, U1(k, d))
28.56/10.07	   A^2 -> H(a, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.07	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.07	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, a), b)
28.56/10.07	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, a), c)
28.56/10.07	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, a), e)
28.56/10.07	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, a), b)
28.56/10.07	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, a), c)
28.56/10.07	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, d), b)
28.56/10.07	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, d), c)
28.56/10.07	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, d), e)
28.56/10.07	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, a), d)
28.56/10.07	   A^2 -> H(U1(c, a), k)
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.07	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.07	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.07	   A^2 -> H(U1(d, c), b)
28.56/10.07	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(d, c), c)
28.56/10.07	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(d, c), e)
28.56/10.07	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, a), d)
28.56/10.07	   A^2 -> H(U1(d, a), k)
28.56/10.07	   A^2 -> H(U1(a, e), b)
28.56/10.07	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(a, e), c)
28.56/10.07	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(a, e), e)
28.56/10.07	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(a, k), b)
28.56/10.07	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(a, k), c)
28.56/10.07	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(a, k), e)
28.56/10.07	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(a, c), d)
28.56/10.07	   A^2 -> H(U1(a, c), k)
28.56/10.07	   A^2 -> H(U1(a, d), d)
28.56/10.07	   A^2 -> H(U1(a, d), k)
28.56/10.07	   A^2 -> H(k, U1(c, b))
28.56/10.07	   A^2 -> H(k, U1(d, b))
28.56/10.07	   A^2 -> H(k, U1(b, c))
28.56/10.07	   A^2 -> H(k, U1(b, d))
28.56/10.07	   A^2 -> H(k, U1(c, c))
28.56/10.07	   A^2 -> H(k, f(e))
28.56/10.07	   A^2 -> H(k, f(k))
28.56/10.07	   A^2 -> H(k, U1(d, d))
28.56/10.07	   A^2 -> H(c, U1(e, b))
28.56/10.07	   A^2 -> H(c, U1(k, b))
28.56/10.07	   A^2 -> H(c, U1(c, d))
28.56/10.07	   A^2 -> H(c, U1(d, c))
28.56/10.07	   A^2 -> H(c, U1(b, e))
28.56/10.07	   A^2 -> H(c, U1(b, k))
28.56/10.07	   A^2 -> H(c, U1(e, c))
28.56/10.07	   A^2 -> H(c, U1(k, c))
28.56/10.07	   A^2 -> H(c, U1(c, e))
28.56/10.07	   A^2 -> H(c, U1(c, k))
28.56/10.07	   A^2 -> H(c, U1(e, e))
28.56/10.07	   A^2 -> H(c, U1(k, k))
28.56/10.07	   A^2 -> H(c, U1(k, d))
28.56/10.07	   A^2 -> H(c, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.07	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.07	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, c), b)
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, c), e)
28.56/10.07	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.07	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.07	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.07	   A^2 -> H(U1(k, c), b)
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, c), c)
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, e), b)
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, e), c)
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, e), e)
28.56/10.07	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, k), b)
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, k), c)
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, k), e)
28.56/10.07	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, c), d)
28.56/10.07	   A^2 -> H(e, U1(e, b))
28.56/10.07	   A^2 -> H(e, U1(c, d))
28.56/10.07	   A^2 -> H(e, U1(d, c))
28.56/10.07	   A^2 -> H(e, U1(b, e))
28.56/10.07	   A^2 -> H(e, U1(b, k))
28.56/10.07	   A^2 -> H(e, U1(e, c))
28.56/10.07	   A^2 -> H(e, U1(c, e))
28.56/10.07	   A^2 -> H(e, U1(c, k))
28.56/10.07	   A^2 -> H(e, U1(e, e))
28.56/10.07	   A^2 -> H(e, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, e), b)
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, e), c)
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.07	   A^2 -> H(f(e), d)
28.56/10.07	   A^2 -> H(f(e), k)
28.56/10.07	   A^2 -> H(U1(k, k), b)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, k), c)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.07	   A^2 -> H(f(k), d)
28.56/10.07	   A^2 -> H(f(k), k)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.07	   A^2 -> H(U1(k, d), b)
28.56/10.07	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, d), c)
28.56/10.07	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, k), b)
28.56/10.07	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(d, k), c)
28.56/10.07	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(d, k), e)
28.56/10.07	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, d), d)
28.56/10.07	   A^2 -> H(U1(d, d), k)
28.56/10.07	   A^2 -> H(U1(e, c), c)
28.56/10.07	   A^2 -> H(U1(c, c), e)
28.56/10.07	   A^2 -> H(U1(c, c), k)
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, e), e)
28.56/10.07	   A^2 -> H(d, U1(e, b))
28.56/10.07	   A^2 -> H(d, U1(k, b))
28.56/10.07	   A^2 -> H(d, U1(c, d))
28.56/10.07	   A^2 -> H(d, U1(d, c))
28.56/10.07	   A^2 -> H(d, U1(b, e))
28.56/10.07	   A^2 -> H(d, U1(b, k))
28.56/10.07	   A^2 -> H(d, U1(e, c))
28.56/10.07	   A^2 -> H(d, U1(k, c))
28.56/10.07	   A^2 -> H(d, U1(c, e))
28.56/10.07	   A^2 -> H(d, U1(c, k))
28.56/10.07	   A^2 -> H(d, U1(e, e))
28.56/10.07	   A^2 -> H(d, U1(k, k))
28.56/10.07	   A^2 -> H(d, U1(k, d))
28.56/10.07	   A^2 -> H(d, U1(d, k))
28.56/10.07	   A^2 -> H(a, b)
28.56/10.07	   A^2 -> H(a, U1(e, d))
28.56/10.07	   A^2 -> H(a, U1(d, e))
28.56/10.07	   A^2 -> H(a, c)
28.56/10.07	   A^2 -> H(a, U1(e, k))
28.56/10.07	
28.56/10.07	The TRS R consists of the following rules:
28.56/10.07	
28.56/10.07	   f(x) -> U1(x, x)
28.56/10.07	   U1(e, x) -> x
28.56/10.07	   a -> c
28.56/10.07	   a -> d
28.56/10.07	   b -> c
28.56/10.07	   b -> d
28.56/10.07	   d -> k
28.56/10.07	   c -> e
28.56/10.07	   c -> k
28.56/10.07	
28.56/10.07	Q is empty.
28.56/10.07	We have to consider all minimal (P,Q,R)-chains.
28.56/10.07	----------------------------------------
28.56/10.07	
28.56/10.07	(1825) TransformationProof (EQUIVALENT)
28.56/10.07	By narrowing [LPAR04] the rule A^2 -> H(a, U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.07	
28.56/10.07	   (A^2 -> H(c, U1(k, c)),A^2 -> H(c, U1(k, c)))
28.56/10.07	   (A^2 -> H(d, U1(k, c)),A^2 -> H(d, U1(k, c)))
28.56/10.07	   (A^2 -> H(a, U1(k, e)),A^2 -> H(a, U1(k, e)))
28.56/10.07	   (A^2 -> H(a, U1(k, k)),A^2 -> H(a, U1(k, k)))
28.56/10.07	
28.56/10.07	
28.56/10.07	----------------------------------------
28.56/10.07	
28.56/10.07	(1826)
28.56/10.07	Obligation:
28.56/10.07	Q DP problem:
28.56/10.07	The TRS P consists of the following rules:
28.56/10.07	
28.56/10.07	   H(x, x) -> G(x, x, f(k))
28.56/10.07	   G(d, x, x) -> A^2
28.56/10.07	   A^2 -> H(f(c), f(c))
28.56/10.07	   A^2 -> H(f(d), f(d))
28.56/10.07	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.07	   A^2 -> H(f(e), f(e))
28.56/10.07	   A^2 -> H(f(k), f(k))
28.56/10.07	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.07	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.07	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.07	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.07	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.07	   A^2 -> H(a, U1(c, e))
28.56/10.07	   A^2 -> H(a, U1(c, k))
28.56/10.07	   A^2 -> H(a, U1(e, e))
28.56/10.07	   A^2 -> H(a, U1(k, k))
28.56/10.07	   A^2 -> H(a, U1(k, d))
28.56/10.07	   A^2 -> H(a, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.07	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.07	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, a), b)
28.56/10.07	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, a), c)
28.56/10.07	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, a), e)
28.56/10.07	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, a), b)
28.56/10.07	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, a), c)
28.56/10.07	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, d), b)
28.56/10.07	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, d), c)
28.56/10.07	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, d), e)
28.56/10.07	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, a), d)
28.56/10.07	   A^2 -> H(U1(c, a), k)
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.07	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.07	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.07	   A^2 -> H(U1(d, c), b)
28.56/10.07	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(d, c), c)
28.56/10.07	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(d, c), e)
28.56/10.07	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, a), d)
28.56/10.07	   A^2 -> H(U1(d, a), k)
28.56/10.07	   A^2 -> H(U1(a, e), b)
28.56/10.07	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(a, e), c)
28.56/10.07	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(a, e), e)
28.56/10.07	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(a, k), b)
28.56/10.07	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(a, k), c)
28.56/10.07	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(a, k), e)
28.56/10.07	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(a, c), d)
28.56/10.07	   A^2 -> H(U1(a, c), k)
28.56/10.07	   A^2 -> H(U1(a, d), d)
28.56/10.07	   A^2 -> H(U1(a, d), k)
28.56/10.07	   A^2 -> H(k, U1(c, b))
28.56/10.07	   A^2 -> H(k, U1(d, b))
28.56/10.07	   A^2 -> H(k, U1(b, c))
28.56/10.07	   A^2 -> H(k, U1(b, d))
28.56/10.07	   A^2 -> H(k, U1(c, c))
28.56/10.07	   A^2 -> H(k, f(e))
28.56/10.07	   A^2 -> H(k, f(k))
28.56/10.07	   A^2 -> H(k, U1(d, d))
28.56/10.07	   A^2 -> H(c, U1(e, b))
28.56/10.07	   A^2 -> H(c, U1(k, b))
28.56/10.07	   A^2 -> H(c, U1(c, d))
28.56/10.07	   A^2 -> H(c, U1(d, c))
28.56/10.07	   A^2 -> H(c, U1(b, e))
28.56/10.07	   A^2 -> H(c, U1(b, k))
28.56/10.07	   A^2 -> H(c, U1(e, c))
28.56/10.07	   A^2 -> H(c, U1(k, c))
28.56/10.07	   A^2 -> H(c, U1(c, e))
28.56/10.07	   A^2 -> H(c, U1(c, k))
28.56/10.07	   A^2 -> H(c, U1(e, e))
28.56/10.07	   A^2 -> H(c, U1(k, k))
28.56/10.07	   A^2 -> H(c, U1(k, d))
28.56/10.07	   A^2 -> H(c, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.07	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.07	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, c), b)
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, c), e)
28.56/10.07	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.07	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.07	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.07	   A^2 -> H(U1(k, c), b)
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, c), c)
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, e), b)
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, e), c)
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, e), e)
28.56/10.07	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, k), b)
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, k), c)
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, k), e)
28.56/10.07	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, c), d)
28.56/10.07	   A^2 -> H(e, U1(e, b))
28.56/10.07	   A^2 -> H(e, U1(c, d))
28.56/10.07	   A^2 -> H(e, U1(d, c))
28.56/10.07	   A^2 -> H(e, U1(b, e))
28.56/10.07	   A^2 -> H(e, U1(b, k))
28.56/10.07	   A^2 -> H(e, U1(e, c))
28.56/10.07	   A^2 -> H(e, U1(c, e))
28.56/10.07	   A^2 -> H(e, U1(c, k))
28.56/10.07	   A^2 -> H(e, U1(e, e))
28.56/10.07	   A^2 -> H(e, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, e), b)
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, e), c)
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.07	   A^2 -> H(f(e), d)
28.56/10.07	   A^2 -> H(f(e), k)
28.56/10.07	   A^2 -> H(U1(k, k), b)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, k), c)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.07	   A^2 -> H(f(k), d)
28.56/10.07	   A^2 -> H(f(k), k)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.07	   A^2 -> H(U1(k, d), b)
28.56/10.07	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, d), c)
28.56/10.07	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, k), b)
28.56/10.07	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(d, k), c)
28.56/10.07	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(d, k), e)
28.56/10.07	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, d), d)
28.56/10.07	   A^2 -> H(U1(d, d), k)
28.56/10.07	   A^2 -> H(U1(e, c), c)
28.56/10.07	   A^2 -> H(U1(c, c), e)
28.56/10.07	   A^2 -> H(U1(c, c), k)
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, e), e)
28.56/10.07	   A^2 -> H(d, U1(e, b))
28.56/10.07	   A^2 -> H(d, U1(k, b))
28.56/10.07	   A^2 -> H(d, U1(c, d))
28.56/10.07	   A^2 -> H(d, U1(d, c))
28.56/10.07	   A^2 -> H(d, U1(b, e))
28.56/10.07	   A^2 -> H(d, U1(b, k))
28.56/10.07	   A^2 -> H(d, U1(e, c))
28.56/10.07	   A^2 -> H(d, U1(k, c))
28.56/10.07	   A^2 -> H(d, U1(c, e))
28.56/10.07	   A^2 -> H(d, U1(c, k))
28.56/10.07	   A^2 -> H(d, U1(e, e))
28.56/10.07	   A^2 -> H(d, U1(k, k))
28.56/10.07	   A^2 -> H(d, U1(k, d))
28.56/10.07	   A^2 -> H(d, U1(d, k))
28.56/10.07	   A^2 -> H(a, b)
28.56/10.07	   A^2 -> H(a, U1(e, d))
28.56/10.07	   A^2 -> H(a, U1(d, e))
28.56/10.07	   A^2 -> H(a, c)
28.56/10.07	   A^2 -> H(a, U1(e, k))
28.56/10.07	   A^2 -> H(a, U1(k, e))
28.56/10.07	
28.56/10.07	The TRS R consists of the following rules:
28.56/10.07	
28.56/10.07	   f(x) -> U1(x, x)
28.56/10.07	   U1(e, x) -> x
28.56/10.07	   a -> c
28.56/10.07	   a -> d
28.56/10.07	   b -> c
28.56/10.07	   b -> d
28.56/10.07	   d -> k
28.56/10.07	   c -> e
28.56/10.07	   c -> k
28.56/10.07	
28.56/10.07	Q is empty.
28.56/10.07	We have to consider all minimal (P,Q,R)-chains.
28.56/10.07	----------------------------------------
28.56/10.07	
28.56/10.07	(1827) TransformationProof (EQUIVALENT)
28.56/10.07	By narrowing [LPAR04] the rule A^2 -> H(a, U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.07	
28.56/10.07	   (A^2 -> H(c, U1(c, e)),A^2 -> H(c, U1(c, e)))
28.56/10.07	   (A^2 -> H(d, U1(c, e)),A^2 -> H(d, U1(c, e)))
28.56/10.07	   (A^2 -> H(a, U1(e, e)),A^2 -> H(a, U1(e, e)))
28.56/10.07	   (A^2 -> H(a, U1(k, e)),A^2 -> H(a, U1(k, e)))
28.56/10.07	
28.56/10.07	
28.56/10.07	----------------------------------------
28.56/10.07	
28.56/10.07	(1828)
28.56/10.07	Obligation:
28.56/10.07	Q DP problem:
28.56/10.07	The TRS P consists of the following rules:
28.56/10.07	
28.56/10.07	   H(x, x) -> G(x, x, f(k))
28.56/10.07	   G(d, x, x) -> A^2
28.56/10.07	   A^2 -> H(f(c), f(c))
28.56/10.07	   A^2 -> H(f(d), f(d))
28.56/10.07	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.07	   A^2 -> H(f(e), f(e))
28.56/10.07	   A^2 -> H(f(k), f(k))
28.56/10.07	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.07	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.07	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.07	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.07	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.07	   A^2 -> H(a, U1(c, k))
28.56/10.07	   A^2 -> H(a, U1(e, e))
28.56/10.07	   A^2 -> H(a, U1(k, k))
28.56/10.07	   A^2 -> H(a, U1(k, d))
28.56/10.07	   A^2 -> H(a, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.07	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.07	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, a), b)
28.56/10.07	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, a), c)
28.56/10.07	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, a), e)
28.56/10.07	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, a), b)
28.56/10.07	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, a), c)
28.56/10.07	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, d), b)
28.56/10.07	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, d), c)
28.56/10.07	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, d), e)
28.56/10.07	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, a), d)
28.56/10.07	   A^2 -> H(U1(c, a), k)
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.07	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.07	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.07	   A^2 -> H(U1(d, c), b)
28.56/10.07	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(d, c), c)
28.56/10.07	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(d, c), e)
28.56/10.07	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, a), d)
28.56/10.07	   A^2 -> H(U1(d, a), k)
28.56/10.07	   A^2 -> H(U1(a, e), b)
28.56/10.07	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(a, e), c)
28.56/10.07	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(a, e), e)
28.56/10.07	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(a, k), b)
28.56/10.07	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(a, k), c)
28.56/10.07	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(a, k), e)
28.56/10.07	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(a, c), d)
28.56/10.07	   A^2 -> H(U1(a, c), k)
28.56/10.07	   A^2 -> H(U1(a, d), d)
28.56/10.07	   A^2 -> H(U1(a, d), k)
28.56/10.07	   A^2 -> H(k, U1(c, b))
28.56/10.07	   A^2 -> H(k, U1(d, b))
28.56/10.07	   A^2 -> H(k, U1(b, c))
28.56/10.07	   A^2 -> H(k, U1(b, d))
28.56/10.07	   A^2 -> H(k, U1(c, c))
28.56/10.07	   A^2 -> H(k, f(e))
28.56/10.07	   A^2 -> H(k, f(k))
28.56/10.07	   A^2 -> H(k, U1(d, d))
28.56/10.07	   A^2 -> H(c, U1(e, b))
28.56/10.07	   A^2 -> H(c, U1(k, b))
28.56/10.07	   A^2 -> H(c, U1(c, d))
28.56/10.07	   A^2 -> H(c, U1(d, c))
28.56/10.07	   A^2 -> H(c, U1(b, e))
28.56/10.07	   A^2 -> H(c, U1(b, k))
28.56/10.07	   A^2 -> H(c, U1(e, c))
28.56/10.07	   A^2 -> H(c, U1(k, c))
28.56/10.07	   A^2 -> H(c, U1(c, e))
28.56/10.07	   A^2 -> H(c, U1(c, k))
28.56/10.07	   A^2 -> H(c, U1(e, e))
28.56/10.07	   A^2 -> H(c, U1(k, k))
28.56/10.07	   A^2 -> H(c, U1(k, d))
28.56/10.07	   A^2 -> H(c, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.07	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.07	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, c), b)
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, c), e)
28.56/10.07	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.07	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.07	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.07	   A^2 -> H(U1(k, c), b)
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, c), c)
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, e), b)
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, e), c)
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, e), e)
28.56/10.07	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, k), b)
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, k), c)
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, k), e)
28.56/10.07	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, c), d)
28.56/10.07	   A^2 -> H(e, U1(e, b))
28.56/10.07	   A^2 -> H(e, U1(c, d))
28.56/10.07	   A^2 -> H(e, U1(d, c))
28.56/10.07	   A^2 -> H(e, U1(b, e))
28.56/10.07	   A^2 -> H(e, U1(b, k))
28.56/10.07	   A^2 -> H(e, U1(e, c))
28.56/10.07	   A^2 -> H(e, U1(c, e))
28.56/10.07	   A^2 -> H(e, U1(c, k))
28.56/10.07	   A^2 -> H(e, U1(e, e))
28.56/10.07	   A^2 -> H(e, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, e), b)
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, e), c)
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.07	   A^2 -> H(f(e), d)
28.56/10.07	   A^2 -> H(f(e), k)
28.56/10.07	   A^2 -> H(U1(k, k), b)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, k), c)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.07	   A^2 -> H(f(k), d)
28.56/10.07	   A^2 -> H(f(k), k)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.07	   A^2 -> H(U1(k, d), b)
28.56/10.07	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, d), c)
28.56/10.07	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, k), b)
28.56/10.07	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(d, k), c)
28.56/10.07	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(d, k), e)
28.56/10.07	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, d), d)
28.56/10.07	   A^2 -> H(U1(d, d), k)
28.56/10.07	   A^2 -> H(U1(e, c), c)
28.56/10.07	   A^2 -> H(U1(c, c), e)
28.56/10.07	   A^2 -> H(U1(c, c), k)
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, e), e)
28.56/10.07	   A^2 -> H(d, U1(e, b))
28.56/10.07	   A^2 -> H(d, U1(k, b))
28.56/10.07	   A^2 -> H(d, U1(c, d))
28.56/10.07	   A^2 -> H(d, U1(d, c))
28.56/10.07	   A^2 -> H(d, U1(b, e))
28.56/10.07	   A^2 -> H(d, U1(b, k))
28.56/10.07	   A^2 -> H(d, U1(e, c))
28.56/10.07	   A^2 -> H(d, U1(k, c))
28.56/10.07	   A^2 -> H(d, U1(c, e))
28.56/10.07	   A^2 -> H(d, U1(c, k))
28.56/10.07	   A^2 -> H(d, U1(e, e))
28.56/10.07	   A^2 -> H(d, U1(k, k))
28.56/10.07	   A^2 -> H(d, U1(k, d))
28.56/10.07	   A^2 -> H(d, U1(d, k))
28.56/10.07	   A^2 -> H(a, b)
28.56/10.07	   A^2 -> H(a, U1(e, d))
28.56/10.07	   A^2 -> H(a, U1(d, e))
28.56/10.07	   A^2 -> H(a, c)
28.56/10.07	   A^2 -> H(a, U1(e, k))
28.56/10.07	   A^2 -> H(a, U1(k, e))
28.56/10.07	
28.56/10.07	The TRS R consists of the following rules:
28.56/10.07	
28.56/10.07	   f(x) -> U1(x, x)
28.56/10.07	   U1(e, x) -> x
28.56/10.07	   a -> c
28.56/10.07	   a -> d
28.56/10.07	   b -> c
28.56/10.07	   b -> d
28.56/10.07	   d -> k
28.56/10.07	   c -> e
28.56/10.07	   c -> k
28.56/10.07	
28.56/10.07	Q is empty.
28.56/10.07	We have to consider all minimal (P,Q,R)-chains.
28.56/10.07	----------------------------------------
28.56/10.07	
28.56/10.07	(1829) TransformationProof (EQUIVALENT)
28.56/10.07	By narrowing [LPAR04] the rule A^2 -> H(a, U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.07	
28.56/10.07	   (A^2 -> H(c, U1(c, k)),A^2 -> H(c, U1(c, k)))
28.56/10.07	   (A^2 -> H(d, U1(c, k)),A^2 -> H(d, U1(c, k)))
28.56/10.07	   (A^2 -> H(a, U1(e, k)),A^2 -> H(a, U1(e, k)))
28.56/10.07	   (A^2 -> H(a, U1(k, k)),A^2 -> H(a, U1(k, k)))
28.56/10.07	
28.56/10.07	
28.56/10.07	----------------------------------------
28.56/10.07	
28.56/10.07	(1830)
28.56/10.07	Obligation:
28.56/10.07	Q DP problem:
28.56/10.07	The TRS P consists of the following rules:
28.56/10.07	
28.56/10.07	   H(x, x) -> G(x, x, f(k))
28.56/10.07	   G(d, x, x) -> A^2
28.56/10.07	   A^2 -> H(f(c), f(c))
28.56/10.07	   A^2 -> H(f(d), f(d))
28.56/10.07	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.07	   A^2 -> H(f(e), f(e))
28.56/10.07	   A^2 -> H(f(k), f(k))
28.56/10.07	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.07	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.07	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.07	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.07	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.07	   A^2 -> H(a, U1(e, e))
28.56/10.07	   A^2 -> H(a, U1(k, k))
28.56/10.07	   A^2 -> H(a, U1(k, d))
28.56/10.07	   A^2 -> H(a, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.07	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.07	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, a), b)
28.56/10.07	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, a), c)
28.56/10.07	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, a), e)
28.56/10.07	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, a), b)
28.56/10.07	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, a), c)
28.56/10.07	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, d), b)
28.56/10.07	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, d), c)
28.56/10.07	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, d), e)
28.56/10.07	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, a), d)
28.56/10.07	   A^2 -> H(U1(c, a), k)
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.07	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.07	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.07	   A^2 -> H(U1(d, c), b)
28.56/10.07	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(d, c), c)
28.56/10.07	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(d, c), e)
28.56/10.07	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, a), d)
28.56/10.07	   A^2 -> H(U1(d, a), k)
28.56/10.07	   A^2 -> H(U1(a, e), b)
28.56/10.07	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(a, e), c)
28.56/10.07	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(a, e), e)
28.56/10.07	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(a, k), b)
28.56/10.07	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(a, k), c)
28.56/10.07	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(a, k), e)
28.56/10.07	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(a, c), d)
28.56/10.07	   A^2 -> H(U1(a, c), k)
28.56/10.07	   A^2 -> H(U1(a, d), d)
28.56/10.07	   A^2 -> H(U1(a, d), k)
28.56/10.07	   A^2 -> H(k, U1(c, b))
28.56/10.07	   A^2 -> H(k, U1(d, b))
28.56/10.07	   A^2 -> H(k, U1(b, c))
28.56/10.07	   A^2 -> H(k, U1(b, d))
28.56/10.07	   A^2 -> H(k, U1(c, c))
28.56/10.07	   A^2 -> H(k, f(e))
28.56/10.07	   A^2 -> H(k, f(k))
28.56/10.07	   A^2 -> H(k, U1(d, d))
28.56/10.07	   A^2 -> H(c, U1(e, b))
28.56/10.07	   A^2 -> H(c, U1(k, b))
28.56/10.07	   A^2 -> H(c, U1(c, d))
28.56/10.07	   A^2 -> H(c, U1(d, c))
28.56/10.07	   A^2 -> H(c, U1(b, e))
28.56/10.07	   A^2 -> H(c, U1(b, k))
28.56/10.07	   A^2 -> H(c, U1(e, c))
28.56/10.07	   A^2 -> H(c, U1(k, c))
28.56/10.07	   A^2 -> H(c, U1(c, e))
28.56/10.07	   A^2 -> H(c, U1(c, k))
28.56/10.07	   A^2 -> H(c, U1(e, e))
28.56/10.07	   A^2 -> H(c, U1(k, k))
28.56/10.07	   A^2 -> H(c, U1(k, d))
28.56/10.07	   A^2 -> H(c, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.07	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.07	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, c), b)
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, c), e)
28.56/10.07	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.07	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.07	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.07	   A^2 -> H(U1(k, c), b)
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, c), c)
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, e), b)
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, e), c)
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, e), e)
28.56/10.07	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, k), b)
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, k), c)
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, k), e)
28.56/10.07	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, c), d)
28.56/10.07	   A^2 -> H(e, U1(e, b))
28.56/10.07	   A^2 -> H(e, U1(c, d))
28.56/10.07	   A^2 -> H(e, U1(d, c))
28.56/10.07	   A^2 -> H(e, U1(b, e))
28.56/10.07	   A^2 -> H(e, U1(b, k))
28.56/10.07	   A^2 -> H(e, U1(e, c))
28.56/10.07	   A^2 -> H(e, U1(c, e))
28.56/10.07	   A^2 -> H(e, U1(c, k))
28.56/10.07	   A^2 -> H(e, U1(e, e))
28.56/10.07	   A^2 -> H(e, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, e), b)
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, e), c)
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.07	   A^2 -> H(f(e), d)
28.56/10.07	   A^2 -> H(f(e), k)
28.56/10.07	   A^2 -> H(U1(k, k), b)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, k), c)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.07	   A^2 -> H(f(k), d)
28.56/10.07	   A^2 -> H(f(k), k)
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.07	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.07	   A^2 -> H(U1(k, d), b)
28.56/10.07	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, d), c)
28.56/10.07	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, k), b)
28.56/10.07	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(d, k), c)
28.56/10.07	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(d, k), e)
28.56/10.07	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, d), d)
28.56/10.07	   A^2 -> H(U1(d, d), k)
28.56/10.07	   A^2 -> H(U1(e, c), c)
28.56/10.07	   A^2 -> H(U1(c, c), e)
28.56/10.07	   A^2 -> H(U1(c, c), k)
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.07	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, e), e)
28.56/10.07	   A^2 -> H(d, U1(e, b))
28.56/10.07	   A^2 -> H(d, U1(k, b))
28.56/10.07	   A^2 -> H(d, U1(c, d))
28.56/10.07	   A^2 -> H(d, U1(d, c))
28.56/10.07	   A^2 -> H(d, U1(b, e))
28.56/10.07	   A^2 -> H(d, U1(b, k))
28.56/10.07	   A^2 -> H(d, U1(e, c))
28.56/10.07	   A^2 -> H(d, U1(k, c))
28.56/10.07	   A^2 -> H(d, U1(c, e))
28.56/10.07	   A^2 -> H(d, U1(c, k))
28.56/10.07	   A^2 -> H(d, U1(e, e))
28.56/10.07	   A^2 -> H(d, U1(k, k))
28.56/10.07	   A^2 -> H(d, U1(k, d))
28.56/10.07	   A^2 -> H(d, U1(d, k))
28.56/10.07	   A^2 -> H(a, b)
28.56/10.07	   A^2 -> H(a, U1(e, d))
28.56/10.07	   A^2 -> H(a, U1(d, e))
28.56/10.07	   A^2 -> H(a, c)
28.56/10.07	   A^2 -> H(a, U1(e, k))
28.56/10.07	   A^2 -> H(a, U1(k, e))
28.56/10.07	
28.56/10.07	The TRS R consists of the following rules:
28.56/10.07	
28.56/10.07	   f(x) -> U1(x, x)
28.56/10.07	   U1(e, x) -> x
28.56/10.07	   a -> c
28.56/10.07	   a -> d
28.56/10.07	   b -> c
28.56/10.07	   b -> d
28.56/10.07	   d -> k
28.56/10.07	   c -> e
28.56/10.07	   c -> k
28.56/10.07	
28.56/10.07	Q is empty.
28.56/10.07	We have to consider all minimal (P,Q,R)-chains.
28.56/10.07	----------------------------------------
28.56/10.07	
28.56/10.07	(1831) TransformationProof (EQUIVALENT)
28.56/10.07	By narrowing [LPAR04] the rule A^2 -> H(a, U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.07	
28.56/10.07	   (A^2 -> H(c, U1(e, e)),A^2 -> H(c, U1(e, e)))
28.56/10.07	   (A^2 -> H(d, U1(e, e)),A^2 -> H(d, U1(e, e)))
28.56/10.07	   (A^2 -> H(a, e),A^2 -> H(a, e))
28.56/10.07	
28.56/10.07	
28.56/10.07	----------------------------------------
28.56/10.07	
28.56/10.07	(1832)
28.56/10.07	Obligation:
28.56/10.07	Q DP problem:
28.56/10.07	The TRS P consists of the following rules:
28.56/10.07	
28.56/10.07	   H(x, x) -> G(x, x, f(k))
28.56/10.07	   G(d, x, x) -> A^2
28.56/10.07	   A^2 -> H(f(c), f(c))
28.56/10.07	   A^2 -> H(f(d), f(d))
28.56/10.07	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.07	   A^2 -> H(f(e), f(e))
28.56/10.07	   A^2 -> H(f(k), f(k))
28.56/10.07	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.07	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.07	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.07	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.07	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.07	   A^2 -> H(a, U1(k, k))
28.56/10.07	   A^2 -> H(a, U1(k, d))
28.56/10.07	   A^2 -> H(a, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.07	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.07	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, a), b)
28.56/10.07	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, a), c)
28.56/10.07	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, a), e)
28.56/10.07	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, a), b)
28.56/10.07	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, a), c)
28.56/10.07	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, d), b)
28.56/10.07	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.07	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.07	   A^2 -> H(U1(c, d), c)
28.56/10.07	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.07	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.07	   A^2 -> H(U1(c, d), e)
28.56/10.07	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.07	   A^2 -> H(U1(c, a), d)
28.56/10.07	   A^2 -> H(U1(c, a), k)
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.07	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.07	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.07	   A^2 -> H(U1(d, c), b)
28.56/10.07	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(d, c), c)
28.56/10.07	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(d, c), e)
28.56/10.07	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(d, a), d)
28.56/10.07	   A^2 -> H(U1(d, a), k)
28.56/10.07	   A^2 -> H(U1(a, e), b)
28.56/10.07	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.07	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.07	   A^2 -> H(U1(a, e), c)
28.56/10.07	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.07	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.07	   A^2 -> H(U1(a, e), e)
28.56/10.07	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.07	   A^2 -> H(U1(a, k), b)
28.56/10.07	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.07	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.07	   A^2 -> H(U1(a, k), c)
28.56/10.07	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.07	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.07	   A^2 -> H(U1(a, k), e)
28.56/10.07	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(a, c), d)
28.56/10.07	   A^2 -> H(U1(a, c), k)
28.56/10.07	   A^2 -> H(U1(a, d), d)
28.56/10.07	   A^2 -> H(U1(a, d), k)
28.56/10.07	   A^2 -> H(k, U1(c, b))
28.56/10.07	   A^2 -> H(k, U1(d, b))
28.56/10.07	   A^2 -> H(k, U1(b, c))
28.56/10.07	   A^2 -> H(k, U1(b, d))
28.56/10.07	   A^2 -> H(k, U1(c, c))
28.56/10.07	   A^2 -> H(k, f(e))
28.56/10.07	   A^2 -> H(k, f(k))
28.56/10.07	   A^2 -> H(k, U1(d, d))
28.56/10.07	   A^2 -> H(c, U1(e, b))
28.56/10.07	   A^2 -> H(c, U1(k, b))
28.56/10.07	   A^2 -> H(c, U1(c, d))
28.56/10.07	   A^2 -> H(c, U1(d, c))
28.56/10.07	   A^2 -> H(c, U1(b, e))
28.56/10.07	   A^2 -> H(c, U1(b, k))
28.56/10.07	   A^2 -> H(c, U1(e, c))
28.56/10.07	   A^2 -> H(c, U1(k, c))
28.56/10.07	   A^2 -> H(c, U1(c, e))
28.56/10.07	   A^2 -> H(c, U1(c, k))
28.56/10.07	   A^2 -> H(c, U1(e, e))
28.56/10.07	   A^2 -> H(c, U1(k, k))
28.56/10.07	   A^2 -> H(c, U1(k, d))
28.56/10.07	   A^2 -> H(c, U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.07	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.07	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.07	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.07	   A^2 -> H(U1(e, c), b)
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(e, c), e)
28.56/10.07	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.07	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.07	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.07	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.07	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.07	   A^2 -> H(U1(k, c), b)
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.07	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.07	   A^2 -> H(U1(k, c), c)
28.56/10.07	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.07	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, e), b)
28.56/10.08	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.08	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.08	   A^2 -> H(U1(c, e), c)
28.56/10.08	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.08	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.08	   A^2 -> H(U1(c, e), e)
28.56/10.08	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, k), b)
28.56/10.08	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(c, k), c)
28.56/10.08	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.08	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.08	   A^2 -> H(U1(c, k), e)
28.56/10.08	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, c), d)
28.56/10.08	   A^2 -> H(e, U1(e, b))
28.56/10.08	   A^2 -> H(e, U1(c, d))
28.56/10.08	   A^2 -> H(e, U1(d, c))
28.56/10.08	   A^2 -> H(e, U1(b, e))
28.56/10.08	   A^2 -> H(e, U1(b, k))
28.56/10.08	   A^2 -> H(e, U1(e, c))
28.56/10.08	   A^2 -> H(e, U1(c, e))
28.56/10.08	   A^2 -> H(e, U1(c, k))
28.56/10.08	   A^2 -> H(e, U1(e, e))
28.56/10.08	   A^2 -> H(e, U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, e), b)
28.56/10.08	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.08	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.08	   A^2 -> H(U1(e, e), c)
28.56/10.08	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.08	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.08	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.08	   A^2 -> H(f(e), d)
28.56/10.08	   A^2 -> H(f(e), k)
28.56/10.08	   A^2 -> H(U1(k, k), b)
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, k), c)
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.08	   A^2 -> H(f(k), d)
28.56/10.08	   A^2 -> H(f(k), k)
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.08	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.08	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.08	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.08	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.08	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.08	   A^2 -> H(U1(k, d), b)
28.56/10.08	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, d), c)
28.56/10.08	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.08	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.08	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, k), b)
28.56/10.08	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(d, k), c)
28.56/10.08	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.08	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.08	   A^2 -> H(U1(d, k), e)
28.56/10.08	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, d), d)
28.56/10.08	   A^2 -> H(U1(d, d), k)
28.56/10.08	   A^2 -> H(U1(e, c), c)
28.56/10.08	   A^2 -> H(U1(c, c), e)
28.56/10.08	   A^2 -> H(U1(c, c), k)
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.08	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.08	   A^2 -> H(U1(e, e), e)
28.56/10.08	   A^2 -> H(d, U1(e, b))
28.56/10.08	   A^2 -> H(d, U1(k, b))
28.56/10.08	   A^2 -> H(d, U1(c, d))
28.56/10.08	   A^2 -> H(d, U1(d, c))
28.56/10.08	   A^2 -> H(d, U1(b, e))
28.56/10.08	   A^2 -> H(d, U1(b, k))
28.56/10.08	   A^2 -> H(d, U1(e, c))
28.56/10.08	   A^2 -> H(d, U1(k, c))
28.56/10.08	   A^2 -> H(d, U1(c, e))
28.56/10.08	   A^2 -> H(d, U1(c, k))
28.56/10.08	   A^2 -> H(d, U1(e, e))
28.56/10.08	   A^2 -> H(d, U1(k, k))
28.56/10.08	   A^2 -> H(d, U1(k, d))
28.56/10.08	   A^2 -> H(d, U1(d, k))
28.56/10.08	   A^2 -> H(a, b)
28.56/10.08	   A^2 -> H(a, U1(e, d))
28.56/10.08	   A^2 -> H(a, U1(d, e))
28.56/10.08	   A^2 -> H(a, c)
28.56/10.08	   A^2 -> H(a, U1(e, k))
28.56/10.08	   A^2 -> H(a, U1(k, e))
28.56/10.08	   A^2 -> H(a, e)
28.56/10.08	
28.56/10.08	The TRS R consists of the following rules:
28.56/10.08	
28.56/10.08	   f(x) -> U1(x, x)
28.56/10.08	   U1(e, x) -> x
28.56/10.08	   a -> c
28.56/10.08	   a -> d
28.56/10.08	   b -> c
28.56/10.08	   b -> d
28.56/10.08	   d -> k
28.56/10.08	   c -> e
28.56/10.08	   c -> k
28.56/10.08	
28.56/10.08	Q is empty.
28.56/10.08	We have to consider all minimal (P,Q,R)-chains.
28.56/10.08	----------------------------------------
28.56/10.08	
28.56/10.08	(1833) TransformationProof (EQUIVALENT)
28.56/10.08	By narrowing [LPAR04] the rule A^2 -> H(a, U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.08	
28.56/10.08	   (A^2 -> H(c, U1(k, k)),A^2 -> H(c, U1(k, k)))
28.56/10.08	   (A^2 -> H(d, U1(k, k)),A^2 -> H(d, U1(k, k)))
28.56/10.08	
28.56/10.08	
28.56/10.08	----------------------------------------
28.56/10.08	
28.56/10.08	(1834)
28.56/10.08	Obligation:
28.56/10.08	Q DP problem:
28.56/10.08	The TRS P consists of the following rules:
28.56/10.08	
28.56/10.08	   H(x, x) -> G(x, x, f(k))
28.56/10.08	   G(d, x, x) -> A^2
28.56/10.08	   A^2 -> H(f(c), f(c))
28.56/10.08	   A^2 -> H(f(d), f(d))
28.56/10.08	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.08	   A^2 -> H(f(e), f(e))
28.56/10.08	   A^2 -> H(f(k), f(k))
28.56/10.08	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.08	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.08	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.08	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.08	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.08	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.08	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.08	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.08	   A^2 -> H(a, U1(k, d))
28.56/10.08	   A^2 -> H(a, U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.08	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.08	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.08	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.08	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.08	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.08	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.08	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, a), b)
28.56/10.08	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.08	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.08	   A^2 -> H(U1(e, a), c)
28.56/10.08	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.08	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.08	   A^2 -> H(U1(e, a), e)
28.56/10.08	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.08	   A^2 -> H(U1(k, a), b)
28.56/10.08	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, a), c)
28.56/10.08	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.08	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.08	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, d), b)
28.56/10.08	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.08	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.08	   A^2 -> H(U1(c, d), c)
28.56/10.08	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.08	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.08	   A^2 -> H(U1(c, d), e)
28.56/10.08	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, a), d)
28.56/10.08	   A^2 -> H(U1(c, a), k)
28.56/10.08	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.08	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.08	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.08	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.08	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.08	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.08	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.08	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.08	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.08	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.08	   A^2 -> H(U1(d, c), b)
28.56/10.08	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.08	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.08	   A^2 -> H(U1(d, c), c)
28.56/10.08	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.08	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.08	   A^2 -> H(U1(d, c), e)
28.56/10.08	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, a), d)
28.56/10.08	   A^2 -> H(U1(d, a), k)
28.56/10.08	   A^2 -> H(U1(a, e), b)
28.56/10.08	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.08	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.08	   A^2 -> H(U1(a, e), c)
28.56/10.08	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.08	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.08	   A^2 -> H(U1(a, e), e)
28.56/10.08	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.08	   A^2 -> H(U1(a, k), b)
28.56/10.08	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(a, k), c)
28.56/10.08	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.08	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.08	   A^2 -> H(U1(a, k), e)
28.56/10.08	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(a, c), d)
28.56/10.08	   A^2 -> H(U1(a, c), k)
28.56/10.08	   A^2 -> H(U1(a, d), d)
28.56/10.08	   A^2 -> H(U1(a, d), k)
28.56/10.08	   A^2 -> H(k, U1(c, b))
28.56/10.08	   A^2 -> H(k, U1(d, b))
28.56/10.08	   A^2 -> H(k, U1(b, c))
28.56/10.08	   A^2 -> H(k, U1(b, d))
28.56/10.08	   A^2 -> H(k, U1(c, c))
28.56/10.08	   A^2 -> H(k, f(e))
28.56/10.08	   A^2 -> H(k, f(k))
28.56/10.08	   A^2 -> H(k, U1(d, d))
28.56/10.08	   A^2 -> H(c, U1(e, b))
28.56/10.08	   A^2 -> H(c, U1(k, b))
28.56/10.08	   A^2 -> H(c, U1(c, d))
28.56/10.08	   A^2 -> H(c, U1(d, c))
28.56/10.08	   A^2 -> H(c, U1(b, e))
28.56/10.08	   A^2 -> H(c, U1(b, k))
28.56/10.08	   A^2 -> H(c, U1(e, c))
28.56/10.08	   A^2 -> H(c, U1(k, c))
28.56/10.08	   A^2 -> H(c, U1(c, e))
28.56/10.08	   A^2 -> H(c, U1(c, k))
28.56/10.08	   A^2 -> H(c, U1(e, e))
28.56/10.08	   A^2 -> H(c, U1(k, k))
28.56/10.08	   A^2 -> H(c, U1(k, d))
28.56/10.08	   A^2 -> H(c, U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.08	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.08	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.08	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.08	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.08	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.08	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.08	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, c), b)
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.08	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.08	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.08	   A^2 -> H(U1(e, c), e)
28.56/10.08	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.08	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.08	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.08	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.08	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.08	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.08	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.08	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.08	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.08	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.08	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.08	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.08	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.08	   A^2 -> H(U1(k, c), b)
28.56/10.08	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, c), c)
28.56/10.08	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.08	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.08	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, e), b)
28.56/10.08	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.08	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.08	   A^2 -> H(U1(c, e), c)
28.56/10.08	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.08	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.08	   A^2 -> H(U1(c, e), e)
28.56/10.08	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, k), b)
28.56/10.08	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(c, k), c)
28.56/10.08	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.08	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.08	   A^2 -> H(U1(c, k), e)
28.56/10.08	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, c), d)
28.56/10.08	   A^2 -> H(e, U1(e, b))
28.56/10.08	   A^2 -> H(e, U1(c, d))
28.56/10.08	   A^2 -> H(e, U1(d, c))
28.56/10.08	   A^2 -> H(e, U1(b, e))
28.56/10.08	   A^2 -> H(e, U1(b, k))
28.56/10.08	   A^2 -> H(e, U1(e, c))
28.56/10.08	   A^2 -> H(e, U1(c, e))
28.56/10.08	   A^2 -> H(e, U1(c, k))
28.56/10.08	   A^2 -> H(e, U1(e, e))
28.56/10.08	   A^2 -> H(e, U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, e), b)
28.56/10.08	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.08	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.08	   A^2 -> H(U1(e, e), c)
28.56/10.08	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.08	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.08	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.08	   A^2 -> H(f(e), d)
28.56/10.08	   A^2 -> H(f(e), k)
28.56/10.08	   A^2 -> H(U1(k, k), b)
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, k), c)
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.08	   A^2 -> H(f(k), d)
28.56/10.08	   A^2 -> H(f(k), k)
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.08	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.08	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.08	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.08	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.08	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.08	   A^2 -> H(U1(k, d), b)
28.56/10.08	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, d), c)
28.56/10.08	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.08	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.08	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, k), b)
28.56/10.08	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(d, k), c)
28.56/10.08	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.08	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.08	   A^2 -> H(U1(d, k), e)
28.56/10.08	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, d), d)
28.56/10.08	   A^2 -> H(U1(d, d), k)
28.56/10.08	   A^2 -> H(U1(e, c), c)
28.56/10.08	   A^2 -> H(U1(c, c), e)
28.56/10.08	   A^2 -> H(U1(c, c), k)
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.08	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.08	   A^2 -> H(U1(e, e), e)
28.56/10.08	   A^2 -> H(d, U1(e, b))
28.56/10.08	   A^2 -> H(d, U1(k, b))
28.56/10.08	   A^2 -> H(d, U1(c, d))
28.56/10.08	   A^2 -> H(d, U1(d, c))
28.56/10.08	   A^2 -> H(d, U1(b, e))
28.56/10.08	   A^2 -> H(d, U1(b, k))
28.56/10.08	   A^2 -> H(d, U1(e, c))
28.56/10.08	   A^2 -> H(d, U1(k, c))
28.56/10.08	   A^2 -> H(d, U1(c, e))
28.56/10.08	   A^2 -> H(d, U1(c, k))
28.56/10.08	   A^2 -> H(d, U1(e, e))
28.56/10.08	   A^2 -> H(d, U1(k, k))
28.56/10.08	   A^2 -> H(d, U1(k, d))
28.56/10.08	   A^2 -> H(d, U1(d, k))
28.56/10.08	   A^2 -> H(a, b)
28.56/10.08	   A^2 -> H(a, U1(e, d))
28.56/10.08	   A^2 -> H(a, U1(d, e))
28.56/10.08	   A^2 -> H(a, c)
28.56/10.08	   A^2 -> H(a, U1(e, k))
28.56/10.08	   A^2 -> H(a, U1(k, e))
28.56/10.08	   A^2 -> H(a, e)
28.56/10.08	
28.56/10.08	The TRS R consists of the following rules:
28.56/10.08	
28.56/10.08	   f(x) -> U1(x, x)
28.56/10.08	   U1(e, x) -> x
28.56/10.08	   a -> c
28.56/10.08	   a -> d
28.56/10.08	   b -> c
28.56/10.08	   b -> d
28.56/10.08	   d -> k
28.56/10.08	   c -> e
28.56/10.08	   c -> k
28.56/10.08	
28.56/10.08	Q is empty.
28.56/10.08	We have to consider all minimal (P,Q,R)-chains.
28.56/10.08	----------------------------------------
28.56/10.08	
28.56/10.08	(1835) TransformationProof (EQUIVALENT)
28.56/10.08	By narrowing [LPAR04] the rule A^2 -> H(a, U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.08	
28.56/10.08	   (A^2 -> H(c, U1(k, d)),A^2 -> H(c, U1(k, d)))
28.56/10.08	   (A^2 -> H(d, U1(k, d)),A^2 -> H(d, U1(k, d)))
28.56/10.08	   (A^2 -> H(a, U1(k, k)),A^2 -> H(a, U1(k, k)))
28.56/10.08	
28.56/10.08	
28.56/10.08	----------------------------------------
28.56/10.08	
28.56/10.08	(1836)
28.56/10.08	Obligation:
28.56/10.08	Q DP problem:
28.56/10.08	The TRS P consists of the following rules:
28.56/10.08	
28.56/10.08	   H(x, x) -> G(x, x, f(k))
28.56/10.08	   G(d, x, x) -> A^2
28.56/10.08	   A^2 -> H(f(c), f(c))
28.56/10.08	   A^2 -> H(f(d), f(d))
28.56/10.08	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.08	   A^2 -> H(f(e), f(e))
28.56/10.08	   A^2 -> H(f(k), f(k))
28.56/10.08	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.08	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.08	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.08	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.08	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.08	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.08	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.08	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.08	   A^2 -> H(a, U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.08	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.08	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.08	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.08	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.08	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.08	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.08	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, a), b)
28.56/10.08	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.08	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.08	   A^2 -> H(U1(e, a), c)
28.56/10.08	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.08	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.08	   A^2 -> H(U1(e, a), e)
28.56/10.08	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.08	   A^2 -> H(U1(k, a), b)
28.56/10.08	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, a), c)
28.56/10.08	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.08	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.08	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, d), b)
28.56/10.08	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.08	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.08	   A^2 -> H(U1(c, d), c)
28.56/10.08	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.08	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.08	   A^2 -> H(U1(c, d), e)
28.56/10.08	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, a), d)
28.56/10.08	   A^2 -> H(U1(c, a), k)
28.56/10.08	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.08	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.08	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.08	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.08	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.08	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.08	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.08	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.08	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.08	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.08	   A^2 -> H(U1(d, c), b)
28.56/10.08	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.08	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.08	   A^2 -> H(U1(d, c), c)
28.56/10.08	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.08	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.08	   A^2 -> H(U1(d, c), e)
28.56/10.08	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, a), d)
28.56/10.08	   A^2 -> H(U1(d, a), k)
28.56/10.08	   A^2 -> H(U1(a, e), b)
28.56/10.08	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.08	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.08	   A^2 -> H(U1(a, e), c)
28.56/10.08	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.08	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.08	   A^2 -> H(U1(a, e), e)
28.56/10.08	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.08	   A^2 -> H(U1(a, k), b)
28.56/10.08	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(a, k), c)
28.56/10.08	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.08	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.08	   A^2 -> H(U1(a, k), e)
28.56/10.08	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(a, c), d)
28.56/10.08	   A^2 -> H(U1(a, c), k)
28.56/10.08	   A^2 -> H(U1(a, d), d)
28.56/10.08	   A^2 -> H(U1(a, d), k)
28.56/10.08	   A^2 -> H(k, U1(c, b))
28.56/10.08	   A^2 -> H(k, U1(d, b))
28.56/10.08	   A^2 -> H(k, U1(b, c))
28.56/10.08	   A^2 -> H(k, U1(b, d))
28.56/10.08	   A^2 -> H(k, U1(c, c))
28.56/10.08	   A^2 -> H(k, f(e))
28.56/10.08	   A^2 -> H(k, f(k))
28.56/10.08	   A^2 -> H(k, U1(d, d))
28.56/10.08	   A^2 -> H(c, U1(e, b))
28.56/10.08	   A^2 -> H(c, U1(k, b))
28.56/10.08	   A^2 -> H(c, U1(c, d))
28.56/10.08	   A^2 -> H(c, U1(d, c))
28.56/10.08	   A^2 -> H(c, U1(b, e))
28.56/10.08	   A^2 -> H(c, U1(b, k))
28.56/10.08	   A^2 -> H(c, U1(e, c))
28.56/10.08	   A^2 -> H(c, U1(k, c))
28.56/10.08	   A^2 -> H(c, U1(c, e))
28.56/10.08	   A^2 -> H(c, U1(c, k))
28.56/10.08	   A^2 -> H(c, U1(e, e))
28.56/10.08	   A^2 -> H(c, U1(k, k))
28.56/10.08	   A^2 -> H(c, U1(k, d))
28.56/10.08	   A^2 -> H(c, U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.08	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.08	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.08	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.08	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.08	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.08	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.08	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, c), b)
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.08	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.08	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.08	   A^2 -> H(U1(e, c), e)
28.56/10.08	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.08	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.08	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.08	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.08	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.08	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.08	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.08	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.08	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.08	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.08	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.08	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.08	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.08	   A^2 -> H(U1(k, c), b)
28.56/10.08	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, c), c)
28.56/10.08	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.08	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.08	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, e), b)
28.56/10.08	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.08	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.08	   A^2 -> H(U1(c, e), c)
28.56/10.08	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.08	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.08	   A^2 -> H(U1(c, e), e)
28.56/10.08	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, k), b)
28.56/10.08	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(c, k), c)
28.56/10.08	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.08	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.08	   A^2 -> H(U1(c, k), e)
28.56/10.08	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, c), d)
28.56/10.08	   A^2 -> H(e, U1(e, b))
28.56/10.08	   A^2 -> H(e, U1(c, d))
28.56/10.08	   A^2 -> H(e, U1(d, c))
28.56/10.08	   A^2 -> H(e, U1(b, e))
28.56/10.08	   A^2 -> H(e, U1(b, k))
28.56/10.08	   A^2 -> H(e, U1(e, c))
28.56/10.08	   A^2 -> H(e, U1(c, e))
28.56/10.08	   A^2 -> H(e, U1(c, k))
28.56/10.08	   A^2 -> H(e, U1(e, e))
28.56/10.08	   A^2 -> H(e, U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, e), b)
28.56/10.08	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.08	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.08	   A^2 -> H(U1(e, e), c)
28.56/10.08	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.08	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.08	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.08	   A^2 -> H(f(e), d)
28.56/10.08	   A^2 -> H(f(e), k)
28.56/10.08	   A^2 -> H(U1(k, k), b)
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, k), c)
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.08	   A^2 -> H(f(k), d)
28.56/10.08	   A^2 -> H(f(k), k)
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.08	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.08	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.08	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.08	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.08	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.08	   A^2 -> H(U1(k, d), b)
28.56/10.08	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, d), c)
28.56/10.08	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.08	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.08	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, k), b)
28.56/10.08	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(d, k), c)
28.56/10.08	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.08	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.08	   A^2 -> H(U1(d, k), e)
28.56/10.08	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, d), d)
28.56/10.08	   A^2 -> H(U1(d, d), k)
28.56/10.08	   A^2 -> H(U1(e, c), c)
28.56/10.08	   A^2 -> H(U1(c, c), e)
28.56/10.08	   A^2 -> H(U1(c, c), k)
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.08	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.08	   A^2 -> H(U1(e, e), e)
28.56/10.08	   A^2 -> H(d, U1(e, b))
28.56/10.08	   A^2 -> H(d, U1(k, b))
28.56/10.08	   A^2 -> H(d, U1(c, d))
28.56/10.08	   A^2 -> H(d, U1(d, c))
28.56/10.08	   A^2 -> H(d, U1(b, e))
28.56/10.08	   A^2 -> H(d, U1(b, k))
28.56/10.08	   A^2 -> H(d, U1(e, c))
28.56/10.08	   A^2 -> H(d, U1(k, c))
28.56/10.08	   A^2 -> H(d, U1(c, e))
28.56/10.08	   A^2 -> H(d, U1(c, k))
28.56/10.08	   A^2 -> H(d, U1(e, e))
28.56/10.08	   A^2 -> H(d, U1(k, k))
28.56/10.08	   A^2 -> H(d, U1(k, d))
28.56/10.08	   A^2 -> H(d, U1(d, k))
28.56/10.08	   A^2 -> H(a, b)
28.56/10.08	   A^2 -> H(a, U1(e, d))
28.56/10.08	   A^2 -> H(a, U1(d, e))
28.56/10.08	   A^2 -> H(a, c)
28.56/10.08	   A^2 -> H(a, U1(e, k))
28.56/10.08	   A^2 -> H(a, U1(k, e))
28.56/10.08	   A^2 -> H(a, e)
28.56/10.08	   A^2 -> H(a, U1(k, k))
28.56/10.08	
28.56/10.08	The TRS R consists of the following rules:
28.56/10.08	
28.56/10.08	   f(x) -> U1(x, x)
28.56/10.08	   U1(e, x) -> x
28.56/10.08	   a -> c
28.56/10.08	   a -> d
28.56/10.08	   b -> c
28.56/10.08	   b -> d
28.56/10.08	   d -> k
28.56/10.08	   c -> e
28.56/10.08	   c -> k
28.56/10.08	
28.56/10.08	Q is empty.
28.56/10.08	We have to consider all minimal (P,Q,R)-chains.
28.56/10.08	----------------------------------------
28.56/10.08	
28.56/10.08	(1837) TransformationProof (EQUIVALENT)
28.56/10.08	By narrowing [LPAR04] the rule A^2 -> H(a, U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.08	
28.56/10.08	   (A^2 -> H(c, U1(d, k)),A^2 -> H(c, U1(d, k)))
28.56/10.08	   (A^2 -> H(d, U1(d, k)),A^2 -> H(d, U1(d, k)))
28.56/10.08	   (A^2 -> H(a, U1(k, k)),A^2 -> H(a, U1(k, k)))
28.56/10.08	
28.56/10.08	
28.56/10.08	----------------------------------------
28.56/10.08	
28.56/10.08	(1838)
28.56/10.08	Obligation:
28.56/10.08	Q DP problem:
28.56/10.08	The TRS P consists of the following rules:
28.56/10.08	
28.56/10.08	   H(x, x) -> G(x, x, f(k))
28.56/10.08	   G(d, x, x) -> A^2
28.56/10.08	   A^2 -> H(f(c), f(c))
28.56/10.08	   A^2 -> H(f(d), f(d))
28.56/10.08	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.08	   A^2 -> H(f(e), f(e))
28.56/10.08	   A^2 -> H(f(k), f(k))
28.56/10.08	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.08	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.08	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.08	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.08	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.08	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.08	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.08	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(e, b))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.08	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.08	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.08	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.08	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.08	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.08	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.08	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, a), b)
28.56/10.08	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.08	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.08	   A^2 -> H(U1(e, a), c)
28.56/10.08	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.08	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.08	   A^2 -> H(U1(e, a), e)
28.56/10.08	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.08	   A^2 -> H(U1(k, a), b)
28.56/10.08	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, a), c)
28.56/10.08	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.08	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.08	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, d), b)
28.56/10.08	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.08	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.08	   A^2 -> H(U1(c, d), c)
28.56/10.08	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.08	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.08	   A^2 -> H(U1(c, d), e)
28.56/10.08	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, a), d)
28.56/10.08	   A^2 -> H(U1(c, a), k)
28.56/10.08	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.08	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.08	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.08	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.08	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.08	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.08	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.08	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.08	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.08	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.08	   A^2 -> H(U1(d, c), b)
28.56/10.08	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.08	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.08	   A^2 -> H(U1(d, c), c)
28.56/10.08	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.08	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.08	   A^2 -> H(U1(d, c), e)
28.56/10.08	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, a), d)
28.56/10.08	   A^2 -> H(U1(d, a), k)
28.56/10.08	   A^2 -> H(U1(a, e), b)
28.56/10.08	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.08	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.08	   A^2 -> H(U1(a, e), c)
28.56/10.08	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.08	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.08	   A^2 -> H(U1(a, e), e)
28.56/10.08	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.08	   A^2 -> H(U1(a, k), b)
28.56/10.08	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(a, k), c)
28.56/10.08	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.08	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.08	   A^2 -> H(U1(a, k), e)
28.56/10.08	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(a, c), d)
28.56/10.08	   A^2 -> H(U1(a, c), k)
28.56/10.08	   A^2 -> H(U1(a, d), d)
28.56/10.08	   A^2 -> H(U1(a, d), k)
28.56/10.08	   A^2 -> H(k, U1(c, b))
28.56/10.08	   A^2 -> H(k, U1(d, b))
28.56/10.08	   A^2 -> H(k, U1(b, c))
28.56/10.08	   A^2 -> H(k, U1(b, d))
28.56/10.08	   A^2 -> H(k, U1(c, c))
28.56/10.08	   A^2 -> H(k, f(e))
28.56/10.08	   A^2 -> H(k, f(k))
28.56/10.08	   A^2 -> H(k, U1(d, d))
28.56/10.08	   A^2 -> H(c, U1(e, b))
28.56/10.08	   A^2 -> H(c, U1(k, b))
28.56/10.08	   A^2 -> H(c, U1(c, d))
28.56/10.08	   A^2 -> H(c, U1(d, c))
28.56/10.08	   A^2 -> H(c, U1(b, e))
28.56/10.08	   A^2 -> H(c, U1(b, k))
28.56/10.08	   A^2 -> H(c, U1(e, c))
28.56/10.08	   A^2 -> H(c, U1(k, c))
28.56/10.08	   A^2 -> H(c, U1(c, e))
28.56/10.08	   A^2 -> H(c, U1(c, k))
28.56/10.08	   A^2 -> H(c, U1(e, e))
28.56/10.08	   A^2 -> H(c, U1(k, k))
28.56/10.08	   A^2 -> H(c, U1(k, d))
28.56/10.08	   A^2 -> H(c, U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.08	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.08	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.08	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.08	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.08	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.08	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.08	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, c), b)
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.08	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.08	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.08	   A^2 -> H(U1(e, c), e)
28.56/10.08	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.08	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.08	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.08	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.08	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.08	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.08	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.08	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.08	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.08	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.08	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.08	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.08	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.08	   A^2 -> H(U1(k, c), b)
28.56/10.08	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, c), c)
28.56/10.08	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.08	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.08	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, e), b)
28.56/10.08	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.08	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.08	   A^2 -> H(U1(c, e), c)
28.56/10.08	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.08	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.08	   A^2 -> H(U1(c, e), e)
28.56/10.08	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, k), b)
28.56/10.08	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(c, k), c)
28.56/10.08	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.08	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.08	   A^2 -> H(U1(c, k), e)
28.56/10.08	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, c), d)
28.56/10.08	   A^2 -> H(e, U1(e, b))
28.56/10.08	   A^2 -> H(e, U1(c, d))
28.56/10.08	   A^2 -> H(e, U1(d, c))
28.56/10.08	   A^2 -> H(e, U1(b, e))
28.56/10.08	   A^2 -> H(e, U1(b, k))
28.56/10.08	   A^2 -> H(e, U1(e, c))
28.56/10.08	   A^2 -> H(e, U1(c, e))
28.56/10.08	   A^2 -> H(e, U1(c, k))
28.56/10.08	   A^2 -> H(e, U1(e, e))
28.56/10.08	   A^2 -> H(e, U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, e), b)
28.56/10.08	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.08	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.08	   A^2 -> H(U1(e, e), c)
28.56/10.08	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.08	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.08	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.08	   A^2 -> H(f(e), d)
28.56/10.08	   A^2 -> H(f(e), k)
28.56/10.08	   A^2 -> H(U1(k, k), b)
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, k), c)
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.08	   A^2 -> H(f(k), d)
28.56/10.08	   A^2 -> H(f(k), k)
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.08	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.08	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.08	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.08	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.08	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.08	   A^2 -> H(U1(k, d), b)
28.56/10.08	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, d), c)
28.56/10.08	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.08	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.08	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, k), b)
28.56/10.08	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(d, k), c)
28.56/10.08	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.08	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.08	   A^2 -> H(U1(d, k), e)
28.56/10.08	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, d), d)
28.56/10.08	   A^2 -> H(U1(d, d), k)
28.56/10.08	   A^2 -> H(U1(e, c), c)
28.56/10.08	   A^2 -> H(U1(c, c), e)
28.56/10.08	   A^2 -> H(U1(c, c), k)
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.08	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.08	   A^2 -> H(U1(e, e), e)
28.56/10.08	   A^2 -> H(d, U1(e, b))
28.56/10.08	   A^2 -> H(d, U1(k, b))
28.56/10.08	   A^2 -> H(d, U1(c, d))
28.56/10.08	   A^2 -> H(d, U1(d, c))
28.56/10.08	   A^2 -> H(d, U1(b, e))
28.56/10.08	   A^2 -> H(d, U1(b, k))
28.56/10.08	   A^2 -> H(d, U1(e, c))
28.56/10.08	   A^2 -> H(d, U1(k, c))
28.56/10.08	   A^2 -> H(d, U1(c, e))
28.56/10.08	   A^2 -> H(d, U1(c, k))
28.56/10.08	   A^2 -> H(d, U1(e, e))
28.56/10.08	   A^2 -> H(d, U1(k, k))
28.56/10.08	   A^2 -> H(d, U1(k, d))
28.56/10.08	   A^2 -> H(d, U1(d, k))
28.56/10.08	   A^2 -> H(a, b)
28.56/10.08	   A^2 -> H(a, U1(e, d))
28.56/10.08	   A^2 -> H(a, U1(d, e))
28.56/10.08	   A^2 -> H(a, c)
28.56/10.08	   A^2 -> H(a, U1(e, k))
28.56/10.08	   A^2 -> H(a, U1(k, e))
28.56/10.08	   A^2 -> H(a, e)
28.56/10.08	   A^2 -> H(a, U1(k, k))
28.56/10.08	
28.56/10.08	The TRS R consists of the following rules:
28.56/10.08	
28.56/10.08	   f(x) -> U1(x, x)
28.56/10.08	   U1(e, x) -> x
28.56/10.08	   a -> c
28.56/10.08	   a -> d
28.56/10.08	   b -> c
28.56/10.08	   b -> d
28.56/10.08	   d -> k
28.56/10.08	   c -> e
28.56/10.08	   c -> k
28.56/10.08	
28.56/10.08	Q is empty.
28.56/10.08	We have to consider all minimal (P,Q,R)-chains.
28.56/10.08	----------------------------------------
28.56/10.08	
28.56/10.08	(1839) TransformationProof (EQUIVALENT)
28.56/10.08	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.08	
28.56/10.08	   (A^2 -> H(d, U1(e, b)),A^2 -> H(d, U1(e, b)))
28.56/10.08	   (A^2 -> H(U1(e, k), U1(e, b)),A^2 -> H(U1(e, k), U1(e, b)))
28.56/10.08	   (A^2 -> H(U1(e, d), b),A^2 -> H(U1(e, d), b))
28.56/10.08	   (A^2 -> H(U1(e, d), U1(e, c)),A^2 -> H(U1(e, d), U1(e, c)))
28.56/10.08	   (A^2 -> H(U1(e, d), U1(e, d)),A^2 -> H(U1(e, d), U1(e, d)))
28.56/10.08	
28.56/10.08	
28.56/10.08	----------------------------------------
28.56/10.08	
28.56/10.08	(1840)
28.56/10.08	Obligation:
28.56/10.08	Q DP problem:
28.56/10.08	The TRS P consists of the following rules:
28.56/10.08	
28.56/10.08	   H(x, x) -> G(x, x, f(k))
28.56/10.08	   G(d, x, x) -> A^2
28.56/10.08	   A^2 -> H(f(c), f(c))
28.56/10.08	   A^2 -> H(f(d), f(d))
28.56/10.08	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.08	   A^2 -> H(f(e), f(e))
28.56/10.08	   A^2 -> H(f(k), f(k))
28.56/10.08	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.08	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.08	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.08	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.08	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.08	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.08	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.08	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, b))
28.56/10.08	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.08	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.08	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.08	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.08	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.08	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.08	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, a), b)
28.56/10.08	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.08	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.08	   A^2 -> H(U1(e, a), c)
28.56/10.08	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.08	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.08	   A^2 -> H(U1(e, a), e)
28.56/10.08	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.08	   A^2 -> H(U1(k, a), b)
28.56/10.08	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, a), c)
28.56/10.08	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.08	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.08	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, d), b)
28.56/10.08	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.08	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.08	   A^2 -> H(U1(c, d), c)
28.56/10.08	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.08	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.08	   A^2 -> H(U1(c, d), e)
28.56/10.08	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, a), d)
28.56/10.08	   A^2 -> H(U1(c, a), k)
28.56/10.08	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.08	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.08	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.08	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.08	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.08	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.08	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.08	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.08	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.08	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.08	   A^2 -> H(U1(d, c), b)
28.56/10.08	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.08	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.08	   A^2 -> H(U1(d, c), c)
28.56/10.08	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.08	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.08	   A^2 -> H(U1(d, c), e)
28.56/10.08	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, a), d)
28.56/10.08	   A^2 -> H(U1(d, a), k)
28.56/10.08	   A^2 -> H(U1(a, e), b)
28.56/10.08	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.08	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.08	   A^2 -> H(U1(a, e), c)
28.56/10.08	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.08	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.08	   A^2 -> H(U1(a, e), e)
28.56/10.08	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.08	   A^2 -> H(U1(a, k), b)
28.56/10.08	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(a, k), c)
28.56/10.08	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.08	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.08	   A^2 -> H(U1(a, k), e)
28.56/10.08	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(a, c), d)
28.56/10.08	   A^2 -> H(U1(a, c), k)
28.56/10.08	   A^2 -> H(U1(a, d), d)
28.56/10.08	   A^2 -> H(U1(a, d), k)
28.56/10.08	   A^2 -> H(k, U1(c, b))
28.56/10.08	   A^2 -> H(k, U1(d, b))
28.56/10.08	   A^2 -> H(k, U1(b, c))
28.56/10.08	   A^2 -> H(k, U1(b, d))
28.56/10.08	   A^2 -> H(k, U1(c, c))
28.56/10.08	   A^2 -> H(k, f(e))
28.56/10.08	   A^2 -> H(k, f(k))
28.56/10.08	   A^2 -> H(k, U1(d, d))
28.56/10.08	   A^2 -> H(c, U1(e, b))
28.56/10.08	   A^2 -> H(c, U1(k, b))
28.56/10.08	   A^2 -> H(c, U1(c, d))
28.56/10.08	   A^2 -> H(c, U1(d, c))
28.56/10.08	   A^2 -> H(c, U1(b, e))
28.56/10.08	   A^2 -> H(c, U1(b, k))
28.56/10.08	   A^2 -> H(c, U1(e, c))
28.56/10.08	   A^2 -> H(c, U1(k, c))
28.56/10.08	   A^2 -> H(c, U1(c, e))
28.56/10.08	   A^2 -> H(c, U1(c, k))
28.56/10.08	   A^2 -> H(c, U1(e, e))
28.56/10.08	   A^2 -> H(c, U1(k, k))
28.56/10.08	   A^2 -> H(c, U1(k, d))
28.56/10.08	   A^2 -> H(c, U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.08	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.08	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.08	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.08	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.08	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.08	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.08	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, c), b)
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.08	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.08	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.08	   A^2 -> H(U1(e, c), e)
28.56/10.08	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.08	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.08	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.08	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.08	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.08	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.08	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.08	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.08	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.08	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.08	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.08	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.08	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.08	   A^2 -> H(U1(k, c), b)
28.56/10.08	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, c), c)
28.56/10.08	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.08	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.08	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, e), b)
28.56/10.08	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.08	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.08	   A^2 -> H(U1(c, e), c)
28.56/10.08	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.08	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.08	   A^2 -> H(U1(c, e), e)
28.56/10.08	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, k), b)
28.56/10.08	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(c, k), c)
28.56/10.08	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.08	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.08	   A^2 -> H(U1(c, k), e)
28.56/10.08	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, c), d)
28.56/10.08	   A^2 -> H(e, U1(e, b))
28.56/10.08	   A^2 -> H(e, U1(c, d))
28.56/10.08	   A^2 -> H(e, U1(d, c))
28.56/10.08	   A^2 -> H(e, U1(b, e))
28.56/10.08	   A^2 -> H(e, U1(b, k))
28.56/10.08	   A^2 -> H(e, U1(e, c))
28.56/10.08	   A^2 -> H(e, U1(c, e))
28.56/10.08	   A^2 -> H(e, U1(c, k))
28.56/10.08	   A^2 -> H(e, U1(e, e))
28.56/10.08	   A^2 -> H(e, U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, e), b)
28.56/10.08	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.08	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.08	   A^2 -> H(U1(e, e), c)
28.56/10.08	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.08	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.08	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.08	   A^2 -> H(f(e), d)
28.56/10.08	   A^2 -> H(f(e), k)
28.56/10.08	   A^2 -> H(U1(k, k), b)
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, k), c)
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.08	   A^2 -> H(f(k), d)
28.56/10.08	   A^2 -> H(f(k), k)
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.08	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.08	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.08	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.08	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.08	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.08	   A^2 -> H(U1(k, d), b)
28.56/10.08	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, d), c)
28.56/10.08	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.08	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.08	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, k), b)
28.56/10.08	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(d, k), c)
28.56/10.08	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.08	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.08	   A^2 -> H(U1(d, k), e)
28.56/10.08	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, d), d)
28.56/10.08	   A^2 -> H(U1(d, d), k)
28.56/10.08	   A^2 -> H(U1(e, c), c)
28.56/10.08	   A^2 -> H(U1(c, c), e)
28.56/10.08	   A^2 -> H(U1(c, c), k)
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.08	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.08	   A^2 -> H(U1(e, e), e)
28.56/10.08	   A^2 -> H(d, U1(e, b))
28.56/10.08	   A^2 -> H(d, U1(k, b))
28.56/10.08	   A^2 -> H(d, U1(c, d))
28.56/10.08	   A^2 -> H(d, U1(d, c))
28.56/10.08	   A^2 -> H(d, U1(b, e))
28.56/10.08	   A^2 -> H(d, U1(b, k))
28.56/10.08	   A^2 -> H(d, U1(e, c))
28.56/10.08	   A^2 -> H(d, U1(k, c))
28.56/10.08	   A^2 -> H(d, U1(c, e))
28.56/10.08	   A^2 -> H(d, U1(c, k))
28.56/10.08	   A^2 -> H(d, U1(e, e))
28.56/10.08	   A^2 -> H(d, U1(k, k))
28.56/10.08	   A^2 -> H(d, U1(k, d))
28.56/10.08	   A^2 -> H(d, U1(d, k))
28.56/10.08	   A^2 -> H(a, b)
28.56/10.08	   A^2 -> H(a, U1(e, d))
28.56/10.08	   A^2 -> H(a, U1(d, e))
28.56/10.08	   A^2 -> H(a, c)
28.56/10.08	   A^2 -> H(a, U1(e, k))
28.56/10.08	   A^2 -> H(a, U1(k, e))
28.56/10.08	   A^2 -> H(a, e)
28.56/10.08	   A^2 -> H(a, U1(k, k))
28.56/10.08	   A^2 -> H(U1(e, d), b)
28.56/10.08	   A^2 -> H(U1(e, d), U1(e, d))
28.56/10.08	
28.56/10.08	The TRS R consists of the following rules:
28.56/10.08	
28.56/10.08	   f(x) -> U1(x, x)
28.56/10.08	   U1(e, x) -> x
28.56/10.08	   a -> c
28.56/10.08	   a -> d
28.56/10.08	   b -> c
28.56/10.08	   b -> d
28.56/10.08	   d -> k
28.56/10.08	   c -> e
28.56/10.08	   c -> k
28.56/10.08	
28.56/10.08	Q is empty.
28.56/10.08	We have to consider all minimal (P,Q,R)-chains.
28.56/10.08	----------------------------------------
28.56/10.08	
28.56/10.08	(1841) TransformationProof (EQUIVALENT)
28.56/10.08	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.08	
28.56/10.08	   (A^2 -> H(d, U1(k, b)),A^2 -> H(d, U1(k, b)))
28.56/10.08	   (A^2 -> H(U1(e, k), U1(k, b)),A^2 -> H(U1(e, k), U1(k, b)))
28.56/10.08	   (A^2 -> H(U1(e, d), U1(k, c)),A^2 -> H(U1(e, d), U1(k, c)))
28.56/10.08	   (A^2 -> H(U1(e, d), U1(k, d)),A^2 -> H(U1(e, d), U1(k, d)))
28.56/10.08	
28.56/10.08	
28.56/10.08	----------------------------------------
28.56/10.08	
28.56/10.08	(1842)
28.56/10.08	Obligation:
28.56/10.08	Q DP problem:
28.56/10.08	The TRS P consists of the following rules:
28.56/10.08	
28.56/10.08	   H(x, x) -> G(x, x, f(k))
28.56/10.08	   G(d, x, x) -> A^2
28.56/10.08	   A^2 -> H(f(c), f(c))
28.56/10.08	   A^2 -> H(f(d), f(d))
28.56/10.08	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.08	   A^2 -> H(f(e), f(e))
28.56/10.08	   A^2 -> H(f(k), f(k))
28.56/10.08	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.08	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.08	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.08	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.08	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.08	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.08	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.08	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(c, d))
28.56/10.08	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.08	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.08	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.08	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.08	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.08	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, a), b)
28.56/10.08	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.08	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.08	   A^2 -> H(U1(e, a), c)
28.56/10.08	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.08	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.08	   A^2 -> H(U1(e, a), e)
28.56/10.08	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.08	   A^2 -> H(U1(k, a), b)
28.56/10.08	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, a), c)
28.56/10.08	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.08	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.08	   A^2 -> H(U1(k, a), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, d), b)
28.56/10.08	   A^2 -> H(U1(c, d), U1(e, d))
28.56/10.08	   A^2 -> H(U1(c, d), U1(d, e))
28.56/10.08	   A^2 -> H(U1(c, d), c)
28.56/10.08	   A^2 -> H(U1(c, d), U1(e, k))
28.56/10.08	   A^2 -> H(U1(c, d), U1(k, e))
28.56/10.08	   A^2 -> H(U1(c, d), e)
28.56/10.08	   A^2 -> H(U1(c, d), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, a), d)
28.56/10.08	   A^2 -> H(U1(c, a), k)
28.56/10.08	   A^2 -> H(U1(d, e), U1(e, b))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, b))
28.56/10.08	   A^2 -> H(U1(d, e), U1(c, d))
28.56/10.08	   A^2 -> H(U1(d, e), U1(d, c))
28.56/10.08	   A^2 -> H(U1(d, e), U1(b, e))
28.56/10.08	   A^2 -> H(U1(d, e), U1(b, k))
28.56/10.08	   A^2 -> H(U1(d, e), U1(e, c))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, c))
28.56/10.08	   A^2 -> H(U1(d, e), U1(c, e))
28.56/10.08	   A^2 -> H(U1(d, e), U1(c, k))
28.56/10.08	   A^2 -> H(U1(d, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, e), U1(k, d))
28.56/10.08	   A^2 -> H(U1(d, e), U1(d, k))
28.56/10.08	   A^2 -> H(U1(d, c), b)
28.56/10.08	   A^2 -> H(U1(d, c), U1(e, d))
28.56/10.08	   A^2 -> H(U1(d, c), U1(d, e))
28.56/10.08	   A^2 -> H(U1(d, c), c)
28.56/10.08	   A^2 -> H(U1(d, c), U1(e, k))
28.56/10.08	   A^2 -> H(U1(d, c), U1(k, e))
28.56/10.08	   A^2 -> H(U1(d, c), e)
28.56/10.08	   A^2 -> H(U1(d, c), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, a), d)
28.56/10.08	   A^2 -> H(U1(d, a), k)
28.56/10.08	   A^2 -> H(U1(a, e), b)
28.56/10.08	   A^2 -> H(U1(a, e), U1(e, d))
28.56/10.08	   A^2 -> H(U1(a, e), U1(d, e))
28.56/10.08	   A^2 -> H(U1(a, e), c)
28.56/10.08	   A^2 -> H(U1(a, e), U1(e, k))
28.56/10.08	   A^2 -> H(U1(a, e), U1(k, e))
28.56/10.08	   A^2 -> H(U1(a, e), e)
28.56/10.08	   A^2 -> H(U1(a, e), U1(k, k))
28.56/10.08	   A^2 -> H(U1(a, k), b)
28.56/10.08	   A^2 -> H(U1(a, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(a, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(a, k), c)
28.56/10.08	   A^2 -> H(U1(a, k), U1(e, k))
28.56/10.08	   A^2 -> H(U1(a, k), U1(k, e))
28.56/10.08	   A^2 -> H(U1(a, k), e)
28.56/10.08	   A^2 -> H(U1(a, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(a, c), d)
28.56/10.08	   A^2 -> H(U1(a, c), k)
28.56/10.08	   A^2 -> H(U1(a, d), d)
28.56/10.08	   A^2 -> H(U1(a, d), k)
28.56/10.08	   A^2 -> H(k, U1(c, b))
28.56/10.08	   A^2 -> H(k, U1(d, b))
28.56/10.08	   A^2 -> H(k, U1(b, c))
28.56/10.08	   A^2 -> H(k, U1(b, d))
28.56/10.08	   A^2 -> H(k, U1(c, c))
28.56/10.08	   A^2 -> H(k, f(e))
28.56/10.08	   A^2 -> H(k, f(k))
28.56/10.08	   A^2 -> H(k, U1(d, d))
28.56/10.08	   A^2 -> H(c, U1(e, b))
28.56/10.08	   A^2 -> H(c, U1(k, b))
28.56/10.08	   A^2 -> H(c, U1(c, d))
28.56/10.08	   A^2 -> H(c, U1(d, c))
28.56/10.08	   A^2 -> H(c, U1(b, e))
28.56/10.08	   A^2 -> H(c, U1(b, k))
28.56/10.08	   A^2 -> H(c, U1(e, c))
28.56/10.08	   A^2 -> H(c, U1(k, c))
28.56/10.08	   A^2 -> H(c, U1(c, e))
28.56/10.08	   A^2 -> H(c, U1(c, k))
28.56/10.08	   A^2 -> H(c, U1(e, e))
28.56/10.08	   A^2 -> H(c, U1(k, k))
28.56/10.08	   A^2 -> H(c, U1(k, d))
28.56/10.08	   A^2 -> H(c, U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(e, b))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, b))
28.56/10.08	   A^2 -> H(U1(e, k), U1(c, d))
28.56/10.08	   A^2 -> H(U1(e, k), U1(d, c))
28.56/10.08	   A^2 -> H(U1(e, k), U1(b, e))
28.56/10.08	   A^2 -> H(U1(e, k), U1(b, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(e, c))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, c))
28.56/10.08	   A^2 -> H(U1(e, k), U1(c, e))
28.56/10.08	   A^2 -> H(U1(e, k), U1(c, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(e, e))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(e, k), U1(k, d))
28.56/10.08	   A^2 -> H(U1(e, k), U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, c), b)
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, d))
28.56/10.08	   A^2 -> H(U1(e, c), U1(d, e))
28.56/10.08	   A^2 -> H(U1(e, c), U1(k, e))
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, k))
28.56/10.08	   A^2 -> H(U1(e, c), e)
28.56/10.08	   A^2 -> H(U1(e, c), U1(k, k))
28.56/10.08	   A^2 -> H(U1(k, e), U1(e, b))
28.56/10.08	   A^2 -> H(U1(k, e), U1(k, b))
28.56/10.08	   A^2 -> H(U1(k, e), U1(c, d))
28.56/10.08	   A^2 -> H(U1(k, e), U1(d, c))
28.56/10.08	   A^2 -> H(U1(k, e), U1(b, e))
28.56/10.08	   A^2 -> H(U1(k, e), U1(b, k))
28.56/10.08	   A^2 -> H(U1(k, e), U1(e, c))
28.56/10.08	   A^2 -> H(U1(k, e), U1(k, c))
28.56/10.08	   A^2 -> H(U1(k, e), U1(c, e))
28.56/10.08	   A^2 -> H(U1(k, e), U1(c, k))
28.56/10.08	   A^2 -> H(U1(k, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, e), U1(k, d))
28.56/10.08	   A^2 -> H(U1(k, e), U1(d, k))
28.56/10.08	   A^2 -> H(U1(k, c), b)
28.56/10.08	   A^2 -> H(U1(k, c), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, c), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, c), c)
28.56/10.08	   A^2 -> H(U1(k, c), U1(e, k))
28.56/10.08	   A^2 -> H(U1(k, c), U1(k, e))
28.56/10.08	   A^2 -> H(U1(k, c), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, e), b)
28.56/10.08	   A^2 -> H(U1(c, e), U1(e, d))
28.56/10.08	   A^2 -> H(U1(c, e), U1(d, e))
28.56/10.08	   A^2 -> H(U1(c, e), c)
28.56/10.08	   A^2 -> H(U1(c, e), U1(e, k))
28.56/10.08	   A^2 -> H(U1(c, e), U1(k, e))
28.56/10.08	   A^2 -> H(U1(c, e), e)
28.56/10.08	   A^2 -> H(U1(c, e), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, k), b)
28.56/10.08	   A^2 -> H(U1(c, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(c, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(c, k), c)
28.56/10.08	   A^2 -> H(U1(c, k), U1(e, k))
28.56/10.08	   A^2 -> H(U1(c, k), U1(k, e))
28.56/10.08	   A^2 -> H(U1(c, k), e)
28.56/10.08	   A^2 -> H(U1(c, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(c, c), d)
28.56/10.08	   A^2 -> H(e, U1(e, b))
28.56/10.08	   A^2 -> H(e, U1(c, d))
28.56/10.08	   A^2 -> H(e, U1(d, c))
28.56/10.08	   A^2 -> H(e, U1(b, e))
28.56/10.08	   A^2 -> H(e, U1(b, k))
28.56/10.08	   A^2 -> H(e, U1(e, c))
28.56/10.08	   A^2 -> H(e, U1(c, e))
28.56/10.08	   A^2 -> H(e, U1(c, k))
28.56/10.08	   A^2 -> H(e, U1(e, e))
28.56/10.08	   A^2 -> H(e, U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, e), b)
28.56/10.08	   A^2 -> H(U1(e, e), U1(e, d))
28.56/10.08	   A^2 -> H(U1(e, e), U1(d, e))
28.56/10.08	   A^2 -> H(U1(e, e), c)
28.56/10.08	   A^2 -> H(U1(e, e), U1(e, k))
28.56/10.08	   A^2 -> H(U1(e, e), U1(k, e))
28.56/10.08	   A^2 -> H(U1(e, e), U1(k, k))
28.56/10.08	   A^2 -> H(f(e), d)
28.56/10.08	   A^2 -> H(f(e), k)
28.56/10.08	   A^2 -> H(U1(k, k), b)
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, k), c)
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, k))
28.56/10.08	   A^2 -> H(f(k), d)
28.56/10.08	   A^2 -> H(f(k), k)
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, b))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, b))
28.56/10.08	   A^2 -> H(U1(k, k), U1(c, d))
28.56/10.08	   A^2 -> H(U1(k, k), U1(d, c))
28.56/10.08	   A^2 -> H(U1(k, k), U1(b, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(b, k))
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, c))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, c))
28.56/10.08	   A^2 -> H(U1(k, k), U1(c, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(c, k))
28.56/10.08	   A^2 -> H(U1(k, k), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, d))
28.56/10.08	   A^2 -> H(U1(k, k), U1(d, k))
28.56/10.08	   A^2 -> H(U1(k, d), b)
28.56/10.08	   A^2 -> H(U1(k, d), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, d), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, d), c)
28.56/10.08	   A^2 -> H(U1(k, d), U1(e, k))
28.56/10.08	   A^2 -> H(U1(k, d), U1(k, e))
28.56/10.08	   A^2 -> H(U1(k, d), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, k), b)
28.56/10.08	   A^2 -> H(U1(d, k), U1(e, d))
28.56/10.08	   A^2 -> H(U1(d, k), U1(d, e))
28.56/10.08	   A^2 -> H(U1(d, k), c)
28.56/10.08	   A^2 -> H(U1(d, k), U1(e, k))
28.56/10.08	   A^2 -> H(U1(d, k), U1(k, e))
28.56/10.08	   A^2 -> H(U1(d, k), e)
28.56/10.08	   A^2 -> H(U1(d, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(d, d), d)
28.56/10.08	   A^2 -> H(U1(d, d), k)
28.56/10.08	   A^2 -> H(U1(e, c), c)
28.56/10.08	   A^2 -> H(U1(c, c), e)
28.56/10.08	   A^2 -> H(U1(c, c), k)
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, c), U1(e, e))
28.56/10.08	   A^2 -> H(U1(c, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(c, k), U1(e, e))
28.56/10.08	   A^2 -> H(U1(e, e), e)
28.56/10.08	   A^2 -> H(d, U1(e, b))
28.56/10.08	   A^2 -> H(d, U1(k, b))
28.56/10.08	   A^2 -> H(d, U1(c, d))
28.56/10.08	   A^2 -> H(d, U1(d, c))
28.56/10.08	   A^2 -> H(d, U1(b, e))
28.56/10.08	   A^2 -> H(d, U1(b, k))
28.56/10.08	   A^2 -> H(d, U1(e, c))
28.56/10.08	   A^2 -> H(d, U1(k, c))
28.56/10.08	   A^2 -> H(d, U1(c, e))
28.56/10.08	   A^2 -> H(d, U1(c, k))
28.56/10.08	   A^2 -> H(d, U1(e, e))
28.56/10.08	   A^2 -> H(d, U1(k, k))
28.56/10.08	   A^2 -> H(d, U1(k, d))
28.56/10.08	   A^2 -> H(d, U1(d, k))
28.56/10.08	   A^2 -> H(a, b)
28.56/10.08	   A^2 -> H(a, U1(e, d))
28.56/10.08	   A^2 -> H(a, U1(d, e))
28.56/10.08	   A^2 -> H(a, c)
28.56/10.08	   A^2 -> H(a, U1(e, k))
28.56/10.08	   A^2 -> H(a, U1(k, e))
28.56/10.08	   A^2 -> H(a, e)
28.56/10.08	   A^2 -> H(a, U1(k, k))
28.56/10.08	   A^2 -> H(U1(e, d), b)
28.56/10.08	   A^2 -> H(U1(e, d), U1(e, d))
28.56/10.08	
28.56/10.08	The TRS R consists of the following rules:
28.56/10.08	
28.56/10.08	   f(x) -> U1(x, x)
28.56/10.08	   U1(e, x) -> x
28.56/10.08	   a -> c
28.56/10.08	   a -> d
28.56/10.08	   b -> c
28.56/10.08	   b -> d
28.56/10.08	   d -> k
28.56/10.08	   c -> e
28.56/10.08	   c -> k
28.56/10.08	
28.56/10.08	Q is empty.
28.56/10.08	We have to consider all minimal (P,Q,R)-chains.
28.56/10.08	----------------------------------------
28.56/10.08	
28.56/10.08	(1843) TransformationProof (EQUIVALENT)
28.56/10.08	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.56/10.08	
28.56/10.08	   (A^2 -> H(d, U1(c, d)),A^2 -> H(d, U1(c, d)))
28.56/10.08	   (A^2 -> H(U1(e, k), U1(c, d)),A^2 -> H(U1(e, k), U1(c, d)))
28.56/10.08	   (A^2 -> H(U1(e, d), U1(e, d)),A^2 -> H(U1(e, d), U1(e, d)))
28.56/10.08	   (A^2 -> H(U1(e, d), U1(k, d)),A^2 -> H(U1(e, d), U1(k, d)))
28.56/10.08	   (A^2 -> H(U1(e, d), U1(c, k)),A^2 -> H(U1(e, d), U1(c, k)))
28.56/10.08	
28.56/10.08	
28.56/10.08	----------------------------------------
28.56/10.08	
28.56/10.08	(1844)
28.56/10.08	Obligation:
28.56/10.08	Q DP problem:
28.56/10.08	The TRS P consists of the following rules:
28.56/10.08	
28.56/10.08	   H(x, x) -> G(x, x, f(k))
28.56/10.08	   G(d, x, x) -> A^2
28.56/10.08	   A^2 -> H(f(c), f(c))
28.56/10.08	   A^2 -> H(f(d), f(d))
28.56/10.08	   A^2 -> H(U1(c, c), U1(c, c))
28.56/10.08	   A^2 -> H(f(e), f(e))
28.56/10.08	   A^2 -> H(f(k), f(k))
28.56/10.08	   A^2 -> H(U1(d, d), U1(d, d))
28.56/10.08	   A^2 -> H(U1(c, d), U1(c, d))
28.56/10.08	   A^2 -> H(U1(d, c), U1(d, c))
28.56/10.08	   A^2 -> H(U1(e, c), U1(e, c))
28.56/10.08	   A^2 -> H(U1(k, c), U1(k, c))
28.56/10.08	   A^2 -> H(U1(c, e), U1(c, e))
28.56/10.08	   A^2 -> H(U1(c, k), U1(c, k))
28.56/10.08	   A^2 -> H(U1(e, e), U1(e, e))
28.56/10.08	   A^2 -> H(U1(k, k), U1(k, k))
28.56/10.08	   A^2 -> H(U1(k, d), U1(k, d))
28.56/10.08	   A^2 -> H(U1(d, k), U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(d, c))
28.56/10.08	   A^2 -> H(U1(e, d), U1(b, e))
28.56/10.08	   A^2 -> H(U1(e, d), U1(b, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(e, c))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, c))
28.56/10.08	   A^2 -> H(U1(e, d), U1(c, e))
28.56/10.08	   A^2 -> H(U1(e, d), U1(c, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(e, e))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, k))
28.56/10.08	   A^2 -> H(U1(e, d), U1(k, d))
28.56/10.08	   A^2 -> H(U1(e, d), U1(d, k))
28.56/10.08	   A^2 -> H(U1(e, a), b)
28.56/10.08	   A^2 -> H(U1(e, a), U1(e, d))
28.56/10.08	   A^2 -> H(U1(e, a), U1(d, e))
28.56/10.08	   A^2 -> H(U1(e, a), c)
28.56/10.08	   A^2 -> H(U1(e, a), U1(e, k))
28.56/10.08	   A^2 -> H(U1(e, a), U1(k, e))
28.56/10.08	   A^2 -> H(U1(e, a), e)
28.56/10.08	   A^2 -> H(U1(e, a), U1(k, k))
28.56/10.08	   A^2 -> H(U1(k, a), b)
28.56/10.08	   A^2 -> H(U1(k, a), U1(e, d))
28.56/10.08	   A^2 -> H(U1(k, a), U1(d, e))
28.56/10.08	   A^2 -> H(U1(k, a), c)
28.56/10.08	   A^2 -> H(U1(k, a), U1(e, k))
28.56/10.08	   A^2 -> H(U1(k, a), U1(k, e))
28.56/10.08	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.08	   A^2 -> H(U1(c, d), b)
28.57/10.08	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.08	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.08	   A^2 -> H(U1(c, d), c)
28.57/10.08	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.08	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.08	   A^2 -> H(U1(c, d), e)
28.57/10.08	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.08	   A^2 -> H(U1(c, a), d)
28.57/10.08	   A^2 -> H(U1(c, a), k)
28.57/10.08	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.08	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.08	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.08	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.08	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.08	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.08	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.08	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.08	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.08	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.08	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.08	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.08	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.08	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.08	   A^2 -> H(U1(d, c), b)
28.57/10.08	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.08	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.08	   A^2 -> H(U1(d, c), c)
28.57/10.08	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.08	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.08	   A^2 -> H(U1(d, c), e)
28.57/10.08	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.08	   A^2 -> H(U1(d, a), d)
28.57/10.08	   A^2 -> H(U1(d, a), k)
28.57/10.08	   A^2 -> H(U1(a, e), b)
28.57/10.08	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.08	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.08	   A^2 -> H(U1(a, e), c)
28.57/10.08	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.08	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.08	   A^2 -> H(U1(a, e), e)
28.57/10.08	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.08	   A^2 -> H(U1(a, k), b)
28.57/10.08	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.08	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.08	   A^2 -> H(U1(a, k), c)
28.57/10.08	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.08	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.08	   A^2 -> H(U1(a, k), e)
28.57/10.08	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.08	   A^2 -> H(U1(a, c), d)
28.57/10.08	   A^2 -> H(U1(a, c), k)
28.57/10.08	   A^2 -> H(U1(a, d), d)
28.57/10.08	   A^2 -> H(U1(a, d), k)
28.57/10.08	   A^2 -> H(k, U1(c, b))
28.57/10.08	   A^2 -> H(k, U1(d, b))
28.57/10.08	   A^2 -> H(k, U1(b, c))
28.57/10.08	   A^2 -> H(k, U1(b, d))
28.57/10.08	   A^2 -> H(k, U1(c, c))
28.57/10.08	   A^2 -> H(k, f(e))
28.57/10.08	   A^2 -> H(k, f(k))
28.57/10.08	   A^2 -> H(k, U1(d, d))
28.57/10.08	   A^2 -> H(c, U1(e, b))
28.57/10.08	   A^2 -> H(c, U1(k, b))
28.57/10.08	   A^2 -> H(c, U1(c, d))
28.57/10.08	   A^2 -> H(c, U1(d, c))
28.57/10.08	   A^2 -> H(c, U1(b, e))
28.57/10.08	   A^2 -> H(c, U1(b, k))
28.57/10.08	   A^2 -> H(c, U1(e, c))
28.57/10.08	   A^2 -> H(c, U1(k, c))
28.57/10.08	   A^2 -> H(c, U1(c, e))
28.57/10.08	   A^2 -> H(c, U1(c, k))
28.57/10.08	   A^2 -> H(c, U1(e, e))
28.57/10.08	   A^2 -> H(c, U1(k, k))
28.57/10.08	   A^2 -> H(c, U1(k, d))
28.57/10.08	   A^2 -> H(c, U1(d, k))
28.57/10.08	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.08	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.08	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.08	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.08	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.08	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.08	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.08	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.08	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.08	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.08	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.08	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.08	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.08	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.08	   A^2 -> H(U1(e, c), b)
28.57/10.08	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.08	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.08	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.08	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.08	   A^2 -> H(U1(e, c), e)
28.57/10.08	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.08	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.08	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.08	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.08	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.08	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.08	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.08	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.08	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.08	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.08	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.08	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.08	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.08	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.08	   A^2 -> H(U1(k, c), b)
28.57/10.08	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.08	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.08	   A^2 -> H(U1(k, c), c)
28.57/10.08	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.08	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.08	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.08	   A^2 -> H(U1(c, e), b)
28.57/10.08	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.08	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.08	   A^2 -> H(U1(c, e), c)
28.57/10.08	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.08	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.08	   A^2 -> H(U1(c, e), e)
28.57/10.08	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.08	   A^2 -> H(U1(c, k), b)
28.57/10.08	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.08	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.08	   A^2 -> H(U1(c, k), c)
28.57/10.08	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.08	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.08	   A^2 -> H(U1(c, k), e)
28.57/10.08	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.08	   A^2 -> H(U1(c, c), d)
28.57/10.08	   A^2 -> H(e, U1(e, b))
28.57/10.08	   A^2 -> H(e, U1(c, d))
28.57/10.08	   A^2 -> H(e, U1(d, c))
28.57/10.08	   A^2 -> H(e, U1(b, e))
28.57/10.08	   A^2 -> H(e, U1(b, k))
28.57/10.08	   A^2 -> H(e, U1(e, c))
28.57/10.08	   A^2 -> H(e, U1(c, e))
28.57/10.08	   A^2 -> H(e, U1(c, k))
28.57/10.08	   A^2 -> H(e, U1(e, e))
28.57/10.08	   A^2 -> H(e, U1(d, k))
28.57/10.08	   A^2 -> H(U1(e, e), b)
28.57/10.08	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.08	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.08	   A^2 -> H(U1(e, e), c)
28.57/10.08	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.08	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.08	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.08	   A^2 -> H(f(e), d)
28.57/10.08	   A^2 -> H(f(e), k)
28.57/10.08	   A^2 -> H(U1(k, k), b)
28.57/10.08	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.08	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.08	   A^2 -> H(U1(k, k), c)
28.57/10.08	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.08	   A^2 -> H(f(k), d)
28.57/10.08	   A^2 -> H(f(k), k)
28.57/10.08	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.08	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.08	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.08	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.08	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.08	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.08	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.08	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.08	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.08	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.08	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.08	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.08	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.08	   A^2 -> H(U1(k, d), b)
28.57/10.08	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.08	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.08	   A^2 -> H(U1(k, d), c)
28.57/10.08	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.08	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.08	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.08	   A^2 -> H(U1(d, k), b)
28.57/10.08	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.08	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.08	   A^2 -> H(U1(d, k), c)
28.57/10.08	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.08	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.08	   A^2 -> H(U1(d, k), e)
28.57/10.08	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.08	   A^2 -> H(U1(d, d), d)
28.57/10.08	   A^2 -> H(U1(d, d), k)
28.57/10.08	   A^2 -> H(U1(e, c), c)
28.57/10.08	   A^2 -> H(U1(c, c), e)
28.57/10.08	   A^2 -> H(U1(c, c), k)
28.57/10.08	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.08	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.08	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.08	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.08	   A^2 -> H(U1(e, e), e)
28.57/10.08	   A^2 -> H(d, U1(e, b))
28.57/10.08	   A^2 -> H(d, U1(k, b))
28.57/10.08	   A^2 -> H(d, U1(c, d))
28.57/10.08	   A^2 -> H(d, U1(d, c))
28.57/10.08	   A^2 -> H(d, U1(b, e))
28.57/10.08	   A^2 -> H(d, U1(b, k))
28.57/10.08	   A^2 -> H(d, U1(e, c))
28.57/10.08	   A^2 -> H(d, U1(k, c))
28.57/10.08	   A^2 -> H(d, U1(c, e))
28.57/10.08	   A^2 -> H(d, U1(c, k))
28.57/10.08	   A^2 -> H(d, U1(e, e))
28.57/10.08	   A^2 -> H(d, U1(k, k))
28.57/10.08	   A^2 -> H(d, U1(k, d))
28.57/10.08	   A^2 -> H(d, U1(d, k))
28.57/10.08	   A^2 -> H(a, b)
28.57/10.08	   A^2 -> H(a, U1(e, d))
28.57/10.08	   A^2 -> H(a, U1(d, e))
28.57/10.08	   A^2 -> H(a, c)
28.57/10.08	   A^2 -> H(a, U1(e, k))
28.57/10.08	   A^2 -> H(a, U1(k, e))
28.57/10.08	   A^2 -> H(a, e)
28.57/10.08	   A^2 -> H(a, U1(k, k))
28.57/10.08	   A^2 -> H(U1(e, d), b)
28.57/10.08	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.08	
28.57/10.08	The TRS R consists of the following rules:
28.57/10.08	
28.57/10.08	   f(x) -> U1(x, x)
28.57/10.08	   U1(e, x) -> x
28.57/10.08	   a -> c
28.57/10.08	   a -> d
28.57/10.08	   b -> c
28.57/10.08	   b -> d
28.57/10.08	   d -> k
28.57/10.08	   c -> e
28.57/10.08	   c -> k
28.57/10.08	
28.57/10.08	Q is empty.
28.57/10.08	We have to consider all minimal (P,Q,R)-chains.
28.57/10.08	----------------------------------------
28.57/10.08	
28.57/10.08	(1845) TransformationProof (EQUIVALENT)
28.57/10.08	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.08	
28.57/10.08	   (A^2 -> H(d, U1(d, c)),A^2 -> H(d, U1(d, c)))
28.57/10.08	   (A^2 -> H(U1(e, k), U1(d, c)),A^2 -> H(U1(e, k), U1(d, c)))
28.57/10.08	   (A^2 -> H(U1(e, d), U1(k, c)),A^2 -> H(U1(e, d), U1(k, c)))
28.57/10.08	   (A^2 -> H(U1(e, d), U1(d, e)),A^2 -> H(U1(e, d), U1(d, e)))
28.57/10.08	   (A^2 -> H(U1(e, d), U1(d, k)),A^2 -> H(U1(e, d), U1(d, k)))
28.57/10.08	
28.57/10.08	
28.57/10.08	----------------------------------------
28.57/10.08	
28.57/10.08	(1846)
28.57/10.08	Obligation:
28.57/10.08	Q DP problem:
28.57/10.08	The TRS P consists of the following rules:
28.57/10.08	
28.57/10.08	   H(x, x) -> G(x, x, f(k))
28.57/10.08	   G(d, x, x) -> A^2
28.57/10.08	   A^2 -> H(f(c), f(c))
28.57/10.08	   A^2 -> H(f(d), f(d))
28.57/10.08	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.08	   A^2 -> H(f(e), f(e))
28.57/10.08	   A^2 -> H(f(k), f(k))
28.57/10.08	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.08	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.08	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.08	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.08	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.08	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.08	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.08	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.08	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.08	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.08	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.08	   A^2 -> H(U1(e, d), U1(b, e))
28.57/10.08	   A^2 -> H(U1(e, d), U1(b, k))
28.57/10.08	   A^2 -> H(U1(e, d), U1(e, c))
28.57/10.08	   A^2 -> H(U1(e, d), U1(k, c))
28.57/10.08	   A^2 -> H(U1(e, d), U1(c, e))
28.57/10.08	   A^2 -> H(U1(e, d), U1(c, k))
28.57/10.08	   A^2 -> H(U1(e, d), U1(e, e))
28.57/10.08	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.08	   A^2 -> H(U1(e, d), U1(k, d))
28.57/10.08	   A^2 -> H(U1(e, d), U1(d, k))
28.57/10.08	   A^2 -> H(U1(e, a), b)
28.57/10.08	   A^2 -> H(U1(e, a), U1(e, d))
28.57/10.08	   A^2 -> H(U1(e, a), U1(d, e))
28.57/10.08	   A^2 -> H(U1(e, a), c)
28.57/10.08	   A^2 -> H(U1(e, a), U1(e, k))
28.57/10.08	   A^2 -> H(U1(e, a), U1(k, e))
28.57/10.08	   A^2 -> H(U1(e, a), e)
28.57/10.08	   A^2 -> H(U1(e, a), U1(k, k))
28.57/10.08	   A^2 -> H(U1(k, a), b)
28.57/10.08	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.08	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.08	   A^2 -> H(U1(k, a), c)
28.57/10.08	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.08	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.08	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.08	   A^2 -> H(U1(c, d), b)
28.57/10.08	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.08	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.08	   A^2 -> H(U1(c, d), c)
28.57/10.08	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.08	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.08	   A^2 -> H(U1(c, d), e)
28.57/10.08	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.08	   A^2 -> H(U1(c, a), d)
28.57/10.08	   A^2 -> H(U1(c, a), k)
28.57/10.08	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.08	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.08	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.08	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.08	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.08	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.08	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.08	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.08	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.08	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.08	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.08	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.08	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.08	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.08	   A^2 -> H(U1(d, c), b)
28.57/10.08	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.08	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.08	   A^2 -> H(U1(d, c), c)
28.57/10.08	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.08	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.08	   A^2 -> H(U1(d, c), e)
28.57/10.08	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.08	   A^2 -> H(U1(d, a), d)
28.57/10.08	   A^2 -> H(U1(d, a), k)
28.57/10.08	   A^2 -> H(U1(a, e), b)
28.57/10.08	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.08	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.08	   A^2 -> H(U1(a, e), c)
28.57/10.08	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.08	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.08	   A^2 -> H(U1(a, e), e)
28.57/10.08	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.08	   A^2 -> H(U1(a, k), b)
28.57/10.08	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.08	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.08	   A^2 -> H(U1(a, k), c)
28.57/10.08	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.08	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.08	   A^2 -> H(U1(a, k), e)
28.57/10.08	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.08	   A^2 -> H(U1(a, c), d)
28.57/10.08	   A^2 -> H(U1(a, c), k)
28.57/10.08	   A^2 -> H(U1(a, d), d)
28.57/10.08	   A^2 -> H(U1(a, d), k)
28.57/10.08	   A^2 -> H(k, U1(c, b))
28.57/10.08	   A^2 -> H(k, U1(d, b))
28.57/10.08	   A^2 -> H(k, U1(b, c))
28.57/10.08	   A^2 -> H(k, U1(b, d))
28.57/10.08	   A^2 -> H(k, U1(c, c))
28.57/10.08	   A^2 -> H(k, f(e))
28.57/10.08	   A^2 -> H(k, f(k))
28.57/10.08	   A^2 -> H(k, U1(d, d))
28.57/10.08	   A^2 -> H(c, U1(e, b))
28.57/10.08	   A^2 -> H(c, U1(k, b))
28.57/10.08	   A^2 -> H(c, U1(c, d))
28.57/10.08	   A^2 -> H(c, U1(d, c))
28.57/10.08	   A^2 -> H(c, U1(b, e))
28.57/10.08	   A^2 -> H(c, U1(b, k))
28.57/10.08	   A^2 -> H(c, U1(e, c))
28.57/10.08	   A^2 -> H(c, U1(k, c))
28.57/10.08	   A^2 -> H(c, U1(c, e))
28.57/10.08	   A^2 -> H(c, U1(c, k))
28.57/10.08	   A^2 -> H(c, U1(e, e))
28.57/10.08	   A^2 -> H(c, U1(k, k))
28.57/10.08	   A^2 -> H(c, U1(k, d))
28.57/10.08	   A^2 -> H(c, U1(d, k))
28.57/10.08	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.08	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.08	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.08	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.08	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.08	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.08	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.08	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.08	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.08	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.08	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.08	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.08	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.08	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.08	   A^2 -> H(U1(e, c), b)
28.57/10.08	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.08	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.08	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.08	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.08	   A^2 -> H(U1(e, c), e)
28.57/10.08	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.08	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.08	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.08	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.08	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.08	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.08	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.08	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.08	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.08	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.08	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.08	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.08	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.08	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.08	   A^2 -> H(U1(k, c), b)
28.57/10.08	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.08	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.08	   A^2 -> H(U1(k, c), c)
28.57/10.08	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.08	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.08	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.08	   A^2 -> H(U1(c, e), b)
28.57/10.08	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.08	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.08	   A^2 -> H(U1(c, e), c)
28.57/10.08	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.08	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.08	   A^2 -> H(U1(c, e), e)
28.57/10.08	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.08	   A^2 -> H(U1(c, k), b)
28.57/10.08	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.08	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.08	   A^2 -> H(U1(c, k), c)
28.57/10.08	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.08	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, k), e)
28.57/10.09	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, c), d)
28.57/10.09	   A^2 -> H(e, U1(e, b))
28.57/10.09	   A^2 -> H(e, U1(c, d))
28.57/10.09	   A^2 -> H(e, U1(d, c))
28.57/10.09	   A^2 -> H(e, U1(b, e))
28.57/10.09	   A^2 -> H(e, U1(b, k))
28.57/10.09	   A^2 -> H(e, U1(e, c))
28.57/10.09	   A^2 -> H(e, U1(c, e))
28.57/10.09	   A^2 -> H(e, U1(c, k))
28.57/10.09	   A^2 -> H(e, U1(e, e))
28.57/10.09	   A^2 -> H(e, U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, e), b)
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, e), c)
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.09	   A^2 -> H(f(e), d)
28.57/10.09	   A^2 -> H(f(e), k)
28.57/10.09	   A^2 -> H(U1(k, k), b)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, k), c)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.09	   A^2 -> H(f(k), d)
28.57/10.09	   A^2 -> H(f(k), k)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(k, d), b)
28.57/10.09	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, d), c)
28.57/10.09	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, k), b)
28.57/10.09	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(d, k), c)
28.57/10.09	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(d, k), e)
28.57/10.09	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, d), d)
28.57/10.09	   A^2 -> H(U1(d, d), k)
28.57/10.09	   A^2 -> H(U1(e, c), c)
28.57/10.09	   A^2 -> H(U1(c, c), e)
28.57/10.09	   A^2 -> H(U1(c, c), k)
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, e), e)
28.57/10.09	   A^2 -> H(d, U1(e, b))
28.57/10.09	   A^2 -> H(d, U1(k, b))
28.57/10.09	   A^2 -> H(d, U1(c, d))
28.57/10.09	   A^2 -> H(d, U1(d, c))
28.57/10.09	   A^2 -> H(d, U1(b, e))
28.57/10.09	   A^2 -> H(d, U1(b, k))
28.57/10.09	   A^2 -> H(d, U1(e, c))
28.57/10.09	   A^2 -> H(d, U1(k, c))
28.57/10.09	   A^2 -> H(d, U1(c, e))
28.57/10.09	   A^2 -> H(d, U1(c, k))
28.57/10.09	   A^2 -> H(d, U1(e, e))
28.57/10.09	   A^2 -> H(d, U1(k, k))
28.57/10.09	   A^2 -> H(d, U1(k, d))
28.57/10.09	   A^2 -> H(d, U1(d, k))
28.57/10.09	   A^2 -> H(a, b)
28.57/10.09	   A^2 -> H(a, U1(e, d))
28.57/10.09	   A^2 -> H(a, U1(d, e))
28.57/10.09	   A^2 -> H(a, c)
28.57/10.09	   A^2 -> H(a, U1(e, k))
28.57/10.09	   A^2 -> H(a, U1(k, e))
28.57/10.09	   A^2 -> H(a, e)
28.57/10.09	   A^2 -> H(a, U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, d), b)
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.09	
28.57/10.09	The TRS R consists of the following rules:
28.57/10.09	
28.57/10.09	   f(x) -> U1(x, x)
28.57/10.09	   U1(e, x) -> x
28.57/10.09	   a -> c
28.57/10.09	   a -> d
28.57/10.09	   b -> c
28.57/10.09	   b -> d
28.57/10.09	   d -> k
28.57/10.09	   c -> e
28.57/10.09	   c -> k
28.57/10.09	
28.57/10.09	Q is empty.
28.57/10.09	We have to consider all minimal (P,Q,R)-chains.
28.57/10.09	----------------------------------------
28.57/10.09	
28.57/10.09	(1847) TransformationProof (EQUIVALENT)
28.57/10.09	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.09	
28.57/10.09	   (A^2 -> H(d, U1(b, e)),A^2 -> H(d, U1(b, e)))
28.57/10.09	   (A^2 -> H(U1(e, k), U1(b, e)),A^2 -> H(U1(e, k), U1(b, e)))
28.57/10.09	   (A^2 -> H(U1(e, d), U1(c, e)),A^2 -> H(U1(e, d), U1(c, e)))
28.57/10.09	   (A^2 -> H(U1(e, d), U1(d, e)),A^2 -> H(U1(e, d), U1(d, e)))
28.57/10.09	
28.57/10.09	
28.57/10.09	----------------------------------------
28.57/10.09	
28.57/10.09	(1848)
28.57/10.09	Obligation:
28.57/10.09	Q DP problem:
28.57/10.09	The TRS P consists of the following rules:
28.57/10.09	
28.57/10.09	   H(x, x) -> G(x, x, f(k))
28.57/10.09	   G(d, x, x) -> A^2
28.57/10.09	   A^2 -> H(f(c), f(c))
28.57/10.09	   A^2 -> H(f(d), f(d))
28.57/10.09	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.09	   A^2 -> H(f(e), f(e))
28.57/10.09	   A^2 -> H(f(k), f(k))
28.57/10.09	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.09	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.09	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.09	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.09	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(b, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, c))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, c))
28.57/10.09	   A^2 -> H(U1(e, d), U1(c, e))
28.57/10.09	   A^2 -> H(U1(e, d), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, d))
28.57/10.09	   A^2 -> H(U1(e, d), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, a), b)
28.57/10.09	   A^2 -> H(U1(e, a), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, a), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, a), c)
28.57/10.09	   A^2 -> H(U1(e, a), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, a), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, a), e)
28.57/10.09	   A^2 -> H(U1(e, a), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, a), b)
28.57/10.09	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, a), c)
28.57/10.09	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, d), b)
28.57/10.09	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, d), c)
28.57/10.09	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, d), e)
28.57/10.09	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, a), d)
28.57/10.09	   A^2 -> H(U1(c, a), k)
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.09	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.09	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.09	   A^2 -> H(U1(d, c), b)
28.57/10.09	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(d, c), c)
28.57/10.09	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(d, c), e)
28.57/10.09	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, a), d)
28.57/10.09	   A^2 -> H(U1(d, a), k)
28.57/10.09	   A^2 -> H(U1(a, e), b)
28.57/10.09	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(a, e), c)
28.57/10.09	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(a, e), e)
28.57/10.09	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(a, k), b)
28.57/10.09	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(a, k), c)
28.57/10.09	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(a, k), e)
28.57/10.09	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(a, c), d)
28.57/10.09	   A^2 -> H(U1(a, c), k)
28.57/10.09	   A^2 -> H(U1(a, d), d)
28.57/10.09	   A^2 -> H(U1(a, d), k)
28.57/10.09	   A^2 -> H(k, U1(c, b))
28.57/10.09	   A^2 -> H(k, U1(d, b))
28.57/10.09	   A^2 -> H(k, U1(b, c))
28.57/10.09	   A^2 -> H(k, U1(b, d))
28.57/10.09	   A^2 -> H(k, U1(c, c))
28.57/10.09	   A^2 -> H(k, f(e))
28.57/10.09	   A^2 -> H(k, f(k))
28.57/10.09	   A^2 -> H(k, U1(d, d))
28.57/10.09	   A^2 -> H(c, U1(e, b))
28.57/10.09	   A^2 -> H(c, U1(k, b))
28.57/10.09	   A^2 -> H(c, U1(c, d))
28.57/10.09	   A^2 -> H(c, U1(d, c))
28.57/10.09	   A^2 -> H(c, U1(b, e))
28.57/10.09	   A^2 -> H(c, U1(b, k))
28.57/10.09	   A^2 -> H(c, U1(e, c))
28.57/10.09	   A^2 -> H(c, U1(k, c))
28.57/10.09	   A^2 -> H(c, U1(c, e))
28.57/10.09	   A^2 -> H(c, U1(c, k))
28.57/10.09	   A^2 -> H(c, U1(e, e))
28.57/10.09	   A^2 -> H(c, U1(k, k))
28.57/10.09	   A^2 -> H(c, U1(k, d))
28.57/10.09	   A^2 -> H(c, U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.09	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.09	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, c), b)
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, c), e)
28.57/10.09	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.09	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.09	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.09	   A^2 -> H(U1(k, c), b)
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, c), c)
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, e), b)
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, e), c)
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, e), e)
28.57/10.09	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, k), b)
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, k), c)
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, k), e)
28.57/10.09	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, c), d)
28.57/10.09	   A^2 -> H(e, U1(e, b))
28.57/10.09	   A^2 -> H(e, U1(c, d))
28.57/10.09	   A^2 -> H(e, U1(d, c))
28.57/10.09	   A^2 -> H(e, U1(b, e))
28.57/10.09	   A^2 -> H(e, U1(b, k))
28.57/10.09	   A^2 -> H(e, U1(e, c))
28.57/10.09	   A^2 -> H(e, U1(c, e))
28.57/10.09	   A^2 -> H(e, U1(c, k))
28.57/10.09	   A^2 -> H(e, U1(e, e))
28.57/10.09	   A^2 -> H(e, U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, e), b)
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, e), c)
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.09	   A^2 -> H(f(e), d)
28.57/10.09	   A^2 -> H(f(e), k)
28.57/10.09	   A^2 -> H(U1(k, k), b)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, k), c)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.09	   A^2 -> H(f(k), d)
28.57/10.09	   A^2 -> H(f(k), k)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(k, d), b)
28.57/10.09	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, d), c)
28.57/10.09	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, k), b)
28.57/10.09	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(d, k), c)
28.57/10.09	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(d, k), e)
28.57/10.09	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, d), d)
28.57/10.09	   A^2 -> H(U1(d, d), k)
28.57/10.09	   A^2 -> H(U1(e, c), c)
28.57/10.09	   A^2 -> H(U1(c, c), e)
28.57/10.09	   A^2 -> H(U1(c, c), k)
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, e), e)
28.57/10.09	   A^2 -> H(d, U1(e, b))
28.57/10.09	   A^2 -> H(d, U1(k, b))
28.57/10.09	   A^2 -> H(d, U1(c, d))
28.57/10.09	   A^2 -> H(d, U1(d, c))
28.57/10.09	   A^2 -> H(d, U1(b, e))
28.57/10.09	   A^2 -> H(d, U1(b, k))
28.57/10.09	   A^2 -> H(d, U1(e, c))
28.57/10.09	   A^2 -> H(d, U1(k, c))
28.57/10.09	   A^2 -> H(d, U1(c, e))
28.57/10.09	   A^2 -> H(d, U1(c, k))
28.57/10.09	   A^2 -> H(d, U1(e, e))
28.57/10.09	   A^2 -> H(d, U1(k, k))
28.57/10.09	   A^2 -> H(d, U1(k, d))
28.57/10.09	   A^2 -> H(d, U1(d, k))
28.57/10.09	   A^2 -> H(a, b)
28.57/10.09	   A^2 -> H(a, U1(e, d))
28.57/10.09	   A^2 -> H(a, U1(d, e))
28.57/10.09	   A^2 -> H(a, c)
28.57/10.09	   A^2 -> H(a, U1(e, k))
28.57/10.09	   A^2 -> H(a, U1(k, e))
28.57/10.09	   A^2 -> H(a, e)
28.57/10.09	   A^2 -> H(a, U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, d), b)
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.09	
28.57/10.09	The TRS R consists of the following rules:
28.57/10.09	
28.57/10.09	   f(x) -> U1(x, x)
28.57/10.09	   U1(e, x) -> x
28.57/10.09	   a -> c
28.57/10.09	   a -> d
28.57/10.09	   b -> c
28.57/10.09	   b -> d
28.57/10.09	   d -> k
28.57/10.09	   c -> e
28.57/10.09	   c -> k
28.57/10.09	
28.57/10.09	Q is empty.
28.57/10.09	We have to consider all minimal (P,Q,R)-chains.
28.57/10.09	----------------------------------------
28.57/10.09	
28.57/10.09	(1849) TransformationProof (EQUIVALENT)
28.57/10.09	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.09	
28.57/10.09	   (A^2 -> H(d, U1(b, k)),A^2 -> H(d, U1(b, k)))
28.57/10.09	   (A^2 -> H(U1(e, k), U1(b, k)),A^2 -> H(U1(e, k), U1(b, k)))
28.57/10.09	   (A^2 -> H(U1(e, d), U1(c, k)),A^2 -> H(U1(e, d), U1(c, k)))
28.57/10.09	   (A^2 -> H(U1(e, d), U1(d, k)),A^2 -> H(U1(e, d), U1(d, k)))
28.57/10.09	
28.57/10.09	
28.57/10.09	----------------------------------------
28.57/10.09	
28.57/10.09	(1850)
28.57/10.09	Obligation:
28.57/10.09	Q DP problem:
28.57/10.09	The TRS P consists of the following rules:
28.57/10.09	
28.57/10.09	   H(x, x) -> G(x, x, f(k))
28.57/10.09	   G(d, x, x) -> A^2
28.57/10.09	   A^2 -> H(f(c), f(c))
28.57/10.09	   A^2 -> H(f(d), f(d))
28.57/10.09	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.09	   A^2 -> H(f(e), f(e))
28.57/10.09	   A^2 -> H(f(k), f(k))
28.57/10.09	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.09	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.09	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.09	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.09	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, c))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, c))
28.57/10.09	   A^2 -> H(U1(e, d), U1(c, e))
28.57/10.09	   A^2 -> H(U1(e, d), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, d))
28.57/10.09	   A^2 -> H(U1(e, d), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, a), b)
28.57/10.09	   A^2 -> H(U1(e, a), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, a), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, a), c)
28.57/10.09	   A^2 -> H(U1(e, a), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, a), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, a), e)
28.57/10.09	   A^2 -> H(U1(e, a), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, a), b)
28.57/10.09	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, a), c)
28.57/10.09	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, d), b)
28.57/10.09	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, d), c)
28.57/10.09	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, d), e)
28.57/10.09	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, a), d)
28.57/10.09	   A^2 -> H(U1(c, a), k)
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.09	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.09	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.09	   A^2 -> H(U1(d, c), b)
28.57/10.09	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(d, c), c)
28.57/10.09	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(d, c), e)
28.57/10.09	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, a), d)
28.57/10.09	   A^2 -> H(U1(d, a), k)
28.57/10.09	   A^2 -> H(U1(a, e), b)
28.57/10.09	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(a, e), c)
28.57/10.09	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(a, e), e)
28.57/10.09	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(a, k), b)
28.57/10.09	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(a, k), c)
28.57/10.09	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(a, k), e)
28.57/10.09	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(a, c), d)
28.57/10.09	   A^2 -> H(U1(a, c), k)
28.57/10.09	   A^2 -> H(U1(a, d), d)
28.57/10.09	   A^2 -> H(U1(a, d), k)
28.57/10.09	   A^2 -> H(k, U1(c, b))
28.57/10.09	   A^2 -> H(k, U1(d, b))
28.57/10.09	   A^2 -> H(k, U1(b, c))
28.57/10.09	   A^2 -> H(k, U1(b, d))
28.57/10.09	   A^2 -> H(k, U1(c, c))
28.57/10.09	   A^2 -> H(k, f(e))
28.57/10.09	   A^2 -> H(k, f(k))
28.57/10.09	   A^2 -> H(k, U1(d, d))
28.57/10.09	   A^2 -> H(c, U1(e, b))
28.57/10.09	   A^2 -> H(c, U1(k, b))
28.57/10.09	   A^2 -> H(c, U1(c, d))
28.57/10.09	   A^2 -> H(c, U1(d, c))
28.57/10.09	   A^2 -> H(c, U1(b, e))
28.57/10.09	   A^2 -> H(c, U1(b, k))
28.57/10.09	   A^2 -> H(c, U1(e, c))
28.57/10.09	   A^2 -> H(c, U1(k, c))
28.57/10.09	   A^2 -> H(c, U1(c, e))
28.57/10.09	   A^2 -> H(c, U1(c, k))
28.57/10.09	   A^2 -> H(c, U1(e, e))
28.57/10.09	   A^2 -> H(c, U1(k, k))
28.57/10.09	   A^2 -> H(c, U1(k, d))
28.57/10.09	   A^2 -> H(c, U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.09	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.09	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, c), b)
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, c), e)
28.57/10.09	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.09	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.09	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.09	   A^2 -> H(U1(k, c), b)
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, c), c)
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, e), b)
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, e), c)
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, e), e)
28.57/10.09	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, k), b)
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, k), c)
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, k), e)
28.57/10.09	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, c), d)
28.57/10.09	   A^2 -> H(e, U1(e, b))
28.57/10.09	   A^2 -> H(e, U1(c, d))
28.57/10.09	   A^2 -> H(e, U1(d, c))
28.57/10.09	   A^2 -> H(e, U1(b, e))
28.57/10.09	   A^2 -> H(e, U1(b, k))
28.57/10.09	   A^2 -> H(e, U1(e, c))
28.57/10.09	   A^2 -> H(e, U1(c, e))
28.57/10.09	   A^2 -> H(e, U1(c, k))
28.57/10.09	   A^2 -> H(e, U1(e, e))
28.57/10.09	   A^2 -> H(e, U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, e), b)
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, e), c)
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.09	   A^2 -> H(f(e), d)
28.57/10.09	   A^2 -> H(f(e), k)
28.57/10.09	   A^2 -> H(U1(k, k), b)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, k), c)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.09	   A^2 -> H(f(k), d)
28.57/10.09	   A^2 -> H(f(k), k)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(k, d), b)
28.57/10.09	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, d), c)
28.57/10.09	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, k), b)
28.57/10.09	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(d, k), c)
28.57/10.09	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(d, k), e)
28.57/10.09	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, d), d)
28.57/10.09	   A^2 -> H(U1(d, d), k)
28.57/10.09	   A^2 -> H(U1(e, c), c)
28.57/10.09	   A^2 -> H(U1(c, c), e)
28.57/10.09	   A^2 -> H(U1(c, c), k)
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, e), e)
28.57/10.09	   A^2 -> H(d, U1(e, b))
28.57/10.09	   A^2 -> H(d, U1(k, b))
28.57/10.09	   A^2 -> H(d, U1(c, d))
28.57/10.09	   A^2 -> H(d, U1(d, c))
28.57/10.09	   A^2 -> H(d, U1(b, e))
28.57/10.09	   A^2 -> H(d, U1(b, k))
28.57/10.09	   A^2 -> H(d, U1(e, c))
28.57/10.09	   A^2 -> H(d, U1(k, c))
28.57/10.09	   A^2 -> H(d, U1(c, e))
28.57/10.09	   A^2 -> H(d, U1(c, k))
28.57/10.09	   A^2 -> H(d, U1(e, e))
28.57/10.09	   A^2 -> H(d, U1(k, k))
28.57/10.09	   A^2 -> H(d, U1(k, d))
28.57/10.09	   A^2 -> H(d, U1(d, k))
28.57/10.09	   A^2 -> H(a, b)
28.57/10.09	   A^2 -> H(a, U1(e, d))
28.57/10.09	   A^2 -> H(a, U1(d, e))
28.57/10.09	   A^2 -> H(a, c)
28.57/10.09	   A^2 -> H(a, U1(e, k))
28.57/10.09	   A^2 -> H(a, U1(k, e))
28.57/10.09	   A^2 -> H(a, e)
28.57/10.09	   A^2 -> H(a, U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, d), b)
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.09	
28.57/10.09	The TRS R consists of the following rules:
28.57/10.09	
28.57/10.09	   f(x) -> U1(x, x)
28.57/10.09	   U1(e, x) -> x
28.57/10.09	   a -> c
28.57/10.09	   a -> d
28.57/10.09	   b -> c
28.57/10.09	   b -> d
28.57/10.09	   d -> k
28.57/10.09	   c -> e
28.57/10.09	   c -> k
28.57/10.09	
28.57/10.09	Q is empty.
28.57/10.09	We have to consider all minimal (P,Q,R)-chains.
28.57/10.09	----------------------------------------
28.57/10.09	
28.57/10.09	(1851) TransformationProof (EQUIVALENT)
28.57/10.09	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.09	
28.57/10.09	   (A^2 -> H(d, U1(e, c)),A^2 -> H(d, U1(e, c)))
28.57/10.09	   (A^2 -> H(U1(e, k), U1(e, c)),A^2 -> H(U1(e, k), U1(e, c)))
28.57/10.09	   (A^2 -> H(U1(e, d), c),A^2 -> H(U1(e, d), c))
28.57/10.09	   (A^2 -> H(U1(e, d), U1(e, e)),A^2 -> H(U1(e, d), U1(e, e)))
28.57/10.09	   (A^2 -> H(U1(e, d), U1(e, k)),A^2 -> H(U1(e, d), U1(e, k)))
28.57/10.09	
28.57/10.09	
28.57/10.09	----------------------------------------
28.57/10.09	
28.57/10.09	(1852)
28.57/10.09	Obligation:
28.57/10.09	Q DP problem:
28.57/10.09	The TRS P consists of the following rules:
28.57/10.09	
28.57/10.09	   H(x, x) -> G(x, x, f(k))
28.57/10.09	   G(d, x, x) -> A^2
28.57/10.09	   A^2 -> H(f(c), f(c))
28.57/10.09	   A^2 -> H(f(d), f(d))
28.57/10.09	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.09	   A^2 -> H(f(e), f(e))
28.57/10.09	   A^2 -> H(f(k), f(k))
28.57/10.09	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.09	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.09	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.09	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.09	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, c))
28.57/10.09	   A^2 -> H(U1(e, d), U1(c, e))
28.57/10.09	   A^2 -> H(U1(e, d), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, d))
28.57/10.09	   A^2 -> H(U1(e, d), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, a), b)
28.57/10.09	   A^2 -> H(U1(e, a), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, a), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, a), c)
28.57/10.09	   A^2 -> H(U1(e, a), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, a), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, a), e)
28.57/10.09	   A^2 -> H(U1(e, a), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, a), b)
28.57/10.09	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, a), c)
28.57/10.09	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, d), b)
28.57/10.09	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, d), c)
28.57/10.09	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, d), e)
28.57/10.09	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, a), d)
28.57/10.09	   A^2 -> H(U1(c, a), k)
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.09	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.09	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.09	   A^2 -> H(U1(d, c), b)
28.57/10.09	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(d, c), c)
28.57/10.09	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(d, c), e)
28.57/10.09	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, a), d)
28.57/10.09	   A^2 -> H(U1(d, a), k)
28.57/10.09	   A^2 -> H(U1(a, e), b)
28.57/10.09	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(a, e), c)
28.57/10.09	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(a, e), e)
28.57/10.09	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(a, k), b)
28.57/10.09	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(a, k), c)
28.57/10.09	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(a, k), e)
28.57/10.09	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(a, c), d)
28.57/10.09	   A^2 -> H(U1(a, c), k)
28.57/10.09	   A^2 -> H(U1(a, d), d)
28.57/10.09	   A^2 -> H(U1(a, d), k)
28.57/10.09	   A^2 -> H(k, U1(c, b))
28.57/10.09	   A^2 -> H(k, U1(d, b))
28.57/10.09	   A^2 -> H(k, U1(b, c))
28.57/10.09	   A^2 -> H(k, U1(b, d))
28.57/10.09	   A^2 -> H(k, U1(c, c))
28.57/10.09	   A^2 -> H(k, f(e))
28.57/10.09	   A^2 -> H(k, f(k))
28.57/10.09	   A^2 -> H(k, U1(d, d))
28.57/10.09	   A^2 -> H(c, U1(e, b))
28.57/10.09	   A^2 -> H(c, U1(k, b))
28.57/10.09	   A^2 -> H(c, U1(c, d))
28.57/10.09	   A^2 -> H(c, U1(d, c))
28.57/10.09	   A^2 -> H(c, U1(b, e))
28.57/10.09	   A^2 -> H(c, U1(b, k))
28.57/10.09	   A^2 -> H(c, U1(e, c))
28.57/10.09	   A^2 -> H(c, U1(k, c))
28.57/10.09	   A^2 -> H(c, U1(c, e))
28.57/10.09	   A^2 -> H(c, U1(c, k))
28.57/10.09	   A^2 -> H(c, U1(e, e))
28.57/10.09	   A^2 -> H(c, U1(k, k))
28.57/10.09	   A^2 -> H(c, U1(k, d))
28.57/10.09	   A^2 -> H(c, U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.09	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.09	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, c), b)
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, c), e)
28.57/10.09	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.09	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.09	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.09	   A^2 -> H(U1(k, c), b)
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, c), c)
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, e), b)
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, e), c)
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, e), e)
28.57/10.09	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, k), b)
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, k), c)
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, k), e)
28.57/10.09	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, c), d)
28.57/10.09	   A^2 -> H(e, U1(e, b))
28.57/10.09	   A^2 -> H(e, U1(c, d))
28.57/10.09	   A^2 -> H(e, U1(d, c))
28.57/10.09	   A^2 -> H(e, U1(b, e))
28.57/10.09	   A^2 -> H(e, U1(b, k))
28.57/10.09	   A^2 -> H(e, U1(e, c))
28.57/10.09	   A^2 -> H(e, U1(c, e))
28.57/10.09	   A^2 -> H(e, U1(c, k))
28.57/10.09	   A^2 -> H(e, U1(e, e))
28.57/10.09	   A^2 -> H(e, U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, e), b)
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, e), c)
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.09	   A^2 -> H(f(e), d)
28.57/10.09	   A^2 -> H(f(e), k)
28.57/10.09	   A^2 -> H(U1(k, k), b)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, k), c)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.09	   A^2 -> H(f(k), d)
28.57/10.09	   A^2 -> H(f(k), k)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(k, d), b)
28.57/10.09	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, d), c)
28.57/10.09	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, k), b)
28.57/10.09	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(d, k), c)
28.57/10.09	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(d, k), e)
28.57/10.09	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, d), d)
28.57/10.09	   A^2 -> H(U1(d, d), k)
28.57/10.09	   A^2 -> H(U1(e, c), c)
28.57/10.09	   A^2 -> H(U1(c, c), e)
28.57/10.09	   A^2 -> H(U1(c, c), k)
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, e), e)
28.57/10.09	   A^2 -> H(d, U1(e, b))
28.57/10.09	   A^2 -> H(d, U1(k, b))
28.57/10.09	   A^2 -> H(d, U1(c, d))
28.57/10.09	   A^2 -> H(d, U1(d, c))
28.57/10.09	   A^2 -> H(d, U1(b, e))
28.57/10.09	   A^2 -> H(d, U1(b, k))
28.57/10.09	   A^2 -> H(d, U1(e, c))
28.57/10.09	   A^2 -> H(d, U1(k, c))
28.57/10.09	   A^2 -> H(d, U1(c, e))
28.57/10.09	   A^2 -> H(d, U1(c, k))
28.57/10.09	   A^2 -> H(d, U1(e, e))
28.57/10.09	   A^2 -> H(d, U1(k, k))
28.57/10.09	   A^2 -> H(d, U1(k, d))
28.57/10.09	   A^2 -> H(d, U1(d, k))
28.57/10.09	   A^2 -> H(a, b)
28.57/10.09	   A^2 -> H(a, U1(e, d))
28.57/10.09	   A^2 -> H(a, U1(d, e))
28.57/10.09	   A^2 -> H(a, c)
28.57/10.09	   A^2 -> H(a, U1(e, k))
28.57/10.09	   A^2 -> H(a, U1(k, e))
28.57/10.09	   A^2 -> H(a, e)
28.57/10.09	   A^2 -> H(a, U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, d), b)
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, d), c)
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.09	
28.57/10.09	The TRS R consists of the following rules:
28.57/10.09	
28.57/10.09	   f(x) -> U1(x, x)
28.57/10.09	   U1(e, x) -> x
28.57/10.09	   a -> c
28.57/10.09	   a -> d
28.57/10.09	   b -> c
28.57/10.09	   b -> d
28.57/10.09	   d -> k
28.57/10.09	   c -> e
28.57/10.09	   c -> k
28.57/10.09	
28.57/10.09	Q is empty.
28.57/10.09	We have to consider all minimal (P,Q,R)-chains.
28.57/10.09	----------------------------------------
28.57/10.09	
28.57/10.09	(1853) TransformationProof (EQUIVALENT)
28.57/10.09	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.09	
28.57/10.09	   (A^2 -> H(d, U1(k, c)),A^2 -> H(d, U1(k, c)))
28.57/10.09	   (A^2 -> H(U1(e, k), U1(k, c)),A^2 -> H(U1(e, k), U1(k, c)))
28.57/10.09	   (A^2 -> H(U1(e, d), U1(k, e)),A^2 -> H(U1(e, d), U1(k, e)))
28.57/10.09	   (A^2 -> H(U1(e, d), U1(k, k)),A^2 -> H(U1(e, d), U1(k, k)))
28.57/10.09	
28.57/10.09	
28.57/10.09	----------------------------------------
28.57/10.09	
28.57/10.09	(1854)
28.57/10.09	Obligation:
28.57/10.09	Q DP problem:
28.57/10.09	The TRS P consists of the following rules:
28.57/10.09	
28.57/10.09	   H(x, x) -> G(x, x, f(k))
28.57/10.09	   G(d, x, x) -> A^2
28.57/10.09	   A^2 -> H(f(c), f(c))
28.57/10.09	   A^2 -> H(f(d), f(d))
28.57/10.09	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.09	   A^2 -> H(f(e), f(e))
28.57/10.09	   A^2 -> H(f(k), f(k))
28.57/10.09	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.09	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.09	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.09	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.09	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(c, e))
28.57/10.09	   A^2 -> H(U1(e, d), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, d))
28.57/10.09	   A^2 -> H(U1(e, d), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, a), b)
28.57/10.09	   A^2 -> H(U1(e, a), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, a), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, a), c)
28.57/10.09	   A^2 -> H(U1(e, a), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, a), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, a), e)
28.57/10.09	   A^2 -> H(U1(e, a), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, a), b)
28.57/10.09	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, a), c)
28.57/10.09	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, d), b)
28.57/10.09	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, d), c)
28.57/10.09	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, d), e)
28.57/10.09	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, a), d)
28.57/10.09	   A^2 -> H(U1(c, a), k)
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.09	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.09	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.09	   A^2 -> H(U1(d, c), b)
28.57/10.09	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(d, c), c)
28.57/10.09	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(d, c), e)
28.57/10.09	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, a), d)
28.57/10.09	   A^2 -> H(U1(d, a), k)
28.57/10.09	   A^2 -> H(U1(a, e), b)
28.57/10.09	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(a, e), c)
28.57/10.09	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(a, e), e)
28.57/10.09	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(a, k), b)
28.57/10.09	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(a, k), c)
28.57/10.09	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(a, k), e)
28.57/10.09	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(a, c), d)
28.57/10.09	   A^2 -> H(U1(a, c), k)
28.57/10.09	   A^2 -> H(U1(a, d), d)
28.57/10.09	   A^2 -> H(U1(a, d), k)
28.57/10.09	   A^2 -> H(k, U1(c, b))
28.57/10.09	   A^2 -> H(k, U1(d, b))
28.57/10.09	   A^2 -> H(k, U1(b, c))
28.57/10.09	   A^2 -> H(k, U1(b, d))
28.57/10.09	   A^2 -> H(k, U1(c, c))
28.57/10.09	   A^2 -> H(k, f(e))
28.57/10.09	   A^2 -> H(k, f(k))
28.57/10.09	   A^2 -> H(k, U1(d, d))
28.57/10.09	   A^2 -> H(c, U1(e, b))
28.57/10.09	   A^2 -> H(c, U1(k, b))
28.57/10.09	   A^2 -> H(c, U1(c, d))
28.57/10.09	   A^2 -> H(c, U1(d, c))
28.57/10.09	   A^2 -> H(c, U1(b, e))
28.57/10.09	   A^2 -> H(c, U1(b, k))
28.57/10.09	   A^2 -> H(c, U1(e, c))
28.57/10.09	   A^2 -> H(c, U1(k, c))
28.57/10.09	   A^2 -> H(c, U1(c, e))
28.57/10.09	   A^2 -> H(c, U1(c, k))
28.57/10.09	   A^2 -> H(c, U1(e, e))
28.57/10.09	   A^2 -> H(c, U1(k, k))
28.57/10.09	   A^2 -> H(c, U1(k, d))
28.57/10.09	   A^2 -> H(c, U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.09	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.09	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, c), b)
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, c), e)
28.57/10.09	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.09	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.09	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.09	   A^2 -> H(U1(k, c), b)
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, c), c)
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, e), b)
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, e), c)
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, e), e)
28.57/10.09	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, k), b)
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, k), c)
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, k), e)
28.57/10.09	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, c), d)
28.57/10.09	   A^2 -> H(e, U1(e, b))
28.57/10.09	   A^2 -> H(e, U1(c, d))
28.57/10.09	   A^2 -> H(e, U1(d, c))
28.57/10.09	   A^2 -> H(e, U1(b, e))
28.57/10.09	   A^2 -> H(e, U1(b, k))
28.57/10.09	   A^2 -> H(e, U1(e, c))
28.57/10.09	   A^2 -> H(e, U1(c, e))
28.57/10.09	   A^2 -> H(e, U1(c, k))
28.57/10.09	   A^2 -> H(e, U1(e, e))
28.57/10.09	   A^2 -> H(e, U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, e), b)
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, e), c)
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.09	   A^2 -> H(f(e), d)
28.57/10.09	   A^2 -> H(f(e), k)
28.57/10.09	   A^2 -> H(U1(k, k), b)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, k), c)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.09	   A^2 -> H(f(k), d)
28.57/10.09	   A^2 -> H(f(k), k)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(k, d), b)
28.57/10.09	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, d), c)
28.57/10.09	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, k), b)
28.57/10.09	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(d, k), c)
28.57/10.09	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(d, k), e)
28.57/10.09	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, d), d)
28.57/10.09	   A^2 -> H(U1(d, d), k)
28.57/10.09	   A^2 -> H(U1(e, c), c)
28.57/10.09	   A^2 -> H(U1(c, c), e)
28.57/10.09	   A^2 -> H(U1(c, c), k)
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, e), e)
28.57/10.09	   A^2 -> H(d, U1(e, b))
28.57/10.09	   A^2 -> H(d, U1(k, b))
28.57/10.09	   A^2 -> H(d, U1(c, d))
28.57/10.09	   A^2 -> H(d, U1(d, c))
28.57/10.09	   A^2 -> H(d, U1(b, e))
28.57/10.09	   A^2 -> H(d, U1(b, k))
28.57/10.09	   A^2 -> H(d, U1(e, c))
28.57/10.09	   A^2 -> H(d, U1(k, c))
28.57/10.09	   A^2 -> H(d, U1(c, e))
28.57/10.09	   A^2 -> H(d, U1(c, k))
28.57/10.09	   A^2 -> H(d, U1(e, e))
28.57/10.09	   A^2 -> H(d, U1(k, k))
28.57/10.09	   A^2 -> H(d, U1(k, d))
28.57/10.09	   A^2 -> H(d, U1(d, k))
28.57/10.09	   A^2 -> H(a, b)
28.57/10.09	   A^2 -> H(a, U1(e, d))
28.57/10.09	   A^2 -> H(a, U1(d, e))
28.57/10.09	   A^2 -> H(a, c)
28.57/10.09	   A^2 -> H(a, U1(e, k))
28.57/10.09	   A^2 -> H(a, U1(k, e))
28.57/10.09	   A^2 -> H(a, e)
28.57/10.09	   A^2 -> H(a, U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, d), b)
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, d), c)
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.09	
28.57/10.09	The TRS R consists of the following rules:
28.57/10.09	
28.57/10.09	   f(x) -> U1(x, x)
28.57/10.09	   U1(e, x) -> x
28.57/10.09	   a -> c
28.57/10.09	   a -> d
28.57/10.09	   b -> c
28.57/10.09	   b -> d
28.57/10.09	   d -> k
28.57/10.09	   c -> e
28.57/10.09	   c -> k
28.57/10.09	
28.57/10.09	Q is empty.
28.57/10.09	We have to consider all minimal (P,Q,R)-chains.
28.57/10.09	----------------------------------------
28.57/10.09	
28.57/10.09	(1855) TransformationProof (EQUIVALENT)
28.57/10.09	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.09	
28.57/10.09	   (A^2 -> H(d, U1(c, e)),A^2 -> H(d, U1(c, e)))
28.57/10.09	   (A^2 -> H(U1(e, k), U1(c, e)),A^2 -> H(U1(e, k), U1(c, e)))
28.57/10.09	   (A^2 -> H(U1(e, d), U1(e, e)),A^2 -> H(U1(e, d), U1(e, e)))
28.57/10.09	   (A^2 -> H(U1(e, d), U1(k, e)),A^2 -> H(U1(e, d), U1(k, e)))
28.57/10.09	
28.57/10.09	
28.57/10.09	----------------------------------------
28.57/10.09	
28.57/10.09	(1856)
28.57/10.09	Obligation:
28.57/10.09	Q DP problem:
28.57/10.09	The TRS P consists of the following rules:
28.57/10.09	
28.57/10.09	   H(x, x) -> G(x, x, f(k))
28.57/10.09	   G(d, x, x) -> A^2
28.57/10.09	   A^2 -> H(f(c), f(c))
28.57/10.09	   A^2 -> H(f(d), f(d))
28.57/10.09	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.09	   A^2 -> H(f(e), f(e))
28.57/10.09	   A^2 -> H(f(k), f(k))
28.57/10.09	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.09	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.09	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.09	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.09	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, d))
28.57/10.09	   A^2 -> H(U1(e, d), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, a), b)
28.57/10.09	   A^2 -> H(U1(e, a), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, a), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, a), c)
28.57/10.09	   A^2 -> H(U1(e, a), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, a), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, a), e)
28.57/10.09	   A^2 -> H(U1(e, a), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, a), b)
28.57/10.09	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, a), c)
28.57/10.09	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, d), b)
28.57/10.09	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, d), c)
28.57/10.09	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, d), e)
28.57/10.09	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, a), d)
28.57/10.09	   A^2 -> H(U1(c, a), k)
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.09	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.09	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.09	   A^2 -> H(U1(d, c), b)
28.57/10.09	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(d, c), c)
28.57/10.09	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(d, c), e)
28.57/10.09	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, a), d)
28.57/10.09	   A^2 -> H(U1(d, a), k)
28.57/10.09	   A^2 -> H(U1(a, e), b)
28.57/10.09	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(a, e), c)
28.57/10.09	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(a, e), e)
28.57/10.09	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(a, k), b)
28.57/10.09	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(a, k), c)
28.57/10.09	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(a, k), e)
28.57/10.09	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(a, c), d)
28.57/10.09	   A^2 -> H(U1(a, c), k)
28.57/10.09	   A^2 -> H(U1(a, d), d)
28.57/10.09	   A^2 -> H(U1(a, d), k)
28.57/10.09	   A^2 -> H(k, U1(c, b))
28.57/10.09	   A^2 -> H(k, U1(d, b))
28.57/10.09	   A^2 -> H(k, U1(b, c))
28.57/10.09	   A^2 -> H(k, U1(b, d))
28.57/10.09	   A^2 -> H(k, U1(c, c))
28.57/10.09	   A^2 -> H(k, f(e))
28.57/10.09	   A^2 -> H(k, f(k))
28.57/10.09	   A^2 -> H(k, U1(d, d))
28.57/10.09	   A^2 -> H(c, U1(e, b))
28.57/10.09	   A^2 -> H(c, U1(k, b))
28.57/10.09	   A^2 -> H(c, U1(c, d))
28.57/10.09	   A^2 -> H(c, U1(d, c))
28.57/10.09	   A^2 -> H(c, U1(b, e))
28.57/10.09	   A^2 -> H(c, U1(b, k))
28.57/10.09	   A^2 -> H(c, U1(e, c))
28.57/10.09	   A^2 -> H(c, U1(k, c))
28.57/10.09	   A^2 -> H(c, U1(c, e))
28.57/10.09	   A^2 -> H(c, U1(c, k))
28.57/10.09	   A^2 -> H(c, U1(e, e))
28.57/10.09	   A^2 -> H(c, U1(k, k))
28.57/10.09	   A^2 -> H(c, U1(k, d))
28.57/10.09	   A^2 -> H(c, U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.09	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.09	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, c), b)
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, c), e)
28.57/10.09	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.09	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.09	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.09	   A^2 -> H(U1(k, c), b)
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, c), c)
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, e), b)
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, e), c)
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, e), e)
28.57/10.09	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, k), b)
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, k), c)
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, k), e)
28.57/10.09	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, c), d)
28.57/10.09	   A^2 -> H(e, U1(e, b))
28.57/10.09	   A^2 -> H(e, U1(c, d))
28.57/10.09	   A^2 -> H(e, U1(d, c))
28.57/10.09	   A^2 -> H(e, U1(b, e))
28.57/10.09	   A^2 -> H(e, U1(b, k))
28.57/10.09	   A^2 -> H(e, U1(e, c))
28.57/10.09	   A^2 -> H(e, U1(c, e))
28.57/10.09	   A^2 -> H(e, U1(c, k))
28.57/10.09	   A^2 -> H(e, U1(e, e))
28.57/10.09	   A^2 -> H(e, U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, e), b)
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, e), c)
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.09	   A^2 -> H(f(e), d)
28.57/10.09	   A^2 -> H(f(e), k)
28.57/10.09	   A^2 -> H(U1(k, k), b)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, k), c)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.09	   A^2 -> H(f(k), d)
28.57/10.09	   A^2 -> H(f(k), k)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(k, d), b)
28.57/10.09	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, d), c)
28.57/10.09	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, k), b)
28.57/10.09	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(d, k), c)
28.57/10.09	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(d, k), e)
28.57/10.09	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, d), d)
28.57/10.09	   A^2 -> H(U1(d, d), k)
28.57/10.09	   A^2 -> H(U1(e, c), c)
28.57/10.09	   A^2 -> H(U1(c, c), e)
28.57/10.09	   A^2 -> H(U1(c, c), k)
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, e), e)
28.57/10.09	   A^2 -> H(d, U1(e, b))
28.57/10.09	   A^2 -> H(d, U1(k, b))
28.57/10.09	   A^2 -> H(d, U1(c, d))
28.57/10.09	   A^2 -> H(d, U1(d, c))
28.57/10.09	   A^2 -> H(d, U1(b, e))
28.57/10.09	   A^2 -> H(d, U1(b, k))
28.57/10.09	   A^2 -> H(d, U1(e, c))
28.57/10.09	   A^2 -> H(d, U1(k, c))
28.57/10.09	   A^2 -> H(d, U1(c, e))
28.57/10.09	   A^2 -> H(d, U1(c, k))
28.57/10.09	   A^2 -> H(d, U1(e, e))
28.57/10.09	   A^2 -> H(d, U1(k, k))
28.57/10.09	   A^2 -> H(d, U1(k, d))
28.57/10.09	   A^2 -> H(d, U1(d, k))
28.57/10.09	   A^2 -> H(a, b)
28.57/10.09	   A^2 -> H(a, U1(e, d))
28.57/10.09	   A^2 -> H(a, U1(d, e))
28.57/10.09	   A^2 -> H(a, c)
28.57/10.09	   A^2 -> H(a, U1(e, k))
28.57/10.09	   A^2 -> H(a, U1(k, e))
28.57/10.09	   A^2 -> H(a, e)
28.57/10.09	   A^2 -> H(a, U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, d), b)
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, d), c)
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.09	
28.57/10.09	The TRS R consists of the following rules:
28.57/10.09	
28.57/10.09	   f(x) -> U1(x, x)
28.57/10.09	   U1(e, x) -> x
28.57/10.09	   a -> c
28.57/10.09	   a -> d
28.57/10.09	   b -> c
28.57/10.09	   b -> d
28.57/10.09	   d -> k
28.57/10.09	   c -> e
28.57/10.09	   c -> k
28.57/10.09	
28.57/10.09	Q is empty.
28.57/10.09	We have to consider all minimal (P,Q,R)-chains.
28.57/10.09	----------------------------------------
28.57/10.09	
28.57/10.09	(1857) TransformationProof (EQUIVALENT)
28.57/10.09	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.09	
28.57/10.09	   (A^2 -> H(d, U1(c, k)),A^2 -> H(d, U1(c, k)))
28.57/10.09	   (A^2 -> H(U1(e, k), U1(c, k)),A^2 -> H(U1(e, k), U1(c, k)))
28.57/10.09	   (A^2 -> H(U1(e, d), U1(e, k)),A^2 -> H(U1(e, d), U1(e, k)))
28.57/10.09	   (A^2 -> H(U1(e, d), U1(k, k)),A^2 -> H(U1(e, d), U1(k, k)))
28.57/10.09	
28.57/10.09	
28.57/10.09	----------------------------------------
28.57/10.09	
28.57/10.09	(1858)
28.57/10.09	Obligation:
28.57/10.09	Q DP problem:
28.57/10.09	The TRS P consists of the following rules:
28.57/10.09	
28.57/10.09	   H(x, x) -> G(x, x, f(k))
28.57/10.09	   G(d, x, x) -> A^2
28.57/10.09	   A^2 -> H(f(c), f(c))
28.57/10.09	   A^2 -> H(f(d), f(d))
28.57/10.09	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.09	   A^2 -> H(f(e), f(e))
28.57/10.09	   A^2 -> H(f(k), f(k))
28.57/10.09	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.09	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.09	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.09	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.09	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, d))
28.57/10.09	   A^2 -> H(U1(e, d), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, a), b)
28.57/10.09	   A^2 -> H(U1(e, a), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, a), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, a), c)
28.57/10.09	   A^2 -> H(U1(e, a), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, a), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, a), e)
28.57/10.09	   A^2 -> H(U1(e, a), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, a), b)
28.57/10.09	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, a), c)
28.57/10.09	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, d), b)
28.57/10.09	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, d), c)
28.57/10.09	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, d), e)
28.57/10.09	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, a), d)
28.57/10.09	   A^2 -> H(U1(c, a), k)
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.09	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.09	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.09	   A^2 -> H(U1(d, c), b)
28.57/10.09	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(d, c), c)
28.57/10.09	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(d, c), e)
28.57/10.09	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, a), d)
28.57/10.09	   A^2 -> H(U1(d, a), k)
28.57/10.09	   A^2 -> H(U1(a, e), b)
28.57/10.09	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(a, e), c)
28.57/10.09	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(a, e), e)
28.57/10.09	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(a, k), b)
28.57/10.09	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(a, k), c)
28.57/10.09	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(a, k), e)
28.57/10.09	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(a, c), d)
28.57/10.09	   A^2 -> H(U1(a, c), k)
28.57/10.09	   A^2 -> H(U1(a, d), d)
28.57/10.09	   A^2 -> H(U1(a, d), k)
28.57/10.09	   A^2 -> H(k, U1(c, b))
28.57/10.09	   A^2 -> H(k, U1(d, b))
28.57/10.09	   A^2 -> H(k, U1(b, c))
28.57/10.09	   A^2 -> H(k, U1(b, d))
28.57/10.09	   A^2 -> H(k, U1(c, c))
28.57/10.09	   A^2 -> H(k, f(e))
28.57/10.09	   A^2 -> H(k, f(k))
28.57/10.09	   A^2 -> H(k, U1(d, d))
28.57/10.09	   A^2 -> H(c, U1(e, b))
28.57/10.09	   A^2 -> H(c, U1(k, b))
28.57/10.09	   A^2 -> H(c, U1(c, d))
28.57/10.09	   A^2 -> H(c, U1(d, c))
28.57/10.09	   A^2 -> H(c, U1(b, e))
28.57/10.09	   A^2 -> H(c, U1(b, k))
28.57/10.09	   A^2 -> H(c, U1(e, c))
28.57/10.09	   A^2 -> H(c, U1(k, c))
28.57/10.09	   A^2 -> H(c, U1(c, e))
28.57/10.09	   A^2 -> H(c, U1(c, k))
28.57/10.09	   A^2 -> H(c, U1(e, e))
28.57/10.09	   A^2 -> H(c, U1(k, k))
28.57/10.09	   A^2 -> H(c, U1(k, d))
28.57/10.09	   A^2 -> H(c, U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.09	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.09	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, c), b)
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, c), e)
28.57/10.09	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.09	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.09	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.09	   A^2 -> H(U1(k, c), b)
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, c), c)
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, e), b)
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, e), c)
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, e), e)
28.57/10.09	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, k), b)
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, k), c)
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, k), e)
28.57/10.09	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, c), d)
28.57/10.09	   A^2 -> H(e, U1(e, b))
28.57/10.09	   A^2 -> H(e, U1(c, d))
28.57/10.09	   A^2 -> H(e, U1(d, c))
28.57/10.09	   A^2 -> H(e, U1(b, e))
28.57/10.09	   A^2 -> H(e, U1(b, k))
28.57/10.09	   A^2 -> H(e, U1(e, c))
28.57/10.09	   A^2 -> H(e, U1(c, e))
28.57/10.09	   A^2 -> H(e, U1(c, k))
28.57/10.09	   A^2 -> H(e, U1(e, e))
28.57/10.09	   A^2 -> H(e, U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, e), b)
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, e), c)
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.09	   A^2 -> H(f(e), d)
28.57/10.09	   A^2 -> H(f(e), k)
28.57/10.09	   A^2 -> H(U1(k, k), b)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, k), c)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.09	   A^2 -> H(f(k), d)
28.57/10.09	   A^2 -> H(f(k), k)
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.09	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(k, d), b)
28.57/10.09	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, d), c)
28.57/10.09	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, k), b)
28.57/10.09	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(d, k), c)
28.57/10.09	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(d, k), e)
28.57/10.09	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, d), d)
28.57/10.09	   A^2 -> H(U1(d, d), k)
28.57/10.09	   A^2 -> H(U1(e, c), c)
28.57/10.09	   A^2 -> H(U1(c, c), e)
28.57/10.09	   A^2 -> H(U1(c, c), k)
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, e), e)
28.57/10.09	   A^2 -> H(d, U1(e, b))
28.57/10.09	   A^2 -> H(d, U1(k, b))
28.57/10.09	   A^2 -> H(d, U1(c, d))
28.57/10.09	   A^2 -> H(d, U1(d, c))
28.57/10.09	   A^2 -> H(d, U1(b, e))
28.57/10.09	   A^2 -> H(d, U1(b, k))
28.57/10.09	   A^2 -> H(d, U1(e, c))
28.57/10.09	   A^2 -> H(d, U1(k, c))
28.57/10.09	   A^2 -> H(d, U1(c, e))
28.57/10.09	   A^2 -> H(d, U1(c, k))
28.57/10.09	   A^2 -> H(d, U1(e, e))
28.57/10.09	   A^2 -> H(d, U1(k, k))
28.57/10.09	   A^2 -> H(d, U1(k, d))
28.57/10.09	   A^2 -> H(d, U1(d, k))
28.57/10.09	   A^2 -> H(a, b)
28.57/10.09	   A^2 -> H(a, U1(e, d))
28.57/10.09	   A^2 -> H(a, U1(d, e))
28.57/10.09	   A^2 -> H(a, c)
28.57/10.09	   A^2 -> H(a, U1(e, k))
28.57/10.09	   A^2 -> H(a, U1(k, e))
28.57/10.09	   A^2 -> H(a, e)
28.57/10.09	   A^2 -> H(a, U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, d), b)
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, d), c)
28.57/10.09	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.09	
28.57/10.09	The TRS R consists of the following rules:
28.57/10.09	
28.57/10.09	   f(x) -> U1(x, x)
28.57/10.09	   U1(e, x) -> x
28.57/10.09	   a -> c
28.57/10.09	   a -> d
28.57/10.09	   b -> c
28.57/10.09	   b -> d
28.57/10.09	   d -> k
28.57/10.09	   c -> e
28.57/10.09	   c -> k
28.57/10.09	
28.57/10.09	Q is empty.
28.57/10.09	We have to consider all minimal (P,Q,R)-chains.
28.57/10.09	----------------------------------------
28.57/10.09	
28.57/10.09	(1859) TransformationProof (EQUIVALENT)
28.57/10.09	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.09	
28.57/10.09	   (A^2 -> H(d, U1(e, e)),A^2 -> H(d, U1(e, e)))
28.57/10.09	   (A^2 -> H(U1(e, k), U1(e, e)),A^2 -> H(U1(e, k), U1(e, e)))
28.57/10.09	   (A^2 -> H(U1(e, d), e),A^2 -> H(U1(e, d), e))
28.57/10.09	
28.57/10.09	
28.57/10.09	----------------------------------------
28.57/10.09	
28.57/10.09	(1860)
28.57/10.09	Obligation:
28.57/10.09	Q DP problem:
28.57/10.09	The TRS P consists of the following rules:
28.57/10.09	
28.57/10.09	   H(x, x) -> G(x, x, f(k))
28.57/10.09	   G(d, x, x) -> A^2
28.57/10.09	   A^2 -> H(f(c), f(c))
28.57/10.09	   A^2 -> H(f(d), f(d))
28.57/10.09	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.09	   A^2 -> H(f(e), f(e))
28.57/10.09	   A^2 -> H(f(k), f(k))
28.57/10.09	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.09	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.09	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.09	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.09	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, d), U1(k, d))
28.57/10.09	   A^2 -> H(U1(e, d), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, a), b)
28.57/10.09	   A^2 -> H(U1(e, a), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, a), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, a), c)
28.57/10.09	   A^2 -> H(U1(e, a), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, a), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, a), e)
28.57/10.09	   A^2 -> H(U1(e, a), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, a), b)
28.57/10.09	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, a), c)
28.57/10.09	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, d), b)
28.57/10.09	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, d), c)
28.57/10.09	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, d), e)
28.57/10.09	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, a), d)
28.57/10.09	   A^2 -> H(U1(c, a), k)
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.09	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.09	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.09	   A^2 -> H(U1(d, c), b)
28.57/10.09	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(d, c), c)
28.57/10.09	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(d, c), e)
28.57/10.09	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(d, a), d)
28.57/10.09	   A^2 -> H(U1(d, a), k)
28.57/10.09	   A^2 -> H(U1(a, e), b)
28.57/10.09	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(a, e), c)
28.57/10.09	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(a, e), e)
28.57/10.09	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(a, k), b)
28.57/10.09	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(a, k), c)
28.57/10.09	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.09	   A^2 -> H(U1(a, k), e)
28.57/10.09	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(a, c), d)
28.57/10.09	   A^2 -> H(U1(a, c), k)
28.57/10.09	   A^2 -> H(U1(a, d), d)
28.57/10.09	   A^2 -> H(U1(a, d), k)
28.57/10.09	   A^2 -> H(k, U1(c, b))
28.57/10.09	   A^2 -> H(k, U1(d, b))
28.57/10.09	   A^2 -> H(k, U1(b, c))
28.57/10.09	   A^2 -> H(k, U1(b, d))
28.57/10.09	   A^2 -> H(k, U1(c, c))
28.57/10.09	   A^2 -> H(k, f(e))
28.57/10.09	   A^2 -> H(k, f(k))
28.57/10.09	   A^2 -> H(k, U1(d, d))
28.57/10.09	   A^2 -> H(c, U1(e, b))
28.57/10.09	   A^2 -> H(c, U1(k, b))
28.57/10.09	   A^2 -> H(c, U1(c, d))
28.57/10.09	   A^2 -> H(c, U1(d, c))
28.57/10.09	   A^2 -> H(c, U1(b, e))
28.57/10.09	   A^2 -> H(c, U1(b, k))
28.57/10.09	   A^2 -> H(c, U1(e, c))
28.57/10.09	   A^2 -> H(c, U1(k, c))
28.57/10.09	   A^2 -> H(c, U1(c, e))
28.57/10.09	   A^2 -> H(c, U1(c, k))
28.57/10.09	   A^2 -> H(c, U1(e, e))
28.57/10.09	   A^2 -> H(c, U1(k, k))
28.57/10.09	   A^2 -> H(c, U1(k, d))
28.57/10.09	   A^2 -> H(c, U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.09	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.09	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.09	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.09	   A^2 -> H(U1(e, c), b)
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(e, c), e)
28.57/10.09	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.09	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.09	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.09	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.09	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.09	   A^2 -> H(U1(k, c), b)
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.09	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.09	   A^2 -> H(U1(k, c), c)
28.57/10.09	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.09	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, e), b)
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, e), c)
28.57/10.09	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.09	   A^2 -> H(U1(c, e), e)
28.57/10.09	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.09	   A^2 -> H(U1(c, k), b)
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.09	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.09	   A^2 -> H(U1(c, k), c)
28.57/10.09	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.09	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, k), e)
28.57/10.10	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, c), d)
28.57/10.10	   A^2 -> H(e, U1(e, b))
28.57/10.10	   A^2 -> H(e, U1(c, d))
28.57/10.10	   A^2 -> H(e, U1(d, c))
28.57/10.10	   A^2 -> H(e, U1(b, e))
28.57/10.10	   A^2 -> H(e, U1(b, k))
28.57/10.10	   A^2 -> H(e, U1(e, c))
28.57/10.10	   A^2 -> H(e, U1(c, e))
28.57/10.10	   A^2 -> H(e, U1(c, k))
28.57/10.10	   A^2 -> H(e, U1(e, e))
28.57/10.10	   A^2 -> H(e, U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, e), b)
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, e), c)
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.10	   A^2 -> H(f(e), d)
28.57/10.10	   A^2 -> H(f(e), k)
28.57/10.10	   A^2 -> H(U1(k, k), b)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, k), c)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.10	   A^2 -> H(f(k), d)
28.57/10.10	   A^2 -> H(f(k), k)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(k, d), b)
28.57/10.10	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, d), c)
28.57/10.10	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, k), b)
28.57/10.10	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(d, k), c)
28.57/10.10	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(d, k), e)
28.57/10.10	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, d), d)
28.57/10.10	   A^2 -> H(U1(d, d), k)
28.57/10.10	   A^2 -> H(U1(e, c), c)
28.57/10.10	   A^2 -> H(U1(c, c), e)
28.57/10.10	   A^2 -> H(U1(c, c), k)
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(e, e), e)
28.57/10.10	   A^2 -> H(d, U1(e, b))
28.57/10.10	   A^2 -> H(d, U1(k, b))
28.57/10.10	   A^2 -> H(d, U1(c, d))
28.57/10.10	   A^2 -> H(d, U1(d, c))
28.57/10.10	   A^2 -> H(d, U1(b, e))
28.57/10.10	   A^2 -> H(d, U1(b, k))
28.57/10.10	   A^2 -> H(d, U1(e, c))
28.57/10.10	   A^2 -> H(d, U1(k, c))
28.57/10.10	   A^2 -> H(d, U1(c, e))
28.57/10.10	   A^2 -> H(d, U1(c, k))
28.57/10.10	   A^2 -> H(d, U1(e, e))
28.57/10.10	   A^2 -> H(d, U1(k, k))
28.57/10.10	   A^2 -> H(d, U1(k, d))
28.57/10.10	   A^2 -> H(d, U1(d, k))
28.57/10.10	   A^2 -> H(a, b)
28.57/10.10	   A^2 -> H(a, U1(e, d))
28.57/10.10	   A^2 -> H(a, U1(d, e))
28.57/10.10	   A^2 -> H(a, c)
28.57/10.10	   A^2 -> H(a, U1(e, k))
28.57/10.10	   A^2 -> H(a, U1(k, e))
28.57/10.10	   A^2 -> H(a, e)
28.57/10.10	   A^2 -> H(a, U1(k, k))
28.57/10.10	   A^2 -> H(U1(e, d), b)
28.57/10.10	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, d), c)
28.57/10.10	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, d), e)
28.57/10.10	
28.57/10.10	The TRS R consists of the following rules:
28.57/10.10	
28.57/10.10	   f(x) -> U1(x, x)
28.57/10.10	   U1(e, x) -> x
28.57/10.10	   a -> c
28.57/10.10	   a -> d
28.57/10.10	   b -> c
28.57/10.10	   b -> d
28.57/10.10	   d -> k
28.57/10.10	   c -> e
28.57/10.10	   c -> k
28.57/10.10	
28.57/10.10	Q is empty.
28.57/10.10	We have to consider all minimal (P,Q,R)-chains.
28.57/10.10	----------------------------------------
28.57/10.10	
28.57/10.10	(1861) TransformationProof (EQUIVALENT)
28.57/10.10	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.10	
28.57/10.10	   (A^2 -> H(d, U1(k, k)),A^2 -> H(d, U1(k, k)))
28.57/10.10	   (A^2 -> H(U1(e, k), U1(k, k)),A^2 -> H(U1(e, k), U1(k, k)))
28.57/10.10	
28.57/10.10	
28.57/10.10	----------------------------------------
28.57/10.10	
28.57/10.10	(1862)
28.57/10.10	Obligation:
28.57/10.10	Q DP problem:
28.57/10.10	The TRS P consists of the following rules:
28.57/10.10	
28.57/10.10	   H(x, x) -> G(x, x, f(k))
28.57/10.10	   G(d, x, x) -> A^2
28.57/10.10	   A^2 -> H(f(c), f(c))
28.57/10.10	   A^2 -> H(f(d), f(d))
28.57/10.10	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.10	   A^2 -> H(f(e), f(e))
28.57/10.10	   A^2 -> H(f(k), f(k))
28.57/10.10	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.10	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.10	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.10	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.10	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, d), U1(k, d))
28.57/10.10	   A^2 -> H(U1(e, d), U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, a), b)
28.57/10.10	   A^2 -> H(U1(e, a), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, a), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, a), c)
28.57/10.10	   A^2 -> H(U1(e, a), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, a), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, a), e)
28.57/10.10	   A^2 -> H(U1(e, a), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, a), b)
28.57/10.10	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, a), c)
28.57/10.10	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, d), b)
28.57/10.10	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, d), c)
28.57/10.10	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, d), e)
28.57/10.10	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, a), d)
28.57/10.10	   A^2 -> H(U1(c, a), k)
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.10	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.10	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.10	   A^2 -> H(U1(d, c), b)
28.57/10.10	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(d, c), c)
28.57/10.10	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(d, c), e)
28.57/10.10	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, a), d)
28.57/10.10	   A^2 -> H(U1(d, a), k)
28.57/10.10	   A^2 -> H(U1(a, e), b)
28.57/10.10	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(a, e), c)
28.57/10.10	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(a, e), e)
28.57/10.10	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(a, k), b)
28.57/10.10	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(a, k), c)
28.57/10.10	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(a, k), e)
28.57/10.10	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(a, c), d)
28.57/10.10	   A^2 -> H(U1(a, c), k)
28.57/10.10	   A^2 -> H(U1(a, d), d)
28.57/10.10	   A^2 -> H(U1(a, d), k)
28.57/10.10	   A^2 -> H(k, U1(c, b))
28.57/10.10	   A^2 -> H(k, U1(d, b))
28.57/10.10	   A^2 -> H(k, U1(b, c))
28.57/10.10	   A^2 -> H(k, U1(b, d))
28.57/10.10	   A^2 -> H(k, U1(c, c))
28.57/10.10	   A^2 -> H(k, f(e))
28.57/10.10	   A^2 -> H(k, f(k))
28.57/10.10	   A^2 -> H(k, U1(d, d))
28.57/10.10	   A^2 -> H(c, U1(e, b))
28.57/10.10	   A^2 -> H(c, U1(k, b))
28.57/10.10	   A^2 -> H(c, U1(c, d))
28.57/10.10	   A^2 -> H(c, U1(d, c))
28.57/10.10	   A^2 -> H(c, U1(b, e))
28.57/10.10	   A^2 -> H(c, U1(b, k))
28.57/10.10	   A^2 -> H(c, U1(e, c))
28.57/10.10	   A^2 -> H(c, U1(k, c))
28.57/10.10	   A^2 -> H(c, U1(c, e))
28.57/10.10	   A^2 -> H(c, U1(c, k))
28.57/10.10	   A^2 -> H(c, U1(e, e))
28.57/10.10	   A^2 -> H(c, U1(k, k))
28.57/10.10	   A^2 -> H(c, U1(k, d))
28.57/10.10	   A^2 -> H(c, U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.10	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.10	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, c), b)
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, c), e)
28.57/10.10	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.10	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.10	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.10	   A^2 -> H(U1(k, c), b)
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, c), c)
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, e), b)
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, e), c)
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, e), e)
28.57/10.10	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, k), b)
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, k), c)
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, k), e)
28.57/10.10	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, c), d)
28.57/10.10	   A^2 -> H(e, U1(e, b))
28.57/10.10	   A^2 -> H(e, U1(c, d))
28.57/10.10	   A^2 -> H(e, U1(d, c))
28.57/10.10	   A^2 -> H(e, U1(b, e))
28.57/10.10	   A^2 -> H(e, U1(b, k))
28.57/10.10	   A^2 -> H(e, U1(e, c))
28.57/10.10	   A^2 -> H(e, U1(c, e))
28.57/10.10	   A^2 -> H(e, U1(c, k))
28.57/10.10	   A^2 -> H(e, U1(e, e))
28.57/10.10	   A^2 -> H(e, U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, e), b)
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, e), c)
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.10	   A^2 -> H(f(e), d)
28.57/10.10	   A^2 -> H(f(e), k)
28.57/10.10	   A^2 -> H(U1(k, k), b)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, k), c)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.10	   A^2 -> H(f(k), d)
28.57/10.10	   A^2 -> H(f(k), k)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(k, d), b)
28.57/10.10	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, d), c)
28.57/10.10	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, k), b)
28.57/10.10	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(d, k), c)
28.57/10.10	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(d, k), e)
28.57/10.10	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, d), d)
28.57/10.10	   A^2 -> H(U1(d, d), k)
28.57/10.10	   A^2 -> H(U1(e, c), c)
28.57/10.10	   A^2 -> H(U1(c, c), e)
28.57/10.10	   A^2 -> H(U1(c, c), k)
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(e, e), e)
28.57/10.10	   A^2 -> H(d, U1(e, b))
28.57/10.10	   A^2 -> H(d, U1(k, b))
28.57/10.10	   A^2 -> H(d, U1(c, d))
28.57/10.10	   A^2 -> H(d, U1(d, c))
28.57/10.10	   A^2 -> H(d, U1(b, e))
28.57/10.10	   A^2 -> H(d, U1(b, k))
28.57/10.10	   A^2 -> H(d, U1(e, c))
28.57/10.10	   A^2 -> H(d, U1(k, c))
28.57/10.10	   A^2 -> H(d, U1(c, e))
28.57/10.10	   A^2 -> H(d, U1(c, k))
28.57/10.10	   A^2 -> H(d, U1(e, e))
28.57/10.10	   A^2 -> H(d, U1(k, k))
28.57/10.10	   A^2 -> H(d, U1(k, d))
28.57/10.10	   A^2 -> H(d, U1(d, k))
28.57/10.10	   A^2 -> H(a, b)
28.57/10.10	   A^2 -> H(a, U1(e, d))
28.57/10.10	   A^2 -> H(a, U1(d, e))
28.57/10.10	   A^2 -> H(a, c)
28.57/10.10	   A^2 -> H(a, U1(e, k))
28.57/10.10	   A^2 -> H(a, U1(k, e))
28.57/10.10	   A^2 -> H(a, e)
28.57/10.10	   A^2 -> H(a, U1(k, k))
28.57/10.10	   A^2 -> H(U1(e, d), b)
28.57/10.10	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, d), c)
28.57/10.10	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, d), e)
28.57/10.10	
28.57/10.10	The TRS R consists of the following rules:
28.57/10.10	
28.57/10.10	   f(x) -> U1(x, x)
28.57/10.10	   U1(e, x) -> x
28.57/10.10	   a -> c
28.57/10.10	   a -> d
28.57/10.10	   b -> c
28.57/10.10	   b -> d
28.57/10.10	   d -> k
28.57/10.10	   c -> e
28.57/10.10	   c -> k
28.57/10.10	
28.57/10.10	Q is empty.
28.57/10.10	We have to consider all minimal (P,Q,R)-chains.
28.57/10.10	----------------------------------------
28.57/10.10	
28.57/10.10	(1863) TransformationProof (EQUIVALENT)
28.57/10.10	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.10	
28.57/10.10	   (A^2 -> H(d, U1(k, d)),A^2 -> H(d, U1(k, d)))
28.57/10.10	   (A^2 -> H(U1(e, k), U1(k, d)),A^2 -> H(U1(e, k), U1(k, d)))
28.57/10.10	   (A^2 -> H(U1(e, d), U1(k, k)),A^2 -> H(U1(e, d), U1(k, k)))
28.57/10.10	
28.57/10.10	
28.57/10.10	----------------------------------------
28.57/10.10	
28.57/10.10	(1864)
28.57/10.10	Obligation:
28.57/10.10	Q DP problem:
28.57/10.10	The TRS P consists of the following rules:
28.57/10.10	
28.57/10.10	   H(x, x) -> G(x, x, f(k))
28.57/10.10	   G(d, x, x) -> A^2
28.57/10.10	   A^2 -> H(f(c), f(c))
28.57/10.10	   A^2 -> H(f(d), f(d))
28.57/10.10	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.10	   A^2 -> H(f(e), f(e))
28.57/10.10	   A^2 -> H(f(k), f(k))
28.57/10.10	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.10	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.10	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.10	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.10	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, d), U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, a), b)
28.57/10.10	   A^2 -> H(U1(e, a), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, a), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, a), c)
28.57/10.10	   A^2 -> H(U1(e, a), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, a), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, a), e)
28.57/10.10	   A^2 -> H(U1(e, a), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, a), b)
28.57/10.10	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, a), c)
28.57/10.10	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, d), b)
28.57/10.10	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, d), c)
28.57/10.10	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, d), e)
28.57/10.10	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, a), d)
28.57/10.10	   A^2 -> H(U1(c, a), k)
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.10	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.10	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.10	   A^2 -> H(U1(d, c), b)
28.57/10.10	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(d, c), c)
28.57/10.10	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(d, c), e)
28.57/10.10	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, a), d)
28.57/10.10	   A^2 -> H(U1(d, a), k)
28.57/10.10	   A^2 -> H(U1(a, e), b)
28.57/10.10	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(a, e), c)
28.57/10.10	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(a, e), e)
28.57/10.10	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(a, k), b)
28.57/10.10	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(a, k), c)
28.57/10.10	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(a, k), e)
28.57/10.10	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(a, c), d)
28.57/10.10	   A^2 -> H(U1(a, c), k)
28.57/10.10	   A^2 -> H(U1(a, d), d)
28.57/10.10	   A^2 -> H(U1(a, d), k)
28.57/10.10	   A^2 -> H(k, U1(c, b))
28.57/10.10	   A^2 -> H(k, U1(d, b))
28.57/10.10	   A^2 -> H(k, U1(b, c))
28.57/10.10	   A^2 -> H(k, U1(b, d))
28.57/10.10	   A^2 -> H(k, U1(c, c))
28.57/10.10	   A^2 -> H(k, f(e))
28.57/10.10	   A^2 -> H(k, f(k))
28.57/10.10	   A^2 -> H(k, U1(d, d))
28.57/10.10	   A^2 -> H(c, U1(e, b))
28.57/10.10	   A^2 -> H(c, U1(k, b))
28.57/10.10	   A^2 -> H(c, U1(c, d))
28.57/10.10	   A^2 -> H(c, U1(d, c))
28.57/10.10	   A^2 -> H(c, U1(b, e))
28.57/10.10	   A^2 -> H(c, U1(b, k))
28.57/10.10	   A^2 -> H(c, U1(e, c))
28.57/10.10	   A^2 -> H(c, U1(k, c))
28.57/10.10	   A^2 -> H(c, U1(c, e))
28.57/10.10	   A^2 -> H(c, U1(c, k))
28.57/10.10	   A^2 -> H(c, U1(e, e))
28.57/10.10	   A^2 -> H(c, U1(k, k))
28.57/10.10	   A^2 -> H(c, U1(k, d))
28.57/10.10	   A^2 -> H(c, U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.10	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.10	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, c), b)
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, c), e)
28.57/10.10	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.10	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.10	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.10	   A^2 -> H(U1(k, c), b)
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, c), c)
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, e), b)
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, e), c)
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, e), e)
28.57/10.10	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, k), b)
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, k), c)
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, k), e)
28.57/10.10	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, c), d)
28.57/10.10	   A^2 -> H(e, U1(e, b))
28.57/10.10	   A^2 -> H(e, U1(c, d))
28.57/10.10	   A^2 -> H(e, U1(d, c))
28.57/10.10	   A^2 -> H(e, U1(b, e))
28.57/10.10	   A^2 -> H(e, U1(b, k))
28.57/10.10	   A^2 -> H(e, U1(e, c))
28.57/10.10	   A^2 -> H(e, U1(c, e))
28.57/10.10	   A^2 -> H(e, U1(c, k))
28.57/10.10	   A^2 -> H(e, U1(e, e))
28.57/10.10	   A^2 -> H(e, U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, e), b)
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, e), c)
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.10	   A^2 -> H(f(e), d)
28.57/10.10	   A^2 -> H(f(e), k)
28.57/10.10	   A^2 -> H(U1(k, k), b)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, k), c)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.10	   A^2 -> H(f(k), d)
28.57/10.10	   A^2 -> H(f(k), k)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(k, d), b)
28.57/10.10	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, d), c)
28.57/10.10	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, k), b)
28.57/10.10	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(d, k), c)
28.57/10.10	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(d, k), e)
28.57/10.10	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, d), d)
28.57/10.10	   A^2 -> H(U1(d, d), k)
28.57/10.10	   A^2 -> H(U1(e, c), c)
28.57/10.10	   A^2 -> H(U1(c, c), e)
28.57/10.10	   A^2 -> H(U1(c, c), k)
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(e, e), e)
28.57/10.10	   A^2 -> H(d, U1(e, b))
28.57/10.10	   A^2 -> H(d, U1(k, b))
28.57/10.10	   A^2 -> H(d, U1(c, d))
28.57/10.10	   A^2 -> H(d, U1(d, c))
28.57/10.10	   A^2 -> H(d, U1(b, e))
28.57/10.10	   A^2 -> H(d, U1(b, k))
28.57/10.10	   A^2 -> H(d, U1(e, c))
28.57/10.10	   A^2 -> H(d, U1(k, c))
28.57/10.10	   A^2 -> H(d, U1(c, e))
28.57/10.10	   A^2 -> H(d, U1(c, k))
28.57/10.10	   A^2 -> H(d, U1(e, e))
28.57/10.10	   A^2 -> H(d, U1(k, k))
28.57/10.10	   A^2 -> H(d, U1(k, d))
28.57/10.10	   A^2 -> H(d, U1(d, k))
28.57/10.10	   A^2 -> H(a, b)
28.57/10.10	   A^2 -> H(a, U1(e, d))
28.57/10.10	   A^2 -> H(a, U1(d, e))
28.57/10.10	   A^2 -> H(a, c)
28.57/10.10	   A^2 -> H(a, U1(e, k))
28.57/10.10	   A^2 -> H(a, U1(k, e))
28.57/10.10	   A^2 -> H(a, e)
28.57/10.10	   A^2 -> H(a, U1(k, k))
28.57/10.10	   A^2 -> H(U1(e, d), b)
28.57/10.10	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, d), c)
28.57/10.10	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, d), e)
28.57/10.10	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.10	
28.57/10.10	The TRS R consists of the following rules:
28.57/10.10	
28.57/10.10	   f(x) -> U1(x, x)
28.57/10.10	   U1(e, x) -> x
28.57/10.10	   a -> c
28.57/10.10	   a -> d
28.57/10.10	   b -> c
28.57/10.10	   b -> d
28.57/10.10	   d -> k
28.57/10.10	   c -> e
28.57/10.10	   c -> k
28.57/10.10	
28.57/10.10	Q is empty.
28.57/10.10	We have to consider all minimal (P,Q,R)-chains.
28.57/10.10	----------------------------------------
28.57/10.10	
28.57/10.10	(1865) TransformationProof (EQUIVALENT)
28.57/10.10	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.10	
28.57/10.10	   (A^2 -> H(d, U1(d, k)),A^2 -> H(d, U1(d, k)))
28.57/10.10	   (A^2 -> H(U1(e, k), U1(d, k)),A^2 -> H(U1(e, k), U1(d, k)))
28.57/10.10	   (A^2 -> H(U1(e, d), U1(k, k)),A^2 -> H(U1(e, d), U1(k, k)))
28.57/10.10	
28.57/10.10	
28.57/10.10	----------------------------------------
28.57/10.10	
28.57/10.10	(1866)
28.57/10.10	Obligation:
28.57/10.10	Q DP problem:
28.57/10.10	The TRS P consists of the following rules:
28.57/10.10	
28.57/10.10	   H(x, x) -> G(x, x, f(k))
28.57/10.10	   G(d, x, x) -> A^2
28.57/10.10	   A^2 -> H(f(c), f(c))
28.57/10.10	   A^2 -> H(f(d), f(d))
28.57/10.10	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.10	   A^2 -> H(f(e), f(e))
28.57/10.10	   A^2 -> H(f(k), f(k))
28.57/10.10	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.10	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.10	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.10	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.10	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, a), b)
28.57/10.10	   A^2 -> H(U1(e, a), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, a), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, a), c)
28.57/10.10	   A^2 -> H(U1(e, a), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, a), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, a), e)
28.57/10.10	   A^2 -> H(U1(e, a), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, a), b)
28.57/10.10	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, a), c)
28.57/10.10	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, d), b)
28.57/10.10	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, d), c)
28.57/10.10	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, d), e)
28.57/10.10	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, a), d)
28.57/10.10	   A^2 -> H(U1(c, a), k)
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.10	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.10	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.10	   A^2 -> H(U1(d, c), b)
28.57/10.10	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(d, c), c)
28.57/10.10	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(d, c), e)
28.57/10.10	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, a), d)
28.57/10.10	   A^2 -> H(U1(d, a), k)
28.57/10.10	   A^2 -> H(U1(a, e), b)
28.57/10.10	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(a, e), c)
28.57/10.10	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(a, e), e)
28.57/10.10	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(a, k), b)
28.57/10.10	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(a, k), c)
28.57/10.10	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(a, k), e)
28.57/10.10	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(a, c), d)
28.57/10.10	   A^2 -> H(U1(a, c), k)
28.57/10.10	   A^2 -> H(U1(a, d), d)
28.57/10.10	   A^2 -> H(U1(a, d), k)
28.57/10.10	   A^2 -> H(k, U1(c, b))
28.57/10.10	   A^2 -> H(k, U1(d, b))
28.57/10.10	   A^2 -> H(k, U1(b, c))
28.57/10.10	   A^2 -> H(k, U1(b, d))
28.57/10.10	   A^2 -> H(k, U1(c, c))
28.57/10.10	   A^2 -> H(k, f(e))
28.57/10.10	   A^2 -> H(k, f(k))
28.57/10.10	   A^2 -> H(k, U1(d, d))
28.57/10.10	   A^2 -> H(c, U1(e, b))
28.57/10.10	   A^2 -> H(c, U1(k, b))
28.57/10.10	   A^2 -> H(c, U1(c, d))
28.57/10.10	   A^2 -> H(c, U1(d, c))
28.57/10.10	   A^2 -> H(c, U1(b, e))
28.57/10.10	   A^2 -> H(c, U1(b, k))
28.57/10.10	   A^2 -> H(c, U1(e, c))
28.57/10.10	   A^2 -> H(c, U1(k, c))
28.57/10.10	   A^2 -> H(c, U1(c, e))
28.57/10.10	   A^2 -> H(c, U1(c, k))
28.57/10.10	   A^2 -> H(c, U1(e, e))
28.57/10.10	   A^2 -> H(c, U1(k, k))
28.57/10.10	   A^2 -> H(c, U1(k, d))
28.57/10.10	   A^2 -> H(c, U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.10	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.10	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, c), b)
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, c), e)
28.57/10.10	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.10	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.10	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.10	   A^2 -> H(U1(k, c), b)
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, c), c)
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, e), b)
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, e), c)
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, e), e)
28.57/10.10	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, k), b)
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, k), c)
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, k), e)
28.57/10.10	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, c), d)
28.57/10.10	   A^2 -> H(e, U1(e, b))
28.57/10.10	   A^2 -> H(e, U1(c, d))
28.57/10.10	   A^2 -> H(e, U1(d, c))
28.57/10.10	   A^2 -> H(e, U1(b, e))
28.57/10.10	   A^2 -> H(e, U1(b, k))
28.57/10.10	   A^2 -> H(e, U1(e, c))
28.57/10.10	   A^2 -> H(e, U1(c, e))
28.57/10.10	   A^2 -> H(e, U1(c, k))
28.57/10.10	   A^2 -> H(e, U1(e, e))
28.57/10.10	   A^2 -> H(e, U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, e), b)
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, e), c)
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.10	   A^2 -> H(f(e), d)
28.57/10.10	   A^2 -> H(f(e), k)
28.57/10.10	   A^2 -> H(U1(k, k), b)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, k), c)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.10	   A^2 -> H(f(k), d)
28.57/10.10	   A^2 -> H(f(k), k)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(k, d), b)
28.57/10.10	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, d), c)
28.57/10.10	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, k), b)
28.57/10.10	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(d, k), c)
28.57/10.10	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(d, k), e)
28.57/10.10	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, d), d)
28.57/10.10	   A^2 -> H(U1(d, d), k)
28.57/10.10	   A^2 -> H(U1(e, c), c)
28.57/10.10	   A^2 -> H(U1(c, c), e)
28.57/10.10	   A^2 -> H(U1(c, c), k)
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(e, e), e)
28.57/10.10	   A^2 -> H(d, U1(e, b))
28.57/10.10	   A^2 -> H(d, U1(k, b))
28.57/10.10	   A^2 -> H(d, U1(c, d))
28.57/10.10	   A^2 -> H(d, U1(d, c))
28.57/10.10	   A^2 -> H(d, U1(b, e))
28.57/10.10	   A^2 -> H(d, U1(b, k))
28.57/10.10	   A^2 -> H(d, U1(e, c))
28.57/10.10	   A^2 -> H(d, U1(k, c))
28.57/10.10	   A^2 -> H(d, U1(c, e))
28.57/10.10	   A^2 -> H(d, U1(c, k))
28.57/10.10	   A^2 -> H(d, U1(e, e))
28.57/10.10	   A^2 -> H(d, U1(k, k))
28.57/10.10	   A^2 -> H(d, U1(k, d))
28.57/10.10	   A^2 -> H(d, U1(d, k))
28.57/10.10	   A^2 -> H(a, b)
28.57/10.10	   A^2 -> H(a, U1(e, d))
28.57/10.10	   A^2 -> H(a, U1(d, e))
28.57/10.10	   A^2 -> H(a, c)
28.57/10.10	   A^2 -> H(a, U1(e, k))
28.57/10.10	   A^2 -> H(a, U1(k, e))
28.57/10.10	   A^2 -> H(a, e)
28.57/10.10	   A^2 -> H(a, U1(k, k))
28.57/10.10	   A^2 -> H(U1(e, d), b)
28.57/10.10	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, d), c)
28.57/10.10	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, d), e)
28.57/10.10	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.10	
28.57/10.10	The TRS R consists of the following rules:
28.57/10.10	
28.57/10.10	   f(x) -> U1(x, x)
28.57/10.10	   U1(e, x) -> x
28.57/10.10	   a -> c
28.57/10.10	   a -> d
28.57/10.10	   b -> c
28.57/10.10	   b -> d
28.57/10.10	   d -> k
28.57/10.10	   c -> e
28.57/10.10	   c -> k
28.57/10.10	
28.57/10.10	Q is empty.
28.57/10.10	We have to consider all minimal (P,Q,R)-chains.
28.57/10.10	----------------------------------------
28.57/10.10	
28.57/10.10	(1867) TransformationProof (EQUIVALENT)
28.57/10.10	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), b) at position [] we obtained the following new rules [LPAR04]:
28.57/10.10	
28.57/10.10	   (A^2 -> H(a, b),A^2 -> H(a, b))
28.57/10.10	   (A^2 -> H(U1(e, c), b),A^2 -> H(U1(e, c), b))
28.57/10.10	   (A^2 -> H(U1(e, d), b),A^2 -> H(U1(e, d), b))
28.57/10.10	   (A^2 -> H(U1(e, a), c),A^2 -> H(U1(e, a), c))
28.57/10.10	   (A^2 -> H(U1(e, a), d),A^2 -> H(U1(e, a), d))
28.57/10.10	
28.57/10.10	
28.57/10.10	----------------------------------------
28.57/10.10	
28.57/10.10	(1868)
28.57/10.10	Obligation:
28.57/10.10	Q DP problem:
28.57/10.10	The TRS P consists of the following rules:
28.57/10.10	
28.57/10.10	   H(x, x) -> G(x, x, f(k))
28.57/10.10	   G(d, x, x) -> A^2
28.57/10.10	   A^2 -> H(f(c), f(c))
28.57/10.10	   A^2 -> H(f(d), f(d))
28.57/10.10	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.10	   A^2 -> H(f(e), f(e))
28.57/10.10	   A^2 -> H(f(k), f(k))
28.57/10.10	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.10	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.10	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.10	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.10	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, a), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, a), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, a), c)
28.57/10.10	   A^2 -> H(U1(e, a), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, a), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, a), e)
28.57/10.10	   A^2 -> H(U1(e, a), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, a), b)
28.57/10.10	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, a), c)
28.57/10.10	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, d), b)
28.57/10.10	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, d), c)
28.57/10.10	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, d), e)
28.57/10.10	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, a), d)
28.57/10.10	   A^2 -> H(U1(c, a), k)
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.10	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.10	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.10	   A^2 -> H(U1(d, c), b)
28.57/10.10	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(d, c), c)
28.57/10.10	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(d, c), e)
28.57/10.10	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, a), d)
28.57/10.10	   A^2 -> H(U1(d, a), k)
28.57/10.10	   A^2 -> H(U1(a, e), b)
28.57/10.10	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(a, e), c)
28.57/10.10	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(a, e), e)
28.57/10.10	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(a, k), b)
28.57/10.10	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(a, k), c)
28.57/10.10	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(a, k), e)
28.57/10.10	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(a, c), d)
28.57/10.10	   A^2 -> H(U1(a, c), k)
28.57/10.10	   A^2 -> H(U1(a, d), d)
28.57/10.10	   A^2 -> H(U1(a, d), k)
28.57/10.10	   A^2 -> H(k, U1(c, b))
28.57/10.10	   A^2 -> H(k, U1(d, b))
28.57/10.10	   A^2 -> H(k, U1(b, c))
28.57/10.10	   A^2 -> H(k, U1(b, d))
28.57/10.10	   A^2 -> H(k, U1(c, c))
28.57/10.10	   A^2 -> H(k, f(e))
28.57/10.10	   A^2 -> H(k, f(k))
28.57/10.10	   A^2 -> H(k, U1(d, d))
28.57/10.10	   A^2 -> H(c, U1(e, b))
28.57/10.10	   A^2 -> H(c, U1(k, b))
28.57/10.10	   A^2 -> H(c, U1(c, d))
28.57/10.10	   A^2 -> H(c, U1(d, c))
28.57/10.10	   A^2 -> H(c, U1(b, e))
28.57/10.10	   A^2 -> H(c, U1(b, k))
28.57/10.10	   A^2 -> H(c, U1(e, c))
28.57/10.10	   A^2 -> H(c, U1(k, c))
28.57/10.10	   A^2 -> H(c, U1(c, e))
28.57/10.10	   A^2 -> H(c, U1(c, k))
28.57/10.10	   A^2 -> H(c, U1(e, e))
28.57/10.10	   A^2 -> H(c, U1(k, k))
28.57/10.10	   A^2 -> H(c, U1(k, d))
28.57/10.10	   A^2 -> H(c, U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.10	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.10	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, c), b)
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, c), e)
28.57/10.10	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.10	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.10	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.10	   A^2 -> H(U1(k, c), b)
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, c), c)
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, e), b)
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, e), c)
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, e), e)
28.57/10.10	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, k), b)
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, k), c)
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, k), e)
28.57/10.10	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, c), d)
28.57/10.10	   A^2 -> H(e, U1(e, b))
28.57/10.10	   A^2 -> H(e, U1(c, d))
28.57/10.10	   A^2 -> H(e, U1(d, c))
28.57/10.10	   A^2 -> H(e, U1(b, e))
28.57/10.10	   A^2 -> H(e, U1(b, k))
28.57/10.10	   A^2 -> H(e, U1(e, c))
28.57/10.10	   A^2 -> H(e, U1(c, e))
28.57/10.10	   A^2 -> H(e, U1(c, k))
28.57/10.10	   A^2 -> H(e, U1(e, e))
28.57/10.10	   A^2 -> H(e, U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, e), b)
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, e), c)
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.10	   A^2 -> H(f(e), d)
28.57/10.10	   A^2 -> H(f(e), k)
28.57/10.10	   A^2 -> H(U1(k, k), b)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, k), c)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.10	   A^2 -> H(f(k), d)
28.57/10.10	   A^2 -> H(f(k), k)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(k, d), b)
28.57/10.10	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, d), c)
28.57/10.10	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, k), b)
28.57/10.10	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(d, k), c)
28.57/10.10	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(d, k), e)
28.57/10.10	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, d), d)
28.57/10.10	   A^2 -> H(U1(d, d), k)
28.57/10.10	   A^2 -> H(U1(e, c), c)
28.57/10.10	   A^2 -> H(U1(c, c), e)
28.57/10.10	   A^2 -> H(U1(c, c), k)
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(e, e), e)
28.57/10.10	   A^2 -> H(d, U1(e, b))
28.57/10.10	   A^2 -> H(d, U1(k, b))
28.57/10.10	   A^2 -> H(d, U1(c, d))
28.57/10.10	   A^2 -> H(d, U1(d, c))
28.57/10.10	   A^2 -> H(d, U1(b, e))
28.57/10.10	   A^2 -> H(d, U1(b, k))
28.57/10.10	   A^2 -> H(d, U1(e, c))
28.57/10.10	   A^2 -> H(d, U1(k, c))
28.57/10.10	   A^2 -> H(d, U1(c, e))
28.57/10.10	   A^2 -> H(d, U1(c, k))
28.57/10.10	   A^2 -> H(d, U1(e, e))
28.57/10.10	   A^2 -> H(d, U1(k, k))
28.57/10.10	   A^2 -> H(d, U1(k, d))
28.57/10.10	   A^2 -> H(d, U1(d, k))
28.57/10.10	   A^2 -> H(a, b)
28.57/10.10	   A^2 -> H(a, U1(e, d))
28.57/10.10	   A^2 -> H(a, U1(d, e))
28.57/10.10	   A^2 -> H(a, c)
28.57/10.10	   A^2 -> H(a, U1(e, k))
28.57/10.10	   A^2 -> H(a, U1(k, e))
28.57/10.10	   A^2 -> H(a, e)
28.57/10.10	   A^2 -> H(a, U1(k, k))
28.57/10.10	   A^2 -> H(U1(e, d), b)
28.57/10.10	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, d), c)
28.57/10.10	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, d), e)
28.57/10.10	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.10	   A^2 -> H(U1(e, a), d)
28.57/10.10	
28.57/10.10	The TRS R consists of the following rules:
28.57/10.10	
28.57/10.10	   f(x) -> U1(x, x)
28.57/10.10	   U1(e, x) -> x
28.57/10.10	   a -> c
28.57/10.10	   a -> d
28.57/10.10	   b -> c
28.57/10.10	   b -> d
28.57/10.10	   d -> k
28.57/10.10	   c -> e
28.57/10.10	   c -> k
28.57/10.10	
28.57/10.10	Q is empty.
28.57/10.10	We have to consider all minimal (P,Q,R)-chains.
28.57/10.10	----------------------------------------
28.57/10.10	
28.57/10.10	(1869) TransformationProof (EQUIVALENT)
28.57/10.10	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.10	
28.57/10.10	   (A^2 -> H(a, U1(e, d)),A^2 -> H(a, U1(e, d)))
28.57/10.10	   (A^2 -> H(U1(e, c), U1(e, d)),A^2 -> H(U1(e, c), U1(e, d)))
28.57/10.10	   (A^2 -> H(U1(e, d), U1(e, d)),A^2 -> H(U1(e, d), U1(e, d)))
28.57/10.10	   (A^2 -> H(U1(e, a), d),A^2 -> H(U1(e, a), d))
28.57/10.10	   (A^2 -> H(U1(e, a), U1(e, k)),A^2 -> H(U1(e, a), U1(e, k)))
28.57/10.10	
28.57/10.10	
28.57/10.10	----------------------------------------
28.57/10.10	
28.57/10.10	(1870)
28.57/10.10	Obligation:
28.57/10.10	Q DP problem:
28.57/10.10	The TRS P consists of the following rules:
28.57/10.10	
28.57/10.10	   H(x, x) -> G(x, x, f(k))
28.57/10.10	   G(d, x, x) -> A^2
28.57/10.10	   A^2 -> H(f(c), f(c))
28.57/10.10	   A^2 -> H(f(d), f(d))
28.57/10.10	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.10	   A^2 -> H(f(e), f(e))
28.57/10.10	   A^2 -> H(f(k), f(k))
28.57/10.10	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.10	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.10	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.10	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.10	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, a), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, a), c)
28.57/10.10	   A^2 -> H(U1(e, a), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, a), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, a), e)
28.57/10.10	   A^2 -> H(U1(e, a), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, a), b)
28.57/10.10	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, a), c)
28.57/10.10	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, d), b)
28.57/10.10	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, d), c)
28.57/10.10	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, d), e)
28.57/10.10	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, a), d)
28.57/10.10	   A^2 -> H(U1(c, a), k)
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.10	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.10	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.10	   A^2 -> H(U1(d, c), b)
28.57/10.10	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(d, c), c)
28.57/10.10	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(d, c), e)
28.57/10.10	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, a), d)
28.57/10.10	   A^2 -> H(U1(d, a), k)
28.57/10.10	   A^2 -> H(U1(a, e), b)
28.57/10.10	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(a, e), c)
28.57/10.10	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(a, e), e)
28.57/10.10	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(a, k), b)
28.57/10.10	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(a, k), c)
28.57/10.10	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(a, k), e)
28.57/10.10	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(a, c), d)
28.57/10.10	   A^2 -> H(U1(a, c), k)
28.57/10.10	   A^2 -> H(U1(a, d), d)
28.57/10.10	   A^2 -> H(U1(a, d), k)
28.57/10.10	   A^2 -> H(k, U1(c, b))
28.57/10.10	   A^2 -> H(k, U1(d, b))
28.57/10.10	   A^2 -> H(k, U1(b, c))
28.57/10.10	   A^2 -> H(k, U1(b, d))
28.57/10.10	   A^2 -> H(k, U1(c, c))
28.57/10.10	   A^2 -> H(k, f(e))
28.57/10.10	   A^2 -> H(k, f(k))
28.57/10.10	   A^2 -> H(k, U1(d, d))
28.57/10.10	   A^2 -> H(c, U1(e, b))
28.57/10.10	   A^2 -> H(c, U1(k, b))
28.57/10.10	   A^2 -> H(c, U1(c, d))
28.57/10.10	   A^2 -> H(c, U1(d, c))
28.57/10.10	   A^2 -> H(c, U1(b, e))
28.57/10.10	   A^2 -> H(c, U1(b, k))
28.57/10.10	   A^2 -> H(c, U1(e, c))
28.57/10.10	   A^2 -> H(c, U1(k, c))
28.57/10.10	   A^2 -> H(c, U1(c, e))
28.57/10.10	   A^2 -> H(c, U1(c, k))
28.57/10.10	   A^2 -> H(c, U1(e, e))
28.57/10.10	   A^2 -> H(c, U1(k, k))
28.57/10.10	   A^2 -> H(c, U1(k, d))
28.57/10.10	   A^2 -> H(c, U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.10	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.10	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, c), b)
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, c), e)
28.57/10.10	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.10	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.10	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.10	   A^2 -> H(U1(k, c), b)
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, c), c)
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, e), b)
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, e), c)
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, e), e)
28.57/10.10	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, k), b)
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, k), c)
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, k), e)
28.57/10.10	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, c), d)
28.57/10.10	   A^2 -> H(e, U1(e, b))
28.57/10.10	   A^2 -> H(e, U1(c, d))
28.57/10.10	   A^2 -> H(e, U1(d, c))
28.57/10.10	   A^2 -> H(e, U1(b, e))
28.57/10.10	   A^2 -> H(e, U1(b, k))
28.57/10.10	   A^2 -> H(e, U1(e, c))
28.57/10.10	   A^2 -> H(e, U1(c, e))
28.57/10.10	   A^2 -> H(e, U1(c, k))
28.57/10.10	   A^2 -> H(e, U1(e, e))
28.57/10.10	   A^2 -> H(e, U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, e), b)
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, e), c)
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.10	   A^2 -> H(f(e), d)
28.57/10.10	   A^2 -> H(f(e), k)
28.57/10.10	   A^2 -> H(U1(k, k), b)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, k), c)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.10	   A^2 -> H(f(k), d)
28.57/10.10	   A^2 -> H(f(k), k)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(k, d), b)
28.57/10.10	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, d), c)
28.57/10.10	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, k), b)
28.57/10.10	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(d, k), c)
28.57/10.10	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(d, k), e)
28.57/10.10	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, d), d)
28.57/10.10	   A^2 -> H(U1(d, d), k)
28.57/10.10	   A^2 -> H(U1(e, c), c)
28.57/10.10	   A^2 -> H(U1(c, c), e)
28.57/10.10	   A^2 -> H(U1(c, c), k)
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(e, e), e)
28.57/10.10	   A^2 -> H(d, U1(e, b))
28.57/10.10	   A^2 -> H(d, U1(k, b))
28.57/10.10	   A^2 -> H(d, U1(c, d))
28.57/10.10	   A^2 -> H(d, U1(d, c))
28.57/10.10	   A^2 -> H(d, U1(b, e))
28.57/10.10	   A^2 -> H(d, U1(b, k))
28.57/10.10	   A^2 -> H(d, U1(e, c))
28.57/10.10	   A^2 -> H(d, U1(k, c))
28.57/10.10	   A^2 -> H(d, U1(c, e))
28.57/10.10	   A^2 -> H(d, U1(c, k))
28.57/10.10	   A^2 -> H(d, U1(e, e))
28.57/10.10	   A^2 -> H(d, U1(k, k))
28.57/10.10	   A^2 -> H(d, U1(k, d))
28.57/10.10	   A^2 -> H(d, U1(d, k))
28.57/10.10	   A^2 -> H(a, b)
28.57/10.10	   A^2 -> H(a, U1(e, d))
28.57/10.10	   A^2 -> H(a, U1(d, e))
28.57/10.10	   A^2 -> H(a, c)
28.57/10.10	   A^2 -> H(a, U1(e, k))
28.57/10.10	   A^2 -> H(a, U1(k, e))
28.57/10.10	   A^2 -> H(a, e)
28.57/10.10	   A^2 -> H(a, U1(k, k))
28.57/10.10	   A^2 -> H(U1(e, d), b)
28.57/10.10	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, d), c)
28.57/10.10	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, d), e)
28.57/10.10	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.10	   A^2 -> H(U1(e, a), d)
28.57/10.10	
28.57/10.10	The TRS R consists of the following rules:
28.57/10.10	
28.57/10.10	   f(x) -> U1(x, x)
28.57/10.10	   U1(e, x) -> x
28.57/10.10	   a -> c
28.57/10.10	   a -> d
28.57/10.10	   b -> c
28.57/10.10	   b -> d
28.57/10.10	   d -> k
28.57/10.10	   c -> e
28.57/10.10	   c -> k
28.57/10.10	
28.57/10.10	Q is empty.
28.57/10.10	We have to consider all minimal (P,Q,R)-chains.
28.57/10.10	----------------------------------------
28.57/10.10	
28.57/10.10	(1871) TransformationProof (EQUIVALENT)
28.57/10.10	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.10	
28.57/10.10	   (A^2 -> H(a, U1(d, e)),A^2 -> H(a, U1(d, e)))
28.57/10.10	   (A^2 -> H(U1(e, c), U1(d, e)),A^2 -> H(U1(e, c), U1(d, e)))
28.57/10.10	   (A^2 -> H(U1(e, d), U1(d, e)),A^2 -> H(U1(e, d), U1(d, e)))
28.57/10.10	   (A^2 -> H(U1(e, a), U1(k, e)),A^2 -> H(U1(e, a), U1(k, e)))
28.57/10.10	
28.57/10.10	
28.57/10.10	----------------------------------------
28.57/10.10	
28.57/10.10	(1872)
28.57/10.10	Obligation:
28.57/10.10	Q DP problem:
28.57/10.10	The TRS P consists of the following rules:
28.57/10.10	
28.57/10.10	   H(x, x) -> G(x, x, f(k))
28.57/10.10	   G(d, x, x) -> A^2
28.57/10.10	   A^2 -> H(f(c), f(c))
28.57/10.10	   A^2 -> H(f(d), f(d))
28.57/10.10	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.10	   A^2 -> H(f(e), f(e))
28.57/10.10	   A^2 -> H(f(k), f(k))
28.57/10.10	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.10	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.10	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.10	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.10	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, a), c)
28.57/10.10	   A^2 -> H(U1(e, a), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, a), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, a), e)
28.57/10.10	   A^2 -> H(U1(e, a), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, a), b)
28.57/10.10	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, a), c)
28.57/10.10	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, d), b)
28.57/10.10	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, d), c)
28.57/10.10	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, d), e)
28.57/10.10	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, a), d)
28.57/10.10	   A^2 -> H(U1(c, a), k)
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.10	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.10	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.10	   A^2 -> H(U1(d, c), b)
28.57/10.10	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(d, c), c)
28.57/10.10	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(d, c), e)
28.57/10.10	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, a), d)
28.57/10.10	   A^2 -> H(U1(d, a), k)
28.57/10.10	   A^2 -> H(U1(a, e), b)
28.57/10.10	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(a, e), c)
28.57/10.10	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(a, e), e)
28.57/10.10	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(a, k), b)
28.57/10.10	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(a, k), c)
28.57/10.10	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(a, k), e)
28.57/10.10	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(a, c), d)
28.57/10.10	   A^2 -> H(U1(a, c), k)
28.57/10.10	   A^2 -> H(U1(a, d), d)
28.57/10.10	   A^2 -> H(U1(a, d), k)
28.57/10.10	   A^2 -> H(k, U1(c, b))
28.57/10.10	   A^2 -> H(k, U1(d, b))
28.57/10.10	   A^2 -> H(k, U1(b, c))
28.57/10.10	   A^2 -> H(k, U1(b, d))
28.57/10.10	   A^2 -> H(k, U1(c, c))
28.57/10.10	   A^2 -> H(k, f(e))
28.57/10.10	   A^2 -> H(k, f(k))
28.57/10.10	   A^2 -> H(k, U1(d, d))
28.57/10.10	   A^2 -> H(c, U1(e, b))
28.57/10.10	   A^2 -> H(c, U1(k, b))
28.57/10.10	   A^2 -> H(c, U1(c, d))
28.57/10.10	   A^2 -> H(c, U1(d, c))
28.57/10.10	   A^2 -> H(c, U1(b, e))
28.57/10.10	   A^2 -> H(c, U1(b, k))
28.57/10.10	   A^2 -> H(c, U1(e, c))
28.57/10.10	   A^2 -> H(c, U1(k, c))
28.57/10.10	   A^2 -> H(c, U1(c, e))
28.57/10.10	   A^2 -> H(c, U1(c, k))
28.57/10.10	   A^2 -> H(c, U1(e, e))
28.57/10.10	   A^2 -> H(c, U1(k, k))
28.57/10.10	   A^2 -> H(c, U1(k, d))
28.57/10.10	   A^2 -> H(c, U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.10	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.10	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, c), b)
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, c), e)
28.57/10.10	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.10	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.10	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.10	   A^2 -> H(U1(k, c), b)
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, c), c)
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, e), b)
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, e), c)
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, e), e)
28.57/10.10	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, k), b)
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, k), c)
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, k), e)
28.57/10.10	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, c), d)
28.57/10.10	   A^2 -> H(e, U1(e, b))
28.57/10.10	   A^2 -> H(e, U1(c, d))
28.57/10.10	   A^2 -> H(e, U1(d, c))
28.57/10.10	   A^2 -> H(e, U1(b, e))
28.57/10.10	   A^2 -> H(e, U1(b, k))
28.57/10.10	   A^2 -> H(e, U1(e, c))
28.57/10.10	   A^2 -> H(e, U1(c, e))
28.57/10.10	   A^2 -> H(e, U1(c, k))
28.57/10.10	   A^2 -> H(e, U1(e, e))
28.57/10.10	   A^2 -> H(e, U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, e), b)
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, e), c)
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.10	   A^2 -> H(f(e), d)
28.57/10.10	   A^2 -> H(f(e), k)
28.57/10.10	   A^2 -> H(U1(k, k), b)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, k), c)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.10	   A^2 -> H(f(k), d)
28.57/10.10	   A^2 -> H(f(k), k)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(k, d), b)
28.57/10.10	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, d), c)
28.57/10.10	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, k), b)
28.57/10.10	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(d, k), c)
28.57/10.10	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(d, k), e)
28.57/10.10	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, d), d)
28.57/10.10	   A^2 -> H(U1(d, d), k)
28.57/10.10	   A^2 -> H(U1(e, c), c)
28.57/10.10	   A^2 -> H(U1(c, c), e)
28.57/10.10	   A^2 -> H(U1(c, c), k)
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(e, e), e)
28.57/10.10	   A^2 -> H(d, U1(e, b))
28.57/10.10	   A^2 -> H(d, U1(k, b))
28.57/10.10	   A^2 -> H(d, U1(c, d))
28.57/10.10	   A^2 -> H(d, U1(d, c))
28.57/10.10	   A^2 -> H(d, U1(b, e))
28.57/10.10	   A^2 -> H(d, U1(b, k))
28.57/10.10	   A^2 -> H(d, U1(e, c))
28.57/10.10	   A^2 -> H(d, U1(k, c))
28.57/10.10	   A^2 -> H(d, U1(c, e))
28.57/10.10	   A^2 -> H(d, U1(c, k))
28.57/10.10	   A^2 -> H(d, U1(e, e))
28.57/10.10	   A^2 -> H(d, U1(k, k))
28.57/10.10	   A^2 -> H(d, U1(k, d))
28.57/10.10	   A^2 -> H(d, U1(d, k))
28.57/10.10	   A^2 -> H(a, b)
28.57/10.10	   A^2 -> H(a, U1(e, d))
28.57/10.10	   A^2 -> H(a, U1(d, e))
28.57/10.10	   A^2 -> H(a, c)
28.57/10.10	   A^2 -> H(a, U1(e, k))
28.57/10.10	   A^2 -> H(a, U1(k, e))
28.57/10.10	   A^2 -> H(a, e)
28.57/10.10	   A^2 -> H(a, U1(k, k))
28.57/10.10	   A^2 -> H(U1(e, d), b)
28.57/10.10	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, d), c)
28.57/10.10	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, d), e)
28.57/10.10	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.10	   A^2 -> H(U1(e, a), d)
28.57/10.10	
28.57/10.10	The TRS R consists of the following rules:
28.57/10.10	
28.57/10.10	   f(x) -> U1(x, x)
28.57/10.10	   U1(e, x) -> x
28.57/10.10	   a -> c
28.57/10.10	   a -> d
28.57/10.10	   b -> c
28.57/10.10	   b -> d
28.57/10.10	   d -> k
28.57/10.10	   c -> e
28.57/10.10	   c -> k
28.57/10.10	
28.57/10.10	Q is empty.
28.57/10.10	We have to consider all minimal (P,Q,R)-chains.
28.57/10.10	----------------------------------------
28.57/10.10	
28.57/10.10	(1873) TransformationProof (EQUIVALENT)
28.57/10.10	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), c) at position [] we obtained the following new rules [LPAR04]:
28.57/10.10	
28.57/10.10	   (A^2 -> H(a, c),A^2 -> H(a, c))
28.57/10.10	   (A^2 -> H(U1(e, c), c),A^2 -> H(U1(e, c), c))
28.57/10.10	   (A^2 -> H(U1(e, d), c),A^2 -> H(U1(e, d), c))
28.57/10.10	   (A^2 -> H(U1(e, a), e),A^2 -> H(U1(e, a), e))
28.57/10.10	   (A^2 -> H(U1(e, a), k),A^2 -> H(U1(e, a), k))
28.57/10.10	
28.57/10.10	
28.57/10.10	----------------------------------------
28.57/10.10	
28.57/10.10	(1874)
28.57/10.10	Obligation:
28.57/10.10	Q DP problem:
28.57/10.10	The TRS P consists of the following rules:
28.57/10.10	
28.57/10.10	   H(x, x) -> G(x, x, f(k))
28.57/10.10	   G(d, x, x) -> A^2
28.57/10.10	   A^2 -> H(f(c), f(c))
28.57/10.10	   A^2 -> H(f(d), f(d))
28.57/10.10	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.10	   A^2 -> H(f(e), f(e))
28.57/10.10	   A^2 -> H(f(k), f(k))
28.57/10.10	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.10	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.10	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.10	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.10	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, a), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, a), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, a), e)
28.57/10.10	   A^2 -> H(U1(e, a), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, a), b)
28.57/10.10	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, a), c)
28.57/10.10	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, d), b)
28.57/10.10	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, d), c)
28.57/10.10	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, d), e)
28.57/10.10	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, a), d)
28.57/10.10	   A^2 -> H(U1(c, a), k)
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.10	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.10	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.10	   A^2 -> H(U1(d, c), b)
28.57/10.10	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(d, c), c)
28.57/10.10	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(d, c), e)
28.57/10.10	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(d, a), d)
28.57/10.10	   A^2 -> H(U1(d, a), k)
28.57/10.10	   A^2 -> H(U1(a, e), b)
28.57/10.10	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(a, e), c)
28.57/10.10	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(a, e), e)
28.57/10.10	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(a, k), b)
28.57/10.10	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(a, k), c)
28.57/10.10	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(a, k), e)
28.57/10.10	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(a, c), d)
28.57/10.10	   A^2 -> H(U1(a, c), k)
28.57/10.10	   A^2 -> H(U1(a, d), d)
28.57/10.10	   A^2 -> H(U1(a, d), k)
28.57/10.10	   A^2 -> H(k, U1(c, b))
28.57/10.10	   A^2 -> H(k, U1(d, b))
28.57/10.10	   A^2 -> H(k, U1(b, c))
28.57/10.10	   A^2 -> H(k, U1(b, d))
28.57/10.10	   A^2 -> H(k, U1(c, c))
28.57/10.10	   A^2 -> H(k, f(e))
28.57/10.10	   A^2 -> H(k, f(k))
28.57/10.10	   A^2 -> H(k, U1(d, d))
28.57/10.10	   A^2 -> H(c, U1(e, b))
28.57/10.10	   A^2 -> H(c, U1(k, b))
28.57/10.10	   A^2 -> H(c, U1(c, d))
28.57/10.10	   A^2 -> H(c, U1(d, c))
28.57/10.10	   A^2 -> H(c, U1(b, e))
28.57/10.10	   A^2 -> H(c, U1(b, k))
28.57/10.10	   A^2 -> H(c, U1(e, c))
28.57/10.10	   A^2 -> H(c, U1(k, c))
28.57/10.10	   A^2 -> H(c, U1(c, e))
28.57/10.10	   A^2 -> H(c, U1(c, k))
28.57/10.10	   A^2 -> H(c, U1(e, e))
28.57/10.10	   A^2 -> H(c, U1(k, k))
28.57/10.10	   A^2 -> H(c, U1(k, d))
28.57/10.10	   A^2 -> H(c, U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.10	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.10	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, c), b)
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, c), e)
28.57/10.10	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.10	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.10	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.10	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.10	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.10	   A^2 -> H(U1(k, c), b)
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, c), c)
28.57/10.10	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.10	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, e), b)
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, e), c)
28.57/10.10	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, e), e)
28.57/10.10	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, k), b)
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(c, k), c)
28.57/10.10	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.10	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.10	   A^2 -> H(U1(c, k), e)
28.57/10.10	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.10	   A^2 -> H(U1(c, c), d)
28.57/10.10	   A^2 -> H(e, U1(e, b))
28.57/10.10	   A^2 -> H(e, U1(c, d))
28.57/10.10	   A^2 -> H(e, U1(d, c))
28.57/10.10	   A^2 -> H(e, U1(b, e))
28.57/10.10	   A^2 -> H(e, U1(b, k))
28.57/10.10	   A^2 -> H(e, U1(e, c))
28.57/10.10	   A^2 -> H(e, U1(c, e))
28.57/10.10	   A^2 -> H(e, U1(c, k))
28.57/10.10	   A^2 -> H(e, U1(e, e))
28.57/10.10	   A^2 -> H(e, U1(d, k))
28.57/10.10	   A^2 -> H(U1(e, e), b)
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.10	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.10	   A^2 -> H(U1(e, e), c)
28.57/10.10	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.10	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.10	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.10	   A^2 -> H(f(e), d)
28.57/10.10	   A^2 -> H(f(e), k)
28.57/10.10	   A^2 -> H(U1(k, k), b)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.10	   A^2 -> H(U1(k, k), c)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.10	   A^2 -> H(f(k), d)
28.57/10.10	   A^2 -> H(f(k), k)
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.10	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.10	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.10	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.10	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.10	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, d), b)
28.57/10.11	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, d), c)
28.57/10.11	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, k), b)
28.57/10.11	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(d, k), c)
28.57/10.11	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(d, k), e)
28.57/10.11	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, d), d)
28.57/10.11	   A^2 -> H(U1(d, d), k)
28.57/10.11	   A^2 -> H(U1(e, c), c)
28.57/10.11	   A^2 -> H(U1(c, c), e)
28.57/10.11	   A^2 -> H(U1(c, c), k)
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(e, e), e)
28.57/10.11	   A^2 -> H(d, U1(e, b))
28.57/10.11	   A^2 -> H(d, U1(k, b))
28.57/10.11	   A^2 -> H(d, U1(c, d))
28.57/10.11	   A^2 -> H(d, U1(d, c))
28.57/10.11	   A^2 -> H(d, U1(b, e))
28.57/10.11	   A^2 -> H(d, U1(b, k))
28.57/10.11	   A^2 -> H(d, U1(e, c))
28.57/10.11	   A^2 -> H(d, U1(k, c))
28.57/10.11	   A^2 -> H(d, U1(c, e))
28.57/10.11	   A^2 -> H(d, U1(c, k))
28.57/10.11	   A^2 -> H(d, U1(e, e))
28.57/10.11	   A^2 -> H(d, U1(k, k))
28.57/10.11	   A^2 -> H(d, U1(k, d))
28.57/10.11	   A^2 -> H(d, U1(d, k))
28.57/10.11	   A^2 -> H(a, b)
28.57/10.11	   A^2 -> H(a, U1(e, d))
28.57/10.11	   A^2 -> H(a, U1(d, e))
28.57/10.11	   A^2 -> H(a, c)
28.57/10.11	   A^2 -> H(a, U1(e, k))
28.57/10.11	   A^2 -> H(a, U1(k, e))
28.57/10.11	   A^2 -> H(a, e)
28.57/10.11	   A^2 -> H(a, U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, d), b)
28.57/10.11	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, d), c)
28.57/10.11	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, d), e)
28.57/10.11	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, a), d)
28.57/10.11	   A^2 -> H(U1(e, a), k)
28.57/10.11	
28.57/10.11	The TRS R consists of the following rules:
28.57/10.11	
28.57/10.11	   f(x) -> U1(x, x)
28.57/10.11	   U1(e, x) -> x
28.57/10.11	   a -> c
28.57/10.11	   a -> d
28.57/10.11	   b -> c
28.57/10.11	   b -> d
28.57/10.11	   d -> k
28.57/10.11	   c -> e
28.57/10.11	   c -> k
28.57/10.11	
28.57/10.11	Q is empty.
28.57/10.11	We have to consider all minimal (P,Q,R)-chains.
28.57/10.11	----------------------------------------
28.57/10.11	
28.57/10.11	(1875) TransformationProof (EQUIVALENT)
28.57/10.11	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.11	
28.57/10.11	   (A^2 -> H(a, U1(e, k)),A^2 -> H(a, U1(e, k)))
28.57/10.11	   (A^2 -> H(U1(e, c), U1(e, k)),A^2 -> H(U1(e, c), U1(e, k)))
28.57/10.11	   (A^2 -> H(U1(e, d), U1(e, k)),A^2 -> H(U1(e, d), U1(e, k)))
28.57/10.11	   (A^2 -> H(U1(e, a), k),A^2 -> H(U1(e, a), k))
28.57/10.11	
28.57/10.11	
28.57/10.11	----------------------------------------
28.57/10.11	
28.57/10.11	(1876)
28.57/10.11	Obligation:
28.57/10.11	Q DP problem:
28.57/10.11	The TRS P consists of the following rules:
28.57/10.11	
28.57/10.11	   H(x, x) -> G(x, x, f(k))
28.57/10.11	   G(d, x, x) -> A^2
28.57/10.11	   A^2 -> H(f(c), f(c))
28.57/10.11	   A^2 -> H(f(d), f(d))
28.57/10.11	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.11	   A^2 -> H(f(e), f(e))
28.57/10.11	   A^2 -> H(f(k), f(k))
28.57/10.11	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.11	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.11	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.11	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.11	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, a), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, a), e)
28.57/10.11	   A^2 -> H(U1(e, a), U1(k, k))
28.57/10.11	   A^2 -> H(U1(k, a), b)
28.57/10.11	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, a), c)
28.57/10.11	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, d), b)
28.57/10.11	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, d), c)
28.57/10.11	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, d), e)
28.57/10.11	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, a), d)
28.57/10.11	   A^2 -> H(U1(c, a), k)
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.11	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.11	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.11	   A^2 -> H(U1(d, c), b)
28.57/10.11	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(d, c), c)
28.57/10.11	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(d, c), e)
28.57/10.11	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, a), d)
28.57/10.11	   A^2 -> H(U1(d, a), k)
28.57/10.11	   A^2 -> H(U1(a, e), b)
28.57/10.11	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(a, e), c)
28.57/10.11	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(a, e), e)
28.57/10.11	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(a, k), b)
28.57/10.11	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(a, k), c)
28.57/10.11	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(a, k), e)
28.57/10.11	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(a, c), d)
28.57/10.11	   A^2 -> H(U1(a, c), k)
28.57/10.11	   A^2 -> H(U1(a, d), d)
28.57/10.11	   A^2 -> H(U1(a, d), k)
28.57/10.11	   A^2 -> H(k, U1(c, b))
28.57/10.11	   A^2 -> H(k, U1(d, b))
28.57/10.11	   A^2 -> H(k, U1(b, c))
28.57/10.11	   A^2 -> H(k, U1(b, d))
28.57/10.11	   A^2 -> H(k, U1(c, c))
28.57/10.11	   A^2 -> H(k, f(e))
28.57/10.11	   A^2 -> H(k, f(k))
28.57/10.11	   A^2 -> H(k, U1(d, d))
28.57/10.11	   A^2 -> H(c, U1(e, b))
28.57/10.11	   A^2 -> H(c, U1(k, b))
28.57/10.11	   A^2 -> H(c, U1(c, d))
28.57/10.11	   A^2 -> H(c, U1(d, c))
28.57/10.11	   A^2 -> H(c, U1(b, e))
28.57/10.11	   A^2 -> H(c, U1(b, k))
28.57/10.11	   A^2 -> H(c, U1(e, c))
28.57/10.11	   A^2 -> H(c, U1(k, c))
28.57/10.11	   A^2 -> H(c, U1(c, e))
28.57/10.11	   A^2 -> H(c, U1(c, k))
28.57/10.11	   A^2 -> H(c, U1(e, e))
28.57/10.11	   A^2 -> H(c, U1(k, k))
28.57/10.11	   A^2 -> H(c, U1(k, d))
28.57/10.11	   A^2 -> H(c, U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.11	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.11	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, c), b)
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, c), e)
28.57/10.11	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.11	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.11	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, c), b)
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, c), c)
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, e), b)
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, e), c)
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, e), e)
28.57/10.11	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, k), b)
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, k), c)
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, k), e)
28.57/10.11	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, c), d)
28.57/10.11	   A^2 -> H(e, U1(e, b))
28.57/10.11	   A^2 -> H(e, U1(c, d))
28.57/10.11	   A^2 -> H(e, U1(d, c))
28.57/10.11	   A^2 -> H(e, U1(b, e))
28.57/10.11	   A^2 -> H(e, U1(b, k))
28.57/10.11	   A^2 -> H(e, U1(e, c))
28.57/10.11	   A^2 -> H(e, U1(c, e))
28.57/10.11	   A^2 -> H(e, U1(c, k))
28.57/10.11	   A^2 -> H(e, U1(e, e))
28.57/10.11	   A^2 -> H(e, U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, e), b)
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, e), c)
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.11	   A^2 -> H(f(e), d)
28.57/10.11	   A^2 -> H(f(e), k)
28.57/10.11	   A^2 -> H(U1(k, k), b)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, k), c)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.11	   A^2 -> H(f(k), d)
28.57/10.11	   A^2 -> H(f(k), k)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, d), b)
28.57/10.11	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, d), c)
28.57/10.11	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, k), b)
28.57/10.11	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(d, k), c)
28.57/10.11	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(d, k), e)
28.57/10.11	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, d), d)
28.57/10.11	   A^2 -> H(U1(d, d), k)
28.57/10.11	   A^2 -> H(U1(e, c), c)
28.57/10.11	   A^2 -> H(U1(c, c), e)
28.57/10.11	   A^2 -> H(U1(c, c), k)
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(e, e), e)
28.57/10.11	   A^2 -> H(d, U1(e, b))
28.57/10.11	   A^2 -> H(d, U1(k, b))
28.57/10.11	   A^2 -> H(d, U1(c, d))
28.57/10.11	   A^2 -> H(d, U1(d, c))
28.57/10.11	   A^2 -> H(d, U1(b, e))
28.57/10.11	   A^2 -> H(d, U1(b, k))
28.57/10.11	   A^2 -> H(d, U1(e, c))
28.57/10.11	   A^2 -> H(d, U1(k, c))
28.57/10.11	   A^2 -> H(d, U1(c, e))
28.57/10.11	   A^2 -> H(d, U1(c, k))
28.57/10.11	   A^2 -> H(d, U1(e, e))
28.57/10.11	   A^2 -> H(d, U1(k, k))
28.57/10.11	   A^2 -> H(d, U1(k, d))
28.57/10.11	   A^2 -> H(d, U1(d, k))
28.57/10.11	   A^2 -> H(a, b)
28.57/10.11	   A^2 -> H(a, U1(e, d))
28.57/10.11	   A^2 -> H(a, U1(d, e))
28.57/10.11	   A^2 -> H(a, c)
28.57/10.11	   A^2 -> H(a, U1(e, k))
28.57/10.11	   A^2 -> H(a, U1(k, e))
28.57/10.11	   A^2 -> H(a, e)
28.57/10.11	   A^2 -> H(a, U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, d), b)
28.57/10.11	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, d), c)
28.57/10.11	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, d), e)
28.57/10.11	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, a), d)
28.57/10.11	   A^2 -> H(U1(e, a), k)
28.57/10.11	
28.57/10.11	The TRS R consists of the following rules:
28.57/10.11	
28.57/10.11	   f(x) -> U1(x, x)
28.57/10.11	   U1(e, x) -> x
28.57/10.11	   a -> c
28.57/10.11	   a -> d
28.57/10.11	   b -> c
28.57/10.11	   b -> d
28.57/10.11	   d -> k
28.57/10.11	   c -> e
28.57/10.11	   c -> k
28.57/10.11	
28.57/10.11	Q is empty.
28.57/10.11	We have to consider all minimal (P,Q,R)-chains.
28.57/10.11	----------------------------------------
28.57/10.11	
28.57/10.11	(1877) TransformationProof (EQUIVALENT)
28.57/10.11	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.11	
28.57/10.11	   (A^2 -> H(a, U1(k, e)),A^2 -> H(a, U1(k, e)))
28.57/10.11	   (A^2 -> H(U1(e, c), U1(k, e)),A^2 -> H(U1(e, c), U1(k, e)))
28.57/10.11	   (A^2 -> H(U1(e, d), U1(k, e)),A^2 -> H(U1(e, d), U1(k, e)))
28.57/10.11	
28.57/10.11	
28.57/10.11	----------------------------------------
28.57/10.11	
28.57/10.11	(1878)
28.57/10.11	Obligation:
28.57/10.11	Q DP problem:
28.57/10.11	The TRS P consists of the following rules:
28.57/10.11	
28.57/10.11	   H(x, x) -> G(x, x, f(k))
28.57/10.11	   G(d, x, x) -> A^2
28.57/10.11	   A^2 -> H(f(c), f(c))
28.57/10.11	   A^2 -> H(f(d), f(d))
28.57/10.11	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.11	   A^2 -> H(f(e), f(e))
28.57/10.11	   A^2 -> H(f(k), f(k))
28.57/10.11	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.11	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.11	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.11	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.11	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, a), e)
28.57/10.11	   A^2 -> H(U1(e, a), U1(k, k))
28.57/10.11	   A^2 -> H(U1(k, a), b)
28.57/10.11	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, a), c)
28.57/10.11	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, d), b)
28.57/10.11	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, d), c)
28.57/10.11	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, d), e)
28.57/10.11	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, a), d)
28.57/10.11	   A^2 -> H(U1(c, a), k)
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.11	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.11	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.11	   A^2 -> H(U1(d, c), b)
28.57/10.11	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(d, c), c)
28.57/10.11	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(d, c), e)
28.57/10.11	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, a), d)
28.57/10.11	   A^2 -> H(U1(d, a), k)
28.57/10.11	   A^2 -> H(U1(a, e), b)
28.57/10.11	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(a, e), c)
28.57/10.11	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(a, e), e)
28.57/10.11	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(a, k), b)
28.57/10.11	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(a, k), c)
28.57/10.11	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(a, k), e)
28.57/10.11	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(a, c), d)
28.57/10.11	   A^2 -> H(U1(a, c), k)
28.57/10.11	   A^2 -> H(U1(a, d), d)
28.57/10.11	   A^2 -> H(U1(a, d), k)
28.57/10.11	   A^2 -> H(k, U1(c, b))
28.57/10.11	   A^2 -> H(k, U1(d, b))
28.57/10.11	   A^2 -> H(k, U1(b, c))
28.57/10.11	   A^2 -> H(k, U1(b, d))
28.57/10.11	   A^2 -> H(k, U1(c, c))
28.57/10.11	   A^2 -> H(k, f(e))
28.57/10.11	   A^2 -> H(k, f(k))
28.57/10.11	   A^2 -> H(k, U1(d, d))
28.57/10.11	   A^2 -> H(c, U1(e, b))
28.57/10.11	   A^2 -> H(c, U1(k, b))
28.57/10.11	   A^2 -> H(c, U1(c, d))
28.57/10.11	   A^2 -> H(c, U1(d, c))
28.57/10.11	   A^2 -> H(c, U1(b, e))
28.57/10.11	   A^2 -> H(c, U1(b, k))
28.57/10.11	   A^2 -> H(c, U1(e, c))
28.57/10.11	   A^2 -> H(c, U1(k, c))
28.57/10.11	   A^2 -> H(c, U1(c, e))
28.57/10.11	   A^2 -> H(c, U1(c, k))
28.57/10.11	   A^2 -> H(c, U1(e, e))
28.57/10.11	   A^2 -> H(c, U1(k, k))
28.57/10.11	   A^2 -> H(c, U1(k, d))
28.57/10.11	   A^2 -> H(c, U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.11	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.11	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, c), b)
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, c), e)
28.57/10.11	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.11	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.11	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, c), b)
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, c), c)
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, e), b)
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, e), c)
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, e), e)
28.57/10.11	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, k), b)
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, k), c)
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, k), e)
28.57/10.11	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, c), d)
28.57/10.11	   A^2 -> H(e, U1(e, b))
28.57/10.11	   A^2 -> H(e, U1(c, d))
28.57/10.11	   A^2 -> H(e, U1(d, c))
28.57/10.11	   A^2 -> H(e, U1(b, e))
28.57/10.11	   A^2 -> H(e, U1(b, k))
28.57/10.11	   A^2 -> H(e, U1(e, c))
28.57/10.11	   A^2 -> H(e, U1(c, e))
28.57/10.11	   A^2 -> H(e, U1(c, k))
28.57/10.11	   A^2 -> H(e, U1(e, e))
28.57/10.11	   A^2 -> H(e, U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, e), b)
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, e), c)
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.11	   A^2 -> H(f(e), d)
28.57/10.11	   A^2 -> H(f(e), k)
28.57/10.11	   A^2 -> H(U1(k, k), b)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, k), c)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.11	   A^2 -> H(f(k), d)
28.57/10.11	   A^2 -> H(f(k), k)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, d), b)
28.57/10.11	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, d), c)
28.57/10.11	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, k), b)
28.57/10.11	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(d, k), c)
28.57/10.11	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(d, k), e)
28.57/10.11	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, d), d)
28.57/10.11	   A^2 -> H(U1(d, d), k)
28.57/10.11	   A^2 -> H(U1(e, c), c)
28.57/10.11	   A^2 -> H(U1(c, c), e)
28.57/10.11	   A^2 -> H(U1(c, c), k)
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(e, e), e)
28.57/10.11	   A^2 -> H(d, U1(e, b))
28.57/10.11	   A^2 -> H(d, U1(k, b))
28.57/10.11	   A^2 -> H(d, U1(c, d))
28.57/10.11	   A^2 -> H(d, U1(d, c))
28.57/10.11	   A^2 -> H(d, U1(b, e))
28.57/10.11	   A^2 -> H(d, U1(b, k))
28.57/10.11	   A^2 -> H(d, U1(e, c))
28.57/10.11	   A^2 -> H(d, U1(k, c))
28.57/10.11	   A^2 -> H(d, U1(c, e))
28.57/10.11	   A^2 -> H(d, U1(c, k))
28.57/10.11	   A^2 -> H(d, U1(e, e))
28.57/10.11	   A^2 -> H(d, U1(k, k))
28.57/10.11	   A^2 -> H(d, U1(k, d))
28.57/10.11	   A^2 -> H(d, U1(d, k))
28.57/10.11	   A^2 -> H(a, b)
28.57/10.11	   A^2 -> H(a, U1(e, d))
28.57/10.11	   A^2 -> H(a, U1(d, e))
28.57/10.11	   A^2 -> H(a, c)
28.57/10.11	   A^2 -> H(a, U1(e, k))
28.57/10.11	   A^2 -> H(a, U1(k, e))
28.57/10.11	   A^2 -> H(a, e)
28.57/10.11	   A^2 -> H(a, U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, d), b)
28.57/10.11	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, d), c)
28.57/10.11	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, d), e)
28.57/10.11	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, a), d)
28.57/10.11	   A^2 -> H(U1(e, a), k)
28.57/10.11	
28.57/10.11	The TRS R consists of the following rules:
28.57/10.11	
28.57/10.11	   f(x) -> U1(x, x)
28.57/10.11	   U1(e, x) -> x
28.57/10.11	   a -> c
28.57/10.11	   a -> d
28.57/10.11	   b -> c
28.57/10.11	   b -> d
28.57/10.11	   d -> k
28.57/10.11	   c -> e
28.57/10.11	   c -> k
28.57/10.11	
28.57/10.11	Q is empty.
28.57/10.11	We have to consider all minimal (P,Q,R)-chains.
28.57/10.11	----------------------------------------
28.57/10.11	
28.57/10.11	(1879) TransformationProof (EQUIVALENT)
28.57/10.11	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), e) at position [] we obtained the following new rules [LPAR04]:
28.57/10.11	
28.57/10.11	   (A^2 -> H(a, e),A^2 -> H(a, e))
28.57/10.11	   (A^2 -> H(U1(e, c), e),A^2 -> H(U1(e, c), e))
28.57/10.11	   (A^2 -> H(U1(e, d), e),A^2 -> H(U1(e, d), e))
28.57/10.11	
28.57/10.11	
28.57/10.11	----------------------------------------
28.57/10.11	
28.57/10.11	(1880)
28.57/10.11	Obligation:
28.57/10.11	Q DP problem:
28.57/10.11	The TRS P consists of the following rules:
28.57/10.11	
28.57/10.11	   H(x, x) -> G(x, x, f(k))
28.57/10.11	   G(d, x, x) -> A^2
28.57/10.11	   A^2 -> H(f(c), f(c))
28.57/10.11	   A^2 -> H(f(d), f(d))
28.57/10.11	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.11	   A^2 -> H(f(e), f(e))
28.57/10.11	   A^2 -> H(f(k), f(k))
28.57/10.11	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.11	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.11	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.11	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.11	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, a), U1(k, k))
28.57/10.11	   A^2 -> H(U1(k, a), b)
28.57/10.11	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, a), c)
28.57/10.11	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, d), b)
28.57/10.11	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, d), c)
28.57/10.11	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, d), e)
28.57/10.11	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, a), d)
28.57/10.11	   A^2 -> H(U1(c, a), k)
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.11	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.11	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.11	   A^2 -> H(U1(d, c), b)
28.57/10.11	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(d, c), c)
28.57/10.11	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(d, c), e)
28.57/10.11	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, a), d)
28.57/10.11	   A^2 -> H(U1(d, a), k)
28.57/10.11	   A^2 -> H(U1(a, e), b)
28.57/10.11	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(a, e), c)
28.57/10.11	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(a, e), e)
28.57/10.11	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(a, k), b)
28.57/10.11	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(a, k), c)
28.57/10.11	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(a, k), e)
28.57/10.11	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(a, c), d)
28.57/10.11	   A^2 -> H(U1(a, c), k)
28.57/10.11	   A^2 -> H(U1(a, d), d)
28.57/10.11	   A^2 -> H(U1(a, d), k)
28.57/10.11	   A^2 -> H(k, U1(c, b))
28.57/10.11	   A^2 -> H(k, U1(d, b))
28.57/10.11	   A^2 -> H(k, U1(b, c))
28.57/10.11	   A^2 -> H(k, U1(b, d))
28.57/10.11	   A^2 -> H(k, U1(c, c))
28.57/10.11	   A^2 -> H(k, f(e))
28.57/10.11	   A^2 -> H(k, f(k))
28.57/10.11	   A^2 -> H(k, U1(d, d))
28.57/10.11	   A^2 -> H(c, U1(e, b))
28.57/10.11	   A^2 -> H(c, U1(k, b))
28.57/10.11	   A^2 -> H(c, U1(c, d))
28.57/10.11	   A^2 -> H(c, U1(d, c))
28.57/10.11	   A^2 -> H(c, U1(b, e))
28.57/10.11	   A^2 -> H(c, U1(b, k))
28.57/10.11	   A^2 -> H(c, U1(e, c))
28.57/10.11	   A^2 -> H(c, U1(k, c))
28.57/10.11	   A^2 -> H(c, U1(c, e))
28.57/10.11	   A^2 -> H(c, U1(c, k))
28.57/10.11	   A^2 -> H(c, U1(e, e))
28.57/10.11	   A^2 -> H(c, U1(k, k))
28.57/10.11	   A^2 -> H(c, U1(k, d))
28.57/10.11	   A^2 -> H(c, U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.11	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.11	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, c), b)
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, c), e)
28.57/10.11	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.11	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.11	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, c), b)
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, c), c)
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, e), b)
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, e), c)
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, e), e)
28.57/10.11	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, k), b)
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, k), c)
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, k), e)
28.57/10.11	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, c), d)
28.57/10.11	   A^2 -> H(e, U1(e, b))
28.57/10.11	   A^2 -> H(e, U1(c, d))
28.57/10.11	   A^2 -> H(e, U1(d, c))
28.57/10.11	   A^2 -> H(e, U1(b, e))
28.57/10.11	   A^2 -> H(e, U1(b, k))
28.57/10.11	   A^2 -> H(e, U1(e, c))
28.57/10.11	   A^2 -> H(e, U1(c, e))
28.57/10.11	   A^2 -> H(e, U1(c, k))
28.57/10.11	   A^2 -> H(e, U1(e, e))
28.57/10.11	   A^2 -> H(e, U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, e), b)
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, e), c)
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.11	   A^2 -> H(f(e), d)
28.57/10.11	   A^2 -> H(f(e), k)
28.57/10.11	   A^2 -> H(U1(k, k), b)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, k), c)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.11	   A^2 -> H(f(k), d)
28.57/10.11	   A^2 -> H(f(k), k)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, d), b)
28.57/10.11	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, d), c)
28.57/10.11	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, k), b)
28.57/10.11	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(d, k), c)
28.57/10.11	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(d, k), e)
28.57/10.11	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, d), d)
28.57/10.11	   A^2 -> H(U1(d, d), k)
28.57/10.11	   A^2 -> H(U1(e, c), c)
28.57/10.11	   A^2 -> H(U1(c, c), e)
28.57/10.11	   A^2 -> H(U1(c, c), k)
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(e, e), e)
28.57/10.11	   A^2 -> H(d, U1(e, b))
28.57/10.11	   A^2 -> H(d, U1(k, b))
28.57/10.11	   A^2 -> H(d, U1(c, d))
28.57/10.11	   A^2 -> H(d, U1(d, c))
28.57/10.11	   A^2 -> H(d, U1(b, e))
28.57/10.11	   A^2 -> H(d, U1(b, k))
28.57/10.11	   A^2 -> H(d, U1(e, c))
28.57/10.11	   A^2 -> H(d, U1(k, c))
28.57/10.11	   A^2 -> H(d, U1(c, e))
28.57/10.11	   A^2 -> H(d, U1(c, k))
28.57/10.11	   A^2 -> H(d, U1(e, e))
28.57/10.11	   A^2 -> H(d, U1(k, k))
28.57/10.11	   A^2 -> H(d, U1(k, d))
28.57/10.11	   A^2 -> H(d, U1(d, k))
28.57/10.11	   A^2 -> H(a, b)
28.57/10.11	   A^2 -> H(a, U1(e, d))
28.57/10.11	   A^2 -> H(a, U1(d, e))
28.57/10.11	   A^2 -> H(a, c)
28.57/10.11	   A^2 -> H(a, U1(e, k))
28.57/10.11	   A^2 -> H(a, U1(k, e))
28.57/10.11	   A^2 -> H(a, e)
28.57/10.11	   A^2 -> H(a, U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, d), b)
28.57/10.11	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, d), c)
28.57/10.11	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, d), e)
28.57/10.11	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, a), d)
28.57/10.11	   A^2 -> H(U1(e, a), k)
28.57/10.11	
28.57/10.11	The TRS R consists of the following rules:
28.57/10.11	
28.57/10.11	   f(x) -> U1(x, x)
28.57/10.11	   U1(e, x) -> x
28.57/10.11	   a -> c
28.57/10.11	   a -> d
28.57/10.11	   b -> c
28.57/10.11	   b -> d
28.57/10.11	   d -> k
28.57/10.11	   c -> e
28.57/10.11	   c -> k
28.57/10.11	
28.57/10.11	Q is empty.
28.57/10.11	We have to consider all minimal (P,Q,R)-chains.
28.57/10.11	----------------------------------------
28.57/10.11	
28.57/10.11	(1881) TransformationProof (EQUIVALENT)
28.57/10.11	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.11	
28.57/10.11	   (A^2 -> H(a, U1(k, k)),A^2 -> H(a, U1(k, k)))
28.57/10.11	   (A^2 -> H(U1(e, c), U1(k, k)),A^2 -> H(U1(e, c), U1(k, k)))
28.57/10.11	   (A^2 -> H(U1(e, d), U1(k, k)),A^2 -> H(U1(e, d), U1(k, k)))
28.57/10.11	
28.57/10.11	
28.57/10.11	----------------------------------------
28.57/10.11	
28.57/10.11	(1882)
28.57/10.11	Obligation:
28.57/10.11	Q DP problem:
28.57/10.11	The TRS P consists of the following rules:
28.57/10.11	
28.57/10.11	   H(x, x) -> G(x, x, f(k))
28.57/10.11	   G(d, x, x) -> A^2
28.57/10.11	   A^2 -> H(f(c), f(c))
28.57/10.11	   A^2 -> H(f(d), f(d))
28.57/10.11	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.11	   A^2 -> H(f(e), f(e))
28.57/10.11	   A^2 -> H(f(k), f(k))
28.57/10.11	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.11	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.11	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.11	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.11	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, a), b)
28.57/10.11	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, a), c)
28.57/10.11	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, d), b)
28.57/10.11	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, d), c)
28.57/10.11	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, d), e)
28.57/10.11	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, a), d)
28.57/10.11	   A^2 -> H(U1(c, a), k)
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.11	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.11	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.11	   A^2 -> H(U1(d, c), b)
28.57/10.11	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(d, c), c)
28.57/10.11	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(d, c), e)
28.57/10.11	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, a), d)
28.57/10.11	   A^2 -> H(U1(d, a), k)
28.57/10.11	   A^2 -> H(U1(a, e), b)
28.57/10.11	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(a, e), c)
28.57/10.11	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(a, e), e)
28.57/10.11	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(a, k), b)
28.57/10.11	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(a, k), c)
28.57/10.11	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(a, k), e)
28.57/10.11	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(a, c), d)
28.57/10.11	   A^2 -> H(U1(a, c), k)
28.57/10.11	   A^2 -> H(U1(a, d), d)
28.57/10.11	   A^2 -> H(U1(a, d), k)
28.57/10.11	   A^2 -> H(k, U1(c, b))
28.57/10.11	   A^2 -> H(k, U1(d, b))
28.57/10.11	   A^2 -> H(k, U1(b, c))
28.57/10.11	   A^2 -> H(k, U1(b, d))
28.57/10.11	   A^2 -> H(k, U1(c, c))
28.57/10.11	   A^2 -> H(k, f(e))
28.57/10.11	   A^2 -> H(k, f(k))
28.57/10.11	   A^2 -> H(k, U1(d, d))
28.57/10.11	   A^2 -> H(c, U1(e, b))
28.57/10.11	   A^2 -> H(c, U1(k, b))
28.57/10.11	   A^2 -> H(c, U1(c, d))
28.57/10.11	   A^2 -> H(c, U1(d, c))
28.57/10.11	   A^2 -> H(c, U1(b, e))
28.57/10.11	   A^2 -> H(c, U1(b, k))
28.57/10.11	   A^2 -> H(c, U1(e, c))
28.57/10.11	   A^2 -> H(c, U1(k, c))
28.57/10.11	   A^2 -> H(c, U1(c, e))
28.57/10.11	   A^2 -> H(c, U1(c, k))
28.57/10.11	   A^2 -> H(c, U1(e, e))
28.57/10.11	   A^2 -> H(c, U1(k, k))
28.57/10.11	   A^2 -> H(c, U1(k, d))
28.57/10.11	   A^2 -> H(c, U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.11	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.11	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, c), b)
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, c), e)
28.57/10.11	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.11	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.11	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, c), b)
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, c), c)
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, e), b)
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, e), c)
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, e), e)
28.57/10.11	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, k), b)
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, k), c)
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, k), e)
28.57/10.11	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, c), d)
28.57/10.11	   A^2 -> H(e, U1(e, b))
28.57/10.11	   A^2 -> H(e, U1(c, d))
28.57/10.11	   A^2 -> H(e, U1(d, c))
28.57/10.11	   A^2 -> H(e, U1(b, e))
28.57/10.11	   A^2 -> H(e, U1(b, k))
28.57/10.11	   A^2 -> H(e, U1(e, c))
28.57/10.11	   A^2 -> H(e, U1(c, e))
28.57/10.11	   A^2 -> H(e, U1(c, k))
28.57/10.11	   A^2 -> H(e, U1(e, e))
28.57/10.11	   A^2 -> H(e, U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, e), b)
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, e), c)
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.11	   A^2 -> H(f(e), d)
28.57/10.11	   A^2 -> H(f(e), k)
28.57/10.11	   A^2 -> H(U1(k, k), b)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, k), c)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.11	   A^2 -> H(f(k), d)
28.57/10.11	   A^2 -> H(f(k), k)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, d), b)
28.57/10.11	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, d), c)
28.57/10.11	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, k), b)
28.57/10.11	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(d, k), c)
28.57/10.11	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(d, k), e)
28.57/10.11	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, d), d)
28.57/10.11	   A^2 -> H(U1(d, d), k)
28.57/10.11	   A^2 -> H(U1(e, c), c)
28.57/10.11	   A^2 -> H(U1(c, c), e)
28.57/10.11	   A^2 -> H(U1(c, c), k)
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(e, e), e)
28.57/10.11	   A^2 -> H(d, U1(e, b))
28.57/10.11	   A^2 -> H(d, U1(k, b))
28.57/10.11	   A^2 -> H(d, U1(c, d))
28.57/10.11	   A^2 -> H(d, U1(d, c))
28.57/10.11	   A^2 -> H(d, U1(b, e))
28.57/10.11	   A^2 -> H(d, U1(b, k))
28.57/10.11	   A^2 -> H(d, U1(e, c))
28.57/10.11	   A^2 -> H(d, U1(k, c))
28.57/10.11	   A^2 -> H(d, U1(c, e))
28.57/10.11	   A^2 -> H(d, U1(c, k))
28.57/10.11	   A^2 -> H(d, U1(e, e))
28.57/10.11	   A^2 -> H(d, U1(k, k))
28.57/10.11	   A^2 -> H(d, U1(k, d))
28.57/10.11	   A^2 -> H(d, U1(d, k))
28.57/10.11	   A^2 -> H(a, b)
28.57/10.11	   A^2 -> H(a, U1(e, d))
28.57/10.11	   A^2 -> H(a, U1(d, e))
28.57/10.11	   A^2 -> H(a, c)
28.57/10.11	   A^2 -> H(a, U1(e, k))
28.57/10.11	   A^2 -> H(a, U1(k, e))
28.57/10.11	   A^2 -> H(a, e)
28.57/10.11	   A^2 -> H(a, U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, d), b)
28.57/10.11	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, d), c)
28.57/10.11	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, d), e)
28.57/10.11	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, a), d)
28.57/10.11	   A^2 -> H(U1(e, a), k)
28.57/10.11	
28.57/10.11	The TRS R consists of the following rules:
28.57/10.11	
28.57/10.11	   f(x) -> U1(x, x)
28.57/10.11	   U1(e, x) -> x
28.57/10.11	   a -> c
28.57/10.11	   a -> d
28.57/10.11	   b -> c
28.57/10.11	   b -> d
28.57/10.11	   d -> k
28.57/10.11	   c -> e
28.57/10.11	   c -> k
28.57/10.11	
28.57/10.11	Q is empty.
28.57/10.11	We have to consider all minimal (P,Q,R)-chains.
28.57/10.11	----------------------------------------
28.57/10.11	
28.57/10.11	(1883) TransformationProof (EQUIVALENT)
28.57/10.11	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), b) at position [] we obtained the following new rules [LPAR04]:
28.57/10.11	
28.57/10.11	   (A^2 -> H(U1(k, c), b),A^2 -> H(U1(k, c), b))
28.57/10.11	   (A^2 -> H(U1(k, d), b),A^2 -> H(U1(k, d), b))
28.57/10.11	   (A^2 -> H(U1(k, a), c),A^2 -> H(U1(k, a), c))
28.57/10.11	   (A^2 -> H(U1(k, a), d),A^2 -> H(U1(k, a), d))
28.57/10.11	
28.57/10.11	
28.57/10.11	----------------------------------------
28.57/10.11	
28.57/10.11	(1884)
28.57/10.11	Obligation:
28.57/10.11	Q DP problem:
28.57/10.11	The TRS P consists of the following rules:
28.57/10.11	
28.57/10.11	   H(x, x) -> G(x, x, f(k))
28.57/10.11	   G(d, x, x) -> A^2
28.57/10.11	   A^2 -> H(f(c), f(c))
28.57/10.11	   A^2 -> H(f(d), f(d))
28.57/10.11	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.11	   A^2 -> H(f(e), f(e))
28.57/10.11	   A^2 -> H(f(k), f(k))
28.57/10.11	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.11	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.11	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.11	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.11	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, a), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, a), c)
28.57/10.11	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, d), b)
28.57/10.11	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, d), c)
28.57/10.11	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, d), e)
28.57/10.11	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, a), d)
28.57/10.11	   A^2 -> H(U1(c, a), k)
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.11	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.11	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.11	   A^2 -> H(U1(d, c), b)
28.57/10.11	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(d, c), c)
28.57/10.11	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(d, c), e)
28.57/10.11	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, a), d)
28.57/10.11	   A^2 -> H(U1(d, a), k)
28.57/10.11	   A^2 -> H(U1(a, e), b)
28.57/10.11	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(a, e), c)
28.57/10.11	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(a, e), e)
28.57/10.11	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(a, k), b)
28.57/10.11	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(a, k), c)
28.57/10.11	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(a, k), e)
28.57/10.11	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(a, c), d)
28.57/10.11	   A^2 -> H(U1(a, c), k)
28.57/10.11	   A^2 -> H(U1(a, d), d)
28.57/10.11	   A^2 -> H(U1(a, d), k)
28.57/10.11	   A^2 -> H(k, U1(c, b))
28.57/10.11	   A^2 -> H(k, U1(d, b))
28.57/10.11	   A^2 -> H(k, U1(b, c))
28.57/10.11	   A^2 -> H(k, U1(b, d))
28.57/10.11	   A^2 -> H(k, U1(c, c))
28.57/10.11	   A^2 -> H(k, f(e))
28.57/10.11	   A^2 -> H(k, f(k))
28.57/10.11	   A^2 -> H(k, U1(d, d))
28.57/10.11	   A^2 -> H(c, U1(e, b))
28.57/10.11	   A^2 -> H(c, U1(k, b))
28.57/10.11	   A^2 -> H(c, U1(c, d))
28.57/10.11	   A^2 -> H(c, U1(d, c))
28.57/10.11	   A^2 -> H(c, U1(b, e))
28.57/10.11	   A^2 -> H(c, U1(b, k))
28.57/10.11	   A^2 -> H(c, U1(e, c))
28.57/10.11	   A^2 -> H(c, U1(k, c))
28.57/10.11	   A^2 -> H(c, U1(c, e))
28.57/10.11	   A^2 -> H(c, U1(c, k))
28.57/10.11	   A^2 -> H(c, U1(e, e))
28.57/10.11	   A^2 -> H(c, U1(k, k))
28.57/10.11	   A^2 -> H(c, U1(k, d))
28.57/10.11	   A^2 -> H(c, U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.11	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.11	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, c), b)
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, c), e)
28.57/10.11	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.11	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.11	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, c), b)
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, c), c)
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, e), b)
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, e), c)
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, e), e)
28.57/10.11	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, k), b)
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, k), c)
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, k), e)
28.57/10.11	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, c), d)
28.57/10.11	   A^2 -> H(e, U1(e, b))
28.57/10.11	   A^2 -> H(e, U1(c, d))
28.57/10.11	   A^2 -> H(e, U1(d, c))
28.57/10.11	   A^2 -> H(e, U1(b, e))
28.57/10.11	   A^2 -> H(e, U1(b, k))
28.57/10.11	   A^2 -> H(e, U1(e, c))
28.57/10.11	   A^2 -> H(e, U1(c, e))
28.57/10.11	   A^2 -> H(e, U1(c, k))
28.57/10.11	   A^2 -> H(e, U1(e, e))
28.57/10.11	   A^2 -> H(e, U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, e), b)
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, e), c)
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.11	   A^2 -> H(f(e), d)
28.57/10.11	   A^2 -> H(f(e), k)
28.57/10.11	   A^2 -> H(U1(k, k), b)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, k), c)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.11	   A^2 -> H(f(k), d)
28.57/10.11	   A^2 -> H(f(k), k)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, d), b)
28.57/10.11	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, d), c)
28.57/10.11	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, k), b)
28.57/10.11	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(d, k), c)
28.57/10.11	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(d, k), e)
28.57/10.11	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, d), d)
28.57/10.11	   A^2 -> H(U1(d, d), k)
28.57/10.11	   A^2 -> H(U1(e, c), c)
28.57/10.11	   A^2 -> H(U1(c, c), e)
28.57/10.11	   A^2 -> H(U1(c, c), k)
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(e, e), e)
28.57/10.11	   A^2 -> H(d, U1(e, b))
28.57/10.11	   A^2 -> H(d, U1(k, b))
28.57/10.11	   A^2 -> H(d, U1(c, d))
28.57/10.11	   A^2 -> H(d, U1(d, c))
28.57/10.11	   A^2 -> H(d, U1(b, e))
28.57/10.11	   A^2 -> H(d, U1(b, k))
28.57/10.11	   A^2 -> H(d, U1(e, c))
28.57/10.11	   A^2 -> H(d, U1(k, c))
28.57/10.11	   A^2 -> H(d, U1(c, e))
28.57/10.11	   A^2 -> H(d, U1(c, k))
28.57/10.11	   A^2 -> H(d, U1(e, e))
28.57/10.11	   A^2 -> H(d, U1(k, k))
28.57/10.11	   A^2 -> H(d, U1(k, d))
28.57/10.11	   A^2 -> H(d, U1(d, k))
28.57/10.11	   A^2 -> H(a, b)
28.57/10.11	   A^2 -> H(a, U1(e, d))
28.57/10.11	   A^2 -> H(a, U1(d, e))
28.57/10.11	   A^2 -> H(a, c)
28.57/10.11	   A^2 -> H(a, U1(e, k))
28.57/10.11	   A^2 -> H(a, U1(k, e))
28.57/10.11	   A^2 -> H(a, e)
28.57/10.11	   A^2 -> H(a, U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, d), b)
28.57/10.11	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, d), c)
28.57/10.11	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, d), e)
28.57/10.11	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, a), d)
28.57/10.11	   A^2 -> H(U1(e, a), k)
28.57/10.11	   A^2 -> H(U1(k, a), d)
28.57/10.11	
28.57/10.11	The TRS R consists of the following rules:
28.57/10.11	
28.57/10.11	   f(x) -> U1(x, x)
28.57/10.11	   U1(e, x) -> x
28.57/10.11	   a -> c
28.57/10.11	   a -> d
28.57/10.11	   b -> c
28.57/10.11	   b -> d
28.57/10.11	   d -> k
28.57/10.11	   c -> e
28.57/10.11	   c -> k
28.57/10.11	
28.57/10.11	Q is empty.
28.57/10.11	We have to consider all minimal (P,Q,R)-chains.
28.57/10.11	----------------------------------------
28.57/10.11	
28.57/10.11	(1885) TransformationProof (EQUIVALENT)
28.57/10.11	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.11	
28.57/10.11	   (A^2 -> H(U1(k, c), U1(e, d)),A^2 -> H(U1(k, c), U1(e, d)))
28.57/10.11	   (A^2 -> H(U1(k, d), U1(e, d)),A^2 -> H(U1(k, d), U1(e, d)))
28.57/10.11	   (A^2 -> H(U1(k, a), d),A^2 -> H(U1(k, a), d))
28.57/10.11	   (A^2 -> H(U1(k, a), U1(e, k)),A^2 -> H(U1(k, a), U1(e, k)))
28.57/10.11	
28.57/10.11	
28.57/10.11	----------------------------------------
28.57/10.11	
28.57/10.11	(1886)
28.57/10.11	Obligation:
28.57/10.11	Q DP problem:
28.57/10.11	The TRS P consists of the following rules:
28.57/10.11	
28.57/10.11	   H(x, x) -> G(x, x, f(k))
28.57/10.11	   G(d, x, x) -> A^2
28.57/10.11	   A^2 -> H(f(c), f(c))
28.57/10.11	   A^2 -> H(f(d), f(d))
28.57/10.11	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.11	   A^2 -> H(f(e), f(e))
28.57/10.11	   A^2 -> H(f(k), f(k))
28.57/10.11	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.11	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.11	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.11	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.11	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, a), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, a), c)
28.57/10.11	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, d), b)
28.57/10.11	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, d), c)
28.57/10.11	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, d), e)
28.57/10.11	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, a), d)
28.57/10.11	   A^2 -> H(U1(c, a), k)
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.11	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.11	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.11	   A^2 -> H(U1(d, c), b)
28.57/10.11	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(d, c), c)
28.57/10.11	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(d, c), e)
28.57/10.11	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, a), d)
28.57/10.11	   A^2 -> H(U1(d, a), k)
28.57/10.11	   A^2 -> H(U1(a, e), b)
28.57/10.11	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(a, e), c)
28.57/10.11	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(a, e), e)
28.57/10.11	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(a, k), b)
28.57/10.11	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(a, k), c)
28.57/10.11	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(a, k), e)
28.57/10.11	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(a, c), d)
28.57/10.11	   A^2 -> H(U1(a, c), k)
28.57/10.11	   A^2 -> H(U1(a, d), d)
28.57/10.11	   A^2 -> H(U1(a, d), k)
28.57/10.11	   A^2 -> H(k, U1(c, b))
28.57/10.11	   A^2 -> H(k, U1(d, b))
28.57/10.11	   A^2 -> H(k, U1(b, c))
28.57/10.11	   A^2 -> H(k, U1(b, d))
28.57/10.11	   A^2 -> H(k, U1(c, c))
28.57/10.11	   A^2 -> H(k, f(e))
28.57/10.11	   A^2 -> H(k, f(k))
28.57/10.11	   A^2 -> H(k, U1(d, d))
28.57/10.11	   A^2 -> H(c, U1(e, b))
28.57/10.11	   A^2 -> H(c, U1(k, b))
28.57/10.11	   A^2 -> H(c, U1(c, d))
28.57/10.11	   A^2 -> H(c, U1(d, c))
28.57/10.11	   A^2 -> H(c, U1(b, e))
28.57/10.11	   A^2 -> H(c, U1(b, k))
28.57/10.11	   A^2 -> H(c, U1(e, c))
28.57/10.11	   A^2 -> H(c, U1(k, c))
28.57/10.11	   A^2 -> H(c, U1(c, e))
28.57/10.11	   A^2 -> H(c, U1(c, k))
28.57/10.11	   A^2 -> H(c, U1(e, e))
28.57/10.11	   A^2 -> H(c, U1(k, k))
28.57/10.11	   A^2 -> H(c, U1(k, d))
28.57/10.11	   A^2 -> H(c, U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.11	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.11	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, c), b)
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, c), e)
28.57/10.11	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.11	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.11	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, c), b)
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, c), c)
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, e), b)
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, e), c)
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, e), e)
28.57/10.11	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, k), b)
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, k), c)
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, k), e)
28.57/10.11	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, c), d)
28.57/10.11	   A^2 -> H(e, U1(e, b))
28.57/10.11	   A^2 -> H(e, U1(c, d))
28.57/10.11	   A^2 -> H(e, U1(d, c))
28.57/10.11	   A^2 -> H(e, U1(b, e))
28.57/10.11	   A^2 -> H(e, U1(b, k))
28.57/10.11	   A^2 -> H(e, U1(e, c))
28.57/10.11	   A^2 -> H(e, U1(c, e))
28.57/10.11	   A^2 -> H(e, U1(c, k))
28.57/10.11	   A^2 -> H(e, U1(e, e))
28.57/10.11	   A^2 -> H(e, U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, e), b)
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, e), c)
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.11	   A^2 -> H(f(e), d)
28.57/10.11	   A^2 -> H(f(e), k)
28.57/10.11	   A^2 -> H(U1(k, k), b)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, k), c)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.11	   A^2 -> H(f(k), d)
28.57/10.11	   A^2 -> H(f(k), k)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, d), b)
28.57/10.11	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, d), c)
28.57/10.11	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, k), b)
28.57/10.11	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(d, k), c)
28.57/10.11	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(d, k), e)
28.57/10.11	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, d), d)
28.57/10.11	   A^2 -> H(U1(d, d), k)
28.57/10.11	   A^2 -> H(U1(e, c), c)
28.57/10.11	   A^2 -> H(U1(c, c), e)
28.57/10.11	   A^2 -> H(U1(c, c), k)
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(e, e), e)
28.57/10.11	   A^2 -> H(d, U1(e, b))
28.57/10.11	   A^2 -> H(d, U1(k, b))
28.57/10.11	   A^2 -> H(d, U1(c, d))
28.57/10.11	   A^2 -> H(d, U1(d, c))
28.57/10.11	   A^2 -> H(d, U1(b, e))
28.57/10.11	   A^2 -> H(d, U1(b, k))
28.57/10.11	   A^2 -> H(d, U1(e, c))
28.57/10.11	   A^2 -> H(d, U1(k, c))
28.57/10.11	   A^2 -> H(d, U1(c, e))
28.57/10.11	   A^2 -> H(d, U1(c, k))
28.57/10.11	   A^2 -> H(d, U1(e, e))
28.57/10.11	   A^2 -> H(d, U1(k, k))
28.57/10.11	   A^2 -> H(d, U1(k, d))
28.57/10.11	   A^2 -> H(d, U1(d, k))
28.57/10.11	   A^2 -> H(a, b)
28.57/10.11	   A^2 -> H(a, U1(e, d))
28.57/10.11	   A^2 -> H(a, U1(d, e))
28.57/10.11	   A^2 -> H(a, c)
28.57/10.11	   A^2 -> H(a, U1(e, k))
28.57/10.11	   A^2 -> H(a, U1(k, e))
28.57/10.11	   A^2 -> H(a, e)
28.57/10.11	   A^2 -> H(a, U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, d), b)
28.57/10.11	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, d), c)
28.57/10.11	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, d), e)
28.57/10.11	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, a), d)
28.57/10.11	   A^2 -> H(U1(e, a), k)
28.57/10.11	   A^2 -> H(U1(k, a), d)
28.57/10.11	
28.57/10.11	The TRS R consists of the following rules:
28.57/10.11	
28.57/10.11	   f(x) -> U1(x, x)
28.57/10.11	   U1(e, x) -> x
28.57/10.11	   a -> c
28.57/10.11	   a -> d
28.57/10.11	   b -> c
28.57/10.11	   b -> d
28.57/10.11	   d -> k
28.57/10.11	   c -> e
28.57/10.11	   c -> k
28.57/10.11	
28.57/10.11	Q is empty.
28.57/10.11	We have to consider all minimal (P,Q,R)-chains.
28.57/10.11	----------------------------------------
28.57/10.11	
28.57/10.11	(1887) TransformationProof (EQUIVALENT)
28.57/10.11	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.11	
28.57/10.11	   (A^2 -> H(U1(k, c), U1(d, e)),A^2 -> H(U1(k, c), U1(d, e)))
28.57/10.11	   (A^2 -> H(U1(k, d), U1(d, e)),A^2 -> H(U1(k, d), U1(d, e)))
28.57/10.11	   (A^2 -> H(U1(k, a), U1(k, e)),A^2 -> H(U1(k, a), U1(k, e)))
28.57/10.11	
28.57/10.11	
28.57/10.11	----------------------------------------
28.57/10.11	
28.57/10.11	(1888)
28.57/10.11	Obligation:
28.57/10.11	Q DP problem:
28.57/10.11	The TRS P consists of the following rules:
28.57/10.11	
28.57/10.11	   H(x, x) -> G(x, x, f(k))
28.57/10.11	   G(d, x, x) -> A^2
28.57/10.11	   A^2 -> H(f(c), f(c))
28.57/10.11	   A^2 -> H(f(d), f(d))
28.57/10.11	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.11	   A^2 -> H(f(e), f(e))
28.57/10.11	   A^2 -> H(f(k), f(k))
28.57/10.11	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.11	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.11	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.11	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.11	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, a), c)
28.57/10.11	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, d), b)
28.57/10.11	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, d), c)
28.57/10.11	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, d), e)
28.57/10.11	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, a), d)
28.57/10.11	   A^2 -> H(U1(c, a), k)
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.11	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.11	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.11	   A^2 -> H(U1(d, c), b)
28.57/10.11	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(d, c), c)
28.57/10.11	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(d, c), e)
28.57/10.11	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, a), d)
28.57/10.11	   A^2 -> H(U1(d, a), k)
28.57/10.11	   A^2 -> H(U1(a, e), b)
28.57/10.11	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(a, e), c)
28.57/10.11	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(a, e), e)
28.57/10.11	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(a, k), b)
28.57/10.11	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(a, k), c)
28.57/10.11	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(a, k), e)
28.57/10.11	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(a, c), d)
28.57/10.11	   A^2 -> H(U1(a, c), k)
28.57/10.11	   A^2 -> H(U1(a, d), d)
28.57/10.11	   A^2 -> H(U1(a, d), k)
28.57/10.11	   A^2 -> H(k, U1(c, b))
28.57/10.11	   A^2 -> H(k, U1(d, b))
28.57/10.11	   A^2 -> H(k, U1(b, c))
28.57/10.11	   A^2 -> H(k, U1(b, d))
28.57/10.11	   A^2 -> H(k, U1(c, c))
28.57/10.11	   A^2 -> H(k, f(e))
28.57/10.11	   A^2 -> H(k, f(k))
28.57/10.11	   A^2 -> H(k, U1(d, d))
28.57/10.11	   A^2 -> H(c, U1(e, b))
28.57/10.11	   A^2 -> H(c, U1(k, b))
28.57/10.11	   A^2 -> H(c, U1(c, d))
28.57/10.11	   A^2 -> H(c, U1(d, c))
28.57/10.11	   A^2 -> H(c, U1(b, e))
28.57/10.11	   A^2 -> H(c, U1(b, k))
28.57/10.11	   A^2 -> H(c, U1(e, c))
28.57/10.11	   A^2 -> H(c, U1(k, c))
28.57/10.11	   A^2 -> H(c, U1(c, e))
28.57/10.11	   A^2 -> H(c, U1(c, k))
28.57/10.11	   A^2 -> H(c, U1(e, e))
28.57/10.11	   A^2 -> H(c, U1(k, k))
28.57/10.11	   A^2 -> H(c, U1(k, d))
28.57/10.11	   A^2 -> H(c, U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.11	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.11	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, c), b)
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, c), e)
28.57/10.11	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.11	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.11	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.11	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, c), b)
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, c), c)
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, e), b)
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, e), c)
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, e), e)
28.57/10.11	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, k), b)
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(c, k), c)
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(c, k), e)
28.57/10.11	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(c, c), d)
28.57/10.11	   A^2 -> H(e, U1(e, b))
28.57/10.11	   A^2 -> H(e, U1(c, d))
28.57/10.11	   A^2 -> H(e, U1(d, c))
28.57/10.11	   A^2 -> H(e, U1(b, e))
28.57/10.11	   A^2 -> H(e, U1(b, k))
28.57/10.11	   A^2 -> H(e, U1(e, c))
28.57/10.11	   A^2 -> H(e, U1(c, e))
28.57/10.11	   A^2 -> H(e, U1(c, k))
28.57/10.11	   A^2 -> H(e, U1(e, e))
28.57/10.11	   A^2 -> H(e, U1(d, k))
28.57/10.11	   A^2 -> H(U1(e, e), b)
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.11	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.11	   A^2 -> H(U1(e, e), c)
28.57/10.11	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.11	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.11	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.11	   A^2 -> H(f(e), d)
28.57/10.11	   A^2 -> H(f(e), k)
28.57/10.11	   A^2 -> H(U1(k, k), b)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, k), c)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.11	   A^2 -> H(f(k), d)
28.57/10.11	   A^2 -> H(f(k), k)
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.11	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.11	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.11	   A^2 -> H(U1(k, d), b)
28.57/10.11	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.11	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.11	   A^2 -> H(U1(k, d), c)
28.57/10.11	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.11	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, k), b)
28.57/10.11	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.11	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.11	   A^2 -> H(U1(d, k), c)
28.57/10.11	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.11	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.11	   A^2 -> H(U1(d, k), e)
28.57/10.11	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.11	   A^2 -> H(U1(d, d), d)
28.57/10.11	   A^2 -> H(U1(d, d), k)
28.57/10.11	   A^2 -> H(U1(e, c), c)
28.57/10.11	   A^2 -> H(U1(c, c), e)
28.57/10.11	   A^2 -> H(U1(c, c), k)
28.57/10.11	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.11	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.11	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.11	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.11	   A^2 -> H(U1(e, e), e)
28.57/10.11	   A^2 -> H(d, U1(e, b))
28.57/10.11	   A^2 -> H(d, U1(k, b))
28.57/10.11	   A^2 -> H(d, U1(c, d))
28.57/10.11	   A^2 -> H(d, U1(d, c))
28.57/10.11	   A^2 -> H(d, U1(b, e))
28.57/10.11	   A^2 -> H(d, U1(b, k))
28.57/10.11	   A^2 -> H(d, U1(e, c))
28.57/10.11	   A^2 -> H(d, U1(k, c))
28.57/10.11	   A^2 -> H(d, U1(c, e))
28.57/10.11	   A^2 -> H(d, U1(c, k))
28.57/10.11	   A^2 -> H(d, U1(e, e))
28.57/10.12	   A^2 -> H(d, U1(k, k))
28.57/10.12	   A^2 -> H(d, U1(k, d))
28.57/10.12	   A^2 -> H(d, U1(d, k))
28.57/10.12	   A^2 -> H(a, b)
28.57/10.12	   A^2 -> H(a, U1(e, d))
28.57/10.12	   A^2 -> H(a, U1(d, e))
28.57/10.12	   A^2 -> H(a, c)
28.57/10.12	   A^2 -> H(a, U1(e, k))
28.57/10.12	   A^2 -> H(a, U1(k, e))
28.57/10.12	   A^2 -> H(a, e)
28.57/10.12	   A^2 -> H(a, U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, d), b)
28.57/10.12	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, d), c)
28.57/10.12	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, d), e)
28.57/10.12	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, a), d)
28.57/10.12	   A^2 -> H(U1(e, a), k)
28.57/10.12	   A^2 -> H(U1(k, a), d)
28.57/10.12	
28.57/10.12	The TRS R consists of the following rules:
28.57/10.12	
28.57/10.12	   f(x) -> U1(x, x)
28.57/10.12	   U1(e, x) -> x
28.57/10.12	   a -> c
28.57/10.12	   a -> d
28.57/10.12	   b -> c
28.57/10.12	   b -> d
28.57/10.12	   d -> k
28.57/10.12	   c -> e
28.57/10.12	   c -> k
28.57/10.12	
28.57/10.12	Q is empty.
28.57/10.12	We have to consider all minimal (P,Q,R)-chains.
28.57/10.12	----------------------------------------
28.57/10.12	
28.57/10.12	(1889) TransformationProof (EQUIVALENT)
28.57/10.12	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), c) at position [] we obtained the following new rules [LPAR04]:
28.57/10.12	
28.57/10.12	   (A^2 -> H(U1(k, c), c),A^2 -> H(U1(k, c), c))
28.57/10.12	   (A^2 -> H(U1(k, d), c),A^2 -> H(U1(k, d), c))
28.57/10.12	   (A^2 -> H(U1(k, a), e),A^2 -> H(U1(k, a), e))
28.57/10.12	   (A^2 -> H(U1(k, a), k),A^2 -> H(U1(k, a), k))
28.57/10.12	
28.57/10.12	
28.57/10.12	----------------------------------------
28.57/10.12	
28.57/10.12	(1890)
28.57/10.12	Obligation:
28.57/10.12	Q DP problem:
28.57/10.12	The TRS P consists of the following rules:
28.57/10.12	
28.57/10.12	   H(x, x) -> G(x, x, f(k))
28.57/10.12	   G(d, x, x) -> A^2
28.57/10.12	   A^2 -> H(f(c), f(c))
28.57/10.12	   A^2 -> H(f(d), f(d))
28.57/10.12	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.12	   A^2 -> H(f(e), f(e))
28.57/10.12	   A^2 -> H(f(k), f(k))
28.57/10.12	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.12	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.12	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.12	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.12	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.12	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.12	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, d), b)
28.57/10.12	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, d), c)
28.57/10.12	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, d), e)
28.57/10.12	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, a), d)
28.57/10.12	   A^2 -> H(U1(c, a), k)
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.12	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.12	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.12	   A^2 -> H(U1(d, c), b)
28.57/10.12	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(d, c), c)
28.57/10.12	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(d, c), e)
28.57/10.12	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, a), d)
28.57/10.12	   A^2 -> H(U1(d, a), k)
28.57/10.12	   A^2 -> H(U1(a, e), b)
28.57/10.12	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(a, e), c)
28.57/10.12	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(a, e), e)
28.57/10.12	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(a, k), b)
28.57/10.12	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(a, k), c)
28.57/10.12	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(a, k), e)
28.57/10.12	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(a, c), d)
28.57/10.12	   A^2 -> H(U1(a, c), k)
28.57/10.12	   A^2 -> H(U1(a, d), d)
28.57/10.12	   A^2 -> H(U1(a, d), k)
28.57/10.12	   A^2 -> H(k, U1(c, b))
28.57/10.12	   A^2 -> H(k, U1(d, b))
28.57/10.12	   A^2 -> H(k, U1(b, c))
28.57/10.12	   A^2 -> H(k, U1(b, d))
28.57/10.12	   A^2 -> H(k, U1(c, c))
28.57/10.12	   A^2 -> H(k, f(e))
28.57/10.12	   A^2 -> H(k, f(k))
28.57/10.12	   A^2 -> H(k, U1(d, d))
28.57/10.12	   A^2 -> H(c, U1(e, b))
28.57/10.12	   A^2 -> H(c, U1(k, b))
28.57/10.12	   A^2 -> H(c, U1(c, d))
28.57/10.12	   A^2 -> H(c, U1(d, c))
28.57/10.12	   A^2 -> H(c, U1(b, e))
28.57/10.12	   A^2 -> H(c, U1(b, k))
28.57/10.12	   A^2 -> H(c, U1(e, c))
28.57/10.12	   A^2 -> H(c, U1(k, c))
28.57/10.12	   A^2 -> H(c, U1(c, e))
28.57/10.12	   A^2 -> H(c, U1(c, k))
28.57/10.12	   A^2 -> H(c, U1(e, e))
28.57/10.12	   A^2 -> H(c, U1(k, k))
28.57/10.12	   A^2 -> H(c, U1(k, d))
28.57/10.12	   A^2 -> H(c, U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.12	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.12	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, c), b)
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, c), e)
28.57/10.12	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.12	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.12	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, c), b)
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, c), c)
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, e), b)
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, e), c)
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, e), e)
28.57/10.12	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, k), b)
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, k), c)
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, k), e)
28.57/10.12	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, c), d)
28.57/10.12	   A^2 -> H(e, U1(e, b))
28.57/10.12	   A^2 -> H(e, U1(c, d))
28.57/10.12	   A^2 -> H(e, U1(d, c))
28.57/10.12	   A^2 -> H(e, U1(b, e))
28.57/10.12	   A^2 -> H(e, U1(b, k))
28.57/10.12	   A^2 -> H(e, U1(e, c))
28.57/10.12	   A^2 -> H(e, U1(c, e))
28.57/10.12	   A^2 -> H(e, U1(c, k))
28.57/10.12	   A^2 -> H(e, U1(e, e))
28.57/10.12	   A^2 -> H(e, U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, e), b)
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, e), c)
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.12	   A^2 -> H(f(e), d)
28.57/10.12	   A^2 -> H(f(e), k)
28.57/10.12	   A^2 -> H(U1(k, k), b)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, k), c)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.12	   A^2 -> H(f(k), d)
28.57/10.12	   A^2 -> H(f(k), k)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, d), b)
28.57/10.12	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, d), c)
28.57/10.12	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, k), b)
28.57/10.12	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(d, k), c)
28.57/10.12	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(d, k), e)
28.57/10.12	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, d), d)
28.57/10.12	   A^2 -> H(U1(d, d), k)
28.57/10.12	   A^2 -> H(U1(e, c), c)
28.57/10.12	   A^2 -> H(U1(c, c), e)
28.57/10.12	   A^2 -> H(U1(c, c), k)
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(e, e), e)
28.57/10.12	   A^2 -> H(d, U1(e, b))
28.57/10.12	   A^2 -> H(d, U1(k, b))
28.57/10.12	   A^2 -> H(d, U1(c, d))
28.57/10.12	   A^2 -> H(d, U1(d, c))
28.57/10.12	   A^2 -> H(d, U1(b, e))
28.57/10.12	   A^2 -> H(d, U1(b, k))
28.57/10.12	   A^2 -> H(d, U1(e, c))
28.57/10.12	   A^2 -> H(d, U1(k, c))
28.57/10.12	   A^2 -> H(d, U1(c, e))
28.57/10.12	   A^2 -> H(d, U1(c, k))
28.57/10.12	   A^2 -> H(d, U1(e, e))
28.57/10.12	   A^2 -> H(d, U1(k, k))
28.57/10.12	   A^2 -> H(d, U1(k, d))
28.57/10.12	   A^2 -> H(d, U1(d, k))
28.57/10.12	   A^2 -> H(a, b)
28.57/10.12	   A^2 -> H(a, U1(e, d))
28.57/10.12	   A^2 -> H(a, U1(d, e))
28.57/10.12	   A^2 -> H(a, c)
28.57/10.12	   A^2 -> H(a, U1(e, k))
28.57/10.12	   A^2 -> H(a, U1(k, e))
28.57/10.12	   A^2 -> H(a, e)
28.57/10.12	   A^2 -> H(a, U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, d), b)
28.57/10.12	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, d), c)
28.57/10.12	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, d), e)
28.57/10.12	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, a), d)
28.57/10.12	   A^2 -> H(U1(e, a), k)
28.57/10.12	   A^2 -> H(U1(k, a), d)
28.57/10.12	   A^2 -> H(U1(k, a), e)
28.57/10.12	   A^2 -> H(U1(k, a), k)
28.57/10.12	
28.57/10.12	The TRS R consists of the following rules:
28.57/10.12	
28.57/10.12	   f(x) -> U1(x, x)
28.57/10.12	   U1(e, x) -> x
28.57/10.12	   a -> c
28.57/10.12	   a -> d
28.57/10.12	   b -> c
28.57/10.12	   b -> d
28.57/10.12	   d -> k
28.57/10.12	   c -> e
28.57/10.12	   c -> k
28.57/10.12	
28.57/10.12	Q is empty.
28.57/10.12	We have to consider all minimal (P,Q,R)-chains.
28.57/10.12	----------------------------------------
28.57/10.12	
28.57/10.12	(1891) DependencyGraphProof (EQUIVALENT)
28.57/10.12	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
28.57/10.12	----------------------------------------
28.57/10.12	
28.57/10.12	(1892)
28.57/10.12	Obligation:
28.57/10.12	Q DP problem:
28.57/10.12	The TRS P consists of the following rules:
28.57/10.12	
28.57/10.12	   G(d, x, x) -> A^2
28.57/10.12	   A^2 -> H(f(c), f(c))
28.57/10.12	   H(x, x) -> G(x, x, f(k))
28.57/10.12	   A^2 -> H(f(d), f(d))
28.57/10.12	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.12	   A^2 -> H(f(e), f(e))
28.57/10.12	   A^2 -> H(f(k), f(k))
28.57/10.12	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.12	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.12	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.12	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.12	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, a), U1(e, k))
28.57/10.12	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.12	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, d), b)
28.57/10.12	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, d), c)
28.57/10.12	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, d), e)
28.57/10.12	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, a), d)
28.57/10.12	   A^2 -> H(U1(c, a), k)
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.12	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.12	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.12	   A^2 -> H(U1(d, c), b)
28.57/10.12	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(d, c), c)
28.57/10.12	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(d, c), e)
28.57/10.12	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, a), d)
28.57/10.12	   A^2 -> H(U1(d, a), k)
28.57/10.12	   A^2 -> H(U1(a, e), b)
28.57/10.12	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(a, e), c)
28.57/10.12	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(a, e), e)
28.57/10.12	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(a, k), b)
28.57/10.12	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(a, k), c)
28.57/10.12	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(a, k), e)
28.57/10.12	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(a, c), d)
28.57/10.12	   A^2 -> H(U1(a, c), k)
28.57/10.12	   A^2 -> H(U1(a, d), d)
28.57/10.12	   A^2 -> H(U1(a, d), k)
28.57/10.12	   A^2 -> H(k, U1(c, b))
28.57/10.12	   A^2 -> H(k, U1(d, b))
28.57/10.12	   A^2 -> H(k, U1(b, c))
28.57/10.12	   A^2 -> H(k, U1(b, d))
28.57/10.12	   A^2 -> H(k, U1(c, c))
28.57/10.12	   A^2 -> H(k, f(e))
28.57/10.12	   A^2 -> H(k, f(k))
28.57/10.12	   A^2 -> H(k, U1(d, d))
28.57/10.12	   A^2 -> H(c, U1(e, b))
28.57/10.12	   A^2 -> H(c, U1(k, b))
28.57/10.12	   A^2 -> H(c, U1(c, d))
28.57/10.12	   A^2 -> H(c, U1(d, c))
28.57/10.12	   A^2 -> H(c, U1(b, e))
28.57/10.12	   A^2 -> H(c, U1(b, k))
28.57/10.12	   A^2 -> H(c, U1(e, c))
28.57/10.12	   A^2 -> H(c, U1(k, c))
28.57/10.12	   A^2 -> H(c, U1(c, e))
28.57/10.12	   A^2 -> H(c, U1(c, k))
28.57/10.12	   A^2 -> H(c, U1(e, e))
28.57/10.12	   A^2 -> H(c, U1(k, k))
28.57/10.12	   A^2 -> H(c, U1(k, d))
28.57/10.12	   A^2 -> H(c, U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.12	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.12	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, c), b)
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, c), e)
28.57/10.12	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.12	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.12	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, c), b)
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, c), c)
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, e), b)
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, e), c)
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, e), e)
28.57/10.12	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, k), b)
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, k), c)
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, k), e)
28.57/10.12	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, c), d)
28.57/10.12	   A^2 -> H(e, U1(e, b))
28.57/10.12	   A^2 -> H(e, U1(c, d))
28.57/10.12	   A^2 -> H(e, U1(d, c))
28.57/10.12	   A^2 -> H(e, U1(b, e))
28.57/10.12	   A^2 -> H(e, U1(b, k))
28.57/10.12	   A^2 -> H(e, U1(e, c))
28.57/10.12	   A^2 -> H(e, U1(c, e))
28.57/10.12	   A^2 -> H(e, U1(c, k))
28.57/10.12	   A^2 -> H(e, U1(e, e))
28.57/10.12	   A^2 -> H(e, U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, e), b)
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, e), c)
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.12	   A^2 -> H(f(e), d)
28.57/10.12	   A^2 -> H(f(e), k)
28.57/10.12	   A^2 -> H(U1(k, k), b)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, k), c)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.12	   A^2 -> H(f(k), d)
28.57/10.12	   A^2 -> H(f(k), k)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, d), b)
28.57/10.12	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, d), c)
28.57/10.12	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, k), b)
28.57/10.12	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(d, k), c)
28.57/10.12	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(d, k), e)
28.57/10.12	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, d), d)
28.57/10.12	   A^2 -> H(U1(d, d), k)
28.57/10.12	   A^2 -> H(U1(e, c), c)
28.57/10.12	   A^2 -> H(U1(c, c), e)
28.57/10.12	   A^2 -> H(U1(c, c), k)
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(e, e), e)
28.57/10.12	   A^2 -> H(d, U1(e, b))
28.57/10.12	   A^2 -> H(d, U1(k, b))
28.57/10.12	   A^2 -> H(d, U1(c, d))
28.57/10.12	   A^2 -> H(d, U1(d, c))
28.57/10.12	   A^2 -> H(d, U1(b, e))
28.57/10.12	   A^2 -> H(d, U1(b, k))
28.57/10.12	   A^2 -> H(d, U1(e, c))
28.57/10.12	   A^2 -> H(d, U1(k, c))
28.57/10.12	   A^2 -> H(d, U1(c, e))
28.57/10.12	   A^2 -> H(d, U1(c, k))
28.57/10.12	   A^2 -> H(d, U1(e, e))
28.57/10.12	   A^2 -> H(d, U1(k, k))
28.57/10.12	   A^2 -> H(d, U1(k, d))
28.57/10.12	   A^2 -> H(d, U1(d, k))
28.57/10.12	   A^2 -> H(a, b)
28.57/10.12	   A^2 -> H(a, U1(e, d))
28.57/10.12	   A^2 -> H(a, U1(d, e))
28.57/10.12	   A^2 -> H(a, c)
28.57/10.12	   A^2 -> H(a, U1(e, k))
28.57/10.12	   A^2 -> H(a, U1(k, e))
28.57/10.12	   A^2 -> H(a, e)
28.57/10.12	   A^2 -> H(a, U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, d), b)
28.57/10.12	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, d), c)
28.57/10.12	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, d), e)
28.57/10.12	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, a), d)
28.57/10.12	   A^2 -> H(U1(e, a), k)
28.57/10.12	   A^2 -> H(U1(k, a), d)
28.57/10.12	
28.57/10.12	The TRS R consists of the following rules:
28.57/10.12	
28.57/10.12	   f(x) -> U1(x, x)
28.57/10.12	   U1(e, x) -> x
28.57/10.12	   a -> c
28.57/10.12	   a -> d
28.57/10.12	   b -> c
28.57/10.12	   b -> d
28.57/10.12	   d -> k
28.57/10.12	   c -> e
28.57/10.12	   c -> k
28.57/10.12	
28.57/10.12	Q is empty.
28.57/10.12	We have to consider all minimal (P,Q,R)-chains.
28.57/10.12	----------------------------------------
28.57/10.12	
28.57/10.12	(1893) TransformationProof (EQUIVALENT)
28.57/10.12	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.12	
28.57/10.12	   (A^2 -> H(U1(k, c), U1(e, k)),A^2 -> H(U1(k, c), U1(e, k)))
28.57/10.12	   (A^2 -> H(U1(k, d), U1(e, k)),A^2 -> H(U1(k, d), U1(e, k)))
28.57/10.12	   (A^2 -> H(U1(k, a), k),A^2 -> H(U1(k, a), k))
28.57/10.12	
28.57/10.12	
28.57/10.12	----------------------------------------
28.57/10.12	
28.57/10.12	(1894)
28.57/10.12	Obligation:
28.57/10.12	Q DP problem:
28.57/10.12	The TRS P consists of the following rules:
28.57/10.12	
28.57/10.12	   G(d, x, x) -> A^2
28.57/10.12	   A^2 -> H(f(c), f(c))
28.57/10.12	   H(x, x) -> G(x, x, f(k))
28.57/10.12	   A^2 -> H(f(d), f(d))
28.57/10.12	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.12	   A^2 -> H(f(e), f(e))
28.57/10.12	   A^2 -> H(f(k), f(k))
28.57/10.12	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.12	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.12	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.12	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.12	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.12	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, d), b)
28.57/10.12	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, d), c)
28.57/10.12	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, d), e)
28.57/10.12	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, a), d)
28.57/10.12	   A^2 -> H(U1(c, a), k)
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.12	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.12	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.12	   A^2 -> H(U1(d, c), b)
28.57/10.12	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(d, c), c)
28.57/10.12	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(d, c), e)
28.57/10.12	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, a), d)
28.57/10.12	   A^2 -> H(U1(d, a), k)
28.57/10.12	   A^2 -> H(U1(a, e), b)
28.57/10.12	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(a, e), c)
28.57/10.12	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(a, e), e)
28.57/10.12	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(a, k), b)
28.57/10.12	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(a, k), c)
28.57/10.12	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(a, k), e)
28.57/10.12	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(a, c), d)
28.57/10.12	   A^2 -> H(U1(a, c), k)
28.57/10.12	   A^2 -> H(U1(a, d), d)
28.57/10.12	   A^2 -> H(U1(a, d), k)
28.57/10.12	   A^2 -> H(k, U1(c, b))
28.57/10.12	   A^2 -> H(k, U1(d, b))
28.57/10.12	   A^2 -> H(k, U1(b, c))
28.57/10.12	   A^2 -> H(k, U1(b, d))
28.57/10.12	   A^2 -> H(k, U1(c, c))
28.57/10.12	   A^2 -> H(k, f(e))
28.57/10.12	   A^2 -> H(k, f(k))
28.57/10.12	   A^2 -> H(k, U1(d, d))
28.57/10.12	   A^2 -> H(c, U1(e, b))
28.57/10.12	   A^2 -> H(c, U1(k, b))
28.57/10.12	   A^2 -> H(c, U1(c, d))
28.57/10.12	   A^2 -> H(c, U1(d, c))
28.57/10.12	   A^2 -> H(c, U1(b, e))
28.57/10.12	   A^2 -> H(c, U1(b, k))
28.57/10.12	   A^2 -> H(c, U1(e, c))
28.57/10.12	   A^2 -> H(c, U1(k, c))
28.57/10.12	   A^2 -> H(c, U1(c, e))
28.57/10.12	   A^2 -> H(c, U1(c, k))
28.57/10.12	   A^2 -> H(c, U1(e, e))
28.57/10.12	   A^2 -> H(c, U1(k, k))
28.57/10.12	   A^2 -> H(c, U1(k, d))
28.57/10.12	   A^2 -> H(c, U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.12	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.12	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, c), b)
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, c), e)
28.57/10.12	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.12	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.12	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, c), b)
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, c), c)
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, e), b)
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, e), c)
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, e), e)
28.57/10.12	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, k), b)
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, k), c)
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, k), e)
28.57/10.12	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, c), d)
28.57/10.12	   A^2 -> H(e, U1(e, b))
28.57/10.12	   A^2 -> H(e, U1(c, d))
28.57/10.12	   A^2 -> H(e, U1(d, c))
28.57/10.12	   A^2 -> H(e, U1(b, e))
28.57/10.12	   A^2 -> H(e, U1(b, k))
28.57/10.12	   A^2 -> H(e, U1(e, c))
28.57/10.12	   A^2 -> H(e, U1(c, e))
28.57/10.12	   A^2 -> H(e, U1(c, k))
28.57/10.12	   A^2 -> H(e, U1(e, e))
28.57/10.12	   A^2 -> H(e, U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, e), b)
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, e), c)
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.12	   A^2 -> H(f(e), d)
28.57/10.12	   A^2 -> H(f(e), k)
28.57/10.12	   A^2 -> H(U1(k, k), b)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, k), c)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.12	   A^2 -> H(f(k), d)
28.57/10.12	   A^2 -> H(f(k), k)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, d), b)
28.57/10.12	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, d), c)
28.57/10.12	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, k), b)
28.57/10.12	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(d, k), c)
28.57/10.12	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(d, k), e)
28.57/10.12	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, d), d)
28.57/10.12	   A^2 -> H(U1(d, d), k)
28.57/10.12	   A^2 -> H(U1(e, c), c)
28.57/10.12	   A^2 -> H(U1(c, c), e)
28.57/10.12	   A^2 -> H(U1(c, c), k)
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(e, e), e)
28.57/10.12	   A^2 -> H(d, U1(e, b))
28.57/10.12	   A^2 -> H(d, U1(k, b))
28.57/10.12	   A^2 -> H(d, U1(c, d))
28.57/10.12	   A^2 -> H(d, U1(d, c))
28.57/10.12	   A^2 -> H(d, U1(b, e))
28.57/10.12	   A^2 -> H(d, U1(b, k))
28.57/10.12	   A^2 -> H(d, U1(e, c))
28.57/10.12	   A^2 -> H(d, U1(k, c))
28.57/10.12	   A^2 -> H(d, U1(c, e))
28.57/10.12	   A^2 -> H(d, U1(c, k))
28.57/10.12	   A^2 -> H(d, U1(e, e))
28.57/10.12	   A^2 -> H(d, U1(k, k))
28.57/10.12	   A^2 -> H(d, U1(k, d))
28.57/10.12	   A^2 -> H(d, U1(d, k))
28.57/10.12	   A^2 -> H(a, b)
28.57/10.12	   A^2 -> H(a, U1(e, d))
28.57/10.12	   A^2 -> H(a, U1(d, e))
28.57/10.12	   A^2 -> H(a, c)
28.57/10.12	   A^2 -> H(a, U1(e, k))
28.57/10.12	   A^2 -> H(a, U1(k, e))
28.57/10.12	   A^2 -> H(a, e)
28.57/10.12	   A^2 -> H(a, U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, d), b)
28.57/10.12	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, d), c)
28.57/10.12	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, d), e)
28.57/10.12	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, a), d)
28.57/10.12	   A^2 -> H(U1(e, a), k)
28.57/10.12	   A^2 -> H(U1(k, a), d)
28.57/10.12	   A^2 -> H(U1(k, a), k)
28.57/10.12	
28.57/10.12	The TRS R consists of the following rules:
28.57/10.12	
28.57/10.12	   f(x) -> U1(x, x)
28.57/10.12	   U1(e, x) -> x
28.57/10.12	   a -> c
28.57/10.12	   a -> d
28.57/10.12	   b -> c
28.57/10.12	   b -> d
28.57/10.12	   d -> k
28.57/10.12	   c -> e
28.57/10.12	   c -> k
28.57/10.12	
28.57/10.12	Q is empty.
28.57/10.12	We have to consider all minimal (P,Q,R)-chains.
28.57/10.12	----------------------------------------
28.57/10.12	
28.57/10.12	(1895) DependencyGraphProof (EQUIVALENT)
28.57/10.12	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.12	----------------------------------------
28.57/10.12	
28.57/10.12	(1896)
28.57/10.12	Obligation:
28.57/10.12	Q DP problem:
28.57/10.12	The TRS P consists of the following rules:
28.57/10.12	
28.57/10.12	   A^2 -> H(f(c), f(c))
28.57/10.12	   H(x, x) -> G(x, x, f(k))
28.57/10.12	   G(d, x, x) -> A^2
28.57/10.12	   A^2 -> H(f(d), f(d))
28.57/10.12	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.12	   A^2 -> H(f(e), f(e))
28.57/10.12	   A^2 -> H(f(k), f(k))
28.57/10.12	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.12	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.12	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.12	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.12	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, a), U1(k, e))
28.57/10.12	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, d), b)
28.57/10.12	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, d), c)
28.57/10.12	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, d), e)
28.57/10.12	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, a), d)
28.57/10.12	   A^2 -> H(U1(c, a), k)
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.12	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.12	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.12	   A^2 -> H(U1(d, c), b)
28.57/10.12	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(d, c), c)
28.57/10.12	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(d, c), e)
28.57/10.12	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, a), d)
28.57/10.12	   A^2 -> H(U1(d, a), k)
28.57/10.12	   A^2 -> H(U1(a, e), b)
28.57/10.12	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(a, e), c)
28.57/10.12	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(a, e), e)
28.57/10.12	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(a, k), b)
28.57/10.12	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(a, k), c)
28.57/10.12	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(a, k), e)
28.57/10.12	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(a, c), d)
28.57/10.12	   A^2 -> H(U1(a, c), k)
28.57/10.12	   A^2 -> H(U1(a, d), d)
28.57/10.12	   A^2 -> H(U1(a, d), k)
28.57/10.12	   A^2 -> H(k, U1(c, b))
28.57/10.12	   A^2 -> H(k, U1(d, b))
28.57/10.12	   A^2 -> H(k, U1(b, c))
28.57/10.12	   A^2 -> H(k, U1(b, d))
28.57/10.12	   A^2 -> H(k, U1(c, c))
28.57/10.12	   A^2 -> H(k, f(e))
28.57/10.12	   A^2 -> H(k, f(k))
28.57/10.12	   A^2 -> H(k, U1(d, d))
28.57/10.12	   A^2 -> H(c, U1(e, b))
28.57/10.12	   A^2 -> H(c, U1(k, b))
28.57/10.12	   A^2 -> H(c, U1(c, d))
28.57/10.12	   A^2 -> H(c, U1(d, c))
28.57/10.12	   A^2 -> H(c, U1(b, e))
28.57/10.12	   A^2 -> H(c, U1(b, k))
28.57/10.12	   A^2 -> H(c, U1(e, c))
28.57/10.12	   A^2 -> H(c, U1(k, c))
28.57/10.12	   A^2 -> H(c, U1(c, e))
28.57/10.12	   A^2 -> H(c, U1(c, k))
28.57/10.12	   A^2 -> H(c, U1(e, e))
28.57/10.12	   A^2 -> H(c, U1(k, k))
28.57/10.12	   A^2 -> H(c, U1(k, d))
28.57/10.12	   A^2 -> H(c, U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.12	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.12	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, c), b)
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, c), e)
28.57/10.12	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.12	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.12	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, c), b)
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, c), c)
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, e), b)
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, e), c)
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, e), e)
28.57/10.12	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, k), b)
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, k), c)
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, k), e)
28.57/10.12	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, c), d)
28.57/10.12	   A^2 -> H(e, U1(e, b))
28.57/10.12	   A^2 -> H(e, U1(c, d))
28.57/10.12	   A^2 -> H(e, U1(d, c))
28.57/10.12	   A^2 -> H(e, U1(b, e))
28.57/10.12	   A^2 -> H(e, U1(b, k))
28.57/10.12	   A^2 -> H(e, U1(e, c))
28.57/10.12	   A^2 -> H(e, U1(c, e))
28.57/10.12	   A^2 -> H(e, U1(c, k))
28.57/10.12	   A^2 -> H(e, U1(e, e))
28.57/10.12	   A^2 -> H(e, U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, e), b)
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, e), c)
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.12	   A^2 -> H(f(e), d)
28.57/10.12	   A^2 -> H(f(e), k)
28.57/10.12	   A^2 -> H(U1(k, k), b)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, k), c)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.12	   A^2 -> H(f(k), d)
28.57/10.12	   A^2 -> H(f(k), k)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, d), b)
28.57/10.12	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, d), c)
28.57/10.12	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, k), b)
28.57/10.12	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(d, k), c)
28.57/10.12	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(d, k), e)
28.57/10.12	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, d), d)
28.57/10.12	   A^2 -> H(U1(d, d), k)
28.57/10.12	   A^2 -> H(U1(e, c), c)
28.57/10.12	   A^2 -> H(U1(c, c), e)
28.57/10.12	   A^2 -> H(U1(c, c), k)
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(e, e), e)
28.57/10.12	   A^2 -> H(d, U1(e, b))
28.57/10.12	   A^2 -> H(d, U1(k, b))
28.57/10.12	   A^2 -> H(d, U1(c, d))
28.57/10.12	   A^2 -> H(d, U1(d, c))
28.57/10.12	   A^2 -> H(d, U1(b, e))
28.57/10.12	   A^2 -> H(d, U1(b, k))
28.57/10.12	   A^2 -> H(d, U1(e, c))
28.57/10.12	   A^2 -> H(d, U1(k, c))
28.57/10.12	   A^2 -> H(d, U1(c, e))
28.57/10.12	   A^2 -> H(d, U1(c, k))
28.57/10.12	   A^2 -> H(d, U1(e, e))
28.57/10.12	   A^2 -> H(d, U1(k, k))
28.57/10.12	   A^2 -> H(d, U1(k, d))
28.57/10.12	   A^2 -> H(d, U1(d, k))
28.57/10.12	   A^2 -> H(a, b)
28.57/10.12	   A^2 -> H(a, U1(e, d))
28.57/10.12	   A^2 -> H(a, U1(d, e))
28.57/10.12	   A^2 -> H(a, c)
28.57/10.12	   A^2 -> H(a, U1(e, k))
28.57/10.12	   A^2 -> H(a, U1(k, e))
28.57/10.12	   A^2 -> H(a, e)
28.57/10.12	   A^2 -> H(a, U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, d), b)
28.57/10.12	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, d), c)
28.57/10.12	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, d), e)
28.57/10.12	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, a), d)
28.57/10.12	   A^2 -> H(U1(e, a), k)
28.57/10.12	   A^2 -> H(U1(k, a), d)
28.57/10.12	
28.57/10.12	The TRS R consists of the following rules:
28.57/10.12	
28.57/10.12	   f(x) -> U1(x, x)
28.57/10.12	   U1(e, x) -> x
28.57/10.12	   a -> c
28.57/10.12	   a -> d
28.57/10.12	   b -> c
28.57/10.12	   b -> d
28.57/10.12	   d -> k
28.57/10.12	   c -> e
28.57/10.12	   c -> k
28.57/10.12	
28.57/10.12	Q is empty.
28.57/10.12	We have to consider all minimal (P,Q,R)-chains.
28.57/10.12	----------------------------------------
28.57/10.12	
28.57/10.12	(1897) TransformationProof (EQUIVALENT)
28.57/10.12	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.12	
28.57/10.12	   (A^2 -> H(U1(k, c), U1(k, e)),A^2 -> H(U1(k, c), U1(k, e)))
28.57/10.12	   (A^2 -> H(U1(k, d), U1(k, e)),A^2 -> H(U1(k, d), U1(k, e)))
28.57/10.12	
28.57/10.12	
28.57/10.12	----------------------------------------
28.57/10.12	
28.57/10.12	(1898)
28.57/10.12	Obligation:
28.57/10.12	Q DP problem:
28.57/10.12	The TRS P consists of the following rules:
28.57/10.12	
28.57/10.12	   A^2 -> H(f(c), f(c))
28.57/10.12	   H(x, x) -> G(x, x, f(k))
28.57/10.12	   G(d, x, x) -> A^2
28.57/10.12	   A^2 -> H(f(d), f(d))
28.57/10.12	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.12	   A^2 -> H(f(e), f(e))
28.57/10.12	   A^2 -> H(f(k), f(k))
28.57/10.12	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.12	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.12	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.12	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.12	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, a), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, d), b)
28.57/10.12	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, d), c)
28.57/10.12	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, d), e)
28.57/10.12	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, a), d)
28.57/10.12	   A^2 -> H(U1(c, a), k)
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.12	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.12	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.12	   A^2 -> H(U1(d, c), b)
28.57/10.12	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(d, c), c)
28.57/10.12	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(d, c), e)
28.57/10.12	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, a), d)
28.57/10.12	   A^2 -> H(U1(d, a), k)
28.57/10.12	   A^2 -> H(U1(a, e), b)
28.57/10.12	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(a, e), c)
28.57/10.12	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(a, e), e)
28.57/10.12	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(a, k), b)
28.57/10.12	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(a, k), c)
28.57/10.12	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(a, k), e)
28.57/10.12	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(a, c), d)
28.57/10.12	   A^2 -> H(U1(a, c), k)
28.57/10.12	   A^2 -> H(U1(a, d), d)
28.57/10.12	   A^2 -> H(U1(a, d), k)
28.57/10.12	   A^2 -> H(k, U1(c, b))
28.57/10.12	   A^2 -> H(k, U1(d, b))
28.57/10.12	   A^2 -> H(k, U1(b, c))
28.57/10.12	   A^2 -> H(k, U1(b, d))
28.57/10.12	   A^2 -> H(k, U1(c, c))
28.57/10.12	   A^2 -> H(k, f(e))
28.57/10.12	   A^2 -> H(k, f(k))
28.57/10.12	   A^2 -> H(k, U1(d, d))
28.57/10.12	   A^2 -> H(c, U1(e, b))
28.57/10.12	   A^2 -> H(c, U1(k, b))
28.57/10.12	   A^2 -> H(c, U1(c, d))
28.57/10.12	   A^2 -> H(c, U1(d, c))
28.57/10.12	   A^2 -> H(c, U1(b, e))
28.57/10.12	   A^2 -> H(c, U1(b, k))
28.57/10.12	   A^2 -> H(c, U1(e, c))
28.57/10.12	   A^2 -> H(c, U1(k, c))
28.57/10.12	   A^2 -> H(c, U1(c, e))
28.57/10.12	   A^2 -> H(c, U1(c, k))
28.57/10.12	   A^2 -> H(c, U1(e, e))
28.57/10.12	   A^2 -> H(c, U1(k, k))
28.57/10.12	   A^2 -> H(c, U1(k, d))
28.57/10.12	   A^2 -> H(c, U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.12	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.12	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, c), b)
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, c), e)
28.57/10.12	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.12	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.12	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, c), b)
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, c), c)
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, e), b)
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, e), c)
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, e), e)
28.57/10.12	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, k), b)
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, k), c)
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, k), e)
28.57/10.12	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, c), d)
28.57/10.12	   A^2 -> H(e, U1(e, b))
28.57/10.12	   A^2 -> H(e, U1(c, d))
28.57/10.12	   A^2 -> H(e, U1(d, c))
28.57/10.12	   A^2 -> H(e, U1(b, e))
28.57/10.12	   A^2 -> H(e, U1(b, k))
28.57/10.12	   A^2 -> H(e, U1(e, c))
28.57/10.12	   A^2 -> H(e, U1(c, e))
28.57/10.12	   A^2 -> H(e, U1(c, k))
28.57/10.12	   A^2 -> H(e, U1(e, e))
28.57/10.12	   A^2 -> H(e, U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, e), b)
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, e), c)
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.12	   A^2 -> H(f(e), d)
28.57/10.12	   A^2 -> H(f(e), k)
28.57/10.12	   A^2 -> H(U1(k, k), b)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, k), c)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.12	   A^2 -> H(f(k), d)
28.57/10.12	   A^2 -> H(f(k), k)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, d), b)
28.57/10.12	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, d), c)
28.57/10.12	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, k), b)
28.57/10.12	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(d, k), c)
28.57/10.12	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(d, k), e)
28.57/10.12	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, d), d)
28.57/10.12	   A^2 -> H(U1(d, d), k)
28.57/10.12	   A^2 -> H(U1(e, c), c)
28.57/10.12	   A^2 -> H(U1(c, c), e)
28.57/10.12	   A^2 -> H(U1(c, c), k)
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(e, e), e)
28.57/10.12	   A^2 -> H(d, U1(e, b))
28.57/10.12	   A^2 -> H(d, U1(k, b))
28.57/10.12	   A^2 -> H(d, U1(c, d))
28.57/10.12	   A^2 -> H(d, U1(d, c))
28.57/10.12	   A^2 -> H(d, U1(b, e))
28.57/10.12	   A^2 -> H(d, U1(b, k))
28.57/10.12	   A^2 -> H(d, U1(e, c))
28.57/10.12	   A^2 -> H(d, U1(k, c))
28.57/10.12	   A^2 -> H(d, U1(c, e))
28.57/10.12	   A^2 -> H(d, U1(c, k))
28.57/10.12	   A^2 -> H(d, U1(e, e))
28.57/10.12	   A^2 -> H(d, U1(k, k))
28.57/10.12	   A^2 -> H(d, U1(k, d))
28.57/10.12	   A^2 -> H(d, U1(d, k))
28.57/10.12	   A^2 -> H(a, b)
28.57/10.12	   A^2 -> H(a, U1(e, d))
28.57/10.12	   A^2 -> H(a, U1(d, e))
28.57/10.12	   A^2 -> H(a, c)
28.57/10.12	   A^2 -> H(a, U1(e, k))
28.57/10.12	   A^2 -> H(a, U1(k, e))
28.57/10.12	   A^2 -> H(a, e)
28.57/10.12	   A^2 -> H(a, U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, d), b)
28.57/10.12	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, d), c)
28.57/10.12	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, d), e)
28.57/10.12	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, a), d)
28.57/10.12	   A^2 -> H(U1(e, a), k)
28.57/10.12	   A^2 -> H(U1(k, a), d)
28.57/10.12	
28.57/10.12	The TRS R consists of the following rules:
28.57/10.12	
28.57/10.12	   f(x) -> U1(x, x)
28.57/10.12	   U1(e, x) -> x
28.57/10.12	   a -> c
28.57/10.12	   a -> d
28.57/10.12	   b -> c
28.57/10.12	   b -> d
28.57/10.12	   d -> k
28.57/10.12	   c -> e
28.57/10.12	   c -> k
28.57/10.12	
28.57/10.12	Q is empty.
28.57/10.12	We have to consider all minimal (P,Q,R)-chains.
28.57/10.12	----------------------------------------
28.57/10.12	
28.57/10.12	(1899) TransformationProof (EQUIVALENT)
28.57/10.12	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.12	
28.57/10.12	   (A^2 -> H(U1(k, c), U1(k, k)),A^2 -> H(U1(k, c), U1(k, k)))
28.57/10.12	   (A^2 -> H(U1(k, d), U1(k, k)),A^2 -> H(U1(k, d), U1(k, k)))
28.57/10.12	
28.57/10.12	
28.57/10.12	----------------------------------------
28.57/10.12	
28.57/10.12	(1900)
28.57/10.12	Obligation:
28.57/10.12	Q DP problem:
28.57/10.12	The TRS P consists of the following rules:
28.57/10.12	
28.57/10.12	   A^2 -> H(f(c), f(c))
28.57/10.12	   H(x, x) -> G(x, x, f(k))
28.57/10.12	   G(d, x, x) -> A^2
28.57/10.12	   A^2 -> H(f(d), f(d))
28.57/10.12	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.12	   A^2 -> H(f(e), f(e))
28.57/10.12	   A^2 -> H(f(k), f(k))
28.57/10.12	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.12	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.12	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.12	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.12	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(c, d), b)
28.57/10.12	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, d), c)
28.57/10.12	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, d), e)
28.57/10.12	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, a), d)
28.57/10.12	   A^2 -> H(U1(c, a), k)
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.12	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.12	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.12	   A^2 -> H(U1(d, c), b)
28.57/10.12	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(d, c), c)
28.57/10.12	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(d, c), e)
28.57/10.12	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, a), d)
28.57/10.12	   A^2 -> H(U1(d, a), k)
28.57/10.12	   A^2 -> H(U1(a, e), b)
28.57/10.12	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(a, e), c)
28.57/10.12	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(a, e), e)
28.57/10.12	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(a, k), b)
28.57/10.12	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(a, k), c)
28.57/10.12	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(a, k), e)
28.57/10.12	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(a, c), d)
28.57/10.12	   A^2 -> H(U1(a, c), k)
28.57/10.12	   A^2 -> H(U1(a, d), d)
28.57/10.12	   A^2 -> H(U1(a, d), k)
28.57/10.12	   A^2 -> H(k, U1(c, b))
28.57/10.12	   A^2 -> H(k, U1(d, b))
28.57/10.12	   A^2 -> H(k, U1(b, c))
28.57/10.12	   A^2 -> H(k, U1(b, d))
28.57/10.12	   A^2 -> H(k, U1(c, c))
28.57/10.12	   A^2 -> H(k, f(e))
28.57/10.12	   A^2 -> H(k, f(k))
28.57/10.12	   A^2 -> H(k, U1(d, d))
28.57/10.12	   A^2 -> H(c, U1(e, b))
28.57/10.12	   A^2 -> H(c, U1(k, b))
28.57/10.12	   A^2 -> H(c, U1(c, d))
28.57/10.12	   A^2 -> H(c, U1(d, c))
28.57/10.12	   A^2 -> H(c, U1(b, e))
28.57/10.12	   A^2 -> H(c, U1(b, k))
28.57/10.12	   A^2 -> H(c, U1(e, c))
28.57/10.12	   A^2 -> H(c, U1(k, c))
28.57/10.12	   A^2 -> H(c, U1(c, e))
28.57/10.12	   A^2 -> H(c, U1(c, k))
28.57/10.12	   A^2 -> H(c, U1(e, e))
28.57/10.12	   A^2 -> H(c, U1(k, k))
28.57/10.12	   A^2 -> H(c, U1(k, d))
28.57/10.12	   A^2 -> H(c, U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.12	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.12	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, c), b)
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, c), e)
28.57/10.12	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.12	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.12	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, c), b)
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, c), c)
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, e), b)
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, e), c)
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, e), e)
28.57/10.12	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, k), b)
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, k), c)
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, k), e)
28.57/10.12	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, c), d)
28.57/10.12	   A^2 -> H(e, U1(e, b))
28.57/10.12	   A^2 -> H(e, U1(c, d))
28.57/10.12	   A^2 -> H(e, U1(d, c))
28.57/10.12	   A^2 -> H(e, U1(b, e))
28.57/10.12	   A^2 -> H(e, U1(b, k))
28.57/10.12	   A^2 -> H(e, U1(e, c))
28.57/10.12	   A^2 -> H(e, U1(c, e))
28.57/10.12	   A^2 -> H(e, U1(c, k))
28.57/10.12	   A^2 -> H(e, U1(e, e))
28.57/10.12	   A^2 -> H(e, U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, e), b)
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, e), c)
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.12	   A^2 -> H(f(e), d)
28.57/10.12	   A^2 -> H(f(e), k)
28.57/10.12	   A^2 -> H(U1(k, k), b)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, k), c)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.12	   A^2 -> H(f(k), d)
28.57/10.12	   A^2 -> H(f(k), k)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, d), b)
28.57/10.12	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, d), c)
28.57/10.12	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, k), b)
28.57/10.12	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(d, k), c)
28.57/10.12	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(d, k), e)
28.57/10.12	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, d), d)
28.57/10.12	   A^2 -> H(U1(d, d), k)
28.57/10.12	   A^2 -> H(U1(e, c), c)
28.57/10.12	   A^2 -> H(U1(c, c), e)
28.57/10.12	   A^2 -> H(U1(c, c), k)
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(e, e), e)
28.57/10.12	   A^2 -> H(d, U1(e, b))
28.57/10.12	   A^2 -> H(d, U1(k, b))
28.57/10.12	   A^2 -> H(d, U1(c, d))
28.57/10.12	   A^2 -> H(d, U1(d, c))
28.57/10.12	   A^2 -> H(d, U1(b, e))
28.57/10.12	   A^2 -> H(d, U1(b, k))
28.57/10.12	   A^2 -> H(d, U1(e, c))
28.57/10.12	   A^2 -> H(d, U1(k, c))
28.57/10.12	   A^2 -> H(d, U1(c, e))
28.57/10.12	   A^2 -> H(d, U1(c, k))
28.57/10.12	   A^2 -> H(d, U1(e, e))
28.57/10.12	   A^2 -> H(d, U1(k, k))
28.57/10.12	   A^2 -> H(d, U1(k, d))
28.57/10.12	   A^2 -> H(d, U1(d, k))
28.57/10.12	   A^2 -> H(a, b)
28.57/10.12	   A^2 -> H(a, U1(e, d))
28.57/10.12	   A^2 -> H(a, U1(d, e))
28.57/10.12	   A^2 -> H(a, c)
28.57/10.12	   A^2 -> H(a, U1(e, k))
28.57/10.12	   A^2 -> H(a, U1(k, e))
28.57/10.12	   A^2 -> H(a, e)
28.57/10.12	   A^2 -> H(a, U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, d), b)
28.57/10.12	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, d), c)
28.57/10.12	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, d), e)
28.57/10.12	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, a), d)
28.57/10.12	   A^2 -> H(U1(e, a), k)
28.57/10.12	   A^2 -> H(U1(k, a), d)
28.57/10.12	
28.57/10.12	The TRS R consists of the following rules:
28.57/10.12	
28.57/10.12	   f(x) -> U1(x, x)
28.57/10.12	   U1(e, x) -> x
28.57/10.12	   a -> c
28.57/10.12	   a -> d
28.57/10.12	   b -> c
28.57/10.12	   b -> d
28.57/10.12	   d -> k
28.57/10.12	   c -> e
28.57/10.12	   c -> k
28.57/10.12	
28.57/10.12	Q is empty.
28.57/10.12	We have to consider all minimal (P,Q,R)-chains.
28.57/10.12	----------------------------------------
28.57/10.12	
28.57/10.12	(1901) TransformationProof (EQUIVALENT)
28.57/10.12	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), b) at position [] we obtained the following new rules [LPAR04]:
28.57/10.12	
28.57/10.12	   (A^2 -> H(U1(e, d), b),A^2 -> H(U1(e, d), b))
28.57/10.12	   (A^2 -> H(U1(k, d), b),A^2 -> H(U1(k, d), b))
28.57/10.12	   (A^2 -> H(U1(c, k), b),A^2 -> H(U1(c, k), b))
28.57/10.12	   (A^2 -> H(U1(c, d), c),A^2 -> H(U1(c, d), c))
28.57/10.12	   (A^2 -> H(U1(c, d), d),A^2 -> H(U1(c, d), d))
28.57/10.12	
28.57/10.12	
28.57/10.12	----------------------------------------
28.57/10.12	
28.57/10.12	(1902)
28.57/10.12	Obligation:
28.57/10.12	Q DP problem:
28.57/10.12	The TRS P consists of the following rules:
28.57/10.12	
28.57/10.12	   A^2 -> H(f(c), f(c))
28.57/10.12	   H(x, x) -> G(x, x, f(k))
28.57/10.12	   G(d, x, x) -> A^2
28.57/10.12	   A^2 -> H(f(d), f(d))
28.57/10.12	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.12	   A^2 -> H(f(e), f(e))
28.57/10.12	   A^2 -> H(f(k), f(k))
28.57/10.12	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.12	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.12	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.12	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.12	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(c, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, d), c)
28.57/10.12	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, d), e)
28.57/10.12	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, a), d)
28.57/10.12	   A^2 -> H(U1(c, a), k)
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.12	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.12	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.12	   A^2 -> H(U1(d, c), b)
28.57/10.12	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(d, c), c)
28.57/10.12	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(d, c), e)
28.57/10.12	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, a), d)
28.57/10.12	   A^2 -> H(U1(d, a), k)
28.57/10.12	   A^2 -> H(U1(a, e), b)
28.57/10.12	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(a, e), c)
28.57/10.12	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(a, e), e)
28.57/10.12	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(a, k), b)
28.57/10.12	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(a, k), c)
28.57/10.12	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(a, k), e)
28.57/10.12	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(a, c), d)
28.57/10.12	   A^2 -> H(U1(a, c), k)
28.57/10.12	   A^2 -> H(U1(a, d), d)
28.57/10.12	   A^2 -> H(U1(a, d), k)
28.57/10.12	   A^2 -> H(k, U1(c, b))
28.57/10.12	   A^2 -> H(k, U1(d, b))
28.57/10.12	   A^2 -> H(k, U1(b, c))
28.57/10.12	   A^2 -> H(k, U1(b, d))
28.57/10.12	   A^2 -> H(k, U1(c, c))
28.57/10.12	   A^2 -> H(k, f(e))
28.57/10.12	   A^2 -> H(k, f(k))
28.57/10.12	   A^2 -> H(k, U1(d, d))
28.57/10.12	   A^2 -> H(c, U1(e, b))
28.57/10.12	   A^2 -> H(c, U1(k, b))
28.57/10.12	   A^2 -> H(c, U1(c, d))
28.57/10.12	   A^2 -> H(c, U1(d, c))
28.57/10.12	   A^2 -> H(c, U1(b, e))
28.57/10.12	   A^2 -> H(c, U1(b, k))
28.57/10.12	   A^2 -> H(c, U1(e, c))
28.57/10.12	   A^2 -> H(c, U1(k, c))
28.57/10.12	   A^2 -> H(c, U1(c, e))
28.57/10.12	   A^2 -> H(c, U1(c, k))
28.57/10.12	   A^2 -> H(c, U1(e, e))
28.57/10.12	   A^2 -> H(c, U1(k, k))
28.57/10.12	   A^2 -> H(c, U1(k, d))
28.57/10.12	   A^2 -> H(c, U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.12	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.12	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, c), b)
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, c), e)
28.57/10.12	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.12	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.12	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.12	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, c), b)
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, c), c)
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.12	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, e), b)
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, e), c)
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, e), e)
28.57/10.12	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, k), b)
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(c, k), c)
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(c, k), e)
28.57/10.12	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(c, c), d)
28.57/10.12	   A^2 -> H(e, U1(e, b))
28.57/10.12	   A^2 -> H(e, U1(c, d))
28.57/10.12	   A^2 -> H(e, U1(d, c))
28.57/10.12	   A^2 -> H(e, U1(b, e))
28.57/10.12	   A^2 -> H(e, U1(b, k))
28.57/10.12	   A^2 -> H(e, U1(e, c))
28.57/10.12	   A^2 -> H(e, U1(c, e))
28.57/10.12	   A^2 -> H(e, U1(c, k))
28.57/10.12	   A^2 -> H(e, U1(e, e))
28.57/10.12	   A^2 -> H(e, U1(d, k))
28.57/10.12	   A^2 -> H(U1(e, e), b)
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, e), c)
28.57/10.12	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.12	   A^2 -> H(f(e), d)
28.57/10.12	   A^2 -> H(f(e), k)
28.57/10.12	   A^2 -> H(U1(k, k), b)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, k), c)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.12	   A^2 -> H(f(k), d)
28.57/10.12	   A^2 -> H(f(k), k)
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.12	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.12	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.12	   A^2 -> H(U1(k, d), b)
28.57/10.12	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(k, d), c)
28.57/10.12	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, k), b)
28.57/10.12	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.12	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.12	   A^2 -> H(U1(d, k), c)
28.57/10.12	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.12	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.12	   A^2 -> H(U1(d, k), e)
28.57/10.12	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.12	   A^2 -> H(U1(d, d), d)
28.57/10.12	   A^2 -> H(U1(d, d), k)
28.57/10.12	   A^2 -> H(U1(e, c), c)
28.57/10.12	   A^2 -> H(U1(c, c), e)
28.57/10.12	   A^2 -> H(U1(c, c), k)
28.57/10.12	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.12	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.12	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.12	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.12	   A^2 -> H(U1(e, e), e)
28.57/10.12	   A^2 -> H(d, U1(e, b))
28.57/10.12	   A^2 -> H(d, U1(k, b))
28.57/10.12	   A^2 -> H(d, U1(c, d))
28.57/10.12	   A^2 -> H(d, U1(d, c))
28.57/10.12	   A^2 -> H(d, U1(b, e))
28.57/10.12	   A^2 -> H(d, U1(b, k))
28.57/10.12	   A^2 -> H(d, U1(e, c))
28.57/10.12	   A^2 -> H(d, U1(k, c))
28.57/10.12	   A^2 -> H(d, U1(c, e))
28.57/10.12	   A^2 -> H(d, U1(c, k))
28.57/10.12	   A^2 -> H(d, U1(e, e))
28.57/10.12	   A^2 -> H(d, U1(k, k))
28.57/10.12	   A^2 -> H(d, U1(k, d))
28.57/10.12	   A^2 -> H(d, U1(d, k))
28.57/10.12	   A^2 -> H(a, b)
28.57/10.12	   A^2 -> H(a, U1(e, d))
28.57/10.12	   A^2 -> H(a, U1(d, e))
28.57/10.12	   A^2 -> H(a, c)
28.57/10.12	   A^2 -> H(a, U1(e, k))
28.57/10.12	   A^2 -> H(a, U1(k, e))
28.57/10.12	   A^2 -> H(a, e)
28.57/10.12	   A^2 -> H(a, U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, d), b)
28.57/10.12	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.12	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.12	   A^2 -> H(U1(e, d), c)
28.57/10.12	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.12	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.12	   A^2 -> H(U1(e, d), e)
28.57/10.12	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.12	   A^2 -> H(U1(e, a), d)
28.57/10.12	   A^2 -> H(U1(e, a), k)
28.57/10.12	   A^2 -> H(U1(k, a), d)
28.57/10.12	   A^2 -> H(U1(c, d), d)
28.57/10.12	
28.57/10.12	The TRS R consists of the following rules:
28.57/10.12	
28.57/10.12	   f(x) -> U1(x, x)
28.57/10.12	   U1(e, x) -> x
28.57/10.12	   a -> c
28.57/10.12	   a -> d
28.57/10.12	   b -> c
28.57/10.12	   b -> d
28.57/10.12	   d -> k
28.57/10.12	   c -> e
28.57/10.12	   c -> k
28.57/10.12	
28.57/10.12	Q is empty.
28.57/10.12	We have to consider all minimal (P,Q,R)-chains.
28.57/10.12	----------------------------------------
28.57/10.12	
28.57/10.12	(1903) TransformationProof (EQUIVALENT)
28.57/10.12	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.12	
28.57/10.12	   (A^2 -> H(U1(e, d), U1(e, d)),A^2 -> H(U1(e, d), U1(e, d)))
28.57/10.12	   (A^2 -> H(U1(k, d), U1(e, d)),A^2 -> H(U1(k, d), U1(e, d)))
28.57/10.12	   (A^2 -> H(U1(c, k), U1(e, d)),A^2 -> H(U1(c, k), U1(e, d)))
28.57/10.12	   (A^2 -> H(U1(c, d), d),A^2 -> H(U1(c, d), d))
28.57/10.12	   (A^2 -> H(U1(c, d), U1(e, k)),A^2 -> H(U1(c, d), U1(e, k)))
28.57/10.12	
28.57/10.12	
28.57/10.12	----------------------------------------
28.57/10.12	
28.57/10.12	(1904)
28.57/10.12	Obligation:
28.57/10.12	Q DP problem:
28.57/10.12	The TRS P consists of the following rules:
28.57/10.12	
28.57/10.12	   A^2 -> H(f(c), f(c))
28.57/10.12	   H(x, x) -> G(x, x, f(k))
28.57/10.12	   G(d, x, x) -> A^2
28.57/10.12	   A^2 -> H(f(d), f(d))
28.57/10.12	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.12	   A^2 -> H(f(e), f(e))
28.57/10.13	   A^2 -> H(f(k), f(k))
28.57/10.13	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.13	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.13	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.13	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.13	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(c, d), U1(d, e))
28.57/10.13	   A^2 -> H(U1(c, d), c)
28.57/10.13	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, d), e)
28.57/10.13	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, a), d)
28.57/10.13	   A^2 -> H(U1(c, a), k)
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.13	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.13	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.13	   A^2 -> H(U1(d, c), b)
28.57/10.13	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(d, c), c)
28.57/10.13	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(d, c), e)
28.57/10.13	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, a), d)
28.57/10.13	   A^2 -> H(U1(d, a), k)
28.57/10.13	   A^2 -> H(U1(a, e), b)
28.57/10.13	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(a, e), c)
28.57/10.13	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(a, e), e)
28.57/10.13	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(a, k), b)
28.57/10.13	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(a, k), c)
28.57/10.13	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(a, k), e)
28.57/10.13	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(a, c), d)
28.57/10.13	   A^2 -> H(U1(a, c), k)
28.57/10.13	   A^2 -> H(U1(a, d), d)
28.57/10.13	   A^2 -> H(U1(a, d), k)
28.57/10.13	   A^2 -> H(k, U1(c, b))
28.57/10.13	   A^2 -> H(k, U1(d, b))
28.57/10.13	   A^2 -> H(k, U1(b, c))
28.57/10.13	   A^2 -> H(k, U1(b, d))
28.57/10.13	   A^2 -> H(k, U1(c, c))
28.57/10.13	   A^2 -> H(k, f(e))
28.57/10.13	   A^2 -> H(k, f(k))
28.57/10.13	   A^2 -> H(k, U1(d, d))
28.57/10.13	   A^2 -> H(c, U1(e, b))
28.57/10.13	   A^2 -> H(c, U1(k, b))
28.57/10.13	   A^2 -> H(c, U1(c, d))
28.57/10.13	   A^2 -> H(c, U1(d, c))
28.57/10.13	   A^2 -> H(c, U1(b, e))
28.57/10.13	   A^2 -> H(c, U1(b, k))
28.57/10.13	   A^2 -> H(c, U1(e, c))
28.57/10.13	   A^2 -> H(c, U1(k, c))
28.57/10.13	   A^2 -> H(c, U1(c, e))
28.57/10.13	   A^2 -> H(c, U1(c, k))
28.57/10.13	   A^2 -> H(c, U1(e, e))
28.57/10.13	   A^2 -> H(c, U1(k, k))
28.57/10.13	   A^2 -> H(c, U1(k, d))
28.57/10.13	   A^2 -> H(c, U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.13	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.13	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, c), b)
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, c), e)
28.57/10.13	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.13	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.13	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.13	   A^2 -> H(U1(k, c), b)
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, c), c)
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, e), b)
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(c, e), c)
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, e), e)
28.57/10.13	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, k), b)
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(c, k), c)
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, k), e)
28.57/10.13	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, c), d)
28.57/10.13	   A^2 -> H(e, U1(e, b))
28.57/10.13	   A^2 -> H(e, U1(c, d))
28.57/10.13	   A^2 -> H(e, U1(d, c))
28.57/10.13	   A^2 -> H(e, U1(b, e))
28.57/10.13	   A^2 -> H(e, U1(b, k))
28.57/10.13	   A^2 -> H(e, U1(e, c))
28.57/10.13	   A^2 -> H(e, U1(c, e))
28.57/10.13	   A^2 -> H(e, U1(c, k))
28.57/10.13	   A^2 -> H(e, U1(e, e))
28.57/10.13	   A^2 -> H(e, U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, e), b)
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, e), c)
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.13	   A^2 -> H(f(e), d)
28.57/10.13	   A^2 -> H(f(e), k)
28.57/10.13	   A^2 -> H(U1(k, k), b)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, k), c)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.13	   A^2 -> H(f(k), d)
28.57/10.13	   A^2 -> H(f(k), k)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(k, d), b)
28.57/10.13	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, d), c)
28.57/10.13	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, k), b)
28.57/10.13	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(d, k), c)
28.57/10.13	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(d, k), e)
28.57/10.13	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, d), d)
28.57/10.13	   A^2 -> H(U1(d, d), k)
28.57/10.13	   A^2 -> H(U1(e, c), c)
28.57/10.13	   A^2 -> H(U1(c, c), e)
28.57/10.13	   A^2 -> H(U1(c, c), k)
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(e, e), e)
28.57/10.13	   A^2 -> H(d, U1(e, b))
28.57/10.13	   A^2 -> H(d, U1(k, b))
28.57/10.13	   A^2 -> H(d, U1(c, d))
28.57/10.13	   A^2 -> H(d, U1(d, c))
28.57/10.13	   A^2 -> H(d, U1(b, e))
28.57/10.13	   A^2 -> H(d, U1(b, k))
28.57/10.13	   A^2 -> H(d, U1(e, c))
28.57/10.13	   A^2 -> H(d, U1(k, c))
28.57/10.13	   A^2 -> H(d, U1(c, e))
28.57/10.13	   A^2 -> H(d, U1(c, k))
28.57/10.13	   A^2 -> H(d, U1(e, e))
28.57/10.13	   A^2 -> H(d, U1(k, k))
28.57/10.13	   A^2 -> H(d, U1(k, d))
28.57/10.13	   A^2 -> H(d, U1(d, k))
28.57/10.13	   A^2 -> H(a, b)
28.57/10.13	   A^2 -> H(a, U1(e, d))
28.57/10.13	   A^2 -> H(a, U1(d, e))
28.57/10.13	   A^2 -> H(a, c)
28.57/10.13	   A^2 -> H(a, U1(e, k))
28.57/10.13	   A^2 -> H(a, U1(k, e))
28.57/10.13	   A^2 -> H(a, e)
28.57/10.13	   A^2 -> H(a, U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, d), b)
28.57/10.13	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, d), c)
28.57/10.13	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, d), e)
28.57/10.13	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, a), d)
28.57/10.13	   A^2 -> H(U1(e, a), k)
28.57/10.13	   A^2 -> H(U1(k, a), d)
28.57/10.13	   A^2 -> H(U1(c, d), d)
28.57/10.13	
28.57/10.13	The TRS R consists of the following rules:
28.57/10.13	
28.57/10.13	   f(x) -> U1(x, x)
28.57/10.13	   U1(e, x) -> x
28.57/10.13	   a -> c
28.57/10.13	   a -> d
28.57/10.13	   b -> c
28.57/10.13	   b -> d
28.57/10.13	   d -> k
28.57/10.13	   c -> e
28.57/10.13	   c -> k
28.57/10.13	
28.57/10.13	Q is empty.
28.57/10.13	We have to consider all minimal (P,Q,R)-chains.
28.57/10.13	----------------------------------------
28.57/10.13	
28.57/10.13	(1905) TransformationProof (EQUIVALENT)
28.57/10.13	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.13	
28.57/10.13	   (A^2 -> H(U1(e, d), U1(d, e)),A^2 -> H(U1(e, d), U1(d, e)))
28.57/10.13	   (A^2 -> H(U1(k, d), U1(d, e)),A^2 -> H(U1(k, d), U1(d, e)))
28.57/10.13	   (A^2 -> H(U1(c, k), U1(d, e)),A^2 -> H(U1(c, k), U1(d, e)))
28.57/10.13	   (A^2 -> H(U1(c, d), U1(k, e)),A^2 -> H(U1(c, d), U1(k, e)))
28.57/10.13	
28.57/10.13	
28.57/10.13	----------------------------------------
28.57/10.13	
28.57/10.13	(1906)
28.57/10.13	Obligation:
28.57/10.13	Q DP problem:
28.57/10.13	The TRS P consists of the following rules:
28.57/10.13	
28.57/10.13	   A^2 -> H(f(c), f(c))
28.57/10.13	   H(x, x) -> G(x, x, f(k))
28.57/10.13	   G(d, x, x) -> A^2
28.57/10.13	   A^2 -> H(f(d), f(d))
28.57/10.13	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.13	   A^2 -> H(f(e), f(e))
28.57/10.13	   A^2 -> H(f(k), f(k))
28.57/10.13	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.13	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.13	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.13	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.13	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(c, d), c)
28.57/10.13	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, d), e)
28.57/10.13	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, a), d)
28.57/10.13	   A^2 -> H(U1(c, a), k)
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.13	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.13	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.13	   A^2 -> H(U1(d, c), b)
28.57/10.13	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(d, c), c)
28.57/10.13	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(d, c), e)
28.57/10.13	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, a), d)
28.57/10.13	   A^2 -> H(U1(d, a), k)
28.57/10.13	   A^2 -> H(U1(a, e), b)
28.57/10.13	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(a, e), c)
28.57/10.13	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(a, e), e)
28.57/10.13	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(a, k), b)
28.57/10.13	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(a, k), c)
28.57/10.13	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(a, k), e)
28.57/10.13	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(a, c), d)
28.57/10.13	   A^2 -> H(U1(a, c), k)
28.57/10.13	   A^2 -> H(U1(a, d), d)
28.57/10.13	   A^2 -> H(U1(a, d), k)
28.57/10.13	   A^2 -> H(k, U1(c, b))
28.57/10.13	   A^2 -> H(k, U1(d, b))
28.57/10.13	   A^2 -> H(k, U1(b, c))
28.57/10.13	   A^2 -> H(k, U1(b, d))
28.57/10.13	   A^2 -> H(k, U1(c, c))
28.57/10.13	   A^2 -> H(k, f(e))
28.57/10.13	   A^2 -> H(k, f(k))
28.57/10.13	   A^2 -> H(k, U1(d, d))
28.57/10.13	   A^2 -> H(c, U1(e, b))
28.57/10.13	   A^2 -> H(c, U1(k, b))
28.57/10.13	   A^2 -> H(c, U1(c, d))
28.57/10.13	   A^2 -> H(c, U1(d, c))
28.57/10.13	   A^2 -> H(c, U1(b, e))
28.57/10.13	   A^2 -> H(c, U1(b, k))
28.57/10.13	   A^2 -> H(c, U1(e, c))
28.57/10.13	   A^2 -> H(c, U1(k, c))
28.57/10.13	   A^2 -> H(c, U1(c, e))
28.57/10.13	   A^2 -> H(c, U1(c, k))
28.57/10.13	   A^2 -> H(c, U1(e, e))
28.57/10.13	   A^2 -> H(c, U1(k, k))
28.57/10.13	   A^2 -> H(c, U1(k, d))
28.57/10.13	   A^2 -> H(c, U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.13	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.13	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, c), b)
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, c), e)
28.57/10.13	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.13	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.13	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.13	   A^2 -> H(U1(k, c), b)
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, c), c)
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, e), b)
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(c, e), c)
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, e), e)
28.57/10.13	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, k), b)
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(c, k), c)
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, k), e)
28.57/10.13	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, c), d)
28.57/10.13	   A^2 -> H(e, U1(e, b))
28.57/10.13	   A^2 -> H(e, U1(c, d))
28.57/10.13	   A^2 -> H(e, U1(d, c))
28.57/10.13	   A^2 -> H(e, U1(b, e))
28.57/10.13	   A^2 -> H(e, U1(b, k))
28.57/10.13	   A^2 -> H(e, U1(e, c))
28.57/10.13	   A^2 -> H(e, U1(c, e))
28.57/10.13	   A^2 -> H(e, U1(c, k))
28.57/10.13	   A^2 -> H(e, U1(e, e))
28.57/10.13	   A^2 -> H(e, U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, e), b)
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, e), c)
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.13	   A^2 -> H(f(e), d)
28.57/10.13	   A^2 -> H(f(e), k)
28.57/10.13	   A^2 -> H(U1(k, k), b)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, k), c)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.13	   A^2 -> H(f(k), d)
28.57/10.13	   A^2 -> H(f(k), k)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(k, d), b)
28.57/10.13	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, d), c)
28.57/10.13	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, k), b)
28.57/10.13	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(d, k), c)
28.57/10.13	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(d, k), e)
28.57/10.13	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, d), d)
28.57/10.13	   A^2 -> H(U1(d, d), k)
28.57/10.13	   A^2 -> H(U1(e, c), c)
28.57/10.13	   A^2 -> H(U1(c, c), e)
28.57/10.13	   A^2 -> H(U1(c, c), k)
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(e, e), e)
28.57/10.13	   A^2 -> H(d, U1(e, b))
28.57/10.13	   A^2 -> H(d, U1(k, b))
28.57/10.13	   A^2 -> H(d, U1(c, d))
28.57/10.13	   A^2 -> H(d, U1(d, c))
28.57/10.13	   A^2 -> H(d, U1(b, e))
28.57/10.13	   A^2 -> H(d, U1(b, k))
28.57/10.13	   A^2 -> H(d, U1(e, c))
28.57/10.13	   A^2 -> H(d, U1(k, c))
28.57/10.13	   A^2 -> H(d, U1(c, e))
28.57/10.13	   A^2 -> H(d, U1(c, k))
28.57/10.13	   A^2 -> H(d, U1(e, e))
28.57/10.13	   A^2 -> H(d, U1(k, k))
28.57/10.13	   A^2 -> H(d, U1(k, d))
28.57/10.13	   A^2 -> H(d, U1(d, k))
28.57/10.13	   A^2 -> H(a, b)
28.57/10.13	   A^2 -> H(a, U1(e, d))
28.57/10.13	   A^2 -> H(a, U1(d, e))
28.57/10.13	   A^2 -> H(a, c)
28.57/10.13	   A^2 -> H(a, U1(e, k))
28.57/10.13	   A^2 -> H(a, U1(k, e))
28.57/10.13	   A^2 -> H(a, e)
28.57/10.13	   A^2 -> H(a, U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, d), b)
28.57/10.13	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, d), c)
28.57/10.13	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, d), e)
28.57/10.13	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, a), d)
28.57/10.13	   A^2 -> H(U1(e, a), k)
28.57/10.13	   A^2 -> H(U1(k, a), d)
28.57/10.13	   A^2 -> H(U1(c, d), d)
28.57/10.13	
28.57/10.13	The TRS R consists of the following rules:
28.57/10.13	
28.57/10.13	   f(x) -> U1(x, x)
28.57/10.13	   U1(e, x) -> x
28.57/10.13	   a -> c
28.57/10.13	   a -> d
28.57/10.13	   b -> c
28.57/10.13	   b -> d
28.57/10.13	   d -> k
28.57/10.13	   c -> e
28.57/10.13	   c -> k
28.57/10.13	
28.57/10.13	Q is empty.
28.57/10.13	We have to consider all minimal (P,Q,R)-chains.
28.57/10.13	----------------------------------------
28.57/10.13	
28.57/10.13	(1907) TransformationProof (EQUIVALENT)
28.57/10.13	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), c) at position [] we obtained the following new rules [LPAR04]:
28.57/10.13	
28.57/10.13	   (A^2 -> H(U1(e, d), c),A^2 -> H(U1(e, d), c))
28.57/10.13	   (A^2 -> H(U1(k, d), c),A^2 -> H(U1(k, d), c))
28.57/10.13	   (A^2 -> H(U1(c, k), c),A^2 -> H(U1(c, k), c))
28.57/10.13	   (A^2 -> H(U1(c, d), e),A^2 -> H(U1(c, d), e))
28.57/10.13	   (A^2 -> H(U1(c, d), k),A^2 -> H(U1(c, d), k))
28.57/10.13	
28.57/10.13	
28.57/10.13	----------------------------------------
28.57/10.13	
28.57/10.13	(1908)
28.57/10.13	Obligation:
28.57/10.13	Q DP problem:
28.57/10.13	The TRS P consists of the following rules:
28.57/10.13	
28.57/10.13	   A^2 -> H(f(c), f(c))
28.57/10.13	   H(x, x) -> G(x, x, f(k))
28.57/10.13	   G(d, x, x) -> A^2
28.57/10.13	   A^2 -> H(f(d), f(d))
28.57/10.13	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.13	   A^2 -> H(f(e), f(e))
28.57/10.13	   A^2 -> H(f(k), f(k))
28.57/10.13	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.13	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.13	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.13	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.13	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(c, d), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, d), e)
28.57/10.13	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, a), d)
28.57/10.13	   A^2 -> H(U1(c, a), k)
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.13	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.13	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.13	   A^2 -> H(U1(d, c), b)
28.57/10.13	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(d, c), c)
28.57/10.13	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(d, c), e)
28.57/10.13	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, a), d)
28.57/10.13	   A^2 -> H(U1(d, a), k)
28.57/10.13	   A^2 -> H(U1(a, e), b)
28.57/10.13	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(a, e), c)
28.57/10.13	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(a, e), e)
28.57/10.13	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(a, k), b)
28.57/10.13	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(a, k), c)
28.57/10.13	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(a, k), e)
28.57/10.13	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(a, c), d)
28.57/10.13	   A^2 -> H(U1(a, c), k)
28.57/10.13	   A^2 -> H(U1(a, d), d)
28.57/10.13	   A^2 -> H(U1(a, d), k)
28.57/10.13	   A^2 -> H(k, U1(c, b))
28.57/10.13	   A^2 -> H(k, U1(d, b))
28.57/10.13	   A^2 -> H(k, U1(b, c))
28.57/10.13	   A^2 -> H(k, U1(b, d))
28.57/10.13	   A^2 -> H(k, U1(c, c))
28.57/10.13	   A^2 -> H(k, f(e))
28.57/10.13	   A^2 -> H(k, f(k))
28.57/10.13	   A^2 -> H(k, U1(d, d))
28.57/10.13	   A^2 -> H(c, U1(e, b))
28.57/10.13	   A^2 -> H(c, U1(k, b))
28.57/10.13	   A^2 -> H(c, U1(c, d))
28.57/10.13	   A^2 -> H(c, U1(d, c))
28.57/10.13	   A^2 -> H(c, U1(b, e))
28.57/10.13	   A^2 -> H(c, U1(b, k))
28.57/10.13	   A^2 -> H(c, U1(e, c))
28.57/10.13	   A^2 -> H(c, U1(k, c))
28.57/10.13	   A^2 -> H(c, U1(c, e))
28.57/10.13	   A^2 -> H(c, U1(c, k))
28.57/10.13	   A^2 -> H(c, U1(e, e))
28.57/10.13	   A^2 -> H(c, U1(k, k))
28.57/10.13	   A^2 -> H(c, U1(k, d))
28.57/10.13	   A^2 -> H(c, U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.13	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.13	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, c), b)
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, c), e)
28.57/10.13	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.13	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.13	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.13	   A^2 -> H(U1(k, c), b)
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, c), c)
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, e), b)
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(c, e), c)
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, e), e)
28.57/10.13	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, k), b)
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(c, k), c)
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, k), e)
28.57/10.13	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, c), d)
28.57/10.13	   A^2 -> H(e, U1(e, b))
28.57/10.13	   A^2 -> H(e, U1(c, d))
28.57/10.13	   A^2 -> H(e, U1(d, c))
28.57/10.13	   A^2 -> H(e, U1(b, e))
28.57/10.13	   A^2 -> H(e, U1(b, k))
28.57/10.13	   A^2 -> H(e, U1(e, c))
28.57/10.13	   A^2 -> H(e, U1(c, e))
28.57/10.13	   A^2 -> H(e, U1(c, k))
28.57/10.13	   A^2 -> H(e, U1(e, e))
28.57/10.13	   A^2 -> H(e, U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, e), b)
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, e), c)
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.13	   A^2 -> H(f(e), d)
28.57/10.13	   A^2 -> H(f(e), k)
28.57/10.13	   A^2 -> H(U1(k, k), b)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, k), c)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.13	   A^2 -> H(f(k), d)
28.57/10.13	   A^2 -> H(f(k), k)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(k, d), b)
28.57/10.13	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, d), c)
28.57/10.13	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, k), b)
28.57/10.13	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(d, k), c)
28.57/10.13	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(d, k), e)
28.57/10.13	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, d), d)
28.57/10.13	   A^2 -> H(U1(d, d), k)
28.57/10.13	   A^2 -> H(U1(e, c), c)
28.57/10.13	   A^2 -> H(U1(c, c), e)
28.57/10.13	   A^2 -> H(U1(c, c), k)
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(e, e), e)
28.57/10.13	   A^2 -> H(d, U1(e, b))
28.57/10.13	   A^2 -> H(d, U1(k, b))
28.57/10.13	   A^2 -> H(d, U1(c, d))
28.57/10.13	   A^2 -> H(d, U1(d, c))
28.57/10.13	   A^2 -> H(d, U1(b, e))
28.57/10.13	   A^2 -> H(d, U1(b, k))
28.57/10.13	   A^2 -> H(d, U1(e, c))
28.57/10.13	   A^2 -> H(d, U1(k, c))
28.57/10.13	   A^2 -> H(d, U1(c, e))
28.57/10.13	   A^2 -> H(d, U1(c, k))
28.57/10.13	   A^2 -> H(d, U1(e, e))
28.57/10.13	   A^2 -> H(d, U1(k, k))
28.57/10.13	   A^2 -> H(d, U1(k, d))
28.57/10.13	   A^2 -> H(d, U1(d, k))
28.57/10.13	   A^2 -> H(a, b)
28.57/10.13	   A^2 -> H(a, U1(e, d))
28.57/10.13	   A^2 -> H(a, U1(d, e))
28.57/10.13	   A^2 -> H(a, c)
28.57/10.13	   A^2 -> H(a, U1(e, k))
28.57/10.13	   A^2 -> H(a, U1(k, e))
28.57/10.13	   A^2 -> H(a, e)
28.57/10.13	   A^2 -> H(a, U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, d), b)
28.57/10.13	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, d), c)
28.57/10.13	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, d), e)
28.57/10.13	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, a), d)
28.57/10.13	   A^2 -> H(U1(e, a), k)
28.57/10.13	   A^2 -> H(U1(k, a), d)
28.57/10.13	   A^2 -> H(U1(c, d), d)
28.57/10.13	   A^2 -> H(U1(c, d), k)
28.57/10.13	
28.57/10.13	The TRS R consists of the following rules:
28.57/10.13	
28.57/10.13	   f(x) -> U1(x, x)
28.57/10.13	   U1(e, x) -> x
28.57/10.13	   a -> c
28.57/10.13	   a -> d
28.57/10.13	   b -> c
28.57/10.13	   b -> d
28.57/10.13	   d -> k
28.57/10.13	   c -> e
28.57/10.13	   c -> k
28.57/10.13	
28.57/10.13	Q is empty.
28.57/10.13	We have to consider all minimal (P,Q,R)-chains.
28.57/10.13	----------------------------------------
28.57/10.13	
28.57/10.13	(1909) TransformationProof (EQUIVALENT)
28.57/10.13	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.13	
28.57/10.13	   (A^2 -> H(U1(e, d), U1(e, k)),A^2 -> H(U1(e, d), U1(e, k)))
28.57/10.13	   (A^2 -> H(U1(k, d), U1(e, k)),A^2 -> H(U1(k, d), U1(e, k)))
28.57/10.13	   (A^2 -> H(U1(c, k), U1(e, k)),A^2 -> H(U1(c, k), U1(e, k)))
28.57/10.13	   (A^2 -> H(U1(c, d), k),A^2 -> H(U1(c, d), k))
28.57/10.13	
28.57/10.13	
28.57/10.13	----------------------------------------
28.57/10.13	
28.57/10.13	(1910)
28.57/10.13	Obligation:
28.57/10.13	Q DP problem:
28.57/10.13	The TRS P consists of the following rules:
28.57/10.13	
28.57/10.13	   A^2 -> H(f(c), f(c))
28.57/10.13	   H(x, x) -> G(x, x, f(k))
28.57/10.13	   G(d, x, x) -> A^2
28.57/10.13	   A^2 -> H(f(d), f(d))
28.57/10.13	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.13	   A^2 -> H(f(e), f(e))
28.57/10.13	   A^2 -> H(f(k), f(k))
28.57/10.13	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.13	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.13	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.13	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.13	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(c, d), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, d), e)
28.57/10.13	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, a), d)
28.57/10.13	   A^2 -> H(U1(c, a), k)
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.13	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.13	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.13	   A^2 -> H(U1(d, c), b)
28.57/10.13	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(d, c), c)
28.57/10.13	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(d, c), e)
28.57/10.13	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, a), d)
28.57/10.13	   A^2 -> H(U1(d, a), k)
28.57/10.13	   A^2 -> H(U1(a, e), b)
28.57/10.13	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(a, e), c)
28.57/10.13	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(a, e), e)
28.57/10.13	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(a, k), b)
28.57/10.13	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(a, k), c)
28.57/10.13	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(a, k), e)
28.57/10.13	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(a, c), d)
28.57/10.13	   A^2 -> H(U1(a, c), k)
28.57/10.13	   A^2 -> H(U1(a, d), d)
28.57/10.13	   A^2 -> H(U1(a, d), k)
28.57/10.13	   A^2 -> H(k, U1(c, b))
28.57/10.13	   A^2 -> H(k, U1(d, b))
28.57/10.13	   A^2 -> H(k, U1(b, c))
28.57/10.13	   A^2 -> H(k, U1(b, d))
28.57/10.13	   A^2 -> H(k, U1(c, c))
28.57/10.13	   A^2 -> H(k, f(e))
28.57/10.13	   A^2 -> H(k, f(k))
28.57/10.13	   A^2 -> H(k, U1(d, d))
28.57/10.13	   A^2 -> H(c, U1(e, b))
28.57/10.13	   A^2 -> H(c, U1(k, b))
28.57/10.13	   A^2 -> H(c, U1(c, d))
28.57/10.13	   A^2 -> H(c, U1(d, c))
28.57/10.13	   A^2 -> H(c, U1(b, e))
28.57/10.13	   A^2 -> H(c, U1(b, k))
28.57/10.13	   A^2 -> H(c, U1(e, c))
28.57/10.13	   A^2 -> H(c, U1(k, c))
28.57/10.13	   A^2 -> H(c, U1(c, e))
28.57/10.13	   A^2 -> H(c, U1(c, k))
28.57/10.13	   A^2 -> H(c, U1(e, e))
28.57/10.13	   A^2 -> H(c, U1(k, k))
28.57/10.13	   A^2 -> H(c, U1(k, d))
28.57/10.13	   A^2 -> H(c, U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.13	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.13	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, c), b)
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, c), e)
28.57/10.13	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.13	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.13	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.13	   A^2 -> H(U1(k, c), b)
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, c), c)
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, e), b)
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(c, e), c)
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, e), e)
28.57/10.13	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, k), b)
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(c, k), c)
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, k), e)
28.57/10.13	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, c), d)
28.57/10.13	   A^2 -> H(e, U1(e, b))
28.57/10.13	   A^2 -> H(e, U1(c, d))
28.57/10.13	   A^2 -> H(e, U1(d, c))
28.57/10.13	   A^2 -> H(e, U1(b, e))
28.57/10.13	   A^2 -> H(e, U1(b, k))
28.57/10.13	   A^2 -> H(e, U1(e, c))
28.57/10.13	   A^2 -> H(e, U1(c, e))
28.57/10.13	   A^2 -> H(e, U1(c, k))
28.57/10.13	   A^2 -> H(e, U1(e, e))
28.57/10.13	   A^2 -> H(e, U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, e), b)
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, e), c)
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.13	   A^2 -> H(f(e), d)
28.57/10.13	   A^2 -> H(f(e), k)
28.57/10.13	   A^2 -> H(U1(k, k), b)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, k), c)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.13	   A^2 -> H(f(k), d)
28.57/10.13	   A^2 -> H(f(k), k)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(k, d), b)
28.57/10.13	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, d), c)
28.57/10.13	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, k), b)
28.57/10.13	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(d, k), c)
28.57/10.13	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(d, k), e)
28.57/10.13	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, d), d)
28.57/10.13	   A^2 -> H(U1(d, d), k)
28.57/10.13	   A^2 -> H(U1(e, c), c)
28.57/10.13	   A^2 -> H(U1(c, c), e)
28.57/10.13	   A^2 -> H(U1(c, c), k)
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(e, e), e)
28.57/10.13	   A^2 -> H(d, U1(e, b))
28.57/10.13	   A^2 -> H(d, U1(k, b))
28.57/10.13	   A^2 -> H(d, U1(c, d))
28.57/10.13	   A^2 -> H(d, U1(d, c))
28.57/10.13	   A^2 -> H(d, U1(b, e))
28.57/10.13	   A^2 -> H(d, U1(b, k))
28.57/10.13	   A^2 -> H(d, U1(e, c))
28.57/10.13	   A^2 -> H(d, U1(k, c))
28.57/10.13	   A^2 -> H(d, U1(c, e))
28.57/10.13	   A^2 -> H(d, U1(c, k))
28.57/10.13	   A^2 -> H(d, U1(e, e))
28.57/10.13	   A^2 -> H(d, U1(k, k))
28.57/10.13	   A^2 -> H(d, U1(k, d))
28.57/10.13	   A^2 -> H(d, U1(d, k))
28.57/10.13	   A^2 -> H(a, b)
28.57/10.13	   A^2 -> H(a, U1(e, d))
28.57/10.13	   A^2 -> H(a, U1(d, e))
28.57/10.13	   A^2 -> H(a, c)
28.57/10.13	   A^2 -> H(a, U1(e, k))
28.57/10.13	   A^2 -> H(a, U1(k, e))
28.57/10.13	   A^2 -> H(a, e)
28.57/10.13	   A^2 -> H(a, U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, d), b)
28.57/10.13	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, d), c)
28.57/10.13	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, d), e)
28.57/10.13	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, a), d)
28.57/10.13	   A^2 -> H(U1(e, a), k)
28.57/10.13	   A^2 -> H(U1(k, a), d)
28.57/10.13	   A^2 -> H(U1(c, d), d)
28.57/10.13	   A^2 -> H(U1(c, d), k)
28.57/10.13	
28.57/10.13	The TRS R consists of the following rules:
28.57/10.13	
28.57/10.13	   f(x) -> U1(x, x)
28.57/10.13	   U1(e, x) -> x
28.57/10.13	   a -> c
28.57/10.13	   a -> d
28.57/10.13	   b -> c
28.57/10.13	   b -> d
28.57/10.13	   d -> k
28.57/10.13	   c -> e
28.57/10.13	   c -> k
28.57/10.13	
28.57/10.13	Q is empty.
28.57/10.13	We have to consider all minimal (P,Q,R)-chains.
28.57/10.13	----------------------------------------
28.57/10.13	
28.57/10.13	(1911) TransformationProof (EQUIVALENT)
28.57/10.13	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.13	
28.57/10.13	   (A^2 -> H(U1(e, d), U1(k, e)),A^2 -> H(U1(e, d), U1(k, e)))
28.57/10.13	   (A^2 -> H(U1(k, d), U1(k, e)),A^2 -> H(U1(k, d), U1(k, e)))
28.57/10.13	   (A^2 -> H(U1(c, k), U1(k, e)),A^2 -> H(U1(c, k), U1(k, e)))
28.57/10.13	
28.57/10.13	
28.57/10.13	----------------------------------------
28.57/10.13	
28.57/10.13	(1912)
28.57/10.13	Obligation:
28.57/10.13	Q DP problem:
28.57/10.13	The TRS P consists of the following rules:
28.57/10.13	
28.57/10.13	   A^2 -> H(f(c), f(c))
28.57/10.13	   H(x, x) -> G(x, x, f(k))
28.57/10.13	   G(d, x, x) -> A^2
28.57/10.13	   A^2 -> H(f(d), f(d))
28.57/10.13	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.13	   A^2 -> H(f(e), f(e))
28.57/10.13	   A^2 -> H(f(k), f(k))
28.57/10.13	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.13	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.13	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.13	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.13	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(c, d), e)
28.57/10.13	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, a), d)
28.57/10.13	   A^2 -> H(U1(c, a), k)
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.13	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.13	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.13	   A^2 -> H(U1(d, c), b)
28.57/10.13	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(d, c), c)
28.57/10.13	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(d, c), e)
28.57/10.13	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, a), d)
28.57/10.13	   A^2 -> H(U1(d, a), k)
28.57/10.13	   A^2 -> H(U1(a, e), b)
28.57/10.13	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(a, e), c)
28.57/10.13	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(a, e), e)
28.57/10.13	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(a, k), b)
28.57/10.13	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(a, k), c)
28.57/10.13	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(a, k), e)
28.57/10.13	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(a, c), d)
28.57/10.13	   A^2 -> H(U1(a, c), k)
28.57/10.13	   A^2 -> H(U1(a, d), d)
28.57/10.13	   A^2 -> H(U1(a, d), k)
28.57/10.13	   A^2 -> H(k, U1(c, b))
28.57/10.13	   A^2 -> H(k, U1(d, b))
28.57/10.13	   A^2 -> H(k, U1(b, c))
28.57/10.13	   A^2 -> H(k, U1(b, d))
28.57/10.13	   A^2 -> H(k, U1(c, c))
28.57/10.13	   A^2 -> H(k, f(e))
28.57/10.13	   A^2 -> H(k, f(k))
28.57/10.13	   A^2 -> H(k, U1(d, d))
28.57/10.13	   A^2 -> H(c, U1(e, b))
28.57/10.13	   A^2 -> H(c, U1(k, b))
28.57/10.13	   A^2 -> H(c, U1(c, d))
28.57/10.13	   A^2 -> H(c, U1(d, c))
28.57/10.13	   A^2 -> H(c, U1(b, e))
28.57/10.13	   A^2 -> H(c, U1(b, k))
28.57/10.13	   A^2 -> H(c, U1(e, c))
28.57/10.13	   A^2 -> H(c, U1(k, c))
28.57/10.13	   A^2 -> H(c, U1(c, e))
28.57/10.13	   A^2 -> H(c, U1(c, k))
28.57/10.13	   A^2 -> H(c, U1(e, e))
28.57/10.13	   A^2 -> H(c, U1(k, k))
28.57/10.13	   A^2 -> H(c, U1(k, d))
28.57/10.13	   A^2 -> H(c, U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.13	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.13	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, c), b)
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, c), e)
28.57/10.13	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.13	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.13	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.13	   A^2 -> H(U1(k, c), b)
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, c), c)
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, e), b)
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(c, e), c)
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, e), e)
28.57/10.13	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, k), b)
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(c, k), c)
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, k), e)
28.57/10.13	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, c), d)
28.57/10.13	   A^2 -> H(e, U1(e, b))
28.57/10.13	   A^2 -> H(e, U1(c, d))
28.57/10.13	   A^2 -> H(e, U1(d, c))
28.57/10.13	   A^2 -> H(e, U1(b, e))
28.57/10.13	   A^2 -> H(e, U1(b, k))
28.57/10.13	   A^2 -> H(e, U1(e, c))
28.57/10.13	   A^2 -> H(e, U1(c, e))
28.57/10.13	   A^2 -> H(e, U1(c, k))
28.57/10.13	   A^2 -> H(e, U1(e, e))
28.57/10.13	   A^2 -> H(e, U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, e), b)
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, e), c)
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.13	   A^2 -> H(f(e), d)
28.57/10.13	   A^2 -> H(f(e), k)
28.57/10.13	   A^2 -> H(U1(k, k), b)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, k), c)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.13	   A^2 -> H(f(k), d)
28.57/10.13	   A^2 -> H(f(k), k)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(k, d), b)
28.57/10.13	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, d), c)
28.57/10.13	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, k), b)
28.57/10.13	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(d, k), c)
28.57/10.13	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(d, k), e)
28.57/10.13	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, d), d)
28.57/10.13	   A^2 -> H(U1(d, d), k)
28.57/10.13	   A^2 -> H(U1(e, c), c)
28.57/10.13	   A^2 -> H(U1(c, c), e)
28.57/10.13	   A^2 -> H(U1(c, c), k)
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(e, e), e)
28.57/10.13	   A^2 -> H(d, U1(e, b))
28.57/10.13	   A^2 -> H(d, U1(k, b))
28.57/10.13	   A^2 -> H(d, U1(c, d))
28.57/10.13	   A^2 -> H(d, U1(d, c))
28.57/10.13	   A^2 -> H(d, U1(b, e))
28.57/10.13	   A^2 -> H(d, U1(b, k))
28.57/10.13	   A^2 -> H(d, U1(e, c))
28.57/10.13	   A^2 -> H(d, U1(k, c))
28.57/10.13	   A^2 -> H(d, U1(c, e))
28.57/10.13	   A^2 -> H(d, U1(c, k))
28.57/10.13	   A^2 -> H(d, U1(e, e))
28.57/10.13	   A^2 -> H(d, U1(k, k))
28.57/10.13	   A^2 -> H(d, U1(k, d))
28.57/10.13	   A^2 -> H(d, U1(d, k))
28.57/10.13	   A^2 -> H(a, b)
28.57/10.13	   A^2 -> H(a, U1(e, d))
28.57/10.13	   A^2 -> H(a, U1(d, e))
28.57/10.13	   A^2 -> H(a, c)
28.57/10.13	   A^2 -> H(a, U1(e, k))
28.57/10.13	   A^2 -> H(a, U1(k, e))
28.57/10.13	   A^2 -> H(a, e)
28.57/10.13	   A^2 -> H(a, U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, d), b)
28.57/10.13	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, d), c)
28.57/10.13	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, d), e)
28.57/10.13	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, a), d)
28.57/10.13	   A^2 -> H(U1(e, a), k)
28.57/10.13	   A^2 -> H(U1(k, a), d)
28.57/10.13	   A^2 -> H(U1(c, d), d)
28.57/10.13	   A^2 -> H(U1(c, d), k)
28.57/10.13	
28.57/10.13	The TRS R consists of the following rules:
28.57/10.13	
28.57/10.13	   f(x) -> U1(x, x)
28.57/10.13	   U1(e, x) -> x
28.57/10.13	   a -> c
28.57/10.13	   a -> d
28.57/10.13	   b -> c
28.57/10.13	   b -> d
28.57/10.13	   d -> k
28.57/10.13	   c -> e
28.57/10.13	   c -> k
28.57/10.13	
28.57/10.13	Q is empty.
28.57/10.13	We have to consider all minimal (P,Q,R)-chains.
28.57/10.13	----------------------------------------
28.57/10.13	
28.57/10.13	(1913) TransformationProof (EQUIVALENT)
28.57/10.13	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), e) at position [] we obtained the following new rules [LPAR04]:
28.57/10.13	
28.57/10.13	   (A^2 -> H(U1(e, d), e),A^2 -> H(U1(e, d), e))
28.57/10.13	   (A^2 -> H(U1(k, d), e),A^2 -> H(U1(k, d), e))
28.57/10.13	   (A^2 -> H(U1(c, k), e),A^2 -> H(U1(c, k), e))
28.57/10.13	
28.57/10.13	
28.57/10.13	----------------------------------------
28.57/10.13	
28.57/10.13	(1914)
28.57/10.13	Obligation:
28.57/10.13	Q DP problem:
28.57/10.13	The TRS P consists of the following rules:
28.57/10.13	
28.57/10.13	   A^2 -> H(f(c), f(c))
28.57/10.13	   H(x, x) -> G(x, x, f(k))
28.57/10.13	   G(d, x, x) -> A^2
28.57/10.13	   A^2 -> H(f(d), f(d))
28.57/10.13	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.13	   A^2 -> H(f(e), f(e))
28.57/10.13	   A^2 -> H(f(k), f(k))
28.57/10.13	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.13	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.13	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.13	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.13	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, a), d)
28.57/10.13	   A^2 -> H(U1(c, a), k)
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.13	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.13	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.13	   A^2 -> H(U1(d, c), b)
28.57/10.13	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(d, c), c)
28.57/10.13	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(d, c), e)
28.57/10.13	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, a), d)
28.57/10.13	   A^2 -> H(U1(d, a), k)
28.57/10.13	   A^2 -> H(U1(a, e), b)
28.57/10.13	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(a, e), c)
28.57/10.13	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(a, e), e)
28.57/10.13	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(a, k), b)
28.57/10.13	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(a, k), c)
28.57/10.13	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(a, k), e)
28.57/10.13	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(a, c), d)
28.57/10.13	   A^2 -> H(U1(a, c), k)
28.57/10.13	   A^2 -> H(U1(a, d), d)
28.57/10.13	   A^2 -> H(U1(a, d), k)
28.57/10.13	   A^2 -> H(k, U1(c, b))
28.57/10.13	   A^2 -> H(k, U1(d, b))
28.57/10.13	   A^2 -> H(k, U1(b, c))
28.57/10.13	   A^2 -> H(k, U1(b, d))
28.57/10.13	   A^2 -> H(k, U1(c, c))
28.57/10.13	   A^2 -> H(k, f(e))
28.57/10.13	   A^2 -> H(k, f(k))
28.57/10.13	   A^2 -> H(k, U1(d, d))
28.57/10.13	   A^2 -> H(c, U1(e, b))
28.57/10.13	   A^2 -> H(c, U1(k, b))
28.57/10.13	   A^2 -> H(c, U1(c, d))
28.57/10.13	   A^2 -> H(c, U1(d, c))
28.57/10.13	   A^2 -> H(c, U1(b, e))
28.57/10.13	   A^2 -> H(c, U1(b, k))
28.57/10.13	   A^2 -> H(c, U1(e, c))
28.57/10.13	   A^2 -> H(c, U1(k, c))
28.57/10.13	   A^2 -> H(c, U1(c, e))
28.57/10.13	   A^2 -> H(c, U1(c, k))
28.57/10.13	   A^2 -> H(c, U1(e, e))
28.57/10.13	   A^2 -> H(c, U1(k, k))
28.57/10.13	   A^2 -> H(c, U1(k, d))
28.57/10.13	   A^2 -> H(c, U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.13	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.13	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, c), b)
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, c), e)
28.57/10.13	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.13	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.13	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.13	   A^2 -> H(U1(k, c), b)
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, c), c)
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, e), b)
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(c, e), c)
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, e), e)
28.57/10.13	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, k), b)
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(c, k), c)
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, k), e)
28.57/10.13	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, c), d)
28.57/10.13	   A^2 -> H(e, U1(e, b))
28.57/10.13	   A^2 -> H(e, U1(c, d))
28.57/10.13	   A^2 -> H(e, U1(d, c))
28.57/10.13	   A^2 -> H(e, U1(b, e))
28.57/10.13	   A^2 -> H(e, U1(b, k))
28.57/10.13	   A^2 -> H(e, U1(e, c))
28.57/10.13	   A^2 -> H(e, U1(c, e))
28.57/10.13	   A^2 -> H(e, U1(c, k))
28.57/10.13	   A^2 -> H(e, U1(e, e))
28.57/10.13	   A^2 -> H(e, U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, e), b)
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, e), c)
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.13	   A^2 -> H(f(e), d)
28.57/10.13	   A^2 -> H(f(e), k)
28.57/10.13	   A^2 -> H(U1(k, k), b)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, k), c)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.13	   A^2 -> H(f(k), d)
28.57/10.13	   A^2 -> H(f(k), k)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(k, d), b)
28.57/10.13	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, d), c)
28.57/10.13	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, k), b)
28.57/10.13	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(d, k), c)
28.57/10.13	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(d, k), e)
28.57/10.13	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, d), d)
28.57/10.13	   A^2 -> H(U1(d, d), k)
28.57/10.13	   A^2 -> H(U1(e, c), c)
28.57/10.13	   A^2 -> H(U1(c, c), e)
28.57/10.13	   A^2 -> H(U1(c, c), k)
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(e, e), e)
28.57/10.13	   A^2 -> H(d, U1(e, b))
28.57/10.13	   A^2 -> H(d, U1(k, b))
28.57/10.13	   A^2 -> H(d, U1(c, d))
28.57/10.13	   A^2 -> H(d, U1(d, c))
28.57/10.13	   A^2 -> H(d, U1(b, e))
28.57/10.13	   A^2 -> H(d, U1(b, k))
28.57/10.13	   A^2 -> H(d, U1(e, c))
28.57/10.13	   A^2 -> H(d, U1(k, c))
28.57/10.13	   A^2 -> H(d, U1(c, e))
28.57/10.13	   A^2 -> H(d, U1(c, k))
28.57/10.13	   A^2 -> H(d, U1(e, e))
28.57/10.13	   A^2 -> H(d, U1(k, k))
28.57/10.13	   A^2 -> H(d, U1(k, d))
28.57/10.13	   A^2 -> H(d, U1(d, k))
28.57/10.13	   A^2 -> H(a, b)
28.57/10.13	   A^2 -> H(a, U1(e, d))
28.57/10.13	   A^2 -> H(a, U1(d, e))
28.57/10.13	   A^2 -> H(a, c)
28.57/10.13	   A^2 -> H(a, U1(e, k))
28.57/10.13	   A^2 -> H(a, U1(k, e))
28.57/10.13	   A^2 -> H(a, e)
28.57/10.13	   A^2 -> H(a, U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, d), b)
28.57/10.13	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, d), c)
28.57/10.13	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, d), e)
28.57/10.13	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, a), d)
28.57/10.13	   A^2 -> H(U1(e, a), k)
28.57/10.13	   A^2 -> H(U1(k, a), d)
28.57/10.13	   A^2 -> H(U1(c, d), d)
28.57/10.13	   A^2 -> H(U1(c, d), k)
28.57/10.13	   A^2 -> H(U1(k, d), e)
28.57/10.13	
28.57/10.13	The TRS R consists of the following rules:
28.57/10.13	
28.57/10.13	   f(x) -> U1(x, x)
28.57/10.13	   U1(e, x) -> x
28.57/10.13	   a -> c
28.57/10.13	   a -> d
28.57/10.13	   b -> c
28.57/10.13	   b -> d
28.57/10.13	   d -> k
28.57/10.13	   c -> e
28.57/10.13	   c -> k
28.57/10.13	
28.57/10.13	Q is empty.
28.57/10.13	We have to consider all minimal (P,Q,R)-chains.
28.57/10.13	----------------------------------------
28.57/10.13	
28.57/10.13	(1915) DependencyGraphProof (EQUIVALENT)
28.57/10.13	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.13	----------------------------------------
28.57/10.13	
28.57/10.13	(1916)
28.57/10.13	Obligation:
28.57/10.13	Q DP problem:
28.57/10.13	The TRS P consists of the following rules:
28.57/10.13	
28.57/10.13	   H(x, x) -> G(x, x, f(k))
28.57/10.13	   G(d, x, x) -> A^2
28.57/10.13	   A^2 -> H(f(c), f(c))
28.57/10.13	   A^2 -> H(f(d), f(d))
28.57/10.13	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.13	   A^2 -> H(f(e), f(e))
28.57/10.13	   A^2 -> H(f(k), f(k))
28.57/10.13	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.13	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.13	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.13	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.13	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(c, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, a), d)
28.57/10.13	   A^2 -> H(U1(c, a), k)
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.13	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.13	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.13	   A^2 -> H(U1(d, c), b)
28.57/10.13	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(d, c), c)
28.57/10.13	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(d, c), e)
28.57/10.13	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, a), d)
28.57/10.13	   A^2 -> H(U1(d, a), k)
28.57/10.13	   A^2 -> H(U1(a, e), b)
28.57/10.13	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(a, e), c)
28.57/10.13	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(a, e), e)
28.57/10.13	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(a, k), b)
28.57/10.13	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(a, k), c)
28.57/10.13	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(a, k), e)
28.57/10.13	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(a, c), d)
28.57/10.13	   A^2 -> H(U1(a, c), k)
28.57/10.13	   A^2 -> H(U1(a, d), d)
28.57/10.13	   A^2 -> H(U1(a, d), k)
28.57/10.13	   A^2 -> H(k, U1(c, b))
28.57/10.13	   A^2 -> H(k, U1(d, b))
28.57/10.13	   A^2 -> H(k, U1(b, c))
28.57/10.13	   A^2 -> H(k, U1(b, d))
28.57/10.13	   A^2 -> H(k, U1(c, c))
28.57/10.13	   A^2 -> H(k, f(e))
28.57/10.13	   A^2 -> H(k, f(k))
28.57/10.13	   A^2 -> H(k, U1(d, d))
28.57/10.13	   A^2 -> H(c, U1(e, b))
28.57/10.13	   A^2 -> H(c, U1(k, b))
28.57/10.13	   A^2 -> H(c, U1(c, d))
28.57/10.13	   A^2 -> H(c, U1(d, c))
28.57/10.13	   A^2 -> H(c, U1(b, e))
28.57/10.13	   A^2 -> H(c, U1(b, k))
28.57/10.13	   A^2 -> H(c, U1(e, c))
28.57/10.13	   A^2 -> H(c, U1(k, c))
28.57/10.13	   A^2 -> H(c, U1(c, e))
28.57/10.13	   A^2 -> H(c, U1(c, k))
28.57/10.13	   A^2 -> H(c, U1(e, e))
28.57/10.13	   A^2 -> H(c, U1(k, k))
28.57/10.13	   A^2 -> H(c, U1(k, d))
28.57/10.13	   A^2 -> H(c, U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.13	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.13	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, c), b)
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, c), e)
28.57/10.13	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.13	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.13	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.13	   A^2 -> H(U1(k, c), b)
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, c), c)
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, e), b)
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(c, e), c)
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, e), e)
28.57/10.13	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, k), b)
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(c, k), c)
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, k), e)
28.57/10.13	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, c), d)
28.57/10.13	   A^2 -> H(e, U1(e, b))
28.57/10.13	   A^2 -> H(e, U1(c, d))
28.57/10.13	   A^2 -> H(e, U1(d, c))
28.57/10.13	   A^2 -> H(e, U1(b, e))
28.57/10.13	   A^2 -> H(e, U1(b, k))
28.57/10.13	   A^2 -> H(e, U1(e, c))
28.57/10.13	   A^2 -> H(e, U1(c, e))
28.57/10.13	   A^2 -> H(e, U1(c, k))
28.57/10.13	   A^2 -> H(e, U1(e, e))
28.57/10.13	   A^2 -> H(e, U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, e), b)
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, e), c)
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.13	   A^2 -> H(f(e), d)
28.57/10.13	   A^2 -> H(f(e), k)
28.57/10.13	   A^2 -> H(U1(k, k), b)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, k), c)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.13	   A^2 -> H(f(k), d)
28.57/10.13	   A^2 -> H(f(k), k)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(k, d), b)
28.57/10.13	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, d), c)
28.57/10.13	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, k), b)
28.57/10.13	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(d, k), c)
28.57/10.13	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(d, k), e)
28.57/10.13	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, d), d)
28.57/10.13	   A^2 -> H(U1(d, d), k)
28.57/10.13	   A^2 -> H(U1(e, c), c)
28.57/10.13	   A^2 -> H(U1(c, c), e)
28.57/10.13	   A^2 -> H(U1(c, c), k)
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(e, e), e)
28.57/10.13	   A^2 -> H(d, U1(e, b))
28.57/10.13	   A^2 -> H(d, U1(k, b))
28.57/10.13	   A^2 -> H(d, U1(c, d))
28.57/10.13	   A^2 -> H(d, U1(d, c))
28.57/10.13	   A^2 -> H(d, U1(b, e))
28.57/10.13	   A^2 -> H(d, U1(b, k))
28.57/10.13	   A^2 -> H(d, U1(e, c))
28.57/10.13	   A^2 -> H(d, U1(k, c))
28.57/10.13	   A^2 -> H(d, U1(c, e))
28.57/10.13	   A^2 -> H(d, U1(c, k))
28.57/10.13	   A^2 -> H(d, U1(e, e))
28.57/10.13	   A^2 -> H(d, U1(k, k))
28.57/10.13	   A^2 -> H(d, U1(k, d))
28.57/10.13	   A^2 -> H(d, U1(d, k))
28.57/10.13	   A^2 -> H(a, b)
28.57/10.13	   A^2 -> H(a, U1(e, d))
28.57/10.13	   A^2 -> H(a, U1(d, e))
28.57/10.13	   A^2 -> H(a, c)
28.57/10.13	   A^2 -> H(a, U1(e, k))
28.57/10.13	   A^2 -> H(a, U1(k, e))
28.57/10.13	   A^2 -> H(a, e)
28.57/10.13	   A^2 -> H(a, U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, d), b)
28.57/10.13	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, d), c)
28.57/10.13	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, d), e)
28.57/10.13	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, a), d)
28.57/10.13	   A^2 -> H(U1(e, a), k)
28.57/10.13	   A^2 -> H(U1(k, a), d)
28.57/10.13	   A^2 -> H(U1(c, d), d)
28.57/10.13	   A^2 -> H(U1(c, d), k)
28.57/10.13	
28.57/10.13	The TRS R consists of the following rules:
28.57/10.13	
28.57/10.13	   f(x) -> U1(x, x)
28.57/10.13	   U1(e, x) -> x
28.57/10.13	   a -> c
28.57/10.13	   a -> d
28.57/10.13	   b -> c
28.57/10.13	   b -> d
28.57/10.13	   d -> k
28.57/10.13	   c -> e
28.57/10.13	   c -> k
28.57/10.13	
28.57/10.13	Q is empty.
28.57/10.13	We have to consider all minimal (P,Q,R)-chains.
28.57/10.13	----------------------------------------
28.57/10.13	
28.57/10.13	(1917) TransformationProof (EQUIVALENT)
28.57/10.13	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.13	
28.57/10.13	   (A^2 -> H(U1(e, d), U1(k, k)),A^2 -> H(U1(e, d), U1(k, k)))
28.57/10.13	   (A^2 -> H(U1(k, d), U1(k, k)),A^2 -> H(U1(k, d), U1(k, k)))
28.57/10.13	   (A^2 -> H(U1(c, k), U1(k, k)),A^2 -> H(U1(c, k), U1(k, k)))
28.57/10.13	
28.57/10.13	
28.57/10.13	----------------------------------------
28.57/10.13	
28.57/10.13	(1918)
28.57/10.13	Obligation:
28.57/10.13	Q DP problem:
28.57/10.13	The TRS P consists of the following rules:
28.57/10.13	
28.57/10.13	   H(x, x) -> G(x, x, f(k))
28.57/10.13	   G(d, x, x) -> A^2
28.57/10.13	   A^2 -> H(f(c), f(c))
28.57/10.13	   A^2 -> H(f(d), f(d))
28.57/10.13	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.13	   A^2 -> H(f(e), f(e))
28.57/10.13	   A^2 -> H(f(k), f(k))
28.57/10.13	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.13	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.13	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.13	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.13	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(c, a), d)
28.57/10.13	   A^2 -> H(U1(c, a), k)
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.13	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.13	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.13	   A^2 -> H(U1(d, c), b)
28.57/10.13	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(d, c), c)
28.57/10.13	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(d, c), e)
28.57/10.13	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(d, a), d)
28.57/10.13	   A^2 -> H(U1(d, a), k)
28.57/10.13	   A^2 -> H(U1(a, e), b)
28.57/10.13	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(a, e), c)
28.57/10.13	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(a, e), e)
28.57/10.13	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(a, k), b)
28.57/10.13	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(a, k), c)
28.57/10.13	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(a, k), e)
28.57/10.13	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(a, c), d)
28.57/10.13	   A^2 -> H(U1(a, c), k)
28.57/10.13	   A^2 -> H(U1(a, d), d)
28.57/10.13	   A^2 -> H(U1(a, d), k)
28.57/10.13	   A^2 -> H(k, U1(c, b))
28.57/10.13	   A^2 -> H(k, U1(d, b))
28.57/10.13	   A^2 -> H(k, U1(b, c))
28.57/10.13	   A^2 -> H(k, U1(b, d))
28.57/10.13	   A^2 -> H(k, U1(c, c))
28.57/10.13	   A^2 -> H(k, f(e))
28.57/10.13	   A^2 -> H(k, f(k))
28.57/10.13	   A^2 -> H(k, U1(d, d))
28.57/10.13	   A^2 -> H(c, U1(e, b))
28.57/10.13	   A^2 -> H(c, U1(k, b))
28.57/10.13	   A^2 -> H(c, U1(c, d))
28.57/10.13	   A^2 -> H(c, U1(d, c))
28.57/10.13	   A^2 -> H(c, U1(b, e))
28.57/10.13	   A^2 -> H(c, U1(b, k))
28.57/10.13	   A^2 -> H(c, U1(e, c))
28.57/10.13	   A^2 -> H(c, U1(k, c))
28.57/10.13	   A^2 -> H(c, U1(c, e))
28.57/10.13	   A^2 -> H(c, U1(c, k))
28.57/10.13	   A^2 -> H(c, U1(e, e))
28.57/10.13	   A^2 -> H(c, U1(k, k))
28.57/10.13	   A^2 -> H(c, U1(k, d))
28.57/10.13	   A^2 -> H(c, U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.13	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.13	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, c), b)
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, c), e)
28.57/10.13	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.13	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.13	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.13	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.13	   A^2 -> H(U1(k, c), b)
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, c), c)
28.57/10.13	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.13	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, e), b)
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(c, e), c)
28.57/10.13	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, e), e)
28.57/10.13	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, k), b)
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(c, k), c)
28.57/10.13	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.13	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.13	   A^2 -> H(U1(c, k), e)
28.57/10.13	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.13	   A^2 -> H(U1(c, c), d)
28.57/10.13	   A^2 -> H(e, U1(e, b))
28.57/10.13	   A^2 -> H(e, U1(c, d))
28.57/10.13	   A^2 -> H(e, U1(d, c))
28.57/10.13	   A^2 -> H(e, U1(b, e))
28.57/10.13	   A^2 -> H(e, U1(b, k))
28.57/10.13	   A^2 -> H(e, U1(e, c))
28.57/10.13	   A^2 -> H(e, U1(c, e))
28.57/10.13	   A^2 -> H(e, U1(c, k))
28.57/10.13	   A^2 -> H(e, U1(e, e))
28.57/10.13	   A^2 -> H(e, U1(d, k))
28.57/10.13	   A^2 -> H(U1(e, e), b)
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.13	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.13	   A^2 -> H(U1(e, e), c)
28.57/10.13	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.13	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.13	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.13	   A^2 -> H(f(e), d)
28.57/10.13	   A^2 -> H(f(e), k)
28.57/10.13	   A^2 -> H(U1(k, k), b)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, k), c)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.13	   A^2 -> H(f(k), d)
28.57/10.13	   A^2 -> H(f(k), k)
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.13	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.13	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.13	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.13	   A^2 -> H(U1(k, d), b)
28.57/10.13	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.13	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.13	   A^2 -> H(U1(k, d), c)
28.57/10.13	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.13	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, k), b)
28.57/10.14	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(d, k), c)
28.57/10.14	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(d, k), e)
28.57/10.14	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, d), d)
28.57/10.14	   A^2 -> H(U1(d, d), k)
28.57/10.14	   A^2 -> H(U1(e, c), c)
28.57/10.14	   A^2 -> H(U1(c, c), e)
28.57/10.14	   A^2 -> H(U1(c, c), k)
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(e, e), e)
28.57/10.14	   A^2 -> H(d, U1(e, b))
28.57/10.14	   A^2 -> H(d, U1(k, b))
28.57/10.14	   A^2 -> H(d, U1(c, d))
28.57/10.14	   A^2 -> H(d, U1(d, c))
28.57/10.14	   A^2 -> H(d, U1(b, e))
28.57/10.14	   A^2 -> H(d, U1(b, k))
28.57/10.14	   A^2 -> H(d, U1(e, c))
28.57/10.14	   A^2 -> H(d, U1(k, c))
28.57/10.14	   A^2 -> H(d, U1(c, e))
28.57/10.14	   A^2 -> H(d, U1(c, k))
28.57/10.14	   A^2 -> H(d, U1(e, e))
28.57/10.14	   A^2 -> H(d, U1(k, k))
28.57/10.14	   A^2 -> H(d, U1(k, d))
28.57/10.14	   A^2 -> H(d, U1(d, k))
28.57/10.14	   A^2 -> H(a, b)
28.57/10.14	   A^2 -> H(a, U1(e, d))
28.57/10.14	   A^2 -> H(a, U1(d, e))
28.57/10.14	   A^2 -> H(a, c)
28.57/10.14	   A^2 -> H(a, U1(e, k))
28.57/10.14	   A^2 -> H(a, U1(k, e))
28.57/10.14	   A^2 -> H(a, e)
28.57/10.14	   A^2 -> H(a, U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, d), b)
28.57/10.14	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, d), c)
28.57/10.14	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, d), e)
28.57/10.14	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, a), d)
28.57/10.14	   A^2 -> H(U1(e, a), k)
28.57/10.14	   A^2 -> H(U1(k, a), d)
28.57/10.14	   A^2 -> H(U1(c, d), d)
28.57/10.14	   A^2 -> H(U1(c, d), k)
28.57/10.14	
28.57/10.14	The TRS R consists of the following rules:
28.57/10.14	
28.57/10.14	   f(x) -> U1(x, x)
28.57/10.14	   U1(e, x) -> x
28.57/10.14	   a -> c
28.57/10.14	   a -> d
28.57/10.14	   b -> c
28.57/10.14	   b -> d
28.57/10.14	   d -> k
28.57/10.14	   c -> e
28.57/10.14	   c -> k
28.57/10.14	
28.57/10.14	Q is empty.
28.57/10.14	We have to consider all minimal (P,Q,R)-chains.
28.57/10.14	----------------------------------------
28.57/10.14	
28.57/10.14	(1919) TransformationProof (EQUIVALENT)
28.57/10.14	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), d) at position [] we obtained the following new rules [LPAR04]:
28.57/10.14	
28.57/10.14	   (A^2 -> H(U1(e, a), d),A^2 -> H(U1(e, a), d))
28.57/10.14	   (A^2 -> H(U1(k, a), d),A^2 -> H(U1(k, a), d))
28.57/10.14	   (A^2 -> H(U1(c, c), d),A^2 -> H(U1(c, c), d))
28.57/10.14	   (A^2 -> H(U1(c, d), d),A^2 -> H(U1(c, d), d))
28.57/10.14	   (A^2 -> H(U1(c, a), k),A^2 -> H(U1(c, a), k))
28.57/10.14	
28.57/10.14	
28.57/10.14	----------------------------------------
28.57/10.14	
28.57/10.14	(1920)
28.57/10.14	Obligation:
28.57/10.14	Q DP problem:
28.57/10.14	The TRS P consists of the following rules:
28.57/10.14	
28.57/10.14	   H(x, x) -> G(x, x, f(k))
28.57/10.14	   G(d, x, x) -> A^2
28.57/10.14	   A^2 -> H(f(c), f(c))
28.57/10.14	   A^2 -> H(f(d), f(d))
28.57/10.14	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.14	   A^2 -> H(f(e), f(e))
28.57/10.14	   A^2 -> H(f(k), f(k))
28.57/10.14	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.14	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.14	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.14	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.14	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(c, a), k)
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.14	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.14	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.14	   A^2 -> H(U1(d, c), b)
28.57/10.14	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(d, c), c)
28.57/10.14	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(d, c), e)
28.57/10.14	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, a), d)
28.57/10.14	   A^2 -> H(U1(d, a), k)
28.57/10.14	   A^2 -> H(U1(a, e), b)
28.57/10.14	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(a, e), c)
28.57/10.14	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(a, e), e)
28.57/10.14	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(a, k), b)
28.57/10.14	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(a, k), c)
28.57/10.14	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(a, k), e)
28.57/10.14	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(a, c), d)
28.57/10.14	   A^2 -> H(U1(a, c), k)
28.57/10.14	   A^2 -> H(U1(a, d), d)
28.57/10.14	   A^2 -> H(U1(a, d), k)
28.57/10.14	   A^2 -> H(k, U1(c, b))
28.57/10.14	   A^2 -> H(k, U1(d, b))
28.57/10.14	   A^2 -> H(k, U1(b, c))
28.57/10.14	   A^2 -> H(k, U1(b, d))
28.57/10.14	   A^2 -> H(k, U1(c, c))
28.57/10.14	   A^2 -> H(k, f(e))
28.57/10.14	   A^2 -> H(k, f(k))
28.57/10.14	   A^2 -> H(k, U1(d, d))
28.57/10.14	   A^2 -> H(c, U1(e, b))
28.57/10.14	   A^2 -> H(c, U1(k, b))
28.57/10.14	   A^2 -> H(c, U1(c, d))
28.57/10.14	   A^2 -> H(c, U1(d, c))
28.57/10.14	   A^2 -> H(c, U1(b, e))
28.57/10.14	   A^2 -> H(c, U1(b, k))
28.57/10.14	   A^2 -> H(c, U1(e, c))
28.57/10.14	   A^2 -> H(c, U1(k, c))
28.57/10.14	   A^2 -> H(c, U1(c, e))
28.57/10.14	   A^2 -> H(c, U1(c, k))
28.57/10.14	   A^2 -> H(c, U1(e, e))
28.57/10.14	   A^2 -> H(c, U1(k, k))
28.57/10.14	   A^2 -> H(c, U1(k, d))
28.57/10.14	   A^2 -> H(c, U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.14	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.14	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, c), b)
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, c), e)
28.57/10.14	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.14	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.14	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.14	   A^2 -> H(U1(k, c), b)
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, c), c)
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, e), b)
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(c, e), c)
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(c, e), e)
28.57/10.14	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, k), b)
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(c, k), c)
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(c, k), e)
28.57/10.14	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, c), d)
28.57/10.14	   A^2 -> H(e, U1(e, b))
28.57/10.14	   A^2 -> H(e, U1(c, d))
28.57/10.14	   A^2 -> H(e, U1(d, c))
28.57/10.14	   A^2 -> H(e, U1(b, e))
28.57/10.14	   A^2 -> H(e, U1(b, k))
28.57/10.14	   A^2 -> H(e, U1(e, c))
28.57/10.14	   A^2 -> H(e, U1(c, e))
28.57/10.14	   A^2 -> H(e, U1(c, k))
28.57/10.14	   A^2 -> H(e, U1(e, e))
28.57/10.14	   A^2 -> H(e, U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, e), b)
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, e), c)
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.14	   A^2 -> H(f(e), d)
28.57/10.14	   A^2 -> H(f(e), k)
28.57/10.14	   A^2 -> H(U1(k, k), b)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, k), c)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.14	   A^2 -> H(f(k), d)
28.57/10.14	   A^2 -> H(f(k), k)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(k, d), b)
28.57/10.14	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, d), c)
28.57/10.14	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, k), b)
28.57/10.14	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(d, k), c)
28.57/10.14	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(d, k), e)
28.57/10.14	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, d), d)
28.57/10.14	   A^2 -> H(U1(d, d), k)
28.57/10.14	   A^2 -> H(U1(e, c), c)
28.57/10.14	   A^2 -> H(U1(c, c), e)
28.57/10.14	   A^2 -> H(U1(c, c), k)
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(e, e), e)
28.57/10.14	   A^2 -> H(d, U1(e, b))
28.57/10.14	   A^2 -> H(d, U1(k, b))
28.57/10.14	   A^2 -> H(d, U1(c, d))
28.57/10.14	   A^2 -> H(d, U1(d, c))
28.57/10.14	   A^2 -> H(d, U1(b, e))
28.57/10.14	   A^2 -> H(d, U1(b, k))
28.57/10.14	   A^2 -> H(d, U1(e, c))
28.57/10.14	   A^2 -> H(d, U1(k, c))
28.57/10.14	   A^2 -> H(d, U1(c, e))
28.57/10.14	   A^2 -> H(d, U1(c, k))
28.57/10.14	   A^2 -> H(d, U1(e, e))
28.57/10.14	   A^2 -> H(d, U1(k, k))
28.57/10.14	   A^2 -> H(d, U1(k, d))
28.57/10.14	   A^2 -> H(d, U1(d, k))
28.57/10.14	   A^2 -> H(a, b)
28.57/10.14	   A^2 -> H(a, U1(e, d))
28.57/10.14	   A^2 -> H(a, U1(d, e))
28.57/10.14	   A^2 -> H(a, c)
28.57/10.14	   A^2 -> H(a, U1(e, k))
28.57/10.14	   A^2 -> H(a, U1(k, e))
28.57/10.14	   A^2 -> H(a, e)
28.57/10.14	   A^2 -> H(a, U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, d), b)
28.57/10.14	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, d), c)
28.57/10.14	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, d), e)
28.57/10.14	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, a), d)
28.57/10.14	   A^2 -> H(U1(e, a), k)
28.57/10.14	   A^2 -> H(U1(k, a), d)
28.57/10.14	   A^2 -> H(U1(c, d), d)
28.57/10.14	   A^2 -> H(U1(c, d), k)
28.57/10.14	
28.57/10.14	The TRS R consists of the following rules:
28.57/10.14	
28.57/10.14	   f(x) -> U1(x, x)
28.57/10.14	   U1(e, x) -> x
28.57/10.14	   a -> c
28.57/10.14	   a -> d
28.57/10.14	   b -> c
28.57/10.14	   b -> d
28.57/10.14	   d -> k
28.57/10.14	   c -> e
28.57/10.14	   c -> k
28.57/10.14	
28.57/10.14	Q is empty.
28.57/10.14	We have to consider all minimal (P,Q,R)-chains.
28.57/10.14	----------------------------------------
28.57/10.14	
28.57/10.14	(1921) TransformationProof (EQUIVALENT)
28.57/10.14	By narrowing [LPAR04] the rule A^2 -> H(U1(c, a), k) at position [] we obtained the following new rules [LPAR04]:
28.57/10.14	
28.57/10.14	   (A^2 -> H(U1(e, a), k),A^2 -> H(U1(e, a), k))
28.57/10.14	   (A^2 -> H(U1(k, a), k),A^2 -> H(U1(k, a), k))
28.57/10.14	   (A^2 -> H(U1(c, c), k),A^2 -> H(U1(c, c), k))
28.57/10.14	   (A^2 -> H(U1(c, d), k),A^2 -> H(U1(c, d), k))
28.57/10.14	
28.57/10.14	
28.57/10.14	----------------------------------------
28.57/10.14	
28.57/10.14	(1922)
28.57/10.14	Obligation:
28.57/10.14	Q DP problem:
28.57/10.14	The TRS P consists of the following rules:
28.57/10.14	
28.57/10.14	   H(x, x) -> G(x, x, f(k))
28.57/10.14	   G(d, x, x) -> A^2
28.57/10.14	   A^2 -> H(f(c), f(c))
28.57/10.14	   A^2 -> H(f(d), f(d))
28.57/10.14	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.14	   A^2 -> H(f(e), f(e))
28.57/10.14	   A^2 -> H(f(k), f(k))
28.57/10.14	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.14	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.14	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.14	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.14	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.14	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.14	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.14	   A^2 -> H(U1(d, c), b)
28.57/10.14	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(d, c), c)
28.57/10.14	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(d, c), e)
28.57/10.14	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, a), d)
28.57/10.14	   A^2 -> H(U1(d, a), k)
28.57/10.14	   A^2 -> H(U1(a, e), b)
28.57/10.14	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(a, e), c)
28.57/10.14	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(a, e), e)
28.57/10.14	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(a, k), b)
28.57/10.14	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(a, k), c)
28.57/10.14	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(a, k), e)
28.57/10.14	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(a, c), d)
28.57/10.14	   A^2 -> H(U1(a, c), k)
28.57/10.14	   A^2 -> H(U1(a, d), d)
28.57/10.14	   A^2 -> H(U1(a, d), k)
28.57/10.14	   A^2 -> H(k, U1(c, b))
28.57/10.14	   A^2 -> H(k, U1(d, b))
28.57/10.14	   A^2 -> H(k, U1(b, c))
28.57/10.14	   A^2 -> H(k, U1(b, d))
28.57/10.14	   A^2 -> H(k, U1(c, c))
28.57/10.14	   A^2 -> H(k, f(e))
28.57/10.14	   A^2 -> H(k, f(k))
28.57/10.14	   A^2 -> H(k, U1(d, d))
28.57/10.14	   A^2 -> H(c, U1(e, b))
28.57/10.14	   A^2 -> H(c, U1(k, b))
28.57/10.14	   A^2 -> H(c, U1(c, d))
28.57/10.14	   A^2 -> H(c, U1(d, c))
28.57/10.14	   A^2 -> H(c, U1(b, e))
28.57/10.14	   A^2 -> H(c, U1(b, k))
28.57/10.14	   A^2 -> H(c, U1(e, c))
28.57/10.14	   A^2 -> H(c, U1(k, c))
28.57/10.14	   A^2 -> H(c, U1(c, e))
28.57/10.14	   A^2 -> H(c, U1(c, k))
28.57/10.14	   A^2 -> H(c, U1(e, e))
28.57/10.14	   A^2 -> H(c, U1(k, k))
28.57/10.14	   A^2 -> H(c, U1(k, d))
28.57/10.14	   A^2 -> H(c, U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.14	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.14	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, c), b)
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, c), e)
28.57/10.14	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.14	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.14	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.14	   A^2 -> H(U1(k, c), b)
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, c), c)
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, e), b)
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(c, e), c)
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(c, e), e)
28.57/10.14	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, k), b)
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(c, k), c)
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(c, k), e)
28.57/10.14	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, c), d)
28.57/10.14	   A^2 -> H(e, U1(e, b))
28.57/10.14	   A^2 -> H(e, U1(c, d))
28.57/10.14	   A^2 -> H(e, U1(d, c))
28.57/10.14	   A^2 -> H(e, U1(b, e))
28.57/10.14	   A^2 -> H(e, U1(b, k))
28.57/10.14	   A^2 -> H(e, U1(e, c))
28.57/10.14	   A^2 -> H(e, U1(c, e))
28.57/10.14	   A^2 -> H(e, U1(c, k))
28.57/10.14	   A^2 -> H(e, U1(e, e))
28.57/10.14	   A^2 -> H(e, U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, e), b)
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, e), c)
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.14	   A^2 -> H(f(e), d)
28.57/10.14	   A^2 -> H(f(e), k)
28.57/10.14	   A^2 -> H(U1(k, k), b)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, k), c)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.14	   A^2 -> H(f(k), d)
28.57/10.14	   A^2 -> H(f(k), k)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(k, d), b)
28.57/10.14	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, d), c)
28.57/10.14	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, k), b)
28.57/10.14	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(d, k), c)
28.57/10.14	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(d, k), e)
28.57/10.14	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, d), d)
28.57/10.14	   A^2 -> H(U1(d, d), k)
28.57/10.14	   A^2 -> H(U1(e, c), c)
28.57/10.14	   A^2 -> H(U1(c, c), e)
28.57/10.14	   A^2 -> H(U1(c, c), k)
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(e, e), e)
28.57/10.14	   A^2 -> H(d, U1(e, b))
28.57/10.14	   A^2 -> H(d, U1(k, b))
28.57/10.14	   A^2 -> H(d, U1(c, d))
28.57/10.14	   A^2 -> H(d, U1(d, c))
28.57/10.14	   A^2 -> H(d, U1(b, e))
28.57/10.14	   A^2 -> H(d, U1(b, k))
28.57/10.14	   A^2 -> H(d, U1(e, c))
28.57/10.14	   A^2 -> H(d, U1(k, c))
28.57/10.14	   A^2 -> H(d, U1(c, e))
28.57/10.14	   A^2 -> H(d, U1(c, k))
28.57/10.14	   A^2 -> H(d, U1(e, e))
28.57/10.14	   A^2 -> H(d, U1(k, k))
28.57/10.14	   A^2 -> H(d, U1(k, d))
28.57/10.14	   A^2 -> H(d, U1(d, k))
28.57/10.14	   A^2 -> H(a, b)
28.57/10.14	   A^2 -> H(a, U1(e, d))
28.57/10.14	   A^2 -> H(a, U1(d, e))
28.57/10.14	   A^2 -> H(a, c)
28.57/10.14	   A^2 -> H(a, U1(e, k))
28.57/10.14	   A^2 -> H(a, U1(k, e))
28.57/10.14	   A^2 -> H(a, e)
28.57/10.14	   A^2 -> H(a, U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, d), b)
28.57/10.14	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, d), c)
28.57/10.14	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, d), e)
28.57/10.14	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, a), d)
28.57/10.14	   A^2 -> H(U1(e, a), k)
28.57/10.14	   A^2 -> H(U1(k, a), d)
28.57/10.14	   A^2 -> H(U1(c, d), d)
28.57/10.14	   A^2 -> H(U1(c, d), k)
28.57/10.14	   A^2 -> H(U1(k, a), k)
28.57/10.14	
28.57/10.14	The TRS R consists of the following rules:
28.57/10.14	
28.57/10.14	   f(x) -> U1(x, x)
28.57/10.14	   U1(e, x) -> x
28.57/10.14	   a -> c
28.57/10.14	   a -> d
28.57/10.14	   b -> c
28.57/10.14	   b -> d
28.57/10.14	   d -> k
28.57/10.14	   c -> e
28.57/10.14	   c -> k
28.57/10.14	
28.57/10.14	Q is empty.
28.57/10.14	We have to consider all minimal (P,Q,R)-chains.
28.57/10.14	----------------------------------------
28.57/10.14	
28.57/10.14	(1923) DependencyGraphProof (EQUIVALENT)
28.57/10.14	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.14	----------------------------------------
28.57/10.14	
28.57/10.14	(1924)
28.57/10.14	Obligation:
28.57/10.14	Q DP problem:
28.57/10.14	The TRS P consists of the following rules:
28.57/10.14	
28.57/10.14	   G(d, x, x) -> A^2
28.57/10.14	   A^2 -> H(f(c), f(c))
28.57/10.14	   H(x, x) -> G(x, x, f(k))
28.57/10.14	   A^2 -> H(f(d), f(d))
28.57/10.14	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.14	   A^2 -> H(f(e), f(e))
28.57/10.14	   A^2 -> H(f(k), f(k))
28.57/10.14	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.14	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.14	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.14	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.14	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, b))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.14	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.14	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.14	   A^2 -> H(U1(d, c), b)
28.57/10.14	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(d, c), c)
28.57/10.14	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(d, c), e)
28.57/10.14	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, a), d)
28.57/10.14	   A^2 -> H(U1(d, a), k)
28.57/10.14	   A^2 -> H(U1(a, e), b)
28.57/10.14	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(a, e), c)
28.57/10.14	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(a, e), e)
28.57/10.14	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(a, k), b)
28.57/10.14	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(a, k), c)
28.57/10.14	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(a, k), e)
28.57/10.14	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(a, c), d)
28.57/10.14	   A^2 -> H(U1(a, c), k)
28.57/10.14	   A^2 -> H(U1(a, d), d)
28.57/10.14	   A^2 -> H(U1(a, d), k)
28.57/10.14	   A^2 -> H(k, U1(c, b))
28.57/10.14	   A^2 -> H(k, U1(d, b))
28.57/10.14	   A^2 -> H(k, U1(b, c))
28.57/10.14	   A^2 -> H(k, U1(b, d))
28.57/10.14	   A^2 -> H(k, U1(c, c))
28.57/10.14	   A^2 -> H(k, f(e))
28.57/10.14	   A^2 -> H(k, f(k))
28.57/10.14	   A^2 -> H(k, U1(d, d))
28.57/10.14	   A^2 -> H(c, U1(e, b))
28.57/10.14	   A^2 -> H(c, U1(k, b))
28.57/10.14	   A^2 -> H(c, U1(c, d))
28.57/10.14	   A^2 -> H(c, U1(d, c))
28.57/10.14	   A^2 -> H(c, U1(b, e))
28.57/10.14	   A^2 -> H(c, U1(b, k))
28.57/10.14	   A^2 -> H(c, U1(e, c))
28.57/10.14	   A^2 -> H(c, U1(k, c))
28.57/10.14	   A^2 -> H(c, U1(c, e))
28.57/10.14	   A^2 -> H(c, U1(c, k))
28.57/10.14	   A^2 -> H(c, U1(e, e))
28.57/10.14	   A^2 -> H(c, U1(k, k))
28.57/10.14	   A^2 -> H(c, U1(k, d))
28.57/10.14	   A^2 -> H(c, U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.14	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.14	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, c), b)
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, c), e)
28.57/10.14	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.14	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.14	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.14	   A^2 -> H(U1(k, c), b)
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, c), c)
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, e), b)
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(c, e), c)
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(c, e), e)
28.57/10.14	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, k), b)
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(c, k), c)
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(c, k), e)
28.57/10.14	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, c), d)
28.57/10.14	   A^2 -> H(e, U1(e, b))
28.57/10.14	   A^2 -> H(e, U1(c, d))
28.57/10.14	   A^2 -> H(e, U1(d, c))
28.57/10.14	   A^2 -> H(e, U1(b, e))
28.57/10.14	   A^2 -> H(e, U1(b, k))
28.57/10.14	   A^2 -> H(e, U1(e, c))
28.57/10.14	   A^2 -> H(e, U1(c, e))
28.57/10.14	   A^2 -> H(e, U1(c, k))
28.57/10.14	   A^2 -> H(e, U1(e, e))
28.57/10.14	   A^2 -> H(e, U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, e), b)
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, e), c)
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.14	   A^2 -> H(f(e), d)
28.57/10.14	   A^2 -> H(f(e), k)
28.57/10.14	   A^2 -> H(U1(k, k), b)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, k), c)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.14	   A^2 -> H(f(k), d)
28.57/10.14	   A^2 -> H(f(k), k)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(k, d), b)
28.57/10.14	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, d), c)
28.57/10.14	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, k), b)
28.57/10.14	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(d, k), c)
28.57/10.14	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(d, k), e)
28.57/10.14	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, d), d)
28.57/10.14	   A^2 -> H(U1(d, d), k)
28.57/10.14	   A^2 -> H(U1(e, c), c)
28.57/10.14	   A^2 -> H(U1(c, c), e)
28.57/10.14	   A^2 -> H(U1(c, c), k)
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(e, e), e)
28.57/10.14	   A^2 -> H(d, U1(e, b))
28.57/10.14	   A^2 -> H(d, U1(k, b))
28.57/10.14	   A^2 -> H(d, U1(c, d))
28.57/10.14	   A^2 -> H(d, U1(d, c))
28.57/10.14	   A^2 -> H(d, U1(b, e))
28.57/10.14	   A^2 -> H(d, U1(b, k))
28.57/10.14	   A^2 -> H(d, U1(e, c))
28.57/10.14	   A^2 -> H(d, U1(k, c))
28.57/10.14	   A^2 -> H(d, U1(c, e))
28.57/10.14	   A^2 -> H(d, U1(c, k))
28.57/10.14	   A^2 -> H(d, U1(e, e))
28.57/10.14	   A^2 -> H(d, U1(k, k))
28.57/10.14	   A^2 -> H(d, U1(k, d))
28.57/10.14	   A^2 -> H(d, U1(d, k))
28.57/10.14	   A^2 -> H(a, b)
28.57/10.14	   A^2 -> H(a, U1(e, d))
28.57/10.14	   A^2 -> H(a, U1(d, e))
28.57/10.14	   A^2 -> H(a, c)
28.57/10.14	   A^2 -> H(a, U1(e, k))
28.57/10.14	   A^2 -> H(a, U1(k, e))
28.57/10.14	   A^2 -> H(a, e)
28.57/10.14	   A^2 -> H(a, U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, d), b)
28.57/10.14	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, d), c)
28.57/10.14	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, d), e)
28.57/10.14	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, a), d)
28.57/10.14	   A^2 -> H(U1(e, a), k)
28.57/10.14	   A^2 -> H(U1(k, a), d)
28.57/10.14	   A^2 -> H(U1(c, d), d)
28.57/10.14	   A^2 -> H(U1(c, d), k)
28.57/10.14	
28.57/10.14	The TRS R consists of the following rules:
28.57/10.14	
28.57/10.14	   f(x) -> U1(x, x)
28.57/10.14	   U1(e, x) -> x
28.57/10.14	   a -> c
28.57/10.14	   a -> d
28.57/10.14	   b -> c
28.57/10.14	   b -> d
28.57/10.14	   d -> k
28.57/10.14	   c -> e
28.57/10.14	   c -> k
28.57/10.14	
28.57/10.14	Q is empty.
28.57/10.14	We have to consider all minimal (P,Q,R)-chains.
28.57/10.14	----------------------------------------
28.57/10.14	
28.57/10.14	(1925) TransformationProof (EQUIVALENT)
28.57/10.14	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.14	
28.57/10.14	   (A^2 -> H(U1(k, e), U1(e, b)),A^2 -> H(U1(k, e), U1(e, b)))
28.57/10.14	   (A^2 -> H(U1(d, e), b),A^2 -> H(U1(d, e), b))
28.57/10.14	   (A^2 -> H(U1(d, e), U1(e, c)),A^2 -> H(U1(d, e), U1(e, c)))
28.57/10.14	   (A^2 -> H(U1(d, e), U1(e, d)),A^2 -> H(U1(d, e), U1(e, d)))
28.57/10.14	
28.57/10.14	
28.57/10.14	----------------------------------------
28.57/10.14	
28.57/10.14	(1926)
28.57/10.14	Obligation:
28.57/10.14	Q DP problem:
28.57/10.14	The TRS P consists of the following rules:
28.57/10.14	
28.57/10.14	   G(d, x, x) -> A^2
28.57/10.14	   A^2 -> H(f(c), f(c))
28.57/10.14	   H(x, x) -> G(x, x, f(k))
28.57/10.14	   A^2 -> H(f(d), f(d))
28.57/10.14	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.14	   A^2 -> H(f(e), f(e))
28.57/10.14	   A^2 -> H(f(k), f(k))
28.57/10.14	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.14	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.14	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.14	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.14	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, b))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.14	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.14	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.14	   A^2 -> H(U1(d, c), b)
28.57/10.14	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(d, c), c)
28.57/10.14	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(d, c), e)
28.57/10.14	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, a), d)
28.57/10.14	   A^2 -> H(U1(d, a), k)
28.57/10.14	   A^2 -> H(U1(a, e), b)
28.57/10.14	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(a, e), c)
28.57/10.14	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(a, e), e)
28.57/10.14	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(a, k), b)
28.57/10.14	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(a, k), c)
28.57/10.14	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(a, k), e)
28.57/10.14	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(a, c), d)
28.57/10.14	   A^2 -> H(U1(a, c), k)
28.57/10.14	   A^2 -> H(U1(a, d), d)
28.57/10.14	   A^2 -> H(U1(a, d), k)
28.57/10.14	   A^2 -> H(k, U1(c, b))
28.57/10.14	   A^2 -> H(k, U1(d, b))
28.57/10.14	   A^2 -> H(k, U1(b, c))
28.57/10.14	   A^2 -> H(k, U1(b, d))
28.57/10.14	   A^2 -> H(k, U1(c, c))
28.57/10.14	   A^2 -> H(k, f(e))
28.57/10.14	   A^2 -> H(k, f(k))
28.57/10.14	   A^2 -> H(k, U1(d, d))
28.57/10.14	   A^2 -> H(c, U1(e, b))
28.57/10.14	   A^2 -> H(c, U1(k, b))
28.57/10.14	   A^2 -> H(c, U1(c, d))
28.57/10.14	   A^2 -> H(c, U1(d, c))
28.57/10.14	   A^2 -> H(c, U1(b, e))
28.57/10.14	   A^2 -> H(c, U1(b, k))
28.57/10.14	   A^2 -> H(c, U1(e, c))
28.57/10.14	   A^2 -> H(c, U1(k, c))
28.57/10.14	   A^2 -> H(c, U1(c, e))
28.57/10.14	   A^2 -> H(c, U1(c, k))
28.57/10.14	   A^2 -> H(c, U1(e, e))
28.57/10.14	   A^2 -> H(c, U1(k, k))
28.57/10.14	   A^2 -> H(c, U1(k, d))
28.57/10.14	   A^2 -> H(c, U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.14	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.14	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, c), b)
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, c), e)
28.57/10.14	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.14	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.14	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.14	   A^2 -> H(U1(k, c), b)
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, c), c)
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, e), b)
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(c, e), c)
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(c, e), e)
28.57/10.14	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, k), b)
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(c, k), c)
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(c, k), e)
28.57/10.14	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, c), d)
28.57/10.14	   A^2 -> H(e, U1(e, b))
28.57/10.14	   A^2 -> H(e, U1(c, d))
28.57/10.14	   A^2 -> H(e, U1(d, c))
28.57/10.14	   A^2 -> H(e, U1(b, e))
28.57/10.14	   A^2 -> H(e, U1(b, k))
28.57/10.14	   A^2 -> H(e, U1(e, c))
28.57/10.14	   A^2 -> H(e, U1(c, e))
28.57/10.14	   A^2 -> H(e, U1(c, k))
28.57/10.14	   A^2 -> H(e, U1(e, e))
28.57/10.14	   A^2 -> H(e, U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, e), b)
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, e), c)
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.14	   A^2 -> H(f(e), d)
28.57/10.14	   A^2 -> H(f(e), k)
28.57/10.14	   A^2 -> H(U1(k, k), b)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, k), c)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.14	   A^2 -> H(f(k), d)
28.57/10.14	   A^2 -> H(f(k), k)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(k, d), b)
28.57/10.14	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, d), c)
28.57/10.14	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, k), b)
28.57/10.14	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(d, k), c)
28.57/10.14	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(d, k), e)
28.57/10.14	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, d), d)
28.57/10.14	   A^2 -> H(U1(d, d), k)
28.57/10.14	   A^2 -> H(U1(e, c), c)
28.57/10.14	   A^2 -> H(U1(c, c), e)
28.57/10.14	   A^2 -> H(U1(c, c), k)
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(e, e), e)
28.57/10.14	   A^2 -> H(d, U1(e, b))
28.57/10.14	   A^2 -> H(d, U1(k, b))
28.57/10.14	   A^2 -> H(d, U1(c, d))
28.57/10.14	   A^2 -> H(d, U1(d, c))
28.57/10.14	   A^2 -> H(d, U1(b, e))
28.57/10.14	   A^2 -> H(d, U1(b, k))
28.57/10.14	   A^2 -> H(d, U1(e, c))
28.57/10.14	   A^2 -> H(d, U1(k, c))
28.57/10.14	   A^2 -> H(d, U1(c, e))
28.57/10.14	   A^2 -> H(d, U1(c, k))
28.57/10.14	   A^2 -> H(d, U1(e, e))
28.57/10.14	   A^2 -> H(d, U1(k, k))
28.57/10.14	   A^2 -> H(d, U1(k, d))
28.57/10.14	   A^2 -> H(d, U1(d, k))
28.57/10.14	   A^2 -> H(a, b)
28.57/10.14	   A^2 -> H(a, U1(e, d))
28.57/10.14	   A^2 -> H(a, U1(d, e))
28.57/10.14	   A^2 -> H(a, c)
28.57/10.14	   A^2 -> H(a, U1(e, k))
28.57/10.14	   A^2 -> H(a, U1(k, e))
28.57/10.14	   A^2 -> H(a, e)
28.57/10.14	   A^2 -> H(a, U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, d), b)
28.57/10.14	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, d), c)
28.57/10.14	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, d), e)
28.57/10.14	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, a), d)
28.57/10.14	   A^2 -> H(U1(e, a), k)
28.57/10.14	   A^2 -> H(U1(k, a), d)
28.57/10.14	   A^2 -> H(U1(c, d), d)
28.57/10.14	   A^2 -> H(U1(c, d), k)
28.57/10.14	   A^2 -> H(U1(d, e), b)
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.14	
28.57/10.14	The TRS R consists of the following rules:
28.57/10.14	
28.57/10.14	   f(x) -> U1(x, x)
28.57/10.14	   U1(e, x) -> x
28.57/10.14	   a -> c
28.57/10.14	   a -> d
28.57/10.14	   b -> c
28.57/10.14	   b -> d
28.57/10.14	   d -> k
28.57/10.14	   c -> e
28.57/10.14	   c -> k
28.57/10.14	
28.57/10.14	Q is empty.
28.57/10.14	We have to consider all minimal (P,Q,R)-chains.
28.57/10.14	----------------------------------------
28.57/10.14	
28.57/10.14	(1927) TransformationProof (EQUIVALENT)
28.57/10.14	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.14	
28.57/10.14	   (A^2 -> H(U1(k, e), U1(k, b)),A^2 -> H(U1(k, e), U1(k, b)))
28.57/10.14	   (A^2 -> H(U1(d, e), U1(k, c)),A^2 -> H(U1(d, e), U1(k, c)))
28.57/10.14	   (A^2 -> H(U1(d, e), U1(k, d)),A^2 -> H(U1(d, e), U1(k, d)))
28.57/10.14	
28.57/10.14	
28.57/10.14	----------------------------------------
28.57/10.14	
28.57/10.14	(1928)
28.57/10.14	Obligation:
28.57/10.14	Q DP problem:
28.57/10.14	The TRS P consists of the following rules:
28.57/10.14	
28.57/10.14	   G(d, x, x) -> A^2
28.57/10.14	   A^2 -> H(f(c), f(c))
28.57/10.14	   H(x, x) -> G(x, x, f(k))
28.57/10.14	   A^2 -> H(f(d), f(d))
28.57/10.14	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.14	   A^2 -> H(f(e), f(e))
28.57/10.14	   A^2 -> H(f(k), f(k))
28.57/10.14	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.14	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.14	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.14	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.14	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, d))
28.57/10.14	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.14	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.14	   A^2 -> H(U1(d, c), b)
28.57/10.14	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(d, c), c)
28.57/10.14	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(d, c), e)
28.57/10.14	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, a), d)
28.57/10.14	   A^2 -> H(U1(d, a), k)
28.57/10.14	   A^2 -> H(U1(a, e), b)
28.57/10.14	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(a, e), c)
28.57/10.14	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(a, e), e)
28.57/10.14	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(a, k), b)
28.57/10.14	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(a, k), c)
28.57/10.14	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(a, k), e)
28.57/10.14	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(a, c), d)
28.57/10.14	   A^2 -> H(U1(a, c), k)
28.57/10.14	   A^2 -> H(U1(a, d), d)
28.57/10.14	   A^2 -> H(U1(a, d), k)
28.57/10.14	   A^2 -> H(k, U1(c, b))
28.57/10.14	   A^2 -> H(k, U1(d, b))
28.57/10.14	   A^2 -> H(k, U1(b, c))
28.57/10.14	   A^2 -> H(k, U1(b, d))
28.57/10.14	   A^2 -> H(k, U1(c, c))
28.57/10.14	   A^2 -> H(k, f(e))
28.57/10.14	   A^2 -> H(k, f(k))
28.57/10.14	   A^2 -> H(k, U1(d, d))
28.57/10.14	   A^2 -> H(c, U1(e, b))
28.57/10.14	   A^2 -> H(c, U1(k, b))
28.57/10.14	   A^2 -> H(c, U1(c, d))
28.57/10.14	   A^2 -> H(c, U1(d, c))
28.57/10.14	   A^2 -> H(c, U1(b, e))
28.57/10.14	   A^2 -> H(c, U1(b, k))
28.57/10.14	   A^2 -> H(c, U1(e, c))
28.57/10.14	   A^2 -> H(c, U1(k, c))
28.57/10.14	   A^2 -> H(c, U1(c, e))
28.57/10.14	   A^2 -> H(c, U1(c, k))
28.57/10.14	   A^2 -> H(c, U1(e, e))
28.57/10.14	   A^2 -> H(c, U1(k, k))
28.57/10.14	   A^2 -> H(c, U1(k, d))
28.57/10.14	   A^2 -> H(c, U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.14	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.14	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, c), b)
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, c), e)
28.57/10.14	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.14	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.14	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.14	   A^2 -> H(U1(k, c), b)
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, c), c)
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, e), b)
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(c, e), c)
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(c, e), e)
28.57/10.14	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, k), b)
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(c, k), c)
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(c, k), e)
28.57/10.14	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, c), d)
28.57/10.14	   A^2 -> H(e, U1(e, b))
28.57/10.14	   A^2 -> H(e, U1(c, d))
28.57/10.14	   A^2 -> H(e, U1(d, c))
28.57/10.14	   A^2 -> H(e, U1(b, e))
28.57/10.14	   A^2 -> H(e, U1(b, k))
28.57/10.14	   A^2 -> H(e, U1(e, c))
28.57/10.14	   A^2 -> H(e, U1(c, e))
28.57/10.14	   A^2 -> H(e, U1(c, k))
28.57/10.14	   A^2 -> H(e, U1(e, e))
28.57/10.14	   A^2 -> H(e, U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, e), b)
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, e), c)
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.14	   A^2 -> H(f(e), d)
28.57/10.14	   A^2 -> H(f(e), k)
28.57/10.14	   A^2 -> H(U1(k, k), b)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, k), c)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.14	   A^2 -> H(f(k), d)
28.57/10.14	   A^2 -> H(f(k), k)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(k, d), b)
28.57/10.14	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, d), c)
28.57/10.14	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, k), b)
28.57/10.14	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(d, k), c)
28.57/10.14	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(d, k), e)
28.57/10.14	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, d), d)
28.57/10.14	   A^2 -> H(U1(d, d), k)
28.57/10.14	   A^2 -> H(U1(e, c), c)
28.57/10.14	   A^2 -> H(U1(c, c), e)
28.57/10.14	   A^2 -> H(U1(c, c), k)
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(e, e), e)
28.57/10.14	   A^2 -> H(d, U1(e, b))
28.57/10.14	   A^2 -> H(d, U1(k, b))
28.57/10.14	   A^2 -> H(d, U1(c, d))
28.57/10.14	   A^2 -> H(d, U1(d, c))
28.57/10.14	   A^2 -> H(d, U1(b, e))
28.57/10.14	   A^2 -> H(d, U1(b, k))
28.57/10.14	   A^2 -> H(d, U1(e, c))
28.57/10.14	   A^2 -> H(d, U1(k, c))
28.57/10.14	   A^2 -> H(d, U1(c, e))
28.57/10.14	   A^2 -> H(d, U1(c, k))
28.57/10.14	   A^2 -> H(d, U1(e, e))
28.57/10.14	   A^2 -> H(d, U1(k, k))
28.57/10.14	   A^2 -> H(d, U1(k, d))
28.57/10.14	   A^2 -> H(d, U1(d, k))
28.57/10.14	   A^2 -> H(a, b)
28.57/10.14	   A^2 -> H(a, U1(e, d))
28.57/10.14	   A^2 -> H(a, U1(d, e))
28.57/10.14	   A^2 -> H(a, c)
28.57/10.14	   A^2 -> H(a, U1(e, k))
28.57/10.14	   A^2 -> H(a, U1(k, e))
28.57/10.14	   A^2 -> H(a, e)
28.57/10.14	   A^2 -> H(a, U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, d), b)
28.57/10.14	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, d), c)
28.57/10.14	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, d), e)
28.57/10.14	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, a), d)
28.57/10.14	   A^2 -> H(U1(e, a), k)
28.57/10.14	   A^2 -> H(U1(k, a), d)
28.57/10.14	   A^2 -> H(U1(c, d), d)
28.57/10.14	   A^2 -> H(U1(c, d), k)
28.57/10.14	   A^2 -> H(U1(d, e), b)
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.14	
28.57/10.14	The TRS R consists of the following rules:
28.57/10.14	
28.57/10.14	   f(x) -> U1(x, x)
28.57/10.14	   U1(e, x) -> x
28.57/10.14	   a -> c
28.57/10.14	   a -> d
28.57/10.14	   b -> c
28.57/10.14	   b -> d
28.57/10.14	   d -> k
28.57/10.14	   c -> e
28.57/10.14	   c -> k
28.57/10.14	
28.57/10.14	Q is empty.
28.57/10.14	We have to consider all minimal (P,Q,R)-chains.
28.57/10.14	----------------------------------------
28.57/10.14	
28.57/10.14	(1929) TransformationProof (EQUIVALENT)
28.57/10.14	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.14	
28.57/10.14	   (A^2 -> H(U1(k, e), U1(c, d)),A^2 -> H(U1(k, e), U1(c, d)))
28.57/10.14	   (A^2 -> H(U1(d, e), U1(e, d)),A^2 -> H(U1(d, e), U1(e, d)))
28.57/10.14	   (A^2 -> H(U1(d, e), U1(k, d)),A^2 -> H(U1(d, e), U1(k, d)))
28.57/10.14	   (A^2 -> H(U1(d, e), U1(c, k)),A^2 -> H(U1(d, e), U1(c, k)))
28.57/10.14	
28.57/10.14	
28.57/10.14	----------------------------------------
28.57/10.14	
28.57/10.14	(1930)
28.57/10.14	Obligation:
28.57/10.14	Q DP problem:
28.57/10.14	The TRS P consists of the following rules:
28.57/10.14	
28.57/10.14	   G(d, x, x) -> A^2
28.57/10.14	   A^2 -> H(f(c), f(c))
28.57/10.14	   H(x, x) -> G(x, x, f(k))
28.57/10.14	   A^2 -> H(f(d), f(d))
28.57/10.14	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.14	   A^2 -> H(f(e), f(e))
28.57/10.14	   A^2 -> H(f(k), f(k))
28.57/10.14	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.14	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.14	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.14	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.14	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(d, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.14	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.14	   A^2 -> H(U1(d, c), b)
28.57/10.14	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(d, c), c)
28.57/10.14	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(d, c), e)
28.57/10.14	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, a), d)
28.57/10.14	   A^2 -> H(U1(d, a), k)
28.57/10.14	   A^2 -> H(U1(a, e), b)
28.57/10.14	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(a, e), c)
28.57/10.14	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(a, e), e)
28.57/10.14	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(a, k), b)
28.57/10.14	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(a, k), c)
28.57/10.14	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(a, k), e)
28.57/10.14	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(a, c), d)
28.57/10.14	   A^2 -> H(U1(a, c), k)
28.57/10.14	   A^2 -> H(U1(a, d), d)
28.57/10.14	   A^2 -> H(U1(a, d), k)
28.57/10.14	   A^2 -> H(k, U1(c, b))
28.57/10.14	   A^2 -> H(k, U1(d, b))
28.57/10.14	   A^2 -> H(k, U1(b, c))
28.57/10.14	   A^2 -> H(k, U1(b, d))
28.57/10.14	   A^2 -> H(k, U1(c, c))
28.57/10.14	   A^2 -> H(k, f(e))
28.57/10.14	   A^2 -> H(k, f(k))
28.57/10.14	   A^2 -> H(k, U1(d, d))
28.57/10.14	   A^2 -> H(c, U1(e, b))
28.57/10.14	   A^2 -> H(c, U1(k, b))
28.57/10.14	   A^2 -> H(c, U1(c, d))
28.57/10.14	   A^2 -> H(c, U1(d, c))
28.57/10.14	   A^2 -> H(c, U1(b, e))
28.57/10.14	   A^2 -> H(c, U1(b, k))
28.57/10.14	   A^2 -> H(c, U1(e, c))
28.57/10.14	   A^2 -> H(c, U1(k, c))
28.57/10.14	   A^2 -> H(c, U1(c, e))
28.57/10.14	   A^2 -> H(c, U1(c, k))
28.57/10.14	   A^2 -> H(c, U1(e, e))
28.57/10.14	   A^2 -> H(c, U1(k, k))
28.57/10.14	   A^2 -> H(c, U1(k, d))
28.57/10.14	   A^2 -> H(c, U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.14	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.14	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, c), b)
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, c), e)
28.57/10.14	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.14	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.14	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.14	   A^2 -> H(U1(k, c), b)
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, c), c)
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, e), b)
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(c, e), c)
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(c, e), e)
28.57/10.14	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, k), b)
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(c, k), c)
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(c, k), e)
28.57/10.14	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, c), d)
28.57/10.14	   A^2 -> H(e, U1(e, b))
28.57/10.14	   A^2 -> H(e, U1(c, d))
28.57/10.14	   A^2 -> H(e, U1(d, c))
28.57/10.14	   A^2 -> H(e, U1(b, e))
28.57/10.14	   A^2 -> H(e, U1(b, k))
28.57/10.14	   A^2 -> H(e, U1(e, c))
28.57/10.14	   A^2 -> H(e, U1(c, e))
28.57/10.14	   A^2 -> H(e, U1(c, k))
28.57/10.14	   A^2 -> H(e, U1(e, e))
28.57/10.14	   A^2 -> H(e, U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, e), b)
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, e), c)
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.14	   A^2 -> H(f(e), d)
28.57/10.14	   A^2 -> H(f(e), k)
28.57/10.14	   A^2 -> H(U1(k, k), b)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, k), c)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.14	   A^2 -> H(f(k), d)
28.57/10.14	   A^2 -> H(f(k), k)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(k, d), b)
28.57/10.14	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, d), c)
28.57/10.14	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, k), b)
28.57/10.14	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(d, k), c)
28.57/10.14	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(d, k), e)
28.57/10.14	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, d), d)
28.57/10.14	   A^2 -> H(U1(d, d), k)
28.57/10.14	   A^2 -> H(U1(e, c), c)
28.57/10.14	   A^2 -> H(U1(c, c), e)
28.57/10.14	   A^2 -> H(U1(c, c), k)
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(e, e), e)
28.57/10.14	   A^2 -> H(d, U1(e, b))
28.57/10.14	   A^2 -> H(d, U1(k, b))
28.57/10.14	   A^2 -> H(d, U1(c, d))
28.57/10.14	   A^2 -> H(d, U1(d, c))
28.57/10.14	   A^2 -> H(d, U1(b, e))
28.57/10.14	   A^2 -> H(d, U1(b, k))
28.57/10.14	   A^2 -> H(d, U1(e, c))
28.57/10.14	   A^2 -> H(d, U1(k, c))
28.57/10.14	   A^2 -> H(d, U1(c, e))
28.57/10.14	   A^2 -> H(d, U1(c, k))
28.57/10.14	   A^2 -> H(d, U1(e, e))
28.57/10.14	   A^2 -> H(d, U1(k, k))
28.57/10.14	   A^2 -> H(d, U1(k, d))
28.57/10.14	   A^2 -> H(d, U1(d, k))
28.57/10.14	   A^2 -> H(a, b)
28.57/10.14	   A^2 -> H(a, U1(e, d))
28.57/10.14	   A^2 -> H(a, U1(d, e))
28.57/10.14	   A^2 -> H(a, c)
28.57/10.14	   A^2 -> H(a, U1(e, k))
28.57/10.14	   A^2 -> H(a, U1(k, e))
28.57/10.14	   A^2 -> H(a, e)
28.57/10.14	   A^2 -> H(a, U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, d), b)
28.57/10.14	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, d), c)
28.57/10.14	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, d), e)
28.57/10.14	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, a), d)
28.57/10.14	   A^2 -> H(U1(e, a), k)
28.57/10.14	   A^2 -> H(U1(k, a), d)
28.57/10.14	   A^2 -> H(U1(c, d), d)
28.57/10.14	   A^2 -> H(U1(c, d), k)
28.57/10.14	   A^2 -> H(U1(d, e), b)
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.14	
28.57/10.14	The TRS R consists of the following rules:
28.57/10.14	
28.57/10.14	   f(x) -> U1(x, x)
28.57/10.14	   U1(e, x) -> x
28.57/10.14	   a -> c
28.57/10.14	   a -> d
28.57/10.14	   b -> c
28.57/10.14	   b -> d
28.57/10.14	   d -> k
28.57/10.14	   c -> e
28.57/10.14	   c -> k
28.57/10.14	
28.57/10.14	Q is empty.
28.57/10.14	We have to consider all minimal (P,Q,R)-chains.
28.57/10.14	----------------------------------------
28.57/10.14	
28.57/10.14	(1931) TransformationProof (EQUIVALENT)
28.57/10.14	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.14	
28.57/10.14	   (A^2 -> H(U1(k, e), U1(d, c)),A^2 -> H(U1(k, e), U1(d, c)))
28.57/10.14	   (A^2 -> H(U1(d, e), U1(k, c)),A^2 -> H(U1(d, e), U1(k, c)))
28.57/10.14	   (A^2 -> H(U1(d, e), U1(d, e)),A^2 -> H(U1(d, e), U1(d, e)))
28.57/10.14	   (A^2 -> H(U1(d, e), U1(d, k)),A^2 -> H(U1(d, e), U1(d, k)))
28.57/10.14	
28.57/10.14	
28.57/10.14	----------------------------------------
28.57/10.14	
28.57/10.14	(1932)
28.57/10.14	Obligation:
28.57/10.14	Q DP problem:
28.57/10.14	The TRS P consists of the following rules:
28.57/10.14	
28.57/10.14	   G(d, x, x) -> A^2
28.57/10.14	   A^2 -> H(f(c), f(c))
28.57/10.14	   H(x, x) -> G(x, x, f(k))
28.57/10.14	   A^2 -> H(f(d), f(d))
28.57/10.14	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.14	   A^2 -> H(f(e), f(e))
28.57/10.14	   A^2 -> H(f(k), f(k))
28.57/10.14	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.14	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.14	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.14	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.14	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(b, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.14	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.14	   A^2 -> H(U1(d, c), b)
28.57/10.14	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(d, c), c)
28.57/10.14	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(d, c), e)
28.57/10.14	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, a), d)
28.57/10.14	   A^2 -> H(U1(d, a), k)
28.57/10.14	   A^2 -> H(U1(a, e), b)
28.57/10.14	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(a, e), c)
28.57/10.14	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(a, e), e)
28.57/10.14	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(a, k), b)
28.57/10.14	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(a, k), c)
28.57/10.14	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(a, k), e)
28.57/10.14	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(a, c), d)
28.57/10.14	   A^2 -> H(U1(a, c), k)
28.57/10.14	   A^2 -> H(U1(a, d), d)
28.57/10.14	   A^2 -> H(U1(a, d), k)
28.57/10.14	   A^2 -> H(k, U1(c, b))
28.57/10.14	   A^2 -> H(k, U1(d, b))
28.57/10.14	   A^2 -> H(k, U1(b, c))
28.57/10.14	   A^2 -> H(k, U1(b, d))
28.57/10.14	   A^2 -> H(k, U1(c, c))
28.57/10.14	   A^2 -> H(k, f(e))
28.57/10.14	   A^2 -> H(k, f(k))
28.57/10.14	   A^2 -> H(k, U1(d, d))
28.57/10.14	   A^2 -> H(c, U1(e, b))
28.57/10.14	   A^2 -> H(c, U1(k, b))
28.57/10.14	   A^2 -> H(c, U1(c, d))
28.57/10.14	   A^2 -> H(c, U1(d, c))
28.57/10.14	   A^2 -> H(c, U1(b, e))
28.57/10.14	   A^2 -> H(c, U1(b, k))
28.57/10.14	   A^2 -> H(c, U1(e, c))
28.57/10.14	   A^2 -> H(c, U1(k, c))
28.57/10.14	   A^2 -> H(c, U1(c, e))
28.57/10.14	   A^2 -> H(c, U1(c, k))
28.57/10.14	   A^2 -> H(c, U1(e, e))
28.57/10.14	   A^2 -> H(c, U1(k, k))
28.57/10.14	   A^2 -> H(c, U1(k, d))
28.57/10.14	   A^2 -> H(c, U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.14	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.14	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, c), b)
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, c), e)
28.57/10.14	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.14	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.14	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.14	   A^2 -> H(U1(k, c), b)
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, c), c)
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, e), b)
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(c, e), c)
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(c, e), e)
28.57/10.14	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, k), b)
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(c, k), c)
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(c, k), e)
28.57/10.14	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(c, c), d)
28.57/10.14	   A^2 -> H(e, U1(e, b))
28.57/10.14	   A^2 -> H(e, U1(c, d))
28.57/10.14	   A^2 -> H(e, U1(d, c))
28.57/10.14	   A^2 -> H(e, U1(b, e))
28.57/10.14	   A^2 -> H(e, U1(b, k))
28.57/10.14	   A^2 -> H(e, U1(e, c))
28.57/10.14	   A^2 -> H(e, U1(c, e))
28.57/10.14	   A^2 -> H(e, U1(c, k))
28.57/10.14	   A^2 -> H(e, U1(e, e))
28.57/10.14	   A^2 -> H(e, U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, e), b)
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, e), c)
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.14	   A^2 -> H(f(e), d)
28.57/10.14	   A^2 -> H(f(e), k)
28.57/10.14	   A^2 -> H(U1(k, k), b)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, k), c)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.14	   A^2 -> H(f(k), d)
28.57/10.14	   A^2 -> H(f(k), k)
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.14	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(k, d), b)
28.57/10.14	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.14	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.14	   A^2 -> H(U1(k, d), c)
28.57/10.14	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, k), b)
28.57/10.14	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(d, k), c)
28.57/10.14	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(d, k), e)
28.57/10.14	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, d), d)
28.57/10.14	   A^2 -> H(U1(d, d), k)
28.57/10.14	   A^2 -> H(U1(e, c), c)
28.57/10.14	   A^2 -> H(U1(c, c), e)
28.57/10.14	   A^2 -> H(U1(c, c), k)
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.14	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(e, e), e)
28.57/10.14	   A^2 -> H(d, U1(e, b))
28.57/10.14	   A^2 -> H(d, U1(k, b))
28.57/10.14	   A^2 -> H(d, U1(c, d))
28.57/10.14	   A^2 -> H(d, U1(d, c))
28.57/10.14	   A^2 -> H(d, U1(b, e))
28.57/10.14	   A^2 -> H(d, U1(b, k))
28.57/10.14	   A^2 -> H(d, U1(e, c))
28.57/10.14	   A^2 -> H(d, U1(k, c))
28.57/10.14	   A^2 -> H(d, U1(c, e))
28.57/10.14	   A^2 -> H(d, U1(c, k))
28.57/10.14	   A^2 -> H(d, U1(e, e))
28.57/10.14	   A^2 -> H(d, U1(k, k))
28.57/10.14	   A^2 -> H(d, U1(k, d))
28.57/10.14	   A^2 -> H(d, U1(d, k))
28.57/10.14	   A^2 -> H(a, b)
28.57/10.14	   A^2 -> H(a, U1(e, d))
28.57/10.14	   A^2 -> H(a, U1(d, e))
28.57/10.14	   A^2 -> H(a, c)
28.57/10.14	   A^2 -> H(a, U1(e, k))
28.57/10.14	   A^2 -> H(a, U1(k, e))
28.57/10.14	   A^2 -> H(a, e)
28.57/10.14	   A^2 -> H(a, U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, d), b)
28.57/10.14	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, d), c)
28.57/10.14	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, d), e)
28.57/10.14	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, a), d)
28.57/10.14	   A^2 -> H(U1(e, a), k)
28.57/10.14	   A^2 -> H(U1(k, a), d)
28.57/10.14	   A^2 -> H(U1(c, d), d)
28.57/10.14	   A^2 -> H(U1(c, d), k)
28.57/10.14	   A^2 -> H(U1(d, e), b)
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.14	
28.57/10.14	The TRS R consists of the following rules:
28.57/10.14	
28.57/10.14	   f(x) -> U1(x, x)
28.57/10.14	   U1(e, x) -> x
28.57/10.14	   a -> c
28.57/10.14	   a -> d
28.57/10.14	   b -> c
28.57/10.14	   b -> d
28.57/10.14	   d -> k
28.57/10.14	   c -> e
28.57/10.14	   c -> k
28.57/10.14	
28.57/10.14	Q is empty.
28.57/10.14	We have to consider all minimal (P,Q,R)-chains.
28.57/10.14	----------------------------------------
28.57/10.14	
28.57/10.14	(1933) TransformationProof (EQUIVALENT)
28.57/10.14	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.14	
28.57/10.14	   (A^2 -> H(U1(k, e), U1(b, e)),A^2 -> H(U1(k, e), U1(b, e)))
28.57/10.14	   (A^2 -> H(U1(d, e), U1(c, e)),A^2 -> H(U1(d, e), U1(c, e)))
28.57/10.14	   (A^2 -> H(U1(d, e), U1(d, e)),A^2 -> H(U1(d, e), U1(d, e)))
28.57/10.14	
28.57/10.14	
28.57/10.14	----------------------------------------
28.57/10.14	
28.57/10.14	(1934)
28.57/10.14	Obligation:
28.57/10.14	Q DP problem:
28.57/10.14	The TRS P consists of the following rules:
28.57/10.14	
28.57/10.14	   G(d, x, x) -> A^2
28.57/10.14	   A^2 -> H(f(c), f(c))
28.57/10.14	   H(x, x) -> G(x, x, f(k))
28.57/10.14	   A^2 -> H(f(d), f(d))
28.57/10.14	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.14	   A^2 -> H(f(e), f(e))
28.57/10.14	   A^2 -> H(f(k), f(k))
28.57/10.14	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.14	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.14	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.14	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.14	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.14	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(b, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.14	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.14	   A^2 -> H(U1(d, c), b)
28.57/10.14	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(d, c), c)
28.57/10.14	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(d, c), e)
28.57/10.14	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(d, a), d)
28.57/10.14	   A^2 -> H(U1(d, a), k)
28.57/10.14	   A^2 -> H(U1(a, e), b)
28.57/10.14	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.14	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.14	   A^2 -> H(U1(a, e), c)
28.57/10.14	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.14	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.14	   A^2 -> H(U1(a, e), e)
28.57/10.14	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.14	   A^2 -> H(U1(a, k), b)
28.57/10.14	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.14	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.14	   A^2 -> H(U1(a, k), c)
28.57/10.14	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.14	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.14	   A^2 -> H(U1(a, k), e)
28.57/10.14	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(a, c), d)
28.57/10.14	   A^2 -> H(U1(a, c), k)
28.57/10.14	   A^2 -> H(U1(a, d), d)
28.57/10.14	   A^2 -> H(U1(a, d), k)
28.57/10.14	   A^2 -> H(k, U1(c, b))
28.57/10.14	   A^2 -> H(k, U1(d, b))
28.57/10.14	   A^2 -> H(k, U1(b, c))
28.57/10.14	   A^2 -> H(k, U1(b, d))
28.57/10.14	   A^2 -> H(k, U1(c, c))
28.57/10.14	   A^2 -> H(k, f(e))
28.57/10.14	   A^2 -> H(k, f(k))
28.57/10.14	   A^2 -> H(k, U1(d, d))
28.57/10.14	   A^2 -> H(c, U1(e, b))
28.57/10.14	   A^2 -> H(c, U1(k, b))
28.57/10.14	   A^2 -> H(c, U1(c, d))
28.57/10.14	   A^2 -> H(c, U1(d, c))
28.57/10.14	   A^2 -> H(c, U1(b, e))
28.57/10.14	   A^2 -> H(c, U1(b, k))
28.57/10.14	   A^2 -> H(c, U1(e, c))
28.57/10.14	   A^2 -> H(c, U1(k, c))
28.57/10.14	   A^2 -> H(c, U1(c, e))
28.57/10.14	   A^2 -> H(c, U1(c, k))
28.57/10.14	   A^2 -> H(c, U1(e, e))
28.57/10.14	   A^2 -> H(c, U1(k, k))
28.57/10.14	   A^2 -> H(c, U1(k, d))
28.57/10.14	   A^2 -> H(c, U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.14	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.14	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.14	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.14	   A^2 -> H(U1(e, c), b)
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.14	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.14	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.14	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.14	   A^2 -> H(U1(e, c), e)
28.57/10.14	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.14	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.14	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.14	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.14	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.14	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.15	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.15	   A^2 -> H(U1(k, c), b)
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, c), c)
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, e), b)
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(c, e), c)
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(c, e), e)
28.57/10.15	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, k), b)
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(c, k), c)
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(c, k), e)
28.57/10.15	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, c), d)
28.57/10.15	   A^2 -> H(e, U1(e, b))
28.57/10.15	   A^2 -> H(e, U1(c, d))
28.57/10.15	   A^2 -> H(e, U1(d, c))
28.57/10.15	   A^2 -> H(e, U1(b, e))
28.57/10.15	   A^2 -> H(e, U1(b, k))
28.57/10.15	   A^2 -> H(e, U1(e, c))
28.57/10.15	   A^2 -> H(e, U1(c, e))
28.57/10.15	   A^2 -> H(e, U1(c, k))
28.57/10.15	   A^2 -> H(e, U1(e, e))
28.57/10.15	   A^2 -> H(e, U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, e), b)
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, e), c)
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.15	   A^2 -> H(f(e), d)
28.57/10.15	   A^2 -> H(f(e), k)
28.57/10.15	   A^2 -> H(U1(k, k), b)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, k), c)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.15	   A^2 -> H(f(k), d)
28.57/10.15	   A^2 -> H(f(k), k)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(k, d), b)
28.57/10.15	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, d), c)
28.57/10.15	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, k), b)
28.57/10.15	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, k), c)
28.57/10.15	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(d, k), e)
28.57/10.15	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, d), d)
28.57/10.15	   A^2 -> H(U1(d, d), k)
28.57/10.15	   A^2 -> H(U1(e, c), c)
28.57/10.15	   A^2 -> H(U1(c, c), e)
28.57/10.15	   A^2 -> H(U1(c, c), k)
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(e, e), e)
28.57/10.15	   A^2 -> H(d, U1(e, b))
28.57/10.15	   A^2 -> H(d, U1(k, b))
28.57/10.15	   A^2 -> H(d, U1(c, d))
28.57/10.15	   A^2 -> H(d, U1(d, c))
28.57/10.15	   A^2 -> H(d, U1(b, e))
28.57/10.15	   A^2 -> H(d, U1(b, k))
28.57/10.15	   A^2 -> H(d, U1(e, c))
28.57/10.15	   A^2 -> H(d, U1(k, c))
28.57/10.15	   A^2 -> H(d, U1(c, e))
28.57/10.15	   A^2 -> H(d, U1(c, k))
28.57/10.15	   A^2 -> H(d, U1(e, e))
28.57/10.15	   A^2 -> H(d, U1(k, k))
28.57/10.15	   A^2 -> H(d, U1(k, d))
28.57/10.15	   A^2 -> H(d, U1(d, k))
28.57/10.15	   A^2 -> H(a, b)
28.57/10.15	   A^2 -> H(a, U1(e, d))
28.57/10.15	   A^2 -> H(a, U1(d, e))
28.57/10.15	   A^2 -> H(a, c)
28.57/10.15	   A^2 -> H(a, U1(e, k))
28.57/10.15	   A^2 -> H(a, U1(k, e))
28.57/10.15	   A^2 -> H(a, e)
28.57/10.15	   A^2 -> H(a, U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, d), b)
28.57/10.15	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, d), c)
28.57/10.15	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, d), e)
28.57/10.15	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, a), d)
28.57/10.15	   A^2 -> H(U1(e, a), k)
28.57/10.15	   A^2 -> H(U1(k, a), d)
28.57/10.15	   A^2 -> H(U1(c, d), d)
28.57/10.15	   A^2 -> H(U1(c, d), k)
28.57/10.15	   A^2 -> H(U1(d, e), b)
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.15	
28.57/10.15	The TRS R consists of the following rules:
28.57/10.15	
28.57/10.15	   f(x) -> U1(x, x)
28.57/10.15	   U1(e, x) -> x
28.57/10.15	   a -> c
28.57/10.15	   a -> d
28.57/10.15	   b -> c
28.57/10.15	   b -> d
28.57/10.15	   d -> k
28.57/10.15	   c -> e
28.57/10.15	   c -> k
28.57/10.15	
28.57/10.15	Q is empty.
28.57/10.15	We have to consider all minimal (P,Q,R)-chains.
28.57/10.15	----------------------------------------
28.57/10.15	
28.57/10.15	(1935) TransformationProof (EQUIVALENT)
28.57/10.15	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.15	
28.57/10.15	   (A^2 -> H(U1(k, e), U1(b, k)),A^2 -> H(U1(k, e), U1(b, k)))
28.57/10.15	   (A^2 -> H(U1(d, e), U1(c, k)),A^2 -> H(U1(d, e), U1(c, k)))
28.57/10.15	   (A^2 -> H(U1(d, e), U1(d, k)),A^2 -> H(U1(d, e), U1(d, k)))
28.57/10.15	
28.57/10.15	
28.57/10.15	----------------------------------------
28.57/10.15	
28.57/10.15	(1936)
28.57/10.15	Obligation:
28.57/10.15	Q DP problem:
28.57/10.15	The TRS P consists of the following rules:
28.57/10.15	
28.57/10.15	   G(d, x, x) -> A^2
28.57/10.15	   A^2 -> H(f(c), f(c))
28.57/10.15	   H(x, x) -> G(x, x, f(k))
28.57/10.15	   A^2 -> H(f(d), f(d))
28.57/10.15	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.15	   A^2 -> H(f(e), f(e))
28.57/10.15	   A^2 -> H(f(k), f(k))
28.57/10.15	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.15	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.15	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.15	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.15	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, c))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.15	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.15	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.15	   A^2 -> H(U1(d, c), b)
28.57/10.15	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, c), c)
28.57/10.15	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(d, c), e)
28.57/10.15	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, a), d)
28.57/10.15	   A^2 -> H(U1(d, a), k)
28.57/10.15	   A^2 -> H(U1(a, e), b)
28.57/10.15	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(a, e), c)
28.57/10.15	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(a, e), e)
28.57/10.15	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(a, k), b)
28.57/10.15	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(a, k), c)
28.57/10.15	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(a, k), e)
28.57/10.15	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(a, c), d)
28.57/10.15	   A^2 -> H(U1(a, c), k)
28.57/10.15	   A^2 -> H(U1(a, d), d)
28.57/10.15	   A^2 -> H(U1(a, d), k)
28.57/10.15	   A^2 -> H(k, U1(c, b))
28.57/10.15	   A^2 -> H(k, U1(d, b))
28.57/10.15	   A^2 -> H(k, U1(b, c))
28.57/10.15	   A^2 -> H(k, U1(b, d))
28.57/10.15	   A^2 -> H(k, U1(c, c))
28.57/10.15	   A^2 -> H(k, f(e))
28.57/10.15	   A^2 -> H(k, f(k))
28.57/10.15	   A^2 -> H(k, U1(d, d))
28.57/10.15	   A^2 -> H(c, U1(e, b))
28.57/10.15	   A^2 -> H(c, U1(k, b))
28.57/10.15	   A^2 -> H(c, U1(c, d))
28.57/10.15	   A^2 -> H(c, U1(d, c))
28.57/10.15	   A^2 -> H(c, U1(b, e))
28.57/10.15	   A^2 -> H(c, U1(b, k))
28.57/10.15	   A^2 -> H(c, U1(e, c))
28.57/10.15	   A^2 -> H(c, U1(k, c))
28.57/10.15	   A^2 -> H(c, U1(c, e))
28.57/10.15	   A^2 -> H(c, U1(c, k))
28.57/10.15	   A^2 -> H(c, U1(e, e))
28.57/10.15	   A^2 -> H(c, U1(k, k))
28.57/10.15	   A^2 -> H(c, U1(k, d))
28.57/10.15	   A^2 -> H(c, U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.15	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.15	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, c), b)
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, c), e)
28.57/10.15	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.15	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.15	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.15	   A^2 -> H(U1(k, c), b)
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, c), c)
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, e), b)
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(c, e), c)
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(c, e), e)
28.57/10.15	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, k), b)
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(c, k), c)
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(c, k), e)
28.57/10.15	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, c), d)
28.57/10.15	   A^2 -> H(e, U1(e, b))
28.57/10.15	   A^2 -> H(e, U1(c, d))
28.57/10.15	   A^2 -> H(e, U1(d, c))
28.57/10.15	   A^2 -> H(e, U1(b, e))
28.57/10.15	   A^2 -> H(e, U1(b, k))
28.57/10.15	   A^2 -> H(e, U1(e, c))
28.57/10.15	   A^2 -> H(e, U1(c, e))
28.57/10.15	   A^2 -> H(e, U1(c, k))
28.57/10.15	   A^2 -> H(e, U1(e, e))
28.57/10.15	   A^2 -> H(e, U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, e), b)
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, e), c)
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.15	   A^2 -> H(f(e), d)
28.57/10.15	   A^2 -> H(f(e), k)
28.57/10.15	   A^2 -> H(U1(k, k), b)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, k), c)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.15	   A^2 -> H(f(k), d)
28.57/10.15	   A^2 -> H(f(k), k)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(k, d), b)
28.57/10.15	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, d), c)
28.57/10.15	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, k), b)
28.57/10.15	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, k), c)
28.57/10.15	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(d, k), e)
28.57/10.15	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, d), d)
28.57/10.15	   A^2 -> H(U1(d, d), k)
28.57/10.15	   A^2 -> H(U1(e, c), c)
28.57/10.15	   A^2 -> H(U1(c, c), e)
28.57/10.15	   A^2 -> H(U1(c, c), k)
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(e, e), e)
28.57/10.15	   A^2 -> H(d, U1(e, b))
28.57/10.15	   A^2 -> H(d, U1(k, b))
28.57/10.15	   A^2 -> H(d, U1(c, d))
28.57/10.15	   A^2 -> H(d, U1(d, c))
28.57/10.15	   A^2 -> H(d, U1(b, e))
28.57/10.15	   A^2 -> H(d, U1(b, k))
28.57/10.15	   A^2 -> H(d, U1(e, c))
28.57/10.15	   A^2 -> H(d, U1(k, c))
28.57/10.15	   A^2 -> H(d, U1(c, e))
28.57/10.15	   A^2 -> H(d, U1(c, k))
28.57/10.15	   A^2 -> H(d, U1(e, e))
28.57/10.15	   A^2 -> H(d, U1(k, k))
28.57/10.15	   A^2 -> H(d, U1(k, d))
28.57/10.15	   A^2 -> H(d, U1(d, k))
28.57/10.15	   A^2 -> H(a, b)
28.57/10.15	   A^2 -> H(a, U1(e, d))
28.57/10.15	   A^2 -> H(a, U1(d, e))
28.57/10.15	   A^2 -> H(a, c)
28.57/10.15	   A^2 -> H(a, U1(e, k))
28.57/10.15	   A^2 -> H(a, U1(k, e))
28.57/10.15	   A^2 -> H(a, e)
28.57/10.15	   A^2 -> H(a, U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, d), b)
28.57/10.15	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, d), c)
28.57/10.15	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, d), e)
28.57/10.15	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, a), d)
28.57/10.15	   A^2 -> H(U1(e, a), k)
28.57/10.15	   A^2 -> H(U1(k, a), d)
28.57/10.15	   A^2 -> H(U1(c, d), d)
28.57/10.15	   A^2 -> H(U1(c, d), k)
28.57/10.15	   A^2 -> H(U1(d, e), b)
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.15	
28.57/10.15	The TRS R consists of the following rules:
28.57/10.15	
28.57/10.15	   f(x) -> U1(x, x)
28.57/10.15	   U1(e, x) -> x
28.57/10.15	   a -> c
28.57/10.15	   a -> d
28.57/10.15	   b -> c
28.57/10.15	   b -> d
28.57/10.15	   d -> k
28.57/10.15	   c -> e
28.57/10.15	   c -> k
28.57/10.15	
28.57/10.15	Q is empty.
28.57/10.15	We have to consider all minimal (P,Q,R)-chains.
28.57/10.15	----------------------------------------
28.57/10.15	
28.57/10.15	(1937) TransformationProof (EQUIVALENT)
28.57/10.15	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.15	
28.57/10.15	   (A^2 -> H(U1(k, e), U1(e, c)),A^2 -> H(U1(k, e), U1(e, c)))
28.57/10.15	   (A^2 -> H(U1(d, e), c),A^2 -> H(U1(d, e), c))
28.57/10.15	   (A^2 -> H(U1(d, e), U1(e, e)),A^2 -> H(U1(d, e), U1(e, e)))
28.57/10.15	   (A^2 -> H(U1(d, e), U1(e, k)),A^2 -> H(U1(d, e), U1(e, k)))
28.57/10.15	
28.57/10.15	
28.57/10.15	----------------------------------------
28.57/10.15	
28.57/10.15	(1938)
28.57/10.15	Obligation:
28.57/10.15	Q DP problem:
28.57/10.15	The TRS P consists of the following rules:
28.57/10.15	
28.57/10.15	   G(d, x, x) -> A^2
28.57/10.15	   A^2 -> H(f(c), f(c))
28.57/10.15	   H(x, x) -> G(x, x, f(k))
28.57/10.15	   A^2 -> H(f(d), f(d))
28.57/10.15	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.15	   A^2 -> H(f(e), f(e))
28.57/10.15	   A^2 -> H(f(k), f(k))
28.57/10.15	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.15	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.15	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.15	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.15	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, c))
28.57/10.15	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.15	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.15	   A^2 -> H(U1(d, c), b)
28.57/10.15	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, c), c)
28.57/10.15	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(d, c), e)
28.57/10.15	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, a), d)
28.57/10.15	   A^2 -> H(U1(d, a), k)
28.57/10.15	   A^2 -> H(U1(a, e), b)
28.57/10.15	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(a, e), c)
28.57/10.15	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(a, e), e)
28.57/10.15	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(a, k), b)
28.57/10.15	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(a, k), c)
28.57/10.15	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(a, k), e)
28.57/10.15	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(a, c), d)
28.57/10.15	   A^2 -> H(U1(a, c), k)
28.57/10.15	   A^2 -> H(U1(a, d), d)
28.57/10.15	   A^2 -> H(U1(a, d), k)
28.57/10.15	   A^2 -> H(k, U1(c, b))
28.57/10.15	   A^2 -> H(k, U1(d, b))
28.57/10.15	   A^2 -> H(k, U1(b, c))
28.57/10.15	   A^2 -> H(k, U1(b, d))
28.57/10.15	   A^2 -> H(k, U1(c, c))
28.57/10.15	   A^2 -> H(k, f(e))
28.57/10.15	   A^2 -> H(k, f(k))
28.57/10.15	   A^2 -> H(k, U1(d, d))
28.57/10.15	   A^2 -> H(c, U1(e, b))
28.57/10.15	   A^2 -> H(c, U1(k, b))
28.57/10.15	   A^2 -> H(c, U1(c, d))
28.57/10.15	   A^2 -> H(c, U1(d, c))
28.57/10.15	   A^2 -> H(c, U1(b, e))
28.57/10.15	   A^2 -> H(c, U1(b, k))
28.57/10.15	   A^2 -> H(c, U1(e, c))
28.57/10.15	   A^2 -> H(c, U1(k, c))
28.57/10.15	   A^2 -> H(c, U1(c, e))
28.57/10.15	   A^2 -> H(c, U1(c, k))
28.57/10.15	   A^2 -> H(c, U1(e, e))
28.57/10.15	   A^2 -> H(c, U1(k, k))
28.57/10.15	   A^2 -> H(c, U1(k, d))
28.57/10.15	   A^2 -> H(c, U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.15	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.15	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, c), b)
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, c), e)
28.57/10.15	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.15	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.15	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.15	   A^2 -> H(U1(k, c), b)
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, c), c)
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, e), b)
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(c, e), c)
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(c, e), e)
28.57/10.15	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, k), b)
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(c, k), c)
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(c, k), e)
28.57/10.15	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, c), d)
28.57/10.15	   A^2 -> H(e, U1(e, b))
28.57/10.15	   A^2 -> H(e, U1(c, d))
28.57/10.15	   A^2 -> H(e, U1(d, c))
28.57/10.15	   A^2 -> H(e, U1(b, e))
28.57/10.15	   A^2 -> H(e, U1(b, k))
28.57/10.15	   A^2 -> H(e, U1(e, c))
28.57/10.15	   A^2 -> H(e, U1(c, e))
28.57/10.15	   A^2 -> H(e, U1(c, k))
28.57/10.15	   A^2 -> H(e, U1(e, e))
28.57/10.15	   A^2 -> H(e, U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, e), b)
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, e), c)
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.15	   A^2 -> H(f(e), d)
28.57/10.15	   A^2 -> H(f(e), k)
28.57/10.15	   A^2 -> H(U1(k, k), b)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, k), c)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.15	   A^2 -> H(f(k), d)
28.57/10.15	   A^2 -> H(f(k), k)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(k, d), b)
28.57/10.15	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, d), c)
28.57/10.15	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, k), b)
28.57/10.15	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, k), c)
28.57/10.15	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(d, k), e)
28.57/10.15	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, d), d)
28.57/10.15	   A^2 -> H(U1(d, d), k)
28.57/10.15	   A^2 -> H(U1(e, c), c)
28.57/10.15	   A^2 -> H(U1(c, c), e)
28.57/10.15	   A^2 -> H(U1(c, c), k)
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(e, e), e)
28.57/10.15	   A^2 -> H(d, U1(e, b))
28.57/10.15	   A^2 -> H(d, U1(k, b))
28.57/10.15	   A^2 -> H(d, U1(c, d))
28.57/10.15	   A^2 -> H(d, U1(d, c))
28.57/10.15	   A^2 -> H(d, U1(b, e))
28.57/10.15	   A^2 -> H(d, U1(b, k))
28.57/10.15	   A^2 -> H(d, U1(e, c))
28.57/10.15	   A^2 -> H(d, U1(k, c))
28.57/10.15	   A^2 -> H(d, U1(c, e))
28.57/10.15	   A^2 -> H(d, U1(c, k))
28.57/10.15	   A^2 -> H(d, U1(e, e))
28.57/10.15	   A^2 -> H(d, U1(k, k))
28.57/10.15	   A^2 -> H(d, U1(k, d))
28.57/10.15	   A^2 -> H(d, U1(d, k))
28.57/10.15	   A^2 -> H(a, b)
28.57/10.15	   A^2 -> H(a, U1(e, d))
28.57/10.15	   A^2 -> H(a, U1(d, e))
28.57/10.15	   A^2 -> H(a, c)
28.57/10.15	   A^2 -> H(a, U1(e, k))
28.57/10.15	   A^2 -> H(a, U1(k, e))
28.57/10.15	   A^2 -> H(a, e)
28.57/10.15	   A^2 -> H(a, U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, d), b)
28.57/10.15	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, d), c)
28.57/10.15	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, d), e)
28.57/10.15	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, a), d)
28.57/10.15	   A^2 -> H(U1(e, a), k)
28.57/10.15	   A^2 -> H(U1(k, a), d)
28.57/10.15	   A^2 -> H(U1(c, d), d)
28.57/10.15	   A^2 -> H(U1(c, d), k)
28.57/10.15	   A^2 -> H(U1(d, e), b)
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, e), c)
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.15	
28.57/10.15	The TRS R consists of the following rules:
28.57/10.15	
28.57/10.15	   f(x) -> U1(x, x)
28.57/10.15	   U1(e, x) -> x
28.57/10.15	   a -> c
28.57/10.15	   a -> d
28.57/10.15	   b -> c
28.57/10.15	   b -> d
28.57/10.15	   d -> k
28.57/10.15	   c -> e
28.57/10.15	   c -> k
28.57/10.15	
28.57/10.15	Q is empty.
28.57/10.15	We have to consider all minimal (P,Q,R)-chains.
28.57/10.15	----------------------------------------
28.57/10.15	
28.57/10.15	(1939) TransformationProof (EQUIVALENT)
28.57/10.15	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.15	
28.57/10.15	   (A^2 -> H(U1(k, e), U1(k, c)),A^2 -> H(U1(k, e), U1(k, c)))
28.57/10.15	   (A^2 -> H(U1(d, e), U1(k, e)),A^2 -> H(U1(d, e), U1(k, e)))
28.57/10.15	   (A^2 -> H(U1(d, e), U1(k, k)),A^2 -> H(U1(d, e), U1(k, k)))
28.57/10.15	
28.57/10.15	
28.57/10.15	----------------------------------------
28.57/10.15	
28.57/10.15	(1940)
28.57/10.15	Obligation:
28.57/10.15	Q DP problem:
28.57/10.15	The TRS P consists of the following rules:
28.57/10.15	
28.57/10.15	   G(d, x, x) -> A^2
28.57/10.15	   A^2 -> H(f(c), f(c))
28.57/10.15	   H(x, x) -> G(x, x, f(k))
28.57/10.15	   A^2 -> H(f(d), f(d))
28.57/10.15	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.15	   A^2 -> H(f(e), f(e))
28.57/10.15	   A^2 -> H(f(k), f(k))
28.57/10.15	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.15	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.15	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.15	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.15	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.15	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.15	   A^2 -> H(U1(d, c), b)
28.57/10.15	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, c), c)
28.57/10.15	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(d, c), e)
28.57/10.15	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, a), d)
28.57/10.15	   A^2 -> H(U1(d, a), k)
28.57/10.15	   A^2 -> H(U1(a, e), b)
28.57/10.15	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(a, e), c)
28.57/10.15	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(a, e), e)
28.57/10.15	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(a, k), b)
28.57/10.15	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(a, k), c)
28.57/10.15	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(a, k), e)
28.57/10.15	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(a, c), d)
28.57/10.15	   A^2 -> H(U1(a, c), k)
28.57/10.15	   A^2 -> H(U1(a, d), d)
28.57/10.15	   A^2 -> H(U1(a, d), k)
28.57/10.15	   A^2 -> H(k, U1(c, b))
28.57/10.15	   A^2 -> H(k, U1(d, b))
28.57/10.15	   A^2 -> H(k, U1(b, c))
28.57/10.15	   A^2 -> H(k, U1(b, d))
28.57/10.15	   A^2 -> H(k, U1(c, c))
28.57/10.15	   A^2 -> H(k, f(e))
28.57/10.15	   A^2 -> H(k, f(k))
28.57/10.15	   A^2 -> H(k, U1(d, d))
28.57/10.15	   A^2 -> H(c, U1(e, b))
28.57/10.15	   A^2 -> H(c, U1(k, b))
28.57/10.15	   A^2 -> H(c, U1(c, d))
28.57/10.15	   A^2 -> H(c, U1(d, c))
28.57/10.15	   A^2 -> H(c, U1(b, e))
28.57/10.15	   A^2 -> H(c, U1(b, k))
28.57/10.15	   A^2 -> H(c, U1(e, c))
28.57/10.15	   A^2 -> H(c, U1(k, c))
28.57/10.15	   A^2 -> H(c, U1(c, e))
28.57/10.15	   A^2 -> H(c, U1(c, k))
28.57/10.15	   A^2 -> H(c, U1(e, e))
28.57/10.15	   A^2 -> H(c, U1(k, k))
28.57/10.15	   A^2 -> H(c, U1(k, d))
28.57/10.15	   A^2 -> H(c, U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.15	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.15	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, c), b)
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, c), e)
28.57/10.15	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.15	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.15	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.15	   A^2 -> H(U1(k, c), b)
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, c), c)
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, e), b)
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(c, e), c)
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(c, e), e)
28.57/10.15	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, k), b)
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(c, k), c)
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(c, k), e)
28.57/10.15	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, c), d)
28.57/10.15	   A^2 -> H(e, U1(e, b))
28.57/10.15	   A^2 -> H(e, U1(c, d))
28.57/10.15	   A^2 -> H(e, U1(d, c))
28.57/10.15	   A^2 -> H(e, U1(b, e))
28.57/10.15	   A^2 -> H(e, U1(b, k))
28.57/10.15	   A^2 -> H(e, U1(e, c))
28.57/10.15	   A^2 -> H(e, U1(c, e))
28.57/10.15	   A^2 -> H(e, U1(c, k))
28.57/10.15	   A^2 -> H(e, U1(e, e))
28.57/10.15	   A^2 -> H(e, U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, e), b)
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, e), c)
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.15	   A^2 -> H(f(e), d)
28.57/10.15	   A^2 -> H(f(e), k)
28.57/10.15	   A^2 -> H(U1(k, k), b)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, k), c)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.15	   A^2 -> H(f(k), d)
28.57/10.15	   A^2 -> H(f(k), k)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(k, d), b)
28.57/10.15	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, d), c)
28.57/10.15	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, k), b)
28.57/10.15	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, k), c)
28.57/10.15	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(d, k), e)
28.57/10.15	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, d), d)
28.57/10.15	   A^2 -> H(U1(d, d), k)
28.57/10.15	   A^2 -> H(U1(e, c), c)
28.57/10.15	   A^2 -> H(U1(c, c), e)
28.57/10.15	   A^2 -> H(U1(c, c), k)
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(e, e), e)
28.57/10.15	   A^2 -> H(d, U1(e, b))
28.57/10.15	   A^2 -> H(d, U1(k, b))
28.57/10.15	   A^2 -> H(d, U1(c, d))
28.57/10.15	   A^2 -> H(d, U1(d, c))
28.57/10.15	   A^2 -> H(d, U1(b, e))
28.57/10.15	   A^2 -> H(d, U1(b, k))
28.57/10.15	   A^2 -> H(d, U1(e, c))
28.57/10.15	   A^2 -> H(d, U1(k, c))
28.57/10.15	   A^2 -> H(d, U1(c, e))
28.57/10.15	   A^2 -> H(d, U1(c, k))
28.57/10.15	   A^2 -> H(d, U1(e, e))
28.57/10.15	   A^2 -> H(d, U1(k, k))
28.57/10.15	   A^2 -> H(d, U1(k, d))
28.57/10.15	   A^2 -> H(d, U1(d, k))
28.57/10.15	   A^2 -> H(a, b)
28.57/10.15	   A^2 -> H(a, U1(e, d))
28.57/10.15	   A^2 -> H(a, U1(d, e))
28.57/10.15	   A^2 -> H(a, c)
28.57/10.15	   A^2 -> H(a, U1(e, k))
28.57/10.15	   A^2 -> H(a, U1(k, e))
28.57/10.15	   A^2 -> H(a, e)
28.57/10.15	   A^2 -> H(a, U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, d), b)
28.57/10.15	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, d), c)
28.57/10.15	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, d), e)
28.57/10.15	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, a), d)
28.57/10.15	   A^2 -> H(U1(e, a), k)
28.57/10.15	   A^2 -> H(U1(k, a), d)
28.57/10.15	   A^2 -> H(U1(c, d), d)
28.57/10.15	   A^2 -> H(U1(c, d), k)
28.57/10.15	   A^2 -> H(U1(d, e), b)
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, e), c)
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.15	
28.57/10.15	The TRS R consists of the following rules:
28.57/10.15	
28.57/10.15	   f(x) -> U1(x, x)
28.57/10.15	   U1(e, x) -> x
28.57/10.15	   a -> c
28.57/10.15	   a -> d
28.57/10.15	   b -> c
28.57/10.15	   b -> d
28.57/10.15	   d -> k
28.57/10.15	   c -> e
28.57/10.15	   c -> k
28.57/10.15	
28.57/10.15	Q is empty.
28.57/10.15	We have to consider all minimal (P,Q,R)-chains.
28.57/10.15	----------------------------------------
28.57/10.15	
28.57/10.15	(1941) TransformationProof (EQUIVALENT)
28.57/10.15	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.15	
28.57/10.15	   (A^2 -> H(U1(k, e), U1(c, e)),A^2 -> H(U1(k, e), U1(c, e)))
28.57/10.15	   (A^2 -> H(U1(d, e), U1(e, e)),A^2 -> H(U1(d, e), U1(e, e)))
28.57/10.15	   (A^2 -> H(U1(d, e), U1(k, e)),A^2 -> H(U1(d, e), U1(k, e)))
28.57/10.15	
28.57/10.15	
28.57/10.15	----------------------------------------
28.57/10.15	
28.57/10.15	(1942)
28.57/10.15	Obligation:
28.57/10.15	Q DP problem:
28.57/10.15	The TRS P consists of the following rules:
28.57/10.15	
28.57/10.15	   G(d, x, x) -> A^2
28.57/10.15	   A^2 -> H(f(c), f(c))
28.57/10.15	   H(x, x) -> G(x, x, f(k))
28.57/10.15	   A^2 -> H(f(d), f(d))
28.57/10.15	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.15	   A^2 -> H(f(e), f(e))
28.57/10.15	   A^2 -> H(f(k), f(k))
28.57/10.15	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.15	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.15	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.15	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.15	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(c, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.15	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.15	   A^2 -> H(U1(d, c), b)
28.57/10.15	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, c), c)
28.57/10.15	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(d, c), e)
28.57/10.15	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, a), d)
28.57/10.15	   A^2 -> H(U1(d, a), k)
28.57/10.15	   A^2 -> H(U1(a, e), b)
28.57/10.15	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(a, e), c)
28.57/10.15	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(a, e), e)
28.57/10.15	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(a, k), b)
28.57/10.15	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(a, k), c)
28.57/10.15	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(a, k), e)
28.57/10.15	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(a, c), d)
28.57/10.15	   A^2 -> H(U1(a, c), k)
28.57/10.15	   A^2 -> H(U1(a, d), d)
28.57/10.15	   A^2 -> H(U1(a, d), k)
28.57/10.15	   A^2 -> H(k, U1(c, b))
28.57/10.15	   A^2 -> H(k, U1(d, b))
28.57/10.15	   A^2 -> H(k, U1(b, c))
28.57/10.15	   A^2 -> H(k, U1(b, d))
28.57/10.15	   A^2 -> H(k, U1(c, c))
28.57/10.15	   A^2 -> H(k, f(e))
28.57/10.15	   A^2 -> H(k, f(k))
28.57/10.15	   A^2 -> H(k, U1(d, d))
28.57/10.15	   A^2 -> H(c, U1(e, b))
28.57/10.15	   A^2 -> H(c, U1(k, b))
28.57/10.15	   A^2 -> H(c, U1(c, d))
28.57/10.15	   A^2 -> H(c, U1(d, c))
28.57/10.15	   A^2 -> H(c, U1(b, e))
28.57/10.15	   A^2 -> H(c, U1(b, k))
28.57/10.15	   A^2 -> H(c, U1(e, c))
28.57/10.15	   A^2 -> H(c, U1(k, c))
28.57/10.15	   A^2 -> H(c, U1(c, e))
28.57/10.15	   A^2 -> H(c, U1(c, k))
28.57/10.15	   A^2 -> H(c, U1(e, e))
28.57/10.15	   A^2 -> H(c, U1(k, k))
28.57/10.15	   A^2 -> H(c, U1(k, d))
28.57/10.15	   A^2 -> H(c, U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.15	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.15	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, c), b)
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, c), e)
28.57/10.15	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.15	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.15	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.15	   A^2 -> H(U1(k, c), b)
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, c), c)
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, e), b)
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(c, e), c)
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(c, e), e)
28.57/10.15	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, k), b)
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(c, k), c)
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(c, k), e)
28.57/10.15	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, c), d)
28.57/10.15	   A^2 -> H(e, U1(e, b))
28.57/10.15	   A^2 -> H(e, U1(c, d))
28.57/10.15	   A^2 -> H(e, U1(d, c))
28.57/10.15	   A^2 -> H(e, U1(b, e))
28.57/10.15	   A^2 -> H(e, U1(b, k))
28.57/10.15	   A^2 -> H(e, U1(e, c))
28.57/10.15	   A^2 -> H(e, U1(c, e))
28.57/10.15	   A^2 -> H(e, U1(c, k))
28.57/10.15	   A^2 -> H(e, U1(e, e))
28.57/10.15	   A^2 -> H(e, U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, e), b)
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, e), c)
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.15	   A^2 -> H(f(e), d)
28.57/10.15	   A^2 -> H(f(e), k)
28.57/10.15	   A^2 -> H(U1(k, k), b)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, k), c)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.15	   A^2 -> H(f(k), d)
28.57/10.15	   A^2 -> H(f(k), k)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(k, d), b)
28.57/10.15	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, d), c)
28.57/10.15	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, k), b)
28.57/10.15	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, k), c)
28.57/10.15	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(d, k), e)
28.57/10.15	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, d), d)
28.57/10.15	   A^2 -> H(U1(d, d), k)
28.57/10.15	   A^2 -> H(U1(e, c), c)
28.57/10.15	   A^2 -> H(U1(c, c), e)
28.57/10.15	   A^2 -> H(U1(c, c), k)
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(e, e), e)
28.57/10.15	   A^2 -> H(d, U1(e, b))
28.57/10.15	   A^2 -> H(d, U1(k, b))
28.57/10.15	   A^2 -> H(d, U1(c, d))
28.57/10.15	   A^2 -> H(d, U1(d, c))
28.57/10.15	   A^2 -> H(d, U1(b, e))
28.57/10.15	   A^2 -> H(d, U1(b, k))
28.57/10.15	   A^2 -> H(d, U1(e, c))
28.57/10.15	   A^2 -> H(d, U1(k, c))
28.57/10.15	   A^2 -> H(d, U1(c, e))
28.57/10.15	   A^2 -> H(d, U1(c, k))
28.57/10.15	   A^2 -> H(d, U1(e, e))
28.57/10.15	   A^2 -> H(d, U1(k, k))
28.57/10.15	   A^2 -> H(d, U1(k, d))
28.57/10.15	   A^2 -> H(d, U1(d, k))
28.57/10.15	   A^2 -> H(a, b)
28.57/10.15	   A^2 -> H(a, U1(e, d))
28.57/10.15	   A^2 -> H(a, U1(d, e))
28.57/10.15	   A^2 -> H(a, c)
28.57/10.15	   A^2 -> H(a, U1(e, k))
28.57/10.15	   A^2 -> H(a, U1(k, e))
28.57/10.15	   A^2 -> H(a, e)
28.57/10.15	   A^2 -> H(a, U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, d), b)
28.57/10.15	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, d), c)
28.57/10.15	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, d), e)
28.57/10.15	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, a), d)
28.57/10.15	   A^2 -> H(U1(e, a), k)
28.57/10.15	   A^2 -> H(U1(k, a), d)
28.57/10.15	   A^2 -> H(U1(c, d), d)
28.57/10.15	   A^2 -> H(U1(c, d), k)
28.57/10.15	   A^2 -> H(U1(d, e), b)
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, e), c)
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.15	
28.57/10.15	The TRS R consists of the following rules:
28.57/10.15	
28.57/10.15	   f(x) -> U1(x, x)
28.57/10.15	   U1(e, x) -> x
28.57/10.15	   a -> c
28.57/10.15	   a -> d
28.57/10.15	   b -> c
28.57/10.15	   b -> d
28.57/10.15	   d -> k
28.57/10.15	   c -> e
28.57/10.15	   c -> k
28.57/10.15	
28.57/10.15	Q is empty.
28.57/10.15	We have to consider all minimal (P,Q,R)-chains.
28.57/10.15	----------------------------------------
28.57/10.15	
28.57/10.15	(1943) TransformationProof (EQUIVALENT)
28.57/10.15	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.15	
28.57/10.15	   (A^2 -> H(U1(k, e), U1(c, k)),A^2 -> H(U1(k, e), U1(c, k)))
28.57/10.15	   (A^2 -> H(U1(d, e), U1(e, k)),A^2 -> H(U1(d, e), U1(e, k)))
28.57/10.15	   (A^2 -> H(U1(d, e), U1(k, k)),A^2 -> H(U1(d, e), U1(k, k)))
28.57/10.15	
28.57/10.15	
28.57/10.15	----------------------------------------
28.57/10.15	
28.57/10.15	(1944)
28.57/10.15	Obligation:
28.57/10.15	Q DP problem:
28.57/10.15	The TRS P consists of the following rules:
28.57/10.15	
28.57/10.15	   G(d, x, x) -> A^2
28.57/10.15	   A^2 -> H(f(c), f(c))
28.57/10.15	   H(x, x) -> G(x, x, f(k))
28.57/10.15	   A^2 -> H(f(d), f(d))
28.57/10.15	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.15	   A^2 -> H(f(e), f(e))
28.57/10.15	   A^2 -> H(f(k), f(k))
28.57/10.15	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.15	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.15	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.15	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.15	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.15	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.15	   A^2 -> H(U1(d, c), b)
28.57/10.15	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, c), c)
28.57/10.15	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(d, c), e)
28.57/10.15	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, a), d)
28.57/10.15	   A^2 -> H(U1(d, a), k)
28.57/10.15	   A^2 -> H(U1(a, e), b)
28.57/10.15	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(a, e), c)
28.57/10.15	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(a, e), e)
28.57/10.15	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(a, k), b)
28.57/10.15	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(a, k), c)
28.57/10.15	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(a, k), e)
28.57/10.15	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(a, c), d)
28.57/10.15	   A^2 -> H(U1(a, c), k)
28.57/10.15	   A^2 -> H(U1(a, d), d)
28.57/10.15	   A^2 -> H(U1(a, d), k)
28.57/10.15	   A^2 -> H(k, U1(c, b))
28.57/10.15	   A^2 -> H(k, U1(d, b))
28.57/10.15	   A^2 -> H(k, U1(b, c))
28.57/10.15	   A^2 -> H(k, U1(b, d))
28.57/10.15	   A^2 -> H(k, U1(c, c))
28.57/10.15	   A^2 -> H(k, f(e))
28.57/10.15	   A^2 -> H(k, f(k))
28.57/10.15	   A^2 -> H(k, U1(d, d))
28.57/10.15	   A^2 -> H(c, U1(e, b))
28.57/10.15	   A^2 -> H(c, U1(k, b))
28.57/10.15	   A^2 -> H(c, U1(c, d))
28.57/10.15	   A^2 -> H(c, U1(d, c))
28.57/10.15	   A^2 -> H(c, U1(b, e))
28.57/10.15	   A^2 -> H(c, U1(b, k))
28.57/10.15	   A^2 -> H(c, U1(e, c))
28.57/10.15	   A^2 -> H(c, U1(k, c))
28.57/10.15	   A^2 -> H(c, U1(c, e))
28.57/10.15	   A^2 -> H(c, U1(c, k))
28.57/10.15	   A^2 -> H(c, U1(e, e))
28.57/10.15	   A^2 -> H(c, U1(k, k))
28.57/10.15	   A^2 -> H(c, U1(k, d))
28.57/10.15	   A^2 -> H(c, U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.15	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.15	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, c), b)
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, c), e)
28.57/10.15	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.15	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.15	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.15	   A^2 -> H(U1(k, c), b)
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, c), c)
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, e), b)
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(c, e), c)
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(c, e), e)
28.57/10.15	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, k), b)
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(c, k), c)
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(c, k), e)
28.57/10.15	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, c), d)
28.57/10.15	   A^2 -> H(e, U1(e, b))
28.57/10.15	   A^2 -> H(e, U1(c, d))
28.57/10.15	   A^2 -> H(e, U1(d, c))
28.57/10.15	   A^2 -> H(e, U1(b, e))
28.57/10.15	   A^2 -> H(e, U1(b, k))
28.57/10.15	   A^2 -> H(e, U1(e, c))
28.57/10.15	   A^2 -> H(e, U1(c, e))
28.57/10.15	   A^2 -> H(e, U1(c, k))
28.57/10.15	   A^2 -> H(e, U1(e, e))
28.57/10.15	   A^2 -> H(e, U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, e), b)
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, e), c)
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.15	   A^2 -> H(f(e), d)
28.57/10.15	   A^2 -> H(f(e), k)
28.57/10.15	   A^2 -> H(U1(k, k), b)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, k), c)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.15	   A^2 -> H(f(k), d)
28.57/10.15	   A^2 -> H(f(k), k)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(k, d), b)
28.57/10.15	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, d), c)
28.57/10.15	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, k), b)
28.57/10.15	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, k), c)
28.57/10.15	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(d, k), e)
28.57/10.15	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, d), d)
28.57/10.15	   A^2 -> H(U1(d, d), k)
28.57/10.15	   A^2 -> H(U1(e, c), c)
28.57/10.15	   A^2 -> H(U1(c, c), e)
28.57/10.15	   A^2 -> H(U1(c, c), k)
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(e, e), e)
28.57/10.15	   A^2 -> H(d, U1(e, b))
28.57/10.15	   A^2 -> H(d, U1(k, b))
28.57/10.15	   A^2 -> H(d, U1(c, d))
28.57/10.15	   A^2 -> H(d, U1(d, c))
28.57/10.15	   A^2 -> H(d, U1(b, e))
28.57/10.15	   A^2 -> H(d, U1(b, k))
28.57/10.15	   A^2 -> H(d, U1(e, c))
28.57/10.15	   A^2 -> H(d, U1(k, c))
28.57/10.15	   A^2 -> H(d, U1(c, e))
28.57/10.15	   A^2 -> H(d, U1(c, k))
28.57/10.15	   A^2 -> H(d, U1(e, e))
28.57/10.15	   A^2 -> H(d, U1(k, k))
28.57/10.15	   A^2 -> H(d, U1(k, d))
28.57/10.15	   A^2 -> H(d, U1(d, k))
28.57/10.15	   A^2 -> H(a, b)
28.57/10.15	   A^2 -> H(a, U1(e, d))
28.57/10.15	   A^2 -> H(a, U1(d, e))
28.57/10.15	   A^2 -> H(a, c)
28.57/10.15	   A^2 -> H(a, U1(e, k))
28.57/10.15	   A^2 -> H(a, U1(k, e))
28.57/10.15	   A^2 -> H(a, e)
28.57/10.15	   A^2 -> H(a, U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, d), b)
28.57/10.15	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, d), c)
28.57/10.15	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, d), e)
28.57/10.15	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, a), d)
28.57/10.15	   A^2 -> H(U1(e, a), k)
28.57/10.15	   A^2 -> H(U1(k, a), d)
28.57/10.15	   A^2 -> H(U1(c, d), d)
28.57/10.15	   A^2 -> H(U1(c, d), k)
28.57/10.15	   A^2 -> H(U1(d, e), b)
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, e), c)
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.15	
28.57/10.15	The TRS R consists of the following rules:
28.57/10.15	
28.57/10.15	   f(x) -> U1(x, x)
28.57/10.15	   U1(e, x) -> x
28.57/10.15	   a -> c
28.57/10.15	   a -> d
28.57/10.15	   b -> c
28.57/10.15	   b -> d
28.57/10.15	   d -> k
28.57/10.15	   c -> e
28.57/10.15	   c -> k
28.57/10.15	
28.57/10.15	Q is empty.
28.57/10.15	We have to consider all minimal (P,Q,R)-chains.
28.57/10.15	----------------------------------------
28.57/10.15	
28.57/10.15	(1945) TransformationProof (EQUIVALENT)
28.57/10.15	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.15	
28.57/10.15	   (A^2 -> H(U1(k, e), U1(e, e)),A^2 -> H(U1(k, e), U1(e, e)))
28.57/10.15	   (A^2 -> H(U1(d, e), e),A^2 -> H(U1(d, e), e))
28.57/10.15	
28.57/10.15	
28.57/10.15	----------------------------------------
28.57/10.15	
28.57/10.15	(1946)
28.57/10.15	Obligation:
28.57/10.15	Q DP problem:
28.57/10.15	The TRS P consists of the following rules:
28.57/10.15	
28.57/10.15	   G(d, x, x) -> A^2
28.57/10.15	   A^2 -> H(f(c), f(c))
28.57/10.15	   H(x, x) -> G(x, x, f(k))
28.57/10.15	   A^2 -> H(f(d), f(d))
28.57/10.15	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.15	   A^2 -> H(f(e), f(e))
28.57/10.15	   A^2 -> H(f(k), f(k))
28.57/10.15	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.15	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.15	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.15	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.15	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.15	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.15	   A^2 -> H(U1(d, c), b)
28.57/10.15	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, c), c)
28.57/10.15	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(d, c), e)
28.57/10.15	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, a), d)
28.57/10.15	   A^2 -> H(U1(d, a), k)
28.57/10.15	   A^2 -> H(U1(a, e), b)
28.57/10.15	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(a, e), c)
28.57/10.15	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(a, e), e)
28.57/10.15	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(a, k), b)
28.57/10.15	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(a, k), c)
28.57/10.15	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(a, k), e)
28.57/10.15	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(a, c), d)
28.57/10.15	   A^2 -> H(U1(a, c), k)
28.57/10.15	   A^2 -> H(U1(a, d), d)
28.57/10.15	   A^2 -> H(U1(a, d), k)
28.57/10.15	   A^2 -> H(k, U1(c, b))
28.57/10.15	   A^2 -> H(k, U1(d, b))
28.57/10.15	   A^2 -> H(k, U1(b, c))
28.57/10.15	   A^2 -> H(k, U1(b, d))
28.57/10.15	   A^2 -> H(k, U1(c, c))
28.57/10.15	   A^2 -> H(k, f(e))
28.57/10.15	   A^2 -> H(k, f(k))
28.57/10.15	   A^2 -> H(k, U1(d, d))
28.57/10.15	   A^2 -> H(c, U1(e, b))
28.57/10.15	   A^2 -> H(c, U1(k, b))
28.57/10.15	   A^2 -> H(c, U1(c, d))
28.57/10.15	   A^2 -> H(c, U1(d, c))
28.57/10.15	   A^2 -> H(c, U1(b, e))
28.57/10.15	   A^2 -> H(c, U1(b, k))
28.57/10.15	   A^2 -> H(c, U1(e, c))
28.57/10.15	   A^2 -> H(c, U1(k, c))
28.57/10.15	   A^2 -> H(c, U1(c, e))
28.57/10.15	   A^2 -> H(c, U1(c, k))
28.57/10.15	   A^2 -> H(c, U1(e, e))
28.57/10.15	   A^2 -> H(c, U1(k, k))
28.57/10.15	   A^2 -> H(c, U1(k, d))
28.57/10.15	   A^2 -> H(c, U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.15	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.15	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, c), b)
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, c), e)
28.57/10.15	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.15	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.15	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.15	   A^2 -> H(U1(k, c), b)
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, c), c)
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, e), b)
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(c, e), c)
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(c, e), e)
28.57/10.15	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, k), b)
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(c, k), c)
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(c, k), e)
28.57/10.15	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, c), d)
28.57/10.15	   A^2 -> H(e, U1(e, b))
28.57/10.15	   A^2 -> H(e, U1(c, d))
28.57/10.15	   A^2 -> H(e, U1(d, c))
28.57/10.15	   A^2 -> H(e, U1(b, e))
28.57/10.15	   A^2 -> H(e, U1(b, k))
28.57/10.15	   A^2 -> H(e, U1(e, c))
28.57/10.15	   A^2 -> H(e, U1(c, e))
28.57/10.15	   A^2 -> H(e, U1(c, k))
28.57/10.15	   A^2 -> H(e, U1(e, e))
28.57/10.15	   A^2 -> H(e, U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, e), b)
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, e), c)
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.15	   A^2 -> H(f(e), d)
28.57/10.15	   A^2 -> H(f(e), k)
28.57/10.15	   A^2 -> H(U1(k, k), b)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, k), c)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.15	   A^2 -> H(f(k), d)
28.57/10.15	   A^2 -> H(f(k), k)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(k, d), b)
28.57/10.15	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, d), c)
28.57/10.15	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, k), b)
28.57/10.15	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, k), c)
28.57/10.15	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(d, k), e)
28.57/10.15	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, d), d)
28.57/10.15	   A^2 -> H(U1(d, d), k)
28.57/10.15	   A^2 -> H(U1(e, c), c)
28.57/10.15	   A^2 -> H(U1(c, c), e)
28.57/10.15	   A^2 -> H(U1(c, c), k)
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(e, e), e)
28.57/10.15	   A^2 -> H(d, U1(e, b))
28.57/10.15	   A^2 -> H(d, U1(k, b))
28.57/10.15	   A^2 -> H(d, U1(c, d))
28.57/10.15	   A^2 -> H(d, U1(d, c))
28.57/10.15	   A^2 -> H(d, U1(b, e))
28.57/10.15	   A^2 -> H(d, U1(b, k))
28.57/10.15	   A^2 -> H(d, U1(e, c))
28.57/10.15	   A^2 -> H(d, U1(k, c))
28.57/10.15	   A^2 -> H(d, U1(c, e))
28.57/10.15	   A^2 -> H(d, U1(c, k))
28.57/10.15	   A^2 -> H(d, U1(e, e))
28.57/10.15	   A^2 -> H(d, U1(k, k))
28.57/10.15	   A^2 -> H(d, U1(k, d))
28.57/10.15	   A^2 -> H(d, U1(d, k))
28.57/10.15	   A^2 -> H(a, b)
28.57/10.15	   A^2 -> H(a, U1(e, d))
28.57/10.15	   A^2 -> H(a, U1(d, e))
28.57/10.15	   A^2 -> H(a, c)
28.57/10.15	   A^2 -> H(a, U1(e, k))
28.57/10.15	   A^2 -> H(a, U1(k, e))
28.57/10.15	   A^2 -> H(a, e)
28.57/10.15	   A^2 -> H(a, U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, d), b)
28.57/10.15	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, d), c)
28.57/10.15	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, d), e)
28.57/10.15	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, a), d)
28.57/10.15	   A^2 -> H(U1(e, a), k)
28.57/10.15	   A^2 -> H(U1(k, a), d)
28.57/10.15	   A^2 -> H(U1(c, d), d)
28.57/10.15	   A^2 -> H(U1(c, d), k)
28.57/10.15	   A^2 -> H(U1(d, e), b)
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, e), c)
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(d, e), e)
28.57/10.15	
28.57/10.15	The TRS R consists of the following rules:
28.57/10.15	
28.57/10.15	   f(x) -> U1(x, x)
28.57/10.15	   U1(e, x) -> x
28.57/10.15	   a -> c
28.57/10.15	   a -> d
28.57/10.15	   b -> c
28.57/10.15	   b -> d
28.57/10.15	   d -> k
28.57/10.15	   c -> e
28.57/10.15	   c -> k
28.57/10.15	
28.57/10.15	Q is empty.
28.57/10.15	We have to consider all minimal (P,Q,R)-chains.
28.57/10.15	----------------------------------------
28.57/10.15	
28.57/10.15	(1947) TransformationProof (EQUIVALENT)
28.57/10.15	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.15	
28.57/10.15	   (A^2 -> H(U1(k, e), U1(k, k)),A^2 -> H(U1(k, e), U1(k, k)))
28.57/10.15	
28.57/10.15	
28.57/10.15	----------------------------------------
28.57/10.15	
28.57/10.15	(1948)
28.57/10.15	Obligation:
28.57/10.15	Q DP problem:
28.57/10.15	The TRS P consists of the following rules:
28.57/10.15	
28.57/10.15	   G(d, x, x) -> A^2
28.57/10.15	   A^2 -> H(f(c), f(c))
28.57/10.15	   H(x, x) -> G(x, x, f(k))
28.57/10.15	   A^2 -> H(f(d), f(d))
28.57/10.15	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.15	   A^2 -> H(f(e), f(e))
28.57/10.15	   A^2 -> H(f(k), f(k))
28.57/10.15	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.15	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.15	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.15	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.15	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.15	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.15	   A^2 -> H(U1(d, c), b)
28.57/10.15	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, c), c)
28.57/10.15	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(d, c), e)
28.57/10.15	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, a), d)
28.57/10.15	   A^2 -> H(U1(d, a), k)
28.57/10.15	   A^2 -> H(U1(a, e), b)
28.57/10.15	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(a, e), c)
28.57/10.15	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(a, e), e)
28.57/10.15	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(a, k), b)
28.57/10.15	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(a, k), c)
28.57/10.15	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(a, k), e)
28.57/10.15	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(a, c), d)
28.57/10.15	   A^2 -> H(U1(a, c), k)
28.57/10.15	   A^2 -> H(U1(a, d), d)
28.57/10.15	   A^2 -> H(U1(a, d), k)
28.57/10.15	   A^2 -> H(k, U1(c, b))
28.57/10.15	   A^2 -> H(k, U1(d, b))
28.57/10.15	   A^2 -> H(k, U1(b, c))
28.57/10.15	   A^2 -> H(k, U1(b, d))
28.57/10.15	   A^2 -> H(k, U1(c, c))
28.57/10.15	   A^2 -> H(k, f(e))
28.57/10.15	   A^2 -> H(k, f(k))
28.57/10.15	   A^2 -> H(k, U1(d, d))
28.57/10.15	   A^2 -> H(c, U1(e, b))
28.57/10.15	   A^2 -> H(c, U1(k, b))
28.57/10.15	   A^2 -> H(c, U1(c, d))
28.57/10.15	   A^2 -> H(c, U1(d, c))
28.57/10.15	   A^2 -> H(c, U1(b, e))
28.57/10.15	   A^2 -> H(c, U1(b, k))
28.57/10.15	   A^2 -> H(c, U1(e, c))
28.57/10.15	   A^2 -> H(c, U1(k, c))
28.57/10.15	   A^2 -> H(c, U1(c, e))
28.57/10.15	   A^2 -> H(c, U1(c, k))
28.57/10.15	   A^2 -> H(c, U1(e, e))
28.57/10.15	   A^2 -> H(c, U1(k, k))
28.57/10.15	   A^2 -> H(c, U1(k, d))
28.57/10.15	   A^2 -> H(c, U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.15	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.15	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, c), b)
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, c), e)
28.57/10.15	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.15	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.15	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.15	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.15	   A^2 -> H(U1(k, c), b)
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, c), c)
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, e), b)
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(c, e), c)
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(c, e), e)
28.57/10.15	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, k), b)
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(c, k), c)
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(c, k), e)
28.57/10.15	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(c, c), d)
28.57/10.15	   A^2 -> H(e, U1(e, b))
28.57/10.15	   A^2 -> H(e, U1(c, d))
28.57/10.15	   A^2 -> H(e, U1(d, c))
28.57/10.15	   A^2 -> H(e, U1(b, e))
28.57/10.15	   A^2 -> H(e, U1(b, k))
28.57/10.15	   A^2 -> H(e, U1(e, c))
28.57/10.15	   A^2 -> H(e, U1(c, e))
28.57/10.15	   A^2 -> H(e, U1(c, k))
28.57/10.15	   A^2 -> H(e, U1(e, e))
28.57/10.15	   A^2 -> H(e, U1(d, k))
28.57/10.15	   A^2 -> H(U1(e, e), b)
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, e), c)
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.15	   A^2 -> H(f(e), d)
28.57/10.15	   A^2 -> H(f(e), k)
28.57/10.15	   A^2 -> H(U1(k, k), b)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, k), c)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.15	   A^2 -> H(f(k), d)
28.57/10.15	   A^2 -> H(f(k), k)
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.15	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(k, d), b)
28.57/10.15	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.15	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.15	   A^2 -> H(U1(k, d), c)
28.57/10.15	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, k), b)
28.57/10.15	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, k), c)
28.57/10.15	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.15	   A^2 -> H(U1(d, k), e)
28.57/10.15	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(d, d), d)
28.57/10.15	   A^2 -> H(U1(d, d), k)
28.57/10.15	   A^2 -> H(U1(e, c), c)
28.57/10.15	   A^2 -> H(U1(c, c), e)
28.57/10.15	   A^2 -> H(U1(c, c), k)
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.15	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.15	   A^2 -> H(U1(e, e), e)
28.57/10.15	   A^2 -> H(d, U1(e, b))
28.57/10.15	   A^2 -> H(d, U1(k, b))
28.57/10.15	   A^2 -> H(d, U1(c, d))
28.57/10.15	   A^2 -> H(d, U1(d, c))
28.57/10.15	   A^2 -> H(d, U1(b, e))
28.57/10.15	   A^2 -> H(d, U1(b, k))
28.57/10.15	   A^2 -> H(d, U1(e, c))
28.57/10.15	   A^2 -> H(d, U1(k, c))
28.57/10.15	   A^2 -> H(d, U1(c, e))
28.57/10.15	   A^2 -> H(d, U1(c, k))
28.57/10.15	   A^2 -> H(d, U1(e, e))
28.57/10.15	   A^2 -> H(d, U1(k, k))
28.57/10.15	   A^2 -> H(d, U1(k, d))
28.57/10.15	   A^2 -> H(d, U1(d, k))
28.57/10.15	   A^2 -> H(a, b)
28.57/10.15	   A^2 -> H(a, U1(e, d))
28.57/10.15	   A^2 -> H(a, U1(d, e))
28.57/10.15	   A^2 -> H(a, c)
28.57/10.15	   A^2 -> H(a, U1(e, k))
28.57/10.15	   A^2 -> H(a, U1(k, e))
28.57/10.15	   A^2 -> H(a, e)
28.57/10.15	   A^2 -> H(a, U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, d), b)
28.57/10.15	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.15	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.15	   A^2 -> H(U1(e, d), c)
28.57/10.15	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.15	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.15	   A^2 -> H(U1(e, d), e)
28.57/10.15	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.15	   A^2 -> H(U1(e, a), d)
28.57/10.15	   A^2 -> H(U1(e, a), k)
28.57/10.15	   A^2 -> H(U1(k, a), d)
28.57/10.15	   A^2 -> H(U1(c, d), d)
28.57/10.15	   A^2 -> H(U1(c, d), k)
28.57/10.15	   A^2 -> H(U1(d, e), b)
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, e), c)
28.57/10.15	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.15	   A^2 -> H(U1(d, e), e)
28.57/10.15	   A^2 -> H(U1(k, e), U1(k, k))
28.57/10.15	
28.57/10.15	The TRS R consists of the following rules:
28.57/10.15	
28.57/10.15	   f(x) -> U1(x, x)
28.57/10.15	   U1(e, x) -> x
28.57/10.15	   a -> c
28.57/10.15	   a -> d
28.57/10.15	   b -> c
28.57/10.15	   b -> d
28.57/10.15	   d -> k
28.57/10.15	   c -> e
28.57/10.15	   c -> k
28.57/10.15	
28.57/10.15	Q is empty.
28.57/10.15	We have to consider all minimal (P,Q,R)-chains.
28.57/10.15	----------------------------------------
28.57/10.15	
28.57/10.15	(1949) DependencyGraphProof (EQUIVALENT)
28.57/10.15	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.15	----------------------------------------
28.57/10.15	
28.57/10.15	(1950)
28.57/10.15	Obligation:
28.57/10.15	Q DP problem:
28.57/10.15	The TRS P consists of the following rules:
28.57/10.15	
28.57/10.15	   A^2 -> H(f(c), f(c))
28.57/10.15	   H(x, x) -> G(x, x, f(k))
28.57/10.15	   G(d, x, x) -> A^2
28.57/10.15	   A^2 -> H(f(d), f(d))
28.57/10.15	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.15	   A^2 -> H(f(e), f(e))
28.57/10.15	   A^2 -> H(f(k), f(k))
28.57/10.15	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.15	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.15	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.15	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.15	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.15	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.15	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.15	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.15	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.15	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.15	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.15	   A^2 -> H(U1(d, e), U1(k, d))
28.57/10.15	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.15	   A^2 -> H(U1(d, c), b)
28.57/10.15	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.15	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.15	   A^2 -> H(U1(d, c), c)
28.57/10.15	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.15	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.15	   A^2 -> H(U1(d, c), e)
28.57/10.15	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, a), d)
28.57/10.16	   A^2 -> H(U1(d, a), k)
28.57/10.16	   A^2 -> H(U1(a, e), b)
28.57/10.16	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(a, e), c)
28.57/10.16	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(a, e), e)
28.57/10.16	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(a, k), b)
28.57/10.16	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(a, k), c)
28.57/10.16	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(a, k), e)
28.57/10.16	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(a, c), d)
28.57/10.16	   A^2 -> H(U1(a, c), k)
28.57/10.16	   A^2 -> H(U1(a, d), d)
28.57/10.16	   A^2 -> H(U1(a, d), k)
28.57/10.16	   A^2 -> H(k, U1(c, b))
28.57/10.16	   A^2 -> H(k, U1(d, b))
28.57/10.16	   A^2 -> H(k, U1(b, c))
28.57/10.16	   A^2 -> H(k, U1(b, d))
28.57/10.16	   A^2 -> H(k, U1(c, c))
28.57/10.16	   A^2 -> H(k, f(e))
28.57/10.16	   A^2 -> H(k, f(k))
28.57/10.16	   A^2 -> H(k, U1(d, d))
28.57/10.16	   A^2 -> H(c, U1(e, b))
28.57/10.16	   A^2 -> H(c, U1(k, b))
28.57/10.16	   A^2 -> H(c, U1(c, d))
28.57/10.16	   A^2 -> H(c, U1(d, c))
28.57/10.16	   A^2 -> H(c, U1(b, e))
28.57/10.16	   A^2 -> H(c, U1(b, k))
28.57/10.16	   A^2 -> H(c, U1(e, c))
28.57/10.16	   A^2 -> H(c, U1(k, c))
28.57/10.16	   A^2 -> H(c, U1(c, e))
28.57/10.16	   A^2 -> H(c, U1(c, k))
28.57/10.16	   A^2 -> H(c, U1(e, e))
28.57/10.16	   A^2 -> H(c, U1(k, k))
28.57/10.16	   A^2 -> H(c, U1(k, d))
28.57/10.16	   A^2 -> H(c, U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.16	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.16	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, c), b)
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, c), e)
28.57/10.16	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.16	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.16	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.16	   A^2 -> H(U1(k, c), b)
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, c), c)
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, e), b)
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(c, e), c)
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(c, e), e)
28.57/10.16	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, k), b)
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(c, k), c)
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(c, k), e)
28.57/10.16	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, c), d)
28.57/10.16	   A^2 -> H(e, U1(e, b))
28.57/10.16	   A^2 -> H(e, U1(c, d))
28.57/10.16	   A^2 -> H(e, U1(d, c))
28.57/10.16	   A^2 -> H(e, U1(b, e))
28.57/10.16	   A^2 -> H(e, U1(b, k))
28.57/10.16	   A^2 -> H(e, U1(e, c))
28.57/10.16	   A^2 -> H(e, U1(c, e))
28.57/10.16	   A^2 -> H(e, U1(c, k))
28.57/10.16	   A^2 -> H(e, U1(e, e))
28.57/10.16	   A^2 -> H(e, U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, e), b)
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, e), c)
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.16	   A^2 -> H(f(e), d)
28.57/10.16	   A^2 -> H(f(e), k)
28.57/10.16	   A^2 -> H(U1(k, k), b)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, k), c)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.16	   A^2 -> H(f(k), d)
28.57/10.16	   A^2 -> H(f(k), k)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(k, d), b)
28.57/10.16	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, d), c)
28.57/10.16	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, k), b)
28.57/10.16	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, k), c)
28.57/10.16	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, k), e)
28.57/10.16	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, d), d)
28.57/10.16	   A^2 -> H(U1(d, d), k)
28.57/10.16	   A^2 -> H(U1(e, c), c)
28.57/10.16	   A^2 -> H(U1(c, c), e)
28.57/10.16	   A^2 -> H(U1(c, c), k)
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(e, e), e)
28.57/10.16	   A^2 -> H(d, U1(e, b))
28.57/10.16	   A^2 -> H(d, U1(k, b))
28.57/10.16	   A^2 -> H(d, U1(c, d))
28.57/10.16	   A^2 -> H(d, U1(d, c))
28.57/10.16	   A^2 -> H(d, U1(b, e))
28.57/10.16	   A^2 -> H(d, U1(b, k))
28.57/10.16	   A^2 -> H(d, U1(e, c))
28.57/10.16	   A^2 -> H(d, U1(k, c))
28.57/10.16	   A^2 -> H(d, U1(c, e))
28.57/10.16	   A^2 -> H(d, U1(c, k))
28.57/10.16	   A^2 -> H(d, U1(e, e))
28.57/10.16	   A^2 -> H(d, U1(k, k))
28.57/10.16	   A^2 -> H(d, U1(k, d))
28.57/10.16	   A^2 -> H(d, U1(d, k))
28.57/10.16	   A^2 -> H(a, b)
28.57/10.16	   A^2 -> H(a, U1(e, d))
28.57/10.16	   A^2 -> H(a, U1(d, e))
28.57/10.16	   A^2 -> H(a, c)
28.57/10.16	   A^2 -> H(a, U1(e, k))
28.57/10.16	   A^2 -> H(a, U1(k, e))
28.57/10.16	   A^2 -> H(a, e)
28.57/10.16	   A^2 -> H(a, U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, d), b)
28.57/10.16	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, d), c)
28.57/10.16	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, d), e)
28.57/10.16	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, a), d)
28.57/10.16	   A^2 -> H(U1(e, a), k)
28.57/10.16	   A^2 -> H(U1(k, a), d)
28.57/10.16	   A^2 -> H(U1(c, d), d)
28.57/10.16	   A^2 -> H(U1(c, d), k)
28.57/10.16	   A^2 -> H(U1(d, e), b)
28.57/10.16	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, e), c)
28.57/10.16	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, e), e)
28.57/10.16	
28.57/10.16	The TRS R consists of the following rules:
28.57/10.16	
28.57/10.16	   f(x) -> U1(x, x)
28.57/10.16	   U1(e, x) -> x
28.57/10.16	   a -> c
28.57/10.16	   a -> d
28.57/10.16	   b -> c
28.57/10.16	   b -> d
28.57/10.16	   d -> k
28.57/10.16	   c -> e
28.57/10.16	   c -> k
28.57/10.16	
28.57/10.16	Q is empty.
28.57/10.16	We have to consider all minimal (P,Q,R)-chains.
28.57/10.16	----------------------------------------
28.57/10.16	
28.57/10.16	(1951) TransformationProof (EQUIVALENT)
28.57/10.16	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.16	
28.57/10.16	   (A^2 -> H(U1(k, e), U1(k, d)),A^2 -> H(U1(k, e), U1(k, d)))
28.57/10.16	   (A^2 -> H(U1(d, e), U1(k, k)),A^2 -> H(U1(d, e), U1(k, k)))
28.57/10.16	
28.57/10.16	
28.57/10.16	----------------------------------------
28.57/10.16	
28.57/10.16	(1952)
28.57/10.16	Obligation:
28.57/10.16	Q DP problem:
28.57/10.16	The TRS P consists of the following rules:
28.57/10.16	
28.57/10.16	   A^2 -> H(f(c), f(c))
28.57/10.16	   H(x, x) -> G(x, x, f(k))
28.57/10.16	   G(d, x, x) -> A^2
28.57/10.16	   A^2 -> H(f(d), f(d))
28.57/10.16	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.16	   A^2 -> H(f(e), f(e))
28.57/10.16	   A^2 -> H(f(k), f(k))
28.57/10.16	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.16	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.16	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.16	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.16	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.16	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(d, e), U1(d, k))
28.57/10.16	   A^2 -> H(U1(d, c), b)
28.57/10.16	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, c), c)
28.57/10.16	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, c), e)
28.57/10.16	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, a), d)
28.57/10.16	   A^2 -> H(U1(d, a), k)
28.57/10.16	   A^2 -> H(U1(a, e), b)
28.57/10.16	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(a, e), c)
28.57/10.16	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(a, e), e)
28.57/10.16	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(a, k), b)
28.57/10.16	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(a, k), c)
28.57/10.16	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(a, k), e)
28.57/10.16	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(a, c), d)
28.57/10.16	   A^2 -> H(U1(a, c), k)
28.57/10.16	   A^2 -> H(U1(a, d), d)
28.57/10.16	   A^2 -> H(U1(a, d), k)
28.57/10.16	   A^2 -> H(k, U1(c, b))
28.57/10.16	   A^2 -> H(k, U1(d, b))
28.57/10.16	   A^2 -> H(k, U1(b, c))
28.57/10.16	   A^2 -> H(k, U1(b, d))
28.57/10.16	   A^2 -> H(k, U1(c, c))
28.57/10.16	   A^2 -> H(k, f(e))
28.57/10.16	   A^2 -> H(k, f(k))
28.57/10.16	   A^2 -> H(k, U1(d, d))
28.57/10.16	   A^2 -> H(c, U1(e, b))
28.57/10.16	   A^2 -> H(c, U1(k, b))
28.57/10.16	   A^2 -> H(c, U1(c, d))
28.57/10.16	   A^2 -> H(c, U1(d, c))
28.57/10.16	   A^2 -> H(c, U1(b, e))
28.57/10.16	   A^2 -> H(c, U1(b, k))
28.57/10.16	   A^2 -> H(c, U1(e, c))
28.57/10.16	   A^2 -> H(c, U1(k, c))
28.57/10.16	   A^2 -> H(c, U1(c, e))
28.57/10.16	   A^2 -> H(c, U1(c, k))
28.57/10.16	   A^2 -> H(c, U1(e, e))
28.57/10.16	   A^2 -> H(c, U1(k, k))
28.57/10.16	   A^2 -> H(c, U1(k, d))
28.57/10.16	   A^2 -> H(c, U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.16	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.16	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, c), b)
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, c), e)
28.57/10.16	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.16	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.16	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.16	   A^2 -> H(U1(k, c), b)
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, c), c)
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, e), b)
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(c, e), c)
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(c, e), e)
28.57/10.16	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, k), b)
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(c, k), c)
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(c, k), e)
28.57/10.16	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, c), d)
28.57/10.16	   A^2 -> H(e, U1(e, b))
28.57/10.16	   A^2 -> H(e, U1(c, d))
28.57/10.16	   A^2 -> H(e, U1(d, c))
28.57/10.16	   A^2 -> H(e, U1(b, e))
28.57/10.16	   A^2 -> H(e, U1(b, k))
28.57/10.16	   A^2 -> H(e, U1(e, c))
28.57/10.16	   A^2 -> H(e, U1(c, e))
28.57/10.16	   A^2 -> H(e, U1(c, k))
28.57/10.16	   A^2 -> H(e, U1(e, e))
28.57/10.16	   A^2 -> H(e, U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, e), b)
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, e), c)
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.16	   A^2 -> H(f(e), d)
28.57/10.16	   A^2 -> H(f(e), k)
28.57/10.16	   A^2 -> H(U1(k, k), b)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, k), c)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.16	   A^2 -> H(f(k), d)
28.57/10.16	   A^2 -> H(f(k), k)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(k, d), b)
28.57/10.16	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, d), c)
28.57/10.16	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, k), b)
28.57/10.16	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, k), c)
28.57/10.16	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, k), e)
28.57/10.16	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, d), d)
28.57/10.16	   A^2 -> H(U1(d, d), k)
28.57/10.16	   A^2 -> H(U1(e, c), c)
28.57/10.16	   A^2 -> H(U1(c, c), e)
28.57/10.16	   A^2 -> H(U1(c, c), k)
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(e, e), e)
28.57/10.16	   A^2 -> H(d, U1(e, b))
28.57/10.16	   A^2 -> H(d, U1(k, b))
28.57/10.16	   A^2 -> H(d, U1(c, d))
28.57/10.16	   A^2 -> H(d, U1(d, c))
28.57/10.16	   A^2 -> H(d, U1(b, e))
28.57/10.16	   A^2 -> H(d, U1(b, k))
28.57/10.16	   A^2 -> H(d, U1(e, c))
28.57/10.16	   A^2 -> H(d, U1(k, c))
28.57/10.16	   A^2 -> H(d, U1(c, e))
28.57/10.16	   A^2 -> H(d, U1(c, k))
28.57/10.16	   A^2 -> H(d, U1(e, e))
28.57/10.16	   A^2 -> H(d, U1(k, k))
28.57/10.16	   A^2 -> H(d, U1(k, d))
28.57/10.16	   A^2 -> H(d, U1(d, k))
28.57/10.16	   A^2 -> H(a, b)
28.57/10.16	   A^2 -> H(a, U1(e, d))
28.57/10.16	   A^2 -> H(a, U1(d, e))
28.57/10.16	   A^2 -> H(a, c)
28.57/10.16	   A^2 -> H(a, U1(e, k))
28.57/10.16	   A^2 -> H(a, U1(k, e))
28.57/10.16	   A^2 -> H(a, e)
28.57/10.16	   A^2 -> H(a, U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, d), b)
28.57/10.16	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, d), c)
28.57/10.16	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, d), e)
28.57/10.16	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, a), d)
28.57/10.16	   A^2 -> H(U1(e, a), k)
28.57/10.16	   A^2 -> H(U1(k, a), d)
28.57/10.16	   A^2 -> H(U1(c, d), d)
28.57/10.16	   A^2 -> H(U1(c, d), k)
28.57/10.16	   A^2 -> H(U1(d, e), b)
28.57/10.16	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, e), c)
28.57/10.16	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, e), e)
28.57/10.16	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.16	
28.57/10.16	The TRS R consists of the following rules:
28.57/10.16	
28.57/10.16	   f(x) -> U1(x, x)
28.57/10.16	   U1(e, x) -> x
28.57/10.16	   a -> c
28.57/10.16	   a -> d
28.57/10.16	   b -> c
28.57/10.16	   b -> d
28.57/10.16	   d -> k
28.57/10.16	   c -> e
28.57/10.16	   c -> k
28.57/10.16	
28.57/10.16	Q is empty.
28.57/10.16	We have to consider all minimal (P,Q,R)-chains.
28.57/10.16	----------------------------------------
28.57/10.16	
28.57/10.16	(1953) TransformationProof (EQUIVALENT)
28.57/10.16	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.16	
28.57/10.16	   (A^2 -> H(U1(k, e), U1(d, k)),A^2 -> H(U1(k, e), U1(d, k)))
28.57/10.16	   (A^2 -> H(U1(d, e), U1(k, k)),A^2 -> H(U1(d, e), U1(k, k)))
28.57/10.16	
28.57/10.16	
28.57/10.16	----------------------------------------
28.57/10.16	
28.57/10.16	(1954)
28.57/10.16	Obligation:
28.57/10.16	Q DP problem:
28.57/10.16	The TRS P consists of the following rules:
28.57/10.16	
28.57/10.16	   A^2 -> H(f(c), f(c))
28.57/10.16	   H(x, x) -> G(x, x, f(k))
28.57/10.16	   G(d, x, x) -> A^2
28.57/10.16	   A^2 -> H(f(d), f(d))
28.57/10.16	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.16	   A^2 -> H(f(e), f(e))
28.57/10.16	   A^2 -> H(f(k), f(k))
28.57/10.16	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.16	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.16	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.16	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.16	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.16	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(d, c), b)
28.57/10.16	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, c), c)
28.57/10.16	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, c), e)
28.57/10.16	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, a), d)
28.57/10.16	   A^2 -> H(U1(d, a), k)
28.57/10.16	   A^2 -> H(U1(a, e), b)
28.57/10.16	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(a, e), c)
28.57/10.16	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(a, e), e)
28.57/10.16	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(a, k), b)
28.57/10.16	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(a, k), c)
28.57/10.16	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(a, k), e)
28.57/10.16	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(a, c), d)
28.57/10.16	   A^2 -> H(U1(a, c), k)
28.57/10.16	   A^2 -> H(U1(a, d), d)
28.57/10.16	   A^2 -> H(U1(a, d), k)
28.57/10.16	   A^2 -> H(k, U1(c, b))
28.57/10.16	   A^2 -> H(k, U1(d, b))
28.57/10.16	   A^2 -> H(k, U1(b, c))
28.57/10.16	   A^2 -> H(k, U1(b, d))
28.57/10.16	   A^2 -> H(k, U1(c, c))
28.57/10.16	   A^2 -> H(k, f(e))
28.57/10.16	   A^2 -> H(k, f(k))
28.57/10.16	   A^2 -> H(k, U1(d, d))
28.57/10.16	   A^2 -> H(c, U1(e, b))
28.57/10.16	   A^2 -> H(c, U1(k, b))
28.57/10.16	   A^2 -> H(c, U1(c, d))
28.57/10.16	   A^2 -> H(c, U1(d, c))
28.57/10.16	   A^2 -> H(c, U1(b, e))
28.57/10.16	   A^2 -> H(c, U1(b, k))
28.57/10.16	   A^2 -> H(c, U1(e, c))
28.57/10.16	   A^2 -> H(c, U1(k, c))
28.57/10.16	   A^2 -> H(c, U1(c, e))
28.57/10.16	   A^2 -> H(c, U1(c, k))
28.57/10.16	   A^2 -> H(c, U1(e, e))
28.57/10.16	   A^2 -> H(c, U1(k, k))
28.57/10.16	   A^2 -> H(c, U1(k, d))
28.57/10.16	   A^2 -> H(c, U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.16	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.16	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, c), b)
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, c), e)
28.57/10.16	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.16	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.16	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.16	   A^2 -> H(U1(k, c), b)
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, c), c)
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, e), b)
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(c, e), c)
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(c, e), e)
28.57/10.16	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, k), b)
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(c, k), c)
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(c, k), e)
28.57/10.16	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, c), d)
28.57/10.16	   A^2 -> H(e, U1(e, b))
28.57/10.16	   A^2 -> H(e, U1(c, d))
28.57/10.16	   A^2 -> H(e, U1(d, c))
28.57/10.16	   A^2 -> H(e, U1(b, e))
28.57/10.16	   A^2 -> H(e, U1(b, k))
28.57/10.16	   A^2 -> H(e, U1(e, c))
28.57/10.16	   A^2 -> H(e, U1(c, e))
28.57/10.16	   A^2 -> H(e, U1(c, k))
28.57/10.16	   A^2 -> H(e, U1(e, e))
28.57/10.16	   A^2 -> H(e, U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, e), b)
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, e), c)
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.16	   A^2 -> H(f(e), d)
28.57/10.16	   A^2 -> H(f(e), k)
28.57/10.16	   A^2 -> H(U1(k, k), b)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, k), c)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.16	   A^2 -> H(f(k), d)
28.57/10.16	   A^2 -> H(f(k), k)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(k, d), b)
28.57/10.16	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, d), c)
28.57/10.16	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, k), b)
28.57/10.16	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, k), c)
28.57/10.16	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, k), e)
28.57/10.16	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, d), d)
28.57/10.16	   A^2 -> H(U1(d, d), k)
28.57/10.16	   A^2 -> H(U1(e, c), c)
28.57/10.16	   A^2 -> H(U1(c, c), e)
28.57/10.16	   A^2 -> H(U1(c, c), k)
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(e, e), e)
28.57/10.16	   A^2 -> H(d, U1(e, b))
28.57/10.16	   A^2 -> H(d, U1(k, b))
28.57/10.16	   A^2 -> H(d, U1(c, d))
28.57/10.16	   A^2 -> H(d, U1(d, c))
28.57/10.16	   A^2 -> H(d, U1(b, e))
28.57/10.16	   A^2 -> H(d, U1(b, k))
28.57/10.16	   A^2 -> H(d, U1(e, c))
28.57/10.16	   A^2 -> H(d, U1(k, c))
28.57/10.16	   A^2 -> H(d, U1(c, e))
28.57/10.16	   A^2 -> H(d, U1(c, k))
28.57/10.16	   A^2 -> H(d, U1(e, e))
28.57/10.16	   A^2 -> H(d, U1(k, k))
28.57/10.16	   A^2 -> H(d, U1(k, d))
28.57/10.16	   A^2 -> H(d, U1(d, k))
28.57/10.16	   A^2 -> H(a, b)
28.57/10.16	   A^2 -> H(a, U1(e, d))
28.57/10.16	   A^2 -> H(a, U1(d, e))
28.57/10.16	   A^2 -> H(a, c)
28.57/10.16	   A^2 -> H(a, U1(e, k))
28.57/10.16	   A^2 -> H(a, U1(k, e))
28.57/10.16	   A^2 -> H(a, e)
28.57/10.16	   A^2 -> H(a, U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, d), b)
28.57/10.16	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, d), c)
28.57/10.16	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, d), e)
28.57/10.16	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, a), d)
28.57/10.16	   A^2 -> H(U1(e, a), k)
28.57/10.16	   A^2 -> H(U1(k, a), d)
28.57/10.16	   A^2 -> H(U1(c, d), d)
28.57/10.16	   A^2 -> H(U1(c, d), k)
28.57/10.16	   A^2 -> H(U1(d, e), b)
28.57/10.16	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, e), c)
28.57/10.16	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, e), e)
28.57/10.16	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.16	
28.57/10.16	The TRS R consists of the following rules:
28.57/10.16	
28.57/10.16	   f(x) -> U1(x, x)
28.57/10.16	   U1(e, x) -> x
28.57/10.16	   a -> c
28.57/10.16	   a -> d
28.57/10.16	   b -> c
28.57/10.16	   b -> d
28.57/10.16	   d -> k
28.57/10.16	   c -> e
28.57/10.16	   c -> k
28.57/10.16	
28.57/10.16	Q is empty.
28.57/10.16	We have to consider all minimal (P,Q,R)-chains.
28.57/10.16	----------------------------------------
28.57/10.16	
28.57/10.16	(1955) TransformationProof (EQUIVALENT)
28.57/10.16	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), b) at position [] we obtained the following new rules [LPAR04]:
28.57/10.16	
28.57/10.16	   (A^2 -> H(U1(k, c), b),A^2 -> H(U1(k, c), b))
28.57/10.16	   (A^2 -> H(U1(d, e), b),A^2 -> H(U1(d, e), b))
28.57/10.16	   (A^2 -> H(U1(d, k), b),A^2 -> H(U1(d, k), b))
28.57/10.16	   (A^2 -> H(U1(d, c), c),A^2 -> H(U1(d, c), c))
28.57/10.16	   (A^2 -> H(U1(d, c), d),A^2 -> H(U1(d, c), d))
28.57/10.16	
28.57/10.16	
28.57/10.16	----------------------------------------
28.57/10.16	
28.57/10.16	(1956)
28.57/10.16	Obligation:
28.57/10.16	Q DP problem:
28.57/10.16	The TRS P consists of the following rules:
28.57/10.16	
28.57/10.16	   A^2 -> H(f(c), f(c))
28.57/10.16	   H(x, x) -> G(x, x, f(k))
28.57/10.16	   G(d, x, x) -> A^2
28.57/10.16	   A^2 -> H(f(d), f(d))
28.57/10.16	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.16	   A^2 -> H(f(e), f(e))
28.57/10.16	   A^2 -> H(f(k), f(k))
28.57/10.16	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.16	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.16	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.16	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.16	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.16	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(d, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, c), c)
28.57/10.16	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, c), e)
28.57/10.16	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, a), d)
28.57/10.16	   A^2 -> H(U1(d, a), k)
28.57/10.16	   A^2 -> H(U1(a, e), b)
28.57/10.16	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(a, e), c)
28.57/10.16	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(a, e), e)
28.57/10.16	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(a, k), b)
28.57/10.16	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(a, k), c)
28.57/10.16	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(a, k), e)
28.57/10.16	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(a, c), d)
28.57/10.16	   A^2 -> H(U1(a, c), k)
28.57/10.16	   A^2 -> H(U1(a, d), d)
28.57/10.16	   A^2 -> H(U1(a, d), k)
28.57/10.16	   A^2 -> H(k, U1(c, b))
28.57/10.16	   A^2 -> H(k, U1(d, b))
28.57/10.16	   A^2 -> H(k, U1(b, c))
28.57/10.16	   A^2 -> H(k, U1(b, d))
28.57/10.16	   A^2 -> H(k, U1(c, c))
28.57/10.16	   A^2 -> H(k, f(e))
28.57/10.16	   A^2 -> H(k, f(k))
28.57/10.16	   A^2 -> H(k, U1(d, d))
28.57/10.16	   A^2 -> H(c, U1(e, b))
28.57/10.16	   A^2 -> H(c, U1(k, b))
28.57/10.16	   A^2 -> H(c, U1(c, d))
28.57/10.16	   A^2 -> H(c, U1(d, c))
28.57/10.16	   A^2 -> H(c, U1(b, e))
28.57/10.16	   A^2 -> H(c, U1(b, k))
28.57/10.16	   A^2 -> H(c, U1(e, c))
28.57/10.16	   A^2 -> H(c, U1(k, c))
28.57/10.16	   A^2 -> H(c, U1(c, e))
28.57/10.16	   A^2 -> H(c, U1(c, k))
28.57/10.16	   A^2 -> H(c, U1(e, e))
28.57/10.16	   A^2 -> H(c, U1(k, k))
28.57/10.16	   A^2 -> H(c, U1(k, d))
28.57/10.16	   A^2 -> H(c, U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.16	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.16	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, c), b)
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, c), e)
28.57/10.16	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.16	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.16	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.16	   A^2 -> H(U1(k, c), b)
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, c), c)
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, e), b)
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(c, e), c)
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(c, e), e)
28.57/10.16	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, k), b)
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(c, k), c)
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(c, k), e)
28.57/10.16	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, c), d)
28.57/10.16	   A^2 -> H(e, U1(e, b))
28.57/10.16	   A^2 -> H(e, U1(c, d))
28.57/10.16	   A^2 -> H(e, U1(d, c))
28.57/10.16	   A^2 -> H(e, U1(b, e))
28.57/10.16	   A^2 -> H(e, U1(b, k))
28.57/10.16	   A^2 -> H(e, U1(e, c))
28.57/10.16	   A^2 -> H(e, U1(c, e))
28.57/10.16	   A^2 -> H(e, U1(c, k))
28.57/10.16	   A^2 -> H(e, U1(e, e))
28.57/10.16	   A^2 -> H(e, U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, e), b)
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, e), c)
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.16	   A^2 -> H(f(e), d)
28.57/10.16	   A^2 -> H(f(e), k)
28.57/10.16	   A^2 -> H(U1(k, k), b)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, k), c)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.16	   A^2 -> H(f(k), d)
28.57/10.16	   A^2 -> H(f(k), k)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(k, d), b)
28.57/10.16	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, d), c)
28.57/10.16	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, k), b)
28.57/10.16	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, k), c)
28.57/10.16	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, k), e)
28.57/10.16	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, d), d)
28.57/10.16	   A^2 -> H(U1(d, d), k)
28.57/10.16	   A^2 -> H(U1(e, c), c)
28.57/10.16	   A^2 -> H(U1(c, c), e)
28.57/10.16	   A^2 -> H(U1(c, c), k)
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(e, e), e)
28.57/10.16	   A^2 -> H(d, U1(e, b))
28.57/10.16	   A^2 -> H(d, U1(k, b))
28.57/10.16	   A^2 -> H(d, U1(c, d))
28.57/10.16	   A^2 -> H(d, U1(d, c))
28.57/10.16	   A^2 -> H(d, U1(b, e))
28.57/10.16	   A^2 -> H(d, U1(b, k))
28.57/10.16	   A^2 -> H(d, U1(e, c))
28.57/10.16	   A^2 -> H(d, U1(k, c))
28.57/10.16	   A^2 -> H(d, U1(c, e))
28.57/10.16	   A^2 -> H(d, U1(c, k))
28.57/10.16	   A^2 -> H(d, U1(e, e))
28.57/10.16	   A^2 -> H(d, U1(k, k))
28.57/10.16	   A^2 -> H(d, U1(k, d))
28.57/10.16	   A^2 -> H(d, U1(d, k))
28.57/10.16	   A^2 -> H(a, b)
28.57/10.16	   A^2 -> H(a, U1(e, d))
28.57/10.16	   A^2 -> H(a, U1(d, e))
28.57/10.16	   A^2 -> H(a, c)
28.57/10.16	   A^2 -> H(a, U1(e, k))
28.57/10.16	   A^2 -> H(a, U1(k, e))
28.57/10.16	   A^2 -> H(a, e)
28.57/10.16	   A^2 -> H(a, U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, d), b)
28.57/10.16	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, d), c)
28.57/10.16	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, d), e)
28.57/10.16	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, a), d)
28.57/10.16	   A^2 -> H(U1(e, a), k)
28.57/10.16	   A^2 -> H(U1(k, a), d)
28.57/10.16	   A^2 -> H(U1(c, d), d)
28.57/10.16	   A^2 -> H(U1(c, d), k)
28.57/10.16	   A^2 -> H(U1(d, e), b)
28.57/10.16	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, e), c)
28.57/10.16	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, e), e)
28.57/10.16	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, c), d)
28.57/10.16	
28.57/10.16	The TRS R consists of the following rules:
28.57/10.16	
28.57/10.16	   f(x) -> U1(x, x)
28.57/10.16	   U1(e, x) -> x
28.57/10.16	   a -> c
28.57/10.16	   a -> d
28.57/10.16	   b -> c
28.57/10.16	   b -> d
28.57/10.16	   d -> k
28.57/10.16	   c -> e
28.57/10.16	   c -> k
28.57/10.16	
28.57/10.16	Q is empty.
28.57/10.16	We have to consider all minimal (P,Q,R)-chains.
28.57/10.16	----------------------------------------
28.57/10.16	
28.57/10.16	(1957) TransformationProof (EQUIVALENT)
28.57/10.16	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.16	
28.57/10.16	   (A^2 -> H(U1(k, c), U1(e, d)),A^2 -> H(U1(k, c), U1(e, d)))
28.57/10.16	   (A^2 -> H(U1(d, e), U1(e, d)),A^2 -> H(U1(d, e), U1(e, d)))
28.57/10.16	   (A^2 -> H(U1(d, k), U1(e, d)),A^2 -> H(U1(d, k), U1(e, d)))
28.57/10.16	   (A^2 -> H(U1(d, c), d),A^2 -> H(U1(d, c), d))
28.57/10.16	   (A^2 -> H(U1(d, c), U1(e, k)),A^2 -> H(U1(d, c), U1(e, k)))
28.57/10.16	
28.57/10.16	
28.57/10.16	----------------------------------------
28.57/10.16	
28.57/10.16	(1958)
28.57/10.16	Obligation:
28.57/10.16	Q DP problem:
28.57/10.16	The TRS P consists of the following rules:
28.57/10.16	
28.57/10.16	   A^2 -> H(f(c), f(c))
28.57/10.16	   H(x, x) -> G(x, x, f(k))
28.57/10.16	   G(d, x, x) -> A^2
28.57/10.16	   A^2 -> H(f(d), f(d))
28.57/10.16	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.16	   A^2 -> H(f(e), f(e))
28.57/10.16	   A^2 -> H(f(k), f(k))
28.57/10.16	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.16	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.16	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.16	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.16	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.16	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(d, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, c), c)
28.57/10.16	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, c), e)
28.57/10.16	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, a), d)
28.57/10.16	   A^2 -> H(U1(d, a), k)
28.57/10.16	   A^2 -> H(U1(a, e), b)
28.57/10.16	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(a, e), c)
28.57/10.16	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(a, e), e)
28.57/10.16	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(a, k), b)
28.57/10.16	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(a, k), c)
28.57/10.16	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(a, k), e)
28.57/10.16	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(a, c), d)
28.57/10.16	   A^2 -> H(U1(a, c), k)
28.57/10.16	   A^2 -> H(U1(a, d), d)
28.57/10.16	   A^2 -> H(U1(a, d), k)
28.57/10.16	   A^2 -> H(k, U1(c, b))
28.57/10.16	   A^2 -> H(k, U1(d, b))
28.57/10.16	   A^2 -> H(k, U1(b, c))
28.57/10.16	   A^2 -> H(k, U1(b, d))
28.57/10.16	   A^2 -> H(k, U1(c, c))
28.57/10.16	   A^2 -> H(k, f(e))
28.57/10.16	   A^2 -> H(k, f(k))
28.57/10.16	   A^2 -> H(k, U1(d, d))
28.57/10.16	   A^2 -> H(c, U1(e, b))
28.57/10.16	   A^2 -> H(c, U1(k, b))
28.57/10.16	   A^2 -> H(c, U1(c, d))
28.57/10.16	   A^2 -> H(c, U1(d, c))
28.57/10.16	   A^2 -> H(c, U1(b, e))
28.57/10.16	   A^2 -> H(c, U1(b, k))
28.57/10.16	   A^2 -> H(c, U1(e, c))
28.57/10.16	   A^2 -> H(c, U1(k, c))
28.57/10.16	   A^2 -> H(c, U1(c, e))
28.57/10.16	   A^2 -> H(c, U1(c, k))
28.57/10.16	   A^2 -> H(c, U1(e, e))
28.57/10.16	   A^2 -> H(c, U1(k, k))
28.57/10.16	   A^2 -> H(c, U1(k, d))
28.57/10.16	   A^2 -> H(c, U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.16	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.16	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, c), b)
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, c), e)
28.57/10.16	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.16	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.16	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.16	   A^2 -> H(U1(k, c), b)
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, c), c)
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, e), b)
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(c, e), c)
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(c, e), e)
28.57/10.16	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, k), b)
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(c, k), c)
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(c, k), e)
28.57/10.16	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, c), d)
28.57/10.16	   A^2 -> H(e, U1(e, b))
28.57/10.16	   A^2 -> H(e, U1(c, d))
28.57/10.16	   A^2 -> H(e, U1(d, c))
28.57/10.16	   A^2 -> H(e, U1(b, e))
28.57/10.16	   A^2 -> H(e, U1(b, k))
28.57/10.16	   A^2 -> H(e, U1(e, c))
28.57/10.16	   A^2 -> H(e, U1(c, e))
28.57/10.16	   A^2 -> H(e, U1(c, k))
28.57/10.16	   A^2 -> H(e, U1(e, e))
28.57/10.16	   A^2 -> H(e, U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, e), b)
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, e), c)
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.16	   A^2 -> H(f(e), d)
28.57/10.16	   A^2 -> H(f(e), k)
28.57/10.16	   A^2 -> H(U1(k, k), b)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, k), c)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.16	   A^2 -> H(f(k), d)
28.57/10.16	   A^2 -> H(f(k), k)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(k, d), b)
28.57/10.16	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, d), c)
28.57/10.16	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, k), b)
28.57/10.16	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, k), c)
28.57/10.16	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, k), e)
28.57/10.16	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, d), d)
28.57/10.16	   A^2 -> H(U1(d, d), k)
28.57/10.16	   A^2 -> H(U1(e, c), c)
28.57/10.16	   A^2 -> H(U1(c, c), e)
28.57/10.16	   A^2 -> H(U1(c, c), k)
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(e, e), e)
28.57/10.16	   A^2 -> H(d, U1(e, b))
28.57/10.16	   A^2 -> H(d, U1(k, b))
28.57/10.16	   A^2 -> H(d, U1(c, d))
28.57/10.16	   A^2 -> H(d, U1(d, c))
28.57/10.16	   A^2 -> H(d, U1(b, e))
28.57/10.16	   A^2 -> H(d, U1(b, k))
28.57/10.16	   A^2 -> H(d, U1(e, c))
28.57/10.16	   A^2 -> H(d, U1(k, c))
28.57/10.16	   A^2 -> H(d, U1(c, e))
28.57/10.16	   A^2 -> H(d, U1(c, k))
28.57/10.16	   A^2 -> H(d, U1(e, e))
28.57/10.16	   A^2 -> H(d, U1(k, k))
28.57/10.16	   A^2 -> H(d, U1(k, d))
28.57/10.16	   A^2 -> H(d, U1(d, k))
28.57/10.16	   A^2 -> H(a, b)
28.57/10.16	   A^2 -> H(a, U1(e, d))
28.57/10.16	   A^2 -> H(a, U1(d, e))
28.57/10.16	   A^2 -> H(a, c)
28.57/10.16	   A^2 -> H(a, U1(e, k))
28.57/10.16	   A^2 -> H(a, U1(k, e))
28.57/10.16	   A^2 -> H(a, e)
28.57/10.16	   A^2 -> H(a, U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, d), b)
28.57/10.16	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, d), c)
28.57/10.16	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, d), e)
28.57/10.16	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, a), d)
28.57/10.16	   A^2 -> H(U1(e, a), k)
28.57/10.16	   A^2 -> H(U1(k, a), d)
28.57/10.16	   A^2 -> H(U1(c, d), d)
28.57/10.16	   A^2 -> H(U1(c, d), k)
28.57/10.16	   A^2 -> H(U1(d, e), b)
28.57/10.16	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, e), c)
28.57/10.16	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, e), e)
28.57/10.16	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, c), d)
28.57/10.16	
28.57/10.16	The TRS R consists of the following rules:
28.57/10.16	
28.57/10.16	   f(x) -> U1(x, x)
28.57/10.16	   U1(e, x) -> x
28.57/10.16	   a -> c
28.57/10.16	   a -> d
28.57/10.16	   b -> c
28.57/10.16	   b -> d
28.57/10.16	   d -> k
28.57/10.16	   c -> e
28.57/10.16	   c -> k
28.57/10.16	
28.57/10.16	Q is empty.
28.57/10.16	We have to consider all minimal (P,Q,R)-chains.
28.57/10.16	----------------------------------------
28.57/10.16	
28.57/10.16	(1959) TransformationProof (EQUIVALENT)
28.57/10.16	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.16	
28.57/10.16	   (A^2 -> H(U1(k, c), U1(d, e)),A^2 -> H(U1(k, c), U1(d, e)))
28.57/10.16	   (A^2 -> H(U1(d, e), U1(d, e)),A^2 -> H(U1(d, e), U1(d, e)))
28.57/10.16	   (A^2 -> H(U1(d, k), U1(d, e)),A^2 -> H(U1(d, k), U1(d, e)))
28.57/10.16	   (A^2 -> H(U1(d, c), U1(k, e)),A^2 -> H(U1(d, c), U1(k, e)))
28.57/10.16	
28.57/10.16	
28.57/10.16	----------------------------------------
28.57/10.16	
28.57/10.16	(1960)
28.57/10.16	Obligation:
28.57/10.16	Q DP problem:
28.57/10.16	The TRS P consists of the following rules:
28.57/10.16	
28.57/10.16	   A^2 -> H(f(c), f(c))
28.57/10.16	   H(x, x) -> G(x, x, f(k))
28.57/10.16	   G(d, x, x) -> A^2
28.57/10.16	   A^2 -> H(f(d), f(d))
28.57/10.16	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.16	   A^2 -> H(f(e), f(e))
28.57/10.16	   A^2 -> H(f(k), f(k))
28.57/10.16	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.16	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.16	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.16	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.16	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.16	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(d, c), c)
28.57/10.16	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, c), e)
28.57/10.16	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, a), d)
28.57/10.16	   A^2 -> H(U1(d, a), k)
28.57/10.16	   A^2 -> H(U1(a, e), b)
28.57/10.16	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(a, e), c)
28.57/10.16	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(a, e), e)
28.57/10.16	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(a, k), b)
28.57/10.16	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(a, k), c)
28.57/10.16	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(a, k), e)
28.57/10.16	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(a, c), d)
28.57/10.16	   A^2 -> H(U1(a, c), k)
28.57/10.16	   A^2 -> H(U1(a, d), d)
28.57/10.16	   A^2 -> H(U1(a, d), k)
28.57/10.16	   A^2 -> H(k, U1(c, b))
28.57/10.16	   A^2 -> H(k, U1(d, b))
28.57/10.16	   A^2 -> H(k, U1(b, c))
28.57/10.16	   A^2 -> H(k, U1(b, d))
28.57/10.16	   A^2 -> H(k, U1(c, c))
28.57/10.16	   A^2 -> H(k, f(e))
28.57/10.16	   A^2 -> H(k, f(k))
28.57/10.16	   A^2 -> H(k, U1(d, d))
28.57/10.16	   A^2 -> H(c, U1(e, b))
28.57/10.16	   A^2 -> H(c, U1(k, b))
28.57/10.16	   A^2 -> H(c, U1(c, d))
28.57/10.16	   A^2 -> H(c, U1(d, c))
28.57/10.16	   A^2 -> H(c, U1(b, e))
28.57/10.16	   A^2 -> H(c, U1(b, k))
28.57/10.16	   A^2 -> H(c, U1(e, c))
28.57/10.16	   A^2 -> H(c, U1(k, c))
28.57/10.16	   A^2 -> H(c, U1(c, e))
28.57/10.16	   A^2 -> H(c, U1(c, k))
28.57/10.16	   A^2 -> H(c, U1(e, e))
28.57/10.16	   A^2 -> H(c, U1(k, k))
28.57/10.16	   A^2 -> H(c, U1(k, d))
28.57/10.16	   A^2 -> H(c, U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.16	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.16	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, c), b)
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, c), e)
28.57/10.16	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.16	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.16	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.16	   A^2 -> H(U1(k, c), b)
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, c), c)
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, e), b)
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(c, e), c)
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(c, e), e)
28.57/10.16	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, k), b)
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(c, k), c)
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(c, k), e)
28.57/10.16	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, c), d)
28.57/10.16	   A^2 -> H(e, U1(e, b))
28.57/10.16	   A^2 -> H(e, U1(c, d))
28.57/10.16	   A^2 -> H(e, U1(d, c))
28.57/10.16	   A^2 -> H(e, U1(b, e))
28.57/10.16	   A^2 -> H(e, U1(b, k))
28.57/10.16	   A^2 -> H(e, U1(e, c))
28.57/10.16	   A^2 -> H(e, U1(c, e))
28.57/10.16	   A^2 -> H(e, U1(c, k))
28.57/10.16	   A^2 -> H(e, U1(e, e))
28.57/10.16	   A^2 -> H(e, U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, e), b)
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, e), c)
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.16	   A^2 -> H(f(e), d)
28.57/10.16	   A^2 -> H(f(e), k)
28.57/10.16	   A^2 -> H(U1(k, k), b)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, k), c)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.16	   A^2 -> H(f(k), d)
28.57/10.16	   A^2 -> H(f(k), k)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(k, d), b)
28.57/10.16	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, d), c)
28.57/10.16	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, k), b)
28.57/10.16	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, k), c)
28.57/10.16	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, k), e)
28.57/10.16	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, d), d)
28.57/10.16	   A^2 -> H(U1(d, d), k)
28.57/10.16	   A^2 -> H(U1(e, c), c)
28.57/10.16	   A^2 -> H(U1(c, c), e)
28.57/10.16	   A^2 -> H(U1(c, c), k)
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(e, e), e)
28.57/10.16	   A^2 -> H(d, U1(e, b))
28.57/10.16	   A^2 -> H(d, U1(k, b))
28.57/10.16	   A^2 -> H(d, U1(c, d))
28.57/10.16	   A^2 -> H(d, U1(d, c))
28.57/10.16	   A^2 -> H(d, U1(b, e))
28.57/10.16	   A^2 -> H(d, U1(b, k))
28.57/10.16	   A^2 -> H(d, U1(e, c))
28.57/10.16	   A^2 -> H(d, U1(k, c))
28.57/10.16	   A^2 -> H(d, U1(c, e))
28.57/10.16	   A^2 -> H(d, U1(c, k))
28.57/10.16	   A^2 -> H(d, U1(e, e))
28.57/10.16	   A^2 -> H(d, U1(k, k))
28.57/10.16	   A^2 -> H(d, U1(k, d))
28.57/10.16	   A^2 -> H(d, U1(d, k))
28.57/10.16	   A^2 -> H(a, b)
28.57/10.16	   A^2 -> H(a, U1(e, d))
28.57/10.16	   A^2 -> H(a, U1(d, e))
28.57/10.16	   A^2 -> H(a, c)
28.57/10.16	   A^2 -> H(a, U1(e, k))
28.57/10.16	   A^2 -> H(a, U1(k, e))
28.57/10.16	   A^2 -> H(a, e)
28.57/10.16	   A^2 -> H(a, U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, d), b)
28.57/10.16	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, d), c)
28.57/10.16	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, d), e)
28.57/10.16	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, a), d)
28.57/10.16	   A^2 -> H(U1(e, a), k)
28.57/10.16	   A^2 -> H(U1(k, a), d)
28.57/10.16	   A^2 -> H(U1(c, d), d)
28.57/10.16	   A^2 -> H(U1(c, d), k)
28.57/10.16	   A^2 -> H(U1(d, e), b)
28.57/10.16	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, e), c)
28.57/10.16	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, e), e)
28.57/10.16	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, c), d)
28.57/10.16	
28.57/10.16	The TRS R consists of the following rules:
28.57/10.16	
28.57/10.16	   f(x) -> U1(x, x)
28.57/10.16	   U1(e, x) -> x
28.57/10.16	   a -> c
28.57/10.16	   a -> d
28.57/10.16	   b -> c
28.57/10.16	   b -> d
28.57/10.16	   d -> k
28.57/10.16	   c -> e
28.57/10.16	   c -> k
28.57/10.16	
28.57/10.16	Q is empty.
28.57/10.16	We have to consider all minimal (P,Q,R)-chains.
28.57/10.16	----------------------------------------
28.57/10.16	
28.57/10.16	(1961) TransformationProof (EQUIVALENT)
28.57/10.16	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), c) at position [] we obtained the following new rules [LPAR04]:
28.57/10.16	
28.57/10.16	   (A^2 -> H(U1(k, c), c),A^2 -> H(U1(k, c), c))
28.57/10.16	   (A^2 -> H(U1(d, e), c),A^2 -> H(U1(d, e), c))
28.57/10.16	   (A^2 -> H(U1(d, k), c),A^2 -> H(U1(d, k), c))
28.57/10.16	   (A^2 -> H(U1(d, c), e),A^2 -> H(U1(d, c), e))
28.57/10.16	   (A^2 -> H(U1(d, c), k),A^2 -> H(U1(d, c), k))
28.57/10.16	
28.57/10.16	
28.57/10.16	----------------------------------------
28.57/10.16	
28.57/10.16	(1962)
28.57/10.16	Obligation:
28.57/10.16	Q DP problem:
28.57/10.16	The TRS P consists of the following rules:
28.57/10.16	
28.57/10.16	   A^2 -> H(f(c), f(c))
28.57/10.16	   H(x, x) -> G(x, x, f(k))
28.57/10.16	   G(d, x, x) -> A^2
28.57/10.16	   A^2 -> H(f(d), f(d))
28.57/10.16	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.16	   A^2 -> H(f(e), f(e))
28.57/10.16	   A^2 -> H(f(k), f(k))
28.57/10.16	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.16	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.16	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.16	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.16	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.16	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(d, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, c), e)
28.57/10.16	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, a), d)
28.57/10.16	   A^2 -> H(U1(d, a), k)
28.57/10.16	   A^2 -> H(U1(a, e), b)
28.57/10.16	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(a, e), c)
28.57/10.16	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(a, e), e)
28.57/10.16	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(a, k), b)
28.57/10.16	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(a, k), c)
28.57/10.16	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(a, k), e)
28.57/10.16	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(a, c), d)
28.57/10.16	   A^2 -> H(U1(a, c), k)
28.57/10.16	   A^2 -> H(U1(a, d), d)
28.57/10.16	   A^2 -> H(U1(a, d), k)
28.57/10.16	   A^2 -> H(k, U1(c, b))
28.57/10.16	   A^2 -> H(k, U1(d, b))
28.57/10.16	   A^2 -> H(k, U1(b, c))
28.57/10.16	   A^2 -> H(k, U1(b, d))
28.57/10.16	   A^2 -> H(k, U1(c, c))
28.57/10.16	   A^2 -> H(k, f(e))
28.57/10.16	   A^2 -> H(k, f(k))
28.57/10.16	   A^2 -> H(k, U1(d, d))
28.57/10.16	   A^2 -> H(c, U1(e, b))
28.57/10.16	   A^2 -> H(c, U1(k, b))
28.57/10.16	   A^2 -> H(c, U1(c, d))
28.57/10.16	   A^2 -> H(c, U1(d, c))
28.57/10.16	   A^2 -> H(c, U1(b, e))
28.57/10.16	   A^2 -> H(c, U1(b, k))
28.57/10.16	   A^2 -> H(c, U1(e, c))
28.57/10.16	   A^2 -> H(c, U1(k, c))
28.57/10.16	   A^2 -> H(c, U1(c, e))
28.57/10.16	   A^2 -> H(c, U1(c, k))
28.57/10.16	   A^2 -> H(c, U1(e, e))
28.57/10.16	   A^2 -> H(c, U1(k, k))
28.57/10.16	   A^2 -> H(c, U1(k, d))
28.57/10.16	   A^2 -> H(c, U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.16	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.16	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, c), b)
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, c), e)
28.57/10.16	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.16	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.16	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.16	   A^2 -> H(U1(k, c), b)
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, c), c)
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, e), b)
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(c, e), c)
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(c, e), e)
28.57/10.16	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, k), b)
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(c, k), c)
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(c, k), e)
28.57/10.16	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, c), d)
28.57/10.16	   A^2 -> H(e, U1(e, b))
28.57/10.16	   A^2 -> H(e, U1(c, d))
28.57/10.16	   A^2 -> H(e, U1(d, c))
28.57/10.16	   A^2 -> H(e, U1(b, e))
28.57/10.16	   A^2 -> H(e, U1(b, k))
28.57/10.16	   A^2 -> H(e, U1(e, c))
28.57/10.16	   A^2 -> H(e, U1(c, e))
28.57/10.16	   A^2 -> H(e, U1(c, k))
28.57/10.16	   A^2 -> H(e, U1(e, e))
28.57/10.16	   A^2 -> H(e, U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, e), b)
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, e), c)
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.16	   A^2 -> H(f(e), d)
28.57/10.16	   A^2 -> H(f(e), k)
28.57/10.16	   A^2 -> H(U1(k, k), b)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, k), c)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.16	   A^2 -> H(f(k), d)
28.57/10.16	   A^2 -> H(f(k), k)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(k, d), b)
28.57/10.16	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, d), c)
28.57/10.16	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, k), b)
28.57/10.16	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, k), c)
28.57/10.16	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, k), e)
28.57/10.16	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, d), d)
28.57/10.16	   A^2 -> H(U1(d, d), k)
28.57/10.16	   A^2 -> H(U1(e, c), c)
28.57/10.16	   A^2 -> H(U1(c, c), e)
28.57/10.16	   A^2 -> H(U1(c, c), k)
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(e, e), e)
28.57/10.16	   A^2 -> H(d, U1(e, b))
28.57/10.16	   A^2 -> H(d, U1(k, b))
28.57/10.16	   A^2 -> H(d, U1(c, d))
28.57/10.16	   A^2 -> H(d, U1(d, c))
28.57/10.16	   A^2 -> H(d, U1(b, e))
28.57/10.16	   A^2 -> H(d, U1(b, k))
28.57/10.16	   A^2 -> H(d, U1(e, c))
28.57/10.16	   A^2 -> H(d, U1(k, c))
28.57/10.16	   A^2 -> H(d, U1(c, e))
28.57/10.16	   A^2 -> H(d, U1(c, k))
28.57/10.16	   A^2 -> H(d, U1(e, e))
28.57/10.16	   A^2 -> H(d, U1(k, k))
28.57/10.16	   A^2 -> H(d, U1(k, d))
28.57/10.16	   A^2 -> H(d, U1(d, k))
28.57/10.16	   A^2 -> H(a, b)
28.57/10.16	   A^2 -> H(a, U1(e, d))
28.57/10.16	   A^2 -> H(a, U1(d, e))
28.57/10.16	   A^2 -> H(a, c)
28.57/10.16	   A^2 -> H(a, U1(e, k))
28.57/10.16	   A^2 -> H(a, U1(k, e))
28.57/10.16	   A^2 -> H(a, e)
28.57/10.16	   A^2 -> H(a, U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, d), b)
28.57/10.16	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, d), c)
28.57/10.16	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, d), e)
28.57/10.16	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, a), d)
28.57/10.16	   A^2 -> H(U1(e, a), k)
28.57/10.16	   A^2 -> H(U1(k, a), d)
28.57/10.16	   A^2 -> H(U1(c, d), d)
28.57/10.16	   A^2 -> H(U1(c, d), k)
28.57/10.16	   A^2 -> H(U1(d, e), b)
28.57/10.16	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, e), c)
28.57/10.16	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, e), e)
28.57/10.16	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, c), d)
28.57/10.16	   A^2 -> H(U1(d, c), k)
28.57/10.16	
28.57/10.16	The TRS R consists of the following rules:
28.57/10.16	
28.57/10.16	   f(x) -> U1(x, x)
28.57/10.16	   U1(e, x) -> x
28.57/10.16	   a -> c
28.57/10.16	   a -> d
28.57/10.16	   b -> c
28.57/10.16	   b -> d
28.57/10.16	   d -> k
28.57/10.16	   c -> e
28.57/10.16	   c -> k
28.57/10.16	
28.57/10.16	Q is empty.
28.57/10.16	We have to consider all minimal (P,Q,R)-chains.
28.57/10.16	----------------------------------------
28.57/10.16	
28.57/10.16	(1963) TransformationProof (EQUIVALENT)
28.57/10.16	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.16	
28.57/10.16	   (A^2 -> H(U1(k, c), U1(e, k)),A^2 -> H(U1(k, c), U1(e, k)))
28.57/10.16	   (A^2 -> H(U1(d, e), U1(e, k)),A^2 -> H(U1(d, e), U1(e, k)))
28.57/10.16	   (A^2 -> H(U1(d, k), U1(e, k)),A^2 -> H(U1(d, k), U1(e, k)))
28.57/10.16	   (A^2 -> H(U1(d, c), k),A^2 -> H(U1(d, c), k))
28.57/10.16	
28.57/10.16	
28.57/10.16	----------------------------------------
28.57/10.16	
28.57/10.16	(1964)
28.57/10.16	Obligation:
28.57/10.16	Q DP problem:
28.57/10.16	The TRS P consists of the following rules:
28.57/10.16	
28.57/10.16	   A^2 -> H(f(c), f(c))
28.57/10.16	   H(x, x) -> G(x, x, f(k))
28.57/10.16	   G(d, x, x) -> A^2
28.57/10.16	   A^2 -> H(f(d), f(d))
28.57/10.16	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.16	   A^2 -> H(f(e), f(e))
28.57/10.16	   A^2 -> H(f(k), f(k))
28.57/10.16	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.16	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.16	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.16	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.16	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.16	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(d, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, c), e)
28.57/10.16	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, a), d)
28.57/10.16	   A^2 -> H(U1(d, a), k)
28.57/10.16	   A^2 -> H(U1(a, e), b)
28.57/10.16	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(a, e), c)
28.57/10.16	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(a, e), e)
28.57/10.16	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(a, k), b)
28.57/10.16	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(a, k), c)
28.57/10.16	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(a, k), e)
28.57/10.16	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(a, c), d)
28.57/10.16	   A^2 -> H(U1(a, c), k)
28.57/10.16	   A^2 -> H(U1(a, d), d)
28.57/10.16	   A^2 -> H(U1(a, d), k)
28.57/10.16	   A^2 -> H(k, U1(c, b))
28.57/10.16	   A^2 -> H(k, U1(d, b))
28.57/10.16	   A^2 -> H(k, U1(b, c))
28.57/10.16	   A^2 -> H(k, U1(b, d))
28.57/10.16	   A^2 -> H(k, U1(c, c))
28.57/10.16	   A^2 -> H(k, f(e))
28.57/10.16	   A^2 -> H(k, f(k))
28.57/10.16	   A^2 -> H(k, U1(d, d))
28.57/10.16	   A^2 -> H(c, U1(e, b))
28.57/10.16	   A^2 -> H(c, U1(k, b))
28.57/10.16	   A^2 -> H(c, U1(c, d))
28.57/10.16	   A^2 -> H(c, U1(d, c))
28.57/10.16	   A^2 -> H(c, U1(b, e))
28.57/10.16	   A^2 -> H(c, U1(b, k))
28.57/10.16	   A^2 -> H(c, U1(e, c))
28.57/10.16	   A^2 -> H(c, U1(k, c))
28.57/10.16	   A^2 -> H(c, U1(c, e))
28.57/10.16	   A^2 -> H(c, U1(c, k))
28.57/10.16	   A^2 -> H(c, U1(e, e))
28.57/10.16	   A^2 -> H(c, U1(k, k))
28.57/10.16	   A^2 -> H(c, U1(k, d))
28.57/10.16	   A^2 -> H(c, U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.16	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.16	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, c), b)
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, c), e)
28.57/10.16	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.16	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.16	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.16	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.16	   A^2 -> H(U1(k, c), b)
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, c), c)
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.16	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, e), b)
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(c, e), c)
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(c, e), e)
28.57/10.16	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, k), b)
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(c, k), c)
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(c, k), e)
28.57/10.16	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(c, c), d)
28.57/10.16	   A^2 -> H(e, U1(e, b))
28.57/10.16	   A^2 -> H(e, U1(c, d))
28.57/10.16	   A^2 -> H(e, U1(d, c))
28.57/10.16	   A^2 -> H(e, U1(b, e))
28.57/10.16	   A^2 -> H(e, U1(b, k))
28.57/10.16	   A^2 -> H(e, U1(e, c))
28.57/10.16	   A^2 -> H(e, U1(c, e))
28.57/10.16	   A^2 -> H(e, U1(c, k))
28.57/10.16	   A^2 -> H(e, U1(e, e))
28.57/10.16	   A^2 -> H(e, U1(d, k))
28.57/10.16	   A^2 -> H(U1(e, e), b)
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, e), c)
28.57/10.16	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.16	   A^2 -> H(f(e), d)
28.57/10.16	   A^2 -> H(f(e), k)
28.57/10.16	   A^2 -> H(U1(k, k), b)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, k), c)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.16	   A^2 -> H(f(k), d)
28.57/10.16	   A^2 -> H(f(k), k)
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.16	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.16	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.16	   A^2 -> H(U1(k, d), b)
28.57/10.16	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.16	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.16	   A^2 -> H(U1(k, d), c)
28.57/10.16	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.16	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, k), b)
28.57/10.16	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, k), c)
28.57/10.16	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, k), e)
28.57/10.16	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, d), d)
28.57/10.16	   A^2 -> H(U1(d, d), k)
28.57/10.16	   A^2 -> H(U1(e, c), c)
28.57/10.16	   A^2 -> H(U1(c, c), e)
28.57/10.16	   A^2 -> H(U1(c, c), k)
28.57/10.16	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.16	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.16	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.16	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.16	   A^2 -> H(U1(e, e), e)
28.57/10.16	   A^2 -> H(d, U1(e, b))
28.57/10.16	   A^2 -> H(d, U1(k, b))
28.57/10.16	   A^2 -> H(d, U1(c, d))
28.57/10.16	   A^2 -> H(d, U1(d, c))
28.57/10.16	   A^2 -> H(d, U1(b, e))
28.57/10.16	   A^2 -> H(d, U1(b, k))
28.57/10.16	   A^2 -> H(d, U1(e, c))
28.57/10.16	   A^2 -> H(d, U1(k, c))
28.57/10.16	   A^2 -> H(d, U1(c, e))
28.57/10.16	   A^2 -> H(d, U1(c, k))
28.57/10.16	   A^2 -> H(d, U1(e, e))
28.57/10.16	   A^2 -> H(d, U1(k, k))
28.57/10.16	   A^2 -> H(d, U1(k, d))
28.57/10.16	   A^2 -> H(d, U1(d, k))
28.57/10.16	   A^2 -> H(a, b)
28.57/10.16	   A^2 -> H(a, U1(e, d))
28.57/10.16	   A^2 -> H(a, U1(d, e))
28.57/10.16	   A^2 -> H(a, c)
28.57/10.16	   A^2 -> H(a, U1(e, k))
28.57/10.16	   A^2 -> H(a, U1(k, e))
28.57/10.16	   A^2 -> H(a, e)
28.57/10.16	   A^2 -> H(a, U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, d), b)
28.57/10.16	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.16	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.16	   A^2 -> H(U1(e, d), c)
28.57/10.16	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.16	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.16	   A^2 -> H(U1(e, d), e)
28.57/10.16	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.16	   A^2 -> H(U1(e, a), d)
28.57/10.16	   A^2 -> H(U1(e, a), k)
28.57/10.16	   A^2 -> H(U1(k, a), d)
28.57/10.16	   A^2 -> H(U1(c, d), d)
28.57/10.16	   A^2 -> H(U1(c, d), k)
28.57/10.16	   A^2 -> H(U1(d, e), b)
28.57/10.16	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.16	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.16	   A^2 -> H(U1(d, e), c)
28.57/10.16	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.16	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.16	   A^2 -> H(U1(d, e), e)
28.57/10.16	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.16	   A^2 -> H(U1(d, c), d)
28.57/10.16	   A^2 -> H(U1(d, c), k)
28.57/10.16	
28.57/10.16	The TRS R consists of the following rules:
28.57/10.16	
28.57/10.16	   f(x) -> U1(x, x)
28.57/10.16	   U1(e, x) -> x
28.57/10.16	   a -> c
28.57/10.16	   a -> d
28.57/10.16	   b -> c
28.57/10.16	   b -> d
28.57/10.16	   d -> k
28.57/10.16	   c -> e
28.57/10.16	   c -> k
28.57/10.16	
28.57/10.16	Q is empty.
28.57/10.16	We have to consider all minimal (P,Q,R)-chains.
28.57/10.16	----------------------------------------
28.57/10.16	
28.57/10.16	(1965) TransformationProof (EQUIVALENT)
28.57/10.16	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.16	
28.57/10.16	   (A^2 -> H(U1(k, c), U1(k, e)),A^2 -> H(U1(k, c), U1(k, e)))
28.57/10.16	   (A^2 -> H(U1(d, e), U1(k, e)),A^2 -> H(U1(d, e), U1(k, e)))
28.57/10.16	   (A^2 -> H(U1(d, k), U1(k, e)),A^2 -> H(U1(d, k), U1(k, e)))
28.57/10.16	
28.57/10.16	
28.57/10.16	----------------------------------------
28.57/10.16	
28.57/10.16	(1966)
28.57/10.16	Obligation:
28.57/10.16	Q DP problem:
28.57/10.16	The TRS P consists of the following rules:
28.57/10.16	
28.57/10.16	   A^2 -> H(f(c), f(c))
28.57/10.16	   H(x, x) -> G(x, x, f(k))
28.57/10.16	   G(d, x, x) -> A^2
28.57/10.16	   A^2 -> H(f(d), f(d))
28.57/10.17	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.17	   A^2 -> H(f(e), f(e))
28.57/10.17	   A^2 -> H(f(k), f(k))
28.57/10.17	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.17	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.17	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.17	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.17	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.17	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(d, c), e)
28.57/10.17	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, a), d)
28.57/10.17	   A^2 -> H(U1(d, a), k)
28.57/10.17	   A^2 -> H(U1(a, e), b)
28.57/10.17	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(a, e), c)
28.57/10.17	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(a, e), e)
28.57/10.17	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(a, k), b)
28.57/10.17	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(a, k), c)
28.57/10.17	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(a, k), e)
28.57/10.17	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(a, c), d)
28.57/10.17	   A^2 -> H(U1(a, c), k)
28.57/10.17	   A^2 -> H(U1(a, d), d)
28.57/10.17	   A^2 -> H(U1(a, d), k)
28.57/10.17	   A^2 -> H(k, U1(c, b))
28.57/10.17	   A^2 -> H(k, U1(d, b))
28.57/10.17	   A^2 -> H(k, U1(b, c))
28.57/10.17	   A^2 -> H(k, U1(b, d))
28.57/10.17	   A^2 -> H(k, U1(c, c))
28.57/10.17	   A^2 -> H(k, f(e))
28.57/10.17	   A^2 -> H(k, f(k))
28.57/10.17	   A^2 -> H(k, U1(d, d))
28.57/10.17	   A^2 -> H(c, U1(e, b))
28.57/10.17	   A^2 -> H(c, U1(k, b))
28.57/10.17	   A^2 -> H(c, U1(c, d))
28.57/10.17	   A^2 -> H(c, U1(d, c))
28.57/10.17	   A^2 -> H(c, U1(b, e))
28.57/10.17	   A^2 -> H(c, U1(b, k))
28.57/10.17	   A^2 -> H(c, U1(e, c))
28.57/10.17	   A^2 -> H(c, U1(k, c))
28.57/10.17	   A^2 -> H(c, U1(c, e))
28.57/10.17	   A^2 -> H(c, U1(c, k))
28.57/10.17	   A^2 -> H(c, U1(e, e))
28.57/10.17	   A^2 -> H(c, U1(k, k))
28.57/10.17	   A^2 -> H(c, U1(k, d))
28.57/10.17	   A^2 -> H(c, U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.17	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.17	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, c), b)
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, c), e)
28.57/10.17	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.17	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.17	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.17	   A^2 -> H(U1(k, c), b)
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, c), c)
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, e), b)
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(c, e), c)
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(c, e), e)
28.57/10.17	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, k), b)
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(c, k), c)
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(c, k), e)
28.57/10.17	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, c), d)
28.57/10.17	   A^2 -> H(e, U1(e, b))
28.57/10.17	   A^2 -> H(e, U1(c, d))
28.57/10.17	   A^2 -> H(e, U1(d, c))
28.57/10.17	   A^2 -> H(e, U1(b, e))
28.57/10.17	   A^2 -> H(e, U1(b, k))
28.57/10.17	   A^2 -> H(e, U1(e, c))
28.57/10.17	   A^2 -> H(e, U1(c, e))
28.57/10.17	   A^2 -> H(e, U1(c, k))
28.57/10.17	   A^2 -> H(e, U1(e, e))
28.57/10.17	   A^2 -> H(e, U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, e), b)
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, e), c)
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.17	   A^2 -> H(f(e), d)
28.57/10.17	   A^2 -> H(f(e), k)
28.57/10.17	   A^2 -> H(U1(k, k), b)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, k), c)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.17	   A^2 -> H(f(k), d)
28.57/10.17	   A^2 -> H(f(k), k)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(k, d), b)
28.57/10.17	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, d), c)
28.57/10.17	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, k), b)
28.57/10.17	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(d, k), c)
28.57/10.17	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(d, k), e)
28.57/10.17	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, d), d)
28.57/10.17	   A^2 -> H(U1(d, d), k)
28.57/10.17	   A^2 -> H(U1(e, c), c)
28.57/10.17	   A^2 -> H(U1(c, c), e)
28.57/10.17	   A^2 -> H(U1(c, c), k)
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(e, e), e)
28.57/10.17	   A^2 -> H(d, U1(e, b))
28.57/10.17	   A^2 -> H(d, U1(k, b))
28.57/10.17	   A^2 -> H(d, U1(c, d))
28.57/10.17	   A^2 -> H(d, U1(d, c))
28.57/10.17	   A^2 -> H(d, U1(b, e))
28.57/10.17	   A^2 -> H(d, U1(b, k))
28.57/10.17	   A^2 -> H(d, U1(e, c))
28.57/10.17	   A^2 -> H(d, U1(k, c))
28.57/10.17	   A^2 -> H(d, U1(c, e))
28.57/10.17	   A^2 -> H(d, U1(c, k))
28.57/10.17	   A^2 -> H(d, U1(e, e))
28.57/10.17	   A^2 -> H(d, U1(k, k))
28.57/10.17	   A^2 -> H(d, U1(k, d))
28.57/10.17	   A^2 -> H(d, U1(d, k))
28.57/10.17	   A^2 -> H(a, b)
28.57/10.17	   A^2 -> H(a, U1(e, d))
28.57/10.17	   A^2 -> H(a, U1(d, e))
28.57/10.17	   A^2 -> H(a, c)
28.57/10.17	   A^2 -> H(a, U1(e, k))
28.57/10.17	   A^2 -> H(a, U1(k, e))
28.57/10.17	   A^2 -> H(a, e)
28.57/10.17	   A^2 -> H(a, U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, d), b)
28.57/10.17	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, d), c)
28.57/10.17	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, d), e)
28.57/10.17	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, a), d)
28.57/10.17	   A^2 -> H(U1(e, a), k)
28.57/10.17	   A^2 -> H(U1(k, a), d)
28.57/10.17	   A^2 -> H(U1(c, d), d)
28.57/10.17	   A^2 -> H(U1(c, d), k)
28.57/10.17	   A^2 -> H(U1(d, e), b)
28.57/10.17	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(d, e), c)
28.57/10.17	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(d, e), e)
28.57/10.17	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, c), d)
28.57/10.17	   A^2 -> H(U1(d, c), k)
28.57/10.17	
28.57/10.17	The TRS R consists of the following rules:
28.57/10.17	
28.57/10.17	   f(x) -> U1(x, x)
28.57/10.17	   U1(e, x) -> x
28.57/10.17	   a -> c
28.57/10.17	   a -> d
28.57/10.17	   b -> c
28.57/10.17	   b -> d
28.57/10.17	   d -> k
28.57/10.17	   c -> e
28.57/10.17	   c -> k
28.57/10.17	
28.57/10.17	Q is empty.
28.57/10.17	We have to consider all minimal (P,Q,R)-chains.
28.57/10.17	----------------------------------------
28.57/10.17	
28.57/10.17	(1967) TransformationProof (EQUIVALENT)
28.57/10.17	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), e) at position [] we obtained the following new rules [LPAR04]:
28.57/10.17	
28.57/10.17	   (A^2 -> H(U1(k, c), e),A^2 -> H(U1(k, c), e))
28.57/10.17	   (A^2 -> H(U1(d, e), e),A^2 -> H(U1(d, e), e))
28.57/10.17	   (A^2 -> H(U1(d, k), e),A^2 -> H(U1(d, k), e))
28.57/10.17	
28.57/10.17	
28.57/10.17	----------------------------------------
28.57/10.17	
28.57/10.17	(1968)
28.57/10.17	Obligation:
28.57/10.17	Q DP problem:
28.57/10.17	The TRS P consists of the following rules:
28.57/10.17	
28.57/10.17	   A^2 -> H(f(c), f(c))
28.57/10.17	   H(x, x) -> G(x, x, f(k))
28.57/10.17	   G(d, x, x) -> A^2
28.57/10.17	   A^2 -> H(f(d), f(d))
28.57/10.17	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.17	   A^2 -> H(f(e), f(e))
28.57/10.17	   A^2 -> H(f(k), f(k))
28.57/10.17	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.17	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.17	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.17	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.17	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.17	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, a), d)
28.57/10.17	   A^2 -> H(U1(d, a), k)
28.57/10.17	   A^2 -> H(U1(a, e), b)
28.57/10.17	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(a, e), c)
28.57/10.17	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(a, e), e)
28.57/10.17	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(a, k), b)
28.57/10.17	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(a, k), c)
28.57/10.17	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(a, k), e)
28.57/10.17	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(a, c), d)
28.57/10.17	   A^2 -> H(U1(a, c), k)
28.57/10.17	   A^2 -> H(U1(a, d), d)
28.57/10.17	   A^2 -> H(U1(a, d), k)
28.57/10.17	   A^2 -> H(k, U1(c, b))
28.57/10.17	   A^2 -> H(k, U1(d, b))
28.57/10.17	   A^2 -> H(k, U1(b, c))
28.57/10.17	   A^2 -> H(k, U1(b, d))
28.57/10.17	   A^2 -> H(k, U1(c, c))
28.57/10.17	   A^2 -> H(k, f(e))
28.57/10.17	   A^2 -> H(k, f(k))
28.57/10.17	   A^2 -> H(k, U1(d, d))
28.57/10.17	   A^2 -> H(c, U1(e, b))
28.57/10.17	   A^2 -> H(c, U1(k, b))
28.57/10.17	   A^2 -> H(c, U1(c, d))
28.57/10.17	   A^2 -> H(c, U1(d, c))
28.57/10.17	   A^2 -> H(c, U1(b, e))
28.57/10.17	   A^2 -> H(c, U1(b, k))
28.57/10.17	   A^2 -> H(c, U1(e, c))
28.57/10.17	   A^2 -> H(c, U1(k, c))
28.57/10.17	   A^2 -> H(c, U1(c, e))
28.57/10.17	   A^2 -> H(c, U1(c, k))
28.57/10.17	   A^2 -> H(c, U1(e, e))
28.57/10.17	   A^2 -> H(c, U1(k, k))
28.57/10.17	   A^2 -> H(c, U1(k, d))
28.57/10.17	   A^2 -> H(c, U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.17	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.17	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, c), b)
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, c), e)
28.57/10.17	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.17	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.17	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.17	   A^2 -> H(U1(k, c), b)
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, c), c)
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, e), b)
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(c, e), c)
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(c, e), e)
28.57/10.17	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, k), b)
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(c, k), c)
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(c, k), e)
28.57/10.17	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, c), d)
28.57/10.17	   A^2 -> H(e, U1(e, b))
28.57/10.17	   A^2 -> H(e, U1(c, d))
28.57/10.17	   A^2 -> H(e, U1(d, c))
28.57/10.17	   A^2 -> H(e, U1(b, e))
28.57/10.17	   A^2 -> H(e, U1(b, k))
28.57/10.17	   A^2 -> H(e, U1(e, c))
28.57/10.17	   A^2 -> H(e, U1(c, e))
28.57/10.17	   A^2 -> H(e, U1(c, k))
28.57/10.17	   A^2 -> H(e, U1(e, e))
28.57/10.17	   A^2 -> H(e, U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, e), b)
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, e), c)
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.17	   A^2 -> H(f(e), d)
28.57/10.17	   A^2 -> H(f(e), k)
28.57/10.17	   A^2 -> H(U1(k, k), b)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, k), c)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.17	   A^2 -> H(f(k), d)
28.57/10.17	   A^2 -> H(f(k), k)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(k, d), b)
28.57/10.17	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, d), c)
28.57/10.17	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, k), b)
28.57/10.17	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(d, k), c)
28.57/10.17	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(d, k), e)
28.57/10.17	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, d), d)
28.57/10.17	   A^2 -> H(U1(d, d), k)
28.57/10.17	   A^2 -> H(U1(e, c), c)
28.57/10.17	   A^2 -> H(U1(c, c), e)
28.57/10.17	   A^2 -> H(U1(c, c), k)
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(e, e), e)
28.57/10.17	   A^2 -> H(d, U1(e, b))
28.57/10.17	   A^2 -> H(d, U1(k, b))
28.57/10.17	   A^2 -> H(d, U1(c, d))
28.57/10.17	   A^2 -> H(d, U1(d, c))
28.57/10.17	   A^2 -> H(d, U1(b, e))
28.57/10.17	   A^2 -> H(d, U1(b, k))
28.57/10.17	   A^2 -> H(d, U1(e, c))
28.57/10.17	   A^2 -> H(d, U1(k, c))
28.57/10.17	   A^2 -> H(d, U1(c, e))
28.57/10.17	   A^2 -> H(d, U1(c, k))
28.57/10.17	   A^2 -> H(d, U1(e, e))
28.57/10.17	   A^2 -> H(d, U1(k, k))
28.57/10.17	   A^2 -> H(d, U1(k, d))
28.57/10.17	   A^2 -> H(d, U1(d, k))
28.57/10.17	   A^2 -> H(a, b)
28.57/10.17	   A^2 -> H(a, U1(e, d))
28.57/10.17	   A^2 -> H(a, U1(d, e))
28.57/10.17	   A^2 -> H(a, c)
28.57/10.17	   A^2 -> H(a, U1(e, k))
28.57/10.17	   A^2 -> H(a, U1(k, e))
28.57/10.17	   A^2 -> H(a, e)
28.57/10.17	   A^2 -> H(a, U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, d), b)
28.57/10.17	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, d), c)
28.57/10.17	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, d), e)
28.57/10.17	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, a), d)
28.57/10.17	   A^2 -> H(U1(e, a), k)
28.57/10.17	   A^2 -> H(U1(k, a), d)
28.57/10.17	   A^2 -> H(U1(c, d), d)
28.57/10.17	   A^2 -> H(U1(c, d), k)
28.57/10.17	   A^2 -> H(U1(d, e), b)
28.57/10.17	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(d, e), c)
28.57/10.17	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(d, e), e)
28.57/10.17	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, c), d)
28.57/10.17	   A^2 -> H(U1(d, c), k)
28.57/10.17	   A^2 -> H(U1(k, c), e)
28.57/10.17	
28.57/10.17	The TRS R consists of the following rules:
28.57/10.17	
28.57/10.17	   f(x) -> U1(x, x)
28.57/10.17	   U1(e, x) -> x
28.57/10.17	   a -> c
28.57/10.17	   a -> d
28.57/10.17	   b -> c
28.57/10.17	   b -> d
28.57/10.17	   d -> k
28.57/10.17	   c -> e
28.57/10.17	   c -> k
28.57/10.17	
28.57/10.17	Q is empty.
28.57/10.17	We have to consider all minimal (P,Q,R)-chains.
28.57/10.17	----------------------------------------
28.57/10.17	
28.57/10.17	(1969) DependencyGraphProof (EQUIVALENT)
28.57/10.17	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.17	----------------------------------------
28.57/10.17	
28.57/10.17	(1970)
28.57/10.17	Obligation:
28.57/10.17	Q DP problem:
28.57/10.17	The TRS P consists of the following rules:
28.57/10.17	
28.57/10.17	   H(x, x) -> G(x, x, f(k))
28.57/10.17	   G(d, x, x) -> A^2
28.57/10.17	   A^2 -> H(f(c), f(c))
28.57/10.17	   A^2 -> H(f(d), f(d))
28.57/10.17	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.17	   A^2 -> H(f(e), f(e))
28.57/10.17	   A^2 -> H(f(k), f(k))
28.57/10.17	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.17	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.17	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.17	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.17	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.17	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(d, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, a), d)
28.57/10.17	   A^2 -> H(U1(d, a), k)
28.57/10.17	   A^2 -> H(U1(a, e), b)
28.57/10.17	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(a, e), c)
28.57/10.17	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(a, e), e)
28.57/10.17	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(a, k), b)
28.57/10.17	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(a, k), c)
28.57/10.17	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(a, k), e)
28.57/10.17	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(a, c), d)
28.57/10.17	   A^2 -> H(U1(a, c), k)
28.57/10.17	   A^2 -> H(U1(a, d), d)
28.57/10.17	   A^2 -> H(U1(a, d), k)
28.57/10.17	   A^2 -> H(k, U1(c, b))
28.57/10.17	   A^2 -> H(k, U1(d, b))
28.57/10.17	   A^2 -> H(k, U1(b, c))
28.57/10.17	   A^2 -> H(k, U1(b, d))
28.57/10.17	   A^2 -> H(k, U1(c, c))
28.57/10.17	   A^2 -> H(k, f(e))
28.57/10.17	   A^2 -> H(k, f(k))
28.57/10.17	   A^2 -> H(k, U1(d, d))
28.57/10.17	   A^2 -> H(c, U1(e, b))
28.57/10.17	   A^2 -> H(c, U1(k, b))
28.57/10.17	   A^2 -> H(c, U1(c, d))
28.57/10.17	   A^2 -> H(c, U1(d, c))
28.57/10.17	   A^2 -> H(c, U1(b, e))
28.57/10.17	   A^2 -> H(c, U1(b, k))
28.57/10.17	   A^2 -> H(c, U1(e, c))
28.57/10.17	   A^2 -> H(c, U1(k, c))
28.57/10.17	   A^2 -> H(c, U1(c, e))
28.57/10.17	   A^2 -> H(c, U1(c, k))
28.57/10.17	   A^2 -> H(c, U1(e, e))
28.57/10.17	   A^2 -> H(c, U1(k, k))
28.57/10.17	   A^2 -> H(c, U1(k, d))
28.57/10.17	   A^2 -> H(c, U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.17	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.17	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, c), b)
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, c), e)
28.57/10.17	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.17	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.17	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.17	   A^2 -> H(U1(k, c), b)
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, c), c)
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, e), b)
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(c, e), c)
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(c, e), e)
28.57/10.17	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, k), b)
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(c, k), c)
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(c, k), e)
28.57/10.17	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, c), d)
28.57/10.17	   A^2 -> H(e, U1(e, b))
28.57/10.17	   A^2 -> H(e, U1(c, d))
28.57/10.17	   A^2 -> H(e, U1(d, c))
28.57/10.17	   A^2 -> H(e, U1(b, e))
28.57/10.17	   A^2 -> H(e, U1(b, k))
28.57/10.17	   A^2 -> H(e, U1(e, c))
28.57/10.17	   A^2 -> H(e, U1(c, e))
28.57/10.17	   A^2 -> H(e, U1(c, k))
28.57/10.17	   A^2 -> H(e, U1(e, e))
28.57/10.17	   A^2 -> H(e, U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, e), b)
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, e), c)
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.17	   A^2 -> H(f(e), d)
28.57/10.17	   A^2 -> H(f(e), k)
28.57/10.17	   A^2 -> H(U1(k, k), b)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, k), c)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.17	   A^2 -> H(f(k), d)
28.57/10.17	   A^2 -> H(f(k), k)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(k, d), b)
28.57/10.17	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, d), c)
28.57/10.17	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, k), b)
28.57/10.17	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(d, k), c)
28.57/10.17	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(d, k), e)
28.57/10.17	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, d), d)
28.57/10.17	   A^2 -> H(U1(d, d), k)
28.57/10.17	   A^2 -> H(U1(e, c), c)
28.57/10.17	   A^2 -> H(U1(c, c), e)
28.57/10.17	   A^2 -> H(U1(c, c), k)
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(e, e), e)
28.57/10.17	   A^2 -> H(d, U1(e, b))
28.57/10.17	   A^2 -> H(d, U1(k, b))
28.57/10.17	   A^2 -> H(d, U1(c, d))
28.57/10.17	   A^2 -> H(d, U1(d, c))
28.57/10.17	   A^2 -> H(d, U1(b, e))
28.57/10.17	   A^2 -> H(d, U1(b, k))
28.57/10.17	   A^2 -> H(d, U1(e, c))
28.57/10.17	   A^2 -> H(d, U1(k, c))
28.57/10.17	   A^2 -> H(d, U1(c, e))
28.57/10.17	   A^2 -> H(d, U1(c, k))
28.57/10.17	   A^2 -> H(d, U1(e, e))
28.57/10.17	   A^2 -> H(d, U1(k, k))
28.57/10.17	   A^2 -> H(d, U1(k, d))
28.57/10.17	   A^2 -> H(d, U1(d, k))
28.57/10.17	   A^2 -> H(a, b)
28.57/10.17	   A^2 -> H(a, U1(e, d))
28.57/10.17	   A^2 -> H(a, U1(d, e))
28.57/10.17	   A^2 -> H(a, c)
28.57/10.17	   A^2 -> H(a, U1(e, k))
28.57/10.17	   A^2 -> H(a, U1(k, e))
28.57/10.17	   A^2 -> H(a, e)
28.57/10.17	   A^2 -> H(a, U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, d), b)
28.57/10.17	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, d), c)
28.57/10.17	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, d), e)
28.57/10.17	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, a), d)
28.57/10.17	   A^2 -> H(U1(e, a), k)
28.57/10.17	   A^2 -> H(U1(k, a), d)
28.57/10.17	   A^2 -> H(U1(c, d), d)
28.57/10.17	   A^2 -> H(U1(c, d), k)
28.57/10.17	   A^2 -> H(U1(d, e), b)
28.57/10.17	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(d, e), c)
28.57/10.17	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(d, e), e)
28.57/10.17	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, c), d)
28.57/10.17	   A^2 -> H(U1(d, c), k)
28.57/10.17	
28.57/10.17	The TRS R consists of the following rules:
28.57/10.17	
28.57/10.17	   f(x) -> U1(x, x)
28.57/10.17	   U1(e, x) -> x
28.57/10.17	   a -> c
28.57/10.17	   a -> d
28.57/10.17	   b -> c
28.57/10.17	   b -> d
28.57/10.17	   d -> k
28.57/10.17	   c -> e
28.57/10.17	   c -> k
28.57/10.17	
28.57/10.17	Q is empty.
28.57/10.17	We have to consider all minimal (P,Q,R)-chains.
28.57/10.17	----------------------------------------
28.57/10.17	
28.57/10.17	(1971) TransformationProof (EQUIVALENT)
28.57/10.17	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.17	
28.57/10.17	   (A^2 -> H(U1(k, c), U1(k, k)),A^2 -> H(U1(k, c), U1(k, k)))
28.57/10.17	   (A^2 -> H(U1(d, e), U1(k, k)),A^2 -> H(U1(d, e), U1(k, k)))
28.57/10.17	   (A^2 -> H(U1(d, k), U1(k, k)),A^2 -> H(U1(d, k), U1(k, k)))
28.57/10.17	
28.57/10.17	
28.57/10.17	----------------------------------------
28.57/10.17	
28.57/10.17	(1972)
28.57/10.17	Obligation:
28.57/10.17	Q DP problem:
28.57/10.17	The TRS P consists of the following rules:
28.57/10.17	
28.57/10.17	   H(x, x) -> G(x, x, f(k))
28.57/10.17	   G(d, x, x) -> A^2
28.57/10.17	   A^2 -> H(f(c), f(c))
28.57/10.17	   A^2 -> H(f(d), f(d))
28.57/10.17	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.17	   A^2 -> H(f(e), f(e))
28.57/10.17	   A^2 -> H(f(k), f(k))
28.57/10.17	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.17	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.17	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.17	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.17	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.17	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(d, a), d)
28.57/10.17	   A^2 -> H(U1(d, a), k)
28.57/10.17	   A^2 -> H(U1(a, e), b)
28.57/10.17	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(a, e), c)
28.57/10.17	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(a, e), e)
28.57/10.17	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(a, k), b)
28.57/10.17	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(a, k), c)
28.57/10.17	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(a, k), e)
28.57/10.17	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(a, c), d)
28.57/10.17	   A^2 -> H(U1(a, c), k)
28.57/10.17	   A^2 -> H(U1(a, d), d)
28.57/10.17	   A^2 -> H(U1(a, d), k)
28.57/10.17	   A^2 -> H(k, U1(c, b))
28.57/10.17	   A^2 -> H(k, U1(d, b))
28.57/10.17	   A^2 -> H(k, U1(b, c))
28.57/10.17	   A^2 -> H(k, U1(b, d))
28.57/10.17	   A^2 -> H(k, U1(c, c))
28.57/10.17	   A^2 -> H(k, f(e))
28.57/10.17	   A^2 -> H(k, f(k))
28.57/10.17	   A^2 -> H(k, U1(d, d))
28.57/10.17	   A^2 -> H(c, U1(e, b))
28.57/10.17	   A^2 -> H(c, U1(k, b))
28.57/10.17	   A^2 -> H(c, U1(c, d))
28.57/10.17	   A^2 -> H(c, U1(d, c))
28.57/10.17	   A^2 -> H(c, U1(b, e))
28.57/10.17	   A^2 -> H(c, U1(b, k))
28.57/10.17	   A^2 -> H(c, U1(e, c))
28.57/10.17	   A^2 -> H(c, U1(k, c))
28.57/10.17	   A^2 -> H(c, U1(c, e))
28.57/10.17	   A^2 -> H(c, U1(c, k))
28.57/10.17	   A^2 -> H(c, U1(e, e))
28.57/10.17	   A^2 -> H(c, U1(k, k))
28.57/10.17	   A^2 -> H(c, U1(k, d))
28.57/10.17	   A^2 -> H(c, U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.17	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.17	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, c), b)
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, c), e)
28.57/10.17	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.17	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.17	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.17	   A^2 -> H(U1(k, c), b)
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, c), c)
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, e), b)
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(c, e), c)
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(c, e), e)
28.57/10.17	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, k), b)
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(c, k), c)
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(c, k), e)
28.57/10.17	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, c), d)
28.57/10.17	   A^2 -> H(e, U1(e, b))
28.57/10.17	   A^2 -> H(e, U1(c, d))
28.57/10.17	   A^2 -> H(e, U1(d, c))
28.57/10.17	   A^2 -> H(e, U1(b, e))
28.57/10.17	   A^2 -> H(e, U1(b, k))
28.57/10.17	   A^2 -> H(e, U1(e, c))
28.57/10.17	   A^2 -> H(e, U1(c, e))
28.57/10.17	   A^2 -> H(e, U1(c, k))
28.57/10.17	   A^2 -> H(e, U1(e, e))
28.57/10.17	   A^2 -> H(e, U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, e), b)
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, e), c)
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.17	   A^2 -> H(f(e), d)
28.57/10.17	   A^2 -> H(f(e), k)
28.57/10.17	   A^2 -> H(U1(k, k), b)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, k), c)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.17	   A^2 -> H(f(k), d)
28.57/10.17	   A^2 -> H(f(k), k)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(k, d), b)
28.57/10.17	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, d), c)
28.57/10.17	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, k), b)
28.57/10.17	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(d, k), c)
28.57/10.17	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(d, k), e)
28.57/10.17	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, d), d)
28.57/10.17	   A^2 -> H(U1(d, d), k)
28.57/10.17	   A^2 -> H(U1(e, c), c)
28.57/10.17	   A^2 -> H(U1(c, c), e)
28.57/10.17	   A^2 -> H(U1(c, c), k)
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(e, e), e)
28.57/10.17	   A^2 -> H(d, U1(e, b))
28.57/10.17	   A^2 -> H(d, U1(k, b))
28.57/10.17	   A^2 -> H(d, U1(c, d))
28.57/10.17	   A^2 -> H(d, U1(d, c))
28.57/10.17	   A^2 -> H(d, U1(b, e))
28.57/10.17	   A^2 -> H(d, U1(b, k))
28.57/10.17	   A^2 -> H(d, U1(e, c))
28.57/10.17	   A^2 -> H(d, U1(k, c))
28.57/10.17	   A^2 -> H(d, U1(c, e))
28.57/10.17	   A^2 -> H(d, U1(c, k))
28.57/10.17	   A^2 -> H(d, U1(e, e))
28.57/10.17	   A^2 -> H(d, U1(k, k))
28.57/10.17	   A^2 -> H(d, U1(k, d))
28.57/10.17	   A^2 -> H(d, U1(d, k))
28.57/10.17	   A^2 -> H(a, b)
28.57/10.17	   A^2 -> H(a, U1(e, d))
28.57/10.17	   A^2 -> H(a, U1(d, e))
28.57/10.17	   A^2 -> H(a, c)
28.57/10.17	   A^2 -> H(a, U1(e, k))
28.57/10.17	   A^2 -> H(a, U1(k, e))
28.57/10.17	   A^2 -> H(a, e)
28.57/10.17	   A^2 -> H(a, U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, d), b)
28.57/10.17	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, d), c)
28.57/10.17	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, d), e)
28.57/10.17	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, a), d)
28.57/10.17	   A^2 -> H(U1(e, a), k)
28.57/10.17	   A^2 -> H(U1(k, a), d)
28.57/10.17	   A^2 -> H(U1(c, d), d)
28.57/10.17	   A^2 -> H(U1(c, d), k)
28.57/10.17	   A^2 -> H(U1(d, e), b)
28.57/10.17	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(d, e), c)
28.57/10.17	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(d, e), e)
28.57/10.17	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, c), d)
28.57/10.17	   A^2 -> H(U1(d, c), k)
28.57/10.17	
28.57/10.17	The TRS R consists of the following rules:
28.57/10.17	
28.57/10.17	   f(x) -> U1(x, x)
28.57/10.17	   U1(e, x) -> x
28.57/10.17	   a -> c
28.57/10.17	   a -> d
28.57/10.17	   b -> c
28.57/10.17	   b -> d
28.57/10.17	   d -> k
28.57/10.17	   c -> e
28.57/10.17	   c -> k
28.57/10.17	
28.57/10.17	Q is empty.
28.57/10.17	We have to consider all minimal (P,Q,R)-chains.
28.57/10.17	----------------------------------------
28.57/10.17	
28.57/10.17	(1973) TransformationProof (EQUIVALENT)
28.57/10.17	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), d) at position [] we obtained the following new rules [LPAR04]:
28.57/10.17	
28.57/10.17	   (A^2 -> H(U1(k, a), d),A^2 -> H(U1(k, a), d))
28.57/10.17	   (A^2 -> H(U1(d, c), d),A^2 -> H(U1(d, c), d))
28.57/10.17	   (A^2 -> H(U1(d, d), d),A^2 -> H(U1(d, d), d))
28.57/10.17	   (A^2 -> H(U1(d, a), k),A^2 -> H(U1(d, a), k))
28.57/10.17	
28.57/10.17	
28.57/10.17	----------------------------------------
28.57/10.17	
28.57/10.17	(1974)
28.57/10.17	Obligation:
28.57/10.17	Q DP problem:
28.57/10.17	The TRS P consists of the following rules:
28.57/10.17	
28.57/10.17	   H(x, x) -> G(x, x, f(k))
28.57/10.17	   G(d, x, x) -> A^2
28.57/10.17	   A^2 -> H(f(c), f(c))
28.57/10.17	   A^2 -> H(f(d), f(d))
28.57/10.17	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.17	   A^2 -> H(f(e), f(e))
28.57/10.17	   A^2 -> H(f(k), f(k))
28.57/10.17	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.17	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.17	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.17	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.17	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.17	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(d, a), k)
28.57/10.17	   A^2 -> H(U1(a, e), b)
28.57/10.17	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(a, e), c)
28.57/10.17	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(a, e), e)
28.57/10.17	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(a, k), b)
28.57/10.17	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(a, k), c)
28.57/10.17	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(a, k), e)
28.57/10.17	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(a, c), d)
28.57/10.17	   A^2 -> H(U1(a, c), k)
28.57/10.17	   A^2 -> H(U1(a, d), d)
28.57/10.17	   A^2 -> H(U1(a, d), k)
28.57/10.17	   A^2 -> H(k, U1(c, b))
28.57/10.17	   A^2 -> H(k, U1(d, b))
28.57/10.17	   A^2 -> H(k, U1(b, c))
28.57/10.17	   A^2 -> H(k, U1(b, d))
28.57/10.17	   A^2 -> H(k, U1(c, c))
28.57/10.17	   A^2 -> H(k, f(e))
28.57/10.17	   A^2 -> H(k, f(k))
28.57/10.17	   A^2 -> H(k, U1(d, d))
28.57/10.17	   A^2 -> H(c, U1(e, b))
28.57/10.17	   A^2 -> H(c, U1(k, b))
28.57/10.17	   A^2 -> H(c, U1(c, d))
28.57/10.17	   A^2 -> H(c, U1(d, c))
28.57/10.17	   A^2 -> H(c, U1(b, e))
28.57/10.17	   A^2 -> H(c, U1(b, k))
28.57/10.17	   A^2 -> H(c, U1(e, c))
28.57/10.17	   A^2 -> H(c, U1(k, c))
28.57/10.17	   A^2 -> H(c, U1(c, e))
28.57/10.17	   A^2 -> H(c, U1(c, k))
28.57/10.17	   A^2 -> H(c, U1(e, e))
28.57/10.17	   A^2 -> H(c, U1(k, k))
28.57/10.17	   A^2 -> H(c, U1(k, d))
28.57/10.17	   A^2 -> H(c, U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.17	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.17	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, c), b)
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, c), e)
28.57/10.17	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.17	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.17	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.17	   A^2 -> H(U1(k, c), b)
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, c), c)
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, e), b)
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(c, e), c)
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(c, e), e)
28.57/10.17	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, k), b)
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(c, k), c)
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(c, k), e)
28.57/10.17	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, c), d)
28.57/10.17	   A^2 -> H(e, U1(e, b))
28.57/10.17	   A^2 -> H(e, U1(c, d))
28.57/10.17	   A^2 -> H(e, U1(d, c))
28.57/10.17	   A^2 -> H(e, U1(b, e))
28.57/10.17	   A^2 -> H(e, U1(b, k))
28.57/10.17	   A^2 -> H(e, U1(e, c))
28.57/10.17	   A^2 -> H(e, U1(c, e))
28.57/10.17	   A^2 -> H(e, U1(c, k))
28.57/10.17	   A^2 -> H(e, U1(e, e))
28.57/10.17	   A^2 -> H(e, U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, e), b)
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, e), c)
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.17	   A^2 -> H(f(e), d)
28.57/10.17	   A^2 -> H(f(e), k)
28.57/10.17	   A^2 -> H(U1(k, k), b)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, k), c)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.17	   A^2 -> H(f(k), d)
28.57/10.17	   A^2 -> H(f(k), k)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(k, d), b)
28.57/10.17	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, d), c)
28.57/10.17	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, k), b)
28.57/10.17	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(d, k), c)
28.57/10.17	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(d, k), e)
28.57/10.17	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, d), d)
28.57/10.17	   A^2 -> H(U1(d, d), k)
28.57/10.17	   A^2 -> H(U1(e, c), c)
28.57/10.17	   A^2 -> H(U1(c, c), e)
28.57/10.17	   A^2 -> H(U1(c, c), k)
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(e, e), e)
28.57/10.17	   A^2 -> H(d, U1(e, b))
28.57/10.17	   A^2 -> H(d, U1(k, b))
28.57/10.17	   A^2 -> H(d, U1(c, d))
28.57/10.17	   A^2 -> H(d, U1(d, c))
28.57/10.17	   A^2 -> H(d, U1(b, e))
28.57/10.17	   A^2 -> H(d, U1(b, k))
28.57/10.17	   A^2 -> H(d, U1(e, c))
28.57/10.17	   A^2 -> H(d, U1(k, c))
28.57/10.17	   A^2 -> H(d, U1(c, e))
28.57/10.17	   A^2 -> H(d, U1(c, k))
28.57/10.17	   A^2 -> H(d, U1(e, e))
28.57/10.17	   A^2 -> H(d, U1(k, k))
28.57/10.17	   A^2 -> H(d, U1(k, d))
28.57/10.17	   A^2 -> H(d, U1(d, k))
28.57/10.17	   A^2 -> H(a, b)
28.57/10.17	   A^2 -> H(a, U1(e, d))
28.57/10.17	   A^2 -> H(a, U1(d, e))
28.57/10.17	   A^2 -> H(a, c)
28.57/10.17	   A^2 -> H(a, U1(e, k))
28.57/10.17	   A^2 -> H(a, U1(k, e))
28.57/10.17	   A^2 -> H(a, e)
28.57/10.17	   A^2 -> H(a, U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, d), b)
28.57/10.17	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, d), c)
28.57/10.17	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, d), e)
28.57/10.17	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, a), d)
28.57/10.17	   A^2 -> H(U1(e, a), k)
28.57/10.17	   A^2 -> H(U1(k, a), d)
28.57/10.17	   A^2 -> H(U1(c, d), d)
28.57/10.17	   A^2 -> H(U1(c, d), k)
28.57/10.17	   A^2 -> H(U1(d, e), b)
28.57/10.17	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(d, e), c)
28.57/10.17	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(d, e), e)
28.57/10.17	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, c), d)
28.57/10.17	   A^2 -> H(U1(d, c), k)
28.57/10.17	
28.57/10.17	The TRS R consists of the following rules:
28.57/10.17	
28.57/10.17	   f(x) -> U1(x, x)
28.57/10.17	   U1(e, x) -> x
28.57/10.17	   a -> c
28.57/10.17	   a -> d
28.57/10.17	   b -> c
28.57/10.17	   b -> d
28.57/10.17	   d -> k
28.57/10.17	   c -> e
28.57/10.17	   c -> k
28.57/10.17	
28.57/10.17	Q is empty.
28.57/10.17	We have to consider all minimal (P,Q,R)-chains.
28.57/10.17	----------------------------------------
28.57/10.17	
28.57/10.17	(1975) TransformationProof (EQUIVALENT)
28.57/10.17	By narrowing [LPAR04] the rule A^2 -> H(U1(d, a), k) at position [] we obtained the following new rules [LPAR04]:
28.57/10.17	
28.57/10.17	   (A^2 -> H(U1(k, a), k),A^2 -> H(U1(k, a), k))
28.57/10.17	   (A^2 -> H(U1(d, c), k),A^2 -> H(U1(d, c), k))
28.57/10.17	   (A^2 -> H(U1(d, d), k),A^2 -> H(U1(d, d), k))
28.57/10.17	
28.57/10.17	
28.57/10.17	----------------------------------------
28.57/10.17	
28.57/10.17	(1976)
28.57/10.17	Obligation:
28.57/10.17	Q DP problem:
28.57/10.17	The TRS P consists of the following rules:
28.57/10.17	
28.57/10.17	   H(x, x) -> G(x, x, f(k))
28.57/10.17	   G(d, x, x) -> A^2
28.57/10.17	   A^2 -> H(f(c), f(c))
28.57/10.17	   A^2 -> H(f(d), f(d))
28.57/10.17	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.17	   A^2 -> H(f(e), f(e))
28.57/10.17	   A^2 -> H(f(k), f(k))
28.57/10.17	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.17	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.17	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.17	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.17	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.17	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(a, e), b)
28.57/10.17	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(a, e), c)
28.57/10.17	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(a, e), e)
28.57/10.17	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(a, k), b)
28.57/10.17	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(a, k), c)
28.57/10.17	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(a, k), e)
28.57/10.17	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(a, c), d)
28.57/10.17	   A^2 -> H(U1(a, c), k)
28.57/10.17	   A^2 -> H(U1(a, d), d)
28.57/10.17	   A^2 -> H(U1(a, d), k)
28.57/10.17	   A^2 -> H(k, U1(c, b))
28.57/10.17	   A^2 -> H(k, U1(d, b))
28.57/10.17	   A^2 -> H(k, U1(b, c))
28.57/10.17	   A^2 -> H(k, U1(b, d))
28.57/10.17	   A^2 -> H(k, U1(c, c))
28.57/10.17	   A^2 -> H(k, f(e))
28.57/10.17	   A^2 -> H(k, f(k))
28.57/10.17	   A^2 -> H(k, U1(d, d))
28.57/10.17	   A^2 -> H(c, U1(e, b))
28.57/10.17	   A^2 -> H(c, U1(k, b))
28.57/10.17	   A^2 -> H(c, U1(c, d))
28.57/10.17	   A^2 -> H(c, U1(d, c))
28.57/10.17	   A^2 -> H(c, U1(b, e))
28.57/10.17	   A^2 -> H(c, U1(b, k))
28.57/10.17	   A^2 -> H(c, U1(e, c))
28.57/10.17	   A^2 -> H(c, U1(k, c))
28.57/10.17	   A^2 -> H(c, U1(c, e))
28.57/10.17	   A^2 -> H(c, U1(c, k))
28.57/10.17	   A^2 -> H(c, U1(e, e))
28.57/10.17	   A^2 -> H(c, U1(k, k))
28.57/10.17	   A^2 -> H(c, U1(k, d))
28.57/10.17	   A^2 -> H(c, U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.17	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.17	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, c), b)
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, c), e)
28.57/10.17	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.17	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.17	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.17	   A^2 -> H(U1(k, c), b)
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, c), c)
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, e), b)
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(c, e), c)
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(c, e), e)
28.57/10.17	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, k), b)
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(c, k), c)
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(c, k), e)
28.57/10.17	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, c), d)
28.57/10.17	   A^2 -> H(e, U1(e, b))
28.57/10.17	   A^2 -> H(e, U1(c, d))
28.57/10.17	   A^2 -> H(e, U1(d, c))
28.57/10.17	   A^2 -> H(e, U1(b, e))
28.57/10.17	   A^2 -> H(e, U1(b, k))
28.57/10.17	   A^2 -> H(e, U1(e, c))
28.57/10.17	   A^2 -> H(e, U1(c, e))
28.57/10.17	   A^2 -> H(e, U1(c, k))
28.57/10.17	   A^2 -> H(e, U1(e, e))
28.57/10.17	   A^2 -> H(e, U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, e), b)
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, e), c)
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.17	   A^2 -> H(f(e), d)
28.57/10.17	   A^2 -> H(f(e), k)
28.57/10.17	   A^2 -> H(U1(k, k), b)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, k), c)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.17	   A^2 -> H(f(k), d)
28.57/10.17	   A^2 -> H(f(k), k)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(k, d), b)
28.57/10.17	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, d), c)
28.57/10.17	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, k), b)
28.57/10.17	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(d, k), c)
28.57/10.17	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(d, k), e)
28.57/10.17	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, d), d)
28.57/10.17	   A^2 -> H(U1(d, d), k)
28.57/10.17	   A^2 -> H(U1(e, c), c)
28.57/10.17	   A^2 -> H(U1(c, c), e)
28.57/10.17	   A^2 -> H(U1(c, c), k)
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(e, e), e)
28.57/10.17	   A^2 -> H(d, U1(e, b))
28.57/10.17	   A^2 -> H(d, U1(k, b))
28.57/10.17	   A^2 -> H(d, U1(c, d))
28.57/10.17	   A^2 -> H(d, U1(d, c))
28.57/10.17	   A^2 -> H(d, U1(b, e))
28.57/10.17	   A^2 -> H(d, U1(b, k))
28.57/10.17	   A^2 -> H(d, U1(e, c))
28.57/10.17	   A^2 -> H(d, U1(k, c))
28.57/10.17	   A^2 -> H(d, U1(c, e))
28.57/10.17	   A^2 -> H(d, U1(c, k))
28.57/10.17	   A^2 -> H(d, U1(e, e))
28.57/10.17	   A^2 -> H(d, U1(k, k))
28.57/10.17	   A^2 -> H(d, U1(k, d))
28.57/10.17	   A^2 -> H(d, U1(d, k))
28.57/10.17	   A^2 -> H(a, b)
28.57/10.17	   A^2 -> H(a, U1(e, d))
28.57/10.17	   A^2 -> H(a, U1(d, e))
28.57/10.17	   A^2 -> H(a, c)
28.57/10.17	   A^2 -> H(a, U1(e, k))
28.57/10.17	   A^2 -> H(a, U1(k, e))
28.57/10.17	   A^2 -> H(a, e)
28.57/10.17	   A^2 -> H(a, U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, d), b)
28.57/10.17	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, d), c)
28.57/10.17	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, d), e)
28.57/10.17	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, a), d)
28.57/10.17	   A^2 -> H(U1(e, a), k)
28.57/10.17	   A^2 -> H(U1(k, a), d)
28.57/10.17	   A^2 -> H(U1(c, d), d)
28.57/10.17	   A^2 -> H(U1(c, d), k)
28.57/10.17	   A^2 -> H(U1(d, e), b)
28.57/10.17	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(d, e), c)
28.57/10.17	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(d, e), e)
28.57/10.17	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, c), d)
28.57/10.17	   A^2 -> H(U1(d, c), k)
28.57/10.17	   A^2 -> H(U1(k, a), k)
28.57/10.17	
28.57/10.17	The TRS R consists of the following rules:
28.57/10.17	
28.57/10.17	   f(x) -> U1(x, x)
28.57/10.17	   U1(e, x) -> x
28.57/10.17	   a -> c
28.57/10.17	   a -> d
28.57/10.17	   b -> c
28.57/10.17	   b -> d
28.57/10.17	   d -> k
28.57/10.17	   c -> e
28.57/10.17	   c -> k
28.57/10.17	
28.57/10.17	Q is empty.
28.57/10.17	We have to consider all minimal (P,Q,R)-chains.
28.57/10.17	----------------------------------------
28.57/10.17	
28.57/10.17	(1977) DependencyGraphProof (EQUIVALENT)
28.57/10.17	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.17	----------------------------------------
28.57/10.17	
28.57/10.17	(1978)
28.57/10.17	Obligation:
28.57/10.17	Q DP problem:
28.57/10.17	The TRS P consists of the following rules:
28.57/10.17	
28.57/10.17	   G(d, x, x) -> A^2
28.57/10.17	   A^2 -> H(f(c), f(c))
28.57/10.17	   H(x, x) -> G(x, x, f(k))
28.57/10.17	   A^2 -> H(f(d), f(d))
28.57/10.17	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.17	   A^2 -> H(f(e), f(e))
28.57/10.17	   A^2 -> H(f(k), f(k))
28.57/10.17	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.17	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.17	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.17	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.17	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.17	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(a, e), b)
28.57/10.17	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(a, e), c)
28.57/10.17	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(a, e), e)
28.57/10.17	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(a, k), b)
28.57/10.17	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(a, k), c)
28.57/10.17	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(a, k), e)
28.57/10.17	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(a, c), d)
28.57/10.17	   A^2 -> H(U1(a, c), k)
28.57/10.17	   A^2 -> H(U1(a, d), d)
28.57/10.17	   A^2 -> H(U1(a, d), k)
28.57/10.17	   A^2 -> H(k, U1(c, b))
28.57/10.17	   A^2 -> H(k, U1(d, b))
28.57/10.17	   A^2 -> H(k, U1(b, c))
28.57/10.17	   A^2 -> H(k, U1(b, d))
28.57/10.17	   A^2 -> H(k, U1(c, c))
28.57/10.17	   A^2 -> H(k, f(e))
28.57/10.17	   A^2 -> H(k, f(k))
28.57/10.17	   A^2 -> H(k, U1(d, d))
28.57/10.17	   A^2 -> H(c, U1(e, b))
28.57/10.17	   A^2 -> H(c, U1(k, b))
28.57/10.17	   A^2 -> H(c, U1(c, d))
28.57/10.17	   A^2 -> H(c, U1(d, c))
28.57/10.17	   A^2 -> H(c, U1(b, e))
28.57/10.17	   A^2 -> H(c, U1(b, k))
28.57/10.17	   A^2 -> H(c, U1(e, c))
28.57/10.17	   A^2 -> H(c, U1(k, c))
28.57/10.17	   A^2 -> H(c, U1(c, e))
28.57/10.17	   A^2 -> H(c, U1(c, k))
28.57/10.17	   A^2 -> H(c, U1(e, e))
28.57/10.17	   A^2 -> H(c, U1(k, k))
28.57/10.17	   A^2 -> H(c, U1(k, d))
28.57/10.17	   A^2 -> H(c, U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.17	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.17	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, c), b)
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, c), e)
28.57/10.17	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.17	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.17	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.17	   A^2 -> H(U1(k, c), b)
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, c), c)
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, e), b)
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(c, e), c)
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(c, e), e)
28.57/10.17	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, k), b)
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(c, k), c)
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(c, k), e)
28.57/10.17	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, c), d)
28.57/10.17	   A^2 -> H(e, U1(e, b))
28.57/10.17	   A^2 -> H(e, U1(c, d))
28.57/10.17	   A^2 -> H(e, U1(d, c))
28.57/10.17	   A^2 -> H(e, U1(b, e))
28.57/10.17	   A^2 -> H(e, U1(b, k))
28.57/10.17	   A^2 -> H(e, U1(e, c))
28.57/10.17	   A^2 -> H(e, U1(c, e))
28.57/10.17	   A^2 -> H(e, U1(c, k))
28.57/10.17	   A^2 -> H(e, U1(e, e))
28.57/10.17	   A^2 -> H(e, U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, e), b)
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, e), c)
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.17	   A^2 -> H(f(e), d)
28.57/10.17	   A^2 -> H(f(e), k)
28.57/10.17	   A^2 -> H(U1(k, k), b)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, k), c)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.17	   A^2 -> H(f(k), d)
28.57/10.17	   A^2 -> H(f(k), k)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(k, d), b)
28.57/10.17	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, d), c)
28.57/10.17	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, k), b)
28.57/10.17	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(d, k), c)
28.57/10.17	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(d, k), e)
28.57/10.17	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, d), d)
28.57/10.17	   A^2 -> H(U1(d, d), k)
28.57/10.17	   A^2 -> H(U1(e, c), c)
28.57/10.17	   A^2 -> H(U1(c, c), e)
28.57/10.17	   A^2 -> H(U1(c, c), k)
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(e, e), e)
28.57/10.17	   A^2 -> H(d, U1(e, b))
28.57/10.17	   A^2 -> H(d, U1(k, b))
28.57/10.17	   A^2 -> H(d, U1(c, d))
28.57/10.17	   A^2 -> H(d, U1(d, c))
28.57/10.17	   A^2 -> H(d, U1(b, e))
28.57/10.17	   A^2 -> H(d, U1(b, k))
28.57/10.17	   A^2 -> H(d, U1(e, c))
28.57/10.17	   A^2 -> H(d, U1(k, c))
28.57/10.17	   A^2 -> H(d, U1(c, e))
28.57/10.17	   A^2 -> H(d, U1(c, k))
28.57/10.17	   A^2 -> H(d, U1(e, e))
28.57/10.17	   A^2 -> H(d, U1(k, k))
28.57/10.17	   A^2 -> H(d, U1(k, d))
28.57/10.17	   A^2 -> H(d, U1(d, k))
28.57/10.17	   A^2 -> H(a, b)
28.57/10.17	   A^2 -> H(a, U1(e, d))
28.57/10.17	   A^2 -> H(a, U1(d, e))
28.57/10.17	   A^2 -> H(a, c)
28.57/10.17	   A^2 -> H(a, U1(e, k))
28.57/10.17	   A^2 -> H(a, U1(k, e))
28.57/10.17	   A^2 -> H(a, e)
28.57/10.17	   A^2 -> H(a, U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, d), b)
28.57/10.17	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, d), c)
28.57/10.17	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, d), e)
28.57/10.17	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, a), d)
28.57/10.17	   A^2 -> H(U1(e, a), k)
28.57/10.17	   A^2 -> H(U1(k, a), d)
28.57/10.17	   A^2 -> H(U1(c, d), d)
28.57/10.17	   A^2 -> H(U1(c, d), k)
28.57/10.17	   A^2 -> H(U1(d, e), b)
28.57/10.17	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(d, e), c)
28.57/10.17	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(d, e), e)
28.57/10.17	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, c), d)
28.57/10.17	   A^2 -> H(U1(d, c), k)
28.57/10.17	
28.57/10.17	The TRS R consists of the following rules:
28.57/10.17	
28.57/10.17	   f(x) -> U1(x, x)
28.57/10.17	   U1(e, x) -> x
28.57/10.17	   a -> c
28.57/10.17	   a -> d
28.57/10.17	   b -> c
28.57/10.17	   b -> d
28.57/10.17	   d -> k
28.57/10.17	   c -> e
28.57/10.17	   c -> k
28.57/10.17	
28.57/10.17	Q is empty.
28.57/10.17	We have to consider all minimal (P,Q,R)-chains.
28.57/10.17	----------------------------------------
28.57/10.17	
28.57/10.17	(1979) TransformationProof (EQUIVALENT)
28.57/10.17	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), b) at position [] we obtained the following new rules [LPAR04]:
28.57/10.17	
28.57/10.17	   (A^2 -> H(U1(c, e), b),A^2 -> H(U1(c, e), b))
28.57/10.17	   (A^2 -> H(U1(d, e), b),A^2 -> H(U1(d, e), b))
28.57/10.17	   (A^2 -> H(U1(a, e), c),A^2 -> H(U1(a, e), c))
28.57/10.17	   (A^2 -> H(U1(a, e), d),A^2 -> H(U1(a, e), d))
28.57/10.17	
28.57/10.17	
28.57/10.17	----------------------------------------
28.57/10.17	
28.57/10.17	(1980)
28.57/10.17	Obligation:
28.57/10.17	Q DP problem:
28.57/10.17	The TRS P consists of the following rules:
28.57/10.17	
28.57/10.17	   G(d, x, x) -> A^2
28.57/10.17	   A^2 -> H(f(c), f(c))
28.57/10.17	   H(x, x) -> G(x, x, f(k))
28.57/10.17	   A^2 -> H(f(d), f(d))
28.57/10.17	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.17	   A^2 -> H(f(e), f(e))
28.57/10.17	   A^2 -> H(f(k), f(k))
28.57/10.17	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.17	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.17	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.17	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.17	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.17	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(a, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(a, e), c)
28.57/10.17	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(a, e), e)
28.57/10.17	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(a, k), b)
28.57/10.17	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(a, k), c)
28.57/10.17	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(a, k), e)
28.57/10.17	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(a, c), d)
28.57/10.17	   A^2 -> H(U1(a, c), k)
28.57/10.17	   A^2 -> H(U1(a, d), d)
28.57/10.17	   A^2 -> H(U1(a, d), k)
28.57/10.17	   A^2 -> H(k, U1(c, b))
28.57/10.17	   A^2 -> H(k, U1(d, b))
28.57/10.17	   A^2 -> H(k, U1(b, c))
28.57/10.17	   A^2 -> H(k, U1(b, d))
28.57/10.17	   A^2 -> H(k, U1(c, c))
28.57/10.17	   A^2 -> H(k, f(e))
28.57/10.17	   A^2 -> H(k, f(k))
28.57/10.17	   A^2 -> H(k, U1(d, d))
28.57/10.17	   A^2 -> H(c, U1(e, b))
28.57/10.17	   A^2 -> H(c, U1(k, b))
28.57/10.17	   A^2 -> H(c, U1(c, d))
28.57/10.17	   A^2 -> H(c, U1(d, c))
28.57/10.17	   A^2 -> H(c, U1(b, e))
28.57/10.17	   A^2 -> H(c, U1(b, k))
28.57/10.17	   A^2 -> H(c, U1(e, c))
28.57/10.17	   A^2 -> H(c, U1(k, c))
28.57/10.17	   A^2 -> H(c, U1(c, e))
28.57/10.17	   A^2 -> H(c, U1(c, k))
28.57/10.17	   A^2 -> H(c, U1(e, e))
28.57/10.17	   A^2 -> H(c, U1(k, k))
28.57/10.17	   A^2 -> H(c, U1(k, d))
28.57/10.17	   A^2 -> H(c, U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.17	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.17	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, c), b)
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, c), e)
28.57/10.17	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.17	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.17	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.17	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.17	   A^2 -> H(U1(k, c), b)
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, c), c)
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, e), b)
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(c, e), c)
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(c, e), e)
28.57/10.17	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, k), b)
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(c, k), c)
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(c, k), e)
28.57/10.17	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(c, c), d)
28.57/10.17	   A^2 -> H(e, U1(e, b))
28.57/10.17	   A^2 -> H(e, U1(c, d))
28.57/10.17	   A^2 -> H(e, U1(d, c))
28.57/10.17	   A^2 -> H(e, U1(b, e))
28.57/10.17	   A^2 -> H(e, U1(b, k))
28.57/10.17	   A^2 -> H(e, U1(e, c))
28.57/10.17	   A^2 -> H(e, U1(c, e))
28.57/10.17	   A^2 -> H(e, U1(c, k))
28.57/10.17	   A^2 -> H(e, U1(e, e))
28.57/10.17	   A^2 -> H(e, U1(d, k))
28.57/10.17	   A^2 -> H(U1(e, e), b)
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, e), c)
28.57/10.17	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.17	   A^2 -> H(f(e), d)
28.57/10.17	   A^2 -> H(f(e), k)
28.57/10.17	   A^2 -> H(U1(k, k), b)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, k), c)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.17	   A^2 -> H(f(k), d)
28.57/10.17	   A^2 -> H(f(k), k)
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.17	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.17	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.17	   A^2 -> H(U1(k, d), b)
28.57/10.17	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.17	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.17	   A^2 -> H(U1(k, d), c)
28.57/10.17	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.17	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, k), b)
28.57/10.17	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.17	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.17	   A^2 -> H(U1(d, k), c)
28.57/10.17	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.17	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.17	   A^2 -> H(U1(d, k), e)
28.57/10.17	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, d), d)
28.57/10.17	   A^2 -> H(U1(d, d), k)
28.57/10.17	   A^2 -> H(U1(e, c), c)
28.57/10.17	   A^2 -> H(U1(c, c), e)
28.57/10.17	   A^2 -> H(U1(c, c), k)
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.17	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.17	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.17	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.17	   A^2 -> H(U1(e, e), e)
28.57/10.17	   A^2 -> H(d, U1(e, b))
28.57/10.17	   A^2 -> H(d, U1(k, b))
28.57/10.17	   A^2 -> H(d, U1(c, d))
28.57/10.17	   A^2 -> H(d, U1(d, c))
28.57/10.17	   A^2 -> H(d, U1(b, e))
28.57/10.17	   A^2 -> H(d, U1(b, k))
28.57/10.17	   A^2 -> H(d, U1(e, c))
28.57/10.17	   A^2 -> H(d, U1(k, c))
28.57/10.17	   A^2 -> H(d, U1(c, e))
28.57/10.17	   A^2 -> H(d, U1(c, k))
28.57/10.17	   A^2 -> H(d, U1(e, e))
28.57/10.17	   A^2 -> H(d, U1(k, k))
28.57/10.17	   A^2 -> H(d, U1(k, d))
28.57/10.17	   A^2 -> H(d, U1(d, k))
28.57/10.17	   A^2 -> H(a, b)
28.57/10.17	   A^2 -> H(a, U1(e, d))
28.57/10.17	   A^2 -> H(a, U1(d, e))
28.57/10.17	   A^2 -> H(a, c)
28.57/10.17	   A^2 -> H(a, U1(e, k))
28.57/10.17	   A^2 -> H(a, U1(k, e))
28.57/10.17	   A^2 -> H(a, e)
28.57/10.17	   A^2 -> H(a, U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, d), b)
28.57/10.17	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.17	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.17	   A^2 -> H(U1(e, d), c)
28.57/10.17	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.17	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.17	   A^2 -> H(U1(e, d), e)
28.57/10.17	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.17	   A^2 -> H(U1(e, a), d)
28.57/10.17	   A^2 -> H(U1(e, a), k)
28.57/10.17	   A^2 -> H(U1(k, a), d)
28.57/10.17	   A^2 -> H(U1(c, d), d)
28.57/10.17	   A^2 -> H(U1(c, d), k)
28.57/10.17	   A^2 -> H(U1(d, e), b)
28.57/10.17	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.17	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.17	   A^2 -> H(U1(d, e), c)
28.57/10.17	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.17	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.17	   A^2 -> H(U1(d, e), e)
28.57/10.17	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.17	   A^2 -> H(U1(d, c), d)
28.57/10.17	   A^2 -> H(U1(d, c), k)
28.57/10.17	   A^2 -> H(U1(a, e), d)
28.57/10.17	
28.57/10.17	The TRS R consists of the following rules:
28.57/10.17	
28.57/10.17	   f(x) -> U1(x, x)
28.57/10.17	   U1(e, x) -> x
28.57/10.17	   a -> c
28.57/10.17	   a -> d
28.57/10.17	   b -> c
28.57/10.17	   b -> d
28.57/10.17	   d -> k
28.57/10.17	   c -> e
28.57/10.17	   c -> k
28.57/10.17	
28.57/10.17	Q is empty.
28.57/10.17	We have to consider all minimal (P,Q,R)-chains.
28.57/10.17	----------------------------------------
28.57/10.17	
28.57/10.17	(1981) TransformationProof (EQUIVALENT)
28.57/10.17	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.17	
28.57/10.17	   (A^2 -> H(U1(c, e), U1(e, d)),A^2 -> H(U1(c, e), U1(e, d)))
28.57/10.17	   (A^2 -> H(U1(d, e), U1(e, d)),A^2 -> H(U1(d, e), U1(e, d)))
28.57/10.17	   (A^2 -> H(U1(a, e), d),A^2 -> H(U1(a, e), d))
28.57/10.17	   (A^2 -> H(U1(a, e), U1(e, k)),A^2 -> H(U1(a, e), U1(e, k)))
28.57/10.17	
28.57/10.17	
28.57/10.17	----------------------------------------
28.57/10.17	
28.57/10.17	(1982)
28.57/10.17	Obligation:
28.57/10.17	Q DP problem:
28.57/10.17	The TRS P consists of the following rules:
28.57/10.17	
28.57/10.17	   G(d, x, x) -> A^2
28.57/10.17	   A^2 -> H(f(c), f(c))
28.57/10.17	   H(x, x) -> G(x, x, f(k))
28.57/10.17	   A^2 -> H(f(d), f(d))
28.57/10.17	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.17	   A^2 -> H(f(e), f(e))
28.57/10.17	   A^2 -> H(f(k), f(k))
28.57/10.17	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.17	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.17	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.17	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.17	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.18	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.18	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.18	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(a, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(a, e), c)
28.57/10.18	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(a, e), e)
28.57/10.18	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(a, k), b)
28.57/10.18	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(a, k), c)
28.57/10.18	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(a, k), e)
28.57/10.18	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(a, c), d)
28.57/10.18	   A^2 -> H(U1(a, c), k)
28.57/10.18	   A^2 -> H(U1(a, d), d)
28.57/10.18	   A^2 -> H(U1(a, d), k)
28.57/10.18	   A^2 -> H(k, U1(c, b))
28.57/10.18	   A^2 -> H(k, U1(d, b))
28.57/10.18	   A^2 -> H(k, U1(b, c))
28.57/10.18	   A^2 -> H(k, U1(b, d))
28.57/10.18	   A^2 -> H(k, U1(c, c))
28.57/10.18	   A^2 -> H(k, f(e))
28.57/10.18	   A^2 -> H(k, f(k))
28.57/10.18	   A^2 -> H(k, U1(d, d))
28.57/10.18	   A^2 -> H(c, U1(e, b))
28.57/10.18	   A^2 -> H(c, U1(k, b))
28.57/10.18	   A^2 -> H(c, U1(c, d))
28.57/10.18	   A^2 -> H(c, U1(d, c))
28.57/10.18	   A^2 -> H(c, U1(b, e))
28.57/10.18	   A^2 -> H(c, U1(b, k))
28.57/10.18	   A^2 -> H(c, U1(e, c))
28.57/10.18	   A^2 -> H(c, U1(k, c))
28.57/10.18	   A^2 -> H(c, U1(c, e))
28.57/10.18	   A^2 -> H(c, U1(c, k))
28.57/10.18	   A^2 -> H(c, U1(e, e))
28.57/10.18	   A^2 -> H(c, U1(k, k))
28.57/10.18	   A^2 -> H(c, U1(k, d))
28.57/10.18	   A^2 -> H(c, U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.18	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.18	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, c), b)
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, c), e)
28.57/10.18	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.18	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.18	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.18	   A^2 -> H(U1(k, c), b)
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, c), c)
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, e), b)
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(c, e), c)
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(c, e), e)
28.57/10.18	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, k), b)
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(c, k), c)
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(c, k), e)
28.57/10.18	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, c), d)
28.57/10.18	   A^2 -> H(e, U1(e, b))
28.57/10.18	   A^2 -> H(e, U1(c, d))
28.57/10.18	   A^2 -> H(e, U1(d, c))
28.57/10.18	   A^2 -> H(e, U1(b, e))
28.57/10.18	   A^2 -> H(e, U1(b, k))
28.57/10.18	   A^2 -> H(e, U1(e, c))
28.57/10.18	   A^2 -> H(e, U1(c, e))
28.57/10.18	   A^2 -> H(e, U1(c, k))
28.57/10.18	   A^2 -> H(e, U1(e, e))
28.57/10.18	   A^2 -> H(e, U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, e), b)
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, e), c)
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.18	   A^2 -> H(f(e), d)
28.57/10.18	   A^2 -> H(f(e), k)
28.57/10.18	   A^2 -> H(U1(k, k), b)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, k), c)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.18	   A^2 -> H(f(k), d)
28.57/10.18	   A^2 -> H(f(k), k)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(k, d), b)
28.57/10.18	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, d), c)
28.57/10.18	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, k), b)
28.57/10.18	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(d, k), c)
28.57/10.18	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(d, k), e)
28.57/10.18	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, d), d)
28.57/10.18	   A^2 -> H(U1(d, d), k)
28.57/10.18	   A^2 -> H(U1(e, c), c)
28.57/10.18	   A^2 -> H(U1(c, c), e)
28.57/10.18	   A^2 -> H(U1(c, c), k)
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(e, e), e)
28.57/10.18	   A^2 -> H(d, U1(e, b))
28.57/10.18	   A^2 -> H(d, U1(k, b))
28.57/10.18	   A^2 -> H(d, U1(c, d))
28.57/10.18	   A^2 -> H(d, U1(d, c))
28.57/10.18	   A^2 -> H(d, U1(b, e))
28.57/10.18	   A^2 -> H(d, U1(b, k))
28.57/10.18	   A^2 -> H(d, U1(e, c))
28.57/10.18	   A^2 -> H(d, U1(k, c))
28.57/10.18	   A^2 -> H(d, U1(c, e))
28.57/10.18	   A^2 -> H(d, U1(c, k))
28.57/10.18	   A^2 -> H(d, U1(e, e))
28.57/10.18	   A^2 -> H(d, U1(k, k))
28.57/10.18	   A^2 -> H(d, U1(k, d))
28.57/10.18	   A^2 -> H(d, U1(d, k))
28.57/10.18	   A^2 -> H(a, b)
28.57/10.18	   A^2 -> H(a, U1(e, d))
28.57/10.18	   A^2 -> H(a, U1(d, e))
28.57/10.18	   A^2 -> H(a, c)
28.57/10.18	   A^2 -> H(a, U1(e, k))
28.57/10.18	   A^2 -> H(a, U1(k, e))
28.57/10.18	   A^2 -> H(a, e)
28.57/10.18	   A^2 -> H(a, U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, d), b)
28.57/10.18	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, d), c)
28.57/10.18	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, d), e)
28.57/10.18	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, a), d)
28.57/10.18	   A^2 -> H(U1(e, a), k)
28.57/10.18	   A^2 -> H(U1(k, a), d)
28.57/10.18	   A^2 -> H(U1(c, d), d)
28.57/10.18	   A^2 -> H(U1(c, d), k)
28.57/10.18	   A^2 -> H(U1(d, e), b)
28.57/10.18	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(d, e), c)
28.57/10.18	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(d, e), e)
28.57/10.18	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, c), d)
28.57/10.18	   A^2 -> H(U1(d, c), k)
28.57/10.18	   A^2 -> H(U1(a, e), d)
28.57/10.18	
28.57/10.18	The TRS R consists of the following rules:
28.57/10.18	
28.57/10.18	   f(x) -> U1(x, x)
28.57/10.18	   U1(e, x) -> x
28.57/10.18	   a -> c
28.57/10.18	   a -> d
28.57/10.18	   b -> c
28.57/10.18	   b -> d
28.57/10.18	   d -> k
28.57/10.18	   c -> e
28.57/10.18	   c -> k
28.57/10.18	
28.57/10.18	Q is empty.
28.57/10.18	We have to consider all minimal (P,Q,R)-chains.
28.57/10.18	----------------------------------------
28.57/10.18	
28.57/10.18	(1983) TransformationProof (EQUIVALENT)
28.57/10.18	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.18	
28.57/10.18	   (A^2 -> H(U1(c, e), U1(d, e)),A^2 -> H(U1(c, e), U1(d, e)))
28.57/10.18	   (A^2 -> H(U1(d, e), U1(d, e)),A^2 -> H(U1(d, e), U1(d, e)))
28.57/10.18	   (A^2 -> H(U1(a, e), U1(k, e)),A^2 -> H(U1(a, e), U1(k, e)))
28.57/10.18	
28.57/10.18	
28.57/10.18	----------------------------------------
28.57/10.18	
28.57/10.18	(1984)
28.57/10.18	Obligation:
28.57/10.18	Q DP problem:
28.57/10.18	The TRS P consists of the following rules:
28.57/10.18	
28.57/10.18	   G(d, x, x) -> A^2
28.57/10.18	   A^2 -> H(f(c), f(c))
28.57/10.18	   H(x, x) -> G(x, x, f(k))
28.57/10.18	   A^2 -> H(f(d), f(d))
28.57/10.18	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.18	   A^2 -> H(f(e), f(e))
28.57/10.18	   A^2 -> H(f(k), f(k))
28.57/10.18	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.18	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.18	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.18	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.18	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.18	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(a, e), c)
28.57/10.18	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(a, e), e)
28.57/10.18	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(a, k), b)
28.57/10.18	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(a, k), c)
28.57/10.18	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(a, k), e)
28.57/10.18	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(a, c), d)
28.57/10.18	   A^2 -> H(U1(a, c), k)
28.57/10.18	   A^2 -> H(U1(a, d), d)
28.57/10.18	   A^2 -> H(U1(a, d), k)
28.57/10.18	   A^2 -> H(k, U1(c, b))
28.57/10.18	   A^2 -> H(k, U1(d, b))
28.57/10.18	   A^2 -> H(k, U1(b, c))
28.57/10.18	   A^2 -> H(k, U1(b, d))
28.57/10.18	   A^2 -> H(k, U1(c, c))
28.57/10.18	   A^2 -> H(k, f(e))
28.57/10.18	   A^2 -> H(k, f(k))
28.57/10.18	   A^2 -> H(k, U1(d, d))
28.57/10.18	   A^2 -> H(c, U1(e, b))
28.57/10.18	   A^2 -> H(c, U1(k, b))
28.57/10.18	   A^2 -> H(c, U1(c, d))
28.57/10.18	   A^2 -> H(c, U1(d, c))
28.57/10.18	   A^2 -> H(c, U1(b, e))
28.57/10.18	   A^2 -> H(c, U1(b, k))
28.57/10.18	   A^2 -> H(c, U1(e, c))
28.57/10.18	   A^2 -> H(c, U1(k, c))
28.57/10.18	   A^2 -> H(c, U1(c, e))
28.57/10.18	   A^2 -> H(c, U1(c, k))
28.57/10.18	   A^2 -> H(c, U1(e, e))
28.57/10.18	   A^2 -> H(c, U1(k, k))
28.57/10.18	   A^2 -> H(c, U1(k, d))
28.57/10.18	   A^2 -> H(c, U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.18	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.18	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, c), b)
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, c), e)
28.57/10.18	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.18	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.18	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.18	   A^2 -> H(U1(k, c), b)
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, c), c)
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, e), b)
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(c, e), c)
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(c, e), e)
28.57/10.18	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, k), b)
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(c, k), c)
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(c, k), e)
28.57/10.18	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, c), d)
28.57/10.18	   A^2 -> H(e, U1(e, b))
28.57/10.18	   A^2 -> H(e, U1(c, d))
28.57/10.18	   A^2 -> H(e, U1(d, c))
28.57/10.18	   A^2 -> H(e, U1(b, e))
28.57/10.18	   A^2 -> H(e, U1(b, k))
28.57/10.18	   A^2 -> H(e, U1(e, c))
28.57/10.18	   A^2 -> H(e, U1(c, e))
28.57/10.18	   A^2 -> H(e, U1(c, k))
28.57/10.18	   A^2 -> H(e, U1(e, e))
28.57/10.18	   A^2 -> H(e, U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, e), b)
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, e), c)
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.18	   A^2 -> H(f(e), d)
28.57/10.18	   A^2 -> H(f(e), k)
28.57/10.18	   A^2 -> H(U1(k, k), b)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, k), c)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.18	   A^2 -> H(f(k), d)
28.57/10.18	   A^2 -> H(f(k), k)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(k, d), b)
28.57/10.18	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, d), c)
28.57/10.18	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, k), b)
28.57/10.18	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(d, k), c)
28.57/10.18	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(d, k), e)
28.57/10.18	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, d), d)
28.57/10.18	   A^2 -> H(U1(d, d), k)
28.57/10.18	   A^2 -> H(U1(e, c), c)
28.57/10.18	   A^2 -> H(U1(c, c), e)
28.57/10.18	   A^2 -> H(U1(c, c), k)
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(e, e), e)
28.57/10.18	   A^2 -> H(d, U1(e, b))
28.57/10.18	   A^2 -> H(d, U1(k, b))
28.57/10.18	   A^2 -> H(d, U1(c, d))
28.57/10.18	   A^2 -> H(d, U1(d, c))
28.57/10.18	   A^2 -> H(d, U1(b, e))
28.57/10.18	   A^2 -> H(d, U1(b, k))
28.57/10.18	   A^2 -> H(d, U1(e, c))
28.57/10.18	   A^2 -> H(d, U1(k, c))
28.57/10.18	   A^2 -> H(d, U1(c, e))
28.57/10.18	   A^2 -> H(d, U1(c, k))
28.57/10.18	   A^2 -> H(d, U1(e, e))
28.57/10.18	   A^2 -> H(d, U1(k, k))
28.57/10.18	   A^2 -> H(d, U1(k, d))
28.57/10.18	   A^2 -> H(d, U1(d, k))
28.57/10.18	   A^2 -> H(a, b)
28.57/10.18	   A^2 -> H(a, U1(e, d))
28.57/10.18	   A^2 -> H(a, U1(d, e))
28.57/10.18	   A^2 -> H(a, c)
28.57/10.18	   A^2 -> H(a, U1(e, k))
28.57/10.18	   A^2 -> H(a, U1(k, e))
28.57/10.18	   A^2 -> H(a, e)
28.57/10.18	   A^2 -> H(a, U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, d), b)
28.57/10.18	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, d), c)
28.57/10.18	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, d), e)
28.57/10.18	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, a), d)
28.57/10.18	   A^2 -> H(U1(e, a), k)
28.57/10.18	   A^2 -> H(U1(k, a), d)
28.57/10.18	   A^2 -> H(U1(c, d), d)
28.57/10.18	   A^2 -> H(U1(c, d), k)
28.57/10.18	   A^2 -> H(U1(d, e), b)
28.57/10.18	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(d, e), c)
28.57/10.18	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(d, e), e)
28.57/10.18	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, c), d)
28.57/10.18	   A^2 -> H(U1(d, c), k)
28.57/10.18	   A^2 -> H(U1(a, e), d)
28.57/10.18	
28.57/10.18	The TRS R consists of the following rules:
28.57/10.18	
28.57/10.18	   f(x) -> U1(x, x)
28.57/10.18	   U1(e, x) -> x
28.57/10.18	   a -> c
28.57/10.18	   a -> d
28.57/10.18	   b -> c
28.57/10.18	   b -> d
28.57/10.18	   d -> k
28.57/10.18	   c -> e
28.57/10.18	   c -> k
28.57/10.18	
28.57/10.18	Q is empty.
28.57/10.18	We have to consider all minimal (P,Q,R)-chains.
28.57/10.18	----------------------------------------
28.57/10.18	
28.57/10.18	(1985) TransformationProof (EQUIVALENT)
28.57/10.18	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), c) at position [] we obtained the following new rules [LPAR04]:
28.57/10.18	
28.57/10.18	   (A^2 -> H(U1(c, e), c),A^2 -> H(U1(c, e), c))
28.57/10.18	   (A^2 -> H(U1(d, e), c),A^2 -> H(U1(d, e), c))
28.57/10.18	   (A^2 -> H(U1(a, e), e),A^2 -> H(U1(a, e), e))
28.57/10.18	   (A^2 -> H(U1(a, e), k),A^2 -> H(U1(a, e), k))
28.57/10.18	
28.57/10.18	
28.57/10.18	----------------------------------------
28.57/10.18	
28.57/10.18	(1986)
28.57/10.18	Obligation:
28.57/10.18	Q DP problem:
28.57/10.18	The TRS P consists of the following rules:
28.57/10.18	
28.57/10.18	   G(d, x, x) -> A^2
28.57/10.18	   A^2 -> H(f(c), f(c))
28.57/10.18	   H(x, x) -> G(x, x, f(k))
28.57/10.18	   A^2 -> H(f(d), f(d))
28.57/10.18	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.18	   A^2 -> H(f(e), f(e))
28.57/10.18	   A^2 -> H(f(k), f(k))
28.57/10.18	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.18	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.18	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.18	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.18	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.18	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(a, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(a, e), e)
28.57/10.18	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(a, k), b)
28.57/10.18	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(a, k), c)
28.57/10.18	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(a, k), e)
28.57/10.18	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(a, c), d)
28.57/10.18	   A^2 -> H(U1(a, c), k)
28.57/10.18	   A^2 -> H(U1(a, d), d)
28.57/10.18	   A^2 -> H(U1(a, d), k)
28.57/10.18	   A^2 -> H(k, U1(c, b))
28.57/10.18	   A^2 -> H(k, U1(d, b))
28.57/10.18	   A^2 -> H(k, U1(b, c))
28.57/10.18	   A^2 -> H(k, U1(b, d))
28.57/10.18	   A^2 -> H(k, U1(c, c))
28.57/10.18	   A^2 -> H(k, f(e))
28.57/10.18	   A^2 -> H(k, f(k))
28.57/10.18	   A^2 -> H(k, U1(d, d))
28.57/10.18	   A^2 -> H(c, U1(e, b))
28.57/10.18	   A^2 -> H(c, U1(k, b))
28.57/10.18	   A^2 -> H(c, U1(c, d))
28.57/10.18	   A^2 -> H(c, U1(d, c))
28.57/10.18	   A^2 -> H(c, U1(b, e))
28.57/10.18	   A^2 -> H(c, U1(b, k))
28.57/10.18	   A^2 -> H(c, U1(e, c))
28.57/10.18	   A^2 -> H(c, U1(k, c))
28.57/10.18	   A^2 -> H(c, U1(c, e))
28.57/10.18	   A^2 -> H(c, U1(c, k))
28.57/10.18	   A^2 -> H(c, U1(e, e))
28.57/10.18	   A^2 -> H(c, U1(k, k))
28.57/10.18	   A^2 -> H(c, U1(k, d))
28.57/10.18	   A^2 -> H(c, U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.18	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.18	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, c), b)
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, c), e)
28.57/10.18	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.18	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.18	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.18	   A^2 -> H(U1(k, c), b)
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, c), c)
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, e), b)
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(c, e), c)
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(c, e), e)
28.57/10.18	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, k), b)
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(c, k), c)
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(c, k), e)
28.57/10.18	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, c), d)
28.57/10.18	   A^2 -> H(e, U1(e, b))
28.57/10.18	   A^2 -> H(e, U1(c, d))
28.57/10.18	   A^2 -> H(e, U1(d, c))
28.57/10.18	   A^2 -> H(e, U1(b, e))
28.57/10.18	   A^2 -> H(e, U1(b, k))
28.57/10.18	   A^2 -> H(e, U1(e, c))
28.57/10.18	   A^2 -> H(e, U1(c, e))
28.57/10.18	   A^2 -> H(e, U1(c, k))
28.57/10.18	   A^2 -> H(e, U1(e, e))
28.57/10.18	   A^2 -> H(e, U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, e), b)
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, e), c)
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.18	   A^2 -> H(f(e), d)
28.57/10.18	   A^2 -> H(f(e), k)
28.57/10.18	   A^2 -> H(U1(k, k), b)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, k), c)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.18	   A^2 -> H(f(k), d)
28.57/10.18	   A^2 -> H(f(k), k)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(k, d), b)
28.57/10.18	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, d), c)
28.57/10.18	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, k), b)
28.57/10.18	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(d, k), c)
28.57/10.18	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(d, k), e)
28.57/10.18	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, d), d)
28.57/10.18	   A^2 -> H(U1(d, d), k)
28.57/10.18	   A^2 -> H(U1(e, c), c)
28.57/10.18	   A^2 -> H(U1(c, c), e)
28.57/10.18	   A^2 -> H(U1(c, c), k)
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(e, e), e)
28.57/10.18	   A^2 -> H(d, U1(e, b))
28.57/10.18	   A^2 -> H(d, U1(k, b))
28.57/10.18	   A^2 -> H(d, U1(c, d))
28.57/10.18	   A^2 -> H(d, U1(d, c))
28.57/10.18	   A^2 -> H(d, U1(b, e))
28.57/10.18	   A^2 -> H(d, U1(b, k))
28.57/10.18	   A^2 -> H(d, U1(e, c))
28.57/10.18	   A^2 -> H(d, U1(k, c))
28.57/10.18	   A^2 -> H(d, U1(c, e))
28.57/10.18	   A^2 -> H(d, U1(c, k))
28.57/10.18	   A^2 -> H(d, U1(e, e))
28.57/10.18	   A^2 -> H(d, U1(k, k))
28.57/10.18	   A^2 -> H(d, U1(k, d))
28.57/10.18	   A^2 -> H(d, U1(d, k))
28.57/10.18	   A^2 -> H(a, b)
28.57/10.18	   A^2 -> H(a, U1(e, d))
28.57/10.18	   A^2 -> H(a, U1(d, e))
28.57/10.18	   A^2 -> H(a, c)
28.57/10.18	   A^2 -> H(a, U1(e, k))
28.57/10.18	   A^2 -> H(a, U1(k, e))
28.57/10.18	   A^2 -> H(a, e)
28.57/10.18	   A^2 -> H(a, U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, d), b)
28.57/10.18	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, d), c)
28.57/10.18	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, d), e)
28.57/10.18	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, a), d)
28.57/10.18	   A^2 -> H(U1(e, a), k)
28.57/10.18	   A^2 -> H(U1(k, a), d)
28.57/10.18	   A^2 -> H(U1(c, d), d)
28.57/10.18	   A^2 -> H(U1(c, d), k)
28.57/10.18	   A^2 -> H(U1(d, e), b)
28.57/10.18	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(d, e), c)
28.57/10.18	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(d, e), e)
28.57/10.18	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, c), d)
28.57/10.18	   A^2 -> H(U1(d, c), k)
28.57/10.18	   A^2 -> H(U1(a, e), d)
28.57/10.18	   A^2 -> H(U1(a, e), k)
28.57/10.18	
28.57/10.18	The TRS R consists of the following rules:
28.57/10.18	
28.57/10.18	   f(x) -> U1(x, x)
28.57/10.18	   U1(e, x) -> x
28.57/10.18	   a -> c
28.57/10.18	   a -> d
28.57/10.18	   b -> c
28.57/10.18	   b -> d
28.57/10.18	   d -> k
28.57/10.18	   c -> e
28.57/10.18	   c -> k
28.57/10.18	
28.57/10.18	Q is empty.
28.57/10.18	We have to consider all minimal (P,Q,R)-chains.
28.57/10.18	----------------------------------------
28.57/10.18	
28.57/10.18	(1987) TransformationProof (EQUIVALENT)
28.57/10.18	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.18	
28.57/10.18	   (A^2 -> H(U1(c, e), U1(e, k)),A^2 -> H(U1(c, e), U1(e, k)))
28.57/10.18	   (A^2 -> H(U1(d, e), U1(e, k)),A^2 -> H(U1(d, e), U1(e, k)))
28.57/10.18	   (A^2 -> H(U1(a, e), k),A^2 -> H(U1(a, e), k))
28.57/10.18	
28.57/10.18	
28.57/10.18	----------------------------------------
28.57/10.18	
28.57/10.18	(1988)
28.57/10.18	Obligation:
28.57/10.18	Q DP problem:
28.57/10.18	The TRS P consists of the following rules:
28.57/10.18	
28.57/10.18	   G(d, x, x) -> A^2
28.57/10.18	   A^2 -> H(f(c), f(c))
28.57/10.18	   H(x, x) -> G(x, x, f(k))
28.57/10.18	   A^2 -> H(f(d), f(d))
28.57/10.18	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.18	   A^2 -> H(f(e), f(e))
28.57/10.18	   A^2 -> H(f(k), f(k))
28.57/10.18	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.18	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.18	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.18	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.18	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.18	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(a, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(a, e), e)
28.57/10.18	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(a, k), b)
28.57/10.18	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(a, k), c)
28.57/10.18	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(a, k), e)
28.57/10.18	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(a, c), d)
28.57/10.18	   A^2 -> H(U1(a, c), k)
28.57/10.18	   A^2 -> H(U1(a, d), d)
28.57/10.18	   A^2 -> H(U1(a, d), k)
28.57/10.18	   A^2 -> H(k, U1(c, b))
28.57/10.18	   A^2 -> H(k, U1(d, b))
28.57/10.18	   A^2 -> H(k, U1(b, c))
28.57/10.18	   A^2 -> H(k, U1(b, d))
28.57/10.18	   A^2 -> H(k, U1(c, c))
28.57/10.18	   A^2 -> H(k, f(e))
28.57/10.18	   A^2 -> H(k, f(k))
28.57/10.18	   A^2 -> H(k, U1(d, d))
28.57/10.18	   A^2 -> H(c, U1(e, b))
28.57/10.18	   A^2 -> H(c, U1(k, b))
28.57/10.18	   A^2 -> H(c, U1(c, d))
28.57/10.18	   A^2 -> H(c, U1(d, c))
28.57/10.18	   A^2 -> H(c, U1(b, e))
28.57/10.18	   A^2 -> H(c, U1(b, k))
28.57/10.18	   A^2 -> H(c, U1(e, c))
28.57/10.18	   A^2 -> H(c, U1(k, c))
28.57/10.18	   A^2 -> H(c, U1(c, e))
28.57/10.18	   A^2 -> H(c, U1(c, k))
28.57/10.18	   A^2 -> H(c, U1(e, e))
28.57/10.18	   A^2 -> H(c, U1(k, k))
28.57/10.18	   A^2 -> H(c, U1(k, d))
28.57/10.18	   A^2 -> H(c, U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.18	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.18	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, c), b)
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, c), e)
28.57/10.18	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.18	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.18	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.18	   A^2 -> H(U1(k, c), b)
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, c), c)
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, e), b)
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(c, e), c)
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(c, e), e)
28.57/10.18	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, k), b)
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(c, k), c)
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(c, k), e)
28.57/10.18	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, c), d)
28.57/10.18	   A^2 -> H(e, U1(e, b))
28.57/10.18	   A^2 -> H(e, U1(c, d))
28.57/10.18	   A^2 -> H(e, U1(d, c))
28.57/10.18	   A^2 -> H(e, U1(b, e))
28.57/10.18	   A^2 -> H(e, U1(b, k))
28.57/10.18	   A^2 -> H(e, U1(e, c))
28.57/10.18	   A^2 -> H(e, U1(c, e))
28.57/10.18	   A^2 -> H(e, U1(c, k))
28.57/10.18	   A^2 -> H(e, U1(e, e))
28.57/10.18	   A^2 -> H(e, U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, e), b)
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, e), c)
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.18	   A^2 -> H(f(e), d)
28.57/10.18	   A^2 -> H(f(e), k)
28.57/10.18	   A^2 -> H(U1(k, k), b)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, k), c)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.18	   A^2 -> H(f(k), d)
28.57/10.18	   A^2 -> H(f(k), k)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(k, d), b)
28.57/10.18	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, d), c)
28.57/10.18	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, k), b)
28.57/10.18	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(d, k), c)
28.57/10.18	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(d, k), e)
28.57/10.18	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, d), d)
28.57/10.18	   A^2 -> H(U1(d, d), k)
28.57/10.18	   A^2 -> H(U1(e, c), c)
28.57/10.18	   A^2 -> H(U1(c, c), e)
28.57/10.18	   A^2 -> H(U1(c, c), k)
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(e, e), e)
28.57/10.18	   A^2 -> H(d, U1(e, b))
28.57/10.18	   A^2 -> H(d, U1(k, b))
28.57/10.18	   A^2 -> H(d, U1(c, d))
28.57/10.18	   A^2 -> H(d, U1(d, c))
28.57/10.18	   A^2 -> H(d, U1(b, e))
28.57/10.18	   A^2 -> H(d, U1(b, k))
28.57/10.18	   A^2 -> H(d, U1(e, c))
28.57/10.18	   A^2 -> H(d, U1(k, c))
28.57/10.18	   A^2 -> H(d, U1(c, e))
28.57/10.18	   A^2 -> H(d, U1(c, k))
28.57/10.18	   A^2 -> H(d, U1(e, e))
28.57/10.18	   A^2 -> H(d, U1(k, k))
28.57/10.18	   A^2 -> H(d, U1(k, d))
28.57/10.18	   A^2 -> H(d, U1(d, k))
28.57/10.18	   A^2 -> H(a, b)
28.57/10.18	   A^2 -> H(a, U1(e, d))
28.57/10.18	   A^2 -> H(a, U1(d, e))
28.57/10.18	   A^2 -> H(a, c)
28.57/10.18	   A^2 -> H(a, U1(e, k))
28.57/10.18	   A^2 -> H(a, U1(k, e))
28.57/10.18	   A^2 -> H(a, e)
28.57/10.18	   A^2 -> H(a, U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, d), b)
28.57/10.18	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, d), c)
28.57/10.18	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, d), e)
28.57/10.18	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, a), d)
28.57/10.18	   A^2 -> H(U1(e, a), k)
28.57/10.18	   A^2 -> H(U1(k, a), d)
28.57/10.18	   A^2 -> H(U1(c, d), d)
28.57/10.18	   A^2 -> H(U1(c, d), k)
28.57/10.18	   A^2 -> H(U1(d, e), b)
28.57/10.18	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(d, e), c)
28.57/10.18	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(d, e), e)
28.57/10.18	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, c), d)
28.57/10.18	   A^2 -> H(U1(d, c), k)
28.57/10.18	   A^2 -> H(U1(a, e), d)
28.57/10.18	   A^2 -> H(U1(a, e), k)
28.57/10.18	
28.57/10.18	The TRS R consists of the following rules:
28.57/10.18	
28.57/10.18	   f(x) -> U1(x, x)
28.57/10.18	   U1(e, x) -> x
28.57/10.18	   a -> c
28.57/10.18	   a -> d
28.57/10.18	   b -> c
28.57/10.18	   b -> d
28.57/10.18	   d -> k
28.57/10.18	   c -> e
28.57/10.18	   c -> k
28.57/10.18	
28.57/10.18	Q is empty.
28.57/10.18	We have to consider all minimal (P,Q,R)-chains.
28.57/10.18	----------------------------------------
28.57/10.18	
28.57/10.18	(1989) TransformationProof (EQUIVALENT)
28.57/10.18	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.18	
28.57/10.18	   (A^2 -> H(U1(c, e), U1(k, e)),A^2 -> H(U1(c, e), U1(k, e)))
28.57/10.18	   (A^2 -> H(U1(d, e), U1(k, e)),A^2 -> H(U1(d, e), U1(k, e)))
28.57/10.18	
28.57/10.18	
28.57/10.18	----------------------------------------
28.57/10.18	
28.57/10.18	(1990)
28.57/10.18	Obligation:
28.57/10.18	Q DP problem:
28.57/10.18	The TRS P consists of the following rules:
28.57/10.18	
28.57/10.18	   G(d, x, x) -> A^2
28.57/10.18	   A^2 -> H(f(c), f(c))
28.57/10.18	   H(x, x) -> G(x, x, f(k))
28.57/10.18	   A^2 -> H(f(d), f(d))
28.57/10.18	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.18	   A^2 -> H(f(e), f(e))
28.57/10.18	   A^2 -> H(f(k), f(k))
28.57/10.18	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.18	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.18	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.18	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.18	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.18	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(a, e), e)
28.57/10.18	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(a, k), b)
28.57/10.18	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(a, k), c)
28.57/10.18	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(a, k), e)
28.57/10.18	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(a, c), d)
28.57/10.18	   A^2 -> H(U1(a, c), k)
28.57/10.18	   A^2 -> H(U1(a, d), d)
28.57/10.18	   A^2 -> H(U1(a, d), k)
28.57/10.18	   A^2 -> H(k, U1(c, b))
28.57/10.18	   A^2 -> H(k, U1(d, b))
28.57/10.18	   A^2 -> H(k, U1(b, c))
28.57/10.18	   A^2 -> H(k, U1(b, d))
28.57/10.18	   A^2 -> H(k, U1(c, c))
28.57/10.18	   A^2 -> H(k, f(e))
28.57/10.18	   A^2 -> H(k, f(k))
28.57/10.18	   A^2 -> H(k, U1(d, d))
28.57/10.18	   A^2 -> H(c, U1(e, b))
28.57/10.18	   A^2 -> H(c, U1(k, b))
28.57/10.18	   A^2 -> H(c, U1(c, d))
28.57/10.18	   A^2 -> H(c, U1(d, c))
28.57/10.18	   A^2 -> H(c, U1(b, e))
28.57/10.18	   A^2 -> H(c, U1(b, k))
28.57/10.18	   A^2 -> H(c, U1(e, c))
28.57/10.18	   A^2 -> H(c, U1(k, c))
28.57/10.18	   A^2 -> H(c, U1(c, e))
28.57/10.18	   A^2 -> H(c, U1(c, k))
28.57/10.18	   A^2 -> H(c, U1(e, e))
28.57/10.18	   A^2 -> H(c, U1(k, k))
28.57/10.18	   A^2 -> H(c, U1(k, d))
28.57/10.18	   A^2 -> H(c, U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.18	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.18	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, c), b)
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, c), e)
28.57/10.18	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.18	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.18	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.18	   A^2 -> H(U1(k, c), b)
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, c), c)
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, e), b)
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(c, e), c)
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(c, e), e)
28.57/10.18	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, k), b)
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(c, k), c)
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(c, k), e)
28.57/10.18	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, c), d)
28.57/10.18	   A^2 -> H(e, U1(e, b))
28.57/10.18	   A^2 -> H(e, U1(c, d))
28.57/10.18	   A^2 -> H(e, U1(d, c))
28.57/10.18	   A^2 -> H(e, U1(b, e))
28.57/10.18	   A^2 -> H(e, U1(b, k))
28.57/10.18	   A^2 -> H(e, U1(e, c))
28.57/10.18	   A^2 -> H(e, U1(c, e))
28.57/10.18	   A^2 -> H(e, U1(c, k))
28.57/10.18	   A^2 -> H(e, U1(e, e))
28.57/10.18	   A^2 -> H(e, U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, e), b)
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, e), c)
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.18	   A^2 -> H(f(e), d)
28.57/10.18	   A^2 -> H(f(e), k)
28.57/10.18	   A^2 -> H(U1(k, k), b)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, k), c)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.18	   A^2 -> H(f(k), d)
28.57/10.18	   A^2 -> H(f(k), k)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(k, d), b)
28.57/10.18	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, d), c)
28.57/10.18	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, k), b)
28.57/10.18	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(d, k), c)
28.57/10.18	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(d, k), e)
28.57/10.18	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, d), d)
28.57/10.18	   A^2 -> H(U1(d, d), k)
28.57/10.18	   A^2 -> H(U1(e, c), c)
28.57/10.18	   A^2 -> H(U1(c, c), e)
28.57/10.18	   A^2 -> H(U1(c, c), k)
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(e, e), e)
28.57/10.18	   A^2 -> H(d, U1(e, b))
28.57/10.18	   A^2 -> H(d, U1(k, b))
28.57/10.18	   A^2 -> H(d, U1(c, d))
28.57/10.18	   A^2 -> H(d, U1(d, c))
28.57/10.18	   A^2 -> H(d, U1(b, e))
28.57/10.18	   A^2 -> H(d, U1(b, k))
28.57/10.18	   A^2 -> H(d, U1(e, c))
28.57/10.18	   A^2 -> H(d, U1(k, c))
28.57/10.18	   A^2 -> H(d, U1(c, e))
28.57/10.18	   A^2 -> H(d, U1(c, k))
28.57/10.18	   A^2 -> H(d, U1(e, e))
28.57/10.18	   A^2 -> H(d, U1(k, k))
28.57/10.18	   A^2 -> H(d, U1(k, d))
28.57/10.18	   A^2 -> H(d, U1(d, k))
28.57/10.18	   A^2 -> H(a, b)
28.57/10.18	   A^2 -> H(a, U1(e, d))
28.57/10.18	   A^2 -> H(a, U1(d, e))
28.57/10.18	   A^2 -> H(a, c)
28.57/10.18	   A^2 -> H(a, U1(e, k))
28.57/10.18	   A^2 -> H(a, U1(k, e))
28.57/10.18	   A^2 -> H(a, e)
28.57/10.18	   A^2 -> H(a, U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, d), b)
28.57/10.18	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, d), c)
28.57/10.18	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, d), e)
28.57/10.18	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, a), d)
28.57/10.18	   A^2 -> H(U1(e, a), k)
28.57/10.18	   A^2 -> H(U1(k, a), d)
28.57/10.18	   A^2 -> H(U1(c, d), d)
28.57/10.18	   A^2 -> H(U1(c, d), k)
28.57/10.18	   A^2 -> H(U1(d, e), b)
28.57/10.18	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(d, e), c)
28.57/10.18	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(d, e), e)
28.57/10.18	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, c), d)
28.57/10.18	   A^2 -> H(U1(d, c), k)
28.57/10.18	   A^2 -> H(U1(a, e), d)
28.57/10.18	   A^2 -> H(U1(a, e), k)
28.57/10.18	
28.57/10.18	The TRS R consists of the following rules:
28.57/10.18	
28.57/10.18	   f(x) -> U1(x, x)
28.57/10.18	   U1(e, x) -> x
28.57/10.18	   a -> c
28.57/10.18	   a -> d
28.57/10.18	   b -> c
28.57/10.18	   b -> d
28.57/10.18	   d -> k
28.57/10.18	   c -> e
28.57/10.18	   c -> k
28.57/10.18	
28.57/10.18	Q is empty.
28.57/10.18	We have to consider all minimal (P,Q,R)-chains.
28.57/10.18	----------------------------------------
28.57/10.18	
28.57/10.18	(1991) TransformationProof (EQUIVALENT)
28.57/10.18	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), e) at position [] we obtained the following new rules [LPAR04]:
28.57/10.18	
28.57/10.18	   (A^2 -> H(U1(c, e), e),A^2 -> H(U1(c, e), e))
28.57/10.18	   (A^2 -> H(U1(d, e), e),A^2 -> H(U1(d, e), e))
28.57/10.18	
28.57/10.18	
28.57/10.18	----------------------------------------
28.57/10.18	
28.57/10.18	(1992)
28.57/10.18	Obligation:
28.57/10.18	Q DP problem:
28.57/10.18	The TRS P consists of the following rules:
28.57/10.18	
28.57/10.18	   G(d, x, x) -> A^2
28.57/10.18	   A^2 -> H(f(c), f(c))
28.57/10.18	   H(x, x) -> G(x, x, f(k))
28.57/10.18	   A^2 -> H(f(d), f(d))
28.57/10.18	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.18	   A^2 -> H(f(e), f(e))
28.57/10.18	   A^2 -> H(f(k), f(k))
28.57/10.18	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.18	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.18	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.18	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.18	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.18	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(a, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(a, k), b)
28.57/10.18	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(a, k), c)
28.57/10.18	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(a, k), e)
28.57/10.18	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(a, c), d)
28.57/10.18	   A^2 -> H(U1(a, c), k)
28.57/10.18	   A^2 -> H(U1(a, d), d)
28.57/10.18	   A^2 -> H(U1(a, d), k)
28.57/10.18	   A^2 -> H(k, U1(c, b))
28.57/10.18	   A^2 -> H(k, U1(d, b))
28.57/10.18	   A^2 -> H(k, U1(b, c))
28.57/10.18	   A^2 -> H(k, U1(b, d))
28.57/10.18	   A^2 -> H(k, U1(c, c))
28.57/10.18	   A^2 -> H(k, f(e))
28.57/10.18	   A^2 -> H(k, f(k))
28.57/10.18	   A^2 -> H(k, U1(d, d))
28.57/10.18	   A^2 -> H(c, U1(e, b))
28.57/10.18	   A^2 -> H(c, U1(k, b))
28.57/10.18	   A^2 -> H(c, U1(c, d))
28.57/10.18	   A^2 -> H(c, U1(d, c))
28.57/10.18	   A^2 -> H(c, U1(b, e))
28.57/10.18	   A^2 -> H(c, U1(b, k))
28.57/10.18	   A^2 -> H(c, U1(e, c))
28.57/10.18	   A^2 -> H(c, U1(k, c))
28.57/10.18	   A^2 -> H(c, U1(c, e))
28.57/10.18	   A^2 -> H(c, U1(c, k))
28.57/10.18	   A^2 -> H(c, U1(e, e))
28.57/10.18	   A^2 -> H(c, U1(k, k))
28.57/10.18	   A^2 -> H(c, U1(k, d))
28.57/10.18	   A^2 -> H(c, U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.18	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.18	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, c), b)
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, c), e)
28.57/10.18	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.18	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.18	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.18	   A^2 -> H(U1(k, c), b)
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, c), c)
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, e), b)
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(c, e), c)
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(c, e), e)
28.57/10.18	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, k), b)
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(c, k), c)
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(c, k), e)
28.57/10.18	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, c), d)
28.57/10.18	   A^2 -> H(e, U1(e, b))
28.57/10.18	   A^2 -> H(e, U1(c, d))
28.57/10.18	   A^2 -> H(e, U1(d, c))
28.57/10.18	   A^2 -> H(e, U1(b, e))
28.57/10.18	   A^2 -> H(e, U1(b, k))
28.57/10.18	   A^2 -> H(e, U1(e, c))
28.57/10.18	   A^2 -> H(e, U1(c, e))
28.57/10.18	   A^2 -> H(e, U1(c, k))
28.57/10.18	   A^2 -> H(e, U1(e, e))
28.57/10.18	   A^2 -> H(e, U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, e), b)
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, e), c)
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.18	   A^2 -> H(f(e), d)
28.57/10.18	   A^2 -> H(f(e), k)
28.57/10.18	   A^2 -> H(U1(k, k), b)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, k), c)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.18	   A^2 -> H(f(k), d)
28.57/10.18	   A^2 -> H(f(k), k)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(k, d), b)
28.57/10.18	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, d), c)
28.57/10.18	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, k), b)
28.57/10.18	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(d, k), c)
28.57/10.18	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(d, k), e)
28.57/10.18	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, d), d)
28.57/10.18	   A^2 -> H(U1(d, d), k)
28.57/10.18	   A^2 -> H(U1(e, c), c)
28.57/10.18	   A^2 -> H(U1(c, c), e)
28.57/10.18	   A^2 -> H(U1(c, c), k)
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(e, e), e)
28.57/10.18	   A^2 -> H(d, U1(e, b))
28.57/10.18	   A^2 -> H(d, U1(k, b))
28.57/10.18	   A^2 -> H(d, U1(c, d))
28.57/10.18	   A^2 -> H(d, U1(d, c))
28.57/10.18	   A^2 -> H(d, U1(b, e))
28.57/10.18	   A^2 -> H(d, U1(b, k))
28.57/10.18	   A^2 -> H(d, U1(e, c))
28.57/10.18	   A^2 -> H(d, U1(k, c))
28.57/10.18	   A^2 -> H(d, U1(c, e))
28.57/10.18	   A^2 -> H(d, U1(c, k))
28.57/10.18	   A^2 -> H(d, U1(e, e))
28.57/10.18	   A^2 -> H(d, U1(k, k))
28.57/10.18	   A^2 -> H(d, U1(k, d))
28.57/10.18	   A^2 -> H(d, U1(d, k))
28.57/10.18	   A^2 -> H(a, b)
28.57/10.18	   A^2 -> H(a, U1(e, d))
28.57/10.18	   A^2 -> H(a, U1(d, e))
28.57/10.18	   A^2 -> H(a, c)
28.57/10.18	   A^2 -> H(a, U1(e, k))
28.57/10.18	   A^2 -> H(a, U1(k, e))
28.57/10.18	   A^2 -> H(a, e)
28.57/10.18	   A^2 -> H(a, U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, d), b)
28.57/10.18	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, d), c)
28.57/10.18	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, d), e)
28.57/10.18	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, a), d)
28.57/10.18	   A^2 -> H(U1(e, a), k)
28.57/10.18	   A^2 -> H(U1(k, a), d)
28.57/10.18	   A^2 -> H(U1(c, d), d)
28.57/10.18	   A^2 -> H(U1(c, d), k)
28.57/10.18	   A^2 -> H(U1(d, e), b)
28.57/10.18	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(d, e), c)
28.57/10.18	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(d, e), e)
28.57/10.18	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, c), d)
28.57/10.18	   A^2 -> H(U1(d, c), k)
28.57/10.18	   A^2 -> H(U1(a, e), d)
28.57/10.18	   A^2 -> H(U1(a, e), k)
28.57/10.18	
28.57/10.18	The TRS R consists of the following rules:
28.57/10.18	
28.57/10.18	   f(x) -> U1(x, x)
28.57/10.18	   U1(e, x) -> x
28.57/10.18	   a -> c
28.57/10.18	   a -> d
28.57/10.18	   b -> c
28.57/10.18	   b -> d
28.57/10.18	   d -> k
28.57/10.18	   c -> e
28.57/10.18	   c -> k
28.57/10.18	
28.57/10.18	Q is empty.
28.57/10.18	We have to consider all minimal (P,Q,R)-chains.
28.57/10.18	----------------------------------------
28.57/10.18	
28.57/10.18	(1993) TransformationProof (EQUIVALENT)
28.57/10.18	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.18	
28.57/10.18	   (A^2 -> H(U1(c, e), U1(k, k)),A^2 -> H(U1(c, e), U1(k, k)))
28.57/10.18	   (A^2 -> H(U1(d, e), U1(k, k)),A^2 -> H(U1(d, e), U1(k, k)))
28.57/10.18	
28.57/10.18	
28.57/10.18	----------------------------------------
28.57/10.18	
28.57/10.18	(1994)
28.57/10.18	Obligation:
28.57/10.18	Q DP problem:
28.57/10.18	The TRS P consists of the following rules:
28.57/10.18	
28.57/10.18	   G(d, x, x) -> A^2
28.57/10.18	   A^2 -> H(f(c), f(c))
28.57/10.18	   H(x, x) -> G(x, x, f(k))
28.57/10.18	   A^2 -> H(f(d), f(d))
28.57/10.18	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.18	   A^2 -> H(f(e), f(e))
28.57/10.18	   A^2 -> H(f(k), f(k))
28.57/10.18	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.18	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.18	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.18	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.18	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.18	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(a, k), b)
28.57/10.18	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(a, k), c)
28.57/10.18	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(a, k), e)
28.57/10.18	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(a, c), d)
28.57/10.18	   A^2 -> H(U1(a, c), k)
28.57/10.18	   A^2 -> H(U1(a, d), d)
28.57/10.18	   A^2 -> H(U1(a, d), k)
28.57/10.18	   A^2 -> H(k, U1(c, b))
28.57/10.18	   A^2 -> H(k, U1(d, b))
28.57/10.18	   A^2 -> H(k, U1(b, c))
28.57/10.18	   A^2 -> H(k, U1(b, d))
28.57/10.18	   A^2 -> H(k, U1(c, c))
28.57/10.18	   A^2 -> H(k, f(e))
28.57/10.18	   A^2 -> H(k, f(k))
28.57/10.18	   A^2 -> H(k, U1(d, d))
28.57/10.18	   A^2 -> H(c, U1(e, b))
28.57/10.18	   A^2 -> H(c, U1(k, b))
28.57/10.18	   A^2 -> H(c, U1(c, d))
28.57/10.18	   A^2 -> H(c, U1(d, c))
28.57/10.18	   A^2 -> H(c, U1(b, e))
28.57/10.18	   A^2 -> H(c, U1(b, k))
28.57/10.18	   A^2 -> H(c, U1(e, c))
28.57/10.18	   A^2 -> H(c, U1(k, c))
28.57/10.18	   A^2 -> H(c, U1(c, e))
28.57/10.18	   A^2 -> H(c, U1(c, k))
28.57/10.18	   A^2 -> H(c, U1(e, e))
28.57/10.18	   A^2 -> H(c, U1(k, k))
28.57/10.18	   A^2 -> H(c, U1(k, d))
28.57/10.18	   A^2 -> H(c, U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.18	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.18	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, c), b)
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, c), e)
28.57/10.18	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.18	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.18	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.18	   A^2 -> H(U1(k, c), b)
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, c), c)
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, e), b)
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(c, e), c)
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(c, e), e)
28.57/10.18	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, k), b)
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(c, k), c)
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(c, k), e)
28.57/10.18	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, c), d)
28.57/10.18	   A^2 -> H(e, U1(e, b))
28.57/10.18	   A^2 -> H(e, U1(c, d))
28.57/10.18	   A^2 -> H(e, U1(d, c))
28.57/10.18	   A^2 -> H(e, U1(b, e))
28.57/10.18	   A^2 -> H(e, U1(b, k))
28.57/10.18	   A^2 -> H(e, U1(e, c))
28.57/10.18	   A^2 -> H(e, U1(c, e))
28.57/10.18	   A^2 -> H(e, U1(c, k))
28.57/10.18	   A^2 -> H(e, U1(e, e))
28.57/10.18	   A^2 -> H(e, U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, e), b)
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, e), c)
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.18	   A^2 -> H(f(e), d)
28.57/10.18	   A^2 -> H(f(e), k)
28.57/10.18	   A^2 -> H(U1(k, k), b)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, k), c)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.18	   A^2 -> H(f(k), d)
28.57/10.18	   A^2 -> H(f(k), k)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(k, d), b)
28.57/10.18	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, d), c)
28.57/10.18	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, k), b)
28.57/10.18	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(d, k), c)
28.57/10.18	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(d, k), e)
28.57/10.18	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, d), d)
28.57/10.18	   A^2 -> H(U1(d, d), k)
28.57/10.18	   A^2 -> H(U1(e, c), c)
28.57/10.18	   A^2 -> H(U1(c, c), e)
28.57/10.18	   A^2 -> H(U1(c, c), k)
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(e, e), e)
28.57/10.18	   A^2 -> H(d, U1(e, b))
28.57/10.18	   A^2 -> H(d, U1(k, b))
28.57/10.18	   A^2 -> H(d, U1(c, d))
28.57/10.18	   A^2 -> H(d, U1(d, c))
28.57/10.18	   A^2 -> H(d, U1(b, e))
28.57/10.18	   A^2 -> H(d, U1(b, k))
28.57/10.18	   A^2 -> H(d, U1(e, c))
28.57/10.18	   A^2 -> H(d, U1(k, c))
28.57/10.18	   A^2 -> H(d, U1(c, e))
28.57/10.18	   A^2 -> H(d, U1(c, k))
28.57/10.18	   A^2 -> H(d, U1(e, e))
28.57/10.18	   A^2 -> H(d, U1(k, k))
28.57/10.18	   A^2 -> H(d, U1(k, d))
28.57/10.18	   A^2 -> H(d, U1(d, k))
28.57/10.18	   A^2 -> H(a, b)
28.57/10.18	   A^2 -> H(a, U1(e, d))
28.57/10.18	   A^2 -> H(a, U1(d, e))
28.57/10.18	   A^2 -> H(a, c)
28.57/10.18	   A^2 -> H(a, U1(e, k))
28.57/10.18	   A^2 -> H(a, U1(k, e))
28.57/10.18	   A^2 -> H(a, e)
28.57/10.18	   A^2 -> H(a, U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, d), b)
28.57/10.18	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, d), c)
28.57/10.18	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, d), e)
28.57/10.18	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, a), d)
28.57/10.18	   A^2 -> H(U1(e, a), k)
28.57/10.18	   A^2 -> H(U1(k, a), d)
28.57/10.18	   A^2 -> H(U1(c, d), d)
28.57/10.18	   A^2 -> H(U1(c, d), k)
28.57/10.18	   A^2 -> H(U1(d, e), b)
28.57/10.18	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(d, e), c)
28.57/10.18	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(d, e), e)
28.57/10.18	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, c), d)
28.57/10.18	   A^2 -> H(U1(d, c), k)
28.57/10.18	   A^2 -> H(U1(a, e), d)
28.57/10.18	   A^2 -> H(U1(a, e), k)
28.57/10.18	
28.57/10.18	The TRS R consists of the following rules:
28.57/10.18	
28.57/10.18	   f(x) -> U1(x, x)
28.57/10.18	   U1(e, x) -> x
28.57/10.18	   a -> c
28.57/10.18	   a -> d
28.57/10.18	   b -> c
28.57/10.18	   b -> d
28.57/10.18	   d -> k
28.57/10.18	   c -> e
28.57/10.18	   c -> k
28.57/10.18	
28.57/10.18	Q is empty.
28.57/10.18	We have to consider all minimal (P,Q,R)-chains.
28.57/10.18	----------------------------------------
28.57/10.18	
28.57/10.18	(1995) TransformationProof (EQUIVALENT)
28.57/10.18	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), b) at position [] we obtained the following new rules [LPAR04]:
28.57/10.18	
28.57/10.18	   (A^2 -> H(U1(c, k), b),A^2 -> H(U1(c, k), b))
28.57/10.18	   (A^2 -> H(U1(d, k), b),A^2 -> H(U1(d, k), b))
28.57/10.18	   (A^2 -> H(U1(a, k), c),A^2 -> H(U1(a, k), c))
28.57/10.18	   (A^2 -> H(U1(a, k), d),A^2 -> H(U1(a, k), d))
28.57/10.18	
28.57/10.18	
28.57/10.18	----------------------------------------
28.57/10.18	
28.57/10.18	(1996)
28.57/10.18	Obligation:
28.57/10.18	Q DP problem:
28.57/10.18	The TRS P consists of the following rules:
28.57/10.18	
28.57/10.18	   G(d, x, x) -> A^2
28.57/10.18	   A^2 -> H(f(c), f(c))
28.57/10.18	   H(x, x) -> G(x, x, f(k))
28.57/10.18	   A^2 -> H(f(d), f(d))
28.57/10.18	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.18	   A^2 -> H(f(e), f(e))
28.57/10.18	   A^2 -> H(f(k), f(k))
28.57/10.18	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.18	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.18	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.18	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.18	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.18	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(a, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(a, k), c)
28.57/10.18	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(a, k), e)
28.57/10.18	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(a, c), d)
28.57/10.18	   A^2 -> H(U1(a, c), k)
28.57/10.18	   A^2 -> H(U1(a, d), d)
28.57/10.18	   A^2 -> H(U1(a, d), k)
28.57/10.18	   A^2 -> H(k, U1(c, b))
28.57/10.18	   A^2 -> H(k, U1(d, b))
28.57/10.18	   A^2 -> H(k, U1(b, c))
28.57/10.18	   A^2 -> H(k, U1(b, d))
28.57/10.18	   A^2 -> H(k, U1(c, c))
28.57/10.18	   A^2 -> H(k, f(e))
28.57/10.18	   A^2 -> H(k, f(k))
28.57/10.18	   A^2 -> H(k, U1(d, d))
28.57/10.18	   A^2 -> H(c, U1(e, b))
28.57/10.18	   A^2 -> H(c, U1(k, b))
28.57/10.18	   A^2 -> H(c, U1(c, d))
28.57/10.18	   A^2 -> H(c, U1(d, c))
28.57/10.18	   A^2 -> H(c, U1(b, e))
28.57/10.18	   A^2 -> H(c, U1(b, k))
28.57/10.18	   A^2 -> H(c, U1(e, c))
28.57/10.18	   A^2 -> H(c, U1(k, c))
28.57/10.18	   A^2 -> H(c, U1(c, e))
28.57/10.18	   A^2 -> H(c, U1(c, k))
28.57/10.18	   A^2 -> H(c, U1(e, e))
28.57/10.18	   A^2 -> H(c, U1(k, k))
28.57/10.18	   A^2 -> H(c, U1(k, d))
28.57/10.18	   A^2 -> H(c, U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.18	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.18	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, c), b)
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, c), e)
28.57/10.18	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.18	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.18	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.18	   A^2 -> H(U1(k, c), b)
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, c), c)
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, e), b)
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(c, e), c)
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(c, e), e)
28.57/10.18	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, k), b)
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(c, k), c)
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(c, k), e)
28.57/10.18	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(c, c), d)
28.57/10.18	   A^2 -> H(e, U1(e, b))
28.57/10.18	   A^2 -> H(e, U1(c, d))
28.57/10.18	   A^2 -> H(e, U1(d, c))
28.57/10.18	   A^2 -> H(e, U1(b, e))
28.57/10.18	   A^2 -> H(e, U1(b, k))
28.57/10.18	   A^2 -> H(e, U1(e, c))
28.57/10.18	   A^2 -> H(e, U1(c, e))
28.57/10.18	   A^2 -> H(e, U1(c, k))
28.57/10.18	   A^2 -> H(e, U1(e, e))
28.57/10.18	   A^2 -> H(e, U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, e), b)
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, e), c)
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.18	   A^2 -> H(f(e), d)
28.57/10.18	   A^2 -> H(f(e), k)
28.57/10.18	   A^2 -> H(U1(k, k), b)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, k), c)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.18	   A^2 -> H(f(k), d)
28.57/10.18	   A^2 -> H(f(k), k)
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.18	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(k, d), b)
28.57/10.18	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, d), c)
28.57/10.18	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, k), b)
28.57/10.18	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.18	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(d, k), c)
28.57/10.18	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(d, k), e)
28.57/10.18	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, d), d)
28.57/10.18	   A^2 -> H(U1(d, d), k)
28.57/10.18	   A^2 -> H(U1(e, c), c)
28.57/10.18	   A^2 -> H(U1(c, c), e)
28.57/10.18	   A^2 -> H(U1(c, c), k)
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.18	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(e, e), e)
28.57/10.18	   A^2 -> H(d, U1(e, b))
28.57/10.18	   A^2 -> H(d, U1(k, b))
28.57/10.18	   A^2 -> H(d, U1(c, d))
28.57/10.18	   A^2 -> H(d, U1(d, c))
28.57/10.18	   A^2 -> H(d, U1(b, e))
28.57/10.18	   A^2 -> H(d, U1(b, k))
28.57/10.18	   A^2 -> H(d, U1(e, c))
28.57/10.18	   A^2 -> H(d, U1(k, c))
28.57/10.18	   A^2 -> H(d, U1(c, e))
28.57/10.18	   A^2 -> H(d, U1(c, k))
28.57/10.18	   A^2 -> H(d, U1(e, e))
28.57/10.18	   A^2 -> H(d, U1(k, k))
28.57/10.18	   A^2 -> H(d, U1(k, d))
28.57/10.18	   A^2 -> H(d, U1(d, k))
28.57/10.18	   A^2 -> H(a, b)
28.57/10.18	   A^2 -> H(a, U1(e, d))
28.57/10.18	   A^2 -> H(a, U1(d, e))
28.57/10.18	   A^2 -> H(a, c)
28.57/10.18	   A^2 -> H(a, U1(e, k))
28.57/10.18	   A^2 -> H(a, U1(k, e))
28.57/10.18	   A^2 -> H(a, e)
28.57/10.18	   A^2 -> H(a, U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, d), b)
28.57/10.18	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, d), c)
28.57/10.18	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, d), e)
28.57/10.18	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, a), d)
28.57/10.18	   A^2 -> H(U1(e, a), k)
28.57/10.18	   A^2 -> H(U1(k, a), d)
28.57/10.18	   A^2 -> H(U1(c, d), d)
28.57/10.18	   A^2 -> H(U1(c, d), k)
28.57/10.18	   A^2 -> H(U1(d, e), b)
28.57/10.18	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.18	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.18	   A^2 -> H(U1(d, e), c)
28.57/10.18	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.18	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.18	   A^2 -> H(U1(d, e), e)
28.57/10.18	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.18	   A^2 -> H(U1(d, c), d)
28.57/10.18	   A^2 -> H(U1(d, c), k)
28.57/10.18	   A^2 -> H(U1(a, e), d)
28.57/10.18	   A^2 -> H(U1(a, e), k)
28.57/10.18	   A^2 -> H(U1(a, k), d)
28.57/10.18	
28.57/10.18	The TRS R consists of the following rules:
28.57/10.18	
28.57/10.18	   f(x) -> U1(x, x)
28.57/10.18	   U1(e, x) -> x
28.57/10.18	   a -> c
28.57/10.18	   a -> d
28.57/10.18	   b -> c
28.57/10.18	   b -> d
28.57/10.18	   d -> k
28.57/10.18	   c -> e
28.57/10.18	   c -> k
28.57/10.18	
28.57/10.18	Q is empty.
28.57/10.18	We have to consider all minimal (P,Q,R)-chains.
28.57/10.18	----------------------------------------
28.57/10.18	
28.57/10.18	(1997) TransformationProof (EQUIVALENT)
28.57/10.18	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.18	
28.57/10.18	   (A^2 -> H(U1(c, k), U1(e, d)),A^2 -> H(U1(c, k), U1(e, d)))
28.57/10.18	   (A^2 -> H(U1(d, k), U1(e, d)),A^2 -> H(U1(d, k), U1(e, d)))
28.57/10.18	   (A^2 -> H(U1(a, k), d),A^2 -> H(U1(a, k), d))
28.57/10.18	   (A^2 -> H(U1(a, k), U1(e, k)),A^2 -> H(U1(a, k), U1(e, k)))
28.57/10.18	
28.57/10.18	
28.57/10.18	----------------------------------------
28.57/10.18	
28.57/10.18	(1998)
28.57/10.18	Obligation:
28.57/10.18	Q DP problem:
28.57/10.18	The TRS P consists of the following rules:
28.57/10.18	
28.57/10.18	   G(d, x, x) -> A^2
28.57/10.18	   A^2 -> H(f(c), f(c))
28.57/10.18	   H(x, x) -> G(x, x, f(k))
28.57/10.18	   A^2 -> H(f(d), f(d))
28.57/10.18	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.18	   A^2 -> H(f(e), f(e))
28.57/10.18	   A^2 -> H(f(k), f(k))
28.57/10.18	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.18	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.18	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.18	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.18	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.18	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(a, k), U1(d, e))
28.57/10.18	   A^2 -> H(U1(a, k), c)
28.57/10.18	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.18	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.18	   A^2 -> H(U1(a, k), e)
28.57/10.18	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(a, c), d)
28.57/10.18	   A^2 -> H(U1(a, c), k)
28.57/10.18	   A^2 -> H(U1(a, d), d)
28.57/10.18	   A^2 -> H(U1(a, d), k)
28.57/10.18	   A^2 -> H(k, U1(c, b))
28.57/10.18	   A^2 -> H(k, U1(d, b))
28.57/10.18	   A^2 -> H(k, U1(b, c))
28.57/10.18	   A^2 -> H(k, U1(b, d))
28.57/10.18	   A^2 -> H(k, U1(c, c))
28.57/10.18	   A^2 -> H(k, f(e))
28.57/10.18	   A^2 -> H(k, f(k))
28.57/10.18	   A^2 -> H(k, U1(d, d))
28.57/10.18	   A^2 -> H(c, U1(e, b))
28.57/10.18	   A^2 -> H(c, U1(k, b))
28.57/10.18	   A^2 -> H(c, U1(c, d))
28.57/10.18	   A^2 -> H(c, U1(d, c))
28.57/10.18	   A^2 -> H(c, U1(b, e))
28.57/10.18	   A^2 -> H(c, U1(b, k))
28.57/10.18	   A^2 -> H(c, U1(e, c))
28.57/10.18	   A^2 -> H(c, U1(k, c))
28.57/10.18	   A^2 -> H(c, U1(c, e))
28.57/10.18	   A^2 -> H(c, U1(c, k))
28.57/10.18	   A^2 -> H(c, U1(e, e))
28.57/10.18	   A^2 -> H(c, U1(k, k))
28.57/10.18	   A^2 -> H(c, U1(k, d))
28.57/10.18	   A^2 -> H(c, U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.18	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.18	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.18	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.18	   A^2 -> H(U1(e, c), b)
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.18	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.18	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.18	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.18	   A^2 -> H(U1(e, c), e)
28.57/10.18	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.18	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.18	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.18	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.18	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.18	   A^2 -> H(U1(k, c), b)
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.18	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.18	   A^2 -> H(U1(k, c), c)
28.57/10.18	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.18	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, e), b)
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(c, e), c)
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(c, e), e)
28.57/10.19	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, k), b)
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(c, k), c)
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(c, k), e)
28.57/10.19	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, c), d)
28.57/10.19	   A^2 -> H(e, U1(e, b))
28.57/10.19	   A^2 -> H(e, U1(c, d))
28.57/10.19	   A^2 -> H(e, U1(d, c))
28.57/10.19	   A^2 -> H(e, U1(b, e))
28.57/10.19	   A^2 -> H(e, U1(b, k))
28.57/10.19	   A^2 -> H(e, U1(e, c))
28.57/10.19	   A^2 -> H(e, U1(c, e))
28.57/10.19	   A^2 -> H(e, U1(c, k))
28.57/10.19	   A^2 -> H(e, U1(e, e))
28.57/10.19	   A^2 -> H(e, U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, e), b)
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, e), c)
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.19	   A^2 -> H(f(e), d)
28.57/10.19	   A^2 -> H(f(e), k)
28.57/10.19	   A^2 -> H(U1(k, k), b)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, k), c)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.19	   A^2 -> H(f(k), d)
28.57/10.19	   A^2 -> H(f(k), k)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(k, d), b)
28.57/10.19	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, d), c)
28.57/10.19	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, k), b)
28.57/10.19	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(d, k), c)
28.57/10.19	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(d, k), e)
28.57/10.19	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, d), d)
28.57/10.19	   A^2 -> H(U1(d, d), k)
28.57/10.19	   A^2 -> H(U1(e, c), c)
28.57/10.19	   A^2 -> H(U1(c, c), e)
28.57/10.19	   A^2 -> H(U1(c, c), k)
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(e, e), e)
28.57/10.19	   A^2 -> H(d, U1(e, b))
28.57/10.19	   A^2 -> H(d, U1(k, b))
28.57/10.19	   A^2 -> H(d, U1(c, d))
28.57/10.19	   A^2 -> H(d, U1(d, c))
28.57/10.19	   A^2 -> H(d, U1(b, e))
28.57/10.19	   A^2 -> H(d, U1(b, k))
28.57/10.19	   A^2 -> H(d, U1(e, c))
28.57/10.19	   A^2 -> H(d, U1(k, c))
28.57/10.19	   A^2 -> H(d, U1(c, e))
28.57/10.19	   A^2 -> H(d, U1(c, k))
28.57/10.19	   A^2 -> H(d, U1(e, e))
28.57/10.19	   A^2 -> H(d, U1(k, k))
28.57/10.19	   A^2 -> H(d, U1(k, d))
28.57/10.19	   A^2 -> H(d, U1(d, k))
28.57/10.19	   A^2 -> H(a, b)
28.57/10.19	   A^2 -> H(a, U1(e, d))
28.57/10.19	   A^2 -> H(a, U1(d, e))
28.57/10.19	   A^2 -> H(a, c)
28.57/10.19	   A^2 -> H(a, U1(e, k))
28.57/10.19	   A^2 -> H(a, U1(k, e))
28.57/10.19	   A^2 -> H(a, e)
28.57/10.19	   A^2 -> H(a, U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, d), b)
28.57/10.19	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, d), c)
28.57/10.19	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, d), e)
28.57/10.19	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, a), d)
28.57/10.19	   A^2 -> H(U1(e, a), k)
28.57/10.19	   A^2 -> H(U1(k, a), d)
28.57/10.19	   A^2 -> H(U1(c, d), d)
28.57/10.19	   A^2 -> H(U1(c, d), k)
28.57/10.19	   A^2 -> H(U1(d, e), b)
28.57/10.19	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(d, e), c)
28.57/10.19	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(d, e), e)
28.57/10.19	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, c), d)
28.57/10.19	   A^2 -> H(U1(d, c), k)
28.57/10.19	   A^2 -> H(U1(a, e), d)
28.57/10.19	   A^2 -> H(U1(a, e), k)
28.57/10.19	   A^2 -> H(U1(a, k), d)
28.57/10.19	
28.57/10.19	The TRS R consists of the following rules:
28.57/10.19	
28.57/10.19	   f(x) -> U1(x, x)
28.57/10.19	   U1(e, x) -> x
28.57/10.19	   a -> c
28.57/10.19	   a -> d
28.57/10.19	   b -> c
28.57/10.19	   b -> d
28.57/10.19	   d -> k
28.57/10.19	   c -> e
28.57/10.19	   c -> k
28.57/10.19	
28.57/10.19	Q is empty.
28.57/10.19	We have to consider all minimal (P,Q,R)-chains.
28.57/10.19	----------------------------------------
28.57/10.19	
28.57/10.19	(1999) TransformationProof (EQUIVALENT)
28.57/10.19	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.19	
28.57/10.19	   (A^2 -> H(U1(c, k), U1(d, e)),A^2 -> H(U1(c, k), U1(d, e)))
28.57/10.19	   (A^2 -> H(U1(d, k), U1(d, e)),A^2 -> H(U1(d, k), U1(d, e)))
28.57/10.19	   (A^2 -> H(U1(a, k), U1(k, e)),A^2 -> H(U1(a, k), U1(k, e)))
28.57/10.19	
28.57/10.19	
28.57/10.19	----------------------------------------
28.57/10.19	
28.57/10.19	(2000)
28.57/10.19	Obligation:
28.57/10.19	Q DP problem:
28.57/10.19	The TRS P consists of the following rules:
28.57/10.19	
28.57/10.19	   G(d, x, x) -> A^2
28.57/10.19	   A^2 -> H(f(c), f(c))
28.57/10.19	   H(x, x) -> G(x, x, f(k))
28.57/10.19	   A^2 -> H(f(d), f(d))
28.57/10.19	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.19	   A^2 -> H(f(e), f(e))
28.57/10.19	   A^2 -> H(f(k), f(k))
28.57/10.19	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.19	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.19	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.19	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.19	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.19	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(a, k), c)
28.57/10.19	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(a, k), e)
28.57/10.19	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(a, c), d)
28.57/10.19	   A^2 -> H(U1(a, c), k)
28.57/10.19	   A^2 -> H(U1(a, d), d)
28.57/10.19	   A^2 -> H(U1(a, d), k)
28.57/10.19	   A^2 -> H(k, U1(c, b))
28.57/10.19	   A^2 -> H(k, U1(d, b))
28.57/10.19	   A^2 -> H(k, U1(b, c))
28.57/10.19	   A^2 -> H(k, U1(b, d))
28.57/10.19	   A^2 -> H(k, U1(c, c))
28.57/10.19	   A^2 -> H(k, f(e))
28.57/10.19	   A^2 -> H(k, f(k))
28.57/10.19	   A^2 -> H(k, U1(d, d))
28.57/10.19	   A^2 -> H(c, U1(e, b))
28.57/10.19	   A^2 -> H(c, U1(k, b))
28.57/10.19	   A^2 -> H(c, U1(c, d))
28.57/10.19	   A^2 -> H(c, U1(d, c))
28.57/10.19	   A^2 -> H(c, U1(b, e))
28.57/10.19	   A^2 -> H(c, U1(b, k))
28.57/10.19	   A^2 -> H(c, U1(e, c))
28.57/10.19	   A^2 -> H(c, U1(k, c))
28.57/10.19	   A^2 -> H(c, U1(c, e))
28.57/10.19	   A^2 -> H(c, U1(c, k))
28.57/10.19	   A^2 -> H(c, U1(e, e))
28.57/10.19	   A^2 -> H(c, U1(k, k))
28.57/10.19	   A^2 -> H(c, U1(k, d))
28.57/10.19	   A^2 -> H(c, U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.19	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.19	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, c), b)
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, c), e)
28.57/10.19	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.19	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.19	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.19	   A^2 -> H(U1(k, c), b)
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, c), c)
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, e), b)
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(c, e), c)
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(c, e), e)
28.57/10.19	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, k), b)
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(c, k), c)
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(c, k), e)
28.57/10.19	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, c), d)
28.57/10.19	   A^2 -> H(e, U1(e, b))
28.57/10.19	   A^2 -> H(e, U1(c, d))
28.57/10.19	   A^2 -> H(e, U1(d, c))
28.57/10.19	   A^2 -> H(e, U1(b, e))
28.57/10.19	   A^2 -> H(e, U1(b, k))
28.57/10.19	   A^2 -> H(e, U1(e, c))
28.57/10.19	   A^2 -> H(e, U1(c, e))
28.57/10.19	   A^2 -> H(e, U1(c, k))
28.57/10.19	   A^2 -> H(e, U1(e, e))
28.57/10.19	   A^2 -> H(e, U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, e), b)
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, e), c)
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.19	   A^2 -> H(f(e), d)
28.57/10.19	   A^2 -> H(f(e), k)
28.57/10.19	   A^2 -> H(U1(k, k), b)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, k), c)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.19	   A^2 -> H(f(k), d)
28.57/10.19	   A^2 -> H(f(k), k)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(k, d), b)
28.57/10.19	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, d), c)
28.57/10.19	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, k), b)
28.57/10.19	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(d, k), c)
28.57/10.19	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(d, k), e)
28.57/10.19	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, d), d)
28.57/10.19	   A^2 -> H(U1(d, d), k)
28.57/10.19	   A^2 -> H(U1(e, c), c)
28.57/10.19	   A^2 -> H(U1(c, c), e)
28.57/10.19	   A^2 -> H(U1(c, c), k)
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(e, e), e)
28.57/10.19	   A^2 -> H(d, U1(e, b))
28.57/10.19	   A^2 -> H(d, U1(k, b))
28.57/10.19	   A^2 -> H(d, U1(c, d))
28.57/10.19	   A^2 -> H(d, U1(d, c))
28.57/10.19	   A^2 -> H(d, U1(b, e))
28.57/10.19	   A^2 -> H(d, U1(b, k))
28.57/10.19	   A^2 -> H(d, U1(e, c))
28.57/10.19	   A^2 -> H(d, U1(k, c))
28.57/10.19	   A^2 -> H(d, U1(c, e))
28.57/10.19	   A^2 -> H(d, U1(c, k))
28.57/10.19	   A^2 -> H(d, U1(e, e))
28.57/10.19	   A^2 -> H(d, U1(k, k))
28.57/10.19	   A^2 -> H(d, U1(k, d))
28.57/10.19	   A^2 -> H(d, U1(d, k))
28.57/10.19	   A^2 -> H(a, b)
28.57/10.19	   A^2 -> H(a, U1(e, d))
28.57/10.19	   A^2 -> H(a, U1(d, e))
28.57/10.19	   A^2 -> H(a, c)
28.57/10.19	   A^2 -> H(a, U1(e, k))
28.57/10.19	   A^2 -> H(a, U1(k, e))
28.57/10.19	   A^2 -> H(a, e)
28.57/10.19	   A^2 -> H(a, U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, d), b)
28.57/10.19	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, d), c)
28.57/10.19	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, d), e)
28.57/10.19	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, a), d)
28.57/10.19	   A^2 -> H(U1(e, a), k)
28.57/10.19	   A^2 -> H(U1(k, a), d)
28.57/10.19	   A^2 -> H(U1(c, d), d)
28.57/10.19	   A^2 -> H(U1(c, d), k)
28.57/10.19	   A^2 -> H(U1(d, e), b)
28.57/10.19	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(d, e), c)
28.57/10.19	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(d, e), e)
28.57/10.19	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, c), d)
28.57/10.19	   A^2 -> H(U1(d, c), k)
28.57/10.19	   A^2 -> H(U1(a, e), d)
28.57/10.19	   A^2 -> H(U1(a, e), k)
28.57/10.19	   A^2 -> H(U1(a, k), d)
28.57/10.19	
28.57/10.19	The TRS R consists of the following rules:
28.57/10.19	
28.57/10.19	   f(x) -> U1(x, x)
28.57/10.19	   U1(e, x) -> x
28.57/10.19	   a -> c
28.57/10.19	   a -> d
28.57/10.19	   b -> c
28.57/10.19	   b -> d
28.57/10.19	   d -> k
28.57/10.19	   c -> e
28.57/10.19	   c -> k
28.57/10.19	
28.57/10.19	Q is empty.
28.57/10.19	We have to consider all minimal (P,Q,R)-chains.
28.57/10.19	----------------------------------------
28.57/10.19	
28.57/10.19	(2001) TransformationProof (EQUIVALENT)
28.57/10.19	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), c) at position [] we obtained the following new rules [LPAR04]:
28.57/10.19	
28.57/10.19	   (A^2 -> H(U1(c, k), c),A^2 -> H(U1(c, k), c))
28.57/10.19	   (A^2 -> H(U1(d, k), c),A^2 -> H(U1(d, k), c))
28.57/10.19	   (A^2 -> H(U1(a, k), e),A^2 -> H(U1(a, k), e))
28.57/10.19	   (A^2 -> H(U1(a, k), k),A^2 -> H(U1(a, k), k))
28.57/10.19	
28.57/10.19	
28.57/10.19	----------------------------------------
28.57/10.19	
28.57/10.19	(2002)
28.57/10.19	Obligation:
28.57/10.19	Q DP problem:
28.57/10.19	The TRS P consists of the following rules:
28.57/10.19	
28.57/10.19	   G(d, x, x) -> A^2
28.57/10.19	   A^2 -> H(f(c), f(c))
28.57/10.19	   H(x, x) -> G(x, x, f(k))
28.57/10.19	   A^2 -> H(f(d), f(d))
28.57/10.19	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.19	   A^2 -> H(f(e), f(e))
28.57/10.19	   A^2 -> H(f(k), f(k))
28.57/10.19	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.19	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.19	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.19	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.19	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.19	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(a, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(a, k), e)
28.57/10.19	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(a, c), d)
28.57/10.19	   A^2 -> H(U1(a, c), k)
28.57/10.19	   A^2 -> H(U1(a, d), d)
28.57/10.19	   A^2 -> H(U1(a, d), k)
28.57/10.19	   A^2 -> H(k, U1(c, b))
28.57/10.19	   A^2 -> H(k, U1(d, b))
28.57/10.19	   A^2 -> H(k, U1(b, c))
28.57/10.19	   A^2 -> H(k, U1(b, d))
28.57/10.19	   A^2 -> H(k, U1(c, c))
28.57/10.19	   A^2 -> H(k, f(e))
28.57/10.19	   A^2 -> H(k, f(k))
28.57/10.19	   A^2 -> H(k, U1(d, d))
28.57/10.19	   A^2 -> H(c, U1(e, b))
28.57/10.19	   A^2 -> H(c, U1(k, b))
28.57/10.19	   A^2 -> H(c, U1(c, d))
28.57/10.19	   A^2 -> H(c, U1(d, c))
28.57/10.19	   A^2 -> H(c, U1(b, e))
28.57/10.19	   A^2 -> H(c, U1(b, k))
28.57/10.19	   A^2 -> H(c, U1(e, c))
28.57/10.19	   A^2 -> H(c, U1(k, c))
28.57/10.19	   A^2 -> H(c, U1(c, e))
28.57/10.19	   A^2 -> H(c, U1(c, k))
28.57/10.19	   A^2 -> H(c, U1(e, e))
28.57/10.19	   A^2 -> H(c, U1(k, k))
28.57/10.19	   A^2 -> H(c, U1(k, d))
28.57/10.19	   A^2 -> H(c, U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.19	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.19	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, c), b)
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, c), e)
28.57/10.19	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.19	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.19	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.19	   A^2 -> H(U1(k, c), b)
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, c), c)
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, e), b)
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(c, e), c)
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(c, e), e)
28.57/10.19	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, k), b)
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(c, k), c)
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(c, k), e)
28.57/10.19	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, c), d)
28.57/10.19	   A^2 -> H(e, U1(e, b))
28.57/10.19	   A^2 -> H(e, U1(c, d))
28.57/10.19	   A^2 -> H(e, U1(d, c))
28.57/10.19	   A^2 -> H(e, U1(b, e))
28.57/10.19	   A^2 -> H(e, U1(b, k))
28.57/10.19	   A^2 -> H(e, U1(e, c))
28.57/10.19	   A^2 -> H(e, U1(c, e))
28.57/10.19	   A^2 -> H(e, U1(c, k))
28.57/10.19	   A^2 -> H(e, U1(e, e))
28.57/10.19	   A^2 -> H(e, U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, e), b)
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, e), c)
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.19	   A^2 -> H(f(e), d)
28.57/10.19	   A^2 -> H(f(e), k)
28.57/10.19	   A^2 -> H(U1(k, k), b)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, k), c)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.19	   A^2 -> H(f(k), d)
28.57/10.19	   A^2 -> H(f(k), k)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(k, d), b)
28.57/10.19	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, d), c)
28.57/10.19	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, k), b)
28.57/10.19	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(d, k), c)
28.57/10.19	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(d, k), e)
28.57/10.19	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, d), d)
28.57/10.19	   A^2 -> H(U1(d, d), k)
28.57/10.19	   A^2 -> H(U1(e, c), c)
28.57/10.19	   A^2 -> H(U1(c, c), e)
28.57/10.19	   A^2 -> H(U1(c, c), k)
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(e, e), e)
28.57/10.19	   A^2 -> H(d, U1(e, b))
28.57/10.19	   A^2 -> H(d, U1(k, b))
28.57/10.19	   A^2 -> H(d, U1(c, d))
28.57/10.19	   A^2 -> H(d, U1(d, c))
28.57/10.19	   A^2 -> H(d, U1(b, e))
28.57/10.19	   A^2 -> H(d, U1(b, k))
28.57/10.19	   A^2 -> H(d, U1(e, c))
28.57/10.19	   A^2 -> H(d, U1(k, c))
28.57/10.19	   A^2 -> H(d, U1(c, e))
28.57/10.19	   A^2 -> H(d, U1(c, k))
28.57/10.19	   A^2 -> H(d, U1(e, e))
28.57/10.19	   A^2 -> H(d, U1(k, k))
28.57/10.19	   A^2 -> H(d, U1(k, d))
28.57/10.19	   A^2 -> H(d, U1(d, k))
28.57/10.19	   A^2 -> H(a, b)
28.57/10.19	   A^2 -> H(a, U1(e, d))
28.57/10.19	   A^2 -> H(a, U1(d, e))
28.57/10.19	   A^2 -> H(a, c)
28.57/10.19	   A^2 -> H(a, U1(e, k))
28.57/10.19	   A^2 -> H(a, U1(k, e))
28.57/10.19	   A^2 -> H(a, e)
28.57/10.19	   A^2 -> H(a, U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, d), b)
28.57/10.19	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, d), c)
28.57/10.19	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, d), e)
28.57/10.19	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, a), d)
28.57/10.19	   A^2 -> H(U1(e, a), k)
28.57/10.19	   A^2 -> H(U1(k, a), d)
28.57/10.19	   A^2 -> H(U1(c, d), d)
28.57/10.19	   A^2 -> H(U1(c, d), k)
28.57/10.19	   A^2 -> H(U1(d, e), b)
28.57/10.19	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(d, e), c)
28.57/10.19	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(d, e), e)
28.57/10.19	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, c), d)
28.57/10.19	   A^2 -> H(U1(d, c), k)
28.57/10.19	   A^2 -> H(U1(a, e), d)
28.57/10.19	   A^2 -> H(U1(a, e), k)
28.57/10.19	   A^2 -> H(U1(a, k), d)
28.57/10.19	   A^2 -> H(U1(a, k), k)
28.57/10.19	
28.57/10.19	The TRS R consists of the following rules:
28.57/10.19	
28.57/10.19	   f(x) -> U1(x, x)
28.57/10.19	   U1(e, x) -> x
28.57/10.19	   a -> c
28.57/10.19	   a -> d
28.57/10.19	   b -> c
28.57/10.19	   b -> d
28.57/10.19	   d -> k
28.57/10.19	   c -> e
28.57/10.19	   c -> k
28.57/10.19	
28.57/10.19	Q is empty.
28.57/10.19	We have to consider all minimal (P,Q,R)-chains.
28.57/10.19	----------------------------------------
28.57/10.19	
28.57/10.19	(2003) TransformationProof (EQUIVALENT)
28.57/10.19	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.19	
28.57/10.19	   (A^2 -> H(U1(c, k), U1(e, k)),A^2 -> H(U1(c, k), U1(e, k)))
28.57/10.19	   (A^2 -> H(U1(d, k), U1(e, k)),A^2 -> H(U1(d, k), U1(e, k)))
28.57/10.19	   (A^2 -> H(U1(a, k), k),A^2 -> H(U1(a, k), k))
28.57/10.19	
28.57/10.19	
28.57/10.19	----------------------------------------
28.57/10.19	
28.57/10.19	(2004)
28.57/10.19	Obligation:
28.57/10.19	Q DP problem:
28.57/10.19	The TRS P consists of the following rules:
28.57/10.19	
28.57/10.19	   G(d, x, x) -> A^2
28.57/10.19	   A^2 -> H(f(c), f(c))
28.57/10.19	   H(x, x) -> G(x, x, f(k))
28.57/10.19	   A^2 -> H(f(d), f(d))
28.57/10.19	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.19	   A^2 -> H(f(e), f(e))
28.57/10.19	   A^2 -> H(f(k), f(k))
28.57/10.19	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.19	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.19	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.19	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.19	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.19	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(a, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(a, k), e)
28.57/10.19	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(a, c), d)
28.57/10.19	   A^2 -> H(U1(a, c), k)
28.57/10.19	   A^2 -> H(U1(a, d), d)
28.57/10.19	   A^2 -> H(U1(a, d), k)
28.57/10.19	   A^2 -> H(k, U1(c, b))
28.57/10.19	   A^2 -> H(k, U1(d, b))
28.57/10.19	   A^2 -> H(k, U1(b, c))
28.57/10.19	   A^2 -> H(k, U1(b, d))
28.57/10.19	   A^2 -> H(k, U1(c, c))
28.57/10.19	   A^2 -> H(k, f(e))
28.57/10.19	   A^2 -> H(k, f(k))
28.57/10.19	   A^2 -> H(k, U1(d, d))
28.57/10.19	   A^2 -> H(c, U1(e, b))
28.57/10.19	   A^2 -> H(c, U1(k, b))
28.57/10.19	   A^2 -> H(c, U1(c, d))
28.57/10.19	   A^2 -> H(c, U1(d, c))
28.57/10.19	   A^2 -> H(c, U1(b, e))
28.57/10.19	   A^2 -> H(c, U1(b, k))
28.57/10.19	   A^2 -> H(c, U1(e, c))
28.57/10.19	   A^2 -> H(c, U1(k, c))
28.57/10.19	   A^2 -> H(c, U1(c, e))
28.57/10.19	   A^2 -> H(c, U1(c, k))
28.57/10.19	   A^2 -> H(c, U1(e, e))
28.57/10.19	   A^2 -> H(c, U1(k, k))
28.57/10.19	   A^2 -> H(c, U1(k, d))
28.57/10.19	   A^2 -> H(c, U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.19	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.19	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, c), b)
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, c), e)
28.57/10.19	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.19	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.19	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.19	   A^2 -> H(U1(k, c), b)
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, c), c)
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, e), b)
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(c, e), c)
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(c, e), e)
28.57/10.19	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, k), b)
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(c, k), c)
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(c, k), e)
28.57/10.19	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, c), d)
28.57/10.19	   A^2 -> H(e, U1(e, b))
28.57/10.19	   A^2 -> H(e, U1(c, d))
28.57/10.19	   A^2 -> H(e, U1(d, c))
28.57/10.19	   A^2 -> H(e, U1(b, e))
28.57/10.19	   A^2 -> H(e, U1(b, k))
28.57/10.19	   A^2 -> H(e, U1(e, c))
28.57/10.19	   A^2 -> H(e, U1(c, e))
28.57/10.19	   A^2 -> H(e, U1(c, k))
28.57/10.19	   A^2 -> H(e, U1(e, e))
28.57/10.19	   A^2 -> H(e, U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, e), b)
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, e), c)
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.19	   A^2 -> H(f(e), d)
28.57/10.19	   A^2 -> H(f(e), k)
28.57/10.19	   A^2 -> H(U1(k, k), b)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, k), c)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.19	   A^2 -> H(f(k), d)
28.57/10.19	   A^2 -> H(f(k), k)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(k, d), b)
28.57/10.19	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, d), c)
28.57/10.19	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, k), b)
28.57/10.19	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(d, k), c)
28.57/10.19	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(d, k), e)
28.57/10.19	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, d), d)
28.57/10.19	   A^2 -> H(U1(d, d), k)
28.57/10.19	   A^2 -> H(U1(e, c), c)
28.57/10.19	   A^2 -> H(U1(c, c), e)
28.57/10.19	   A^2 -> H(U1(c, c), k)
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(e, e), e)
28.57/10.19	   A^2 -> H(d, U1(e, b))
28.57/10.19	   A^2 -> H(d, U1(k, b))
28.57/10.19	   A^2 -> H(d, U1(c, d))
28.57/10.19	   A^2 -> H(d, U1(d, c))
28.57/10.19	   A^2 -> H(d, U1(b, e))
28.57/10.19	   A^2 -> H(d, U1(b, k))
28.57/10.19	   A^2 -> H(d, U1(e, c))
28.57/10.19	   A^2 -> H(d, U1(k, c))
28.57/10.19	   A^2 -> H(d, U1(c, e))
28.57/10.19	   A^2 -> H(d, U1(c, k))
28.57/10.19	   A^2 -> H(d, U1(e, e))
28.57/10.19	   A^2 -> H(d, U1(k, k))
28.57/10.19	   A^2 -> H(d, U1(k, d))
28.57/10.19	   A^2 -> H(d, U1(d, k))
28.57/10.19	   A^2 -> H(a, b)
28.57/10.19	   A^2 -> H(a, U1(e, d))
28.57/10.19	   A^2 -> H(a, U1(d, e))
28.57/10.19	   A^2 -> H(a, c)
28.57/10.19	   A^2 -> H(a, U1(e, k))
28.57/10.19	   A^2 -> H(a, U1(k, e))
28.57/10.19	   A^2 -> H(a, e)
28.57/10.19	   A^2 -> H(a, U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, d), b)
28.57/10.19	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, d), c)
28.57/10.19	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, d), e)
28.57/10.19	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, a), d)
28.57/10.19	   A^2 -> H(U1(e, a), k)
28.57/10.19	   A^2 -> H(U1(k, a), d)
28.57/10.19	   A^2 -> H(U1(c, d), d)
28.57/10.19	   A^2 -> H(U1(c, d), k)
28.57/10.19	   A^2 -> H(U1(d, e), b)
28.57/10.19	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(d, e), c)
28.57/10.19	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(d, e), e)
28.57/10.19	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, c), d)
28.57/10.19	   A^2 -> H(U1(d, c), k)
28.57/10.19	   A^2 -> H(U1(a, e), d)
28.57/10.19	   A^2 -> H(U1(a, e), k)
28.57/10.19	   A^2 -> H(U1(a, k), d)
28.57/10.19	   A^2 -> H(U1(a, k), k)
28.57/10.19	
28.57/10.19	The TRS R consists of the following rules:
28.57/10.19	
28.57/10.19	   f(x) -> U1(x, x)
28.57/10.19	   U1(e, x) -> x
28.57/10.19	   a -> c
28.57/10.19	   a -> d
28.57/10.19	   b -> c
28.57/10.19	   b -> d
28.57/10.19	   d -> k
28.57/10.19	   c -> e
28.57/10.19	   c -> k
28.57/10.19	
28.57/10.19	Q is empty.
28.57/10.19	We have to consider all minimal (P,Q,R)-chains.
28.57/10.19	----------------------------------------
28.57/10.19	
28.57/10.19	(2005) TransformationProof (EQUIVALENT)
28.57/10.19	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.19	
28.57/10.19	   (A^2 -> H(U1(c, k), U1(k, e)),A^2 -> H(U1(c, k), U1(k, e)))
28.57/10.19	   (A^2 -> H(U1(d, k), U1(k, e)),A^2 -> H(U1(d, k), U1(k, e)))
28.57/10.19	
28.57/10.19	
28.57/10.19	----------------------------------------
28.57/10.19	
28.57/10.19	(2006)
28.57/10.19	Obligation:
28.57/10.19	Q DP problem:
28.57/10.19	The TRS P consists of the following rules:
28.57/10.19	
28.57/10.19	   G(d, x, x) -> A^2
28.57/10.19	   A^2 -> H(f(c), f(c))
28.57/10.19	   H(x, x) -> G(x, x, f(k))
28.57/10.19	   A^2 -> H(f(d), f(d))
28.57/10.19	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.19	   A^2 -> H(f(e), f(e))
28.57/10.19	   A^2 -> H(f(k), f(k))
28.57/10.19	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.19	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.19	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.19	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.19	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.19	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(a, k), e)
28.57/10.19	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(a, c), d)
28.57/10.19	   A^2 -> H(U1(a, c), k)
28.57/10.19	   A^2 -> H(U1(a, d), d)
28.57/10.19	   A^2 -> H(U1(a, d), k)
28.57/10.19	   A^2 -> H(k, U1(c, b))
28.57/10.19	   A^2 -> H(k, U1(d, b))
28.57/10.19	   A^2 -> H(k, U1(b, c))
28.57/10.19	   A^2 -> H(k, U1(b, d))
28.57/10.19	   A^2 -> H(k, U1(c, c))
28.57/10.19	   A^2 -> H(k, f(e))
28.57/10.19	   A^2 -> H(k, f(k))
28.57/10.19	   A^2 -> H(k, U1(d, d))
28.57/10.19	   A^2 -> H(c, U1(e, b))
28.57/10.19	   A^2 -> H(c, U1(k, b))
28.57/10.19	   A^2 -> H(c, U1(c, d))
28.57/10.19	   A^2 -> H(c, U1(d, c))
28.57/10.19	   A^2 -> H(c, U1(b, e))
28.57/10.19	   A^2 -> H(c, U1(b, k))
28.57/10.19	   A^2 -> H(c, U1(e, c))
28.57/10.19	   A^2 -> H(c, U1(k, c))
28.57/10.19	   A^2 -> H(c, U1(c, e))
28.57/10.19	   A^2 -> H(c, U1(c, k))
28.57/10.19	   A^2 -> H(c, U1(e, e))
28.57/10.19	   A^2 -> H(c, U1(k, k))
28.57/10.19	   A^2 -> H(c, U1(k, d))
28.57/10.19	   A^2 -> H(c, U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.19	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.19	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, c), b)
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, c), e)
28.57/10.19	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.19	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.19	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.19	   A^2 -> H(U1(k, c), b)
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, c), c)
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, e), b)
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(c, e), c)
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(c, e), e)
28.57/10.19	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, k), b)
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(c, k), c)
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(c, k), e)
28.57/10.19	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, c), d)
28.57/10.19	   A^2 -> H(e, U1(e, b))
28.57/10.19	   A^2 -> H(e, U1(c, d))
28.57/10.19	   A^2 -> H(e, U1(d, c))
28.57/10.19	   A^2 -> H(e, U1(b, e))
28.57/10.19	   A^2 -> H(e, U1(b, k))
28.57/10.19	   A^2 -> H(e, U1(e, c))
28.57/10.19	   A^2 -> H(e, U1(c, e))
28.57/10.19	   A^2 -> H(e, U1(c, k))
28.57/10.19	   A^2 -> H(e, U1(e, e))
28.57/10.19	   A^2 -> H(e, U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, e), b)
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, e), c)
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.19	   A^2 -> H(f(e), d)
28.57/10.19	   A^2 -> H(f(e), k)
28.57/10.19	   A^2 -> H(U1(k, k), b)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, k), c)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.19	   A^2 -> H(f(k), d)
28.57/10.19	   A^2 -> H(f(k), k)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(k, d), b)
28.57/10.19	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, d), c)
28.57/10.19	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, k), b)
28.57/10.19	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(d, k), c)
28.57/10.19	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(d, k), e)
28.57/10.19	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, d), d)
28.57/10.19	   A^2 -> H(U1(d, d), k)
28.57/10.19	   A^2 -> H(U1(e, c), c)
28.57/10.19	   A^2 -> H(U1(c, c), e)
28.57/10.19	   A^2 -> H(U1(c, c), k)
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(e, e), e)
28.57/10.19	   A^2 -> H(d, U1(e, b))
28.57/10.19	   A^2 -> H(d, U1(k, b))
28.57/10.19	   A^2 -> H(d, U1(c, d))
28.57/10.19	   A^2 -> H(d, U1(d, c))
28.57/10.19	   A^2 -> H(d, U1(b, e))
28.57/10.19	   A^2 -> H(d, U1(b, k))
28.57/10.19	   A^2 -> H(d, U1(e, c))
28.57/10.19	   A^2 -> H(d, U1(k, c))
28.57/10.19	   A^2 -> H(d, U1(c, e))
28.57/10.19	   A^2 -> H(d, U1(c, k))
28.57/10.19	   A^2 -> H(d, U1(e, e))
28.57/10.19	   A^2 -> H(d, U1(k, k))
28.57/10.19	   A^2 -> H(d, U1(k, d))
28.57/10.19	   A^2 -> H(d, U1(d, k))
28.57/10.19	   A^2 -> H(a, b)
28.57/10.19	   A^2 -> H(a, U1(e, d))
28.57/10.19	   A^2 -> H(a, U1(d, e))
28.57/10.19	   A^2 -> H(a, c)
28.57/10.19	   A^2 -> H(a, U1(e, k))
28.57/10.19	   A^2 -> H(a, U1(k, e))
28.57/10.19	   A^2 -> H(a, e)
28.57/10.19	   A^2 -> H(a, U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, d), b)
28.57/10.19	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, d), c)
28.57/10.19	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, d), e)
28.57/10.19	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, a), d)
28.57/10.19	   A^2 -> H(U1(e, a), k)
28.57/10.19	   A^2 -> H(U1(k, a), d)
28.57/10.19	   A^2 -> H(U1(c, d), d)
28.57/10.19	   A^2 -> H(U1(c, d), k)
28.57/10.19	   A^2 -> H(U1(d, e), b)
28.57/10.19	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(d, e), c)
28.57/10.19	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(d, e), e)
28.57/10.19	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, c), d)
28.57/10.19	   A^2 -> H(U1(d, c), k)
28.57/10.19	   A^2 -> H(U1(a, e), d)
28.57/10.19	   A^2 -> H(U1(a, e), k)
28.57/10.19	   A^2 -> H(U1(a, k), d)
28.57/10.19	   A^2 -> H(U1(a, k), k)
28.57/10.19	
28.57/10.19	The TRS R consists of the following rules:
28.57/10.19	
28.57/10.19	   f(x) -> U1(x, x)
28.57/10.19	   U1(e, x) -> x
28.57/10.19	   a -> c
28.57/10.19	   a -> d
28.57/10.19	   b -> c
28.57/10.19	   b -> d
28.57/10.19	   d -> k
28.57/10.19	   c -> e
28.57/10.19	   c -> k
28.57/10.19	
28.57/10.19	Q is empty.
28.57/10.19	We have to consider all minimal (P,Q,R)-chains.
28.57/10.19	----------------------------------------
28.57/10.19	
28.57/10.19	(2007) TransformationProof (EQUIVALENT)
28.57/10.19	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), e) at position [] we obtained the following new rules [LPAR04]:
28.57/10.19	
28.57/10.19	   (A^2 -> H(U1(c, k), e),A^2 -> H(U1(c, k), e))
28.57/10.19	   (A^2 -> H(U1(d, k), e),A^2 -> H(U1(d, k), e))
28.57/10.19	
28.57/10.19	
28.57/10.19	----------------------------------------
28.57/10.19	
28.57/10.19	(2008)
28.57/10.19	Obligation:
28.57/10.19	Q DP problem:
28.57/10.19	The TRS P consists of the following rules:
28.57/10.19	
28.57/10.19	   G(d, x, x) -> A^2
28.57/10.19	   A^2 -> H(f(c), f(c))
28.57/10.19	   H(x, x) -> G(x, x, f(k))
28.57/10.19	   A^2 -> H(f(d), f(d))
28.57/10.19	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.19	   A^2 -> H(f(e), f(e))
28.57/10.19	   A^2 -> H(f(k), f(k))
28.57/10.19	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.19	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.19	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.19	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.19	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.19	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(a, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(a, c), d)
28.57/10.19	   A^2 -> H(U1(a, c), k)
28.57/10.19	   A^2 -> H(U1(a, d), d)
28.57/10.19	   A^2 -> H(U1(a, d), k)
28.57/10.19	   A^2 -> H(k, U1(c, b))
28.57/10.19	   A^2 -> H(k, U1(d, b))
28.57/10.19	   A^2 -> H(k, U1(b, c))
28.57/10.19	   A^2 -> H(k, U1(b, d))
28.57/10.19	   A^2 -> H(k, U1(c, c))
28.57/10.19	   A^2 -> H(k, f(e))
28.57/10.19	   A^2 -> H(k, f(k))
28.57/10.19	   A^2 -> H(k, U1(d, d))
28.57/10.19	   A^2 -> H(c, U1(e, b))
28.57/10.19	   A^2 -> H(c, U1(k, b))
28.57/10.19	   A^2 -> H(c, U1(c, d))
28.57/10.19	   A^2 -> H(c, U1(d, c))
28.57/10.19	   A^2 -> H(c, U1(b, e))
28.57/10.19	   A^2 -> H(c, U1(b, k))
28.57/10.19	   A^2 -> H(c, U1(e, c))
28.57/10.19	   A^2 -> H(c, U1(k, c))
28.57/10.19	   A^2 -> H(c, U1(c, e))
28.57/10.19	   A^2 -> H(c, U1(c, k))
28.57/10.19	   A^2 -> H(c, U1(e, e))
28.57/10.19	   A^2 -> H(c, U1(k, k))
28.57/10.19	   A^2 -> H(c, U1(k, d))
28.57/10.19	   A^2 -> H(c, U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.19	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.19	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, c), b)
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, c), e)
28.57/10.19	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.19	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.19	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.19	   A^2 -> H(U1(k, c), b)
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, c), c)
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, e), b)
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(c, e), c)
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(c, e), e)
28.57/10.19	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, k), b)
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(c, k), c)
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(c, k), e)
28.57/10.19	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, c), d)
28.57/10.19	   A^2 -> H(e, U1(e, b))
28.57/10.19	   A^2 -> H(e, U1(c, d))
28.57/10.19	   A^2 -> H(e, U1(d, c))
28.57/10.19	   A^2 -> H(e, U1(b, e))
28.57/10.19	   A^2 -> H(e, U1(b, k))
28.57/10.19	   A^2 -> H(e, U1(e, c))
28.57/10.19	   A^2 -> H(e, U1(c, e))
28.57/10.19	   A^2 -> H(e, U1(c, k))
28.57/10.19	   A^2 -> H(e, U1(e, e))
28.57/10.19	   A^2 -> H(e, U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, e), b)
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, e), c)
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.19	   A^2 -> H(f(e), d)
28.57/10.19	   A^2 -> H(f(e), k)
28.57/10.19	   A^2 -> H(U1(k, k), b)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, k), c)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.19	   A^2 -> H(f(k), d)
28.57/10.19	   A^2 -> H(f(k), k)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(k, d), b)
28.57/10.19	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, d), c)
28.57/10.19	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, k), b)
28.57/10.19	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(d, k), c)
28.57/10.19	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(d, k), e)
28.57/10.19	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, d), d)
28.57/10.19	   A^2 -> H(U1(d, d), k)
28.57/10.19	   A^2 -> H(U1(e, c), c)
28.57/10.19	   A^2 -> H(U1(c, c), e)
28.57/10.19	   A^2 -> H(U1(c, c), k)
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(e, e), e)
28.57/10.19	   A^2 -> H(d, U1(e, b))
28.57/10.19	   A^2 -> H(d, U1(k, b))
28.57/10.19	   A^2 -> H(d, U1(c, d))
28.57/10.19	   A^2 -> H(d, U1(d, c))
28.57/10.19	   A^2 -> H(d, U1(b, e))
28.57/10.19	   A^2 -> H(d, U1(b, k))
28.57/10.19	   A^2 -> H(d, U1(e, c))
28.57/10.19	   A^2 -> H(d, U1(k, c))
28.57/10.19	   A^2 -> H(d, U1(c, e))
28.57/10.19	   A^2 -> H(d, U1(c, k))
28.57/10.19	   A^2 -> H(d, U1(e, e))
28.57/10.19	   A^2 -> H(d, U1(k, k))
28.57/10.19	   A^2 -> H(d, U1(k, d))
28.57/10.19	   A^2 -> H(d, U1(d, k))
28.57/10.19	   A^2 -> H(a, b)
28.57/10.19	   A^2 -> H(a, U1(e, d))
28.57/10.19	   A^2 -> H(a, U1(d, e))
28.57/10.19	   A^2 -> H(a, c)
28.57/10.19	   A^2 -> H(a, U1(e, k))
28.57/10.19	   A^2 -> H(a, U1(k, e))
28.57/10.19	   A^2 -> H(a, e)
28.57/10.19	   A^2 -> H(a, U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, d), b)
28.57/10.19	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, d), c)
28.57/10.19	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, d), e)
28.57/10.19	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, a), d)
28.57/10.19	   A^2 -> H(U1(e, a), k)
28.57/10.19	   A^2 -> H(U1(k, a), d)
28.57/10.19	   A^2 -> H(U1(c, d), d)
28.57/10.19	   A^2 -> H(U1(c, d), k)
28.57/10.19	   A^2 -> H(U1(d, e), b)
28.57/10.19	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(d, e), c)
28.57/10.19	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(d, e), e)
28.57/10.19	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, c), d)
28.57/10.19	   A^2 -> H(U1(d, c), k)
28.57/10.19	   A^2 -> H(U1(a, e), d)
28.57/10.19	   A^2 -> H(U1(a, e), k)
28.57/10.19	   A^2 -> H(U1(a, k), d)
28.57/10.19	   A^2 -> H(U1(a, k), k)
28.57/10.19	
28.57/10.19	The TRS R consists of the following rules:
28.57/10.19	
28.57/10.19	   f(x) -> U1(x, x)
28.57/10.19	   U1(e, x) -> x
28.57/10.19	   a -> c
28.57/10.19	   a -> d
28.57/10.19	   b -> c
28.57/10.19	   b -> d
28.57/10.19	   d -> k
28.57/10.19	   c -> e
28.57/10.19	   c -> k
28.57/10.19	
28.57/10.19	Q is empty.
28.57/10.19	We have to consider all minimal (P,Q,R)-chains.
28.57/10.19	----------------------------------------
28.57/10.19	
28.57/10.19	(2009) TransformationProof (EQUIVALENT)
28.57/10.19	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.19	
28.57/10.19	   (A^2 -> H(U1(c, k), U1(k, k)),A^2 -> H(U1(c, k), U1(k, k)))
28.57/10.19	   (A^2 -> H(U1(d, k), U1(k, k)),A^2 -> H(U1(d, k), U1(k, k)))
28.57/10.19	
28.57/10.19	
28.57/10.19	----------------------------------------
28.57/10.19	
28.57/10.19	(2010)
28.57/10.19	Obligation:
28.57/10.19	Q DP problem:
28.57/10.19	The TRS P consists of the following rules:
28.57/10.19	
28.57/10.19	   G(d, x, x) -> A^2
28.57/10.19	   A^2 -> H(f(c), f(c))
28.57/10.19	   H(x, x) -> G(x, x, f(k))
28.57/10.19	   A^2 -> H(f(d), f(d))
28.57/10.19	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.19	   A^2 -> H(f(e), f(e))
28.57/10.19	   A^2 -> H(f(k), f(k))
28.57/10.19	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.19	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.19	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.19	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.19	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.19	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(a, c), d)
28.57/10.19	   A^2 -> H(U1(a, c), k)
28.57/10.19	   A^2 -> H(U1(a, d), d)
28.57/10.19	   A^2 -> H(U1(a, d), k)
28.57/10.19	   A^2 -> H(k, U1(c, b))
28.57/10.19	   A^2 -> H(k, U1(d, b))
28.57/10.19	   A^2 -> H(k, U1(b, c))
28.57/10.19	   A^2 -> H(k, U1(b, d))
28.57/10.19	   A^2 -> H(k, U1(c, c))
28.57/10.19	   A^2 -> H(k, f(e))
28.57/10.19	   A^2 -> H(k, f(k))
28.57/10.19	   A^2 -> H(k, U1(d, d))
28.57/10.19	   A^2 -> H(c, U1(e, b))
28.57/10.19	   A^2 -> H(c, U1(k, b))
28.57/10.19	   A^2 -> H(c, U1(c, d))
28.57/10.19	   A^2 -> H(c, U1(d, c))
28.57/10.19	   A^2 -> H(c, U1(b, e))
28.57/10.19	   A^2 -> H(c, U1(b, k))
28.57/10.19	   A^2 -> H(c, U1(e, c))
28.57/10.19	   A^2 -> H(c, U1(k, c))
28.57/10.19	   A^2 -> H(c, U1(c, e))
28.57/10.19	   A^2 -> H(c, U1(c, k))
28.57/10.19	   A^2 -> H(c, U1(e, e))
28.57/10.19	   A^2 -> H(c, U1(k, k))
28.57/10.19	   A^2 -> H(c, U1(k, d))
28.57/10.19	   A^2 -> H(c, U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.19	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.19	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, c), b)
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, c), e)
28.57/10.19	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.19	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.19	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.19	   A^2 -> H(U1(k, c), b)
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, c), c)
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, e), b)
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(c, e), c)
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(c, e), e)
28.57/10.19	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, k), b)
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(c, k), c)
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(c, k), e)
28.57/10.19	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, c), d)
28.57/10.19	   A^2 -> H(e, U1(e, b))
28.57/10.19	   A^2 -> H(e, U1(c, d))
28.57/10.19	   A^2 -> H(e, U1(d, c))
28.57/10.19	   A^2 -> H(e, U1(b, e))
28.57/10.19	   A^2 -> H(e, U1(b, k))
28.57/10.19	   A^2 -> H(e, U1(e, c))
28.57/10.19	   A^2 -> H(e, U1(c, e))
28.57/10.19	   A^2 -> H(e, U1(c, k))
28.57/10.19	   A^2 -> H(e, U1(e, e))
28.57/10.19	   A^2 -> H(e, U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, e), b)
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, e), c)
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.19	   A^2 -> H(f(e), d)
28.57/10.19	   A^2 -> H(f(e), k)
28.57/10.19	   A^2 -> H(U1(k, k), b)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, k), c)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.19	   A^2 -> H(f(k), d)
28.57/10.19	   A^2 -> H(f(k), k)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(k, d), b)
28.57/10.19	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, d), c)
28.57/10.19	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, k), b)
28.57/10.19	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(d, k), c)
28.57/10.19	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(d, k), e)
28.57/10.19	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, d), d)
28.57/10.19	   A^2 -> H(U1(d, d), k)
28.57/10.19	   A^2 -> H(U1(e, c), c)
28.57/10.19	   A^2 -> H(U1(c, c), e)
28.57/10.19	   A^2 -> H(U1(c, c), k)
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(e, e), e)
28.57/10.19	   A^2 -> H(d, U1(e, b))
28.57/10.19	   A^2 -> H(d, U1(k, b))
28.57/10.19	   A^2 -> H(d, U1(c, d))
28.57/10.19	   A^2 -> H(d, U1(d, c))
28.57/10.19	   A^2 -> H(d, U1(b, e))
28.57/10.19	   A^2 -> H(d, U1(b, k))
28.57/10.19	   A^2 -> H(d, U1(e, c))
28.57/10.19	   A^2 -> H(d, U1(k, c))
28.57/10.19	   A^2 -> H(d, U1(c, e))
28.57/10.19	   A^2 -> H(d, U1(c, k))
28.57/10.19	   A^2 -> H(d, U1(e, e))
28.57/10.19	   A^2 -> H(d, U1(k, k))
28.57/10.19	   A^2 -> H(d, U1(k, d))
28.57/10.19	   A^2 -> H(d, U1(d, k))
28.57/10.19	   A^2 -> H(a, b)
28.57/10.19	   A^2 -> H(a, U1(e, d))
28.57/10.19	   A^2 -> H(a, U1(d, e))
28.57/10.19	   A^2 -> H(a, c)
28.57/10.19	   A^2 -> H(a, U1(e, k))
28.57/10.19	   A^2 -> H(a, U1(k, e))
28.57/10.19	   A^2 -> H(a, e)
28.57/10.19	   A^2 -> H(a, U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, d), b)
28.57/10.19	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, d), c)
28.57/10.19	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, d), e)
28.57/10.19	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, a), d)
28.57/10.19	   A^2 -> H(U1(e, a), k)
28.57/10.19	   A^2 -> H(U1(k, a), d)
28.57/10.19	   A^2 -> H(U1(c, d), d)
28.57/10.19	   A^2 -> H(U1(c, d), k)
28.57/10.19	   A^2 -> H(U1(d, e), b)
28.57/10.19	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(d, e), c)
28.57/10.19	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(d, e), e)
28.57/10.19	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, c), d)
28.57/10.19	   A^2 -> H(U1(d, c), k)
28.57/10.19	   A^2 -> H(U1(a, e), d)
28.57/10.19	   A^2 -> H(U1(a, e), k)
28.57/10.19	   A^2 -> H(U1(a, k), d)
28.57/10.19	   A^2 -> H(U1(a, k), k)
28.57/10.19	
28.57/10.19	The TRS R consists of the following rules:
28.57/10.19	
28.57/10.19	   f(x) -> U1(x, x)
28.57/10.19	   U1(e, x) -> x
28.57/10.19	   a -> c
28.57/10.19	   a -> d
28.57/10.19	   b -> c
28.57/10.19	   b -> d
28.57/10.19	   d -> k
28.57/10.19	   c -> e
28.57/10.19	   c -> k
28.57/10.19	
28.57/10.19	Q is empty.
28.57/10.19	We have to consider all minimal (P,Q,R)-chains.
28.57/10.19	----------------------------------------
28.57/10.19	
28.57/10.19	(2011) TransformationProof (EQUIVALENT)
28.57/10.19	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), d) at position [] we obtained the following new rules [LPAR04]:
28.57/10.19	
28.57/10.19	   (A^2 -> H(U1(c, c), d),A^2 -> H(U1(c, c), d))
28.57/10.19	   (A^2 -> H(U1(d, c), d),A^2 -> H(U1(d, c), d))
28.57/10.19	   (A^2 -> H(U1(a, e), d),A^2 -> H(U1(a, e), d))
28.57/10.19	   (A^2 -> H(U1(a, k), d),A^2 -> H(U1(a, k), d))
28.57/10.19	   (A^2 -> H(U1(a, c), k),A^2 -> H(U1(a, c), k))
28.57/10.19	
28.57/10.19	
28.57/10.19	----------------------------------------
28.57/10.19	
28.57/10.19	(2012)
28.57/10.19	Obligation:
28.57/10.19	Q DP problem:
28.57/10.19	The TRS P consists of the following rules:
28.57/10.19	
28.57/10.19	   G(d, x, x) -> A^2
28.57/10.19	   A^2 -> H(f(c), f(c))
28.57/10.19	   H(x, x) -> G(x, x, f(k))
28.57/10.19	   A^2 -> H(f(d), f(d))
28.57/10.19	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.19	   A^2 -> H(f(e), f(e))
28.57/10.19	   A^2 -> H(f(k), f(k))
28.57/10.19	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.19	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.19	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.19	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.19	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.19	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(a, c), k)
28.57/10.19	   A^2 -> H(U1(a, d), d)
28.57/10.19	   A^2 -> H(U1(a, d), k)
28.57/10.19	   A^2 -> H(k, U1(c, b))
28.57/10.19	   A^2 -> H(k, U1(d, b))
28.57/10.19	   A^2 -> H(k, U1(b, c))
28.57/10.19	   A^2 -> H(k, U1(b, d))
28.57/10.19	   A^2 -> H(k, U1(c, c))
28.57/10.19	   A^2 -> H(k, f(e))
28.57/10.19	   A^2 -> H(k, f(k))
28.57/10.19	   A^2 -> H(k, U1(d, d))
28.57/10.19	   A^2 -> H(c, U1(e, b))
28.57/10.19	   A^2 -> H(c, U1(k, b))
28.57/10.19	   A^2 -> H(c, U1(c, d))
28.57/10.19	   A^2 -> H(c, U1(d, c))
28.57/10.19	   A^2 -> H(c, U1(b, e))
28.57/10.19	   A^2 -> H(c, U1(b, k))
28.57/10.19	   A^2 -> H(c, U1(e, c))
28.57/10.19	   A^2 -> H(c, U1(k, c))
28.57/10.19	   A^2 -> H(c, U1(c, e))
28.57/10.19	   A^2 -> H(c, U1(c, k))
28.57/10.19	   A^2 -> H(c, U1(e, e))
28.57/10.19	   A^2 -> H(c, U1(k, k))
28.57/10.19	   A^2 -> H(c, U1(k, d))
28.57/10.19	   A^2 -> H(c, U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.19	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.19	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, c), b)
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, c), e)
28.57/10.19	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.19	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.19	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.19	   A^2 -> H(U1(k, c), b)
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, c), c)
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, e), b)
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(c, e), c)
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(c, e), e)
28.57/10.19	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, k), b)
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(c, k), c)
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(c, k), e)
28.57/10.19	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, c), d)
28.57/10.19	   A^2 -> H(e, U1(e, b))
28.57/10.19	   A^2 -> H(e, U1(c, d))
28.57/10.19	   A^2 -> H(e, U1(d, c))
28.57/10.19	   A^2 -> H(e, U1(b, e))
28.57/10.19	   A^2 -> H(e, U1(b, k))
28.57/10.19	   A^2 -> H(e, U1(e, c))
28.57/10.19	   A^2 -> H(e, U1(c, e))
28.57/10.19	   A^2 -> H(e, U1(c, k))
28.57/10.19	   A^2 -> H(e, U1(e, e))
28.57/10.19	   A^2 -> H(e, U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, e), b)
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, e), c)
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.19	   A^2 -> H(f(e), d)
28.57/10.19	   A^2 -> H(f(e), k)
28.57/10.19	   A^2 -> H(U1(k, k), b)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, k), c)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.19	   A^2 -> H(f(k), d)
28.57/10.19	   A^2 -> H(f(k), k)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(k, d), b)
28.57/10.19	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, d), c)
28.57/10.19	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, k), b)
28.57/10.19	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(d, k), c)
28.57/10.19	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(d, k), e)
28.57/10.19	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, d), d)
28.57/10.19	   A^2 -> H(U1(d, d), k)
28.57/10.19	   A^2 -> H(U1(e, c), c)
28.57/10.19	   A^2 -> H(U1(c, c), e)
28.57/10.19	   A^2 -> H(U1(c, c), k)
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(e, e), e)
28.57/10.19	   A^2 -> H(d, U1(e, b))
28.57/10.19	   A^2 -> H(d, U1(k, b))
28.57/10.19	   A^2 -> H(d, U1(c, d))
28.57/10.19	   A^2 -> H(d, U1(d, c))
28.57/10.19	   A^2 -> H(d, U1(b, e))
28.57/10.19	   A^2 -> H(d, U1(b, k))
28.57/10.19	   A^2 -> H(d, U1(e, c))
28.57/10.19	   A^2 -> H(d, U1(k, c))
28.57/10.19	   A^2 -> H(d, U1(c, e))
28.57/10.19	   A^2 -> H(d, U1(c, k))
28.57/10.19	   A^2 -> H(d, U1(e, e))
28.57/10.19	   A^2 -> H(d, U1(k, k))
28.57/10.19	   A^2 -> H(d, U1(k, d))
28.57/10.19	   A^2 -> H(d, U1(d, k))
28.57/10.19	   A^2 -> H(a, b)
28.57/10.19	   A^2 -> H(a, U1(e, d))
28.57/10.19	   A^2 -> H(a, U1(d, e))
28.57/10.19	   A^2 -> H(a, c)
28.57/10.19	   A^2 -> H(a, U1(e, k))
28.57/10.19	   A^2 -> H(a, U1(k, e))
28.57/10.19	   A^2 -> H(a, e)
28.57/10.19	   A^2 -> H(a, U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, d), b)
28.57/10.19	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, d), c)
28.57/10.19	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, d), e)
28.57/10.19	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, a), d)
28.57/10.19	   A^2 -> H(U1(e, a), k)
28.57/10.19	   A^2 -> H(U1(k, a), d)
28.57/10.19	   A^2 -> H(U1(c, d), d)
28.57/10.19	   A^2 -> H(U1(c, d), k)
28.57/10.19	   A^2 -> H(U1(d, e), b)
28.57/10.19	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(d, e), c)
28.57/10.19	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(d, e), e)
28.57/10.19	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, c), d)
28.57/10.19	   A^2 -> H(U1(d, c), k)
28.57/10.19	   A^2 -> H(U1(a, e), d)
28.57/10.19	   A^2 -> H(U1(a, e), k)
28.57/10.19	   A^2 -> H(U1(a, k), d)
28.57/10.19	   A^2 -> H(U1(a, k), k)
28.57/10.19	
28.57/10.19	The TRS R consists of the following rules:
28.57/10.19	
28.57/10.19	   f(x) -> U1(x, x)
28.57/10.19	   U1(e, x) -> x
28.57/10.19	   a -> c
28.57/10.19	   a -> d
28.57/10.19	   b -> c
28.57/10.19	   b -> d
28.57/10.19	   d -> k
28.57/10.19	   c -> e
28.57/10.19	   c -> k
28.57/10.19	
28.57/10.19	Q is empty.
28.57/10.19	We have to consider all minimal (P,Q,R)-chains.
28.57/10.19	----------------------------------------
28.57/10.19	
28.57/10.19	(2013) TransformationProof (EQUIVALENT)
28.57/10.19	By narrowing [LPAR04] the rule A^2 -> H(U1(a, c), k) at position [] we obtained the following new rules [LPAR04]:
28.57/10.19	
28.57/10.19	   (A^2 -> H(U1(c, c), k),A^2 -> H(U1(c, c), k))
28.57/10.19	   (A^2 -> H(U1(d, c), k),A^2 -> H(U1(d, c), k))
28.57/10.19	   (A^2 -> H(U1(a, e), k),A^2 -> H(U1(a, e), k))
28.57/10.19	   (A^2 -> H(U1(a, k), k),A^2 -> H(U1(a, k), k))
28.57/10.19	
28.57/10.19	
28.57/10.19	----------------------------------------
28.57/10.19	
28.57/10.19	(2014)
28.57/10.19	Obligation:
28.57/10.19	Q DP problem:
28.57/10.19	The TRS P consists of the following rules:
28.57/10.19	
28.57/10.19	   G(d, x, x) -> A^2
28.57/10.19	   A^2 -> H(f(c), f(c))
28.57/10.19	   H(x, x) -> G(x, x, f(k))
28.57/10.19	   A^2 -> H(f(d), f(d))
28.57/10.19	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.19	   A^2 -> H(f(e), f(e))
28.57/10.19	   A^2 -> H(f(k), f(k))
28.57/10.19	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.19	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.19	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.19	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.19	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.19	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(a, d), d)
28.57/10.19	   A^2 -> H(U1(a, d), k)
28.57/10.19	   A^2 -> H(k, U1(c, b))
28.57/10.19	   A^2 -> H(k, U1(d, b))
28.57/10.19	   A^2 -> H(k, U1(b, c))
28.57/10.19	   A^2 -> H(k, U1(b, d))
28.57/10.19	   A^2 -> H(k, U1(c, c))
28.57/10.19	   A^2 -> H(k, f(e))
28.57/10.19	   A^2 -> H(k, f(k))
28.57/10.19	   A^2 -> H(k, U1(d, d))
28.57/10.19	   A^2 -> H(c, U1(e, b))
28.57/10.19	   A^2 -> H(c, U1(k, b))
28.57/10.19	   A^2 -> H(c, U1(c, d))
28.57/10.19	   A^2 -> H(c, U1(d, c))
28.57/10.19	   A^2 -> H(c, U1(b, e))
28.57/10.19	   A^2 -> H(c, U1(b, k))
28.57/10.19	   A^2 -> H(c, U1(e, c))
28.57/10.19	   A^2 -> H(c, U1(k, c))
28.57/10.19	   A^2 -> H(c, U1(c, e))
28.57/10.19	   A^2 -> H(c, U1(c, k))
28.57/10.19	   A^2 -> H(c, U1(e, e))
28.57/10.19	   A^2 -> H(c, U1(k, k))
28.57/10.19	   A^2 -> H(c, U1(k, d))
28.57/10.19	   A^2 -> H(c, U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.19	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.19	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, c), b)
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, c), e)
28.57/10.19	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.19	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.19	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.19	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.19	   A^2 -> H(U1(k, c), b)
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, c), c)
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.19	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, e), b)
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(c, e), c)
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(c, e), e)
28.57/10.19	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, k), b)
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(c, k), c)
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(c, k), e)
28.57/10.19	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(c, c), d)
28.57/10.19	   A^2 -> H(e, U1(e, b))
28.57/10.19	   A^2 -> H(e, U1(c, d))
28.57/10.19	   A^2 -> H(e, U1(d, c))
28.57/10.19	   A^2 -> H(e, U1(b, e))
28.57/10.19	   A^2 -> H(e, U1(b, k))
28.57/10.19	   A^2 -> H(e, U1(e, c))
28.57/10.19	   A^2 -> H(e, U1(c, e))
28.57/10.19	   A^2 -> H(e, U1(c, k))
28.57/10.19	   A^2 -> H(e, U1(e, e))
28.57/10.19	   A^2 -> H(e, U1(d, k))
28.57/10.19	   A^2 -> H(U1(e, e), b)
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.19	   A^2 -> H(U1(e, e), c)
28.57/10.19	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.19	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.19	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.19	   A^2 -> H(f(e), d)
28.57/10.19	   A^2 -> H(f(e), k)
28.57/10.19	   A^2 -> H(U1(k, k), b)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, k), c)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.19	   A^2 -> H(f(k), d)
28.57/10.19	   A^2 -> H(f(k), k)
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.19	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.19	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.19	   A^2 -> H(U1(k, d), b)
28.57/10.19	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.19	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.19	   A^2 -> H(U1(k, d), c)
28.57/10.19	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.19	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, k), b)
28.57/10.19	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.19	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.19	   A^2 -> H(U1(d, k), c)
28.57/10.19	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.19	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.19	   A^2 -> H(U1(d, k), e)
28.57/10.19	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.19	   A^2 -> H(U1(d, d), d)
28.57/10.19	   A^2 -> H(U1(d, d), k)
28.57/10.19	   A^2 -> H(U1(e, c), c)
28.57/10.19	   A^2 -> H(U1(c, c), e)
28.57/10.19	   A^2 -> H(U1(c, c), k)
28.57/10.19	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.19	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.19	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.19	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.19	   A^2 -> H(U1(e, e), e)
28.57/10.19	   A^2 -> H(d, U1(e, b))
28.57/10.19	   A^2 -> H(d, U1(k, b))
28.57/10.19	   A^2 -> H(d, U1(c, d))
28.57/10.19	   A^2 -> H(d, U1(d, c))
28.57/10.19	   A^2 -> H(d, U1(b, e))
28.57/10.19	   A^2 -> H(d, U1(b, k))
28.57/10.19	   A^2 -> H(d, U1(e, c))
28.57/10.19	   A^2 -> H(d, U1(k, c))
28.57/10.19	   A^2 -> H(d, U1(c, e))
28.57/10.19	   A^2 -> H(d, U1(c, k))
28.57/10.19	   A^2 -> H(d, U1(e, e))
28.57/10.19	   A^2 -> H(d, U1(k, k))
28.57/10.19	   A^2 -> H(d, U1(k, d))
28.57/10.19	   A^2 -> H(d, U1(d, k))
28.57/10.19	   A^2 -> H(a, b)
28.57/10.19	   A^2 -> H(a, U1(e, d))
28.57/10.19	   A^2 -> H(a, U1(d, e))
28.57/10.19	   A^2 -> H(a, c)
28.57/10.19	   A^2 -> H(a, U1(e, k))
28.57/10.19	   A^2 -> H(a, U1(k, e))
28.57/10.19	   A^2 -> H(a, e)
28.57/10.19	   A^2 -> H(a, U1(k, k))
28.57/10.19	   A^2 -> H(U1(e, d), b)
28.57/10.19	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.19	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, d), c)
28.57/10.20	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, d), e)
28.57/10.20	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, a), d)
28.57/10.20	   A^2 -> H(U1(e, a), k)
28.57/10.20	   A^2 -> H(U1(k, a), d)
28.57/10.20	   A^2 -> H(U1(c, d), d)
28.57/10.20	   A^2 -> H(U1(c, d), k)
28.57/10.20	   A^2 -> H(U1(d, e), b)
28.57/10.20	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(d, e), c)
28.57/10.20	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(d, e), e)
28.57/10.20	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, c), d)
28.57/10.20	   A^2 -> H(U1(d, c), k)
28.57/10.20	   A^2 -> H(U1(a, e), d)
28.57/10.20	   A^2 -> H(U1(a, e), k)
28.57/10.20	   A^2 -> H(U1(a, k), d)
28.57/10.20	   A^2 -> H(U1(a, k), k)
28.57/10.20	
28.57/10.20	The TRS R consists of the following rules:
28.57/10.20	
28.57/10.20	   f(x) -> U1(x, x)
28.57/10.20	   U1(e, x) -> x
28.57/10.20	   a -> c
28.57/10.20	   a -> d
28.57/10.20	   b -> c
28.57/10.20	   b -> d
28.57/10.20	   d -> k
28.57/10.20	   c -> e
28.57/10.20	   c -> k
28.57/10.20	
28.57/10.20	Q is empty.
28.57/10.20	We have to consider all minimal (P,Q,R)-chains.
28.57/10.20	----------------------------------------
28.57/10.20	
28.57/10.20	(2015) TransformationProof (EQUIVALENT)
28.57/10.20	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), d) at position [] we obtained the following new rules [LPAR04]:
28.57/10.20	
28.57/10.20	   (A^2 -> H(U1(c, d), d),A^2 -> H(U1(c, d), d))
28.57/10.20	   (A^2 -> H(U1(d, d), d),A^2 -> H(U1(d, d), d))
28.57/10.20	   (A^2 -> H(U1(a, k), d),A^2 -> H(U1(a, k), d))
28.57/10.20	   (A^2 -> H(U1(a, d), k),A^2 -> H(U1(a, d), k))
28.57/10.20	
28.57/10.20	
28.57/10.20	----------------------------------------
28.57/10.20	
28.57/10.20	(2016)
28.57/10.20	Obligation:
28.57/10.20	Q DP problem:
28.57/10.20	The TRS P consists of the following rules:
28.57/10.20	
28.57/10.20	   G(d, x, x) -> A^2
28.57/10.20	   A^2 -> H(f(c), f(c))
28.57/10.20	   H(x, x) -> G(x, x, f(k))
28.57/10.20	   A^2 -> H(f(d), f(d))
28.57/10.20	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.20	   A^2 -> H(f(e), f(e))
28.57/10.20	   A^2 -> H(f(k), f(k))
28.57/10.20	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.20	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.20	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.20	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.20	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.20	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.20	   A^2 -> H(U1(a, d), k)
28.57/10.20	   A^2 -> H(k, U1(c, b))
28.57/10.20	   A^2 -> H(k, U1(d, b))
28.57/10.20	   A^2 -> H(k, U1(b, c))
28.57/10.20	   A^2 -> H(k, U1(b, d))
28.57/10.20	   A^2 -> H(k, U1(c, c))
28.57/10.20	   A^2 -> H(k, f(e))
28.57/10.20	   A^2 -> H(k, f(k))
28.57/10.20	   A^2 -> H(k, U1(d, d))
28.57/10.20	   A^2 -> H(c, U1(e, b))
28.57/10.20	   A^2 -> H(c, U1(k, b))
28.57/10.20	   A^2 -> H(c, U1(c, d))
28.57/10.20	   A^2 -> H(c, U1(d, c))
28.57/10.20	   A^2 -> H(c, U1(b, e))
28.57/10.20	   A^2 -> H(c, U1(b, k))
28.57/10.20	   A^2 -> H(c, U1(e, c))
28.57/10.20	   A^2 -> H(c, U1(k, c))
28.57/10.20	   A^2 -> H(c, U1(c, e))
28.57/10.20	   A^2 -> H(c, U1(c, k))
28.57/10.20	   A^2 -> H(c, U1(e, e))
28.57/10.20	   A^2 -> H(c, U1(k, k))
28.57/10.20	   A^2 -> H(c, U1(k, d))
28.57/10.20	   A^2 -> H(c, U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.20	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.20	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, c), b)
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, c), e)
28.57/10.20	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.20	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.20	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.20	   A^2 -> H(U1(k, c), b)
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, c), c)
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, e), b)
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(c, e), c)
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(c, e), e)
28.57/10.20	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, k), b)
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(c, k), c)
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.20	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.20	   A^2 -> H(U1(c, k), e)
28.57/10.20	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, c), d)
28.57/10.20	   A^2 -> H(e, U1(e, b))
28.57/10.20	   A^2 -> H(e, U1(c, d))
28.57/10.20	   A^2 -> H(e, U1(d, c))
28.57/10.20	   A^2 -> H(e, U1(b, e))
28.57/10.20	   A^2 -> H(e, U1(b, k))
28.57/10.20	   A^2 -> H(e, U1(e, c))
28.57/10.20	   A^2 -> H(e, U1(c, e))
28.57/10.20	   A^2 -> H(e, U1(c, k))
28.57/10.20	   A^2 -> H(e, U1(e, e))
28.57/10.20	   A^2 -> H(e, U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, e), b)
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, e), c)
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.20	   A^2 -> H(f(e), d)
28.57/10.20	   A^2 -> H(f(e), k)
28.57/10.20	   A^2 -> H(U1(k, k), b)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, k), c)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.20	   A^2 -> H(f(k), d)
28.57/10.20	   A^2 -> H(f(k), k)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.20	   A^2 -> H(U1(k, d), b)
28.57/10.20	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, d), c)
28.57/10.20	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, k), b)
28.57/10.20	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(d, k), c)
28.57/10.20	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.20	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.20	   A^2 -> H(U1(d, k), e)
28.57/10.20	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, d), d)
28.57/10.20	   A^2 -> H(U1(d, d), k)
28.57/10.20	   A^2 -> H(U1(e, c), c)
28.57/10.20	   A^2 -> H(U1(c, c), e)
28.57/10.20	   A^2 -> H(U1(c, c), k)
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(e, e), e)
28.57/10.20	   A^2 -> H(d, U1(e, b))
28.57/10.20	   A^2 -> H(d, U1(k, b))
28.57/10.20	   A^2 -> H(d, U1(c, d))
28.57/10.20	   A^2 -> H(d, U1(d, c))
28.57/10.20	   A^2 -> H(d, U1(b, e))
28.57/10.20	   A^2 -> H(d, U1(b, k))
28.57/10.20	   A^2 -> H(d, U1(e, c))
28.57/10.20	   A^2 -> H(d, U1(k, c))
28.57/10.20	   A^2 -> H(d, U1(c, e))
28.57/10.20	   A^2 -> H(d, U1(c, k))
28.57/10.20	   A^2 -> H(d, U1(e, e))
28.57/10.20	   A^2 -> H(d, U1(k, k))
28.57/10.20	   A^2 -> H(d, U1(k, d))
28.57/10.20	   A^2 -> H(d, U1(d, k))
28.57/10.20	   A^2 -> H(a, b)
28.57/10.20	   A^2 -> H(a, U1(e, d))
28.57/10.20	   A^2 -> H(a, U1(d, e))
28.57/10.20	   A^2 -> H(a, c)
28.57/10.20	   A^2 -> H(a, U1(e, k))
28.57/10.20	   A^2 -> H(a, U1(k, e))
28.57/10.20	   A^2 -> H(a, e)
28.57/10.20	   A^2 -> H(a, U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, d), b)
28.57/10.20	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, d), c)
28.57/10.20	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, d), e)
28.57/10.20	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, a), d)
28.57/10.20	   A^2 -> H(U1(e, a), k)
28.57/10.20	   A^2 -> H(U1(k, a), d)
28.57/10.20	   A^2 -> H(U1(c, d), d)
28.57/10.20	   A^2 -> H(U1(c, d), k)
28.57/10.20	   A^2 -> H(U1(d, e), b)
28.57/10.20	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(d, e), c)
28.57/10.20	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(d, e), e)
28.57/10.20	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, c), d)
28.57/10.20	   A^2 -> H(U1(d, c), k)
28.57/10.20	   A^2 -> H(U1(a, e), d)
28.57/10.20	   A^2 -> H(U1(a, e), k)
28.57/10.20	   A^2 -> H(U1(a, k), d)
28.57/10.20	   A^2 -> H(U1(a, k), k)
28.57/10.20	
28.57/10.20	The TRS R consists of the following rules:
28.57/10.20	
28.57/10.20	   f(x) -> U1(x, x)
28.57/10.20	   U1(e, x) -> x
28.57/10.20	   a -> c
28.57/10.20	   a -> d
28.57/10.20	   b -> c
28.57/10.20	   b -> d
28.57/10.20	   d -> k
28.57/10.20	   c -> e
28.57/10.20	   c -> k
28.57/10.20	
28.57/10.20	Q is empty.
28.57/10.20	We have to consider all minimal (P,Q,R)-chains.
28.57/10.20	----------------------------------------
28.57/10.20	
28.57/10.20	(2017) TransformationProof (EQUIVALENT)
28.57/10.20	By narrowing [LPAR04] the rule A^2 -> H(U1(a, d), k) at position [] we obtained the following new rules [LPAR04]:
28.57/10.20	
28.57/10.20	   (A^2 -> H(U1(c, d), k),A^2 -> H(U1(c, d), k))
28.57/10.20	   (A^2 -> H(U1(d, d), k),A^2 -> H(U1(d, d), k))
28.57/10.20	   (A^2 -> H(U1(a, k), k),A^2 -> H(U1(a, k), k))
28.57/10.20	
28.57/10.20	
28.57/10.20	----------------------------------------
28.57/10.20	
28.57/10.20	(2018)
28.57/10.20	Obligation:
28.57/10.20	Q DP problem:
28.57/10.20	The TRS P consists of the following rules:
28.57/10.20	
28.57/10.20	   G(d, x, x) -> A^2
28.57/10.20	   A^2 -> H(f(c), f(c))
28.57/10.20	   H(x, x) -> G(x, x, f(k))
28.57/10.20	   A^2 -> H(f(d), f(d))
28.57/10.20	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.20	   A^2 -> H(f(e), f(e))
28.57/10.20	   A^2 -> H(f(k), f(k))
28.57/10.20	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.20	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.20	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.20	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.20	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.20	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.20	   A^2 -> H(k, U1(c, b))
28.57/10.20	   A^2 -> H(k, U1(d, b))
28.57/10.20	   A^2 -> H(k, U1(b, c))
28.57/10.20	   A^2 -> H(k, U1(b, d))
28.57/10.20	   A^2 -> H(k, U1(c, c))
28.57/10.20	   A^2 -> H(k, f(e))
28.57/10.20	   A^2 -> H(k, f(k))
28.57/10.20	   A^2 -> H(k, U1(d, d))
28.57/10.20	   A^2 -> H(c, U1(e, b))
28.57/10.20	   A^2 -> H(c, U1(k, b))
28.57/10.20	   A^2 -> H(c, U1(c, d))
28.57/10.20	   A^2 -> H(c, U1(d, c))
28.57/10.20	   A^2 -> H(c, U1(b, e))
28.57/10.20	   A^2 -> H(c, U1(b, k))
28.57/10.20	   A^2 -> H(c, U1(e, c))
28.57/10.20	   A^2 -> H(c, U1(k, c))
28.57/10.20	   A^2 -> H(c, U1(c, e))
28.57/10.20	   A^2 -> H(c, U1(c, k))
28.57/10.20	   A^2 -> H(c, U1(e, e))
28.57/10.20	   A^2 -> H(c, U1(k, k))
28.57/10.20	   A^2 -> H(c, U1(k, d))
28.57/10.20	   A^2 -> H(c, U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.20	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.20	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, c), b)
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, c), e)
28.57/10.20	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.20	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.20	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.20	   A^2 -> H(U1(k, c), b)
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, c), c)
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, e), b)
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(c, e), c)
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(c, e), e)
28.57/10.20	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, k), b)
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(c, k), c)
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.20	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.20	   A^2 -> H(U1(c, k), e)
28.57/10.20	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, c), d)
28.57/10.20	   A^2 -> H(e, U1(e, b))
28.57/10.20	   A^2 -> H(e, U1(c, d))
28.57/10.20	   A^2 -> H(e, U1(d, c))
28.57/10.20	   A^2 -> H(e, U1(b, e))
28.57/10.20	   A^2 -> H(e, U1(b, k))
28.57/10.20	   A^2 -> H(e, U1(e, c))
28.57/10.20	   A^2 -> H(e, U1(c, e))
28.57/10.20	   A^2 -> H(e, U1(c, k))
28.57/10.20	   A^2 -> H(e, U1(e, e))
28.57/10.20	   A^2 -> H(e, U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, e), b)
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, e), c)
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.20	   A^2 -> H(f(e), d)
28.57/10.20	   A^2 -> H(f(e), k)
28.57/10.20	   A^2 -> H(U1(k, k), b)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, k), c)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.20	   A^2 -> H(f(k), d)
28.57/10.20	   A^2 -> H(f(k), k)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.20	   A^2 -> H(U1(k, d), b)
28.57/10.20	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, d), c)
28.57/10.20	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, k), b)
28.57/10.20	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(d, k), c)
28.57/10.20	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.20	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.20	   A^2 -> H(U1(d, k), e)
28.57/10.20	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, d), d)
28.57/10.20	   A^2 -> H(U1(d, d), k)
28.57/10.20	   A^2 -> H(U1(e, c), c)
28.57/10.20	   A^2 -> H(U1(c, c), e)
28.57/10.20	   A^2 -> H(U1(c, c), k)
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(e, e), e)
28.57/10.20	   A^2 -> H(d, U1(e, b))
28.57/10.20	   A^2 -> H(d, U1(k, b))
28.57/10.20	   A^2 -> H(d, U1(c, d))
28.57/10.20	   A^2 -> H(d, U1(d, c))
28.57/10.20	   A^2 -> H(d, U1(b, e))
28.57/10.20	   A^2 -> H(d, U1(b, k))
28.57/10.20	   A^2 -> H(d, U1(e, c))
28.57/10.20	   A^2 -> H(d, U1(k, c))
28.57/10.20	   A^2 -> H(d, U1(c, e))
28.57/10.20	   A^2 -> H(d, U1(c, k))
28.57/10.20	   A^2 -> H(d, U1(e, e))
28.57/10.20	   A^2 -> H(d, U1(k, k))
28.57/10.20	   A^2 -> H(d, U1(k, d))
28.57/10.20	   A^2 -> H(d, U1(d, k))
28.57/10.20	   A^2 -> H(a, b)
28.57/10.20	   A^2 -> H(a, U1(e, d))
28.57/10.20	   A^2 -> H(a, U1(d, e))
28.57/10.20	   A^2 -> H(a, c)
28.57/10.20	   A^2 -> H(a, U1(e, k))
28.57/10.20	   A^2 -> H(a, U1(k, e))
28.57/10.20	   A^2 -> H(a, e)
28.57/10.20	   A^2 -> H(a, U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, d), b)
28.57/10.20	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, d), c)
28.57/10.20	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, d), e)
28.57/10.20	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, a), d)
28.57/10.20	   A^2 -> H(U1(e, a), k)
28.57/10.20	   A^2 -> H(U1(k, a), d)
28.57/10.20	   A^2 -> H(U1(c, d), d)
28.57/10.20	   A^2 -> H(U1(c, d), k)
28.57/10.20	   A^2 -> H(U1(d, e), b)
28.57/10.20	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(d, e), c)
28.57/10.20	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(d, e), e)
28.57/10.20	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, c), d)
28.57/10.20	   A^2 -> H(U1(d, c), k)
28.57/10.20	   A^2 -> H(U1(a, e), d)
28.57/10.20	   A^2 -> H(U1(a, e), k)
28.57/10.20	   A^2 -> H(U1(a, k), d)
28.57/10.20	   A^2 -> H(U1(a, k), k)
28.57/10.20	
28.57/10.20	The TRS R consists of the following rules:
28.57/10.20	
28.57/10.20	   f(x) -> U1(x, x)
28.57/10.20	   U1(e, x) -> x
28.57/10.20	   a -> c
28.57/10.20	   a -> d
28.57/10.20	   b -> c
28.57/10.20	   b -> d
28.57/10.20	   d -> k
28.57/10.20	   c -> e
28.57/10.20	   c -> k
28.57/10.20	
28.57/10.20	Q is empty.
28.57/10.20	We have to consider all minimal (P,Q,R)-chains.
28.57/10.20	----------------------------------------
28.57/10.20	
28.57/10.20	(2019) TransformationProof (EQUIVALENT)
28.57/10.20	By narrowing [LPAR04] the rule A^2 -> H(k, U1(c, b)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.20	
28.57/10.20	   (A^2 -> H(k, U1(e, b)),A^2 -> H(k, U1(e, b)))
28.57/10.20	   (A^2 -> H(k, U1(k, b)),A^2 -> H(k, U1(k, b)))
28.57/10.20	   (A^2 -> H(k, U1(c, c)),A^2 -> H(k, U1(c, c)))
28.57/10.20	   (A^2 -> H(k, U1(c, d)),A^2 -> H(k, U1(c, d)))
28.57/10.20	
28.57/10.20	
28.57/10.20	----------------------------------------
28.57/10.20	
28.57/10.20	(2020)
28.57/10.20	Obligation:
28.57/10.20	Q DP problem:
28.57/10.20	The TRS P consists of the following rules:
28.57/10.20	
28.57/10.20	   G(d, x, x) -> A^2
28.57/10.20	   A^2 -> H(f(c), f(c))
28.57/10.20	   H(x, x) -> G(x, x, f(k))
28.57/10.20	   A^2 -> H(f(d), f(d))
28.57/10.20	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.20	   A^2 -> H(f(e), f(e))
28.57/10.20	   A^2 -> H(f(k), f(k))
28.57/10.20	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.20	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.20	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.20	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.20	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.20	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.20	   A^2 -> H(k, U1(d, b))
28.57/10.20	   A^2 -> H(k, U1(b, c))
28.57/10.20	   A^2 -> H(k, U1(b, d))
28.57/10.20	   A^2 -> H(k, U1(c, c))
28.57/10.20	   A^2 -> H(k, f(e))
28.57/10.20	   A^2 -> H(k, f(k))
28.57/10.20	   A^2 -> H(k, U1(d, d))
28.57/10.20	   A^2 -> H(c, U1(e, b))
28.57/10.20	   A^2 -> H(c, U1(k, b))
28.57/10.20	   A^2 -> H(c, U1(c, d))
28.57/10.20	   A^2 -> H(c, U1(d, c))
28.57/10.20	   A^2 -> H(c, U1(b, e))
28.57/10.20	   A^2 -> H(c, U1(b, k))
28.57/10.20	   A^2 -> H(c, U1(e, c))
28.57/10.20	   A^2 -> H(c, U1(k, c))
28.57/10.20	   A^2 -> H(c, U1(c, e))
28.57/10.20	   A^2 -> H(c, U1(c, k))
28.57/10.20	   A^2 -> H(c, U1(e, e))
28.57/10.20	   A^2 -> H(c, U1(k, k))
28.57/10.20	   A^2 -> H(c, U1(k, d))
28.57/10.20	   A^2 -> H(c, U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.20	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.20	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, c), b)
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, c), e)
28.57/10.20	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.20	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.20	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.20	   A^2 -> H(U1(k, c), b)
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, c), c)
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, e), b)
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(c, e), c)
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(c, e), e)
28.57/10.20	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, k), b)
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(c, k), c)
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.20	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.20	   A^2 -> H(U1(c, k), e)
28.57/10.20	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, c), d)
28.57/10.20	   A^2 -> H(e, U1(e, b))
28.57/10.20	   A^2 -> H(e, U1(c, d))
28.57/10.20	   A^2 -> H(e, U1(d, c))
28.57/10.20	   A^2 -> H(e, U1(b, e))
28.57/10.20	   A^2 -> H(e, U1(b, k))
28.57/10.20	   A^2 -> H(e, U1(e, c))
28.57/10.20	   A^2 -> H(e, U1(c, e))
28.57/10.20	   A^2 -> H(e, U1(c, k))
28.57/10.20	   A^2 -> H(e, U1(e, e))
28.57/10.20	   A^2 -> H(e, U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, e), b)
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, e), c)
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.20	   A^2 -> H(f(e), d)
28.57/10.20	   A^2 -> H(f(e), k)
28.57/10.20	   A^2 -> H(U1(k, k), b)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, k), c)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.20	   A^2 -> H(f(k), d)
28.57/10.20	   A^2 -> H(f(k), k)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.20	   A^2 -> H(U1(k, d), b)
28.57/10.20	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, d), c)
28.57/10.20	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, k), b)
28.57/10.20	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(d, k), c)
28.57/10.20	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.20	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.20	   A^2 -> H(U1(d, k), e)
28.57/10.20	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, d), d)
28.57/10.20	   A^2 -> H(U1(d, d), k)
28.57/10.20	   A^2 -> H(U1(e, c), c)
28.57/10.20	   A^2 -> H(U1(c, c), e)
28.57/10.20	   A^2 -> H(U1(c, c), k)
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(e, e), e)
28.57/10.20	   A^2 -> H(d, U1(e, b))
28.57/10.20	   A^2 -> H(d, U1(k, b))
28.57/10.20	   A^2 -> H(d, U1(c, d))
28.57/10.20	   A^2 -> H(d, U1(d, c))
28.57/10.20	   A^2 -> H(d, U1(b, e))
28.57/10.20	   A^2 -> H(d, U1(b, k))
28.57/10.20	   A^2 -> H(d, U1(e, c))
28.57/10.20	   A^2 -> H(d, U1(k, c))
28.57/10.20	   A^2 -> H(d, U1(c, e))
28.57/10.20	   A^2 -> H(d, U1(c, k))
28.57/10.20	   A^2 -> H(d, U1(e, e))
28.57/10.20	   A^2 -> H(d, U1(k, k))
28.57/10.20	   A^2 -> H(d, U1(k, d))
28.57/10.20	   A^2 -> H(d, U1(d, k))
28.57/10.20	   A^2 -> H(a, b)
28.57/10.20	   A^2 -> H(a, U1(e, d))
28.57/10.20	   A^2 -> H(a, U1(d, e))
28.57/10.20	   A^2 -> H(a, c)
28.57/10.20	   A^2 -> H(a, U1(e, k))
28.57/10.20	   A^2 -> H(a, U1(k, e))
28.57/10.20	   A^2 -> H(a, e)
28.57/10.20	   A^2 -> H(a, U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, d), b)
28.57/10.20	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, d), c)
28.57/10.20	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, d), e)
28.57/10.20	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, a), d)
28.57/10.20	   A^2 -> H(U1(e, a), k)
28.57/10.20	   A^2 -> H(U1(k, a), d)
28.57/10.20	   A^2 -> H(U1(c, d), d)
28.57/10.20	   A^2 -> H(U1(c, d), k)
28.57/10.20	   A^2 -> H(U1(d, e), b)
28.57/10.20	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(d, e), c)
28.57/10.20	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(d, e), e)
28.57/10.20	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, c), d)
28.57/10.20	   A^2 -> H(U1(d, c), k)
28.57/10.20	   A^2 -> H(U1(a, e), d)
28.57/10.20	   A^2 -> H(U1(a, e), k)
28.57/10.20	   A^2 -> H(U1(a, k), d)
28.57/10.20	   A^2 -> H(U1(a, k), k)
28.57/10.20	   A^2 -> H(k, U1(e, b))
28.57/10.20	   A^2 -> H(k, U1(k, b))
28.57/10.20	   A^2 -> H(k, U1(c, d))
28.57/10.20	
28.57/10.20	The TRS R consists of the following rules:
28.57/10.20	
28.57/10.20	   f(x) -> U1(x, x)
28.57/10.20	   U1(e, x) -> x
28.57/10.20	   a -> c
28.57/10.20	   a -> d
28.57/10.20	   b -> c
28.57/10.20	   b -> d
28.57/10.20	   d -> k
28.57/10.20	   c -> e
28.57/10.20	   c -> k
28.57/10.20	
28.57/10.20	Q is empty.
28.57/10.20	We have to consider all minimal (P,Q,R)-chains.
28.57/10.20	----------------------------------------
28.57/10.20	
28.57/10.20	(2021) DependencyGraphProof (EQUIVALENT)
28.57/10.20	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.20	----------------------------------------
28.57/10.20	
28.57/10.20	(2022)
28.57/10.20	Obligation:
28.57/10.20	Q DP problem:
28.57/10.20	The TRS P consists of the following rules:
28.57/10.20	
28.57/10.20	   A^2 -> H(f(c), f(c))
28.57/10.20	   H(x, x) -> G(x, x, f(k))
28.57/10.20	   G(d, x, x) -> A^2
28.57/10.20	   A^2 -> H(f(d), f(d))
28.57/10.20	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.20	   A^2 -> H(f(e), f(e))
28.57/10.20	   A^2 -> H(f(k), f(k))
28.57/10.20	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.20	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.20	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.20	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.20	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.20	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.20	   A^2 -> H(k, U1(d, b))
28.57/10.20	   A^2 -> H(k, U1(b, c))
28.57/10.20	   A^2 -> H(k, U1(b, d))
28.57/10.20	   A^2 -> H(k, U1(c, c))
28.57/10.20	   A^2 -> H(k, f(e))
28.57/10.20	   A^2 -> H(k, f(k))
28.57/10.20	   A^2 -> H(k, U1(d, d))
28.57/10.20	   A^2 -> H(c, U1(e, b))
28.57/10.20	   A^2 -> H(c, U1(k, b))
28.57/10.20	   A^2 -> H(c, U1(c, d))
28.57/10.20	   A^2 -> H(c, U1(d, c))
28.57/10.20	   A^2 -> H(c, U1(b, e))
28.57/10.20	   A^2 -> H(c, U1(b, k))
28.57/10.20	   A^2 -> H(c, U1(e, c))
28.57/10.20	   A^2 -> H(c, U1(k, c))
28.57/10.20	   A^2 -> H(c, U1(c, e))
28.57/10.20	   A^2 -> H(c, U1(c, k))
28.57/10.20	   A^2 -> H(c, U1(e, e))
28.57/10.20	   A^2 -> H(c, U1(k, k))
28.57/10.20	   A^2 -> H(c, U1(k, d))
28.57/10.20	   A^2 -> H(c, U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.20	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.20	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, c), b)
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, c), e)
28.57/10.20	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.20	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.20	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.20	   A^2 -> H(U1(k, c), b)
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, c), c)
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, e), b)
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(c, e), c)
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(c, e), e)
28.57/10.20	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, k), b)
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(c, k), c)
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.20	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.20	   A^2 -> H(U1(c, k), e)
28.57/10.20	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, c), d)
28.57/10.20	   A^2 -> H(e, U1(e, b))
28.57/10.20	   A^2 -> H(e, U1(c, d))
28.57/10.20	   A^2 -> H(e, U1(d, c))
28.57/10.20	   A^2 -> H(e, U1(b, e))
28.57/10.20	   A^2 -> H(e, U1(b, k))
28.57/10.20	   A^2 -> H(e, U1(e, c))
28.57/10.20	   A^2 -> H(e, U1(c, e))
28.57/10.20	   A^2 -> H(e, U1(c, k))
28.57/10.20	   A^2 -> H(e, U1(e, e))
28.57/10.20	   A^2 -> H(e, U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, e), b)
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, e), c)
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.20	   A^2 -> H(f(e), d)
28.57/10.20	   A^2 -> H(f(e), k)
28.57/10.20	   A^2 -> H(U1(k, k), b)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, k), c)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.20	   A^2 -> H(f(k), d)
28.57/10.20	   A^2 -> H(f(k), k)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.20	   A^2 -> H(U1(k, d), b)
28.57/10.20	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, d), c)
28.57/10.20	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, k), b)
28.57/10.20	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(d, k), c)
28.57/10.20	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.20	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.20	   A^2 -> H(U1(d, k), e)
28.57/10.20	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, d), d)
28.57/10.20	   A^2 -> H(U1(d, d), k)
28.57/10.20	   A^2 -> H(U1(e, c), c)
28.57/10.20	   A^2 -> H(U1(c, c), e)
28.57/10.20	   A^2 -> H(U1(c, c), k)
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(e, e), e)
28.57/10.20	   A^2 -> H(d, U1(e, b))
28.57/10.20	   A^2 -> H(d, U1(k, b))
28.57/10.20	   A^2 -> H(d, U1(c, d))
28.57/10.20	   A^2 -> H(d, U1(d, c))
28.57/10.20	   A^2 -> H(d, U1(b, e))
28.57/10.20	   A^2 -> H(d, U1(b, k))
28.57/10.20	   A^2 -> H(d, U1(e, c))
28.57/10.20	   A^2 -> H(d, U1(k, c))
28.57/10.20	   A^2 -> H(d, U1(c, e))
28.57/10.20	   A^2 -> H(d, U1(c, k))
28.57/10.20	   A^2 -> H(d, U1(e, e))
28.57/10.20	   A^2 -> H(d, U1(k, k))
28.57/10.20	   A^2 -> H(d, U1(k, d))
28.57/10.20	   A^2 -> H(d, U1(d, k))
28.57/10.20	   A^2 -> H(a, b)
28.57/10.20	   A^2 -> H(a, U1(e, d))
28.57/10.20	   A^2 -> H(a, U1(d, e))
28.57/10.20	   A^2 -> H(a, c)
28.57/10.20	   A^2 -> H(a, U1(e, k))
28.57/10.20	   A^2 -> H(a, U1(k, e))
28.57/10.20	   A^2 -> H(a, e)
28.57/10.20	   A^2 -> H(a, U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, d), b)
28.57/10.20	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, d), c)
28.57/10.20	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, d), e)
28.57/10.20	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, a), d)
28.57/10.20	   A^2 -> H(U1(e, a), k)
28.57/10.20	   A^2 -> H(U1(k, a), d)
28.57/10.20	   A^2 -> H(U1(c, d), d)
28.57/10.20	   A^2 -> H(U1(c, d), k)
28.57/10.20	   A^2 -> H(U1(d, e), b)
28.57/10.20	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(d, e), c)
28.57/10.20	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(d, e), e)
28.57/10.20	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, c), d)
28.57/10.20	   A^2 -> H(U1(d, c), k)
28.57/10.20	   A^2 -> H(U1(a, e), d)
28.57/10.20	   A^2 -> H(U1(a, e), k)
28.57/10.20	   A^2 -> H(U1(a, k), d)
28.57/10.20	   A^2 -> H(U1(a, k), k)
28.57/10.20	   A^2 -> H(k, U1(e, b))
28.57/10.20	   A^2 -> H(k, U1(c, d))
28.57/10.20	
28.57/10.20	The TRS R consists of the following rules:
28.57/10.20	
28.57/10.20	   f(x) -> U1(x, x)
28.57/10.20	   U1(e, x) -> x
28.57/10.20	   a -> c
28.57/10.20	   a -> d
28.57/10.20	   b -> c
28.57/10.20	   b -> d
28.57/10.20	   d -> k
28.57/10.20	   c -> e
28.57/10.20	   c -> k
28.57/10.20	
28.57/10.20	Q is empty.
28.57/10.20	We have to consider all minimal (P,Q,R)-chains.
28.57/10.20	----------------------------------------
28.57/10.20	
28.57/10.20	(2023) TransformationProof (EQUIVALENT)
28.57/10.20	By narrowing [LPAR04] the rule A^2 -> H(k, U1(d, b)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.20	
28.57/10.20	   (A^2 -> H(k, U1(k, b)),A^2 -> H(k, U1(k, b)))
28.57/10.20	   (A^2 -> H(k, U1(d, c)),A^2 -> H(k, U1(d, c)))
28.57/10.20	   (A^2 -> H(k, U1(d, d)),A^2 -> H(k, U1(d, d)))
28.57/10.20	
28.57/10.20	
28.57/10.20	----------------------------------------
28.57/10.20	
28.57/10.20	(2024)
28.57/10.20	Obligation:
28.57/10.20	Q DP problem:
28.57/10.20	The TRS P consists of the following rules:
28.57/10.20	
28.57/10.20	   A^2 -> H(f(c), f(c))
28.57/10.20	   H(x, x) -> G(x, x, f(k))
28.57/10.20	   G(d, x, x) -> A^2
28.57/10.20	   A^2 -> H(f(d), f(d))
28.57/10.20	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.20	   A^2 -> H(f(e), f(e))
28.57/10.20	   A^2 -> H(f(k), f(k))
28.57/10.20	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.20	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.20	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.20	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.20	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.20	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.20	   A^2 -> H(k, U1(b, c))
28.57/10.20	   A^2 -> H(k, U1(b, d))
28.57/10.20	   A^2 -> H(k, U1(c, c))
28.57/10.20	   A^2 -> H(k, f(e))
28.57/10.20	   A^2 -> H(k, f(k))
28.57/10.20	   A^2 -> H(k, U1(d, d))
28.57/10.20	   A^2 -> H(c, U1(e, b))
28.57/10.20	   A^2 -> H(c, U1(k, b))
28.57/10.20	   A^2 -> H(c, U1(c, d))
28.57/10.20	   A^2 -> H(c, U1(d, c))
28.57/10.20	   A^2 -> H(c, U1(b, e))
28.57/10.20	   A^2 -> H(c, U1(b, k))
28.57/10.20	   A^2 -> H(c, U1(e, c))
28.57/10.20	   A^2 -> H(c, U1(k, c))
28.57/10.20	   A^2 -> H(c, U1(c, e))
28.57/10.20	   A^2 -> H(c, U1(c, k))
28.57/10.20	   A^2 -> H(c, U1(e, e))
28.57/10.20	   A^2 -> H(c, U1(k, k))
28.57/10.20	   A^2 -> H(c, U1(k, d))
28.57/10.20	   A^2 -> H(c, U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.20	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.20	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, c), b)
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, c), e)
28.57/10.20	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.20	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.20	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.20	   A^2 -> H(U1(k, c), b)
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, c), c)
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, e), b)
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(c, e), c)
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(c, e), e)
28.57/10.20	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, k), b)
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(c, k), c)
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.20	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.20	   A^2 -> H(U1(c, k), e)
28.57/10.20	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, c), d)
28.57/10.20	   A^2 -> H(e, U1(e, b))
28.57/10.20	   A^2 -> H(e, U1(c, d))
28.57/10.20	   A^2 -> H(e, U1(d, c))
28.57/10.20	   A^2 -> H(e, U1(b, e))
28.57/10.20	   A^2 -> H(e, U1(b, k))
28.57/10.20	   A^2 -> H(e, U1(e, c))
28.57/10.20	   A^2 -> H(e, U1(c, e))
28.57/10.20	   A^2 -> H(e, U1(c, k))
28.57/10.20	   A^2 -> H(e, U1(e, e))
28.57/10.20	   A^2 -> H(e, U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, e), b)
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, e), c)
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.20	   A^2 -> H(f(e), d)
28.57/10.20	   A^2 -> H(f(e), k)
28.57/10.20	   A^2 -> H(U1(k, k), b)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, k), c)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.20	   A^2 -> H(f(k), d)
28.57/10.20	   A^2 -> H(f(k), k)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.20	   A^2 -> H(U1(k, d), b)
28.57/10.20	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, d), c)
28.57/10.20	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, k), b)
28.57/10.20	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(d, k), c)
28.57/10.20	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.20	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.20	   A^2 -> H(U1(d, k), e)
28.57/10.20	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, d), d)
28.57/10.20	   A^2 -> H(U1(d, d), k)
28.57/10.20	   A^2 -> H(U1(e, c), c)
28.57/10.20	   A^2 -> H(U1(c, c), e)
28.57/10.20	   A^2 -> H(U1(c, c), k)
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(e, e), e)
28.57/10.20	   A^2 -> H(d, U1(e, b))
28.57/10.20	   A^2 -> H(d, U1(k, b))
28.57/10.20	   A^2 -> H(d, U1(c, d))
28.57/10.20	   A^2 -> H(d, U1(d, c))
28.57/10.20	   A^2 -> H(d, U1(b, e))
28.57/10.20	   A^2 -> H(d, U1(b, k))
28.57/10.20	   A^2 -> H(d, U1(e, c))
28.57/10.20	   A^2 -> H(d, U1(k, c))
28.57/10.20	   A^2 -> H(d, U1(c, e))
28.57/10.20	   A^2 -> H(d, U1(c, k))
28.57/10.20	   A^2 -> H(d, U1(e, e))
28.57/10.20	   A^2 -> H(d, U1(k, k))
28.57/10.20	   A^2 -> H(d, U1(k, d))
28.57/10.20	   A^2 -> H(d, U1(d, k))
28.57/10.20	   A^2 -> H(a, b)
28.57/10.20	   A^2 -> H(a, U1(e, d))
28.57/10.20	   A^2 -> H(a, U1(d, e))
28.57/10.20	   A^2 -> H(a, c)
28.57/10.20	   A^2 -> H(a, U1(e, k))
28.57/10.20	   A^2 -> H(a, U1(k, e))
28.57/10.20	   A^2 -> H(a, e)
28.57/10.20	   A^2 -> H(a, U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, d), b)
28.57/10.20	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, d), c)
28.57/10.20	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, d), e)
28.57/10.20	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, a), d)
28.57/10.20	   A^2 -> H(U1(e, a), k)
28.57/10.20	   A^2 -> H(U1(k, a), d)
28.57/10.20	   A^2 -> H(U1(c, d), d)
28.57/10.20	   A^2 -> H(U1(c, d), k)
28.57/10.20	   A^2 -> H(U1(d, e), b)
28.57/10.20	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(d, e), c)
28.57/10.20	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(d, e), e)
28.57/10.20	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, c), d)
28.57/10.20	   A^2 -> H(U1(d, c), k)
28.57/10.20	   A^2 -> H(U1(a, e), d)
28.57/10.20	   A^2 -> H(U1(a, e), k)
28.57/10.20	   A^2 -> H(U1(a, k), d)
28.57/10.20	   A^2 -> H(U1(a, k), k)
28.57/10.20	   A^2 -> H(k, U1(e, b))
28.57/10.20	   A^2 -> H(k, U1(c, d))
28.57/10.20	   A^2 -> H(k, U1(k, b))
28.57/10.20	   A^2 -> H(k, U1(d, c))
28.57/10.20	
28.57/10.20	The TRS R consists of the following rules:
28.57/10.20	
28.57/10.20	   f(x) -> U1(x, x)
28.57/10.20	   U1(e, x) -> x
28.57/10.20	   a -> c
28.57/10.20	   a -> d
28.57/10.20	   b -> c
28.57/10.20	   b -> d
28.57/10.20	   d -> k
28.57/10.20	   c -> e
28.57/10.20	   c -> k
28.57/10.20	
28.57/10.20	Q is empty.
28.57/10.20	We have to consider all minimal (P,Q,R)-chains.
28.57/10.20	----------------------------------------
28.57/10.20	
28.57/10.20	(2025) DependencyGraphProof (EQUIVALENT)
28.57/10.20	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.20	----------------------------------------
28.57/10.20	
28.57/10.20	(2026)
28.57/10.20	Obligation:
28.57/10.20	Q DP problem:
28.57/10.20	The TRS P consists of the following rules:
28.57/10.20	
28.57/10.20	   H(x, x) -> G(x, x, f(k))
28.57/10.20	   G(d, x, x) -> A^2
28.57/10.20	   A^2 -> H(f(c), f(c))
28.57/10.20	   A^2 -> H(f(d), f(d))
28.57/10.20	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.20	   A^2 -> H(f(e), f(e))
28.57/10.20	   A^2 -> H(f(k), f(k))
28.57/10.20	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.20	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.20	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.20	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.20	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.20	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.20	   A^2 -> H(k, U1(b, c))
28.57/10.20	   A^2 -> H(k, U1(b, d))
28.57/10.20	   A^2 -> H(k, U1(c, c))
28.57/10.20	   A^2 -> H(k, f(e))
28.57/10.20	   A^2 -> H(k, f(k))
28.57/10.20	   A^2 -> H(k, U1(d, d))
28.57/10.20	   A^2 -> H(c, U1(e, b))
28.57/10.20	   A^2 -> H(c, U1(k, b))
28.57/10.20	   A^2 -> H(c, U1(c, d))
28.57/10.20	   A^2 -> H(c, U1(d, c))
28.57/10.20	   A^2 -> H(c, U1(b, e))
28.57/10.20	   A^2 -> H(c, U1(b, k))
28.57/10.20	   A^2 -> H(c, U1(e, c))
28.57/10.20	   A^2 -> H(c, U1(k, c))
28.57/10.20	   A^2 -> H(c, U1(c, e))
28.57/10.20	   A^2 -> H(c, U1(c, k))
28.57/10.20	   A^2 -> H(c, U1(e, e))
28.57/10.20	   A^2 -> H(c, U1(k, k))
28.57/10.20	   A^2 -> H(c, U1(k, d))
28.57/10.20	   A^2 -> H(c, U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.20	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.20	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, c), b)
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, c), e)
28.57/10.20	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.20	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.20	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.20	   A^2 -> H(U1(k, c), b)
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, c), c)
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, e), b)
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(c, e), c)
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(c, e), e)
28.57/10.20	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, k), b)
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(c, k), c)
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.20	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.20	   A^2 -> H(U1(c, k), e)
28.57/10.20	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, c), d)
28.57/10.20	   A^2 -> H(e, U1(e, b))
28.57/10.20	   A^2 -> H(e, U1(c, d))
28.57/10.20	   A^2 -> H(e, U1(d, c))
28.57/10.20	   A^2 -> H(e, U1(b, e))
28.57/10.20	   A^2 -> H(e, U1(b, k))
28.57/10.20	   A^2 -> H(e, U1(e, c))
28.57/10.20	   A^2 -> H(e, U1(c, e))
28.57/10.20	   A^2 -> H(e, U1(c, k))
28.57/10.20	   A^2 -> H(e, U1(e, e))
28.57/10.20	   A^2 -> H(e, U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, e), b)
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, e), c)
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.20	   A^2 -> H(f(e), d)
28.57/10.20	   A^2 -> H(f(e), k)
28.57/10.20	   A^2 -> H(U1(k, k), b)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, k), c)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.20	   A^2 -> H(f(k), d)
28.57/10.20	   A^2 -> H(f(k), k)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.20	   A^2 -> H(U1(k, d), b)
28.57/10.20	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, d), c)
28.57/10.20	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, k), b)
28.57/10.20	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(d, k), c)
28.57/10.20	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.20	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.20	   A^2 -> H(U1(d, k), e)
28.57/10.20	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, d), d)
28.57/10.20	   A^2 -> H(U1(d, d), k)
28.57/10.20	   A^2 -> H(U1(e, c), c)
28.57/10.20	   A^2 -> H(U1(c, c), e)
28.57/10.20	   A^2 -> H(U1(c, c), k)
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(e, e), e)
28.57/10.20	   A^2 -> H(d, U1(e, b))
28.57/10.20	   A^2 -> H(d, U1(k, b))
28.57/10.20	   A^2 -> H(d, U1(c, d))
28.57/10.20	   A^2 -> H(d, U1(d, c))
28.57/10.20	   A^2 -> H(d, U1(b, e))
28.57/10.20	   A^2 -> H(d, U1(b, k))
28.57/10.20	   A^2 -> H(d, U1(e, c))
28.57/10.20	   A^2 -> H(d, U1(k, c))
28.57/10.20	   A^2 -> H(d, U1(c, e))
28.57/10.20	   A^2 -> H(d, U1(c, k))
28.57/10.20	   A^2 -> H(d, U1(e, e))
28.57/10.20	   A^2 -> H(d, U1(k, k))
28.57/10.20	   A^2 -> H(d, U1(k, d))
28.57/10.20	   A^2 -> H(d, U1(d, k))
28.57/10.20	   A^2 -> H(a, b)
28.57/10.20	   A^2 -> H(a, U1(e, d))
28.57/10.20	   A^2 -> H(a, U1(d, e))
28.57/10.20	   A^2 -> H(a, c)
28.57/10.20	   A^2 -> H(a, U1(e, k))
28.57/10.20	   A^2 -> H(a, U1(k, e))
28.57/10.20	   A^2 -> H(a, e)
28.57/10.20	   A^2 -> H(a, U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, d), b)
28.57/10.20	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, d), c)
28.57/10.20	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, d), e)
28.57/10.20	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, a), d)
28.57/10.20	   A^2 -> H(U1(e, a), k)
28.57/10.20	   A^2 -> H(U1(k, a), d)
28.57/10.20	   A^2 -> H(U1(c, d), d)
28.57/10.20	   A^2 -> H(U1(c, d), k)
28.57/10.20	   A^2 -> H(U1(d, e), b)
28.57/10.20	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(d, e), c)
28.57/10.20	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(d, e), e)
28.57/10.20	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, c), d)
28.57/10.20	   A^2 -> H(U1(d, c), k)
28.57/10.20	   A^2 -> H(U1(a, e), d)
28.57/10.20	   A^2 -> H(U1(a, e), k)
28.57/10.20	   A^2 -> H(U1(a, k), d)
28.57/10.20	   A^2 -> H(U1(a, k), k)
28.57/10.20	   A^2 -> H(k, U1(e, b))
28.57/10.20	   A^2 -> H(k, U1(c, d))
28.57/10.20	   A^2 -> H(k, U1(d, c))
28.57/10.20	
28.57/10.20	The TRS R consists of the following rules:
28.57/10.20	
28.57/10.20	   f(x) -> U1(x, x)
28.57/10.20	   U1(e, x) -> x
28.57/10.20	   a -> c
28.57/10.20	   a -> d
28.57/10.20	   b -> c
28.57/10.20	   b -> d
28.57/10.20	   d -> k
28.57/10.20	   c -> e
28.57/10.20	   c -> k
28.57/10.20	
28.57/10.20	Q is empty.
28.57/10.20	We have to consider all minimal (P,Q,R)-chains.
28.57/10.20	----------------------------------------
28.57/10.20	
28.57/10.20	(2027) TransformationProof (EQUIVALENT)
28.57/10.20	By narrowing [LPAR04] the rule A^2 -> H(k, U1(b, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.20	
28.57/10.20	   (A^2 -> H(k, U1(c, c)),A^2 -> H(k, U1(c, c)))
28.57/10.20	   (A^2 -> H(k, U1(d, c)),A^2 -> H(k, U1(d, c)))
28.57/10.20	   (A^2 -> H(k, U1(b, e)),A^2 -> H(k, U1(b, e)))
28.57/10.20	   (A^2 -> H(k, U1(b, k)),A^2 -> H(k, U1(b, k)))
28.57/10.20	
28.57/10.20	
28.57/10.20	----------------------------------------
28.57/10.20	
28.57/10.20	(2028)
28.57/10.20	Obligation:
28.57/10.20	Q DP problem:
28.57/10.20	The TRS P consists of the following rules:
28.57/10.20	
28.57/10.20	   H(x, x) -> G(x, x, f(k))
28.57/10.20	   G(d, x, x) -> A^2
28.57/10.20	   A^2 -> H(f(c), f(c))
28.57/10.20	   A^2 -> H(f(d), f(d))
28.57/10.20	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.20	   A^2 -> H(f(e), f(e))
28.57/10.20	   A^2 -> H(f(k), f(k))
28.57/10.20	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.20	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.20	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.20	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.20	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.20	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.20	   A^2 -> H(k, U1(b, d))
28.57/10.20	   A^2 -> H(k, U1(c, c))
28.57/10.20	   A^2 -> H(k, f(e))
28.57/10.20	   A^2 -> H(k, f(k))
28.57/10.20	   A^2 -> H(k, U1(d, d))
28.57/10.20	   A^2 -> H(c, U1(e, b))
28.57/10.20	   A^2 -> H(c, U1(k, b))
28.57/10.20	   A^2 -> H(c, U1(c, d))
28.57/10.20	   A^2 -> H(c, U1(d, c))
28.57/10.20	   A^2 -> H(c, U1(b, e))
28.57/10.20	   A^2 -> H(c, U1(b, k))
28.57/10.20	   A^2 -> H(c, U1(e, c))
28.57/10.20	   A^2 -> H(c, U1(k, c))
28.57/10.20	   A^2 -> H(c, U1(c, e))
28.57/10.20	   A^2 -> H(c, U1(c, k))
28.57/10.20	   A^2 -> H(c, U1(e, e))
28.57/10.20	   A^2 -> H(c, U1(k, k))
28.57/10.20	   A^2 -> H(c, U1(k, d))
28.57/10.20	   A^2 -> H(c, U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.20	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.20	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, c), b)
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, c), e)
28.57/10.20	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.20	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.20	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.20	   A^2 -> H(U1(k, c), b)
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, c), c)
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, e), b)
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(c, e), c)
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(c, e), e)
28.57/10.20	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, k), b)
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(c, k), c)
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.20	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.20	   A^2 -> H(U1(c, k), e)
28.57/10.20	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, c), d)
28.57/10.20	   A^2 -> H(e, U1(e, b))
28.57/10.20	   A^2 -> H(e, U1(c, d))
28.57/10.20	   A^2 -> H(e, U1(d, c))
28.57/10.20	   A^2 -> H(e, U1(b, e))
28.57/10.20	   A^2 -> H(e, U1(b, k))
28.57/10.20	   A^2 -> H(e, U1(e, c))
28.57/10.20	   A^2 -> H(e, U1(c, e))
28.57/10.20	   A^2 -> H(e, U1(c, k))
28.57/10.20	   A^2 -> H(e, U1(e, e))
28.57/10.20	   A^2 -> H(e, U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, e), b)
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, e), c)
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.20	   A^2 -> H(f(e), d)
28.57/10.20	   A^2 -> H(f(e), k)
28.57/10.20	   A^2 -> H(U1(k, k), b)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, k), c)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.20	   A^2 -> H(f(k), d)
28.57/10.20	   A^2 -> H(f(k), k)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.20	   A^2 -> H(U1(k, d), b)
28.57/10.20	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, d), c)
28.57/10.20	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, k), b)
28.57/10.20	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(d, k), c)
28.57/10.20	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.20	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.20	   A^2 -> H(U1(d, k), e)
28.57/10.20	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, d), d)
28.57/10.20	   A^2 -> H(U1(d, d), k)
28.57/10.20	   A^2 -> H(U1(e, c), c)
28.57/10.20	   A^2 -> H(U1(c, c), e)
28.57/10.20	   A^2 -> H(U1(c, c), k)
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(e, e), e)
28.57/10.20	   A^2 -> H(d, U1(e, b))
28.57/10.20	   A^2 -> H(d, U1(k, b))
28.57/10.20	   A^2 -> H(d, U1(c, d))
28.57/10.20	   A^2 -> H(d, U1(d, c))
28.57/10.20	   A^2 -> H(d, U1(b, e))
28.57/10.20	   A^2 -> H(d, U1(b, k))
28.57/10.20	   A^2 -> H(d, U1(e, c))
28.57/10.20	   A^2 -> H(d, U1(k, c))
28.57/10.20	   A^2 -> H(d, U1(c, e))
28.57/10.20	   A^2 -> H(d, U1(c, k))
28.57/10.20	   A^2 -> H(d, U1(e, e))
28.57/10.20	   A^2 -> H(d, U1(k, k))
28.57/10.20	   A^2 -> H(d, U1(k, d))
28.57/10.20	   A^2 -> H(d, U1(d, k))
28.57/10.20	   A^2 -> H(a, b)
28.57/10.20	   A^2 -> H(a, U1(e, d))
28.57/10.20	   A^2 -> H(a, U1(d, e))
28.57/10.20	   A^2 -> H(a, c)
28.57/10.20	   A^2 -> H(a, U1(e, k))
28.57/10.20	   A^2 -> H(a, U1(k, e))
28.57/10.20	   A^2 -> H(a, e)
28.57/10.20	   A^2 -> H(a, U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, d), b)
28.57/10.20	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, d), c)
28.57/10.20	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, d), e)
28.57/10.20	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, a), d)
28.57/10.20	   A^2 -> H(U1(e, a), k)
28.57/10.20	   A^2 -> H(U1(k, a), d)
28.57/10.20	   A^2 -> H(U1(c, d), d)
28.57/10.20	   A^2 -> H(U1(c, d), k)
28.57/10.20	   A^2 -> H(U1(d, e), b)
28.57/10.20	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(d, e), c)
28.57/10.20	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(d, e), e)
28.57/10.20	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, c), d)
28.57/10.20	   A^2 -> H(U1(d, c), k)
28.57/10.20	   A^2 -> H(U1(a, e), d)
28.57/10.20	   A^2 -> H(U1(a, e), k)
28.57/10.20	   A^2 -> H(U1(a, k), d)
28.57/10.20	   A^2 -> H(U1(a, k), k)
28.57/10.20	   A^2 -> H(k, U1(e, b))
28.57/10.20	   A^2 -> H(k, U1(c, d))
28.57/10.20	   A^2 -> H(k, U1(d, c))
28.57/10.20	   A^2 -> H(k, U1(b, e))
28.57/10.20	   A^2 -> H(k, U1(b, k))
28.57/10.20	
28.57/10.20	The TRS R consists of the following rules:
28.57/10.20	
28.57/10.20	   f(x) -> U1(x, x)
28.57/10.20	   U1(e, x) -> x
28.57/10.20	   a -> c
28.57/10.20	   a -> d
28.57/10.20	   b -> c
28.57/10.20	   b -> d
28.57/10.20	   d -> k
28.57/10.20	   c -> e
28.57/10.20	   c -> k
28.57/10.20	
28.57/10.20	Q is empty.
28.57/10.20	We have to consider all minimal (P,Q,R)-chains.
28.57/10.20	----------------------------------------
28.57/10.20	
28.57/10.20	(2029) TransformationProof (EQUIVALENT)
28.57/10.20	By narrowing [LPAR04] the rule A^2 -> H(k, U1(b, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.20	
28.57/10.20	   (A^2 -> H(k, U1(c, d)),A^2 -> H(k, U1(c, d)))
28.57/10.20	   (A^2 -> H(k, U1(d, d)),A^2 -> H(k, U1(d, d)))
28.57/10.20	   (A^2 -> H(k, U1(b, k)),A^2 -> H(k, U1(b, k)))
28.57/10.20	
28.57/10.20	
28.57/10.20	----------------------------------------
28.57/10.20	
28.57/10.20	(2030)
28.57/10.20	Obligation:
28.57/10.20	Q DP problem:
28.57/10.20	The TRS P consists of the following rules:
28.57/10.20	
28.57/10.20	   H(x, x) -> G(x, x, f(k))
28.57/10.20	   G(d, x, x) -> A^2
28.57/10.20	   A^2 -> H(f(c), f(c))
28.57/10.20	   A^2 -> H(f(d), f(d))
28.57/10.20	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.20	   A^2 -> H(f(e), f(e))
28.57/10.20	   A^2 -> H(f(k), f(k))
28.57/10.20	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.20	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.20	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.20	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.20	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.20	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.20	   A^2 -> H(k, U1(c, c))
28.57/10.20	   A^2 -> H(k, f(e))
28.57/10.20	   A^2 -> H(k, f(k))
28.57/10.20	   A^2 -> H(k, U1(d, d))
28.57/10.20	   A^2 -> H(c, U1(e, b))
28.57/10.20	   A^2 -> H(c, U1(k, b))
28.57/10.20	   A^2 -> H(c, U1(c, d))
28.57/10.20	   A^2 -> H(c, U1(d, c))
28.57/10.20	   A^2 -> H(c, U1(b, e))
28.57/10.20	   A^2 -> H(c, U1(b, k))
28.57/10.20	   A^2 -> H(c, U1(e, c))
28.57/10.20	   A^2 -> H(c, U1(k, c))
28.57/10.20	   A^2 -> H(c, U1(c, e))
28.57/10.20	   A^2 -> H(c, U1(c, k))
28.57/10.20	   A^2 -> H(c, U1(e, e))
28.57/10.20	   A^2 -> H(c, U1(k, k))
28.57/10.20	   A^2 -> H(c, U1(k, d))
28.57/10.20	   A^2 -> H(c, U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.20	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.20	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, c), b)
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, c), e)
28.57/10.20	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.20	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.20	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.20	   A^2 -> H(U1(k, c), b)
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, c), c)
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, e), b)
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(c, e), c)
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(c, e), e)
28.57/10.20	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, k), b)
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(c, k), c)
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.20	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.20	   A^2 -> H(U1(c, k), e)
28.57/10.20	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, c), d)
28.57/10.20	   A^2 -> H(e, U1(e, b))
28.57/10.20	   A^2 -> H(e, U1(c, d))
28.57/10.20	   A^2 -> H(e, U1(d, c))
28.57/10.20	   A^2 -> H(e, U1(b, e))
28.57/10.20	   A^2 -> H(e, U1(b, k))
28.57/10.20	   A^2 -> H(e, U1(e, c))
28.57/10.20	   A^2 -> H(e, U1(c, e))
28.57/10.20	   A^2 -> H(e, U1(c, k))
28.57/10.20	   A^2 -> H(e, U1(e, e))
28.57/10.20	   A^2 -> H(e, U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, e), b)
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, e), c)
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.20	   A^2 -> H(f(e), d)
28.57/10.20	   A^2 -> H(f(e), k)
28.57/10.20	   A^2 -> H(U1(k, k), b)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, k), c)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.20	   A^2 -> H(f(k), d)
28.57/10.20	   A^2 -> H(f(k), k)
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.20	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.20	   A^2 -> H(U1(k, d), b)
28.57/10.20	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, d), c)
28.57/10.20	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, k), b)
28.57/10.20	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(d, k), c)
28.57/10.20	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.20	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.20	   A^2 -> H(U1(d, k), e)
28.57/10.20	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, d), d)
28.57/10.20	   A^2 -> H(U1(d, d), k)
28.57/10.20	   A^2 -> H(U1(e, c), c)
28.57/10.20	   A^2 -> H(U1(c, c), e)
28.57/10.20	   A^2 -> H(U1(c, c), k)
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(e, e), e)
28.57/10.20	   A^2 -> H(d, U1(e, b))
28.57/10.20	   A^2 -> H(d, U1(k, b))
28.57/10.20	   A^2 -> H(d, U1(c, d))
28.57/10.20	   A^2 -> H(d, U1(d, c))
28.57/10.20	   A^2 -> H(d, U1(b, e))
28.57/10.20	   A^2 -> H(d, U1(b, k))
28.57/10.20	   A^2 -> H(d, U1(e, c))
28.57/10.20	   A^2 -> H(d, U1(k, c))
28.57/10.20	   A^2 -> H(d, U1(c, e))
28.57/10.20	   A^2 -> H(d, U1(c, k))
28.57/10.20	   A^2 -> H(d, U1(e, e))
28.57/10.20	   A^2 -> H(d, U1(k, k))
28.57/10.20	   A^2 -> H(d, U1(k, d))
28.57/10.20	   A^2 -> H(d, U1(d, k))
28.57/10.20	   A^2 -> H(a, b)
28.57/10.20	   A^2 -> H(a, U1(e, d))
28.57/10.20	   A^2 -> H(a, U1(d, e))
28.57/10.20	   A^2 -> H(a, c)
28.57/10.20	   A^2 -> H(a, U1(e, k))
28.57/10.20	   A^2 -> H(a, U1(k, e))
28.57/10.20	   A^2 -> H(a, e)
28.57/10.20	   A^2 -> H(a, U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, d), b)
28.57/10.20	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, d), c)
28.57/10.20	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, d), e)
28.57/10.20	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, a), d)
28.57/10.20	   A^2 -> H(U1(e, a), k)
28.57/10.20	   A^2 -> H(U1(k, a), d)
28.57/10.20	   A^2 -> H(U1(c, d), d)
28.57/10.20	   A^2 -> H(U1(c, d), k)
28.57/10.20	   A^2 -> H(U1(d, e), b)
28.57/10.20	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(d, e), c)
28.57/10.20	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(d, e), e)
28.57/10.20	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.20	   A^2 -> H(U1(d, c), d)
28.57/10.20	   A^2 -> H(U1(d, c), k)
28.57/10.20	   A^2 -> H(U1(a, e), d)
28.57/10.20	   A^2 -> H(U1(a, e), k)
28.57/10.20	   A^2 -> H(U1(a, k), d)
28.57/10.20	   A^2 -> H(U1(a, k), k)
28.57/10.20	   A^2 -> H(k, U1(e, b))
28.57/10.20	   A^2 -> H(k, U1(c, d))
28.57/10.20	   A^2 -> H(k, U1(d, c))
28.57/10.20	   A^2 -> H(k, U1(b, e))
28.57/10.20	   A^2 -> H(k, U1(b, k))
28.57/10.20	
28.57/10.20	The TRS R consists of the following rules:
28.57/10.20	
28.57/10.20	   f(x) -> U1(x, x)
28.57/10.20	   U1(e, x) -> x
28.57/10.20	   a -> c
28.57/10.20	   a -> d
28.57/10.20	   b -> c
28.57/10.20	   b -> d
28.57/10.20	   d -> k
28.57/10.20	   c -> e
28.57/10.20	   c -> k
28.57/10.20	
28.57/10.20	Q is empty.
28.57/10.20	We have to consider all minimal (P,Q,R)-chains.
28.57/10.20	----------------------------------------
28.57/10.20	
28.57/10.20	(2031) TransformationProof (EQUIVALENT)
28.57/10.20	By narrowing [LPAR04] the rule A^2 -> H(k, U1(c, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.20	
28.57/10.20	   (A^2 -> H(k, U1(e, c)),A^2 -> H(k, U1(e, c)))
28.57/10.20	   (A^2 -> H(k, U1(k, c)),A^2 -> H(k, U1(k, c)))
28.57/10.20	   (A^2 -> H(k, U1(c, e)),A^2 -> H(k, U1(c, e)))
28.57/10.20	   (A^2 -> H(k, U1(c, k)),A^2 -> H(k, U1(c, k)))
28.57/10.20	
28.57/10.20	
28.57/10.20	----------------------------------------
28.57/10.20	
28.57/10.20	(2032)
28.57/10.20	Obligation:
28.57/10.20	Q DP problem:
28.57/10.20	The TRS P consists of the following rules:
28.57/10.20	
28.57/10.20	   H(x, x) -> G(x, x, f(k))
28.57/10.20	   G(d, x, x) -> A^2
28.57/10.20	   A^2 -> H(f(c), f(c))
28.57/10.20	   A^2 -> H(f(d), f(d))
28.57/10.20	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.20	   A^2 -> H(f(e), f(e))
28.57/10.20	   A^2 -> H(f(k), f(k))
28.57/10.20	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.20	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.20	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.20	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.20	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.20	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.20	   A^2 -> H(k, f(e))
28.57/10.20	   A^2 -> H(k, f(k))
28.57/10.20	   A^2 -> H(k, U1(d, d))
28.57/10.20	   A^2 -> H(c, U1(e, b))
28.57/10.20	   A^2 -> H(c, U1(k, b))
28.57/10.20	   A^2 -> H(c, U1(c, d))
28.57/10.20	   A^2 -> H(c, U1(d, c))
28.57/10.20	   A^2 -> H(c, U1(b, e))
28.57/10.20	   A^2 -> H(c, U1(b, k))
28.57/10.20	   A^2 -> H(c, U1(e, c))
28.57/10.20	   A^2 -> H(c, U1(k, c))
28.57/10.20	   A^2 -> H(c, U1(c, e))
28.57/10.20	   A^2 -> H(c, U1(c, k))
28.57/10.20	   A^2 -> H(c, U1(e, e))
28.57/10.20	   A^2 -> H(c, U1(k, k))
28.57/10.20	   A^2 -> H(c, U1(k, d))
28.57/10.20	   A^2 -> H(c, U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.20	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.20	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.20	   A^2 -> H(U1(e, c), b)
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.20	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.20	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.20	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.20	   A^2 -> H(U1(e, c), e)
28.57/10.20	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.20	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.20	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.20	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.20	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.20	   A^2 -> H(U1(k, c), b)
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.20	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.20	   A^2 -> H(U1(k, c), c)
28.57/10.20	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.20	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, e), b)
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.20	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.20	   A^2 -> H(U1(c, e), c)
28.57/10.20	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.20	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.20	   A^2 -> H(U1(c, e), e)
28.57/10.20	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, k), b)
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.20	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.20	   A^2 -> H(U1(c, k), c)
28.57/10.20	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.20	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.20	   A^2 -> H(U1(c, k), e)
28.57/10.20	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.20	   A^2 -> H(U1(c, c), d)
28.57/10.20	   A^2 -> H(e, U1(e, b))
28.57/10.20	   A^2 -> H(e, U1(c, d))
28.57/10.20	   A^2 -> H(e, U1(d, c))
28.57/10.20	   A^2 -> H(e, U1(b, e))
28.57/10.21	   A^2 -> H(e, U1(b, k))
28.57/10.21	   A^2 -> H(e, U1(e, c))
28.57/10.21	   A^2 -> H(e, U1(c, e))
28.57/10.21	   A^2 -> H(e, U1(c, k))
28.57/10.21	   A^2 -> H(e, U1(e, e))
28.57/10.21	   A^2 -> H(e, U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, e), b)
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, e), c)
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.21	   A^2 -> H(f(e), d)
28.57/10.21	   A^2 -> H(f(e), k)
28.57/10.21	   A^2 -> H(U1(k, k), b)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, k), c)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.21	   A^2 -> H(f(k), d)
28.57/10.21	   A^2 -> H(f(k), k)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.21	   A^2 -> H(U1(k, d), b)
28.57/10.21	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, d), c)
28.57/10.21	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, k), b)
28.57/10.21	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(d, k), c)
28.57/10.21	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.21	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.21	   A^2 -> H(U1(d, k), e)
28.57/10.21	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, d), d)
28.57/10.21	   A^2 -> H(U1(d, d), k)
28.57/10.21	   A^2 -> H(U1(e, c), c)
28.57/10.21	   A^2 -> H(U1(c, c), e)
28.57/10.21	   A^2 -> H(U1(c, c), k)
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(e, e), e)
28.57/10.21	   A^2 -> H(d, U1(e, b))
28.57/10.21	   A^2 -> H(d, U1(k, b))
28.57/10.21	   A^2 -> H(d, U1(c, d))
28.57/10.21	   A^2 -> H(d, U1(d, c))
28.57/10.21	   A^2 -> H(d, U1(b, e))
28.57/10.21	   A^2 -> H(d, U1(b, k))
28.57/10.21	   A^2 -> H(d, U1(e, c))
28.57/10.21	   A^2 -> H(d, U1(k, c))
28.57/10.21	   A^2 -> H(d, U1(c, e))
28.57/10.21	   A^2 -> H(d, U1(c, k))
28.57/10.21	   A^2 -> H(d, U1(e, e))
28.57/10.21	   A^2 -> H(d, U1(k, k))
28.57/10.21	   A^2 -> H(d, U1(k, d))
28.57/10.21	   A^2 -> H(d, U1(d, k))
28.57/10.21	   A^2 -> H(a, b)
28.57/10.21	   A^2 -> H(a, U1(e, d))
28.57/10.21	   A^2 -> H(a, U1(d, e))
28.57/10.21	   A^2 -> H(a, c)
28.57/10.21	   A^2 -> H(a, U1(e, k))
28.57/10.21	   A^2 -> H(a, U1(k, e))
28.57/10.21	   A^2 -> H(a, e)
28.57/10.21	   A^2 -> H(a, U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, d), b)
28.57/10.21	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, d), c)
28.57/10.21	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, d), e)
28.57/10.21	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, a), d)
28.57/10.21	   A^2 -> H(U1(e, a), k)
28.57/10.21	   A^2 -> H(U1(k, a), d)
28.57/10.21	   A^2 -> H(U1(c, d), d)
28.57/10.21	   A^2 -> H(U1(c, d), k)
28.57/10.21	   A^2 -> H(U1(d, e), b)
28.57/10.21	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(d, e), c)
28.57/10.21	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(d, e), e)
28.57/10.21	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, c), d)
28.57/10.21	   A^2 -> H(U1(d, c), k)
28.57/10.21	   A^2 -> H(U1(a, e), d)
28.57/10.21	   A^2 -> H(U1(a, e), k)
28.57/10.21	   A^2 -> H(U1(a, k), d)
28.57/10.21	   A^2 -> H(U1(a, k), k)
28.57/10.21	   A^2 -> H(k, U1(e, b))
28.57/10.21	   A^2 -> H(k, U1(c, d))
28.57/10.21	   A^2 -> H(k, U1(d, c))
28.57/10.21	   A^2 -> H(k, U1(b, e))
28.57/10.21	   A^2 -> H(k, U1(b, k))
28.57/10.21	   A^2 -> H(k, U1(e, c))
28.57/10.21	   A^2 -> H(k, U1(k, c))
28.57/10.21	   A^2 -> H(k, U1(c, e))
28.57/10.21	   A^2 -> H(k, U1(c, k))
28.57/10.21	
28.57/10.21	The TRS R consists of the following rules:
28.57/10.21	
28.57/10.21	   f(x) -> U1(x, x)
28.57/10.21	   U1(e, x) -> x
28.57/10.21	   a -> c
28.57/10.21	   a -> d
28.57/10.21	   b -> c
28.57/10.21	   b -> d
28.57/10.21	   d -> k
28.57/10.21	   c -> e
28.57/10.21	   c -> k
28.57/10.21	
28.57/10.21	Q is empty.
28.57/10.21	We have to consider all minimal (P,Q,R)-chains.
28.57/10.21	----------------------------------------
28.57/10.21	
28.57/10.21	(2033) DependencyGraphProof (EQUIVALENT)
28.57/10.21	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.21	----------------------------------------
28.57/10.21	
28.57/10.21	(2034)
28.57/10.21	Obligation:
28.57/10.21	Q DP problem:
28.57/10.21	The TRS P consists of the following rules:
28.57/10.21	
28.57/10.21	   G(d, x, x) -> A^2
28.57/10.21	   A^2 -> H(f(c), f(c))
28.57/10.21	   H(x, x) -> G(x, x, f(k))
28.57/10.21	   A^2 -> H(f(d), f(d))
28.57/10.21	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.21	   A^2 -> H(f(e), f(e))
28.57/10.21	   A^2 -> H(f(k), f(k))
28.57/10.21	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.21	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.21	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.21	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.21	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.21	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.21	   A^2 -> H(k, f(e))
28.57/10.21	   A^2 -> H(k, f(k))
28.57/10.21	   A^2 -> H(k, U1(d, d))
28.57/10.21	   A^2 -> H(c, U1(e, b))
28.57/10.21	   A^2 -> H(c, U1(k, b))
28.57/10.21	   A^2 -> H(c, U1(c, d))
28.57/10.21	   A^2 -> H(c, U1(d, c))
28.57/10.21	   A^2 -> H(c, U1(b, e))
28.57/10.21	   A^2 -> H(c, U1(b, k))
28.57/10.21	   A^2 -> H(c, U1(e, c))
28.57/10.21	   A^2 -> H(c, U1(k, c))
28.57/10.21	   A^2 -> H(c, U1(c, e))
28.57/10.21	   A^2 -> H(c, U1(c, k))
28.57/10.21	   A^2 -> H(c, U1(e, e))
28.57/10.21	   A^2 -> H(c, U1(k, k))
28.57/10.21	   A^2 -> H(c, U1(k, d))
28.57/10.21	   A^2 -> H(c, U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.21	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.21	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, c), b)
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, c), e)
28.57/10.21	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.21	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.21	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.21	   A^2 -> H(U1(k, c), b)
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, c), c)
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, e), b)
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(c, e), c)
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(c, e), e)
28.57/10.21	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, k), b)
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(c, k), c)
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.21	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.21	   A^2 -> H(U1(c, k), e)
28.57/10.21	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, c), d)
28.57/10.21	   A^2 -> H(e, U1(e, b))
28.57/10.21	   A^2 -> H(e, U1(c, d))
28.57/10.21	   A^2 -> H(e, U1(d, c))
28.57/10.21	   A^2 -> H(e, U1(b, e))
28.57/10.21	   A^2 -> H(e, U1(b, k))
28.57/10.21	   A^2 -> H(e, U1(e, c))
28.57/10.21	   A^2 -> H(e, U1(c, e))
28.57/10.21	   A^2 -> H(e, U1(c, k))
28.57/10.21	   A^2 -> H(e, U1(e, e))
28.57/10.21	   A^2 -> H(e, U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, e), b)
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, e), c)
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.21	   A^2 -> H(f(e), d)
28.57/10.21	   A^2 -> H(f(e), k)
28.57/10.21	   A^2 -> H(U1(k, k), b)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, k), c)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.21	   A^2 -> H(f(k), d)
28.57/10.21	   A^2 -> H(f(k), k)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.21	   A^2 -> H(U1(k, d), b)
28.57/10.21	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, d), c)
28.57/10.21	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, k), b)
28.57/10.21	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(d, k), c)
28.57/10.21	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.21	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.21	   A^2 -> H(U1(d, k), e)
28.57/10.21	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, d), d)
28.57/10.21	   A^2 -> H(U1(d, d), k)
28.57/10.21	   A^2 -> H(U1(e, c), c)
28.57/10.21	   A^2 -> H(U1(c, c), e)
28.57/10.21	   A^2 -> H(U1(c, c), k)
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(e, e), e)
28.57/10.21	   A^2 -> H(d, U1(e, b))
28.57/10.21	   A^2 -> H(d, U1(k, b))
28.57/10.21	   A^2 -> H(d, U1(c, d))
28.57/10.21	   A^2 -> H(d, U1(d, c))
28.57/10.21	   A^2 -> H(d, U1(b, e))
28.57/10.21	   A^2 -> H(d, U1(b, k))
28.57/10.21	   A^2 -> H(d, U1(e, c))
28.57/10.21	   A^2 -> H(d, U1(k, c))
28.57/10.21	   A^2 -> H(d, U1(c, e))
28.57/10.21	   A^2 -> H(d, U1(c, k))
28.57/10.21	   A^2 -> H(d, U1(e, e))
28.57/10.21	   A^2 -> H(d, U1(k, k))
28.57/10.21	   A^2 -> H(d, U1(k, d))
28.57/10.21	   A^2 -> H(d, U1(d, k))
28.57/10.21	   A^2 -> H(a, b)
28.57/10.21	   A^2 -> H(a, U1(e, d))
28.57/10.21	   A^2 -> H(a, U1(d, e))
28.57/10.21	   A^2 -> H(a, c)
28.57/10.21	   A^2 -> H(a, U1(e, k))
28.57/10.21	   A^2 -> H(a, U1(k, e))
28.57/10.21	   A^2 -> H(a, e)
28.57/10.21	   A^2 -> H(a, U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, d), b)
28.57/10.21	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, d), c)
28.57/10.21	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, d), e)
28.57/10.21	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, a), d)
28.57/10.21	   A^2 -> H(U1(e, a), k)
28.57/10.21	   A^2 -> H(U1(k, a), d)
28.57/10.21	   A^2 -> H(U1(c, d), d)
28.57/10.21	   A^2 -> H(U1(c, d), k)
28.57/10.21	   A^2 -> H(U1(d, e), b)
28.57/10.21	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(d, e), c)
28.57/10.21	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(d, e), e)
28.57/10.21	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, c), d)
28.57/10.21	   A^2 -> H(U1(d, c), k)
28.57/10.21	   A^2 -> H(U1(a, e), d)
28.57/10.21	   A^2 -> H(U1(a, e), k)
28.57/10.21	   A^2 -> H(U1(a, k), d)
28.57/10.21	   A^2 -> H(U1(a, k), k)
28.57/10.21	   A^2 -> H(k, U1(e, b))
28.57/10.21	   A^2 -> H(k, U1(c, d))
28.57/10.21	   A^2 -> H(k, U1(d, c))
28.57/10.21	   A^2 -> H(k, U1(b, e))
28.57/10.21	   A^2 -> H(k, U1(b, k))
28.57/10.21	   A^2 -> H(k, U1(e, c))
28.57/10.21	   A^2 -> H(k, U1(c, e))
28.57/10.21	   A^2 -> H(k, U1(c, k))
28.57/10.21	
28.57/10.21	The TRS R consists of the following rules:
28.57/10.21	
28.57/10.21	   f(x) -> U1(x, x)
28.57/10.21	   U1(e, x) -> x
28.57/10.21	   a -> c
28.57/10.21	   a -> d
28.57/10.21	   b -> c
28.57/10.21	   b -> d
28.57/10.21	   d -> k
28.57/10.21	   c -> e
28.57/10.21	   c -> k
28.57/10.21	
28.57/10.21	Q is empty.
28.57/10.21	We have to consider all minimal (P,Q,R)-chains.
28.57/10.21	----------------------------------------
28.57/10.21	
28.57/10.21	(2035) TransformationProof (EQUIVALENT)
28.57/10.21	By narrowing [LPAR04] the rule A^2 -> H(k, f(e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.21	
28.57/10.21	   (A^2 -> H(k, U1(e, e)),A^2 -> H(k, U1(e, e)))
28.57/10.21	
28.57/10.21	
28.57/10.21	----------------------------------------
28.57/10.21	
28.57/10.21	(2036)
28.57/10.21	Obligation:
28.57/10.21	Q DP problem:
28.57/10.21	The TRS P consists of the following rules:
28.57/10.21	
28.57/10.21	   G(d, x, x) -> A^2
28.57/10.21	   A^2 -> H(f(c), f(c))
28.57/10.21	   H(x, x) -> G(x, x, f(k))
28.57/10.21	   A^2 -> H(f(d), f(d))
28.57/10.21	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.21	   A^2 -> H(f(e), f(e))
28.57/10.21	   A^2 -> H(f(k), f(k))
28.57/10.21	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.21	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.21	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.21	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.21	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.21	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.21	   A^2 -> H(k, f(k))
28.57/10.21	   A^2 -> H(k, U1(d, d))
28.57/10.21	   A^2 -> H(c, U1(e, b))
28.57/10.21	   A^2 -> H(c, U1(k, b))
28.57/10.21	   A^2 -> H(c, U1(c, d))
28.57/10.21	   A^2 -> H(c, U1(d, c))
28.57/10.21	   A^2 -> H(c, U1(b, e))
28.57/10.21	   A^2 -> H(c, U1(b, k))
28.57/10.21	   A^2 -> H(c, U1(e, c))
28.57/10.21	   A^2 -> H(c, U1(k, c))
28.57/10.21	   A^2 -> H(c, U1(c, e))
28.57/10.21	   A^2 -> H(c, U1(c, k))
28.57/10.21	   A^2 -> H(c, U1(e, e))
28.57/10.21	   A^2 -> H(c, U1(k, k))
28.57/10.21	   A^2 -> H(c, U1(k, d))
28.57/10.21	   A^2 -> H(c, U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.21	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.21	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, c), b)
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, c), e)
28.57/10.21	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.21	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.21	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.21	   A^2 -> H(U1(k, c), b)
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, c), c)
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, e), b)
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(c, e), c)
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(c, e), e)
28.57/10.21	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, k), b)
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(c, k), c)
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.21	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.21	   A^2 -> H(U1(c, k), e)
28.57/10.21	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, c), d)
28.57/10.21	   A^2 -> H(e, U1(e, b))
28.57/10.21	   A^2 -> H(e, U1(c, d))
28.57/10.21	   A^2 -> H(e, U1(d, c))
28.57/10.21	   A^2 -> H(e, U1(b, e))
28.57/10.21	   A^2 -> H(e, U1(b, k))
28.57/10.21	   A^2 -> H(e, U1(e, c))
28.57/10.21	   A^2 -> H(e, U1(c, e))
28.57/10.21	   A^2 -> H(e, U1(c, k))
28.57/10.21	   A^2 -> H(e, U1(e, e))
28.57/10.21	   A^2 -> H(e, U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, e), b)
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, e), c)
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.21	   A^2 -> H(f(e), d)
28.57/10.21	   A^2 -> H(f(e), k)
28.57/10.21	   A^2 -> H(U1(k, k), b)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, k), c)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.21	   A^2 -> H(f(k), d)
28.57/10.21	   A^2 -> H(f(k), k)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.21	   A^2 -> H(U1(k, d), b)
28.57/10.21	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, d), c)
28.57/10.21	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, k), b)
28.57/10.21	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(d, k), c)
28.57/10.21	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.21	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.21	   A^2 -> H(U1(d, k), e)
28.57/10.21	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, d), d)
28.57/10.21	   A^2 -> H(U1(d, d), k)
28.57/10.21	   A^2 -> H(U1(e, c), c)
28.57/10.21	   A^2 -> H(U1(c, c), e)
28.57/10.21	   A^2 -> H(U1(c, c), k)
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(e, e), e)
28.57/10.21	   A^2 -> H(d, U1(e, b))
28.57/10.21	   A^2 -> H(d, U1(k, b))
28.57/10.21	   A^2 -> H(d, U1(c, d))
28.57/10.21	   A^2 -> H(d, U1(d, c))
28.57/10.21	   A^2 -> H(d, U1(b, e))
28.57/10.21	   A^2 -> H(d, U1(b, k))
28.57/10.21	   A^2 -> H(d, U1(e, c))
28.57/10.21	   A^2 -> H(d, U1(k, c))
28.57/10.21	   A^2 -> H(d, U1(c, e))
28.57/10.21	   A^2 -> H(d, U1(c, k))
28.57/10.21	   A^2 -> H(d, U1(e, e))
28.57/10.21	   A^2 -> H(d, U1(k, k))
28.57/10.21	   A^2 -> H(d, U1(k, d))
28.57/10.21	   A^2 -> H(d, U1(d, k))
28.57/10.21	   A^2 -> H(a, b)
28.57/10.21	   A^2 -> H(a, U1(e, d))
28.57/10.21	   A^2 -> H(a, U1(d, e))
28.57/10.21	   A^2 -> H(a, c)
28.57/10.21	   A^2 -> H(a, U1(e, k))
28.57/10.21	   A^2 -> H(a, U1(k, e))
28.57/10.21	   A^2 -> H(a, e)
28.57/10.21	   A^2 -> H(a, U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, d), b)
28.57/10.21	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, d), c)
28.57/10.21	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, d), e)
28.57/10.21	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, a), d)
28.57/10.21	   A^2 -> H(U1(e, a), k)
28.57/10.21	   A^2 -> H(U1(k, a), d)
28.57/10.21	   A^2 -> H(U1(c, d), d)
28.57/10.21	   A^2 -> H(U1(c, d), k)
28.57/10.21	   A^2 -> H(U1(d, e), b)
28.57/10.21	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(d, e), c)
28.57/10.21	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(d, e), e)
28.57/10.21	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, c), d)
28.57/10.21	   A^2 -> H(U1(d, c), k)
28.57/10.21	   A^2 -> H(U1(a, e), d)
28.57/10.21	   A^2 -> H(U1(a, e), k)
28.57/10.21	   A^2 -> H(U1(a, k), d)
28.57/10.21	   A^2 -> H(U1(a, k), k)
28.57/10.21	   A^2 -> H(k, U1(e, b))
28.57/10.21	   A^2 -> H(k, U1(c, d))
28.57/10.21	   A^2 -> H(k, U1(d, c))
28.57/10.21	   A^2 -> H(k, U1(b, e))
28.57/10.21	   A^2 -> H(k, U1(b, k))
28.57/10.21	   A^2 -> H(k, U1(e, c))
28.57/10.21	   A^2 -> H(k, U1(c, e))
28.57/10.21	   A^2 -> H(k, U1(c, k))
28.57/10.21	   A^2 -> H(k, U1(e, e))
28.57/10.21	
28.57/10.21	The TRS R consists of the following rules:
28.57/10.21	
28.57/10.21	   f(x) -> U1(x, x)
28.57/10.21	   U1(e, x) -> x
28.57/10.21	   a -> c
28.57/10.21	   a -> d
28.57/10.21	   b -> c
28.57/10.21	   b -> d
28.57/10.21	   d -> k
28.57/10.21	   c -> e
28.57/10.21	   c -> k
28.57/10.21	
28.57/10.21	Q is empty.
28.57/10.21	We have to consider all minimal (P,Q,R)-chains.
28.57/10.21	----------------------------------------
28.57/10.21	
28.57/10.21	(2037) TransformationProof (EQUIVALENT)
28.57/10.21	By narrowing [LPAR04] the rule A^2 -> H(k, f(k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.21	
28.57/10.21	   (A^2 -> H(k, U1(k, k)),A^2 -> H(k, U1(k, k)))
28.57/10.21	
28.57/10.21	
28.57/10.21	----------------------------------------
28.57/10.21	
28.57/10.21	(2038)
28.57/10.21	Obligation:
28.57/10.21	Q DP problem:
28.57/10.21	The TRS P consists of the following rules:
28.57/10.21	
28.57/10.21	   G(d, x, x) -> A^2
28.57/10.21	   A^2 -> H(f(c), f(c))
28.57/10.21	   H(x, x) -> G(x, x, f(k))
28.57/10.21	   A^2 -> H(f(d), f(d))
28.57/10.21	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.21	   A^2 -> H(f(e), f(e))
28.57/10.21	   A^2 -> H(f(k), f(k))
28.57/10.21	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.21	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.21	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.21	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.21	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.21	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.21	   A^2 -> H(k, U1(d, d))
28.57/10.21	   A^2 -> H(c, U1(e, b))
28.57/10.21	   A^2 -> H(c, U1(k, b))
28.57/10.21	   A^2 -> H(c, U1(c, d))
28.57/10.21	   A^2 -> H(c, U1(d, c))
28.57/10.21	   A^2 -> H(c, U1(b, e))
28.57/10.21	   A^2 -> H(c, U1(b, k))
28.57/10.21	   A^2 -> H(c, U1(e, c))
28.57/10.21	   A^2 -> H(c, U1(k, c))
28.57/10.21	   A^2 -> H(c, U1(c, e))
28.57/10.21	   A^2 -> H(c, U1(c, k))
28.57/10.21	   A^2 -> H(c, U1(e, e))
28.57/10.21	   A^2 -> H(c, U1(k, k))
28.57/10.21	   A^2 -> H(c, U1(k, d))
28.57/10.21	   A^2 -> H(c, U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.21	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.21	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, c), b)
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, c), e)
28.57/10.21	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.21	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.21	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.21	   A^2 -> H(U1(k, c), b)
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, c), c)
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, e), b)
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(c, e), c)
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(c, e), e)
28.57/10.21	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, k), b)
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(c, k), c)
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.21	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.21	   A^2 -> H(U1(c, k), e)
28.57/10.21	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, c), d)
28.57/10.21	   A^2 -> H(e, U1(e, b))
28.57/10.21	   A^2 -> H(e, U1(c, d))
28.57/10.21	   A^2 -> H(e, U1(d, c))
28.57/10.21	   A^2 -> H(e, U1(b, e))
28.57/10.21	   A^2 -> H(e, U1(b, k))
28.57/10.21	   A^2 -> H(e, U1(e, c))
28.57/10.21	   A^2 -> H(e, U1(c, e))
28.57/10.21	   A^2 -> H(e, U1(c, k))
28.57/10.21	   A^2 -> H(e, U1(e, e))
28.57/10.21	   A^2 -> H(e, U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, e), b)
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, e), c)
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.21	   A^2 -> H(f(e), d)
28.57/10.21	   A^2 -> H(f(e), k)
28.57/10.21	   A^2 -> H(U1(k, k), b)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, k), c)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.21	   A^2 -> H(f(k), d)
28.57/10.21	   A^2 -> H(f(k), k)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.21	   A^2 -> H(U1(k, d), b)
28.57/10.21	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, d), c)
28.57/10.21	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, k), b)
28.57/10.21	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(d, k), c)
28.57/10.21	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.21	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.21	   A^2 -> H(U1(d, k), e)
28.57/10.21	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, d), d)
28.57/10.21	   A^2 -> H(U1(d, d), k)
28.57/10.21	   A^2 -> H(U1(e, c), c)
28.57/10.21	   A^2 -> H(U1(c, c), e)
28.57/10.21	   A^2 -> H(U1(c, c), k)
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(e, e), e)
28.57/10.21	   A^2 -> H(d, U1(e, b))
28.57/10.21	   A^2 -> H(d, U1(k, b))
28.57/10.21	   A^2 -> H(d, U1(c, d))
28.57/10.21	   A^2 -> H(d, U1(d, c))
28.57/10.21	   A^2 -> H(d, U1(b, e))
28.57/10.21	   A^2 -> H(d, U1(b, k))
28.57/10.21	   A^2 -> H(d, U1(e, c))
28.57/10.21	   A^2 -> H(d, U1(k, c))
28.57/10.21	   A^2 -> H(d, U1(c, e))
28.57/10.21	   A^2 -> H(d, U1(c, k))
28.57/10.21	   A^2 -> H(d, U1(e, e))
28.57/10.21	   A^2 -> H(d, U1(k, k))
28.57/10.21	   A^2 -> H(d, U1(k, d))
28.57/10.21	   A^2 -> H(d, U1(d, k))
28.57/10.21	   A^2 -> H(a, b)
28.57/10.21	   A^2 -> H(a, U1(e, d))
28.57/10.21	   A^2 -> H(a, U1(d, e))
28.57/10.21	   A^2 -> H(a, c)
28.57/10.21	   A^2 -> H(a, U1(e, k))
28.57/10.21	   A^2 -> H(a, U1(k, e))
28.57/10.21	   A^2 -> H(a, e)
28.57/10.21	   A^2 -> H(a, U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, d), b)
28.57/10.21	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, d), c)
28.57/10.21	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, d), e)
28.57/10.21	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, a), d)
28.57/10.21	   A^2 -> H(U1(e, a), k)
28.57/10.21	   A^2 -> H(U1(k, a), d)
28.57/10.21	   A^2 -> H(U1(c, d), d)
28.57/10.21	   A^2 -> H(U1(c, d), k)
28.57/10.21	   A^2 -> H(U1(d, e), b)
28.57/10.21	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(d, e), c)
28.57/10.21	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(d, e), e)
28.57/10.21	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, c), d)
28.57/10.21	   A^2 -> H(U1(d, c), k)
28.57/10.21	   A^2 -> H(U1(a, e), d)
28.57/10.21	   A^2 -> H(U1(a, e), k)
28.57/10.21	   A^2 -> H(U1(a, k), d)
28.57/10.21	   A^2 -> H(U1(a, k), k)
28.57/10.21	   A^2 -> H(k, U1(e, b))
28.57/10.21	   A^2 -> H(k, U1(c, d))
28.57/10.21	   A^2 -> H(k, U1(d, c))
28.57/10.21	   A^2 -> H(k, U1(b, e))
28.57/10.21	   A^2 -> H(k, U1(b, k))
28.57/10.21	   A^2 -> H(k, U1(e, c))
28.57/10.21	   A^2 -> H(k, U1(c, e))
28.57/10.21	   A^2 -> H(k, U1(c, k))
28.57/10.21	   A^2 -> H(k, U1(e, e))
28.57/10.21	   A^2 -> H(k, U1(k, k))
28.57/10.21	
28.57/10.21	The TRS R consists of the following rules:
28.57/10.21	
28.57/10.21	   f(x) -> U1(x, x)
28.57/10.21	   U1(e, x) -> x
28.57/10.21	   a -> c
28.57/10.21	   a -> d
28.57/10.21	   b -> c
28.57/10.21	   b -> d
28.57/10.21	   d -> k
28.57/10.21	   c -> e
28.57/10.21	   c -> k
28.57/10.21	
28.57/10.21	Q is empty.
28.57/10.21	We have to consider all minimal (P,Q,R)-chains.
28.57/10.21	----------------------------------------
28.57/10.21	
28.57/10.21	(2039) DependencyGraphProof (EQUIVALENT)
28.57/10.21	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.21	----------------------------------------
28.57/10.21	
28.57/10.21	(2040)
28.57/10.21	Obligation:
28.57/10.21	Q DP problem:
28.57/10.21	The TRS P consists of the following rules:
28.57/10.21	
28.57/10.21	   A^2 -> H(f(c), f(c))
28.57/10.21	   H(x, x) -> G(x, x, f(k))
28.57/10.21	   G(d, x, x) -> A^2
28.57/10.21	   A^2 -> H(f(d), f(d))
28.57/10.21	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.21	   A^2 -> H(f(e), f(e))
28.57/10.21	   A^2 -> H(f(k), f(k))
28.57/10.21	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.21	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.21	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.21	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.21	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.21	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.21	   A^2 -> H(k, U1(d, d))
28.57/10.21	   A^2 -> H(c, U1(e, b))
28.57/10.21	   A^2 -> H(c, U1(k, b))
28.57/10.21	   A^2 -> H(c, U1(c, d))
28.57/10.21	   A^2 -> H(c, U1(d, c))
28.57/10.21	   A^2 -> H(c, U1(b, e))
28.57/10.21	   A^2 -> H(c, U1(b, k))
28.57/10.21	   A^2 -> H(c, U1(e, c))
28.57/10.21	   A^2 -> H(c, U1(k, c))
28.57/10.21	   A^2 -> H(c, U1(c, e))
28.57/10.21	   A^2 -> H(c, U1(c, k))
28.57/10.21	   A^2 -> H(c, U1(e, e))
28.57/10.21	   A^2 -> H(c, U1(k, k))
28.57/10.21	   A^2 -> H(c, U1(k, d))
28.57/10.21	   A^2 -> H(c, U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.21	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.21	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, c), b)
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, c), e)
28.57/10.21	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.21	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.21	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.21	   A^2 -> H(U1(k, c), b)
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, c), c)
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, e), b)
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(c, e), c)
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(c, e), e)
28.57/10.21	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, k), b)
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(c, k), c)
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.21	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.21	   A^2 -> H(U1(c, k), e)
28.57/10.21	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, c), d)
28.57/10.21	   A^2 -> H(e, U1(e, b))
28.57/10.21	   A^2 -> H(e, U1(c, d))
28.57/10.21	   A^2 -> H(e, U1(d, c))
28.57/10.21	   A^2 -> H(e, U1(b, e))
28.57/10.21	   A^2 -> H(e, U1(b, k))
28.57/10.21	   A^2 -> H(e, U1(e, c))
28.57/10.21	   A^2 -> H(e, U1(c, e))
28.57/10.21	   A^2 -> H(e, U1(c, k))
28.57/10.21	   A^2 -> H(e, U1(e, e))
28.57/10.21	   A^2 -> H(e, U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, e), b)
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, e), c)
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.21	   A^2 -> H(f(e), d)
28.57/10.21	   A^2 -> H(f(e), k)
28.57/10.21	   A^2 -> H(U1(k, k), b)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, k), c)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.21	   A^2 -> H(f(k), d)
28.57/10.21	   A^2 -> H(f(k), k)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.21	   A^2 -> H(U1(k, d), b)
28.57/10.21	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, d), c)
28.57/10.21	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, k), b)
28.57/10.21	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(d, k), c)
28.57/10.21	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.21	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.21	   A^2 -> H(U1(d, k), e)
28.57/10.21	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, d), d)
28.57/10.21	   A^2 -> H(U1(d, d), k)
28.57/10.21	   A^2 -> H(U1(e, c), c)
28.57/10.21	   A^2 -> H(U1(c, c), e)
28.57/10.21	   A^2 -> H(U1(c, c), k)
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(e, e), e)
28.57/10.21	   A^2 -> H(d, U1(e, b))
28.57/10.21	   A^2 -> H(d, U1(k, b))
28.57/10.21	   A^2 -> H(d, U1(c, d))
28.57/10.21	   A^2 -> H(d, U1(d, c))
28.57/10.21	   A^2 -> H(d, U1(b, e))
28.57/10.21	   A^2 -> H(d, U1(b, k))
28.57/10.21	   A^2 -> H(d, U1(e, c))
28.57/10.21	   A^2 -> H(d, U1(k, c))
28.57/10.21	   A^2 -> H(d, U1(c, e))
28.57/10.21	   A^2 -> H(d, U1(c, k))
28.57/10.21	   A^2 -> H(d, U1(e, e))
28.57/10.21	   A^2 -> H(d, U1(k, k))
28.57/10.21	   A^2 -> H(d, U1(k, d))
28.57/10.21	   A^2 -> H(d, U1(d, k))
28.57/10.21	   A^2 -> H(a, b)
28.57/10.21	   A^2 -> H(a, U1(e, d))
28.57/10.21	   A^2 -> H(a, U1(d, e))
28.57/10.21	   A^2 -> H(a, c)
28.57/10.21	   A^2 -> H(a, U1(e, k))
28.57/10.21	   A^2 -> H(a, U1(k, e))
28.57/10.21	   A^2 -> H(a, e)
28.57/10.21	   A^2 -> H(a, U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, d), b)
28.57/10.21	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, d), c)
28.57/10.21	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, d), e)
28.57/10.21	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, a), d)
28.57/10.21	   A^2 -> H(U1(e, a), k)
28.57/10.21	   A^2 -> H(U1(k, a), d)
28.57/10.21	   A^2 -> H(U1(c, d), d)
28.57/10.21	   A^2 -> H(U1(c, d), k)
28.57/10.21	   A^2 -> H(U1(d, e), b)
28.57/10.21	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(d, e), c)
28.57/10.21	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(d, e), e)
28.57/10.21	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, c), d)
28.57/10.21	   A^2 -> H(U1(d, c), k)
28.57/10.21	   A^2 -> H(U1(a, e), d)
28.57/10.21	   A^2 -> H(U1(a, e), k)
28.57/10.21	   A^2 -> H(U1(a, k), d)
28.57/10.21	   A^2 -> H(U1(a, k), k)
28.57/10.21	   A^2 -> H(k, U1(e, b))
28.57/10.21	   A^2 -> H(k, U1(c, d))
28.57/10.21	   A^2 -> H(k, U1(d, c))
28.57/10.21	   A^2 -> H(k, U1(b, e))
28.57/10.21	   A^2 -> H(k, U1(b, k))
28.57/10.21	   A^2 -> H(k, U1(e, c))
28.57/10.21	   A^2 -> H(k, U1(c, e))
28.57/10.21	   A^2 -> H(k, U1(c, k))
28.57/10.21	   A^2 -> H(k, U1(e, e))
28.57/10.21	
28.57/10.21	The TRS R consists of the following rules:
28.57/10.21	
28.57/10.21	   f(x) -> U1(x, x)
28.57/10.21	   U1(e, x) -> x
28.57/10.21	   a -> c
28.57/10.21	   a -> d
28.57/10.21	   b -> c
28.57/10.21	   b -> d
28.57/10.21	   d -> k
28.57/10.21	   c -> e
28.57/10.21	   c -> k
28.57/10.21	
28.57/10.21	Q is empty.
28.57/10.21	We have to consider all minimal (P,Q,R)-chains.
28.57/10.21	----------------------------------------
28.57/10.21	
28.57/10.21	(2041) TransformationProof (EQUIVALENT)
28.57/10.21	By narrowing [LPAR04] the rule A^2 -> H(k, U1(d, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.21	
28.57/10.21	   (A^2 -> H(k, U1(k, d)),A^2 -> H(k, U1(k, d)))
28.57/10.21	   (A^2 -> H(k, U1(d, k)),A^2 -> H(k, U1(d, k)))
28.57/10.21	
28.57/10.21	
28.57/10.21	----------------------------------------
28.57/10.21	
28.57/10.21	(2042)
28.57/10.21	Obligation:
28.57/10.21	Q DP problem:
28.57/10.21	The TRS P consists of the following rules:
28.57/10.21	
28.57/10.21	   A^2 -> H(f(c), f(c))
28.57/10.21	   H(x, x) -> G(x, x, f(k))
28.57/10.21	   G(d, x, x) -> A^2
28.57/10.21	   A^2 -> H(f(d), f(d))
28.57/10.21	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.21	   A^2 -> H(f(e), f(e))
28.57/10.21	   A^2 -> H(f(k), f(k))
28.57/10.21	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.21	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.21	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.21	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.21	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.21	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.21	   A^2 -> H(c, U1(e, b))
28.57/10.21	   A^2 -> H(c, U1(k, b))
28.57/10.21	   A^2 -> H(c, U1(c, d))
28.57/10.21	   A^2 -> H(c, U1(d, c))
28.57/10.21	   A^2 -> H(c, U1(b, e))
28.57/10.21	   A^2 -> H(c, U1(b, k))
28.57/10.21	   A^2 -> H(c, U1(e, c))
28.57/10.21	   A^2 -> H(c, U1(k, c))
28.57/10.21	   A^2 -> H(c, U1(c, e))
28.57/10.21	   A^2 -> H(c, U1(c, k))
28.57/10.21	   A^2 -> H(c, U1(e, e))
28.57/10.21	   A^2 -> H(c, U1(k, k))
28.57/10.21	   A^2 -> H(c, U1(k, d))
28.57/10.21	   A^2 -> H(c, U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.21	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.21	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, c), b)
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, c), e)
28.57/10.21	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.21	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.21	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.21	   A^2 -> H(U1(k, c), b)
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, c), c)
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, e), b)
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(c, e), c)
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(c, e), e)
28.57/10.21	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, k), b)
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(c, k), c)
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.21	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.21	   A^2 -> H(U1(c, k), e)
28.57/10.21	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, c), d)
28.57/10.21	   A^2 -> H(e, U1(e, b))
28.57/10.21	   A^2 -> H(e, U1(c, d))
28.57/10.21	   A^2 -> H(e, U1(d, c))
28.57/10.21	   A^2 -> H(e, U1(b, e))
28.57/10.21	   A^2 -> H(e, U1(b, k))
28.57/10.21	   A^2 -> H(e, U1(e, c))
28.57/10.21	   A^2 -> H(e, U1(c, e))
28.57/10.21	   A^2 -> H(e, U1(c, k))
28.57/10.21	   A^2 -> H(e, U1(e, e))
28.57/10.21	   A^2 -> H(e, U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, e), b)
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, e), c)
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.21	   A^2 -> H(f(e), d)
28.57/10.21	   A^2 -> H(f(e), k)
28.57/10.21	   A^2 -> H(U1(k, k), b)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, k), c)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.21	   A^2 -> H(f(k), d)
28.57/10.21	   A^2 -> H(f(k), k)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.21	   A^2 -> H(U1(k, d), b)
28.57/10.21	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, d), c)
28.57/10.21	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, k), b)
28.57/10.21	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(d, k), c)
28.57/10.21	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.21	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.21	   A^2 -> H(U1(d, k), e)
28.57/10.21	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, d), d)
28.57/10.21	   A^2 -> H(U1(d, d), k)
28.57/10.21	   A^2 -> H(U1(e, c), c)
28.57/10.21	   A^2 -> H(U1(c, c), e)
28.57/10.21	   A^2 -> H(U1(c, c), k)
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(e, e), e)
28.57/10.21	   A^2 -> H(d, U1(e, b))
28.57/10.21	   A^2 -> H(d, U1(k, b))
28.57/10.21	   A^2 -> H(d, U1(c, d))
28.57/10.21	   A^2 -> H(d, U1(d, c))
28.57/10.21	   A^2 -> H(d, U1(b, e))
28.57/10.21	   A^2 -> H(d, U1(b, k))
28.57/10.21	   A^2 -> H(d, U1(e, c))
28.57/10.21	   A^2 -> H(d, U1(k, c))
28.57/10.21	   A^2 -> H(d, U1(c, e))
28.57/10.21	   A^2 -> H(d, U1(c, k))
28.57/10.21	   A^2 -> H(d, U1(e, e))
28.57/10.21	   A^2 -> H(d, U1(k, k))
28.57/10.21	   A^2 -> H(d, U1(k, d))
28.57/10.21	   A^2 -> H(d, U1(d, k))
28.57/10.21	   A^2 -> H(a, b)
28.57/10.21	   A^2 -> H(a, U1(e, d))
28.57/10.21	   A^2 -> H(a, U1(d, e))
28.57/10.21	   A^2 -> H(a, c)
28.57/10.21	   A^2 -> H(a, U1(e, k))
28.57/10.21	   A^2 -> H(a, U1(k, e))
28.57/10.21	   A^2 -> H(a, e)
28.57/10.21	   A^2 -> H(a, U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, d), b)
28.57/10.21	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, d), c)
28.57/10.21	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, d), e)
28.57/10.21	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, a), d)
28.57/10.21	   A^2 -> H(U1(e, a), k)
28.57/10.21	   A^2 -> H(U1(k, a), d)
28.57/10.21	   A^2 -> H(U1(c, d), d)
28.57/10.21	   A^2 -> H(U1(c, d), k)
28.57/10.21	   A^2 -> H(U1(d, e), b)
28.57/10.21	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(d, e), c)
28.57/10.21	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(d, e), e)
28.57/10.21	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, c), d)
28.57/10.21	   A^2 -> H(U1(d, c), k)
28.57/10.21	   A^2 -> H(U1(a, e), d)
28.57/10.21	   A^2 -> H(U1(a, e), k)
28.57/10.21	   A^2 -> H(U1(a, k), d)
28.57/10.21	   A^2 -> H(U1(a, k), k)
28.57/10.21	   A^2 -> H(k, U1(e, b))
28.57/10.21	   A^2 -> H(k, U1(c, d))
28.57/10.21	   A^2 -> H(k, U1(d, c))
28.57/10.21	   A^2 -> H(k, U1(b, e))
28.57/10.21	   A^2 -> H(k, U1(b, k))
28.57/10.21	   A^2 -> H(k, U1(e, c))
28.57/10.21	   A^2 -> H(k, U1(c, e))
28.57/10.21	   A^2 -> H(k, U1(c, k))
28.57/10.21	   A^2 -> H(k, U1(e, e))
28.57/10.21	   A^2 -> H(k, U1(k, d))
28.57/10.21	   A^2 -> H(k, U1(d, k))
28.57/10.21	
28.57/10.21	The TRS R consists of the following rules:
28.57/10.21	
28.57/10.21	   f(x) -> U1(x, x)
28.57/10.21	   U1(e, x) -> x
28.57/10.21	   a -> c
28.57/10.21	   a -> d
28.57/10.21	   b -> c
28.57/10.21	   b -> d
28.57/10.21	   d -> k
28.57/10.21	   c -> e
28.57/10.21	   c -> k
28.57/10.21	
28.57/10.21	Q is empty.
28.57/10.21	We have to consider all minimal (P,Q,R)-chains.
28.57/10.21	----------------------------------------
28.57/10.21	
28.57/10.21	(2043) DependencyGraphProof (EQUIVALENT)
28.57/10.21	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.21	----------------------------------------
28.57/10.21	
28.57/10.21	(2044)
28.57/10.21	Obligation:
28.57/10.21	Q DP problem:
28.57/10.21	The TRS P consists of the following rules:
28.57/10.21	
28.57/10.21	   H(x, x) -> G(x, x, f(k))
28.57/10.21	   G(d, x, x) -> A^2
28.57/10.21	   A^2 -> H(f(c), f(c))
28.57/10.21	   A^2 -> H(f(d), f(d))
28.57/10.21	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.21	   A^2 -> H(f(e), f(e))
28.57/10.21	   A^2 -> H(f(k), f(k))
28.57/10.21	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.21	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.21	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.21	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.21	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.21	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.21	   A^2 -> H(c, U1(e, b))
28.57/10.21	   A^2 -> H(c, U1(k, b))
28.57/10.21	   A^2 -> H(c, U1(c, d))
28.57/10.21	   A^2 -> H(c, U1(d, c))
28.57/10.21	   A^2 -> H(c, U1(b, e))
28.57/10.21	   A^2 -> H(c, U1(b, k))
28.57/10.21	   A^2 -> H(c, U1(e, c))
28.57/10.21	   A^2 -> H(c, U1(k, c))
28.57/10.21	   A^2 -> H(c, U1(c, e))
28.57/10.21	   A^2 -> H(c, U1(c, k))
28.57/10.21	   A^2 -> H(c, U1(e, e))
28.57/10.21	   A^2 -> H(c, U1(k, k))
28.57/10.21	   A^2 -> H(c, U1(k, d))
28.57/10.21	   A^2 -> H(c, U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.21	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.21	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, c), b)
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, c), e)
28.57/10.21	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.21	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.21	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.21	   A^2 -> H(U1(k, c), b)
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, c), c)
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, e), b)
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(c, e), c)
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(c, e), e)
28.57/10.21	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, k), b)
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(c, k), c)
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.21	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.21	   A^2 -> H(U1(c, k), e)
28.57/10.21	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, c), d)
28.57/10.21	   A^2 -> H(e, U1(e, b))
28.57/10.21	   A^2 -> H(e, U1(c, d))
28.57/10.21	   A^2 -> H(e, U1(d, c))
28.57/10.21	   A^2 -> H(e, U1(b, e))
28.57/10.21	   A^2 -> H(e, U1(b, k))
28.57/10.21	   A^2 -> H(e, U1(e, c))
28.57/10.21	   A^2 -> H(e, U1(c, e))
28.57/10.21	   A^2 -> H(e, U1(c, k))
28.57/10.21	   A^2 -> H(e, U1(e, e))
28.57/10.21	   A^2 -> H(e, U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, e), b)
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, e), c)
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.21	   A^2 -> H(f(e), d)
28.57/10.21	   A^2 -> H(f(e), k)
28.57/10.21	   A^2 -> H(U1(k, k), b)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, k), c)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.21	   A^2 -> H(f(k), d)
28.57/10.21	   A^2 -> H(f(k), k)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.21	   A^2 -> H(U1(k, d), b)
28.57/10.21	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, d), c)
28.57/10.21	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, k), b)
28.57/10.21	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(d, k), c)
28.57/10.21	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.21	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.21	   A^2 -> H(U1(d, k), e)
28.57/10.21	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, d), d)
28.57/10.21	   A^2 -> H(U1(d, d), k)
28.57/10.21	   A^2 -> H(U1(e, c), c)
28.57/10.21	   A^2 -> H(U1(c, c), e)
28.57/10.21	   A^2 -> H(U1(c, c), k)
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(e, e), e)
28.57/10.21	   A^2 -> H(d, U1(e, b))
28.57/10.21	   A^2 -> H(d, U1(k, b))
28.57/10.21	   A^2 -> H(d, U1(c, d))
28.57/10.21	   A^2 -> H(d, U1(d, c))
28.57/10.21	   A^2 -> H(d, U1(b, e))
28.57/10.21	   A^2 -> H(d, U1(b, k))
28.57/10.21	   A^2 -> H(d, U1(e, c))
28.57/10.21	   A^2 -> H(d, U1(k, c))
28.57/10.21	   A^2 -> H(d, U1(c, e))
28.57/10.21	   A^2 -> H(d, U1(c, k))
28.57/10.21	   A^2 -> H(d, U1(e, e))
28.57/10.21	   A^2 -> H(d, U1(k, k))
28.57/10.21	   A^2 -> H(d, U1(k, d))
28.57/10.21	   A^2 -> H(d, U1(d, k))
28.57/10.21	   A^2 -> H(a, b)
28.57/10.21	   A^2 -> H(a, U1(e, d))
28.57/10.21	   A^2 -> H(a, U1(d, e))
28.57/10.21	   A^2 -> H(a, c)
28.57/10.21	   A^2 -> H(a, U1(e, k))
28.57/10.21	   A^2 -> H(a, U1(k, e))
28.57/10.21	   A^2 -> H(a, e)
28.57/10.21	   A^2 -> H(a, U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, d), b)
28.57/10.21	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, d), c)
28.57/10.21	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, d), e)
28.57/10.21	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, a), d)
28.57/10.21	   A^2 -> H(U1(e, a), k)
28.57/10.21	   A^2 -> H(U1(k, a), d)
28.57/10.21	   A^2 -> H(U1(c, d), d)
28.57/10.21	   A^2 -> H(U1(c, d), k)
28.57/10.21	   A^2 -> H(U1(d, e), b)
28.57/10.21	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(d, e), c)
28.57/10.21	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(d, e), e)
28.57/10.21	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, c), d)
28.57/10.21	   A^2 -> H(U1(d, c), k)
28.57/10.21	   A^2 -> H(U1(a, e), d)
28.57/10.21	   A^2 -> H(U1(a, e), k)
28.57/10.21	   A^2 -> H(U1(a, k), d)
28.57/10.21	   A^2 -> H(U1(a, k), k)
28.57/10.21	   A^2 -> H(k, U1(e, b))
28.57/10.21	   A^2 -> H(k, U1(c, d))
28.57/10.21	   A^2 -> H(k, U1(d, c))
28.57/10.21	   A^2 -> H(k, U1(b, e))
28.57/10.21	   A^2 -> H(k, U1(b, k))
28.57/10.21	   A^2 -> H(k, U1(e, c))
28.57/10.21	   A^2 -> H(k, U1(c, e))
28.57/10.21	   A^2 -> H(k, U1(c, k))
28.57/10.21	   A^2 -> H(k, U1(e, e))
28.57/10.21	   A^2 -> H(k, U1(d, k))
28.57/10.21	
28.57/10.21	The TRS R consists of the following rules:
28.57/10.21	
28.57/10.21	   f(x) -> U1(x, x)
28.57/10.21	   U1(e, x) -> x
28.57/10.21	   a -> c
28.57/10.21	   a -> d
28.57/10.21	   b -> c
28.57/10.21	   b -> d
28.57/10.21	   d -> k
28.57/10.21	   c -> e
28.57/10.21	   c -> k
28.57/10.21	
28.57/10.21	Q is empty.
28.57/10.21	We have to consider all minimal (P,Q,R)-chains.
28.57/10.21	----------------------------------------
28.57/10.21	
28.57/10.21	(2045) TransformationProof (EQUIVALENT)
28.57/10.21	By narrowing [LPAR04] the rule A^2 -> H(c, U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.21	
28.57/10.21	   (A^2 -> H(e, U1(e, b)),A^2 -> H(e, U1(e, b)))
28.57/10.21	   (A^2 -> H(k, U1(e, b)),A^2 -> H(k, U1(e, b)))
28.57/10.21	   (A^2 -> H(c, b),A^2 -> H(c, b))
28.57/10.21	   (A^2 -> H(c, U1(e, c)),A^2 -> H(c, U1(e, c)))
28.57/10.21	   (A^2 -> H(c, U1(e, d)),A^2 -> H(c, U1(e, d)))
28.57/10.21	
28.57/10.21	
28.57/10.21	----------------------------------------
28.57/10.21	
28.57/10.21	(2046)
28.57/10.21	Obligation:
28.57/10.21	Q DP problem:
28.57/10.21	The TRS P consists of the following rules:
28.57/10.21	
28.57/10.21	   H(x, x) -> G(x, x, f(k))
28.57/10.21	   G(d, x, x) -> A^2
28.57/10.21	   A^2 -> H(f(c), f(c))
28.57/10.21	   A^2 -> H(f(d), f(d))
28.57/10.21	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.21	   A^2 -> H(f(e), f(e))
28.57/10.21	   A^2 -> H(f(k), f(k))
28.57/10.21	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.21	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.21	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.21	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.21	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.21	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.21	   A^2 -> H(c, U1(k, b))
28.57/10.21	   A^2 -> H(c, U1(c, d))
28.57/10.21	   A^2 -> H(c, U1(d, c))
28.57/10.21	   A^2 -> H(c, U1(b, e))
28.57/10.21	   A^2 -> H(c, U1(b, k))
28.57/10.21	   A^2 -> H(c, U1(e, c))
28.57/10.21	   A^2 -> H(c, U1(k, c))
28.57/10.21	   A^2 -> H(c, U1(c, e))
28.57/10.21	   A^2 -> H(c, U1(c, k))
28.57/10.21	   A^2 -> H(c, U1(e, e))
28.57/10.21	   A^2 -> H(c, U1(k, k))
28.57/10.21	   A^2 -> H(c, U1(k, d))
28.57/10.21	   A^2 -> H(c, U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.21	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.21	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, c), b)
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, c), e)
28.57/10.21	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.21	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.21	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.21	   A^2 -> H(U1(k, c), b)
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, c), c)
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, e), b)
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(c, e), c)
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(c, e), e)
28.57/10.21	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, k), b)
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(c, k), c)
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.21	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.21	   A^2 -> H(U1(c, k), e)
28.57/10.21	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, c), d)
28.57/10.21	   A^2 -> H(e, U1(e, b))
28.57/10.21	   A^2 -> H(e, U1(c, d))
28.57/10.21	   A^2 -> H(e, U1(d, c))
28.57/10.21	   A^2 -> H(e, U1(b, e))
28.57/10.21	   A^2 -> H(e, U1(b, k))
28.57/10.21	   A^2 -> H(e, U1(e, c))
28.57/10.21	   A^2 -> H(e, U1(c, e))
28.57/10.21	   A^2 -> H(e, U1(c, k))
28.57/10.21	   A^2 -> H(e, U1(e, e))
28.57/10.21	   A^2 -> H(e, U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, e), b)
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, e), c)
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.21	   A^2 -> H(f(e), d)
28.57/10.21	   A^2 -> H(f(e), k)
28.57/10.21	   A^2 -> H(U1(k, k), b)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, k), c)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.21	   A^2 -> H(f(k), d)
28.57/10.21	   A^2 -> H(f(k), k)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.21	   A^2 -> H(U1(k, d), b)
28.57/10.21	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, d), c)
28.57/10.21	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, k), b)
28.57/10.21	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(d, k), c)
28.57/10.21	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.21	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.21	   A^2 -> H(U1(d, k), e)
28.57/10.21	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, d), d)
28.57/10.21	   A^2 -> H(U1(d, d), k)
28.57/10.21	   A^2 -> H(U1(e, c), c)
28.57/10.21	   A^2 -> H(U1(c, c), e)
28.57/10.21	   A^2 -> H(U1(c, c), k)
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(e, e), e)
28.57/10.21	   A^2 -> H(d, U1(e, b))
28.57/10.21	   A^2 -> H(d, U1(k, b))
28.57/10.21	   A^2 -> H(d, U1(c, d))
28.57/10.21	   A^2 -> H(d, U1(d, c))
28.57/10.21	   A^2 -> H(d, U1(b, e))
28.57/10.21	   A^2 -> H(d, U1(b, k))
28.57/10.21	   A^2 -> H(d, U1(e, c))
28.57/10.21	   A^2 -> H(d, U1(k, c))
28.57/10.21	   A^2 -> H(d, U1(c, e))
28.57/10.21	   A^2 -> H(d, U1(c, k))
28.57/10.21	   A^2 -> H(d, U1(e, e))
28.57/10.21	   A^2 -> H(d, U1(k, k))
28.57/10.21	   A^2 -> H(d, U1(k, d))
28.57/10.21	   A^2 -> H(d, U1(d, k))
28.57/10.21	   A^2 -> H(a, b)
28.57/10.21	   A^2 -> H(a, U1(e, d))
28.57/10.21	   A^2 -> H(a, U1(d, e))
28.57/10.21	   A^2 -> H(a, c)
28.57/10.21	   A^2 -> H(a, U1(e, k))
28.57/10.21	   A^2 -> H(a, U1(k, e))
28.57/10.21	   A^2 -> H(a, e)
28.57/10.21	   A^2 -> H(a, U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, d), b)
28.57/10.21	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, d), c)
28.57/10.21	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, d), e)
28.57/10.21	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, a), d)
28.57/10.21	   A^2 -> H(U1(e, a), k)
28.57/10.21	   A^2 -> H(U1(k, a), d)
28.57/10.21	   A^2 -> H(U1(c, d), d)
28.57/10.21	   A^2 -> H(U1(c, d), k)
28.57/10.21	   A^2 -> H(U1(d, e), b)
28.57/10.21	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(d, e), c)
28.57/10.21	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(d, e), e)
28.57/10.21	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, c), d)
28.57/10.21	   A^2 -> H(U1(d, c), k)
28.57/10.21	   A^2 -> H(U1(a, e), d)
28.57/10.21	   A^2 -> H(U1(a, e), k)
28.57/10.21	   A^2 -> H(U1(a, k), d)
28.57/10.21	   A^2 -> H(U1(a, k), k)
28.57/10.21	   A^2 -> H(k, U1(e, b))
28.57/10.21	   A^2 -> H(k, U1(c, d))
28.57/10.21	   A^2 -> H(k, U1(d, c))
28.57/10.21	   A^2 -> H(k, U1(b, e))
28.57/10.21	   A^2 -> H(k, U1(b, k))
28.57/10.21	   A^2 -> H(k, U1(e, c))
28.57/10.21	   A^2 -> H(k, U1(c, e))
28.57/10.21	   A^2 -> H(k, U1(c, k))
28.57/10.21	   A^2 -> H(k, U1(e, e))
28.57/10.21	   A^2 -> H(k, U1(d, k))
28.57/10.21	   A^2 -> H(c, b)
28.57/10.21	   A^2 -> H(c, U1(e, d))
28.57/10.21	
28.57/10.21	The TRS R consists of the following rules:
28.57/10.21	
28.57/10.21	   f(x) -> U1(x, x)
28.57/10.21	   U1(e, x) -> x
28.57/10.21	   a -> c
28.57/10.21	   a -> d
28.57/10.21	   b -> c
28.57/10.21	   b -> d
28.57/10.21	   d -> k
28.57/10.21	   c -> e
28.57/10.21	   c -> k
28.57/10.21	
28.57/10.21	Q is empty.
28.57/10.21	We have to consider all minimal (P,Q,R)-chains.
28.57/10.21	----------------------------------------
28.57/10.21	
28.57/10.21	(2047) TransformationProof (EQUIVALENT)
28.57/10.21	By narrowing [LPAR04] the rule A^2 -> H(c, U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.21	
28.57/10.21	   (A^2 -> H(e, U1(k, b)),A^2 -> H(e, U1(k, b)))
28.57/10.21	   (A^2 -> H(k, U1(k, b)),A^2 -> H(k, U1(k, b)))
28.57/10.21	   (A^2 -> H(c, U1(k, c)),A^2 -> H(c, U1(k, c)))
28.57/10.21	   (A^2 -> H(c, U1(k, d)),A^2 -> H(c, U1(k, d)))
28.57/10.21	
28.57/10.21	
28.57/10.21	----------------------------------------
28.57/10.21	
28.57/10.21	(2048)
28.57/10.21	Obligation:
28.57/10.21	Q DP problem:
28.57/10.21	The TRS P consists of the following rules:
28.57/10.21	
28.57/10.21	   H(x, x) -> G(x, x, f(k))
28.57/10.21	   G(d, x, x) -> A^2
28.57/10.21	   A^2 -> H(f(c), f(c))
28.57/10.21	   A^2 -> H(f(d), f(d))
28.57/10.21	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.21	   A^2 -> H(f(e), f(e))
28.57/10.21	   A^2 -> H(f(k), f(k))
28.57/10.21	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.21	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.21	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.21	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.21	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.21	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.21	   A^2 -> H(c, U1(c, d))
28.57/10.21	   A^2 -> H(c, U1(d, c))
28.57/10.21	   A^2 -> H(c, U1(b, e))
28.57/10.21	   A^2 -> H(c, U1(b, k))
28.57/10.21	   A^2 -> H(c, U1(e, c))
28.57/10.21	   A^2 -> H(c, U1(k, c))
28.57/10.21	   A^2 -> H(c, U1(c, e))
28.57/10.21	   A^2 -> H(c, U1(c, k))
28.57/10.21	   A^2 -> H(c, U1(e, e))
28.57/10.21	   A^2 -> H(c, U1(k, k))
28.57/10.21	   A^2 -> H(c, U1(k, d))
28.57/10.21	   A^2 -> H(c, U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.21	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.21	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, c), b)
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, c), e)
28.57/10.21	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.21	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.21	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.21	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.21	   A^2 -> H(U1(k, c), b)
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, c), c)
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, e), b)
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(c, e), c)
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(c, e), e)
28.57/10.21	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, k), b)
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(c, k), c)
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.21	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.21	   A^2 -> H(U1(c, k), e)
28.57/10.21	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(c, c), d)
28.57/10.21	   A^2 -> H(e, U1(e, b))
28.57/10.21	   A^2 -> H(e, U1(c, d))
28.57/10.21	   A^2 -> H(e, U1(d, c))
28.57/10.21	   A^2 -> H(e, U1(b, e))
28.57/10.21	   A^2 -> H(e, U1(b, k))
28.57/10.21	   A^2 -> H(e, U1(e, c))
28.57/10.21	   A^2 -> H(e, U1(c, e))
28.57/10.21	   A^2 -> H(e, U1(c, k))
28.57/10.21	   A^2 -> H(e, U1(e, e))
28.57/10.21	   A^2 -> H(e, U1(d, k))
28.57/10.21	   A^2 -> H(U1(e, e), b)
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, e), c)
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.21	   A^2 -> H(f(e), d)
28.57/10.21	   A^2 -> H(f(e), k)
28.57/10.21	   A^2 -> H(U1(k, k), b)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, k), c)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.21	   A^2 -> H(f(k), d)
28.57/10.21	   A^2 -> H(f(k), k)
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.21	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.21	   A^2 -> H(U1(k, d), b)
28.57/10.21	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.21	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.21	   A^2 -> H(U1(k, d), c)
28.57/10.21	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, k), b)
28.57/10.21	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.21	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.21	   A^2 -> H(U1(d, k), c)
28.57/10.21	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.21	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.21	   A^2 -> H(U1(d, k), e)
28.57/10.21	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, d), d)
28.57/10.21	   A^2 -> H(U1(d, d), k)
28.57/10.21	   A^2 -> H(U1(e, c), c)
28.57/10.21	   A^2 -> H(U1(c, c), e)
28.57/10.21	   A^2 -> H(U1(c, c), k)
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.21	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.21	   A^2 -> H(U1(e, e), e)
28.57/10.21	   A^2 -> H(d, U1(e, b))
28.57/10.21	   A^2 -> H(d, U1(k, b))
28.57/10.21	   A^2 -> H(d, U1(c, d))
28.57/10.21	   A^2 -> H(d, U1(d, c))
28.57/10.21	   A^2 -> H(d, U1(b, e))
28.57/10.21	   A^2 -> H(d, U1(b, k))
28.57/10.21	   A^2 -> H(d, U1(e, c))
28.57/10.21	   A^2 -> H(d, U1(k, c))
28.57/10.21	   A^2 -> H(d, U1(c, e))
28.57/10.21	   A^2 -> H(d, U1(c, k))
28.57/10.21	   A^2 -> H(d, U1(e, e))
28.57/10.21	   A^2 -> H(d, U1(k, k))
28.57/10.21	   A^2 -> H(d, U1(k, d))
28.57/10.21	   A^2 -> H(d, U1(d, k))
28.57/10.21	   A^2 -> H(a, b)
28.57/10.21	   A^2 -> H(a, U1(e, d))
28.57/10.21	   A^2 -> H(a, U1(d, e))
28.57/10.21	   A^2 -> H(a, c)
28.57/10.21	   A^2 -> H(a, U1(e, k))
28.57/10.21	   A^2 -> H(a, U1(k, e))
28.57/10.21	   A^2 -> H(a, e)
28.57/10.21	   A^2 -> H(a, U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, d), b)
28.57/10.21	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.21	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.21	   A^2 -> H(U1(e, d), c)
28.57/10.21	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.21	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.21	   A^2 -> H(U1(e, d), e)
28.57/10.21	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.21	   A^2 -> H(U1(e, a), d)
28.57/10.21	   A^2 -> H(U1(e, a), k)
28.57/10.21	   A^2 -> H(U1(k, a), d)
28.57/10.21	   A^2 -> H(U1(c, d), d)
28.57/10.21	   A^2 -> H(U1(c, d), k)
28.57/10.21	   A^2 -> H(U1(d, e), b)
28.57/10.21	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.21	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.21	   A^2 -> H(U1(d, e), c)
28.57/10.21	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.21	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.21	   A^2 -> H(U1(d, e), e)
28.57/10.21	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.21	   A^2 -> H(U1(d, c), d)
28.57/10.21	   A^2 -> H(U1(d, c), k)
28.57/10.21	   A^2 -> H(U1(a, e), d)
28.57/10.21	   A^2 -> H(U1(a, e), k)
28.57/10.21	   A^2 -> H(U1(a, k), d)
28.57/10.21	   A^2 -> H(U1(a, k), k)
28.57/10.21	   A^2 -> H(k, U1(e, b))
28.57/10.21	   A^2 -> H(k, U1(c, d))
28.57/10.21	   A^2 -> H(k, U1(d, c))
28.57/10.21	   A^2 -> H(k, U1(b, e))
28.57/10.21	   A^2 -> H(k, U1(b, k))
28.57/10.21	   A^2 -> H(k, U1(e, c))
28.57/10.21	   A^2 -> H(k, U1(c, e))
28.57/10.21	   A^2 -> H(k, U1(c, k))
28.57/10.21	   A^2 -> H(k, U1(e, e))
28.57/10.21	   A^2 -> H(k, U1(d, k))
28.57/10.21	   A^2 -> H(c, b)
28.57/10.21	   A^2 -> H(c, U1(e, d))
28.57/10.21	   A^2 -> H(e, U1(k, b))
28.57/10.21	   A^2 -> H(k, U1(k, b))
28.57/10.21	
28.57/10.21	The TRS R consists of the following rules:
28.57/10.21	
28.57/10.21	   f(x) -> U1(x, x)
28.57/10.21	   U1(e, x) -> x
28.57/10.21	   a -> c
28.57/10.21	   a -> d
28.57/10.21	   b -> c
28.57/10.21	   b -> d
28.57/10.21	   d -> k
28.57/10.21	   c -> e
28.57/10.21	   c -> k
28.57/10.21	
28.57/10.21	Q is empty.
28.57/10.21	We have to consider all minimal (P,Q,R)-chains.
28.57/10.21	----------------------------------------
28.57/10.21	
28.57/10.21	(2049) DependencyGraphProof (EQUIVALENT)
28.57/10.21	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
28.57/10.21	----------------------------------------
28.57/10.21	
28.57/10.21	(2050)
28.57/10.21	Obligation:
28.57/10.21	Q DP problem:
28.57/10.21	The TRS P consists of the following rules:
28.57/10.21	
28.57/10.21	   G(d, x, x) -> A^2
28.57/10.21	   A^2 -> H(f(c), f(c))
28.57/10.21	   H(x, x) -> G(x, x, f(k))
28.57/10.21	   A^2 -> H(f(d), f(d))
28.57/10.21	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.21	   A^2 -> H(f(e), f(e))
28.57/10.21	   A^2 -> H(f(k), f(k))
28.57/10.21	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.21	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.21	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.21	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.21	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.21	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.21	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.21	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.21	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.21	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.21	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.21	   A^2 -> H(c, U1(c, d))
28.57/10.22	   A^2 -> H(c, U1(d, c))
28.57/10.22	   A^2 -> H(c, U1(b, e))
28.57/10.22	   A^2 -> H(c, U1(b, k))
28.57/10.22	   A^2 -> H(c, U1(e, c))
28.57/10.22	   A^2 -> H(c, U1(k, c))
28.57/10.22	   A^2 -> H(c, U1(c, e))
28.57/10.22	   A^2 -> H(c, U1(c, k))
28.57/10.22	   A^2 -> H(c, U1(e, e))
28.57/10.22	   A^2 -> H(c, U1(k, k))
28.57/10.22	   A^2 -> H(c, U1(k, d))
28.57/10.22	   A^2 -> H(c, U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.22	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.22	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, c), b)
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, c), e)
28.57/10.22	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.22	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.22	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.22	   A^2 -> H(U1(k, c), b)
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, c), c)
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, e), b)
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(c, e), c)
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(c, e), e)
28.57/10.22	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, k), b)
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(c, k), c)
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.22	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.22	   A^2 -> H(U1(c, k), e)
28.57/10.22	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, c), d)
28.57/10.22	   A^2 -> H(e, U1(e, b))
28.57/10.22	   A^2 -> H(e, U1(c, d))
28.57/10.22	   A^2 -> H(e, U1(d, c))
28.57/10.22	   A^2 -> H(e, U1(b, e))
28.57/10.22	   A^2 -> H(e, U1(b, k))
28.57/10.22	   A^2 -> H(e, U1(e, c))
28.57/10.22	   A^2 -> H(e, U1(c, e))
28.57/10.22	   A^2 -> H(e, U1(c, k))
28.57/10.22	   A^2 -> H(e, U1(e, e))
28.57/10.22	   A^2 -> H(e, U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, e), b)
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, e), c)
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.22	   A^2 -> H(f(e), d)
28.57/10.22	   A^2 -> H(f(e), k)
28.57/10.22	   A^2 -> H(U1(k, k), b)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, k), c)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.22	   A^2 -> H(f(k), d)
28.57/10.22	   A^2 -> H(f(k), k)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.22	   A^2 -> H(U1(k, d), b)
28.57/10.22	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, d), c)
28.57/10.22	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, k), b)
28.57/10.22	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(d, k), c)
28.57/10.22	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.22	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.22	   A^2 -> H(U1(d, k), e)
28.57/10.22	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, d), d)
28.57/10.22	   A^2 -> H(U1(d, d), k)
28.57/10.22	   A^2 -> H(U1(e, c), c)
28.57/10.22	   A^2 -> H(U1(c, c), e)
28.57/10.22	   A^2 -> H(U1(c, c), k)
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(e, e), e)
28.57/10.22	   A^2 -> H(d, U1(e, b))
28.57/10.22	   A^2 -> H(d, U1(k, b))
28.57/10.22	   A^2 -> H(d, U1(c, d))
28.57/10.22	   A^2 -> H(d, U1(d, c))
28.57/10.22	   A^2 -> H(d, U1(b, e))
28.57/10.22	   A^2 -> H(d, U1(b, k))
28.57/10.22	   A^2 -> H(d, U1(e, c))
28.57/10.22	   A^2 -> H(d, U1(k, c))
28.57/10.22	   A^2 -> H(d, U1(c, e))
28.57/10.22	   A^2 -> H(d, U1(c, k))
28.57/10.22	   A^2 -> H(d, U1(e, e))
28.57/10.22	   A^2 -> H(d, U1(k, k))
28.57/10.22	   A^2 -> H(d, U1(k, d))
28.57/10.22	   A^2 -> H(d, U1(d, k))
28.57/10.22	   A^2 -> H(a, b)
28.57/10.22	   A^2 -> H(a, U1(e, d))
28.57/10.22	   A^2 -> H(a, U1(d, e))
28.57/10.22	   A^2 -> H(a, c)
28.57/10.22	   A^2 -> H(a, U1(e, k))
28.57/10.22	   A^2 -> H(a, U1(k, e))
28.57/10.22	   A^2 -> H(a, e)
28.57/10.22	   A^2 -> H(a, U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, d), b)
28.57/10.22	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, d), c)
28.57/10.22	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, d), e)
28.57/10.22	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, a), d)
28.57/10.22	   A^2 -> H(U1(e, a), k)
28.57/10.22	   A^2 -> H(U1(k, a), d)
28.57/10.22	   A^2 -> H(U1(c, d), d)
28.57/10.22	   A^2 -> H(U1(c, d), k)
28.57/10.22	   A^2 -> H(U1(d, e), b)
28.57/10.22	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(d, e), c)
28.57/10.22	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(d, e), e)
28.57/10.22	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, c), d)
28.57/10.22	   A^2 -> H(U1(d, c), k)
28.57/10.22	   A^2 -> H(U1(a, e), d)
28.57/10.22	   A^2 -> H(U1(a, e), k)
28.57/10.22	   A^2 -> H(U1(a, k), d)
28.57/10.22	   A^2 -> H(U1(a, k), k)
28.57/10.22	   A^2 -> H(k, U1(e, b))
28.57/10.22	   A^2 -> H(k, U1(c, d))
28.57/10.22	   A^2 -> H(k, U1(d, c))
28.57/10.22	   A^2 -> H(k, U1(b, e))
28.57/10.22	   A^2 -> H(k, U1(b, k))
28.57/10.22	   A^2 -> H(k, U1(e, c))
28.57/10.22	   A^2 -> H(k, U1(c, e))
28.57/10.22	   A^2 -> H(k, U1(c, k))
28.57/10.22	   A^2 -> H(k, U1(e, e))
28.57/10.22	   A^2 -> H(k, U1(d, k))
28.57/10.22	   A^2 -> H(c, b)
28.57/10.22	   A^2 -> H(c, U1(e, d))
28.57/10.22	
28.57/10.22	The TRS R consists of the following rules:
28.57/10.22	
28.57/10.22	   f(x) -> U1(x, x)
28.57/10.22	   U1(e, x) -> x
28.57/10.22	   a -> c
28.57/10.22	   a -> d
28.57/10.22	   b -> c
28.57/10.22	   b -> d
28.57/10.22	   d -> k
28.57/10.22	   c -> e
28.57/10.22	   c -> k
28.57/10.22	
28.57/10.22	Q is empty.
28.57/10.22	We have to consider all minimal (P,Q,R)-chains.
28.57/10.22	----------------------------------------
28.57/10.22	
28.57/10.22	(2051) TransformationProof (EQUIVALENT)
28.57/10.22	By narrowing [LPAR04] the rule A^2 -> H(c, U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.22	
28.57/10.22	   (A^2 -> H(e, U1(c, d)),A^2 -> H(e, U1(c, d)))
28.57/10.22	   (A^2 -> H(k, U1(c, d)),A^2 -> H(k, U1(c, d)))
28.57/10.22	   (A^2 -> H(c, U1(e, d)),A^2 -> H(c, U1(e, d)))
28.57/10.22	   (A^2 -> H(c, U1(k, d)),A^2 -> H(c, U1(k, d)))
28.57/10.22	   (A^2 -> H(c, U1(c, k)),A^2 -> H(c, U1(c, k)))
28.57/10.22	
28.57/10.22	
28.57/10.22	----------------------------------------
28.57/10.22	
28.57/10.22	(2052)
28.57/10.22	Obligation:
28.57/10.22	Q DP problem:
28.57/10.22	The TRS P consists of the following rules:
28.57/10.22	
28.57/10.22	   G(d, x, x) -> A^2
28.57/10.22	   A^2 -> H(f(c), f(c))
28.57/10.22	   H(x, x) -> G(x, x, f(k))
28.57/10.22	   A^2 -> H(f(d), f(d))
28.57/10.22	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.22	   A^2 -> H(f(e), f(e))
28.57/10.22	   A^2 -> H(f(k), f(k))
28.57/10.22	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.22	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.22	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.22	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.22	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.22	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.22	   A^2 -> H(c, U1(d, c))
28.57/10.22	   A^2 -> H(c, U1(b, e))
28.57/10.22	   A^2 -> H(c, U1(b, k))
28.57/10.22	   A^2 -> H(c, U1(e, c))
28.57/10.22	   A^2 -> H(c, U1(k, c))
28.57/10.22	   A^2 -> H(c, U1(c, e))
28.57/10.22	   A^2 -> H(c, U1(c, k))
28.57/10.22	   A^2 -> H(c, U1(e, e))
28.57/10.22	   A^2 -> H(c, U1(k, k))
28.57/10.22	   A^2 -> H(c, U1(k, d))
28.57/10.22	   A^2 -> H(c, U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.22	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.22	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, c), b)
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, c), e)
28.57/10.22	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.22	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.22	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.22	   A^2 -> H(U1(k, c), b)
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, c), c)
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, e), b)
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(c, e), c)
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(c, e), e)
28.57/10.22	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, k), b)
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(c, k), c)
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.22	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.22	   A^2 -> H(U1(c, k), e)
28.57/10.22	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, c), d)
28.57/10.22	   A^2 -> H(e, U1(e, b))
28.57/10.22	   A^2 -> H(e, U1(c, d))
28.57/10.22	   A^2 -> H(e, U1(d, c))
28.57/10.22	   A^2 -> H(e, U1(b, e))
28.57/10.22	   A^2 -> H(e, U1(b, k))
28.57/10.22	   A^2 -> H(e, U1(e, c))
28.57/10.22	   A^2 -> H(e, U1(c, e))
28.57/10.22	   A^2 -> H(e, U1(c, k))
28.57/10.22	   A^2 -> H(e, U1(e, e))
28.57/10.22	   A^2 -> H(e, U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, e), b)
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, e), c)
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.22	   A^2 -> H(f(e), d)
28.57/10.22	   A^2 -> H(f(e), k)
28.57/10.22	   A^2 -> H(U1(k, k), b)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, k), c)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.22	   A^2 -> H(f(k), d)
28.57/10.22	   A^2 -> H(f(k), k)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.22	   A^2 -> H(U1(k, d), b)
28.57/10.22	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, d), c)
28.57/10.22	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, k), b)
28.57/10.22	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(d, k), c)
28.57/10.22	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.22	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.22	   A^2 -> H(U1(d, k), e)
28.57/10.22	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, d), d)
28.57/10.22	   A^2 -> H(U1(d, d), k)
28.57/10.22	   A^2 -> H(U1(e, c), c)
28.57/10.22	   A^2 -> H(U1(c, c), e)
28.57/10.22	   A^2 -> H(U1(c, c), k)
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(e, e), e)
28.57/10.22	   A^2 -> H(d, U1(e, b))
28.57/10.22	   A^2 -> H(d, U1(k, b))
28.57/10.22	   A^2 -> H(d, U1(c, d))
28.57/10.22	   A^2 -> H(d, U1(d, c))
28.57/10.22	   A^2 -> H(d, U1(b, e))
28.57/10.22	   A^2 -> H(d, U1(b, k))
28.57/10.22	   A^2 -> H(d, U1(e, c))
28.57/10.22	   A^2 -> H(d, U1(k, c))
28.57/10.22	   A^2 -> H(d, U1(c, e))
28.57/10.22	   A^2 -> H(d, U1(c, k))
28.57/10.22	   A^2 -> H(d, U1(e, e))
28.57/10.22	   A^2 -> H(d, U1(k, k))
28.57/10.22	   A^2 -> H(d, U1(k, d))
28.57/10.22	   A^2 -> H(d, U1(d, k))
28.57/10.22	   A^2 -> H(a, b)
28.57/10.22	   A^2 -> H(a, U1(e, d))
28.57/10.22	   A^2 -> H(a, U1(d, e))
28.57/10.22	   A^2 -> H(a, c)
28.57/10.22	   A^2 -> H(a, U1(e, k))
28.57/10.22	   A^2 -> H(a, U1(k, e))
28.57/10.22	   A^2 -> H(a, e)
28.57/10.22	   A^2 -> H(a, U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, d), b)
28.57/10.22	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, d), c)
28.57/10.22	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, d), e)
28.57/10.22	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, a), d)
28.57/10.22	   A^2 -> H(U1(e, a), k)
28.57/10.22	   A^2 -> H(U1(k, a), d)
28.57/10.22	   A^2 -> H(U1(c, d), d)
28.57/10.22	   A^2 -> H(U1(c, d), k)
28.57/10.22	   A^2 -> H(U1(d, e), b)
28.57/10.22	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(d, e), c)
28.57/10.22	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(d, e), e)
28.57/10.22	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, c), d)
28.57/10.22	   A^2 -> H(U1(d, c), k)
28.57/10.22	   A^2 -> H(U1(a, e), d)
28.57/10.22	   A^2 -> H(U1(a, e), k)
28.57/10.22	   A^2 -> H(U1(a, k), d)
28.57/10.22	   A^2 -> H(U1(a, k), k)
28.57/10.22	   A^2 -> H(k, U1(e, b))
28.57/10.22	   A^2 -> H(k, U1(c, d))
28.57/10.22	   A^2 -> H(k, U1(d, c))
28.57/10.22	   A^2 -> H(k, U1(b, e))
28.57/10.22	   A^2 -> H(k, U1(b, k))
28.57/10.22	   A^2 -> H(k, U1(e, c))
28.57/10.22	   A^2 -> H(k, U1(c, e))
28.57/10.22	   A^2 -> H(k, U1(c, k))
28.57/10.22	   A^2 -> H(k, U1(e, e))
28.57/10.22	   A^2 -> H(k, U1(d, k))
28.57/10.22	   A^2 -> H(c, b)
28.57/10.22	   A^2 -> H(c, U1(e, d))
28.57/10.22	
28.57/10.22	The TRS R consists of the following rules:
28.57/10.22	
28.57/10.22	   f(x) -> U1(x, x)
28.57/10.22	   U1(e, x) -> x
28.57/10.22	   a -> c
28.57/10.22	   a -> d
28.57/10.22	   b -> c
28.57/10.22	   b -> d
28.57/10.22	   d -> k
28.57/10.22	   c -> e
28.57/10.22	   c -> k
28.57/10.22	
28.57/10.22	Q is empty.
28.57/10.22	We have to consider all minimal (P,Q,R)-chains.
28.57/10.22	----------------------------------------
28.57/10.22	
28.57/10.22	(2053) TransformationProof (EQUIVALENT)
28.57/10.22	By narrowing [LPAR04] the rule A^2 -> H(c, U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.22	
28.57/10.22	   (A^2 -> H(e, U1(d, c)),A^2 -> H(e, U1(d, c)))
28.57/10.22	   (A^2 -> H(k, U1(d, c)),A^2 -> H(k, U1(d, c)))
28.57/10.22	   (A^2 -> H(c, U1(k, c)),A^2 -> H(c, U1(k, c)))
28.57/10.22	   (A^2 -> H(c, U1(d, e)),A^2 -> H(c, U1(d, e)))
28.57/10.22	   (A^2 -> H(c, U1(d, k)),A^2 -> H(c, U1(d, k)))
28.57/10.22	
28.57/10.22	
28.57/10.22	----------------------------------------
28.57/10.22	
28.57/10.22	(2054)
28.57/10.22	Obligation:
28.57/10.22	Q DP problem:
28.57/10.22	The TRS P consists of the following rules:
28.57/10.22	
28.57/10.22	   G(d, x, x) -> A^2
28.57/10.22	   A^2 -> H(f(c), f(c))
28.57/10.22	   H(x, x) -> G(x, x, f(k))
28.57/10.22	   A^2 -> H(f(d), f(d))
28.57/10.22	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.22	   A^2 -> H(f(e), f(e))
28.57/10.22	   A^2 -> H(f(k), f(k))
28.57/10.22	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.22	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.22	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.22	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.22	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.22	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.22	   A^2 -> H(c, U1(b, e))
28.57/10.22	   A^2 -> H(c, U1(b, k))
28.57/10.22	   A^2 -> H(c, U1(e, c))
28.57/10.22	   A^2 -> H(c, U1(k, c))
28.57/10.22	   A^2 -> H(c, U1(c, e))
28.57/10.22	   A^2 -> H(c, U1(c, k))
28.57/10.22	   A^2 -> H(c, U1(e, e))
28.57/10.22	   A^2 -> H(c, U1(k, k))
28.57/10.22	   A^2 -> H(c, U1(k, d))
28.57/10.22	   A^2 -> H(c, U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.22	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.22	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, c), b)
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, c), e)
28.57/10.22	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.22	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.22	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.22	   A^2 -> H(U1(k, c), b)
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, c), c)
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, e), b)
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(c, e), c)
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(c, e), e)
28.57/10.22	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, k), b)
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(c, k), c)
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.22	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.22	   A^2 -> H(U1(c, k), e)
28.57/10.22	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, c), d)
28.57/10.22	   A^2 -> H(e, U1(e, b))
28.57/10.22	   A^2 -> H(e, U1(c, d))
28.57/10.22	   A^2 -> H(e, U1(d, c))
28.57/10.22	   A^2 -> H(e, U1(b, e))
28.57/10.22	   A^2 -> H(e, U1(b, k))
28.57/10.22	   A^2 -> H(e, U1(e, c))
28.57/10.22	   A^2 -> H(e, U1(c, e))
28.57/10.22	   A^2 -> H(e, U1(c, k))
28.57/10.22	   A^2 -> H(e, U1(e, e))
28.57/10.22	   A^2 -> H(e, U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, e), b)
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, e), c)
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.22	   A^2 -> H(f(e), d)
28.57/10.22	   A^2 -> H(f(e), k)
28.57/10.22	   A^2 -> H(U1(k, k), b)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, k), c)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.22	   A^2 -> H(f(k), d)
28.57/10.22	   A^2 -> H(f(k), k)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.22	   A^2 -> H(U1(k, d), b)
28.57/10.22	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, d), c)
28.57/10.22	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, k), b)
28.57/10.22	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(d, k), c)
28.57/10.22	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.22	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.22	   A^2 -> H(U1(d, k), e)
28.57/10.22	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, d), d)
28.57/10.22	   A^2 -> H(U1(d, d), k)
28.57/10.22	   A^2 -> H(U1(e, c), c)
28.57/10.22	   A^2 -> H(U1(c, c), e)
28.57/10.22	   A^2 -> H(U1(c, c), k)
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(e, e), e)
28.57/10.22	   A^2 -> H(d, U1(e, b))
28.57/10.22	   A^2 -> H(d, U1(k, b))
28.57/10.22	   A^2 -> H(d, U1(c, d))
28.57/10.22	   A^2 -> H(d, U1(d, c))
28.57/10.22	   A^2 -> H(d, U1(b, e))
28.57/10.22	   A^2 -> H(d, U1(b, k))
28.57/10.22	   A^2 -> H(d, U1(e, c))
28.57/10.22	   A^2 -> H(d, U1(k, c))
28.57/10.22	   A^2 -> H(d, U1(c, e))
28.57/10.22	   A^2 -> H(d, U1(c, k))
28.57/10.22	   A^2 -> H(d, U1(e, e))
28.57/10.22	   A^2 -> H(d, U1(k, k))
28.57/10.22	   A^2 -> H(d, U1(k, d))
28.57/10.22	   A^2 -> H(d, U1(d, k))
28.57/10.22	   A^2 -> H(a, b)
28.57/10.22	   A^2 -> H(a, U1(e, d))
28.57/10.22	   A^2 -> H(a, U1(d, e))
28.57/10.22	   A^2 -> H(a, c)
28.57/10.22	   A^2 -> H(a, U1(e, k))
28.57/10.22	   A^2 -> H(a, U1(k, e))
28.57/10.22	   A^2 -> H(a, e)
28.57/10.22	   A^2 -> H(a, U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, d), b)
28.57/10.22	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, d), c)
28.57/10.22	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, d), e)
28.57/10.22	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, a), d)
28.57/10.22	   A^2 -> H(U1(e, a), k)
28.57/10.22	   A^2 -> H(U1(k, a), d)
28.57/10.22	   A^2 -> H(U1(c, d), d)
28.57/10.22	   A^2 -> H(U1(c, d), k)
28.57/10.22	   A^2 -> H(U1(d, e), b)
28.57/10.22	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(d, e), c)
28.57/10.22	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(d, e), e)
28.57/10.22	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, c), d)
28.57/10.22	   A^2 -> H(U1(d, c), k)
28.57/10.22	   A^2 -> H(U1(a, e), d)
28.57/10.22	   A^2 -> H(U1(a, e), k)
28.57/10.22	   A^2 -> H(U1(a, k), d)
28.57/10.22	   A^2 -> H(U1(a, k), k)
28.57/10.22	   A^2 -> H(k, U1(e, b))
28.57/10.22	   A^2 -> H(k, U1(c, d))
28.57/10.22	   A^2 -> H(k, U1(d, c))
28.57/10.22	   A^2 -> H(k, U1(b, e))
28.57/10.22	   A^2 -> H(k, U1(b, k))
28.57/10.22	   A^2 -> H(k, U1(e, c))
28.57/10.22	   A^2 -> H(k, U1(c, e))
28.57/10.22	   A^2 -> H(k, U1(c, k))
28.57/10.22	   A^2 -> H(k, U1(e, e))
28.57/10.22	   A^2 -> H(k, U1(d, k))
28.57/10.22	   A^2 -> H(c, b)
28.57/10.22	   A^2 -> H(c, U1(e, d))
28.57/10.22	   A^2 -> H(c, U1(d, e))
28.57/10.22	
28.57/10.22	The TRS R consists of the following rules:
28.57/10.22	
28.57/10.22	   f(x) -> U1(x, x)
28.57/10.22	   U1(e, x) -> x
28.57/10.22	   a -> c
28.57/10.22	   a -> d
28.57/10.22	   b -> c
28.57/10.22	   b -> d
28.57/10.22	   d -> k
28.57/10.22	   c -> e
28.57/10.22	   c -> k
28.57/10.22	
28.57/10.22	Q is empty.
28.57/10.22	We have to consider all minimal (P,Q,R)-chains.
28.57/10.22	----------------------------------------
28.57/10.22	
28.57/10.22	(2055) TransformationProof (EQUIVALENT)
28.57/10.22	By narrowing [LPAR04] the rule A^2 -> H(c, U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.22	
28.57/10.22	   (A^2 -> H(e, U1(b, e)),A^2 -> H(e, U1(b, e)))
28.57/10.22	   (A^2 -> H(k, U1(b, e)),A^2 -> H(k, U1(b, e)))
28.57/10.22	   (A^2 -> H(c, U1(c, e)),A^2 -> H(c, U1(c, e)))
28.57/10.22	   (A^2 -> H(c, U1(d, e)),A^2 -> H(c, U1(d, e)))
28.57/10.22	
28.57/10.22	
28.57/10.22	----------------------------------------
28.57/10.22	
28.57/10.22	(2056)
28.57/10.22	Obligation:
28.57/10.22	Q DP problem:
28.57/10.22	The TRS P consists of the following rules:
28.57/10.22	
28.57/10.22	   G(d, x, x) -> A^2
28.57/10.22	   A^2 -> H(f(c), f(c))
28.57/10.22	   H(x, x) -> G(x, x, f(k))
28.57/10.22	   A^2 -> H(f(d), f(d))
28.57/10.22	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.22	   A^2 -> H(f(e), f(e))
28.57/10.22	   A^2 -> H(f(k), f(k))
28.57/10.22	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.22	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.22	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.22	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.22	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.22	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.22	   A^2 -> H(c, U1(b, k))
28.57/10.22	   A^2 -> H(c, U1(e, c))
28.57/10.22	   A^2 -> H(c, U1(k, c))
28.57/10.22	   A^2 -> H(c, U1(c, e))
28.57/10.22	   A^2 -> H(c, U1(c, k))
28.57/10.22	   A^2 -> H(c, U1(e, e))
28.57/10.22	   A^2 -> H(c, U1(k, k))
28.57/10.22	   A^2 -> H(c, U1(k, d))
28.57/10.22	   A^2 -> H(c, U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.22	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.22	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, c), b)
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, c), e)
28.57/10.22	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.22	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.22	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.22	   A^2 -> H(U1(k, c), b)
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, c), c)
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, e), b)
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(c, e), c)
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(c, e), e)
28.57/10.22	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, k), b)
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(c, k), c)
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.22	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.22	   A^2 -> H(U1(c, k), e)
28.57/10.22	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, c), d)
28.57/10.22	   A^2 -> H(e, U1(e, b))
28.57/10.22	   A^2 -> H(e, U1(c, d))
28.57/10.22	   A^2 -> H(e, U1(d, c))
28.57/10.22	   A^2 -> H(e, U1(b, e))
28.57/10.22	   A^2 -> H(e, U1(b, k))
28.57/10.22	   A^2 -> H(e, U1(e, c))
28.57/10.22	   A^2 -> H(e, U1(c, e))
28.57/10.22	   A^2 -> H(e, U1(c, k))
28.57/10.22	   A^2 -> H(e, U1(e, e))
28.57/10.22	   A^2 -> H(e, U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, e), b)
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, e), c)
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.22	   A^2 -> H(f(e), d)
28.57/10.22	   A^2 -> H(f(e), k)
28.57/10.22	   A^2 -> H(U1(k, k), b)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, k), c)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.22	   A^2 -> H(f(k), d)
28.57/10.22	   A^2 -> H(f(k), k)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.22	   A^2 -> H(U1(k, d), b)
28.57/10.22	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, d), c)
28.57/10.22	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, k), b)
28.57/10.22	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(d, k), c)
28.57/10.22	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.22	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.22	   A^2 -> H(U1(d, k), e)
28.57/10.22	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, d), d)
28.57/10.22	   A^2 -> H(U1(d, d), k)
28.57/10.22	   A^2 -> H(U1(e, c), c)
28.57/10.22	   A^2 -> H(U1(c, c), e)
28.57/10.22	   A^2 -> H(U1(c, c), k)
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(e, e), e)
28.57/10.22	   A^2 -> H(d, U1(e, b))
28.57/10.22	   A^2 -> H(d, U1(k, b))
28.57/10.22	   A^2 -> H(d, U1(c, d))
28.57/10.22	   A^2 -> H(d, U1(d, c))
28.57/10.22	   A^2 -> H(d, U1(b, e))
28.57/10.22	   A^2 -> H(d, U1(b, k))
28.57/10.22	   A^2 -> H(d, U1(e, c))
28.57/10.22	   A^2 -> H(d, U1(k, c))
28.57/10.22	   A^2 -> H(d, U1(c, e))
28.57/10.22	   A^2 -> H(d, U1(c, k))
28.57/10.22	   A^2 -> H(d, U1(e, e))
28.57/10.22	   A^2 -> H(d, U1(k, k))
28.57/10.22	   A^2 -> H(d, U1(k, d))
28.57/10.22	   A^2 -> H(d, U1(d, k))
28.57/10.22	   A^2 -> H(a, b)
28.57/10.22	   A^2 -> H(a, U1(e, d))
28.57/10.22	   A^2 -> H(a, U1(d, e))
28.57/10.22	   A^2 -> H(a, c)
28.57/10.22	   A^2 -> H(a, U1(e, k))
28.57/10.22	   A^2 -> H(a, U1(k, e))
28.57/10.22	   A^2 -> H(a, e)
28.57/10.22	   A^2 -> H(a, U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, d), b)
28.57/10.22	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, d), c)
28.57/10.22	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, d), e)
28.57/10.22	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, a), d)
28.57/10.22	   A^2 -> H(U1(e, a), k)
28.57/10.22	   A^2 -> H(U1(k, a), d)
28.57/10.22	   A^2 -> H(U1(c, d), d)
28.57/10.22	   A^2 -> H(U1(c, d), k)
28.57/10.22	   A^2 -> H(U1(d, e), b)
28.57/10.22	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(d, e), c)
28.57/10.22	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(d, e), e)
28.57/10.22	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, c), d)
28.57/10.22	   A^2 -> H(U1(d, c), k)
28.57/10.22	   A^2 -> H(U1(a, e), d)
28.57/10.22	   A^2 -> H(U1(a, e), k)
28.57/10.22	   A^2 -> H(U1(a, k), d)
28.57/10.22	   A^2 -> H(U1(a, k), k)
28.57/10.22	   A^2 -> H(k, U1(e, b))
28.57/10.22	   A^2 -> H(k, U1(c, d))
28.57/10.22	   A^2 -> H(k, U1(d, c))
28.57/10.22	   A^2 -> H(k, U1(b, e))
28.57/10.22	   A^2 -> H(k, U1(b, k))
28.57/10.22	   A^2 -> H(k, U1(e, c))
28.57/10.22	   A^2 -> H(k, U1(c, e))
28.57/10.22	   A^2 -> H(k, U1(c, k))
28.57/10.22	   A^2 -> H(k, U1(e, e))
28.57/10.22	   A^2 -> H(k, U1(d, k))
28.57/10.22	   A^2 -> H(c, b)
28.57/10.22	   A^2 -> H(c, U1(e, d))
28.57/10.22	   A^2 -> H(c, U1(d, e))
28.57/10.22	
28.57/10.22	The TRS R consists of the following rules:
28.57/10.22	
28.57/10.22	   f(x) -> U1(x, x)
28.57/10.22	   U1(e, x) -> x
28.57/10.22	   a -> c
28.57/10.22	   a -> d
28.57/10.22	   b -> c
28.57/10.22	   b -> d
28.57/10.22	   d -> k
28.57/10.22	   c -> e
28.57/10.22	   c -> k
28.57/10.22	
28.57/10.22	Q is empty.
28.57/10.22	We have to consider all minimal (P,Q,R)-chains.
28.57/10.22	----------------------------------------
28.57/10.22	
28.57/10.22	(2057) TransformationProof (EQUIVALENT)
28.57/10.22	By narrowing [LPAR04] the rule A^2 -> H(c, U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.22	
28.57/10.22	   (A^2 -> H(e, U1(b, k)),A^2 -> H(e, U1(b, k)))
28.57/10.22	   (A^2 -> H(k, U1(b, k)),A^2 -> H(k, U1(b, k)))
28.57/10.22	   (A^2 -> H(c, U1(c, k)),A^2 -> H(c, U1(c, k)))
28.57/10.22	   (A^2 -> H(c, U1(d, k)),A^2 -> H(c, U1(d, k)))
28.57/10.22	
28.57/10.22	
28.57/10.22	----------------------------------------
28.57/10.22	
28.57/10.22	(2058)
28.57/10.22	Obligation:
28.57/10.22	Q DP problem:
28.57/10.22	The TRS P consists of the following rules:
28.57/10.22	
28.57/10.22	   G(d, x, x) -> A^2
28.57/10.22	   A^2 -> H(f(c), f(c))
28.57/10.22	   H(x, x) -> G(x, x, f(k))
28.57/10.22	   A^2 -> H(f(d), f(d))
28.57/10.22	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.22	   A^2 -> H(f(e), f(e))
28.57/10.22	   A^2 -> H(f(k), f(k))
28.57/10.22	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.22	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.22	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.22	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.22	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.22	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.22	   A^2 -> H(c, U1(e, c))
28.57/10.22	   A^2 -> H(c, U1(k, c))
28.57/10.22	   A^2 -> H(c, U1(c, e))
28.57/10.22	   A^2 -> H(c, U1(c, k))
28.57/10.22	   A^2 -> H(c, U1(e, e))
28.57/10.22	   A^2 -> H(c, U1(k, k))
28.57/10.22	   A^2 -> H(c, U1(k, d))
28.57/10.22	   A^2 -> H(c, U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.22	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.22	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, c), b)
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, c), e)
28.57/10.22	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.22	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.22	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.22	   A^2 -> H(U1(k, c), b)
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, c), c)
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, e), b)
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(c, e), c)
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(c, e), e)
28.57/10.22	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, k), b)
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(c, k), c)
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.22	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.22	   A^2 -> H(U1(c, k), e)
28.57/10.22	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, c), d)
28.57/10.22	   A^2 -> H(e, U1(e, b))
28.57/10.22	   A^2 -> H(e, U1(c, d))
28.57/10.22	   A^2 -> H(e, U1(d, c))
28.57/10.22	   A^2 -> H(e, U1(b, e))
28.57/10.22	   A^2 -> H(e, U1(b, k))
28.57/10.22	   A^2 -> H(e, U1(e, c))
28.57/10.22	   A^2 -> H(e, U1(c, e))
28.57/10.22	   A^2 -> H(e, U1(c, k))
28.57/10.22	   A^2 -> H(e, U1(e, e))
28.57/10.22	   A^2 -> H(e, U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, e), b)
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, e), c)
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.22	   A^2 -> H(f(e), d)
28.57/10.22	   A^2 -> H(f(e), k)
28.57/10.22	   A^2 -> H(U1(k, k), b)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, k), c)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.22	   A^2 -> H(f(k), d)
28.57/10.22	   A^2 -> H(f(k), k)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.22	   A^2 -> H(U1(k, d), b)
28.57/10.22	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, d), c)
28.57/10.22	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, k), b)
28.57/10.22	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(d, k), c)
28.57/10.22	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.22	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.22	   A^2 -> H(U1(d, k), e)
28.57/10.22	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, d), d)
28.57/10.22	   A^2 -> H(U1(d, d), k)
28.57/10.22	   A^2 -> H(U1(e, c), c)
28.57/10.22	   A^2 -> H(U1(c, c), e)
28.57/10.22	   A^2 -> H(U1(c, c), k)
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(e, e), e)
28.57/10.22	   A^2 -> H(d, U1(e, b))
28.57/10.22	   A^2 -> H(d, U1(k, b))
28.57/10.22	   A^2 -> H(d, U1(c, d))
28.57/10.22	   A^2 -> H(d, U1(d, c))
28.57/10.22	   A^2 -> H(d, U1(b, e))
28.57/10.22	   A^2 -> H(d, U1(b, k))
28.57/10.22	   A^2 -> H(d, U1(e, c))
28.57/10.22	   A^2 -> H(d, U1(k, c))
28.57/10.22	   A^2 -> H(d, U1(c, e))
28.57/10.22	   A^2 -> H(d, U1(c, k))
28.57/10.22	   A^2 -> H(d, U1(e, e))
28.57/10.22	   A^2 -> H(d, U1(k, k))
28.57/10.22	   A^2 -> H(d, U1(k, d))
28.57/10.22	   A^2 -> H(d, U1(d, k))
28.57/10.22	   A^2 -> H(a, b)
28.57/10.22	   A^2 -> H(a, U1(e, d))
28.57/10.22	   A^2 -> H(a, U1(d, e))
28.57/10.22	   A^2 -> H(a, c)
28.57/10.22	   A^2 -> H(a, U1(e, k))
28.57/10.22	   A^2 -> H(a, U1(k, e))
28.57/10.22	   A^2 -> H(a, e)
28.57/10.22	   A^2 -> H(a, U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, d), b)
28.57/10.22	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, d), c)
28.57/10.22	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, d), e)
28.57/10.22	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, a), d)
28.57/10.22	   A^2 -> H(U1(e, a), k)
28.57/10.22	   A^2 -> H(U1(k, a), d)
28.57/10.22	   A^2 -> H(U1(c, d), d)
28.57/10.22	   A^2 -> H(U1(c, d), k)
28.57/10.22	   A^2 -> H(U1(d, e), b)
28.57/10.22	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(d, e), c)
28.57/10.22	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(d, e), e)
28.57/10.22	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, c), d)
28.57/10.22	   A^2 -> H(U1(d, c), k)
28.57/10.22	   A^2 -> H(U1(a, e), d)
28.57/10.22	   A^2 -> H(U1(a, e), k)
28.57/10.22	   A^2 -> H(U1(a, k), d)
28.57/10.22	   A^2 -> H(U1(a, k), k)
28.57/10.22	   A^2 -> H(k, U1(e, b))
28.57/10.22	   A^2 -> H(k, U1(c, d))
28.57/10.22	   A^2 -> H(k, U1(d, c))
28.57/10.22	   A^2 -> H(k, U1(b, e))
28.57/10.22	   A^2 -> H(k, U1(b, k))
28.57/10.22	   A^2 -> H(k, U1(e, c))
28.57/10.22	   A^2 -> H(k, U1(c, e))
28.57/10.22	   A^2 -> H(k, U1(c, k))
28.57/10.22	   A^2 -> H(k, U1(e, e))
28.57/10.22	   A^2 -> H(k, U1(d, k))
28.57/10.22	   A^2 -> H(c, b)
28.57/10.22	   A^2 -> H(c, U1(e, d))
28.57/10.22	   A^2 -> H(c, U1(d, e))
28.57/10.22	
28.57/10.22	The TRS R consists of the following rules:
28.57/10.22	
28.57/10.22	   f(x) -> U1(x, x)
28.57/10.22	   U1(e, x) -> x
28.57/10.22	   a -> c
28.57/10.22	   a -> d
28.57/10.22	   b -> c
28.57/10.22	   b -> d
28.57/10.22	   d -> k
28.57/10.22	   c -> e
28.57/10.22	   c -> k
28.57/10.22	
28.57/10.22	Q is empty.
28.57/10.22	We have to consider all minimal (P,Q,R)-chains.
28.57/10.22	----------------------------------------
28.57/10.22	
28.57/10.22	(2059) TransformationProof (EQUIVALENT)
28.57/10.22	By narrowing [LPAR04] the rule A^2 -> H(c, U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.22	
28.57/10.22	   (A^2 -> H(e, U1(e, c)),A^2 -> H(e, U1(e, c)))
28.57/10.22	   (A^2 -> H(k, U1(e, c)),A^2 -> H(k, U1(e, c)))
28.57/10.22	   (A^2 -> H(c, c),A^2 -> H(c, c))
28.57/10.22	   (A^2 -> H(c, U1(e, e)),A^2 -> H(c, U1(e, e)))
28.57/10.22	   (A^2 -> H(c, U1(e, k)),A^2 -> H(c, U1(e, k)))
28.57/10.22	
28.57/10.22	
28.57/10.22	----------------------------------------
28.57/10.22	
28.57/10.22	(2060)
28.57/10.22	Obligation:
28.57/10.22	Q DP problem:
28.57/10.22	The TRS P consists of the following rules:
28.57/10.22	
28.57/10.22	   G(d, x, x) -> A^2
28.57/10.22	   A^2 -> H(f(c), f(c))
28.57/10.22	   H(x, x) -> G(x, x, f(k))
28.57/10.22	   A^2 -> H(f(d), f(d))
28.57/10.22	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.22	   A^2 -> H(f(e), f(e))
28.57/10.22	   A^2 -> H(f(k), f(k))
28.57/10.22	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.22	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.22	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.22	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.22	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.22	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.22	   A^2 -> H(c, U1(k, c))
28.57/10.22	   A^2 -> H(c, U1(c, e))
28.57/10.22	   A^2 -> H(c, U1(c, k))
28.57/10.22	   A^2 -> H(c, U1(e, e))
28.57/10.22	   A^2 -> H(c, U1(k, k))
28.57/10.22	   A^2 -> H(c, U1(k, d))
28.57/10.22	   A^2 -> H(c, U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.22	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.22	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, c), b)
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, c), e)
28.57/10.22	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.22	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.22	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.22	   A^2 -> H(U1(k, c), b)
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, c), c)
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, e), b)
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(c, e), c)
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(c, e), e)
28.57/10.22	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, k), b)
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(c, k), c)
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.22	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.22	   A^2 -> H(U1(c, k), e)
28.57/10.22	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, c), d)
28.57/10.22	   A^2 -> H(e, U1(e, b))
28.57/10.22	   A^2 -> H(e, U1(c, d))
28.57/10.22	   A^2 -> H(e, U1(d, c))
28.57/10.22	   A^2 -> H(e, U1(b, e))
28.57/10.22	   A^2 -> H(e, U1(b, k))
28.57/10.22	   A^2 -> H(e, U1(e, c))
28.57/10.22	   A^2 -> H(e, U1(c, e))
28.57/10.22	   A^2 -> H(e, U1(c, k))
28.57/10.22	   A^2 -> H(e, U1(e, e))
28.57/10.22	   A^2 -> H(e, U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, e), b)
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, e), c)
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.22	   A^2 -> H(f(e), d)
28.57/10.22	   A^2 -> H(f(e), k)
28.57/10.22	   A^2 -> H(U1(k, k), b)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, k), c)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.22	   A^2 -> H(f(k), d)
28.57/10.22	   A^2 -> H(f(k), k)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.22	   A^2 -> H(U1(k, d), b)
28.57/10.22	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, d), c)
28.57/10.22	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, k), b)
28.57/10.22	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(d, k), c)
28.57/10.22	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.22	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.22	   A^2 -> H(U1(d, k), e)
28.57/10.22	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, d), d)
28.57/10.22	   A^2 -> H(U1(d, d), k)
28.57/10.22	   A^2 -> H(U1(e, c), c)
28.57/10.22	   A^2 -> H(U1(c, c), e)
28.57/10.22	   A^2 -> H(U1(c, c), k)
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(e, e), e)
28.57/10.22	   A^2 -> H(d, U1(e, b))
28.57/10.22	   A^2 -> H(d, U1(k, b))
28.57/10.22	   A^2 -> H(d, U1(c, d))
28.57/10.22	   A^2 -> H(d, U1(d, c))
28.57/10.22	   A^2 -> H(d, U1(b, e))
28.57/10.22	   A^2 -> H(d, U1(b, k))
28.57/10.22	   A^2 -> H(d, U1(e, c))
28.57/10.22	   A^2 -> H(d, U1(k, c))
28.57/10.22	   A^2 -> H(d, U1(c, e))
28.57/10.22	   A^2 -> H(d, U1(c, k))
28.57/10.22	   A^2 -> H(d, U1(e, e))
28.57/10.22	   A^2 -> H(d, U1(k, k))
28.57/10.22	   A^2 -> H(d, U1(k, d))
28.57/10.22	   A^2 -> H(d, U1(d, k))
28.57/10.22	   A^2 -> H(a, b)
28.57/10.22	   A^2 -> H(a, U1(e, d))
28.57/10.22	   A^2 -> H(a, U1(d, e))
28.57/10.22	   A^2 -> H(a, c)
28.57/10.22	   A^2 -> H(a, U1(e, k))
28.57/10.22	   A^2 -> H(a, U1(k, e))
28.57/10.22	   A^2 -> H(a, e)
28.57/10.22	   A^2 -> H(a, U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, d), b)
28.57/10.22	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, d), c)
28.57/10.22	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, d), e)
28.57/10.22	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, a), d)
28.57/10.22	   A^2 -> H(U1(e, a), k)
28.57/10.22	   A^2 -> H(U1(k, a), d)
28.57/10.22	   A^2 -> H(U1(c, d), d)
28.57/10.22	   A^2 -> H(U1(c, d), k)
28.57/10.22	   A^2 -> H(U1(d, e), b)
28.57/10.22	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(d, e), c)
28.57/10.22	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(d, e), e)
28.57/10.22	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, c), d)
28.57/10.22	   A^2 -> H(U1(d, c), k)
28.57/10.22	   A^2 -> H(U1(a, e), d)
28.57/10.22	   A^2 -> H(U1(a, e), k)
28.57/10.22	   A^2 -> H(U1(a, k), d)
28.57/10.22	   A^2 -> H(U1(a, k), k)
28.57/10.22	   A^2 -> H(k, U1(e, b))
28.57/10.22	   A^2 -> H(k, U1(c, d))
28.57/10.22	   A^2 -> H(k, U1(d, c))
28.57/10.22	   A^2 -> H(k, U1(b, e))
28.57/10.22	   A^2 -> H(k, U1(b, k))
28.57/10.22	   A^2 -> H(k, U1(e, c))
28.57/10.22	   A^2 -> H(k, U1(c, e))
28.57/10.22	   A^2 -> H(k, U1(c, k))
28.57/10.22	   A^2 -> H(k, U1(e, e))
28.57/10.22	   A^2 -> H(k, U1(d, k))
28.57/10.22	   A^2 -> H(c, b)
28.57/10.22	   A^2 -> H(c, U1(e, d))
28.57/10.22	   A^2 -> H(c, U1(d, e))
28.57/10.22	   A^2 -> H(c, c)
28.57/10.22	   A^2 -> H(c, U1(e, k))
28.57/10.22	
28.57/10.22	The TRS R consists of the following rules:
28.57/10.22	
28.57/10.22	   f(x) -> U1(x, x)
28.57/10.22	   U1(e, x) -> x
28.57/10.22	   a -> c
28.57/10.22	   a -> d
28.57/10.22	   b -> c
28.57/10.22	   b -> d
28.57/10.22	   d -> k
28.57/10.22	   c -> e
28.57/10.22	   c -> k
28.57/10.22	
28.57/10.22	Q is empty.
28.57/10.22	We have to consider all minimal (P,Q,R)-chains.
28.57/10.22	----------------------------------------
28.57/10.22	
28.57/10.22	(2061) TransformationProof (EQUIVALENT)
28.57/10.22	By narrowing [LPAR04] the rule A^2 -> H(c, U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.22	
28.57/10.22	   (A^2 -> H(e, U1(k, c)),A^2 -> H(e, U1(k, c)))
28.57/10.22	   (A^2 -> H(k, U1(k, c)),A^2 -> H(k, U1(k, c)))
28.57/10.22	   (A^2 -> H(c, U1(k, e)),A^2 -> H(c, U1(k, e)))
28.57/10.22	   (A^2 -> H(c, U1(k, k)),A^2 -> H(c, U1(k, k)))
28.57/10.22	
28.57/10.22	
28.57/10.22	----------------------------------------
28.57/10.22	
28.57/10.22	(2062)
28.57/10.22	Obligation:
28.57/10.22	Q DP problem:
28.57/10.22	The TRS P consists of the following rules:
28.57/10.22	
28.57/10.22	   G(d, x, x) -> A^2
28.57/10.22	   A^2 -> H(f(c), f(c))
28.57/10.22	   H(x, x) -> G(x, x, f(k))
28.57/10.22	   A^2 -> H(f(d), f(d))
28.57/10.22	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.22	   A^2 -> H(f(e), f(e))
28.57/10.22	   A^2 -> H(f(k), f(k))
28.57/10.22	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.22	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.22	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.22	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.22	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.22	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.22	   A^2 -> H(c, U1(c, e))
28.57/10.22	   A^2 -> H(c, U1(c, k))
28.57/10.22	   A^2 -> H(c, U1(e, e))
28.57/10.22	   A^2 -> H(c, U1(k, k))
28.57/10.22	   A^2 -> H(c, U1(k, d))
28.57/10.22	   A^2 -> H(c, U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.22	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.22	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, c), b)
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, c), e)
28.57/10.22	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.22	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.22	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.22	   A^2 -> H(U1(k, c), b)
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, c), c)
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, e), b)
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(c, e), c)
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(c, e), e)
28.57/10.22	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, k), b)
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(c, k), c)
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.22	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.22	   A^2 -> H(U1(c, k), e)
28.57/10.22	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, c), d)
28.57/10.22	   A^2 -> H(e, U1(e, b))
28.57/10.22	   A^2 -> H(e, U1(c, d))
28.57/10.22	   A^2 -> H(e, U1(d, c))
28.57/10.22	   A^2 -> H(e, U1(b, e))
28.57/10.22	   A^2 -> H(e, U1(b, k))
28.57/10.22	   A^2 -> H(e, U1(e, c))
28.57/10.22	   A^2 -> H(e, U1(c, e))
28.57/10.22	   A^2 -> H(e, U1(c, k))
28.57/10.22	   A^2 -> H(e, U1(e, e))
28.57/10.22	   A^2 -> H(e, U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, e), b)
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, e), c)
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.22	   A^2 -> H(f(e), d)
28.57/10.22	   A^2 -> H(f(e), k)
28.57/10.22	   A^2 -> H(U1(k, k), b)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, k), c)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.22	   A^2 -> H(f(k), d)
28.57/10.22	   A^2 -> H(f(k), k)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.22	   A^2 -> H(U1(k, d), b)
28.57/10.22	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, d), c)
28.57/10.22	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, k), b)
28.57/10.22	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(d, k), c)
28.57/10.22	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.22	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.22	   A^2 -> H(U1(d, k), e)
28.57/10.22	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, d), d)
28.57/10.22	   A^2 -> H(U1(d, d), k)
28.57/10.22	   A^2 -> H(U1(e, c), c)
28.57/10.22	   A^2 -> H(U1(c, c), e)
28.57/10.22	   A^2 -> H(U1(c, c), k)
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(e, e), e)
28.57/10.22	   A^2 -> H(d, U1(e, b))
28.57/10.22	   A^2 -> H(d, U1(k, b))
28.57/10.22	   A^2 -> H(d, U1(c, d))
28.57/10.22	   A^2 -> H(d, U1(d, c))
28.57/10.22	   A^2 -> H(d, U1(b, e))
28.57/10.22	   A^2 -> H(d, U1(b, k))
28.57/10.22	   A^2 -> H(d, U1(e, c))
28.57/10.22	   A^2 -> H(d, U1(k, c))
28.57/10.22	   A^2 -> H(d, U1(c, e))
28.57/10.22	   A^2 -> H(d, U1(c, k))
28.57/10.22	   A^2 -> H(d, U1(e, e))
28.57/10.22	   A^2 -> H(d, U1(k, k))
28.57/10.22	   A^2 -> H(d, U1(k, d))
28.57/10.22	   A^2 -> H(d, U1(d, k))
28.57/10.22	   A^2 -> H(a, b)
28.57/10.22	   A^2 -> H(a, U1(e, d))
28.57/10.22	   A^2 -> H(a, U1(d, e))
28.57/10.22	   A^2 -> H(a, c)
28.57/10.22	   A^2 -> H(a, U1(e, k))
28.57/10.22	   A^2 -> H(a, U1(k, e))
28.57/10.22	   A^2 -> H(a, e)
28.57/10.22	   A^2 -> H(a, U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, d), b)
28.57/10.22	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, d), c)
28.57/10.22	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, d), e)
28.57/10.22	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, a), d)
28.57/10.22	   A^2 -> H(U1(e, a), k)
28.57/10.22	   A^2 -> H(U1(k, a), d)
28.57/10.22	   A^2 -> H(U1(c, d), d)
28.57/10.22	   A^2 -> H(U1(c, d), k)
28.57/10.22	   A^2 -> H(U1(d, e), b)
28.57/10.22	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(d, e), c)
28.57/10.22	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(d, e), e)
28.57/10.22	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, c), d)
28.57/10.22	   A^2 -> H(U1(d, c), k)
28.57/10.22	   A^2 -> H(U1(a, e), d)
28.57/10.22	   A^2 -> H(U1(a, e), k)
28.57/10.22	   A^2 -> H(U1(a, k), d)
28.57/10.22	   A^2 -> H(U1(a, k), k)
28.57/10.22	   A^2 -> H(k, U1(e, b))
28.57/10.22	   A^2 -> H(k, U1(c, d))
28.57/10.22	   A^2 -> H(k, U1(d, c))
28.57/10.22	   A^2 -> H(k, U1(b, e))
28.57/10.22	   A^2 -> H(k, U1(b, k))
28.57/10.22	   A^2 -> H(k, U1(e, c))
28.57/10.22	   A^2 -> H(k, U1(c, e))
28.57/10.22	   A^2 -> H(k, U1(c, k))
28.57/10.22	   A^2 -> H(k, U1(e, e))
28.57/10.22	   A^2 -> H(k, U1(d, k))
28.57/10.22	   A^2 -> H(c, b)
28.57/10.22	   A^2 -> H(c, U1(e, d))
28.57/10.22	   A^2 -> H(c, U1(d, e))
28.57/10.22	   A^2 -> H(c, c)
28.57/10.22	   A^2 -> H(c, U1(e, k))
28.57/10.22	   A^2 -> H(e, U1(k, c))
28.57/10.22	   A^2 -> H(k, U1(k, c))
28.57/10.22	   A^2 -> H(c, U1(k, e))
28.57/10.22	
28.57/10.22	The TRS R consists of the following rules:
28.57/10.22	
28.57/10.22	   f(x) -> U1(x, x)
28.57/10.22	   U1(e, x) -> x
28.57/10.22	   a -> c
28.57/10.22	   a -> d
28.57/10.22	   b -> c
28.57/10.22	   b -> d
28.57/10.22	   d -> k
28.57/10.22	   c -> e
28.57/10.22	   c -> k
28.57/10.22	
28.57/10.22	Q is empty.
28.57/10.22	We have to consider all minimal (P,Q,R)-chains.
28.57/10.22	----------------------------------------
28.57/10.22	
28.57/10.22	(2063) DependencyGraphProof (EQUIVALENT)
28.57/10.22	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
28.57/10.22	----------------------------------------
28.57/10.22	
28.57/10.22	(2064)
28.57/10.22	Obligation:
28.57/10.22	Q DP problem:
28.57/10.22	The TRS P consists of the following rules:
28.57/10.22	
28.57/10.22	   A^2 -> H(f(c), f(c))
28.57/10.22	   H(x, x) -> G(x, x, f(k))
28.57/10.22	   G(d, x, x) -> A^2
28.57/10.22	   A^2 -> H(f(d), f(d))
28.57/10.22	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.22	   A^2 -> H(f(e), f(e))
28.57/10.22	   A^2 -> H(f(k), f(k))
28.57/10.22	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.22	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.22	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.22	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.22	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.22	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.22	   A^2 -> H(c, U1(c, e))
28.57/10.22	   A^2 -> H(c, U1(c, k))
28.57/10.22	   A^2 -> H(c, U1(e, e))
28.57/10.22	   A^2 -> H(c, U1(k, k))
28.57/10.22	   A^2 -> H(c, U1(k, d))
28.57/10.22	   A^2 -> H(c, U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.22	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.22	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, c), b)
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, c), e)
28.57/10.22	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.22	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.22	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.22	   A^2 -> H(U1(k, c), b)
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, c), c)
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, e), b)
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(c, e), c)
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(c, e), e)
28.57/10.22	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, k), b)
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(c, k), c)
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.22	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.22	   A^2 -> H(U1(c, k), e)
28.57/10.22	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, c), d)
28.57/10.22	   A^2 -> H(e, U1(e, b))
28.57/10.22	   A^2 -> H(e, U1(c, d))
28.57/10.22	   A^2 -> H(e, U1(d, c))
28.57/10.22	   A^2 -> H(e, U1(b, e))
28.57/10.22	   A^2 -> H(e, U1(b, k))
28.57/10.22	   A^2 -> H(e, U1(e, c))
28.57/10.22	   A^2 -> H(e, U1(c, e))
28.57/10.22	   A^2 -> H(e, U1(c, k))
28.57/10.22	   A^2 -> H(e, U1(e, e))
28.57/10.22	   A^2 -> H(e, U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, e), b)
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, e), c)
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.22	   A^2 -> H(f(e), d)
28.57/10.22	   A^2 -> H(f(e), k)
28.57/10.22	   A^2 -> H(U1(k, k), b)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, k), c)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.22	   A^2 -> H(f(k), d)
28.57/10.22	   A^2 -> H(f(k), k)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.22	   A^2 -> H(U1(k, d), b)
28.57/10.22	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, d), c)
28.57/10.22	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, k), b)
28.57/10.22	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(d, k), c)
28.57/10.22	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.22	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.22	   A^2 -> H(U1(d, k), e)
28.57/10.22	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, d), d)
28.57/10.22	   A^2 -> H(U1(d, d), k)
28.57/10.22	   A^2 -> H(U1(e, c), c)
28.57/10.22	   A^2 -> H(U1(c, c), e)
28.57/10.22	   A^2 -> H(U1(c, c), k)
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(e, e), e)
28.57/10.22	   A^2 -> H(d, U1(e, b))
28.57/10.22	   A^2 -> H(d, U1(k, b))
28.57/10.22	   A^2 -> H(d, U1(c, d))
28.57/10.22	   A^2 -> H(d, U1(d, c))
28.57/10.22	   A^2 -> H(d, U1(b, e))
28.57/10.22	   A^2 -> H(d, U1(b, k))
28.57/10.22	   A^2 -> H(d, U1(e, c))
28.57/10.22	   A^2 -> H(d, U1(k, c))
28.57/10.22	   A^2 -> H(d, U1(c, e))
28.57/10.22	   A^2 -> H(d, U1(c, k))
28.57/10.22	   A^2 -> H(d, U1(e, e))
28.57/10.22	   A^2 -> H(d, U1(k, k))
28.57/10.22	   A^2 -> H(d, U1(k, d))
28.57/10.22	   A^2 -> H(d, U1(d, k))
28.57/10.22	   A^2 -> H(a, b)
28.57/10.22	   A^2 -> H(a, U1(e, d))
28.57/10.22	   A^2 -> H(a, U1(d, e))
28.57/10.22	   A^2 -> H(a, c)
28.57/10.22	   A^2 -> H(a, U1(e, k))
28.57/10.22	   A^2 -> H(a, U1(k, e))
28.57/10.22	   A^2 -> H(a, e)
28.57/10.22	   A^2 -> H(a, U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, d), b)
28.57/10.22	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, d), c)
28.57/10.22	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, d), e)
28.57/10.22	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, a), d)
28.57/10.22	   A^2 -> H(U1(e, a), k)
28.57/10.22	   A^2 -> H(U1(k, a), d)
28.57/10.22	   A^2 -> H(U1(c, d), d)
28.57/10.22	   A^2 -> H(U1(c, d), k)
28.57/10.22	   A^2 -> H(U1(d, e), b)
28.57/10.22	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(d, e), c)
28.57/10.22	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(d, e), e)
28.57/10.22	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, c), d)
28.57/10.22	   A^2 -> H(U1(d, c), k)
28.57/10.22	   A^2 -> H(U1(a, e), d)
28.57/10.22	   A^2 -> H(U1(a, e), k)
28.57/10.22	   A^2 -> H(U1(a, k), d)
28.57/10.22	   A^2 -> H(U1(a, k), k)
28.57/10.22	   A^2 -> H(k, U1(e, b))
28.57/10.22	   A^2 -> H(k, U1(c, d))
28.57/10.22	   A^2 -> H(k, U1(d, c))
28.57/10.22	   A^2 -> H(k, U1(b, e))
28.57/10.22	   A^2 -> H(k, U1(b, k))
28.57/10.22	   A^2 -> H(k, U1(e, c))
28.57/10.22	   A^2 -> H(k, U1(c, e))
28.57/10.22	   A^2 -> H(k, U1(c, k))
28.57/10.22	   A^2 -> H(k, U1(e, e))
28.57/10.22	   A^2 -> H(k, U1(d, k))
28.57/10.22	   A^2 -> H(c, b)
28.57/10.22	   A^2 -> H(c, U1(e, d))
28.57/10.22	   A^2 -> H(c, U1(d, e))
28.57/10.22	   A^2 -> H(c, c)
28.57/10.22	   A^2 -> H(c, U1(e, k))
28.57/10.22	   A^2 -> H(c, U1(k, e))
28.57/10.22	
28.57/10.22	The TRS R consists of the following rules:
28.57/10.22	
28.57/10.22	   f(x) -> U1(x, x)
28.57/10.22	   U1(e, x) -> x
28.57/10.22	   a -> c
28.57/10.22	   a -> d
28.57/10.22	   b -> c
28.57/10.22	   b -> d
28.57/10.22	   d -> k
28.57/10.22	   c -> e
28.57/10.22	   c -> k
28.57/10.22	
28.57/10.22	Q is empty.
28.57/10.22	We have to consider all minimal (P,Q,R)-chains.
28.57/10.22	----------------------------------------
28.57/10.22	
28.57/10.22	(2065) TransformationProof (EQUIVALENT)
28.57/10.22	By narrowing [LPAR04] the rule A^2 -> H(c, U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.22	
28.57/10.22	   (A^2 -> H(e, U1(c, e)),A^2 -> H(e, U1(c, e)))
28.57/10.22	   (A^2 -> H(k, U1(c, e)),A^2 -> H(k, U1(c, e)))
28.57/10.22	   (A^2 -> H(c, U1(e, e)),A^2 -> H(c, U1(e, e)))
28.57/10.22	   (A^2 -> H(c, U1(k, e)),A^2 -> H(c, U1(k, e)))
28.57/10.22	
28.57/10.22	
28.57/10.22	----------------------------------------
28.57/10.22	
28.57/10.22	(2066)
28.57/10.22	Obligation:
28.57/10.22	Q DP problem:
28.57/10.22	The TRS P consists of the following rules:
28.57/10.22	
28.57/10.22	   A^2 -> H(f(c), f(c))
28.57/10.22	   H(x, x) -> G(x, x, f(k))
28.57/10.22	   G(d, x, x) -> A^2
28.57/10.22	   A^2 -> H(f(d), f(d))
28.57/10.22	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.22	   A^2 -> H(f(e), f(e))
28.57/10.22	   A^2 -> H(f(k), f(k))
28.57/10.22	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.22	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.22	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.22	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.22	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.22	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.22	   A^2 -> H(c, U1(c, k))
28.57/10.22	   A^2 -> H(c, U1(e, e))
28.57/10.22	   A^2 -> H(c, U1(k, k))
28.57/10.22	   A^2 -> H(c, U1(k, d))
28.57/10.22	   A^2 -> H(c, U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.22	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.22	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, c), b)
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, c), e)
28.57/10.22	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.22	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.22	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.22	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.22	   A^2 -> H(U1(k, c), b)
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, c), c)
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.22	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, e), b)
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(c, e), c)
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(c, e), e)
28.57/10.22	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, k), b)
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(c, k), c)
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.22	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.22	   A^2 -> H(U1(c, k), e)
28.57/10.22	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(c, c), d)
28.57/10.22	   A^2 -> H(e, U1(e, b))
28.57/10.22	   A^2 -> H(e, U1(c, d))
28.57/10.22	   A^2 -> H(e, U1(d, c))
28.57/10.22	   A^2 -> H(e, U1(b, e))
28.57/10.22	   A^2 -> H(e, U1(b, k))
28.57/10.22	   A^2 -> H(e, U1(e, c))
28.57/10.22	   A^2 -> H(e, U1(c, e))
28.57/10.22	   A^2 -> H(e, U1(c, k))
28.57/10.22	   A^2 -> H(e, U1(e, e))
28.57/10.22	   A^2 -> H(e, U1(d, k))
28.57/10.22	   A^2 -> H(U1(e, e), b)
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.22	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.22	   A^2 -> H(U1(e, e), c)
28.57/10.22	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.22	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.22	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.22	   A^2 -> H(f(e), d)
28.57/10.22	   A^2 -> H(f(e), k)
28.57/10.22	   A^2 -> H(U1(k, k), b)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, k), c)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.22	   A^2 -> H(f(k), d)
28.57/10.22	   A^2 -> H(f(k), k)
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.22	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.22	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.22	   A^2 -> H(U1(k, d), b)
28.57/10.22	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.22	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.22	   A^2 -> H(U1(k, d), c)
28.57/10.22	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.22	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, k), b)
28.57/10.22	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.22	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.22	   A^2 -> H(U1(d, k), c)
28.57/10.22	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.22	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.22	   A^2 -> H(U1(d, k), e)
28.57/10.22	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.22	   A^2 -> H(U1(d, d), d)
28.57/10.22	   A^2 -> H(U1(d, d), k)
28.57/10.22	   A^2 -> H(U1(e, c), c)
28.57/10.22	   A^2 -> H(U1(c, c), e)
28.57/10.22	   A^2 -> H(U1(c, c), k)
28.57/10.22	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.22	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.22	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.22	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.22	   A^2 -> H(U1(e, e), e)
28.57/10.22	   A^2 -> H(d, U1(e, b))
28.57/10.22	   A^2 -> H(d, U1(k, b))
28.57/10.22	   A^2 -> H(d, U1(c, d))
28.57/10.22	   A^2 -> H(d, U1(d, c))
28.57/10.22	   A^2 -> H(d, U1(b, e))
28.57/10.22	   A^2 -> H(d, U1(b, k))
28.57/10.23	   A^2 -> H(d, U1(e, c))
28.57/10.23	   A^2 -> H(d, U1(k, c))
28.57/10.23	   A^2 -> H(d, U1(c, e))
28.57/10.23	   A^2 -> H(d, U1(c, k))
28.57/10.23	   A^2 -> H(d, U1(e, e))
28.57/10.23	   A^2 -> H(d, U1(k, k))
28.57/10.23	   A^2 -> H(d, U1(k, d))
28.57/10.23	   A^2 -> H(d, U1(d, k))
28.57/10.23	   A^2 -> H(a, b)
28.57/10.23	   A^2 -> H(a, U1(e, d))
28.57/10.23	   A^2 -> H(a, U1(d, e))
28.57/10.23	   A^2 -> H(a, c)
28.57/10.23	   A^2 -> H(a, U1(e, k))
28.57/10.23	   A^2 -> H(a, U1(k, e))
28.57/10.23	   A^2 -> H(a, e)
28.57/10.23	   A^2 -> H(a, U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, d), b)
28.57/10.23	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, d), c)
28.57/10.23	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, d), e)
28.57/10.23	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, a), d)
28.57/10.23	   A^2 -> H(U1(e, a), k)
28.57/10.23	   A^2 -> H(U1(k, a), d)
28.57/10.23	   A^2 -> H(U1(c, d), d)
28.57/10.23	   A^2 -> H(U1(c, d), k)
28.57/10.23	   A^2 -> H(U1(d, e), b)
28.57/10.23	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(d, e), c)
28.57/10.23	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(d, e), e)
28.57/10.23	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, c), d)
28.57/10.23	   A^2 -> H(U1(d, c), k)
28.57/10.23	   A^2 -> H(U1(a, e), d)
28.57/10.23	   A^2 -> H(U1(a, e), k)
28.57/10.23	   A^2 -> H(U1(a, k), d)
28.57/10.23	   A^2 -> H(U1(a, k), k)
28.57/10.23	   A^2 -> H(k, U1(e, b))
28.57/10.23	   A^2 -> H(k, U1(c, d))
28.57/10.23	   A^2 -> H(k, U1(d, c))
28.57/10.23	   A^2 -> H(k, U1(b, e))
28.57/10.23	   A^2 -> H(k, U1(b, k))
28.57/10.23	   A^2 -> H(k, U1(e, c))
28.57/10.23	   A^2 -> H(k, U1(c, e))
28.57/10.23	   A^2 -> H(k, U1(c, k))
28.57/10.23	   A^2 -> H(k, U1(e, e))
28.57/10.23	   A^2 -> H(k, U1(d, k))
28.57/10.23	   A^2 -> H(c, b)
28.57/10.23	   A^2 -> H(c, U1(e, d))
28.57/10.23	   A^2 -> H(c, U1(d, e))
28.57/10.23	   A^2 -> H(c, c)
28.57/10.23	   A^2 -> H(c, U1(e, k))
28.57/10.23	   A^2 -> H(c, U1(k, e))
28.57/10.23	
28.57/10.23	The TRS R consists of the following rules:
28.57/10.23	
28.57/10.23	   f(x) -> U1(x, x)
28.57/10.23	   U1(e, x) -> x
28.57/10.23	   a -> c
28.57/10.23	   a -> d
28.57/10.23	   b -> c
28.57/10.23	   b -> d
28.57/10.23	   d -> k
28.57/10.23	   c -> e
28.57/10.23	   c -> k
28.57/10.23	
28.57/10.23	Q is empty.
28.57/10.23	We have to consider all minimal (P,Q,R)-chains.
28.57/10.23	----------------------------------------
28.57/10.23	
28.57/10.23	(2067) TransformationProof (EQUIVALENT)
28.57/10.23	By narrowing [LPAR04] the rule A^2 -> H(c, U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.23	
28.57/10.23	   (A^2 -> H(e, U1(c, k)),A^2 -> H(e, U1(c, k)))
28.57/10.23	   (A^2 -> H(k, U1(c, k)),A^2 -> H(k, U1(c, k)))
28.57/10.23	   (A^2 -> H(c, U1(e, k)),A^2 -> H(c, U1(e, k)))
28.57/10.23	   (A^2 -> H(c, U1(k, k)),A^2 -> H(c, U1(k, k)))
28.57/10.23	
28.57/10.23	
28.57/10.23	----------------------------------------
28.57/10.23	
28.57/10.23	(2068)
28.57/10.23	Obligation:
28.57/10.23	Q DP problem:
28.57/10.23	The TRS P consists of the following rules:
28.57/10.23	
28.57/10.23	   A^2 -> H(f(c), f(c))
28.57/10.23	   H(x, x) -> G(x, x, f(k))
28.57/10.23	   G(d, x, x) -> A^2
28.57/10.23	   A^2 -> H(f(d), f(d))
28.57/10.23	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.23	   A^2 -> H(f(e), f(e))
28.57/10.23	   A^2 -> H(f(k), f(k))
28.57/10.23	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.23	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.23	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.23	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.23	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.23	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.23	   A^2 -> H(c, U1(e, e))
28.57/10.23	   A^2 -> H(c, U1(k, k))
28.57/10.23	   A^2 -> H(c, U1(k, d))
28.57/10.23	   A^2 -> H(c, U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.23	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.23	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, c), b)
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, c), e)
28.57/10.23	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.23	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.23	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.23	   A^2 -> H(U1(k, c), b)
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, c), c)
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, e), b)
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(c, e), c)
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(c, e), e)
28.57/10.23	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, k), b)
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(c, k), c)
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.23	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.23	   A^2 -> H(U1(c, k), e)
28.57/10.23	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, c), d)
28.57/10.23	   A^2 -> H(e, U1(e, b))
28.57/10.23	   A^2 -> H(e, U1(c, d))
28.57/10.23	   A^2 -> H(e, U1(d, c))
28.57/10.23	   A^2 -> H(e, U1(b, e))
28.57/10.23	   A^2 -> H(e, U1(b, k))
28.57/10.23	   A^2 -> H(e, U1(e, c))
28.57/10.23	   A^2 -> H(e, U1(c, e))
28.57/10.23	   A^2 -> H(e, U1(c, k))
28.57/10.23	   A^2 -> H(e, U1(e, e))
28.57/10.23	   A^2 -> H(e, U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, e), b)
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, e), c)
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.23	   A^2 -> H(f(e), d)
28.57/10.23	   A^2 -> H(f(e), k)
28.57/10.23	   A^2 -> H(U1(k, k), b)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, k), c)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.23	   A^2 -> H(f(k), d)
28.57/10.23	   A^2 -> H(f(k), k)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(k, d), b)
28.57/10.23	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, d), c)
28.57/10.23	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, k), b)
28.57/10.23	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(d, k), c)
28.57/10.23	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.23	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.23	   A^2 -> H(U1(d, k), e)
28.57/10.23	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, d), d)
28.57/10.23	   A^2 -> H(U1(d, d), k)
28.57/10.23	   A^2 -> H(U1(e, c), c)
28.57/10.23	   A^2 -> H(U1(c, c), e)
28.57/10.23	   A^2 -> H(U1(c, c), k)
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(e, e), e)
28.57/10.23	   A^2 -> H(d, U1(e, b))
28.57/10.23	   A^2 -> H(d, U1(k, b))
28.57/10.23	   A^2 -> H(d, U1(c, d))
28.57/10.23	   A^2 -> H(d, U1(d, c))
28.57/10.23	   A^2 -> H(d, U1(b, e))
28.57/10.23	   A^2 -> H(d, U1(b, k))
28.57/10.23	   A^2 -> H(d, U1(e, c))
28.57/10.23	   A^2 -> H(d, U1(k, c))
28.57/10.23	   A^2 -> H(d, U1(c, e))
28.57/10.23	   A^2 -> H(d, U1(c, k))
28.57/10.23	   A^2 -> H(d, U1(e, e))
28.57/10.23	   A^2 -> H(d, U1(k, k))
28.57/10.23	   A^2 -> H(d, U1(k, d))
28.57/10.23	   A^2 -> H(d, U1(d, k))
28.57/10.23	   A^2 -> H(a, b)
28.57/10.23	   A^2 -> H(a, U1(e, d))
28.57/10.23	   A^2 -> H(a, U1(d, e))
28.57/10.23	   A^2 -> H(a, c)
28.57/10.23	   A^2 -> H(a, U1(e, k))
28.57/10.23	   A^2 -> H(a, U1(k, e))
28.57/10.23	   A^2 -> H(a, e)
28.57/10.23	   A^2 -> H(a, U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, d), b)
28.57/10.23	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, d), c)
28.57/10.23	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, d), e)
28.57/10.23	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, a), d)
28.57/10.23	   A^2 -> H(U1(e, a), k)
28.57/10.23	   A^2 -> H(U1(k, a), d)
28.57/10.23	   A^2 -> H(U1(c, d), d)
28.57/10.23	   A^2 -> H(U1(c, d), k)
28.57/10.23	   A^2 -> H(U1(d, e), b)
28.57/10.23	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(d, e), c)
28.57/10.23	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(d, e), e)
28.57/10.23	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, c), d)
28.57/10.23	   A^2 -> H(U1(d, c), k)
28.57/10.23	   A^2 -> H(U1(a, e), d)
28.57/10.23	   A^2 -> H(U1(a, e), k)
28.57/10.23	   A^2 -> H(U1(a, k), d)
28.57/10.23	   A^2 -> H(U1(a, k), k)
28.57/10.23	   A^2 -> H(k, U1(e, b))
28.57/10.23	   A^2 -> H(k, U1(c, d))
28.57/10.23	   A^2 -> H(k, U1(d, c))
28.57/10.23	   A^2 -> H(k, U1(b, e))
28.57/10.23	   A^2 -> H(k, U1(b, k))
28.57/10.23	   A^2 -> H(k, U1(e, c))
28.57/10.23	   A^2 -> H(k, U1(c, e))
28.57/10.23	   A^2 -> H(k, U1(c, k))
28.57/10.23	   A^2 -> H(k, U1(e, e))
28.57/10.23	   A^2 -> H(k, U1(d, k))
28.57/10.23	   A^2 -> H(c, b)
28.57/10.23	   A^2 -> H(c, U1(e, d))
28.57/10.23	   A^2 -> H(c, U1(d, e))
28.57/10.23	   A^2 -> H(c, c)
28.57/10.23	   A^2 -> H(c, U1(e, k))
28.57/10.23	   A^2 -> H(c, U1(k, e))
28.57/10.23	
28.57/10.23	The TRS R consists of the following rules:
28.57/10.23	
28.57/10.23	   f(x) -> U1(x, x)
28.57/10.23	   U1(e, x) -> x
28.57/10.23	   a -> c
28.57/10.23	   a -> d
28.57/10.23	   b -> c
28.57/10.23	   b -> d
28.57/10.23	   d -> k
28.57/10.23	   c -> e
28.57/10.23	   c -> k
28.57/10.23	
28.57/10.23	Q is empty.
28.57/10.23	We have to consider all minimal (P,Q,R)-chains.
28.57/10.23	----------------------------------------
28.57/10.23	
28.57/10.23	(2069) TransformationProof (EQUIVALENT)
28.57/10.23	By narrowing [LPAR04] the rule A^2 -> H(c, U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.23	
28.57/10.23	   (A^2 -> H(e, U1(e, e)),A^2 -> H(e, U1(e, e)))
28.57/10.23	   (A^2 -> H(k, U1(e, e)),A^2 -> H(k, U1(e, e)))
28.57/10.23	   (A^2 -> H(c, e),A^2 -> H(c, e))
28.57/10.23	
28.57/10.23	
28.57/10.23	----------------------------------------
28.57/10.23	
28.57/10.23	(2070)
28.57/10.23	Obligation:
28.57/10.23	Q DP problem:
28.57/10.23	The TRS P consists of the following rules:
28.57/10.23	
28.57/10.23	   A^2 -> H(f(c), f(c))
28.57/10.23	   H(x, x) -> G(x, x, f(k))
28.57/10.23	   G(d, x, x) -> A^2
28.57/10.23	   A^2 -> H(f(d), f(d))
28.57/10.23	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.23	   A^2 -> H(f(e), f(e))
28.57/10.23	   A^2 -> H(f(k), f(k))
28.57/10.23	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.23	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.23	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.23	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.23	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.23	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.23	   A^2 -> H(c, U1(k, k))
28.57/10.23	   A^2 -> H(c, U1(k, d))
28.57/10.23	   A^2 -> H(c, U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.23	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.23	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, c), b)
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, c), e)
28.57/10.23	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.23	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.23	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.23	   A^2 -> H(U1(k, c), b)
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, c), c)
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, e), b)
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(c, e), c)
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(c, e), e)
28.57/10.23	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, k), b)
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(c, k), c)
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.23	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.23	   A^2 -> H(U1(c, k), e)
28.57/10.23	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, c), d)
28.57/10.23	   A^2 -> H(e, U1(e, b))
28.57/10.23	   A^2 -> H(e, U1(c, d))
28.57/10.23	   A^2 -> H(e, U1(d, c))
28.57/10.23	   A^2 -> H(e, U1(b, e))
28.57/10.23	   A^2 -> H(e, U1(b, k))
28.57/10.23	   A^2 -> H(e, U1(e, c))
28.57/10.23	   A^2 -> H(e, U1(c, e))
28.57/10.23	   A^2 -> H(e, U1(c, k))
28.57/10.23	   A^2 -> H(e, U1(e, e))
28.57/10.23	   A^2 -> H(e, U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, e), b)
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, e), c)
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.23	   A^2 -> H(f(e), d)
28.57/10.23	   A^2 -> H(f(e), k)
28.57/10.23	   A^2 -> H(U1(k, k), b)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, k), c)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.23	   A^2 -> H(f(k), d)
28.57/10.23	   A^2 -> H(f(k), k)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(k, d), b)
28.57/10.23	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, d), c)
28.57/10.23	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, k), b)
28.57/10.23	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(d, k), c)
28.57/10.23	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.23	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.23	   A^2 -> H(U1(d, k), e)
28.57/10.23	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, d), d)
28.57/10.23	   A^2 -> H(U1(d, d), k)
28.57/10.23	   A^2 -> H(U1(e, c), c)
28.57/10.23	   A^2 -> H(U1(c, c), e)
28.57/10.23	   A^2 -> H(U1(c, c), k)
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(e, e), e)
28.57/10.23	   A^2 -> H(d, U1(e, b))
28.57/10.23	   A^2 -> H(d, U1(k, b))
28.57/10.23	   A^2 -> H(d, U1(c, d))
28.57/10.23	   A^2 -> H(d, U1(d, c))
28.57/10.23	   A^2 -> H(d, U1(b, e))
28.57/10.23	   A^2 -> H(d, U1(b, k))
28.57/10.23	   A^2 -> H(d, U1(e, c))
28.57/10.23	   A^2 -> H(d, U1(k, c))
28.57/10.23	   A^2 -> H(d, U1(c, e))
28.57/10.23	   A^2 -> H(d, U1(c, k))
28.57/10.23	   A^2 -> H(d, U1(e, e))
28.57/10.23	   A^2 -> H(d, U1(k, k))
28.57/10.23	   A^2 -> H(d, U1(k, d))
28.57/10.23	   A^2 -> H(d, U1(d, k))
28.57/10.23	   A^2 -> H(a, b)
28.57/10.23	   A^2 -> H(a, U1(e, d))
28.57/10.23	   A^2 -> H(a, U1(d, e))
28.57/10.23	   A^2 -> H(a, c)
28.57/10.23	   A^2 -> H(a, U1(e, k))
28.57/10.23	   A^2 -> H(a, U1(k, e))
28.57/10.23	   A^2 -> H(a, e)
28.57/10.23	   A^2 -> H(a, U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, d), b)
28.57/10.23	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, d), c)
28.57/10.23	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, d), e)
28.57/10.23	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, a), d)
28.57/10.23	   A^2 -> H(U1(e, a), k)
28.57/10.23	   A^2 -> H(U1(k, a), d)
28.57/10.23	   A^2 -> H(U1(c, d), d)
28.57/10.23	   A^2 -> H(U1(c, d), k)
28.57/10.23	   A^2 -> H(U1(d, e), b)
28.57/10.23	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(d, e), c)
28.57/10.23	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(d, e), e)
28.57/10.23	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, c), d)
28.57/10.23	   A^2 -> H(U1(d, c), k)
28.57/10.23	   A^2 -> H(U1(a, e), d)
28.57/10.23	   A^2 -> H(U1(a, e), k)
28.57/10.23	   A^2 -> H(U1(a, k), d)
28.57/10.23	   A^2 -> H(U1(a, k), k)
28.57/10.23	   A^2 -> H(k, U1(e, b))
28.57/10.23	   A^2 -> H(k, U1(c, d))
28.57/10.23	   A^2 -> H(k, U1(d, c))
28.57/10.23	   A^2 -> H(k, U1(b, e))
28.57/10.23	   A^2 -> H(k, U1(b, k))
28.57/10.23	   A^2 -> H(k, U1(e, c))
28.57/10.23	   A^2 -> H(k, U1(c, e))
28.57/10.23	   A^2 -> H(k, U1(c, k))
28.57/10.23	   A^2 -> H(k, U1(e, e))
28.57/10.23	   A^2 -> H(k, U1(d, k))
28.57/10.23	   A^2 -> H(c, b)
28.57/10.23	   A^2 -> H(c, U1(e, d))
28.57/10.23	   A^2 -> H(c, U1(d, e))
28.57/10.23	   A^2 -> H(c, c)
28.57/10.23	   A^2 -> H(c, U1(e, k))
28.57/10.23	   A^2 -> H(c, U1(k, e))
28.57/10.23	   A^2 -> H(c, e)
28.57/10.23	
28.57/10.23	The TRS R consists of the following rules:
28.57/10.23	
28.57/10.23	   f(x) -> U1(x, x)
28.57/10.23	   U1(e, x) -> x
28.57/10.23	   a -> c
28.57/10.23	   a -> d
28.57/10.23	   b -> c
28.57/10.23	   b -> d
28.57/10.23	   d -> k
28.57/10.23	   c -> e
28.57/10.23	   c -> k
28.57/10.23	
28.57/10.23	Q is empty.
28.57/10.23	We have to consider all minimal (P,Q,R)-chains.
28.57/10.23	----------------------------------------
28.57/10.23	
28.57/10.23	(2071) TransformationProof (EQUIVALENT)
28.57/10.23	By narrowing [LPAR04] the rule A^2 -> H(c, U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.23	
28.57/10.23	   (A^2 -> H(e, U1(k, k)),A^2 -> H(e, U1(k, k)))
28.57/10.23	   (A^2 -> H(k, U1(k, k)),A^2 -> H(k, U1(k, k)))
28.57/10.23	
28.57/10.23	
28.57/10.23	----------------------------------------
28.57/10.23	
28.57/10.23	(2072)
28.57/10.23	Obligation:
28.57/10.23	Q DP problem:
28.57/10.23	The TRS P consists of the following rules:
28.57/10.23	
28.57/10.23	   A^2 -> H(f(c), f(c))
28.57/10.23	   H(x, x) -> G(x, x, f(k))
28.57/10.23	   G(d, x, x) -> A^2
28.57/10.23	   A^2 -> H(f(d), f(d))
28.57/10.23	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.23	   A^2 -> H(f(e), f(e))
28.57/10.23	   A^2 -> H(f(k), f(k))
28.57/10.23	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.23	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.23	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.23	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.23	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.23	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.23	   A^2 -> H(c, U1(k, d))
28.57/10.23	   A^2 -> H(c, U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.23	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.23	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, c), b)
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, c), e)
28.57/10.23	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.23	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.23	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.23	   A^2 -> H(U1(k, c), b)
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, c), c)
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, e), b)
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(c, e), c)
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(c, e), e)
28.57/10.23	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, k), b)
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(c, k), c)
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.23	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.23	   A^2 -> H(U1(c, k), e)
28.57/10.23	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, c), d)
28.57/10.23	   A^2 -> H(e, U1(e, b))
28.57/10.23	   A^2 -> H(e, U1(c, d))
28.57/10.23	   A^2 -> H(e, U1(d, c))
28.57/10.23	   A^2 -> H(e, U1(b, e))
28.57/10.23	   A^2 -> H(e, U1(b, k))
28.57/10.23	   A^2 -> H(e, U1(e, c))
28.57/10.23	   A^2 -> H(e, U1(c, e))
28.57/10.23	   A^2 -> H(e, U1(c, k))
28.57/10.23	   A^2 -> H(e, U1(e, e))
28.57/10.23	   A^2 -> H(e, U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, e), b)
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, e), c)
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.23	   A^2 -> H(f(e), d)
28.57/10.23	   A^2 -> H(f(e), k)
28.57/10.23	   A^2 -> H(U1(k, k), b)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, k), c)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.23	   A^2 -> H(f(k), d)
28.57/10.23	   A^2 -> H(f(k), k)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(k, d), b)
28.57/10.23	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, d), c)
28.57/10.23	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, k), b)
28.57/10.23	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(d, k), c)
28.57/10.23	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.23	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.23	   A^2 -> H(U1(d, k), e)
28.57/10.23	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, d), d)
28.57/10.23	   A^2 -> H(U1(d, d), k)
28.57/10.23	   A^2 -> H(U1(e, c), c)
28.57/10.23	   A^2 -> H(U1(c, c), e)
28.57/10.23	   A^2 -> H(U1(c, c), k)
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(e, e), e)
28.57/10.23	   A^2 -> H(d, U1(e, b))
28.57/10.23	   A^2 -> H(d, U1(k, b))
28.57/10.23	   A^2 -> H(d, U1(c, d))
28.57/10.23	   A^2 -> H(d, U1(d, c))
28.57/10.23	   A^2 -> H(d, U1(b, e))
28.57/10.23	   A^2 -> H(d, U1(b, k))
28.57/10.23	   A^2 -> H(d, U1(e, c))
28.57/10.23	   A^2 -> H(d, U1(k, c))
28.57/10.23	   A^2 -> H(d, U1(c, e))
28.57/10.23	   A^2 -> H(d, U1(c, k))
28.57/10.23	   A^2 -> H(d, U1(e, e))
28.57/10.23	   A^2 -> H(d, U1(k, k))
28.57/10.23	   A^2 -> H(d, U1(k, d))
28.57/10.23	   A^2 -> H(d, U1(d, k))
28.57/10.23	   A^2 -> H(a, b)
28.57/10.23	   A^2 -> H(a, U1(e, d))
28.57/10.23	   A^2 -> H(a, U1(d, e))
28.57/10.23	   A^2 -> H(a, c)
28.57/10.23	   A^2 -> H(a, U1(e, k))
28.57/10.23	   A^2 -> H(a, U1(k, e))
28.57/10.23	   A^2 -> H(a, e)
28.57/10.23	   A^2 -> H(a, U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, d), b)
28.57/10.23	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, d), c)
28.57/10.23	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, d), e)
28.57/10.23	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, a), d)
28.57/10.23	   A^2 -> H(U1(e, a), k)
28.57/10.23	   A^2 -> H(U1(k, a), d)
28.57/10.23	   A^2 -> H(U1(c, d), d)
28.57/10.23	   A^2 -> H(U1(c, d), k)
28.57/10.23	   A^2 -> H(U1(d, e), b)
28.57/10.23	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(d, e), c)
28.57/10.23	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(d, e), e)
28.57/10.23	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, c), d)
28.57/10.23	   A^2 -> H(U1(d, c), k)
28.57/10.23	   A^2 -> H(U1(a, e), d)
28.57/10.23	   A^2 -> H(U1(a, e), k)
28.57/10.23	   A^2 -> H(U1(a, k), d)
28.57/10.23	   A^2 -> H(U1(a, k), k)
28.57/10.23	   A^2 -> H(k, U1(e, b))
28.57/10.23	   A^2 -> H(k, U1(c, d))
28.57/10.23	   A^2 -> H(k, U1(d, c))
28.57/10.23	   A^2 -> H(k, U1(b, e))
28.57/10.23	   A^2 -> H(k, U1(b, k))
28.57/10.23	   A^2 -> H(k, U1(e, c))
28.57/10.23	   A^2 -> H(k, U1(c, e))
28.57/10.23	   A^2 -> H(k, U1(c, k))
28.57/10.23	   A^2 -> H(k, U1(e, e))
28.57/10.23	   A^2 -> H(k, U1(d, k))
28.57/10.23	   A^2 -> H(c, b)
28.57/10.23	   A^2 -> H(c, U1(e, d))
28.57/10.23	   A^2 -> H(c, U1(d, e))
28.57/10.23	   A^2 -> H(c, c)
28.57/10.23	   A^2 -> H(c, U1(e, k))
28.57/10.23	   A^2 -> H(c, U1(k, e))
28.57/10.23	   A^2 -> H(c, e)
28.57/10.23	   A^2 -> H(e, U1(k, k))
28.57/10.23	   A^2 -> H(k, U1(k, k))
28.57/10.23	
28.57/10.23	The TRS R consists of the following rules:
28.57/10.23	
28.57/10.23	   f(x) -> U1(x, x)
28.57/10.23	   U1(e, x) -> x
28.57/10.23	   a -> c
28.57/10.23	   a -> d
28.57/10.23	   b -> c
28.57/10.23	   b -> d
28.57/10.23	   d -> k
28.57/10.23	   c -> e
28.57/10.23	   c -> k
28.57/10.23	
28.57/10.23	Q is empty.
28.57/10.23	We have to consider all minimal (P,Q,R)-chains.
28.57/10.23	----------------------------------------
28.57/10.23	
28.57/10.23	(2073) DependencyGraphProof (EQUIVALENT)
28.57/10.23	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
28.57/10.23	----------------------------------------
28.57/10.23	
28.57/10.23	(2074)
28.57/10.23	Obligation:
28.57/10.23	Q DP problem:
28.57/10.23	The TRS P consists of the following rules:
28.57/10.23	
28.57/10.23	   H(x, x) -> G(x, x, f(k))
28.57/10.23	   G(d, x, x) -> A^2
28.57/10.23	   A^2 -> H(f(c), f(c))
28.57/10.23	   A^2 -> H(f(d), f(d))
28.57/10.23	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.23	   A^2 -> H(f(e), f(e))
28.57/10.23	   A^2 -> H(f(k), f(k))
28.57/10.23	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.23	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.23	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.23	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.23	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.23	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.23	   A^2 -> H(c, U1(k, d))
28.57/10.23	   A^2 -> H(c, U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.23	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.23	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, c), b)
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, c), e)
28.57/10.23	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.23	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.23	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.23	   A^2 -> H(U1(k, c), b)
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, c), c)
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, e), b)
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(c, e), c)
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(c, e), e)
28.57/10.23	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, k), b)
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(c, k), c)
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.23	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.23	   A^2 -> H(U1(c, k), e)
28.57/10.23	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, c), d)
28.57/10.23	   A^2 -> H(e, U1(e, b))
28.57/10.23	   A^2 -> H(e, U1(c, d))
28.57/10.23	   A^2 -> H(e, U1(d, c))
28.57/10.23	   A^2 -> H(e, U1(b, e))
28.57/10.23	   A^2 -> H(e, U1(b, k))
28.57/10.23	   A^2 -> H(e, U1(e, c))
28.57/10.23	   A^2 -> H(e, U1(c, e))
28.57/10.23	   A^2 -> H(e, U1(c, k))
28.57/10.23	   A^2 -> H(e, U1(e, e))
28.57/10.23	   A^2 -> H(e, U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, e), b)
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, e), c)
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.23	   A^2 -> H(f(e), d)
28.57/10.23	   A^2 -> H(f(e), k)
28.57/10.23	   A^2 -> H(U1(k, k), b)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, k), c)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.23	   A^2 -> H(f(k), d)
28.57/10.23	   A^2 -> H(f(k), k)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(k, d), b)
28.57/10.23	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, d), c)
28.57/10.23	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, k), b)
28.57/10.23	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(d, k), c)
28.57/10.23	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.23	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.23	   A^2 -> H(U1(d, k), e)
28.57/10.23	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, d), d)
28.57/10.23	   A^2 -> H(U1(d, d), k)
28.57/10.23	   A^2 -> H(U1(e, c), c)
28.57/10.23	   A^2 -> H(U1(c, c), e)
28.57/10.23	   A^2 -> H(U1(c, c), k)
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(e, e), e)
28.57/10.23	   A^2 -> H(d, U1(e, b))
28.57/10.23	   A^2 -> H(d, U1(k, b))
28.57/10.23	   A^2 -> H(d, U1(c, d))
28.57/10.23	   A^2 -> H(d, U1(d, c))
28.57/10.23	   A^2 -> H(d, U1(b, e))
28.57/10.23	   A^2 -> H(d, U1(b, k))
28.57/10.23	   A^2 -> H(d, U1(e, c))
28.57/10.23	   A^2 -> H(d, U1(k, c))
28.57/10.23	   A^2 -> H(d, U1(c, e))
28.57/10.23	   A^2 -> H(d, U1(c, k))
28.57/10.23	   A^2 -> H(d, U1(e, e))
28.57/10.23	   A^2 -> H(d, U1(k, k))
28.57/10.23	   A^2 -> H(d, U1(k, d))
28.57/10.23	   A^2 -> H(d, U1(d, k))
28.57/10.23	   A^2 -> H(a, b)
28.57/10.23	   A^2 -> H(a, U1(e, d))
28.57/10.23	   A^2 -> H(a, U1(d, e))
28.57/10.23	   A^2 -> H(a, c)
28.57/10.23	   A^2 -> H(a, U1(e, k))
28.57/10.23	   A^2 -> H(a, U1(k, e))
28.57/10.23	   A^2 -> H(a, e)
28.57/10.23	   A^2 -> H(a, U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, d), b)
28.57/10.23	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, d), c)
28.57/10.23	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, d), e)
28.57/10.23	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, a), d)
28.57/10.23	   A^2 -> H(U1(e, a), k)
28.57/10.23	   A^2 -> H(U1(k, a), d)
28.57/10.23	   A^2 -> H(U1(c, d), d)
28.57/10.23	   A^2 -> H(U1(c, d), k)
28.57/10.23	   A^2 -> H(U1(d, e), b)
28.57/10.23	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(d, e), c)
28.57/10.23	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(d, e), e)
28.57/10.23	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, c), d)
28.57/10.23	   A^2 -> H(U1(d, c), k)
28.57/10.23	   A^2 -> H(U1(a, e), d)
28.57/10.23	   A^2 -> H(U1(a, e), k)
28.57/10.23	   A^2 -> H(U1(a, k), d)
28.57/10.23	   A^2 -> H(U1(a, k), k)
28.57/10.23	   A^2 -> H(k, U1(e, b))
28.57/10.23	   A^2 -> H(k, U1(c, d))
28.57/10.23	   A^2 -> H(k, U1(d, c))
28.57/10.23	   A^2 -> H(k, U1(b, e))
28.57/10.23	   A^2 -> H(k, U1(b, k))
28.57/10.23	   A^2 -> H(k, U1(e, c))
28.57/10.23	   A^2 -> H(k, U1(c, e))
28.57/10.23	   A^2 -> H(k, U1(c, k))
28.57/10.23	   A^2 -> H(k, U1(e, e))
28.57/10.23	   A^2 -> H(k, U1(d, k))
28.57/10.23	   A^2 -> H(c, b)
28.57/10.23	   A^2 -> H(c, U1(e, d))
28.57/10.23	   A^2 -> H(c, U1(d, e))
28.57/10.23	   A^2 -> H(c, c)
28.57/10.23	   A^2 -> H(c, U1(e, k))
28.57/10.23	   A^2 -> H(c, U1(k, e))
28.57/10.23	   A^2 -> H(c, e)
28.57/10.23	
28.57/10.23	The TRS R consists of the following rules:
28.57/10.23	
28.57/10.23	   f(x) -> U1(x, x)
28.57/10.23	   U1(e, x) -> x
28.57/10.23	   a -> c
28.57/10.23	   a -> d
28.57/10.23	   b -> c
28.57/10.23	   b -> d
28.57/10.23	   d -> k
28.57/10.23	   c -> e
28.57/10.23	   c -> k
28.57/10.23	
28.57/10.23	Q is empty.
28.57/10.23	We have to consider all minimal (P,Q,R)-chains.
28.57/10.23	----------------------------------------
28.57/10.23	
28.57/10.23	(2075) TransformationProof (EQUIVALENT)
28.57/10.23	By narrowing [LPAR04] the rule A^2 -> H(c, U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.23	
28.57/10.23	   (A^2 -> H(e, U1(k, d)),A^2 -> H(e, U1(k, d)))
28.57/10.23	   (A^2 -> H(k, U1(k, d)),A^2 -> H(k, U1(k, d)))
28.57/10.23	   (A^2 -> H(c, U1(k, k)),A^2 -> H(c, U1(k, k)))
28.57/10.23	
28.57/10.23	
28.57/10.23	----------------------------------------
28.57/10.23	
28.57/10.23	(2076)
28.57/10.23	Obligation:
28.57/10.23	Q DP problem:
28.57/10.23	The TRS P consists of the following rules:
28.57/10.23	
28.57/10.23	   H(x, x) -> G(x, x, f(k))
28.57/10.23	   G(d, x, x) -> A^2
28.57/10.23	   A^2 -> H(f(c), f(c))
28.57/10.23	   A^2 -> H(f(d), f(d))
28.57/10.23	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.23	   A^2 -> H(f(e), f(e))
28.57/10.23	   A^2 -> H(f(k), f(k))
28.57/10.23	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.23	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.23	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.23	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.23	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.23	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.23	   A^2 -> H(c, U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.23	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.23	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, c), b)
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, c), e)
28.57/10.23	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.23	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.23	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.23	   A^2 -> H(U1(k, c), b)
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, c), c)
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, e), b)
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(c, e), c)
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(c, e), e)
28.57/10.23	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, k), b)
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(c, k), c)
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.23	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.23	   A^2 -> H(U1(c, k), e)
28.57/10.23	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, c), d)
28.57/10.23	   A^2 -> H(e, U1(e, b))
28.57/10.23	   A^2 -> H(e, U1(c, d))
28.57/10.23	   A^2 -> H(e, U1(d, c))
28.57/10.23	   A^2 -> H(e, U1(b, e))
28.57/10.23	   A^2 -> H(e, U1(b, k))
28.57/10.23	   A^2 -> H(e, U1(e, c))
28.57/10.23	   A^2 -> H(e, U1(c, e))
28.57/10.23	   A^2 -> H(e, U1(c, k))
28.57/10.23	   A^2 -> H(e, U1(e, e))
28.57/10.23	   A^2 -> H(e, U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, e), b)
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, e), c)
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.23	   A^2 -> H(f(e), d)
28.57/10.23	   A^2 -> H(f(e), k)
28.57/10.23	   A^2 -> H(U1(k, k), b)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, k), c)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.23	   A^2 -> H(f(k), d)
28.57/10.23	   A^2 -> H(f(k), k)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(k, d), b)
28.57/10.23	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, d), c)
28.57/10.23	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, k), b)
28.57/10.23	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(d, k), c)
28.57/10.23	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.23	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.23	   A^2 -> H(U1(d, k), e)
28.57/10.23	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, d), d)
28.57/10.23	   A^2 -> H(U1(d, d), k)
28.57/10.23	   A^2 -> H(U1(e, c), c)
28.57/10.23	   A^2 -> H(U1(c, c), e)
28.57/10.23	   A^2 -> H(U1(c, c), k)
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(e, e), e)
28.57/10.23	   A^2 -> H(d, U1(e, b))
28.57/10.23	   A^2 -> H(d, U1(k, b))
28.57/10.23	   A^2 -> H(d, U1(c, d))
28.57/10.23	   A^2 -> H(d, U1(d, c))
28.57/10.23	   A^2 -> H(d, U1(b, e))
28.57/10.23	   A^2 -> H(d, U1(b, k))
28.57/10.23	   A^2 -> H(d, U1(e, c))
28.57/10.23	   A^2 -> H(d, U1(k, c))
28.57/10.23	   A^2 -> H(d, U1(c, e))
28.57/10.23	   A^2 -> H(d, U1(c, k))
28.57/10.23	   A^2 -> H(d, U1(e, e))
28.57/10.23	   A^2 -> H(d, U1(k, k))
28.57/10.23	   A^2 -> H(d, U1(k, d))
28.57/10.23	   A^2 -> H(d, U1(d, k))
28.57/10.23	   A^2 -> H(a, b)
28.57/10.23	   A^2 -> H(a, U1(e, d))
28.57/10.23	   A^2 -> H(a, U1(d, e))
28.57/10.23	   A^2 -> H(a, c)
28.57/10.23	   A^2 -> H(a, U1(e, k))
28.57/10.23	   A^2 -> H(a, U1(k, e))
28.57/10.23	   A^2 -> H(a, e)
28.57/10.23	   A^2 -> H(a, U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, d), b)
28.57/10.23	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, d), c)
28.57/10.23	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, d), e)
28.57/10.23	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, a), d)
28.57/10.23	   A^2 -> H(U1(e, a), k)
28.57/10.23	   A^2 -> H(U1(k, a), d)
28.57/10.23	   A^2 -> H(U1(c, d), d)
28.57/10.23	   A^2 -> H(U1(c, d), k)
28.57/10.23	   A^2 -> H(U1(d, e), b)
28.57/10.23	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(d, e), c)
28.57/10.23	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(d, e), e)
28.57/10.23	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, c), d)
28.57/10.23	   A^2 -> H(U1(d, c), k)
28.57/10.23	   A^2 -> H(U1(a, e), d)
28.57/10.23	   A^2 -> H(U1(a, e), k)
28.57/10.23	   A^2 -> H(U1(a, k), d)
28.57/10.23	   A^2 -> H(U1(a, k), k)
28.57/10.23	   A^2 -> H(k, U1(e, b))
28.57/10.23	   A^2 -> H(k, U1(c, d))
28.57/10.23	   A^2 -> H(k, U1(d, c))
28.57/10.23	   A^2 -> H(k, U1(b, e))
28.57/10.23	   A^2 -> H(k, U1(b, k))
28.57/10.23	   A^2 -> H(k, U1(e, c))
28.57/10.23	   A^2 -> H(k, U1(c, e))
28.57/10.23	   A^2 -> H(k, U1(c, k))
28.57/10.23	   A^2 -> H(k, U1(e, e))
28.57/10.23	   A^2 -> H(k, U1(d, k))
28.57/10.23	   A^2 -> H(c, b)
28.57/10.23	   A^2 -> H(c, U1(e, d))
28.57/10.23	   A^2 -> H(c, U1(d, e))
28.57/10.23	   A^2 -> H(c, c)
28.57/10.23	   A^2 -> H(c, U1(e, k))
28.57/10.23	   A^2 -> H(c, U1(k, e))
28.57/10.23	   A^2 -> H(c, e)
28.57/10.23	   A^2 -> H(e, U1(k, d))
28.57/10.23	   A^2 -> H(k, U1(k, d))
28.57/10.23	   A^2 -> H(c, U1(k, k))
28.57/10.23	
28.57/10.23	The TRS R consists of the following rules:
28.57/10.23	
28.57/10.23	   f(x) -> U1(x, x)
28.57/10.23	   U1(e, x) -> x
28.57/10.23	   a -> c
28.57/10.23	   a -> d
28.57/10.23	   b -> c
28.57/10.23	   b -> d
28.57/10.23	   d -> k
28.57/10.23	   c -> e
28.57/10.23	   c -> k
28.57/10.23	
28.57/10.23	Q is empty.
28.57/10.23	We have to consider all minimal (P,Q,R)-chains.
28.57/10.23	----------------------------------------
28.57/10.23	
28.57/10.23	(2077) DependencyGraphProof (EQUIVALENT)
28.57/10.23	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
28.57/10.23	----------------------------------------
28.57/10.23	
28.57/10.23	(2078)
28.57/10.23	Obligation:
28.57/10.23	Q DP problem:
28.57/10.23	The TRS P consists of the following rules:
28.57/10.23	
28.57/10.23	   G(d, x, x) -> A^2
28.57/10.23	   A^2 -> H(f(c), f(c))
28.57/10.23	   H(x, x) -> G(x, x, f(k))
28.57/10.23	   A^2 -> H(f(d), f(d))
28.57/10.23	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.23	   A^2 -> H(f(e), f(e))
28.57/10.23	   A^2 -> H(f(k), f(k))
28.57/10.23	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.23	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.23	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.23	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.23	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.23	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.23	   A^2 -> H(c, U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.23	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.23	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, c), b)
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, c), e)
28.57/10.23	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.23	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.23	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.23	   A^2 -> H(U1(k, c), b)
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, c), c)
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, e), b)
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(c, e), c)
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(c, e), e)
28.57/10.23	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, k), b)
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(c, k), c)
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.23	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.23	   A^2 -> H(U1(c, k), e)
28.57/10.23	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, c), d)
28.57/10.23	   A^2 -> H(e, U1(e, b))
28.57/10.23	   A^2 -> H(e, U1(c, d))
28.57/10.23	   A^2 -> H(e, U1(d, c))
28.57/10.23	   A^2 -> H(e, U1(b, e))
28.57/10.23	   A^2 -> H(e, U1(b, k))
28.57/10.23	   A^2 -> H(e, U1(e, c))
28.57/10.23	   A^2 -> H(e, U1(c, e))
28.57/10.23	   A^2 -> H(e, U1(c, k))
28.57/10.23	   A^2 -> H(e, U1(e, e))
28.57/10.23	   A^2 -> H(e, U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, e), b)
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, e), c)
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.23	   A^2 -> H(f(e), d)
28.57/10.23	   A^2 -> H(f(e), k)
28.57/10.23	   A^2 -> H(U1(k, k), b)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, k), c)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.23	   A^2 -> H(f(k), d)
28.57/10.23	   A^2 -> H(f(k), k)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(k, d), b)
28.57/10.23	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, d), c)
28.57/10.23	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, k), b)
28.57/10.23	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(d, k), c)
28.57/10.23	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.23	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.23	   A^2 -> H(U1(d, k), e)
28.57/10.23	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, d), d)
28.57/10.23	   A^2 -> H(U1(d, d), k)
28.57/10.23	   A^2 -> H(U1(e, c), c)
28.57/10.23	   A^2 -> H(U1(c, c), e)
28.57/10.23	   A^2 -> H(U1(c, c), k)
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(e, e), e)
28.57/10.23	   A^2 -> H(d, U1(e, b))
28.57/10.23	   A^2 -> H(d, U1(k, b))
28.57/10.23	   A^2 -> H(d, U1(c, d))
28.57/10.23	   A^2 -> H(d, U1(d, c))
28.57/10.23	   A^2 -> H(d, U1(b, e))
28.57/10.23	   A^2 -> H(d, U1(b, k))
28.57/10.23	   A^2 -> H(d, U1(e, c))
28.57/10.23	   A^2 -> H(d, U1(k, c))
28.57/10.23	   A^2 -> H(d, U1(c, e))
28.57/10.23	   A^2 -> H(d, U1(c, k))
28.57/10.23	   A^2 -> H(d, U1(e, e))
28.57/10.23	   A^2 -> H(d, U1(k, k))
28.57/10.23	   A^2 -> H(d, U1(k, d))
28.57/10.23	   A^2 -> H(d, U1(d, k))
28.57/10.23	   A^2 -> H(a, b)
28.57/10.23	   A^2 -> H(a, U1(e, d))
28.57/10.23	   A^2 -> H(a, U1(d, e))
28.57/10.23	   A^2 -> H(a, c)
28.57/10.23	   A^2 -> H(a, U1(e, k))
28.57/10.23	   A^2 -> H(a, U1(k, e))
28.57/10.23	   A^2 -> H(a, e)
28.57/10.23	   A^2 -> H(a, U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, d), b)
28.57/10.23	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, d), c)
28.57/10.23	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, d), e)
28.57/10.23	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, a), d)
28.57/10.23	   A^2 -> H(U1(e, a), k)
28.57/10.23	   A^2 -> H(U1(k, a), d)
28.57/10.23	   A^2 -> H(U1(c, d), d)
28.57/10.23	   A^2 -> H(U1(c, d), k)
28.57/10.23	   A^2 -> H(U1(d, e), b)
28.57/10.23	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(d, e), c)
28.57/10.23	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(d, e), e)
28.57/10.23	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, c), d)
28.57/10.23	   A^2 -> H(U1(d, c), k)
28.57/10.23	   A^2 -> H(U1(a, e), d)
28.57/10.23	   A^2 -> H(U1(a, e), k)
28.57/10.23	   A^2 -> H(U1(a, k), d)
28.57/10.23	   A^2 -> H(U1(a, k), k)
28.57/10.23	   A^2 -> H(k, U1(e, b))
28.57/10.23	   A^2 -> H(k, U1(c, d))
28.57/10.23	   A^2 -> H(k, U1(d, c))
28.57/10.23	   A^2 -> H(k, U1(b, e))
28.57/10.23	   A^2 -> H(k, U1(b, k))
28.57/10.23	   A^2 -> H(k, U1(e, c))
28.57/10.23	   A^2 -> H(k, U1(c, e))
28.57/10.23	   A^2 -> H(k, U1(c, k))
28.57/10.23	   A^2 -> H(k, U1(e, e))
28.57/10.23	   A^2 -> H(k, U1(d, k))
28.57/10.23	   A^2 -> H(c, b)
28.57/10.23	   A^2 -> H(c, U1(e, d))
28.57/10.23	   A^2 -> H(c, U1(d, e))
28.57/10.23	   A^2 -> H(c, c)
28.57/10.23	   A^2 -> H(c, U1(e, k))
28.57/10.23	   A^2 -> H(c, U1(k, e))
28.57/10.23	   A^2 -> H(c, e)
28.57/10.23	   A^2 -> H(c, U1(k, k))
28.57/10.23	
28.57/10.23	The TRS R consists of the following rules:
28.57/10.23	
28.57/10.23	   f(x) -> U1(x, x)
28.57/10.23	   U1(e, x) -> x
28.57/10.23	   a -> c
28.57/10.23	   a -> d
28.57/10.23	   b -> c
28.57/10.23	   b -> d
28.57/10.23	   d -> k
28.57/10.23	   c -> e
28.57/10.23	   c -> k
28.57/10.23	
28.57/10.23	Q is empty.
28.57/10.23	We have to consider all minimal (P,Q,R)-chains.
28.57/10.23	----------------------------------------
28.57/10.23	
28.57/10.23	(2079) TransformationProof (EQUIVALENT)
28.57/10.23	By narrowing [LPAR04] the rule A^2 -> H(c, U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.23	
28.57/10.23	   (A^2 -> H(e, U1(d, k)),A^2 -> H(e, U1(d, k)))
28.57/10.23	   (A^2 -> H(k, U1(d, k)),A^2 -> H(k, U1(d, k)))
28.57/10.23	   (A^2 -> H(c, U1(k, k)),A^2 -> H(c, U1(k, k)))
28.57/10.23	
28.57/10.23	
28.57/10.23	----------------------------------------
28.57/10.23	
28.57/10.23	(2080)
28.57/10.23	Obligation:
28.57/10.23	Q DP problem:
28.57/10.23	The TRS P consists of the following rules:
28.57/10.23	
28.57/10.23	   G(d, x, x) -> A^2
28.57/10.23	   A^2 -> H(f(c), f(c))
28.57/10.23	   H(x, x) -> G(x, x, f(k))
28.57/10.23	   A^2 -> H(f(d), f(d))
28.57/10.23	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.23	   A^2 -> H(f(e), f(e))
28.57/10.23	   A^2 -> H(f(k), f(k))
28.57/10.23	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.23	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.23	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.23	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.23	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.23	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, b))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.23	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.23	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, c), b)
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, c), e)
28.57/10.23	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.23	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.23	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.23	   A^2 -> H(U1(k, c), b)
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, c), c)
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, e), b)
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(c, e), c)
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(c, e), e)
28.57/10.23	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, k), b)
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(c, k), c)
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.23	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.23	   A^2 -> H(U1(c, k), e)
28.57/10.23	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, c), d)
28.57/10.23	   A^2 -> H(e, U1(e, b))
28.57/10.23	   A^2 -> H(e, U1(c, d))
28.57/10.23	   A^2 -> H(e, U1(d, c))
28.57/10.23	   A^2 -> H(e, U1(b, e))
28.57/10.23	   A^2 -> H(e, U1(b, k))
28.57/10.23	   A^2 -> H(e, U1(e, c))
28.57/10.23	   A^2 -> H(e, U1(c, e))
28.57/10.23	   A^2 -> H(e, U1(c, k))
28.57/10.23	   A^2 -> H(e, U1(e, e))
28.57/10.23	   A^2 -> H(e, U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, e), b)
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, e), c)
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.23	   A^2 -> H(f(e), d)
28.57/10.23	   A^2 -> H(f(e), k)
28.57/10.23	   A^2 -> H(U1(k, k), b)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, k), c)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.23	   A^2 -> H(f(k), d)
28.57/10.23	   A^2 -> H(f(k), k)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(k, d), b)
28.57/10.23	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, d), c)
28.57/10.23	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, k), b)
28.57/10.23	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(d, k), c)
28.57/10.23	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.23	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.23	   A^2 -> H(U1(d, k), e)
28.57/10.23	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, d), d)
28.57/10.23	   A^2 -> H(U1(d, d), k)
28.57/10.23	   A^2 -> H(U1(e, c), c)
28.57/10.23	   A^2 -> H(U1(c, c), e)
28.57/10.23	   A^2 -> H(U1(c, c), k)
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(e, e), e)
28.57/10.23	   A^2 -> H(d, U1(e, b))
28.57/10.23	   A^2 -> H(d, U1(k, b))
28.57/10.23	   A^2 -> H(d, U1(c, d))
28.57/10.23	   A^2 -> H(d, U1(d, c))
28.57/10.23	   A^2 -> H(d, U1(b, e))
28.57/10.23	   A^2 -> H(d, U1(b, k))
28.57/10.23	   A^2 -> H(d, U1(e, c))
28.57/10.23	   A^2 -> H(d, U1(k, c))
28.57/10.23	   A^2 -> H(d, U1(c, e))
28.57/10.23	   A^2 -> H(d, U1(c, k))
28.57/10.23	   A^2 -> H(d, U1(e, e))
28.57/10.23	   A^2 -> H(d, U1(k, k))
28.57/10.23	   A^2 -> H(d, U1(k, d))
28.57/10.23	   A^2 -> H(d, U1(d, k))
28.57/10.23	   A^2 -> H(a, b)
28.57/10.23	   A^2 -> H(a, U1(e, d))
28.57/10.23	   A^2 -> H(a, U1(d, e))
28.57/10.23	   A^2 -> H(a, c)
28.57/10.23	   A^2 -> H(a, U1(e, k))
28.57/10.23	   A^2 -> H(a, U1(k, e))
28.57/10.23	   A^2 -> H(a, e)
28.57/10.23	   A^2 -> H(a, U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, d), b)
28.57/10.23	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, d), c)
28.57/10.23	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, d), e)
28.57/10.23	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, a), d)
28.57/10.23	   A^2 -> H(U1(e, a), k)
28.57/10.23	   A^2 -> H(U1(k, a), d)
28.57/10.23	   A^2 -> H(U1(c, d), d)
28.57/10.23	   A^2 -> H(U1(c, d), k)
28.57/10.23	   A^2 -> H(U1(d, e), b)
28.57/10.23	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(d, e), c)
28.57/10.23	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(d, e), e)
28.57/10.23	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, c), d)
28.57/10.23	   A^2 -> H(U1(d, c), k)
28.57/10.23	   A^2 -> H(U1(a, e), d)
28.57/10.23	   A^2 -> H(U1(a, e), k)
28.57/10.23	   A^2 -> H(U1(a, k), d)
28.57/10.23	   A^2 -> H(U1(a, k), k)
28.57/10.23	   A^2 -> H(k, U1(e, b))
28.57/10.23	   A^2 -> H(k, U1(c, d))
28.57/10.23	   A^2 -> H(k, U1(d, c))
28.57/10.23	   A^2 -> H(k, U1(b, e))
28.57/10.23	   A^2 -> H(k, U1(b, k))
28.57/10.23	   A^2 -> H(k, U1(e, c))
28.57/10.23	   A^2 -> H(k, U1(c, e))
28.57/10.23	   A^2 -> H(k, U1(c, k))
28.57/10.23	   A^2 -> H(k, U1(e, e))
28.57/10.23	   A^2 -> H(k, U1(d, k))
28.57/10.23	   A^2 -> H(c, b)
28.57/10.23	   A^2 -> H(c, U1(e, d))
28.57/10.23	   A^2 -> H(c, U1(d, e))
28.57/10.23	   A^2 -> H(c, c)
28.57/10.23	   A^2 -> H(c, U1(e, k))
28.57/10.23	   A^2 -> H(c, U1(k, e))
28.57/10.23	   A^2 -> H(c, e)
28.57/10.23	   A^2 -> H(c, U1(k, k))
28.57/10.23	
28.57/10.23	The TRS R consists of the following rules:
28.57/10.23	
28.57/10.23	   f(x) -> U1(x, x)
28.57/10.23	   U1(e, x) -> x
28.57/10.23	   a -> c
28.57/10.23	   a -> d
28.57/10.23	   b -> c
28.57/10.23	   b -> d
28.57/10.23	   d -> k
28.57/10.23	   c -> e
28.57/10.23	   c -> k
28.57/10.23	
28.57/10.23	Q is empty.
28.57/10.23	We have to consider all minimal (P,Q,R)-chains.
28.57/10.23	----------------------------------------
28.57/10.23	
28.57/10.23	(2081) TransformationProof (EQUIVALENT)
28.57/10.23	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.23	
28.57/10.23	   (A^2 -> H(k, U1(e, b)),A^2 -> H(k, U1(e, b)))
28.57/10.23	   (A^2 -> H(U1(e, k), b),A^2 -> H(U1(e, k), b))
28.57/10.23	   (A^2 -> H(U1(e, k), U1(e, c)),A^2 -> H(U1(e, k), U1(e, c)))
28.57/10.23	   (A^2 -> H(U1(e, k), U1(e, d)),A^2 -> H(U1(e, k), U1(e, d)))
28.57/10.23	
28.57/10.23	
28.57/10.23	----------------------------------------
28.57/10.23	
28.57/10.23	(2082)
28.57/10.23	Obligation:
28.57/10.23	Q DP problem:
28.57/10.23	The TRS P consists of the following rules:
28.57/10.23	
28.57/10.23	   G(d, x, x) -> A^2
28.57/10.23	   A^2 -> H(f(c), f(c))
28.57/10.23	   H(x, x) -> G(x, x, f(k))
28.57/10.23	   A^2 -> H(f(d), f(d))
28.57/10.23	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.23	   A^2 -> H(f(e), f(e))
28.57/10.23	   A^2 -> H(f(k), f(k))
28.57/10.23	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.23	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.23	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.23	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.23	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.23	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, b))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.23	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.23	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, c), b)
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, c), e)
28.57/10.23	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.23	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.23	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.23	   A^2 -> H(U1(k, c), b)
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, c), c)
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, e), b)
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(c, e), c)
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(c, e), e)
28.57/10.23	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, k), b)
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(c, k), c)
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.23	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.23	   A^2 -> H(U1(c, k), e)
28.57/10.23	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, c), d)
28.57/10.23	   A^2 -> H(e, U1(e, b))
28.57/10.23	   A^2 -> H(e, U1(c, d))
28.57/10.23	   A^2 -> H(e, U1(d, c))
28.57/10.23	   A^2 -> H(e, U1(b, e))
28.57/10.23	   A^2 -> H(e, U1(b, k))
28.57/10.23	   A^2 -> H(e, U1(e, c))
28.57/10.23	   A^2 -> H(e, U1(c, e))
28.57/10.23	   A^2 -> H(e, U1(c, k))
28.57/10.23	   A^2 -> H(e, U1(e, e))
28.57/10.23	   A^2 -> H(e, U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, e), b)
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, e), c)
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.23	   A^2 -> H(f(e), d)
28.57/10.23	   A^2 -> H(f(e), k)
28.57/10.23	   A^2 -> H(U1(k, k), b)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, k), c)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.23	   A^2 -> H(f(k), d)
28.57/10.23	   A^2 -> H(f(k), k)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(k, d), b)
28.57/10.23	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, d), c)
28.57/10.23	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, k), b)
28.57/10.23	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(d, k), c)
28.57/10.23	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.23	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.23	   A^2 -> H(U1(d, k), e)
28.57/10.23	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, d), d)
28.57/10.23	   A^2 -> H(U1(d, d), k)
28.57/10.23	   A^2 -> H(U1(e, c), c)
28.57/10.23	   A^2 -> H(U1(c, c), e)
28.57/10.23	   A^2 -> H(U1(c, c), k)
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(e, e), e)
28.57/10.23	   A^2 -> H(d, U1(e, b))
28.57/10.23	   A^2 -> H(d, U1(k, b))
28.57/10.23	   A^2 -> H(d, U1(c, d))
28.57/10.23	   A^2 -> H(d, U1(d, c))
28.57/10.23	   A^2 -> H(d, U1(b, e))
28.57/10.23	   A^2 -> H(d, U1(b, k))
28.57/10.23	   A^2 -> H(d, U1(e, c))
28.57/10.23	   A^2 -> H(d, U1(k, c))
28.57/10.23	   A^2 -> H(d, U1(c, e))
28.57/10.23	   A^2 -> H(d, U1(c, k))
28.57/10.23	   A^2 -> H(d, U1(e, e))
28.57/10.23	   A^2 -> H(d, U1(k, k))
28.57/10.23	   A^2 -> H(d, U1(k, d))
28.57/10.23	   A^2 -> H(d, U1(d, k))
28.57/10.23	   A^2 -> H(a, b)
28.57/10.23	   A^2 -> H(a, U1(e, d))
28.57/10.23	   A^2 -> H(a, U1(d, e))
28.57/10.23	   A^2 -> H(a, c)
28.57/10.23	   A^2 -> H(a, U1(e, k))
28.57/10.23	   A^2 -> H(a, U1(k, e))
28.57/10.23	   A^2 -> H(a, e)
28.57/10.23	   A^2 -> H(a, U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, d), b)
28.57/10.23	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, d), c)
28.57/10.23	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, d), e)
28.57/10.23	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, a), d)
28.57/10.23	   A^2 -> H(U1(e, a), k)
28.57/10.23	   A^2 -> H(U1(k, a), d)
28.57/10.23	   A^2 -> H(U1(c, d), d)
28.57/10.23	   A^2 -> H(U1(c, d), k)
28.57/10.23	   A^2 -> H(U1(d, e), b)
28.57/10.23	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(d, e), c)
28.57/10.23	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(d, e), e)
28.57/10.23	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.23	   A^2 -> H(U1(d, c), d)
28.57/10.23	   A^2 -> H(U1(d, c), k)
28.57/10.23	   A^2 -> H(U1(a, e), d)
28.57/10.23	   A^2 -> H(U1(a, e), k)
28.57/10.23	   A^2 -> H(U1(a, k), d)
28.57/10.23	   A^2 -> H(U1(a, k), k)
28.57/10.23	   A^2 -> H(k, U1(e, b))
28.57/10.23	   A^2 -> H(k, U1(c, d))
28.57/10.23	   A^2 -> H(k, U1(d, c))
28.57/10.23	   A^2 -> H(k, U1(b, e))
28.57/10.23	   A^2 -> H(k, U1(b, k))
28.57/10.23	   A^2 -> H(k, U1(e, c))
28.57/10.23	   A^2 -> H(k, U1(c, e))
28.57/10.23	   A^2 -> H(k, U1(c, k))
28.57/10.23	   A^2 -> H(k, U1(e, e))
28.57/10.23	   A^2 -> H(k, U1(d, k))
28.57/10.23	   A^2 -> H(c, b)
28.57/10.23	   A^2 -> H(c, U1(e, d))
28.57/10.23	   A^2 -> H(c, U1(d, e))
28.57/10.23	   A^2 -> H(c, c)
28.57/10.23	   A^2 -> H(c, U1(e, k))
28.57/10.23	   A^2 -> H(c, U1(k, e))
28.57/10.23	   A^2 -> H(c, e)
28.57/10.23	   A^2 -> H(c, U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, k), b)
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.23	
28.57/10.23	The TRS R consists of the following rules:
28.57/10.23	
28.57/10.23	   f(x) -> U1(x, x)
28.57/10.23	   U1(e, x) -> x
28.57/10.23	   a -> c
28.57/10.23	   a -> d
28.57/10.23	   b -> c
28.57/10.23	   b -> d
28.57/10.23	   d -> k
28.57/10.23	   c -> e
28.57/10.23	   c -> k
28.57/10.23	
28.57/10.23	Q is empty.
28.57/10.23	We have to consider all minimal (P,Q,R)-chains.
28.57/10.23	----------------------------------------
28.57/10.23	
28.57/10.23	(2083) TransformationProof (EQUIVALENT)
28.57/10.23	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.23	
28.57/10.23	   (A^2 -> H(k, U1(k, b)),A^2 -> H(k, U1(k, b)))
28.57/10.23	   (A^2 -> H(U1(e, k), U1(k, c)),A^2 -> H(U1(e, k), U1(k, c)))
28.57/10.23	   (A^2 -> H(U1(e, k), U1(k, d)),A^2 -> H(U1(e, k), U1(k, d)))
28.57/10.23	
28.57/10.23	
28.57/10.23	----------------------------------------
28.57/10.23	
28.57/10.23	(2084)
28.57/10.23	Obligation:
28.57/10.23	Q DP problem:
28.57/10.23	The TRS P consists of the following rules:
28.57/10.23	
28.57/10.23	   G(d, x, x) -> A^2
28.57/10.23	   A^2 -> H(f(c), f(c))
28.57/10.23	   H(x, x) -> G(x, x, f(k))
28.57/10.23	   A^2 -> H(f(d), f(d))
28.57/10.23	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.23	   A^2 -> H(f(e), f(e))
28.57/10.23	   A^2 -> H(f(k), f(k))
28.57/10.23	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.23	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.23	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.23	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.23	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.23	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.23	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.23	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, c), b)
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, c), e)
28.57/10.23	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.23	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.23	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.23	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.23	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.23	   A^2 -> H(U1(k, c), b)
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, c), c)
28.57/10.23	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.23	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, e), b)
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(c, e), c)
28.57/10.23	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(c, e), e)
28.57/10.23	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, k), b)
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(c, k), c)
28.57/10.23	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.23	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.23	   A^2 -> H(U1(c, k), e)
28.57/10.23	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.23	   A^2 -> H(U1(c, c), d)
28.57/10.23	   A^2 -> H(e, U1(e, b))
28.57/10.23	   A^2 -> H(e, U1(c, d))
28.57/10.23	   A^2 -> H(e, U1(d, c))
28.57/10.23	   A^2 -> H(e, U1(b, e))
28.57/10.23	   A^2 -> H(e, U1(b, k))
28.57/10.23	   A^2 -> H(e, U1(e, c))
28.57/10.23	   A^2 -> H(e, U1(c, e))
28.57/10.23	   A^2 -> H(e, U1(c, k))
28.57/10.23	   A^2 -> H(e, U1(e, e))
28.57/10.23	   A^2 -> H(e, U1(d, k))
28.57/10.23	   A^2 -> H(U1(e, e), b)
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.23	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.23	   A^2 -> H(U1(e, e), c)
28.57/10.23	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.23	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.23	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.23	   A^2 -> H(f(e), d)
28.57/10.23	   A^2 -> H(f(e), k)
28.57/10.23	   A^2 -> H(U1(k, k), b)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.23	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.23	   A^2 -> H(U1(k, k), c)
28.57/10.23	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.24	   A^2 -> H(f(k), d)
28.57/10.24	   A^2 -> H(f(k), k)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(k, d), b)
28.57/10.24	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, d), c)
28.57/10.24	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, k), b)
28.57/10.24	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(d, k), c)
28.57/10.24	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.24	   A^2 -> H(U1(d, k), e)
28.57/10.24	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, d), d)
28.57/10.24	   A^2 -> H(U1(d, d), k)
28.57/10.24	   A^2 -> H(U1(e, c), c)
28.57/10.24	   A^2 -> H(U1(c, c), e)
28.57/10.24	   A^2 -> H(U1(c, c), k)
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(e, e), e)
28.57/10.24	   A^2 -> H(d, U1(e, b))
28.57/10.24	   A^2 -> H(d, U1(k, b))
28.57/10.24	   A^2 -> H(d, U1(c, d))
28.57/10.24	   A^2 -> H(d, U1(d, c))
28.57/10.24	   A^2 -> H(d, U1(b, e))
28.57/10.24	   A^2 -> H(d, U1(b, k))
28.57/10.24	   A^2 -> H(d, U1(e, c))
28.57/10.24	   A^2 -> H(d, U1(k, c))
28.57/10.24	   A^2 -> H(d, U1(c, e))
28.57/10.24	   A^2 -> H(d, U1(c, k))
28.57/10.24	   A^2 -> H(d, U1(e, e))
28.57/10.24	   A^2 -> H(d, U1(k, k))
28.57/10.24	   A^2 -> H(d, U1(k, d))
28.57/10.24	   A^2 -> H(d, U1(d, k))
28.57/10.24	   A^2 -> H(a, b)
28.57/10.24	   A^2 -> H(a, U1(e, d))
28.57/10.24	   A^2 -> H(a, U1(d, e))
28.57/10.24	   A^2 -> H(a, c)
28.57/10.24	   A^2 -> H(a, U1(e, k))
28.57/10.24	   A^2 -> H(a, U1(k, e))
28.57/10.24	   A^2 -> H(a, e)
28.57/10.24	   A^2 -> H(a, U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, d), b)
28.57/10.24	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, d), c)
28.57/10.24	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, d), e)
28.57/10.24	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, a), d)
28.57/10.24	   A^2 -> H(U1(e, a), k)
28.57/10.24	   A^2 -> H(U1(k, a), d)
28.57/10.24	   A^2 -> H(U1(c, d), d)
28.57/10.24	   A^2 -> H(U1(c, d), k)
28.57/10.24	   A^2 -> H(U1(d, e), b)
28.57/10.24	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(d, e), c)
28.57/10.24	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(d, e), e)
28.57/10.24	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, c), d)
28.57/10.24	   A^2 -> H(U1(d, c), k)
28.57/10.24	   A^2 -> H(U1(a, e), d)
28.57/10.24	   A^2 -> H(U1(a, e), k)
28.57/10.24	   A^2 -> H(U1(a, k), d)
28.57/10.24	   A^2 -> H(U1(a, k), k)
28.57/10.24	   A^2 -> H(k, U1(e, b))
28.57/10.24	   A^2 -> H(k, U1(c, d))
28.57/10.24	   A^2 -> H(k, U1(d, c))
28.57/10.24	   A^2 -> H(k, U1(b, e))
28.57/10.24	   A^2 -> H(k, U1(b, k))
28.57/10.24	   A^2 -> H(k, U1(e, c))
28.57/10.24	   A^2 -> H(k, U1(c, e))
28.57/10.24	   A^2 -> H(k, U1(c, k))
28.57/10.24	   A^2 -> H(k, U1(e, e))
28.57/10.24	   A^2 -> H(k, U1(d, k))
28.57/10.24	   A^2 -> H(c, b)
28.57/10.24	   A^2 -> H(c, U1(e, d))
28.57/10.24	   A^2 -> H(c, U1(d, e))
28.57/10.24	   A^2 -> H(c, c)
28.57/10.24	   A^2 -> H(c, U1(e, k))
28.57/10.24	   A^2 -> H(c, U1(k, e))
28.57/10.24	   A^2 -> H(c, e)
28.57/10.24	   A^2 -> H(c, U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, k), b)
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.24	   A^2 -> H(k, U1(k, b))
28.57/10.24	
28.57/10.24	The TRS R consists of the following rules:
28.57/10.24	
28.57/10.24	   f(x) -> U1(x, x)
28.57/10.24	   U1(e, x) -> x
28.57/10.24	   a -> c
28.57/10.24	   a -> d
28.57/10.24	   b -> c
28.57/10.24	   b -> d
28.57/10.24	   d -> k
28.57/10.24	   c -> e
28.57/10.24	   c -> k
28.57/10.24	
28.57/10.24	Q is empty.
28.57/10.24	We have to consider all minimal (P,Q,R)-chains.
28.57/10.24	----------------------------------------
28.57/10.24	
28.57/10.24	(2085) DependencyGraphProof (EQUIVALENT)
28.57/10.24	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.24	----------------------------------------
28.57/10.24	
28.57/10.24	(2086)
28.57/10.24	Obligation:
28.57/10.24	Q DP problem:
28.57/10.24	The TRS P consists of the following rules:
28.57/10.24	
28.57/10.24	   A^2 -> H(f(c), f(c))
28.57/10.24	   H(x, x) -> G(x, x, f(k))
28.57/10.24	   G(d, x, x) -> A^2
28.57/10.24	   A^2 -> H(f(d), f(d))
28.57/10.24	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.24	   A^2 -> H(f(e), f(e))
28.57/10.24	   A^2 -> H(f(k), f(k))
28.57/10.24	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.24	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.24	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.24	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.24	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.24	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(c, d))
28.57/10.24	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.24	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.24	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.24	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, c), b)
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, c), e)
28.57/10.24	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.24	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.24	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.24	   A^2 -> H(U1(k, c), b)
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, c), c)
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, e), b)
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(c, e), c)
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(c, e), e)
28.57/10.24	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, k), b)
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(c, k), c)
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.24	   A^2 -> H(U1(c, k), e)
28.57/10.24	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, c), d)
28.57/10.24	   A^2 -> H(e, U1(e, b))
28.57/10.24	   A^2 -> H(e, U1(c, d))
28.57/10.24	   A^2 -> H(e, U1(d, c))
28.57/10.24	   A^2 -> H(e, U1(b, e))
28.57/10.24	   A^2 -> H(e, U1(b, k))
28.57/10.24	   A^2 -> H(e, U1(e, c))
28.57/10.24	   A^2 -> H(e, U1(c, e))
28.57/10.24	   A^2 -> H(e, U1(c, k))
28.57/10.24	   A^2 -> H(e, U1(e, e))
28.57/10.24	   A^2 -> H(e, U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, e), b)
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, e), c)
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.24	   A^2 -> H(f(e), d)
28.57/10.24	   A^2 -> H(f(e), k)
28.57/10.24	   A^2 -> H(U1(k, k), b)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, k), c)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.24	   A^2 -> H(f(k), d)
28.57/10.24	   A^2 -> H(f(k), k)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(k, d), b)
28.57/10.24	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, d), c)
28.57/10.24	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, k), b)
28.57/10.24	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(d, k), c)
28.57/10.24	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.24	   A^2 -> H(U1(d, k), e)
28.57/10.24	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, d), d)
28.57/10.24	   A^2 -> H(U1(d, d), k)
28.57/10.24	   A^2 -> H(U1(e, c), c)
28.57/10.24	   A^2 -> H(U1(c, c), e)
28.57/10.24	   A^2 -> H(U1(c, c), k)
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(e, e), e)
28.57/10.24	   A^2 -> H(d, U1(e, b))
28.57/10.24	   A^2 -> H(d, U1(k, b))
28.57/10.24	   A^2 -> H(d, U1(c, d))
28.57/10.24	   A^2 -> H(d, U1(d, c))
28.57/10.24	   A^2 -> H(d, U1(b, e))
28.57/10.24	   A^2 -> H(d, U1(b, k))
28.57/10.24	   A^2 -> H(d, U1(e, c))
28.57/10.24	   A^2 -> H(d, U1(k, c))
28.57/10.24	   A^2 -> H(d, U1(c, e))
28.57/10.24	   A^2 -> H(d, U1(c, k))
28.57/10.24	   A^2 -> H(d, U1(e, e))
28.57/10.24	   A^2 -> H(d, U1(k, k))
28.57/10.24	   A^2 -> H(d, U1(k, d))
28.57/10.24	   A^2 -> H(d, U1(d, k))
28.57/10.24	   A^2 -> H(a, b)
28.57/10.24	   A^2 -> H(a, U1(e, d))
28.57/10.24	   A^2 -> H(a, U1(d, e))
28.57/10.24	   A^2 -> H(a, c)
28.57/10.24	   A^2 -> H(a, U1(e, k))
28.57/10.24	   A^2 -> H(a, U1(k, e))
28.57/10.24	   A^2 -> H(a, e)
28.57/10.24	   A^2 -> H(a, U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, d), b)
28.57/10.24	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, d), c)
28.57/10.24	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, d), e)
28.57/10.24	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, a), d)
28.57/10.24	   A^2 -> H(U1(e, a), k)
28.57/10.24	   A^2 -> H(U1(k, a), d)
28.57/10.24	   A^2 -> H(U1(c, d), d)
28.57/10.24	   A^2 -> H(U1(c, d), k)
28.57/10.24	   A^2 -> H(U1(d, e), b)
28.57/10.24	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(d, e), c)
28.57/10.24	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(d, e), e)
28.57/10.24	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, c), d)
28.57/10.24	   A^2 -> H(U1(d, c), k)
28.57/10.24	   A^2 -> H(U1(a, e), d)
28.57/10.24	   A^2 -> H(U1(a, e), k)
28.57/10.24	   A^2 -> H(U1(a, k), d)
28.57/10.24	   A^2 -> H(U1(a, k), k)
28.57/10.24	   A^2 -> H(k, U1(e, b))
28.57/10.24	   A^2 -> H(k, U1(c, d))
28.57/10.24	   A^2 -> H(k, U1(d, c))
28.57/10.24	   A^2 -> H(k, U1(b, e))
28.57/10.24	   A^2 -> H(k, U1(b, k))
28.57/10.24	   A^2 -> H(k, U1(e, c))
28.57/10.24	   A^2 -> H(k, U1(c, e))
28.57/10.24	   A^2 -> H(k, U1(c, k))
28.57/10.24	   A^2 -> H(k, U1(e, e))
28.57/10.24	   A^2 -> H(k, U1(d, k))
28.57/10.24	   A^2 -> H(c, b)
28.57/10.24	   A^2 -> H(c, U1(e, d))
28.57/10.24	   A^2 -> H(c, U1(d, e))
28.57/10.24	   A^2 -> H(c, c)
28.57/10.24	   A^2 -> H(c, U1(e, k))
28.57/10.24	   A^2 -> H(c, U1(k, e))
28.57/10.24	   A^2 -> H(c, e)
28.57/10.24	   A^2 -> H(c, U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, k), b)
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.24	
28.57/10.24	The TRS R consists of the following rules:
28.57/10.24	
28.57/10.24	   f(x) -> U1(x, x)
28.57/10.24	   U1(e, x) -> x
28.57/10.24	   a -> c
28.57/10.24	   a -> d
28.57/10.24	   b -> c
28.57/10.24	   b -> d
28.57/10.24	   d -> k
28.57/10.24	   c -> e
28.57/10.24	   c -> k
28.57/10.24	
28.57/10.24	Q is empty.
28.57/10.24	We have to consider all minimal (P,Q,R)-chains.
28.57/10.24	----------------------------------------
28.57/10.24	
28.57/10.24	(2087) TransformationProof (EQUIVALENT)
28.57/10.24	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.24	
28.57/10.24	   (A^2 -> H(k, U1(c, d)),A^2 -> H(k, U1(c, d)))
28.57/10.24	   (A^2 -> H(U1(e, k), U1(e, d)),A^2 -> H(U1(e, k), U1(e, d)))
28.57/10.24	   (A^2 -> H(U1(e, k), U1(k, d)),A^2 -> H(U1(e, k), U1(k, d)))
28.57/10.24	   (A^2 -> H(U1(e, k), U1(c, k)),A^2 -> H(U1(e, k), U1(c, k)))
28.57/10.24	
28.57/10.24	
28.57/10.24	----------------------------------------
28.57/10.24	
28.57/10.24	(2088)
28.57/10.24	Obligation:
28.57/10.24	Q DP problem:
28.57/10.24	The TRS P consists of the following rules:
28.57/10.24	
28.57/10.24	   A^2 -> H(f(c), f(c))
28.57/10.24	   H(x, x) -> G(x, x, f(k))
28.57/10.24	   G(d, x, x) -> A^2
28.57/10.24	   A^2 -> H(f(d), f(d))
28.57/10.24	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.24	   A^2 -> H(f(e), f(e))
28.57/10.24	   A^2 -> H(f(k), f(k))
28.57/10.24	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.24	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.24	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.24	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.24	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.24	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(d, c))
28.57/10.24	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.24	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.24	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, c), b)
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, c), e)
28.57/10.24	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.24	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.24	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.24	   A^2 -> H(U1(k, c), b)
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, c), c)
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, e), b)
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(c, e), c)
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(c, e), e)
28.57/10.24	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, k), b)
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(c, k), c)
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.24	   A^2 -> H(U1(c, k), e)
28.57/10.24	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, c), d)
28.57/10.24	   A^2 -> H(e, U1(e, b))
28.57/10.24	   A^2 -> H(e, U1(c, d))
28.57/10.24	   A^2 -> H(e, U1(d, c))
28.57/10.24	   A^2 -> H(e, U1(b, e))
28.57/10.24	   A^2 -> H(e, U1(b, k))
28.57/10.24	   A^2 -> H(e, U1(e, c))
28.57/10.24	   A^2 -> H(e, U1(c, e))
28.57/10.24	   A^2 -> H(e, U1(c, k))
28.57/10.24	   A^2 -> H(e, U1(e, e))
28.57/10.24	   A^2 -> H(e, U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, e), b)
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, e), c)
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.24	   A^2 -> H(f(e), d)
28.57/10.24	   A^2 -> H(f(e), k)
28.57/10.24	   A^2 -> H(U1(k, k), b)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, k), c)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.24	   A^2 -> H(f(k), d)
28.57/10.24	   A^2 -> H(f(k), k)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(k, d), b)
28.57/10.24	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, d), c)
28.57/10.24	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, k), b)
28.57/10.24	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(d, k), c)
28.57/10.24	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.24	   A^2 -> H(U1(d, k), e)
28.57/10.24	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, d), d)
28.57/10.24	   A^2 -> H(U1(d, d), k)
28.57/10.24	   A^2 -> H(U1(e, c), c)
28.57/10.24	   A^2 -> H(U1(c, c), e)
28.57/10.24	   A^2 -> H(U1(c, c), k)
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(e, e), e)
28.57/10.24	   A^2 -> H(d, U1(e, b))
28.57/10.24	   A^2 -> H(d, U1(k, b))
28.57/10.24	   A^2 -> H(d, U1(c, d))
28.57/10.24	   A^2 -> H(d, U1(d, c))
28.57/10.24	   A^2 -> H(d, U1(b, e))
28.57/10.24	   A^2 -> H(d, U1(b, k))
28.57/10.24	   A^2 -> H(d, U1(e, c))
28.57/10.24	   A^2 -> H(d, U1(k, c))
28.57/10.24	   A^2 -> H(d, U1(c, e))
28.57/10.24	   A^2 -> H(d, U1(c, k))
28.57/10.24	   A^2 -> H(d, U1(e, e))
28.57/10.24	   A^2 -> H(d, U1(k, k))
28.57/10.24	   A^2 -> H(d, U1(k, d))
28.57/10.24	   A^2 -> H(d, U1(d, k))
28.57/10.24	   A^2 -> H(a, b)
28.57/10.24	   A^2 -> H(a, U1(e, d))
28.57/10.24	   A^2 -> H(a, U1(d, e))
28.57/10.24	   A^2 -> H(a, c)
28.57/10.24	   A^2 -> H(a, U1(e, k))
28.57/10.24	   A^2 -> H(a, U1(k, e))
28.57/10.24	   A^2 -> H(a, e)
28.57/10.24	   A^2 -> H(a, U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, d), b)
28.57/10.24	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, d), c)
28.57/10.24	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, d), e)
28.57/10.24	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, a), d)
28.57/10.24	   A^2 -> H(U1(e, a), k)
28.57/10.24	   A^2 -> H(U1(k, a), d)
28.57/10.24	   A^2 -> H(U1(c, d), d)
28.57/10.24	   A^2 -> H(U1(c, d), k)
28.57/10.24	   A^2 -> H(U1(d, e), b)
28.57/10.24	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(d, e), c)
28.57/10.24	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(d, e), e)
28.57/10.24	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, c), d)
28.57/10.24	   A^2 -> H(U1(d, c), k)
28.57/10.24	   A^2 -> H(U1(a, e), d)
28.57/10.24	   A^2 -> H(U1(a, e), k)
28.57/10.24	   A^2 -> H(U1(a, k), d)
28.57/10.24	   A^2 -> H(U1(a, k), k)
28.57/10.24	   A^2 -> H(k, U1(e, b))
28.57/10.24	   A^2 -> H(k, U1(c, d))
28.57/10.24	   A^2 -> H(k, U1(d, c))
28.57/10.24	   A^2 -> H(k, U1(b, e))
28.57/10.24	   A^2 -> H(k, U1(b, k))
28.57/10.24	   A^2 -> H(k, U1(e, c))
28.57/10.24	   A^2 -> H(k, U1(c, e))
28.57/10.24	   A^2 -> H(k, U1(c, k))
28.57/10.24	   A^2 -> H(k, U1(e, e))
28.57/10.24	   A^2 -> H(k, U1(d, k))
28.57/10.24	   A^2 -> H(c, b)
28.57/10.24	   A^2 -> H(c, U1(e, d))
28.57/10.24	   A^2 -> H(c, U1(d, e))
28.57/10.24	   A^2 -> H(c, c)
28.57/10.24	   A^2 -> H(c, U1(e, k))
28.57/10.24	   A^2 -> H(c, U1(k, e))
28.57/10.24	   A^2 -> H(c, e)
28.57/10.24	   A^2 -> H(c, U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, k), b)
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.24	
28.57/10.24	The TRS R consists of the following rules:
28.57/10.24	
28.57/10.24	   f(x) -> U1(x, x)
28.57/10.24	   U1(e, x) -> x
28.57/10.24	   a -> c
28.57/10.24	   a -> d
28.57/10.24	   b -> c
28.57/10.24	   b -> d
28.57/10.24	   d -> k
28.57/10.24	   c -> e
28.57/10.24	   c -> k
28.57/10.24	
28.57/10.24	Q is empty.
28.57/10.24	We have to consider all minimal (P,Q,R)-chains.
28.57/10.24	----------------------------------------
28.57/10.24	
28.57/10.24	(2089) TransformationProof (EQUIVALENT)
28.57/10.24	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.24	
28.57/10.24	   (A^2 -> H(k, U1(d, c)),A^2 -> H(k, U1(d, c)))
28.57/10.24	   (A^2 -> H(U1(e, k), U1(k, c)),A^2 -> H(U1(e, k), U1(k, c)))
28.57/10.24	   (A^2 -> H(U1(e, k), U1(d, e)),A^2 -> H(U1(e, k), U1(d, e)))
28.57/10.24	   (A^2 -> H(U1(e, k), U1(d, k)),A^2 -> H(U1(e, k), U1(d, k)))
28.57/10.24	
28.57/10.24	
28.57/10.24	----------------------------------------
28.57/10.24	
28.57/10.24	(2090)
28.57/10.24	Obligation:
28.57/10.24	Q DP problem:
28.57/10.24	The TRS P consists of the following rules:
28.57/10.24	
28.57/10.24	   A^2 -> H(f(c), f(c))
28.57/10.24	   H(x, x) -> G(x, x, f(k))
28.57/10.24	   G(d, x, x) -> A^2
28.57/10.24	   A^2 -> H(f(d), f(d))
28.57/10.24	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.24	   A^2 -> H(f(e), f(e))
28.57/10.24	   A^2 -> H(f(k), f(k))
28.57/10.24	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.24	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.24	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.24	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.24	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.24	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(b, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.24	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.24	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, c), b)
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, c), e)
28.57/10.24	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.24	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.24	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.24	   A^2 -> H(U1(k, c), b)
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, c), c)
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, e), b)
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(c, e), c)
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(c, e), e)
28.57/10.24	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, k), b)
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(c, k), c)
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.24	   A^2 -> H(U1(c, k), e)
28.57/10.24	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, c), d)
28.57/10.24	   A^2 -> H(e, U1(e, b))
28.57/10.24	   A^2 -> H(e, U1(c, d))
28.57/10.24	   A^2 -> H(e, U1(d, c))
28.57/10.24	   A^2 -> H(e, U1(b, e))
28.57/10.24	   A^2 -> H(e, U1(b, k))
28.57/10.24	   A^2 -> H(e, U1(e, c))
28.57/10.24	   A^2 -> H(e, U1(c, e))
28.57/10.24	   A^2 -> H(e, U1(c, k))
28.57/10.24	   A^2 -> H(e, U1(e, e))
28.57/10.24	   A^2 -> H(e, U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, e), b)
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, e), c)
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.24	   A^2 -> H(f(e), d)
28.57/10.24	   A^2 -> H(f(e), k)
28.57/10.24	   A^2 -> H(U1(k, k), b)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, k), c)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.24	   A^2 -> H(f(k), d)
28.57/10.24	   A^2 -> H(f(k), k)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(k, d), b)
28.57/10.24	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, d), c)
28.57/10.24	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, k), b)
28.57/10.24	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(d, k), c)
28.57/10.24	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.24	   A^2 -> H(U1(d, k), e)
28.57/10.24	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, d), d)
28.57/10.24	   A^2 -> H(U1(d, d), k)
28.57/10.24	   A^2 -> H(U1(e, c), c)
28.57/10.24	   A^2 -> H(U1(c, c), e)
28.57/10.24	   A^2 -> H(U1(c, c), k)
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(e, e), e)
28.57/10.24	   A^2 -> H(d, U1(e, b))
28.57/10.24	   A^2 -> H(d, U1(k, b))
28.57/10.24	   A^2 -> H(d, U1(c, d))
28.57/10.24	   A^2 -> H(d, U1(d, c))
28.57/10.24	   A^2 -> H(d, U1(b, e))
28.57/10.24	   A^2 -> H(d, U1(b, k))
28.57/10.24	   A^2 -> H(d, U1(e, c))
28.57/10.24	   A^2 -> H(d, U1(k, c))
28.57/10.24	   A^2 -> H(d, U1(c, e))
28.57/10.24	   A^2 -> H(d, U1(c, k))
28.57/10.24	   A^2 -> H(d, U1(e, e))
28.57/10.24	   A^2 -> H(d, U1(k, k))
28.57/10.24	   A^2 -> H(d, U1(k, d))
28.57/10.24	   A^2 -> H(d, U1(d, k))
28.57/10.24	   A^2 -> H(a, b)
28.57/10.24	   A^2 -> H(a, U1(e, d))
28.57/10.24	   A^2 -> H(a, U1(d, e))
28.57/10.24	   A^2 -> H(a, c)
28.57/10.24	   A^2 -> H(a, U1(e, k))
28.57/10.24	   A^2 -> H(a, U1(k, e))
28.57/10.24	   A^2 -> H(a, e)
28.57/10.24	   A^2 -> H(a, U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, d), b)
28.57/10.24	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, d), c)
28.57/10.24	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, d), e)
28.57/10.24	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, a), d)
28.57/10.24	   A^2 -> H(U1(e, a), k)
28.57/10.24	   A^2 -> H(U1(k, a), d)
28.57/10.24	   A^2 -> H(U1(c, d), d)
28.57/10.24	   A^2 -> H(U1(c, d), k)
28.57/10.24	   A^2 -> H(U1(d, e), b)
28.57/10.24	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(d, e), c)
28.57/10.24	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(d, e), e)
28.57/10.24	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, c), d)
28.57/10.24	   A^2 -> H(U1(d, c), k)
28.57/10.24	   A^2 -> H(U1(a, e), d)
28.57/10.24	   A^2 -> H(U1(a, e), k)
28.57/10.24	   A^2 -> H(U1(a, k), d)
28.57/10.24	   A^2 -> H(U1(a, k), k)
28.57/10.24	   A^2 -> H(k, U1(e, b))
28.57/10.24	   A^2 -> H(k, U1(c, d))
28.57/10.24	   A^2 -> H(k, U1(d, c))
28.57/10.24	   A^2 -> H(k, U1(b, e))
28.57/10.24	   A^2 -> H(k, U1(b, k))
28.57/10.24	   A^2 -> H(k, U1(e, c))
28.57/10.24	   A^2 -> H(k, U1(c, e))
28.57/10.24	   A^2 -> H(k, U1(c, k))
28.57/10.24	   A^2 -> H(k, U1(e, e))
28.57/10.24	   A^2 -> H(k, U1(d, k))
28.57/10.24	   A^2 -> H(c, b)
28.57/10.24	   A^2 -> H(c, U1(e, d))
28.57/10.24	   A^2 -> H(c, U1(d, e))
28.57/10.24	   A^2 -> H(c, c)
28.57/10.24	   A^2 -> H(c, U1(e, k))
28.57/10.24	   A^2 -> H(c, U1(k, e))
28.57/10.24	   A^2 -> H(c, e)
28.57/10.24	   A^2 -> H(c, U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, k), b)
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.24	
28.57/10.24	The TRS R consists of the following rules:
28.57/10.24	
28.57/10.24	   f(x) -> U1(x, x)
28.57/10.24	   U1(e, x) -> x
28.57/10.24	   a -> c
28.57/10.24	   a -> d
28.57/10.24	   b -> c
28.57/10.24	   b -> d
28.57/10.24	   d -> k
28.57/10.24	   c -> e
28.57/10.24	   c -> k
28.57/10.24	
28.57/10.24	Q is empty.
28.57/10.24	We have to consider all minimal (P,Q,R)-chains.
28.57/10.24	----------------------------------------
28.57/10.24	
28.57/10.24	(2091) TransformationProof (EQUIVALENT)
28.57/10.24	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.24	
28.57/10.24	   (A^2 -> H(k, U1(b, e)),A^2 -> H(k, U1(b, e)))
28.57/10.24	   (A^2 -> H(U1(e, k), U1(c, e)),A^2 -> H(U1(e, k), U1(c, e)))
28.57/10.24	   (A^2 -> H(U1(e, k), U1(d, e)),A^2 -> H(U1(e, k), U1(d, e)))
28.57/10.24	
28.57/10.24	
28.57/10.24	----------------------------------------
28.57/10.24	
28.57/10.24	(2092)
28.57/10.24	Obligation:
28.57/10.24	Q DP problem:
28.57/10.24	The TRS P consists of the following rules:
28.57/10.24	
28.57/10.24	   A^2 -> H(f(c), f(c))
28.57/10.24	   H(x, x) -> G(x, x, f(k))
28.57/10.24	   G(d, x, x) -> A^2
28.57/10.24	   A^2 -> H(f(d), f(d))
28.57/10.24	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.24	   A^2 -> H(f(e), f(e))
28.57/10.24	   A^2 -> H(f(k), f(k))
28.57/10.24	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.24	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.24	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.24	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.24	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.24	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(b, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.24	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.24	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, c), b)
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, c), e)
28.57/10.24	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.24	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.24	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.24	   A^2 -> H(U1(k, c), b)
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, c), c)
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, e), b)
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(c, e), c)
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(c, e), e)
28.57/10.24	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, k), b)
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(c, k), c)
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.24	   A^2 -> H(U1(c, k), e)
28.57/10.24	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, c), d)
28.57/10.24	   A^2 -> H(e, U1(e, b))
28.57/10.24	   A^2 -> H(e, U1(c, d))
28.57/10.24	   A^2 -> H(e, U1(d, c))
28.57/10.24	   A^2 -> H(e, U1(b, e))
28.57/10.24	   A^2 -> H(e, U1(b, k))
28.57/10.24	   A^2 -> H(e, U1(e, c))
28.57/10.24	   A^2 -> H(e, U1(c, e))
28.57/10.24	   A^2 -> H(e, U1(c, k))
28.57/10.24	   A^2 -> H(e, U1(e, e))
28.57/10.24	   A^2 -> H(e, U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, e), b)
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, e), c)
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.24	   A^2 -> H(f(e), d)
28.57/10.24	   A^2 -> H(f(e), k)
28.57/10.24	   A^2 -> H(U1(k, k), b)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, k), c)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.24	   A^2 -> H(f(k), d)
28.57/10.24	   A^2 -> H(f(k), k)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(k, d), b)
28.57/10.24	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, d), c)
28.57/10.24	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, k), b)
28.57/10.24	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(d, k), c)
28.57/10.24	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.24	   A^2 -> H(U1(d, k), e)
28.57/10.24	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, d), d)
28.57/10.24	   A^2 -> H(U1(d, d), k)
28.57/10.24	   A^2 -> H(U1(e, c), c)
28.57/10.24	   A^2 -> H(U1(c, c), e)
28.57/10.24	   A^2 -> H(U1(c, c), k)
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(e, e), e)
28.57/10.24	   A^2 -> H(d, U1(e, b))
28.57/10.24	   A^2 -> H(d, U1(k, b))
28.57/10.24	   A^2 -> H(d, U1(c, d))
28.57/10.24	   A^2 -> H(d, U1(d, c))
28.57/10.24	   A^2 -> H(d, U1(b, e))
28.57/10.24	   A^2 -> H(d, U1(b, k))
28.57/10.24	   A^2 -> H(d, U1(e, c))
28.57/10.24	   A^2 -> H(d, U1(k, c))
28.57/10.24	   A^2 -> H(d, U1(c, e))
28.57/10.24	   A^2 -> H(d, U1(c, k))
28.57/10.24	   A^2 -> H(d, U1(e, e))
28.57/10.24	   A^2 -> H(d, U1(k, k))
28.57/10.24	   A^2 -> H(d, U1(k, d))
28.57/10.24	   A^2 -> H(d, U1(d, k))
28.57/10.24	   A^2 -> H(a, b)
28.57/10.24	   A^2 -> H(a, U1(e, d))
28.57/10.24	   A^2 -> H(a, U1(d, e))
28.57/10.24	   A^2 -> H(a, c)
28.57/10.24	   A^2 -> H(a, U1(e, k))
28.57/10.24	   A^2 -> H(a, U1(k, e))
28.57/10.24	   A^2 -> H(a, e)
28.57/10.24	   A^2 -> H(a, U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, d), b)
28.57/10.24	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, d), c)
28.57/10.24	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, d), e)
28.57/10.24	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, a), d)
28.57/10.24	   A^2 -> H(U1(e, a), k)
28.57/10.24	   A^2 -> H(U1(k, a), d)
28.57/10.24	   A^2 -> H(U1(c, d), d)
28.57/10.24	   A^2 -> H(U1(c, d), k)
28.57/10.24	   A^2 -> H(U1(d, e), b)
28.57/10.24	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(d, e), c)
28.57/10.24	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(d, e), e)
28.57/10.24	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, c), d)
28.57/10.24	   A^2 -> H(U1(d, c), k)
28.57/10.24	   A^2 -> H(U1(a, e), d)
28.57/10.24	   A^2 -> H(U1(a, e), k)
28.57/10.24	   A^2 -> H(U1(a, k), d)
28.57/10.24	   A^2 -> H(U1(a, k), k)
28.57/10.24	   A^2 -> H(k, U1(e, b))
28.57/10.24	   A^2 -> H(k, U1(c, d))
28.57/10.24	   A^2 -> H(k, U1(d, c))
28.57/10.24	   A^2 -> H(k, U1(b, e))
28.57/10.24	   A^2 -> H(k, U1(b, k))
28.57/10.24	   A^2 -> H(k, U1(e, c))
28.57/10.24	   A^2 -> H(k, U1(c, e))
28.57/10.24	   A^2 -> H(k, U1(c, k))
28.57/10.24	   A^2 -> H(k, U1(e, e))
28.57/10.24	   A^2 -> H(k, U1(d, k))
28.57/10.24	   A^2 -> H(c, b)
28.57/10.24	   A^2 -> H(c, U1(e, d))
28.57/10.24	   A^2 -> H(c, U1(d, e))
28.57/10.24	   A^2 -> H(c, c)
28.57/10.24	   A^2 -> H(c, U1(e, k))
28.57/10.24	   A^2 -> H(c, U1(k, e))
28.57/10.24	   A^2 -> H(c, e)
28.57/10.24	   A^2 -> H(c, U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, k), b)
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.24	
28.57/10.24	The TRS R consists of the following rules:
28.57/10.24	
28.57/10.24	   f(x) -> U1(x, x)
28.57/10.24	   U1(e, x) -> x
28.57/10.24	   a -> c
28.57/10.24	   a -> d
28.57/10.24	   b -> c
28.57/10.24	   b -> d
28.57/10.24	   d -> k
28.57/10.24	   c -> e
28.57/10.24	   c -> k
28.57/10.24	
28.57/10.24	Q is empty.
28.57/10.24	We have to consider all minimal (P,Q,R)-chains.
28.57/10.24	----------------------------------------
28.57/10.24	
28.57/10.24	(2093) TransformationProof (EQUIVALENT)
28.57/10.24	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.24	
28.57/10.24	   (A^2 -> H(k, U1(b, k)),A^2 -> H(k, U1(b, k)))
28.57/10.24	   (A^2 -> H(U1(e, k), U1(c, k)),A^2 -> H(U1(e, k), U1(c, k)))
28.57/10.24	   (A^2 -> H(U1(e, k), U1(d, k)),A^2 -> H(U1(e, k), U1(d, k)))
28.57/10.24	
28.57/10.24	
28.57/10.24	----------------------------------------
28.57/10.24	
28.57/10.24	(2094)
28.57/10.24	Obligation:
28.57/10.24	Q DP problem:
28.57/10.24	The TRS P consists of the following rules:
28.57/10.24	
28.57/10.24	   A^2 -> H(f(c), f(c))
28.57/10.24	   H(x, x) -> G(x, x, f(k))
28.57/10.24	   G(d, x, x) -> A^2
28.57/10.24	   A^2 -> H(f(d), f(d))
28.57/10.24	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.24	   A^2 -> H(f(e), f(e))
28.57/10.24	   A^2 -> H(f(k), f(k))
28.57/10.24	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.24	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.24	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.24	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.24	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.24	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, c))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.24	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.24	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, c), b)
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, c), e)
28.57/10.24	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.24	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.24	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.24	   A^2 -> H(U1(k, c), b)
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, c), c)
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, e), b)
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(c, e), c)
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(c, e), e)
28.57/10.24	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, k), b)
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(c, k), c)
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.24	   A^2 -> H(U1(c, k), e)
28.57/10.24	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, c), d)
28.57/10.24	   A^2 -> H(e, U1(e, b))
28.57/10.24	   A^2 -> H(e, U1(c, d))
28.57/10.24	   A^2 -> H(e, U1(d, c))
28.57/10.24	   A^2 -> H(e, U1(b, e))
28.57/10.24	   A^2 -> H(e, U1(b, k))
28.57/10.24	   A^2 -> H(e, U1(e, c))
28.57/10.24	   A^2 -> H(e, U1(c, e))
28.57/10.24	   A^2 -> H(e, U1(c, k))
28.57/10.24	   A^2 -> H(e, U1(e, e))
28.57/10.24	   A^2 -> H(e, U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, e), b)
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, e), c)
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.24	   A^2 -> H(f(e), d)
28.57/10.24	   A^2 -> H(f(e), k)
28.57/10.24	   A^2 -> H(U1(k, k), b)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, k), c)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.24	   A^2 -> H(f(k), d)
28.57/10.24	   A^2 -> H(f(k), k)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(k, d), b)
28.57/10.24	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, d), c)
28.57/10.24	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, k), b)
28.57/10.24	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(d, k), c)
28.57/10.24	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.24	   A^2 -> H(U1(d, k), e)
28.57/10.24	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, d), d)
28.57/10.24	   A^2 -> H(U1(d, d), k)
28.57/10.24	   A^2 -> H(U1(e, c), c)
28.57/10.24	   A^2 -> H(U1(c, c), e)
28.57/10.24	   A^2 -> H(U1(c, c), k)
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(e, e), e)
28.57/10.24	   A^2 -> H(d, U1(e, b))
28.57/10.24	   A^2 -> H(d, U1(k, b))
28.57/10.24	   A^2 -> H(d, U1(c, d))
28.57/10.24	   A^2 -> H(d, U1(d, c))
28.57/10.24	   A^2 -> H(d, U1(b, e))
28.57/10.24	   A^2 -> H(d, U1(b, k))
28.57/10.24	   A^2 -> H(d, U1(e, c))
28.57/10.24	   A^2 -> H(d, U1(k, c))
28.57/10.24	   A^2 -> H(d, U1(c, e))
28.57/10.24	   A^2 -> H(d, U1(c, k))
28.57/10.24	   A^2 -> H(d, U1(e, e))
28.57/10.24	   A^2 -> H(d, U1(k, k))
28.57/10.24	   A^2 -> H(d, U1(k, d))
28.57/10.24	   A^2 -> H(d, U1(d, k))
28.57/10.24	   A^2 -> H(a, b)
28.57/10.24	   A^2 -> H(a, U1(e, d))
28.57/10.24	   A^2 -> H(a, U1(d, e))
28.57/10.24	   A^2 -> H(a, c)
28.57/10.24	   A^2 -> H(a, U1(e, k))
28.57/10.24	   A^2 -> H(a, U1(k, e))
28.57/10.24	   A^2 -> H(a, e)
28.57/10.24	   A^2 -> H(a, U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, d), b)
28.57/10.24	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, d), c)
28.57/10.24	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, d), e)
28.57/10.24	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, a), d)
28.57/10.24	   A^2 -> H(U1(e, a), k)
28.57/10.24	   A^2 -> H(U1(k, a), d)
28.57/10.24	   A^2 -> H(U1(c, d), d)
28.57/10.24	   A^2 -> H(U1(c, d), k)
28.57/10.24	   A^2 -> H(U1(d, e), b)
28.57/10.24	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(d, e), c)
28.57/10.24	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(d, e), e)
28.57/10.24	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, c), d)
28.57/10.24	   A^2 -> H(U1(d, c), k)
28.57/10.24	   A^2 -> H(U1(a, e), d)
28.57/10.24	   A^2 -> H(U1(a, e), k)
28.57/10.24	   A^2 -> H(U1(a, k), d)
28.57/10.24	   A^2 -> H(U1(a, k), k)
28.57/10.24	   A^2 -> H(k, U1(e, b))
28.57/10.24	   A^2 -> H(k, U1(c, d))
28.57/10.24	   A^2 -> H(k, U1(d, c))
28.57/10.24	   A^2 -> H(k, U1(b, e))
28.57/10.24	   A^2 -> H(k, U1(b, k))
28.57/10.24	   A^2 -> H(k, U1(e, c))
28.57/10.24	   A^2 -> H(k, U1(c, e))
28.57/10.24	   A^2 -> H(k, U1(c, k))
28.57/10.24	   A^2 -> H(k, U1(e, e))
28.57/10.24	   A^2 -> H(k, U1(d, k))
28.57/10.24	   A^2 -> H(c, b)
28.57/10.24	   A^2 -> H(c, U1(e, d))
28.57/10.24	   A^2 -> H(c, U1(d, e))
28.57/10.24	   A^2 -> H(c, c)
28.57/10.24	   A^2 -> H(c, U1(e, k))
28.57/10.24	   A^2 -> H(c, U1(k, e))
28.57/10.24	   A^2 -> H(c, e)
28.57/10.24	   A^2 -> H(c, U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, k), b)
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.24	
28.57/10.24	The TRS R consists of the following rules:
28.57/10.24	
28.57/10.24	   f(x) -> U1(x, x)
28.57/10.24	   U1(e, x) -> x
28.57/10.24	   a -> c
28.57/10.24	   a -> d
28.57/10.24	   b -> c
28.57/10.24	   b -> d
28.57/10.24	   d -> k
28.57/10.24	   c -> e
28.57/10.24	   c -> k
28.57/10.24	
28.57/10.24	Q is empty.
28.57/10.24	We have to consider all minimal (P,Q,R)-chains.
28.57/10.24	----------------------------------------
28.57/10.24	
28.57/10.24	(2095) TransformationProof (EQUIVALENT)
28.57/10.24	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.24	
28.57/10.24	   (A^2 -> H(k, U1(e, c)),A^2 -> H(k, U1(e, c)))
28.57/10.24	   (A^2 -> H(U1(e, k), c),A^2 -> H(U1(e, k), c))
28.57/10.24	   (A^2 -> H(U1(e, k), U1(e, e)),A^2 -> H(U1(e, k), U1(e, e)))
28.57/10.24	   (A^2 -> H(U1(e, k), U1(e, k)),A^2 -> H(U1(e, k), U1(e, k)))
28.57/10.24	
28.57/10.24	
28.57/10.24	----------------------------------------
28.57/10.24	
28.57/10.24	(2096)
28.57/10.24	Obligation:
28.57/10.24	Q DP problem:
28.57/10.24	The TRS P consists of the following rules:
28.57/10.24	
28.57/10.24	   A^2 -> H(f(c), f(c))
28.57/10.24	   H(x, x) -> G(x, x, f(k))
28.57/10.24	   G(d, x, x) -> A^2
28.57/10.24	   A^2 -> H(f(d), f(d))
28.57/10.24	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.24	   A^2 -> H(f(e), f(e))
28.57/10.24	   A^2 -> H(f(k), f(k))
28.57/10.24	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.24	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.24	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.24	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.24	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.24	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, c))
28.57/10.24	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.24	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, c), b)
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, c), e)
28.57/10.24	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.24	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.24	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.24	   A^2 -> H(U1(k, c), b)
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, c), c)
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, e), b)
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(c, e), c)
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(c, e), e)
28.57/10.24	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, k), b)
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(c, k), c)
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.24	   A^2 -> H(U1(c, k), e)
28.57/10.24	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, c), d)
28.57/10.24	   A^2 -> H(e, U1(e, b))
28.57/10.24	   A^2 -> H(e, U1(c, d))
28.57/10.24	   A^2 -> H(e, U1(d, c))
28.57/10.24	   A^2 -> H(e, U1(b, e))
28.57/10.24	   A^2 -> H(e, U1(b, k))
28.57/10.24	   A^2 -> H(e, U1(e, c))
28.57/10.24	   A^2 -> H(e, U1(c, e))
28.57/10.24	   A^2 -> H(e, U1(c, k))
28.57/10.24	   A^2 -> H(e, U1(e, e))
28.57/10.24	   A^2 -> H(e, U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, e), b)
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, e), c)
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.24	   A^2 -> H(f(e), d)
28.57/10.24	   A^2 -> H(f(e), k)
28.57/10.24	   A^2 -> H(U1(k, k), b)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, k), c)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.24	   A^2 -> H(f(k), d)
28.57/10.24	   A^2 -> H(f(k), k)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(k, d), b)
28.57/10.24	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, d), c)
28.57/10.24	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, k), b)
28.57/10.24	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(d, k), c)
28.57/10.24	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.24	   A^2 -> H(U1(d, k), e)
28.57/10.24	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, d), d)
28.57/10.24	   A^2 -> H(U1(d, d), k)
28.57/10.24	   A^2 -> H(U1(e, c), c)
28.57/10.24	   A^2 -> H(U1(c, c), e)
28.57/10.24	   A^2 -> H(U1(c, c), k)
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(e, e), e)
28.57/10.24	   A^2 -> H(d, U1(e, b))
28.57/10.24	   A^2 -> H(d, U1(k, b))
28.57/10.24	   A^2 -> H(d, U1(c, d))
28.57/10.24	   A^2 -> H(d, U1(d, c))
28.57/10.24	   A^2 -> H(d, U1(b, e))
28.57/10.24	   A^2 -> H(d, U1(b, k))
28.57/10.24	   A^2 -> H(d, U1(e, c))
28.57/10.24	   A^2 -> H(d, U1(k, c))
28.57/10.24	   A^2 -> H(d, U1(c, e))
28.57/10.24	   A^2 -> H(d, U1(c, k))
28.57/10.24	   A^2 -> H(d, U1(e, e))
28.57/10.24	   A^2 -> H(d, U1(k, k))
28.57/10.24	   A^2 -> H(d, U1(k, d))
28.57/10.24	   A^2 -> H(d, U1(d, k))
28.57/10.24	   A^2 -> H(a, b)
28.57/10.24	   A^2 -> H(a, U1(e, d))
28.57/10.24	   A^2 -> H(a, U1(d, e))
28.57/10.24	   A^2 -> H(a, c)
28.57/10.24	   A^2 -> H(a, U1(e, k))
28.57/10.24	   A^2 -> H(a, U1(k, e))
28.57/10.24	   A^2 -> H(a, e)
28.57/10.24	   A^2 -> H(a, U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, d), b)
28.57/10.24	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, d), c)
28.57/10.24	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, d), e)
28.57/10.24	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, a), d)
28.57/10.24	   A^2 -> H(U1(e, a), k)
28.57/10.24	   A^2 -> H(U1(k, a), d)
28.57/10.24	   A^2 -> H(U1(c, d), d)
28.57/10.24	   A^2 -> H(U1(c, d), k)
28.57/10.24	   A^2 -> H(U1(d, e), b)
28.57/10.24	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(d, e), c)
28.57/10.24	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(d, e), e)
28.57/10.24	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, c), d)
28.57/10.24	   A^2 -> H(U1(d, c), k)
28.57/10.24	   A^2 -> H(U1(a, e), d)
28.57/10.24	   A^2 -> H(U1(a, e), k)
28.57/10.24	   A^2 -> H(U1(a, k), d)
28.57/10.24	   A^2 -> H(U1(a, k), k)
28.57/10.24	   A^2 -> H(k, U1(e, b))
28.57/10.24	   A^2 -> H(k, U1(c, d))
28.57/10.24	   A^2 -> H(k, U1(d, c))
28.57/10.24	   A^2 -> H(k, U1(b, e))
28.57/10.24	   A^2 -> H(k, U1(b, k))
28.57/10.24	   A^2 -> H(k, U1(e, c))
28.57/10.24	   A^2 -> H(k, U1(c, e))
28.57/10.24	   A^2 -> H(k, U1(c, k))
28.57/10.24	   A^2 -> H(k, U1(e, e))
28.57/10.24	   A^2 -> H(k, U1(d, k))
28.57/10.24	   A^2 -> H(c, b)
28.57/10.24	   A^2 -> H(c, U1(e, d))
28.57/10.24	   A^2 -> H(c, U1(d, e))
28.57/10.24	   A^2 -> H(c, c)
28.57/10.24	   A^2 -> H(c, U1(e, k))
28.57/10.24	   A^2 -> H(c, U1(k, e))
28.57/10.24	   A^2 -> H(c, e)
28.57/10.24	   A^2 -> H(c, U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, k), b)
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, k), c)
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.24	
28.57/10.24	The TRS R consists of the following rules:
28.57/10.24	
28.57/10.24	   f(x) -> U1(x, x)
28.57/10.24	   U1(e, x) -> x
28.57/10.24	   a -> c
28.57/10.24	   a -> d
28.57/10.24	   b -> c
28.57/10.24	   b -> d
28.57/10.24	   d -> k
28.57/10.24	   c -> e
28.57/10.24	   c -> k
28.57/10.24	
28.57/10.24	Q is empty.
28.57/10.24	We have to consider all minimal (P,Q,R)-chains.
28.57/10.24	----------------------------------------
28.57/10.24	
28.57/10.24	(2097) TransformationProof (EQUIVALENT)
28.57/10.24	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.24	
28.57/10.24	   (A^2 -> H(k, U1(k, c)),A^2 -> H(k, U1(k, c)))
28.57/10.24	   (A^2 -> H(U1(e, k), U1(k, e)),A^2 -> H(U1(e, k), U1(k, e)))
28.57/10.24	   (A^2 -> H(U1(e, k), U1(k, k)),A^2 -> H(U1(e, k), U1(k, k)))
28.57/10.24	
28.57/10.24	
28.57/10.24	----------------------------------------
28.57/10.24	
28.57/10.24	(2098)
28.57/10.24	Obligation:
28.57/10.24	Q DP problem:
28.57/10.24	The TRS P consists of the following rules:
28.57/10.24	
28.57/10.24	   A^2 -> H(f(c), f(c))
28.57/10.24	   H(x, x) -> G(x, x, f(k))
28.57/10.24	   G(d, x, x) -> A^2
28.57/10.24	   A^2 -> H(f(d), f(d))
28.57/10.24	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.24	   A^2 -> H(f(e), f(e))
28.57/10.24	   A^2 -> H(f(k), f(k))
28.57/10.24	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.24	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.24	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.24	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.24	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.24	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.24	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, c), b)
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, c), e)
28.57/10.24	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.24	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.24	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.24	   A^2 -> H(U1(k, c), b)
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, c), c)
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, e), b)
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(c, e), c)
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(c, e), e)
28.57/10.24	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, k), b)
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(c, k), c)
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.24	   A^2 -> H(U1(c, k), e)
28.57/10.24	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, c), d)
28.57/10.24	   A^2 -> H(e, U1(e, b))
28.57/10.24	   A^2 -> H(e, U1(c, d))
28.57/10.24	   A^2 -> H(e, U1(d, c))
28.57/10.24	   A^2 -> H(e, U1(b, e))
28.57/10.24	   A^2 -> H(e, U1(b, k))
28.57/10.24	   A^2 -> H(e, U1(e, c))
28.57/10.24	   A^2 -> H(e, U1(c, e))
28.57/10.24	   A^2 -> H(e, U1(c, k))
28.57/10.24	   A^2 -> H(e, U1(e, e))
28.57/10.24	   A^2 -> H(e, U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, e), b)
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, e), c)
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.24	   A^2 -> H(f(e), d)
28.57/10.24	   A^2 -> H(f(e), k)
28.57/10.24	   A^2 -> H(U1(k, k), b)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, k), c)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.24	   A^2 -> H(f(k), d)
28.57/10.24	   A^2 -> H(f(k), k)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(k, d), b)
28.57/10.24	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, d), c)
28.57/10.24	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, k), b)
28.57/10.24	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(d, k), c)
28.57/10.24	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.24	   A^2 -> H(U1(d, k), e)
28.57/10.24	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, d), d)
28.57/10.24	   A^2 -> H(U1(d, d), k)
28.57/10.24	   A^2 -> H(U1(e, c), c)
28.57/10.24	   A^2 -> H(U1(c, c), e)
28.57/10.24	   A^2 -> H(U1(c, c), k)
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(e, e), e)
28.57/10.24	   A^2 -> H(d, U1(e, b))
28.57/10.24	   A^2 -> H(d, U1(k, b))
28.57/10.24	   A^2 -> H(d, U1(c, d))
28.57/10.24	   A^2 -> H(d, U1(d, c))
28.57/10.24	   A^2 -> H(d, U1(b, e))
28.57/10.24	   A^2 -> H(d, U1(b, k))
28.57/10.24	   A^2 -> H(d, U1(e, c))
28.57/10.24	   A^2 -> H(d, U1(k, c))
28.57/10.24	   A^2 -> H(d, U1(c, e))
28.57/10.24	   A^2 -> H(d, U1(c, k))
28.57/10.24	   A^2 -> H(d, U1(e, e))
28.57/10.24	   A^2 -> H(d, U1(k, k))
28.57/10.24	   A^2 -> H(d, U1(k, d))
28.57/10.24	   A^2 -> H(d, U1(d, k))
28.57/10.24	   A^2 -> H(a, b)
28.57/10.24	   A^2 -> H(a, U1(e, d))
28.57/10.24	   A^2 -> H(a, U1(d, e))
28.57/10.24	   A^2 -> H(a, c)
28.57/10.24	   A^2 -> H(a, U1(e, k))
28.57/10.24	   A^2 -> H(a, U1(k, e))
28.57/10.24	   A^2 -> H(a, e)
28.57/10.24	   A^2 -> H(a, U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, d), b)
28.57/10.24	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, d), c)
28.57/10.24	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, d), e)
28.57/10.24	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, a), d)
28.57/10.24	   A^2 -> H(U1(e, a), k)
28.57/10.24	   A^2 -> H(U1(k, a), d)
28.57/10.24	   A^2 -> H(U1(c, d), d)
28.57/10.24	   A^2 -> H(U1(c, d), k)
28.57/10.24	   A^2 -> H(U1(d, e), b)
28.57/10.24	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(d, e), c)
28.57/10.24	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(d, e), e)
28.57/10.24	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, c), d)
28.57/10.24	   A^2 -> H(U1(d, c), k)
28.57/10.24	   A^2 -> H(U1(a, e), d)
28.57/10.24	   A^2 -> H(U1(a, e), k)
28.57/10.24	   A^2 -> H(U1(a, k), d)
28.57/10.24	   A^2 -> H(U1(a, k), k)
28.57/10.24	   A^2 -> H(k, U1(e, b))
28.57/10.24	   A^2 -> H(k, U1(c, d))
28.57/10.24	   A^2 -> H(k, U1(d, c))
28.57/10.24	   A^2 -> H(k, U1(b, e))
28.57/10.24	   A^2 -> H(k, U1(b, k))
28.57/10.24	   A^2 -> H(k, U1(e, c))
28.57/10.24	   A^2 -> H(k, U1(c, e))
28.57/10.24	   A^2 -> H(k, U1(c, k))
28.57/10.24	   A^2 -> H(k, U1(e, e))
28.57/10.24	   A^2 -> H(k, U1(d, k))
28.57/10.24	   A^2 -> H(c, b)
28.57/10.24	   A^2 -> H(c, U1(e, d))
28.57/10.24	   A^2 -> H(c, U1(d, e))
28.57/10.24	   A^2 -> H(c, c)
28.57/10.24	   A^2 -> H(c, U1(e, k))
28.57/10.24	   A^2 -> H(c, U1(k, e))
28.57/10.24	   A^2 -> H(c, e)
28.57/10.24	   A^2 -> H(c, U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, k), b)
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, k), c)
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.24	   A^2 -> H(k, U1(k, c))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.24	
28.57/10.24	The TRS R consists of the following rules:
28.57/10.24	
28.57/10.24	   f(x) -> U1(x, x)
28.57/10.24	   U1(e, x) -> x
28.57/10.24	   a -> c
28.57/10.24	   a -> d
28.57/10.24	   b -> c
28.57/10.24	   b -> d
28.57/10.24	   d -> k
28.57/10.24	   c -> e
28.57/10.24	   c -> k
28.57/10.24	
28.57/10.24	Q is empty.
28.57/10.24	We have to consider all minimal (P,Q,R)-chains.
28.57/10.24	----------------------------------------
28.57/10.24	
28.57/10.24	(2099) DependencyGraphProof (EQUIVALENT)
28.57/10.24	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.24	----------------------------------------
28.57/10.24	
28.57/10.24	(2100)
28.57/10.24	Obligation:
28.57/10.24	Q DP problem:
28.57/10.24	The TRS P consists of the following rules:
28.57/10.24	
28.57/10.24	   H(x, x) -> G(x, x, f(k))
28.57/10.24	   G(d, x, x) -> A^2
28.57/10.24	   A^2 -> H(f(c), f(c))
28.57/10.24	   A^2 -> H(f(d), f(d))
28.57/10.24	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.24	   A^2 -> H(f(e), f(e))
28.57/10.24	   A^2 -> H(f(k), f(k))
28.57/10.24	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.24	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.24	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.24	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.24	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.24	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(c, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.24	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, c), b)
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, c), e)
28.57/10.24	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.24	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.24	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.24	   A^2 -> H(U1(k, c), b)
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, c), c)
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, e), b)
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(c, e), c)
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(c, e), e)
28.57/10.24	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, k), b)
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(c, k), c)
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.24	   A^2 -> H(U1(c, k), e)
28.57/10.24	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, c), d)
28.57/10.24	   A^2 -> H(e, U1(e, b))
28.57/10.24	   A^2 -> H(e, U1(c, d))
28.57/10.24	   A^2 -> H(e, U1(d, c))
28.57/10.24	   A^2 -> H(e, U1(b, e))
28.57/10.24	   A^2 -> H(e, U1(b, k))
28.57/10.24	   A^2 -> H(e, U1(e, c))
28.57/10.24	   A^2 -> H(e, U1(c, e))
28.57/10.24	   A^2 -> H(e, U1(c, k))
28.57/10.24	   A^2 -> H(e, U1(e, e))
28.57/10.24	   A^2 -> H(e, U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, e), b)
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, e), c)
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.24	   A^2 -> H(f(e), d)
28.57/10.24	   A^2 -> H(f(e), k)
28.57/10.24	   A^2 -> H(U1(k, k), b)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, k), c)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.24	   A^2 -> H(f(k), d)
28.57/10.24	   A^2 -> H(f(k), k)
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.24	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(k, d), b)
28.57/10.24	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, d), c)
28.57/10.24	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, k), b)
28.57/10.24	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(d, k), c)
28.57/10.24	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.24	   A^2 -> H(U1(d, k), e)
28.57/10.24	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, d), d)
28.57/10.24	   A^2 -> H(U1(d, d), k)
28.57/10.24	   A^2 -> H(U1(e, c), c)
28.57/10.24	   A^2 -> H(U1(c, c), e)
28.57/10.24	   A^2 -> H(U1(c, c), k)
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(e, e), e)
28.57/10.24	   A^2 -> H(d, U1(e, b))
28.57/10.24	   A^2 -> H(d, U1(k, b))
28.57/10.24	   A^2 -> H(d, U1(c, d))
28.57/10.24	   A^2 -> H(d, U1(d, c))
28.57/10.24	   A^2 -> H(d, U1(b, e))
28.57/10.24	   A^2 -> H(d, U1(b, k))
28.57/10.24	   A^2 -> H(d, U1(e, c))
28.57/10.24	   A^2 -> H(d, U1(k, c))
28.57/10.24	   A^2 -> H(d, U1(c, e))
28.57/10.24	   A^2 -> H(d, U1(c, k))
28.57/10.24	   A^2 -> H(d, U1(e, e))
28.57/10.24	   A^2 -> H(d, U1(k, k))
28.57/10.24	   A^2 -> H(d, U1(k, d))
28.57/10.24	   A^2 -> H(d, U1(d, k))
28.57/10.24	   A^2 -> H(a, b)
28.57/10.24	   A^2 -> H(a, U1(e, d))
28.57/10.24	   A^2 -> H(a, U1(d, e))
28.57/10.24	   A^2 -> H(a, c)
28.57/10.24	   A^2 -> H(a, U1(e, k))
28.57/10.24	   A^2 -> H(a, U1(k, e))
28.57/10.24	   A^2 -> H(a, e)
28.57/10.24	   A^2 -> H(a, U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, d), b)
28.57/10.24	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, d), c)
28.57/10.24	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, d), e)
28.57/10.24	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, a), d)
28.57/10.24	   A^2 -> H(U1(e, a), k)
28.57/10.24	   A^2 -> H(U1(k, a), d)
28.57/10.24	   A^2 -> H(U1(c, d), d)
28.57/10.24	   A^2 -> H(U1(c, d), k)
28.57/10.24	   A^2 -> H(U1(d, e), b)
28.57/10.24	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(d, e), c)
28.57/10.24	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(d, e), e)
28.57/10.24	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.24	   A^2 -> H(U1(d, c), d)
28.57/10.24	   A^2 -> H(U1(d, c), k)
28.57/10.24	   A^2 -> H(U1(a, e), d)
28.57/10.24	   A^2 -> H(U1(a, e), k)
28.57/10.24	   A^2 -> H(U1(a, k), d)
28.57/10.24	   A^2 -> H(U1(a, k), k)
28.57/10.24	   A^2 -> H(k, U1(e, b))
28.57/10.24	   A^2 -> H(k, U1(c, d))
28.57/10.24	   A^2 -> H(k, U1(d, c))
28.57/10.24	   A^2 -> H(k, U1(b, e))
28.57/10.24	   A^2 -> H(k, U1(b, k))
28.57/10.24	   A^2 -> H(k, U1(e, c))
28.57/10.24	   A^2 -> H(k, U1(c, e))
28.57/10.24	   A^2 -> H(k, U1(c, k))
28.57/10.24	   A^2 -> H(k, U1(e, e))
28.57/10.24	   A^2 -> H(k, U1(d, k))
28.57/10.24	   A^2 -> H(c, b)
28.57/10.24	   A^2 -> H(c, U1(e, d))
28.57/10.24	   A^2 -> H(c, U1(d, e))
28.57/10.24	   A^2 -> H(c, c)
28.57/10.24	   A^2 -> H(c, U1(e, k))
28.57/10.24	   A^2 -> H(c, U1(k, e))
28.57/10.24	   A^2 -> H(c, e)
28.57/10.24	   A^2 -> H(c, U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, k), b)
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, k), c)
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.24	
28.57/10.24	The TRS R consists of the following rules:
28.57/10.24	
28.57/10.24	   f(x) -> U1(x, x)
28.57/10.24	   U1(e, x) -> x
28.57/10.24	   a -> c
28.57/10.24	   a -> d
28.57/10.24	   b -> c
28.57/10.24	   b -> d
28.57/10.24	   d -> k
28.57/10.24	   c -> e
28.57/10.24	   c -> k
28.57/10.24	
28.57/10.24	Q is empty.
28.57/10.24	We have to consider all minimal (P,Q,R)-chains.
28.57/10.24	----------------------------------------
28.57/10.24	
28.57/10.24	(2101) TransformationProof (EQUIVALENT)
28.57/10.24	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.24	
28.57/10.24	   (A^2 -> H(k, U1(c, e)),A^2 -> H(k, U1(c, e)))
28.57/10.24	   (A^2 -> H(U1(e, k), U1(e, e)),A^2 -> H(U1(e, k), U1(e, e)))
28.57/10.24	   (A^2 -> H(U1(e, k), U1(k, e)),A^2 -> H(U1(e, k), U1(k, e)))
28.57/10.24	
28.57/10.24	
28.57/10.24	----------------------------------------
28.57/10.24	
28.57/10.24	(2102)
28.57/10.24	Obligation:
28.57/10.24	Q DP problem:
28.57/10.24	The TRS P consists of the following rules:
28.57/10.24	
28.57/10.24	   H(x, x) -> G(x, x, f(k))
28.57/10.24	   G(d, x, x) -> A^2
28.57/10.24	   A^2 -> H(f(c), f(c))
28.57/10.24	   A^2 -> H(f(d), f(d))
28.57/10.24	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.24	   A^2 -> H(f(e), f(e))
28.57/10.24	   A^2 -> H(f(k), f(k))
28.57/10.24	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.24	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.24	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.24	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.24	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.24	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(c, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.24	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.24	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.24	   A^2 -> H(U1(e, c), b)
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.24	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.24	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.24	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.24	   A^2 -> H(U1(e, c), e)
28.57/10.24	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.24	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.24	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.24	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.24	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.24	   A^2 -> H(U1(k, c), b)
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.24	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.24	   A^2 -> H(U1(k, c), c)
28.57/10.24	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.24	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, e), b)
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.24	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.24	   A^2 -> H(U1(c, e), c)
28.57/10.24	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.24	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.24	   A^2 -> H(U1(c, e), e)
28.57/10.24	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.24	   A^2 -> H(U1(c, k), b)
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.24	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.24	   A^2 -> H(U1(c, k), c)
28.57/10.24	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.24	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, k), e)
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, c), d)
28.57/10.25	   A^2 -> H(e, U1(e, b))
28.57/10.25	   A^2 -> H(e, U1(c, d))
28.57/10.25	   A^2 -> H(e, U1(d, c))
28.57/10.25	   A^2 -> H(e, U1(b, e))
28.57/10.25	   A^2 -> H(e, U1(b, k))
28.57/10.25	   A^2 -> H(e, U1(e, c))
28.57/10.25	   A^2 -> H(e, U1(c, e))
28.57/10.25	   A^2 -> H(e, U1(c, k))
28.57/10.25	   A^2 -> H(e, U1(e, e))
28.57/10.25	   A^2 -> H(e, U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, e), b)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, e), c)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.25	   A^2 -> H(f(e), d)
28.57/10.25	   A^2 -> H(f(e), k)
28.57/10.25	   A^2 -> H(U1(k, k), b)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, k), c)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.25	   A^2 -> H(f(k), d)
28.57/10.25	   A^2 -> H(f(k), k)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(k, d), b)
28.57/10.25	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, d), c)
28.57/10.25	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, k), b)
28.57/10.25	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(d, k), c)
28.57/10.25	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(d, k), e)
28.57/10.25	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, d), d)
28.57/10.25	   A^2 -> H(U1(d, d), k)
28.57/10.25	   A^2 -> H(U1(e, c), c)
28.57/10.25	   A^2 -> H(U1(c, c), e)
28.57/10.25	   A^2 -> H(U1(c, c), k)
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(e, e), e)
28.57/10.25	   A^2 -> H(d, U1(e, b))
28.57/10.25	   A^2 -> H(d, U1(k, b))
28.57/10.25	   A^2 -> H(d, U1(c, d))
28.57/10.25	   A^2 -> H(d, U1(d, c))
28.57/10.25	   A^2 -> H(d, U1(b, e))
28.57/10.25	   A^2 -> H(d, U1(b, k))
28.57/10.25	   A^2 -> H(d, U1(e, c))
28.57/10.25	   A^2 -> H(d, U1(k, c))
28.57/10.25	   A^2 -> H(d, U1(c, e))
28.57/10.25	   A^2 -> H(d, U1(c, k))
28.57/10.25	   A^2 -> H(d, U1(e, e))
28.57/10.25	   A^2 -> H(d, U1(k, k))
28.57/10.25	   A^2 -> H(d, U1(k, d))
28.57/10.25	   A^2 -> H(d, U1(d, k))
28.57/10.25	   A^2 -> H(a, b)
28.57/10.25	   A^2 -> H(a, U1(e, d))
28.57/10.25	   A^2 -> H(a, U1(d, e))
28.57/10.25	   A^2 -> H(a, c)
28.57/10.25	   A^2 -> H(a, U1(e, k))
28.57/10.25	   A^2 -> H(a, U1(k, e))
28.57/10.25	   A^2 -> H(a, e)
28.57/10.25	   A^2 -> H(a, U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, d), b)
28.57/10.25	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, d), c)
28.57/10.25	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, d), e)
28.57/10.25	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, a), d)
28.57/10.25	   A^2 -> H(U1(e, a), k)
28.57/10.25	   A^2 -> H(U1(k, a), d)
28.57/10.25	   A^2 -> H(U1(c, d), d)
28.57/10.25	   A^2 -> H(U1(c, d), k)
28.57/10.25	   A^2 -> H(U1(d, e), b)
28.57/10.25	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(d, e), c)
28.57/10.25	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(d, e), e)
28.57/10.25	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, c), d)
28.57/10.25	   A^2 -> H(U1(d, c), k)
28.57/10.25	   A^2 -> H(U1(a, e), d)
28.57/10.25	   A^2 -> H(U1(a, e), k)
28.57/10.25	   A^2 -> H(U1(a, k), d)
28.57/10.25	   A^2 -> H(U1(a, k), k)
28.57/10.25	   A^2 -> H(k, U1(e, b))
28.57/10.25	   A^2 -> H(k, U1(c, d))
28.57/10.25	   A^2 -> H(k, U1(d, c))
28.57/10.25	   A^2 -> H(k, U1(b, e))
28.57/10.25	   A^2 -> H(k, U1(b, k))
28.57/10.25	   A^2 -> H(k, U1(e, c))
28.57/10.25	   A^2 -> H(k, U1(c, e))
28.57/10.25	   A^2 -> H(k, U1(c, k))
28.57/10.25	   A^2 -> H(k, U1(e, e))
28.57/10.25	   A^2 -> H(k, U1(d, k))
28.57/10.25	   A^2 -> H(c, b)
28.57/10.25	   A^2 -> H(c, U1(e, d))
28.57/10.25	   A^2 -> H(c, U1(d, e))
28.57/10.25	   A^2 -> H(c, c)
28.57/10.25	   A^2 -> H(c, U1(e, k))
28.57/10.25	   A^2 -> H(c, U1(k, e))
28.57/10.25	   A^2 -> H(c, e)
28.57/10.25	   A^2 -> H(c, U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, k), b)
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, k), c)
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.25	
28.57/10.25	The TRS R consists of the following rules:
28.57/10.25	
28.57/10.25	   f(x) -> U1(x, x)
28.57/10.25	   U1(e, x) -> x
28.57/10.25	   a -> c
28.57/10.25	   a -> d
28.57/10.25	   b -> c
28.57/10.25	   b -> d
28.57/10.25	   d -> k
28.57/10.25	   c -> e
28.57/10.25	   c -> k
28.57/10.25	
28.57/10.25	Q is empty.
28.57/10.25	We have to consider all minimal (P,Q,R)-chains.
28.57/10.25	----------------------------------------
28.57/10.25	
28.57/10.25	(2103) TransformationProof (EQUIVALENT)
28.57/10.25	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.25	
28.57/10.25	   (A^2 -> H(k, U1(c, k)),A^2 -> H(k, U1(c, k)))
28.57/10.25	   (A^2 -> H(U1(e, k), U1(e, k)),A^2 -> H(U1(e, k), U1(e, k)))
28.57/10.25	   (A^2 -> H(U1(e, k), U1(k, k)),A^2 -> H(U1(e, k), U1(k, k)))
28.57/10.25	
28.57/10.25	
28.57/10.25	----------------------------------------
28.57/10.25	
28.57/10.25	(2104)
28.57/10.25	Obligation:
28.57/10.25	Q DP problem:
28.57/10.25	The TRS P consists of the following rules:
28.57/10.25	
28.57/10.25	   H(x, x) -> G(x, x, f(k))
28.57/10.25	   G(d, x, x) -> A^2
28.57/10.25	   A^2 -> H(f(c), f(c))
28.57/10.25	   A^2 -> H(f(d), f(d))
28.57/10.25	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.25	   A^2 -> H(f(e), f(e))
28.57/10.25	   A^2 -> H(f(k), f(k))
28.57/10.25	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.25	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.25	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.25	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.25	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.25	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.25	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, c), b)
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, c), e)
28.57/10.25	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.25	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.25	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.25	   A^2 -> H(U1(k, c), b)
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, c), c)
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, e), b)
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(c, e), c)
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, e), e)
28.57/10.25	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, k), b)
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(c, k), c)
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, k), e)
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, c), d)
28.57/10.25	   A^2 -> H(e, U1(e, b))
28.57/10.25	   A^2 -> H(e, U1(c, d))
28.57/10.25	   A^2 -> H(e, U1(d, c))
28.57/10.25	   A^2 -> H(e, U1(b, e))
28.57/10.25	   A^2 -> H(e, U1(b, k))
28.57/10.25	   A^2 -> H(e, U1(e, c))
28.57/10.25	   A^2 -> H(e, U1(c, e))
28.57/10.25	   A^2 -> H(e, U1(c, k))
28.57/10.25	   A^2 -> H(e, U1(e, e))
28.57/10.25	   A^2 -> H(e, U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, e), b)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, e), c)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.25	   A^2 -> H(f(e), d)
28.57/10.25	   A^2 -> H(f(e), k)
28.57/10.25	   A^2 -> H(U1(k, k), b)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, k), c)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.25	   A^2 -> H(f(k), d)
28.57/10.25	   A^2 -> H(f(k), k)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(k, d), b)
28.57/10.25	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, d), c)
28.57/10.25	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, k), b)
28.57/10.25	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(d, k), c)
28.57/10.25	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(d, k), e)
28.57/10.25	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, d), d)
28.57/10.25	   A^2 -> H(U1(d, d), k)
28.57/10.25	   A^2 -> H(U1(e, c), c)
28.57/10.25	   A^2 -> H(U1(c, c), e)
28.57/10.25	   A^2 -> H(U1(c, c), k)
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(e, e), e)
28.57/10.25	   A^2 -> H(d, U1(e, b))
28.57/10.25	   A^2 -> H(d, U1(k, b))
28.57/10.25	   A^2 -> H(d, U1(c, d))
28.57/10.25	   A^2 -> H(d, U1(d, c))
28.57/10.25	   A^2 -> H(d, U1(b, e))
28.57/10.25	   A^2 -> H(d, U1(b, k))
28.57/10.25	   A^2 -> H(d, U1(e, c))
28.57/10.25	   A^2 -> H(d, U1(k, c))
28.57/10.25	   A^2 -> H(d, U1(c, e))
28.57/10.25	   A^2 -> H(d, U1(c, k))
28.57/10.25	   A^2 -> H(d, U1(e, e))
28.57/10.25	   A^2 -> H(d, U1(k, k))
28.57/10.25	   A^2 -> H(d, U1(k, d))
28.57/10.25	   A^2 -> H(d, U1(d, k))
28.57/10.25	   A^2 -> H(a, b)
28.57/10.25	   A^2 -> H(a, U1(e, d))
28.57/10.25	   A^2 -> H(a, U1(d, e))
28.57/10.25	   A^2 -> H(a, c)
28.57/10.25	   A^2 -> H(a, U1(e, k))
28.57/10.25	   A^2 -> H(a, U1(k, e))
28.57/10.25	   A^2 -> H(a, e)
28.57/10.25	   A^2 -> H(a, U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, d), b)
28.57/10.25	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, d), c)
28.57/10.25	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, d), e)
28.57/10.25	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, a), d)
28.57/10.25	   A^2 -> H(U1(e, a), k)
28.57/10.25	   A^2 -> H(U1(k, a), d)
28.57/10.25	   A^2 -> H(U1(c, d), d)
28.57/10.25	   A^2 -> H(U1(c, d), k)
28.57/10.25	   A^2 -> H(U1(d, e), b)
28.57/10.25	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(d, e), c)
28.57/10.25	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(d, e), e)
28.57/10.25	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, c), d)
28.57/10.25	   A^2 -> H(U1(d, c), k)
28.57/10.25	   A^2 -> H(U1(a, e), d)
28.57/10.25	   A^2 -> H(U1(a, e), k)
28.57/10.25	   A^2 -> H(U1(a, k), d)
28.57/10.25	   A^2 -> H(U1(a, k), k)
28.57/10.25	   A^2 -> H(k, U1(e, b))
28.57/10.25	   A^2 -> H(k, U1(c, d))
28.57/10.25	   A^2 -> H(k, U1(d, c))
28.57/10.25	   A^2 -> H(k, U1(b, e))
28.57/10.25	   A^2 -> H(k, U1(b, k))
28.57/10.25	   A^2 -> H(k, U1(e, c))
28.57/10.25	   A^2 -> H(k, U1(c, e))
28.57/10.25	   A^2 -> H(k, U1(c, k))
28.57/10.25	   A^2 -> H(k, U1(e, e))
28.57/10.25	   A^2 -> H(k, U1(d, k))
28.57/10.25	   A^2 -> H(c, b)
28.57/10.25	   A^2 -> H(c, U1(e, d))
28.57/10.25	   A^2 -> H(c, U1(d, e))
28.57/10.25	   A^2 -> H(c, c)
28.57/10.25	   A^2 -> H(c, U1(e, k))
28.57/10.25	   A^2 -> H(c, U1(k, e))
28.57/10.25	   A^2 -> H(c, e)
28.57/10.25	   A^2 -> H(c, U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, k), b)
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, k), c)
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.25	
28.57/10.25	The TRS R consists of the following rules:
28.57/10.25	
28.57/10.25	   f(x) -> U1(x, x)
28.57/10.25	   U1(e, x) -> x
28.57/10.25	   a -> c
28.57/10.25	   a -> d
28.57/10.25	   b -> c
28.57/10.25	   b -> d
28.57/10.25	   d -> k
28.57/10.25	   c -> e
28.57/10.25	   c -> k
28.57/10.25	
28.57/10.25	Q is empty.
28.57/10.25	We have to consider all minimal (P,Q,R)-chains.
28.57/10.25	----------------------------------------
28.57/10.25	
28.57/10.25	(2105) TransformationProof (EQUIVALENT)
28.57/10.25	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.25	
28.57/10.25	   (A^2 -> H(k, U1(e, e)),A^2 -> H(k, U1(e, e)))
28.57/10.25	   (A^2 -> H(U1(e, k), e),A^2 -> H(U1(e, k), e))
28.57/10.25	
28.57/10.25	
28.57/10.25	----------------------------------------
28.57/10.25	
28.57/10.25	(2106)
28.57/10.25	Obligation:
28.57/10.25	Q DP problem:
28.57/10.25	The TRS P consists of the following rules:
28.57/10.25	
28.57/10.25	   H(x, x) -> G(x, x, f(k))
28.57/10.25	   G(d, x, x) -> A^2
28.57/10.25	   A^2 -> H(f(c), f(c))
28.57/10.25	   A^2 -> H(f(d), f(d))
28.57/10.25	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.25	   A^2 -> H(f(e), f(e))
28.57/10.25	   A^2 -> H(f(k), f(k))
28.57/10.25	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.25	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.25	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.25	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.25	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.25	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.25	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, c), b)
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, c), e)
28.57/10.25	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.25	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.25	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.25	   A^2 -> H(U1(k, c), b)
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, c), c)
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, e), b)
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(c, e), c)
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, e), e)
28.57/10.25	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, k), b)
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(c, k), c)
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, k), e)
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, c), d)
28.57/10.25	   A^2 -> H(e, U1(e, b))
28.57/10.25	   A^2 -> H(e, U1(c, d))
28.57/10.25	   A^2 -> H(e, U1(d, c))
28.57/10.25	   A^2 -> H(e, U1(b, e))
28.57/10.25	   A^2 -> H(e, U1(b, k))
28.57/10.25	   A^2 -> H(e, U1(e, c))
28.57/10.25	   A^2 -> H(e, U1(c, e))
28.57/10.25	   A^2 -> H(e, U1(c, k))
28.57/10.25	   A^2 -> H(e, U1(e, e))
28.57/10.25	   A^2 -> H(e, U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, e), b)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, e), c)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.25	   A^2 -> H(f(e), d)
28.57/10.25	   A^2 -> H(f(e), k)
28.57/10.25	   A^2 -> H(U1(k, k), b)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, k), c)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.25	   A^2 -> H(f(k), d)
28.57/10.25	   A^2 -> H(f(k), k)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(k, d), b)
28.57/10.25	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, d), c)
28.57/10.25	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, k), b)
28.57/10.25	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(d, k), c)
28.57/10.25	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(d, k), e)
28.57/10.25	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, d), d)
28.57/10.25	   A^2 -> H(U1(d, d), k)
28.57/10.25	   A^2 -> H(U1(e, c), c)
28.57/10.25	   A^2 -> H(U1(c, c), e)
28.57/10.25	   A^2 -> H(U1(c, c), k)
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(e, e), e)
28.57/10.25	   A^2 -> H(d, U1(e, b))
28.57/10.25	   A^2 -> H(d, U1(k, b))
28.57/10.25	   A^2 -> H(d, U1(c, d))
28.57/10.25	   A^2 -> H(d, U1(d, c))
28.57/10.25	   A^2 -> H(d, U1(b, e))
28.57/10.25	   A^2 -> H(d, U1(b, k))
28.57/10.25	   A^2 -> H(d, U1(e, c))
28.57/10.25	   A^2 -> H(d, U1(k, c))
28.57/10.25	   A^2 -> H(d, U1(c, e))
28.57/10.25	   A^2 -> H(d, U1(c, k))
28.57/10.25	   A^2 -> H(d, U1(e, e))
28.57/10.25	   A^2 -> H(d, U1(k, k))
28.57/10.25	   A^2 -> H(d, U1(k, d))
28.57/10.25	   A^2 -> H(d, U1(d, k))
28.57/10.25	   A^2 -> H(a, b)
28.57/10.25	   A^2 -> H(a, U1(e, d))
28.57/10.25	   A^2 -> H(a, U1(d, e))
28.57/10.25	   A^2 -> H(a, c)
28.57/10.25	   A^2 -> H(a, U1(e, k))
28.57/10.25	   A^2 -> H(a, U1(k, e))
28.57/10.25	   A^2 -> H(a, e)
28.57/10.25	   A^2 -> H(a, U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, d), b)
28.57/10.25	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, d), c)
28.57/10.25	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, d), e)
28.57/10.25	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, a), d)
28.57/10.25	   A^2 -> H(U1(e, a), k)
28.57/10.25	   A^2 -> H(U1(k, a), d)
28.57/10.25	   A^2 -> H(U1(c, d), d)
28.57/10.25	   A^2 -> H(U1(c, d), k)
28.57/10.25	   A^2 -> H(U1(d, e), b)
28.57/10.25	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(d, e), c)
28.57/10.25	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(d, e), e)
28.57/10.25	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, c), d)
28.57/10.25	   A^2 -> H(U1(d, c), k)
28.57/10.25	   A^2 -> H(U1(a, e), d)
28.57/10.25	   A^2 -> H(U1(a, e), k)
28.57/10.25	   A^2 -> H(U1(a, k), d)
28.57/10.25	   A^2 -> H(U1(a, k), k)
28.57/10.25	   A^2 -> H(k, U1(e, b))
28.57/10.25	   A^2 -> H(k, U1(c, d))
28.57/10.25	   A^2 -> H(k, U1(d, c))
28.57/10.25	   A^2 -> H(k, U1(b, e))
28.57/10.25	   A^2 -> H(k, U1(b, k))
28.57/10.25	   A^2 -> H(k, U1(e, c))
28.57/10.25	   A^2 -> H(k, U1(c, e))
28.57/10.25	   A^2 -> H(k, U1(c, k))
28.57/10.25	   A^2 -> H(k, U1(e, e))
28.57/10.25	   A^2 -> H(k, U1(d, k))
28.57/10.25	   A^2 -> H(c, b)
28.57/10.25	   A^2 -> H(c, U1(e, d))
28.57/10.25	   A^2 -> H(c, U1(d, e))
28.57/10.25	   A^2 -> H(c, c)
28.57/10.25	   A^2 -> H(c, U1(e, k))
28.57/10.25	   A^2 -> H(c, U1(k, e))
28.57/10.25	   A^2 -> H(c, e)
28.57/10.25	   A^2 -> H(c, U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, k), b)
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, k), c)
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, k), e)
28.57/10.25	
28.57/10.25	The TRS R consists of the following rules:
28.57/10.25	
28.57/10.25	   f(x) -> U1(x, x)
28.57/10.25	   U1(e, x) -> x
28.57/10.25	   a -> c
28.57/10.25	   a -> d
28.57/10.25	   b -> c
28.57/10.25	   b -> d
28.57/10.25	   d -> k
28.57/10.25	   c -> e
28.57/10.25	   c -> k
28.57/10.25	
28.57/10.25	Q is empty.
28.57/10.25	We have to consider all minimal (P,Q,R)-chains.
28.57/10.25	----------------------------------------
28.57/10.25	
28.57/10.25	(2107) TransformationProof (EQUIVALENT)
28.57/10.25	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.25	
28.57/10.25	   (A^2 -> H(k, U1(k, k)),A^2 -> H(k, U1(k, k)))
28.57/10.25	
28.57/10.25	
28.57/10.25	----------------------------------------
28.57/10.25	
28.57/10.25	(2108)
28.57/10.25	Obligation:
28.57/10.25	Q DP problem:
28.57/10.25	The TRS P consists of the following rules:
28.57/10.25	
28.57/10.25	   H(x, x) -> G(x, x, f(k))
28.57/10.25	   G(d, x, x) -> A^2
28.57/10.25	   A^2 -> H(f(c), f(c))
28.57/10.25	   A^2 -> H(f(d), f(d))
28.57/10.25	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.25	   A^2 -> H(f(e), f(e))
28.57/10.25	   A^2 -> H(f(k), f(k))
28.57/10.25	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.25	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.25	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.25	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.25	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.25	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.25	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, c), b)
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, c), e)
28.57/10.25	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.25	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.25	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.25	   A^2 -> H(U1(k, c), b)
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, c), c)
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, e), b)
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(c, e), c)
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, e), e)
28.57/10.25	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, k), b)
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(c, k), c)
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, k), e)
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, c), d)
28.57/10.25	   A^2 -> H(e, U1(e, b))
28.57/10.25	   A^2 -> H(e, U1(c, d))
28.57/10.25	   A^2 -> H(e, U1(d, c))
28.57/10.25	   A^2 -> H(e, U1(b, e))
28.57/10.25	   A^2 -> H(e, U1(b, k))
28.57/10.25	   A^2 -> H(e, U1(e, c))
28.57/10.25	   A^2 -> H(e, U1(c, e))
28.57/10.25	   A^2 -> H(e, U1(c, k))
28.57/10.25	   A^2 -> H(e, U1(e, e))
28.57/10.25	   A^2 -> H(e, U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, e), b)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, e), c)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.25	   A^2 -> H(f(e), d)
28.57/10.25	   A^2 -> H(f(e), k)
28.57/10.25	   A^2 -> H(U1(k, k), b)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, k), c)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.25	   A^2 -> H(f(k), d)
28.57/10.25	   A^2 -> H(f(k), k)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(k, d), b)
28.57/10.25	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, d), c)
28.57/10.25	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, k), b)
28.57/10.25	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(d, k), c)
28.57/10.25	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(d, k), e)
28.57/10.25	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, d), d)
28.57/10.25	   A^2 -> H(U1(d, d), k)
28.57/10.25	   A^2 -> H(U1(e, c), c)
28.57/10.25	   A^2 -> H(U1(c, c), e)
28.57/10.25	   A^2 -> H(U1(c, c), k)
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(e, e), e)
28.57/10.25	   A^2 -> H(d, U1(e, b))
28.57/10.25	   A^2 -> H(d, U1(k, b))
28.57/10.25	   A^2 -> H(d, U1(c, d))
28.57/10.25	   A^2 -> H(d, U1(d, c))
28.57/10.25	   A^2 -> H(d, U1(b, e))
28.57/10.25	   A^2 -> H(d, U1(b, k))
28.57/10.25	   A^2 -> H(d, U1(e, c))
28.57/10.25	   A^2 -> H(d, U1(k, c))
28.57/10.25	   A^2 -> H(d, U1(c, e))
28.57/10.25	   A^2 -> H(d, U1(c, k))
28.57/10.25	   A^2 -> H(d, U1(e, e))
28.57/10.25	   A^2 -> H(d, U1(k, k))
28.57/10.25	   A^2 -> H(d, U1(k, d))
28.57/10.25	   A^2 -> H(d, U1(d, k))
28.57/10.25	   A^2 -> H(a, b)
28.57/10.25	   A^2 -> H(a, U1(e, d))
28.57/10.25	   A^2 -> H(a, U1(d, e))
28.57/10.25	   A^2 -> H(a, c)
28.57/10.25	   A^2 -> H(a, U1(e, k))
28.57/10.25	   A^2 -> H(a, U1(k, e))
28.57/10.25	   A^2 -> H(a, e)
28.57/10.25	   A^2 -> H(a, U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, d), b)
28.57/10.25	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, d), c)
28.57/10.25	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, d), e)
28.57/10.25	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, a), d)
28.57/10.25	   A^2 -> H(U1(e, a), k)
28.57/10.25	   A^2 -> H(U1(k, a), d)
28.57/10.25	   A^2 -> H(U1(c, d), d)
28.57/10.25	   A^2 -> H(U1(c, d), k)
28.57/10.25	   A^2 -> H(U1(d, e), b)
28.57/10.25	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(d, e), c)
28.57/10.25	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(d, e), e)
28.57/10.25	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, c), d)
28.57/10.25	   A^2 -> H(U1(d, c), k)
28.57/10.25	   A^2 -> H(U1(a, e), d)
28.57/10.25	   A^2 -> H(U1(a, e), k)
28.57/10.25	   A^2 -> H(U1(a, k), d)
28.57/10.25	   A^2 -> H(U1(a, k), k)
28.57/10.25	   A^2 -> H(k, U1(e, b))
28.57/10.25	   A^2 -> H(k, U1(c, d))
28.57/10.25	   A^2 -> H(k, U1(d, c))
28.57/10.25	   A^2 -> H(k, U1(b, e))
28.57/10.25	   A^2 -> H(k, U1(b, k))
28.57/10.25	   A^2 -> H(k, U1(e, c))
28.57/10.25	   A^2 -> H(k, U1(c, e))
28.57/10.25	   A^2 -> H(k, U1(c, k))
28.57/10.25	   A^2 -> H(k, U1(e, e))
28.57/10.25	   A^2 -> H(k, U1(d, k))
28.57/10.25	   A^2 -> H(c, b)
28.57/10.25	   A^2 -> H(c, U1(e, d))
28.57/10.25	   A^2 -> H(c, U1(d, e))
28.57/10.25	   A^2 -> H(c, c)
28.57/10.25	   A^2 -> H(c, U1(e, k))
28.57/10.25	   A^2 -> H(c, U1(k, e))
28.57/10.25	   A^2 -> H(c, e)
28.57/10.25	   A^2 -> H(c, U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, k), b)
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, k), c)
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, k), e)
28.57/10.25	   A^2 -> H(k, U1(k, k))
28.57/10.25	
28.57/10.25	The TRS R consists of the following rules:
28.57/10.25	
28.57/10.25	   f(x) -> U1(x, x)
28.57/10.25	   U1(e, x) -> x
28.57/10.25	   a -> c
28.57/10.25	   a -> d
28.57/10.25	   b -> c
28.57/10.25	   b -> d
28.57/10.25	   d -> k
28.57/10.25	   c -> e
28.57/10.25	   c -> k
28.57/10.25	
28.57/10.25	Q is empty.
28.57/10.25	We have to consider all minimal (P,Q,R)-chains.
28.57/10.25	----------------------------------------
28.57/10.25	
28.57/10.25	(2109) DependencyGraphProof (EQUIVALENT)
28.57/10.25	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.25	----------------------------------------
28.57/10.25	
28.57/10.25	(2110)
28.57/10.25	Obligation:
28.57/10.25	Q DP problem:
28.57/10.25	The TRS P consists of the following rules:
28.57/10.25	
28.57/10.25	   G(d, x, x) -> A^2
28.57/10.25	   A^2 -> H(f(c), f(c))
28.57/10.25	   H(x, x) -> G(x, x, f(k))
28.57/10.25	   A^2 -> H(f(d), f(d))
28.57/10.25	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.25	   A^2 -> H(f(e), f(e))
28.57/10.25	   A^2 -> H(f(k), f(k))
28.57/10.25	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.25	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.25	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.25	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.25	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.25	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, d))
28.57/10.25	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, c), b)
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, c), e)
28.57/10.25	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.25	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.25	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.25	   A^2 -> H(U1(k, c), b)
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, c), c)
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, e), b)
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(c, e), c)
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, e), e)
28.57/10.25	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, k), b)
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(c, k), c)
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, k), e)
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, c), d)
28.57/10.25	   A^2 -> H(e, U1(e, b))
28.57/10.25	   A^2 -> H(e, U1(c, d))
28.57/10.25	   A^2 -> H(e, U1(d, c))
28.57/10.25	   A^2 -> H(e, U1(b, e))
28.57/10.25	   A^2 -> H(e, U1(b, k))
28.57/10.25	   A^2 -> H(e, U1(e, c))
28.57/10.25	   A^2 -> H(e, U1(c, e))
28.57/10.25	   A^2 -> H(e, U1(c, k))
28.57/10.25	   A^2 -> H(e, U1(e, e))
28.57/10.25	   A^2 -> H(e, U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, e), b)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, e), c)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.25	   A^2 -> H(f(e), d)
28.57/10.25	   A^2 -> H(f(e), k)
28.57/10.25	   A^2 -> H(U1(k, k), b)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, k), c)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.25	   A^2 -> H(f(k), d)
28.57/10.25	   A^2 -> H(f(k), k)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(k, d), b)
28.57/10.25	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, d), c)
28.57/10.25	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, k), b)
28.57/10.25	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(d, k), c)
28.57/10.25	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(d, k), e)
28.57/10.25	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, d), d)
28.57/10.25	   A^2 -> H(U1(d, d), k)
28.57/10.25	   A^2 -> H(U1(e, c), c)
28.57/10.25	   A^2 -> H(U1(c, c), e)
28.57/10.25	   A^2 -> H(U1(c, c), k)
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(e, e), e)
28.57/10.25	   A^2 -> H(d, U1(e, b))
28.57/10.25	   A^2 -> H(d, U1(k, b))
28.57/10.25	   A^2 -> H(d, U1(c, d))
28.57/10.25	   A^2 -> H(d, U1(d, c))
28.57/10.25	   A^2 -> H(d, U1(b, e))
28.57/10.25	   A^2 -> H(d, U1(b, k))
28.57/10.25	   A^2 -> H(d, U1(e, c))
28.57/10.25	   A^2 -> H(d, U1(k, c))
28.57/10.25	   A^2 -> H(d, U1(c, e))
28.57/10.25	   A^2 -> H(d, U1(c, k))
28.57/10.25	   A^2 -> H(d, U1(e, e))
28.57/10.25	   A^2 -> H(d, U1(k, k))
28.57/10.25	   A^2 -> H(d, U1(k, d))
28.57/10.25	   A^2 -> H(d, U1(d, k))
28.57/10.25	   A^2 -> H(a, b)
28.57/10.25	   A^2 -> H(a, U1(e, d))
28.57/10.25	   A^2 -> H(a, U1(d, e))
28.57/10.25	   A^2 -> H(a, c)
28.57/10.25	   A^2 -> H(a, U1(e, k))
28.57/10.25	   A^2 -> H(a, U1(k, e))
28.57/10.25	   A^2 -> H(a, e)
28.57/10.25	   A^2 -> H(a, U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, d), b)
28.57/10.25	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, d), c)
28.57/10.25	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, d), e)
28.57/10.25	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, a), d)
28.57/10.25	   A^2 -> H(U1(e, a), k)
28.57/10.25	   A^2 -> H(U1(k, a), d)
28.57/10.25	   A^2 -> H(U1(c, d), d)
28.57/10.25	   A^2 -> H(U1(c, d), k)
28.57/10.25	   A^2 -> H(U1(d, e), b)
28.57/10.25	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(d, e), c)
28.57/10.25	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(d, e), e)
28.57/10.25	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, c), d)
28.57/10.25	   A^2 -> H(U1(d, c), k)
28.57/10.25	   A^2 -> H(U1(a, e), d)
28.57/10.25	   A^2 -> H(U1(a, e), k)
28.57/10.25	   A^2 -> H(U1(a, k), d)
28.57/10.25	   A^2 -> H(U1(a, k), k)
28.57/10.25	   A^2 -> H(k, U1(e, b))
28.57/10.25	   A^2 -> H(k, U1(c, d))
28.57/10.25	   A^2 -> H(k, U1(d, c))
28.57/10.25	   A^2 -> H(k, U1(b, e))
28.57/10.25	   A^2 -> H(k, U1(b, k))
28.57/10.25	   A^2 -> H(k, U1(e, c))
28.57/10.25	   A^2 -> H(k, U1(c, e))
28.57/10.25	   A^2 -> H(k, U1(c, k))
28.57/10.25	   A^2 -> H(k, U1(e, e))
28.57/10.25	   A^2 -> H(k, U1(d, k))
28.57/10.25	   A^2 -> H(c, b)
28.57/10.25	   A^2 -> H(c, U1(e, d))
28.57/10.25	   A^2 -> H(c, U1(d, e))
28.57/10.25	   A^2 -> H(c, c)
28.57/10.25	   A^2 -> H(c, U1(e, k))
28.57/10.25	   A^2 -> H(c, U1(k, e))
28.57/10.25	   A^2 -> H(c, e)
28.57/10.25	   A^2 -> H(c, U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, k), b)
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, k), c)
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, k), e)
28.57/10.25	
28.57/10.25	The TRS R consists of the following rules:
28.57/10.25	
28.57/10.25	   f(x) -> U1(x, x)
28.57/10.25	   U1(e, x) -> x
28.57/10.25	   a -> c
28.57/10.25	   a -> d
28.57/10.25	   b -> c
28.57/10.25	   b -> d
28.57/10.25	   d -> k
28.57/10.25	   c -> e
28.57/10.25	   c -> k
28.57/10.25	
28.57/10.25	Q is empty.
28.57/10.25	We have to consider all minimal (P,Q,R)-chains.
28.57/10.25	----------------------------------------
28.57/10.25	
28.57/10.25	(2111) TransformationProof (EQUIVALENT)
28.57/10.25	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.25	
28.57/10.25	   (A^2 -> H(k, U1(k, d)),A^2 -> H(k, U1(k, d)))
28.57/10.25	   (A^2 -> H(U1(e, k), U1(k, k)),A^2 -> H(U1(e, k), U1(k, k)))
28.57/10.25	
28.57/10.25	
28.57/10.25	----------------------------------------
28.57/10.25	
28.57/10.25	(2112)
28.57/10.25	Obligation:
28.57/10.25	Q DP problem:
28.57/10.25	The TRS P consists of the following rules:
28.57/10.25	
28.57/10.25	   G(d, x, x) -> A^2
28.57/10.25	   A^2 -> H(f(c), f(c))
28.57/10.25	   H(x, x) -> G(x, x, f(k))
28.57/10.25	   A^2 -> H(f(d), f(d))
28.57/10.25	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.25	   A^2 -> H(f(e), f(e))
28.57/10.25	   A^2 -> H(f(k), f(k))
28.57/10.25	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.25	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.25	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.25	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.25	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.25	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, c), b)
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, c), e)
28.57/10.25	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.25	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.25	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.25	   A^2 -> H(U1(k, c), b)
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, c), c)
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, e), b)
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(c, e), c)
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, e), e)
28.57/10.25	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, k), b)
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(c, k), c)
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, k), e)
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, c), d)
28.57/10.25	   A^2 -> H(e, U1(e, b))
28.57/10.25	   A^2 -> H(e, U1(c, d))
28.57/10.25	   A^2 -> H(e, U1(d, c))
28.57/10.25	   A^2 -> H(e, U1(b, e))
28.57/10.25	   A^2 -> H(e, U1(b, k))
28.57/10.25	   A^2 -> H(e, U1(e, c))
28.57/10.25	   A^2 -> H(e, U1(c, e))
28.57/10.25	   A^2 -> H(e, U1(c, k))
28.57/10.25	   A^2 -> H(e, U1(e, e))
28.57/10.25	   A^2 -> H(e, U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, e), b)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, e), c)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.25	   A^2 -> H(f(e), d)
28.57/10.25	   A^2 -> H(f(e), k)
28.57/10.25	   A^2 -> H(U1(k, k), b)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, k), c)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.25	   A^2 -> H(f(k), d)
28.57/10.25	   A^2 -> H(f(k), k)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(k, d), b)
28.57/10.25	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, d), c)
28.57/10.25	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, k), b)
28.57/10.25	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(d, k), c)
28.57/10.25	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(d, k), e)
28.57/10.25	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, d), d)
28.57/10.25	   A^2 -> H(U1(d, d), k)
28.57/10.25	   A^2 -> H(U1(e, c), c)
28.57/10.25	   A^2 -> H(U1(c, c), e)
28.57/10.25	   A^2 -> H(U1(c, c), k)
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(e, e), e)
28.57/10.25	   A^2 -> H(d, U1(e, b))
28.57/10.25	   A^2 -> H(d, U1(k, b))
28.57/10.25	   A^2 -> H(d, U1(c, d))
28.57/10.25	   A^2 -> H(d, U1(d, c))
28.57/10.25	   A^2 -> H(d, U1(b, e))
28.57/10.25	   A^2 -> H(d, U1(b, k))
28.57/10.25	   A^2 -> H(d, U1(e, c))
28.57/10.25	   A^2 -> H(d, U1(k, c))
28.57/10.25	   A^2 -> H(d, U1(c, e))
28.57/10.25	   A^2 -> H(d, U1(c, k))
28.57/10.25	   A^2 -> H(d, U1(e, e))
28.57/10.25	   A^2 -> H(d, U1(k, k))
28.57/10.25	   A^2 -> H(d, U1(k, d))
28.57/10.25	   A^2 -> H(d, U1(d, k))
28.57/10.25	   A^2 -> H(a, b)
28.57/10.25	   A^2 -> H(a, U1(e, d))
28.57/10.25	   A^2 -> H(a, U1(d, e))
28.57/10.25	   A^2 -> H(a, c)
28.57/10.25	   A^2 -> H(a, U1(e, k))
28.57/10.25	   A^2 -> H(a, U1(k, e))
28.57/10.25	   A^2 -> H(a, e)
28.57/10.25	   A^2 -> H(a, U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, d), b)
28.57/10.25	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, d), c)
28.57/10.25	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, d), e)
28.57/10.25	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, a), d)
28.57/10.25	   A^2 -> H(U1(e, a), k)
28.57/10.25	   A^2 -> H(U1(k, a), d)
28.57/10.25	   A^2 -> H(U1(c, d), d)
28.57/10.25	   A^2 -> H(U1(c, d), k)
28.57/10.25	   A^2 -> H(U1(d, e), b)
28.57/10.25	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(d, e), c)
28.57/10.25	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(d, e), e)
28.57/10.25	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, c), d)
28.57/10.25	   A^2 -> H(U1(d, c), k)
28.57/10.25	   A^2 -> H(U1(a, e), d)
28.57/10.25	   A^2 -> H(U1(a, e), k)
28.57/10.25	   A^2 -> H(U1(a, k), d)
28.57/10.25	   A^2 -> H(U1(a, k), k)
28.57/10.25	   A^2 -> H(k, U1(e, b))
28.57/10.25	   A^2 -> H(k, U1(c, d))
28.57/10.25	   A^2 -> H(k, U1(d, c))
28.57/10.25	   A^2 -> H(k, U1(b, e))
28.57/10.25	   A^2 -> H(k, U1(b, k))
28.57/10.25	   A^2 -> H(k, U1(e, c))
28.57/10.25	   A^2 -> H(k, U1(c, e))
28.57/10.25	   A^2 -> H(k, U1(c, k))
28.57/10.25	   A^2 -> H(k, U1(e, e))
28.57/10.25	   A^2 -> H(k, U1(d, k))
28.57/10.25	   A^2 -> H(c, b)
28.57/10.25	   A^2 -> H(c, U1(e, d))
28.57/10.25	   A^2 -> H(c, U1(d, e))
28.57/10.25	   A^2 -> H(c, c)
28.57/10.25	   A^2 -> H(c, U1(e, k))
28.57/10.25	   A^2 -> H(c, U1(k, e))
28.57/10.25	   A^2 -> H(c, e)
28.57/10.25	   A^2 -> H(c, U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, k), b)
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, k), c)
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, k), e)
28.57/10.25	   A^2 -> H(k, U1(k, d))
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.25	
28.57/10.25	The TRS R consists of the following rules:
28.57/10.25	
28.57/10.25	   f(x) -> U1(x, x)
28.57/10.25	   U1(e, x) -> x
28.57/10.25	   a -> c
28.57/10.25	   a -> d
28.57/10.25	   b -> c
28.57/10.25	   b -> d
28.57/10.25	   d -> k
28.57/10.25	   c -> e
28.57/10.25	   c -> k
28.57/10.25	
28.57/10.25	Q is empty.
28.57/10.25	We have to consider all minimal (P,Q,R)-chains.
28.57/10.25	----------------------------------------
28.57/10.25	
28.57/10.25	(2113) DependencyGraphProof (EQUIVALENT)
28.57/10.25	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.25	----------------------------------------
28.57/10.25	
28.57/10.25	(2114)
28.57/10.25	Obligation:
28.57/10.25	Q DP problem:
28.57/10.25	The TRS P consists of the following rules:
28.57/10.25	
28.57/10.25	   A^2 -> H(f(c), f(c))
28.57/10.25	   H(x, x) -> G(x, x, f(k))
28.57/10.25	   G(d, x, x) -> A^2
28.57/10.25	   A^2 -> H(f(d), f(d))
28.57/10.25	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.25	   A^2 -> H(f(e), f(e))
28.57/10.25	   A^2 -> H(f(k), f(k))
28.57/10.25	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.25	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.25	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.25	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.25	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.25	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, c), b)
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, c), e)
28.57/10.25	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.25	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.25	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.25	   A^2 -> H(U1(k, c), b)
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, c), c)
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, e), b)
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(c, e), c)
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, e), e)
28.57/10.25	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, k), b)
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(c, k), c)
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, k), e)
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, c), d)
28.57/10.25	   A^2 -> H(e, U1(e, b))
28.57/10.25	   A^2 -> H(e, U1(c, d))
28.57/10.25	   A^2 -> H(e, U1(d, c))
28.57/10.25	   A^2 -> H(e, U1(b, e))
28.57/10.25	   A^2 -> H(e, U1(b, k))
28.57/10.25	   A^2 -> H(e, U1(e, c))
28.57/10.25	   A^2 -> H(e, U1(c, e))
28.57/10.25	   A^2 -> H(e, U1(c, k))
28.57/10.25	   A^2 -> H(e, U1(e, e))
28.57/10.25	   A^2 -> H(e, U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, e), b)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, e), c)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.25	   A^2 -> H(f(e), d)
28.57/10.25	   A^2 -> H(f(e), k)
28.57/10.25	   A^2 -> H(U1(k, k), b)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, k), c)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.25	   A^2 -> H(f(k), d)
28.57/10.25	   A^2 -> H(f(k), k)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(k, d), b)
28.57/10.25	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, d), c)
28.57/10.25	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, k), b)
28.57/10.25	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(d, k), c)
28.57/10.25	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(d, k), e)
28.57/10.25	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, d), d)
28.57/10.25	   A^2 -> H(U1(d, d), k)
28.57/10.25	   A^2 -> H(U1(e, c), c)
28.57/10.25	   A^2 -> H(U1(c, c), e)
28.57/10.25	   A^2 -> H(U1(c, c), k)
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(e, e), e)
28.57/10.25	   A^2 -> H(d, U1(e, b))
28.57/10.25	   A^2 -> H(d, U1(k, b))
28.57/10.25	   A^2 -> H(d, U1(c, d))
28.57/10.25	   A^2 -> H(d, U1(d, c))
28.57/10.25	   A^2 -> H(d, U1(b, e))
28.57/10.25	   A^2 -> H(d, U1(b, k))
28.57/10.25	   A^2 -> H(d, U1(e, c))
28.57/10.25	   A^2 -> H(d, U1(k, c))
28.57/10.25	   A^2 -> H(d, U1(c, e))
28.57/10.25	   A^2 -> H(d, U1(c, k))
28.57/10.25	   A^2 -> H(d, U1(e, e))
28.57/10.25	   A^2 -> H(d, U1(k, k))
28.57/10.25	   A^2 -> H(d, U1(k, d))
28.57/10.25	   A^2 -> H(d, U1(d, k))
28.57/10.25	   A^2 -> H(a, b)
28.57/10.25	   A^2 -> H(a, U1(e, d))
28.57/10.25	   A^2 -> H(a, U1(d, e))
28.57/10.25	   A^2 -> H(a, c)
28.57/10.25	   A^2 -> H(a, U1(e, k))
28.57/10.25	   A^2 -> H(a, U1(k, e))
28.57/10.25	   A^2 -> H(a, e)
28.57/10.25	   A^2 -> H(a, U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, d), b)
28.57/10.25	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, d), c)
28.57/10.25	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, d), e)
28.57/10.25	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, a), d)
28.57/10.25	   A^2 -> H(U1(e, a), k)
28.57/10.25	   A^2 -> H(U1(k, a), d)
28.57/10.25	   A^2 -> H(U1(c, d), d)
28.57/10.25	   A^2 -> H(U1(c, d), k)
28.57/10.25	   A^2 -> H(U1(d, e), b)
28.57/10.25	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(d, e), c)
28.57/10.25	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(d, e), e)
28.57/10.25	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, c), d)
28.57/10.25	   A^2 -> H(U1(d, c), k)
28.57/10.25	   A^2 -> H(U1(a, e), d)
28.57/10.25	   A^2 -> H(U1(a, e), k)
28.57/10.25	   A^2 -> H(U1(a, k), d)
28.57/10.25	   A^2 -> H(U1(a, k), k)
28.57/10.25	   A^2 -> H(k, U1(e, b))
28.57/10.25	   A^2 -> H(k, U1(c, d))
28.57/10.25	   A^2 -> H(k, U1(d, c))
28.57/10.25	   A^2 -> H(k, U1(b, e))
28.57/10.25	   A^2 -> H(k, U1(b, k))
28.57/10.25	   A^2 -> H(k, U1(e, c))
28.57/10.25	   A^2 -> H(k, U1(c, e))
28.57/10.25	   A^2 -> H(k, U1(c, k))
28.57/10.25	   A^2 -> H(k, U1(e, e))
28.57/10.25	   A^2 -> H(k, U1(d, k))
28.57/10.25	   A^2 -> H(c, b)
28.57/10.25	   A^2 -> H(c, U1(e, d))
28.57/10.25	   A^2 -> H(c, U1(d, e))
28.57/10.25	   A^2 -> H(c, c)
28.57/10.25	   A^2 -> H(c, U1(e, k))
28.57/10.25	   A^2 -> H(c, U1(k, e))
28.57/10.25	   A^2 -> H(c, e)
28.57/10.25	   A^2 -> H(c, U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, k), b)
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, k), c)
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, k), e)
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.25	
28.57/10.25	The TRS R consists of the following rules:
28.57/10.25	
28.57/10.25	   f(x) -> U1(x, x)
28.57/10.25	   U1(e, x) -> x
28.57/10.25	   a -> c
28.57/10.25	   a -> d
28.57/10.25	   b -> c
28.57/10.25	   b -> d
28.57/10.25	   d -> k
28.57/10.25	   c -> e
28.57/10.25	   c -> k
28.57/10.25	
28.57/10.25	Q is empty.
28.57/10.25	We have to consider all minimal (P,Q,R)-chains.
28.57/10.25	----------------------------------------
28.57/10.25	
28.57/10.25	(2115) TransformationProof (EQUIVALENT)
28.57/10.25	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.25	
28.57/10.25	   (A^2 -> H(k, U1(d, k)),A^2 -> H(k, U1(d, k)))
28.57/10.25	   (A^2 -> H(U1(e, k), U1(k, k)),A^2 -> H(U1(e, k), U1(k, k)))
28.57/10.25	
28.57/10.25	
28.57/10.25	----------------------------------------
28.57/10.25	
28.57/10.25	(2116)
28.57/10.25	Obligation:
28.57/10.25	Q DP problem:
28.57/10.25	The TRS P consists of the following rules:
28.57/10.25	
28.57/10.25	   A^2 -> H(f(c), f(c))
28.57/10.25	   H(x, x) -> G(x, x, f(k))
28.57/10.25	   G(d, x, x) -> A^2
28.57/10.25	   A^2 -> H(f(d), f(d))
28.57/10.25	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.25	   A^2 -> H(f(e), f(e))
28.57/10.25	   A^2 -> H(f(k), f(k))
28.57/10.25	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.25	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.25	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.25	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.25	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.25	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, c), b)
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, c), e)
28.57/10.25	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.25	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.25	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.25	   A^2 -> H(U1(k, c), b)
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, c), c)
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, e), b)
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(c, e), c)
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, e), e)
28.57/10.25	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, k), b)
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(c, k), c)
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, k), e)
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, c), d)
28.57/10.25	   A^2 -> H(e, U1(e, b))
28.57/10.25	   A^2 -> H(e, U1(c, d))
28.57/10.25	   A^2 -> H(e, U1(d, c))
28.57/10.25	   A^2 -> H(e, U1(b, e))
28.57/10.25	   A^2 -> H(e, U1(b, k))
28.57/10.25	   A^2 -> H(e, U1(e, c))
28.57/10.25	   A^2 -> H(e, U1(c, e))
28.57/10.25	   A^2 -> H(e, U1(c, k))
28.57/10.25	   A^2 -> H(e, U1(e, e))
28.57/10.25	   A^2 -> H(e, U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, e), b)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, e), c)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.25	   A^2 -> H(f(e), d)
28.57/10.25	   A^2 -> H(f(e), k)
28.57/10.25	   A^2 -> H(U1(k, k), b)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, k), c)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.25	   A^2 -> H(f(k), d)
28.57/10.25	   A^2 -> H(f(k), k)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(k, d), b)
28.57/10.25	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, d), c)
28.57/10.25	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, k), b)
28.57/10.25	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(d, k), c)
28.57/10.25	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(d, k), e)
28.57/10.25	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, d), d)
28.57/10.25	   A^2 -> H(U1(d, d), k)
28.57/10.25	   A^2 -> H(U1(e, c), c)
28.57/10.25	   A^2 -> H(U1(c, c), e)
28.57/10.25	   A^2 -> H(U1(c, c), k)
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(e, e), e)
28.57/10.25	   A^2 -> H(d, U1(e, b))
28.57/10.25	   A^2 -> H(d, U1(k, b))
28.57/10.25	   A^2 -> H(d, U1(c, d))
28.57/10.25	   A^2 -> H(d, U1(d, c))
28.57/10.25	   A^2 -> H(d, U1(b, e))
28.57/10.25	   A^2 -> H(d, U1(b, k))
28.57/10.25	   A^2 -> H(d, U1(e, c))
28.57/10.25	   A^2 -> H(d, U1(k, c))
28.57/10.25	   A^2 -> H(d, U1(c, e))
28.57/10.25	   A^2 -> H(d, U1(c, k))
28.57/10.25	   A^2 -> H(d, U1(e, e))
28.57/10.25	   A^2 -> H(d, U1(k, k))
28.57/10.25	   A^2 -> H(d, U1(k, d))
28.57/10.25	   A^2 -> H(d, U1(d, k))
28.57/10.25	   A^2 -> H(a, b)
28.57/10.25	   A^2 -> H(a, U1(e, d))
28.57/10.25	   A^2 -> H(a, U1(d, e))
28.57/10.25	   A^2 -> H(a, c)
28.57/10.25	   A^2 -> H(a, U1(e, k))
28.57/10.25	   A^2 -> H(a, U1(k, e))
28.57/10.25	   A^2 -> H(a, e)
28.57/10.25	   A^2 -> H(a, U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, d), b)
28.57/10.25	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, d), c)
28.57/10.25	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, d), e)
28.57/10.25	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, a), d)
28.57/10.25	   A^2 -> H(U1(e, a), k)
28.57/10.25	   A^2 -> H(U1(k, a), d)
28.57/10.25	   A^2 -> H(U1(c, d), d)
28.57/10.25	   A^2 -> H(U1(c, d), k)
28.57/10.25	   A^2 -> H(U1(d, e), b)
28.57/10.25	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(d, e), c)
28.57/10.25	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(d, e), e)
28.57/10.25	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, c), d)
28.57/10.25	   A^2 -> H(U1(d, c), k)
28.57/10.25	   A^2 -> H(U1(a, e), d)
28.57/10.25	   A^2 -> H(U1(a, e), k)
28.57/10.25	   A^2 -> H(U1(a, k), d)
28.57/10.25	   A^2 -> H(U1(a, k), k)
28.57/10.25	   A^2 -> H(k, U1(e, b))
28.57/10.25	   A^2 -> H(k, U1(c, d))
28.57/10.25	   A^2 -> H(k, U1(d, c))
28.57/10.25	   A^2 -> H(k, U1(b, e))
28.57/10.25	   A^2 -> H(k, U1(b, k))
28.57/10.25	   A^2 -> H(k, U1(e, c))
28.57/10.25	   A^2 -> H(k, U1(c, e))
28.57/10.25	   A^2 -> H(k, U1(c, k))
28.57/10.25	   A^2 -> H(k, U1(e, e))
28.57/10.25	   A^2 -> H(k, U1(d, k))
28.57/10.25	   A^2 -> H(c, b)
28.57/10.25	   A^2 -> H(c, U1(e, d))
28.57/10.25	   A^2 -> H(c, U1(d, e))
28.57/10.25	   A^2 -> H(c, c)
28.57/10.25	   A^2 -> H(c, U1(e, k))
28.57/10.25	   A^2 -> H(c, U1(k, e))
28.57/10.25	   A^2 -> H(c, e)
28.57/10.25	   A^2 -> H(c, U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, k), b)
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, k), c)
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, k), e)
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.25	
28.57/10.25	The TRS R consists of the following rules:
28.57/10.25	
28.57/10.25	   f(x) -> U1(x, x)
28.57/10.25	   U1(e, x) -> x
28.57/10.25	   a -> c
28.57/10.25	   a -> d
28.57/10.25	   b -> c
28.57/10.25	   b -> d
28.57/10.25	   d -> k
28.57/10.25	   c -> e
28.57/10.25	   c -> k
28.57/10.25	
28.57/10.25	Q is empty.
28.57/10.25	We have to consider all minimal (P,Q,R)-chains.
28.57/10.25	----------------------------------------
28.57/10.25	
28.57/10.25	(2117) TransformationProof (EQUIVALENT)
28.57/10.25	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), b) at position [] we obtained the following new rules [LPAR04]:
28.57/10.25	
28.57/10.25	   (A^2 -> H(c, b),A^2 -> H(c, b))
28.57/10.25	   (A^2 -> H(U1(e, e), b),A^2 -> H(U1(e, e), b))
28.57/10.25	   (A^2 -> H(U1(e, k), b),A^2 -> H(U1(e, k), b))
28.57/10.25	   (A^2 -> H(U1(e, c), c),A^2 -> H(U1(e, c), c))
28.57/10.25	   (A^2 -> H(U1(e, c), d),A^2 -> H(U1(e, c), d))
28.57/10.25	
28.57/10.25	
28.57/10.25	----------------------------------------
28.57/10.25	
28.57/10.25	(2118)
28.57/10.25	Obligation:
28.57/10.25	Q DP problem:
28.57/10.25	The TRS P consists of the following rules:
28.57/10.25	
28.57/10.25	   A^2 -> H(f(c), f(c))
28.57/10.25	   H(x, x) -> G(x, x, f(k))
28.57/10.25	   G(d, x, x) -> A^2
28.57/10.25	   A^2 -> H(f(d), f(d))
28.57/10.25	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.25	   A^2 -> H(f(e), f(e))
28.57/10.25	   A^2 -> H(f(k), f(k))
28.57/10.25	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.25	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.25	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.25	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.25	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.25	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, c), e)
28.57/10.25	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.25	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.25	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.25	   A^2 -> H(U1(k, c), b)
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, c), c)
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, e), b)
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(c, e), c)
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, e), e)
28.57/10.25	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, k), b)
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(c, k), c)
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, k), e)
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, c), d)
28.57/10.25	   A^2 -> H(e, U1(e, b))
28.57/10.25	   A^2 -> H(e, U1(c, d))
28.57/10.25	   A^2 -> H(e, U1(d, c))
28.57/10.25	   A^2 -> H(e, U1(b, e))
28.57/10.25	   A^2 -> H(e, U1(b, k))
28.57/10.25	   A^2 -> H(e, U1(e, c))
28.57/10.25	   A^2 -> H(e, U1(c, e))
28.57/10.25	   A^2 -> H(e, U1(c, k))
28.57/10.25	   A^2 -> H(e, U1(e, e))
28.57/10.25	   A^2 -> H(e, U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, e), b)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, e), c)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.25	   A^2 -> H(f(e), d)
28.57/10.25	   A^2 -> H(f(e), k)
28.57/10.25	   A^2 -> H(U1(k, k), b)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, k), c)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.25	   A^2 -> H(f(k), d)
28.57/10.25	   A^2 -> H(f(k), k)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.25	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(k, d), b)
28.57/10.25	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, d), c)
28.57/10.25	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, k), b)
28.57/10.25	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(d, k), c)
28.57/10.25	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(d, k), e)
28.57/10.25	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, d), d)
28.57/10.25	   A^2 -> H(U1(d, d), k)
28.57/10.25	   A^2 -> H(U1(e, c), c)
28.57/10.25	   A^2 -> H(U1(c, c), e)
28.57/10.25	   A^2 -> H(U1(c, c), k)
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.25	   A^2 -> H(U1(e, e), e)
28.57/10.25	   A^2 -> H(d, U1(e, b))
28.57/10.25	   A^2 -> H(d, U1(k, b))
28.57/10.25	   A^2 -> H(d, U1(c, d))
28.57/10.25	   A^2 -> H(d, U1(d, c))
28.57/10.25	   A^2 -> H(d, U1(b, e))
28.57/10.25	   A^2 -> H(d, U1(b, k))
28.57/10.25	   A^2 -> H(d, U1(e, c))
28.57/10.25	   A^2 -> H(d, U1(k, c))
28.57/10.25	   A^2 -> H(d, U1(c, e))
28.57/10.25	   A^2 -> H(d, U1(c, k))
28.57/10.25	   A^2 -> H(d, U1(e, e))
28.57/10.25	   A^2 -> H(d, U1(k, k))
28.57/10.25	   A^2 -> H(d, U1(k, d))
28.57/10.25	   A^2 -> H(d, U1(d, k))
28.57/10.25	   A^2 -> H(a, b)
28.57/10.25	   A^2 -> H(a, U1(e, d))
28.57/10.25	   A^2 -> H(a, U1(d, e))
28.57/10.25	   A^2 -> H(a, c)
28.57/10.25	   A^2 -> H(a, U1(e, k))
28.57/10.25	   A^2 -> H(a, U1(k, e))
28.57/10.25	   A^2 -> H(a, e)
28.57/10.25	   A^2 -> H(a, U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, d), b)
28.57/10.25	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, d), c)
28.57/10.25	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, d), e)
28.57/10.25	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, a), d)
28.57/10.25	   A^2 -> H(U1(e, a), k)
28.57/10.25	   A^2 -> H(U1(k, a), d)
28.57/10.25	   A^2 -> H(U1(c, d), d)
28.57/10.25	   A^2 -> H(U1(c, d), k)
28.57/10.25	   A^2 -> H(U1(d, e), b)
28.57/10.25	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(d, e), c)
28.57/10.25	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(d, e), e)
28.57/10.25	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.25	   A^2 -> H(U1(d, c), d)
28.57/10.25	   A^2 -> H(U1(d, c), k)
28.57/10.25	   A^2 -> H(U1(a, e), d)
28.57/10.25	   A^2 -> H(U1(a, e), k)
28.57/10.25	   A^2 -> H(U1(a, k), d)
28.57/10.25	   A^2 -> H(U1(a, k), k)
28.57/10.25	   A^2 -> H(k, U1(e, b))
28.57/10.25	   A^2 -> H(k, U1(c, d))
28.57/10.25	   A^2 -> H(k, U1(d, c))
28.57/10.25	   A^2 -> H(k, U1(b, e))
28.57/10.25	   A^2 -> H(k, U1(b, k))
28.57/10.25	   A^2 -> H(k, U1(e, c))
28.57/10.25	   A^2 -> H(k, U1(c, e))
28.57/10.25	   A^2 -> H(k, U1(c, k))
28.57/10.25	   A^2 -> H(k, U1(e, e))
28.57/10.25	   A^2 -> H(k, U1(d, k))
28.57/10.25	   A^2 -> H(c, b)
28.57/10.25	   A^2 -> H(c, U1(e, d))
28.57/10.25	   A^2 -> H(c, U1(d, e))
28.57/10.25	   A^2 -> H(c, c)
28.57/10.25	   A^2 -> H(c, U1(e, k))
28.57/10.25	   A^2 -> H(c, U1(k, e))
28.57/10.25	   A^2 -> H(c, e)
28.57/10.25	   A^2 -> H(c, U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, k), b)
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, k), c)
28.57/10.25	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, k), e)
28.57/10.25	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(e, c), d)
28.57/10.25	
28.57/10.25	The TRS R consists of the following rules:
28.57/10.25	
28.57/10.25	   f(x) -> U1(x, x)
28.57/10.25	   U1(e, x) -> x
28.57/10.25	   a -> c
28.57/10.25	   a -> d
28.57/10.25	   b -> c
28.57/10.25	   b -> d
28.57/10.25	   d -> k
28.57/10.25	   c -> e
28.57/10.25	   c -> k
28.57/10.25	
28.57/10.25	Q is empty.
28.57/10.25	We have to consider all minimal (P,Q,R)-chains.
28.57/10.25	----------------------------------------
28.57/10.25	
28.57/10.25	(2119) TransformationProof (EQUIVALENT)
28.57/10.25	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.25	
28.57/10.25	   (A^2 -> H(c, U1(e, d)),A^2 -> H(c, U1(e, d)))
28.57/10.25	   (A^2 -> H(U1(e, e), U1(e, d)),A^2 -> H(U1(e, e), U1(e, d)))
28.57/10.25	   (A^2 -> H(U1(e, k), U1(e, d)),A^2 -> H(U1(e, k), U1(e, d)))
28.57/10.25	   (A^2 -> H(U1(e, c), d),A^2 -> H(U1(e, c), d))
28.57/10.25	   (A^2 -> H(U1(e, c), U1(e, k)),A^2 -> H(U1(e, c), U1(e, k)))
28.57/10.25	
28.57/10.25	
28.57/10.25	----------------------------------------
28.57/10.25	
28.57/10.25	(2120)
28.57/10.25	Obligation:
28.57/10.25	Q DP problem:
28.57/10.25	The TRS P consists of the following rules:
28.57/10.25	
28.57/10.25	   A^2 -> H(f(c), f(c))
28.57/10.25	   H(x, x) -> G(x, x, f(k))
28.57/10.25	   G(d, x, x) -> A^2
28.57/10.25	   A^2 -> H(f(d), f(d))
28.57/10.25	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.25	   A^2 -> H(f(e), f(e))
28.57/10.25	   A^2 -> H(f(k), f(k))
28.57/10.25	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.25	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.25	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.25	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.25	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.25	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, c), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, c), e)
28.57/10.25	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.25	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.25	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.25	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.25	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.25	   A^2 -> H(U1(k, c), b)
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.25	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.25	   A^2 -> H(U1(k, c), c)
28.57/10.25	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.25	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, e), b)
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(c, e), c)
28.57/10.25	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, e), e)
28.57/10.25	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, k), b)
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.25	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.25	   A^2 -> H(U1(c, k), c)
28.57/10.25	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.25	   A^2 -> H(U1(c, k), e)
28.57/10.25	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.25	   A^2 -> H(U1(c, c), d)
28.57/10.25	   A^2 -> H(e, U1(e, b))
28.57/10.25	   A^2 -> H(e, U1(c, d))
28.57/10.25	   A^2 -> H(e, U1(d, c))
28.57/10.25	   A^2 -> H(e, U1(b, e))
28.57/10.25	   A^2 -> H(e, U1(b, k))
28.57/10.25	   A^2 -> H(e, U1(e, c))
28.57/10.25	   A^2 -> H(e, U1(c, e))
28.57/10.25	   A^2 -> H(e, U1(c, k))
28.57/10.25	   A^2 -> H(e, U1(e, e))
28.57/10.25	   A^2 -> H(e, U1(d, k))
28.57/10.25	   A^2 -> H(U1(e, e), b)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.25	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.25	   A^2 -> H(U1(e, e), c)
28.57/10.25	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.25	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.25	   A^2 -> H(f(e), d)
28.57/10.25	   A^2 -> H(f(e), k)
28.57/10.25	   A^2 -> H(U1(k, k), b)
28.57/10.25	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, k), c)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.26	   A^2 -> H(f(k), d)
28.57/10.26	   A^2 -> H(f(k), k)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, d), b)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, d), c)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, k), b)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, k), c)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, k), e)
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, d), d)
28.57/10.26	   A^2 -> H(U1(d, d), k)
28.57/10.26	   A^2 -> H(U1(e, c), c)
28.57/10.26	   A^2 -> H(U1(c, c), e)
28.57/10.26	   A^2 -> H(U1(c, c), k)
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(e, e), e)
28.57/10.26	   A^2 -> H(d, U1(e, b))
28.57/10.26	   A^2 -> H(d, U1(k, b))
28.57/10.26	   A^2 -> H(d, U1(c, d))
28.57/10.26	   A^2 -> H(d, U1(d, c))
28.57/10.26	   A^2 -> H(d, U1(b, e))
28.57/10.26	   A^2 -> H(d, U1(b, k))
28.57/10.26	   A^2 -> H(d, U1(e, c))
28.57/10.26	   A^2 -> H(d, U1(k, c))
28.57/10.26	   A^2 -> H(d, U1(c, e))
28.57/10.26	   A^2 -> H(d, U1(c, k))
28.57/10.26	   A^2 -> H(d, U1(e, e))
28.57/10.26	   A^2 -> H(d, U1(k, k))
28.57/10.26	   A^2 -> H(d, U1(k, d))
28.57/10.26	   A^2 -> H(d, U1(d, k))
28.57/10.26	   A^2 -> H(a, b)
28.57/10.26	   A^2 -> H(a, U1(e, d))
28.57/10.26	   A^2 -> H(a, U1(d, e))
28.57/10.26	   A^2 -> H(a, c)
28.57/10.26	   A^2 -> H(a, U1(e, k))
28.57/10.26	   A^2 -> H(a, U1(k, e))
28.57/10.26	   A^2 -> H(a, e)
28.57/10.26	   A^2 -> H(a, U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, d), b)
28.57/10.26	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, d), c)
28.57/10.26	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, d), e)
28.57/10.26	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, a), d)
28.57/10.26	   A^2 -> H(U1(e, a), k)
28.57/10.26	   A^2 -> H(U1(k, a), d)
28.57/10.26	   A^2 -> H(U1(c, d), d)
28.57/10.26	   A^2 -> H(U1(c, d), k)
28.57/10.26	   A^2 -> H(U1(d, e), b)
28.57/10.26	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, e), c)
28.57/10.26	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, e), e)
28.57/10.26	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, c), d)
28.57/10.26	   A^2 -> H(U1(d, c), k)
28.57/10.26	   A^2 -> H(U1(a, e), d)
28.57/10.26	   A^2 -> H(U1(a, e), k)
28.57/10.26	   A^2 -> H(U1(a, k), d)
28.57/10.26	   A^2 -> H(U1(a, k), k)
28.57/10.26	   A^2 -> H(k, U1(e, b))
28.57/10.26	   A^2 -> H(k, U1(c, d))
28.57/10.26	   A^2 -> H(k, U1(d, c))
28.57/10.26	   A^2 -> H(k, U1(b, e))
28.57/10.26	   A^2 -> H(k, U1(b, k))
28.57/10.26	   A^2 -> H(k, U1(e, c))
28.57/10.26	   A^2 -> H(k, U1(c, e))
28.57/10.26	   A^2 -> H(k, U1(c, k))
28.57/10.26	   A^2 -> H(k, U1(e, e))
28.57/10.26	   A^2 -> H(k, U1(d, k))
28.57/10.26	   A^2 -> H(c, b)
28.57/10.26	   A^2 -> H(c, U1(e, d))
28.57/10.26	   A^2 -> H(c, U1(d, e))
28.57/10.26	   A^2 -> H(c, c)
28.57/10.26	   A^2 -> H(c, U1(e, k))
28.57/10.26	   A^2 -> H(c, U1(k, e))
28.57/10.26	   A^2 -> H(c, e)
28.57/10.26	   A^2 -> H(c, U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, k), b)
28.57/10.26	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, k), c)
28.57/10.26	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, k), e)
28.57/10.26	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, c), d)
28.57/10.26	
28.57/10.26	The TRS R consists of the following rules:
28.57/10.26	
28.57/10.26	   f(x) -> U1(x, x)
28.57/10.26	   U1(e, x) -> x
28.57/10.26	   a -> c
28.57/10.26	   a -> d
28.57/10.26	   b -> c
28.57/10.26	   b -> d
28.57/10.26	   d -> k
28.57/10.26	   c -> e
28.57/10.26	   c -> k
28.57/10.26	
28.57/10.26	Q is empty.
28.57/10.26	We have to consider all minimal (P,Q,R)-chains.
28.57/10.26	----------------------------------------
28.57/10.26	
28.57/10.26	(2121) TransformationProof (EQUIVALENT)
28.57/10.26	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.26	
28.57/10.26	   (A^2 -> H(c, U1(d, e)),A^2 -> H(c, U1(d, e)))
28.57/10.26	   (A^2 -> H(U1(e, e), U1(d, e)),A^2 -> H(U1(e, e), U1(d, e)))
28.57/10.26	   (A^2 -> H(U1(e, k), U1(d, e)),A^2 -> H(U1(e, k), U1(d, e)))
28.57/10.26	   (A^2 -> H(U1(e, c), U1(k, e)),A^2 -> H(U1(e, c), U1(k, e)))
28.57/10.26	
28.57/10.26	
28.57/10.26	----------------------------------------
28.57/10.26	
28.57/10.26	(2122)
28.57/10.26	Obligation:
28.57/10.26	Q DP problem:
28.57/10.26	The TRS P consists of the following rules:
28.57/10.26	
28.57/10.26	   A^2 -> H(f(c), f(c))
28.57/10.26	   H(x, x) -> G(x, x, f(k))
28.57/10.26	   G(d, x, x) -> A^2
28.57/10.26	   A^2 -> H(f(d), f(d))
28.57/10.26	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.26	   A^2 -> H(f(e), f(e))
28.57/10.26	   A^2 -> H(f(k), f(k))
28.57/10.26	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.26	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.26	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.26	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(e, c), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, c), e)
28.57/10.26	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.26	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, c), b)
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, c), c)
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, e), b)
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(c, e), c)
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(c, e), e)
28.57/10.26	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, k), b)
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(c, k), c)
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(c, k), e)
28.57/10.26	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, c), d)
28.57/10.26	   A^2 -> H(e, U1(e, b))
28.57/10.26	   A^2 -> H(e, U1(c, d))
28.57/10.26	   A^2 -> H(e, U1(d, c))
28.57/10.26	   A^2 -> H(e, U1(b, e))
28.57/10.26	   A^2 -> H(e, U1(b, k))
28.57/10.26	   A^2 -> H(e, U1(e, c))
28.57/10.26	   A^2 -> H(e, U1(c, e))
28.57/10.26	   A^2 -> H(e, U1(c, k))
28.57/10.26	   A^2 -> H(e, U1(e, e))
28.57/10.26	   A^2 -> H(e, U1(d, k))
28.57/10.26	   A^2 -> H(U1(e, e), b)
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, e), c)
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.26	   A^2 -> H(f(e), d)
28.57/10.26	   A^2 -> H(f(e), k)
28.57/10.26	   A^2 -> H(U1(k, k), b)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, k), c)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.26	   A^2 -> H(f(k), d)
28.57/10.26	   A^2 -> H(f(k), k)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, d), b)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, d), c)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, k), b)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, k), c)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, k), e)
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, d), d)
28.57/10.26	   A^2 -> H(U1(d, d), k)
28.57/10.26	   A^2 -> H(U1(e, c), c)
28.57/10.26	   A^2 -> H(U1(c, c), e)
28.57/10.26	   A^2 -> H(U1(c, c), k)
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(e, e), e)
28.57/10.26	   A^2 -> H(d, U1(e, b))
28.57/10.26	   A^2 -> H(d, U1(k, b))
28.57/10.26	   A^2 -> H(d, U1(c, d))
28.57/10.26	   A^2 -> H(d, U1(d, c))
28.57/10.26	   A^2 -> H(d, U1(b, e))
28.57/10.26	   A^2 -> H(d, U1(b, k))
28.57/10.26	   A^2 -> H(d, U1(e, c))
28.57/10.26	   A^2 -> H(d, U1(k, c))
28.57/10.26	   A^2 -> H(d, U1(c, e))
28.57/10.26	   A^2 -> H(d, U1(c, k))
28.57/10.26	   A^2 -> H(d, U1(e, e))
28.57/10.26	   A^2 -> H(d, U1(k, k))
28.57/10.26	   A^2 -> H(d, U1(k, d))
28.57/10.26	   A^2 -> H(d, U1(d, k))
28.57/10.26	   A^2 -> H(a, b)
28.57/10.26	   A^2 -> H(a, U1(e, d))
28.57/10.26	   A^2 -> H(a, U1(d, e))
28.57/10.26	   A^2 -> H(a, c)
28.57/10.26	   A^2 -> H(a, U1(e, k))
28.57/10.26	   A^2 -> H(a, U1(k, e))
28.57/10.26	   A^2 -> H(a, e)
28.57/10.26	   A^2 -> H(a, U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, d), b)
28.57/10.26	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, d), c)
28.57/10.26	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, d), e)
28.57/10.26	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, a), d)
28.57/10.26	   A^2 -> H(U1(e, a), k)
28.57/10.26	   A^2 -> H(U1(k, a), d)
28.57/10.26	   A^2 -> H(U1(c, d), d)
28.57/10.26	   A^2 -> H(U1(c, d), k)
28.57/10.26	   A^2 -> H(U1(d, e), b)
28.57/10.26	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, e), c)
28.57/10.26	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, e), e)
28.57/10.26	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, c), d)
28.57/10.26	   A^2 -> H(U1(d, c), k)
28.57/10.26	   A^2 -> H(U1(a, e), d)
28.57/10.26	   A^2 -> H(U1(a, e), k)
28.57/10.26	   A^2 -> H(U1(a, k), d)
28.57/10.26	   A^2 -> H(U1(a, k), k)
28.57/10.26	   A^2 -> H(k, U1(e, b))
28.57/10.26	   A^2 -> H(k, U1(c, d))
28.57/10.26	   A^2 -> H(k, U1(d, c))
28.57/10.26	   A^2 -> H(k, U1(b, e))
28.57/10.26	   A^2 -> H(k, U1(b, k))
28.57/10.26	   A^2 -> H(k, U1(e, c))
28.57/10.26	   A^2 -> H(k, U1(c, e))
28.57/10.26	   A^2 -> H(k, U1(c, k))
28.57/10.26	   A^2 -> H(k, U1(e, e))
28.57/10.26	   A^2 -> H(k, U1(d, k))
28.57/10.26	   A^2 -> H(c, b)
28.57/10.26	   A^2 -> H(c, U1(e, d))
28.57/10.26	   A^2 -> H(c, U1(d, e))
28.57/10.26	   A^2 -> H(c, c)
28.57/10.26	   A^2 -> H(c, U1(e, k))
28.57/10.26	   A^2 -> H(c, U1(k, e))
28.57/10.26	   A^2 -> H(c, e)
28.57/10.26	   A^2 -> H(c, U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, k), b)
28.57/10.26	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, k), c)
28.57/10.26	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, k), e)
28.57/10.26	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, c), d)
28.57/10.26	
28.57/10.26	The TRS R consists of the following rules:
28.57/10.26	
28.57/10.26	   f(x) -> U1(x, x)
28.57/10.26	   U1(e, x) -> x
28.57/10.26	   a -> c
28.57/10.26	   a -> d
28.57/10.26	   b -> c
28.57/10.26	   b -> d
28.57/10.26	   d -> k
28.57/10.26	   c -> e
28.57/10.26	   c -> k
28.57/10.26	
28.57/10.26	Q is empty.
28.57/10.26	We have to consider all minimal (P,Q,R)-chains.
28.57/10.26	----------------------------------------
28.57/10.26	
28.57/10.26	(2123) TransformationProof (EQUIVALENT)
28.57/10.26	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.26	
28.57/10.26	   (A^2 -> H(c, U1(k, e)),A^2 -> H(c, U1(k, e)))
28.57/10.26	   (A^2 -> H(U1(e, e), U1(k, e)),A^2 -> H(U1(e, e), U1(k, e)))
28.57/10.26	   (A^2 -> H(U1(e, k), U1(k, e)),A^2 -> H(U1(e, k), U1(k, e)))
28.57/10.26	
28.57/10.26	
28.57/10.26	----------------------------------------
28.57/10.26	
28.57/10.26	(2124)
28.57/10.26	Obligation:
28.57/10.26	Q DP problem:
28.57/10.26	The TRS P consists of the following rules:
28.57/10.26	
28.57/10.26	   A^2 -> H(f(c), f(c))
28.57/10.26	   H(x, x) -> G(x, x, f(k))
28.57/10.26	   G(d, x, x) -> A^2
28.57/10.26	   A^2 -> H(f(d), f(d))
28.57/10.26	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.26	   A^2 -> H(f(e), f(e))
28.57/10.26	   A^2 -> H(f(k), f(k))
28.57/10.26	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.26	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.26	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.26	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, c), e)
28.57/10.26	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.26	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, c), b)
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, c), c)
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, e), b)
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(c, e), c)
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(c, e), e)
28.57/10.26	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, k), b)
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(c, k), c)
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(c, k), e)
28.57/10.26	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, c), d)
28.57/10.26	   A^2 -> H(e, U1(e, b))
28.57/10.26	   A^2 -> H(e, U1(c, d))
28.57/10.26	   A^2 -> H(e, U1(d, c))
28.57/10.26	   A^2 -> H(e, U1(b, e))
28.57/10.26	   A^2 -> H(e, U1(b, k))
28.57/10.26	   A^2 -> H(e, U1(e, c))
28.57/10.26	   A^2 -> H(e, U1(c, e))
28.57/10.26	   A^2 -> H(e, U1(c, k))
28.57/10.26	   A^2 -> H(e, U1(e, e))
28.57/10.26	   A^2 -> H(e, U1(d, k))
28.57/10.26	   A^2 -> H(U1(e, e), b)
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, e), c)
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.26	   A^2 -> H(f(e), d)
28.57/10.26	   A^2 -> H(f(e), k)
28.57/10.26	   A^2 -> H(U1(k, k), b)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, k), c)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.26	   A^2 -> H(f(k), d)
28.57/10.26	   A^2 -> H(f(k), k)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, d), b)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, d), c)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, k), b)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, k), c)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, k), e)
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, d), d)
28.57/10.26	   A^2 -> H(U1(d, d), k)
28.57/10.26	   A^2 -> H(U1(e, c), c)
28.57/10.26	   A^2 -> H(U1(c, c), e)
28.57/10.26	   A^2 -> H(U1(c, c), k)
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(e, e), e)
28.57/10.26	   A^2 -> H(d, U1(e, b))
28.57/10.26	   A^2 -> H(d, U1(k, b))
28.57/10.26	   A^2 -> H(d, U1(c, d))
28.57/10.26	   A^2 -> H(d, U1(d, c))
28.57/10.26	   A^2 -> H(d, U1(b, e))
28.57/10.26	   A^2 -> H(d, U1(b, k))
28.57/10.26	   A^2 -> H(d, U1(e, c))
28.57/10.26	   A^2 -> H(d, U1(k, c))
28.57/10.26	   A^2 -> H(d, U1(c, e))
28.57/10.26	   A^2 -> H(d, U1(c, k))
28.57/10.26	   A^2 -> H(d, U1(e, e))
28.57/10.26	   A^2 -> H(d, U1(k, k))
28.57/10.26	   A^2 -> H(d, U1(k, d))
28.57/10.26	   A^2 -> H(d, U1(d, k))
28.57/10.26	   A^2 -> H(a, b)
28.57/10.26	   A^2 -> H(a, U1(e, d))
28.57/10.26	   A^2 -> H(a, U1(d, e))
28.57/10.26	   A^2 -> H(a, c)
28.57/10.26	   A^2 -> H(a, U1(e, k))
28.57/10.26	   A^2 -> H(a, U1(k, e))
28.57/10.26	   A^2 -> H(a, e)
28.57/10.26	   A^2 -> H(a, U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, d), b)
28.57/10.26	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, d), c)
28.57/10.26	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, d), e)
28.57/10.26	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, a), d)
28.57/10.26	   A^2 -> H(U1(e, a), k)
28.57/10.26	   A^2 -> H(U1(k, a), d)
28.57/10.26	   A^2 -> H(U1(c, d), d)
28.57/10.26	   A^2 -> H(U1(c, d), k)
28.57/10.26	   A^2 -> H(U1(d, e), b)
28.57/10.26	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, e), c)
28.57/10.26	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, e), e)
28.57/10.26	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, c), d)
28.57/10.26	   A^2 -> H(U1(d, c), k)
28.57/10.26	   A^2 -> H(U1(a, e), d)
28.57/10.26	   A^2 -> H(U1(a, e), k)
28.57/10.26	   A^2 -> H(U1(a, k), d)
28.57/10.26	   A^2 -> H(U1(a, k), k)
28.57/10.26	   A^2 -> H(k, U1(e, b))
28.57/10.26	   A^2 -> H(k, U1(c, d))
28.57/10.26	   A^2 -> H(k, U1(d, c))
28.57/10.26	   A^2 -> H(k, U1(b, e))
28.57/10.26	   A^2 -> H(k, U1(b, k))
28.57/10.26	   A^2 -> H(k, U1(e, c))
28.57/10.26	   A^2 -> H(k, U1(c, e))
28.57/10.26	   A^2 -> H(k, U1(c, k))
28.57/10.26	   A^2 -> H(k, U1(e, e))
28.57/10.26	   A^2 -> H(k, U1(d, k))
28.57/10.26	   A^2 -> H(c, b)
28.57/10.26	   A^2 -> H(c, U1(e, d))
28.57/10.26	   A^2 -> H(c, U1(d, e))
28.57/10.26	   A^2 -> H(c, c)
28.57/10.26	   A^2 -> H(c, U1(e, k))
28.57/10.26	   A^2 -> H(c, U1(k, e))
28.57/10.26	   A^2 -> H(c, e)
28.57/10.26	   A^2 -> H(c, U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, k), b)
28.57/10.26	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, k), c)
28.57/10.26	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, k), e)
28.57/10.26	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, c), d)
28.57/10.26	
28.57/10.26	The TRS R consists of the following rules:
28.57/10.26	
28.57/10.26	   f(x) -> U1(x, x)
28.57/10.26	   U1(e, x) -> x
28.57/10.26	   a -> c
28.57/10.26	   a -> d
28.57/10.26	   b -> c
28.57/10.26	   b -> d
28.57/10.26	   d -> k
28.57/10.26	   c -> e
28.57/10.26	   c -> k
28.57/10.26	
28.57/10.26	Q is empty.
28.57/10.26	We have to consider all minimal (P,Q,R)-chains.
28.57/10.26	----------------------------------------
28.57/10.26	
28.57/10.26	(2125) TransformationProof (EQUIVALENT)
28.57/10.26	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.26	
28.57/10.26	   (A^2 -> H(c, U1(e, k)),A^2 -> H(c, U1(e, k)))
28.57/10.26	   (A^2 -> H(U1(e, e), U1(e, k)),A^2 -> H(U1(e, e), U1(e, k)))
28.57/10.26	   (A^2 -> H(U1(e, k), U1(e, k)),A^2 -> H(U1(e, k), U1(e, k)))
28.57/10.26	   (A^2 -> H(U1(e, c), k),A^2 -> H(U1(e, c), k))
28.57/10.26	
28.57/10.26	
28.57/10.26	----------------------------------------
28.57/10.26	
28.57/10.26	(2126)
28.57/10.26	Obligation:
28.57/10.26	Q DP problem:
28.57/10.26	The TRS P consists of the following rules:
28.57/10.26	
28.57/10.26	   A^2 -> H(f(c), f(c))
28.57/10.26	   H(x, x) -> G(x, x, f(k))
28.57/10.26	   G(d, x, x) -> A^2
28.57/10.26	   A^2 -> H(f(d), f(d))
28.57/10.26	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.26	   A^2 -> H(f(e), f(e))
28.57/10.26	   A^2 -> H(f(k), f(k))
28.57/10.26	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.26	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.26	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.26	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(e, c), e)
28.57/10.26	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.26	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, c), b)
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, c), c)
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, e), b)
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(c, e), c)
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(c, e), e)
28.57/10.26	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, k), b)
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(c, k), c)
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(c, k), e)
28.57/10.26	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, c), d)
28.57/10.26	   A^2 -> H(e, U1(e, b))
28.57/10.26	   A^2 -> H(e, U1(c, d))
28.57/10.26	   A^2 -> H(e, U1(d, c))
28.57/10.26	   A^2 -> H(e, U1(b, e))
28.57/10.26	   A^2 -> H(e, U1(b, k))
28.57/10.26	   A^2 -> H(e, U1(e, c))
28.57/10.26	   A^2 -> H(e, U1(c, e))
28.57/10.26	   A^2 -> H(e, U1(c, k))
28.57/10.26	   A^2 -> H(e, U1(e, e))
28.57/10.26	   A^2 -> H(e, U1(d, k))
28.57/10.26	   A^2 -> H(U1(e, e), b)
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, e), c)
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.26	   A^2 -> H(f(e), d)
28.57/10.26	   A^2 -> H(f(e), k)
28.57/10.26	   A^2 -> H(U1(k, k), b)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, k), c)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.26	   A^2 -> H(f(k), d)
28.57/10.26	   A^2 -> H(f(k), k)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, d), b)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, d), c)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, k), b)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, k), c)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, k), e)
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, d), d)
28.57/10.26	   A^2 -> H(U1(d, d), k)
28.57/10.26	   A^2 -> H(U1(e, c), c)
28.57/10.26	   A^2 -> H(U1(c, c), e)
28.57/10.26	   A^2 -> H(U1(c, c), k)
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(e, e), e)
28.57/10.26	   A^2 -> H(d, U1(e, b))
28.57/10.26	   A^2 -> H(d, U1(k, b))
28.57/10.26	   A^2 -> H(d, U1(c, d))
28.57/10.26	   A^2 -> H(d, U1(d, c))
28.57/10.26	   A^2 -> H(d, U1(b, e))
28.57/10.26	   A^2 -> H(d, U1(b, k))
28.57/10.26	   A^2 -> H(d, U1(e, c))
28.57/10.26	   A^2 -> H(d, U1(k, c))
28.57/10.26	   A^2 -> H(d, U1(c, e))
28.57/10.26	   A^2 -> H(d, U1(c, k))
28.57/10.26	   A^2 -> H(d, U1(e, e))
28.57/10.26	   A^2 -> H(d, U1(k, k))
28.57/10.26	   A^2 -> H(d, U1(k, d))
28.57/10.26	   A^2 -> H(d, U1(d, k))
28.57/10.26	   A^2 -> H(a, b)
28.57/10.26	   A^2 -> H(a, U1(e, d))
28.57/10.26	   A^2 -> H(a, U1(d, e))
28.57/10.26	   A^2 -> H(a, c)
28.57/10.26	   A^2 -> H(a, U1(e, k))
28.57/10.26	   A^2 -> H(a, U1(k, e))
28.57/10.26	   A^2 -> H(a, e)
28.57/10.26	   A^2 -> H(a, U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, d), b)
28.57/10.26	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, d), c)
28.57/10.26	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, d), e)
28.57/10.26	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, a), d)
28.57/10.26	   A^2 -> H(U1(e, a), k)
28.57/10.26	   A^2 -> H(U1(k, a), d)
28.57/10.26	   A^2 -> H(U1(c, d), d)
28.57/10.26	   A^2 -> H(U1(c, d), k)
28.57/10.26	   A^2 -> H(U1(d, e), b)
28.57/10.26	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, e), c)
28.57/10.26	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, e), e)
28.57/10.26	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, c), d)
28.57/10.26	   A^2 -> H(U1(d, c), k)
28.57/10.26	   A^2 -> H(U1(a, e), d)
28.57/10.26	   A^2 -> H(U1(a, e), k)
28.57/10.26	   A^2 -> H(U1(a, k), d)
28.57/10.26	   A^2 -> H(U1(a, k), k)
28.57/10.26	   A^2 -> H(k, U1(e, b))
28.57/10.26	   A^2 -> H(k, U1(c, d))
28.57/10.26	   A^2 -> H(k, U1(d, c))
28.57/10.26	   A^2 -> H(k, U1(b, e))
28.57/10.26	   A^2 -> H(k, U1(b, k))
28.57/10.26	   A^2 -> H(k, U1(e, c))
28.57/10.26	   A^2 -> H(k, U1(c, e))
28.57/10.26	   A^2 -> H(k, U1(c, k))
28.57/10.26	   A^2 -> H(k, U1(e, e))
28.57/10.26	   A^2 -> H(k, U1(d, k))
28.57/10.26	   A^2 -> H(c, b)
28.57/10.26	   A^2 -> H(c, U1(e, d))
28.57/10.26	   A^2 -> H(c, U1(d, e))
28.57/10.26	   A^2 -> H(c, c)
28.57/10.26	   A^2 -> H(c, U1(e, k))
28.57/10.26	   A^2 -> H(c, U1(k, e))
28.57/10.26	   A^2 -> H(c, e)
28.57/10.26	   A^2 -> H(c, U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, k), b)
28.57/10.26	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, k), c)
28.57/10.26	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, k), e)
28.57/10.26	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, c), d)
28.57/10.26	   A^2 -> H(U1(e, c), k)
28.57/10.26	
28.57/10.26	The TRS R consists of the following rules:
28.57/10.26	
28.57/10.26	   f(x) -> U1(x, x)
28.57/10.26	   U1(e, x) -> x
28.57/10.26	   a -> c
28.57/10.26	   a -> d
28.57/10.26	   b -> c
28.57/10.26	   b -> d
28.57/10.26	   d -> k
28.57/10.26	   c -> e
28.57/10.26	   c -> k
28.57/10.26	
28.57/10.26	Q is empty.
28.57/10.26	We have to consider all minimal (P,Q,R)-chains.
28.57/10.26	----------------------------------------
28.57/10.26	
28.57/10.26	(2127) TransformationProof (EQUIVALENT)
28.57/10.26	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), e) at position [] we obtained the following new rules [LPAR04]:
28.57/10.26	
28.57/10.26	   (A^2 -> H(c, e),A^2 -> H(c, e))
28.57/10.26	   (A^2 -> H(U1(e, e), e),A^2 -> H(U1(e, e), e))
28.57/10.26	   (A^2 -> H(U1(e, k), e),A^2 -> H(U1(e, k), e))
28.57/10.26	
28.57/10.26	
28.57/10.26	----------------------------------------
28.57/10.26	
28.57/10.26	(2128)
28.57/10.26	Obligation:
28.57/10.26	Q DP problem:
28.57/10.26	The TRS P consists of the following rules:
28.57/10.26	
28.57/10.26	   A^2 -> H(f(c), f(c))
28.57/10.26	   H(x, x) -> G(x, x, f(k))
28.57/10.26	   G(d, x, x) -> A^2
28.57/10.26	   A^2 -> H(f(d), f(d))
28.57/10.26	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.26	   A^2 -> H(f(e), f(e))
28.57/10.26	   A^2 -> H(f(k), f(k))
28.57/10.26	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.26	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.26	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.26	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(e, c), U1(k, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.26	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, c), b)
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, c), c)
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, e), b)
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(c, e), c)
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(c, e), e)
28.57/10.26	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, k), b)
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(c, k), c)
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(c, k), e)
28.57/10.26	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, c), d)
28.57/10.26	   A^2 -> H(e, U1(e, b))
28.57/10.26	   A^2 -> H(e, U1(c, d))
28.57/10.26	   A^2 -> H(e, U1(d, c))
28.57/10.26	   A^2 -> H(e, U1(b, e))
28.57/10.26	   A^2 -> H(e, U1(b, k))
28.57/10.26	   A^2 -> H(e, U1(e, c))
28.57/10.26	   A^2 -> H(e, U1(c, e))
28.57/10.26	   A^2 -> H(e, U1(c, k))
28.57/10.26	   A^2 -> H(e, U1(e, e))
28.57/10.26	   A^2 -> H(e, U1(d, k))
28.57/10.26	   A^2 -> H(U1(e, e), b)
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, e), c)
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.26	   A^2 -> H(f(e), d)
28.57/10.26	   A^2 -> H(f(e), k)
28.57/10.26	   A^2 -> H(U1(k, k), b)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, k), c)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.26	   A^2 -> H(f(k), d)
28.57/10.26	   A^2 -> H(f(k), k)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, d), b)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, d), c)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, k), b)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, k), c)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, k), e)
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, d), d)
28.57/10.26	   A^2 -> H(U1(d, d), k)
28.57/10.26	   A^2 -> H(U1(e, c), c)
28.57/10.26	   A^2 -> H(U1(c, c), e)
28.57/10.26	   A^2 -> H(U1(c, c), k)
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(e, e), e)
28.57/10.26	   A^2 -> H(d, U1(e, b))
28.57/10.26	   A^2 -> H(d, U1(k, b))
28.57/10.26	   A^2 -> H(d, U1(c, d))
28.57/10.26	   A^2 -> H(d, U1(d, c))
28.57/10.26	   A^2 -> H(d, U1(b, e))
28.57/10.26	   A^2 -> H(d, U1(b, k))
28.57/10.26	   A^2 -> H(d, U1(e, c))
28.57/10.26	   A^2 -> H(d, U1(k, c))
28.57/10.26	   A^2 -> H(d, U1(c, e))
28.57/10.26	   A^2 -> H(d, U1(c, k))
28.57/10.26	   A^2 -> H(d, U1(e, e))
28.57/10.26	   A^2 -> H(d, U1(k, k))
28.57/10.26	   A^2 -> H(d, U1(k, d))
28.57/10.26	   A^2 -> H(d, U1(d, k))
28.57/10.26	   A^2 -> H(a, b)
28.57/10.26	   A^2 -> H(a, U1(e, d))
28.57/10.26	   A^2 -> H(a, U1(d, e))
28.57/10.26	   A^2 -> H(a, c)
28.57/10.26	   A^2 -> H(a, U1(e, k))
28.57/10.26	   A^2 -> H(a, U1(k, e))
28.57/10.26	   A^2 -> H(a, e)
28.57/10.26	   A^2 -> H(a, U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, d), b)
28.57/10.26	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, d), c)
28.57/10.26	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, d), e)
28.57/10.26	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, a), d)
28.57/10.26	   A^2 -> H(U1(e, a), k)
28.57/10.26	   A^2 -> H(U1(k, a), d)
28.57/10.26	   A^2 -> H(U1(c, d), d)
28.57/10.26	   A^2 -> H(U1(c, d), k)
28.57/10.26	   A^2 -> H(U1(d, e), b)
28.57/10.26	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, e), c)
28.57/10.26	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, e), e)
28.57/10.26	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, c), d)
28.57/10.26	   A^2 -> H(U1(d, c), k)
28.57/10.26	   A^2 -> H(U1(a, e), d)
28.57/10.26	   A^2 -> H(U1(a, e), k)
28.57/10.26	   A^2 -> H(U1(a, k), d)
28.57/10.26	   A^2 -> H(U1(a, k), k)
28.57/10.26	   A^2 -> H(k, U1(e, b))
28.57/10.26	   A^2 -> H(k, U1(c, d))
28.57/10.26	   A^2 -> H(k, U1(d, c))
28.57/10.26	   A^2 -> H(k, U1(b, e))
28.57/10.26	   A^2 -> H(k, U1(b, k))
28.57/10.26	   A^2 -> H(k, U1(e, c))
28.57/10.26	   A^2 -> H(k, U1(c, e))
28.57/10.26	   A^2 -> H(k, U1(c, k))
28.57/10.26	   A^2 -> H(k, U1(e, e))
28.57/10.26	   A^2 -> H(k, U1(d, k))
28.57/10.26	   A^2 -> H(c, b)
28.57/10.26	   A^2 -> H(c, U1(e, d))
28.57/10.26	   A^2 -> H(c, U1(d, e))
28.57/10.26	   A^2 -> H(c, c)
28.57/10.26	   A^2 -> H(c, U1(e, k))
28.57/10.26	   A^2 -> H(c, U1(k, e))
28.57/10.26	   A^2 -> H(c, e)
28.57/10.26	   A^2 -> H(c, U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, k), b)
28.57/10.26	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, k), c)
28.57/10.26	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, k), e)
28.57/10.26	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, c), d)
28.57/10.26	   A^2 -> H(U1(e, c), k)
28.57/10.26	
28.57/10.26	The TRS R consists of the following rules:
28.57/10.26	
28.57/10.26	   f(x) -> U1(x, x)
28.57/10.26	   U1(e, x) -> x
28.57/10.26	   a -> c
28.57/10.26	   a -> d
28.57/10.26	   b -> c
28.57/10.26	   b -> d
28.57/10.26	   d -> k
28.57/10.26	   c -> e
28.57/10.26	   c -> k
28.57/10.26	
28.57/10.26	Q is empty.
28.57/10.26	We have to consider all minimal (P,Q,R)-chains.
28.57/10.26	----------------------------------------
28.57/10.26	
28.57/10.26	(2129) TransformationProof (EQUIVALENT)
28.57/10.26	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.26	
28.57/10.26	   (A^2 -> H(c, U1(k, k)),A^2 -> H(c, U1(k, k)))
28.57/10.26	   (A^2 -> H(U1(e, e), U1(k, k)),A^2 -> H(U1(e, e), U1(k, k)))
28.57/10.26	   (A^2 -> H(U1(e, k), U1(k, k)),A^2 -> H(U1(e, k), U1(k, k)))
28.57/10.26	
28.57/10.26	
28.57/10.26	----------------------------------------
28.57/10.26	
28.57/10.26	(2130)
28.57/10.26	Obligation:
28.57/10.26	Q DP problem:
28.57/10.26	The TRS P consists of the following rules:
28.57/10.26	
28.57/10.26	   A^2 -> H(f(c), f(c))
28.57/10.26	   H(x, x) -> G(x, x, f(k))
28.57/10.26	   G(d, x, x) -> A^2
28.57/10.26	   A^2 -> H(f(d), f(d))
28.57/10.26	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.26	   A^2 -> H(f(e), f(e))
28.57/10.26	   A^2 -> H(f(k), f(k))
28.57/10.26	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.26	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.26	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.26	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, b))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.26	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, c), b)
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, c), c)
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, e), b)
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(c, e), c)
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(c, e), e)
28.57/10.26	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, k), b)
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(c, k), c)
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(c, k), e)
28.57/10.26	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, c), d)
28.57/10.26	   A^2 -> H(e, U1(e, b))
28.57/10.26	   A^2 -> H(e, U1(c, d))
28.57/10.26	   A^2 -> H(e, U1(d, c))
28.57/10.26	   A^2 -> H(e, U1(b, e))
28.57/10.26	   A^2 -> H(e, U1(b, k))
28.57/10.26	   A^2 -> H(e, U1(e, c))
28.57/10.26	   A^2 -> H(e, U1(c, e))
28.57/10.26	   A^2 -> H(e, U1(c, k))
28.57/10.26	   A^2 -> H(e, U1(e, e))
28.57/10.26	   A^2 -> H(e, U1(d, k))
28.57/10.26	   A^2 -> H(U1(e, e), b)
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, e), c)
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.26	   A^2 -> H(f(e), d)
28.57/10.26	   A^2 -> H(f(e), k)
28.57/10.26	   A^2 -> H(U1(k, k), b)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, k), c)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.26	   A^2 -> H(f(k), d)
28.57/10.26	   A^2 -> H(f(k), k)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, d), b)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, d), c)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, k), b)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, k), c)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, k), e)
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, d), d)
28.57/10.26	   A^2 -> H(U1(d, d), k)
28.57/10.26	   A^2 -> H(U1(e, c), c)
28.57/10.26	   A^2 -> H(U1(c, c), e)
28.57/10.26	   A^2 -> H(U1(c, c), k)
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(e, e), e)
28.57/10.26	   A^2 -> H(d, U1(e, b))
28.57/10.26	   A^2 -> H(d, U1(k, b))
28.57/10.26	   A^2 -> H(d, U1(c, d))
28.57/10.26	   A^2 -> H(d, U1(d, c))
28.57/10.26	   A^2 -> H(d, U1(b, e))
28.57/10.26	   A^2 -> H(d, U1(b, k))
28.57/10.26	   A^2 -> H(d, U1(e, c))
28.57/10.26	   A^2 -> H(d, U1(k, c))
28.57/10.26	   A^2 -> H(d, U1(c, e))
28.57/10.26	   A^2 -> H(d, U1(c, k))
28.57/10.26	   A^2 -> H(d, U1(e, e))
28.57/10.26	   A^2 -> H(d, U1(k, k))
28.57/10.26	   A^2 -> H(d, U1(k, d))
28.57/10.26	   A^2 -> H(d, U1(d, k))
28.57/10.26	   A^2 -> H(a, b)
28.57/10.26	   A^2 -> H(a, U1(e, d))
28.57/10.26	   A^2 -> H(a, U1(d, e))
28.57/10.26	   A^2 -> H(a, c)
28.57/10.26	   A^2 -> H(a, U1(e, k))
28.57/10.26	   A^2 -> H(a, U1(k, e))
28.57/10.26	   A^2 -> H(a, e)
28.57/10.26	   A^2 -> H(a, U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, d), b)
28.57/10.26	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, d), c)
28.57/10.26	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, d), e)
28.57/10.26	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, a), d)
28.57/10.26	   A^2 -> H(U1(e, a), k)
28.57/10.26	   A^2 -> H(U1(k, a), d)
28.57/10.26	   A^2 -> H(U1(c, d), d)
28.57/10.26	   A^2 -> H(U1(c, d), k)
28.57/10.26	   A^2 -> H(U1(d, e), b)
28.57/10.26	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, e), c)
28.57/10.26	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, e), e)
28.57/10.26	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, c), d)
28.57/10.26	   A^2 -> H(U1(d, c), k)
28.57/10.26	   A^2 -> H(U1(a, e), d)
28.57/10.26	   A^2 -> H(U1(a, e), k)
28.57/10.26	   A^2 -> H(U1(a, k), d)
28.57/10.26	   A^2 -> H(U1(a, k), k)
28.57/10.26	   A^2 -> H(k, U1(e, b))
28.57/10.26	   A^2 -> H(k, U1(c, d))
28.57/10.26	   A^2 -> H(k, U1(d, c))
28.57/10.26	   A^2 -> H(k, U1(b, e))
28.57/10.26	   A^2 -> H(k, U1(b, k))
28.57/10.26	   A^2 -> H(k, U1(e, c))
28.57/10.26	   A^2 -> H(k, U1(c, e))
28.57/10.26	   A^2 -> H(k, U1(c, k))
28.57/10.26	   A^2 -> H(k, U1(e, e))
28.57/10.26	   A^2 -> H(k, U1(d, k))
28.57/10.26	   A^2 -> H(c, b)
28.57/10.26	   A^2 -> H(c, U1(e, d))
28.57/10.26	   A^2 -> H(c, U1(d, e))
28.57/10.26	   A^2 -> H(c, c)
28.57/10.26	   A^2 -> H(c, U1(e, k))
28.57/10.26	   A^2 -> H(c, U1(k, e))
28.57/10.26	   A^2 -> H(c, e)
28.57/10.26	   A^2 -> H(c, U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, k), b)
28.57/10.26	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, k), c)
28.57/10.26	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, k), e)
28.57/10.26	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, c), d)
28.57/10.26	   A^2 -> H(U1(e, c), k)
28.57/10.26	
28.57/10.26	The TRS R consists of the following rules:
28.57/10.26	
28.57/10.26	   f(x) -> U1(x, x)
28.57/10.26	   U1(e, x) -> x
28.57/10.26	   a -> c
28.57/10.26	   a -> d
28.57/10.26	   b -> c
28.57/10.26	   b -> d
28.57/10.26	   d -> k
28.57/10.26	   c -> e
28.57/10.26	   c -> k
28.57/10.26	
28.57/10.26	Q is empty.
28.57/10.26	We have to consider all minimal (P,Q,R)-chains.
28.57/10.26	----------------------------------------
28.57/10.26	
28.57/10.26	(2131) TransformationProof (EQUIVALENT)
28.57/10.26	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.26	
28.57/10.26	   (A^2 -> H(U1(k, e), b),A^2 -> H(U1(k, e), b))
28.57/10.26	   (A^2 -> H(U1(k, e), U1(e, c)),A^2 -> H(U1(k, e), U1(e, c)))
28.57/10.26	   (A^2 -> H(U1(k, e), U1(e, d)),A^2 -> H(U1(k, e), U1(e, d)))
28.57/10.26	
28.57/10.26	
28.57/10.26	----------------------------------------
28.57/10.26	
28.57/10.26	(2132)
28.57/10.26	Obligation:
28.57/10.26	Q DP problem:
28.57/10.26	The TRS P consists of the following rules:
28.57/10.26	
28.57/10.26	   A^2 -> H(f(c), f(c))
28.57/10.26	   H(x, x) -> G(x, x, f(k))
28.57/10.26	   G(d, x, x) -> A^2
28.57/10.26	   A^2 -> H(f(d), f(d))
28.57/10.26	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.26	   A^2 -> H(f(e), f(e))
28.57/10.26	   A^2 -> H(f(k), f(k))
28.57/10.26	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.26	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.26	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.26	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, b))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.26	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, c), b)
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, c), c)
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, e), b)
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(c, e), c)
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(c, e), e)
28.57/10.26	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, k), b)
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(c, k), c)
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(c, k), e)
28.57/10.26	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, c), d)
28.57/10.26	   A^2 -> H(e, U1(e, b))
28.57/10.26	   A^2 -> H(e, U1(c, d))
28.57/10.26	   A^2 -> H(e, U1(d, c))
28.57/10.26	   A^2 -> H(e, U1(b, e))
28.57/10.26	   A^2 -> H(e, U1(b, k))
28.57/10.26	   A^2 -> H(e, U1(e, c))
28.57/10.26	   A^2 -> H(e, U1(c, e))
28.57/10.26	   A^2 -> H(e, U1(c, k))
28.57/10.26	   A^2 -> H(e, U1(e, e))
28.57/10.26	   A^2 -> H(e, U1(d, k))
28.57/10.26	   A^2 -> H(U1(e, e), b)
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, e), c)
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.26	   A^2 -> H(f(e), d)
28.57/10.26	   A^2 -> H(f(e), k)
28.57/10.26	   A^2 -> H(U1(k, k), b)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, k), c)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.26	   A^2 -> H(f(k), d)
28.57/10.26	   A^2 -> H(f(k), k)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, d), b)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, d), c)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, k), b)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, k), c)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, k), e)
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, d), d)
28.57/10.26	   A^2 -> H(U1(d, d), k)
28.57/10.26	   A^2 -> H(U1(e, c), c)
28.57/10.26	   A^2 -> H(U1(c, c), e)
28.57/10.26	   A^2 -> H(U1(c, c), k)
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(e, e), e)
28.57/10.26	   A^2 -> H(d, U1(e, b))
28.57/10.26	   A^2 -> H(d, U1(k, b))
28.57/10.26	   A^2 -> H(d, U1(c, d))
28.57/10.26	   A^2 -> H(d, U1(d, c))
28.57/10.26	   A^2 -> H(d, U1(b, e))
28.57/10.26	   A^2 -> H(d, U1(b, k))
28.57/10.26	   A^2 -> H(d, U1(e, c))
28.57/10.26	   A^2 -> H(d, U1(k, c))
28.57/10.26	   A^2 -> H(d, U1(c, e))
28.57/10.26	   A^2 -> H(d, U1(c, k))
28.57/10.26	   A^2 -> H(d, U1(e, e))
28.57/10.26	   A^2 -> H(d, U1(k, k))
28.57/10.26	   A^2 -> H(d, U1(k, d))
28.57/10.26	   A^2 -> H(d, U1(d, k))
28.57/10.26	   A^2 -> H(a, b)
28.57/10.26	   A^2 -> H(a, U1(e, d))
28.57/10.26	   A^2 -> H(a, U1(d, e))
28.57/10.26	   A^2 -> H(a, c)
28.57/10.26	   A^2 -> H(a, U1(e, k))
28.57/10.26	   A^2 -> H(a, U1(k, e))
28.57/10.26	   A^2 -> H(a, e)
28.57/10.26	   A^2 -> H(a, U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, d), b)
28.57/10.26	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, d), c)
28.57/10.26	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, d), e)
28.57/10.26	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, a), d)
28.57/10.26	   A^2 -> H(U1(e, a), k)
28.57/10.26	   A^2 -> H(U1(k, a), d)
28.57/10.26	   A^2 -> H(U1(c, d), d)
28.57/10.26	   A^2 -> H(U1(c, d), k)
28.57/10.26	   A^2 -> H(U1(d, e), b)
28.57/10.26	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, e), c)
28.57/10.26	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, e), e)
28.57/10.26	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, c), d)
28.57/10.26	   A^2 -> H(U1(d, c), k)
28.57/10.26	   A^2 -> H(U1(a, e), d)
28.57/10.26	   A^2 -> H(U1(a, e), k)
28.57/10.26	   A^2 -> H(U1(a, k), d)
28.57/10.26	   A^2 -> H(U1(a, k), k)
28.57/10.26	   A^2 -> H(k, U1(e, b))
28.57/10.26	   A^2 -> H(k, U1(c, d))
28.57/10.26	   A^2 -> H(k, U1(d, c))
28.57/10.26	   A^2 -> H(k, U1(b, e))
28.57/10.26	   A^2 -> H(k, U1(b, k))
28.57/10.26	   A^2 -> H(k, U1(e, c))
28.57/10.26	   A^2 -> H(k, U1(c, e))
28.57/10.26	   A^2 -> H(k, U1(c, k))
28.57/10.26	   A^2 -> H(k, U1(e, e))
28.57/10.26	   A^2 -> H(k, U1(d, k))
28.57/10.26	   A^2 -> H(c, b)
28.57/10.26	   A^2 -> H(c, U1(e, d))
28.57/10.26	   A^2 -> H(c, U1(d, e))
28.57/10.26	   A^2 -> H(c, c)
28.57/10.26	   A^2 -> H(c, U1(e, k))
28.57/10.26	   A^2 -> H(c, U1(k, e))
28.57/10.26	   A^2 -> H(c, e)
28.57/10.26	   A^2 -> H(c, U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, k), b)
28.57/10.26	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, k), c)
28.57/10.26	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, k), e)
28.57/10.26	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, c), d)
28.57/10.26	   A^2 -> H(U1(e, c), k)
28.57/10.26	   A^2 -> H(U1(k, e), b)
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.26	
28.57/10.26	The TRS R consists of the following rules:
28.57/10.26	
28.57/10.26	   f(x) -> U1(x, x)
28.57/10.26	   U1(e, x) -> x
28.57/10.26	   a -> c
28.57/10.26	   a -> d
28.57/10.26	   b -> c
28.57/10.26	   b -> d
28.57/10.26	   d -> k
28.57/10.26	   c -> e
28.57/10.26	   c -> k
28.57/10.26	
28.57/10.26	Q is empty.
28.57/10.26	We have to consider all minimal (P,Q,R)-chains.
28.57/10.26	----------------------------------------
28.57/10.26	
28.57/10.26	(2133) TransformationProof (EQUIVALENT)
28.57/10.26	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.26	
28.57/10.26	   (A^2 -> H(U1(k, e), U1(k, c)),A^2 -> H(U1(k, e), U1(k, c)))
28.57/10.26	   (A^2 -> H(U1(k, e), U1(k, d)),A^2 -> H(U1(k, e), U1(k, d)))
28.57/10.26	
28.57/10.26	
28.57/10.26	----------------------------------------
28.57/10.26	
28.57/10.26	(2134)
28.57/10.26	Obligation:
28.57/10.26	Q DP problem:
28.57/10.26	The TRS P consists of the following rules:
28.57/10.26	
28.57/10.26	   A^2 -> H(f(c), f(c))
28.57/10.26	   H(x, x) -> G(x, x, f(k))
28.57/10.26	   G(d, x, x) -> A^2
28.57/10.26	   A^2 -> H(f(d), f(d))
28.57/10.26	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.26	   A^2 -> H(f(e), f(e))
28.57/10.26	   A^2 -> H(f(k), f(k))
28.57/10.26	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.26	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.26	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.26	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, d))
28.57/10.26	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, c), b)
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, c), c)
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, e), b)
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(c, e), c)
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(c, e), e)
28.57/10.26	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, k), b)
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(c, k), c)
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(c, k), e)
28.57/10.26	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, c), d)
28.57/10.26	   A^2 -> H(e, U1(e, b))
28.57/10.26	   A^2 -> H(e, U1(c, d))
28.57/10.26	   A^2 -> H(e, U1(d, c))
28.57/10.26	   A^2 -> H(e, U1(b, e))
28.57/10.26	   A^2 -> H(e, U1(b, k))
28.57/10.26	   A^2 -> H(e, U1(e, c))
28.57/10.26	   A^2 -> H(e, U1(c, e))
28.57/10.26	   A^2 -> H(e, U1(c, k))
28.57/10.26	   A^2 -> H(e, U1(e, e))
28.57/10.26	   A^2 -> H(e, U1(d, k))
28.57/10.26	   A^2 -> H(U1(e, e), b)
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, e), c)
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.26	   A^2 -> H(f(e), d)
28.57/10.26	   A^2 -> H(f(e), k)
28.57/10.26	   A^2 -> H(U1(k, k), b)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, k), c)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.26	   A^2 -> H(f(k), d)
28.57/10.26	   A^2 -> H(f(k), k)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, d), b)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, d), c)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, k), b)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, k), c)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, k), e)
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, d), d)
28.57/10.26	   A^2 -> H(U1(d, d), k)
28.57/10.26	   A^2 -> H(U1(e, c), c)
28.57/10.26	   A^2 -> H(U1(c, c), e)
28.57/10.26	   A^2 -> H(U1(c, c), k)
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(e, e), e)
28.57/10.26	   A^2 -> H(d, U1(e, b))
28.57/10.26	   A^2 -> H(d, U1(k, b))
28.57/10.26	   A^2 -> H(d, U1(c, d))
28.57/10.26	   A^2 -> H(d, U1(d, c))
28.57/10.26	   A^2 -> H(d, U1(b, e))
28.57/10.26	   A^2 -> H(d, U1(b, k))
28.57/10.26	   A^2 -> H(d, U1(e, c))
28.57/10.26	   A^2 -> H(d, U1(k, c))
28.57/10.26	   A^2 -> H(d, U1(c, e))
28.57/10.26	   A^2 -> H(d, U1(c, k))
28.57/10.26	   A^2 -> H(d, U1(e, e))
28.57/10.26	   A^2 -> H(d, U1(k, k))
28.57/10.26	   A^2 -> H(d, U1(k, d))
28.57/10.26	   A^2 -> H(d, U1(d, k))
28.57/10.26	   A^2 -> H(a, b)
28.57/10.26	   A^2 -> H(a, U1(e, d))
28.57/10.26	   A^2 -> H(a, U1(d, e))
28.57/10.26	   A^2 -> H(a, c)
28.57/10.26	   A^2 -> H(a, U1(e, k))
28.57/10.26	   A^2 -> H(a, U1(k, e))
28.57/10.26	   A^2 -> H(a, e)
28.57/10.26	   A^2 -> H(a, U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, d), b)
28.57/10.26	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, d), c)
28.57/10.26	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, d), e)
28.57/10.26	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, a), d)
28.57/10.26	   A^2 -> H(U1(e, a), k)
28.57/10.26	   A^2 -> H(U1(k, a), d)
28.57/10.26	   A^2 -> H(U1(c, d), d)
28.57/10.26	   A^2 -> H(U1(c, d), k)
28.57/10.26	   A^2 -> H(U1(d, e), b)
28.57/10.26	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, e), c)
28.57/10.26	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, e), e)
28.57/10.26	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, c), d)
28.57/10.26	   A^2 -> H(U1(d, c), k)
28.57/10.26	   A^2 -> H(U1(a, e), d)
28.57/10.26	   A^2 -> H(U1(a, e), k)
28.57/10.26	   A^2 -> H(U1(a, k), d)
28.57/10.26	   A^2 -> H(U1(a, k), k)
28.57/10.26	   A^2 -> H(k, U1(e, b))
28.57/10.26	   A^2 -> H(k, U1(c, d))
28.57/10.26	   A^2 -> H(k, U1(d, c))
28.57/10.26	   A^2 -> H(k, U1(b, e))
28.57/10.26	   A^2 -> H(k, U1(b, k))
28.57/10.26	   A^2 -> H(k, U1(e, c))
28.57/10.26	   A^2 -> H(k, U1(c, e))
28.57/10.26	   A^2 -> H(k, U1(c, k))
28.57/10.26	   A^2 -> H(k, U1(e, e))
28.57/10.26	   A^2 -> H(k, U1(d, k))
28.57/10.26	   A^2 -> H(c, b)
28.57/10.26	   A^2 -> H(c, U1(e, d))
28.57/10.26	   A^2 -> H(c, U1(d, e))
28.57/10.26	   A^2 -> H(c, c)
28.57/10.26	   A^2 -> H(c, U1(e, k))
28.57/10.26	   A^2 -> H(c, U1(k, e))
28.57/10.26	   A^2 -> H(c, e)
28.57/10.26	   A^2 -> H(c, U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, k), b)
28.57/10.26	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, k), c)
28.57/10.26	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, k), e)
28.57/10.26	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, c), d)
28.57/10.26	   A^2 -> H(U1(e, c), k)
28.57/10.26	   A^2 -> H(U1(k, e), b)
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.26	
28.57/10.26	The TRS R consists of the following rules:
28.57/10.26	
28.57/10.26	   f(x) -> U1(x, x)
28.57/10.26	   U1(e, x) -> x
28.57/10.26	   a -> c
28.57/10.26	   a -> d
28.57/10.26	   b -> c
28.57/10.26	   b -> d
28.57/10.26	   d -> k
28.57/10.26	   c -> e
28.57/10.26	   c -> k
28.57/10.26	
28.57/10.26	Q is empty.
28.57/10.26	We have to consider all minimal (P,Q,R)-chains.
28.57/10.26	----------------------------------------
28.57/10.26	
28.57/10.26	(2135) TransformationProof (EQUIVALENT)
28.57/10.26	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.26	
28.57/10.26	   (A^2 -> H(U1(k, e), U1(e, d)),A^2 -> H(U1(k, e), U1(e, d)))
28.57/10.26	   (A^2 -> H(U1(k, e), U1(k, d)),A^2 -> H(U1(k, e), U1(k, d)))
28.57/10.26	   (A^2 -> H(U1(k, e), U1(c, k)),A^2 -> H(U1(k, e), U1(c, k)))
28.57/10.26	
28.57/10.26	
28.57/10.26	----------------------------------------
28.57/10.26	
28.57/10.26	(2136)
28.57/10.26	Obligation:
28.57/10.26	Q DP problem:
28.57/10.26	The TRS P consists of the following rules:
28.57/10.26	
28.57/10.26	   A^2 -> H(f(c), f(c))
28.57/10.26	   H(x, x) -> G(x, x, f(k))
28.57/10.26	   G(d, x, x) -> A^2
28.57/10.26	   A^2 -> H(f(d), f(d))
28.57/10.26	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.26	   A^2 -> H(f(e), f(e))
28.57/10.26	   A^2 -> H(f(k), f(k))
28.57/10.26	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.26	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.26	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.26	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(d, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, c), b)
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, c), c)
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, e), b)
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(c, e), c)
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(c, e), e)
28.57/10.26	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, k), b)
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(c, k), c)
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(c, k), e)
28.57/10.26	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, c), d)
28.57/10.26	   A^2 -> H(e, U1(e, b))
28.57/10.26	   A^2 -> H(e, U1(c, d))
28.57/10.26	   A^2 -> H(e, U1(d, c))
28.57/10.26	   A^2 -> H(e, U1(b, e))
28.57/10.26	   A^2 -> H(e, U1(b, k))
28.57/10.26	   A^2 -> H(e, U1(e, c))
28.57/10.26	   A^2 -> H(e, U1(c, e))
28.57/10.26	   A^2 -> H(e, U1(c, k))
28.57/10.26	   A^2 -> H(e, U1(e, e))
28.57/10.26	   A^2 -> H(e, U1(d, k))
28.57/10.26	   A^2 -> H(U1(e, e), b)
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, e), c)
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.26	   A^2 -> H(f(e), d)
28.57/10.26	   A^2 -> H(f(e), k)
28.57/10.26	   A^2 -> H(U1(k, k), b)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, k), c)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.26	   A^2 -> H(f(k), d)
28.57/10.26	   A^2 -> H(f(k), k)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, d), b)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, d), c)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, k), b)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, k), c)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, k), e)
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, d), d)
28.57/10.26	   A^2 -> H(U1(d, d), k)
28.57/10.26	   A^2 -> H(U1(e, c), c)
28.57/10.26	   A^2 -> H(U1(c, c), e)
28.57/10.26	   A^2 -> H(U1(c, c), k)
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(e, e), e)
28.57/10.26	   A^2 -> H(d, U1(e, b))
28.57/10.26	   A^2 -> H(d, U1(k, b))
28.57/10.26	   A^2 -> H(d, U1(c, d))
28.57/10.26	   A^2 -> H(d, U1(d, c))
28.57/10.26	   A^2 -> H(d, U1(b, e))
28.57/10.26	   A^2 -> H(d, U1(b, k))
28.57/10.26	   A^2 -> H(d, U1(e, c))
28.57/10.26	   A^2 -> H(d, U1(k, c))
28.57/10.26	   A^2 -> H(d, U1(c, e))
28.57/10.26	   A^2 -> H(d, U1(c, k))
28.57/10.26	   A^2 -> H(d, U1(e, e))
28.57/10.26	   A^2 -> H(d, U1(k, k))
28.57/10.26	   A^2 -> H(d, U1(k, d))
28.57/10.26	   A^2 -> H(d, U1(d, k))
28.57/10.26	   A^2 -> H(a, b)
28.57/10.26	   A^2 -> H(a, U1(e, d))
28.57/10.26	   A^2 -> H(a, U1(d, e))
28.57/10.26	   A^2 -> H(a, c)
28.57/10.26	   A^2 -> H(a, U1(e, k))
28.57/10.26	   A^2 -> H(a, U1(k, e))
28.57/10.26	   A^2 -> H(a, e)
28.57/10.26	   A^2 -> H(a, U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, d), b)
28.57/10.26	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, d), c)
28.57/10.26	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, d), e)
28.57/10.26	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, a), d)
28.57/10.26	   A^2 -> H(U1(e, a), k)
28.57/10.26	   A^2 -> H(U1(k, a), d)
28.57/10.26	   A^2 -> H(U1(c, d), d)
28.57/10.26	   A^2 -> H(U1(c, d), k)
28.57/10.26	   A^2 -> H(U1(d, e), b)
28.57/10.26	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, e), c)
28.57/10.26	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, e), e)
28.57/10.26	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, c), d)
28.57/10.26	   A^2 -> H(U1(d, c), k)
28.57/10.26	   A^2 -> H(U1(a, e), d)
28.57/10.26	   A^2 -> H(U1(a, e), k)
28.57/10.26	   A^2 -> H(U1(a, k), d)
28.57/10.26	   A^2 -> H(U1(a, k), k)
28.57/10.26	   A^2 -> H(k, U1(e, b))
28.57/10.26	   A^2 -> H(k, U1(c, d))
28.57/10.26	   A^2 -> H(k, U1(d, c))
28.57/10.26	   A^2 -> H(k, U1(b, e))
28.57/10.26	   A^2 -> H(k, U1(b, k))
28.57/10.26	   A^2 -> H(k, U1(e, c))
28.57/10.26	   A^2 -> H(k, U1(c, e))
28.57/10.26	   A^2 -> H(k, U1(c, k))
28.57/10.26	   A^2 -> H(k, U1(e, e))
28.57/10.26	   A^2 -> H(k, U1(d, k))
28.57/10.26	   A^2 -> H(c, b)
28.57/10.26	   A^2 -> H(c, U1(e, d))
28.57/10.26	   A^2 -> H(c, U1(d, e))
28.57/10.26	   A^2 -> H(c, c)
28.57/10.26	   A^2 -> H(c, U1(e, k))
28.57/10.26	   A^2 -> H(c, U1(k, e))
28.57/10.26	   A^2 -> H(c, e)
28.57/10.26	   A^2 -> H(c, U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, k), b)
28.57/10.26	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, k), c)
28.57/10.26	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, k), e)
28.57/10.26	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(e, c), d)
28.57/10.26	   A^2 -> H(U1(e, c), k)
28.57/10.26	   A^2 -> H(U1(k, e), b)
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.26	
28.57/10.26	The TRS R consists of the following rules:
28.57/10.26	
28.57/10.26	   f(x) -> U1(x, x)
28.57/10.26	   U1(e, x) -> x
28.57/10.26	   a -> c
28.57/10.26	   a -> d
28.57/10.26	   b -> c
28.57/10.26	   b -> d
28.57/10.26	   d -> k
28.57/10.26	   c -> e
28.57/10.26	   c -> k
28.57/10.26	
28.57/10.26	Q is empty.
28.57/10.26	We have to consider all minimal (P,Q,R)-chains.
28.57/10.26	----------------------------------------
28.57/10.26	
28.57/10.26	(2137) TransformationProof (EQUIVALENT)
28.57/10.26	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.26	
28.57/10.26	   (A^2 -> H(U1(k, e), U1(k, c)),A^2 -> H(U1(k, e), U1(k, c)))
28.57/10.26	   (A^2 -> H(U1(k, e), U1(d, e)),A^2 -> H(U1(k, e), U1(d, e)))
28.57/10.26	   (A^2 -> H(U1(k, e), U1(d, k)),A^2 -> H(U1(k, e), U1(d, k)))
28.57/10.26	
28.57/10.26	
28.57/10.26	----------------------------------------
28.57/10.26	
28.57/10.26	(2138)
28.57/10.26	Obligation:
28.57/10.26	Q DP problem:
28.57/10.26	The TRS P consists of the following rules:
28.57/10.26	
28.57/10.26	   A^2 -> H(f(c), f(c))
28.57/10.26	   H(x, x) -> G(x, x, f(k))
28.57/10.26	   G(d, x, x) -> A^2
28.57/10.26	   A^2 -> H(f(d), f(d))
28.57/10.26	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.26	   A^2 -> H(f(e), f(e))
28.57/10.26	   A^2 -> H(f(k), f(k))
28.57/10.26	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.26	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.26	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.26	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, c), b)
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, c), c)
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, e), b)
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(c, e), c)
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(c, e), e)
28.57/10.26	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, k), b)
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(c, k), c)
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(c, k), e)
28.57/10.26	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(c, c), d)
28.57/10.26	   A^2 -> H(e, U1(e, b))
28.57/10.26	   A^2 -> H(e, U1(c, d))
28.57/10.26	   A^2 -> H(e, U1(d, c))
28.57/10.26	   A^2 -> H(e, U1(b, e))
28.57/10.26	   A^2 -> H(e, U1(b, k))
28.57/10.26	   A^2 -> H(e, U1(e, c))
28.57/10.26	   A^2 -> H(e, U1(c, e))
28.57/10.26	   A^2 -> H(e, U1(c, k))
28.57/10.26	   A^2 -> H(e, U1(e, e))
28.57/10.26	   A^2 -> H(e, U1(d, k))
28.57/10.26	   A^2 -> H(U1(e, e), b)
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.26	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.26	   A^2 -> H(U1(e, e), c)
28.57/10.26	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.26	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.26	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.26	   A^2 -> H(f(e), d)
28.57/10.26	   A^2 -> H(f(e), k)
28.57/10.26	   A^2 -> H(U1(k, k), b)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, k), c)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.26	   A^2 -> H(f(k), d)
28.57/10.26	   A^2 -> H(f(k), k)
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.26	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.26	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.26	   A^2 -> H(U1(k, d), b)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.26	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.26	   A^2 -> H(U1(k, d), c)
28.57/10.26	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.26	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, k), b)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.26	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.26	   A^2 -> H(U1(d, k), c)
28.57/10.26	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.26	   A^2 -> H(U1(d, k), e)
28.57/10.26	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.26	   A^2 -> H(U1(d, d), d)
28.57/10.26	   A^2 -> H(U1(d, d), k)
28.57/10.26	   A^2 -> H(U1(e, c), c)
28.57/10.26	   A^2 -> H(U1(c, c), e)
28.57/10.26	   A^2 -> H(U1(c, c), k)
28.57/10.26	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.26	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.26	   A^2 -> H(U1(e, e), e)
28.57/10.26	   A^2 -> H(d, U1(e, b))
28.57/10.26	   A^2 -> H(d, U1(k, b))
28.57/10.26	   A^2 -> H(d, U1(c, d))
28.57/10.26	   A^2 -> H(d, U1(d, c))
28.57/10.26	   A^2 -> H(d, U1(b, e))
28.57/10.26	   A^2 -> H(d, U1(b, k))
28.57/10.26	   A^2 -> H(d, U1(e, c))
28.57/10.26	   A^2 -> H(d, U1(k, c))
28.57/10.26	   A^2 -> H(d, U1(c, e))
28.57/10.26	   A^2 -> H(d, U1(c, k))
28.57/10.26	   A^2 -> H(d, U1(e, e))
28.57/10.26	   A^2 -> H(d, U1(k, k))
28.57/10.26	   A^2 -> H(d, U1(k, d))
28.57/10.26	   A^2 -> H(d, U1(d, k))
28.57/10.27	   A^2 -> H(a, b)
28.57/10.27	   A^2 -> H(a, U1(e, d))
28.57/10.27	   A^2 -> H(a, U1(d, e))
28.57/10.27	   A^2 -> H(a, c)
28.57/10.27	   A^2 -> H(a, U1(e, k))
28.57/10.27	   A^2 -> H(a, U1(k, e))
28.57/10.27	   A^2 -> H(a, e)
28.57/10.27	   A^2 -> H(a, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, d), b)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, d), c)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, d), e)
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, a), d)
28.57/10.27	   A^2 -> H(U1(e, a), k)
28.57/10.27	   A^2 -> H(U1(k, a), d)
28.57/10.27	   A^2 -> H(U1(c, d), d)
28.57/10.27	   A^2 -> H(U1(c, d), k)
28.57/10.27	   A^2 -> H(U1(d, e), b)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, e), c)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, e), e)
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, c), d)
28.57/10.27	   A^2 -> H(U1(d, c), k)
28.57/10.27	   A^2 -> H(U1(a, e), d)
28.57/10.27	   A^2 -> H(U1(a, e), k)
28.57/10.27	   A^2 -> H(U1(a, k), d)
28.57/10.27	   A^2 -> H(U1(a, k), k)
28.57/10.27	   A^2 -> H(k, U1(e, b))
28.57/10.27	   A^2 -> H(k, U1(c, d))
28.57/10.27	   A^2 -> H(k, U1(d, c))
28.57/10.27	   A^2 -> H(k, U1(b, e))
28.57/10.27	   A^2 -> H(k, U1(b, k))
28.57/10.27	   A^2 -> H(k, U1(e, c))
28.57/10.27	   A^2 -> H(k, U1(c, e))
28.57/10.27	   A^2 -> H(k, U1(c, k))
28.57/10.27	   A^2 -> H(k, U1(e, e))
28.57/10.27	   A^2 -> H(k, U1(d, k))
28.57/10.27	   A^2 -> H(c, b)
28.57/10.27	   A^2 -> H(c, U1(e, d))
28.57/10.27	   A^2 -> H(c, U1(d, e))
28.57/10.27	   A^2 -> H(c, c)
28.57/10.27	   A^2 -> H(c, U1(e, k))
28.57/10.27	   A^2 -> H(c, U1(k, e))
28.57/10.27	   A^2 -> H(c, e)
28.57/10.27	   A^2 -> H(c, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, k), b)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, k), c)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, k), e)
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, c), d)
28.57/10.27	   A^2 -> H(U1(e, c), k)
28.57/10.27	   A^2 -> H(U1(k, e), b)
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.27	
28.57/10.27	The TRS R consists of the following rules:
28.57/10.27	
28.57/10.27	   f(x) -> U1(x, x)
28.57/10.27	   U1(e, x) -> x
28.57/10.27	   a -> c
28.57/10.27	   a -> d
28.57/10.27	   b -> c
28.57/10.27	   b -> d
28.57/10.27	   d -> k
28.57/10.27	   c -> e
28.57/10.27	   c -> k
28.57/10.27	
28.57/10.27	Q is empty.
28.57/10.27	We have to consider all minimal (P,Q,R)-chains.
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2139) TransformationProof (EQUIVALENT)
28.57/10.27	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.27	
28.57/10.27	   (A^2 -> H(U1(k, e), U1(c, e)),A^2 -> H(U1(k, e), U1(c, e)))
28.57/10.27	   (A^2 -> H(U1(k, e), U1(d, e)),A^2 -> H(U1(k, e), U1(d, e)))
28.57/10.27	
28.57/10.27	
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2140)
28.57/10.27	Obligation:
28.57/10.27	Q DP problem:
28.57/10.27	The TRS P consists of the following rules:
28.57/10.27	
28.57/10.27	   A^2 -> H(f(c), f(c))
28.57/10.27	   H(x, x) -> G(x, x, f(k))
28.57/10.27	   G(d, x, x) -> A^2
28.57/10.27	   A^2 -> H(f(d), f(d))
28.57/10.27	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.27	   A^2 -> H(f(e), f(e))
28.57/10.27	   A^2 -> H(f(k), f(k))
28.57/10.27	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.27	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.27	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.27	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.27	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.27	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.27	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(b, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.27	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.27	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, c), b)
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, c), c)
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, e), b)
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(c, e), c)
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(c, e), e)
28.57/10.27	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, k), b)
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(c, k), c)
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(c, k), e)
28.57/10.27	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, c), d)
28.57/10.27	   A^2 -> H(e, U1(e, b))
28.57/10.27	   A^2 -> H(e, U1(c, d))
28.57/10.27	   A^2 -> H(e, U1(d, c))
28.57/10.27	   A^2 -> H(e, U1(b, e))
28.57/10.27	   A^2 -> H(e, U1(b, k))
28.57/10.27	   A^2 -> H(e, U1(e, c))
28.57/10.27	   A^2 -> H(e, U1(c, e))
28.57/10.27	   A^2 -> H(e, U1(c, k))
28.57/10.27	   A^2 -> H(e, U1(e, e))
28.57/10.27	   A^2 -> H(e, U1(d, k))
28.57/10.27	   A^2 -> H(U1(e, e), b)
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, e), c)
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.27	   A^2 -> H(f(e), d)
28.57/10.27	   A^2 -> H(f(e), k)
28.57/10.27	   A^2 -> H(U1(k, k), b)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, k), c)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.27	   A^2 -> H(f(k), d)
28.57/10.27	   A^2 -> H(f(k), k)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, d), b)
28.57/10.27	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, d), c)
28.57/10.27	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, k), b)
28.57/10.27	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, k), c)
28.57/10.27	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, k), e)
28.57/10.27	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, d), d)
28.57/10.27	   A^2 -> H(U1(d, d), k)
28.57/10.27	   A^2 -> H(U1(e, c), c)
28.57/10.27	   A^2 -> H(U1(c, c), e)
28.57/10.27	   A^2 -> H(U1(c, c), k)
28.57/10.27	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.27	   A^2 -> H(U1(e, e), e)
28.57/10.27	   A^2 -> H(d, U1(e, b))
28.57/10.27	   A^2 -> H(d, U1(k, b))
28.57/10.27	   A^2 -> H(d, U1(c, d))
28.57/10.27	   A^2 -> H(d, U1(d, c))
28.57/10.27	   A^2 -> H(d, U1(b, e))
28.57/10.27	   A^2 -> H(d, U1(b, k))
28.57/10.27	   A^2 -> H(d, U1(e, c))
28.57/10.27	   A^2 -> H(d, U1(k, c))
28.57/10.27	   A^2 -> H(d, U1(c, e))
28.57/10.27	   A^2 -> H(d, U1(c, k))
28.57/10.27	   A^2 -> H(d, U1(e, e))
28.57/10.27	   A^2 -> H(d, U1(k, k))
28.57/10.27	   A^2 -> H(d, U1(k, d))
28.57/10.27	   A^2 -> H(d, U1(d, k))
28.57/10.27	   A^2 -> H(a, b)
28.57/10.27	   A^2 -> H(a, U1(e, d))
28.57/10.27	   A^2 -> H(a, U1(d, e))
28.57/10.27	   A^2 -> H(a, c)
28.57/10.27	   A^2 -> H(a, U1(e, k))
28.57/10.27	   A^2 -> H(a, U1(k, e))
28.57/10.27	   A^2 -> H(a, e)
28.57/10.27	   A^2 -> H(a, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, d), b)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, d), c)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, d), e)
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, a), d)
28.57/10.27	   A^2 -> H(U1(e, a), k)
28.57/10.27	   A^2 -> H(U1(k, a), d)
28.57/10.27	   A^2 -> H(U1(c, d), d)
28.57/10.27	   A^2 -> H(U1(c, d), k)
28.57/10.27	   A^2 -> H(U1(d, e), b)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, e), c)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, e), e)
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, c), d)
28.57/10.27	   A^2 -> H(U1(d, c), k)
28.57/10.27	   A^2 -> H(U1(a, e), d)
28.57/10.27	   A^2 -> H(U1(a, e), k)
28.57/10.27	   A^2 -> H(U1(a, k), d)
28.57/10.27	   A^2 -> H(U1(a, k), k)
28.57/10.27	   A^2 -> H(k, U1(e, b))
28.57/10.27	   A^2 -> H(k, U1(c, d))
28.57/10.27	   A^2 -> H(k, U1(d, c))
28.57/10.27	   A^2 -> H(k, U1(b, e))
28.57/10.27	   A^2 -> H(k, U1(b, k))
28.57/10.27	   A^2 -> H(k, U1(e, c))
28.57/10.27	   A^2 -> H(k, U1(c, e))
28.57/10.27	   A^2 -> H(k, U1(c, k))
28.57/10.27	   A^2 -> H(k, U1(e, e))
28.57/10.27	   A^2 -> H(k, U1(d, k))
28.57/10.27	   A^2 -> H(c, b)
28.57/10.27	   A^2 -> H(c, U1(e, d))
28.57/10.27	   A^2 -> H(c, U1(d, e))
28.57/10.27	   A^2 -> H(c, c)
28.57/10.27	   A^2 -> H(c, U1(e, k))
28.57/10.27	   A^2 -> H(c, U1(k, e))
28.57/10.27	   A^2 -> H(c, e)
28.57/10.27	   A^2 -> H(c, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, k), b)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, k), c)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, k), e)
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, c), d)
28.57/10.27	   A^2 -> H(U1(e, c), k)
28.57/10.27	   A^2 -> H(U1(k, e), b)
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.27	
28.57/10.27	The TRS R consists of the following rules:
28.57/10.27	
28.57/10.27	   f(x) -> U1(x, x)
28.57/10.27	   U1(e, x) -> x
28.57/10.27	   a -> c
28.57/10.27	   a -> d
28.57/10.27	   b -> c
28.57/10.27	   b -> d
28.57/10.27	   d -> k
28.57/10.27	   c -> e
28.57/10.27	   c -> k
28.57/10.27	
28.57/10.27	Q is empty.
28.57/10.27	We have to consider all minimal (P,Q,R)-chains.
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2141) TransformationProof (EQUIVALENT)
28.57/10.27	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.27	
28.57/10.27	   (A^2 -> H(U1(k, e), U1(c, k)),A^2 -> H(U1(k, e), U1(c, k)))
28.57/10.27	   (A^2 -> H(U1(k, e), U1(d, k)),A^2 -> H(U1(k, e), U1(d, k)))
28.57/10.27	
28.57/10.27	
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2142)
28.57/10.27	Obligation:
28.57/10.27	Q DP problem:
28.57/10.27	The TRS P consists of the following rules:
28.57/10.27	
28.57/10.27	   A^2 -> H(f(c), f(c))
28.57/10.27	   H(x, x) -> G(x, x, f(k))
28.57/10.27	   G(d, x, x) -> A^2
28.57/10.27	   A^2 -> H(f(d), f(d))
28.57/10.27	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.27	   A^2 -> H(f(e), f(e))
28.57/10.27	   A^2 -> H(f(k), f(k))
28.57/10.27	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.27	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.27	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.27	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.27	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.27	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.27	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.27	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.27	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, c), b)
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, c), c)
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, e), b)
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(c, e), c)
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(c, e), e)
28.57/10.27	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, k), b)
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(c, k), c)
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(c, k), e)
28.57/10.27	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, c), d)
28.57/10.27	   A^2 -> H(e, U1(e, b))
28.57/10.27	   A^2 -> H(e, U1(c, d))
28.57/10.27	   A^2 -> H(e, U1(d, c))
28.57/10.27	   A^2 -> H(e, U1(b, e))
28.57/10.27	   A^2 -> H(e, U1(b, k))
28.57/10.27	   A^2 -> H(e, U1(e, c))
28.57/10.27	   A^2 -> H(e, U1(c, e))
28.57/10.27	   A^2 -> H(e, U1(c, k))
28.57/10.27	   A^2 -> H(e, U1(e, e))
28.57/10.27	   A^2 -> H(e, U1(d, k))
28.57/10.27	   A^2 -> H(U1(e, e), b)
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, e), c)
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.27	   A^2 -> H(f(e), d)
28.57/10.27	   A^2 -> H(f(e), k)
28.57/10.27	   A^2 -> H(U1(k, k), b)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, k), c)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.27	   A^2 -> H(f(k), d)
28.57/10.27	   A^2 -> H(f(k), k)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, d), b)
28.57/10.27	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, d), c)
28.57/10.27	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, k), b)
28.57/10.27	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, k), c)
28.57/10.27	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, k), e)
28.57/10.27	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, d), d)
28.57/10.27	   A^2 -> H(U1(d, d), k)
28.57/10.27	   A^2 -> H(U1(e, c), c)
28.57/10.27	   A^2 -> H(U1(c, c), e)
28.57/10.27	   A^2 -> H(U1(c, c), k)
28.57/10.27	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.27	   A^2 -> H(U1(e, e), e)
28.57/10.27	   A^2 -> H(d, U1(e, b))
28.57/10.27	   A^2 -> H(d, U1(k, b))
28.57/10.27	   A^2 -> H(d, U1(c, d))
28.57/10.27	   A^2 -> H(d, U1(d, c))
28.57/10.27	   A^2 -> H(d, U1(b, e))
28.57/10.27	   A^2 -> H(d, U1(b, k))
28.57/10.27	   A^2 -> H(d, U1(e, c))
28.57/10.27	   A^2 -> H(d, U1(k, c))
28.57/10.27	   A^2 -> H(d, U1(c, e))
28.57/10.27	   A^2 -> H(d, U1(c, k))
28.57/10.27	   A^2 -> H(d, U1(e, e))
28.57/10.27	   A^2 -> H(d, U1(k, k))
28.57/10.27	   A^2 -> H(d, U1(k, d))
28.57/10.27	   A^2 -> H(d, U1(d, k))
28.57/10.27	   A^2 -> H(a, b)
28.57/10.27	   A^2 -> H(a, U1(e, d))
28.57/10.27	   A^2 -> H(a, U1(d, e))
28.57/10.27	   A^2 -> H(a, c)
28.57/10.27	   A^2 -> H(a, U1(e, k))
28.57/10.27	   A^2 -> H(a, U1(k, e))
28.57/10.27	   A^2 -> H(a, e)
28.57/10.27	   A^2 -> H(a, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, d), b)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, d), c)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, d), e)
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, a), d)
28.57/10.27	   A^2 -> H(U1(e, a), k)
28.57/10.27	   A^2 -> H(U1(k, a), d)
28.57/10.27	   A^2 -> H(U1(c, d), d)
28.57/10.27	   A^2 -> H(U1(c, d), k)
28.57/10.27	   A^2 -> H(U1(d, e), b)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, e), c)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, e), e)
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, c), d)
28.57/10.27	   A^2 -> H(U1(d, c), k)
28.57/10.27	   A^2 -> H(U1(a, e), d)
28.57/10.27	   A^2 -> H(U1(a, e), k)
28.57/10.27	   A^2 -> H(U1(a, k), d)
28.57/10.27	   A^2 -> H(U1(a, k), k)
28.57/10.27	   A^2 -> H(k, U1(e, b))
28.57/10.27	   A^2 -> H(k, U1(c, d))
28.57/10.27	   A^2 -> H(k, U1(d, c))
28.57/10.27	   A^2 -> H(k, U1(b, e))
28.57/10.27	   A^2 -> H(k, U1(b, k))
28.57/10.27	   A^2 -> H(k, U1(e, c))
28.57/10.27	   A^2 -> H(k, U1(c, e))
28.57/10.27	   A^2 -> H(k, U1(c, k))
28.57/10.27	   A^2 -> H(k, U1(e, e))
28.57/10.27	   A^2 -> H(k, U1(d, k))
28.57/10.27	   A^2 -> H(c, b)
28.57/10.27	   A^2 -> H(c, U1(e, d))
28.57/10.27	   A^2 -> H(c, U1(d, e))
28.57/10.27	   A^2 -> H(c, c)
28.57/10.27	   A^2 -> H(c, U1(e, k))
28.57/10.27	   A^2 -> H(c, U1(k, e))
28.57/10.27	   A^2 -> H(c, e)
28.57/10.27	   A^2 -> H(c, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, k), b)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, k), c)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, k), e)
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, c), d)
28.57/10.27	   A^2 -> H(U1(e, c), k)
28.57/10.27	   A^2 -> H(U1(k, e), b)
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.27	
28.57/10.27	The TRS R consists of the following rules:
28.57/10.27	
28.57/10.27	   f(x) -> U1(x, x)
28.57/10.27	   U1(e, x) -> x
28.57/10.27	   a -> c
28.57/10.27	   a -> d
28.57/10.27	   b -> c
28.57/10.27	   b -> d
28.57/10.27	   d -> k
28.57/10.27	   c -> e
28.57/10.27	   c -> k
28.57/10.27	
28.57/10.27	Q is empty.
28.57/10.27	We have to consider all minimal (P,Q,R)-chains.
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2143) TransformationProof (EQUIVALENT)
28.57/10.27	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.27	
28.57/10.27	   (A^2 -> H(U1(k, e), c),A^2 -> H(U1(k, e), c))
28.57/10.27	   (A^2 -> H(U1(k, e), U1(e, e)),A^2 -> H(U1(k, e), U1(e, e)))
28.57/10.27	   (A^2 -> H(U1(k, e), U1(e, k)),A^2 -> H(U1(k, e), U1(e, k)))
28.57/10.27	
28.57/10.27	
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2144)
28.57/10.27	Obligation:
28.57/10.27	Q DP problem:
28.57/10.27	The TRS P consists of the following rules:
28.57/10.27	
28.57/10.27	   A^2 -> H(f(c), f(c))
28.57/10.27	   H(x, x) -> G(x, x, f(k))
28.57/10.27	   G(d, x, x) -> A^2
28.57/10.27	   A^2 -> H(f(d), f(d))
28.57/10.27	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.27	   A^2 -> H(f(e), f(e))
28.57/10.27	   A^2 -> H(f(k), f(k))
28.57/10.27	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.27	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.27	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.27	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.27	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.27	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.27	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, c))
28.57/10.27	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.27	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, c), b)
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, c), c)
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, e), b)
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(c, e), c)
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(c, e), e)
28.57/10.27	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, k), b)
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(c, k), c)
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(c, k), e)
28.57/10.27	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, c), d)
28.57/10.27	   A^2 -> H(e, U1(e, b))
28.57/10.27	   A^2 -> H(e, U1(c, d))
28.57/10.27	   A^2 -> H(e, U1(d, c))
28.57/10.27	   A^2 -> H(e, U1(b, e))
28.57/10.27	   A^2 -> H(e, U1(b, k))
28.57/10.27	   A^2 -> H(e, U1(e, c))
28.57/10.27	   A^2 -> H(e, U1(c, e))
28.57/10.27	   A^2 -> H(e, U1(c, k))
28.57/10.27	   A^2 -> H(e, U1(e, e))
28.57/10.27	   A^2 -> H(e, U1(d, k))
28.57/10.27	   A^2 -> H(U1(e, e), b)
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, e), c)
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.27	   A^2 -> H(f(e), d)
28.57/10.27	   A^2 -> H(f(e), k)
28.57/10.27	   A^2 -> H(U1(k, k), b)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, k), c)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.27	   A^2 -> H(f(k), d)
28.57/10.27	   A^2 -> H(f(k), k)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, d), b)
28.57/10.27	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, d), c)
28.57/10.27	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, k), b)
28.57/10.27	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, k), c)
28.57/10.27	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, k), e)
28.57/10.27	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, d), d)
28.57/10.27	   A^2 -> H(U1(d, d), k)
28.57/10.27	   A^2 -> H(U1(e, c), c)
28.57/10.27	   A^2 -> H(U1(c, c), e)
28.57/10.27	   A^2 -> H(U1(c, c), k)
28.57/10.27	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.27	   A^2 -> H(U1(e, e), e)
28.57/10.27	   A^2 -> H(d, U1(e, b))
28.57/10.27	   A^2 -> H(d, U1(k, b))
28.57/10.27	   A^2 -> H(d, U1(c, d))
28.57/10.27	   A^2 -> H(d, U1(d, c))
28.57/10.27	   A^2 -> H(d, U1(b, e))
28.57/10.27	   A^2 -> H(d, U1(b, k))
28.57/10.27	   A^2 -> H(d, U1(e, c))
28.57/10.27	   A^2 -> H(d, U1(k, c))
28.57/10.27	   A^2 -> H(d, U1(c, e))
28.57/10.27	   A^2 -> H(d, U1(c, k))
28.57/10.27	   A^2 -> H(d, U1(e, e))
28.57/10.27	   A^2 -> H(d, U1(k, k))
28.57/10.27	   A^2 -> H(d, U1(k, d))
28.57/10.27	   A^2 -> H(d, U1(d, k))
28.57/10.27	   A^2 -> H(a, b)
28.57/10.27	   A^2 -> H(a, U1(e, d))
28.57/10.27	   A^2 -> H(a, U1(d, e))
28.57/10.27	   A^2 -> H(a, c)
28.57/10.27	   A^2 -> H(a, U1(e, k))
28.57/10.27	   A^2 -> H(a, U1(k, e))
28.57/10.27	   A^2 -> H(a, e)
28.57/10.27	   A^2 -> H(a, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, d), b)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, d), c)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, d), e)
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, a), d)
28.57/10.27	   A^2 -> H(U1(e, a), k)
28.57/10.27	   A^2 -> H(U1(k, a), d)
28.57/10.27	   A^2 -> H(U1(c, d), d)
28.57/10.27	   A^2 -> H(U1(c, d), k)
28.57/10.27	   A^2 -> H(U1(d, e), b)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, e), c)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, e), e)
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, c), d)
28.57/10.27	   A^2 -> H(U1(d, c), k)
28.57/10.27	   A^2 -> H(U1(a, e), d)
28.57/10.27	   A^2 -> H(U1(a, e), k)
28.57/10.27	   A^2 -> H(U1(a, k), d)
28.57/10.27	   A^2 -> H(U1(a, k), k)
28.57/10.27	   A^2 -> H(k, U1(e, b))
28.57/10.27	   A^2 -> H(k, U1(c, d))
28.57/10.27	   A^2 -> H(k, U1(d, c))
28.57/10.27	   A^2 -> H(k, U1(b, e))
28.57/10.27	   A^2 -> H(k, U1(b, k))
28.57/10.27	   A^2 -> H(k, U1(e, c))
28.57/10.27	   A^2 -> H(k, U1(c, e))
28.57/10.27	   A^2 -> H(k, U1(c, k))
28.57/10.27	   A^2 -> H(k, U1(e, e))
28.57/10.27	   A^2 -> H(k, U1(d, k))
28.57/10.27	   A^2 -> H(c, b)
28.57/10.27	   A^2 -> H(c, U1(e, d))
28.57/10.27	   A^2 -> H(c, U1(d, e))
28.57/10.27	   A^2 -> H(c, c)
28.57/10.27	   A^2 -> H(c, U1(e, k))
28.57/10.27	   A^2 -> H(c, U1(k, e))
28.57/10.27	   A^2 -> H(c, e)
28.57/10.27	   A^2 -> H(c, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, k), b)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, k), c)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, k), e)
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, c), d)
28.57/10.27	   A^2 -> H(U1(e, c), k)
28.57/10.27	   A^2 -> H(U1(k, e), b)
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, e), c)
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.27	
28.57/10.27	The TRS R consists of the following rules:
28.57/10.27	
28.57/10.27	   f(x) -> U1(x, x)
28.57/10.27	   U1(e, x) -> x
28.57/10.27	   a -> c
28.57/10.27	   a -> d
28.57/10.27	   b -> c
28.57/10.27	   b -> d
28.57/10.27	   d -> k
28.57/10.27	   c -> e
28.57/10.27	   c -> k
28.57/10.27	
28.57/10.27	Q is empty.
28.57/10.27	We have to consider all minimal (P,Q,R)-chains.
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2145) TransformationProof (EQUIVALENT)
28.57/10.27	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.27	
28.57/10.27	   (A^2 -> H(U1(k, e), U1(k, e)),A^2 -> H(U1(k, e), U1(k, e)))
28.57/10.27	   (A^2 -> H(U1(k, e), U1(k, k)),A^2 -> H(U1(k, e), U1(k, k)))
28.57/10.27	
28.57/10.27	
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2146)
28.57/10.27	Obligation:
28.57/10.27	Q DP problem:
28.57/10.27	The TRS P consists of the following rules:
28.57/10.27	
28.57/10.27	   A^2 -> H(f(c), f(c))
28.57/10.27	   H(x, x) -> G(x, x, f(k))
28.57/10.27	   G(d, x, x) -> A^2
28.57/10.27	   A^2 -> H(f(d), f(d))
28.57/10.27	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.27	   A^2 -> H(f(e), f(e))
28.57/10.27	   A^2 -> H(f(k), f(k))
28.57/10.27	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.27	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.27	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.27	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.27	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.27	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.27	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.27	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, c), b)
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, c), c)
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, e), b)
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(c, e), c)
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(c, e), e)
28.57/10.27	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, k), b)
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(c, k), c)
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(c, k), e)
28.57/10.27	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, c), d)
28.57/10.27	   A^2 -> H(e, U1(e, b))
28.57/10.27	   A^2 -> H(e, U1(c, d))
28.57/10.27	   A^2 -> H(e, U1(d, c))
28.57/10.27	   A^2 -> H(e, U1(b, e))
28.57/10.27	   A^2 -> H(e, U1(b, k))
28.57/10.27	   A^2 -> H(e, U1(e, c))
28.57/10.27	   A^2 -> H(e, U1(c, e))
28.57/10.27	   A^2 -> H(e, U1(c, k))
28.57/10.27	   A^2 -> H(e, U1(e, e))
28.57/10.27	   A^2 -> H(e, U1(d, k))
28.57/10.27	   A^2 -> H(U1(e, e), b)
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, e), c)
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.27	   A^2 -> H(f(e), d)
28.57/10.27	   A^2 -> H(f(e), k)
28.57/10.27	   A^2 -> H(U1(k, k), b)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, k), c)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.27	   A^2 -> H(f(k), d)
28.57/10.27	   A^2 -> H(f(k), k)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, d), b)
28.57/10.27	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, d), c)
28.57/10.27	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, k), b)
28.57/10.27	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, k), c)
28.57/10.27	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, k), e)
28.57/10.27	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, d), d)
28.57/10.27	   A^2 -> H(U1(d, d), k)
28.57/10.27	   A^2 -> H(U1(e, c), c)
28.57/10.27	   A^2 -> H(U1(c, c), e)
28.57/10.27	   A^2 -> H(U1(c, c), k)
28.57/10.27	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.27	   A^2 -> H(U1(e, e), e)
28.57/10.27	   A^2 -> H(d, U1(e, b))
28.57/10.27	   A^2 -> H(d, U1(k, b))
28.57/10.27	   A^2 -> H(d, U1(c, d))
28.57/10.27	   A^2 -> H(d, U1(d, c))
28.57/10.27	   A^2 -> H(d, U1(b, e))
28.57/10.27	   A^2 -> H(d, U1(b, k))
28.57/10.27	   A^2 -> H(d, U1(e, c))
28.57/10.27	   A^2 -> H(d, U1(k, c))
28.57/10.27	   A^2 -> H(d, U1(c, e))
28.57/10.27	   A^2 -> H(d, U1(c, k))
28.57/10.27	   A^2 -> H(d, U1(e, e))
28.57/10.27	   A^2 -> H(d, U1(k, k))
28.57/10.27	   A^2 -> H(d, U1(k, d))
28.57/10.27	   A^2 -> H(d, U1(d, k))
28.57/10.27	   A^2 -> H(a, b)
28.57/10.27	   A^2 -> H(a, U1(e, d))
28.57/10.27	   A^2 -> H(a, U1(d, e))
28.57/10.27	   A^2 -> H(a, c)
28.57/10.27	   A^2 -> H(a, U1(e, k))
28.57/10.27	   A^2 -> H(a, U1(k, e))
28.57/10.27	   A^2 -> H(a, e)
28.57/10.27	   A^2 -> H(a, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, d), b)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, d), c)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, d), e)
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, a), d)
28.57/10.27	   A^2 -> H(U1(e, a), k)
28.57/10.27	   A^2 -> H(U1(k, a), d)
28.57/10.27	   A^2 -> H(U1(c, d), d)
28.57/10.27	   A^2 -> H(U1(c, d), k)
28.57/10.27	   A^2 -> H(U1(d, e), b)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, e), c)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, e), e)
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, c), d)
28.57/10.27	   A^2 -> H(U1(d, c), k)
28.57/10.27	   A^2 -> H(U1(a, e), d)
28.57/10.27	   A^2 -> H(U1(a, e), k)
28.57/10.27	   A^2 -> H(U1(a, k), d)
28.57/10.27	   A^2 -> H(U1(a, k), k)
28.57/10.27	   A^2 -> H(k, U1(e, b))
28.57/10.27	   A^2 -> H(k, U1(c, d))
28.57/10.27	   A^2 -> H(k, U1(d, c))
28.57/10.27	   A^2 -> H(k, U1(b, e))
28.57/10.27	   A^2 -> H(k, U1(b, k))
28.57/10.27	   A^2 -> H(k, U1(e, c))
28.57/10.27	   A^2 -> H(k, U1(c, e))
28.57/10.27	   A^2 -> H(k, U1(c, k))
28.57/10.27	   A^2 -> H(k, U1(e, e))
28.57/10.27	   A^2 -> H(k, U1(d, k))
28.57/10.27	   A^2 -> H(c, b)
28.57/10.27	   A^2 -> H(c, U1(e, d))
28.57/10.27	   A^2 -> H(c, U1(d, e))
28.57/10.27	   A^2 -> H(c, c)
28.57/10.27	   A^2 -> H(c, U1(e, k))
28.57/10.27	   A^2 -> H(c, U1(k, e))
28.57/10.27	   A^2 -> H(c, e)
28.57/10.27	   A^2 -> H(c, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, k), b)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, k), c)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, k), e)
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, c), d)
28.57/10.27	   A^2 -> H(U1(e, c), k)
28.57/10.27	   A^2 -> H(U1(k, e), b)
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, e), c)
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, k))
28.57/10.27	
28.57/10.27	The TRS R consists of the following rules:
28.57/10.27	
28.57/10.27	   f(x) -> U1(x, x)
28.57/10.27	   U1(e, x) -> x
28.57/10.27	   a -> c
28.57/10.27	   a -> d
28.57/10.27	   b -> c
28.57/10.27	   b -> d
28.57/10.27	   d -> k
28.57/10.27	   c -> e
28.57/10.27	   c -> k
28.57/10.27	
28.57/10.27	Q is empty.
28.57/10.27	We have to consider all minimal (P,Q,R)-chains.
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2147) DependencyGraphProof (EQUIVALENT)
28.57/10.27	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2148)
28.57/10.27	Obligation:
28.57/10.27	Q DP problem:
28.57/10.27	The TRS P consists of the following rules:
28.57/10.27	
28.57/10.27	   H(x, x) -> G(x, x, f(k))
28.57/10.27	   G(d, x, x) -> A^2
28.57/10.27	   A^2 -> H(f(c), f(c))
28.57/10.27	   A^2 -> H(f(d), f(d))
28.57/10.27	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.27	   A^2 -> H(f(e), f(e))
28.57/10.27	   A^2 -> H(f(k), f(k))
28.57/10.27	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.27	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.27	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.27	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.27	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.27	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.27	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(c, e))
28.57/10.27	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, c), b)
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, c), c)
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, e), b)
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(c, e), c)
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(c, e), e)
28.57/10.27	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, k), b)
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(c, k), c)
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(c, k), e)
28.57/10.27	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, c), d)
28.57/10.27	   A^2 -> H(e, U1(e, b))
28.57/10.27	   A^2 -> H(e, U1(c, d))
28.57/10.27	   A^2 -> H(e, U1(d, c))
28.57/10.27	   A^2 -> H(e, U1(b, e))
28.57/10.27	   A^2 -> H(e, U1(b, k))
28.57/10.27	   A^2 -> H(e, U1(e, c))
28.57/10.27	   A^2 -> H(e, U1(c, e))
28.57/10.27	   A^2 -> H(e, U1(c, k))
28.57/10.27	   A^2 -> H(e, U1(e, e))
28.57/10.27	   A^2 -> H(e, U1(d, k))
28.57/10.27	   A^2 -> H(U1(e, e), b)
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, e), c)
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.27	   A^2 -> H(f(e), d)
28.57/10.27	   A^2 -> H(f(e), k)
28.57/10.27	   A^2 -> H(U1(k, k), b)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, k), c)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.27	   A^2 -> H(f(k), d)
28.57/10.27	   A^2 -> H(f(k), k)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, d), b)
28.57/10.27	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, d), c)
28.57/10.27	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, k), b)
28.57/10.27	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, k), c)
28.57/10.27	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, k), e)
28.57/10.27	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, d), d)
28.57/10.27	   A^2 -> H(U1(d, d), k)
28.57/10.27	   A^2 -> H(U1(e, c), c)
28.57/10.27	   A^2 -> H(U1(c, c), e)
28.57/10.27	   A^2 -> H(U1(c, c), k)
28.57/10.27	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.27	   A^2 -> H(U1(e, e), e)
28.57/10.27	   A^2 -> H(d, U1(e, b))
28.57/10.27	   A^2 -> H(d, U1(k, b))
28.57/10.27	   A^2 -> H(d, U1(c, d))
28.57/10.27	   A^2 -> H(d, U1(d, c))
28.57/10.27	   A^2 -> H(d, U1(b, e))
28.57/10.27	   A^2 -> H(d, U1(b, k))
28.57/10.27	   A^2 -> H(d, U1(e, c))
28.57/10.27	   A^2 -> H(d, U1(k, c))
28.57/10.27	   A^2 -> H(d, U1(c, e))
28.57/10.27	   A^2 -> H(d, U1(c, k))
28.57/10.27	   A^2 -> H(d, U1(e, e))
28.57/10.27	   A^2 -> H(d, U1(k, k))
28.57/10.27	   A^2 -> H(d, U1(k, d))
28.57/10.27	   A^2 -> H(d, U1(d, k))
28.57/10.27	   A^2 -> H(a, b)
28.57/10.27	   A^2 -> H(a, U1(e, d))
28.57/10.27	   A^2 -> H(a, U1(d, e))
28.57/10.27	   A^2 -> H(a, c)
28.57/10.27	   A^2 -> H(a, U1(e, k))
28.57/10.27	   A^2 -> H(a, U1(k, e))
28.57/10.27	   A^2 -> H(a, e)
28.57/10.27	   A^2 -> H(a, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, d), b)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, d), c)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, d), e)
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, a), d)
28.57/10.27	   A^2 -> H(U1(e, a), k)
28.57/10.27	   A^2 -> H(U1(k, a), d)
28.57/10.27	   A^2 -> H(U1(c, d), d)
28.57/10.27	   A^2 -> H(U1(c, d), k)
28.57/10.27	   A^2 -> H(U1(d, e), b)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, e), c)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, e), e)
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, c), d)
28.57/10.27	   A^2 -> H(U1(d, c), k)
28.57/10.27	   A^2 -> H(U1(a, e), d)
28.57/10.27	   A^2 -> H(U1(a, e), k)
28.57/10.27	   A^2 -> H(U1(a, k), d)
28.57/10.27	   A^2 -> H(U1(a, k), k)
28.57/10.27	   A^2 -> H(k, U1(e, b))
28.57/10.27	   A^2 -> H(k, U1(c, d))
28.57/10.27	   A^2 -> H(k, U1(d, c))
28.57/10.27	   A^2 -> H(k, U1(b, e))
28.57/10.27	   A^2 -> H(k, U1(b, k))
28.57/10.27	   A^2 -> H(k, U1(e, c))
28.57/10.27	   A^2 -> H(k, U1(c, e))
28.57/10.27	   A^2 -> H(k, U1(c, k))
28.57/10.27	   A^2 -> H(k, U1(e, e))
28.57/10.27	   A^2 -> H(k, U1(d, k))
28.57/10.27	   A^2 -> H(c, b)
28.57/10.27	   A^2 -> H(c, U1(e, d))
28.57/10.27	   A^2 -> H(c, U1(d, e))
28.57/10.27	   A^2 -> H(c, c)
28.57/10.27	   A^2 -> H(c, U1(e, k))
28.57/10.27	   A^2 -> H(c, U1(k, e))
28.57/10.27	   A^2 -> H(c, e)
28.57/10.27	   A^2 -> H(c, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, k), b)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, k), c)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, k), e)
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, c), d)
28.57/10.27	   A^2 -> H(U1(e, c), k)
28.57/10.27	   A^2 -> H(U1(k, e), b)
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, e), c)
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.27	
28.57/10.27	The TRS R consists of the following rules:
28.57/10.27	
28.57/10.27	   f(x) -> U1(x, x)
28.57/10.27	   U1(e, x) -> x
28.57/10.27	   a -> c
28.57/10.27	   a -> d
28.57/10.27	   b -> c
28.57/10.27	   b -> d
28.57/10.27	   d -> k
28.57/10.27	   c -> e
28.57/10.27	   c -> k
28.57/10.27	
28.57/10.27	Q is empty.
28.57/10.27	We have to consider all minimal (P,Q,R)-chains.
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2149) TransformationProof (EQUIVALENT)
28.57/10.27	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.27	
28.57/10.27	   (A^2 -> H(U1(k, e), U1(e, e)),A^2 -> H(U1(k, e), U1(e, e)))
28.57/10.27	   (A^2 -> H(U1(k, e), U1(k, e)),A^2 -> H(U1(k, e), U1(k, e)))
28.57/10.27	
28.57/10.27	
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2150)
28.57/10.27	Obligation:
28.57/10.27	Q DP problem:
28.57/10.27	The TRS P consists of the following rules:
28.57/10.27	
28.57/10.27	   H(x, x) -> G(x, x, f(k))
28.57/10.27	   G(d, x, x) -> A^2
28.57/10.27	   A^2 -> H(f(c), f(c))
28.57/10.27	   A^2 -> H(f(d), f(d))
28.57/10.27	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.27	   A^2 -> H(f(e), f(e))
28.57/10.27	   A^2 -> H(f(k), f(k))
28.57/10.27	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.27	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.27	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.27	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.27	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.27	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.27	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(c, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, c), b)
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, c), c)
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, e), b)
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(c, e), c)
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(c, e), e)
28.57/10.27	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, k), b)
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(c, k), c)
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(c, k), e)
28.57/10.27	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, c), d)
28.57/10.27	   A^2 -> H(e, U1(e, b))
28.57/10.27	   A^2 -> H(e, U1(c, d))
28.57/10.27	   A^2 -> H(e, U1(d, c))
28.57/10.27	   A^2 -> H(e, U1(b, e))
28.57/10.27	   A^2 -> H(e, U1(b, k))
28.57/10.27	   A^2 -> H(e, U1(e, c))
28.57/10.27	   A^2 -> H(e, U1(c, e))
28.57/10.27	   A^2 -> H(e, U1(c, k))
28.57/10.27	   A^2 -> H(e, U1(e, e))
28.57/10.27	   A^2 -> H(e, U1(d, k))
28.57/10.27	   A^2 -> H(U1(e, e), b)
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, e), c)
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.27	   A^2 -> H(f(e), d)
28.57/10.27	   A^2 -> H(f(e), k)
28.57/10.27	   A^2 -> H(U1(k, k), b)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, k), c)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.27	   A^2 -> H(f(k), d)
28.57/10.27	   A^2 -> H(f(k), k)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, d), b)
28.57/10.27	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, d), c)
28.57/10.27	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, k), b)
28.57/10.27	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, k), c)
28.57/10.27	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, k), e)
28.57/10.27	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, d), d)
28.57/10.27	   A^2 -> H(U1(d, d), k)
28.57/10.27	   A^2 -> H(U1(e, c), c)
28.57/10.27	   A^2 -> H(U1(c, c), e)
28.57/10.27	   A^2 -> H(U1(c, c), k)
28.57/10.27	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.27	   A^2 -> H(U1(e, e), e)
28.57/10.27	   A^2 -> H(d, U1(e, b))
28.57/10.27	   A^2 -> H(d, U1(k, b))
28.57/10.27	   A^2 -> H(d, U1(c, d))
28.57/10.27	   A^2 -> H(d, U1(d, c))
28.57/10.27	   A^2 -> H(d, U1(b, e))
28.57/10.27	   A^2 -> H(d, U1(b, k))
28.57/10.27	   A^2 -> H(d, U1(e, c))
28.57/10.27	   A^2 -> H(d, U1(k, c))
28.57/10.27	   A^2 -> H(d, U1(c, e))
28.57/10.27	   A^2 -> H(d, U1(c, k))
28.57/10.27	   A^2 -> H(d, U1(e, e))
28.57/10.27	   A^2 -> H(d, U1(k, k))
28.57/10.27	   A^2 -> H(d, U1(k, d))
28.57/10.27	   A^2 -> H(d, U1(d, k))
28.57/10.27	   A^2 -> H(a, b)
28.57/10.27	   A^2 -> H(a, U1(e, d))
28.57/10.27	   A^2 -> H(a, U1(d, e))
28.57/10.27	   A^2 -> H(a, c)
28.57/10.27	   A^2 -> H(a, U1(e, k))
28.57/10.27	   A^2 -> H(a, U1(k, e))
28.57/10.27	   A^2 -> H(a, e)
28.57/10.27	   A^2 -> H(a, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, d), b)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, d), c)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, d), e)
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, a), d)
28.57/10.27	   A^2 -> H(U1(e, a), k)
28.57/10.27	   A^2 -> H(U1(k, a), d)
28.57/10.27	   A^2 -> H(U1(c, d), d)
28.57/10.27	   A^2 -> H(U1(c, d), k)
28.57/10.27	   A^2 -> H(U1(d, e), b)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, e), c)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, e), e)
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, c), d)
28.57/10.27	   A^2 -> H(U1(d, c), k)
28.57/10.27	   A^2 -> H(U1(a, e), d)
28.57/10.27	   A^2 -> H(U1(a, e), k)
28.57/10.27	   A^2 -> H(U1(a, k), d)
28.57/10.27	   A^2 -> H(U1(a, k), k)
28.57/10.27	   A^2 -> H(k, U1(e, b))
28.57/10.27	   A^2 -> H(k, U1(c, d))
28.57/10.27	   A^2 -> H(k, U1(d, c))
28.57/10.27	   A^2 -> H(k, U1(b, e))
28.57/10.27	   A^2 -> H(k, U1(b, k))
28.57/10.27	   A^2 -> H(k, U1(e, c))
28.57/10.27	   A^2 -> H(k, U1(c, e))
28.57/10.27	   A^2 -> H(k, U1(c, k))
28.57/10.27	   A^2 -> H(k, U1(e, e))
28.57/10.27	   A^2 -> H(k, U1(d, k))
28.57/10.27	   A^2 -> H(c, b)
28.57/10.27	   A^2 -> H(c, U1(e, d))
28.57/10.27	   A^2 -> H(c, U1(d, e))
28.57/10.27	   A^2 -> H(c, c)
28.57/10.27	   A^2 -> H(c, U1(e, k))
28.57/10.27	   A^2 -> H(c, U1(k, e))
28.57/10.27	   A^2 -> H(c, e)
28.57/10.27	   A^2 -> H(c, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, k), b)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, k), c)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, k), e)
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, c), d)
28.57/10.27	   A^2 -> H(U1(e, c), k)
28.57/10.27	   A^2 -> H(U1(k, e), b)
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, e), c)
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.27	
28.57/10.27	The TRS R consists of the following rules:
28.57/10.27	
28.57/10.27	   f(x) -> U1(x, x)
28.57/10.27	   U1(e, x) -> x
28.57/10.27	   a -> c
28.57/10.27	   a -> d
28.57/10.27	   b -> c
28.57/10.27	   b -> d
28.57/10.27	   d -> k
28.57/10.27	   c -> e
28.57/10.27	   c -> k
28.57/10.27	
28.57/10.27	Q is empty.
28.57/10.27	We have to consider all minimal (P,Q,R)-chains.
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2151) TransformationProof (EQUIVALENT)
28.57/10.27	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.27	
28.57/10.27	   (A^2 -> H(U1(k, e), U1(e, k)),A^2 -> H(U1(k, e), U1(e, k)))
28.57/10.27	   (A^2 -> H(U1(k, e), U1(k, k)),A^2 -> H(U1(k, e), U1(k, k)))
28.57/10.27	
28.57/10.27	
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2152)
28.57/10.27	Obligation:
28.57/10.27	Q DP problem:
28.57/10.27	The TRS P consists of the following rules:
28.57/10.27	
28.57/10.27	   H(x, x) -> G(x, x, f(k))
28.57/10.27	   G(d, x, x) -> A^2
28.57/10.27	   A^2 -> H(f(c), f(c))
28.57/10.27	   A^2 -> H(f(d), f(d))
28.57/10.27	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.27	   A^2 -> H(f(e), f(e))
28.57/10.27	   A^2 -> H(f(k), f(k))
28.57/10.27	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.27	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.27	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.27	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.27	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.27	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.27	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, c), b)
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, c), c)
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, e), b)
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(c, e), c)
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(c, e), e)
28.57/10.27	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, k), b)
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(c, k), c)
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(c, k), e)
28.57/10.27	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, c), d)
28.57/10.27	   A^2 -> H(e, U1(e, b))
28.57/10.27	   A^2 -> H(e, U1(c, d))
28.57/10.27	   A^2 -> H(e, U1(d, c))
28.57/10.27	   A^2 -> H(e, U1(b, e))
28.57/10.27	   A^2 -> H(e, U1(b, k))
28.57/10.27	   A^2 -> H(e, U1(e, c))
28.57/10.27	   A^2 -> H(e, U1(c, e))
28.57/10.27	   A^2 -> H(e, U1(c, k))
28.57/10.27	   A^2 -> H(e, U1(e, e))
28.57/10.27	   A^2 -> H(e, U1(d, k))
28.57/10.27	   A^2 -> H(U1(e, e), b)
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, e), c)
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.27	   A^2 -> H(f(e), d)
28.57/10.27	   A^2 -> H(f(e), k)
28.57/10.27	   A^2 -> H(U1(k, k), b)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, k), c)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.27	   A^2 -> H(f(k), d)
28.57/10.27	   A^2 -> H(f(k), k)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, d), b)
28.57/10.27	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, d), c)
28.57/10.27	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, k), b)
28.57/10.27	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, k), c)
28.57/10.27	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, k), e)
28.57/10.27	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, d), d)
28.57/10.27	   A^2 -> H(U1(d, d), k)
28.57/10.27	   A^2 -> H(U1(e, c), c)
28.57/10.27	   A^2 -> H(U1(c, c), e)
28.57/10.27	   A^2 -> H(U1(c, c), k)
28.57/10.27	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.27	   A^2 -> H(U1(e, e), e)
28.57/10.27	   A^2 -> H(d, U1(e, b))
28.57/10.27	   A^2 -> H(d, U1(k, b))
28.57/10.27	   A^2 -> H(d, U1(c, d))
28.57/10.27	   A^2 -> H(d, U1(d, c))
28.57/10.27	   A^2 -> H(d, U1(b, e))
28.57/10.27	   A^2 -> H(d, U1(b, k))
28.57/10.27	   A^2 -> H(d, U1(e, c))
28.57/10.27	   A^2 -> H(d, U1(k, c))
28.57/10.27	   A^2 -> H(d, U1(c, e))
28.57/10.27	   A^2 -> H(d, U1(c, k))
28.57/10.27	   A^2 -> H(d, U1(e, e))
28.57/10.27	   A^2 -> H(d, U1(k, k))
28.57/10.27	   A^2 -> H(d, U1(k, d))
28.57/10.27	   A^2 -> H(d, U1(d, k))
28.57/10.27	   A^2 -> H(a, b)
28.57/10.27	   A^2 -> H(a, U1(e, d))
28.57/10.27	   A^2 -> H(a, U1(d, e))
28.57/10.27	   A^2 -> H(a, c)
28.57/10.27	   A^2 -> H(a, U1(e, k))
28.57/10.27	   A^2 -> H(a, U1(k, e))
28.57/10.27	   A^2 -> H(a, e)
28.57/10.27	   A^2 -> H(a, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, d), b)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, d), c)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, d), e)
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, a), d)
28.57/10.27	   A^2 -> H(U1(e, a), k)
28.57/10.27	   A^2 -> H(U1(k, a), d)
28.57/10.27	   A^2 -> H(U1(c, d), d)
28.57/10.27	   A^2 -> H(U1(c, d), k)
28.57/10.27	   A^2 -> H(U1(d, e), b)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, e), c)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, e), e)
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, c), d)
28.57/10.27	   A^2 -> H(U1(d, c), k)
28.57/10.27	   A^2 -> H(U1(a, e), d)
28.57/10.27	   A^2 -> H(U1(a, e), k)
28.57/10.27	   A^2 -> H(U1(a, k), d)
28.57/10.27	   A^2 -> H(U1(a, k), k)
28.57/10.27	   A^2 -> H(k, U1(e, b))
28.57/10.27	   A^2 -> H(k, U1(c, d))
28.57/10.27	   A^2 -> H(k, U1(d, c))
28.57/10.27	   A^2 -> H(k, U1(b, e))
28.57/10.27	   A^2 -> H(k, U1(b, k))
28.57/10.27	   A^2 -> H(k, U1(e, c))
28.57/10.27	   A^2 -> H(k, U1(c, e))
28.57/10.27	   A^2 -> H(k, U1(c, k))
28.57/10.27	   A^2 -> H(k, U1(e, e))
28.57/10.27	   A^2 -> H(k, U1(d, k))
28.57/10.27	   A^2 -> H(c, b)
28.57/10.27	   A^2 -> H(c, U1(e, d))
28.57/10.27	   A^2 -> H(c, U1(d, e))
28.57/10.27	   A^2 -> H(c, c)
28.57/10.27	   A^2 -> H(c, U1(e, k))
28.57/10.27	   A^2 -> H(c, U1(k, e))
28.57/10.27	   A^2 -> H(c, e)
28.57/10.27	   A^2 -> H(c, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, k), b)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, k), c)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, k), e)
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, c), d)
28.57/10.27	   A^2 -> H(U1(e, c), k)
28.57/10.27	   A^2 -> H(U1(k, e), b)
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, e), c)
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, k))
28.57/10.27	
28.57/10.27	The TRS R consists of the following rules:
28.57/10.27	
28.57/10.27	   f(x) -> U1(x, x)
28.57/10.27	   U1(e, x) -> x
28.57/10.27	   a -> c
28.57/10.27	   a -> d
28.57/10.27	   b -> c
28.57/10.27	   b -> d
28.57/10.27	   d -> k
28.57/10.27	   c -> e
28.57/10.27	   c -> k
28.57/10.27	
28.57/10.27	Q is empty.
28.57/10.27	We have to consider all minimal (P,Q,R)-chains.
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2153) DependencyGraphProof (EQUIVALENT)
28.57/10.27	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2154)
28.57/10.27	Obligation:
28.57/10.27	Q DP problem:
28.57/10.27	The TRS P consists of the following rules:
28.57/10.27	
28.57/10.27	   G(d, x, x) -> A^2
28.57/10.27	   A^2 -> H(f(c), f(c))
28.57/10.27	   H(x, x) -> G(x, x, f(k))
28.57/10.27	   A^2 -> H(f(d), f(d))
28.57/10.27	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.27	   A^2 -> H(f(e), f(e))
28.57/10.27	   A^2 -> H(f(k), f(k))
28.57/10.27	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.27	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.27	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.27	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.27	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.27	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.27	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, c), b)
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, c), c)
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, e), b)
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(c, e), c)
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(c, e), e)
28.57/10.27	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, k), b)
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(c, k), c)
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(c, k), e)
28.57/10.27	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, c), d)
28.57/10.27	   A^2 -> H(e, U1(e, b))
28.57/10.27	   A^2 -> H(e, U1(c, d))
28.57/10.27	   A^2 -> H(e, U1(d, c))
28.57/10.27	   A^2 -> H(e, U1(b, e))
28.57/10.27	   A^2 -> H(e, U1(b, k))
28.57/10.27	   A^2 -> H(e, U1(e, c))
28.57/10.27	   A^2 -> H(e, U1(c, e))
28.57/10.27	   A^2 -> H(e, U1(c, k))
28.57/10.27	   A^2 -> H(e, U1(e, e))
28.57/10.27	   A^2 -> H(e, U1(d, k))
28.57/10.27	   A^2 -> H(U1(e, e), b)
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, e), c)
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.27	   A^2 -> H(f(e), d)
28.57/10.27	   A^2 -> H(f(e), k)
28.57/10.27	   A^2 -> H(U1(k, k), b)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, k), c)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.27	   A^2 -> H(f(k), d)
28.57/10.27	   A^2 -> H(f(k), k)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, d), b)
28.57/10.27	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, d), c)
28.57/10.27	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, k), b)
28.57/10.27	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, k), c)
28.57/10.27	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, k), e)
28.57/10.27	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, d), d)
28.57/10.27	   A^2 -> H(U1(d, d), k)
28.57/10.27	   A^2 -> H(U1(e, c), c)
28.57/10.27	   A^2 -> H(U1(c, c), e)
28.57/10.27	   A^2 -> H(U1(c, c), k)
28.57/10.27	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.27	   A^2 -> H(U1(e, e), e)
28.57/10.27	   A^2 -> H(d, U1(e, b))
28.57/10.27	   A^2 -> H(d, U1(k, b))
28.57/10.27	   A^2 -> H(d, U1(c, d))
28.57/10.27	   A^2 -> H(d, U1(d, c))
28.57/10.27	   A^2 -> H(d, U1(b, e))
28.57/10.27	   A^2 -> H(d, U1(b, k))
28.57/10.27	   A^2 -> H(d, U1(e, c))
28.57/10.27	   A^2 -> H(d, U1(k, c))
28.57/10.27	   A^2 -> H(d, U1(c, e))
28.57/10.27	   A^2 -> H(d, U1(c, k))
28.57/10.27	   A^2 -> H(d, U1(e, e))
28.57/10.27	   A^2 -> H(d, U1(k, k))
28.57/10.27	   A^2 -> H(d, U1(k, d))
28.57/10.27	   A^2 -> H(d, U1(d, k))
28.57/10.27	   A^2 -> H(a, b)
28.57/10.27	   A^2 -> H(a, U1(e, d))
28.57/10.27	   A^2 -> H(a, U1(d, e))
28.57/10.27	   A^2 -> H(a, c)
28.57/10.27	   A^2 -> H(a, U1(e, k))
28.57/10.27	   A^2 -> H(a, U1(k, e))
28.57/10.27	   A^2 -> H(a, e)
28.57/10.27	   A^2 -> H(a, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, d), b)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, d), c)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, d), e)
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, a), d)
28.57/10.27	   A^2 -> H(U1(e, a), k)
28.57/10.27	   A^2 -> H(U1(k, a), d)
28.57/10.27	   A^2 -> H(U1(c, d), d)
28.57/10.27	   A^2 -> H(U1(c, d), k)
28.57/10.27	   A^2 -> H(U1(d, e), b)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, e), c)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, e), e)
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, c), d)
28.57/10.27	   A^2 -> H(U1(d, c), k)
28.57/10.27	   A^2 -> H(U1(a, e), d)
28.57/10.27	   A^2 -> H(U1(a, e), k)
28.57/10.27	   A^2 -> H(U1(a, k), d)
28.57/10.27	   A^2 -> H(U1(a, k), k)
28.57/10.27	   A^2 -> H(k, U1(e, b))
28.57/10.27	   A^2 -> H(k, U1(c, d))
28.57/10.27	   A^2 -> H(k, U1(d, c))
28.57/10.27	   A^2 -> H(k, U1(b, e))
28.57/10.27	   A^2 -> H(k, U1(b, k))
28.57/10.27	   A^2 -> H(k, U1(e, c))
28.57/10.27	   A^2 -> H(k, U1(c, e))
28.57/10.27	   A^2 -> H(k, U1(c, k))
28.57/10.27	   A^2 -> H(k, U1(e, e))
28.57/10.27	   A^2 -> H(k, U1(d, k))
28.57/10.27	   A^2 -> H(c, b)
28.57/10.27	   A^2 -> H(c, U1(e, d))
28.57/10.27	   A^2 -> H(c, U1(d, e))
28.57/10.27	   A^2 -> H(c, c)
28.57/10.27	   A^2 -> H(c, U1(e, k))
28.57/10.27	   A^2 -> H(c, U1(k, e))
28.57/10.27	   A^2 -> H(c, e)
28.57/10.27	   A^2 -> H(c, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, k), b)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, k), c)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, k), e)
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, c), d)
28.57/10.27	   A^2 -> H(U1(e, c), k)
28.57/10.27	   A^2 -> H(U1(k, e), b)
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, e), c)
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.27	
28.57/10.27	The TRS R consists of the following rules:
28.57/10.27	
28.57/10.27	   f(x) -> U1(x, x)
28.57/10.27	   U1(e, x) -> x
28.57/10.27	   a -> c
28.57/10.27	   a -> d
28.57/10.27	   b -> c
28.57/10.27	   b -> d
28.57/10.27	   d -> k
28.57/10.27	   c -> e
28.57/10.27	   c -> k
28.57/10.27	
28.57/10.27	Q is empty.
28.57/10.27	We have to consider all minimal (P,Q,R)-chains.
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2155) TransformationProof (EQUIVALENT)
28.57/10.27	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.27	
28.57/10.27	   (A^2 -> H(U1(k, e), e),A^2 -> H(U1(k, e), e))
28.57/10.27	
28.57/10.27	
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2156)
28.57/10.27	Obligation:
28.57/10.27	Q DP problem:
28.57/10.27	The TRS P consists of the following rules:
28.57/10.27	
28.57/10.27	   G(d, x, x) -> A^2
28.57/10.27	   A^2 -> H(f(c), f(c))
28.57/10.27	   H(x, x) -> G(x, x, f(k))
28.57/10.27	   A^2 -> H(f(d), f(d))
28.57/10.27	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.27	   A^2 -> H(f(e), f(e))
28.57/10.27	   A^2 -> H(f(k), f(k))
28.57/10.27	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.27	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.27	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.27	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.27	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.27	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.27	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, c), b)
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, c), c)
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, e), b)
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(c, e), c)
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(c, e), e)
28.57/10.27	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, k), b)
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(c, k), c)
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(c, k), e)
28.57/10.27	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(c, c), d)
28.57/10.27	   A^2 -> H(e, U1(e, b))
28.57/10.27	   A^2 -> H(e, U1(c, d))
28.57/10.27	   A^2 -> H(e, U1(d, c))
28.57/10.27	   A^2 -> H(e, U1(b, e))
28.57/10.27	   A^2 -> H(e, U1(b, k))
28.57/10.27	   A^2 -> H(e, U1(e, c))
28.57/10.27	   A^2 -> H(e, U1(c, e))
28.57/10.27	   A^2 -> H(e, U1(c, k))
28.57/10.27	   A^2 -> H(e, U1(e, e))
28.57/10.27	   A^2 -> H(e, U1(d, k))
28.57/10.27	   A^2 -> H(U1(e, e), b)
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, e), c)
28.57/10.27	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.27	   A^2 -> H(f(e), d)
28.57/10.27	   A^2 -> H(f(e), k)
28.57/10.27	   A^2 -> H(U1(k, k), b)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, k), c)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.27	   A^2 -> H(f(k), d)
28.57/10.27	   A^2 -> H(f(k), k)
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.27	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.27	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.27	   A^2 -> H(U1(k, d), b)
28.57/10.27	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, d), c)
28.57/10.27	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, k), b)
28.57/10.27	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, k), c)
28.57/10.27	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, k), e)
28.57/10.27	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, d), d)
28.57/10.27	   A^2 -> H(U1(d, d), k)
28.57/10.27	   A^2 -> H(U1(e, c), c)
28.57/10.27	   A^2 -> H(U1(c, c), e)
28.57/10.27	   A^2 -> H(U1(c, c), k)
28.57/10.27	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.27	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.27	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.27	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.27	   A^2 -> H(U1(e, e), e)
28.57/10.27	   A^2 -> H(d, U1(e, b))
28.57/10.27	   A^2 -> H(d, U1(k, b))
28.57/10.27	   A^2 -> H(d, U1(c, d))
28.57/10.27	   A^2 -> H(d, U1(d, c))
28.57/10.27	   A^2 -> H(d, U1(b, e))
28.57/10.27	   A^2 -> H(d, U1(b, k))
28.57/10.27	   A^2 -> H(d, U1(e, c))
28.57/10.27	   A^2 -> H(d, U1(k, c))
28.57/10.27	   A^2 -> H(d, U1(c, e))
28.57/10.27	   A^2 -> H(d, U1(c, k))
28.57/10.27	   A^2 -> H(d, U1(e, e))
28.57/10.27	   A^2 -> H(d, U1(k, k))
28.57/10.27	   A^2 -> H(d, U1(k, d))
28.57/10.27	   A^2 -> H(d, U1(d, k))
28.57/10.27	   A^2 -> H(a, b)
28.57/10.27	   A^2 -> H(a, U1(e, d))
28.57/10.27	   A^2 -> H(a, U1(d, e))
28.57/10.27	   A^2 -> H(a, c)
28.57/10.27	   A^2 -> H(a, U1(e, k))
28.57/10.27	   A^2 -> H(a, U1(k, e))
28.57/10.27	   A^2 -> H(a, e)
28.57/10.27	   A^2 -> H(a, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, d), b)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, d), c)
28.57/10.27	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, d), e)
28.57/10.27	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, a), d)
28.57/10.27	   A^2 -> H(U1(e, a), k)
28.57/10.27	   A^2 -> H(U1(k, a), d)
28.57/10.27	   A^2 -> H(U1(c, d), d)
28.57/10.27	   A^2 -> H(U1(c, d), k)
28.57/10.27	   A^2 -> H(U1(d, e), b)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(d, e), c)
28.57/10.27	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(d, e), e)
28.57/10.27	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.27	   A^2 -> H(U1(d, c), d)
28.57/10.27	   A^2 -> H(U1(d, c), k)
28.57/10.27	   A^2 -> H(U1(a, e), d)
28.57/10.27	   A^2 -> H(U1(a, e), k)
28.57/10.27	   A^2 -> H(U1(a, k), d)
28.57/10.27	   A^2 -> H(U1(a, k), k)
28.57/10.27	   A^2 -> H(k, U1(e, b))
28.57/10.27	   A^2 -> H(k, U1(c, d))
28.57/10.27	   A^2 -> H(k, U1(d, c))
28.57/10.27	   A^2 -> H(k, U1(b, e))
28.57/10.27	   A^2 -> H(k, U1(b, k))
28.57/10.27	   A^2 -> H(k, U1(e, c))
28.57/10.27	   A^2 -> H(k, U1(c, e))
28.57/10.27	   A^2 -> H(k, U1(c, k))
28.57/10.27	   A^2 -> H(k, U1(e, e))
28.57/10.27	   A^2 -> H(k, U1(d, k))
28.57/10.27	   A^2 -> H(c, b)
28.57/10.27	   A^2 -> H(c, U1(e, d))
28.57/10.27	   A^2 -> H(c, U1(d, e))
28.57/10.27	   A^2 -> H(c, c)
28.57/10.27	   A^2 -> H(c, U1(e, k))
28.57/10.27	   A^2 -> H(c, U1(k, e))
28.57/10.27	   A^2 -> H(c, e)
28.57/10.27	   A^2 -> H(c, U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, k), b)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.27	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.27	   A^2 -> H(U1(e, k), c)
28.57/10.27	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.27	   A^2 -> H(U1(e, k), e)
28.57/10.27	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.27	   A^2 -> H(U1(e, c), d)
28.57/10.27	   A^2 -> H(U1(e, c), k)
28.57/10.27	   A^2 -> H(U1(k, e), b)
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.27	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.27	   A^2 -> H(U1(k, e), c)
28.57/10.27	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.27	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.27	   A^2 -> H(U1(k, e), e)
28.57/10.27	
28.57/10.27	The TRS R consists of the following rules:
28.57/10.27	
28.57/10.27	   f(x) -> U1(x, x)
28.57/10.27	   U1(e, x) -> x
28.57/10.27	   a -> c
28.57/10.27	   a -> d
28.57/10.27	   b -> c
28.57/10.27	   b -> d
28.57/10.27	   d -> k
28.57/10.27	   c -> e
28.57/10.27	   c -> k
28.57/10.27	
28.57/10.27	Q is empty.
28.57/10.27	We have to consider all minimal (P,Q,R)-chains.
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2157) DependencyGraphProof (EQUIVALENT)
28.57/10.27	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.27	----------------------------------------
28.57/10.27	
28.57/10.27	(2158)
28.57/10.27	Obligation:
28.57/10.27	Q DP problem:
28.57/10.27	The TRS P consists of the following rules:
28.57/10.27	
28.57/10.27	   A^2 -> H(f(c), f(c))
28.57/10.27	   H(x, x) -> G(x, x, f(k))
28.57/10.27	   G(d, x, x) -> A^2
28.57/10.27	   A^2 -> H(f(d), f(d))
28.57/10.28	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.28	   A^2 -> H(f(e), f(e))
28.57/10.28	   A^2 -> H(f(k), f(k))
28.57/10.28	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.28	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.28	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.28	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, e), U1(k, d))
28.57/10.28	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, c), b)
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, c), c)
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, e), b)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, e), c)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, e), e)
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, k), b)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, k), c)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, k), e)
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, c), d)
28.57/10.28	   A^2 -> H(e, U1(e, b))
28.57/10.28	   A^2 -> H(e, U1(c, d))
28.57/10.28	   A^2 -> H(e, U1(d, c))
28.57/10.28	   A^2 -> H(e, U1(b, e))
28.57/10.28	   A^2 -> H(e, U1(b, k))
28.57/10.28	   A^2 -> H(e, U1(e, c))
28.57/10.28	   A^2 -> H(e, U1(c, e))
28.57/10.28	   A^2 -> H(e, U1(c, k))
28.57/10.28	   A^2 -> H(e, U1(e, e))
28.57/10.28	   A^2 -> H(e, U1(d, k))
28.57/10.28	   A^2 -> H(U1(e, e), b)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, e), c)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.28	   A^2 -> H(f(e), d)
28.57/10.28	   A^2 -> H(f(e), k)
28.57/10.28	   A^2 -> H(U1(k, k), b)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, k), c)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.28	   A^2 -> H(f(k), d)
28.57/10.28	   A^2 -> H(f(k), k)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, d), b)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, d), c)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, k), b)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, k), c)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, k), e)
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, d), d)
28.57/10.28	   A^2 -> H(U1(d, d), k)
28.57/10.28	   A^2 -> H(U1(e, c), c)
28.57/10.28	   A^2 -> H(U1(c, c), e)
28.57/10.28	   A^2 -> H(U1(c, c), k)
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(e, e), e)
28.57/10.28	   A^2 -> H(d, U1(e, b))
28.57/10.28	   A^2 -> H(d, U1(k, b))
28.57/10.28	   A^2 -> H(d, U1(c, d))
28.57/10.28	   A^2 -> H(d, U1(d, c))
28.57/10.28	   A^2 -> H(d, U1(b, e))
28.57/10.28	   A^2 -> H(d, U1(b, k))
28.57/10.28	   A^2 -> H(d, U1(e, c))
28.57/10.28	   A^2 -> H(d, U1(k, c))
28.57/10.28	   A^2 -> H(d, U1(c, e))
28.57/10.28	   A^2 -> H(d, U1(c, k))
28.57/10.28	   A^2 -> H(d, U1(e, e))
28.57/10.28	   A^2 -> H(d, U1(k, k))
28.57/10.28	   A^2 -> H(d, U1(k, d))
28.57/10.28	   A^2 -> H(d, U1(d, k))
28.57/10.28	   A^2 -> H(a, b)
28.57/10.28	   A^2 -> H(a, U1(e, d))
28.57/10.28	   A^2 -> H(a, U1(d, e))
28.57/10.28	   A^2 -> H(a, c)
28.57/10.28	   A^2 -> H(a, U1(e, k))
28.57/10.28	   A^2 -> H(a, U1(k, e))
28.57/10.28	   A^2 -> H(a, e)
28.57/10.28	   A^2 -> H(a, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, d), b)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, d), c)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, d), e)
28.57/10.28	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, a), d)
28.57/10.28	   A^2 -> H(U1(e, a), k)
28.57/10.28	   A^2 -> H(U1(k, a), d)
28.57/10.28	   A^2 -> H(U1(c, d), d)
28.57/10.28	   A^2 -> H(U1(c, d), k)
28.57/10.28	   A^2 -> H(U1(d, e), b)
28.57/10.28	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, e), c)
28.57/10.28	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, e), e)
28.57/10.28	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, c), d)
28.57/10.28	   A^2 -> H(U1(d, c), k)
28.57/10.28	   A^2 -> H(U1(a, e), d)
28.57/10.28	   A^2 -> H(U1(a, e), k)
28.57/10.28	   A^2 -> H(U1(a, k), d)
28.57/10.28	   A^2 -> H(U1(a, k), k)
28.57/10.28	   A^2 -> H(k, U1(e, b))
28.57/10.28	   A^2 -> H(k, U1(c, d))
28.57/10.28	   A^2 -> H(k, U1(d, c))
28.57/10.28	   A^2 -> H(k, U1(b, e))
28.57/10.28	   A^2 -> H(k, U1(b, k))
28.57/10.28	   A^2 -> H(k, U1(e, c))
28.57/10.28	   A^2 -> H(k, U1(c, e))
28.57/10.28	   A^2 -> H(k, U1(c, k))
28.57/10.28	   A^2 -> H(k, U1(e, e))
28.57/10.28	   A^2 -> H(k, U1(d, k))
28.57/10.28	   A^2 -> H(c, b)
28.57/10.28	   A^2 -> H(c, U1(e, d))
28.57/10.28	   A^2 -> H(c, U1(d, e))
28.57/10.28	   A^2 -> H(c, c)
28.57/10.28	   A^2 -> H(c, U1(e, k))
28.57/10.28	   A^2 -> H(c, U1(k, e))
28.57/10.28	   A^2 -> H(c, e)
28.57/10.28	   A^2 -> H(c, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, k), b)
28.57/10.28	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, k), c)
28.57/10.28	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, k), e)
28.57/10.28	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, c), d)
28.57/10.28	   A^2 -> H(U1(e, c), k)
28.57/10.28	   A^2 -> H(U1(k, e), b)
28.57/10.28	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, e), c)
28.57/10.28	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.28	
28.57/10.28	The TRS R consists of the following rules:
28.57/10.28	
28.57/10.28	   f(x) -> U1(x, x)
28.57/10.28	   U1(e, x) -> x
28.57/10.28	   a -> c
28.57/10.28	   a -> d
28.57/10.28	   b -> c
28.57/10.28	   b -> d
28.57/10.28	   d -> k
28.57/10.28	   c -> e
28.57/10.28	   c -> k
28.57/10.28	
28.57/10.28	Q is empty.
28.57/10.28	We have to consider all minimal (P,Q,R)-chains.
28.57/10.28	----------------------------------------
28.57/10.28	
28.57/10.28	(2159) TransformationProof (EQUIVALENT)
28.57/10.28	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.28	
28.57/10.28	   (A^2 -> H(U1(k, e), U1(k, k)),A^2 -> H(U1(k, e), U1(k, k)))
28.57/10.28	
28.57/10.28	
28.57/10.28	----------------------------------------
28.57/10.28	
28.57/10.28	(2160)
28.57/10.28	Obligation:
28.57/10.28	Q DP problem:
28.57/10.28	The TRS P consists of the following rules:
28.57/10.28	
28.57/10.28	   A^2 -> H(f(c), f(c))
28.57/10.28	   H(x, x) -> G(x, x, f(k))
28.57/10.28	   G(d, x, x) -> A^2
28.57/10.28	   A^2 -> H(f(d), f(d))
28.57/10.28	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.28	   A^2 -> H(f(e), f(e))
28.57/10.28	   A^2 -> H(f(k), f(k))
28.57/10.28	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.28	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.28	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.28	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, c), b)
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, c), c)
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, e), b)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, e), c)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, e), e)
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, k), b)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, k), c)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, k), e)
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, c), d)
28.57/10.28	   A^2 -> H(e, U1(e, b))
28.57/10.28	   A^2 -> H(e, U1(c, d))
28.57/10.28	   A^2 -> H(e, U1(d, c))
28.57/10.28	   A^2 -> H(e, U1(b, e))
28.57/10.28	   A^2 -> H(e, U1(b, k))
28.57/10.28	   A^2 -> H(e, U1(e, c))
28.57/10.28	   A^2 -> H(e, U1(c, e))
28.57/10.28	   A^2 -> H(e, U1(c, k))
28.57/10.28	   A^2 -> H(e, U1(e, e))
28.57/10.28	   A^2 -> H(e, U1(d, k))
28.57/10.28	   A^2 -> H(U1(e, e), b)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, e), c)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.28	   A^2 -> H(f(e), d)
28.57/10.28	   A^2 -> H(f(e), k)
28.57/10.28	   A^2 -> H(U1(k, k), b)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, k), c)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.28	   A^2 -> H(f(k), d)
28.57/10.28	   A^2 -> H(f(k), k)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, d), b)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, d), c)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, k), b)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, k), c)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, k), e)
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, d), d)
28.57/10.28	   A^2 -> H(U1(d, d), k)
28.57/10.28	   A^2 -> H(U1(e, c), c)
28.57/10.28	   A^2 -> H(U1(c, c), e)
28.57/10.28	   A^2 -> H(U1(c, c), k)
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(e, e), e)
28.57/10.28	   A^2 -> H(d, U1(e, b))
28.57/10.28	   A^2 -> H(d, U1(k, b))
28.57/10.28	   A^2 -> H(d, U1(c, d))
28.57/10.28	   A^2 -> H(d, U1(d, c))
28.57/10.28	   A^2 -> H(d, U1(b, e))
28.57/10.28	   A^2 -> H(d, U1(b, k))
28.57/10.28	   A^2 -> H(d, U1(e, c))
28.57/10.28	   A^2 -> H(d, U1(k, c))
28.57/10.28	   A^2 -> H(d, U1(c, e))
28.57/10.28	   A^2 -> H(d, U1(c, k))
28.57/10.28	   A^2 -> H(d, U1(e, e))
28.57/10.28	   A^2 -> H(d, U1(k, k))
28.57/10.28	   A^2 -> H(d, U1(k, d))
28.57/10.28	   A^2 -> H(d, U1(d, k))
28.57/10.28	   A^2 -> H(a, b)
28.57/10.28	   A^2 -> H(a, U1(e, d))
28.57/10.28	   A^2 -> H(a, U1(d, e))
28.57/10.28	   A^2 -> H(a, c)
28.57/10.28	   A^2 -> H(a, U1(e, k))
28.57/10.28	   A^2 -> H(a, U1(k, e))
28.57/10.28	   A^2 -> H(a, e)
28.57/10.28	   A^2 -> H(a, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, d), b)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, d), c)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, d), e)
28.57/10.28	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, a), d)
28.57/10.28	   A^2 -> H(U1(e, a), k)
28.57/10.28	   A^2 -> H(U1(k, a), d)
28.57/10.28	   A^2 -> H(U1(c, d), d)
28.57/10.28	   A^2 -> H(U1(c, d), k)
28.57/10.28	   A^2 -> H(U1(d, e), b)
28.57/10.28	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, e), c)
28.57/10.28	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, e), e)
28.57/10.28	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, c), d)
28.57/10.28	   A^2 -> H(U1(d, c), k)
28.57/10.28	   A^2 -> H(U1(a, e), d)
28.57/10.28	   A^2 -> H(U1(a, e), k)
28.57/10.28	   A^2 -> H(U1(a, k), d)
28.57/10.28	   A^2 -> H(U1(a, k), k)
28.57/10.28	   A^2 -> H(k, U1(e, b))
28.57/10.28	   A^2 -> H(k, U1(c, d))
28.57/10.28	   A^2 -> H(k, U1(d, c))
28.57/10.28	   A^2 -> H(k, U1(b, e))
28.57/10.28	   A^2 -> H(k, U1(b, k))
28.57/10.28	   A^2 -> H(k, U1(e, c))
28.57/10.28	   A^2 -> H(k, U1(c, e))
28.57/10.28	   A^2 -> H(k, U1(c, k))
28.57/10.28	   A^2 -> H(k, U1(e, e))
28.57/10.28	   A^2 -> H(k, U1(d, k))
28.57/10.28	   A^2 -> H(c, b)
28.57/10.28	   A^2 -> H(c, U1(e, d))
28.57/10.28	   A^2 -> H(c, U1(d, e))
28.57/10.28	   A^2 -> H(c, c)
28.57/10.28	   A^2 -> H(c, U1(e, k))
28.57/10.28	   A^2 -> H(c, U1(k, e))
28.57/10.28	   A^2 -> H(c, e)
28.57/10.28	   A^2 -> H(c, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, k), b)
28.57/10.28	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, k), c)
28.57/10.28	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, k), e)
28.57/10.28	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, c), d)
28.57/10.28	   A^2 -> H(U1(e, c), k)
28.57/10.28	   A^2 -> H(U1(k, e), b)
28.57/10.28	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, e), c)
28.57/10.28	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, e), U1(k, k))
28.57/10.28	
28.57/10.28	The TRS R consists of the following rules:
28.57/10.28	
28.57/10.28	   f(x) -> U1(x, x)
28.57/10.28	   U1(e, x) -> x
28.57/10.28	   a -> c
28.57/10.28	   a -> d
28.57/10.28	   b -> c
28.57/10.28	   b -> d
28.57/10.28	   d -> k
28.57/10.28	   c -> e
28.57/10.28	   c -> k
28.57/10.28	
28.57/10.28	Q is empty.
28.57/10.28	We have to consider all minimal (P,Q,R)-chains.
28.57/10.28	----------------------------------------
28.57/10.28	
28.57/10.28	(2161) DependencyGraphProof (EQUIVALENT)
28.57/10.28	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.28	----------------------------------------
28.57/10.28	
28.57/10.28	(2162)
28.57/10.28	Obligation:
28.57/10.28	Q DP problem:
28.57/10.28	The TRS P consists of the following rules:
28.57/10.28	
28.57/10.28	   H(x, x) -> G(x, x, f(k))
28.57/10.28	   G(d, x, x) -> A^2
28.57/10.28	   A^2 -> H(f(c), f(c))
28.57/10.28	   A^2 -> H(f(d), f(d))
28.57/10.28	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.28	   A^2 -> H(f(e), f(e))
28.57/10.28	   A^2 -> H(f(k), f(k))
28.57/10.28	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.28	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.28	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.28	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, e), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, c), b)
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, c), c)
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, e), b)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, e), c)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, e), e)
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, k), b)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, k), c)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, k), e)
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, c), d)
28.57/10.28	   A^2 -> H(e, U1(e, b))
28.57/10.28	   A^2 -> H(e, U1(c, d))
28.57/10.28	   A^2 -> H(e, U1(d, c))
28.57/10.28	   A^2 -> H(e, U1(b, e))
28.57/10.28	   A^2 -> H(e, U1(b, k))
28.57/10.28	   A^2 -> H(e, U1(e, c))
28.57/10.28	   A^2 -> H(e, U1(c, e))
28.57/10.28	   A^2 -> H(e, U1(c, k))
28.57/10.28	   A^2 -> H(e, U1(e, e))
28.57/10.28	   A^2 -> H(e, U1(d, k))
28.57/10.28	   A^2 -> H(U1(e, e), b)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, e), c)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.28	   A^2 -> H(f(e), d)
28.57/10.28	   A^2 -> H(f(e), k)
28.57/10.28	   A^2 -> H(U1(k, k), b)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, k), c)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.28	   A^2 -> H(f(k), d)
28.57/10.28	   A^2 -> H(f(k), k)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, d), b)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, d), c)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, k), b)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, k), c)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, k), e)
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, d), d)
28.57/10.28	   A^2 -> H(U1(d, d), k)
28.57/10.28	   A^2 -> H(U1(e, c), c)
28.57/10.28	   A^2 -> H(U1(c, c), e)
28.57/10.28	   A^2 -> H(U1(c, c), k)
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(e, e), e)
28.57/10.28	   A^2 -> H(d, U1(e, b))
28.57/10.28	   A^2 -> H(d, U1(k, b))
28.57/10.28	   A^2 -> H(d, U1(c, d))
28.57/10.28	   A^2 -> H(d, U1(d, c))
28.57/10.28	   A^2 -> H(d, U1(b, e))
28.57/10.28	   A^2 -> H(d, U1(b, k))
28.57/10.28	   A^2 -> H(d, U1(e, c))
28.57/10.28	   A^2 -> H(d, U1(k, c))
28.57/10.28	   A^2 -> H(d, U1(c, e))
28.57/10.28	   A^2 -> H(d, U1(c, k))
28.57/10.28	   A^2 -> H(d, U1(e, e))
28.57/10.28	   A^2 -> H(d, U1(k, k))
28.57/10.28	   A^2 -> H(d, U1(k, d))
28.57/10.28	   A^2 -> H(d, U1(d, k))
28.57/10.28	   A^2 -> H(a, b)
28.57/10.28	   A^2 -> H(a, U1(e, d))
28.57/10.28	   A^2 -> H(a, U1(d, e))
28.57/10.28	   A^2 -> H(a, c)
28.57/10.28	   A^2 -> H(a, U1(e, k))
28.57/10.28	   A^2 -> H(a, U1(k, e))
28.57/10.28	   A^2 -> H(a, e)
28.57/10.28	   A^2 -> H(a, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, d), b)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, d), c)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, d), e)
28.57/10.28	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, a), d)
28.57/10.28	   A^2 -> H(U1(e, a), k)
28.57/10.28	   A^2 -> H(U1(k, a), d)
28.57/10.28	   A^2 -> H(U1(c, d), d)
28.57/10.28	   A^2 -> H(U1(c, d), k)
28.57/10.28	   A^2 -> H(U1(d, e), b)
28.57/10.28	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, e), c)
28.57/10.28	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, e), e)
28.57/10.28	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, c), d)
28.57/10.28	   A^2 -> H(U1(d, c), k)
28.57/10.28	   A^2 -> H(U1(a, e), d)
28.57/10.28	   A^2 -> H(U1(a, e), k)
28.57/10.28	   A^2 -> H(U1(a, k), d)
28.57/10.28	   A^2 -> H(U1(a, k), k)
28.57/10.28	   A^2 -> H(k, U1(e, b))
28.57/10.28	   A^2 -> H(k, U1(c, d))
28.57/10.28	   A^2 -> H(k, U1(d, c))
28.57/10.28	   A^2 -> H(k, U1(b, e))
28.57/10.28	   A^2 -> H(k, U1(b, k))
28.57/10.28	   A^2 -> H(k, U1(e, c))
28.57/10.28	   A^2 -> H(k, U1(c, e))
28.57/10.28	   A^2 -> H(k, U1(c, k))
28.57/10.28	   A^2 -> H(k, U1(e, e))
28.57/10.28	   A^2 -> H(k, U1(d, k))
28.57/10.28	   A^2 -> H(c, b)
28.57/10.28	   A^2 -> H(c, U1(e, d))
28.57/10.28	   A^2 -> H(c, U1(d, e))
28.57/10.28	   A^2 -> H(c, c)
28.57/10.28	   A^2 -> H(c, U1(e, k))
28.57/10.28	   A^2 -> H(c, U1(k, e))
28.57/10.28	   A^2 -> H(c, e)
28.57/10.28	   A^2 -> H(c, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, k), b)
28.57/10.28	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, k), c)
28.57/10.28	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, k), e)
28.57/10.28	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, c), d)
28.57/10.28	   A^2 -> H(U1(e, c), k)
28.57/10.28	   A^2 -> H(U1(k, e), b)
28.57/10.28	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, e), c)
28.57/10.28	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.28	
28.57/10.28	The TRS R consists of the following rules:
28.57/10.28	
28.57/10.28	   f(x) -> U1(x, x)
28.57/10.28	   U1(e, x) -> x
28.57/10.28	   a -> c
28.57/10.28	   a -> d
28.57/10.28	   b -> c
28.57/10.28	   b -> d
28.57/10.28	   d -> k
28.57/10.28	   c -> e
28.57/10.28	   c -> k
28.57/10.28	
28.57/10.28	Q is empty.
28.57/10.28	We have to consider all minimal (P,Q,R)-chains.
28.57/10.28	----------------------------------------
28.57/10.28	
28.57/10.28	(2163) TransformationProof (EQUIVALENT)
28.57/10.28	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.28	
28.57/10.28	   (A^2 -> H(U1(k, e), U1(k, k)),A^2 -> H(U1(k, e), U1(k, k)))
28.57/10.28	
28.57/10.28	
28.57/10.28	----------------------------------------
28.57/10.28	
28.57/10.28	(2164)
28.57/10.28	Obligation:
28.57/10.28	Q DP problem:
28.57/10.28	The TRS P consists of the following rules:
28.57/10.28	
28.57/10.28	   H(x, x) -> G(x, x, f(k))
28.57/10.28	   G(d, x, x) -> A^2
28.57/10.28	   A^2 -> H(f(c), f(c))
28.57/10.28	   A^2 -> H(f(d), f(d))
28.57/10.28	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.28	   A^2 -> H(f(e), f(e))
28.57/10.28	   A^2 -> H(f(k), f(k))
28.57/10.28	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.28	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.28	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.28	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, c), b)
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, c), c)
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, e), b)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, e), c)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, e), e)
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, k), b)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, k), c)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, k), e)
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, c), d)
28.57/10.28	   A^2 -> H(e, U1(e, b))
28.57/10.28	   A^2 -> H(e, U1(c, d))
28.57/10.28	   A^2 -> H(e, U1(d, c))
28.57/10.28	   A^2 -> H(e, U1(b, e))
28.57/10.28	   A^2 -> H(e, U1(b, k))
28.57/10.28	   A^2 -> H(e, U1(e, c))
28.57/10.28	   A^2 -> H(e, U1(c, e))
28.57/10.28	   A^2 -> H(e, U1(c, k))
28.57/10.28	   A^2 -> H(e, U1(e, e))
28.57/10.28	   A^2 -> H(e, U1(d, k))
28.57/10.28	   A^2 -> H(U1(e, e), b)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, e), c)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.28	   A^2 -> H(f(e), d)
28.57/10.28	   A^2 -> H(f(e), k)
28.57/10.28	   A^2 -> H(U1(k, k), b)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, k), c)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.28	   A^2 -> H(f(k), d)
28.57/10.28	   A^2 -> H(f(k), k)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, d), b)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, d), c)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, k), b)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, k), c)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, k), e)
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, d), d)
28.57/10.28	   A^2 -> H(U1(d, d), k)
28.57/10.28	   A^2 -> H(U1(e, c), c)
28.57/10.28	   A^2 -> H(U1(c, c), e)
28.57/10.28	   A^2 -> H(U1(c, c), k)
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(e, e), e)
28.57/10.28	   A^2 -> H(d, U1(e, b))
28.57/10.28	   A^2 -> H(d, U1(k, b))
28.57/10.28	   A^2 -> H(d, U1(c, d))
28.57/10.28	   A^2 -> H(d, U1(d, c))
28.57/10.28	   A^2 -> H(d, U1(b, e))
28.57/10.28	   A^2 -> H(d, U1(b, k))
28.57/10.28	   A^2 -> H(d, U1(e, c))
28.57/10.28	   A^2 -> H(d, U1(k, c))
28.57/10.28	   A^2 -> H(d, U1(c, e))
28.57/10.28	   A^2 -> H(d, U1(c, k))
28.57/10.28	   A^2 -> H(d, U1(e, e))
28.57/10.28	   A^2 -> H(d, U1(k, k))
28.57/10.28	   A^2 -> H(d, U1(k, d))
28.57/10.28	   A^2 -> H(d, U1(d, k))
28.57/10.28	   A^2 -> H(a, b)
28.57/10.28	   A^2 -> H(a, U1(e, d))
28.57/10.28	   A^2 -> H(a, U1(d, e))
28.57/10.28	   A^2 -> H(a, c)
28.57/10.28	   A^2 -> H(a, U1(e, k))
28.57/10.28	   A^2 -> H(a, U1(k, e))
28.57/10.28	   A^2 -> H(a, e)
28.57/10.28	   A^2 -> H(a, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, d), b)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, d), c)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, d), e)
28.57/10.28	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, a), d)
28.57/10.28	   A^2 -> H(U1(e, a), k)
28.57/10.28	   A^2 -> H(U1(k, a), d)
28.57/10.28	   A^2 -> H(U1(c, d), d)
28.57/10.28	   A^2 -> H(U1(c, d), k)
28.57/10.28	   A^2 -> H(U1(d, e), b)
28.57/10.28	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, e), c)
28.57/10.28	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, e), e)
28.57/10.28	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, c), d)
28.57/10.28	   A^2 -> H(U1(d, c), k)
28.57/10.28	   A^2 -> H(U1(a, e), d)
28.57/10.28	   A^2 -> H(U1(a, e), k)
28.57/10.28	   A^2 -> H(U1(a, k), d)
28.57/10.28	   A^2 -> H(U1(a, k), k)
28.57/10.28	   A^2 -> H(k, U1(e, b))
28.57/10.28	   A^2 -> H(k, U1(c, d))
28.57/10.28	   A^2 -> H(k, U1(d, c))
28.57/10.28	   A^2 -> H(k, U1(b, e))
28.57/10.28	   A^2 -> H(k, U1(b, k))
28.57/10.28	   A^2 -> H(k, U1(e, c))
28.57/10.28	   A^2 -> H(k, U1(c, e))
28.57/10.28	   A^2 -> H(k, U1(c, k))
28.57/10.28	   A^2 -> H(k, U1(e, e))
28.57/10.28	   A^2 -> H(k, U1(d, k))
28.57/10.28	   A^2 -> H(c, b)
28.57/10.28	   A^2 -> H(c, U1(e, d))
28.57/10.28	   A^2 -> H(c, U1(d, e))
28.57/10.28	   A^2 -> H(c, c)
28.57/10.28	   A^2 -> H(c, U1(e, k))
28.57/10.28	   A^2 -> H(c, U1(k, e))
28.57/10.28	   A^2 -> H(c, e)
28.57/10.28	   A^2 -> H(c, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, k), b)
28.57/10.28	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, k), c)
28.57/10.28	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, k), e)
28.57/10.28	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, c), d)
28.57/10.28	   A^2 -> H(U1(e, c), k)
28.57/10.28	   A^2 -> H(U1(k, e), b)
28.57/10.28	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, e), c)
28.57/10.28	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, e), U1(k, k))
28.57/10.28	
28.57/10.28	The TRS R consists of the following rules:
28.57/10.28	
28.57/10.28	   f(x) -> U1(x, x)
28.57/10.28	   U1(e, x) -> x
28.57/10.28	   a -> c
28.57/10.28	   a -> d
28.57/10.28	   b -> c
28.57/10.28	   b -> d
28.57/10.28	   d -> k
28.57/10.28	   c -> e
28.57/10.28	   c -> k
28.57/10.28	
28.57/10.28	Q is empty.
28.57/10.28	We have to consider all minimal (P,Q,R)-chains.
28.57/10.28	----------------------------------------
28.57/10.28	
28.57/10.28	(2165) DependencyGraphProof (EQUIVALENT)
28.57/10.28	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.28	----------------------------------------
28.57/10.28	
28.57/10.28	(2166)
28.57/10.28	Obligation:
28.57/10.28	Q DP problem:
28.57/10.28	The TRS P consists of the following rules:
28.57/10.28	
28.57/10.28	   G(d, x, x) -> A^2
28.57/10.28	   A^2 -> H(f(c), f(c))
28.57/10.28	   H(x, x) -> G(x, x, f(k))
28.57/10.28	   A^2 -> H(f(d), f(d))
28.57/10.28	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.28	   A^2 -> H(f(e), f(e))
28.57/10.28	   A^2 -> H(f(k), f(k))
28.57/10.28	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.28	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.28	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.28	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, c), b)
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, c), c)
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, e), b)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, e), c)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, e), e)
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, k), b)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, k), c)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, k), e)
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, c), d)
28.57/10.28	   A^2 -> H(e, U1(e, b))
28.57/10.28	   A^2 -> H(e, U1(c, d))
28.57/10.28	   A^2 -> H(e, U1(d, c))
28.57/10.28	   A^2 -> H(e, U1(b, e))
28.57/10.28	   A^2 -> H(e, U1(b, k))
28.57/10.28	   A^2 -> H(e, U1(e, c))
28.57/10.28	   A^2 -> H(e, U1(c, e))
28.57/10.28	   A^2 -> H(e, U1(c, k))
28.57/10.28	   A^2 -> H(e, U1(e, e))
28.57/10.28	   A^2 -> H(e, U1(d, k))
28.57/10.28	   A^2 -> H(U1(e, e), b)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, e), c)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.28	   A^2 -> H(f(e), d)
28.57/10.28	   A^2 -> H(f(e), k)
28.57/10.28	   A^2 -> H(U1(k, k), b)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, k), c)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.28	   A^2 -> H(f(k), d)
28.57/10.28	   A^2 -> H(f(k), k)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, d), b)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, d), c)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, k), b)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, k), c)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, k), e)
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, d), d)
28.57/10.28	   A^2 -> H(U1(d, d), k)
28.57/10.28	   A^2 -> H(U1(e, c), c)
28.57/10.28	   A^2 -> H(U1(c, c), e)
28.57/10.28	   A^2 -> H(U1(c, c), k)
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(e, e), e)
28.57/10.28	   A^2 -> H(d, U1(e, b))
28.57/10.28	   A^2 -> H(d, U1(k, b))
28.57/10.28	   A^2 -> H(d, U1(c, d))
28.57/10.28	   A^2 -> H(d, U1(d, c))
28.57/10.28	   A^2 -> H(d, U1(b, e))
28.57/10.28	   A^2 -> H(d, U1(b, k))
28.57/10.28	   A^2 -> H(d, U1(e, c))
28.57/10.28	   A^2 -> H(d, U1(k, c))
28.57/10.28	   A^2 -> H(d, U1(c, e))
28.57/10.28	   A^2 -> H(d, U1(c, k))
28.57/10.28	   A^2 -> H(d, U1(e, e))
28.57/10.28	   A^2 -> H(d, U1(k, k))
28.57/10.28	   A^2 -> H(d, U1(k, d))
28.57/10.28	   A^2 -> H(d, U1(d, k))
28.57/10.28	   A^2 -> H(a, b)
28.57/10.28	   A^2 -> H(a, U1(e, d))
28.57/10.28	   A^2 -> H(a, U1(d, e))
28.57/10.28	   A^2 -> H(a, c)
28.57/10.28	   A^2 -> H(a, U1(e, k))
28.57/10.28	   A^2 -> H(a, U1(k, e))
28.57/10.28	   A^2 -> H(a, e)
28.57/10.28	   A^2 -> H(a, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, d), b)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, d), c)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, d), e)
28.57/10.28	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, a), d)
28.57/10.28	   A^2 -> H(U1(e, a), k)
28.57/10.28	   A^2 -> H(U1(k, a), d)
28.57/10.28	   A^2 -> H(U1(c, d), d)
28.57/10.28	   A^2 -> H(U1(c, d), k)
28.57/10.28	   A^2 -> H(U1(d, e), b)
28.57/10.28	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, e), c)
28.57/10.28	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, e), e)
28.57/10.28	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, c), d)
28.57/10.28	   A^2 -> H(U1(d, c), k)
28.57/10.28	   A^2 -> H(U1(a, e), d)
28.57/10.28	   A^2 -> H(U1(a, e), k)
28.57/10.28	   A^2 -> H(U1(a, k), d)
28.57/10.28	   A^2 -> H(U1(a, k), k)
28.57/10.28	   A^2 -> H(k, U1(e, b))
28.57/10.28	   A^2 -> H(k, U1(c, d))
28.57/10.28	   A^2 -> H(k, U1(d, c))
28.57/10.28	   A^2 -> H(k, U1(b, e))
28.57/10.28	   A^2 -> H(k, U1(b, k))
28.57/10.28	   A^2 -> H(k, U1(e, c))
28.57/10.28	   A^2 -> H(k, U1(c, e))
28.57/10.28	   A^2 -> H(k, U1(c, k))
28.57/10.28	   A^2 -> H(k, U1(e, e))
28.57/10.28	   A^2 -> H(k, U1(d, k))
28.57/10.28	   A^2 -> H(c, b)
28.57/10.28	   A^2 -> H(c, U1(e, d))
28.57/10.28	   A^2 -> H(c, U1(d, e))
28.57/10.28	   A^2 -> H(c, c)
28.57/10.28	   A^2 -> H(c, U1(e, k))
28.57/10.28	   A^2 -> H(c, U1(k, e))
28.57/10.28	   A^2 -> H(c, e)
28.57/10.28	   A^2 -> H(c, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, k), b)
28.57/10.28	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, k), c)
28.57/10.28	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, k), e)
28.57/10.28	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, c), d)
28.57/10.28	   A^2 -> H(U1(e, c), k)
28.57/10.28	   A^2 -> H(U1(k, e), b)
28.57/10.28	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, e), c)
28.57/10.28	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.28	
28.57/10.28	The TRS R consists of the following rules:
28.57/10.28	
28.57/10.28	   f(x) -> U1(x, x)
28.57/10.28	   U1(e, x) -> x
28.57/10.28	   a -> c
28.57/10.28	   a -> d
28.57/10.28	   b -> c
28.57/10.28	   b -> d
28.57/10.28	   d -> k
28.57/10.28	   c -> e
28.57/10.28	   c -> k
28.57/10.28	
28.57/10.28	Q is empty.
28.57/10.28	We have to consider all minimal (P,Q,R)-chains.
28.57/10.28	----------------------------------------
28.57/10.28	
28.57/10.28	(2167) TransformationProof (EQUIVALENT)
28.57/10.28	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), b) at position [] we obtained the following new rules [LPAR04]:
28.57/10.28	
28.57/10.28	   (A^2 -> H(U1(k, e), b),A^2 -> H(U1(k, e), b))
28.57/10.28	   (A^2 -> H(U1(k, k), b),A^2 -> H(U1(k, k), b))
28.57/10.28	   (A^2 -> H(U1(k, c), c),A^2 -> H(U1(k, c), c))
28.57/10.28	   (A^2 -> H(U1(k, c), d),A^2 -> H(U1(k, c), d))
28.57/10.28	
28.57/10.28	
28.57/10.28	----------------------------------------
28.57/10.28	
28.57/10.28	(2168)
28.57/10.28	Obligation:
28.57/10.28	Q DP problem:
28.57/10.28	The TRS P consists of the following rules:
28.57/10.28	
28.57/10.28	   G(d, x, x) -> A^2
28.57/10.28	   A^2 -> H(f(c), f(c))
28.57/10.28	   H(x, x) -> G(x, x, f(k))
28.57/10.28	   A^2 -> H(f(d), f(d))
28.57/10.28	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.28	   A^2 -> H(f(e), f(e))
28.57/10.28	   A^2 -> H(f(k), f(k))
28.57/10.28	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.28	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.28	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.28	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, c), c)
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, e), b)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, e), c)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, e), e)
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, k), b)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, k), c)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, k), e)
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, c), d)
28.57/10.28	   A^2 -> H(e, U1(e, b))
28.57/10.28	   A^2 -> H(e, U1(c, d))
28.57/10.28	   A^2 -> H(e, U1(d, c))
28.57/10.28	   A^2 -> H(e, U1(b, e))
28.57/10.28	   A^2 -> H(e, U1(b, k))
28.57/10.28	   A^2 -> H(e, U1(e, c))
28.57/10.28	   A^2 -> H(e, U1(c, e))
28.57/10.28	   A^2 -> H(e, U1(c, k))
28.57/10.28	   A^2 -> H(e, U1(e, e))
28.57/10.28	   A^2 -> H(e, U1(d, k))
28.57/10.28	   A^2 -> H(U1(e, e), b)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, e), c)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.28	   A^2 -> H(f(e), d)
28.57/10.28	   A^2 -> H(f(e), k)
28.57/10.28	   A^2 -> H(U1(k, k), b)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, k), c)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.28	   A^2 -> H(f(k), d)
28.57/10.28	   A^2 -> H(f(k), k)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, d), b)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, d), c)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, k), b)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, k), c)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, k), e)
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, d), d)
28.57/10.28	   A^2 -> H(U1(d, d), k)
28.57/10.28	   A^2 -> H(U1(e, c), c)
28.57/10.28	   A^2 -> H(U1(c, c), e)
28.57/10.28	   A^2 -> H(U1(c, c), k)
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(e, e), e)
28.57/10.28	   A^2 -> H(d, U1(e, b))
28.57/10.28	   A^2 -> H(d, U1(k, b))
28.57/10.28	   A^2 -> H(d, U1(c, d))
28.57/10.28	   A^2 -> H(d, U1(d, c))
28.57/10.28	   A^2 -> H(d, U1(b, e))
28.57/10.28	   A^2 -> H(d, U1(b, k))
28.57/10.28	   A^2 -> H(d, U1(e, c))
28.57/10.28	   A^2 -> H(d, U1(k, c))
28.57/10.28	   A^2 -> H(d, U1(c, e))
28.57/10.28	   A^2 -> H(d, U1(c, k))
28.57/10.28	   A^2 -> H(d, U1(e, e))
28.57/10.28	   A^2 -> H(d, U1(k, k))
28.57/10.28	   A^2 -> H(d, U1(k, d))
28.57/10.28	   A^2 -> H(d, U1(d, k))
28.57/10.28	   A^2 -> H(a, b)
28.57/10.28	   A^2 -> H(a, U1(e, d))
28.57/10.28	   A^2 -> H(a, U1(d, e))
28.57/10.28	   A^2 -> H(a, c)
28.57/10.28	   A^2 -> H(a, U1(e, k))
28.57/10.28	   A^2 -> H(a, U1(k, e))
28.57/10.28	   A^2 -> H(a, e)
28.57/10.28	   A^2 -> H(a, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, d), b)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, d), c)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, d), e)
28.57/10.28	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, a), d)
28.57/10.28	   A^2 -> H(U1(e, a), k)
28.57/10.28	   A^2 -> H(U1(k, a), d)
28.57/10.28	   A^2 -> H(U1(c, d), d)
28.57/10.28	   A^2 -> H(U1(c, d), k)
28.57/10.28	   A^2 -> H(U1(d, e), b)
28.57/10.28	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, e), c)
28.57/10.28	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, e), e)
28.57/10.28	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, c), d)
28.57/10.28	   A^2 -> H(U1(d, c), k)
28.57/10.28	   A^2 -> H(U1(a, e), d)
28.57/10.28	   A^2 -> H(U1(a, e), k)
28.57/10.28	   A^2 -> H(U1(a, k), d)
28.57/10.28	   A^2 -> H(U1(a, k), k)
28.57/10.28	   A^2 -> H(k, U1(e, b))
28.57/10.28	   A^2 -> H(k, U1(c, d))
28.57/10.28	   A^2 -> H(k, U1(d, c))
28.57/10.28	   A^2 -> H(k, U1(b, e))
28.57/10.28	   A^2 -> H(k, U1(b, k))
28.57/10.28	   A^2 -> H(k, U1(e, c))
28.57/10.28	   A^2 -> H(k, U1(c, e))
28.57/10.28	   A^2 -> H(k, U1(c, k))
28.57/10.28	   A^2 -> H(k, U1(e, e))
28.57/10.28	   A^2 -> H(k, U1(d, k))
28.57/10.28	   A^2 -> H(c, b)
28.57/10.28	   A^2 -> H(c, U1(e, d))
28.57/10.28	   A^2 -> H(c, U1(d, e))
28.57/10.28	   A^2 -> H(c, c)
28.57/10.28	   A^2 -> H(c, U1(e, k))
28.57/10.28	   A^2 -> H(c, U1(k, e))
28.57/10.28	   A^2 -> H(c, e)
28.57/10.28	   A^2 -> H(c, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, k), b)
28.57/10.28	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, k), c)
28.57/10.28	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, k), e)
28.57/10.28	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, c), d)
28.57/10.28	   A^2 -> H(U1(e, c), k)
28.57/10.28	   A^2 -> H(U1(k, e), b)
28.57/10.28	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, e), c)
28.57/10.28	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, c), d)
28.57/10.28	
28.57/10.28	The TRS R consists of the following rules:
28.57/10.28	
28.57/10.28	   f(x) -> U1(x, x)
28.57/10.28	   U1(e, x) -> x
28.57/10.28	   a -> c
28.57/10.28	   a -> d
28.57/10.28	   b -> c
28.57/10.28	   b -> d
28.57/10.28	   d -> k
28.57/10.28	   c -> e
28.57/10.28	   c -> k
28.57/10.28	
28.57/10.28	Q is empty.
28.57/10.28	We have to consider all minimal (P,Q,R)-chains.
28.57/10.28	----------------------------------------
28.57/10.28	
28.57/10.28	(2169) TransformationProof (EQUIVALENT)
28.57/10.28	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.28	
28.57/10.28	   (A^2 -> H(U1(k, e), U1(e, d)),A^2 -> H(U1(k, e), U1(e, d)))
28.57/10.28	   (A^2 -> H(U1(k, k), U1(e, d)),A^2 -> H(U1(k, k), U1(e, d)))
28.57/10.28	   (A^2 -> H(U1(k, c), d),A^2 -> H(U1(k, c), d))
28.57/10.28	   (A^2 -> H(U1(k, c), U1(e, k)),A^2 -> H(U1(k, c), U1(e, k)))
28.57/10.28	
28.57/10.28	
28.57/10.28	----------------------------------------
28.57/10.28	
28.57/10.28	(2170)
28.57/10.28	Obligation:
28.57/10.28	Q DP problem:
28.57/10.28	The TRS P consists of the following rules:
28.57/10.28	
28.57/10.28	   G(d, x, x) -> A^2
28.57/10.28	   A^2 -> H(f(c), f(c))
28.57/10.28	   H(x, x) -> G(x, x, f(k))
28.57/10.28	   A^2 -> H(f(d), f(d))
28.57/10.28	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.28	   A^2 -> H(f(e), f(e))
28.57/10.28	   A^2 -> H(f(k), f(k))
28.57/10.28	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.28	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.28	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.28	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, c), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, c), c)
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, e), b)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, e), c)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, e), e)
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, k), b)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, k), c)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, k), e)
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, c), d)
28.57/10.28	   A^2 -> H(e, U1(e, b))
28.57/10.28	   A^2 -> H(e, U1(c, d))
28.57/10.28	   A^2 -> H(e, U1(d, c))
28.57/10.28	   A^2 -> H(e, U1(b, e))
28.57/10.28	   A^2 -> H(e, U1(b, k))
28.57/10.28	   A^2 -> H(e, U1(e, c))
28.57/10.28	   A^2 -> H(e, U1(c, e))
28.57/10.28	   A^2 -> H(e, U1(c, k))
28.57/10.28	   A^2 -> H(e, U1(e, e))
28.57/10.28	   A^2 -> H(e, U1(d, k))
28.57/10.28	   A^2 -> H(U1(e, e), b)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, e), c)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.28	   A^2 -> H(f(e), d)
28.57/10.28	   A^2 -> H(f(e), k)
28.57/10.28	   A^2 -> H(U1(k, k), b)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, k), c)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.28	   A^2 -> H(f(k), d)
28.57/10.28	   A^2 -> H(f(k), k)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, d), b)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, d), c)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, k), b)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, k), c)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, k), e)
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, d), d)
28.57/10.28	   A^2 -> H(U1(d, d), k)
28.57/10.28	   A^2 -> H(U1(e, c), c)
28.57/10.28	   A^2 -> H(U1(c, c), e)
28.57/10.28	   A^2 -> H(U1(c, c), k)
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(e, e), e)
28.57/10.28	   A^2 -> H(d, U1(e, b))
28.57/10.28	   A^2 -> H(d, U1(k, b))
28.57/10.28	   A^2 -> H(d, U1(c, d))
28.57/10.28	   A^2 -> H(d, U1(d, c))
28.57/10.28	   A^2 -> H(d, U1(b, e))
28.57/10.28	   A^2 -> H(d, U1(b, k))
28.57/10.28	   A^2 -> H(d, U1(e, c))
28.57/10.28	   A^2 -> H(d, U1(k, c))
28.57/10.28	   A^2 -> H(d, U1(c, e))
28.57/10.28	   A^2 -> H(d, U1(c, k))
28.57/10.28	   A^2 -> H(d, U1(e, e))
28.57/10.28	   A^2 -> H(d, U1(k, k))
28.57/10.28	   A^2 -> H(d, U1(k, d))
28.57/10.28	   A^2 -> H(d, U1(d, k))
28.57/10.28	   A^2 -> H(a, b)
28.57/10.28	   A^2 -> H(a, U1(e, d))
28.57/10.28	   A^2 -> H(a, U1(d, e))
28.57/10.28	   A^2 -> H(a, c)
28.57/10.28	   A^2 -> H(a, U1(e, k))
28.57/10.28	   A^2 -> H(a, U1(k, e))
28.57/10.28	   A^2 -> H(a, e)
28.57/10.28	   A^2 -> H(a, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, d), b)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, d), c)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, d), e)
28.57/10.28	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, a), d)
28.57/10.28	   A^2 -> H(U1(e, a), k)
28.57/10.28	   A^2 -> H(U1(k, a), d)
28.57/10.28	   A^2 -> H(U1(c, d), d)
28.57/10.28	   A^2 -> H(U1(c, d), k)
28.57/10.28	   A^2 -> H(U1(d, e), b)
28.57/10.28	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, e), c)
28.57/10.28	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, e), e)
28.57/10.28	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, c), d)
28.57/10.28	   A^2 -> H(U1(d, c), k)
28.57/10.28	   A^2 -> H(U1(a, e), d)
28.57/10.28	   A^2 -> H(U1(a, e), k)
28.57/10.28	   A^2 -> H(U1(a, k), d)
28.57/10.28	   A^2 -> H(U1(a, k), k)
28.57/10.28	   A^2 -> H(k, U1(e, b))
28.57/10.28	   A^2 -> H(k, U1(c, d))
28.57/10.28	   A^2 -> H(k, U1(d, c))
28.57/10.28	   A^2 -> H(k, U1(b, e))
28.57/10.28	   A^2 -> H(k, U1(b, k))
28.57/10.28	   A^2 -> H(k, U1(e, c))
28.57/10.28	   A^2 -> H(k, U1(c, e))
28.57/10.28	   A^2 -> H(k, U1(c, k))
28.57/10.28	   A^2 -> H(k, U1(e, e))
28.57/10.28	   A^2 -> H(k, U1(d, k))
28.57/10.28	   A^2 -> H(c, b)
28.57/10.28	   A^2 -> H(c, U1(e, d))
28.57/10.28	   A^2 -> H(c, U1(d, e))
28.57/10.28	   A^2 -> H(c, c)
28.57/10.28	   A^2 -> H(c, U1(e, k))
28.57/10.28	   A^2 -> H(c, U1(k, e))
28.57/10.28	   A^2 -> H(c, e)
28.57/10.28	   A^2 -> H(c, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, k), b)
28.57/10.28	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, k), c)
28.57/10.28	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, k), e)
28.57/10.28	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, c), d)
28.57/10.28	   A^2 -> H(U1(e, c), k)
28.57/10.28	   A^2 -> H(U1(k, e), b)
28.57/10.28	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, e), c)
28.57/10.28	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, c), d)
28.57/10.28	
28.57/10.28	The TRS R consists of the following rules:
28.57/10.28	
28.57/10.28	   f(x) -> U1(x, x)
28.57/10.28	   U1(e, x) -> x
28.57/10.28	   a -> c
28.57/10.28	   a -> d
28.57/10.28	   b -> c
28.57/10.28	   b -> d
28.57/10.28	   d -> k
28.57/10.28	   c -> e
28.57/10.28	   c -> k
28.57/10.28	
28.57/10.28	Q is empty.
28.57/10.28	We have to consider all minimal (P,Q,R)-chains.
28.57/10.28	----------------------------------------
28.57/10.28	
28.57/10.28	(2171) TransformationProof (EQUIVALENT)
28.57/10.28	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.28	
28.57/10.28	   (A^2 -> H(U1(k, e), U1(d, e)),A^2 -> H(U1(k, e), U1(d, e)))
28.57/10.28	   (A^2 -> H(U1(k, k), U1(d, e)),A^2 -> H(U1(k, k), U1(d, e)))
28.57/10.28	   (A^2 -> H(U1(k, c), U1(k, e)),A^2 -> H(U1(k, c), U1(k, e)))
28.57/10.28	
28.57/10.28	
28.57/10.28	----------------------------------------
28.57/10.28	
28.57/10.28	(2172)
28.57/10.28	Obligation:
28.57/10.28	Q DP problem:
28.57/10.28	The TRS P consists of the following rules:
28.57/10.28	
28.57/10.28	   G(d, x, x) -> A^2
28.57/10.28	   A^2 -> H(f(c), f(c))
28.57/10.28	   H(x, x) -> G(x, x, f(k))
28.57/10.28	   A^2 -> H(f(d), f(d))
28.57/10.28	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.28	   A^2 -> H(f(e), f(e))
28.57/10.28	   A^2 -> H(f(k), f(k))
28.57/10.28	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.28	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.28	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.28	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, c), c)
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, e), b)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, e), c)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, e), e)
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, k), b)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, k), c)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, k), e)
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, c), d)
28.57/10.28	   A^2 -> H(e, U1(e, b))
28.57/10.28	   A^2 -> H(e, U1(c, d))
28.57/10.28	   A^2 -> H(e, U1(d, c))
28.57/10.28	   A^2 -> H(e, U1(b, e))
28.57/10.28	   A^2 -> H(e, U1(b, k))
28.57/10.28	   A^2 -> H(e, U1(e, c))
28.57/10.28	   A^2 -> H(e, U1(c, e))
28.57/10.28	   A^2 -> H(e, U1(c, k))
28.57/10.28	   A^2 -> H(e, U1(e, e))
28.57/10.28	   A^2 -> H(e, U1(d, k))
28.57/10.28	   A^2 -> H(U1(e, e), b)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, e), c)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.28	   A^2 -> H(f(e), d)
28.57/10.28	   A^2 -> H(f(e), k)
28.57/10.28	   A^2 -> H(U1(k, k), b)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, k), c)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.28	   A^2 -> H(f(k), d)
28.57/10.28	   A^2 -> H(f(k), k)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, d), b)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, d), c)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, k), b)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, k), c)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, k), e)
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, d), d)
28.57/10.28	   A^2 -> H(U1(d, d), k)
28.57/10.28	   A^2 -> H(U1(e, c), c)
28.57/10.28	   A^2 -> H(U1(c, c), e)
28.57/10.28	   A^2 -> H(U1(c, c), k)
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(e, e), e)
28.57/10.28	   A^2 -> H(d, U1(e, b))
28.57/10.28	   A^2 -> H(d, U1(k, b))
28.57/10.28	   A^2 -> H(d, U1(c, d))
28.57/10.28	   A^2 -> H(d, U1(d, c))
28.57/10.28	   A^2 -> H(d, U1(b, e))
28.57/10.28	   A^2 -> H(d, U1(b, k))
28.57/10.28	   A^2 -> H(d, U1(e, c))
28.57/10.28	   A^2 -> H(d, U1(k, c))
28.57/10.28	   A^2 -> H(d, U1(c, e))
28.57/10.28	   A^2 -> H(d, U1(c, k))
28.57/10.28	   A^2 -> H(d, U1(e, e))
28.57/10.28	   A^2 -> H(d, U1(k, k))
28.57/10.28	   A^2 -> H(d, U1(k, d))
28.57/10.28	   A^2 -> H(d, U1(d, k))
28.57/10.28	   A^2 -> H(a, b)
28.57/10.28	   A^2 -> H(a, U1(e, d))
28.57/10.28	   A^2 -> H(a, U1(d, e))
28.57/10.28	   A^2 -> H(a, c)
28.57/10.28	   A^2 -> H(a, U1(e, k))
28.57/10.28	   A^2 -> H(a, U1(k, e))
28.57/10.28	   A^2 -> H(a, e)
28.57/10.28	   A^2 -> H(a, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, d), b)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, d), c)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, d), e)
28.57/10.28	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, a), d)
28.57/10.28	   A^2 -> H(U1(e, a), k)
28.57/10.28	   A^2 -> H(U1(k, a), d)
28.57/10.28	   A^2 -> H(U1(c, d), d)
28.57/10.28	   A^2 -> H(U1(c, d), k)
28.57/10.28	   A^2 -> H(U1(d, e), b)
28.57/10.28	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, e), c)
28.57/10.28	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, e), e)
28.57/10.28	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, c), d)
28.57/10.28	   A^2 -> H(U1(d, c), k)
28.57/10.28	   A^2 -> H(U1(a, e), d)
28.57/10.28	   A^2 -> H(U1(a, e), k)
28.57/10.28	   A^2 -> H(U1(a, k), d)
28.57/10.28	   A^2 -> H(U1(a, k), k)
28.57/10.28	   A^2 -> H(k, U1(e, b))
28.57/10.28	   A^2 -> H(k, U1(c, d))
28.57/10.28	   A^2 -> H(k, U1(d, c))
28.57/10.28	   A^2 -> H(k, U1(b, e))
28.57/10.28	   A^2 -> H(k, U1(b, k))
28.57/10.28	   A^2 -> H(k, U1(e, c))
28.57/10.28	   A^2 -> H(k, U1(c, e))
28.57/10.28	   A^2 -> H(k, U1(c, k))
28.57/10.28	   A^2 -> H(k, U1(e, e))
28.57/10.28	   A^2 -> H(k, U1(d, k))
28.57/10.28	   A^2 -> H(c, b)
28.57/10.28	   A^2 -> H(c, U1(e, d))
28.57/10.28	   A^2 -> H(c, U1(d, e))
28.57/10.28	   A^2 -> H(c, c)
28.57/10.28	   A^2 -> H(c, U1(e, k))
28.57/10.28	   A^2 -> H(c, U1(k, e))
28.57/10.28	   A^2 -> H(c, e)
28.57/10.28	   A^2 -> H(c, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, k), b)
28.57/10.28	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, k), c)
28.57/10.28	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, k), e)
28.57/10.28	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, c), d)
28.57/10.28	   A^2 -> H(U1(e, c), k)
28.57/10.28	   A^2 -> H(U1(k, e), b)
28.57/10.28	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, e), c)
28.57/10.28	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, c), d)
28.57/10.28	
28.57/10.28	The TRS R consists of the following rules:
28.57/10.28	
28.57/10.28	   f(x) -> U1(x, x)
28.57/10.28	   U1(e, x) -> x
28.57/10.28	   a -> c
28.57/10.28	   a -> d
28.57/10.28	   b -> c
28.57/10.28	   b -> d
28.57/10.28	   d -> k
28.57/10.28	   c -> e
28.57/10.28	   c -> k
28.57/10.28	
28.57/10.28	Q is empty.
28.57/10.28	We have to consider all minimal (P,Q,R)-chains.
28.57/10.28	----------------------------------------
28.57/10.28	
28.57/10.28	(2173) TransformationProof (EQUIVALENT)
28.57/10.28	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), c) at position [] we obtained the following new rules [LPAR04]:
28.57/10.28	
28.57/10.28	   (A^2 -> H(U1(k, e), c),A^2 -> H(U1(k, e), c))
28.57/10.28	   (A^2 -> H(U1(k, k), c),A^2 -> H(U1(k, k), c))
28.57/10.28	   (A^2 -> H(U1(k, c), e),A^2 -> H(U1(k, c), e))
28.57/10.28	   (A^2 -> H(U1(k, c), k),A^2 -> H(U1(k, c), k))
28.57/10.28	
28.57/10.28	
28.57/10.28	----------------------------------------
28.57/10.28	
28.57/10.28	(2174)
28.57/10.28	Obligation:
28.57/10.28	Q DP problem:
28.57/10.28	The TRS P consists of the following rules:
28.57/10.28	
28.57/10.28	   G(d, x, x) -> A^2
28.57/10.28	   A^2 -> H(f(c), f(c))
28.57/10.28	   H(x, x) -> G(x, x, f(k))
28.57/10.28	   A^2 -> H(f(d), f(d))
28.57/10.28	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.28	   A^2 -> H(f(e), f(e))
28.57/10.28	   A^2 -> H(f(k), f(k))
28.57/10.28	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.28	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.28	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.28	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, e), b)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, e), c)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, e), e)
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, k), b)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, k), c)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, k), e)
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, c), d)
28.57/10.28	   A^2 -> H(e, U1(e, b))
28.57/10.28	   A^2 -> H(e, U1(c, d))
28.57/10.28	   A^2 -> H(e, U1(d, c))
28.57/10.28	   A^2 -> H(e, U1(b, e))
28.57/10.28	   A^2 -> H(e, U1(b, k))
28.57/10.28	   A^2 -> H(e, U1(e, c))
28.57/10.28	   A^2 -> H(e, U1(c, e))
28.57/10.28	   A^2 -> H(e, U1(c, k))
28.57/10.28	   A^2 -> H(e, U1(e, e))
28.57/10.28	   A^2 -> H(e, U1(d, k))
28.57/10.28	   A^2 -> H(U1(e, e), b)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, e), c)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.28	   A^2 -> H(f(e), d)
28.57/10.28	   A^2 -> H(f(e), k)
28.57/10.28	   A^2 -> H(U1(k, k), b)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, k), c)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.28	   A^2 -> H(f(k), d)
28.57/10.28	   A^2 -> H(f(k), k)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, d), b)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, d), c)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, k), b)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, k), c)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, k), e)
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, d), d)
28.57/10.28	   A^2 -> H(U1(d, d), k)
28.57/10.28	   A^2 -> H(U1(e, c), c)
28.57/10.28	   A^2 -> H(U1(c, c), e)
28.57/10.28	   A^2 -> H(U1(c, c), k)
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(e, e), e)
28.57/10.28	   A^2 -> H(d, U1(e, b))
28.57/10.28	   A^2 -> H(d, U1(k, b))
28.57/10.28	   A^2 -> H(d, U1(c, d))
28.57/10.28	   A^2 -> H(d, U1(d, c))
28.57/10.28	   A^2 -> H(d, U1(b, e))
28.57/10.28	   A^2 -> H(d, U1(b, k))
28.57/10.28	   A^2 -> H(d, U1(e, c))
28.57/10.28	   A^2 -> H(d, U1(k, c))
28.57/10.28	   A^2 -> H(d, U1(c, e))
28.57/10.28	   A^2 -> H(d, U1(c, k))
28.57/10.28	   A^2 -> H(d, U1(e, e))
28.57/10.28	   A^2 -> H(d, U1(k, k))
28.57/10.28	   A^2 -> H(d, U1(k, d))
28.57/10.28	   A^2 -> H(d, U1(d, k))
28.57/10.28	   A^2 -> H(a, b)
28.57/10.28	   A^2 -> H(a, U1(e, d))
28.57/10.28	   A^2 -> H(a, U1(d, e))
28.57/10.28	   A^2 -> H(a, c)
28.57/10.28	   A^2 -> H(a, U1(e, k))
28.57/10.28	   A^2 -> H(a, U1(k, e))
28.57/10.28	   A^2 -> H(a, e)
28.57/10.28	   A^2 -> H(a, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, d), b)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, d), c)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, d), e)
28.57/10.28	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, a), d)
28.57/10.28	   A^2 -> H(U1(e, a), k)
28.57/10.28	   A^2 -> H(U1(k, a), d)
28.57/10.28	   A^2 -> H(U1(c, d), d)
28.57/10.28	   A^2 -> H(U1(c, d), k)
28.57/10.28	   A^2 -> H(U1(d, e), b)
28.57/10.28	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, e), c)
28.57/10.28	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, e), e)
28.57/10.28	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, c), d)
28.57/10.28	   A^2 -> H(U1(d, c), k)
28.57/10.28	   A^2 -> H(U1(a, e), d)
28.57/10.28	   A^2 -> H(U1(a, e), k)
28.57/10.28	   A^2 -> H(U1(a, k), d)
28.57/10.28	   A^2 -> H(U1(a, k), k)
28.57/10.28	   A^2 -> H(k, U1(e, b))
28.57/10.28	   A^2 -> H(k, U1(c, d))
28.57/10.28	   A^2 -> H(k, U1(d, c))
28.57/10.28	   A^2 -> H(k, U1(b, e))
28.57/10.28	   A^2 -> H(k, U1(b, k))
28.57/10.28	   A^2 -> H(k, U1(e, c))
28.57/10.28	   A^2 -> H(k, U1(c, e))
28.57/10.28	   A^2 -> H(k, U1(c, k))
28.57/10.28	   A^2 -> H(k, U1(e, e))
28.57/10.28	   A^2 -> H(k, U1(d, k))
28.57/10.28	   A^2 -> H(c, b)
28.57/10.28	   A^2 -> H(c, U1(e, d))
28.57/10.28	   A^2 -> H(c, U1(d, e))
28.57/10.28	   A^2 -> H(c, c)
28.57/10.28	   A^2 -> H(c, U1(e, k))
28.57/10.28	   A^2 -> H(c, U1(k, e))
28.57/10.28	   A^2 -> H(c, e)
28.57/10.28	   A^2 -> H(c, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, k), b)
28.57/10.28	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, k), c)
28.57/10.28	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, k), e)
28.57/10.28	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, c), d)
28.57/10.28	   A^2 -> H(U1(e, c), k)
28.57/10.28	   A^2 -> H(U1(k, e), b)
28.57/10.28	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, e), c)
28.57/10.28	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, c), d)
28.57/10.28	   A^2 -> H(U1(k, c), e)
28.57/10.28	   A^2 -> H(U1(k, c), k)
28.57/10.28	
28.57/10.28	The TRS R consists of the following rules:
28.57/10.28	
28.57/10.28	   f(x) -> U1(x, x)
28.57/10.28	   U1(e, x) -> x
28.57/10.28	   a -> c
28.57/10.28	   a -> d
28.57/10.28	   b -> c
28.57/10.28	   b -> d
28.57/10.28	   d -> k
28.57/10.28	   c -> e
28.57/10.28	   c -> k
28.57/10.28	
28.57/10.28	Q is empty.
28.57/10.28	We have to consider all minimal (P,Q,R)-chains.
28.57/10.28	----------------------------------------
28.57/10.28	
28.57/10.28	(2175) DependencyGraphProof (EQUIVALENT)
28.57/10.28	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
28.57/10.28	----------------------------------------
28.57/10.28	
28.57/10.28	(2176)
28.57/10.28	Obligation:
28.57/10.28	Q DP problem:
28.57/10.28	The TRS P consists of the following rules:
28.57/10.28	
28.57/10.28	   A^2 -> H(f(c), f(c))
28.57/10.28	   H(x, x) -> G(x, x, f(k))
28.57/10.28	   G(d, x, x) -> A^2
28.57/10.28	   A^2 -> H(f(d), f(d))
28.57/10.28	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.28	   A^2 -> H(f(e), f(e))
28.57/10.28	   A^2 -> H(f(k), f(k))
28.57/10.28	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.28	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.28	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.28	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, e), b)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, e), c)
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, e), e)
28.57/10.28	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, k), b)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(c, k), c)
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(c, k), e)
28.57/10.28	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(c, c), d)
28.57/10.28	   A^2 -> H(e, U1(e, b))
28.57/10.28	   A^2 -> H(e, U1(c, d))
28.57/10.28	   A^2 -> H(e, U1(d, c))
28.57/10.28	   A^2 -> H(e, U1(b, e))
28.57/10.28	   A^2 -> H(e, U1(b, k))
28.57/10.28	   A^2 -> H(e, U1(e, c))
28.57/10.28	   A^2 -> H(e, U1(c, e))
28.57/10.28	   A^2 -> H(e, U1(c, k))
28.57/10.28	   A^2 -> H(e, U1(e, e))
28.57/10.28	   A^2 -> H(e, U1(d, k))
28.57/10.28	   A^2 -> H(U1(e, e), b)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, e), c)
28.57/10.28	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.28	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.28	   A^2 -> H(f(e), d)
28.57/10.28	   A^2 -> H(f(e), k)
28.57/10.28	   A^2 -> H(U1(k, k), b)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, k), c)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.28	   A^2 -> H(f(k), d)
28.57/10.28	   A^2 -> H(f(k), k)
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.28	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.28	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.28	   A^2 -> H(U1(k, d), b)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(k, d), c)
28.57/10.28	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.28	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, k), b)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.28	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.28	   A^2 -> H(U1(d, k), c)
28.57/10.28	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.28	   A^2 -> H(U1(d, k), e)
28.57/10.28	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.28	   A^2 -> H(U1(d, d), d)
28.57/10.28	   A^2 -> H(U1(d, d), k)
28.57/10.28	   A^2 -> H(U1(e, c), c)
28.57/10.28	   A^2 -> H(U1(c, c), e)
28.57/10.28	   A^2 -> H(U1(c, c), k)
28.57/10.28	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.28	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.28	   A^2 -> H(U1(e, e), e)
28.57/10.28	   A^2 -> H(d, U1(e, b))
28.57/10.28	   A^2 -> H(d, U1(k, b))
28.57/10.28	   A^2 -> H(d, U1(c, d))
28.57/10.28	   A^2 -> H(d, U1(d, c))
28.57/10.28	   A^2 -> H(d, U1(b, e))
28.57/10.28	   A^2 -> H(d, U1(b, k))
28.57/10.28	   A^2 -> H(d, U1(e, c))
28.57/10.28	   A^2 -> H(d, U1(k, c))
28.57/10.28	   A^2 -> H(d, U1(c, e))
28.57/10.28	   A^2 -> H(d, U1(c, k))
28.57/10.28	   A^2 -> H(d, U1(e, e))
28.57/10.28	   A^2 -> H(d, U1(k, k))
28.57/10.28	   A^2 -> H(d, U1(k, d))
28.57/10.28	   A^2 -> H(d, U1(d, k))
28.57/10.28	   A^2 -> H(a, b)
28.57/10.28	   A^2 -> H(a, U1(e, d))
28.57/10.28	   A^2 -> H(a, U1(d, e))
28.57/10.28	   A^2 -> H(a, c)
28.57/10.28	   A^2 -> H(a, U1(e, k))
28.57/10.28	   A^2 -> H(a, U1(k, e))
28.57/10.28	   A^2 -> H(a, e)
28.57/10.28	   A^2 -> H(a, U1(k, k))
28.57/10.28	   A^2 -> H(U1(e, d), b)
28.57/10.28	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.28	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.28	   A^2 -> H(U1(e, d), c)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, d), e)
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, a), d)
28.57/10.29	   A^2 -> H(U1(e, a), k)
28.57/10.29	   A^2 -> H(U1(k, a), d)
28.57/10.29	   A^2 -> H(U1(c, d), d)
28.57/10.29	   A^2 -> H(U1(c, d), k)
28.57/10.29	   A^2 -> H(U1(d, e), b)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, e), c)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, e), e)
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, c), d)
28.57/10.29	   A^2 -> H(U1(d, c), k)
28.57/10.29	   A^2 -> H(U1(a, e), d)
28.57/10.29	   A^2 -> H(U1(a, e), k)
28.57/10.29	   A^2 -> H(U1(a, k), d)
28.57/10.29	   A^2 -> H(U1(a, k), k)
28.57/10.29	   A^2 -> H(k, U1(e, b))
28.57/10.29	   A^2 -> H(k, U1(c, d))
28.57/10.29	   A^2 -> H(k, U1(d, c))
28.57/10.29	   A^2 -> H(k, U1(b, e))
28.57/10.29	   A^2 -> H(k, U1(b, k))
28.57/10.29	   A^2 -> H(k, U1(e, c))
28.57/10.29	   A^2 -> H(k, U1(c, e))
28.57/10.29	   A^2 -> H(k, U1(c, k))
28.57/10.29	   A^2 -> H(k, U1(e, e))
28.57/10.29	   A^2 -> H(k, U1(d, k))
28.57/10.29	   A^2 -> H(c, b)
28.57/10.29	   A^2 -> H(c, U1(e, d))
28.57/10.29	   A^2 -> H(c, U1(d, e))
28.57/10.29	   A^2 -> H(c, c)
28.57/10.29	   A^2 -> H(c, U1(e, k))
28.57/10.29	   A^2 -> H(c, U1(k, e))
28.57/10.29	   A^2 -> H(c, e)
28.57/10.29	   A^2 -> H(c, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, k), b)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, k), c)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, k), e)
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, c), d)
28.57/10.29	   A^2 -> H(U1(e, c), k)
28.57/10.29	   A^2 -> H(U1(k, e), b)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, e), c)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, c), d)
28.57/10.29	
28.57/10.29	The TRS R consists of the following rules:
28.57/10.29	
28.57/10.29	   f(x) -> U1(x, x)
28.57/10.29	   U1(e, x) -> x
28.57/10.29	   a -> c
28.57/10.29	   a -> d
28.57/10.29	   b -> c
28.57/10.29	   b -> d
28.57/10.29	   d -> k
28.57/10.29	   c -> e
28.57/10.29	   c -> k
28.57/10.29	
28.57/10.29	Q is empty.
28.57/10.29	We have to consider all minimal (P,Q,R)-chains.
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2177) TransformationProof (EQUIVALENT)
28.57/10.29	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.29	
28.57/10.29	   (A^2 -> H(U1(k, e), U1(e, k)),A^2 -> H(U1(k, e), U1(e, k)))
28.57/10.29	   (A^2 -> H(U1(k, k), U1(e, k)),A^2 -> H(U1(k, k), U1(e, k)))
28.57/10.29	   (A^2 -> H(U1(k, c), k),A^2 -> H(U1(k, c), k))
28.57/10.29	
28.57/10.29	
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2178)
28.57/10.29	Obligation:
28.57/10.29	Q DP problem:
28.57/10.29	The TRS P consists of the following rules:
28.57/10.29	
28.57/10.29	   A^2 -> H(f(c), f(c))
28.57/10.29	   H(x, x) -> G(x, x, f(k))
28.57/10.29	   G(d, x, x) -> A^2
28.57/10.29	   A^2 -> H(f(d), f(d))
28.57/10.29	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.29	   A^2 -> H(f(e), f(e))
28.57/10.29	   A^2 -> H(f(k), f(k))
28.57/10.29	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.29	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.29	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.29	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, e), b)
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(c, e), c)
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, e), e)
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, k), b)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(c, k), c)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, k), e)
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, c), d)
28.57/10.29	   A^2 -> H(e, U1(e, b))
28.57/10.29	   A^2 -> H(e, U1(c, d))
28.57/10.29	   A^2 -> H(e, U1(d, c))
28.57/10.29	   A^2 -> H(e, U1(b, e))
28.57/10.29	   A^2 -> H(e, U1(b, k))
28.57/10.29	   A^2 -> H(e, U1(e, c))
28.57/10.29	   A^2 -> H(e, U1(c, e))
28.57/10.29	   A^2 -> H(e, U1(c, k))
28.57/10.29	   A^2 -> H(e, U1(e, e))
28.57/10.29	   A^2 -> H(e, U1(d, k))
28.57/10.29	   A^2 -> H(U1(e, e), b)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, e), c)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.29	   A^2 -> H(f(e), d)
28.57/10.29	   A^2 -> H(f(e), k)
28.57/10.29	   A^2 -> H(U1(k, k), b)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, k), c)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.29	   A^2 -> H(f(k), d)
28.57/10.29	   A^2 -> H(f(k), k)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(k, d), b)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, d), c)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, k), b)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, k), c)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, k), e)
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, d), d)
28.57/10.29	   A^2 -> H(U1(d, d), k)
28.57/10.29	   A^2 -> H(U1(e, c), c)
28.57/10.29	   A^2 -> H(U1(c, c), e)
28.57/10.29	   A^2 -> H(U1(c, c), k)
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(e, e), e)
28.57/10.29	   A^2 -> H(d, U1(e, b))
28.57/10.29	   A^2 -> H(d, U1(k, b))
28.57/10.29	   A^2 -> H(d, U1(c, d))
28.57/10.29	   A^2 -> H(d, U1(d, c))
28.57/10.29	   A^2 -> H(d, U1(b, e))
28.57/10.29	   A^2 -> H(d, U1(b, k))
28.57/10.29	   A^2 -> H(d, U1(e, c))
28.57/10.29	   A^2 -> H(d, U1(k, c))
28.57/10.29	   A^2 -> H(d, U1(c, e))
28.57/10.29	   A^2 -> H(d, U1(c, k))
28.57/10.29	   A^2 -> H(d, U1(e, e))
28.57/10.29	   A^2 -> H(d, U1(k, k))
28.57/10.29	   A^2 -> H(d, U1(k, d))
28.57/10.29	   A^2 -> H(d, U1(d, k))
28.57/10.29	   A^2 -> H(a, b)
28.57/10.29	   A^2 -> H(a, U1(e, d))
28.57/10.29	   A^2 -> H(a, U1(d, e))
28.57/10.29	   A^2 -> H(a, c)
28.57/10.29	   A^2 -> H(a, U1(e, k))
28.57/10.29	   A^2 -> H(a, U1(k, e))
28.57/10.29	   A^2 -> H(a, e)
28.57/10.29	   A^2 -> H(a, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, d), b)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, d), c)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, d), e)
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, a), d)
28.57/10.29	   A^2 -> H(U1(e, a), k)
28.57/10.29	   A^2 -> H(U1(k, a), d)
28.57/10.29	   A^2 -> H(U1(c, d), d)
28.57/10.29	   A^2 -> H(U1(c, d), k)
28.57/10.29	   A^2 -> H(U1(d, e), b)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, e), c)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, e), e)
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, c), d)
28.57/10.29	   A^2 -> H(U1(d, c), k)
28.57/10.29	   A^2 -> H(U1(a, e), d)
28.57/10.29	   A^2 -> H(U1(a, e), k)
28.57/10.29	   A^2 -> H(U1(a, k), d)
28.57/10.29	   A^2 -> H(U1(a, k), k)
28.57/10.29	   A^2 -> H(k, U1(e, b))
28.57/10.29	   A^2 -> H(k, U1(c, d))
28.57/10.29	   A^2 -> H(k, U1(d, c))
28.57/10.29	   A^2 -> H(k, U1(b, e))
28.57/10.29	   A^2 -> H(k, U1(b, k))
28.57/10.29	   A^2 -> H(k, U1(e, c))
28.57/10.29	   A^2 -> H(k, U1(c, e))
28.57/10.29	   A^2 -> H(k, U1(c, k))
28.57/10.29	   A^2 -> H(k, U1(e, e))
28.57/10.29	   A^2 -> H(k, U1(d, k))
28.57/10.29	   A^2 -> H(c, b)
28.57/10.29	   A^2 -> H(c, U1(e, d))
28.57/10.29	   A^2 -> H(c, U1(d, e))
28.57/10.29	   A^2 -> H(c, c)
28.57/10.29	   A^2 -> H(c, U1(e, k))
28.57/10.29	   A^2 -> H(c, U1(k, e))
28.57/10.29	   A^2 -> H(c, e)
28.57/10.29	   A^2 -> H(c, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, k), b)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, k), c)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, k), e)
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, c), d)
28.57/10.29	   A^2 -> H(U1(e, c), k)
28.57/10.29	   A^2 -> H(U1(k, e), b)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, e), c)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, c), d)
28.57/10.29	   A^2 -> H(U1(k, c), k)
28.57/10.29	
28.57/10.29	The TRS R consists of the following rules:
28.57/10.29	
28.57/10.29	   f(x) -> U1(x, x)
28.57/10.29	   U1(e, x) -> x
28.57/10.29	   a -> c
28.57/10.29	   a -> d
28.57/10.29	   b -> c
28.57/10.29	   b -> d
28.57/10.29	   d -> k
28.57/10.29	   c -> e
28.57/10.29	   c -> k
28.57/10.29	
28.57/10.29	Q is empty.
28.57/10.29	We have to consider all minimal (P,Q,R)-chains.
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2179) DependencyGraphProof (EQUIVALENT)
28.57/10.29	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2180)
28.57/10.29	Obligation:
28.57/10.29	Q DP problem:
28.57/10.29	The TRS P consists of the following rules:
28.57/10.29	
28.57/10.29	   H(x, x) -> G(x, x, f(k))
28.57/10.29	   G(d, x, x) -> A^2
28.57/10.29	   A^2 -> H(f(c), f(c))
28.57/10.29	   A^2 -> H(f(d), f(d))
28.57/10.29	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.29	   A^2 -> H(f(e), f(e))
28.57/10.29	   A^2 -> H(f(k), f(k))
28.57/10.29	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.29	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.29	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.29	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(k, c), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, e), b)
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(c, e), c)
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, e), e)
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, k), b)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(c, k), c)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, k), e)
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, c), d)
28.57/10.29	   A^2 -> H(e, U1(e, b))
28.57/10.29	   A^2 -> H(e, U1(c, d))
28.57/10.29	   A^2 -> H(e, U1(d, c))
28.57/10.29	   A^2 -> H(e, U1(b, e))
28.57/10.29	   A^2 -> H(e, U1(b, k))
28.57/10.29	   A^2 -> H(e, U1(e, c))
28.57/10.29	   A^2 -> H(e, U1(c, e))
28.57/10.29	   A^2 -> H(e, U1(c, k))
28.57/10.29	   A^2 -> H(e, U1(e, e))
28.57/10.29	   A^2 -> H(e, U1(d, k))
28.57/10.29	   A^2 -> H(U1(e, e), b)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, e), c)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.29	   A^2 -> H(f(e), d)
28.57/10.29	   A^2 -> H(f(e), k)
28.57/10.29	   A^2 -> H(U1(k, k), b)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, k), c)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.29	   A^2 -> H(f(k), d)
28.57/10.29	   A^2 -> H(f(k), k)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(k, d), b)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, d), c)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, k), b)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, k), c)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, k), e)
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, d), d)
28.57/10.29	   A^2 -> H(U1(d, d), k)
28.57/10.29	   A^2 -> H(U1(e, c), c)
28.57/10.29	   A^2 -> H(U1(c, c), e)
28.57/10.29	   A^2 -> H(U1(c, c), k)
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(e, e), e)
28.57/10.29	   A^2 -> H(d, U1(e, b))
28.57/10.29	   A^2 -> H(d, U1(k, b))
28.57/10.29	   A^2 -> H(d, U1(c, d))
28.57/10.29	   A^2 -> H(d, U1(d, c))
28.57/10.29	   A^2 -> H(d, U1(b, e))
28.57/10.29	   A^2 -> H(d, U1(b, k))
28.57/10.29	   A^2 -> H(d, U1(e, c))
28.57/10.29	   A^2 -> H(d, U1(k, c))
28.57/10.29	   A^2 -> H(d, U1(c, e))
28.57/10.29	   A^2 -> H(d, U1(c, k))
28.57/10.29	   A^2 -> H(d, U1(e, e))
28.57/10.29	   A^2 -> H(d, U1(k, k))
28.57/10.29	   A^2 -> H(d, U1(k, d))
28.57/10.29	   A^2 -> H(d, U1(d, k))
28.57/10.29	   A^2 -> H(a, b)
28.57/10.29	   A^2 -> H(a, U1(e, d))
28.57/10.29	   A^2 -> H(a, U1(d, e))
28.57/10.29	   A^2 -> H(a, c)
28.57/10.29	   A^2 -> H(a, U1(e, k))
28.57/10.29	   A^2 -> H(a, U1(k, e))
28.57/10.29	   A^2 -> H(a, e)
28.57/10.29	   A^2 -> H(a, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, d), b)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, d), c)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, d), e)
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, a), d)
28.57/10.29	   A^2 -> H(U1(e, a), k)
28.57/10.29	   A^2 -> H(U1(k, a), d)
28.57/10.29	   A^2 -> H(U1(c, d), d)
28.57/10.29	   A^2 -> H(U1(c, d), k)
28.57/10.29	   A^2 -> H(U1(d, e), b)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, e), c)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, e), e)
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, c), d)
28.57/10.29	   A^2 -> H(U1(d, c), k)
28.57/10.29	   A^2 -> H(U1(a, e), d)
28.57/10.29	   A^2 -> H(U1(a, e), k)
28.57/10.29	   A^2 -> H(U1(a, k), d)
28.57/10.29	   A^2 -> H(U1(a, k), k)
28.57/10.29	   A^2 -> H(k, U1(e, b))
28.57/10.29	   A^2 -> H(k, U1(c, d))
28.57/10.29	   A^2 -> H(k, U1(d, c))
28.57/10.29	   A^2 -> H(k, U1(b, e))
28.57/10.29	   A^2 -> H(k, U1(b, k))
28.57/10.29	   A^2 -> H(k, U1(e, c))
28.57/10.29	   A^2 -> H(k, U1(c, e))
28.57/10.29	   A^2 -> H(k, U1(c, k))
28.57/10.29	   A^2 -> H(k, U1(e, e))
28.57/10.29	   A^2 -> H(k, U1(d, k))
28.57/10.29	   A^2 -> H(c, b)
28.57/10.29	   A^2 -> H(c, U1(e, d))
28.57/10.29	   A^2 -> H(c, U1(d, e))
28.57/10.29	   A^2 -> H(c, c)
28.57/10.29	   A^2 -> H(c, U1(e, k))
28.57/10.29	   A^2 -> H(c, U1(k, e))
28.57/10.29	   A^2 -> H(c, e)
28.57/10.29	   A^2 -> H(c, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, k), b)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, k), c)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, k), e)
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, c), d)
28.57/10.29	   A^2 -> H(U1(e, c), k)
28.57/10.29	   A^2 -> H(U1(k, e), b)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, e), c)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, c), d)
28.57/10.29	
28.57/10.29	The TRS R consists of the following rules:
28.57/10.29	
28.57/10.29	   f(x) -> U1(x, x)
28.57/10.29	   U1(e, x) -> x
28.57/10.29	   a -> c
28.57/10.29	   a -> d
28.57/10.29	   b -> c
28.57/10.29	   b -> d
28.57/10.29	   d -> k
28.57/10.29	   c -> e
28.57/10.29	   c -> k
28.57/10.29	
28.57/10.29	Q is empty.
28.57/10.29	We have to consider all minimal (P,Q,R)-chains.
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2181) TransformationProof (EQUIVALENT)
28.57/10.29	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.29	
28.57/10.29	   (A^2 -> H(U1(k, e), U1(k, e)),A^2 -> H(U1(k, e), U1(k, e)))
28.57/10.29	   (A^2 -> H(U1(k, k), U1(k, e)),A^2 -> H(U1(k, k), U1(k, e)))
28.57/10.29	
28.57/10.29	
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2182)
28.57/10.29	Obligation:
28.57/10.29	Q DP problem:
28.57/10.29	The TRS P consists of the following rules:
28.57/10.29	
28.57/10.29	   H(x, x) -> G(x, x, f(k))
28.57/10.29	   G(d, x, x) -> A^2
28.57/10.29	   A^2 -> H(f(c), f(c))
28.57/10.29	   A^2 -> H(f(d), f(d))
28.57/10.29	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.29	   A^2 -> H(f(e), f(e))
28.57/10.29	   A^2 -> H(f(k), f(k))
28.57/10.29	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.29	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.29	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.29	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, e), b)
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(c, e), c)
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, e), e)
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, k), b)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(c, k), c)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, k), e)
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, c), d)
28.57/10.29	   A^2 -> H(e, U1(e, b))
28.57/10.29	   A^2 -> H(e, U1(c, d))
28.57/10.29	   A^2 -> H(e, U1(d, c))
28.57/10.29	   A^2 -> H(e, U1(b, e))
28.57/10.29	   A^2 -> H(e, U1(b, k))
28.57/10.29	   A^2 -> H(e, U1(e, c))
28.57/10.29	   A^2 -> H(e, U1(c, e))
28.57/10.29	   A^2 -> H(e, U1(c, k))
28.57/10.29	   A^2 -> H(e, U1(e, e))
28.57/10.29	   A^2 -> H(e, U1(d, k))
28.57/10.29	   A^2 -> H(U1(e, e), b)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, e), c)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.29	   A^2 -> H(f(e), d)
28.57/10.29	   A^2 -> H(f(e), k)
28.57/10.29	   A^2 -> H(U1(k, k), b)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, k), c)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.29	   A^2 -> H(f(k), d)
28.57/10.29	   A^2 -> H(f(k), k)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(k, d), b)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, d), c)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, k), b)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, k), c)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, k), e)
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, d), d)
28.57/10.29	   A^2 -> H(U1(d, d), k)
28.57/10.29	   A^2 -> H(U1(e, c), c)
28.57/10.29	   A^2 -> H(U1(c, c), e)
28.57/10.29	   A^2 -> H(U1(c, c), k)
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(e, e), e)
28.57/10.29	   A^2 -> H(d, U1(e, b))
28.57/10.29	   A^2 -> H(d, U1(k, b))
28.57/10.29	   A^2 -> H(d, U1(c, d))
28.57/10.29	   A^2 -> H(d, U1(d, c))
28.57/10.29	   A^2 -> H(d, U1(b, e))
28.57/10.29	   A^2 -> H(d, U1(b, k))
28.57/10.29	   A^2 -> H(d, U1(e, c))
28.57/10.29	   A^2 -> H(d, U1(k, c))
28.57/10.29	   A^2 -> H(d, U1(c, e))
28.57/10.29	   A^2 -> H(d, U1(c, k))
28.57/10.29	   A^2 -> H(d, U1(e, e))
28.57/10.29	   A^2 -> H(d, U1(k, k))
28.57/10.29	   A^2 -> H(d, U1(k, d))
28.57/10.29	   A^2 -> H(d, U1(d, k))
28.57/10.29	   A^2 -> H(a, b)
28.57/10.29	   A^2 -> H(a, U1(e, d))
28.57/10.29	   A^2 -> H(a, U1(d, e))
28.57/10.29	   A^2 -> H(a, c)
28.57/10.29	   A^2 -> H(a, U1(e, k))
28.57/10.29	   A^2 -> H(a, U1(k, e))
28.57/10.29	   A^2 -> H(a, e)
28.57/10.29	   A^2 -> H(a, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, d), b)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, d), c)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, d), e)
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, a), d)
28.57/10.29	   A^2 -> H(U1(e, a), k)
28.57/10.29	   A^2 -> H(U1(k, a), d)
28.57/10.29	   A^2 -> H(U1(c, d), d)
28.57/10.29	   A^2 -> H(U1(c, d), k)
28.57/10.29	   A^2 -> H(U1(d, e), b)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, e), c)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, e), e)
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, c), d)
28.57/10.29	   A^2 -> H(U1(d, c), k)
28.57/10.29	   A^2 -> H(U1(a, e), d)
28.57/10.29	   A^2 -> H(U1(a, e), k)
28.57/10.29	   A^2 -> H(U1(a, k), d)
28.57/10.29	   A^2 -> H(U1(a, k), k)
28.57/10.29	   A^2 -> H(k, U1(e, b))
28.57/10.29	   A^2 -> H(k, U1(c, d))
28.57/10.29	   A^2 -> H(k, U1(d, c))
28.57/10.29	   A^2 -> H(k, U1(b, e))
28.57/10.29	   A^2 -> H(k, U1(b, k))
28.57/10.29	   A^2 -> H(k, U1(e, c))
28.57/10.29	   A^2 -> H(k, U1(c, e))
28.57/10.29	   A^2 -> H(k, U1(c, k))
28.57/10.29	   A^2 -> H(k, U1(e, e))
28.57/10.29	   A^2 -> H(k, U1(d, k))
28.57/10.29	   A^2 -> H(c, b)
28.57/10.29	   A^2 -> H(c, U1(e, d))
28.57/10.29	   A^2 -> H(c, U1(d, e))
28.57/10.29	   A^2 -> H(c, c)
28.57/10.29	   A^2 -> H(c, U1(e, k))
28.57/10.29	   A^2 -> H(c, U1(k, e))
28.57/10.29	   A^2 -> H(c, e)
28.57/10.29	   A^2 -> H(c, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, k), b)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, k), c)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, k), e)
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, c), d)
28.57/10.29	   A^2 -> H(U1(e, c), k)
28.57/10.29	   A^2 -> H(U1(k, e), b)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, e), c)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, c), d)
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, e))
28.57/10.29	
28.57/10.29	The TRS R consists of the following rules:
28.57/10.29	
28.57/10.29	   f(x) -> U1(x, x)
28.57/10.29	   U1(e, x) -> x
28.57/10.29	   a -> c
28.57/10.29	   a -> d
28.57/10.29	   b -> c
28.57/10.29	   b -> d
28.57/10.29	   d -> k
28.57/10.29	   c -> e
28.57/10.29	   c -> k
28.57/10.29	
28.57/10.29	Q is empty.
28.57/10.29	We have to consider all minimal (P,Q,R)-chains.
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2183) DependencyGraphProof (EQUIVALENT)
28.57/10.29	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2184)
28.57/10.29	Obligation:
28.57/10.29	Q DP problem:
28.57/10.29	The TRS P consists of the following rules:
28.57/10.29	
28.57/10.29	   G(d, x, x) -> A^2
28.57/10.29	   A^2 -> H(f(c), f(c))
28.57/10.29	   H(x, x) -> G(x, x, f(k))
28.57/10.29	   A^2 -> H(f(d), f(d))
28.57/10.29	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.29	   A^2 -> H(f(e), f(e))
28.57/10.29	   A^2 -> H(f(k), f(k))
28.57/10.29	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.29	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.29	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.29	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(k, c), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, e), b)
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(c, e), c)
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, e), e)
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, k), b)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(c, k), c)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, k), e)
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, c), d)
28.57/10.29	   A^2 -> H(e, U1(e, b))
28.57/10.29	   A^2 -> H(e, U1(c, d))
28.57/10.29	   A^2 -> H(e, U1(d, c))
28.57/10.29	   A^2 -> H(e, U1(b, e))
28.57/10.29	   A^2 -> H(e, U1(b, k))
28.57/10.29	   A^2 -> H(e, U1(e, c))
28.57/10.29	   A^2 -> H(e, U1(c, e))
28.57/10.29	   A^2 -> H(e, U1(c, k))
28.57/10.29	   A^2 -> H(e, U1(e, e))
28.57/10.29	   A^2 -> H(e, U1(d, k))
28.57/10.29	   A^2 -> H(U1(e, e), b)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, e), c)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.29	   A^2 -> H(f(e), d)
28.57/10.29	   A^2 -> H(f(e), k)
28.57/10.29	   A^2 -> H(U1(k, k), b)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, k), c)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.29	   A^2 -> H(f(k), d)
28.57/10.29	   A^2 -> H(f(k), k)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(k, d), b)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, d), c)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, k), b)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, k), c)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, k), e)
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, d), d)
28.57/10.29	   A^2 -> H(U1(d, d), k)
28.57/10.29	   A^2 -> H(U1(e, c), c)
28.57/10.29	   A^2 -> H(U1(c, c), e)
28.57/10.29	   A^2 -> H(U1(c, c), k)
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(e, e), e)
28.57/10.29	   A^2 -> H(d, U1(e, b))
28.57/10.29	   A^2 -> H(d, U1(k, b))
28.57/10.29	   A^2 -> H(d, U1(c, d))
28.57/10.29	   A^2 -> H(d, U1(d, c))
28.57/10.29	   A^2 -> H(d, U1(b, e))
28.57/10.29	   A^2 -> H(d, U1(b, k))
28.57/10.29	   A^2 -> H(d, U1(e, c))
28.57/10.29	   A^2 -> H(d, U1(k, c))
28.57/10.29	   A^2 -> H(d, U1(c, e))
28.57/10.29	   A^2 -> H(d, U1(c, k))
28.57/10.29	   A^2 -> H(d, U1(e, e))
28.57/10.29	   A^2 -> H(d, U1(k, k))
28.57/10.29	   A^2 -> H(d, U1(k, d))
28.57/10.29	   A^2 -> H(d, U1(d, k))
28.57/10.29	   A^2 -> H(a, b)
28.57/10.29	   A^2 -> H(a, U1(e, d))
28.57/10.29	   A^2 -> H(a, U1(d, e))
28.57/10.29	   A^2 -> H(a, c)
28.57/10.29	   A^2 -> H(a, U1(e, k))
28.57/10.29	   A^2 -> H(a, U1(k, e))
28.57/10.29	   A^2 -> H(a, e)
28.57/10.29	   A^2 -> H(a, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, d), b)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, d), c)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, d), e)
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, a), d)
28.57/10.29	   A^2 -> H(U1(e, a), k)
28.57/10.29	   A^2 -> H(U1(k, a), d)
28.57/10.29	   A^2 -> H(U1(c, d), d)
28.57/10.29	   A^2 -> H(U1(c, d), k)
28.57/10.29	   A^2 -> H(U1(d, e), b)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, e), c)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, e), e)
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, c), d)
28.57/10.29	   A^2 -> H(U1(d, c), k)
28.57/10.29	   A^2 -> H(U1(a, e), d)
28.57/10.29	   A^2 -> H(U1(a, e), k)
28.57/10.29	   A^2 -> H(U1(a, k), d)
28.57/10.29	   A^2 -> H(U1(a, k), k)
28.57/10.29	   A^2 -> H(k, U1(e, b))
28.57/10.29	   A^2 -> H(k, U1(c, d))
28.57/10.29	   A^2 -> H(k, U1(d, c))
28.57/10.29	   A^2 -> H(k, U1(b, e))
28.57/10.29	   A^2 -> H(k, U1(b, k))
28.57/10.29	   A^2 -> H(k, U1(e, c))
28.57/10.29	   A^2 -> H(k, U1(c, e))
28.57/10.29	   A^2 -> H(k, U1(c, k))
28.57/10.29	   A^2 -> H(k, U1(e, e))
28.57/10.29	   A^2 -> H(k, U1(d, k))
28.57/10.29	   A^2 -> H(c, b)
28.57/10.29	   A^2 -> H(c, U1(e, d))
28.57/10.29	   A^2 -> H(c, U1(d, e))
28.57/10.29	   A^2 -> H(c, c)
28.57/10.29	   A^2 -> H(c, U1(e, k))
28.57/10.29	   A^2 -> H(c, U1(k, e))
28.57/10.29	   A^2 -> H(c, e)
28.57/10.29	   A^2 -> H(c, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, k), b)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, k), c)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, k), e)
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, c), d)
28.57/10.29	   A^2 -> H(U1(e, c), k)
28.57/10.29	   A^2 -> H(U1(k, e), b)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, e), c)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, c), d)
28.57/10.29	
28.57/10.29	The TRS R consists of the following rules:
28.57/10.29	
28.57/10.29	   f(x) -> U1(x, x)
28.57/10.29	   U1(e, x) -> x
28.57/10.29	   a -> c
28.57/10.29	   a -> d
28.57/10.29	   b -> c
28.57/10.29	   b -> d
28.57/10.29	   d -> k
28.57/10.29	   c -> e
28.57/10.29	   c -> k
28.57/10.29	
28.57/10.29	Q is empty.
28.57/10.29	We have to consider all minimal (P,Q,R)-chains.
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2185) TransformationProof (EQUIVALENT)
28.57/10.29	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.29	
28.57/10.29	   (A^2 -> H(U1(k, e), U1(k, k)),A^2 -> H(U1(k, e), U1(k, k)))
28.57/10.29	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.57/10.29	
28.57/10.29	
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2186)
28.57/10.29	Obligation:
28.57/10.29	Q DP problem:
28.57/10.29	The TRS P consists of the following rules:
28.57/10.29	
28.57/10.29	   G(d, x, x) -> A^2
28.57/10.29	   A^2 -> H(f(c), f(c))
28.57/10.29	   H(x, x) -> G(x, x, f(k))
28.57/10.29	   A^2 -> H(f(d), f(d))
28.57/10.29	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.29	   A^2 -> H(f(e), f(e))
28.57/10.29	   A^2 -> H(f(k), f(k))
28.57/10.29	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.29	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.29	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.29	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(c, e), b)
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(c, e), c)
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, e), e)
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, k), b)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(c, k), c)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, k), e)
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, c), d)
28.57/10.29	   A^2 -> H(e, U1(e, b))
28.57/10.29	   A^2 -> H(e, U1(c, d))
28.57/10.29	   A^2 -> H(e, U1(d, c))
28.57/10.29	   A^2 -> H(e, U1(b, e))
28.57/10.29	   A^2 -> H(e, U1(b, k))
28.57/10.29	   A^2 -> H(e, U1(e, c))
28.57/10.29	   A^2 -> H(e, U1(c, e))
28.57/10.29	   A^2 -> H(e, U1(c, k))
28.57/10.29	   A^2 -> H(e, U1(e, e))
28.57/10.29	   A^2 -> H(e, U1(d, k))
28.57/10.29	   A^2 -> H(U1(e, e), b)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, e), c)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.29	   A^2 -> H(f(e), d)
28.57/10.29	   A^2 -> H(f(e), k)
28.57/10.29	   A^2 -> H(U1(k, k), b)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, k), c)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.29	   A^2 -> H(f(k), d)
28.57/10.29	   A^2 -> H(f(k), k)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(k, d), b)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, d), c)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, k), b)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, k), c)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, k), e)
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, d), d)
28.57/10.29	   A^2 -> H(U1(d, d), k)
28.57/10.29	   A^2 -> H(U1(e, c), c)
28.57/10.29	   A^2 -> H(U1(c, c), e)
28.57/10.29	   A^2 -> H(U1(c, c), k)
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(e, e), e)
28.57/10.29	   A^2 -> H(d, U1(e, b))
28.57/10.29	   A^2 -> H(d, U1(k, b))
28.57/10.29	   A^2 -> H(d, U1(c, d))
28.57/10.29	   A^2 -> H(d, U1(d, c))
28.57/10.29	   A^2 -> H(d, U1(b, e))
28.57/10.29	   A^2 -> H(d, U1(b, k))
28.57/10.29	   A^2 -> H(d, U1(e, c))
28.57/10.29	   A^2 -> H(d, U1(k, c))
28.57/10.29	   A^2 -> H(d, U1(c, e))
28.57/10.29	   A^2 -> H(d, U1(c, k))
28.57/10.29	   A^2 -> H(d, U1(e, e))
28.57/10.29	   A^2 -> H(d, U1(k, k))
28.57/10.29	   A^2 -> H(d, U1(k, d))
28.57/10.29	   A^2 -> H(d, U1(d, k))
28.57/10.29	   A^2 -> H(a, b)
28.57/10.29	   A^2 -> H(a, U1(e, d))
28.57/10.29	   A^2 -> H(a, U1(d, e))
28.57/10.29	   A^2 -> H(a, c)
28.57/10.29	   A^2 -> H(a, U1(e, k))
28.57/10.29	   A^2 -> H(a, U1(k, e))
28.57/10.29	   A^2 -> H(a, e)
28.57/10.29	   A^2 -> H(a, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, d), b)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, d), c)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, d), e)
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, a), d)
28.57/10.29	   A^2 -> H(U1(e, a), k)
28.57/10.29	   A^2 -> H(U1(k, a), d)
28.57/10.29	   A^2 -> H(U1(c, d), d)
28.57/10.29	   A^2 -> H(U1(c, d), k)
28.57/10.29	   A^2 -> H(U1(d, e), b)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, e), c)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, e), e)
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, c), d)
28.57/10.29	   A^2 -> H(U1(d, c), k)
28.57/10.29	   A^2 -> H(U1(a, e), d)
28.57/10.29	   A^2 -> H(U1(a, e), k)
28.57/10.29	   A^2 -> H(U1(a, k), d)
28.57/10.29	   A^2 -> H(U1(a, k), k)
28.57/10.29	   A^2 -> H(k, U1(e, b))
28.57/10.29	   A^2 -> H(k, U1(c, d))
28.57/10.29	   A^2 -> H(k, U1(d, c))
28.57/10.29	   A^2 -> H(k, U1(b, e))
28.57/10.29	   A^2 -> H(k, U1(b, k))
28.57/10.29	   A^2 -> H(k, U1(e, c))
28.57/10.29	   A^2 -> H(k, U1(c, e))
28.57/10.29	   A^2 -> H(k, U1(c, k))
28.57/10.29	   A^2 -> H(k, U1(e, e))
28.57/10.29	   A^2 -> H(k, U1(d, k))
28.57/10.29	   A^2 -> H(c, b)
28.57/10.29	   A^2 -> H(c, U1(e, d))
28.57/10.29	   A^2 -> H(c, U1(d, e))
28.57/10.29	   A^2 -> H(c, c)
28.57/10.29	   A^2 -> H(c, U1(e, k))
28.57/10.29	   A^2 -> H(c, U1(k, e))
28.57/10.29	   A^2 -> H(c, e)
28.57/10.29	   A^2 -> H(c, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, k), b)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, k), c)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, k), e)
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, c), d)
28.57/10.29	   A^2 -> H(U1(e, c), k)
28.57/10.29	   A^2 -> H(U1(k, e), b)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, e), c)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, c), d)
28.57/10.29	   A^2 -> H(U1(k, e), U1(k, k))
28.57/10.29	
28.57/10.29	The TRS R consists of the following rules:
28.57/10.29	
28.57/10.29	   f(x) -> U1(x, x)
28.57/10.29	   U1(e, x) -> x
28.57/10.29	   a -> c
28.57/10.29	   a -> d
28.57/10.29	   b -> c
28.57/10.29	   b -> d
28.57/10.29	   d -> k
28.57/10.29	   c -> e
28.57/10.29	   c -> k
28.57/10.29	
28.57/10.29	Q is empty.
28.57/10.29	We have to consider all minimal (P,Q,R)-chains.
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2187) DependencyGraphProof (EQUIVALENT)
28.57/10.29	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2188)
28.57/10.29	Obligation:
28.57/10.29	Q DP problem:
28.57/10.29	The TRS P consists of the following rules:
28.57/10.29	
28.57/10.29	   A^2 -> H(f(c), f(c))
28.57/10.29	   H(x, x) -> G(x, x, f(k))
28.57/10.29	   G(d, x, x) -> A^2
28.57/10.29	   A^2 -> H(f(d), f(d))
28.57/10.29	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.29	   A^2 -> H(f(e), f(e))
28.57/10.29	   A^2 -> H(f(k), f(k))
28.57/10.29	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.29	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.29	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.29	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(c, e), b)
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(c, e), c)
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, e), e)
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, k), b)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(c, k), c)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, k), e)
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, c), d)
28.57/10.29	   A^2 -> H(e, U1(e, b))
28.57/10.29	   A^2 -> H(e, U1(c, d))
28.57/10.29	   A^2 -> H(e, U1(d, c))
28.57/10.29	   A^2 -> H(e, U1(b, e))
28.57/10.29	   A^2 -> H(e, U1(b, k))
28.57/10.29	   A^2 -> H(e, U1(e, c))
28.57/10.29	   A^2 -> H(e, U1(c, e))
28.57/10.29	   A^2 -> H(e, U1(c, k))
28.57/10.29	   A^2 -> H(e, U1(e, e))
28.57/10.29	   A^2 -> H(e, U1(d, k))
28.57/10.29	   A^2 -> H(U1(e, e), b)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, e), c)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.29	   A^2 -> H(f(e), d)
28.57/10.29	   A^2 -> H(f(e), k)
28.57/10.29	   A^2 -> H(U1(k, k), b)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, k), c)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.29	   A^2 -> H(f(k), d)
28.57/10.29	   A^2 -> H(f(k), k)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(k, d), b)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, d), c)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, k), b)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, k), c)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, k), e)
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, d), d)
28.57/10.29	   A^2 -> H(U1(d, d), k)
28.57/10.29	   A^2 -> H(U1(e, c), c)
28.57/10.29	   A^2 -> H(U1(c, c), e)
28.57/10.29	   A^2 -> H(U1(c, c), k)
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(e, e), e)
28.57/10.29	   A^2 -> H(d, U1(e, b))
28.57/10.29	   A^2 -> H(d, U1(k, b))
28.57/10.29	   A^2 -> H(d, U1(c, d))
28.57/10.29	   A^2 -> H(d, U1(d, c))
28.57/10.29	   A^2 -> H(d, U1(b, e))
28.57/10.29	   A^2 -> H(d, U1(b, k))
28.57/10.29	   A^2 -> H(d, U1(e, c))
28.57/10.29	   A^2 -> H(d, U1(k, c))
28.57/10.29	   A^2 -> H(d, U1(c, e))
28.57/10.29	   A^2 -> H(d, U1(c, k))
28.57/10.29	   A^2 -> H(d, U1(e, e))
28.57/10.29	   A^2 -> H(d, U1(k, k))
28.57/10.29	   A^2 -> H(d, U1(k, d))
28.57/10.29	   A^2 -> H(d, U1(d, k))
28.57/10.29	   A^2 -> H(a, b)
28.57/10.29	   A^2 -> H(a, U1(e, d))
28.57/10.29	   A^2 -> H(a, U1(d, e))
28.57/10.29	   A^2 -> H(a, c)
28.57/10.29	   A^2 -> H(a, U1(e, k))
28.57/10.29	   A^2 -> H(a, U1(k, e))
28.57/10.29	   A^2 -> H(a, e)
28.57/10.29	   A^2 -> H(a, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, d), b)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, d), c)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, d), e)
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, a), d)
28.57/10.29	   A^2 -> H(U1(e, a), k)
28.57/10.29	   A^2 -> H(U1(k, a), d)
28.57/10.29	   A^2 -> H(U1(c, d), d)
28.57/10.29	   A^2 -> H(U1(c, d), k)
28.57/10.29	   A^2 -> H(U1(d, e), b)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, e), c)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, e), e)
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, c), d)
28.57/10.29	   A^2 -> H(U1(d, c), k)
28.57/10.29	   A^2 -> H(U1(a, e), d)
28.57/10.29	   A^2 -> H(U1(a, e), k)
28.57/10.29	   A^2 -> H(U1(a, k), d)
28.57/10.29	   A^2 -> H(U1(a, k), k)
28.57/10.29	   A^2 -> H(k, U1(e, b))
28.57/10.29	   A^2 -> H(k, U1(c, d))
28.57/10.29	   A^2 -> H(k, U1(d, c))
28.57/10.29	   A^2 -> H(k, U1(b, e))
28.57/10.29	   A^2 -> H(k, U1(b, k))
28.57/10.29	   A^2 -> H(k, U1(e, c))
28.57/10.29	   A^2 -> H(k, U1(c, e))
28.57/10.29	   A^2 -> H(k, U1(c, k))
28.57/10.29	   A^2 -> H(k, U1(e, e))
28.57/10.29	   A^2 -> H(k, U1(d, k))
28.57/10.29	   A^2 -> H(c, b)
28.57/10.29	   A^2 -> H(c, U1(e, d))
28.57/10.29	   A^2 -> H(c, U1(d, e))
28.57/10.29	   A^2 -> H(c, c)
28.57/10.29	   A^2 -> H(c, U1(e, k))
28.57/10.29	   A^2 -> H(c, U1(k, e))
28.57/10.29	   A^2 -> H(c, e)
28.57/10.29	   A^2 -> H(c, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, k), b)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, k), c)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, k), e)
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, c), d)
28.57/10.29	   A^2 -> H(U1(e, c), k)
28.57/10.29	   A^2 -> H(U1(k, e), b)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, e), c)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, c), d)
28.57/10.29	
28.57/10.29	The TRS R consists of the following rules:
28.57/10.29	
28.57/10.29	   f(x) -> U1(x, x)
28.57/10.29	   U1(e, x) -> x
28.57/10.29	   a -> c
28.57/10.29	   a -> d
28.57/10.29	   b -> c
28.57/10.29	   b -> d
28.57/10.29	   d -> k
28.57/10.29	   c -> e
28.57/10.29	   c -> k
28.57/10.29	
28.57/10.29	Q is empty.
28.57/10.29	We have to consider all minimal (P,Q,R)-chains.
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2189) TransformationProof (EQUIVALENT)
28.57/10.29	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), b) at position [] we obtained the following new rules [LPAR04]:
28.57/10.29	
28.57/10.29	   (A^2 -> H(U1(e, e), b),A^2 -> H(U1(e, e), b))
28.57/10.29	   (A^2 -> H(U1(k, e), b),A^2 -> H(U1(k, e), b))
28.57/10.29	   (A^2 -> H(U1(c, e), c),A^2 -> H(U1(c, e), c))
28.57/10.29	   (A^2 -> H(U1(c, e), d),A^2 -> H(U1(c, e), d))
28.57/10.29	
28.57/10.29	
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2190)
28.57/10.29	Obligation:
28.57/10.29	Q DP problem:
28.57/10.29	The TRS P consists of the following rules:
28.57/10.29	
28.57/10.29	   A^2 -> H(f(c), f(c))
28.57/10.29	   H(x, x) -> G(x, x, f(k))
28.57/10.29	   G(d, x, x) -> A^2
28.57/10.29	   A^2 -> H(f(d), f(d))
28.57/10.29	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.29	   A^2 -> H(f(e), f(e))
28.57/10.29	   A^2 -> H(f(k), f(k))
28.57/10.29	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.29	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.29	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.29	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(c, e), c)
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, e), e)
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, k), b)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(c, k), c)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, k), e)
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, c), d)
28.57/10.29	   A^2 -> H(e, U1(e, b))
28.57/10.29	   A^2 -> H(e, U1(c, d))
28.57/10.29	   A^2 -> H(e, U1(d, c))
28.57/10.29	   A^2 -> H(e, U1(b, e))
28.57/10.29	   A^2 -> H(e, U1(b, k))
28.57/10.29	   A^2 -> H(e, U1(e, c))
28.57/10.29	   A^2 -> H(e, U1(c, e))
28.57/10.29	   A^2 -> H(e, U1(c, k))
28.57/10.29	   A^2 -> H(e, U1(e, e))
28.57/10.29	   A^2 -> H(e, U1(d, k))
28.57/10.29	   A^2 -> H(U1(e, e), b)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, e), c)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.29	   A^2 -> H(f(e), d)
28.57/10.29	   A^2 -> H(f(e), k)
28.57/10.29	   A^2 -> H(U1(k, k), b)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, k), c)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.29	   A^2 -> H(f(k), d)
28.57/10.29	   A^2 -> H(f(k), k)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(k, d), b)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, d), c)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, k), b)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, k), c)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, k), e)
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, d), d)
28.57/10.29	   A^2 -> H(U1(d, d), k)
28.57/10.29	   A^2 -> H(U1(e, c), c)
28.57/10.29	   A^2 -> H(U1(c, c), e)
28.57/10.29	   A^2 -> H(U1(c, c), k)
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(e, e), e)
28.57/10.29	   A^2 -> H(d, U1(e, b))
28.57/10.29	   A^2 -> H(d, U1(k, b))
28.57/10.29	   A^2 -> H(d, U1(c, d))
28.57/10.29	   A^2 -> H(d, U1(d, c))
28.57/10.29	   A^2 -> H(d, U1(b, e))
28.57/10.29	   A^2 -> H(d, U1(b, k))
28.57/10.29	   A^2 -> H(d, U1(e, c))
28.57/10.29	   A^2 -> H(d, U1(k, c))
28.57/10.29	   A^2 -> H(d, U1(c, e))
28.57/10.29	   A^2 -> H(d, U1(c, k))
28.57/10.29	   A^2 -> H(d, U1(e, e))
28.57/10.29	   A^2 -> H(d, U1(k, k))
28.57/10.29	   A^2 -> H(d, U1(k, d))
28.57/10.29	   A^2 -> H(d, U1(d, k))
28.57/10.29	   A^2 -> H(a, b)
28.57/10.29	   A^2 -> H(a, U1(e, d))
28.57/10.29	   A^2 -> H(a, U1(d, e))
28.57/10.29	   A^2 -> H(a, c)
28.57/10.29	   A^2 -> H(a, U1(e, k))
28.57/10.29	   A^2 -> H(a, U1(k, e))
28.57/10.29	   A^2 -> H(a, e)
28.57/10.29	   A^2 -> H(a, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, d), b)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, d), c)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, d), e)
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, a), d)
28.57/10.29	   A^2 -> H(U1(e, a), k)
28.57/10.29	   A^2 -> H(U1(k, a), d)
28.57/10.29	   A^2 -> H(U1(c, d), d)
28.57/10.29	   A^2 -> H(U1(c, d), k)
28.57/10.29	   A^2 -> H(U1(d, e), b)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, e), c)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, e), e)
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, c), d)
28.57/10.29	   A^2 -> H(U1(d, c), k)
28.57/10.29	   A^2 -> H(U1(a, e), d)
28.57/10.29	   A^2 -> H(U1(a, e), k)
28.57/10.29	   A^2 -> H(U1(a, k), d)
28.57/10.29	   A^2 -> H(U1(a, k), k)
28.57/10.29	   A^2 -> H(k, U1(e, b))
28.57/10.29	   A^2 -> H(k, U1(c, d))
28.57/10.29	   A^2 -> H(k, U1(d, c))
28.57/10.29	   A^2 -> H(k, U1(b, e))
28.57/10.29	   A^2 -> H(k, U1(b, k))
28.57/10.29	   A^2 -> H(k, U1(e, c))
28.57/10.29	   A^2 -> H(k, U1(c, e))
28.57/10.29	   A^2 -> H(k, U1(c, k))
28.57/10.29	   A^2 -> H(k, U1(e, e))
28.57/10.29	   A^2 -> H(k, U1(d, k))
28.57/10.29	   A^2 -> H(c, b)
28.57/10.29	   A^2 -> H(c, U1(e, d))
28.57/10.29	   A^2 -> H(c, U1(d, e))
28.57/10.29	   A^2 -> H(c, c)
28.57/10.29	   A^2 -> H(c, U1(e, k))
28.57/10.29	   A^2 -> H(c, U1(k, e))
28.57/10.29	   A^2 -> H(c, e)
28.57/10.29	   A^2 -> H(c, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, k), b)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, k), c)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, k), e)
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, c), d)
28.57/10.29	   A^2 -> H(U1(e, c), k)
28.57/10.29	   A^2 -> H(U1(k, e), b)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, e), c)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, c), d)
28.57/10.29	   A^2 -> H(U1(c, e), d)
28.57/10.29	
28.57/10.29	The TRS R consists of the following rules:
28.57/10.29	
28.57/10.29	   f(x) -> U1(x, x)
28.57/10.29	   U1(e, x) -> x
28.57/10.29	   a -> c
28.57/10.29	   a -> d
28.57/10.29	   b -> c
28.57/10.29	   b -> d
28.57/10.29	   d -> k
28.57/10.29	   c -> e
28.57/10.29	   c -> k
28.57/10.29	
28.57/10.29	Q is empty.
28.57/10.29	We have to consider all minimal (P,Q,R)-chains.
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2191) TransformationProof (EQUIVALENT)
28.57/10.29	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.29	
28.57/10.29	   (A^2 -> H(U1(e, e), U1(e, d)),A^2 -> H(U1(e, e), U1(e, d)))
28.57/10.29	   (A^2 -> H(U1(k, e), U1(e, d)),A^2 -> H(U1(k, e), U1(e, d)))
28.57/10.29	   (A^2 -> H(U1(c, e), d),A^2 -> H(U1(c, e), d))
28.57/10.29	   (A^2 -> H(U1(c, e), U1(e, k)),A^2 -> H(U1(c, e), U1(e, k)))
28.57/10.29	
28.57/10.29	
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2192)
28.57/10.29	Obligation:
28.57/10.29	Q DP problem:
28.57/10.29	The TRS P consists of the following rules:
28.57/10.29	
28.57/10.29	   A^2 -> H(f(c), f(c))
28.57/10.29	   H(x, x) -> G(x, x, f(k))
28.57/10.29	   G(d, x, x) -> A^2
28.57/10.29	   A^2 -> H(f(d), f(d))
28.57/10.29	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.29	   A^2 -> H(f(e), f(e))
28.57/10.29	   A^2 -> H(f(k), f(k))
28.57/10.29	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.29	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.29	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.29	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(c, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(c, e), c)
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, e), e)
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, k), b)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(c, k), c)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, k), e)
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, c), d)
28.57/10.29	   A^2 -> H(e, U1(e, b))
28.57/10.29	   A^2 -> H(e, U1(c, d))
28.57/10.29	   A^2 -> H(e, U1(d, c))
28.57/10.29	   A^2 -> H(e, U1(b, e))
28.57/10.29	   A^2 -> H(e, U1(b, k))
28.57/10.29	   A^2 -> H(e, U1(e, c))
28.57/10.29	   A^2 -> H(e, U1(c, e))
28.57/10.29	   A^2 -> H(e, U1(c, k))
28.57/10.29	   A^2 -> H(e, U1(e, e))
28.57/10.29	   A^2 -> H(e, U1(d, k))
28.57/10.29	   A^2 -> H(U1(e, e), b)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, e), c)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.29	   A^2 -> H(f(e), d)
28.57/10.29	   A^2 -> H(f(e), k)
28.57/10.29	   A^2 -> H(U1(k, k), b)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, k), c)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.29	   A^2 -> H(f(k), d)
28.57/10.29	   A^2 -> H(f(k), k)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(k, d), b)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, d), c)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, k), b)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, k), c)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, k), e)
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, d), d)
28.57/10.29	   A^2 -> H(U1(d, d), k)
28.57/10.29	   A^2 -> H(U1(e, c), c)
28.57/10.29	   A^2 -> H(U1(c, c), e)
28.57/10.29	   A^2 -> H(U1(c, c), k)
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(e, e), e)
28.57/10.29	   A^2 -> H(d, U1(e, b))
28.57/10.29	   A^2 -> H(d, U1(k, b))
28.57/10.29	   A^2 -> H(d, U1(c, d))
28.57/10.29	   A^2 -> H(d, U1(d, c))
28.57/10.29	   A^2 -> H(d, U1(b, e))
28.57/10.29	   A^2 -> H(d, U1(b, k))
28.57/10.29	   A^2 -> H(d, U1(e, c))
28.57/10.29	   A^2 -> H(d, U1(k, c))
28.57/10.29	   A^2 -> H(d, U1(c, e))
28.57/10.29	   A^2 -> H(d, U1(c, k))
28.57/10.29	   A^2 -> H(d, U1(e, e))
28.57/10.29	   A^2 -> H(d, U1(k, k))
28.57/10.29	   A^2 -> H(d, U1(k, d))
28.57/10.29	   A^2 -> H(d, U1(d, k))
28.57/10.29	   A^2 -> H(a, b)
28.57/10.29	   A^2 -> H(a, U1(e, d))
28.57/10.29	   A^2 -> H(a, U1(d, e))
28.57/10.29	   A^2 -> H(a, c)
28.57/10.29	   A^2 -> H(a, U1(e, k))
28.57/10.29	   A^2 -> H(a, U1(k, e))
28.57/10.29	   A^2 -> H(a, e)
28.57/10.29	   A^2 -> H(a, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, d), b)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, d), c)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, d), e)
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, a), d)
28.57/10.29	   A^2 -> H(U1(e, a), k)
28.57/10.29	   A^2 -> H(U1(k, a), d)
28.57/10.29	   A^2 -> H(U1(c, d), d)
28.57/10.29	   A^2 -> H(U1(c, d), k)
28.57/10.29	   A^2 -> H(U1(d, e), b)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, e), c)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, e), e)
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, c), d)
28.57/10.29	   A^2 -> H(U1(d, c), k)
28.57/10.29	   A^2 -> H(U1(a, e), d)
28.57/10.29	   A^2 -> H(U1(a, e), k)
28.57/10.29	   A^2 -> H(U1(a, k), d)
28.57/10.29	   A^2 -> H(U1(a, k), k)
28.57/10.29	   A^2 -> H(k, U1(e, b))
28.57/10.29	   A^2 -> H(k, U1(c, d))
28.57/10.29	   A^2 -> H(k, U1(d, c))
28.57/10.29	   A^2 -> H(k, U1(b, e))
28.57/10.29	   A^2 -> H(k, U1(b, k))
28.57/10.29	   A^2 -> H(k, U1(e, c))
28.57/10.29	   A^2 -> H(k, U1(c, e))
28.57/10.29	   A^2 -> H(k, U1(c, k))
28.57/10.29	   A^2 -> H(k, U1(e, e))
28.57/10.29	   A^2 -> H(k, U1(d, k))
28.57/10.29	   A^2 -> H(c, b)
28.57/10.29	   A^2 -> H(c, U1(e, d))
28.57/10.29	   A^2 -> H(c, U1(d, e))
28.57/10.29	   A^2 -> H(c, c)
28.57/10.29	   A^2 -> H(c, U1(e, k))
28.57/10.29	   A^2 -> H(c, U1(k, e))
28.57/10.29	   A^2 -> H(c, e)
28.57/10.29	   A^2 -> H(c, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, k), b)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, k), c)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, k), e)
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, c), d)
28.57/10.29	   A^2 -> H(U1(e, c), k)
28.57/10.29	   A^2 -> H(U1(k, e), b)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, e), c)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, c), d)
28.57/10.29	   A^2 -> H(U1(c, e), d)
28.57/10.29	
28.57/10.29	The TRS R consists of the following rules:
28.57/10.29	
28.57/10.29	   f(x) -> U1(x, x)
28.57/10.29	   U1(e, x) -> x
28.57/10.29	   a -> c
28.57/10.29	   a -> d
28.57/10.29	   b -> c
28.57/10.29	   b -> d
28.57/10.29	   d -> k
28.57/10.29	   c -> e
28.57/10.29	   c -> k
28.57/10.29	
28.57/10.29	Q is empty.
28.57/10.29	We have to consider all minimal (P,Q,R)-chains.
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2193) TransformationProof (EQUIVALENT)
28.57/10.29	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.29	
28.57/10.29	   (A^2 -> H(U1(e, e), U1(d, e)),A^2 -> H(U1(e, e), U1(d, e)))
28.57/10.29	   (A^2 -> H(U1(k, e), U1(d, e)),A^2 -> H(U1(k, e), U1(d, e)))
28.57/10.29	   (A^2 -> H(U1(c, e), U1(k, e)),A^2 -> H(U1(c, e), U1(k, e)))
28.57/10.29	
28.57/10.29	
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2194)
28.57/10.29	Obligation:
28.57/10.29	Q DP problem:
28.57/10.29	The TRS P consists of the following rules:
28.57/10.29	
28.57/10.29	   A^2 -> H(f(c), f(c))
28.57/10.29	   H(x, x) -> G(x, x, f(k))
28.57/10.29	   G(d, x, x) -> A^2
28.57/10.29	   A^2 -> H(f(d), f(d))
28.57/10.29	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.29	   A^2 -> H(f(e), f(e))
28.57/10.29	   A^2 -> H(f(k), f(k))
28.57/10.29	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.29	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.29	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.29	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(c, e), c)
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, e), e)
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, k), b)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(c, k), c)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, k), e)
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, c), d)
28.57/10.29	   A^2 -> H(e, U1(e, b))
28.57/10.29	   A^2 -> H(e, U1(c, d))
28.57/10.29	   A^2 -> H(e, U1(d, c))
28.57/10.29	   A^2 -> H(e, U1(b, e))
28.57/10.29	   A^2 -> H(e, U1(b, k))
28.57/10.29	   A^2 -> H(e, U1(e, c))
28.57/10.29	   A^2 -> H(e, U1(c, e))
28.57/10.29	   A^2 -> H(e, U1(c, k))
28.57/10.29	   A^2 -> H(e, U1(e, e))
28.57/10.29	   A^2 -> H(e, U1(d, k))
28.57/10.29	   A^2 -> H(U1(e, e), b)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, e), c)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.29	   A^2 -> H(f(e), d)
28.57/10.29	   A^2 -> H(f(e), k)
28.57/10.29	   A^2 -> H(U1(k, k), b)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, k), c)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.29	   A^2 -> H(f(k), d)
28.57/10.29	   A^2 -> H(f(k), k)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(k, d), b)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, d), c)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, k), b)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, k), c)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, k), e)
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, d), d)
28.57/10.29	   A^2 -> H(U1(d, d), k)
28.57/10.29	   A^2 -> H(U1(e, c), c)
28.57/10.29	   A^2 -> H(U1(c, c), e)
28.57/10.29	   A^2 -> H(U1(c, c), k)
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(e, e), e)
28.57/10.29	   A^2 -> H(d, U1(e, b))
28.57/10.29	   A^2 -> H(d, U1(k, b))
28.57/10.29	   A^2 -> H(d, U1(c, d))
28.57/10.29	   A^2 -> H(d, U1(d, c))
28.57/10.29	   A^2 -> H(d, U1(b, e))
28.57/10.29	   A^2 -> H(d, U1(b, k))
28.57/10.29	   A^2 -> H(d, U1(e, c))
28.57/10.29	   A^2 -> H(d, U1(k, c))
28.57/10.29	   A^2 -> H(d, U1(c, e))
28.57/10.29	   A^2 -> H(d, U1(c, k))
28.57/10.29	   A^2 -> H(d, U1(e, e))
28.57/10.29	   A^2 -> H(d, U1(k, k))
28.57/10.29	   A^2 -> H(d, U1(k, d))
28.57/10.29	   A^2 -> H(d, U1(d, k))
28.57/10.29	   A^2 -> H(a, b)
28.57/10.29	   A^2 -> H(a, U1(e, d))
28.57/10.29	   A^2 -> H(a, U1(d, e))
28.57/10.29	   A^2 -> H(a, c)
28.57/10.29	   A^2 -> H(a, U1(e, k))
28.57/10.29	   A^2 -> H(a, U1(k, e))
28.57/10.29	   A^2 -> H(a, e)
28.57/10.29	   A^2 -> H(a, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, d), b)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, d), c)
28.57/10.29	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, d), e)
28.57/10.29	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, a), d)
28.57/10.29	   A^2 -> H(U1(e, a), k)
28.57/10.29	   A^2 -> H(U1(k, a), d)
28.57/10.29	   A^2 -> H(U1(c, d), d)
28.57/10.29	   A^2 -> H(U1(c, d), k)
28.57/10.29	   A^2 -> H(U1(d, e), b)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, e), c)
28.57/10.29	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, e), e)
28.57/10.29	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, c), d)
28.57/10.29	   A^2 -> H(U1(d, c), k)
28.57/10.29	   A^2 -> H(U1(a, e), d)
28.57/10.29	   A^2 -> H(U1(a, e), k)
28.57/10.29	   A^2 -> H(U1(a, k), d)
28.57/10.29	   A^2 -> H(U1(a, k), k)
28.57/10.29	   A^2 -> H(k, U1(e, b))
28.57/10.29	   A^2 -> H(k, U1(c, d))
28.57/10.29	   A^2 -> H(k, U1(d, c))
28.57/10.29	   A^2 -> H(k, U1(b, e))
28.57/10.29	   A^2 -> H(k, U1(b, k))
28.57/10.29	   A^2 -> H(k, U1(e, c))
28.57/10.29	   A^2 -> H(k, U1(c, e))
28.57/10.29	   A^2 -> H(k, U1(c, k))
28.57/10.29	   A^2 -> H(k, U1(e, e))
28.57/10.29	   A^2 -> H(k, U1(d, k))
28.57/10.29	   A^2 -> H(c, b)
28.57/10.29	   A^2 -> H(c, U1(e, d))
28.57/10.29	   A^2 -> H(c, U1(d, e))
28.57/10.29	   A^2 -> H(c, c)
28.57/10.29	   A^2 -> H(c, U1(e, k))
28.57/10.29	   A^2 -> H(c, U1(k, e))
28.57/10.29	   A^2 -> H(c, e)
28.57/10.29	   A^2 -> H(c, U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, k), b)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, k), c)
28.57/10.29	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, k), e)
28.57/10.29	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(e, c), d)
28.57/10.29	   A^2 -> H(U1(e, c), k)
28.57/10.29	   A^2 -> H(U1(k, e), b)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, e), c)
28.57/10.29	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, c), d)
28.57/10.29	   A^2 -> H(U1(c, e), d)
28.57/10.29	
28.57/10.29	The TRS R consists of the following rules:
28.57/10.29	
28.57/10.29	   f(x) -> U1(x, x)
28.57/10.29	   U1(e, x) -> x
28.57/10.29	   a -> c
28.57/10.29	   a -> d
28.57/10.29	   b -> c
28.57/10.29	   b -> d
28.57/10.29	   d -> k
28.57/10.29	   c -> e
28.57/10.29	   c -> k
28.57/10.29	
28.57/10.29	Q is empty.
28.57/10.29	We have to consider all minimal (P,Q,R)-chains.
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2195) TransformationProof (EQUIVALENT)
28.57/10.29	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), c) at position [] we obtained the following new rules [LPAR04]:
28.57/10.29	
28.57/10.29	   (A^2 -> H(U1(e, e), c),A^2 -> H(U1(e, e), c))
28.57/10.29	   (A^2 -> H(U1(k, e), c),A^2 -> H(U1(k, e), c))
28.57/10.29	   (A^2 -> H(U1(c, e), e),A^2 -> H(U1(c, e), e))
28.57/10.29	   (A^2 -> H(U1(c, e), k),A^2 -> H(U1(c, e), k))
28.57/10.29	
28.57/10.29	
28.57/10.29	----------------------------------------
28.57/10.29	
28.57/10.29	(2196)
28.57/10.29	Obligation:
28.57/10.29	Q DP problem:
28.57/10.29	The TRS P consists of the following rules:
28.57/10.29	
28.57/10.29	   A^2 -> H(f(c), f(c))
28.57/10.29	   H(x, x) -> G(x, x, f(k))
28.57/10.29	   G(d, x, x) -> A^2
28.57/10.29	   A^2 -> H(f(d), f(d))
28.57/10.29	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.29	   A^2 -> H(f(e), f(e))
28.57/10.29	   A^2 -> H(f(k), f(k))
28.57/10.29	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.29	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.29	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.29	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.29	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(c, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, e), e)
28.57/10.29	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, k), b)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(c, k), c)
28.57/10.29	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(c, k), e)
28.57/10.29	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(c, c), d)
28.57/10.29	   A^2 -> H(e, U1(e, b))
28.57/10.29	   A^2 -> H(e, U1(c, d))
28.57/10.29	   A^2 -> H(e, U1(d, c))
28.57/10.29	   A^2 -> H(e, U1(b, e))
28.57/10.29	   A^2 -> H(e, U1(b, k))
28.57/10.29	   A^2 -> H(e, U1(e, c))
28.57/10.29	   A^2 -> H(e, U1(c, e))
28.57/10.29	   A^2 -> H(e, U1(c, k))
28.57/10.29	   A^2 -> H(e, U1(e, e))
28.57/10.29	   A^2 -> H(e, U1(d, k))
28.57/10.29	   A^2 -> H(U1(e, e), b)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.29	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.29	   A^2 -> H(U1(e, e), c)
28.57/10.29	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.29	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.29	   A^2 -> H(f(e), d)
28.57/10.29	   A^2 -> H(f(e), k)
28.57/10.29	   A^2 -> H(U1(k, k), b)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, k), c)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.29	   A^2 -> H(f(k), d)
28.57/10.29	   A^2 -> H(f(k), k)
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.29	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.29	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.29	   A^2 -> H(U1(k, d), b)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.29	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.29	   A^2 -> H(U1(k, d), c)
28.57/10.29	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.29	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, k), b)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.29	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.29	   A^2 -> H(U1(d, k), c)
28.57/10.29	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.29	   A^2 -> H(U1(d, k), e)
28.57/10.29	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.29	   A^2 -> H(U1(d, d), d)
28.57/10.29	   A^2 -> H(U1(d, d), k)
28.57/10.29	   A^2 -> H(U1(e, c), c)
28.57/10.29	   A^2 -> H(U1(c, c), e)
28.57/10.29	   A^2 -> H(U1(c, c), k)
28.57/10.29	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.29	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(e, e), e)
28.57/10.30	   A^2 -> H(d, U1(e, b))
28.57/10.30	   A^2 -> H(d, U1(k, b))
28.57/10.30	   A^2 -> H(d, U1(c, d))
28.57/10.30	   A^2 -> H(d, U1(d, c))
28.57/10.30	   A^2 -> H(d, U1(b, e))
28.57/10.30	   A^2 -> H(d, U1(b, k))
28.57/10.30	   A^2 -> H(d, U1(e, c))
28.57/10.30	   A^2 -> H(d, U1(k, c))
28.57/10.30	   A^2 -> H(d, U1(c, e))
28.57/10.30	   A^2 -> H(d, U1(c, k))
28.57/10.30	   A^2 -> H(d, U1(e, e))
28.57/10.30	   A^2 -> H(d, U1(k, k))
28.57/10.30	   A^2 -> H(d, U1(k, d))
28.57/10.30	   A^2 -> H(d, U1(d, k))
28.57/10.30	   A^2 -> H(a, b)
28.57/10.30	   A^2 -> H(a, U1(e, d))
28.57/10.30	   A^2 -> H(a, U1(d, e))
28.57/10.30	   A^2 -> H(a, c)
28.57/10.30	   A^2 -> H(a, U1(e, k))
28.57/10.30	   A^2 -> H(a, U1(k, e))
28.57/10.30	   A^2 -> H(a, e)
28.57/10.30	   A^2 -> H(a, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, d), b)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, d), c)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, d), e)
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, a), d)
28.57/10.30	   A^2 -> H(U1(e, a), k)
28.57/10.30	   A^2 -> H(U1(k, a), d)
28.57/10.30	   A^2 -> H(U1(c, d), d)
28.57/10.30	   A^2 -> H(U1(c, d), k)
28.57/10.30	   A^2 -> H(U1(d, e), b)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, e), c)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, e), e)
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, c), d)
28.57/10.30	   A^2 -> H(U1(d, c), k)
28.57/10.30	   A^2 -> H(U1(a, e), d)
28.57/10.30	   A^2 -> H(U1(a, e), k)
28.57/10.30	   A^2 -> H(U1(a, k), d)
28.57/10.30	   A^2 -> H(U1(a, k), k)
28.57/10.30	   A^2 -> H(k, U1(e, b))
28.57/10.30	   A^2 -> H(k, U1(c, d))
28.57/10.30	   A^2 -> H(k, U1(d, c))
28.57/10.30	   A^2 -> H(k, U1(b, e))
28.57/10.30	   A^2 -> H(k, U1(b, k))
28.57/10.30	   A^2 -> H(k, U1(e, c))
28.57/10.30	   A^2 -> H(k, U1(c, e))
28.57/10.30	   A^2 -> H(k, U1(c, k))
28.57/10.30	   A^2 -> H(k, U1(e, e))
28.57/10.30	   A^2 -> H(k, U1(d, k))
28.57/10.30	   A^2 -> H(c, b)
28.57/10.30	   A^2 -> H(c, U1(e, d))
28.57/10.30	   A^2 -> H(c, U1(d, e))
28.57/10.30	   A^2 -> H(c, c)
28.57/10.30	   A^2 -> H(c, U1(e, k))
28.57/10.30	   A^2 -> H(c, U1(k, e))
28.57/10.30	   A^2 -> H(c, e)
28.57/10.30	   A^2 -> H(c, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, k), b)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, k), c)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, k), e)
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, c), d)
28.57/10.30	   A^2 -> H(U1(e, c), k)
28.57/10.30	   A^2 -> H(U1(k, e), b)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, e), c)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, c), d)
28.57/10.30	   A^2 -> H(U1(c, e), d)
28.57/10.30	   A^2 -> H(U1(c, e), k)
28.57/10.30	
28.57/10.30	The TRS R consists of the following rules:
28.57/10.30	
28.57/10.30	   f(x) -> U1(x, x)
28.57/10.30	   U1(e, x) -> x
28.57/10.30	   a -> c
28.57/10.30	   a -> d
28.57/10.30	   b -> c
28.57/10.30	   b -> d
28.57/10.30	   d -> k
28.57/10.30	   c -> e
28.57/10.30	   c -> k
28.57/10.30	
28.57/10.30	Q is empty.
28.57/10.30	We have to consider all minimal (P,Q,R)-chains.
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2197) TransformationProof (EQUIVALENT)
28.57/10.30	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.30	
28.57/10.30	   (A^2 -> H(U1(e, e), U1(e, k)),A^2 -> H(U1(e, e), U1(e, k)))
28.57/10.30	   (A^2 -> H(U1(k, e), U1(e, k)),A^2 -> H(U1(k, e), U1(e, k)))
28.57/10.30	   (A^2 -> H(U1(c, e), k),A^2 -> H(U1(c, e), k))
28.57/10.30	
28.57/10.30	
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2198)
28.57/10.30	Obligation:
28.57/10.30	Q DP problem:
28.57/10.30	The TRS P consists of the following rules:
28.57/10.30	
28.57/10.30	   A^2 -> H(f(c), f(c))
28.57/10.30	   H(x, x) -> G(x, x, f(k))
28.57/10.30	   G(d, x, x) -> A^2
28.57/10.30	   A^2 -> H(f(d), f(d))
28.57/10.30	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.30	   A^2 -> H(f(e), f(e))
28.57/10.30	   A^2 -> H(f(k), f(k))
28.57/10.30	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.30	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.30	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.30	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(c, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(c, e), e)
28.57/10.30	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.30	   A^2 -> H(U1(c, k), b)
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(c, k), c)
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(c, k), e)
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(c, c), d)
28.57/10.30	   A^2 -> H(e, U1(e, b))
28.57/10.30	   A^2 -> H(e, U1(c, d))
28.57/10.30	   A^2 -> H(e, U1(d, c))
28.57/10.30	   A^2 -> H(e, U1(b, e))
28.57/10.30	   A^2 -> H(e, U1(b, k))
28.57/10.30	   A^2 -> H(e, U1(e, c))
28.57/10.30	   A^2 -> H(e, U1(c, e))
28.57/10.30	   A^2 -> H(e, U1(c, k))
28.57/10.30	   A^2 -> H(e, U1(e, e))
28.57/10.30	   A^2 -> H(e, U1(d, k))
28.57/10.30	   A^2 -> H(U1(e, e), b)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, e), c)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.30	   A^2 -> H(f(e), d)
28.57/10.30	   A^2 -> H(f(e), k)
28.57/10.30	   A^2 -> H(U1(k, k), b)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, k), c)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.30	   A^2 -> H(f(k), d)
28.57/10.30	   A^2 -> H(f(k), k)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(k, d), b)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, d), c)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, k), b)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, k), c)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, k), e)
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, d), d)
28.57/10.30	   A^2 -> H(U1(d, d), k)
28.57/10.30	   A^2 -> H(U1(e, c), c)
28.57/10.30	   A^2 -> H(U1(c, c), e)
28.57/10.30	   A^2 -> H(U1(c, c), k)
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(e, e), e)
28.57/10.30	   A^2 -> H(d, U1(e, b))
28.57/10.30	   A^2 -> H(d, U1(k, b))
28.57/10.30	   A^2 -> H(d, U1(c, d))
28.57/10.30	   A^2 -> H(d, U1(d, c))
28.57/10.30	   A^2 -> H(d, U1(b, e))
28.57/10.30	   A^2 -> H(d, U1(b, k))
28.57/10.30	   A^2 -> H(d, U1(e, c))
28.57/10.30	   A^2 -> H(d, U1(k, c))
28.57/10.30	   A^2 -> H(d, U1(c, e))
28.57/10.30	   A^2 -> H(d, U1(c, k))
28.57/10.30	   A^2 -> H(d, U1(e, e))
28.57/10.30	   A^2 -> H(d, U1(k, k))
28.57/10.30	   A^2 -> H(d, U1(k, d))
28.57/10.30	   A^2 -> H(d, U1(d, k))
28.57/10.30	   A^2 -> H(a, b)
28.57/10.30	   A^2 -> H(a, U1(e, d))
28.57/10.30	   A^2 -> H(a, U1(d, e))
28.57/10.30	   A^2 -> H(a, c)
28.57/10.30	   A^2 -> H(a, U1(e, k))
28.57/10.30	   A^2 -> H(a, U1(k, e))
28.57/10.30	   A^2 -> H(a, e)
28.57/10.30	   A^2 -> H(a, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, d), b)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, d), c)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, d), e)
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, a), d)
28.57/10.30	   A^2 -> H(U1(e, a), k)
28.57/10.30	   A^2 -> H(U1(k, a), d)
28.57/10.30	   A^2 -> H(U1(c, d), d)
28.57/10.30	   A^2 -> H(U1(c, d), k)
28.57/10.30	   A^2 -> H(U1(d, e), b)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, e), c)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, e), e)
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, c), d)
28.57/10.30	   A^2 -> H(U1(d, c), k)
28.57/10.30	   A^2 -> H(U1(a, e), d)
28.57/10.30	   A^2 -> H(U1(a, e), k)
28.57/10.30	   A^2 -> H(U1(a, k), d)
28.57/10.30	   A^2 -> H(U1(a, k), k)
28.57/10.30	   A^2 -> H(k, U1(e, b))
28.57/10.30	   A^2 -> H(k, U1(c, d))
28.57/10.30	   A^2 -> H(k, U1(d, c))
28.57/10.30	   A^2 -> H(k, U1(b, e))
28.57/10.30	   A^2 -> H(k, U1(b, k))
28.57/10.30	   A^2 -> H(k, U1(e, c))
28.57/10.30	   A^2 -> H(k, U1(c, e))
28.57/10.30	   A^2 -> H(k, U1(c, k))
28.57/10.30	   A^2 -> H(k, U1(e, e))
28.57/10.30	   A^2 -> H(k, U1(d, k))
28.57/10.30	   A^2 -> H(c, b)
28.57/10.30	   A^2 -> H(c, U1(e, d))
28.57/10.30	   A^2 -> H(c, U1(d, e))
28.57/10.30	   A^2 -> H(c, c)
28.57/10.30	   A^2 -> H(c, U1(e, k))
28.57/10.30	   A^2 -> H(c, U1(k, e))
28.57/10.30	   A^2 -> H(c, e)
28.57/10.30	   A^2 -> H(c, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, k), b)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, k), c)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, k), e)
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, c), d)
28.57/10.30	   A^2 -> H(U1(e, c), k)
28.57/10.30	   A^2 -> H(U1(k, e), b)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, e), c)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, c), d)
28.57/10.30	   A^2 -> H(U1(c, e), d)
28.57/10.30	   A^2 -> H(U1(c, e), k)
28.57/10.30	
28.57/10.30	The TRS R consists of the following rules:
28.57/10.30	
28.57/10.30	   f(x) -> U1(x, x)
28.57/10.30	   U1(e, x) -> x
28.57/10.30	   a -> c
28.57/10.30	   a -> d
28.57/10.30	   b -> c
28.57/10.30	   b -> d
28.57/10.30	   d -> k
28.57/10.30	   c -> e
28.57/10.30	   c -> k
28.57/10.30	
28.57/10.30	Q is empty.
28.57/10.30	We have to consider all minimal (P,Q,R)-chains.
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2199) TransformationProof (EQUIVALENT)
28.57/10.30	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.30	
28.57/10.30	   (A^2 -> H(U1(e, e), U1(k, e)),A^2 -> H(U1(e, e), U1(k, e)))
28.57/10.30	   (A^2 -> H(U1(k, e), U1(k, e)),A^2 -> H(U1(k, e), U1(k, e)))
28.57/10.30	
28.57/10.30	
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2200)
28.57/10.30	Obligation:
28.57/10.30	Q DP problem:
28.57/10.30	The TRS P consists of the following rules:
28.57/10.30	
28.57/10.30	   A^2 -> H(f(c), f(c))
28.57/10.30	   H(x, x) -> G(x, x, f(k))
28.57/10.30	   G(d, x, x) -> A^2
28.57/10.30	   A^2 -> H(f(d), f(d))
28.57/10.30	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.30	   A^2 -> H(f(e), f(e))
28.57/10.30	   A^2 -> H(f(k), f(k))
28.57/10.30	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.30	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.30	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.30	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(c, e), e)
28.57/10.30	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.30	   A^2 -> H(U1(c, k), b)
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(c, k), c)
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(c, k), e)
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(c, c), d)
28.57/10.30	   A^2 -> H(e, U1(e, b))
28.57/10.30	   A^2 -> H(e, U1(c, d))
28.57/10.30	   A^2 -> H(e, U1(d, c))
28.57/10.30	   A^2 -> H(e, U1(b, e))
28.57/10.30	   A^2 -> H(e, U1(b, k))
28.57/10.30	   A^2 -> H(e, U1(e, c))
28.57/10.30	   A^2 -> H(e, U1(c, e))
28.57/10.30	   A^2 -> H(e, U1(c, k))
28.57/10.30	   A^2 -> H(e, U1(e, e))
28.57/10.30	   A^2 -> H(e, U1(d, k))
28.57/10.30	   A^2 -> H(U1(e, e), b)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, e), c)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.30	   A^2 -> H(f(e), d)
28.57/10.30	   A^2 -> H(f(e), k)
28.57/10.30	   A^2 -> H(U1(k, k), b)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, k), c)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.30	   A^2 -> H(f(k), d)
28.57/10.30	   A^2 -> H(f(k), k)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(k, d), b)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, d), c)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, k), b)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, k), c)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, k), e)
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, d), d)
28.57/10.30	   A^2 -> H(U1(d, d), k)
28.57/10.30	   A^2 -> H(U1(e, c), c)
28.57/10.30	   A^2 -> H(U1(c, c), e)
28.57/10.30	   A^2 -> H(U1(c, c), k)
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(e, e), e)
28.57/10.30	   A^2 -> H(d, U1(e, b))
28.57/10.30	   A^2 -> H(d, U1(k, b))
28.57/10.30	   A^2 -> H(d, U1(c, d))
28.57/10.30	   A^2 -> H(d, U1(d, c))
28.57/10.30	   A^2 -> H(d, U1(b, e))
28.57/10.30	   A^2 -> H(d, U1(b, k))
28.57/10.30	   A^2 -> H(d, U1(e, c))
28.57/10.30	   A^2 -> H(d, U1(k, c))
28.57/10.30	   A^2 -> H(d, U1(c, e))
28.57/10.30	   A^2 -> H(d, U1(c, k))
28.57/10.30	   A^2 -> H(d, U1(e, e))
28.57/10.30	   A^2 -> H(d, U1(k, k))
28.57/10.30	   A^2 -> H(d, U1(k, d))
28.57/10.30	   A^2 -> H(d, U1(d, k))
28.57/10.30	   A^2 -> H(a, b)
28.57/10.30	   A^2 -> H(a, U1(e, d))
28.57/10.30	   A^2 -> H(a, U1(d, e))
28.57/10.30	   A^2 -> H(a, c)
28.57/10.30	   A^2 -> H(a, U1(e, k))
28.57/10.30	   A^2 -> H(a, U1(k, e))
28.57/10.30	   A^2 -> H(a, e)
28.57/10.30	   A^2 -> H(a, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, d), b)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, d), c)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, d), e)
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, a), d)
28.57/10.30	   A^2 -> H(U1(e, a), k)
28.57/10.30	   A^2 -> H(U1(k, a), d)
28.57/10.30	   A^2 -> H(U1(c, d), d)
28.57/10.30	   A^2 -> H(U1(c, d), k)
28.57/10.30	   A^2 -> H(U1(d, e), b)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, e), c)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, e), e)
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, c), d)
28.57/10.30	   A^2 -> H(U1(d, c), k)
28.57/10.30	   A^2 -> H(U1(a, e), d)
28.57/10.30	   A^2 -> H(U1(a, e), k)
28.57/10.30	   A^2 -> H(U1(a, k), d)
28.57/10.30	   A^2 -> H(U1(a, k), k)
28.57/10.30	   A^2 -> H(k, U1(e, b))
28.57/10.30	   A^2 -> H(k, U1(c, d))
28.57/10.30	   A^2 -> H(k, U1(d, c))
28.57/10.30	   A^2 -> H(k, U1(b, e))
28.57/10.30	   A^2 -> H(k, U1(b, k))
28.57/10.30	   A^2 -> H(k, U1(e, c))
28.57/10.30	   A^2 -> H(k, U1(c, e))
28.57/10.30	   A^2 -> H(k, U1(c, k))
28.57/10.30	   A^2 -> H(k, U1(e, e))
28.57/10.30	   A^2 -> H(k, U1(d, k))
28.57/10.30	   A^2 -> H(c, b)
28.57/10.30	   A^2 -> H(c, U1(e, d))
28.57/10.30	   A^2 -> H(c, U1(d, e))
28.57/10.30	   A^2 -> H(c, c)
28.57/10.30	   A^2 -> H(c, U1(e, k))
28.57/10.30	   A^2 -> H(c, U1(k, e))
28.57/10.30	   A^2 -> H(c, e)
28.57/10.30	   A^2 -> H(c, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, k), b)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, k), c)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, k), e)
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, c), d)
28.57/10.30	   A^2 -> H(U1(e, c), k)
28.57/10.30	   A^2 -> H(U1(k, e), b)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, e), c)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, c), d)
28.57/10.30	   A^2 -> H(U1(c, e), d)
28.57/10.30	   A^2 -> H(U1(c, e), k)
28.57/10.30	
28.57/10.30	The TRS R consists of the following rules:
28.57/10.30	
28.57/10.30	   f(x) -> U1(x, x)
28.57/10.30	   U1(e, x) -> x
28.57/10.30	   a -> c
28.57/10.30	   a -> d
28.57/10.30	   b -> c
28.57/10.30	   b -> d
28.57/10.30	   d -> k
28.57/10.30	   c -> e
28.57/10.30	   c -> k
28.57/10.30	
28.57/10.30	Q is empty.
28.57/10.30	We have to consider all minimal (P,Q,R)-chains.
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2201) TransformationProof (EQUIVALENT)
28.57/10.30	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), e) at position [] we obtained the following new rules [LPAR04]:
28.57/10.30	
28.57/10.30	   (A^2 -> H(U1(e, e), e),A^2 -> H(U1(e, e), e))
28.57/10.30	   (A^2 -> H(U1(k, e), e),A^2 -> H(U1(k, e), e))
28.57/10.30	
28.57/10.30	
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2202)
28.57/10.30	Obligation:
28.57/10.30	Q DP problem:
28.57/10.30	The TRS P consists of the following rules:
28.57/10.30	
28.57/10.30	   A^2 -> H(f(c), f(c))
28.57/10.30	   H(x, x) -> G(x, x, f(k))
28.57/10.30	   G(d, x, x) -> A^2
28.57/10.30	   A^2 -> H(f(d), f(d))
28.57/10.30	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.30	   A^2 -> H(f(e), f(e))
28.57/10.30	   A^2 -> H(f(k), f(k))
28.57/10.30	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.30	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.30	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.30	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.30	   A^2 -> H(U1(c, k), b)
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(c, k), c)
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(c, k), e)
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(c, c), d)
28.57/10.30	   A^2 -> H(e, U1(e, b))
28.57/10.30	   A^2 -> H(e, U1(c, d))
28.57/10.30	   A^2 -> H(e, U1(d, c))
28.57/10.30	   A^2 -> H(e, U1(b, e))
28.57/10.30	   A^2 -> H(e, U1(b, k))
28.57/10.30	   A^2 -> H(e, U1(e, c))
28.57/10.30	   A^2 -> H(e, U1(c, e))
28.57/10.30	   A^2 -> H(e, U1(c, k))
28.57/10.30	   A^2 -> H(e, U1(e, e))
28.57/10.30	   A^2 -> H(e, U1(d, k))
28.57/10.30	   A^2 -> H(U1(e, e), b)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, e), c)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.30	   A^2 -> H(f(e), d)
28.57/10.30	   A^2 -> H(f(e), k)
28.57/10.30	   A^2 -> H(U1(k, k), b)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, k), c)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.30	   A^2 -> H(f(k), d)
28.57/10.30	   A^2 -> H(f(k), k)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(k, d), b)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, d), c)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, k), b)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, k), c)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, k), e)
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, d), d)
28.57/10.30	   A^2 -> H(U1(d, d), k)
28.57/10.30	   A^2 -> H(U1(e, c), c)
28.57/10.30	   A^2 -> H(U1(c, c), e)
28.57/10.30	   A^2 -> H(U1(c, c), k)
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(e, e), e)
28.57/10.30	   A^2 -> H(d, U1(e, b))
28.57/10.30	   A^2 -> H(d, U1(k, b))
28.57/10.30	   A^2 -> H(d, U1(c, d))
28.57/10.30	   A^2 -> H(d, U1(d, c))
28.57/10.30	   A^2 -> H(d, U1(b, e))
28.57/10.30	   A^2 -> H(d, U1(b, k))
28.57/10.30	   A^2 -> H(d, U1(e, c))
28.57/10.30	   A^2 -> H(d, U1(k, c))
28.57/10.30	   A^2 -> H(d, U1(c, e))
28.57/10.30	   A^2 -> H(d, U1(c, k))
28.57/10.30	   A^2 -> H(d, U1(e, e))
28.57/10.30	   A^2 -> H(d, U1(k, k))
28.57/10.30	   A^2 -> H(d, U1(k, d))
28.57/10.30	   A^2 -> H(d, U1(d, k))
28.57/10.30	   A^2 -> H(a, b)
28.57/10.30	   A^2 -> H(a, U1(e, d))
28.57/10.30	   A^2 -> H(a, U1(d, e))
28.57/10.30	   A^2 -> H(a, c)
28.57/10.30	   A^2 -> H(a, U1(e, k))
28.57/10.30	   A^2 -> H(a, U1(k, e))
28.57/10.30	   A^2 -> H(a, e)
28.57/10.30	   A^2 -> H(a, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, d), b)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, d), c)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, d), e)
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, a), d)
28.57/10.30	   A^2 -> H(U1(e, a), k)
28.57/10.30	   A^2 -> H(U1(k, a), d)
28.57/10.30	   A^2 -> H(U1(c, d), d)
28.57/10.30	   A^2 -> H(U1(c, d), k)
28.57/10.30	   A^2 -> H(U1(d, e), b)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, e), c)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, e), e)
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, c), d)
28.57/10.30	   A^2 -> H(U1(d, c), k)
28.57/10.30	   A^2 -> H(U1(a, e), d)
28.57/10.30	   A^2 -> H(U1(a, e), k)
28.57/10.30	   A^2 -> H(U1(a, k), d)
28.57/10.30	   A^2 -> H(U1(a, k), k)
28.57/10.30	   A^2 -> H(k, U1(e, b))
28.57/10.30	   A^2 -> H(k, U1(c, d))
28.57/10.30	   A^2 -> H(k, U1(d, c))
28.57/10.30	   A^2 -> H(k, U1(b, e))
28.57/10.30	   A^2 -> H(k, U1(b, k))
28.57/10.30	   A^2 -> H(k, U1(e, c))
28.57/10.30	   A^2 -> H(k, U1(c, e))
28.57/10.30	   A^2 -> H(k, U1(c, k))
28.57/10.30	   A^2 -> H(k, U1(e, e))
28.57/10.30	   A^2 -> H(k, U1(d, k))
28.57/10.30	   A^2 -> H(c, b)
28.57/10.30	   A^2 -> H(c, U1(e, d))
28.57/10.30	   A^2 -> H(c, U1(d, e))
28.57/10.30	   A^2 -> H(c, c)
28.57/10.30	   A^2 -> H(c, U1(e, k))
28.57/10.30	   A^2 -> H(c, U1(k, e))
28.57/10.30	   A^2 -> H(c, e)
28.57/10.30	   A^2 -> H(c, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, k), b)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, k), c)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, k), e)
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, c), d)
28.57/10.30	   A^2 -> H(U1(e, c), k)
28.57/10.30	   A^2 -> H(U1(k, e), b)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, e), c)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, c), d)
28.57/10.30	   A^2 -> H(U1(c, e), d)
28.57/10.30	   A^2 -> H(U1(c, e), k)
28.57/10.30	   A^2 -> H(U1(k, e), e)
28.57/10.30	
28.57/10.30	The TRS R consists of the following rules:
28.57/10.30	
28.57/10.30	   f(x) -> U1(x, x)
28.57/10.30	   U1(e, x) -> x
28.57/10.30	   a -> c
28.57/10.30	   a -> d
28.57/10.30	   b -> c
28.57/10.30	   b -> d
28.57/10.30	   d -> k
28.57/10.30	   c -> e
28.57/10.30	   c -> k
28.57/10.30	
28.57/10.30	Q is empty.
28.57/10.30	We have to consider all minimal (P,Q,R)-chains.
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2203) DependencyGraphProof (EQUIVALENT)
28.57/10.30	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2204)
28.57/10.30	Obligation:
28.57/10.30	Q DP problem:
28.57/10.30	The TRS P consists of the following rules:
28.57/10.30	
28.57/10.30	   H(x, x) -> G(x, x, f(k))
28.57/10.30	   G(d, x, x) -> A^2
28.57/10.30	   A^2 -> H(f(c), f(c))
28.57/10.30	   A^2 -> H(f(d), f(d))
28.57/10.30	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.30	   A^2 -> H(f(e), f(e))
28.57/10.30	   A^2 -> H(f(k), f(k))
28.57/10.30	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.30	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.30	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.30	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(c, e), U1(k, k))
28.57/10.30	   A^2 -> H(U1(c, k), b)
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(c, k), c)
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(c, k), e)
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(c, c), d)
28.57/10.30	   A^2 -> H(e, U1(e, b))
28.57/10.30	   A^2 -> H(e, U1(c, d))
28.57/10.30	   A^2 -> H(e, U1(d, c))
28.57/10.30	   A^2 -> H(e, U1(b, e))
28.57/10.30	   A^2 -> H(e, U1(b, k))
28.57/10.30	   A^2 -> H(e, U1(e, c))
28.57/10.30	   A^2 -> H(e, U1(c, e))
28.57/10.30	   A^2 -> H(e, U1(c, k))
28.57/10.30	   A^2 -> H(e, U1(e, e))
28.57/10.30	   A^2 -> H(e, U1(d, k))
28.57/10.30	   A^2 -> H(U1(e, e), b)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, e), c)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.30	   A^2 -> H(f(e), d)
28.57/10.30	   A^2 -> H(f(e), k)
28.57/10.30	   A^2 -> H(U1(k, k), b)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, k), c)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.30	   A^2 -> H(f(k), d)
28.57/10.30	   A^2 -> H(f(k), k)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(k, d), b)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, d), c)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, k), b)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, k), c)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, k), e)
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, d), d)
28.57/10.30	   A^2 -> H(U1(d, d), k)
28.57/10.30	   A^2 -> H(U1(e, c), c)
28.57/10.30	   A^2 -> H(U1(c, c), e)
28.57/10.30	   A^2 -> H(U1(c, c), k)
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(e, e), e)
28.57/10.30	   A^2 -> H(d, U1(e, b))
28.57/10.30	   A^2 -> H(d, U1(k, b))
28.57/10.30	   A^2 -> H(d, U1(c, d))
28.57/10.30	   A^2 -> H(d, U1(d, c))
28.57/10.30	   A^2 -> H(d, U1(b, e))
28.57/10.30	   A^2 -> H(d, U1(b, k))
28.57/10.30	   A^2 -> H(d, U1(e, c))
28.57/10.30	   A^2 -> H(d, U1(k, c))
28.57/10.30	   A^2 -> H(d, U1(c, e))
28.57/10.30	   A^2 -> H(d, U1(c, k))
28.57/10.30	   A^2 -> H(d, U1(e, e))
28.57/10.30	   A^2 -> H(d, U1(k, k))
28.57/10.30	   A^2 -> H(d, U1(k, d))
28.57/10.30	   A^2 -> H(d, U1(d, k))
28.57/10.30	   A^2 -> H(a, b)
28.57/10.30	   A^2 -> H(a, U1(e, d))
28.57/10.30	   A^2 -> H(a, U1(d, e))
28.57/10.30	   A^2 -> H(a, c)
28.57/10.30	   A^2 -> H(a, U1(e, k))
28.57/10.30	   A^2 -> H(a, U1(k, e))
28.57/10.30	   A^2 -> H(a, e)
28.57/10.30	   A^2 -> H(a, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, d), b)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, d), c)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, d), e)
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, a), d)
28.57/10.30	   A^2 -> H(U1(e, a), k)
28.57/10.30	   A^2 -> H(U1(k, a), d)
28.57/10.30	   A^2 -> H(U1(c, d), d)
28.57/10.30	   A^2 -> H(U1(c, d), k)
28.57/10.30	   A^2 -> H(U1(d, e), b)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, e), c)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, e), e)
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, c), d)
28.57/10.30	   A^2 -> H(U1(d, c), k)
28.57/10.30	   A^2 -> H(U1(a, e), d)
28.57/10.30	   A^2 -> H(U1(a, e), k)
28.57/10.30	   A^2 -> H(U1(a, k), d)
28.57/10.30	   A^2 -> H(U1(a, k), k)
28.57/10.30	   A^2 -> H(k, U1(e, b))
28.57/10.30	   A^2 -> H(k, U1(c, d))
28.57/10.30	   A^2 -> H(k, U1(d, c))
28.57/10.30	   A^2 -> H(k, U1(b, e))
28.57/10.30	   A^2 -> H(k, U1(b, k))
28.57/10.30	   A^2 -> H(k, U1(e, c))
28.57/10.30	   A^2 -> H(k, U1(c, e))
28.57/10.30	   A^2 -> H(k, U1(c, k))
28.57/10.30	   A^2 -> H(k, U1(e, e))
28.57/10.30	   A^2 -> H(k, U1(d, k))
28.57/10.30	   A^2 -> H(c, b)
28.57/10.30	   A^2 -> H(c, U1(e, d))
28.57/10.30	   A^2 -> H(c, U1(d, e))
28.57/10.30	   A^2 -> H(c, c)
28.57/10.30	   A^2 -> H(c, U1(e, k))
28.57/10.30	   A^2 -> H(c, U1(k, e))
28.57/10.30	   A^2 -> H(c, e)
28.57/10.30	   A^2 -> H(c, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, k), b)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, k), c)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, k), e)
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, c), d)
28.57/10.30	   A^2 -> H(U1(e, c), k)
28.57/10.30	   A^2 -> H(U1(k, e), b)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, e), c)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, c), d)
28.57/10.30	   A^2 -> H(U1(c, e), d)
28.57/10.30	   A^2 -> H(U1(c, e), k)
28.57/10.30	
28.57/10.30	The TRS R consists of the following rules:
28.57/10.30	
28.57/10.30	   f(x) -> U1(x, x)
28.57/10.30	   U1(e, x) -> x
28.57/10.30	   a -> c
28.57/10.30	   a -> d
28.57/10.30	   b -> c
28.57/10.30	   b -> d
28.57/10.30	   d -> k
28.57/10.30	   c -> e
28.57/10.30	   c -> k
28.57/10.30	
28.57/10.30	Q is empty.
28.57/10.30	We have to consider all minimal (P,Q,R)-chains.
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2205) TransformationProof (EQUIVALENT)
28.57/10.30	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.30	
28.57/10.30	   (A^2 -> H(U1(e, e), U1(k, k)),A^2 -> H(U1(e, e), U1(k, k)))
28.57/10.30	   (A^2 -> H(U1(k, e), U1(k, k)),A^2 -> H(U1(k, e), U1(k, k)))
28.57/10.30	
28.57/10.30	
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2206)
28.57/10.30	Obligation:
28.57/10.30	Q DP problem:
28.57/10.30	The TRS P consists of the following rules:
28.57/10.30	
28.57/10.30	   H(x, x) -> G(x, x, f(k))
28.57/10.30	   G(d, x, x) -> A^2
28.57/10.30	   A^2 -> H(f(c), f(c))
28.57/10.30	   A^2 -> H(f(d), f(d))
28.57/10.30	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.30	   A^2 -> H(f(e), f(e))
28.57/10.30	   A^2 -> H(f(k), f(k))
28.57/10.30	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.30	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.30	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.30	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(c, k), b)
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(c, k), c)
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(c, k), e)
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(c, c), d)
28.57/10.30	   A^2 -> H(e, U1(e, b))
28.57/10.30	   A^2 -> H(e, U1(c, d))
28.57/10.30	   A^2 -> H(e, U1(d, c))
28.57/10.30	   A^2 -> H(e, U1(b, e))
28.57/10.30	   A^2 -> H(e, U1(b, k))
28.57/10.30	   A^2 -> H(e, U1(e, c))
28.57/10.30	   A^2 -> H(e, U1(c, e))
28.57/10.30	   A^2 -> H(e, U1(c, k))
28.57/10.30	   A^2 -> H(e, U1(e, e))
28.57/10.30	   A^2 -> H(e, U1(d, k))
28.57/10.30	   A^2 -> H(U1(e, e), b)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, e), c)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.30	   A^2 -> H(f(e), d)
28.57/10.30	   A^2 -> H(f(e), k)
28.57/10.30	   A^2 -> H(U1(k, k), b)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, k), c)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.30	   A^2 -> H(f(k), d)
28.57/10.30	   A^2 -> H(f(k), k)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(k, d), b)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, d), c)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, k), b)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, k), c)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, k), e)
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, d), d)
28.57/10.30	   A^2 -> H(U1(d, d), k)
28.57/10.30	   A^2 -> H(U1(e, c), c)
28.57/10.30	   A^2 -> H(U1(c, c), e)
28.57/10.30	   A^2 -> H(U1(c, c), k)
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(e, e), e)
28.57/10.30	   A^2 -> H(d, U1(e, b))
28.57/10.30	   A^2 -> H(d, U1(k, b))
28.57/10.30	   A^2 -> H(d, U1(c, d))
28.57/10.30	   A^2 -> H(d, U1(d, c))
28.57/10.30	   A^2 -> H(d, U1(b, e))
28.57/10.30	   A^2 -> H(d, U1(b, k))
28.57/10.30	   A^2 -> H(d, U1(e, c))
28.57/10.30	   A^2 -> H(d, U1(k, c))
28.57/10.30	   A^2 -> H(d, U1(c, e))
28.57/10.30	   A^2 -> H(d, U1(c, k))
28.57/10.30	   A^2 -> H(d, U1(e, e))
28.57/10.30	   A^2 -> H(d, U1(k, k))
28.57/10.30	   A^2 -> H(d, U1(k, d))
28.57/10.30	   A^2 -> H(d, U1(d, k))
28.57/10.30	   A^2 -> H(a, b)
28.57/10.30	   A^2 -> H(a, U1(e, d))
28.57/10.30	   A^2 -> H(a, U1(d, e))
28.57/10.30	   A^2 -> H(a, c)
28.57/10.30	   A^2 -> H(a, U1(e, k))
28.57/10.30	   A^2 -> H(a, U1(k, e))
28.57/10.30	   A^2 -> H(a, e)
28.57/10.30	   A^2 -> H(a, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, d), b)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, d), c)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, d), e)
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, a), d)
28.57/10.30	   A^2 -> H(U1(e, a), k)
28.57/10.30	   A^2 -> H(U1(k, a), d)
28.57/10.30	   A^2 -> H(U1(c, d), d)
28.57/10.30	   A^2 -> H(U1(c, d), k)
28.57/10.30	   A^2 -> H(U1(d, e), b)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, e), c)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, e), e)
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, c), d)
28.57/10.30	   A^2 -> H(U1(d, c), k)
28.57/10.30	   A^2 -> H(U1(a, e), d)
28.57/10.30	   A^2 -> H(U1(a, e), k)
28.57/10.30	   A^2 -> H(U1(a, k), d)
28.57/10.30	   A^2 -> H(U1(a, k), k)
28.57/10.30	   A^2 -> H(k, U1(e, b))
28.57/10.30	   A^2 -> H(k, U1(c, d))
28.57/10.30	   A^2 -> H(k, U1(d, c))
28.57/10.30	   A^2 -> H(k, U1(b, e))
28.57/10.30	   A^2 -> H(k, U1(b, k))
28.57/10.30	   A^2 -> H(k, U1(e, c))
28.57/10.30	   A^2 -> H(k, U1(c, e))
28.57/10.30	   A^2 -> H(k, U1(c, k))
28.57/10.30	   A^2 -> H(k, U1(e, e))
28.57/10.30	   A^2 -> H(k, U1(d, k))
28.57/10.30	   A^2 -> H(c, b)
28.57/10.30	   A^2 -> H(c, U1(e, d))
28.57/10.30	   A^2 -> H(c, U1(d, e))
28.57/10.30	   A^2 -> H(c, c)
28.57/10.30	   A^2 -> H(c, U1(e, k))
28.57/10.30	   A^2 -> H(c, U1(k, e))
28.57/10.30	   A^2 -> H(c, e)
28.57/10.30	   A^2 -> H(c, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, k), b)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, k), c)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, k), e)
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, c), d)
28.57/10.30	   A^2 -> H(U1(e, c), k)
28.57/10.30	   A^2 -> H(U1(k, e), b)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, e), c)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, c), d)
28.57/10.30	   A^2 -> H(U1(c, e), d)
28.57/10.30	   A^2 -> H(U1(c, e), k)
28.57/10.30	   A^2 -> H(U1(k, e), U1(k, k))
28.57/10.30	
28.57/10.30	The TRS R consists of the following rules:
28.57/10.30	
28.57/10.30	   f(x) -> U1(x, x)
28.57/10.30	   U1(e, x) -> x
28.57/10.30	   a -> c
28.57/10.30	   a -> d
28.57/10.30	   b -> c
28.57/10.30	   b -> d
28.57/10.30	   d -> k
28.57/10.30	   c -> e
28.57/10.30	   c -> k
28.57/10.30	
28.57/10.30	Q is empty.
28.57/10.30	We have to consider all minimal (P,Q,R)-chains.
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2207) DependencyGraphProof (EQUIVALENT)
28.57/10.30	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2208)
28.57/10.30	Obligation:
28.57/10.30	Q DP problem:
28.57/10.30	The TRS P consists of the following rules:
28.57/10.30	
28.57/10.30	   G(d, x, x) -> A^2
28.57/10.30	   A^2 -> H(f(c), f(c))
28.57/10.30	   H(x, x) -> G(x, x, f(k))
28.57/10.30	   A^2 -> H(f(d), f(d))
28.57/10.30	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.30	   A^2 -> H(f(e), f(e))
28.57/10.30	   A^2 -> H(f(k), f(k))
28.57/10.30	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.30	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.30	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.30	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(c, k), b)
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(c, k), c)
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(c, k), e)
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(c, c), d)
28.57/10.30	   A^2 -> H(e, U1(e, b))
28.57/10.30	   A^2 -> H(e, U1(c, d))
28.57/10.30	   A^2 -> H(e, U1(d, c))
28.57/10.30	   A^2 -> H(e, U1(b, e))
28.57/10.30	   A^2 -> H(e, U1(b, k))
28.57/10.30	   A^2 -> H(e, U1(e, c))
28.57/10.30	   A^2 -> H(e, U1(c, e))
28.57/10.30	   A^2 -> H(e, U1(c, k))
28.57/10.30	   A^2 -> H(e, U1(e, e))
28.57/10.30	   A^2 -> H(e, U1(d, k))
28.57/10.30	   A^2 -> H(U1(e, e), b)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, e), c)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.30	   A^2 -> H(f(e), d)
28.57/10.30	   A^2 -> H(f(e), k)
28.57/10.30	   A^2 -> H(U1(k, k), b)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, k), c)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.30	   A^2 -> H(f(k), d)
28.57/10.30	   A^2 -> H(f(k), k)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(k, d), b)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, d), c)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, k), b)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, k), c)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, k), e)
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, d), d)
28.57/10.30	   A^2 -> H(U1(d, d), k)
28.57/10.30	   A^2 -> H(U1(e, c), c)
28.57/10.30	   A^2 -> H(U1(c, c), e)
28.57/10.30	   A^2 -> H(U1(c, c), k)
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(e, e), e)
28.57/10.30	   A^2 -> H(d, U1(e, b))
28.57/10.30	   A^2 -> H(d, U1(k, b))
28.57/10.30	   A^2 -> H(d, U1(c, d))
28.57/10.30	   A^2 -> H(d, U1(d, c))
28.57/10.30	   A^2 -> H(d, U1(b, e))
28.57/10.30	   A^2 -> H(d, U1(b, k))
28.57/10.30	   A^2 -> H(d, U1(e, c))
28.57/10.30	   A^2 -> H(d, U1(k, c))
28.57/10.30	   A^2 -> H(d, U1(c, e))
28.57/10.30	   A^2 -> H(d, U1(c, k))
28.57/10.30	   A^2 -> H(d, U1(e, e))
28.57/10.30	   A^2 -> H(d, U1(k, k))
28.57/10.30	   A^2 -> H(d, U1(k, d))
28.57/10.30	   A^2 -> H(d, U1(d, k))
28.57/10.30	   A^2 -> H(a, b)
28.57/10.30	   A^2 -> H(a, U1(e, d))
28.57/10.30	   A^2 -> H(a, U1(d, e))
28.57/10.30	   A^2 -> H(a, c)
28.57/10.30	   A^2 -> H(a, U1(e, k))
28.57/10.30	   A^2 -> H(a, U1(k, e))
28.57/10.30	   A^2 -> H(a, e)
28.57/10.30	   A^2 -> H(a, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, d), b)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, d), c)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, d), e)
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, a), d)
28.57/10.30	   A^2 -> H(U1(e, a), k)
28.57/10.30	   A^2 -> H(U1(k, a), d)
28.57/10.30	   A^2 -> H(U1(c, d), d)
28.57/10.30	   A^2 -> H(U1(c, d), k)
28.57/10.30	   A^2 -> H(U1(d, e), b)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, e), c)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, e), e)
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, c), d)
28.57/10.30	   A^2 -> H(U1(d, c), k)
28.57/10.30	   A^2 -> H(U1(a, e), d)
28.57/10.30	   A^2 -> H(U1(a, e), k)
28.57/10.30	   A^2 -> H(U1(a, k), d)
28.57/10.30	   A^2 -> H(U1(a, k), k)
28.57/10.30	   A^2 -> H(k, U1(e, b))
28.57/10.30	   A^2 -> H(k, U1(c, d))
28.57/10.30	   A^2 -> H(k, U1(d, c))
28.57/10.30	   A^2 -> H(k, U1(b, e))
28.57/10.30	   A^2 -> H(k, U1(b, k))
28.57/10.30	   A^2 -> H(k, U1(e, c))
28.57/10.30	   A^2 -> H(k, U1(c, e))
28.57/10.30	   A^2 -> H(k, U1(c, k))
28.57/10.30	   A^2 -> H(k, U1(e, e))
28.57/10.30	   A^2 -> H(k, U1(d, k))
28.57/10.30	   A^2 -> H(c, b)
28.57/10.30	   A^2 -> H(c, U1(e, d))
28.57/10.30	   A^2 -> H(c, U1(d, e))
28.57/10.30	   A^2 -> H(c, c)
28.57/10.30	   A^2 -> H(c, U1(e, k))
28.57/10.30	   A^2 -> H(c, U1(k, e))
28.57/10.30	   A^2 -> H(c, e)
28.57/10.30	   A^2 -> H(c, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, k), b)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, k), c)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, k), e)
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, c), d)
28.57/10.30	   A^2 -> H(U1(e, c), k)
28.57/10.30	   A^2 -> H(U1(k, e), b)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, e), c)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, c), d)
28.57/10.30	   A^2 -> H(U1(c, e), d)
28.57/10.30	   A^2 -> H(U1(c, e), k)
28.57/10.30	
28.57/10.30	The TRS R consists of the following rules:
28.57/10.30	
28.57/10.30	   f(x) -> U1(x, x)
28.57/10.30	   U1(e, x) -> x
28.57/10.30	   a -> c
28.57/10.30	   a -> d
28.57/10.30	   b -> c
28.57/10.30	   b -> d
28.57/10.30	   d -> k
28.57/10.30	   c -> e
28.57/10.30	   c -> k
28.57/10.30	
28.57/10.30	Q is empty.
28.57/10.30	We have to consider all minimal (P,Q,R)-chains.
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2209) TransformationProof (EQUIVALENT)
28.57/10.30	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), b) at position [] we obtained the following new rules [LPAR04]:
28.57/10.30	
28.57/10.30	   (A^2 -> H(U1(e, k), b),A^2 -> H(U1(e, k), b))
28.57/10.30	   (A^2 -> H(U1(k, k), b),A^2 -> H(U1(k, k), b))
28.57/10.30	   (A^2 -> H(U1(c, k), c),A^2 -> H(U1(c, k), c))
28.57/10.30	   (A^2 -> H(U1(c, k), d),A^2 -> H(U1(c, k), d))
28.57/10.30	
28.57/10.30	
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2210)
28.57/10.30	Obligation:
28.57/10.30	Q DP problem:
28.57/10.30	The TRS P consists of the following rules:
28.57/10.30	
28.57/10.30	   G(d, x, x) -> A^2
28.57/10.30	   A^2 -> H(f(c), f(c))
28.57/10.30	   H(x, x) -> G(x, x, f(k))
28.57/10.30	   A^2 -> H(f(d), f(d))
28.57/10.30	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.30	   A^2 -> H(f(e), f(e))
28.57/10.30	   A^2 -> H(f(k), f(k))
28.57/10.30	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.30	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.30	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.30	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(c, k), c)
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(c, k), e)
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(c, c), d)
28.57/10.30	   A^2 -> H(e, U1(e, b))
28.57/10.30	   A^2 -> H(e, U1(c, d))
28.57/10.30	   A^2 -> H(e, U1(d, c))
28.57/10.30	   A^2 -> H(e, U1(b, e))
28.57/10.30	   A^2 -> H(e, U1(b, k))
28.57/10.30	   A^2 -> H(e, U1(e, c))
28.57/10.30	   A^2 -> H(e, U1(c, e))
28.57/10.30	   A^2 -> H(e, U1(c, k))
28.57/10.30	   A^2 -> H(e, U1(e, e))
28.57/10.30	   A^2 -> H(e, U1(d, k))
28.57/10.30	   A^2 -> H(U1(e, e), b)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, e), c)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.30	   A^2 -> H(f(e), d)
28.57/10.30	   A^2 -> H(f(e), k)
28.57/10.30	   A^2 -> H(U1(k, k), b)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, k), c)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.30	   A^2 -> H(f(k), d)
28.57/10.30	   A^2 -> H(f(k), k)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(k, d), b)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, d), c)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, k), b)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, k), c)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, k), e)
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, d), d)
28.57/10.30	   A^2 -> H(U1(d, d), k)
28.57/10.30	   A^2 -> H(U1(e, c), c)
28.57/10.30	   A^2 -> H(U1(c, c), e)
28.57/10.30	   A^2 -> H(U1(c, c), k)
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(e, e), e)
28.57/10.30	   A^2 -> H(d, U1(e, b))
28.57/10.30	   A^2 -> H(d, U1(k, b))
28.57/10.30	   A^2 -> H(d, U1(c, d))
28.57/10.30	   A^2 -> H(d, U1(d, c))
28.57/10.30	   A^2 -> H(d, U1(b, e))
28.57/10.30	   A^2 -> H(d, U1(b, k))
28.57/10.30	   A^2 -> H(d, U1(e, c))
28.57/10.30	   A^2 -> H(d, U1(k, c))
28.57/10.30	   A^2 -> H(d, U1(c, e))
28.57/10.30	   A^2 -> H(d, U1(c, k))
28.57/10.30	   A^2 -> H(d, U1(e, e))
28.57/10.30	   A^2 -> H(d, U1(k, k))
28.57/10.30	   A^2 -> H(d, U1(k, d))
28.57/10.30	   A^2 -> H(d, U1(d, k))
28.57/10.30	   A^2 -> H(a, b)
28.57/10.30	   A^2 -> H(a, U1(e, d))
28.57/10.30	   A^2 -> H(a, U1(d, e))
28.57/10.30	   A^2 -> H(a, c)
28.57/10.30	   A^2 -> H(a, U1(e, k))
28.57/10.30	   A^2 -> H(a, U1(k, e))
28.57/10.30	   A^2 -> H(a, e)
28.57/10.30	   A^2 -> H(a, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, d), b)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, d), c)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, d), e)
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, a), d)
28.57/10.30	   A^2 -> H(U1(e, a), k)
28.57/10.30	   A^2 -> H(U1(k, a), d)
28.57/10.30	   A^2 -> H(U1(c, d), d)
28.57/10.30	   A^2 -> H(U1(c, d), k)
28.57/10.30	   A^2 -> H(U1(d, e), b)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, e), c)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, e), e)
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, c), d)
28.57/10.30	   A^2 -> H(U1(d, c), k)
28.57/10.30	   A^2 -> H(U1(a, e), d)
28.57/10.30	   A^2 -> H(U1(a, e), k)
28.57/10.30	   A^2 -> H(U1(a, k), d)
28.57/10.30	   A^2 -> H(U1(a, k), k)
28.57/10.30	   A^2 -> H(k, U1(e, b))
28.57/10.30	   A^2 -> H(k, U1(c, d))
28.57/10.30	   A^2 -> H(k, U1(d, c))
28.57/10.30	   A^2 -> H(k, U1(b, e))
28.57/10.30	   A^2 -> H(k, U1(b, k))
28.57/10.30	   A^2 -> H(k, U1(e, c))
28.57/10.30	   A^2 -> H(k, U1(c, e))
28.57/10.30	   A^2 -> H(k, U1(c, k))
28.57/10.30	   A^2 -> H(k, U1(e, e))
28.57/10.30	   A^2 -> H(k, U1(d, k))
28.57/10.30	   A^2 -> H(c, b)
28.57/10.30	   A^2 -> H(c, U1(e, d))
28.57/10.30	   A^2 -> H(c, U1(d, e))
28.57/10.30	   A^2 -> H(c, c)
28.57/10.30	   A^2 -> H(c, U1(e, k))
28.57/10.30	   A^2 -> H(c, U1(k, e))
28.57/10.30	   A^2 -> H(c, e)
28.57/10.30	   A^2 -> H(c, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, k), b)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, k), c)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, k), e)
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, c), d)
28.57/10.30	   A^2 -> H(U1(e, c), k)
28.57/10.30	   A^2 -> H(U1(k, e), b)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, e), c)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, c), d)
28.57/10.30	   A^2 -> H(U1(c, e), d)
28.57/10.30	   A^2 -> H(U1(c, e), k)
28.57/10.30	   A^2 -> H(U1(c, k), d)
28.57/10.30	
28.57/10.30	The TRS R consists of the following rules:
28.57/10.30	
28.57/10.30	   f(x) -> U1(x, x)
28.57/10.30	   U1(e, x) -> x
28.57/10.30	   a -> c
28.57/10.30	   a -> d
28.57/10.30	   b -> c
28.57/10.30	   b -> d
28.57/10.30	   d -> k
28.57/10.30	   c -> e
28.57/10.30	   c -> k
28.57/10.30	
28.57/10.30	Q is empty.
28.57/10.30	We have to consider all minimal (P,Q,R)-chains.
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2211) TransformationProof (EQUIVALENT)
28.57/10.30	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.30	
28.57/10.30	   (A^2 -> H(U1(e, k), U1(e, d)),A^2 -> H(U1(e, k), U1(e, d)))
28.57/10.30	   (A^2 -> H(U1(k, k), U1(e, d)),A^2 -> H(U1(k, k), U1(e, d)))
28.57/10.30	   (A^2 -> H(U1(c, k), d),A^2 -> H(U1(c, k), d))
28.57/10.30	   (A^2 -> H(U1(c, k), U1(e, k)),A^2 -> H(U1(c, k), U1(e, k)))
28.57/10.30	
28.57/10.30	
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2212)
28.57/10.30	Obligation:
28.57/10.30	Q DP problem:
28.57/10.30	The TRS P consists of the following rules:
28.57/10.30	
28.57/10.30	   G(d, x, x) -> A^2
28.57/10.30	   A^2 -> H(f(c), f(c))
28.57/10.30	   H(x, x) -> G(x, x, f(k))
28.57/10.30	   A^2 -> H(f(d), f(d))
28.57/10.30	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.30	   A^2 -> H(f(e), f(e))
28.57/10.30	   A^2 -> H(f(k), f(k))
28.57/10.30	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.30	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.30	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.30	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(c, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(c, k), c)
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(c, k), e)
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(c, c), d)
28.57/10.30	   A^2 -> H(e, U1(e, b))
28.57/10.30	   A^2 -> H(e, U1(c, d))
28.57/10.30	   A^2 -> H(e, U1(d, c))
28.57/10.30	   A^2 -> H(e, U1(b, e))
28.57/10.30	   A^2 -> H(e, U1(b, k))
28.57/10.30	   A^2 -> H(e, U1(e, c))
28.57/10.30	   A^2 -> H(e, U1(c, e))
28.57/10.30	   A^2 -> H(e, U1(c, k))
28.57/10.30	   A^2 -> H(e, U1(e, e))
28.57/10.30	   A^2 -> H(e, U1(d, k))
28.57/10.30	   A^2 -> H(U1(e, e), b)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, e), c)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.30	   A^2 -> H(f(e), d)
28.57/10.30	   A^2 -> H(f(e), k)
28.57/10.30	   A^2 -> H(U1(k, k), b)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, k), c)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.30	   A^2 -> H(f(k), d)
28.57/10.30	   A^2 -> H(f(k), k)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(k, d), b)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, d), c)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, k), b)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, k), c)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, k), e)
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, d), d)
28.57/10.30	   A^2 -> H(U1(d, d), k)
28.57/10.30	   A^2 -> H(U1(e, c), c)
28.57/10.30	   A^2 -> H(U1(c, c), e)
28.57/10.30	   A^2 -> H(U1(c, c), k)
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(e, e), e)
28.57/10.30	   A^2 -> H(d, U1(e, b))
28.57/10.30	   A^2 -> H(d, U1(k, b))
28.57/10.30	   A^2 -> H(d, U1(c, d))
28.57/10.30	   A^2 -> H(d, U1(d, c))
28.57/10.30	   A^2 -> H(d, U1(b, e))
28.57/10.30	   A^2 -> H(d, U1(b, k))
28.57/10.30	   A^2 -> H(d, U1(e, c))
28.57/10.30	   A^2 -> H(d, U1(k, c))
28.57/10.30	   A^2 -> H(d, U1(c, e))
28.57/10.30	   A^2 -> H(d, U1(c, k))
28.57/10.30	   A^2 -> H(d, U1(e, e))
28.57/10.30	   A^2 -> H(d, U1(k, k))
28.57/10.30	   A^2 -> H(d, U1(k, d))
28.57/10.30	   A^2 -> H(d, U1(d, k))
28.57/10.30	   A^2 -> H(a, b)
28.57/10.30	   A^2 -> H(a, U1(e, d))
28.57/10.30	   A^2 -> H(a, U1(d, e))
28.57/10.30	   A^2 -> H(a, c)
28.57/10.30	   A^2 -> H(a, U1(e, k))
28.57/10.30	   A^2 -> H(a, U1(k, e))
28.57/10.30	   A^2 -> H(a, e)
28.57/10.30	   A^2 -> H(a, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, d), b)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, d), c)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, d), e)
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, a), d)
28.57/10.30	   A^2 -> H(U1(e, a), k)
28.57/10.30	   A^2 -> H(U1(k, a), d)
28.57/10.30	   A^2 -> H(U1(c, d), d)
28.57/10.30	   A^2 -> H(U1(c, d), k)
28.57/10.30	   A^2 -> H(U1(d, e), b)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, e), c)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, e), e)
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, c), d)
28.57/10.30	   A^2 -> H(U1(d, c), k)
28.57/10.30	   A^2 -> H(U1(a, e), d)
28.57/10.30	   A^2 -> H(U1(a, e), k)
28.57/10.30	   A^2 -> H(U1(a, k), d)
28.57/10.30	   A^2 -> H(U1(a, k), k)
28.57/10.30	   A^2 -> H(k, U1(e, b))
28.57/10.30	   A^2 -> H(k, U1(c, d))
28.57/10.30	   A^2 -> H(k, U1(d, c))
28.57/10.30	   A^2 -> H(k, U1(b, e))
28.57/10.30	   A^2 -> H(k, U1(b, k))
28.57/10.30	   A^2 -> H(k, U1(e, c))
28.57/10.30	   A^2 -> H(k, U1(c, e))
28.57/10.30	   A^2 -> H(k, U1(c, k))
28.57/10.30	   A^2 -> H(k, U1(e, e))
28.57/10.30	   A^2 -> H(k, U1(d, k))
28.57/10.30	   A^2 -> H(c, b)
28.57/10.30	   A^2 -> H(c, U1(e, d))
28.57/10.30	   A^2 -> H(c, U1(d, e))
28.57/10.30	   A^2 -> H(c, c)
28.57/10.30	   A^2 -> H(c, U1(e, k))
28.57/10.30	   A^2 -> H(c, U1(k, e))
28.57/10.30	   A^2 -> H(c, e)
28.57/10.30	   A^2 -> H(c, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, k), b)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, k), c)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, k), e)
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, c), d)
28.57/10.30	   A^2 -> H(U1(e, c), k)
28.57/10.30	   A^2 -> H(U1(k, e), b)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, e), c)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, c), d)
28.57/10.30	   A^2 -> H(U1(c, e), d)
28.57/10.30	   A^2 -> H(U1(c, e), k)
28.57/10.30	   A^2 -> H(U1(c, k), d)
28.57/10.30	
28.57/10.30	The TRS R consists of the following rules:
28.57/10.30	
28.57/10.30	   f(x) -> U1(x, x)
28.57/10.30	   U1(e, x) -> x
28.57/10.30	   a -> c
28.57/10.30	   a -> d
28.57/10.30	   b -> c
28.57/10.30	   b -> d
28.57/10.30	   d -> k
28.57/10.30	   c -> e
28.57/10.30	   c -> k
28.57/10.30	
28.57/10.30	Q is empty.
28.57/10.30	We have to consider all minimal (P,Q,R)-chains.
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2213) TransformationProof (EQUIVALENT)
28.57/10.30	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.30	
28.57/10.30	   (A^2 -> H(U1(e, k), U1(d, e)),A^2 -> H(U1(e, k), U1(d, e)))
28.57/10.30	   (A^2 -> H(U1(k, k), U1(d, e)),A^2 -> H(U1(k, k), U1(d, e)))
28.57/10.30	   (A^2 -> H(U1(c, k), U1(k, e)),A^2 -> H(U1(c, k), U1(k, e)))
28.57/10.30	
28.57/10.30	
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2214)
28.57/10.30	Obligation:
28.57/10.30	Q DP problem:
28.57/10.30	The TRS P consists of the following rules:
28.57/10.30	
28.57/10.30	   G(d, x, x) -> A^2
28.57/10.30	   A^2 -> H(f(c), f(c))
28.57/10.30	   H(x, x) -> G(x, x, f(k))
28.57/10.30	   A^2 -> H(f(d), f(d))
28.57/10.30	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.30	   A^2 -> H(f(e), f(e))
28.57/10.30	   A^2 -> H(f(k), f(k))
28.57/10.30	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.30	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.30	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.30	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(c, k), c)
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(c, k), e)
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(c, c), d)
28.57/10.30	   A^2 -> H(e, U1(e, b))
28.57/10.30	   A^2 -> H(e, U1(c, d))
28.57/10.30	   A^2 -> H(e, U1(d, c))
28.57/10.30	   A^2 -> H(e, U1(b, e))
28.57/10.30	   A^2 -> H(e, U1(b, k))
28.57/10.30	   A^2 -> H(e, U1(e, c))
28.57/10.30	   A^2 -> H(e, U1(c, e))
28.57/10.30	   A^2 -> H(e, U1(c, k))
28.57/10.30	   A^2 -> H(e, U1(e, e))
28.57/10.30	   A^2 -> H(e, U1(d, k))
28.57/10.30	   A^2 -> H(U1(e, e), b)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, e), c)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.30	   A^2 -> H(f(e), d)
28.57/10.30	   A^2 -> H(f(e), k)
28.57/10.30	   A^2 -> H(U1(k, k), b)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, k), c)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.30	   A^2 -> H(f(k), d)
28.57/10.30	   A^2 -> H(f(k), k)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(k, d), b)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, d), c)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, k), b)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, k), c)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, k), e)
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, d), d)
28.57/10.30	   A^2 -> H(U1(d, d), k)
28.57/10.30	   A^2 -> H(U1(e, c), c)
28.57/10.30	   A^2 -> H(U1(c, c), e)
28.57/10.30	   A^2 -> H(U1(c, c), k)
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(e, e), e)
28.57/10.30	   A^2 -> H(d, U1(e, b))
28.57/10.30	   A^2 -> H(d, U1(k, b))
28.57/10.30	   A^2 -> H(d, U1(c, d))
28.57/10.30	   A^2 -> H(d, U1(d, c))
28.57/10.30	   A^2 -> H(d, U1(b, e))
28.57/10.30	   A^2 -> H(d, U1(b, k))
28.57/10.30	   A^2 -> H(d, U1(e, c))
28.57/10.30	   A^2 -> H(d, U1(k, c))
28.57/10.30	   A^2 -> H(d, U1(c, e))
28.57/10.30	   A^2 -> H(d, U1(c, k))
28.57/10.30	   A^2 -> H(d, U1(e, e))
28.57/10.30	   A^2 -> H(d, U1(k, k))
28.57/10.30	   A^2 -> H(d, U1(k, d))
28.57/10.30	   A^2 -> H(d, U1(d, k))
28.57/10.30	   A^2 -> H(a, b)
28.57/10.30	   A^2 -> H(a, U1(e, d))
28.57/10.30	   A^2 -> H(a, U1(d, e))
28.57/10.30	   A^2 -> H(a, c)
28.57/10.30	   A^2 -> H(a, U1(e, k))
28.57/10.30	   A^2 -> H(a, U1(k, e))
28.57/10.30	   A^2 -> H(a, e)
28.57/10.30	   A^2 -> H(a, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, d), b)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, d), c)
28.57/10.30	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, d), e)
28.57/10.30	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, a), d)
28.57/10.30	   A^2 -> H(U1(e, a), k)
28.57/10.30	   A^2 -> H(U1(k, a), d)
28.57/10.30	   A^2 -> H(U1(c, d), d)
28.57/10.30	   A^2 -> H(U1(c, d), k)
28.57/10.30	   A^2 -> H(U1(d, e), b)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, e), c)
28.57/10.30	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, e), e)
28.57/10.30	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, c), d)
28.57/10.30	   A^2 -> H(U1(d, c), k)
28.57/10.30	   A^2 -> H(U1(a, e), d)
28.57/10.30	   A^2 -> H(U1(a, e), k)
28.57/10.30	   A^2 -> H(U1(a, k), d)
28.57/10.30	   A^2 -> H(U1(a, k), k)
28.57/10.30	   A^2 -> H(k, U1(e, b))
28.57/10.30	   A^2 -> H(k, U1(c, d))
28.57/10.30	   A^2 -> H(k, U1(d, c))
28.57/10.30	   A^2 -> H(k, U1(b, e))
28.57/10.30	   A^2 -> H(k, U1(b, k))
28.57/10.30	   A^2 -> H(k, U1(e, c))
28.57/10.30	   A^2 -> H(k, U1(c, e))
28.57/10.30	   A^2 -> H(k, U1(c, k))
28.57/10.30	   A^2 -> H(k, U1(e, e))
28.57/10.30	   A^2 -> H(k, U1(d, k))
28.57/10.30	   A^2 -> H(c, b)
28.57/10.30	   A^2 -> H(c, U1(e, d))
28.57/10.30	   A^2 -> H(c, U1(d, e))
28.57/10.30	   A^2 -> H(c, c)
28.57/10.30	   A^2 -> H(c, U1(e, k))
28.57/10.30	   A^2 -> H(c, U1(k, e))
28.57/10.30	   A^2 -> H(c, e)
28.57/10.30	   A^2 -> H(c, U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, k), b)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, k), c)
28.57/10.30	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, k), e)
28.57/10.30	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(e, c), d)
28.57/10.30	   A^2 -> H(U1(e, c), k)
28.57/10.30	   A^2 -> H(U1(k, e), b)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, e), c)
28.57/10.30	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, c), d)
28.57/10.30	   A^2 -> H(U1(c, e), d)
28.57/10.30	   A^2 -> H(U1(c, e), k)
28.57/10.30	   A^2 -> H(U1(c, k), d)
28.57/10.30	
28.57/10.30	The TRS R consists of the following rules:
28.57/10.30	
28.57/10.30	   f(x) -> U1(x, x)
28.57/10.30	   U1(e, x) -> x
28.57/10.30	   a -> c
28.57/10.30	   a -> d
28.57/10.30	   b -> c
28.57/10.30	   b -> d
28.57/10.30	   d -> k
28.57/10.30	   c -> e
28.57/10.30	   c -> k
28.57/10.30	
28.57/10.30	Q is empty.
28.57/10.30	We have to consider all minimal (P,Q,R)-chains.
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2215) TransformationProof (EQUIVALENT)
28.57/10.30	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), c) at position [] we obtained the following new rules [LPAR04]:
28.57/10.30	
28.57/10.30	   (A^2 -> H(U1(e, k), c),A^2 -> H(U1(e, k), c))
28.57/10.30	   (A^2 -> H(U1(k, k), c),A^2 -> H(U1(k, k), c))
28.57/10.30	   (A^2 -> H(U1(c, k), e),A^2 -> H(U1(c, k), e))
28.57/10.30	   (A^2 -> H(U1(c, k), k),A^2 -> H(U1(c, k), k))
28.57/10.30	
28.57/10.30	
28.57/10.30	----------------------------------------
28.57/10.30	
28.57/10.30	(2216)
28.57/10.30	Obligation:
28.57/10.30	Q DP problem:
28.57/10.30	The TRS P consists of the following rules:
28.57/10.30	
28.57/10.30	   G(d, x, x) -> A^2
28.57/10.30	   A^2 -> H(f(c), f(c))
28.57/10.30	   H(x, x) -> G(x, x, f(k))
28.57/10.30	   A^2 -> H(f(d), f(d))
28.57/10.30	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.30	   A^2 -> H(f(e), f(e))
28.57/10.30	   A^2 -> H(f(k), f(k))
28.57/10.30	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.30	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.30	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.30	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.30	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(c, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(c, k), e)
28.57/10.30	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(c, c), d)
28.57/10.30	   A^2 -> H(e, U1(e, b))
28.57/10.30	   A^2 -> H(e, U1(c, d))
28.57/10.30	   A^2 -> H(e, U1(d, c))
28.57/10.30	   A^2 -> H(e, U1(b, e))
28.57/10.30	   A^2 -> H(e, U1(b, k))
28.57/10.30	   A^2 -> H(e, U1(e, c))
28.57/10.30	   A^2 -> H(e, U1(c, e))
28.57/10.30	   A^2 -> H(e, U1(c, k))
28.57/10.30	   A^2 -> H(e, U1(e, e))
28.57/10.30	   A^2 -> H(e, U1(d, k))
28.57/10.30	   A^2 -> H(U1(e, e), b)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.30	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.30	   A^2 -> H(U1(e, e), c)
28.57/10.30	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.30	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.30	   A^2 -> H(f(e), d)
28.57/10.30	   A^2 -> H(f(e), k)
28.57/10.30	   A^2 -> H(U1(k, k), b)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, k), c)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.30	   A^2 -> H(f(k), d)
28.57/10.30	   A^2 -> H(f(k), k)
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.30	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.30	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.30	   A^2 -> H(U1(k, d), b)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.30	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.30	   A^2 -> H(U1(k, d), c)
28.57/10.30	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.30	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, k), b)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.30	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.30	   A^2 -> H(U1(d, k), c)
28.57/10.30	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.30	   A^2 -> H(U1(d, k), e)
28.57/10.30	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.30	   A^2 -> H(U1(d, d), d)
28.57/10.30	   A^2 -> H(U1(d, d), k)
28.57/10.30	   A^2 -> H(U1(e, c), c)
28.57/10.30	   A^2 -> H(U1(c, c), e)
28.57/10.30	   A^2 -> H(U1(c, c), k)
28.57/10.30	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.30	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(e, e), e)
28.57/10.31	   A^2 -> H(d, U1(e, b))
28.57/10.31	   A^2 -> H(d, U1(k, b))
28.57/10.31	   A^2 -> H(d, U1(c, d))
28.57/10.31	   A^2 -> H(d, U1(d, c))
28.57/10.31	   A^2 -> H(d, U1(b, e))
28.57/10.31	   A^2 -> H(d, U1(b, k))
28.57/10.31	   A^2 -> H(d, U1(e, c))
28.57/10.31	   A^2 -> H(d, U1(k, c))
28.57/10.31	   A^2 -> H(d, U1(c, e))
28.57/10.31	   A^2 -> H(d, U1(c, k))
28.57/10.31	   A^2 -> H(d, U1(e, e))
28.57/10.31	   A^2 -> H(d, U1(k, k))
28.57/10.31	   A^2 -> H(d, U1(k, d))
28.57/10.31	   A^2 -> H(d, U1(d, k))
28.57/10.31	   A^2 -> H(a, b)
28.57/10.31	   A^2 -> H(a, U1(e, d))
28.57/10.31	   A^2 -> H(a, U1(d, e))
28.57/10.31	   A^2 -> H(a, c)
28.57/10.31	   A^2 -> H(a, U1(e, k))
28.57/10.31	   A^2 -> H(a, U1(k, e))
28.57/10.31	   A^2 -> H(a, e)
28.57/10.31	   A^2 -> H(a, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, d), b)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, d), c)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, d), e)
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, a), d)
28.57/10.31	   A^2 -> H(U1(e, a), k)
28.57/10.31	   A^2 -> H(U1(k, a), d)
28.57/10.31	   A^2 -> H(U1(c, d), d)
28.57/10.31	   A^2 -> H(U1(c, d), k)
28.57/10.31	   A^2 -> H(U1(d, e), b)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, e), c)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, e), e)
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, c), d)
28.57/10.31	   A^2 -> H(U1(d, c), k)
28.57/10.31	   A^2 -> H(U1(a, e), d)
28.57/10.31	   A^2 -> H(U1(a, e), k)
28.57/10.31	   A^2 -> H(U1(a, k), d)
28.57/10.31	   A^2 -> H(U1(a, k), k)
28.57/10.31	   A^2 -> H(k, U1(e, b))
28.57/10.31	   A^2 -> H(k, U1(c, d))
28.57/10.31	   A^2 -> H(k, U1(d, c))
28.57/10.31	   A^2 -> H(k, U1(b, e))
28.57/10.31	   A^2 -> H(k, U1(b, k))
28.57/10.31	   A^2 -> H(k, U1(e, c))
28.57/10.31	   A^2 -> H(k, U1(c, e))
28.57/10.31	   A^2 -> H(k, U1(c, k))
28.57/10.31	   A^2 -> H(k, U1(e, e))
28.57/10.31	   A^2 -> H(k, U1(d, k))
28.57/10.31	   A^2 -> H(c, b)
28.57/10.31	   A^2 -> H(c, U1(e, d))
28.57/10.31	   A^2 -> H(c, U1(d, e))
28.57/10.31	   A^2 -> H(c, c)
28.57/10.31	   A^2 -> H(c, U1(e, k))
28.57/10.31	   A^2 -> H(c, U1(k, e))
28.57/10.31	   A^2 -> H(c, e)
28.57/10.31	   A^2 -> H(c, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, k), b)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, k), c)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, k), e)
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, c), d)
28.57/10.31	   A^2 -> H(U1(e, c), k)
28.57/10.31	   A^2 -> H(U1(k, e), b)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, e), c)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, c), d)
28.57/10.31	   A^2 -> H(U1(c, e), d)
28.57/10.31	   A^2 -> H(U1(c, e), k)
28.57/10.31	   A^2 -> H(U1(c, k), d)
28.57/10.31	   A^2 -> H(U1(c, k), k)
28.57/10.31	
28.57/10.31	The TRS R consists of the following rules:
28.57/10.31	
28.57/10.31	   f(x) -> U1(x, x)
28.57/10.31	   U1(e, x) -> x
28.57/10.31	   a -> c
28.57/10.31	   a -> d
28.57/10.31	   b -> c
28.57/10.31	   b -> d
28.57/10.31	   d -> k
28.57/10.31	   c -> e
28.57/10.31	   c -> k
28.57/10.31	
28.57/10.31	Q is empty.
28.57/10.31	We have to consider all minimal (P,Q,R)-chains.
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2217) TransformationProof (EQUIVALENT)
28.57/10.31	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.31	
28.57/10.31	   (A^2 -> H(U1(e, k), U1(e, k)),A^2 -> H(U1(e, k), U1(e, k)))
28.57/10.31	   (A^2 -> H(U1(k, k), U1(e, k)),A^2 -> H(U1(k, k), U1(e, k)))
28.57/10.31	   (A^2 -> H(U1(c, k), k),A^2 -> H(U1(c, k), k))
28.57/10.31	
28.57/10.31	
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2218)
28.57/10.31	Obligation:
28.57/10.31	Q DP problem:
28.57/10.31	The TRS P consists of the following rules:
28.57/10.31	
28.57/10.31	   G(d, x, x) -> A^2
28.57/10.31	   A^2 -> H(f(c), f(c))
28.57/10.31	   H(x, x) -> G(x, x, f(k))
28.57/10.31	   A^2 -> H(f(d), f(d))
28.57/10.31	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.31	   A^2 -> H(f(e), f(e))
28.57/10.31	   A^2 -> H(f(k), f(k))
28.57/10.31	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.31	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.31	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.31	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.31	   A^2 -> H(U1(c, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(c, k), e)
28.57/10.31	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(c, c), d)
28.57/10.31	   A^2 -> H(e, U1(e, b))
28.57/10.31	   A^2 -> H(e, U1(c, d))
28.57/10.31	   A^2 -> H(e, U1(d, c))
28.57/10.31	   A^2 -> H(e, U1(b, e))
28.57/10.31	   A^2 -> H(e, U1(b, k))
28.57/10.31	   A^2 -> H(e, U1(e, c))
28.57/10.31	   A^2 -> H(e, U1(c, e))
28.57/10.31	   A^2 -> H(e, U1(c, k))
28.57/10.31	   A^2 -> H(e, U1(e, e))
28.57/10.31	   A^2 -> H(e, U1(d, k))
28.57/10.31	   A^2 -> H(U1(e, e), b)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, e), c)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.31	   A^2 -> H(f(e), d)
28.57/10.31	   A^2 -> H(f(e), k)
28.57/10.31	   A^2 -> H(U1(k, k), b)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, k), c)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.31	   A^2 -> H(f(k), d)
28.57/10.31	   A^2 -> H(f(k), k)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.31	   A^2 -> H(U1(k, d), b)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, d), c)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, k), b)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, k), c)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, k), e)
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, d), d)
28.57/10.31	   A^2 -> H(U1(d, d), k)
28.57/10.31	   A^2 -> H(U1(e, c), c)
28.57/10.31	   A^2 -> H(U1(c, c), e)
28.57/10.31	   A^2 -> H(U1(c, c), k)
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(e, e), e)
28.57/10.31	   A^2 -> H(d, U1(e, b))
28.57/10.31	   A^2 -> H(d, U1(k, b))
28.57/10.31	   A^2 -> H(d, U1(c, d))
28.57/10.31	   A^2 -> H(d, U1(d, c))
28.57/10.31	   A^2 -> H(d, U1(b, e))
28.57/10.31	   A^2 -> H(d, U1(b, k))
28.57/10.31	   A^2 -> H(d, U1(e, c))
28.57/10.31	   A^2 -> H(d, U1(k, c))
28.57/10.31	   A^2 -> H(d, U1(c, e))
28.57/10.31	   A^2 -> H(d, U1(c, k))
28.57/10.31	   A^2 -> H(d, U1(e, e))
28.57/10.31	   A^2 -> H(d, U1(k, k))
28.57/10.31	   A^2 -> H(d, U1(k, d))
28.57/10.31	   A^2 -> H(d, U1(d, k))
28.57/10.31	   A^2 -> H(a, b)
28.57/10.31	   A^2 -> H(a, U1(e, d))
28.57/10.31	   A^2 -> H(a, U1(d, e))
28.57/10.31	   A^2 -> H(a, c)
28.57/10.31	   A^2 -> H(a, U1(e, k))
28.57/10.31	   A^2 -> H(a, U1(k, e))
28.57/10.31	   A^2 -> H(a, e)
28.57/10.31	   A^2 -> H(a, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, d), b)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, d), c)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, d), e)
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, a), d)
28.57/10.31	   A^2 -> H(U1(e, a), k)
28.57/10.31	   A^2 -> H(U1(k, a), d)
28.57/10.31	   A^2 -> H(U1(c, d), d)
28.57/10.31	   A^2 -> H(U1(c, d), k)
28.57/10.31	   A^2 -> H(U1(d, e), b)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, e), c)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, e), e)
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, c), d)
28.57/10.31	   A^2 -> H(U1(d, c), k)
28.57/10.31	   A^2 -> H(U1(a, e), d)
28.57/10.31	   A^2 -> H(U1(a, e), k)
28.57/10.31	   A^2 -> H(U1(a, k), d)
28.57/10.31	   A^2 -> H(U1(a, k), k)
28.57/10.31	   A^2 -> H(k, U1(e, b))
28.57/10.31	   A^2 -> H(k, U1(c, d))
28.57/10.31	   A^2 -> H(k, U1(d, c))
28.57/10.31	   A^2 -> H(k, U1(b, e))
28.57/10.31	   A^2 -> H(k, U1(b, k))
28.57/10.31	   A^2 -> H(k, U1(e, c))
28.57/10.31	   A^2 -> H(k, U1(c, e))
28.57/10.31	   A^2 -> H(k, U1(c, k))
28.57/10.31	   A^2 -> H(k, U1(e, e))
28.57/10.31	   A^2 -> H(k, U1(d, k))
28.57/10.31	   A^2 -> H(c, b)
28.57/10.31	   A^2 -> H(c, U1(e, d))
28.57/10.31	   A^2 -> H(c, U1(d, e))
28.57/10.31	   A^2 -> H(c, c)
28.57/10.31	   A^2 -> H(c, U1(e, k))
28.57/10.31	   A^2 -> H(c, U1(k, e))
28.57/10.31	   A^2 -> H(c, e)
28.57/10.31	   A^2 -> H(c, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, k), b)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, k), c)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, k), e)
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, c), d)
28.57/10.31	   A^2 -> H(U1(e, c), k)
28.57/10.31	   A^2 -> H(U1(k, e), b)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, e), c)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, c), d)
28.57/10.31	   A^2 -> H(U1(c, e), d)
28.57/10.31	   A^2 -> H(U1(c, e), k)
28.57/10.31	   A^2 -> H(U1(c, k), d)
28.57/10.31	   A^2 -> H(U1(c, k), k)
28.57/10.31	
28.57/10.31	The TRS R consists of the following rules:
28.57/10.31	
28.57/10.31	   f(x) -> U1(x, x)
28.57/10.31	   U1(e, x) -> x
28.57/10.31	   a -> c
28.57/10.31	   a -> d
28.57/10.31	   b -> c
28.57/10.31	   b -> d
28.57/10.31	   d -> k
28.57/10.31	   c -> e
28.57/10.31	   c -> k
28.57/10.31	
28.57/10.31	Q is empty.
28.57/10.31	We have to consider all minimal (P,Q,R)-chains.
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2219) TransformationProof (EQUIVALENT)
28.57/10.31	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.31	
28.57/10.31	   (A^2 -> H(U1(e, k), U1(k, e)),A^2 -> H(U1(e, k), U1(k, e)))
28.57/10.31	   (A^2 -> H(U1(k, k), U1(k, e)),A^2 -> H(U1(k, k), U1(k, e)))
28.57/10.31	
28.57/10.31	
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2220)
28.57/10.31	Obligation:
28.57/10.31	Q DP problem:
28.57/10.31	The TRS P consists of the following rules:
28.57/10.31	
28.57/10.31	   G(d, x, x) -> A^2
28.57/10.31	   A^2 -> H(f(c), f(c))
28.57/10.31	   H(x, x) -> G(x, x, f(k))
28.57/10.31	   A^2 -> H(f(d), f(d))
28.57/10.31	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.31	   A^2 -> H(f(e), f(e))
28.57/10.31	   A^2 -> H(f(k), f(k))
28.57/10.31	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.31	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.31	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.31	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.31	   A^2 -> H(U1(c, k), e)
28.57/10.31	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(c, c), d)
28.57/10.31	   A^2 -> H(e, U1(e, b))
28.57/10.31	   A^2 -> H(e, U1(c, d))
28.57/10.31	   A^2 -> H(e, U1(d, c))
28.57/10.31	   A^2 -> H(e, U1(b, e))
28.57/10.31	   A^2 -> H(e, U1(b, k))
28.57/10.31	   A^2 -> H(e, U1(e, c))
28.57/10.31	   A^2 -> H(e, U1(c, e))
28.57/10.31	   A^2 -> H(e, U1(c, k))
28.57/10.31	   A^2 -> H(e, U1(e, e))
28.57/10.31	   A^2 -> H(e, U1(d, k))
28.57/10.31	   A^2 -> H(U1(e, e), b)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, e), c)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.31	   A^2 -> H(f(e), d)
28.57/10.31	   A^2 -> H(f(e), k)
28.57/10.31	   A^2 -> H(U1(k, k), b)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, k), c)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.31	   A^2 -> H(f(k), d)
28.57/10.31	   A^2 -> H(f(k), k)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.31	   A^2 -> H(U1(k, d), b)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, d), c)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, k), b)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, k), c)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, k), e)
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, d), d)
28.57/10.31	   A^2 -> H(U1(d, d), k)
28.57/10.31	   A^2 -> H(U1(e, c), c)
28.57/10.31	   A^2 -> H(U1(c, c), e)
28.57/10.31	   A^2 -> H(U1(c, c), k)
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(e, e), e)
28.57/10.31	   A^2 -> H(d, U1(e, b))
28.57/10.31	   A^2 -> H(d, U1(k, b))
28.57/10.31	   A^2 -> H(d, U1(c, d))
28.57/10.31	   A^2 -> H(d, U1(d, c))
28.57/10.31	   A^2 -> H(d, U1(b, e))
28.57/10.31	   A^2 -> H(d, U1(b, k))
28.57/10.31	   A^2 -> H(d, U1(e, c))
28.57/10.31	   A^2 -> H(d, U1(k, c))
28.57/10.31	   A^2 -> H(d, U1(c, e))
28.57/10.31	   A^2 -> H(d, U1(c, k))
28.57/10.31	   A^2 -> H(d, U1(e, e))
28.57/10.31	   A^2 -> H(d, U1(k, k))
28.57/10.31	   A^2 -> H(d, U1(k, d))
28.57/10.31	   A^2 -> H(d, U1(d, k))
28.57/10.31	   A^2 -> H(a, b)
28.57/10.31	   A^2 -> H(a, U1(e, d))
28.57/10.31	   A^2 -> H(a, U1(d, e))
28.57/10.31	   A^2 -> H(a, c)
28.57/10.31	   A^2 -> H(a, U1(e, k))
28.57/10.31	   A^2 -> H(a, U1(k, e))
28.57/10.31	   A^2 -> H(a, e)
28.57/10.31	   A^2 -> H(a, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, d), b)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, d), c)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, d), e)
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, a), d)
28.57/10.31	   A^2 -> H(U1(e, a), k)
28.57/10.31	   A^2 -> H(U1(k, a), d)
28.57/10.31	   A^2 -> H(U1(c, d), d)
28.57/10.31	   A^2 -> H(U1(c, d), k)
28.57/10.31	   A^2 -> H(U1(d, e), b)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, e), c)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, e), e)
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, c), d)
28.57/10.31	   A^2 -> H(U1(d, c), k)
28.57/10.31	   A^2 -> H(U1(a, e), d)
28.57/10.31	   A^2 -> H(U1(a, e), k)
28.57/10.31	   A^2 -> H(U1(a, k), d)
28.57/10.31	   A^2 -> H(U1(a, k), k)
28.57/10.31	   A^2 -> H(k, U1(e, b))
28.57/10.31	   A^2 -> H(k, U1(c, d))
28.57/10.31	   A^2 -> H(k, U1(d, c))
28.57/10.31	   A^2 -> H(k, U1(b, e))
28.57/10.31	   A^2 -> H(k, U1(b, k))
28.57/10.31	   A^2 -> H(k, U1(e, c))
28.57/10.31	   A^2 -> H(k, U1(c, e))
28.57/10.31	   A^2 -> H(k, U1(c, k))
28.57/10.31	   A^2 -> H(k, U1(e, e))
28.57/10.31	   A^2 -> H(k, U1(d, k))
28.57/10.31	   A^2 -> H(c, b)
28.57/10.31	   A^2 -> H(c, U1(e, d))
28.57/10.31	   A^2 -> H(c, U1(d, e))
28.57/10.31	   A^2 -> H(c, c)
28.57/10.31	   A^2 -> H(c, U1(e, k))
28.57/10.31	   A^2 -> H(c, U1(k, e))
28.57/10.31	   A^2 -> H(c, e)
28.57/10.31	   A^2 -> H(c, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, k), b)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, k), c)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, k), e)
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, c), d)
28.57/10.31	   A^2 -> H(U1(e, c), k)
28.57/10.31	   A^2 -> H(U1(k, e), b)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, e), c)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, c), d)
28.57/10.31	   A^2 -> H(U1(c, e), d)
28.57/10.31	   A^2 -> H(U1(c, e), k)
28.57/10.31	   A^2 -> H(U1(c, k), d)
28.57/10.31	   A^2 -> H(U1(c, k), k)
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, e))
28.57/10.31	
28.57/10.31	The TRS R consists of the following rules:
28.57/10.31	
28.57/10.31	   f(x) -> U1(x, x)
28.57/10.31	   U1(e, x) -> x
28.57/10.31	   a -> c
28.57/10.31	   a -> d
28.57/10.31	   b -> c
28.57/10.31	   b -> d
28.57/10.31	   d -> k
28.57/10.31	   c -> e
28.57/10.31	   c -> k
28.57/10.31	
28.57/10.31	Q is empty.
28.57/10.31	We have to consider all minimal (P,Q,R)-chains.
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2221) DependencyGraphProof (EQUIVALENT)
28.57/10.31	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2222)
28.57/10.31	Obligation:
28.57/10.31	Q DP problem:
28.57/10.31	The TRS P consists of the following rules:
28.57/10.31	
28.57/10.31	   A^2 -> H(f(c), f(c))
28.57/10.31	   H(x, x) -> G(x, x, f(k))
28.57/10.31	   G(d, x, x) -> A^2
28.57/10.31	   A^2 -> H(f(d), f(d))
28.57/10.31	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.31	   A^2 -> H(f(e), f(e))
28.57/10.31	   A^2 -> H(f(k), f(k))
28.57/10.31	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.31	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.31	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.31	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.31	   A^2 -> H(U1(c, k), e)
28.57/10.31	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(c, c), d)
28.57/10.31	   A^2 -> H(e, U1(e, b))
28.57/10.31	   A^2 -> H(e, U1(c, d))
28.57/10.31	   A^2 -> H(e, U1(d, c))
28.57/10.31	   A^2 -> H(e, U1(b, e))
28.57/10.31	   A^2 -> H(e, U1(b, k))
28.57/10.31	   A^2 -> H(e, U1(e, c))
28.57/10.31	   A^2 -> H(e, U1(c, e))
28.57/10.31	   A^2 -> H(e, U1(c, k))
28.57/10.31	   A^2 -> H(e, U1(e, e))
28.57/10.31	   A^2 -> H(e, U1(d, k))
28.57/10.31	   A^2 -> H(U1(e, e), b)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, e), c)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.31	   A^2 -> H(f(e), d)
28.57/10.31	   A^2 -> H(f(e), k)
28.57/10.31	   A^2 -> H(U1(k, k), b)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, k), c)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.31	   A^2 -> H(f(k), d)
28.57/10.31	   A^2 -> H(f(k), k)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.31	   A^2 -> H(U1(k, d), b)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, d), c)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, k), b)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, k), c)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, k), e)
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, d), d)
28.57/10.31	   A^2 -> H(U1(d, d), k)
28.57/10.31	   A^2 -> H(U1(e, c), c)
28.57/10.31	   A^2 -> H(U1(c, c), e)
28.57/10.31	   A^2 -> H(U1(c, c), k)
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(e, e), e)
28.57/10.31	   A^2 -> H(d, U1(e, b))
28.57/10.31	   A^2 -> H(d, U1(k, b))
28.57/10.31	   A^2 -> H(d, U1(c, d))
28.57/10.31	   A^2 -> H(d, U1(d, c))
28.57/10.31	   A^2 -> H(d, U1(b, e))
28.57/10.31	   A^2 -> H(d, U1(b, k))
28.57/10.31	   A^2 -> H(d, U1(e, c))
28.57/10.31	   A^2 -> H(d, U1(k, c))
28.57/10.31	   A^2 -> H(d, U1(c, e))
28.57/10.31	   A^2 -> H(d, U1(c, k))
28.57/10.31	   A^2 -> H(d, U1(e, e))
28.57/10.31	   A^2 -> H(d, U1(k, k))
28.57/10.31	   A^2 -> H(d, U1(k, d))
28.57/10.31	   A^2 -> H(d, U1(d, k))
28.57/10.31	   A^2 -> H(a, b)
28.57/10.31	   A^2 -> H(a, U1(e, d))
28.57/10.31	   A^2 -> H(a, U1(d, e))
28.57/10.31	   A^2 -> H(a, c)
28.57/10.31	   A^2 -> H(a, U1(e, k))
28.57/10.31	   A^2 -> H(a, U1(k, e))
28.57/10.31	   A^2 -> H(a, e)
28.57/10.31	   A^2 -> H(a, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, d), b)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, d), c)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, d), e)
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, a), d)
28.57/10.31	   A^2 -> H(U1(e, a), k)
28.57/10.31	   A^2 -> H(U1(k, a), d)
28.57/10.31	   A^2 -> H(U1(c, d), d)
28.57/10.31	   A^2 -> H(U1(c, d), k)
28.57/10.31	   A^2 -> H(U1(d, e), b)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, e), c)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, e), e)
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, c), d)
28.57/10.31	   A^2 -> H(U1(d, c), k)
28.57/10.31	   A^2 -> H(U1(a, e), d)
28.57/10.31	   A^2 -> H(U1(a, e), k)
28.57/10.31	   A^2 -> H(U1(a, k), d)
28.57/10.31	   A^2 -> H(U1(a, k), k)
28.57/10.31	   A^2 -> H(k, U1(e, b))
28.57/10.31	   A^2 -> H(k, U1(c, d))
28.57/10.31	   A^2 -> H(k, U1(d, c))
28.57/10.31	   A^2 -> H(k, U1(b, e))
28.57/10.31	   A^2 -> H(k, U1(b, k))
28.57/10.31	   A^2 -> H(k, U1(e, c))
28.57/10.31	   A^2 -> H(k, U1(c, e))
28.57/10.31	   A^2 -> H(k, U1(c, k))
28.57/10.31	   A^2 -> H(k, U1(e, e))
28.57/10.31	   A^2 -> H(k, U1(d, k))
28.57/10.31	   A^2 -> H(c, b)
28.57/10.31	   A^2 -> H(c, U1(e, d))
28.57/10.31	   A^2 -> H(c, U1(d, e))
28.57/10.31	   A^2 -> H(c, c)
28.57/10.31	   A^2 -> H(c, U1(e, k))
28.57/10.31	   A^2 -> H(c, U1(k, e))
28.57/10.31	   A^2 -> H(c, e)
28.57/10.31	   A^2 -> H(c, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, k), b)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, k), c)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, k), e)
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, c), d)
28.57/10.31	   A^2 -> H(U1(e, c), k)
28.57/10.31	   A^2 -> H(U1(k, e), b)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, e), c)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, c), d)
28.57/10.31	   A^2 -> H(U1(c, e), d)
28.57/10.31	   A^2 -> H(U1(c, e), k)
28.57/10.31	   A^2 -> H(U1(c, k), d)
28.57/10.31	   A^2 -> H(U1(c, k), k)
28.57/10.31	
28.57/10.31	The TRS R consists of the following rules:
28.57/10.31	
28.57/10.31	   f(x) -> U1(x, x)
28.57/10.31	   U1(e, x) -> x
28.57/10.31	   a -> c
28.57/10.31	   a -> d
28.57/10.31	   b -> c
28.57/10.31	   b -> d
28.57/10.31	   d -> k
28.57/10.31	   c -> e
28.57/10.31	   c -> k
28.57/10.31	
28.57/10.31	Q is empty.
28.57/10.31	We have to consider all minimal (P,Q,R)-chains.
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2223) TransformationProof (EQUIVALENT)
28.57/10.31	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), e) at position [] we obtained the following new rules [LPAR04]:
28.57/10.31	
28.57/10.31	   (A^2 -> H(U1(e, k), e),A^2 -> H(U1(e, k), e))
28.57/10.31	   (A^2 -> H(U1(k, k), e),A^2 -> H(U1(k, k), e))
28.57/10.31	
28.57/10.31	
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2224)
28.57/10.31	Obligation:
28.57/10.31	Q DP problem:
28.57/10.31	The TRS P consists of the following rules:
28.57/10.31	
28.57/10.31	   A^2 -> H(f(c), f(c))
28.57/10.31	   H(x, x) -> G(x, x, f(k))
28.57/10.31	   G(d, x, x) -> A^2
28.57/10.31	   A^2 -> H(f(d), f(d))
28.57/10.31	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.31	   A^2 -> H(f(e), f(e))
28.57/10.31	   A^2 -> H(f(k), f(k))
28.57/10.31	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.31	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.31	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.31	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.31	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(c, c), d)
28.57/10.31	   A^2 -> H(e, U1(e, b))
28.57/10.31	   A^2 -> H(e, U1(c, d))
28.57/10.31	   A^2 -> H(e, U1(d, c))
28.57/10.31	   A^2 -> H(e, U1(b, e))
28.57/10.31	   A^2 -> H(e, U1(b, k))
28.57/10.31	   A^2 -> H(e, U1(e, c))
28.57/10.31	   A^2 -> H(e, U1(c, e))
28.57/10.31	   A^2 -> H(e, U1(c, k))
28.57/10.31	   A^2 -> H(e, U1(e, e))
28.57/10.31	   A^2 -> H(e, U1(d, k))
28.57/10.31	   A^2 -> H(U1(e, e), b)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, e), c)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.31	   A^2 -> H(f(e), d)
28.57/10.31	   A^2 -> H(f(e), k)
28.57/10.31	   A^2 -> H(U1(k, k), b)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, k), c)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.31	   A^2 -> H(f(k), d)
28.57/10.31	   A^2 -> H(f(k), k)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.31	   A^2 -> H(U1(k, d), b)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, d), c)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, k), b)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, k), c)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, k), e)
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, d), d)
28.57/10.31	   A^2 -> H(U1(d, d), k)
28.57/10.31	   A^2 -> H(U1(e, c), c)
28.57/10.31	   A^2 -> H(U1(c, c), e)
28.57/10.31	   A^2 -> H(U1(c, c), k)
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(e, e), e)
28.57/10.31	   A^2 -> H(d, U1(e, b))
28.57/10.31	   A^2 -> H(d, U1(k, b))
28.57/10.31	   A^2 -> H(d, U1(c, d))
28.57/10.31	   A^2 -> H(d, U1(d, c))
28.57/10.31	   A^2 -> H(d, U1(b, e))
28.57/10.31	   A^2 -> H(d, U1(b, k))
28.57/10.31	   A^2 -> H(d, U1(e, c))
28.57/10.31	   A^2 -> H(d, U1(k, c))
28.57/10.31	   A^2 -> H(d, U1(c, e))
28.57/10.31	   A^2 -> H(d, U1(c, k))
28.57/10.31	   A^2 -> H(d, U1(e, e))
28.57/10.31	   A^2 -> H(d, U1(k, k))
28.57/10.31	   A^2 -> H(d, U1(k, d))
28.57/10.31	   A^2 -> H(d, U1(d, k))
28.57/10.31	   A^2 -> H(a, b)
28.57/10.31	   A^2 -> H(a, U1(e, d))
28.57/10.31	   A^2 -> H(a, U1(d, e))
28.57/10.31	   A^2 -> H(a, c)
28.57/10.31	   A^2 -> H(a, U1(e, k))
28.57/10.31	   A^2 -> H(a, U1(k, e))
28.57/10.31	   A^2 -> H(a, e)
28.57/10.31	   A^2 -> H(a, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, d), b)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, d), c)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, d), e)
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, a), d)
28.57/10.31	   A^2 -> H(U1(e, a), k)
28.57/10.31	   A^2 -> H(U1(k, a), d)
28.57/10.31	   A^2 -> H(U1(c, d), d)
28.57/10.31	   A^2 -> H(U1(c, d), k)
28.57/10.31	   A^2 -> H(U1(d, e), b)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, e), c)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, e), e)
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, c), d)
28.57/10.31	   A^2 -> H(U1(d, c), k)
28.57/10.31	   A^2 -> H(U1(a, e), d)
28.57/10.31	   A^2 -> H(U1(a, e), k)
28.57/10.31	   A^2 -> H(U1(a, k), d)
28.57/10.31	   A^2 -> H(U1(a, k), k)
28.57/10.31	   A^2 -> H(k, U1(e, b))
28.57/10.31	   A^2 -> H(k, U1(c, d))
28.57/10.31	   A^2 -> H(k, U1(d, c))
28.57/10.31	   A^2 -> H(k, U1(b, e))
28.57/10.31	   A^2 -> H(k, U1(b, k))
28.57/10.31	   A^2 -> H(k, U1(e, c))
28.57/10.31	   A^2 -> H(k, U1(c, e))
28.57/10.31	   A^2 -> H(k, U1(c, k))
28.57/10.31	   A^2 -> H(k, U1(e, e))
28.57/10.31	   A^2 -> H(k, U1(d, k))
28.57/10.31	   A^2 -> H(c, b)
28.57/10.31	   A^2 -> H(c, U1(e, d))
28.57/10.31	   A^2 -> H(c, U1(d, e))
28.57/10.31	   A^2 -> H(c, c)
28.57/10.31	   A^2 -> H(c, U1(e, k))
28.57/10.31	   A^2 -> H(c, U1(k, e))
28.57/10.31	   A^2 -> H(c, e)
28.57/10.31	   A^2 -> H(c, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, k), b)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, k), c)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, k), e)
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, c), d)
28.57/10.31	   A^2 -> H(U1(e, c), k)
28.57/10.31	   A^2 -> H(U1(k, e), b)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, e), c)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, c), d)
28.57/10.31	   A^2 -> H(U1(c, e), d)
28.57/10.31	   A^2 -> H(U1(c, e), k)
28.57/10.31	   A^2 -> H(U1(c, k), d)
28.57/10.31	   A^2 -> H(U1(c, k), k)
28.57/10.31	   A^2 -> H(U1(k, k), e)
28.57/10.31	
28.57/10.31	The TRS R consists of the following rules:
28.57/10.31	
28.57/10.31	   f(x) -> U1(x, x)
28.57/10.31	   U1(e, x) -> x
28.57/10.31	   a -> c
28.57/10.31	   a -> d
28.57/10.31	   b -> c
28.57/10.31	   b -> d
28.57/10.31	   d -> k
28.57/10.31	   c -> e
28.57/10.31	   c -> k
28.57/10.31	
28.57/10.31	Q is empty.
28.57/10.31	We have to consider all minimal (P,Q,R)-chains.
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2225) DependencyGraphProof (EQUIVALENT)
28.57/10.31	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2226)
28.57/10.31	Obligation:
28.57/10.31	Q DP problem:
28.57/10.31	The TRS P consists of the following rules:
28.57/10.31	
28.57/10.31	   H(x, x) -> G(x, x, f(k))
28.57/10.31	   G(d, x, x) -> A^2
28.57/10.31	   A^2 -> H(f(c), f(c))
28.57/10.31	   A^2 -> H(f(d), f(d))
28.57/10.31	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.31	   A^2 -> H(f(e), f(e))
28.57/10.31	   A^2 -> H(f(k), f(k))
28.57/10.31	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.31	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.31	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.31	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.31	   A^2 -> H(U1(c, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(c, c), d)
28.57/10.31	   A^2 -> H(e, U1(e, b))
28.57/10.31	   A^2 -> H(e, U1(c, d))
28.57/10.31	   A^2 -> H(e, U1(d, c))
28.57/10.31	   A^2 -> H(e, U1(b, e))
28.57/10.31	   A^2 -> H(e, U1(b, k))
28.57/10.31	   A^2 -> H(e, U1(e, c))
28.57/10.31	   A^2 -> H(e, U1(c, e))
28.57/10.31	   A^2 -> H(e, U1(c, k))
28.57/10.31	   A^2 -> H(e, U1(e, e))
28.57/10.31	   A^2 -> H(e, U1(d, k))
28.57/10.31	   A^2 -> H(U1(e, e), b)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, e), c)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.31	   A^2 -> H(f(e), d)
28.57/10.31	   A^2 -> H(f(e), k)
28.57/10.31	   A^2 -> H(U1(k, k), b)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, k), c)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.31	   A^2 -> H(f(k), d)
28.57/10.31	   A^2 -> H(f(k), k)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.31	   A^2 -> H(U1(k, d), b)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, d), c)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, k), b)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, k), c)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, k), e)
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, d), d)
28.57/10.31	   A^2 -> H(U1(d, d), k)
28.57/10.31	   A^2 -> H(U1(e, c), c)
28.57/10.31	   A^2 -> H(U1(c, c), e)
28.57/10.31	   A^2 -> H(U1(c, c), k)
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(e, e), e)
28.57/10.31	   A^2 -> H(d, U1(e, b))
28.57/10.31	   A^2 -> H(d, U1(k, b))
28.57/10.31	   A^2 -> H(d, U1(c, d))
28.57/10.31	   A^2 -> H(d, U1(d, c))
28.57/10.31	   A^2 -> H(d, U1(b, e))
28.57/10.31	   A^2 -> H(d, U1(b, k))
28.57/10.31	   A^2 -> H(d, U1(e, c))
28.57/10.31	   A^2 -> H(d, U1(k, c))
28.57/10.31	   A^2 -> H(d, U1(c, e))
28.57/10.31	   A^2 -> H(d, U1(c, k))
28.57/10.31	   A^2 -> H(d, U1(e, e))
28.57/10.31	   A^2 -> H(d, U1(k, k))
28.57/10.31	   A^2 -> H(d, U1(k, d))
28.57/10.31	   A^2 -> H(d, U1(d, k))
28.57/10.31	   A^2 -> H(a, b)
28.57/10.31	   A^2 -> H(a, U1(e, d))
28.57/10.31	   A^2 -> H(a, U1(d, e))
28.57/10.31	   A^2 -> H(a, c)
28.57/10.31	   A^2 -> H(a, U1(e, k))
28.57/10.31	   A^2 -> H(a, U1(k, e))
28.57/10.31	   A^2 -> H(a, e)
28.57/10.31	   A^2 -> H(a, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, d), b)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, d), c)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, d), e)
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, a), d)
28.57/10.31	   A^2 -> H(U1(e, a), k)
28.57/10.31	   A^2 -> H(U1(k, a), d)
28.57/10.31	   A^2 -> H(U1(c, d), d)
28.57/10.31	   A^2 -> H(U1(c, d), k)
28.57/10.31	   A^2 -> H(U1(d, e), b)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, e), c)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, e), e)
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, c), d)
28.57/10.31	   A^2 -> H(U1(d, c), k)
28.57/10.31	   A^2 -> H(U1(a, e), d)
28.57/10.31	   A^2 -> H(U1(a, e), k)
28.57/10.31	   A^2 -> H(U1(a, k), d)
28.57/10.31	   A^2 -> H(U1(a, k), k)
28.57/10.31	   A^2 -> H(k, U1(e, b))
28.57/10.31	   A^2 -> H(k, U1(c, d))
28.57/10.31	   A^2 -> H(k, U1(d, c))
28.57/10.31	   A^2 -> H(k, U1(b, e))
28.57/10.31	   A^2 -> H(k, U1(b, k))
28.57/10.31	   A^2 -> H(k, U1(e, c))
28.57/10.31	   A^2 -> H(k, U1(c, e))
28.57/10.31	   A^2 -> H(k, U1(c, k))
28.57/10.31	   A^2 -> H(k, U1(e, e))
28.57/10.31	   A^2 -> H(k, U1(d, k))
28.57/10.31	   A^2 -> H(c, b)
28.57/10.31	   A^2 -> H(c, U1(e, d))
28.57/10.31	   A^2 -> H(c, U1(d, e))
28.57/10.31	   A^2 -> H(c, c)
28.57/10.31	   A^2 -> H(c, U1(e, k))
28.57/10.31	   A^2 -> H(c, U1(k, e))
28.57/10.31	   A^2 -> H(c, e)
28.57/10.31	   A^2 -> H(c, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, k), b)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, k), c)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, k), e)
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, c), d)
28.57/10.31	   A^2 -> H(U1(e, c), k)
28.57/10.31	   A^2 -> H(U1(k, e), b)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, e), c)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, c), d)
28.57/10.31	   A^2 -> H(U1(c, e), d)
28.57/10.31	   A^2 -> H(U1(c, e), k)
28.57/10.31	   A^2 -> H(U1(c, k), d)
28.57/10.31	   A^2 -> H(U1(c, k), k)
28.57/10.31	
28.57/10.31	The TRS R consists of the following rules:
28.57/10.31	
28.57/10.31	   f(x) -> U1(x, x)
28.57/10.31	   U1(e, x) -> x
28.57/10.31	   a -> c
28.57/10.31	   a -> d
28.57/10.31	   b -> c
28.57/10.31	   b -> d
28.57/10.31	   d -> k
28.57/10.31	   c -> e
28.57/10.31	   c -> k
28.57/10.31	
28.57/10.31	Q is empty.
28.57/10.31	We have to consider all minimal (P,Q,R)-chains.
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2227) TransformationProof (EQUIVALENT)
28.57/10.31	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.31	
28.57/10.31	   (A^2 -> H(U1(e, k), U1(k, k)),A^2 -> H(U1(e, k), U1(k, k)))
28.57/10.31	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.57/10.31	
28.57/10.31	
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2228)
28.57/10.31	Obligation:
28.57/10.31	Q DP problem:
28.57/10.31	The TRS P consists of the following rules:
28.57/10.31	
28.57/10.31	   H(x, x) -> G(x, x, f(k))
28.57/10.31	   G(d, x, x) -> A^2
28.57/10.31	   A^2 -> H(f(c), f(c))
28.57/10.31	   A^2 -> H(f(d), f(d))
28.57/10.31	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.31	   A^2 -> H(f(e), f(e))
28.57/10.31	   A^2 -> H(f(k), f(k))
28.57/10.31	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.31	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.31	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.31	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.31	   A^2 -> H(U1(c, c), d)
28.57/10.31	   A^2 -> H(e, U1(e, b))
28.57/10.31	   A^2 -> H(e, U1(c, d))
28.57/10.31	   A^2 -> H(e, U1(d, c))
28.57/10.31	   A^2 -> H(e, U1(b, e))
28.57/10.31	   A^2 -> H(e, U1(b, k))
28.57/10.31	   A^2 -> H(e, U1(e, c))
28.57/10.31	   A^2 -> H(e, U1(c, e))
28.57/10.31	   A^2 -> H(e, U1(c, k))
28.57/10.31	   A^2 -> H(e, U1(e, e))
28.57/10.31	   A^2 -> H(e, U1(d, k))
28.57/10.31	   A^2 -> H(U1(e, e), b)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, e), c)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.31	   A^2 -> H(f(e), d)
28.57/10.31	   A^2 -> H(f(e), k)
28.57/10.31	   A^2 -> H(U1(k, k), b)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, k), c)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.31	   A^2 -> H(f(k), d)
28.57/10.31	   A^2 -> H(f(k), k)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.31	   A^2 -> H(U1(k, d), b)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, d), c)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, k), b)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, k), c)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, k), e)
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, d), d)
28.57/10.31	   A^2 -> H(U1(d, d), k)
28.57/10.31	   A^2 -> H(U1(e, c), c)
28.57/10.31	   A^2 -> H(U1(c, c), e)
28.57/10.31	   A^2 -> H(U1(c, c), k)
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(e, e), e)
28.57/10.31	   A^2 -> H(d, U1(e, b))
28.57/10.31	   A^2 -> H(d, U1(k, b))
28.57/10.31	   A^2 -> H(d, U1(c, d))
28.57/10.31	   A^2 -> H(d, U1(d, c))
28.57/10.31	   A^2 -> H(d, U1(b, e))
28.57/10.31	   A^2 -> H(d, U1(b, k))
28.57/10.31	   A^2 -> H(d, U1(e, c))
28.57/10.31	   A^2 -> H(d, U1(k, c))
28.57/10.31	   A^2 -> H(d, U1(c, e))
28.57/10.31	   A^2 -> H(d, U1(c, k))
28.57/10.31	   A^2 -> H(d, U1(e, e))
28.57/10.31	   A^2 -> H(d, U1(k, k))
28.57/10.31	   A^2 -> H(d, U1(k, d))
28.57/10.31	   A^2 -> H(d, U1(d, k))
28.57/10.31	   A^2 -> H(a, b)
28.57/10.31	   A^2 -> H(a, U1(e, d))
28.57/10.31	   A^2 -> H(a, U1(d, e))
28.57/10.31	   A^2 -> H(a, c)
28.57/10.31	   A^2 -> H(a, U1(e, k))
28.57/10.31	   A^2 -> H(a, U1(k, e))
28.57/10.31	   A^2 -> H(a, e)
28.57/10.31	   A^2 -> H(a, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, d), b)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, d), c)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, d), e)
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, a), d)
28.57/10.31	   A^2 -> H(U1(e, a), k)
28.57/10.31	   A^2 -> H(U1(k, a), d)
28.57/10.31	   A^2 -> H(U1(c, d), d)
28.57/10.31	   A^2 -> H(U1(c, d), k)
28.57/10.31	   A^2 -> H(U1(d, e), b)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, e), c)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, e), e)
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, c), d)
28.57/10.31	   A^2 -> H(U1(d, c), k)
28.57/10.31	   A^2 -> H(U1(a, e), d)
28.57/10.31	   A^2 -> H(U1(a, e), k)
28.57/10.31	   A^2 -> H(U1(a, k), d)
28.57/10.31	   A^2 -> H(U1(a, k), k)
28.57/10.31	   A^2 -> H(k, U1(e, b))
28.57/10.31	   A^2 -> H(k, U1(c, d))
28.57/10.31	   A^2 -> H(k, U1(d, c))
28.57/10.31	   A^2 -> H(k, U1(b, e))
28.57/10.31	   A^2 -> H(k, U1(b, k))
28.57/10.31	   A^2 -> H(k, U1(e, c))
28.57/10.31	   A^2 -> H(k, U1(c, e))
28.57/10.31	   A^2 -> H(k, U1(c, k))
28.57/10.31	   A^2 -> H(k, U1(e, e))
28.57/10.31	   A^2 -> H(k, U1(d, k))
28.57/10.31	   A^2 -> H(c, b)
28.57/10.31	   A^2 -> H(c, U1(e, d))
28.57/10.31	   A^2 -> H(c, U1(d, e))
28.57/10.31	   A^2 -> H(c, c)
28.57/10.31	   A^2 -> H(c, U1(e, k))
28.57/10.31	   A^2 -> H(c, U1(k, e))
28.57/10.31	   A^2 -> H(c, e)
28.57/10.31	   A^2 -> H(c, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, k), b)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, k), c)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, k), e)
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, c), d)
28.57/10.31	   A^2 -> H(U1(e, c), k)
28.57/10.31	   A^2 -> H(U1(k, e), b)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, e), c)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, c), d)
28.57/10.31	   A^2 -> H(U1(c, e), d)
28.57/10.31	   A^2 -> H(U1(c, e), k)
28.57/10.31	   A^2 -> H(U1(c, k), d)
28.57/10.31	   A^2 -> H(U1(c, k), k)
28.57/10.31	
28.57/10.31	The TRS R consists of the following rules:
28.57/10.31	
28.57/10.31	   f(x) -> U1(x, x)
28.57/10.31	   U1(e, x) -> x
28.57/10.31	   a -> c
28.57/10.31	   a -> d
28.57/10.31	   b -> c
28.57/10.31	   b -> d
28.57/10.31	   d -> k
28.57/10.31	   c -> e
28.57/10.31	   c -> k
28.57/10.31	
28.57/10.31	Q is empty.
28.57/10.31	We have to consider all minimal (P,Q,R)-chains.
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2229) TransformationProof (EQUIVALENT)
28.57/10.31	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), d) at position [] we obtained the following new rules [LPAR04]:
28.57/10.31	
28.57/10.31	   (A^2 -> H(U1(e, c), d),A^2 -> H(U1(e, c), d))
28.57/10.31	   (A^2 -> H(U1(k, c), d),A^2 -> H(U1(k, c), d))
28.57/10.31	   (A^2 -> H(U1(c, e), d),A^2 -> H(U1(c, e), d))
28.57/10.31	   (A^2 -> H(U1(c, k), d),A^2 -> H(U1(c, k), d))
28.57/10.31	   (A^2 -> H(U1(c, c), k),A^2 -> H(U1(c, c), k))
28.57/10.31	
28.57/10.31	
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2230)
28.57/10.31	Obligation:
28.57/10.31	Q DP problem:
28.57/10.31	The TRS P consists of the following rules:
28.57/10.31	
28.57/10.31	   H(x, x) -> G(x, x, f(k))
28.57/10.31	   G(d, x, x) -> A^2
28.57/10.31	   A^2 -> H(f(c), f(c))
28.57/10.31	   A^2 -> H(f(d), f(d))
28.57/10.31	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.31	   A^2 -> H(f(e), f(e))
28.57/10.31	   A^2 -> H(f(k), f(k))
28.57/10.31	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.31	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.31	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.31	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.31	   A^2 -> H(e, U1(e, b))
28.57/10.31	   A^2 -> H(e, U1(c, d))
28.57/10.31	   A^2 -> H(e, U1(d, c))
28.57/10.31	   A^2 -> H(e, U1(b, e))
28.57/10.31	   A^2 -> H(e, U1(b, k))
28.57/10.31	   A^2 -> H(e, U1(e, c))
28.57/10.31	   A^2 -> H(e, U1(c, e))
28.57/10.31	   A^2 -> H(e, U1(c, k))
28.57/10.31	   A^2 -> H(e, U1(e, e))
28.57/10.31	   A^2 -> H(e, U1(d, k))
28.57/10.31	   A^2 -> H(U1(e, e), b)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, e), c)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.31	   A^2 -> H(f(e), d)
28.57/10.31	   A^2 -> H(f(e), k)
28.57/10.31	   A^2 -> H(U1(k, k), b)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, k), c)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.31	   A^2 -> H(f(k), d)
28.57/10.31	   A^2 -> H(f(k), k)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.31	   A^2 -> H(U1(k, d), b)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, d), c)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, k), b)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, k), c)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, k), e)
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, d), d)
28.57/10.31	   A^2 -> H(U1(d, d), k)
28.57/10.31	   A^2 -> H(U1(e, c), c)
28.57/10.31	   A^2 -> H(U1(c, c), e)
28.57/10.31	   A^2 -> H(U1(c, c), k)
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(e, e), e)
28.57/10.31	   A^2 -> H(d, U1(e, b))
28.57/10.31	   A^2 -> H(d, U1(k, b))
28.57/10.31	   A^2 -> H(d, U1(c, d))
28.57/10.31	   A^2 -> H(d, U1(d, c))
28.57/10.31	   A^2 -> H(d, U1(b, e))
28.57/10.31	   A^2 -> H(d, U1(b, k))
28.57/10.31	   A^2 -> H(d, U1(e, c))
28.57/10.31	   A^2 -> H(d, U1(k, c))
28.57/10.31	   A^2 -> H(d, U1(c, e))
28.57/10.31	   A^2 -> H(d, U1(c, k))
28.57/10.31	   A^2 -> H(d, U1(e, e))
28.57/10.31	   A^2 -> H(d, U1(k, k))
28.57/10.31	   A^2 -> H(d, U1(k, d))
28.57/10.31	   A^2 -> H(d, U1(d, k))
28.57/10.31	   A^2 -> H(a, b)
28.57/10.31	   A^2 -> H(a, U1(e, d))
28.57/10.31	   A^2 -> H(a, U1(d, e))
28.57/10.31	   A^2 -> H(a, c)
28.57/10.31	   A^2 -> H(a, U1(e, k))
28.57/10.31	   A^2 -> H(a, U1(k, e))
28.57/10.31	   A^2 -> H(a, e)
28.57/10.31	   A^2 -> H(a, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, d), b)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, d), c)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, d), e)
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, a), d)
28.57/10.31	   A^2 -> H(U1(e, a), k)
28.57/10.31	   A^2 -> H(U1(k, a), d)
28.57/10.31	   A^2 -> H(U1(c, d), d)
28.57/10.31	   A^2 -> H(U1(c, d), k)
28.57/10.31	   A^2 -> H(U1(d, e), b)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, e), c)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, e), e)
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, c), d)
28.57/10.31	   A^2 -> H(U1(d, c), k)
28.57/10.31	   A^2 -> H(U1(a, e), d)
28.57/10.31	   A^2 -> H(U1(a, e), k)
28.57/10.31	   A^2 -> H(U1(a, k), d)
28.57/10.31	   A^2 -> H(U1(a, k), k)
28.57/10.31	   A^2 -> H(k, U1(e, b))
28.57/10.31	   A^2 -> H(k, U1(c, d))
28.57/10.31	   A^2 -> H(k, U1(d, c))
28.57/10.31	   A^2 -> H(k, U1(b, e))
28.57/10.31	   A^2 -> H(k, U1(b, k))
28.57/10.31	   A^2 -> H(k, U1(e, c))
28.57/10.31	   A^2 -> H(k, U1(c, e))
28.57/10.31	   A^2 -> H(k, U1(c, k))
28.57/10.31	   A^2 -> H(k, U1(e, e))
28.57/10.31	   A^2 -> H(k, U1(d, k))
28.57/10.31	   A^2 -> H(c, b)
28.57/10.31	   A^2 -> H(c, U1(e, d))
28.57/10.31	   A^2 -> H(c, U1(d, e))
28.57/10.31	   A^2 -> H(c, c)
28.57/10.31	   A^2 -> H(c, U1(e, k))
28.57/10.31	   A^2 -> H(c, U1(k, e))
28.57/10.31	   A^2 -> H(c, e)
28.57/10.31	   A^2 -> H(c, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, k), b)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, k), c)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, k), e)
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, c), d)
28.57/10.31	   A^2 -> H(U1(e, c), k)
28.57/10.31	   A^2 -> H(U1(k, e), b)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, e), c)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, c), d)
28.57/10.31	   A^2 -> H(U1(c, e), d)
28.57/10.31	   A^2 -> H(U1(c, e), k)
28.57/10.31	   A^2 -> H(U1(c, k), d)
28.57/10.31	   A^2 -> H(U1(c, k), k)
28.57/10.31	
28.57/10.31	The TRS R consists of the following rules:
28.57/10.31	
28.57/10.31	   f(x) -> U1(x, x)
28.57/10.31	   U1(e, x) -> x
28.57/10.31	   a -> c
28.57/10.31	   a -> d
28.57/10.31	   b -> c
28.57/10.31	   b -> d
28.57/10.31	   d -> k
28.57/10.31	   c -> e
28.57/10.31	   c -> k
28.57/10.31	
28.57/10.31	Q is empty.
28.57/10.31	We have to consider all minimal (P,Q,R)-chains.
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2231) TransformationProof (EQUIVALENT)
28.57/10.31	By narrowing [LPAR04] the rule A^2 -> H(e, U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.31	
28.57/10.31	   (A^2 -> H(e, b),A^2 -> H(e, b))
28.57/10.31	   (A^2 -> H(e, U1(e, c)),A^2 -> H(e, U1(e, c)))
28.57/10.31	   (A^2 -> H(e, U1(e, d)),A^2 -> H(e, U1(e, d)))
28.57/10.31	
28.57/10.31	
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2232)
28.57/10.31	Obligation:
28.57/10.31	Q DP problem:
28.57/10.31	The TRS P consists of the following rules:
28.57/10.31	
28.57/10.31	   H(x, x) -> G(x, x, f(k))
28.57/10.31	   G(d, x, x) -> A^2
28.57/10.31	   A^2 -> H(f(c), f(c))
28.57/10.31	   A^2 -> H(f(d), f(d))
28.57/10.31	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.31	   A^2 -> H(f(e), f(e))
28.57/10.31	   A^2 -> H(f(k), f(k))
28.57/10.31	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.31	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.31	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.31	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.31	   A^2 -> H(e, U1(c, d))
28.57/10.31	   A^2 -> H(e, U1(d, c))
28.57/10.31	   A^2 -> H(e, U1(b, e))
28.57/10.31	   A^2 -> H(e, U1(b, k))
28.57/10.31	   A^2 -> H(e, U1(e, c))
28.57/10.31	   A^2 -> H(e, U1(c, e))
28.57/10.31	   A^2 -> H(e, U1(c, k))
28.57/10.31	   A^2 -> H(e, U1(e, e))
28.57/10.31	   A^2 -> H(e, U1(d, k))
28.57/10.31	   A^2 -> H(U1(e, e), b)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, e), c)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.31	   A^2 -> H(f(e), d)
28.57/10.31	   A^2 -> H(f(e), k)
28.57/10.31	   A^2 -> H(U1(k, k), b)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, k), c)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.31	   A^2 -> H(f(k), d)
28.57/10.31	   A^2 -> H(f(k), k)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.31	   A^2 -> H(U1(k, d), b)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, d), c)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, k), b)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, k), c)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, k), e)
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, d), d)
28.57/10.31	   A^2 -> H(U1(d, d), k)
28.57/10.31	   A^2 -> H(U1(e, c), c)
28.57/10.31	   A^2 -> H(U1(c, c), e)
28.57/10.31	   A^2 -> H(U1(c, c), k)
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(e, e), e)
28.57/10.31	   A^2 -> H(d, U1(e, b))
28.57/10.31	   A^2 -> H(d, U1(k, b))
28.57/10.31	   A^2 -> H(d, U1(c, d))
28.57/10.31	   A^2 -> H(d, U1(d, c))
28.57/10.31	   A^2 -> H(d, U1(b, e))
28.57/10.31	   A^2 -> H(d, U1(b, k))
28.57/10.31	   A^2 -> H(d, U1(e, c))
28.57/10.31	   A^2 -> H(d, U1(k, c))
28.57/10.31	   A^2 -> H(d, U1(c, e))
28.57/10.31	   A^2 -> H(d, U1(c, k))
28.57/10.31	   A^2 -> H(d, U1(e, e))
28.57/10.31	   A^2 -> H(d, U1(k, k))
28.57/10.31	   A^2 -> H(d, U1(k, d))
28.57/10.31	   A^2 -> H(d, U1(d, k))
28.57/10.31	   A^2 -> H(a, b)
28.57/10.31	   A^2 -> H(a, U1(e, d))
28.57/10.31	   A^2 -> H(a, U1(d, e))
28.57/10.31	   A^2 -> H(a, c)
28.57/10.31	   A^2 -> H(a, U1(e, k))
28.57/10.31	   A^2 -> H(a, U1(k, e))
28.57/10.31	   A^2 -> H(a, e)
28.57/10.31	   A^2 -> H(a, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, d), b)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, d), c)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, d), e)
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, a), d)
28.57/10.31	   A^2 -> H(U1(e, a), k)
28.57/10.31	   A^2 -> H(U1(k, a), d)
28.57/10.31	   A^2 -> H(U1(c, d), d)
28.57/10.31	   A^2 -> H(U1(c, d), k)
28.57/10.31	   A^2 -> H(U1(d, e), b)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, e), c)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, e), e)
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, c), d)
28.57/10.31	   A^2 -> H(U1(d, c), k)
28.57/10.31	   A^2 -> H(U1(a, e), d)
28.57/10.31	   A^2 -> H(U1(a, e), k)
28.57/10.31	   A^2 -> H(U1(a, k), d)
28.57/10.31	   A^2 -> H(U1(a, k), k)
28.57/10.31	   A^2 -> H(k, U1(e, b))
28.57/10.31	   A^2 -> H(k, U1(c, d))
28.57/10.31	   A^2 -> H(k, U1(d, c))
28.57/10.31	   A^2 -> H(k, U1(b, e))
28.57/10.31	   A^2 -> H(k, U1(b, k))
28.57/10.31	   A^2 -> H(k, U1(e, c))
28.57/10.31	   A^2 -> H(k, U1(c, e))
28.57/10.31	   A^2 -> H(k, U1(c, k))
28.57/10.31	   A^2 -> H(k, U1(e, e))
28.57/10.31	   A^2 -> H(k, U1(d, k))
28.57/10.31	   A^2 -> H(c, b)
28.57/10.31	   A^2 -> H(c, U1(e, d))
28.57/10.31	   A^2 -> H(c, U1(d, e))
28.57/10.31	   A^2 -> H(c, c)
28.57/10.31	   A^2 -> H(c, U1(e, k))
28.57/10.31	   A^2 -> H(c, U1(k, e))
28.57/10.31	   A^2 -> H(c, e)
28.57/10.31	   A^2 -> H(c, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, k), b)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, k), c)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, k), e)
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, c), d)
28.57/10.31	   A^2 -> H(U1(e, c), k)
28.57/10.31	   A^2 -> H(U1(k, e), b)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, e), c)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, c), d)
28.57/10.31	   A^2 -> H(U1(c, e), d)
28.57/10.31	   A^2 -> H(U1(c, e), k)
28.57/10.31	   A^2 -> H(U1(c, k), d)
28.57/10.31	   A^2 -> H(U1(c, k), k)
28.57/10.31	   A^2 -> H(e, b)
28.57/10.31	   A^2 -> H(e, U1(e, d))
28.57/10.31	
28.57/10.31	The TRS R consists of the following rules:
28.57/10.31	
28.57/10.31	   f(x) -> U1(x, x)
28.57/10.31	   U1(e, x) -> x
28.57/10.31	   a -> c
28.57/10.31	   a -> d
28.57/10.31	   b -> c
28.57/10.31	   b -> d
28.57/10.31	   d -> k
28.57/10.31	   c -> e
28.57/10.31	   c -> k
28.57/10.31	
28.57/10.31	Q is empty.
28.57/10.31	We have to consider all minimal (P,Q,R)-chains.
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2233) TransformationProof (EQUIVALENT)
28.57/10.31	By narrowing [LPAR04] the rule A^2 -> H(e, U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.31	
28.57/10.31	   (A^2 -> H(e, U1(e, d)),A^2 -> H(e, U1(e, d)))
28.57/10.31	   (A^2 -> H(e, U1(k, d)),A^2 -> H(e, U1(k, d)))
28.57/10.31	   (A^2 -> H(e, U1(c, k)),A^2 -> H(e, U1(c, k)))
28.57/10.31	
28.57/10.31	
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2234)
28.57/10.31	Obligation:
28.57/10.31	Q DP problem:
28.57/10.31	The TRS P consists of the following rules:
28.57/10.31	
28.57/10.31	   H(x, x) -> G(x, x, f(k))
28.57/10.31	   G(d, x, x) -> A^2
28.57/10.31	   A^2 -> H(f(c), f(c))
28.57/10.31	   A^2 -> H(f(d), f(d))
28.57/10.31	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.31	   A^2 -> H(f(e), f(e))
28.57/10.31	   A^2 -> H(f(k), f(k))
28.57/10.31	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.31	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.31	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.31	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.31	   A^2 -> H(e, U1(d, c))
28.57/10.31	   A^2 -> H(e, U1(b, e))
28.57/10.31	   A^2 -> H(e, U1(b, k))
28.57/10.31	   A^2 -> H(e, U1(e, c))
28.57/10.31	   A^2 -> H(e, U1(c, e))
28.57/10.31	   A^2 -> H(e, U1(c, k))
28.57/10.31	   A^2 -> H(e, U1(e, e))
28.57/10.31	   A^2 -> H(e, U1(d, k))
28.57/10.31	   A^2 -> H(U1(e, e), b)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, e), c)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.31	   A^2 -> H(f(e), d)
28.57/10.31	   A^2 -> H(f(e), k)
28.57/10.31	   A^2 -> H(U1(k, k), b)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, k), c)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.31	   A^2 -> H(f(k), d)
28.57/10.31	   A^2 -> H(f(k), k)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.31	   A^2 -> H(U1(k, d), b)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, d), c)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, k), b)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, k), c)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, k), e)
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, d), d)
28.57/10.31	   A^2 -> H(U1(d, d), k)
28.57/10.31	   A^2 -> H(U1(e, c), c)
28.57/10.31	   A^2 -> H(U1(c, c), e)
28.57/10.31	   A^2 -> H(U1(c, c), k)
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(e, e), e)
28.57/10.31	   A^2 -> H(d, U1(e, b))
28.57/10.31	   A^2 -> H(d, U1(k, b))
28.57/10.31	   A^2 -> H(d, U1(c, d))
28.57/10.31	   A^2 -> H(d, U1(d, c))
28.57/10.31	   A^2 -> H(d, U1(b, e))
28.57/10.31	   A^2 -> H(d, U1(b, k))
28.57/10.31	   A^2 -> H(d, U1(e, c))
28.57/10.31	   A^2 -> H(d, U1(k, c))
28.57/10.31	   A^2 -> H(d, U1(c, e))
28.57/10.31	   A^2 -> H(d, U1(c, k))
28.57/10.31	   A^2 -> H(d, U1(e, e))
28.57/10.31	   A^2 -> H(d, U1(k, k))
28.57/10.31	   A^2 -> H(d, U1(k, d))
28.57/10.31	   A^2 -> H(d, U1(d, k))
28.57/10.31	   A^2 -> H(a, b)
28.57/10.31	   A^2 -> H(a, U1(e, d))
28.57/10.31	   A^2 -> H(a, U1(d, e))
28.57/10.31	   A^2 -> H(a, c)
28.57/10.31	   A^2 -> H(a, U1(e, k))
28.57/10.31	   A^2 -> H(a, U1(k, e))
28.57/10.31	   A^2 -> H(a, e)
28.57/10.31	   A^2 -> H(a, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, d), b)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, d), c)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, d), e)
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, a), d)
28.57/10.31	   A^2 -> H(U1(e, a), k)
28.57/10.31	   A^2 -> H(U1(k, a), d)
28.57/10.31	   A^2 -> H(U1(c, d), d)
28.57/10.31	   A^2 -> H(U1(c, d), k)
28.57/10.31	   A^2 -> H(U1(d, e), b)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, e), c)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, e), e)
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, c), d)
28.57/10.31	   A^2 -> H(U1(d, c), k)
28.57/10.31	   A^2 -> H(U1(a, e), d)
28.57/10.31	   A^2 -> H(U1(a, e), k)
28.57/10.31	   A^2 -> H(U1(a, k), d)
28.57/10.31	   A^2 -> H(U1(a, k), k)
28.57/10.31	   A^2 -> H(k, U1(e, b))
28.57/10.31	   A^2 -> H(k, U1(c, d))
28.57/10.31	   A^2 -> H(k, U1(d, c))
28.57/10.31	   A^2 -> H(k, U1(b, e))
28.57/10.31	   A^2 -> H(k, U1(b, k))
28.57/10.31	   A^2 -> H(k, U1(e, c))
28.57/10.31	   A^2 -> H(k, U1(c, e))
28.57/10.31	   A^2 -> H(k, U1(c, k))
28.57/10.31	   A^2 -> H(k, U1(e, e))
28.57/10.31	   A^2 -> H(k, U1(d, k))
28.57/10.31	   A^2 -> H(c, b)
28.57/10.31	   A^2 -> H(c, U1(e, d))
28.57/10.31	   A^2 -> H(c, U1(d, e))
28.57/10.31	   A^2 -> H(c, c)
28.57/10.31	   A^2 -> H(c, U1(e, k))
28.57/10.31	   A^2 -> H(c, U1(k, e))
28.57/10.31	   A^2 -> H(c, e)
28.57/10.31	   A^2 -> H(c, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, k), b)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, k), c)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, k), e)
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, c), d)
28.57/10.31	   A^2 -> H(U1(e, c), k)
28.57/10.31	   A^2 -> H(U1(k, e), b)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, e), c)
28.57/10.31	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, c), d)
28.57/10.31	   A^2 -> H(U1(c, e), d)
28.57/10.31	   A^2 -> H(U1(c, e), k)
28.57/10.31	   A^2 -> H(U1(c, k), d)
28.57/10.31	   A^2 -> H(U1(c, k), k)
28.57/10.31	   A^2 -> H(e, b)
28.57/10.31	   A^2 -> H(e, U1(e, d))
28.57/10.31	   A^2 -> H(e, U1(k, d))
28.57/10.31	
28.57/10.31	The TRS R consists of the following rules:
28.57/10.31	
28.57/10.31	   f(x) -> U1(x, x)
28.57/10.31	   U1(e, x) -> x
28.57/10.31	   a -> c
28.57/10.31	   a -> d
28.57/10.31	   b -> c
28.57/10.31	   b -> d
28.57/10.31	   d -> k
28.57/10.31	   c -> e
28.57/10.31	   c -> k
28.57/10.31	
28.57/10.31	Q is empty.
28.57/10.31	We have to consider all minimal (P,Q,R)-chains.
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2235) DependencyGraphProof (EQUIVALENT)
28.57/10.31	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.31	----------------------------------------
28.57/10.31	
28.57/10.31	(2236)
28.57/10.31	Obligation:
28.57/10.31	Q DP problem:
28.57/10.31	The TRS P consists of the following rules:
28.57/10.31	
28.57/10.31	   G(d, x, x) -> A^2
28.57/10.31	   A^2 -> H(f(c), f(c))
28.57/10.31	   H(x, x) -> G(x, x, f(k))
28.57/10.31	   A^2 -> H(f(d), f(d))
28.57/10.31	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.31	   A^2 -> H(f(e), f(e))
28.57/10.31	   A^2 -> H(f(k), f(k))
28.57/10.31	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.31	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.31	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.31	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.31	   A^2 -> H(e, U1(d, c))
28.57/10.31	   A^2 -> H(e, U1(b, e))
28.57/10.31	   A^2 -> H(e, U1(b, k))
28.57/10.31	   A^2 -> H(e, U1(e, c))
28.57/10.31	   A^2 -> H(e, U1(c, e))
28.57/10.31	   A^2 -> H(e, U1(c, k))
28.57/10.31	   A^2 -> H(e, U1(e, e))
28.57/10.31	   A^2 -> H(e, U1(d, k))
28.57/10.31	   A^2 -> H(U1(e, e), b)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, e), c)
28.57/10.31	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.31	   A^2 -> H(f(e), d)
28.57/10.31	   A^2 -> H(f(e), k)
28.57/10.31	   A^2 -> H(U1(k, k), b)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, k), c)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.31	   A^2 -> H(f(k), d)
28.57/10.31	   A^2 -> H(f(k), k)
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.31	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.31	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.31	   A^2 -> H(U1(k, d), b)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(k, d), c)
28.57/10.31	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, k), b)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, k), c)
28.57/10.31	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, k), e)
28.57/10.31	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, d), d)
28.57/10.31	   A^2 -> H(U1(d, d), k)
28.57/10.31	   A^2 -> H(U1(e, c), c)
28.57/10.31	   A^2 -> H(U1(c, c), e)
28.57/10.31	   A^2 -> H(U1(c, c), k)
28.57/10.31	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.31	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.31	   A^2 -> H(U1(e, e), e)
28.57/10.31	   A^2 -> H(d, U1(e, b))
28.57/10.31	   A^2 -> H(d, U1(k, b))
28.57/10.31	   A^2 -> H(d, U1(c, d))
28.57/10.31	   A^2 -> H(d, U1(d, c))
28.57/10.31	   A^2 -> H(d, U1(b, e))
28.57/10.31	   A^2 -> H(d, U1(b, k))
28.57/10.31	   A^2 -> H(d, U1(e, c))
28.57/10.31	   A^2 -> H(d, U1(k, c))
28.57/10.31	   A^2 -> H(d, U1(c, e))
28.57/10.31	   A^2 -> H(d, U1(c, k))
28.57/10.31	   A^2 -> H(d, U1(e, e))
28.57/10.31	   A^2 -> H(d, U1(k, k))
28.57/10.31	   A^2 -> H(d, U1(k, d))
28.57/10.31	   A^2 -> H(d, U1(d, k))
28.57/10.31	   A^2 -> H(a, b)
28.57/10.31	   A^2 -> H(a, U1(e, d))
28.57/10.31	   A^2 -> H(a, U1(d, e))
28.57/10.31	   A^2 -> H(a, c)
28.57/10.31	   A^2 -> H(a, U1(e, k))
28.57/10.31	   A^2 -> H(a, U1(k, e))
28.57/10.31	   A^2 -> H(a, e)
28.57/10.31	   A^2 -> H(a, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, d), b)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, d), c)
28.57/10.31	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, d), e)
28.57/10.31	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, a), d)
28.57/10.31	   A^2 -> H(U1(e, a), k)
28.57/10.31	   A^2 -> H(U1(k, a), d)
28.57/10.31	   A^2 -> H(U1(c, d), d)
28.57/10.31	   A^2 -> H(U1(c, d), k)
28.57/10.31	   A^2 -> H(U1(d, e), b)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.31	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.31	   A^2 -> H(U1(d, e), c)
28.57/10.31	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.31	   A^2 -> H(U1(d, e), e)
28.57/10.31	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.31	   A^2 -> H(U1(d, c), d)
28.57/10.31	   A^2 -> H(U1(d, c), k)
28.57/10.31	   A^2 -> H(U1(a, e), d)
28.57/10.31	   A^2 -> H(U1(a, e), k)
28.57/10.31	   A^2 -> H(U1(a, k), d)
28.57/10.31	   A^2 -> H(U1(a, k), k)
28.57/10.31	   A^2 -> H(k, U1(e, b))
28.57/10.31	   A^2 -> H(k, U1(c, d))
28.57/10.31	   A^2 -> H(k, U1(d, c))
28.57/10.31	   A^2 -> H(k, U1(b, e))
28.57/10.31	   A^2 -> H(k, U1(b, k))
28.57/10.31	   A^2 -> H(k, U1(e, c))
28.57/10.31	   A^2 -> H(k, U1(c, e))
28.57/10.31	   A^2 -> H(k, U1(c, k))
28.57/10.31	   A^2 -> H(k, U1(e, e))
28.57/10.31	   A^2 -> H(k, U1(d, k))
28.57/10.31	   A^2 -> H(c, b)
28.57/10.31	   A^2 -> H(c, U1(e, d))
28.57/10.31	   A^2 -> H(c, U1(d, e))
28.57/10.31	   A^2 -> H(c, c)
28.57/10.31	   A^2 -> H(c, U1(e, k))
28.57/10.31	   A^2 -> H(c, U1(k, e))
28.57/10.31	   A^2 -> H(c, e)
28.57/10.31	   A^2 -> H(c, U1(k, k))
28.57/10.31	   A^2 -> H(U1(e, k), b)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.31	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.31	   A^2 -> H(U1(e, k), c)
28.57/10.31	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.31	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.31	   A^2 -> H(U1(e, k), e)
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, c), d)
28.57/10.32	   A^2 -> H(U1(e, c), k)
28.57/10.32	   A^2 -> H(U1(k, e), b)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, e), c)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, c), d)
28.57/10.32	   A^2 -> H(U1(c, e), d)
28.57/10.32	   A^2 -> H(U1(c, e), k)
28.57/10.32	   A^2 -> H(U1(c, k), d)
28.57/10.32	   A^2 -> H(U1(c, k), k)
28.57/10.32	   A^2 -> H(e, b)
28.57/10.32	   A^2 -> H(e, U1(e, d))
28.57/10.32	
28.57/10.32	The TRS R consists of the following rules:
28.57/10.32	
28.57/10.32	   f(x) -> U1(x, x)
28.57/10.32	   U1(e, x) -> x
28.57/10.32	   a -> c
28.57/10.32	   a -> d
28.57/10.32	   b -> c
28.57/10.32	   b -> d
28.57/10.32	   d -> k
28.57/10.32	   c -> e
28.57/10.32	   c -> k
28.57/10.32	
28.57/10.32	Q is empty.
28.57/10.32	We have to consider all minimal (P,Q,R)-chains.
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2237) TransformationProof (EQUIVALENT)
28.57/10.32	By narrowing [LPAR04] the rule A^2 -> H(e, U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.32	
28.57/10.32	   (A^2 -> H(e, U1(k, c)),A^2 -> H(e, U1(k, c)))
28.57/10.32	   (A^2 -> H(e, U1(d, e)),A^2 -> H(e, U1(d, e)))
28.57/10.32	   (A^2 -> H(e, U1(d, k)),A^2 -> H(e, U1(d, k)))
28.57/10.32	
28.57/10.32	
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2238)
28.57/10.32	Obligation:
28.57/10.32	Q DP problem:
28.57/10.32	The TRS P consists of the following rules:
28.57/10.32	
28.57/10.32	   G(d, x, x) -> A^2
28.57/10.32	   A^2 -> H(f(c), f(c))
28.57/10.32	   H(x, x) -> G(x, x, f(k))
28.57/10.32	   A^2 -> H(f(d), f(d))
28.57/10.32	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.32	   A^2 -> H(f(e), f(e))
28.57/10.32	   A^2 -> H(f(k), f(k))
28.57/10.32	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.32	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.32	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.32	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.32	   A^2 -> H(e, U1(b, e))
28.57/10.32	   A^2 -> H(e, U1(b, k))
28.57/10.32	   A^2 -> H(e, U1(e, c))
28.57/10.32	   A^2 -> H(e, U1(c, e))
28.57/10.32	   A^2 -> H(e, U1(c, k))
28.57/10.32	   A^2 -> H(e, U1(e, e))
28.57/10.32	   A^2 -> H(e, U1(d, k))
28.57/10.32	   A^2 -> H(U1(e, e), b)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, e), c)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.32	   A^2 -> H(f(e), d)
28.57/10.32	   A^2 -> H(f(e), k)
28.57/10.32	   A^2 -> H(U1(k, k), b)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, k), c)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.32	   A^2 -> H(f(k), d)
28.57/10.32	   A^2 -> H(f(k), k)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.32	   A^2 -> H(U1(k, d), b)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, d), c)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, k), b)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, k), c)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, k), e)
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, d), d)
28.57/10.32	   A^2 -> H(U1(d, d), k)
28.57/10.32	   A^2 -> H(U1(e, c), c)
28.57/10.32	   A^2 -> H(U1(c, c), e)
28.57/10.32	   A^2 -> H(U1(c, c), k)
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(e, e), e)
28.57/10.32	   A^2 -> H(d, U1(e, b))
28.57/10.32	   A^2 -> H(d, U1(k, b))
28.57/10.32	   A^2 -> H(d, U1(c, d))
28.57/10.32	   A^2 -> H(d, U1(d, c))
28.57/10.32	   A^2 -> H(d, U1(b, e))
28.57/10.32	   A^2 -> H(d, U1(b, k))
28.57/10.32	   A^2 -> H(d, U1(e, c))
28.57/10.32	   A^2 -> H(d, U1(k, c))
28.57/10.32	   A^2 -> H(d, U1(c, e))
28.57/10.32	   A^2 -> H(d, U1(c, k))
28.57/10.32	   A^2 -> H(d, U1(e, e))
28.57/10.32	   A^2 -> H(d, U1(k, k))
28.57/10.32	   A^2 -> H(d, U1(k, d))
28.57/10.32	   A^2 -> H(d, U1(d, k))
28.57/10.32	   A^2 -> H(a, b)
28.57/10.32	   A^2 -> H(a, U1(e, d))
28.57/10.32	   A^2 -> H(a, U1(d, e))
28.57/10.32	   A^2 -> H(a, c)
28.57/10.32	   A^2 -> H(a, U1(e, k))
28.57/10.32	   A^2 -> H(a, U1(k, e))
28.57/10.32	   A^2 -> H(a, e)
28.57/10.32	   A^2 -> H(a, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, d), b)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, d), c)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, d), e)
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, a), d)
28.57/10.32	   A^2 -> H(U1(e, a), k)
28.57/10.32	   A^2 -> H(U1(k, a), d)
28.57/10.32	   A^2 -> H(U1(c, d), d)
28.57/10.32	   A^2 -> H(U1(c, d), k)
28.57/10.32	   A^2 -> H(U1(d, e), b)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, e), c)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, e), e)
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, c), d)
28.57/10.32	   A^2 -> H(U1(d, c), k)
28.57/10.32	   A^2 -> H(U1(a, e), d)
28.57/10.32	   A^2 -> H(U1(a, e), k)
28.57/10.32	   A^2 -> H(U1(a, k), d)
28.57/10.32	   A^2 -> H(U1(a, k), k)
28.57/10.32	   A^2 -> H(k, U1(e, b))
28.57/10.32	   A^2 -> H(k, U1(c, d))
28.57/10.32	   A^2 -> H(k, U1(d, c))
28.57/10.32	   A^2 -> H(k, U1(b, e))
28.57/10.32	   A^2 -> H(k, U1(b, k))
28.57/10.32	   A^2 -> H(k, U1(e, c))
28.57/10.32	   A^2 -> H(k, U1(c, e))
28.57/10.32	   A^2 -> H(k, U1(c, k))
28.57/10.32	   A^2 -> H(k, U1(e, e))
28.57/10.32	   A^2 -> H(k, U1(d, k))
28.57/10.32	   A^2 -> H(c, b)
28.57/10.32	   A^2 -> H(c, U1(e, d))
28.57/10.32	   A^2 -> H(c, U1(d, e))
28.57/10.32	   A^2 -> H(c, c)
28.57/10.32	   A^2 -> H(c, U1(e, k))
28.57/10.32	   A^2 -> H(c, U1(k, e))
28.57/10.32	   A^2 -> H(c, e)
28.57/10.32	   A^2 -> H(c, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, k), b)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, k), c)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, k), e)
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, c), d)
28.57/10.32	   A^2 -> H(U1(e, c), k)
28.57/10.32	   A^2 -> H(U1(k, e), b)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, e), c)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, c), d)
28.57/10.32	   A^2 -> H(U1(c, e), d)
28.57/10.32	   A^2 -> H(U1(c, e), k)
28.57/10.32	   A^2 -> H(U1(c, k), d)
28.57/10.32	   A^2 -> H(U1(c, k), k)
28.57/10.32	   A^2 -> H(e, b)
28.57/10.32	   A^2 -> H(e, U1(e, d))
28.57/10.32	   A^2 -> H(e, U1(k, c))
28.57/10.32	   A^2 -> H(e, U1(d, e))
28.57/10.32	
28.57/10.32	The TRS R consists of the following rules:
28.57/10.32	
28.57/10.32	   f(x) -> U1(x, x)
28.57/10.32	   U1(e, x) -> x
28.57/10.32	   a -> c
28.57/10.32	   a -> d
28.57/10.32	   b -> c
28.57/10.32	   b -> d
28.57/10.32	   d -> k
28.57/10.32	   c -> e
28.57/10.32	   c -> k
28.57/10.32	
28.57/10.32	Q is empty.
28.57/10.32	We have to consider all minimal (P,Q,R)-chains.
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2239) DependencyGraphProof (EQUIVALENT)
28.57/10.32	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2240)
28.57/10.32	Obligation:
28.57/10.32	Q DP problem:
28.57/10.32	The TRS P consists of the following rules:
28.57/10.32	
28.57/10.32	   A^2 -> H(f(c), f(c))
28.57/10.32	   H(x, x) -> G(x, x, f(k))
28.57/10.32	   G(d, x, x) -> A^2
28.57/10.32	   A^2 -> H(f(d), f(d))
28.57/10.32	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.32	   A^2 -> H(f(e), f(e))
28.57/10.32	   A^2 -> H(f(k), f(k))
28.57/10.32	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.32	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.32	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.32	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.32	   A^2 -> H(e, U1(b, e))
28.57/10.32	   A^2 -> H(e, U1(b, k))
28.57/10.32	   A^2 -> H(e, U1(e, c))
28.57/10.32	   A^2 -> H(e, U1(c, e))
28.57/10.32	   A^2 -> H(e, U1(c, k))
28.57/10.32	   A^2 -> H(e, U1(e, e))
28.57/10.32	   A^2 -> H(e, U1(d, k))
28.57/10.32	   A^2 -> H(U1(e, e), b)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, e), c)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.32	   A^2 -> H(f(e), d)
28.57/10.32	   A^2 -> H(f(e), k)
28.57/10.32	   A^2 -> H(U1(k, k), b)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, k), c)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.32	   A^2 -> H(f(k), d)
28.57/10.32	   A^2 -> H(f(k), k)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.32	   A^2 -> H(U1(k, d), b)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, d), c)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, k), b)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, k), c)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, k), e)
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, d), d)
28.57/10.32	   A^2 -> H(U1(d, d), k)
28.57/10.32	   A^2 -> H(U1(e, c), c)
28.57/10.32	   A^2 -> H(U1(c, c), e)
28.57/10.32	   A^2 -> H(U1(c, c), k)
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(e, e), e)
28.57/10.32	   A^2 -> H(d, U1(e, b))
28.57/10.32	   A^2 -> H(d, U1(k, b))
28.57/10.32	   A^2 -> H(d, U1(c, d))
28.57/10.32	   A^2 -> H(d, U1(d, c))
28.57/10.32	   A^2 -> H(d, U1(b, e))
28.57/10.32	   A^2 -> H(d, U1(b, k))
28.57/10.32	   A^2 -> H(d, U1(e, c))
28.57/10.32	   A^2 -> H(d, U1(k, c))
28.57/10.32	   A^2 -> H(d, U1(c, e))
28.57/10.32	   A^2 -> H(d, U1(c, k))
28.57/10.32	   A^2 -> H(d, U1(e, e))
28.57/10.32	   A^2 -> H(d, U1(k, k))
28.57/10.32	   A^2 -> H(d, U1(k, d))
28.57/10.32	   A^2 -> H(d, U1(d, k))
28.57/10.32	   A^2 -> H(a, b)
28.57/10.32	   A^2 -> H(a, U1(e, d))
28.57/10.32	   A^2 -> H(a, U1(d, e))
28.57/10.32	   A^2 -> H(a, c)
28.57/10.32	   A^2 -> H(a, U1(e, k))
28.57/10.32	   A^2 -> H(a, U1(k, e))
28.57/10.32	   A^2 -> H(a, e)
28.57/10.32	   A^2 -> H(a, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, d), b)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, d), c)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, d), e)
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, a), d)
28.57/10.32	   A^2 -> H(U1(e, a), k)
28.57/10.32	   A^2 -> H(U1(k, a), d)
28.57/10.32	   A^2 -> H(U1(c, d), d)
28.57/10.32	   A^2 -> H(U1(c, d), k)
28.57/10.32	   A^2 -> H(U1(d, e), b)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, e), c)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, e), e)
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, c), d)
28.57/10.32	   A^2 -> H(U1(d, c), k)
28.57/10.32	   A^2 -> H(U1(a, e), d)
28.57/10.32	   A^2 -> H(U1(a, e), k)
28.57/10.32	   A^2 -> H(U1(a, k), d)
28.57/10.32	   A^2 -> H(U1(a, k), k)
28.57/10.32	   A^2 -> H(k, U1(e, b))
28.57/10.32	   A^2 -> H(k, U1(c, d))
28.57/10.32	   A^2 -> H(k, U1(d, c))
28.57/10.32	   A^2 -> H(k, U1(b, e))
28.57/10.32	   A^2 -> H(k, U1(b, k))
28.57/10.32	   A^2 -> H(k, U1(e, c))
28.57/10.32	   A^2 -> H(k, U1(c, e))
28.57/10.32	   A^2 -> H(k, U1(c, k))
28.57/10.32	   A^2 -> H(k, U1(e, e))
28.57/10.32	   A^2 -> H(k, U1(d, k))
28.57/10.32	   A^2 -> H(c, b)
28.57/10.32	   A^2 -> H(c, U1(e, d))
28.57/10.32	   A^2 -> H(c, U1(d, e))
28.57/10.32	   A^2 -> H(c, c)
28.57/10.32	   A^2 -> H(c, U1(e, k))
28.57/10.32	   A^2 -> H(c, U1(k, e))
28.57/10.32	   A^2 -> H(c, e)
28.57/10.32	   A^2 -> H(c, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, k), b)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, k), c)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, k), e)
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, c), d)
28.57/10.32	   A^2 -> H(U1(e, c), k)
28.57/10.32	   A^2 -> H(U1(k, e), b)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, e), c)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, c), d)
28.57/10.32	   A^2 -> H(U1(c, e), d)
28.57/10.32	   A^2 -> H(U1(c, e), k)
28.57/10.32	   A^2 -> H(U1(c, k), d)
28.57/10.32	   A^2 -> H(U1(c, k), k)
28.57/10.32	   A^2 -> H(e, b)
28.57/10.32	   A^2 -> H(e, U1(e, d))
28.57/10.32	   A^2 -> H(e, U1(d, e))
28.57/10.32	
28.57/10.32	The TRS R consists of the following rules:
28.57/10.32	
28.57/10.32	   f(x) -> U1(x, x)
28.57/10.32	   U1(e, x) -> x
28.57/10.32	   a -> c
28.57/10.32	   a -> d
28.57/10.32	   b -> c
28.57/10.32	   b -> d
28.57/10.32	   d -> k
28.57/10.32	   c -> e
28.57/10.32	   c -> k
28.57/10.32	
28.57/10.32	Q is empty.
28.57/10.32	We have to consider all minimal (P,Q,R)-chains.
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2241) TransformationProof (EQUIVALENT)
28.57/10.32	By narrowing [LPAR04] the rule A^2 -> H(e, U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.32	
28.57/10.32	   (A^2 -> H(e, U1(c, e)),A^2 -> H(e, U1(c, e)))
28.57/10.32	   (A^2 -> H(e, U1(d, e)),A^2 -> H(e, U1(d, e)))
28.57/10.32	
28.57/10.32	
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2242)
28.57/10.32	Obligation:
28.57/10.32	Q DP problem:
28.57/10.32	The TRS P consists of the following rules:
28.57/10.32	
28.57/10.32	   A^2 -> H(f(c), f(c))
28.57/10.32	   H(x, x) -> G(x, x, f(k))
28.57/10.32	   G(d, x, x) -> A^2
28.57/10.32	   A^2 -> H(f(d), f(d))
28.57/10.32	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.32	   A^2 -> H(f(e), f(e))
28.57/10.32	   A^2 -> H(f(k), f(k))
28.57/10.32	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.32	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.32	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.32	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.32	   A^2 -> H(e, U1(b, k))
28.57/10.32	   A^2 -> H(e, U1(e, c))
28.57/10.32	   A^2 -> H(e, U1(c, e))
28.57/10.32	   A^2 -> H(e, U1(c, k))
28.57/10.32	   A^2 -> H(e, U1(e, e))
28.57/10.32	   A^2 -> H(e, U1(d, k))
28.57/10.32	   A^2 -> H(U1(e, e), b)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, e), c)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.32	   A^2 -> H(f(e), d)
28.57/10.32	   A^2 -> H(f(e), k)
28.57/10.32	   A^2 -> H(U1(k, k), b)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, k), c)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.32	   A^2 -> H(f(k), d)
28.57/10.32	   A^2 -> H(f(k), k)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.32	   A^2 -> H(U1(k, d), b)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, d), c)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, k), b)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, k), c)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, k), e)
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, d), d)
28.57/10.32	   A^2 -> H(U1(d, d), k)
28.57/10.32	   A^2 -> H(U1(e, c), c)
28.57/10.32	   A^2 -> H(U1(c, c), e)
28.57/10.32	   A^2 -> H(U1(c, c), k)
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(e, e), e)
28.57/10.32	   A^2 -> H(d, U1(e, b))
28.57/10.32	   A^2 -> H(d, U1(k, b))
28.57/10.32	   A^2 -> H(d, U1(c, d))
28.57/10.32	   A^2 -> H(d, U1(d, c))
28.57/10.32	   A^2 -> H(d, U1(b, e))
28.57/10.32	   A^2 -> H(d, U1(b, k))
28.57/10.32	   A^2 -> H(d, U1(e, c))
28.57/10.32	   A^2 -> H(d, U1(k, c))
28.57/10.32	   A^2 -> H(d, U1(c, e))
28.57/10.32	   A^2 -> H(d, U1(c, k))
28.57/10.32	   A^2 -> H(d, U1(e, e))
28.57/10.32	   A^2 -> H(d, U1(k, k))
28.57/10.32	   A^2 -> H(d, U1(k, d))
28.57/10.32	   A^2 -> H(d, U1(d, k))
28.57/10.32	   A^2 -> H(a, b)
28.57/10.32	   A^2 -> H(a, U1(e, d))
28.57/10.32	   A^2 -> H(a, U1(d, e))
28.57/10.32	   A^2 -> H(a, c)
28.57/10.32	   A^2 -> H(a, U1(e, k))
28.57/10.32	   A^2 -> H(a, U1(k, e))
28.57/10.32	   A^2 -> H(a, e)
28.57/10.32	   A^2 -> H(a, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, d), b)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, d), c)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, d), e)
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, a), d)
28.57/10.32	   A^2 -> H(U1(e, a), k)
28.57/10.32	   A^2 -> H(U1(k, a), d)
28.57/10.32	   A^2 -> H(U1(c, d), d)
28.57/10.32	   A^2 -> H(U1(c, d), k)
28.57/10.32	   A^2 -> H(U1(d, e), b)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, e), c)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, e), e)
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, c), d)
28.57/10.32	   A^2 -> H(U1(d, c), k)
28.57/10.32	   A^2 -> H(U1(a, e), d)
28.57/10.32	   A^2 -> H(U1(a, e), k)
28.57/10.32	   A^2 -> H(U1(a, k), d)
28.57/10.32	   A^2 -> H(U1(a, k), k)
28.57/10.32	   A^2 -> H(k, U1(e, b))
28.57/10.32	   A^2 -> H(k, U1(c, d))
28.57/10.32	   A^2 -> H(k, U1(d, c))
28.57/10.32	   A^2 -> H(k, U1(b, e))
28.57/10.32	   A^2 -> H(k, U1(b, k))
28.57/10.32	   A^2 -> H(k, U1(e, c))
28.57/10.32	   A^2 -> H(k, U1(c, e))
28.57/10.32	   A^2 -> H(k, U1(c, k))
28.57/10.32	   A^2 -> H(k, U1(e, e))
28.57/10.32	   A^2 -> H(k, U1(d, k))
28.57/10.32	   A^2 -> H(c, b)
28.57/10.32	   A^2 -> H(c, U1(e, d))
28.57/10.32	   A^2 -> H(c, U1(d, e))
28.57/10.32	   A^2 -> H(c, c)
28.57/10.32	   A^2 -> H(c, U1(e, k))
28.57/10.32	   A^2 -> H(c, U1(k, e))
28.57/10.32	   A^2 -> H(c, e)
28.57/10.32	   A^2 -> H(c, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, k), b)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, k), c)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, k), e)
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, c), d)
28.57/10.32	   A^2 -> H(U1(e, c), k)
28.57/10.32	   A^2 -> H(U1(k, e), b)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, e), c)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, c), d)
28.57/10.32	   A^2 -> H(U1(c, e), d)
28.57/10.32	   A^2 -> H(U1(c, e), k)
28.57/10.32	   A^2 -> H(U1(c, k), d)
28.57/10.32	   A^2 -> H(U1(c, k), k)
28.57/10.32	   A^2 -> H(e, b)
28.57/10.32	   A^2 -> H(e, U1(e, d))
28.57/10.32	   A^2 -> H(e, U1(d, e))
28.57/10.32	
28.57/10.32	The TRS R consists of the following rules:
28.57/10.32	
28.57/10.32	   f(x) -> U1(x, x)
28.57/10.32	   U1(e, x) -> x
28.57/10.32	   a -> c
28.57/10.32	   a -> d
28.57/10.32	   b -> c
28.57/10.32	   b -> d
28.57/10.32	   d -> k
28.57/10.32	   c -> e
28.57/10.32	   c -> k
28.57/10.32	
28.57/10.32	Q is empty.
28.57/10.32	We have to consider all minimal (P,Q,R)-chains.
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2243) TransformationProof (EQUIVALENT)
28.57/10.32	By narrowing [LPAR04] the rule A^2 -> H(e, U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.32	
28.57/10.32	   (A^2 -> H(e, U1(c, k)),A^2 -> H(e, U1(c, k)))
28.57/10.32	   (A^2 -> H(e, U1(d, k)),A^2 -> H(e, U1(d, k)))
28.57/10.32	
28.57/10.32	
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2244)
28.57/10.32	Obligation:
28.57/10.32	Q DP problem:
28.57/10.32	The TRS P consists of the following rules:
28.57/10.32	
28.57/10.32	   A^2 -> H(f(c), f(c))
28.57/10.32	   H(x, x) -> G(x, x, f(k))
28.57/10.32	   G(d, x, x) -> A^2
28.57/10.32	   A^2 -> H(f(d), f(d))
28.57/10.32	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.32	   A^2 -> H(f(e), f(e))
28.57/10.32	   A^2 -> H(f(k), f(k))
28.57/10.32	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.32	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.32	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.32	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.32	   A^2 -> H(e, U1(e, c))
28.57/10.32	   A^2 -> H(e, U1(c, e))
28.57/10.32	   A^2 -> H(e, U1(c, k))
28.57/10.32	   A^2 -> H(e, U1(e, e))
28.57/10.32	   A^2 -> H(e, U1(d, k))
28.57/10.32	   A^2 -> H(U1(e, e), b)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, e), c)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.32	   A^2 -> H(f(e), d)
28.57/10.32	   A^2 -> H(f(e), k)
28.57/10.32	   A^2 -> H(U1(k, k), b)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, k), c)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.32	   A^2 -> H(f(k), d)
28.57/10.32	   A^2 -> H(f(k), k)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.32	   A^2 -> H(U1(k, d), b)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, d), c)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, k), b)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, k), c)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, k), e)
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, d), d)
28.57/10.32	   A^2 -> H(U1(d, d), k)
28.57/10.32	   A^2 -> H(U1(e, c), c)
28.57/10.32	   A^2 -> H(U1(c, c), e)
28.57/10.32	   A^2 -> H(U1(c, c), k)
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(e, e), e)
28.57/10.32	   A^2 -> H(d, U1(e, b))
28.57/10.32	   A^2 -> H(d, U1(k, b))
28.57/10.32	   A^2 -> H(d, U1(c, d))
28.57/10.32	   A^2 -> H(d, U1(d, c))
28.57/10.32	   A^2 -> H(d, U1(b, e))
28.57/10.32	   A^2 -> H(d, U1(b, k))
28.57/10.32	   A^2 -> H(d, U1(e, c))
28.57/10.32	   A^2 -> H(d, U1(k, c))
28.57/10.32	   A^2 -> H(d, U1(c, e))
28.57/10.32	   A^2 -> H(d, U1(c, k))
28.57/10.32	   A^2 -> H(d, U1(e, e))
28.57/10.32	   A^2 -> H(d, U1(k, k))
28.57/10.32	   A^2 -> H(d, U1(k, d))
28.57/10.32	   A^2 -> H(d, U1(d, k))
28.57/10.32	   A^2 -> H(a, b)
28.57/10.32	   A^2 -> H(a, U1(e, d))
28.57/10.32	   A^2 -> H(a, U1(d, e))
28.57/10.32	   A^2 -> H(a, c)
28.57/10.32	   A^2 -> H(a, U1(e, k))
28.57/10.32	   A^2 -> H(a, U1(k, e))
28.57/10.32	   A^2 -> H(a, e)
28.57/10.32	   A^2 -> H(a, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, d), b)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, d), c)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, d), e)
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, a), d)
28.57/10.32	   A^2 -> H(U1(e, a), k)
28.57/10.32	   A^2 -> H(U1(k, a), d)
28.57/10.32	   A^2 -> H(U1(c, d), d)
28.57/10.32	   A^2 -> H(U1(c, d), k)
28.57/10.32	   A^2 -> H(U1(d, e), b)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, e), c)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, e), e)
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, c), d)
28.57/10.32	   A^2 -> H(U1(d, c), k)
28.57/10.32	   A^2 -> H(U1(a, e), d)
28.57/10.32	   A^2 -> H(U1(a, e), k)
28.57/10.32	   A^2 -> H(U1(a, k), d)
28.57/10.32	   A^2 -> H(U1(a, k), k)
28.57/10.32	   A^2 -> H(k, U1(e, b))
28.57/10.32	   A^2 -> H(k, U1(c, d))
28.57/10.32	   A^2 -> H(k, U1(d, c))
28.57/10.32	   A^2 -> H(k, U1(b, e))
28.57/10.32	   A^2 -> H(k, U1(b, k))
28.57/10.32	   A^2 -> H(k, U1(e, c))
28.57/10.32	   A^2 -> H(k, U1(c, e))
28.57/10.32	   A^2 -> H(k, U1(c, k))
28.57/10.32	   A^2 -> H(k, U1(e, e))
28.57/10.32	   A^2 -> H(k, U1(d, k))
28.57/10.32	   A^2 -> H(c, b)
28.57/10.32	   A^2 -> H(c, U1(e, d))
28.57/10.32	   A^2 -> H(c, U1(d, e))
28.57/10.32	   A^2 -> H(c, c)
28.57/10.32	   A^2 -> H(c, U1(e, k))
28.57/10.32	   A^2 -> H(c, U1(k, e))
28.57/10.32	   A^2 -> H(c, e)
28.57/10.32	   A^2 -> H(c, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, k), b)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, k), c)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, k), e)
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, c), d)
28.57/10.32	   A^2 -> H(U1(e, c), k)
28.57/10.32	   A^2 -> H(U1(k, e), b)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, e), c)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, c), d)
28.57/10.32	   A^2 -> H(U1(c, e), d)
28.57/10.32	   A^2 -> H(U1(c, e), k)
28.57/10.32	   A^2 -> H(U1(c, k), d)
28.57/10.32	   A^2 -> H(U1(c, k), k)
28.57/10.32	   A^2 -> H(e, b)
28.57/10.32	   A^2 -> H(e, U1(e, d))
28.57/10.32	   A^2 -> H(e, U1(d, e))
28.57/10.32	
28.57/10.32	The TRS R consists of the following rules:
28.57/10.32	
28.57/10.32	   f(x) -> U1(x, x)
28.57/10.32	   U1(e, x) -> x
28.57/10.32	   a -> c
28.57/10.32	   a -> d
28.57/10.32	   b -> c
28.57/10.32	   b -> d
28.57/10.32	   d -> k
28.57/10.32	   c -> e
28.57/10.32	   c -> k
28.57/10.32	
28.57/10.32	Q is empty.
28.57/10.32	We have to consider all minimal (P,Q,R)-chains.
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2245) TransformationProof (EQUIVALENT)
28.57/10.32	By narrowing [LPAR04] the rule A^2 -> H(e, U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.32	
28.57/10.32	   (A^2 -> H(e, c),A^2 -> H(e, c))
28.57/10.32	   (A^2 -> H(e, U1(e, e)),A^2 -> H(e, U1(e, e)))
28.57/10.32	   (A^2 -> H(e, U1(e, k)),A^2 -> H(e, U1(e, k)))
28.57/10.32	
28.57/10.32	
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2246)
28.57/10.32	Obligation:
28.57/10.32	Q DP problem:
28.57/10.32	The TRS P consists of the following rules:
28.57/10.32	
28.57/10.32	   A^2 -> H(f(c), f(c))
28.57/10.32	   H(x, x) -> G(x, x, f(k))
28.57/10.32	   G(d, x, x) -> A^2
28.57/10.32	   A^2 -> H(f(d), f(d))
28.57/10.32	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.32	   A^2 -> H(f(e), f(e))
28.57/10.32	   A^2 -> H(f(k), f(k))
28.57/10.32	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.32	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.32	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.32	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.32	   A^2 -> H(e, U1(c, e))
28.57/10.32	   A^2 -> H(e, U1(c, k))
28.57/10.32	   A^2 -> H(e, U1(e, e))
28.57/10.32	   A^2 -> H(e, U1(d, k))
28.57/10.32	   A^2 -> H(U1(e, e), b)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, e), c)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.32	   A^2 -> H(f(e), d)
28.57/10.32	   A^2 -> H(f(e), k)
28.57/10.32	   A^2 -> H(U1(k, k), b)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, k), c)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.32	   A^2 -> H(f(k), d)
28.57/10.32	   A^2 -> H(f(k), k)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.32	   A^2 -> H(U1(k, d), b)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, d), c)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, k), b)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, k), c)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, k), e)
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, d), d)
28.57/10.32	   A^2 -> H(U1(d, d), k)
28.57/10.32	   A^2 -> H(U1(e, c), c)
28.57/10.32	   A^2 -> H(U1(c, c), e)
28.57/10.32	   A^2 -> H(U1(c, c), k)
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(e, e), e)
28.57/10.32	   A^2 -> H(d, U1(e, b))
28.57/10.32	   A^2 -> H(d, U1(k, b))
28.57/10.32	   A^2 -> H(d, U1(c, d))
28.57/10.32	   A^2 -> H(d, U1(d, c))
28.57/10.32	   A^2 -> H(d, U1(b, e))
28.57/10.32	   A^2 -> H(d, U1(b, k))
28.57/10.32	   A^2 -> H(d, U1(e, c))
28.57/10.32	   A^2 -> H(d, U1(k, c))
28.57/10.32	   A^2 -> H(d, U1(c, e))
28.57/10.32	   A^2 -> H(d, U1(c, k))
28.57/10.32	   A^2 -> H(d, U1(e, e))
28.57/10.32	   A^2 -> H(d, U1(k, k))
28.57/10.32	   A^2 -> H(d, U1(k, d))
28.57/10.32	   A^2 -> H(d, U1(d, k))
28.57/10.32	   A^2 -> H(a, b)
28.57/10.32	   A^2 -> H(a, U1(e, d))
28.57/10.32	   A^2 -> H(a, U1(d, e))
28.57/10.32	   A^2 -> H(a, c)
28.57/10.32	   A^2 -> H(a, U1(e, k))
28.57/10.32	   A^2 -> H(a, U1(k, e))
28.57/10.32	   A^2 -> H(a, e)
28.57/10.32	   A^2 -> H(a, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, d), b)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, d), c)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, d), e)
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, a), d)
28.57/10.32	   A^2 -> H(U1(e, a), k)
28.57/10.32	   A^2 -> H(U1(k, a), d)
28.57/10.32	   A^2 -> H(U1(c, d), d)
28.57/10.32	   A^2 -> H(U1(c, d), k)
28.57/10.32	   A^2 -> H(U1(d, e), b)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, e), c)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, e), e)
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, c), d)
28.57/10.32	   A^2 -> H(U1(d, c), k)
28.57/10.32	   A^2 -> H(U1(a, e), d)
28.57/10.32	   A^2 -> H(U1(a, e), k)
28.57/10.32	   A^2 -> H(U1(a, k), d)
28.57/10.32	   A^2 -> H(U1(a, k), k)
28.57/10.32	   A^2 -> H(k, U1(e, b))
28.57/10.32	   A^2 -> H(k, U1(c, d))
28.57/10.32	   A^2 -> H(k, U1(d, c))
28.57/10.32	   A^2 -> H(k, U1(b, e))
28.57/10.32	   A^2 -> H(k, U1(b, k))
28.57/10.32	   A^2 -> H(k, U1(e, c))
28.57/10.32	   A^2 -> H(k, U1(c, e))
28.57/10.32	   A^2 -> H(k, U1(c, k))
28.57/10.32	   A^2 -> H(k, U1(e, e))
28.57/10.32	   A^2 -> H(k, U1(d, k))
28.57/10.32	   A^2 -> H(c, b)
28.57/10.32	   A^2 -> H(c, U1(e, d))
28.57/10.32	   A^2 -> H(c, U1(d, e))
28.57/10.32	   A^2 -> H(c, c)
28.57/10.32	   A^2 -> H(c, U1(e, k))
28.57/10.32	   A^2 -> H(c, U1(k, e))
28.57/10.32	   A^2 -> H(c, e)
28.57/10.32	   A^2 -> H(c, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, k), b)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, k), c)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, k), e)
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, c), d)
28.57/10.32	   A^2 -> H(U1(e, c), k)
28.57/10.32	   A^2 -> H(U1(k, e), b)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, e), c)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, c), d)
28.57/10.32	   A^2 -> H(U1(c, e), d)
28.57/10.32	   A^2 -> H(U1(c, e), k)
28.57/10.32	   A^2 -> H(U1(c, k), d)
28.57/10.32	   A^2 -> H(U1(c, k), k)
28.57/10.32	   A^2 -> H(e, b)
28.57/10.32	   A^2 -> H(e, U1(e, d))
28.57/10.32	   A^2 -> H(e, U1(d, e))
28.57/10.32	   A^2 -> H(e, c)
28.57/10.32	   A^2 -> H(e, U1(e, k))
28.57/10.32	
28.57/10.32	The TRS R consists of the following rules:
28.57/10.32	
28.57/10.32	   f(x) -> U1(x, x)
28.57/10.32	   U1(e, x) -> x
28.57/10.32	   a -> c
28.57/10.32	   a -> d
28.57/10.32	   b -> c
28.57/10.32	   b -> d
28.57/10.32	   d -> k
28.57/10.32	   c -> e
28.57/10.32	   c -> k
28.57/10.32	
28.57/10.32	Q is empty.
28.57/10.32	We have to consider all minimal (P,Q,R)-chains.
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2247) TransformationProof (EQUIVALENT)
28.57/10.32	By narrowing [LPAR04] the rule A^2 -> H(e, U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.32	
28.57/10.32	   (A^2 -> H(e, U1(e, e)),A^2 -> H(e, U1(e, e)))
28.57/10.32	   (A^2 -> H(e, U1(k, e)),A^2 -> H(e, U1(k, e)))
28.57/10.32	
28.57/10.32	
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2248)
28.57/10.32	Obligation:
28.57/10.32	Q DP problem:
28.57/10.32	The TRS P consists of the following rules:
28.57/10.32	
28.57/10.32	   A^2 -> H(f(c), f(c))
28.57/10.32	   H(x, x) -> G(x, x, f(k))
28.57/10.32	   G(d, x, x) -> A^2
28.57/10.32	   A^2 -> H(f(d), f(d))
28.57/10.32	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.32	   A^2 -> H(f(e), f(e))
28.57/10.32	   A^2 -> H(f(k), f(k))
28.57/10.32	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.32	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.32	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.32	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.32	   A^2 -> H(e, U1(c, k))
28.57/10.32	   A^2 -> H(e, U1(e, e))
28.57/10.32	   A^2 -> H(e, U1(d, k))
28.57/10.32	   A^2 -> H(U1(e, e), b)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, e), c)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.32	   A^2 -> H(f(e), d)
28.57/10.32	   A^2 -> H(f(e), k)
28.57/10.32	   A^2 -> H(U1(k, k), b)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, k), c)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.32	   A^2 -> H(f(k), d)
28.57/10.32	   A^2 -> H(f(k), k)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.32	   A^2 -> H(U1(k, d), b)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, d), c)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, k), b)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, k), c)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, k), e)
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, d), d)
28.57/10.32	   A^2 -> H(U1(d, d), k)
28.57/10.32	   A^2 -> H(U1(e, c), c)
28.57/10.32	   A^2 -> H(U1(c, c), e)
28.57/10.32	   A^2 -> H(U1(c, c), k)
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(e, e), e)
28.57/10.32	   A^2 -> H(d, U1(e, b))
28.57/10.32	   A^2 -> H(d, U1(k, b))
28.57/10.32	   A^2 -> H(d, U1(c, d))
28.57/10.32	   A^2 -> H(d, U1(d, c))
28.57/10.32	   A^2 -> H(d, U1(b, e))
28.57/10.32	   A^2 -> H(d, U1(b, k))
28.57/10.32	   A^2 -> H(d, U1(e, c))
28.57/10.32	   A^2 -> H(d, U1(k, c))
28.57/10.32	   A^2 -> H(d, U1(c, e))
28.57/10.32	   A^2 -> H(d, U1(c, k))
28.57/10.32	   A^2 -> H(d, U1(e, e))
28.57/10.32	   A^2 -> H(d, U1(k, k))
28.57/10.32	   A^2 -> H(d, U1(k, d))
28.57/10.32	   A^2 -> H(d, U1(d, k))
28.57/10.32	   A^2 -> H(a, b)
28.57/10.32	   A^2 -> H(a, U1(e, d))
28.57/10.32	   A^2 -> H(a, U1(d, e))
28.57/10.32	   A^2 -> H(a, c)
28.57/10.32	   A^2 -> H(a, U1(e, k))
28.57/10.32	   A^2 -> H(a, U1(k, e))
28.57/10.32	   A^2 -> H(a, e)
28.57/10.32	   A^2 -> H(a, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, d), b)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, d), c)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, d), e)
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, a), d)
28.57/10.32	   A^2 -> H(U1(e, a), k)
28.57/10.32	   A^2 -> H(U1(k, a), d)
28.57/10.32	   A^2 -> H(U1(c, d), d)
28.57/10.32	   A^2 -> H(U1(c, d), k)
28.57/10.32	   A^2 -> H(U1(d, e), b)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, e), c)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, e), e)
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, c), d)
28.57/10.32	   A^2 -> H(U1(d, c), k)
28.57/10.32	   A^2 -> H(U1(a, e), d)
28.57/10.32	   A^2 -> H(U1(a, e), k)
28.57/10.32	   A^2 -> H(U1(a, k), d)
28.57/10.32	   A^2 -> H(U1(a, k), k)
28.57/10.32	   A^2 -> H(k, U1(e, b))
28.57/10.32	   A^2 -> H(k, U1(c, d))
28.57/10.32	   A^2 -> H(k, U1(d, c))
28.57/10.32	   A^2 -> H(k, U1(b, e))
28.57/10.32	   A^2 -> H(k, U1(b, k))
28.57/10.32	   A^2 -> H(k, U1(e, c))
28.57/10.32	   A^2 -> H(k, U1(c, e))
28.57/10.32	   A^2 -> H(k, U1(c, k))
28.57/10.32	   A^2 -> H(k, U1(e, e))
28.57/10.32	   A^2 -> H(k, U1(d, k))
28.57/10.32	   A^2 -> H(c, b)
28.57/10.32	   A^2 -> H(c, U1(e, d))
28.57/10.32	   A^2 -> H(c, U1(d, e))
28.57/10.32	   A^2 -> H(c, c)
28.57/10.32	   A^2 -> H(c, U1(e, k))
28.57/10.32	   A^2 -> H(c, U1(k, e))
28.57/10.32	   A^2 -> H(c, e)
28.57/10.32	   A^2 -> H(c, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, k), b)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, k), c)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, k), e)
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, c), d)
28.57/10.32	   A^2 -> H(U1(e, c), k)
28.57/10.32	   A^2 -> H(U1(k, e), b)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, e), c)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, c), d)
28.57/10.32	   A^2 -> H(U1(c, e), d)
28.57/10.32	   A^2 -> H(U1(c, e), k)
28.57/10.32	   A^2 -> H(U1(c, k), d)
28.57/10.32	   A^2 -> H(U1(c, k), k)
28.57/10.32	   A^2 -> H(e, b)
28.57/10.32	   A^2 -> H(e, U1(e, d))
28.57/10.32	   A^2 -> H(e, U1(d, e))
28.57/10.32	   A^2 -> H(e, c)
28.57/10.32	   A^2 -> H(e, U1(e, k))
28.57/10.32	   A^2 -> H(e, U1(k, e))
28.57/10.32	
28.57/10.32	The TRS R consists of the following rules:
28.57/10.32	
28.57/10.32	   f(x) -> U1(x, x)
28.57/10.32	   U1(e, x) -> x
28.57/10.32	   a -> c
28.57/10.32	   a -> d
28.57/10.32	   b -> c
28.57/10.32	   b -> d
28.57/10.32	   d -> k
28.57/10.32	   c -> e
28.57/10.32	   c -> k
28.57/10.32	
28.57/10.32	Q is empty.
28.57/10.32	We have to consider all minimal (P,Q,R)-chains.
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2249) DependencyGraphProof (EQUIVALENT)
28.57/10.32	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2250)
28.57/10.32	Obligation:
28.57/10.32	Q DP problem:
28.57/10.32	The TRS P consists of the following rules:
28.57/10.32	
28.57/10.32	   H(x, x) -> G(x, x, f(k))
28.57/10.32	   G(d, x, x) -> A^2
28.57/10.32	   A^2 -> H(f(c), f(c))
28.57/10.32	   A^2 -> H(f(d), f(d))
28.57/10.32	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.32	   A^2 -> H(f(e), f(e))
28.57/10.32	   A^2 -> H(f(k), f(k))
28.57/10.32	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.32	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.32	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.32	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.32	   A^2 -> H(e, U1(c, k))
28.57/10.32	   A^2 -> H(e, U1(e, e))
28.57/10.32	   A^2 -> H(e, U1(d, k))
28.57/10.32	   A^2 -> H(U1(e, e), b)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, e), c)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.32	   A^2 -> H(f(e), d)
28.57/10.32	   A^2 -> H(f(e), k)
28.57/10.32	   A^2 -> H(U1(k, k), b)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, k), c)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.32	   A^2 -> H(f(k), d)
28.57/10.32	   A^2 -> H(f(k), k)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.32	   A^2 -> H(U1(k, d), b)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, d), c)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, k), b)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, k), c)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, k), e)
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, d), d)
28.57/10.32	   A^2 -> H(U1(d, d), k)
28.57/10.32	   A^2 -> H(U1(e, c), c)
28.57/10.32	   A^2 -> H(U1(c, c), e)
28.57/10.32	   A^2 -> H(U1(c, c), k)
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(e, e), e)
28.57/10.32	   A^2 -> H(d, U1(e, b))
28.57/10.32	   A^2 -> H(d, U1(k, b))
28.57/10.32	   A^2 -> H(d, U1(c, d))
28.57/10.32	   A^2 -> H(d, U1(d, c))
28.57/10.32	   A^2 -> H(d, U1(b, e))
28.57/10.32	   A^2 -> H(d, U1(b, k))
28.57/10.32	   A^2 -> H(d, U1(e, c))
28.57/10.32	   A^2 -> H(d, U1(k, c))
28.57/10.32	   A^2 -> H(d, U1(c, e))
28.57/10.32	   A^2 -> H(d, U1(c, k))
28.57/10.32	   A^2 -> H(d, U1(e, e))
28.57/10.32	   A^2 -> H(d, U1(k, k))
28.57/10.32	   A^2 -> H(d, U1(k, d))
28.57/10.32	   A^2 -> H(d, U1(d, k))
28.57/10.32	   A^2 -> H(a, b)
28.57/10.32	   A^2 -> H(a, U1(e, d))
28.57/10.32	   A^2 -> H(a, U1(d, e))
28.57/10.32	   A^2 -> H(a, c)
28.57/10.32	   A^2 -> H(a, U1(e, k))
28.57/10.32	   A^2 -> H(a, U1(k, e))
28.57/10.32	   A^2 -> H(a, e)
28.57/10.32	   A^2 -> H(a, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, d), b)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, d), c)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, d), e)
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, a), d)
28.57/10.32	   A^2 -> H(U1(e, a), k)
28.57/10.32	   A^2 -> H(U1(k, a), d)
28.57/10.32	   A^2 -> H(U1(c, d), d)
28.57/10.32	   A^2 -> H(U1(c, d), k)
28.57/10.32	   A^2 -> H(U1(d, e), b)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, e), c)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, e), e)
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, c), d)
28.57/10.32	   A^2 -> H(U1(d, c), k)
28.57/10.32	   A^2 -> H(U1(a, e), d)
28.57/10.32	   A^2 -> H(U1(a, e), k)
28.57/10.32	   A^2 -> H(U1(a, k), d)
28.57/10.32	   A^2 -> H(U1(a, k), k)
28.57/10.32	   A^2 -> H(k, U1(e, b))
28.57/10.32	   A^2 -> H(k, U1(c, d))
28.57/10.32	   A^2 -> H(k, U1(d, c))
28.57/10.32	   A^2 -> H(k, U1(b, e))
28.57/10.32	   A^2 -> H(k, U1(b, k))
28.57/10.32	   A^2 -> H(k, U1(e, c))
28.57/10.32	   A^2 -> H(k, U1(c, e))
28.57/10.32	   A^2 -> H(k, U1(c, k))
28.57/10.32	   A^2 -> H(k, U1(e, e))
28.57/10.32	   A^2 -> H(k, U1(d, k))
28.57/10.32	   A^2 -> H(c, b)
28.57/10.32	   A^2 -> H(c, U1(e, d))
28.57/10.32	   A^2 -> H(c, U1(d, e))
28.57/10.32	   A^2 -> H(c, c)
28.57/10.32	   A^2 -> H(c, U1(e, k))
28.57/10.32	   A^2 -> H(c, U1(k, e))
28.57/10.32	   A^2 -> H(c, e)
28.57/10.32	   A^2 -> H(c, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, k), b)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, k), c)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, k), e)
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, c), d)
28.57/10.32	   A^2 -> H(U1(e, c), k)
28.57/10.32	   A^2 -> H(U1(k, e), b)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, e), c)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, c), d)
28.57/10.32	   A^2 -> H(U1(c, e), d)
28.57/10.32	   A^2 -> H(U1(c, e), k)
28.57/10.32	   A^2 -> H(U1(c, k), d)
28.57/10.32	   A^2 -> H(U1(c, k), k)
28.57/10.32	   A^2 -> H(e, b)
28.57/10.32	   A^2 -> H(e, U1(e, d))
28.57/10.32	   A^2 -> H(e, U1(d, e))
28.57/10.32	   A^2 -> H(e, c)
28.57/10.32	   A^2 -> H(e, U1(e, k))
28.57/10.32	
28.57/10.32	The TRS R consists of the following rules:
28.57/10.32	
28.57/10.32	   f(x) -> U1(x, x)
28.57/10.32	   U1(e, x) -> x
28.57/10.32	   a -> c
28.57/10.32	   a -> d
28.57/10.32	   b -> c
28.57/10.32	   b -> d
28.57/10.32	   d -> k
28.57/10.32	   c -> e
28.57/10.32	   c -> k
28.57/10.32	
28.57/10.32	Q is empty.
28.57/10.32	We have to consider all minimal (P,Q,R)-chains.
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2251) TransformationProof (EQUIVALENT)
28.57/10.32	By narrowing [LPAR04] the rule A^2 -> H(e, U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.32	
28.57/10.32	   (A^2 -> H(e, U1(e, k)),A^2 -> H(e, U1(e, k)))
28.57/10.32	   (A^2 -> H(e, U1(k, k)),A^2 -> H(e, U1(k, k)))
28.57/10.32	
28.57/10.32	
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2252)
28.57/10.32	Obligation:
28.57/10.32	Q DP problem:
28.57/10.32	The TRS P consists of the following rules:
28.57/10.32	
28.57/10.32	   H(x, x) -> G(x, x, f(k))
28.57/10.32	   G(d, x, x) -> A^2
28.57/10.32	   A^2 -> H(f(c), f(c))
28.57/10.32	   A^2 -> H(f(d), f(d))
28.57/10.32	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.32	   A^2 -> H(f(e), f(e))
28.57/10.32	   A^2 -> H(f(k), f(k))
28.57/10.32	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.32	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.32	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.32	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.32	   A^2 -> H(e, U1(e, e))
28.57/10.32	   A^2 -> H(e, U1(d, k))
28.57/10.32	   A^2 -> H(U1(e, e), b)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, e), c)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.32	   A^2 -> H(f(e), d)
28.57/10.32	   A^2 -> H(f(e), k)
28.57/10.32	   A^2 -> H(U1(k, k), b)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, k), c)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.32	   A^2 -> H(f(k), d)
28.57/10.32	   A^2 -> H(f(k), k)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.32	   A^2 -> H(U1(k, d), b)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, d), c)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, k), b)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, k), c)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, k), e)
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, d), d)
28.57/10.32	   A^2 -> H(U1(d, d), k)
28.57/10.32	   A^2 -> H(U1(e, c), c)
28.57/10.32	   A^2 -> H(U1(c, c), e)
28.57/10.32	   A^2 -> H(U1(c, c), k)
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(e, e), e)
28.57/10.32	   A^2 -> H(d, U1(e, b))
28.57/10.32	   A^2 -> H(d, U1(k, b))
28.57/10.32	   A^2 -> H(d, U1(c, d))
28.57/10.32	   A^2 -> H(d, U1(d, c))
28.57/10.32	   A^2 -> H(d, U1(b, e))
28.57/10.32	   A^2 -> H(d, U1(b, k))
28.57/10.32	   A^2 -> H(d, U1(e, c))
28.57/10.32	   A^2 -> H(d, U1(k, c))
28.57/10.32	   A^2 -> H(d, U1(c, e))
28.57/10.32	   A^2 -> H(d, U1(c, k))
28.57/10.32	   A^2 -> H(d, U1(e, e))
28.57/10.32	   A^2 -> H(d, U1(k, k))
28.57/10.32	   A^2 -> H(d, U1(k, d))
28.57/10.32	   A^2 -> H(d, U1(d, k))
28.57/10.32	   A^2 -> H(a, b)
28.57/10.32	   A^2 -> H(a, U1(e, d))
28.57/10.32	   A^2 -> H(a, U1(d, e))
28.57/10.32	   A^2 -> H(a, c)
28.57/10.32	   A^2 -> H(a, U1(e, k))
28.57/10.32	   A^2 -> H(a, U1(k, e))
28.57/10.32	   A^2 -> H(a, e)
28.57/10.32	   A^2 -> H(a, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, d), b)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, d), c)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, d), e)
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, a), d)
28.57/10.32	   A^2 -> H(U1(e, a), k)
28.57/10.32	   A^2 -> H(U1(k, a), d)
28.57/10.32	   A^2 -> H(U1(c, d), d)
28.57/10.32	   A^2 -> H(U1(c, d), k)
28.57/10.32	   A^2 -> H(U1(d, e), b)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, e), c)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, e), e)
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, c), d)
28.57/10.32	   A^2 -> H(U1(d, c), k)
28.57/10.32	   A^2 -> H(U1(a, e), d)
28.57/10.32	   A^2 -> H(U1(a, e), k)
28.57/10.32	   A^2 -> H(U1(a, k), d)
28.57/10.32	   A^2 -> H(U1(a, k), k)
28.57/10.32	   A^2 -> H(k, U1(e, b))
28.57/10.32	   A^2 -> H(k, U1(c, d))
28.57/10.32	   A^2 -> H(k, U1(d, c))
28.57/10.32	   A^2 -> H(k, U1(b, e))
28.57/10.32	   A^2 -> H(k, U1(b, k))
28.57/10.32	   A^2 -> H(k, U1(e, c))
28.57/10.32	   A^2 -> H(k, U1(c, e))
28.57/10.32	   A^2 -> H(k, U1(c, k))
28.57/10.32	   A^2 -> H(k, U1(e, e))
28.57/10.32	   A^2 -> H(k, U1(d, k))
28.57/10.32	   A^2 -> H(c, b)
28.57/10.32	   A^2 -> H(c, U1(e, d))
28.57/10.32	   A^2 -> H(c, U1(d, e))
28.57/10.32	   A^2 -> H(c, c)
28.57/10.32	   A^2 -> H(c, U1(e, k))
28.57/10.32	   A^2 -> H(c, U1(k, e))
28.57/10.32	   A^2 -> H(c, e)
28.57/10.32	   A^2 -> H(c, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, k), b)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, k), c)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, k), e)
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, c), d)
28.57/10.32	   A^2 -> H(U1(e, c), k)
28.57/10.32	   A^2 -> H(U1(k, e), b)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, e), c)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, c), d)
28.57/10.32	   A^2 -> H(U1(c, e), d)
28.57/10.32	   A^2 -> H(U1(c, e), k)
28.57/10.32	   A^2 -> H(U1(c, k), d)
28.57/10.32	   A^2 -> H(U1(c, k), k)
28.57/10.32	   A^2 -> H(e, b)
28.57/10.32	   A^2 -> H(e, U1(e, d))
28.57/10.32	   A^2 -> H(e, U1(d, e))
28.57/10.32	   A^2 -> H(e, c)
28.57/10.32	   A^2 -> H(e, U1(e, k))
28.57/10.32	   A^2 -> H(e, U1(k, k))
28.57/10.32	
28.57/10.32	The TRS R consists of the following rules:
28.57/10.32	
28.57/10.32	   f(x) -> U1(x, x)
28.57/10.32	   U1(e, x) -> x
28.57/10.32	   a -> c
28.57/10.32	   a -> d
28.57/10.32	   b -> c
28.57/10.32	   b -> d
28.57/10.32	   d -> k
28.57/10.32	   c -> e
28.57/10.32	   c -> k
28.57/10.32	
28.57/10.32	Q is empty.
28.57/10.32	We have to consider all minimal (P,Q,R)-chains.
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2253) DependencyGraphProof (EQUIVALENT)
28.57/10.32	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2254)
28.57/10.32	Obligation:
28.57/10.32	Q DP problem:
28.57/10.32	The TRS P consists of the following rules:
28.57/10.32	
28.57/10.32	   G(d, x, x) -> A^2
28.57/10.32	   A^2 -> H(f(c), f(c))
28.57/10.32	   H(x, x) -> G(x, x, f(k))
28.57/10.32	   A^2 -> H(f(d), f(d))
28.57/10.32	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.32	   A^2 -> H(f(e), f(e))
28.57/10.32	   A^2 -> H(f(k), f(k))
28.57/10.32	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.32	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.32	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.32	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.32	   A^2 -> H(e, U1(e, e))
28.57/10.32	   A^2 -> H(e, U1(d, k))
28.57/10.32	   A^2 -> H(U1(e, e), b)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, e), c)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.32	   A^2 -> H(f(e), d)
28.57/10.32	   A^2 -> H(f(e), k)
28.57/10.32	   A^2 -> H(U1(k, k), b)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, k), c)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.32	   A^2 -> H(f(k), d)
28.57/10.32	   A^2 -> H(f(k), k)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.32	   A^2 -> H(U1(k, d), b)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, d), c)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, k), b)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, k), c)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, k), e)
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, d), d)
28.57/10.32	   A^2 -> H(U1(d, d), k)
28.57/10.32	   A^2 -> H(U1(e, c), c)
28.57/10.32	   A^2 -> H(U1(c, c), e)
28.57/10.32	   A^2 -> H(U1(c, c), k)
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(e, e), e)
28.57/10.32	   A^2 -> H(d, U1(e, b))
28.57/10.32	   A^2 -> H(d, U1(k, b))
28.57/10.32	   A^2 -> H(d, U1(c, d))
28.57/10.32	   A^2 -> H(d, U1(d, c))
28.57/10.32	   A^2 -> H(d, U1(b, e))
28.57/10.32	   A^2 -> H(d, U1(b, k))
28.57/10.32	   A^2 -> H(d, U1(e, c))
28.57/10.32	   A^2 -> H(d, U1(k, c))
28.57/10.32	   A^2 -> H(d, U1(c, e))
28.57/10.32	   A^2 -> H(d, U1(c, k))
28.57/10.32	   A^2 -> H(d, U1(e, e))
28.57/10.32	   A^2 -> H(d, U1(k, k))
28.57/10.32	   A^2 -> H(d, U1(k, d))
28.57/10.32	   A^2 -> H(d, U1(d, k))
28.57/10.32	   A^2 -> H(a, b)
28.57/10.32	   A^2 -> H(a, U1(e, d))
28.57/10.32	   A^2 -> H(a, U1(d, e))
28.57/10.32	   A^2 -> H(a, c)
28.57/10.32	   A^2 -> H(a, U1(e, k))
28.57/10.32	   A^2 -> H(a, U1(k, e))
28.57/10.32	   A^2 -> H(a, e)
28.57/10.32	   A^2 -> H(a, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, d), b)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, d), c)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, d), e)
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, a), d)
28.57/10.32	   A^2 -> H(U1(e, a), k)
28.57/10.32	   A^2 -> H(U1(k, a), d)
28.57/10.32	   A^2 -> H(U1(c, d), d)
28.57/10.32	   A^2 -> H(U1(c, d), k)
28.57/10.32	   A^2 -> H(U1(d, e), b)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, e), c)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, e), e)
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, c), d)
28.57/10.32	   A^2 -> H(U1(d, c), k)
28.57/10.32	   A^2 -> H(U1(a, e), d)
28.57/10.32	   A^2 -> H(U1(a, e), k)
28.57/10.32	   A^2 -> H(U1(a, k), d)
28.57/10.32	   A^2 -> H(U1(a, k), k)
28.57/10.32	   A^2 -> H(k, U1(e, b))
28.57/10.32	   A^2 -> H(k, U1(c, d))
28.57/10.32	   A^2 -> H(k, U1(d, c))
28.57/10.32	   A^2 -> H(k, U1(b, e))
28.57/10.32	   A^2 -> H(k, U1(b, k))
28.57/10.32	   A^2 -> H(k, U1(e, c))
28.57/10.32	   A^2 -> H(k, U1(c, e))
28.57/10.32	   A^2 -> H(k, U1(c, k))
28.57/10.32	   A^2 -> H(k, U1(e, e))
28.57/10.32	   A^2 -> H(k, U1(d, k))
28.57/10.32	   A^2 -> H(c, b)
28.57/10.32	   A^2 -> H(c, U1(e, d))
28.57/10.32	   A^2 -> H(c, U1(d, e))
28.57/10.32	   A^2 -> H(c, c)
28.57/10.32	   A^2 -> H(c, U1(e, k))
28.57/10.32	   A^2 -> H(c, U1(k, e))
28.57/10.32	   A^2 -> H(c, e)
28.57/10.32	   A^2 -> H(c, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, k), b)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, k), c)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, k), e)
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, c), d)
28.57/10.32	   A^2 -> H(U1(e, c), k)
28.57/10.32	   A^2 -> H(U1(k, e), b)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, e), c)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, c), d)
28.57/10.32	   A^2 -> H(U1(c, e), d)
28.57/10.32	   A^2 -> H(U1(c, e), k)
28.57/10.32	   A^2 -> H(U1(c, k), d)
28.57/10.32	   A^2 -> H(U1(c, k), k)
28.57/10.32	   A^2 -> H(e, b)
28.57/10.32	   A^2 -> H(e, U1(e, d))
28.57/10.32	   A^2 -> H(e, U1(d, e))
28.57/10.32	   A^2 -> H(e, c)
28.57/10.32	   A^2 -> H(e, U1(e, k))
28.57/10.32	
28.57/10.32	The TRS R consists of the following rules:
28.57/10.32	
28.57/10.32	   f(x) -> U1(x, x)
28.57/10.32	   U1(e, x) -> x
28.57/10.32	   a -> c
28.57/10.32	   a -> d
28.57/10.32	   b -> c
28.57/10.32	   b -> d
28.57/10.32	   d -> k
28.57/10.32	   c -> e
28.57/10.32	   c -> k
28.57/10.32	
28.57/10.32	Q is empty.
28.57/10.32	We have to consider all minimal (P,Q,R)-chains.
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2255) TransformationProof (EQUIVALENT)
28.57/10.32	By narrowing [LPAR04] the rule A^2 -> H(e, U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.32	
28.57/10.32	   (A^2 -> H(e, e),A^2 -> H(e, e))
28.57/10.32	
28.57/10.32	
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2256)
28.57/10.32	Obligation:
28.57/10.32	Q DP problem:
28.57/10.32	The TRS P consists of the following rules:
28.57/10.32	
28.57/10.32	   G(d, x, x) -> A^2
28.57/10.32	   A^2 -> H(f(c), f(c))
28.57/10.32	   H(x, x) -> G(x, x, f(k))
28.57/10.32	   A^2 -> H(f(d), f(d))
28.57/10.32	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.32	   A^2 -> H(f(e), f(e))
28.57/10.32	   A^2 -> H(f(k), f(k))
28.57/10.32	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.32	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.32	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.32	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.32	   A^2 -> H(e, U1(d, k))
28.57/10.32	   A^2 -> H(U1(e, e), b)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, e), c)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.32	   A^2 -> H(f(e), d)
28.57/10.32	   A^2 -> H(f(e), k)
28.57/10.32	   A^2 -> H(U1(k, k), b)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, k), c)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.32	   A^2 -> H(f(k), d)
28.57/10.32	   A^2 -> H(f(k), k)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.32	   A^2 -> H(U1(k, d), b)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, d), c)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, k), b)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, k), c)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, k), e)
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, d), d)
28.57/10.32	   A^2 -> H(U1(d, d), k)
28.57/10.32	   A^2 -> H(U1(e, c), c)
28.57/10.32	   A^2 -> H(U1(c, c), e)
28.57/10.32	   A^2 -> H(U1(c, c), k)
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(e, e), e)
28.57/10.32	   A^2 -> H(d, U1(e, b))
28.57/10.32	   A^2 -> H(d, U1(k, b))
28.57/10.32	   A^2 -> H(d, U1(c, d))
28.57/10.32	   A^2 -> H(d, U1(d, c))
28.57/10.32	   A^2 -> H(d, U1(b, e))
28.57/10.32	   A^2 -> H(d, U1(b, k))
28.57/10.32	   A^2 -> H(d, U1(e, c))
28.57/10.32	   A^2 -> H(d, U1(k, c))
28.57/10.32	   A^2 -> H(d, U1(c, e))
28.57/10.32	   A^2 -> H(d, U1(c, k))
28.57/10.32	   A^2 -> H(d, U1(e, e))
28.57/10.32	   A^2 -> H(d, U1(k, k))
28.57/10.32	   A^2 -> H(d, U1(k, d))
28.57/10.32	   A^2 -> H(d, U1(d, k))
28.57/10.32	   A^2 -> H(a, b)
28.57/10.32	   A^2 -> H(a, U1(e, d))
28.57/10.32	   A^2 -> H(a, U1(d, e))
28.57/10.32	   A^2 -> H(a, c)
28.57/10.32	   A^2 -> H(a, U1(e, k))
28.57/10.32	   A^2 -> H(a, U1(k, e))
28.57/10.32	   A^2 -> H(a, e)
28.57/10.32	   A^2 -> H(a, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, d), b)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, d), c)
28.57/10.32	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, d), e)
28.57/10.32	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, a), d)
28.57/10.32	   A^2 -> H(U1(e, a), k)
28.57/10.32	   A^2 -> H(U1(k, a), d)
28.57/10.32	   A^2 -> H(U1(c, d), d)
28.57/10.32	   A^2 -> H(U1(c, d), k)
28.57/10.32	   A^2 -> H(U1(d, e), b)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, e), c)
28.57/10.32	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, e), e)
28.57/10.32	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, c), d)
28.57/10.32	   A^2 -> H(U1(d, c), k)
28.57/10.32	   A^2 -> H(U1(a, e), d)
28.57/10.32	   A^2 -> H(U1(a, e), k)
28.57/10.32	   A^2 -> H(U1(a, k), d)
28.57/10.32	   A^2 -> H(U1(a, k), k)
28.57/10.32	   A^2 -> H(k, U1(e, b))
28.57/10.32	   A^2 -> H(k, U1(c, d))
28.57/10.32	   A^2 -> H(k, U1(d, c))
28.57/10.32	   A^2 -> H(k, U1(b, e))
28.57/10.32	   A^2 -> H(k, U1(b, k))
28.57/10.32	   A^2 -> H(k, U1(e, c))
28.57/10.32	   A^2 -> H(k, U1(c, e))
28.57/10.32	   A^2 -> H(k, U1(c, k))
28.57/10.32	   A^2 -> H(k, U1(e, e))
28.57/10.32	   A^2 -> H(k, U1(d, k))
28.57/10.32	   A^2 -> H(c, b)
28.57/10.32	   A^2 -> H(c, U1(e, d))
28.57/10.32	   A^2 -> H(c, U1(d, e))
28.57/10.32	   A^2 -> H(c, c)
28.57/10.32	   A^2 -> H(c, U1(e, k))
28.57/10.32	   A^2 -> H(c, U1(k, e))
28.57/10.32	   A^2 -> H(c, e)
28.57/10.32	   A^2 -> H(c, U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, k), b)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, k), c)
28.57/10.32	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, k), e)
28.57/10.32	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(e, c), d)
28.57/10.32	   A^2 -> H(U1(e, c), k)
28.57/10.32	   A^2 -> H(U1(k, e), b)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, e), c)
28.57/10.32	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, c), d)
28.57/10.32	   A^2 -> H(U1(c, e), d)
28.57/10.32	   A^2 -> H(U1(c, e), k)
28.57/10.32	   A^2 -> H(U1(c, k), d)
28.57/10.32	   A^2 -> H(U1(c, k), k)
28.57/10.32	   A^2 -> H(e, b)
28.57/10.32	   A^2 -> H(e, U1(e, d))
28.57/10.32	   A^2 -> H(e, U1(d, e))
28.57/10.32	   A^2 -> H(e, c)
28.57/10.32	   A^2 -> H(e, U1(e, k))
28.57/10.32	   A^2 -> H(e, e)
28.57/10.32	
28.57/10.32	The TRS R consists of the following rules:
28.57/10.32	
28.57/10.32	   f(x) -> U1(x, x)
28.57/10.32	   U1(e, x) -> x
28.57/10.32	   a -> c
28.57/10.32	   a -> d
28.57/10.32	   b -> c
28.57/10.32	   b -> d
28.57/10.32	   d -> k
28.57/10.32	   c -> e
28.57/10.32	   c -> k
28.57/10.32	
28.57/10.32	Q is empty.
28.57/10.32	We have to consider all minimal (P,Q,R)-chains.
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2257) TransformationProof (EQUIVALENT)
28.57/10.32	By narrowing [LPAR04] the rule A^2 -> H(e, U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.32	
28.57/10.32	   (A^2 -> H(e, U1(k, k)),A^2 -> H(e, U1(k, k)))
28.57/10.32	
28.57/10.32	
28.57/10.32	----------------------------------------
28.57/10.32	
28.57/10.32	(2258)
28.57/10.32	Obligation:
28.57/10.32	Q DP problem:
28.57/10.32	The TRS P consists of the following rules:
28.57/10.32	
28.57/10.32	   G(d, x, x) -> A^2
28.57/10.32	   A^2 -> H(f(c), f(c))
28.57/10.32	   H(x, x) -> G(x, x, f(k))
28.57/10.32	   A^2 -> H(f(d), f(d))
28.57/10.32	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.32	   A^2 -> H(f(e), f(e))
28.57/10.32	   A^2 -> H(f(k), f(k))
28.57/10.32	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.32	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.32	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.32	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.32	   A^2 -> H(U1(e, e), b)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.32	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.32	   A^2 -> H(U1(e, e), c)
28.57/10.32	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.32	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.32	   A^2 -> H(f(e), d)
28.57/10.32	   A^2 -> H(f(e), k)
28.57/10.32	   A^2 -> H(U1(k, k), b)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, k), c)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.32	   A^2 -> H(f(k), d)
28.57/10.32	   A^2 -> H(f(k), k)
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.32	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.32	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.32	   A^2 -> H(U1(k, d), b)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.32	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.32	   A^2 -> H(U1(k, d), c)
28.57/10.32	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.32	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, k), b)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.32	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.32	   A^2 -> H(U1(d, k), c)
28.57/10.32	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.32	   A^2 -> H(U1(d, k), e)
28.57/10.32	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.32	   A^2 -> H(U1(d, d), d)
28.57/10.32	   A^2 -> H(U1(d, d), k)
28.57/10.32	   A^2 -> H(U1(e, c), c)
28.57/10.32	   A^2 -> H(U1(c, c), e)
28.57/10.32	   A^2 -> H(U1(c, c), k)
28.57/10.32	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.32	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.32	   A^2 -> H(U1(e, e), e)
28.57/10.32	   A^2 -> H(d, U1(e, b))
28.57/10.32	   A^2 -> H(d, U1(k, b))
28.57/10.32	   A^2 -> H(d, U1(c, d))
28.57/10.32	   A^2 -> H(d, U1(d, c))
28.57/10.32	   A^2 -> H(d, U1(b, e))
28.57/10.32	   A^2 -> H(d, U1(b, k))
28.57/10.32	   A^2 -> H(d, U1(e, c))
28.57/10.32	   A^2 -> H(d, U1(k, c))
28.57/10.33	   A^2 -> H(d, U1(c, e))
28.57/10.33	   A^2 -> H(d, U1(c, k))
28.57/10.33	   A^2 -> H(d, U1(e, e))
28.57/10.33	   A^2 -> H(d, U1(k, k))
28.57/10.33	   A^2 -> H(d, U1(k, d))
28.57/10.33	   A^2 -> H(d, U1(d, k))
28.57/10.33	   A^2 -> H(a, b)
28.57/10.33	   A^2 -> H(a, U1(e, d))
28.57/10.33	   A^2 -> H(a, U1(d, e))
28.57/10.33	   A^2 -> H(a, c)
28.57/10.33	   A^2 -> H(a, U1(e, k))
28.57/10.33	   A^2 -> H(a, U1(k, e))
28.57/10.33	   A^2 -> H(a, e)
28.57/10.33	   A^2 -> H(a, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, d), b)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, d), c)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, d), e)
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, a), d)
28.57/10.33	   A^2 -> H(U1(e, a), k)
28.57/10.33	   A^2 -> H(U1(k, a), d)
28.57/10.33	   A^2 -> H(U1(c, d), d)
28.57/10.33	   A^2 -> H(U1(c, d), k)
28.57/10.33	   A^2 -> H(U1(d, e), b)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, e), c)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, e), e)
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, c), d)
28.57/10.33	   A^2 -> H(U1(d, c), k)
28.57/10.33	   A^2 -> H(U1(a, e), d)
28.57/10.33	   A^2 -> H(U1(a, e), k)
28.57/10.33	   A^2 -> H(U1(a, k), d)
28.57/10.33	   A^2 -> H(U1(a, k), k)
28.57/10.33	   A^2 -> H(k, U1(e, b))
28.57/10.33	   A^2 -> H(k, U1(c, d))
28.57/10.33	   A^2 -> H(k, U1(d, c))
28.57/10.33	   A^2 -> H(k, U1(b, e))
28.57/10.33	   A^2 -> H(k, U1(b, k))
28.57/10.33	   A^2 -> H(k, U1(e, c))
28.57/10.33	   A^2 -> H(k, U1(c, e))
28.57/10.33	   A^2 -> H(k, U1(c, k))
28.57/10.33	   A^2 -> H(k, U1(e, e))
28.57/10.33	   A^2 -> H(k, U1(d, k))
28.57/10.33	   A^2 -> H(c, b)
28.57/10.33	   A^2 -> H(c, U1(e, d))
28.57/10.33	   A^2 -> H(c, U1(d, e))
28.57/10.33	   A^2 -> H(c, c)
28.57/10.33	   A^2 -> H(c, U1(e, k))
28.57/10.33	   A^2 -> H(c, U1(k, e))
28.57/10.33	   A^2 -> H(c, e)
28.57/10.33	   A^2 -> H(c, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, k), b)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, k), c)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, k), e)
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, c), d)
28.57/10.33	   A^2 -> H(U1(e, c), k)
28.57/10.33	   A^2 -> H(U1(k, e), b)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, e), c)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, c), d)
28.57/10.33	   A^2 -> H(U1(c, e), d)
28.57/10.33	   A^2 -> H(U1(c, e), k)
28.57/10.33	   A^2 -> H(U1(c, k), d)
28.57/10.33	   A^2 -> H(U1(c, k), k)
28.57/10.33	   A^2 -> H(e, b)
28.57/10.33	   A^2 -> H(e, U1(e, d))
28.57/10.33	   A^2 -> H(e, U1(d, e))
28.57/10.33	   A^2 -> H(e, c)
28.57/10.33	   A^2 -> H(e, U1(e, k))
28.57/10.33	   A^2 -> H(e, e)
28.57/10.33	   A^2 -> H(e, U1(k, k))
28.57/10.33	
28.57/10.33	The TRS R consists of the following rules:
28.57/10.33	
28.57/10.33	   f(x) -> U1(x, x)
28.57/10.33	   U1(e, x) -> x
28.57/10.33	   a -> c
28.57/10.33	   a -> d
28.57/10.33	   b -> c
28.57/10.33	   b -> d
28.57/10.33	   d -> k
28.57/10.33	   c -> e
28.57/10.33	   c -> k
28.57/10.33	
28.57/10.33	Q is empty.
28.57/10.33	We have to consider all minimal (P,Q,R)-chains.
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2259) DependencyGraphProof (EQUIVALENT)
28.57/10.33	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2260)
28.57/10.33	Obligation:
28.57/10.33	Q DP problem:
28.57/10.33	The TRS P consists of the following rules:
28.57/10.33	
28.57/10.33	   A^2 -> H(f(c), f(c))
28.57/10.33	   H(x, x) -> G(x, x, f(k))
28.57/10.33	   G(d, x, x) -> A^2
28.57/10.33	   A^2 -> H(f(d), f(d))
28.57/10.33	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.33	   A^2 -> H(f(e), f(e))
28.57/10.33	   A^2 -> H(f(k), f(k))
28.57/10.33	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.33	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.33	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.33	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(e, e), b)
28.57/10.33	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, e), c)
28.57/10.33	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.33	   A^2 -> H(f(e), d)
28.57/10.33	   A^2 -> H(f(e), k)
28.57/10.33	   A^2 -> H(U1(k, k), b)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, k), c)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.33	   A^2 -> H(f(k), d)
28.57/10.33	   A^2 -> H(f(k), k)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(k, d), b)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, d), c)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, k), b)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, k), c)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, k), e)
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, d), d)
28.57/10.33	   A^2 -> H(U1(d, d), k)
28.57/10.33	   A^2 -> H(U1(e, c), c)
28.57/10.33	   A^2 -> H(U1(c, c), e)
28.57/10.33	   A^2 -> H(U1(c, c), k)
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(e, e), e)
28.57/10.33	   A^2 -> H(d, U1(e, b))
28.57/10.33	   A^2 -> H(d, U1(k, b))
28.57/10.33	   A^2 -> H(d, U1(c, d))
28.57/10.33	   A^2 -> H(d, U1(d, c))
28.57/10.33	   A^2 -> H(d, U1(b, e))
28.57/10.33	   A^2 -> H(d, U1(b, k))
28.57/10.33	   A^2 -> H(d, U1(e, c))
28.57/10.33	   A^2 -> H(d, U1(k, c))
28.57/10.33	   A^2 -> H(d, U1(c, e))
28.57/10.33	   A^2 -> H(d, U1(c, k))
28.57/10.33	   A^2 -> H(d, U1(e, e))
28.57/10.33	   A^2 -> H(d, U1(k, k))
28.57/10.33	   A^2 -> H(d, U1(k, d))
28.57/10.33	   A^2 -> H(d, U1(d, k))
28.57/10.33	   A^2 -> H(a, b)
28.57/10.33	   A^2 -> H(a, U1(e, d))
28.57/10.33	   A^2 -> H(a, U1(d, e))
28.57/10.33	   A^2 -> H(a, c)
28.57/10.33	   A^2 -> H(a, U1(e, k))
28.57/10.33	   A^2 -> H(a, U1(k, e))
28.57/10.33	   A^2 -> H(a, e)
28.57/10.33	   A^2 -> H(a, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, d), b)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, d), c)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, d), e)
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, a), d)
28.57/10.33	   A^2 -> H(U1(e, a), k)
28.57/10.33	   A^2 -> H(U1(k, a), d)
28.57/10.33	   A^2 -> H(U1(c, d), d)
28.57/10.33	   A^2 -> H(U1(c, d), k)
28.57/10.33	   A^2 -> H(U1(d, e), b)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, e), c)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, e), e)
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, c), d)
28.57/10.33	   A^2 -> H(U1(d, c), k)
28.57/10.33	   A^2 -> H(U1(a, e), d)
28.57/10.33	   A^2 -> H(U1(a, e), k)
28.57/10.33	   A^2 -> H(U1(a, k), d)
28.57/10.33	   A^2 -> H(U1(a, k), k)
28.57/10.33	   A^2 -> H(k, U1(e, b))
28.57/10.33	   A^2 -> H(k, U1(c, d))
28.57/10.33	   A^2 -> H(k, U1(d, c))
28.57/10.33	   A^2 -> H(k, U1(b, e))
28.57/10.33	   A^2 -> H(k, U1(b, k))
28.57/10.33	   A^2 -> H(k, U1(e, c))
28.57/10.33	   A^2 -> H(k, U1(c, e))
28.57/10.33	   A^2 -> H(k, U1(c, k))
28.57/10.33	   A^2 -> H(k, U1(e, e))
28.57/10.33	   A^2 -> H(k, U1(d, k))
28.57/10.33	   A^2 -> H(c, b)
28.57/10.33	   A^2 -> H(c, U1(e, d))
28.57/10.33	   A^2 -> H(c, U1(d, e))
28.57/10.33	   A^2 -> H(c, c)
28.57/10.33	   A^2 -> H(c, U1(e, k))
28.57/10.33	   A^2 -> H(c, U1(k, e))
28.57/10.33	   A^2 -> H(c, e)
28.57/10.33	   A^2 -> H(c, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, k), b)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, k), c)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, k), e)
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, c), d)
28.57/10.33	   A^2 -> H(U1(e, c), k)
28.57/10.33	   A^2 -> H(U1(k, e), b)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, e), c)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, c), d)
28.57/10.33	   A^2 -> H(U1(c, e), d)
28.57/10.33	   A^2 -> H(U1(c, e), k)
28.57/10.33	   A^2 -> H(U1(c, k), d)
28.57/10.33	   A^2 -> H(U1(c, k), k)
28.57/10.33	   A^2 -> H(e, b)
28.57/10.33	   A^2 -> H(e, U1(e, d))
28.57/10.33	   A^2 -> H(e, U1(d, e))
28.57/10.33	   A^2 -> H(e, c)
28.57/10.33	   A^2 -> H(e, U1(e, k))
28.57/10.33	   A^2 -> H(e, e)
28.57/10.33	
28.57/10.33	The TRS R consists of the following rules:
28.57/10.33	
28.57/10.33	   f(x) -> U1(x, x)
28.57/10.33	   U1(e, x) -> x
28.57/10.33	   a -> c
28.57/10.33	   a -> d
28.57/10.33	   b -> c
28.57/10.33	   b -> d
28.57/10.33	   d -> k
28.57/10.33	   c -> e
28.57/10.33	   c -> k
28.57/10.33	
28.57/10.33	Q is empty.
28.57/10.33	We have to consider all minimal (P,Q,R)-chains.
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2261) TransformationProof (EQUIVALENT)
28.57/10.33	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), b) at position [] we obtained the following new rules [LPAR04]:
28.57/10.33	
28.57/10.33	   (A^2 -> H(e, b),A^2 -> H(e, b))
28.57/10.33	   (A^2 -> H(U1(e, e), c),A^2 -> H(U1(e, e), c))
28.57/10.33	   (A^2 -> H(U1(e, e), d),A^2 -> H(U1(e, e), d))
28.57/10.33	
28.57/10.33	
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2262)
28.57/10.33	Obligation:
28.57/10.33	Q DP problem:
28.57/10.33	The TRS P consists of the following rules:
28.57/10.33	
28.57/10.33	   A^2 -> H(f(c), f(c))
28.57/10.33	   H(x, x) -> G(x, x, f(k))
28.57/10.33	   G(d, x, x) -> A^2
28.57/10.33	   A^2 -> H(f(d), f(d))
28.57/10.33	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.33	   A^2 -> H(f(e), f(e))
28.57/10.33	   A^2 -> H(f(k), f(k))
28.57/10.33	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.33	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.33	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.33	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, e), c)
28.57/10.33	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.33	   A^2 -> H(f(e), d)
28.57/10.33	   A^2 -> H(f(e), k)
28.57/10.33	   A^2 -> H(U1(k, k), b)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, k), c)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.33	   A^2 -> H(f(k), d)
28.57/10.33	   A^2 -> H(f(k), k)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(k, d), b)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, d), c)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, k), b)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, k), c)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, k), e)
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, d), d)
28.57/10.33	   A^2 -> H(U1(d, d), k)
28.57/10.33	   A^2 -> H(U1(e, c), c)
28.57/10.33	   A^2 -> H(U1(c, c), e)
28.57/10.33	   A^2 -> H(U1(c, c), k)
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(e, e), e)
28.57/10.33	   A^2 -> H(d, U1(e, b))
28.57/10.33	   A^2 -> H(d, U1(k, b))
28.57/10.33	   A^2 -> H(d, U1(c, d))
28.57/10.33	   A^2 -> H(d, U1(d, c))
28.57/10.33	   A^2 -> H(d, U1(b, e))
28.57/10.33	   A^2 -> H(d, U1(b, k))
28.57/10.33	   A^2 -> H(d, U1(e, c))
28.57/10.33	   A^2 -> H(d, U1(k, c))
28.57/10.33	   A^2 -> H(d, U1(c, e))
28.57/10.33	   A^2 -> H(d, U1(c, k))
28.57/10.33	   A^2 -> H(d, U1(e, e))
28.57/10.33	   A^2 -> H(d, U1(k, k))
28.57/10.33	   A^2 -> H(d, U1(k, d))
28.57/10.33	   A^2 -> H(d, U1(d, k))
28.57/10.33	   A^2 -> H(a, b)
28.57/10.33	   A^2 -> H(a, U1(e, d))
28.57/10.33	   A^2 -> H(a, U1(d, e))
28.57/10.33	   A^2 -> H(a, c)
28.57/10.33	   A^2 -> H(a, U1(e, k))
28.57/10.33	   A^2 -> H(a, U1(k, e))
28.57/10.33	   A^2 -> H(a, e)
28.57/10.33	   A^2 -> H(a, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, d), b)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, d), c)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, d), e)
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, a), d)
28.57/10.33	   A^2 -> H(U1(e, a), k)
28.57/10.33	   A^2 -> H(U1(k, a), d)
28.57/10.33	   A^2 -> H(U1(c, d), d)
28.57/10.33	   A^2 -> H(U1(c, d), k)
28.57/10.33	   A^2 -> H(U1(d, e), b)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, e), c)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, e), e)
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, c), d)
28.57/10.33	   A^2 -> H(U1(d, c), k)
28.57/10.33	   A^2 -> H(U1(a, e), d)
28.57/10.33	   A^2 -> H(U1(a, e), k)
28.57/10.33	   A^2 -> H(U1(a, k), d)
28.57/10.33	   A^2 -> H(U1(a, k), k)
28.57/10.33	   A^2 -> H(k, U1(e, b))
28.57/10.33	   A^2 -> H(k, U1(c, d))
28.57/10.33	   A^2 -> H(k, U1(d, c))
28.57/10.33	   A^2 -> H(k, U1(b, e))
28.57/10.33	   A^2 -> H(k, U1(b, k))
28.57/10.33	   A^2 -> H(k, U1(e, c))
28.57/10.33	   A^2 -> H(k, U1(c, e))
28.57/10.33	   A^2 -> H(k, U1(c, k))
28.57/10.33	   A^2 -> H(k, U1(e, e))
28.57/10.33	   A^2 -> H(k, U1(d, k))
28.57/10.33	   A^2 -> H(c, b)
28.57/10.33	   A^2 -> H(c, U1(e, d))
28.57/10.33	   A^2 -> H(c, U1(d, e))
28.57/10.33	   A^2 -> H(c, c)
28.57/10.33	   A^2 -> H(c, U1(e, k))
28.57/10.33	   A^2 -> H(c, U1(k, e))
28.57/10.33	   A^2 -> H(c, e)
28.57/10.33	   A^2 -> H(c, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, k), b)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, k), c)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, k), e)
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, c), d)
28.57/10.33	   A^2 -> H(U1(e, c), k)
28.57/10.33	   A^2 -> H(U1(k, e), b)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, e), c)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, c), d)
28.57/10.33	   A^2 -> H(U1(c, e), d)
28.57/10.33	   A^2 -> H(U1(c, e), k)
28.57/10.33	   A^2 -> H(U1(c, k), d)
28.57/10.33	   A^2 -> H(U1(c, k), k)
28.57/10.33	   A^2 -> H(e, b)
28.57/10.33	   A^2 -> H(e, U1(e, d))
28.57/10.33	   A^2 -> H(e, U1(d, e))
28.57/10.33	   A^2 -> H(e, c)
28.57/10.33	   A^2 -> H(e, U1(e, k))
28.57/10.33	   A^2 -> H(e, e)
28.57/10.33	   A^2 -> H(U1(e, e), d)
28.57/10.33	
28.57/10.33	The TRS R consists of the following rules:
28.57/10.33	
28.57/10.33	   f(x) -> U1(x, x)
28.57/10.33	   U1(e, x) -> x
28.57/10.33	   a -> c
28.57/10.33	   a -> d
28.57/10.33	   b -> c
28.57/10.33	   b -> d
28.57/10.33	   d -> k
28.57/10.33	   c -> e
28.57/10.33	   c -> k
28.57/10.33	
28.57/10.33	Q is empty.
28.57/10.33	We have to consider all minimal (P,Q,R)-chains.
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2263) TransformationProof (EQUIVALENT)
28.57/10.33	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.33	
28.57/10.33	   (A^2 -> H(e, U1(e, d)),A^2 -> H(e, U1(e, d)))
28.57/10.33	   (A^2 -> H(U1(e, e), d),A^2 -> H(U1(e, e), d))
28.57/10.33	   (A^2 -> H(U1(e, e), U1(e, k)),A^2 -> H(U1(e, e), U1(e, k)))
28.57/10.33	
28.57/10.33	
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2264)
28.57/10.33	Obligation:
28.57/10.33	Q DP problem:
28.57/10.33	The TRS P consists of the following rules:
28.57/10.33	
28.57/10.33	   A^2 -> H(f(c), f(c))
28.57/10.33	   H(x, x) -> G(x, x, f(k))
28.57/10.33	   G(d, x, x) -> A^2
28.57/10.33	   A^2 -> H(f(d), f(d))
28.57/10.33	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.33	   A^2 -> H(f(e), f(e))
28.57/10.33	   A^2 -> H(f(k), f(k))
28.57/10.33	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.33	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.33	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.33	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, e), c)
28.57/10.33	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.33	   A^2 -> H(f(e), d)
28.57/10.33	   A^2 -> H(f(e), k)
28.57/10.33	   A^2 -> H(U1(k, k), b)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, k), c)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.33	   A^2 -> H(f(k), d)
28.57/10.33	   A^2 -> H(f(k), k)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(k, d), b)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, d), c)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, k), b)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, k), c)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, k), e)
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, d), d)
28.57/10.33	   A^2 -> H(U1(d, d), k)
28.57/10.33	   A^2 -> H(U1(e, c), c)
28.57/10.33	   A^2 -> H(U1(c, c), e)
28.57/10.33	   A^2 -> H(U1(c, c), k)
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(e, e), e)
28.57/10.33	   A^2 -> H(d, U1(e, b))
28.57/10.33	   A^2 -> H(d, U1(k, b))
28.57/10.33	   A^2 -> H(d, U1(c, d))
28.57/10.33	   A^2 -> H(d, U1(d, c))
28.57/10.33	   A^2 -> H(d, U1(b, e))
28.57/10.33	   A^2 -> H(d, U1(b, k))
28.57/10.33	   A^2 -> H(d, U1(e, c))
28.57/10.33	   A^2 -> H(d, U1(k, c))
28.57/10.33	   A^2 -> H(d, U1(c, e))
28.57/10.33	   A^2 -> H(d, U1(c, k))
28.57/10.33	   A^2 -> H(d, U1(e, e))
28.57/10.33	   A^2 -> H(d, U1(k, k))
28.57/10.33	   A^2 -> H(d, U1(k, d))
28.57/10.33	   A^2 -> H(d, U1(d, k))
28.57/10.33	   A^2 -> H(a, b)
28.57/10.33	   A^2 -> H(a, U1(e, d))
28.57/10.33	   A^2 -> H(a, U1(d, e))
28.57/10.33	   A^2 -> H(a, c)
28.57/10.33	   A^2 -> H(a, U1(e, k))
28.57/10.33	   A^2 -> H(a, U1(k, e))
28.57/10.33	   A^2 -> H(a, e)
28.57/10.33	   A^2 -> H(a, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, d), b)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, d), c)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, d), e)
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, a), d)
28.57/10.33	   A^2 -> H(U1(e, a), k)
28.57/10.33	   A^2 -> H(U1(k, a), d)
28.57/10.33	   A^2 -> H(U1(c, d), d)
28.57/10.33	   A^2 -> H(U1(c, d), k)
28.57/10.33	   A^2 -> H(U1(d, e), b)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, e), c)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, e), e)
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, c), d)
28.57/10.33	   A^2 -> H(U1(d, c), k)
28.57/10.33	   A^2 -> H(U1(a, e), d)
28.57/10.33	   A^2 -> H(U1(a, e), k)
28.57/10.33	   A^2 -> H(U1(a, k), d)
28.57/10.33	   A^2 -> H(U1(a, k), k)
28.57/10.33	   A^2 -> H(k, U1(e, b))
28.57/10.33	   A^2 -> H(k, U1(c, d))
28.57/10.33	   A^2 -> H(k, U1(d, c))
28.57/10.33	   A^2 -> H(k, U1(b, e))
28.57/10.33	   A^2 -> H(k, U1(b, k))
28.57/10.33	   A^2 -> H(k, U1(e, c))
28.57/10.33	   A^2 -> H(k, U1(c, e))
28.57/10.33	   A^2 -> H(k, U1(c, k))
28.57/10.33	   A^2 -> H(k, U1(e, e))
28.57/10.33	   A^2 -> H(k, U1(d, k))
28.57/10.33	   A^2 -> H(c, b)
28.57/10.33	   A^2 -> H(c, U1(e, d))
28.57/10.33	   A^2 -> H(c, U1(d, e))
28.57/10.33	   A^2 -> H(c, c)
28.57/10.33	   A^2 -> H(c, U1(e, k))
28.57/10.33	   A^2 -> H(c, U1(k, e))
28.57/10.33	   A^2 -> H(c, e)
28.57/10.33	   A^2 -> H(c, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, k), b)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, k), c)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, k), e)
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, c), d)
28.57/10.33	   A^2 -> H(U1(e, c), k)
28.57/10.33	   A^2 -> H(U1(k, e), b)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, e), c)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, c), d)
28.57/10.33	   A^2 -> H(U1(c, e), d)
28.57/10.33	   A^2 -> H(U1(c, e), k)
28.57/10.33	   A^2 -> H(U1(c, k), d)
28.57/10.33	   A^2 -> H(U1(c, k), k)
28.57/10.33	   A^2 -> H(e, b)
28.57/10.33	   A^2 -> H(e, U1(e, d))
28.57/10.33	   A^2 -> H(e, U1(d, e))
28.57/10.33	   A^2 -> H(e, c)
28.57/10.33	   A^2 -> H(e, U1(e, k))
28.57/10.33	   A^2 -> H(e, e)
28.57/10.33	   A^2 -> H(U1(e, e), d)
28.57/10.33	
28.57/10.33	The TRS R consists of the following rules:
28.57/10.33	
28.57/10.33	   f(x) -> U1(x, x)
28.57/10.33	   U1(e, x) -> x
28.57/10.33	   a -> c
28.57/10.33	   a -> d
28.57/10.33	   b -> c
28.57/10.33	   b -> d
28.57/10.33	   d -> k
28.57/10.33	   c -> e
28.57/10.33	   c -> k
28.57/10.33	
28.57/10.33	Q is empty.
28.57/10.33	We have to consider all minimal (P,Q,R)-chains.
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2265) TransformationProof (EQUIVALENT)
28.57/10.33	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.33	
28.57/10.33	   (A^2 -> H(e, U1(d, e)),A^2 -> H(e, U1(d, e)))
28.57/10.33	   (A^2 -> H(U1(e, e), U1(k, e)),A^2 -> H(U1(e, e), U1(k, e)))
28.57/10.33	
28.57/10.33	
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2266)
28.57/10.33	Obligation:
28.57/10.33	Q DP problem:
28.57/10.33	The TRS P consists of the following rules:
28.57/10.33	
28.57/10.33	   A^2 -> H(f(c), f(c))
28.57/10.33	   H(x, x) -> G(x, x, f(k))
28.57/10.33	   G(d, x, x) -> A^2
28.57/10.33	   A^2 -> H(f(d), f(d))
28.57/10.33	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.33	   A^2 -> H(f(e), f(e))
28.57/10.33	   A^2 -> H(f(k), f(k))
28.57/10.33	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.33	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.33	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.33	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(e, e), c)
28.57/10.33	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.33	   A^2 -> H(f(e), d)
28.57/10.33	   A^2 -> H(f(e), k)
28.57/10.33	   A^2 -> H(U1(k, k), b)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, k), c)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.33	   A^2 -> H(f(k), d)
28.57/10.33	   A^2 -> H(f(k), k)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(k, d), b)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, d), c)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, k), b)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, k), c)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, k), e)
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, d), d)
28.57/10.33	   A^2 -> H(U1(d, d), k)
28.57/10.33	   A^2 -> H(U1(e, c), c)
28.57/10.33	   A^2 -> H(U1(c, c), e)
28.57/10.33	   A^2 -> H(U1(c, c), k)
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(e, e), e)
28.57/10.33	   A^2 -> H(d, U1(e, b))
28.57/10.33	   A^2 -> H(d, U1(k, b))
28.57/10.33	   A^2 -> H(d, U1(c, d))
28.57/10.33	   A^2 -> H(d, U1(d, c))
28.57/10.33	   A^2 -> H(d, U1(b, e))
28.57/10.33	   A^2 -> H(d, U1(b, k))
28.57/10.33	   A^2 -> H(d, U1(e, c))
28.57/10.33	   A^2 -> H(d, U1(k, c))
28.57/10.33	   A^2 -> H(d, U1(c, e))
28.57/10.33	   A^2 -> H(d, U1(c, k))
28.57/10.33	   A^2 -> H(d, U1(e, e))
28.57/10.33	   A^2 -> H(d, U1(k, k))
28.57/10.33	   A^2 -> H(d, U1(k, d))
28.57/10.33	   A^2 -> H(d, U1(d, k))
28.57/10.33	   A^2 -> H(a, b)
28.57/10.33	   A^2 -> H(a, U1(e, d))
28.57/10.33	   A^2 -> H(a, U1(d, e))
28.57/10.33	   A^2 -> H(a, c)
28.57/10.33	   A^2 -> H(a, U1(e, k))
28.57/10.33	   A^2 -> H(a, U1(k, e))
28.57/10.33	   A^2 -> H(a, e)
28.57/10.33	   A^2 -> H(a, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, d), b)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, d), c)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, d), e)
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, a), d)
28.57/10.33	   A^2 -> H(U1(e, a), k)
28.57/10.33	   A^2 -> H(U1(k, a), d)
28.57/10.33	   A^2 -> H(U1(c, d), d)
28.57/10.33	   A^2 -> H(U1(c, d), k)
28.57/10.33	   A^2 -> H(U1(d, e), b)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, e), c)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, e), e)
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, c), d)
28.57/10.33	   A^2 -> H(U1(d, c), k)
28.57/10.33	   A^2 -> H(U1(a, e), d)
28.57/10.33	   A^2 -> H(U1(a, e), k)
28.57/10.33	   A^2 -> H(U1(a, k), d)
28.57/10.33	   A^2 -> H(U1(a, k), k)
28.57/10.33	   A^2 -> H(k, U1(e, b))
28.57/10.33	   A^2 -> H(k, U1(c, d))
28.57/10.33	   A^2 -> H(k, U1(d, c))
28.57/10.33	   A^2 -> H(k, U1(b, e))
28.57/10.33	   A^2 -> H(k, U1(b, k))
28.57/10.33	   A^2 -> H(k, U1(e, c))
28.57/10.33	   A^2 -> H(k, U1(c, e))
28.57/10.33	   A^2 -> H(k, U1(c, k))
28.57/10.33	   A^2 -> H(k, U1(e, e))
28.57/10.33	   A^2 -> H(k, U1(d, k))
28.57/10.33	   A^2 -> H(c, b)
28.57/10.33	   A^2 -> H(c, U1(e, d))
28.57/10.33	   A^2 -> H(c, U1(d, e))
28.57/10.33	   A^2 -> H(c, c)
28.57/10.33	   A^2 -> H(c, U1(e, k))
28.57/10.33	   A^2 -> H(c, U1(k, e))
28.57/10.33	   A^2 -> H(c, e)
28.57/10.33	   A^2 -> H(c, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, k), b)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, k), c)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, k), e)
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, c), d)
28.57/10.33	   A^2 -> H(U1(e, c), k)
28.57/10.33	   A^2 -> H(U1(k, e), b)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, e), c)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, c), d)
28.57/10.33	   A^2 -> H(U1(c, e), d)
28.57/10.33	   A^2 -> H(U1(c, e), k)
28.57/10.33	   A^2 -> H(U1(c, k), d)
28.57/10.33	   A^2 -> H(U1(c, k), k)
28.57/10.33	   A^2 -> H(e, b)
28.57/10.33	   A^2 -> H(e, U1(e, d))
28.57/10.33	   A^2 -> H(e, U1(d, e))
28.57/10.33	   A^2 -> H(e, c)
28.57/10.33	   A^2 -> H(e, U1(e, k))
28.57/10.33	   A^2 -> H(e, e)
28.57/10.33	   A^2 -> H(U1(e, e), d)
28.57/10.33	
28.57/10.33	The TRS R consists of the following rules:
28.57/10.33	
28.57/10.33	   f(x) -> U1(x, x)
28.57/10.33	   U1(e, x) -> x
28.57/10.33	   a -> c
28.57/10.33	   a -> d
28.57/10.33	   b -> c
28.57/10.33	   b -> d
28.57/10.33	   d -> k
28.57/10.33	   c -> e
28.57/10.33	   c -> k
28.57/10.33	
28.57/10.33	Q is empty.
28.57/10.33	We have to consider all minimal (P,Q,R)-chains.
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2267) TransformationProof (EQUIVALENT)
28.57/10.33	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), c) at position [] we obtained the following new rules [LPAR04]:
28.57/10.33	
28.57/10.33	   (A^2 -> H(e, c),A^2 -> H(e, c))
28.57/10.33	   (A^2 -> H(U1(e, e), e),A^2 -> H(U1(e, e), e))
28.57/10.33	   (A^2 -> H(U1(e, e), k),A^2 -> H(U1(e, e), k))
28.57/10.33	
28.57/10.33	
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2268)
28.57/10.33	Obligation:
28.57/10.33	Q DP problem:
28.57/10.33	The TRS P consists of the following rules:
28.57/10.33	
28.57/10.33	   A^2 -> H(f(c), f(c))
28.57/10.33	   H(x, x) -> G(x, x, f(k))
28.57/10.33	   G(d, x, x) -> A^2
28.57/10.33	   A^2 -> H(f(d), f(d))
28.57/10.33	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.33	   A^2 -> H(f(e), f(e))
28.57/10.33	   A^2 -> H(f(k), f(k))
28.57/10.33	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.33	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.33	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.33	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.33	   A^2 -> H(f(e), d)
28.57/10.33	   A^2 -> H(f(e), k)
28.57/10.33	   A^2 -> H(U1(k, k), b)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, k), c)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.33	   A^2 -> H(f(k), d)
28.57/10.33	   A^2 -> H(f(k), k)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(k, d), b)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, d), c)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, k), b)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, k), c)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, k), e)
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, d), d)
28.57/10.33	   A^2 -> H(U1(d, d), k)
28.57/10.33	   A^2 -> H(U1(e, c), c)
28.57/10.33	   A^2 -> H(U1(c, c), e)
28.57/10.33	   A^2 -> H(U1(c, c), k)
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(e, e), e)
28.57/10.33	   A^2 -> H(d, U1(e, b))
28.57/10.33	   A^2 -> H(d, U1(k, b))
28.57/10.33	   A^2 -> H(d, U1(c, d))
28.57/10.33	   A^2 -> H(d, U1(d, c))
28.57/10.33	   A^2 -> H(d, U1(b, e))
28.57/10.33	   A^2 -> H(d, U1(b, k))
28.57/10.33	   A^2 -> H(d, U1(e, c))
28.57/10.33	   A^2 -> H(d, U1(k, c))
28.57/10.33	   A^2 -> H(d, U1(c, e))
28.57/10.33	   A^2 -> H(d, U1(c, k))
28.57/10.33	   A^2 -> H(d, U1(e, e))
28.57/10.33	   A^2 -> H(d, U1(k, k))
28.57/10.33	   A^2 -> H(d, U1(k, d))
28.57/10.33	   A^2 -> H(d, U1(d, k))
28.57/10.33	   A^2 -> H(a, b)
28.57/10.33	   A^2 -> H(a, U1(e, d))
28.57/10.33	   A^2 -> H(a, U1(d, e))
28.57/10.33	   A^2 -> H(a, c)
28.57/10.33	   A^2 -> H(a, U1(e, k))
28.57/10.33	   A^2 -> H(a, U1(k, e))
28.57/10.33	   A^2 -> H(a, e)
28.57/10.33	   A^2 -> H(a, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, d), b)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, d), c)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, d), e)
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, a), d)
28.57/10.33	   A^2 -> H(U1(e, a), k)
28.57/10.33	   A^2 -> H(U1(k, a), d)
28.57/10.33	   A^2 -> H(U1(c, d), d)
28.57/10.33	   A^2 -> H(U1(c, d), k)
28.57/10.33	   A^2 -> H(U1(d, e), b)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, e), c)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, e), e)
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, c), d)
28.57/10.33	   A^2 -> H(U1(d, c), k)
28.57/10.33	   A^2 -> H(U1(a, e), d)
28.57/10.33	   A^2 -> H(U1(a, e), k)
28.57/10.33	   A^2 -> H(U1(a, k), d)
28.57/10.33	   A^2 -> H(U1(a, k), k)
28.57/10.33	   A^2 -> H(k, U1(e, b))
28.57/10.33	   A^2 -> H(k, U1(c, d))
28.57/10.33	   A^2 -> H(k, U1(d, c))
28.57/10.33	   A^2 -> H(k, U1(b, e))
28.57/10.33	   A^2 -> H(k, U1(b, k))
28.57/10.33	   A^2 -> H(k, U1(e, c))
28.57/10.33	   A^2 -> H(k, U1(c, e))
28.57/10.33	   A^2 -> H(k, U1(c, k))
28.57/10.33	   A^2 -> H(k, U1(e, e))
28.57/10.33	   A^2 -> H(k, U1(d, k))
28.57/10.33	   A^2 -> H(c, b)
28.57/10.33	   A^2 -> H(c, U1(e, d))
28.57/10.33	   A^2 -> H(c, U1(d, e))
28.57/10.33	   A^2 -> H(c, c)
28.57/10.33	   A^2 -> H(c, U1(e, k))
28.57/10.33	   A^2 -> H(c, U1(k, e))
28.57/10.33	   A^2 -> H(c, e)
28.57/10.33	   A^2 -> H(c, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, k), b)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, k), c)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, k), e)
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, c), d)
28.57/10.33	   A^2 -> H(U1(e, c), k)
28.57/10.33	   A^2 -> H(U1(k, e), b)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, e), c)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, c), d)
28.57/10.33	   A^2 -> H(U1(c, e), d)
28.57/10.33	   A^2 -> H(U1(c, e), k)
28.57/10.33	   A^2 -> H(U1(c, k), d)
28.57/10.33	   A^2 -> H(U1(c, k), k)
28.57/10.33	   A^2 -> H(e, b)
28.57/10.33	   A^2 -> H(e, U1(e, d))
28.57/10.33	   A^2 -> H(e, U1(d, e))
28.57/10.33	   A^2 -> H(e, c)
28.57/10.33	   A^2 -> H(e, U1(e, k))
28.57/10.33	   A^2 -> H(e, e)
28.57/10.33	   A^2 -> H(U1(e, e), d)
28.57/10.33	   A^2 -> H(U1(e, e), k)
28.57/10.33	
28.57/10.33	The TRS R consists of the following rules:
28.57/10.33	
28.57/10.33	   f(x) -> U1(x, x)
28.57/10.33	   U1(e, x) -> x
28.57/10.33	   a -> c
28.57/10.33	   a -> d
28.57/10.33	   b -> c
28.57/10.33	   b -> d
28.57/10.33	   d -> k
28.57/10.33	   c -> e
28.57/10.33	   c -> k
28.57/10.33	
28.57/10.33	Q is empty.
28.57/10.33	We have to consider all minimal (P,Q,R)-chains.
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2269) TransformationProof (EQUIVALENT)
28.57/10.33	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.33	
28.57/10.33	   (A^2 -> H(e, U1(e, k)),A^2 -> H(e, U1(e, k)))
28.57/10.33	   (A^2 -> H(U1(e, e), k),A^2 -> H(U1(e, e), k))
28.57/10.33	
28.57/10.33	
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2270)
28.57/10.33	Obligation:
28.57/10.33	Q DP problem:
28.57/10.33	The TRS P consists of the following rules:
28.57/10.33	
28.57/10.33	   A^2 -> H(f(c), f(c))
28.57/10.33	   H(x, x) -> G(x, x, f(k))
28.57/10.33	   G(d, x, x) -> A^2
28.57/10.33	   A^2 -> H(f(d), f(d))
28.57/10.33	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.33	   A^2 -> H(f(e), f(e))
28.57/10.33	   A^2 -> H(f(k), f(k))
28.57/10.33	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.33	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.33	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.33	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.33	   A^2 -> H(f(e), d)
28.57/10.33	   A^2 -> H(f(e), k)
28.57/10.33	   A^2 -> H(U1(k, k), b)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, k), c)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.33	   A^2 -> H(f(k), d)
28.57/10.33	   A^2 -> H(f(k), k)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(k, d), b)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, d), c)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, k), b)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, k), c)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, k), e)
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, d), d)
28.57/10.33	   A^2 -> H(U1(d, d), k)
28.57/10.33	   A^2 -> H(U1(e, c), c)
28.57/10.33	   A^2 -> H(U1(c, c), e)
28.57/10.33	   A^2 -> H(U1(c, c), k)
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(e, e), e)
28.57/10.33	   A^2 -> H(d, U1(e, b))
28.57/10.33	   A^2 -> H(d, U1(k, b))
28.57/10.33	   A^2 -> H(d, U1(c, d))
28.57/10.33	   A^2 -> H(d, U1(d, c))
28.57/10.33	   A^2 -> H(d, U1(b, e))
28.57/10.33	   A^2 -> H(d, U1(b, k))
28.57/10.33	   A^2 -> H(d, U1(e, c))
28.57/10.33	   A^2 -> H(d, U1(k, c))
28.57/10.33	   A^2 -> H(d, U1(c, e))
28.57/10.33	   A^2 -> H(d, U1(c, k))
28.57/10.33	   A^2 -> H(d, U1(e, e))
28.57/10.33	   A^2 -> H(d, U1(k, k))
28.57/10.33	   A^2 -> H(d, U1(k, d))
28.57/10.33	   A^2 -> H(d, U1(d, k))
28.57/10.33	   A^2 -> H(a, b)
28.57/10.33	   A^2 -> H(a, U1(e, d))
28.57/10.33	   A^2 -> H(a, U1(d, e))
28.57/10.33	   A^2 -> H(a, c)
28.57/10.33	   A^2 -> H(a, U1(e, k))
28.57/10.33	   A^2 -> H(a, U1(k, e))
28.57/10.33	   A^2 -> H(a, e)
28.57/10.33	   A^2 -> H(a, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, d), b)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, d), c)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, d), e)
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, a), d)
28.57/10.33	   A^2 -> H(U1(e, a), k)
28.57/10.33	   A^2 -> H(U1(k, a), d)
28.57/10.33	   A^2 -> H(U1(c, d), d)
28.57/10.33	   A^2 -> H(U1(c, d), k)
28.57/10.33	   A^2 -> H(U1(d, e), b)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, e), c)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, e), e)
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, c), d)
28.57/10.33	   A^2 -> H(U1(d, c), k)
28.57/10.33	   A^2 -> H(U1(a, e), d)
28.57/10.33	   A^2 -> H(U1(a, e), k)
28.57/10.33	   A^2 -> H(U1(a, k), d)
28.57/10.33	   A^2 -> H(U1(a, k), k)
28.57/10.33	   A^2 -> H(k, U1(e, b))
28.57/10.33	   A^2 -> H(k, U1(c, d))
28.57/10.33	   A^2 -> H(k, U1(d, c))
28.57/10.33	   A^2 -> H(k, U1(b, e))
28.57/10.33	   A^2 -> H(k, U1(b, k))
28.57/10.33	   A^2 -> H(k, U1(e, c))
28.57/10.33	   A^2 -> H(k, U1(c, e))
28.57/10.33	   A^2 -> H(k, U1(c, k))
28.57/10.33	   A^2 -> H(k, U1(e, e))
28.57/10.33	   A^2 -> H(k, U1(d, k))
28.57/10.33	   A^2 -> H(c, b)
28.57/10.33	   A^2 -> H(c, U1(e, d))
28.57/10.33	   A^2 -> H(c, U1(d, e))
28.57/10.33	   A^2 -> H(c, c)
28.57/10.33	   A^2 -> H(c, U1(e, k))
28.57/10.33	   A^2 -> H(c, U1(k, e))
28.57/10.33	   A^2 -> H(c, e)
28.57/10.33	   A^2 -> H(c, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, k), b)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, k), c)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, k), e)
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, c), d)
28.57/10.33	   A^2 -> H(U1(e, c), k)
28.57/10.33	   A^2 -> H(U1(k, e), b)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, e), c)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, c), d)
28.57/10.33	   A^2 -> H(U1(c, e), d)
28.57/10.33	   A^2 -> H(U1(c, e), k)
28.57/10.33	   A^2 -> H(U1(c, k), d)
28.57/10.33	   A^2 -> H(U1(c, k), k)
28.57/10.33	   A^2 -> H(e, b)
28.57/10.33	   A^2 -> H(e, U1(e, d))
28.57/10.33	   A^2 -> H(e, U1(d, e))
28.57/10.33	   A^2 -> H(e, c)
28.57/10.33	   A^2 -> H(e, U1(e, k))
28.57/10.33	   A^2 -> H(e, e)
28.57/10.33	   A^2 -> H(U1(e, e), d)
28.57/10.33	   A^2 -> H(U1(e, e), k)
28.57/10.33	
28.57/10.33	The TRS R consists of the following rules:
28.57/10.33	
28.57/10.33	   f(x) -> U1(x, x)
28.57/10.33	   U1(e, x) -> x
28.57/10.33	   a -> c
28.57/10.33	   a -> d
28.57/10.33	   b -> c
28.57/10.33	   b -> d
28.57/10.33	   d -> k
28.57/10.33	   c -> e
28.57/10.33	   c -> k
28.57/10.33	
28.57/10.33	Q is empty.
28.57/10.33	We have to consider all minimal (P,Q,R)-chains.
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2271) TransformationProof (EQUIVALENT)
28.57/10.33	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.33	
28.57/10.33	   (A^2 -> H(e, U1(k, e)),A^2 -> H(e, U1(k, e)))
28.57/10.33	
28.57/10.33	
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2272)
28.57/10.33	Obligation:
28.57/10.33	Q DP problem:
28.57/10.33	The TRS P consists of the following rules:
28.57/10.33	
28.57/10.33	   A^2 -> H(f(c), f(c))
28.57/10.33	   H(x, x) -> G(x, x, f(k))
28.57/10.33	   G(d, x, x) -> A^2
28.57/10.33	   A^2 -> H(f(d), f(d))
28.57/10.33	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.33	   A^2 -> H(f(e), f(e))
28.57/10.33	   A^2 -> H(f(k), f(k))
28.57/10.33	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.33	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.33	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.33	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.33	   A^2 -> H(f(e), d)
28.57/10.33	   A^2 -> H(f(e), k)
28.57/10.33	   A^2 -> H(U1(k, k), b)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, k), c)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.33	   A^2 -> H(f(k), d)
28.57/10.33	   A^2 -> H(f(k), k)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(k, d), b)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, d), c)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, k), b)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, k), c)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, k), e)
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, d), d)
28.57/10.33	   A^2 -> H(U1(d, d), k)
28.57/10.33	   A^2 -> H(U1(e, c), c)
28.57/10.33	   A^2 -> H(U1(c, c), e)
28.57/10.33	   A^2 -> H(U1(c, c), k)
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(e, e), e)
28.57/10.33	   A^2 -> H(d, U1(e, b))
28.57/10.33	   A^2 -> H(d, U1(k, b))
28.57/10.33	   A^2 -> H(d, U1(c, d))
28.57/10.33	   A^2 -> H(d, U1(d, c))
28.57/10.33	   A^2 -> H(d, U1(b, e))
28.57/10.33	   A^2 -> H(d, U1(b, k))
28.57/10.33	   A^2 -> H(d, U1(e, c))
28.57/10.33	   A^2 -> H(d, U1(k, c))
28.57/10.33	   A^2 -> H(d, U1(c, e))
28.57/10.33	   A^2 -> H(d, U1(c, k))
28.57/10.33	   A^2 -> H(d, U1(e, e))
28.57/10.33	   A^2 -> H(d, U1(k, k))
28.57/10.33	   A^2 -> H(d, U1(k, d))
28.57/10.33	   A^2 -> H(d, U1(d, k))
28.57/10.33	   A^2 -> H(a, b)
28.57/10.33	   A^2 -> H(a, U1(e, d))
28.57/10.33	   A^2 -> H(a, U1(d, e))
28.57/10.33	   A^2 -> H(a, c)
28.57/10.33	   A^2 -> H(a, U1(e, k))
28.57/10.33	   A^2 -> H(a, U1(k, e))
28.57/10.33	   A^2 -> H(a, e)
28.57/10.33	   A^2 -> H(a, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, d), b)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, d), c)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, d), e)
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, a), d)
28.57/10.33	   A^2 -> H(U1(e, a), k)
28.57/10.33	   A^2 -> H(U1(k, a), d)
28.57/10.33	   A^2 -> H(U1(c, d), d)
28.57/10.33	   A^2 -> H(U1(c, d), k)
28.57/10.33	   A^2 -> H(U1(d, e), b)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, e), c)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, e), e)
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, c), d)
28.57/10.33	   A^2 -> H(U1(d, c), k)
28.57/10.33	   A^2 -> H(U1(a, e), d)
28.57/10.33	   A^2 -> H(U1(a, e), k)
28.57/10.33	   A^2 -> H(U1(a, k), d)
28.57/10.33	   A^2 -> H(U1(a, k), k)
28.57/10.33	   A^2 -> H(k, U1(e, b))
28.57/10.33	   A^2 -> H(k, U1(c, d))
28.57/10.33	   A^2 -> H(k, U1(d, c))
28.57/10.33	   A^2 -> H(k, U1(b, e))
28.57/10.33	   A^2 -> H(k, U1(b, k))
28.57/10.33	   A^2 -> H(k, U1(e, c))
28.57/10.33	   A^2 -> H(k, U1(c, e))
28.57/10.33	   A^2 -> H(k, U1(c, k))
28.57/10.33	   A^2 -> H(k, U1(e, e))
28.57/10.33	   A^2 -> H(k, U1(d, k))
28.57/10.33	   A^2 -> H(c, b)
28.57/10.33	   A^2 -> H(c, U1(e, d))
28.57/10.33	   A^2 -> H(c, U1(d, e))
28.57/10.33	   A^2 -> H(c, c)
28.57/10.33	   A^2 -> H(c, U1(e, k))
28.57/10.33	   A^2 -> H(c, U1(k, e))
28.57/10.33	   A^2 -> H(c, e)
28.57/10.33	   A^2 -> H(c, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, k), b)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, k), c)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, k), e)
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, c), d)
28.57/10.33	   A^2 -> H(U1(e, c), k)
28.57/10.33	   A^2 -> H(U1(k, e), b)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, e), c)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, c), d)
28.57/10.33	   A^2 -> H(U1(c, e), d)
28.57/10.33	   A^2 -> H(U1(c, e), k)
28.57/10.33	   A^2 -> H(U1(c, k), d)
28.57/10.33	   A^2 -> H(U1(c, k), k)
28.57/10.33	   A^2 -> H(e, b)
28.57/10.33	   A^2 -> H(e, U1(e, d))
28.57/10.33	   A^2 -> H(e, U1(d, e))
28.57/10.33	   A^2 -> H(e, c)
28.57/10.33	   A^2 -> H(e, U1(e, k))
28.57/10.33	   A^2 -> H(e, e)
28.57/10.33	   A^2 -> H(U1(e, e), d)
28.57/10.33	   A^2 -> H(U1(e, e), k)
28.57/10.33	   A^2 -> H(e, U1(k, e))
28.57/10.33	
28.57/10.33	The TRS R consists of the following rules:
28.57/10.33	
28.57/10.33	   f(x) -> U1(x, x)
28.57/10.33	   U1(e, x) -> x
28.57/10.33	   a -> c
28.57/10.33	   a -> d
28.57/10.33	   b -> c
28.57/10.33	   b -> d
28.57/10.33	   d -> k
28.57/10.33	   c -> e
28.57/10.33	   c -> k
28.57/10.33	
28.57/10.33	Q is empty.
28.57/10.33	We have to consider all minimal (P,Q,R)-chains.
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2273) DependencyGraphProof (EQUIVALENT)
28.57/10.33	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2274)
28.57/10.33	Obligation:
28.57/10.33	Q DP problem:
28.57/10.33	The TRS P consists of the following rules:
28.57/10.33	
28.57/10.33	   H(x, x) -> G(x, x, f(k))
28.57/10.33	   G(d, x, x) -> A^2
28.57/10.33	   A^2 -> H(f(c), f(c))
28.57/10.33	   A^2 -> H(f(d), f(d))
28.57/10.33	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.33	   A^2 -> H(f(e), f(e))
28.57/10.33	   A^2 -> H(f(k), f(k))
28.57/10.33	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.33	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.33	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.33	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(k, k))
28.57/10.33	   A^2 -> H(f(e), d)
28.57/10.33	   A^2 -> H(f(e), k)
28.57/10.33	   A^2 -> H(U1(k, k), b)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, k), c)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.33	   A^2 -> H(f(k), d)
28.57/10.33	   A^2 -> H(f(k), k)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(k, d), b)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, d), c)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, k), b)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, k), c)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, k), e)
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, d), d)
28.57/10.33	   A^2 -> H(U1(d, d), k)
28.57/10.33	   A^2 -> H(U1(e, c), c)
28.57/10.33	   A^2 -> H(U1(c, c), e)
28.57/10.33	   A^2 -> H(U1(c, c), k)
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(e, e), e)
28.57/10.33	   A^2 -> H(d, U1(e, b))
28.57/10.33	   A^2 -> H(d, U1(k, b))
28.57/10.33	   A^2 -> H(d, U1(c, d))
28.57/10.33	   A^2 -> H(d, U1(d, c))
28.57/10.33	   A^2 -> H(d, U1(b, e))
28.57/10.33	   A^2 -> H(d, U1(b, k))
28.57/10.33	   A^2 -> H(d, U1(e, c))
28.57/10.33	   A^2 -> H(d, U1(k, c))
28.57/10.33	   A^2 -> H(d, U1(c, e))
28.57/10.33	   A^2 -> H(d, U1(c, k))
28.57/10.33	   A^2 -> H(d, U1(e, e))
28.57/10.33	   A^2 -> H(d, U1(k, k))
28.57/10.33	   A^2 -> H(d, U1(k, d))
28.57/10.33	   A^2 -> H(d, U1(d, k))
28.57/10.33	   A^2 -> H(a, b)
28.57/10.33	   A^2 -> H(a, U1(e, d))
28.57/10.33	   A^2 -> H(a, U1(d, e))
28.57/10.33	   A^2 -> H(a, c)
28.57/10.33	   A^2 -> H(a, U1(e, k))
28.57/10.33	   A^2 -> H(a, U1(k, e))
28.57/10.33	   A^2 -> H(a, e)
28.57/10.33	   A^2 -> H(a, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, d), b)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, d), c)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, d), e)
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, a), d)
28.57/10.33	   A^2 -> H(U1(e, a), k)
28.57/10.33	   A^2 -> H(U1(k, a), d)
28.57/10.33	   A^2 -> H(U1(c, d), d)
28.57/10.33	   A^2 -> H(U1(c, d), k)
28.57/10.33	   A^2 -> H(U1(d, e), b)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, e), c)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, e), e)
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, c), d)
28.57/10.33	   A^2 -> H(U1(d, c), k)
28.57/10.33	   A^2 -> H(U1(a, e), d)
28.57/10.33	   A^2 -> H(U1(a, e), k)
28.57/10.33	   A^2 -> H(U1(a, k), d)
28.57/10.33	   A^2 -> H(U1(a, k), k)
28.57/10.33	   A^2 -> H(k, U1(e, b))
28.57/10.33	   A^2 -> H(k, U1(c, d))
28.57/10.33	   A^2 -> H(k, U1(d, c))
28.57/10.33	   A^2 -> H(k, U1(b, e))
28.57/10.33	   A^2 -> H(k, U1(b, k))
28.57/10.33	   A^2 -> H(k, U1(e, c))
28.57/10.33	   A^2 -> H(k, U1(c, e))
28.57/10.33	   A^2 -> H(k, U1(c, k))
28.57/10.33	   A^2 -> H(k, U1(e, e))
28.57/10.33	   A^2 -> H(k, U1(d, k))
28.57/10.33	   A^2 -> H(c, b)
28.57/10.33	   A^2 -> H(c, U1(e, d))
28.57/10.33	   A^2 -> H(c, U1(d, e))
28.57/10.33	   A^2 -> H(c, c)
28.57/10.33	   A^2 -> H(c, U1(e, k))
28.57/10.33	   A^2 -> H(c, U1(k, e))
28.57/10.33	   A^2 -> H(c, e)
28.57/10.33	   A^2 -> H(c, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, k), b)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, k), c)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, k), e)
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, c), d)
28.57/10.33	   A^2 -> H(U1(e, c), k)
28.57/10.33	   A^2 -> H(U1(k, e), b)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, e), c)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, c), d)
28.57/10.33	   A^2 -> H(U1(c, e), d)
28.57/10.33	   A^2 -> H(U1(c, e), k)
28.57/10.33	   A^2 -> H(U1(c, k), d)
28.57/10.33	   A^2 -> H(U1(c, k), k)
28.57/10.33	   A^2 -> H(e, b)
28.57/10.33	   A^2 -> H(e, U1(e, d))
28.57/10.33	   A^2 -> H(e, U1(d, e))
28.57/10.33	   A^2 -> H(e, c)
28.57/10.33	   A^2 -> H(e, U1(e, k))
28.57/10.33	   A^2 -> H(e, e)
28.57/10.33	   A^2 -> H(U1(e, e), d)
28.57/10.33	   A^2 -> H(U1(e, e), k)
28.57/10.33	
28.57/10.33	The TRS R consists of the following rules:
28.57/10.33	
28.57/10.33	   f(x) -> U1(x, x)
28.57/10.33	   U1(e, x) -> x
28.57/10.33	   a -> c
28.57/10.33	   a -> d
28.57/10.33	   b -> c
28.57/10.33	   b -> d
28.57/10.33	   d -> k
28.57/10.33	   c -> e
28.57/10.33	   c -> k
28.57/10.33	
28.57/10.33	Q is empty.
28.57/10.33	We have to consider all minimal (P,Q,R)-chains.
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2275) TransformationProof (EQUIVALENT)
28.57/10.33	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.33	
28.57/10.33	   (A^2 -> H(e, U1(k, k)),A^2 -> H(e, U1(k, k)))
28.57/10.33	
28.57/10.33	
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2276)
28.57/10.33	Obligation:
28.57/10.33	Q DP problem:
28.57/10.33	The TRS P consists of the following rules:
28.57/10.33	
28.57/10.33	   H(x, x) -> G(x, x, f(k))
28.57/10.33	   G(d, x, x) -> A^2
28.57/10.33	   A^2 -> H(f(c), f(c))
28.57/10.33	   A^2 -> H(f(d), f(d))
28.57/10.33	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.33	   A^2 -> H(f(e), f(e))
28.57/10.33	   A^2 -> H(f(k), f(k))
28.57/10.33	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.33	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.33	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.33	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.33	   A^2 -> H(f(e), d)
28.57/10.33	   A^2 -> H(f(e), k)
28.57/10.33	   A^2 -> H(U1(k, k), b)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, k), c)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.33	   A^2 -> H(f(k), d)
28.57/10.33	   A^2 -> H(f(k), k)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(k, d), b)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, d), c)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, k), b)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, k), c)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, k), e)
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, d), d)
28.57/10.33	   A^2 -> H(U1(d, d), k)
28.57/10.33	   A^2 -> H(U1(e, c), c)
28.57/10.33	   A^2 -> H(U1(c, c), e)
28.57/10.33	   A^2 -> H(U1(c, c), k)
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(e, e), e)
28.57/10.33	   A^2 -> H(d, U1(e, b))
28.57/10.33	   A^2 -> H(d, U1(k, b))
28.57/10.33	   A^2 -> H(d, U1(c, d))
28.57/10.33	   A^2 -> H(d, U1(d, c))
28.57/10.33	   A^2 -> H(d, U1(b, e))
28.57/10.33	   A^2 -> H(d, U1(b, k))
28.57/10.33	   A^2 -> H(d, U1(e, c))
28.57/10.33	   A^2 -> H(d, U1(k, c))
28.57/10.33	   A^2 -> H(d, U1(c, e))
28.57/10.33	   A^2 -> H(d, U1(c, k))
28.57/10.33	   A^2 -> H(d, U1(e, e))
28.57/10.33	   A^2 -> H(d, U1(k, k))
28.57/10.33	   A^2 -> H(d, U1(k, d))
28.57/10.33	   A^2 -> H(d, U1(d, k))
28.57/10.33	   A^2 -> H(a, b)
28.57/10.33	   A^2 -> H(a, U1(e, d))
28.57/10.33	   A^2 -> H(a, U1(d, e))
28.57/10.33	   A^2 -> H(a, c)
28.57/10.33	   A^2 -> H(a, U1(e, k))
28.57/10.33	   A^2 -> H(a, U1(k, e))
28.57/10.33	   A^2 -> H(a, e)
28.57/10.33	   A^2 -> H(a, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, d), b)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, d), c)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, d), e)
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, a), d)
28.57/10.33	   A^2 -> H(U1(e, a), k)
28.57/10.33	   A^2 -> H(U1(k, a), d)
28.57/10.33	   A^2 -> H(U1(c, d), d)
28.57/10.33	   A^2 -> H(U1(c, d), k)
28.57/10.33	   A^2 -> H(U1(d, e), b)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, e), c)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, e), e)
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, c), d)
28.57/10.33	   A^2 -> H(U1(d, c), k)
28.57/10.33	   A^2 -> H(U1(a, e), d)
28.57/10.33	   A^2 -> H(U1(a, e), k)
28.57/10.33	   A^2 -> H(U1(a, k), d)
28.57/10.33	   A^2 -> H(U1(a, k), k)
28.57/10.33	   A^2 -> H(k, U1(e, b))
28.57/10.33	   A^2 -> H(k, U1(c, d))
28.57/10.33	   A^2 -> H(k, U1(d, c))
28.57/10.33	   A^2 -> H(k, U1(b, e))
28.57/10.33	   A^2 -> H(k, U1(b, k))
28.57/10.33	   A^2 -> H(k, U1(e, c))
28.57/10.33	   A^2 -> H(k, U1(c, e))
28.57/10.33	   A^2 -> H(k, U1(c, k))
28.57/10.33	   A^2 -> H(k, U1(e, e))
28.57/10.33	   A^2 -> H(k, U1(d, k))
28.57/10.33	   A^2 -> H(c, b)
28.57/10.33	   A^2 -> H(c, U1(e, d))
28.57/10.33	   A^2 -> H(c, U1(d, e))
28.57/10.33	   A^2 -> H(c, c)
28.57/10.33	   A^2 -> H(c, U1(e, k))
28.57/10.33	   A^2 -> H(c, U1(k, e))
28.57/10.33	   A^2 -> H(c, e)
28.57/10.33	   A^2 -> H(c, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, k), b)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, k), c)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, k), e)
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, c), d)
28.57/10.33	   A^2 -> H(U1(e, c), k)
28.57/10.33	   A^2 -> H(U1(k, e), b)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, e), c)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, c), d)
28.57/10.33	   A^2 -> H(U1(c, e), d)
28.57/10.33	   A^2 -> H(U1(c, e), k)
28.57/10.33	   A^2 -> H(U1(c, k), d)
28.57/10.33	   A^2 -> H(U1(c, k), k)
28.57/10.33	   A^2 -> H(e, b)
28.57/10.33	   A^2 -> H(e, U1(e, d))
28.57/10.33	   A^2 -> H(e, U1(d, e))
28.57/10.33	   A^2 -> H(e, c)
28.57/10.33	   A^2 -> H(e, U1(e, k))
28.57/10.33	   A^2 -> H(e, e)
28.57/10.33	   A^2 -> H(U1(e, e), d)
28.57/10.33	   A^2 -> H(U1(e, e), k)
28.57/10.33	   A^2 -> H(e, U1(k, k))
28.57/10.33	
28.57/10.33	The TRS R consists of the following rules:
28.57/10.33	
28.57/10.33	   f(x) -> U1(x, x)
28.57/10.33	   U1(e, x) -> x
28.57/10.33	   a -> c
28.57/10.33	   a -> d
28.57/10.33	   b -> c
28.57/10.33	   b -> d
28.57/10.33	   d -> k
28.57/10.33	   c -> e
28.57/10.33	   c -> k
28.57/10.33	
28.57/10.33	Q is empty.
28.57/10.33	We have to consider all minimal (P,Q,R)-chains.
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2277) DependencyGraphProof (EQUIVALENT)
28.57/10.33	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2278)
28.57/10.33	Obligation:
28.57/10.33	Q DP problem:
28.57/10.33	The TRS P consists of the following rules:
28.57/10.33	
28.57/10.33	   G(d, x, x) -> A^2
28.57/10.33	   A^2 -> H(f(c), f(c))
28.57/10.33	   H(x, x) -> G(x, x, f(k))
28.57/10.33	   A^2 -> H(f(d), f(d))
28.57/10.33	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.33	   A^2 -> H(f(e), f(e))
28.57/10.33	   A^2 -> H(f(k), f(k))
28.57/10.33	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.33	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.33	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.33	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.33	   A^2 -> H(f(e), d)
28.57/10.33	   A^2 -> H(f(e), k)
28.57/10.33	   A^2 -> H(U1(k, k), b)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, k), c)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.33	   A^2 -> H(f(k), d)
28.57/10.33	   A^2 -> H(f(k), k)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(k, d), b)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, d), c)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, k), b)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, k), c)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, k), e)
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, d), d)
28.57/10.33	   A^2 -> H(U1(d, d), k)
28.57/10.33	   A^2 -> H(U1(e, c), c)
28.57/10.33	   A^2 -> H(U1(c, c), e)
28.57/10.33	   A^2 -> H(U1(c, c), k)
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(e, e), e)
28.57/10.33	   A^2 -> H(d, U1(e, b))
28.57/10.33	   A^2 -> H(d, U1(k, b))
28.57/10.33	   A^2 -> H(d, U1(c, d))
28.57/10.33	   A^2 -> H(d, U1(d, c))
28.57/10.33	   A^2 -> H(d, U1(b, e))
28.57/10.33	   A^2 -> H(d, U1(b, k))
28.57/10.33	   A^2 -> H(d, U1(e, c))
28.57/10.33	   A^2 -> H(d, U1(k, c))
28.57/10.33	   A^2 -> H(d, U1(c, e))
28.57/10.33	   A^2 -> H(d, U1(c, k))
28.57/10.33	   A^2 -> H(d, U1(e, e))
28.57/10.33	   A^2 -> H(d, U1(k, k))
28.57/10.33	   A^2 -> H(d, U1(k, d))
28.57/10.33	   A^2 -> H(d, U1(d, k))
28.57/10.33	   A^2 -> H(a, b)
28.57/10.33	   A^2 -> H(a, U1(e, d))
28.57/10.33	   A^2 -> H(a, U1(d, e))
28.57/10.33	   A^2 -> H(a, c)
28.57/10.33	   A^2 -> H(a, U1(e, k))
28.57/10.33	   A^2 -> H(a, U1(k, e))
28.57/10.33	   A^2 -> H(a, e)
28.57/10.33	   A^2 -> H(a, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, d), b)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, d), c)
28.57/10.33	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, d), e)
28.57/10.33	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, a), d)
28.57/10.33	   A^2 -> H(U1(e, a), k)
28.57/10.33	   A^2 -> H(U1(k, a), d)
28.57/10.33	   A^2 -> H(U1(c, d), d)
28.57/10.33	   A^2 -> H(U1(c, d), k)
28.57/10.33	   A^2 -> H(U1(d, e), b)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, e), c)
28.57/10.33	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, e), e)
28.57/10.33	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, c), d)
28.57/10.33	   A^2 -> H(U1(d, c), k)
28.57/10.33	   A^2 -> H(U1(a, e), d)
28.57/10.33	   A^2 -> H(U1(a, e), k)
28.57/10.33	   A^2 -> H(U1(a, k), d)
28.57/10.33	   A^2 -> H(U1(a, k), k)
28.57/10.33	   A^2 -> H(k, U1(e, b))
28.57/10.33	   A^2 -> H(k, U1(c, d))
28.57/10.33	   A^2 -> H(k, U1(d, c))
28.57/10.33	   A^2 -> H(k, U1(b, e))
28.57/10.33	   A^2 -> H(k, U1(b, k))
28.57/10.33	   A^2 -> H(k, U1(e, c))
28.57/10.33	   A^2 -> H(k, U1(c, e))
28.57/10.33	   A^2 -> H(k, U1(c, k))
28.57/10.33	   A^2 -> H(k, U1(e, e))
28.57/10.33	   A^2 -> H(k, U1(d, k))
28.57/10.33	   A^2 -> H(c, b)
28.57/10.33	   A^2 -> H(c, U1(e, d))
28.57/10.33	   A^2 -> H(c, U1(d, e))
28.57/10.33	   A^2 -> H(c, c)
28.57/10.33	   A^2 -> H(c, U1(e, k))
28.57/10.33	   A^2 -> H(c, U1(k, e))
28.57/10.33	   A^2 -> H(c, e)
28.57/10.33	   A^2 -> H(c, U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, k), b)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(e, k), c)
28.57/10.33	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(e, k), e)
28.57/10.33	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(e, c), d)
28.57/10.33	   A^2 -> H(U1(e, c), k)
28.57/10.33	   A^2 -> H(U1(k, e), b)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, e), c)
28.57/10.33	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, c), d)
28.57/10.33	   A^2 -> H(U1(c, e), d)
28.57/10.33	   A^2 -> H(U1(c, e), k)
28.57/10.33	   A^2 -> H(U1(c, k), d)
28.57/10.33	   A^2 -> H(U1(c, k), k)
28.57/10.33	   A^2 -> H(e, b)
28.57/10.33	   A^2 -> H(e, U1(e, d))
28.57/10.33	   A^2 -> H(e, U1(d, e))
28.57/10.33	   A^2 -> H(e, c)
28.57/10.33	   A^2 -> H(e, U1(e, k))
28.57/10.33	   A^2 -> H(e, e)
28.57/10.33	   A^2 -> H(U1(e, e), d)
28.57/10.33	   A^2 -> H(U1(e, e), k)
28.57/10.33	
28.57/10.33	The TRS R consists of the following rules:
28.57/10.33	
28.57/10.33	   f(x) -> U1(x, x)
28.57/10.33	   U1(e, x) -> x
28.57/10.33	   a -> c
28.57/10.33	   a -> d
28.57/10.33	   b -> c
28.57/10.33	   b -> d
28.57/10.33	   d -> k
28.57/10.33	   c -> e
28.57/10.33	   c -> k
28.57/10.33	
28.57/10.33	Q is empty.
28.57/10.33	We have to consider all minimal (P,Q,R)-chains.
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2279) TransformationProof (EQUIVALENT)
28.57/10.33	By narrowing [LPAR04] the rule A^2 -> H(f(e), d) at position [] we obtained the following new rules [LPAR04]:
28.57/10.33	
28.57/10.33	   (A^2 -> H(U1(e, e), d),A^2 -> H(U1(e, e), d))
28.57/10.33	   (A^2 -> H(f(e), k),A^2 -> H(f(e), k))
28.57/10.33	
28.57/10.33	
28.57/10.33	----------------------------------------
28.57/10.33	
28.57/10.33	(2280)
28.57/10.33	Obligation:
28.57/10.33	Q DP problem:
28.57/10.33	The TRS P consists of the following rules:
28.57/10.33	
28.57/10.33	   G(d, x, x) -> A^2
28.57/10.33	   A^2 -> H(f(c), f(c))
28.57/10.33	   H(x, x) -> G(x, x, f(k))
28.57/10.33	   A^2 -> H(f(d), f(d))
28.57/10.33	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.33	   A^2 -> H(f(e), f(e))
28.57/10.33	   A^2 -> H(f(k), f(k))
28.57/10.33	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.33	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.33	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.33	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.33	   A^2 -> H(f(e), k)
28.57/10.33	   A^2 -> H(U1(k, k), b)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, k), c)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.33	   A^2 -> H(f(k), d)
28.57/10.33	   A^2 -> H(f(k), k)
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.33	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.33	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.33	   A^2 -> H(U1(k, d), b)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.33	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.33	   A^2 -> H(U1(k, d), c)
28.57/10.33	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.33	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, k), b)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.33	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.33	   A^2 -> H(U1(d, k), c)
28.57/10.33	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.33	   A^2 -> H(U1(d, k), e)
28.57/10.33	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.33	   A^2 -> H(U1(d, d), d)
28.57/10.33	   A^2 -> H(U1(d, d), k)
28.57/10.33	   A^2 -> H(U1(e, c), c)
28.57/10.33	   A^2 -> H(U1(c, c), e)
28.57/10.33	   A^2 -> H(U1(c, c), k)
28.57/10.33	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.33	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.33	   A^2 -> H(U1(e, e), e)
28.57/10.33	   A^2 -> H(d, U1(e, b))
28.57/10.34	   A^2 -> H(d, U1(k, b))
28.57/10.34	   A^2 -> H(d, U1(c, d))
28.57/10.34	   A^2 -> H(d, U1(d, c))
28.57/10.34	   A^2 -> H(d, U1(b, e))
28.57/10.34	   A^2 -> H(d, U1(b, k))
28.57/10.34	   A^2 -> H(d, U1(e, c))
28.57/10.34	   A^2 -> H(d, U1(k, c))
28.57/10.34	   A^2 -> H(d, U1(c, e))
28.57/10.34	   A^2 -> H(d, U1(c, k))
28.57/10.34	   A^2 -> H(d, U1(e, e))
28.57/10.34	   A^2 -> H(d, U1(k, k))
28.57/10.34	   A^2 -> H(d, U1(k, d))
28.57/10.34	   A^2 -> H(d, U1(d, k))
28.57/10.34	   A^2 -> H(a, b)
28.57/10.34	   A^2 -> H(a, U1(e, d))
28.57/10.34	   A^2 -> H(a, U1(d, e))
28.57/10.34	   A^2 -> H(a, c)
28.57/10.34	   A^2 -> H(a, U1(e, k))
28.57/10.34	   A^2 -> H(a, U1(k, e))
28.57/10.34	   A^2 -> H(a, e)
28.57/10.34	   A^2 -> H(a, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, d), b)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, d), c)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, d), e)
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, a), d)
28.57/10.34	   A^2 -> H(U1(e, a), k)
28.57/10.34	   A^2 -> H(U1(k, a), d)
28.57/10.34	   A^2 -> H(U1(c, d), d)
28.57/10.34	   A^2 -> H(U1(c, d), k)
28.57/10.34	   A^2 -> H(U1(d, e), b)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, e), c)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, e), e)
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, c), d)
28.57/10.34	   A^2 -> H(U1(d, c), k)
28.57/10.34	   A^2 -> H(U1(a, e), d)
28.57/10.34	   A^2 -> H(U1(a, e), k)
28.57/10.34	   A^2 -> H(U1(a, k), d)
28.57/10.34	   A^2 -> H(U1(a, k), k)
28.57/10.34	   A^2 -> H(k, U1(e, b))
28.57/10.34	   A^2 -> H(k, U1(c, d))
28.57/10.34	   A^2 -> H(k, U1(d, c))
28.57/10.34	   A^2 -> H(k, U1(b, e))
28.57/10.34	   A^2 -> H(k, U1(b, k))
28.57/10.34	   A^2 -> H(k, U1(e, c))
28.57/10.34	   A^2 -> H(k, U1(c, e))
28.57/10.34	   A^2 -> H(k, U1(c, k))
28.57/10.34	   A^2 -> H(k, U1(e, e))
28.57/10.34	   A^2 -> H(k, U1(d, k))
28.57/10.34	   A^2 -> H(c, b)
28.57/10.34	   A^2 -> H(c, U1(e, d))
28.57/10.34	   A^2 -> H(c, U1(d, e))
28.57/10.34	   A^2 -> H(c, c)
28.57/10.34	   A^2 -> H(c, U1(e, k))
28.57/10.34	   A^2 -> H(c, U1(k, e))
28.57/10.34	   A^2 -> H(c, e)
28.57/10.34	   A^2 -> H(c, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, k), b)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, k), c)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, k), e)
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, c), d)
28.57/10.34	   A^2 -> H(U1(e, c), k)
28.57/10.34	   A^2 -> H(U1(k, e), b)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, e), c)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, c), d)
28.57/10.34	   A^2 -> H(U1(c, e), d)
28.57/10.34	   A^2 -> H(U1(c, e), k)
28.57/10.34	   A^2 -> H(U1(c, k), d)
28.57/10.34	   A^2 -> H(U1(c, k), k)
28.57/10.34	   A^2 -> H(e, b)
28.57/10.34	   A^2 -> H(e, U1(e, d))
28.57/10.34	   A^2 -> H(e, U1(d, e))
28.57/10.34	   A^2 -> H(e, c)
28.57/10.34	   A^2 -> H(e, U1(e, k))
28.57/10.34	   A^2 -> H(e, e)
28.57/10.34	   A^2 -> H(U1(e, e), d)
28.57/10.34	   A^2 -> H(U1(e, e), k)
28.57/10.34	
28.57/10.34	The TRS R consists of the following rules:
28.57/10.34	
28.57/10.34	   f(x) -> U1(x, x)
28.57/10.34	   U1(e, x) -> x
28.57/10.34	   a -> c
28.57/10.34	   a -> d
28.57/10.34	   b -> c
28.57/10.34	   b -> d
28.57/10.34	   d -> k
28.57/10.34	   c -> e
28.57/10.34	   c -> k
28.57/10.34	
28.57/10.34	Q is empty.
28.57/10.34	We have to consider all minimal (P,Q,R)-chains.
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2281) TransformationProof (EQUIVALENT)
28.57/10.34	By narrowing [LPAR04] the rule A^2 -> H(f(e), k) at position [] we obtained the following new rules [LPAR04]:
28.57/10.34	
28.57/10.34	   (A^2 -> H(U1(e, e), k),A^2 -> H(U1(e, e), k))
28.57/10.34	
28.57/10.34	
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2282)
28.57/10.34	Obligation:
28.57/10.34	Q DP problem:
28.57/10.34	The TRS P consists of the following rules:
28.57/10.34	
28.57/10.34	   G(d, x, x) -> A^2
28.57/10.34	   A^2 -> H(f(c), f(c))
28.57/10.34	   H(x, x) -> G(x, x, f(k))
28.57/10.34	   A^2 -> H(f(d), f(d))
28.57/10.34	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.34	   A^2 -> H(f(e), f(e))
28.57/10.34	   A^2 -> H(f(k), f(k))
28.57/10.34	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.34	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.34	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.34	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, k), b)
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, k), c)
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.34	   A^2 -> H(f(k), d)
28.57/10.34	   A^2 -> H(f(k), k)
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, d), b)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, d), c)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, k), b)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, k), c)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, k), e)
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, d), d)
28.57/10.34	   A^2 -> H(U1(d, d), k)
28.57/10.34	   A^2 -> H(U1(e, c), c)
28.57/10.34	   A^2 -> H(U1(c, c), e)
28.57/10.34	   A^2 -> H(U1(c, c), k)
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(e, e), e)
28.57/10.34	   A^2 -> H(d, U1(e, b))
28.57/10.34	   A^2 -> H(d, U1(k, b))
28.57/10.34	   A^2 -> H(d, U1(c, d))
28.57/10.34	   A^2 -> H(d, U1(d, c))
28.57/10.34	   A^2 -> H(d, U1(b, e))
28.57/10.34	   A^2 -> H(d, U1(b, k))
28.57/10.34	   A^2 -> H(d, U1(e, c))
28.57/10.34	   A^2 -> H(d, U1(k, c))
28.57/10.34	   A^2 -> H(d, U1(c, e))
28.57/10.34	   A^2 -> H(d, U1(c, k))
28.57/10.34	   A^2 -> H(d, U1(e, e))
28.57/10.34	   A^2 -> H(d, U1(k, k))
28.57/10.34	   A^2 -> H(d, U1(k, d))
28.57/10.34	   A^2 -> H(d, U1(d, k))
28.57/10.34	   A^2 -> H(a, b)
28.57/10.34	   A^2 -> H(a, U1(e, d))
28.57/10.34	   A^2 -> H(a, U1(d, e))
28.57/10.34	   A^2 -> H(a, c)
28.57/10.34	   A^2 -> H(a, U1(e, k))
28.57/10.34	   A^2 -> H(a, U1(k, e))
28.57/10.34	   A^2 -> H(a, e)
28.57/10.34	   A^2 -> H(a, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, d), b)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, d), c)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, d), e)
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, a), d)
28.57/10.34	   A^2 -> H(U1(e, a), k)
28.57/10.34	   A^2 -> H(U1(k, a), d)
28.57/10.34	   A^2 -> H(U1(c, d), d)
28.57/10.34	   A^2 -> H(U1(c, d), k)
28.57/10.34	   A^2 -> H(U1(d, e), b)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, e), c)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, e), e)
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, c), d)
28.57/10.34	   A^2 -> H(U1(d, c), k)
28.57/10.34	   A^2 -> H(U1(a, e), d)
28.57/10.34	   A^2 -> H(U1(a, e), k)
28.57/10.34	   A^2 -> H(U1(a, k), d)
28.57/10.34	   A^2 -> H(U1(a, k), k)
28.57/10.34	   A^2 -> H(k, U1(e, b))
28.57/10.34	   A^2 -> H(k, U1(c, d))
28.57/10.34	   A^2 -> H(k, U1(d, c))
28.57/10.34	   A^2 -> H(k, U1(b, e))
28.57/10.34	   A^2 -> H(k, U1(b, k))
28.57/10.34	   A^2 -> H(k, U1(e, c))
28.57/10.34	   A^2 -> H(k, U1(c, e))
28.57/10.34	   A^2 -> H(k, U1(c, k))
28.57/10.34	   A^2 -> H(k, U1(e, e))
28.57/10.34	   A^2 -> H(k, U1(d, k))
28.57/10.34	   A^2 -> H(c, b)
28.57/10.34	   A^2 -> H(c, U1(e, d))
28.57/10.34	   A^2 -> H(c, U1(d, e))
28.57/10.34	   A^2 -> H(c, c)
28.57/10.34	   A^2 -> H(c, U1(e, k))
28.57/10.34	   A^2 -> H(c, U1(k, e))
28.57/10.34	   A^2 -> H(c, e)
28.57/10.34	   A^2 -> H(c, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, k), b)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, k), c)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, k), e)
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, c), d)
28.57/10.34	   A^2 -> H(U1(e, c), k)
28.57/10.34	   A^2 -> H(U1(k, e), b)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, e), c)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, c), d)
28.57/10.34	   A^2 -> H(U1(c, e), d)
28.57/10.34	   A^2 -> H(U1(c, e), k)
28.57/10.34	   A^2 -> H(U1(c, k), d)
28.57/10.34	   A^2 -> H(U1(c, k), k)
28.57/10.34	   A^2 -> H(e, b)
28.57/10.34	   A^2 -> H(e, U1(e, d))
28.57/10.34	   A^2 -> H(e, U1(d, e))
28.57/10.34	   A^2 -> H(e, c)
28.57/10.34	   A^2 -> H(e, U1(e, k))
28.57/10.34	   A^2 -> H(e, e)
28.57/10.34	   A^2 -> H(U1(e, e), d)
28.57/10.34	   A^2 -> H(U1(e, e), k)
28.57/10.34	
28.57/10.34	The TRS R consists of the following rules:
28.57/10.34	
28.57/10.34	   f(x) -> U1(x, x)
28.57/10.34	   U1(e, x) -> x
28.57/10.34	   a -> c
28.57/10.34	   a -> d
28.57/10.34	   b -> c
28.57/10.34	   b -> d
28.57/10.34	   d -> k
28.57/10.34	   c -> e
28.57/10.34	   c -> k
28.57/10.34	
28.57/10.34	Q is empty.
28.57/10.34	We have to consider all minimal (P,Q,R)-chains.
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2283) TransformationProof (EQUIVALENT)
28.57/10.34	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), b) at position [] we obtained the following new rules [LPAR04]:
28.57/10.34	
28.57/10.34	   (A^2 -> H(U1(k, k), c),A^2 -> H(U1(k, k), c))
28.57/10.34	   (A^2 -> H(U1(k, k), d),A^2 -> H(U1(k, k), d))
28.57/10.34	
28.57/10.34	
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2284)
28.57/10.34	Obligation:
28.57/10.34	Q DP problem:
28.57/10.34	The TRS P consists of the following rules:
28.57/10.34	
28.57/10.34	   G(d, x, x) -> A^2
28.57/10.34	   A^2 -> H(f(c), f(c))
28.57/10.34	   H(x, x) -> G(x, x, f(k))
28.57/10.34	   A^2 -> H(f(d), f(d))
28.57/10.34	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.34	   A^2 -> H(f(e), f(e))
28.57/10.34	   A^2 -> H(f(k), f(k))
28.57/10.34	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.34	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.34	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.34	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, k), c)
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.34	   A^2 -> H(f(k), d)
28.57/10.34	   A^2 -> H(f(k), k)
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, d), b)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, d), c)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, k), b)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, k), c)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, k), e)
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, d), d)
28.57/10.34	   A^2 -> H(U1(d, d), k)
28.57/10.34	   A^2 -> H(U1(e, c), c)
28.57/10.34	   A^2 -> H(U1(c, c), e)
28.57/10.34	   A^2 -> H(U1(c, c), k)
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(e, e), e)
28.57/10.34	   A^2 -> H(d, U1(e, b))
28.57/10.34	   A^2 -> H(d, U1(k, b))
28.57/10.34	   A^2 -> H(d, U1(c, d))
28.57/10.34	   A^2 -> H(d, U1(d, c))
28.57/10.34	   A^2 -> H(d, U1(b, e))
28.57/10.34	   A^2 -> H(d, U1(b, k))
28.57/10.34	   A^2 -> H(d, U1(e, c))
28.57/10.34	   A^2 -> H(d, U1(k, c))
28.57/10.34	   A^2 -> H(d, U1(c, e))
28.57/10.34	   A^2 -> H(d, U1(c, k))
28.57/10.34	   A^2 -> H(d, U1(e, e))
28.57/10.34	   A^2 -> H(d, U1(k, k))
28.57/10.34	   A^2 -> H(d, U1(k, d))
28.57/10.34	   A^2 -> H(d, U1(d, k))
28.57/10.34	   A^2 -> H(a, b)
28.57/10.34	   A^2 -> H(a, U1(e, d))
28.57/10.34	   A^2 -> H(a, U1(d, e))
28.57/10.34	   A^2 -> H(a, c)
28.57/10.34	   A^2 -> H(a, U1(e, k))
28.57/10.34	   A^2 -> H(a, U1(k, e))
28.57/10.34	   A^2 -> H(a, e)
28.57/10.34	   A^2 -> H(a, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, d), b)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, d), c)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, d), e)
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, a), d)
28.57/10.34	   A^2 -> H(U1(e, a), k)
28.57/10.34	   A^2 -> H(U1(k, a), d)
28.57/10.34	   A^2 -> H(U1(c, d), d)
28.57/10.34	   A^2 -> H(U1(c, d), k)
28.57/10.34	   A^2 -> H(U1(d, e), b)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, e), c)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, e), e)
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, c), d)
28.57/10.34	   A^2 -> H(U1(d, c), k)
28.57/10.34	   A^2 -> H(U1(a, e), d)
28.57/10.34	   A^2 -> H(U1(a, e), k)
28.57/10.34	   A^2 -> H(U1(a, k), d)
28.57/10.34	   A^2 -> H(U1(a, k), k)
28.57/10.34	   A^2 -> H(k, U1(e, b))
28.57/10.34	   A^2 -> H(k, U1(c, d))
28.57/10.34	   A^2 -> H(k, U1(d, c))
28.57/10.34	   A^2 -> H(k, U1(b, e))
28.57/10.34	   A^2 -> H(k, U1(b, k))
28.57/10.34	   A^2 -> H(k, U1(e, c))
28.57/10.34	   A^2 -> H(k, U1(c, e))
28.57/10.34	   A^2 -> H(k, U1(c, k))
28.57/10.34	   A^2 -> H(k, U1(e, e))
28.57/10.34	   A^2 -> H(k, U1(d, k))
28.57/10.34	   A^2 -> H(c, b)
28.57/10.34	   A^2 -> H(c, U1(e, d))
28.57/10.34	   A^2 -> H(c, U1(d, e))
28.57/10.34	   A^2 -> H(c, c)
28.57/10.34	   A^2 -> H(c, U1(e, k))
28.57/10.34	   A^2 -> H(c, U1(k, e))
28.57/10.34	   A^2 -> H(c, e)
28.57/10.34	   A^2 -> H(c, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, k), b)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, k), c)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, k), e)
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, c), d)
28.57/10.34	   A^2 -> H(U1(e, c), k)
28.57/10.34	   A^2 -> H(U1(k, e), b)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, e), c)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, c), d)
28.57/10.34	   A^2 -> H(U1(c, e), d)
28.57/10.34	   A^2 -> H(U1(c, e), k)
28.57/10.34	   A^2 -> H(U1(c, k), d)
28.57/10.34	   A^2 -> H(U1(c, k), k)
28.57/10.34	   A^2 -> H(e, b)
28.57/10.34	   A^2 -> H(e, U1(e, d))
28.57/10.34	   A^2 -> H(e, U1(d, e))
28.57/10.34	   A^2 -> H(e, c)
28.57/10.34	   A^2 -> H(e, U1(e, k))
28.57/10.34	   A^2 -> H(e, e)
28.57/10.34	   A^2 -> H(U1(e, e), d)
28.57/10.34	   A^2 -> H(U1(e, e), k)
28.57/10.34	   A^2 -> H(U1(k, k), d)
28.57/10.34	
28.57/10.34	The TRS R consists of the following rules:
28.57/10.34	
28.57/10.34	   f(x) -> U1(x, x)
28.57/10.34	   U1(e, x) -> x
28.57/10.34	   a -> c
28.57/10.34	   a -> d
28.57/10.34	   b -> c
28.57/10.34	   b -> d
28.57/10.34	   d -> k
28.57/10.34	   c -> e
28.57/10.34	   c -> k
28.57/10.34	
28.57/10.34	Q is empty.
28.57/10.34	We have to consider all minimal (P,Q,R)-chains.
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2285) TransformationProof (EQUIVALENT)
28.57/10.34	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.34	
28.57/10.34	   (A^2 -> H(U1(k, k), d),A^2 -> H(U1(k, k), d))
28.57/10.34	   (A^2 -> H(U1(k, k), U1(e, k)),A^2 -> H(U1(k, k), U1(e, k)))
28.57/10.34	
28.57/10.34	
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2286)
28.57/10.34	Obligation:
28.57/10.34	Q DP problem:
28.57/10.34	The TRS P consists of the following rules:
28.57/10.34	
28.57/10.34	   G(d, x, x) -> A^2
28.57/10.34	   A^2 -> H(f(c), f(c))
28.57/10.34	   H(x, x) -> G(x, x, f(k))
28.57/10.34	   A^2 -> H(f(d), f(d))
28.57/10.34	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.34	   A^2 -> H(f(e), f(e))
28.57/10.34	   A^2 -> H(f(k), f(k))
28.57/10.34	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.34	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.34	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.34	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, k), c)
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.34	   A^2 -> H(f(k), d)
28.57/10.34	   A^2 -> H(f(k), k)
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, d), b)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, d), c)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, k), b)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, k), c)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, k), e)
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, d), d)
28.57/10.34	   A^2 -> H(U1(d, d), k)
28.57/10.34	   A^2 -> H(U1(e, c), c)
28.57/10.34	   A^2 -> H(U1(c, c), e)
28.57/10.34	   A^2 -> H(U1(c, c), k)
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(e, e), e)
28.57/10.34	   A^2 -> H(d, U1(e, b))
28.57/10.34	   A^2 -> H(d, U1(k, b))
28.57/10.34	   A^2 -> H(d, U1(c, d))
28.57/10.34	   A^2 -> H(d, U1(d, c))
28.57/10.34	   A^2 -> H(d, U1(b, e))
28.57/10.34	   A^2 -> H(d, U1(b, k))
28.57/10.34	   A^2 -> H(d, U1(e, c))
28.57/10.34	   A^2 -> H(d, U1(k, c))
28.57/10.34	   A^2 -> H(d, U1(c, e))
28.57/10.34	   A^2 -> H(d, U1(c, k))
28.57/10.34	   A^2 -> H(d, U1(e, e))
28.57/10.34	   A^2 -> H(d, U1(k, k))
28.57/10.34	   A^2 -> H(d, U1(k, d))
28.57/10.34	   A^2 -> H(d, U1(d, k))
28.57/10.34	   A^2 -> H(a, b)
28.57/10.34	   A^2 -> H(a, U1(e, d))
28.57/10.34	   A^2 -> H(a, U1(d, e))
28.57/10.34	   A^2 -> H(a, c)
28.57/10.34	   A^2 -> H(a, U1(e, k))
28.57/10.34	   A^2 -> H(a, U1(k, e))
28.57/10.34	   A^2 -> H(a, e)
28.57/10.34	   A^2 -> H(a, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, d), b)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, d), c)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, d), e)
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, a), d)
28.57/10.34	   A^2 -> H(U1(e, a), k)
28.57/10.34	   A^2 -> H(U1(k, a), d)
28.57/10.34	   A^2 -> H(U1(c, d), d)
28.57/10.34	   A^2 -> H(U1(c, d), k)
28.57/10.34	   A^2 -> H(U1(d, e), b)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, e), c)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, e), e)
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, c), d)
28.57/10.34	   A^2 -> H(U1(d, c), k)
28.57/10.34	   A^2 -> H(U1(a, e), d)
28.57/10.34	   A^2 -> H(U1(a, e), k)
28.57/10.34	   A^2 -> H(U1(a, k), d)
28.57/10.34	   A^2 -> H(U1(a, k), k)
28.57/10.34	   A^2 -> H(k, U1(e, b))
28.57/10.34	   A^2 -> H(k, U1(c, d))
28.57/10.34	   A^2 -> H(k, U1(d, c))
28.57/10.34	   A^2 -> H(k, U1(b, e))
28.57/10.34	   A^2 -> H(k, U1(b, k))
28.57/10.34	   A^2 -> H(k, U1(e, c))
28.57/10.34	   A^2 -> H(k, U1(c, e))
28.57/10.34	   A^2 -> H(k, U1(c, k))
28.57/10.34	   A^2 -> H(k, U1(e, e))
28.57/10.34	   A^2 -> H(k, U1(d, k))
28.57/10.34	   A^2 -> H(c, b)
28.57/10.34	   A^2 -> H(c, U1(e, d))
28.57/10.34	   A^2 -> H(c, U1(d, e))
28.57/10.34	   A^2 -> H(c, c)
28.57/10.34	   A^2 -> H(c, U1(e, k))
28.57/10.34	   A^2 -> H(c, U1(k, e))
28.57/10.34	   A^2 -> H(c, e)
28.57/10.34	   A^2 -> H(c, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, k), b)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, k), c)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, k), e)
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, c), d)
28.57/10.34	   A^2 -> H(U1(e, c), k)
28.57/10.34	   A^2 -> H(U1(k, e), b)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, e), c)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, c), d)
28.57/10.34	   A^2 -> H(U1(c, e), d)
28.57/10.34	   A^2 -> H(U1(c, e), k)
28.57/10.34	   A^2 -> H(U1(c, k), d)
28.57/10.34	   A^2 -> H(U1(c, k), k)
28.57/10.34	   A^2 -> H(e, b)
28.57/10.34	   A^2 -> H(e, U1(e, d))
28.57/10.34	   A^2 -> H(e, U1(d, e))
28.57/10.34	   A^2 -> H(e, c)
28.57/10.34	   A^2 -> H(e, U1(e, k))
28.57/10.34	   A^2 -> H(e, e)
28.57/10.34	   A^2 -> H(U1(e, e), d)
28.57/10.34	   A^2 -> H(U1(e, e), k)
28.57/10.34	   A^2 -> H(U1(k, k), d)
28.57/10.34	
28.57/10.34	The TRS R consists of the following rules:
28.57/10.34	
28.57/10.34	   f(x) -> U1(x, x)
28.57/10.34	   U1(e, x) -> x
28.57/10.34	   a -> c
28.57/10.34	   a -> d
28.57/10.34	   b -> c
28.57/10.34	   b -> d
28.57/10.34	   d -> k
28.57/10.34	   c -> e
28.57/10.34	   c -> k
28.57/10.34	
28.57/10.34	Q is empty.
28.57/10.34	We have to consider all minimal (P,Q,R)-chains.
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2287) TransformationProof (EQUIVALENT)
28.57/10.34	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.34	
28.57/10.34	   (A^2 -> H(U1(k, k), U1(k, e)),A^2 -> H(U1(k, k), U1(k, e)))
28.57/10.34	
28.57/10.34	
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2288)
28.57/10.34	Obligation:
28.57/10.34	Q DP problem:
28.57/10.34	The TRS P consists of the following rules:
28.57/10.34	
28.57/10.34	   G(d, x, x) -> A^2
28.57/10.34	   A^2 -> H(f(c), f(c))
28.57/10.34	   H(x, x) -> G(x, x, f(k))
28.57/10.34	   A^2 -> H(f(d), f(d))
28.57/10.34	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.34	   A^2 -> H(f(e), f(e))
28.57/10.34	   A^2 -> H(f(k), f(k))
28.57/10.34	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.34	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.34	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.34	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, k), c)
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.34	   A^2 -> H(f(k), d)
28.57/10.34	   A^2 -> H(f(k), k)
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, d), b)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, d), c)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, k), b)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, k), c)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, k), e)
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, d), d)
28.57/10.34	   A^2 -> H(U1(d, d), k)
28.57/10.34	   A^2 -> H(U1(e, c), c)
28.57/10.34	   A^2 -> H(U1(c, c), e)
28.57/10.34	   A^2 -> H(U1(c, c), k)
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(e, e), e)
28.57/10.34	   A^2 -> H(d, U1(e, b))
28.57/10.34	   A^2 -> H(d, U1(k, b))
28.57/10.34	   A^2 -> H(d, U1(c, d))
28.57/10.34	   A^2 -> H(d, U1(d, c))
28.57/10.34	   A^2 -> H(d, U1(b, e))
28.57/10.34	   A^2 -> H(d, U1(b, k))
28.57/10.34	   A^2 -> H(d, U1(e, c))
28.57/10.34	   A^2 -> H(d, U1(k, c))
28.57/10.34	   A^2 -> H(d, U1(c, e))
28.57/10.34	   A^2 -> H(d, U1(c, k))
28.57/10.34	   A^2 -> H(d, U1(e, e))
28.57/10.34	   A^2 -> H(d, U1(k, k))
28.57/10.34	   A^2 -> H(d, U1(k, d))
28.57/10.34	   A^2 -> H(d, U1(d, k))
28.57/10.34	   A^2 -> H(a, b)
28.57/10.34	   A^2 -> H(a, U1(e, d))
28.57/10.34	   A^2 -> H(a, U1(d, e))
28.57/10.34	   A^2 -> H(a, c)
28.57/10.34	   A^2 -> H(a, U1(e, k))
28.57/10.34	   A^2 -> H(a, U1(k, e))
28.57/10.34	   A^2 -> H(a, e)
28.57/10.34	   A^2 -> H(a, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, d), b)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, d), c)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, d), e)
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, a), d)
28.57/10.34	   A^2 -> H(U1(e, a), k)
28.57/10.34	   A^2 -> H(U1(k, a), d)
28.57/10.34	   A^2 -> H(U1(c, d), d)
28.57/10.34	   A^2 -> H(U1(c, d), k)
28.57/10.34	   A^2 -> H(U1(d, e), b)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, e), c)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, e), e)
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, c), d)
28.57/10.34	   A^2 -> H(U1(d, c), k)
28.57/10.34	   A^2 -> H(U1(a, e), d)
28.57/10.34	   A^2 -> H(U1(a, e), k)
28.57/10.34	   A^2 -> H(U1(a, k), d)
28.57/10.34	   A^2 -> H(U1(a, k), k)
28.57/10.34	   A^2 -> H(k, U1(e, b))
28.57/10.34	   A^2 -> H(k, U1(c, d))
28.57/10.34	   A^2 -> H(k, U1(d, c))
28.57/10.34	   A^2 -> H(k, U1(b, e))
28.57/10.34	   A^2 -> H(k, U1(b, k))
28.57/10.34	   A^2 -> H(k, U1(e, c))
28.57/10.34	   A^2 -> H(k, U1(c, e))
28.57/10.34	   A^2 -> H(k, U1(c, k))
28.57/10.34	   A^2 -> H(k, U1(e, e))
28.57/10.34	   A^2 -> H(k, U1(d, k))
28.57/10.34	   A^2 -> H(c, b)
28.57/10.34	   A^2 -> H(c, U1(e, d))
28.57/10.34	   A^2 -> H(c, U1(d, e))
28.57/10.34	   A^2 -> H(c, c)
28.57/10.34	   A^2 -> H(c, U1(e, k))
28.57/10.34	   A^2 -> H(c, U1(k, e))
28.57/10.34	   A^2 -> H(c, e)
28.57/10.34	   A^2 -> H(c, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, k), b)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, k), c)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, k), e)
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, c), d)
28.57/10.34	   A^2 -> H(U1(e, c), k)
28.57/10.34	   A^2 -> H(U1(k, e), b)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, e), c)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, c), d)
28.57/10.34	   A^2 -> H(U1(c, e), d)
28.57/10.34	   A^2 -> H(U1(c, e), k)
28.57/10.34	   A^2 -> H(U1(c, k), d)
28.57/10.34	   A^2 -> H(U1(c, k), k)
28.57/10.34	   A^2 -> H(e, b)
28.57/10.34	   A^2 -> H(e, U1(e, d))
28.57/10.34	   A^2 -> H(e, U1(d, e))
28.57/10.34	   A^2 -> H(e, c)
28.57/10.34	   A^2 -> H(e, U1(e, k))
28.57/10.34	   A^2 -> H(e, e)
28.57/10.34	   A^2 -> H(U1(e, e), d)
28.57/10.34	   A^2 -> H(U1(e, e), k)
28.57/10.34	   A^2 -> H(U1(k, k), d)
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, e))
28.57/10.34	
28.57/10.34	The TRS R consists of the following rules:
28.57/10.34	
28.57/10.34	   f(x) -> U1(x, x)
28.57/10.34	   U1(e, x) -> x
28.57/10.34	   a -> c
28.57/10.34	   a -> d
28.57/10.34	   b -> c
28.57/10.34	   b -> d
28.57/10.34	   d -> k
28.57/10.34	   c -> e
28.57/10.34	   c -> k
28.57/10.34	
28.57/10.34	Q is empty.
28.57/10.34	We have to consider all minimal (P,Q,R)-chains.
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2289) DependencyGraphProof (EQUIVALENT)
28.57/10.34	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2290)
28.57/10.34	Obligation:
28.57/10.34	Q DP problem:
28.57/10.34	The TRS P consists of the following rules:
28.57/10.34	
28.57/10.34	   A^2 -> H(f(c), f(c))
28.57/10.34	   H(x, x) -> G(x, x, f(k))
28.57/10.34	   G(d, x, x) -> A^2
28.57/10.34	   A^2 -> H(f(d), f(d))
28.57/10.34	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.34	   A^2 -> H(f(e), f(e))
28.57/10.34	   A^2 -> H(f(k), f(k))
28.57/10.34	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.34	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.34	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.34	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, k), c)
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.34	   A^2 -> H(f(k), d)
28.57/10.34	   A^2 -> H(f(k), k)
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, d), b)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, d), c)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, k), b)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, k), c)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, k), e)
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, d), d)
28.57/10.34	   A^2 -> H(U1(d, d), k)
28.57/10.34	   A^2 -> H(U1(e, c), c)
28.57/10.34	   A^2 -> H(U1(c, c), e)
28.57/10.34	   A^2 -> H(U1(c, c), k)
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(e, e), e)
28.57/10.34	   A^2 -> H(d, U1(e, b))
28.57/10.34	   A^2 -> H(d, U1(k, b))
28.57/10.34	   A^2 -> H(d, U1(c, d))
28.57/10.34	   A^2 -> H(d, U1(d, c))
28.57/10.34	   A^2 -> H(d, U1(b, e))
28.57/10.34	   A^2 -> H(d, U1(b, k))
28.57/10.34	   A^2 -> H(d, U1(e, c))
28.57/10.34	   A^2 -> H(d, U1(k, c))
28.57/10.34	   A^2 -> H(d, U1(c, e))
28.57/10.34	   A^2 -> H(d, U1(c, k))
28.57/10.34	   A^2 -> H(d, U1(e, e))
28.57/10.34	   A^2 -> H(d, U1(k, k))
28.57/10.34	   A^2 -> H(d, U1(k, d))
28.57/10.34	   A^2 -> H(d, U1(d, k))
28.57/10.34	   A^2 -> H(a, b)
28.57/10.34	   A^2 -> H(a, U1(e, d))
28.57/10.34	   A^2 -> H(a, U1(d, e))
28.57/10.34	   A^2 -> H(a, c)
28.57/10.34	   A^2 -> H(a, U1(e, k))
28.57/10.34	   A^2 -> H(a, U1(k, e))
28.57/10.34	   A^2 -> H(a, e)
28.57/10.34	   A^2 -> H(a, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, d), b)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, d), c)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, d), e)
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, a), d)
28.57/10.34	   A^2 -> H(U1(e, a), k)
28.57/10.34	   A^2 -> H(U1(k, a), d)
28.57/10.34	   A^2 -> H(U1(c, d), d)
28.57/10.34	   A^2 -> H(U1(c, d), k)
28.57/10.34	   A^2 -> H(U1(d, e), b)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, e), c)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, e), e)
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, c), d)
28.57/10.34	   A^2 -> H(U1(d, c), k)
28.57/10.34	   A^2 -> H(U1(a, e), d)
28.57/10.34	   A^2 -> H(U1(a, e), k)
28.57/10.34	   A^2 -> H(U1(a, k), d)
28.57/10.34	   A^2 -> H(U1(a, k), k)
28.57/10.34	   A^2 -> H(k, U1(e, b))
28.57/10.34	   A^2 -> H(k, U1(c, d))
28.57/10.34	   A^2 -> H(k, U1(d, c))
28.57/10.34	   A^2 -> H(k, U1(b, e))
28.57/10.34	   A^2 -> H(k, U1(b, k))
28.57/10.34	   A^2 -> H(k, U1(e, c))
28.57/10.34	   A^2 -> H(k, U1(c, e))
28.57/10.34	   A^2 -> H(k, U1(c, k))
28.57/10.34	   A^2 -> H(k, U1(e, e))
28.57/10.34	   A^2 -> H(k, U1(d, k))
28.57/10.34	   A^2 -> H(c, b)
28.57/10.34	   A^2 -> H(c, U1(e, d))
28.57/10.34	   A^2 -> H(c, U1(d, e))
28.57/10.34	   A^2 -> H(c, c)
28.57/10.34	   A^2 -> H(c, U1(e, k))
28.57/10.34	   A^2 -> H(c, U1(k, e))
28.57/10.34	   A^2 -> H(c, e)
28.57/10.34	   A^2 -> H(c, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, k), b)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, k), c)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, k), e)
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, c), d)
28.57/10.34	   A^2 -> H(U1(e, c), k)
28.57/10.34	   A^2 -> H(U1(k, e), b)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, e), c)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, c), d)
28.57/10.34	   A^2 -> H(U1(c, e), d)
28.57/10.34	   A^2 -> H(U1(c, e), k)
28.57/10.34	   A^2 -> H(U1(c, k), d)
28.57/10.34	   A^2 -> H(U1(c, k), k)
28.57/10.34	   A^2 -> H(e, b)
28.57/10.34	   A^2 -> H(e, U1(e, d))
28.57/10.34	   A^2 -> H(e, U1(d, e))
28.57/10.34	   A^2 -> H(e, c)
28.57/10.34	   A^2 -> H(e, U1(e, k))
28.57/10.34	   A^2 -> H(e, e)
28.57/10.34	   A^2 -> H(U1(e, e), d)
28.57/10.34	   A^2 -> H(U1(e, e), k)
28.57/10.34	   A^2 -> H(U1(k, k), d)
28.57/10.34	
28.57/10.34	The TRS R consists of the following rules:
28.57/10.34	
28.57/10.34	   f(x) -> U1(x, x)
28.57/10.34	   U1(e, x) -> x
28.57/10.34	   a -> c
28.57/10.34	   a -> d
28.57/10.34	   b -> c
28.57/10.34	   b -> d
28.57/10.34	   d -> k
28.57/10.34	   c -> e
28.57/10.34	   c -> k
28.57/10.34	
28.57/10.34	Q is empty.
28.57/10.34	We have to consider all minimal (P,Q,R)-chains.
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2291) TransformationProof (EQUIVALENT)
28.57/10.34	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), c) at position [] we obtained the following new rules [LPAR04]:
28.57/10.34	
28.57/10.34	   (A^2 -> H(U1(k, k), e),A^2 -> H(U1(k, k), e))
28.57/10.34	   (A^2 -> H(U1(k, k), k),A^2 -> H(U1(k, k), k))
28.57/10.34	
28.57/10.34	
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2292)
28.57/10.34	Obligation:
28.57/10.34	Q DP problem:
28.57/10.34	The TRS P consists of the following rules:
28.57/10.34	
28.57/10.34	   A^2 -> H(f(c), f(c))
28.57/10.34	   H(x, x) -> G(x, x, f(k))
28.57/10.34	   G(d, x, x) -> A^2
28.57/10.34	   A^2 -> H(f(d), f(d))
28.57/10.34	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.34	   A^2 -> H(f(e), f(e))
28.57/10.34	   A^2 -> H(f(k), f(k))
28.57/10.34	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.34	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.34	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.34	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.34	   A^2 -> H(f(k), d)
28.57/10.34	   A^2 -> H(f(k), k)
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, d), b)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, d), c)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, k), b)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, k), c)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, k), e)
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, d), d)
28.57/10.34	   A^2 -> H(U1(d, d), k)
28.57/10.34	   A^2 -> H(U1(e, c), c)
28.57/10.34	   A^2 -> H(U1(c, c), e)
28.57/10.34	   A^2 -> H(U1(c, c), k)
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(e, e), e)
28.57/10.34	   A^2 -> H(d, U1(e, b))
28.57/10.34	   A^2 -> H(d, U1(k, b))
28.57/10.34	   A^2 -> H(d, U1(c, d))
28.57/10.34	   A^2 -> H(d, U1(d, c))
28.57/10.34	   A^2 -> H(d, U1(b, e))
28.57/10.34	   A^2 -> H(d, U1(b, k))
28.57/10.34	   A^2 -> H(d, U1(e, c))
28.57/10.34	   A^2 -> H(d, U1(k, c))
28.57/10.34	   A^2 -> H(d, U1(c, e))
28.57/10.34	   A^2 -> H(d, U1(c, k))
28.57/10.34	   A^2 -> H(d, U1(e, e))
28.57/10.34	   A^2 -> H(d, U1(k, k))
28.57/10.34	   A^2 -> H(d, U1(k, d))
28.57/10.34	   A^2 -> H(d, U1(d, k))
28.57/10.34	   A^2 -> H(a, b)
28.57/10.34	   A^2 -> H(a, U1(e, d))
28.57/10.34	   A^2 -> H(a, U1(d, e))
28.57/10.34	   A^2 -> H(a, c)
28.57/10.34	   A^2 -> H(a, U1(e, k))
28.57/10.34	   A^2 -> H(a, U1(k, e))
28.57/10.34	   A^2 -> H(a, e)
28.57/10.34	   A^2 -> H(a, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, d), b)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, d), c)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, d), e)
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, a), d)
28.57/10.34	   A^2 -> H(U1(e, a), k)
28.57/10.34	   A^2 -> H(U1(k, a), d)
28.57/10.34	   A^2 -> H(U1(c, d), d)
28.57/10.34	   A^2 -> H(U1(c, d), k)
28.57/10.34	   A^2 -> H(U1(d, e), b)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, e), c)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, e), e)
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, c), d)
28.57/10.34	   A^2 -> H(U1(d, c), k)
28.57/10.34	   A^2 -> H(U1(a, e), d)
28.57/10.34	   A^2 -> H(U1(a, e), k)
28.57/10.34	   A^2 -> H(U1(a, k), d)
28.57/10.34	   A^2 -> H(U1(a, k), k)
28.57/10.34	   A^2 -> H(k, U1(e, b))
28.57/10.34	   A^2 -> H(k, U1(c, d))
28.57/10.34	   A^2 -> H(k, U1(d, c))
28.57/10.34	   A^2 -> H(k, U1(b, e))
28.57/10.34	   A^2 -> H(k, U1(b, k))
28.57/10.34	   A^2 -> H(k, U1(e, c))
28.57/10.34	   A^2 -> H(k, U1(c, e))
28.57/10.34	   A^2 -> H(k, U1(c, k))
28.57/10.34	   A^2 -> H(k, U1(e, e))
28.57/10.34	   A^2 -> H(k, U1(d, k))
28.57/10.34	   A^2 -> H(c, b)
28.57/10.34	   A^2 -> H(c, U1(e, d))
28.57/10.34	   A^2 -> H(c, U1(d, e))
28.57/10.34	   A^2 -> H(c, c)
28.57/10.34	   A^2 -> H(c, U1(e, k))
28.57/10.34	   A^2 -> H(c, U1(k, e))
28.57/10.34	   A^2 -> H(c, e)
28.57/10.34	   A^2 -> H(c, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, k), b)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, k), c)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, k), e)
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, c), d)
28.57/10.34	   A^2 -> H(U1(e, c), k)
28.57/10.34	   A^2 -> H(U1(k, e), b)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, e), c)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, c), d)
28.57/10.34	   A^2 -> H(U1(c, e), d)
28.57/10.34	   A^2 -> H(U1(c, e), k)
28.57/10.34	   A^2 -> H(U1(c, k), d)
28.57/10.34	   A^2 -> H(U1(c, k), k)
28.57/10.34	   A^2 -> H(e, b)
28.57/10.34	   A^2 -> H(e, U1(e, d))
28.57/10.34	   A^2 -> H(e, U1(d, e))
28.57/10.34	   A^2 -> H(e, c)
28.57/10.34	   A^2 -> H(e, U1(e, k))
28.57/10.34	   A^2 -> H(e, e)
28.57/10.34	   A^2 -> H(U1(e, e), d)
28.57/10.34	   A^2 -> H(U1(e, e), k)
28.57/10.34	   A^2 -> H(U1(k, k), d)
28.57/10.34	   A^2 -> H(U1(k, k), e)
28.57/10.34	   A^2 -> H(U1(k, k), k)
28.57/10.34	
28.57/10.34	The TRS R consists of the following rules:
28.57/10.34	
28.57/10.34	   f(x) -> U1(x, x)
28.57/10.34	   U1(e, x) -> x
28.57/10.34	   a -> c
28.57/10.34	   a -> d
28.57/10.34	   b -> c
28.57/10.34	   b -> d
28.57/10.34	   d -> k
28.57/10.34	   c -> e
28.57/10.34	   c -> k
28.57/10.34	
28.57/10.34	Q is empty.
28.57/10.34	We have to consider all minimal (P,Q,R)-chains.
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2293) DependencyGraphProof (EQUIVALENT)
28.57/10.34	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2294)
28.57/10.34	Obligation:
28.57/10.34	Q DP problem:
28.57/10.34	The TRS P consists of the following rules:
28.57/10.34	
28.57/10.34	   H(x, x) -> G(x, x, f(k))
28.57/10.34	   G(d, x, x) -> A^2
28.57/10.34	   A^2 -> H(f(c), f(c))
28.57/10.34	   A^2 -> H(f(d), f(d))
28.57/10.34	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.34	   A^2 -> H(f(e), f(e))
28.57/10.34	   A^2 -> H(f(k), f(k))
28.57/10.34	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.34	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.34	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.34	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.34	   A^2 -> H(f(k), d)
28.57/10.34	   A^2 -> H(f(k), k)
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, d), b)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, d), c)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, k), b)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, k), c)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, k), e)
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, d), d)
28.57/10.34	   A^2 -> H(U1(d, d), k)
28.57/10.34	   A^2 -> H(U1(e, c), c)
28.57/10.34	   A^2 -> H(U1(c, c), e)
28.57/10.34	   A^2 -> H(U1(c, c), k)
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(e, e), e)
28.57/10.34	   A^2 -> H(d, U1(e, b))
28.57/10.34	   A^2 -> H(d, U1(k, b))
28.57/10.34	   A^2 -> H(d, U1(c, d))
28.57/10.34	   A^2 -> H(d, U1(d, c))
28.57/10.34	   A^2 -> H(d, U1(b, e))
28.57/10.34	   A^2 -> H(d, U1(b, k))
28.57/10.34	   A^2 -> H(d, U1(e, c))
28.57/10.34	   A^2 -> H(d, U1(k, c))
28.57/10.34	   A^2 -> H(d, U1(c, e))
28.57/10.34	   A^2 -> H(d, U1(c, k))
28.57/10.34	   A^2 -> H(d, U1(e, e))
28.57/10.34	   A^2 -> H(d, U1(k, k))
28.57/10.34	   A^2 -> H(d, U1(k, d))
28.57/10.34	   A^2 -> H(d, U1(d, k))
28.57/10.34	   A^2 -> H(a, b)
28.57/10.34	   A^2 -> H(a, U1(e, d))
28.57/10.34	   A^2 -> H(a, U1(d, e))
28.57/10.34	   A^2 -> H(a, c)
28.57/10.34	   A^2 -> H(a, U1(e, k))
28.57/10.34	   A^2 -> H(a, U1(k, e))
28.57/10.34	   A^2 -> H(a, e)
28.57/10.34	   A^2 -> H(a, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, d), b)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, d), c)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, d), e)
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, a), d)
28.57/10.34	   A^2 -> H(U1(e, a), k)
28.57/10.34	   A^2 -> H(U1(k, a), d)
28.57/10.34	   A^2 -> H(U1(c, d), d)
28.57/10.34	   A^2 -> H(U1(c, d), k)
28.57/10.34	   A^2 -> H(U1(d, e), b)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, e), c)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, e), e)
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, c), d)
28.57/10.34	   A^2 -> H(U1(d, c), k)
28.57/10.34	   A^2 -> H(U1(a, e), d)
28.57/10.34	   A^2 -> H(U1(a, e), k)
28.57/10.34	   A^2 -> H(U1(a, k), d)
28.57/10.34	   A^2 -> H(U1(a, k), k)
28.57/10.34	   A^2 -> H(k, U1(e, b))
28.57/10.34	   A^2 -> H(k, U1(c, d))
28.57/10.34	   A^2 -> H(k, U1(d, c))
28.57/10.34	   A^2 -> H(k, U1(b, e))
28.57/10.34	   A^2 -> H(k, U1(b, k))
28.57/10.34	   A^2 -> H(k, U1(e, c))
28.57/10.34	   A^2 -> H(k, U1(c, e))
28.57/10.34	   A^2 -> H(k, U1(c, k))
28.57/10.34	   A^2 -> H(k, U1(e, e))
28.57/10.34	   A^2 -> H(k, U1(d, k))
28.57/10.34	   A^2 -> H(c, b)
28.57/10.34	   A^2 -> H(c, U1(e, d))
28.57/10.34	   A^2 -> H(c, U1(d, e))
28.57/10.34	   A^2 -> H(c, c)
28.57/10.34	   A^2 -> H(c, U1(e, k))
28.57/10.34	   A^2 -> H(c, U1(k, e))
28.57/10.34	   A^2 -> H(c, e)
28.57/10.34	   A^2 -> H(c, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, k), b)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, k), c)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, k), e)
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, c), d)
28.57/10.34	   A^2 -> H(U1(e, c), k)
28.57/10.34	   A^2 -> H(U1(k, e), b)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, e), c)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, c), d)
28.57/10.34	   A^2 -> H(U1(c, e), d)
28.57/10.34	   A^2 -> H(U1(c, e), k)
28.57/10.34	   A^2 -> H(U1(c, k), d)
28.57/10.34	   A^2 -> H(U1(c, k), k)
28.57/10.34	   A^2 -> H(e, b)
28.57/10.34	   A^2 -> H(e, U1(e, d))
28.57/10.34	   A^2 -> H(e, U1(d, e))
28.57/10.34	   A^2 -> H(e, c)
28.57/10.34	   A^2 -> H(e, U1(e, k))
28.57/10.34	   A^2 -> H(e, e)
28.57/10.34	   A^2 -> H(U1(e, e), d)
28.57/10.34	   A^2 -> H(U1(e, e), k)
28.57/10.34	   A^2 -> H(U1(k, k), d)
28.57/10.34	
28.57/10.34	The TRS R consists of the following rules:
28.57/10.34	
28.57/10.34	   f(x) -> U1(x, x)
28.57/10.34	   U1(e, x) -> x
28.57/10.34	   a -> c
28.57/10.34	   a -> d
28.57/10.34	   b -> c
28.57/10.34	   b -> d
28.57/10.34	   d -> k
28.57/10.34	   c -> e
28.57/10.34	   c -> k
28.57/10.34	
28.57/10.34	Q is empty.
28.57/10.34	We have to consider all minimal (P,Q,R)-chains.
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2295) TransformationProof (EQUIVALENT)
28.57/10.34	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.34	
28.57/10.34	   (A^2 -> H(U1(k, k), k),A^2 -> H(U1(k, k), k))
28.57/10.34	
28.57/10.34	
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2296)
28.57/10.34	Obligation:
28.57/10.34	Q DP problem:
28.57/10.34	The TRS P consists of the following rules:
28.57/10.34	
28.57/10.34	   H(x, x) -> G(x, x, f(k))
28.57/10.34	   G(d, x, x) -> A^2
28.57/10.34	   A^2 -> H(f(c), f(c))
28.57/10.34	   A^2 -> H(f(d), f(d))
28.57/10.34	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.34	   A^2 -> H(f(e), f(e))
28.57/10.34	   A^2 -> H(f(k), f(k))
28.57/10.34	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.34	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.34	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.34	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.34	   A^2 -> H(f(k), d)
28.57/10.34	   A^2 -> H(f(k), k)
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, d), b)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, d), c)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, k), b)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, k), c)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, k), e)
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, d), d)
28.57/10.34	   A^2 -> H(U1(d, d), k)
28.57/10.34	   A^2 -> H(U1(e, c), c)
28.57/10.34	   A^2 -> H(U1(c, c), e)
28.57/10.34	   A^2 -> H(U1(c, c), k)
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(e, e), e)
28.57/10.34	   A^2 -> H(d, U1(e, b))
28.57/10.34	   A^2 -> H(d, U1(k, b))
28.57/10.34	   A^2 -> H(d, U1(c, d))
28.57/10.34	   A^2 -> H(d, U1(d, c))
28.57/10.34	   A^2 -> H(d, U1(b, e))
28.57/10.34	   A^2 -> H(d, U1(b, k))
28.57/10.34	   A^2 -> H(d, U1(e, c))
28.57/10.34	   A^2 -> H(d, U1(k, c))
28.57/10.34	   A^2 -> H(d, U1(c, e))
28.57/10.34	   A^2 -> H(d, U1(c, k))
28.57/10.34	   A^2 -> H(d, U1(e, e))
28.57/10.34	   A^2 -> H(d, U1(k, k))
28.57/10.34	   A^2 -> H(d, U1(k, d))
28.57/10.34	   A^2 -> H(d, U1(d, k))
28.57/10.34	   A^2 -> H(a, b)
28.57/10.34	   A^2 -> H(a, U1(e, d))
28.57/10.34	   A^2 -> H(a, U1(d, e))
28.57/10.34	   A^2 -> H(a, c)
28.57/10.34	   A^2 -> H(a, U1(e, k))
28.57/10.34	   A^2 -> H(a, U1(k, e))
28.57/10.34	   A^2 -> H(a, e)
28.57/10.34	   A^2 -> H(a, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, d), b)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, d), c)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, d), e)
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, a), d)
28.57/10.34	   A^2 -> H(U1(e, a), k)
28.57/10.34	   A^2 -> H(U1(k, a), d)
28.57/10.34	   A^2 -> H(U1(c, d), d)
28.57/10.34	   A^2 -> H(U1(c, d), k)
28.57/10.34	   A^2 -> H(U1(d, e), b)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, e), c)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, e), e)
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, c), d)
28.57/10.34	   A^2 -> H(U1(d, c), k)
28.57/10.34	   A^2 -> H(U1(a, e), d)
28.57/10.34	   A^2 -> H(U1(a, e), k)
28.57/10.34	   A^2 -> H(U1(a, k), d)
28.57/10.34	   A^2 -> H(U1(a, k), k)
28.57/10.34	   A^2 -> H(k, U1(e, b))
28.57/10.34	   A^2 -> H(k, U1(c, d))
28.57/10.34	   A^2 -> H(k, U1(d, c))
28.57/10.34	   A^2 -> H(k, U1(b, e))
28.57/10.34	   A^2 -> H(k, U1(b, k))
28.57/10.34	   A^2 -> H(k, U1(e, c))
28.57/10.34	   A^2 -> H(k, U1(c, e))
28.57/10.34	   A^2 -> H(k, U1(c, k))
28.57/10.34	   A^2 -> H(k, U1(e, e))
28.57/10.34	   A^2 -> H(k, U1(d, k))
28.57/10.34	   A^2 -> H(c, b)
28.57/10.34	   A^2 -> H(c, U1(e, d))
28.57/10.34	   A^2 -> H(c, U1(d, e))
28.57/10.34	   A^2 -> H(c, c)
28.57/10.34	   A^2 -> H(c, U1(e, k))
28.57/10.34	   A^2 -> H(c, U1(k, e))
28.57/10.34	   A^2 -> H(c, e)
28.57/10.34	   A^2 -> H(c, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, k), b)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, k), c)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, k), e)
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, c), d)
28.57/10.34	   A^2 -> H(U1(e, c), k)
28.57/10.34	   A^2 -> H(U1(k, e), b)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, e), c)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, c), d)
28.57/10.34	   A^2 -> H(U1(c, e), d)
28.57/10.34	   A^2 -> H(U1(c, e), k)
28.57/10.34	   A^2 -> H(U1(c, k), d)
28.57/10.34	   A^2 -> H(U1(c, k), k)
28.57/10.34	   A^2 -> H(e, b)
28.57/10.34	   A^2 -> H(e, U1(e, d))
28.57/10.34	   A^2 -> H(e, U1(d, e))
28.57/10.34	   A^2 -> H(e, c)
28.57/10.34	   A^2 -> H(e, U1(e, k))
28.57/10.34	   A^2 -> H(e, e)
28.57/10.34	   A^2 -> H(U1(e, e), d)
28.57/10.34	   A^2 -> H(U1(e, e), k)
28.57/10.34	   A^2 -> H(U1(k, k), d)
28.57/10.34	   A^2 -> H(U1(k, k), k)
28.57/10.34	
28.57/10.34	The TRS R consists of the following rules:
28.57/10.34	
28.57/10.34	   f(x) -> U1(x, x)
28.57/10.34	   U1(e, x) -> x
28.57/10.34	   a -> c
28.57/10.34	   a -> d
28.57/10.34	   b -> c
28.57/10.34	   b -> d
28.57/10.34	   d -> k
28.57/10.34	   c -> e
28.57/10.34	   c -> k
28.57/10.34	
28.57/10.34	Q is empty.
28.57/10.34	We have to consider all minimal (P,Q,R)-chains.
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2297) DependencyGraphProof (EQUIVALENT)
28.57/10.34	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2298)
28.57/10.34	Obligation:
28.57/10.34	Q DP problem:
28.57/10.34	The TRS P consists of the following rules:
28.57/10.34	
28.57/10.34	   G(d, x, x) -> A^2
28.57/10.34	   A^2 -> H(f(c), f(c))
28.57/10.34	   H(x, x) -> G(x, x, f(k))
28.57/10.34	   A^2 -> H(f(d), f(d))
28.57/10.34	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.34	   A^2 -> H(f(e), f(e))
28.57/10.34	   A^2 -> H(f(k), f(k))
28.57/10.34	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.34	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.34	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.34	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.34	   A^2 -> H(f(k), d)
28.57/10.34	   A^2 -> H(f(k), k)
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, d), b)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, d), c)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, k), b)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, k), c)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, k), e)
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, d), d)
28.57/10.34	   A^2 -> H(U1(d, d), k)
28.57/10.34	   A^2 -> H(U1(e, c), c)
28.57/10.34	   A^2 -> H(U1(c, c), e)
28.57/10.34	   A^2 -> H(U1(c, c), k)
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(e, e), e)
28.57/10.34	   A^2 -> H(d, U1(e, b))
28.57/10.34	   A^2 -> H(d, U1(k, b))
28.57/10.34	   A^2 -> H(d, U1(c, d))
28.57/10.34	   A^2 -> H(d, U1(d, c))
28.57/10.34	   A^2 -> H(d, U1(b, e))
28.57/10.34	   A^2 -> H(d, U1(b, k))
28.57/10.34	   A^2 -> H(d, U1(e, c))
28.57/10.34	   A^2 -> H(d, U1(k, c))
28.57/10.34	   A^2 -> H(d, U1(c, e))
28.57/10.34	   A^2 -> H(d, U1(c, k))
28.57/10.34	   A^2 -> H(d, U1(e, e))
28.57/10.34	   A^2 -> H(d, U1(k, k))
28.57/10.34	   A^2 -> H(d, U1(k, d))
28.57/10.34	   A^2 -> H(d, U1(d, k))
28.57/10.34	   A^2 -> H(a, b)
28.57/10.34	   A^2 -> H(a, U1(e, d))
28.57/10.34	   A^2 -> H(a, U1(d, e))
28.57/10.34	   A^2 -> H(a, c)
28.57/10.34	   A^2 -> H(a, U1(e, k))
28.57/10.34	   A^2 -> H(a, U1(k, e))
28.57/10.34	   A^2 -> H(a, e)
28.57/10.34	   A^2 -> H(a, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, d), b)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, d), c)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, d), e)
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, a), d)
28.57/10.34	   A^2 -> H(U1(e, a), k)
28.57/10.34	   A^2 -> H(U1(k, a), d)
28.57/10.34	   A^2 -> H(U1(c, d), d)
28.57/10.34	   A^2 -> H(U1(c, d), k)
28.57/10.34	   A^2 -> H(U1(d, e), b)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, e), c)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, e), e)
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, c), d)
28.57/10.34	   A^2 -> H(U1(d, c), k)
28.57/10.34	   A^2 -> H(U1(a, e), d)
28.57/10.34	   A^2 -> H(U1(a, e), k)
28.57/10.34	   A^2 -> H(U1(a, k), d)
28.57/10.34	   A^2 -> H(U1(a, k), k)
28.57/10.34	   A^2 -> H(k, U1(e, b))
28.57/10.34	   A^2 -> H(k, U1(c, d))
28.57/10.34	   A^2 -> H(k, U1(d, c))
28.57/10.34	   A^2 -> H(k, U1(b, e))
28.57/10.34	   A^2 -> H(k, U1(b, k))
28.57/10.34	   A^2 -> H(k, U1(e, c))
28.57/10.34	   A^2 -> H(k, U1(c, e))
28.57/10.34	   A^2 -> H(k, U1(c, k))
28.57/10.34	   A^2 -> H(k, U1(e, e))
28.57/10.34	   A^2 -> H(k, U1(d, k))
28.57/10.34	   A^2 -> H(c, b)
28.57/10.34	   A^2 -> H(c, U1(e, d))
28.57/10.34	   A^2 -> H(c, U1(d, e))
28.57/10.34	   A^2 -> H(c, c)
28.57/10.34	   A^2 -> H(c, U1(e, k))
28.57/10.34	   A^2 -> H(c, U1(k, e))
28.57/10.34	   A^2 -> H(c, e)
28.57/10.34	   A^2 -> H(c, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, k), b)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, k), c)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, k), e)
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, c), d)
28.57/10.34	   A^2 -> H(U1(e, c), k)
28.57/10.34	   A^2 -> H(U1(k, e), b)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, e), c)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, c), d)
28.57/10.34	   A^2 -> H(U1(c, e), d)
28.57/10.34	   A^2 -> H(U1(c, e), k)
28.57/10.34	   A^2 -> H(U1(c, k), d)
28.57/10.34	   A^2 -> H(U1(c, k), k)
28.57/10.34	   A^2 -> H(e, b)
28.57/10.34	   A^2 -> H(e, U1(e, d))
28.57/10.34	   A^2 -> H(e, U1(d, e))
28.57/10.34	   A^2 -> H(e, c)
28.57/10.34	   A^2 -> H(e, U1(e, k))
28.57/10.34	   A^2 -> H(e, e)
28.57/10.34	   A^2 -> H(U1(e, e), d)
28.57/10.34	   A^2 -> H(U1(e, e), k)
28.57/10.34	   A^2 -> H(U1(k, k), d)
28.57/10.34	
28.57/10.34	The TRS R consists of the following rules:
28.57/10.34	
28.57/10.34	   f(x) -> U1(x, x)
28.57/10.34	   U1(e, x) -> x
28.57/10.34	   a -> c
28.57/10.34	   a -> d
28.57/10.34	   b -> c
28.57/10.34	   b -> d
28.57/10.34	   d -> k
28.57/10.34	   c -> e
28.57/10.34	   c -> k
28.57/10.34	
28.57/10.34	Q is empty.
28.57/10.34	We have to consider all minimal (P,Q,R)-chains.
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2299) TransformationProof (EQUIVALENT)
28.57/10.34	By narrowing [LPAR04] the rule A^2 -> H(f(k), d) at position [] we obtained the following new rules [LPAR04]:
28.57/10.34	
28.57/10.34	   (A^2 -> H(U1(k, k), d),A^2 -> H(U1(k, k), d))
28.57/10.34	   (A^2 -> H(f(k), k),A^2 -> H(f(k), k))
28.57/10.34	
28.57/10.34	
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2300)
28.57/10.34	Obligation:
28.57/10.34	Q DP problem:
28.57/10.34	The TRS P consists of the following rules:
28.57/10.34	
28.57/10.34	   G(d, x, x) -> A^2
28.57/10.34	   A^2 -> H(f(c), f(c))
28.57/10.34	   H(x, x) -> G(x, x, f(k))
28.57/10.34	   A^2 -> H(f(d), f(d))
28.57/10.34	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.34	   A^2 -> H(f(e), f(e))
28.57/10.34	   A^2 -> H(f(k), f(k))
28.57/10.34	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.34	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.34	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.34	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.34	   A^2 -> H(f(k), k)
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, d), b)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, d), c)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, k), b)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, k), c)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, k), e)
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, d), d)
28.57/10.34	   A^2 -> H(U1(d, d), k)
28.57/10.34	   A^2 -> H(U1(e, c), c)
28.57/10.34	   A^2 -> H(U1(c, c), e)
28.57/10.34	   A^2 -> H(U1(c, c), k)
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(e, e), e)
28.57/10.34	   A^2 -> H(d, U1(e, b))
28.57/10.34	   A^2 -> H(d, U1(k, b))
28.57/10.34	   A^2 -> H(d, U1(c, d))
28.57/10.34	   A^2 -> H(d, U1(d, c))
28.57/10.34	   A^2 -> H(d, U1(b, e))
28.57/10.34	   A^2 -> H(d, U1(b, k))
28.57/10.34	   A^2 -> H(d, U1(e, c))
28.57/10.34	   A^2 -> H(d, U1(k, c))
28.57/10.34	   A^2 -> H(d, U1(c, e))
28.57/10.34	   A^2 -> H(d, U1(c, k))
28.57/10.34	   A^2 -> H(d, U1(e, e))
28.57/10.34	   A^2 -> H(d, U1(k, k))
28.57/10.34	   A^2 -> H(d, U1(k, d))
28.57/10.34	   A^2 -> H(d, U1(d, k))
28.57/10.34	   A^2 -> H(a, b)
28.57/10.34	   A^2 -> H(a, U1(e, d))
28.57/10.34	   A^2 -> H(a, U1(d, e))
28.57/10.34	   A^2 -> H(a, c)
28.57/10.34	   A^2 -> H(a, U1(e, k))
28.57/10.34	   A^2 -> H(a, U1(k, e))
28.57/10.34	   A^2 -> H(a, e)
28.57/10.34	   A^2 -> H(a, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, d), b)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, d), c)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, d), e)
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, a), d)
28.57/10.34	   A^2 -> H(U1(e, a), k)
28.57/10.34	   A^2 -> H(U1(k, a), d)
28.57/10.34	   A^2 -> H(U1(c, d), d)
28.57/10.34	   A^2 -> H(U1(c, d), k)
28.57/10.34	   A^2 -> H(U1(d, e), b)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, e), c)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, e), e)
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, c), d)
28.57/10.34	   A^2 -> H(U1(d, c), k)
28.57/10.34	   A^2 -> H(U1(a, e), d)
28.57/10.34	   A^2 -> H(U1(a, e), k)
28.57/10.34	   A^2 -> H(U1(a, k), d)
28.57/10.34	   A^2 -> H(U1(a, k), k)
28.57/10.34	   A^2 -> H(k, U1(e, b))
28.57/10.34	   A^2 -> H(k, U1(c, d))
28.57/10.34	   A^2 -> H(k, U1(d, c))
28.57/10.34	   A^2 -> H(k, U1(b, e))
28.57/10.34	   A^2 -> H(k, U1(b, k))
28.57/10.34	   A^2 -> H(k, U1(e, c))
28.57/10.34	   A^2 -> H(k, U1(c, e))
28.57/10.34	   A^2 -> H(k, U1(c, k))
28.57/10.34	   A^2 -> H(k, U1(e, e))
28.57/10.34	   A^2 -> H(k, U1(d, k))
28.57/10.34	   A^2 -> H(c, b)
28.57/10.34	   A^2 -> H(c, U1(e, d))
28.57/10.34	   A^2 -> H(c, U1(d, e))
28.57/10.34	   A^2 -> H(c, c)
28.57/10.34	   A^2 -> H(c, U1(e, k))
28.57/10.34	   A^2 -> H(c, U1(k, e))
28.57/10.34	   A^2 -> H(c, e)
28.57/10.34	   A^2 -> H(c, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, k), b)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, k), c)
28.57/10.34	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, k), e)
28.57/10.34	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, c), d)
28.57/10.34	   A^2 -> H(U1(e, c), k)
28.57/10.34	   A^2 -> H(U1(k, e), b)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, e), c)
28.57/10.34	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, c), d)
28.57/10.34	   A^2 -> H(U1(c, e), d)
28.57/10.34	   A^2 -> H(U1(c, e), k)
28.57/10.34	   A^2 -> H(U1(c, k), d)
28.57/10.34	   A^2 -> H(U1(c, k), k)
28.57/10.34	   A^2 -> H(e, b)
28.57/10.34	   A^2 -> H(e, U1(e, d))
28.57/10.34	   A^2 -> H(e, U1(d, e))
28.57/10.34	   A^2 -> H(e, c)
28.57/10.34	   A^2 -> H(e, U1(e, k))
28.57/10.34	   A^2 -> H(e, e)
28.57/10.34	   A^2 -> H(U1(e, e), d)
28.57/10.34	   A^2 -> H(U1(e, e), k)
28.57/10.34	   A^2 -> H(U1(k, k), d)
28.57/10.34	
28.57/10.34	The TRS R consists of the following rules:
28.57/10.34	
28.57/10.34	   f(x) -> U1(x, x)
28.57/10.34	   U1(e, x) -> x
28.57/10.34	   a -> c
28.57/10.34	   a -> d
28.57/10.34	   b -> c
28.57/10.34	   b -> d
28.57/10.34	   d -> k
28.57/10.34	   c -> e
28.57/10.34	   c -> k
28.57/10.34	
28.57/10.34	Q is empty.
28.57/10.34	We have to consider all minimal (P,Q,R)-chains.
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2301) TransformationProof (EQUIVALENT)
28.57/10.34	By narrowing [LPAR04] the rule A^2 -> H(f(k), k) at position [] we obtained the following new rules [LPAR04]:
28.57/10.34	
28.57/10.34	   (A^2 -> H(U1(k, k), k),A^2 -> H(U1(k, k), k))
28.57/10.34	
28.57/10.34	
28.57/10.34	----------------------------------------
28.57/10.34	
28.57/10.34	(2302)
28.57/10.34	Obligation:
28.57/10.34	Q DP problem:
28.57/10.34	The TRS P consists of the following rules:
28.57/10.34	
28.57/10.34	   G(d, x, x) -> A^2
28.57/10.34	   A^2 -> H(f(c), f(c))
28.57/10.34	   H(x, x) -> G(x, x, f(k))
28.57/10.34	   A^2 -> H(f(d), f(d))
28.57/10.34	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.34	   A^2 -> H(f(e), f(e))
28.57/10.34	   A^2 -> H(f(k), f(k))
28.57/10.34	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.34	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.34	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.34	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.34	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.34	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.34	   A^2 -> H(U1(k, d), b)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(k, d), c)
28.57/10.34	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, k), b)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, k), c)
28.57/10.34	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, k), e)
28.57/10.34	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.34	   A^2 -> H(U1(d, d), d)
28.57/10.34	   A^2 -> H(U1(d, d), k)
28.57/10.34	   A^2 -> H(U1(e, c), c)
28.57/10.34	   A^2 -> H(U1(c, c), e)
28.57/10.34	   A^2 -> H(U1(c, c), k)
28.57/10.34	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.34	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.34	   A^2 -> H(U1(e, e), e)
28.57/10.34	   A^2 -> H(d, U1(e, b))
28.57/10.34	   A^2 -> H(d, U1(k, b))
28.57/10.34	   A^2 -> H(d, U1(c, d))
28.57/10.34	   A^2 -> H(d, U1(d, c))
28.57/10.34	   A^2 -> H(d, U1(b, e))
28.57/10.34	   A^2 -> H(d, U1(b, k))
28.57/10.34	   A^2 -> H(d, U1(e, c))
28.57/10.34	   A^2 -> H(d, U1(k, c))
28.57/10.34	   A^2 -> H(d, U1(c, e))
28.57/10.34	   A^2 -> H(d, U1(c, k))
28.57/10.34	   A^2 -> H(d, U1(e, e))
28.57/10.34	   A^2 -> H(d, U1(k, k))
28.57/10.34	   A^2 -> H(d, U1(k, d))
28.57/10.34	   A^2 -> H(d, U1(d, k))
28.57/10.34	   A^2 -> H(a, b)
28.57/10.34	   A^2 -> H(a, U1(e, d))
28.57/10.34	   A^2 -> H(a, U1(d, e))
28.57/10.34	   A^2 -> H(a, c)
28.57/10.34	   A^2 -> H(a, U1(e, k))
28.57/10.34	   A^2 -> H(a, U1(k, e))
28.57/10.34	   A^2 -> H(a, e)
28.57/10.34	   A^2 -> H(a, U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, d), b)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.34	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.34	   A^2 -> H(U1(e, d), c)
28.57/10.34	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.34	   A^2 -> H(U1(e, d), e)
28.57/10.34	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.34	   A^2 -> H(U1(e, a), d)
28.57/10.34	   A^2 -> H(U1(e, a), k)
28.57/10.34	   A^2 -> H(U1(k, a), d)
28.57/10.34	   A^2 -> H(U1(c, d), d)
28.57/10.34	   A^2 -> H(U1(c, d), k)
28.57/10.34	   A^2 -> H(U1(d, e), b)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.34	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.34	   A^2 -> H(U1(d, e), c)
28.57/10.34	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.34	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.34	   A^2 -> H(U1(d, e), e)
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, c), d)
28.57/10.35	   A^2 -> H(U1(d, c), k)
28.57/10.35	   A^2 -> H(U1(a, e), d)
28.57/10.35	   A^2 -> H(U1(a, e), k)
28.57/10.35	   A^2 -> H(U1(a, k), d)
28.57/10.35	   A^2 -> H(U1(a, k), k)
28.57/10.35	   A^2 -> H(k, U1(e, b))
28.57/10.35	   A^2 -> H(k, U1(c, d))
28.57/10.35	   A^2 -> H(k, U1(d, c))
28.57/10.35	   A^2 -> H(k, U1(b, e))
28.57/10.35	   A^2 -> H(k, U1(b, k))
28.57/10.35	   A^2 -> H(k, U1(e, c))
28.57/10.35	   A^2 -> H(k, U1(c, e))
28.57/10.35	   A^2 -> H(k, U1(c, k))
28.57/10.35	   A^2 -> H(k, U1(e, e))
28.57/10.35	   A^2 -> H(k, U1(d, k))
28.57/10.35	   A^2 -> H(c, b)
28.57/10.35	   A^2 -> H(c, U1(e, d))
28.57/10.35	   A^2 -> H(c, U1(d, e))
28.57/10.35	   A^2 -> H(c, c)
28.57/10.35	   A^2 -> H(c, U1(e, k))
28.57/10.35	   A^2 -> H(c, U1(k, e))
28.57/10.35	   A^2 -> H(c, e)
28.57/10.35	   A^2 -> H(c, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, k), b)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, k), c)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, k), e)
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, c), d)
28.57/10.35	   A^2 -> H(U1(e, c), k)
28.57/10.35	   A^2 -> H(U1(k, e), b)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, e), c)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, c), d)
28.57/10.35	   A^2 -> H(U1(c, e), d)
28.57/10.35	   A^2 -> H(U1(c, e), k)
28.57/10.35	   A^2 -> H(U1(c, k), d)
28.57/10.35	   A^2 -> H(U1(c, k), k)
28.57/10.35	   A^2 -> H(e, b)
28.57/10.35	   A^2 -> H(e, U1(e, d))
28.57/10.35	   A^2 -> H(e, U1(d, e))
28.57/10.35	   A^2 -> H(e, c)
28.57/10.35	   A^2 -> H(e, U1(e, k))
28.57/10.35	   A^2 -> H(e, e)
28.57/10.35	   A^2 -> H(U1(e, e), d)
28.57/10.35	   A^2 -> H(U1(e, e), k)
28.57/10.35	   A^2 -> H(U1(k, k), d)
28.57/10.35	   A^2 -> H(U1(k, k), k)
28.57/10.35	
28.57/10.35	The TRS R consists of the following rules:
28.57/10.35	
28.57/10.35	   f(x) -> U1(x, x)
28.57/10.35	   U1(e, x) -> x
28.57/10.35	   a -> c
28.57/10.35	   a -> d
28.57/10.35	   b -> c
28.57/10.35	   b -> d
28.57/10.35	   d -> k
28.57/10.35	   c -> e
28.57/10.35	   c -> k
28.57/10.35	
28.57/10.35	Q is empty.
28.57/10.35	We have to consider all minimal (P,Q,R)-chains.
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2303) DependencyGraphProof (EQUIVALENT)
28.57/10.35	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2304)
28.57/10.35	Obligation:
28.57/10.35	Q DP problem:
28.57/10.35	The TRS P consists of the following rules:
28.57/10.35	
28.57/10.35	   A^2 -> H(f(c), f(c))
28.57/10.35	   H(x, x) -> G(x, x, f(k))
28.57/10.35	   G(d, x, x) -> A^2
28.57/10.35	   A^2 -> H(f(d), f(d))
28.57/10.35	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.35	   A^2 -> H(f(e), f(e))
28.57/10.35	   A^2 -> H(f(k), f(k))
28.57/10.35	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.35	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.35	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.35	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, b))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, d), b)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, d), c)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, k), b)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, k), c)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, k), e)
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, d), d)
28.57/10.35	   A^2 -> H(U1(d, d), k)
28.57/10.35	   A^2 -> H(U1(e, c), c)
28.57/10.35	   A^2 -> H(U1(c, c), e)
28.57/10.35	   A^2 -> H(U1(c, c), k)
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(e, e), e)
28.57/10.35	   A^2 -> H(d, U1(e, b))
28.57/10.35	   A^2 -> H(d, U1(k, b))
28.57/10.35	   A^2 -> H(d, U1(c, d))
28.57/10.35	   A^2 -> H(d, U1(d, c))
28.57/10.35	   A^2 -> H(d, U1(b, e))
28.57/10.35	   A^2 -> H(d, U1(b, k))
28.57/10.35	   A^2 -> H(d, U1(e, c))
28.57/10.35	   A^2 -> H(d, U1(k, c))
28.57/10.35	   A^2 -> H(d, U1(c, e))
28.57/10.35	   A^2 -> H(d, U1(c, k))
28.57/10.35	   A^2 -> H(d, U1(e, e))
28.57/10.35	   A^2 -> H(d, U1(k, k))
28.57/10.35	   A^2 -> H(d, U1(k, d))
28.57/10.35	   A^2 -> H(d, U1(d, k))
28.57/10.35	   A^2 -> H(a, b)
28.57/10.35	   A^2 -> H(a, U1(e, d))
28.57/10.35	   A^2 -> H(a, U1(d, e))
28.57/10.35	   A^2 -> H(a, c)
28.57/10.35	   A^2 -> H(a, U1(e, k))
28.57/10.35	   A^2 -> H(a, U1(k, e))
28.57/10.35	   A^2 -> H(a, e)
28.57/10.35	   A^2 -> H(a, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, d), b)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, d), c)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, d), e)
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, a), d)
28.57/10.35	   A^2 -> H(U1(e, a), k)
28.57/10.35	   A^2 -> H(U1(k, a), d)
28.57/10.35	   A^2 -> H(U1(c, d), d)
28.57/10.35	   A^2 -> H(U1(c, d), k)
28.57/10.35	   A^2 -> H(U1(d, e), b)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, e), c)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, e), e)
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, c), d)
28.57/10.35	   A^2 -> H(U1(d, c), k)
28.57/10.35	   A^2 -> H(U1(a, e), d)
28.57/10.35	   A^2 -> H(U1(a, e), k)
28.57/10.35	   A^2 -> H(U1(a, k), d)
28.57/10.35	   A^2 -> H(U1(a, k), k)
28.57/10.35	   A^2 -> H(k, U1(e, b))
28.57/10.35	   A^2 -> H(k, U1(c, d))
28.57/10.35	   A^2 -> H(k, U1(d, c))
28.57/10.35	   A^2 -> H(k, U1(b, e))
28.57/10.35	   A^2 -> H(k, U1(b, k))
28.57/10.35	   A^2 -> H(k, U1(e, c))
28.57/10.35	   A^2 -> H(k, U1(c, e))
28.57/10.35	   A^2 -> H(k, U1(c, k))
28.57/10.35	   A^2 -> H(k, U1(e, e))
28.57/10.35	   A^2 -> H(k, U1(d, k))
28.57/10.35	   A^2 -> H(c, b)
28.57/10.35	   A^2 -> H(c, U1(e, d))
28.57/10.35	   A^2 -> H(c, U1(d, e))
28.57/10.35	   A^2 -> H(c, c)
28.57/10.35	   A^2 -> H(c, U1(e, k))
28.57/10.35	   A^2 -> H(c, U1(k, e))
28.57/10.35	   A^2 -> H(c, e)
28.57/10.35	   A^2 -> H(c, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, k), b)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, k), c)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, k), e)
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, c), d)
28.57/10.35	   A^2 -> H(U1(e, c), k)
28.57/10.35	   A^2 -> H(U1(k, e), b)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, e), c)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, c), d)
28.57/10.35	   A^2 -> H(U1(c, e), d)
28.57/10.35	   A^2 -> H(U1(c, e), k)
28.57/10.35	   A^2 -> H(U1(c, k), d)
28.57/10.35	   A^2 -> H(U1(c, k), k)
28.57/10.35	   A^2 -> H(e, b)
28.57/10.35	   A^2 -> H(e, U1(e, d))
28.57/10.35	   A^2 -> H(e, U1(d, e))
28.57/10.35	   A^2 -> H(e, c)
28.57/10.35	   A^2 -> H(e, U1(e, k))
28.57/10.35	   A^2 -> H(e, e)
28.57/10.35	   A^2 -> H(U1(e, e), d)
28.57/10.35	   A^2 -> H(U1(e, e), k)
28.57/10.35	   A^2 -> H(U1(k, k), d)
28.57/10.35	
28.57/10.35	The TRS R consists of the following rules:
28.57/10.35	
28.57/10.35	   f(x) -> U1(x, x)
28.57/10.35	   U1(e, x) -> x
28.57/10.35	   a -> c
28.57/10.35	   a -> d
28.57/10.35	   b -> c
28.57/10.35	   b -> d
28.57/10.35	   d -> k
28.57/10.35	   c -> e
28.57/10.35	   c -> k
28.57/10.35	
28.57/10.35	Q is empty.
28.57/10.35	We have to consider all minimal (P,Q,R)-chains.
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2305) TransformationProof (EQUIVALENT)
28.57/10.35	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.35	
28.57/10.35	   (A^2 -> H(U1(k, k), b),A^2 -> H(U1(k, k), b))
28.57/10.35	   (A^2 -> H(U1(k, k), U1(e, c)),A^2 -> H(U1(k, k), U1(e, c)))
28.57/10.35	   (A^2 -> H(U1(k, k), U1(e, d)),A^2 -> H(U1(k, k), U1(e, d)))
28.57/10.35	
28.57/10.35	
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2306)
28.57/10.35	Obligation:
28.57/10.35	Q DP problem:
28.57/10.35	The TRS P consists of the following rules:
28.57/10.35	
28.57/10.35	   A^2 -> H(f(c), f(c))
28.57/10.35	   H(x, x) -> G(x, x, f(k))
28.57/10.35	   G(d, x, x) -> A^2
28.57/10.35	   A^2 -> H(f(d), f(d))
28.57/10.35	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.35	   A^2 -> H(f(e), f(e))
28.57/10.35	   A^2 -> H(f(k), f(k))
28.57/10.35	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.35	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.35	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.35	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, b))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, d), b)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, d), c)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, k), b)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, k), c)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, k), e)
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, d), d)
28.57/10.35	   A^2 -> H(U1(d, d), k)
28.57/10.35	   A^2 -> H(U1(e, c), c)
28.57/10.35	   A^2 -> H(U1(c, c), e)
28.57/10.35	   A^2 -> H(U1(c, c), k)
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(e, e), e)
28.57/10.35	   A^2 -> H(d, U1(e, b))
28.57/10.35	   A^2 -> H(d, U1(k, b))
28.57/10.35	   A^2 -> H(d, U1(c, d))
28.57/10.35	   A^2 -> H(d, U1(d, c))
28.57/10.35	   A^2 -> H(d, U1(b, e))
28.57/10.35	   A^2 -> H(d, U1(b, k))
28.57/10.35	   A^2 -> H(d, U1(e, c))
28.57/10.35	   A^2 -> H(d, U1(k, c))
28.57/10.35	   A^2 -> H(d, U1(c, e))
28.57/10.35	   A^2 -> H(d, U1(c, k))
28.57/10.35	   A^2 -> H(d, U1(e, e))
28.57/10.35	   A^2 -> H(d, U1(k, k))
28.57/10.35	   A^2 -> H(d, U1(k, d))
28.57/10.35	   A^2 -> H(d, U1(d, k))
28.57/10.35	   A^2 -> H(a, b)
28.57/10.35	   A^2 -> H(a, U1(e, d))
28.57/10.35	   A^2 -> H(a, U1(d, e))
28.57/10.35	   A^2 -> H(a, c)
28.57/10.35	   A^2 -> H(a, U1(e, k))
28.57/10.35	   A^2 -> H(a, U1(k, e))
28.57/10.35	   A^2 -> H(a, e)
28.57/10.35	   A^2 -> H(a, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, d), b)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, d), c)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, d), e)
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, a), d)
28.57/10.35	   A^2 -> H(U1(e, a), k)
28.57/10.35	   A^2 -> H(U1(k, a), d)
28.57/10.35	   A^2 -> H(U1(c, d), d)
28.57/10.35	   A^2 -> H(U1(c, d), k)
28.57/10.35	   A^2 -> H(U1(d, e), b)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, e), c)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, e), e)
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, c), d)
28.57/10.35	   A^2 -> H(U1(d, c), k)
28.57/10.35	   A^2 -> H(U1(a, e), d)
28.57/10.35	   A^2 -> H(U1(a, e), k)
28.57/10.35	   A^2 -> H(U1(a, k), d)
28.57/10.35	   A^2 -> H(U1(a, k), k)
28.57/10.35	   A^2 -> H(k, U1(e, b))
28.57/10.35	   A^2 -> H(k, U1(c, d))
28.57/10.35	   A^2 -> H(k, U1(d, c))
28.57/10.35	   A^2 -> H(k, U1(b, e))
28.57/10.35	   A^2 -> H(k, U1(b, k))
28.57/10.35	   A^2 -> H(k, U1(e, c))
28.57/10.35	   A^2 -> H(k, U1(c, e))
28.57/10.35	   A^2 -> H(k, U1(c, k))
28.57/10.35	   A^2 -> H(k, U1(e, e))
28.57/10.35	   A^2 -> H(k, U1(d, k))
28.57/10.35	   A^2 -> H(c, b)
28.57/10.35	   A^2 -> H(c, U1(e, d))
28.57/10.35	   A^2 -> H(c, U1(d, e))
28.57/10.35	   A^2 -> H(c, c)
28.57/10.35	   A^2 -> H(c, U1(e, k))
28.57/10.35	   A^2 -> H(c, U1(k, e))
28.57/10.35	   A^2 -> H(c, e)
28.57/10.35	   A^2 -> H(c, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, k), b)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, k), c)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, k), e)
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, c), d)
28.57/10.35	   A^2 -> H(U1(e, c), k)
28.57/10.35	   A^2 -> H(U1(k, e), b)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, e), c)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, c), d)
28.57/10.35	   A^2 -> H(U1(c, e), d)
28.57/10.35	   A^2 -> H(U1(c, e), k)
28.57/10.35	   A^2 -> H(U1(c, k), d)
28.57/10.35	   A^2 -> H(U1(c, k), k)
28.57/10.35	   A^2 -> H(e, b)
28.57/10.35	   A^2 -> H(e, U1(e, d))
28.57/10.35	   A^2 -> H(e, U1(d, e))
28.57/10.35	   A^2 -> H(e, c)
28.57/10.35	   A^2 -> H(e, U1(e, k))
28.57/10.35	   A^2 -> H(e, e)
28.57/10.35	   A^2 -> H(U1(e, e), d)
28.57/10.35	   A^2 -> H(U1(e, e), k)
28.57/10.35	   A^2 -> H(U1(k, k), d)
28.57/10.35	   A^2 -> H(U1(k, k), b)
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.35	
28.57/10.35	The TRS R consists of the following rules:
28.57/10.35	
28.57/10.35	   f(x) -> U1(x, x)
28.57/10.35	   U1(e, x) -> x
28.57/10.35	   a -> c
28.57/10.35	   a -> d
28.57/10.35	   b -> c
28.57/10.35	   b -> d
28.57/10.35	   d -> k
28.57/10.35	   c -> e
28.57/10.35	   c -> k
28.57/10.35	
28.57/10.35	Q is empty.
28.57/10.35	We have to consider all minimal (P,Q,R)-chains.
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2307) TransformationProof (EQUIVALENT)
28.57/10.35	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.35	
28.57/10.35	   (A^2 -> H(U1(k, k), U1(k, c)),A^2 -> H(U1(k, k), U1(k, c)))
28.57/10.35	   (A^2 -> H(U1(k, k), U1(k, d)),A^2 -> H(U1(k, k), U1(k, d)))
28.57/10.35	
28.57/10.35	
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2308)
28.57/10.35	Obligation:
28.57/10.35	Q DP problem:
28.57/10.35	The TRS P consists of the following rules:
28.57/10.35	
28.57/10.35	   A^2 -> H(f(c), f(c))
28.57/10.35	   H(x, x) -> G(x, x, f(k))
28.57/10.35	   G(d, x, x) -> A^2
28.57/10.35	   A^2 -> H(f(d), f(d))
28.57/10.35	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.35	   A^2 -> H(f(e), f(e))
28.57/10.35	   A^2 -> H(f(k), f(k))
28.57/10.35	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.35	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.35	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.35	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, d), b)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, d), c)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, k), b)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, k), c)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, k), e)
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, d), d)
28.57/10.35	   A^2 -> H(U1(d, d), k)
28.57/10.35	   A^2 -> H(U1(e, c), c)
28.57/10.35	   A^2 -> H(U1(c, c), e)
28.57/10.35	   A^2 -> H(U1(c, c), k)
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(e, e), e)
28.57/10.35	   A^2 -> H(d, U1(e, b))
28.57/10.35	   A^2 -> H(d, U1(k, b))
28.57/10.35	   A^2 -> H(d, U1(c, d))
28.57/10.35	   A^2 -> H(d, U1(d, c))
28.57/10.35	   A^2 -> H(d, U1(b, e))
28.57/10.35	   A^2 -> H(d, U1(b, k))
28.57/10.35	   A^2 -> H(d, U1(e, c))
28.57/10.35	   A^2 -> H(d, U1(k, c))
28.57/10.35	   A^2 -> H(d, U1(c, e))
28.57/10.35	   A^2 -> H(d, U1(c, k))
28.57/10.35	   A^2 -> H(d, U1(e, e))
28.57/10.35	   A^2 -> H(d, U1(k, k))
28.57/10.35	   A^2 -> H(d, U1(k, d))
28.57/10.35	   A^2 -> H(d, U1(d, k))
28.57/10.35	   A^2 -> H(a, b)
28.57/10.35	   A^2 -> H(a, U1(e, d))
28.57/10.35	   A^2 -> H(a, U1(d, e))
28.57/10.35	   A^2 -> H(a, c)
28.57/10.35	   A^2 -> H(a, U1(e, k))
28.57/10.35	   A^2 -> H(a, U1(k, e))
28.57/10.35	   A^2 -> H(a, e)
28.57/10.35	   A^2 -> H(a, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, d), b)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, d), c)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, d), e)
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, a), d)
28.57/10.35	   A^2 -> H(U1(e, a), k)
28.57/10.35	   A^2 -> H(U1(k, a), d)
28.57/10.35	   A^2 -> H(U1(c, d), d)
28.57/10.35	   A^2 -> H(U1(c, d), k)
28.57/10.35	   A^2 -> H(U1(d, e), b)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, e), c)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, e), e)
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, c), d)
28.57/10.35	   A^2 -> H(U1(d, c), k)
28.57/10.35	   A^2 -> H(U1(a, e), d)
28.57/10.35	   A^2 -> H(U1(a, e), k)
28.57/10.35	   A^2 -> H(U1(a, k), d)
28.57/10.35	   A^2 -> H(U1(a, k), k)
28.57/10.35	   A^2 -> H(k, U1(e, b))
28.57/10.35	   A^2 -> H(k, U1(c, d))
28.57/10.35	   A^2 -> H(k, U1(d, c))
28.57/10.35	   A^2 -> H(k, U1(b, e))
28.57/10.35	   A^2 -> H(k, U1(b, k))
28.57/10.35	   A^2 -> H(k, U1(e, c))
28.57/10.35	   A^2 -> H(k, U1(c, e))
28.57/10.35	   A^2 -> H(k, U1(c, k))
28.57/10.35	   A^2 -> H(k, U1(e, e))
28.57/10.35	   A^2 -> H(k, U1(d, k))
28.57/10.35	   A^2 -> H(c, b)
28.57/10.35	   A^2 -> H(c, U1(e, d))
28.57/10.35	   A^2 -> H(c, U1(d, e))
28.57/10.35	   A^2 -> H(c, c)
28.57/10.35	   A^2 -> H(c, U1(e, k))
28.57/10.35	   A^2 -> H(c, U1(k, e))
28.57/10.35	   A^2 -> H(c, e)
28.57/10.35	   A^2 -> H(c, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, k), b)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, k), c)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, k), e)
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, c), d)
28.57/10.35	   A^2 -> H(U1(e, c), k)
28.57/10.35	   A^2 -> H(U1(k, e), b)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, e), c)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, c), d)
28.57/10.35	   A^2 -> H(U1(c, e), d)
28.57/10.35	   A^2 -> H(U1(c, e), k)
28.57/10.35	   A^2 -> H(U1(c, k), d)
28.57/10.35	   A^2 -> H(U1(c, k), k)
28.57/10.35	   A^2 -> H(e, b)
28.57/10.35	   A^2 -> H(e, U1(e, d))
28.57/10.35	   A^2 -> H(e, U1(d, e))
28.57/10.35	   A^2 -> H(e, c)
28.57/10.35	   A^2 -> H(e, U1(e, k))
28.57/10.35	   A^2 -> H(e, e)
28.57/10.35	   A^2 -> H(U1(e, e), d)
28.57/10.35	   A^2 -> H(U1(e, e), k)
28.57/10.35	   A^2 -> H(U1(k, k), d)
28.57/10.35	   A^2 -> H(U1(k, k), b)
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.35	
28.57/10.35	The TRS R consists of the following rules:
28.57/10.35	
28.57/10.35	   f(x) -> U1(x, x)
28.57/10.35	   U1(e, x) -> x
28.57/10.35	   a -> c
28.57/10.35	   a -> d
28.57/10.35	   b -> c
28.57/10.35	   b -> d
28.57/10.35	   d -> k
28.57/10.35	   c -> e
28.57/10.35	   c -> k
28.57/10.35	
28.57/10.35	Q is empty.
28.57/10.35	We have to consider all minimal (P,Q,R)-chains.
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2309) TransformationProof (EQUIVALENT)
28.57/10.35	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.35	
28.57/10.35	   (A^2 -> H(U1(k, k), U1(e, d)),A^2 -> H(U1(k, k), U1(e, d)))
28.57/10.35	   (A^2 -> H(U1(k, k), U1(k, d)),A^2 -> H(U1(k, k), U1(k, d)))
28.57/10.35	   (A^2 -> H(U1(k, k), U1(c, k)),A^2 -> H(U1(k, k), U1(c, k)))
28.57/10.35	
28.57/10.35	
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2310)
28.57/10.35	Obligation:
28.57/10.35	Q DP problem:
28.57/10.35	The TRS P consists of the following rules:
28.57/10.35	
28.57/10.35	   A^2 -> H(f(c), f(c))
28.57/10.35	   H(x, x) -> G(x, x, f(k))
28.57/10.35	   G(d, x, x) -> A^2
28.57/10.35	   A^2 -> H(f(d), f(d))
28.57/10.35	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.35	   A^2 -> H(f(e), f(e))
28.57/10.35	   A^2 -> H(f(k), f(k))
28.57/10.35	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.35	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.35	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.35	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, d), b)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, d), c)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, k), b)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, k), c)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, k), e)
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, d), d)
28.57/10.35	   A^2 -> H(U1(d, d), k)
28.57/10.35	   A^2 -> H(U1(e, c), c)
28.57/10.35	   A^2 -> H(U1(c, c), e)
28.57/10.35	   A^2 -> H(U1(c, c), k)
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(e, e), e)
28.57/10.35	   A^2 -> H(d, U1(e, b))
28.57/10.35	   A^2 -> H(d, U1(k, b))
28.57/10.35	   A^2 -> H(d, U1(c, d))
28.57/10.35	   A^2 -> H(d, U1(d, c))
28.57/10.35	   A^2 -> H(d, U1(b, e))
28.57/10.35	   A^2 -> H(d, U1(b, k))
28.57/10.35	   A^2 -> H(d, U1(e, c))
28.57/10.35	   A^2 -> H(d, U1(k, c))
28.57/10.35	   A^2 -> H(d, U1(c, e))
28.57/10.35	   A^2 -> H(d, U1(c, k))
28.57/10.35	   A^2 -> H(d, U1(e, e))
28.57/10.35	   A^2 -> H(d, U1(k, k))
28.57/10.35	   A^2 -> H(d, U1(k, d))
28.57/10.35	   A^2 -> H(d, U1(d, k))
28.57/10.35	   A^2 -> H(a, b)
28.57/10.35	   A^2 -> H(a, U1(e, d))
28.57/10.35	   A^2 -> H(a, U1(d, e))
28.57/10.35	   A^2 -> H(a, c)
28.57/10.35	   A^2 -> H(a, U1(e, k))
28.57/10.35	   A^2 -> H(a, U1(k, e))
28.57/10.35	   A^2 -> H(a, e)
28.57/10.35	   A^2 -> H(a, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, d), b)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, d), c)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, d), e)
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, a), d)
28.57/10.35	   A^2 -> H(U1(e, a), k)
28.57/10.35	   A^2 -> H(U1(k, a), d)
28.57/10.35	   A^2 -> H(U1(c, d), d)
28.57/10.35	   A^2 -> H(U1(c, d), k)
28.57/10.35	   A^2 -> H(U1(d, e), b)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, e), c)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, e), e)
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, c), d)
28.57/10.35	   A^2 -> H(U1(d, c), k)
28.57/10.35	   A^2 -> H(U1(a, e), d)
28.57/10.35	   A^2 -> H(U1(a, e), k)
28.57/10.35	   A^2 -> H(U1(a, k), d)
28.57/10.35	   A^2 -> H(U1(a, k), k)
28.57/10.35	   A^2 -> H(k, U1(e, b))
28.57/10.35	   A^2 -> H(k, U1(c, d))
28.57/10.35	   A^2 -> H(k, U1(d, c))
28.57/10.35	   A^2 -> H(k, U1(b, e))
28.57/10.35	   A^2 -> H(k, U1(b, k))
28.57/10.35	   A^2 -> H(k, U1(e, c))
28.57/10.35	   A^2 -> H(k, U1(c, e))
28.57/10.35	   A^2 -> H(k, U1(c, k))
28.57/10.35	   A^2 -> H(k, U1(e, e))
28.57/10.35	   A^2 -> H(k, U1(d, k))
28.57/10.35	   A^2 -> H(c, b)
28.57/10.35	   A^2 -> H(c, U1(e, d))
28.57/10.35	   A^2 -> H(c, U1(d, e))
28.57/10.35	   A^2 -> H(c, c)
28.57/10.35	   A^2 -> H(c, U1(e, k))
28.57/10.35	   A^2 -> H(c, U1(k, e))
28.57/10.35	   A^2 -> H(c, e)
28.57/10.35	   A^2 -> H(c, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, k), b)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, k), c)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, k), e)
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, c), d)
28.57/10.35	   A^2 -> H(U1(e, c), k)
28.57/10.35	   A^2 -> H(U1(k, e), b)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, e), c)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, c), d)
28.57/10.35	   A^2 -> H(U1(c, e), d)
28.57/10.35	   A^2 -> H(U1(c, e), k)
28.57/10.35	   A^2 -> H(U1(c, k), d)
28.57/10.35	   A^2 -> H(U1(c, k), k)
28.57/10.35	   A^2 -> H(e, b)
28.57/10.35	   A^2 -> H(e, U1(e, d))
28.57/10.35	   A^2 -> H(e, U1(d, e))
28.57/10.35	   A^2 -> H(e, c)
28.57/10.35	   A^2 -> H(e, U1(e, k))
28.57/10.35	   A^2 -> H(e, e)
28.57/10.35	   A^2 -> H(U1(e, e), d)
28.57/10.35	   A^2 -> H(U1(e, e), k)
28.57/10.35	   A^2 -> H(U1(k, k), d)
28.57/10.35	   A^2 -> H(U1(k, k), b)
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.35	
28.57/10.35	The TRS R consists of the following rules:
28.57/10.35	
28.57/10.35	   f(x) -> U1(x, x)
28.57/10.35	   U1(e, x) -> x
28.57/10.35	   a -> c
28.57/10.35	   a -> d
28.57/10.35	   b -> c
28.57/10.35	   b -> d
28.57/10.35	   d -> k
28.57/10.35	   c -> e
28.57/10.35	   c -> k
28.57/10.35	
28.57/10.35	Q is empty.
28.57/10.35	We have to consider all minimal (P,Q,R)-chains.
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2311) TransformationProof (EQUIVALENT)
28.57/10.35	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.35	
28.57/10.35	   (A^2 -> H(U1(k, k), U1(k, c)),A^2 -> H(U1(k, k), U1(k, c)))
28.57/10.35	   (A^2 -> H(U1(k, k), U1(d, e)),A^2 -> H(U1(k, k), U1(d, e)))
28.57/10.35	   (A^2 -> H(U1(k, k), U1(d, k)),A^2 -> H(U1(k, k), U1(d, k)))
28.57/10.35	
28.57/10.35	
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2312)
28.57/10.35	Obligation:
28.57/10.35	Q DP problem:
28.57/10.35	The TRS P consists of the following rules:
28.57/10.35	
28.57/10.35	   A^2 -> H(f(c), f(c))
28.57/10.35	   H(x, x) -> G(x, x, f(k))
28.57/10.35	   G(d, x, x) -> A^2
28.57/10.35	   A^2 -> H(f(d), f(d))
28.57/10.35	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.35	   A^2 -> H(f(e), f(e))
28.57/10.35	   A^2 -> H(f(k), f(k))
28.57/10.35	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.35	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.35	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.35	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(b, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, d), b)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, d), c)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, k), b)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, k), c)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, k), e)
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, d), d)
28.57/10.35	   A^2 -> H(U1(d, d), k)
28.57/10.35	   A^2 -> H(U1(e, c), c)
28.57/10.35	   A^2 -> H(U1(c, c), e)
28.57/10.35	   A^2 -> H(U1(c, c), k)
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(e, e), e)
28.57/10.35	   A^2 -> H(d, U1(e, b))
28.57/10.35	   A^2 -> H(d, U1(k, b))
28.57/10.35	   A^2 -> H(d, U1(c, d))
28.57/10.35	   A^2 -> H(d, U1(d, c))
28.57/10.35	   A^2 -> H(d, U1(b, e))
28.57/10.35	   A^2 -> H(d, U1(b, k))
28.57/10.35	   A^2 -> H(d, U1(e, c))
28.57/10.35	   A^2 -> H(d, U1(k, c))
28.57/10.35	   A^2 -> H(d, U1(c, e))
28.57/10.35	   A^2 -> H(d, U1(c, k))
28.57/10.35	   A^2 -> H(d, U1(e, e))
28.57/10.35	   A^2 -> H(d, U1(k, k))
28.57/10.35	   A^2 -> H(d, U1(k, d))
28.57/10.35	   A^2 -> H(d, U1(d, k))
28.57/10.35	   A^2 -> H(a, b)
28.57/10.35	   A^2 -> H(a, U1(e, d))
28.57/10.35	   A^2 -> H(a, U1(d, e))
28.57/10.35	   A^2 -> H(a, c)
28.57/10.35	   A^2 -> H(a, U1(e, k))
28.57/10.35	   A^2 -> H(a, U1(k, e))
28.57/10.35	   A^2 -> H(a, e)
28.57/10.35	   A^2 -> H(a, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, d), b)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, d), c)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, d), e)
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, a), d)
28.57/10.35	   A^2 -> H(U1(e, a), k)
28.57/10.35	   A^2 -> H(U1(k, a), d)
28.57/10.35	   A^2 -> H(U1(c, d), d)
28.57/10.35	   A^2 -> H(U1(c, d), k)
28.57/10.35	   A^2 -> H(U1(d, e), b)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, e), c)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, e), e)
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, c), d)
28.57/10.35	   A^2 -> H(U1(d, c), k)
28.57/10.35	   A^2 -> H(U1(a, e), d)
28.57/10.35	   A^2 -> H(U1(a, e), k)
28.57/10.35	   A^2 -> H(U1(a, k), d)
28.57/10.35	   A^2 -> H(U1(a, k), k)
28.57/10.35	   A^2 -> H(k, U1(e, b))
28.57/10.35	   A^2 -> H(k, U1(c, d))
28.57/10.35	   A^2 -> H(k, U1(d, c))
28.57/10.35	   A^2 -> H(k, U1(b, e))
28.57/10.35	   A^2 -> H(k, U1(b, k))
28.57/10.35	   A^2 -> H(k, U1(e, c))
28.57/10.35	   A^2 -> H(k, U1(c, e))
28.57/10.35	   A^2 -> H(k, U1(c, k))
28.57/10.35	   A^2 -> H(k, U1(e, e))
28.57/10.35	   A^2 -> H(k, U1(d, k))
28.57/10.35	   A^2 -> H(c, b)
28.57/10.35	   A^2 -> H(c, U1(e, d))
28.57/10.35	   A^2 -> H(c, U1(d, e))
28.57/10.35	   A^2 -> H(c, c)
28.57/10.35	   A^2 -> H(c, U1(e, k))
28.57/10.35	   A^2 -> H(c, U1(k, e))
28.57/10.35	   A^2 -> H(c, e)
28.57/10.35	   A^2 -> H(c, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, k), b)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, k), c)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, k), e)
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, c), d)
28.57/10.35	   A^2 -> H(U1(e, c), k)
28.57/10.35	   A^2 -> H(U1(k, e), b)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, e), c)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, c), d)
28.57/10.35	   A^2 -> H(U1(c, e), d)
28.57/10.35	   A^2 -> H(U1(c, e), k)
28.57/10.35	   A^2 -> H(U1(c, k), d)
28.57/10.35	   A^2 -> H(U1(c, k), k)
28.57/10.35	   A^2 -> H(e, b)
28.57/10.35	   A^2 -> H(e, U1(e, d))
28.57/10.35	   A^2 -> H(e, U1(d, e))
28.57/10.35	   A^2 -> H(e, c)
28.57/10.35	   A^2 -> H(e, U1(e, k))
28.57/10.35	   A^2 -> H(e, e)
28.57/10.35	   A^2 -> H(U1(e, e), d)
28.57/10.35	   A^2 -> H(U1(e, e), k)
28.57/10.35	   A^2 -> H(U1(k, k), d)
28.57/10.35	   A^2 -> H(U1(k, k), b)
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.35	
28.57/10.35	The TRS R consists of the following rules:
28.57/10.35	
28.57/10.35	   f(x) -> U1(x, x)
28.57/10.35	   U1(e, x) -> x
28.57/10.35	   a -> c
28.57/10.35	   a -> d
28.57/10.35	   b -> c
28.57/10.35	   b -> d
28.57/10.35	   d -> k
28.57/10.35	   c -> e
28.57/10.35	   c -> k
28.57/10.35	
28.57/10.35	Q is empty.
28.57/10.35	We have to consider all minimal (P,Q,R)-chains.
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2313) TransformationProof (EQUIVALENT)
28.57/10.35	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.35	
28.57/10.35	   (A^2 -> H(U1(k, k), U1(c, e)),A^2 -> H(U1(k, k), U1(c, e)))
28.57/10.35	   (A^2 -> H(U1(k, k), U1(d, e)),A^2 -> H(U1(k, k), U1(d, e)))
28.57/10.35	
28.57/10.35	
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2314)
28.57/10.35	Obligation:
28.57/10.35	Q DP problem:
28.57/10.35	The TRS P consists of the following rules:
28.57/10.35	
28.57/10.35	   A^2 -> H(f(c), f(c))
28.57/10.35	   H(x, x) -> G(x, x, f(k))
28.57/10.35	   G(d, x, x) -> A^2
28.57/10.35	   A^2 -> H(f(d), f(d))
28.57/10.35	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.35	   A^2 -> H(f(e), f(e))
28.57/10.35	   A^2 -> H(f(k), f(k))
28.57/10.35	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.35	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.35	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.35	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(b, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, d), b)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, d), c)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, k), b)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, k), c)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, k), e)
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, d), d)
28.57/10.35	   A^2 -> H(U1(d, d), k)
28.57/10.35	   A^2 -> H(U1(e, c), c)
28.57/10.35	   A^2 -> H(U1(c, c), e)
28.57/10.35	   A^2 -> H(U1(c, c), k)
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(e, e), e)
28.57/10.35	   A^2 -> H(d, U1(e, b))
28.57/10.35	   A^2 -> H(d, U1(k, b))
28.57/10.35	   A^2 -> H(d, U1(c, d))
28.57/10.35	   A^2 -> H(d, U1(d, c))
28.57/10.35	   A^2 -> H(d, U1(b, e))
28.57/10.35	   A^2 -> H(d, U1(b, k))
28.57/10.35	   A^2 -> H(d, U1(e, c))
28.57/10.35	   A^2 -> H(d, U1(k, c))
28.57/10.35	   A^2 -> H(d, U1(c, e))
28.57/10.35	   A^2 -> H(d, U1(c, k))
28.57/10.35	   A^2 -> H(d, U1(e, e))
28.57/10.35	   A^2 -> H(d, U1(k, k))
28.57/10.35	   A^2 -> H(d, U1(k, d))
28.57/10.35	   A^2 -> H(d, U1(d, k))
28.57/10.35	   A^2 -> H(a, b)
28.57/10.35	   A^2 -> H(a, U1(e, d))
28.57/10.35	   A^2 -> H(a, U1(d, e))
28.57/10.35	   A^2 -> H(a, c)
28.57/10.35	   A^2 -> H(a, U1(e, k))
28.57/10.35	   A^2 -> H(a, U1(k, e))
28.57/10.35	   A^2 -> H(a, e)
28.57/10.35	   A^2 -> H(a, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, d), b)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, d), c)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, d), e)
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, a), d)
28.57/10.35	   A^2 -> H(U1(e, a), k)
28.57/10.35	   A^2 -> H(U1(k, a), d)
28.57/10.35	   A^2 -> H(U1(c, d), d)
28.57/10.35	   A^2 -> H(U1(c, d), k)
28.57/10.35	   A^2 -> H(U1(d, e), b)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, e), c)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, e), e)
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, c), d)
28.57/10.35	   A^2 -> H(U1(d, c), k)
28.57/10.35	   A^2 -> H(U1(a, e), d)
28.57/10.35	   A^2 -> H(U1(a, e), k)
28.57/10.35	   A^2 -> H(U1(a, k), d)
28.57/10.35	   A^2 -> H(U1(a, k), k)
28.57/10.35	   A^2 -> H(k, U1(e, b))
28.57/10.35	   A^2 -> H(k, U1(c, d))
28.57/10.35	   A^2 -> H(k, U1(d, c))
28.57/10.35	   A^2 -> H(k, U1(b, e))
28.57/10.35	   A^2 -> H(k, U1(b, k))
28.57/10.35	   A^2 -> H(k, U1(e, c))
28.57/10.35	   A^2 -> H(k, U1(c, e))
28.57/10.35	   A^2 -> H(k, U1(c, k))
28.57/10.35	   A^2 -> H(k, U1(e, e))
28.57/10.35	   A^2 -> H(k, U1(d, k))
28.57/10.35	   A^2 -> H(c, b)
28.57/10.35	   A^2 -> H(c, U1(e, d))
28.57/10.35	   A^2 -> H(c, U1(d, e))
28.57/10.35	   A^2 -> H(c, c)
28.57/10.35	   A^2 -> H(c, U1(e, k))
28.57/10.35	   A^2 -> H(c, U1(k, e))
28.57/10.35	   A^2 -> H(c, e)
28.57/10.35	   A^2 -> H(c, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, k), b)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, k), c)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, k), e)
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, c), d)
28.57/10.35	   A^2 -> H(U1(e, c), k)
28.57/10.35	   A^2 -> H(U1(k, e), b)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, e), c)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, c), d)
28.57/10.35	   A^2 -> H(U1(c, e), d)
28.57/10.35	   A^2 -> H(U1(c, e), k)
28.57/10.35	   A^2 -> H(U1(c, k), d)
28.57/10.35	   A^2 -> H(U1(c, k), k)
28.57/10.35	   A^2 -> H(e, b)
28.57/10.35	   A^2 -> H(e, U1(e, d))
28.57/10.35	   A^2 -> H(e, U1(d, e))
28.57/10.35	   A^2 -> H(e, c)
28.57/10.35	   A^2 -> H(e, U1(e, k))
28.57/10.35	   A^2 -> H(e, e)
28.57/10.35	   A^2 -> H(U1(e, e), d)
28.57/10.35	   A^2 -> H(U1(e, e), k)
28.57/10.35	   A^2 -> H(U1(k, k), d)
28.57/10.35	   A^2 -> H(U1(k, k), b)
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.35	
28.57/10.35	The TRS R consists of the following rules:
28.57/10.35	
28.57/10.35	   f(x) -> U1(x, x)
28.57/10.35	   U1(e, x) -> x
28.57/10.35	   a -> c
28.57/10.35	   a -> d
28.57/10.35	   b -> c
28.57/10.35	   b -> d
28.57/10.35	   d -> k
28.57/10.35	   c -> e
28.57/10.35	   c -> k
28.57/10.35	
28.57/10.35	Q is empty.
28.57/10.35	We have to consider all minimal (P,Q,R)-chains.
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2315) TransformationProof (EQUIVALENT)
28.57/10.35	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.35	
28.57/10.35	   (A^2 -> H(U1(k, k), U1(c, k)),A^2 -> H(U1(k, k), U1(c, k)))
28.57/10.35	   (A^2 -> H(U1(k, k), U1(d, k)),A^2 -> H(U1(k, k), U1(d, k)))
28.57/10.35	
28.57/10.35	
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2316)
28.57/10.35	Obligation:
28.57/10.35	Q DP problem:
28.57/10.35	The TRS P consists of the following rules:
28.57/10.35	
28.57/10.35	   A^2 -> H(f(c), f(c))
28.57/10.35	   H(x, x) -> G(x, x, f(k))
28.57/10.35	   G(d, x, x) -> A^2
28.57/10.35	   A^2 -> H(f(d), f(d))
28.57/10.35	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.35	   A^2 -> H(f(e), f(e))
28.57/10.35	   A^2 -> H(f(k), f(k))
28.57/10.35	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.35	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.35	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.35	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, d), b)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, d), c)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, k), b)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, k), c)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, k), e)
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, d), d)
28.57/10.35	   A^2 -> H(U1(d, d), k)
28.57/10.35	   A^2 -> H(U1(e, c), c)
28.57/10.35	   A^2 -> H(U1(c, c), e)
28.57/10.35	   A^2 -> H(U1(c, c), k)
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(e, e), e)
28.57/10.35	   A^2 -> H(d, U1(e, b))
28.57/10.35	   A^2 -> H(d, U1(k, b))
28.57/10.35	   A^2 -> H(d, U1(c, d))
28.57/10.35	   A^2 -> H(d, U1(d, c))
28.57/10.35	   A^2 -> H(d, U1(b, e))
28.57/10.35	   A^2 -> H(d, U1(b, k))
28.57/10.35	   A^2 -> H(d, U1(e, c))
28.57/10.35	   A^2 -> H(d, U1(k, c))
28.57/10.35	   A^2 -> H(d, U1(c, e))
28.57/10.35	   A^2 -> H(d, U1(c, k))
28.57/10.35	   A^2 -> H(d, U1(e, e))
28.57/10.35	   A^2 -> H(d, U1(k, k))
28.57/10.35	   A^2 -> H(d, U1(k, d))
28.57/10.35	   A^2 -> H(d, U1(d, k))
28.57/10.35	   A^2 -> H(a, b)
28.57/10.35	   A^2 -> H(a, U1(e, d))
28.57/10.35	   A^2 -> H(a, U1(d, e))
28.57/10.35	   A^2 -> H(a, c)
28.57/10.35	   A^2 -> H(a, U1(e, k))
28.57/10.35	   A^2 -> H(a, U1(k, e))
28.57/10.35	   A^2 -> H(a, e)
28.57/10.35	   A^2 -> H(a, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, d), b)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, d), c)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, d), e)
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, a), d)
28.57/10.35	   A^2 -> H(U1(e, a), k)
28.57/10.35	   A^2 -> H(U1(k, a), d)
28.57/10.35	   A^2 -> H(U1(c, d), d)
28.57/10.35	   A^2 -> H(U1(c, d), k)
28.57/10.35	   A^2 -> H(U1(d, e), b)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, e), c)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, e), e)
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, c), d)
28.57/10.35	   A^2 -> H(U1(d, c), k)
28.57/10.35	   A^2 -> H(U1(a, e), d)
28.57/10.35	   A^2 -> H(U1(a, e), k)
28.57/10.35	   A^2 -> H(U1(a, k), d)
28.57/10.35	   A^2 -> H(U1(a, k), k)
28.57/10.35	   A^2 -> H(k, U1(e, b))
28.57/10.35	   A^2 -> H(k, U1(c, d))
28.57/10.35	   A^2 -> H(k, U1(d, c))
28.57/10.35	   A^2 -> H(k, U1(b, e))
28.57/10.35	   A^2 -> H(k, U1(b, k))
28.57/10.35	   A^2 -> H(k, U1(e, c))
28.57/10.35	   A^2 -> H(k, U1(c, e))
28.57/10.35	   A^2 -> H(k, U1(c, k))
28.57/10.35	   A^2 -> H(k, U1(e, e))
28.57/10.35	   A^2 -> H(k, U1(d, k))
28.57/10.35	   A^2 -> H(c, b)
28.57/10.35	   A^2 -> H(c, U1(e, d))
28.57/10.35	   A^2 -> H(c, U1(d, e))
28.57/10.35	   A^2 -> H(c, c)
28.57/10.35	   A^2 -> H(c, U1(e, k))
28.57/10.35	   A^2 -> H(c, U1(k, e))
28.57/10.35	   A^2 -> H(c, e)
28.57/10.35	   A^2 -> H(c, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, k), b)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, k), c)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, k), e)
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, c), d)
28.57/10.35	   A^2 -> H(U1(e, c), k)
28.57/10.35	   A^2 -> H(U1(k, e), b)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, e), c)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, c), d)
28.57/10.35	   A^2 -> H(U1(c, e), d)
28.57/10.35	   A^2 -> H(U1(c, e), k)
28.57/10.35	   A^2 -> H(U1(c, k), d)
28.57/10.35	   A^2 -> H(U1(c, k), k)
28.57/10.35	   A^2 -> H(e, b)
28.57/10.35	   A^2 -> H(e, U1(e, d))
28.57/10.35	   A^2 -> H(e, U1(d, e))
28.57/10.35	   A^2 -> H(e, c)
28.57/10.35	   A^2 -> H(e, U1(e, k))
28.57/10.35	   A^2 -> H(e, e)
28.57/10.35	   A^2 -> H(U1(e, e), d)
28.57/10.35	   A^2 -> H(U1(e, e), k)
28.57/10.35	   A^2 -> H(U1(k, k), d)
28.57/10.35	   A^2 -> H(U1(k, k), b)
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.35	
28.57/10.35	The TRS R consists of the following rules:
28.57/10.35	
28.57/10.35	   f(x) -> U1(x, x)
28.57/10.35	   U1(e, x) -> x
28.57/10.35	   a -> c
28.57/10.35	   a -> d
28.57/10.35	   b -> c
28.57/10.35	   b -> d
28.57/10.35	   d -> k
28.57/10.35	   c -> e
28.57/10.35	   c -> k
28.57/10.35	
28.57/10.35	Q is empty.
28.57/10.35	We have to consider all minimal (P,Q,R)-chains.
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2317) TransformationProof (EQUIVALENT)
28.57/10.35	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.35	
28.57/10.35	   (A^2 -> H(U1(k, k), c),A^2 -> H(U1(k, k), c))
28.57/10.35	   (A^2 -> H(U1(k, k), U1(e, e)),A^2 -> H(U1(k, k), U1(e, e)))
28.57/10.35	   (A^2 -> H(U1(k, k), U1(e, k)),A^2 -> H(U1(k, k), U1(e, k)))
28.57/10.35	
28.57/10.35	
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2318)
28.57/10.35	Obligation:
28.57/10.35	Q DP problem:
28.57/10.35	The TRS P consists of the following rules:
28.57/10.35	
28.57/10.35	   A^2 -> H(f(c), f(c))
28.57/10.35	   H(x, x) -> G(x, x, f(k))
28.57/10.35	   G(d, x, x) -> A^2
28.57/10.35	   A^2 -> H(f(d), f(d))
28.57/10.35	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.35	   A^2 -> H(f(e), f(e))
28.57/10.35	   A^2 -> H(f(k), f(k))
28.57/10.35	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.35	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.35	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.35	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, c))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, d), b)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, d), c)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, k), b)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, k), c)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, k), e)
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, d), d)
28.57/10.35	   A^2 -> H(U1(d, d), k)
28.57/10.35	   A^2 -> H(U1(e, c), c)
28.57/10.35	   A^2 -> H(U1(c, c), e)
28.57/10.35	   A^2 -> H(U1(c, c), k)
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(e, e), e)
28.57/10.35	   A^2 -> H(d, U1(e, b))
28.57/10.35	   A^2 -> H(d, U1(k, b))
28.57/10.35	   A^2 -> H(d, U1(c, d))
28.57/10.35	   A^2 -> H(d, U1(d, c))
28.57/10.35	   A^2 -> H(d, U1(b, e))
28.57/10.35	   A^2 -> H(d, U1(b, k))
28.57/10.35	   A^2 -> H(d, U1(e, c))
28.57/10.35	   A^2 -> H(d, U1(k, c))
28.57/10.35	   A^2 -> H(d, U1(c, e))
28.57/10.35	   A^2 -> H(d, U1(c, k))
28.57/10.35	   A^2 -> H(d, U1(e, e))
28.57/10.35	   A^2 -> H(d, U1(k, k))
28.57/10.35	   A^2 -> H(d, U1(k, d))
28.57/10.35	   A^2 -> H(d, U1(d, k))
28.57/10.35	   A^2 -> H(a, b)
28.57/10.35	   A^2 -> H(a, U1(e, d))
28.57/10.35	   A^2 -> H(a, U1(d, e))
28.57/10.35	   A^2 -> H(a, c)
28.57/10.35	   A^2 -> H(a, U1(e, k))
28.57/10.35	   A^2 -> H(a, U1(k, e))
28.57/10.35	   A^2 -> H(a, e)
28.57/10.35	   A^2 -> H(a, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, d), b)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, d), c)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, d), e)
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, a), d)
28.57/10.35	   A^2 -> H(U1(e, a), k)
28.57/10.35	   A^2 -> H(U1(k, a), d)
28.57/10.35	   A^2 -> H(U1(c, d), d)
28.57/10.35	   A^2 -> H(U1(c, d), k)
28.57/10.35	   A^2 -> H(U1(d, e), b)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, e), c)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, e), e)
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, c), d)
28.57/10.35	   A^2 -> H(U1(d, c), k)
28.57/10.35	   A^2 -> H(U1(a, e), d)
28.57/10.35	   A^2 -> H(U1(a, e), k)
28.57/10.35	   A^2 -> H(U1(a, k), d)
28.57/10.35	   A^2 -> H(U1(a, k), k)
28.57/10.35	   A^2 -> H(k, U1(e, b))
28.57/10.35	   A^2 -> H(k, U1(c, d))
28.57/10.35	   A^2 -> H(k, U1(d, c))
28.57/10.35	   A^2 -> H(k, U1(b, e))
28.57/10.35	   A^2 -> H(k, U1(b, k))
28.57/10.35	   A^2 -> H(k, U1(e, c))
28.57/10.35	   A^2 -> H(k, U1(c, e))
28.57/10.35	   A^2 -> H(k, U1(c, k))
28.57/10.35	   A^2 -> H(k, U1(e, e))
28.57/10.35	   A^2 -> H(k, U1(d, k))
28.57/10.35	   A^2 -> H(c, b)
28.57/10.35	   A^2 -> H(c, U1(e, d))
28.57/10.35	   A^2 -> H(c, U1(d, e))
28.57/10.35	   A^2 -> H(c, c)
28.57/10.35	   A^2 -> H(c, U1(e, k))
28.57/10.35	   A^2 -> H(c, U1(k, e))
28.57/10.35	   A^2 -> H(c, e)
28.57/10.35	   A^2 -> H(c, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, k), b)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, k), c)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, k), e)
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, c), d)
28.57/10.35	   A^2 -> H(U1(e, c), k)
28.57/10.35	   A^2 -> H(U1(k, e), b)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, e), c)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, c), d)
28.57/10.35	   A^2 -> H(U1(c, e), d)
28.57/10.35	   A^2 -> H(U1(c, e), k)
28.57/10.35	   A^2 -> H(U1(c, k), d)
28.57/10.35	   A^2 -> H(U1(c, k), k)
28.57/10.35	   A^2 -> H(e, b)
28.57/10.35	   A^2 -> H(e, U1(e, d))
28.57/10.35	   A^2 -> H(e, U1(d, e))
28.57/10.35	   A^2 -> H(e, c)
28.57/10.35	   A^2 -> H(e, U1(e, k))
28.57/10.35	   A^2 -> H(e, e)
28.57/10.35	   A^2 -> H(U1(e, e), d)
28.57/10.35	   A^2 -> H(U1(e, e), k)
28.57/10.35	   A^2 -> H(U1(k, k), d)
28.57/10.35	   A^2 -> H(U1(k, k), b)
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, k), c)
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.35	
28.57/10.35	The TRS R consists of the following rules:
28.57/10.35	
28.57/10.35	   f(x) -> U1(x, x)
28.57/10.35	   U1(e, x) -> x
28.57/10.35	   a -> c
28.57/10.35	   a -> d
28.57/10.35	   b -> c
28.57/10.35	   b -> d
28.57/10.35	   d -> k
28.57/10.35	   c -> e
28.57/10.35	   c -> k
28.57/10.35	
28.57/10.35	Q is empty.
28.57/10.35	We have to consider all minimal (P,Q,R)-chains.
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2319) TransformationProof (EQUIVALENT)
28.57/10.35	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.35	
28.57/10.35	   (A^2 -> H(U1(k, k), U1(k, e)),A^2 -> H(U1(k, k), U1(k, e)))
28.57/10.35	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.57/10.35	
28.57/10.35	
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2320)
28.57/10.35	Obligation:
28.57/10.35	Q DP problem:
28.57/10.35	The TRS P consists of the following rules:
28.57/10.35	
28.57/10.35	   A^2 -> H(f(c), f(c))
28.57/10.35	   H(x, x) -> G(x, x, f(k))
28.57/10.35	   G(d, x, x) -> A^2
28.57/10.35	   A^2 -> H(f(d), f(d))
28.57/10.35	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.35	   A^2 -> H(f(e), f(e))
28.57/10.35	   A^2 -> H(f(k), f(k))
28.57/10.35	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.35	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.35	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.35	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, d), b)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, d), c)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, k), b)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, k), c)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, k), e)
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, d), d)
28.57/10.35	   A^2 -> H(U1(d, d), k)
28.57/10.35	   A^2 -> H(U1(e, c), c)
28.57/10.35	   A^2 -> H(U1(c, c), e)
28.57/10.35	   A^2 -> H(U1(c, c), k)
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(e, e), e)
28.57/10.35	   A^2 -> H(d, U1(e, b))
28.57/10.35	   A^2 -> H(d, U1(k, b))
28.57/10.35	   A^2 -> H(d, U1(c, d))
28.57/10.35	   A^2 -> H(d, U1(d, c))
28.57/10.35	   A^2 -> H(d, U1(b, e))
28.57/10.35	   A^2 -> H(d, U1(b, k))
28.57/10.35	   A^2 -> H(d, U1(e, c))
28.57/10.35	   A^2 -> H(d, U1(k, c))
28.57/10.35	   A^2 -> H(d, U1(c, e))
28.57/10.35	   A^2 -> H(d, U1(c, k))
28.57/10.35	   A^2 -> H(d, U1(e, e))
28.57/10.35	   A^2 -> H(d, U1(k, k))
28.57/10.35	   A^2 -> H(d, U1(k, d))
28.57/10.35	   A^2 -> H(d, U1(d, k))
28.57/10.35	   A^2 -> H(a, b)
28.57/10.35	   A^2 -> H(a, U1(e, d))
28.57/10.35	   A^2 -> H(a, U1(d, e))
28.57/10.35	   A^2 -> H(a, c)
28.57/10.35	   A^2 -> H(a, U1(e, k))
28.57/10.35	   A^2 -> H(a, U1(k, e))
28.57/10.35	   A^2 -> H(a, e)
28.57/10.35	   A^2 -> H(a, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, d), b)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, d), c)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, d), e)
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, a), d)
28.57/10.35	   A^2 -> H(U1(e, a), k)
28.57/10.35	   A^2 -> H(U1(k, a), d)
28.57/10.35	   A^2 -> H(U1(c, d), d)
28.57/10.35	   A^2 -> H(U1(c, d), k)
28.57/10.35	   A^2 -> H(U1(d, e), b)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, e), c)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, e), e)
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, c), d)
28.57/10.35	   A^2 -> H(U1(d, c), k)
28.57/10.35	   A^2 -> H(U1(a, e), d)
28.57/10.35	   A^2 -> H(U1(a, e), k)
28.57/10.35	   A^2 -> H(U1(a, k), d)
28.57/10.35	   A^2 -> H(U1(a, k), k)
28.57/10.35	   A^2 -> H(k, U1(e, b))
28.57/10.35	   A^2 -> H(k, U1(c, d))
28.57/10.35	   A^2 -> H(k, U1(d, c))
28.57/10.35	   A^2 -> H(k, U1(b, e))
28.57/10.35	   A^2 -> H(k, U1(b, k))
28.57/10.35	   A^2 -> H(k, U1(e, c))
28.57/10.35	   A^2 -> H(k, U1(c, e))
28.57/10.35	   A^2 -> H(k, U1(c, k))
28.57/10.35	   A^2 -> H(k, U1(e, e))
28.57/10.35	   A^2 -> H(k, U1(d, k))
28.57/10.35	   A^2 -> H(c, b)
28.57/10.35	   A^2 -> H(c, U1(e, d))
28.57/10.35	   A^2 -> H(c, U1(d, e))
28.57/10.35	   A^2 -> H(c, c)
28.57/10.35	   A^2 -> H(c, U1(e, k))
28.57/10.35	   A^2 -> H(c, U1(k, e))
28.57/10.35	   A^2 -> H(c, e)
28.57/10.35	   A^2 -> H(c, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, k), b)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, k), c)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, k), e)
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, c), d)
28.57/10.35	   A^2 -> H(U1(e, c), k)
28.57/10.35	   A^2 -> H(U1(k, e), b)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, e), c)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, c), d)
28.57/10.35	   A^2 -> H(U1(c, e), d)
28.57/10.35	   A^2 -> H(U1(c, e), k)
28.57/10.35	   A^2 -> H(U1(c, k), d)
28.57/10.35	   A^2 -> H(U1(c, k), k)
28.57/10.35	   A^2 -> H(e, b)
28.57/10.35	   A^2 -> H(e, U1(e, d))
28.57/10.35	   A^2 -> H(e, U1(d, e))
28.57/10.35	   A^2 -> H(e, c)
28.57/10.35	   A^2 -> H(e, U1(e, k))
28.57/10.35	   A^2 -> H(e, e)
28.57/10.35	   A^2 -> H(U1(e, e), d)
28.57/10.35	   A^2 -> H(U1(e, e), k)
28.57/10.35	   A^2 -> H(U1(k, k), d)
28.57/10.35	   A^2 -> H(U1(k, k), b)
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, k), c)
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, e))
28.57/10.35	
28.57/10.35	The TRS R consists of the following rules:
28.57/10.35	
28.57/10.35	   f(x) -> U1(x, x)
28.57/10.35	   U1(e, x) -> x
28.57/10.35	   a -> c
28.57/10.35	   a -> d
28.57/10.35	   b -> c
28.57/10.35	   b -> d
28.57/10.35	   d -> k
28.57/10.35	   c -> e
28.57/10.35	   c -> k
28.57/10.35	
28.57/10.35	Q is empty.
28.57/10.35	We have to consider all minimal (P,Q,R)-chains.
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2321) DependencyGraphProof (EQUIVALENT)
28.57/10.35	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2322)
28.57/10.35	Obligation:
28.57/10.35	Q DP problem:
28.57/10.35	The TRS P consists of the following rules:
28.57/10.35	
28.57/10.35	   H(x, x) -> G(x, x, f(k))
28.57/10.35	   G(d, x, x) -> A^2
28.57/10.35	   A^2 -> H(f(c), f(c))
28.57/10.35	   A^2 -> H(f(d), f(d))
28.57/10.35	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.35	   A^2 -> H(f(e), f(e))
28.57/10.35	   A^2 -> H(f(k), f(k))
28.57/10.35	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.35	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.35	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.35	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, d), b)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, d), c)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, k), b)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, k), c)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, k), e)
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, d), d)
28.57/10.35	   A^2 -> H(U1(d, d), k)
28.57/10.35	   A^2 -> H(U1(e, c), c)
28.57/10.35	   A^2 -> H(U1(c, c), e)
28.57/10.35	   A^2 -> H(U1(c, c), k)
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(e, e), e)
28.57/10.35	   A^2 -> H(d, U1(e, b))
28.57/10.35	   A^2 -> H(d, U1(k, b))
28.57/10.35	   A^2 -> H(d, U1(c, d))
28.57/10.35	   A^2 -> H(d, U1(d, c))
28.57/10.35	   A^2 -> H(d, U1(b, e))
28.57/10.35	   A^2 -> H(d, U1(b, k))
28.57/10.35	   A^2 -> H(d, U1(e, c))
28.57/10.35	   A^2 -> H(d, U1(k, c))
28.57/10.35	   A^2 -> H(d, U1(c, e))
28.57/10.35	   A^2 -> H(d, U1(c, k))
28.57/10.35	   A^2 -> H(d, U1(e, e))
28.57/10.35	   A^2 -> H(d, U1(k, k))
28.57/10.35	   A^2 -> H(d, U1(k, d))
28.57/10.35	   A^2 -> H(d, U1(d, k))
28.57/10.35	   A^2 -> H(a, b)
28.57/10.35	   A^2 -> H(a, U1(e, d))
28.57/10.35	   A^2 -> H(a, U1(d, e))
28.57/10.35	   A^2 -> H(a, c)
28.57/10.35	   A^2 -> H(a, U1(e, k))
28.57/10.35	   A^2 -> H(a, U1(k, e))
28.57/10.35	   A^2 -> H(a, e)
28.57/10.35	   A^2 -> H(a, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, d), b)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, d), c)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, d), e)
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, a), d)
28.57/10.35	   A^2 -> H(U1(e, a), k)
28.57/10.35	   A^2 -> H(U1(k, a), d)
28.57/10.35	   A^2 -> H(U1(c, d), d)
28.57/10.35	   A^2 -> H(U1(c, d), k)
28.57/10.35	   A^2 -> H(U1(d, e), b)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, e), c)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, e), e)
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, c), d)
28.57/10.35	   A^2 -> H(U1(d, c), k)
28.57/10.35	   A^2 -> H(U1(a, e), d)
28.57/10.35	   A^2 -> H(U1(a, e), k)
28.57/10.35	   A^2 -> H(U1(a, k), d)
28.57/10.35	   A^2 -> H(U1(a, k), k)
28.57/10.35	   A^2 -> H(k, U1(e, b))
28.57/10.35	   A^2 -> H(k, U1(c, d))
28.57/10.35	   A^2 -> H(k, U1(d, c))
28.57/10.35	   A^2 -> H(k, U1(b, e))
28.57/10.35	   A^2 -> H(k, U1(b, k))
28.57/10.35	   A^2 -> H(k, U1(e, c))
28.57/10.35	   A^2 -> H(k, U1(c, e))
28.57/10.35	   A^2 -> H(k, U1(c, k))
28.57/10.35	   A^2 -> H(k, U1(e, e))
28.57/10.35	   A^2 -> H(k, U1(d, k))
28.57/10.35	   A^2 -> H(c, b)
28.57/10.35	   A^2 -> H(c, U1(e, d))
28.57/10.35	   A^2 -> H(c, U1(d, e))
28.57/10.35	   A^2 -> H(c, c)
28.57/10.35	   A^2 -> H(c, U1(e, k))
28.57/10.35	   A^2 -> H(c, U1(k, e))
28.57/10.35	   A^2 -> H(c, e)
28.57/10.35	   A^2 -> H(c, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, k), b)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, k), c)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, k), e)
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, c), d)
28.57/10.35	   A^2 -> H(U1(e, c), k)
28.57/10.35	   A^2 -> H(U1(k, e), b)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, e), c)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, c), d)
28.57/10.35	   A^2 -> H(U1(c, e), d)
28.57/10.35	   A^2 -> H(U1(c, e), k)
28.57/10.35	   A^2 -> H(U1(c, k), d)
28.57/10.35	   A^2 -> H(U1(c, k), k)
28.57/10.35	   A^2 -> H(e, b)
28.57/10.35	   A^2 -> H(e, U1(e, d))
28.57/10.35	   A^2 -> H(e, U1(d, e))
28.57/10.35	   A^2 -> H(e, c)
28.57/10.35	   A^2 -> H(e, U1(e, k))
28.57/10.35	   A^2 -> H(e, e)
28.57/10.35	   A^2 -> H(U1(e, e), d)
28.57/10.35	   A^2 -> H(U1(e, e), k)
28.57/10.35	   A^2 -> H(U1(k, k), d)
28.57/10.35	   A^2 -> H(U1(k, k), b)
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, k), c)
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.35	
28.57/10.35	The TRS R consists of the following rules:
28.57/10.35	
28.57/10.35	   f(x) -> U1(x, x)
28.57/10.35	   U1(e, x) -> x
28.57/10.35	   a -> c
28.57/10.35	   a -> d
28.57/10.35	   b -> c
28.57/10.35	   b -> d
28.57/10.35	   d -> k
28.57/10.35	   c -> e
28.57/10.35	   c -> k
28.57/10.35	
28.57/10.35	Q is empty.
28.57/10.35	We have to consider all minimal (P,Q,R)-chains.
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2323) TransformationProof (EQUIVALENT)
28.57/10.35	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.35	
28.57/10.35	   (A^2 -> H(U1(k, k), U1(e, e)),A^2 -> H(U1(k, k), U1(e, e)))
28.57/10.35	   (A^2 -> H(U1(k, k), U1(k, e)),A^2 -> H(U1(k, k), U1(k, e)))
28.57/10.35	
28.57/10.35	
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2324)
28.57/10.35	Obligation:
28.57/10.35	Q DP problem:
28.57/10.35	The TRS P consists of the following rules:
28.57/10.35	
28.57/10.35	   H(x, x) -> G(x, x, f(k))
28.57/10.35	   G(d, x, x) -> A^2
28.57/10.35	   A^2 -> H(f(c), f(c))
28.57/10.35	   A^2 -> H(f(d), f(d))
28.57/10.35	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.35	   A^2 -> H(f(e), f(e))
28.57/10.35	   A^2 -> H(f(k), f(k))
28.57/10.35	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.35	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.35	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.35	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, d), b)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, d), c)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, k), b)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, k), c)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, k), e)
28.57/10.35	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, d), d)
28.57/10.35	   A^2 -> H(U1(d, d), k)
28.57/10.35	   A^2 -> H(U1(e, c), c)
28.57/10.35	   A^2 -> H(U1(c, c), e)
28.57/10.35	   A^2 -> H(U1(c, c), k)
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(e, e), e)
28.57/10.35	   A^2 -> H(d, U1(e, b))
28.57/10.35	   A^2 -> H(d, U1(k, b))
28.57/10.35	   A^2 -> H(d, U1(c, d))
28.57/10.35	   A^2 -> H(d, U1(d, c))
28.57/10.35	   A^2 -> H(d, U1(b, e))
28.57/10.35	   A^2 -> H(d, U1(b, k))
28.57/10.35	   A^2 -> H(d, U1(e, c))
28.57/10.35	   A^2 -> H(d, U1(k, c))
28.57/10.35	   A^2 -> H(d, U1(c, e))
28.57/10.35	   A^2 -> H(d, U1(c, k))
28.57/10.35	   A^2 -> H(d, U1(e, e))
28.57/10.35	   A^2 -> H(d, U1(k, k))
28.57/10.35	   A^2 -> H(d, U1(k, d))
28.57/10.35	   A^2 -> H(d, U1(d, k))
28.57/10.35	   A^2 -> H(a, b)
28.57/10.35	   A^2 -> H(a, U1(e, d))
28.57/10.35	   A^2 -> H(a, U1(d, e))
28.57/10.35	   A^2 -> H(a, c)
28.57/10.35	   A^2 -> H(a, U1(e, k))
28.57/10.35	   A^2 -> H(a, U1(k, e))
28.57/10.35	   A^2 -> H(a, e)
28.57/10.35	   A^2 -> H(a, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, d), b)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, d), c)
28.57/10.35	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, d), e)
28.57/10.35	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, a), d)
28.57/10.35	   A^2 -> H(U1(e, a), k)
28.57/10.35	   A^2 -> H(U1(k, a), d)
28.57/10.35	   A^2 -> H(U1(c, d), d)
28.57/10.35	   A^2 -> H(U1(c, d), k)
28.57/10.35	   A^2 -> H(U1(d, e), b)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(d, e), c)
28.57/10.35	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(d, e), e)
28.57/10.35	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, c), d)
28.57/10.35	   A^2 -> H(U1(d, c), k)
28.57/10.35	   A^2 -> H(U1(a, e), d)
28.57/10.35	   A^2 -> H(U1(a, e), k)
28.57/10.35	   A^2 -> H(U1(a, k), d)
28.57/10.35	   A^2 -> H(U1(a, k), k)
28.57/10.35	   A^2 -> H(k, U1(e, b))
28.57/10.35	   A^2 -> H(k, U1(c, d))
28.57/10.35	   A^2 -> H(k, U1(d, c))
28.57/10.35	   A^2 -> H(k, U1(b, e))
28.57/10.35	   A^2 -> H(k, U1(b, k))
28.57/10.35	   A^2 -> H(k, U1(e, c))
28.57/10.35	   A^2 -> H(k, U1(c, e))
28.57/10.35	   A^2 -> H(k, U1(c, k))
28.57/10.35	   A^2 -> H(k, U1(e, e))
28.57/10.35	   A^2 -> H(k, U1(d, k))
28.57/10.35	   A^2 -> H(c, b)
28.57/10.35	   A^2 -> H(c, U1(e, d))
28.57/10.35	   A^2 -> H(c, U1(d, e))
28.57/10.35	   A^2 -> H(c, c)
28.57/10.35	   A^2 -> H(c, U1(e, k))
28.57/10.35	   A^2 -> H(c, U1(k, e))
28.57/10.35	   A^2 -> H(c, e)
28.57/10.35	   A^2 -> H(c, U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, k), b)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(e, k), c)
28.57/10.35	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.35	   A^2 -> H(U1(e, k), e)
28.57/10.35	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(e, c), d)
28.57/10.35	   A^2 -> H(U1(e, c), k)
28.57/10.35	   A^2 -> H(U1(k, e), b)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, e), c)
28.57/10.35	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, c), d)
28.57/10.35	   A^2 -> H(U1(c, e), d)
28.57/10.35	   A^2 -> H(U1(c, e), k)
28.57/10.35	   A^2 -> H(U1(c, k), d)
28.57/10.35	   A^2 -> H(U1(c, k), k)
28.57/10.35	   A^2 -> H(e, b)
28.57/10.35	   A^2 -> H(e, U1(e, d))
28.57/10.35	   A^2 -> H(e, U1(d, e))
28.57/10.35	   A^2 -> H(e, c)
28.57/10.35	   A^2 -> H(e, U1(e, k))
28.57/10.35	   A^2 -> H(e, e)
28.57/10.35	   A^2 -> H(U1(e, e), d)
28.57/10.35	   A^2 -> H(U1(e, e), k)
28.57/10.35	   A^2 -> H(U1(k, k), d)
28.57/10.35	   A^2 -> H(U1(k, k), b)
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, k), c)
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, e))
28.57/10.35	
28.57/10.35	The TRS R consists of the following rules:
28.57/10.35	
28.57/10.35	   f(x) -> U1(x, x)
28.57/10.35	   U1(e, x) -> x
28.57/10.35	   a -> c
28.57/10.35	   a -> d
28.57/10.35	   b -> c
28.57/10.35	   b -> d
28.57/10.35	   d -> k
28.57/10.35	   c -> e
28.57/10.35	   c -> k
28.57/10.35	
28.57/10.35	Q is empty.
28.57/10.35	We have to consider all minimal (P,Q,R)-chains.
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2325) DependencyGraphProof (EQUIVALENT)
28.57/10.35	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.35	----------------------------------------
28.57/10.35	
28.57/10.35	(2326)
28.57/10.35	Obligation:
28.57/10.35	Q DP problem:
28.57/10.35	The TRS P consists of the following rules:
28.57/10.35	
28.57/10.35	   G(d, x, x) -> A^2
28.57/10.35	   A^2 -> H(f(c), f(c))
28.57/10.35	   H(x, x) -> G(x, x, f(k))
28.57/10.35	   A^2 -> H(f(d), f(d))
28.57/10.35	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.35	   A^2 -> H(f(e), f(e))
28.57/10.35	   A^2 -> H(f(k), f(k))
28.57/10.35	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.35	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.35	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.35	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.35	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.35	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.35	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.35	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(c, k))
28.57/10.35	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.35	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.35	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.35	   A^2 -> H(U1(k, d), b)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.35	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.35	   A^2 -> H(U1(k, d), c)
28.57/10.35	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.35	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.35	   A^2 -> H(U1(d, k), b)
28.57/10.35	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, k), c)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, k), e)
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, d), d)
28.57/10.36	   A^2 -> H(U1(d, d), k)
28.57/10.36	   A^2 -> H(U1(e, c), c)
28.57/10.36	   A^2 -> H(U1(c, c), e)
28.57/10.36	   A^2 -> H(U1(c, c), k)
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.36	   A^2 -> H(U1(e, e), e)
28.57/10.36	   A^2 -> H(d, U1(e, b))
28.57/10.36	   A^2 -> H(d, U1(k, b))
28.57/10.36	   A^2 -> H(d, U1(c, d))
28.57/10.36	   A^2 -> H(d, U1(d, c))
28.57/10.36	   A^2 -> H(d, U1(b, e))
28.57/10.36	   A^2 -> H(d, U1(b, k))
28.57/10.36	   A^2 -> H(d, U1(e, c))
28.57/10.36	   A^2 -> H(d, U1(k, c))
28.57/10.36	   A^2 -> H(d, U1(c, e))
28.57/10.36	   A^2 -> H(d, U1(c, k))
28.57/10.36	   A^2 -> H(d, U1(e, e))
28.57/10.36	   A^2 -> H(d, U1(k, k))
28.57/10.36	   A^2 -> H(d, U1(k, d))
28.57/10.36	   A^2 -> H(d, U1(d, k))
28.57/10.36	   A^2 -> H(a, b)
28.57/10.36	   A^2 -> H(a, U1(e, d))
28.57/10.36	   A^2 -> H(a, U1(d, e))
28.57/10.36	   A^2 -> H(a, c)
28.57/10.36	   A^2 -> H(a, U1(e, k))
28.57/10.36	   A^2 -> H(a, U1(k, e))
28.57/10.36	   A^2 -> H(a, e)
28.57/10.36	   A^2 -> H(a, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, d), b)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, d), c)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, d), e)
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, a), d)
28.57/10.36	   A^2 -> H(U1(e, a), k)
28.57/10.36	   A^2 -> H(U1(k, a), d)
28.57/10.36	   A^2 -> H(U1(c, d), d)
28.57/10.36	   A^2 -> H(U1(c, d), k)
28.57/10.36	   A^2 -> H(U1(d, e), b)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, e), c)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, e), e)
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, c), d)
28.57/10.36	   A^2 -> H(U1(d, c), k)
28.57/10.36	   A^2 -> H(U1(a, e), d)
28.57/10.36	   A^2 -> H(U1(a, e), k)
28.57/10.36	   A^2 -> H(U1(a, k), d)
28.57/10.36	   A^2 -> H(U1(a, k), k)
28.57/10.36	   A^2 -> H(k, U1(e, b))
28.57/10.36	   A^2 -> H(k, U1(c, d))
28.57/10.36	   A^2 -> H(k, U1(d, c))
28.57/10.36	   A^2 -> H(k, U1(b, e))
28.57/10.36	   A^2 -> H(k, U1(b, k))
28.57/10.36	   A^2 -> H(k, U1(e, c))
28.57/10.36	   A^2 -> H(k, U1(c, e))
28.57/10.36	   A^2 -> H(k, U1(c, k))
28.57/10.36	   A^2 -> H(k, U1(e, e))
28.57/10.36	   A^2 -> H(k, U1(d, k))
28.57/10.36	   A^2 -> H(c, b)
28.57/10.36	   A^2 -> H(c, U1(e, d))
28.57/10.36	   A^2 -> H(c, U1(d, e))
28.57/10.36	   A^2 -> H(c, c)
28.57/10.36	   A^2 -> H(c, U1(e, k))
28.57/10.36	   A^2 -> H(c, U1(k, e))
28.57/10.36	   A^2 -> H(c, e)
28.57/10.36	   A^2 -> H(c, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, k), b)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, k), c)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, k), e)
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, c), d)
28.57/10.36	   A^2 -> H(U1(e, c), k)
28.57/10.36	   A^2 -> H(U1(k, e), b)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, e), c)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, c), d)
28.57/10.36	   A^2 -> H(U1(c, e), d)
28.57/10.36	   A^2 -> H(U1(c, e), k)
28.57/10.36	   A^2 -> H(U1(c, k), d)
28.57/10.36	   A^2 -> H(U1(c, k), k)
28.57/10.36	   A^2 -> H(e, b)
28.57/10.36	   A^2 -> H(e, U1(e, d))
28.57/10.36	   A^2 -> H(e, U1(d, e))
28.57/10.36	   A^2 -> H(e, c)
28.57/10.36	   A^2 -> H(e, U1(e, k))
28.57/10.36	   A^2 -> H(e, e)
28.57/10.36	   A^2 -> H(U1(e, e), d)
28.57/10.36	   A^2 -> H(U1(e, e), k)
28.57/10.36	   A^2 -> H(U1(k, k), d)
28.57/10.36	   A^2 -> H(U1(k, k), b)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, k), c)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.36	
28.57/10.36	The TRS R consists of the following rules:
28.57/10.36	
28.57/10.36	   f(x) -> U1(x, x)
28.57/10.36	   U1(e, x) -> x
28.57/10.36	   a -> c
28.57/10.36	   a -> d
28.57/10.36	   b -> c
28.57/10.36	   b -> d
28.57/10.36	   d -> k
28.57/10.36	   c -> e
28.57/10.36	   c -> k
28.57/10.36	
28.57/10.36	Q is empty.
28.57/10.36	We have to consider all minimal (P,Q,R)-chains.
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2327) TransformationProof (EQUIVALENT)
28.57/10.36	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.36	
28.57/10.36	   (A^2 -> H(U1(k, k), U1(e, k)),A^2 -> H(U1(k, k), U1(e, k)))
28.57/10.36	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.57/10.36	
28.57/10.36	
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2328)
28.57/10.36	Obligation:
28.57/10.36	Q DP problem:
28.57/10.36	The TRS P consists of the following rules:
28.57/10.36	
28.57/10.36	   G(d, x, x) -> A^2
28.57/10.36	   A^2 -> H(f(c), f(c))
28.57/10.36	   H(x, x) -> G(x, x, f(k))
28.57/10.36	   A^2 -> H(f(d), f(d))
28.57/10.36	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.36	   A^2 -> H(f(e), f(e))
28.57/10.36	   A^2 -> H(f(k), f(k))
28.57/10.36	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.36	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.36	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.36	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.36	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.36	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.36	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.36	   A^2 -> H(U1(k, d), b)
28.57/10.36	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, d), c)
28.57/10.36	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, k), b)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, k), c)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, k), e)
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, d), d)
28.57/10.36	   A^2 -> H(U1(d, d), k)
28.57/10.36	   A^2 -> H(U1(e, c), c)
28.57/10.36	   A^2 -> H(U1(c, c), e)
28.57/10.36	   A^2 -> H(U1(c, c), k)
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.36	   A^2 -> H(U1(e, e), e)
28.57/10.36	   A^2 -> H(d, U1(e, b))
28.57/10.36	   A^2 -> H(d, U1(k, b))
28.57/10.36	   A^2 -> H(d, U1(c, d))
28.57/10.36	   A^2 -> H(d, U1(d, c))
28.57/10.36	   A^2 -> H(d, U1(b, e))
28.57/10.36	   A^2 -> H(d, U1(b, k))
28.57/10.36	   A^2 -> H(d, U1(e, c))
28.57/10.36	   A^2 -> H(d, U1(k, c))
28.57/10.36	   A^2 -> H(d, U1(c, e))
28.57/10.36	   A^2 -> H(d, U1(c, k))
28.57/10.36	   A^2 -> H(d, U1(e, e))
28.57/10.36	   A^2 -> H(d, U1(k, k))
28.57/10.36	   A^2 -> H(d, U1(k, d))
28.57/10.36	   A^2 -> H(d, U1(d, k))
28.57/10.36	   A^2 -> H(a, b)
28.57/10.36	   A^2 -> H(a, U1(e, d))
28.57/10.36	   A^2 -> H(a, U1(d, e))
28.57/10.36	   A^2 -> H(a, c)
28.57/10.36	   A^2 -> H(a, U1(e, k))
28.57/10.36	   A^2 -> H(a, U1(k, e))
28.57/10.36	   A^2 -> H(a, e)
28.57/10.36	   A^2 -> H(a, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, d), b)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, d), c)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, d), e)
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, a), d)
28.57/10.36	   A^2 -> H(U1(e, a), k)
28.57/10.36	   A^2 -> H(U1(k, a), d)
28.57/10.36	   A^2 -> H(U1(c, d), d)
28.57/10.36	   A^2 -> H(U1(c, d), k)
28.57/10.36	   A^2 -> H(U1(d, e), b)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, e), c)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, e), e)
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, c), d)
28.57/10.36	   A^2 -> H(U1(d, c), k)
28.57/10.36	   A^2 -> H(U1(a, e), d)
28.57/10.36	   A^2 -> H(U1(a, e), k)
28.57/10.36	   A^2 -> H(U1(a, k), d)
28.57/10.36	   A^2 -> H(U1(a, k), k)
28.57/10.36	   A^2 -> H(k, U1(e, b))
28.57/10.36	   A^2 -> H(k, U1(c, d))
28.57/10.36	   A^2 -> H(k, U1(d, c))
28.57/10.36	   A^2 -> H(k, U1(b, e))
28.57/10.36	   A^2 -> H(k, U1(b, k))
28.57/10.36	   A^2 -> H(k, U1(e, c))
28.57/10.36	   A^2 -> H(k, U1(c, e))
28.57/10.36	   A^2 -> H(k, U1(c, k))
28.57/10.36	   A^2 -> H(k, U1(e, e))
28.57/10.36	   A^2 -> H(k, U1(d, k))
28.57/10.36	   A^2 -> H(c, b)
28.57/10.36	   A^2 -> H(c, U1(e, d))
28.57/10.36	   A^2 -> H(c, U1(d, e))
28.57/10.36	   A^2 -> H(c, c)
28.57/10.36	   A^2 -> H(c, U1(e, k))
28.57/10.36	   A^2 -> H(c, U1(k, e))
28.57/10.36	   A^2 -> H(c, e)
28.57/10.36	   A^2 -> H(c, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, k), b)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, k), c)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, k), e)
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, c), d)
28.57/10.36	   A^2 -> H(U1(e, c), k)
28.57/10.36	   A^2 -> H(U1(k, e), b)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, e), c)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, c), d)
28.57/10.36	   A^2 -> H(U1(c, e), d)
28.57/10.36	   A^2 -> H(U1(c, e), k)
28.57/10.36	   A^2 -> H(U1(c, k), d)
28.57/10.36	   A^2 -> H(U1(c, k), k)
28.57/10.36	   A^2 -> H(e, b)
28.57/10.36	   A^2 -> H(e, U1(e, d))
28.57/10.36	   A^2 -> H(e, U1(d, e))
28.57/10.36	   A^2 -> H(e, c)
28.57/10.36	   A^2 -> H(e, U1(e, k))
28.57/10.36	   A^2 -> H(e, e)
28.57/10.36	   A^2 -> H(U1(e, e), d)
28.57/10.36	   A^2 -> H(U1(e, e), k)
28.57/10.36	   A^2 -> H(U1(k, k), d)
28.57/10.36	   A^2 -> H(U1(k, k), b)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, k), c)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.36	
28.57/10.36	The TRS R consists of the following rules:
28.57/10.36	
28.57/10.36	   f(x) -> U1(x, x)
28.57/10.36	   U1(e, x) -> x
28.57/10.36	   a -> c
28.57/10.36	   a -> d
28.57/10.36	   b -> c
28.57/10.36	   b -> d
28.57/10.36	   d -> k
28.57/10.36	   c -> e
28.57/10.36	   c -> k
28.57/10.36	
28.57/10.36	Q is empty.
28.57/10.36	We have to consider all minimal (P,Q,R)-chains.
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2329) TransformationProof (EQUIVALENT)
28.57/10.36	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.36	
28.57/10.36	   (A^2 -> H(U1(k, k), e),A^2 -> H(U1(k, k), e))
28.57/10.36	
28.57/10.36	
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2330)
28.57/10.36	Obligation:
28.57/10.36	Q DP problem:
28.57/10.36	The TRS P consists of the following rules:
28.57/10.36	
28.57/10.36	   G(d, x, x) -> A^2
28.57/10.36	   A^2 -> H(f(c), f(c))
28.57/10.36	   H(x, x) -> G(x, x, f(k))
28.57/10.36	   A^2 -> H(f(d), f(d))
28.57/10.36	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.36	   A^2 -> H(f(e), f(e))
28.57/10.36	   A^2 -> H(f(k), f(k))
28.57/10.36	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.36	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.36	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.36	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.36	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.36	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.36	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.36	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.36	   A^2 -> H(U1(k, d), b)
28.57/10.36	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, d), c)
28.57/10.36	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, k), b)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, k), c)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, k), e)
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, d), d)
28.57/10.36	   A^2 -> H(U1(d, d), k)
28.57/10.36	   A^2 -> H(U1(e, c), c)
28.57/10.36	   A^2 -> H(U1(c, c), e)
28.57/10.36	   A^2 -> H(U1(c, c), k)
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.36	   A^2 -> H(U1(e, e), e)
28.57/10.36	   A^2 -> H(d, U1(e, b))
28.57/10.36	   A^2 -> H(d, U1(k, b))
28.57/10.36	   A^2 -> H(d, U1(c, d))
28.57/10.36	   A^2 -> H(d, U1(d, c))
28.57/10.36	   A^2 -> H(d, U1(b, e))
28.57/10.36	   A^2 -> H(d, U1(b, k))
28.57/10.36	   A^2 -> H(d, U1(e, c))
28.57/10.36	   A^2 -> H(d, U1(k, c))
28.57/10.36	   A^2 -> H(d, U1(c, e))
28.57/10.36	   A^2 -> H(d, U1(c, k))
28.57/10.36	   A^2 -> H(d, U1(e, e))
28.57/10.36	   A^2 -> H(d, U1(k, k))
28.57/10.36	   A^2 -> H(d, U1(k, d))
28.57/10.36	   A^2 -> H(d, U1(d, k))
28.57/10.36	   A^2 -> H(a, b)
28.57/10.36	   A^2 -> H(a, U1(e, d))
28.57/10.36	   A^2 -> H(a, U1(d, e))
28.57/10.36	   A^2 -> H(a, c)
28.57/10.36	   A^2 -> H(a, U1(e, k))
28.57/10.36	   A^2 -> H(a, U1(k, e))
28.57/10.36	   A^2 -> H(a, e)
28.57/10.36	   A^2 -> H(a, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, d), b)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, d), c)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, d), e)
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, a), d)
28.57/10.36	   A^2 -> H(U1(e, a), k)
28.57/10.36	   A^2 -> H(U1(k, a), d)
28.57/10.36	   A^2 -> H(U1(c, d), d)
28.57/10.36	   A^2 -> H(U1(c, d), k)
28.57/10.36	   A^2 -> H(U1(d, e), b)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, e), c)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, e), e)
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, c), d)
28.57/10.36	   A^2 -> H(U1(d, c), k)
28.57/10.36	   A^2 -> H(U1(a, e), d)
28.57/10.36	   A^2 -> H(U1(a, e), k)
28.57/10.36	   A^2 -> H(U1(a, k), d)
28.57/10.36	   A^2 -> H(U1(a, k), k)
28.57/10.36	   A^2 -> H(k, U1(e, b))
28.57/10.36	   A^2 -> H(k, U1(c, d))
28.57/10.36	   A^2 -> H(k, U1(d, c))
28.57/10.36	   A^2 -> H(k, U1(b, e))
28.57/10.36	   A^2 -> H(k, U1(b, k))
28.57/10.36	   A^2 -> H(k, U1(e, c))
28.57/10.36	   A^2 -> H(k, U1(c, e))
28.57/10.36	   A^2 -> H(k, U1(c, k))
28.57/10.36	   A^2 -> H(k, U1(e, e))
28.57/10.36	   A^2 -> H(k, U1(d, k))
28.57/10.36	   A^2 -> H(c, b)
28.57/10.36	   A^2 -> H(c, U1(e, d))
28.57/10.36	   A^2 -> H(c, U1(d, e))
28.57/10.36	   A^2 -> H(c, c)
28.57/10.36	   A^2 -> H(c, U1(e, k))
28.57/10.36	   A^2 -> H(c, U1(k, e))
28.57/10.36	   A^2 -> H(c, e)
28.57/10.36	   A^2 -> H(c, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, k), b)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, k), c)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, k), e)
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, c), d)
28.57/10.36	   A^2 -> H(U1(e, c), k)
28.57/10.36	   A^2 -> H(U1(k, e), b)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, e), c)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, c), d)
28.57/10.36	   A^2 -> H(U1(c, e), d)
28.57/10.36	   A^2 -> H(U1(c, e), k)
28.57/10.36	   A^2 -> H(U1(c, k), d)
28.57/10.36	   A^2 -> H(U1(c, k), k)
28.57/10.36	   A^2 -> H(e, b)
28.57/10.36	   A^2 -> H(e, U1(e, d))
28.57/10.36	   A^2 -> H(e, U1(d, e))
28.57/10.36	   A^2 -> H(e, c)
28.57/10.36	   A^2 -> H(e, U1(e, k))
28.57/10.36	   A^2 -> H(e, e)
28.57/10.36	   A^2 -> H(U1(e, e), d)
28.57/10.36	   A^2 -> H(U1(e, e), k)
28.57/10.36	   A^2 -> H(U1(k, k), d)
28.57/10.36	   A^2 -> H(U1(k, k), b)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, k), c)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, k), e)
28.57/10.36	
28.57/10.36	The TRS R consists of the following rules:
28.57/10.36	
28.57/10.36	   f(x) -> U1(x, x)
28.57/10.36	   U1(e, x) -> x
28.57/10.36	   a -> c
28.57/10.36	   a -> d
28.57/10.36	   b -> c
28.57/10.36	   b -> d
28.57/10.36	   d -> k
28.57/10.36	   c -> e
28.57/10.36	   c -> k
28.57/10.36	
28.57/10.36	Q is empty.
28.57/10.36	We have to consider all minimal (P,Q,R)-chains.
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2331) DependencyGraphProof (EQUIVALENT)
28.57/10.36	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2332)
28.57/10.36	Obligation:
28.57/10.36	Q DP problem:
28.57/10.36	The TRS P consists of the following rules:
28.57/10.36	
28.57/10.36	   A^2 -> H(f(c), f(c))
28.57/10.36	   H(x, x) -> G(x, x, f(k))
28.57/10.36	   G(d, x, x) -> A^2
28.57/10.36	   A^2 -> H(f(d), f(d))
28.57/10.36	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.36	   A^2 -> H(f(e), f(e))
28.57/10.36	   A^2 -> H(f(k), f(k))
28.57/10.36	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.36	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.36	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.36	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.36	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.36	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.36	   A^2 -> H(U1(k, k), U1(k, d))
28.57/10.36	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.36	   A^2 -> H(U1(k, d), b)
28.57/10.36	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, d), c)
28.57/10.36	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, k), b)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, k), c)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, k), e)
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, d), d)
28.57/10.36	   A^2 -> H(U1(d, d), k)
28.57/10.36	   A^2 -> H(U1(e, c), c)
28.57/10.36	   A^2 -> H(U1(c, c), e)
28.57/10.36	   A^2 -> H(U1(c, c), k)
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.36	   A^2 -> H(U1(e, e), e)
28.57/10.36	   A^2 -> H(d, U1(e, b))
28.57/10.36	   A^2 -> H(d, U1(k, b))
28.57/10.36	   A^2 -> H(d, U1(c, d))
28.57/10.36	   A^2 -> H(d, U1(d, c))
28.57/10.36	   A^2 -> H(d, U1(b, e))
28.57/10.36	   A^2 -> H(d, U1(b, k))
28.57/10.36	   A^2 -> H(d, U1(e, c))
28.57/10.36	   A^2 -> H(d, U1(k, c))
28.57/10.36	   A^2 -> H(d, U1(c, e))
28.57/10.36	   A^2 -> H(d, U1(c, k))
28.57/10.36	   A^2 -> H(d, U1(e, e))
28.57/10.36	   A^2 -> H(d, U1(k, k))
28.57/10.36	   A^2 -> H(d, U1(k, d))
28.57/10.36	   A^2 -> H(d, U1(d, k))
28.57/10.36	   A^2 -> H(a, b)
28.57/10.36	   A^2 -> H(a, U1(e, d))
28.57/10.36	   A^2 -> H(a, U1(d, e))
28.57/10.36	   A^2 -> H(a, c)
28.57/10.36	   A^2 -> H(a, U1(e, k))
28.57/10.36	   A^2 -> H(a, U1(k, e))
28.57/10.36	   A^2 -> H(a, e)
28.57/10.36	   A^2 -> H(a, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, d), b)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, d), c)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, d), e)
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, a), d)
28.57/10.36	   A^2 -> H(U1(e, a), k)
28.57/10.36	   A^2 -> H(U1(k, a), d)
28.57/10.36	   A^2 -> H(U1(c, d), d)
28.57/10.36	   A^2 -> H(U1(c, d), k)
28.57/10.36	   A^2 -> H(U1(d, e), b)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, e), c)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, e), e)
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, c), d)
28.57/10.36	   A^2 -> H(U1(d, c), k)
28.57/10.36	   A^2 -> H(U1(a, e), d)
28.57/10.36	   A^2 -> H(U1(a, e), k)
28.57/10.36	   A^2 -> H(U1(a, k), d)
28.57/10.36	   A^2 -> H(U1(a, k), k)
28.57/10.36	   A^2 -> H(k, U1(e, b))
28.57/10.36	   A^2 -> H(k, U1(c, d))
28.57/10.36	   A^2 -> H(k, U1(d, c))
28.57/10.36	   A^2 -> H(k, U1(b, e))
28.57/10.36	   A^2 -> H(k, U1(b, k))
28.57/10.36	   A^2 -> H(k, U1(e, c))
28.57/10.36	   A^2 -> H(k, U1(c, e))
28.57/10.36	   A^2 -> H(k, U1(c, k))
28.57/10.36	   A^2 -> H(k, U1(e, e))
28.57/10.36	   A^2 -> H(k, U1(d, k))
28.57/10.36	   A^2 -> H(c, b)
28.57/10.36	   A^2 -> H(c, U1(e, d))
28.57/10.36	   A^2 -> H(c, U1(d, e))
28.57/10.36	   A^2 -> H(c, c)
28.57/10.36	   A^2 -> H(c, U1(e, k))
28.57/10.36	   A^2 -> H(c, U1(k, e))
28.57/10.36	   A^2 -> H(c, e)
28.57/10.36	   A^2 -> H(c, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, k), b)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, k), c)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, k), e)
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, c), d)
28.57/10.36	   A^2 -> H(U1(e, c), k)
28.57/10.36	   A^2 -> H(U1(k, e), b)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, e), c)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, c), d)
28.57/10.36	   A^2 -> H(U1(c, e), d)
28.57/10.36	   A^2 -> H(U1(c, e), k)
28.57/10.36	   A^2 -> H(U1(c, k), d)
28.57/10.36	   A^2 -> H(U1(c, k), k)
28.57/10.36	   A^2 -> H(e, b)
28.57/10.36	   A^2 -> H(e, U1(e, d))
28.57/10.36	   A^2 -> H(e, U1(d, e))
28.57/10.36	   A^2 -> H(e, c)
28.57/10.36	   A^2 -> H(e, U1(e, k))
28.57/10.36	   A^2 -> H(e, e)
28.57/10.36	   A^2 -> H(U1(e, e), d)
28.57/10.36	   A^2 -> H(U1(e, e), k)
28.57/10.36	   A^2 -> H(U1(k, k), d)
28.57/10.36	   A^2 -> H(U1(k, k), b)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, k), c)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.36	
28.57/10.36	The TRS R consists of the following rules:
28.57/10.36	
28.57/10.36	   f(x) -> U1(x, x)
28.57/10.36	   U1(e, x) -> x
28.57/10.36	   a -> c
28.57/10.36	   a -> d
28.57/10.36	   b -> c
28.57/10.36	   b -> d
28.57/10.36	   d -> k
28.57/10.36	   c -> e
28.57/10.36	   c -> k
28.57/10.36	
28.57/10.36	Q is empty.
28.57/10.36	We have to consider all minimal (P,Q,R)-chains.
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2333) TransformationProof (EQUIVALENT)
28.57/10.36	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.36	
28.57/10.36	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.57/10.36	
28.57/10.36	
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2334)
28.57/10.36	Obligation:
28.57/10.36	Q DP problem:
28.57/10.36	The TRS P consists of the following rules:
28.57/10.36	
28.57/10.36	   A^2 -> H(f(c), f(c))
28.57/10.36	   H(x, x) -> G(x, x, f(k))
28.57/10.36	   G(d, x, x) -> A^2
28.57/10.36	   A^2 -> H(f(d), f(d))
28.57/10.36	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.36	   A^2 -> H(f(e), f(e))
28.57/10.36	   A^2 -> H(f(k), f(k))
28.57/10.36	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.36	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.36	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.36	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.36	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.36	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.36	   A^2 -> H(U1(k, k), U1(d, k))
28.57/10.36	   A^2 -> H(U1(k, d), b)
28.57/10.36	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, d), c)
28.57/10.36	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, k), b)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, k), c)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, k), e)
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, d), d)
28.57/10.36	   A^2 -> H(U1(d, d), k)
28.57/10.36	   A^2 -> H(U1(e, c), c)
28.57/10.36	   A^2 -> H(U1(c, c), e)
28.57/10.36	   A^2 -> H(U1(c, c), k)
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.36	   A^2 -> H(U1(e, e), e)
28.57/10.36	   A^2 -> H(d, U1(e, b))
28.57/10.36	   A^2 -> H(d, U1(k, b))
28.57/10.36	   A^2 -> H(d, U1(c, d))
28.57/10.36	   A^2 -> H(d, U1(d, c))
28.57/10.36	   A^2 -> H(d, U1(b, e))
28.57/10.36	   A^2 -> H(d, U1(b, k))
28.57/10.36	   A^2 -> H(d, U1(e, c))
28.57/10.36	   A^2 -> H(d, U1(k, c))
28.57/10.36	   A^2 -> H(d, U1(c, e))
28.57/10.36	   A^2 -> H(d, U1(c, k))
28.57/10.36	   A^2 -> H(d, U1(e, e))
28.57/10.36	   A^2 -> H(d, U1(k, k))
28.57/10.36	   A^2 -> H(d, U1(k, d))
28.57/10.36	   A^2 -> H(d, U1(d, k))
28.57/10.36	   A^2 -> H(a, b)
28.57/10.36	   A^2 -> H(a, U1(e, d))
28.57/10.36	   A^2 -> H(a, U1(d, e))
28.57/10.36	   A^2 -> H(a, c)
28.57/10.36	   A^2 -> H(a, U1(e, k))
28.57/10.36	   A^2 -> H(a, U1(k, e))
28.57/10.36	   A^2 -> H(a, e)
28.57/10.36	   A^2 -> H(a, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, d), b)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, d), c)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, d), e)
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, a), d)
28.57/10.36	   A^2 -> H(U1(e, a), k)
28.57/10.36	   A^2 -> H(U1(k, a), d)
28.57/10.36	   A^2 -> H(U1(c, d), d)
28.57/10.36	   A^2 -> H(U1(c, d), k)
28.57/10.36	   A^2 -> H(U1(d, e), b)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, e), c)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, e), e)
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, c), d)
28.57/10.36	   A^2 -> H(U1(d, c), k)
28.57/10.36	   A^2 -> H(U1(a, e), d)
28.57/10.36	   A^2 -> H(U1(a, e), k)
28.57/10.36	   A^2 -> H(U1(a, k), d)
28.57/10.36	   A^2 -> H(U1(a, k), k)
28.57/10.36	   A^2 -> H(k, U1(e, b))
28.57/10.36	   A^2 -> H(k, U1(c, d))
28.57/10.36	   A^2 -> H(k, U1(d, c))
28.57/10.36	   A^2 -> H(k, U1(b, e))
28.57/10.36	   A^2 -> H(k, U1(b, k))
28.57/10.36	   A^2 -> H(k, U1(e, c))
28.57/10.36	   A^2 -> H(k, U1(c, e))
28.57/10.36	   A^2 -> H(k, U1(c, k))
28.57/10.36	   A^2 -> H(k, U1(e, e))
28.57/10.36	   A^2 -> H(k, U1(d, k))
28.57/10.36	   A^2 -> H(c, b)
28.57/10.36	   A^2 -> H(c, U1(e, d))
28.57/10.36	   A^2 -> H(c, U1(d, e))
28.57/10.36	   A^2 -> H(c, c)
28.57/10.36	   A^2 -> H(c, U1(e, k))
28.57/10.36	   A^2 -> H(c, U1(k, e))
28.57/10.36	   A^2 -> H(c, e)
28.57/10.36	   A^2 -> H(c, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, k), b)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, k), c)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, k), e)
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, c), d)
28.57/10.36	   A^2 -> H(U1(e, c), k)
28.57/10.36	   A^2 -> H(U1(k, e), b)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, e), c)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, c), d)
28.57/10.36	   A^2 -> H(U1(c, e), d)
28.57/10.36	   A^2 -> H(U1(c, e), k)
28.57/10.36	   A^2 -> H(U1(c, k), d)
28.57/10.36	   A^2 -> H(U1(c, k), k)
28.57/10.36	   A^2 -> H(e, b)
28.57/10.36	   A^2 -> H(e, U1(e, d))
28.57/10.36	   A^2 -> H(e, U1(d, e))
28.57/10.36	   A^2 -> H(e, c)
28.57/10.36	   A^2 -> H(e, U1(e, k))
28.57/10.36	   A^2 -> H(e, e)
28.57/10.36	   A^2 -> H(U1(e, e), d)
28.57/10.36	   A^2 -> H(U1(e, e), k)
28.57/10.36	   A^2 -> H(U1(k, k), d)
28.57/10.36	   A^2 -> H(U1(k, k), b)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, k), c)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.36	
28.57/10.36	The TRS R consists of the following rules:
28.57/10.36	
28.57/10.36	   f(x) -> U1(x, x)
28.57/10.36	   U1(e, x) -> x
28.57/10.36	   a -> c
28.57/10.36	   a -> d
28.57/10.36	   b -> c
28.57/10.36	   b -> d
28.57/10.36	   d -> k
28.57/10.36	   c -> e
28.57/10.36	   c -> k
28.57/10.36	
28.57/10.36	Q is empty.
28.57/10.36	We have to consider all minimal (P,Q,R)-chains.
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2335) TransformationProof (EQUIVALENT)
28.57/10.36	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.36	
28.57/10.36	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.57/10.36	
28.57/10.36	
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2336)
28.57/10.36	Obligation:
28.57/10.36	Q DP problem:
28.57/10.36	The TRS P consists of the following rules:
28.57/10.36	
28.57/10.36	   A^2 -> H(f(c), f(c))
28.57/10.36	   H(x, x) -> G(x, x, f(k))
28.57/10.36	   G(d, x, x) -> A^2
28.57/10.36	   A^2 -> H(f(d), f(d))
28.57/10.36	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.36	   A^2 -> H(f(e), f(e))
28.57/10.36	   A^2 -> H(f(k), f(k))
28.57/10.36	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.36	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.36	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.36	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.36	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.36	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.36	   A^2 -> H(U1(k, d), b)
28.57/10.36	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, d), c)
28.57/10.36	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, k), b)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, k), c)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, k), e)
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, d), d)
28.57/10.36	   A^2 -> H(U1(d, d), k)
28.57/10.36	   A^2 -> H(U1(e, c), c)
28.57/10.36	   A^2 -> H(U1(c, c), e)
28.57/10.36	   A^2 -> H(U1(c, c), k)
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.36	   A^2 -> H(U1(e, e), e)
28.57/10.36	   A^2 -> H(d, U1(e, b))
28.57/10.36	   A^2 -> H(d, U1(k, b))
28.57/10.36	   A^2 -> H(d, U1(c, d))
28.57/10.36	   A^2 -> H(d, U1(d, c))
28.57/10.36	   A^2 -> H(d, U1(b, e))
28.57/10.36	   A^2 -> H(d, U1(b, k))
28.57/10.36	   A^2 -> H(d, U1(e, c))
28.57/10.36	   A^2 -> H(d, U1(k, c))
28.57/10.36	   A^2 -> H(d, U1(c, e))
28.57/10.36	   A^2 -> H(d, U1(c, k))
28.57/10.36	   A^2 -> H(d, U1(e, e))
28.57/10.36	   A^2 -> H(d, U1(k, k))
28.57/10.36	   A^2 -> H(d, U1(k, d))
28.57/10.36	   A^2 -> H(d, U1(d, k))
28.57/10.36	   A^2 -> H(a, b)
28.57/10.36	   A^2 -> H(a, U1(e, d))
28.57/10.36	   A^2 -> H(a, U1(d, e))
28.57/10.36	   A^2 -> H(a, c)
28.57/10.36	   A^2 -> H(a, U1(e, k))
28.57/10.36	   A^2 -> H(a, U1(k, e))
28.57/10.36	   A^2 -> H(a, e)
28.57/10.36	   A^2 -> H(a, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, d), b)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, d), c)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, d), e)
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, a), d)
28.57/10.36	   A^2 -> H(U1(e, a), k)
28.57/10.36	   A^2 -> H(U1(k, a), d)
28.57/10.36	   A^2 -> H(U1(c, d), d)
28.57/10.36	   A^2 -> H(U1(c, d), k)
28.57/10.36	   A^2 -> H(U1(d, e), b)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, e), c)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, e), e)
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, c), d)
28.57/10.36	   A^2 -> H(U1(d, c), k)
28.57/10.36	   A^2 -> H(U1(a, e), d)
28.57/10.36	   A^2 -> H(U1(a, e), k)
28.57/10.36	   A^2 -> H(U1(a, k), d)
28.57/10.36	   A^2 -> H(U1(a, k), k)
28.57/10.36	   A^2 -> H(k, U1(e, b))
28.57/10.36	   A^2 -> H(k, U1(c, d))
28.57/10.36	   A^2 -> H(k, U1(d, c))
28.57/10.36	   A^2 -> H(k, U1(b, e))
28.57/10.36	   A^2 -> H(k, U1(b, k))
28.57/10.36	   A^2 -> H(k, U1(e, c))
28.57/10.36	   A^2 -> H(k, U1(c, e))
28.57/10.36	   A^2 -> H(k, U1(c, k))
28.57/10.36	   A^2 -> H(k, U1(e, e))
28.57/10.36	   A^2 -> H(k, U1(d, k))
28.57/10.36	   A^2 -> H(c, b)
28.57/10.36	   A^2 -> H(c, U1(e, d))
28.57/10.36	   A^2 -> H(c, U1(d, e))
28.57/10.36	   A^2 -> H(c, c)
28.57/10.36	   A^2 -> H(c, U1(e, k))
28.57/10.36	   A^2 -> H(c, U1(k, e))
28.57/10.36	   A^2 -> H(c, e)
28.57/10.36	   A^2 -> H(c, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, k), b)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, k), c)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, k), e)
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, c), d)
28.57/10.36	   A^2 -> H(U1(e, c), k)
28.57/10.36	   A^2 -> H(U1(k, e), b)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, e), c)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, c), d)
28.57/10.36	   A^2 -> H(U1(c, e), d)
28.57/10.36	   A^2 -> H(U1(c, e), k)
28.57/10.36	   A^2 -> H(U1(c, k), d)
28.57/10.36	   A^2 -> H(U1(c, k), k)
28.57/10.36	   A^2 -> H(e, b)
28.57/10.36	   A^2 -> H(e, U1(e, d))
28.57/10.36	   A^2 -> H(e, U1(d, e))
28.57/10.36	   A^2 -> H(e, c)
28.57/10.36	   A^2 -> H(e, U1(e, k))
28.57/10.36	   A^2 -> H(e, e)
28.57/10.36	   A^2 -> H(U1(e, e), d)
28.57/10.36	   A^2 -> H(U1(e, e), k)
28.57/10.36	   A^2 -> H(U1(k, k), d)
28.57/10.36	   A^2 -> H(U1(k, k), b)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, k), c)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.36	
28.57/10.36	The TRS R consists of the following rules:
28.57/10.36	
28.57/10.36	   f(x) -> U1(x, x)
28.57/10.36	   U1(e, x) -> x
28.57/10.36	   a -> c
28.57/10.36	   a -> d
28.57/10.36	   b -> c
28.57/10.36	   b -> d
28.57/10.36	   d -> k
28.57/10.36	   c -> e
28.57/10.36	   c -> k
28.57/10.36	
28.57/10.36	Q is empty.
28.57/10.36	We have to consider all minimal (P,Q,R)-chains.
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2337) TransformationProof (EQUIVALENT)
28.57/10.36	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), b) at position [] we obtained the following new rules [LPAR04]:
28.57/10.36	
28.57/10.36	   (A^2 -> H(U1(k, k), b),A^2 -> H(U1(k, k), b))
28.57/10.36	   (A^2 -> H(U1(k, d), c),A^2 -> H(U1(k, d), c))
28.57/10.36	   (A^2 -> H(U1(k, d), d),A^2 -> H(U1(k, d), d))
28.57/10.36	
28.57/10.36	
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2338)
28.57/10.36	Obligation:
28.57/10.36	Q DP problem:
28.57/10.36	The TRS P consists of the following rules:
28.57/10.36	
28.57/10.36	   A^2 -> H(f(c), f(c))
28.57/10.36	   H(x, x) -> G(x, x, f(k))
28.57/10.36	   G(d, x, x) -> A^2
28.57/10.36	   A^2 -> H(f(d), f(d))
28.57/10.36	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.36	   A^2 -> H(f(e), f(e))
28.57/10.36	   A^2 -> H(f(k), f(k))
28.57/10.36	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.36	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.36	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.36	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.36	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.36	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, d), c)
28.57/10.36	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, k), b)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, k), c)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, k), e)
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, d), d)
28.57/10.36	   A^2 -> H(U1(d, d), k)
28.57/10.36	   A^2 -> H(U1(e, c), c)
28.57/10.36	   A^2 -> H(U1(c, c), e)
28.57/10.36	   A^2 -> H(U1(c, c), k)
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.36	   A^2 -> H(U1(e, e), e)
28.57/10.36	   A^2 -> H(d, U1(e, b))
28.57/10.36	   A^2 -> H(d, U1(k, b))
28.57/10.36	   A^2 -> H(d, U1(c, d))
28.57/10.36	   A^2 -> H(d, U1(d, c))
28.57/10.36	   A^2 -> H(d, U1(b, e))
28.57/10.36	   A^2 -> H(d, U1(b, k))
28.57/10.36	   A^2 -> H(d, U1(e, c))
28.57/10.36	   A^2 -> H(d, U1(k, c))
28.57/10.36	   A^2 -> H(d, U1(c, e))
28.57/10.36	   A^2 -> H(d, U1(c, k))
28.57/10.36	   A^2 -> H(d, U1(e, e))
28.57/10.36	   A^2 -> H(d, U1(k, k))
28.57/10.36	   A^2 -> H(d, U1(k, d))
28.57/10.36	   A^2 -> H(d, U1(d, k))
28.57/10.36	   A^2 -> H(a, b)
28.57/10.36	   A^2 -> H(a, U1(e, d))
28.57/10.36	   A^2 -> H(a, U1(d, e))
28.57/10.36	   A^2 -> H(a, c)
28.57/10.36	   A^2 -> H(a, U1(e, k))
28.57/10.36	   A^2 -> H(a, U1(k, e))
28.57/10.36	   A^2 -> H(a, e)
28.57/10.36	   A^2 -> H(a, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, d), b)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, d), c)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, d), e)
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, a), d)
28.57/10.36	   A^2 -> H(U1(e, a), k)
28.57/10.36	   A^2 -> H(U1(k, a), d)
28.57/10.36	   A^2 -> H(U1(c, d), d)
28.57/10.36	   A^2 -> H(U1(c, d), k)
28.57/10.36	   A^2 -> H(U1(d, e), b)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, e), c)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, e), e)
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, c), d)
28.57/10.36	   A^2 -> H(U1(d, c), k)
28.57/10.36	   A^2 -> H(U1(a, e), d)
28.57/10.36	   A^2 -> H(U1(a, e), k)
28.57/10.36	   A^2 -> H(U1(a, k), d)
28.57/10.36	   A^2 -> H(U1(a, k), k)
28.57/10.36	   A^2 -> H(k, U1(e, b))
28.57/10.36	   A^2 -> H(k, U1(c, d))
28.57/10.36	   A^2 -> H(k, U1(d, c))
28.57/10.36	   A^2 -> H(k, U1(b, e))
28.57/10.36	   A^2 -> H(k, U1(b, k))
28.57/10.36	   A^2 -> H(k, U1(e, c))
28.57/10.36	   A^2 -> H(k, U1(c, e))
28.57/10.36	   A^2 -> H(k, U1(c, k))
28.57/10.36	   A^2 -> H(k, U1(e, e))
28.57/10.36	   A^2 -> H(k, U1(d, k))
28.57/10.36	   A^2 -> H(c, b)
28.57/10.36	   A^2 -> H(c, U1(e, d))
28.57/10.36	   A^2 -> H(c, U1(d, e))
28.57/10.36	   A^2 -> H(c, c)
28.57/10.36	   A^2 -> H(c, U1(e, k))
28.57/10.36	   A^2 -> H(c, U1(k, e))
28.57/10.36	   A^2 -> H(c, e)
28.57/10.36	   A^2 -> H(c, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, k), b)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, k), c)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, k), e)
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, c), d)
28.57/10.36	   A^2 -> H(U1(e, c), k)
28.57/10.36	   A^2 -> H(U1(k, e), b)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, e), c)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, c), d)
28.57/10.36	   A^2 -> H(U1(c, e), d)
28.57/10.36	   A^2 -> H(U1(c, e), k)
28.57/10.36	   A^2 -> H(U1(c, k), d)
28.57/10.36	   A^2 -> H(U1(c, k), k)
28.57/10.36	   A^2 -> H(e, b)
28.57/10.36	   A^2 -> H(e, U1(e, d))
28.57/10.36	   A^2 -> H(e, U1(d, e))
28.57/10.36	   A^2 -> H(e, c)
28.57/10.36	   A^2 -> H(e, U1(e, k))
28.57/10.36	   A^2 -> H(e, e)
28.57/10.36	   A^2 -> H(U1(e, e), d)
28.57/10.36	   A^2 -> H(U1(e, e), k)
28.57/10.36	   A^2 -> H(U1(k, k), d)
28.57/10.36	   A^2 -> H(U1(k, k), b)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, k), c)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, d), d)
28.57/10.36	
28.57/10.36	The TRS R consists of the following rules:
28.57/10.36	
28.57/10.36	   f(x) -> U1(x, x)
28.57/10.36	   U1(e, x) -> x
28.57/10.36	   a -> c
28.57/10.36	   a -> d
28.57/10.36	   b -> c
28.57/10.36	   b -> d
28.57/10.36	   d -> k
28.57/10.36	   c -> e
28.57/10.36	   c -> k
28.57/10.36	
28.57/10.36	Q is empty.
28.57/10.36	We have to consider all minimal (P,Q,R)-chains.
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2339) TransformationProof (EQUIVALENT)
28.57/10.36	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.36	
28.57/10.36	   (A^2 -> H(U1(k, k), U1(e, d)),A^2 -> H(U1(k, k), U1(e, d)))
28.57/10.36	   (A^2 -> H(U1(k, d), d),A^2 -> H(U1(k, d), d))
28.57/10.36	   (A^2 -> H(U1(k, d), U1(e, k)),A^2 -> H(U1(k, d), U1(e, k)))
28.57/10.36	
28.57/10.36	
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2340)
28.57/10.36	Obligation:
28.57/10.36	Q DP problem:
28.57/10.36	The TRS P consists of the following rules:
28.57/10.36	
28.57/10.36	   A^2 -> H(f(c), f(c))
28.57/10.36	   H(x, x) -> G(x, x, f(k))
28.57/10.36	   G(d, x, x) -> A^2
28.57/10.36	   A^2 -> H(f(d), f(d))
28.57/10.36	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.36	   A^2 -> H(f(e), f(e))
28.57/10.36	   A^2 -> H(f(k), f(k))
28.57/10.36	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.36	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.36	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.36	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.36	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.36	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, d), c)
28.57/10.36	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, k), b)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, k), c)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, k), e)
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, d), d)
28.57/10.36	   A^2 -> H(U1(d, d), k)
28.57/10.36	   A^2 -> H(U1(e, c), c)
28.57/10.36	   A^2 -> H(U1(c, c), e)
28.57/10.36	   A^2 -> H(U1(c, c), k)
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.36	   A^2 -> H(U1(e, e), e)
28.57/10.36	   A^2 -> H(d, U1(e, b))
28.57/10.36	   A^2 -> H(d, U1(k, b))
28.57/10.36	   A^2 -> H(d, U1(c, d))
28.57/10.36	   A^2 -> H(d, U1(d, c))
28.57/10.36	   A^2 -> H(d, U1(b, e))
28.57/10.36	   A^2 -> H(d, U1(b, k))
28.57/10.36	   A^2 -> H(d, U1(e, c))
28.57/10.36	   A^2 -> H(d, U1(k, c))
28.57/10.36	   A^2 -> H(d, U1(c, e))
28.57/10.36	   A^2 -> H(d, U1(c, k))
28.57/10.36	   A^2 -> H(d, U1(e, e))
28.57/10.36	   A^2 -> H(d, U1(k, k))
28.57/10.36	   A^2 -> H(d, U1(k, d))
28.57/10.36	   A^2 -> H(d, U1(d, k))
28.57/10.36	   A^2 -> H(a, b)
28.57/10.36	   A^2 -> H(a, U1(e, d))
28.57/10.36	   A^2 -> H(a, U1(d, e))
28.57/10.36	   A^2 -> H(a, c)
28.57/10.36	   A^2 -> H(a, U1(e, k))
28.57/10.36	   A^2 -> H(a, U1(k, e))
28.57/10.36	   A^2 -> H(a, e)
28.57/10.36	   A^2 -> H(a, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, d), b)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, d), c)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, d), e)
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, a), d)
28.57/10.36	   A^2 -> H(U1(e, a), k)
28.57/10.36	   A^2 -> H(U1(k, a), d)
28.57/10.36	   A^2 -> H(U1(c, d), d)
28.57/10.36	   A^2 -> H(U1(c, d), k)
28.57/10.36	   A^2 -> H(U1(d, e), b)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, e), c)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, e), e)
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, c), d)
28.57/10.36	   A^2 -> H(U1(d, c), k)
28.57/10.36	   A^2 -> H(U1(a, e), d)
28.57/10.36	   A^2 -> H(U1(a, e), k)
28.57/10.36	   A^2 -> H(U1(a, k), d)
28.57/10.36	   A^2 -> H(U1(a, k), k)
28.57/10.36	   A^2 -> H(k, U1(e, b))
28.57/10.36	   A^2 -> H(k, U1(c, d))
28.57/10.36	   A^2 -> H(k, U1(d, c))
28.57/10.36	   A^2 -> H(k, U1(b, e))
28.57/10.36	   A^2 -> H(k, U1(b, k))
28.57/10.36	   A^2 -> H(k, U1(e, c))
28.57/10.36	   A^2 -> H(k, U1(c, e))
28.57/10.36	   A^2 -> H(k, U1(c, k))
28.57/10.36	   A^2 -> H(k, U1(e, e))
28.57/10.36	   A^2 -> H(k, U1(d, k))
28.57/10.36	   A^2 -> H(c, b)
28.57/10.36	   A^2 -> H(c, U1(e, d))
28.57/10.36	   A^2 -> H(c, U1(d, e))
28.57/10.36	   A^2 -> H(c, c)
28.57/10.36	   A^2 -> H(c, U1(e, k))
28.57/10.36	   A^2 -> H(c, U1(k, e))
28.57/10.36	   A^2 -> H(c, e)
28.57/10.36	   A^2 -> H(c, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, k), b)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, k), c)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, k), e)
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, c), d)
28.57/10.36	   A^2 -> H(U1(e, c), k)
28.57/10.36	   A^2 -> H(U1(k, e), b)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, e), c)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, c), d)
28.57/10.36	   A^2 -> H(U1(c, e), d)
28.57/10.36	   A^2 -> H(U1(c, e), k)
28.57/10.36	   A^2 -> H(U1(c, k), d)
28.57/10.36	   A^2 -> H(U1(c, k), k)
28.57/10.36	   A^2 -> H(e, b)
28.57/10.36	   A^2 -> H(e, U1(e, d))
28.57/10.36	   A^2 -> H(e, U1(d, e))
28.57/10.36	   A^2 -> H(e, c)
28.57/10.36	   A^2 -> H(e, U1(e, k))
28.57/10.36	   A^2 -> H(e, e)
28.57/10.36	   A^2 -> H(U1(e, e), d)
28.57/10.36	   A^2 -> H(U1(e, e), k)
28.57/10.36	   A^2 -> H(U1(k, k), d)
28.57/10.36	   A^2 -> H(U1(k, k), b)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, k), c)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, d), d)
28.57/10.36	
28.57/10.36	The TRS R consists of the following rules:
28.57/10.36	
28.57/10.36	   f(x) -> U1(x, x)
28.57/10.36	   U1(e, x) -> x
28.57/10.36	   a -> c
28.57/10.36	   a -> d
28.57/10.36	   b -> c
28.57/10.36	   b -> d
28.57/10.36	   d -> k
28.57/10.36	   c -> e
28.57/10.36	   c -> k
28.57/10.36	
28.57/10.36	Q is empty.
28.57/10.36	We have to consider all minimal (P,Q,R)-chains.
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2341) TransformationProof (EQUIVALENT)
28.57/10.36	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.36	
28.57/10.36	   (A^2 -> H(U1(k, k), U1(d, e)),A^2 -> H(U1(k, k), U1(d, e)))
28.57/10.36	   (A^2 -> H(U1(k, d), U1(k, e)),A^2 -> H(U1(k, d), U1(k, e)))
28.57/10.36	
28.57/10.36	
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2342)
28.57/10.36	Obligation:
28.57/10.36	Q DP problem:
28.57/10.36	The TRS P consists of the following rules:
28.57/10.36	
28.57/10.36	   A^2 -> H(f(c), f(c))
28.57/10.36	   H(x, x) -> G(x, x, f(k))
28.57/10.36	   G(d, x, x) -> A^2
28.57/10.36	   A^2 -> H(f(d), f(d))
28.57/10.36	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.36	   A^2 -> H(f(e), f(e))
28.57/10.36	   A^2 -> H(f(k), f(k))
28.57/10.36	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.36	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.36	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.36	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.36	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.36	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.36	   A^2 -> H(U1(k, d), c)
28.57/10.36	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, k), b)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, k), c)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, k), e)
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, d), d)
28.57/10.36	   A^2 -> H(U1(d, d), k)
28.57/10.36	   A^2 -> H(U1(e, c), c)
28.57/10.36	   A^2 -> H(U1(c, c), e)
28.57/10.36	   A^2 -> H(U1(c, c), k)
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.36	   A^2 -> H(U1(e, e), e)
28.57/10.36	   A^2 -> H(d, U1(e, b))
28.57/10.36	   A^2 -> H(d, U1(k, b))
28.57/10.36	   A^2 -> H(d, U1(c, d))
28.57/10.36	   A^2 -> H(d, U1(d, c))
28.57/10.36	   A^2 -> H(d, U1(b, e))
28.57/10.36	   A^2 -> H(d, U1(b, k))
28.57/10.36	   A^2 -> H(d, U1(e, c))
28.57/10.36	   A^2 -> H(d, U1(k, c))
28.57/10.36	   A^2 -> H(d, U1(c, e))
28.57/10.36	   A^2 -> H(d, U1(c, k))
28.57/10.36	   A^2 -> H(d, U1(e, e))
28.57/10.36	   A^2 -> H(d, U1(k, k))
28.57/10.36	   A^2 -> H(d, U1(k, d))
28.57/10.36	   A^2 -> H(d, U1(d, k))
28.57/10.36	   A^2 -> H(a, b)
28.57/10.36	   A^2 -> H(a, U1(e, d))
28.57/10.36	   A^2 -> H(a, U1(d, e))
28.57/10.36	   A^2 -> H(a, c)
28.57/10.36	   A^2 -> H(a, U1(e, k))
28.57/10.36	   A^2 -> H(a, U1(k, e))
28.57/10.36	   A^2 -> H(a, e)
28.57/10.36	   A^2 -> H(a, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, d), b)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, d), c)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, d), e)
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, a), d)
28.57/10.36	   A^2 -> H(U1(e, a), k)
28.57/10.36	   A^2 -> H(U1(k, a), d)
28.57/10.36	   A^2 -> H(U1(c, d), d)
28.57/10.36	   A^2 -> H(U1(c, d), k)
28.57/10.36	   A^2 -> H(U1(d, e), b)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, e), c)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, e), e)
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, c), d)
28.57/10.36	   A^2 -> H(U1(d, c), k)
28.57/10.36	   A^2 -> H(U1(a, e), d)
28.57/10.36	   A^2 -> H(U1(a, e), k)
28.57/10.36	   A^2 -> H(U1(a, k), d)
28.57/10.36	   A^2 -> H(U1(a, k), k)
28.57/10.36	   A^2 -> H(k, U1(e, b))
28.57/10.36	   A^2 -> H(k, U1(c, d))
28.57/10.36	   A^2 -> H(k, U1(d, c))
28.57/10.36	   A^2 -> H(k, U1(b, e))
28.57/10.36	   A^2 -> H(k, U1(b, k))
28.57/10.36	   A^2 -> H(k, U1(e, c))
28.57/10.36	   A^2 -> H(k, U1(c, e))
28.57/10.36	   A^2 -> H(k, U1(c, k))
28.57/10.36	   A^2 -> H(k, U1(e, e))
28.57/10.36	   A^2 -> H(k, U1(d, k))
28.57/10.36	   A^2 -> H(c, b)
28.57/10.36	   A^2 -> H(c, U1(e, d))
28.57/10.36	   A^2 -> H(c, U1(d, e))
28.57/10.36	   A^2 -> H(c, c)
28.57/10.36	   A^2 -> H(c, U1(e, k))
28.57/10.36	   A^2 -> H(c, U1(k, e))
28.57/10.36	   A^2 -> H(c, e)
28.57/10.36	   A^2 -> H(c, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, k), b)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, k), c)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, k), e)
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, c), d)
28.57/10.36	   A^2 -> H(U1(e, c), k)
28.57/10.36	   A^2 -> H(U1(k, e), b)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, e), c)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, c), d)
28.57/10.36	   A^2 -> H(U1(c, e), d)
28.57/10.36	   A^2 -> H(U1(c, e), k)
28.57/10.36	   A^2 -> H(U1(c, k), d)
28.57/10.36	   A^2 -> H(U1(c, k), k)
28.57/10.36	   A^2 -> H(e, b)
28.57/10.36	   A^2 -> H(e, U1(e, d))
28.57/10.36	   A^2 -> H(e, U1(d, e))
28.57/10.36	   A^2 -> H(e, c)
28.57/10.36	   A^2 -> H(e, U1(e, k))
28.57/10.36	   A^2 -> H(e, e)
28.57/10.36	   A^2 -> H(U1(e, e), d)
28.57/10.36	   A^2 -> H(U1(e, e), k)
28.57/10.36	   A^2 -> H(U1(k, k), d)
28.57/10.36	   A^2 -> H(U1(k, k), b)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, k), c)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, d), d)
28.57/10.36	
28.57/10.36	The TRS R consists of the following rules:
28.57/10.36	
28.57/10.36	   f(x) -> U1(x, x)
28.57/10.36	   U1(e, x) -> x
28.57/10.36	   a -> c
28.57/10.36	   a -> d
28.57/10.36	   b -> c
28.57/10.36	   b -> d
28.57/10.36	   d -> k
28.57/10.36	   c -> e
28.57/10.36	   c -> k
28.57/10.36	
28.57/10.36	Q is empty.
28.57/10.36	We have to consider all minimal (P,Q,R)-chains.
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2343) TransformationProof (EQUIVALENT)
28.57/10.36	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), c) at position [] we obtained the following new rules [LPAR04]:
28.57/10.36	
28.57/10.36	   (A^2 -> H(U1(k, k), c),A^2 -> H(U1(k, k), c))
28.57/10.36	   (A^2 -> H(U1(k, d), e),A^2 -> H(U1(k, d), e))
28.57/10.36	   (A^2 -> H(U1(k, d), k),A^2 -> H(U1(k, d), k))
28.57/10.36	
28.57/10.36	
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2344)
28.57/10.36	Obligation:
28.57/10.36	Q DP problem:
28.57/10.36	The TRS P consists of the following rules:
28.57/10.36	
28.57/10.36	   A^2 -> H(f(c), f(c))
28.57/10.36	   H(x, x) -> G(x, x, f(k))
28.57/10.36	   G(d, x, x) -> A^2
28.57/10.36	   A^2 -> H(f(d), f(d))
28.57/10.36	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.36	   A^2 -> H(f(e), f(e))
28.57/10.36	   A^2 -> H(f(k), f(k))
28.57/10.36	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.36	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.36	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.36	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.36	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.36	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, k), b)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, k), c)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, k), e)
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, d), d)
28.57/10.36	   A^2 -> H(U1(d, d), k)
28.57/10.36	   A^2 -> H(U1(e, c), c)
28.57/10.36	   A^2 -> H(U1(c, c), e)
28.57/10.36	   A^2 -> H(U1(c, c), k)
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.36	   A^2 -> H(U1(e, e), e)
28.57/10.36	   A^2 -> H(d, U1(e, b))
28.57/10.36	   A^2 -> H(d, U1(k, b))
28.57/10.36	   A^2 -> H(d, U1(c, d))
28.57/10.36	   A^2 -> H(d, U1(d, c))
28.57/10.36	   A^2 -> H(d, U1(b, e))
28.57/10.36	   A^2 -> H(d, U1(b, k))
28.57/10.36	   A^2 -> H(d, U1(e, c))
28.57/10.36	   A^2 -> H(d, U1(k, c))
28.57/10.36	   A^2 -> H(d, U1(c, e))
28.57/10.36	   A^2 -> H(d, U1(c, k))
28.57/10.36	   A^2 -> H(d, U1(e, e))
28.57/10.36	   A^2 -> H(d, U1(k, k))
28.57/10.36	   A^2 -> H(d, U1(k, d))
28.57/10.36	   A^2 -> H(d, U1(d, k))
28.57/10.36	   A^2 -> H(a, b)
28.57/10.36	   A^2 -> H(a, U1(e, d))
28.57/10.36	   A^2 -> H(a, U1(d, e))
28.57/10.36	   A^2 -> H(a, c)
28.57/10.36	   A^2 -> H(a, U1(e, k))
28.57/10.36	   A^2 -> H(a, U1(k, e))
28.57/10.36	   A^2 -> H(a, e)
28.57/10.36	   A^2 -> H(a, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, d), b)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, d), c)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, d), e)
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, a), d)
28.57/10.36	   A^2 -> H(U1(e, a), k)
28.57/10.36	   A^2 -> H(U1(k, a), d)
28.57/10.36	   A^2 -> H(U1(c, d), d)
28.57/10.36	   A^2 -> H(U1(c, d), k)
28.57/10.36	   A^2 -> H(U1(d, e), b)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, e), c)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, e), e)
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, c), d)
28.57/10.36	   A^2 -> H(U1(d, c), k)
28.57/10.36	   A^2 -> H(U1(a, e), d)
28.57/10.36	   A^2 -> H(U1(a, e), k)
28.57/10.36	   A^2 -> H(U1(a, k), d)
28.57/10.36	   A^2 -> H(U1(a, k), k)
28.57/10.36	   A^2 -> H(k, U1(e, b))
28.57/10.36	   A^2 -> H(k, U1(c, d))
28.57/10.36	   A^2 -> H(k, U1(d, c))
28.57/10.36	   A^2 -> H(k, U1(b, e))
28.57/10.36	   A^2 -> H(k, U1(b, k))
28.57/10.36	   A^2 -> H(k, U1(e, c))
28.57/10.36	   A^2 -> H(k, U1(c, e))
28.57/10.36	   A^2 -> H(k, U1(c, k))
28.57/10.36	   A^2 -> H(k, U1(e, e))
28.57/10.36	   A^2 -> H(k, U1(d, k))
28.57/10.36	   A^2 -> H(c, b)
28.57/10.36	   A^2 -> H(c, U1(e, d))
28.57/10.36	   A^2 -> H(c, U1(d, e))
28.57/10.36	   A^2 -> H(c, c)
28.57/10.36	   A^2 -> H(c, U1(e, k))
28.57/10.36	   A^2 -> H(c, U1(k, e))
28.57/10.36	   A^2 -> H(c, e)
28.57/10.36	   A^2 -> H(c, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, k), b)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, k), c)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, k), e)
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, c), d)
28.57/10.36	   A^2 -> H(U1(e, c), k)
28.57/10.36	   A^2 -> H(U1(k, e), b)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, e), c)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, c), d)
28.57/10.36	   A^2 -> H(U1(c, e), d)
28.57/10.36	   A^2 -> H(U1(c, e), k)
28.57/10.36	   A^2 -> H(U1(c, k), d)
28.57/10.36	   A^2 -> H(U1(c, k), k)
28.57/10.36	   A^2 -> H(e, b)
28.57/10.36	   A^2 -> H(e, U1(e, d))
28.57/10.36	   A^2 -> H(e, U1(d, e))
28.57/10.36	   A^2 -> H(e, c)
28.57/10.36	   A^2 -> H(e, U1(e, k))
28.57/10.36	   A^2 -> H(e, e)
28.57/10.36	   A^2 -> H(U1(e, e), d)
28.57/10.36	   A^2 -> H(U1(e, e), k)
28.57/10.36	   A^2 -> H(U1(k, k), d)
28.57/10.36	   A^2 -> H(U1(k, k), b)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, k), c)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, d), d)
28.57/10.36	   A^2 -> H(U1(k, d), e)
28.57/10.36	   A^2 -> H(U1(k, d), k)
28.57/10.36	
28.57/10.36	The TRS R consists of the following rules:
28.57/10.36	
28.57/10.36	   f(x) -> U1(x, x)
28.57/10.36	   U1(e, x) -> x
28.57/10.36	   a -> c
28.57/10.36	   a -> d
28.57/10.36	   b -> c
28.57/10.36	   b -> d
28.57/10.36	   d -> k
28.57/10.36	   c -> e
28.57/10.36	   c -> k
28.57/10.36	
28.57/10.36	Q is empty.
28.57/10.36	We have to consider all minimal (P,Q,R)-chains.
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2345) DependencyGraphProof (EQUIVALENT)
28.57/10.36	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2346)
28.57/10.36	Obligation:
28.57/10.36	Q DP problem:
28.57/10.36	The TRS P consists of the following rules:
28.57/10.36	
28.57/10.36	   H(x, x) -> G(x, x, f(k))
28.57/10.36	   G(d, x, x) -> A^2
28.57/10.36	   A^2 -> H(f(c), f(c))
28.57/10.36	   A^2 -> H(f(d), f(d))
28.57/10.36	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.36	   A^2 -> H(f(e), f(e))
28.57/10.36	   A^2 -> H(f(k), f(k))
28.57/10.36	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.36	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.36	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.36	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.36	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.36	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, k), b)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, k), c)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, k), e)
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, d), d)
28.57/10.36	   A^2 -> H(U1(d, d), k)
28.57/10.36	   A^2 -> H(U1(e, c), c)
28.57/10.36	   A^2 -> H(U1(c, c), e)
28.57/10.36	   A^2 -> H(U1(c, c), k)
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.36	   A^2 -> H(U1(e, e), e)
28.57/10.36	   A^2 -> H(d, U1(e, b))
28.57/10.36	   A^2 -> H(d, U1(k, b))
28.57/10.36	   A^2 -> H(d, U1(c, d))
28.57/10.36	   A^2 -> H(d, U1(d, c))
28.57/10.36	   A^2 -> H(d, U1(b, e))
28.57/10.36	   A^2 -> H(d, U1(b, k))
28.57/10.36	   A^2 -> H(d, U1(e, c))
28.57/10.36	   A^2 -> H(d, U1(k, c))
28.57/10.36	   A^2 -> H(d, U1(c, e))
28.57/10.36	   A^2 -> H(d, U1(c, k))
28.57/10.36	   A^2 -> H(d, U1(e, e))
28.57/10.36	   A^2 -> H(d, U1(k, k))
28.57/10.36	   A^2 -> H(d, U1(k, d))
28.57/10.36	   A^2 -> H(d, U1(d, k))
28.57/10.36	   A^2 -> H(a, b)
28.57/10.36	   A^2 -> H(a, U1(e, d))
28.57/10.36	   A^2 -> H(a, U1(d, e))
28.57/10.36	   A^2 -> H(a, c)
28.57/10.36	   A^2 -> H(a, U1(e, k))
28.57/10.36	   A^2 -> H(a, U1(k, e))
28.57/10.36	   A^2 -> H(a, e)
28.57/10.36	   A^2 -> H(a, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, d), b)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, d), c)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, d), e)
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, a), d)
28.57/10.36	   A^2 -> H(U1(e, a), k)
28.57/10.36	   A^2 -> H(U1(k, a), d)
28.57/10.36	   A^2 -> H(U1(c, d), d)
28.57/10.36	   A^2 -> H(U1(c, d), k)
28.57/10.36	   A^2 -> H(U1(d, e), b)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, e), c)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, e), e)
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, c), d)
28.57/10.36	   A^2 -> H(U1(d, c), k)
28.57/10.36	   A^2 -> H(U1(a, e), d)
28.57/10.36	   A^2 -> H(U1(a, e), k)
28.57/10.36	   A^2 -> H(U1(a, k), d)
28.57/10.36	   A^2 -> H(U1(a, k), k)
28.57/10.36	   A^2 -> H(k, U1(e, b))
28.57/10.36	   A^2 -> H(k, U1(c, d))
28.57/10.36	   A^2 -> H(k, U1(d, c))
28.57/10.36	   A^2 -> H(k, U1(b, e))
28.57/10.36	   A^2 -> H(k, U1(b, k))
28.57/10.36	   A^2 -> H(k, U1(e, c))
28.57/10.36	   A^2 -> H(k, U1(c, e))
28.57/10.36	   A^2 -> H(k, U1(c, k))
28.57/10.36	   A^2 -> H(k, U1(e, e))
28.57/10.36	   A^2 -> H(k, U1(d, k))
28.57/10.36	   A^2 -> H(c, b)
28.57/10.36	   A^2 -> H(c, U1(e, d))
28.57/10.36	   A^2 -> H(c, U1(d, e))
28.57/10.36	   A^2 -> H(c, c)
28.57/10.36	   A^2 -> H(c, U1(e, k))
28.57/10.36	   A^2 -> H(c, U1(k, e))
28.57/10.36	   A^2 -> H(c, e)
28.57/10.36	   A^2 -> H(c, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, k), b)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, k), c)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, k), e)
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, c), d)
28.57/10.36	   A^2 -> H(U1(e, c), k)
28.57/10.36	   A^2 -> H(U1(k, e), b)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, e), c)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, c), d)
28.57/10.36	   A^2 -> H(U1(c, e), d)
28.57/10.36	   A^2 -> H(U1(c, e), k)
28.57/10.36	   A^2 -> H(U1(c, k), d)
28.57/10.36	   A^2 -> H(U1(c, k), k)
28.57/10.36	   A^2 -> H(e, b)
28.57/10.36	   A^2 -> H(e, U1(e, d))
28.57/10.36	   A^2 -> H(e, U1(d, e))
28.57/10.36	   A^2 -> H(e, c)
28.57/10.36	   A^2 -> H(e, U1(e, k))
28.57/10.36	   A^2 -> H(e, e)
28.57/10.36	   A^2 -> H(U1(e, e), d)
28.57/10.36	   A^2 -> H(U1(e, e), k)
28.57/10.36	   A^2 -> H(U1(k, k), d)
28.57/10.36	   A^2 -> H(U1(k, k), b)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, k), c)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, d), d)
28.57/10.36	
28.57/10.36	The TRS R consists of the following rules:
28.57/10.36	
28.57/10.36	   f(x) -> U1(x, x)
28.57/10.36	   U1(e, x) -> x
28.57/10.36	   a -> c
28.57/10.36	   a -> d
28.57/10.36	   b -> c
28.57/10.36	   b -> d
28.57/10.36	   d -> k
28.57/10.36	   c -> e
28.57/10.36	   c -> k
28.57/10.36	
28.57/10.36	Q is empty.
28.57/10.36	We have to consider all minimal (P,Q,R)-chains.
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2347) TransformationProof (EQUIVALENT)
28.57/10.36	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.36	
28.57/10.36	   (A^2 -> H(U1(k, k), U1(e, k)),A^2 -> H(U1(k, k), U1(e, k)))
28.57/10.36	   (A^2 -> H(U1(k, d), k),A^2 -> H(U1(k, d), k))
28.57/10.36	
28.57/10.36	
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2348)
28.57/10.36	Obligation:
28.57/10.36	Q DP problem:
28.57/10.36	The TRS P consists of the following rules:
28.57/10.36	
28.57/10.36	   H(x, x) -> G(x, x, f(k))
28.57/10.36	   G(d, x, x) -> A^2
28.57/10.36	   A^2 -> H(f(c), f(c))
28.57/10.36	   A^2 -> H(f(d), f(d))
28.57/10.36	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.36	   A^2 -> H(f(e), f(e))
28.57/10.36	   A^2 -> H(f(k), f(k))
28.57/10.36	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.36	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.36	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.36	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.36	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.36	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, k), b)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, k), c)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, k), e)
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, d), d)
28.57/10.36	   A^2 -> H(U1(d, d), k)
28.57/10.36	   A^2 -> H(U1(e, c), c)
28.57/10.36	   A^2 -> H(U1(c, c), e)
28.57/10.36	   A^2 -> H(U1(c, c), k)
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.36	   A^2 -> H(U1(e, e), e)
28.57/10.36	   A^2 -> H(d, U1(e, b))
28.57/10.36	   A^2 -> H(d, U1(k, b))
28.57/10.36	   A^2 -> H(d, U1(c, d))
28.57/10.36	   A^2 -> H(d, U1(d, c))
28.57/10.36	   A^2 -> H(d, U1(b, e))
28.57/10.36	   A^2 -> H(d, U1(b, k))
28.57/10.36	   A^2 -> H(d, U1(e, c))
28.57/10.36	   A^2 -> H(d, U1(k, c))
28.57/10.36	   A^2 -> H(d, U1(c, e))
28.57/10.36	   A^2 -> H(d, U1(c, k))
28.57/10.36	   A^2 -> H(d, U1(e, e))
28.57/10.36	   A^2 -> H(d, U1(k, k))
28.57/10.36	   A^2 -> H(d, U1(k, d))
28.57/10.36	   A^2 -> H(d, U1(d, k))
28.57/10.36	   A^2 -> H(a, b)
28.57/10.36	   A^2 -> H(a, U1(e, d))
28.57/10.36	   A^2 -> H(a, U1(d, e))
28.57/10.36	   A^2 -> H(a, c)
28.57/10.36	   A^2 -> H(a, U1(e, k))
28.57/10.36	   A^2 -> H(a, U1(k, e))
28.57/10.36	   A^2 -> H(a, e)
28.57/10.36	   A^2 -> H(a, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, d), b)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, d), c)
28.57/10.36	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, d), e)
28.57/10.36	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, a), d)
28.57/10.36	   A^2 -> H(U1(e, a), k)
28.57/10.36	   A^2 -> H(U1(k, a), d)
28.57/10.36	   A^2 -> H(U1(c, d), d)
28.57/10.36	   A^2 -> H(U1(c, d), k)
28.57/10.36	   A^2 -> H(U1(d, e), b)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, e), c)
28.57/10.36	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, e), e)
28.57/10.36	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, c), d)
28.57/10.36	   A^2 -> H(U1(d, c), k)
28.57/10.36	   A^2 -> H(U1(a, e), d)
28.57/10.36	   A^2 -> H(U1(a, e), k)
28.57/10.36	   A^2 -> H(U1(a, k), d)
28.57/10.36	   A^2 -> H(U1(a, k), k)
28.57/10.36	   A^2 -> H(k, U1(e, b))
28.57/10.36	   A^2 -> H(k, U1(c, d))
28.57/10.36	   A^2 -> H(k, U1(d, c))
28.57/10.36	   A^2 -> H(k, U1(b, e))
28.57/10.36	   A^2 -> H(k, U1(b, k))
28.57/10.36	   A^2 -> H(k, U1(e, c))
28.57/10.36	   A^2 -> H(k, U1(c, e))
28.57/10.36	   A^2 -> H(k, U1(c, k))
28.57/10.36	   A^2 -> H(k, U1(e, e))
28.57/10.36	   A^2 -> H(k, U1(d, k))
28.57/10.36	   A^2 -> H(c, b)
28.57/10.36	   A^2 -> H(c, U1(e, d))
28.57/10.36	   A^2 -> H(c, U1(d, e))
28.57/10.36	   A^2 -> H(c, c)
28.57/10.36	   A^2 -> H(c, U1(e, k))
28.57/10.36	   A^2 -> H(c, U1(k, e))
28.57/10.36	   A^2 -> H(c, e)
28.57/10.36	   A^2 -> H(c, U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, k), b)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(e, k), c)
28.57/10.36	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(e, k), e)
28.57/10.36	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(e, c), d)
28.57/10.36	   A^2 -> H(U1(e, c), k)
28.57/10.36	   A^2 -> H(U1(k, e), b)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, e), c)
28.57/10.36	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, c), d)
28.57/10.36	   A^2 -> H(U1(c, e), d)
28.57/10.36	   A^2 -> H(U1(c, e), k)
28.57/10.36	   A^2 -> H(U1(c, k), d)
28.57/10.36	   A^2 -> H(U1(c, k), k)
28.57/10.36	   A^2 -> H(e, b)
28.57/10.36	   A^2 -> H(e, U1(e, d))
28.57/10.36	   A^2 -> H(e, U1(d, e))
28.57/10.36	   A^2 -> H(e, c)
28.57/10.36	   A^2 -> H(e, U1(e, k))
28.57/10.36	   A^2 -> H(e, e)
28.57/10.36	   A^2 -> H(U1(e, e), d)
28.57/10.36	   A^2 -> H(U1(e, e), k)
28.57/10.36	   A^2 -> H(U1(k, k), d)
28.57/10.36	   A^2 -> H(U1(k, k), b)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(k, k), c)
28.57/10.36	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(k, d), d)
28.57/10.36	   A^2 -> H(U1(k, d), k)
28.57/10.36	
28.57/10.36	The TRS R consists of the following rules:
28.57/10.36	
28.57/10.36	   f(x) -> U1(x, x)
28.57/10.36	   U1(e, x) -> x
28.57/10.36	   a -> c
28.57/10.36	   a -> d
28.57/10.36	   b -> c
28.57/10.36	   b -> d
28.57/10.36	   d -> k
28.57/10.36	   c -> e
28.57/10.36	   c -> k
28.57/10.36	
28.57/10.36	Q is empty.
28.57/10.36	We have to consider all minimal (P,Q,R)-chains.
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2349) DependencyGraphProof (EQUIVALENT)
28.57/10.36	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.36	----------------------------------------
28.57/10.36	
28.57/10.36	(2350)
28.57/10.36	Obligation:
28.57/10.36	Q DP problem:
28.57/10.36	The TRS P consists of the following rules:
28.57/10.36	
28.57/10.36	   G(d, x, x) -> A^2
28.57/10.36	   A^2 -> H(f(c), f(c))
28.57/10.36	   H(x, x) -> G(x, x, f(k))
28.57/10.36	   A^2 -> H(f(d), f(d))
28.57/10.36	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.36	   A^2 -> H(f(e), f(e))
28.57/10.36	   A^2 -> H(f(k), f(k))
28.57/10.36	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.36	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.36	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.36	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.36	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.36	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.36	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, e))
28.57/10.36	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, k), b)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.36	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.36	   A^2 -> H(U1(d, k), c)
28.57/10.36	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.36	   A^2 -> H(U1(d, k), e)
28.57/10.36	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.36	   A^2 -> H(U1(d, d), d)
28.57/10.36	   A^2 -> H(U1(d, d), k)
28.57/10.36	   A^2 -> H(U1(e, c), c)
28.57/10.36	   A^2 -> H(U1(c, c), e)
28.57/10.36	   A^2 -> H(U1(c, c), k)
28.57/10.36	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.36	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.37	   A^2 -> H(U1(e, e), e)
28.57/10.37	   A^2 -> H(d, U1(e, b))
28.57/10.37	   A^2 -> H(d, U1(k, b))
28.57/10.37	   A^2 -> H(d, U1(c, d))
28.57/10.37	   A^2 -> H(d, U1(d, c))
28.57/10.37	   A^2 -> H(d, U1(b, e))
28.57/10.37	   A^2 -> H(d, U1(b, k))
28.57/10.37	   A^2 -> H(d, U1(e, c))
28.57/10.37	   A^2 -> H(d, U1(k, c))
28.57/10.37	   A^2 -> H(d, U1(c, e))
28.57/10.37	   A^2 -> H(d, U1(c, k))
28.57/10.37	   A^2 -> H(d, U1(e, e))
28.57/10.37	   A^2 -> H(d, U1(k, k))
28.57/10.37	   A^2 -> H(d, U1(k, d))
28.57/10.37	   A^2 -> H(d, U1(d, k))
28.57/10.37	   A^2 -> H(a, b)
28.57/10.37	   A^2 -> H(a, U1(e, d))
28.57/10.37	   A^2 -> H(a, U1(d, e))
28.57/10.37	   A^2 -> H(a, c)
28.57/10.37	   A^2 -> H(a, U1(e, k))
28.57/10.37	   A^2 -> H(a, U1(k, e))
28.57/10.37	   A^2 -> H(a, e)
28.57/10.37	   A^2 -> H(a, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, d), b)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, d), c)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, d), e)
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, a), d)
28.57/10.37	   A^2 -> H(U1(e, a), k)
28.57/10.37	   A^2 -> H(U1(k, a), d)
28.57/10.37	   A^2 -> H(U1(c, d), d)
28.57/10.37	   A^2 -> H(U1(c, d), k)
28.57/10.37	   A^2 -> H(U1(d, e), b)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(d, e), c)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, e), e)
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, c), d)
28.57/10.37	   A^2 -> H(U1(d, c), k)
28.57/10.37	   A^2 -> H(U1(a, e), d)
28.57/10.37	   A^2 -> H(U1(a, e), k)
28.57/10.37	   A^2 -> H(U1(a, k), d)
28.57/10.37	   A^2 -> H(U1(a, k), k)
28.57/10.37	   A^2 -> H(k, U1(e, b))
28.57/10.37	   A^2 -> H(k, U1(c, d))
28.57/10.37	   A^2 -> H(k, U1(d, c))
28.57/10.37	   A^2 -> H(k, U1(b, e))
28.57/10.37	   A^2 -> H(k, U1(b, k))
28.57/10.37	   A^2 -> H(k, U1(e, c))
28.57/10.37	   A^2 -> H(k, U1(c, e))
28.57/10.37	   A^2 -> H(k, U1(c, k))
28.57/10.37	   A^2 -> H(k, U1(e, e))
28.57/10.37	   A^2 -> H(k, U1(d, k))
28.57/10.37	   A^2 -> H(c, b)
28.57/10.37	   A^2 -> H(c, U1(e, d))
28.57/10.37	   A^2 -> H(c, U1(d, e))
28.57/10.37	   A^2 -> H(c, c)
28.57/10.37	   A^2 -> H(c, U1(e, k))
28.57/10.37	   A^2 -> H(c, U1(k, e))
28.57/10.37	   A^2 -> H(c, e)
28.57/10.37	   A^2 -> H(c, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, k), b)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, k), c)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, k), e)
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, c), d)
28.57/10.37	   A^2 -> H(U1(e, c), k)
28.57/10.37	   A^2 -> H(U1(k, e), b)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, e), c)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(k, c), d)
28.57/10.37	   A^2 -> H(U1(c, e), d)
28.57/10.37	   A^2 -> H(U1(c, e), k)
28.57/10.37	   A^2 -> H(U1(c, k), d)
28.57/10.37	   A^2 -> H(U1(c, k), k)
28.57/10.37	   A^2 -> H(e, b)
28.57/10.37	   A^2 -> H(e, U1(e, d))
28.57/10.37	   A^2 -> H(e, U1(d, e))
28.57/10.37	   A^2 -> H(e, c)
28.57/10.37	   A^2 -> H(e, U1(e, k))
28.57/10.37	   A^2 -> H(e, e)
28.57/10.37	   A^2 -> H(U1(e, e), d)
28.57/10.37	   A^2 -> H(U1(e, e), k)
28.57/10.37	   A^2 -> H(U1(k, k), d)
28.57/10.37	   A^2 -> H(U1(k, k), b)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, k), c)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, d), d)
28.57/10.37	
28.57/10.37	The TRS R consists of the following rules:
28.57/10.37	
28.57/10.37	   f(x) -> U1(x, x)
28.57/10.37	   U1(e, x) -> x
28.57/10.37	   a -> c
28.57/10.37	   a -> d
28.57/10.37	   b -> c
28.57/10.37	   b -> d
28.57/10.37	   d -> k
28.57/10.37	   c -> e
28.57/10.37	   c -> k
28.57/10.37	
28.57/10.37	Q is empty.
28.57/10.37	We have to consider all minimal (P,Q,R)-chains.
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2351) TransformationProof (EQUIVALENT)
28.57/10.37	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.37	
28.57/10.37	   (A^2 -> H(U1(k, k), U1(k, e)),A^2 -> H(U1(k, k), U1(k, e)))
28.57/10.37	
28.57/10.37	
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2352)
28.57/10.37	Obligation:
28.57/10.37	Q DP problem:
28.57/10.37	The TRS P consists of the following rules:
28.57/10.37	
28.57/10.37	   G(d, x, x) -> A^2
28.57/10.37	   A^2 -> H(f(c), f(c))
28.57/10.37	   H(x, x) -> G(x, x, f(k))
28.57/10.37	   A^2 -> H(f(d), f(d))
28.57/10.37	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.37	   A^2 -> H(f(e), f(e))
28.57/10.37	   A^2 -> H(f(k), f(k))
28.57/10.37	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.37	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.37	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.37	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.37	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.37	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.37	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.37	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, k), b)
28.57/10.37	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(d, k), c)
28.57/10.37	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, k), e)
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, d), d)
28.57/10.37	   A^2 -> H(U1(d, d), k)
28.57/10.37	   A^2 -> H(U1(e, c), c)
28.57/10.37	   A^2 -> H(U1(c, c), e)
28.57/10.37	   A^2 -> H(U1(c, c), k)
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.37	   A^2 -> H(U1(e, e), e)
28.57/10.37	   A^2 -> H(d, U1(e, b))
28.57/10.37	   A^2 -> H(d, U1(k, b))
28.57/10.37	   A^2 -> H(d, U1(c, d))
28.57/10.37	   A^2 -> H(d, U1(d, c))
28.57/10.37	   A^2 -> H(d, U1(b, e))
28.57/10.37	   A^2 -> H(d, U1(b, k))
28.57/10.37	   A^2 -> H(d, U1(e, c))
28.57/10.37	   A^2 -> H(d, U1(k, c))
28.57/10.37	   A^2 -> H(d, U1(c, e))
28.57/10.37	   A^2 -> H(d, U1(c, k))
28.57/10.37	   A^2 -> H(d, U1(e, e))
28.57/10.37	   A^2 -> H(d, U1(k, k))
28.57/10.37	   A^2 -> H(d, U1(k, d))
28.57/10.37	   A^2 -> H(d, U1(d, k))
28.57/10.37	   A^2 -> H(a, b)
28.57/10.37	   A^2 -> H(a, U1(e, d))
28.57/10.37	   A^2 -> H(a, U1(d, e))
28.57/10.37	   A^2 -> H(a, c)
28.57/10.37	   A^2 -> H(a, U1(e, k))
28.57/10.37	   A^2 -> H(a, U1(k, e))
28.57/10.37	   A^2 -> H(a, e)
28.57/10.37	   A^2 -> H(a, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, d), b)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, d), c)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, d), e)
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, a), d)
28.57/10.37	   A^2 -> H(U1(e, a), k)
28.57/10.37	   A^2 -> H(U1(k, a), d)
28.57/10.37	   A^2 -> H(U1(c, d), d)
28.57/10.37	   A^2 -> H(U1(c, d), k)
28.57/10.37	   A^2 -> H(U1(d, e), b)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(d, e), c)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, e), e)
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, c), d)
28.57/10.37	   A^2 -> H(U1(d, c), k)
28.57/10.37	   A^2 -> H(U1(a, e), d)
28.57/10.37	   A^2 -> H(U1(a, e), k)
28.57/10.37	   A^2 -> H(U1(a, k), d)
28.57/10.37	   A^2 -> H(U1(a, k), k)
28.57/10.37	   A^2 -> H(k, U1(e, b))
28.57/10.37	   A^2 -> H(k, U1(c, d))
28.57/10.37	   A^2 -> H(k, U1(d, c))
28.57/10.37	   A^2 -> H(k, U1(b, e))
28.57/10.37	   A^2 -> H(k, U1(b, k))
28.57/10.37	   A^2 -> H(k, U1(e, c))
28.57/10.37	   A^2 -> H(k, U1(c, e))
28.57/10.37	   A^2 -> H(k, U1(c, k))
28.57/10.37	   A^2 -> H(k, U1(e, e))
28.57/10.37	   A^2 -> H(k, U1(d, k))
28.57/10.37	   A^2 -> H(c, b)
28.57/10.37	   A^2 -> H(c, U1(e, d))
28.57/10.37	   A^2 -> H(c, U1(d, e))
28.57/10.37	   A^2 -> H(c, c)
28.57/10.37	   A^2 -> H(c, U1(e, k))
28.57/10.37	   A^2 -> H(c, U1(k, e))
28.57/10.37	   A^2 -> H(c, e)
28.57/10.37	   A^2 -> H(c, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, k), b)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, k), c)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, k), e)
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, c), d)
28.57/10.37	   A^2 -> H(U1(e, c), k)
28.57/10.37	   A^2 -> H(U1(k, e), b)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, e), c)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(k, c), d)
28.57/10.37	   A^2 -> H(U1(c, e), d)
28.57/10.37	   A^2 -> H(U1(c, e), k)
28.57/10.37	   A^2 -> H(U1(c, k), d)
28.57/10.37	   A^2 -> H(U1(c, k), k)
28.57/10.37	   A^2 -> H(e, b)
28.57/10.37	   A^2 -> H(e, U1(e, d))
28.57/10.37	   A^2 -> H(e, U1(d, e))
28.57/10.37	   A^2 -> H(e, c)
28.57/10.37	   A^2 -> H(e, U1(e, k))
28.57/10.37	   A^2 -> H(e, e)
28.57/10.37	   A^2 -> H(U1(e, e), d)
28.57/10.37	   A^2 -> H(U1(e, e), k)
28.57/10.37	   A^2 -> H(U1(k, k), d)
28.57/10.37	   A^2 -> H(U1(k, k), b)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, k), c)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, d), d)
28.57/10.37	   A^2 -> H(U1(k, k), U1(k, e))
28.57/10.37	
28.57/10.37	The TRS R consists of the following rules:
28.57/10.37	
28.57/10.37	   f(x) -> U1(x, x)
28.57/10.37	   U1(e, x) -> x
28.57/10.37	   a -> c
28.57/10.37	   a -> d
28.57/10.37	   b -> c
28.57/10.37	   b -> d
28.57/10.37	   d -> k
28.57/10.37	   c -> e
28.57/10.37	   c -> k
28.57/10.37	
28.57/10.37	Q is empty.
28.57/10.37	We have to consider all minimal (P,Q,R)-chains.
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2353) DependencyGraphProof (EQUIVALENT)
28.57/10.37	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2354)
28.57/10.37	Obligation:
28.57/10.37	Q DP problem:
28.57/10.37	The TRS P consists of the following rules:
28.57/10.37	
28.57/10.37	   A^2 -> H(f(c), f(c))
28.57/10.37	   H(x, x) -> G(x, x, f(k))
28.57/10.37	   G(d, x, x) -> A^2
28.57/10.37	   A^2 -> H(f(d), f(d))
28.57/10.37	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.37	   A^2 -> H(f(e), f(e))
28.57/10.37	   A^2 -> H(f(k), f(k))
28.57/10.37	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.37	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.37	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.37	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.37	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.37	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.37	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.37	   A^2 -> H(U1(k, d), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, k), b)
28.57/10.37	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(d, k), c)
28.57/10.37	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, k), e)
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, d), d)
28.57/10.37	   A^2 -> H(U1(d, d), k)
28.57/10.37	   A^2 -> H(U1(e, c), c)
28.57/10.37	   A^2 -> H(U1(c, c), e)
28.57/10.37	   A^2 -> H(U1(c, c), k)
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.37	   A^2 -> H(U1(e, e), e)
28.57/10.37	   A^2 -> H(d, U1(e, b))
28.57/10.37	   A^2 -> H(d, U1(k, b))
28.57/10.37	   A^2 -> H(d, U1(c, d))
28.57/10.37	   A^2 -> H(d, U1(d, c))
28.57/10.37	   A^2 -> H(d, U1(b, e))
28.57/10.37	   A^2 -> H(d, U1(b, k))
28.57/10.37	   A^2 -> H(d, U1(e, c))
28.57/10.37	   A^2 -> H(d, U1(k, c))
28.57/10.37	   A^2 -> H(d, U1(c, e))
28.57/10.37	   A^2 -> H(d, U1(c, k))
28.57/10.37	   A^2 -> H(d, U1(e, e))
28.57/10.37	   A^2 -> H(d, U1(k, k))
28.57/10.37	   A^2 -> H(d, U1(k, d))
28.57/10.37	   A^2 -> H(d, U1(d, k))
28.57/10.37	   A^2 -> H(a, b)
28.57/10.37	   A^2 -> H(a, U1(e, d))
28.57/10.37	   A^2 -> H(a, U1(d, e))
28.57/10.37	   A^2 -> H(a, c)
28.57/10.37	   A^2 -> H(a, U1(e, k))
28.57/10.37	   A^2 -> H(a, U1(k, e))
28.57/10.37	   A^2 -> H(a, e)
28.57/10.37	   A^2 -> H(a, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, d), b)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, d), c)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, d), e)
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, a), d)
28.57/10.37	   A^2 -> H(U1(e, a), k)
28.57/10.37	   A^2 -> H(U1(k, a), d)
28.57/10.37	   A^2 -> H(U1(c, d), d)
28.57/10.37	   A^2 -> H(U1(c, d), k)
28.57/10.37	   A^2 -> H(U1(d, e), b)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(d, e), c)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, e), e)
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, c), d)
28.57/10.37	   A^2 -> H(U1(d, c), k)
28.57/10.37	   A^2 -> H(U1(a, e), d)
28.57/10.37	   A^2 -> H(U1(a, e), k)
28.57/10.37	   A^2 -> H(U1(a, k), d)
28.57/10.37	   A^2 -> H(U1(a, k), k)
28.57/10.37	   A^2 -> H(k, U1(e, b))
28.57/10.37	   A^2 -> H(k, U1(c, d))
28.57/10.37	   A^2 -> H(k, U1(d, c))
28.57/10.37	   A^2 -> H(k, U1(b, e))
28.57/10.37	   A^2 -> H(k, U1(b, k))
28.57/10.37	   A^2 -> H(k, U1(e, c))
28.57/10.37	   A^2 -> H(k, U1(c, e))
28.57/10.37	   A^2 -> H(k, U1(c, k))
28.57/10.37	   A^2 -> H(k, U1(e, e))
28.57/10.37	   A^2 -> H(k, U1(d, k))
28.57/10.37	   A^2 -> H(c, b)
28.57/10.37	   A^2 -> H(c, U1(e, d))
28.57/10.37	   A^2 -> H(c, U1(d, e))
28.57/10.37	   A^2 -> H(c, c)
28.57/10.37	   A^2 -> H(c, U1(e, k))
28.57/10.37	   A^2 -> H(c, U1(k, e))
28.57/10.37	   A^2 -> H(c, e)
28.57/10.37	   A^2 -> H(c, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, k), b)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, k), c)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, k), e)
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, c), d)
28.57/10.37	   A^2 -> H(U1(e, c), k)
28.57/10.37	   A^2 -> H(U1(k, e), b)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, e), c)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(k, c), d)
28.57/10.37	   A^2 -> H(U1(c, e), d)
28.57/10.37	   A^2 -> H(U1(c, e), k)
28.57/10.37	   A^2 -> H(U1(c, k), d)
28.57/10.37	   A^2 -> H(U1(c, k), k)
28.57/10.37	   A^2 -> H(e, b)
28.57/10.37	   A^2 -> H(e, U1(e, d))
28.57/10.37	   A^2 -> H(e, U1(d, e))
28.57/10.37	   A^2 -> H(e, c)
28.57/10.37	   A^2 -> H(e, U1(e, k))
28.57/10.37	   A^2 -> H(e, e)
28.57/10.37	   A^2 -> H(U1(e, e), d)
28.57/10.37	   A^2 -> H(U1(e, e), k)
28.57/10.37	   A^2 -> H(U1(k, k), d)
28.57/10.37	   A^2 -> H(U1(k, k), b)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, k), c)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, d), d)
28.57/10.37	
28.57/10.37	The TRS R consists of the following rules:
28.57/10.37	
28.57/10.37	   f(x) -> U1(x, x)
28.57/10.37	   U1(e, x) -> x
28.57/10.37	   a -> c
28.57/10.37	   a -> d
28.57/10.37	   b -> c
28.57/10.37	   b -> d
28.57/10.37	   d -> k
28.57/10.37	   c -> e
28.57/10.37	   c -> k
28.57/10.37	
28.57/10.37	Q is empty.
28.57/10.37	We have to consider all minimal (P,Q,R)-chains.
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2355) TransformationProof (EQUIVALENT)
28.57/10.37	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.37	
28.57/10.37	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.57/10.37	
28.57/10.37	
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2356)
28.57/10.37	Obligation:
28.57/10.37	Q DP problem:
28.57/10.37	The TRS P consists of the following rules:
28.57/10.37	
28.57/10.37	   A^2 -> H(f(c), f(c))
28.57/10.37	   H(x, x) -> G(x, x, f(k))
28.57/10.37	   G(d, x, x) -> A^2
28.57/10.37	   A^2 -> H(f(d), f(d))
28.57/10.37	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.37	   A^2 -> H(f(e), f(e))
28.57/10.37	   A^2 -> H(f(k), f(k))
28.57/10.37	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.37	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.37	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.37	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.37	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.37	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.37	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.37	   A^2 -> H(U1(d, k), b)
28.57/10.37	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(d, k), c)
28.57/10.37	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, k), e)
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, d), d)
28.57/10.37	   A^2 -> H(U1(d, d), k)
28.57/10.37	   A^2 -> H(U1(e, c), c)
28.57/10.37	   A^2 -> H(U1(c, c), e)
28.57/10.37	   A^2 -> H(U1(c, c), k)
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.37	   A^2 -> H(U1(e, e), e)
28.57/10.37	   A^2 -> H(d, U1(e, b))
28.57/10.37	   A^2 -> H(d, U1(k, b))
28.57/10.37	   A^2 -> H(d, U1(c, d))
28.57/10.37	   A^2 -> H(d, U1(d, c))
28.57/10.37	   A^2 -> H(d, U1(b, e))
28.57/10.37	   A^2 -> H(d, U1(b, k))
28.57/10.37	   A^2 -> H(d, U1(e, c))
28.57/10.37	   A^2 -> H(d, U1(k, c))
28.57/10.37	   A^2 -> H(d, U1(c, e))
28.57/10.37	   A^2 -> H(d, U1(c, k))
28.57/10.37	   A^2 -> H(d, U1(e, e))
28.57/10.37	   A^2 -> H(d, U1(k, k))
28.57/10.37	   A^2 -> H(d, U1(k, d))
28.57/10.37	   A^2 -> H(d, U1(d, k))
28.57/10.37	   A^2 -> H(a, b)
28.57/10.37	   A^2 -> H(a, U1(e, d))
28.57/10.37	   A^2 -> H(a, U1(d, e))
28.57/10.37	   A^2 -> H(a, c)
28.57/10.37	   A^2 -> H(a, U1(e, k))
28.57/10.37	   A^2 -> H(a, U1(k, e))
28.57/10.37	   A^2 -> H(a, e)
28.57/10.37	   A^2 -> H(a, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, d), b)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, d), c)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, d), e)
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, a), d)
28.57/10.37	   A^2 -> H(U1(e, a), k)
28.57/10.37	   A^2 -> H(U1(k, a), d)
28.57/10.37	   A^2 -> H(U1(c, d), d)
28.57/10.37	   A^2 -> H(U1(c, d), k)
28.57/10.37	   A^2 -> H(U1(d, e), b)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(d, e), c)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, e), e)
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, c), d)
28.57/10.37	   A^2 -> H(U1(d, c), k)
28.57/10.37	   A^2 -> H(U1(a, e), d)
28.57/10.37	   A^2 -> H(U1(a, e), k)
28.57/10.37	   A^2 -> H(U1(a, k), d)
28.57/10.37	   A^2 -> H(U1(a, k), k)
28.57/10.37	   A^2 -> H(k, U1(e, b))
28.57/10.37	   A^2 -> H(k, U1(c, d))
28.57/10.37	   A^2 -> H(k, U1(d, c))
28.57/10.37	   A^2 -> H(k, U1(b, e))
28.57/10.37	   A^2 -> H(k, U1(b, k))
28.57/10.37	   A^2 -> H(k, U1(e, c))
28.57/10.37	   A^2 -> H(k, U1(c, e))
28.57/10.37	   A^2 -> H(k, U1(c, k))
28.57/10.37	   A^2 -> H(k, U1(e, e))
28.57/10.37	   A^2 -> H(k, U1(d, k))
28.57/10.37	   A^2 -> H(c, b)
28.57/10.37	   A^2 -> H(c, U1(e, d))
28.57/10.37	   A^2 -> H(c, U1(d, e))
28.57/10.37	   A^2 -> H(c, c)
28.57/10.37	   A^2 -> H(c, U1(e, k))
28.57/10.37	   A^2 -> H(c, U1(k, e))
28.57/10.37	   A^2 -> H(c, e)
28.57/10.37	   A^2 -> H(c, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, k), b)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, k), c)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, k), e)
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, c), d)
28.57/10.37	   A^2 -> H(U1(e, c), k)
28.57/10.37	   A^2 -> H(U1(k, e), b)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, e), c)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(k, c), d)
28.57/10.37	   A^2 -> H(U1(c, e), d)
28.57/10.37	   A^2 -> H(U1(c, e), k)
28.57/10.37	   A^2 -> H(U1(c, k), d)
28.57/10.37	   A^2 -> H(U1(c, k), k)
28.57/10.37	   A^2 -> H(e, b)
28.57/10.37	   A^2 -> H(e, U1(e, d))
28.57/10.37	   A^2 -> H(e, U1(d, e))
28.57/10.37	   A^2 -> H(e, c)
28.57/10.37	   A^2 -> H(e, U1(e, k))
28.57/10.37	   A^2 -> H(e, e)
28.57/10.37	   A^2 -> H(U1(e, e), d)
28.57/10.37	   A^2 -> H(U1(e, e), k)
28.57/10.37	   A^2 -> H(U1(k, k), d)
28.57/10.37	   A^2 -> H(U1(k, k), b)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, k), c)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, d), d)
28.57/10.37	
28.57/10.37	The TRS R consists of the following rules:
28.57/10.37	
28.57/10.37	   f(x) -> U1(x, x)
28.57/10.37	   U1(e, x) -> x
28.57/10.37	   a -> c
28.57/10.37	   a -> d
28.57/10.37	   b -> c
28.57/10.37	   b -> d
28.57/10.37	   d -> k
28.57/10.37	   c -> e
28.57/10.37	   c -> k
28.57/10.37	
28.57/10.37	Q is empty.
28.57/10.37	We have to consider all minimal (P,Q,R)-chains.
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2357) TransformationProof (EQUIVALENT)
28.57/10.37	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), b) at position [] we obtained the following new rules [LPAR04]:
28.57/10.37	
28.57/10.37	   (A^2 -> H(U1(k, k), b),A^2 -> H(U1(k, k), b))
28.57/10.37	   (A^2 -> H(U1(d, k), c),A^2 -> H(U1(d, k), c))
28.57/10.37	   (A^2 -> H(U1(d, k), d),A^2 -> H(U1(d, k), d))
28.57/10.37	
28.57/10.37	
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2358)
28.57/10.37	Obligation:
28.57/10.37	Q DP problem:
28.57/10.37	The TRS P consists of the following rules:
28.57/10.37	
28.57/10.37	   A^2 -> H(f(c), f(c))
28.57/10.37	   H(x, x) -> G(x, x, f(k))
28.57/10.37	   G(d, x, x) -> A^2
28.57/10.37	   A^2 -> H(f(d), f(d))
28.57/10.37	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.37	   A^2 -> H(f(e), f(e))
28.57/10.37	   A^2 -> H(f(k), f(k))
28.57/10.37	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.37	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.37	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.37	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.37	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.37	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.37	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.37	   A^2 -> H(U1(d, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(d, k), c)
28.57/10.37	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, k), e)
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, d), d)
28.57/10.37	   A^2 -> H(U1(d, d), k)
28.57/10.37	   A^2 -> H(U1(e, c), c)
28.57/10.37	   A^2 -> H(U1(c, c), e)
28.57/10.37	   A^2 -> H(U1(c, c), k)
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.37	   A^2 -> H(U1(e, e), e)
28.57/10.37	   A^2 -> H(d, U1(e, b))
28.57/10.37	   A^2 -> H(d, U1(k, b))
28.57/10.37	   A^2 -> H(d, U1(c, d))
28.57/10.37	   A^2 -> H(d, U1(d, c))
28.57/10.37	   A^2 -> H(d, U1(b, e))
28.57/10.37	   A^2 -> H(d, U1(b, k))
28.57/10.37	   A^2 -> H(d, U1(e, c))
28.57/10.37	   A^2 -> H(d, U1(k, c))
28.57/10.37	   A^2 -> H(d, U1(c, e))
28.57/10.37	   A^2 -> H(d, U1(c, k))
28.57/10.37	   A^2 -> H(d, U1(e, e))
28.57/10.37	   A^2 -> H(d, U1(k, k))
28.57/10.37	   A^2 -> H(d, U1(k, d))
28.57/10.37	   A^2 -> H(d, U1(d, k))
28.57/10.37	   A^2 -> H(a, b)
28.57/10.37	   A^2 -> H(a, U1(e, d))
28.57/10.37	   A^2 -> H(a, U1(d, e))
28.57/10.37	   A^2 -> H(a, c)
28.57/10.37	   A^2 -> H(a, U1(e, k))
28.57/10.37	   A^2 -> H(a, U1(k, e))
28.57/10.37	   A^2 -> H(a, e)
28.57/10.37	   A^2 -> H(a, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, d), b)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, d), c)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, d), e)
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, a), d)
28.57/10.37	   A^2 -> H(U1(e, a), k)
28.57/10.37	   A^2 -> H(U1(k, a), d)
28.57/10.37	   A^2 -> H(U1(c, d), d)
28.57/10.37	   A^2 -> H(U1(c, d), k)
28.57/10.37	   A^2 -> H(U1(d, e), b)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(d, e), c)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, e), e)
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, c), d)
28.57/10.37	   A^2 -> H(U1(d, c), k)
28.57/10.37	   A^2 -> H(U1(a, e), d)
28.57/10.37	   A^2 -> H(U1(a, e), k)
28.57/10.37	   A^2 -> H(U1(a, k), d)
28.57/10.37	   A^2 -> H(U1(a, k), k)
28.57/10.37	   A^2 -> H(k, U1(e, b))
28.57/10.37	   A^2 -> H(k, U1(c, d))
28.57/10.37	   A^2 -> H(k, U1(d, c))
28.57/10.37	   A^2 -> H(k, U1(b, e))
28.57/10.37	   A^2 -> H(k, U1(b, k))
28.57/10.37	   A^2 -> H(k, U1(e, c))
28.57/10.37	   A^2 -> H(k, U1(c, e))
28.57/10.37	   A^2 -> H(k, U1(c, k))
28.57/10.37	   A^2 -> H(k, U1(e, e))
28.57/10.37	   A^2 -> H(k, U1(d, k))
28.57/10.37	   A^2 -> H(c, b)
28.57/10.37	   A^2 -> H(c, U1(e, d))
28.57/10.37	   A^2 -> H(c, U1(d, e))
28.57/10.37	   A^2 -> H(c, c)
28.57/10.37	   A^2 -> H(c, U1(e, k))
28.57/10.37	   A^2 -> H(c, U1(k, e))
28.57/10.37	   A^2 -> H(c, e)
28.57/10.37	   A^2 -> H(c, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, k), b)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, k), c)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, k), e)
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, c), d)
28.57/10.37	   A^2 -> H(U1(e, c), k)
28.57/10.37	   A^2 -> H(U1(k, e), b)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, e), c)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(k, c), d)
28.57/10.37	   A^2 -> H(U1(c, e), d)
28.57/10.37	   A^2 -> H(U1(c, e), k)
28.57/10.37	   A^2 -> H(U1(c, k), d)
28.57/10.37	   A^2 -> H(U1(c, k), k)
28.57/10.37	   A^2 -> H(e, b)
28.57/10.37	   A^2 -> H(e, U1(e, d))
28.57/10.37	   A^2 -> H(e, U1(d, e))
28.57/10.37	   A^2 -> H(e, c)
28.57/10.37	   A^2 -> H(e, U1(e, k))
28.57/10.37	   A^2 -> H(e, e)
28.57/10.37	   A^2 -> H(U1(e, e), d)
28.57/10.37	   A^2 -> H(U1(e, e), k)
28.57/10.37	   A^2 -> H(U1(k, k), d)
28.57/10.37	   A^2 -> H(U1(k, k), b)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, k), c)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, d), d)
28.57/10.37	   A^2 -> H(U1(d, k), d)
28.57/10.37	
28.57/10.37	The TRS R consists of the following rules:
28.57/10.37	
28.57/10.37	   f(x) -> U1(x, x)
28.57/10.37	   U1(e, x) -> x
28.57/10.37	   a -> c
28.57/10.37	   a -> d
28.57/10.37	   b -> c
28.57/10.37	   b -> d
28.57/10.37	   d -> k
28.57/10.37	   c -> e
28.57/10.37	   c -> k
28.57/10.37	
28.57/10.37	Q is empty.
28.57/10.37	We have to consider all minimal (P,Q,R)-chains.
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2359) TransformationProof (EQUIVALENT)
28.57/10.37	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.37	
28.57/10.37	   (A^2 -> H(U1(k, k), U1(e, d)),A^2 -> H(U1(k, k), U1(e, d)))
28.57/10.37	   (A^2 -> H(U1(d, k), d),A^2 -> H(U1(d, k), d))
28.57/10.37	   (A^2 -> H(U1(d, k), U1(e, k)),A^2 -> H(U1(d, k), U1(e, k)))
28.57/10.37	
28.57/10.37	
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2360)
28.57/10.37	Obligation:
28.57/10.37	Q DP problem:
28.57/10.37	The TRS P consists of the following rules:
28.57/10.37	
28.57/10.37	   A^2 -> H(f(c), f(c))
28.57/10.37	   H(x, x) -> G(x, x, f(k))
28.57/10.37	   G(d, x, x) -> A^2
28.57/10.37	   A^2 -> H(f(d), f(d))
28.57/10.37	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.37	   A^2 -> H(f(e), f(e))
28.57/10.37	   A^2 -> H(f(k), f(k))
28.57/10.37	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.37	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.37	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.37	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.37	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.37	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.37	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.37	   A^2 -> H(U1(d, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(d, k), c)
28.57/10.37	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, k), e)
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, d), d)
28.57/10.37	   A^2 -> H(U1(d, d), k)
28.57/10.37	   A^2 -> H(U1(e, c), c)
28.57/10.37	   A^2 -> H(U1(c, c), e)
28.57/10.37	   A^2 -> H(U1(c, c), k)
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.37	   A^2 -> H(U1(e, e), e)
28.57/10.37	   A^2 -> H(d, U1(e, b))
28.57/10.37	   A^2 -> H(d, U1(k, b))
28.57/10.37	   A^2 -> H(d, U1(c, d))
28.57/10.37	   A^2 -> H(d, U1(d, c))
28.57/10.37	   A^2 -> H(d, U1(b, e))
28.57/10.37	   A^2 -> H(d, U1(b, k))
28.57/10.37	   A^2 -> H(d, U1(e, c))
28.57/10.37	   A^2 -> H(d, U1(k, c))
28.57/10.37	   A^2 -> H(d, U1(c, e))
28.57/10.37	   A^2 -> H(d, U1(c, k))
28.57/10.37	   A^2 -> H(d, U1(e, e))
28.57/10.37	   A^2 -> H(d, U1(k, k))
28.57/10.37	   A^2 -> H(d, U1(k, d))
28.57/10.37	   A^2 -> H(d, U1(d, k))
28.57/10.37	   A^2 -> H(a, b)
28.57/10.37	   A^2 -> H(a, U1(e, d))
28.57/10.37	   A^2 -> H(a, U1(d, e))
28.57/10.37	   A^2 -> H(a, c)
28.57/10.37	   A^2 -> H(a, U1(e, k))
28.57/10.37	   A^2 -> H(a, U1(k, e))
28.57/10.37	   A^2 -> H(a, e)
28.57/10.37	   A^2 -> H(a, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, d), b)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, d), c)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, d), e)
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, a), d)
28.57/10.37	   A^2 -> H(U1(e, a), k)
28.57/10.37	   A^2 -> H(U1(k, a), d)
28.57/10.37	   A^2 -> H(U1(c, d), d)
28.57/10.37	   A^2 -> H(U1(c, d), k)
28.57/10.37	   A^2 -> H(U1(d, e), b)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(d, e), c)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, e), e)
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, c), d)
28.57/10.37	   A^2 -> H(U1(d, c), k)
28.57/10.37	   A^2 -> H(U1(a, e), d)
28.57/10.37	   A^2 -> H(U1(a, e), k)
28.57/10.37	   A^2 -> H(U1(a, k), d)
28.57/10.37	   A^2 -> H(U1(a, k), k)
28.57/10.37	   A^2 -> H(k, U1(e, b))
28.57/10.37	   A^2 -> H(k, U1(c, d))
28.57/10.37	   A^2 -> H(k, U1(d, c))
28.57/10.37	   A^2 -> H(k, U1(b, e))
28.57/10.37	   A^2 -> H(k, U1(b, k))
28.57/10.37	   A^2 -> H(k, U1(e, c))
28.57/10.37	   A^2 -> H(k, U1(c, e))
28.57/10.37	   A^2 -> H(k, U1(c, k))
28.57/10.37	   A^2 -> H(k, U1(e, e))
28.57/10.37	   A^2 -> H(k, U1(d, k))
28.57/10.37	   A^2 -> H(c, b)
28.57/10.37	   A^2 -> H(c, U1(e, d))
28.57/10.37	   A^2 -> H(c, U1(d, e))
28.57/10.37	   A^2 -> H(c, c)
28.57/10.37	   A^2 -> H(c, U1(e, k))
28.57/10.37	   A^2 -> H(c, U1(k, e))
28.57/10.37	   A^2 -> H(c, e)
28.57/10.37	   A^2 -> H(c, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, k), b)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, k), c)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, k), e)
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, c), d)
28.57/10.37	   A^2 -> H(U1(e, c), k)
28.57/10.37	   A^2 -> H(U1(k, e), b)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, e), c)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(k, c), d)
28.57/10.37	   A^2 -> H(U1(c, e), d)
28.57/10.37	   A^2 -> H(U1(c, e), k)
28.57/10.37	   A^2 -> H(U1(c, k), d)
28.57/10.37	   A^2 -> H(U1(c, k), k)
28.57/10.37	   A^2 -> H(e, b)
28.57/10.37	   A^2 -> H(e, U1(e, d))
28.57/10.37	   A^2 -> H(e, U1(d, e))
28.57/10.37	   A^2 -> H(e, c)
28.57/10.37	   A^2 -> H(e, U1(e, k))
28.57/10.37	   A^2 -> H(e, e)
28.57/10.37	   A^2 -> H(U1(e, e), d)
28.57/10.37	   A^2 -> H(U1(e, e), k)
28.57/10.37	   A^2 -> H(U1(k, k), d)
28.57/10.37	   A^2 -> H(U1(k, k), b)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, k), c)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, d), d)
28.57/10.37	   A^2 -> H(U1(d, k), d)
28.57/10.37	
28.57/10.37	The TRS R consists of the following rules:
28.57/10.37	
28.57/10.37	   f(x) -> U1(x, x)
28.57/10.37	   U1(e, x) -> x
28.57/10.37	   a -> c
28.57/10.37	   a -> d
28.57/10.37	   b -> c
28.57/10.37	   b -> d
28.57/10.37	   d -> k
28.57/10.37	   c -> e
28.57/10.37	   c -> k
28.57/10.37	
28.57/10.37	Q is empty.
28.57/10.37	We have to consider all minimal (P,Q,R)-chains.
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2361) TransformationProof (EQUIVALENT)
28.57/10.37	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.37	
28.57/10.37	   (A^2 -> H(U1(k, k), U1(d, e)),A^2 -> H(U1(k, k), U1(d, e)))
28.57/10.37	   (A^2 -> H(U1(d, k), U1(k, e)),A^2 -> H(U1(d, k), U1(k, e)))
28.57/10.37	
28.57/10.37	
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2362)
28.57/10.37	Obligation:
28.57/10.37	Q DP problem:
28.57/10.37	The TRS P consists of the following rules:
28.57/10.37	
28.57/10.37	   A^2 -> H(f(c), f(c))
28.57/10.37	   H(x, x) -> G(x, x, f(k))
28.57/10.37	   G(d, x, x) -> A^2
28.57/10.37	   A^2 -> H(f(d), f(d))
28.57/10.37	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.37	   A^2 -> H(f(e), f(e))
28.57/10.37	   A^2 -> H(f(k), f(k))
28.57/10.37	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.37	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.37	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.37	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.37	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.37	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.37	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.37	   A^2 -> H(U1(d, k), c)
28.57/10.37	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, k), e)
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, d), d)
28.57/10.37	   A^2 -> H(U1(d, d), k)
28.57/10.37	   A^2 -> H(U1(e, c), c)
28.57/10.37	   A^2 -> H(U1(c, c), e)
28.57/10.37	   A^2 -> H(U1(c, c), k)
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.37	   A^2 -> H(U1(e, e), e)
28.57/10.37	   A^2 -> H(d, U1(e, b))
28.57/10.37	   A^2 -> H(d, U1(k, b))
28.57/10.37	   A^2 -> H(d, U1(c, d))
28.57/10.37	   A^2 -> H(d, U1(d, c))
28.57/10.37	   A^2 -> H(d, U1(b, e))
28.57/10.37	   A^2 -> H(d, U1(b, k))
28.57/10.37	   A^2 -> H(d, U1(e, c))
28.57/10.37	   A^2 -> H(d, U1(k, c))
28.57/10.37	   A^2 -> H(d, U1(c, e))
28.57/10.37	   A^2 -> H(d, U1(c, k))
28.57/10.37	   A^2 -> H(d, U1(e, e))
28.57/10.37	   A^2 -> H(d, U1(k, k))
28.57/10.37	   A^2 -> H(d, U1(k, d))
28.57/10.37	   A^2 -> H(d, U1(d, k))
28.57/10.37	   A^2 -> H(a, b)
28.57/10.37	   A^2 -> H(a, U1(e, d))
28.57/10.37	   A^2 -> H(a, U1(d, e))
28.57/10.37	   A^2 -> H(a, c)
28.57/10.37	   A^2 -> H(a, U1(e, k))
28.57/10.37	   A^2 -> H(a, U1(k, e))
28.57/10.37	   A^2 -> H(a, e)
28.57/10.37	   A^2 -> H(a, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, d), b)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, d), c)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, d), e)
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, a), d)
28.57/10.37	   A^2 -> H(U1(e, a), k)
28.57/10.37	   A^2 -> H(U1(k, a), d)
28.57/10.37	   A^2 -> H(U1(c, d), d)
28.57/10.37	   A^2 -> H(U1(c, d), k)
28.57/10.37	   A^2 -> H(U1(d, e), b)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(d, e), c)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, e), e)
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, c), d)
28.57/10.37	   A^2 -> H(U1(d, c), k)
28.57/10.37	   A^2 -> H(U1(a, e), d)
28.57/10.37	   A^2 -> H(U1(a, e), k)
28.57/10.37	   A^2 -> H(U1(a, k), d)
28.57/10.37	   A^2 -> H(U1(a, k), k)
28.57/10.37	   A^2 -> H(k, U1(e, b))
28.57/10.37	   A^2 -> H(k, U1(c, d))
28.57/10.37	   A^2 -> H(k, U1(d, c))
28.57/10.37	   A^2 -> H(k, U1(b, e))
28.57/10.37	   A^2 -> H(k, U1(b, k))
28.57/10.37	   A^2 -> H(k, U1(e, c))
28.57/10.37	   A^2 -> H(k, U1(c, e))
28.57/10.37	   A^2 -> H(k, U1(c, k))
28.57/10.37	   A^2 -> H(k, U1(e, e))
28.57/10.37	   A^2 -> H(k, U1(d, k))
28.57/10.37	   A^2 -> H(c, b)
28.57/10.37	   A^2 -> H(c, U1(e, d))
28.57/10.37	   A^2 -> H(c, U1(d, e))
28.57/10.37	   A^2 -> H(c, c)
28.57/10.37	   A^2 -> H(c, U1(e, k))
28.57/10.37	   A^2 -> H(c, U1(k, e))
28.57/10.37	   A^2 -> H(c, e)
28.57/10.37	   A^2 -> H(c, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, k), b)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, k), c)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, k), e)
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, c), d)
28.57/10.37	   A^2 -> H(U1(e, c), k)
28.57/10.37	   A^2 -> H(U1(k, e), b)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, e), c)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(k, c), d)
28.57/10.37	   A^2 -> H(U1(c, e), d)
28.57/10.37	   A^2 -> H(U1(c, e), k)
28.57/10.37	   A^2 -> H(U1(c, k), d)
28.57/10.37	   A^2 -> H(U1(c, k), k)
28.57/10.37	   A^2 -> H(e, b)
28.57/10.37	   A^2 -> H(e, U1(e, d))
28.57/10.37	   A^2 -> H(e, U1(d, e))
28.57/10.37	   A^2 -> H(e, c)
28.57/10.37	   A^2 -> H(e, U1(e, k))
28.57/10.37	   A^2 -> H(e, e)
28.57/10.37	   A^2 -> H(U1(e, e), d)
28.57/10.37	   A^2 -> H(U1(e, e), k)
28.57/10.37	   A^2 -> H(U1(k, k), d)
28.57/10.37	   A^2 -> H(U1(k, k), b)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, k), c)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, d), d)
28.57/10.37	   A^2 -> H(U1(d, k), d)
28.57/10.37	
28.57/10.37	The TRS R consists of the following rules:
28.57/10.37	
28.57/10.37	   f(x) -> U1(x, x)
28.57/10.37	   U1(e, x) -> x
28.57/10.37	   a -> c
28.57/10.37	   a -> d
28.57/10.37	   b -> c
28.57/10.37	   b -> d
28.57/10.37	   d -> k
28.57/10.37	   c -> e
28.57/10.37	   c -> k
28.57/10.37	
28.57/10.37	Q is empty.
28.57/10.37	We have to consider all minimal (P,Q,R)-chains.
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2363) TransformationProof (EQUIVALENT)
28.57/10.37	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), c) at position [] we obtained the following new rules [LPAR04]:
28.57/10.37	
28.57/10.37	   (A^2 -> H(U1(k, k), c),A^2 -> H(U1(k, k), c))
28.57/10.37	   (A^2 -> H(U1(d, k), e),A^2 -> H(U1(d, k), e))
28.57/10.37	   (A^2 -> H(U1(d, k), k),A^2 -> H(U1(d, k), k))
28.57/10.37	
28.57/10.37	
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2364)
28.57/10.37	Obligation:
28.57/10.37	Q DP problem:
28.57/10.37	The TRS P consists of the following rules:
28.57/10.37	
28.57/10.37	   A^2 -> H(f(c), f(c))
28.57/10.37	   H(x, x) -> G(x, x, f(k))
28.57/10.37	   G(d, x, x) -> A^2
28.57/10.37	   A^2 -> H(f(d), f(d))
28.57/10.37	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.37	   A^2 -> H(f(e), f(e))
28.57/10.37	   A^2 -> H(f(k), f(k))
28.57/10.37	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.37	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.37	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.37	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.37	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.37	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.37	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.37	   A^2 -> H(U1(d, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, k), e)
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, d), d)
28.57/10.37	   A^2 -> H(U1(d, d), k)
28.57/10.37	   A^2 -> H(U1(e, c), c)
28.57/10.37	   A^2 -> H(U1(c, c), e)
28.57/10.37	   A^2 -> H(U1(c, c), k)
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.37	   A^2 -> H(U1(e, e), e)
28.57/10.37	   A^2 -> H(d, U1(e, b))
28.57/10.37	   A^2 -> H(d, U1(k, b))
28.57/10.37	   A^2 -> H(d, U1(c, d))
28.57/10.37	   A^2 -> H(d, U1(d, c))
28.57/10.37	   A^2 -> H(d, U1(b, e))
28.57/10.37	   A^2 -> H(d, U1(b, k))
28.57/10.37	   A^2 -> H(d, U1(e, c))
28.57/10.37	   A^2 -> H(d, U1(k, c))
28.57/10.37	   A^2 -> H(d, U1(c, e))
28.57/10.37	   A^2 -> H(d, U1(c, k))
28.57/10.37	   A^2 -> H(d, U1(e, e))
28.57/10.37	   A^2 -> H(d, U1(k, k))
28.57/10.37	   A^2 -> H(d, U1(k, d))
28.57/10.37	   A^2 -> H(d, U1(d, k))
28.57/10.37	   A^2 -> H(a, b)
28.57/10.37	   A^2 -> H(a, U1(e, d))
28.57/10.37	   A^2 -> H(a, U1(d, e))
28.57/10.37	   A^2 -> H(a, c)
28.57/10.37	   A^2 -> H(a, U1(e, k))
28.57/10.37	   A^2 -> H(a, U1(k, e))
28.57/10.37	   A^2 -> H(a, e)
28.57/10.37	   A^2 -> H(a, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, d), b)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, d), c)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, d), e)
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, a), d)
28.57/10.37	   A^2 -> H(U1(e, a), k)
28.57/10.37	   A^2 -> H(U1(k, a), d)
28.57/10.37	   A^2 -> H(U1(c, d), d)
28.57/10.37	   A^2 -> H(U1(c, d), k)
28.57/10.37	   A^2 -> H(U1(d, e), b)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(d, e), c)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, e), e)
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, c), d)
28.57/10.37	   A^2 -> H(U1(d, c), k)
28.57/10.37	   A^2 -> H(U1(a, e), d)
28.57/10.37	   A^2 -> H(U1(a, e), k)
28.57/10.37	   A^2 -> H(U1(a, k), d)
28.57/10.37	   A^2 -> H(U1(a, k), k)
28.57/10.37	   A^2 -> H(k, U1(e, b))
28.57/10.37	   A^2 -> H(k, U1(c, d))
28.57/10.37	   A^2 -> H(k, U1(d, c))
28.57/10.37	   A^2 -> H(k, U1(b, e))
28.57/10.37	   A^2 -> H(k, U1(b, k))
28.57/10.37	   A^2 -> H(k, U1(e, c))
28.57/10.37	   A^2 -> H(k, U1(c, e))
28.57/10.37	   A^2 -> H(k, U1(c, k))
28.57/10.37	   A^2 -> H(k, U1(e, e))
28.57/10.37	   A^2 -> H(k, U1(d, k))
28.57/10.37	   A^2 -> H(c, b)
28.57/10.37	   A^2 -> H(c, U1(e, d))
28.57/10.37	   A^2 -> H(c, U1(d, e))
28.57/10.37	   A^2 -> H(c, c)
28.57/10.37	   A^2 -> H(c, U1(e, k))
28.57/10.37	   A^2 -> H(c, U1(k, e))
28.57/10.37	   A^2 -> H(c, e)
28.57/10.37	   A^2 -> H(c, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, k), b)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, k), c)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, k), e)
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, c), d)
28.57/10.37	   A^2 -> H(U1(e, c), k)
28.57/10.37	   A^2 -> H(U1(k, e), b)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, e), c)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(k, c), d)
28.57/10.37	   A^2 -> H(U1(c, e), d)
28.57/10.37	   A^2 -> H(U1(c, e), k)
28.57/10.37	   A^2 -> H(U1(c, k), d)
28.57/10.37	   A^2 -> H(U1(c, k), k)
28.57/10.37	   A^2 -> H(e, b)
28.57/10.37	   A^2 -> H(e, U1(e, d))
28.57/10.37	   A^2 -> H(e, U1(d, e))
28.57/10.37	   A^2 -> H(e, c)
28.57/10.37	   A^2 -> H(e, U1(e, k))
28.57/10.37	   A^2 -> H(e, e)
28.57/10.37	   A^2 -> H(U1(e, e), d)
28.57/10.37	   A^2 -> H(U1(e, e), k)
28.57/10.37	   A^2 -> H(U1(k, k), d)
28.57/10.37	   A^2 -> H(U1(k, k), b)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, k), c)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, d), d)
28.57/10.37	   A^2 -> H(U1(d, k), d)
28.57/10.37	   A^2 -> H(U1(d, k), k)
28.57/10.37	
28.57/10.37	The TRS R consists of the following rules:
28.57/10.37	
28.57/10.37	   f(x) -> U1(x, x)
28.57/10.37	   U1(e, x) -> x
28.57/10.37	   a -> c
28.57/10.37	   a -> d
28.57/10.37	   b -> c
28.57/10.37	   b -> d
28.57/10.37	   d -> k
28.57/10.37	   c -> e
28.57/10.37	   c -> k
28.57/10.37	
28.57/10.37	Q is empty.
28.57/10.37	We have to consider all minimal (P,Q,R)-chains.
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2365) TransformationProof (EQUIVALENT)
28.57/10.37	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.37	
28.57/10.37	   (A^2 -> H(U1(k, k), U1(e, k)),A^2 -> H(U1(k, k), U1(e, k)))
28.57/10.37	   (A^2 -> H(U1(d, k), k),A^2 -> H(U1(d, k), k))
28.57/10.37	
28.57/10.37	
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2366)
28.57/10.37	Obligation:
28.57/10.37	Q DP problem:
28.57/10.37	The TRS P consists of the following rules:
28.57/10.37	
28.57/10.37	   A^2 -> H(f(c), f(c))
28.57/10.37	   H(x, x) -> G(x, x, f(k))
28.57/10.37	   G(d, x, x) -> A^2
28.57/10.37	   A^2 -> H(f(d), f(d))
28.57/10.37	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.37	   A^2 -> H(f(e), f(e))
28.57/10.37	   A^2 -> H(f(k), f(k))
28.57/10.37	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.37	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.37	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.37	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.37	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.37	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.37	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, k), e)
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, d), d)
28.57/10.37	   A^2 -> H(U1(d, d), k)
28.57/10.37	   A^2 -> H(U1(e, c), c)
28.57/10.37	   A^2 -> H(U1(c, c), e)
28.57/10.37	   A^2 -> H(U1(c, c), k)
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.37	   A^2 -> H(U1(e, e), e)
28.57/10.37	   A^2 -> H(d, U1(e, b))
28.57/10.37	   A^2 -> H(d, U1(k, b))
28.57/10.37	   A^2 -> H(d, U1(c, d))
28.57/10.37	   A^2 -> H(d, U1(d, c))
28.57/10.37	   A^2 -> H(d, U1(b, e))
28.57/10.37	   A^2 -> H(d, U1(b, k))
28.57/10.37	   A^2 -> H(d, U1(e, c))
28.57/10.37	   A^2 -> H(d, U1(k, c))
28.57/10.37	   A^2 -> H(d, U1(c, e))
28.57/10.37	   A^2 -> H(d, U1(c, k))
28.57/10.37	   A^2 -> H(d, U1(e, e))
28.57/10.37	   A^2 -> H(d, U1(k, k))
28.57/10.37	   A^2 -> H(d, U1(k, d))
28.57/10.37	   A^2 -> H(d, U1(d, k))
28.57/10.37	   A^2 -> H(a, b)
28.57/10.37	   A^2 -> H(a, U1(e, d))
28.57/10.37	   A^2 -> H(a, U1(d, e))
28.57/10.37	   A^2 -> H(a, c)
28.57/10.37	   A^2 -> H(a, U1(e, k))
28.57/10.37	   A^2 -> H(a, U1(k, e))
28.57/10.37	   A^2 -> H(a, e)
28.57/10.37	   A^2 -> H(a, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, d), b)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, d), c)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, d), e)
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, a), d)
28.57/10.37	   A^2 -> H(U1(e, a), k)
28.57/10.37	   A^2 -> H(U1(k, a), d)
28.57/10.37	   A^2 -> H(U1(c, d), d)
28.57/10.37	   A^2 -> H(U1(c, d), k)
28.57/10.37	   A^2 -> H(U1(d, e), b)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(d, e), c)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, e), e)
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, c), d)
28.57/10.37	   A^2 -> H(U1(d, c), k)
28.57/10.37	   A^2 -> H(U1(a, e), d)
28.57/10.37	   A^2 -> H(U1(a, e), k)
28.57/10.37	   A^2 -> H(U1(a, k), d)
28.57/10.37	   A^2 -> H(U1(a, k), k)
28.57/10.37	   A^2 -> H(k, U1(e, b))
28.57/10.37	   A^2 -> H(k, U1(c, d))
28.57/10.37	   A^2 -> H(k, U1(d, c))
28.57/10.37	   A^2 -> H(k, U1(b, e))
28.57/10.37	   A^2 -> H(k, U1(b, k))
28.57/10.37	   A^2 -> H(k, U1(e, c))
28.57/10.37	   A^2 -> H(k, U1(c, e))
28.57/10.37	   A^2 -> H(k, U1(c, k))
28.57/10.37	   A^2 -> H(k, U1(e, e))
28.57/10.37	   A^2 -> H(k, U1(d, k))
28.57/10.37	   A^2 -> H(c, b)
28.57/10.37	   A^2 -> H(c, U1(e, d))
28.57/10.37	   A^2 -> H(c, U1(d, e))
28.57/10.37	   A^2 -> H(c, c)
28.57/10.37	   A^2 -> H(c, U1(e, k))
28.57/10.37	   A^2 -> H(c, U1(k, e))
28.57/10.37	   A^2 -> H(c, e)
28.57/10.37	   A^2 -> H(c, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, k), b)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, k), c)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, k), e)
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, c), d)
28.57/10.37	   A^2 -> H(U1(e, c), k)
28.57/10.37	   A^2 -> H(U1(k, e), b)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, e), c)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(k, c), d)
28.57/10.37	   A^2 -> H(U1(c, e), d)
28.57/10.37	   A^2 -> H(U1(c, e), k)
28.57/10.37	   A^2 -> H(U1(c, k), d)
28.57/10.37	   A^2 -> H(U1(c, k), k)
28.57/10.37	   A^2 -> H(e, b)
28.57/10.37	   A^2 -> H(e, U1(e, d))
28.57/10.37	   A^2 -> H(e, U1(d, e))
28.57/10.37	   A^2 -> H(e, c)
28.57/10.37	   A^2 -> H(e, U1(e, k))
28.57/10.37	   A^2 -> H(e, e)
28.57/10.37	   A^2 -> H(U1(e, e), d)
28.57/10.37	   A^2 -> H(U1(e, e), k)
28.57/10.37	   A^2 -> H(U1(k, k), d)
28.57/10.37	   A^2 -> H(U1(k, k), b)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, k), c)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, d), d)
28.57/10.37	   A^2 -> H(U1(d, k), d)
28.57/10.37	   A^2 -> H(U1(d, k), k)
28.57/10.37	
28.57/10.37	The TRS R consists of the following rules:
28.57/10.37	
28.57/10.37	   f(x) -> U1(x, x)
28.57/10.37	   U1(e, x) -> x
28.57/10.37	   a -> c
28.57/10.37	   a -> d
28.57/10.37	   b -> c
28.57/10.37	   b -> d
28.57/10.37	   d -> k
28.57/10.37	   c -> e
28.57/10.37	   c -> k
28.57/10.37	
28.57/10.37	Q is empty.
28.57/10.37	We have to consider all minimal (P,Q,R)-chains.
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2367) TransformationProof (EQUIVALENT)
28.57/10.37	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.37	
28.57/10.37	   (A^2 -> H(U1(k, k), U1(k, e)),A^2 -> H(U1(k, k), U1(k, e)))
28.57/10.37	
28.57/10.37	
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2368)
28.57/10.37	Obligation:
28.57/10.37	Q DP problem:
28.57/10.37	The TRS P consists of the following rules:
28.57/10.37	
28.57/10.37	   A^2 -> H(f(c), f(c))
28.57/10.37	   H(x, x) -> G(x, x, f(k))
28.57/10.37	   G(d, x, x) -> A^2
28.57/10.37	   A^2 -> H(f(d), f(d))
28.57/10.37	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.37	   A^2 -> H(f(e), f(e))
28.57/10.37	   A^2 -> H(f(k), f(k))
28.57/10.37	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.37	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.37	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.37	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.37	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.37	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.37	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.37	   A^2 -> H(U1(d, k), e)
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, d), d)
28.57/10.37	   A^2 -> H(U1(d, d), k)
28.57/10.37	   A^2 -> H(U1(e, c), c)
28.57/10.37	   A^2 -> H(U1(c, c), e)
28.57/10.37	   A^2 -> H(U1(c, c), k)
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.37	   A^2 -> H(U1(e, e), e)
28.57/10.37	   A^2 -> H(d, U1(e, b))
28.57/10.37	   A^2 -> H(d, U1(k, b))
28.57/10.37	   A^2 -> H(d, U1(c, d))
28.57/10.37	   A^2 -> H(d, U1(d, c))
28.57/10.37	   A^2 -> H(d, U1(b, e))
28.57/10.37	   A^2 -> H(d, U1(b, k))
28.57/10.37	   A^2 -> H(d, U1(e, c))
28.57/10.37	   A^2 -> H(d, U1(k, c))
28.57/10.37	   A^2 -> H(d, U1(c, e))
28.57/10.37	   A^2 -> H(d, U1(c, k))
28.57/10.37	   A^2 -> H(d, U1(e, e))
28.57/10.37	   A^2 -> H(d, U1(k, k))
28.57/10.37	   A^2 -> H(d, U1(k, d))
28.57/10.37	   A^2 -> H(d, U1(d, k))
28.57/10.37	   A^2 -> H(a, b)
28.57/10.37	   A^2 -> H(a, U1(e, d))
28.57/10.37	   A^2 -> H(a, U1(d, e))
28.57/10.37	   A^2 -> H(a, c)
28.57/10.37	   A^2 -> H(a, U1(e, k))
28.57/10.37	   A^2 -> H(a, U1(k, e))
28.57/10.37	   A^2 -> H(a, e)
28.57/10.37	   A^2 -> H(a, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, d), b)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, d), c)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, d), e)
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, a), d)
28.57/10.37	   A^2 -> H(U1(e, a), k)
28.57/10.37	   A^2 -> H(U1(k, a), d)
28.57/10.37	   A^2 -> H(U1(c, d), d)
28.57/10.37	   A^2 -> H(U1(c, d), k)
28.57/10.37	   A^2 -> H(U1(d, e), b)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(d, e), c)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, e), e)
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, c), d)
28.57/10.37	   A^2 -> H(U1(d, c), k)
28.57/10.37	   A^2 -> H(U1(a, e), d)
28.57/10.37	   A^2 -> H(U1(a, e), k)
28.57/10.37	   A^2 -> H(U1(a, k), d)
28.57/10.37	   A^2 -> H(U1(a, k), k)
28.57/10.37	   A^2 -> H(k, U1(e, b))
28.57/10.37	   A^2 -> H(k, U1(c, d))
28.57/10.37	   A^2 -> H(k, U1(d, c))
28.57/10.37	   A^2 -> H(k, U1(b, e))
28.57/10.37	   A^2 -> H(k, U1(b, k))
28.57/10.37	   A^2 -> H(k, U1(e, c))
28.57/10.37	   A^2 -> H(k, U1(c, e))
28.57/10.37	   A^2 -> H(k, U1(c, k))
28.57/10.37	   A^2 -> H(k, U1(e, e))
28.57/10.37	   A^2 -> H(k, U1(d, k))
28.57/10.37	   A^2 -> H(c, b)
28.57/10.37	   A^2 -> H(c, U1(e, d))
28.57/10.37	   A^2 -> H(c, U1(d, e))
28.57/10.37	   A^2 -> H(c, c)
28.57/10.37	   A^2 -> H(c, U1(e, k))
28.57/10.37	   A^2 -> H(c, U1(k, e))
28.57/10.37	   A^2 -> H(c, e)
28.57/10.37	   A^2 -> H(c, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, k), b)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, k), c)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, k), e)
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, c), d)
28.57/10.37	   A^2 -> H(U1(e, c), k)
28.57/10.37	   A^2 -> H(U1(k, e), b)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, e), c)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(k, c), d)
28.57/10.37	   A^2 -> H(U1(c, e), d)
28.57/10.37	   A^2 -> H(U1(c, e), k)
28.57/10.37	   A^2 -> H(U1(c, k), d)
28.57/10.37	   A^2 -> H(U1(c, k), k)
28.57/10.37	   A^2 -> H(e, b)
28.57/10.37	   A^2 -> H(e, U1(e, d))
28.57/10.37	   A^2 -> H(e, U1(d, e))
28.57/10.37	   A^2 -> H(e, c)
28.57/10.37	   A^2 -> H(e, U1(e, k))
28.57/10.37	   A^2 -> H(e, e)
28.57/10.37	   A^2 -> H(U1(e, e), d)
28.57/10.37	   A^2 -> H(U1(e, e), k)
28.57/10.37	   A^2 -> H(U1(k, k), d)
28.57/10.37	   A^2 -> H(U1(k, k), b)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, k), c)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, d), d)
28.57/10.37	   A^2 -> H(U1(d, k), d)
28.57/10.37	   A^2 -> H(U1(d, k), k)
28.57/10.37	   A^2 -> H(U1(k, k), U1(k, e))
28.57/10.37	
28.57/10.37	The TRS R consists of the following rules:
28.57/10.37	
28.57/10.37	   f(x) -> U1(x, x)
28.57/10.37	   U1(e, x) -> x
28.57/10.37	   a -> c
28.57/10.37	   a -> d
28.57/10.37	   b -> c
28.57/10.37	   b -> d
28.57/10.37	   d -> k
28.57/10.37	   c -> e
28.57/10.37	   c -> k
28.57/10.37	
28.57/10.37	Q is empty.
28.57/10.37	We have to consider all minimal (P,Q,R)-chains.
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2369) DependencyGraphProof (EQUIVALENT)
28.57/10.37	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2370)
28.57/10.37	Obligation:
28.57/10.37	Q DP problem:
28.57/10.37	The TRS P consists of the following rules:
28.57/10.37	
28.57/10.37	   H(x, x) -> G(x, x, f(k))
28.57/10.37	   G(d, x, x) -> A^2
28.57/10.37	   A^2 -> H(f(c), f(c))
28.57/10.37	   A^2 -> H(f(d), f(d))
28.57/10.37	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.37	   A^2 -> H(f(e), f(e))
28.57/10.37	   A^2 -> H(f(k), f(k))
28.57/10.37	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.37	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.37	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.37	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.37	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.37	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.37	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.37	   A^2 -> H(U1(d, k), e)
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, d), d)
28.57/10.37	   A^2 -> H(U1(d, d), k)
28.57/10.37	   A^2 -> H(U1(e, c), c)
28.57/10.37	   A^2 -> H(U1(c, c), e)
28.57/10.37	   A^2 -> H(U1(c, c), k)
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.37	   A^2 -> H(U1(e, e), e)
28.57/10.37	   A^2 -> H(d, U1(e, b))
28.57/10.37	   A^2 -> H(d, U1(k, b))
28.57/10.37	   A^2 -> H(d, U1(c, d))
28.57/10.37	   A^2 -> H(d, U1(d, c))
28.57/10.37	   A^2 -> H(d, U1(b, e))
28.57/10.37	   A^2 -> H(d, U1(b, k))
28.57/10.37	   A^2 -> H(d, U1(e, c))
28.57/10.37	   A^2 -> H(d, U1(k, c))
28.57/10.37	   A^2 -> H(d, U1(c, e))
28.57/10.37	   A^2 -> H(d, U1(c, k))
28.57/10.37	   A^2 -> H(d, U1(e, e))
28.57/10.37	   A^2 -> H(d, U1(k, k))
28.57/10.37	   A^2 -> H(d, U1(k, d))
28.57/10.37	   A^2 -> H(d, U1(d, k))
28.57/10.37	   A^2 -> H(a, b)
28.57/10.37	   A^2 -> H(a, U1(e, d))
28.57/10.37	   A^2 -> H(a, U1(d, e))
28.57/10.37	   A^2 -> H(a, c)
28.57/10.37	   A^2 -> H(a, U1(e, k))
28.57/10.37	   A^2 -> H(a, U1(k, e))
28.57/10.37	   A^2 -> H(a, e)
28.57/10.37	   A^2 -> H(a, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, d), b)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, d), c)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, d), e)
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, a), d)
28.57/10.37	   A^2 -> H(U1(e, a), k)
28.57/10.37	   A^2 -> H(U1(k, a), d)
28.57/10.37	   A^2 -> H(U1(c, d), d)
28.57/10.37	   A^2 -> H(U1(c, d), k)
28.57/10.37	   A^2 -> H(U1(d, e), b)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(d, e), c)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, e), e)
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, c), d)
28.57/10.37	   A^2 -> H(U1(d, c), k)
28.57/10.37	   A^2 -> H(U1(a, e), d)
28.57/10.37	   A^2 -> H(U1(a, e), k)
28.57/10.37	   A^2 -> H(U1(a, k), d)
28.57/10.37	   A^2 -> H(U1(a, k), k)
28.57/10.37	   A^2 -> H(k, U1(e, b))
28.57/10.37	   A^2 -> H(k, U1(c, d))
28.57/10.37	   A^2 -> H(k, U1(d, c))
28.57/10.37	   A^2 -> H(k, U1(b, e))
28.57/10.37	   A^2 -> H(k, U1(b, k))
28.57/10.37	   A^2 -> H(k, U1(e, c))
28.57/10.37	   A^2 -> H(k, U1(c, e))
28.57/10.37	   A^2 -> H(k, U1(c, k))
28.57/10.37	   A^2 -> H(k, U1(e, e))
28.57/10.37	   A^2 -> H(k, U1(d, k))
28.57/10.37	   A^2 -> H(c, b)
28.57/10.37	   A^2 -> H(c, U1(e, d))
28.57/10.37	   A^2 -> H(c, U1(d, e))
28.57/10.37	   A^2 -> H(c, c)
28.57/10.37	   A^2 -> H(c, U1(e, k))
28.57/10.37	   A^2 -> H(c, U1(k, e))
28.57/10.37	   A^2 -> H(c, e)
28.57/10.37	   A^2 -> H(c, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, k), b)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, k), c)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, k), e)
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, c), d)
28.57/10.37	   A^2 -> H(U1(e, c), k)
28.57/10.37	   A^2 -> H(U1(k, e), b)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, e), c)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(k, c), d)
28.57/10.37	   A^2 -> H(U1(c, e), d)
28.57/10.37	   A^2 -> H(U1(c, e), k)
28.57/10.37	   A^2 -> H(U1(c, k), d)
28.57/10.37	   A^2 -> H(U1(c, k), k)
28.57/10.37	   A^2 -> H(e, b)
28.57/10.37	   A^2 -> H(e, U1(e, d))
28.57/10.37	   A^2 -> H(e, U1(d, e))
28.57/10.37	   A^2 -> H(e, c)
28.57/10.37	   A^2 -> H(e, U1(e, k))
28.57/10.37	   A^2 -> H(e, e)
28.57/10.37	   A^2 -> H(U1(e, e), d)
28.57/10.37	   A^2 -> H(U1(e, e), k)
28.57/10.37	   A^2 -> H(U1(k, k), d)
28.57/10.37	   A^2 -> H(U1(k, k), b)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, k), c)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, d), d)
28.57/10.37	   A^2 -> H(U1(d, k), d)
28.57/10.37	   A^2 -> H(U1(d, k), k)
28.57/10.37	
28.57/10.37	The TRS R consists of the following rules:
28.57/10.37	
28.57/10.37	   f(x) -> U1(x, x)
28.57/10.37	   U1(e, x) -> x
28.57/10.37	   a -> c
28.57/10.37	   a -> d
28.57/10.37	   b -> c
28.57/10.37	   b -> d
28.57/10.37	   d -> k
28.57/10.37	   c -> e
28.57/10.37	   c -> k
28.57/10.37	
28.57/10.37	Q is empty.
28.57/10.37	We have to consider all minimal (P,Q,R)-chains.
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2371) TransformationProof (EQUIVALENT)
28.57/10.37	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), e) at position [] we obtained the following new rules [LPAR04]:
28.57/10.37	
28.57/10.37	   (A^2 -> H(U1(k, k), e),A^2 -> H(U1(k, k), e))
28.57/10.37	
28.57/10.37	
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2372)
28.57/10.37	Obligation:
28.57/10.37	Q DP problem:
28.57/10.37	The TRS P consists of the following rules:
28.57/10.37	
28.57/10.37	   H(x, x) -> G(x, x, f(k))
28.57/10.37	   G(d, x, x) -> A^2
28.57/10.37	   A^2 -> H(f(c), f(c))
28.57/10.37	   A^2 -> H(f(d), f(d))
28.57/10.37	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.37	   A^2 -> H(f(e), f(e))
28.57/10.37	   A^2 -> H(f(k), f(k))
28.57/10.37	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.37	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.37	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.37	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.37	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.37	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.37	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, d), d)
28.57/10.37	   A^2 -> H(U1(d, d), k)
28.57/10.37	   A^2 -> H(U1(e, c), c)
28.57/10.37	   A^2 -> H(U1(c, c), e)
28.57/10.37	   A^2 -> H(U1(c, c), k)
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.37	   A^2 -> H(U1(e, e), e)
28.57/10.37	   A^2 -> H(d, U1(e, b))
28.57/10.37	   A^2 -> H(d, U1(k, b))
28.57/10.37	   A^2 -> H(d, U1(c, d))
28.57/10.37	   A^2 -> H(d, U1(d, c))
28.57/10.37	   A^2 -> H(d, U1(b, e))
28.57/10.37	   A^2 -> H(d, U1(b, k))
28.57/10.37	   A^2 -> H(d, U1(e, c))
28.57/10.37	   A^2 -> H(d, U1(k, c))
28.57/10.37	   A^2 -> H(d, U1(c, e))
28.57/10.37	   A^2 -> H(d, U1(c, k))
28.57/10.37	   A^2 -> H(d, U1(e, e))
28.57/10.37	   A^2 -> H(d, U1(k, k))
28.57/10.37	   A^2 -> H(d, U1(k, d))
28.57/10.37	   A^2 -> H(d, U1(d, k))
28.57/10.37	   A^2 -> H(a, b)
28.57/10.37	   A^2 -> H(a, U1(e, d))
28.57/10.37	   A^2 -> H(a, U1(d, e))
28.57/10.37	   A^2 -> H(a, c)
28.57/10.37	   A^2 -> H(a, U1(e, k))
28.57/10.37	   A^2 -> H(a, U1(k, e))
28.57/10.37	   A^2 -> H(a, e)
28.57/10.37	   A^2 -> H(a, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, d), b)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, d), c)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, d), e)
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, a), d)
28.57/10.37	   A^2 -> H(U1(e, a), k)
28.57/10.37	   A^2 -> H(U1(k, a), d)
28.57/10.37	   A^2 -> H(U1(c, d), d)
28.57/10.37	   A^2 -> H(U1(c, d), k)
28.57/10.37	   A^2 -> H(U1(d, e), b)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(d, e), c)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, e), e)
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, c), d)
28.57/10.37	   A^2 -> H(U1(d, c), k)
28.57/10.37	   A^2 -> H(U1(a, e), d)
28.57/10.37	   A^2 -> H(U1(a, e), k)
28.57/10.37	   A^2 -> H(U1(a, k), d)
28.57/10.37	   A^2 -> H(U1(a, k), k)
28.57/10.37	   A^2 -> H(k, U1(e, b))
28.57/10.37	   A^2 -> H(k, U1(c, d))
28.57/10.37	   A^2 -> H(k, U1(d, c))
28.57/10.37	   A^2 -> H(k, U1(b, e))
28.57/10.37	   A^2 -> H(k, U1(b, k))
28.57/10.37	   A^2 -> H(k, U1(e, c))
28.57/10.37	   A^2 -> H(k, U1(c, e))
28.57/10.37	   A^2 -> H(k, U1(c, k))
28.57/10.37	   A^2 -> H(k, U1(e, e))
28.57/10.37	   A^2 -> H(k, U1(d, k))
28.57/10.37	   A^2 -> H(c, b)
28.57/10.37	   A^2 -> H(c, U1(e, d))
28.57/10.37	   A^2 -> H(c, U1(d, e))
28.57/10.37	   A^2 -> H(c, c)
28.57/10.37	   A^2 -> H(c, U1(e, k))
28.57/10.37	   A^2 -> H(c, U1(k, e))
28.57/10.37	   A^2 -> H(c, e)
28.57/10.37	   A^2 -> H(c, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, k), b)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, k), c)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, k), e)
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, c), d)
28.57/10.37	   A^2 -> H(U1(e, c), k)
28.57/10.37	   A^2 -> H(U1(k, e), b)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, e), c)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(k, c), d)
28.57/10.37	   A^2 -> H(U1(c, e), d)
28.57/10.37	   A^2 -> H(U1(c, e), k)
28.57/10.37	   A^2 -> H(U1(c, k), d)
28.57/10.37	   A^2 -> H(U1(c, k), k)
28.57/10.37	   A^2 -> H(e, b)
28.57/10.37	   A^2 -> H(e, U1(e, d))
28.57/10.37	   A^2 -> H(e, U1(d, e))
28.57/10.37	   A^2 -> H(e, c)
28.57/10.37	   A^2 -> H(e, U1(e, k))
28.57/10.37	   A^2 -> H(e, e)
28.57/10.37	   A^2 -> H(U1(e, e), d)
28.57/10.37	   A^2 -> H(U1(e, e), k)
28.57/10.37	   A^2 -> H(U1(k, k), d)
28.57/10.37	   A^2 -> H(U1(k, k), b)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, k), c)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, d), d)
28.57/10.37	   A^2 -> H(U1(d, k), d)
28.57/10.37	   A^2 -> H(U1(d, k), k)
28.57/10.37	   A^2 -> H(U1(k, k), e)
28.57/10.37	
28.57/10.37	The TRS R consists of the following rules:
28.57/10.37	
28.57/10.37	   f(x) -> U1(x, x)
28.57/10.37	   U1(e, x) -> x
28.57/10.37	   a -> c
28.57/10.37	   a -> d
28.57/10.37	   b -> c
28.57/10.37	   b -> d
28.57/10.37	   d -> k
28.57/10.37	   c -> e
28.57/10.37	   c -> k
28.57/10.37	
28.57/10.37	Q is empty.
28.57/10.37	We have to consider all minimal (P,Q,R)-chains.
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2373) DependencyGraphProof (EQUIVALENT)
28.57/10.37	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2374)
28.57/10.37	Obligation:
28.57/10.37	Q DP problem:
28.57/10.37	The TRS P consists of the following rules:
28.57/10.37	
28.57/10.37	   G(d, x, x) -> A^2
28.57/10.37	   A^2 -> H(f(c), f(c))
28.57/10.37	   H(x, x) -> G(x, x, f(k))
28.57/10.37	   A^2 -> H(f(d), f(d))
28.57/10.37	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.37	   A^2 -> H(f(e), f(e))
28.57/10.37	   A^2 -> H(f(k), f(k))
28.57/10.37	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.37	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.37	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.37	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.37	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.37	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.37	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.37	   A^2 -> H(U1(d, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, d), d)
28.57/10.37	   A^2 -> H(U1(d, d), k)
28.57/10.37	   A^2 -> H(U1(e, c), c)
28.57/10.37	   A^2 -> H(U1(c, c), e)
28.57/10.37	   A^2 -> H(U1(c, c), k)
28.57/10.37	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.37	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.37	   A^2 -> H(U1(e, e), e)
28.57/10.37	   A^2 -> H(d, U1(e, b))
28.57/10.37	   A^2 -> H(d, U1(k, b))
28.57/10.37	   A^2 -> H(d, U1(c, d))
28.57/10.37	   A^2 -> H(d, U1(d, c))
28.57/10.37	   A^2 -> H(d, U1(b, e))
28.57/10.37	   A^2 -> H(d, U1(b, k))
28.57/10.37	   A^2 -> H(d, U1(e, c))
28.57/10.37	   A^2 -> H(d, U1(k, c))
28.57/10.37	   A^2 -> H(d, U1(c, e))
28.57/10.37	   A^2 -> H(d, U1(c, k))
28.57/10.37	   A^2 -> H(d, U1(e, e))
28.57/10.37	   A^2 -> H(d, U1(k, k))
28.57/10.37	   A^2 -> H(d, U1(k, d))
28.57/10.37	   A^2 -> H(d, U1(d, k))
28.57/10.37	   A^2 -> H(a, b)
28.57/10.37	   A^2 -> H(a, U1(e, d))
28.57/10.37	   A^2 -> H(a, U1(d, e))
28.57/10.37	   A^2 -> H(a, c)
28.57/10.37	   A^2 -> H(a, U1(e, k))
28.57/10.37	   A^2 -> H(a, U1(k, e))
28.57/10.37	   A^2 -> H(a, e)
28.57/10.37	   A^2 -> H(a, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, d), b)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, d), c)
28.57/10.37	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, d), e)
28.57/10.37	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, a), d)
28.57/10.37	   A^2 -> H(U1(e, a), k)
28.57/10.37	   A^2 -> H(U1(k, a), d)
28.57/10.37	   A^2 -> H(U1(c, d), d)
28.57/10.37	   A^2 -> H(U1(c, d), k)
28.57/10.37	   A^2 -> H(U1(d, e), b)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(d, e), c)
28.57/10.37	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(d, e), e)
28.57/10.37	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.37	   A^2 -> H(U1(d, c), d)
28.57/10.37	   A^2 -> H(U1(d, c), k)
28.57/10.37	   A^2 -> H(U1(a, e), d)
28.57/10.37	   A^2 -> H(U1(a, e), k)
28.57/10.37	   A^2 -> H(U1(a, k), d)
28.57/10.37	   A^2 -> H(U1(a, k), k)
28.57/10.37	   A^2 -> H(k, U1(e, b))
28.57/10.37	   A^2 -> H(k, U1(c, d))
28.57/10.37	   A^2 -> H(k, U1(d, c))
28.57/10.37	   A^2 -> H(k, U1(b, e))
28.57/10.37	   A^2 -> H(k, U1(b, k))
28.57/10.37	   A^2 -> H(k, U1(e, c))
28.57/10.37	   A^2 -> H(k, U1(c, e))
28.57/10.37	   A^2 -> H(k, U1(c, k))
28.57/10.37	   A^2 -> H(k, U1(e, e))
28.57/10.37	   A^2 -> H(k, U1(d, k))
28.57/10.37	   A^2 -> H(c, b)
28.57/10.37	   A^2 -> H(c, U1(e, d))
28.57/10.37	   A^2 -> H(c, U1(d, e))
28.57/10.37	   A^2 -> H(c, c)
28.57/10.37	   A^2 -> H(c, U1(e, k))
28.57/10.37	   A^2 -> H(c, U1(k, e))
28.57/10.37	   A^2 -> H(c, e)
28.57/10.37	   A^2 -> H(c, U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, k), b)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(e, k), c)
28.57/10.37	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.37	   A^2 -> H(U1(e, k), e)
28.57/10.37	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.37	   A^2 -> H(U1(e, c), d)
28.57/10.37	   A^2 -> H(U1(e, c), k)
28.57/10.37	   A^2 -> H(U1(k, e), b)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, e), c)
28.57/10.37	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.37	   A^2 -> H(U1(k, c), d)
28.57/10.37	   A^2 -> H(U1(c, e), d)
28.57/10.37	   A^2 -> H(U1(c, e), k)
28.57/10.37	   A^2 -> H(U1(c, k), d)
28.57/10.37	   A^2 -> H(U1(c, k), k)
28.57/10.37	   A^2 -> H(e, b)
28.57/10.37	   A^2 -> H(e, U1(e, d))
28.57/10.37	   A^2 -> H(e, U1(d, e))
28.57/10.37	   A^2 -> H(e, c)
28.57/10.37	   A^2 -> H(e, U1(e, k))
28.57/10.37	   A^2 -> H(e, e)
28.57/10.37	   A^2 -> H(U1(e, e), d)
28.57/10.37	   A^2 -> H(U1(e, e), k)
28.57/10.37	   A^2 -> H(U1(k, k), d)
28.57/10.37	   A^2 -> H(U1(k, k), b)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.37	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.37	   A^2 -> H(U1(k, k), c)
28.57/10.37	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.37	   A^2 -> H(U1(k, d), d)
28.57/10.37	   A^2 -> H(U1(d, k), d)
28.57/10.37	   A^2 -> H(U1(d, k), k)
28.57/10.37	
28.57/10.37	The TRS R consists of the following rules:
28.57/10.37	
28.57/10.37	   f(x) -> U1(x, x)
28.57/10.37	   U1(e, x) -> x
28.57/10.37	   a -> c
28.57/10.37	   a -> d
28.57/10.37	   b -> c
28.57/10.37	   b -> d
28.57/10.37	   d -> k
28.57/10.37	   c -> e
28.57/10.37	   c -> k
28.57/10.37	
28.57/10.37	Q is empty.
28.57/10.37	We have to consider all minimal (P,Q,R)-chains.
28.57/10.37	----------------------------------------
28.57/10.37	
28.57/10.37	(2375) TransformationProof (EQUIVALENT)
28.57/10.37	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.38	
28.57/10.38	   (A^2 -> H(U1(k, k), U1(k, k)),A^2 -> H(U1(k, k), U1(k, k)))
28.57/10.38	
28.57/10.38	
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2376)
28.57/10.38	Obligation:
28.57/10.38	Q DP problem:
28.57/10.38	The TRS P consists of the following rules:
28.57/10.38	
28.57/10.38	   G(d, x, x) -> A^2
28.57/10.38	   A^2 -> H(f(c), f(c))
28.57/10.38	   H(x, x) -> G(x, x, f(k))
28.57/10.38	   A^2 -> H(f(d), f(d))
28.57/10.38	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.38	   A^2 -> H(f(e), f(e))
28.57/10.38	   A^2 -> H(f(k), f(k))
28.57/10.38	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.38	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.38	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.38	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.38	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.38	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.38	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.38	   A^2 -> H(U1(d, d), d)
28.57/10.38	   A^2 -> H(U1(d, d), k)
28.57/10.38	   A^2 -> H(U1(e, c), c)
28.57/10.38	   A^2 -> H(U1(c, c), e)
28.57/10.38	   A^2 -> H(U1(c, c), k)
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.38	   A^2 -> H(U1(e, e), e)
28.57/10.38	   A^2 -> H(d, U1(e, b))
28.57/10.38	   A^2 -> H(d, U1(k, b))
28.57/10.38	   A^2 -> H(d, U1(c, d))
28.57/10.38	   A^2 -> H(d, U1(d, c))
28.57/10.38	   A^2 -> H(d, U1(b, e))
28.57/10.38	   A^2 -> H(d, U1(b, k))
28.57/10.38	   A^2 -> H(d, U1(e, c))
28.57/10.38	   A^2 -> H(d, U1(k, c))
28.57/10.38	   A^2 -> H(d, U1(c, e))
28.57/10.38	   A^2 -> H(d, U1(c, k))
28.57/10.38	   A^2 -> H(d, U1(e, e))
28.57/10.38	   A^2 -> H(d, U1(k, k))
28.57/10.38	   A^2 -> H(d, U1(k, d))
28.57/10.38	   A^2 -> H(d, U1(d, k))
28.57/10.38	   A^2 -> H(a, b)
28.57/10.38	   A^2 -> H(a, U1(e, d))
28.57/10.38	   A^2 -> H(a, U1(d, e))
28.57/10.38	   A^2 -> H(a, c)
28.57/10.38	   A^2 -> H(a, U1(e, k))
28.57/10.38	   A^2 -> H(a, U1(k, e))
28.57/10.38	   A^2 -> H(a, e)
28.57/10.38	   A^2 -> H(a, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, d), b)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, d), c)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, d), e)
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, a), d)
28.57/10.38	   A^2 -> H(U1(e, a), k)
28.57/10.38	   A^2 -> H(U1(k, a), d)
28.57/10.38	   A^2 -> H(U1(c, d), d)
28.57/10.38	   A^2 -> H(U1(c, d), k)
28.57/10.38	   A^2 -> H(U1(d, e), b)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(d, e), c)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(d, e), e)
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.38	   A^2 -> H(U1(d, c), d)
28.57/10.38	   A^2 -> H(U1(d, c), k)
28.57/10.38	   A^2 -> H(U1(a, e), d)
28.57/10.38	   A^2 -> H(U1(a, e), k)
28.57/10.38	   A^2 -> H(U1(a, k), d)
28.57/10.38	   A^2 -> H(U1(a, k), k)
28.57/10.38	   A^2 -> H(k, U1(e, b))
28.57/10.38	   A^2 -> H(k, U1(c, d))
28.57/10.38	   A^2 -> H(k, U1(d, c))
28.57/10.38	   A^2 -> H(k, U1(b, e))
28.57/10.38	   A^2 -> H(k, U1(b, k))
28.57/10.38	   A^2 -> H(k, U1(e, c))
28.57/10.38	   A^2 -> H(k, U1(c, e))
28.57/10.38	   A^2 -> H(k, U1(c, k))
28.57/10.38	   A^2 -> H(k, U1(e, e))
28.57/10.38	   A^2 -> H(k, U1(d, k))
28.57/10.38	   A^2 -> H(c, b)
28.57/10.38	   A^2 -> H(c, U1(e, d))
28.57/10.38	   A^2 -> H(c, U1(d, e))
28.57/10.38	   A^2 -> H(c, c)
28.57/10.38	   A^2 -> H(c, U1(e, k))
28.57/10.38	   A^2 -> H(c, U1(k, e))
28.57/10.38	   A^2 -> H(c, e)
28.57/10.38	   A^2 -> H(c, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, k), b)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, k), c)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, k), e)
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, c), d)
28.57/10.38	   A^2 -> H(U1(e, c), k)
28.57/10.38	   A^2 -> H(U1(k, e), b)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, e), c)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(k, c), d)
28.57/10.38	   A^2 -> H(U1(c, e), d)
28.57/10.38	   A^2 -> H(U1(c, e), k)
28.57/10.38	   A^2 -> H(U1(c, k), d)
28.57/10.38	   A^2 -> H(U1(c, k), k)
28.57/10.38	   A^2 -> H(e, b)
28.57/10.38	   A^2 -> H(e, U1(e, d))
28.57/10.38	   A^2 -> H(e, U1(d, e))
28.57/10.38	   A^2 -> H(e, c)
28.57/10.38	   A^2 -> H(e, U1(e, k))
28.57/10.38	   A^2 -> H(e, e)
28.57/10.38	   A^2 -> H(U1(e, e), d)
28.57/10.38	   A^2 -> H(U1(e, e), k)
28.57/10.38	   A^2 -> H(U1(k, k), d)
28.57/10.38	   A^2 -> H(U1(k, k), b)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, k), c)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, d), d)
28.57/10.38	   A^2 -> H(U1(d, k), d)
28.57/10.38	   A^2 -> H(U1(d, k), k)
28.57/10.38	
28.57/10.38	The TRS R consists of the following rules:
28.57/10.38	
28.57/10.38	   f(x) -> U1(x, x)
28.57/10.38	   U1(e, x) -> x
28.57/10.38	   a -> c
28.57/10.38	   a -> d
28.57/10.38	   b -> c
28.57/10.38	   b -> d
28.57/10.38	   d -> k
28.57/10.38	   c -> e
28.57/10.38	   c -> k
28.57/10.38	
28.57/10.38	Q is empty.
28.57/10.38	We have to consider all minimal (P,Q,R)-chains.
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2377) TransformationProof (EQUIVALENT)
28.57/10.38	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), d) at position [] we obtained the following new rules [LPAR04]:
28.57/10.38	
28.57/10.38	   (A^2 -> H(U1(k, d), d),A^2 -> H(U1(k, d), d))
28.57/10.38	   (A^2 -> H(U1(d, k), d),A^2 -> H(U1(d, k), d))
28.57/10.38	   (A^2 -> H(U1(d, d), k),A^2 -> H(U1(d, d), k))
28.57/10.38	
28.57/10.38	
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2378)
28.57/10.38	Obligation:
28.57/10.38	Q DP problem:
28.57/10.38	The TRS P consists of the following rules:
28.57/10.38	
28.57/10.38	   G(d, x, x) -> A^2
28.57/10.38	   A^2 -> H(f(c), f(c))
28.57/10.38	   H(x, x) -> G(x, x, f(k))
28.57/10.38	   A^2 -> H(f(d), f(d))
28.57/10.38	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.38	   A^2 -> H(f(e), f(e))
28.57/10.38	   A^2 -> H(f(k), f(k))
28.57/10.38	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.38	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.38	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.38	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.38	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.38	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.38	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.38	   A^2 -> H(U1(d, d), k)
28.57/10.38	   A^2 -> H(U1(e, c), c)
28.57/10.38	   A^2 -> H(U1(c, c), e)
28.57/10.38	   A^2 -> H(U1(c, c), k)
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.38	   A^2 -> H(U1(e, e), e)
28.57/10.38	   A^2 -> H(d, U1(e, b))
28.57/10.38	   A^2 -> H(d, U1(k, b))
28.57/10.38	   A^2 -> H(d, U1(c, d))
28.57/10.38	   A^2 -> H(d, U1(d, c))
28.57/10.38	   A^2 -> H(d, U1(b, e))
28.57/10.38	   A^2 -> H(d, U1(b, k))
28.57/10.38	   A^2 -> H(d, U1(e, c))
28.57/10.38	   A^2 -> H(d, U1(k, c))
28.57/10.38	   A^2 -> H(d, U1(c, e))
28.57/10.38	   A^2 -> H(d, U1(c, k))
28.57/10.38	   A^2 -> H(d, U1(e, e))
28.57/10.38	   A^2 -> H(d, U1(k, k))
28.57/10.38	   A^2 -> H(d, U1(k, d))
28.57/10.38	   A^2 -> H(d, U1(d, k))
28.57/10.38	   A^2 -> H(a, b)
28.57/10.38	   A^2 -> H(a, U1(e, d))
28.57/10.38	   A^2 -> H(a, U1(d, e))
28.57/10.38	   A^2 -> H(a, c)
28.57/10.38	   A^2 -> H(a, U1(e, k))
28.57/10.38	   A^2 -> H(a, U1(k, e))
28.57/10.38	   A^2 -> H(a, e)
28.57/10.38	   A^2 -> H(a, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, d), b)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, d), c)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, d), e)
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, a), d)
28.57/10.38	   A^2 -> H(U1(e, a), k)
28.57/10.38	   A^2 -> H(U1(k, a), d)
28.57/10.38	   A^2 -> H(U1(c, d), d)
28.57/10.38	   A^2 -> H(U1(c, d), k)
28.57/10.38	   A^2 -> H(U1(d, e), b)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(d, e), c)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(d, e), e)
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.38	   A^2 -> H(U1(d, c), d)
28.57/10.38	   A^2 -> H(U1(d, c), k)
28.57/10.38	   A^2 -> H(U1(a, e), d)
28.57/10.38	   A^2 -> H(U1(a, e), k)
28.57/10.38	   A^2 -> H(U1(a, k), d)
28.57/10.38	   A^2 -> H(U1(a, k), k)
28.57/10.38	   A^2 -> H(k, U1(e, b))
28.57/10.38	   A^2 -> H(k, U1(c, d))
28.57/10.38	   A^2 -> H(k, U1(d, c))
28.57/10.38	   A^2 -> H(k, U1(b, e))
28.57/10.38	   A^2 -> H(k, U1(b, k))
28.57/10.38	   A^2 -> H(k, U1(e, c))
28.57/10.38	   A^2 -> H(k, U1(c, e))
28.57/10.38	   A^2 -> H(k, U1(c, k))
28.57/10.38	   A^2 -> H(k, U1(e, e))
28.57/10.38	   A^2 -> H(k, U1(d, k))
28.57/10.38	   A^2 -> H(c, b)
28.57/10.38	   A^2 -> H(c, U1(e, d))
28.57/10.38	   A^2 -> H(c, U1(d, e))
28.57/10.38	   A^2 -> H(c, c)
28.57/10.38	   A^2 -> H(c, U1(e, k))
28.57/10.38	   A^2 -> H(c, U1(k, e))
28.57/10.38	   A^2 -> H(c, e)
28.57/10.38	   A^2 -> H(c, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, k), b)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, k), c)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, k), e)
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, c), d)
28.57/10.38	   A^2 -> H(U1(e, c), k)
28.57/10.38	   A^2 -> H(U1(k, e), b)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, e), c)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(k, c), d)
28.57/10.38	   A^2 -> H(U1(c, e), d)
28.57/10.38	   A^2 -> H(U1(c, e), k)
28.57/10.38	   A^2 -> H(U1(c, k), d)
28.57/10.38	   A^2 -> H(U1(c, k), k)
28.57/10.38	   A^2 -> H(e, b)
28.57/10.38	   A^2 -> H(e, U1(e, d))
28.57/10.38	   A^2 -> H(e, U1(d, e))
28.57/10.38	   A^2 -> H(e, c)
28.57/10.38	   A^2 -> H(e, U1(e, k))
28.57/10.38	   A^2 -> H(e, e)
28.57/10.38	   A^2 -> H(U1(e, e), d)
28.57/10.38	   A^2 -> H(U1(e, e), k)
28.57/10.38	   A^2 -> H(U1(k, k), d)
28.57/10.38	   A^2 -> H(U1(k, k), b)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, k), c)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, d), d)
28.57/10.38	   A^2 -> H(U1(d, k), d)
28.57/10.38	   A^2 -> H(U1(d, k), k)
28.57/10.38	
28.57/10.38	The TRS R consists of the following rules:
28.57/10.38	
28.57/10.38	   f(x) -> U1(x, x)
28.57/10.38	   U1(e, x) -> x
28.57/10.38	   a -> c
28.57/10.38	   a -> d
28.57/10.38	   b -> c
28.57/10.38	   b -> d
28.57/10.38	   d -> k
28.57/10.38	   c -> e
28.57/10.38	   c -> k
28.57/10.38	
28.57/10.38	Q is empty.
28.57/10.38	We have to consider all minimal (P,Q,R)-chains.
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2379) TransformationProof (EQUIVALENT)
28.57/10.38	By narrowing [LPAR04] the rule A^2 -> H(U1(d, d), k) at position [] we obtained the following new rules [LPAR04]:
28.57/10.38	
28.57/10.38	   (A^2 -> H(U1(k, d), k),A^2 -> H(U1(k, d), k))
28.57/10.38	   (A^2 -> H(U1(d, k), k),A^2 -> H(U1(d, k), k))
28.57/10.38	
28.57/10.38	
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2380)
28.57/10.38	Obligation:
28.57/10.38	Q DP problem:
28.57/10.38	The TRS P consists of the following rules:
28.57/10.38	
28.57/10.38	   G(d, x, x) -> A^2
28.57/10.38	   A^2 -> H(f(c), f(c))
28.57/10.38	   H(x, x) -> G(x, x, f(k))
28.57/10.38	   A^2 -> H(f(d), f(d))
28.57/10.38	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.38	   A^2 -> H(f(e), f(e))
28.57/10.38	   A^2 -> H(f(k), f(k))
28.57/10.38	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.38	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.38	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.38	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.38	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.38	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.38	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.38	   A^2 -> H(U1(e, c), c)
28.57/10.38	   A^2 -> H(U1(c, c), e)
28.57/10.38	   A^2 -> H(U1(c, c), k)
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.38	   A^2 -> H(U1(e, e), e)
28.57/10.38	   A^2 -> H(d, U1(e, b))
28.57/10.38	   A^2 -> H(d, U1(k, b))
28.57/10.38	   A^2 -> H(d, U1(c, d))
28.57/10.38	   A^2 -> H(d, U1(d, c))
28.57/10.38	   A^2 -> H(d, U1(b, e))
28.57/10.38	   A^2 -> H(d, U1(b, k))
28.57/10.38	   A^2 -> H(d, U1(e, c))
28.57/10.38	   A^2 -> H(d, U1(k, c))
28.57/10.38	   A^2 -> H(d, U1(c, e))
28.57/10.38	   A^2 -> H(d, U1(c, k))
28.57/10.38	   A^2 -> H(d, U1(e, e))
28.57/10.38	   A^2 -> H(d, U1(k, k))
28.57/10.38	   A^2 -> H(d, U1(k, d))
28.57/10.38	   A^2 -> H(d, U1(d, k))
28.57/10.38	   A^2 -> H(a, b)
28.57/10.38	   A^2 -> H(a, U1(e, d))
28.57/10.38	   A^2 -> H(a, U1(d, e))
28.57/10.38	   A^2 -> H(a, c)
28.57/10.38	   A^2 -> H(a, U1(e, k))
28.57/10.38	   A^2 -> H(a, U1(k, e))
28.57/10.38	   A^2 -> H(a, e)
28.57/10.38	   A^2 -> H(a, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, d), b)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, d), c)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, d), e)
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, a), d)
28.57/10.38	   A^2 -> H(U1(e, a), k)
28.57/10.38	   A^2 -> H(U1(k, a), d)
28.57/10.38	   A^2 -> H(U1(c, d), d)
28.57/10.38	   A^2 -> H(U1(c, d), k)
28.57/10.38	   A^2 -> H(U1(d, e), b)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(d, e), c)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(d, e), e)
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.38	   A^2 -> H(U1(d, c), d)
28.57/10.38	   A^2 -> H(U1(d, c), k)
28.57/10.38	   A^2 -> H(U1(a, e), d)
28.57/10.38	   A^2 -> H(U1(a, e), k)
28.57/10.38	   A^2 -> H(U1(a, k), d)
28.57/10.38	   A^2 -> H(U1(a, k), k)
28.57/10.38	   A^2 -> H(k, U1(e, b))
28.57/10.38	   A^2 -> H(k, U1(c, d))
28.57/10.38	   A^2 -> H(k, U1(d, c))
28.57/10.38	   A^2 -> H(k, U1(b, e))
28.57/10.38	   A^2 -> H(k, U1(b, k))
28.57/10.38	   A^2 -> H(k, U1(e, c))
28.57/10.38	   A^2 -> H(k, U1(c, e))
28.57/10.38	   A^2 -> H(k, U1(c, k))
28.57/10.38	   A^2 -> H(k, U1(e, e))
28.57/10.38	   A^2 -> H(k, U1(d, k))
28.57/10.38	   A^2 -> H(c, b)
28.57/10.38	   A^2 -> H(c, U1(e, d))
28.57/10.38	   A^2 -> H(c, U1(d, e))
28.57/10.38	   A^2 -> H(c, c)
28.57/10.38	   A^2 -> H(c, U1(e, k))
28.57/10.38	   A^2 -> H(c, U1(k, e))
28.57/10.38	   A^2 -> H(c, e)
28.57/10.38	   A^2 -> H(c, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, k), b)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, k), c)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, k), e)
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, c), d)
28.57/10.38	   A^2 -> H(U1(e, c), k)
28.57/10.38	   A^2 -> H(U1(k, e), b)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, e), c)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(k, c), d)
28.57/10.38	   A^2 -> H(U1(c, e), d)
28.57/10.38	   A^2 -> H(U1(c, e), k)
28.57/10.38	   A^2 -> H(U1(c, k), d)
28.57/10.38	   A^2 -> H(U1(c, k), k)
28.57/10.38	   A^2 -> H(e, b)
28.57/10.38	   A^2 -> H(e, U1(e, d))
28.57/10.38	   A^2 -> H(e, U1(d, e))
28.57/10.38	   A^2 -> H(e, c)
28.57/10.38	   A^2 -> H(e, U1(e, k))
28.57/10.38	   A^2 -> H(e, e)
28.57/10.38	   A^2 -> H(U1(e, e), d)
28.57/10.38	   A^2 -> H(U1(e, e), k)
28.57/10.38	   A^2 -> H(U1(k, k), d)
28.57/10.38	   A^2 -> H(U1(k, k), b)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, k), c)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, d), d)
28.57/10.38	   A^2 -> H(U1(d, k), d)
28.57/10.38	   A^2 -> H(U1(d, k), k)
28.57/10.38	   A^2 -> H(U1(k, d), k)
28.57/10.38	
28.57/10.38	The TRS R consists of the following rules:
28.57/10.38	
28.57/10.38	   f(x) -> U1(x, x)
28.57/10.38	   U1(e, x) -> x
28.57/10.38	   a -> c
28.57/10.38	   a -> d
28.57/10.38	   b -> c
28.57/10.38	   b -> d
28.57/10.38	   d -> k
28.57/10.38	   c -> e
28.57/10.38	   c -> k
28.57/10.38	
28.57/10.38	Q is empty.
28.57/10.38	We have to consider all minimal (P,Q,R)-chains.
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2381) DependencyGraphProof (EQUIVALENT)
28.57/10.38	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2382)
28.57/10.38	Obligation:
28.57/10.38	Q DP problem:
28.57/10.38	The TRS P consists of the following rules:
28.57/10.38	
28.57/10.38	   A^2 -> H(f(c), f(c))
28.57/10.38	   H(x, x) -> G(x, x, f(k))
28.57/10.38	   G(d, x, x) -> A^2
28.57/10.38	   A^2 -> H(f(d), f(d))
28.57/10.38	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.38	   A^2 -> H(f(e), f(e))
28.57/10.38	   A^2 -> H(f(k), f(k))
28.57/10.38	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.38	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.38	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.38	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.38	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.38	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.38	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.38	   A^2 -> H(U1(e, c), c)
28.57/10.38	   A^2 -> H(U1(c, c), e)
28.57/10.38	   A^2 -> H(U1(c, c), k)
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.38	   A^2 -> H(U1(e, e), e)
28.57/10.38	   A^2 -> H(d, U1(e, b))
28.57/10.38	   A^2 -> H(d, U1(k, b))
28.57/10.38	   A^2 -> H(d, U1(c, d))
28.57/10.38	   A^2 -> H(d, U1(d, c))
28.57/10.38	   A^2 -> H(d, U1(b, e))
28.57/10.38	   A^2 -> H(d, U1(b, k))
28.57/10.38	   A^2 -> H(d, U1(e, c))
28.57/10.38	   A^2 -> H(d, U1(k, c))
28.57/10.38	   A^2 -> H(d, U1(c, e))
28.57/10.38	   A^2 -> H(d, U1(c, k))
28.57/10.38	   A^2 -> H(d, U1(e, e))
28.57/10.38	   A^2 -> H(d, U1(k, k))
28.57/10.38	   A^2 -> H(d, U1(k, d))
28.57/10.38	   A^2 -> H(d, U1(d, k))
28.57/10.38	   A^2 -> H(a, b)
28.57/10.38	   A^2 -> H(a, U1(e, d))
28.57/10.38	   A^2 -> H(a, U1(d, e))
28.57/10.38	   A^2 -> H(a, c)
28.57/10.38	   A^2 -> H(a, U1(e, k))
28.57/10.38	   A^2 -> H(a, U1(k, e))
28.57/10.38	   A^2 -> H(a, e)
28.57/10.38	   A^2 -> H(a, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, d), b)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, d), c)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, d), e)
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, a), d)
28.57/10.38	   A^2 -> H(U1(e, a), k)
28.57/10.38	   A^2 -> H(U1(k, a), d)
28.57/10.38	   A^2 -> H(U1(c, d), d)
28.57/10.38	   A^2 -> H(U1(c, d), k)
28.57/10.38	   A^2 -> H(U1(d, e), b)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(d, e), c)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(d, e), e)
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.38	   A^2 -> H(U1(d, c), d)
28.57/10.38	   A^2 -> H(U1(d, c), k)
28.57/10.38	   A^2 -> H(U1(a, e), d)
28.57/10.38	   A^2 -> H(U1(a, e), k)
28.57/10.38	   A^2 -> H(U1(a, k), d)
28.57/10.38	   A^2 -> H(U1(a, k), k)
28.57/10.38	   A^2 -> H(k, U1(e, b))
28.57/10.38	   A^2 -> H(k, U1(c, d))
28.57/10.38	   A^2 -> H(k, U1(d, c))
28.57/10.38	   A^2 -> H(k, U1(b, e))
28.57/10.38	   A^2 -> H(k, U1(b, k))
28.57/10.38	   A^2 -> H(k, U1(e, c))
28.57/10.38	   A^2 -> H(k, U1(c, e))
28.57/10.38	   A^2 -> H(k, U1(c, k))
28.57/10.38	   A^2 -> H(k, U1(e, e))
28.57/10.38	   A^2 -> H(k, U1(d, k))
28.57/10.38	   A^2 -> H(c, b)
28.57/10.38	   A^2 -> H(c, U1(e, d))
28.57/10.38	   A^2 -> H(c, U1(d, e))
28.57/10.38	   A^2 -> H(c, c)
28.57/10.38	   A^2 -> H(c, U1(e, k))
28.57/10.38	   A^2 -> H(c, U1(k, e))
28.57/10.38	   A^2 -> H(c, e)
28.57/10.38	   A^2 -> H(c, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, k), b)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, k), c)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, k), e)
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, c), d)
28.57/10.38	   A^2 -> H(U1(e, c), k)
28.57/10.38	   A^2 -> H(U1(k, e), b)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, e), c)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(k, c), d)
28.57/10.38	   A^2 -> H(U1(c, e), d)
28.57/10.38	   A^2 -> H(U1(c, e), k)
28.57/10.38	   A^2 -> H(U1(c, k), d)
28.57/10.38	   A^2 -> H(U1(c, k), k)
28.57/10.38	   A^2 -> H(e, b)
28.57/10.38	   A^2 -> H(e, U1(e, d))
28.57/10.38	   A^2 -> H(e, U1(d, e))
28.57/10.38	   A^2 -> H(e, c)
28.57/10.38	   A^2 -> H(e, U1(e, k))
28.57/10.38	   A^2 -> H(e, e)
28.57/10.38	   A^2 -> H(U1(e, e), d)
28.57/10.38	   A^2 -> H(U1(e, e), k)
28.57/10.38	   A^2 -> H(U1(k, k), d)
28.57/10.38	   A^2 -> H(U1(k, k), b)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, k), c)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, d), d)
28.57/10.38	   A^2 -> H(U1(d, k), d)
28.57/10.38	   A^2 -> H(U1(d, k), k)
28.57/10.38	
28.57/10.38	The TRS R consists of the following rules:
28.57/10.38	
28.57/10.38	   f(x) -> U1(x, x)
28.57/10.38	   U1(e, x) -> x
28.57/10.38	   a -> c
28.57/10.38	   a -> d
28.57/10.38	   b -> c
28.57/10.38	   b -> d
28.57/10.38	   d -> k
28.57/10.38	   c -> e
28.57/10.38	   c -> k
28.57/10.38	
28.57/10.38	Q is empty.
28.57/10.38	We have to consider all minimal (P,Q,R)-chains.
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2383) TransformationProof (EQUIVALENT)
28.57/10.38	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), c) at position [] we obtained the following new rules [LPAR04]:
28.57/10.38	
28.57/10.38	   (A^2 -> H(c, c),A^2 -> H(c, c))
28.57/10.38	   (A^2 -> H(U1(e, e), c),A^2 -> H(U1(e, e), c))
28.57/10.38	   (A^2 -> H(U1(e, k), c),A^2 -> H(U1(e, k), c))
28.57/10.38	   (A^2 -> H(U1(e, c), e),A^2 -> H(U1(e, c), e))
28.57/10.38	   (A^2 -> H(U1(e, c), k),A^2 -> H(U1(e, c), k))
28.57/10.38	
28.57/10.38	
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2384)
28.57/10.38	Obligation:
28.57/10.38	Q DP problem:
28.57/10.38	The TRS P consists of the following rules:
28.57/10.38	
28.57/10.38	   A^2 -> H(f(c), f(c))
28.57/10.38	   H(x, x) -> G(x, x, f(k))
28.57/10.38	   G(d, x, x) -> A^2
28.57/10.38	   A^2 -> H(f(d), f(d))
28.57/10.38	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.38	   A^2 -> H(f(e), f(e))
28.57/10.38	   A^2 -> H(f(k), f(k))
28.57/10.38	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.38	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.38	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.38	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.38	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.38	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.38	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.38	   A^2 -> H(U1(c, c), e)
28.57/10.38	   A^2 -> H(U1(c, c), k)
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.38	   A^2 -> H(U1(e, e), e)
28.57/10.38	   A^2 -> H(d, U1(e, b))
28.57/10.38	   A^2 -> H(d, U1(k, b))
28.57/10.38	   A^2 -> H(d, U1(c, d))
28.57/10.38	   A^2 -> H(d, U1(d, c))
28.57/10.38	   A^2 -> H(d, U1(b, e))
28.57/10.38	   A^2 -> H(d, U1(b, k))
28.57/10.38	   A^2 -> H(d, U1(e, c))
28.57/10.38	   A^2 -> H(d, U1(k, c))
28.57/10.38	   A^2 -> H(d, U1(c, e))
28.57/10.38	   A^2 -> H(d, U1(c, k))
28.57/10.38	   A^2 -> H(d, U1(e, e))
28.57/10.38	   A^2 -> H(d, U1(k, k))
28.57/10.38	   A^2 -> H(d, U1(k, d))
28.57/10.38	   A^2 -> H(d, U1(d, k))
28.57/10.38	   A^2 -> H(a, b)
28.57/10.38	   A^2 -> H(a, U1(e, d))
28.57/10.38	   A^2 -> H(a, U1(d, e))
28.57/10.38	   A^2 -> H(a, c)
28.57/10.38	   A^2 -> H(a, U1(e, k))
28.57/10.38	   A^2 -> H(a, U1(k, e))
28.57/10.38	   A^2 -> H(a, e)
28.57/10.38	   A^2 -> H(a, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, d), b)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, d), c)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, d), e)
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, a), d)
28.57/10.38	   A^2 -> H(U1(e, a), k)
28.57/10.38	   A^2 -> H(U1(k, a), d)
28.57/10.38	   A^2 -> H(U1(c, d), d)
28.57/10.38	   A^2 -> H(U1(c, d), k)
28.57/10.38	   A^2 -> H(U1(d, e), b)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(d, e), c)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(d, e), e)
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.38	   A^2 -> H(U1(d, c), d)
28.57/10.38	   A^2 -> H(U1(d, c), k)
28.57/10.38	   A^2 -> H(U1(a, e), d)
28.57/10.38	   A^2 -> H(U1(a, e), k)
28.57/10.38	   A^2 -> H(U1(a, k), d)
28.57/10.38	   A^2 -> H(U1(a, k), k)
28.57/10.38	   A^2 -> H(k, U1(e, b))
28.57/10.38	   A^2 -> H(k, U1(c, d))
28.57/10.38	   A^2 -> H(k, U1(d, c))
28.57/10.38	   A^2 -> H(k, U1(b, e))
28.57/10.38	   A^2 -> H(k, U1(b, k))
28.57/10.38	   A^2 -> H(k, U1(e, c))
28.57/10.38	   A^2 -> H(k, U1(c, e))
28.57/10.38	   A^2 -> H(k, U1(c, k))
28.57/10.38	   A^2 -> H(k, U1(e, e))
28.57/10.38	   A^2 -> H(k, U1(d, k))
28.57/10.38	   A^2 -> H(c, b)
28.57/10.38	   A^2 -> H(c, U1(e, d))
28.57/10.38	   A^2 -> H(c, U1(d, e))
28.57/10.38	   A^2 -> H(c, c)
28.57/10.38	   A^2 -> H(c, U1(e, k))
28.57/10.38	   A^2 -> H(c, U1(k, e))
28.57/10.38	   A^2 -> H(c, e)
28.57/10.38	   A^2 -> H(c, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, k), b)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, k), c)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, k), e)
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, c), d)
28.57/10.38	   A^2 -> H(U1(e, c), k)
28.57/10.38	   A^2 -> H(U1(k, e), b)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, e), c)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(k, c), d)
28.57/10.38	   A^2 -> H(U1(c, e), d)
28.57/10.38	   A^2 -> H(U1(c, e), k)
28.57/10.38	   A^2 -> H(U1(c, k), d)
28.57/10.38	   A^2 -> H(U1(c, k), k)
28.57/10.38	   A^2 -> H(e, b)
28.57/10.38	   A^2 -> H(e, U1(e, d))
28.57/10.38	   A^2 -> H(e, U1(d, e))
28.57/10.38	   A^2 -> H(e, c)
28.57/10.38	   A^2 -> H(e, U1(e, k))
28.57/10.38	   A^2 -> H(e, e)
28.57/10.38	   A^2 -> H(U1(e, e), d)
28.57/10.38	   A^2 -> H(U1(e, e), k)
28.57/10.38	   A^2 -> H(U1(k, k), d)
28.57/10.38	   A^2 -> H(U1(k, k), b)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, k), c)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, d), d)
28.57/10.38	   A^2 -> H(U1(d, k), d)
28.57/10.38	   A^2 -> H(U1(d, k), k)
28.57/10.38	   A^2 -> H(U1(e, e), c)
28.57/10.38	   A^2 -> H(U1(e, c), e)
28.57/10.38	
28.57/10.38	The TRS R consists of the following rules:
28.57/10.38	
28.57/10.38	   f(x) -> U1(x, x)
28.57/10.38	   U1(e, x) -> x
28.57/10.38	   a -> c
28.57/10.38	   a -> d
28.57/10.38	   b -> c
28.57/10.38	   b -> d
28.57/10.38	   d -> k
28.57/10.38	   c -> e
28.57/10.38	   c -> k
28.57/10.38	
28.57/10.38	Q is empty.
28.57/10.38	We have to consider all minimal (P,Q,R)-chains.
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2385) TransformationProof (EQUIVALENT)
28.57/10.38	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), e) at position [] we obtained the following new rules [LPAR04]:
28.57/10.38	
28.57/10.38	   (A^2 -> H(U1(e, c), e),A^2 -> H(U1(e, c), e))
28.57/10.38	   (A^2 -> H(U1(k, c), e),A^2 -> H(U1(k, c), e))
28.57/10.38	   (A^2 -> H(U1(c, e), e),A^2 -> H(U1(c, e), e))
28.57/10.38	   (A^2 -> H(U1(c, k), e),A^2 -> H(U1(c, k), e))
28.57/10.38	
28.57/10.38	
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2386)
28.57/10.38	Obligation:
28.57/10.38	Q DP problem:
28.57/10.38	The TRS P consists of the following rules:
28.57/10.38	
28.57/10.38	   A^2 -> H(f(c), f(c))
28.57/10.38	   H(x, x) -> G(x, x, f(k))
28.57/10.38	   G(d, x, x) -> A^2
28.57/10.38	   A^2 -> H(f(d), f(d))
28.57/10.38	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.38	   A^2 -> H(f(e), f(e))
28.57/10.38	   A^2 -> H(f(k), f(k))
28.57/10.38	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.38	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.38	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.38	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.38	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.38	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.38	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.38	   A^2 -> H(U1(c, c), k)
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.38	   A^2 -> H(U1(e, e), e)
28.57/10.38	   A^2 -> H(d, U1(e, b))
28.57/10.38	   A^2 -> H(d, U1(k, b))
28.57/10.38	   A^2 -> H(d, U1(c, d))
28.57/10.38	   A^2 -> H(d, U1(d, c))
28.57/10.38	   A^2 -> H(d, U1(b, e))
28.57/10.38	   A^2 -> H(d, U1(b, k))
28.57/10.38	   A^2 -> H(d, U1(e, c))
28.57/10.38	   A^2 -> H(d, U1(k, c))
28.57/10.38	   A^2 -> H(d, U1(c, e))
28.57/10.38	   A^2 -> H(d, U1(c, k))
28.57/10.38	   A^2 -> H(d, U1(e, e))
28.57/10.38	   A^2 -> H(d, U1(k, k))
28.57/10.38	   A^2 -> H(d, U1(k, d))
28.57/10.38	   A^2 -> H(d, U1(d, k))
28.57/10.38	   A^2 -> H(a, b)
28.57/10.38	   A^2 -> H(a, U1(e, d))
28.57/10.38	   A^2 -> H(a, U1(d, e))
28.57/10.38	   A^2 -> H(a, c)
28.57/10.38	   A^2 -> H(a, U1(e, k))
28.57/10.38	   A^2 -> H(a, U1(k, e))
28.57/10.38	   A^2 -> H(a, e)
28.57/10.38	   A^2 -> H(a, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, d), b)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, d), c)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, d), e)
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, a), d)
28.57/10.38	   A^2 -> H(U1(e, a), k)
28.57/10.38	   A^2 -> H(U1(k, a), d)
28.57/10.38	   A^2 -> H(U1(c, d), d)
28.57/10.38	   A^2 -> H(U1(c, d), k)
28.57/10.38	   A^2 -> H(U1(d, e), b)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(d, e), c)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(d, e), e)
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.38	   A^2 -> H(U1(d, c), d)
28.57/10.38	   A^2 -> H(U1(d, c), k)
28.57/10.38	   A^2 -> H(U1(a, e), d)
28.57/10.38	   A^2 -> H(U1(a, e), k)
28.57/10.38	   A^2 -> H(U1(a, k), d)
28.57/10.38	   A^2 -> H(U1(a, k), k)
28.57/10.38	   A^2 -> H(k, U1(e, b))
28.57/10.38	   A^2 -> H(k, U1(c, d))
28.57/10.38	   A^2 -> H(k, U1(d, c))
28.57/10.38	   A^2 -> H(k, U1(b, e))
28.57/10.38	   A^2 -> H(k, U1(b, k))
28.57/10.38	   A^2 -> H(k, U1(e, c))
28.57/10.38	   A^2 -> H(k, U1(c, e))
28.57/10.38	   A^2 -> H(k, U1(c, k))
28.57/10.38	   A^2 -> H(k, U1(e, e))
28.57/10.38	   A^2 -> H(k, U1(d, k))
28.57/10.38	   A^2 -> H(c, b)
28.57/10.38	   A^2 -> H(c, U1(e, d))
28.57/10.38	   A^2 -> H(c, U1(d, e))
28.57/10.38	   A^2 -> H(c, c)
28.57/10.38	   A^2 -> H(c, U1(e, k))
28.57/10.38	   A^2 -> H(c, U1(k, e))
28.57/10.38	   A^2 -> H(c, e)
28.57/10.38	   A^2 -> H(c, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, k), b)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, k), c)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, k), e)
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, c), d)
28.57/10.38	   A^2 -> H(U1(e, c), k)
28.57/10.38	   A^2 -> H(U1(k, e), b)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, e), c)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(k, c), d)
28.57/10.38	   A^2 -> H(U1(c, e), d)
28.57/10.38	   A^2 -> H(U1(c, e), k)
28.57/10.38	   A^2 -> H(U1(c, k), d)
28.57/10.38	   A^2 -> H(U1(c, k), k)
28.57/10.38	   A^2 -> H(e, b)
28.57/10.38	   A^2 -> H(e, U1(e, d))
28.57/10.38	   A^2 -> H(e, U1(d, e))
28.57/10.38	   A^2 -> H(e, c)
28.57/10.38	   A^2 -> H(e, U1(e, k))
28.57/10.38	   A^2 -> H(e, e)
28.57/10.38	   A^2 -> H(U1(e, e), d)
28.57/10.38	   A^2 -> H(U1(e, e), k)
28.57/10.38	   A^2 -> H(U1(k, k), d)
28.57/10.38	   A^2 -> H(U1(k, k), b)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, k), c)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, d), d)
28.57/10.38	   A^2 -> H(U1(d, k), d)
28.57/10.38	   A^2 -> H(U1(d, k), k)
28.57/10.38	   A^2 -> H(U1(e, e), c)
28.57/10.38	   A^2 -> H(U1(e, c), e)
28.57/10.38	   A^2 -> H(U1(k, c), e)
28.57/10.38	   A^2 -> H(U1(c, e), e)
28.57/10.38	   A^2 -> H(U1(c, k), e)
28.57/10.38	
28.57/10.38	The TRS R consists of the following rules:
28.57/10.38	
28.57/10.38	   f(x) -> U1(x, x)
28.57/10.38	   U1(e, x) -> x
28.57/10.38	   a -> c
28.57/10.38	   a -> d
28.57/10.38	   b -> c
28.57/10.38	   b -> d
28.57/10.38	   d -> k
28.57/10.38	   c -> e
28.57/10.38	   c -> k
28.57/10.38	
28.57/10.38	Q is empty.
28.57/10.38	We have to consider all minimal (P,Q,R)-chains.
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2387) DependencyGraphProof (EQUIVALENT)
28.57/10.38	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2388)
28.57/10.38	Obligation:
28.57/10.38	Q DP problem:
28.57/10.38	The TRS P consists of the following rules:
28.57/10.38	
28.57/10.38	   H(x, x) -> G(x, x, f(k))
28.57/10.38	   G(d, x, x) -> A^2
28.57/10.38	   A^2 -> H(f(c), f(c))
28.57/10.38	   A^2 -> H(f(d), f(d))
28.57/10.38	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.38	   A^2 -> H(f(e), f(e))
28.57/10.38	   A^2 -> H(f(k), f(k))
28.57/10.38	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.38	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.38	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.38	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.38	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.38	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.38	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.38	   A^2 -> H(U1(c, c), k)
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.38	   A^2 -> H(U1(e, e), e)
28.57/10.38	   A^2 -> H(d, U1(e, b))
28.57/10.38	   A^2 -> H(d, U1(k, b))
28.57/10.38	   A^2 -> H(d, U1(c, d))
28.57/10.38	   A^2 -> H(d, U1(d, c))
28.57/10.38	   A^2 -> H(d, U1(b, e))
28.57/10.38	   A^2 -> H(d, U1(b, k))
28.57/10.38	   A^2 -> H(d, U1(e, c))
28.57/10.38	   A^2 -> H(d, U1(k, c))
28.57/10.38	   A^2 -> H(d, U1(c, e))
28.57/10.38	   A^2 -> H(d, U1(c, k))
28.57/10.38	   A^2 -> H(d, U1(e, e))
28.57/10.38	   A^2 -> H(d, U1(k, k))
28.57/10.38	   A^2 -> H(d, U1(k, d))
28.57/10.38	   A^2 -> H(d, U1(d, k))
28.57/10.38	   A^2 -> H(a, b)
28.57/10.38	   A^2 -> H(a, U1(e, d))
28.57/10.38	   A^2 -> H(a, U1(d, e))
28.57/10.38	   A^2 -> H(a, c)
28.57/10.38	   A^2 -> H(a, U1(e, k))
28.57/10.38	   A^2 -> H(a, U1(k, e))
28.57/10.38	   A^2 -> H(a, e)
28.57/10.38	   A^2 -> H(a, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, d), b)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, d), c)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, d), e)
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, a), d)
28.57/10.38	   A^2 -> H(U1(e, a), k)
28.57/10.38	   A^2 -> H(U1(k, a), d)
28.57/10.38	   A^2 -> H(U1(c, d), d)
28.57/10.38	   A^2 -> H(U1(c, d), k)
28.57/10.38	   A^2 -> H(U1(d, e), b)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(d, e), c)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(d, e), e)
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.38	   A^2 -> H(U1(d, c), d)
28.57/10.38	   A^2 -> H(U1(d, c), k)
28.57/10.38	   A^2 -> H(U1(a, e), d)
28.57/10.38	   A^2 -> H(U1(a, e), k)
28.57/10.38	   A^2 -> H(U1(a, k), d)
28.57/10.38	   A^2 -> H(U1(a, k), k)
28.57/10.38	   A^2 -> H(k, U1(e, b))
28.57/10.38	   A^2 -> H(k, U1(c, d))
28.57/10.38	   A^2 -> H(k, U1(d, c))
28.57/10.38	   A^2 -> H(k, U1(b, e))
28.57/10.38	   A^2 -> H(k, U1(b, k))
28.57/10.38	   A^2 -> H(k, U1(e, c))
28.57/10.38	   A^2 -> H(k, U1(c, e))
28.57/10.38	   A^2 -> H(k, U1(c, k))
28.57/10.38	   A^2 -> H(k, U1(e, e))
28.57/10.38	   A^2 -> H(k, U1(d, k))
28.57/10.38	   A^2 -> H(c, b)
28.57/10.38	   A^2 -> H(c, U1(e, d))
28.57/10.38	   A^2 -> H(c, U1(d, e))
28.57/10.38	   A^2 -> H(c, c)
28.57/10.38	   A^2 -> H(c, U1(e, k))
28.57/10.38	   A^2 -> H(c, U1(k, e))
28.57/10.38	   A^2 -> H(c, e)
28.57/10.38	   A^2 -> H(c, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, k), b)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, k), c)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, k), e)
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, c), d)
28.57/10.38	   A^2 -> H(U1(e, c), k)
28.57/10.38	   A^2 -> H(U1(k, e), b)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, e), c)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(k, c), d)
28.57/10.38	   A^2 -> H(U1(c, e), d)
28.57/10.38	   A^2 -> H(U1(c, e), k)
28.57/10.38	   A^2 -> H(U1(c, k), d)
28.57/10.38	   A^2 -> H(U1(c, k), k)
28.57/10.38	   A^2 -> H(e, b)
28.57/10.38	   A^2 -> H(e, U1(e, d))
28.57/10.38	   A^2 -> H(e, U1(d, e))
28.57/10.38	   A^2 -> H(e, c)
28.57/10.38	   A^2 -> H(e, U1(e, k))
28.57/10.38	   A^2 -> H(e, e)
28.57/10.38	   A^2 -> H(U1(e, e), d)
28.57/10.38	   A^2 -> H(U1(e, e), k)
28.57/10.38	   A^2 -> H(U1(k, k), d)
28.57/10.38	   A^2 -> H(U1(k, k), b)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, k), c)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, d), d)
28.57/10.38	   A^2 -> H(U1(d, k), d)
28.57/10.38	   A^2 -> H(U1(d, k), k)
28.57/10.38	   A^2 -> H(U1(e, e), c)
28.57/10.38	   A^2 -> H(U1(e, c), e)
28.57/10.38	   A^2 -> H(U1(c, e), e)
28.57/10.38	   A^2 -> H(U1(c, k), e)
28.57/10.38	
28.57/10.38	The TRS R consists of the following rules:
28.57/10.38	
28.57/10.38	   f(x) -> U1(x, x)
28.57/10.38	   U1(e, x) -> x
28.57/10.38	   a -> c
28.57/10.38	   a -> d
28.57/10.38	   b -> c
28.57/10.38	   b -> d
28.57/10.38	   d -> k
28.57/10.38	   c -> e
28.57/10.38	   c -> k
28.57/10.38	
28.57/10.38	Q is empty.
28.57/10.38	We have to consider all minimal (P,Q,R)-chains.
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2389) TransformationProof (EQUIVALENT)
28.57/10.38	By narrowing [LPAR04] the rule A^2 -> H(U1(c, c), k) at position [] we obtained the following new rules [LPAR04]:
28.57/10.38	
28.57/10.38	   (A^2 -> H(U1(e, c), k),A^2 -> H(U1(e, c), k))
28.57/10.38	   (A^2 -> H(U1(k, c), k),A^2 -> H(U1(k, c), k))
28.57/10.38	   (A^2 -> H(U1(c, e), k),A^2 -> H(U1(c, e), k))
28.57/10.38	   (A^2 -> H(U1(c, k), k),A^2 -> H(U1(c, k), k))
28.57/10.38	
28.57/10.38	
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2390)
28.57/10.38	Obligation:
28.57/10.38	Q DP problem:
28.57/10.38	The TRS P consists of the following rules:
28.57/10.38	
28.57/10.38	   H(x, x) -> G(x, x, f(k))
28.57/10.38	   G(d, x, x) -> A^2
28.57/10.38	   A^2 -> H(f(c), f(c))
28.57/10.38	   A^2 -> H(f(d), f(d))
28.57/10.38	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.38	   A^2 -> H(f(e), f(e))
28.57/10.38	   A^2 -> H(f(k), f(k))
28.57/10.38	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.38	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.38	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.38	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.38	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.38	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.38	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.38	   A^2 -> H(U1(e, e), e)
28.57/10.38	   A^2 -> H(d, U1(e, b))
28.57/10.38	   A^2 -> H(d, U1(k, b))
28.57/10.38	   A^2 -> H(d, U1(c, d))
28.57/10.38	   A^2 -> H(d, U1(d, c))
28.57/10.38	   A^2 -> H(d, U1(b, e))
28.57/10.38	   A^2 -> H(d, U1(b, k))
28.57/10.38	   A^2 -> H(d, U1(e, c))
28.57/10.38	   A^2 -> H(d, U1(k, c))
28.57/10.38	   A^2 -> H(d, U1(c, e))
28.57/10.38	   A^2 -> H(d, U1(c, k))
28.57/10.38	   A^2 -> H(d, U1(e, e))
28.57/10.38	   A^2 -> H(d, U1(k, k))
28.57/10.38	   A^2 -> H(d, U1(k, d))
28.57/10.38	   A^2 -> H(d, U1(d, k))
28.57/10.38	   A^2 -> H(a, b)
28.57/10.38	   A^2 -> H(a, U1(e, d))
28.57/10.38	   A^2 -> H(a, U1(d, e))
28.57/10.38	   A^2 -> H(a, c)
28.57/10.38	   A^2 -> H(a, U1(e, k))
28.57/10.38	   A^2 -> H(a, U1(k, e))
28.57/10.38	   A^2 -> H(a, e)
28.57/10.38	   A^2 -> H(a, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, d), b)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, d), c)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, d), e)
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, a), d)
28.57/10.38	   A^2 -> H(U1(e, a), k)
28.57/10.38	   A^2 -> H(U1(k, a), d)
28.57/10.38	   A^2 -> H(U1(c, d), d)
28.57/10.38	   A^2 -> H(U1(c, d), k)
28.57/10.38	   A^2 -> H(U1(d, e), b)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(d, e), c)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(d, e), e)
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.38	   A^2 -> H(U1(d, c), d)
28.57/10.38	   A^2 -> H(U1(d, c), k)
28.57/10.38	   A^2 -> H(U1(a, e), d)
28.57/10.38	   A^2 -> H(U1(a, e), k)
28.57/10.38	   A^2 -> H(U1(a, k), d)
28.57/10.38	   A^2 -> H(U1(a, k), k)
28.57/10.38	   A^2 -> H(k, U1(e, b))
28.57/10.38	   A^2 -> H(k, U1(c, d))
28.57/10.38	   A^2 -> H(k, U1(d, c))
28.57/10.38	   A^2 -> H(k, U1(b, e))
28.57/10.38	   A^2 -> H(k, U1(b, k))
28.57/10.38	   A^2 -> H(k, U1(e, c))
28.57/10.38	   A^2 -> H(k, U1(c, e))
28.57/10.38	   A^2 -> H(k, U1(c, k))
28.57/10.38	   A^2 -> H(k, U1(e, e))
28.57/10.38	   A^2 -> H(k, U1(d, k))
28.57/10.38	   A^2 -> H(c, b)
28.57/10.38	   A^2 -> H(c, U1(e, d))
28.57/10.38	   A^2 -> H(c, U1(d, e))
28.57/10.38	   A^2 -> H(c, c)
28.57/10.38	   A^2 -> H(c, U1(e, k))
28.57/10.38	   A^2 -> H(c, U1(k, e))
28.57/10.38	   A^2 -> H(c, e)
28.57/10.38	   A^2 -> H(c, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, k), b)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, k), c)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, k), e)
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, c), d)
28.57/10.38	   A^2 -> H(U1(e, c), k)
28.57/10.38	   A^2 -> H(U1(k, e), b)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, e), c)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(k, c), d)
28.57/10.38	   A^2 -> H(U1(c, e), d)
28.57/10.38	   A^2 -> H(U1(c, e), k)
28.57/10.38	   A^2 -> H(U1(c, k), d)
28.57/10.38	   A^2 -> H(U1(c, k), k)
28.57/10.38	   A^2 -> H(e, b)
28.57/10.38	   A^2 -> H(e, U1(e, d))
28.57/10.38	   A^2 -> H(e, U1(d, e))
28.57/10.38	   A^2 -> H(e, c)
28.57/10.38	   A^2 -> H(e, U1(e, k))
28.57/10.38	   A^2 -> H(e, e)
28.57/10.38	   A^2 -> H(U1(e, e), d)
28.57/10.38	   A^2 -> H(U1(e, e), k)
28.57/10.38	   A^2 -> H(U1(k, k), d)
28.57/10.38	   A^2 -> H(U1(k, k), b)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, k), c)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, d), d)
28.57/10.38	   A^2 -> H(U1(d, k), d)
28.57/10.38	   A^2 -> H(U1(d, k), k)
28.57/10.38	   A^2 -> H(U1(e, e), c)
28.57/10.38	   A^2 -> H(U1(e, c), e)
28.57/10.38	   A^2 -> H(U1(c, e), e)
28.57/10.38	   A^2 -> H(U1(c, k), e)
28.57/10.38	   A^2 -> H(U1(k, c), k)
28.57/10.38	
28.57/10.38	The TRS R consists of the following rules:
28.57/10.38	
28.57/10.38	   f(x) -> U1(x, x)
28.57/10.38	   U1(e, x) -> x
28.57/10.38	   a -> c
28.57/10.38	   a -> d
28.57/10.38	   b -> c
28.57/10.38	   b -> d
28.57/10.38	   d -> k
28.57/10.38	   c -> e
28.57/10.38	   c -> k
28.57/10.38	
28.57/10.38	Q is empty.
28.57/10.38	We have to consider all minimal (P,Q,R)-chains.
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2391) DependencyGraphProof (EQUIVALENT)
28.57/10.38	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2392)
28.57/10.38	Obligation:
28.57/10.38	Q DP problem:
28.57/10.38	The TRS P consists of the following rules:
28.57/10.38	
28.57/10.38	   G(d, x, x) -> A^2
28.57/10.38	   A^2 -> H(f(c), f(c))
28.57/10.38	   H(x, x) -> G(x, x, f(k))
28.57/10.38	   A^2 -> H(f(d), f(d))
28.57/10.38	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.38	   A^2 -> H(f(e), f(e))
28.57/10.38	   A^2 -> H(f(k), f(k))
28.57/10.38	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.38	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.38	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.38	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.38	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.38	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.38	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.38	   A^2 -> H(U1(e, e), e)
28.57/10.38	   A^2 -> H(d, U1(e, b))
28.57/10.38	   A^2 -> H(d, U1(k, b))
28.57/10.38	   A^2 -> H(d, U1(c, d))
28.57/10.38	   A^2 -> H(d, U1(d, c))
28.57/10.38	   A^2 -> H(d, U1(b, e))
28.57/10.38	   A^2 -> H(d, U1(b, k))
28.57/10.38	   A^2 -> H(d, U1(e, c))
28.57/10.38	   A^2 -> H(d, U1(k, c))
28.57/10.38	   A^2 -> H(d, U1(c, e))
28.57/10.38	   A^2 -> H(d, U1(c, k))
28.57/10.38	   A^2 -> H(d, U1(e, e))
28.57/10.38	   A^2 -> H(d, U1(k, k))
28.57/10.38	   A^2 -> H(d, U1(k, d))
28.57/10.38	   A^2 -> H(d, U1(d, k))
28.57/10.38	   A^2 -> H(a, b)
28.57/10.38	   A^2 -> H(a, U1(e, d))
28.57/10.38	   A^2 -> H(a, U1(d, e))
28.57/10.38	   A^2 -> H(a, c)
28.57/10.38	   A^2 -> H(a, U1(e, k))
28.57/10.38	   A^2 -> H(a, U1(k, e))
28.57/10.38	   A^2 -> H(a, e)
28.57/10.38	   A^2 -> H(a, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, d), b)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, d), c)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, d), e)
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, a), d)
28.57/10.38	   A^2 -> H(U1(e, a), k)
28.57/10.38	   A^2 -> H(U1(k, a), d)
28.57/10.38	   A^2 -> H(U1(c, d), d)
28.57/10.38	   A^2 -> H(U1(c, d), k)
28.57/10.38	   A^2 -> H(U1(d, e), b)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(d, e), c)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(d, e), e)
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.38	   A^2 -> H(U1(d, c), d)
28.57/10.38	   A^2 -> H(U1(d, c), k)
28.57/10.38	   A^2 -> H(U1(a, e), d)
28.57/10.38	   A^2 -> H(U1(a, e), k)
28.57/10.38	   A^2 -> H(U1(a, k), d)
28.57/10.38	   A^2 -> H(U1(a, k), k)
28.57/10.38	   A^2 -> H(k, U1(e, b))
28.57/10.38	   A^2 -> H(k, U1(c, d))
28.57/10.38	   A^2 -> H(k, U1(d, c))
28.57/10.38	   A^2 -> H(k, U1(b, e))
28.57/10.38	   A^2 -> H(k, U1(b, k))
28.57/10.38	   A^2 -> H(k, U1(e, c))
28.57/10.38	   A^2 -> H(k, U1(c, e))
28.57/10.38	   A^2 -> H(k, U1(c, k))
28.57/10.38	   A^2 -> H(k, U1(e, e))
28.57/10.38	   A^2 -> H(k, U1(d, k))
28.57/10.38	   A^2 -> H(c, b)
28.57/10.38	   A^2 -> H(c, U1(e, d))
28.57/10.38	   A^2 -> H(c, U1(d, e))
28.57/10.38	   A^2 -> H(c, c)
28.57/10.38	   A^2 -> H(c, U1(e, k))
28.57/10.38	   A^2 -> H(c, U1(k, e))
28.57/10.38	   A^2 -> H(c, e)
28.57/10.38	   A^2 -> H(c, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, k), b)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, k), c)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, k), e)
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, c), d)
28.57/10.38	   A^2 -> H(U1(e, c), k)
28.57/10.38	   A^2 -> H(U1(k, e), b)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, e), c)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(k, c), d)
28.57/10.38	   A^2 -> H(U1(c, e), d)
28.57/10.38	   A^2 -> H(U1(c, e), k)
28.57/10.38	   A^2 -> H(U1(c, k), d)
28.57/10.38	   A^2 -> H(U1(c, k), k)
28.57/10.38	   A^2 -> H(e, b)
28.57/10.38	   A^2 -> H(e, U1(e, d))
28.57/10.38	   A^2 -> H(e, U1(d, e))
28.57/10.38	   A^2 -> H(e, c)
28.57/10.38	   A^2 -> H(e, U1(e, k))
28.57/10.38	   A^2 -> H(e, e)
28.57/10.38	   A^2 -> H(U1(e, e), d)
28.57/10.38	   A^2 -> H(U1(e, e), k)
28.57/10.38	   A^2 -> H(U1(k, k), d)
28.57/10.38	   A^2 -> H(U1(k, k), b)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, k), c)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, d), d)
28.57/10.38	   A^2 -> H(U1(d, k), d)
28.57/10.38	   A^2 -> H(U1(d, k), k)
28.57/10.38	   A^2 -> H(U1(e, e), c)
28.57/10.38	   A^2 -> H(U1(e, c), e)
28.57/10.38	   A^2 -> H(U1(c, e), e)
28.57/10.38	   A^2 -> H(U1(c, k), e)
28.57/10.38	
28.57/10.38	The TRS R consists of the following rules:
28.57/10.38	
28.57/10.38	   f(x) -> U1(x, x)
28.57/10.38	   U1(e, x) -> x
28.57/10.38	   a -> c
28.57/10.38	   a -> d
28.57/10.38	   b -> c
28.57/10.38	   b -> d
28.57/10.38	   d -> k
28.57/10.38	   c -> e
28.57/10.38	   c -> k
28.57/10.38	
28.57/10.38	Q is empty.
28.57/10.38	We have to consider all minimal (P,Q,R)-chains.
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2393) TransformationProof (EQUIVALENT)
28.57/10.38	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.38	
28.57/10.38	   (A^2 -> H(c, U1(e, e)),A^2 -> H(c, U1(e, e)))
28.57/10.38	   (A^2 -> H(U1(e, e), U1(e, e)),A^2 -> H(U1(e, e), U1(e, e)))
28.57/10.38	   (A^2 -> H(U1(e, k), U1(e, e)),A^2 -> H(U1(e, k), U1(e, e)))
28.57/10.38	   (A^2 -> H(U1(e, c), e),A^2 -> H(U1(e, c), e))
28.57/10.38	
28.57/10.38	
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2394)
28.57/10.38	Obligation:
28.57/10.38	Q DP problem:
28.57/10.38	The TRS P consists of the following rules:
28.57/10.38	
28.57/10.38	   G(d, x, x) -> A^2
28.57/10.38	   A^2 -> H(f(c), f(c))
28.57/10.38	   H(x, x) -> G(x, x, f(k))
28.57/10.38	   A^2 -> H(f(d), f(d))
28.57/10.38	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.38	   A^2 -> H(f(e), f(e))
28.57/10.38	   A^2 -> H(f(k), f(k))
28.57/10.38	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.38	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.38	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.38	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.38	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.38	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.38	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.38	   A^2 -> H(U1(k, c), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.38	   A^2 -> H(U1(e, e), e)
28.57/10.38	   A^2 -> H(d, U1(e, b))
28.57/10.38	   A^2 -> H(d, U1(k, b))
28.57/10.38	   A^2 -> H(d, U1(c, d))
28.57/10.38	   A^2 -> H(d, U1(d, c))
28.57/10.38	   A^2 -> H(d, U1(b, e))
28.57/10.38	   A^2 -> H(d, U1(b, k))
28.57/10.38	   A^2 -> H(d, U1(e, c))
28.57/10.38	   A^2 -> H(d, U1(k, c))
28.57/10.38	   A^2 -> H(d, U1(c, e))
28.57/10.38	   A^2 -> H(d, U1(c, k))
28.57/10.38	   A^2 -> H(d, U1(e, e))
28.57/10.38	   A^2 -> H(d, U1(k, k))
28.57/10.38	   A^2 -> H(d, U1(k, d))
28.57/10.38	   A^2 -> H(d, U1(d, k))
28.57/10.38	   A^2 -> H(a, b)
28.57/10.38	   A^2 -> H(a, U1(e, d))
28.57/10.38	   A^2 -> H(a, U1(d, e))
28.57/10.38	   A^2 -> H(a, c)
28.57/10.38	   A^2 -> H(a, U1(e, k))
28.57/10.38	   A^2 -> H(a, U1(k, e))
28.57/10.38	   A^2 -> H(a, e)
28.57/10.38	   A^2 -> H(a, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, d), b)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, d), c)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, d), e)
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, a), d)
28.57/10.38	   A^2 -> H(U1(e, a), k)
28.57/10.38	   A^2 -> H(U1(k, a), d)
28.57/10.38	   A^2 -> H(U1(c, d), d)
28.57/10.38	   A^2 -> H(U1(c, d), k)
28.57/10.38	   A^2 -> H(U1(d, e), b)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(d, e), c)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(d, e), e)
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.38	   A^2 -> H(U1(d, c), d)
28.57/10.38	   A^2 -> H(U1(d, c), k)
28.57/10.38	   A^2 -> H(U1(a, e), d)
28.57/10.38	   A^2 -> H(U1(a, e), k)
28.57/10.38	   A^2 -> H(U1(a, k), d)
28.57/10.38	   A^2 -> H(U1(a, k), k)
28.57/10.38	   A^2 -> H(k, U1(e, b))
28.57/10.38	   A^2 -> H(k, U1(c, d))
28.57/10.38	   A^2 -> H(k, U1(d, c))
28.57/10.38	   A^2 -> H(k, U1(b, e))
28.57/10.38	   A^2 -> H(k, U1(b, k))
28.57/10.38	   A^2 -> H(k, U1(e, c))
28.57/10.38	   A^2 -> H(k, U1(c, e))
28.57/10.38	   A^2 -> H(k, U1(c, k))
28.57/10.38	   A^2 -> H(k, U1(e, e))
28.57/10.38	   A^2 -> H(k, U1(d, k))
28.57/10.38	   A^2 -> H(c, b)
28.57/10.38	   A^2 -> H(c, U1(e, d))
28.57/10.38	   A^2 -> H(c, U1(d, e))
28.57/10.38	   A^2 -> H(c, c)
28.57/10.38	   A^2 -> H(c, U1(e, k))
28.57/10.38	   A^2 -> H(c, U1(k, e))
28.57/10.38	   A^2 -> H(c, e)
28.57/10.38	   A^2 -> H(c, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, k), b)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, k), c)
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, k), e)
28.57/10.38	   A^2 -> H(U1(e, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, c), d)
28.57/10.38	   A^2 -> H(U1(e, c), k)
28.57/10.38	   A^2 -> H(U1(k, e), b)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, e), c)
28.57/10.38	   A^2 -> H(U1(k, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(k, c), d)
28.57/10.38	   A^2 -> H(U1(c, e), d)
28.57/10.38	   A^2 -> H(U1(c, e), k)
28.57/10.38	   A^2 -> H(U1(c, k), d)
28.57/10.38	   A^2 -> H(U1(c, k), k)
28.57/10.38	   A^2 -> H(e, b)
28.57/10.38	   A^2 -> H(e, U1(e, d))
28.57/10.38	   A^2 -> H(e, U1(d, e))
28.57/10.38	   A^2 -> H(e, c)
28.57/10.38	   A^2 -> H(e, U1(e, k))
28.57/10.38	   A^2 -> H(e, e)
28.57/10.38	   A^2 -> H(U1(e, e), d)
28.57/10.38	   A^2 -> H(U1(e, e), k)
28.57/10.38	   A^2 -> H(U1(k, k), d)
28.57/10.38	   A^2 -> H(U1(k, k), b)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, d))
28.57/10.38	   A^2 -> H(U1(k, k), U1(d, e))
28.57/10.38	   A^2 -> H(U1(k, k), c)
28.57/10.38	   A^2 -> H(U1(k, k), U1(e, k))
28.57/10.38	   A^2 -> H(U1(k, d), d)
28.57/10.38	   A^2 -> H(U1(d, k), d)
28.57/10.38	   A^2 -> H(U1(d, k), k)
28.57/10.38	   A^2 -> H(U1(e, e), c)
28.57/10.38	   A^2 -> H(U1(e, c), e)
28.57/10.38	   A^2 -> H(U1(c, e), e)
28.57/10.38	   A^2 -> H(U1(c, k), e)
28.57/10.38	   A^2 -> H(c, U1(e, e))
28.57/10.38	   A^2 -> H(U1(e, k), U1(e, e))
28.57/10.38	
28.57/10.38	The TRS R consists of the following rules:
28.57/10.38	
28.57/10.38	   f(x) -> U1(x, x)
28.57/10.38	   U1(e, x) -> x
28.57/10.38	   a -> c
28.57/10.38	   a -> d
28.57/10.38	   b -> c
28.57/10.38	   b -> d
28.57/10.38	   d -> k
28.57/10.38	   c -> e
28.57/10.38	   c -> k
28.57/10.38	
28.57/10.38	Q is empty.
28.57/10.38	We have to consider all minimal (P,Q,R)-chains.
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2395) TransformationProof (EQUIVALENT)
28.57/10.38	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.57/10.38	
28.57/10.38	   (A^2 -> H(U1(k, e), U1(e, e)),A^2 -> H(U1(k, e), U1(e, e)))
28.57/10.38	   (A^2 -> H(U1(k, k), U1(e, e)),A^2 -> H(U1(k, k), U1(e, e)))
28.57/10.38	   (A^2 -> H(U1(k, c), e),A^2 -> H(U1(k, c), e))
28.57/10.38	
28.57/10.38	
28.57/10.38	----------------------------------------
28.57/10.38	
28.57/10.38	(2396)
28.57/10.38	Obligation:
28.57/10.38	Q DP problem:
28.57/10.38	The TRS P consists of the following rules:
28.57/10.38	
28.57/10.38	   G(d, x, x) -> A^2
28.57/10.38	   A^2 -> H(f(c), f(c))
28.57/10.38	   H(x, x) -> G(x, x, f(k))
28.57/10.38	   A^2 -> H(f(d), f(d))
28.57/10.38	   A^2 -> H(U1(c, c), U1(c, c))
28.57/10.38	   A^2 -> H(f(e), f(e))
28.57/10.38	   A^2 -> H(f(k), f(k))
28.57/10.38	   A^2 -> H(U1(d, d), U1(d, d))
28.57/10.38	   A^2 -> H(U1(c, d), U1(c, d))
28.57/10.38	   A^2 -> H(U1(d, c), U1(d, c))
28.57/10.38	   A^2 -> H(U1(e, c), U1(e, c))
28.57/10.38	   A^2 -> H(U1(k, c), U1(k, c))
28.57/10.38	   A^2 -> H(U1(c, e), U1(c, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(c, k))
28.57/10.38	   A^2 -> H(U1(e, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(k, k), U1(k, k))
28.57/10.38	   A^2 -> H(U1(k, d), U1(k, d))
28.57/10.38	   A^2 -> H(U1(d, k), U1(d, k))
28.57/10.38	   A^2 -> H(U1(c, e), U1(e, e))
28.57/10.38	   A^2 -> H(U1(c, k), U1(e, e))
28.57/10.38	   A^2 -> H(U1(e, e), e)
28.57/10.38	   A^2 -> H(d, U1(e, b))
28.57/10.38	   A^2 -> H(d, U1(k, b))
28.57/10.38	   A^2 -> H(d, U1(c, d))
28.57/10.38	   A^2 -> H(d, U1(d, c))
28.57/10.38	   A^2 -> H(d, U1(b, e))
28.57/10.38	   A^2 -> H(d, U1(b, k))
28.57/10.38	   A^2 -> H(d, U1(e, c))
28.57/10.38	   A^2 -> H(d, U1(k, c))
28.57/10.38	   A^2 -> H(d, U1(c, e))
28.57/10.38	   A^2 -> H(d, U1(c, k))
28.57/10.38	   A^2 -> H(d, U1(e, e))
28.57/10.38	   A^2 -> H(d, U1(k, k))
28.57/10.38	   A^2 -> H(d, U1(k, d))
28.57/10.38	   A^2 -> H(d, U1(d, k))
28.57/10.38	   A^2 -> H(a, b)
28.57/10.38	   A^2 -> H(a, U1(e, d))
28.57/10.38	   A^2 -> H(a, U1(d, e))
28.57/10.38	   A^2 -> H(a, c)
28.57/10.38	   A^2 -> H(a, U1(e, k))
28.57/10.38	   A^2 -> H(a, U1(k, e))
28.57/10.38	   A^2 -> H(a, e)
28.57/10.38	   A^2 -> H(a, U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, d), b)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, d))
28.57/10.38	   A^2 -> H(U1(e, d), U1(d, e))
28.57/10.38	   A^2 -> H(U1(e, d), c)
28.57/10.38	   A^2 -> H(U1(e, d), U1(e, k))
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, e))
28.57/10.38	   A^2 -> H(U1(e, d), e)
28.57/10.38	   A^2 -> H(U1(e, d), U1(k, k))
28.57/10.38	   A^2 -> H(U1(e, a), d)
28.57/10.38	   A^2 -> H(U1(e, a), k)
28.57/10.38	   A^2 -> H(U1(k, a), d)
28.57/10.38	   A^2 -> H(U1(c, d), d)
28.57/10.38	   A^2 -> H(U1(c, d), k)
28.57/10.38	   A^2 -> H(U1(d, e), b)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, d))
28.57/10.38	   A^2 -> H(U1(d, e), U1(d, e))
28.57/10.38	   A^2 -> H(U1(d, e), c)
28.57/10.38	   A^2 -> H(U1(d, e), U1(e, k))
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, e))
28.57/10.38	   A^2 -> H(U1(d, e), e)
28.57/10.38	   A^2 -> H(U1(d, e), U1(k, k))
28.57/10.38	   A^2 -> H(U1(d, c), d)
28.57/10.38	   A^2 -> H(U1(d, c), k)
28.57/10.38	   A^2 -> H(U1(a, e), d)
28.57/10.38	   A^2 -> H(U1(a, e), k)
28.57/10.38	   A^2 -> H(U1(a, k), d)
28.57/10.38	   A^2 -> H(U1(a, k), k)
28.57/10.38	   A^2 -> H(k, U1(e, b))
28.57/10.38	   A^2 -> H(k, U1(c, d))
28.57/10.38	   A^2 -> H(k, U1(d, c))
28.57/10.38	   A^2 -> H(k, U1(b, e))
28.57/10.38	   A^2 -> H(k, U1(b, k))
28.57/10.38	   A^2 -> H(k, U1(e, c))
28.57/10.38	   A^2 -> H(k, U1(c, e))
28.57/10.38	   A^2 -> H(k, U1(c, k))
28.57/10.38	   A^2 -> H(k, U1(e, e))
28.57/10.38	   A^2 -> H(k, U1(d, k))
28.58/10.38	   A^2 -> H(c, b)
28.58/10.38	   A^2 -> H(c, U1(e, d))
28.58/10.38	   A^2 -> H(c, U1(d, e))
28.58/10.38	   A^2 -> H(c, c)
28.58/10.38	   A^2 -> H(c, U1(e, k))
28.58/10.38	   A^2 -> H(c, U1(k, e))
28.58/10.38	   A^2 -> H(c, e)
28.58/10.38	   A^2 -> H(c, U1(k, k))
28.58/10.38	   A^2 -> H(U1(e, k), b)
28.58/10.38	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.38	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.38	   A^2 -> H(U1(e, k), c)
28.58/10.38	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.38	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.38	   A^2 -> H(U1(e, k), e)
28.58/10.38	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.38	   A^2 -> H(U1(e, c), d)
28.58/10.38	   A^2 -> H(U1(e, c), k)
28.58/10.38	   A^2 -> H(U1(k, e), b)
28.58/10.38	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.38	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.38	   A^2 -> H(U1(k, e), c)
28.58/10.38	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.38	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.38	   A^2 -> H(U1(k, c), d)
28.58/10.38	   A^2 -> H(U1(c, e), d)
28.58/10.38	   A^2 -> H(U1(c, e), k)
28.58/10.38	   A^2 -> H(U1(c, k), d)
28.58/10.38	   A^2 -> H(U1(c, k), k)
28.58/10.38	   A^2 -> H(e, b)
28.58/10.38	   A^2 -> H(e, U1(e, d))
28.58/10.38	   A^2 -> H(e, U1(d, e))
28.58/10.38	   A^2 -> H(e, c)
28.58/10.38	   A^2 -> H(e, U1(e, k))
28.58/10.38	   A^2 -> H(e, e)
28.58/10.38	   A^2 -> H(U1(e, e), d)
28.58/10.38	   A^2 -> H(U1(e, e), k)
28.58/10.38	   A^2 -> H(U1(k, k), d)
28.58/10.38	   A^2 -> H(U1(k, k), b)
28.58/10.38	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.38	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.38	   A^2 -> H(U1(k, k), c)
28.58/10.38	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.38	   A^2 -> H(U1(k, d), d)
28.58/10.38	   A^2 -> H(U1(d, k), d)
28.58/10.38	   A^2 -> H(U1(d, k), k)
28.58/10.38	   A^2 -> H(U1(e, e), c)
28.58/10.38	   A^2 -> H(U1(e, c), e)
28.58/10.38	   A^2 -> H(U1(c, e), e)
28.58/10.38	   A^2 -> H(U1(c, k), e)
28.58/10.38	   A^2 -> H(c, U1(e, e))
28.58/10.38	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.38	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.38	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.38	   A^2 -> H(U1(k, c), e)
28.58/10.38	
28.58/10.38	The TRS R consists of the following rules:
28.58/10.38	
28.58/10.38	   f(x) -> U1(x, x)
28.58/10.38	   U1(e, x) -> x
28.58/10.38	   a -> c
28.58/10.38	   a -> d
28.58/10.38	   b -> c
28.58/10.38	   b -> d
28.58/10.38	   d -> k
28.58/10.38	   c -> e
28.58/10.38	   c -> k
28.58/10.38	
28.58/10.38	Q is empty.
28.58/10.38	We have to consider all minimal (P,Q,R)-chains.
28.58/10.38	----------------------------------------
28.58/10.38	
28.58/10.38	(2397) DependencyGraphProof (EQUIVALENT)
28.58/10.38	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.38	----------------------------------------
28.58/10.38	
28.58/10.38	(2398)
28.58/10.38	Obligation:
28.58/10.38	Q DP problem:
28.58/10.38	The TRS P consists of the following rules:
28.58/10.38	
28.58/10.38	   A^2 -> H(f(c), f(c))
28.58/10.38	   H(x, x) -> G(x, x, f(k))
28.58/10.38	   G(d, x, x) -> A^2
28.58/10.38	   A^2 -> H(f(d), f(d))
28.58/10.38	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.38	   A^2 -> H(f(e), f(e))
28.58/10.38	   A^2 -> H(f(k), f(k))
28.58/10.38	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.38	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.38	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.38	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.38	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.38	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.38	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.38	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.38	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.38	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.38	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.38	   A^2 -> H(U1(c, e), U1(e, e))
28.58/10.38	   A^2 -> H(U1(c, k), U1(e, e))
28.58/10.38	   A^2 -> H(U1(e, e), e)
28.58/10.38	   A^2 -> H(d, U1(e, b))
28.58/10.38	   A^2 -> H(d, U1(k, b))
28.58/10.38	   A^2 -> H(d, U1(c, d))
28.58/10.38	   A^2 -> H(d, U1(d, c))
28.58/10.38	   A^2 -> H(d, U1(b, e))
28.58/10.38	   A^2 -> H(d, U1(b, k))
28.58/10.38	   A^2 -> H(d, U1(e, c))
28.58/10.38	   A^2 -> H(d, U1(k, c))
28.58/10.38	   A^2 -> H(d, U1(c, e))
28.58/10.38	   A^2 -> H(d, U1(c, k))
28.58/10.38	   A^2 -> H(d, U1(e, e))
28.58/10.38	   A^2 -> H(d, U1(k, k))
28.58/10.38	   A^2 -> H(d, U1(k, d))
28.58/10.38	   A^2 -> H(d, U1(d, k))
28.58/10.38	   A^2 -> H(a, b)
28.58/10.38	   A^2 -> H(a, U1(e, d))
28.58/10.38	   A^2 -> H(a, U1(d, e))
28.58/10.38	   A^2 -> H(a, c)
28.58/10.38	   A^2 -> H(a, U1(e, k))
28.58/10.38	   A^2 -> H(a, U1(k, e))
28.58/10.38	   A^2 -> H(a, e)
28.58/10.38	   A^2 -> H(a, U1(k, k))
28.58/10.38	   A^2 -> H(U1(e, d), b)
28.58/10.38	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.38	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.38	   A^2 -> H(U1(e, d), c)
28.58/10.38	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.38	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.38	   A^2 -> H(U1(e, d), e)
28.58/10.38	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.38	   A^2 -> H(U1(e, a), d)
28.58/10.38	   A^2 -> H(U1(e, a), k)
28.58/10.38	   A^2 -> H(U1(k, a), d)
28.58/10.38	   A^2 -> H(U1(c, d), d)
28.58/10.38	   A^2 -> H(U1(c, d), k)
28.58/10.38	   A^2 -> H(U1(d, e), b)
28.58/10.38	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.38	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.38	   A^2 -> H(U1(d, e), c)
28.58/10.38	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.38	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.38	   A^2 -> H(U1(d, e), e)
28.58/10.38	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.38	   A^2 -> H(U1(d, c), d)
28.58/10.38	   A^2 -> H(U1(d, c), k)
28.58/10.38	   A^2 -> H(U1(a, e), d)
28.58/10.38	   A^2 -> H(U1(a, e), k)
28.58/10.38	   A^2 -> H(U1(a, k), d)
28.58/10.38	   A^2 -> H(U1(a, k), k)
28.58/10.38	   A^2 -> H(k, U1(e, b))
28.58/10.38	   A^2 -> H(k, U1(c, d))
28.58/10.38	   A^2 -> H(k, U1(d, c))
28.58/10.38	   A^2 -> H(k, U1(b, e))
28.58/10.38	   A^2 -> H(k, U1(b, k))
28.58/10.38	   A^2 -> H(k, U1(e, c))
28.58/10.38	   A^2 -> H(k, U1(c, e))
28.58/10.38	   A^2 -> H(k, U1(c, k))
28.58/10.38	   A^2 -> H(k, U1(e, e))
28.58/10.38	   A^2 -> H(k, U1(d, k))
28.58/10.38	   A^2 -> H(c, b)
28.58/10.38	   A^2 -> H(c, U1(e, d))
28.58/10.38	   A^2 -> H(c, U1(d, e))
28.58/10.38	   A^2 -> H(c, c)
28.58/10.38	   A^2 -> H(c, U1(e, k))
28.58/10.38	   A^2 -> H(c, U1(k, e))
28.58/10.38	   A^2 -> H(c, e)
28.58/10.38	   A^2 -> H(c, U1(k, k))
28.58/10.38	   A^2 -> H(U1(e, k), b)
28.58/10.38	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.38	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.38	   A^2 -> H(U1(e, k), c)
28.58/10.38	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.38	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.38	   A^2 -> H(U1(e, k), e)
28.58/10.38	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.38	   A^2 -> H(U1(e, c), d)
28.58/10.38	   A^2 -> H(U1(e, c), k)
28.58/10.38	   A^2 -> H(U1(k, e), b)
28.58/10.38	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.38	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.38	   A^2 -> H(U1(k, e), c)
28.58/10.38	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.38	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.38	   A^2 -> H(U1(k, c), d)
28.58/10.38	   A^2 -> H(U1(c, e), d)
28.58/10.38	   A^2 -> H(U1(c, e), k)
28.58/10.38	   A^2 -> H(U1(c, k), d)
28.58/10.38	   A^2 -> H(U1(c, k), k)
28.58/10.38	   A^2 -> H(e, b)
28.58/10.38	   A^2 -> H(e, U1(e, d))
28.58/10.38	   A^2 -> H(e, U1(d, e))
28.58/10.38	   A^2 -> H(e, c)
28.58/10.38	   A^2 -> H(e, U1(e, k))
28.58/10.38	   A^2 -> H(e, e)
28.58/10.38	   A^2 -> H(U1(e, e), d)
28.58/10.38	   A^2 -> H(U1(e, e), k)
28.58/10.38	   A^2 -> H(U1(k, k), d)
28.58/10.38	   A^2 -> H(U1(k, k), b)
28.58/10.38	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.38	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.38	   A^2 -> H(U1(k, k), c)
28.58/10.38	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.38	   A^2 -> H(U1(k, d), d)
28.58/10.38	   A^2 -> H(U1(d, k), d)
28.58/10.38	   A^2 -> H(U1(d, k), k)
28.58/10.38	   A^2 -> H(U1(e, e), c)
28.58/10.38	   A^2 -> H(U1(e, c), e)
28.58/10.38	   A^2 -> H(U1(c, e), e)
28.58/10.38	   A^2 -> H(U1(c, k), e)
28.58/10.38	   A^2 -> H(c, U1(e, e))
28.58/10.38	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.38	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.38	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.38	
28.58/10.38	The TRS R consists of the following rules:
28.58/10.38	
28.58/10.38	   f(x) -> U1(x, x)
28.58/10.38	   U1(e, x) -> x
28.58/10.38	   a -> c
28.58/10.38	   a -> d
28.58/10.38	   b -> c
28.58/10.38	   b -> d
28.58/10.38	   d -> k
28.58/10.38	   c -> e
28.58/10.38	   c -> k
28.58/10.38	
28.58/10.38	Q is empty.
28.58/10.38	We have to consider all minimal (P,Q,R)-chains.
28.58/10.38	----------------------------------------
28.58/10.38	
28.58/10.38	(2399) TransformationProof (EQUIVALENT)
28.58/10.38	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.38	
28.58/10.38	   (A^2 -> H(U1(e, e), U1(e, e)),A^2 -> H(U1(e, e), U1(e, e)))
28.58/10.38	   (A^2 -> H(U1(k, e), U1(e, e)),A^2 -> H(U1(k, e), U1(e, e)))
28.58/10.38	   (A^2 -> H(U1(c, e), e),A^2 -> H(U1(c, e), e))
28.58/10.38	
28.58/10.38	
28.58/10.38	----------------------------------------
28.58/10.38	
28.58/10.38	(2400)
28.58/10.38	Obligation:
28.58/10.38	Q DP problem:
28.58/10.38	The TRS P consists of the following rules:
28.58/10.38	
28.58/10.38	   A^2 -> H(f(c), f(c))
28.58/10.38	   H(x, x) -> G(x, x, f(k))
28.58/10.38	   G(d, x, x) -> A^2
28.58/10.38	   A^2 -> H(f(d), f(d))
28.58/10.38	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.38	   A^2 -> H(f(e), f(e))
28.58/10.38	   A^2 -> H(f(k), f(k))
28.58/10.38	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.38	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.38	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.38	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.38	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.38	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.38	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.38	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.38	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.38	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.38	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.38	   A^2 -> H(U1(c, k), U1(e, e))
28.58/10.38	   A^2 -> H(U1(e, e), e)
28.58/10.38	   A^2 -> H(d, U1(e, b))
28.58/10.38	   A^2 -> H(d, U1(k, b))
28.58/10.38	   A^2 -> H(d, U1(c, d))
28.58/10.38	   A^2 -> H(d, U1(d, c))
28.58/10.38	   A^2 -> H(d, U1(b, e))
28.58/10.38	   A^2 -> H(d, U1(b, k))
28.58/10.38	   A^2 -> H(d, U1(e, c))
28.58/10.38	   A^2 -> H(d, U1(k, c))
28.58/10.38	   A^2 -> H(d, U1(c, e))
28.58/10.38	   A^2 -> H(d, U1(c, k))
28.58/10.38	   A^2 -> H(d, U1(e, e))
28.58/10.38	   A^2 -> H(d, U1(k, k))
28.58/10.38	   A^2 -> H(d, U1(k, d))
28.58/10.38	   A^2 -> H(d, U1(d, k))
28.58/10.38	   A^2 -> H(a, b)
28.58/10.38	   A^2 -> H(a, U1(e, d))
28.58/10.38	   A^2 -> H(a, U1(d, e))
28.58/10.38	   A^2 -> H(a, c)
28.58/10.38	   A^2 -> H(a, U1(e, k))
28.58/10.38	   A^2 -> H(a, U1(k, e))
28.58/10.38	   A^2 -> H(a, e)
28.58/10.38	   A^2 -> H(a, U1(k, k))
28.58/10.38	   A^2 -> H(U1(e, d), b)
28.58/10.38	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.38	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.38	   A^2 -> H(U1(e, d), c)
28.58/10.38	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.38	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.38	   A^2 -> H(U1(e, d), e)
28.58/10.38	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.38	   A^2 -> H(U1(e, a), d)
28.58/10.38	   A^2 -> H(U1(e, a), k)
28.58/10.38	   A^2 -> H(U1(k, a), d)
28.58/10.38	   A^2 -> H(U1(c, d), d)
28.58/10.38	   A^2 -> H(U1(c, d), k)
28.58/10.38	   A^2 -> H(U1(d, e), b)
28.58/10.38	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.38	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.38	   A^2 -> H(U1(d, e), c)
28.58/10.38	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.38	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.38	   A^2 -> H(U1(d, e), e)
28.58/10.38	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.38	   A^2 -> H(U1(d, c), d)
28.58/10.38	   A^2 -> H(U1(d, c), k)
28.58/10.38	   A^2 -> H(U1(a, e), d)
28.58/10.38	   A^2 -> H(U1(a, e), k)
28.58/10.38	   A^2 -> H(U1(a, k), d)
28.58/10.38	   A^2 -> H(U1(a, k), k)
28.58/10.38	   A^2 -> H(k, U1(e, b))
28.58/10.38	   A^2 -> H(k, U1(c, d))
28.58/10.38	   A^2 -> H(k, U1(d, c))
28.58/10.38	   A^2 -> H(k, U1(b, e))
28.58/10.38	   A^2 -> H(k, U1(b, k))
28.58/10.38	   A^2 -> H(k, U1(e, c))
28.58/10.38	   A^2 -> H(k, U1(c, e))
28.58/10.38	   A^2 -> H(k, U1(c, k))
28.58/10.38	   A^2 -> H(k, U1(e, e))
28.58/10.38	   A^2 -> H(k, U1(d, k))
28.58/10.38	   A^2 -> H(c, b)
28.58/10.38	   A^2 -> H(c, U1(e, d))
28.58/10.38	   A^2 -> H(c, U1(d, e))
28.58/10.38	   A^2 -> H(c, c)
28.58/10.38	   A^2 -> H(c, U1(e, k))
28.58/10.38	   A^2 -> H(c, U1(k, e))
28.58/10.38	   A^2 -> H(c, e)
28.58/10.38	   A^2 -> H(c, U1(k, k))
28.58/10.38	   A^2 -> H(U1(e, k), b)
28.58/10.38	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.38	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.38	   A^2 -> H(U1(e, k), c)
28.58/10.38	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.38	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.38	   A^2 -> H(U1(e, k), e)
28.58/10.38	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.38	   A^2 -> H(U1(e, c), d)
28.58/10.38	   A^2 -> H(U1(e, c), k)
28.58/10.38	   A^2 -> H(U1(k, e), b)
28.58/10.38	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.38	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.38	   A^2 -> H(U1(k, e), c)
28.58/10.38	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.38	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.38	   A^2 -> H(U1(k, c), d)
28.58/10.38	   A^2 -> H(U1(c, e), d)
28.58/10.38	   A^2 -> H(U1(c, e), k)
28.58/10.38	   A^2 -> H(U1(c, k), d)
28.58/10.38	   A^2 -> H(U1(c, k), k)
28.58/10.38	   A^2 -> H(e, b)
28.58/10.38	   A^2 -> H(e, U1(e, d))
28.58/10.38	   A^2 -> H(e, U1(d, e))
28.58/10.38	   A^2 -> H(e, c)
28.58/10.38	   A^2 -> H(e, U1(e, k))
28.58/10.38	   A^2 -> H(e, e)
28.58/10.39	   A^2 -> H(U1(e, e), d)
28.58/10.39	   A^2 -> H(U1(e, e), k)
28.58/10.39	   A^2 -> H(U1(k, k), d)
28.58/10.39	   A^2 -> H(U1(k, k), b)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, k), c)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, d), d)
28.58/10.39	   A^2 -> H(U1(d, k), d)
28.58/10.39	   A^2 -> H(U1(d, k), k)
28.58/10.39	   A^2 -> H(U1(e, e), c)
28.58/10.39	   A^2 -> H(U1(e, c), e)
28.58/10.39	   A^2 -> H(U1(c, e), e)
28.58/10.39	   A^2 -> H(U1(c, k), e)
28.58/10.39	   A^2 -> H(c, U1(e, e))
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.39	
28.58/10.39	The TRS R consists of the following rules:
28.58/10.39	
28.58/10.39	   f(x) -> U1(x, x)
28.58/10.39	   U1(e, x) -> x
28.58/10.39	   a -> c
28.58/10.39	   a -> d
28.58/10.39	   b -> c
28.58/10.39	   b -> d
28.58/10.39	   d -> k
28.58/10.39	   c -> e
28.58/10.39	   c -> k
28.58/10.39	
28.58/10.39	Q is empty.
28.58/10.39	We have to consider all minimal (P,Q,R)-chains.
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2401) TransformationProof (EQUIVALENT)
28.58/10.39	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.39	
28.58/10.39	   (A^2 -> H(U1(e, k), U1(e, e)),A^2 -> H(U1(e, k), U1(e, e)))
28.58/10.39	   (A^2 -> H(U1(k, k), U1(e, e)),A^2 -> H(U1(k, k), U1(e, e)))
28.58/10.39	   (A^2 -> H(U1(c, k), e),A^2 -> H(U1(c, k), e))
28.58/10.39	
28.58/10.39	
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2402)
28.58/10.39	Obligation:
28.58/10.39	Q DP problem:
28.58/10.39	The TRS P consists of the following rules:
28.58/10.39	
28.58/10.39	   A^2 -> H(f(c), f(c))
28.58/10.39	   H(x, x) -> G(x, x, f(k))
28.58/10.39	   G(d, x, x) -> A^2
28.58/10.39	   A^2 -> H(f(d), f(d))
28.58/10.39	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.39	   A^2 -> H(f(e), f(e))
28.58/10.39	   A^2 -> H(f(k), f(k))
28.58/10.39	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.39	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.39	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.39	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.39	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.39	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.39	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.39	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.39	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.39	   A^2 -> H(U1(e, e), e)
28.58/10.39	   A^2 -> H(d, U1(e, b))
28.58/10.39	   A^2 -> H(d, U1(k, b))
28.58/10.39	   A^2 -> H(d, U1(c, d))
28.58/10.39	   A^2 -> H(d, U1(d, c))
28.58/10.39	   A^2 -> H(d, U1(b, e))
28.58/10.39	   A^2 -> H(d, U1(b, k))
28.58/10.39	   A^2 -> H(d, U1(e, c))
28.58/10.39	   A^2 -> H(d, U1(k, c))
28.58/10.39	   A^2 -> H(d, U1(c, e))
28.58/10.39	   A^2 -> H(d, U1(c, k))
28.58/10.39	   A^2 -> H(d, U1(e, e))
28.58/10.39	   A^2 -> H(d, U1(k, k))
28.58/10.39	   A^2 -> H(d, U1(k, d))
28.58/10.39	   A^2 -> H(d, U1(d, k))
28.58/10.39	   A^2 -> H(a, b)
28.58/10.39	   A^2 -> H(a, U1(e, d))
28.58/10.39	   A^2 -> H(a, U1(d, e))
28.58/10.39	   A^2 -> H(a, c)
28.58/10.39	   A^2 -> H(a, U1(e, k))
28.58/10.39	   A^2 -> H(a, U1(k, e))
28.58/10.39	   A^2 -> H(a, e)
28.58/10.39	   A^2 -> H(a, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, d), b)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, d), c)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, d), e)
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, a), d)
28.58/10.39	   A^2 -> H(U1(e, a), k)
28.58/10.39	   A^2 -> H(U1(k, a), d)
28.58/10.39	   A^2 -> H(U1(c, d), d)
28.58/10.39	   A^2 -> H(U1(c, d), k)
28.58/10.39	   A^2 -> H(U1(d, e), b)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(d, e), c)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(d, e), e)
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.39	   A^2 -> H(U1(d, c), d)
28.58/10.39	   A^2 -> H(U1(d, c), k)
28.58/10.39	   A^2 -> H(U1(a, e), d)
28.58/10.39	   A^2 -> H(U1(a, e), k)
28.58/10.39	   A^2 -> H(U1(a, k), d)
28.58/10.39	   A^2 -> H(U1(a, k), k)
28.58/10.39	   A^2 -> H(k, U1(e, b))
28.58/10.39	   A^2 -> H(k, U1(c, d))
28.58/10.39	   A^2 -> H(k, U1(d, c))
28.58/10.39	   A^2 -> H(k, U1(b, e))
28.58/10.39	   A^2 -> H(k, U1(b, k))
28.58/10.39	   A^2 -> H(k, U1(e, c))
28.58/10.39	   A^2 -> H(k, U1(c, e))
28.58/10.39	   A^2 -> H(k, U1(c, k))
28.58/10.39	   A^2 -> H(k, U1(e, e))
28.58/10.39	   A^2 -> H(k, U1(d, k))
28.58/10.39	   A^2 -> H(c, b)
28.58/10.39	   A^2 -> H(c, U1(e, d))
28.58/10.39	   A^2 -> H(c, U1(d, e))
28.58/10.39	   A^2 -> H(c, c)
28.58/10.39	   A^2 -> H(c, U1(e, k))
28.58/10.39	   A^2 -> H(c, U1(k, e))
28.58/10.39	   A^2 -> H(c, e)
28.58/10.39	   A^2 -> H(c, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, k), b)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, k), c)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, k), e)
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, c), d)
28.58/10.39	   A^2 -> H(U1(e, c), k)
28.58/10.39	   A^2 -> H(U1(k, e), b)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, e), c)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(k, c), d)
28.58/10.39	   A^2 -> H(U1(c, e), d)
28.58/10.39	   A^2 -> H(U1(c, e), k)
28.58/10.39	   A^2 -> H(U1(c, k), d)
28.58/10.39	   A^2 -> H(U1(c, k), k)
28.58/10.39	   A^2 -> H(e, b)
28.58/10.39	   A^2 -> H(e, U1(e, d))
28.58/10.39	   A^2 -> H(e, U1(d, e))
28.58/10.39	   A^2 -> H(e, c)
28.58/10.39	   A^2 -> H(e, U1(e, k))
28.58/10.39	   A^2 -> H(e, e)
28.58/10.39	   A^2 -> H(U1(e, e), d)
28.58/10.39	   A^2 -> H(U1(e, e), k)
28.58/10.39	   A^2 -> H(U1(k, k), d)
28.58/10.39	   A^2 -> H(U1(k, k), b)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, k), c)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, d), d)
28.58/10.39	   A^2 -> H(U1(d, k), d)
28.58/10.39	   A^2 -> H(U1(d, k), k)
28.58/10.39	   A^2 -> H(U1(e, e), c)
28.58/10.39	   A^2 -> H(U1(e, c), e)
28.58/10.39	   A^2 -> H(U1(c, e), e)
28.58/10.39	   A^2 -> H(U1(c, k), e)
28.58/10.39	   A^2 -> H(c, U1(e, e))
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.39	
28.58/10.39	The TRS R consists of the following rules:
28.58/10.39	
28.58/10.39	   f(x) -> U1(x, x)
28.58/10.39	   U1(e, x) -> x
28.58/10.39	   a -> c
28.58/10.39	   a -> d
28.58/10.39	   b -> c
28.58/10.39	   b -> d
28.58/10.39	   d -> k
28.58/10.39	   c -> e
28.58/10.39	   c -> k
28.58/10.39	
28.58/10.39	Q is empty.
28.58/10.39	We have to consider all minimal (P,Q,R)-chains.
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2403) TransformationProof (EQUIVALENT)
28.58/10.39	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), e) at position [] we obtained the following new rules [LPAR04]:
28.58/10.39	
28.58/10.39	   (A^2 -> H(e, e),A^2 -> H(e, e))
28.58/10.39	
28.58/10.39	
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2404)
28.58/10.39	Obligation:
28.58/10.39	Q DP problem:
28.58/10.39	The TRS P consists of the following rules:
28.58/10.39	
28.58/10.39	   A^2 -> H(f(c), f(c))
28.58/10.39	   H(x, x) -> G(x, x, f(k))
28.58/10.39	   G(d, x, x) -> A^2
28.58/10.39	   A^2 -> H(f(d), f(d))
28.58/10.39	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.39	   A^2 -> H(f(e), f(e))
28.58/10.39	   A^2 -> H(f(k), f(k))
28.58/10.39	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.39	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.39	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.39	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.39	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.39	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.39	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.39	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.39	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.39	   A^2 -> H(d, U1(e, b))
28.58/10.39	   A^2 -> H(d, U1(k, b))
28.58/10.39	   A^2 -> H(d, U1(c, d))
28.58/10.39	   A^2 -> H(d, U1(d, c))
28.58/10.39	   A^2 -> H(d, U1(b, e))
28.58/10.39	   A^2 -> H(d, U1(b, k))
28.58/10.39	   A^2 -> H(d, U1(e, c))
28.58/10.39	   A^2 -> H(d, U1(k, c))
28.58/10.39	   A^2 -> H(d, U1(c, e))
28.58/10.39	   A^2 -> H(d, U1(c, k))
28.58/10.39	   A^2 -> H(d, U1(e, e))
28.58/10.39	   A^2 -> H(d, U1(k, k))
28.58/10.39	   A^2 -> H(d, U1(k, d))
28.58/10.39	   A^2 -> H(d, U1(d, k))
28.58/10.39	   A^2 -> H(a, b)
28.58/10.39	   A^2 -> H(a, U1(e, d))
28.58/10.39	   A^2 -> H(a, U1(d, e))
28.58/10.39	   A^2 -> H(a, c)
28.58/10.39	   A^2 -> H(a, U1(e, k))
28.58/10.39	   A^2 -> H(a, U1(k, e))
28.58/10.39	   A^2 -> H(a, e)
28.58/10.39	   A^2 -> H(a, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, d), b)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, d), c)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, d), e)
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, a), d)
28.58/10.39	   A^2 -> H(U1(e, a), k)
28.58/10.39	   A^2 -> H(U1(k, a), d)
28.58/10.39	   A^2 -> H(U1(c, d), d)
28.58/10.39	   A^2 -> H(U1(c, d), k)
28.58/10.39	   A^2 -> H(U1(d, e), b)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(d, e), c)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(d, e), e)
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.39	   A^2 -> H(U1(d, c), d)
28.58/10.39	   A^2 -> H(U1(d, c), k)
28.58/10.39	   A^2 -> H(U1(a, e), d)
28.58/10.39	   A^2 -> H(U1(a, e), k)
28.58/10.39	   A^2 -> H(U1(a, k), d)
28.58/10.39	   A^2 -> H(U1(a, k), k)
28.58/10.39	   A^2 -> H(k, U1(e, b))
28.58/10.39	   A^2 -> H(k, U1(c, d))
28.58/10.39	   A^2 -> H(k, U1(d, c))
28.58/10.39	   A^2 -> H(k, U1(b, e))
28.58/10.39	   A^2 -> H(k, U1(b, k))
28.58/10.39	   A^2 -> H(k, U1(e, c))
28.58/10.39	   A^2 -> H(k, U1(c, e))
28.58/10.39	   A^2 -> H(k, U1(c, k))
28.58/10.39	   A^2 -> H(k, U1(e, e))
28.58/10.39	   A^2 -> H(k, U1(d, k))
28.58/10.39	   A^2 -> H(c, b)
28.58/10.39	   A^2 -> H(c, U1(e, d))
28.58/10.39	   A^2 -> H(c, U1(d, e))
28.58/10.39	   A^2 -> H(c, c)
28.58/10.39	   A^2 -> H(c, U1(e, k))
28.58/10.39	   A^2 -> H(c, U1(k, e))
28.58/10.39	   A^2 -> H(c, e)
28.58/10.39	   A^2 -> H(c, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, k), b)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, k), c)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, k), e)
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, c), d)
28.58/10.39	   A^2 -> H(U1(e, c), k)
28.58/10.39	   A^2 -> H(U1(k, e), b)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, e), c)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(k, c), d)
28.58/10.39	   A^2 -> H(U1(c, e), d)
28.58/10.39	   A^2 -> H(U1(c, e), k)
28.58/10.39	   A^2 -> H(U1(c, k), d)
28.58/10.39	   A^2 -> H(U1(c, k), k)
28.58/10.39	   A^2 -> H(e, b)
28.58/10.39	   A^2 -> H(e, U1(e, d))
28.58/10.39	   A^2 -> H(e, U1(d, e))
28.58/10.39	   A^2 -> H(e, c)
28.58/10.39	   A^2 -> H(e, U1(e, k))
28.58/10.39	   A^2 -> H(e, e)
28.58/10.39	   A^2 -> H(U1(e, e), d)
28.58/10.39	   A^2 -> H(U1(e, e), k)
28.58/10.39	   A^2 -> H(U1(k, k), d)
28.58/10.39	   A^2 -> H(U1(k, k), b)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, k), c)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, d), d)
28.58/10.39	   A^2 -> H(U1(d, k), d)
28.58/10.39	   A^2 -> H(U1(d, k), k)
28.58/10.39	   A^2 -> H(U1(e, e), c)
28.58/10.39	   A^2 -> H(U1(e, c), e)
28.58/10.39	   A^2 -> H(U1(c, e), e)
28.58/10.39	   A^2 -> H(U1(c, k), e)
28.58/10.39	   A^2 -> H(c, U1(e, e))
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.39	
28.58/10.39	The TRS R consists of the following rules:
28.58/10.39	
28.58/10.39	   f(x) -> U1(x, x)
28.58/10.39	   U1(e, x) -> x
28.58/10.39	   a -> c
28.58/10.39	   a -> d
28.58/10.39	   b -> c
28.58/10.39	   b -> d
28.58/10.39	   d -> k
28.58/10.39	   c -> e
28.58/10.39	   c -> k
28.58/10.39	
28.58/10.39	Q is empty.
28.58/10.39	We have to consider all minimal (P,Q,R)-chains.
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2405) TransformationProof (EQUIVALENT)
28.58/10.39	By narrowing [LPAR04] the rule A^2 -> H(d, U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.39	
28.58/10.39	   (A^2 -> H(k, U1(e, b)),A^2 -> H(k, U1(e, b)))
28.58/10.39	   (A^2 -> H(d, b),A^2 -> H(d, b))
28.58/10.39	   (A^2 -> H(d, U1(e, c)),A^2 -> H(d, U1(e, c)))
28.58/10.39	   (A^2 -> H(d, U1(e, d)),A^2 -> H(d, U1(e, d)))
28.58/10.39	
28.58/10.39	
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2406)
28.58/10.39	Obligation:
28.58/10.39	Q DP problem:
28.58/10.39	The TRS P consists of the following rules:
28.58/10.39	
28.58/10.39	   A^2 -> H(f(c), f(c))
28.58/10.39	   H(x, x) -> G(x, x, f(k))
28.58/10.39	   G(d, x, x) -> A^2
28.58/10.39	   A^2 -> H(f(d), f(d))
28.58/10.39	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.39	   A^2 -> H(f(e), f(e))
28.58/10.39	   A^2 -> H(f(k), f(k))
28.58/10.39	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.39	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.39	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.39	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.39	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.39	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.39	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.39	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.39	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.39	   A^2 -> H(d, U1(k, b))
28.58/10.39	   A^2 -> H(d, U1(c, d))
28.58/10.39	   A^2 -> H(d, U1(d, c))
28.58/10.39	   A^2 -> H(d, U1(b, e))
28.58/10.39	   A^2 -> H(d, U1(b, k))
28.58/10.39	   A^2 -> H(d, U1(e, c))
28.58/10.39	   A^2 -> H(d, U1(k, c))
28.58/10.39	   A^2 -> H(d, U1(c, e))
28.58/10.39	   A^2 -> H(d, U1(c, k))
28.58/10.39	   A^2 -> H(d, U1(e, e))
28.58/10.39	   A^2 -> H(d, U1(k, k))
28.58/10.39	   A^2 -> H(d, U1(k, d))
28.58/10.39	   A^2 -> H(d, U1(d, k))
28.58/10.39	   A^2 -> H(a, b)
28.58/10.39	   A^2 -> H(a, U1(e, d))
28.58/10.39	   A^2 -> H(a, U1(d, e))
28.58/10.39	   A^2 -> H(a, c)
28.58/10.39	   A^2 -> H(a, U1(e, k))
28.58/10.39	   A^2 -> H(a, U1(k, e))
28.58/10.39	   A^2 -> H(a, e)
28.58/10.39	   A^2 -> H(a, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, d), b)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, d), c)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, d), e)
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, a), d)
28.58/10.39	   A^2 -> H(U1(e, a), k)
28.58/10.39	   A^2 -> H(U1(k, a), d)
28.58/10.39	   A^2 -> H(U1(c, d), d)
28.58/10.39	   A^2 -> H(U1(c, d), k)
28.58/10.39	   A^2 -> H(U1(d, e), b)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(d, e), c)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(d, e), e)
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.39	   A^2 -> H(U1(d, c), d)
28.58/10.39	   A^2 -> H(U1(d, c), k)
28.58/10.39	   A^2 -> H(U1(a, e), d)
28.58/10.39	   A^2 -> H(U1(a, e), k)
28.58/10.39	   A^2 -> H(U1(a, k), d)
28.58/10.39	   A^2 -> H(U1(a, k), k)
28.58/10.39	   A^2 -> H(k, U1(e, b))
28.58/10.39	   A^2 -> H(k, U1(c, d))
28.58/10.39	   A^2 -> H(k, U1(d, c))
28.58/10.39	   A^2 -> H(k, U1(b, e))
28.58/10.39	   A^2 -> H(k, U1(b, k))
28.58/10.39	   A^2 -> H(k, U1(e, c))
28.58/10.39	   A^2 -> H(k, U1(c, e))
28.58/10.39	   A^2 -> H(k, U1(c, k))
28.58/10.39	   A^2 -> H(k, U1(e, e))
28.58/10.39	   A^2 -> H(k, U1(d, k))
28.58/10.39	   A^2 -> H(c, b)
28.58/10.39	   A^2 -> H(c, U1(e, d))
28.58/10.39	   A^2 -> H(c, U1(d, e))
28.58/10.39	   A^2 -> H(c, c)
28.58/10.39	   A^2 -> H(c, U1(e, k))
28.58/10.39	   A^2 -> H(c, U1(k, e))
28.58/10.39	   A^2 -> H(c, e)
28.58/10.39	   A^2 -> H(c, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, k), b)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, k), c)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, k), e)
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, c), d)
28.58/10.39	   A^2 -> H(U1(e, c), k)
28.58/10.39	   A^2 -> H(U1(k, e), b)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, e), c)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(k, c), d)
28.58/10.39	   A^2 -> H(U1(c, e), d)
28.58/10.39	   A^2 -> H(U1(c, e), k)
28.58/10.39	   A^2 -> H(U1(c, k), d)
28.58/10.39	   A^2 -> H(U1(c, k), k)
28.58/10.39	   A^2 -> H(e, b)
28.58/10.39	   A^2 -> H(e, U1(e, d))
28.58/10.39	   A^2 -> H(e, U1(d, e))
28.58/10.39	   A^2 -> H(e, c)
28.58/10.39	   A^2 -> H(e, U1(e, k))
28.58/10.39	   A^2 -> H(e, e)
28.58/10.39	   A^2 -> H(U1(e, e), d)
28.58/10.39	   A^2 -> H(U1(e, e), k)
28.58/10.39	   A^2 -> H(U1(k, k), d)
28.58/10.39	   A^2 -> H(U1(k, k), b)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, k), c)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, d), d)
28.58/10.39	   A^2 -> H(U1(d, k), d)
28.58/10.39	   A^2 -> H(U1(d, k), k)
28.58/10.39	   A^2 -> H(U1(e, e), c)
28.58/10.39	   A^2 -> H(U1(e, c), e)
28.58/10.39	   A^2 -> H(U1(c, e), e)
28.58/10.39	   A^2 -> H(U1(c, k), e)
28.58/10.39	   A^2 -> H(c, U1(e, e))
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.39	   A^2 -> H(d, b)
28.58/10.39	   A^2 -> H(d, U1(e, d))
28.58/10.39	
28.58/10.39	The TRS R consists of the following rules:
28.58/10.39	
28.58/10.39	   f(x) -> U1(x, x)
28.58/10.39	   U1(e, x) -> x
28.58/10.39	   a -> c
28.58/10.39	   a -> d
28.58/10.39	   b -> c
28.58/10.39	   b -> d
28.58/10.39	   d -> k
28.58/10.39	   c -> e
28.58/10.39	   c -> k
28.58/10.39	
28.58/10.39	Q is empty.
28.58/10.39	We have to consider all minimal (P,Q,R)-chains.
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2407) TransformationProof (EQUIVALENT)
28.58/10.39	By narrowing [LPAR04] the rule A^2 -> H(d, U1(k, b)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.39	
28.58/10.39	   (A^2 -> H(k, U1(k, b)),A^2 -> H(k, U1(k, b)))
28.58/10.39	   (A^2 -> H(d, U1(k, c)),A^2 -> H(d, U1(k, c)))
28.58/10.39	   (A^2 -> H(d, U1(k, d)),A^2 -> H(d, U1(k, d)))
28.58/10.39	
28.58/10.39	
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2408)
28.58/10.39	Obligation:
28.58/10.39	Q DP problem:
28.58/10.39	The TRS P consists of the following rules:
28.58/10.39	
28.58/10.39	   A^2 -> H(f(c), f(c))
28.58/10.39	   H(x, x) -> G(x, x, f(k))
28.58/10.39	   G(d, x, x) -> A^2
28.58/10.39	   A^2 -> H(f(d), f(d))
28.58/10.39	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.39	   A^2 -> H(f(e), f(e))
28.58/10.39	   A^2 -> H(f(k), f(k))
28.58/10.39	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.39	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.39	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.39	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.39	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.39	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.39	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.39	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.39	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.39	   A^2 -> H(d, U1(c, d))
28.58/10.39	   A^2 -> H(d, U1(d, c))
28.58/10.39	   A^2 -> H(d, U1(b, e))
28.58/10.39	   A^2 -> H(d, U1(b, k))
28.58/10.39	   A^2 -> H(d, U1(e, c))
28.58/10.39	   A^2 -> H(d, U1(k, c))
28.58/10.39	   A^2 -> H(d, U1(c, e))
28.58/10.39	   A^2 -> H(d, U1(c, k))
28.58/10.39	   A^2 -> H(d, U1(e, e))
28.58/10.39	   A^2 -> H(d, U1(k, k))
28.58/10.39	   A^2 -> H(d, U1(k, d))
28.58/10.39	   A^2 -> H(d, U1(d, k))
28.58/10.39	   A^2 -> H(a, b)
28.58/10.39	   A^2 -> H(a, U1(e, d))
28.58/10.39	   A^2 -> H(a, U1(d, e))
28.58/10.39	   A^2 -> H(a, c)
28.58/10.39	   A^2 -> H(a, U1(e, k))
28.58/10.39	   A^2 -> H(a, U1(k, e))
28.58/10.39	   A^2 -> H(a, e)
28.58/10.39	   A^2 -> H(a, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, d), b)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, d), c)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, d), e)
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, a), d)
28.58/10.39	   A^2 -> H(U1(e, a), k)
28.58/10.39	   A^2 -> H(U1(k, a), d)
28.58/10.39	   A^2 -> H(U1(c, d), d)
28.58/10.39	   A^2 -> H(U1(c, d), k)
28.58/10.39	   A^2 -> H(U1(d, e), b)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(d, e), c)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(d, e), e)
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.39	   A^2 -> H(U1(d, c), d)
28.58/10.39	   A^2 -> H(U1(d, c), k)
28.58/10.39	   A^2 -> H(U1(a, e), d)
28.58/10.39	   A^2 -> H(U1(a, e), k)
28.58/10.39	   A^2 -> H(U1(a, k), d)
28.58/10.39	   A^2 -> H(U1(a, k), k)
28.58/10.39	   A^2 -> H(k, U1(e, b))
28.58/10.39	   A^2 -> H(k, U1(c, d))
28.58/10.39	   A^2 -> H(k, U1(d, c))
28.58/10.39	   A^2 -> H(k, U1(b, e))
28.58/10.39	   A^2 -> H(k, U1(b, k))
28.58/10.39	   A^2 -> H(k, U1(e, c))
28.58/10.39	   A^2 -> H(k, U1(c, e))
28.58/10.39	   A^2 -> H(k, U1(c, k))
28.58/10.39	   A^2 -> H(k, U1(e, e))
28.58/10.39	   A^2 -> H(k, U1(d, k))
28.58/10.39	   A^2 -> H(c, b)
28.58/10.39	   A^2 -> H(c, U1(e, d))
28.58/10.39	   A^2 -> H(c, U1(d, e))
28.58/10.39	   A^2 -> H(c, c)
28.58/10.39	   A^2 -> H(c, U1(e, k))
28.58/10.39	   A^2 -> H(c, U1(k, e))
28.58/10.39	   A^2 -> H(c, e)
28.58/10.39	   A^2 -> H(c, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, k), b)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, k), c)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, k), e)
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, c), d)
28.58/10.39	   A^2 -> H(U1(e, c), k)
28.58/10.39	   A^2 -> H(U1(k, e), b)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, e), c)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(k, c), d)
28.58/10.39	   A^2 -> H(U1(c, e), d)
28.58/10.39	   A^2 -> H(U1(c, e), k)
28.58/10.39	   A^2 -> H(U1(c, k), d)
28.58/10.39	   A^2 -> H(U1(c, k), k)
28.58/10.39	   A^2 -> H(e, b)
28.58/10.39	   A^2 -> H(e, U1(e, d))
28.58/10.39	   A^2 -> H(e, U1(d, e))
28.58/10.39	   A^2 -> H(e, c)
28.58/10.39	   A^2 -> H(e, U1(e, k))
28.58/10.39	   A^2 -> H(e, e)
28.58/10.39	   A^2 -> H(U1(e, e), d)
28.58/10.39	   A^2 -> H(U1(e, e), k)
28.58/10.39	   A^2 -> H(U1(k, k), d)
28.58/10.39	   A^2 -> H(U1(k, k), b)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, k), c)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, d), d)
28.58/10.39	   A^2 -> H(U1(d, k), d)
28.58/10.39	   A^2 -> H(U1(d, k), k)
28.58/10.39	   A^2 -> H(U1(e, e), c)
28.58/10.39	   A^2 -> H(U1(e, c), e)
28.58/10.39	   A^2 -> H(U1(c, e), e)
28.58/10.39	   A^2 -> H(U1(c, k), e)
28.58/10.39	   A^2 -> H(c, U1(e, e))
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.39	   A^2 -> H(d, b)
28.58/10.39	   A^2 -> H(d, U1(e, d))
28.58/10.39	   A^2 -> H(k, U1(k, b))
28.58/10.39	
28.58/10.39	The TRS R consists of the following rules:
28.58/10.39	
28.58/10.39	   f(x) -> U1(x, x)
28.58/10.39	   U1(e, x) -> x
28.58/10.39	   a -> c
28.58/10.39	   a -> d
28.58/10.39	   b -> c
28.58/10.39	   b -> d
28.58/10.39	   d -> k
28.58/10.39	   c -> e
28.58/10.39	   c -> k
28.58/10.39	
28.58/10.39	Q is empty.
28.58/10.39	We have to consider all minimal (P,Q,R)-chains.
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2409) DependencyGraphProof (EQUIVALENT)
28.58/10.39	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2410)
28.58/10.39	Obligation:
28.58/10.39	Q DP problem:
28.58/10.39	The TRS P consists of the following rules:
28.58/10.39	
28.58/10.39	   H(x, x) -> G(x, x, f(k))
28.58/10.39	   G(d, x, x) -> A^2
28.58/10.39	   A^2 -> H(f(c), f(c))
28.58/10.39	   A^2 -> H(f(d), f(d))
28.58/10.39	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.39	   A^2 -> H(f(e), f(e))
28.58/10.39	   A^2 -> H(f(k), f(k))
28.58/10.39	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.39	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.39	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.39	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.39	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.39	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.39	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.39	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.39	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.39	   A^2 -> H(d, U1(c, d))
28.58/10.39	   A^2 -> H(d, U1(d, c))
28.58/10.39	   A^2 -> H(d, U1(b, e))
28.58/10.39	   A^2 -> H(d, U1(b, k))
28.58/10.39	   A^2 -> H(d, U1(e, c))
28.58/10.39	   A^2 -> H(d, U1(k, c))
28.58/10.39	   A^2 -> H(d, U1(c, e))
28.58/10.39	   A^2 -> H(d, U1(c, k))
28.58/10.39	   A^2 -> H(d, U1(e, e))
28.58/10.39	   A^2 -> H(d, U1(k, k))
28.58/10.39	   A^2 -> H(d, U1(k, d))
28.58/10.39	   A^2 -> H(d, U1(d, k))
28.58/10.39	   A^2 -> H(a, b)
28.58/10.39	   A^2 -> H(a, U1(e, d))
28.58/10.39	   A^2 -> H(a, U1(d, e))
28.58/10.39	   A^2 -> H(a, c)
28.58/10.39	   A^2 -> H(a, U1(e, k))
28.58/10.39	   A^2 -> H(a, U1(k, e))
28.58/10.39	   A^2 -> H(a, e)
28.58/10.39	   A^2 -> H(a, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, d), b)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, d), c)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, d), e)
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, a), d)
28.58/10.39	   A^2 -> H(U1(e, a), k)
28.58/10.39	   A^2 -> H(U1(k, a), d)
28.58/10.39	   A^2 -> H(U1(c, d), d)
28.58/10.39	   A^2 -> H(U1(c, d), k)
28.58/10.39	   A^2 -> H(U1(d, e), b)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(d, e), c)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(d, e), e)
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.39	   A^2 -> H(U1(d, c), d)
28.58/10.39	   A^2 -> H(U1(d, c), k)
28.58/10.39	   A^2 -> H(U1(a, e), d)
28.58/10.39	   A^2 -> H(U1(a, e), k)
28.58/10.39	   A^2 -> H(U1(a, k), d)
28.58/10.39	   A^2 -> H(U1(a, k), k)
28.58/10.39	   A^2 -> H(k, U1(e, b))
28.58/10.39	   A^2 -> H(k, U1(c, d))
28.58/10.39	   A^2 -> H(k, U1(d, c))
28.58/10.39	   A^2 -> H(k, U1(b, e))
28.58/10.39	   A^2 -> H(k, U1(b, k))
28.58/10.39	   A^2 -> H(k, U1(e, c))
28.58/10.39	   A^2 -> H(k, U1(c, e))
28.58/10.39	   A^2 -> H(k, U1(c, k))
28.58/10.39	   A^2 -> H(k, U1(e, e))
28.58/10.39	   A^2 -> H(k, U1(d, k))
28.58/10.39	   A^2 -> H(c, b)
28.58/10.39	   A^2 -> H(c, U1(e, d))
28.58/10.39	   A^2 -> H(c, U1(d, e))
28.58/10.39	   A^2 -> H(c, c)
28.58/10.39	   A^2 -> H(c, U1(e, k))
28.58/10.39	   A^2 -> H(c, U1(k, e))
28.58/10.39	   A^2 -> H(c, e)
28.58/10.39	   A^2 -> H(c, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, k), b)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, k), c)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, k), e)
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, c), d)
28.58/10.39	   A^2 -> H(U1(e, c), k)
28.58/10.39	   A^2 -> H(U1(k, e), b)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, e), c)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(k, c), d)
28.58/10.39	   A^2 -> H(U1(c, e), d)
28.58/10.39	   A^2 -> H(U1(c, e), k)
28.58/10.39	   A^2 -> H(U1(c, k), d)
28.58/10.39	   A^2 -> H(U1(c, k), k)
28.58/10.39	   A^2 -> H(e, b)
28.58/10.39	   A^2 -> H(e, U1(e, d))
28.58/10.39	   A^2 -> H(e, U1(d, e))
28.58/10.39	   A^2 -> H(e, c)
28.58/10.39	   A^2 -> H(e, U1(e, k))
28.58/10.39	   A^2 -> H(e, e)
28.58/10.39	   A^2 -> H(U1(e, e), d)
28.58/10.39	   A^2 -> H(U1(e, e), k)
28.58/10.39	   A^2 -> H(U1(k, k), d)
28.58/10.39	   A^2 -> H(U1(k, k), b)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, k), c)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, d), d)
28.58/10.39	   A^2 -> H(U1(d, k), d)
28.58/10.39	   A^2 -> H(U1(d, k), k)
28.58/10.39	   A^2 -> H(U1(e, e), c)
28.58/10.39	   A^2 -> H(U1(e, c), e)
28.58/10.39	   A^2 -> H(U1(c, e), e)
28.58/10.39	   A^2 -> H(U1(c, k), e)
28.58/10.39	   A^2 -> H(c, U1(e, e))
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.39	   A^2 -> H(d, b)
28.58/10.39	   A^2 -> H(d, U1(e, d))
28.58/10.39	
28.58/10.39	The TRS R consists of the following rules:
28.58/10.39	
28.58/10.39	   f(x) -> U1(x, x)
28.58/10.39	   U1(e, x) -> x
28.58/10.39	   a -> c
28.58/10.39	   a -> d
28.58/10.39	   b -> c
28.58/10.39	   b -> d
28.58/10.39	   d -> k
28.58/10.39	   c -> e
28.58/10.39	   c -> k
28.58/10.39	
28.58/10.39	Q is empty.
28.58/10.39	We have to consider all minimal (P,Q,R)-chains.
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2411) TransformationProof (EQUIVALENT)
28.58/10.39	By narrowing [LPAR04] the rule A^2 -> H(d, U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.39	
28.58/10.39	   (A^2 -> H(k, U1(c, d)),A^2 -> H(k, U1(c, d)))
28.58/10.39	   (A^2 -> H(d, U1(e, d)),A^2 -> H(d, U1(e, d)))
28.58/10.39	   (A^2 -> H(d, U1(k, d)),A^2 -> H(d, U1(k, d)))
28.58/10.39	   (A^2 -> H(d, U1(c, k)),A^2 -> H(d, U1(c, k)))
28.58/10.39	
28.58/10.39	
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2412)
28.58/10.39	Obligation:
28.58/10.39	Q DP problem:
28.58/10.39	The TRS P consists of the following rules:
28.58/10.39	
28.58/10.39	   H(x, x) -> G(x, x, f(k))
28.58/10.39	   G(d, x, x) -> A^2
28.58/10.39	   A^2 -> H(f(c), f(c))
28.58/10.39	   A^2 -> H(f(d), f(d))
28.58/10.39	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.39	   A^2 -> H(f(e), f(e))
28.58/10.39	   A^2 -> H(f(k), f(k))
28.58/10.39	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.39	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.39	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.39	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.39	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.39	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.39	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.39	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.39	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.39	   A^2 -> H(d, U1(d, c))
28.58/10.39	   A^2 -> H(d, U1(b, e))
28.58/10.39	   A^2 -> H(d, U1(b, k))
28.58/10.39	   A^2 -> H(d, U1(e, c))
28.58/10.39	   A^2 -> H(d, U1(k, c))
28.58/10.39	   A^2 -> H(d, U1(c, e))
28.58/10.39	   A^2 -> H(d, U1(c, k))
28.58/10.39	   A^2 -> H(d, U1(e, e))
28.58/10.39	   A^2 -> H(d, U1(k, k))
28.58/10.39	   A^2 -> H(d, U1(k, d))
28.58/10.39	   A^2 -> H(d, U1(d, k))
28.58/10.39	   A^2 -> H(a, b)
28.58/10.39	   A^2 -> H(a, U1(e, d))
28.58/10.39	   A^2 -> H(a, U1(d, e))
28.58/10.39	   A^2 -> H(a, c)
28.58/10.39	   A^2 -> H(a, U1(e, k))
28.58/10.39	   A^2 -> H(a, U1(k, e))
28.58/10.39	   A^2 -> H(a, e)
28.58/10.39	   A^2 -> H(a, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, d), b)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, d), c)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, d), e)
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, a), d)
28.58/10.39	   A^2 -> H(U1(e, a), k)
28.58/10.39	   A^2 -> H(U1(k, a), d)
28.58/10.39	   A^2 -> H(U1(c, d), d)
28.58/10.39	   A^2 -> H(U1(c, d), k)
28.58/10.39	   A^2 -> H(U1(d, e), b)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(d, e), c)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(d, e), e)
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.39	   A^2 -> H(U1(d, c), d)
28.58/10.39	   A^2 -> H(U1(d, c), k)
28.58/10.39	   A^2 -> H(U1(a, e), d)
28.58/10.39	   A^2 -> H(U1(a, e), k)
28.58/10.39	   A^2 -> H(U1(a, k), d)
28.58/10.39	   A^2 -> H(U1(a, k), k)
28.58/10.39	   A^2 -> H(k, U1(e, b))
28.58/10.39	   A^2 -> H(k, U1(c, d))
28.58/10.39	   A^2 -> H(k, U1(d, c))
28.58/10.39	   A^2 -> H(k, U1(b, e))
28.58/10.39	   A^2 -> H(k, U1(b, k))
28.58/10.39	   A^2 -> H(k, U1(e, c))
28.58/10.39	   A^2 -> H(k, U1(c, e))
28.58/10.39	   A^2 -> H(k, U1(c, k))
28.58/10.39	   A^2 -> H(k, U1(e, e))
28.58/10.39	   A^2 -> H(k, U1(d, k))
28.58/10.39	   A^2 -> H(c, b)
28.58/10.39	   A^2 -> H(c, U1(e, d))
28.58/10.39	   A^2 -> H(c, U1(d, e))
28.58/10.39	   A^2 -> H(c, c)
28.58/10.39	   A^2 -> H(c, U1(e, k))
28.58/10.39	   A^2 -> H(c, U1(k, e))
28.58/10.39	   A^2 -> H(c, e)
28.58/10.39	   A^2 -> H(c, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, k), b)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, k), c)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, k), e)
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, c), d)
28.58/10.39	   A^2 -> H(U1(e, c), k)
28.58/10.39	   A^2 -> H(U1(k, e), b)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, e), c)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(k, c), d)
28.58/10.39	   A^2 -> H(U1(c, e), d)
28.58/10.39	   A^2 -> H(U1(c, e), k)
28.58/10.39	   A^2 -> H(U1(c, k), d)
28.58/10.39	   A^2 -> H(U1(c, k), k)
28.58/10.39	   A^2 -> H(e, b)
28.58/10.39	   A^2 -> H(e, U1(e, d))
28.58/10.39	   A^2 -> H(e, U1(d, e))
28.58/10.39	   A^2 -> H(e, c)
28.58/10.39	   A^2 -> H(e, U1(e, k))
28.58/10.39	   A^2 -> H(e, e)
28.58/10.39	   A^2 -> H(U1(e, e), d)
28.58/10.39	   A^2 -> H(U1(e, e), k)
28.58/10.39	   A^2 -> H(U1(k, k), d)
28.58/10.39	   A^2 -> H(U1(k, k), b)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, k), c)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, d), d)
28.58/10.39	   A^2 -> H(U1(d, k), d)
28.58/10.39	   A^2 -> H(U1(d, k), k)
28.58/10.39	   A^2 -> H(U1(e, e), c)
28.58/10.39	   A^2 -> H(U1(e, c), e)
28.58/10.39	   A^2 -> H(U1(c, e), e)
28.58/10.39	   A^2 -> H(U1(c, k), e)
28.58/10.39	   A^2 -> H(c, U1(e, e))
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.39	   A^2 -> H(d, b)
28.58/10.39	   A^2 -> H(d, U1(e, d))
28.58/10.39	
28.58/10.39	The TRS R consists of the following rules:
28.58/10.39	
28.58/10.39	   f(x) -> U1(x, x)
28.58/10.39	   U1(e, x) -> x
28.58/10.39	   a -> c
28.58/10.39	   a -> d
28.58/10.39	   b -> c
28.58/10.39	   b -> d
28.58/10.39	   d -> k
28.58/10.39	   c -> e
28.58/10.39	   c -> k
28.58/10.39	
28.58/10.39	Q is empty.
28.58/10.39	We have to consider all minimal (P,Q,R)-chains.
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2413) TransformationProof (EQUIVALENT)
28.58/10.39	By narrowing [LPAR04] the rule A^2 -> H(d, U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.39	
28.58/10.39	   (A^2 -> H(k, U1(d, c)),A^2 -> H(k, U1(d, c)))
28.58/10.39	   (A^2 -> H(d, U1(k, c)),A^2 -> H(d, U1(k, c)))
28.58/10.39	   (A^2 -> H(d, U1(d, e)),A^2 -> H(d, U1(d, e)))
28.58/10.39	   (A^2 -> H(d, U1(d, k)),A^2 -> H(d, U1(d, k)))
28.58/10.39	
28.58/10.39	
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2414)
28.58/10.39	Obligation:
28.58/10.39	Q DP problem:
28.58/10.39	The TRS P consists of the following rules:
28.58/10.39	
28.58/10.39	   H(x, x) -> G(x, x, f(k))
28.58/10.39	   G(d, x, x) -> A^2
28.58/10.39	   A^2 -> H(f(c), f(c))
28.58/10.39	   A^2 -> H(f(d), f(d))
28.58/10.39	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.39	   A^2 -> H(f(e), f(e))
28.58/10.39	   A^2 -> H(f(k), f(k))
28.58/10.39	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.39	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.39	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.39	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.39	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.39	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.39	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.39	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.39	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.39	   A^2 -> H(d, U1(b, e))
28.58/10.39	   A^2 -> H(d, U1(b, k))
28.58/10.39	   A^2 -> H(d, U1(e, c))
28.58/10.39	   A^2 -> H(d, U1(k, c))
28.58/10.39	   A^2 -> H(d, U1(c, e))
28.58/10.39	   A^2 -> H(d, U1(c, k))
28.58/10.39	   A^2 -> H(d, U1(e, e))
28.58/10.39	   A^2 -> H(d, U1(k, k))
28.58/10.39	   A^2 -> H(d, U1(k, d))
28.58/10.39	   A^2 -> H(d, U1(d, k))
28.58/10.39	   A^2 -> H(a, b)
28.58/10.39	   A^2 -> H(a, U1(e, d))
28.58/10.39	   A^2 -> H(a, U1(d, e))
28.58/10.39	   A^2 -> H(a, c)
28.58/10.39	   A^2 -> H(a, U1(e, k))
28.58/10.39	   A^2 -> H(a, U1(k, e))
28.58/10.39	   A^2 -> H(a, e)
28.58/10.39	   A^2 -> H(a, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, d), b)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, d), c)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, d), e)
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, a), d)
28.58/10.39	   A^2 -> H(U1(e, a), k)
28.58/10.39	   A^2 -> H(U1(k, a), d)
28.58/10.39	   A^2 -> H(U1(c, d), d)
28.58/10.39	   A^2 -> H(U1(c, d), k)
28.58/10.39	   A^2 -> H(U1(d, e), b)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(d, e), c)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(d, e), e)
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.39	   A^2 -> H(U1(d, c), d)
28.58/10.39	   A^2 -> H(U1(d, c), k)
28.58/10.39	   A^2 -> H(U1(a, e), d)
28.58/10.39	   A^2 -> H(U1(a, e), k)
28.58/10.39	   A^2 -> H(U1(a, k), d)
28.58/10.39	   A^2 -> H(U1(a, k), k)
28.58/10.39	   A^2 -> H(k, U1(e, b))
28.58/10.39	   A^2 -> H(k, U1(c, d))
28.58/10.39	   A^2 -> H(k, U1(d, c))
28.58/10.39	   A^2 -> H(k, U1(b, e))
28.58/10.39	   A^2 -> H(k, U1(b, k))
28.58/10.39	   A^2 -> H(k, U1(e, c))
28.58/10.39	   A^2 -> H(k, U1(c, e))
28.58/10.39	   A^2 -> H(k, U1(c, k))
28.58/10.39	   A^2 -> H(k, U1(e, e))
28.58/10.39	   A^2 -> H(k, U1(d, k))
28.58/10.39	   A^2 -> H(c, b)
28.58/10.39	   A^2 -> H(c, U1(e, d))
28.58/10.39	   A^2 -> H(c, U1(d, e))
28.58/10.39	   A^2 -> H(c, c)
28.58/10.39	   A^2 -> H(c, U1(e, k))
28.58/10.39	   A^2 -> H(c, U1(k, e))
28.58/10.39	   A^2 -> H(c, e)
28.58/10.39	   A^2 -> H(c, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, k), b)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, k), c)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, k), e)
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, c), d)
28.58/10.39	   A^2 -> H(U1(e, c), k)
28.58/10.39	   A^2 -> H(U1(k, e), b)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, e), c)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(k, c), d)
28.58/10.39	   A^2 -> H(U1(c, e), d)
28.58/10.39	   A^2 -> H(U1(c, e), k)
28.58/10.39	   A^2 -> H(U1(c, k), d)
28.58/10.39	   A^2 -> H(U1(c, k), k)
28.58/10.39	   A^2 -> H(e, b)
28.58/10.39	   A^2 -> H(e, U1(e, d))
28.58/10.39	   A^2 -> H(e, U1(d, e))
28.58/10.39	   A^2 -> H(e, c)
28.58/10.39	   A^2 -> H(e, U1(e, k))
28.58/10.39	   A^2 -> H(e, e)
28.58/10.39	   A^2 -> H(U1(e, e), d)
28.58/10.39	   A^2 -> H(U1(e, e), k)
28.58/10.39	   A^2 -> H(U1(k, k), d)
28.58/10.39	   A^2 -> H(U1(k, k), b)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, k), c)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, d), d)
28.58/10.39	   A^2 -> H(U1(d, k), d)
28.58/10.39	   A^2 -> H(U1(d, k), k)
28.58/10.39	   A^2 -> H(U1(e, e), c)
28.58/10.39	   A^2 -> H(U1(e, c), e)
28.58/10.39	   A^2 -> H(U1(c, e), e)
28.58/10.39	   A^2 -> H(U1(c, k), e)
28.58/10.39	   A^2 -> H(c, U1(e, e))
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.39	   A^2 -> H(d, b)
28.58/10.39	   A^2 -> H(d, U1(e, d))
28.58/10.39	   A^2 -> H(d, U1(d, e))
28.58/10.39	
28.58/10.39	The TRS R consists of the following rules:
28.58/10.39	
28.58/10.39	   f(x) -> U1(x, x)
28.58/10.39	   U1(e, x) -> x
28.58/10.39	   a -> c
28.58/10.39	   a -> d
28.58/10.39	   b -> c
28.58/10.39	   b -> d
28.58/10.39	   d -> k
28.58/10.39	   c -> e
28.58/10.39	   c -> k
28.58/10.39	
28.58/10.39	Q is empty.
28.58/10.39	We have to consider all minimal (P,Q,R)-chains.
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2415) TransformationProof (EQUIVALENT)
28.58/10.39	By narrowing [LPAR04] the rule A^2 -> H(d, U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.39	
28.58/10.39	   (A^2 -> H(k, U1(b, e)),A^2 -> H(k, U1(b, e)))
28.58/10.39	   (A^2 -> H(d, U1(c, e)),A^2 -> H(d, U1(c, e)))
28.58/10.39	   (A^2 -> H(d, U1(d, e)),A^2 -> H(d, U1(d, e)))
28.58/10.39	
28.58/10.39	
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2416)
28.58/10.39	Obligation:
28.58/10.39	Q DP problem:
28.58/10.39	The TRS P consists of the following rules:
28.58/10.39	
28.58/10.39	   H(x, x) -> G(x, x, f(k))
28.58/10.39	   G(d, x, x) -> A^2
28.58/10.39	   A^2 -> H(f(c), f(c))
28.58/10.39	   A^2 -> H(f(d), f(d))
28.58/10.39	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.39	   A^2 -> H(f(e), f(e))
28.58/10.39	   A^2 -> H(f(k), f(k))
28.58/10.39	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.39	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.39	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.39	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.39	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.39	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.39	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.39	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.39	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.39	   A^2 -> H(d, U1(b, k))
28.58/10.39	   A^2 -> H(d, U1(e, c))
28.58/10.39	   A^2 -> H(d, U1(k, c))
28.58/10.39	   A^2 -> H(d, U1(c, e))
28.58/10.39	   A^2 -> H(d, U1(c, k))
28.58/10.39	   A^2 -> H(d, U1(e, e))
28.58/10.39	   A^2 -> H(d, U1(k, k))
28.58/10.39	   A^2 -> H(d, U1(k, d))
28.58/10.39	   A^2 -> H(d, U1(d, k))
28.58/10.39	   A^2 -> H(a, b)
28.58/10.39	   A^2 -> H(a, U1(e, d))
28.58/10.39	   A^2 -> H(a, U1(d, e))
28.58/10.39	   A^2 -> H(a, c)
28.58/10.39	   A^2 -> H(a, U1(e, k))
28.58/10.39	   A^2 -> H(a, U1(k, e))
28.58/10.39	   A^2 -> H(a, e)
28.58/10.39	   A^2 -> H(a, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, d), b)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, d), c)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, d), e)
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, a), d)
28.58/10.39	   A^2 -> H(U1(e, a), k)
28.58/10.39	   A^2 -> H(U1(k, a), d)
28.58/10.39	   A^2 -> H(U1(c, d), d)
28.58/10.39	   A^2 -> H(U1(c, d), k)
28.58/10.39	   A^2 -> H(U1(d, e), b)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(d, e), c)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(d, e), e)
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.39	   A^2 -> H(U1(d, c), d)
28.58/10.39	   A^2 -> H(U1(d, c), k)
28.58/10.39	   A^2 -> H(U1(a, e), d)
28.58/10.39	   A^2 -> H(U1(a, e), k)
28.58/10.39	   A^2 -> H(U1(a, k), d)
28.58/10.39	   A^2 -> H(U1(a, k), k)
28.58/10.39	   A^2 -> H(k, U1(e, b))
28.58/10.39	   A^2 -> H(k, U1(c, d))
28.58/10.39	   A^2 -> H(k, U1(d, c))
28.58/10.39	   A^2 -> H(k, U1(b, e))
28.58/10.39	   A^2 -> H(k, U1(b, k))
28.58/10.39	   A^2 -> H(k, U1(e, c))
28.58/10.39	   A^2 -> H(k, U1(c, e))
28.58/10.39	   A^2 -> H(k, U1(c, k))
28.58/10.39	   A^2 -> H(k, U1(e, e))
28.58/10.39	   A^2 -> H(k, U1(d, k))
28.58/10.39	   A^2 -> H(c, b)
28.58/10.39	   A^2 -> H(c, U1(e, d))
28.58/10.39	   A^2 -> H(c, U1(d, e))
28.58/10.39	   A^2 -> H(c, c)
28.58/10.39	   A^2 -> H(c, U1(e, k))
28.58/10.39	   A^2 -> H(c, U1(k, e))
28.58/10.39	   A^2 -> H(c, e)
28.58/10.39	   A^2 -> H(c, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, k), b)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, k), c)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, k), e)
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, c), d)
28.58/10.39	   A^2 -> H(U1(e, c), k)
28.58/10.39	   A^2 -> H(U1(k, e), b)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, e), c)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(k, c), d)
28.58/10.39	   A^2 -> H(U1(c, e), d)
28.58/10.39	   A^2 -> H(U1(c, e), k)
28.58/10.39	   A^2 -> H(U1(c, k), d)
28.58/10.39	   A^2 -> H(U1(c, k), k)
28.58/10.39	   A^2 -> H(e, b)
28.58/10.39	   A^2 -> H(e, U1(e, d))
28.58/10.39	   A^2 -> H(e, U1(d, e))
28.58/10.39	   A^2 -> H(e, c)
28.58/10.39	   A^2 -> H(e, U1(e, k))
28.58/10.39	   A^2 -> H(e, e)
28.58/10.39	   A^2 -> H(U1(e, e), d)
28.58/10.39	   A^2 -> H(U1(e, e), k)
28.58/10.39	   A^2 -> H(U1(k, k), d)
28.58/10.39	   A^2 -> H(U1(k, k), b)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, k), c)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, d), d)
28.58/10.39	   A^2 -> H(U1(d, k), d)
28.58/10.39	   A^2 -> H(U1(d, k), k)
28.58/10.39	   A^2 -> H(U1(e, e), c)
28.58/10.39	   A^2 -> H(U1(e, c), e)
28.58/10.39	   A^2 -> H(U1(c, e), e)
28.58/10.39	   A^2 -> H(U1(c, k), e)
28.58/10.39	   A^2 -> H(c, U1(e, e))
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.39	   A^2 -> H(d, b)
28.58/10.39	   A^2 -> H(d, U1(e, d))
28.58/10.39	   A^2 -> H(d, U1(d, e))
28.58/10.39	
28.58/10.39	The TRS R consists of the following rules:
28.58/10.39	
28.58/10.39	   f(x) -> U1(x, x)
28.58/10.39	   U1(e, x) -> x
28.58/10.39	   a -> c
28.58/10.39	   a -> d
28.58/10.39	   b -> c
28.58/10.39	   b -> d
28.58/10.39	   d -> k
28.58/10.39	   c -> e
28.58/10.39	   c -> k
28.58/10.39	
28.58/10.39	Q is empty.
28.58/10.39	We have to consider all minimal (P,Q,R)-chains.
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2417) TransformationProof (EQUIVALENT)
28.58/10.39	By narrowing [LPAR04] the rule A^2 -> H(d, U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.39	
28.58/10.39	   (A^2 -> H(k, U1(b, k)),A^2 -> H(k, U1(b, k)))
28.58/10.39	   (A^2 -> H(d, U1(c, k)),A^2 -> H(d, U1(c, k)))
28.58/10.39	   (A^2 -> H(d, U1(d, k)),A^2 -> H(d, U1(d, k)))
28.58/10.39	
28.58/10.39	
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2418)
28.58/10.39	Obligation:
28.58/10.39	Q DP problem:
28.58/10.39	The TRS P consists of the following rules:
28.58/10.39	
28.58/10.39	   H(x, x) -> G(x, x, f(k))
28.58/10.39	   G(d, x, x) -> A^2
28.58/10.39	   A^2 -> H(f(c), f(c))
28.58/10.39	   A^2 -> H(f(d), f(d))
28.58/10.39	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.39	   A^2 -> H(f(e), f(e))
28.58/10.39	   A^2 -> H(f(k), f(k))
28.58/10.39	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.39	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.39	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.39	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.39	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.39	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.39	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.39	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.39	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.39	   A^2 -> H(d, U1(e, c))
28.58/10.39	   A^2 -> H(d, U1(k, c))
28.58/10.39	   A^2 -> H(d, U1(c, e))
28.58/10.39	   A^2 -> H(d, U1(c, k))
28.58/10.39	   A^2 -> H(d, U1(e, e))
28.58/10.39	   A^2 -> H(d, U1(k, k))
28.58/10.39	   A^2 -> H(d, U1(k, d))
28.58/10.39	   A^2 -> H(d, U1(d, k))
28.58/10.39	   A^2 -> H(a, b)
28.58/10.39	   A^2 -> H(a, U1(e, d))
28.58/10.39	   A^2 -> H(a, U1(d, e))
28.58/10.39	   A^2 -> H(a, c)
28.58/10.39	   A^2 -> H(a, U1(e, k))
28.58/10.39	   A^2 -> H(a, U1(k, e))
28.58/10.39	   A^2 -> H(a, e)
28.58/10.39	   A^2 -> H(a, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, d), b)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, d), c)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, d), e)
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, a), d)
28.58/10.39	   A^2 -> H(U1(e, a), k)
28.58/10.39	   A^2 -> H(U1(k, a), d)
28.58/10.39	   A^2 -> H(U1(c, d), d)
28.58/10.39	   A^2 -> H(U1(c, d), k)
28.58/10.39	   A^2 -> H(U1(d, e), b)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(d, e), c)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(d, e), e)
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.39	   A^2 -> H(U1(d, c), d)
28.58/10.39	   A^2 -> H(U1(d, c), k)
28.58/10.39	   A^2 -> H(U1(a, e), d)
28.58/10.39	   A^2 -> H(U1(a, e), k)
28.58/10.39	   A^2 -> H(U1(a, k), d)
28.58/10.39	   A^2 -> H(U1(a, k), k)
28.58/10.39	   A^2 -> H(k, U1(e, b))
28.58/10.39	   A^2 -> H(k, U1(c, d))
28.58/10.39	   A^2 -> H(k, U1(d, c))
28.58/10.39	   A^2 -> H(k, U1(b, e))
28.58/10.39	   A^2 -> H(k, U1(b, k))
28.58/10.39	   A^2 -> H(k, U1(e, c))
28.58/10.39	   A^2 -> H(k, U1(c, e))
28.58/10.39	   A^2 -> H(k, U1(c, k))
28.58/10.39	   A^2 -> H(k, U1(e, e))
28.58/10.39	   A^2 -> H(k, U1(d, k))
28.58/10.39	   A^2 -> H(c, b)
28.58/10.39	   A^2 -> H(c, U1(e, d))
28.58/10.39	   A^2 -> H(c, U1(d, e))
28.58/10.39	   A^2 -> H(c, c)
28.58/10.39	   A^2 -> H(c, U1(e, k))
28.58/10.39	   A^2 -> H(c, U1(k, e))
28.58/10.39	   A^2 -> H(c, e)
28.58/10.39	   A^2 -> H(c, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, k), b)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, k), c)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, k), e)
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, c), d)
28.58/10.39	   A^2 -> H(U1(e, c), k)
28.58/10.39	   A^2 -> H(U1(k, e), b)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, e), c)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(k, c), d)
28.58/10.39	   A^2 -> H(U1(c, e), d)
28.58/10.39	   A^2 -> H(U1(c, e), k)
28.58/10.39	   A^2 -> H(U1(c, k), d)
28.58/10.39	   A^2 -> H(U1(c, k), k)
28.58/10.39	   A^2 -> H(e, b)
28.58/10.39	   A^2 -> H(e, U1(e, d))
28.58/10.39	   A^2 -> H(e, U1(d, e))
28.58/10.39	   A^2 -> H(e, c)
28.58/10.39	   A^2 -> H(e, U1(e, k))
28.58/10.39	   A^2 -> H(e, e)
28.58/10.39	   A^2 -> H(U1(e, e), d)
28.58/10.39	   A^2 -> H(U1(e, e), k)
28.58/10.39	   A^2 -> H(U1(k, k), d)
28.58/10.39	   A^2 -> H(U1(k, k), b)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, k), c)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, d), d)
28.58/10.39	   A^2 -> H(U1(d, k), d)
28.58/10.39	   A^2 -> H(U1(d, k), k)
28.58/10.39	   A^2 -> H(U1(e, e), c)
28.58/10.39	   A^2 -> H(U1(e, c), e)
28.58/10.39	   A^2 -> H(U1(c, e), e)
28.58/10.39	   A^2 -> H(U1(c, k), e)
28.58/10.39	   A^2 -> H(c, U1(e, e))
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.39	   A^2 -> H(d, b)
28.58/10.39	   A^2 -> H(d, U1(e, d))
28.58/10.39	   A^2 -> H(d, U1(d, e))
28.58/10.39	
28.58/10.39	The TRS R consists of the following rules:
28.58/10.39	
28.58/10.39	   f(x) -> U1(x, x)
28.58/10.39	   U1(e, x) -> x
28.58/10.39	   a -> c
28.58/10.39	   a -> d
28.58/10.39	   b -> c
28.58/10.39	   b -> d
28.58/10.39	   d -> k
28.58/10.39	   c -> e
28.58/10.39	   c -> k
28.58/10.39	
28.58/10.39	Q is empty.
28.58/10.39	We have to consider all minimal (P,Q,R)-chains.
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2419) TransformationProof (EQUIVALENT)
28.58/10.39	By narrowing [LPAR04] the rule A^2 -> H(d, U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.39	
28.58/10.39	   (A^2 -> H(k, U1(e, c)),A^2 -> H(k, U1(e, c)))
28.58/10.39	   (A^2 -> H(d, c),A^2 -> H(d, c))
28.58/10.39	   (A^2 -> H(d, U1(e, e)),A^2 -> H(d, U1(e, e)))
28.58/10.39	   (A^2 -> H(d, U1(e, k)),A^2 -> H(d, U1(e, k)))
28.58/10.39	
28.58/10.39	
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2420)
28.58/10.39	Obligation:
28.58/10.39	Q DP problem:
28.58/10.39	The TRS P consists of the following rules:
28.58/10.39	
28.58/10.39	   H(x, x) -> G(x, x, f(k))
28.58/10.39	   G(d, x, x) -> A^2
28.58/10.39	   A^2 -> H(f(c), f(c))
28.58/10.39	   A^2 -> H(f(d), f(d))
28.58/10.39	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.39	   A^2 -> H(f(e), f(e))
28.58/10.39	   A^2 -> H(f(k), f(k))
28.58/10.39	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.39	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.39	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.39	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.39	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.39	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.39	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.39	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.39	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.39	   A^2 -> H(d, U1(k, c))
28.58/10.39	   A^2 -> H(d, U1(c, e))
28.58/10.39	   A^2 -> H(d, U1(c, k))
28.58/10.39	   A^2 -> H(d, U1(e, e))
28.58/10.39	   A^2 -> H(d, U1(k, k))
28.58/10.39	   A^2 -> H(d, U1(k, d))
28.58/10.39	   A^2 -> H(d, U1(d, k))
28.58/10.39	   A^2 -> H(a, b)
28.58/10.39	   A^2 -> H(a, U1(e, d))
28.58/10.39	   A^2 -> H(a, U1(d, e))
28.58/10.39	   A^2 -> H(a, c)
28.58/10.39	   A^2 -> H(a, U1(e, k))
28.58/10.39	   A^2 -> H(a, U1(k, e))
28.58/10.39	   A^2 -> H(a, e)
28.58/10.39	   A^2 -> H(a, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, d), b)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, d), c)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, d), e)
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, a), d)
28.58/10.39	   A^2 -> H(U1(e, a), k)
28.58/10.39	   A^2 -> H(U1(k, a), d)
28.58/10.39	   A^2 -> H(U1(c, d), d)
28.58/10.39	   A^2 -> H(U1(c, d), k)
28.58/10.39	   A^2 -> H(U1(d, e), b)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(d, e), c)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(d, e), e)
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.39	   A^2 -> H(U1(d, c), d)
28.58/10.39	   A^2 -> H(U1(d, c), k)
28.58/10.39	   A^2 -> H(U1(a, e), d)
28.58/10.39	   A^2 -> H(U1(a, e), k)
28.58/10.39	   A^2 -> H(U1(a, k), d)
28.58/10.39	   A^2 -> H(U1(a, k), k)
28.58/10.39	   A^2 -> H(k, U1(e, b))
28.58/10.39	   A^2 -> H(k, U1(c, d))
28.58/10.39	   A^2 -> H(k, U1(d, c))
28.58/10.39	   A^2 -> H(k, U1(b, e))
28.58/10.39	   A^2 -> H(k, U1(b, k))
28.58/10.39	   A^2 -> H(k, U1(e, c))
28.58/10.39	   A^2 -> H(k, U1(c, e))
28.58/10.39	   A^2 -> H(k, U1(c, k))
28.58/10.39	   A^2 -> H(k, U1(e, e))
28.58/10.39	   A^2 -> H(k, U1(d, k))
28.58/10.39	   A^2 -> H(c, b)
28.58/10.39	   A^2 -> H(c, U1(e, d))
28.58/10.39	   A^2 -> H(c, U1(d, e))
28.58/10.39	   A^2 -> H(c, c)
28.58/10.39	   A^2 -> H(c, U1(e, k))
28.58/10.39	   A^2 -> H(c, U1(k, e))
28.58/10.39	   A^2 -> H(c, e)
28.58/10.39	   A^2 -> H(c, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, k), b)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, k), c)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, k), e)
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, c), d)
28.58/10.39	   A^2 -> H(U1(e, c), k)
28.58/10.39	   A^2 -> H(U1(k, e), b)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, e), c)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(k, c), d)
28.58/10.39	   A^2 -> H(U1(c, e), d)
28.58/10.39	   A^2 -> H(U1(c, e), k)
28.58/10.39	   A^2 -> H(U1(c, k), d)
28.58/10.39	   A^2 -> H(U1(c, k), k)
28.58/10.39	   A^2 -> H(e, b)
28.58/10.39	   A^2 -> H(e, U1(e, d))
28.58/10.39	   A^2 -> H(e, U1(d, e))
28.58/10.39	   A^2 -> H(e, c)
28.58/10.39	   A^2 -> H(e, U1(e, k))
28.58/10.39	   A^2 -> H(e, e)
28.58/10.39	   A^2 -> H(U1(e, e), d)
28.58/10.39	   A^2 -> H(U1(e, e), k)
28.58/10.39	   A^2 -> H(U1(k, k), d)
28.58/10.39	   A^2 -> H(U1(k, k), b)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, k), c)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, d), d)
28.58/10.39	   A^2 -> H(U1(d, k), d)
28.58/10.39	   A^2 -> H(U1(d, k), k)
28.58/10.39	   A^2 -> H(U1(e, e), c)
28.58/10.39	   A^2 -> H(U1(e, c), e)
28.58/10.39	   A^2 -> H(U1(c, e), e)
28.58/10.39	   A^2 -> H(U1(c, k), e)
28.58/10.39	   A^2 -> H(c, U1(e, e))
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.39	   A^2 -> H(d, b)
28.58/10.39	   A^2 -> H(d, U1(e, d))
28.58/10.39	   A^2 -> H(d, U1(d, e))
28.58/10.39	   A^2 -> H(d, c)
28.58/10.39	   A^2 -> H(d, U1(e, k))
28.58/10.39	
28.58/10.39	The TRS R consists of the following rules:
28.58/10.39	
28.58/10.39	   f(x) -> U1(x, x)
28.58/10.39	   U1(e, x) -> x
28.58/10.39	   a -> c
28.58/10.39	   a -> d
28.58/10.39	   b -> c
28.58/10.39	   b -> d
28.58/10.39	   d -> k
28.58/10.39	   c -> e
28.58/10.39	   c -> k
28.58/10.39	
28.58/10.39	Q is empty.
28.58/10.39	We have to consider all minimal (P,Q,R)-chains.
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2421) TransformationProof (EQUIVALENT)
28.58/10.39	By narrowing [LPAR04] the rule A^2 -> H(d, U1(k, c)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.39	
28.58/10.39	   (A^2 -> H(k, U1(k, c)),A^2 -> H(k, U1(k, c)))
28.58/10.39	   (A^2 -> H(d, U1(k, e)),A^2 -> H(d, U1(k, e)))
28.58/10.39	   (A^2 -> H(d, U1(k, k)),A^2 -> H(d, U1(k, k)))
28.58/10.39	
28.58/10.39	
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2422)
28.58/10.39	Obligation:
28.58/10.39	Q DP problem:
28.58/10.39	The TRS P consists of the following rules:
28.58/10.39	
28.58/10.39	   H(x, x) -> G(x, x, f(k))
28.58/10.39	   G(d, x, x) -> A^2
28.58/10.39	   A^2 -> H(f(c), f(c))
28.58/10.39	   A^2 -> H(f(d), f(d))
28.58/10.39	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.39	   A^2 -> H(f(e), f(e))
28.58/10.39	   A^2 -> H(f(k), f(k))
28.58/10.39	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.39	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.39	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.39	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.39	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.39	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.39	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.39	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.39	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.39	   A^2 -> H(d, U1(c, e))
28.58/10.39	   A^2 -> H(d, U1(c, k))
28.58/10.39	   A^2 -> H(d, U1(e, e))
28.58/10.39	   A^2 -> H(d, U1(k, k))
28.58/10.39	   A^2 -> H(d, U1(k, d))
28.58/10.39	   A^2 -> H(d, U1(d, k))
28.58/10.39	   A^2 -> H(a, b)
28.58/10.39	   A^2 -> H(a, U1(e, d))
28.58/10.39	   A^2 -> H(a, U1(d, e))
28.58/10.39	   A^2 -> H(a, c)
28.58/10.39	   A^2 -> H(a, U1(e, k))
28.58/10.39	   A^2 -> H(a, U1(k, e))
28.58/10.39	   A^2 -> H(a, e)
28.58/10.39	   A^2 -> H(a, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, d), b)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, d), c)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, d), e)
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, a), d)
28.58/10.39	   A^2 -> H(U1(e, a), k)
28.58/10.39	   A^2 -> H(U1(k, a), d)
28.58/10.39	   A^2 -> H(U1(c, d), d)
28.58/10.39	   A^2 -> H(U1(c, d), k)
28.58/10.39	   A^2 -> H(U1(d, e), b)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(d, e), c)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(d, e), e)
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.39	   A^2 -> H(U1(d, c), d)
28.58/10.39	   A^2 -> H(U1(d, c), k)
28.58/10.39	   A^2 -> H(U1(a, e), d)
28.58/10.39	   A^2 -> H(U1(a, e), k)
28.58/10.39	   A^2 -> H(U1(a, k), d)
28.58/10.39	   A^2 -> H(U1(a, k), k)
28.58/10.39	   A^2 -> H(k, U1(e, b))
28.58/10.39	   A^2 -> H(k, U1(c, d))
28.58/10.39	   A^2 -> H(k, U1(d, c))
28.58/10.39	   A^2 -> H(k, U1(b, e))
28.58/10.39	   A^2 -> H(k, U1(b, k))
28.58/10.39	   A^2 -> H(k, U1(e, c))
28.58/10.39	   A^2 -> H(k, U1(c, e))
28.58/10.39	   A^2 -> H(k, U1(c, k))
28.58/10.39	   A^2 -> H(k, U1(e, e))
28.58/10.39	   A^2 -> H(k, U1(d, k))
28.58/10.39	   A^2 -> H(c, b)
28.58/10.39	   A^2 -> H(c, U1(e, d))
28.58/10.39	   A^2 -> H(c, U1(d, e))
28.58/10.39	   A^2 -> H(c, c)
28.58/10.39	   A^2 -> H(c, U1(e, k))
28.58/10.39	   A^2 -> H(c, U1(k, e))
28.58/10.39	   A^2 -> H(c, e)
28.58/10.39	   A^2 -> H(c, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, k), b)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, k), c)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, k), e)
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, c), d)
28.58/10.39	   A^2 -> H(U1(e, c), k)
28.58/10.39	   A^2 -> H(U1(k, e), b)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, e), c)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(k, c), d)
28.58/10.39	   A^2 -> H(U1(c, e), d)
28.58/10.39	   A^2 -> H(U1(c, e), k)
28.58/10.39	   A^2 -> H(U1(c, k), d)
28.58/10.39	   A^2 -> H(U1(c, k), k)
28.58/10.39	   A^2 -> H(e, b)
28.58/10.39	   A^2 -> H(e, U1(e, d))
28.58/10.39	   A^2 -> H(e, U1(d, e))
28.58/10.39	   A^2 -> H(e, c)
28.58/10.39	   A^2 -> H(e, U1(e, k))
28.58/10.39	   A^2 -> H(e, e)
28.58/10.39	   A^2 -> H(U1(e, e), d)
28.58/10.39	   A^2 -> H(U1(e, e), k)
28.58/10.39	   A^2 -> H(U1(k, k), d)
28.58/10.39	   A^2 -> H(U1(k, k), b)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, k), c)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, d), d)
28.58/10.39	   A^2 -> H(U1(d, k), d)
28.58/10.39	   A^2 -> H(U1(d, k), k)
28.58/10.39	   A^2 -> H(U1(e, e), c)
28.58/10.39	   A^2 -> H(U1(e, c), e)
28.58/10.39	   A^2 -> H(U1(c, e), e)
28.58/10.39	   A^2 -> H(U1(c, k), e)
28.58/10.39	   A^2 -> H(c, U1(e, e))
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.39	   A^2 -> H(d, b)
28.58/10.39	   A^2 -> H(d, U1(e, d))
28.58/10.39	   A^2 -> H(d, U1(d, e))
28.58/10.39	   A^2 -> H(d, c)
28.58/10.39	   A^2 -> H(d, U1(e, k))
28.58/10.39	   A^2 -> H(k, U1(k, c))
28.58/10.39	   A^2 -> H(d, U1(k, e))
28.58/10.39	
28.58/10.39	The TRS R consists of the following rules:
28.58/10.39	
28.58/10.39	   f(x) -> U1(x, x)
28.58/10.39	   U1(e, x) -> x
28.58/10.39	   a -> c
28.58/10.39	   a -> d
28.58/10.39	   b -> c
28.58/10.39	   b -> d
28.58/10.39	   d -> k
28.58/10.39	   c -> e
28.58/10.39	   c -> k
28.58/10.39	
28.58/10.39	Q is empty.
28.58/10.39	We have to consider all minimal (P,Q,R)-chains.
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2423) DependencyGraphProof (EQUIVALENT)
28.58/10.39	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2424)
28.58/10.39	Obligation:
28.58/10.39	Q DP problem:
28.58/10.39	The TRS P consists of the following rules:
28.58/10.39	
28.58/10.39	   G(d, x, x) -> A^2
28.58/10.39	   A^2 -> H(f(c), f(c))
28.58/10.39	   H(x, x) -> G(x, x, f(k))
28.58/10.39	   A^2 -> H(f(d), f(d))
28.58/10.39	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.39	   A^2 -> H(f(e), f(e))
28.58/10.39	   A^2 -> H(f(k), f(k))
28.58/10.39	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.39	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.39	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.39	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.39	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.39	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.39	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.39	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.39	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.39	   A^2 -> H(d, U1(c, e))
28.58/10.39	   A^2 -> H(d, U1(c, k))
28.58/10.39	   A^2 -> H(d, U1(e, e))
28.58/10.39	   A^2 -> H(d, U1(k, k))
28.58/10.39	   A^2 -> H(d, U1(k, d))
28.58/10.39	   A^2 -> H(d, U1(d, k))
28.58/10.39	   A^2 -> H(a, b)
28.58/10.39	   A^2 -> H(a, U1(e, d))
28.58/10.39	   A^2 -> H(a, U1(d, e))
28.58/10.39	   A^2 -> H(a, c)
28.58/10.39	   A^2 -> H(a, U1(e, k))
28.58/10.39	   A^2 -> H(a, U1(k, e))
28.58/10.39	   A^2 -> H(a, e)
28.58/10.39	   A^2 -> H(a, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, d), b)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, d), c)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, d), e)
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, a), d)
28.58/10.39	   A^2 -> H(U1(e, a), k)
28.58/10.39	   A^2 -> H(U1(k, a), d)
28.58/10.39	   A^2 -> H(U1(c, d), d)
28.58/10.39	   A^2 -> H(U1(c, d), k)
28.58/10.39	   A^2 -> H(U1(d, e), b)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(d, e), c)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(d, e), e)
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.39	   A^2 -> H(U1(d, c), d)
28.58/10.39	   A^2 -> H(U1(d, c), k)
28.58/10.39	   A^2 -> H(U1(a, e), d)
28.58/10.39	   A^2 -> H(U1(a, e), k)
28.58/10.39	   A^2 -> H(U1(a, k), d)
28.58/10.39	   A^2 -> H(U1(a, k), k)
28.58/10.39	   A^2 -> H(k, U1(e, b))
28.58/10.39	   A^2 -> H(k, U1(c, d))
28.58/10.39	   A^2 -> H(k, U1(d, c))
28.58/10.39	   A^2 -> H(k, U1(b, e))
28.58/10.39	   A^2 -> H(k, U1(b, k))
28.58/10.39	   A^2 -> H(k, U1(e, c))
28.58/10.39	   A^2 -> H(k, U1(c, e))
28.58/10.39	   A^2 -> H(k, U1(c, k))
28.58/10.39	   A^2 -> H(k, U1(e, e))
28.58/10.39	   A^2 -> H(k, U1(d, k))
28.58/10.39	   A^2 -> H(c, b)
28.58/10.39	   A^2 -> H(c, U1(e, d))
28.58/10.39	   A^2 -> H(c, U1(d, e))
28.58/10.39	   A^2 -> H(c, c)
28.58/10.39	   A^2 -> H(c, U1(e, k))
28.58/10.39	   A^2 -> H(c, U1(k, e))
28.58/10.39	   A^2 -> H(c, e)
28.58/10.39	   A^2 -> H(c, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, k), b)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, k), c)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, k), e)
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, c), d)
28.58/10.39	   A^2 -> H(U1(e, c), k)
28.58/10.39	   A^2 -> H(U1(k, e), b)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, e), c)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(k, c), d)
28.58/10.39	   A^2 -> H(U1(c, e), d)
28.58/10.39	   A^2 -> H(U1(c, e), k)
28.58/10.39	   A^2 -> H(U1(c, k), d)
28.58/10.39	   A^2 -> H(U1(c, k), k)
28.58/10.39	   A^2 -> H(e, b)
28.58/10.39	   A^2 -> H(e, U1(e, d))
28.58/10.39	   A^2 -> H(e, U1(d, e))
28.58/10.39	   A^2 -> H(e, c)
28.58/10.39	   A^2 -> H(e, U1(e, k))
28.58/10.39	   A^2 -> H(e, e)
28.58/10.39	   A^2 -> H(U1(e, e), d)
28.58/10.39	   A^2 -> H(U1(e, e), k)
28.58/10.39	   A^2 -> H(U1(k, k), d)
28.58/10.39	   A^2 -> H(U1(k, k), b)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, k), c)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, d), d)
28.58/10.39	   A^2 -> H(U1(d, k), d)
28.58/10.39	   A^2 -> H(U1(d, k), k)
28.58/10.39	   A^2 -> H(U1(e, e), c)
28.58/10.39	   A^2 -> H(U1(e, c), e)
28.58/10.39	   A^2 -> H(U1(c, e), e)
28.58/10.39	   A^2 -> H(U1(c, k), e)
28.58/10.39	   A^2 -> H(c, U1(e, e))
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.39	   A^2 -> H(d, b)
28.58/10.39	   A^2 -> H(d, U1(e, d))
28.58/10.39	   A^2 -> H(d, U1(d, e))
28.58/10.39	   A^2 -> H(d, c)
28.58/10.39	   A^2 -> H(d, U1(e, k))
28.58/10.39	   A^2 -> H(d, U1(k, e))
28.58/10.39	
28.58/10.39	The TRS R consists of the following rules:
28.58/10.39	
28.58/10.39	   f(x) -> U1(x, x)
28.58/10.39	   U1(e, x) -> x
28.58/10.39	   a -> c
28.58/10.39	   a -> d
28.58/10.39	   b -> c
28.58/10.39	   b -> d
28.58/10.39	   d -> k
28.58/10.39	   c -> e
28.58/10.39	   c -> k
28.58/10.39	
28.58/10.39	Q is empty.
28.58/10.39	We have to consider all minimal (P,Q,R)-chains.
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2425) TransformationProof (EQUIVALENT)
28.58/10.39	By narrowing [LPAR04] the rule A^2 -> H(d, U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.39	
28.58/10.39	   (A^2 -> H(k, U1(c, e)),A^2 -> H(k, U1(c, e)))
28.58/10.39	   (A^2 -> H(d, U1(e, e)),A^2 -> H(d, U1(e, e)))
28.58/10.39	   (A^2 -> H(d, U1(k, e)),A^2 -> H(d, U1(k, e)))
28.58/10.39	
28.58/10.39	
28.58/10.39	----------------------------------------
28.58/10.39	
28.58/10.39	(2426)
28.58/10.39	Obligation:
28.58/10.39	Q DP problem:
28.58/10.39	The TRS P consists of the following rules:
28.58/10.39	
28.58/10.39	   G(d, x, x) -> A^2
28.58/10.39	   A^2 -> H(f(c), f(c))
28.58/10.39	   H(x, x) -> G(x, x, f(k))
28.58/10.39	   A^2 -> H(f(d), f(d))
28.58/10.39	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.39	   A^2 -> H(f(e), f(e))
28.58/10.39	   A^2 -> H(f(k), f(k))
28.58/10.39	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.39	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.39	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.39	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.39	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.39	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.39	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.39	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.39	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.39	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.39	   A^2 -> H(d, U1(c, k))
28.58/10.39	   A^2 -> H(d, U1(e, e))
28.58/10.39	   A^2 -> H(d, U1(k, k))
28.58/10.39	   A^2 -> H(d, U1(k, d))
28.58/10.39	   A^2 -> H(d, U1(d, k))
28.58/10.39	   A^2 -> H(a, b)
28.58/10.39	   A^2 -> H(a, U1(e, d))
28.58/10.39	   A^2 -> H(a, U1(d, e))
28.58/10.39	   A^2 -> H(a, c)
28.58/10.39	   A^2 -> H(a, U1(e, k))
28.58/10.39	   A^2 -> H(a, U1(k, e))
28.58/10.39	   A^2 -> H(a, e)
28.58/10.39	   A^2 -> H(a, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, d), b)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, d), c)
28.58/10.39	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, d), e)
28.58/10.39	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, a), d)
28.58/10.39	   A^2 -> H(U1(e, a), k)
28.58/10.39	   A^2 -> H(U1(k, a), d)
28.58/10.39	   A^2 -> H(U1(c, d), d)
28.58/10.39	   A^2 -> H(U1(c, d), k)
28.58/10.39	   A^2 -> H(U1(d, e), b)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(d, e), c)
28.58/10.39	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(d, e), e)
28.58/10.39	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.39	   A^2 -> H(U1(d, c), d)
28.58/10.39	   A^2 -> H(U1(d, c), k)
28.58/10.39	   A^2 -> H(U1(a, e), d)
28.58/10.39	   A^2 -> H(U1(a, e), k)
28.58/10.39	   A^2 -> H(U1(a, k), d)
28.58/10.39	   A^2 -> H(U1(a, k), k)
28.58/10.39	   A^2 -> H(k, U1(e, b))
28.58/10.39	   A^2 -> H(k, U1(c, d))
28.58/10.39	   A^2 -> H(k, U1(d, c))
28.58/10.39	   A^2 -> H(k, U1(b, e))
28.58/10.39	   A^2 -> H(k, U1(b, k))
28.58/10.39	   A^2 -> H(k, U1(e, c))
28.58/10.39	   A^2 -> H(k, U1(c, e))
28.58/10.39	   A^2 -> H(k, U1(c, k))
28.58/10.39	   A^2 -> H(k, U1(e, e))
28.58/10.39	   A^2 -> H(k, U1(d, k))
28.58/10.39	   A^2 -> H(c, b)
28.58/10.39	   A^2 -> H(c, U1(e, d))
28.58/10.39	   A^2 -> H(c, U1(d, e))
28.58/10.39	   A^2 -> H(c, c)
28.58/10.39	   A^2 -> H(c, U1(e, k))
28.58/10.39	   A^2 -> H(c, U1(k, e))
28.58/10.39	   A^2 -> H(c, e)
28.58/10.39	   A^2 -> H(c, U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, k), b)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.39	   A^2 -> H(U1(e, k), c)
28.58/10.39	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.39	   A^2 -> H(U1(e, k), e)
28.58/10.39	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.39	   A^2 -> H(U1(e, c), d)
28.58/10.39	   A^2 -> H(U1(e, c), k)
28.58/10.39	   A^2 -> H(U1(k, e), b)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.39	   A^2 -> H(U1(k, e), c)
28.58/10.39	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.39	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.39	   A^2 -> H(U1(k, c), d)
28.58/10.39	   A^2 -> H(U1(c, e), d)
28.58/10.39	   A^2 -> H(U1(c, e), k)
28.58/10.39	   A^2 -> H(U1(c, k), d)
28.58/10.39	   A^2 -> H(U1(c, k), k)
28.58/10.39	   A^2 -> H(e, b)
28.58/10.39	   A^2 -> H(e, U1(e, d))
28.58/10.39	   A^2 -> H(e, U1(d, e))
28.58/10.39	   A^2 -> H(e, c)
28.58/10.39	   A^2 -> H(e, U1(e, k))
28.58/10.39	   A^2 -> H(e, e)
28.58/10.39	   A^2 -> H(U1(e, e), d)
28.58/10.39	   A^2 -> H(U1(e, e), k)
28.58/10.39	   A^2 -> H(U1(k, k), d)
28.58/10.39	   A^2 -> H(U1(k, k), b)
28.58/10.39	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.39	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, k), c)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, d), d)
28.58/10.40	   A^2 -> H(U1(d, k), d)
28.58/10.40	   A^2 -> H(U1(d, k), k)
28.58/10.40	   A^2 -> H(U1(e, e), c)
28.58/10.40	   A^2 -> H(U1(e, c), e)
28.58/10.40	   A^2 -> H(U1(c, e), e)
28.58/10.40	   A^2 -> H(U1(c, k), e)
28.58/10.40	   A^2 -> H(c, U1(e, e))
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.40	   A^2 -> H(d, b)
28.58/10.40	   A^2 -> H(d, U1(e, d))
28.58/10.40	   A^2 -> H(d, U1(d, e))
28.58/10.40	   A^2 -> H(d, c)
28.58/10.40	   A^2 -> H(d, U1(e, k))
28.58/10.40	   A^2 -> H(d, U1(k, e))
28.58/10.40	
28.58/10.40	The TRS R consists of the following rules:
28.58/10.40	
28.58/10.40	   f(x) -> U1(x, x)
28.58/10.40	   U1(e, x) -> x
28.58/10.40	   a -> c
28.58/10.40	   a -> d
28.58/10.40	   b -> c
28.58/10.40	   b -> d
28.58/10.40	   d -> k
28.58/10.40	   c -> e
28.58/10.40	   c -> k
28.58/10.40	
28.58/10.40	Q is empty.
28.58/10.40	We have to consider all minimal (P,Q,R)-chains.
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2427) TransformationProof (EQUIVALENT)
28.58/10.40	By narrowing [LPAR04] the rule A^2 -> H(d, U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.40	
28.58/10.40	   (A^2 -> H(k, U1(c, k)),A^2 -> H(k, U1(c, k)))
28.58/10.40	   (A^2 -> H(d, U1(e, k)),A^2 -> H(d, U1(e, k)))
28.58/10.40	   (A^2 -> H(d, U1(k, k)),A^2 -> H(d, U1(k, k)))
28.58/10.40	
28.58/10.40	
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2428)
28.58/10.40	Obligation:
28.58/10.40	Q DP problem:
28.58/10.40	The TRS P consists of the following rules:
28.58/10.40	
28.58/10.40	   G(d, x, x) -> A^2
28.58/10.40	   A^2 -> H(f(c), f(c))
28.58/10.40	   H(x, x) -> G(x, x, f(k))
28.58/10.40	   A^2 -> H(f(d), f(d))
28.58/10.40	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.40	   A^2 -> H(f(e), f(e))
28.58/10.40	   A^2 -> H(f(k), f(k))
28.58/10.40	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.40	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.40	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.40	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.40	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.40	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.40	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.40	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.40	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.40	   A^2 -> H(d, U1(e, e))
28.58/10.40	   A^2 -> H(d, U1(k, k))
28.58/10.40	   A^2 -> H(d, U1(k, d))
28.58/10.40	   A^2 -> H(d, U1(d, k))
28.58/10.40	   A^2 -> H(a, b)
28.58/10.40	   A^2 -> H(a, U1(e, d))
28.58/10.40	   A^2 -> H(a, U1(d, e))
28.58/10.40	   A^2 -> H(a, c)
28.58/10.40	   A^2 -> H(a, U1(e, k))
28.58/10.40	   A^2 -> H(a, U1(k, e))
28.58/10.40	   A^2 -> H(a, e)
28.58/10.40	   A^2 -> H(a, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, d), b)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, d), c)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, d), e)
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, a), d)
28.58/10.40	   A^2 -> H(U1(e, a), k)
28.58/10.40	   A^2 -> H(U1(k, a), d)
28.58/10.40	   A^2 -> H(U1(c, d), d)
28.58/10.40	   A^2 -> H(U1(c, d), k)
28.58/10.40	   A^2 -> H(U1(d, e), b)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(d, e), c)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(d, e), e)
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.40	   A^2 -> H(U1(d, c), d)
28.58/10.40	   A^2 -> H(U1(d, c), k)
28.58/10.40	   A^2 -> H(U1(a, e), d)
28.58/10.40	   A^2 -> H(U1(a, e), k)
28.58/10.40	   A^2 -> H(U1(a, k), d)
28.58/10.40	   A^2 -> H(U1(a, k), k)
28.58/10.40	   A^2 -> H(k, U1(e, b))
28.58/10.40	   A^2 -> H(k, U1(c, d))
28.58/10.40	   A^2 -> H(k, U1(d, c))
28.58/10.40	   A^2 -> H(k, U1(b, e))
28.58/10.40	   A^2 -> H(k, U1(b, k))
28.58/10.40	   A^2 -> H(k, U1(e, c))
28.58/10.40	   A^2 -> H(k, U1(c, e))
28.58/10.40	   A^2 -> H(k, U1(c, k))
28.58/10.40	   A^2 -> H(k, U1(e, e))
28.58/10.40	   A^2 -> H(k, U1(d, k))
28.58/10.40	   A^2 -> H(c, b)
28.58/10.40	   A^2 -> H(c, U1(e, d))
28.58/10.40	   A^2 -> H(c, U1(d, e))
28.58/10.40	   A^2 -> H(c, c)
28.58/10.40	   A^2 -> H(c, U1(e, k))
28.58/10.40	   A^2 -> H(c, U1(k, e))
28.58/10.40	   A^2 -> H(c, e)
28.58/10.40	   A^2 -> H(c, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, k), b)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, k), c)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, k), e)
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, c), d)
28.58/10.40	   A^2 -> H(U1(e, c), k)
28.58/10.40	   A^2 -> H(U1(k, e), b)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, e), c)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(k, c), d)
28.58/10.40	   A^2 -> H(U1(c, e), d)
28.58/10.40	   A^2 -> H(U1(c, e), k)
28.58/10.40	   A^2 -> H(U1(c, k), d)
28.58/10.40	   A^2 -> H(U1(c, k), k)
28.58/10.40	   A^2 -> H(e, b)
28.58/10.40	   A^2 -> H(e, U1(e, d))
28.58/10.40	   A^2 -> H(e, U1(d, e))
28.58/10.40	   A^2 -> H(e, c)
28.58/10.40	   A^2 -> H(e, U1(e, k))
28.58/10.40	   A^2 -> H(e, e)
28.58/10.40	   A^2 -> H(U1(e, e), d)
28.58/10.40	   A^2 -> H(U1(e, e), k)
28.58/10.40	   A^2 -> H(U1(k, k), d)
28.58/10.40	   A^2 -> H(U1(k, k), b)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, k), c)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, d), d)
28.58/10.40	   A^2 -> H(U1(d, k), d)
28.58/10.40	   A^2 -> H(U1(d, k), k)
28.58/10.40	   A^2 -> H(U1(e, e), c)
28.58/10.40	   A^2 -> H(U1(e, c), e)
28.58/10.40	   A^2 -> H(U1(c, e), e)
28.58/10.40	   A^2 -> H(U1(c, k), e)
28.58/10.40	   A^2 -> H(c, U1(e, e))
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.40	   A^2 -> H(d, b)
28.58/10.40	   A^2 -> H(d, U1(e, d))
28.58/10.40	   A^2 -> H(d, U1(d, e))
28.58/10.40	   A^2 -> H(d, c)
28.58/10.40	   A^2 -> H(d, U1(e, k))
28.58/10.40	   A^2 -> H(d, U1(k, e))
28.58/10.40	
28.58/10.40	The TRS R consists of the following rules:
28.58/10.40	
28.58/10.40	   f(x) -> U1(x, x)
28.58/10.40	   U1(e, x) -> x
28.58/10.40	   a -> c
28.58/10.40	   a -> d
28.58/10.40	   b -> c
28.58/10.40	   b -> d
28.58/10.40	   d -> k
28.58/10.40	   c -> e
28.58/10.40	   c -> k
28.58/10.40	
28.58/10.40	Q is empty.
28.58/10.40	We have to consider all minimal (P,Q,R)-chains.
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2429) TransformationProof (EQUIVALENT)
28.58/10.40	By narrowing [LPAR04] the rule A^2 -> H(d, U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.40	
28.58/10.40	   (A^2 -> H(k, U1(e, e)),A^2 -> H(k, U1(e, e)))
28.58/10.40	   (A^2 -> H(d, e),A^2 -> H(d, e))
28.58/10.40	
28.58/10.40	
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2430)
28.58/10.40	Obligation:
28.58/10.40	Q DP problem:
28.58/10.40	The TRS P consists of the following rules:
28.58/10.40	
28.58/10.40	   G(d, x, x) -> A^2
28.58/10.40	   A^2 -> H(f(c), f(c))
28.58/10.40	   H(x, x) -> G(x, x, f(k))
28.58/10.40	   A^2 -> H(f(d), f(d))
28.58/10.40	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.40	   A^2 -> H(f(e), f(e))
28.58/10.40	   A^2 -> H(f(k), f(k))
28.58/10.40	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.40	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.40	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.40	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.40	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.40	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.40	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.40	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.40	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.40	   A^2 -> H(d, U1(k, k))
28.58/10.40	   A^2 -> H(d, U1(k, d))
28.58/10.40	   A^2 -> H(d, U1(d, k))
28.58/10.40	   A^2 -> H(a, b)
28.58/10.40	   A^2 -> H(a, U1(e, d))
28.58/10.40	   A^2 -> H(a, U1(d, e))
28.58/10.40	   A^2 -> H(a, c)
28.58/10.40	   A^2 -> H(a, U1(e, k))
28.58/10.40	   A^2 -> H(a, U1(k, e))
28.58/10.40	   A^2 -> H(a, e)
28.58/10.40	   A^2 -> H(a, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, d), b)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, d), c)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, d), e)
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, a), d)
28.58/10.40	   A^2 -> H(U1(e, a), k)
28.58/10.40	   A^2 -> H(U1(k, a), d)
28.58/10.40	   A^2 -> H(U1(c, d), d)
28.58/10.40	   A^2 -> H(U1(c, d), k)
28.58/10.40	   A^2 -> H(U1(d, e), b)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(d, e), c)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(d, e), e)
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.40	   A^2 -> H(U1(d, c), d)
28.58/10.40	   A^2 -> H(U1(d, c), k)
28.58/10.40	   A^2 -> H(U1(a, e), d)
28.58/10.40	   A^2 -> H(U1(a, e), k)
28.58/10.40	   A^2 -> H(U1(a, k), d)
28.58/10.40	   A^2 -> H(U1(a, k), k)
28.58/10.40	   A^2 -> H(k, U1(e, b))
28.58/10.40	   A^2 -> H(k, U1(c, d))
28.58/10.40	   A^2 -> H(k, U1(d, c))
28.58/10.40	   A^2 -> H(k, U1(b, e))
28.58/10.40	   A^2 -> H(k, U1(b, k))
28.58/10.40	   A^2 -> H(k, U1(e, c))
28.58/10.40	   A^2 -> H(k, U1(c, e))
28.58/10.40	   A^2 -> H(k, U1(c, k))
28.58/10.40	   A^2 -> H(k, U1(e, e))
28.58/10.40	   A^2 -> H(k, U1(d, k))
28.58/10.40	   A^2 -> H(c, b)
28.58/10.40	   A^2 -> H(c, U1(e, d))
28.58/10.40	   A^2 -> H(c, U1(d, e))
28.58/10.40	   A^2 -> H(c, c)
28.58/10.40	   A^2 -> H(c, U1(e, k))
28.58/10.40	   A^2 -> H(c, U1(k, e))
28.58/10.40	   A^2 -> H(c, e)
28.58/10.40	   A^2 -> H(c, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, k), b)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, k), c)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, k), e)
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, c), d)
28.58/10.40	   A^2 -> H(U1(e, c), k)
28.58/10.40	   A^2 -> H(U1(k, e), b)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, e), c)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(k, c), d)
28.58/10.40	   A^2 -> H(U1(c, e), d)
28.58/10.40	   A^2 -> H(U1(c, e), k)
28.58/10.40	   A^2 -> H(U1(c, k), d)
28.58/10.40	   A^2 -> H(U1(c, k), k)
28.58/10.40	   A^2 -> H(e, b)
28.58/10.40	   A^2 -> H(e, U1(e, d))
28.58/10.40	   A^2 -> H(e, U1(d, e))
28.58/10.40	   A^2 -> H(e, c)
28.58/10.40	   A^2 -> H(e, U1(e, k))
28.58/10.40	   A^2 -> H(e, e)
28.58/10.40	   A^2 -> H(U1(e, e), d)
28.58/10.40	   A^2 -> H(U1(e, e), k)
28.58/10.40	   A^2 -> H(U1(k, k), d)
28.58/10.40	   A^2 -> H(U1(k, k), b)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, k), c)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, d), d)
28.58/10.40	   A^2 -> H(U1(d, k), d)
28.58/10.40	   A^2 -> H(U1(d, k), k)
28.58/10.40	   A^2 -> H(U1(e, e), c)
28.58/10.40	   A^2 -> H(U1(e, c), e)
28.58/10.40	   A^2 -> H(U1(c, e), e)
28.58/10.40	   A^2 -> H(U1(c, k), e)
28.58/10.40	   A^2 -> H(c, U1(e, e))
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.40	   A^2 -> H(d, b)
28.58/10.40	   A^2 -> H(d, U1(e, d))
28.58/10.40	   A^2 -> H(d, U1(d, e))
28.58/10.40	   A^2 -> H(d, c)
28.58/10.40	   A^2 -> H(d, U1(e, k))
28.58/10.40	   A^2 -> H(d, U1(k, e))
28.58/10.40	   A^2 -> H(d, e)
28.58/10.40	
28.58/10.40	The TRS R consists of the following rules:
28.58/10.40	
28.58/10.40	   f(x) -> U1(x, x)
28.58/10.40	   U1(e, x) -> x
28.58/10.40	   a -> c
28.58/10.40	   a -> d
28.58/10.40	   b -> c
28.58/10.40	   b -> d
28.58/10.40	   d -> k
28.58/10.40	   c -> e
28.58/10.40	   c -> k
28.58/10.40	
28.58/10.40	Q is empty.
28.58/10.40	We have to consider all minimal (P,Q,R)-chains.
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2431) TransformationProof (EQUIVALENT)
28.58/10.40	By narrowing [LPAR04] the rule A^2 -> H(d, U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.40	
28.58/10.40	   (A^2 -> H(k, U1(k, k)),A^2 -> H(k, U1(k, k)))
28.58/10.40	
28.58/10.40	
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2432)
28.58/10.40	Obligation:
28.58/10.40	Q DP problem:
28.58/10.40	The TRS P consists of the following rules:
28.58/10.40	
28.58/10.40	   G(d, x, x) -> A^2
28.58/10.40	   A^2 -> H(f(c), f(c))
28.58/10.40	   H(x, x) -> G(x, x, f(k))
28.58/10.40	   A^2 -> H(f(d), f(d))
28.58/10.40	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.40	   A^2 -> H(f(e), f(e))
28.58/10.40	   A^2 -> H(f(k), f(k))
28.58/10.40	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.40	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.40	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.40	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.40	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.40	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.40	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.40	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.40	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.40	   A^2 -> H(d, U1(k, d))
28.58/10.40	   A^2 -> H(d, U1(d, k))
28.58/10.40	   A^2 -> H(a, b)
28.58/10.40	   A^2 -> H(a, U1(e, d))
28.58/10.40	   A^2 -> H(a, U1(d, e))
28.58/10.40	   A^2 -> H(a, c)
28.58/10.40	   A^2 -> H(a, U1(e, k))
28.58/10.40	   A^2 -> H(a, U1(k, e))
28.58/10.40	   A^2 -> H(a, e)
28.58/10.40	   A^2 -> H(a, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, d), b)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, d), c)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, d), e)
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, a), d)
28.58/10.40	   A^2 -> H(U1(e, a), k)
28.58/10.40	   A^2 -> H(U1(k, a), d)
28.58/10.40	   A^2 -> H(U1(c, d), d)
28.58/10.40	   A^2 -> H(U1(c, d), k)
28.58/10.40	   A^2 -> H(U1(d, e), b)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(d, e), c)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(d, e), e)
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.40	   A^2 -> H(U1(d, c), d)
28.58/10.40	   A^2 -> H(U1(d, c), k)
28.58/10.40	   A^2 -> H(U1(a, e), d)
28.58/10.40	   A^2 -> H(U1(a, e), k)
28.58/10.40	   A^2 -> H(U1(a, k), d)
28.58/10.40	   A^2 -> H(U1(a, k), k)
28.58/10.40	   A^2 -> H(k, U1(e, b))
28.58/10.40	   A^2 -> H(k, U1(c, d))
28.58/10.40	   A^2 -> H(k, U1(d, c))
28.58/10.40	   A^2 -> H(k, U1(b, e))
28.58/10.40	   A^2 -> H(k, U1(b, k))
28.58/10.40	   A^2 -> H(k, U1(e, c))
28.58/10.40	   A^2 -> H(k, U1(c, e))
28.58/10.40	   A^2 -> H(k, U1(c, k))
28.58/10.40	   A^2 -> H(k, U1(e, e))
28.58/10.40	   A^2 -> H(k, U1(d, k))
28.58/10.40	   A^2 -> H(c, b)
28.58/10.40	   A^2 -> H(c, U1(e, d))
28.58/10.40	   A^2 -> H(c, U1(d, e))
28.58/10.40	   A^2 -> H(c, c)
28.58/10.40	   A^2 -> H(c, U1(e, k))
28.58/10.40	   A^2 -> H(c, U1(k, e))
28.58/10.40	   A^2 -> H(c, e)
28.58/10.40	   A^2 -> H(c, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, k), b)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, k), c)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, k), e)
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, c), d)
28.58/10.40	   A^2 -> H(U1(e, c), k)
28.58/10.40	   A^2 -> H(U1(k, e), b)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, e), c)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(k, c), d)
28.58/10.40	   A^2 -> H(U1(c, e), d)
28.58/10.40	   A^2 -> H(U1(c, e), k)
28.58/10.40	   A^2 -> H(U1(c, k), d)
28.58/10.40	   A^2 -> H(U1(c, k), k)
28.58/10.40	   A^2 -> H(e, b)
28.58/10.40	   A^2 -> H(e, U1(e, d))
28.58/10.40	   A^2 -> H(e, U1(d, e))
28.58/10.40	   A^2 -> H(e, c)
28.58/10.40	   A^2 -> H(e, U1(e, k))
28.58/10.40	   A^2 -> H(e, e)
28.58/10.40	   A^2 -> H(U1(e, e), d)
28.58/10.40	   A^2 -> H(U1(e, e), k)
28.58/10.40	   A^2 -> H(U1(k, k), d)
28.58/10.40	   A^2 -> H(U1(k, k), b)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, k), c)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, d), d)
28.58/10.40	   A^2 -> H(U1(d, k), d)
28.58/10.40	   A^2 -> H(U1(d, k), k)
28.58/10.40	   A^2 -> H(U1(e, e), c)
28.58/10.40	   A^2 -> H(U1(e, c), e)
28.58/10.40	   A^2 -> H(U1(c, e), e)
28.58/10.40	   A^2 -> H(U1(c, k), e)
28.58/10.40	   A^2 -> H(c, U1(e, e))
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.40	   A^2 -> H(d, b)
28.58/10.40	   A^2 -> H(d, U1(e, d))
28.58/10.40	   A^2 -> H(d, U1(d, e))
28.58/10.40	   A^2 -> H(d, c)
28.58/10.40	   A^2 -> H(d, U1(e, k))
28.58/10.40	   A^2 -> H(d, U1(k, e))
28.58/10.40	   A^2 -> H(d, e)
28.58/10.40	   A^2 -> H(k, U1(k, k))
28.58/10.40	
28.58/10.40	The TRS R consists of the following rules:
28.58/10.40	
28.58/10.40	   f(x) -> U1(x, x)
28.58/10.40	   U1(e, x) -> x
28.58/10.40	   a -> c
28.58/10.40	   a -> d
28.58/10.40	   b -> c
28.58/10.40	   b -> d
28.58/10.40	   d -> k
28.58/10.40	   c -> e
28.58/10.40	   c -> k
28.58/10.40	
28.58/10.40	Q is empty.
28.58/10.40	We have to consider all minimal (P,Q,R)-chains.
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2433) DependencyGraphProof (EQUIVALENT)
28.58/10.40	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2434)
28.58/10.40	Obligation:
28.58/10.40	Q DP problem:
28.58/10.40	The TRS P consists of the following rules:
28.58/10.40	
28.58/10.40	   A^2 -> H(f(c), f(c))
28.58/10.40	   H(x, x) -> G(x, x, f(k))
28.58/10.40	   G(d, x, x) -> A^2
28.58/10.40	   A^2 -> H(f(d), f(d))
28.58/10.40	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.40	   A^2 -> H(f(e), f(e))
28.58/10.40	   A^2 -> H(f(k), f(k))
28.58/10.40	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.40	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.40	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.40	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.40	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.40	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.40	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.40	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.40	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.40	   A^2 -> H(d, U1(k, d))
28.58/10.40	   A^2 -> H(d, U1(d, k))
28.58/10.40	   A^2 -> H(a, b)
28.58/10.40	   A^2 -> H(a, U1(e, d))
28.58/10.40	   A^2 -> H(a, U1(d, e))
28.58/10.40	   A^2 -> H(a, c)
28.58/10.40	   A^2 -> H(a, U1(e, k))
28.58/10.40	   A^2 -> H(a, U1(k, e))
28.58/10.40	   A^2 -> H(a, e)
28.58/10.40	   A^2 -> H(a, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, d), b)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, d), c)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, d), e)
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, a), d)
28.58/10.40	   A^2 -> H(U1(e, a), k)
28.58/10.40	   A^2 -> H(U1(k, a), d)
28.58/10.40	   A^2 -> H(U1(c, d), d)
28.58/10.40	   A^2 -> H(U1(c, d), k)
28.58/10.40	   A^2 -> H(U1(d, e), b)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(d, e), c)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(d, e), e)
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.40	   A^2 -> H(U1(d, c), d)
28.58/10.40	   A^2 -> H(U1(d, c), k)
28.58/10.40	   A^2 -> H(U1(a, e), d)
28.58/10.40	   A^2 -> H(U1(a, e), k)
28.58/10.40	   A^2 -> H(U1(a, k), d)
28.58/10.40	   A^2 -> H(U1(a, k), k)
28.58/10.40	   A^2 -> H(k, U1(e, b))
28.58/10.40	   A^2 -> H(k, U1(c, d))
28.58/10.40	   A^2 -> H(k, U1(d, c))
28.58/10.40	   A^2 -> H(k, U1(b, e))
28.58/10.40	   A^2 -> H(k, U1(b, k))
28.58/10.40	   A^2 -> H(k, U1(e, c))
28.58/10.40	   A^2 -> H(k, U1(c, e))
28.58/10.40	   A^2 -> H(k, U1(c, k))
28.58/10.40	   A^2 -> H(k, U1(e, e))
28.58/10.40	   A^2 -> H(k, U1(d, k))
28.58/10.40	   A^2 -> H(c, b)
28.58/10.40	   A^2 -> H(c, U1(e, d))
28.58/10.40	   A^2 -> H(c, U1(d, e))
28.58/10.40	   A^2 -> H(c, c)
28.58/10.40	   A^2 -> H(c, U1(e, k))
28.58/10.40	   A^2 -> H(c, U1(k, e))
28.58/10.40	   A^2 -> H(c, e)
28.58/10.40	   A^2 -> H(c, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, k), b)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, k), c)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, k), e)
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, c), d)
28.58/10.40	   A^2 -> H(U1(e, c), k)
28.58/10.40	   A^2 -> H(U1(k, e), b)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, e), c)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(k, c), d)
28.58/10.40	   A^2 -> H(U1(c, e), d)
28.58/10.40	   A^2 -> H(U1(c, e), k)
28.58/10.40	   A^2 -> H(U1(c, k), d)
28.58/10.40	   A^2 -> H(U1(c, k), k)
28.58/10.40	   A^2 -> H(e, b)
28.58/10.40	   A^2 -> H(e, U1(e, d))
28.58/10.40	   A^2 -> H(e, U1(d, e))
28.58/10.40	   A^2 -> H(e, c)
28.58/10.40	   A^2 -> H(e, U1(e, k))
28.58/10.40	   A^2 -> H(e, e)
28.58/10.40	   A^2 -> H(U1(e, e), d)
28.58/10.40	   A^2 -> H(U1(e, e), k)
28.58/10.40	   A^2 -> H(U1(k, k), d)
28.58/10.40	   A^2 -> H(U1(k, k), b)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, k), c)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, d), d)
28.58/10.40	   A^2 -> H(U1(d, k), d)
28.58/10.40	   A^2 -> H(U1(d, k), k)
28.58/10.40	   A^2 -> H(U1(e, e), c)
28.58/10.40	   A^2 -> H(U1(e, c), e)
28.58/10.40	   A^2 -> H(U1(c, e), e)
28.58/10.40	   A^2 -> H(U1(c, k), e)
28.58/10.40	   A^2 -> H(c, U1(e, e))
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.40	   A^2 -> H(d, b)
28.58/10.40	   A^2 -> H(d, U1(e, d))
28.58/10.40	   A^2 -> H(d, U1(d, e))
28.58/10.40	   A^2 -> H(d, c)
28.58/10.40	   A^2 -> H(d, U1(e, k))
28.58/10.40	   A^2 -> H(d, U1(k, e))
28.58/10.40	   A^2 -> H(d, e)
28.58/10.40	
28.58/10.40	The TRS R consists of the following rules:
28.58/10.40	
28.58/10.40	   f(x) -> U1(x, x)
28.58/10.40	   U1(e, x) -> x
28.58/10.40	   a -> c
28.58/10.40	   a -> d
28.58/10.40	   b -> c
28.58/10.40	   b -> d
28.58/10.40	   d -> k
28.58/10.40	   c -> e
28.58/10.40	   c -> k
28.58/10.40	
28.58/10.40	Q is empty.
28.58/10.40	We have to consider all minimal (P,Q,R)-chains.
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2435) TransformationProof (EQUIVALENT)
28.58/10.40	By narrowing [LPAR04] the rule A^2 -> H(d, U1(k, d)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.40	
28.58/10.40	   (A^2 -> H(k, U1(k, d)),A^2 -> H(k, U1(k, d)))
28.58/10.40	   (A^2 -> H(d, U1(k, k)),A^2 -> H(d, U1(k, k)))
28.58/10.40	
28.58/10.40	
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2436)
28.58/10.40	Obligation:
28.58/10.40	Q DP problem:
28.58/10.40	The TRS P consists of the following rules:
28.58/10.40	
28.58/10.40	   A^2 -> H(f(c), f(c))
28.58/10.40	   H(x, x) -> G(x, x, f(k))
28.58/10.40	   G(d, x, x) -> A^2
28.58/10.40	   A^2 -> H(f(d), f(d))
28.58/10.40	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.40	   A^2 -> H(f(e), f(e))
28.58/10.40	   A^2 -> H(f(k), f(k))
28.58/10.40	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.40	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.40	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.40	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.40	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.40	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.40	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.40	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.40	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.40	   A^2 -> H(d, U1(d, k))
28.58/10.40	   A^2 -> H(a, b)
28.58/10.40	   A^2 -> H(a, U1(e, d))
28.58/10.40	   A^2 -> H(a, U1(d, e))
28.58/10.40	   A^2 -> H(a, c)
28.58/10.40	   A^2 -> H(a, U1(e, k))
28.58/10.40	   A^2 -> H(a, U1(k, e))
28.58/10.40	   A^2 -> H(a, e)
28.58/10.40	   A^2 -> H(a, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, d), b)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, d), c)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, d), e)
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, a), d)
28.58/10.40	   A^2 -> H(U1(e, a), k)
28.58/10.40	   A^2 -> H(U1(k, a), d)
28.58/10.40	   A^2 -> H(U1(c, d), d)
28.58/10.40	   A^2 -> H(U1(c, d), k)
28.58/10.40	   A^2 -> H(U1(d, e), b)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(d, e), c)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(d, e), e)
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.40	   A^2 -> H(U1(d, c), d)
28.58/10.40	   A^2 -> H(U1(d, c), k)
28.58/10.40	   A^2 -> H(U1(a, e), d)
28.58/10.40	   A^2 -> H(U1(a, e), k)
28.58/10.40	   A^2 -> H(U1(a, k), d)
28.58/10.40	   A^2 -> H(U1(a, k), k)
28.58/10.40	   A^2 -> H(k, U1(e, b))
28.58/10.40	   A^2 -> H(k, U1(c, d))
28.58/10.40	   A^2 -> H(k, U1(d, c))
28.58/10.40	   A^2 -> H(k, U1(b, e))
28.58/10.40	   A^2 -> H(k, U1(b, k))
28.58/10.40	   A^2 -> H(k, U1(e, c))
28.58/10.40	   A^2 -> H(k, U1(c, e))
28.58/10.40	   A^2 -> H(k, U1(c, k))
28.58/10.40	   A^2 -> H(k, U1(e, e))
28.58/10.40	   A^2 -> H(k, U1(d, k))
28.58/10.40	   A^2 -> H(c, b)
28.58/10.40	   A^2 -> H(c, U1(e, d))
28.58/10.40	   A^2 -> H(c, U1(d, e))
28.58/10.40	   A^2 -> H(c, c)
28.58/10.40	   A^2 -> H(c, U1(e, k))
28.58/10.40	   A^2 -> H(c, U1(k, e))
28.58/10.40	   A^2 -> H(c, e)
28.58/10.40	   A^2 -> H(c, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, k), b)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, k), c)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, k), e)
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, c), d)
28.58/10.40	   A^2 -> H(U1(e, c), k)
28.58/10.40	   A^2 -> H(U1(k, e), b)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, e), c)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(k, c), d)
28.58/10.40	   A^2 -> H(U1(c, e), d)
28.58/10.40	   A^2 -> H(U1(c, e), k)
28.58/10.40	   A^2 -> H(U1(c, k), d)
28.58/10.40	   A^2 -> H(U1(c, k), k)
28.58/10.40	   A^2 -> H(e, b)
28.58/10.40	   A^2 -> H(e, U1(e, d))
28.58/10.40	   A^2 -> H(e, U1(d, e))
28.58/10.40	   A^2 -> H(e, c)
28.58/10.40	   A^2 -> H(e, U1(e, k))
28.58/10.40	   A^2 -> H(e, e)
28.58/10.40	   A^2 -> H(U1(e, e), d)
28.58/10.40	   A^2 -> H(U1(e, e), k)
28.58/10.40	   A^2 -> H(U1(k, k), d)
28.58/10.40	   A^2 -> H(U1(k, k), b)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, k), c)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, d), d)
28.58/10.40	   A^2 -> H(U1(d, k), d)
28.58/10.40	   A^2 -> H(U1(d, k), k)
28.58/10.40	   A^2 -> H(U1(e, e), c)
28.58/10.40	   A^2 -> H(U1(e, c), e)
28.58/10.40	   A^2 -> H(U1(c, e), e)
28.58/10.40	   A^2 -> H(U1(c, k), e)
28.58/10.40	   A^2 -> H(c, U1(e, e))
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.40	   A^2 -> H(d, b)
28.58/10.40	   A^2 -> H(d, U1(e, d))
28.58/10.40	   A^2 -> H(d, U1(d, e))
28.58/10.40	   A^2 -> H(d, c)
28.58/10.40	   A^2 -> H(d, U1(e, k))
28.58/10.40	   A^2 -> H(d, U1(k, e))
28.58/10.40	   A^2 -> H(d, e)
28.58/10.40	   A^2 -> H(k, U1(k, d))
28.58/10.40	   A^2 -> H(d, U1(k, k))
28.58/10.40	
28.58/10.40	The TRS R consists of the following rules:
28.58/10.40	
28.58/10.40	   f(x) -> U1(x, x)
28.58/10.40	   U1(e, x) -> x
28.58/10.40	   a -> c
28.58/10.40	   a -> d
28.58/10.40	   b -> c
28.58/10.40	   b -> d
28.58/10.40	   d -> k
28.58/10.40	   c -> e
28.58/10.40	   c -> k
28.58/10.40	
28.58/10.40	Q is empty.
28.58/10.40	We have to consider all minimal (P,Q,R)-chains.
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2437) DependencyGraphProof (EQUIVALENT)
28.58/10.40	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2438)
28.58/10.40	Obligation:
28.58/10.40	Q DP problem:
28.58/10.40	The TRS P consists of the following rules:
28.58/10.40	
28.58/10.40	   H(x, x) -> G(x, x, f(k))
28.58/10.40	   G(d, x, x) -> A^2
28.58/10.40	   A^2 -> H(f(c), f(c))
28.58/10.40	   A^2 -> H(f(d), f(d))
28.58/10.40	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.40	   A^2 -> H(f(e), f(e))
28.58/10.40	   A^2 -> H(f(k), f(k))
28.58/10.40	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.40	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.40	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.40	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.40	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.40	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.40	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.40	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.40	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.40	   A^2 -> H(d, U1(d, k))
28.58/10.40	   A^2 -> H(a, b)
28.58/10.40	   A^2 -> H(a, U1(e, d))
28.58/10.40	   A^2 -> H(a, U1(d, e))
28.58/10.40	   A^2 -> H(a, c)
28.58/10.40	   A^2 -> H(a, U1(e, k))
28.58/10.40	   A^2 -> H(a, U1(k, e))
28.58/10.40	   A^2 -> H(a, e)
28.58/10.40	   A^2 -> H(a, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, d), b)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, d), c)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, d), e)
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, a), d)
28.58/10.40	   A^2 -> H(U1(e, a), k)
28.58/10.40	   A^2 -> H(U1(k, a), d)
28.58/10.40	   A^2 -> H(U1(c, d), d)
28.58/10.40	   A^2 -> H(U1(c, d), k)
28.58/10.40	   A^2 -> H(U1(d, e), b)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(d, e), c)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(d, e), e)
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.40	   A^2 -> H(U1(d, c), d)
28.58/10.40	   A^2 -> H(U1(d, c), k)
28.58/10.40	   A^2 -> H(U1(a, e), d)
28.58/10.40	   A^2 -> H(U1(a, e), k)
28.58/10.40	   A^2 -> H(U1(a, k), d)
28.58/10.40	   A^2 -> H(U1(a, k), k)
28.58/10.40	   A^2 -> H(k, U1(e, b))
28.58/10.40	   A^2 -> H(k, U1(c, d))
28.58/10.40	   A^2 -> H(k, U1(d, c))
28.58/10.40	   A^2 -> H(k, U1(b, e))
28.58/10.40	   A^2 -> H(k, U1(b, k))
28.58/10.40	   A^2 -> H(k, U1(e, c))
28.58/10.40	   A^2 -> H(k, U1(c, e))
28.58/10.40	   A^2 -> H(k, U1(c, k))
28.58/10.40	   A^2 -> H(k, U1(e, e))
28.58/10.40	   A^2 -> H(k, U1(d, k))
28.58/10.40	   A^2 -> H(c, b)
28.58/10.40	   A^2 -> H(c, U1(e, d))
28.58/10.40	   A^2 -> H(c, U1(d, e))
28.58/10.40	   A^2 -> H(c, c)
28.58/10.40	   A^2 -> H(c, U1(e, k))
28.58/10.40	   A^2 -> H(c, U1(k, e))
28.58/10.40	   A^2 -> H(c, e)
28.58/10.40	   A^2 -> H(c, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, k), b)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, k), c)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, k), e)
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, c), d)
28.58/10.40	   A^2 -> H(U1(e, c), k)
28.58/10.40	   A^2 -> H(U1(k, e), b)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, e), c)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(k, c), d)
28.58/10.40	   A^2 -> H(U1(c, e), d)
28.58/10.40	   A^2 -> H(U1(c, e), k)
28.58/10.40	   A^2 -> H(U1(c, k), d)
28.58/10.40	   A^2 -> H(U1(c, k), k)
28.58/10.40	   A^2 -> H(e, b)
28.58/10.40	   A^2 -> H(e, U1(e, d))
28.58/10.40	   A^2 -> H(e, U1(d, e))
28.58/10.40	   A^2 -> H(e, c)
28.58/10.40	   A^2 -> H(e, U1(e, k))
28.58/10.40	   A^2 -> H(e, e)
28.58/10.40	   A^2 -> H(U1(e, e), d)
28.58/10.40	   A^2 -> H(U1(e, e), k)
28.58/10.40	   A^2 -> H(U1(k, k), d)
28.58/10.40	   A^2 -> H(U1(k, k), b)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, k), c)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, d), d)
28.58/10.40	   A^2 -> H(U1(d, k), d)
28.58/10.40	   A^2 -> H(U1(d, k), k)
28.58/10.40	   A^2 -> H(U1(e, e), c)
28.58/10.40	   A^2 -> H(U1(e, c), e)
28.58/10.40	   A^2 -> H(U1(c, e), e)
28.58/10.40	   A^2 -> H(U1(c, k), e)
28.58/10.40	   A^2 -> H(c, U1(e, e))
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.40	   A^2 -> H(d, b)
28.58/10.40	   A^2 -> H(d, U1(e, d))
28.58/10.40	   A^2 -> H(d, U1(d, e))
28.58/10.40	   A^2 -> H(d, c)
28.58/10.40	   A^2 -> H(d, U1(e, k))
28.58/10.40	   A^2 -> H(d, U1(k, e))
28.58/10.40	   A^2 -> H(d, e)
28.58/10.40	   A^2 -> H(d, U1(k, k))
28.58/10.40	
28.58/10.40	The TRS R consists of the following rules:
28.58/10.40	
28.58/10.40	   f(x) -> U1(x, x)
28.58/10.40	   U1(e, x) -> x
28.58/10.40	   a -> c
28.58/10.40	   a -> d
28.58/10.40	   b -> c
28.58/10.40	   b -> d
28.58/10.40	   d -> k
28.58/10.40	   c -> e
28.58/10.40	   c -> k
28.58/10.40	
28.58/10.40	Q is empty.
28.58/10.40	We have to consider all minimal (P,Q,R)-chains.
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2439) TransformationProof (EQUIVALENT)
28.58/10.40	By narrowing [LPAR04] the rule A^2 -> H(d, U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.40	
28.58/10.40	   (A^2 -> H(k, U1(d, k)),A^2 -> H(k, U1(d, k)))
28.58/10.40	   (A^2 -> H(d, U1(k, k)),A^2 -> H(d, U1(k, k)))
28.58/10.40	
28.58/10.40	
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2440)
28.58/10.40	Obligation:
28.58/10.40	Q DP problem:
28.58/10.40	The TRS P consists of the following rules:
28.58/10.40	
28.58/10.40	   H(x, x) -> G(x, x, f(k))
28.58/10.40	   G(d, x, x) -> A^2
28.58/10.40	   A^2 -> H(f(c), f(c))
28.58/10.40	   A^2 -> H(f(d), f(d))
28.58/10.40	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.40	   A^2 -> H(f(e), f(e))
28.58/10.40	   A^2 -> H(f(k), f(k))
28.58/10.40	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.40	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.40	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.40	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.40	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.40	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.40	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.40	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.40	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.40	   A^2 -> H(a, b)
28.58/10.40	   A^2 -> H(a, U1(e, d))
28.58/10.40	   A^2 -> H(a, U1(d, e))
28.58/10.40	   A^2 -> H(a, c)
28.58/10.40	   A^2 -> H(a, U1(e, k))
28.58/10.40	   A^2 -> H(a, U1(k, e))
28.58/10.40	   A^2 -> H(a, e)
28.58/10.40	   A^2 -> H(a, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, d), b)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, d), c)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, d), e)
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, a), d)
28.58/10.40	   A^2 -> H(U1(e, a), k)
28.58/10.40	   A^2 -> H(U1(k, a), d)
28.58/10.40	   A^2 -> H(U1(c, d), d)
28.58/10.40	   A^2 -> H(U1(c, d), k)
28.58/10.40	   A^2 -> H(U1(d, e), b)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(d, e), c)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(d, e), e)
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.40	   A^2 -> H(U1(d, c), d)
28.58/10.40	   A^2 -> H(U1(d, c), k)
28.58/10.40	   A^2 -> H(U1(a, e), d)
28.58/10.40	   A^2 -> H(U1(a, e), k)
28.58/10.40	   A^2 -> H(U1(a, k), d)
28.58/10.40	   A^2 -> H(U1(a, k), k)
28.58/10.40	   A^2 -> H(k, U1(e, b))
28.58/10.40	   A^2 -> H(k, U1(c, d))
28.58/10.40	   A^2 -> H(k, U1(d, c))
28.58/10.40	   A^2 -> H(k, U1(b, e))
28.58/10.40	   A^2 -> H(k, U1(b, k))
28.58/10.40	   A^2 -> H(k, U1(e, c))
28.58/10.40	   A^2 -> H(k, U1(c, e))
28.58/10.40	   A^2 -> H(k, U1(c, k))
28.58/10.40	   A^2 -> H(k, U1(e, e))
28.58/10.40	   A^2 -> H(k, U1(d, k))
28.58/10.40	   A^2 -> H(c, b)
28.58/10.40	   A^2 -> H(c, U1(e, d))
28.58/10.40	   A^2 -> H(c, U1(d, e))
28.58/10.40	   A^2 -> H(c, c)
28.58/10.40	   A^2 -> H(c, U1(e, k))
28.58/10.40	   A^2 -> H(c, U1(k, e))
28.58/10.40	   A^2 -> H(c, e)
28.58/10.40	   A^2 -> H(c, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, k), b)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, k), c)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, k), e)
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, c), d)
28.58/10.40	   A^2 -> H(U1(e, c), k)
28.58/10.40	   A^2 -> H(U1(k, e), b)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, e), c)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(k, c), d)
28.58/10.40	   A^2 -> H(U1(c, e), d)
28.58/10.40	   A^2 -> H(U1(c, e), k)
28.58/10.40	   A^2 -> H(U1(c, k), d)
28.58/10.40	   A^2 -> H(U1(c, k), k)
28.58/10.40	   A^2 -> H(e, b)
28.58/10.40	   A^2 -> H(e, U1(e, d))
28.58/10.40	   A^2 -> H(e, U1(d, e))
28.58/10.40	   A^2 -> H(e, c)
28.58/10.40	   A^2 -> H(e, U1(e, k))
28.58/10.40	   A^2 -> H(e, e)
28.58/10.40	   A^2 -> H(U1(e, e), d)
28.58/10.40	   A^2 -> H(U1(e, e), k)
28.58/10.40	   A^2 -> H(U1(k, k), d)
28.58/10.40	   A^2 -> H(U1(k, k), b)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, k), c)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, d), d)
28.58/10.40	   A^2 -> H(U1(d, k), d)
28.58/10.40	   A^2 -> H(U1(d, k), k)
28.58/10.40	   A^2 -> H(U1(e, e), c)
28.58/10.40	   A^2 -> H(U1(e, c), e)
28.58/10.40	   A^2 -> H(U1(c, e), e)
28.58/10.40	   A^2 -> H(U1(c, k), e)
28.58/10.40	   A^2 -> H(c, U1(e, e))
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.40	   A^2 -> H(d, b)
28.58/10.40	   A^2 -> H(d, U1(e, d))
28.58/10.40	   A^2 -> H(d, U1(d, e))
28.58/10.40	   A^2 -> H(d, c)
28.58/10.40	   A^2 -> H(d, U1(e, k))
28.58/10.40	   A^2 -> H(d, U1(k, e))
28.58/10.40	   A^2 -> H(d, e)
28.58/10.40	   A^2 -> H(d, U1(k, k))
28.58/10.40	
28.58/10.40	The TRS R consists of the following rules:
28.58/10.40	
28.58/10.40	   f(x) -> U1(x, x)
28.58/10.40	   U1(e, x) -> x
28.58/10.40	   a -> c
28.58/10.40	   a -> d
28.58/10.40	   b -> c
28.58/10.40	   b -> d
28.58/10.40	   d -> k
28.58/10.40	   c -> e
28.58/10.40	   c -> k
28.58/10.40	
28.58/10.40	Q is empty.
28.58/10.40	We have to consider all minimal (P,Q,R)-chains.
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2441) TransformationProof (EQUIVALENT)
28.58/10.40	By narrowing [LPAR04] the rule A^2 -> H(a, b) at position [] we obtained the following new rules [LPAR04]:
28.58/10.40	
28.58/10.40	   (A^2 -> H(c, b),A^2 -> H(c, b))
28.58/10.40	   (A^2 -> H(d, b),A^2 -> H(d, b))
28.58/10.40	   (A^2 -> H(a, c),A^2 -> H(a, c))
28.58/10.40	   (A^2 -> H(a, d),A^2 -> H(a, d))
28.58/10.40	
28.58/10.40	
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2442)
28.58/10.40	Obligation:
28.58/10.40	Q DP problem:
28.58/10.40	The TRS P consists of the following rules:
28.58/10.40	
28.58/10.40	   H(x, x) -> G(x, x, f(k))
28.58/10.40	   G(d, x, x) -> A^2
28.58/10.40	   A^2 -> H(f(c), f(c))
28.58/10.40	   A^2 -> H(f(d), f(d))
28.58/10.40	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.40	   A^2 -> H(f(e), f(e))
28.58/10.40	   A^2 -> H(f(k), f(k))
28.58/10.40	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.40	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.40	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.40	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.40	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.40	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.40	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.40	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.40	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.40	   A^2 -> H(a, U1(e, d))
28.58/10.40	   A^2 -> H(a, U1(d, e))
28.58/10.40	   A^2 -> H(a, c)
28.58/10.40	   A^2 -> H(a, U1(e, k))
28.58/10.40	   A^2 -> H(a, U1(k, e))
28.58/10.40	   A^2 -> H(a, e)
28.58/10.40	   A^2 -> H(a, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, d), b)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, d), c)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, d), e)
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, a), d)
28.58/10.40	   A^2 -> H(U1(e, a), k)
28.58/10.40	   A^2 -> H(U1(k, a), d)
28.58/10.40	   A^2 -> H(U1(c, d), d)
28.58/10.40	   A^2 -> H(U1(c, d), k)
28.58/10.40	   A^2 -> H(U1(d, e), b)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(d, e), c)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(d, e), e)
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.40	   A^2 -> H(U1(d, c), d)
28.58/10.40	   A^2 -> H(U1(d, c), k)
28.58/10.40	   A^2 -> H(U1(a, e), d)
28.58/10.40	   A^2 -> H(U1(a, e), k)
28.58/10.40	   A^2 -> H(U1(a, k), d)
28.58/10.40	   A^2 -> H(U1(a, k), k)
28.58/10.40	   A^2 -> H(k, U1(e, b))
28.58/10.40	   A^2 -> H(k, U1(c, d))
28.58/10.40	   A^2 -> H(k, U1(d, c))
28.58/10.40	   A^2 -> H(k, U1(b, e))
28.58/10.40	   A^2 -> H(k, U1(b, k))
28.58/10.40	   A^2 -> H(k, U1(e, c))
28.58/10.40	   A^2 -> H(k, U1(c, e))
28.58/10.40	   A^2 -> H(k, U1(c, k))
28.58/10.40	   A^2 -> H(k, U1(e, e))
28.58/10.40	   A^2 -> H(k, U1(d, k))
28.58/10.40	   A^2 -> H(c, b)
28.58/10.40	   A^2 -> H(c, U1(e, d))
28.58/10.40	   A^2 -> H(c, U1(d, e))
28.58/10.40	   A^2 -> H(c, c)
28.58/10.40	   A^2 -> H(c, U1(e, k))
28.58/10.40	   A^2 -> H(c, U1(k, e))
28.58/10.40	   A^2 -> H(c, e)
28.58/10.40	   A^2 -> H(c, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, k), b)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, k), c)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, k), e)
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, c), d)
28.58/10.40	   A^2 -> H(U1(e, c), k)
28.58/10.40	   A^2 -> H(U1(k, e), b)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, e), c)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(k, c), d)
28.58/10.40	   A^2 -> H(U1(c, e), d)
28.58/10.40	   A^2 -> H(U1(c, e), k)
28.58/10.40	   A^2 -> H(U1(c, k), d)
28.58/10.40	   A^2 -> H(U1(c, k), k)
28.58/10.40	   A^2 -> H(e, b)
28.58/10.40	   A^2 -> H(e, U1(e, d))
28.58/10.40	   A^2 -> H(e, U1(d, e))
28.58/10.40	   A^2 -> H(e, c)
28.58/10.40	   A^2 -> H(e, U1(e, k))
28.58/10.40	   A^2 -> H(e, e)
28.58/10.40	   A^2 -> H(U1(e, e), d)
28.58/10.40	   A^2 -> H(U1(e, e), k)
28.58/10.40	   A^2 -> H(U1(k, k), d)
28.58/10.40	   A^2 -> H(U1(k, k), b)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, k), c)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, d), d)
28.58/10.40	   A^2 -> H(U1(d, k), d)
28.58/10.40	   A^2 -> H(U1(d, k), k)
28.58/10.40	   A^2 -> H(U1(e, e), c)
28.58/10.40	   A^2 -> H(U1(e, c), e)
28.58/10.40	   A^2 -> H(U1(c, e), e)
28.58/10.40	   A^2 -> H(U1(c, k), e)
28.58/10.40	   A^2 -> H(c, U1(e, e))
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.40	   A^2 -> H(d, b)
28.58/10.40	   A^2 -> H(d, U1(e, d))
28.58/10.40	   A^2 -> H(d, U1(d, e))
28.58/10.40	   A^2 -> H(d, c)
28.58/10.40	   A^2 -> H(d, U1(e, k))
28.58/10.40	   A^2 -> H(d, U1(k, e))
28.58/10.40	   A^2 -> H(d, e)
28.58/10.40	   A^2 -> H(d, U1(k, k))
28.58/10.40	   A^2 -> H(a, d)
28.58/10.40	
28.58/10.40	The TRS R consists of the following rules:
28.58/10.40	
28.58/10.40	   f(x) -> U1(x, x)
28.58/10.40	   U1(e, x) -> x
28.58/10.40	   a -> c
28.58/10.40	   a -> d
28.58/10.40	   b -> c
28.58/10.40	   b -> d
28.58/10.40	   d -> k
28.58/10.40	   c -> e
28.58/10.40	   c -> k
28.58/10.40	
28.58/10.40	Q is empty.
28.58/10.40	We have to consider all minimal (P,Q,R)-chains.
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2443) TransformationProof (EQUIVALENT)
28.58/10.40	By narrowing [LPAR04] the rule A^2 -> H(a, U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.40	
28.58/10.40	   (A^2 -> H(c, U1(e, d)),A^2 -> H(c, U1(e, d)))
28.58/10.40	   (A^2 -> H(d, U1(e, d)),A^2 -> H(d, U1(e, d)))
28.58/10.40	   (A^2 -> H(a, d),A^2 -> H(a, d))
28.58/10.40	   (A^2 -> H(a, U1(e, k)),A^2 -> H(a, U1(e, k)))
28.58/10.40	
28.58/10.40	
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2444)
28.58/10.40	Obligation:
28.58/10.40	Q DP problem:
28.58/10.40	The TRS P consists of the following rules:
28.58/10.40	
28.58/10.40	   H(x, x) -> G(x, x, f(k))
28.58/10.40	   G(d, x, x) -> A^2
28.58/10.40	   A^2 -> H(f(c), f(c))
28.58/10.40	   A^2 -> H(f(d), f(d))
28.58/10.40	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.40	   A^2 -> H(f(e), f(e))
28.58/10.40	   A^2 -> H(f(k), f(k))
28.58/10.40	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.40	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.40	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.40	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.40	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.40	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.40	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.40	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.40	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.40	   A^2 -> H(a, U1(d, e))
28.58/10.40	   A^2 -> H(a, c)
28.58/10.40	   A^2 -> H(a, U1(e, k))
28.58/10.40	   A^2 -> H(a, U1(k, e))
28.58/10.40	   A^2 -> H(a, e)
28.58/10.40	   A^2 -> H(a, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, d), b)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, d), c)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, d), e)
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, a), d)
28.58/10.40	   A^2 -> H(U1(e, a), k)
28.58/10.40	   A^2 -> H(U1(k, a), d)
28.58/10.40	   A^2 -> H(U1(c, d), d)
28.58/10.40	   A^2 -> H(U1(c, d), k)
28.58/10.40	   A^2 -> H(U1(d, e), b)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(d, e), c)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(d, e), e)
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.40	   A^2 -> H(U1(d, c), d)
28.58/10.40	   A^2 -> H(U1(d, c), k)
28.58/10.40	   A^2 -> H(U1(a, e), d)
28.58/10.40	   A^2 -> H(U1(a, e), k)
28.58/10.40	   A^2 -> H(U1(a, k), d)
28.58/10.40	   A^2 -> H(U1(a, k), k)
28.58/10.40	   A^2 -> H(k, U1(e, b))
28.58/10.40	   A^2 -> H(k, U1(c, d))
28.58/10.40	   A^2 -> H(k, U1(d, c))
28.58/10.40	   A^2 -> H(k, U1(b, e))
28.58/10.40	   A^2 -> H(k, U1(b, k))
28.58/10.40	   A^2 -> H(k, U1(e, c))
28.58/10.40	   A^2 -> H(k, U1(c, e))
28.58/10.40	   A^2 -> H(k, U1(c, k))
28.58/10.40	   A^2 -> H(k, U1(e, e))
28.58/10.40	   A^2 -> H(k, U1(d, k))
28.58/10.40	   A^2 -> H(c, b)
28.58/10.40	   A^2 -> H(c, U1(e, d))
28.58/10.40	   A^2 -> H(c, U1(d, e))
28.58/10.40	   A^2 -> H(c, c)
28.58/10.40	   A^2 -> H(c, U1(e, k))
28.58/10.40	   A^2 -> H(c, U1(k, e))
28.58/10.40	   A^2 -> H(c, e)
28.58/10.40	   A^2 -> H(c, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, k), b)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, k), c)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, k), e)
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, c), d)
28.58/10.40	   A^2 -> H(U1(e, c), k)
28.58/10.40	   A^2 -> H(U1(k, e), b)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, e), c)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(k, c), d)
28.58/10.40	   A^2 -> H(U1(c, e), d)
28.58/10.40	   A^2 -> H(U1(c, e), k)
28.58/10.40	   A^2 -> H(U1(c, k), d)
28.58/10.40	   A^2 -> H(U1(c, k), k)
28.58/10.40	   A^2 -> H(e, b)
28.58/10.40	   A^2 -> H(e, U1(e, d))
28.58/10.40	   A^2 -> H(e, U1(d, e))
28.58/10.40	   A^2 -> H(e, c)
28.58/10.40	   A^2 -> H(e, U1(e, k))
28.58/10.40	   A^2 -> H(e, e)
28.58/10.40	   A^2 -> H(U1(e, e), d)
28.58/10.40	   A^2 -> H(U1(e, e), k)
28.58/10.40	   A^2 -> H(U1(k, k), d)
28.58/10.40	   A^2 -> H(U1(k, k), b)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, k), c)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, d), d)
28.58/10.40	   A^2 -> H(U1(d, k), d)
28.58/10.40	   A^2 -> H(U1(d, k), k)
28.58/10.40	   A^2 -> H(U1(e, e), c)
28.58/10.40	   A^2 -> H(U1(e, c), e)
28.58/10.40	   A^2 -> H(U1(c, e), e)
28.58/10.40	   A^2 -> H(U1(c, k), e)
28.58/10.40	   A^2 -> H(c, U1(e, e))
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.40	   A^2 -> H(d, b)
28.58/10.40	   A^2 -> H(d, U1(e, d))
28.58/10.40	   A^2 -> H(d, U1(d, e))
28.58/10.40	   A^2 -> H(d, c)
28.58/10.40	   A^2 -> H(d, U1(e, k))
28.58/10.40	   A^2 -> H(d, U1(k, e))
28.58/10.40	   A^2 -> H(d, e)
28.58/10.40	   A^2 -> H(d, U1(k, k))
28.58/10.40	   A^2 -> H(a, d)
28.58/10.40	
28.58/10.40	The TRS R consists of the following rules:
28.58/10.40	
28.58/10.40	   f(x) -> U1(x, x)
28.58/10.40	   U1(e, x) -> x
28.58/10.40	   a -> c
28.58/10.40	   a -> d
28.58/10.40	   b -> c
28.58/10.40	   b -> d
28.58/10.40	   d -> k
28.58/10.40	   c -> e
28.58/10.40	   c -> k
28.58/10.40	
28.58/10.40	Q is empty.
28.58/10.40	We have to consider all minimal (P,Q,R)-chains.
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2445) TransformationProof (EQUIVALENT)
28.58/10.40	By narrowing [LPAR04] the rule A^2 -> H(a, U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.40	
28.58/10.40	   (A^2 -> H(c, U1(d, e)),A^2 -> H(c, U1(d, e)))
28.58/10.40	   (A^2 -> H(d, U1(d, e)),A^2 -> H(d, U1(d, e)))
28.58/10.40	   (A^2 -> H(a, U1(k, e)),A^2 -> H(a, U1(k, e)))
28.58/10.40	
28.58/10.40	
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2446)
28.58/10.40	Obligation:
28.58/10.40	Q DP problem:
28.58/10.40	The TRS P consists of the following rules:
28.58/10.40	
28.58/10.40	   H(x, x) -> G(x, x, f(k))
28.58/10.40	   G(d, x, x) -> A^2
28.58/10.40	   A^2 -> H(f(c), f(c))
28.58/10.40	   A^2 -> H(f(d), f(d))
28.58/10.40	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.40	   A^2 -> H(f(e), f(e))
28.58/10.40	   A^2 -> H(f(k), f(k))
28.58/10.40	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.40	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.40	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.40	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.40	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.40	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.40	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.40	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.40	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.40	   A^2 -> H(a, c)
28.58/10.40	   A^2 -> H(a, U1(e, k))
28.58/10.40	   A^2 -> H(a, U1(k, e))
28.58/10.40	   A^2 -> H(a, e)
28.58/10.40	   A^2 -> H(a, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, d), b)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, d), c)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, d), e)
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, a), d)
28.58/10.40	   A^2 -> H(U1(e, a), k)
28.58/10.40	   A^2 -> H(U1(k, a), d)
28.58/10.40	   A^2 -> H(U1(c, d), d)
28.58/10.40	   A^2 -> H(U1(c, d), k)
28.58/10.40	   A^2 -> H(U1(d, e), b)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(d, e), c)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(d, e), e)
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.40	   A^2 -> H(U1(d, c), d)
28.58/10.40	   A^2 -> H(U1(d, c), k)
28.58/10.40	   A^2 -> H(U1(a, e), d)
28.58/10.40	   A^2 -> H(U1(a, e), k)
28.58/10.40	   A^2 -> H(U1(a, k), d)
28.58/10.40	   A^2 -> H(U1(a, k), k)
28.58/10.40	   A^2 -> H(k, U1(e, b))
28.58/10.40	   A^2 -> H(k, U1(c, d))
28.58/10.40	   A^2 -> H(k, U1(d, c))
28.58/10.40	   A^2 -> H(k, U1(b, e))
28.58/10.40	   A^2 -> H(k, U1(b, k))
28.58/10.40	   A^2 -> H(k, U1(e, c))
28.58/10.40	   A^2 -> H(k, U1(c, e))
28.58/10.40	   A^2 -> H(k, U1(c, k))
28.58/10.40	   A^2 -> H(k, U1(e, e))
28.58/10.40	   A^2 -> H(k, U1(d, k))
28.58/10.40	   A^2 -> H(c, b)
28.58/10.40	   A^2 -> H(c, U1(e, d))
28.58/10.40	   A^2 -> H(c, U1(d, e))
28.58/10.40	   A^2 -> H(c, c)
28.58/10.40	   A^2 -> H(c, U1(e, k))
28.58/10.40	   A^2 -> H(c, U1(k, e))
28.58/10.40	   A^2 -> H(c, e)
28.58/10.40	   A^2 -> H(c, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, k), b)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, k), c)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, k), e)
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, c), d)
28.58/10.40	   A^2 -> H(U1(e, c), k)
28.58/10.40	   A^2 -> H(U1(k, e), b)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, e), c)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(k, c), d)
28.58/10.40	   A^2 -> H(U1(c, e), d)
28.58/10.40	   A^2 -> H(U1(c, e), k)
28.58/10.40	   A^2 -> H(U1(c, k), d)
28.58/10.40	   A^2 -> H(U1(c, k), k)
28.58/10.40	   A^2 -> H(e, b)
28.58/10.40	   A^2 -> H(e, U1(e, d))
28.58/10.40	   A^2 -> H(e, U1(d, e))
28.58/10.40	   A^2 -> H(e, c)
28.58/10.40	   A^2 -> H(e, U1(e, k))
28.58/10.40	   A^2 -> H(e, e)
28.58/10.40	   A^2 -> H(U1(e, e), d)
28.58/10.40	   A^2 -> H(U1(e, e), k)
28.58/10.40	   A^2 -> H(U1(k, k), d)
28.58/10.40	   A^2 -> H(U1(k, k), b)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, k), c)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, d), d)
28.58/10.40	   A^2 -> H(U1(d, k), d)
28.58/10.40	   A^2 -> H(U1(d, k), k)
28.58/10.40	   A^2 -> H(U1(e, e), c)
28.58/10.40	   A^2 -> H(U1(e, c), e)
28.58/10.40	   A^2 -> H(U1(c, e), e)
28.58/10.40	   A^2 -> H(U1(c, k), e)
28.58/10.40	   A^2 -> H(c, U1(e, e))
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.40	   A^2 -> H(d, b)
28.58/10.40	   A^2 -> H(d, U1(e, d))
28.58/10.40	   A^2 -> H(d, U1(d, e))
28.58/10.40	   A^2 -> H(d, c)
28.58/10.40	   A^2 -> H(d, U1(e, k))
28.58/10.40	   A^2 -> H(d, U1(k, e))
28.58/10.40	   A^2 -> H(d, e)
28.58/10.40	   A^2 -> H(d, U1(k, k))
28.58/10.40	   A^2 -> H(a, d)
28.58/10.40	
28.58/10.40	The TRS R consists of the following rules:
28.58/10.40	
28.58/10.40	   f(x) -> U1(x, x)
28.58/10.40	   U1(e, x) -> x
28.58/10.40	   a -> c
28.58/10.40	   a -> d
28.58/10.40	   b -> c
28.58/10.40	   b -> d
28.58/10.40	   d -> k
28.58/10.40	   c -> e
28.58/10.40	   c -> k
28.58/10.40	
28.58/10.40	Q is empty.
28.58/10.40	We have to consider all minimal (P,Q,R)-chains.
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2447) TransformationProof (EQUIVALENT)
28.58/10.40	By narrowing [LPAR04] the rule A^2 -> H(a, c) at position [] we obtained the following new rules [LPAR04]:
28.58/10.40	
28.58/10.40	   (A^2 -> H(c, c),A^2 -> H(c, c))
28.58/10.40	   (A^2 -> H(d, c),A^2 -> H(d, c))
28.58/10.40	   (A^2 -> H(a, e),A^2 -> H(a, e))
28.58/10.40	   (A^2 -> H(a, k),A^2 -> H(a, k))
28.58/10.40	
28.58/10.40	
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2448)
28.58/10.40	Obligation:
28.58/10.40	Q DP problem:
28.58/10.40	The TRS P consists of the following rules:
28.58/10.40	
28.58/10.40	   H(x, x) -> G(x, x, f(k))
28.58/10.40	   G(d, x, x) -> A^2
28.58/10.40	   A^2 -> H(f(c), f(c))
28.58/10.40	   A^2 -> H(f(d), f(d))
28.58/10.40	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.40	   A^2 -> H(f(e), f(e))
28.58/10.40	   A^2 -> H(f(k), f(k))
28.58/10.40	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.40	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.40	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.40	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.40	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.40	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.40	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.40	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.40	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.40	   A^2 -> H(a, U1(e, k))
28.58/10.40	   A^2 -> H(a, U1(k, e))
28.58/10.40	   A^2 -> H(a, e)
28.58/10.40	   A^2 -> H(a, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, d), b)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, d), c)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, d), e)
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, a), d)
28.58/10.40	   A^2 -> H(U1(e, a), k)
28.58/10.40	   A^2 -> H(U1(k, a), d)
28.58/10.40	   A^2 -> H(U1(c, d), d)
28.58/10.40	   A^2 -> H(U1(c, d), k)
28.58/10.40	   A^2 -> H(U1(d, e), b)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(d, e), c)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(d, e), e)
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.40	   A^2 -> H(U1(d, c), d)
28.58/10.40	   A^2 -> H(U1(d, c), k)
28.58/10.40	   A^2 -> H(U1(a, e), d)
28.58/10.40	   A^2 -> H(U1(a, e), k)
28.58/10.40	   A^2 -> H(U1(a, k), d)
28.58/10.40	   A^2 -> H(U1(a, k), k)
28.58/10.40	   A^2 -> H(k, U1(e, b))
28.58/10.40	   A^2 -> H(k, U1(c, d))
28.58/10.40	   A^2 -> H(k, U1(d, c))
28.58/10.40	   A^2 -> H(k, U1(b, e))
28.58/10.40	   A^2 -> H(k, U1(b, k))
28.58/10.40	   A^2 -> H(k, U1(e, c))
28.58/10.40	   A^2 -> H(k, U1(c, e))
28.58/10.40	   A^2 -> H(k, U1(c, k))
28.58/10.40	   A^2 -> H(k, U1(e, e))
28.58/10.40	   A^2 -> H(k, U1(d, k))
28.58/10.40	   A^2 -> H(c, b)
28.58/10.40	   A^2 -> H(c, U1(e, d))
28.58/10.40	   A^2 -> H(c, U1(d, e))
28.58/10.40	   A^2 -> H(c, c)
28.58/10.40	   A^2 -> H(c, U1(e, k))
28.58/10.40	   A^2 -> H(c, U1(k, e))
28.58/10.40	   A^2 -> H(c, e)
28.58/10.40	   A^2 -> H(c, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, k), b)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, k), c)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, k), e)
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, c), d)
28.58/10.40	   A^2 -> H(U1(e, c), k)
28.58/10.40	   A^2 -> H(U1(k, e), b)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, e), c)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(k, c), d)
28.58/10.40	   A^2 -> H(U1(c, e), d)
28.58/10.40	   A^2 -> H(U1(c, e), k)
28.58/10.40	   A^2 -> H(U1(c, k), d)
28.58/10.40	   A^2 -> H(U1(c, k), k)
28.58/10.40	   A^2 -> H(e, b)
28.58/10.40	   A^2 -> H(e, U1(e, d))
28.58/10.40	   A^2 -> H(e, U1(d, e))
28.58/10.40	   A^2 -> H(e, c)
28.58/10.40	   A^2 -> H(e, U1(e, k))
28.58/10.40	   A^2 -> H(e, e)
28.58/10.40	   A^2 -> H(U1(e, e), d)
28.58/10.40	   A^2 -> H(U1(e, e), k)
28.58/10.40	   A^2 -> H(U1(k, k), d)
28.58/10.40	   A^2 -> H(U1(k, k), b)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, k), c)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, d), d)
28.58/10.40	   A^2 -> H(U1(d, k), d)
28.58/10.40	   A^2 -> H(U1(d, k), k)
28.58/10.40	   A^2 -> H(U1(e, e), c)
28.58/10.40	   A^2 -> H(U1(e, c), e)
28.58/10.40	   A^2 -> H(U1(c, e), e)
28.58/10.40	   A^2 -> H(U1(c, k), e)
28.58/10.40	   A^2 -> H(c, U1(e, e))
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.40	   A^2 -> H(d, b)
28.58/10.40	   A^2 -> H(d, U1(e, d))
28.58/10.40	   A^2 -> H(d, U1(d, e))
28.58/10.40	   A^2 -> H(d, c)
28.58/10.40	   A^2 -> H(d, U1(e, k))
28.58/10.40	   A^2 -> H(d, U1(k, e))
28.58/10.40	   A^2 -> H(d, e)
28.58/10.40	   A^2 -> H(d, U1(k, k))
28.58/10.40	   A^2 -> H(a, d)
28.58/10.40	   A^2 -> H(a, k)
28.58/10.40	
28.58/10.40	The TRS R consists of the following rules:
28.58/10.40	
28.58/10.40	   f(x) -> U1(x, x)
28.58/10.40	   U1(e, x) -> x
28.58/10.40	   a -> c
28.58/10.40	   a -> d
28.58/10.40	   b -> c
28.58/10.40	   b -> d
28.58/10.40	   d -> k
28.58/10.40	   c -> e
28.58/10.40	   c -> k
28.58/10.40	
28.58/10.40	Q is empty.
28.58/10.40	We have to consider all minimal (P,Q,R)-chains.
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2449) TransformationProof (EQUIVALENT)
28.58/10.40	By narrowing [LPAR04] the rule A^2 -> H(a, U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.40	
28.58/10.40	   (A^2 -> H(c, U1(e, k)),A^2 -> H(c, U1(e, k)))
28.58/10.40	   (A^2 -> H(d, U1(e, k)),A^2 -> H(d, U1(e, k)))
28.58/10.40	   (A^2 -> H(a, k),A^2 -> H(a, k))
28.58/10.40	
28.58/10.40	
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2450)
28.58/10.40	Obligation:
28.58/10.40	Q DP problem:
28.58/10.40	The TRS P consists of the following rules:
28.58/10.40	
28.58/10.40	   H(x, x) -> G(x, x, f(k))
28.58/10.40	   G(d, x, x) -> A^2
28.58/10.40	   A^2 -> H(f(c), f(c))
28.58/10.40	   A^2 -> H(f(d), f(d))
28.58/10.40	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.40	   A^2 -> H(f(e), f(e))
28.58/10.40	   A^2 -> H(f(k), f(k))
28.58/10.40	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.40	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.40	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.40	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.40	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.40	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.40	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.40	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.40	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.40	   A^2 -> H(a, U1(k, e))
28.58/10.40	   A^2 -> H(a, e)
28.58/10.40	   A^2 -> H(a, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, d), b)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, d), c)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, d), e)
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, a), d)
28.58/10.40	   A^2 -> H(U1(e, a), k)
28.58/10.40	   A^2 -> H(U1(k, a), d)
28.58/10.40	   A^2 -> H(U1(c, d), d)
28.58/10.40	   A^2 -> H(U1(c, d), k)
28.58/10.40	   A^2 -> H(U1(d, e), b)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(d, e), c)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(d, e), e)
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.40	   A^2 -> H(U1(d, c), d)
28.58/10.40	   A^2 -> H(U1(d, c), k)
28.58/10.40	   A^2 -> H(U1(a, e), d)
28.58/10.40	   A^2 -> H(U1(a, e), k)
28.58/10.40	   A^2 -> H(U1(a, k), d)
28.58/10.40	   A^2 -> H(U1(a, k), k)
28.58/10.40	   A^2 -> H(k, U1(e, b))
28.58/10.40	   A^2 -> H(k, U1(c, d))
28.58/10.40	   A^2 -> H(k, U1(d, c))
28.58/10.40	   A^2 -> H(k, U1(b, e))
28.58/10.40	   A^2 -> H(k, U1(b, k))
28.58/10.40	   A^2 -> H(k, U1(e, c))
28.58/10.40	   A^2 -> H(k, U1(c, e))
28.58/10.40	   A^2 -> H(k, U1(c, k))
28.58/10.40	   A^2 -> H(k, U1(e, e))
28.58/10.40	   A^2 -> H(k, U1(d, k))
28.58/10.40	   A^2 -> H(c, b)
28.58/10.40	   A^2 -> H(c, U1(e, d))
28.58/10.40	   A^2 -> H(c, U1(d, e))
28.58/10.40	   A^2 -> H(c, c)
28.58/10.40	   A^2 -> H(c, U1(e, k))
28.58/10.40	   A^2 -> H(c, U1(k, e))
28.58/10.40	   A^2 -> H(c, e)
28.58/10.40	   A^2 -> H(c, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, k), b)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, k), c)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, k), e)
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, c), d)
28.58/10.40	   A^2 -> H(U1(e, c), k)
28.58/10.40	   A^2 -> H(U1(k, e), b)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, e), c)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(k, c), d)
28.58/10.40	   A^2 -> H(U1(c, e), d)
28.58/10.40	   A^2 -> H(U1(c, e), k)
28.58/10.40	   A^2 -> H(U1(c, k), d)
28.58/10.40	   A^2 -> H(U1(c, k), k)
28.58/10.40	   A^2 -> H(e, b)
28.58/10.40	   A^2 -> H(e, U1(e, d))
28.58/10.40	   A^2 -> H(e, U1(d, e))
28.58/10.40	   A^2 -> H(e, c)
28.58/10.40	   A^2 -> H(e, U1(e, k))
28.58/10.40	   A^2 -> H(e, e)
28.58/10.40	   A^2 -> H(U1(e, e), d)
28.58/10.40	   A^2 -> H(U1(e, e), k)
28.58/10.40	   A^2 -> H(U1(k, k), d)
28.58/10.40	   A^2 -> H(U1(k, k), b)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, k), c)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, d), d)
28.58/10.40	   A^2 -> H(U1(d, k), d)
28.58/10.40	   A^2 -> H(U1(d, k), k)
28.58/10.40	   A^2 -> H(U1(e, e), c)
28.58/10.40	   A^2 -> H(U1(e, c), e)
28.58/10.40	   A^2 -> H(U1(c, e), e)
28.58/10.40	   A^2 -> H(U1(c, k), e)
28.58/10.40	   A^2 -> H(c, U1(e, e))
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.40	   A^2 -> H(d, b)
28.58/10.40	   A^2 -> H(d, U1(e, d))
28.58/10.40	   A^2 -> H(d, U1(d, e))
28.58/10.40	   A^2 -> H(d, c)
28.58/10.40	   A^2 -> H(d, U1(e, k))
28.58/10.40	   A^2 -> H(d, U1(k, e))
28.58/10.40	   A^2 -> H(d, e)
28.58/10.40	   A^2 -> H(d, U1(k, k))
28.58/10.40	   A^2 -> H(a, d)
28.58/10.40	   A^2 -> H(a, k)
28.58/10.40	
28.58/10.40	The TRS R consists of the following rules:
28.58/10.40	
28.58/10.40	   f(x) -> U1(x, x)
28.58/10.40	   U1(e, x) -> x
28.58/10.40	   a -> c
28.58/10.40	   a -> d
28.58/10.40	   b -> c
28.58/10.40	   b -> d
28.58/10.40	   d -> k
28.58/10.40	   c -> e
28.58/10.40	   c -> k
28.58/10.40	
28.58/10.40	Q is empty.
28.58/10.40	We have to consider all minimal (P,Q,R)-chains.
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2451) TransformationProof (EQUIVALENT)
28.58/10.40	By narrowing [LPAR04] the rule A^2 -> H(a, U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.40	
28.58/10.40	   (A^2 -> H(c, U1(k, e)),A^2 -> H(c, U1(k, e)))
28.58/10.40	   (A^2 -> H(d, U1(k, e)),A^2 -> H(d, U1(k, e)))
28.58/10.40	
28.58/10.40	
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2452)
28.58/10.40	Obligation:
28.58/10.40	Q DP problem:
28.58/10.40	The TRS P consists of the following rules:
28.58/10.40	
28.58/10.40	   H(x, x) -> G(x, x, f(k))
28.58/10.40	   G(d, x, x) -> A^2
28.58/10.40	   A^2 -> H(f(c), f(c))
28.58/10.40	   A^2 -> H(f(d), f(d))
28.58/10.40	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.40	   A^2 -> H(f(e), f(e))
28.58/10.40	   A^2 -> H(f(k), f(k))
28.58/10.40	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.40	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.40	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.40	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.40	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.40	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.40	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.40	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.40	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.40	   A^2 -> H(a, e)
28.58/10.40	   A^2 -> H(a, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, d), b)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, d), c)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, d), e)
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, a), d)
28.58/10.40	   A^2 -> H(U1(e, a), k)
28.58/10.40	   A^2 -> H(U1(k, a), d)
28.58/10.40	   A^2 -> H(U1(c, d), d)
28.58/10.40	   A^2 -> H(U1(c, d), k)
28.58/10.40	   A^2 -> H(U1(d, e), b)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(d, e), c)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(d, e), e)
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.40	   A^2 -> H(U1(d, c), d)
28.58/10.40	   A^2 -> H(U1(d, c), k)
28.58/10.40	   A^2 -> H(U1(a, e), d)
28.58/10.40	   A^2 -> H(U1(a, e), k)
28.58/10.40	   A^2 -> H(U1(a, k), d)
28.58/10.40	   A^2 -> H(U1(a, k), k)
28.58/10.40	   A^2 -> H(k, U1(e, b))
28.58/10.40	   A^2 -> H(k, U1(c, d))
28.58/10.40	   A^2 -> H(k, U1(d, c))
28.58/10.40	   A^2 -> H(k, U1(b, e))
28.58/10.40	   A^2 -> H(k, U1(b, k))
28.58/10.40	   A^2 -> H(k, U1(e, c))
28.58/10.40	   A^2 -> H(k, U1(c, e))
28.58/10.40	   A^2 -> H(k, U1(c, k))
28.58/10.40	   A^2 -> H(k, U1(e, e))
28.58/10.40	   A^2 -> H(k, U1(d, k))
28.58/10.40	   A^2 -> H(c, b)
28.58/10.40	   A^2 -> H(c, U1(e, d))
28.58/10.40	   A^2 -> H(c, U1(d, e))
28.58/10.40	   A^2 -> H(c, c)
28.58/10.40	   A^2 -> H(c, U1(e, k))
28.58/10.40	   A^2 -> H(c, U1(k, e))
28.58/10.40	   A^2 -> H(c, e)
28.58/10.40	   A^2 -> H(c, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, k), b)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, k), c)
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, k), e)
28.58/10.40	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, c), d)
28.58/10.40	   A^2 -> H(U1(e, c), k)
28.58/10.40	   A^2 -> H(U1(k, e), b)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, e), c)
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(k, c), d)
28.58/10.40	   A^2 -> H(U1(c, e), d)
28.58/10.40	   A^2 -> H(U1(c, e), k)
28.58/10.40	   A^2 -> H(U1(c, k), d)
28.58/10.40	   A^2 -> H(U1(c, k), k)
28.58/10.40	   A^2 -> H(e, b)
28.58/10.40	   A^2 -> H(e, U1(e, d))
28.58/10.40	   A^2 -> H(e, U1(d, e))
28.58/10.40	   A^2 -> H(e, c)
28.58/10.40	   A^2 -> H(e, U1(e, k))
28.58/10.40	   A^2 -> H(e, e)
28.58/10.40	   A^2 -> H(U1(e, e), d)
28.58/10.40	   A^2 -> H(U1(e, e), k)
28.58/10.40	   A^2 -> H(U1(k, k), d)
28.58/10.40	   A^2 -> H(U1(k, k), b)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.40	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.40	   A^2 -> H(U1(k, k), c)
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.40	   A^2 -> H(U1(k, d), d)
28.58/10.40	   A^2 -> H(U1(d, k), d)
28.58/10.40	   A^2 -> H(U1(d, k), k)
28.58/10.40	   A^2 -> H(U1(e, e), c)
28.58/10.40	   A^2 -> H(U1(e, c), e)
28.58/10.40	   A^2 -> H(U1(c, e), e)
28.58/10.40	   A^2 -> H(U1(c, k), e)
28.58/10.40	   A^2 -> H(c, U1(e, e))
28.58/10.40	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.40	   A^2 -> H(d, b)
28.58/10.40	   A^2 -> H(d, U1(e, d))
28.58/10.40	   A^2 -> H(d, U1(d, e))
28.58/10.40	   A^2 -> H(d, c)
28.58/10.40	   A^2 -> H(d, U1(e, k))
28.58/10.40	   A^2 -> H(d, U1(k, e))
28.58/10.40	   A^2 -> H(d, e)
28.58/10.40	   A^2 -> H(d, U1(k, k))
28.58/10.40	   A^2 -> H(a, d)
28.58/10.40	   A^2 -> H(a, k)
28.58/10.40	
28.58/10.40	The TRS R consists of the following rules:
28.58/10.40	
28.58/10.40	   f(x) -> U1(x, x)
28.58/10.40	   U1(e, x) -> x
28.58/10.40	   a -> c
28.58/10.40	   a -> d
28.58/10.40	   b -> c
28.58/10.40	   b -> d
28.58/10.40	   d -> k
28.58/10.40	   c -> e
28.58/10.40	   c -> k
28.58/10.40	
28.58/10.40	Q is empty.
28.58/10.40	We have to consider all minimal (P,Q,R)-chains.
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2453) TransformationProof (EQUIVALENT)
28.58/10.40	By narrowing [LPAR04] the rule A^2 -> H(a, e) at position [] we obtained the following new rules [LPAR04]:
28.58/10.40	
28.58/10.40	   (A^2 -> H(c, e),A^2 -> H(c, e))
28.58/10.40	   (A^2 -> H(d, e),A^2 -> H(d, e))
28.58/10.40	
28.58/10.40	
28.58/10.40	----------------------------------------
28.58/10.40	
28.58/10.40	(2454)
28.58/10.40	Obligation:
28.58/10.40	Q DP problem:
28.58/10.40	The TRS P consists of the following rules:
28.58/10.40	
28.58/10.40	   H(x, x) -> G(x, x, f(k))
28.58/10.40	   G(d, x, x) -> A^2
28.58/10.40	   A^2 -> H(f(c), f(c))
28.58/10.40	   A^2 -> H(f(d), f(d))
28.58/10.40	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.40	   A^2 -> H(f(e), f(e))
28.58/10.40	   A^2 -> H(f(k), f(k))
28.58/10.40	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.40	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.40	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.40	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.40	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.40	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.40	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.40	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.40	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.40	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.40	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.40	   A^2 -> H(a, U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, d), b)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.40	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.40	   A^2 -> H(U1(e, d), c)
28.58/10.40	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.40	   A^2 -> H(U1(e, d), e)
28.58/10.40	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.40	   A^2 -> H(U1(e, a), d)
28.58/10.40	   A^2 -> H(U1(e, a), k)
28.58/10.40	   A^2 -> H(U1(k, a), d)
28.58/10.40	   A^2 -> H(U1(c, d), d)
28.58/10.40	   A^2 -> H(U1(c, d), k)
28.58/10.40	   A^2 -> H(U1(d, e), b)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.40	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.40	   A^2 -> H(U1(d, e), c)
28.58/10.40	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.40	   A^2 -> H(U1(d, e), e)
28.58/10.40	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.40	   A^2 -> H(U1(d, c), d)
28.58/10.41	   A^2 -> H(U1(d, c), k)
28.58/10.41	   A^2 -> H(U1(a, e), d)
28.58/10.41	   A^2 -> H(U1(a, e), k)
28.58/10.41	   A^2 -> H(U1(a, k), d)
28.58/10.41	   A^2 -> H(U1(a, k), k)
28.58/10.41	   A^2 -> H(k, U1(e, b))
28.58/10.41	   A^2 -> H(k, U1(c, d))
28.58/10.41	   A^2 -> H(k, U1(d, c))
28.58/10.41	   A^2 -> H(k, U1(b, e))
28.58/10.41	   A^2 -> H(k, U1(b, k))
28.58/10.41	   A^2 -> H(k, U1(e, c))
28.58/10.41	   A^2 -> H(k, U1(c, e))
28.58/10.41	   A^2 -> H(k, U1(c, k))
28.58/10.41	   A^2 -> H(k, U1(e, e))
28.58/10.41	   A^2 -> H(k, U1(d, k))
28.58/10.41	   A^2 -> H(c, b)
28.58/10.41	   A^2 -> H(c, U1(e, d))
28.58/10.41	   A^2 -> H(c, U1(d, e))
28.58/10.41	   A^2 -> H(c, c)
28.58/10.41	   A^2 -> H(c, U1(e, k))
28.58/10.41	   A^2 -> H(c, U1(k, e))
28.58/10.41	   A^2 -> H(c, e)
28.58/10.41	   A^2 -> H(c, U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, k), b)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(e, k), c)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, k), e)
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, c), d)
28.58/10.41	   A^2 -> H(U1(e, c), k)
28.58/10.41	   A^2 -> H(U1(k, e), b)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, e), c)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(k, c), d)
28.58/10.41	   A^2 -> H(U1(c, e), d)
28.58/10.41	   A^2 -> H(U1(c, e), k)
28.58/10.41	   A^2 -> H(U1(c, k), d)
28.58/10.41	   A^2 -> H(U1(c, k), k)
28.58/10.41	   A^2 -> H(e, b)
28.58/10.41	   A^2 -> H(e, U1(e, d))
28.58/10.41	   A^2 -> H(e, U1(d, e))
28.58/10.41	   A^2 -> H(e, c)
28.58/10.41	   A^2 -> H(e, U1(e, k))
28.58/10.41	   A^2 -> H(e, e)
28.58/10.41	   A^2 -> H(U1(e, e), d)
28.58/10.41	   A^2 -> H(U1(e, e), k)
28.58/10.41	   A^2 -> H(U1(k, k), d)
28.58/10.41	   A^2 -> H(U1(k, k), b)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, k), c)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, d), d)
28.58/10.41	   A^2 -> H(U1(d, k), d)
28.58/10.41	   A^2 -> H(U1(d, k), k)
28.58/10.41	   A^2 -> H(U1(e, e), c)
28.58/10.41	   A^2 -> H(U1(e, c), e)
28.58/10.41	   A^2 -> H(U1(c, e), e)
28.58/10.41	   A^2 -> H(U1(c, k), e)
28.58/10.41	   A^2 -> H(c, U1(e, e))
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.41	   A^2 -> H(d, b)
28.58/10.41	   A^2 -> H(d, U1(e, d))
28.58/10.41	   A^2 -> H(d, U1(d, e))
28.58/10.41	   A^2 -> H(d, c)
28.58/10.41	   A^2 -> H(d, U1(e, k))
28.58/10.41	   A^2 -> H(d, U1(k, e))
28.58/10.41	   A^2 -> H(d, e)
28.58/10.41	   A^2 -> H(d, U1(k, k))
28.58/10.41	   A^2 -> H(a, d)
28.58/10.41	   A^2 -> H(a, k)
28.58/10.41	
28.58/10.41	The TRS R consists of the following rules:
28.58/10.41	
28.58/10.41	   f(x) -> U1(x, x)
28.58/10.41	   U1(e, x) -> x
28.58/10.41	   a -> c
28.58/10.41	   a -> d
28.58/10.41	   b -> c
28.58/10.41	   b -> d
28.58/10.41	   d -> k
28.58/10.41	   c -> e
28.58/10.41	   c -> k
28.58/10.41	
28.58/10.41	Q is empty.
28.58/10.41	We have to consider all minimal (P,Q,R)-chains.
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2455) TransformationProof (EQUIVALENT)
28.58/10.41	By narrowing [LPAR04] the rule A^2 -> H(a, U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.41	
28.58/10.41	   (A^2 -> H(c, U1(k, k)),A^2 -> H(c, U1(k, k)))
28.58/10.41	   (A^2 -> H(d, U1(k, k)),A^2 -> H(d, U1(k, k)))
28.58/10.41	
28.58/10.41	
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2456)
28.58/10.41	Obligation:
28.58/10.41	Q DP problem:
28.58/10.41	The TRS P consists of the following rules:
28.58/10.41	
28.58/10.41	   H(x, x) -> G(x, x, f(k))
28.58/10.41	   G(d, x, x) -> A^2
28.58/10.41	   A^2 -> H(f(c), f(c))
28.58/10.41	   A^2 -> H(f(d), f(d))
28.58/10.41	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.41	   A^2 -> H(f(e), f(e))
28.58/10.41	   A^2 -> H(f(k), f(k))
28.58/10.41	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.41	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.41	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.41	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.41	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.41	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.41	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.41	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.41	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.41	   A^2 -> H(U1(e, d), b)
28.58/10.41	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.41	   A^2 -> H(U1(e, d), c)
28.58/10.41	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, d), e)
28.58/10.41	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, a), d)
28.58/10.41	   A^2 -> H(U1(e, a), k)
28.58/10.41	   A^2 -> H(U1(k, a), d)
28.58/10.41	   A^2 -> H(U1(c, d), d)
28.58/10.41	   A^2 -> H(U1(c, d), k)
28.58/10.41	   A^2 -> H(U1(d, e), b)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(d, e), c)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(d, e), e)
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.41	   A^2 -> H(U1(d, c), d)
28.58/10.41	   A^2 -> H(U1(d, c), k)
28.58/10.41	   A^2 -> H(U1(a, e), d)
28.58/10.41	   A^2 -> H(U1(a, e), k)
28.58/10.41	   A^2 -> H(U1(a, k), d)
28.58/10.41	   A^2 -> H(U1(a, k), k)
28.58/10.41	   A^2 -> H(k, U1(e, b))
28.58/10.41	   A^2 -> H(k, U1(c, d))
28.58/10.41	   A^2 -> H(k, U1(d, c))
28.58/10.41	   A^2 -> H(k, U1(b, e))
28.58/10.41	   A^2 -> H(k, U1(b, k))
28.58/10.41	   A^2 -> H(k, U1(e, c))
28.58/10.41	   A^2 -> H(k, U1(c, e))
28.58/10.41	   A^2 -> H(k, U1(c, k))
28.58/10.41	   A^2 -> H(k, U1(e, e))
28.58/10.41	   A^2 -> H(k, U1(d, k))
28.58/10.41	   A^2 -> H(c, b)
28.58/10.41	   A^2 -> H(c, U1(e, d))
28.58/10.41	   A^2 -> H(c, U1(d, e))
28.58/10.41	   A^2 -> H(c, c)
28.58/10.41	   A^2 -> H(c, U1(e, k))
28.58/10.41	   A^2 -> H(c, U1(k, e))
28.58/10.41	   A^2 -> H(c, e)
28.58/10.41	   A^2 -> H(c, U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, k), b)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(e, k), c)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, k), e)
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, c), d)
28.58/10.41	   A^2 -> H(U1(e, c), k)
28.58/10.41	   A^2 -> H(U1(k, e), b)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, e), c)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(k, c), d)
28.58/10.41	   A^2 -> H(U1(c, e), d)
28.58/10.41	   A^2 -> H(U1(c, e), k)
28.58/10.41	   A^2 -> H(U1(c, k), d)
28.58/10.41	   A^2 -> H(U1(c, k), k)
28.58/10.41	   A^2 -> H(e, b)
28.58/10.41	   A^2 -> H(e, U1(e, d))
28.58/10.41	   A^2 -> H(e, U1(d, e))
28.58/10.41	   A^2 -> H(e, c)
28.58/10.41	   A^2 -> H(e, U1(e, k))
28.58/10.41	   A^2 -> H(e, e)
28.58/10.41	   A^2 -> H(U1(e, e), d)
28.58/10.41	   A^2 -> H(U1(e, e), k)
28.58/10.41	   A^2 -> H(U1(k, k), d)
28.58/10.41	   A^2 -> H(U1(k, k), b)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, k), c)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, d), d)
28.58/10.41	   A^2 -> H(U1(d, k), d)
28.58/10.41	   A^2 -> H(U1(d, k), k)
28.58/10.41	   A^2 -> H(U1(e, e), c)
28.58/10.41	   A^2 -> H(U1(e, c), e)
28.58/10.41	   A^2 -> H(U1(c, e), e)
28.58/10.41	   A^2 -> H(U1(c, k), e)
28.58/10.41	   A^2 -> H(c, U1(e, e))
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.41	   A^2 -> H(d, b)
28.58/10.41	   A^2 -> H(d, U1(e, d))
28.58/10.41	   A^2 -> H(d, U1(d, e))
28.58/10.41	   A^2 -> H(d, c)
28.58/10.41	   A^2 -> H(d, U1(e, k))
28.58/10.41	   A^2 -> H(d, U1(k, e))
28.58/10.41	   A^2 -> H(d, e)
28.58/10.41	   A^2 -> H(d, U1(k, k))
28.58/10.41	   A^2 -> H(a, d)
28.58/10.41	   A^2 -> H(a, k)
28.58/10.41	
28.58/10.41	The TRS R consists of the following rules:
28.58/10.41	
28.58/10.41	   f(x) -> U1(x, x)
28.58/10.41	   U1(e, x) -> x
28.58/10.41	   a -> c
28.58/10.41	   a -> d
28.58/10.41	   b -> c
28.58/10.41	   b -> d
28.58/10.41	   d -> k
28.58/10.41	   c -> e
28.58/10.41	   c -> k
28.58/10.41	
28.58/10.41	Q is empty.
28.58/10.41	We have to consider all minimal (P,Q,R)-chains.
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2457) TransformationProof (EQUIVALENT)
28.58/10.41	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), b) at position [] we obtained the following new rules [LPAR04]:
28.58/10.41	
28.58/10.41	   (A^2 -> H(d, b),A^2 -> H(d, b))
28.58/10.41	   (A^2 -> H(U1(e, k), b),A^2 -> H(U1(e, k), b))
28.58/10.41	   (A^2 -> H(U1(e, d), c),A^2 -> H(U1(e, d), c))
28.58/10.41	   (A^2 -> H(U1(e, d), d),A^2 -> H(U1(e, d), d))
28.58/10.41	
28.58/10.41	
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2458)
28.58/10.41	Obligation:
28.58/10.41	Q DP problem:
28.58/10.41	The TRS P consists of the following rules:
28.58/10.41	
28.58/10.41	   H(x, x) -> G(x, x, f(k))
28.58/10.41	   G(d, x, x) -> A^2
28.58/10.41	   A^2 -> H(f(c), f(c))
28.58/10.41	   A^2 -> H(f(d), f(d))
28.58/10.41	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.41	   A^2 -> H(f(e), f(e))
28.58/10.41	   A^2 -> H(f(k), f(k))
28.58/10.41	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.41	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.41	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.41	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.41	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.41	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.41	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.41	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.41	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.41	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, d), U1(d, e))
28.58/10.41	   A^2 -> H(U1(e, d), c)
28.58/10.41	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, d), e)
28.58/10.41	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, a), d)
28.58/10.41	   A^2 -> H(U1(e, a), k)
28.58/10.41	   A^2 -> H(U1(k, a), d)
28.58/10.41	   A^2 -> H(U1(c, d), d)
28.58/10.41	   A^2 -> H(U1(c, d), k)
28.58/10.41	   A^2 -> H(U1(d, e), b)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(d, e), c)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(d, e), e)
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.41	   A^2 -> H(U1(d, c), d)
28.58/10.41	   A^2 -> H(U1(d, c), k)
28.58/10.41	   A^2 -> H(U1(a, e), d)
28.58/10.41	   A^2 -> H(U1(a, e), k)
28.58/10.41	   A^2 -> H(U1(a, k), d)
28.58/10.41	   A^2 -> H(U1(a, k), k)
28.58/10.41	   A^2 -> H(k, U1(e, b))
28.58/10.41	   A^2 -> H(k, U1(c, d))
28.58/10.41	   A^2 -> H(k, U1(d, c))
28.58/10.41	   A^2 -> H(k, U1(b, e))
28.58/10.41	   A^2 -> H(k, U1(b, k))
28.58/10.41	   A^2 -> H(k, U1(e, c))
28.58/10.41	   A^2 -> H(k, U1(c, e))
28.58/10.41	   A^2 -> H(k, U1(c, k))
28.58/10.41	   A^2 -> H(k, U1(e, e))
28.58/10.41	   A^2 -> H(k, U1(d, k))
28.58/10.41	   A^2 -> H(c, b)
28.58/10.41	   A^2 -> H(c, U1(e, d))
28.58/10.41	   A^2 -> H(c, U1(d, e))
28.58/10.41	   A^2 -> H(c, c)
28.58/10.41	   A^2 -> H(c, U1(e, k))
28.58/10.41	   A^2 -> H(c, U1(k, e))
28.58/10.41	   A^2 -> H(c, e)
28.58/10.41	   A^2 -> H(c, U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, k), b)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(e, k), c)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, k), e)
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, c), d)
28.58/10.41	   A^2 -> H(U1(e, c), k)
28.58/10.41	   A^2 -> H(U1(k, e), b)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, e), c)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(k, c), d)
28.58/10.41	   A^2 -> H(U1(c, e), d)
28.58/10.41	   A^2 -> H(U1(c, e), k)
28.58/10.41	   A^2 -> H(U1(c, k), d)
28.58/10.41	   A^2 -> H(U1(c, k), k)
28.58/10.41	   A^2 -> H(e, b)
28.58/10.41	   A^2 -> H(e, U1(e, d))
28.58/10.41	   A^2 -> H(e, U1(d, e))
28.58/10.41	   A^2 -> H(e, c)
28.58/10.41	   A^2 -> H(e, U1(e, k))
28.58/10.41	   A^2 -> H(e, e)
28.58/10.41	   A^2 -> H(U1(e, e), d)
28.58/10.41	   A^2 -> H(U1(e, e), k)
28.58/10.41	   A^2 -> H(U1(k, k), d)
28.58/10.41	   A^2 -> H(U1(k, k), b)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, k), c)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, d), d)
28.58/10.41	   A^2 -> H(U1(d, k), d)
28.58/10.41	   A^2 -> H(U1(d, k), k)
28.58/10.41	   A^2 -> H(U1(e, e), c)
28.58/10.41	   A^2 -> H(U1(e, c), e)
28.58/10.41	   A^2 -> H(U1(c, e), e)
28.58/10.41	   A^2 -> H(U1(c, k), e)
28.58/10.41	   A^2 -> H(c, U1(e, e))
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.41	   A^2 -> H(d, b)
28.58/10.41	   A^2 -> H(d, U1(e, d))
28.58/10.41	   A^2 -> H(d, U1(d, e))
28.58/10.41	   A^2 -> H(d, c)
28.58/10.41	   A^2 -> H(d, U1(e, k))
28.58/10.41	   A^2 -> H(d, U1(k, e))
28.58/10.41	   A^2 -> H(d, e)
28.58/10.41	   A^2 -> H(d, U1(k, k))
28.58/10.41	   A^2 -> H(a, d)
28.58/10.41	   A^2 -> H(a, k)
28.58/10.41	   A^2 -> H(U1(e, d), d)
28.58/10.41	
28.58/10.41	The TRS R consists of the following rules:
28.58/10.41	
28.58/10.41	   f(x) -> U1(x, x)
28.58/10.41	   U1(e, x) -> x
28.58/10.41	   a -> c
28.58/10.41	   a -> d
28.58/10.41	   b -> c
28.58/10.41	   b -> d
28.58/10.41	   d -> k
28.58/10.41	   c -> e
28.58/10.41	   c -> k
28.58/10.41	
28.58/10.41	Q is empty.
28.58/10.41	We have to consider all minimal (P,Q,R)-chains.
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2459) TransformationProof (EQUIVALENT)
28.58/10.41	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.41	
28.58/10.41	   (A^2 -> H(d, U1(d, e)),A^2 -> H(d, U1(d, e)))
28.58/10.41	   (A^2 -> H(U1(e, k), U1(d, e)),A^2 -> H(U1(e, k), U1(d, e)))
28.58/10.41	   (A^2 -> H(U1(e, d), U1(k, e)),A^2 -> H(U1(e, d), U1(k, e)))
28.58/10.41	
28.58/10.41	
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2460)
28.58/10.41	Obligation:
28.58/10.41	Q DP problem:
28.58/10.41	The TRS P consists of the following rules:
28.58/10.41	
28.58/10.41	   H(x, x) -> G(x, x, f(k))
28.58/10.41	   G(d, x, x) -> A^2
28.58/10.41	   A^2 -> H(f(c), f(c))
28.58/10.41	   A^2 -> H(f(d), f(d))
28.58/10.41	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.41	   A^2 -> H(f(e), f(e))
28.58/10.41	   A^2 -> H(f(k), f(k))
28.58/10.41	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.41	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.41	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.41	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.41	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.41	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.41	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.41	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.41	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.41	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, d), c)
28.58/10.41	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, d), e)
28.58/10.41	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, a), d)
28.58/10.41	   A^2 -> H(U1(e, a), k)
28.58/10.41	   A^2 -> H(U1(k, a), d)
28.58/10.41	   A^2 -> H(U1(c, d), d)
28.58/10.41	   A^2 -> H(U1(c, d), k)
28.58/10.41	   A^2 -> H(U1(d, e), b)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(d, e), c)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(d, e), e)
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.41	   A^2 -> H(U1(d, c), d)
28.58/10.41	   A^2 -> H(U1(d, c), k)
28.58/10.41	   A^2 -> H(U1(a, e), d)
28.58/10.41	   A^2 -> H(U1(a, e), k)
28.58/10.41	   A^2 -> H(U1(a, k), d)
28.58/10.41	   A^2 -> H(U1(a, k), k)
28.58/10.41	   A^2 -> H(k, U1(e, b))
28.58/10.41	   A^2 -> H(k, U1(c, d))
28.58/10.41	   A^2 -> H(k, U1(d, c))
28.58/10.41	   A^2 -> H(k, U1(b, e))
28.58/10.41	   A^2 -> H(k, U1(b, k))
28.58/10.41	   A^2 -> H(k, U1(e, c))
28.58/10.41	   A^2 -> H(k, U1(c, e))
28.58/10.41	   A^2 -> H(k, U1(c, k))
28.58/10.41	   A^2 -> H(k, U1(e, e))
28.58/10.41	   A^2 -> H(k, U1(d, k))
28.58/10.41	   A^2 -> H(c, b)
28.58/10.41	   A^2 -> H(c, U1(e, d))
28.58/10.41	   A^2 -> H(c, U1(d, e))
28.58/10.41	   A^2 -> H(c, c)
28.58/10.41	   A^2 -> H(c, U1(e, k))
28.58/10.41	   A^2 -> H(c, U1(k, e))
28.58/10.41	   A^2 -> H(c, e)
28.58/10.41	   A^2 -> H(c, U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, k), b)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(e, k), c)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, k), e)
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, c), d)
28.58/10.41	   A^2 -> H(U1(e, c), k)
28.58/10.41	   A^2 -> H(U1(k, e), b)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, e), c)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(k, c), d)
28.58/10.41	   A^2 -> H(U1(c, e), d)
28.58/10.41	   A^2 -> H(U1(c, e), k)
28.58/10.41	   A^2 -> H(U1(c, k), d)
28.58/10.41	   A^2 -> H(U1(c, k), k)
28.58/10.41	   A^2 -> H(e, b)
28.58/10.41	   A^2 -> H(e, U1(e, d))
28.58/10.41	   A^2 -> H(e, U1(d, e))
28.58/10.41	   A^2 -> H(e, c)
28.58/10.41	   A^2 -> H(e, U1(e, k))
28.58/10.41	   A^2 -> H(e, e)
28.58/10.41	   A^2 -> H(U1(e, e), d)
28.58/10.41	   A^2 -> H(U1(e, e), k)
28.58/10.41	   A^2 -> H(U1(k, k), d)
28.58/10.41	   A^2 -> H(U1(k, k), b)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, k), c)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, d), d)
28.58/10.41	   A^2 -> H(U1(d, k), d)
28.58/10.41	   A^2 -> H(U1(d, k), k)
28.58/10.41	   A^2 -> H(U1(e, e), c)
28.58/10.41	   A^2 -> H(U1(e, c), e)
28.58/10.41	   A^2 -> H(U1(c, e), e)
28.58/10.41	   A^2 -> H(U1(c, k), e)
28.58/10.41	   A^2 -> H(c, U1(e, e))
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.41	   A^2 -> H(d, b)
28.58/10.41	   A^2 -> H(d, U1(e, d))
28.58/10.41	   A^2 -> H(d, U1(d, e))
28.58/10.41	   A^2 -> H(d, c)
28.58/10.41	   A^2 -> H(d, U1(e, k))
28.58/10.41	   A^2 -> H(d, U1(k, e))
28.58/10.41	   A^2 -> H(d, e)
28.58/10.41	   A^2 -> H(d, U1(k, k))
28.58/10.41	   A^2 -> H(a, d)
28.58/10.41	   A^2 -> H(a, k)
28.58/10.41	   A^2 -> H(U1(e, d), d)
28.58/10.41	
28.58/10.41	The TRS R consists of the following rules:
28.58/10.41	
28.58/10.41	   f(x) -> U1(x, x)
28.58/10.41	   U1(e, x) -> x
28.58/10.41	   a -> c
28.58/10.41	   a -> d
28.58/10.41	   b -> c
28.58/10.41	   b -> d
28.58/10.41	   d -> k
28.58/10.41	   c -> e
28.58/10.41	   c -> k
28.58/10.41	
28.58/10.41	Q is empty.
28.58/10.41	We have to consider all minimal (P,Q,R)-chains.
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2461) TransformationProof (EQUIVALENT)
28.58/10.41	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), c) at position [] we obtained the following new rules [LPAR04]:
28.58/10.41	
28.58/10.41	   (A^2 -> H(d, c),A^2 -> H(d, c))
28.58/10.41	   (A^2 -> H(U1(e, k), c),A^2 -> H(U1(e, k), c))
28.58/10.41	   (A^2 -> H(U1(e, d), e),A^2 -> H(U1(e, d), e))
28.58/10.41	   (A^2 -> H(U1(e, d), k),A^2 -> H(U1(e, d), k))
28.58/10.41	
28.58/10.41	
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2462)
28.58/10.41	Obligation:
28.58/10.41	Q DP problem:
28.58/10.41	The TRS P consists of the following rules:
28.58/10.41	
28.58/10.41	   H(x, x) -> G(x, x, f(k))
28.58/10.41	   G(d, x, x) -> A^2
28.58/10.41	   A^2 -> H(f(c), f(c))
28.58/10.41	   A^2 -> H(f(d), f(d))
28.58/10.41	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.41	   A^2 -> H(f(e), f(e))
28.58/10.41	   A^2 -> H(f(k), f(k))
28.58/10.41	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.41	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.41	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.41	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.41	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.41	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.41	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.41	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.41	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.41	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, d), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, d), e)
28.58/10.41	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, a), d)
28.58/10.41	   A^2 -> H(U1(e, a), k)
28.58/10.41	   A^2 -> H(U1(k, a), d)
28.58/10.41	   A^2 -> H(U1(c, d), d)
28.58/10.41	   A^2 -> H(U1(c, d), k)
28.58/10.41	   A^2 -> H(U1(d, e), b)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(d, e), c)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(d, e), e)
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.41	   A^2 -> H(U1(d, c), d)
28.58/10.41	   A^2 -> H(U1(d, c), k)
28.58/10.41	   A^2 -> H(U1(a, e), d)
28.58/10.41	   A^2 -> H(U1(a, e), k)
28.58/10.41	   A^2 -> H(U1(a, k), d)
28.58/10.41	   A^2 -> H(U1(a, k), k)
28.58/10.41	   A^2 -> H(k, U1(e, b))
28.58/10.41	   A^2 -> H(k, U1(c, d))
28.58/10.41	   A^2 -> H(k, U1(d, c))
28.58/10.41	   A^2 -> H(k, U1(b, e))
28.58/10.41	   A^2 -> H(k, U1(b, k))
28.58/10.41	   A^2 -> H(k, U1(e, c))
28.58/10.41	   A^2 -> H(k, U1(c, e))
28.58/10.41	   A^2 -> H(k, U1(c, k))
28.58/10.41	   A^2 -> H(k, U1(e, e))
28.58/10.41	   A^2 -> H(k, U1(d, k))
28.58/10.41	   A^2 -> H(c, b)
28.58/10.41	   A^2 -> H(c, U1(e, d))
28.58/10.41	   A^2 -> H(c, U1(d, e))
28.58/10.41	   A^2 -> H(c, c)
28.58/10.41	   A^2 -> H(c, U1(e, k))
28.58/10.41	   A^2 -> H(c, U1(k, e))
28.58/10.41	   A^2 -> H(c, e)
28.58/10.41	   A^2 -> H(c, U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, k), b)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(e, k), c)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, k), e)
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, c), d)
28.58/10.41	   A^2 -> H(U1(e, c), k)
28.58/10.41	   A^2 -> H(U1(k, e), b)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, e), c)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(k, c), d)
28.58/10.41	   A^2 -> H(U1(c, e), d)
28.58/10.41	   A^2 -> H(U1(c, e), k)
28.58/10.41	   A^2 -> H(U1(c, k), d)
28.58/10.41	   A^2 -> H(U1(c, k), k)
28.58/10.41	   A^2 -> H(e, b)
28.58/10.41	   A^2 -> H(e, U1(e, d))
28.58/10.41	   A^2 -> H(e, U1(d, e))
28.58/10.41	   A^2 -> H(e, c)
28.58/10.41	   A^2 -> H(e, U1(e, k))
28.58/10.41	   A^2 -> H(e, e)
28.58/10.41	   A^2 -> H(U1(e, e), d)
28.58/10.41	   A^2 -> H(U1(e, e), k)
28.58/10.41	   A^2 -> H(U1(k, k), d)
28.58/10.41	   A^2 -> H(U1(k, k), b)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, k), c)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, d), d)
28.58/10.41	   A^2 -> H(U1(d, k), d)
28.58/10.41	   A^2 -> H(U1(d, k), k)
28.58/10.41	   A^2 -> H(U1(e, e), c)
28.58/10.41	   A^2 -> H(U1(e, c), e)
28.58/10.41	   A^2 -> H(U1(c, e), e)
28.58/10.41	   A^2 -> H(U1(c, k), e)
28.58/10.41	   A^2 -> H(c, U1(e, e))
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.41	   A^2 -> H(d, b)
28.58/10.41	   A^2 -> H(d, U1(e, d))
28.58/10.41	   A^2 -> H(d, U1(d, e))
28.58/10.41	   A^2 -> H(d, c)
28.58/10.41	   A^2 -> H(d, U1(e, k))
28.58/10.41	   A^2 -> H(d, U1(k, e))
28.58/10.41	   A^2 -> H(d, e)
28.58/10.41	   A^2 -> H(d, U1(k, k))
28.58/10.41	   A^2 -> H(a, d)
28.58/10.41	   A^2 -> H(a, k)
28.58/10.41	   A^2 -> H(U1(e, d), d)
28.58/10.41	   A^2 -> H(U1(e, d), k)
28.58/10.41	
28.58/10.41	The TRS R consists of the following rules:
28.58/10.41	
28.58/10.41	   f(x) -> U1(x, x)
28.58/10.41	   U1(e, x) -> x
28.58/10.41	   a -> c
28.58/10.41	   a -> d
28.58/10.41	   b -> c
28.58/10.41	   b -> d
28.58/10.41	   d -> k
28.58/10.41	   c -> e
28.58/10.41	   c -> k
28.58/10.41	
28.58/10.41	Q is empty.
28.58/10.41	We have to consider all minimal (P,Q,R)-chains.
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2463) TransformationProof (EQUIVALENT)
28.58/10.41	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.41	
28.58/10.41	   (A^2 -> H(d, U1(e, k)),A^2 -> H(d, U1(e, k)))
28.58/10.41	   (A^2 -> H(U1(e, k), U1(e, k)),A^2 -> H(U1(e, k), U1(e, k)))
28.58/10.41	   (A^2 -> H(U1(e, d), k),A^2 -> H(U1(e, d), k))
28.58/10.41	
28.58/10.41	
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2464)
28.58/10.41	Obligation:
28.58/10.41	Q DP problem:
28.58/10.41	The TRS P consists of the following rules:
28.58/10.41	
28.58/10.41	   H(x, x) -> G(x, x, f(k))
28.58/10.41	   G(d, x, x) -> A^2
28.58/10.41	   A^2 -> H(f(c), f(c))
28.58/10.41	   A^2 -> H(f(d), f(d))
28.58/10.41	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.41	   A^2 -> H(f(e), f(e))
28.58/10.41	   A^2 -> H(f(k), f(k))
28.58/10.41	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.41	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.41	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.41	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.41	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.41	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.41	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.41	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.41	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.41	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, d), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, d), e)
28.58/10.41	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, a), d)
28.58/10.41	   A^2 -> H(U1(e, a), k)
28.58/10.41	   A^2 -> H(U1(k, a), d)
28.58/10.41	   A^2 -> H(U1(c, d), d)
28.58/10.41	   A^2 -> H(U1(c, d), k)
28.58/10.41	   A^2 -> H(U1(d, e), b)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(d, e), c)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(d, e), e)
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.41	   A^2 -> H(U1(d, c), d)
28.58/10.41	   A^2 -> H(U1(d, c), k)
28.58/10.41	   A^2 -> H(U1(a, e), d)
28.58/10.41	   A^2 -> H(U1(a, e), k)
28.58/10.41	   A^2 -> H(U1(a, k), d)
28.58/10.41	   A^2 -> H(U1(a, k), k)
28.58/10.41	   A^2 -> H(k, U1(e, b))
28.58/10.41	   A^2 -> H(k, U1(c, d))
28.58/10.41	   A^2 -> H(k, U1(d, c))
28.58/10.41	   A^2 -> H(k, U1(b, e))
28.58/10.41	   A^2 -> H(k, U1(b, k))
28.58/10.41	   A^2 -> H(k, U1(e, c))
28.58/10.41	   A^2 -> H(k, U1(c, e))
28.58/10.41	   A^2 -> H(k, U1(c, k))
28.58/10.41	   A^2 -> H(k, U1(e, e))
28.58/10.41	   A^2 -> H(k, U1(d, k))
28.58/10.41	   A^2 -> H(c, b)
28.58/10.41	   A^2 -> H(c, U1(e, d))
28.58/10.41	   A^2 -> H(c, U1(d, e))
28.58/10.41	   A^2 -> H(c, c)
28.58/10.41	   A^2 -> H(c, U1(e, k))
28.58/10.41	   A^2 -> H(c, U1(k, e))
28.58/10.41	   A^2 -> H(c, e)
28.58/10.41	   A^2 -> H(c, U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, k), b)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(e, k), c)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, k), e)
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, c), d)
28.58/10.41	   A^2 -> H(U1(e, c), k)
28.58/10.41	   A^2 -> H(U1(k, e), b)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, e), c)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(k, c), d)
28.58/10.41	   A^2 -> H(U1(c, e), d)
28.58/10.41	   A^2 -> H(U1(c, e), k)
28.58/10.41	   A^2 -> H(U1(c, k), d)
28.58/10.41	   A^2 -> H(U1(c, k), k)
28.58/10.41	   A^2 -> H(e, b)
28.58/10.41	   A^2 -> H(e, U1(e, d))
28.58/10.41	   A^2 -> H(e, U1(d, e))
28.58/10.41	   A^2 -> H(e, c)
28.58/10.41	   A^2 -> H(e, U1(e, k))
28.58/10.41	   A^2 -> H(e, e)
28.58/10.41	   A^2 -> H(U1(e, e), d)
28.58/10.41	   A^2 -> H(U1(e, e), k)
28.58/10.41	   A^2 -> H(U1(k, k), d)
28.58/10.41	   A^2 -> H(U1(k, k), b)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, k), c)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, d), d)
28.58/10.41	   A^2 -> H(U1(d, k), d)
28.58/10.41	   A^2 -> H(U1(d, k), k)
28.58/10.41	   A^2 -> H(U1(e, e), c)
28.58/10.41	   A^2 -> H(U1(e, c), e)
28.58/10.41	   A^2 -> H(U1(c, e), e)
28.58/10.41	   A^2 -> H(U1(c, k), e)
28.58/10.41	   A^2 -> H(c, U1(e, e))
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.41	   A^2 -> H(d, b)
28.58/10.41	   A^2 -> H(d, U1(e, d))
28.58/10.41	   A^2 -> H(d, U1(d, e))
28.58/10.41	   A^2 -> H(d, c)
28.58/10.41	   A^2 -> H(d, U1(e, k))
28.58/10.41	   A^2 -> H(d, U1(k, e))
28.58/10.41	   A^2 -> H(d, e)
28.58/10.41	   A^2 -> H(d, U1(k, k))
28.58/10.41	   A^2 -> H(a, d)
28.58/10.41	   A^2 -> H(a, k)
28.58/10.41	   A^2 -> H(U1(e, d), d)
28.58/10.41	   A^2 -> H(U1(e, d), k)
28.58/10.41	
28.58/10.41	The TRS R consists of the following rules:
28.58/10.41	
28.58/10.41	   f(x) -> U1(x, x)
28.58/10.41	   U1(e, x) -> x
28.58/10.41	   a -> c
28.58/10.41	   a -> d
28.58/10.41	   b -> c
28.58/10.41	   b -> d
28.58/10.41	   d -> k
28.58/10.41	   c -> e
28.58/10.41	   c -> k
28.58/10.41	
28.58/10.41	Q is empty.
28.58/10.41	We have to consider all minimal (P,Q,R)-chains.
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2465) TransformationProof (EQUIVALENT)
28.58/10.41	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.41	
28.58/10.41	   (A^2 -> H(d, U1(k, e)),A^2 -> H(d, U1(k, e)))
28.58/10.41	   (A^2 -> H(U1(e, k), U1(k, e)),A^2 -> H(U1(e, k), U1(k, e)))
28.58/10.41	
28.58/10.41	
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2466)
28.58/10.41	Obligation:
28.58/10.41	Q DP problem:
28.58/10.41	The TRS P consists of the following rules:
28.58/10.41	
28.58/10.41	   H(x, x) -> G(x, x, f(k))
28.58/10.41	   G(d, x, x) -> A^2
28.58/10.41	   A^2 -> H(f(c), f(c))
28.58/10.41	   A^2 -> H(f(d), f(d))
28.58/10.41	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.41	   A^2 -> H(f(e), f(e))
28.58/10.41	   A^2 -> H(f(k), f(k))
28.58/10.41	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.41	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.41	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.41	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.41	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.41	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.41	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.41	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.41	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.41	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, d), e)
28.58/10.41	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, a), d)
28.58/10.41	   A^2 -> H(U1(e, a), k)
28.58/10.41	   A^2 -> H(U1(k, a), d)
28.58/10.41	   A^2 -> H(U1(c, d), d)
28.58/10.41	   A^2 -> H(U1(c, d), k)
28.58/10.41	   A^2 -> H(U1(d, e), b)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(d, e), c)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(d, e), e)
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.41	   A^2 -> H(U1(d, c), d)
28.58/10.41	   A^2 -> H(U1(d, c), k)
28.58/10.41	   A^2 -> H(U1(a, e), d)
28.58/10.41	   A^2 -> H(U1(a, e), k)
28.58/10.41	   A^2 -> H(U1(a, k), d)
28.58/10.41	   A^2 -> H(U1(a, k), k)
28.58/10.41	   A^2 -> H(k, U1(e, b))
28.58/10.41	   A^2 -> H(k, U1(c, d))
28.58/10.41	   A^2 -> H(k, U1(d, c))
28.58/10.41	   A^2 -> H(k, U1(b, e))
28.58/10.41	   A^2 -> H(k, U1(b, k))
28.58/10.41	   A^2 -> H(k, U1(e, c))
28.58/10.41	   A^2 -> H(k, U1(c, e))
28.58/10.41	   A^2 -> H(k, U1(c, k))
28.58/10.41	   A^2 -> H(k, U1(e, e))
28.58/10.41	   A^2 -> H(k, U1(d, k))
28.58/10.41	   A^2 -> H(c, b)
28.58/10.41	   A^2 -> H(c, U1(e, d))
28.58/10.41	   A^2 -> H(c, U1(d, e))
28.58/10.41	   A^2 -> H(c, c)
28.58/10.41	   A^2 -> H(c, U1(e, k))
28.58/10.41	   A^2 -> H(c, U1(k, e))
28.58/10.41	   A^2 -> H(c, e)
28.58/10.41	   A^2 -> H(c, U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, k), b)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(e, k), c)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, k), e)
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, c), d)
28.58/10.41	   A^2 -> H(U1(e, c), k)
28.58/10.41	   A^2 -> H(U1(k, e), b)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, e), c)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(k, c), d)
28.58/10.41	   A^2 -> H(U1(c, e), d)
28.58/10.41	   A^2 -> H(U1(c, e), k)
28.58/10.41	   A^2 -> H(U1(c, k), d)
28.58/10.41	   A^2 -> H(U1(c, k), k)
28.58/10.41	   A^2 -> H(e, b)
28.58/10.41	   A^2 -> H(e, U1(e, d))
28.58/10.41	   A^2 -> H(e, U1(d, e))
28.58/10.41	   A^2 -> H(e, c)
28.58/10.41	   A^2 -> H(e, U1(e, k))
28.58/10.41	   A^2 -> H(e, e)
28.58/10.41	   A^2 -> H(U1(e, e), d)
28.58/10.41	   A^2 -> H(U1(e, e), k)
28.58/10.41	   A^2 -> H(U1(k, k), d)
28.58/10.41	   A^2 -> H(U1(k, k), b)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, k), c)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, d), d)
28.58/10.41	   A^2 -> H(U1(d, k), d)
28.58/10.41	   A^2 -> H(U1(d, k), k)
28.58/10.41	   A^2 -> H(U1(e, e), c)
28.58/10.41	   A^2 -> H(U1(e, c), e)
28.58/10.41	   A^2 -> H(U1(c, e), e)
28.58/10.41	   A^2 -> H(U1(c, k), e)
28.58/10.41	   A^2 -> H(c, U1(e, e))
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.41	   A^2 -> H(d, b)
28.58/10.41	   A^2 -> H(d, U1(e, d))
28.58/10.41	   A^2 -> H(d, U1(d, e))
28.58/10.41	   A^2 -> H(d, c)
28.58/10.41	   A^2 -> H(d, U1(e, k))
28.58/10.41	   A^2 -> H(d, U1(k, e))
28.58/10.41	   A^2 -> H(d, e)
28.58/10.41	   A^2 -> H(d, U1(k, k))
28.58/10.41	   A^2 -> H(a, d)
28.58/10.41	   A^2 -> H(a, k)
28.58/10.41	   A^2 -> H(U1(e, d), d)
28.58/10.41	   A^2 -> H(U1(e, d), k)
28.58/10.41	
28.58/10.41	The TRS R consists of the following rules:
28.58/10.41	
28.58/10.41	   f(x) -> U1(x, x)
28.58/10.41	   U1(e, x) -> x
28.58/10.41	   a -> c
28.58/10.41	   a -> d
28.58/10.41	   b -> c
28.58/10.41	   b -> d
28.58/10.41	   d -> k
28.58/10.41	   c -> e
28.58/10.41	   c -> k
28.58/10.41	
28.58/10.41	Q is empty.
28.58/10.41	We have to consider all minimal (P,Q,R)-chains.
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2467) TransformationProof (EQUIVALENT)
28.58/10.41	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), e) at position [] we obtained the following new rules [LPAR04]:
28.58/10.41	
28.58/10.41	   (A^2 -> H(d, e),A^2 -> H(d, e))
28.58/10.41	   (A^2 -> H(U1(e, k), e),A^2 -> H(U1(e, k), e))
28.58/10.41	
28.58/10.41	
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2468)
28.58/10.41	Obligation:
28.58/10.41	Q DP problem:
28.58/10.41	The TRS P consists of the following rules:
28.58/10.41	
28.58/10.41	   H(x, x) -> G(x, x, f(k))
28.58/10.41	   G(d, x, x) -> A^2
28.58/10.41	   A^2 -> H(f(c), f(c))
28.58/10.41	   A^2 -> H(f(d), f(d))
28.58/10.41	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.41	   A^2 -> H(f(e), f(e))
28.58/10.41	   A^2 -> H(f(k), f(k))
28.58/10.41	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.41	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.41	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.41	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.41	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.41	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.41	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.41	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.41	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.41	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, d), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, a), d)
28.58/10.41	   A^2 -> H(U1(e, a), k)
28.58/10.41	   A^2 -> H(U1(k, a), d)
28.58/10.41	   A^2 -> H(U1(c, d), d)
28.58/10.41	   A^2 -> H(U1(c, d), k)
28.58/10.41	   A^2 -> H(U1(d, e), b)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(d, e), c)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(d, e), e)
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.41	   A^2 -> H(U1(d, c), d)
28.58/10.41	   A^2 -> H(U1(d, c), k)
28.58/10.41	   A^2 -> H(U1(a, e), d)
28.58/10.41	   A^2 -> H(U1(a, e), k)
28.58/10.41	   A^2 -> H(U1(a, k), d)
28.58/10.41	   A^2 -> H(U1(a, k), k)
28.58/10.41	   A^2 -> H(k, U1(e, b))
28.58/10.41	   A^2 -> H(k, U1(c, d))
28.58/10.41	   A^2 -> H(k, U1(d, c))
28.58/10.41	   A^2 -> H(k, U1(b, e))
28.58/10.41	   A^2 -> H(k, U1(b, k))
28.58/10.41	   A^2 -> H(k, U1(e, c))
28.58/10.41	   A^2 -> H(k, U1(c, e))
28.58/10.41	   A^2 -> H(k, U1(c, k))
28.58/10.41	   A^2 -> H(k, U1(e, e))
28.58/10.41	   A^2 -> H(k, U1(d, k))
28.58/10.41	   A^2 -> H(c, b)
28.58/10.41	   A^2 -> H(c, U1(e, d))
28.58/10.41	   A^2 -> H(c, U1(d, e))
28.58/10.41	   A^2 -> H(c, c)
28.58/10.41	   A^2 -> H(c, U1(e, k))
28.58/10.41	   A^2 -> H(c, U1(k, e))
28.58/10.41	   A^2 -> H(c, e)
28.58/10.41	   A^2 -> H(c, U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, k), b)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(e, k), c)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, k), e)
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, c), d)
28.58/10.41	   A^2 -> H(U1(e, c), k)
28.58/10.41	   A^2 -> H(U1(k, e), b)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, e), c)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(k, c), d)
28.58/10.41	   A^2 -> H(U1(c, e), d)
28.58/10.41	   A^2 -> H(U1(c, e), k)
28.58/10.41	   A^2 -> H(U1(c, k), d)
28.58/10.41	   A^2 -> H(U1(c, k), k)
28.58/10.41	   A^2 -> H(e, b)
28.58/10.41	   A^2 -> H(e, U1(e, d))
28.58/10.41	   A^2 -> H(e, U1(d, e))
28.58/10.41	   A^2 -> H(e, c)
28.58/10.41	   A^2 -> H(e, U1(e, k))
28.58/10.41	   A^2 -> H(e, e)
28.58/10.41	   A^2 -> H(U1(e, e), d)
28.58/10.41	   A^2 -> H(U1(e, e), k)
28.58/10.41	   A^2 -> H(U1(k, k), d)
28.58/10.41	   A^2 -> H(U1(k, k), b)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, k), c)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, d), d)
28.58/10.41	   A^2 -> H(U1(d, k), d)
28.58/10.41	   A^2 -> H(U1(d, k), k)
28.58/10.41	   A^2 -> H(U1(e, e), c)
28.58/10.41	   A^2 -> H(U1(e, c), e)
28.58/10.41	   A^2 -> H(U1(c, e), e)
28.58/10.41	   A^2 -> H(U1(c, k), e)
28.58/10.41	   A^2 -> H(c, U1(e, e))
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.41	   A^2 -> H(d, b)
28.58/10.41	   A^2 -> H(d, U1(e, d))
28.58/10.41	   A^2 -> H(d, U1(d, e))
28.58/10.41	   A^2 -> H(d, c)
28.58/10.41	   A^2 -> H(d, U1(e, k))
28.58/10.41	   A^2 -> H(d, U1(k, e))
28.58/10.41	   A^2 -> H(d, e)
28.58/10.41	   A^2 -> H(d, U1(k, k))
28.58/10.41	   A^2 -> H(a, d)
28.58/10.41	   A^2 -> H(a, k)
28.58/10.41	   A^2 -> H(U1(e, d), d)
28.58/10.41	   A^2 -> H(U1(e, d), k)
28.58/10.41	
28.58/10.41	The TRS R consists of the following rules:
28.58/10.41	
28.58/10.41	   f(x) -> U1(x, x)
28.58/10.41	   U1(e, x) -> x
28.58/10.41	   a -> c
28.58/10.41	   a -> d
28.58/10.41	   b -> c
28.58/10.41	   b -> d
28.58/10.41	   d -> k
28.58/10.41	   c -> e
28.58/10.41	   c -> k
28.58/10.41	
28.58/10.41	Q is empty.
28.58/10.41	We have to consider all minimal (P,Q,R)-chains.
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2469) TransformationProof (EQUIVALENT)
28.58/10.41	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.41	
28.58/10.41	   (A^2 -> H(d, U1(k, k)),A^2 -> H(d, U1(k, k)))
28.58/10.41	   (A^2 -> H(U1(e, k), U1(k, k)),A^2 -> H(U1(e, k), U1(k, k)))
28.58/10.41	
28.58/10.41	
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2470)
28.58/10.41	Obligation:
28.58/10.41	Q DP problem:
28.58/10.41	The TRS P consists of the following rules:
28.58/10.41	
28.58/10.41	   H(x, x) -> G(x, x, f(k))
28.58/10.41	   G(d, x, x) -> A^2
28.58/10.41	   A^2 -> H(f(c), f(c))
28.58/10.41	   A^2 -> H(f(d), f(d))
28.58/10.41	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.41	   A^2 -> H(f(e), f(e))
28.58/10.41	   A^2 -> H(f(k), f(k))
28.58/10.41	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.41	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.41	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.41	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.41	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.41	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.41	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.41	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.41	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.41	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, a), d)
28.58/10.41	   A^2 -> H(U1(e, a), k)
28.58/10.41	   A^2 -> H(U1(k, a), d)
28.58/10.41	   A^2 -> H(U1(c, d), d)
28.58/10.41	   A^2 -> H(U1(c, d), k)
28.58/10.41	   A^2 -> H(U1(d, e), b)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(d, e), c)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(d, e), e)
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.41	   A^2 -> H(U1(d, c), d)
28.58/10.41	   A^2 -> H(U1(d, c), k)
28.58/10.41	   A^2 -> H(U1(a, e), d)
28.58/10.41	   A^2 -> H(U1(a, e), k)
28.58/10.41	   A^2 -> H(U1(a, k), d)
28.58/10.41	   A^2 -> H(U1(a, k), k)
28.58/10.41	   A^2 -> H(k, U1(e, b))
28.58/10.41	   A^2 -> H(k, U1(c, d))
28.58/10.41	   A^2 -> H(k, U1(d, c))
28.58/10.41	   A^2 -> H(k, U1(b, e))
28.58/10.41	   A^2 -> H(k, U1(b, k))
28.58/10.41	   A^2 -> H(k, U1(e, c))
28.58/10.41	   A^2 -> H(k, U1(c, e))
28.58/10.41	   A^2 -> H(k, U1(c, k))
28.58/10.41	   A^2 -> H(k, U1(e, e))
28.58/10.41	   A^2 -> H(k, U1(d, k))
28.58/10.41	   A^2 -> H(c, b)
28.58/10.41	   A^2 -> H(c, U1(e, d))
28.58/10.41	   A^2 -> H(c, U1(d, e))
28.58/10.41	   A^2 -> H(c, c)
28.58/10.41	   A^2 -> H(c, U1(e, k))
28.58/10.41	   A^2 -> H(c, U1(k, e))
28.58/10.41	   A^2 -> H(c, e)
28.58/10.41	   A^2 -> H(c, U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, k), b)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(e, k), c)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, k), e)
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, c), d)
28.58/10.41	   A^2 -> H(U1(e, c), k)
28.58/10.41	   A^2 -> H(U1(k, e), b)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, e), c)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(k, c), d)
28.58/10.41	   A^2 -> H(U1(c, e), d)
28.58/10.41	   A^2 -> H(U1(c, e), k)
28.58/10.41	   A^2 -> H(U1(c, k), d)
28.58/10.41	   A^2 -> H(U1(c, k), k)
28.58/10.41	   A^2 -> H(e, b)
28.58/10.41	   A^2 -> H(e, U1(e, d))
28.58/10.41	   A^2 -> H(e, U1(d, e))
28.58/10.41	   A^2 -> H(e, c)
28.58/10.41	   A^2 -> H(e, U1(e, k))
28.58/10.41	   A^2 -> H(e, e)
28.58/10.41	   A^2 -> H(U1(e, e), d)
28.58/10.41	   A^2 -> H(U1(e, e), k)
28.58/10.41	   A^2 -> H(U1(k, k), d)
28.58/10.41	   A^2 -> H(U1(k, k), b)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, k), c)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, d), d)
28.58/10.41	   A^2 -> H(U1(d, k), d)
28.58/10.41	   A^2 -> H(U1(d, k), k)
28.58/10.41	   A^2 -> H(U1(e, e), c)
28.58/10.41	   A^2 -> H(U1(e, c), e)
28.58/10.41	   A^2 -> H(U1(c, e), e)
28.58/10.41	   A^2 -> H(U1(c, k), e)
28.58/10.41	   A^2 -> H(c, U1(e, e))
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.41	   A^2 -> H(d, b)
28.58/10.41	   A^2 -> H(d, U1(e, d))
28.58/10.41	   A^2 -> H(d, U1(d, e))
28.58/10.41	   A^2 -> H(d, c)
28.58/10.41	   A^2 -> H(d, U1(e, k))
28.58/10.41	   A^2 -> H(d, U1(k, e))
28.58/10.41	   A^2 -> H(d, e)
28.58/10.41	   A^2 -> H(d, U1(k, k))
28.58/10.41	   A^2 -> H(a, d)
28.58/10.41	   A^2 -> H(a, k)
28.58/10.41	   A^2 -> H(U1(e, d), d)
28.58/10.41	   A^2 -> H(U1(e, d), k)
28.58/10.41	
28.58/10.41	The TRS R consists of the following rules:
28.58/10.41	
28.58/10.41	   f(x) -> U1(x, x)
28.58/10.41	   U1(e, x) -> x
28.58/10.41	   a -> c
28.58/10.41	   a -> d
28.58/10.41	   b -> c
28.58/10.41	   b -> d
28.58/10.41	   d -> k
28.58/10.41	   c -> e
28.58/10.41	   c -> k
28.58/10.41	
28.58/10.41	Q is empty.
28.58/10.41	We have to consider all minimal (P,Q,R)-chains.
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2471) TransformationProof (EQUIVALENT)
28.58/10.41	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.41	
28.58/10.41	   (A^2 -> H(a, d),A^2 -> H(a, d))
28.58/10.41	   (A^2 -> H(U1(e, c), d),A^2 -> H(U1(e, c), d))
28.58/10.41	   (A^2 -> H(U1(e, d), d),A^2 -> H(U1(e, d), d))
28.58/10.41	   (A^2 -> H(U1(e, a), k),A^2 -> H(U1(e, a), k))
28.58/10.41	
28.58/10.41	
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2472)
28.58/10.41	Obligation:
28.58/10.41	Q DP problem:
28.58/10.41	The TRS P consists of the following rules:
28.58/10.41	
28.58/10.41	   H(x, x) -> G(x, x, f(k))
28.58/10.41	   G(d, x, x) -> A^2
28.58/10.41	   A^2 -> H(f(c), f(c))
28.58/10.41	   A^2 -> H(f(d), f(d))
28.58/10.41	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.41	   A^2 -> H(f(e), f(e))
28.58/10.41	   A^2 -> H(f(k), f(k))
28.58/10.41	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.41	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.41	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.41	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.41	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.41	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.41	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.41	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.41	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.41	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, a), k)
28.58/10.41	   A^2 -> H(U1(k, a), d)
28.58/10.41	   A^2 -> H(U1(c, d), d)
28.58/10.41	   A^2 -> H(U1(c, d), k)
28.58/10.41	   A^2 -> H(U1(d, e), b)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(d, e), c)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(d, e), e)
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.41	   A^2 -> H(U1(d, c), d)
28.58/10.41	   A^2 -> H(U1(d, c), k)
28.58/10.41	   A^2 -> H(U1(a, e), d)
28.58/10.41	   A^2 -> H(U1(a, e), k)
28.58/10.41	   A^2 -> H(U1(a, k), d)
28.58/10.41	   A^2 -> H(U1(a, k), k)
28.58/10.41	   A^2 -> H(k, U1(e, b))
28.58/10.41	   A^2 -> H(k, U1(c, d))
28.58/10.41	   A^2 -> H(k, U1(d, c))
28.58/10.41	   A^2 -> H(k, U1(b, e))
28.58/10.41	   A^2 -> H(k, U1(b, k))
28.58/10.41	   A^2 -> H(k, U1(e, c))
28.58/10.41	   A^2 -> H(k, U1(c, e))
28.58/10.41	   A^2 -> H(k, U1(c, k))
28.58/10.41	   A^2 -> H(k, U1(e, e))
28.58/10.41	   A^2 -> H(k, U1(d, k))
28.58/10.41	   A^2 -> H(c, b)
28.58/10.41	   A^2 -> H(c, U1(e, d))
28.58/10.41	   A^2 -> H(c, U1(d, e))
28.58/10.41	   A^2 -> H(c, c)
28.58/10.41	   A^2 -> H(c, U1(e, k))
28.58/10.41	   A^2 -> H(c, U1(k, e))
28.58/10.41	   A^2 -> H(c, e)
28.58/10.41	   A^2 -> H(c, U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, k), b)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(e, k), c)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, k), e)
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, c), d)
28.58/10.41	   A^2 -> H(U1(e, c), k)
28.58/10.41	   A^2 -> H(U1(k, e), b)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, e), c)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(k, c), d)
28.58/10.41	   A^2 -> H(U1(c, e), d)
28.58/10.41	   A^2 -> H(U1(c, e), k)
28.58/10.41	   A^2 -> H(U1(c, k), d)
28.58/10.41	   A^2 -> H(U1(c, k), k)
28.58/10.41	   A^2 -> H(e, b)
28.58/10.41	   A^2 -> H(e, U1(e, d))
28.58/10.41	   A^2 -> H(e, U1(d, e))
28.58/10.41	   A^2 -> H(e, c)
28.58/10.41	   A^2 -> H(e, U1(e, k))
28.58/10.41	   A^2 -> H(e, e)
28.58/10.41	   A^2 -> H(U1(e, e), d)
28.58/10.41	   A^2 -> H(U1(e, e), k)
28.58/10.41	   A^2 -> H(U1(k, k), d)
28.58/10.41	   A^2 -> H(U1(k, k), b)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, k), c)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, d), d)
28.58/10.41	   A^2 -> H(U1(d, k), d)
28.58/10.41	   A^2 -> H(U1(d, k), k)
28.58/10.41	   A^2 -> H(U1(e, e), c)
28.58/10.41	   A^2 -> H(U1(e, c), e)
28.58/10.41	   A^2 -> H(U1(c, e), e)
28.58/10.41	   A^2 -> H(U1(c, k), e)
28.58/10.41	   A^2 -> H(c, U1(e, e))
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.41	   A^2 -> H(d, b)
28.58/10.41	   A^2 -> H(d, U1(e, d))
28.58/10.41	   A^2 -> H(d, U1(d, e))
28.58/10.41	   A^2 -> H(d, c)
28.58/10.41	   A^2 -> H(d, U1(e, k))
28.58/10.41	   A^2 -> H(d, U1(k, e))
28.58/10.41	   A^2 -> H(d, e)
28.58/10.41	   A^2 -> H(d, U1(k, k))
28.58/10.41	   A^2 -> H(a, d)
28.58/10.41	   A^2 -> H(a, k)
28.58/10.41	   A^2 -> H(U1(e, d), d)
28.58/10.41	   A^2 -> H(U1(e, d), k)
28.58/10.41	
28.58/10.41	The TRS R consists of the following rules:
28.58/10.41	
28.58/10.41	   f(x) -> U1(x, x)
28.58/10.41	   U1(e, x) -> x
28.58/10.41	   a -> c
28.58/10.41	   a -> d
28.58/10.41	   b -> c
28.58/10.41	   b -> d
28.58/10.41	   d -> k
28.58/10.41	   c -> e
28.58/10.41	   c -> k
28.58/10.41	
28.58/10.41	Q is empty.
28.58/10.41	We have to consider all minimal (P,Q,R)-chains.
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2473) TransformationProof (EQUIVALENT)
28.58/10.41	By narrowing [LPAR04] the rule A^2 -> H(U1(e, a), k) at position [] we obtained the following new rules [LPAR04]:
28.58/10.41	
28.58/10.41	   (A^2 -> H(a, k),A^2 -> H(a, k))
28.58/10.41	   (A^2 -> H(U1(e, c), k),A^2 -> H(U1(e, c), k))
28.58/10.41	   (A^2 -> H(U1(e, d), k),A^2 -> H(U1(e, d), k))
28.58/10.41	
28.58/10.41	
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2474)
28.58/10.41	Obligation:
28.58/10.41	Q DP problem:
28.58/10.41	The TRS P consists of the following rules:
28.58/10.41	
28.58/10.41	   H(x, x) -> G(x, x, f(k))
28.58/10.41	   G(d, x, x) -> A^2
28.58/10.41	   A^2 -> H(f(c), f(c))
28.58/10.41	   A^2 -> H(f(d), f(d))
28.58/10.41	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.41	   A^2 -> H(f(e), f(e))
28.58/10.41	   A^2 -> H(f(k), f(k))
28.58/10.41	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.41	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.41	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.41	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.41	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.41	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.41	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.41	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.41	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.41	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, a), d)
28.58/10.41	   A^2 -> H(U1(c, d), d)
28.58/10.41	   A^2 -> H(U1(c, d), k)
28.58/10.41	   A^2 -> H(U1(d, e), b)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(d, e), c)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(d, e), e)
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.41	   A^2 -> H(U1(d, c), d)
28.58/10.41	   A^2 -> H(U1(d, c), k)
28.58/10.41	   A^2 -> H(U1(a, e), d)
28.58/10.41	   A^2 -> H(U1(a, e), k)
28.58/10.41	   A^2 -> H(U1(a, k), d)
28.58/10.41	   A^2 -> H(U1(a, k), k)
28.58/10.41	   A^2 -> H(k, U1(e, b))
28.58/10.41	   A^2 -> H(k, U1(c, d))
28.58/10.41	   A^2 -> H(k, U1(d, c))
28.58/10.41	   A^2 -> H(k, U1(b, e))
28.58/10.41	   A^2 -> H(k, U1(b, k))
28.58/10.41	   A^2 -> H(k, U1(e, c))
28.58/10.41	   A^2 -> H(k, U1(c, e))
28.58/10.41	   A^2 -> H(k, U1(c, k))
28.58/10.41	   A^2 -> H(k, U1(e, e))
28.58/10.41	   A^2 -> H(k, U1(d, k))
28.58/10.41	   A^2 -> H(c, b)
28.58/10.41	   A^2 -> H(c, U1(e, d))
28.58/10.41	   A^2 -> H(c, U1(d, e))
28.58/10.41	   A^2 -> H(c, c)
28.58/10.41	   A^2 -> H(c, U1(e, k))
28.58/10.41	   A^2 -> H(c, U1(k, e))
28.58/10.41	   A^2 -> H(c, e)
28.58/10.41	   A^2 -> H(c, U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, k), b)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(e, k), c)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, k), e)
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, c), d)
28.58/10.41	   A^2 -> H(U1(e, c), k)
28.58/10.41	   A^2 -> H(U1(k, e), b)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, e), c)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(k, c), d)
28.58/10.41	   A^2 -> H(U1(c, e), d)
28.58/10.41	   A^2 -> H(U1(c, e), k)
28.58/10.41	   A^2 -> H(U1(c, k), d)
28.58/10.41	   A^2 -> H(U1(c, k), k)
28.58/10.41	   A^2 -> H(e, b)
28.58/10.41	   A^2 -> H(e, U1(e, d))
28.58/10.41	   A^2 -> H(e, U1(d, e))
28.58/10.41	   A^2 -> H(e, c)
28.58/10.41	   A^2 -> H(e, U1(e, k))
28.58/10.41	   A^2 -> H(e, e)
28.58/10.41	   A^2 -> H(U1(e, e), d)
28.58/10.41	   A^2 -> H(U1(e, e), k)
28.58/10.41	   A^2 -> H(U1(k, k), d)
28.58/10.41	   A^2 -> H(U1(k, k), b)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, k), c)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, d), d)
28.58/10.41	   A^2 -> H(U1(d, k), d)
28.58/10.41	   A^2 -> H(U1(d, k), k)
28.58/10.41	   A^2 -> H(U1(e, e), c)
28.58/10.41	   A^2 -> H(U1(e, c), e)
28.58/10.41	   A^2 -> H(U1(c, e), e)
28.58/10.41	   A^2 -> H(U1(c, k), e)
28.58/10.41	   A^2 -> H(c, U1(e, e))
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.41	   A^2 -> H(d, b)
28.58/10.41	   A^2 -> H(d, U1(e, d))
28.58/10.41	   A^2 -> H(d, U1(d, e))
28.58/10.41	   A^2 -> H(d, c)
28.58/10.41	   A^2 -> H(d, U1(e, k))
28.58/10.41	   A^2 -> H(d, U1(k, e))
28.58/10.41	   A^2 -> H(d, e)
28.58/10.41	   A^2 -> H(d, U1(k, k))
28.58/10.41	   A^2 -> H(a, d)
28.58/10.41	   A^2 -> H(a, k)
28.58/10.41	   A^2 -> H(U1(e, d), d)
28.58/10.41	   A^2 -> H(U1(e, d), k)
28.58/10.41	
28.58/10.41	The TRS R consists of the following rules:
28.58/10.41	
28.58/10.41	   f(x) -> U1(x, x)
28.58/10.41	   U1(e, x) -> x
28.58/10.41	   a -> c
28.58/10.41	   a -> d
28.58/10.41	   b -> c
28.58/10.41	   b -> d
28.58/10.41	   d -> k
28.58/10.41	   c -> e
28.58/10.41	   c -> k
28.58/10.41	
28.58/10.41	Q is empty.
28.58/10.41	We have to consider all minimal (P,Q,R)-chains.
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2475) TransformationProof (EQUIVALENT)
28.58/10.41	By narrowing [LPAR04] the rule A^2 -> H(U1(k, a), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.41	
28.58/10.41	   (A^2 -> H(U1(k, c), d),A^2 -> H(U1(k, c), d))
28.58/10.41	   (A^2 -> H(U1(k, d), d),A^2 -> H(U1(k, d), d))
28.58/10.41	   (A^2 -> H(U1(k, a), k),A^2 -> H(U1(k, a), k))
28.58/10.41	
28.58/10.41	
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2476)
28.58/10.41	Obligation:
28.58/10.41	Q DP problem:
28.58/10.41	The TRS P consists of the following rules:
28.58/10.41	
28.58/10.41	   H(x, x) -> G(x, x, f(k))
28.58/10.41	   G(d, x, x) -> A^2
28.58/10.41	   A^2 -> H(f(c), f(c))
28.58/10.41	   A^2 -> H(f(d), f(d))
28.58/10.41	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.41	   A^2 -> H(f(e), f(e))
28.58/10.41	   A^2 -> H(f(k), f(k))
28.58/10.41	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.41	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.41	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.41	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.41	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.41	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.41	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.41	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.41	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.41	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.41	   A^2 -> H(U1(c, d), d)
28.58/10.41	   A^2 -> H(U1(c, d), k)
28.58/10.41	   A^2 -> H(U1(d, e), b)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(d, e), c)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(d, e), e)
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.41	   A^2 -> H(U1(d, c), d)
28.58/10.41	   A^2 -> H(U1(d, c), k)
28.58/10.41	   A^2 -> H(U1(a, e), d)
28.58/10.41	   A^2 -> H(U1(a, e), k)
28.58/10.41	   A^2 -> H(U1(a, k), d)
28.58/10.41	   A^2 -> H(U1(a, k), k)
28.58/10.41	   A^2 -> H(k, U1(e, b))
28.58/10.41	   A^2 -> H(k, U1(c, d))
28.58/10.41	   A^2 -> H(k, U1(d, c))
28.58/10.41	   A^2 -> H(k, U1(b, e))
28.58/10.41	   A^2 -> H(k, U1(b, k))
28.58/10.41	   A^2 -> H(k, U1(e, c))
28.58/10.41	   A^2 -> H(k, U1(c, e))
28.58/10.41	   A^2 -> H(k, U1(c, k))
28.58/10.41	   A^2 -> H(k, U1(e, e))
28.58/10.41	   A^2 -> H(k, U1(d, k))
28.58/10.41	   A^2 -> H(c, b)
28.58/10.41	   A^2 -> H(c, U1(e, d))
28.58/10.41	   A^2 -> H(c, U1(d, e))
28.58/10.41	   A^2 -> H(c, c)
28.58/10.41	   A^2 -> H(c, U1(e, k))
28.58/10.41	   A^2 -> H(c, U1(k, e))
28.58/10.41	   A^2 -> H(c, e)
28.58/10.41	   A^2 -> H(c, U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, k), b)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(e, k), c)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, k), e)
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, c), d)
28.58/10.41	   A^2 -> H(U1(e, c), k)
28.58/10.41	   A^2 -> H(U1(k, e), b)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, e), c)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(k, c), d)
28.58/10.41	   A^2 -> H(U1(c, e), d)
28.58/10.41	   A^2 -> H(U1(c, e), k)
28.58/10.41	   A^2 -> H(U1(c, k), d)
28.58/10.41	   A^2 -> H(U1(c, k), k)
28.58/10.41	   A^2 -> H(e, b)
28.58/10.41	   A^2 -> H(e, U1(e, d))
28.58/10.41	   A^2 -> H(e, U1(d, e))
28.58/10.41	   A^2 -> H(e, c)
28.58/10.41	   A^2 -> H(e, U1(e, k))
28.58/10.41	   A^2 -> H(e, e)
28.58/10.41	   A^2 -> H(U1(e, e), d)
28.58/10.41	   A^2 -> H(U1(e, e), k)
28.58/10.41	   A^2 -> H(U1(k, k), d)
28.58/10.41	   A^2 -> H(U1(k, k), b)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, k), c)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, d), d)
28.58/10.41	   A^2 -> H(U1(d, k), d)
28.58/10.41	   A^2 -> H(U1(d, k), k)
28.58/10.41	   A^2 -> H(U1(e, e), c)
28.58/10.41	   A^2 -> H(U1(e, c), e)
28.58/10.41	   A^2 -> H(U1(c, e), e)
28.58/10.41	   A^2 -> H(U1(c, k), e)
28.58/10.41	   A^2 -> H(c, U1(e, e))
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.41	   A^2 -> H(d, b)
28.58/10.41	   A^2 -> H(d, U1(e, d))
28.58/10.41	   A^2 -> H(d, U1(d, e))
28.58/10.41	   A^2 -> H(d, c)
28.58/10.41	   A^2 -> H(d, U1(e, k))
28.58/10.41	   A^2 -> H(d, U1(k, e))
28.58/10.41	   A^2 -> H(d, e)
28.58/10.41	   A^2 -> H(d, U1(k, k))
28.58/10.41	   A^2 -> H(a, d)
28.58/10.41	   A^2 -> H(a, k)
28.58/10.41	   A^2 -> H(U1(e, d), d)
28.58/10.41	   A^2 -> H(U1(e, d), k)
28.58/10.41	   A^2 -> H(U1(k, a), k)
28.58/10.41	
28.58/10.41	The TRS R consists of the following rules:
28.58/10.41	
28.58/10.41	   f(x) -> U1(x, x)
28.58/10.41	   U1(e, x) -> x
28.58/10.41	   a -> c
28.58/10.41	   a -> d
28.58/10.41	   b -> c
28.58/10.41	   b -> d
28.58/10.41	   d -> k
28.58/10.41	   c -> e
28.58/10.41	   c -> k
28.58/10.41	
28.58/10.41	Q is empty.
28.58/10.41	We have to consider all minimal (P,Q,R)-chains.
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2477) DependencyGraphProof (EQUIVALENT)
28.58/10.41	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2478)
28.58/10.41	Obligation:
28.58/10.41	Q DP problem:
28.58/10.41	The TRS P consists of the following rules:
28.58/10.41	
28.58/10.41	   G(d, x, x) -> A^2
28.58/10.41	   A^2 -> H(f(c), f(c))
28.58/10.41	   H(x, x) -> G(x, x, f(k))
28.58/10.41	   A^2 -> H(f(d), f(d))
28.58/10.41	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.41	   A^2 -> H(f(e), f(e))
28.58/10.41	   A^2 -> H(f(k), f(k))
28.58/10.41	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.41	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.41	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.41	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.41	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.41	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.41	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.41	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.41	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.41	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.41	   A^2 -> H(U1(c, d), d)
28.58/10.41	   A^2 -> H(U1(c, d), k)
28.58/10.41	   A^2 -> H(U1(d, e), b)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(d, e), c)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(d, e), e)
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.41	   A^2 -> H(U1(d, c), d)
28.58/10.41	   A^2 -> H(U1(d, c), k)
28.58/10.41	   A^2 -> H(U1(a, e), d)
28.58/10.41	   A^2 -> H(U1(a, e), k)
28.58/10.41	   A^2 -> H(U1(a, k), d)
28.58/10.41	   A^2 -> H(U1(a, k), k)
28.58/10.41	   A^2 -> H(k, U1(e, b))
28.58/10.41	   A^2 -> H(k, U1(c, d))
28.58/10.41	   A^2 -> H(k, U1(d, c))
28.58/10.41	   A^2 -> H(k, U1(b, e))
28.58/10.41	   A^2 -> H(k, U1(b, k))
28.58/10.41	   A^2 -> H(k, U1(e, c))
28.58/10.41	   A^2 -> H(k, U1(c, e))
28.58/10.41	   A^2 -> H(k, U1(c, k))
28.58/10.41	   A^2 -> H(k, U1(e, e))
28.58/10.41	   A^2 -> H(k, U1(d, k))
28.58/10.41	   A^2 -> H(c, b)
28.58/10.41	   A^2 -> H(c, U1(e, d))
28.58/10.41	   A^2 -> H(c, U1(d, e))
28.58/10.41	   A^2 -> H(c, c)
28.58/10.41	   A^2 -> H(c, U1(e, k))
28.58/10.41	   A^2 -> H(c, U1(k, e))
28.58/10.41	   A^2 -> H(c, e)
28.58/10.41	   A^2 -> H(c, U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, k), b)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(e, k), c)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, k), e)
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, c), d)
28.58/10.41	   A^2 -> H(U1(e, c), k)
28.58/10.41	   A^2 -> H(U1(k, e), b)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, e), c)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(k, c), d)
28.58/10.41	   A^2 -> H(U1(c, e), d)
28.58/10.41	   A^2 -> H(U1(c, e), k)
28.58/10.41	   A^2 -> H(U1(c, k), d)
28.58/10.41	   A^2 -> H(U1(c, k), k)
28.58/10.41	   A^2 -> H(e, b)
28.58/10.41	   A^2 -> H(e, U1(e, d))
28.58/10.41	   A^2 -> H(e, U1(d, e))
28.58/10.41	   A^2 -> H(e, c)
28.58/10.41	   A^2 -> H(e, U1(e, k))
28.58/10.41	   A^2 -> H(e, e)
28.58/10.41	   A^2 -> H(U1(e, e), d)
28.58/10.41	   A^2 -> H(U1(e, e), k)
28.58/10.41	   A^2 -> H(U1(k, k), d)
28.58/10.41	   A^2 -> H(U1(k, k), b)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, k), c)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, d), d)
28.58/10.41	   A^2 -> H(U1(d, k), d)
28.58/10.41	   A^2 -> H(U1(d, k), k)
28.58/10.41	   A^2 -> H(U1(e, e), c)
28.58/10.41	   A^2 -> H(U1(e, c), e)
28.58/10.41	   A^2 -> H(U1(c, e), e)
28.58/10.41	   A^2 -> H(U1(c, k), e)
28.58/10.41	   A^2 -> H(c, U1(e, e))
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.41	   A^2 -> H(d, b)
28.58/10.41	   A^2 -> H(d, U1(e, d))
28.58/10.41	   A^2 -> H(d, U1(d, e))
28.58/10.41	   A^2 -> H(d, c)
28.58/10.41	   A^2 -> H(d, U1(e, k))
28.58/10.41	   A^2 -> H(d, U1(k, e))
28.58/10.41	   A^2 -> H(d, e)
28.58/10.41	   A^2 -> H(d, U1(k, k))
28.58/10.41	   A^2 -> H(a, d)
28.58/10.41	   A^2 -> H(a, k)
28.58/10.41	   A^2 -> H(U1(e, d), d)
28.58/10.41	   A^2 -> H(U1(e, d), k)
28.58/10.41	
28.58/10.41	The TRS R consists of the following rules:
28.58/10.41	
28.58/10.41	   f(x) -> U1(x, x)
28.58/10.41	   U1(e, x) -> x
28.58/10.41	   a -> c
28.58/10.41	   a -> d
28.58/10.41	   b -> c
28.58/10.41	   b -> d
28.58/10.41	   d -> k
28.58/10.41	   c -> e
28.58/10.41	   c -> k
28.58/10.41	
28.58/10.41	Q is empty.
28.58/10.41	We have to consider all minimal (P,Q,R)-chains.
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2479) TransformationProof (EQUIVALENT)
28.58/10.41	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.41	
28.58/10.41	   (A^2 -> H(U1(e, d), d),A^2 -> H(U1(e, d), d))
28.58/10.41	   (A^2 -> H(U1(k, d), d),A^2 -> H(U1(k, d), d))
28.58/10.41	   (A^2 -> H(U1(c, k), d),A^2 -> H(U1(c, k), d))
28.58/10.41	   (A^2 -> H(U1(c, d), k),A^2 -> H(U1(c, d), k))
28.58/10.41	
28.58/10.41	
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2480)
28.58/10.41	Obligation:
28.58/10.41	Q DP problem:
28.58/10.41	The TRS P consists of the following rules:
28.58/10.41	
28.58/10.41	   G(d, x, x) -> A^2
28.58/10.41	   A^2 -> H(f(c), f(c))
28.58/10.41	   H(x, x) -> G(x, x, f(k))
28.58/10.41	   A^2 -> H(f(d), f(d))
28.58/10.41	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.41	   A^2 -> H(f(e), f(e))
28.58/10.41	   A^2 -> H(f(k), f(k))
28.58/10.41	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.41	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.41	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.41	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.41	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.41	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.41	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.41	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.41	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.41	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.41	   A^2 -> H(U1(c, d), k)
28.58/10.41	   A^2 -> H(U1(d, e), b)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(d, e), c)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(d, e), e)
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.41	   A^2 -> H(U1(d, c), d)
28.58/10.41	   A^2 -> H(U1(d, c), k)
28.58/10.41	   A^2 -> H(U1(a, e), d)
28.58/10.41	   A^2 -> H(U1(a, e), k)
28.58/10.41	   A^2 -> H(U1(a, k), d)
28.58/10.41	   A^2 -> H(U1(a, k), k)
28.58/10.41	   A^2 -> H(k, U1(e, b))
28.58/10.41	   A^2 -> H(k, U1(c, d))
28.58/10.41	   A^2 -> H(k, U1(d, c))
28.58/10.41	   A^2 -> H(k, U1(b, e))
28.58/10.41	   A^2 -> H(k, U1(b, k))
28.58/10.41	   A^2 -> H(k, U1(e, c))
28.58/10.41	   A^2 -> H(k, U1(c, e))
28.58/10.41	   A^2 -> H(k, U1(c, k))
28.58/10.41	   A^2 -> H(k, U1(e, e))
28.58/10.41	   A^2 -> H(k, U1(d, k))
28.58/10.41	   A^2 -> H(c, b)
28.58/10.41	   A^2 -> H(c, U1(e, d))
28.58/10.41	   A^2 -> H(c, U1(d, e))
28.58/10.41	   A^2 -> H(c, c)
28.58/10.41	   A^2 -> H(c, U1(e, k))
28.58/10.41	   A^2 -> H(c, U1(k, e))
28.58/10.41	   A^2 -> H(c, e)
28.58/10.41	   A^2 -> H(c, U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, k), b)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(e, k), c)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, k), e)
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, c), d)
28.58/10.41	   A^2 -> H(U1(e, c), k)
28.58/10.41	   A^2 -> H(U1(k, e), b)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, e), c)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(k, c), d)
28.58/10.41	   A^2 -> H(U1(c, e), d)
28.58/10.41	   A^2 -> H(U1(c, e), k)
28.58/10.41	   A^2 -> H(U1(c, k), d)
28.58/10.41	   A^2 -> H(U1(c, k), k)
28.58/10.41	   A^2 -> H(e, b)
28.58/10.41	   A^2 -> H(e, U1(e, d))
28.58/10.41	   A^2 -> H(e, U1(d, e))
28.58/10.41	   A^2 -> H(e, c)
28.58/10.41	   A^2 -> H(e, U1(e, k))
28.58/10.41	   A^2 -> H(e, e)
28.58/10.41	   A^2 -> H(U1(e, e), d)
28.58/10.41	   A^2 -> H(U1(e, e), k)
28.58/10.41	   A^2 -> H(U1(k, k), d)
28.58/10.41	   A^2 -> H(U1(k, k), b)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, k), c)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, d), d)
28.58/10.41	   A^2 -> H(U1(d, k), d)
28.58/10.41	   A^2 -> H(U1(d, k), k)
28.58/10.41	   A^2 -> H(U1(e, e), c)
28.58/10.41	   A^2 -> H(U1(e, c), e)
28.58/10.41	   A^2 -> H(U1(c, e), e)
28.58/10.41	   A^2 -> H(U1(c, k), e)
28.58/10.41	   A^2 -> H(c, U1(e, e))
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.41	   A^2 -> H(d, b)
28.58/10.41	   A^2 -> H(d, U1(e, d))
28.58/10.41	   A^2 -> H(d, U1(d, e))
28.58/10.41	   A^2 -> H(d, c)
28.58/10.41	   A^2 -> H(d, U1(e, k))
28.58/10.41	   A^2 -> H(d, U1(k, e))
28.58/10.41	   A^2 -> H(d, e)
28.58/10.41	   A^2 -> H(d, U1(k, k))
28.58/10.41	   A^2 -> H(a, d)
28.58/10.41	   A^2 -> H(a, k)
28.58/10.41	   A^2 -> H(U1(e, d), d)
28.58/10.41	   A^2 -> H(U1(e, d), k)
28.58/10.41	
28.58/10.41	The TRS R consists of the following rules:
28.58/10.41	
28.58/10.41	   f(x) -> U1(x, x)
28.58/10.41	   U1(e, x) -> x
28.58/10.41	   a -> c
28.58/10.41	   a -> d
28.58/10.41	   b -> c
28.58/10.41	   b -> d
28.58/10.41	   d -> k
28.58/10.41	   c -> e
28.58/10.41	   c -> k
28.58/10.41	
28.58/10.41	Q is empty.
28.58/10.41	We have to consider all minimal (P,Q,R)-chains.
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2481) TransformationProof (EQUIVALENT)
28.58/10.41	By narrowing [LPAR04] the rule A^2 -> H(U1(c, d), k) at position [] we obtained the following new rules [LPAR04]:
28.58/10.41	
28.58/10.41	   (A^2 -> H(U1(e, d), k),A^2 -> H(U1(e, d), k))
28.58/10.41	   (A^2 -> H(U1(k, d), k),A^2 -> H(U1(k, d), k))
28.58/10.41	   (A^2 -> H(U1(c, k), k),A^2 -> H(U1(c, k), k))
28.58/10.41	
28.58/10.41	
28.58/10.41	----------------------------------------
28.58/10.41	
28.58/10.41	(2482)
28.58/10.41	Obligation:
28.58/10.41	Q DP problem:
28.58/10.41	The TRS P consists of the following rules:
28.58/10.41	
28.58/10.41	   G(d, x, x) -> A^2
28.58/10.41	   A^2 -> H(f(c), f(c))
28.58/10.41	   H(x, x) -> G(x, x, f(k))
28.58/10.41	   A^2 -> H(f(d), f(d))
28.58/10.41	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.41	   A^2 -> H(f(e), f(e))
28.58/10.41	   A^2 -> H(f(k), f(k))
28.58/10.41	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.41	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.41	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.41	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.41	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.41	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.41	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.41	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.41	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.41	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.41	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.41	   A^2 -> H(U1(d, e), b)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(d, e), c)
28.58/10.41	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(d, e), e)
28.58/10.41	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.41	   A^2 -> H(U1(d, c), d)
28.58/10.41	   A^2 -> H(U1(d, c), k)
28.58/10.41	   A^2 -> H(U1(a, e), d)
28.58/10.41	   A^2 -> H(U1(a, e), k)
28.58/10.41	   A^2 -> H(U1(a, k), d)
28.58/10.41	   A^2 -> H(U1(a, k), k)
28.58/10.41	   A^2 -> H(k, U1(e, b))
28.58/10.41	   A^2 -> H(k, U1(c, d))
28.58/10.41	   A^2 -> H(k, U1(d, c))
28.58/10.41	   A^2 -> H(k, U1(b, e))
28.58/10.41	   A^2 -> H(k, U1(b, k))
28.58/10.41	   A^2 -> H(k, U1(e, c))
28.58/10.41	   A^2 -> H(k, U1(c, e))
28.58/10.41	   A^2 -> H(k, U1(c, k))
28.58/10.41	   A^2 -> H(k, U1(e, e))
28.58/10.41	   A^2 -> H(k, U1(d, k))
28.58/10.41	   A^2 -> H(c, b)
28.58/10.41	   A^2 -> H(c, U1(e, d))
28.58/10.41	   A^2 -> H(c, U1(d, e))
28.58/10.41	   A^2 -> H(c, c)
28.58/10.41	   A^2 -> H(c, U1(e, k))
28.58/10.41	   A^2 -> H(c, U1(k, e))
28.58/10.41	   A^2 -> H(c, e)
28.58/10.41	   A^2 -> H(c, U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, k), b)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(e, k), c)
28.58/10.41	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.41	   A^2 -> H(U1(e, k), e)
28.58/10.41	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.41	   A^2 -> H(U1(e, c), d)
28.58/10.41	   A^2 -> H(U1(e, c), k)
28.58/10.41	   A^2 -> H(U1(k, e), b)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, e), c)
28.58/10.41	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.41	   A^2 -> H(U1(k, c), d)
28.58/10.41	   A^2 -> H(U1(c, e), d)
28.58/10.41	   A^2 -> H(U1(c, e), k)
28.58/10.41	   A^2 -> H(U1(c, k), d)
28.58/10.41	   A^2 -> H(U1(c, k), k)
28.58/10.41	   A^2 -> H(e, b)
28.58/10.41	   A^2 -> H(e, U1(e, d))
28.58/10.41	   A^2 -> H(e, U1(d, e))
28.58/10.41	   A^2 -> H(e, c)
28.58/10.41	   A^2 -> H(e, U1(e, k))
28.58/10.41	   A^2 -> H(e, e)
28.58/10.41	   A^2 -> H(U1(e, e), d)
28.58/10.41	   A^2 -> H(U1(e, e), k)
28.58/10.41	   A^2 -> H(U1(k, k), d)
28.58/10.41	   A^2 -> H(U1(k, k), b)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.41	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.41	   A^2 -> H(U1(k, k), c)
28.58/10.41	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.41	   A^2 -> H(U1(k, d), d)
28.58/10.41	   A^2 -> H(U1(d, k), d)
28.58/10.41	   A^2 -> H(U1(d, k), k)
28.58/10.41	   A^2 -> H(U1(e, e), c)
28.58/10.41	   A^2 -> H(U1(e, c), e)
28.58/10.41	   A^2 -> H(U1(c, e), e)
28.58/10.41	   A^2 -> H(U1(c, k), e)
28.58/10.42	   A^2 -> H(c, U1(e, e))
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.42	   A^2 -> H(d, b)
28.58/10.42	   A^2 -> H(d, U1(e, d))
28.58/10.42	   A^2 -> H(d, U1(d, e))
28.58/10.42	   A^2 -> H(d, c)
28.58/10.42	   A^2 -> H(d, U1(e, k))
28.58/10.42	   A^2 -> H(d, U1(k, e))
28.58/10.42	   A^2 -> H(d, e)
28.58/10.42	   A^2 -> H(d, U1(k, k))
28.58/10.42	   A^2 -> H(a, d)
28.58/10.42	   A^2 -> H(a, k)
28.58/10.42	   A^2 -> H(U1(e, d), d)
28.58/10.42	   A^2 -> H(U1(e, d), k)
28.58/10.42	   A^2 -> H(U1(k, d), k)
28.58/10.42	
28.58/10.42	The TRS R consists of the following rules:
28.58/10.42	
28.58/10.42	   f(x) -> U1(x, x)
28.58/10.42	   U1(e, x) -> x
28.58/10.42	   a -> c
28.58/10.42	   a -> d
28.58/10.42	   b -> c
28.58/10.42	   b -> d
28.58/10.42	   d -> k
28.58/10.42	   c -> e
28.58/10.42	   c -> k
28.58/10.42	
28.58/10.42	Q is empty.
28.58/10.42	We have to consider all minimal (P,Q,R)-chains.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2483) DependencyGraphProof (EQUIVALENT)
28.58/10.42	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2484)
28.58/10.42	Obligation:
28.58/10.42	Q DP problem:
28.58/10.42	The TRS P consists of the following rules:
28.58/10.42	
28.58/10.42	   A^2 -> H(f(c), f(c))
28.58/10.42	   H(x, x) -> G(x, x, f(k))
28.58/10.42	   G(d, x, x) -> A^2
28.58/10.42	   A^2 -> H(f(d), f(d))
28.58/10.42	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.42	   A^2 -> H(f(e), f(e))
28.58/10.42	   A^2 -> H(f(k), f(k))
28.58/10.42	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.42	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.42	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.42	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.42	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.42	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.42	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.42	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.42	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.42	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.42	   A^2 -> H(U1(d, e), b)
28.58/10.42	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.42	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(d, e), c)
28.58/10.42	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(d, e), e)
28.58/10.42	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.42	   A^2 -> H(U1(d, c), d)
28.58/10.42	   A^2 -> H(U1(d, c), k)
28.58/10.42	   A^2 -> H(U1(a, e), d)
28.58/10.42	   A^2 -> H(U1(a, e), k)
28.58/10.42	   A^2 -> H(U1(a, k), d)
28.58/10.42	   A^2 -> H(U1(a, k), k)
28.58/10.42	   A^2 -> H(k, U1(e, b))
28.58/10.42	   A^2 -> H(k, U1(c, d))
28.58/10.42	   A^2 -> H(k, U1(d, c))
28.58/10.42	   A^2 -> H(k, U1(b, e))
28.58/10.42	   A^2 -> H(k, U1(b, k))
28.58/10.42	   A^2 -> H(k, U1(e, c))
28.58/10.42	   A^2 -> H(k, U1(c, e))
28.58/10.42	   A^2 -> H(k, U1(c, k))
28.58/10.42	   A^2 -> H(k, U1(e, e))
28.58/10.42	   A^2 -> H(k, U1(d, k))
28.58/10.42	   A^2 -> H(c, b)
28.58/10.42	   A^2 -> H(c, U1(e, d))
28.58/10.42	   A^2 -> H(c, U1(d, e))
28.58/10.42	   A^2 -> H(c, c)
28.58/10.42	   A^2 -> H(c, U1(e, k))
28.58/10.42	   A^2 -> H(c, U1(k, e))
28.58/10.42	   A^2 -> H(c, e)
28.58/10.42	   A^2 -> H(c, U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, k), b)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(e, k), c)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.42	   A^2 -> H(U1(e, k), e)
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, c), d)
28.58/10.42	   A^2 -> H(U1(e, c), k)
28.58/10.42	   A^2 -> H(U1(k, e), b)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, e), c)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(k, c), d)
28.58/10.42	   A^2 -> H(U1(c, e), d)
28.58/10.42	   A^2 -> H(U1(c, e), k)
28.58/10.42	   A^2 -> H(U1(c, k), d)
28.58/10.42	   A^2 -> H(U1(c, k), k)
28.58/10.42	   A^2 -> H(e, b)
28.58/10.42	   A^2 -> H(e, U1(e, d))
28.58/10.42	   A^2 -> H(e, U1(d, e))
28.58/10.42	   A^2 -> H(e, c)
28.58/10.42	   A^2 -> H(e, U1(e, k))
28.58/10.42	   A^2 -> H(e, e)
28.58/10.42	   A^2 -> H(U1(e, e), d)
28.58/10.42	   A^2 -> H(U1(e, e), k)
28.58/10.42	   A^2 -> H(U1(k, k), d)
28.58/10.42	   A^2 -> H(U1(k, k), b)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, k), c)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, d), d)
28.58/10.42	   A^2 -> H(U1(d, k), d)
28.58/10.42	   A^2 -> H(U1(d, k), k)
28.58/10.42	   A^2 -> H(U1(e, e), c)
28.58/10.42	   A^2 -> H(U1(e, c), e)
28.58/10.42	   A^2 -> H(U1(c, e), e)
28.58/10.42	   A^2 -> H(U1(c, k), e)
28.58/10.42	   A^2 -> H(c, U1(e, e))
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.42	   A^2 -> H(d, b)
28.58/10.42	   A^2 -> H(d, U1(e, d))
28.58/10.42	   A^2 -> H(d, U1(d, e))
28.58/10.42	   A^2 -> H(d, c)
28.58/10.42	   A^2 -> H(d, U1(e, k))
28.58/10.42	   A^2 -> H(d, U1(k, e))
28.58/10.42	   A^2 -> H(d, e)
28.58/10.42	   A^2 -> H(d, U1(k, k))
28.58/10.42	   A^2 -> H(a, d)
28.58/10.42	   A^2 -> H(a, k)
28.58/10.42	   A^2 -> H(U1(e, d), d)
28.58/10.42	   A^2 -> H(U1(e, d), k)
28.58/10.42	
28.58/10.42	The TRS R consists of the following rules:
28.58/10.42	
28.58/10.42	   f(x) -> U1(x, x)
28.58/10.42	   U1(e, x) -> x
28.58/10.42	   a -> c
28.58/10.42	   a -> d
28.58/10.42	   b -> c
28.58/10.42	   b -> d
28.58/10.42	   d -> k
28.58/10.42	   c -> e
28.58/10.42	   c -> k
28.58/10.42	
28.58/10.42	Q is empty.
28.58/10.42	We have to consider all minimal (P,Q,R)-chains.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2485) TransformationProof (EQUIVALENT)
28.58/10.42	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), b) at position [] we obtained the following new rules [LPAR04]:
28.58/10.42	
28.58/10.42	   (A^2 -> H(U1(k, e), b),A^2 -> H(U1(k, e), b))
28.58/10.42	   (A^2 -> H(U1(d, e), c),A^2 -> H(U1(d, e), c))
28.58/10.42	   (A^2 -> H(U1(d, e), d),A^2 -> H(U1(d, e), d))
28.58/10.42	
28.58/10.42	
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2486)
28.58/10.42	Obligation:
28.58/10.42	Q DP problem:
28.58/10.42	The TRS P consists of the following rules:
28.58/10.42	
28.58/10.42	   A^2 -> H(f(c), f(c))
28.58/10.42	   H(x, x) -> G(x, x, f(k))
28.58/10.42	   G(d, x, x) -> A^2
28.58/10.42	   A^2 -> H(f(d), f(d))
28.58/10.42	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.42	   A^2 -> H(f(e), f(e))
28.58/10.42	   A^2 -> H(f(k), f(k))
28.58/10.42	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.42	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.42	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.42	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.42	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.42	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.42	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.42	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.42	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.42	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.42	   A^2 -> H(U1(d, e), U1(e, d))
28.58/10.42	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(d, e), c)
28.58/10.42	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(d, e), e)
28.58/10.42	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.42	   A^2 -> H(U1(d, c), d)
28.58/10.42	   A^2 -> H(U1(d, c), k)
28.58/10.42	   A^2 -> H(U1(a, e), d)
28.58/10.42	   A^2 -> H(U1(a, e), k)
28.58/10.42	   A^2 -> H(U1(a, k), d)
28.58/10.42	   A^2 -> H(U1(a, k), k)
28.58/10.42	   A^2 -> H(k, U1(e, b))
28.58/10.42	   A^2 -> H(k, U1(c, d))
28.58/10.42	   A^2 -> H(k, U1(d, c))
28.58/10.42	   A^2 -> H(k, U1(b, e))
28.58/10.42	   A^2 -> H(k, U1(b, k))
28.58/10.42	   A^2 -> H(k, U1(e, c))
28.58/10.42	   A^2 -> H(k, U1(c, e))
28.58/10.42	   A^2 -> H(k, U1(c, k))
28.58/10.42	   A^2 -> H(k, U1(e, e))
28.58/10.42	   A^2 -> H(k, U1(d, k))
28.58/10.42	   A^2 -> H(c, b)
28.58/10.42	   A^2 -> H(c, U1(e, d))
28.58/10.42	   A^2 -> H(c, U1(d, e))
28.58/10.42	   A^2 -> H(c, c)
28.58/10.42	   A^2 -> H(c, U1(e, k))
28.58/10.42	   A^2 -> H(c, U1(k, e))
28.58/10.42	   A^2 -> H(c, e)
28.58/10.42	   A^2 -> H(c, U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, k), b)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(e, k), c)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.42	   A^2 -> H(U1(e, k), e)
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, c), d)
28.58/10.42	   A^2 -> H(U1(e, c), k)
28.58/10.42	   A^2 -> H(U1(k, e), b)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, e), c)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(k, c), d)
28.58/10.42	   A^2 -> H(U1(c, e), d)
28.58/10.42	   A^2 -> H(U1(c, e), k)
28.58/10.42	   A^2 -> H(U1(c, k), d)
28.58/10.42	   A^2 -> H(U1(c, k), k)
28.58/10.42	   A^2 -> H(e, b)
28.58/10.42	   A^2 -> H(e, U1(e, d))
28.58/10.42	   A^2 -> H(e, U1(d, e))
28.58/10.42	   A^2 -> H(e, c)
28.58/10.42	   A^2 -> H(e, U1(e, k))
28.58/10.42	   A^2 -> H(e, e)
28.58/10.42	   A^2 -> H(U1(e, e), d)
28.58/10.42	   A^2 -> H(U1(e, e), k)
28.58/10.42	   A^2 -> H(U1(k, k), d)
28.58/10.42	   A^2 -> H(U1(k, k), b)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, k), c)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, d), d)
28.58/10.42	   A^2 -> H(U1(d, k), d)
28.58/10.42	   A^2 -> H(U1(d, k), k)
28.58/10.42	   A^2 -> H(U1(e, e), c)
28.58/10.42	   A^2 -> H(U1(e, c), e)
28.58/10.42	   A^2 -> H(U1(c, e), e)
28.58/10.42	   A^2 -> H(U1(c, k), e)
28.58/10.42	   A^2 -> H(c, U1(e, e))
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.42	   A^2 -> H(d, b)
28.58/10.42	   A^2 -> H(d, U1(e, d))
28.58/10.42	   A^2 -> H(d, U1(d, e))
28.58/10.42	   A^2 -> H(d, c)
28.58/10.42	   A^2 -> H(d, U1(e, k))
28.58/10.42	   A^2 -> H(d, U1(k, e))
28.58/10.42	   A^2 -> H(d, e)
28.58/10.42	   A^2 -> H(d, U1(k, k))
28.58/10.42	   A^2 -> H(a, d)
28.58/10.42	   A^2 -> H(a, k)
28.58/10.42	   A^2 -> H(U1(e, d), d)
28.58/10.42	   A^2 -> H(U1(e, d), k)
28.58/10.42	   A^2 -> H(U1(d, e), d)
28.58/10.42	
28.58/10.42	The TRS R consists of the following rules:
28.58/10.42	
28.58/10.42	   f(x) -> U1(x, x)
28.58/10.42	   U1(e, x) -> x
28.58/10.42	   a -> c
28.58/10.42	   a -> d
28.58/10.42	   b -> c
28.58/10.42	   b -> d
28.58/10.42	   d -> k
28.58/10.42	   c -> e
28.58/10.42	   c -> k
28.58/10.42	
28.58/10.42	Q is empty.
28.58/10.42	We have to consider all minimal (P,Q,R)-chains.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2487) TransformationProof (EQUIVALENT)
28.58/10.42	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.42	
28.58/10.42	   (A^2 -> H(U1(k, e), U1(e, d)),A^2 -> H(U1(k, e), U1(e, d)))
28.58/10.42	   (A^2 -> H(U1(d, e), d),A^2 -> H(U1(d, e), d))
28.58/10.42	   (A^2 -> H(U1(d, e), U1(e, k)),A^2 -> H(U1(d, e), U1(e, k)))
28.58/10.42	
28.58/10.42	
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2488)
28.58/10.42	Obligation:
28.58/10.42	Q DP problem:
28.58/10.42	The TRS P consists of the following rules:
28.58/10.42	
28.58/10.42	   A^2 -> H(f(c), f(c))
28.58/10.42	   H(x, x) -> G(x, x, f(k))
28.58/10.42	   G(d, x, x) -> A^2
28.58/10.42	   A^2 -> H(f(d), f(d))
28.58/10.42	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.42	   A^2 -> H(f(e), f(e))
28.58/10.42	   A^2 -> H(f(k), f(k))
28.58/10.42	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.42	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.42	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.42	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.42	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.42	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.42	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.42	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.42	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.42	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.42	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(d, e), c)
28.58/10.42	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(d, e), e)
28.58/10.42	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.42	   A^2 -> H(U1(d, c), d)
28.58/10.42	   A^2 -> H(U1(d, c), k)
28.58/10.42	   A^2 -> H(U1(a, e), d)
28.58/10.42	   A^2 -> H(U1(a, e), k)
28.58/10.42	   A^2 -> H(U1(a, k), d)
28.58/10.42	   A^2 -> H(U1(a, k), k)
28.58/10.42	   A^2 -> H(k, U1(e, b))
28.58/10.42	   A^2 -> H(k, U1(c, d))
28.58/10.42	   A^2 -> H(k, U1(d, c))
28.58/10.42	   A^2 -> H(k, U1(b, e))
28.58/10.42	   A^2 -> H(k, U1(b, k))
28.58/10.42	   A^2 -> H(k, U1(e, c))
28.58/10.42	   A^2 -> H(k, U1(c, e))
28.58/10.42	   A^2 -> H(k, U1(c, k))
28.58/10.42	   A^2 -> H(k, U1(e, e))
28.58/10.42	   A^2 -> H(k, U1(d, k))
28.58/10.42	   A^2 -> H(c, b)
28.58/10.42	   A^2 -> H(c, U1(e, d))
28.58/10.42	   A^2 -> H(c, U1(d, e))
28.58/10.42	   A^2 -> H(c, c)
28.58/10.42	   A^2 -> H(c, U1(e, k))
28.58/10.42	   A^2 -> H(c, U1(k, e))
28.58/10.42	   A^2 -> H(c, e)
28.58/10.42	   A^2 -> H(c, U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, k), b)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(e, k), c)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.42	   A^2 -> H(U1(e, k), e)
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, c), d)
28.58/10.42	   A^2 -> H(U1(e, c), k)
28.58/10.42	   A^2 -> H(U1(k, e), b)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, e), c)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(k, c), d)
28.58/10.42	   A^2 -> H(U1(c, e), d)
28.58/10.42	   A^2 -> H(U1(c, e), k)
28.58/10.42	   A^2 -> H(U1(c, k), d)
28.58/10.42	   A^2 -> H(U1(c, k), k)
28.58/10.42	   A^2 -> H(e, b)
28.58/10.42	   A^2 -> H(e, U1(e, d))
28.58/10.42	   A^2 -> H(e, U1(d, e))
28.58/10.42	   A^2 -> H(e, c)
28.58/10.42	   A^2 -> H(e, U1(e, k))
28.58/10.42	   A^2 -> H(e, e)
28.58/10.42	   A^2 -> H(U1(e, e), d)
28.58/10.42	   A^2 -> H(U1(e, e), k)
28.58/10.42	   A^2 -> H(U1(k, k), d)
28.58/10.42	   A^2 -> H(U1(k, k), b)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, k), c)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, d), d)
28.58/10.42	   A^2 -> H(U1(d, k), d)
28.58/10.42	   A^2 -> H(U1(d, k), k)
28.58/10.42	   A^2 -> H(U1(e, e), c)
28.58/10.42	   A^2 -> H(U1(e, c), e)
28.58/10.42	   A^2 -> H(U1(c, e), e)
28.58/10.42	   A^2 -> H(U1(c, k), e)
28.58/10.42	   A^2 -> H(c, U1(e, e))
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.42	   A^2 -> H(d, b)
28.58/10.42	   A^2 -> H(d, U1(e, d))
28.58/10.42	   A^2 -> H(d, U1(d, e))
28.58/10.42	   A^2 -> H(d, c)
28.58/10.42	   A^2 -> H(d, U1(e, k))
28.58/10.42	   A^2 -> H(d, U1(k, e))
28.58/10.42	   A^2 -> H(d, e)
28.58/10.42	   A^2 -> H(d, U1(k, k))
28.58/10.42	   A^2 -> H(a, d)
28.58/10.42	   A^2 -> H(a, k)
28.58/10.42	   A^2 -> H(U1(e, d), d)
28.58/10.42	   A^2 -> H(U1(e, d), k)
28.58/10.42	   A^2 -> H(U1(d, e), d)
28.58/10.42	
28.58/10.42	The TRS R consists of the following rules:
28.58/10.42	
28.58/10.42	   f(x) -> U1(x, x)
28.58/10.42	   U1(e, x) -> x
28.58/10.42	   a -> c
28.58/10.42	   a -> d
28.58/10.42	   b -> c
28.58/10.42	   b -> d
28.58/10.42	   d -> k
28.58/10.42	   c -> e
28.58/10.42	   c -> k
28.58/10.42	
28.58/10.42	Q is empty.
28.58/10.42	We have to consider all minimal (P,Q,R)-chains.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2489) TransformationProof (EQUIVALENT)
28.58/10.42	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), c) at position [] we obtained the following new rules [LPAR04]:
28.58/10.42	
28.58/10.42	   (A^2 -> H(U1(k, e), c),A^2 -> H(U1(k, e), c))
28.58/10.42	   (A^2 -> H(U1(d, e), e),A^2 -> H(U1(d, e), e))
28.58/10.42	   (A^2 -> H(U1(d, e), k),A^2 -> H(U1(d, e), k))
28.58/10.42	
28.58/10.42	
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2490)
28.58/10.42	Obligation:
28.58/10.42	Q DP problem:
28.58/10.42	The TRS P consists of the following rules:
28.58/10.42	
28.58/10.42	   A^2 -> H(f(c), f(c))
28.58/10.42	   H(x, x) -> G(x, x, f(k))
28.58/10.42	   G(d, x, x) -> A^2
28.58/10.42	   A^2 -> H(f(d), f(d))
28.58/10.42	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.42	   A^2 -> H(f(e), f(e))
28.58/10.42	   A^2 -> H(f(k), f(k))
28.58/10.42	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.42	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.42	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.42	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.42	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.42	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.42	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.42	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.42	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.42	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.42	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(d, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(d, e), e)
28.58/10.42	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.42	   A^2 -> H(U1(d, c), d)
28.58/10.42	   A^2 -> H(U1(d, c), k)
28.58/10.42	   A^2 -> H(U1(a, e), d)
28.58/10.42	   A^2 -> H(U1(a, e), k)
28.58/10.42	   A^2 -> H(U1(a, k), d)
28.58/10.42	   A^2 -> H(U1(a, k), k)
28.58/10.42	   A^2 -> H(k, U1(e, b))
28.58/10.42	   A^2 -> H(k, U1(c, d))
28.58/10.42	   A^2 -> H(k, U1(d, c))
28.58/10.42	   A^2 -> H(k, U1(b, e))
28.58/10.42	   A^2 -> H(k, U1(b, k))
28.58/10.42	   A^2 -> H(k, U1(e, c))
28.58/10.42	   A^2 -> H(k, U1(c, e))
28.58/10.42	   A^2 -> H(k, U1(c, k))
28.58/10.42	   A^2 -> H(k, U1(e, e))
28.58/10.42	   A^2 -> H(k, U1(d, k))
28.58/10.42	   A^2 -> H(c, b)
28.58/10.42	   A^2 -> H(c, U1(e, d))
28.58/10.42	   A^2 -> H(c, U1(d, e))
28.58/10.42	   A^2 -> H(c, c)
28.58/10.42	   A^2 -> H(c, U1(e, k))
28.58/10.42	   A^2 -> H(c, U1(k, e))
28.58/10.42	   A^2 -> H(c, e)
28.58/10.42	   A^2 -> H(c, U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, k), b)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(e, k), c)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.42	   A^2 -> H(U1(e, k), e)
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, c), d)
28.58/10.42	   A^2 -> H(U1(e, c), k)
28.58/10.42	   A^2 -> H(U1(k, e), b)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, e), c)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(k, c), d)
28.58/10.42	   A^2 -> H(U1(c, e), d)
28.58/10.42	   A^2 -> H(U1(c, e), k)
28.58/10.42	   A^2 -> H(U1(c, k), d)
28.58/10.42	   A^2 -> H(U1(c, k), k)
28.58/10.42	   A^2 -> H(e, b)
28.58/10.42	   A^2 -> H(e, U1(e, d))
28.58/10.42	   A^2 -> H(e, U1(d, e))
28.58/10.42	   A^2 -> H(e, c)
28.58/10.42	   A^2 -> H(e, U1(e, k))
28.58/10.42	   A^2 -> H(e, e)
28.58/10.42	   A^2 -> H(U1(e, e), d)
28.58/10.42	   A^2 -> H(U1(e, e), k)
28.58/10.42	   A^2 -> H(U1(k, k), d)
28.58/10.42	   A^2 -> H(U1(k, k), b)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, k), c)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, d), d)
28.58/10.42	   A^2 -> H(U1(d, k), d)
28.58/10.42	   A^2 -> H(U1(d, k), k)
28.58/10.42	   A^2 -> H(U1(e, e), c)
28.58/10.42	   A^2 -> H(U1(e, c), e)
28.58/10.42	   A^2 -> H(U1(c, e), e)
28.58/10.42	   A^2 -> H(U1(c, k), e)
28.58/10.42	   A^2 -> H(c, U1(e, e))
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.42	   A^2 -> H(d, b)
28.58/10.42	   A^2 -> H(d, U1(e, d))
28.58/10.42	   A^2 -> H(d, U1(d, e))
28.58/10.42	   A^2 -> H(d, c)
28.58/10.42	   A^2 -> H(d, U1(e, k))
28.58/10.42	   A^2 -> H(d, U1(k, e))
28.58/10.42	   A^2 -> H(d, e)
28.58/10.42	   A^2 -> H(d, U1(k, k))
28.58/10.42	   A^2 -> H(a, d)
28.58/10.42	   A^2 -> H(a, k)
28.58/10.42	   A^2 -> H(U1(e, d), d)
28.58/10.42	   A^2 -> H(U1(e, d), k)
28.58/10.42	   A^2 -> H(U1(d, e), d)
28.58/10.42	   A^2 -> H(U1(d, e), k)
28.58/10.42	
28.58/10.42	The TRS R consists of the following rules:
28.58/10.42	
28.58/10.42	   f(x) -> U1(x, x)
28.58/10.42	   U1(e, x) -> x
28.58/10.42	   a -> c
28.58/10.42	   a -> d
28.58/10.42	   b -> c
28.58/10.42	   b -> d
28.58/10.42	   d -> k
28.58/10.42	   c -> e
28.58/10.42	   c -> k
28.58/10.42	
28.58/10.42	Q is empty.
28.58/10.42	We have to consider all minimal (P,Q,R)-chains.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2491) TransformationProof (EQUIVALENT)
28.58/10.42	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.42	
28.58/10.42	   (A^2 -> H(U1(k, e), U1(e, k)),A^2 -> H(U1(k, e), U1(e, k)))
28.58/10.42	   (A^2 -> H(U1(d, e), k),A^2 -> H(U1(d, e), k))
28.58/10.42	
28.58/10.42	
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2492)
28.58/10.42	Obligation:
28.58/10.42	Q DP problem:
28.58/10.42	The TRS P consists of the following rules:
28.58/10.42	
28.58/10.42	   A^2 -> H(f(c), f(c))
28.58/10.42	   H(x, x) -> G(x, x, f(k))
28.58/10.42	   G(d, x, x) -> A^2
28.58/10.42	   A^2 -> H(f(d), f(d))
28.58/10.42	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.42	   A^2 -> H(f(e), f(e))
28.58/10.42	   A^2 -> H(f(k), f(k))
28.58/10.42	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.42	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.42	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.42	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.42	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.42	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.42	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.42	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.42	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.42	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.42	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(d, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(d, e), e)
28.58/10.42	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.42	   A^2 -> H(U1(d, c), d)
28.58/10.42	   A^2 -> H(U1(d, c), k)
28.58/10.42	   A^2 -> H(U1(a, e), d)
28.58/10.42	   A^2 -> H(U1(a, e), k)
28.58/10.42	   A^2 -> H(U1(a, k), d)
28.58/10.42	   A^2 -> H(U1(a, k), k)
28.58/10.42	   A^2 -> H(k, U1(e, b))
28.58/10.42	   A^2 -> H(k, U1(c, d))
28.58/10.42	   A^2 -> H(k, U1(d, c))
28.58/10.42	   A^2 -> H(k, U1(b, e))
28.58/10.42	   A^2 -> H(k, U1(b, k))
28.58/10.42	   A^2 -> H(k, U1(e, c))
28.58/10.42	   A^2 -> H(k, U1(c, e))
28.58/10.42	   A^2 -> H(k, U1(c, k))
28.58/10.42	   A^2 -> H(k, U1(e, e))
28.58/10.42	   A^2 -> H(k, U1(d, k))
28.58/10.42	   A^2 -> H(c, b)
28.58/10.42	   A^2 -> H(c, U1(e, d))
28.58/10.42	   A^2 -> H(c, U1(d, e))
28.58/10.42	   A^2 -> H(c, c)
28.58/10.42	   A^2 -> H(c, U1(e, k))
28.58/10.42	   A^2 -> H(c, U1(k, e))
28.58/10.42	   A^2 -> H(c, e)
28.58/10.42	   A^2 -> H(c, U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, k), b)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(e, k), c)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.42	   A^2 -> H(U1(e, k), e)
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, c), d)
28.58/10.42	   A^2 -> H(U1(e, c), k)
28.58/10.42	   A^2 -> H(U1(k, e), b)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, e), c)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(k, c), d)
28.58/10.42	   A^2 -> H(U1(c, e), d)
28.58/10.42	   A^2 -> H(U1(c, e), k)
28.58/10.42	   A^2 -> H(U1(c, k), d)
28.58/10.42	   A^2 -> H(U1(c, k), k)
28.58/10.42	   A^2 -> H(e, b)
28.58/10.42	   A^2 -> H(e, U1(e, d))
28.58/10.42	   A^2 -> H(e, U1(d, e))
28.58/10.42	   A^2 -> H(e, c)
28.58/10.42	   A^2 -> H(e, U1(e, k))
28.58/10.42	   A^2 -> H(e, e)
28.58/10.42	   A^2 -> H(U1(e, e), d)
28.58/10.42	   A^2 -> H(U1(e, e), k)
28.58/10.42	   A^2 -> H(U1(k, k), d)
28.58/10.42	   A^2 -> H(U1(k, k), b)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, k), c)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, d), d)
28.58/10.42	   A^2 -> H(U1(d, k), d)
28.58/10.42	   A^2 -> H(U1(d, k), k)
28.58/10.42	   A^2 -> H(U1(e, e), c)
28.58/10.42	   A^2 -> H(U1(e, c), e)
28.58/10.42	   A^2 -> H(U1(c, e), e)
28.58/10.42	   A^2 -> H(U1(c, k), e)
28.58/10.42	   A^2 -> H(c, U1(e, e))
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.42	   A^2 -> H(d, b)
28.58/10.42	   A^2 -> H(d, U1(e, d))
28.58/10.42	   A^2 -> H(d, U1(d, e))
28.58/10.42	   A^2 -> H(d, c)
28.58/10.42	   A^2 -> H(d, U1(e, k))
28.58/10.42	   A^2 -> H(d, U1(k, e))
28.58/10.42	   A^2 -> H(d, e)
28.58/10.42	   A^2 -> H(d, U1(k, k))
28.58/10.42	   A^2 -> H(a, d)
28.58/10.42	   A^2 -> H(a, k)
28.58/10.42	   A^2 -> H(U1(e, d), d)
28.58/10.42	   A^2 -> H(U1(e, d), k)
28.58/10.42	   A^2 -> H(U1(d, e), d)
28.58/10.42	   A^2 -> H(U1(d, e), k)
28.58/10.42	
28.58/10.42	The TRS R consists of the following rules:
28.58/10.42	
28.58/10.42	   f(x) -> U1(x, x)
28.58/10.42	   U1(e, x) -> x
28.58/10.42	   a -> c
28.58/10.42	   a -> d
28.58/10.42	   b -> c
28.58/10.42	   b -> d
28.58/10.42	   d -> k
28.58/10.42	   c -> e
28.58/10.42	   c -> k
28.58/10.42	
28.58/10.42	Q is empty.
28.58/10.42	We have to consider all minimal (P,Q,R)-chains.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2493) TransformationProof (EQUIVALENT)
28.58/10.42	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.42	
28.58/10.42	   (A^2 -> H(U1(k, e), U1(k, e)),A^2 -> H(U1(k, e), U1(k, e)))
28.58/10.42	
28.58/10.42	
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2494)
28.58/10.42	Obligation:
28.58/10.42	Q DP problem:
28.58/10.42	The TRS P consists of the following rules:
28.58/10.42	
28.58/10.42	   A^2 -> H(f(c), f(c))
28.58/10.42	   H(x, x) -> G(x, x, f(k))
28.58/10.42	   G(d, x, x) -> A^2
28.58/10.42	   A^2 -> H(f(d), f(d))
28.58/10.42	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.42	   A^2 -> H(f(e), f(e))
28.58/10.42	   A^2 -> H(f(k), f(k))
28.58/10.42	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.42	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.42	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.42	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.42	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.42	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.42	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.42	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.42	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.42	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.42	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(d, e), e)
28.58/10.42	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.42	   A^2 -> H(U1(d, c), d)
28.58/10.42	   A^2 -> H(U1(d, c), k)
28.58/10.42	   A^2 -> H(U1(a, e), d)
28.58/10.42	   A^2 -> H(U1(a, e), k)
28.58/10.42	   A^2 -> H(U1(a, k), d)
28.58/10.42	   A^2 -> H(U1(a, k), k)
28.58/10.42	   A^2 -> H(k, U1(e, b))
28.58/10.42	   A^2 -> H(k, U1(c, d))
28.58/10.42	   A^2 -> H(k, U1(d, c))
28.58/10.42	   A^2 -> H(k, U1(b, e))
28.58/10.42	   A^2 -> H(k, U1(b, k))
28.58/10.42	   A^2 -> H(k, U1(e, c))
28.58/10.42	   A^2 -> H(k, U1(c, e))
28.58/10.42	   A^2 -> H(k, U1(c, k))
28.58/10.42	   A^2 -> H(k, U1(e, e))
28.58/10.42	   A^2 -> H(k, U1(d, k))
28.58/10.42	   A^2 -> H(c, b)
28.58/10.42	   A^2 -> H(c, U1(e, d))
28.58/10.42	   A^2 -> H(c, U1(d, e))
28.58/10.42	   A^2 -> H(c, c)
28.58/10.42	   A^2 -> H(c, U1(e, k))
28.58/10.42	   A^2 -> H(c, U1(k, e))
28.58/10.42	   A^2 -> H(c, e)
28.58/10.42	   A^2 -> H(c, U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, k), b)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(e, k), c)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.42	   A^2 -> H(U1(e, k), e)
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, c), d)
28.58/10.42	   A^2 -> H(U1(e, c), k)
28.58/10.42	   A^2 -> H(U1(k, e), b)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, e), c)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(k, c), d)
28.58/10.42	   A^2 -> H(U1(c, e), d)
28.58/10.42	   A^2 -> H(U1(c, e), k)
28.58/10.42	   A^2 -> H(U1(c, k), d)
28.58/10.42	   A^2 -> H(U1(c, k), k)
28.58/10.42	   A^2 -> H(e, b)
28.58/10.42	   A^2 -> H(e, U1(e, d))
28.58/10.42	   A^2 -> H(e, U1(d, e))
28.58/10.42	   A^2 -> H(e, c)
28.58/10.42	   A^2 -> H(e, U1(e, k))
28.58/10.42	   A^2 -> H(e, e)
28.58/10.42	   A^2 -> H(U1(e, e), d)
28.58/10.42	   A^2 -> H(U1(e, e), k)
28.58/10.42	   A^2 -> H(U1(k, k), d)
28.58/10.42	   A^2 -> H(U1(k, k), b)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, k), c)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, d), d)
28.58/10.42	   A^2 -> H(U1(d, k), d)
28.58/10.42	   A^2 -> H(U1(d, k), k)
28.58/10.42	   A^2 -> H(U1(e, e), c)
28.58/10.42	   A^2 -> H(U1(e, c), e)
28.58/10.42	   A^2 -> H(U1(c, e), e)
28.58/10.42	   A^2 -> H(U1(c, k), e)
28.58/10.42	   A^2 -> H(c, U1(e, e))
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.42	   A^2 -> H(d, b)
28.58/10.42	   A^2 -> H(d, U1(e, d))
28.58/10.42	   A^2 -> H(d, U1(d, e))
28.58/10.42	   A^2 -> H(d, c)
28.58/10.42	   A^2 -> H(d, U1(e, k))
28.58/10.42	   A^2 -> H(d, U1(k, e))
28.58/10.42	   A^2 -> H(d, e)
28.58/10.42	   A^2 -> H(d, U1(k, k))
28.58/10.42	   A^2 -> H(a, d)
28.58/10.42	   A^2 -> H(a, k)
28.58/10.42	   A^2 -> H(U1(e, d), d)
28.58/10.42	   A^2 -> H(U1(e, d), k)
28.58/10.42	   A^2 -> H(U1(d, e), d)
28.58/10.42	   A^2 -> H(U1(d, e), k)
28.58/10.42	
28.58/10.42	The TRS R consists of the following rules:
28.58/10.42	
28.58/10.42	   f(x) -> U1(x, x)
28.58/10.42	   U1(e, x) -> x
28.58/10.42	   a -> c
28.58/10.42	   a -> d
28.58/10.42	   b -> c
28.58/10.42	   b -> d
28.58/10.42	   d -> k
28.58/10.42	   c -> e
28.58/10.42	   c -> k
28.58/10.42	
28.58/10.42	Q is empty.
28.58/10.42	We have to consider all minimal (P,Q,R)-chains.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2495) TransformationProof (EQUIVALENT)
28.58/10.42	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), e) at position [] we obtained the following new rules [LPAR04]:
28.58/10.42	
28.58/10.42	   (A^2 -> H(U1(k, e), e),A^2 -> H(U1(k, e), e))
28.58/10.42	
28.58/10.42	
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2496)
28.58/10.42	Obligation:
28.58/10.42	Q DP problem:
28.58/10.42	The TRS P consists of the following rules:
28.58/10.42	
28.58/10.42	   A^2 -> H(f(c), f(c))
28.58/10.42	   H(x, x) -> G(x, x, f(k))
28.58/10.42	   G(d, x, x) -> A^2
28.58/10.42	   A^2 -> H(f(d), f(d))
28.58/10.42	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.42	   A^2 -> H(f(e), f(e))
28.58/10.42	   A^2 -> H(f(k), f(k))
28.58/10.42	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.42	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.42	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.42	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.42	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.42	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.42	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.42	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.42	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.42	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.42	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.42	   A^2 -> H(U1(d, c), d)
28.58/10.42	   A^2 -> H(U1(d, c), k)
28.58/10.42	   A^2 -> H(U1(a, e), d)
28.58/10.42	   A^2 -> H(U1(a, e), k)
28.58/10.42	   A^2 -> H(U1(a, k), d)
28.58/10.42	   A^2 -> H(U1(a, k), k)
28.58/10.42	   A^2 -> H(k, U1(e, b))
28.58/10.42	   A^2 -> H(k, U1(c, d))
28.58/10.42	   A^2 -> H(k, U1(d, c))
28.58/10.42	   A^2 -> H(k, U1(b, e))
28.58/10.42	   A^2 -> H(k, U1(b, k))
28.58/10.42	   A^2 -> H(k, U1(e, c))
28.58/10.42	   A^2 -> H(k, U1(c, e))
28.58/10.42	   A^2 -> H(k, U1(c, k))
28.58/10.42	   A^2 -> H(k, U1(e, e))
28.58/10.42	   A^2 -> H(k, U1(d, k))
28.58/10.42	   A^2 -> H(c, b)
28.58/10.42	   A^2 -> H(c, U1(e, d))
28.58/10.42	   A^2 -> H(c, U1(d, e))
28.58/10.42	   A^2 -> H(c, c)
28.58/10.42	   A^2 -> H(c, U1(e, k))
28.58/10.42	   A^2 -> H(c, U1(k, e))
28.58/10.42	   A^2 -> H(c, e)
28.58/10.42	   A^2 -> H(c, U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, k), b)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(e, k), c)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.42	   A^2 -> H(U1(e, k), e)
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, c), d)
28.58/10.42	   A^2 -> H(U1(e, c), k)
28.58/10.42	   A^2 -> H(U1(k, e), b)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, e), c)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(k, c), d)
28.58/10.42	   A^2 -> H(U1(c, e), d)
28.58/10.42	   A^2 -> H(U1(c, e), k)
28.58/10.42	   A^2 -> H(U1(c, k), d)
28.58/10.42	   A^2 -> H(U1(c, k), k)
28.58/10.42	   A^2 -> H(e, b)
28.58/10.42	   A^2 -> H(e, U1(e, d))
28.58/10.42	   A^2 -> H(e, U1(d, e))
28.58/10.42	   A^2 -> H(e, c)
28.58/10.42	   A^2 -> H(e, U1(e, k))
28.58/10.42	   A^2 -> H(e, e)
28.58/10.42	   A^2 -> H(U1(e, e), d)
28.58/10.42	   A^2 -> H(U1(e, e), k)
28.58/10.42	   A^2 -> H(U1(k, k), d)
28.58/10.42	   A^2 -> H(U1(k, k), b)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, k), c)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, d), d)
28.58/10.42	   A^2 -> H(U1(d, k), d)
28.58/10.42	   A^2 -> H(U1(d, k), k)
28.58/10.42	   A^2 -> H(U1(e, e), c)
28.58/10.42	   A^2 -> H(U1(e, c), e)
28.58/10.42	   A^2 -> H(U1(c, e), e)
28.58/10.42	   A^2 -> H(U1(c, k), e)
28.58/10.42	   A^2 -> H(c, U1(e, e))
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.42	   A^2 -> H(d, b)
28.58/10.42	   A^2 -> H(d, U1(e, d))
28.58/10.42	   A^2 -> H(d, U1(d, e))
28.58/10.42	   A^2 -> H(d, c)
28.58/10.42	   A^2 -> H(d, U1(e, k))
28.58/10.42	   A^2 -> H(d, U1(k, e))
28.58/10.42	   A^2 -> H(d, e)
28.58/10.42	   A^2 -> H(d, U1(k, k))
28.58/10.42	   A^2 -> H(a, d)
28.58/10.42	   A^2 -> H(a, k)
28.58/10.42	   A^2 -> H(U1(e, d), d)
28.58/10.42	   A^2 -> H(U1(e, d), k)
28.58/10.42	   A^2 -> H(U1(d, e), d)
28.58/10.42	   A^2 -> H(U1(d, e), k)
28.58/10.42	   A^2 -> H(U1(k, e), e)
28.58/10.42	
28.58/10.42	The TRS R consists of the following rules:
28.58/10.42	
28.58/10.42	   f(x) -> U1(x, x)
28.58/10.42	   U1(e, x) -> x
28.58/10.42	   a -> c
28.58/10.42	   a -> d
28.58/10.42	   b -> c
28.58/10.42	   b -> d
28.58/10.42	   d -> k
28.58/10.42	   c -> e
28.58/10.42	   c -> k
28.58/10.42	
28.58/10.42	Q is empty.
28.58/10.42	We have to consider all minimal (P,Q,R)-chains.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2497) DependencyGraphProof (EQUIVALENT)
28.58/10.42	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2498)
28.58/10.42	Obligation:
28.58/10.42	Q DP problem:
28.58/10.42	The TRS P consists of the following rules:
28.58/10.42	
28.58/10.42	   H(x, x) -> G(x, x, f(k))
28.58/10.42	   G(d, x, x) -> A^2
28.58/10.42	   A^2 -> H(f(c), f(c))
28.58/10.42	   A^2 -> H(f(d), f(d))
28.58/10.42	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.42	   A^2 -> H(f(e), f(e))
28.58/10.42	   A^2 -> H(f(k), f(k))
28.58/10.42	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.42	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.42	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.42	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.42	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.42	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.42	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.42	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.42	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.42	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.42	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(d, e), U1(k, k))
28.58/10.42	   A^2 -> H(U1(d, c), d)
28.58/10.42	   A^2 -> H(U1(d, c), k)
28.58/10.42	   A^2 -> H(U1(a, e), d)
28.58/10.42	   A^2 -> H(U1(a, e), k)
28.58/10.42	   A^2 -> H(U1(a, k), d)
28.58/10.42	   A^2 -> H(U1(a, k), k)
28.58/10.42	   A^2 -> H(k, U1(e, b))
28.58/10.42	   A^2 -> H(k, U1(c, d))
28.58/10.42	   A^2 -> H(k, U1(d, c))
28.58/10.42	   A^2 -> H(k, U1(b, e))
28.58/10.42	   A^2 -> H(k, U1(b, k))
28.58/10.42	   A^2 -> H(k, U1(e, c))
28.58/10.42	   A^2 -> H(k, U1(c, e))
28.58/10.42	   A^2 -> H(k, U1(c, k))
28.58/10.42	   A^2 -> H(k, U1(e, e))
28.58/10.42	   A^2 -> H(k, U1(d, k))
28.58/10.42	   A^2 -> H(c, b)
28.58/10.42	   A^2 -> H(c, U1(e, d))
28.58/10.42	   A^2 -> H(c, U1(d, e))
28.58/10.42	   A^2 -> H(c, c)
28.58/10.42	   A^2 -> H(c, U1(e, k))
28.58/10.42	   A^2 -> H(c, U1(k, e))
28.58/10.42	   A^2 -> H(c, e)
28.58/10.42	   A^2 -> H(c, U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, k), b)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(e, k), c)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.42	   A^2 -> H(U1(e, k), e)
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, c), d)
28.58/10.42	   A^2 -> H(U1(e, c), k)
28.58/10.42	   A^2 -> H(U1(k, e), b)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, e), c)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(k, c), d)
28.58/10.42	   A^2 -> H(U1(c, e), d)
28.58/10.42	   A^2 -> H(U1(c, e), k)
28.58/10.42	   A^2 -> H(U1(c, k), d)
28.58/10.42	   A^2 -> H(U1(c, k), k)
28.58/10.42	   A^2 -> H(e, b)
28.58/10.42	   A^2 -> H(e, U1(e, d))
28.58/10.42	   A^2 -> H(e, U1(d, e))
28.58/10.42	   A^2 -> H(e, c)
28.58/10.42	   A^2 -> H(e, U1(e, k))
28.58/10.42	   A^2 -> H(e, e)
28.58/10.42	   A^2 -> H(U1(e, e), d)
28.58/10.42	   A^2 -> H(U1(e, e), k)
28.58/10.42	   A^2 -> H(U1(k, k), d)
28.58/10.42	   A^2 -> H(U1(k, k), b)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, k), c)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, d), d)
28.58/10.42	   A^2 -> H(U1(d, k), d)
28.58/10.42	   A^2 -> H(U1(d, k), k)
28.58/10.42	   A^2 -> H(U1(e, e), c)
28.58/10.42	   A^2 -> H(U1(e, c), e)
28.58/10.42	   A^2 -> H(U1(c, e), e)
28.58/10.42	   A^2 -> H(U1(c, k), e)
28.58/10.42	   A^2 -> H(c, U1(e, e))
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.42	   A^2 -> H(d, b)
28.58/10.42	   A^2 -> H(d, U1(e, d))
28.58/10.42	   A^2 -> H(d, U1(d, e))
28.58/10.42	   A^2 -> H(d, c)
28.58/10.42	   A^2 -> H(d, U1(e, k))
28.58/10.42	   A^2 -> H(d, U1(k, e))
28.58/10.42	   A^2 -> H(d, e)
28.58/10.42	   A^2 -> H(d, U1(k, k))
28.58/10.42	   A^2 -> H(a, d)
28.58/10.42	   A^2 -> H(a, k)
28.58/10.42	   A^2 -> H(U1(e, d), d)
28.58/10.42	   A^2 -> H(U1(e, d), k)
28.58/10.42	   A^2 -> H(U1(d, e), d)
28.58/10.42	   A^2 -> H(U1(d, e), k)
28.58/10.42	
28.58/10.42	The TRS R consists of the following rules:
28.58/10.42	
28.58/10.42	   f(x) -> U1(x, x)
28.58/10.42	   U1(e, x) -> x
28.58/10.42	   a -> c
28.58/10.42	   a -> d
28.58/10.42	   b -> c
28.58/10.42	   b -> d
28.58/10.42	   d -> k
28.58/10.42	   c -> e
28.58/10.42	   c -> k
28.58/10.42	
28.58/10.42	Q is empty.
28.58/10.42	We have to consider all minimal (P,Q,R)-chains.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2499) TransformationProof (EQUIVALENT)
28.58/10.42	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.42	
28.58/10.42	   (A^2 -> H(U1(k, e), U1(k, k)),A^2 -> H(U1(k, e), U1(k, k)))
28.58/10.42	
28.58/10.42	
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2500)
28.58/10.42	Obligation:
28.58/10.42	Q DP problem:
28.58/10.42	The TRS P consists of the following rules:
28.58/10.42	
28.58/10.42	   H(x, x) -> G(x, x, f(k))
28.58/10.42	   G(d, x, x) -> A^2
28.58/10.42	   A^2 -> H(f(c), f(c))
28.58/10.42	   A^2 -> H(f(d), f(d))
28.58/10.42	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.42	   A^2 -> H(f(e), f(e))
28.58/10.42	   A^2 -> H(f(k), f(k))
28.58/10.42	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.42	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.42	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.42	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.42	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.42	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.42	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.42	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.42	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.42	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.42	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(d, c), d)
28.58/10.42	   A^2 -> H(U1(d, c), k)
28.58/10.42	   A^2 -> H(U1(a, e), d)
28.58/10.42	   A^2 -> H(U1(a, e), k)
28.58/10.42	   A^2 -> H(U1(a, k), d)
28.58/10.42	   A^2 -> H(U1(a, k), k)
28.58/10.42	   A^2 -> H(k, U1(e, b))
28.58/10.42	   A^2 -> H(k, U1(c, d))
28.58/10.42	   A^2 -> H(k, U1(d, c))
28.58/10.42	   A^2 -> H(k, U1(b, e))
28.58/10.42	   A^2 -> H(k, U1(b, k))
28.58/10.42	   A^2 -> H(k, U1(e, c))
28.58/10.42	   A^2 -> H(k, U1(c, e))
28.58/10.42	   A^2 -> H(k, U1(c, k))
28.58/10.42	   A^2 -> H(k, U1(e, e))
28.58/10.42	   A^2 -> H(k, U1(d, k))
28.58/10.42	   A^2 -> H(c, b)
28.58/10.42	   A^2 -> H(c, U1(e, d))
28.58/10.42	   A^2 -> H(c, U1(d, e))
28.58/10.42	   A^2 -> H(c, c)
28.58/10.42	   A^2 -> H(c, U1(e, k))
28.58/10.42	   A^2 -> H(c, U1(k, e))
28.58/10.42	   A^2 -> H(c, e)
28.58/10.42	   A^2 -> H(c, U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, k), b)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(e, k), c)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.42	   A^2 -> H(U1(e, k), e)
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, c), d)
28.58/10.42	   A^2 -> H(U1(e, c), k)
28.58/10.42	   A^2 -> H(U1(k, e), b)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, e), c)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(k, c), d)
28.58/10.42	   A^2 -> H(U1(c, e), d)
28.58/10.42	   A^2 -> H(U1(c, e), k)
28.58/10.42	   A^2 -> H(U1(c, k), d)
28.58/10.42	   A^2 -> H(U1(c, k), k)
28.58/10.42	   A^2 -> H(e, b)
28.58/10.42	   A^2 -> H(e, U1(e, d))
28.58/10.42	   A^2 -> H(e, U1(d, e))
28.58/10.42	   A^2 -> H(e, c)
28.58/10.42	   A^2 -> H(e, U1(e, k))
28.58/10.42	   A^2 -> H(e, e)
28.58/10.42	   A^2 -> H(U1(e, e), d)
28.58/10.42	   A^2 -> H(U1(e, e), k)
28.58/10.42	   A^2 -> H(U1(k, k), d)
28.58/10.42	   A^2 -> H(U1(k, k), b)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, k), c)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, d), d)
28.58/10.42	   A^2 -> H(U1(d, k), d)
28.58/10.42	   A^2 -> H(U1(d, k), k)
28.58/10.42	   A^2 -> H(U1(e, e), c)
28.58/10.42	   A^2 -> H(U1(e, c), e)
28.58/10.42	   A^2 -> H(U1(c, e), e)
28.58/10.42	   A^2 -> H(U1(c, k), e)
28.58/10.42	   A^2 -> H(c, U1(e, e))
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.42	   A^2 -> H(d, b)
28.58/10.42	   A^2 -> H(d, U1(e, d))
28.58/10.42	   A^2 -> H(d, U1(d, e))
28.58/10.42	   A^2 -> H(d, c)
28.58/10.42	   A^2 -> H(d, U1(e, k))
28.58/10.42	   A^2 -> H(d, U1(k, e))
28.58/10.42	   A^2 -> H(d, e)
28.58/10.42	   A^2 -> H(d, U1(k, k))
28.58/10.42	   A^2 -> H(a, d)
28.58/10.42	   A^2 -> H(a, k)
28.58/10.42	   A^2 -> H(U1(e, d), d)
28.58/10.42	   A^2 -> H(U1(e, d), k)
28.58/10.42	   A^2 -> H(U1(d, e), d)
28.58/10.42	   A^2 -> H(U1(d, e), k)
28.58/10.42	   A^2 -> H(U1(k, e), U1(k, k))
28.58/10.42	
28.58/10.42	The TRS R consists of the following rules:
28.58/10.42	
28.58/10.42	   f(x) -> U1(x, x)
28.58/10.42	   U1(e, x) -> x
28.58/10.42	   a -> c
28.58/10.42	   a -> d
28.58/10.42	   b -> c
28.58/10.42	   b -> d
28.58/10.42	   d -> k
28.58/10.42	   c -> e
28.58/10.42	   c -> k
28.58/10.42	
28.58/10.42	Q is empty.
28.58/10.42	We have to consider all minimal (P,Q,R)-chains.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2501) DependencyGraphProof (EQUIVALENT)
28.58/10.42	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2502)
28.58/10.42	Obligation:
28.58/10.42	Q DP problem:
28.58/10.42	The TRS P consists of the following rules:
28.58/10.42	
28.58/10.42	   G(d, x, x) -> A^2
28.58/10.42	   A^2 -> H(f(c), f(c))
28.58/10.42	   H(x, x) -> G(x, x, f(k))
28.58/10.42	   A^2 -> H(f(d), f(d))
28.58/10.42	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.42	   A^2 -> H(f(e), f(e))
28.58/10.42	   A^2 -> H(f(k), f(k))
28.58/10.42	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.42	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.42	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.42	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.42	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.42	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.42	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.42	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.42	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.42	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.42	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(d, c), d)
28.58/10.42	   A^2 -> H(U1(d, c), k)
28.58/10.42	   A^2 -> H(U1(a, e), d)
28.58/10.42	   A^2 -> H(U1(a, e), k)
28.58/10.42	   A^2 -> H(U1(a, k), d)
28.58/10.42	   A^2 -> H(U1(a, k), k)
28.58/10.42	   A^2 -> H(k, U1(e, b))
28.58/10.42	   A^2 -> H(k, U1(c, d))
28.58/10.42	   A^2 -> H(k, U1(d, c))
28.58/10.42	   A^2 -> H(k, U1(b, e))
28.58/10.42	   A^2 -> H(k, U1(b, k))
28.58/10.42	   A^2 -> H(k, U1(e, c))
28.58/10.42	   A^2 -> H(k, U1(c, e))
28.58/10.42	   A^2 -> H(k, U1(c, k))
28.58/10.42	   A^2 -> H(k, U1(e, e))
28.58/10.42	   A^2 -> H(k, U1(d, k))
28.58/10.42	   A^2 -> H(c, b)
28.58/10.42	   A^2 -> H(c, U1(e, d))
28.58/10.42	   A^2 -> H(c, U1(d, e))
28.58/10.42	   A^2 -> H(c, c)
28.58/10.42	   A^2 -> H(c, U1(e, k))
28.58/10.42	   A^2 -> H(c, U1(k, e))
28.58/10.42	   A^2 -> H(c, e)
28.58/10.42	   A^2 -> H(c, U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, k), b)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(e, k), c)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.42	   A^2 -> H(U1(e, k), e)
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, c), d)
28.58/10.42	   A^2 -> H(U1(e, c), k)
28.58/10.42	   A^2 -> H(U1(k, e), b)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, e), c)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(k, c), d)
28.58/10.42	   A^2 -> H(U1(c, e), d)
28.58/10.42	   A^2 -> H(U1(c, e), k)
28.58/10.42	   A^2 -> H(U1(c, k), d)
28.58/10.42	   A^2 -> H(U1(c, k), k)
28.58/10.42	   A^2 -> H(e, b)
28.58/10.42	   A^2 -> H(e, U1(e, d))
28.58/10.42	   A^2 -> H(e, U1(d, e))
28.58/10.42	   A^2 -> H(e, c)
28.58/10.42	   A^2 -> H(e, U1(e, k))
28.58/10.42	   A^2 -> H(e, e)
28.58/10.42	   A^2 -> H(U1(e, e), d)
28.58/10.42	   A^2 -> H(U1(e, e), k)
28.58/10.42	   A^2 -> H(U1(k, k), d)
28.58/10.42	   A^2 -> H(U1(k, k), b)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, k), c)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, d), d)
28.58/10.42	   A^2 -> H(U1(d, k), d)
28.58/10.42	   A^2 -> H(U1(d, k), k)
28.58/10.42	   A^2 -> H(U1(e, e), c)
28.58/10.42	   A^2 -> H(U1(e, c), e)
28.58/10.42	   A^2 -> H(U1(c, e), e)
28.58/10.42	   A^2 -> H(U1(c, k), e)
28.58/10.42	   A^2 -> H(c, U1(e, e))
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.42	   A^2 -> H(d, b)
28.58/10.42	   A^2 -> H(d, U1(e, d))
28.58/10.42	   A^2 -> H(d, U1(d, e))
28.58/10.42	   A^2 -> H(d, c)
28.58/10.42	   A^2 -> H(d, U1(e, k))
28.58/10.42	   A^2 -> H(d, U1(k, e))
28.58/10.42	   A^2 -> H(d, e)
28.58/10.42	   A^2 -> H(d, U1(k, k))
28.58/10.42	   A^2 -> H(a, d)
28.58/10.42	   A^2 -> H(a, k)
28.58/10.42	   A^2 -> H(U1(e, d), d)
28.58/10.42	   A^2 -> H(U1(e, d), k)
28.58/10.42	   A^2 -> H(U1(d, e), d)
28.58/10.42	   A^2 -> H(U1(d, e), k)
28.58/10.42	
28.58/10.42	The TRS R consists of the following rules:
28.58/10.42	
28.58/10.42	   f(x) -> U1(x, x)
28.58/10.42	   U1(e, x) -> x
28.58/10.42	   a -> c
28.58/10.42	   a -> d
28.58/10.42	   b -> c
28.58/10.42	   b -> d
28.58/10.42	   d -> k
28.58/10.42	   c -> e
28.58/10.42	   c -> k
28.58/10.42	
28.58/10.42	Q is empty.
28.58/10.42	We have to consider all minimal (P,Q,R)-chains.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2503) TransformationProof (EQUIVALENT)
28.58/10.42	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.42	
28.58/10.42	   (A^2 -> H(U1(k, c), d),A^2 -> H(U1(k, c), d))
28.58/10.42	   (A^2 -> H(U1(d, e), d),A^2 -> H(U1(d, e), d))
28.58/10.42	   (A^2 -> H(U1(d, k), d),A^2 -> H(U1(d, k), d))
28.58/10.42	   (A^2 -> H(U1(d, c), k),A^2 -> H(U1(d, c), k))
28.58/10.42	
28.58/10.42	
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2504)
28.58/10.42	Obligation:
28.58/10.42	Q DP problem:
28.58/10.42	The TRS P consists of the following rules:
28.58/10.42	
28.58/10.42	   G(d, x, x) -> A^2
28.58/10.42	   A^2 -> H(f(c), f(c))
28.58/10.42	   H(x, x) -> G(x, x, f(k))
28.58/10.42	   A^2 -> H(f(d), f(d))
28.58/10.42	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.42	   A^2 -> H(f(e), f(e))
28.58/10.42	   A^2 -> H(f(k), f(k))
28.58/10.42	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.42	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.42	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.42	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.42	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.42	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.42	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.42	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.42	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.42	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.42	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(d, c), k)
28.58/10.42	   A^2 -> H(U1(a, e), d)
28.58/10.42	   A^2 -> H(U1(a, e), k)
28.58/10.42	   A^2 -> H(U1(a, k), d)
28.58/10.42	   A^2 -> H(U1(a, k), k)
28.58/10.42	   A^2 -> H(k, U1(e, b))
28.58/10.42	   A^2 -> H(k, U1(c, d))
28.58/10.42	   A^2 -> H(k, U1(d, c))
28.58/10.42	   A^2 -> H(k, U1(b, e))
28.58/10.42	   A^2 -> H(k, U1(b, k))
28.58/10.42	   A^2 -> H(k, U1(e, c))
28.58/10.42	   A^2 -> H(k, U1(c, e))
28.58/10.42	   A^2 -> H(k, U1(c, k))
28.58/10.42	   A^2 -> H(k, U1(e, e))
28.58/10.42	   A^2 -> H(k, U1(d, k))
28.58/10.42	   A^2 -> H(c, b)
28.58/10.42	   A^2 -> H(c, U1(e, d))
28.58/10.42	   A^2 -> H(c, U1(d, e))
28.58/10.42	   A^2 -> H(c, c)
28.58/10.42	   A^2 -> H(c, U1(e, k))
28.58/10.42	   A^2 -> H(c, U1(k, e))
28.58/10.42	   A^2 -> H(c, e)
28.58/10.42	   A^2 -> H(c, U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, k), b)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(e, k), c)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.42	   A^2 -> H(U1(e, k), e)
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, c), d)
28.58/10.42	   A^2 -> H(U1(e, c), k)
28.58/10.42	   A^2 -> H(U1(k, e), b)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, e), c)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(k, c), d)
28.58/10.42	   A^2 -> H(U1(c, e), d)
28.58/10.42	   A^2 -> H(U1(c, e), k)
28.58/10.42	   A^2 -> H(U1(c, k), d)
28.58/10.42	   A^2 -> H(U1(c, k), k)
28.58/10.42	   A^2 -> H(e, b)
28.58/10.42	   A^2 -> H(e, U1(e, d))
28.58/10.42	   A^2 -> H(e, U1(d, e))
28.58/10.42	   A^2 -> H(e, c)
28.58/10.42	   A^2 -> H(e, U1(e, k))
28.58/10.42	   A^2 -> H(e, e)
28.58/10.42	   A^2 -> H(U1(e, e), d)
28.58/10.42	   A^2 -> H(U1(e, e), k)
28.58/10.42	   A^2 -> H(U1(k, k), d)
28.58/10.42	   A^2 -> H(U1(k, k), b)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, k), c)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, d), d)
28.58/10.42	   A^2 -> H(U1(d, k), d)
28.58/10.42	   A^2 -> H(U1(d, k), k)
28.58/10.42	   A^2 -> H(U1(e, e), c)
28.58/10.42	   A^2 -> H(U1(e, c), e)
28.58/10.42	   A^2 -> H(U1(c, e), e)
28.58/10.42	   A^2 -> H(U1(c, k), e)
28.58/10.42	   A^2 -> H(c, U1(e, e))
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.42	   A^2 -> H(d, b)
28.58/10.42	   A^2 -> H(d, U1(e, d))
28.58/10.42	   A^2 -> H(d, U1(d, e))
28.58/10.42	   A^2 -> H(d, c)
28.58/10.42	   A^2 -> H(d, U1(e, k))
28.58/10.42	   A^2 -> H(d, U1(k, e))
28.58/10.42	   A^2 -> H(d, e)
28.58/10.42	   A^2 -> H(d, U1(k, k))
28.58/10.42	   A^2 -> H(a, d)
28.58/10.42	   A^2 -> H(a, k)
28.58/10.42	   A^2 -> H(U1(e, d), d)
28.58/10.42	   A^2 -> H(U1(e, d), k)
28.58/10.42	   A^2 -> H(U1(d, e), d)
28.58/10.42	   A^2 -> H(U1(d, e), k)
28.58/10.42	
28.58/10.42	The TRS R consists of the following rules:
28.58/10.42	
28.58/10.42	   f(x) -> U1(x, x)
28.58/10.42	   U1(e, x) -> x
28.58/10.42	   a -> c
28.58/10.42	   a -> d
28.58/10.42	   b -> c
28.58/10.42	   b -> d
28.58/10.42	   d -> k
28.58/10.42	   c -> e
28.58/10.42	   c -> k
28.58/10.42	
28.58/10.42	Q is empty.
28.58/10.42	We have to consider all minimal (P,Q,R)-chains.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2505) TransformationProof (EQUIVALENT)
28.58/10.42	By narrowing [LPAR04] the rule A^2 -> H(U1(d, c), k) at position [] we obtained the following new rules [LPAR04]:
28.58/10.42	
28.58/10.42	   (A^2 -> H(U1(k, c), k),A^2 -> H(U1(k, c), k))
28.58/10.42	   (A^2 -> H(U1(d, e), k),A^2 -> H(U1(d, e), k))
28.58/10.42	   (A^2 -> H(U1(d, k), k),A^2 -> H(U1(d, k), k))
28.58/10.42	
28.58/10.42	
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2506)
28.58/10.42	Obligation:
28.58/10.42	Q DP problem:
28.58/10.42	The TRS P consists of the following rules:
28.58/10.42	
28.58/10.42	   G(d, x, x) -> A^2
28.58/10.42	   A^2 -> H(f(c), f(c))
28.58/10.42	   H(x, x) -> G(x, x, f(k))
28.58/10.42	   A^2 -> H(f(d), f(d))
28.58/10.42	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.42	   A^2 -> H(f(e), f(e))
28.58/10.42	   A^2 -> H(f(k), f(k))
28.58/10.42	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.42	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.42	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.42	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.42	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.42	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.42	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.42	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.42	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.42	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.42	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(a, e), d)
28.58/10.42	   A^2 -> H(U1(a, e), k)
28.58/10.42	   A^2 -> H(U1(a, k), d)
28.58/10.42	   A^2 -> H(U1(a, k), k)
28.58/10.42	   A^2 -> H(k, U1(e, b))
28.58/10.42	   A^2 -> H(k, U1(c, d))
28.58/10.42	   A^2 -> H(k, U1(d, c))
28.58/10.42	   A^2 -> H(k, U1(b, e))
28.58/10.42	   A^2 -> H(k, U1(b, k))
28.58/10.42	   A^2 -> H(k, U1(e, c))
28.58/10.42	   A^2 -> H(k, U1(c, e))
28.58/10.42	   A^2 -> H(k, U1(c, k))
28.58/10.42	   A^2 -> H(k, U1(e, e))
28.58/10.42	   A^2 -> H(k, U1(d, k))
28.58/10.42	   A^2 -> H(c, b)
28.58/10.42	   A^2 -> H(c, U1(e, d))
28.58/10.42	   A^2 -> H(c, U1(d, e))
28.58/10.42	   A^2 -> H(c, c)
28.58/10.42	   A^2 -> H(c, U1(e, k))
28.58/10.42	   A^2 -> H(c, U1(k, e))
28.58/10.42	   A^2 -> H(c, e)
28.58/10.42	   A^2 -> H(c, U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, k), b)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(e, k), c)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.42	   A^2 -> H(U1(e, k), e)
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, c), d)
28.58/10.42	   A^2 -> H(U1(e, c), k)
28.58/10.42	   A^2 -> H(U1(k, e), b)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, e), c)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(k, c), d)
28.58/10.42	   A^2 -> H(U1(c, e), d)
28.58/10.42	   A^2 -> H(U1(c, e), k)
28.58/10.42	   A^2 -> H(U1(c, k), d)
28.58/10.42	   A^2 -> H(U1(c, k), k)
28.58/10.42	   A^2 -> H(e, b)
28.58/10.42	   A^2 -> H(e, U1(e, d))
28.58/10.42	   A^2 -> H(e, U1(d, e))
28.58/10.42	   A^2 -> H(e, c)
28.58/10.42	   A^2 -> H(e, U1(e, k))
28.58/10.42	   A^2 -> H(e, e)
28.58/10.42	   A^2 -> H(U1(e, e), d)
28.58/10.42	   A^2 -> H(U1(e, e), k)
28.58/10.42	   A^2 -> H(U1(k, k), d)
28.58/10.42	   A^2 -> H(U1(k, k), b)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, k), c)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, d), d)
28.58/10.42	   A^2 -> H(U1(d, k), d)
28.58/10.42	   A^2 -> H(U1(d, k), k)
28.58/10.42	   A^2 -> H(U1(e, e), c)
28.58/10.42	   A^2 -> H(U1(e, c), e)
28.58/10.42	   A^2 -> H(U1(c, e), e)
28.58/10.42	   A^2 -> H(U1(c, k), e)
28.58/10.42	   A^2 -> H(c, U1(e, e))
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.42	   A^2 -> H(d, b)
28.58/10.42	   A^2 -> H(d, U1(e, d))
28.58/10.42	   A^2 -> H(d, U1(d, e))
28.58/10.42	   A^2 -> H(d, c)
28.58/10.42	   A^2 -> H(d, U1(e, k))
28.58/10.42	   A^2 -> H(d, U1(k, e))
28.58/10.42	   A^2 -> H(d, e)
28.58/10.42	   A^2 -> H(d, U1(k, k))
28.58/10.42	   A^2 -> H(a, d)
28.58/10.42	   A^2 -> H(a, k)
28.58/10.42	   A^2 -> H(U1(e, d), d)
28.58/10.42	   A^2 -> H(U1(e, d), k)
28.58/10.42	   A^2 -> H(U1(d, e), d)
28.58/10.42	   A^2 -> H(U1(d, e), k)
28.58/10.42	   A^2 -> H(U1(k, c), k)
28.58/10.42	
28.58/10.42	The TRS R consists of the following rules:
28.58/10.42	
28.58/10.42	   f(x) -> U1(x, x)
28.58/10.42	   U1(e, x) -> x
28.58/10.42	   a -> c
28.58/10.42	   a -> d
28.58/10.42	   b -> c
28.58/10.42	   b -> d
28.58/10.42	   d -> k
28.58/10.42	   c -> e
28.58/10.42	   c -> k
28.58/10.42	
28.58/10.42	Q is empty.
28.58/10.42	We have to consider all minimal (P,Q,R)-chains.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2507) DependencyGraphProof (EQUIVALENT)
28.58/10.42	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2508)
28.58/10.42	Obligation:
28.58/10.42	Q DP problem:
28.58/10.42	The TRS P consists of the following rules:
28.58/10.42	
28.58/10.42	   A^2 -> H(f(c), f(c))
28.58/10.42	   H(x, x) -> G(x, x, f(k))
28.58/10.42	   G(d, x, x) -> A^2
28.58/10.42	   A^2 -> H(f(d), f(d))
28.58/10.42	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.42	   A^2 -> H(f(e), f(e))
28.58/10.42	   A^2 -> H(f(k), f(k))
28.58/10.42	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.42	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.42	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.42	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.42	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.42	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.42	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.42	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.42	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.42	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.42	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(a, e), d)
28.58/10.42	   A^2 -> H(U1(a, e), k)
28.58/10.42	   A^2 -> H(U1(a, k), d)
28.58/10.42	   A^2 -> H(U1(a, k), k)
28.58/10.42	   A^2 -> H(k, U1(e, b))
28.58/10.42	   A^2 -> H(k, U1(c, d))
28.58/10.42	   A^2 -> H(k, U1(d, c))
28.58/10.42	   A^2 -> H(k, U1(b, e))
28.58/10.42	   A^2 -> H(k, U1(b, k))
28.58/10.42	   A^2 -> H(k, U1(e, c))
28.58/10.42	   A^2 -> H(k, U1(c, e))
28.58/10.42	   A^2 -> H(k, U1(c, k))
28.58/10.42	   A^2 -> H(k, U1(e, e))
28.58/10.42	   A^2 -> H(k, U1(d, k))
28.58/10.42	   A^2 -> H(c, b)
28.58/10.42	   A^2 -> H(c, U1(e, d))
28.58/10.42	   A^2 -> H(c, U1(d, e))
28.58/10.42	   A^2 -> H(c, c)
28.58/10.42	   A^2 -> H(c, U1(e, k))
28.58/10.42	   A^2 -> H(c, U1(k, e))
28.58/10.42	   A^2 -> H(c, e)
28.58/10.42	   A^2 -> H(c, U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, k), b)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(e, k), c)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.42	   A^2 -> H(U1(e, k), e)
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, c), d)
28.58/10.42	   A^2 -> H(U1(e, c), k)
28.58/10.42	   A^2 -> H(U1(k, e), b)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, e), c)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(k, c), d)
28.58/10.42	   A^2 -> H(U1(c, e), d)
28.58/10.42	   A^2 -> H(U1(c, e), k)
28.58/10.42	   A^2 -> H(U1(c, k), d)
28.58/10.42	   A^2 -> H(U1(c, k), k)
28.58/10.42	   A^2 -> H(e, b)
28.58/10.42	   A^2 -> H(e, U1(e, d))
28.58/10.42	   A^2 -> H(e, U1(d, e))
28.58/10.42	   A^2 -> H(e, c)
28.58/10.42	   A^2 -> H(e, U1(e, k))
28.58/10.42	   A^2 -> H(e, e)
28.58/10.42	   A^2 -> H(U1(e, e), d)
28.58/10.42	   A^2 -> H(U1(e, e), k)
28.58/10.42	   A^2 -> H(U1(k, k), d)
28.58/10.42	   A^2 -> H(U1(k, k), b)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, k), c)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, d), d)
28.58/10.42	   A^2 -> H(U1(d, k), d)
28.58/10.42	   A^2 -> H(U1(d, k), k)
28.58/10.42	   A^2 -> H(U1(e, e), c)
28.58/10.42	   A^2 -> H(U1(e, c), e)
28.58/10.42	   A^2 -> H(U1(c, e), e)
28.58/10.42	   A^2 -> H(U1(c, k), e)
28.58/10.42	   A^2 -> H(c, U1(e, e))
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.42	   A^2 -> H(d, b)
28.58/10.42	   A^2 -> H(d, U1(e, d))
28.58/10.42	   A^2 -> H(d, U1(d, e))
28.58/10.42	   A^2 -> H(d, c)
28.58/10.42	   A^2 -> H(d, U1(e, k))
28.58/10.42	   A^2 -> H(d, U1(k, e))
28.58/10.42	   A^2 -> H(d, e)
28.58/10.42	   A^2 -> H(d, U1(k, k))
28.58/10.42	   A^2 -> H(a, d)
28.58/10.42	   A^2 -> H(a, k)
28.58/10.42	   A^2 -> H(U1(e, d), d)
28.58/10.42	   A^2 -> H(U1(e, d), k)
28.58/10.42	   A^2 -> H(U1(d, e), d)
28.58/10.42	   A^2 -> H(U1(d, e), k)
28.58/10.42	
28.58/10.42	The TRS R consists of the following rules:
28.58/10.42	
28.58/10.42	   f(x) -> U1(x, x)
28.58/10.42	   U1(e, x) -> x
28.58/10.42	   a -> c
28.58/10.42	   a -> d
28.58/10.42	   b -> c
28.58/10.42	   b -> d
28.58/10.42	   d -> k
28.58/10.42	   c -> e
28.58/10.42	   c -> k
28.58/10.42	
28.58/10.42	Q is empty.
28.58/10.42	We have to consider all minimal (P,Q,R)-chains.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2509) TransformationProof (EQUIVALENT)
28.58/10.42	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.42	
28.58/10.42	   (A^2 -> H(U1(c, e), d),A^2 -> H(U1(c, e), d))
28.58/10.42	   (A^2 -> H(U1(d, e), d),A^2 -> H(U1(d, e), d))
28.58/10.42	   (A^2 -> H(U1(a, e), k),A^2 -> H(U1(a, e), k))
28.58/10.42	
28.58/10.42	
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2510)
28.58/10.42	Obligation:
28.58/10.42	Q DP problem:
28.58/10.42	The TRS P consists of the following rules:
28.58/10.42	
28.58/10.42	   A^2 -> H(f(c), f(c))
28.58/10.42	   H(x, x) -> G(x, x, f(k))
28.58/10.42	   G(d, x, x) -> A^2
28.58/10.42	   A^2 -> H(f(d), f(d))
28.58/10.42	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.42	   A^2 -> H(f(e), f(e))
28.58/10.42	   A^2 -> H(f(k), f(k))
28.58/10.42	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.42	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.42	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.42	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.42	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.42	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.42	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.42	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.42	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.42	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.42	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(a, e), k)
28.58/10.42	   A^2 -> H(U1(a, k), d)
28.58/10.42	   A^2 -> H(U1(a, k), k)
28.58/10.42	   A^2 -> H(k, U1(e, b))
28.58/10.42	   A^2 -> H(k, U1(c, d))
28.58/10.42	   A^2 -> H(k, U1(d, c))
28.58/10.42	   A^2 -> H(k, U1(b, e))
28.58/10.42	   A^2 -> H(k, U1(b, k))
28.58/10.42	   A^2 -> H(k, U1(e, c))
28.58/10.42	   A^2 -> H(k, U1(c, e))
28.58/10.42	   A^2 -> H(k, U1(c, k))
28.58/10.42	   A^2 -> H(k, U1(e, e))
28.58/10.42	   A^2 -> H(k, U1(d, k))
28.58/10.42	   A^2 -> H(c, b)
28.58/10.42	   A^2 -> H(c, U1(e, d))
28.58/10.42	   A^2 -> H(c, U1(d, e))
28.58/10.42	   A^2 -> H(c, c)
28.58/10.42	   A^2 -> H(c, U1(e, k))
28.58/10.42	   A^2 -> H(c, U1(k, e))
28.58/10.42	   A^2 -> H(c, e)
28.58/10.42	   A^2 -> H(c, U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, k), b)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(e, k), c)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.42	   A^2 -> H(U1(e, k), e)
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, c), d)
28.58/10.42	   A^2 -> H(U1(e, c), k)
28.58/10.42	   A^2 -> H(U1(k, e), b)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, e), c)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(k, c), d)
28.58/10.42	   A^2 -> H(U1(c, e), d)
28.58/10.42	   A^2 -> H(U1(c, e), k)
28.58/10.42	   A^2 -> H(U1(c, k), d)
28.58/10.42	   A^2 -> H(U1(c, k), k)
28.58/10.42	   A^2 -> H(e, b)
28.58/10.42	   A^2 -> H(e, U1(e, d))
28.58/10.42	   A^2 -> H(e, U1(d, e))
28.58/10.42	   A^2 -> H(e, c)
28.58/10.42	   A^2 -> H(e, U1(e, k))
28.58/10.42	   A^2 -> H(e, e)
28.58/10.42	   A^2 -> H(U1(e, e), d)
28.58/10.42	   A^2 -> H(U1(e, e), k)
28.58/10.42	   A^2 -> H(U1(k, k), d)
28.58/10.42	   A^2 -> H(U1(k, k), b)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, k), c)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, d), d)
28.58/10.42	   A^2 -> H(U1(d, k), d)
28.58/10.42	   A^2 -> H(U1(d, k), k)
28.58/10.42	   A^2 -> H(U1(e, e), c)
28.58/10.42	   A^2 -> H(U1(e, c), e)
28.58/10.42	   A^2 -> H(U1(c, e), e)
28.58/10.42	   A^2 -> H(U1(c, k), e)
28.58/10.42	   A^2 -> H(c, U1(e, e))
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.42	   A^2 -> H(d, b)
28.58/10.42	   A^2 -> H(d, U1(e, d))
28.58/10.42	   A^2 -> H(d, U1(d, e))
28.58/10.42	   A^2 -> H(d, c)
28.58/10.42	   A^2 -> H(d, U1(e, k))
28.58/10.42	   A^2 -> H(d, U1(k, e))
28.58/10.42	   A^2 -> H(d, e)
28.58/10.42	   A^2 -> H(d, U1(k, k))
28.58/10.42	   A^2 -> H(a, d)
28.58/10.42	   A^2 -> H(a, k)
28.58/10.42	   A^2 -> H(U1(e, d), d)
28.58/10.42	   A^2 -> H(U1(e, d), k)
28.58/10.42	   A^2 -> H(U1(d, e), d)
28.58/10.42	   A^2 -> H(U1(d, e), k)
28.58/10.42	
28.58/10.42	The TRS R consists of the following rules:
28.58/10.42	
28.58/10.42	   f(x) -> U1(x, x)
28.58/10.42	   U1(e, x) -> x
28.58/10.42	   a -> c
28.58/10.42	   a -> d
28.58/10.42	   b -> c
28.58/10.42	   b -> d
28.58/10.42	   d -> k
28.58/10.42	   c -> e
28.58/10.42	   c -> k
28.58/10.42	
28.58/10.42	Q is empty.
28.58/10.42	We have to consider all minimal (P,Q,R)-chains.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2511) TransformationProof (EQUIVALENT)
28.58/10.42	By narrowing [LPAR04] the rule A^2 -> H(U1(a, e), k) at position [] we obtained the following new rules [LPAR04]:
28.58/10.42	
28.58/10.42	   (A^2 -> H(U1(c, e), k),A^2 -> H(U1(c, e), k))
28.58/10.42	   (A^2 -> H(U1(d, e), k),A^2 -> H(U1(d, e), k))
28.58/10.42	
28.58/10.42	
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2512)
28.58/10.42	Obligation:
28.58/10.42	Q DP problem:
28.58/10.42	The TRS P consists of the following rules:
28.58/10.42	
28.58/10.42	   A^2 -> H(f(c), f(c))
28.58/10.42	   H(x, x) -> G(x, x, f(k))
28.58/10.42	   G(d, x, x) -> A^2
28.58/10.42	   A^2 -> H(f(d), f(d))
28.58/10.42	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.42	   A^2 -> H(f(e), f(e))
28.58/10.42	   A^2 -> H(f(k), f(k))
28.58/10.42	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.42	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.42	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.42	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.42	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.42	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.42	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.42	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.42	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.42	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.42	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(a, k), d)
28.58/10.42	   A^2 -> H(U1(a, k), k)
28.58/10.42	   A^2 -> H(k, U1(e, b))
28.58/10.42	   A^2 -> H(k, U1(c, d))
28.58/10.42	   A^2 -> H(k, U1(d, c))
28.58/10.42	   A^2 -> H(k, U1(b, e))
28.58/10.42	   A^2 -> H(k, U1(b, k))
28.58/10.42	   A^2 -> H(k, U1(e, c))
28.58/10.42	   A^2 -> H(k, U1(c, e))
28.58/10.42	   A^2 -> H(k, U1(c, k))
28.58/10.42	   A^2 -> H(k, U1(e, e))
28.58/10.42	   A^2 -> H(k, U1(d, k))
28.58/10.42	   A^2 -> H(c, b)
28.58/10.42	   A^2 -> H(c, U1(e, d))
28.58/10.42	   A^2 -> H(c, U1(d, e))
28.58/10.42	   A^2 -> H(c, c)
28.58/10.42	   A^2 -> H(c, U1(e, k))
28.58/10.42	   A^2 -> H(c, U1(k, e))
28.58/10.42	   A^2 -> H(c, e)
28.58/10.42	   A^2 -> H(c, U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, k), b)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(e, k), c)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.42	   A^2 -> H(U1(e, k), e)
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, c), d)
28.58/10.42	   A^2 -> H(U1(e, c), k)
28.58/10.42	   A^2 -> H(U1(k, e), b)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, e), c)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.42	   A^2 -> H(U1(k, c), d)
28.58/10.42	   A^2 -> H(U1(c, e), d)
28.58/10.42	   A^2 -> H(U1(c, e), k)
28.58/10.42	   A^2 -> H(U1(c, k), d)
28.58/10.42	   A^2 -> H(U1(c, k), k)
28.58/10.42	   A^2 -> H(e, b)
28.58/10.42	   A^2 -> H(e, U1(e, d))
28.58/10.42	   A^2 -> H(e, U1(d, e))
28.58/10.42	   A^2 -> H(e, c)
28.58/10.42	   A^2 -> H(e, U1(e, k))
28.58/10.42	   A^2 -> H(e, e)
28.58/10.42	   A^2 -> H(U1(e, e), d)
28.58/10.42	   A^2 -> H(U1(e, e), k)
28.58/10.42	   A^2 -> H(U1(k, k), d)
28.58/10.42	   A^2 -> H(U1(k, k), b)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, k), c)
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, d), d)
28.58/10.42	   A^2 -> H(U1(d, k), d)
28.58/10.42	   A^2 -> H(U1(d, k), k)
28.58/10.42	   A^2 -> H(U1(e, e), c)
28.58/10.42	   A^2 -> H(U1(e, c), e)
28.58/10.42	   A^2 -> H(U1(c, e), e)
28.58/10.42	   A^2 -> H(U1(c, k), e)
28.58/10.42	   A^2 -> H(c, U1(e, e))
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.42	   A^2 -> H(d, b)
28.58/10.42	   A^2 -> H(d, U1(e, d))
28.58/10.42	   A^2 -> H(d, U1(d, e))
28.58/10.42	   A^2 -> H(d, c)
28.58/10.42	   A^2 -> H(d, U1(e, k))
28.58/10.42	   A^2 -> H(d, U1(k, e))
28.58/10.42	   A^2 -> H(d, e)
28.58/10.42	   A^2 -> H(d, U1(k, k))
28.58/10.42	   A^2 -> H(a, d)
28.58/10.42	   A^2 -> H(a, k)
28.58/10.42	   A^2 -> H(U1(e, d), d)
28.58/10.42	   A^2 -> H(U1(e, d), k)
28.58/10.42	   A^2 -> H(U1(d, e), d)
28.58/10.42	   A^2 -> H(U1(d, e), k)
28.58/10.42	
28.58/10.42	The TRS R consists of the following rules:
28.58/10.42	
28.58/10.42	   f(x) -> U1(x, x)
28.58/10.42	   U1(e, x) -> x
28.58/10.42	   a -> c
28.58/10.42	   a -> d
28.58/10.42	   b -> c
28.58/10.42	   b -> d
28.58/10.42	   d -> k
28.58/10.42	   c -> e
28.58/10.42	   c -> k
28.58/10.42	
28.58/10.42	Q is empty.
28.58/10.42	We have to consider all minimal (P,Q,R)-chains.
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2513) TransformationProof (EQUIVALENT)
28.58/10.42	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.42	
28.58/10.42	   (A^2 -> H(U1(c, k), d),A^2 -> H(U1(c, k), d))
28.58/10.42	   (A^2 -> H(U1(d, k), d),A^2 -> H(U1(d, k), d))
28.58/10.42	   (A^2 -> H(U1(a, k), k),A^2 -> H(U1(a, k), k))
28.58/10.42	
28.58/10.42	
28.58/10.42	----------------------------------------
28.58/10.42	
28.58/10.42	(2514)
28.58/10.42	Obligation:
28.58/10.42	Q DP problem:
28.58/10.42	The TRS P consists of the following rules:
28.58/10.42	
28.58/10.42	   A^2 -> H(f(c), f(c))
28.58/10.42	   H(x, x) -> G(x, x, f(k))
28.58/10.42	   G(d, x, x) -> A^2
28.58/10.42	   A^2 -> H(f(d), f(d))
28.58/10.42	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.42	   A^2 -> H(f(e), f(e))
28.58/10.42	   A^2 -> H(f(k), f(k))
28.58/10.42	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.42	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.42	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.42	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.42	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.42	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.42	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.42	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.42	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.42	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.42	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.42	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(a, k), k)
28.58/10.42	   A^2 -> H(k, U1(e, b))
28.58/10.42	   A^2 -> H(k, U1(c, d))
28.58/10.42	   A^2 -> H(k, U1(d, c))
28.58/10.42	   A^2 -> H(k, U1(b, e))
28.58/10.42	   A^2 -> H(k, U1(b, k))
28.58/10.42	   A^2 -> H(k, U1(e, c))
28.58/10.42	   A^2 -> H(k, U1(c, e))
28.58/10.42	   A^2 -> H(k, U1(c, k))
28.58/10.42	   A^2 -> H(k, U1(e, e))
28.58/10.42	   A^2 -> H(k, U1(d, k))
28.58/10.42	   A^2 -> H(c, b)
28.58/10.42	   A^2 -> H(c, U1(e, d))
28.58/10.42	   A^2 -> H(c, U1(d, e))
28.58/10.42	   A^2 -> H(c, c)
28.58/10.42	   A^2 -> H(c, U1(e, k))
28.58/10.42	   A^2 -> H(c, U1(k, e))
28.58/10.42	   A^2 -> H(c, e)
28.58/10.42	   A^2 -> H(c, U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, k), b)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.42	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.42	   A^2 -> H(U1(e, k), c)
28.58/10.42	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.42	   A^2 -> H(U1(e, k), e)
28.58/10.42	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.42	   A^2 -> H(U1(e, c), d)
28.58/10.42	   A^2 -> H(U1(e, c), k)
28.58/10.42	   A^2 -> H(U1(k, e), b)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.42	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.42	   A^2 -> H(U1(k, e), c)
28.58/10.42	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.42	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.43	   A^2 -> H(U1(k, c), d)
28.58/10.43	   A^2 -> H(U1(c, e), d)
28.58/10.43	   A^2 -> H(U1(c, e), k)
28.58/10.43	   A^2 -> H(U1(c, k), d)
28.58/10.43	   A^2 -> H(U1(c, k), k)
28.58/10.43	   A^2 -> H(e, b)
28.58/10.43	   A^2 -> H(e, U1(e, d))
28.58/10.43	   A^2 -> H(e, U1(d, e))
28.58/10.43	   A^2 -> H(e, c)
28.58/10.43	   A^2 -> H(e, U1(e, k))
28.58/10.43	   A^2 -> H(e, e)
28.58/10.43	   A^2 -> H(U1(e, e), d)
28.58/10.43	   A^2 -> H(U1(e, e), k)
28.58/10.43	   A^2 -> H(U1(k, k), d)
28.58/10.43	   A^2 -> H(U1(k, k), b)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, k), c)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, d), d)
28.58/10.43	   A^2 -> H(U1(d, k), d)
28.58/10.43	   A^2 -> H(U1(d, k), k)
28.58/10.43	   A^2 -> H(U1(e, e), c)
28.58/10.43	   A^2 -> H(U1(e, c), e)
28.58/10.43	   A^2 -> H(U1(c, e), e)
28.58/10.43	   A^2 -> H(U1(c, k), e)
28.58/10.43	   A^2 -> H(c, U1(e, e))
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.43	   A^2 -> H(d, b)
28.58/10.43	   A^2 -> H(d, U1(e, d))
28.58/10.43	   A^2 -> H(d, U1(d, e))
28.58/10.43	   A^2 -> H(d, c)
28.58/10.43	   A^2 -> H(d, U1(e, k))
28.58/10.43	   A^2 -> H(d, U1(k, e))
28.58/10.43	   A^2 -> H(d, e)
28.58/10.43	   A^2 -> H(d, U1(k, k))
28.58/10.43	   A^2 -> H(a, d)
28.58/10.43	   A^2 -> H(a, k)
28.58/10.43	   A^2 -> H(U1(e, d), d)
28.58/10.43	   A^2 -> H(U1(e, d), k)
28.58/10.43	   A^2 -> H(U1(d, e), d)
28.58/10.43	   A^2 -> H(U1(d, e), k)
28.58/10.43	
28.58/10.43	The TRS R consists of the following rules:
28.58/10.43	
28.58/10.43	   f(x) -> U1(x, x)
28.58/10.43	   U1(e, x) -> x
28.58/10.43	   a -> c
28.58/10.43	   a -> d
28.58/10.43	   b -> c
28.58/10.43	   b -> d
28.58/10.43	   d -> k
28.58/10.43	   c -> e
28.58/10.43	   c -> k
28.58/10.43	
28.58/10.43	Q is empty.
28.58/10.43	We have to consider all minimal (P,Q,R)-chains.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2515) TransformationProof (EQUIVALENT)
28.58/10.43	By narrowing [LPAR04] the rule A^2 -> H(U1(a, k), k) at position [] we obtained the following new rules [LPAR04]:
28.58/10.43	
28.58/10.43	   (A^2 -> H(U1(c, k), k),A^2 -> H(U1(c, k), k))
28.58/10.43	   (A^2 -> H(U1(d, k), k),A^2 -> H(U1(d, k), k))
28.58/10.43	
28.58/10.43	
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2516)
28.58/10.43	Obligation:
28.58/10.43	Q DP problem:
28.58/10.43	The TRS P consists of the following rules:
28.58/10.43	
28.58/10.43	   A^2 -> H(f(c), f(c))
28.58/10.43	   H(x, x) -> G(x, x, f(k))
28.58/10.43	   G(d, x, x) -> A^2
28.58/10.43	   A^2 -> H(f(d), f(d))
28.58/10.43	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.43	   A^2 -> H(f(e), f(e))
28.58/10.43	   A^2 -> H(f(k), f(k))
28.58/10.43	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.43	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.43	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.43	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.43	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.43	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.43	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.43	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.43	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.43	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.43	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.43	   A^2 -> H(k, U1(e, b))
28.58/10.43	   A^2 -> H(k, U1(c, d))
28.58/10.43	   A^2 -> H(k, U1(d, c))
28.58/10.43	   A^2 -> H(k, U1(b, e))
28.58/10.43	   A^2 -> H(k, U1(b, k))
28.58/10.43	   A^2 -> H(k, U1(e, c))
28.58/10.43	   A^2 -> H(k, U1(c, e))
28.58/10.43	   A^2 -> H(k, U1(c, k))
28.58/10.43	   A^2 -> H(k, U1(e, e))
28.58/10.43	   A^2 -> H(k, U1(d, k))
28.58/10.43	   A^2 -> H(c, b)
28.58/10.43	   A^2 -> H(c, U1(e, d))
28.58/10.43	   A^2 -> H(c, U1(d, e))
28.58/10.43	   A^2 -> H(c, c)
28.58/10.43	   A^2 -> H(c, U1(e, k))
28.58/10.43	   A^2 -> H(c, U1(k, e))
28.58/10.43	   A^2 -> H(c, e)
28.58/10.43	   A^2 -> H(c, U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, k), b)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(e, k), c)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.43	   A^2 -> H(U1(e, k), e)
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, c), d)
28.58/10.43	   A^2 -> H(U1(e, c), k)
28.58/10.43	   A^2 -> H(U1(k, e), b)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, e), c)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.43	   A^2 -> H(U1(k, c), d)
28.58/10.43	   A^2 -> H(U1(c, e), d)
28.58/10.43	   A^2 -> H(U1(c, e), k)
28.58/10.43	   A^2 -> H(U1(c, k), d)
28.58/10.43	   A^2 -> H(U1(c, k), k)
28.58/10.43	   A^2 -> H(e, b)
28.58/10.43	   A^2 -> H(e, U1(e, d))
28.58/10.43	   A^2 -> H(e, U1(d, e))
28.58/10.43	   A^2 -> H(e, c)
28.58/10.43	   A^2 -> H(e, U1(e, k))
28.58/10.43	   A^2 -> H(e, e)
28.58/10.43	   A^2 -> H(U1(e, e), d)
28.58/10.43	   A^2 -> H(U1(e, e), k)
28.58/10.43	   A^2 -> H(U1(k, k), d)
28.58/10.43	   A^2 -> H(U1(k, k), b)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, k), c)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, d), d)
28.58/10.43	   A^2 -> H(U1(d, k), d)
28.58/10.43	   A^2 -> H(U1(d, k), k)
28.58/10.43	   A^2 -> H(U1(e, e), c)
28.58/10.43	   A^2 -> H(U1(e, c), e)
28.58/10.43	   A^2 -> H(U1(c, e), e)
28.58/10.43	   A^2 -> H(U1(c, k), e)
28.58/10.43	   A^2 -> H(c, U1(e, e))
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.43	   A^2 -> H(d, b)
28.58/10.43	   A^2 -> H(d, U1(e, d))
28.58/10.43	   A^2 -> H(d, U1(d, e))
28.58/10.43	   A^2 -> H(d, c)
28.58/10.43	   A^2 -> H(d, U1(e, k))
28.58/10.43	   A^2 -> H(d, U1(k, e))
28.58/10.43	   A^2 -> H(d, e)
28.58/10.43	   A^2 -> H(d, U1(k, k))
28.58/10.43	   A^2 -> H(a, d)
28.58/10.43	   A^2 -> H(a, k)
28.58/10.43	   A^2 -> H(U1(e, d), d)
28.58/10.43	   A^2 -> H(U1(e, d), k)
28.58/10.43	   A^2 -> H(U1(d, e), d)
28.58/10.43	   A^2 -> H(U1(d, e), k)
28.58/10.43	
28.58/10.43	The TRS R consists of the following rules:
28.58/10.43	
28.58/10.43	   f(x) -> U1(x, x)
28.58/10.43	   U1(e, x) -> x
28.58/10.43	   a -> c
28.58/10.43	   a -> d
28.58/10.43	   b -> c
28.58/10.43	   b -> d
28.58/10.43	   d -> k
28.58/10.43	   c -> e
28.58/10.43	   c -> k
28.58/10.43	
28.58/10.43	Q is empty.
28.58/10.43	We have to consider all minimal (P,Q,R)-chains.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2517) TransformationProof (EQUIVALENT)
28.58/10.43	By narrowing [LPAR04] the rule A^2 -> H(k, U1(e, b)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.43	
28.58/10.43	   (A^2 -> H(k, b),A^2 -> H(k, b))
28.58/10.43	   (A^2 -> H(k, U1(e, c)),A^2 -> H(k, U1(e, c)))
28.58/10.43	   (A^2 -> H(k, U1(e, d)),A^2 -> H(k, U1(e, d)))
28.58/10.43	
28.58/10.43	
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2518)
28.58/10.43	Obligation:
28.58/10.43	Q DP problem:
28.58/10.43	The TRS P consists of the following rules:
28.58/10.43	
28.58/10.43	   A^2 -> H(f(c), f(c))
28.58/10.43	   H(x, x) -> G(x, x, f(k))
28.58/10.43	   G(d, x, x) -> A^2
28.58/10.43	   A^2 -> H(f(d), f(d))
28.58/10.43	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.43	   A^2 -> H(f(e), f(e))
28.58/10.43	   A^2 -> H(f(k), f(k))
28.58/10.43	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.43	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.43	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.43	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.43	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.43	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.43	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.43	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.43	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.43	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.43	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.43	   A^2 -> H(k, U1(c, d))
28.58/10.43	   A^2 -> H(k, U1(d, c))
28.58/10.43	   A^2 -> H(k, U1(b, e))
28.58/10.43	   A^2 -> H(k, U1(b, k))
28.58/10.43	   A^2 -> H(k, U1(e, c))
28.58/10.43	   A^2 -> H(k, U1(c, e))
28.58/10.43	   A^2 -> H(k, U1(c, k))
28.58/10.43	   A^2 -> H(k, U1(e, e))
28.58/10.43	   A^2 -> H(k, U1(d, k))
28.58/10.43	   A^2 -> H(c, b)
28.58/10.43	   A^2 -> H(c, U1(e, d))
28.58/10.43	   A^2 -> H(c, U1(d, e))
28.58/10.43	   A^2 -> H(c, c)
28.58/10.43	   A^2 -> H(c, U1(e, k))
28.58/10.43	   A^2 -> H(c, U1(k, e))
28.58/10.43	   A^2 -> H(c, e)
28.58/10.43	   A^2 -> H(c, U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, k), b)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(e, k), c)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.43	   A^2 -> H(U1(e, k), e)
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, c), d)
28.58/10.43	   A^2 -> H(U1(e, c), k)
28.58/10.43	   A^2 -> H(U1(k, e), b)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, e), c)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.43	   A^2 -> H(U1(k, c), d)
28.58/10.43	   A^2 -> H(U1(c, e), d)
28.58/10.43	   A^2 -> H(U1(c, e), k)
28.58/10.43	   A^2 -> H(U1(c, k), d)
28.58/10.43	   A^2 -> H(U1(c, k), k)
28.58/10.43	   A^2 -> H(e, b)
28.58/10.43	   A^2 -> H(e, U1(e, d))
28.58/10.43	   A^2 -> H(e, U1(d, e))
28.58/10.43	   A^2 -> H(e, c)
28.58/10.43	   A^2 -> H(e, U1(e, k))
28.58/10.43	   A^2 -> H(e, e)
28.58/10.43	   A^2 -> H(U1(e, e), d)
28.58/10.43	   A^2 -> H(U1(e, e), k)
28.58/10.43	   A^2 -> H(U1(k, k), d)
28.58/10.43	   A^2 -> H(U1(k, k), b)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, k), c)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, d), d)
28.58/10.43	   A^2 -> H(U1(d, k), d)
28.58/10.43	   A^2 -> H(U1(d, k), k)
28.58/10.43	   A^2 -> H(U1(e, e), c)
28.58/10.43	   A^2 -> H(U1(e, c), e)
28.58/10.43	   A^2 -> H(U1(c, e), e)
28.58/10.43	   A^2 -> H(U1(c, k), e)
28.58/10.43	   A^2 -> H(c, U1(e, e))
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.43	   A^2 -> H(d, b)
28.58/10.43	   A^2 -> H(d, U1(e, d))
28.58/10.43	   A^2 -> H(d, U1(d, e))
28.58/10.43	   A^2 -> H(d, c)
28.58/10.43	   A^2 -> H(d, U1(e, k))
28.58/10.43	   A^2 -> H(d, U1(k, e))
28.58/10.43	   A^2 -> H(d, e)
28.58/10.43	   A^2 -> H(d, U1(k, k))
28.58/10.43	   A^2 -> H(a, d)
28.58/10.43	   A^2 -> H(a, k)
28.58/10.43	   A^2 -> H(U1(e, d), d)
28.58/10.43	   A^2 -> H(U1(e, d), k)
28.58/10.43	   A^2 -> H(U1(d, e), d)
28.58/10.43	   A^2 -> H(U1(d, e), k)
28.58/10.43	   A^2 -> H(k, b)
28.58/10.43	   A^2 -> H(k, U1(e, d))
28.58/10.43	
28.58/10.43	The TRS R consists of the following rules:
28.58/10.43	
28.58/10.43	   f(x) -> U1(x, x)
28.58/10.43	   U1(e, x) -> x
28.58/10.43	   a -> c
28.58/10.43	   a -> d
28.58/10.43	   b -> c
28.58/10.43	   b -> d
28.58/10.43	   d -> k
28.58/10.43	   c -> e
28.58/10.43	   c -> k
28.58/10.43	
28.58/10.43	Q is empty.
28.58/10.43	We have to consider all minimal (P,Q,R)-chains.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2519) TransformationProof (EQUIVALENT)
28.58/10.43	By narrowing [LPAR04] the rule A^2 -> H(k, U1(c, d)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.43	
28.58/10.43	   (A^2 -> H(k, U1(e, d)),A^2 -> H(k, U1(e, d)))
28.58/10.43	   (A^2 -> H(k, U1(k, d)),A^2 -> H(k, U1(k, d)))
28.58/10.43	   (A^2 -> H(k, U1(c, k)),A^2 -> H(k, U1(c, k)))
28.58/10.43	
28.58/10.43	
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2520)
28.58/10.43	Obligation:
28.58/10.43	Q DP problem:
28.58/10.43	The TRS P consists of the following rules:
28.58/10.43	
28.58/10.43	   A^2 -> H(f(c), f(c))
28.58/10.43	   H(x, x) -> G(x, x, f(k))
28.58/10.43	   G(d, x, x) -> A^2
28.58/10.43	   A^2 -> H(f(d), f(d))
28.58/10.43	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.43	   A^2 -> H(f(e), f(e))
28.58/10.43	   A^2 -> H(f(k), f(k))
28.58/10.43	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.43	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.43	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.43	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.43	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.43	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.43	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.43	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.43	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.43	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.43	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.43	   A^2 -> H(k, U1(d, c))
28.58/10.43	   A^2 -> H(k, U1(b, e))
28.58/10.43	   A^2 -> H(k, U1(b, k))
28.58/10.43	   A^2 -> H(k, U1(e, c))
28.58/10.43	   A^2 -> H(k, U1(c, e))
28.58/10.43	   A^2 -> H(k, U1(c, k))
28.58/10.43	   A^2 -> H(k, U1(e, e))
28.58/10.43	   A^2 -> H(k, U1(d, k))
28.58/10.43	   A^2 -> H(c, b)
28.58/10.43	   A^2 -> H(c, U1(e, d))
28.58/10.43	   A^2 -> H(c, U1(d, e))
28.58/10.43	   A^2 -> H(c, c)
28.58/10.43	   A^2 -> H(c, U1(e, k))
28.58/10.43	   A^2 -> H(c, U1(k, e))
28.58/10.43	   A^2 -> H(c, e)
28.58/10.43	   A^2 -> H(c, U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, k), b)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(e, k), c)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.43	   A^2 -> H(U1(e, k), e)
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, c), d)
28.58/10.43	   A^2 -> H(U1(e, c), k)
28.58/10.43	   A^2 -> H(U1(k, e), b)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, e), c)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.43	   A^2 -> H(U1(k, c), d)
28.58/10.43	   A^2 -> H(U1(c, e), d)
28.58/10.43	   A^2 -> H(U1(c, e), k)
28.58/10.43	   A^2 -> H(U1(c, k), d)
28.58/10.43	   A^2 -> H(U1(c, k), k)
28.58/10.43	   A^2 -> H(e, b)
28.58/10.43	   A^2 -> H(e, U1(e, d))
28.58/10.43	   A^2 -> H(e, U1(d, e))
28.58/10.43	   A^2 -> H(e, c)
28.58/10.43	   A^2 -> H(e, U1(e, k))
28.58/10.43	   A^2 -> H(e, e)
28.58/10.43	   A^2 -> H(U1(e, e), d)
28.58/10.43	   A^2 -> H(U1(e, e), k)
28.58/10.43	   A^2 -> H(U1(k, k), d)
28.58/10.43	   A^2 -> H(U1(k, k), b)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, k), c)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, d), d)
28.58/10.43	   A^2 -> H(U1(d, k), d)
28.58/10.43	   A^2 -> H(U1(d, k), k)
28.58/10.43	   A^2 -> H(U1(e, e), c)
28.58/10.43	   A^2 -> H(U1(e, c), e)
28.58/10.43	   A^2 -> H(U1(c, e), e)
28.58/10.43	   A^2 -> H(U1(c, k), e)
28.58/10.43	   A^2 -> H(c, U1(e, e))
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.43	   A^2 -> H(d, b)
28.58/10.43	   A^2 -> H(d, U1(e, d))
28.58/10.43	   A^2 -> H(d, U1(d, e))
28.58/10.43	   A^2 -> H(d, c)
28.58/10.43	   A^2 -> H(d, U1(e, k))
28.58/10.43	   A^2 -> H(d, U1(k, e))
28.58/10.43	   A^2 -> H(d, e)
28.58/10.43	   A^2 -> H(d, U1(k, k))
28.58/10.43	   A^2 -> H(a, d)
28.58/10.43	   A^2 -> H(a, k)
28.58/10.43	   A^2 -> H(U1(e, d), d)
28.58/10.43	   A^2 -> H(U1(e, d), k)
28.58/10.43	   A^2 -> H(U1(d, e), d)
28.58/10.43	   A^2 -> H(U1(d, e), k)
28.58/10.43	   A^2 -> H(k, b)
28.58/10.43	   A^2 -> H(k, U1(e, d))
28.58/10.43	   A^2 -> H(k, U1(k, d))
28.58/10.43	
28.58/10.43	The TRS R consists of the following rules:
28.58/10.43	
28.58/10.43	   f(x) -> U1(x, x)
28.58/10.43	   U1(e, x) -> x
28.58/10.43	   a -> c
28.58/10.43	   a -> d
28.58/10.43	   b -> c
28.58/10.43	   b -> d
28.58/10.43	   d -> k
28.58/10.43	   c -> e
28.58/10.43	   c -> k
28.58/10.43	
28.58/10.43	Q is empty.
28.58/10.43	We have to consider all minimal (P,Q,R)-chains.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2521) DependencyGraphProof (EQUIVALENT)
28.58/10.43	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2522)
28.58/10.43	Obligation:
28.58/10.43	Q DP problem:
28.58/10.43	The TRS P consists of the following rules:
28.58/10.43	
28.58/10.43	   H(x, x) -> G(x, x, f(k))
28.58/10.43	   G(d, x, x) -> A^2
28.58/10.43	   A^2 -> H(f(c), f(c))
28.58/10.43	   A^2 -> H(f(d), f(d))
28.58/10.43	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.43	   A^2 -> H(f(e), f(e))
28.58/10.43	   A^2 -> H(f(k), f(k))
28.58/10.43	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.43	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.43	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.43	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.43	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.43	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.43	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.43	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.43	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.43	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.43	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.43	   A^2 -> H(k, U1(d, c))
28.58/10.43	   A^2 -> H(k, U1(b, e))
28.58/10.43	   A^2 -> H(k, U1(b, k))
28.58/10.43	   A^2 -> H(k, U1(e, c))
28.58/10.43	   A^2 -> H(k, U1(c, e))
28.58/10.43	   A^2 -> H(k, U1(c, k))
28.58/10.43	   A^2 -> H(k, U1(e, e))
28.58/10.43	   A^2 -> H(k, U1(d, k))
28.58/10.43	   A^2 -> H(c, b)
28.58/10.43	   A^2 -> H(c, U1(e, d))
28.58/10.43	   A^2 -> H(c, U1(d, e))
28.58/10.43	   A^2 -> H(c, c)
28.58/10.43	   A^2 -> H(c, U1(e, k))
28.58/10.43	   A^2 -> H(c, U1(k, e))
28.58/10.43	   A^2 -> H(c, e)
28.58/10.43	   A^2 -> H(c, U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, k), b)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(e, k), c)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.43	   A^2 -> H(U1(e, k), e)
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, c), d)
28.58/10.43	   A^2 -> H(U1(e, c), k)
28.58/10.43	   A^2 -> H(U1(k, e), b)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, e), c)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.43	   A^2 -> H(U1(k, c), d)
28.58/10.43	   A^2 -> H(U1(c, e), d)
28.58/10.43	   A^2 -> H(U1(c, e), k)
28.58/10.43	   A^2 -> H(U1(c, k), d)
28.58/10.43	   A^2 -> H(U1(c, k), k)
28.58/10.43	   A^2 -> H(e, b)
28.58/10.43	   A^2 -> H(e, U1(e, d))
28.58/10.43	   A^2 -> H(e, U1(d, e))
28.58/10.43	   A^2 -> H(e, c)
28.58/10.43	   A^2 -> H(e, U1(e, k))
28.58/10.43	   A^2 -> H(e, e)
28.58/10.43	   A^2 -> H(U1(e, e), d)
28.58/10.43	   A^2 -> H(U1(e, e), k)
28.58/10.43	   A^2 -> H(U1(k, k), d)
28.58/10.43	   A^2 -> H(U1(k, k), b)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, k), c)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, d), d)
28.58/10.43	   A^2 -> H(U1(d, k), d)
28.58/10.43	   A^2 -> H(U1(d, k), k)
28.58/10.43	   A^2 -> H(U1(e, e), c)
28.58/10.43	   A^2 -> H(U1(e, c), e)
28.58/10.43	   A^2 -> H(U1(c, e), e)
28.58/10.43	   A^2 -> H(U1(c, k), e)
28.58/10.43	   A^2 -> H(c, U1(e, e))
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.43	   A^2 -> H(d, b)
28.58/10.43	   A^2 -> H(d, U1(e, d))
28.58/10.43	   A^2 -> H(d, U1(d, e))
28.58/10.43	   A^2 -> H(d, c)
28.58/10.43	   A^2 -> H(d, U1(e, k))
28.58/10.43	   A^2 -> H(d, U1(k, e))
28.58/10.43	   A^2 -> H(d, e)
28.58/10.43	   A^2 -> H(d, U1(k, k))
28.58/10.43	   A^2 -> H(a, d)
28.58/10.43	   A^2 -> H(a, k)
28.58/10.43	   A^2 -> H(U1(e, d), d)
28.58/10.43	   A^2 -> H(U1(e, d), k)
28.58/10.43	   A^2 -> H(U1(d, e), d)
28.58/10.43	   A^2 -> H(U1(d, e), k)
28.58/10.43	   A^2 -> H(k, b)
28.58/10.43	   A^2 -> H(k, U1(e, d))
28.58/10.43	
28.58/10.43	The TRS R consists of the following rules:
28.58/10.43	
28.58/10.43	   f(x) -> U1(x, x)
28.58/10.43	   U1(e, x) -> x
28.58/10.43	   a -> c
28.58/10.43	   a -> d
28.58/10.43	   b -> c
28.58/10.43	   b -> d
28.58/10.43	   d -> k
28.58/10.43	   c -> e
28.58/10.43	   c -> k
28.58/10.43	
28.58/10.43	Q is empty.
28.58/10.43	We have to consider all minimal (P,Q,R)-chains.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2523) TransformationProof (EQUIVALENT)
28.58/10.43	By narrowing [LPAR04] the rule A^2 -> H(k, U1(d, c)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.43	
28.58/10.43	   (A^2 -> H(k, U1(k, c)),A^2 -> H(k, U1(k, c)))
28.58/10.43	   (A^2 -> H(k, U1(d, e)),A^2 -> H(k, U1(d, e)))
28.58/10.43	   (A^2 -> H(k, U1(d, k)),A^2 -> H(k, U1(d, k)))
28.58/10.43	
28.58/10.43	
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2524)
28.58/10.43	Obligation:
28.58/10.43	Q DP problem:
28.58/10.43	The TRS P consists of the following rules:
28.58/10.43	
28.58/10.43	   H(x, x) -> G(x, x, f(k))
28.58/10.43	   G(d, x, x) -> A^2
28.58/10.43	   A^2 -> H(f(c), f(c))
28.58/10.43	   A^2 -> H(f(d), f(d))
28.58/10.43	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.43	   A^2 -> H(f(e), f(e))
28.58/10.43	   A^2 -> H(f(k), f(k))
28.58/10.43	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.43	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.43	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.43	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.43	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.43	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.43	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.43	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.43	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.43	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.43	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.43	   A^2 -> H(k, U1(b, e))
28.58/10.43	   A^2 -> H(k, U1(b, k))
28.58/10.43	   A^2 -> H(k, U1(e, c))
28.58/10.43	   A^2 -> H(k, U1(c, e))
28.58/10.43	   A^2 -> H(k, U1(c, k))
28.58/10.43	   A^2 -> H(k, U1(e, e))
28.58/10.43	   A^2 -> H(k, U1(d, k))
28.58/10.43	   A^2 -> H(c, b)
28.58/10.43	   A^2 -> H(c, U1(e, d))
28.58/10.43	   A^2 -> H(c, U1(d, e))
28.58/10.43	   A^2 -> H(c, c)
28.58/10.43	   A^2 -> H(c, U1(e, k))
28.58/10.43	   A^2 -> H(c, U1(k, e))
28.58/10.43	   A^2 -> H(c, e)
28.58/10.43	   A^2 -> H(c, U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, k), b)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(e, k), c)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.43	   A^2 -> H(U1(e, k), e)
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, c), d)
28.58/10.43	   A^2 -> H(U1(e, c), k)
28.58/10.43	   A^2 -> H(U1(k, e), b)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, e), c)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.43	   A^2 -> H(U1(k, c), d)
28.58/10.43	   A^2 -> H(U1(c, e), d)
28.58/10.43	   A^2 -> H(U1(c, e), k)
28.58/10.43	   A^2 -> H(U1(c, k), d)
28.58/10.43	   A^2 -> H(U1(c, k), k)
28.58/10.43	   A^2 -> H(e, b)
28.58/10.43	   A^2 -> H(e, U1(e, d))
28.58/10.43	   A^2 -> H(e, U1(d, e))
28.58/10.43	   A^2 -> H(e, c)
28.58/10.43	   A^2 -> H(e, U1(e, k))
28.58/10.43	   A^2 -> H(e, e)
28.58/10.43	   A^2 -> H(U1(e, e), d)
28.58/10.43	   A^2 -> H(U1(e, e), k)
28.58/10.43	   A^2 -> H(U1(k, k), d)
28.58/10.43	   A^2 -> H(U1(k, k), b)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, k), c)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, d), d)
28.58/10.43	   A^2 -> H(U1(d, k), d)
28.58/10.43	   A^2 -> H(U1(d, k), k)
28.58/10.43	   A^2 -> H(U1(e, e), c)
28.58/10.43	   A^2 -> H(U1(e, c), e)
28.58/10.43	   A^2 -> H(U1(c, e), e)
28.58/10.43	   A^2 -> H(U1(c, k), e)
28.58/10.43	   A^2 -> H(c, U1(e, e))
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.43	   A^2 -> H(d, b)
28.58/10.43	   A^2 -> H(d, U1(e, d))
28.58/10.43	   A^2 -> H(d, U1(d, e))
28.58/10.43	   A^2 -> H(d, c)
28.58/10.43	   A^2 -> H(d, U1(e, k))
28.58/10.43	   A^2 -> H(d, U1(k, e))
28.58/10.43	   A^2 -> H(d, e)
28.58/10.43	   A^2 -> H(d, U1(k, k))
28.58/10.43	   A^2 -> H(a, d)
28.58/10.43	   A^2 -> H(a, k)
28.58/10.43	   A^2 -> H(U1(e, d), d)
28.58/10.43	   A^2 -> H(U1(e, d), k)
28.58/10.43	   A^2 -> H(U1(d, e), d)
28.58/10.43	   A^2 -> H(U1(d, e), k)
28.58/10.43	   A^2 -> H(k, b)
28.58/10.43	   A^2 -> H(k, U1(e, d))
28.58/10.43	   A^2 -> H(k, U1(k, c))
28.58/10.43	   A^2 -> H(k, U1(d, e))
28.58/10.43	
28.58/10.43	The TRS R consists of the following rules:
28.58/10.43	
28.58/10.43	   f(x) -> U1(x, x)
28.58/10.43	   U1(e, x) -> x
28.58/10.43	   a -> c
28.58/10.43	   a -> d
28.58/10.43	   b -> c
28.58/10.43	   b -> d
28.58/10.43	   d -> k
28.58/10.43	   c -> e
28.58/10.43	   c -> k
28.58/10.43	
28.58/10.43	Q is empty.
28.58/10.43	We have to consider all minimal (P,Q,R)-chains.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2525) DependencyGraphProof (EQUIVALENT)
28.58/10.43	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2526)
28.58/10.43	Obligation:
28.58/10.43	Q DP problem:
28.58/10.43	The TRS P consists of the following rules:
28.58/10.43	
28.58/10.43	   G(d, x, x) -> A^2
28.58/10.43	   A^2 -> H(f(c), f(c))
28.58/10.43	   H(x, x) -> G(x, x, f(k))
28.58/10.43	   A^2 -> H(f(d), f(d))
28.58/10.43	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.43	   A^2 -> H(f(e), f(e))
28.58/10.43	   A^2 -> H(f(k), f(k))
28.58/10.43	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.43	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.43	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.43	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.43	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.43	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.43	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.43	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.43	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.43	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.43	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.43	   A^2 -> H(k, U1(b, e))
28.58/10.43	   A^2 -> H(k, U1(b, k))
28.58/10.43	   A^2 -> H(k, U1(e, c))
28.58/10.43	   A^2 -> H(k, U1(c, e))
28.58/10.43	   A^2 -> H(k, U1(c, k))
28.58/10.43	   A^2 -> H(k, U1(e, e))
28.58/10.43	   A^2 -> H(k, U1(d, k))
28.58/10.43	   A^2 -> H(c, b)
28.58/10.43	   A^2 -> H(c, U1(e, d))
28.58/10.43	   A^2 -> H(c, U1(d, e))
28.58/10.43	   A^2 -> H(c, c)
28.58/10.43	   A^2 -> H(c, U1(e, k))
28.58/10.43	   A^2 -> H(c, U1(k, e))
28.58/10.43	   A^2 -> H(c, e)
28.58/10.43	   A^2 -> H(c, U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, k), b)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(e, k), c)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.43	   A^2 -> H(U1(e, k), e)
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, c), d)
28.58/10.43	   A^2 -> H(U1(e, c), k)
28.58/10.43	   A^2 -> H(U1(k, e), b)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, e), c)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.43	   A^2 -> H(U1(k, c), d)
28.58/10.43	   A^2 -> H(U1(c, e), d)
28.58/10.43	   A^2 -> H(U1(c, e), k)
28.58/10.43	   A^2 -> H(U1(c, k), d)
28.58/10.43	   A^2 -> H(U1(c, k), k)
28.58/10.43	   A^2 -> H(e, b)
28.58/10.43	   A^2 -> H(e, U1(e, d))
28.58/10.43	   A^2 -> H(e, U1(d, e))
28.58/10.43	   A^2 -> H(e, c)
28.58/10.43	   A^2 -> H(e, U1(e, k))
28.58/10.43	   A^2 -> H(e, e)
28.58/10.43	   A^2 -> H(U1(e, e), d)
28.58/10.43	   A^2 -> H(U1(e, e), k)
28.58/10.43	   A^2 -> H(U1(k, k), d)
28.58/10.43	   A^2 -> H(U1(k, k), b)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, k), c)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, d), d)
28.58/10.43	   A^2 -> H(U1(d, k), d)
28.58/10.43	   A^2 -> H(U1(d, k), k)
28.58/10.43	   A^2 -> H(U1(e, e), c)
28.58/10.43	   A^2 -> H(U1(e, c), e)
28.58/10.43	   A^2 -> H(U1(c, e), e)
28.58/10.43	   A^2 -> H(U1(c, k), e)
28.58/10.43	   A^2 -> H(c, U1(e, e))
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.43	   A^2 -> H(d, b)
28.58/10.43	   A^2 -> H(d, U1(e, d))
28.58/10.43	   A^2 -> H(d, U1(d, e))
28.58/10.43	   A^2 -> H(d, c)
28.58/10.43	   A^2 -> H(d, U1(e, k))
28.58/10.43	   A^2 -> H(d, U1(k, e))
28.58/10.43	   A^2 -> H(d, e)
28.58/10.43	   A^2 -> H(d, U1(k, k))
28.58/10.43	   A^2 -> H(a, d)
28.58/10.43	   A^2 -> H(a, k)
28.58/10.43	   A^2 -> H(U1(e, d), d)
28.58/10.43	   A^2 -> H(U1(e, d), k)
28.58/10.43	   A^2 -> H(U1(d, e), d)
28.58/10.43	   A^2 -> H(U1(d, e), k)
28.58/10.43	   A^2 -> H(k, b)
28.58/10.43	   A^2 -> H(k, U1(e, d))
28.58/10.43	   A^2 -> H(k, U1(d, e))
28.58/10.43	
28.58/10.43	The TRS R consists of the following rules:
28.58/10.43	
28.58/10.43	   f(x) -> U1(x, x)
28.58/10.43	   U1(e, x) -> x
28.58/10.43	   a -> c
28.58/10.43	   a -> d
28.58/10.43	   b -> c
28.58/10.43	   b -> d
28.58/10.43	   d -> k
28.58/10.43	   c -> e
28.58/10.43	   c -> k
28.58/10.43	
28.58/10.43	Q is empty.
28.58/10.43	We have to consider all minimal (P,Q,R)-chains.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2527) TransformationProof (EQUIVALENT)
28.58/10.43	By narrowing [LPAR04] the rule A^2 -> H(k, U1(b, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.43	
28.58/10.43	   (A^2 -> H(k, U1(c, e)),A^2 -> H(k, U1(c, e)))
28.58/10.43	   (A^2 -> H(k, U1(d, e)),A^2 -> H(k, U1(d, e)))
28.58/10.43	
28.58/10.43	
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2528)
28.58/10.43	Obligation:
28.58/10.43	Q DP problem:
28.58/10.43	The TRS P consists of the following rules:
28.58/10.43	
28.58/10.43	   G(d, x, x) -> A^2
28.58/10.43	   A^2 -> H(f(c), f(c))
28.58/10.43	   H(x, x) -> G(x, x, f(k))
28.58/10.43	   A^2 -> H(f(d), f(d))
28.58/10.43	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.43	   A^2 -> H(f(e), f(e))
28.58/10.43	   A^2 -> H(f(k), f(k))
28.58/10.43	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.43	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.43	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.43	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.43	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.43	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.43	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.43	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.43	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.43	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.43	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.43	   A^2 -> H(k, U1(b, k))
28.58/10.43	   A^2 -> H(k, U1(e, c))
28.58/10.43	   A^2 -> H(k, U1(c, e))
28.58/10.43	   A^2 -> H(k, U1(c, k))
28.58/10.43	   A^2 -> H(k, U1(e, e))
28.58/10.43	   A^2 -> H(k, U1(d, k))
28.58/10.43	   A^2 -> H(c, b)
28.58/10.43	   A^2 -> H(c, U1(e, d))
28.58/10.43	   A^2 -> H(c, U1(d, e))
28.58/10.43	   A^2 -> H(c, c)
28.58/10.43	   A^2 -> H(c, U1(e, k))
28.58/10.43	   A^2 -> H(c, U1(k, e))
28.58/10.43	   A^2 -> H(c, e)
28.58/10.43	   A^2 -> H(c, U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, k), b)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(e, k), c)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.43	   A^2 -> H(U1(e, k), e)
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, c), d)
28.58/10.43	   A^2 -> H(U1(e, c), k)
28.58/10.43	   A^2 -> H(U1(k, e), b)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, e), c)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.43	   A^2 -> H(U1(k, c), d)
28.58/10.43	   A^2 -> H(U1(c, e), d)
28.58/10.43	   A^2 -> H(U1(c, e), k)
28.58/10.43	   A^2 -> H(U1(c, k), d)
28.58/10.43	   A^2 -> H(U1(c, k), k)
28.58/10.43	   A^2 -> H(e, b)
28.58/10.43	   A^2 -> H(e, U1(e, d))
28.58/10.43	   A^2 -> H(e, U1(d, e))
28.58/10.43	   A^2 -> H(e, c)
28.58/10.43	   A^2 -> H(e, U1(e, k))
28.58/10.43	   A^2 -> H(e, e)
28.58/10.43	   A^2 -> H(U1(e, e), d)
28.58/10.43	   A^2 -> H(U1(e, e), k)
28.58/10.43	   A^2 -> H(U1(k, k), d)
28.58/10.43	   A^2 -> H(U1(k, k), b)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, k), c)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, d), d)
28.58/10.43	   A^2 -> H(U1(d, k), d)
28.58/10.43	   A^2 -> H(U1(d, k), k)
28.58/10.43	   A^2 -> H(U1(e, e), c)
28.58/10.43	   A^2 -> H(U1(e, c), e)
28.58/10.43	   A^2 -> H(U1(c, e), e)
28.58/10.43	   A^2 -> H(U1(c, k), e)
28.58/10.43	   A^2 -> H(c, U1(e, e))
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.43	   A^2 -> H(d, b)
28.58/10.43	   A^2 -> H(d, U1(e, d))
28.58/10.43	   A^2 -> H(d, U1(d, e))
28.58/10.43	   A^2 -> H(d, c)
28.58/10.43	   A^2 -> H(d, U1(e, k))
28.58/10.43	   A^2 -> H(d, U1(k, e))
28.58/10.43	   A^2 -> H(d, e)
28.58/10.43	   A^2 -> H(d, U1(k, k))
28.58/10.43	   A^2 -> H(a, d)
28.58/10.43	   A^2 -> H(a, k)
28.58/10.43	   A^2 -> H(U1(e, d), d)
28.58/10.43	   A^2 -> H(U1(e, d), k)
28.58/10.43	   A^2 -> H(U1(d, e), d)
28.58/10.43	   A^2 -> H(U1(d, e), k)
28.58/10.43	   A^2 -> H(k, b)
28.58/10.43	   A^2 -> H(k, U1(e, d))
28.58/10.43	   A^2 -> H(k, U1(d, e))
28.58/10.43	
28.58/10.43	The TRS R consists of the following rules:
28.58/10.43	
28.58/10.43	   f(x) -> U1(x, x)
28.58/10.43	   U1(e, x) -> x
28.58/10.43	   a -> c
28.58/10.43	   a -> d
28.58/10.43	   b -> c
28.58/10.43	   b -> d
28.58/10.43	   d -> k
28.58/10.43	   c -> e
28.58/10.43	   c -> k
28.58/10.43	
28.58/10.43	Q is empty.
28.58/10.43	We have to consider all minimal (P,Q,R)-chains.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2529) TransformationProof (EQUIVALENT)
28.58/10.43	By narrowing [LPAR04] the rule A^2 -> H(k, U1(b, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.43	
28.58/10.43	   (A^2 -> H(k, U1(c, k)),A^2 -> H(k, U1(c, k)))
28.58/10.43	   (A^2 -> H(k, U1(d, k)),A^2 -> H(k, U1(d, k)))
28.58/10.43	
28.58/10.43	
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2530)
28.58/10.43	Obligation:
28.58/10.43	Q DP problem:
28.58/10.43	The TRS P consists of the following rules:
28.58/10.43	
28.58/10.43	   G(d, x, x) -> A^2
28.58/10.43	   A^2 -> H(f(c), f(c))
28.58/10.43	   H(x, x) -> G(x, x, f(k))
28.58/10.43	   A^2 -> H(f(d), f(d))
28.58/10.43	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.43	   A^2 -> H(f(e), f(e))
28.58/10.43	   A^2 -> H(f(k), f(k))
28.58/10.43	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.43	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.43	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.43	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.43	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.43	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.43	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.43	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.43	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.43	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.43	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.43	   A^2 -> H(k, U1(e, c))
28.58/10.43	   A^2 -> H(k, U1(c, e))
28.58/10.43	   A^2 -> H(k, U1(c, k))
28.58/10.43	   A^2 -> H(k, U1(e, e))
28.58/10.43	   A^2 -> H(k, U1(d, k))
28.58/10.43	   A^2 -> H(c, b)
28.58/10.43	   A^2 -> H(c, U1(e, d))
28.58/10.43	   A^2 -> H(c, U1(d, e))
28.58/10.43	   A^2 -> H(c, c)
28.58/10.43	   A^2 -> H(c, U1(e, k))
28.58/10.43	   A^2 -> H(c, U1(k, e))
28.58/10.43	   A^2 -> H(c, e)
28.58/10.43	   A^2 -> H(c, U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, k), b)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(e, k), c)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.43	   A^2 -> H(U1(e, k), e)
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, c), d)
28.58/10.43	   A^2 -> H(U1(e, c), k)
28.58/10.43	   A^2 -> H(U1(k, e), b)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, e), c)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.43	   A^2 -> H(U1(k, c), d)
28.58/10.43	   A^2 -> H(U1(c, e), d)
28.58/10.43	   A^2 -> H(U1(c, e), k)
28.58/10.43	   A^2 -> H(U1(c, k), d)
28.58/10.43	   A^2 -> H(U1(c, k), k)
28.58/10.43	   A^2 -> H(e, b)
28.58/10.43	   A^2 -> H(e, U1(e, d))
28.58/10.43	   A^2 -> H(e, U1(d, e))
28.58/10.43	   A^2 -> H(e, c)
28.58/10.43	   A^2 -> H(e, U1(e, k))
28.58/10.43	   A^2 -> H(e, e)
28.58/10.43	   A^2 -> H(U1(e, e), d)
28.58/10.43	   A^2 -> H(U1(e, e), k)
28.58/10.43	   A^2 -> H(U1(k, k), d)
28.58/10.43	   A^2 -> H(U1(k, k), b)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, k), c)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, d), d)
28.58/10.43	   A^2 -> H(U1(d, k), d)
28.58/10.43	   A^2 -> H(U1(d, k), k)
28.58/10.43	   A^2 -> H(U1(e, e), c)
28.58/10.43	   A^2 -> H(U1(e, c), e)
28.58/10.43	   A^2 -> H(U1(c, e), e)
28.58/10.43	   A^2 -> H(U1(c, k), e)
28.58/10.43	   A^2 -> H(c, U1(e, e))
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.43	   A^2 -> H(d, b)
28.58/10.43	   A^2 -> H(d, U1(e, d))
28.58/10.43	   A^2 -> H(d, U1(d, e))
28.58/10.43	   A^2 -> H(d, c)
28.58/10.43	   A^2 -> H(d, U1(e, k))
28.58/10.43	   A^2 -> H(d, U1(k, e))
28.58/10.43	   A^2 -> H(d, e)
28.58/10.43	   A^2 -> H(d, U1(k, k))
28.58/10.43	   A^2 -> H(a, d)
28.58/10.43	   A^2 -> H(a, k)
28.58/10.43	   A^2 -> H(U1(e, d), d)
28.58/10.43	   A^2 -> H(U1(e, d), k)
28.58/10.43	   A^2 -> H(U1(d, e), d)
28.58/10.43	   A^2 -> H(U1(d, e), k)
28.58/10.43	   A^2 -> H(k, b)
28.58/10.43	   A^2 -> H(k, U1(e, d))
28.58/10.43	   A^2 -> H(k, U1(d, e))
28.58/10.43	
28.58/10.43	The TRS R consists of the following rules:
28.58/10.43	
28.58/10.43	   f(x) -> U1(x, x)
28.58/10.43	   U1(e, x) -> x
28.58/10.43	   a -> c
28.58/10.43	   a -> d
28.58/10.43	   b -> c
28.58/10.43	   b -> d
28.58/10.43	   d -> k
28.58/10.43	   c -> e
28.58/10.43	   c -> k
28.58/10.43	
28.58/10.43	Q is empty.
28.58/10.43	We have to consider all minimal (P,Q,R)-chains.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2531) TransformationProof (EQUIVALENT)
28.58/10.43	By narrowing [LPAR04] the rule A^2 -> H(k, U1(e, c)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.43	
28.58/10.43	   (A^2 -> H(k, c),A^2 -> H(k, c))
28.58/10.43	   (A^2 -> H(k, U1(e, e)),A^2 -> H(k, U1(e, e)))
28.58/10.43	   (A^2 -> H(k, U1(e, k)),A^2 -> H(k, U1(e, k)))
28.58/10.43	
28.58/10.43	
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2532)
28.58/10.43	Obligation:
28.58/10.43	Q DP problem:
28.58/10.43	The TRS P consists of the following rules:
28.58/10.43	
28.58/10.43	   G(d, x, x) -> A^2
28.58/10.43	   A^2 -> H(f(c), f(c))
28.58/10.43	   H(x, x) -> G(x, x, f(k))
28.58/10.43	   A^2 -> H(f(d), f(d))
28.58/10.43	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.43	   A^2 -> H(f(e), f(e))
28.58/10.43	   A^2 -> H(f(k), f(k))
28.58/10.43	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.43	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.43	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.43	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.43	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.43	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.43	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.43	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.43	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.43	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.43	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.43	   A^2 -> H(k, U1(c, e))
28.58/10.43	   A^2 -> H(k, U1(c, k))
28.58/10.43	   A^2 -> H(k, U1(e, e))
28.58/10.43	   A^2 -> H(k, U1(d, k))
28.58/10.43	   A^2 -> H(c, b)
28.58/10.43	   A^2 -> H(c, U1(e, d))
28.58/10.43	   A^2 -> H(c, U1(d, e))
28.58/10.43	   A^2 -> H(c, c)
28.58/10.43	   A^2 -> H(c, U1(e, k))
28.58/10.43	   A^2 -> H(c, U1(k, e))
28.58/10.43	   A^2 -> H(c, e)
28.58/10.43	   A^2 -> H(c, U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, k), b)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(e, k), c)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.43	   A^2 -> H(U1(e, k), e)
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, c), d)
28.58/10.43	   A^2 -> H(U1(e, c), k)
28.58/10.43	   A^2 -> H(U1(k, e), b)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, e), c)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.43	   A^2 -> H(U1(k, c), d)
28.58/10.43	   A^2 -> H(U1(c, e), d)
28.58/10.43	   A^2 -> H(U1(c, e), k)
28.58/10.43	   A^2 -> H(U1(c, k), d)
28.58/10.43	   A^2 -> H(U1(c, k), k)
28.58/10.43	   A^2 -> H(e, b)
28.58/10.43	   A^2 -> H(e, U1(e, d))
28.58/10.43	   A^2 -> H(e, U1(d, e))
28.58/10.43	   A^2 -> H(e, c)
28.58/10.43	   A^2 -> H(e, U1(e, k))
28.58/10.43	   A^2 -> H(e, e)
28.58/10.43	   A^2 -> H(U1(e, e), d)
28.58/10.43	   A^2 -> H(U1(e, e), k)
28.58/10.43	   A^2 -> H(U1(k, k), d)
28.58/10.43	   A^2 -> H(U1(k, k), b)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, k), c)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, d), d)
28.58/10.43	   A^2 -> H(U1(d, k), d)
28.58/10.43	   A^2 -> H(U1(d, k), k)
28.58/10.43	   A^2 -> H(U1(e, e), c)
28.58/10.43	   A^2 -> H(U1(e, c), e)
28.58/10.43	   A^2 -> H(U1(c, e), e)
28.58/10.43	   A^2 -> H(U1(c, k), e)
28.58/10.43	   A^2 -> H(c, U1(e, e))
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.43	   A^2 -> H(d, b)
28.58/10.43	   A^2 -> H(d, U1(e, d))
28.58/10.43	   A^2 -> H(d, U1(d, e))
28.58/10.43	   A^2 -> H(d, c)
28.58/10.43	   A^2 -> H(d, U1(e, k))
28.58/10.43	   A^2 -> H(d, U1(k, e))
28.58/10.43	   A^2 -> H(d, e)
28.58/10.43	   A^2 -> H(d, U1(k, k))
28.58/10.43	   A^2 -> H(a, d)
28.58/10.43	   A^2 -> H(a, k)
28.58/10.43	   A^2 -> H(U1(e, d), d)
28.58/10.43	   A^2 -> H(U1(e, d), k)
28.58/10.43	   A^2 -> H(U1(d, e), d)
28.58/10.43	   A^2 -> H(U1(d, e), k)
28.58/10.43	   A^2 -> H(k, b)
28.58/10.43	   A^2 -> H(k, U1(e, d))
28.58/10.43	   A^2 -> H(k, U1(d, e))
28.58/10.43	   A^2 -> H(k, c)
28.58/10.43	   A^2 -> H(k, U1(e, k))
28.58/10.43	
28.58/10.43	The TRS R consists of the following rules:
28.58/10.43	
28.58/10.43	   f(x) -> U1(x, x)
28.58/10.43	   U1(e, x) -> x
28.58/10.43	   a -> c
28.58/10.43	   a -> d
28.58/10.43	   b -> c
28.58/10.43	   b -> d
28.58/10.43	   d -> k
28.58/10.43	   c -> e
28.58/10.43	   c -> k
28.58/10.43	
28.58/10.43	Q is empty.
28.58/10.43	We have to consider all minimal (P,Q,R)-chains.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2533) TransformationProof (EQUIVALENT)
28.58/10.43	By narrowing [LPAR04] the rule A^2 -> H(k, U1(c, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.43	
28.58/10.43	   (A^2 -> H(k, U1(e, e)),A^2 -> H(k, U1(e, e)))
28.58/10.43	   (A^2 -> H(k, U1(k, e)),A^2 -> H(k, U1(k, e)))
28.58/10.43	
28.58/10.43	
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2534)
28.58/10.43	Obligation:
28.58/10.43	Q DP problem:
28.58/10.43	The TRS P consists of the following rules:
28.58/10.43	
28.58/10.43	   G(d, x, x) -> A^2
28.58/10.43	   A^2 -> H(f(c), f(c))
28.58/10.43	   H(x, x) -> G(x, x, f(k))
28.58/10.43	   A^2 -> H(f(d), f(d))
28.58/10.43	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.43	   A^2 -> H(f(e), f(e))
28.58/10.43	   A^2 -> H(f(k), f(k))
28.58/10.43	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.43	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.43	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.43	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.43	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.43	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.43	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.43	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.43	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.43	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.43	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.43	   A^2 -> H(k, U1(c, k))
28.58/10.43	   A^2 -> H(k, U1(e, e))
28.58/10.43	   A^2 -> H(k, U1(d, k))
28.58/10.43	   A^2 -> H(c, b)
28.58/10.43	   A^2 -> H(c, U1(e, d))
28.58/10.43	   A^2 -> H(c, U1(d, e))
28.58/10.43	   A^2 -> H(c, c)
28.58/10.43	   A^2 -> H(c, U1(e, k))
28.58/10.43	   A^2 -> H(c, U1(k, e))
28.58/10.43	   A^2 -> H(c, e)
28.58/10.43	   A^2 -> H(c, U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, k), b)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(e, k), c)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.43	   A^2 -> H(U1(e, k), e)
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, c), d)
28.58/10.43	   A^2 -> H(U1(e, c), k)
28.58/10.43	   A^2 -> H(U1(k, e), b)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, e), c)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.43	   A^2 -> H(U1(k, c), d)
28.58/10.43	   A^2 -> H(U1(c, e), d)
28.58/10.43	   A^2 -> H(U1(c, e), k)
28.58/10.43	   A^2 -> H(U1(c, k), d)
28.58/10.43	   A^2 -> H(U1(c, k), k)
28.58/10.43	   A^2 -> H(e, b)
28.58/10.43	   A^2 -> H(e, U1(e, d))
28.58/10.43	   A^2 -> H(e, U1(d, e))
28.58/10.43	   A^2 -> H(e, c)
28.58/10.43	   A^2 -> H(e, U1(e, k))
28.58/10.43	   A^2 -> H(e, e)
28.58/10.43	   A^2 -> H(U1(e, e), d)
28.58/10.43	   A^2 -> H(U1(e, e), k)
28.58/10.43	   A^2 -> H(U1(k, k), d)
28.58/10.43	   A^2 -> H(U1(k, k), b)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, k), c)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, d), d)
28.58/10.43	   A^2 -> H(U1(d, k), d)
28.58/10.43	   A^2 -> H(U1(d, k), k)
28.58/10.43	   A^2 -> H(U1(e, e), c)
28.58/10.43	   A^2 -> H(U1(e, c), e)
28.58/10.43	   A^2 -> H(U1(c, e), e)
28.58/10.43	   A^2 -> H(U1(c, k), e)
28.58/10.43	   A^2 -> H(c, U1(e, e))
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.43	   A^2 -> H(d, b)
28.58/10.43	   A^2 -> H(d, U1(e, d))
28.58/10.43	   A^2 -> H(d, U1(d, e))
28.58/10.43	   A^2 -> H(d, c)
28.58/10.43	   A^2 -> H(d, U1(e, k))
28.58/10.43	   A^2 -> H(d, U1(k, e))
28.58/10.43	   A^2 -> H(d, e)
28.58/10.43	   A^2 -> H(d, U1(k, k))
28.58/10.43	   A^2 -> H(a, d)
28.58/10.43	   A^2 -> H(a, k)
28.58/10.43	   A^2 -> H(U1(e, d), d)
28.58/10.43	   A^2 -> H(U1(e, d), k)
28.58/10.43	   A^2 -> H(U1(d, e), d)
28.58/10.43	   A^2 -> H(U1(d, e), k)
28.58/10.43	   A^2 -> H(k, b)
28.58/10.43	   A^2 -> H(k, U1(e, d))
28.58/10.43	   A^2 -> H(k, U1(d, e))
28.58/10.43	   A^2 -> H(k, c)
28.58/10.43	   A^2 -> H(k, U1(e, k))
28.58/10.43	   A^2 -> H(k, U1(k, e))
28.58/10.43	
28.58/10.43	The TRS R consists of the following rules:
28.58/10.43	
28.58/10.43	   f(x) -> U1(x, x)
28.58/10.43	   U1(e, x) -> x
28.58/10.43	   a -> c
28.58/10.43	   a -> d
28.58/10.43	   b -> c
28.58/10.43	   b -> d
28.58/10.43	   d -> k
28.58/10.43	   c -> e
28.58/10.43	   c -> k
28.58/10.43	
28.58/10.43	Q is empty.
28.58/10.43	We have to consider all minimal (P,Q,R)-chains.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2535) DependencyGraphProof (EQUIVALENT)
28.58/10.43	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2536)
28.58/10.43	Obligation:
28.58/10.43	Q DP problem:
28.58/10.43	The TRS P consists of the following rules:
28.58/10.43	
28.58/10.43	   A^2 -> H(f(c), f(c))
28.58/10.43	   H(x, x) -> G(x, x, f(k))
28.58/10.43	   G(d, x, x) -> A^2
28.58/10.43	   A^2 -> H(f(d), f(d))
28.58/10.43	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.43	   A^2 -> H(f(e), f(e))
28.58/10.43	   A^2 -> H(f(k), f(k))
28.58/10.43	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.43	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.43	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.43	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.43	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.43	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.43	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.43	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.43	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.43	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.43	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.43	   A^2 -> H(k, U1(c, k))
28.58/10.43	   A^2 -> H(k, U1(e, e))
28.58/10.43	   A^2 -> H(k, U1(d, k))
28.58/10.43	   A^2 -> H(c, b)
28.58/10.43	   A^2 -> H(c, U1(e, d))
28.58/10.43	   A^2 -> H(c, U1(d, e))
28.58/10.43	   A^2 -> H(c, c)
28.58/10.43	   A^2 -> H(c, U1(e, k))
28.58/10.43	   A^2 -> H(c, U1(k, e))
28.58/10.43	   A^2 -> H(c, e)
28.58/10.43	   A^2 -> H(c, U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, k), b)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(e, k), c)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.43	   A^2 -> H(U1(e, k), e)
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, c), d)
28.58/10.43	   A^2 -> H(U1(e, c), k)
28.58/10.43	   A^2 -> H(U1(k, e), b)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, e), c)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.43	   A^2 -> H(U1(k, c), d)
28.58/10.43	   A^2 -> H(U1(c, e), d)
28.58/10.43	   A^2 -> H(U1(c, e), k)
28.58/10.43	   A^2 -> H(U1(c, k), d)
28.58/10.43	   A^2 -> H(U1(c, k), k)
28.58/10.43	   A^2 -> H(e, b)
28.58/10.43	   A^2 -> H(e, U1(e, d))
28.58/10.43	   A^2 -> H(e, U1(d, e))
28.58/10.43	   A^2 -> H(e, c)
28.58/10.43	   A^2 -> H(e, U1(e, k))
28.58/10.43	   A^2 -> H(e, e)
28.58/10.43	   A^2 -> H(U1(e, e), d)
28.58/10.43	   A^2 -> H(U1(e, e), k)
28.58/10.43	   A^2 -> H(U1(k, k), d)
28.58/10.43	   A^2 -> H(U1(k, k), b)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, k), c)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, d), d)
28.58/10.43	   A^2 -> H(U1(d, k), d)
28.58/10.43	   A^2 -> H(U1(d, k), k)
28.58/10.43	   A^2 -> H(U1(e, e), c)
28.58/10.43	   A^2 -> H(U1(e, c), e)
28.58/10.43	   A^2 -> H(U1(c, e), e)
28.58/10.43	   A^2 -> H(U1(c, k), e)
28.58/10.43	   A^2 -> H(c, U1(e, e))
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.43	   A^2 -> H(d, b)
28.58/10.43	   A^2 -> H(d, U1(e, d))
28.58/10.43	   A^2 -> H(d, U1(d, e))
28.58/10.43	   A^2 -> H(d, c)
28.58/10.43	   A^2 -> H(d, U1(e, k))
28.58/10.43	   A^2 -> H(d, U1(k, e))
28.58/10.43	   A^2 -> H(d, e)
28.58/10.43	   A^2 -> H(d, U1(k, k))
28.58/10.43	   A^2 -> H(a, d)
28.58/10.43	   A^2 -> H(a, k)
28.58/10.43	   A^2 -> H(U1(e, d), d)
28.58/10.43	   A^2 -> H(U1(e, d), k)
28.58/10.43	   A^2 -> H(U1(d, e), d)
28.58/10.43	   A^2 -> H(U1(d, e), k)
28.58/10.43	   A^2 -> H(k, b)
28.58/10.43	   A^2 -> H(k, U1(e, d))
28.58/10.43	   A^2 -> H(k, U1(d, e))
28.58/10.43	   A^2 -> H(k, c)
28.58/10.43	   A^2 -> H(k, U1(e, k))
28.58/10.43	
28.58/10.43	The TRS R consists of the following rules:
28.58/10.43	
28.58/10.43	   f(x) -> U1(x, x)
28.58/10.43	   U1(e, x) -> x
28.58/10.43	   a -> c
28.58/10.43	   a -> d
28.58/10.43	   b -> c
28.58/10.43	   b -> d
28.58/10.43	   d -> k
28.58/10.43	   c -> e
28.58/10.43	   c -> k
28.58/10.43	
28.58/10.43	Q is empty.
28.58/10.43	We have to consider all minimal (P,Q,R)-chains.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2537) TransformationProof (EQUIVALENT)
28.58/10.43	By narrowing [LPAR04] the rule A^2 -> H(k, U1(c, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.43	
28.58/10.43	   (A^2 -> H(k, U1(e, k)),A^2 -> H(k, U1(e, k)))
28.58/10.43	   (A^2 -> H(k, U1(k, k)),A^2 -> H(k, U1(k, k)))
28.58/10.43	
28.58/10.43	
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2538)
28.58/10.43	Obligation:
28.58/10.43	Q DP problem:
28.58/10.43	The TRS P consists of the following rules:
28.58/10.43	
28.58/10.43	   A^2 -> H(f(c), f(c))
28.58/10.43	   H(x, x) -> G(x, x, f(k))
28.58/10.43	   G(d, x, x) -> A^2
28.58/10.43	   A^2 -> H(f(d), f(d))
28.58/10.43	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.43	   A^2 -> H(f(e), f(e))
28.58/10.43	   A^2 -> H(f(k), f(k))
28.58/10.43	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.43	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.43	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.43	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.43	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.43	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.43	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.43	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.43	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.43	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.43	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.43	   A^2 -> H(k, U1(e, e))
28.58/10.43	   A^2 -> H(k, U1(d, k))
28.58/10.43	   A^2 -> H(c, b)
28.58/10.43	   A^2 -> H(c, U1(e, d))
28.58/10.43	   A^2 -> H(c, U1(d, e))
28.58/10.43	   A^2 -> H(c, c)
28.58/10.43	   A^2 -> H(c, U1(e, k))
28.58/10.43	   A^2 -> H(c, U1(k, e))
28.58/10.43	   A^2 -> H(c, e)
28.58/10.43	   A^2 -> H(c, U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, k), b)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(e, k), c)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.43	   A^2 -> H(U1(e, k), e)
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, c), d)
28.58/10.43	   A^2 -> H(U1(e, c), k)
28.58/10.43	   A^2 -> H(U1(k, e), b)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, e), c)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.43	   A^2 -> H(U1(k, c), d)
28.58/10.43	   A^2 -> H(U1(c, e), d)
28.58/10.43	   A^2 -> H(U1(c, e), k)
28.58/10.43	   A^2 -> H(U1(c, k), d)
28.58/10.43	   A^2 -> H(U1(c, k), k)
28.58/10.43	   A^2 -> H(e, b)
28.58/10.43	   A^2 -> H(e, U1(e, d))
28.58/10.43	   A^2 -> H(e, U1(d, e))
28.58/10.43	   A^2 -> H(e, c)
28.58/10.43	   A^2 -> H(e, U1(e, k))
28.58/10.43	   A^2 -> H(e, e)
28.58/10.43	   A^2 -> H(U1(e, e), d)
28.58/10.43	   A^2 -> H(U1(e, e), k)
28.58/10.43	   A^2 -> H(U1(k, k), d)
28.58/10.43	   A^2 -> H(U1(k, k), b)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, k), c)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, d), d)
28.58/10.43	   A^2 -> H(U1(d, k), d)
28.58/10.43	   A^2 -> H(U1(d, k), k)
28.58/10.43	   A^2 -> H(U1(e, e), c)
28.58/10.43	   A^2 -> H(U1(e, c), e)
28.58/10.43	   A^2 -> H(U1(c, e), e)
28.58/10.43	   A^2 -> H(U1(c, k), e)
28.58/10.43	   A^2 -> H(c, U1(e, e))
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.43	   A^2 -> H(d, b)
28.58/10.43	   A^2 -> H(d, U1(e, d))
28.58/10.43	   A^2 -> H(d, U1(d, e))
28.58/10.43	   A^2 -> H(d, c)
28.58/10.43	   A^2 -> H(d, U1(e, k))
28.58/10.43	   A^2 -> H(d, U1(k, e))
28.58/10.43	   A^2 -> H(d, e)
28.58/10.43	   A^2 -> H(d, U1(k, k))
28.58/10.43	   A^2 -> H(a, d)
28.58/10.43	   A^2 -> H(a, k)
28.58/10.43	   A^2 -> H(U1(e, d), d)
28.58/10.43	   A^2 -> H(U1(e, d), k)
28.58/10.43	   A^2 -> H(U1(d, e), d)
28.58/10.43	   A^2 -> H(U1(d, e), k)
28.58/10.43	   A^2 -> H(k, b)
28.58/10.43	   A^2 -> H(k, U1(e, d))
28.58/10.43	   A^2 -> H(k, U1(d, e))
28.58/10.43	   A^2 -> H(k, c)
28.58/10.43	   A^2 -> H(k, U1(e, k))
28.58/10.43	   A^2 -> H(k, U1(k, k))
28.58/10.43	
28.58/10.43	The TRS R consists of the following rules:
28.58/10.43	
28.58/10.43	   f(x) -> U1(x, x)
28.58/10.43	   U1(e, x) -> x
28.58/10.43	   a -> c
28.58/10.43	   a -> d
28.58/10.43	   b -> c
28.58/10.43	   b -> d
28.58/10.43	   d -> k
28.58/10.43	   c -> e
28.58/10.43	   c -> k
28.58/10.43	
28.58/10.43	Q is empty.
28.58/10.43	We have to consider all minimal (P,Q,R)-chains.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2539) DependencyGraphProof (EQUIVALENT)
28.58/10.43	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2540)
28.58/10.43	Obligation:
28.58/10.43	Q DP problem:
28.58/10.43	The TRS P consists of the following rules:
28.58/10.43	
28.58/10.43	   H(x, x) -> G(x, x, f(k))
28.58/10.43	   G(d, x, x) -> A^2
28.58/10.43	   A^2 -> H(f(c), f(c))
28.58/10.43	   A^2 -> H(f(d), f(d))
28.58/10.43	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.43	   A^2 -> H(f(e), f(e))
28.58/10.43	   A^2 -> H(f(k), f(k))
28.58/10.43	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.43	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.43	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.43	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.43	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.43	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.43	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.43	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.43	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.43	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.43	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.43	   A^2 -> H(k, U1(e, e))
28.58/10.43	   A^2 -> H(k, U1(d, k))
28.58/10.43	   A^2 -> H(c, b)
28.58/10.43	   A^2 -> H(c, U1(e, d))
28.58/10.43	   A^2 -> H(c, U1(d, e))
28.58/10.43	   A^2 -> H(c, c)
28.58/10.43	   A^2 -> H(c, U1(e, k))
28.58/10.43	   A^2 -> H(c, U1(k, e))
28.58/10.43	   A^2 -> H(c, e)
28.58/10.43	   A^2 -> H(c, U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, k), b)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(e, k), c)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.43	   A^2 -> H(U1(e, k), e)
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, c), d)
28.58/10.43	   A^2 -> H(U1(e, c), k)
28.58/10.43	   A^2 -> H(U1(k, e), b)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, e), c)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.43	   A^2 -> H(U1(k, c), d)
28.58/10.43	   A^2 -> H(U1(c, e), d)
28.58/10.43	   A^2 -> H(U1(c, e), k)
28.58/10.43	   A^2 -> H(U1(c, k), d)
28.58/10.43	   A^2 -> H(U1(c, k), k)
28.58/10.43	   A^2 -> H(e, b)
28.58/10.43	   A^2 -> H(e, U1(e, d))
28.58/10.43	   A^2 -> H(e, U1(d, e))
28.58/10.43	   A^2 -> H(e, c)
28.58/10.43	   A^2 -> H(e, U1(e, k))
28.58/10.43	   A^2 -> H(e, e)
28.58/10.43	   A^2 -> H(U1(e, e), d)
28.58/10.43	   A^2 -> H(U1(e, e), k)
28.58/10.43	   A^2 -> H(U1(k, k), d)
28.58/10.43	   A^2 -> H(U1(k, k), b)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, k), c)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, d), d)
28.58/10.43	   A^2 -> H(U1(d, k), d)
28.58/10.43	   A^2 -> H(U1(d, k), k)
28.58/10.43	   A^2 -> H(U1(e, e), c)
28.58/10.43	   A^2 -> H(U1(e, c), e)
28.58/10.43	   A^2 -> H(U1(c, e), e)
28.58/10.43	   A^2 -> H(U1(c, k), e)
28.58/10.43	   A^2 -> H(c, U1(e, e))
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.43	   A^2 -> H(d, b)
28.58/10.43	   A^2 -> H(d, U1(e, d))
28.58/10.43	   A^2 -> H(d, U1(d, e))
28.58/10.43	   A^2 -> H(d, c)
28.58/10.43	   A^2 -> H(d, U1(e, k))
28.58/10.43	   A^2 -> H(d, U1(k, e))
28.58/10.43	   A^2 -> H(d, e)
28.58/10.43	   A^2 -> H(d, U1(k, k))
28.58/10.43	   A^2 -> H(a, d)
28.58/10.43	   A^2 -> H(a, k)
28.58/10.43	   A^2 -> H(U1(e, d), d)
28.58/10.43	   A^2 -> H(U1(e, d), k)
28.58/10.43	   A^2 -> H(U1(d, e), d)
28.58/10.43	   A^2 -> H(U1(d, e), k)
28.58/10.43	   A^2 -> H(k, b)
28.58/10.43	   A^2 -> H(k, U1(e, d))
28.58/10.43	   A^2 -> H(k, U1(d, e))
28.58/10.43	   A^2 -> H(k, c)
28.58/10.43	   A^2 -> H(k, U1(e, k))
28.58/10.43	
28.58/10.43	The TRS R consists of the following rules:
28.58/10.43	
28.58/10.43	   f(x) -> U1(x, x)
28.58/10.43	   U1(e, x) -> x
28.58/10.43	   a -> c
28.58/10.43	   a -> d
28.58/10.43	   b -> c
28.58/10.43	   b -> d
28.58/10.43	   d -> k
28.58/10.43	   c -> e
28.58/10.43	   c -> k
28.58/10.43	
28.58/10.43	Q is empty.
28.58/10.43	We have to consider all minimal (P,Q,R)-chains.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2541) TransformationProof (EQUIVALENT)
28.58/10.43	By narrowing [LPAR04] the rule A^2 -> H(k, U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.43	
28.58/10.43	   (A^2 -> H(k, e),A^2 -> H(k, e))
28.58/10.43	
28.58/10.43	
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2542)
28.58/10.43	Obligation:
28.58/10.43	Q DP problem:
28.58/10.43	The TRS P consists of the following rules:
28.58/10.43	
28.58/10.43	   H(x, x) -> G(x, x, f(k))
28.58/10.43	   G(d, x, x) -> A^2
28.58/10.43	   A^2 -> H(f(c), f(c))
28.58/10.43	   A^2 -> H(f(d), f(d))
28.58/10.43	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.43	   A^2 -> H(f(e), f(e))
28.58/10.43	   A^2 -> H(f(k), f(k))
28.58/10.43	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.43	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.43	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.43	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.43	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.43	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.43	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.43	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.43	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.43	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.43	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.43	   A^2 -> H(k, U1(d, k))
28.58/10.43	   A^2 -> H(c, b)
28.58/10.43	   A^2 -> H(c, U1(e, d))
28.58/10.43	   A^2 -> H(c, U1(d, e))
28.58/10.43	   A^2 -> H(c, c)
28.58/10.43	   A^2 -> H(c, U1(e, k))
28.58/10.43	   A^2 -> H(c, U1(k, e))
28.58/10.43	   A^2 -> H(c, e)
28.58/10.43	   A^2 -> H(c, U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, k), b)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(e, k), c)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.43	   A^2 -> H(U1(e, k), e)
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, c), d)
28.58/10.43	   A^2 -> H(U1(e, c), k)
28.58/10.43	   A^2 -> H(U1(k, e), b)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, e), c)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.43	   A^2 -> H(U1(k, c), d)
28.58/10.43	   A^2 -> H(U1(c, e), d)
28.58/10.43	   A^2 -> H(U1(c, e), k)
28.58/10.43	   A^2 -> H(U1(c, k), d)
28.58/10.43	   A^2 -> H(U1(c, k), k)
28.58/10.43	   A^2 -> H(e, b)
28.58/10.43	   A^2 -> H(e, U1(e, d))
28.58/10.43	   A^2 -> H(e, U1(d, e))
28.58/10.43	   A^2 -> H(e, c)
28.58/10.43	   A^2 -> H(e, U1(e, k))
28.58/10.43	   A^2 -> H(e, e)
28.58/10.43	   A^2 -> H(U1(e, e), d)
28.58/10.43	   A^2 -> H(U1(e, e), k)
28.58/10.43	   A^2 -> H(U1(k, k), d)
28.58/10.43	   A^2 -> H(U1(k, k), b)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, k), c)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, d), d)
28.58/10.43	   A^2 -> H(U1(d, k), d)
28.58/10.43	   A^2 -> H(U1(d, k), k)
28.58/10.43	   A^2 -> H(U1(e, e), c)
28.58/10.43	   A^2 -> H(U1(e, c), e)
28.58/10.43	   A^2 -> H(U1(c, e), e)
28.58/10.43	   A^2 -> H(U1(c, k), e)
28.58/10.43	   A^2 -> H(c, U1(e, e))
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.43	   A^2 -> H(d, b)
28.58/10.43	   A^2 -> H(d, U1(e, d))
28.58/10.43	   A^2 -> H(d, U1(d, e))
28.58/10.43	   A^2 -> H(d, c)
28.58/10.43	   A^2 -> H(d, U1(e, k))
28.58/10.43	   A^2 -> H(d, U1(k, e))
28.58/10.43	   A^2 -> H(d, e)
28.58/10.43	   A^2 -> H(d, U1(k, k))
28.58/10.43	   A^2 -> H(a, d)
28.58/10.43	   A^2 -> H(a, k)
28.58/10.43	   A^2 -> H(U1(e, d), d)
28.58/10.43	   A^2 -> H(U1(e, d), k)
28.58/10.43	   A^2 -> H(U1(d, e), d)
28.58/10.43	   A^2 -> H(U1(d, e), k)
28.58/10.43	   A^2 -> H(k, b)
28.58/10.43	   A^2 -> H(k, U1(e, d))
28.58/10.43	   A^2 -> H(k, U1(d, e))
28.58/10.43	   A^2 -> H(k, c)
28.58/10.43	   A^2 -> H(k, U1(e, k))
28.58/10.43	   A^2 -> H(k, e)
28.58/10.43	
28.58/10.43	The TRS R consists of the following rules:
28.58/10.43	
28.58/10.43	   f(x) -> U1(x, x)
28.58/10.43	   U1(e, x) -> x
28.58/10.43	   a -> c
28.58/10.43	   a -> d
28.58/10.43	   b -> c
28.58/10.43	   b -> d
28.58/10.43	   d -> k
28.58/10.43	   c -> e
28.58/10.43	   c -> k
28.58/10.43	
28.58/10.43	Q is empty.
28.58/10.43	We have to consider all minimal (P,Q,R)-chains.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2543) DependencyGraphProof (EQUIVALENT)
28.58/10.43	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2544)
28.58/10.43	Obligation:
28.58/10.43	Q DP problem:
28.58/10.43	The TRS P consists of the following rules:
28.58/10.43	
28.58/10.43	   G(d, x, x) -> A^2
28.58/10.43	   A^2 -> H(f(c), f(c))
28.58/10.43	   H(x, x) -> G(x, x, f(k))
28.58/10.43	   A^2 -> H(f(d), f(d))
28.58/10.43	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.43	   A^2 -> H(f(e), f(e))
28.58/10.43	   A^2 -> H(f(k), f(k))
28.58/10.43	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.43	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.43	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.43	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.43	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.43	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.43	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.43	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.43	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.43	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.43	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.43	   A^2 -> H(k, U1(d, k))
28.58/10.43	   A^2 -> H(c, b)
28.58/10.43	   A^2 -> H(c, U1(e, d))
28.58/10.43	   A^2 -> H(c, U1(d, e))
28.58/10.43	   A^2 -> H(c, c)
28.58/10.43	   A^2 -> H(c, U1(e, k))
28.58/10.43	   A^2 -> H(c, U1(k, e))
28.58/10.43	   A^2 -> H(c, e)
28.58/10.43	   A^2 -> H(c, U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, k), b)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(e, k), c)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.43	   A^2 -> H(U1(e, k), e)
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, c), d)
28.58/10.43	   A^2 -> H(U1(e, c), k)
28.58/10.43	   A^2 -> H(U1(k, e), b)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, e), c)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.43	   A^2 -> H(U1(k, c), d)
28.58/10.43	   A^2 -> H(U1(c, e), d)
28.58/10.43	   A^2 -> H(U1(c, e), k)
28.58/10.43	   A^2 -> H(U1(c, k), d)
28.58/10.43	   A^2 -> H(U1(c, k), k)
28.58/10.43	   A^2 -> H(e, b)
28.58/10.43	   A^2 -> H(e, U1(e, d))
28.58/10.43	   A^2 -> H(e, U1(d, e))
28.58/10.43	   A^2 -> H(e, c)
28.58/10.43	   A^2 -> H(e, U1(e, k))
28.58/10.43	   A^2 -> H(e, e)
28.58/10.43	   A^2 -> H(U1(e, e), d)
28.58/10.43	   A^2 -> H(U1(e, e), k)
28.58/10.43	   A^2 -> H(U1(k, k), d)
28.58/10.43	   A^2 -> H(U1(k, k), b)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, k), c)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, d), d)
28.58/10.43	   A^2 -> H(U1(d, k), d)
28.58/10.43	   A^2 -> H(U1(d, k), k)
28.58/10.43	   A^2 -> H(U1(e, e), c)
28.58/10.43	   A^2 -> H(U1(e, c), e)
28.58/10.43	   A^2 -> H(U1(c, e), e)
28.58/10.43	   A^2 -> H(U1(c, k), e)
28.58/10.43	   A^2 -> H(c, U1(e, e))
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.43	   A^2 -> H(d, b)
28.58/10.43	   A^2 -> H(d, U1(e, d))
28.58/10.43	   A^2 -> H(d, U1(d, e))
28.58/10.43	   A^2 -> H(d, c)
28.58/10.43	   A^2 -> H(d, U1(e, k))
28.58/10.43	   A^2 -> H(d, U1(k, e))
28.58/10.43	   A^2 -> H(d, e)
28.58/10.43	   A^2 -> H(d, U1(k, k))
28.58/10.43	   A^2 -> H(a, d)
28.58/10.43	   A^2 -> H(a, k)
28.58/10.43	   A^2 -> H(U1(e, d), d)
28.58/10.43	   A^2 -> H(U1(e, d), k)
28.58/10.43	   A^2 -> H(U1(d, e), d)
28.58/10.43	   A^2 -> H(U1(d, e), k)
28.58/10.43	   A^2 -> H(k, b)
28.58/10.43	   A^2 -> H(k, U1(e, d))
28.58/10.43	   A^2 -> H(k, U1(d, e))
28.58/10.43	   A^2 -> H(k, c)
28.58/10.43	   A^2 -> H(k, U1(e, k))
28.58/10.43	
28.58/10.43	The TRS R consists of the following rules:
28.58/10.43	
28.58/10.43	   f(x) -> U1(x, x)
28.58/10.43	   U1(e, x) -> x
28.58/10.43	   a -> c
28.58/10.43	   a -> d
28.58/10.43	   b -> c
28.58/10.43	   b -> d
28.58/10.43	   d -> k
28.58/10.43	   c -> e
28.58/10.43	   c -> k
28.58/10.43	
28.58/10.43	Q is empty.
28.58/10.43	We have to consider all minimal (P,Q,R)-chains.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2545) TransformationProof (EQUIVALENT)
28.58/10.43	By narrowing [LPAR04] the rule A^2 -> H(k, U1(d, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.43	
28.58/10.43	   (A^2 -> H(k, U1(k, k)),A^2 -> H(k, U1(k, k)))
28.58/10.43	
28.58/10.43	
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2546)
28.58/10.43	Obligation:
28.58/10.43	Q DP problem:
28.58/10.43	The TRS P consists of the following rules:
28.58/10.43	
28.58/10.43	   G(d, x, x) -> A^2
28.58/10.43	   A^2 -> H(f(c), f(c))
28.58/10.43	   H(x, x) -> G(x, x, f(k))
28.58/10.43	   A^2 -> H(f(d), f(d))
28.58/10.43	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.43	   A^2 -> H(f(e), f(e))
28.58/10.43	   A^2 -> H(f(k), f(k))
28.58/10.43	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.43	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.43	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.43	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.43	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.43	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.43	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.43	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.43	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.43	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.43	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.43	   A^2 -> H(c, b)
28.58/10.43	   A^2 -> H(c, U1(e, d))
28.58/10.43	   A^2 -> H(c, U1(d, e))
28.58/10.43	   A^2 -> H(c, c)
28.58/10.43	   A^2 -> H(c, U1(e, k))
28.58/10.43	   A^2 -> H(c, U1(k, e))
28.58/10.43	   A^2 -> H(c, e)
28.58/10.43	   A^2 -> H(c, U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, k), b)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(e, k), c)
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.43	   A^2 -> H(U1(e, k), e)
28.58/10.43	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(e, c), d)
28.58/10.43	   A^2 -> H(U1(e, c), k)
28.58/10.43	   A^2 -> H(U1(k, e), b)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, e), c)
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.43	   A^2 -> H(U1(k, c), d)
28.58/10.43	   A^2 -> H(U1(c, e), d)
28.58/10.43	   A^2 -> H(U1(c, e), k)
28.58/10.43	   A^2 -> H(U1(c, k), d)
28.58/10.43	   A^2 -> H(U1(c, k), k)
28.58/10.43	   A^2 -> H(e, b)
28.58/10.43	   A^2 -> H(e, U1(e, d))
28.58/10.43	   A^2 -> H(e, U1(d, e))
28.58/10.43	   A^2 -> H(e, c)
28.58/10.43	   A^2 -> H(e, U1(e, k))
28.58/10.43	   A^2 -> H(e, e)
28.58/10.43	   A^2 -> H(U1(e, e), d)
28.58/10.43	   A^2 -> H(U1(e, e), k)
28.58/10.43	   A^2 -> H(U1(k, k), d)
28.58/10.43	   A^2 -> H(U1(k, k), b)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.43	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.43	   A^2 -> H(U1(k, k), c)
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.43	   A^2 -> H(U1(k, d), d)
28.58/10.43	   A^2 -> H(U1(d, k), d)
28.58/10.43	   A^2 -> H(U1(d, k), k)
28.58/10.43	   A^2 -> H(U1(e, e), c)
28.58/10.43	   A^2 -> H(U1(e, c), e)
28.58/10.43	   A^2 -> H(U1(c, e), e)
28.58/10.43	   A^2 -> H(U1(c, k), e)
28.58/10.43	   A^2 -> H(c, U1(e, e))
28.58/10.43	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.43	   A^2 -> H(d, b)
28.58/10.43	   A^2 -> H(d, U1(e, d))
28.58/10.43	   A^2 -> H(d, U1(d, e))
28.58/10.43	   A^2 -> H(d, c)
28.58/10.43	   A^2 -> H(d, U1(e, k))
28.58/10.43	   A^2 -> H(d, U1(k, e))
28.58/10.43	   A^2 -> H(d, e)
28.58/10.43	   A^2 -> H(d, U1(k, k))
28.58/10.43	   A^2 -> H(a, d)
28.58/10.43	   A^2 -> H(a, k)
28.58/10.43	   A^2 -> H(U1(e, d), d)
28.58/10.43	   A^2 -> H(U1(e, d), k)
28.58/10.43	   A^2 -> H(U1(d, e), d)
28.58/10.43	   A^2 -> H(U1(d, e), k)
28.58/10.43	   A^2 -> H(k, b)
28.58/10.43	   A^2 -> H(k, U1(e, d))
28.58/10.43	   A^2 -> H(k, U1(d, e))
28.58/10.43	   A^2 -> H(k, c)
28.58/10.43	   A^2 -> H(k, U1(e, k))
28.58/10.43	   A^2 -> H(k, U1(k, k))
28.58/10.43	
28.58/10.43	The TRS R consists of the following rules:
28.58/10.43	
28.58/10.43	   f(x) -> U1(x, x)
28.58/10.43	   U1(e, x) -> x
28.58/10.43	   a -> c
28.58/10.43	   a -> d
28.58/10.43	   b -> c
28.58/10.43	   b -> d
28.58/10.43	   d -> k
28.58/10.43	   c -> e
28.58/10.43	   c -> k
28.58/10.43	
28.58/10.43	Q is empty.
28.58/10.43	We have to consider all minimal (P,Q,R)-chains.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2547) DependencyGraphProof (EQUIVALENT)
28.58/10.43	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.43	----------------------------------------
28.58/10.43	
28.58/10.43	(2548)
28.58/10.43	Obligation:
28.58/10.43	Q DP problem:
28.58/10.43	The TRS P consists of the following rules:
28.58/10.43	
28.58/10.43	   A^2 -> H(f(c), f(c))
28.58/10.43	   H(x, x) -> G(x, x, f(k))
28.58/10.43	   G(d, x, x) -> A^2
28.58/10.43	   A^2 -> H(f(d), f(d))
28.58/10.43	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.43	   A^2 -> H(f(e), f(e))
28.58/10.43	   A^2 -> H(f(k), f(k))
28.58/10.43	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.43	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.43	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.43	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.43	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.43	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.43	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.43	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.43	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.43	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.43	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.43	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.43	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.43	   A^2 -> H(c, b)
28.58/10.44	   A^2 -> H(c, U1(e, d))
28.58/10.44	   A^2 -> H(c, U1(d, e))
28.58/10.44	   A^2 -> H(c, c)
28.58/10.44	   A^2 -> H(c, U1(e, k))
28.58/10.44	   A^2 -> H(c, U1(k, e))
28.58/10.44	   A^2 -> H(c, e)
28.58/10.44	   A^2 -> H(c, U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, k), b)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(e, k), c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.44	   A^2 -> H(U1(e, k), e)
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, c), d)
28.58/10.44	   A^2 -> H(U1(e, c), k)
28.58/10.44	   A^2 -> H(U1(k, e), b)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, e), c)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.44	   A^2 -> H(U1(k, c), d)
28.58/10.44	   A^2 -> H(U1(c, e), d)
28.58/10.44	   A^2 -> H(U1(c, e), k)
28.58/10.44	   A^2 -> H(U1(c, k), d)
28.58/10.44	   A^2 -> H(U1(c, k), k)
28.58/10.44	   A^2 -> H(e, b)
28.58/10.44	   A^2 -> H(e, U1(e, d))
28.58/10.44	   A^2 -> H(e, U1(d, e))
28.58/10.44	   A^2 -> H(e, c)
28.58/10.44	   A^2 -> H(e, U1(e, k))
28.58/10.44	   A^2 -> H(e, e)
28.58/10.44	   A^2 -> H(U1(e, e), d)
28.58/10.44	   A^2 -> H(U1(e, e), k)
28.58/10.44	   A^2 -> H(U1(k, k), d)
28.58/10.44	   A^2 -> H(U1(k, k), b)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, k), c)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, d), d)
28.58/10.44	   A^2 -> H(U1(d, k), d)
28.58/10.44	   A^2 -> H(U1(d, k), k)
28.58/10.44	   A^2 -> H(U1(e, e), c)
28.58/10.44	   A^2 -> H(U1(e, c), e)
28.58/10.44	   A^2 -> H(U1(c, e), e)
28.58/10.44	   A^2 -> H(U1(c, k), e)
28.58/10.44	   A^2 -> H(c, U1(e, e))
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.44	   A^2 -> H(d, b)
28.58/10.44	   A^2 -> H(d, U1(e, d))
28.58/10.44	   A^2 -> H(d, U1(d, e))
28.58/10.44	   A^2 -> H(d, c)
28.58/10.44	   A^2 -> H(d, U1(e, k))
28.58/10.44	   A^2 -> H(d, U1(k, e))
28.58/10.44	   A^2 -> H(d, e)
28.58/10.44	   A^2 -> H(d, U1(k, k))
28.58/10.44	   A^2 -> H(a, d)
28.58/10.44	   A^2 -> H(a, k)
28.58/10.44	   A^2 -> H(U1(e, d), d)
28.58/10.44	   A^2 -> H(U1(e, d), k)
28.58/10.44	   A^2 -> H(U1(d, e), d)
28.58/10.44	   A^2 -> H(U1(d, e), k)
28.58/10.44	   A^2 -> H(k, b)
28.58/10.44	   A^2 -> H(k, U1(e, d))
28.58/10.44	   A^2 -> H(k, U1(d, e))
28.58/10.44	   A^2 -> H(k, c)
28.58/10.44	   A^2 -> H(k, U1(e, k))
28.58/10.44	
28.58/10.44	The TRS R consists of the following rules:
28.58/10.44	
28.58/10.44	   f(x) -> U1(x, x)
28.58/10.44	   U1(e, x) -> x
28.58/10.44	   a -> c
28.58/10.44	   a -> d
28.58/10.44	   b -> c
28.58/10.44	   b -> d
28.58/10.44	   d -> k
28.58/10.44	   c -> e
28.58/10.44	   c -> k
28.58/10.44	
28.58/10.44	Q is empty.
28.58/10.44	We have to consider all minimal (P,Q,R)-chains.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2549) TransformationProof (EQUIVALENT)
28.58/10.44	By narrowing [LPAR04] the rule A^2 -> H(c, b) at position [] we obtained the following new rules [LPAR04]:
28.58/10.44	
28.58/10.44	   (A^2 -> H(e, b),A^2 -> H(e, b))
28.58/10.44	   (A^2 -> H(k, b),A^2 -> H(k, b))
28.58/10.44	   (A^2 -> H(c, c),A^2 -> H(c, c))
28.58/10.44	   (A^2 -> H(c, d),A^2 -> H(c, d))
28.58/10.44	
28.58/10.44	
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2550)
28.58/10.44	Obligation:
28.58/10.44	Q DP problem:
28.58/10.44	The TRS P consists of the following rules:
28.58/10.44	
28.58/10.44	   A^2 -> H(f(c), f(c))
28.58/10.44	   H(x, x) -> G(x, x, f(k))
28.58/10.44	   G(d, x, x) -> A^2
28.58/10.44	   A^2 -> H(f(d), f(d))
28.58/10.44	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.44	   A^2 -> H(f(e), f(e))
28.58/10.44	   A^2 -> H(f(k), f(k))
28.58/10.44	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.44	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.44	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.44	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.44	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.44	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.44	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.44	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.44	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.44	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.44	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.44	   A^2 -> H(c, U1(e, d))
28.58/10.44	   A^2 -> H(c, U1(d, e))
28.58/10.44	   A^2 -> H(c, c)
28.58/10.44	   A^2 -> H(c, U1(e, k))
28.58/10.44	   A^2 -> H(c, U1(k, e))
28.58/10.44	   A^2 -> H(c, e)
28.58/10.44	   A^2 -> H(c, U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, k), b)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(e, k), c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.44	   A^2 -> H(U1(e, k), e)
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, c), d)
28.58/10.44	   A^2 -> H(U1(e, c), k)
28.58/10.44	   A^2 -> H(U1(k, e), b)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, e), c)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.44	   A^2 -> H(U1(k, c), d)
28.58/10.44	   A^2 -> H(U1(c, e), d)
28.58/10.44	   A^2 -> H(U1(c, e), k)
28.58/10.44	   A^2 -> H(U1(c, k), d)
28.58/10.44	   A^2 -> H(U1(c, k), k)
28.58/10.44	   A^2 -> H(e, b)
28.58/10.44	   A^2 -> H(e, U1(e, d))
28.58/10.44	   A^2 -> H(e, U1(d, e))
28.58/10.44	   A^2 -> H(e, c)
28.58/10.44	   A^2 -> H(e, U1(e, k))
28.58/10.44	   A^2 -> H(e, e)
28.58/10.44	   A^2 -> H(U1(e, e), d)
28.58/10.44	   A^2 -> H(U1(e, e), k)
28.58/10.44	   A^2 -> H(U1(k, k), d)
28.58/10.44	   A^2 -> H(U1(k, k), b)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, k), c)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, d), d)
28.58/10.44	   A^2 -> H(U1(d, k), d)
28.58/10.44	   A^2 -> H(U1(d, k), k)
28.58/10.44	   A^2 -> H(U1(e, e), c)
28.58/10.44	   A^2 -> H(U1(e, c), e)
28.58/10.44	   A^2 -> H(U1(c, e), e)
28.58/10.44	   A^2 -> H(U1(c, k), e)
28.58/10.44	   A^2 -> H(c, U1(e, e))
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.44	   A^2 -> H(d, b)
28.58/10.44	   A^2 -> H(d, U1(e, d))
28.58/10.44	   A^2 -> H(d, U1(d, e))
28.58/10.44	   A^2 -> H(d, c)
28.58/10.44	   A^2 -> H(d, U1(e, k))
28.58/10.44	   A^2 -> H(d, U1(k, e))
28.58/10.44	   A^2 -> H(d, e)
28.58/10.44	   A^2 -> H(d, U1(k, k))
28.58/10.44	   A^2 -> H(a, d)
28.58/10.44	   A^2 -> H(a, k)
28.58/10.44	   A^2 -> H(U1(e, d), d)
28.58/10.44	   A^2 -> H(U1(e, d), k)
28.58/10.44	   A^2 -> H(U1(d, e), d)
28.58/10.44	   A^2 -> H(U1(d, e), k)
28.58/10.44	   A^2 -> H(k, b)
28.58/10.44	   A^2 -> H(k, U1(e, d))
28.58/10.44	   A^2 -> H(k, U1(d, e))
28.58/10.44	   A^2 -> H(k, c)
28.58/10.44	   A^2 -> H(k, U1(e, k))
28.58/10.44	   A^2 -> H(c, d)
28.58/10.44	
28.58/10.44	The TRS R consists of the following rules:
28.58/10.44	
28.58/10.44	   f(x) -> U1(x, x)
28.58/10.44	   U1(e, x) -> x
28.58/10.44	   a -> c
28.58/10.44	   a -> d
28.58/10.44	   b -> c
28.58/10.44	   b -> d
28.58/10.44	   d -> k
28.58/10.44	   c -> e
28.58/10.44	   c -> k
28.58/10.44	
28.58/10.44	Q is empty.
28.58/10.44	We have to consider all minimal (P,Q,R)-chains.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2551) TransformationProof (EQUIVALENT)
28.58/10.44	By narrowing [LPAR04] the rule A^2 -> H(c, U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.44	
28.58/10.44	   (A^2 -> H(e, U1(e, d)),A^2 -> H(e, U1(e, d)))
28.58/10.44	   (A^2 -> H(k, U1(e, d)),A^2 -> H(k, U1(e, d)))
28.58/10.44	   (A^2 -> H(c, d),A^2 -> H(c, d))
28.58/10.44	   (A^2 -> H(c, U1(e, k)),A^2 -> H(c, U1(e, k)))
28.58/10.44	
28.58/10.44	
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2552)
28.58/10.44	Obligation:
28.58/10.44	Q DP problem:
28.58/10.44	The TRS P consists of the following rules:
28.58/10.44	
28.58/10.44	   A^2 -> H(f(c), f(c))
28.58/10.44	   H(x, x) -> G(x, x, f(k))
28.58/10.44	   G(d, x, x) -> A^2
28.58/10.44	   A^2 -> H(f(d), f(d))
28.58/10.44	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.44	   A^2 -> H(f(e), f(e))
28.58/10.44	   A^2 -> H(f(k), f(k))
28.58/10.44	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.44	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.44	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.44	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.44	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.44	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.44	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.44	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.44	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.44	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.44	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.44	   A^2 -> H(c, U1(d, e))
28.58/10.44	   A^2 -> H(c, c)
28.58/10.44	   A^2 -> H(c, U1(e, k))
28.58/10.44	   A^2 -> H(c, U1(k, e))
28.58/10.44	   A^2 -> H(c, e)
28.58/10.44	   A^2 -> H(c, U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, k), b)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(e, k), c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.44	   A^2 -> H(U1(e, k), e)
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, c), d)
28.58/10.44	   A^2 -> H(U1(e, c), k)
28.58/10.44	   A^2 -> H(U1(k, e), b)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, e), c)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.44	   A^2 -> H(U1(k, c), d)
28.58/10.44	   A^2 -> H(U1(c, e), d)
28.58/10.44	   A^2 -> H(U1(c, e), k)
28.58/10.44	   A^2 -> H(U1(c, k), d)
28.58/10.44	   A^2 -> H(U1(c, k), k)
28.58/10.44	   A^2 -> H(e, b)
28.58/10.44	   A^2 -> H(e, U1(e, d))
28.58/10.44	   A^2 -> H(e, U1(d, e))
28.58/10.44	   A^2 -> H(e, c)
28.58/10.44	   A^2 -> H(e, U1(e, k))
28.58/10.44	   A^2 -> H(e, e)
28.58/10.44	   A^2 -> H(U1(e, e), d)
28.58/10.44	   A^2 -> H(U1(e, e), k)
28.58/10.44	   A^2 -> H(U1(k, k), d)
28.58/10.44	   A^2 -> H(U1(k, k), b)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, k), c)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, d), d)
28.58/10.44	   A^2 -> H(U1(d, k), d)
28.58/10.44	   A^2 -> H(U1(d, k), k)
28.58/10.44	   A^2 -> H(U1(e, e), c)
28.58/10.44	   A^2 -> H(U1(e, c), e)
28.58/10.44	   A^2 -> H(U1(c, e), e)
28.58/10.44	   A^2 -> H(U1(c, k), e)
28.58/10.44	   A^2 -> H(c, U1(e, e))
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.44	   A^2 -> H(d, b)
28.58/10.44	   A^2 -> H(d, U1(e, d))
28.58/10.44	   A^2 -> H(d, U1(d, e))
28.58/10.44	   A^2 -> H(d, c)
28.58/10.44	   A^2 -> H(d, U1(e, k))
28.58/10.44	   A^2 -> H(d, U1(k, e))
28.58/10.44	   A^2 -> H(d, e)
28.58/10.44	   A^2 -> H(d, U1(k, k))
28.58/10.44	   A^2 -> H(a, d)
28.58/10.44	   A^2 -> H(a, k)
28.58/10.44	   A^2 -> H(U1(e, d), d)
28.58/10.44	   A^2 -> H(U1(e, d), k)
28.58/10.44	   A^2 -> H(U1(d, e), d)
28.58/10.44	   A^2 -> H(U1(d, e), k)
28.58/10.44	   A^2 -> H(k, b)
28.58/10.44	   A^2 -> H(k, U1(e, d))
28.58/10.44	   A^2 -> H(k, U1(d, e))
28.58/10.44	   A^2 -> H(k, c)
28.58/10.44	   A^2 -> H(k, U1(e, k))
28.58/10.44	   A^2 -> H(c, d)
28.58/10.44	
28.58/10.44	The TRS R consists of the following rules:
28.58/10.44	
28.58/10.44	   f(x) -> U1(x, x)
28.58/10.44	   U1(e, x) -> x
28.58/10.44	   a -> c
28.58/10.44	   a -> d
28.58/10.44	   b -> c
28.58/10.44	   b -> d
28.58/10.44	   d -> k
28.58/10.44	   c -> e
28.58/10.44	   c -> k
28.58/10.44	
28.58/10.44	Q is empty.
28.58/10.44	We have to consider all minimal (P,Q,R)-chains.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2553) TransformationProof (EQUIVALENT)
28.58/10.44	By narrowing [LPAR04] the rule A^2 -> H(c, U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.44	
28.58/10.44	   (A^2 -> H(e, U1(d, e)),A^2 -> H(e, U1(d, e)))
28.58/10.44	   (A^2 -> H(k, U1(d, e)),A^2 -> H(k, U1(d, e)))
28.58/10.44	   (A^2 -> H(c, U1(k, e)),A^2 -> H(c, U1(k, e)))
28.58/10.44	
28.58/10.44	
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2554)
28.58/10.44	Obligation:
28.58/10.44	Q DP problem:
28.58/10.44	The TRS P consists of the following rules:
28.58/10.44	
28.58/10.44	   A^2 -> H(f(c), f(c))
28.58/10.44	   H(x, x) -> G(x, x, f(k))
28.58/10.44	   G(d, x, x) -> A^2
28.58/10.44	   A^2 -> H(f(d), f(d))
28.58/10.44	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.44	   A^2 -> H(f(e), f(e))
28.58/10.44	   A^2 -> H(f(k), f(k))
28.58/10.44	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.44	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.44	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.44	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.44	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.44	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.44	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.44	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.44	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.44	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.44	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.44	   A^2 -> H(c, c)
28.58/10.44	   A^2 -> H(c, U1(e, k))
28.58/10.44	   A^2 -> H(c, U1(k, e))
28.58/10.44	   A^2 -> H(c, e)
28.58/10.44	   A^2 -> H(c, U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, k), b)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(e, k), c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.44	   A^2 -> H(U1(e, k), e)
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, c), d)
28.58/10.44	   A^2 -> H(U1(e, c), k)
28.58/10.44	   A^2 -> H(U1(k, e), b)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, e), c)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.44	   A^2 -> H(U1(k, c), d)
28.58/10.44	   A^2 -> H(U1(c, e), d)
28.58/10.44	   A^2 -> H(U1(c, e), k)
28.58/10.44	   A^2 -> H(U1(c, k), d)
28.58/10.44	   A^2 -> H(U1(c, k), k)
28.58/10.44	   A^2 -> H(e, b)
28.58/10.44	   A^2 -> H(e, U1(e, d))
28.58/10.44	   A^2 -> H(e, U1(d, e))
28.58/10.44	   A^2 -> H(e, c)
28.58/10.44	   A^2 -> H(e, U1(e, k))
28.58/10.44	   A^2 -> H(e, e)
28.58/10.44	   A^2 -> H(U1(e, e), d)
28.58/10.44	   A^2 -> H(U1(e, e), k)
28.58/10.44	   A^2 -> H(U1(k, k), d)
28.58/10.44	   A^2 -> H(U1(k, k), b)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, k), c)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, d), d)
28.58/10.44	   A^2 -> H(U1(d, k), d)
28.58/10.44	   A^2 -> H(U1(d, k), k)
28.58/10.44	   A^2 -> H(U1(e, e), c)
28.58/10.44	   A^2 -> H(U1(e, c), e)
28.58/10.44	   A^2 -> H(U1(c, e), e)
28.58/10.44	   A^2 -> H(U1(c, k), e)
28.58/10.44	   A^2 -> H(c, U1(e, e))
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.44	   A^2 -> H(d, b)
28.58/10.44	   A^2 -> H(d, U1(e, d))
28.58/10.44	   A^2 -> H(d, U1(d, e))
28.58/10.44	   A^2 -> H(d, c)
28.58/10.44	   A^2 -> H(d, U1(e, k))
28.58/10.44	   A^2 -> H(d, U1(k, e))
28.58/10.44	   A^2 -> H(d, e)
28.58/10.44	   A^2 -> H(d, U1(k, k))
28.58/10.44	   A^2 -> H(a, d)
28.58/10.44	   A^2 -> H(a, k)
28.58/10.44	   A^2 -> H(U1(e, d), d)
28.58/10.44	   A^2 -> H(U1(e, d), k)
28.58/10.44	   A^2 -> H(U1(d, e), d)
28.58/10.44	   A^2 -> H(U1(d, e), k)
28.58/10.44	   A^2 -> H(k, b)
28.58/10.44	   A^2 -> H(k, U1(e, d))
28.58/10.44	   A^2 -> H(k, U1(d, e))
28.58/10.44	   A^2 -> H(k, c)
28.58/10.44	   A^2 -> H(k, U1(e, k))
28.58/10.44	   A^2 -> H(c, d)
28.58/10.44	
28.58/10.44	The TRS R consists of the following rules:
28.58/10.44	
28.58/10.44	   f(x) -> U1(x, x)
28.58/10.44	   U1(e, x) -> x
28.58/10.44	   a -> c
28.58/10.44	   a -> d
28.58/10.44	   b -> c
28.58/10.44	   b -> d
28.58/10.44	   d -> k
28.58/10.44	   c -> e
28.58/10.44	   c -> k
28.58/10.44	
28.58/10.44	Q is empty.
28.58/10.44	We have to consider all minimal (P,Q,R)-chains.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2555) TransformationProof (EQUIVALENT)
28.58/10.44	By narrowing [LPAR04] the rule A^2 -> H(c, U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.44	
28.58/10.44	   (A^2 -> H(e, U1(e, k)),A^2 -> H(e, U1(e, k)))
28.58/10.44	   (A^2 -> H(k, U1(e, k)),A^2 -> H(k, U1(e, k)))
28.58/10.44	   (A^2 -> H(c, k),A^2 -> H(c, k))
28.58/10.44	
28.58/10.44	
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2556)
28.58/10.44	Obligation:
28.58/10.44	Q DP problem:
28.58/10.44	The TRS P consists of the following rules:
28.58/10.44	
28.58/10.44	   A^2 -> H(f(c), f(c))
28.58/10.44	   H(x, x) -> G(x, x, f(k))
28.58/10.44	   G(d, x, x) -> A^2
28.58/10.44	   A^2 -> H(f(d), f(d))
28.58/10.44	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.44	   A^2 -> H(f(e), f(e))
28.58/10.44	   A^2 -> H(f(k), f(k))
28.58/10.44	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.44	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.44	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.44	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.44	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.44	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.44	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.44	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.44	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.44	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.44	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.44	   A^2 -> H(c, c)
28.58/10.44	   A^2 -> H(c, U1(k, e))
28.58/10.44	   A^2 -> H(c, e)
28.58/10.44	   A^2 -> H(c, U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, k), b)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(e, k), c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.44	   A^2 -> H(U1(e, k), e)
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, c), d)
28.58/10.44	   A^2 -> H(U1(e, c), k)
28.58/10.44	   A^2 -> H(U1(k, e), b)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, e), c)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.44	   A^2 -> H(U1(k, c), d)
28.58/10.44	   A^2 -> H(U1(c, e), d)
28.58/10.44	   A^2 -> H(U1(c, e), k)
28.58/10.44	   A^2 -> H(U1(c, k), d)
28.58/10.44	   A^2 -> H(U1(c, k), k)
28.58/10.44	   A^2 -> H(e, b)
28.58/10.44	   A^2 -> H(e, U1(e, d))
28.58/10.44	   A^2 -> H(e, U1(d, e))
28.58/10.44	   A^2 -> H(e, c)
28.58/10.44	   A^2 -> H(e, U1(e, k))
28.58/10.44	   A^2 -> H(e, e)
28.58/10.44	   A^2 -> H(U1(e, e), d)
28.58/10.44	   A^2 -> H(U1(e, e), k)
28.58/10.44	   A^2 -> H(U1(k, k), d)
28.58/10.44	   A^2 -> H(U1(k, k), b)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, k), c)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, d), d)
28.58/10.44	   A^2 -> H(U1(d, k), d)
28.58/10.44	   A^2 -> H(U1(d, k), k)
28.58/10.44	   A^2 -> H(U1(e, e), c)
28.58/10.44	   A^2 -> H(U1(e, c), e)
28.58/10.44	   A^2 -> H(U1(c, e), e)
28.58/10.44	   A^2 -> H(U1(c, k), e)
28.58/10.44	   A^2 -> H(c, U1(e, e))
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.44	   A^2 -> H(d, b)
28.58/10.44	   A^2 -> H(d, U1(e, d))
28.58/10.44	   A^2 -> H(d, U1(d, e))
28.58/10.44	   A^2 -> H(d, c)
28.58/10.44	   A^2 -> H(d, U1(e, k))
28.58/10.44	   A^2 -> H(d, U1(k, e))
28.58/10.44	   A^2 -> H(d, e)
28.58/10.44	   A^2 -> H(d, U1(k, k))
28.58/10.44	   A^2 -> H(a, d)
28.58/10.44	   A^2 -> H(a, k)
28.58/10.44	   A^2 -> H(U1(e, d), d)
28.58/10.44	   A^2 -> H(U1(e, d), k)
28.58/10.44	   A^2 -> H(U1(d, e), d)
28.58/10.44	   A^2 -> H(U1(d, e), k)
28.58/10.44	   A^2 -> H(k, b)
28.58/10.44	   A^2 -> H(k, U1(e, d))
28.58/10.44	   A^2 -> H(k, U1(d, e))
28.58/10.44	   A^2 -> H(k, c)
28.58/10.44	   A^2 -> H(k, U1(e, k))
28.58/10.44	   A^2 -> H(c, d)
28.58/10.44	   A^2 -> H(c, k)
28.58/10.44	
28.58/10.44	The TRS R consists of the following rules:
28.58/10.44	
28.58/10.44	   f(x) -> U1(x, x)
28.58/10.44	   U1(e, x) -> x
28.58/10.44	   a -> c
28.58/10.44	   a -> d
28.58/10.44	   b -> c
28.58/10.44	   b -> d
28.58/10.44	   d -> k
28.58/10.44	   c -> e
28.58/10.44	   c -> k
28.58/10.44	
28.58/10.44	Q is empty.
28.58/10.44	We have to consider all minimal (P,Q,R)-chains.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2557) TransformationProof (EQUIVALENT)
28.58/10.44	By narrowing [LPAR04] the rule A^2 -> H(c, U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.44	
28.58/10.44	   (A^2 -> H(e, U1(k, e)),A^2 -> H(e, U1(k, e)))
28.58/10.44	   (A^2 -> H(k, U1(k, e)),A^2 -> H(k, U1(k, e)))
28.58/10.44	
28.58/10.44	
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2558)
28.58/10.44	Obligation:
28.58/10.44	Q DP problem:
28.58/10.44	The TRS P consists of the following rules:
28.58/10.44	
28.58/10.44	   A^2 -> H(f(c), f(c))
28.58/10.44	   H(x, x) -> G(x, x, f(k))
28.58/10.44	   G(d, x, x) -> A^2
28.58/10.44	   A^2 -> H(f(d), f(d))
28.58/10.44	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.44	   A^2 -> H(f(e), f(e))
28.58/10.44	   A^2 -> H(f(k), f(k))
28.58/10.44	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.44	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.44	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.44	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.44	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.44	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.44	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.44	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.44	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.44	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.44	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.44	   A^2 -> H(c, c)
28.58/10.44	   A^2 -> H(c, e)
28.58/10.44	   A^2 -> H(c, U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, k), b)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(e, k), c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.44	   A^2 -> H(U1(e, k), e)
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, c), d)
28.58/10.44	   A^2 -> H(U1(e, c), k)
28.58/10.44	   A^2 -> H(U1(k, e), b)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, e), c)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.44	   A^2 -> H(U1(k, c), d)
28.58/10.44	   A^2 -> H(U1(c, e), d)
28.58/10.44	   A^2 -> H(U1(c, e), k)
28.58/10.44	   A^2 -> H(U1(c, k), d)
28.58/10.44	   A^2 -> H(U1(c, k), k)
28.58/10.44	   A^2 -> H(e, b)
28.58/10.44	   A^2 -> H(e, U1(e, d))
28.58/10.44	   A^2 -> H(e, U1(d, e))
28.58/10.44	   A^2 -> H(e, c)
28.58/10.44	   A^2 -> H(e, U1(e, k))
28.58/10.44	   A^2 -> H(e, e)
28.58/10.44	   A^2 -> H(U1(e, e), d)
28.58/10.44	   A^2 -> H(U1(e, e), k)
28.58/10.44	   A^2 -> H(U1(k, k), d)
28.58/10.44	   A^2 -> H(U1(k, k), b)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, k), c)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, d), d)
28.58/10.44	   A^2 -> H(U1(d, k), d)
28.58/10.44	   A^2 -> H(U1(d, k), k)
28.58/10.44	   A^2 -> H(U1(e, e), c)
28.58/10.44	   A^2 -> H(U1(e, c), e)
28.58/10.44	   A^2 -> H(U1(c, e), e)
28.58/10.44	   A^2 -> H(U1(c, k), e)
28.58/10.44	   A^2 -> H(c, U1(e, e))
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.44	   A^2 -> H(d, b)
28.58/10.44	   A^2 -> H(d, U1(e, d))
28.58/10.44	   A^2 -> H(d, U1(d, e))
28.58/10.44	   A^2 -> H(d, c)
28.58/10.44	   A^2 -> H(d, U1(e, k))
28.58/10.44	   A^2 -> H(d, U1(k, e))
28.58/10.44	   A^2 -> H(d, e)
28.58/10.44	   A^2 -> H(d, U1(k, k))
28.58/10.44	   A^2 -> H(a, d)
28.58/10.44	   A^2 -> H(a, k)
28.58/10.44	   A^2 -> H(U1(e, d), d)
28.58/10.44	   A^2 -> H(U1(e, d), k)
28.58/10.44	   A^2 -> H(U1(d, e), d)
28.58/10.44	   A^2 -> H(U1(d, e), k)
28.58/10.44	   A^2 -> H(k, b)
28.58/10.44	   A^2 -> H(k, U1(e, d))
28.58/10.44	   A^2 -> H(k, U1(d, e))
28.58/10.44	   A^2 -> H(k, c)
28.58/10.44	   A^2 -> H(k, U1(e, k))
28.58/10.44	   A^2 -> H(c, d)
28.58/10.44	   A^2 -> H(c, k)
28.58/10.44	   A^2 -> H(e, U1(k, e))
28.58/10.44	   A^2 -> H(k, U1(k, e))
28.58/10.44	
28.58/10.44	The TRS R consists of the following rules:
28.58/10.44	
28.58/10.44	   f(x) -> U1(x, x)
28.58/10.44	   U1(e, x) -> x
28.58/10.44	   a -> c
28.58/10.44	   a -> d
28.58/10.44	   b -> c
28.58/10.44	   b -> d
28.58/10.44	   d -> k
28.58/10.44	   c -> e
28.58/10.44	   c -> k
28.58/10.44	
28.58/10.44	Q is empty.
28.58/10.44	We have to consider all minimal (P,Q,R)-chains.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2559) DependencyGraphProof (EQUIVALENT)
28.58/10.44	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2560)
28.58/10.44	Obligation:
28.58/10.44	Q DP problem:
28.58/10.44	The TRS P consists of the following rules:
28.58/10.44	
28.58/10.44	   H(x, x) -> G(x, x, f(k))
28.58/10.44	   G(d, x, x) -> A^2
28.58/10.44	   A^2 -> H(f(c), f(c))
28.58/10.44	   A^2 -> H(f(d), f(d))
28.58/10.44	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.44	   A^2 -> H(f(e), f(e))
28.58/10.44	   A^2 -> H(f(k), f(k))
28.58/10.44	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.44	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.44	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.44	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.44	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.44	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.44	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.44	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.44	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.44	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.44	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.44	   A^2 -> H(c, c)
28.58/10.44	   A^2 -> H(c, e)
28.58/10.44	   A^2 -> H(c, U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, k), b)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(e, k), c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.44	   A^2 -> H(U1(e, k), e)
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, c), d)
28.58/10.44	   A^2 -> H(U1(e, c), k)
28.58/10.44	   A^2 -> H(U1(k, e), b)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, e), c)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.44	   A^2 -> H(U1(k, c), d)
28.58/10.44	   A^2 -> H(U1(c, e), d)
28.58/10.44	   A^2 -> H(U1(c, e), k)
28.58/10.44	   A^2 -> H(U1(c, k), d)
28.58/10.44	   A^2 -> H(U1(c, k), k)
28.58/10.44	   A^2 -> H(e, b)
28.58/10.44	   A^2 -> H(e, U1(e, d))
28.58/10.44	   A^2 -> H(e, U1(d, e))
28.58/10.44	   A^2 -> H(e, c)
28.58/10.44	   A^2 -> H(e, U1(e, k))
28.58/10.44	   A^2 -> H(e, e)
28.58/10.44	   A^2 -> H(U1(e, e), d)
28.58/10.44	   A^2 -> H(U1(e, e), k)
28.58/10.44	   A^2 -> H(U1(k, k), d)
28.58/10.44	   A^2 -> H(U1(k, k), b)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, k), c)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, d), d)
28.58/10.44	   A^2 -> H(U1(d, k), d)
28.58/10.44	   A^2 -> H(U1(d, k), k)
28.58/10.44	   A^2 -> H(U1(e, e), c)
28.58/10.44	   A^2 -> H(U1(e, c), e)
28.58/10.44	   A^2 -> H(U1(c, e), e)
28.58/10.44	   A^2 -> H(U1(c, k), e)
28.58/10.44	   A^2 -> H(c, U1(e, e))
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.44	   A^2 -> H(d, b)
28.58/10.44	   A^2 -> H(d, U1(e, d))
28.58/10.44	   A^2 -> H(d, U1(d, e))
28.58/10.44	   A^2 -> H(d, c)
28.58/10.44	   A^2 -> H(d, U1(e, k))
28.58/10.44	   A^2 -> H(d, U1(k, e))
28.58/10.44	   A^2 -> H(d, e)
28.58/10.44	   A^2 -> H(d, U1(k, k))
28.58/10.44	   A^2 -> H(a, d)
28.58/10.44	   A^2 -> H(a, k)
28.58/10.44	   A^2 -> H(U1(e, d), d)
28.58/10.44	   A^2 -> H(U1(e, d), k)
28.58/10.44	   A^2 -> H(U1(d, e), d)
28.58/10.44	   A^2 -> H(U1(d, e), k)
28.58/10.44	   A^2 -> H(k, b)
28.58/10.44	   A^2 -> H(k, U1(e, d))
28.58/10.44	   A^2 -> H(k, U1(d, e))
28.58/10.44	   A^2 -> H(k, c)
28.58/10.44	   A^2 -> H(k, U1(e, k))
28.58/10.44	   A^2 -> H(c, d)
28.58/10.44	   A^2 -> H(c, k)
28.58/10.44	
28.58/10.44	The TRS R consists of the following rules:
28.58/10.44	
28.58/10.44	   f(x) -> U1(x, x)
28.58/10.44	   U1(e, x) -> x
28.58/10.44	   a -> c
28.58/10.44	   a -> d
28.58/10.44	   b -> c
28.58/10.44	   b -> d
28.58/10.44	   d -> k
28.58/10.44	   c -> e
28.58/10.44	   c -> k
28.58/10.44	
28.58/10.44	Q is empty.
28.58/10.44	We have to consider all minimal (P,Q,R)-chains.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2561) TransformationProof (EQUIVALENT)
28.58/10.44	By narrowing [LPAR04] the rule A^2 -> H(c, e) at position [] we obtained the following new rules [LPAR04]:
28.58/10.44	
28.58/10.44	   (A^2 -> H(e, e),A^2 -> H(e, e))
28.58/10.44	   (A^2 -> H(k, e),A^2 -> H(k, e))
28.58/10.44	
28.58/10.44	
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2562)
28.58/10.44	Obligation:
28.58/10.44	Q DP problem:
28.58/10.44	The TRS P consists of the following rules:
28.58/10.44	
28.58/10.44	   H(x, x) -> G(x, x, f(k))
28.58/10.44	   G(d, x, x) -> A^2
28.58/10.44	   A^2 -> H(f(c), f(c))
28.58/10.44	   A^2 -> H(f(d), f(d))
28.58/10.44	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.44	   A^2 -> H(f(e), f(e))
28.58/10.44	   A^2 -> H(f(k), f(k))
28.58/10.44	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.44	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.44	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.44	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.44	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.44	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.44	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.44	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.44	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.44	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.44	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.44	   A^2 -> H(c, c)
28.58/10.44	   A^2 -> H(c, U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, k), b)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(e, k), c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.44	   A^2 -> H(U1(e, k), e)
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, c), d)
28.58/10.44	   A^2 -> H(U1(e, c), k)
28.58/10.44	   A^2 -> H(U1(k, e), b)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, e), c)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.44	   A^2 -> H(U1(k, c), d)
28.58/10.44	   A^2 -> H(U1(c, e), d)
28.58/10.44	   A^2 -> H(U1(c, e), k)
28.58/10.44	   A^2 -> H(U1(c, k), d)
28.58/10.44	   A^2 -> H(U1(c, k), k)
28.58/10.44	   A^2 -> H(e, b)
28.58/10.44	   A^2 -> H(e, U1(e, d))
28.58/10.44	   A^2 -> H(e, U1(d, e))
28.58/10.44	   A^2 -> H(e, c)
28.58/10.44	   A^2 -> H(e, U1(e, k))
28.58/10.44	   A^2 -> H(e, e)
28.58/10.44	   A^2 -> H(U1(e, e), d)
28.58/10.44	   A^2 -> H(U1(e, e), k)
28.58/10.44	   A^2 -> H(U1(k, k), d)
28.58/10.44	   A^2 -> H(U1(k, k), b)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, k), c)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, d), d)
28.58/10.44	   A^2 -> H(U1(d, k), d)
28.58/10.44	   A^2 -> H(U1(d, k), k)
28.58/10.44	   A^2 -> H(U1(e, e), c)
28.58/10.44	   A^2 -> H(U1(e, c), e)
28.58/10.44	   A^2 -> H(U1(c, e), e)
28.58/10.44	   A^2 -> H(U1(c, k), e)
28.58/10.44	   A^2 -> H(c, U1(e, e))
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.44	   A^2 -> H(d, b)
28.58/10.44	   A^2 -> H(d, U1(e, d))
28.58/10.44	   A^2 -> H(d, U1(d, e))
28.58/10.44	   A^2 -> H(d, c)
28.58/10.44	   A^2 -> H(d, U1(e, k))
28.58/10.44	   A^2 -> H(d, U1(k, e))
28.58/10.44	   A^2 -> H(d, e)
28.58/10.44	   A^2 -> H(d, U1(k, k))
28.58/10.44	   A^2 -> H(a, d)
28.58/10.44	   A^2 -> H(a, k)
28.58/10.44	   A^2 -> H(U1(e, d), d)
28.58/10.44	   A^2 -> H(U1(e, d), k)
28.58/10.44	   A^2 -> H(U1(d, e), d)
28.58/10.44	   A^2 -> H(U1(d, e), k)
28.58/10.44	   A^2 -> H(k, b)
28.58/10.44	   A^2 -> H(k, U1(e, d))
28.58/10.44	   A^2 -> H(k, U1(d, e))
28.58/10.44	   A^2 -> H(k, c)
28.58/10.44	   A^2 -> H(k, U1(e, k))
28.58/10.44	   A^2 -> H(c, d)
28.58/10.44	   A^2 -> H(c, k)
28.58/10.44	   A^2 -> H(k, e)
28.58/10.44	
28.58/10.44	The TRS R consists of the following rules:
28.58/10.44	
28.58/10.44	   f(x) -> U1(x, x)
28.58/10.44	   U1(e, x) -> x
28.58/10.44	   a -> c
28.58/10.44	   a -> d
28.58/10.44	   b -> c
28.58/10.44	   b -> d
28.58/10.44	   d -> k
28.58/10.44	   c -> e
28.58/10.44	   c -> k
28.58/10.44	
28.58/10.44	Q is empty.
28.58/10.44	We have to consider all minimal (P,Q,R)-chains.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2563) DependencyGraphProof (EQUIVALENT)
28.58/10.44	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2564)
28.58/10.44	Obligation:
28.58/10.44	Q DP problem:
28.58/10.44	The TRS P consists of the following rules:
28.58/10.44	
28.58/10.44	   G(d, x, x) -> A^2
28.58/10.44	   A^2 -> H(f(c), f(c))
28.58/10.44	   H(x, x) -> G(x, x, f(k))
28.58/10.44	   A^2 -> H(f(d), f(d))
28.58/10.44	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.44	   A^2 -> H(f(e), f(e))
28.58/10.44	   A^2 -> H(f(k), f(k))
28.58/10.44	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.44	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.44	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.44	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.44	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.44	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.44	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.44	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.44	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.44	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.44	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.44	   A^2 -> H(c, c)
28.58/10.44	   A^2 -> H(c, U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, k), b)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(e, k), c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.44	   A^2 -> H(U1(e, k), e)
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, c), d)
28.58/10.44	   A^2 -> H(U1(e, c), k)
28.58/10.44	   A^2 -> H(U1(k, e), b)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, e), c)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.44	   A^2 -> H(U1(k, c), d)
28.58/10.44	   A^2 -> H(U1(c, e), d)
28.58/10.44	   A^2 -> H(U1(c, e), k)
28.58/10.44	   A^2 -> H(U1(c, k), d)
28.58/10.44	   A^2 -> H(U1(c, k), k)
28.58/10.44	   A^2 -> H(e, b)
28.58/10.44	   A^2 -> H(e, U1(e, d))
28.58/10.44	   A^2 -> H(e, U1(d, e))
28.58/10.44	   A^2 -> H(e, c)
28.58/10.44	   A^2 -> H(e, U1(e, k))
28.58/10.44	   A^2 -> H(e, e)
28.58/10.44	   A^2 -> H(U1(e, e), d)
28.58/10.44	   A^2 -> H(U1(e, e), k)
28.58/10.44	   A^2 -> H(U1(k, k), d)
28.58/10.44	   A^2 -> H(U1(k, k), b)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, k), c)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, d), d)
28.58/10.44	   A^2 -> H(U1(d, k), d)
28.58/10.44	   A^2 -> H(U1(d, k), k)
28.58/10.44	   A^2 -> H(U1(e, e), c)
28.58/10.44	   A^2 -> H(U1(e, c), e)
28.58/10.44	   A^2 -> H(U1(c, e), e)
28.58/10.44	   A^2 -> H(U1(c, k), e)
28.58/10.44	   A^2 -> H(c, U1(e, e))
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.44	   A^2 -> H(d, b)
28.58/10.44	   A^2 -> H(d, U1(e, d))
28.58/10.44	   A^2 -> H(d, U1(d, e))
28.58/10.44	   A^2 -> H(d, c)
28.58/10.44	   A^2 -> H(d, U1(e, k))
28.58/10.44	   A^2 -> H(d, U1(k, e))
28.58/10.44	   A^2 -> H(d, e)
28.58/10.44	   A^2 -> H(d, U1(k, k))
28.58/10.44	   A^2 -> H(a, d)
28.58/10.44	   A^2 -> H(a, k)
28.58/10.44	   A^2 -> H(U1(e, d), d)
28.58/10.44	   A^2 -> H(U1(e, d), k)
28.58/10.44	   A^2 -> H(U1(d, e), d)
28.58/10.44	   A^2 -> H(U1(d, e), k)
28.58/10.44	   A^2 -> H(k, b)
28.58/10.44	   A^2 -> H(k, U1(e, d))
28.58/10.44	   A^2 -> H(k, U1(d, e))
28.58/10.44	   A^2 -> H(k, c)
28.58/10.44	   A^2 -> H(k, U1(e, k))
28.58/10.44	   A^2 -> H(c, d)
28.58/10.44	   A^2 -> H(c, k)
28.58/10.44	
28.58/10.44	The TRS R consists of the following rules:
28.58/10.44	
28.58/10.44	   f(x) -> U1(x, x)
28.58/10.44	   U1(e, x) -> x
28.58/10.44	   a -> c
28.58/10.44	   a -> d
28.58/10.44	   b -> c
28.58/10.44	   b -> d
28.58/10.44	   d -> k
28.58/10.44	   c -> e
28.58/10.44	   c -> k
28.58/10.44	
28.58/10.44	Q is empty.
28.58/10.44	We have to consider all minimal (P,Q,R)-chains.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2565) TransformationProof (EQUIVALENT)
28.58/10.44	By narrowing [LPAR04] the rule A^2 -> H(c, U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.44	
28.58/10.44	   (A^2 -> H(e, U1(k, k)),A^2 -> H(e, U1(k, k)))
28.58/10.44	   (A^2 -> H(k, U1(k, k)),A^2 -> H(k, U1(k, k)))
28.58/10.44	
28.58/10.44	
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2566)
28.58/10.44	Obligation:
28.58/10.44	Q DP problem:
28.58/10.44	The TRS P consists of the following rules:
28.58/10.44	
28.58/10.44	   G(d, x, x) -> A^2
28.58/10.44	   A^2 -> H(f(c), f(c))
28.58/10.44	   H(x, x) -> G(x, x, f(k))
28.58/10.44	   A^2 -> H(f(d), f(d))
28.58/10.44	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.44	   A^2 -> H(f(e), f(e))
28.58/10.44	   A^2 -> H(f(k), f(k))
28.58/10.44	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.44	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.44	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.44	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.44	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.44	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.44	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.44	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.44	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.44	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.44	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.44	   A^2 -> H(c, c)
28.58/10.44	   A^2 -> H(U1(e, k), b)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(e, k), c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.44	   A^2 -> H(U1(e, k), e)
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, c), d)
28.58/10.44	   A^2 -> H(U1(e, c), k)
28.58/10.44	   A^2 -> H(U1(k, e), b)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, e), c)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.44	   A^2 -> H(U1(k, c), d)
28.58/10.44	   A^2 -> H(U1(c, e), d)
28.58/10.44	   A^2 -> H(U1(c, e), k)
28.58/10.44	   A^2 -> H(U1(c, k), d)
28.58/10.44	   A^2 -> H(U1(c, k), k)
28.58/10.44	   A^2 -> H(e, b)
28.58/10.44	   A^2 -> H(e, U1(e, d))
28.58/10.44	   A^2 -> H(e, U1(d, e))
28.58/10.44	   A^2 -> H(e, c)
28.58/10.44	   A^2 -> H(e, U1(e, k))
28.58/10.44	   A^2 -> H(e, e)
28.58/10.44	   A^2 -> H(U1(e, e), d)
28.58/10.44	   A^2 -> H(U1(e, e), k)
28.58/10.44	   A^2 -> H(U1(k, k), d)
28.58/10.44	   A^2 -> H(U1(k, k), b)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, k), c)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, d), d)
28.58/10.44	   A^2 -> H(U1(d, k), d)
28.58/10.44	   A^2 -> H(U1(d, k), k)
28.58/10.44	   A^2 -> H(U1(e, e), c)
28.58/10.44	   A^2 -> H(U1(e, c), e)
28.58/10.44	   A^2 -> H(U1(c, e), e)
28.58/10.44	   A^2 -> H(U1(c, k), e)
28.58/10.44	   A^2 -> H(c, U1(e, e))
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.44	   A^2 -> H(d, b)
28.58/10.44	   A^2 -> H(d, U1(e, d))
28.58/10.44	   A^2 -> H(d, U1(d, e))
28.58/10.44	   A^2 -> H(d, c)
28.58/10.44	   A^2 -> H(d, U1(e, k))
28.58/10.44	   A^2 -> H(d, U1(k, e))
28.58/10.44	   A^2 -> H(d, e)
28.58/10.44	   A^2 -> H(d, U1(k, k))
28.58/10.44	   A^2 -> H(a, d)
28.58/10.44	   A^2 -> H(a, k)
28.58/10.44	   A^2 -> H(U1(e, d), d)
28.58/10.44	   A^2 -> H(U1(e, d), k)
28.58/10.44	   A^2 -> H(U1(d, e), d)
28.58/10.44	   A^2 -> H(U1(d, e), k)
28.58/10.44	   A^2 -> H(k, b)
28.58/10.44	   A^2 -> H(k, U1(e, d))
28.58/10.44	   A^2 -> H(k, U1(d, e))
28.58/10.44	   A^2 -> H(k, c)
28.58/10.44	   A^2 -> H(k, U1(e, k))
28.58/10.44	   A^2 -> H(c, d)
28.58/10.44	   A^2 -> H(c, k)
28.58/10.44	   A^2 -> H(e, U1(k, k))
28.58/10.44	   A^2 -> H(k, U1(k, k))
28.58/10.44	
28.58/10.44	The TRS R consists of the following rules:
28.58/10.44	
28.58/10.44	   f(x) -> U1(x, x)
28.58/10.44	   U1(e, x) -> x
28.58/10.44	   a -> c
28.58/10.44	   a -> d
28.58/10.44	   b -> c
28.58/10.44	   b -> d
28.58/10.44	   d -> k
28.58/10.44	   c -> e
28.58/10.44	   c -> k
28.58/10.44	
28.58/10.44	Q is empty.
28.58/10.44	We have to consider all minimal (P,Q,R)-chains.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2567) DependencyGraphProof (EQUIVALENT)
28.58/10.44	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2568)
28.58/10.44	Obligation:
28.58/10.44	Q DP problem:
28.58/10.44	The TRS P consists of the following rules:
28.58/10.44	
28.58/10.44	   A^2 -> H(f(c), f(c))
28.58/10.44	   H(x, x) -> G(x, x, f(k))
28.58/10.44	   G(d, x, x) -> A^2
28.58/10.44	   A^2 -> H(f(d), f(d))
28.58/10.44	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.44	   A^2 -> H(f(e), f(e))
28.58/10.44	   A^2 -> H(f(k), f(k))
28.58/10.44	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.44	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.44	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.44	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.44	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.44	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.44	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.44	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.44	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.44	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.44	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.44	   A^2 -> H(c, c)
28.58/10.44	   A^2 -> H(U1(e, k), b)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(e, k), c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.44	   A^2 -> H(U1(e, k), e)
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, c), d)
28.58/10.44	   A^2 -> H(U1(e, c), k)
28.58/10.44	   A^2 -> H(U1(k, e), b)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, e), c)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.44	   A^2 -> H(U1(k, c), d)
28.58/10.44	   A^2 -> H(U1(c, e), d)
28.58/10.44	   A^2 -> H(U1(c, e), k)
28.58/10.44	   A^2 -> H(U1(c, k), d)
28.58/10.44	   A^2 -> H(U1(c, k), k)
28.58/10.44	   A^2 -> H(e, b)
28.58/10.44	   A^2 -> H(e, U1(e, d))
28.58/10.44	   A^2 -> H(e, U1(d, e))
28.58/10.44	   A^2 -> H(e, c)
28.58/10.44	   A^2 -> H(e, U1(e, k))
28.58/10.44	   A^2 -> H(e, e)
28.58/10.44	   A^2 -> H(U1(e, e), d)
28.58/10.44	   A^2 -> H(U1(e, e), k)
28.58/10.44	   A^2 -> H(U1(k, k), d)
28.58/10.44	   A^2 -> H(U1(k, k), b)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, k), c)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, d), d)
28.58/10.44	   A^2 -> H(U1(d, k), d)
28.58/10.44	   A^2 -> H(U1(d, k), k)
28.58/10.44	   A^2 -> H(U1(e, e), c)
28.58/10.44	   A^2 -> H(U1(e, c), e)
28.58/10.44	   A^2 -> H(U1(c, e), e)
28.58/10.44	   A^2 -> H(U1(c, k), e)
28.58/10.44	   A^2 -> H(c, U1(e, e))
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.44	   A^2 -> H(d, b)
28.58/10.44	   A^2 -> H(d, U1(e, d))
28.58/10.44	   A^2 -> H(d, U1(d, e))
28.58/10.44	   A^2 -> H(d, c)
28.58/10.44	   A^2 -> H(d, U1(e, k))
28.58/10.44	   A^2 -> H(d, U1(k, e))
28.58/10.44	   A^2 -> H(d, e)
28.58/10.44	   A^2 -> H(d, U1(k, k))
28.58/10.44	   A^2 -> H(a, d)
28.58/10.44	   A^2 -> H(a, k)
28.58/10.44	   A^2 -> H(U1(e, d), d)
28.58/10.44	   A^2 -> H(U1(e, d), k)
28.58/10.44	   A^2 -> H(U1(d, e), d)
28.58/10.44	   A^2 -> H(U1(d, e), k)
28.58/10.44	   A^2 -> H(k, b)
28.58/10.44	   A^2 -> H(k, U1(e, d))
28.58/10.44	   A^2 -> H(k, U1(d, e))
28.58/10.44	   A^2 -> H(k, c)
28.58/10.44	   A^2 -> H(k, U1(e, k))
28.58/10.44	   A^2 -> H(c, d)
28.58/10.44	   A^2 -> H(c, k)
28.58/10.44	
28.58/10.44	The TRS R consists of the following rules:
28.58/10.44	
28.58/10.44	   f(x) -> U1(x, x)
28.58/10.44	   U1(e, x) -> x
28.58/10.44	   a -> c
28.58/10.44	   a -> d
28.58/10.44	   b -> c
28.58/10.44	   b -> d
28.58/10.44	   d -> k
28.58/10.44	   c -> e
28.58/10.44	   c -> k
28.58/10.44	
28.58/10.44	Q is empty.
28.58/10.44	We have to consider all minimal (P,Q,R)-chains.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2569) TransformationProof (EQUIVALENT)
28.58/10.44	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), b) at position [] we obtained the following new rules [LPAR04]:
28.58/10.44	
28.58/10.44	   (A^2 -> H(k, b),A^2 -> H(k, b))
28.58/10.44	   (A^2 -> H(U1(e, k), c),A^2 -> H(U1(e, k), c))
28.58/10.44	   (A^2 -> H(U1(e, k), d),A^2 -> H(U1(e, k), d))
28.58/10.44	
28.58/10.44	
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2570)
28.58/10.44	Obligation:
28.58/10.44	Q DP problem:
28.58/10.44	The TRS P consists of the following rules:
28.58/10.44	
28.58/10.44	   A^2 -> H(f(c), f(c))
28.58/10.44	   H(x, x) -> G(x, x, f(k))
28.58/10.44	   G(d, x, x) -> A^2
28.58/10.44	   A^2 -> H(f(d), f(d))
28.58/10.44	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.44	   A^2 -> H(f(e), f(e))
28.58/10.44	   A^2 -> H(f(k), f(k))
28.58/10.44	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.44	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.44	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.44	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.44	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.44	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.44	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.44	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.44	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.44	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.44	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.44	   A^2 -> H(c, c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(e, k), c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.44	   A^2 -> H(U1(e, k), e)
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, c), d)
28.58/10.44	   A^2 -> H(U1(e, c), k)
28.58/10.44	   A^2 -> H(U1(k, e), b)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, e), c)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.44	   A^2 -> H(U1(k, c), d)
28.58/10.44	   A^2 -> H(U1(c, e), d)
28.58/10.44	   A^2 -> H(U1(c, e), k)
28.58/10.44	   A^2 -> H(U1(c, k), d)
28.58/10.44	   A^2 -> H(U1(c, k), k)
28.58/10.44	   A^2 -> H(e, b)
28.58/10.44	   A^2 -> H(e, U1(e, d))
28.58/10.44	   A^2 -> H(e, U1(d, e))
28.58/10.44	   A^2 -> H(e, c)
28.58/10.44	   A^2 -> H(e, U1(e, k))
28.58/10.44	   A^2 -> H(e, e)
28.58/10.44	   A^2 -> H(U1(e, e), d)
28.58/10.44	   A^2 -> H(U1(e, e), k)
28.58/10.44	   A^2 -> H(U1(k, k), d)
28.58/10.44	   A^2 -> H(U1(k, k), b)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, k), c)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, d), d)
28.58/10.44	   A^2 -> H(U1(d, k), d)
28.58/10.44	   A^2 -> H(U1(d, k), k)
28.58/10.44	   A^2 -> H(U1(e, e), c)
28.58/10.44	   A^2 -> H(U1(e, c), e)
28.58/10.44	   A^2 -> H(U1(c, e), e)
28.58/10.44	   A^2 -> H(U1(c, k), e)
28.58/10.44	   A^2 -> H(c, U1(e, e))
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.44	   A^2 -> H(d, b)
28.58/10.44	   A^2 -> H(d, U1(e, d))
28.58/10.44	   A^2 -> H(d, U1(d, e))
28.58/10.44	   A^2 -> H(d, c)
28.58/10.44	   A^2 -> H(d, U1(e, k))
28.58/10.44	   A^2 -> H(d, U1(k, e))
28.58/10.44	   A^2 -> H(d, e)
28.58/10.44	   A^2 -> H(d, U1(k, k))
28.58/10.44	   A^2 -> H(a, d)
28.58/10.44	   A^2 -> H(a, k)
28.58/10.44	   A^2 -> H(U1(e, d), d)
28.58/10.44	   A^2 -> H(U1(e, d), k)
28.58/10.44	   A^2 -> H(U1(d, e), d)
28.58/10.44	   A^2 -> H(U1(d, e), k)
28.58/10.44	   A^2 -> H(k, b)
28.58/10.44	   A^2 -> H(k, U1(e, d))
28.58/10.44	   A^2 -> H(k, U1(d, e))
28.58/10.44	   A^2 -> H(k, c)
28.58/10.44	   A^2 -> H(k, U1(e, k))
28.58/10.44	   A^2 -> H(c, d)
28.58/10.44	   A^2 -> H(c, k)
28.58/10.44	   A^2 -> H(U1(e, k), d)
28.58/10.44	
28.58/10.44	The TRS R consists of the following rules:
28.58/10.44	
28.58/10.44	   f(x) -> U1(x, x)
28.58/10.44	   U1(e, x) -> x
28.58/10.44	   a -> c
28.58/10.44	   a -> d
28.58/10.44	   b -> c
28.58/10.44	   b -> d
28.58/10.44	   d -> k
28.58/10.44	   c -> e
28.58/10.44	   c -> k
28.58/10.44	
28.58/10.44	Q is empty.
28.58/10.44	We have to consider all minimal (P,Q,R)-chains.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2571) TransformationProof (EQUIVALENT)
28.58/10.44	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.44	
28.58/10.44	   (A^2 -> H(k, U1(e, d)),A^2 -> H(k, U1(e, d)))
28.58/10.44	   (A^2 -> H(U1(e, k), d),A^2 -> H(U1(e, k), d))
28.58/10.44	   (A^2 -> H(U1(e, k), U1(e, k)),A^2 -> H(U1(e, k), U1(e, k)))
28.58/10.44	
28.58/10.44	
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2572)
28.58/10.44	Obligation:
28.58/10.44	Q DP problem:
28.58/10.44	The TRS P consists of the following rules:
28.58/10.44	
28.58/10.44	   A^2 -> H(f(c), f(c))
28.58/10.44	   H(x, x) -> G(x, x, f(k))
28.58/10.44	   G(d, x, x) -> A^2
28.58/10.44	   A^2 -> H(f(d), f(d))
28.58/10.44	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.44	   A^2 -> H(f(e), f(e))
28.58/10.44	   A^2 -> H(f(k), f(k))
28.58/10.44	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.44	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.44	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.44	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.44	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.44	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.44	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.44	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.44	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.44	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.44	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.44	   A^2 -> H(c, c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(e, k), c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.44	   A^2 -> H(U1(e, k), e)
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, c), d)
28.58/10.44	   A^2 -> H(U1(e, c), k)
28.58/10.44	   A^2 -> H(U1(k, e), b)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, e), c)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.44	   A^2 -> H(U1(k, c), d)
28.58/10.44	   A^2 -> H(U1(c, e), d)
28.58/10.44	   A^2 -> H(U1(c, e), k)
28.58/10.44	   A^2 -> H(U1(c, k), d)
28.58/10.44	   A^2 -> H(U1(c, k), k)
28.58/10.44	   A^2 -> H(e, b)
28.58/10.44	   A^2 -> H(e, U1(e, d))
28.58/10.44	   A^2 -> H(e, U1(d, e))
28.58/10.44	   A^2 -> H(e, c)
28.58/10.44	   A^2 -> H(e, U1(e, k))
28.58/10.44	   A^2 -> H(e, e)
28.58/10.44	   A^2 -> H(U1(e, e), d)
28.58/10.44	   A^2 -> H(U1(e, e), k)
28.58/10.44	   A^2 -> H(U1(k, k), d)
28.58/10.44	   A^2 -> H(U1(k, k), b)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, k), c)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, d), d)
28.58/10.44	   A^2 -> H(U1(d, k), d)
28.58/10.44	   A^2 -> H(U1(d, k), k)
28.58/10.44	   A^2 -> H(U1(e, e), c)
28.58/10.44	   A^2 -> H(U1(e, c), e)
28.58/10.44	   A^2 -> H(U1(c, e), e)
28.58/10.44	   A^2 -> H(U1(c, k), e)
28.58/10.44	   A^2 -> H(c, U1(e, e))
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.44	   A^2 -> H(d, b)
28.58/10.44	   A^2 -> H(d, U1(e, d))
28.58/10.44	   A^2 -> H(d, U1(d, e))
28.58/10.44	   A^2 -> H(d, c)
28.58/10.44	   A^2 -> H(d, U1(e, k))
28.58/10.44	   A^2 -> H(d, U1(k, e))
28.58/10.44	   A^2 -> H(d, e)
28.58/10.44	   A^2 -> H(d, U1(k, k))
28.58/10.44	   A^2 -> H(a, d)
28.58/10.44	   A^2 -> H(a, k)
28.58/10.44	   A^2 -> H(U1(e, d), d)
28.58/10.44	   A^2 -> H(U1(e, d), k)
28.58/10.44	   A^2 -> H(U1(d, e), d)
28.58/10.44	   A^2 -> H(U1(d, e), k)
28.58/10.44	   A^2 -> H(k, b)
28.58/10.44	   A^2 -> H(k, U1(e, d))
28.58/10.44	   A^2 -> H(k, U1(d, e))
28.58/10.44	   A^2 -> H(k, c)
28.58/10.44	   A^2 -> H(k, U1(e, k))
28.58/10.44	   A^2 -> H(c, d)
28.58/10.44	   A^2 -> H(c, k)
28.58/10.44	   A^2 -> H(U1(e, k), d)
28.58/10.44	
28.58/10.44	The TRS R consists of the following rules:
28.58/10.44	
28.58/10.44	   f(x) -> U1(x, x)
28.58/10.44	   U1(e, x) -> x
28.58/10.44	   a -> c
28.58/10.44	   a -> d
28.58/10.44	   b -> c
28.58/10.44	   b -> d
28.58/10.44	   d -> k
28.58/10.44	   c -> e
28.58/10.44	   c -> k
28.58/10.44	
28.58/10.44	Q is empty.
28.58/10.44	We have to consider all minimal (P,Q,R)-chains.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2573) TransformationProof (EQUIVALENT)
28.58/10.44	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.44	
28.58/10.44	   (A^2 -> H(k, U1(d, e)),A^2 -> H(k, U1(d, e)))
28.58/10.44	   (A^2 -> H(U1(e, k), U1(k, e)),A^2 -> H(U1(e, k), U1(k, e)))
28.58/10.44	
28.58/10.44	
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2574)
28.58/10.44	Obligation:
28.58/10.44	Q DP problem:
28.58/10.44	The TRS P consists of the following rules:
28.58/10.44	
28.58/10.44	   A^2 -> H(f(c), f(c))
28.58/10.44	   H(x, x) -> G(x, x, f(k))
28.58/10.44	   G(d, x, x) -> A^2
28.58/10.44	   A^2 -> H(f(d), f(d))
28.58/10.44	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.44	   A^2 -> H(f(e), f(e))
28.58/10.44	   A^2 -> H(f(k), f(k))
28.58/10.44	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.44	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.44	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.44	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.44	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.44	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.44	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.44	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.44	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.44	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.44	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.44	   A^2 -> H(c, c)
28.58/10.44	   A^2 -> H(U1(e, k), c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.44	   A^2 -> H(U1(e, k), e)
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, c), d)
28.58/10.44	   A^2 -> H(U1(e, c), k)
28.58/10.44	   A^2 -> H(U1(k, e), b)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, e), c)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.44	   A^2 -> H(U1(k, c), d)
28.58/10.44	   A^2 -> H(U1(c, e), d)
28.58/10.44	   A^2 -> H(U1(c, e), k)
28.58/10.44	   A^2 -> H(U1(c, k), d)
28.58/10.44	   A^2 -> H(U1(c, k), k)
28.58/10.44	   A^2 -> H(e, b)
28.58/10.44	   A^2 -> H(e, U1(e, d))
28.58/10.44	   A^2 -> H(e, U1(d, e))
28.58/10.44	   A^2 -> H(e, c)
28.58/10.44	   A^2 -> H(e, U1(e, k))
28.58/10.44	   A^2 -> H(e, e)
28.58/10.44	   A^2 -> H(U1(e, e), d)
28.58/10.44	   A^2 -> H(U1(e, e), k)
28.58/10.44	   A^2 -> H(U1(k, k), d)
28.58/10.44	   A^2 -> H(U1(k, k), b)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, k), c)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, d), d)
28.58/10.44	   A^2 -> H(U1(d, k), d)
28.58/10.44	   A^2 -> H(U1(d, k), k)
28.58/10.44	   A^2 -> H(U1(e, e), c)
28.58/10.44	   A^2 -> H(U1(e, c), e)
28.58/10.44	   A^2 -> H(U1(c, e), e)
28.58/10.44	   A^2 -> H(U1(c, k), e)
28.58/10.44	   A^2 -> H(c, U1(e, e))
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.44	   A^2 -> H(d, b)
28.58/10.44	   A^2 -> H(d, U1(e, d))
28.58/10.44	   A^2 -> H(d, U1(d, e))
28.58/10.44	   A^2 -> H(d, c)
28.58/10.44	   A^2 -> H(d, U1(e, k))
28.58/10.44	   A^2 -> H(d, U1(k, e))
28.58/10.44	   A^2 -> H(d, e)
28.58/10.44	   A^2 -> H(d, U1(k, k))
28.58/10.44	   A^2 -> H(a, d)
28.58/10.44	   A^2 -> H(a, k)
28.58/10.44	   A^2 -> H(U1(e, d), d)
28.58/10.44	   A^2 -> H(U1(e, d), k)
28.58/10.44	   A^2 -> H(U1(d, e), d)
28.58/10.44	   A^2 -> H(U1(d, e), k)
28.58/10.44	   A^2 -> H(k, b)
28.58/10.44	   A^2 -> H(k, U1(e, d))
28.58/10.44	   A^2 -> H(k, U1(d, e))
28.58/10.44	   A^2 -> H(k, c)
28.58/10.44	   A^2 -> H(k, U1(e, k))
28.58/10.44	   A^2 -> H(c, d)
28.58/10.44	   A^2 -> H(c, k)
28.58/10.44	   A^2 -> H(U1(e, k), d)
28.58/10.44	
28.58/10.44	The TRS R consists of the following rules:
28.58/10.44	
28.58/10.44	   f(x) -> U1(x, x)
28.58/10.44	   U1(e, x) -> x
28.58/10.44	   a -> c
28.58/10.44	   a -> d
28.58/10.44	   b -> c
28.58/10.44	   b -> d
28.58/10.44	   d -> k
28.58/10.44	   c -> e
28.58/10.44	   c -> k
28.58/10.44	
28.58/10.44	Q is empty.
28.58/10.44	We have to consider all minimal (P,Q,R)-chains.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2575) TransformationProof (EQUIVALENT)
28.58/10.44	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), c) at position [] we obtained the following new rules [LPAR04]:
28.58/10.44	
28.58/10.44	   (A^2 -> H(k, c),A^2 -> H(k, c))
28.58/10.44	   (A^2 -> H(U1(e, k), e),A^2 -> H(U1(e, k), e))
28.58/10.44	   (A^2 -> H(U1(e, k), k),A^2 -> H(U1(e, k), k))
28.58/10.44	
28.58/10.44	
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2576)
28.58/10.44	Obligation:
28.58/10.44	Q DP problem:
28.58/10.44	The TRS P consists of the following rules:
28.58/10.44	
28.58/10.44	   A^2 -> H(f(c), f(c))
28.58/10.44	   H(x, x) -> G(x, x, f(k))
28.58/10.44	   G(d, x, x) -> A^2
28.58/10.44	   A^2 -> H(f(d), f(d))
28.58/10.44	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.44	   A^2 -> H(f(e), f(e))
28.58/10.44	   A^2 -> H(f(k), f(k))
28.58/10.44	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.44	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.44	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.44	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.44	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.44	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.44	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.44	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.44	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.44	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.44	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.44	   A^2 -> H(c, c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, e))
28.58/10.44	   A^2 -> H(U1(e, k), e)
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, c), d)
28.58/10.44	   A^2 -> H(U1(e, c), k)
28.58/10.44	   A^2 -> H(U1(k, e), b)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, e), c)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.44	   A^2 -> H(U1(k, c), d)
28.58/10.44	   A^2 -> H(U1(c, e), d)
28.58/10.44	   A^2 -> H(U1(c, e), k)
28.58/10.44	   A^2 -> H(U1(c, k), d)
28.58/10.44	   A^2 -> H(U1(c, k), k)
28.58/10.44	   A^2 -> H(e, b)
28.58/10.44	   A^2 -> H(e, U1(e, d))
28.58/10.44	   A^2 -> H(e, U1(d, e))
28.58/10.44	   A^2 -> H(e, c)
28.58/10.44	   A^2 -> H(e, U1(e, k))
28.58/10.44	   A^2 -> H(e, e)
28.58/10.44	   A^2 -> H(U1(e, e), d)
28.58/10.44	   A^2 -> H(U1(e, e), k)
28.58/10.44	   A^2 -> H(U1(k, k), d)
28.58/10.44	   A^2 -> H(U1(k, k), b)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, k), c)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, d), d)
28.58/10.44	   A^2 -> H(U1(d, k), d)
28.58/10.44	   A^2 -> H(U1(d, k), k)
28.58/10.44	   A^2 -> H(U1(e, e), c)
28.58/10.44	   A^2 -> H(U1(e, c), e)
28.58/10.44	   A^2 -> H(U1(c, e), e)
28.58/10.44	   A^2 -> H(U1(c, k), e)
28.58/10.44	   A^2 -> H(c, U1(e, e))
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.44	   A^2 -> H(d, b)
28.58/10.44	   A^2 -> H(d, U1(e, d))
28.58/10.44	   A^2 -> H(d, U1(d, e))
28.58/10.44	   A^2 -> H(d, c)
28.58/10.44	   A^2 -> H(d, U1(e, k))
28.58/10.44	   A^2 -> H(d, U1(k, e))
28.58/10.44	   A^2 -> H(d, e)
28.58/10.44	   A^2 -> H(d, U1(k, k))
28.58/10.44	   A^2 -> H(a, d)
28.58/10.44	   A^2 -> H(a, k)
28.58/10.44	   A^2 -> H(U1(e, d), d)
28.58/10.44	   A^2 -> H(U1(e, d), k)
28.58/10.44	   A^2 -> H(U1(d, e), d)
28.58/10.44	   A^2 -> H(U1(d, e), k)
28.58/10.44	   A^2 -> H(k, b)
28.58/10.44	   A^2 -> H(k, U1(e, d))
28.58/10.44	   A^2 -> H(k, U1(d, e))
28.58/10.44	   A^2 -> H(k, c)
28.58/10.44	   A^2 -> H(k, U1(e, k))
28.58/10.44	   A^2 -> H(c, d)
28.58/10.44	   A^2 -> H(c, k)
28.58/10.44	   A^2 -> H(U1(e, k), d)
28.58/10.44	   A^2 -> H(U1(e, k), k)
28.58/10.44	
28.58/10.44	The TRS R consists of the following rules:
28.58/10.44	
28.58/10.44	   f(x) -> U1(x, x)
28.58/10.44	   U1(e, x) -> x
28.58/10.44	   a -> c
28.58/10.44	   a -> d
28.58/10.44	   b -> c
28.58/10.44	   b -> d
28.58/10.44	   d -> k
28.58/10.44	   c -> e
28.58/10.44	   c -> k
28.58/10.44	
28.58/10.44	Q is empty.
28.58/10.44	We have to consider all minimal (P,Q,R)-chains.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2577) TransformationProof (EQUIVALENT)
28.58/10.44	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.44	
28.58/10.44	   (A^2 -> H(k, U1(k, e)),A^2 -> H(k, U1(k, e)))
28.58/10.44	
28.58/10.44	
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2578)
28.58/10.44	Obligation:
28.58/10.44	Q DP problem:
28.58/10.44	The TRS P consists of the following rules:
28.58/10.44	
28.58/10.44	   A^2 -> H(f(c), f(c))
28.58/10.44	   H(x, x) -> G(x, x, f(k))
28.58/10.44	   G(d, x, x) -> A^2
28.58/10.44	   A^2 -> H(f(d), f(d))
28.58/10.44	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.44	   A^2 -> H(f(e), f(e))
28.58/10.44	   A^2 -> H(f(k), f(k))
28.58/10.44	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.44	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.44	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.44	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.44	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.44	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.44	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.44	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.44	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.44	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.44	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.44	   A^2 -> H(c, c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(e, k), e)
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, c), d)
28.58/10.44	   A^2 -> H(U1(e, c), k)
28.58/10.44	   A^2 -> H(U1(k, e), b)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, e), c)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.44	   A^2 -> H(U1(k, c), d)
28.58/10.44	   A^2 -> H(U1(c, e), d)
28.58/10.44	   A^2 -> H(U1(c, e), k)
28.58/10.44	   A^2 -> H(U1(c, k), d)
28.58/10.44	   A^2 -> H(U1(c, k), k)
28.58/10.44	   A^2 -> H(e, b)
28.58/10.44	   A^2 -> H(e, U1(e, d))
28.58/10.44	   A^2 -> H(e, U1(d, e))
28.58/10.44	   A^2 -> H(e, c)
28.58/10.44	   A^2 -> H(e, U1(e, k))
28.58/10.44	   A^2 -> H(e, e)
28.58/10.44	   A^2 -> H(U1(e, e), d)
28.58/10.44	   A^2 -> H(U1(e, e), k)
28.58/10.44	   A^2 -> H(U1(k, k), d)
28.58/10.44	   A^2 -> H(U1(k, k), b)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, k), c)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, d), d)
28.58/10.44	   A^2 -> H(U1(d, k), d)
28.58/10.44	   A^2 -> H(U1(d, k), k)
28.58/10.44	   A^2 -> H(U1(e, e), c)
28.58/10.44	   A^2 -> H(U1(e, c), e)
28.58/10.44	   A^2 -> H(U1(c, e), e)
28.58/10.44	   A^2 -> H(U1(c, k), e)
28.58/10.44	   A^2 -> H(c, U1(e, e))
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.44	   A^2 -> H(d, b)
28.58/10.44	   A^2 -> H(d, U1(e, d))
28.58/10.44	   A^2 -> H(d, U1(d, e))
28.58/10.44	   A^2 -> H(d, c)
28.58/10.44	   A^2 -> H(d, U1(e, k))
28.58/10.44	   A^2 -> H(d, U1(k, e))
28.58/10.44	   A^2 -> H(d, e)
28.58/10.44	   A^2 -> H(d, U1(k, k))
28.58/10.44	   A^2 -> H(a, d)
28.58/10.44	   A^2 -> H(a, k)
28.58/10.44	   A^2 -> H(U1(e, d), d)
28.58/10.44	   A^2 -> H(U1(e, d), k)
28.58/10.44	   A^2 -> H(U1(d, e), d)
28.58/10.44	   A^2 -> H(U1(d, e), k)
28.58/10.44	   A^2 -> H(k, b)
28.58/10.44	   A^2 -> H(k, U1(e, d))
28.58/10.44	   A^2 -> H(k, U1(d, e))
28.58/10.44	   A^2 -> H(k, c)
28.58/10.44	   A^2 -> H(k, U1(e, k))
28.58/10.44	   A^2 -> H(c, d)
28.58/10.44	   A^2 -> H(c, k)
28.58/10.44	   A^2 -> H(U1(e, k), d)
28.58/10.44	   A^2 -> H(U1(e, k), k)
28.58/10.44	   A^2 -> H(k, U1(k, e))
28.58/10.44	
28.58/10.44	The TRS R consists of the following rules:
28.58/10.44	
28.58/10.44	   f(x) -> U1(x, x)
28.58/10.44	   U1(e, x) -> x
28.58/10.44	   a -> c
28.58/10.44	   a -> d
28.58/10.44	   b -> c
28.58/10.44	   b -> d
28.58/10.44	   d -> k
28.58/10.44	   c -> e
28.58/10.44	   c -> k
28.58/10.44	
28.58/10.44	Q is empty.
28.58/10.44	We have to consider all minimal (P,Q,R)-chains.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2579) DependencyGraphProof (EQUIVALENT)
28.58/10.44	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2580)
28.58/10.44	Obligation:
28.58/10.44	Q DP problem:
28.58/10.44	The TRS P consists of the following rules:
28.58/10.44	
28.58/10.44	   H(x, x) -> G(x, x, f(k))
28.58/10.44	   G(d, x, x) -> A^2
28.58/10.44	   A^2 -> H(f(c), f(c))
28.58/10.44	   A^2 -> H(f(d), f(d))
28.58/10.44	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.44	   A^2 -> H(f(e), f(e))
28.58/10.44	   A^2 -> H(f(k), f(k))
28.58/10.44	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.44	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.44	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.44	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.44	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.44	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.44	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.44	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.44	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.44	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.44	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.44	   A^2 -> H(c, c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(e, k), e)
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, c), d)
28.58/10.44	   A^2 -> H(U1(e, c), k)
28.58/10.44	   A^2 -> H(U1(k, e), b)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, e), c)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.44	   A^2 -> H(U1(k, c), d)
28.58/10.44	   A^2 -> H(U1(c, e), d)
28.58/10.44	   A^2 -> H(U1(c, e), k)
28.58/10.44	   A^2 -> H(U1(c, k), d)
28.58/10.44	   A^2 -> H(U1(c, k), k)
28.58/10.44	   A^2 -> H(e, b)
28.58/10.44	   A^2 -> H(e, U1(e, d))
28.58/10.44	   A^2 -> H(e, U1(d, e))
28.58/10.44	   A^2 -> H(e, c)
28.58/10.44	   A^2 -> H(e, U1(e, k))
28.58/10.44	   A^2 -> H(e, e)
28.58/10.44	   A^2 -> H(U1(e, e), d)
28.58/10.44	   A^2 -> H(U1(e, e), k)
28.58/10.44	   A^2 -> H(U1(k, k), d)
28.58/10.44	   A^2 -> H(U1(k, k), b)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, k), c)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, d), d)
28.58/10.44	   A^2 -> H(U1(d, k), d)
28.58/10.44	   A^2 -> H(U1(d, k), k)
28.58/10.44	   A^2 -> H(U1(e, e), c)
28.58/10.44	   A^2 -> H(U1(e, c), e)
28.58/10.44	   A^2 -> H(U1(c, e), e)
28.58/10.44	   A^2 -> H(U1(c, k), e)
28.58/10.44	   A^2 -> H(c, U1(e, e))
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.44	   A^2 -> H(d, b)
28.58/10.44	   A^2 -> H(d, U1(e, d))
28.58/10.44	   A^2 -> H(d, U1(d, e))
28.58/10.44	   A^2 -> H(d, c)
28.58/10.44	   A^2 -> H(d, U1(e, k))
28.58/10.44	   A^2 -> H(d, U1(k, e))
28.58/10.44	   A^2 -> H(d, e)
28.58/10.44	   A^2 -> H(d, U1(k, k))
28.58/10.44	   A^2 -> H(a, d)
28.58/10.44	   A^2 -> H(a, k)
28.58/10.44	   A^2 -> H(U1(e, d), d)
28.58/10.44	   A^2 -> H(U1(e, d), k)
28.58/10.44	   A^2 -> H(U1(d, e), d)
28.58/10.44	   A^2 -> H(U1(d, e), k)
28.58/10.44	   A^2 -> H(k, b)
28.58/10.44	   A^2 -> H(k, U1(e, d))
28.58/10.44	   A^2 -> H(k, U1(d, e))
28.58/10.44	   A^2 -> H(k, c)
28.58/10.44	   A^2 -> H(k, U1(e, k))
28.58/10.44	   A^2 -> H(c, d)
28.58/10.44	   A^2 -> H(c, k)
28.58/10.44	   A^2 -> H(U1(e, k), d)
28.58/10.44	   A^2 -> H(U1(e, k), k)
28.58/10.44	
28.58/10.44	The TRS R consists of the following rules:
28.58/10.44	
28.58/10.44	   f(x) -> U1(x, x)
28.58/10.44	   U1(e, x) -> x
28.58/10.44	   a -> c
28.58/10.44	   a -> d
28.58/10.44	   b -> c
28.58/10.44	   b -> d
28.58/10.44	   d -> k
28.58/10.44	   c -> e
28.58/10.44	   c -> k
28.58/10.44	
28.58/10.44	Q is empty.
28.58/10.44	We have to consider all minimal (P,Q,R)-chains.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2581) TransformationProof (EQUIVALENT)
28.58/10.44	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), e) at position [] we obtained the following new rules [LPAR04]:
28.58/10.44	
28.58/10.44	   (A^2 -> H(k, e),A^2 -> H(k, e))
28.58/10.44	
28.58/10.44	
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2582)
28.58/10.44	Obligation:
28.58/10.44	Q DP problem:
28.58/10.44	The TRS P consists of the following rules:
28.58/10.44	
28.58/10.44	   H(x, x) -> G(x, x, f(k))
28.58/10.44	   G(d, x, x) -> A^2
28.58/10.44	   A^2 -> H(f(c), f(c))
28.58/10.44	   A^2 -> H(f(d), f(d))
28.58/10.44	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.44	   A^2 -> H(f(e), f(e))
28.58/10.44	   A^2 -> H(f(k), f(k))
28.58/10.44	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.44	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.44	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.44	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.44	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.44	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.44	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.44	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.44	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.44	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.44	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.44	   A^2 -> H(c, c)
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.44	   A^2 -> H(U1(e, c), d)
28.58/10.44	   A^2 -> H(U1(e, c), k)
28.58/10.44	   A^2 -> H(U1(k, e), b)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, e), c)
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.44	   A^2 -> H(U1(k, c), d)
28.58/10.44	   A^2 -> H(U1(c, e), d)
28.58/10.44	   A^2 -> H(U1(c, e), k)
28.58/10.44	   A^2 -> H(U1(c, k), d)
28.58/10.44	   A^2 -> H(U1(c, k), k)
28.58/10.44	   A^2 -> H(e, b)
28.58/10.44	   A^2 -> H(e, U1(e, d))
28.58/10.44	   A^2 -> H(e, U1(d, e))
28.58/10.44	   A^2 -> H(e, c)
28.58/10.44	   A^2 -> H(e, U1(e, k))
28.58/10.44	   A^2 -> H(e, e)
28.58/10.44	   A^2 -> H(U1(e, e), d)
28.58/10.44	   A^2 -> H(U1(e, e), k)
28.58/10.44	   A^2 -> H(U1(k, k), d)
28.58/10.44	   A^2 -> H(U1(k, k), b)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.44	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.44	   A^2 -> H(U1(k, k), c)
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.44	   A^2 -> H(U1(k, d), d)
28.58/10.44	   A^2 -> H(U1(d, k), d)
28.58/10.44	   A^2 -> H(U1(d, k), k)
28.58/10.44	   A^2 -> H(U1(e, e), c)
28.58/10.44	   A^2 -> H(U1(e, c), e)
28.58/10.44	   A^2 -> H(U1(c, e), e)
28.58/10.44	   A^2 -> H(U1(c, k), e)
28.58/10.44	   A^2 -> H(c, U1(e, e))
28.58/10.44	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.44	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.44	   A^2 -> H(d, b)
28.58/10.44	   A^2 -> H(d, U1(e, d))
28.58/10.44	   A^2 -> H(d, U1(d, e))
28.58/10.44	   A^2 -> H(d, c)
28.58/10.44	   A^2 -> H(d, U1(e, k))
28.58/10.44	   A^2 -> H(d, U1(k, e))
28.58/10.44	   A^2 -> H(d, e)
28.58/10.44	   A^2 -> H(d, U1(k, k))
28.58/10.44	   A^2 -> H(a, d)
28.58/10.44	   A^2 -> H(a, k)
28.58/10.44	   A^2 -> H(U1(e, d), d)
28.58/10.44	   A^2 -> H(U1(e, d), k)
28.58/10.44	   A^2 -> H(U1(d, e), d)
28.58/10.44	   A^2 -> H(U1(d, e), k)
28.58/10.44	   A^2 -> H(k, b)
28.58/10.44	   A^2 -> H(k, U1(e, d))
28.58/10.44	   A^2 -> H(k, U1(d, e))
28.58/10.44	   A^2 -> H(k, c)
28.58/10.44	   A^2 -> H(k, U1(e, k))
28.58/10.44	   A^2 -> H(c, d)
28.58/10.44	   A^2 -> H(c, k)
28.58/10.44	   A^2 -> H(U1(e, k), d)
28.58/10.44	   A^2 -> H(U1(e, k), k)
28.58/10.44	   A^2 -> H(k, e)
28.58/10.44	
28.58/10.44	The TRS R consists of the following rules:
28.58/10.44	
28.58/10.44	   f(x) -> U1(x, x)
28.58/10.44	   U1(e, x) -> x
28.58/10.44	   a -> c
28.58/10.44	   a -> d
28.58/10.44	   b -> c
28.58/10.44	   b -> d
28.58/10.44	   d -> k
28.58/10.44	   c -> e
28.58/10.44	   c -> k
28.58/10.44	
28.58/10.44	Q is empty.
28.58/10.44	We have to consider all minimal (P,Q,R)-chains.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2583) DependencyGraphProof (EQUIVALENT)
28.58/10.44	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.44	----------------------------------------
28.58/10.44	
28.58/10.44	(2584)
28.58/10.44	Obligation:
28.58/10.44	Q DP problem:
28.58/10.44	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(e, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(e, c), d)
28.58/10.45	   A^2 -> H(U1(e, c), k)
28.58/10.45	   A^2 -> H(U1(k, e), b)
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, e), c)
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(U1(k, c), d)
28.58/10.45	   A^2 -> H(U1(c, e), d)
28.58/10.45	   A^2 -> H(U1(c, e), k)
28.58/10.45	   A^2 -> H(U1(c, k), d)
28.58/10.45	   A^2 -> H(U1(c, k), k)
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2585) TransformationProof (EQUIVALENT)
28.58/10.45	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.45	
28.58/10.45	   (A^2 -> H(k, U1(k, k)),A^2 -> H(k, U1(k, k)))
28.58/10.45	
28.58/10.45	
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2586)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(e, c), d)
28.58/10.45	   A^2 -> H(U1(e, c), k)
28.58/10.45	   A^2 -> H(U1(k, e), b)
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, e), c)
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(U1(k, c), d)
28.58/10.45	   A^2 -> H(U1(c, e), d)
28.58/10.45	   A^2 -> H(U1(c, e), k)
28.58/10.45	   A^2 -> H(U1(c, k), d)
28.58/10.45	   A^2 -> H(U1(c, k), k)
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	   A^2 -> H(k, U1(k, k))
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2587) DependencyGraphProof (EQUIVALENT)
28.58/10.45	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2588)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(e, c), d)
28.58/10.45	   A^2 -> H(U1(e, c), k)
28.58/10.45	   A^2 -> H(U1(k, e), b)
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, e), c)
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(U1(k, c), d)
28.58/10.45	   A^2 -> H(U1(c, e), d)
28.58/10.45	   A^2 -> H(U1(c, e), k)
28.58/10.45	   A^2 -> H(U1(c, k), d)
28.58/10.45	   A^2 -> H(U1(c, k), k)
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2589) TransformationProof (EQUIVALENT)
28.58/10.45	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.45	
28.58/10.45	   (A^2 -> H(c, d),A^2 -> H(c, d))
28.58/10.45	   (A^2 -> H(U1(e, e), d),A^2 -> H(U1(e, e), d))
28.58/10.45	   (A^2 -> H(U1(e, k), d),A^2 -> H(U1(e, k), d))
28.58/10.45	   (A^2 -> H(U1(e, c), k),A^2 -> H(U1(e, c), k))
28.58/10.45	
28.58/10.45	
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2590)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(e, c), k)
28.58/10.45	   A^2 -> H(U1(k, e), b)
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, e), c)
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(U1(k, c), d)
28.58/10.45	   A^2 -> H(U1(c, e), d)
28.58/10.45	   A^2 -> H(U1(c, e), k)
28.58/10.45	   A^2 -> H(U1(c, k), d)
28.58/10.45	   A^2 -> H(U1(c, k), k)
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2591) TransformationProof (EQUIVALENT)
28.58/10.45	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), k) at position [] we obtained the following new rules [LPAR04]:
28.58/10.45	
28.58/10.45	   (A^2 -> H(c, k),A^2 -> H(c, k))
28.58/10.45	   (A^2 -> H(U1(e, e), k),A^2 -> H(U1(e, e), k))
28.58/10.45	   (A^2 -> H(U1(e, k), k),A^2 -> H(U1(e, k), k))
28.58/10.45	
28.58/10.45	
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2592)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), b)
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, e), c)
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(U1(k, c), d)
28.58/10.45	   A^2 -> H(U1(c, e), d)
28.58/10.45	   A^2 -> H(U1(c, e), k)
28.58/10.45	   A^2 -> H(U1(c, k), d)
28.58/10.45	   A^2 -> H(U1(c, k), k)
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2593) TransformationProof (EQUIVALENT)
28.58/10.45	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), b) at position [] we obtained the following new rules [LPAR04]:
28.58/10.45	
28.58/10.45	   (A^2 -> H(U1(k, e), c),A^2 -> H(U1(k, e), c))
28.58/10.45	   (A^2 -> H(U1(k, e), d),A^2 -> H(U1(k, e), d))
28.58/10.45	
28.58/10.45	
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2594)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, e), c)
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(U1(k, c), d)
28.58/10.45	   A^2 -> H(U1(c, e), d)
28.58/10.45	   A^2 -> H(U1(c, e), k)
28.58/10.45	   A^2 -> H(U1(c, k), d)
28.58/10.45	   A^2 -> H(U1(c, k), k)
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	   A^2 -> H(U1(k, e), d)
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2595) TransformationProof (EQUIVALENT)
28.58/10.45	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.45	
28.58/10.45	   (A^2 -> H(U1(k, e), d),A^2 -> H(U1(k, e), d))
28.58/10.45	   (A^2 -> H(U1(k, e), U1(e, k)),A^2 -> H(U1(k, e), U1(e, k)))
28.58/10.45	
28.58/10.45	
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2596)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, e), c)
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(U1(k, c), d)
28.58/10.45	   A^2 -> H(U1(c, e), d)
28.58/10.45	   A^2 -> H(U1(c, e), k)
28.58/10.45	   A^2 -> H(U1(c, k), d)
28.58/10.45	   A^2 -> H(U1(c, k), k)
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	   A^2 -> H(U1(k, e), d)
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2597) TransformationProof (EQUIVALENT)
28.58/10.45	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.45	
28.58/10.45	   (A^2 -> H(U1(k, e), U1(k, e)),A^2 -> H(U1(k, e), U1(k, e)))
28.58/10.45	
28.58/10.45	
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2598)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), c)
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(U1(k, c), d)
28.58/10.45	   A^2 -> H(U1(c, e), d)
28.58/10.45	   A^2 -> H(U1(c, e), k)
28.58/10.45	   A^2 -> H(U1(c, k), d)
28.58/10.45	   A^2 -> H(U1(c, k), k)
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	   A^2 -> H(U1(k, e), d)
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2599) TransformationProof (EQUIVALENT)
28.58/10.45	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), c) at position [] we obtained the following new rules [LPAR04]:
28.58/10.45	
28.58/10.45	   (A^2 -> H(U1(k, e), e),A^2 -> H(U1(k, e), e))
28.58/10.45	   (A^2 -> H(U1(k, e), k),A^2 -> H(U1(k, e), k))
28.58/10.45	
28.58/10.45	
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2600)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(U1(k, c), d)
28.58/10.45	   A^2 -> H(U1(c, e), d)
28.58/10.45	   A^2 -> H(U1(c, e), k)
28.58/10.45	   A^2 -> H(U1(c, k), d)
28.58/10.45	   A^2 -> H(U1(c, k), k)
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	   A^2 -> H(U1(k, e), d)
28.58/10.45	   A^2 -> H(U1(k, e), e)
28.58/10.45	   A^2 -> H(U1(k, e), k)
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2601) DependencyGraphProof (EQUIVALENT)
28.58/10.45	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2602)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(U1(k, c), d)
28.58/10.45	   A^2 -> H(U1(c, e), d)
28.58/10.45	   A^2 -> H(U1(c, e), k)
28.58/10.45	   A^2 -> H(U1(c, k), d)
28.58/10.45	   A^2 -> H(U1(c, k), k)
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	   A^2 -> H(U1(k, e), d)
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2603) TransformationProof (EQUIVALENT)
28.58/10.45	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.45	
28.58/10.45	   (A^2 -> H(U1(k, e), k),A^2 -> H(U1(k, e), k))
28.58/10.45	
28.58/10.45	
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2604)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(U1(k, c), d)
28.58/10.45	   A^2 -> H(U1(c, e), d)
28.58/10.45	   A^2 -> H(U1(c, e), k)
28.58/10.45	   A^2 -> H(U1(c, k), d)
28.58/10.45	   A^2 -> H(U1(c, k), k)
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	   A^2 -> H(U1(k, e), d)
28.58/10.45	   A^2 -> H(U1(k, e), k)
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2605) DependencyGraphProof (EQUIVALENT)
28.58/10.45	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2606)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(U1(k, c), d)
28.58/10.45	   A^2 -> H(U1(c, e), d)
28.58/10.45	   A^2 -> H(U1(c, e), k)
28.58/10.45	   A^2 -> H(U1(c, k), d)
28.58/10.45	   A^2 -> H(U1(c, k), k)
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	   A^2 -> H(U1(k, e), d)
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2607) TransformationProof (EQUIVALENT)
28.58/10.45	By narrowing [LPAR04] the rule A^2 -> H(U1(k, c), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.45	
28.58/10.45	   (A^2 -> H(U1(k, e), d),A^2 -> H(U1(k, e), d))
28.58/10.45	   (A^2 -> H(U1(k, k), d),A^2 -> H(U1(k, k), d))
28.58/10.45	   (A^2 -> H(U1(k, c), k),A^2 -> H(U1(k, c), k))
28.58/10.45	
28.58/10.45	
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2608)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(U1(c, e), d)
28.58/10.45	   A^2 -> H(U1(c, e), k)
28.58/10.45	   A^2 -> H(U1(c, k), d)
28.58/10.45	   A^2 -> H(U1(c, k), k)
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	   A^2 -> H(U1(k, e), d)
28.58/10.45	   A^2 -> H(U1(k, c), k)
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2609) DependencyGraphProof (EQUIVALENT)
28.58/10.45	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2610)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(U1(c, e), d)
28.58/10.45	   A^2 -> H(U1(c, e), k)
28.58/10.45	   A^2 -> H(U1(c, k), d)
28.58/10.45	   A^2 -> H(U1(c, k), k)
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	   A^2 -> H(U1(k, e), d)
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2611) TransformationProof (EQUIVALENT)
28.58/10.45	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.45	
28.58/10.45	   (A^2 -> H(U1(e, e), d),A^2 -> H(U1(e, e), d))
28.58/10.45	   (A^2 -> H(U1(k, e), d),A^2 -> H(U1(k, e), d))
28.58/10.45	   (A^2 -> H(U1(c, e), k),A^2 -> H(U1(c, e), k))
28.58/10.45	
28.58/10.45	
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2612)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(U1(c, e), k)
28.58/10.45	   A^2 -> H(U1(c, k), d)
28.58/10.45	   A^2 -> H(U1(c, k), k)
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	   A^2 -> H(U1(k, e), d)
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2613) TransformationProof (EQUIVALENT)
28.58/10.45	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), k) at position [] we obtained the following new rules [LPAR04]:
28.58/10.45	
28.58/10.45	   (A^2 -> H(U1(e, e), k),A^2 -> H(U1(e, e), k))
28.58/10.45	   (A^2 -> H(U1(k, e), k),A^2 -> H(U1(k, e), k))
28.58/10.45	
28.58/10.45	
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2614)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(U1(c, k), d)
28.58/10.45	   A^2 -> H(U1(c, k), k)
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	   A^2 -> H(U1(k, e), d)
28.58/10.45	   A^2 -> H(U1(k, e), k)
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2615) DependencyGraphProof (EQUIVALENT)
28.58/10.45	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2616)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(U1(c, k), d)
28.58/10.45	   A^2 -> H(U1(c, k), k)
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	   A^2 -> H(U1(k, e), d)
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2617) TransformationProof (EQUIVALENT)
28.58/10.45	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.45	
28.58/10.45	   (A^2 -> H(U1(e, k), d),A^2 -> H(U1(e, k), d))
28.58/10.45	   (A^2 -> H(U1(k, k), d),A^2 -> H(U1(k, k), d))
28.58/10.45	   (A^2 -> H(U1(c, k), k),A^2 -> H(U1(c, k), k))
28.58/10.45	
28.58/10.45	
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2618)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(U1(c, k), k)
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	   A^2 -> H(U1(k, e), d)
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2619) TransformationProof (EQUIVALENT)
28.58/10.45	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), k) at position [] we obtained the following new rules [LPAR04]:
28.58/10.45	
28.58/10.45	   (A^2 -> H(U1(e, k), k),A^2 -> H(U1(e, k), k))
28.58/10.45	   (A^2 -> H(U1(k, k), k),A^2 -> H(U1(k, k), k))
28.58/10.45	
28.58/10.45	
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2620)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.45	   A^2 -> H(d, b)
28.58/10.45	   A^2 -> H(d, U1(e, d))
28.58/10.45	   A^2 -> H(d, U1(d, e))
28.58/10.45	   A^2 -> H(d, c)
28.58/10.45	   A^2 -> H(d, U1(e, k))
28.58/10.45	   A^2 -> H(d, U1(k, e))
28.58/10.45	   A^2 -> H(d, e)
28.58/10.45	   A^2 -> H(d, U1(k, k))
28.58/10.45	   A^2 -> H(a, d)
28.58/10.45	   A^2 -> H(a, k)
28.58/10.45	   A^2 -> H(U1(e, d), d)
28.58/10.45	   A^2 -> H(U1(e, d), k)
28.58/10.45	   A^2 -> H(U1(d, e), d)
28.58/10.45	   A^2 -> H(U1(d, e), k)
28.58/10.45	   A^2 -> H(k, b)
28.58/10.45	   A^2 -> H(k, U1(e, d))
28.58/10.45	   A^2 -> H(k, U1(d, e))
28.58/10.45	   A^2 -> H(k, c)
28.58/10.45	   A^2 -> H(k, U1(e, k))
28.58/10.45	   A^2 -> H(c, d)
28.58/10.45	   A^2 -> H(c, k)
28.58/10.45	   A^2 -> H(U1(e, k), d)
28.58/10.45	   A^2 -> H(U1(e, k), k)
28.58/10.45	   A^2 -> H(U1(k, e), d)
28.58/10.45	   A^2 -> H(U1(k, k), k)
28.58/10.45	
28.58/10.45	The TRS R consists of the following rules:
28.58/10.45	
28.58/10.45	   f(x) -> U1(x, x)
28.58/10.45	   U1(e, x) -> x
28.58/10.45	   a -> c
28.58/10.45	   a -> d
28.58/10.45	   b -> c
28.58/10.45	   b -> d
28.58/10.45	   d -> k
28.58/10.45	   c -> e
28.58/10.45	   c -> k
28.58/10.45	
28.58/10.45	Q is empty.
28.58/10.45	We have to consider all minimal (P,Q,R)-chains.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2621) DependencyGraphProof (EQUIVALENT)
28.58/10.45	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.45	----------------------------------------
28.58/10.45	
28.58/10.45	(2622)
28.58/10.45	Obligation:
28.58/10.45	Q DP problem:
28.58/10.45	The TRS P consists of the following rules:
28.58/10.45	
28.58/10.45	   G(d, x, x) -> A^2
28.58/10.45	   A^2 -> H(f(c), f(c))
28.58/10.45	   H(x, x) -> G(x, x, f(k))
28.58/10.45	   A^2 -> H(f(d), f(d))
28.58/10.45	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.45	   A^2 -> H(f(e), f(e))
28.58/10.45	   A^2 -> H(f(k), f(k))
28.58/10.45	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.45	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.45	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.45	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.45	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.45	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.45	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.45	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.45	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.45	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.45	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.45	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.45	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.45	   A^2 -> H(c, c)
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.45	   A^2 -> H(e, b)
28.58/10.45	   A^2 -> H(e, U1(e, d))
28.58/10.45	   A^2 -> H(e, U1(d, e))
28.58/10.45	   A^2 -> H(e, c)
28.58/10.45	   A^2 -> H(e, U1(e, k))
28.58/10.45	   A^2 -> H(e, e)
28.58/10.45	   A^2 -> H(U1(e, e), d)
28.58/10.45	   A^2 -> H(U1(e, e), k)
28.58/10.45	   A^2 -> H(U1(k, k), d)
28.58/10.45	   A^2 -> H(U1(k, k), b)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.45	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.45	   A^2 -> H(U1(k, k), c)
28.58/10.45	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.45	   A^2 -> H(U1(k, d), d)
28.58/10.45	   A^2 -> H(U1(d, k), d)
28.58/10.45	   A^2 -> H(U1(d, k), k)
28.58/10.45	   A^2 -> H(U1(e, e), c)
28.58/10.45	   A^2 -> H(U1(e, c), e)
28.58/10.45	   A^2 -> H(U1(c, e), e)
28.58/10.45	   A^2 -> H(U1(c, k), e)
28.58/10.45	   A^2 -> H(c, U1(e, e))
28.58/10.45	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2623) TransformationProof (EQUIVALENT)
28.58/10.46	By narrowing [LPAR04] the rule A^2 -> H(e, b) at position [] we obtained the following new rules [LPAR04]:
28.58/10.46	
28.58/10.46	   (A^2 -> H(e, c),A^2 -> H(e, c))
28.58/10.46	   (A^2 -> H(e, d),A^2 -> H(e, d))
28.58/10.46	
28.58/10.46	
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2624)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, U1(e, d))
28.58/10.46	   A^2 -> H(e, U1(d, e))
28.58/10.46	   A^2 -> H(e, c)
28.58/10.46	   A^2 -> H(e, U1(e, k))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(e, e), d)
28.58/10.46	   A^2 -> H(U1(e, e), k)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	   A^2 -> H(U1(k, k), b)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.46	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.46	   A^2 -> H(U1(k, k), c)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2625) TransformationProof (EQUIVALENT)
28.58/10.46	By narrowing [LPAR04] the rule A^2 -> H(e, U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.46	
28.58/10.46	   (A^2 -> H(e, d),A^2 -> H(e, d))
28.58/10.46	   (A^2 -> H(e, U1(e, k)),A^2 -> H(e, U1(e, k)))
28.58/10.46	
28.58/10.46	
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2626)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, U1(d, e))
28.58/10.46	   A^2 -> H(e, c)
28.58/10.46	   A^2 -> H(e, U1(e, k))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(e, e), d)
28.58/10.46	   A^2 -> H(U1(e, e), k)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	   A^2 -> H(U1(k, k), b)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.46	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.46	   A^2 -> H(U1(k, k), c)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2627) TransformationProof (EQUIVALENT)
28.58/10.46	By narrowing [LPAR04] the rule A^2 -> H(e, U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.46	
28.58/10.46	   (A^2 -> H(e, U1(k, e)),A^2 -> H(e, U1(k, e)))
28.58/10.46	
28.58/10.46	
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2628)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, c)
28.58/10.46	   A^2 -> H(e, U1(e, k))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(e, e), d)
28.58/10.46	   A^2 -> H(U1(e, e), k)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	   A^2 -> H(U1(k, k), b)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.46	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.46	   A^2 -> H(U1(k, k), c)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	   A^2 -> H(e, U1(k, e))
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2629) DependencyGraphProof (EQUIVALENT)
28.58/10.46	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2630)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, c)
28.58/10.46	   A^2 -> H(e, U1(e, k))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(e, e), d)
28.58/10.46	   A^2 -> H(U1(e, e), k)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	   A^2 -> H(U1(k, k), b)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.46	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.46	   A^2 -> H(U1(k, k), c)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2631) TransformationProof (EQUIVALENT)
28.58/10.46	By narrowing [LPAR04] the rule A^2 -> H(e, c) at position [] we obtained the following new rules [LPAR04]:
28.58/10.46	
28.58/10.46	   (A^2 -> H(e, e),A^2 -> H(e, e))
28.58/10.46	   (A^2 -> H(e, k),A^2 -> H(e, k))
28.58/10.46	
28.58/10.46	
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2632)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, U1(e, k))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(e, e), d)
28.58/10.46	   A^2 -> H(U1(e, e), k)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	   A^2 -> H(U1(k, k), b)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.46	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.46	   A^2 -> H(U1(k, k), c)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	   A^2 -> H(e, k)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2633) DependencyGraphProof (EQUIVALENT)
28.58/10.46	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2634)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, U1(e, k))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(e, e), d)
28.58/10.46	   A^2 -> H(U1(e, e), k)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	   A^2 -> H(U1(k, k), b)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.46	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.46	   A^2 -> H(U1(k, k), c)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2635) TransformationProof (EQUIVALENT)
28.58/10.46	By narrowing [LPAR04] the rule A^2 -> H(e, U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.46	
28.58/10.46	   (A^2 -> H(e, k),A^2 -> H(e, k))
28.58/10.46	
28.58/10.46	
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2636)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(e, e), d)
28.58/10.46	   A^2 -> H(U1(e, e), k)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	   A^2 -> H(U1(k, k), b)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.46	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.46	   A^2 -> H(U1(k, k), c)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	   A^2 -> H(e, k)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2637) DependencyGraphProof (EQUIVALENT)
28.58/10.46	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2638)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(e, e), d)
28.58/10.46	   A^2 -> H(U1(e, e), k)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	   A^2 -> H(U1(k, k), b)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.46	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.46	   A^2 -> H(U1(k, k), c)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2639) TransformationProof (EQUIVALENT)
28.58/10.46	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.46	
28.58/10.46	   (A^2 -> H(e, d),A^2 -> H(e, d))
28.58/10.46	   (A^2 -> H(U1(e, e), k),A^2 -> H(U1(e, e), k))
28.58/10.46	
28.58/10.46	
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2640)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(e, e), k)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	   A^2 -> H(U1(k, k), b)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.46	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.46	   A^2 -> H(U1(k, k), c)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2641) TransformationProof (EQUIVALENT)
28.58/10.46	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), k) at position [] we obtained the following new rules [LPAR04]:
28.58/10.46	
28.58/10.46	   (A^2 -> H(e, k),A^2 -> H(e, k))
28.58/10.46	
28.58/10.46	
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2642)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	   A^2 -> H(U1(k, k), b)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.46	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.46	   A^2 -> H(U1(k, k), c)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	   A^2 -> H(e, k)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2643) DependencyGraphProof (EQUIVALENT)
28.58/10.46	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2644)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	   A^2 -> H(U1(k, k), b)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.46	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.46	   A^2 -> H(U1(k, k), c)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2645) TransformationProof (EQUIVALENT)
28.58/10.46	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.46	
28.58/10.46	   (A^2 -> H(U1(k, k), k),A^2 -> H(U1(k, k), k))
28.58/10.46	
28.58/10.46	
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2646)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(k, k), b)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.46	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.46	   A^2 -> H(U1(k, k), c)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	   A^2 -> H(U1(k, k), k)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2647) DependencyGraphProof (EQUIVALENT)
28.58/10.46	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2648)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(k, k), b)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.46	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.46	   A^2 -> H(U1(k, k), c)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2649) TransformationProof (EQUIVALENT)
28.58/10.46	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), b) at position [] we obtained the following new rules [LPAR04]:
28.58/10.46	
28.58/10.46	   (A^2 -> H(U1(k, k), c),A^2 -> H(U1(k, k), c))
28.58/10.46	   (A^2 -> H(U1(k, k), d),A^2 -> H(U1(k, k), d))
28.58/10.46	
28.58/10.46	
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2650)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, d))
28.58/10.46	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.46	   A^2 -> H(U1(k, k), c)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2651) TransformationProof (EQUIVALENT)
28.58/10.46	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.46	
28.58/10.46	   (A^2 -> H(U1(k, k), d),A^2 -> H(U1(k, k), d))
28.58/10.46	   (A^2 -> H(U1(k, k), U1(e, k)),A^2 -> H(U1(k, k), U1(e, k)))
28.58/10.46	
28.58/10.46	
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2652)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(k, k), U1(d, e))
28.58/10.46	   A^2 -> H(U1(k, k), c)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2653) TransformationProof (EQUIVALENT)
28.58/10.46	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.46	
28.58/10.46	   (A^2 -> H(U1(k, k), U1(k, e)),A^2 -> H(U1(k, k), U1(k, e)))
28.58/10.46	
28.58/10.46	
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2654)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(k, k), c)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, e))
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2655) DependencyGraphProof (EQUIVALENT)
28.58/10.46	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2656)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(k, k), c)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2657) TransformationProof (EQUIVALENT)
28.58/10.46	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), c) at position [] we obtained the following new rules [LPAR04]:
28.58/10.46	
28.58/10.46	   (A^2 -> H(U1(k, k), e),A^2 -> H(U1(k, k), e))
28.58/10.46	   (A^2 -> H(U1(k, k), k),A^2 -> H(U1(k, k), k))
28.58/10.46	
28.58/10.46	
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2658)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	   A^2 -> H(U1(k, k), e)
28.58/10.46	   A^2 -> H(U1(k, k), k)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2659) DependencyGraphProof (EQUIVALENT)
28.58/10.46	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2660)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2661) TransformationProof (EQUIVALENT)
28.58/10.46	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.46	
28.58/10.46	   (A^2 -> H(U1(k, k), k),A^2 -> H(U1(k, k), k))
28.58/10.46	
28.58/10.46	
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2662)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	   A^2 -> H(U1(k, k), k)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2663) DependencyGraphProof (EQUIVALENT)
28.58/10.46	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2664)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(k, d), d)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.46	   A^2 -> H(d, b)
28.58/10.46	   A^2 -> H(d, U1(e, d))
28.58/10.46	   A^2 -> H(d, U1(d, e))
28.58/10.46	   A^2 -> H(d, c)
28.58/10.46	   A^2 -> H(d, U1(e, k))
28.58/10.46	   A^2 -> H(d, U1(k, e))
28.58/10.46	   A^2 -> H(d, e)
28.58/10.46	   A^2 -> H(d, U1(k, k))
28.58/10.46	   A^2 -> H(a, d)
28.58/10.46	   A^2 -> H(a, k)
28.58/10.46	   A^2 -> H(U1(e, d), d)
28.58/10.46	   A^2 -> H(U1(e, d), k)
28.58/10.46	   A^2 -> H(U1(d, e), d)
28.58/10.46	   A^2 -> H(U1(d, e), k)
28.58/10.46	   A^2 -> H(k, b)
28.58/10.46	   A^2 -> H(k, U1(e, d))
28.58/10.46	   A^2 -> H(k, U1(d, e))
28.58/10.46	   A^2 -> H(k, c)
28.58/10.46	   A^2 -> H(k, U1(e, k))
28.58/10.46	   A^2 -> H(c, d)
28.58/10.46	   A^2 -> H(c, k)
28.58/10.46	   A^2 -> H(U1(e, k), d)
28.58/10.46	   A^2 -> H(U1(e, k), k)
28.58/10.46	   A^2 -> H(U1(k, e), d)
28.58/10.46	   A^2 -> H(e, d)
28.58/10.46	   A^2 -> H(U1(k, k), d)
28.58/10.46	
28.58/10.46	The TRS R consists of the following rules:
28.58/10.46	
28.58/10.46	   f(x) -> U1(x, x)
28.58/10.46	   U1(e, x) -> x
28.58/10.46	   a -> c
28.58/10.46	   a -> d
28.58/10.46	   b -> c
28.58/10.46	   b -> d
28.58/10.46	   d -> k
28.58/10.46	   c -> e
28.58/10.46	   c -> k
28.58/10.46	
28.58/10.46	Q is empty.
28.58/10.46	We have to consider all minimal (P,Q,R)-chains.
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2665) TransformationProof (EQUIVALENT)
28.58/10.46	By narrowing [LPAR04] the rule A^2 -> H(U1(k, d), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.46	
28.58/10.46	   (A^2 -> H(U1(k, k), d),A^2 -> H(U1(k, k), d))
28.58/10.46	   (A^2 -> H(U1(k, d), k),A^2 -> H(U1(k, d), k))
28.58/10.46	
28.58/10.46	
28.58/10.46	----------------------------------------
28.58/10.46	
28.58/10.46	(2666)
28.58/10.46	Obligation:
28.58/10.46	Q DP problem:
28.58/10.46	The TRS P consists of the following rules:
28.58/10.46	
28.58/10.46	   H(x, x) -> G(x, x, f(k))
28.58/10.46	   G(d, x, x) -> A^2
28.58/10.46	   A^2 -> H(f(c), f(c))
28.58/10.46	   A^2 -> H(f(d), f(d))
28.58/10.46	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.46	   A^2 -> H(f(e), f(e))
28.58/10.46	   A^2 -> H(f(k), f(k))
28.58/10.46	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.46	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.46	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.46	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.46	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.46	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.46	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.46	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.46	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.46	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.46	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.46	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.46	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.46	   A^2 -> H(c, c)
28.58/10.46	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.46	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.46	   A^2 -> H(e, e)
28.58/10.46	   A^2 -> H(U1(d, k), d)
28.58/10.46	   A^2 -> H(U1(d, k), k)
28.58/10.46	   A^2 -> H(U1(e, e), c)
28.58/10.46	   A^2 -> H(U1(e, c), e)
28.58/10.46	   A^2 -> H(U1(c, e), e)
28.58/10.46	   A^2 -> H(U1(c, k), e)
28.58/10.46	   A^2 -> H(c, U1(e, e))
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.47	   A^2 -> H(d, b)
28.58/10.47	   A^2 -> H(d, U1(e, d))
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(U1(k, d), k)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2667) DependencyGraphProof (EQUIVALENT)
28.58/10.47	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2668)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(U1(d, k), d)
28.58/10.47	   A^2 -> H(U1(d, k), k)
28.58/10.47	   A^2 -> H(U1(e, e), c)
28.58/10.47	   A^2 -> H(U1(e, c), e)
28.58/10.47	   A^2 -> H(U1(c, e), e)
28.58/10.47	   A^2 -> H(U1(c, k), e)
28.58/10.47	   A^2 -> H(c, U1(e, e))
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.47	   A^2 -> H(d, b)
28.58/10.47	   A^2 -> H(d, U1(e, d))
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2669) TransformationProof (EQUIVALENT)
28.58/10.47	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.47	
28.58/10.47	   (A^2 -> H(U1(k, k), d),A^2 -> H(U1(k, k), d))
28.58/10.47	   (A^2 -> H(U1(d, k), k),A^2 -> H(U1(d, k), k))
28.58/10.47	
28.58/10.47	
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2670)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(U1(d, k), k)
28.58/10.47	   A^2 -> H(U1(e, e), c)
28.58/10.47	   A^2 -> H(U1(e, c), e)
28.58/10.47	   A^2 -> H(U1(c, e), e)
28.58/10.47	   A^2 -> H(U1(c, k), e)
28.58/10.47	   A^2 -> H(c, U1(e, e))
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.47	   A^2 -> H(d, b)
28.58/10.47	   A^2 -> H(d, U1(e, d))
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2671) TransformationProof (EQUIVALENT)
28.58/10.47	By narrowing [LPAR04] the rule A^2 -> H(U1(d, k), k) at position [] we obtained the following new rules [LPAR04]:
28.58/10.47	
28.58/10.47	   (A^2 -> H(U1(k, k), k),A^2 -> H(U1(k, k), k))
28.58/10.47	
28.58/10.47	
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2672)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(U1(e, e), c)
28.58/10.47	   A^2 -> H(U1(e, c), e)
28.58/10.47	   A^2 -> H(U1(c, e), e)
28.58/10.47	   A^2 -> H(U1(c, k), e)
28.58/10.47	   A^2 -> H(c, U1(e, e))
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.47	   A^2 -> H(d, b)
28.58/10.47	   A^2 -> H(d, U1(e, d))
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(U1(k, k), k)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2673) DependencyGraphProof (EQUIVALENT)
28.58/10.47	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2674)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(U1(e, e), c)
28.58/10.47	   A^2 -> H(U1(e, c), e)
28.58/10.47	   A^2 -> H(U1(c, e), e)
28.58/10.47	   A^2 -> H(U1(c, k), e)
28.58/10.47	   A^2 -> H(c, U1(e, e))
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.47	   A^2 -> H(d, b)
28.58/10.47	   A^2 -> H(d, U1(e, d))
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2675) TransformationProof (EQUIVALENT)
28.58/10.47	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), c) at position [] we obtained the following new rules [LPAR04]:
28.58/10.47	
28.58/10.47	   (A^2 -> H(e, c),A^2 -> H(e, c))
28.58/10.47	   (A^2 -> H(U1(e, e), e),A^2 -> H(U1(e, e), e))
28.58/10.47	   (A^2 -> H(U1(e, e), k),A^2 -> H(U1(e, e), k))
28.58/10.47	
28.58/10.47	
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2676)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(U1(e, c), e)
28.58/10.47	   A^2 -> H(U1(c, e), e)
28.58/10.47	   A^2 -> H(U1(c, k), e)
28.58/10.47	   A^2 -> H(c, U1(e, e))
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.47	   A^2 -> H(d, b)
28.58/10.47	   A^2 -> H(d, U1(e, d))
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2677) TransformationProof (EQUIVALENT)
28.58/10.47	By narrowing [LPAR04] the rule A^2 -> H(U1(e, c), e) at position [] we obtained the following new rules [LPAR04]:
28.58/10.47	
28.58/10.47	   (A^2 -> H(c, e),A^2 -> H(c, e))
28.58/10.47	   (A^2 -> H(U1(e, e), e),A^2 -> H(U1(e, e), e))
28.58/10.47	   (A^2 -> H(U1(e, k), e),A^2 -> H(U1(e, k), e))
28.58/10.47	
28.58/10.47	
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2678)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(U1(c, e), e)
28.58/10.47	   A^2 -> H(U1(c, k), e)
28.58/10.47	   A^2 -> H(c, U1(e, e))
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.47	   A^2 -> H(d, b)
28.58/10.47	   A^2 -> H(d, U1(e, d))
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2679) TransformationProof (EQUIVALENT)
28.58/10.47	By narrowing [LPAR04] the rule A^2 -> H(U1(c, e), e) at position [] we obtained the following new rules [LPAR04]:
28.58/10.47	
28.58/10.47	   (A^2 -> H(U1(e, e), e),A^2 -> H(U1(e, e), e))
28.58/10.47	   (A^2 -> H(U1(k, e), e),A^2 -> H(U1(k, e), e))
28.58/10.47	
28.58/10.47	
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2680)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(U1(c, k), e)
28.58/10.47	   A^2 -> H(c, U1(e, e))
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.47	   A^2 -> H(d, b)
28.58/10.47	   A^2 -> H(d, U1(e, d))
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	   A^2 -> H(U1(k, e), e)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2681) DependencyGraphProof (EQUIVALENT)
28.58/10.47	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2682)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(U1(c, k), e)
28.58/10.47	   A^2 -> H(c, U1(e, e))
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.47	   A^2 -> H(d, b)
28.58/10.47	   A^2 -> H(d, U1(e, d))
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2683) TransformationProof (EQUIVALENT)
28.58/10.47	By narrowing [LPAR04] the rule A^2 -> H(U1(c, k), e) at position [] we obtained the following new rules [LPAR04]:
28.58/10.47	
28.58/10.47	   (A^2 -> H(U1(e, k), e),A^2 -> H(U1(e, k), e))
28.58/10.47	   (A^2 -> H(U1(k, k), e),A^2 -> H(U1(k, k), e))
28.58/10.47	
28.58/10.47	
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2684)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(c, U1(e, e))
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.47	   A^2 -> H(d, b)
28.58/10.47	   A^2 -> H(d, U1(e, d))
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	   A^2 -> H(U1(k, k), e)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2685) DependencyGraphProof (EQUIVALENT)
28.58/10.47	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2686)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(c, U1(e, e))
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.47	   A^2 -> H(d, b)
28.58/10.47	   A^2 -> H(d, U1(e, d))
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2687) TransformationProof (EQUIVALENT)
28.58/10.47	By narrowing [LPAR04] the rule A^2 -> H(c, U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.47	
28.58/10.47	   (A^2 -> H(e, U1(e, e)),A^2 -> H(e, U1(e, e)))
28.58/10.47	   (A^2 -> H(k, U1(e, e)),A^2 -> H(k, U1(e, e)))
28.58/10.47	   (A^2 -> H(c, e),A^2 -> H(c, e))
28.58/10.47	
28.58/10.47	
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2688)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.47	   A^2 -> H(d, b)
28.58/10.47	   A^2 -> H(d, U1(e, d))
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	   A^2 -> H(e, U1(e, e))
28.58/10.47	   A^2 -> H(k, U1(e, e))
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2689) TransformationProof (EQUIVALENT)
28.58/10.47	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.47	
28.58/10.47	   (A^2 -> H(k, U1(e, e)),A^2 -> H(k, U1(e, e)))
28.58/10.47	   (A^2 -> H(U1(e, k), e),A^2 -> H(U1(e, k), e))
28.58/10.47	
28.58/10.47	
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2690)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(U1(k, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.47	   A^2 -> H(d, b)
28.58/10.47	   A^2 -> H(d, U1(e, d))
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	   A^2 -> H(e, U1(e, e))
28.58/10.47	   A^2 -> H(k, U1(e, e))
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2691) TransformationProof (EQUIVALENT)
28.58/10.47	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.47	
28.58/10.47	   (A^2 -> H(U1(k, e), e),A^2 -> H(U1(k, e), e))
28.58/10.47	
28.58/10.47	
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2692)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.47	   A^2 -> H(d, b)
28.58/10.47	   A^2 -> H(d, U1(e, d))
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	   A^2 -> H(e, U1(e, e))
28.58/10.47	   A^2 -> H(k, U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, e), e)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2693) DependencyGraphProof (EQUIVALENT)
28.58/10.47	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2694)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(U1(k, k), U1(e, e))
28.58/10.47	   A^2 -> H(d, b)
28.58/10.47	   A^2 -> H(d, U1(e, d))
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	   A^2 -> H(e, U1(e, e))
28.58/10.47	   A^2 -> H(k, U1(e, e))
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2695) TransformationProof (EQUIVALENT)
28.58/10.47	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.47	
28.58/10.47	   (A^2 -> H(U1(k, k), e),A^2 -> H(U1(k, k), e))
28.58/10.47	
28.58/10.47	
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2696)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(d, b)
28.58/10.47	   A^2 -> H(d, U1(e, d))
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	   A^2 -> H(e, U1(e, e))
28.58/10.47	   A^2 -> H(k, U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), e)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2697) DependencyGraphProof (EQUIVALENT)
28.58/10.47	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2698)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(d, b)
28.58/10.47	   A^2 -> H(d, U1(e, d))
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	   A^2 -> H(e, U1(e, e))
28.58/10.47	   A^2 -> H(k, U1(e, e))
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2699) TransformationProof (EQUIVALENT)
28.58/10.47	By narrowing [LPAR04] the rule A^2 -> H(d, b) at position [] we obtained the following new rules [LPAR04]:
28.58/10.47	
28.58/10.47	   (A^2 -> H(k, b),A^2 -> H(k, b))
28.58/10.47	   (A^2 -> H(d, c),A^2 -> H(d, c))
28.58/10.47	   (A^2 -> H(d, d),A^2 -> H(d, d))
28.58/10.47	
28.58/10.47	
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2700)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(d, U1(e, d))
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	   A^2 -> H(e, U1(e, e))
28.58/10.47	   A^2 -> H(k, U1(e, e))
28.58/10.47	   A^2 -> H(d, d)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2701) TransformationProof (EQUIVALENT)
28.58/10.47	By narrowing [LPAR04] the rule A^2 -> H(d, U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.47	
28.58/10.47	   (A^2 -> H(k, U1(e, d)),A^2 -> H(k, U1(e, d)))
28.58/10.47	   (A^2 -> H(d, d),A^2 -> H(d, d))
28.58/10.47	   (A^2 -> H(d, U1(e, k)),A^2 -> H(d, U1(e, k)))
28.58/10.47	
28.58/10.47	
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2702)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(d, U1(d, e))
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	   A^2 -> H(e, U1(e, e))
28.58/10.47	   A^2 -> H(k, U1(e, e))
28.58/10.47	   A^2 -> H(d, d)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2703) TransformationProof (EQUIVALENT)
28.58/10.47	By narrowing [LPAR04] the rule A^2 -> H(d, U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.47	
28.58/10.47	   (A^2 -> H(k, U1(d, e)),A^2 -> H(k, U1(d, e)))
28.58/10.47	   (A^2 -> H(d, U1(k, e)),A^2 -> H(d, U1(k, e)))
28.58/10.47	
28.58/10.47	
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2704)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(d, c)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	   A^2 -> H(e, U1(e, e))
28.58/10.47	   A^2 -> H(k, U1(e, e))
28.58/10.47	   A^2 -> H(d, d)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2705) TransformationProof (EQUIVALENT)
28.58/10.47	By narrowing [LPAR04] the rule A^2 -> H(d, c) at position [] we obtained the following new rules [LPAR04]:
28.58/10.47	
28.58/10.47	   (A^2 -> H(k, c),A^2 -> H(k, c))
28.58/10.47	   (A^2 -> H(d, e),A^2 -> H(d, e))
28.58/10.47	   (A^2 -> H(d, k),A^2 -> H(d, k))
28.58/10.47	
28.58/10.47	
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2706)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(d, U1(e, k))
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	   A^2 -> H(e, U1(e, e))
28.58/10.47	   A^2 -> H(k, U1(e, e))
28.58/10.47	   A^2 -> H(d, d)
28.58/10.47	   A^2 -> H(d, k)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2707) TransformationProof (EQUIVALENT)
28.58/10.47	By narrowing [LPAR04] the rule A^2 -> H(d, U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.47	
28.58/10.47	   (A^2 -> H(k, U1(e, k)),A^2 -> H(k, U1(e, k)))
28.58/10.47	   (A^2 -> H(d, k),A^2 -> H(d, k))
28.58/10.47	
28.58/10.47	
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2708)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(d, U1(k, e))
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	   A^2 -> H(e, U1(e, e))
28.58/10.47	   A^2 -> H(k, U1(e, e))
28.58/10.47	   A^2 -> H(d, d)
28.58/10.47	   A^2 -> H(d, k)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2709) TransformationProof (EQUIVALENT)
28.58/10.47	By narrowing [LPAR04] the rule A^2 -> H(d, U1(k, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.47	
28.58/10.47	   (A^2 -> H(k, U1(k, e)),A^2 -> H(k, U1(k, e)))
28.58/10.47	
28.58/10.47	
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2710)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	   A^2 -> H(e, U1(e, e))
28.58/10.47	   A^2 -> H(k, U1(e, e))
28.58/10.47	   A^2 -> H(d, d)
28.58/10.47	   A^2 -> H(d, k)
28.58/10.47	   A^2 -> H(k, U1(k, e))
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2711) DependencyGraphProof (EQUIVALENT)
28.58/10.47	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2712)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(d, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	   A^2 -> H(e, U1(e, e))
28.58/10.47	   A^2 -> H(k, U1(e, e))
28.58/10.47	   A^2 -> H(d, d)
28.58/10.47	   A^2 -> H(d, k)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.47	   d -> k
28.58/10.47	   c -> e
28.58/10.47	   c -> k
28.58/10.47	
28.58/10.47	Q is empty.
28.58/10.47	We have to consider all minimal (P,Q,R)-chains.
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2713) TransformationProof (EQUIVALENT)
28.58/10.47	By narrowing [LPAR04] the rule A^2 -> H(d, e) at position [] we obtained the following new rules [LPAR04]:
28.58/10.47	
28.58/10.47	   (A^2 -> H(k, e),A^2 -> H(k, e))
28.58/10.47	
28.58/10.47	
28.58/10.47	----------------------------------------
28.58/10.47	
28.58/10.47	(2714)
28.58/10.47	Obligation:
28.58/10.47	Q DP problem:
28.58/10.47	The TRS P consists of the following rules:
28.58/10.47	
28.58/10.47	   G(d, x, x) -> A^2
28.58/10.47	   A^2 -> H(f(c), f(c))
28.58/10.47	   H(x, x) -> G(x, x, f(k))
28.58/10.47	   A^2 -> H(f(d), f(d))
28.58/10.47	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.47	   A^2 -> H(f(e), f(e))
28.58/10.47	   A^2 -> H(f(k), f(k))
28.58/10.47	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.47	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.47	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.47	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.47	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.47	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.47	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.47	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.47	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.47	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.47	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.47	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.47	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.47	   A^2 -> H(c, c)
28.58/10.47	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.47	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.47	   A^2 -> H(e, e)
28.58/10.47	   A^2 -> H(d, U1(k, k))
28.58/10.47	   A^2 -> H(a, d)
28.58/10.47	   A^2 -> H(a, k)
28.58/10.47	   A^2 -> H(U1(e, d), d)
28.58/10.47	   A^2 -> H(U1(e, d), k)
28.58/10.47	   A^2 -> H(U1(d, e), d)
28.58/10.47	   A^2 -> H(U1(d, e), k)
28.58/10.47	   A^2 -> H(k, b)
28.58/10.47	   A^2 -> H(k, U1(e, d))
28.58/10.47	   A^2 -> H(k, U1(d, e))
28.58/10.47	   A^2 -> H(k, c)
28.58/10.47	   A^2 -> H(k, U1(e, k))
28.58/10.47	   A^2 -> H(c, d)
28.58/10.47	   A^2 -> H(c, k)
28.58/10.47	   A^2 -> H(U1(e, k), d)
28.58/10.47	   A^2 -> H(U1(e, k), k)
28.58/10.47	   A^2 -> H(U1(k, e), d)
28.58/10.47	   A^2 -> H(e, d)
28.58/10.47	   A^2 -> H(U1(k, k), d)
28.58/10.47	   A^2 -> H(e, c)
28.58/10.47	   A^2 -> H(U1(e, e), e)
28.58/10.47	   A^2 -> H(U1(e, e), k)
28.58/10.47	   A^2 -> H(c, e)
28.58/10.47	   A^2 -> H(U1(e, k), e)
28.58/10.47	   A^2 -> H(e, U1(e, e))
28.58/10.47	   A^2 -> H(k, U1(e, e))
28.58/10.47	   A^2 -> H(d, d)
28.58/10.47	   A^2 -> H(d, k)
28.58/10.47	   A^2 -> H(k, e)
28.58/10.47	
28.58/10.47	The TRS R consists of the following rules:
28.58/10.47	
28.58/10.47	   f(x) -> U1(x, x)
28.58/10.47	   U1(e, x) -> x
28.58/10.47	   a -> c
28.58/10.47	   a -> d
28.58/10.47	   b -> c
28.58/10.47	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2715) DependencyGraphProof (EQUIVALENT)
28.58/10.48	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2716)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(d, U1(k, k))
28.58/10.48	   A^2 -> H(a, d)
28.58/10.48	   A^2 -> H(a, k)
28.58/10.48	   A^2 -> H(U1(e, d), d)
28.58/10.48	   A^2 -> H(U1(e, d), k)
28.58/10.48	   A^2 -> H(U1(d, e), d)
28.58/10.48	   A^2 -> H(U1(d, e), k)
28.58/10.48	   A^2 -> H(k, b)
28.58/10.48	   A^2 -> H(k, U1(e, d))
28.58/10.48	   A^2 -> H(k, U1(d, e))
28.58/10.48	   A^2 -> H(k, c)
28.58/10.48	   A^2 -> H(k, U1(e, k))
28.58/10.48	   A^2 -> H(c, d)
28.58/10.48	   A^2 -> H(c, k)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2717) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(d, U1(k, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(k, U1(k, k)),A^2 -> H(k, U1(k, k)))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2718)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(a, d)
28.58/10.48	   A^2 -> H(a, k)
28.58/10.48	   A^2 -> H(U1(e, d), d)
28.58/10.48	   A^2 -> H(U1(e, d), k)
28.58/10.48	   A^2 -> H(U1(d, e), d)
28.58/10.48	   A^2 -> H(U1(d, e), k)
28.58/10.48	   A^2 -> H(k, b)
28.58/10.48	   A^2 -> H(k, U1(e, d))
28.58/10.48	   A^2 -> H(k, U1(d, e))
28.58/10.48	   A^2 -> H(k, c)
28.58/10.48	   A^2 -> H(k, U1(e, k))
28.58/10.48	   A^2 -> H(c, d)
28.58/10.48	   A^2 -> H(c, k)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, U1(k, k))
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2719) DependencyGraphProof (EQUIVALENT)
28.58/10.48	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2720)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(a, d)
28.58/10.48	   A^2 -> H(a, k)
28.58/10.48	   A^2 -> H(U1(e, d), d)
28.58/10.48	   A^2 -> H(U1(e, d), k)
28.58/10.48	   A^2 -> H(U1(d, e), d)
28.58/10.48	   A^2 -> H(U1(d, e), k)
28.58/10.48	   A^2 -> H(k, b)
28.58/10.48	   A^2 -> H(k, U1(e, d))
28.58/10.48	   A^2 -> H(k, U1(d, e))
28.58/10.48	   A^2 -> H(k, c)
28.58/10.48	   A^2 -> H(k, U1(e, k))
28.58/10.48	   A^2 -> H(c, d)
28.58/10.48	   A^2 -> H(c, k)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2721) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(a, d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(c, d),A^2 -> H(c, d))
28.58/10.48	   (A^2 -> H(d, d),A^2 -> H(d, d))
28.58/10.48	   (A^2 -> H(a, k),A^2 -> H(a, k))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2722)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(a, k)
28.58/10.48	   A^2 -> H(U1(e, d), d)
28.58/10.48	   A^2 -> H(U1(e, d), k)
28.58/10.48	   A^2 -> H(U1(d, e), d)
28.58/10.48	   A^2 -> H(U1(d, e), k)
28.58/10.48	   A^2 -> H(k, b)
28.58/10.48	   A^2 -> H(k, U1(e, d))
28.58/10.48	   A^2 -> H(k, U1(d, e))
28.58/10.48	   A^2 -> H(k, c)
28.58/10.48	   A^2 -> H(k, U1(e, k))
28.58/10.48	   A^2 -> H(c, d)
28.58/10.48	   A^2 -> H(c, k)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2723) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(a, k) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(c, k),A^2 -> H(c, k))
28.58/10.48	   (A^2 -> H(d, k),A^2 -> H(d, k))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2724)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(U1(e, d), d)
28.58/10.48	   A^2 -> H(U1(e, d), k)
28.58/10.48	   A^2 -> H(U1(d, e), d)
28.58/10.48	   A^2 -> H(U1(d, e), k)
28.58/10.48	   A^2 -> H(k, b)
28.58/10.48	   A^2 -> H(k, U1(e, d))
28.58/10.48	   A^2 -> H(k, U1(d, e))
28.58/10.48	   A^2 -> H(k, c)
28.58/10.48	   A^2 -> H(k, U1(e, k))
28.58/10.48	   A^2 -> H(c, d)
28.58/10.48	   A^2 -> H(c, k)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2725) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(d, d),A^2 -> H(d, d))
28.58/10.48	   (A^2 -> H(U1(e, k), d),A^2 -> H(U1(e, k), d))
28.58/10.48	   (A^2 -> H(U1(e, d), k),A^2 -> H(U1(e, d), k))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2726)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(U1(e, d), k)
28.58/10.48	   A^2 -> H(U1(d, e), d)
28.58/10.48	   A^2 -> H(U1(d, e), k)
28.58/10.48	   A^2 -> H(k, b)
28.58/10.48	   A^2 -> H(k, U1(e, d))
28.58/10.48	   A^2 -> H(k, U1(d, e))
28.58/10.48	   A^2 -> H(k, c)
28.58/10.48	   A^2 -> H(k, U1(e, k))
28.58/10.48	   A^2 -> H(c, d)
28.58/10.48	   A^2 -> H(c, k)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2727) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(U1(e, d), k) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(d, k),A^2 -> H(d, k))
28.58/10.48	   (A^2 -> H(U1(e, k), k),A^2 -> H(U1(e, k), k))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2728)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(U1(d, e), d)
28.58/10.48	   A^2 -> H(U1(d, e), k)
28.58/10.48	   A^2 -> H(k, b)
28.58/10.48	   A^2 -> H(k, U1(e, d))
28.58/10.48	   A^2 -> H(k, U1(d, e))
28.58/10.48	   A^2 -> H(k, c)
28.58/10.48	   A^2 -> H(k, U1(e, k))
28.58/10.48	   A^2 -> H(c, d)
28.58/10.48	   A^2 -> H(c, k)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2729) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(U1(k, e), d),A^2 -> H(U1(k, e), d))
28.58/10.48	   (A^2 -> H(U1(d, e), k),A^2 -> H(U1(d, e), k))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2730)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(U1(d, e), k)
28.58/10.48	   A^2 -> H(k, b)
28.58/10.48	   A^2 -> H(k, U1(e, d))
28.58/10.48	   A^2 -> H(k, U1(d, e))
28.58/10.48	   A^2 -> H(k, c)
28.58/10.48	   A^2 -> H(k, U1(e, k))
28.58/10.48	   A^2 -> H(c, d)
28.58/10.48	   A^2 -> H(c, k)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2731) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(U1(d, e), k) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(U1(k, e), k),A^2 -> H(U1(k, e), k))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2732)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(k, b)
28.58/10.48	   A^2 -> H(k, U1(e, d))
28.58/10.48	   A^2 -> H(k, U1(d, e))
28.58/10.48	   A^2 -> H(k, c)
28.58/10.48	   A^2 -> H(k, U1(e, k))
28.58/10.48	   A^2 -> H(c, d)
28.58/10.48	   A^2 -> H(c, k)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(U1(k, e), k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2733) DependencyGraphProof (EQUIVALENT)
28.58/10.48	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2734)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(k, b)
28.58/10.48	   A^2 -> H(k, U1(e, d))
28.58/10.48	   A^2 -> H(k, U1(d, e))
28.58/10.48	   A^2 -> H(k, c)
28.58/10.48	   A^2 -> H(k, U1(e, k))
28.58/10.48	   A^2 -> H(c, d)
28.58/10.48	   A^2 -> H(c, k)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2735) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(k, b) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(k, c),A^2 -> H(k, c))
28.58/10.48	   (A^2 -> H(k, d),A^2 -> H(k, d))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2736)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(k, U1(e, d))
28.58/10.48	   A^2 -> H(k, U1(d, e))
28.58/10.48	   A^2 -> H(k, c)
28.58/10.48	   A^2 -> H(k, U1(e, k))
28.58/10.48	   A^2 -> H(c, d)
28.58/10.48	   A^2 -> H(c, k)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, d)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2737) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(k, U1(e, d)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(k, d),A^2 -> H(k, d))
28.58/10.48	   (A^2 -> H(k, U1(e, k)),A^2 -> H(k, U1(e, k)))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2738)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(k, U1(d, e))
28.58/10.48	   A^2 -> H(k, c)
28.58/10.48	   A^2 -> H(k, U1(e, k))
28.58/10.48	   A^2 -> H(c, d)
28.58/10.48	   A^2 -> H(c, k)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, d)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2739) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(k, U1(d, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(k, U1(k, e)),A^2 -> H(k, U1(k, e)))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2740)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(k, c)
28.58/10.48	   A^2 -> H(k, U1(e, k))
28.58/10.48	   A^2 -> H(c, d)
28.58/10.48	   A^2 -> H(c, k)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, d)
28.58/10.48	   A^2 -> H(k, U1(k, e))
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2741) DependencyGraphProof (EQUIVALENT)
28.58/10.48	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2742)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(k, c)
28.58/10.48	   A^2 -> H(k, U1(e, k))
28.58/10.48	   A^2 -> H(c, d)
28.58/10.48	   A^2 -> H(c, k)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, d)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2743) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(k, c) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(k, e),A^2 -> H(k, e))
28.58/10.48	   (A^2 -> H(k, k),A^2 -> H(k, k))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2744)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(k, U1(e, k))
28.58/10.48	   A^2 -> H(c, d)
28.58/10.48	   A^2 -> H(c, k)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, d)
28.58/10.48	   A^2 -> H(k, e)
28.58/10.48	   A^2 -> H(k, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2745) DependencyGraphProof (EQUIVALENT)
28.58/10.48	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2746)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(k, U1(e, k))
28.58/10.48	   A^2 -> H(c, d)
28.58/10.48	   A^2 -> H(c, k)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, d)
28.58/10.48	   A^2 -> H(k, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2747) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(k, U1(e, k)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(k, k),A^2 -> H(k, k))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2748)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(c, d)
28.58/10.48	   A^2 -> H(c, k)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, d)
28.58/10.48	   A^2 -> H(k, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2749) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(c, d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(e, d),A^2 -> H(e, d))
28.58/10.48	   (A^2 -> H(k, d),A^2 -> H(k, d))
28.58/10.48	   (A^2 -> H(c, k),A^2 -> H(c, k))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2750)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(c, k)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, d)
28.58/10.48	   A^2 -> H(k, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2751) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(c, k) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(e, k),A^2 -> H(e, k))
28.58/10.48	   (A^2 -> H(k, k),A^2 -> H(k, k))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2752)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, d)
28.58/10.48	   A^2 -> H(k, k)
28.58/10.48	   A^2 -> H(e, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2753) DependencyGraphProof (EQUIVALENT)
28.58/10.48	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2754)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(U1(e, k), d)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, d)
28.58/10.48	   A^2 -> H(k, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2755) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(k, d),A^2 -> H(k, d))
28.58/10.48	   (A^2 -> H(U1(e, k), k),A^2 -> H(U1(e, k), k))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2756)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(U1(e, k), k)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, d)
28.58/10.48	   A^2 -> H(k, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2757) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), k) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(k, k),A^2 -> H(k, k))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2758)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(U1(k, e), d)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, d)
28.58/10.48	   A^2 -> H(k, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2759) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(U1(k, e), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(U1(k, e), k),A^2 -> H(U1(k, e), k))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2760)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, d)
28.58/10.48	   A^2 -> H(k, k)
28.58/10.48	   A^2 -> H(U1(k, e), k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2761) DependencyGraphProof (EQUIVALENT)
28.58/10.48	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2762)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(e, d)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, d)
28.58/10.48	   A^2 -> H(k, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2763) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(e, d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(e, k),A^2 -> H(e, k))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2764)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, d)
28.58/10.48	   A^2 -> H(k, k)
28.58/10.48	   A^2 -> H(e, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2765) DependencyGraphProof (EQUIVALENT)
28.58/10.48	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2766)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(U1(k, k), d)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, d)
28.58/10.48	   A^2 -> H(k, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2767) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(U1(k, k), d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(U1(k, k), k),A^2 -> H(U1(k, k), k))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2768)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, d)
28.58/10.48	   A^2 -> H(k, k)
28.58/10.48	   A^2 -> H(U1(k, k), k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2769) DependencyGraphProof (EQUIVALENT)
28.58/10.48	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2770)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.48	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.48	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.48	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.48	   A^2 -> H(c, c)
28.58/10.48	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.48	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.48	   A^2 -> H(e, e)
28.58/10.48	   A^2 -> H(e, c)
28.58/10.48	   A^2 -> H(U1(e, e), e)
28.58/10.48	   A^2 -> H(U1(e, e), k)
28.58/10.48	   A^2 -> H(c, e)
28.58/10.48	   A^2 -> H(U1(e, k), e)
28.58/10.48	   A^2 -> H(e, U1(e, e))
28.58/10.48	   A^2 -> H(k, U1(e, e))
28.58/10.48	   A^2 -> H(d, d)
28.58/10.48	   A^2 -> H(d, k)
28.58/10.48	   A^2 -> H(k, d)
28.58/10.48	   A^2 -> H(k, k)
28.58/10.48	
28.58/10.48	The TRS R consists of the following rules:
28.58/10.48	
28.58/10.48	   f(x) -> U1(x, x)
28.58/10.48	   U1(e, x) -> x
28.58/10.48	   a -> c
28.58/10.48	   a -> d
28.58/10.48	   b -> c
28.58/10.48	   b -> d
28.58/10.48	   d -> k
28.58/10.48	   c -> e
28.58/10.48	   c -> k
28.58/10.48	
28.58/10.48	Q is empty.
28.58/10.48	We have to consider all minimal (P,Q,R)-chains.
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2771) TransformationProof (EQUIVALENT)
28.58/10.48	By narrowing [LPAR04] the rule A^2 -> H(e, c) at position [] we obtained the following new rules [LPAR04]:
28.58/10.48	
28.58/10.48	   (A^2 -> H(e, e),A^2 -> H(e, e))
28.58/10.48	   (A^2 -> H(e, k),A^2 -> H(e, k))
28.58/10.48	
28.58/10.48	
28.58/10.48	----------------------------------------
28.58/10.48	
28.58/10.48	(2772)
28.58/10.48	Obligation:
28.58/10.48	Q DP problem:
28.58/10.48	The TRS P consists of the following rules:
28.58/10.48	
28.58/10.48	   G(d, x, x) -> A^2
28.58/10.48	   A^2 -> H(f(c), f(c))
28.58/10.48	   H(x, x) -> G(x, x, f(k))
28.58/10.48	   A^2 -> H(f(d), f(d))
28.58/10.48	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.48	   A^2 -> H(f(e), f(e))
28.58/10.48	   A^2 -> H(f(k), f(k))
28.58/10.48	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.48	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.48	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.48	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.48	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.48	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.48	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.48	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.48	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.48	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.49	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.49	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.49	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.49	   A^2 -> H(c, c)
28.58/10.49	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.49	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.49	   A^2 -> H(e, e)
28.58/10.49	   A^2 -> H(U1(e, e), e)
28.58/10.49	   A^2 -> H(U1(e, e), k)
28.58/10.49	   A^2 -> H(c, e)
28.58/10.49	   A^2 -> H(U1(e, k), e)
28.58/10.49	   A^2 -> H(e, U1(e, e))
28.58/10.49	   A^2 -> H(k, U1(e, e))
28.58/10.49	   A^2 -> H(d, d)
28.58/10.49	   A^2 -> H(d, k)
28.58/10.49	   A^2 -> H(k, d)
28.58/10.49	   A^2 -> H(k, k)
28.58/10.49	   A^2 -> H(e, k)
28.58/10.49	
28.58/10.49	The TRS R consists of the following rules:
28.58/10.49	
28.58/10.49	   f(x) -> U1(x, x)
28.58/10.49	   U1(e, x) -> x
28.58/10.49	   a -> c
28.58/10.49	   a -> d
28.58/10.49	   b -> c
28.58/10.49	   b -> d
28.58/10.49	   d -> k
28.58/10.49	   c -> e
28.58/10.49	   c -> k
28.58/10.49	
28.58/10.49	Q is empty.
28.58/10.49	We have to consider all minimal (P,Q,R)-chains.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2773) DependencyGraphProof (EQUIVALENT)
28.58/10.49	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2774)
28.58/10.49	Obligation:
28.58/10.49	Q DP problem:
28.58/10.49	The TRS P consists of the following rules:
28.58/10.49	
28.58/10.49	   A^2 -> H(f(c), f(c))
28.58/10.49	   H(x, x) -> G(x, x, f(k))
28.58/10.49	   G(d, x, x) -> A^2
28.58/10.49	   A^2 -> H(f(d), f(d))
28.58/10.49	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.49	   A^2 -> H(f(e), f(e))
28.58/10.49	   A^2 -> H(f(k), f(k))
28.58/10.49	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.49	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.49	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.49	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.49	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.49	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.49	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.49	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.49	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.49	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.49	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.49	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.49	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.49	   A^2 -> H(c, c)
28.58/10.49	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.49	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.49	   A^2 -> H(e, e)
28.58/10.49	   A^2 -> H(U1(e, e), e)
28.58/10.49	   A^2 -> H(U1(e, e), k)
28.58/10.49	   A^2 -> H(c, e)
28.58/10.49	   A^2 -> H(U1(e, k), e)
28.58/10.49	   A^2 -> H(e, U1(e, e))
28.58/10.49	   A^2 -> H(k, U1(e, e))
28.58/10.49	   A^2 -> H(d, d)
28.58/10.49	   A^2 -> H(d, k)
28.58/10.49	   A^2 -> H(k, d)
28.58/10.49	   A^2 -> H(k, k)
28.58/10.49	
28.58/10.49	The TRS R consists of the following rules:
28.58/10.49	
28.58/10.49	   f(x) -> U1(x, x)
28.58/10.49	   U1(e, x) -> x
28.58/10.49	   a -> c
28.58/10.49	   a -> d
28.58/10.49	   b -> c
28.58/10.49	   b -> d
28.58/10.49	   d -> k
28.58/10.49	   c -> e
28.58/10.49	   c -> k
28.58/10.49	
28.58/10.49	Q is empty.
28.58/10.49	We have to consider all minimal (P,Q,R)-chains.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2775) TransformationProof (EQUIVALENT)
28.58/10.49	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), e) at position [] we obtained the following new rules [LPAR04]:
28.58/10.49	
28.58/10.49	   (A^2 -> H(e, e),A^2 -> H(e, e))
28.58/10.49	
28.58/10.49	
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2776)
28.58/10.49	Obligation:
28.58/10.49	Q DP problem:
28.58/10.49	The TRS P consists of the following rules:
28.58/10.49	
28.58/10.49	   A^2 -> H(f(c), f(c))
28.58/10.49	   H(x, x) -> G(x, x, f(k))
28.58/10.49	   G(d, x, x) -> A^2
28.58/10.49	   A^2 -> H(f(d), f(d))
28.58/10.49	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.49	   A^2 -> H(f(e), f(e))
28.58/10.49	   A^2 -> H(f(k), f(k))
28.58/10.49	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.49	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.49	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.49	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.49	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.49	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.49	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.49	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.49	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.49	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.49	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.49	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.49	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.49	   A^2 -> H(c, c)
28.58/10.49	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.49	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.49	   A^2 -> H(e, e)
28.58/10.49	   A^2 -> H(U1(e, e), k)
28.58/10.49	   A^2 -> H(c, e)
28.58/10.49	   A^2 -> H(U1(e, k), e)
28.58/10.49	   A^2 -> H(e, U1(e, e))
28.58/10.49	   A^2 -> H(k, U1(e, e))
28.58/10.49	   A^2 -> H(d, d)
28.58/10.49	   A^2 -> H(d, k)
28.58/10.49	   A^2 -> H(k, d)
28.58/10.49	   A^2 -> H(k, k)
28.58/10.49	
28.58/10.49	The TRS R consists of the following rules:
28.58/10.49	
28.58/10.49	   f(x) -> U1(x, x)
28.58/10.49	   U1(e, x) -> x
28.58/10.49	   a -> c
28.58/10.49	   a -> d
28.58/10.49	   b -> c
28.58/10.49	   b -> d
28.58/10.49	   d -> k
28.58/10.49	   c -> e
28.58/10.49	   c -> k
28.58/10.49	
28.58/10.49	Q is empty.
28.58/10.49	We have to consider all minimal (P,Q,R)-chains.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2777) TransformationProof (EQUIVALENT)
28.58/10.49	By narrowing [LPAR04] the rule A^2 -> H(U1(e, e), k) at position [] we obtained the following new rules [LPAR04]:
28.58/10.49	
28.58/10.49	   (A^2 -> H(e, k),A^2 -> H(e, k))
28.58/10.49	
28.58/10.49	
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2778)
28.58/10.49	Obligation:
28.58/10.49	Q DP problem:
28.58/10.49	The TRS P consists of the following rules:
28.58/10.49	
28.58/10.49	   A^2 -> H(f(c), f(c))
28.58/10.49	   H(x, x) -> G(x, x, f(k))
28.58/10.49	   G(d, x, x) -> A^2
28.58/10.49	   A^2 -> H(f(d), f(d))
28.58/10.49	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.49	   A^2 -> H(f(e), f(e))
28.58/10.49	   A^2 -> H(f(k), f(k))
28.58/10.49	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.49	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.49	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.49	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.49	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.49	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.49	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.49	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.49	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.49	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.49	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.49	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.49	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.49	   A^2 -> H(c, c)
28.58/10.49	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.49	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.49	   A^2 -> H(e, e)
28.58/10.49	   A^2 -> H(c, e)
28.58/10.49	   A^2 -> H(U1(e, k), e)
28.58/10.49	   A^2 -> H(e, U1(e, e))
28.58/10.49	   A^2 -> H(k, U1(e, e))
28.58/10.49	   A^2 -> H(d, d)
28.58/10.49	   A^2 -> H(d, k)
28.58/10.49	   A^2 -> H(k, d)
28.58/10.49	   A^2 -> H(k, k)
28.58/10.49	   A^2 -> H(e, k)
28.58/10.49	
28.58/10.49	The TRS R consists of the following rules:
28.58/10.49	
28.58/10.49	   f(x) -> U1(x, x)
28.58/10.49	   U1(e, x) -> x
28.58/10.49	   a -> c
28.58/10.49	   a -> d
28.58/10.49	   b -> c
28.58/10.49	   b -> d
28.58/10.49	   d -> k
28.58/10.49	   c -> e
28.58/10.49	   c -> k
28.58/10.49	
28.58/10.49	Q is empty.
28.58/10.49	We have to consider all minimal (P,Q,R)-chains.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2779) DependencyGraphProof (EQUIVALENT)
28.58/10.49	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2780)
28.58/10.49	Obligation:
28.58/10.49	Q DP problem:
28.58/10.49	The TRS P consists of the following rules:
28.58/10.49	
28.58/10.49	   H(x, x) -> G(x, x, f(k))
28.58/10.49	   G(d, x, x) -> A^2
28.58/10.49	   A^2 -> H(f(c), f(c))
28.58/10.49	   A^2 -> H(f(d), f(d))
28.58/10.49	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.49	   A^2 -> H(f(e), f(e))
28.58/10.49	   A^2 -> H(f(k), f(k))
28.58/10.49	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.49	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.49	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.49	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.49	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.49	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.49	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.49	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.49	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.49	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.49	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.49	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.49	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.49	   A^2 -> H(c, c)
28.58/10.49	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.49	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.49	   A^2 -> H(e, e)
28.58/10.49	   A^2 -> H(c, e)
28.58/10.49	   A^2 -> H(U1(e, k), e)
28.58/10.49	   A^2 -> H(e, U1(e, e))
28.58/10.49	   A^2 -> H(k, U1(e, e))
28.58/10.49	   A^2 -> H(d, d)
28.58/10.49	   A^2 -> H(d, k)
28.58/10.49	   A^2 -> H(k, d)
28.58/10.49	   A^2 -> H(k, k)
28.58/10.49	
28.58/10.49	The TRS R consists of the following rules:
28.58/10.49	
28.58/10.49	   f(x) -> U1(x, x)
28.58/10.49	   U1(e, x) -> x
28.58/10.49	   a -> c
28.58/10.49	   a -> d
28.58/10.49	   b -> c
28.58/10.49	   b -> d
28.58/10.49	   d -> k
28.58/10.49	   c -> e
28.58/10.49	   c -> k
28.58/10.49	
28.58/10.49	Q is empty.
28.58/10.49	We have to consider all minimal (P,Q,R)-chains.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2781) TransformationProof (EQUIVALENT)
28.58/10.49	By narrowing [LPAR04] the rule A^2 -> H(c, e) at position [] we obtained the following new rules [LPAR04]:
28.58/10.49	
28.58/10.49	   (A^2 -> H(e, e),A^2 -> H(e, e))
28.58/10.49	   (A^2 -> H(k, e),A^2 -> H(k, e))
28.58/10.49	
28.58/10.49	
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2782)
28.58/10.49	Obligation:
28.58/10.49	Q DP problem:
28.58/10.49	The TRS P consists of the following rules:
28.58/10.49	
28.58/10.49	   H(x, x) -> G(x, x, f(k))
28.58/10.49	   G(d, x, x) -> A^2
28.58/10.49	   A^2 -> H(f(c), f(c))
28.58/10.49	   A^2 -> H(f(d), f(d))
28.58/10.49	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.49	   A^2 -> H(f(e), f(e))
28.58/10.49	   A^2 -> H(f(k), f(k))
28.58/10.49	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.49	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.49	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.49	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.49	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.49	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.49	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.49	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.49	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.49	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.49	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.49	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.49	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.49	   A^2 -> H(c, c)
28.58/10.49	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.49	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.49	   A^2 -> H(e, e)
28.58/10.49	   A^2 -> H(U1(e, k), e)
28.58/10.49	   A^2 -> H(e, U1(e, e))
28.58/10.49	   A^2 -> H(k, U1(e, e))
28.58/10.49	   A^2 -> H(d, d)
28.58/10.49	   A^2 -> H(d, k)
28.58/10.49	   A^2 -> H(k, d)
28.58/10.49	   A^2 -> H(k, k)
28.58/10.49	   A^2 -> H(k, e)
28.58/10.49	
28.58/10.49	The TRS R consists of the following rules:
28.58/10.49	
28.58/10.49	   f(x) -> U1(x, x)
28.58/10.49	   U1(e, x) -> x
28.58/10.49	   a -> c
28.58/10.49	   a -> d
28.58/10.49	   b -> c
28.58/10.49	   b -> d
28.58/10.49	   d -> k
28.58/10.49	   c -> e
28.58/10.49	   c -> k
28.58/10.49	
28.58/10.49	Q is empty.
28.58/10.49	We have to consider all minimal (P,Q,R)-chains.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2783) DependencyGraphProof (EQUIVALENT)
28.58/10.49	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2784)
28.58/10.49	Obligation:
28.58/10.49	Q DP problem:
28.58/10.49	The TRS P consists of the following rules:
28.58/10.49	
28.58/10.49	   G(d, x, x) -> A^2
28.58/10.49	   A^2 -> H(f(c), f(c))
28.58/10.49	   H(x, x) -> G(x, x, f(k))
28.58/10.49	   A^2 -> H(f(d), f(d))
28.58/10.49	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.49	   A^2 -> H(f(e), f(e))
28.58/10.49	   A^2 -> H(f(k), f(k))
28.58/10.49	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.49	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.49	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.49	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.49	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.49	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.49	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.49	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.49	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.49	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.49	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.49	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.49	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.49	   A^2 -> H(c, c)
28.58/10.49	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.49	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.49	   A^2 -> H(e, e)
28.58/10.49	   A^2 -> H(U1(e, k), e)
28.58/10.49	   A^2 -> H(e, U1(e, e))
28.58/10.49	   A^2 -> H(k, U1(e, e))
28.58/10.49	   A^2 -> H(d, d)
28.58/10.49	   A^2 -> H(d, k)
28.58/10.49	   A^2 -> H(k, d)
28.58/10.49	   A^2 -> H(k, k)
28.58/10.49	
28.58/10.49	The TRS R consists of the following rules:
28.58/10.49	
28.58/10.49	   f(x) -> U1(x, x)
28.58/10.49	   U1(e, x) -> x
28.58/10.49	   a -> c
28.58/10.49	   a -> d
28.58/10.49	   b -> c
28.58/10.49	   b -> d
28.58/10.49	   d -> k
28.58/10.49	   c -> e
28.58/10.49	   c -> k
28.58/10.49	
28.58/10.49	Q is empty.
28.58/10.49	We have to consider all minimal (P,Q,R)-chains.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2785) TransformationProof (EQUIVALENT)
28.58/10.49	By narrowing [LPAR04] the rule A^2 -> H(U1(e, k), e) at position [] we obtained the following new rules [LPAR04]:
28.58/10.49	
28.58/10.49	   (A^2 -> H(k, e),A^2 -> H(k, e))
28.58/10.49	
28.58/10.49	
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2786)
28.58/10.49	Obligation:
28.58/10.49	Q DP problem:
28.58/10.49	The TRS P consists of the following rules:
28.58/10.49	
28.58/10.49	   G(d, x, x) -> A^2
28.58/10.49	   A^2 -> H(f(c), f(c))
28.58/10.49	   H(x, x) -> G(x, x, f(k))
28.58/10.49	   A^2 -> H(f(d), f(d))
28.58/10.49	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.49	   A^2 -> H(f(e), f(e))
28.58/10.49	   A^2 -> H(f(k), f(k))
28.58/10.49	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.49	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.49	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.49	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.49	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.49	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.49	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.49	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.49	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.49	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.49	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.49	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.49	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.49	   A^2 -> H(c, c)
28.58/10.49	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.49	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.49	   A^2 -> H(e, e)
28.58/10.49	   A^2 -> H(e, U1(e, e))
28.58/10.49	   A^2 -> H(k, U1(e, e))
28.58/10.49	   A^2 -> H(d, d)
28.58/10.49	   A^2 -> H(d, k)
28.58/10.49	   A^2 -> H(k, d)
28.58/10.49	   A^2 -> H(k, k)
28.58/10.49	   A^2 -> H(k, e)
28.58/10.49	
28.58/10.49	The TRS R consists of the following rules:
28.58/10.49	
28.58/10.49	   f(x) -> U1(x, x)
28.58/10.49	   U1(e, x) -> x
28.58/10.49	   a -> c
28.58/10.49	   a -> d
28.58/10.49	   b -> c
28.58/10.49	   b -> d
28.58/10.49	   d -> k
28.58/10.49	   c -> e
28.58/10.49	   c -> k
28.58/10.49	
28.58/10.49	Q is empty.
28.58/10.49	We have to consider all minimal (P,Q,R)-chains.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2787) DependencyGraphProof (EQUIVALENT)
28.58/10.49	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2788)
28.58/10.49	Obligation:
28.58/10.49	Q DP problem:
28.58/10.49	The TRS P consists of the following rules:
28.58/10.49	
28.58/10.49	   A^2 -> H(f(c), f(c))
28.58/10.49	   H(x, x) -> G(x, x, f(k))
28.58/10.49	   G(d, x, x) -> A^2
28.58/10.49	   A^2 -> H(f(d), f(d))
28.58/10.49	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.49	   A^2 -> H(f(e), f(e))
28.58/10.49	   A^2 -> H(f(k), f(k))
28.58/10.49	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.49	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.49	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.49	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.49	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.49	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.49	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.49	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.49	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.49	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.49	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.49	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.49	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.49	   A^2 -> H(c, c)
28.58/10.49	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.49	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.49	   A^2 -> H(e, e)
28.58/10.49	   A^2 -> H(e, U1(e, e))
28.58/10.49	   A^2 -> H(k, U1(e, e))
28.58/10.49	   A^2 -> H(d, d)
28.58/10.49	   A^2 -> H(d, k)
28.58/10.49	   A^2 -> H(k, d)
28.58/10.49	   A^2 -> H(k, k)
28.58/10.49	
28.58/10.49	The TRS R consists of the following rules:
28.58/10.49	
28.58/10.49	   f(x) -> U1(x, x)
28.58/10.49	   U1(e, x) -> x
28.58/10.49	   a -> c
28.58/10.49	   a -> d
28.58/10.49	   b -> c
28.58/10.49	   b -> d
28.58/10.49	   d -> k
28.58/10.49	   c -> e
28.58/10.49	   c -> k
28.58/10.49	
28.58/10.49	Q is empty.
28.58/10.49	We have to consider all minimal (P,Q,R)-chains.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2789) TransformationProof (EQUIVALENT)
28.58/10.49	By narrowing [LPAR04] the rule A^2 -> H(e, U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.49	
28.58/10.49	   (A^2 -> H(e, e),A^2 -> H(e, e))
28.58/10.49	
28.58/10.49	
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2790)
28.58/10.49	Obligation:
28.58/10.49	Q DP problem:
28.58/10.49	The TRS P consists of the following rules:
28.58/10.49	
28.58/10.49	   A^2 -> H(f(c), f(c))
28.58/10.49	   H(x, x) -> G(x, x, f(k))
28.58/10.49	   G(d, x, x) -> A^2
28.58/10.49	   A^2 -> H(f(d), f(d))
28.58/10.49	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.49	   A^2 -> H(f(e), f(e))
28.58/10.49	   A^2 -> H(f(k), f(k))
28.58/10.49	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.49	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.49	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.49	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.49	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.49	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.49	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.49	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.49	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.49	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.49	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.49	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.49	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.49	   A^2 -> H(c, c)
28.58/10.49	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.49	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.49	   A^2 -> H(e, e)
28.58/10.49	   A^2 -> H(k, U1(e, e))
28.58/10.49	   A^2 -> H(d, d)
28.58/10.49	   A^2 -> H(d, k)
28.58/10.49	   A^2 -> H(k, d)
28.58/10.49	   A^2 -> H(k, k)
28.58/10.49	
28.58/10.49	The TRS R consists of the following rules:
28.58/10.49	
28.58/10.49	   f(x) -> U1(x, x)
28.58/10.49	   U1(e, x) -> x
28.58/10.49	   a -> c
28.58/10.49	   a -> d
28.58/10.49	   b -> c
28.58/10.49	   b -> d
28.58/10.49	   d -> k
28.58/10.49	   c -> e
28.58/10.49	   c -> k
28.58/10.49	
28.58/10.49	Q is empty.
28.58/10.49	We have to consider all minimal (P,Q,R)-chains.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2791) TransformationProof (EQUIVALENT)
28.58/10.49	By narrowing [LPAR04] the rule A^2 -> H(k, U1(e, e)) at position [] we obtained the following new rules [LPAR04]:
28.58/10.49	
28.58/10.49	   (A^2 -> H(k, e),A^2 -> H(k, e))
28.58/10.49	
28.58/10.49	
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2792)
28.58/10.49	Obligation:
28.58/10.49	Q DP problem:
28.58/10.49	The TRS P consists of the following rules:
28.58/10.49	
28.58/10.49	   A^2 -> H(f(c), f(c))
28.58/10.49	   H(x, x) -> G(x, x, f(k))
28.58/10.49	   G(d, x, x) -> A^2
28.58/10.49	   A^2 -> H(f(d), f(d))
28.58/10.49	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.49	   A^2 -> H(f(e), f(e))
28.58/10.49	   A^2 -> H(f(k), f(k))
28.58/10.49	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.49	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.49	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.49	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.49	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.49	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.49	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.49	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.49	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.49	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.49	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.49	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.49	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.49	   A^2 -> H(c, c)
28.58/10.49	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.49	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.49	   A^2 -> H(e, e)
28.58/10.49	   A^2 -> H(d, d)
28.58/10.49	   A^2 -> H(d, k)
28.58/10.49	   A^2 -> H(k, d)
28.58/10.49	   A^2 -> H(k, k)
28.58/10.49	   A^2 -> H(k, e)
28.58/10.49	
28.58/10.49	The TRS R consists of the following rules:
28.58/10.49	
28.58/10.49	   f(x) -> U1(x, x)
28.58/10.49	   U1(e, x) -> x
28.58/10.49	   a -> c
28.58/10.49	   a -> d
28.58/10.49	   b -> c
28.58/10.49	   b -> d
28.58/10.49	   d -> k
28.58/10.49	   c -> e
28.58/10.49	   c -> k
28.58/10.49	
28.58/10.49	Q is empty.
28.58/10.49	We have to consider all minimal (P,Q,R)-chains.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2793) DependencyGraphProof (EQUIVALENT)
28.58/10.49	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2794)
28.58/10.49	Obligation:
28.58/10.49	Q DP problem:
28.58/10.49	The TRS P consists of the following rules:
28.58/10.49	
28.58/10.49	   H(x, x) -> G(x, x, f(k))
28.58/10.49	   G(d, x, x) -> A^2
28.58/10.49	   A^2 -> H(f(c), f(c))
28.58/10.49	   A^2 -> H(f(d), f(d))
28.58/10.49	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.49	   A^2 -> H(f(e), f(e))
28.58/10.49	   A^2 -> H(f(k), f(k))
28.58/10.49	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.49	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.49	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.49	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.49	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.49	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.49	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.49	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.49	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.49	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.49	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.49	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.49	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.49	   A^2 -> H(c, c)
28.58/10.49	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.49	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.49	   A^2 -> H(e, e)
28.58/10.49	   A^2 -> H(d, d)
28.58/10.49	   A^2 -> H(d, k)
28.58/10.49	   A^2 -> H(k, d)
28.58/10.49	   A^2 -> H(k, k)
28.58/10.49	
28.58/10.49	The TRS R consists of the following rules:
28.58/10.49	
28.58/10.49	   f(x) -> U1(x, x)
28.58/10.49	   U1(e, x) -> x
28.58/10.49	   a -> c
28.58/10.49	   a -> d
28.58/10.49	   b -> c
28.58/10.49	   b -> d
28.58/10.49	   d -> k
28.58/10.49	   c -> e
28.58/10.49	   c -> k
28.58/10.49	
28.58/10.49	Q is empty.
28.58/10.49	We have to consider all minimal (P,Q,R)-chains.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2795) TransformationProof (EQUIVALENT)
28.58/10.49	By narrowing [LPAR04] the rule A^2 -> H(d, k) at position [] we obtained the following new rules [LPAR04]:
28.58/10.49	
28.58/10.49	   (A^2 -> H(k, k),A^2 -> H(k, k))
28.58/10.49	
28.58/10.49	
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2796)
28.58/10.49	Obligation:
28.58/10.49	Q DP problem:
28.58/10.49	The TRS P consists of the following rules:
28.58/10.49	
28.58/10.49	   H(x, x) -> G(x, x, f(k))
28.58/10.49	   G(d, x, x) -> A^2
28.58/10.49	   A^2 -> H(f(c), f(c))
28.58/10.49	   A^2 -> H(f(d), f(d))
28.58/10.49	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.49	   A^2 -> H(f(e), f(e))
28.58/10.49	   A^2 -> H(f(k), f(k))
28.58/10.49	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.49	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.49	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.49	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.49	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.49	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.49	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.49	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.49	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.49	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.49	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.49	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.49	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.49	   A^2 -> H(c, c)
28.58/10.49	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.49	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.49	   A^2 -> H(e, e)
28.58/10.49	   A^2 -> H(d, d)
28.58/10.49	   A^2 -> H(k, d)
28.58/10.49	   A^2 -> H(k, k)
28.58/10.49	
28.58/10.49	The TRS R consists of the following rules:
28.58/10.49	
28.58/10.49	   f(x) -> U1(x, x)
28.58/10.49	   U1(e, x) -> x
28.58/10.49	   a -> c
28.58/10.49	   a -> d
28.58/10.49	   b -> c
28.58/10.49	   b -> d
28.58/10.49	   d -> k
28.58/10.49	   c -> e
28.58/10.49	   c -> k
28.58/10.49	
28.58/10.49	Q is empty.
28.58/10.49	We have to consider all minimal (P,Q,R)-chains.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2797) TransformationProof (EQUIVALENT)
28.58/10.49	By narrowing [LPAR04] the rule A^2 -> H(k, d) at position [] we obtained the following new rules [LPAR04]:
28.58/10.49	
28.58/10.49	   (A^2 -> H(k, k),A^2 -> H(k, k))
28.58/10.49	
28.58/10.49	
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2798)
28.58/10.49	Obligation:
28.58/10.49	Q DP problem:
28.58/10.49	The TRS P consists of the following rules:
28.58/10.49	
28.58/10.49	   H(x, x) -> G(x, x, f(k))
28.58/10.49	   G(d, x, x) -> A^2
28.58/10.49	   A^2 -> H(f(c), f(c))
28.58/10.49	   A^2 -> H(f(d), f(d))
28.58/10.49	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.49	   A^2 -> H(f(e), f(e))
28.58/10.49	   A^2 -> H(f(k), f(k))
28.58/10.49	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.49	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.49	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.49	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.49	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.49	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.49	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.49	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.49	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.49	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.49	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.49	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.49	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.49	   A^2 -> H(c, c)
28.58/10.49	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.49	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.49	   A^2 -> H(e, e)
28.58/10.49	   A^2 -> H(d, d)
28.58/10.49	   A^2 -> H(k, k)
28.58/10.49	
28.58/10.49	The TRS R consists of the following rules:
28.58/10.49	
28.58/10.49	   f(x) -> U1(x, x)
28.58/10.49	   U1(e, x) -> x
28.58/10.49	   a -> c
28.58/10.49	   a -> d
28.58/10.49	   b -> c
28.58/10.49	   b -> d
28.58/10.49	   d -> k
28.58/10.49	   c -> e
28.58/10.49	   c -> k
28.58/10.49	
28.58/10.49	Q is empty.
28.58/10.49	We have to consider all minimal (P,Q,R)-chains.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2799) UsableRulesReductionPairsProof (EQUIVALENT)
28.58/10.49	By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.
28.58/10.49	
28.58/10.49	No dependency pairs are removed.
28.58/10.49	
28.58/10.49	The following rules are removed from R:
28.58/10.49	
28.58/10.49	   a -> c
28.58/10.49	   a -> d
28.58/10.49	   b -> c
28.58/10.49	   b -> d
28.58/10.49	Used ordering: POLO with Polynomial interpretation [POLO]:
28.58/10.49	
28.58/10.49	   POL(A^2) = 0
28.58/10.49	   POL(G(x_1, x_2, x_3)) = x_1 + x_2 + 2*x_3
28.58/10.49	   POL(H(x_1, x_2)) = x_1 + x_2
28.58/10.49	   POL(U1(x_1, x_2)) = x_1 + x_2
28.58/10.49	   POL(c) = 0
28.58/10.49	   POL(d) = 0
28.58/10.49	   POL(e) = 0
28.58/10.49	   POL(f(x_1)) = 2*x_1
28.58/10.49	   POL(k) = 0
28.58/10.49	
28.58/10.49	
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2800)
28.58/10.49	Obligation:
28.58/10.49	Q DP problem:
28.58/10.49	The TRS P consists of the following rules:
28.58/10.49	
28.58/10.49	   H(x, x) -> G(x, x, f(k))
28.58/10.49	   G(d, x, x) -> A^2
28.58/10.49	   A^2 -> H(f(c), f(c))
28.58/10.49	   A^2 -> H(f(d), f(d))
28.58/10.49	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.49	   A^2 -> H(f(e), f(e))
28.58/10.49	   A^2 -> H(f(k), f(k))
28.58/10.49	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.49	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.49	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.49	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.49	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.49	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.49	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.49	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.49	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.49	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.49	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.49	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.49	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.49	   A^2 -> H(c, c)
28.58/10.49	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.49	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.49	   A^2 -> H(e, e)
28.58/10.49	   A^2 -> H(d, d)
28.58/10.49	   A^2 -> H(k, k)
28.58/10.49	
28.58/10.49	The TRS R consists of the following rules:
28.58/10.49	
28.58/10.49	   d -> k
28.58/10.49	   U1(e, x) -> x
28.58/10.49	   c -> e
28.58/10.49	   c -> k
28.58/10.49	   f(x) -> U1(x, x)
28.58/10.49	
28.58/10.49	Q is empty.
28.58/10.49	We have to consider all minimal (P,Q,R)-chains.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2801) QDPOrderProof (EQUIVALENT)
28.58/10.49	We use the reduction pair processor [LPAR04,JAR06].
28.58/10.49	
28.58/10.49	
28.58/10.49	The following pairs can be oriented strictly and are deleted.
28.58/10.49	
28.58/10.49	   A^2 -> H(f(c), f(c))
28.58/10.49	   A^2 -> H(U1(c, c), U1(c, c))
28.58/10.49	   A^2 -> H(f(e), f(e))
28.58/10.49	   A^2 -> H(f(k), f(k))
28.58/10.49	   A^2 -> H(U1(d, c), U1(d, c))
28.58/10.49	   A^2 -> H(U1(e, c), U1(e, c))
28.58/10.49	   A^2 -> H(U1(k, c), U1(k, c))
28.58/10.49	   A^2 -> H(U1(c, e), U1(c, e))
28.58/10.49	   A^2 -> H(U1(c, k), U1(c, k))
28.58/10.49	   A^2 -> H(U1(e, e), U1(e, e))
28.58/10.49	   A^2 -> H(U1(k, k), U1(k, k))
28.58/10.49	   A^2 -> H(U1(d, k), U1(d, k))
28.58/10.49	   A^2 -> H(U1(d, e), U1(d, e))
28.58/10.49	   A^2 -> H(c, c)
28.58/10.49	   A^2 -> H(U1(e, k), U1(e, k))
28.58/10.49	   A^2 -> H(U1(k, e), U1(k, e))
28.58/10.49	   A^2 -> H(e, e)
28.58/10.49	   A^2 -> H(k, k)
28.58/10.49	The remaining pairs can at least be oriented weakly.
28.58/10.49	Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:
28.58/10.49	
28.58/10.49	POL( G_3(x_1, ..., x_3) ) = 2x_1
28.58/10.49	POL( H_2(x_1, x_2) ) = 2x_1
28.58/10.49	POL( f_1(x_1) ) = x_1
28.58/10.49	POL( U1_2(x_1, x_2) ) = x_2
28.58/10.49	POL( c ) = 0
28.58/10.49	POL( e ) = 0
28.58/10.49	POL( k ) = 0
28.58/10.49	POL( d ) = 1
28.58/10.49	POL( A^2 ) = 2
28.58/10.49	
28.58/10.49	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
28.58/10.49	
28.58/10.49	   f(x) -> U1(x, x)
28.58/10.49	   c -> e
28.58/10.49	   c -> k
28.58/10.49	   d -> k
28.58/10.49	   U1(e, x) -> x
28.58/10.49	
28.58/10.49	
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2802)
28.58/10.49	Obligation:
28.58/10.49	Q DP problem:
28.58/10.49	The TRS P consists of the following rules:
28.58/10.49	
28.58/10.49	   H(x, x) -> G(x, x, f(k))
28.58/10.49	   G(d, x, x) -> A^2
28.58/10.49	   A^2 -> H(f(d), f(d))
28.58/10.49	   A^2 -> H(U1(d, d), U1(d, d))
28.58/10.49	   A^2 -> H(U1(c, d), U1(c, d))
28.58/10.49	   A^2 -> H(U1(k, d), U1(k, d))
28.58/10.49	   A^2 -> H(U1(e, d), U1(e, d))
28.58/10.49	   A^2 -> H(d, d)
28.58/10.49	
28.58/10.49	The TRS R consists of the following rules:
28.58/10.49	
28.58/10.49	   d -> k
28.58/10.49	   U1(e, x) -> x
28.58/10.49	   c -> e
28.58/10.49	   c -> k
28.58/10.49	   f(x) -> U1(x, x)
28.58/10.49	
28.58/10.49	Q is empty.
28.58/10.49	We have to consider all minimal (P,Q,R)-chains.
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2803) NonTerminationLoopProof (COMPLETE)
28.58/10.49	We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
28.58/10.49	Found a loop by narrowing to the left:
28.58/10.49	
28.58/10.49	s = G(U1(c, d), U1(c, d), f(k)) evaluates to  t =G(U1(c, d), U1(c, d), f(k))
28.58/10.49	
28.58/10.49	Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
28.58/10.49	* Matcher: [ ]
28.58/10.49	* Semiunifier: [ ]
28.58/10.49	
28.58/10.49	--------------------------------------------------------------------------------
28.58/10.49	Rewriting sequence
28.58/10.49	
28.58/10.49	G(U1(c, d), U1(c, d), f(k)) -> G(U1(c, d), U1(c, k), f(k))
28.58/10.49	with rule d -> k at position [1,1] and matcher [ ]
28.58/10.49	
28.58/10.49	G(U1(c, d), U1(c, k), f(k)) -> G(U1(c, d), U1(k, k), f(k))
28.58/10.49	with rule c -> k at position [1,0] and matcher [ ]
28.58/10.49	
28.58/10.49	G(U1(c, d), U1(k, k), f(k)) -> G(U1(c, d), U1(k, k), U1(k, k))
28.58/10.49	with rule f(x') -> U1(x', x') at position [2] and matcher [x' / k]
28.58/10.49	
28.58/10.49	G(U1(c, d), U1(k, k), U1(k, k)) -> G(U1(e, d), U1(k, k), U1(k, k))
28.58/10.49	with rule c -> e at position [0,0] and matcher [ ]
28.58/10.49	
28.58/10.49	G(U1(e, d), U1(k, k), U1(k, k)) -> G(d, U1(k, k), U1(k, k))
28.58/10.49	with rule U1(e, x') -> x' at position [0] and matcher [x' / d]
28.58/10.49	
28.58/10.49	G(d, U1(k, k), U1(k, k)) -> A^2
28.58/10.49	with rule G(d, x, x) -> A^2 at position [] and matcher [x / U1(k, k)]
28.58/10.49	
28.58/10.49	A^2 -> H(U1(c, d), U1(c, d))
28.58/10.49	with rule A^2 -> H(U1(c, d), U1(c, d)) at position [] and matcher [ ]
28.58/10.49	
28.58/10.49	H(U1(c, d), U1(c, d)) -> G(U1(c, d), U1(c, d), f(k))
28.58/10.49	with rule H(x, x) -> G(x, x, f(k))
28.58/10.49	
28.58/10.49	Now applying the matcher to the start term leads to a term which is equal to the last term in the rewriting sequence
28.58/10.49	
28.58/10.49	
28.58/10.49	All these steps are and every following step will be a correct step w.r.t to Q.
28.58/10.49	
28.58/10.49	
28.58/10.49	
28.58/10.49	
28.58/10.49	----------------------------------------
28.58/10.49	
28.58/10.49	(2804)
28.58/10.49	NO
28.60/10.51	EOF